0.11/0.11	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.11/0.13	% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.1fadFdPJ8i true
0.12/0.34	% Computer : n026.cluster.edu
0.12/0.34	% Model    : x86_64 x86_64
0.12/0.34	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.34	% Memory   : 8042.1875MB
0.12/0.34	% OS       : Linux 3.10.0-693.el7.x86_64
0.12/0.34	% CPULimit : 960
0.12/0.34	% WCLimit  : 120
0.12/0.34	% DateTime : Tue Aug  9 05:07:34 EDT 2022
0.12/0.34	% CPUTime  : 
0.12/0.34	% Running portfolio for 960 s
0.12/0.34	% File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.12/0.34	% Number of cores: 8
0.12/0.34	% Python version: Python 3.6.8
0.12/0.34	% Running in HO mode
0.51/0.65	% Total configuration time : 828
0.51/0.65	% Estimated wc time : 1656
0.51/0.65	% Estimated cpu time (8 cpus) : 207.0
0.51/0.71	% /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
0.51/0.72	% /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
0.51/0.72	% /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
0.51/0.73	% /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
0.52/0.73	% /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
0.52/0.73	% /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
0.52/0.74	% /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
0.52/0.74	% /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
0.52/0.80	% /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
99.32/13.16	% Solved by lams/40_b.comb.sh.
99.32/13.16	% running E: timeout 28 /export/starexec/sandbox2/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox2/tmp/tmp.1fadFdPJ8i/e_input5e90d4 --cpu-limit=26 --auto-schedule -s -p
99.32/13.16	% done 655 iterations in 12.292s
99.32/13.16	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
99.32/13.16	% SZS output start Refutation
99.32/13.16	thf(setadjoin_type, type, setadjoin: $i > $i > $i).
99.32/13.16	thf(setadjoinSub_type, type, setadjoinSub: $o).
99.32/13.16	thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
99.32/13.16	thf(setunion_type, type, setunion: $i > $i).
99.32/13.16	thf(vacuousDall_type, type, vacuousDall: $o).
99.32/13.16	thf(setadjoinIR_type, type, setadjoinIR: $o).
99.32/13.16	thf(omega0Ax_type, type, omega0Ax: $o).
99.32/13.16	thf(subsetE_type, type, subsetE: $o).
99.32/13.16	thf(setadjoinSub2_type, type, setadjoinSub2: $o).
99.32/13.16	thf(powersetE_type, type, powersetE: $o).
99.32/13.16	thf('#sk12_type', type, '#sk12': $i > $i > $i).
99.32/13.16	thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
99.32/13.16	thf(powerset__Cong_type, type, powerset__Cong: $o).
99.32/13.16	thf(omegaIndAx_type, type, omegaIndAx: $o).
99.32/13.16	thf(uniqinunit_type, type, uniqinunit: $o).
99.32/13.16	thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
99.32/13.16	thf(exu__Cong_type, type, exu__Cong: $o).
99.32/13.16	thf(subset2powerset_type, type, subset2powerset: $o).
99.32/13.16	thf(setoftrueEq_type, type, setoftrueEq: $o).
99.32/13.16	thf(upairsetIL_type, type, upairsetIL: $o).
99.32/13.16	thf(emptyI_type, type, emptyI: $o).
99.32/13.16	thf(exuI3_type, type, exuI3: $o).
99.32/13.16	thf(emptysetAx_type, type, emptysetAx: $o).
99.32/13.16	thf(emptyInPowerset_type, type, emptyInPowerset: $o).
99.32/13.16	thf(setadjoinIL_type, type, setadjoinIL: $o).
99.32/13.16	thf(emptyinunitempty_type, type, emptyinunitempty: $o).
99.32/13.16	thf(upairsetIR_type, type, upairsetIR: $o).
99.32/13.16	thf(emptyset__Cong_type, type, emptyset__Cong: $o).
99.32/13.16	thf(descrp_type, type, descrp: $o).
99.32/13.16	thf('#sk29_type', type, '#sk29': $i).
99.32/13.16	thf(nonemptyI1_type, type, nonemptyI1: $o).
99.32/13.16	thf(emptysetsubset_type, type, emptysetsubset: $o).
99.32/13.16	thf(setunionAx_type, type, setunionAx: $o).
99.32/13.16	thf(notsubsetI_type, type, notsubsetI: $o).
99.32/13.16	thf(subsetRefl_type, type, subsetRefl: $o).
99.32/13.16	thf(nonemptyI_type, type, nonemptyI: $o).
99.32/13.16	thf(emptysetE_type, type, emptysetE: $o).
99.32/13.16	thf(sepInPowerset_type, type, sepInPowerset: $o).
99.32/13.16	thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
99.32/13.16	thf(powersetI_type, type, powersetI: $o).
99.32/13.16	thf('#sk30_type', type, '#sk30': $i).
99.32/13.16	thf(exuE2_type, type, exuE2: $o).
99.32/13.16	thf(exuE3e_type, type, exuE3e: $o).
99.32/13.16	thf(notequalI2_type, type, notequalI2: $o).
99.32/13.16	thf(descr__Cong_type, type, descr__Cong: $o).
99.32/13.16	thf(setextAx_type, type, setextAx: $o).
99.32/13.16	thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
99.32/13.16	thf(eqinunit_type, type, eqinunit: $o).
99.32/13.16	thf(powersetAx_type, type, powersetAx: $o).
99.32/13.16	thf(subsetI2_type, type, subsetI2: $o).
99.32/13.16	thf(binunion_type, type, binunion: $i > $i > $i).
99.32/13.16	thf(subsetI1_type, type, subsetI1: $o).
99.32/13.16	thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
99.32/13.16	thf(replAx_type, type, replAx: $o).
99.32/13.16	thf(subPowSU_type, type, subPowSU: $o).
99.32/13.16	thf(setunionE_type, type, setunionE: $o).
99.32/13.16	thf(setunion__Cong_type, type, setunion__Cong: $o).
99.32/13.16	thf(powersetE1_type, type, powersetE1: $o).
99.32/13.16	thf(omegaSAx_type, type, omegaSAx: $o).
99.32/13.16	thf(setext_type, type, setext: $o).
99.32/13.16	thf(notequalI1_type, type, notequalI1: $o).
99.32/13.16	thf(setextsub_type, type, setextsub: $o).
99.32/13.16	thf(omega__Cong_type, type, omega__Cong: $o).
99.32/13.16	thf(omega_type, type, omega: $i).
99.32/13.16	thf(setbeta_type, type, setbeta: $o).
99.32/13.16	thf(dsetconstrER_type, type, dsetconstrER: $o).
99.32/13.16	thf(nonemptyE1_type, type, nonemptyE1: $o).
99.32/13.16	thf(prop2setE_type, type, prop2setE: $o).
99.32/13.16	thf(prop2set2propI_type, type, prop2set2propI: $o).
99.32/13.16	thf(notdallE_type, type, notdallE: $o).
99.32/13.16	thf(eqimpsubset1_type, type, eqimpsubset1: $o).
99.32/13.16	thf(exuEu_type, type, exuEu: $o).
99.32/13.16	thf(notinsingleton_type, type, notinsingleton: $o).
99.32/13.16	thf(upairsetE_type, type, upairsetE: $o).
99.32/13.16	thf(emptyE1_type, type, emptyE1: $o).
99.32/13.16	thf(emptyinPowerset_type, type, emptyinPowerset: $o).
99.32/13.16	thf(wellorderingAx_type, type, wellorderingAx: $o).
99.32/13.16	thf(powersetsubset_type, type, powersetsubset: $o).
99.32/13.16	thf(emptyset_type, type, emptyset: $i).
99.32/13.16	thf(noeltsimpempty_type, type, noeltsimpempty: $o).
99.32/13.16	thf(exuE1_type, type, exuE1: $o).
99.32/13.16	thf(inPowerset_type, type, inPowerset: $o).
99.32/13.16	thf(in_type, type, in: $i > $i > $o).
99.32/13.16	thf(setunionI_type, type, setunionI: $o).
99.32/13.16	thf(in__Cong_type, type, in__Cong: $o).
99.32/13.16	thf(setadjoinE_type, type, setadjoinE: $o).
99.32/13.16	thf(subsetTrans_type, type, subsetTrans: $o).
99.32/13.16	thf(dsetconstrEL_type, type, dsetconstrEL: $o).
99.32/13.16	thf(foundationAx_type, type, foundationAx: $o).
99.32/13.16	thf(sepSubset_type, type, sepSubset: $o).
99.32/13.16	thf(exuE3u_type, type, exuE3u: $o).
99.32/13.16	thf(setadjoinOr_type, type, setadjoinOr: $o).
99.32/13.16	thf(exuI1_type, type, exuI1: $o).
99.32/13.16	thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
99.32/13.16	thf(inCongP_type, type, inCongP: $o).
99.32/13.16	thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
99.32/13.16	thf(eqimpsubset2_type, type, eqimpsubset2: $o).
99.32/13.16	thf(exuI2_type, type, exuI2: $o).
99.32/13.16	thf(powersetI1_type, type, powersetI1: $o).
99.32/13.16	thf(dsetconstrI_type, type, dsetconstrI: $o).
99.32/13.16	thf(subsetE2_type, type, subsetE2: $o).
99.32/13.16	thf(singletonsswitch_type, type, singletonsswitch: $o).
99.32/13.16	thf(setadjoinAx_type, type, setadjoinAx: $o).
99.32/13.16	thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
99.32/13.16	thf(notinemptyset_type, type, notinemptyset: $o).
99.32/13.16	thf(prop2setI_type, type, prop2setI: $o).
99.32/13.16	thf(notdexE_type, type, notdexE: $o).
99.32/13.16	thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
99.32/13.16	thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
99.32/13.16	thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
99.32/13.16	thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
99.32/13.16	thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
99.32/13.16	thf(binunionIL, conjecture,
99.32/13.16	  (( setextAx ) =>
99.32/13.16	   ( ( emptysetAx ) =>
99.32/13.16	     ( ( setadjoinAx ) =>
99.32/13.16	       ( ( powersetAx ) =>
99.32/13.16	         ( ( setunionAx ) =>
99.32/13.16	           ( ( omega0Ax ) =>
99.32/13.16	             ( ( omegaSAx ) =>
99.32/13.16	               ( ( omegaIndAx ) =>
99.32/13.16	                 ( ( replAx ) =>
99.32/13.16	                   ( ( foundationAx ) =>
99.32/13.16	                     ( ( wellorderingAx ) =>
99.32/13.16	                       ( ( descrp ) =>
99.32/13.16	                         ( ( dsetconstrI ) =>
99.32/13.16	                           ( ( dsetconstrEL ) =>
99.32/13.16	                             ( ( dsetconstrER ) =>
99.32/13.16	                               ( ( exuE1 ) =>
99.32/13.16	                                 ( ( prop2setE ) =>
99.32/13.16	                                   ( ( emptysetE ) =>
99.32/13.16	                                     ( ( emptysetimpfalse ) =>
99.32/13.16	                                       ( ( notinemptyset ) =>
99.32/13.16	                                         ( ( exuE3e ) =>
99.32/13.16	                                           ( ( setext ) =>
99.32/13.16	                                             ( ( emptyI ) =>
99.32/13.16	                                               ( ( noeltsimpempty ) =>
99.32/13.16	                                                 ( ( setbeta ) =>
99.32/13.16	                                                   ( ( nonemptyE1 ) =>
99.32/13.16	                                                     ( ( nonemptyI ) =>
99.32/13.16	                                                       ( ( nonemptyI1 ) =>
99.32/13.16	                                                         ( ( setadjoinIL ) =>
99.32/13.16	                                                           ( ( emptyinunitempty ) =>
99.32/13.16	                                                             ( ( setadjoinIR ) =>
99.32/13.16	                                                               ( ( setadjoinE ) =>
99.32/13.16	                                                                 ( ( 
99.32/13.16	                                                                   setadjoinOr ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   setoftrueEq ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   powersetI ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   emptyinPowerset ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   emptyInPowerset ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   powersetE ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   setunionI ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   setunionE ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   subPowSU ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   exuE2 ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   nonemptyImpWitness ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   uniqinunit ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   notinsingleton ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   eqinunit ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   singletonsswitch ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   upairsetE ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   upairsetIL ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   upairsetIR ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   emptyE1 ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   vacuousDall ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   quantDeMorgan1 ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   quantDeMorgan2 ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   quantDeMorgan3 ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   quantDeMorgan4 ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   prop2setI ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   prop2set2propI ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   notdexE ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   notdallE ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   exuI1 ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   exuI3 ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   exuI2 ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   inCongP ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   in__Cong ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   exuE3u ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   exu__Cong ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   emptyset__Cong ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   setadjoin__Cong ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   powerset__Cong ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   setunion__Cong ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   omega__Cong ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   exuEu ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   descr__Cong ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   dsetconstr__Cong ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   subsetI1 ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   eqimpsubset2 ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   eqimpsubset1 ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   subsetI2 ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   emptysetsubset ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   subsetE ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   subsetE2 ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   notsubsetI ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   notequalI1 ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   notequalI2 ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   subsetRefl ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   subsetTrans ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   setadjoinSub ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   setadjoinSub2 ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   subset2powerset ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   setextsub ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   subsetemptysetimpeq ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   powersetI1 ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   powersetE1 ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   inPowerset ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   powersetsubset ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   sepInPowerset ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   sepSubset ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ![
99.32/13.16	                                                                   A:$i,B:$i,
99.32/13.16	                                                                   Xx:$i]:
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   in @
99.32/13.16	                                                                   Xx @ A ) =>
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   in @
99.32/13.16	                                                                   Xx @ 
99.32/13.16	                                                                   ( 
99.32/13.16	                                                                   binunion @
99.32/13.16	                                                                   A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
99.32/13.16	thf(zf_stmt_0, negated_conjecture,
99.32/13.16	  (~( ( setextAx ) =>
99.32/13.16	      ( ( emptysetAx ) =>
99.32/13.16	        ( ( setadjoinAx ) =>
99.32/13.16	          ( ( powersetAx ) =>
99.32/13.16	            ( ( setunionAx ) =>
99.32/13.16	              ( ( omega0Ax ) =>
99.32/13.16	                ( ( omegaSAx ) =>
99.32/13.16	                  ( ( omegaIndAx ) =>
99.32/13.16	                    ( ( replAx ) =>
99.32/13.16	                      ( ( foundationAx ) =>
99.32/13.16	                        ( ( wellorderingAx ) =>
99.32/13.16	                          ( ( descrp ) =>
99.32/13.16	                            ( ( dsetconstrI ) =>
99.32/13.16	                              ( ( dsetconstrEL ) =>
99.32/13.16	                                ( ( dsetconstrER ) =>
99.32/13.16	                                  ( ( exuE1 ) =>
99.32/13.16	                                    ( ( prop2setE ) =>
99.32/13.16	                                      ( ( emptysetE ) =>
99.32/13.16	                                        ( ( emptysetimpfalse ) =>
99.32/13.16	                                          ( ( notinemptyset ) =>
99.32/13.16	                                            ( ( exuE3e ) =>
99.32/13.16	                                              ( ( setext ) =>
99.32/13.16	                                                ( ( emptyI ) =>
99.32/13.16	                                                  ( ( noeltsimpempty ) =>
99.32/13.16	                                                    ( ( setbeta ) =>
99.32/13.16	                                                      ( ( nonemptyE1 ) =>
99.32/13.16	                                                        ( ( nonemptyI ) =>
99.32/13.16	                                                          ( ( nonemptyI1 ) =>
99.32/13.16	                                                            ( ( setadjoinIL ) =>
99.32/13.16	                                                              ( ( emptyinunitempty ) =>
99.32/13.16	                                                                ( ( setadjoinIR ) =>
99.32/13.16	                                                                  ( ( 
99.32/13.16	                                                                    setadjoinE ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    setadjoinOr ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    setoftrueEq ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    powersetI ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    emptyinPowerset ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    emptyInPowerset ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    powersetE ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    setunionI ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    setunionE ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    subPowSU ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    exuE2 ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    nonemptyImpWitness ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    uniqinunit ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    notinsingleton ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    eqinunit ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    singletonsswitch ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    upairsetE ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    upairsetIL ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    upairsetIR ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    emptyE1 ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    vacuousDall ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    quantDeMorgan1 ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    quantDeMorgan2 ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    quantDeMorgan3 ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    quantDeMorgan4 ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    prop2setI ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    prop2set2propI ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    notdexE ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    notdallE ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    exuI1 ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    exuI3 ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    exuI2 ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    inCongP ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    in__Cong ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    exuE3u ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    exu__Cong ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    emptyset__Cong ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    setadjoin__Cong ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    powerset__Cong ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    setunion__Cong ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    omega__Cong ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    exuEu ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    descr__Cong ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    dsetconstr__Cong ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    subsetI1 ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    eqimpsubset2 ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    eqimpsubset1 ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    subsetI2 ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    emptysetsubset ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    subsetE ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    subsetE2 ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    notsubsetI ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    notequalI1 ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    notequalI2 ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    subsetRefl ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    subsetTrans ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    setadjoinSub ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    setadjoinSub2 ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    subset2powerset ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    setextsub ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    subsetemptysetimpeq ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    powersetI1 ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    powersetE1 ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    inPowerset ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    powersetsubset ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    sepInPowerset ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    sepSubset ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ![
99.32/13.16	                                                                    A:$i,
99.32/13.16	                                                                    B:$i,
99.32/13.16	                                                                    Xx:$i]:
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    in @
99.32/13.16	                                                                    Xx @ A ) =>
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    in @
99.32/13.16	                                                                    Xx @ 
99.32/13.16	                                                                    ( 
99.32/13.16	                                                                    binunion
99.32/13.16	                                                                    @ 
99.32/13.16	                                                                    A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
99.32/13.16	  inference('cnf.neg', [status(esa)], [binunionIL])).
99.32/13.16	thf(zip_derived_cl0, plain,
99.32/13.16	    (~ (((setextAx) =>
99.32/13.16	         (((emptysetAx) =>
99.32/13.16	           (((setadjoinAx) =>
99.32/13.16	             (((powersetAx) =>
99.32/13.16	               (((setunionAx) =>
99.32/13.16	                 (((omega0Ax) =>
99.32/13.16	                   (((omegaSAx) =>
99.32/13.16	                     (((omegaIndAx) =>
99.32/13.16	                       (((replAx) =>
99.32/13.16	                         (((foundationAx) =>
99.32/13.16	                           (((wellorderingAx) =>
99.32/13.16	                             (((descrp) =>
99.32/13.16	                               (((dsetconstrI) =>
99.32/13.16	                                 (((dsetconstrEL) =>
99.32/13.16	                                   (((dsetconstrER) =>
99.32/13.16	                                     (((exuE1) =>
99.32/13.16	                                       (((prop2setE) =>
99.32/13.16	                                         (((emptysetE) =>
99.32/13.16	                                           (((emptysetimpfalse) =>
99.32/13.16	                                             (((notinemptyset) =>
99.32/13.16	                                               (((exuE3e) =>
99.32/13.16	                                                 (((setext) =>
99.32/13.16	                                                   (((emptyI) =>
99.32/13.16	                                                     (((noeltsimpempty) =>
99.32/13.16	                                                       (((setbeta) =>
99.32/13.16	                                                         (((nonemptyE1) =>
99.32/13.16	                                                           (((nonemptyI) =>
99.32/13.16	                                                             (((nonemptyI1) =>
99.32/13.16	                                                               (((setadjoinIL) =>
99.32/13.16	                                                                 (((emptyinunitempty) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setadjoinIR) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setadjoinE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setadjoinOr) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setoftrueEq) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powersetI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (emptyinPowerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (emptyInPowerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powersetE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setunionI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setunionE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subPowSU) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuE2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (nonemptyImpWitness) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (uniqinunit) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notinsingleton) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (eqinunit) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (singletonsswitch) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (upairsetE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (upairsetIL) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (upairsetIR) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (emptyE1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (vacuousDall) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (quantDeMorgan1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (quantDeMorgan2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (quantDeMorgan3) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (quantDeMorgan4) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (prop2setI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (prop2set2propI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notdexE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notdallE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuI1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuI3) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuI2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (inCongP) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (in__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuE3u) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exu__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (emptyset__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setadjoin__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powerset__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setunion__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (omega__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuEu) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (descr__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (dsetconstr__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetI1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (eqimpsubset2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (eqimpsubset1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetI2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (emptysetsubset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetE2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notsubsetI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notequalI1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notequalI2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetRefl) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetTrans) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setadjoinSub) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setadjoinSub2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subset2powerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setextsub) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetemptysetimpeq) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powersetI1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powersetE1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (inPowerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powersetsubset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (sepInPowerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (sepSubset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (!!) @ (
99.32/13.16	                                                                   ^[Y0 : $i]:
99.32/13.16	                                                                    ((
99.32/13.16	                                                                    (!!) @ (
99.32/13.16	                                                                    ^[Y1 : $i]:
99.32/13.16	                                                                    ((
99.32/13.16	                                                                    (!!) @ (
99.32/13.16	                                                                    ^[Y2 : $i]:
99.32/13.16	                                                                    ((
99.32/13.16	                                                                    (in @ 
99.32/13.16	                                                                    Y2 @ 
99.32/13.16	                                                                    Y0) =>
99.32/13.16	                                                                    (in @ 
99.32/13.16	                                                                    Y2 @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    binunion @ 
99.32/13.16	                                                                    Y0 @ Y1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.16	    inference('cnf', [status(esa)], [zf_stmt_0])).
99.32/13.16	thf(zip_derived_cl1, plain,
99.32/13.16	    (~ (((setextAx) =>
99.32/13.16	         (((emptysetAx) =>
99.32/13.16	           (((setadjoinAx) =>
99.32/13.16	             (((powersetAx) =>
99.32/13.16	               (((setunionAx) =>
99.32/13.16	                 (((omega0Ax) =>
99.32/13.16	                   (((omegaSAx) =>
99.32/13.16	                     (((omegaIndAx) =>
99.32/13.16	                       (((replAx) =>
99.32/13.16	                         (((foundationAx) =>
99.32/13.16	                           (((wellorderingAx) =>
99.32/13.16	                             (((descrp) =>
99.32/13.16	                               (((dsetconstrI) =>
99.32/13.16	                                 (((dsetconstrEL) =>
99.32/13.16	                                   (((dsetconstrER) =>
99.32/13.16	                                     (((exuE1) =>
99.32/13.16	                                       (((prop2setE) =>
99.32/13.16	                                         (((emptysetE) =>
99.32/13.16	                                           (((emptysetimpfalse) =>
99.32/13.16	                                             (((notinemptyset) =>
99.32/13.16	                                               (((exuE3e) =>
99.32/13.16	                                                 (((setext) =>
99.32/13.16	                                                   (((emptyI) =>
99.32/13.16	                                                     (((noeltsimpempty) =>
99.32/13.16	                                                       (((setbeta) =>
99.32/13.16	                                                         (((nonemptyE1) =>
99.32/13.16	                                                           (((nonemptyI) =>
99.32/13.16	                                                             (((nonemptyI1) =>
99.32/13.16	                                                               (((setadjoinIL) =>
99.32/13.16	                                                                 (((emptyinunitempty) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setadjoinIR) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setadjoinE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setadjoinOr) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setoftrueEq) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powersetI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (emptyinPowerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (emptyInPowerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powersetE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setunionI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setunionE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subPowSU) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuE2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (nonemptyImpWitness) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (uniqinunit) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notinsingleton) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (eqinunit) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (singletonsswitch) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (upairsetE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (upairsetIL) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (upairsetIR) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (emptyE1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (vacuousDall) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (quantDeMorgan1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (quantDeMorgan2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (quantDeMorgan3) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (quantDeMorgan4) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (prop2setI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (prop2set2propI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notdexE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notdallE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuI1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuI3) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuI2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (inCongP) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (in__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuE3u) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exu__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (emptyset__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setadjoin__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powerset__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setunion__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (omega__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuEu) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (descr__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (dsetconstr__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetI1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (eqimpsubset2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (eqimpsubset1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetI2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (emptysetsubset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetE2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notsubsetI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notequalI1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notequalI2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetRefl) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetTrans) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setadjoinSub) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setadjoinSub2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subset2powerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setextsub) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetemptysetimpeq) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powersetI1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powersetE1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (inPowerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powersetsubset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (sepInPowerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (sepSubset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (!!) @ (
99.32/13.16	                                                                   (('#B') @ (
99.32/13.16	                                                                    !!) @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    !!))) @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#S') @ (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    '#B') @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    '#S') @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    =>))) @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#C') @ in)))))))) @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#C') @ in)))) @ 
99.32/13.16	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.16	    inference('lams2combs', [status(thm)], [zip_derived_cl0])).
99.32/13.16	thf(omega0Ax, axiom,(( omega0Ax  ) = ((in @ emptyset @ omega)))).
99.32/13.16	thf('0', plain, (( omega0Ax ) = ( in @ emptyset @ omega )),
99.32/13.16	    define([status(thm)])).
99.32/13.16	thf(emptyinunitempty, axiom,(( emptyinunitempty  ) =
99.32/13.16	  ((in @ emptyset @ (setadjoin @ emptyset @ emptyset))))).
99.32/13.16	thf('1', plain,
99.32/13.16	    (( emptyinunitempty ) =
99.32/13.16	     ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
99.32/13.16	    define([status(thm)])).
99.32/13.16	thf(emptyset__Cong, axiom,(( emptyset__Cong  ) =
99.32/13.16	  ((((emptyset) = (emptyset)))))).
99.32/13.16	thf('2', plain, (( emptyset__Cong ) = ( ( emptyset ) = ( emptyset ) )),
99.32/13.16	    define([status(thm)])).
99.32/13.16	thf(omega__Cong, axiom,(( omega__Cong  ) = ((((omega) = (omega)))))).
99.32/13.16	thf('3', plain, (( omega__Cong ) = ( ( omega ) = ( omega ) )),
99.32/13.16	    define([status(thm)])).
99.32/13.16	thf(zip_derived_cl2, plain,
99.32/13.16	    (~ (((setextAx) =>
99.32/13.16	         (((emptysetAx) =>
99.32/13.16	           (((setadjoinAx) =>
99.32/13.16	             (((powersetAx) =>
99.32/13.16	               (((setunionAx) =>
99.32/13.16	                 (((in @ emptyset @ omega) =>
99.32/13.16	                   (((omegaSAx) =>
99.32/13.16	                     (((omegaIndAx) =>
99.32/13.16	                       (((replAx) =>
99.32/13.16	                         (((foundationAx) =>
99.32/13.16	                           (((wellorderingAx) =>
99.32/13.16	                             (((descrp) =>
99.32/13.16	                               (((dsetconstrI) =>
99.32/13.16	                                 (((dsetconstrEL) =>
99.32/13.16	                                   (((dsetconstrER) =>
99.32/13.16	                                     (((exuE1) =>
99.32/13.16	                                       (((prop2setE) =>
99.32/13.16	                                         (((emptysetE) =>
99.32/13.16	                                           (((emptysetimpfalse) =>
99.32/13.16	                                             (((notinemptyset) =>
99.32/13.16	                                               (((exuE3e) =>
99.32/13.16	                                                 (((setext) =>
99.32/13.16	                                                   (((emptyI) =>
99.32/13.16	                                                     (((noeltsimpempty) =>
99.32/13.16	                                                       (((setbeta) =>
99.32/13.16	                                                         (((nonemptyE1) =>
99.32/13.16	                                                           (((nonemptyI) =>
99.32/13.16	                                                             (((nonemptyI1) =>
99.32/13.16	                                                               (((setadjoinIL) =>
99.32/13.16	                                                                 (((in @ 
99.32/13.16	                                                                   emptyset @ 
99.32/13.16	                                                                   (setadjoin @ 
99.32/13.16	                                                                    emptyset @ 
99.32/13.16	                                                                    emptyset)) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setadjoinIR) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setadjoinE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setadjoinOr) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setoftrueEq) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powersetI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (emptyinPowerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (emptyInPowerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powersetE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setunionI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setunionE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subPowSU) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuE2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (nonemptyImpWitness) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (uniqinunit) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notinsingleton) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (eqinunit) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (singletonsswitch) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (upairsetE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (upairsetIL) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (upairsetIR) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (emptyE1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (vacuousDall) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (quantDeMorgan1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (quantDeMorgan2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (quantDeMorgan3) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (quantDeMorgan4) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (prop2setI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (prop2set2propI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notdexE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notdallE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuI1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuI3) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuI2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (inCongP) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (in__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuE3u) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exu__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (emptyset) =
99.32/13.16	                                                                   (emptyset))) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setadjoin__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powerset__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setunion__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (omega) =
99.32/13.16	                                                                   (omega))) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuEu) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (descr__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (dsetconstr__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetI1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (eqimpsubset2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (eqimpsubset1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetI2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (emptysetsubset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetE2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notsubsetI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notequalI1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notequalI2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetRefl) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetTrans) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setadjoinSub) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setadjoinSub2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subset2powerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setextsub) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetemptysetimpeq) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powersetI1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powersetE1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (inPowerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powersetsubset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (sepInPowerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (sepSubset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (!!) @ (
99.32/13.16	                                                                   (('#B') @ (
99.32/13.16	                                                                    !!) @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    !!))) @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#S') @ (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    '#B') @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    '#S') @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    =>))) @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#C') @ in)))))))) @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#C') @ in)))) @ 
99.32/13.16	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.16	    inference('rw', [status(thm)], [zip_derived_cl1, '0', '1', '2', '3'])).
