0.07/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.15 % Command : run_portfolio.sh /export/starexec/sandbox2/benchmark/theBenchmark.p /export/starexec/sandbox2/tmp/tmp.gkNOTGXmUq 0.14/0.35 % Computer : n002.cluster.edu 0.14/0.35 % Model : x86_64 x86_64 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.35 % Memory : 8042.1875MB 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.35 % CPULimit : 1200 0.14/0.35 % DateTime : Tue Jul 13 12:35:48 EDT 2021 0.14/0.35 % CPUTime : 0.14/0.35 % Running portfolio for 120 s 0.14/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.14/0.35 % Number of cores: 8 0.14/0.36 % Python version: Python 3.6.8 0.14/0.36 % Running in HO mode 0.55/0.64 % Estimated wc time : 1286 0.55/0.64 % Estimated cpu time (7 cpus) : 183.71428571428572 0.57/0.72 % /export/starexec/sandbox2/solver/bin/lams/s6.sh running for 21s 0.57/0.73 % /export/starexec/sandbox2/solver/bin/lams/new_b3.2.norw.sh running for 15s 0.57/0.75 % /export/starexec/sandbox2/solver/bin/lams/b.rpo.sh running for 21s 0.57/0.76 % /export/starexec/sandbox2/solver/bin/lams/s6.ds.sh running for 10s 0.57/0.76 % /export/starexec/sandbox2/solver/bin/lams/c.s.2.sh running for 68s 0.57/0.76 % /export/starexec/sandbox2/solver/bin/lams/c.easy.sh running for 26s 0.57/0.77 % /export/starexec/sandbox2/solver/bin/lams/old_b3.avatar.sh running for 15s 69.39/10.58 % /export/starexec/sandbox2/solver/bin/lams/old_sp2.sh running for 17s 105.89/15.75 % /export/starexec/sandbox2/solver/bin/lams/b.sh running for 31s 106.06/15.78 % /export/starexec/sandbox2/solver/bin/lams/sh1.sh running for 26s 146.72/21.59 % /export/starexec/sandbox2/solver/bin/lams/b.lsimp.sh running for 17s 147.61/21.74 % /export/starexec/sandbox2/solver/bin/lams/b.split.sh running for 31s 181.50/26.62 % /export/starexec/sandbox2/solver/bin/lams/s4.sh running for 15s 182.11/26.71 % Solved by lams/b.lsimp.sh. 182.11/26.71 % done 2182 iterations in 5.080s 182.11/26.71 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 182.11/26.71 % SZS output start Refutation 182.11/26.71 tff(setextsub, conjecture, 182.11/26.71 (setextAx => 182.11/26.71 (emptysetAx => 182.11/26.71 (setadjoinAx => 182.11/26.71 (powersetAx => 182.11/26.71 (setunionAx => 182.11/26.71 (omega0Ax => 182.11/26.71 (omegaSAx => 182.11/26.71 (omegaIndAx => 182.11/26.71 (replAx => 182.11/26.71 (foundationAx => 182.11/26.71 (wellorderingAx => 182.11/26.71 (descrp => 182.11/26.71 (dsetconstrI => 182.11/26.71 (dsetconstrEL => 182.11/26.71 (dsetconstrER => 182.11/26.71 (exuE1 => 182.11/26.71 (prop2setE => 182.11/26.71 (emptysetE => 182.11/26.71 (emptysetimpfalse => 182.11/26.71 (notinemptyset => 182.11/26.71 (exuE3e => 182.11/26.71 (setext => 182.11/26.71 (emptyI => 182.11/26.71 (noeltsimpempty => 182.11/26.71 (setbeta => 182.11/26.71 (nonemptyE1 => 182.11/26.71 (nonemptyI => 182.11/26.71 (nonemptyI1 => 182.11/26.71 (setadjoinIL => 182.11/26.71 (emptyinunitempty => 182.11/26.71 (setadjoinIR => 182.11/26.71 (setadjoinE => 182.11/26.71 (setadjoinOr => 182.11/26.71 (setoftrueEq => 182.11/26.71 (powersetI => 182.11/26.71 (emptyinPowerset => 182.11/26.71 (emptyInPowerset => 182.11/26.71 (powersetE => 182.11/26.71 (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 (in__Cong => 182.11/26.71 (exuE3u => 182.11/26.71 ( 182.11/26.71 exu__Cong => 182.11/26.71 ( 182.11/26.71 emptyset__Cong => 182.11/26.71 ( 182.11/26.71 setadjoin__Cong => 182.11/26.71 ( 182.11/26.71 powerset__Cong => 182.11/26.71 ( 182.11/26.71 setunion__Cong => 182.11/26.71 ( 182.11/26.71 omega__Cong => 182.11/26.71 ( 182.11/26.71 exuEu => 182.11/26.71 ( 182.11/26.71 descr__Cong => 182.11/26.71 ( 182.11/26.71 dsetconstr__Cong => 182.11/26.71 ( 182.11/26.71 subsetI1 => 182.11/26.71 ( 182.11/26.71 eqimpsubset2 => 182.11/26.71 ( 182.11/26.71 eqimpsubset1 => 182.11/26.71 ( 182.11/26.71 subsetI2 => 182.11/26.71 ( 182.11/26.71 emptysetsubset => 182.11/26.71 ( 182.11/26.71 subsetE => 182.11/26.71 ( 182.11/26.71 subsetE2 => 182.11/26.71 ( 182.11/26.71 notsubsetI => 182.11/26.71 ( 182.11/26.71 notequalI1 => 182.11/26.71 ( 182.11/26.71 notequalI2 => 182.11/26.71 ( 182.11/26.71 subsetRefl => 182.11/26.71 ( 182.11/26.71 subsetTrans => 182.11/26.71 ( 182.11/26.71 setadjoinSub => 182.11/26.71 ( 182.11/26.71 setadjoinSub2 => 182.11/26.71 ( 182.11/26.71 subset2powerset => 182.11/26.71 ( 182.11/26.71 ![A,B]: 182.11/26.71 (subset( 182.11/26.71 A,B) => 182.11/26.71 (subset( 182.11/26.71 B,A) => 182.11/26.71 (A = B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 182.11/26.71 tff(zf_stmt_0, negated_conjecture, 182.11/26.71 (~ 182.11/26.71 (setextAx => 182.11/26.71 (emptysetAx => 182.11/26.71 (setadjoinAx => 182.11/26.71 (powersetAx => 182.11/26.71 (setunionAx => 182.11/26.71 (omega0Ax => 182.11/26.71 (omegaSAx => 182.11/26.71 (omegaIndAx => 182.11/26.71 (replAx => 182.11/26.71 (foundationAx => 182.11/26.71 (wellorderingAx => 182.11/26.71 (descrp => 182.11/26.71 (dsetconstrI => 182.11/26.71 (dsetconstrEL => 182.11/26.71 (dsetconstrER => 182.11/26.71 (exuE1 => 182.11/26.71 (prop2setE => 182.11/26.71 (emptysetE => 182.11/26.71 (emptysetimpfalse => 182.11/26.71 (notinemptyset => 182.11/26.71 (exuE3e => 182.11/26.71 (setext => 182.11/26.71 (emptyI => 182.11/26.71 (noeltsimpempty => 182.11/26.71 (setbeta => 182.11/26.71 (nonemptyE1 => 182.11/26.71 (nonemptyI => 182.11/26.71 (nonemptyI1 => 182.11/26.71 (setadjoinIL => 182.11/26.71 (emptyinunitempty => 182.11/26.71 (setadjoinIR => 182.11/26.71 (setadjoinE => 182.11/26.71 (setadjoinOr => 182.11/26.71 (setoftrueEq => 182.11/26.71 (powersetI => 182.11/26.71 (emptyinPowerset => 182.11/26.71 (emptyInPowerset => 182.11/26.71 (powersetE => 182.11/26.71 (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 ( 182.11/26.71 in__Cong => 182.11/26.71 ( 182.11/26.71 exuE3u => 182.11/26.71 ( 182.11/26.71 exu__Cong => 182.11/26.71 ( 182.11/26.71 emptyset__Cong => 182.11/26.71 ( 182.11/26.71 setadjoin__Cong => 182.11/26.71 ( 182.11/26.71 powerset__Cong => 182.11/26.71 ( 182.11/26.71 setunion__Cong => 182.11/26.71 ( 182.11/26.71 omega__Cong => 182.11/26.71 ( 182.11/26.71 exuEu => 182.11/26.71 ( 182.11/26.71 descr__Cong => 182.11/26.71 ( 182.11/26.71 dsetconstr__Cong => 182.11/26.71 ( 182.11/26.71 subsetI1 => 182.11/26.71 ( 182.11/26.71 eqimpsubset2 => 182.11/26.71 ( 182.11/26.71 eqimpsubset1 => 182.11/26.71 ( 182.11/26.71 subsetI2 => 182.11/26.71 ( 182.11/26.71 emptysetsubset => 182.11/26.71 ( 182.11/26.71 subsetE => 182.11/26.71 ( 182.11/26.71 subsetE2 => 182.11/26.71 ( 182.11/26.71 notsubsetI => 182.11/26.71 ( 182.11/26.71 notequalI1 => 182.11/26.71 ( 182.11/26.71 notequalI2 => 182.11/26.71 ( 182.11/26.71 subsetRefl => 182.11/26.71 ( 182.11/26.71 subsetTrans => 182.11/26.71 ( 182.11/26.71 setadjoinSub => 182.11/26.71 ( 182.11/26.71 setadjoinSub2 => 182.11/26.71 ( 182.11/26.71 subset2powerset => 182.11/26.71 ( 182.11/26.71 ![A,B]: 182.11/26.71 (subset( 182.11/26.71 A,B) => 182.11/26.71 (subset( 182.11/26.71 B,A) => 182.11/26.71 (A = B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 182.11/26.71 tff('0', plain, 182.11/26.71 ~ (setextAx => 182.11/26.71 (emptysetAx => 182.11/26.71 (setadjoinAx => 182.11/26.71 (powersetAx => 182.11/26.71 (setunionAx => 182.11/26.71 (omega0Ax => 182.11/26.71 (omegaSAx => 182.11/26.71 (omegaIndAx => 182.11/26.71 (replAx => 182.11/26.71 (foundationAx => 182.11/26.71 (wellorderingAx => 182.11/26.71 (descrp => 182.11/26.71 (dsetconstrI => 182.11/26.71 (dsetconstrEL => 182.11/26.71 (dsetconstrER => 182.11/26.71 (exuE1 => 182.11/26.71 (prop2setE => 182.11/26.71 (emptysetE => 182.11/26.71 (emptysetimpfalse => 182.11/26.71 (notinemptyset => 182.11/26.71 (exuE3e => 182.11/26.71 (setext => 182.11/26.71 (emptyI => 182.11/26.71 (noeltsimpempty => 182.11/26.71 (setbeta => 182.11/26.71 (nonemptyE1 => 182.11/26.71 (nonemptyI => 182.11/26.71 (nonemptyI1 => 182.11/26.71 (setadjoinIL => 182.11/26.71 (emptyinunitempty => 182.11/26.71 (setadjoinIR => 182.11/26.71 (setadjoinE => 182.11/26.71 (setadjoinOr => 182.11/26.71 (setoftrueEq => 182.11/26.71 (powersetI => 182.11/26.71 (emptyinPowerset => 182.11/26.71 (emptyInPowerset => 182.11/26.71 (powersetE => 182.11/26.71 (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 ( 182.11/26.71 exuI2 => 182.11/26.71 ( 182.11/26.71 inCongP => 182.11/26.71 ( 182.11/26.71 in__Cong => 182.11/26.71 ( 182.11/26.71 exuE3u => 182.11/26.71 ( 182.11/26.71 exu__Cong => 182.11/26.71 ( 182.11/26.71 emptyset__Cong => 182.11/26.71 ( 182.11/26.71 setadjoin__Cong => 182.11/26.71 ( 182.11/26.71 powerset__Cong => 182.11/26.71 ( 182.11/26.71 setunion__Cong => 182.11/26.71 ( 182.11/26.71 omega__Cong => 182.11/26.71 ( 182.11/26.71 exuEu => 182.11/26.71 ( 182.11/26.71 descr__Cong => 182.11/26.71 ( 182.11/26.71 dsetconstr__Cong => 182.11/26.71 ( 182.11/26.71 subsetI1 => 182.11/26.71 ( 182.11/26.71 eqimpsubset2 => 182.11/26.71 ( 182.11/26.71 eqimpsubset1 => 182.11/26.71 ( 182.11/26.71 subsetI2 => 182.11/26.71 ( 182.11/26.71 emptysetsubset => 182.11/26.71 ( 182.11/26.71 subsetE => 182.11/26.71 ( 182.11/26.71 subsetE2 => 182.11/26.71 ( 182.11/26.71 notsubsetI => 182.11/26.71 ( 182.11/26.71 notequalI1 => 182.11/26.71 ( 182.11/26.71 notequalI2 => 182.11/26.71 ( 182.11/26.71 subsetRefl => 182.11/26.71 ( 182.11/26.71 subsetTrans => 182.11/26.71 ( 182.11/26.71 setadjoinSub => 182.11/26.71 ( 182.11/26.71 setadjoinSub2 => 182.11/26.71 ( 182.11/26.71 subset2powerset => 182.11/26.71 ( 182.11/26.71 !!(( 182.11/26.71 ^[Y0 : $i]: 182.11/26.71 (!!(( 182.11/26.71 ^[Y1 : $i]: 182.11/26.71 (subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 (subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 (Y0 = Y1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('cnf', [status(esa)], [zf_stmt_0])). 182.11/26.71 tff(emptyinunitempty, axiom, emptyinunitempty() = 182.11/26.71 in(emptyset, setadjoin(emptyset, emptyset))). 182.11/26.71 tff('1', plain, emptyinunitempty = in(emptyset,setadjoin(emptyset,emptyset)), 182.11/26.71 define([status(thm)])). 182.11/26.71 tff(emptyset__Cong, axiom, emptyset__Cong() = (emptyset = emptyset)). 182.11/26.71 tff('2', plain, emptyset__Cong = (emptyset = emptyset), define([status(thm)])). 182.11/26.71 tff('3', plain, 182.11/26.71 ~ (setextAx => 182.11/26.71 (emptysetAx => 182.11/26.71 (setadjoinAx => 182.11/26.71 (powersetAx => 182.11/26.71 (setunionAx => 182.11/26.71 (omega0Ax => 182.11/26.71 (omegaSAx => 182.11/26.71 (omegaIndAx => 182.11/26.71 (replAx => 182.11/26.71 (foundationAx => 182.11/26.71 (wellorderingAx => 182.11/26.71 (descrp => 182.11/26.71 (dsetconstrI => 182.11/26.71 (dsetconstrEL => 182.11/26.71 (dsetconstrER => 182.11/26.71 (exuE1 => 182.11/26.71 (prop2setE => 182.11/26.71 (emptysetE => 182.11/26.71 (emptysetimpfalse => 182.11/26.71 (notinemptyset => 182.11/26.71 (exuE3e => 182.11/26.71 (setext => 182.11/26.71 (emptyI => 182.11/26.71 (noeltsimpempty => 182.11/26.71 (setbeta => 182.11/26.71 (nonemptyE1 => 182.11/26.71 (nonemptyI => 182.11/26.71 (nonemptyI1 => 182.11/26.71 (setadjoinIL => 182.11/26.71 (in(emptyset, 182.11/26.71 setadjoin(emptyset, emptyset)) => 182.11/26.71 (setadjoinIR => 182.11/26.71 (setadjoinE => 182.11/26.71 (setadjoinOr => 182.11/26.71 (setoftrueEq => 182.11/26.71 (powersetI => 182.11/26.71 (emptyinPowerset => 182.11/26.71 (emptyInPowerset => 182.11/26.71 (powersetE => 182.11/26.71 (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 ( 182.11/26.71 exuI2 => 182.11/26.71 ( 182.11/26.71 inCongP => 182.11/26.71 ( 182.11/26.71 in__Cong => 182.11/26.71 ( 182.11/26.71 exuE3u => 182.11/26.71 ( 182.11/26.71 exu__Cong => 182.11/26.71 ( 182.11/26.71 ( 182.11/26.71 emptyset = 182.11/26.71 emptyset) => 182.11/26.71 ( 182.11/26.71 setadjoin__Cong => 182.11/26.71 ( 182.11/26.71 powerset__Cong => 182.11/26.71 ( 182.11/26.71 setunion__Cong => 182.11/26.71 ( 182.11/26.71 omega__Cong => 182.11/26.71 ( 182.11/26.71 exuEu => 182.11/26.71 ( 182.11/26.71 descr__Cong => 182.11/26.71 ( 182.11/26.71 dsetconstr__Cong => 182.11/26.71 ( 182.11/26.71 subsetI1 => 182.11/26.71 ( 182.11/26.71 eqimpsubset2 => 182.11/26.71 ( 182.11/26.71 eqimpsubset1 => 182.11/26.71 ( 182.11/26.71 subsetI2 => 182.11/26.71 ( 182.11/26.71 emptysetsubset => 182.11/26.71 ( 182.11/26.71 subsetE => 182.11/26.71 ( 182.11/26.71 subsetE2 => 182.11/26.71 ( 182.11/26.71 notsubsetI => 182.11/26.71 ( 182.11/26.71 notequalI1 => 182.11/26.71 ( 182.11/26.71 notequalI2 => 182.11/26.71 ( 182.11/26.71 subsetRefl => 182.11/26.71 ( 182.11/26.71 subsetTrans => 182.11/26.71 ( 182.11/26.71 setadjoinSub => 182.11/26.71 ( 182.11/26.71 setadjoinSub2 => 182.11/26.71 ( 182.11/26.71 subset2powerset => 182.11/26.71 ( 182.11/26.71 !!(( 182.11/26.71 ^[Y0 : $i]: 182.11/26.71 (!!(( 182.11/26.71 ^[Y1 : $i]: 182.11/26.71 (subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 (subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 (Y0 = Y1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('rw', [status(thm)], ['0', '1', '2'])). 182.11/26.71 tff('4', plain, 182.11/26.71 ~ (setextAx => 182.11/26.71 (emptysetAx => 182.11/26.71 (setadjoinAx => 182.11/26.71 (powersetAx => 182.11/26.71 (setunionAx => 182.11/26.71 (omega0Ax => 182.11/26.71 (omegaSAx => 182.11/26.71 (omegaIndAx => 182.11/26.71 (replAx => 182.11/26.71 (foundationAx => 182.11/26.71 (wellorderingAx => 182.11/26.71 (descrp => 182.11/26.71 (dsetconstrI => 182.11/26.71 (dsetconstrEL => 182.11/26.71 (dsetconstrER => 182.11/26.71 (exuE1 => 182.11/26.71 (prop2setE => 182.11/26.71 (emptysetE => 182.11/26.71 (emptysetimpfalse => 182.11/26.71 (notinemptyset => 182.11/26.71 (exuE3e => 182.11/26.71 (setext => 182.11/26.71 (emptyI => 182.11/26.71 (noeltsimpempty => 182.11/26.71 (setbeta => 182.11/26.71 (nonemptyE1 => 182.11/26.71 (nonemptyI => 182.11/26.71 (nonemptyI1 => 182.11/26.71 (setadjoinIL => 182.11/26.71 (in(emptyset, 182.11/26.71 setadjoin(emptyset, emptyset)) => 182.11/26.71 (setadjoinIR => 182.11/26.71 (setadjoinE => 182.11/26.71 (setadjoinOr => 182.11/26.71 (setoftrueEq => 182.11/26.71 (powersetI => 182.11/26.71 (emptyinPowerset => 182.11/26.71 (emptyInPowerset => 182.11/26.71 (powersetE => 182.11/26.71 (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 ( 182.11/26.71 exuI2 => 182.11/26.71 ( 182.11/26.71 inCongP => 182.11/26.71 ( 182.11/26.71 in__Cong => 182.11/26.71 ( 182.11/26.71 exuE3u => 182.11/26.71 ( 182.11/26.71 exu__Cong => 182.11/26.71 ( 182.11/26.71 setadjoin__Cong => 182.11/26.71 ( 182.11/26.71 powerset__Cong => 182.11/26.71 ( 182.11/26.71 setunion__Cong => 182.11/26.71 ( 182.11/26.71 omega__Cong => 182.11/26.71 ( 182.11/26.71 exuEu => 182.11/26.71 ( 182.11/26.71 descr__Cong => 182.11/26.71 ( 182.11/26.71 dsetconstr__Cong => 182.11/26.71 ( 182.11/26.71 subsetI1 => 182.11/26.71 ( 182.11/26.71 eqimpsubset2 => 182.11/26.71 ( 182.11/26.71 eqimpsubset1 => 182.11/26.71 ( 182.11/26.71 subsetI2 => 182.11/26.71 ( 182.11/26.71 emptysetsubset => 182.11/26.71 ( 182.11/26.71 subsetE => 182.11/26.71 ( 182.11/26.71 subsetE2 => 182.11/26.71 ( 182.11/26.71 notsubsetI => 182.11/26.71 ( 182.11/26.71 notequalI1 => 182.11/26.71 ( 182.11/26.71 notequalI2 => 182.11/26.71 ( 182.11/26.71 subsetRefl => 182.11/26.71 ( 182.11/26.71 subsetTrans => 182.11/26.71 ( 182.11/26.71 setadjoinSub => 182.11/26.71 ( 182.11/26.71 setadjoinSub2 => 182.11/26.71 ( 182.11/26.71 subset2powerset => 182.11/26.71 ( 182.11/26.71 !!