99.32/13.16	thf(zip_derived_cl3, plain,
99.32/13.16	    (~ (((setextAx) =>
99.32/13.16	         (((emptysetAx) =>
99.32/13.16	           (((setadjoinAx) =>
99.32/13.16	             (((powersetAx) =>
99.32/13.16	               (((setunionAx) =>
99.32/13.16	                 (((in @ emptyset @ omega) =>
99.32/13.16	                   (((omegaSAx) =>
99.32/13.16	                     (((omegaIndAx) =>
99.32/13.16	                       (((replAx) =>
99.32/13.16	                         (((foundationAx) =>
99.32/13.16	                           (((wellorderingAx) =>
99.32/13.16	                             (((descrp) =>
99.32/13.16	                               (((dsetconstrI) =>
99.32/13.16	                                 (((dsetconstrEL) =>
99.32/13.16	                                   (((dsetconstrER) =>
99.32/13.16	                                     (((exuE1) =>
99.32/13.16	                                       (((prop2setE) =>
99.32/13.16	                                         (((emptysetE) =>
99.32/13.16	                                           (((emptysetimpfalse) =>
99.32/13.16	                                             (((notinemptyset) =>
99.32/13.16	                                               (((exuE3e) =>
99.32/13.16	                                                 (((setext) =>
99.32/13.16	                                                   (((emptyI) =>
99.32/13.16	                                                     (((noeltsimpempty) =>
99.32/13.16	                                                       (((setbeta) =>
99.32/13.16	                                                         (((nonemptyE1) =>
99.32/13.16	                                                           (((nonemptyI) =>
99.32/13.16	                                                             (((nonemptyI1) =>
99.32/13.16	                                                               (((setadjoinIL) =>
99.32/13.16	                                                                 (((in @ 
99.32/13.16	                                                                   emptyset @ 
99.32/13.16	                                                                   (setadjoin @ 
99.32/13.16	                                                                    emptyset @ 
99.32/13.16	                                                                    emptyset)) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setadjoinIR) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setadjoinE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setadjoinOr) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setoftrueEq) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powersetI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (emptyinPowerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (emptyInPowerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powersetE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setunionI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setunionE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subPowSU) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuE2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (nonemptyImpWitness) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (uniqinunit) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notinsingleton) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (eqinunit) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (singletonsswitch) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (upairsetE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (upairsetIL) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (upairsetIR) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (emptyE1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (vacuousDall) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (quantDeMorgan1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (quantDeMorgan2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (quantDeMorgan3) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (quantDeMorgan4) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (prop2setI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (prop2set2propI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notdexE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notdallE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuI1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuI3) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuI2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (inCongP) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (in__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuE3u) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exu__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setadjoin__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powerset__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setunion__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuEu) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (descr__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (dsetconstr__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetI1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (eqimpsubset2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (eqimpsubset1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetI2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (emptysetsubset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetE2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notsubsetI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notequalI1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notequalI2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetRefl) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetTrans) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setadjoinSub) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setadjoinSub2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subset2powerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setextsub) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetemptysetimpeq) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powersetI1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powersetE1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (inPowerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powersetsubset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (sepInPowerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (sepSubset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (!!) @ (
99.32/13.16	                                                                   (('#B') @ (
99.32/13.16	                                                                    !!) @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    !!))) @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#S') @ (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    '#B') @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    '#S') @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    =>))) @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#C') @ in)))))))) @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#C') @ in)))) @ 
99.32/13.16	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.16	    inference('simplify boolean subterms', [status(thm)], [zip_derived_cl2])).
99.32/13.16	thf(zip_derived_cl5, plain,
99.32/13.16	    (~ (((emptysetAx) =>
99.32/13.16	         (((setadjoinAx) =>
99.32/13.16	           (((powersetAx) =>
99.32/13.16	             (((setunionAx) =>
99.32/13.16	               (((in @ emptyset @ omega) =>
99.32/13.16	                 (((omegaSAx) =>
99.32/13.16	                   (((omegaIndAx) =>
99.32/13.16	                     (((replAx) =>
99.32/13.16	                       (((foundationAx) =>
99.32/13.16	                         (((wellorderingAx) =>
99.32/13.16	                           (((descrp) =>
99.32/13.16	                             (((dsetconstrI) =>
99.32/13.16	                               (((dsetconstrEL) =>
99.32/13.16	                                 (((dsetconstrER) =>
99.32/13.16	                                   (((exuE1) =>
99.32/13.16	                                     (((prop2setE) =>
99.32/13.16	                                       (((emptysetE) =>
99.32/13.16	                                         (((emptysetimpfalse) =>
99.32/13.16	                                           (((notinemptyset) =>
99.32/13.16	                                             (((exuE3e) =>
99.32/13.16	                                               (((setext) =>
99.32/13.16	                                                 (((emptyI) =>
99.32/13.16	                                                   (((noeltsimpempty) =>
99.32/13.16	                                                     (((setbeta) =>
99.32/13.16	                                                       (((nonemptyE1) =>
99.32/13.16	                                                         (((nonemptyI) =>
99.32/13.16	                                                           (((nonemptyI1) =>
99.32/13.16	                                                             (((setadjoinIL) =>
99.32/13.16	                                                               (((in @ 
99.32/13.16	                                                                 emptyset @ 
99.32/13.16	                                                                 (setadjoin @ 
99.32/13.16	                                                                  emptyset @ 
99.32/13.16	                                                                  emptyset)) =>
99.32/13.16	                                                                 (((setadjoinIR) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setadjoinE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setadjoinOr) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setoftrueEq) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powersetI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (emptyinPowerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (emptyInPowerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powersetE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setunionI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setunionE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subPowSU) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuE2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (nonemptyImpWitness) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (uniqinunit) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notinsingleton) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (eqinunit) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (singletonsswitch) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (upairsetE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (upairsetIL) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (upairsetIR) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (emptyE1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (vacuousDall) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (quantDeMorgan1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (quantDeMorgan2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (quantDeMorgan3) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (quantDeMorgan4) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (prop2setI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (prop2set2propI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notdexE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notdallE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuI1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuI3) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuI2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (inCongP) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (in__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuE3u) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exu__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setadjoin__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powerset__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setunion__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuEu) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (descr__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (dsetconstr__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetI1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (eqimpsubset2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (eqimpsubset1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetI2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (emptysetsubset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetE2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notsubsetI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notequalI1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notequalI2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetRefl) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetTrans) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setadjoinSub) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setadjoinSub2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subset2powerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setextsub) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetemptysetimpeq) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powersetI1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powersetE1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (inPowerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powersetsubset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (sepInPowerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (sepSubset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (!!) @ (
99.32/13.16	                                                                   (('#B') @ (
99.32/13.16	                                                                    !!) @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    !!))) @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#S') @ (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    '#B') @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    '#S') @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    =>))) @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#C') @ in)))))))) @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#C') @ in)))) @ 
99.32/13.16	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.16	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3])).
99.32/13.16	thf(zip_derived_cl8, plain,
99.32/13.16	    (~ (((setadjoinAx) =>
99.32/13.16	         (((powersetAx) =>
99.32/13.16	           (((setunionAx) =>
99.32/13.16	             (((in @ emptyset @ omega) =>
99.32/13.16	               (((omegaSAx) =>
99.32/13.16	                 (((omegaIndAx) =>
99.32/13.16	                   (((replAx) =>
99.32/13.16	                     (((foundationAx) =>
99.32/13.16	                       (((wellorderingAx) =>
99.32/13.16	                         (((descrp) =>
99.32/13.16	                           (((dsetconstrI) =>
99.32/13.16	                             (((dsetconstrEL) =>
99.32/13.16	                               (((dsetconstrER) =>
99.32/13.16	                                 (((exuE1) =>
99.32/13.16	                                   (((prop2setE) =>
99.32/13.16	                                     (((emptysetE) =>
99.32/13.16	                                       (((emptysetimpfalse) =>
99.32/13.16	                                         (((notinemptyset) =>
99.32/13.16	                                           (((exuE3e) =>
99.32/13.16	                                             (((setext) =>
99.32/13.16	                                               (((emptyI) =>
99.32/13.16	                                                 (((noeltsimpempty) =>
99.32/13.16	                                                   (((setbeta) =>
99.32/13.16	                                                     (((nonemptyE1) =>
99.32/13.16	                                                       (((nonemptyI) =>
99.32/13.16	                                                         (((nonemptyI1) =>
99.32/13.16	                                                           (((setadjoinIL) =>
99.32/13.16	                                                             (((in @ 
99.32/13.16	                                                               emptyset @ 
99.32/13.16	                                                               (setadjoin @ 
99.32/13.16	                                                                emptyset @ 
99.32/13.16	                                                                emptyset)) =>
99.32/13.16	                                                               (((setadjoinIR) =>
99.32/13.16	                                                                 (((setadjoinE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setadjoinOr) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setoftrueEq) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powersetI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (emptyinPowerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (emptyInPowerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powersetE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setunionI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setunionE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subPowSU) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuE2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (nonemptyImpWitness) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (uniqinunit) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notinsingleton) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (eqinunit) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (singletonsswitch) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (upairsetE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (upairsetIL) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (upairsetIR) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (emptyE1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (vacuousDall) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (quantDeMorgan1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (quantDeMorgan2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (quantDeMorgan3) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (quantDeMorgan4) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (prop2setI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (prop2set2propI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notdexE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notdallE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuI1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuI3) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuI2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (inCongP) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (in__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuE3u) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exu__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setadjoin__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powerset__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setunion__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuEu) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (descr__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (dsetconstr__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetI1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (eqimpsubset2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (eqimpsubset1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetI2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (emptysetsubset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetE2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notsubsetI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notequalI1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notequalI2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetRefl) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetTrans) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setadjoinSub) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setadjoinSub2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subset2powerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setextsub) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetemptysetimpeq) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powersetI1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powersetE1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (inPowerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powersetsubset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (sepInPowerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (sepSubset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (!!) @ (
99.32/13.16	                                                                   (('#B') @ (
99.32/13.16	                                                                    !!) @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    !!))) @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#S') @ (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    '#B') @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    '#S') @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    =>))) @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#C') @ in)))))))) @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#C') @ in)))) @ 
99.32/13.16	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.16	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5])).
99.32/13.16	thf(zip_derived_cl13, plain,
99.32/13.16	    (~ (((powersetAx) =>
99.32/13.16	         (((setunionAx) =>
99.32/13.16	           (((in @ emptyset @ omega) =>
99.32/13.16	             (((omegaSAx) =>
99.32/13.16	               (((omegaIndAx) =>
99.32/13.16	                 (((replAx) =>
99.32/13.16	                   (((foundationAx) =>
99.32/13.16	                     (((wellorderingAx) =>
99.32/13.16	                       (((descrp) =>
99.32/13.16	                         (((dsetconstrI) =>
99.32/13.16	                           (((dsetconstrEL) =>
99.32/13.16	                             (((dsetconstrER) =>
99.32/13.16	                               (((exuE1) =>
99.32/13.16	                                 (((prop2setE) =>
99.32/13.16	                                   (((emptysetE) =>
99.32/13.16	                                     (((emptysetimpfalse) =>
99.32/13.16	                                       (((notinemptyset) =>
99.32/13.16	                                         (((exuE3e) =>
99.32/13.16	                                           (((setext) =>
99.32/13.16	                                             (((emptyI) =>
99.32/13.16	                                               (((noeltsimpempty) =>
99.32/13.16	                                                 (((setbeta) =>
99.32/13.16	                                                   (((nonemptyE1) =>
99.32/13.16	                                                     (((nonemptyI) =>
99.32/13.16	                                                       (((nonemptyI1) =>
99.32/13.16	                                                         (((setadjoinIL) =>
99.32/13.16	                                                           (((in @ 
99.32/13.16	                                                             emptyset @ 
99.32/13.16	                                                             (setadjoin @ 
99.32/13.16	                                                              emptyset @ 
99.32/13.16	                                                              emptyset)) =>
99.32/13.16	                                                             (((setadjoinIR) =>
99.32/13.16	                                                               (((setadjoinE) =>
99.32/13.16	                                                                 (((setadjoinOr) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setoftrueEq) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powersetI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (emptyinPowerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (emptyInPowerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powersetE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setunionI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setunionE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subPowSU) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuE2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (nonemptyImpWitness) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (uniqinunit) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notinsingleton) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (eqinunit) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (singletonsswitch) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (upairsetE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (upairsetIL) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (upairsetIR) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (emptyE1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (vacuousDall) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (quantDeMorgan1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (quantDeMorgan2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (quantDeMorgan3) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (quantDeMorgan4) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (prop2setI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (prop2set2propI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notdexE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notdallE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuI1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuI3) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuI2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (inCongP) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (in__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuE3u) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exu__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setadjoin__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powerset__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setunion__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuEu) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (descr__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (dsetconstr__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetI1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (eqimpsubset2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (eqimpsubset1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetI2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (emptysetsubset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetE2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notsubsetI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notequalI1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notequalI2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetRefl) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetTrans) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setadjoinSub) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setadjoinSub2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subset2powerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setextsub) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetemptysetimpeq) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powersetI1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powersetE1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (inPowerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powersetsubset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (sepInPowerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (sepSubset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (!!) @ (
99.32/13.16	                                                                   (('#B') @ (
99.32/13.16	                                                                    !!) @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    !!))) @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#S') @ (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    '#B') @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    '#S') @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    =>))) @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#C') @ in)))))))) @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#C') @ in)))) @ 
99.32/13.16	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.16	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])).
99.32/13.16	thf(zip_derived_cl19, plain,
99.32/13.16	    (~ (((setunionAx) =>
99.32/13.16	         (((in @ emptyset @ omega) =>
99.32/13.16	           (((omegaSAx) =>
99.32/13.16	             (((omegaIndAx) =>
99.32/13.16	               (((replAx) =>
99.32/13.16	                 (((foundationAx) =>
99.32/13.16	                   (((wellorderingAx) =>
99.32/13.16	                     (((descrp) =>
99.32/13.16	                       (((dsetconstrI) =>
99.32/13.16	                         (((dsetconstrEL) =>
99.32/13.16	                           (((dsetconstrER) =>
99.32/13.16	                             (((exuE1) =>
99.32/13.16	                               (((prop2setE) =>
99.32/13.16	                                 (((emptysetE) =>
99.32/13.16	                                   (((emptysetimpfalse) =>
99.32/13.16	                                     (((notinemptyset) =>
99.32/13.16	                                       (((exuE3e) =>
99.32/13.16	                                         (((setext) =>
99.32/13.16	                                           (((emptyI) =>
99.32/13.16	                                             (((noeltsimpempty) =>
99.32/13.16	                                               (((setbeta) =>
99.32/13.16	                                                 (((nonemptyE1) =>
99.32/13.16	                                                   (((nonemptyI) =>
99.32/13.16	                                                     (((nonemptyI1) =>
99.32/13.16	                                                       (((setadjoinIL) =>
99.32/13.16	                                                         (((in @ emptyset @ 
99.32/13.16	                                                           (setadjoin @ 
99.32/13.16	                                                            emptyset @ 
99.32/13.16	                                                            emptyset)) =>
99.32/13.16	                                                           (((setadjoinIR) =>
99.32/13.16	                                                             (((setadjoinE) =>
99.32/13.16	                                                               (((setadjoinOr) =>
99.32/13.16	                                                                 (((setoftrueEq) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powersetI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (emptyinPowerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (emptyInPowerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powersetE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setunionI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setunionE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subPowSU) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuE2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (nonemptyImpWitness) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (uniqinunit) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notinsingleton) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (eqinunit) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (singletonsswitch) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (upairsetE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (upairsetIL) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (upairsetIR) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (emptyE1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (vacuousDall) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (quantDeMorgan1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (quantDeMorgan2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (quantDeMorgan3) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (quantDeMorgan4) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (prop2setI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (prop2set2propI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notdexE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notdallE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuI1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuI3) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuI2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (inCongP) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (in__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuE3u) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exu__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setadjoin__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powerset__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setunion__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuEu) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (descr__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (dsetconstr__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetI1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (eqimpsubset2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (eqimpsubset1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetI2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (emptysetsubset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetE2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notsubsetI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notequalI1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notequalI2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetRefl) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetTrans) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setadjoinSub) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setadjoinSub2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subset2powerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setextsub) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetemptysetimpeq) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powersetI1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powersetE1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (inPowerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powersetsubset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (sepInPowerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (sepSubset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (!!) @ (
99.32/13.16	                                                                   (('#B') @ (
99.32/13.16	                                                                    !!) @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    !!))) @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#S') @ (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    '#B') @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    '#S') @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    =>))) @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#C') @ in)))))))) @ 
99.32/13.16	                                                                    (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#B') @ (
99.32/13.16	                                                                    (
99.32/13.16	                                                                    ('#C') @ in)))) @ 
99.32/13.16	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.16	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl13])).
99.32/13.16	thf(zip_derived_cl25, plain,
99.32/13.16	    (~ (((in @ emptyset @ omega) =>
99.32/13.16	         (((omegaSAx) =>
99.32/13.16	           (((omegaIndAx) =>
99.32/13.16	             (((replAx) =>
99.32/13.16	               (((foundationAx) =>
99.32/13.16	                 (((wellorderingAx) =>
99.32/13.16	                   (((descrp) =>
99.32/13.16	                     (((dsetconstrI) =>
99.32/13.16	                       (((dsetconstrEL) =>
99.32/13.16	                         (((dsetconstrER) =>
99.32/13.16	                           (((exuE1) =>
99.32/13.16	                             (((prop2setE) =>
99.32/13.16	                               (((emptysetE) =>
99.32/13.16	                                 (((emptysetimpfalse) =>
99.32/13.16	                                   (((notinemptyset) =>
99.32/13.16	                                     (((exuE3e) =>
99.32/13.16	                                       (((setext) =>
99.32/13.16	                                         (((emptyI) =>
99.32/13.16	                                           (((noeltsimpempty) =>
99.32/13.16	                                             (((setbeta) =>
99.32/13.16	                                               (((nonemptyE1) =>
99.32/13.16	                                                 (((nonemptyI) =>
99.32/13.16	                                                   (((nonemptyI1) =>
99.32/13.16	                                                     (((setadjoinIL) =>
99.32/13.16	                                                       (((in @ emptyset @ 
99.32/13.16	                                                         (setadjoin @ 
99.32/13.16	                                                          emptyset @ emptyset)) =>
99.32/13.16	                                                         (((setadjoinIR) =>
99.32/13.16	                                                           (((setadjoinE) =>
99.32/13.16	                                                             (((setadjoinOr) =>
99.32/13.16	                                                               (((setoftrueEq) =>
99.32/13.16	                                                                 (((powersetI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (emptyinPowerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (emptyInPowerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powersetE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setunionI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setunionE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subPowSU) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuE2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (nonemptyImpWitness) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (uniqinunit) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notinsingleton) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (eqinunit) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (singletonsswitch) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (upairsetE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (upairsetIL) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (upairsetIR) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (emptyE1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (vacuousDall) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (quantDeMorgan1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (quantDeMorgan2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (quantDeMorgan3) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (quantDeMorgan4) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (prop2setI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (prop2set2propI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notdexE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notdallE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuI1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuI3) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuI2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (inCongP) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (in__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuE3u) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exu__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setadjoin__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (powerset__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setunion__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (exuEu) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (descr__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (dsetconstr__Cong) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetI1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (eqimpsubset2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (eqimpsubset1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetI2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (emptysetsubset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetE) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetE2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notsubsetI) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notequalI1) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (notequalI2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetRefl) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetTrans) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setadjoinSub) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setadjoinSub2) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subset2powerset) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (setextsub) =>
99.32/13.16	                                                                   ((
99.32/13.16	                                                                   (subsetemptysetimpeq) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetE1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (inPowerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetsubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (sepInPowerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (sepSubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (!!) @ (
99.32/13.17	                                                                   (('#B') @ (
99.32/13.17	                                                                    !!) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    !!))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#S') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    '#B') @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    '#S') @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    =>))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#C') @ in)))))))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#C') @ in)))) @ 
99.32/13.17	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.17	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl19])).
99.32/13.17	thf(zip_derived_cl33, plain,
99.32/13.17	    (~ (((omegaSAx) =>
99.32/13.17	         (((omegaIndAx) =>
99.32/13.17	           (((replAx) =>
99.32/13.17	             (((foundationAx) =>
99.32/13.17	               (((wellorderingAx) =>
99.32/13.17	                 (((descrp) =>
99.32/13.17	                   (((dsetconstrI) =>
99.32/13.17	                     (((dsetconstrEL) =>
99.32/13.17	                       (((dsetconstrER) =>
99.32/13.17	                         (((exuE1) =>
99.32/13.17	                           (((prop2setE) =>
99.32/13.17	                             (((emptysetE) =>
99.32/13.17	                               (((emptysetimpfalse) =>
99.32/13.17	                                 (((notinemptyset) =>
99.32/13.17	                                   (((exuE3e) =>
99.32/13.17	                                     (((setext) =>
99.32/13.17	                                       (((emptyI) =>
99.32/13.17	                                         (((noeltsimpempty) =>
99.32/13.17	                                           (((setbeta) =>
99.32/13.17	                                             (((nonemptyE1) =>
99.32/13.17	                                               (((nonemptyI) =>
99.32/13.17	                                                 (((nonemptyI1) =>
99.32/13.17	                                                   (((setadjoinIL) =>
99.32/13.17	                                                     (((in @ emptyset @ 
99.32/13.17	                                                       (setadjoin @ 
99.32/13.17	                                                        emptyset @ emptyset)) =>
99.32/13.17	                                                       (((setadjoinIR) =>
99.32/13.17	                                                         (((setadjoinE) =>
99.32/13.17	                                                           (((setadjoinOr) =>
99.32/13.17	                                                             (((setoftrueEq) =>
99.32/13.17	                                                               (((powersetI) =>
99.32/13.17	                                                                 (((emptyinPowerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (emptyInPowerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setunionI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setunionE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subPowSU) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuE2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (nonemptyImpWitness) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (uniqinunit) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notinsingleton) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (eqinunit) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (singletonsswitch) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (upairsetE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (upairsetIL) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (upairsetIR) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (emptyE1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (vacuousDall) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan3) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan4) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (prop2setI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (prop2set2propI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notdexE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notdallE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI3) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (inCongP) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (in__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuE3u) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exu__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoin__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powerset__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setunion__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuEu) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (descr__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (dsetconstr__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (eqimpsubset2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (eqimpsubset1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (emptysetsubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetE2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notsubsetI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notequalI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notequalI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetRefl) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetTrans) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoinSub) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoinSub2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subset2powerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setextsub) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetemptysetimpeq) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetE1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (inPowerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetsubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (sepInPowerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (sepSubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (!!) @ (
99.32/13.17	                                                                   (('#B') @ (
99.32/13.17	                                                                    !!) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    !!))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#S') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    '#B') @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    '#S') @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    =>))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#C') @ in)))))))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#C') @ in)))) @ 
99.32/13.17	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.17	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl25])).
99.32/13.17	thf(zip_derived_cl40, plain,
99.32/13.17	    (~ (((omegaIndAx) =>
99.32/13.17	         (((replAx) =>
99.32/13.17	           (((foundationAx) =>
99.32/13.17	             (((wellorderingAx) =>
99.32/13.17	               (((descrp) =>
99.32/13.17	                 (((dsetconstrI) =>
99.32/13.17	                   (((dsetconstrEL) =>
99.32/13.17	                     (((dsetconstrER) =>
99.32/13.17	                       (((exuE1) =>
99.32/13.17	                         (((prop2setE) =>
99.32/13.17	                           (((emptysetE) =>
99.32/13.17	                             (((emptysetimpfalse) =>
99.32/13.17	                               (((notinemptyset) =>
99.32/13.17	                                 (((exuE3e) =>
99.32/13.17	                                   (((setext) =>
99.32/13.17	                                     (((emptyI) =>
99.32/13.17	                                       (((noeltsimpempty) =>
99.32/13.17	                                         (((setbeta) =>
99.32/13.17	                                           (((nonemptyE1) =>
99.32/13.17	                                             (((nonemptyI) =>
99.32/13.17	                                               (((nonemptyI1) =>
99.32/13.17	                                                 (((setadjoinIL) =>
99.32/13.17	                                                   (((in @ emptyset @ 
99.32/13.17	                                                     (setadjoin @ emptyset @ 
99.32/13.17	                                                      emptyset)) =>
99.32/13.17	                                                     (((setadjoinIR) =>
99.32/13.17	                                                       (((setadjoinE) =>
99.32/13.17	                                                         (((setadjoinOr) =>
99.32/13.17	                                                           (((setoftrueEq) =>
99.32/13.17	                                                             (((powersetI) =>
99.32/13.17	                                                               (((emptyinPowerset) =>
99.32/13.17	                                                                 (((emptyInPowerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setunionI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setunionE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subPowSU) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuE2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (nonemptyImpWitness) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (uniqinunit) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notinsingleton) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (eqinunit) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (singletonsswitch) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (upairsetE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (upairsetIL) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (upairsetIR) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (emptyE1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (vacuousDall) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan3) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan4) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (prop2setI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (prop2set2propI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notdexE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notdallE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI3) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (inCongP) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (in__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuE3u) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exu__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoin__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powerset__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setunion__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuEu) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (descr__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (dsetconstr__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (eqimpsubset2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (eqimpsubset1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (emptysetsubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetE2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notsubsetI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notequalI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notequalI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetRefl) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetTrans) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoinSub) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoinSub2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subset2powerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setextsub) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetemptysetimpeq) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetE1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (inPowerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetsubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (sepInPowerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (sepSubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (!!) @ (
99.32/13.17	                                                                   (('#B') @ (
99.32/13.17	                                                                    !!) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    !!))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#S') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    '#B') @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    '#S') @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    =>))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#C') @ in)))))))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#C') @ in)))) @ 
99.32/13.17	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.17	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl33])).
99.32/13.17	thf(zip_derived_cl46, plain,
99.32/13.17	    (~ (((replAx) =>
99.32/13.17	         (((foundationAx) =>
99.32/13.17	           (((wellorderingAx) =>
99.32/13.17	             (((descrp) =>
99.32/13.17	               (((dsetconstrI) =>
99.32/13.17	                 (((dsetconstrEL) =>
99.32/13.17	                   (((dsetconstrER) =>
99.32/13.17	                     (((exuE1) =>
99.32/13.17	                       (((prop2setE) =>
99.32/13.17	                         (((emptysetE) =>
99.32/13.17	                           (((emptysetimpfalse) =>
99.32/13.17	                             (((notinemptyset) =>
99.32/13.17	                               (((exuE3e) =>
99.32/13.17	                                 (((setext) =>
99.32/13.17	                                   (((emptyI) =>
99.32/13.17	                                     (((noeltsimpempty) =>
99.32/13.17	                                       (((setbeta) =>
99.32/13.17	                                         (((nonemptyE1) =>
99.32/13.17	                                           (((nonemptyI) =>
99.32/13.17	                                             (((nonemptyI1) =>
99.32/13.17	                                               (((setadjoinIL) =>
99.32/13.17	                                                 (((in @ emptyset @ 
99.32/13.17	                                                   (setadjoin @ emptyset @ 
99.32/13.17	                                                    emptyset)) =>
99.32/13.17	                                                   (((setadjoinIR) =>
99.32/13.17	                                                     (((setadjoinE) =>
99.32/13.17	                                                       (((setadjoinOr) =>
99.32/13.17	                                                         (((setoftrueEq) =>
99.32/13.17	                                                           (((powersetI) =>
99.32/13.17	                                                             (((emptyinPowerset) =>
99.32/13.17	                                                               (((emptyInPowerset) =>
99.32/13.17	                                                                 (((powersetE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setunionI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setunionE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subPowSU) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuE2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (nonemptyImpWitness) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (uniqinunit) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notinsingleton) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (eqinunit) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (singletonsswitch) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (upairsetE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (upairsetIL) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (upairsetIR) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (emptyE1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (vacuousDall) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan3) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan4) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (prop2setI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (prop2set2propI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notdexE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notdallE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI3) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (inCongP) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (in__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuE3u) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exu__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoin__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powerset__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setunion__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuEu) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (descr__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (dsetconstr__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (eqimpsubset2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (eqimpsubset1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (emptysetsubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetE2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notsubsetI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notequalI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notequalI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetRefl) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetTrans) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoinSub) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoinSub2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subset2powerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setextsub) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetemptysetimpeq) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetE1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (inPowerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetsubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (sepInPowerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (sepSubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (!!) @ (
99.32/13.17	                                                                   (('#B') @ (
99.32/13.17	                                                                    !!) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    !!))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#S') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    '#B') @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    '#S') @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    =>))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#C') @ in)))))))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#C') @ in)))) @ 
99.32/13.17	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.17	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl40])).
99.32/13.17	thf(zip_derived_cl52, plain,
99.32/13.17	    (~ (((foundationAx) =>
99.32/13.17	         (((wellorderingAx) =>
99.32/13.17	           (((descrp) =>
99.32/13.17	             (((dsetconstrI) =>
99.32/13.17	               (((dsetconstrEL) =>
99.32/13.17	                 (((dsetconstrER) =>
99.32/13.17	                   (((exuE1) =>
99.32/13.17	                     (((prop2setE) =>
99.32/13.17	                       (((emptysetE) =>
99.32/13.17	                         (((emptysetimpfalse) =>
99.32/13.17	                           (((notinemptyset) =>
99.32/13.17	                             (((exuE3e) =>
99.32/13.17	                               (((setext) =>
99.32/13.17	                                 (((emptyI) =>
99.32/13.17	                                   (((noeltsimpempty) =>
99.32/13.17	                                     (((setbeta) =>
99.32/13.17	                                       (((nonemptyE1) =>
99.32/13.17	                                         (((nonemptyI) =>
99.32/13.17	                                           (((nonemptyI1) =>
99.32/13.17	                                             (((setadjoinIL) =>
99.32/13.17	                                               (((in @ emptyset @ 
99.32/13.17	                                                 (setadjoin @ emptyset @ 
99.32/13.17	                                                  emptyset)) =>
99.32/13.17	                                                 (((setadjoinIR) =>
99.32/13.17	                                                   (((setadjoinE) =>
99.32/13.17	                                                     (((setadjoinOr) =>
99.32/13.17	                                                       (((setoftrueEq) =>
99.32/13.17	                                                         (((powersetI) =>
99.32/13.17	                                                           (((emptyinPowerset) =>
99.32/13.17	                                                             (((emptyInPowerset) =>
99.32/13.17	                                                               (((powersetE) =>
99.32/13.17	                                                                 (((setunionI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setunionE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subPowSU) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuE2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (nonemptyImpWitness) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (uniqinunit) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notinsingleton) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (eqinunit) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (singletonsswitch) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (upairsetE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (upairsetIL) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (upairsetIR) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (emptyE1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (vacuousDall) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan3) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan4) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (prop2setI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (prop2set2propI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notdexE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notdallE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI3) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (inCongP) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (in__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuE3u) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exu__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoin__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powerset__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setunion__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuEu) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (descr__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (dsetconstr__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (eqimpsubset2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (eqimpsubset1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (emptysetsubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetE2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notsubsetI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notequalI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notequalI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetRefl) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetTrans) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoinSub) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoinSub2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subset2powerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setextsub) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetemptysetimpeq) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetE1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (inPowerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetsubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (sepInPowerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (sepSubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (!!) @ (
99.32/13.17	                                                                   (('#B') @ (
99.32/13.17	                                                                    !!) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    !!))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#S') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    '#B') @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    '#S') @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    =>))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#C') @ in)))))))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#C') @ in)))) @ 
99.32/13.17	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.17	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl46])).