(( 182.11/26.71 ^[Y0 : $i]: 182.11/26.71 (!!(( 182.11/26.71 ^[Y1 : $i]: 182.11/26.71 (subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 (subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 (Y0 = Y1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('simplify boolean subterms', [status(thm)], ['3'])). 182.11/26.71 tff('5', plain, 182.11/26.71 ~ (emptysetAx => 182.11/26.71 (setadjoinAx => 182.11/26.71 (powersetAx => 182.11/26.71 (setunionAx => 182.11/26.71 (omega0Ax => 182.11/26.71 (omegaSAx => 182.11/26.71 (omegaIndAx => 182.11/26.71 (replAx => 182.11/26.71 (foundationAx => 182.11/26.71 (wellorderingAx => 182.11/26.71 (descrp => 182.11/26.71 (dsetconstrI => 182.11/26.71 (dsetconstrEL => 182.11/26.71 (dsetconstrER => 182.11/26.71 (exuE1 => 182.11/26.71 (prop2setE => 182.11/26.71 (emptysetE => 182.11/26.71 (emptysetimpfalse => 182.11/26.71 (notinemptyset => 182.11/26.71 (exuE3e => 182.11/26.71 (setext => 182.11/26.71 (emptyI => 182.11/26.71 (noeltsimpempty => 182.11/26.71 (setbeta => 182.11/26.71 (nonemptyE1 => 182.11/26.71 (nonemptyI => 182.11/26.71 (nonemptyI1 => 182.11/26.71 (setadjoinIL => 182.11/26.71 (in(emptyset, 182.11/26.71 setadjoin(emptyset, emptyset)) => 182.11/26.71 (setadjoinIR => 182.11/26.71 (setadjoinE => 182.11/26.71 (setadjoinOr => 182.11/26.71 (setoftrueEq => 182.11/26.71 (powersetI => 182.11/26.71 (emptyinPowerset => 182.11/26.71 (emptyInPowerset => 182.11/26.71 (powersetE => 182.11/26.71 (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 ( 182.11/26.71 inCongP => 182.11/26.71 ( 182.11/26.71 in__Cong => 182.11/26.71 ( 182.11/26.71 exuE3u => 182.11/26.71 ( 182.11/26.71 exu__Cong => 182.11/26.71 ( 182.11/26.71 setadjoin__Cong => 182.11/26.71 ( 182.11/26.71 powerset__Cong => 182.11/26.71 ( 182.11/26.71 setunion__Cong => 182.11/26.71 ( 182.11/26.71 omega__Cong => 182.11/26.71 ( 182.11/26.71 exuEu => 182.11/26.71 ( 182.11/26.71 descr__Cong => 182.11/26.71 ( 182.11/26.71 dsetconstr__Cong => 182.11/26.71 ( 182.11/26.71 subsetI1 => 182.11/26.71 ( 182.11/26.71 eqimpsubset2 => 182.11/26.71 ( 182.11/26.71 eqimpsubset1 => 182.11/26.71 ( 182.11/26.71 subsetI2 => 182.11/26.71 ( 182.11/26.71 emptysetsubset => 182.11/26.71 ( 182.11/26.71 subsetE => 182.11/26.71 ( 182.11/26.71 subsetE2 => 182.11/26.71 ( 182.11/26.71 notsubsetI => 182.11/26.71 ( 182.11/26.71 notequalI1 => 182.11/26.71 ( 182.11/26.71 notequalI2 => 182.11/26.71 ( 182.11/26.71 subsetRefl => 182.11/26.71 ( 182.11/26.71 subsetTrans => 182.11/26.71 ( 182.11/26.71 setadjoinSub => 182.11/26.71 ( 182.11/26.71 setadjoinSub2 => 182.11/26.71 ( 182.11/26.71 subset2powerset => 182.11/26.71 ( 182.11/26.71 !!(( 182.11/26.71 ^[Y0 : $i]: 182.11/26.71 (!!(( 182.11/26.71 ^[Y1 : $i]: 182.11/26.71 (subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 (subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 (Y0 = Y1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['4'])). 182.11/26.71 tff('6', plain, 182.11/26.71 ~ (setadjoinAx => 182.11/26.71 (powersetAx => 182.11/26.71 (setunionAx => 182.11/26.71 (omega0Ax => 182.11/26.71 (omegaSAx => 182.11/26.71 (omegaIndAx => 182.11/26.71 (replAx => 182.11/26.71 (foundationAx => 182.11/26.71 (wellorderingAx => 182.11/26.71 (descrp => 182.11/26.71 (dsetconstrI => 182.11/26.71 (dsetconstrEL => 182.11/26.71 (dsetconstrER => 182.11/26.71 (exuE1 => 182.11/26.71 (prop2setE => 182.11/26.71 (emptysetE => 182.11/26.71 (emptysetimpfalse => 182.11/26.71 (notinemptyset => 182.11/26.71 (exuE3e => 182.11/26.71 (setext => 182.11/26.71 (emptyI => 182.11/26.71 (noeltsimpempty => 182.11/26.71 (setbeta => 182.11/26.71 (nonemptyE1 => 182.11/26.71 (nonemptyI => 182.11/26.71 (nonemptyI1 => 182.11/26.71 (setadjoinIL => 182.11/26.71 (in(emptyset, setadjoin(emptyset, emptyset)) => 182.11/26.71 (setadjoinIR => 182.11/26.71 (setadjoinE => 182.11/26.71 (setadjoinOr => 182.11/26.71 (setoftrueEq => 182.11/26.71 (powersetI => 182.11/26.71 (emptyinPowerset => 182.11/26.71 (emptyInPowerset => 182.11/26.71 (powersetE => 182.11/26.71 (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 ( 182.11/26.71 in__Cong => 182.11/26.71 ( 182.11/26.71 exuE3u => 182.11/26.71 ( 182.11/26.71 exu__Cong => 182.11/26.71 ( 182.11/26.71 setadjoin__Cong => 182.11/26.71 ( 182.11/26.71 powerset__Cong => 182.11/26.71 ( 182.11/26.71 setunion__Cong => 182.11/26.71 ( 182.11/26.71 omega__Cong => 182.11/26.71 ( 182.11/26.71 exuEu => 182.11/26.71 ( 182.11/26.71 descr__Cong => 182.11/26.71 ( 182.11/26.71 dsetconstr__Cong => 182.11/26.71 ( 182.11/26.71 subsetI1 => 182.11/26.71 ( 182.11/26.71 eqimpsubset2 => 182.11/26.71 ( 182.11/26.71 eqimpsubset1 => 182.11/26.71 ( 182.11/26.71 subsetI2 => 182.11/26.71 ( 182.11/26.71 emptysetsubset => 182.11/26.71 ( 182.11/26.71 subsetE => 182.11/26.71 ( 182.11/26.71 subsetE2 => 182.11/26.71 ( 182.11/26.71 notsubsetI => 182.11/26.71 ( 182.11/26.71 notequalI1 => 182.11/26.71 ( 182.11/26.71 notequalI2 => 182.11/26.71 ( 182.11/26.71 subsetRefl => 182.11/26.71 ( 182.11/26.71 subsetTrans => 182.11/26.71 ( 182.11/26.71 setadjoinSub => 182.11/26.71 ( 182.11/26.71 setadjoinSub2 => 182.11/26.71 ( 182.11/26.71 subset2powerset => 182.11/26.71 ( 182.11/26.71 !!(( 182.11/26.71 ^[Y0 : $i]: 182.11/26.71 (!!(( 182.11/26.71 ^[Y1 : $i]: 182.11/26.71 (subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 (subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 (Y0 = Y1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['5'])). 182.11/26.71 tff('7', plain, 182.11/26.71 ~ (powersetAx => 182.11/26.71 (setunionAx => 182.11/26.71 (omega0Ax => 182.11/26.71 (omegaSAx => 182.11/26.71 (omegaIndAx => 182.11/26.71 (replAx => 182.11/26.71 (foundationAx => 182.11/26.71 (wellorderingAx => 182.11/26.71 (descrp => 182.11/26.71 (dsetconstrI => 182.11/26.71 (dsetconstrEL => 182.11/26.71 (dsetconstrER => 182.11/26.71 (exuE1 => 182.11/26.71 (prop2setE => 182.11/26.71 (emptysetE => 182.11/26.71 (emptysetimpfalse => 182.11/26.71 (notinemptyset => 182.11/26.71 (exuE3e => 182.11/26.71 (setext => 182.11/26.71 (emptyI => 182.11/26.71 (noeltsimpempty => 182.11/26.71 (setbeta => 182.11/26.71 (nonemptyE1 => 182.11/26.71 (nonemptyI => 182.11/26.71 (nonemptyI1 => 182.11/26.71 (setadjoinIL => 182.11/26.71 (in(emptyset, setadjoin(emptyset, emptyset)) => 182.11/26.71 (setadjoinIR => 182.11/26.71 (setadjoinE => 182.11/26.71 (setadjoinOr => 182.11/26.71 (setoftrueEq => 182.11/26.71 (powersetI => 182.11/26.71 (emptyinPowerset => 182.11/26.71 (emptyInPowerset => 182.11/26.71 (powersetE => 182.11/26.71 (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 (in__Cong => 182.11/26.71 ( 182.11/26.71 exuE3u => 182.11/26.71 ( 182.11/26.71 exu__Cong => 182.11/26.71 ( 182.11/26.71 setadjoin__Cong => 182.11/26.71 ( 182.11/26.71 powerset__Cong => 182.11/26.71 ( 182.11/26.71 setunion__Cong => 182.11/26.71 ( 182.11/26.71 omega__Cong => 182.11/26.71 ( 182.11/26.71 exuEu => 182.11/26.71 ( 182.11/26.71 descr__Cong => 182.11/26.71 ( 182.11/26.71 dsetconstr__Cong => 182.11/26.71 ( 182.11/26.71 subsetI1 => 182.11/26.71 ( 182.11/26.71 eqimpsubset2 => 182.11/26.71 ( 182.11/26.71 eqimpsubset1 => 182.11/26.71 ( 182.11/26.71 subsetI2 => 182.11/26.71 ( 182.11/26.71 emptysetsubset => 182.11/26.71 ( 182.11/26.71 subsetE => 182.11/26.71 ( 182.11/26.71 subsetE2 => 182.11/26.71 ( 182.11/26.71 notsubsetI => 182.11/26.71 ( 182.11/26.71 notequalI1 => 182.11/26.71 ( 182.11/26.71 notequalI2 => 182.11/26.71 ( 182.11/26.71 subsetRefl => 182.11/26.71 ( 182.11/26.71 subsetTrans => 182.11/26.71 ( 182.11/26.71 setadjoinSub => 182.11/26.71 ( 182.11/26.71 setadjoinSub2 => 182.11/26.71 ( 182.11/26.71 subset2powerset => 182.11/26.71 ( 182.11/26.71 !!