99.32/13.17	thf(zip_derived_cl58, plain,
99.32/13.17	    (~ (((wellorderingAx) =>
99.32/13.17	         (((descrp) =>
99.32/13.17	           (((dsetconstrI) =>
99.32/13.17	             (((dsetconstrEL) =>
99.32/13.17	               (((dsetconstrER) =>
99.32/13.17	                 (((exuE1) =>
99.32/13.17	                   (((prop2setE) =>
99.32/13.17	                     (((emptysetE) =>
99.32/13.17	                       (((emptysetimpfalse) =>
99.32/13.17	                         (((notinemptyset) =>
99.32/13.17	                           (((exuE3e) =>
99.32/13.17	                             (((setext) =>
99.32/13.17	                               (((emptyI) =>
99.32/13.17	                                 (((noeltsimpempty) =>
99.32/13.17	                                   (((setbeta) =>
99.32/13.17	                                     (((nonemptyE1) =>
99.32/13.17	                                       (((nonemptyI) =>
99.32/13.17	                                         (((nonemptyI1) =>
99.32/13.17	                                           (((setadjoinIL) =>
99.32/13.17	                                             (((in @ emptyset @ 
99.32/13.17	                                               (setadjoin @ emptyset @ 
99.32/13.17	                                                emptyset)) =>
99.32/13.17	                                               (((setadjoinIR) =>
99.32/13.17	                                                 (((setadjoinE) =>
99.32/13.17	                                                   (((setadjoinOr) =>
99.32/13.17	                                                     (((setoftrueEq) =>
99.32/13.17	                                                       (((powersetI) =>
99.32/13.17	                                                         (((emptyinPowerset) =>
99.32/13.17	                                                           (((emptyInPowerset) =>
99.32/13.17	                                                             (((powersetE) =>
99.32/13.17	                                                               (((setunionI) =>
99.32/13.17	                                                                 (((setunionE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subPowSU) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuE2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (nonemptyImpWitness) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (uniqinunit) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notinsingleton) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (eqinunit) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (singletonsswitch) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (upairsetE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (upairsetIL) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (upairsetIR) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (emptyE1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (vacuousDall) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan3) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan4) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (prop2setI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (prop2set2propI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notdexE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notdallE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI3) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (inCongP) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (in__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuE3u) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exu__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoin__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powerset__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setunion__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuEu) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (descr__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (dsetconstr__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (eqimpsubset2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (eqimpsubset1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (emptysetsubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetE2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notsubsetI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notequalI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notequalI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetRefl) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetTrans) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoinSub) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoinSub2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subset2powerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setextsub) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetemptysetimpeq) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetE1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (inPowerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetsubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (sepInPowerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (sepSubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (!!) @ (
99.32/13.17	                                                                   (('#B') @ (
99.32/13.17	                                                                    !!) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    !!))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#S') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    '#B') @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    '#S') @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    =>))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#C') @ in)))))))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#C') @ in)))) @ 
99.32/13.17	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.17	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl52])).
99.32/13.17	thf(zip_derived_cl64, plain,
99.32/13.17	    (~ (((descrp) =>
99.32/13.17	         (((dsetconstrI) =>
99.32/13.17	           (((dsetconstrEL) =>
99.32/13.17	             (((dsetconstrER) =>
99.32/13.17	               (((exuE1) =>
99.32/13.17	                 (((prop2setE) =>
99.32/13.17	                   (((emptysetE) =>
99.32/13.17	                     (((emptysetimpfalse) =>
99.32/13.17	                       (((notinemptyset) =>
99.32/13.17	                         (((exuE3e) =>
99.32/13.17	                           (((setext) =>
99.32/13.17	                             (((emptyI) =>
99.32/13.17	                               (((noeltsimpempty) =>
99.32/13.17	                                 (((setbeta) =>
99.32/13.17	                                   (((nonemptyE1) =>
99.32/13.17	                                     (((nonemptyI) =>
99.32/13.17	                                       (((nonemptyI1) =>
99.32/13.17	                                         (((setadjoinIL) =>
99.32/13.17	                                           (((in @ emptyset @ 
99.32/13.17	                                             (setadjoin @ emptyset @ emptyset)) =>
99.32/13.17	                                             (((setadjoinIR) =>
99.32/13.17	                                               (((setadjoinE) =>
99.32/13.17	                                                 (((setadjoinOr) =>
99.32/13.17	                                                   (((setoftrueEq) =>
99.32/13.17	                                                     (((powersetI) =>
99.32/13.17	                                                       (((emptyinPowerset) =>
99.32/13.17	                                                         (((emptyInPowerset) =>
99.32/13.17	                                                           (((powersetE) =>
99.32/13.17	                                                             (((setunionI) =>
99.32/13.17	                                                               (((setunionE) =>
99.32/13.17	                                                                 (((subPowSU) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuE2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (nonemptyImpWitness) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (uniqinunit) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notinsingleton) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (eqinunit) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (singletonsswitch) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (upairsetE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (upairsetIL) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (upairsetIR) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (emptyE1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (vacuousDall) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan3) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan4) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (prop2setI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (prop2set2propI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notdexE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notdallE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI3) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (inCongP) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (in__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuE3u) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exu__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoin__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powerset__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setunion__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuEu) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (descr__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (dsetconstr__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (eqimpsubset2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (eqimpsubset1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (emptysetsubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetE2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notsubsetI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notequalI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notequalI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetRefl) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetTrans) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoinSub) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoinSub2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subset2powerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setextsub) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetemptysetimpeq) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetE1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (inPowerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetsubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (sepInPowerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (sepSubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (!!) @ (
99.32/13.17	                                                                   (('#B') @ (
99.32/13.17	                                                                    !!) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    !!))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#S') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    '#B') @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    '#S') @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    =>))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#C') @ in)))))))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#C') @ in)))) @ 
99.32/13.17	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.17	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl58])).
99.32/13.17	thf(zip_derived_cl71, plain,
99.32/13.17	    (~ (((dsetconstrI) =>
99.32/13.17	         (((dsetconstrEL) =>
99.32/13.17	           (((dsetconstrER) =>
99.32/13.17	             (((exuE1) =>
99.32/13.17	               (((prop2setE) =>
99.32/13.17	                 (((emptysetE) =>
99.32/13.17	                   (((emptysetimpfalse) =>
99.32/13.17	                     (((notinemptyset) =>
99.32/13.17	                       (((exuE3e) =>
99.32/13.17	                         (((setext) =>
99.32/13.17	                           (((emptyI) =>
99.32/13.17	                             (((noeltsimpempty) =>
99.32/13.17	                               (((setbeta) =>
99.32/13.17	                                 (((nonemptyE1) =>
99.32/13.17	                                   (((nonemptyI) =>
99.32/13.17	                                     (((nonemptyI1) =>
99.32/13.17	                                       (((setadjoinIL) =>
99.32/13.17	                                         (((in @ emptyset @ 
99.32/13.17	                                           (setadjoin @ emptyset @ emptyset)) =>
99.32/13.17	                                           (((setadjoinIR) =>
99.32/13.17	                                             (((setadjoinE) =>
99.32/13.17	                                               (((setadjoinOr) =>
99.32/13.17	                                                 (((setoftrueEq) =>
99.32/13.17	                                                   (((powersetI) =>
99.32/13.17	                                                     (((emptyinPowerset) =>
99.32/13.17	                                                       (((emptyInPowerset) =>
99.32/13.17	                                                         (((powersetE) =>
99.32/13.17	                                                           (((setunionI) =>
99.32/13.17	                                                             (((setunionE) =>
99.32/13.17	                                                               (((subPowSU) =>
99.32/13.17	                                                                 (((exuE2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (nonemptyImpWitness) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (uniqinunit) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notinsingleton) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (eqinunit) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (singletonsswitch) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (upairsetE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (upairsetIL) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (upairsetIR) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (emptyE1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (vacuousDall) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan3) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan4) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (prop2setI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (prop2set2propI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notdexE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notdallE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI3) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (inCongP) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (in__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuE3u) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exu__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoin__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powerset__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setunion__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuEu) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (descr__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (dsetconstr__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (eqimpsubset2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (eqimpsubset1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (emptysetsubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetE2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notsubsetI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notequalI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notequalI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetRefl) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetTrans) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoinSub) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoinSub2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subset2powerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setextsub) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetemptysetimpeq) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetE1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (inPowerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetsubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (sepInPowerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (sepSubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (!!) @ (
99.32/13.17	                                                                   (('#B') @ (
99.32/13.17	                                                                    !!) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    !!))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#S') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    '#B') @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    '#S') @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    =>))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#C') @ in)))))))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#C') @ in)))) @ 
99.32/13.17	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.17	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl64])).
99.32/13.17	thf(zip_derived_cl79, plain,
99.32/13.17	    (~ (((dsetconstrEL) =>
99.32/13.17	         (((dsetconstrER) =>
99.32/13.17	           (((exuE1) =>
99.32/13.17	             (((prop2setE) =>
99.32/13.17	               (((emptysetE) =>
99.32/13.17	                 (((emptysetimpfalse) =>
99.32/13.17	                   (((notinemptyset) =>
99.32/13.17	                     (((exuE3e) =>
99.32/13.17	                       (((setext) =>
99.32/13.17	                         (((emptyI) =>
99.32/13.17	                           (((noeltsimpempty) =>
99.32/13.17	                             (((setbeta) =>
99.32/13.17	                               (((nonemptyE1) =>
99.32/13.17	                                 (((nonemptyI) =>
99.32/13.17	                                   (((nonemptyI1) =>
99.32/13.17	                                     (((setadjoinIL) =>
99.32/13.17	                                       (((in @ emptyset @ 
99.32/13.17	                                         (setadjoin @ emptyset @ emptyset)) =>
99.32/13.17	                                         (((setadjoinIR) =>
99.32/13.17	                                           (((setadjoinE) =>
99.32/13.17	                                             (((setadjoinOr) =>
99.32/13.17	                                               (((setoftrueEq) =>
99.32/13.17	                                                 (((powersetI) =>
99.32/13.17	                                                   (((emptyinPowerset) =>
99.32/13.17	                                                     (((emptyInPowerset) =>
99.32/13.17	                                                       (((powersetE) =>
99.32/13.17	                                                         (((setunionI) =>
99.32/13.17	                                                           (((setunionE) =>
99.32/13.17	                                                             (((subPowSU) =>
99.32/13.17	                                                               (((exuE2) =>
99.32/13.17	                                                                 (((nonemptyImpWitness) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (uniqinunit) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notinsingleton) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (eqinunit) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (singletonsswitch) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (upairsetE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (upairsetIL) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (upairsetIR) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (emptyE1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (vacuousDall) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan3) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan4) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (prop2setI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (prop2set2propI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notdexE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notdallE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI3) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (inCongP) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (in__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuE3u) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exu__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoin__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powerset__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setunion__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuEu) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (descr__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (dsetconstr__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (eqimpsubset2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (eqimpsubset1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (emptysetsubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetE2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notsubsetI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notequalI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notequalI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetRefl) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetTrans) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoinSub) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoinSub2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subset2powerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setextsub) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetemptysetimpeq) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetE1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (inPowerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetsubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (sepInPowerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (sepSubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (!!) @ (
99.32/13.17	                                                                   (('#B') @ (
99.32/13.17	                                                                    !!) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    !!))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#S') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    '#B') @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    '#S') @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    =>))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#C') @ in)))))))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#C') @ in)))) @ 
99.32/13.17	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.17	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl71])).
99.32/13.17	thf(zip_derived_cl89, plain,
99.32/13.17	    (~ (((dsetconstrER) =>
99.32/13.17	         (((exuE1) =>
99.32/13.17	           (((prop2setE) =>
99.32/13.17	             (((emptysetE) =>
99.32/13.17	               (((emptysetimpfalse) =>
99.32/13.17	                 (((notinemptyset) =>
99.32/13.17	                   (((exuE3e) =>
99.32/13.17	                     (((setext) =>
99.32/13.17	                       (((emptyI) =>
99.32/13.17	                         (((noeltsimpempty) =>
99.32/13.17	                           (((setbeta) =>
99.32/13.17	                             (((nonemptyE1) =>
99.32/13.17	                               (((nonemptyI) =>
99.32/13.17	                                 (((nonemptyI1) =>
99.32/13.17	                                   (((setadjoinIL) =>
99.32/13.17	                                     (((in @ emptyset @ 
99.32/13.17	                                       (setadjoin @ emptyset @ emptyset)) =>
99.32/13.17	                                       (((setadjoinIR) =>
99.32/13.17	                                         (((setadjoinE) =>
99.32/13.17	                                           (((setadjoinOr) =>
99.32/13.17	                                             (((setoftrueEq) =>
99.32/13.17	                                               (((powersetI) =>
99.32/13.17	                                                 (((emptyinPowerset) =>
99.32/13.17	                                                   (((emptyInPowerset) =>
99.32/13.17	                                                     (((powersetE) =>
99.32/13.17	                                                       (((setunionI) =>
99.32/13.17	                                                         (((setunionE) =>
99.32/13.17	                                                           (((subPowSU) =>
99.32/13.17	                                                             (((exuE2) =>
99.32/13.17	                                                               (((nonemptyImpWitness) =>
99.32/13.17	                                                                 (((uniqinunit) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notinsingleton) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (eqinunit) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (singletonsswitch) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (upairsetE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (upairsetIL) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (upairsetIR) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (emptyE1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (vacuousDall) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan3) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan4) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (prop2setI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (prop2set2propI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notdexE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notdallE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI3) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (inCongP) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (in__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuE3u) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exu__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoin__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powerset__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setunion__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuEu) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (descr__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (dsetconstr__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (eqimpsubset2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (eqimpsubset1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (emptysetsubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetE2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notsubsetI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notequalI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notequalI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetRefl) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetTrans) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoinSub) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoinSub2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subset2powerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setextsub) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetemptysetimpeq) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetE1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (inPowerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetsubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (sepInPowerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (sepSubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (!!) @ (
99.32/13.17	                                                                   (('#B') @ (
99.32/13.17	                                                                    !!) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    !!))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#S') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    '#B') @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    '#S') @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    =>))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#C') @ in)))))))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#C') @ in)))) @ 
99.32/13.17	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.17	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl79])).
99.32/13.17	thf(zip_derived_cl105, plain,
99.32/13.17	    (~ (((exuE1) =>
99.32/13.17	         (((prop2setE) =>
99.32/13.17	           (((emptysetE) =>
99.32/13.17	             (((emptysetimpfalse) =>
99.32/13.17	               (((notinemptyset) =>
99.32/13.17	                 (((exuE3e) =>
99.32/13.17	                   (((setext) =>
99.32/13.17	                     (((emptyI) =>
99.32/13.17	                       (((noeltsimpempty) =>
99.32/13.17	                         (((setbeta) =>
99.32/13.17	                           (((nonemptyE1) =>
99.32/13.17	                             (((nonemptyI) =>
99.32/13.17	                               (((nonemptyI1) =>
99.32/13.17	                                 (((setadjoinIL) =>
99.32/13.17	                                   (((in @ emptyset @ 
99.32/13.17	                                     (setadjoin @ emptyset @ emptyset)) =>
99.32/13.17	                                     (((setadjoinIR) =>
99.32/13.17	                                       (((setadjoinE) =>
99.32/13.17	                                         (((setadjoinOr) =>
99.32/13.17	                                           (((setoftrueEq) =>
99.32/13.17	                                             (((powersetI) =>
99.32/13.17	                                               (((emptyinPowerset) =>
99.32/13.17	                                                 (((emptyInPowerset) =>
99.32/13.17	                                                   (((powersetE) =>
99.32/13.17	                                                     (((setunionI) =>
99.32/13.17	                                                       (((setunionE) =>
99.32/13.17	                                                         (((subPowSU) =>
99.32/13.17	                                                           (((exuE2) =>
99.32/13.17	                                                             (((nonemptyImpWitness) =>
99.32/13.17	                                                               (((uniqinunit) =>
99.32/13.17	                                                                 (((notinsingleton) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (eqinunit) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (singletonsswitch) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (upairsetE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (upairsetIL) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (upairsetIR) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (emptyE1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (vacuousDall) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan3) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan4) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (prop2setI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (prop2set2propI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notdexE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notdallE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI3) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (inCongP) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (in__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuE3u) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exu__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoin__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powerset__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setunion__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuEu) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (descr__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (dsetconstr__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (eqimpsubset2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (eqimpsubset1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (emptysetsubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetE2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notsubsetI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notequalI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notequalI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetRefl) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetTrans) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoinSub) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoinSub2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subset2powerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setextsub) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetemptysetimpeq) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetE1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (inPowerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetsubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (sepInPowerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (sepSubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (!!) @ (
99.32/13.17	                                                                   (('#B') @ (
99.32/13.17	                                                                    !!) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    !!))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#S') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    '#B') @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    '#S') @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    =>))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#C') @ in)))))))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#C') @ in)))) @ 
99.32/13.17	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.17	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl89])).
99.32/13.17	thf(zip_derived_cl123, plain,
99.32/13.17	    (~ (((prop2setE) =>
99.32/13.17	         (((emptysetE) =>
99.32/13.17	           (((emptysetimpfalse) =>
99.32/13.17	             (((notinemptyset) =>
99.32/13.17	               (((exuE3e) =>
99.32/13.17	                 (((setext) =>
99.32/13.17	                   (((emptyI) =>
99.32/13.17	                     (((noeltsimpempty) =>
99.32/13.17	                       (((setbeta) =>
99.32/13.17	                         (((nonemptyE1) =>
99.32/13.17	                           (((nonemptyI) =>
99.32/13.17	                             (((nonemptyI1) =>
99.32/13.17	                               (((setadjoinIL) =>
99.32/13.17	                                 (((in @ emptyset @ 
99.32/13.17	                                   (setadjoin @ emptyset @ emptyset)) =>
99.32/13.17	                                   (((setadjoinIR) =>
99.32/13.17	                                     (((setadjoinE) =>
99.32/13.17	                                       (((setadjoinOr) =>
99.32/13.17	                                         (((setoftrueEq) =>
99.32/13.17	                                           (((powersetI) =>
99.32/13.17	                                             (((emptyinPowerset) =>
99.32/13.17	                                               (((emptyInPowerset) =>
99.32/13.17	                                                 (((powersetE) =>
99.32/13.17	                                                   (((setunionI) =>
99.32/13.17	                                                     (((setunionE) =>
99.32/13.17	                                                       (((subPowSU) =>
99.32/13.17	                                                         (((exuE2) =>
99.32/13.17	                                                           (((nonemptyImpWitness) =>
99.32/13.17	                                                             (((uniqinunit) =>
99.32/13.17	                                                               (((notinsingleton) =>
99.32/13.17	                                                                 (((eqinunit) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (singletonsswitch) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (upairsetE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (upairsetIL) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (upairsetIR) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (emptyE1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (vacuousDall) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan3) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan4) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (prop2setI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (prop2set2propI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notdexE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notdallE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI3) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (inCongP) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (in__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuE3u) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exu__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoin__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powerset__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setunion__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuEu) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (descr__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (dsetconstr__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (eqimpsubset2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (eqimpsubset1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (emptysetsubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetE2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notsubsetI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notequalI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notequalI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetRefl) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetTrans) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoinSub) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoinSub2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subset2powerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setextsub) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetemptysetimpeq) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetE1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (inPowerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetsubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (sepInPowerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (sepSubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (!!) @ (
99.32/13.17	                                                                   (('#B') @ (
99.32/13.17	                                                                    !!) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    !!))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#S') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    '#B') @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    '#S') @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    =>))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#C') @ in)))))))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#C') @ in)))) @ 
99.32/13.17	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.17	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl105])).
99.32/13.17	thf(zip_derived_cl142, plain,
99.32/13.17	    (~ (((emptysetE) =>
99.32/13.17	         (((emptysetimpfalse) =>
99.32/13.17	           (((notinemptyset) =>
99.32/13.17	             (((exuE3e) =>
99.32/13.17	               (((setext) =>
99.32/13.17	                 (((emptyI) =>
99.32/13.17	                   (((noeltsimpempty) =>
99.32/13.17	                     (((setbeta) =>
99.32/13.17	                       (((nonemptyE1) =>
99.32/13.17	                         (((nonemptyI) =>
99.32/13.17	                           (((nonemptyI1) =>
99.32/13.17	                             (((setadjoinIL) =>
99.32/13.17	                               (((in @ emptyset @ 
99.32/13.17	                                 (setadjoin @ emptyset @ emptyset)) =>
99.32/13.17	                                 (((setadjoinIR) =>
99.32/13.17	                                   (((setadjoinE) =>
99.32/13.17	                                     (((setadjoinOr) =>
99.32/13.17	                                       (((setoftrueEq) =>
99.32/13.17	                                         (((powersetI) =>
99.32/13.17	                                           (((emptyinPowerset) =>
99.32/13.17	                                             (((emptyInPowerset) =>
99.32/13.17	                                               (((powersetE) =>
99.32/13.17	                                                 (((setunionI) =>
99.32/13.17	                                                   (((setunionE) =>
99.32/13.17	                                                     (((subPowSU) =>
99.32/13.17	                                                       (((exuE2) =>
99.32/13.17	                                                         (((nonemptyImpWitness) =>
99.32/13.17	                                                           (((uniqinunit) =>
99.32/13.17	                                                             (((notinsingleton) =>
99.32/13.17	                                                               (((eqinunit) =>
99.32/13.17	                                                                 (((singletonsswitch) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (upairsetE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (upairsetIL) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (upairsetIR) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (emptyE1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (vacuousDall) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan3) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan4) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (prop2setI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (prop2set2propI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notdexE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notdallE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI3) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (inCongP) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (in__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuE3u) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exu__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoin__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powerset__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setunion__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuEu) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (descr__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (dsetconstr__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (eqimpsubset2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (eqimpsubset1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (emptysetsubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetE2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notsubsetI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notequalI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notequalI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetRefl) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetTrans) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoinSub) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoinSub2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subset2powerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setextsub) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetemptysetimpeq) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetE1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (inPowerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetsubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (sepInPowerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (sepSubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (!!) @ (
99.32/13.17	                                                                   (('#B') @ (
99.32/13.17	                                                                    !!) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    !!))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#S') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    '#B') @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    '#S') @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    =>))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#C') @ in)))))))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#C') @ in)))) @ 
99.32/13.17	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.17	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl123])).
99.32/13.17	thf(zip_derived_cl158, plain,
99.32/13.17	    (~ (((emptysetimpfalse) =>
99.32/13.17	         (((notinemptyset) =>
99.32/13.17	           (((exuE3e) =>
99.32/13.17	             (((setext) =>
99.32/13.17	               (((emptyI) =>
99.32/13.17	                 (((noeltsimpempty) =>
99.32/13.17	                   (((setbeta) =>
99.32/13.17	                     (((nonemptyE1) =>
99.32/13.17	                       (((nonemptyI) =>
99.32/13.17	                         (((nonemptyI1) =>
99.32/13.17	                           (((setadjoinIL) =>
99.32/13.17	                             (((in @ emptyset @ 
99.32/13.17	                               (setadjoin @ emptyset @ emptyset)) =>
99.32/13.17	                               (((setadjoinIR) =>
99.32/13.17	                                 (((setadjoinE) =>
99.32/13.17	                                   (((setadjoinOr) =>
99.32/13.17	                                     (((setoftrueEq) =>
99.32/13.17	                                       (((powersetI) =>
99.32/13.17	                                         (((emptyinPowerset) =>
99.32/13.17	                                           (((emptyInPowerset) =>
99.32/13.17	                                             (((powersetE) =>
99.32/13.17	                                               (((setunionI) =>
99.32/13.17	                                                 (((setunionE) =>
99.32/13.17	                                                   (((subPowSU) =>
99.32/13.17	                                                     (((exuE2) =>
99.32/13.17	                                                       (((nonemptyImpWitness) =>
99.32/13.17	                                                         (((uniqinunit) =>
99.32/13.17	                                                           (((notinsingleton) =>
99.32/13.17	                                                             (((eqinunit) =>
99.32/13.17	                                                               (((singletonsswitch) =>
99.32/13.17	                                                                 (((upairsetE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (upairsetIL) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (upairsetIR) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (emptyE1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (vacuousDall) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan3) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan4) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (prop2setI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (prop2set2propI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notdexE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notdallE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI3) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (inCongP) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (in__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuE3u) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exu__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoin__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powerset__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setunion__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuEu) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (descr__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (dsetconstr__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (eqimpsubset2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (eqimpsubset1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (emptysetsubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetE2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notsubsetI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notequalI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notequalI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetRefl) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetTrans) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoinSub) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoinSub2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subset2powerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setextsub) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetemptysetimpeq) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetE1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (inPowerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetsubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (sepInPowerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (sepSubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (!!) @ (
99.32/13.17	                                                                   (('#B') @ (
99.32/13.17	                                                                    !!) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    !!))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#S') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    '#B') @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    '#S') @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    =>))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#C') @ in)))))))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#C') @ in)))) @ 
99.32/13.17	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.17	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl142])).
99.32/13.17	thf(zip_derived_cl174, plain,
99.32/13.17	    (~ (((notinemptyset) =>
99.32/13.17	         (((exuE3e) =>
99.32/13.17	           (((setext) =>
99.32/13.17	             (((emptyI) =>
99.32/13.17	               (((noeltsimpempty) =>
99.32/13.17	                 (((setbeta) =>
99.32/13.17	                   (((nonemptyE1) =>
99.32/13.17	                     (((nonemptyI) =>
99.32/13.17	                       (((nonemptyI1) =>
99.32/13.17	                         (((setadjoinIL) =>
99.32/13.17	                           (((in @ emptyset @ 
99.32/13.17	                             (setadjoin @ emptyset @ emptyset)) =>
99.32/13.17	                             (((setadjoinIR) =>
99.32/13.17	                               (((setadjoinE) =>
99.32/13.17	                                 (((setadjoinOr) =>
99.32/13.17	                                   (((setoftrueEq) =>
99.32/13.17	                                     (((powersetI) =>
99.32/13.17	                                       (((emptyinPowerset) =>
99.32/13.17	                                         (((emptyInPowerset) =>
99.32/13.17	                                           (((powersetE) =>
99.32/13.17	                                             (((setunionI) =>
99.32/13.17	                                               (((setunionE) =>
99.32/13.17	                                                 (((subPowSU) =>
99.32/13.17	                                                   (((exuE2) =>
99.32/13.17	                                                     (((nonemptyImpWitness) =>
99.32/13.17	                                                       (((uniqinunit) =>
99.32/13.17	                                                         (((notinsingleton) =>
99.32/13.17	                                                           (((eqinunit) =>
99.32/13.17	                                                             (((singletonsswitch) =>
99.32/13.17	                                                               (((upairsetE) =>
99.32/13.17	                                                                 (((upairsetIL) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (upairsetIR) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (emptyE1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (vacuousDall) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan3) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan4) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (prop2setI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (prop2set2propI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notdexE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notdallE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI3) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (inCongP) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (in__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuE3u) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exu__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoin__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powerset__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setunion__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuEu) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (descr__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (dsetconstr__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (eqimpsubset2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (eqimpsubset1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (emptysetsubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetE2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notsubsetI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notequalI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notequalI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetRefl) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetTrans) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoinSub) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoinSub2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subset2powerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setextsub) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetemptysetimpeq) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetE1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (inPowerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powersetsubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (sepInPowerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (sepSubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (!!) @ (
99.32/13.17	                                                                   (('#B') @ (
99.32/13.17	                                                                    !!) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    !!))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#S') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    '#B') @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    '#S') @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    =>))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#C') @ in)))))))) @ 
99.32/13.17	                                                                    (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#B') @ (
99.32/13.17	                                                                    (
99.32/13.17	                                                                    ('#C') @ in)))) @ 
99.32/13.17	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.17	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl158])).
99.32/13.17	thf(zip_derived_cl189, plain,
99.32/13.17	    (~ (((exuE3e) =>
99.32/13.17	         (((setext) =>
99.32/13.17	           (((emptyI) =>
99.32/13.17	             (((noeltsimpempty) =>
99.32/13.17	               (((setbeta) =>
99.32/13.17	                 (((nonemptyE1) =>
99.32/13.17	                   (((nonemptyI) =>
99.32/13.17	                     (((nonemptyI1) =>
99.32/13.17	                       (((setadjoinIL) =>
99.32/13.17	                         (((in @ emptyset @ 
99.32/13.17	                           (setadjoin @ emptyset @ emptyset)) =>
99.32/13.17	                           (((setadjoinIR) =>
99.32/13.17	                             (((setadjoinE) =>
99.32/13.17	                               (((setadjoinOr) =>
99.32/13.17	                                 (((setoftrueEq) =>
99.32/13.17	                                   (((powersetI) =>
99.32/13.17	                                     (((emptyinPowerset) =>
99.32/13.17	                                       (((emptyInPowerset) =>
99.32/13.17	                                         (((powersetE) =>
99.32/13.17	                                           (((setunionI) =>
99.32/13.17	                                             (((setunionE) =>
99.32/13.17	                                               (((subPowSU) =>
99.32/13.17	                                                 (((exuE2) =>
99.32/13.17	                                                   (((nonemptyImpWitness) =>
99.32/13.17	                                                     (((uniqinunit) =>
99.32/13.17	                                                       (((notinsingleton) =>
99.32/13.17	                                                         (((eqinunit) =>
99.32/13.17	                                                           (((singletonsswitch) =>
99.32/13.17	                                                             (((upairsetE) =>
99.32/13.17	                                                               (((upairsetIL) =>
99.32/13.17	                                                                 (((upairsetIR) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (emptyE1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (vacuousDall) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan3) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (quantDeMorgan4) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (prop2setI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (prop2set2propI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notdexE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notdallE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI3) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (inCongP) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (in__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuE3u) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exu__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoin__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (powerset__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setunion__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (exuEu) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (descr__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (dsetconstr__Cong) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (eqimpsubset2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (eqimpsubset1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (emptysetsubset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetE) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetE2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notsubsetI) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notequalI1) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (notequalI2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetRefl) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subsetTrans) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoinSub) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setadjoinSub2) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (subset2powerset) =>
99.32/13.17	                                                                   ((
99.32/13.17	                                                                   (setextsub) =>
99.32/13.17	                                                                   ((
99.32/13.18	                                                                   (subsetemptysetimpeq) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetE1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (inPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepInPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepSubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (!!) @ (
99.32/13.18	                                                                   (('#B') @ (
99.32/13.18	                                                                    !!) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    !!))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#S') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#B') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#S') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    =>))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))))))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))) @ 
99.32/13.18	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.18	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl174])).