(( 182.11/26.71 ^[Y0 : $i]: 182.11/26.71 (!!(( 182.11/26.71 ^[Y1 : $i]: 182.11/26.71 (subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 (subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 (Y0 = Y1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['6'])). 182.11/26.71 tff('8', plain, 182.11/26.71 ~ (setunionAx => 182.11/26.71 (omega0Ax => 182.11/26.71 (omegaSAx => 182.11/26.71 (omegaIndAx => 182.11/26.71 (replAx => 182.11/26.71 (foundationAx => 182.11/26.71 (wellorderingAx => 182.11/26.71 (descrp => 182.11/26.71 (dsetconstrI => 182.11/26.71 (dsetconstrEL => 182.11/26.71 (dsetconstrER => 182.11/26.71 (exuE1 => 182.11/26.71 (prop2setE => 182.11/26.71 (emptysetE => 182.11/26.71 (emptysetimpfalse => 182.11/26.71 (notinemptyset => 182.11/26.71 (exuE3e => 182.11/26.71 (setext => 182.11/26.71 (emptyI => 182.11/26.71 (noeltsimpempty => 182.11/26.71 (setbeta => 182.11/26.71 (nonemptyE1 => 182.11/26.71 (nonemptyI => 182.11/26.71 (nonemptyI1 => 182.11/26.71 (setadjoinIL => 182.11/26.71 (in(emptyset, setadjoin(emptyset, emptyset)) => 182.11/26.71 (setadjoinIR => 182.11/26.71 (setadjoinE => 182.11/26.71 (setadjoinOr => 182.11/26.71 (setoftrueEq => 182.11/26.71 (powersetI => 182.11/26.71 (emptyinPowerset => 182.11/26.71 (emptyInPowerset => 182.11/26.71 (powersetE => 182.11/26.71 (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 (in__Cong => 182.11/26.71 (exuE3u => 182.11/26.71 ( 182.11/26.71 exu__Cong => 182.11/26.71 ( 182.11/26.71 setadjoin__Cong => 182.11/26.71 ( 182.11/26.71 powerset__Cong => 182.11/26.71 ( 182.11/26.71 setunion__Cong => 182.11/26.71 ( 182.11/26.71 omega__Cong => 182.11/26.71 ( 182.11/26.71 exuEu => 182.11/26.71 ( 182.11/26.71 descr__Cong => 182.11/26.71 ( 182.11/26.71 dsetconstr__Cong => 182.11/26.71 ( 182.11/26.71 subsetI1 => 182.11/26.71 ( 182.11/26.71 eqimpsubset2 => 182.11/26.71 ( 182.11/26.71 eqimpsubset1 => 182.11/26.71 ( 182.11/26.71 subsetI2 => 182.11/26.71 ( 182.11/26.71 emptysetsubset => 182.11/26.71 ( 182.11/26.71 subsetE => 182.11/26.71 ( 182.11/26.71 subsetE2 => 182.11/26.71 ( 182.11/26.71 notsubsetI => 182.11/26.71 ( 182.11/26.71 notequalI1 => 182.11/26.71 ( 182.11/26.71 notequalI2 => 182.11/26.71 ( 182.11/26.71 subsetRefl => 182.11/26.71 ( 182.11/26.71 subsetTrans => 182.11/26.71 ( 182.11/26.71 setadjoinSub => 182.11/26.71 ( 182.11/26.71 setadjoinSub2 => 182.11/26.71 ( 182.11/26.71 subset2powerset => 182.11/26.71 ( 182.11/26.71 !!(( 182.11/26.71 ^[Y0 : $i]: 182.11/26.71 (!!(( 182.11/26.71 ^[Y1 : $i]: 182.11/26.71 (subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 (subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 (Y0 = Y1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['7'])). 182.11/26.71 tff('9', plain, 182.11/26.71 ~ (omega0Ax => 182.11/26.71 (omegaSAx => 182.11/26.71 (omegaIndAx => 182.11/26.71 (replAx => 182.11/26.71 (foundationAx => 182.11/26.71 (wellorderingAx => 182.11/26.71 (descrp => 182.11/26.71 (dsetconstrI => 182.11/26.71 (dsetconstrEL => 182.11/26.71 (dsetconstrER => 182.11/26.71 (exuE1 => 182.11/26.71 (prop2setE => 182.11/26.71 (emptysetE => 182.11/26.71 (emptysetimpfalse => 182.11/26.71 (notinemptyset => 182.11/26.71 (exuE3e => 182.11/26.71 (setext => 182.11/26.71 (emptyI => 182.11/26.71 (noeltsimpempty => 182.11/26.71 (setbeta => 182.11/26.71 (nonemptyE1 => 182.11/26.71 (nonemptyI => 182.11/26.71 (nonemptyI1 => 182.11/26.71 (setadjoinIL => 182.11/26.71 (in(emptyset, setadjoin(emptyset, emptyset)) => 182.11/26.71 (setadjoinIR => 182.11/26.71 (setadjoinE => 182.11/26.71 (setadjoinOr => 182.11/26.71 (setoftrueEq => 182.11/26.71 (powersetI => 182.11/26.71 (emptyinPowerset => 182.11/26.71 (emptyInPowerset => 182.11/26.71 (powersetE => 182.11/26.71 (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 (in__Cong => 182.11/26.71 (exuE3u => 182.11/26.71 (exu__Cong => 182.11/26.71 ( 182.11/26.71 setadjoin__Cong => 182.11/26.71 ( 182.11/26.71 powerset__Cong => 182.11/26.71 ( 182.11/26.71 setunion__Cong => 182.11/26.71 ( 182.11/26.71 omega__Cong => 182.11/26.71 ( 182.11/26.71 exuEu => 182.11/26.71 ( 182.11/26.71 descr__Cong => 182.11/26.71 ( 182.11/26.71 dsetconstr__Cong => 182.11/26.71 ( 182.11/26.71 subsetI1 => 182.11/26.71 ( 182.11/26.71 eqimpsubset2 => 182.11/26.71 ( 182.11/26.71 eqimpsubset1 => 182.11/26.71 ( 182.11/26.71 subsetI2 => 182.11/26.71 ( 182.11/26.71 emptysetsubset => 182.11/26.71 ( 182.11/26.71 subsetE => 182.11/26.71 ( 182.11/26.71 subsetE2 => 182.11/26.71 ( 182.11/26.71 notsubsetI => 182.11/26.71 ( 182.11/26.71 notequalI1 => 182.11/26.71 ( 182.11/26.71 notequalI2 => 182.11/26.71 ( 182.11/26.71 subsetRefl => 182.11/26.71 ( 182.11/26.71 subsetTrans => 182.11/26.71 ( 182.11/26.71 setadjoinSub => 182.11/26.71 ( 182.11/26.71 setadjoinSub2 => 182.11/26.71 ( 182.11/26.71 subset2powerset => 182.11/26.71 ( 182.11/26.71 !!(( 182.11/26.71 ^[Y0 : $i]: 182.11/26.71 (!!(( 182.11/26.71 ^[Y1 : $i]: 182.11/26.71 (subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 (subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 (Y0 = Y1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['8'])). 182.11/26.71 tff('10', plain, 182.11/26.71 ~ (omegaSAx => 182.11/26.71 (omegaIndAx => 182.11/26.71 (replAx => 182.11/26.71 (foundationAx => 182.11/26.71 (wellorderingAx => 182.11/26.71 (descrp => 182.11/26.71 (dsetconstrI => 182.11/26.71 (dsetconstrEL => 182.11/26.71 (dsetconstrER => 182.11/26.71 (exuE1 => 182.11/26.71 (prop2setE => 182.11/26.71 (emptysetE => 182.11/26.71 (emptysetimpfalse => 182.11/26.71 (notinemptyset => 182.11/26.71 (exuE3e => 182.11/26.71 (setext => 182.11/26.71 (emptyI => 182.11/26.71 (noeltsimpempty => 182.11/26.71 (setbeta => 182.11/26.71 (nonemptyE1 => 182.11/26.71 (nonemptyI => 182.11/26.71 (nonemptyI1 => 182.11/26.71 (setadjoinIL => 182.11/26.71 (in(emptyset, setadjoin(emptyset, emptyset)) => 182.11/26.71 (setadjoinIR => 182.11/26.71 (setadjoinE => 182.11/26.71 (setadjoinOr => 182.11/26.71 (setoftrueEq => 182.11/26.71 (powersetI => 182.11/26.71 (emptyinPowerset => 182.11/26.71 (emptyInPowerset => 182.11/26.71 (powersetE => 182.11/26.71 (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 (in__Cong => 182.11/26.71 (exuE3u => 182.11/26.71 (exu__Cong => 182.11/26.71 (setadjoin__Cong => 182.11/26.71 ( 182.11/26.71 powerset__Cong => 182.11/26.71 ( 182.11/26.71 setunion__Cong => 182.11/26.71 ( 182.11/26.71 omega__Cong => 182.11/26.71 ( 182.11/26.71 exuEu => 182.11/26.71 ( 182.11/26.71 descr__Cong => 182.11/26.71 ( 182.11/26.71 dsetconstr__Cong => 182.11/26.71 ( 182.11/26.71 subsetI1 => 182.11/26.71 ( 182.11/26.71 eqimpsubset2 => 182.11/26.71 ( 182.11/26.71 eqimpsubset1 => 182.11/26.71 ( 182.11/26.71 subsetI2 => 182.11/26.71 ( 182.11/26.71 emptysetsubset => 182.11/26.71 ( 182.11/26.71 subsetE => 182.11/26.71 ( 182.11/26.71 subsetE2 => 182.11/26.71 ( 182.11/26.71 notsubsetI => 182.11/26.71 ( 182.11/26.71 notequalI1 => 182.11/26.71 ( 182.11/26.71 notequalI2 => 182.11/26.71 ( 182.11/26.71 subsetRefl => 182.11/26.71 ( 182.11/26.71 subsetTrans => 182.11/26.71 ( 182.11/26.71 setadjoinSub => 182.11/26.71 ( 182.11/26.71 setadjoinSub2 => 182.11/26.71 ( 182.11/26.71 subset2powerset => 182.11/26.71 ( 182.11/26.71 !!(( 182.11/26.71 ^[Y0 : $i]: 182.11/26.71 (!!(( 182.11/26.71 ^[Y1 : $i]: 182.11/26.71 (subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 (subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 (Y0 = Y1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['9'])). 