99.32/13.18	thf(zip_derived_cl206, plain,
99.32/13.18	    (~ (((setext) =>
99.32/13.18	         (((emptyI) =>
99.32/13.18	           (((noeltsimpempty) =>
99.32/13.18	             (((setbeta) =>
99.32/13.18	               (((nonemptyE1) =>
99.32/13.18	                 (((nonemptyI) =>
99.32/13.18	                   (((nonemptyI1) =>
99.32/13.18	                     (((setadjoinIL) =>
99.32/13.18	                       (((in @ emptyset @ 
99.32/13.18	                         (setadjoin @ emptyset @ emptyset)) =>
99.32/13.18	                         (((setadjoinIR) =>
99.32/13.18	                           (((setadjoinE) =>
99.32/13.18	                             (((setadjoinOr) =>
99.32/13.18	                               (((setoftrueEq) =>
99.32/13.18	                                 (((powersetI) =>
99.32/13.18	                                   (((emptyinPowerset) =>
99.32/13.18	                                     (((emptyInPowerset) =>
99.32/13.18	                                       (((powersetE) =>
99.32/13.18	                                         (((setunionI) =>
99.32/13.18	                                           (((setunionE) =>
99.32/13.18	                                             (((subPowSU) =>
99.32/13.18	                                               (((exuE2) =>
99.32/13.18	                                                 (((nonemptyImpWitness) =>
99.32/13.18	                                                   (((uniqinunit) =>
99.32/13.18	                                                     (((notinsingleton) =>
99.32/13.18	                                                       (((eqinunit) =>
99.32/13.18	                                                         (((singletonsswitch) =>
99.32/13.18	                                                           (((upairsetE) =>
99.32/13.18	                                                             (((upairsetIL) =>
99.32/13.18	                                                               (((upairsetIR) =>
99.32/13.18	                                                                 (((emptyE1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (vacuousDall) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (quantDeMorgan1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (quantDeMorgan2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (quantDeMorgan3) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (quantDeMorgan4) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (prop2setI) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (prop2set2propI) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notdexE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notdallE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuI3) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (inCongP) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (in__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuE3u) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exu__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoin__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powerset__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setunion__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuEu) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (descr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (dsetconstr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (emptysetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notsubsetI) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetRefl) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetTrans) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subset2powerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setextsub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetemptysetimpeq) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetE1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (inPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepInPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepSubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (!!) @ (
99.32/13.18	                                                                   (('#B') @ (
99.32/13.18	                                                                    !!) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    !!))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#S') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#B') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#S') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    =>))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))))))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))) @ 
99.32/13.18	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.18	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl189])).
99.32/13.18	thf(zip_derived_cl222, plain,
99.32/13.18	    (~ (((emptyI) =>
99.32/13.18	         (((noeltsimpempty) =>
99.32/13.18	           (((setbeta) =>
99.32/13.18	             (((nonemptyE1) =>
99.32/13.18	               (((nonemptyI) =>
99.32/13.18	                 (((nonemptyI1) =>
99.32/13.18	                   (((setadjoinIL) =>
99.32/13.18	                     (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
99.32/13.18	                       (((setadjoinIR) =>
99.32/13.18	                         (((setadjoinE) =>
99.32/13.18	                           (((setadjoinOr) =>
99.32/13.18	                             (((setoftrueEq) =>
99.32/13.18	                               (((powersetI) =>
99.32/13.18	                                 (((emptyinPowerset) =>
99.32/13.18	                                   (((emptyInPowerset) =>
99.32/13.18	                                     (((powersetE) =>
99.32/13.18	                                       (((setunionI) =>
99.32/13.18	                                         (((setunionE) =>
99.32/13.18	                                           (((subPowSU) =>
99.32/13.18	                                             (((exuE2) =>
99.32/13.18	                                               (((nonemptyImpWitness) =>
99.32/13.18	                                                 (((uniqinunit) =>
99.32/13.18	                                                   (((notinsingleton) =>
99.32/13.18	                                                     (((eqinunit) =>
99.32/13.18	                                                       (((singletonsswitch) =>
99.32/13.18	                                                         (((upairsetE) =>
99.32/13.18	                                                           (((upairsetIL) =>
99.32/13.18	                                                             (((upairsetIR) =>
99.32/13.18	                                                               (((emptyE1) =>
99.32/13.18	                                                                 (((vacuousDall) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (quantDeMorgan1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (quantDeMorgan2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (quantDeMorgan3) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (quantDeMorgan4) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (prop2setI) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (prop2set2propI) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notdexE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notdallE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuI3) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (inCongP) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (in__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuE3u) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exu__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoin__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powerset__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setunion__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuEu) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (descr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (dsetconstr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (emptysetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notsubsetI) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetRefl) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetTrans) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subset2powerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setextsub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetemptysetimpeq) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetE1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (inPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepInPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepSubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (!!) @ (
99.32/13.18	                                                                   (('#B') @ (
99.32/13.18	                                                                    !!) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    !!))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#S') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#B') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#S') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    =>))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))))))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))) @ 
99.32/13.18	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.18	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl206])).
99.32/13.18	thf(zip_derived_cl236, plain,
99.32/13.18	    (~ (((noeltsimpempty) =>
99.32/13.18	         (((setbeta) =>
99.32/13.18	           (((nonemptyE1) =>
99.32/13.18	             (((nonemptyI) =>
99.32/13.18	               (((nonemptyI1) =>
99.32/13.18	                 (((setadjoinIL) =>
99.32/13.18	                   (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
99.32/13.18	                     (((setadjoinIR) =>
99.32/13.18	                       (((setadjoinE) =>
99.32/13.18	                         (((setadjoinOr) =>
99.32/13.18	                           (((setoftrueEq) =>
99.32/13.18	                             (((powersetI) =>
99.32/13.18	                               (((emptyinPowerset) =>
99.32/13.18	                                 (((emptyInPowerset) =>
99.32/13.18	                                   (((powersetE) =>
99.32/13.18	                                     (((setunionI) =>
99.32/13.18	                                       (((setunionE) =>
99.32/13.18	                                         (((subPowSU) =>
99.32/13.18	                                           (((exuE2) =>
99.32/13.18	                                             (((nonemptyImpWitness) =>
99.32/13.18	                                               (((uniqinunit) =>
99.32/13.18	                                                 (((notinsingleton) =>
99.32/13.18	                                                   (((eqinunit) =>
99.32/13.18	                                                     (((singletonsswitch) =>
99.32/13.18	                                                       (((upairsetE) =>
99.32/13.18	                                                         (((upairsetIL) =>
99.32/13.18	                                                           (((upairsetIR) =>
99.32/13.18	                                                             (((emptyE1) =>
99.32/13.18	                                                               (((vacuousDall) =>
99.32/13.18	                                                                 (((quantDeMorgan1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (quantDeMorgan2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (quantDeMorgan3) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (quantDeMorgan4) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (prop2setI) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (prop2set2propI) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notdexE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notdallE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuI3) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (inCongP) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (in__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuE3u) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exu__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoin__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powerset__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setunion__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuEu) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (descr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (dsetconstr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (emptysetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notsubsetI) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetRefl) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetTrans) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subset2powerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setextsub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetemptysetimpeq) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetE1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (inPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepInPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepSubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (!!) @ (
99.32/13.18	                                                                   (('#B') @ (
99.32/13.18	                                                                    !!) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    !!))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#S') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#B') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#S') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    =>))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))))))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))) @ 
99.32/13.18	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.18	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl222])).
99.32/13.18	thf(zip_derived_cl251, plain,
99.32/13.18	    (~ (((setbeta) =>
99.32/13.18	         (((nonemptyE1) =>
99.32/13.18	           (((nonemptyI) =>
99.32/13.18	             (((nonemptyI1) =>
99.32/13.18	               (((setadjoinIL) =>
99.32/13.18	                 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
99.32/13.18	                   (((setadjoinIR) =>
99.32/13.18	                     (((setadjoinE) =>
99.32/13.18	                       (((setadjoinOr) =>
99.32/13.18	                         (((setoftrueEq) =>
99.32/13.18	                           (((powersetI) =>
99.32/13.18	                             (((emptyinPowerset) =>
99.32/13.18	                               (((emptyInPowerset) =>
99.32/13.18	                                 (((powersetE) =>
99.32/13.18	                                   (((setunionI) =>
99.32/13.18	                                     (((setunionE) =>
99.32/13.18	                                       (((subPowSU) =>
99.32/13.18	                                         (((exuE2) =>
99.32/13.18	                                           (((nonemptyImpWitness) =>
99.32/13.18	                                             (((uniqinunit) =>
99.32/13.18	                                               (((notinsingleton) =>
99.32/13.18	                                                 (((eqinunit) =>
99.32/13.18	                                                   (((singletonsswitch) =>
99.32/13.18	                                                     (((upairsetE) =>
99.32/13.18	                                                       (((upairsetIL) =>
99.32/13.18	                                                         (((upairsetIR) =>
99.32/13.18	                                                           (((emptyE1) =>
99.32/13.18	                                                             (((vacuousDall) =>
99.32/13.18	                                                               (((quantDeMorgan1) =>
99.32/13.18	                                                                 (((quantDeMorgan2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (quantDeMorgan3) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (quantDeMorgan4) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (prop2setI) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (prop2set2propI) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notdexE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notdallE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuI3) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (inCongP) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (in__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuE3u) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exu__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoin__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powerset__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setunion__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuEu) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (descr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (dsetconstr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (emptysetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notsubsetI) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetRefl) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetTrans) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subset2powerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setextsub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetemptysetimpeq) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetE1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (inPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepInPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepSubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (!!) @ (
99.32/13.18	                                                                   (('#B') @ (
99.32/13.18	                                                                    !!) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    !!))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#S') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#B') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#S') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    =>))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))))))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))) @ 
99.32/13.18	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.18	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl236])).
99.32/13.18	thf(zip_derived_cl264, plain,
99.32/13.18	    (~ (((nonemptyE1) =>
99.32/13.18	         (((nonemptyI) =>
99.32/13.18	           (((nonemptyI1) =>
99.32/13.18	             (((setadjoinIL) =>
99.32/13.18	               (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
99.32/13.18	                 (((setadjoinIR) =>
99.32/13.18	                   (((setadjoinE) =>
99.32/13.18	                     (((setadjoinOr) =>
99.32/13.18	                       (((setoftrueEq) =>
99.32/13.18	                         (((powersetI) =>
99.32/13.18	                           (((emptyinPowerset) =>
99.32/13.18	                             (((emptyInPowerset) =>
99.32/13.18	                               (((powersetE) =>
99.32/13.18	                                 (((setunionI) =>
99.32/13.18	                                   (((setunionE) =>
99.32/13.18	                                     (((subPowSU) =>
99.32/13.18	                                       (((exuE2) =>
99.32/13.18	                                         (((nonemptyImpWitness) =>
99.32/13.18	                                           (((uniqinunit) =>
99.32/13.18	                                             (((notinsingleton) =>
99.32/13.18	                                               (((eqinunit) =>
99.32/13.18	                                                 (((singletonsswitch) =>
99.32/13.18	                                                   (((upairsetE) =>
99.32/13.18	                                                     (((upairsetIL) =>
99.32/13.18	                                                       (((upairsetIR) =>
99.32/13.18	                                                         (((emptyE1) =>
99.32/13.18	                                                           (((vacuousDall) =>
99.32/13.18	                                                             (((quantDeMorgan1) =>
99.32/13.18	                                                               (((quantDeMorgan2) =>
99.32/13.18	                                                                 (((quantDeMorgan3) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (quantDeMorgan4) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (prop2setI) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (prop2set2propI) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notdexE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notdallE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuI3) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (inCongP) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (in__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuE3u) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exu__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoin__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powerset__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setunion__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuEu) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (descr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (dsetconstr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (emptysetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notsubsetI) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetRefl) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetTrans) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subset2powerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setextsub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetemptysetimpeq) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetE1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (inPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepInPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepSubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (!!) @ (
99.32/13.18	                                                                   (('#B') @ (
99.32/13.18	                                                                    !!) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    !!))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#S') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#B') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#S') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    =>))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))))))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))) @ 
99.32/13.18	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.18	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl251])).
99.32/13.18	thf(zip_derived_cl280, plain,
99.32/13.18	    (~ (((nonemptyI) =>
99.32/13.18	         (((nonemptyI1) =>
99.32/13.18	           (((setadjoinIL) =>
99.32/13.18	             (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
99.32/13.18	               (((setadjoinIR) =>
99.32/13.18	                 (((setadjoinE) =>
99.32/13.18	                   (((setadjoinOr) =>
99.32/13.18	                     (((setoftrueEq) =>
99.32/13.18	                       (((powersetI) =>
99.32/13.18	                         (((emptyinPowerset) =>
99.32/13.18	                           (((emptyInPowerset) =>
99.32/13.18	                             (((powersetE) =>
99.32/13.18	                               (((setunionI) =>
99.32/13.18	                                 (((setunionE) =>
99.32/13.18	                                   (((subPowSU) =>
99.32/13.18	                                     (((exuE2) =>
99.32/13.18	                                       (((nonemptyImpWitness) =>
99.32/13.18	                                         (((uniqinunit) =>
99.32/13.18	                                           (((notinsingleton) =>
99.32/13.18	                                             (((eqinunit) =>
99.32/13.18	                                               (((singletonsswitch) =>
99.32/13.18	                                                 (((upairsetE) =>
99.32/13.18	                                                   (((upairsetIL) =>
99.32/13.18	                                                     (((upairsetIR) =>
99.32/13.18	                                                       (((emptyE1) =>
99.32/13.18	                                                         (((vacuousDall) =>
99.32/13.18	                                                           (((quantDeMorgan1) =>
99.32/13.18	                                                             (((quantDeMorgan2) =>
99.32/13.18	                                                               (((quantDeMorgan3) =>
99.32/13.18	                                                                 (((quantDeMorgan4) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (prop2setI) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (prop2set2propI) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notdexE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notdallE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuI3) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (inCongP) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (in__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuE3u) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exu__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoin__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powerset__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setunion__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuEu) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (descr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (dsetconstr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (emptysetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notsubsetI) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetRefl) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetTrans) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subset2powerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setextsub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetemptysetimpeq) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetE1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (inPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepInPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepSubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (!!) @ (
99.32/13.18	                                                                   (('#B') @ (
99.32/13.18	                                                                    !!) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    !!))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#S') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#B') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#S') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    =>))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))))))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))) @ 
99.32/13.18	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.18	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl264])).
99.32/13.18	thf(zip_derived_cl293, plain,
99.32/13.18	    (~ (((nonemptyI1) =>
99.32/13.18	         (((setadjoinIL) =>
99.32/13.18	           (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
99.32/13.18	             (((setadjoinIR) =>
99.32/13.18	               (((setadjoinE) =>
99.32/13.18	                 (((setadjoinOr) =>
99.32/13.18	                   (((setoftrueEq) =>
99.32/13.18	                     (((powersetI) =>
99.32/13.18	                       (((emptyinPowerset) =>
99.32/13.18	                         (((emptyInPowerset) =>
99.32/13.18	                           (((powersetE) =>
99.32/13.18	                             (((setunionI) =>
99.32/13.18	                               (((setunionE) =>
99.32/13.18	                                 (((subPowSU) =>
99.32/13.18	                                   (((exuE2) =>
99.32/13.18	                                     (((nonemptyImpWitness) =>
99.32/13.18	                                       (((uniqinunit) =>
99.32/13.18	                                         (((notinsingleton) =>
99.32/13.18	                                           (((eqinunit) =>
99.32/13.18	                                             (((singletonsswitch) =>
99.32/13.18	                                               (((upairsetE) =>
99.32/13.18	                                                 (((upairsetIL) =>
99.32/13.18	                                                   (((upairsetIR) =>
99.32/13.18	                                                     (((emptyE1) =>
99.32/13.18	                                                       (((vacuousDall) =>
99.32/13.18	                                                         (((quantDeMorgan1) =>
99.32/13.18	                                                           (((quantDeMorgan2) =>
99.32/13.18	                                                             (((quantDeMorgan3) =>
99.32/13.18	                                                               (((quantDeMorgan4) =>
99.32/13.18	                                                                 (((prop2setI) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (prop2set2propI) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notdexE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notdallE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuI3) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (inCongP) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (in__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuE3u) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exu__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoin__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powerset__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setunion__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuEu) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (descr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (dsetconstr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (emptysetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notsubsetI) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetRefl) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetTrans) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subset2powerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setextsub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetemptysetimpeq) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetE1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (inPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepInPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepSubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (!!) @ (
99.32/13.18	                                                                   (('#B') @ (
99.32/13.18	                                                                    !!) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    !!))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#S') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#B') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#S') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    =>))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))))))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))) @ 
99.32/13.18	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.18	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl280])).
99.32/13.18	thf(zip_derived_cl307, plain,
99.32/13.18	    (~ (((setadjoinIL) =>
99.32/13.18	         (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
99.32/13.18	           (((setadjoinIR) =>
99.32/13.18	             (((setadjoinE) =>
99.32/13.18	               (((setadjoinOr) =>
99.32/13.18	                 (((setoftrueEq) =>
99.32/13.18	                   (((powersetI) =>
99.32/13.18	                     (((emptyinPowerset) =>
99.32/13.18	                       (((emptyInPowerset) =>
99.32/13.18	                         (((powersetE) =>
99.32/13.18	                           (((setunionI) =>
99.32/13.18	                             (((setunionE) =>
99.32/13.18	                               (((subPowSU) =>
99.32/13.18	                                 (((exuE2) =>
99.32/13.18	                                   (((nonemptyImpWitness) =>
99.32/13.18	                                     (((uniqinunit) =>
99.32/13.18	                                       (((notinsingleton) =>
99.32/13.18	                                         (((eqinunit) =>
99.32/13.18	                                           (((singletonsswitch) =>
99.32/13.18	                                             (((upairsetE) =>
99.32/13.18	                                               (((upairsetIL) =>
99.32/13.18	                                                 (((upairsetIR) =>
99.32/13.18	                                                   (((emptyE1) =>
99.32/13.18	                                                     (((vacuousDall) =>
99.32/13.18	                                                       (((quantDeMorgan1) =>
99.32/13.18	                                                         (((quantDeMorgan2) =>
99.32/13.18	                                                           (((quantDeMorgan3) =>
99.32/13.18	                                                             (((quantDeMorgan4) =>
99.32/13.18	                                                               (((prop2setI) =>
99.32/13.18	                                                                 (((prop2set2propI) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notdexE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notdallE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuI3) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (inCongP) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (in__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuE3u) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exu__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoin__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powerset__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setunion__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuEu) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (descr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (dsetconstr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (emptysetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notsubsetI) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetRefl) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetTrans) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subset2powerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setextsub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetemptysetimpeq) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetE1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (inPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepInPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepSubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (!!) @ (
99.32/13.18	                                                                   (('#B') @ (
99.32/13.18	                                                                    !!) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    !!))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#S') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#B') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#S') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    =>))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))))))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))) @ 
99.32/13.18	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.18	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl293])).
99.32/13.18	thf(zip_derived_cl321, plain, ( (setadjoinIL)),
99.32/13.18	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl307])).
99.32/13.18	thf(setadjoinIL, axiom, (setadjoinIL) =>
99.32/13.18	  ((((!!) @ (^[Y0 : $i]:
99.32/13.18	               (((!!) @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1))))))))
99.32/13.18	   = ($true))).
99.32/13.18	thf('4', plain,
99.32/13.18	    (( setadjoinIL ) <=>
99.32/13.18	     ( ![X5:$i,X7:$i]: ( in @ X5 @ ( setadjoin @ X5 @ X7 ) ) )),
99.32/13.18	    inference('rw.lit', [status(esa)], [setadjoinIL])).
99.32/13.18	thf(zip_derived_cl335, plain,
99.32/13.18	    ( (((!!) @ (^[Y0 : $i]:
99.32/13.18	                  (((!!) @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1))))))))),
99.32/13.18	    inference('rw_clause', [status(thm)], [zip_derived_cl321, '4'])).
99.32/13.18	thf(zip_derived_cl346, plain,
99.32/13.18	    ( (((!!) @ ((('#B') @ (!!) @ 
99.32/13.18	                 ((('#S') @ ((('#B') @ ('#B') @ in)) @ setadjoin))))))),
99.32/13.18	    inference('comb-normalize', [status(thm)], [zip_derived_cl335])).
99.32/13.18	thf(zip_derived_cl347, plain,
99.32/13.18	    (![X2 : $i]:  (((!!) @ ((('#B') @ (in @ X2) @ (setadjoin @ X2)))))),
99.32/13.18	    inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl346])).
99.32/13.18	thf(zip_derived_cl352, plain,
99.32/13.18	    (![X2 : $i, X4 : $i]:  (in @ X2 @ (setadjoin @ X2 @ X4))),
99.32/13.18	    inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl347])).
99.32/13.18	thf(zip_derived_cl322, plain,
99.32/13.18	    (~ (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
99.32/13.18	         (((setadjoinIR) =>
99.32/13.18	           (((setadjoinE) =>
99.32/13.18	             (((setadjoinOr) =>
99.32/13.18	               (((setoftrueEq) =>
99.32/13.18	                 (((powersetI) =>
99.32/13.18	                   (((emptyinPowerset) =>
99.32/13.18	                     (((emptyInPowerset) =>
99.32/13.18	                       (((powersetE) =>
99.32/13.18	                         (((setunionI) =>
99.32/13.18	                           (((setunionE) =>
99.32/13.18	                             (((subPowSU) =>
99.32/13.18	                               (((exuE2) =>
99.32/13.18	                                 (((nonemptyImpWitness) =>
99.32/13.18	                                   (((uniqinunit) =>
99.32/13.18	                                     (((notinsingleton) =>
99.32/13.18	                                       (((eqinunit) =>
99.32/13.18	                                         (((singletonsswitch) =>
99.32/13.18	                                           (((upairsetE) =>
99.32/13.18	                                             (((upairsetIL) =>
99.32/13.18	                                               (((upairsetIR) =>
99.32/13.18	                                                 (((emptyE1) =>
99.32/13.18	                                                   (((vacuousDall) =>
99.32/13.18	                                                     (((quantDeMorgan1) =>
99.32/13.18	                                                       (((quantDeMorgan2) =>
99.32/13.18	                                                         (((quantDeMorgan3) =>
99.32/13.18	                                                           (((quantDeMorgan4) =>
99.32/13.18	                                                             (((prop2setI) =>
99.32/13.18	                                                               (((prop2set2propI) =>
99.32/13.18	                                                                 (((notdexE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notdallE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuI3) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (inCongP) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (in__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuE3u) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exu__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoin__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powerset__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setunion__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuEu) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (descr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (dsetconstr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (emptysetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notsubsetI) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetRefl) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetTrans) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subset2powerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setextsub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetemptysetimpeq) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetE1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (inPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepInPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepSubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (!!) @ (
99.32/13.18	                                                                   (('#B') @ (
99.32/13.18	                                                                    !!) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    !!))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#S') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#B') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#S') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    =>))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))))))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))) @ 
99.32/13.18	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.18	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl307])).
99.32/13.18	thf(zip_derived_cl337, plain,
99.32/13.18	    (~ (((setadjoinIR) =>
99.32/13.18	         (((setadjoinE) =>
99.32/13.18	           (((setadjoinOr) =>
99.32/13.18	             (((setoftrueEq) =>
99.32/13.18	               (((powersetI) =>
99.32/13.18	                 (((emptyinPowerset) =>
99.32/13.18	                   (((emptyInPowerset) =>
99.32/13.18	                     (((powersetE) =>
99.32/13.18	                       (((setunionI) =>
99.32/13.18	                         (((setunionE) =>
99.32/13.18	                           (((subPowSU) =>
99.32/13.18	                             (((exuE2) =>
99.32/13.18	                               (((nonemptyImpWitness) =>
99.32/13.18	                                 (((uniqinunit) =>
99.32/13.18	                                   (((notinsingleton) =>
99.32/13.18	                                     (((eqinunit) =>
99.32/13.18	                                       (((singletonsswitch) =>
99.32/13.18	                                         (((upairsetE) =>
99.32/13.18	                                           (((upairsetIL) =>
99.32/13.18	                                             (((upairsetIR) =>
99.32/13.18	                                               (((emptyE1) =>
99.32/13.18	                                                 (((vacuousDall) =>
99.32/13.18	                                                   (((quantDeMorgan1) =>
99.32/13.18	                                                     (((quantDeMorgan2) =>
99.32/13.18	                                                       (((quantDeMorgan3) =>
99.32/13.18	                                                         (((quantDeMorgan4) =>
99.32/13.18	                                                           (((prop2setI) =>
99.32/13.18	                                                             (((prop2set2propI) =>
99.32/13.18	                                                               (((notdexE) =>
99.32/13.18	                                                                 (((notdallE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuI3) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (inCongP) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (in__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuE3u) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exu__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoin__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powerset__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setunion__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuEu) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (descr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (dsetconstr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (emptysetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notsubsetI) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetRefl) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetTrans) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subset2powerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setextsub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetemptysetimpeq) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetE1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (inPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepInPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepSubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (!!) @ (
99.32/13.18	                                                                   (('#B') @ (
99.32/13.18	                                                                    !!) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    !!))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#S') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#B') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#S') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    =>))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))))))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))) @ 
99.32/13.18	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.18	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl322])).
99.32/13.18	thf(zip_derived_cl349, plain,
99.32/13.18	    (~ (((setadjoinE) =>
99.32/13.18	         (((setadjoinOr) =>
99.32/13.18	           (((setoftrueEq) =>
99.32/13.18	             (((powersetI) =>
99.32/13.18	               (((emptyinPowerset) =>
99.32/13.18	                 (((emptyInPowerset) =>
99.32/13.18	                   (((powersetE) =>
99.32/13.18	                     (((setunionI) =>
99.32/13.18	                       (((setunionE) =>
99.32/13.18	                         (((subPowSU) =>
99.32/13.18	                           (((exuE2) =>
99.32/13.18	                             (((nonemptyImpWitness) =>
99.32/13.18	                               (((uniqinunit) =>
99.32/13.18	                                 (((notinsingleton) =>
99.32/13.18	                                   (((eqinunit) =>
99.32/13.18	                                     (((singletonsswitch) =>
99.32/13.18	                                       (((upairsetE) =>
99.32/13.18	                                         (((upairsetIL) =>
99.32/13.18	                                           (((upairsetIR) =>
99.32/13.18	                                             (((emptyE1) =>
99.32/13.18	                                               (((vacuousDall) =>
99.32/13.18	                                                 (((quantDeMorgan1) =>
99.32/13.18	                                                   (((quantDeMorgan2) =>
99.32/13.18	                                                     (((quantDeMorgan3) =>
99.32/13.18	                                                       (((quantDeMorgan4) =>
99.32/13.18	                                                         (((prop2setI) =>
99.32/13.18	                                                           (((prop2set2propI) =>
99.32/13.18	                                                             (((notdexE) =>
99.32/13.18	                                                               (((notdallE) =>
99.32/13.18	                                                                 (((exuI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuI3) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (inCongP) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (in__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuE3u) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exu__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoin__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powerset__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setunion__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuEu) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (descr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (dsetconstr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (emptysetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notsubsetI) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetRefl) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetTrans) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subset2powerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setextsub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetemptysetimpeq) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetE1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (inPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepInPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepSubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (!!) @ (
99.32/13.18	                                                                   (('#B') @ (
99.32/13.18	                                                                    !!) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    !!))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#S') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#B') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#S') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    =>))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))))))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))) @ 
99.32/13.18	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.18	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl337])).
99.32/13.18	thf(zip_derived_cl355, plain,
99.32/13.18	    (~ (((setadjoinOr) =>
99.32/13.18	         (((setoftrueEq) =>
99.32/13.18	           (((powersetI) =>
99.32/13.18	             (((emptyinPowerset) =>
99.32/13.18	               (((emptyInPowerset) =>
99.32/13.18	                 (((powersetE) =>
99.32/13.18	                   (((setunionI) =>
99.32/13.18	                     (((setunionE) =>
99.32/13.18	                       (((subPowSU) =>
99.32/13.18	                         (((exuE2) =>
99.32/13.18	                           (((nonemptyImpWitness) =>
99.32/13.18	                             (((uniqinunit) =>
99.32/13.18	                               (((notinsingleton) =>
99.32/13.18	                                 (((eqinunit) =>
99.32/13.18	                                   (((singletonsswitch) =>
99.32/13.18	                                     (((upairsetE) =>
99.32/13.18	                                       (((upairsetIL) =>
99.32/13.18	                                         (((upairsetIR) =>
99.32/13.18	                                           (((emptyE1) =>
99.32/13.18	                                             (((vacuousDall) =>
99.32/13.18	                                               (((quantDeMorgan1) =>
99.32/13.18	                                                 (((quantDeMorgan2) =>
99.32/13.18	                                                   (((quantDeMorgan3) =>
99.32/13.18	                                                     (((quantDeMorgan4) =>
99.32/13.18	                                                       (((prop2setI) =>
99.32/13.18	                                                         (((prop2set2propI) =>
99.32/13.18	                                                           (((notdexE) =>
99.32/13.18	                                                             (((notdallE) =>
99.32/13.18	                                                               (((exuI1) =>
99.32/13.18	                                                                 (((exuI3) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (inCongP) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (in__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuE3u) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exu__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoin__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powerset__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setunion__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuEu) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (descr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (dsetconstr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (emptysetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notsubsetI) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetRefl) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetTrans) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subset2powerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setextsub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetemptysetimpeq) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetE1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (inPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepInPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepSubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (!!) @ (
99.32/13.18	                                                                   (('#B') @ (
99.32/13.18	                                                                    !!) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    !!))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#S') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#B') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#S') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    =>))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))))))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))) @ 
99.32/13.18	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.18	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl349])).
99.32/13.18	thf(zip_derived_cl362, plain,
99.32/13.18	    (~ (((setoftrueEq) =>
99.32/13.18	         (((powersetI) =>
99.32/13.18	           (((emptyinPowerset) =>
99.32/13.18	             (((emptyInPowerset) =>
99.32/13.18	               (((powersetE) =>
99.32/13.18	                 (((setunionI) =>
99.32/13.18	                   (((setunionE) =>
99.32/13.18	                     (((subPowSU) =>
99.32/13.18	                       (((exuE2) =>
99.32/13.18	                         (((nonemptyImpWitness) =>
99.32/13.18	                           (((uniqinunit) =>
99.32/13.18	                             (((notinsingleton) =>
99.32/13.18	                               (((eqinunit) =>
99.32/13.18	                                 (((singletonsswitch) =>
99.32/13.18	                                   (((upairsetE) =>
99.32/13.18	                                     (((upairsetIL) =>
99.32/13.18	                                       (((upairsetIR) =>
99.32/13.18	                                         (((emptyE1) =>
99.32/13.18	                                           (((vacuousDall) =>
99.32/13.18	                                             (((quantDeMorgan1) =>
99.32/13.18	                                               (((quantDeMorgan2) =>
99.32/13.18	                                                 (((quantDeMorgan3) =>
99.32/13.18	                                                   (((quantDeMorgan4) =>
99.32/13.18	                                                     (((prop2setI) =>
99.32/13.18	                                                       (((prop2set2propI) =>
99.32/13.18	                                                         (((notdexE) =>
99.32/13.18	                                                           (((notdallE) =>
99.32/13.18	                                                             (((exuI1) =>
99.32/13.18	                                                               (((exuI3) =>
99.32/13.18	                                                                 (((exuI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (inCongP) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (in__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuE3u) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exu__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoin__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powerset__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setunion__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuEu) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (descr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (dsetconstr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (emptysetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notsubsetI) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetRefl) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetTrans) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subset2powerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setextsub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetemptysetimpeq) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetE1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (inPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepInPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepSubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (!!) @ (
99.32/13.18	                                                                   (('#B') @ (
99.32/13.18	                                                                    !!) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    !!))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#S') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#B') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#S') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    =>))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))))))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))) @ 
99.32/13.18	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.18	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl355])).