182.11/26.71 tff('11', plain, 182.11/26.71 ~ (omegaIndAx => 182.11/26.71 (replAx => 182.11/26.71 (foundationAx => 182.11/26.71 (wellorderingAx => 182.11/26.71 (descrp => 182.11/26.71 (dsetconstrI => 182.11/26.71 (dsetconstrEL => 182.11/26.71 (dsetconstrER => 182.11/26.71 (exuE1 => 182.11/26.71 (prop2setE => 182.11/26.71 (emptysetE => 182.11/26.71 (emptysetimpfalse => 182.11/26.71 (notinemptyset => 182.11/26.71 (exuE3e => 182.11/26.71 (setext => 182.11/26.71 (emptyI => 182.11/26.71 (noeltsimpempty => 182.11/26.71 (setbeta => 182.11/26.71 (nonemptyE1 => 182.11/26.71 (nonemptyI => 182.11/26.71 (nonemptyI1 => 182.11/26.71 (setadjoinIL => 182.11/26.71 (in(emptyset, setadjoin(emptyset, emptyset)) => 182.11/26.71 (setadjoinIR => 182.11/26.71 (setadjoinE => 182.11/26.71 (setadjoinOr => 182.11/26.71 (setoftrueEq => 182.11/26.71 (powersetI => 182.11/26.71 (emptyinPowerset => 182.11/26.71 (emptyInPowerset => 182.11/26.71 (powersetE => 182.11/26.71 (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 (in__Cong => 182.11/26.71 (exuE3u => 182.11/26.71 (exu__Cong => 182.11/26.71 (setadjoin__Cong => 182.11/26.71 (powerset__Cong => 182.11/26.71 ( 182.11/26.71 setunion__Cong => 182.11/26.71 ( 182.11/26.71 omega__Cong => 182.11/26.71 ( 182.11/26.71 exuEu => 182.11/26.71 ( 182.11/26.71 descr__Cong => 182.11/26.71 ( 182.11/26.71 dsetconstr__Cong => 182.11/26.71 ( 182.11/26.71 subsetI1 => 182.11/26.71 ( 182.11/26.71 eqimpsubset2 => 182.11/26.71 ( 182.11/26.71 eqimpsubset1 => 182.11/26.71 ( 182.11/26.71 subsetI2 => 182.11/26.71 ( 182.11/26.71 emptysetsubset => 182.11/26.71 ( 182.11/26.71 subsetE => 182.11/26.71 ( 182.11/26.71 subsetE2 => 182.11/26.71 ( 182.11/26.71 notsubsetI => 182.11/26.71 ( 182.11/26.71 notequalI1 => 182.11/26.71 ( 182.11/26.71 notequalI2 => 182.11/26.71 ( 182.11/26.71 subsetRefl => 182.11/26.71 ( 182.11/26.71 subsetTrans => 182.11/26.71 ( 182.11/26.71 setadjoinSub => 182.11/26.71 ( 182.11/26.71 setadjoinSub2 => 182.11/26.71 ( 182.11/26.71 subset2powerset => 182.11/26.71 ( 182.11/26.71 !!(( 182.11/26.71 ^[Y0 : $i]: 182.11/26.71 (!!(( 182.11/26.71 ^[Y1 : $i]: 182.11/26.71 (subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 (subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 (Y0 = Y1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['10'])). 182.11/26.71 tff('12', plain, 182.11/26.71 ~ (replAx => 182.11/26.71 (foundationAx => 182.11/26.71 (wellorderingAx => 182.11/26.71 (descrp => 182.11/26.71 (dsetconstrI => 182.11/26.71 (dsetconstrEL => 182.11/26.71 (dsetconstrER => 182.11/26.71 (exuE1 => 182.11/26.71 (prop2setE => 182.11/26.71 (emptysetE => 182.11/26.71 (emptysetimpfalse => 182.11/26.71 (notinemptyset => 182.11/26.71 (exuE3e => 182.11/26.71 (setext => 182.11/26.71 (emptyI => 182.11/26.71 (noeltsimpempty => 182.11/26.71 (setbeta => 182.11/26.71 (nonemptyE1 => 182.11/26.71 (nonemptyI => 182.11/26.71 (nonemptyI1 => 182.11/26.71 (setadjoinIL => 182.11/26.71 (in(emptyset, setadjoin(emptyset, emptyset)) => 182.11/26.71 (setadjoinIR => 182.11/26.71 (setadjoinE => 182.11/26.71 (setadjoinOr => 182.11/26.71 (setoftrueEq => 182.11/26.71 (powersetI => 182.11/26.71 (emptyinPowerset => 182.11/26.71 (emptyInPowerset => 182.11/26.71 (powersetE => 182.11/26.71 (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 (in__Cong => 182.11/26.71 (exuE3u => 182.11/26.71 (exu__Cong => 182.11/26.71 (setadjoin__Cong => 182.11/26.71 (powerset__Cong => 182.11/26.71 (setunion__Cong => 182.11/26.71 ( 182.11/26.71 omega__Cong => 182.11/26.71 ( 182.11/26.71 exuEu => 182.11/26.71 ( 182.11/26.71 descr__Cong => 182.11/26.71 ( 182.11/26.71 dsetconstr__Cong => 182.11/26.71 ( 182.11/26.71 subsetI1 => 182.11/26.71 ( 182.11/26.71 eqimpsubset2 => 182.11/26.71 ( 182.11/26.71 eqimpsubset1 => 182.11/26.71 ( 182.11/26.71 subsetI2 => 182.11/26.71 ( 182.11/26.71 emptysetsubset => 182.11/26.71 ( 182.11/26.71 subsetE => 182.11/26.71 ( 182.11/26.71 subsetE2 => 182.11/26.71 ( 182.11/26.71 notsubsetI => 182.11/26.71 ( 182.11/26.71 notequalI1 => 182.11/26.71 ( 182.11/26.71 notequalI2 => 182.11/26.71 ( 182.11/26.71 subsetRefl => 182.11/26.71 ( 182.11/26.71 subsetTrans => 182.11/26.71 ( 182.11/26.71 setadjoinSub => 182.11/26.71 ( 182.11/26.71 setadjoinSub2 => 182.11/26.71 ( 182.11/26.71 subset2powerset => 182.11/26.71 ( 182.11/26.71 !!(( 182.11/26.71 ^[Y0 : $i]: 182.11/26.71 (!!(( 182.11/26.71 ^[Y1 : $i]: 182.11/26.71 (subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 (subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 (Y0 = Y1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['11'])). 182.11/26.71 tff('13', plain, 182.11/26.71 ~ (foundationAx => 182.11/26.71 (wellorderingAx => 182.11/26.71 (descrp => 182.11/26.71 (dsetconstrI => 182.11/26.71 (dsetconstrEL => 182.11/26.71 (dsetconstrER => 182.11/26.71 (exuE1 => 182.11/26.71 (prop2setE => 182.11/26.71 (emptysetE => 182.11/26.71 (emptysetimpfalse => 182.11/26.71 (notinemptyset => 182.11/26.71 (exuE3e => 182.11/26.71 (setext => 182.11/26.71 (emptyI => 182.11/26.71 (noeltsimpempty => 182.11/26.71 (setbeta => 182.11/26.71 (nonemptyE1 => 182.11/26.71 (nonemptyI => 182.11/26.71 (nonemptyI1 => 182.11/26.71 (setadjoinIL => 182.11/26.71 (in(emptyset, setadjoin(emptyset, emptyset)) => 182.11/26.71 (setadjoinIR => 182.11/26.71 (setadjoinE => 182.11/26.71 (setadjoinOr => 182.11/26.71 (setoftrueEq => 182.11/26.71 (powersetI => 182.11/26.71 (emptyinPowerset => 182.11/26.71 (emptyInPowerset => 182.11/26.71 (powersetE => 182.11/26.71 (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 (in__Cong => 182.11/26.71 (exuE3u => 182.11/26.71 (exu__Cong => 182.11/26.71 (setadjoin__Cong => 182.11/26.71 (powerset__Cong => 182.11/26.71 (setunion__Cong => 182.11/26.71 (omega__Cong => 182.11/26.71 ( 182.11/26.71 exuEu => 182.11/26.71 ( 182.11/26.71 descr__Cong => 182.11/26.71 ( 182.11/26.71 dsetconstr__Cong => 182.11/26.71 ( 182.11/26.71 subsetI1 => 182.11/26.71 ( 182.11/26.71 eqimpsubset2 => 182.11/26.71 ( 182.11/26.71 eqimpsubset1 => 182.11/26.71 ( 182.11/26.71 subsetI2 => 182.11/26.71 ( 182.11/26.71 emptysetsubset => 182.11/26.71 ( 182.11/26.71 subsetE => 182.11/26.71 ( 182.11/26.71 subsetE2 => 182.11/26.71 ( 182.11/26.71 notsubsetI => 182.11/26.71 ( 182.11/26.71 notequalI1 => 182.11/26.71 ( 182.11/26.71 notequalI2 => 182.11/26.71 ( 182.11/26.71 subsetRefl => 182.11/26.71 ( 182.11/26.71 subsetTrans => 182.11/26.71 ( 182.11/26.71 setadjoinSub => 182.11/26.71 ( 182.11/26.71 setadjoinSub2 => 182.11/26.71 ( 182.11/26.71 subset2powerset => 182.11/26.71 ( 182.11/26.71 !!(( 182.11/26.71 ^[Y0 : $i]: 182.11/26.71 (!!(( 182.11/26.71 ^[Y1 : $i]: 182.11/26.71 (subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 (subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 (Y0 = Y1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['12'])). 182.11/26.71 tff('14', plain, 182.11/26.71 ~ (wellorderingAx => 182.11/26.71 (descrp => 182.11/26.71 (dsetconstrI => 182.11/26.71 (dsetconstrEL => 182.11/26.71 (dsetconstrER => 182.11/26.71 (exuE1 => 182.11/26.71 (prop2setE => 182.11/26.71 (emptysetE => 182.11/26.71 (emptysetimpfalse => 182.11/26.71 (notinemptyset => 182.11/26.71 (exuE3e => 182.11/26.71 (setext => 182.11/26.71 (emptyI => 182.11/26.71 (noeltsimpempty => 182.11/26.71 (setbeta => 182.11/26.71 (nonemptyE1 => 182.11/26.71 (nonemptyI => 182.11/26.71 (nonemptyI1 => 182.11/26.71 (setadjoinIL => 182.11/26.71 (in(emptyset, setadjoin(emptyset, emptyset)) => 182.11/26.71 (setadjoinIR => 182.11/26.71 (setadjoinE => 182.11/26.71 (setadjoinOr => 182.11/26.71 (setoftrueEq => 182.11/26.71 (powersetI => 182.11/26.71 (emptyinPowerset => 182.11/26.71 (emptyInPowerset => 182.11/26.71 (powersetE => 182.11/26.71 (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 (in__Cong => 182.11/26.71 (exuE3u => 182.11/26.71 (exu__Cong => 182.11/26.71 (setadjoin__Cong => 182.11/26.71 (powerset__Cong => 182.11/26.71 (setunion__Cong => 182.11/26.71 (omega__Cong => 182.11/26.71 (exuEu => 182.11/26.71 ( 182.11/26.71 descr__Cong => 182.11/26.71 ( 182.11/26.71 dsetconstr__Cong => 182.11/26.71 ( 182.11/26.71 subsetI1 => 182.11/26.71 ( 182.11/26.71 eqimpsubset2 => 182.11/26.71 ( 182.11/26.71 eqimpsubset1 => 182.11/26.71 ( 182.11/26.71 subsetI2 => 182.11/26.71 ( 182.11/26.71 emptysetsubset => 182.11/26.71 ( 182.11/26.71 subsetE => 182.11/26.71 ( 182.11/26.71 subsetE2 => 182.11/26.71 ( 182.11/26.71 notsubsetI => 182.11/26.71 ( 182.11/26.71 notequalI1 => 182.11/26.71 ( 182.11/26.71 notequalI2 => 182.11/26.71 ( 182.11/26.71 subsetRefl => 182.11/26.71 ( 182.11/26.71 subsetTrans => 182.11/26.71 ( 182.11/26.71 setadjoinSub => 182.11/26.71 ( 182.11/26.71 setadjoinSub2 => 182.11/26.71 ( 182.11/26.71 subset2powerset => 182.11/26.71 ( 182.11/26.71 !!(( 182.11/26.71 ^[Y0 : $i]: 182.11/26.71 (!!(( 182.11/26.71 ^[Y1 : $i]: 182.11/26.71 (subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 (subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 (Y0 = Y1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['13'])). 182.11/26.71 tff('15', plain, wellorderingAx, 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['14'])). 182.11/26.71 tff(wellorderingAx, axiom, wellorderingAx => 182.11/26.71 ((!!((^[Y0 : $i]: 182.11/26.71 (??((^[Y1 : $i]: 182.11/26.71 ((!!((^[Y2 : $i]: 182.11/26.71 (in(Y2, Y1) => 182.11/26.71 (!!((^[Y3 : $i]: (in(Y3, Y2) => in(Y3, Y0)))))))))& 182.11/26.71 (!!((^[Y2 : $i]: 182.11/26.71 (!!((^[Y3 : $i]: 182.11/26.71 ((in(Y3, Y0) & in(Y2, Y0)) => 182.11/26.71 ((!!((^[Y4 : $i]: 182.11/26.71 (in(Y4, Y1) => 182.11/26.71 (in(Y2, Y4) <=> in(Y3, Y4)))))) => 182.11/26.71 (Y2 = Y3)))))))))& 182.11/26.71 (!!((^[Y2 : $i]: 182.11/26.71 (!!((^[Y3 : $i]: 182.11/26.71 ((in(Y3, Y1) & in(Y2, Y1)) => 182.11/26.71 ((!!((^[Y4 : $i]: (in(Y4, Y3) => in(Y4, Y2))))) | 182.11/26.71 (!!((^[Y4 : $i]: (in(Y4, Y2) => in(Y4, Y3)))))))))))))& 182.11/26.71 (!!((^[Y2 : $i]: 182.11/26.71 (((??((^[Y3 : $i]: in(Y3, Y2)))) & 182.11/26.71 (!!((^[Y3 : $i]: (in(Y3, Y2) => in(Y3, Y0)))))) => 182.11/26.71 (??((^[Y3 : $i]: 182.11/26.71 (??((^[Y4 : $i]: 182.11/26.71 (in(Y3, Y1)&in(Y4, Y2)& 182.11/26.71 (~((??((^[Y5 : $i]: 182.11/26.71 (in(Y5, Y3) & in(Y5, Y2)))))))& 182.11/26.71 (!!((^[Y5 : $i]: 182.11/26.71 (in(Y5, Y1) => 182.11/26.71 (in(Y4, Y5) | 182.11/26.71 (!!((^[Y6 : $i]: 182.11/26.71 (in(Y6, Y5) => 182.11/26.71 in(Y6, Y3)))))))))))))))))))))))))))) 182.11/26.71 = $true)). 182.11/26.71 tff('16', plain, 182.11/26.71 wellorderingAx <=> 182.11/26.71 (![X5]: 182.11/26.71 (?[X7]: 182.11/26.71 ((![X9]: (in(X9,X7) => (![X11]: (in(X11,X9) => in(X11,X5))))) & 182.11/26.71 (![X13,X15]: 182.11/26.71 ((in(X15,X5) & in(X13,X5)) => 182.11/26.71 ((![X17]: (in(X17,X7) => (in(X13,X17) <=> in(X15,X17)))) => 182.11/26.71 (X13 = X15)))) & 182.11/26.71 (![X19,X21]: 182.11/26.71 ((in(X21,X7) & in(X19,X7)) => 182.11/26.71 ((![X23]: (in(X23,X21) => in(X23,X19))) | 182.11/26.71 (![X25]: (in(X25,X19) => in(X25,X21)))))) & 182.11/26.71 (![X27]: 182.11/26.71 (((?[X29]: in(X29,X27)) & (![X31]: (in(X31,X27) => in(X31,X5)))) => 182.11/26.71 (?[X33,X35]: 182.11/26.71 (in(X33,X7) & in(X35,X27) & 182.11/26.71 (~(?[X37]: (in(X37,X33) & in(X37,X27)))) & 182.11/26.71 (![X39]: 182.11/26.71 (in(X39,X7) => 182.11/26.71 (in(X35,X39) | (![X41]: (in(X41,X39) => in(X41,X33))))))))))))), 182.11/26.71 inference('rw.lit', [status(esa)], [wellorderingAx])). 182.11/26.71 tff('17', plain, 182.11/26.71 (!!((^[Y0 : $i]: 182.11/26.71 (??((^[Y1 : $i]: 182.11/26.71 ((!!((^[Y2 : $i]: 182.11/26.71 (in(Y2, Y1) => 182.11/26.71 (!!((^[Y3 : $i]: (in(Y3, Y2) => in(Y3, Y0)))))))))& 182.11/26.71 (!!((^[Y2 : $i]: 182.11/26.71 (!!((^[Y3 : $i]: 182.11/26.71 ((in(Y3, Y0) & in(Y2, Y0)) => 182.11/26.71 ((!!((^[Y4 : $i]: 182.11/26.71 (in(Y4, Y1) => 182.11/26.71 (in(Y2, Y4) <=> in(Y3, Y4)))))) => 182.11/26.71 (Y2 = Y3)))))))))& 182.11/26.71 (!!((^[Y2 : $i]: 182.11/26.71 (!!((^[Y3 : $i]: 182.11/26.71 ((in(Y3, Y1) & in(Y2, Y1)) => 182.11/26.71 ((!!((^[Y4 : $i]: 182.11/26.71 (in(Y4, Y3) => in(Y4, Y2))))) | 182.11/26.71 (!!((^[Y4 : $i]: 182.11/26.71 (in(Y4, Y2) => in(Y4, Y3)))))))))))))& 182.11/26.71 (!!((^[Y2 : $i]: 182.11/26.71 (((??((^[Y3 : $i]: in(Y3, Y2)))) & 182.11/26.71 (!!((^[Y3 : $i]: (in(Y3, Y2) => in(Y3, Y0)))))) => 182.11/26.71 (??((^[Y3 : $i]: 182.11/26.71 (??((^[Y4 : $i]: 182.11/26.71 (in(Y3, Y1)&in(Y4, Y2)& 182.11/26.71 (~((??((^[Y5 : $i]: 182.11/26.71 (in(Y5, Y3) & in(Y5, Y2)))))))& 182.11/26.71 (!!((^[Y5 : $i]: 182.11/26.71 (in(Y5, Y1) => 182.11/26.71 (in(Y4, Y5) | 182.11/26.71 (!!((^[Y6 : $i]: 182.11/26.71 (in(Y6, Y5) => 182.11/26.71 in(Y6, Y3)))))))))))))))))))))))))))), 182.11/26.71 inference('rw_clause', [status(thm)], ['15', '16'])). 182.11/26.71 tff('18', plain, 182.11/26.71 ![X1]: 182.11/26.71 (??((^[Y0 : $i]: 182.11/26.71 ((!!((^[Y1 : $i]: 182.11/26.71 (in(Y1, Y0) => 182.11/26.71 (!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, X1)))))))))& 182.11/26.71 (!!((^[Y1 : $i]: 182.11/26.71 (!!((^[Y2 : $i]: 182.11/26.71 ((in(Y2, X1) & in(Y1, X1)) => 182.11/26.71 ((!!((^[Y3 : $i]: 182.11/26.71 (in(Y3, Y0) => 182.11/26.71 (in(Y1, Y3) <=> in(Y2, Y3)))))) => 182.11/26.71 (Y1 = Y2)))))))))& 182.11/26.71 (!!((^[Y1 : $i]: 182.11/26.71 (!!((^[Y2 : $i]: 182.11/26.71 ((in(Y2, Y0) & in(Y1, Y0)) => 182.11/26.71 ((!!((^[Y3 : $i]: (in(Y3, Y2) => in(Y3, Y1))))) | 182.11/26.71 (!!((^[Y3 : $i]: (in(Y3, Y1) => in(Y3, Y2)))))))))))))& 182.11/26.71 (!!((^[Y1 : $i]: 182.11/26.71 (((??((^[Y2 : $i]: in(Y2, Y1)))) & 182.11/26.71 (!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, X1)))))) => 182.11/26.71 (??((^[Y2 : $i]: 182.11/26.71 (??((^[Y3 : $i]: 182.11/26.71 (in(Y2, Y0)&in(Y3, Y1)& 182.11/26.71 (~((??((^[Y4 : $i]: 182.11/26.71 (in(Y4, Y2) & in(Y4, Y1)))))))& 182.11/26.71 (!!((^[Y4 : $i]: 182.11/26.71 (in(Y4, Y0) => 182.11/26.71 (in(Y3, Y4) | 182.11/26.71 (!!((^[Y5 : $i]: 182.11/26.71 (in(Y5, Y4) => 182.11/26.71 in(Y5, Y2))))))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_forall', [status(thm)], ['17'])). 182.11/26.71 tff('19', plain, 182.11/26.71 ![X1]: 182.11/26.71 ((!!((^[Y0 : $i]: 182.11/26.71 (in(Y0, '#sk2'(X1)) => 182.11/26.71 (!!((^[Y1 : $i]: (in(Y1, Y0) => in(Y1, X1)))))))))& 182.11/26.71 (!!((^[Y0 : $i]: 182.11/26.71 (!!((^[Y1 : $i]: 182.11/26.71 ((in(Y1, X1) & in(Y0, X1)) => 182.11/26.71 ((!!((^[Y2 : $i]: 182.11/26.71 (in(Y2, '#sk2'(X1)) => 182.11/26.71 (in(Y0, Y2) <=> in(Y1, Y2)))))) => 182.11/26.71 (Y0 = Y1)))))))))& 182.11/26.71 (!!((^[Y0 : $i]: 182.11/26.71 (!!((^[Y1 : $i]: 182.11/26.71 ((in(Y1, '#sk2'(X1)) & in(Y0, '#sk2'(X1))) => 182.11/26.71 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) | 182.11/26.71 (!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1)))))))))))))& 182.11/26.71 (!!((^[Y0 : $i]: 182.11/26.71 (((??((^[Y1 : $i]: in(Y1, Y0)))) & 182.11/26.71 (!!((^[Y1 : $i]: (in(Y1, Y0) => in(Y1, X1)))))) => 182.11/26.71 (??((^[Y1 : $i]: 182.11/26.71 (??((^[Y2 : $i]: 182.11/26.71 (in(Y1, '#sk2'(X1))&in(Y2, Y0)& 182.11/26.71 (~((??((^[Y3 : $i]: (in(Y3, Y1) & in(Y3, Y0)))))))& 182.11/26.71 (!!((^[Y3 : $i]: 182.11/26.71 (in(Y3, '#sk2'(X1)) => 182.11/26.71 (in(Y2, Y3) | 182.11/26.71 (!!