99.32/13.18	thf(zip_derived_cl369, plain,
99.32/13.18	    (~ (((powersetI) =>
99.32/13.18	         (((emptyinPowerset) =>
99.32/13.18	           (((emptyInPowerset) =>
99.32/13.18	             (((powersetE) =>
99.32/13.18	               (((setunionI) =>
99.32/13.18	                 (((setunionE) =>
99.32/13.18	                   (((subPowSU) =>
99.32/13.18	                     (((exuE2) =>
99.32/13.18	                       (((nonemptyImpWitness) =>
99.32/13.18	                         (((uniqinunit) =>
99.32/13.18	                           (((notinsingleton) =>
99.32/13.18	                             (((eqinunit) =>
99.32/13.18	                               (((singletonsswitch) =>
99.32/13.18	                                 (((upairsetE) =>
99.32/13.18	                                   (((upairsetIL) =>
99.32/13.18	                                     (((upairsetIR) =>
99.32/13.18	                                       (((emptyE1) =>
99.32/13.18	                                         (((vacuousDall) =>
99.32/13.18	                                           (((quantDeMorgan1) =>
99.32/13.18	                                             (((quantDeMorgan2) =>
99.32/13.18	                                               (((quantDeMorgan3) =>
99.32/13.18	                                                 (((quantDeMorgan4) =>
99.32/13.18	                                                   (((prop2setI) =>
99.32/13.18	                                                     (((prop2set2propI) =>
99.32/13.18	                                                       (((notdexE) =>
99.32/13.18	                                                         (((notdallE) =>
99.32/13.18	                                                           (((exuI1) =>
99.32/13.18	                                                             (((exuI3) =>
99.32/13.18	                                                               (((exuI2) =>
99.32/13.18	                                                                 (((inCongP) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (in__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuE3u) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exu__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoin__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powerset__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setunion__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuEu) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (descr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (dsetconstr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (emptysetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notsubsetI) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetRefl) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetTrans) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subset2powerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setextsub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetemptysetimpeq) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetE1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (inPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepInPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepSubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (!!) @ (
99.32/13.18	                                                                   (('#B') @ (
99.32/13.18	                                                                    !!) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    !!))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#S') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#B') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#S') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    =>))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))))))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))) @ 
99.32/13.18	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.18	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl362])).
99.32/13.18	thf(zip_derived_cl376, plain,
99.32/13.18	    (~ (((emptyinPowerset) =>
99.32/13.18	         (((emptyInPowerset) =>
99.32/13.18	           (((powersetE) =>
99.32/13.18	             (((setunionI) =>
99.32/13.18	               (((setunionE) =>
99.32/13.18	                 (((subPowSU) =>
99.32/13.18	                   (((exuE2) =>
99.32/13.18	                     (((nonemptyImpWitness) =>
99.32/13.18	                       (((uniqinunit) =>
99.32/13.18	                         (((notinsingleton) =>
99.32/13.18	                           (((eqinunit) =>
99.32/13.18	                             (((singletonsswitch) =>
99.32/13.18	                               (((upairsetE) =>
99.32/13.18	                                 (((upairsetIL) =>
99.32/13.18	                                   (((upairsetIR) =>
99.32/13.18	                                     (((emptyE1) =>
99.32/13.18	                                       (((vacuousDall) =>
99.32/13.18	                                         (((quantDeMorgan1) =>
99.32/13.18	                                           (((quantDeMorgan2) =>
99.32/13.18	                                             (((quantDeMorgan3) =>
99.32/13.18	                                               (((quantDeMorgan4) =>
99.32/13.18	                                                 (((prop2setI) =>
99.32/13.18	                                                   (((prop2set2propI) =>
99.32/13.18	                                                     (((notdexE) =>
99.32/13.18	                                                       (((notdallE) =>
99.32/13.18	                                                         (((exuI1) =>
99.32/13.18	                                                           (((exuI3) =>
99.32/13.18	                                                             (((exuI2) =>
99.32/13.18	                                                               (((inCongP) =>
99.32/13.18	                                                                 (((in__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuE3u) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exu__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoin__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powerset__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setunion__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuEu) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (descr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (dsetconstr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (emptysetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notsubsetI) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetRefl) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetTrans) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subset2powerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setextsub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetemptysetimpeq) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetE1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (inPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepInPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepSubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (!!) @ (
99.32/13.18	                                                                   (('#B') @ (
99.32/13.18	                                                                    !!) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    !!))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#S') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#B') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#S') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    =>))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))))))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))) @ 
99.32/13.18	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.18	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl369])).
99.32/13.18	thf(zip_derived_cl384, plain,
99.32/13.18	    (~ (((emptyInPowerset) =>
99.32/13.18	         (((powersetE) =>
99.32/13.18	           (((setunionI) =>
99.32/13.18	             (((setunionE) =>
99.32/13.18	               (((subPowSU) =>
99.32/13.18	                 (((exuE2) =>
99.32/13.18	                   (((nonemptyImpWitness) =>
99.32/13.18	                     (((uniqinunit) =>
99.32/13.18	                       (((notinsingleton) =>
99.32/13.18	                         (((eqinunit) =>
99.32/13.18	                           (((singletonsswitch) =>
99.32/13.18	                             (((upairsetE) =>
99.32/13.18	                               (((upairsetIL) =>
99.32/13.18	                                 (((upairsetIR) =>
99.32/13.18	                                   (((emptyE1) =>
99.32/13.18	                                     (((vacuousDall) =>
99.32/13.18	                                       (((quantDeMorgan1) =>
99.32/13.18	                                         (((quantDeMorgan2) =>
99.32/13.18	                                           (((quantDeMorgan3) =>
99.32/13.18	                                             (((quantDeMorgan4) =>
99.32/13.18	                                               (((prop2setI) =>
99.32/13.18	                                                 (((prop2set2propI) =>
99.32/13.18	                                                   (((notdexE) =>
99.32/13.18	                                                     (((notdallE) =>
99.32/13.18	                                                       (((exuI1) =>
99.32/13.18	                                                         (((exuI3) =>
99.32/13.18	                                                           (((exuI2) =>
99.32/13.18	                                                             (((inCongP) =>
99.32/13.18	                                                               (((in__Cong) =>
99.32/13.18	                                                                 (((exuE3u) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exu__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoin__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powerset__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setunion__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuEu) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (descr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (dsetconstr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (emptysetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notsubsetI) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetRefl) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetTrans) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subset2powerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setextsub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetemptysetimpeq) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetE1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (inPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepInPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepSubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (!!) @ (
99.32/13.18	                                                                   (('#B') @ (
99.32/13.18	                                                                    !!) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    !!))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#S') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#B') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#S') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    =>))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))))))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))) @ 
99.32/13.18	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.18	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl376])).
99.32/13.18	thf(zip_derived_cl392, plain,
99.32/13.18	    (~ (((powersetE) =>
99.32/13.18	         (((setunionI) =>
99.32/13.18	           (((setunionE) =>
99.32/13.18	             (((subPowSU) =>
99.32/13.18	               (((exuE2) =>
99.32/13.18	                 (((nonemptyImpWitness) =>
99.32/13.18	                   (((uniqinunit) =>
99.32/13.18	                     (((notinsingleton) =>
99.32/13.18	                       (((eqinunit) =>
99.32/13.18	                         (((singletonsswitch) =>
99.32/13.18	                           (((upairsetE) =>
99.32/13.18	                             (((upairsetIL) =>
99.32/13.18	                               (((upairsetIR) =>
99.32/13.18	                                 (((emptyE1) =>
99.32/13.18	                                   (((vacuousDall) =>
99.32/13.18	                                     (((quantDeMorgan1) =>
99.32/13.18	                                       (((quantDeMorgan2) =>
99.32/13.18	                                         (((quantDeMorgan3) =>
99.32/13.18	                                           (((quantDeMorgan4) =>
99.32/13.18	                                             (((prop2setI) =>
99.32/13.18	                                               (((prop2set2propI) =>
99.32/13.18	                                                 (((notdexE) =>
99.32/13.18	                                                   (((notdallE) =>
99.32/13.18	                                                     (((exuI1) =>
99.32/13.18	                                                       (((exuI3) =>
99.32/13.18	                                                         (((exuI2) =>
99.32/13.18	                                                           (((inCongP) =>
99.32/13.18	                                                             (((in__Cong) =>
99.32/13.18	                                                               (((exuE3u) =>
99.32/13.18	                                                                 (((exu__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoin__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powerset__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setunion__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuEu) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (descr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (dsetconstr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (emptysetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notsubsetI) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetRefl) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetTrans) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subset2powerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setextsub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetemptysetimpeq) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetE1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (inPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepInPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepSubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (!!) @ (
99.32/13.18	                                                                   (('#B') @ (
99.32/13.18	                                                                    !!) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    !!))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#S') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#B') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#S') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    =>))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))))))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))) @ 
99.32/13.18	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.18	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl384])).
99.32/13.18	thf(zip_derived_cl400, plain,
99.32/13.18	    (~ (((setunionI) =>
99.32/13.18	         (((setunionE) =>
99.32/13.18	           (((subPowSU) =>
99.32/13.18	             (((exuE2) =>
99.32/13.18	               (((nonemptyImpWitness) =>
99.32/13.18	                 (((uniqinunit) =>
99.32/13.18	                   (((notinsingleton) =>
99.32/13.18	                     (((eqinunit) =>
99.32/13.18	                       (((singletonsswitch) =>
99.32/13.18	                         (((upairsetE) =>
99.32/13.18	                           (((upairsetIL) =>
99.32/13.18	                             (((upairsetIR) =>
99.32/13.18	                               (((emptyE1) =>
99.32/13.18	                                 (((vacuousDall) =>
99.32/13.18	                                   (((quantDeMorgan1) =>
99.32/13.18	                                     (((quantDeMorgan2) =>
99.32/13.18	                                       (((quantDeMorgan3) =>
99.32/13.18	                                         (((quantDeMorgan4) =>
99.32/13.18	                                           (((prop2setI) =>
99.32/13.18	                                             (((prop2set2propI) =>
99.32/13.18	                                               (((notdexE) =>
99.32/13.18	                                                 (((notdallE) =>
99.32/13.18	                                                   (((exuI1) =>
99.32/13.18	                                                     (((exuI3) =>
99.32/13.18	                                                       (((exuI2) =>
99.32/13.18	                                                         (((inCongP) =>
99.32/13.18	                                                           (((in__Cong) =>
99.32/13.18	                                                             (((exuE3u) =>
99.32/13.18	                                                               (((exu__Cong) =>
99.32/13.18	                                                                 (((setadjoin__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powerset__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setunion__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuEu) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (descr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (dsetconstr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (emptysetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notsubsetI) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetRefl) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetTrans) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subset2powerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setextsub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetemptysetimpeq) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetE1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (inPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepInPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepSubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (!!) @ (
99.32/13.18	                                                                   (('#B') @ (
99.32/13.18	                                                                    !!) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    !!))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#S') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#B') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#S') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    =>))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))))))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))) @ 
99.32/13.18	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.18	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl392])).
99.32/13.18	thf(zip_derived_cl408, plain,
99.32/13.18	    (~ (((setunionE) =>
99.32/13.18	         (((subPowSU) =>
99.32/13.18	           (((exuE2) =>
99.32/13.18	             (((nonemptyImpWitness) =>
99.32/13.18	               (((uniqinunit) =>
99.32/13.18	                 (((notinsingleton) =>
99.32/13.18	                   (((eqinunit) =>
99.32/13.18	                     (((singletonsswitch) =>
99.32/13.18	                       (((upairsetE) =>
99.32/13.18	                         (((upairsetIL) =>
99.32/13.18	                           (((upairsetIR) =>
99.32/13.18	                             (((emptyE1) =>
99.32/13.18	                               (((vacuousDall) =>
99.32/13.18	                                 (((quantDeMorgan1) =>
99.32/13.18	                                   (((quantDeMorgan2) =>
99.32/13.18	                                     (((quantDeMorgan3) =>
99.32/13.18	                                       (((quantDeMorgan4) =>
99.32/13.18	                                         (((prop2setI) =>
99.32/13.18	                                           (((prop2set2propI) =>
99.32/13.18	                                             (((notdexE) =>
99.32/13.18	                                               (((notdallE) =>
99.32/13.18	                                                 (((exuI1) =>
99.32/13.18	                                                   (((exuI3) =>
99.32/13.18	                                                     (((exuI2) =>
99.32/13.18	                                                       (((inCongP) =>
99.32/13.18	                                                         (((in__Cong) =>
99.32/13.18	                                                           (((exuE3u) =>
99.32/13.18	                                                             (((exu__Cong) =>
99.32/13.18	                                                               (((setadjoin__Cong) =>
99.32/13.18	                                                                 (((powerset__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setunion__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuEu) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (descr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (dsetconstr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (emptysetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notsubsetI) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetRefl) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetTrans) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subset2powerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setextsub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetemptysetimpeq) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetE1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (inPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepInPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepSubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (!!) @ (
99.32/13.18	                                                                   (('#B') @ (
99.32/13.18	                                                                    !!) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    !!))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#S') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#B') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#S') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    =>))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))))))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))) @ 
99.32/13.18	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.18	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl400])).
99.32/13.18	thf(zip_derived_cl417, plain,
99.32/13.18	    (~ (((subPowSU) =>
99.32/13.18	         (((exuE2) =>
99.32/13.18	           (((nonemptyImpWitness) =>
99.32/13.18	             (((uniqinunit) =>
99.32/13.18	               (((notinsingleton) =>
99.32/13.18	                 (((eqinunit) =>
99.32/13.18	                   (((singletonsswitch) =>
99.32/13.18	                     (((upairsetE) =>
99.32/13.18	                       (((upairsetIL) =>
99.32/13.18	                         (((upairsetIR) =>
99.32/13.18	                           (((emptyE1) =>
99.32/13.18	                             (((vacuousDall) =>
99.32/13.18	                               (((quantDeMorgan1) =>
99.32/13.18	                                 (((quantDeMorgan2) =>
99.32/13.18	                                   (((quantDeMorgan3) =>
99.32/13.18	                                     (((quantDeMorgan4) =>
99.32/13.18	                                       (((prop2setI) =>
99.32/13.18	                                         (((prop2set2propI) =>
99.32/13.18	                                           (((notdexE) =>
99.32/13.18	                                             (((notdallE) =>
99.32/13.18	                                               (((exuI1) =>
99.32/13.18	                                                 (((exuI3) =>
99.32/13.18	                                                   (((exuI2) =>
99.32/13.18	                                                     (((inCongP) =>
99.32/13.18	                                                       (((in__Cong) =>
99.32/13.18	                                                         (((exuE3u) =>
99.32/13.18	                                                           (((exu__Cong) =>
99.32/13.18	                                                             (((setadjoin__Cong) =>
99.32/13.18	                                                               (((powerset__Cong) =>
99.32/13.18	                                                                 (((setunion__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (exuEu) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (descr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (dsetconstr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (emptysetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notsubsetI) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetRefl) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetTrans) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subset2powerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setextsub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetemptysetimpeq) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetE1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (inPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepInPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepSubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (!!) @ (
99.32/13.18	                                                                   (('#B') @ (
99.32/13.18	                                                                    !!) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    !!))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#S') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#B') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#S') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    =>))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))))))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))) @ 
99.32/13.18	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.18	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl408])).
99.32/13.18	thf(zip_derived_cl428, plain,
99.32/13.18	    (~ (((exuE2) =>
99.32/13.18	         (((nonemptyImpWitness) =>
99.32/13.18	           (((uniqinunit) =>
99.32/13.18	             (((notinsingleton) =>
99.32/13.18	               (((eqinunit) =>
99.32/13.18	                 (((singletonsswitch) =>
99.32/13.18	                   (((upairsetE) =>
99.32/13.18	                     (((upairsetIL) =>
99.32/13.18	                       (((upairsetIR) =>
99.32/13.18	                         (((emptyE1) =>
99.32/13.18	                           (((vacuousDall) =>
99.32/13.18	                             (((quantDeMorgan1) =>
99.32/13.18	                               (((quantDeMorgan2) =>
99.32/13.18	                                 (((quantDeMorgan3) =>
99.32/13.18	                                   (((quantDeMorgan4) =>
99.32/13.18	                                     (((prop2setI) =>
99.32/13.18	                                       (((prop2set2propI) =>
99.32/13.18	                                         (((notdexE) =>
99.32/13.18	                                           (((notdallE) =>
99.32/13.18	                                             (((exuI1) =>
99.32/13.18	                                               (((exuI3) =>
99.32/13.18	                                                 (((exuI2) =>
99.32/13.18	                                                   (((inCongP) =>
99.32/13.18	                                                     (((in__Cong) =>
99.32/13.18	                                                       (((exuE3u) =>
99.32/13.18	                                                         (((exu__Cong) =>
99.32/13.18	                                                           (((setadjoin__Cong) =>
99.32/13.18	                                                             (((powerset__Cong) =>
99.32/13.18	                                                               (((setunion__Cong) =>
99.32/13.18	                                                                 (((exuEu) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (descr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (dsetconstr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (emptysetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notsubsetI) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetRefl) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetTrans) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subset2powerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setextsub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetemptysetimpeq) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetE1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (inPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepInPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepSubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (!!) @ (
99.32/13.18	                                                                   (('#B') @ (
99.32/13.18	                                                                    !!) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    !!))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#S') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#B') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#S') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    =>))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))))))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))) @ 
99.32/13.18	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.18	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl417])).
99.32/13.18	thf(zip_derived_cl439, plain,
99.32/13.18	    (~ (((nonemptyImpWitness) =>
99.32/13.18	         (((uniqinunit) =>
99.32/13.18	           (((notinsingleton) =>
99.32/13.18	             (((eqinunit) =>
99.32/13.18	               (((singletonsswitch) =>
99.32/13.18	                 (((upairsetE) =>
99.32/13.18	                   (((upairsetIL) =>
99.32/13.18	                     (((upairsetIR) =>
99.32/13.18	                       (((emptyE1) =>
99.32/13.18	                         (((vacuousDall) =>
99.32/13.18	                           (((quantDeMorgan1) =>
99.32/13.18	                             (((quantDeMorgan2) =>
99.32/13.18	                               (((quantDeMorgan3) =>
99.32/13.18	                                 (((quantDeMorgan4) =>
99.32/13.18	                                   (((prop2setI) =>
99.32/13.18	                                     (((prop2set2propI) =>
99.32/13.18	                                       (((notdexE) =>
99.32/13.18	                                         (((notdallE) =>
99.32/13.18	                                           (((exuI1) =>
99.32/13.18	                                             (((exuI3) =>
99.32/13.18	                                               (((exuI2) =>
99.32/13.18	                                                 (((inCongP) =>
99.32/13.18	                                                   (((in__Cong) =>
99.32/13.18	                                                     (((exuE3u) =>
99.32/13.18	                                                       (((exu__Cong) =>
99.32/13.18	                                                         (((setadjoin__Cong) =>
99.32/13.18	                                                           (((powerset__Cong) =>
99.32/13.18	                                                             (((setunion__Cong) =>
99.32/13.18	                                                               (((exuEu) =>
99.32/13.18	                                                                 (((descr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (dsetconstr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (emptysetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notsubsetI) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetRefl) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetTrans) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subset2powerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setextsub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetemptysetimpeq) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetE1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (inPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepInPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepSubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (!!) @ (
99.32/13.18	                                                                   (('#B') @ (
99.32/13.18	                                                                    !!) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    !!))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#S') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#B') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#S') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    =>))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))))))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))) @ 
99.32/13.18	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.18	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl428])).
99.32/13.18	thf(zip_derived_cl449, plain,
99.32/13.18	    (~ (((uniqinunit) =>
99.32/13.18	         (((notinsingleton) =>
99.32/13.18	           (((eqinunit) =>
99.32/13.18	             (((singletonsswitch) =>
99.32/13.18	               (((upairsetE) =>
99.32/13.18	                 (((upairsetIL) =>
99.32/13.18	                   (((upairsetIR) =>
99.32/13.18	                     (((emptyE1) =>
99.32/13.18	                       (((vacuousDall) =>
99.32/13.18	                         (((quantDeMorgan1) =>
99.32/13.18	                           (((quantDeMorgan2) =>
99.32/13.18	                             (((quantDeMorgan3) =>
99.32/13.18	                               (((quantDeMorgan4) =>
99.32/13.18	                                 (((prop2setI) =>
99.32/13.18	                                   (((prop2set2propI) =>
99.32/13.18	                                     (((notdexE) =>
99.32/13.18	                                       (((notdallE) =>
99.32/13.18	                                         (((exuI1) =>
99.32/13.18	                                           (((exuI3) =>
99.32/13.18	                                             (((exuI2) =>
99.32/13.18	                                               (((inCongP) =>
99.32/13.18	                                                 (((in__Cong) =>
99.32/13.18	                                                   (((exuE3u) =>
99.32/13.18	                                                     (((exu__Cong) =>
99.32/13.18	                                                       (((setadjoin__Cong) =>
99.32/13.18	                                                         (((powerset__Cong) =>
99.32/13.18	                                                           (((setunion__Cong) =>
99.32/13.18	                                                             (((exuEu) =>
99.32/13.18	                                                               (((descr__Cong) =>
99.32/13.18	                                                                 (((dsetconstr__Cong) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (emptysetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notsubsetI) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetRefl) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetTrans) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subset2powerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setextsub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetemptysetimpeq) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetE1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (inPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepInPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepSubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (!!) @ (
99.32/13.18	                                                                   (('#B') @ (
99.32/13.18	                                                                    !!) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    !!))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#S') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#B') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#S') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    =>))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))))))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))) @ 
99.32/13.18	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.18	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl439])).
99.32/13.18	thf(zip_derived_cl458, plain,
99.32/13.18	    (~ (((notinsingleton) =>
99.32/13.18	         (((eqinunit) =>
99.32/13.18	           (((singletonsswitch) =>
99.32/13.18	             (((upairsetE) =>
99.32/13.18	               (((upairsetIL) =>
99.32/13.18	                 (((upairsetIR) =>
99.32/13.18	                   (((emptyE1) =>
99.32/13.18	                     (((vacuousDall) =>
99.32/13.18	                       (((quantDeMorgan1) =>
99.32/13.18	                         (((quantDeMorgan2) =>
99.32/13.18	                           (((quantDeMorgan3) =>
99.32/13.18	                             (((quantDeMorgan4) =>
99.32/13.18	                               (((prop2setI) =>
99.32/13.18	                                 (((prop2set2propI) =>
99.32/13.18	                                   (((notdexE) =>
99.32/13.18	                                     (((notdallE) =>
99.32/13.18	                                       (((exuI1) =>
99.32/13.18	                                         (((exuI3) =>
99.32/13.18	                                           (((exuI2) =>
99.32/13.18	                                             (((inCongP) =>
99.32/13.18	                                               (((in__Cong) =>
99.32/13.18	                                                 (((exuE3u) =>
99.32/13.18	                                                   (((exu__Cong) =>
99.32/13.18	                                                     (((setadjoin__Cong) =>
99.32/13.18	                                                       (((powerset__Cong) =>
99.32/13.18	                                                         (((setunion__Cong) =>
99.32/13.18	                                                           (((exuEu) =>
99.32/13.18	                                                             (((descr__Cong) =>
99.32/13.18	                                                               (((dsetconstr__Cong) =>
99.32/13.18	                                                                 (((subsetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (emptysetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notsubsetI) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetRefl) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetTrans) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subset2powerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setextsub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetemptysetimpeq) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetE1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (inPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepInPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepSubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (!!) @ (
99.32/13.18	                                                                   (('#B') @ (
99.32/13.18	                                                                    !!) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    !!))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#S') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#B') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#S') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    =>))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))))))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))) @ 
99.32/13.18	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.18	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl449])).
99.32/13.18	thf(zip_derived_cl467, plain,
99.32/13.18	    (~ (((eqinunit) =>
99.32/13.18	         (((singletonsswitch) =>
99.32/13.18	           (((upairsetE) =>
99.32/13.18	             (((upairsetIL) =>
99.32/13.18	               (((upairsetIR) =>
99.32/13.18	                 (((emptyE1) =>
99.32/13.18	                   (((vacuousDall) =>
99.32/13.18	                     (((quantDeMorgan1) =>
99.32/13.18	                       (((quantDeMorgan2) =>
99.32/13.18	                         (((quantDeMorgan3) =>
99.32/13.18	                           (((quantDeMorgan4) =>
99.32/13.18	                             (((prop2setI) =>
99.32/13.18	                               (((prop2set2propI) =>
99.32/13.18	                                 (((notdexE) =>
99.32/13.18	                                   (((notdallE) =>
99.32/13.18	                                     (((exuI1) =>
99.32/13.18	                                       (((exuI3) =>
99.32/13.18	                                         (((exuI2) =>
99.32/13.18	                                           (((inCongP) =>
99.32/13.18	                                             (((in__Cong) =>
99.32/13.18	                                               (((exuE3u) =>
99.32/13.18	                                                 (((exu__Cong) =>
99.32/13.18	                                                   (((setadjoin__Cong) =>
99.32/13.18	                                                     (((powerset__Cong) =>
99.32/13.18	                                                       (((setunion__Cong) =>
99.32/13.18	                                                         (((exuEu) =>
99.32/13.18	                                                           (((descr__Cong) =>
99.32/13.18	                                                             (((dsetconstr__Cong) =>
99.32/13.18	                                                               (((subsetI1) =>
99.32/13.18	                                                                 (((eqimpsubset2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (eqimpsubset1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (emptysetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notsubsetI) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetRefl) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetTrans) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subset2powerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setextsub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetemptysetimpeq) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetE1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (inPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepInPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepSubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (!!) @ (
99.32/13.18	                                                                   (('#B') @ (
99.32/13.18	                                                                    !!) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    !!))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#S') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#B') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#S') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    =>))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))))))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))) @ 
99.32/13.18	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.18	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl458])).
99.32/13.18	thf(zip_derived_cl475, plain,
99.32/13.18	    (~ (((singletonsswitch) =>
99.32/13.18	         (((upairsetE) =>
99.32/13.18	           (((upairsetIL) =>
99.32/13.18	             (((upairsetIR) =>
99.32/13.18	               (((emptyE1) =>
99.32/13.18	                 (((vacuousDall) =>
99.32/13.18	                   (((quantDeMorgan1) =>
99.32/13.18	                     (((quantDeMorgan2) =>
99.32/13.18	                       (((quantDeMorgan3) =>
99.32/13.18	                         (((quantDeMorgan4) =>
99.32/13.18	                           (((prop2setI) =>
99.32/13.18	                             (((prop2set2propI) =>
99.32/13.18	                               (((notdexE) =>
99.32/13.18	                                 (((notdallE) =>
99.32/13.18	                                   (((exuI1) =>
99.32/13.18	                                     (((exuI3) =>
99.32/13.18	                                       (((exuI2) =>
99.32/13.18	                                         (((inCongP) =>
99.32/13.18	                                           (((in__Cong) =>
99.32/13.18	                                             (((exuE3u) =>
99.32/13.18	                                               (((exu__Cong) =>
99.32/13.18	                                                 (((setadjoin__Cong) =>
99.32/13.18	                                                   (((powerset__Cong) =>
99.32/13.18	                                                     (((setunion__Cong) =>
99.32/13.18	                                                       (((exuEu) =>
99.32/13.18	                                                         (((descr__Cong) =>
99.32/13.18	                                                           (((dsetconstr__Cong) =>
99.32/13.18	                                                             (((subsetI1) =>
99.32/13.18	                                                               (((eqimpsubset2) =>
99.32/13.18	                                                                 (((eqimpsubset1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (emptysetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notsubsetI) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetRefl) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetTrans) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subset2powerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setextsub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetemptysetimpeq) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetE1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (inPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepInPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepSubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (!!) @ (
99.32/13.18	                                                                   (('#B') @ (
99.32/13.18	                                                                    !!) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    !!))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#S') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#B') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#S') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    =>))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))))))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))) @ 
99.32/13.18	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.18	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl467])).
99.32/13.18	thf(zip_derived_cl485, plain,
99.32/13.18	    (~ (((upairsetE) =>
99.32/13.18	         (((upairsetIL) =>
99.32/13.18	           (((upairsetIR) =>
99.32/13.18	             (((emptyE1) =>
99.32/13.18	               (((vacuousDall) =>
99.32/13.18	                 (((quantDeMorgan1) =>
99.32/13.18	                   (((quantDeMorgan2) =>
99.32/13.18	                     (((quantDeMorgan3) =>
99.32/13.18	                       (((quantDeMorgan4) =>
99.32/13.18	                         (((prop2setI) =>
99.32/13.18	                           (((prop2set2propI) =>
99.32/13.18	                             (((notdexE) =>
99.32/13.18	                               (((notdallE) =>
99.32/13.18	                                 (((exuI1) =>
99.32/13.18	                                   (((exuI3) =>
99.32/13.18	                                     (((exuI2) =>
99.32/13.18	                                       (((inCongP) =>
99.32/13.18	                                         (((in__Cong) =>
99.32/13.18	                                           (((exuE3u) =>
99.32/13.18	                                             (((exu__Cong) =>
99.32/13.18	                                               (((setadjoin__Cong) =>
99.32/13.18	                                                 (((powerset__Cong) =>
99.32/13.18	                                                   (((setunion__Cong) =>
99.32/13.18	                                                     (((exuEu) =>
99.32/13.18	                                                       (((descr__Cong) =>
99.32/13.18	                                                         (((dsetconstr__Cong) =>
99.32/13.18	                                                           (((subsetI1) =>
99.32/13.18	                                                             (((eqimpsubset2) =>
99.32/13.18	                                                               (((eqimpsubset1) =>
99.32/13.18	                                                                 (((subsetI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (emptysetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetE2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notsubsetI) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (notequalI2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetRefl) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetTrans) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setadjoinSub2) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subset2powerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (setextsub) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (subsetemptysetimpeq) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetI1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetE1) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (inPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (powersetsubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepInPowerset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (sepSubset) =>
99.32/13.18	                                                                   ((
99.32/13.18	                                                                   (!!) @ (
99.32/13.18	                                                                   (('#B') @ (
99.32/13.18	                                                                    !!) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    !!))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#S') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#B') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    '#S') @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    =>))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))))))) @ 
99.32/13.18	                                                                    (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#B') @ (
99.32/13.18	                                                                    (
99.32/13.18	                                                                    ('#C') @ in)))) @ 
99.32/13.18	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.18	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl475])).