((^[Y4 : $i]: 182.11/26.71 (in(Y4, Y3) => in(Y4, Y1)))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_exists', [status(thm)], ['18'])). 182.11/26.71 tff('20', plain, 182.11/26.71 ![X1]: 182.11/26.71 (!!((^[Y0 : $i]: 182.11/26.71 (((??((^[Y1 : $i]: in(Y1, Y0)))) & 182.11/26.71 (!!((^[Y1 : $i]: (in(Y1, Y0) => in(Y1, X1)))))) => 182.11/26.71 (??((^[Y1 : $i]: 182.11/26.71 (??((^[Y2 : $i]: 182.11/26.71 (in(Y1, '#sk2'(X1))&in(Y2, Y0)& 182.11/26.71 (~((??((^[Y3 : $i]: (in(Y3, Y1) & in(Y3, Y0)))))))& 182.11/26.71 (!!((^[Y3 : $i]: 182.11/26.71 (in(Y3, '#sk2'(X1)) => 182.11/26.71 (in(Y2, Y3) | 182.11/26.71 (!!((^[Y4 : $i]: 182.11/26.71 (in(Y4, Y3) => in(Y4, Y1))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_and', [status(thm)], ['19'])). 182.11/26.71 tff('21', plain, 182.11/26.71 ![X1, X2]: 182.11/26.71 (((??((^[Y0 : $i]: in(Y0, X2)))) & 182.11/26.71 (!!((^[Y0 : $i]: (in(Y0, X2) => in(Y0, X1)))))) => 182.11/26.71 (??((^[Y0 : $i]: 182.11/26.71 (??((^[Y1 : $i]: 182.11/26.71 (in(Y0, '#sk2'(X1))&in(Y1, X2)& 182.11/26.71 (~((??((^[Y2 : $i]: (in(Y2, Y0) & in(Y2, X2)))))))& 182.11/26.71 (!!((^[Y2 : $i]: 182.11/26.71 (in(Y2, '#sk2'(X1)) => 182.11/26.71 (in(Y1, Y2) | 182.11/26.71 (!!((^[Y3 : $i]: (in(Y3, Y2) => in(Y3, Y0)))))))))))))))))), 182.11/26.71 inference('lazy_cnf_forall', [status(thm)], ['20'])). 182.11/26.71 tff('22', plain, 182.11/26.71 ![X1, X2]: 182.11/26.71 (~ ((??((^[Y0 : $i]: in(Y0, X2)))) & 182.11/26.71 (!!((^[Y0 : $i]: (in(Y0, X2) => in(Y0, X1)))))) 182.11/26.71 | (??((^[Y0 : $i]: 182.11/26.71 (??((^[Y1 : $i]: 182.11/26.71 (in(Y0, '#sk2'(X1))&in(Y1, X2)& 182.11/26.71 (~((??((^[Y2 : $i]: (in(Y2, Y0) & in(Y2, X2)))))))& 182.11/26.71 (!!((^[Y2 : $i]: 182.11/26.71 (in(Y2, '#sk2'(X1)) => 182.11/26.71 (in(Y1, Y2) | 182.11/26.71 (!!((^[Y3 : $i]: (in(Y3, Y2) => in(Y3, Y0)))))))))))))))))), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['21'])). 182.11/26.71 tff('23', plain, 182.11/26.71 ![X1, X2]: 182.11/26.71 (~ (??((^[Y0 : $i]: in(Y0, X2)))) 182.11/26.71 | ~ (!!((^[Y0 : $i]: (in(Y0, X2) => in(Y0, X1))))) 182.11/26.71 | (??((^[Y0 : $i]: 182.11/26.71 (??((^[Y1 : $i]: 182.11/26.71 (in(Y0, '#sk2'(X1))&in(Y1, X2)& 182.11/26.71 (~((??((^[Y2 : $i]: (in(Y2, Y0) & in(Y2, X2)))))))& 182.11/26.71 (!!((^[Y2 : $i]: 182.11/26.71 (in(Y2, '#sk2'(X1)) => 182.11/26.71 (in(Y1, Y2) | 182.11/26.71 (!!((^[Y3 : $i]: (in(Y3, Y2) => in(Y3, Y0)))))))))))))))))), 182.11/26.71 inference('lazy_cnf_and', [status(thm)], ['22'])). 182.11/26.71 tff('24', plain, 182.11/26.71 ![X1, X2, X3]: 182.11/26.71 (~ in(X3, X2) 182.11/26.71 | (??((^[Y0 : $i]: 182.11/26.71 (??((^[Y1 : $i]: 182.11/26.71 (in(Y0, '#sk2'(X1))&in(Y1, X2)& 182.11/26.71 (~((??((^[Y2 : $i]: (in(Y2, Y0) & in(Y2, X2)))))))& 182.11/26.71 (!!((^[Y2 : $i]: 182.11/26.71 (in(Y2, '#sk2'(X1)) => 182.11/26.71 (in(Y1, Y2) | 182.11/26.71 (!!((^[Y3 : $i]: (in(Y3, Y2) => in(Y3, Y0))))))))))))))))) 182.11/26.71 | ~ (!!((^[Y0 : $i]: (in(Y0, X2) => in(Y0, X1)))))), 182.11/26.71 inference('lazy_cnf_forall', [status(thm)], ['23'])). 182.11/26.71 tff('25', plain, 182.11/26.71 ![X1, X2, X3]: 182.11/26.71 ( (??((^[Y0 : $i]: 182.11/26.71 (in('#sk4'(X1, X2), '#sk2'(X1))&in(Y0, X2)& 182.11/26.71 (~((??((^[Y1 : $i]: (in(Y1, '#sk4'(X1, X2)) & in(Y1, X2)))))))& 182.11/26.71 (!!((^[Y1 : $i]: 182.11/26.71 (in(Y1, '#sk2'(X1)) => 182.11/26.71 (in(Y0, Y1) | 182.11/26.71 (!!((^[Y2 : $i]: 182.11/26.71 (in(Y2, Y1) => in(Y2, '#sk4'(X1, X2))))))))))))))) 182.11/26.71 | ~ (!!((^[Y0 : $i]: (in(Y0, X2) => in(Y0, X1))))) 182.11/26.71 | ~ in(X3, X2)), 182.11/26.71 inference('lazy_cnf_exists', [status(thm)], ['24'])). 182.11/26.71 tff('26', plain, 182.11/26.71 ![X1, X2]: 182.11/26.71 ( '#form6'(X1, X2) | ~ (!!((^[Y0 : $i]: (in(Y0, X2) => in(Y0, X1)))))), 182.11/26.71 define([status(thm)])). 182.11/26.71 tff('27', plain, 182.11/26.71 ![X1, X2]: 182.11/26.71 (~ (in('#sk8'(X1, X2), X2) => in('#sk8'(X1, X2), X1)) 182.11/26.71 | '#form6'(X1, X2)), 182.11/26.71 inference('lazy_cnf_exists', [status(thm)], ['26'])). 182.11/26.71 tff('28', plain, ![X1, X2]: ( in('#sk8'(X1, X2), X2) | '#form6'(X1, X2)), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['27'])). 182.11/26.71 tff('29', plain, 182.11/26.71 ~ (descrp => 182.11/26.71 (dsetconstrI => 182.11/26.71 (dsetconstrEL => 182.11/26.71 (dsetconstrER => 182.11/26.71 (exuE1 => 182.11/26.71 (prop2setE => 182.11/26.71 (emptysetE => 182.11/26.71 (emptysetimpfalse => 182.11/26.71 (notinemptyset => 182.11/26.71 (exuE3e => 182.11/26.71 (setext => 182.11/26.71 (emptyI => 182.11/26.71 (noeltsimpempty => 182.11/26.71 (setbeta => 182.11/26.71 (nonemptyE1 => 182.11/26.71 (nonemptyI => 182.11/26.71 (nonemptyI1 => 182.11/26.71 (setadjoinIL => 182.11/26.71 (in(emptyset, setadjoin(emptyset, emptyset)) => 182.11/26.71 (setadjoinIR => 182.11/26.71 (setadjoinE => 182.11/26.71 (setadjoinOr => 182.11/26.71 (setoftrueEq => 182.11/26.71 (powersetI => 182.11/26.71 (emptyinPowerset => 182.11/26.71 (emptyInPowerset => 182.11/26.71 (powersetE => 182.11/26.71 (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 (in__Cong => 182.11/26.71 (exuE3u => 182.11/26.71 (exu__Cong => 182.11/26.71 (setadjoin__Cong => 182.11/26.71 (powerset__Cong => 182.11/26.71 (setunion__Cong => 182.11/26.71 (omega__Cong => 182.11/26.71 (exuEu => 182.11/26.71 (descr__Cong => 182.11/26.71 ( 182.11/26.71 dsetconstr__Cong => 182.11/26.71 ( 182.11/26.71 subsetI1 => 182.11/26.71 ( 182.11/26.71 eqimpsubset2 => 182.11/26.71 ( 182.11/26.71 eqimpsubset1 => 182.11/26.71 ( 182.11/26.71 subsetI2 => 182.11/26.71 ( 182.11/26.71 emptysetsubset => 182.11/26.71 ( 182.11/26.71 subsetE => 182.11/26.71 ( 182.11/26.71 subsetE2 => 182.11/26.71 ( 182.11/26.71 notsubsetI => 182.11/26.71 ( 182.11/26.71 notequalI1 => 182.11/26.71 ( 182.11/26.71 notequalI2 => 182.11/26.71 ( 182.11/26.71 subsetRefl => 182.11/26.71 ( 182.11/26.71 subsetTrans => 182.11/26.71 ( 182.11/26.71 setadjoinSub => 182.11/26.71 ( 182.11/26.71 setadjoinSub2 => 182.11/26.71 ( 182.11/26.71 subset2powerset => 182.11/26.71 ( 182.11/26.71 !!(( 182.11/26.71 ^[Y0 : $i]: 182.11/26.71 (!!(( 182.11/26.71 ^[Y1 : $i]: 182.11/26.71 (subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 (subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 (Y0 = Y1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['14'])). 182.11/26.71 tff('30', plain, 182.11/26.71 ~ (dsetconstrI => 182.11/26.71 (dsetconstrEL => 182.11/26.71 (dsetconstrER => 182.11/26.71 (exuE1 => 182.11/26.71 (prop2setE => 182.11/26.71 (emptysetE => 182.11/26.71 (emptysetimpfalse => 182.11/26.71 (notinemptyset => 182.11/26.71 (exuE3e => 182.11/26.71 (setext => 182.11/26.71 (emptyI => 182.11/26.71 (noeltsimpempty => 182.11/26.71 (setbeta => 182.11/26.71 (nonemptyE1 => 182.11/26.71 (nonemptyI => 182.11/26.71 (nonemptyI1 => 182.11/26.71 (setadjoinIL => 182.11/26.71 (in(emptyset, setadjoin(emptyset, emptyset)) => 182.11/26.71 (setadjoinIR => 182.11/26.71 (setadjoinE => 182.11/26.71 (setadjoinOr => 182.11/26.71 (setoftrueEq => 182.11/26.71 (powersetI => 182.11/26.71 (emptyinPowerset => 182.11/26.71 (emptyInPowerset => 182.11/26.71 (powersetE => 182.11/26.71 (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 (in__Cong => 182.11/26.71 (exuE3u => 182.11/26.71 (exu__Cong => 182.11/26.71 (setadjoin__Cong => 182.11/26.71 (powerset__Cong => 182.11/26.71 (setunion__Cong => 182.11/26.71 (omega__Cong => 182.11/26.71 (exuEu => 182.11/26.71 (descr__Cong => 182.11/26.71 (dsetconstr__Cong => 182.11/26.71 ( 182.11/26.71 subsetI1 => 182.11/26.71 ( 182.11/26.71 eqimpsubset2 => 182.11/26.71 ( 182.11/26.71 eqimpsubset1 => 182.11/26.71 ( 182.11/26.71 subsetI2 => 182.11/26.71 ( 182.11/26.71 emptysetsubset => 182.11/26.71 ( 182.11/26.71 subsetE => 182.11/26.71 ( 182.11/26.71 subsetE2 => 182.11/26.71 ( 182.11/26.71 notsubsetI => 182.11/26.71 ( 182.11/26.71 notequalI1 => 182.11/26.71 ( 182.11/26.71 notequalI2 => 182.11/26.71 ( 182.11/26.71 subsetRefl => 182.11/26.71 ( 182.11/26.71 subsetTrans => 182.11/26.71 ( 182.11/26.71 setadjoinSub => 182.11/26.71 ( 182.11/26.71 setadjoinSub2 => 182.11/26.71 ( 182.11/26.71 subset2powerset => 182.11/26.71 ( 182.11/26.71 !!