99.32/13.18	thf(zip_derived_cl496, plain,
99.32/13.18	    (~ (((upairsetIL) =>
99.32/13.18	         (((upairsetIR) =>
99.32/13.18	           (((emptyE1) =>
99.32/13.18	             (((vacuousDall) =>
99.32/13.18	               (((quantDeMorgan1) =>
99.32/13.18	                 (((quantDeMorgan2) =>
99.32/13.18	                   (((quantDeMorgan3) =>
99.32/13.18	                     (((quantDeMorgan4) =>
99.32/13.18	                       (((prop2setI) =>
99.32/13.18	                         (((prop2set2propI) =>
99.32/13.18	                           (((notdexE) =>
99.32/13.18	                             (((notdallE) =>
99.32/13.18	                               (((exuI1) =>
99.32/13.18	                                 (((exuI3) =>
99.32/13.18	                                   (((exuI2) =>
99.32/13.18	                                     (((inCongP) =>
99.32/13.19	                                       (((in__Cong) =>
99.32/13.19	                                         (((exuE3u) =>
99.32/13.19	                                           (((exu__Cong) =>
99.32/13.19	                                             (((setadjoin__Cong) =>
99.32/13.19	                                               (((powerset__Cong) =>
99.32/13.19	                                                 (((setunion__Cong) =>
99.32/13.19	                                                   (((exuEu) =>
99.32/13.19	                                                     (((descr__Cong) =>
99.32/13.19	                                                       (((dsetconstr__Cong) =>
99.32/13.19	                                                         (((subsetI1) =>
99.32/13.19	                                                           (((eqimpsubset2) =>
99.32/13.19	                                                             (((eqimpsubset1) =>
99.32/13.19	                                                               (((subsetI2) =>
99.32/13.19	                                                                 (((emptysetsubset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (subsetE) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (subsetE2) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (notsubsetI) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (notequalI1) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (notequalI2) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (subsetRefl) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (subsetTrans) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (setadjoinSub) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (setadjoinSub2) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (subset2powerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (setextsub) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (subsetemptysetimpeq) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetI1) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetE1) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (inPowerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetsubset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (sepInPowerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (sepSubset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (!!) @ (
99.32/13.19	                                                                   (('#B') @ (
99.32/13.19	                                                                    !!) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    !!))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#S') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#B') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#S') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    =>))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))))))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))) @ 
99.32/13.19	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl485])).
99.32/13.19	thf(zip_derived_cl507, plain,
99.32/13.19	    (~ (((upairsetIR) =>
99.32/13.19	         (((emptyE1) =>
99.32/13.19	           (((vacuousDall) =>
99.32/13.19	             (((quantDeMorgan1) =>
99.32/13.19	               (((quantDeMorgan2) =>
99.32/13.19	                 (((quantDeMorgan3) =>
99.32/13.19	                   (((quantDeMorgan4) =>
99.32/13.19	                     (((prop2setI) =>
99.32/13.19	                       (((prop2set2propI) =>
99.32/13.19	                         (((notdexE) =>
99.32/13.19	                           (((notdallE) =>
99.32/13.19	                             (((exuI1) =>
99.32/13.19	                               (((exuI3) =>
99.32/13.19	                                 (((exuI2) =>
99.32/13.19	                                   (((inCongP) =>
99.32/13.19	                                     (((in__Cong) =>
99.32/13.19	                                       (((exuE3u) =>
99.32/13.19	                                         (((exu__Cong) =>
99.32/13.19	                                           (((setadjoin__Cong) =>
99.32/13.19	                                             (((powerset__Cong) =>
99.32/13.19	                                               (((setunion__Cong) =>
99.32/13.19	                                                 (((exuEu) =>
99.32/13.19	                                                   (((descr__Cong) =>
99.32/13.19	                                                     (((dsetconstr__Cong) =>
99.32/13.19	                                                       (((subsetI1) =>
99.32/13.19	                                                         (((eqimpsubset2) =>
99.32/13.19	                                                           (((eqimpsubset1) =>
99.32/13.19	                                                             (((subsetI2) =>
99.32/13.19	                                                               (((emptysetsubset) =>
99.32/13.19	                                                                 (((subsetE) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (subsetE2) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (notsubsetI) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (notequalI1) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (notequalI2) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (subsetRefl) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (subsetTrans) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (setadjoinSub) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (setadjoinSub2) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (subset2powerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (setextsub) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (subsetemptysetimpeq) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetI1) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetE1) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (inPowerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetsubset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (sepInPowerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (sepSubset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (!!) @ (
99.32/13.19	                                                                   (('#B') @ (
99.32/13.19	                                                                    !!) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    !!))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#S') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#B') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#S') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    =>))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))))))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))) @ 
99.32/13.19	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl496])).
99.32/13.19	thf(zip_derived_cl517, plain,
99.32/13.19	    (~ (((emptyE1) =>
99.32/13.19	         (((vacuousDall) =>
99.32/13.19	           (((quantDeMorgan1) =>
99.32/13.19	             (((quantDeMorgan2) =>
99.32/13.19	               (((quantDeMorgan3) =>
99.32/13.19	                 (((quantDeMorgan4) =>
99.32/13.19	                   (((prop2setI) =>
99.32/13.19	                     (((prop2set2propI) =>
99.32/13.19	                       (((notdexE) =>
99.32/13.19	                         (((notdallE) =>
99.32/13.19	                           (((exuI1) =>
99.32/13.19	                             (((exuI3) =>
99.32/13.19	                               (((exuI2) =>
99.32/13.19	                                 (((inCongP) =>
99.32/13.19	                                   (((in__Cong) =>
99.32/13.19	                                     (((exuE3u) =>
99.32/13.19	                                       (((exu__Cong) =>
99.32/13.19	                                         (((setadjoin__Cong) =>
99.32/13.19	                                           (((powerset__Cong) =>
99.32/13.19	                                             (((setunion__Cong) =>
99.32/13.19	                                               (((exuEu) =>
99.32/13.19	                                                 (((descr__Cong) =>
99.32/13.19	                                                   (((dsetconstr__Cong) =>
99.32/13.19	                                                     (((subsetI1) =>
99.32/13.19	                                                       (((eqimpsubset2) =>
99.32/13.19	                                                         (((eqimpsubset1) =>
99.32/13.19	                                                           (((subsetI2) =>
99.32/13.19	                                                             (((emptysetsubset) =>
99.32/13.19	                                                               (((subsetE) =>
99.32/13.19	                                                                 (((subsetE2) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (notsubsetI) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (notequalI1) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (notequalI2) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (subsetRefl) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (subsetTrans) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (setadjoinSub) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (setadjoinSub2) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (subset2powerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (setextsub) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (subsetemptysetimpeq) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetI1) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetE1) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (inPowerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetsubset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (sepInPowerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (sepSubset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (!!) @ (
99.32/13.19	                                                                   (('#B') @ (
99.32/13.19	                                                                    !!) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    !!))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#S') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#B') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#S') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    =>))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))))))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))) @ 
99.32/13.19	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl507])).
99.32/13.19	thf(zip_derived_cl528, plain,
99.32/13.19	    (~ (((vacuousDall) =>
99.32/13.19	         (((quantDeMorgan1) =>
99.32/13.19	           (((quantDeMorgan2) =>
99.32/13.19	             (((quantDeMorgan3) =>
99.32/13.19	               (((quantDeMorgan4) =>
99.32/13.19	                 (((prop2setI) =>
99.32/13.19	                   (((prop2set2propI) =>
99.32/13.19	                     (((notdexE) =>
99.32/13.19	                       (((notdallE) =>
99.32/13.19	                         (((exuI1) =>
99.32/13.19	                           (((exuI3) =>
99.32/13.19	                             (((exuI2) =>
99.32/13.19	                               (((inCongP) =>
99.32/13.19	                                 (((in__Cong) =>
99.32/13.19	                                   (((exuE3u) =>
99.32/13.19	                                     (((exu__Cong) =>
99.32/13.19	                                       (((setadjoin__Cong) =>
99.32/13.19	                                         (((powerset__Cong) =>
99.32/13.19	                                           (((setunion__Cong) =>
99.32/13.19	                                             (((exuEu) =>
99.32/13.19	                                               (((descr__Cong) =>
99.32/13.19	                                                 (((dsetconstr__Cong) =>
99.32/13.19	                                                   (((subsetI1) =>
99.32/13.19	                                                     (((eqimpsubset2) =>
99.32/13.19	                                                       (((eqimpsubset1) =>
99.32/13.19	                                                         (((subsetI2) =>
99.32/13.19	                                                           (((emptysetsubset) =>
99.32/13.19	                                                             (((subsetE) =>
99.32/13.19	                                                               (((subsetE2) =>
99.32/13.19	                                                                 (((notsubsetI) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (notequalI1) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (notequalI2) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (subsetRefl) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (subsetTrans) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (setadjoinSub) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (setadjoinSub2) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (subset2powerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (setextsub) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (subsetemptysetimpeq) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetI1) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetE1) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (inPowerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetsubset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (sepInPowerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (sepSubset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (!!) @ (
99.32/13.19	                                                                   (('#B') @ (
99.32/13.19	                                                                    !!) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    !!))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#S') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#B') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#S') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    =>))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))))))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))) @ 
99.32/13.19	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl517])).
99.32/13.19	thf(zip_derived_cl537, plain,
99.32/13.19	    (~ (((quantDeMorgan1) =>
99.32/13.19	         (((quantDeMorgan2) =>
99.32/13.19	           (((quantDeMorgan3) =>
99.32/13.19	             (((quantDeMorgan4) =>
99.32/13.19	               (((prop2setI) =>
99.32/13.19	                 (((prop2set2propI) =>
99.32/13.19	                   (((notdexE) =>
99.32/13.19	                     (((notdallE) =>
99.32/13.19	                       (((exuI1) =>
99.32/13.19	                         (((exuI3) =>
99.32/13.19	                           (((exuI2) =>
99.32/13.19	                             (((inCongP) =>
99.32/13.19	                               (((in__Cong) =>
99.32/13.19	                                 (((exuE3u) =>
99.32/13.19	                                   (((exu__Cong) =>
99.32/13.19	                                     (((setadjoin__Cong) =>
99.32/13.19	                                       (((powerset__Cong) =>
99.32/13.19	                                         (((setunion__Cong) =>
99.32/13.19	                                           (((exuEu) =>
99.32/13.19	                                             (((descr__Cong) =>
99.32/13.19	                                               (((dsetconstr__Cong) =>
99.32/13.19	                                                 (((subsetI1) =>
99.32/13.19	                                                   (((eqimpsubset2) =>
99.32/13.19	                                                     (((eqimpsubset1) =>
99.32/13.19	                                                       (((subsetI2) =>
99.32/13.19	                                                         (((emptysetsubset) =>
99.32/13.19	                                                           (((subsetE) =>
99.32/13.19	                                                             (((subsetE2) =>
99.32/13.19	                                                               (((notsubsetI) =>
99.32/13.19	                                                                 (((notequalI1) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (notequalI2) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (subsetRefl) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (subsetTrans) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (setadjoinSub) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (setadjoinSub2) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (subset2powerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (setextsub) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (subsetemptysetimpeq) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetI1) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetE1) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (inPowerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetsubset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (sepInPowerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (sepSubset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (!!) @ (
99.32/13.19	                                                                   (('#B') @ (
99.32/13.19	                                                                    !!) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    !!))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#S') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#B') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#S') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    =>))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))))))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))) @ 
99.32/13.19	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl528])).
99.32/13.19	thf(zip_derived_cl546, plain,
99.32/13.19	    (~ (((quantDeMorgan2) =>
99.32/13.19	         (((quantDeMorgan3) =>
99.32/13.19	           (((quantDeMorgan4) =>
99.32/13.19	             (((prop2setI) =>
99.32/13.19	               (((prop2set2propI) =>
99.32/13.19	                 (((notdexE) =>
99.32/13.19	                   (((notdallE) =>
99.32/13.19	                     (((exuI1) =>
99.32/13.19	                       (((exuI3) =>
99.32/13.19	                         (((exuI2) =>
99.32/13.19	                           (((inCongP) =>
99.32/13.19	                             (((in__Cong) =>
99.32/13.19	                               (((exuE3u) =>
99.32/13.19	                                 (((exu__Cong) =>
99.32/13.19	                                   (((setadjoin__Cong) =>
99.32/13.19	                                     (((powerset__Cong) =>
99.32/13.19	                                       (((setunion__Cong) =>
99.32/13.19	                                         (((exuEu) =>
99.32/13.19	                                           (((descr__Cong) =>
99.32/13.19	                                             (((dsetconstr__Cong) =>
99.32/13.19	                                               (((subsetI1) =>
99.32/13.19	                                                 (((eqimpsubset2) =>
99.32/13.19	                                                   (((eqimpsubset1) =>
99.32/13.19	                                                     (((subsetI2) =>
99.32/13.19	                                                       (((emptysetsubset) =>
99.32/13.19	                                                         (((subsetE) =>
99.32/13.19	                                                           (((subsetE2) =>
99.32/13.19	                                                             (((notsubsetI) =>
99.32/13.19	                                                               (((notequalI1) =>
99.32/13.19	                                                                 (((notequalI2) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (subsetRefl) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (subsetTrans) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (setadjoinSub) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (setadjoinSub2) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (subset2powerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (setextsub) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (subsetemptysetimpeq) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetI1) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetE1) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (inPowerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetsubset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (sepInPowerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (sepSubset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (!!) @ (
99.32/13.19	                                                                   (('#B') @ (
99.32/13.19	                                                                    !!) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    !!))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#S') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#B') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#S') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    =>))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))))))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))) @ 
99.32/13.19	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl537])).
99.32/13.19	thf(zip_derived_cl553, plain,
99.32/13.19	    (~ (((quantDeMorgan3) =>
99.32/13.19	         (((quantDeMorgan4) =>
99.32/13.19	           (((prop2setI) =>
99.32/13.19	             (((prop2set2propI) =>
99.32/13.19	               (((notdexE) =>
99.32/13.19	                 (((notdallE) =>
99.32/13.19	                   (((exuI1) =>
99.32/13.19	                     (((exuI3) =>
99.32/13.19	                       (((exuI2) =>
99.32/13.19	                         (((inCongP) =>
99.32/13.19	                           (((in__Cong) =>
99.32/13.19	                             (((exuE3u) =>
99.32/13.19	                               (((exu__Cong) =>
99.32/13.19	                                 (((setadjoin__Cong) =>
99.32/13.19	                                   (((powerset__Cong) =>
99.32/13.19	                                     (((setunion__Cong) =>
99.32/13.19	                                       (((exuEu) =>
99.32/13.19	                                         (((descr__Cong) =>
99.32/13.19	                                           (((dsetconstr__Cong) =>
99.32/13.19	                                             (((subsetI1) =>
99.32/13.19	                                               (((eqimpsubset2) =>
99.32/13.19	                                                 (((eqimpsubset1) =>
99.32/13.19	                                                   (((subsetI2) =>
99.32/13.19	                                                     (((emptysetsubset) =>
99.32/13.19	                                                       (((subsetE) =>
99.32/13.19	                                                         (((subsetE2) =>
99.32/13.19	                                                           (((notsubsetI) =>
99.32/13.19	                                                             (((notequalI1) =>
99.32/13.19	                                                               (((notequalI2) =>
99.32/13.19	                                                                 (((subsetRefl) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (subsetTrans) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (setadjoinSub) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (setadjoinSub2) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (subset2powerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (setextsub) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (subsetemptysetimpeq) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetI1) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetE1) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (inPowerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetsubset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (sepInPowerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (sepSubset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (!!) @ (
99.32/13.19	                                                                   (('#B') @ (
99.32/13.19	                                                                    !!) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    !!))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#S') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#B') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#S') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    =>))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))))))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))) @ 
99.32/13.19	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl546])).
99.32/13.19	thf(zip_derived_cl561, plain,
99.32/13.19	    (~ (((quantDeMorgan4) =>
99.32/13.19	         (((prop2setI) =>
99.32/13.19	           (((prop2set2propI) =>
99.32/13.19	             (((notdexE) =>
99.32/13.19	               (((notdallE) =>
99.32/13.19	                 (((exuI1) =>
99.32/13.19	                   (((exuI3) =>
99.32/13.19	                     (((exuI2) =>
99.32/13.19	                       (((inCongP) =>
99.32/13.19	                         (((in__Cong) =>
99.32/13.19	                           (((exuE3u) =>
99.32/13.19	                             (((exu__Cong) =>
99.32/13.19	                               (((setadjoin__Cong) =>
99.32/13.19	                                 (((powerset__Cong) =>
99.32/13.19	                                   (((setunion__Cong) =>
99.32/13.19	                                     (((exuEu) =>
99.32/13.19	                                       (((descr__Cong) =>
99.32/13.19	                                         (((dsetconstr__Cong) =>
99.32/13.19	                                           (((subsetI1) =>
99.32/13.19	                                             (((eqimpsubset2) =>
99.32/13.19	                                               (((eqimpsubset1) =>
99.32/13.19	                                                 (((subsetI2) =>
99.32/13.19	                                                   (((emptysetsubset) =>
99.32/13.19	                                                     (((subsetE) =>
99.32/13.19	                                                       (((subsetE2) =>
99.32/13.19	                                                         (((notsubsetI) =>
99.32/13.19	                                                           (((notequalI1) =>
99.32/13.19	                                                             (((notequalI2) =>
99.32/13.19	                                                               (((subsetRefl) =>
99.32/13.19	                                                                 (((subsetTrans) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (setadjoinSub) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (setadjoinSub2) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (subset2powerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (setextsub) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (subsetemptysetimpeq) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetI1) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetE1) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (inPowerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetsubset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (sepInPowerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (sepSubset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (!!) @ (
99.32/13.19	                                                                   (('#B') @ (
99.32/13.19	                                                                    !!) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    !!))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#S') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#B') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#S') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    =>))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))))))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))) @ 
99.32/13.19	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl553])).
99.32/13.19	thf(zip_derived_cl570, plain,
99.32/13.19	    (~ (((prop2setI) =>
99.32/13.19	         (((prop2set2propI) =>
99.32/13.19	           (((notdexE) =>
99.32/13.19	             (((notdallE) =>
99.32/13.19	               (((exuI1) =>
99.32/13.19	                 (((exuI3) =>
99.32/13.19	                   (((exuI2) =>
99.32/13.19	                     (((inCongP) =>
99.32/13.19	                       (((in__Cong) =>
99.32/13.19	                         (((exuE3u) =>
99.32/13.19	                           (((exu__Cong) =>
99.32/13.19	                             (((setadjoin__Cong) =>
99.32/13.19	                               (((powerset__Cong) =>
99.32/13.19	                                 (((setunion__Cong) =>
99.32/13.19	                                   (((exuEu) =>
99.32/13.19	                                     (((descr__Cong) =>
99.32/13.19	                                       (((dsetconstr__Cong) =>
99.32/13.19	                                         (((subsetI1) =>
99.32/13.19	                                           (((eqimpsubset2) =>
99.32/13.19	                                             (((eqimpsubset1) =>
99.32/13.19	                                               (((subsetI2) =>
99.32/13.19	                                                 (((emptysetsubset) =>
99.32/13.19	                                                   (((subsetE) =>
99.32/13.19	                                                     (((subsetE2) =>
99.32/13.19	                                                       (((notsubsetI) =>
99.32/13.19	                                                         (((notequalI1) =>
99.32/13.19	                                                           (((notequalI2) =>
99.32/13.19	                                                             (((subsetRefl) =>
99.32/13.19	                                                               (((subsetTrans) =>
99.32/13.19	                                                                 (((setadjoinSub) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (setadjoinSub2) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (subset2powerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (setextsub) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (subsetemptysetimpeq) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetI1) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetE1) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (inPowerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetsubset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (sepInPowerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (sepSubset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (!!) @ (
99.32/13.19	                                                                   (('#B') @ (
99.32/13.19	                                                                    !!) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    !!))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#S') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#B') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#S') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    =>))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))))))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))) @ 
99.32/13.19	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl561])).
99.32/13.19	thf(zip_derived_cl578, plain,
99.32/13.19	    (~ (((prop2set2propI) =>
99.32/13.19	         (((notdexE) =>
99.32/13.19	           (((notdallE) =>
99.32/13.19	             (((exuI1) =>
99.32/13.19	               (((exuI3) =>
99.32/13.19	                 (((exuI2) =>
99.32/13.19	                   (((inCongP) =>
99.32/13.19	                     (((in__Cong) =>
99.32/13.19	                       (((exuE3u) =>
99.32/13.19	                         (((exu__Cong) =>
99.32/13.19	                           (((setadjoin__Cong) =>
99.32/13.19	                             (((powerset__Cong) =>
99.32/13.19	                               (((setunion__Cong) =>
99.32/13.19	                                 (((exuEu) =>
99.32/13.19	                                   (((descr__Cong) =>
99.32/13.19	                                     (((dsetconstr__Cong) =>
99.32/13.19	                                       (((subsetI1) =>
99.32/13.19	                                         (((eqimpsubset2) =>
99.32/13.19	                                           (((eqimpsubset1) =>
99.32/13.19	                                             (((subsetI2) =>
99.32/13.19	                                               (((emptysetsubset) =>
99.32/13.19	                                                 (((subsetE) =>
99.32/13.19	                                                   (((subsetE2) =>
99.32/13.19	                                                     (((notsubsetI) =>
99.32/13.19	                                                       (((notequalI1) =>
99.32/13.19	                                                         (((notequalI2) =>
99.32/13.19	                                                           (((subsetRefl) =>
99.32/13.19	                                                             (((subsetTrans) =>
99.32/13.19	                                                               (((setadjoinSub) =>
99.32/13.19	                                                                 (((setadjoinSub2) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (subset2powerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (setextsub) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (subsetemptysetimpeq) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetI1) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetE1) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (inPowerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetsubset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (sepInPowerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (sepSubset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (!!) @ (
99.32/13.19	                                                                   (('#B') @ (
99.32/13.19	                                                                    !!) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    !!))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#S') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#B') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#S') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    =>))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))))))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))) @ 
99.32/13.19	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl570])).
99.32/13.19	thf(zip_derived_cl586, plain,
99.32/13.19	    (~ (((notdexE) =>
99.32/13.19	         (((notdallE) =>
99.32/13.19	           (((exuI1) =>
99.32/13.19	             (((exuI3) =>
99.32/13.19	               (((exuI2) =>
99.32/13.19	                 (((inCongP) =>
99.32/13.19	                   (((in__Cong) =>
99.32/13.19	                     (((exuE3u) =>
99.32/13.19	                       (((exu__Cong) =>
99.32/13.19	                         (((setadjoin__Cong) =>
99.32/13.19	                           (((powerset__Cong) =>
99.32/13.19	                             (((setunion__Cong) =>
99.32/13.19	                               (((exuEu) =>
99.32/13.19	                                 (((descr__Cong) =>
99.32/13.19	                                   (((dsetconstr__Cong) =>
99.32/13.19	                                     (((subsetI1) =>
99.32/13.19	                                       (((eqimpsubset2) =>
99.32/13.19	                                         (((eqimpsubset1) =>
99.32/13.19	                                           (((subsetI2) =>
99.32/13.19	                                             (((emptysetsubset) =>
99.32/13.19	                                               (((subsetE) =>
99.32/13.19	                                                 (((subsetE2) =>
99.32/13.19	                                                   (((notsubsetI) =>
99.32/13.19	                                                     (((notequalI1) =>
99.32/13.19	                                                       (((notequalI2) =>
99.32/13.19	                                                         (((subsetRefl) =>
99.32/13.19	                                                           (((subsetTrans) =>
99.32/13.19	                                                             (((setadjoinSub) =>
99.32/13.19	                                                               (((setadjoinSub2) =>
99.32/13.19	                                                                 (((subset2powerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (setextsub) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (subsetemptysetimpeq) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetI1) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetE1) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (inPowerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetsubset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (sepInPowerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (sepSubset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (!!) @ (
99.32/13.19	                                                                   (('#B') @ (
99.32/13.19	                                                                    !!) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    !!))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#S') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#B') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#S') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    =>))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))))))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))) @ 
99.32/13.19	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl578])).
99.32/13.19	thf(zip_derived_cl595, plain,
99.32/13.19	    (~ (((notdallE) =>
99.32/13.19	         (((exuI1) =>
99.32/13.19	           (((exuI3) =>
99.32/13.19	             (((exuI2) =>
99.32/13.19	               (((inCongP) =>
99.32/13.19	                 (((in__Cong) =>
99.32/13.19	                   (((exuE3u) =>
99.32/13.19	                     (((exu__Cong) =>
99.32/13.19	                       (((setadjoin__Cong) =>
99.32/13.19	                         (((powerset__Cong) =>
99.32/13.19	                           (((setunion__Cong) =>
99.32/13.19	                             (((exuEu) =>
99.32/13.19	                               (((descr__Cong) =>
99.32/13.19	                                 (((dsetconstr__Cong) =>
99.32/13.19	                                   (((subsetI1) =>
99.32/13.19	                                     (((eqimpsubset2) =>
99.32/13.19	                                       (((eqimpsubset1) =>
99.32/13.19	                                         (((subsetI2) =>
99.32/13.19	                                           (((emptysetsubset) =>
99.32/13.19	                                             (((subsetE) =>
99.32/13.19	                                               (((subsetE2) =>
99.32/13.19	                                                 (((notsubsetI) =>
99.32/13.19	                                                   (((notequalI1) =>
99.32/13.19	                                                     (((notequalI2) =>
99.32/13.19	                                                       (((subsetRefl) =>
99.32/13.19	                                                         (((subsetTrans) =>
99.32/13.19	                                                           (((setadjoinSub) =>
99.32/13.19	                                                             (((setadjoinSub2) =>
99.32/13.19	                                                               (((subset2powerset) =>
99.32/13.19	                                                                 (((setextsub) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (subsetemptysetimpeq) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetI1) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetE1) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (inPowerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetsubset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (sepInPowerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (sepSubset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (!!) @ (
99.32/13.19	                                                                   (('#B') @ (
99.32/13.19	                                                                    !!) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    !!))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#S') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#B') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#S') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    =>))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))))))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))) @ 
99.32/13.19	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl586])).
99.32/13.19	thf(zip_derived_cl606, plain,
99.32/13.19	    (~ (((exuI1) =>
99.32/13.19	         (((exuI3) =>
99.32/13.19	           (((exuI2) =>
99.32/13.19	             (((inCongP) =>
99.32/13.19	               (((in__Cong) =>
99.32/13.19	                 (((exuE3u) =>
99.32/13.19	                   (((exu__Cong) =>
99.32/13.19	                     (((setadjoin__Cong) =>
99.32/13.19	                       (((powerset__Cong) =>
99.32/13.19	                         (((setunion__Cong) =>
99.32/13.19	                           (((exuEu) =>
99.32/13.19	                             (((descr__Cong) =>
99.32/13.19	                               (((dsetconstr__Cong) =>
99.32/13.19	                                 (((subsetI1) =>
99.32/13.19	                                   (((eqimpsubset2) =>
99.32/13.19	                                     (((eqimpsubset1) =>
99.32/13.19	                                       (((subsetI2) =>
99.32/13.19	                                         (((emptysetsubset) =>
99.32/13.19	                                           (((subsetE) =>
99.32/13.19	                                             (((subsetE2) =>
99.32/13.19	                                               (((notsubsetI) =>
99.32/13.19	                                                 (((notequalI1) =>
99.32/13.19	                                                   (((notequalI2) =>
99.32/13.19	                                                     (((subsetRefl) =>
99.32/13.19	                                                       (((subsetTrans) =>
99.32/13.19	                                                         (((setadjoinSub) =>
99.32/13.19	                                                           (((setadjoinSub2) =>
99.32/13.19	                                                             (((subset2powerset) =>
99.32/13.19	                                                               (((setextsub) =>
99.32/13.19	                                                                 (((subsetemptysetimpeq) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetI1) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetE1) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (inPowerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetsubset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (sepInPowerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (sepSubset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (!!) @ (
99.32/13.19	                                                                   (('#B') @ (
99.32/13.19	                                                                    !!) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    !!))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#S') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#B') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#S') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    =>))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))))))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))) @ 
99.32/13.19	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl595])).
99.32/13.19	thf(zip_derived_cl619, plain,
99.32/13.19	    (~ (((exuI3) =>
99.32/13.19	         (((exuI2) =>
99.32/13.19	           (((inCongP) =>
99.32/13.19	             (((in__Cong) =>
99.32/13.19	               (((exuE3u) =>
99.32/13.19	                 (((exu__Cong) =>
99.32/13.19	                   (((setadjoin__Cong) =>
99.32/13.19	                     (((powerset__Cong) =>
99.32/13.19	                       (((setunion__Cong) =>
99.32/13.19	                         (((exuEu) =>
99.32/13.19	                           (((descr__Cong) =>
99.32/13.19	                             (((dsetconstr__Cong) =>
99.32/13.19	                               (((subsetI1) =>
99.32/13.19	                                 (((eqimpsubset2) =>
99.32/13.19	                                   (((eqimpsubset1) =>
99.32/13.19	                                     (((subsetI2) =>
99.32/13.19	                                       (((emptysetsubset) =>
99.32/13.19	                                         (((subsetE) =>
99.32/13.19	                                           (((subsetE2) =>
99.32/13.19	                                             (((notsubsetI) =>
99.32/13.19	                                               (((notequalI1) =>
99.32/13.19	                                                 (((notequalI2) =>
99.32/13.19	                                                   (((subsetRefl) =>
99.32/13.19	                                                     (((subsetTrans) =>
99.32/13.19	                                                       (((setadjoinSub) =>
99.32/13.19	                                                         (((setadjoinSub2) =>
99.32/13.19	                                                           (((subset2powerset) =>
99.32/13.19	                                                             (((setextsub) =>
99.32/13.19	                                                               (((subsetemptysetimpeq) =>
99.32/13.19	                                                                 (((powersetI1) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetE1) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (inPowerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetsubset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (sepInPowerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (sepSubset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (!!) @ (
99.32/13.19	                                                                   (('#B') @ (
99.32/13.19	                                                                    !!) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    !!))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#S') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#B') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#S') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    =>))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))))))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))) @ 
99.32/13.19	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl606])).
99.32/13.19	thf(zip_derived_cl630, plain,
99.32/13.19	    (~ (((exuI2) =>
99.32/13.19	         (((inCongP) =>
99.32/13.19	           (((in__Cong) =>
99.32/13.19	             (((exuE3u) =>
99.32/13.19	               (((exu__Cong) =>
99.32/13.19	                 (((setadjoin__Cong) =>
99.32/13.19	                   (((powerset__Cong) =>
99.32/13.19	                     (((setunion__Cong) =>
99.32/13.19	                       (((exuEu) =>
99.32/13.19	                         (((descr__Cong) =>
99.32/13.19	                           (((dsetconstr__Cong) =>
99.32/13.19	                             (((subsetI1) =>
99.32/13.19	                               (((eqimpsubset2) =>
99.32/13.19	                                 (((eqimpsubset1) =>
99.32/13.19	                                   (((subsetI2) =>
99.32/13.19	                                     (((emptysetsubset) =>
99.32/13.19	                                       (((subsetE) =>
99.32/13.19	                                         (((subsetE2) =>
99.32/13.19	                                           (((notsubsetI) =>
99.32/13.19	                                             (((notequalI1) =>
99.32/13.19	                                               (((notequalI2) =>
99.32/13.19	                                                 (((subsetRefl) =>
99.32/13.19	                                                   (((subsetTrans) =>
99.32/13.19	                                                     (((setadjoinSub) =>
99.32/13.19	                                                       (((setadjoinSub2) =>
99.32/13.19	                                                         (((subset2powerset) =>
99.32/13.19	                                                           (((setextsub) =>
99.32/13.19	                                                             (((subsetemptysetimpeq) =>
99.32/13.19	                                                               (((powersetI1) =>
99.32/13.19	                                                                 (((powersetE1) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (inPowerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetsubset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (sepInPowerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (sepSubset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (!!) @ (
99.32/13.19	                                                                   (('#B') @ (
99.32/13.19	                                                                    !!) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    !!))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#S') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#B') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#S') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    =>))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))))))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))) @ 
99.32/13.19	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl619])).
99.32/13.19	thf(zip_derived_cl640, plain,
99.32/13.19	    (~ (((inCongP) =>
99.32/13.19	         (((in__Cong) =>
99.32/13.19	           (((exuE3u) =>
99.32/13.19	             (((exu__Cong) =>
99.32/13.19	               (((setadjoin__Cong) =>
99.32/13.19	                 (((powerset__Cong) =>
99.32/13.19	                   (((setunion__Cong) =>
99.32/13.19	                     (((exuEu) =>
99.32/13.19	                       (((descr__Cong) =>
99.32/13.19	                         (((dsetconstr__Cong) =>
99.32/13.19	                           (((subsetI1) =>
99.32/13.19	                             (((eqimpsubset2) =>
99.32/13.19	                               (((eqimpsubset1) =>
99.32/13.19	                                 (((subsetI2) =>
99.32/13.19	                                   (((emptysetsubset) =>
99.32/13.19	                                     (((subsetE) =>
99.32/13.19	                                       (((subsetE2) =>
99.32/13.19	                                         (((notsubsetI) =>
99.32/13.19	                                           (((notequalI1) =>
99.32/13.19	                                             (((notequalI2) =>
99.32/13.19	                                               (((subsetRefl) =>
99.32/13.19	                                                 (((subsetTrans) =>
99.32/13.19	                                                   (((setadjoinSub) =>
99.32/13.19	                                                     (((setadjoinSub2) =>
99.32/13.19	                                                       (((subset2powerset) =>
99.32/13.19	                                                         (((setextsub) =>
99.32/13.19	                                                           (((subsetemptysetimpeq) =>
99.32/13.19	                                                             (((powersetI1) =>
99.32/13.19	                                                               (((powersetE1) =>
99.32/13.19	                                                                 (((inPowerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (powersetsubset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (sepInPowerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (sepSubset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (!!) @ (
99.32/13.19	                                                                   (('#B') @ (
99.32/13.19	                                                                    !!) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    !!))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#S') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#B') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#S') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    =>))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))))))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))) @ 
99.32/13.19	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl630])).
99.32/13.19	thf(zip_derived_cl650, plain,
99.32/13.19	    (~ (((in__Cong) =>
99.32/13.19	         (((exuE3u) =>
99.32/13.19	           (((exu__Cong) =>
99.32/13.19	             (((setadjoin__Cong) =>
99.32/13.19	               (((powerset__Cong) =>
99.32/13.19	                 (((setunion__Cong) =>
99.32/13.19	                   (((exuEu) =>
99.32/13.19	                     (((descr__Cong) =>
99.32/13.19	                       (((dsetconstr__Cong) =>
99.32/13.19	                         (((subsetI1) =>
99.32/13.19	                           (((eqimpsubset2) =>
99.32/13.19	                             (((eqimpsubset1) =>
99.32/13.19	                               (((subsetI2) =>
99.32/13.19	                                 (((emptysetsubset) =>
99.32/13.19	                                   (((subsetE) =>
99.32/13.19	                                     (((subsetE2) =>
99.32/13.19	                                       (((notsubsetI) =>
99.32/13.19	                                         (((notequalI1) =>
99.32/13.19	                                           (((notequalI2) =>
99.32/13.19	                                             (((subsetRefl) =>
99.32/13.19	                                               (((subsetTrans) =>
99.32/13.19	                                                 (((setadjoinSub) =>
99.32/13.19	                                                   (((setadjoinSub2) =>
99.32/13.19	                                                     (((subset2powerset) =>
99.32/13.19	                                                       (((setextsub) =>
99.32/13.19	                                                         (((subsetemptysetimpeq) =>
99.32/13.19	                                                           (((powersetI1) =>
99.32/13.19	                                                             (((powersetE1) =>
99.32/13.19	                                                               (((inPowerset) =>
99.32/13.19	                                                                 (((powersetsubset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (sepInPowerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (sepSubset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (!!) @ (
99.32/13.19	                                                                   (('#B') @ (
99.32/13.19	                                                                    !!) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    !!))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#S') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#B') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#S') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    =>))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))))))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))) @ 
99.32/13.19	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl640])).
99.32/13.19	thf(zip_derived_cl660, plain,
99.32/13.19	    (~ (((exuE3u) =>
99.32/13.19	         (((exu__Cong) =>
99.32/13.19	           (((setadjoin__Cong) =>
99.32/13.19	             (((powerset__Cong) =>
99.32/13.19	               (((setunion__Cong) =>
99.32/13.19	                 (((exuEu) =>
99.32/13.19	                   (((descr__Cong) =>
99.32/13.19	                     (((dsetconstr__Cong) =>
99.32/13.19	                       (((subsetI1) =>
99.32/13.19	                         (((eqimpsubset2) =>
99.32/13.19	                           (((eqimpsubset1) =>
99.32/13.19	                             (((subsetI2) =>
99.32/13.19	                               (((emptysetsubset) =>
99.32/13.19	                                 (((subsetE) =>
99.32/13.19	                                   (((subsetE2) =>
99.32/13.19	                                     (((notsubsetI) =>
99.32/13.19	                                       (((notequalI1) =>
99.32/13.19	                                         (((notequalI2) =>
99.32/13.19	                                           (((subsetRefl) =>
99.32/13.19	                                             (((subsetTrans) =>
99.32/13.19	                                               (((setadjoinSub) =>
99.32/13.19	                                                 (((setadjoinSub2) =>
99.32/13.19	                                                   (((subset2powerset) =>
99.32/13.19	                                                     (((setextsub) =>
99.32/13.19	                                                       (((subsetemptysetimpeq) =>
99.32/13.19	                                                         (((powersetI1) =>
99.32/13.19	                                                           (((powersetE1) =>
99.32/13.19	                                                             (((inPowerset) =>
99.32/13.19	                                                               (((powersetsubset) =>
99.32/13.19	                                                                 (((sepInPowerset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (sepSubset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (!!) @ (
99.32/13.19	                                                                   (('#B') @ (
99.32/13.19	                                                                    !!) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    !!))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#S') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#B') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#S') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    =>))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))))))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))) @ 
99.32/13.19	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl650])).
99.32/13.19	thf(zip_derived_cl672, plain,
99.32/13.19	    (~ (((exu__Cong) =>
99.32/13.19	         (((setadjoin__Cong) =>
99.32/13.19	           (((powerset__Cong) =>
99.32/13.19	             (((setunion__Cong) =>
99.32/13.19	               (((exuEu) =>
99.32/13.19	                 (((descr__Cong) =>
99.32/13.19	                   (((dsetconstr__Cong) =>
99.32/13.19	                     (((subsetI1) =>
99.32/13.19	                       (((eqimpsubset2) =>
99.32/13.19	                         (((eqimpsubset1) =>
99.32/13.19	                           (((subsetI2) =>
99.32/13.19	                             (((emptysetsubset) =>
99.32/13.19	                               (((subsetE) =>
99.32/13.19	                                 (((subsetE2) =>
99.32/13.19	                                   (((notsubsetI) =>
99.32/13.19	                                     (((notequalI1) =>
99.32/13.19	                                       (((notequalI2) =>
99.32/13.19	                                         (((subsetRefl) =>
99.32/13.19	                                           (((subsetTrans) =>
99.32/13.19	                                             (((setadjoinSub) =>
99.32/13.19	                                               (((setadjoinSub2) =>
99.32/13.19	                                                 (((subset2powerset) =>
99.32/13.19	                                                   (((setextsub) =>
99.32/13.19	                                                     (((subsetemptysetimpeq) =>
99.32/13.19	                                                       (((powersetI1) =>
99.32/13.19	                                                         (((powersetE1) =>
99.32/13.19	                                                           (((inPowerset) =>
99.32/13.19	                                                             (((powersetsubset) =>
99.32/13.19	                                                               (((sepInPowerset) =>
99.32/13.19	                                                                 (((sepSubset) =>
99.32/13.19	                                                                   ((
99.32/13.19	                                                                   (!!) @ (
99.32/13.19	                                                                   (('#B') @ (
99.32/13.19	                                                                    !!) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    !!))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#S') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#B') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#S') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    =>))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))))))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))) @ 
99.32/13.19	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl660])).
99.32/13.19	thf(zip_derived_cl685, plain,
99.32/13.19	    (~ (((setadjoin__Cong) =>
99.32/13.19	         (((powerset__Cong) =>
99.32/13.19	           (((setunion__Cong) =>
99.32/13.19	             (((exuEu) =>
99.32/13.19	               (((descr__Cong) =>
99.32/13.19	                 (((dsetconstr__Cong) =>
99.32/13.19	                   (((subsetI1) =>
99.32/13.19	                     (((eqimpsubset2) =>
99.32/13.19	                       (((eqimpsubset1) =>
99.32/13.19	                         (((subsetI2) =>
99.32/13.19	                           (((emptysetsubset) =>
99.32/13.19	                             (((subsetE) =>
99.32/13.19	                               (((subsetE2) =>
99.32/13.19	                                 (((notsubsetI) =>
99.32/13.19	                                   (((notequalI1) =>
99.32/13.19	                                     (((notequalI2) =>
99.32/13.19	                                       (((subsetRefl) =>
99.32/13.19	                                         (((subsetTrans) =>
99.32/13.19	                                           (((setadjoinSub) =>
99.32/13.19	                                             (((setadjoinSub2) =>
99.32/13.19	                                               (((subset2powerset) =>
99.32/13.19	                                                 (((setextsub) =>
99.32/13.19	                                                   (((subsetemptysetimpeq) =>
99.32/13.19	                                                     (((powersetI1) =>
99.32/13.19	                                                       (((powersetE1) =>
99.32/13.19	                                                         (((inPowerset) =>
99.32/13.19	                                                           (((powersetsubset) =>
99.32/13.19	                                                             (((sepInPowerset) =>
99.32/13.19	                                                               (((sepSubset) =>
99.32/13.19	                                                                 (((!!) @ (
99.32/13.19	                                                                   (('#B') @ (
99.32/13.19	                                                                    !!) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    !!))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#S') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#B') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#S') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    =>))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))))))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))) @ 
99.32/13.19	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl672])).
99.32/13.19	thf(zip_derived_cl699, plain,
99.32/13.19	    (~ (((powerset__Cong) =>
99.32/13.19	         (((setunion__Cong) =>
99.32/13.19	           (((exuEu) =>
99.32/13.19	             (((descr__Cong) =>
99.32/13.19	               (((dsetconstr__Cong) =>
99.32/13.19	                 (((subsetI1) =>
99.32/13.19	                   (((eqimpsubset2) =>
99.32/13.19	                     (((eqimpsubset1) =>
99.32/13.19	                       (((subsetI2) =>
99.32/13.19	                         (((emptysetsubset) =>
99.32/13.19	                           (((subsetE) =>
99.32/13.19	                             (((subsetE2) =>
99.32/13.19	                               (((notsubsetI) =>
99.32/13.19	                                 (((notequalI1) =>
99.32/13.19	                                   (((notequalI2) =>
99.32/13.19	                                     (((subsetRefl) =>
99.32/13.19	                                       (((subsetTrans) =>
99.32/13.19	                                         (((setadjoinSub) =>
99.32/13.19	                                           (((setadjoinSub2) =>
99.32/13.19	                                             (((subset2powerset) =>
99.32/13.19	                                               (((setextsub) =>
99.32/13.19	                                                 (((subsetemptysetimpeq) =>
99.32/13.19	                                                   (((powersetI1) =>
99.32/13.19	                                                     (((powersetE1) =>
99.32/13.19	                                                       (((inPowerset) =>
99.32/13.19	                                                         (((powersetsubset) =>
99.32/13.19	                                                           (((sepInPowerset) =>
99.32/13.19	                                                             (((sepSubset) =>
99.32/13.19	                                                               (((!!) @ (
99.32/13.19	                                                                 (('#B') @ (
99.32/13.19	                                                                  !!) @ 
99.32/13.19	                                                                  ((('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    !!))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#S') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#B') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#S') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    =>))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))))))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))) @ 
99.32/13.19	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl685])).
99.32/13.19	thf(zip_derived_cl714, plain,
99.32/13.19	    (~ (((setunion__Cong) =>
99.32/13.19	         (((exuEu) =>
99.32/13.19	           (((descr__Cong) =>
99.32/13.19	             (((dsetconstr__Cong) =>
99.32/13.19	               (((subsetI1) =>
99.32/13.19	                 (((eqimpsubset2) =>
99.32/13.19	                   (((eqimpsubset1) =>
99.32/13.19	                     (((subsetI2) =>
99.32/13.19	                       (((emptysetsubset) =>
99.32/13.19	                         (((subsetE) =>
99.32/13.19	                           (((subsetE2) =>
99.32/13.19	                             (((notsubsetI) =>
99.32/13.19	                               (((notequalI1) =>
99.32/13.19	                                 (((notequalI2) =>
99.32/13.19	                                   (((subsetRefl) =>
99.32/13.19	                                     (((subsetTrans) =>
99.32/13.19	                                       (((setadjoinSub) =>
99.32/13.19	                                         (((setadjoinSub2) =>
99.32/13.19	                                           (((subset2powerset) =>
99.32/13.19	                                             (((setextsub) =>
99.32/13.19	                                               (((subsetemptysetimpeq) =>
99.32/13.19	                                                 (((powersetI1) =>
99.32/13.19	                                                   (((powersetE1) =>
99.32/13.19	                                                     (((inPowerset) =>
99.32/13.19	                                                       (((powersetsubset) =>
99.32/13.19	                                                         (((sepInPowerset) =>
99.32/13.19	                                                           (((sepSubset) =>
99.32/13.19	                                                             (((!!) @ (
99.32/13.19	                                                               (('#B') @ (
99.32/13.19	                                                                !!) @ 
99.32/13.19	                                                                ((('#B') @ (
99.32/13.19	                                                                  (('#B') @ (
99.32/13.19	                                                                   !!))) @ 
99.32/13.19	                                                                  ((('#S') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#B') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#S') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    =>))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))))))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))) @ 
99.32/13.19	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl699])).
99.32/13.19	thf(zip_derived_cl731, plain,
99.32/13.19	    (~ (((exuEu) =>
99.32/13.19	         (((descr__Cong) =>
99.32/13.19	           (((dsetconstr__Cong) =>
99.32/13.19	             (((subsetI1) =>
99.32/13.19	               (((eqimpsubset2) =>
99.32/13.19	                 (((eqimpsubset1) =>
99.32/13.19	                   (((subsetI2) =>
99.32/13.19	                     (((emptysetsubset) =>
99.32/13.19	                       (((subsetE) =>
99.32/13.19	                         (((subsetE2) =>
99.32/13.19	                           (((notsubsetI) =>
99.32/13.19	                             (((notequalI1) =>
99.32/13.19	                               (((notequalI2) =>
99.32/13.19	                                 (((subsetRefl) =>
99.32/13.19	                                   (((subsetTrans) =>
99.32/13.19	                                     (((setadjoinSub) =>
99.32/13.19	                                       (((setadjoinSub2) =>
99.32/13.19	                                         (((subset2powerset) =>
99.32/13.19	                                           (((setextsub) =>
99.32/13.19	                                             (((subsetemptysetimpeq) =>
99.32/13.19	                                               (((powersetI1) =>
99.32/13.19	                                                 (((powersetE1) =>
99.32/13.19	                                                   (((inPowerset) =>
99.32/13.19	                                                     (((powersetsubset) =>
99.32/13.19	                                                       (((sepInPowerset) =>
99.32/13.19	                                                         (((sepSubset) =>
99.32/13.19	                                                           (((!!) @ (
99.32/13.19	                                                             (('#B') @ (
99.32/13.19	                                                              !!) @ 
99.32/13.19	                                                              ((('#B') @ (
99.32/13.19	                                                                (('#B') @ (
99.32/13.19	                                                                 !!))) @ 
99.32/13.19	                                                                ((('#S') @ (
99.32/13.19	                                                                  (('#B') @ (
99.32/13.19	                                                                   '#B') @ 
99.32/13.19	                                                                   ((
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#S') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    =>))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))))))) @ 
99.32/13.19	                                                                  ((('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))) @ 
99.32/13.19	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl714])).
99.32/13.19	thf(zip_derived_cl749, plain,
99.32/13.19	    (~ (((descr__Cong) =>
99.32/13.19	         (((dsetconstr__Cong) =>
99.32/13.19	           (((subsetI1) =>
99.32/13.19	             (((eqimpsubset2) =>
99.32/13.19	               (((eqimpsubset1) =>
99.32/13.19	                 (((subsetI2) =>
99.32/13.19	                   (((emptysetsubset) =>
99.32/13.19	                     (((subsetE) =>
99.32/13.19	                       (((subsetE2) =>
99.32/13.19	                         (((notsubsetI) =>
99.32/13.19	                           (((notequalI1) =>
99.32/13.19	                             (((notequalI2) =>
99.32/13.19	                               (((subsetRefl) =>
99.32/13.19	                                 (((subsetTrans) =>
99.32/13.19	                                   (((setadjoinSub) =>
99.32/13.19	                                     (((setadjoinSub2) =>
99.32/13.19	                                       (((subset2powerset) =>
99.32/13.19	                                         (((setextsub) =>
99.32/13.19	                                           (((subsetemptysetimpeq) =>
99.32/13.19	                                             (((powersetI1) =>
99.32/13.19	                                               (((powersetE1) =>
99.32/13.19	                                                 (((inPowerset) =>
99.32/13.19	                                                   (((powersetsubset) =>
99.32/13.19	                                                     (((sepInPowerset) =>
99.32/13.19	                                                       (((sepSubset) =>
99.32/13.19	                                                         (((!!) @ ((('#B') @ (
99.32/13.19	                                                                    !!) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    !!))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#S') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#B') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#S') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    =>))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))))))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))) @ 
99.32/13.19	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl731])).
99.32/13.19	thf(zip_derived_cl769, plain,
99.32/13.19	    (~ (((dsetconstr__Cong) =>
99.32/13.19	         (((subsetI1) =>
99.32/13.19	           (((eqimpsubset2) =>
99.32/13.19	             (((eqimpsubset1) =>
99.32/13.19	               (((subsetI2) =>
99.32/13.19	                 (((emptysetsubset) =>
99.32/13.19	                   (((subsetE) =>
99.32/13.19	                     (((subsetE2) =>
99.32/13.19	                       (((notsubsetI) =>
99.32/13.19	                         (((notequalI1) =>
99.32/13.19	                           (((notequalI2) =>
99.32/13.19	                             (((subsetRefl) =>
99.32/13.19	                               (((subsetTrans) =>
99.32/13.19	                                 (((setadjoinSub) =>
99.32/13.19	                                   (((setadjoinSub2) =>
99.32/13.19	                                     (((subset2powerset) =>
99.32/13.19	                                       (((setextsub) =>
99.32/13.19	                                         (((subsetemptysetimpeq) =>
99.32/13.19	                                           (((powersetI1) =>
99.32/13.19	                                             (((powersetE1) =>
99.32/13.19	                                               (((inPowerset) =>
99.32/13.19	                                                 (((powersetsubset) =>
99.32/13.19	                                                   (((sepInPowerset) =>
99.32/13.19	                                                     (((sepSubset) =>
99.32/13.19	                                                       (((!!) @ ((('#B') @ (
99.32/13.19	                                                                  !!) @ 
99.32/13.19	                                                                  ((('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    !!))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#S') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#B') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#S') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    =>))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))))))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))) @ 
99.32/13.19	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl749])).
99.32/13.19	thf(zip_derived_cl789, plain,
99.32/13.19	    (~ (((subsetI1) =>
99.32/13.19	         (((eqimpsubset2) =>
99.32/13.19	           (((eqimpsubset1) =>
99.32/13.19	             (((subsetI2) =>
99.32/13.19	               (((emptysetsubset) =>
99.32/13.19	                 (((subsetE) =>
99.32/13.19	                   (((subsetE2) =>
99.32/13.19	                     (((notsubsetI) =>
99.32/13.19	                       (((notequalI1) =>
99.32/13.19	                         (((notequalI2) =>
99.32/13.19	                           (((subsetRefl) =>
99.32/13.19	                             (((subsetTrans) =>
99.32/13.19	                               (((setadjoinSub) =>
99.32/13.19	                                 (((setadjoinSub2) =>
99.32/13.19	                                   (((subset2powerset) =>
99.32/13.19	                                     (((setextsub) =>
99.32/13.19	                                       (((subsetemptysetimpeq) =>
99.32/13.19	                                         (((powersetI1) =>
99.32/13.19	                                           (((powersetE1) =>
99.32/13.19	                                             (((inPowerset) =>
99.32/13.19	                                               (((powersetsubset) =>
99.32/13.19	                                                 (((sepInPowerset) =>
99.32/13.19	                                                   (((sepSubset) =>
99.32/13.19	                                                     (((!!) @ ((('#B') @ (
99.32/13.19	                                                                !!) @ 
99.32/13.19	                                                                ((('#B') @ (
99.32/13.19	                                                                  (('#B') @ (
99.32/13.19	                                                                   !!))) @ 
99.32/13.19	                                                                  ((('#S') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#B') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#S') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    =>))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))))))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))) @ 
99.32/13.19	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl769])).
99.32/13.19	thf(zip_derived_cl807, plain,
99.32/13.19	    (~ (((eqimpsubset2) =>
99.32/13.19	         (((eqimpsubset1) =>
99.32/13.19	           (((subsetI2) =>
99.32/13.19	             (((emptysetsubset) =>
99.32/13.19	               (((subsetE) =>
99.32/13.19	                 (((subsetE2) =>
99.32/13.19	                   (((notsubsetI) =>
99.32/13.19	                     (((notequalI1) =>
99.32/13.19	                       (((notequalI2) =>
99.32/13.19	                         (((subsetRefl) =>
99.32/13.19	                           (((subsetTrans) =>
99.32/13.19	                             (((setadjoinSub) =>
99.32/13.19	                               (((setadjoinSub2) =>
99.32/13.19	                                 (((subset2powerset) =>
99.32/13.19	                                   (((setextsub) =>
99.32/13.19	                                     (((subsetemptysetimpeq) =>
99.32/13.19	                                       (((powersetI1) =>
99.32/13.19	                                         (((powersetE1) =>
99.32/13.19	                                           (((inPowerset) =>
99.32/13.19	                                             (((powersetsubset) =>
99.32/13.19	                                               (((sepInPowerset) =>
99.32/13.19	                                                 (((sepSubset) =>
99.32/13.19	                                                   (((!!) @ ((('#B') @ (
99.32/13.19	                                                              !!) @ 
99.32/13.19	                                                              ((('#B') @ (
99.32/13.19	                                                                (('#B') @ (
99.32/13.19	                                                                 !!))) @ 
99.32/13.19	                                                                ((('#S') @ (
99.32/13.19	                                                                  (('#B') @ (
99.32/13.19	                                                                   '#B') @ 
99.32/13.19	                                                                   ((
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#S') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    =>))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))))))) @ 
99.32/13.19	                                                                  ((('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))) @ 
99.32/13.19	                                                                    binunion))))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl789])).
99.32/13.19	thf(zip_derived_cl824, plain,
99.32/13.19	    (~ (((eqimpsubset1) =>
99.32/13.19	         (((subsetI2) =>
99.32/13.19	           (((emptysetsubset) =>
99.32/13.19	             (((subsetE) =>
99.32/13.19	               (((subsetE2) =>
99.32/13.19	                 (((notsubsetI) =>
99.32/13.19	                   (((notequalI1) =>
99.32/13.19	                     (((notequalI2) =>
99.32/13.19	                       (((subsetRefl) =>
99.32/13.19	                         (((subsetTrans) =>
99.32/13.19	                           (((setadjoinSub) =>
99.32/13.19	                             (((setadjoinSub2) =>
99.32/13.19	                               (((subset2powerset) =>
99.32/13.19	                                 (((setextsub) =>
99.32/13.19	                                   (((subsetemptysetimpeq) =>
99.32/13.19	                                     (((powersetI1) =>
99.32/13.19	                                       (((powersetE1) =>
99.32/13.19	                                         (((inPowerset) =>
99.32/13.19	                                           (((powersetsubset) =>
99.32/13.19	                                             (((sepInPowerset) =>
99.32/13.19	                                               (((sepSubset) =>
99.32/13.19	                                                 (((!!) @ ((('#B') @ (
99.32/13.19	                                                            !!) @ 
99.32/13.19	                                                            ((('#B') @ (
99.32/13.19	                                                              (('#B') @ (!!))) @ 
99.32/13.19	                                                              ((('#S') @ (
99.32/13.19	                                                                (('#B') @ (
99.32/13.19	                                                                 '#B') @ 
99.32/13.19	                                                                 ((('#B') @ (
99.32/13.19	                                                                   '#S') @ 
99.32/13.19	                                                                   ((
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    =>))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))))))) @ 
99.32/13.19	                                                                ((('#B') @ (
99.32/13.19	                                                                  (('#B') @ (
99.32/13.19	                                                                   (('#C') @ in)))) @ 
99.32/13.19	                                                                  binunion))))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl807])).
99.32/13.19	thf(zip_derived_cl838, plain,
99.32/13.19	    (~ (((subsetI2) =>
99.32/13.19	         (((emptysetsubset) =>
99.32/13.19	           (((subsetE) =>
99.32/13.19	             (((subsetE2) =>
99.32/13.19	               (((notsubsetI) =>
99.32/13.19	                 (((notequalI1) =>
99.32/13.19	                   (((notequalI2) =>
99.32/13.19	                     (((subsetRefl) =>
99.32/13.19	                       (((subsetTrans) =>
99.32/13.19	                         (((setadjoinSub) =>
99.32/13.19	                           (((setadjoinSub2) =>
99.32/13.19	                             (((subset2powerset) =>
99.32/13.19	                               (((setextsub) =>
99.32/13.19	                                 (((subsetemptysetimpeq) =>
99.32/13.19	                                   (((powersetI1) =>
99.32/13.19	                                     (((powersetE1) =>
99.32/13.19	                                       (((inPowerset) =>
99.32/13.19	                                         (((powersetsubset) =>
99.32/13.19	                                           (((sepInPowerset) =>
99.32/13.19	                                             (((sepSubset) =>
99.32/13.19	                                               (((!!) @ ((('#B') @ (!!) @ 
99.32/13.19	                                                          ((('#B') @ (
99.32/13.19	                                                            (('#B') @ (!!))) @ 
99.32/13.19	                                                            ((('#S') @ (
99.32/13.19	                                                              (('#B') @ (
99.32/13.19	                                                               '#B') @ 
99.32/13.19	                                                               ((('#B') @ (
99.32/13.19	                                                                 '#S') @ 
99.32/13.19	                                                                 ((('#B') @ (
99.32/13.19	                                                                   (('#B') @ (
99.32/13.19	                                                                    =>))) @ 
99.32/13.19	                                                                   ((
99.32/13.19	                                                                    ('#C') @ in)))))))) @ 
99.32/13.19	                                                              ((('#B') @ (
99.32/13.19	                                                                (('#B') @ (
99.32/13.19	                                                                 (('#C') @ in)))) @ 
99.32/13.19	                                                                binunion))))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl824])).
99.32/13.19	thf(zip_derived_cl850, plain,
99.32/13.19	    (~ (((emptysetsubset) =>
99.32/13.19	         (((subsetE) =>
99.32/13.19	           (((subsetE2) =>
99.32/13.19	             (((notsubsetI) =>
99.32/13.19	               (((notequalI1) =>
99.32/13.19	                 (((notequalI2) =>
99.32/13.19	                   (((subsetRefl) =>
99.32/13.19	                     (((subsetTrans) =>
99.32/13.19	                       (((setadjoinSub) =>
99.32/13.19	                         (((setadjoinSub2) =>
99.32/13.19	                           (((subset2powerset) =>
99.32/13.19	                             (((setextsub) =>
99.32/13.19	                               (((subsetemptysetimpeq) =>
99.32/13.19	                                 (((powersetI1) =>
99.32/13.19	                                   (((powersetE1) =>
99.32/13.19	                                     (((inPowerset) =>
99.32/13.19	                                       (((powersetsubset) =>
99.32/13.19	                                         (((sepInPowerset) =>
99.32/13.19	                                           (((sepSubset) =>
99.32/13.19	                                             (((!!) @ ((('#B') @ (!!) @ 
99.32/13.19	                                                        ((('#B') @ ((
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    !!))) @ 
99.32/13.19	                                                          ((('#S') @ (
99.32/13.19	                                                            (('#B') @ (
99.32/13.19	                                                             '#B') @ 
99.32/13.19	                                                             ((('#B') @ (
99.32/13.19	                                                               '#S') @ 
99.32/13.19	                                                               ((('#B') @ (
99.32/13.19	                                                                 (('#B') @ (
99.32/13.19	                                                                  =>))) @ 
99.32/13.19	                                                                 ((('#C') @ in)))))))) @ 
99.32/13.19	                                                            ((('#B') @ (
99.32/13.19	                                                              (('#B') @ (
99.32/13.19	                                                               (('#C') @ in)))) @ 
99.32/13.19	                                                              binunion))))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl838])).
99.32/13.19	thf(zip_derived_cl863, plain,
99.32/13.19	    (~ (((subsetE) =>
99.32/13.19	         (((subsetE2) =>
99.32/13.19	           (((notsubsetI) =>
99.32/13.19	             (((notequalI1) =>
99.32/13.19	               (((notequalI2) =>
99.32/13.19	                 (((subsetRefl) =>
99.32/13.19	                   (((subsetTrans) =>
99.32/13.19	                     (((setadjoinSub) =>
99.32/13.19	                       (((setadjoinSub2) =>
99.32/13.19	                         (((subset2powerset) =>
99.32/13.19	                           (((setextsub) =>
99.32/13.19	                             (((subsetemptysetimpeq) =>
99.32/13.19	                               (((powersetI1) =>
99.32/13.19	                                 (((powersetE1) =>
99.32/13.19	                                   (((inPowerset) =>
99.32/13.19	                                     (((powersetsubset) =>
99.32/13.19	                                       (((sepInPowerset) =>
99.32/13.19	                                         (((sepSubset) =>
99.32/13.19	                                           (((!!) @ ((('#B') @ (!!) @ 
99.32/13.19	                                                      ((('#B') @ ((('#B') @ (
99.32/13.19	                                                                   !!))) @ 
99.32/13.19	                                                        ((('#S') @ ((
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#B') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#S') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    =>))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))))))) @ 
99.32/13.19	                                                          ((('#B') @ (
99.32/13.19	                                                            (('#B') @ (
99.32/13.19	                                                             (('#C') @ in)))) @ 
99.32/13.19	                                                            binunion))))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl850])).
99.32/13.19	thf(zip_derived_cl878, plain,
99.32/13.19	    (~ (((subsetE2) =>
99.32/13.19	         (((notsubsetI) =>
99.32/13.19	           (((notequalI1) =>
99.32/13.19	             (((notequalI2) =>
99.32/13.19	               (((subsetRefl) =>
99.32/13.19	                 (((subsetTrans) =>
99.32/13.19	                   (((setadjoinSub) =>
99.32/13.19	                     (((setadjoinSub2) =>
99.32/13.19	                       (((subset2powerset) =>
99.32/13.19	                         (((setextsub) =>
99.32/13.19	                           (((subsetemptysetimpeq) =>
99.32/13.19	                             (((powersetI1) =>
99.32/13.19	                               (((powersetE1) =>
99.32/13.19	                                 (((inPowerset) =>
99.32/13.19	                                   (((powersetsubset) =>
99.32/13.19	                                     (((sepInPowerset) =>
99.32/13.19	                                       (((sepSubset) =>
99.32/13.19	                                         (((!!) @ ((('#B') @ (!!) @ 
99.32/13.19	                                                    ((('#B') @ ((('#B') @ (
99.32/13.19	                                                                 !!))) @ 
99.32/13.19	                                                      ((('#S') @ ((('#B') @ (
99.32/13.19	                                                                   '#B') @ 
99.32/13.19	                                                                   ((
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    '#S') @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    =>))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))))))) @ 
99.32/13.19	                                                        ((('#B') @ ((
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))) @ 
99.32/13.19	                                                          binunion))))))))))))))))))))))))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl863])).
99.32/13.19	thf(zip_derived_cl896, plain,
99.32/13.19	    (~ (((notsubsetI) =>
99.32/13.19	         (((notequalI1) =>
99.32/13.19	           (((notequalI2) =>
99.32/13.19	             (((subsetRefl) =>
99.32/13.19	               (((subsetTrans) =>
99.32/13.19	                 (((setadjoinSub) =>
99.32/13.19	                   (((setadjoinSub2) =>
99.32/13.19	                     (((subset2powerset) =>
99.32/13.19	                       (((setextsub) =>
99.32/13.19	                         (((subsetemptysetimpeq) =>
99.32/13.19	                           (((powersetI1) =>
99.32/13.19	                             (((powersetE1) =>
99.32/13.19	                               (((inPowerset) =>
99.32/13.19	                                 (((powersetsubset) =>
99.32/13.19	                                   (((sepInPowerset) =>
99.32/13.19	                                     (((sepSubset) =>
99.32/13.19	                                       (((!!) @ ((('#B') @ (!!) @ 
99.32/13.19	                                                  ((('#B') @ ((('#B') @ (!!))) @ 
99.32/13.19	                                                    ((('#S') @ ((('#B') @ (
99.32/13.19	                                                                 '#B') @ 
99.32/13.19	                                                                 ((('#B') @ (
99.32/13.19	                                                                   '#S') @ 
99.32/13.19	                                                                   ((
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#B') @ (
99.32/13.19	                                                                    =>))) @ 
99.32/13.19	                                                                    (
99.32/13.19	                                                                    (
99.32/13.19	                                                                    ('#C') @ in)))))))) @ 
99.32/13.19	                                                      ((('#B') @ ((('#B') @ (
99.32/13.19	                                                                   (('#C') @ in)))) @ 
99.32/13.19	                                                        binunion))))))))))))))))))))))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl878])).
99.32/13.19	thf(zip_derived_cl909, plain,
99.32/13.19	    (~ (((notequalI1) =>
99.32/13.19	         (((notequalI2) =>
99.32/13.19	           (((subsetRefl) =>
99.32/13.19	             (((subsetTrans) =>
99.32/13.19	               (((setadjoinSub) =>
99.32/13.19	                 (((setadjoinSub2) =>
99.32/13.19	                   (((subset2powerset) =>
99.32/13.19	                     (((setextsub) =>
99.32/13.19	                       (((subsetemptysetimpeq) =>
99.32/13.19	                         (((powersetI1) =>
99.32/13.19	                           (((powersetE1) =>
99.32/13.19	                             (((inPowerset) =>
99.32/13.19	                               (((powersetsubset) =>
99.32/13.19	                                 (((sepInPowerset) =>
99.32/13.19	                                   (((sepSubset) =>
99.32/13.19	                                     (((!!) @ ((('#B') @ (!!) @ 
99.32/13.19	                                                ((('#B') @ ((('#B') @ (!!))) @ 
99.32/13.19	                                                  ((('#S') @ ((('#B') @ (
99.32/13.19	                                                               '#B') @ 
99.32/13.19	                                                               ((('#B') @ (
99.32/13.19	                                                                 '#S') @ 
99.32/13.19	                                                                 ((('#B') @ (
99.32/13.19	                                                                   (('#B') @ (
99.32/13.19	                                                                    =>))) @ 
99.32/13.19	                                                                   ((
99.32/13.19	                                                                    ('#C') @ in)))))))) @ 
99.32/13.19	                                                    ((('#B') @ ((('#B') @ (
99.32/13.19	                                                                 (('#C') @ in)))) @ 
99.32/13.19	                                                      binunion))))))))))))))))))))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl896])).
99.32/13.19	thf(zip_derived_cl924, plain,
99.32/13.19	    (~ (((notequalI2) =>
99.32/13.19	         (((subsetRefl) =>
99.32/13.19	           (((subsetTrans) =>
99.32/13.19	             (((setadjoinSub) =>
99.32/13.19	               (((setadjoinSub2) =>
99.32/13.19	                 (((subset2powerset) =>
99.32/13.19	                   (((setextsub) =>
99.32/13.19	                     (((subsetemptysetimpeq) =>
99.32/13.19	                       (((powersetI1) =>
99.32/13.19	                         (((powersetE1) =>
99.32/13.19	                           (((inPowerset) =>
99.32/13.19	                             (((powersetsubset) =>
99.32/13.19	                               (((sepInPowerset) =>
99.32/13.19	                                 (((sepSubset) =>
99.32/13.19	                                   (((!!) @ ((('#B') @ (!!) @ 
99.32/13.19	                                              ((('#B') @ ((('#B') @ (!!))) @ 
99.32/13.19	                                                ((('#S') @ ((('#B') @ (
99.32/13.19	                                                             '#B') @ 
99.32/13.19	                                                             ((('#B') @ (
99.32/13.19	                                                               '#S') @ 
99.32/13.19	                                                               ((('#B') @ (
99.32/13.19	                                                                 (('#B') @ (
99.32/13.19	                                                                  =>))) @ 
99.32/13.19	                                                                 ((('#C') @ in)))))))) @ 
99.32/13.19	                                                  ((('#B') @ ((('#B') @ (
99.32/13.19	                                                               (('#C') @ in)))) @ 
99.32/13.19	                                                    binunion))))))))))))))))))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl909])).
99.32/13.19	thf(zip_derived_cl938, plain,
99.32/13.19	    (~ (((subsetRefl) =>
99.32/13.19	         (((subsetTrans) =>
99.32/13.19	           (((setadjoinSub) =>
99.32/13.19	             (((setadjoinSub2) =>
99.32/13.19	               (((subset2powerset) =>
99.32/13.19	                 (((setextsub) =>
99.32/13.19	                   (((subsetemptysetimpeq) =>
99.32/13.19	                     (((powersetI1) =>
99.32/13.19	                       (((powersetE1) =>
99.32/13.19	                         (((inPowerset) =>
99.32/13.19	                           (((powersetsubset) =>
99.32/13.19	                             (((sepInPowerset) =>
99.32/13.19	                               (((sepSubset) =>
99.32/13.19	                                 (((!!) @ ((('#B') @ (!!) @ 
99.32/13.19	                                            ((('#B') @ ((('#B') @ (!!))) @ 
99.32/13.19	                                              ((('#S') @ ((('#B') @ (
99.32/13.19	                                                           '#B') @ 
99.32/13.19	                                                           ((('#B') @ (
99.32/13.19	                                                             '#S') @ 
99.32/13.19	                                                             ((('#B') @ (
99.32/13.19	                                                               (('#B') @ (=>))) @ 
99.32/13.19	                                                               ((('#C') @ in)))))))) @ 
99.32/13.19	                                                ((('#B') @ ((('#B') @ (
99.32/13.19	                                                             (('#C') @ in)))) @ 
99.32/13.19	                                                  binunion))))))))))))))))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl924])).
99.32/13.19	thf(zip_derived_cl952, plain,
99.32/13.19	    (~ (((subsetTrans) =>
99.32/13.19	         (((setadjoinSub) =>
99.32/13.19	           (((setadjoinSub2) =>
99.32/13.19	             (((subset2powerset) =>
99.32/13.19	               (((setextsub) =>
99.32/13.19	                 (((subsetemptysetimpeq) =>
99.32/13.19	                   (((powersetI1) =>
99.32/13.19	                     (((powersetE1) =>
99.32/13.19	                       (((inPowerset) =>
99.32/13.19	                         (((powersetsubset) =>
99.32/13.19	                           (((sepInPowerset) =>
99.32/13.19	                             (((sepSubset) =>
99.32/13.19	                               (((!!) @ ((('#B') @ (!!) @ 
99.32/13.19	                                          ((('#B') @ ((('#B') @ (!!))) @ 
99.32/13.19	                                            ((('#S') @ ((('#B') @ ('#B') @ 
99.32/13.19	                                                         ((('#B') @ (
99.32/13.19	                                                           '#S') @ 
99.32/13.19	                                                           ((('#B') @ (
99.32/13.19	                                                             (('#B') @ (=>))) @ 
99.32/13.19	                                                             ((('#C') @ in)))))))) @ 
99.32/13.19	                                              ((('#B') @ ((('#B') @ (
99.32/13.19	                                                           (('#C') @ in)))) @ 
99.32/13.19	                                                binunion))))))))))))))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl938])).
99.32/13.19	thf(zip_derived_cl967, plain,
99.32/13.19	    (~ (((setadjoinSub) =>
99.32/13.19	         (((setadjoinSub2) =>
99.32/13.19	           (((subset2powerset) =>
99.32/13.19	             (((setextsub) =>
99.32/13.19	               (((subsetemptysetimpeq) =>
99.32/13.19	                 (((powersetI1) =>
99.32/13.19	                   (((powersetE1) =>
99.32/13.19	                     (((inPowerset) =>
99.32/13.19	                       (((powersetsubset) =>
99.32/13.19	                         (((sepInPowerset) =>
99.32/13.19	                           (((sepSubset) =>
99.32/13.19	                             (((!!) @ ((('#B') @ (!!) @ 
99.32/13.19	                                        ((('#B') @ ((('#B') @ (!!))) @ 
99.32/13.19	                                          ((('#S') @ ((('#B') @ ('#B') @ 
99.32/13.19	                                                       ((('#B') @ ('#S') @ 
99.32/13.19	                                                         ((('#B') @ (
99.32/13.19	                                                           (('#B') @ (=>))) @ 
99.32/13.19	                                                           ((('#C') @ in)))))))) @ 
99.32/13.19	                                            ((('#B') @ ((('#B') @ ((('#C') @ in)))) @ 
99.32/13.19	                                              binunion))))))))))))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl952])).
99.32/13.19	thf(zip_derived_cl984, plain,
99.32/13.19	    (~ (((setadjoinSub2) =>
99.32/13.19	         (((subset2powerset) =>
99.32/13.19	           (((setextsub) =>
99.32/13.19	             (((subsetemptysetimpeq) =>
99.32/13.19	               (((powersetI1) =>
99.32/13.19	                 (((powersetE1) =>
99.32/13.19	                   (((inPowerset) =>
99.32/13.19	                     (((powersetsubset) =>
99.32/13.19	                       (((sepInPowerset) =>
99.32/13.19	                         (((sepSubset) =>
99.32/13.19	                           (((!!) @ ((('#B') @ (!!) @ 
99.32/13.19	                                      ((('#B') @ ((('#B') @ (!!))) @ 
99.32/13.19	                                        ((('#S') @ ((('#B') @ ('#B') @ 
99.32/13.19	                                                     ((('#B') @ ('#S') @ 
99.32/13.19	                                                       ((('#B') @ ((('#B') @ (
99.32/13.19	                                                                    =>))) @ 
99.32/13.19	                                                         ((('#C') @ in)))))))) @ 
99.32/13.19	                                          ((('#B') @ ((('#B') @ ((('#C') @ in)))) @ 
99.32/13.19	                                            binunion))))))))))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl967])).
99.32/13.19	thf(zip_derived_cl1000, plain,
99.32/13.19	    (~ (((subset2powerset) =>
99.32/13.19	         (((setextsub) =>
99.32/13.19	           (((subsetemptysetimpeq) =>
99.32/13.19	             (((powersetI1) =>
99.32/13.19	               (((powersetE1) =>
99.32/13.19	                 (((inPowerset) =>
99.32/13.19	                   (((powersetsubset) =>
99.32/13.19	                     (((sepInPowerset) =>
99.32/13.19	                       (((sepSubset) =>
99.32/13.19	                         (((!!) @ ((('#B') @ (!!) @ 
99.32/13.19	                                    ((('#B') @ ((('#B') @ (!!))) @ 
99.32/13.19	                                      ((('#S') @ ((('#B') @ ('#B') @ 
99.32/13.19	                                                   ((('#B') @ ('#S') @ 
99.32/13.19	                                                     ((('#B') @ ((('#B') @ (
99.32/13.19	                                                                  =>))) @ 
99.32/13.19	                                                       ((('#C') @ in)))))))) @ 
99.32/13.19	                                        ((('#B') @ ((('#B') @ ((('#C') @ in)))) @ 
99.32/13.19	                                          binunion))))))))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl984])).
99.32/13.19	thf(zip_derived_cl1015, plain,
99.32/13.19	    (~ (((setextsub) =>
99.32/13.19	         (((subsetemptysetimpeq) =>
99.32/13.19	           (((powersetI1) =>
99.32/13.19	             (((powersetE1) =>
99.32/13.19	               (((inPowerset) =>
99.32/13.19	                 (((powersetsubset) =>
99.32/13.19	                   (((sepInPowerset) =>
99.32/13.19	                     (((sepSubset) =>
99.32/13.19	                       (((!!) @ ((('#B') @ (!!) @ 
99.32/13.19	                                  ((('#B') @ ((('#B') @ (!!))) @ 
99.32/13.19	                                    ((('#S') @ ((('#B') @ ('#B') @ 
99.32/13.19	                                                 ((('#B') @ ('#S') @ 
99.32/13.19	                                                   ((('#B') @ ((('#B') @ (=>))) @ 
99.32/13.19	                                                     ((('#C') @ in)))))))) @ 
99.32/13.19	                                      ((('#B') @ ((('#B') @ ((('#C') @ in)))) @ 
99.32/13.19	                                        binunion))))))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1000])).
99.32/13.19	thf(zip_derived_cl1027, plain,
99.32/13.19	    (~ (((subsetemptysetimpeq) =>
99.32/13.19	         (((powersetI1) =>
99.32/13.19	           (((powersetE1) =>
99.32/13.19	             (((inPowerset) =>
99.32/13.19	               (((powersetsubset) =>
99.32/13.19	                 (((sepInPowerset) =>
99.32/13.19	                   (((sepSubset) =>
99.32/13.19	                     (((!!) @ ((('#B') @ (!!) @ 
99.32/13.19	                                ((('#B') @ ((('#B') @ (!!))) @ 
99.32/13.19	                                  ((('#S') @ ((('#B') @ ('#B') @ 
99.32/13.19	                                               ((('#B') @ ('#S') @ 
99.32/13.19	                                                 ((('#B') @ ((('#B') @ (=>))) @ 
99.32/13.19	                                                   ((('#C') @ in)))))))) @ 
99.32/13.19	                                    ((('#B') @ ((('#B') @ ((('#C') @ in)))) @ 
99.32/13.19	                                      binunion))))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1015])).
99.32/13.19	thf(zip_derived_cl1039, plain,
99.32/13.19	    (~ (((powersetI1) =>
99.32/13.19	         (((powersetE1) =>
99.32/13.19	           (((inPowerset) =>
99.32/13.19	             (((powersetsubset) =>
99.32/13.19	               (((sepInPowerset) =>
99.32/13.19	                 (((sepSubset) =>
99.32/13.19	                   (((!!) @ ((('#B') @ (!!) @ 
99.32/13.19	                              ((('#B') @ ((('#B') @ (!!))) @ 
99.32/13.19	                                ((('#S') @ ((('#B') @ ('#B') @ 
99.32/13.19	                                             ((('#B') @ ('#S') @ 
99.32/13.19	                                               ((('#B') @ ((('#B') @ (=>))) @ 
99.32/13.19	                                                 ((('#C') @ in)))))))) @ 
99.32/13.19	                                  ((('#B') @ ((('#B') @ ((('#C') @ in)))) @ 
99.32/13.19	                                    binunion))))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1027])).
99.32/13.19	thf(zip_derived_cl1055, plain,
99.32/13.19	    (~ (((powersetE1) =>
99.32/13.19	         (((inPowerset) =>
99.32/13.19	           (((powersetsubset) =>
99.32/13.19	             (((sepInPowerset) =>
99.32/13.19	               (((sepSubset) =>
99.32/13.19	                 (((!!) @ ((('#B') @ (!!) @ 
99.32/13.19	                            ((('#B') @ ((('#B') @ (!!))) @ 
99.32/13.19	                              ((('#S') @ ((('#B') @ ('#B') @ 
99.32/13.19	                                           ((('#B') @ ('#S') @ 
99.32/13.19	                                             ((('#B') @ ((('#B') @ (=>))) @ 
99.32/13.19	                                               ((('#C') @ in)))))))) @ 
99.32/13.19	                                ((('#B') @ ((('#B') @ ((('#C') @ in)))) @ 
99.32/13.19	                                  binunion))))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1039])).
99.32/13.19	thf(zip_derived_cl1067, plain,
99.32/13.19	    (~ (((inPowerset) =>
99.32/13.19	         (((powersetsubset) =>
99.32/13.19	           (((sepInPowerset) =>
99.32/13.19	             (((sepSubset) =>
99.32/13.19	               (((!!) @ ((('#B') @ (!!) @ 
99.32/13.19	                          ((('#B') @ ((('#B') @ (!!))) @ 
99.32/13.19	                            ((('#S') @ ((('#B') @ ('#B') @ 
99.32/13.19	                                         ((('#B') @ ('#S') @ 
99.32/13.19	                                           ((('#B') @ ((('#B') @ (=>))) @ 
99.32/13.19	                                             ((('#C') @ in)))))))) @ 
99.32/13.19	                              ((('#B') @ ((('#B') @ ((('#C') @ in)))) @ 
99.32/13.19	                                binunion))))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1055])).
99.32/13.19	thf(zip_derived_cl1074, plain,
99.32/13.19	    (~ (((powersetsubset) =>
99.32/13.19	         (((sepInPowerset) =>
99.32/13.19	           (((sepSubset) =>
99.32/13.19	             (((!!) @ ((('#B') @ (!!) @ 
99.32/13.19	                        ((('#B') @ ((('#B') @ (!!))) @ 
99.32/13.19	                          ((('#S') @ ((('#B') @ ('#B') @ 
99.32/13.19	                                       ((('#B') @ ('#S') @ 
99.32/13.19	                                         ((('#B') @ ((('#B') @ (=>))) @ 
99.32/13.19	                                           ((('#C') @ in)))))))) @ 
99.32/13.19	                            ((('#B') @ ((('#B') @ ((('#C') @ in)))) @ 
99.32/13.19	                              binunion))))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1067])).
99.32/13.19	thf(zip_derived_cl1082, plain,
99.32/13.19	    (~ (((sepInPowerset) =>
99.32/13.19	         (((sepSubset) =>
99.32/13.19	           (((!!) @ ((('#B') @ (!!) @ 
99.32/13.19	                      ((('#B') @ ((('#B') @ (!!))) @ 
99.32/13.19	                        ((('#S') @ ((('#B') @ ('#B') @ 
99.32/13.19	                                     ((('#B') @ ('#S') @ 
99.32/13.19	                                       ((('#B') @ ((('#B') @ (=>))) @ 
99.32/13.19	                                         ((('#C') @ in)))))))) @ 
99.32/13.19	                          ((('#B') @ ((('#B') @ ((('#C') @ in)))) @ binunion))))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1074])).
99.32/13.19	thf(zip_derived_cl1090, plain,
99.32/13.19	    (~ (((sepSubset) =>
99.32/13.19	         (((!!) @ ((('#B') @ (!!) @ 
99.32/13.19	                    ((('#B') @ ((('#B') @ (!!))) @ 
99.32/13.19	                      ((('#S') @ ((('#B') @ ('#B') @ 
99.32/13.19	                                   ((('#B') @ ('#S') @ 
99.32/13.19	                                     ((('#B') @ ((('#B') @ (=>))) @ 
99.32/13.19	                                       ((('#C') @ in)))))))) @ 
99.32/13.19	                        ((('#B') @ ((('#B') @ ((('#C') @ in)))) @ binunion))))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1082])).
99.32/13.19	thf(zip_derived_cl1096, plain,
99.32/13.19	    (~ (((!!) @ ((('#B') @ (!!) @ 
99.32/13.19	                  ((('#B') @ ((('#B') @ (!!))) @ 
99.32/13.19	                    ((('#S') @ ((('#B') @ ('#B') @ 
99.32/13.19	                                 ((('#B') @ ('#S') @ 
99.32/13.19	                                   ((('#B') @ ((('#B') @ (=>))) @ 
99.32/13.19	                                     ((('#C') @ in)))))))) @ 
99.32/13.19	                      ((('#B') @ ((('#B') @ ((('#C') @ in)))) @ binunion))))))))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1090])).
99.32/13.19	thf(zip_derived_cl1101, plain,
99.32/13.19	    (~ (((!!) @ ((('#B') @ (!!) @ 
99.32/13.19	                  ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 
99.32/13.19	                                          ((('#C') @ in @ '#sk29')))))) @ 
99.32/13.19	                    ((('#B') @ ((('#C') @ in)) @ (binunion @ '#sk29')))))))))),
99.32/13.19	    inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1096])).
99.32/13.19	thf(zip_derived_cl1106, plain,
99.32/13.19	    (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ '#sk29')))) @ 
99.32/13.19	                  ((('#C') @ in @ (binunion @ '#sk29' @ '#sk30')))))))),
99.32/13.19	    inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1101])).
99.32/13.19	thf(binunion, axiom,(( binunion @ (X0)@ (X1)) =
99.32/13.19	  ((setunion @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)))))).
99.32/13.19	thf('5', plain,
99.32/13.19	    (![X1:$i,X0:$i]:
99.32/13.19	     ( ( binunion @ X0 @ X1 ) =
99.32/13.19	       ( setunion @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) )),
99.32/13.19	    define([status(thm)])).
99.32/13.19	thf(zip_derived_cl1108, plain,
99.32/13.19	    (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ '#sk29')))) @ 
99.32/13.19	                  ((('#C') @ in @ 
99.32/13.19	                    (setunion @ 
99.32/13.19	                     (setadjoin @ '#sk29' @ (setadjoin @ '#sk30' @ emptyset)))))))))),
99.32/13.19	    inference('rw', [status(thm)], [zip_derived_cl1106, '5'])).
99.32/13.19	thf(zip_derived_cl1109, plain,
99.32/13.19	    (~ (((in @ 
99.32/13.19	         ('#sk12' @ 
99.32/13.19	          (setunion @ 
99.32/13.19	           (setadjoin @ '#sk29' @ (setadjoin @ '#sk30' @ emptyset))) @ 
99.32/13.19	          '#sk29') @ 
99.32/13.19	         '#sk29') => (in @ 
99.32/13.19	         ('#sk12' @ 
99.32/13.19	          (setunion @ 
99.32/13.19	           (setadjoin @ '#sk29' @ (setadjoin @ '#sk30' @ emptyset))) @ 
99.32/13.19	          '#sk29') @ 
99.32/13.19	         (setunion @ (setadjoin @ '#sk29' @ (setadjoin @ '#sk30' @ emptyset))))))),
99.32/13.19	    inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1108])).
99.32/13.19	thf(zip_derived_cl1110, plain,
99.32/13.19	    ( (in @ 
99.32/13.19	       ('#sk12' @ 
99.32/13.19	        (setunion @ (setadjoin @ '#sk29' @ (setadjoin @ '#sk30' @ emptyset))) @ 
99.32/13.19	        '#sk29') @ 
99.32/13.19	       '#sk29')),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1109])).
99.32/13.19	thf(zip_derived_cl1111, plain,
99.32/13.19	    (~ (in @ 
99.32/13.19	        ('#sk12' @ 
99.32/13.19	         (setunion @ (setadjoin @ '#sk29' @ (setadjoin @ '#sk30' @ emptyset))) @ 
99.32/13.19	         '#sk29') @ 
99.32/13.19	        (setunion @ (setadjoin @ '#sk29' @ (setadjoin @ '#sk30' @ emptyset))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1109])).
99.32/13.19	thf(zip_derived_cl407, plain, ( (setunionI)),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl400])).
99.32/13.19	thf(setunionI, axiom, (setunionI) =>
99.32/13.19	  ((((!!) @ (^[Y0 : $i]:
99.32/13.19	               (((!!) @ (^[Y1 : $i]:
99.32/13.19	                           (((!!) @ (^[Y2 : $i]:
99.32/13.19	                                       (((in @ Y1 @ Y2) =>
99.32/13.19	                                         (((in @ Y2 @ Y0) => (in @ Y1 @ 
99.32/13.19	                                           (setunion @ Y0)))))))))))))))
99.32/13.19	   = ($true))).
99.32/13.19	thf('6', plain,
99.32/13.19	    (( setunionI ) <=>
99.32/13.19	     ( ![X5:$i,X7:$i,X9:$i]:
99.32/13.19	       ( ( in @ X7 @ X9 ) =>
99.32/13.19	         ( ( in @ X9 @ X5 ) => ( in @ X7 @ ( setunion @ X5 ) ) ) ) )),
99.32/13.19	    inference('rw.lit', [status(esa)], [setunionI])).
99.32/13.19	thf(zip_derived_cl415, plain,
99.32/13.19	    ( (((!!) @ (^[Y0 : $i]:
99.32/13.19	                  (((!!) @ (^[Y1 : $i]:
99.32/13.19	                              (((!!) @ (^[Y2 : $i]:
99.32/13.19	                                          (((in @ Y1 @ Y2) =>
99.32/13.19	                                            (((in @ Y2 @ Y0) => (in @ Y1 @ 
99.32/13.19	                                              (setunion @ Y0)))))))))))))))),
99.32/13.19	    inference('rw_clause', [status(thm)], [zip_derived_cl407, '6'])).
99.32/13.19	thf(zip_derived_cl424, plain,
99.32/13.19	    ( (((!!) @ ((('#B') @ (!!) @ 
99.32/13.19	                 ((('#B') @ ((('#B') @ (!!))) @ 
99.32/13.19	                   ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 
99.32/13.19	                                           ((('#B') @ ((('#B') @ (=>))) @ in)))))) @ 
99.32/13.19	                     ((('#S') @ ((('#B') @ ('#B') @ 
99.32/13.19	                                  ((('#B') @ ('#C') @ 
99.32/13.19	                                    ((('#B') @ ((('#B') @ (=>))) @ 
99.32/13.19	                                      ((('#C') @ in)))))))) @ 
99.32/13.19	                       ((('#B') @ ((('#C') @ in)) @ setunion))))))))))))),
99.32/13.19	    inference('comb-normalize', [status(thm)], [zip_derived_cl415])).
99.32/13.19	thf(zip_derived_cl425, plain,
99.32/13.19	    (![X2 : $i]:
99.32/13.19	        (((!!) @ ((('#B') @ (!!) @ 
99.32/13.19	                   ((('#S') @ ((('#B') @ ('#S') @ 
99.32/13.19	                                ((('#B') @ ((('#B') @ (=>))) @ in)))) @ 
99.32/13.19	                     ((('#B') @ ((('#C') @ ((('#B') @ (=>) @ 
99.32/13.19	                                             ((('#C') @ in @ X2)))))) @ 
99.32/13.19	                       ((('#C') @ in @ (setunion @ X2)))))))))))),
99.32/13.19	    inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl424])).
99.32/13.19	thf(zip_derived_cl434, plain,
99.32/13.19	    (![X2 : $i, X4 : $i]:
99.32/13.19	        (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (in @ X4))) @ 
99.32/13.19	                   ((('#C') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @ 
99.32/13.19	                     (in @ X4 @ (setunion @ X2))))))))),
99.32/13.19	    inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl425])).
99.32/13.19	thf(zip_derived_cl443, plain,
99.32/13.19	    (![X2 : $i, X4 : $i, X6 : $i]:
99.32/13.19	        (((in @ X4 @ X6) => (((in @ X6 @ X2) => (in @ X4 @ (setunion @ X2))))))),
99.32/13.19	    inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl434])).
99.32/13.19	thf(zip_derived_cl451, plain,
99.32/13.19	    (![X2 : $i, X4 : $i, X6 : $i]:
99.32/13.19	       (~ (in @ X4 @ X6) |  (((in @ X6 @ X2) => (in @ X4 @ (setunion @ X2)))))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl443])).
99.32/13.19	thf(zip_derived_cl459, plain,
99.32/13.19	    (![X2 : $i, X4 : $i, X6 : $i]:
99.32/13.19	       (~ (in @ X6 @ X2) |  (in @ X4 @ (setunion @ X2)) | ~ (in @ X4 @ X6))),
99.32/13.19	    inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl451])).
99.32/13.19	thf(zip_derived_cl13556, plain, ($false),
99.32/13.19	    inference('eprover', [status(thm)],
99.32/13.19	              [zip_derived_cl352, zip_derived_cl1110, zip_derived_cl1111, 
99.32/13.19	               zip_derived_cl459])).
99.32/13.19	
99.32/13.19	% SZS output end Refutation
99.32/13.19	
99.32/13.19	
99.32/13.19	% /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s
99.32/13.19	% Terminating...
99.64/13.34	% Runner terminated.
99.64/13.35	% Zipperpin 1.5 exiting
99.64/13.37	EOF