(( 182.11/26.71 ^[Y0 : $i]: 182.11/26.71 (!!(( 182.11/26.71 ^[Y1 : $i]: 182.11/26.71 (subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 (subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 (Y0 = Y1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['29'])). 182.11/26.71 tff('31', plain, 182.11/26.71 ~ (dsetconstrEL => 182.11/26.71 (dsetconstrER => 182.11/26.71 (exuE1 => 182.11/26.71 (prop2setE => 182.11/26.71 (emptysetE => 182.11/26.71 (emptysetimpfalse => 182.11/26.71 (notinemptyset => 182.11/26.71 (exuE3e => 182.11/26.71 (setext => 182.11/26.71 (emptyI => 182.11/26.71 (noeltsimpempty => 182.11/26.71 (setbeta => 182.11/26.71 (nonemptyE1 => 182.11/26.71 (nonemptyI => 182.11/26.71 (nonemptyI1 => 182.11/26.71 (setadjoinIL => 182.11/26.71 (in(emptyset, setadjoin(emptyset, emptyset)) => 182.11/26.71 (setadjoinIR => 182.11/26.71 (setadjoinE => 182.11/26.71 (setadjoinOr => 182.11/26.71 (setoftrueEq => 182.11/26.71 (powersetI => 182.11/26.71 (emptyinPowerset => 182.11/26.71 (emptyInPowerset => 182.11/26.71 (powersetE => 182.11/26.71 (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 (in__Cong => 182.11/26.71 (exuE3u => 182.11/26.71 (exu__Cong => 182.11/26.71 (setadjoin__Cong => 182.11/26.71 (powerset__Cong => 182.11/26.71 (setunion__Cong => 182.11/26.71 (omega__Cong => 182.11/26.71 (exuEu => 182.11/26.71 (descr__Cong => 182.11/26.71 (dsetconstr__Cong => 182.11/26.71 (subsetI1 => 182.11/26.71 ( 182.11/26.71 eqimpsubset2 => 182.11/26.71 ( 182.11/26.71 eqimpsubset1 => 182.11/26.71 ( 182.11/26.71 subsetI2 => 182.11/26.71 ( 182.11/26.71 emptysetsubset => 182.11/26.71 ( 182.11/26.71 subsetE => 182.11/26.71 ( 182.11/26.71 subsetE2 => 182.11/26.71 ( 182.11/26.71 notsubsetI => 182.11/26.71 ( 182.11/26.71 notequalI1 => 182.11/26.71 ( 182.11/26.71 notequalI2 => 182.11/26.71 ( 182.11/26.71 subsetRefl => 182.11/26.71 ( 182.11/26.71 subsetTrans => 182.11/26.71 ( 182.11/26.71 setadjoinSub => 182.11/26.71 ( 182.11/26.71 setadjoinSub2 => 182.11/26.71 ( 182.11/26.71 subset2powerset => 182.11/26.71 ( 182.11/26.71 !!(( 182.11/26.71 ^[Y0 : $i]: 182.11/26.71 (!!(( 182.11/26.71 ^[Y1 : $i]: 182.11/26.71 (subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 (subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 (Y0 = Y1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['30'])). 182.11/26.71 tff('32', plain, 182.11/26.71 ~ (dsetconstrER => 182.11/26.71 (exuE1 => 182.11/26.71 (prop2setE => 182.11/26.71 (emptysetE => 182.11/26.71 (emptysetimpfalse => 182.11/26.71 (notinemptyset => 182.11/26.71 (exuE3e => 182.11/26.71 (setext => 182.11/26.71 (emptyI => 182.11/26.71 (noeltsimpempty => 182.11/26.71 (setbeta => 182.11/26.71 (nonemptyE1 => 182.11/26.71 (nonemptyI => 182.11/26.71 (nonemptyI1 => 182.11/26.71 (setadjoinIL => 182.11/26.71 (in(emptyset, setadjoin(emptyset, emptyset)) => 182.11/26.71 (setadjoinIR => 182.11/26.71 (setadjoinE => 182.11/26.71 (setadjoinOr => 182.11/26.71 (setoftrueEq => 182.11/26.71 (powersetI => 182.11/26.71 (emptyinPowerset => 182.11/26.71 (emptyInPowerset => 182.11/26.71 (powersetE => 182.11/26.71 (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 (in__Cong => 182.11/26.71 (exuE3u => 182.11/26.71 (exu__Cong => 182.11/26.71 (setadjoin__Cong => 182.11/26.71 (powerset__Cong => 182.11/26.71 (setunion__Cong => 182.11/26.71 (omega__Cong => 182.11/26.71 (exuEu => 182.11/26.71 (descr__Cong => 182.11/26.71 (dsetconstr__Cong => 182.11/26.71 (subsetI1 => 182.11/26.71 (eqimpsubset2 => 182.11/26.71 ( 182.11/26.71 eqimpsubset1 => 182.11/26.71 ( 182.11/26.71 subsetI2 => 182.11/26.71 ( 182.11/26.71 emptysetsubset => 182.11/26.71 ( 182.11/26.71 subsetE => 182.11/26.71 ( 182.11/26.71 subsetE2 => 182.11/26.71 ( 182.11/26.71 notsubsetI => 182.11/26.71 ( 182.11/26.71 notequalI1 => 182.11/26.71 ( 182.11/26.71 notequalI2 => 182.11/26.71 ( 182.11/26.71 subsetRefl => 182.11/26.71 ( 182.11/26.71 subsetTrans => 182.11/26.71 ( 182.11/26.71 setadjoinSub => 182.11/26.71 ( 182.11/26.71 setadjoinSub2 => 182.11/26.71 ( 182.11/26.71 subset2powerset => 182.11/26.71 ( 182.11/26.71 !!(( 182.11/26.71 ^[Y0 : $i]: 182.11/26.71 (!!(( 182.11/26.71 ^[Y1 : $i]: 182.11/26.71 (subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 (subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 (Y0 = Y1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['31'])). 182.11/26.71 tff('33', plain, 182.11/26.71 ~ (exuE1 => 182.11/26.71 (prop2setE => 182.11/26.71 (emptysetE => 182.11/26.71 (emptysetimpfalse => 182.11/26.71 (notinemptyset => 182.11/26.71 (exuE3e => 182.11/26.71 (setext => 182.11/26.71 (emptyI => 182.11/26.71 (noeltsimpempty => 182.11/26.71 (setbeta => 182.11/26.71 (nonemptyE1 => 182.11/26.71 (nonemptyI => 182.11/26.71 (nonemptyI1 => 182.11/26.71 (setadjoinIL => 182.11/26.71 (in(emptyset, setadjoin(emptyset, emptyset)) => 182.11/26.71 (setadjoinIR => 182.11/26.71 (setadjoinE => 182.11/26.71 (setadjoinOr => 182.11/26.71 (setoftrueEq => 182.11/26.71 (powersetI => 182.11/26.71 (emptyinPowerset => 182.11/26.71 (emptyInPowerset => 182.11/26.71 (powersetE => 182.11/26.71 (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 (in__Cong => 182.11/26.71 (exuE3u => 182.11/26.71 (exu__Cong => 182.11/26.71 (setadjoin__Cong => 182.11/26.71 (powerset__Cong => 182.11/26.71 (setunion__Cong => 182.11/26.71 (omega__Cong => 182.11/26.71 (exuEu => 182.11/26.71 (descr__Cong => 182.11/26.71 (dsetconstr__Cong => 182.11/26.71 (subsetI1 => 182.11/26.71 (eqimpsubset2 => 182.11/26.71 (eqimpsubset1 => 182.11/26.71 ( 182.11/26.71 subsetI2 => 182.11/26.71 ( 182.11/26.71 emptysetsubset => 182.11/26.71 ( 182.11/26.71 subsetE => 182.11/26.71 ( 182.11/26.71 subsetE2 => 182.11/26.71 ( 182.11/26.71 notsubsetI => 182.11/26.71 ( 182.11/26.71 notequalI1 => 182.11/26.71 ( 182.11/26.71 notequalI2 => 182.11/26.71 ( 182.11/26.71 subsetRefl => 182.11/26.71 ( 182.11/26.71 subsetTrans => 182.11/26.71 ( 182.11/26.71 setadjoinSub => 182.11/26.71 ( 182.11/26.71 setadjoinSub2 => 182.11/26.71 ( 182.11/26.71 subset2powerset => 182.11/26.71 ( 182.11/26.71 !!(( 182.11/26.71 ^[Y0 : $i]: 182.11/26.71 (!!(( 182.11/26.71 ^[Y1 : $i]: 182.11/26.71 (subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 (subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 (Y0 = Y1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['32'])). 182.11/26.71 tff('34', plain, 182.11/26.71 ~ (prop2setE => 182.11/26.71 (emptysetE => 182.11/26.71 (emptysetimpfalse => 182.11/26.71 (notinemptyset => 182.11/26.71 (exuE3e => 182.11/26.71 (setext => 182.11/26.71 (emptyI => 182.11/26.71 (noeltsimpempty => 182.11/26.71 (setbeta => 182.11/26.71 (nonemptyE1 => 182.11/26.71 (nonemptyI => 182.11/26.71 (nonemptyI1 => 182.11/26.71 (setadjoinIL => 182.11/26.71 (in(emptyset, setadjoin(emptyset, emptyset)) => 182.11/26.71 (setadjoinIR => 182.11/26.71 (setadjoinE => 182.11/26.71 (setadjoinOr => 182.11/26.71 (setoftrueEq => 182.11/26.71 (powersetI => 182.11/26.71 (emptyinPowerset => 182.11/26.71 (emptyInPowerset => 182.11/26.71 (powersetE => 182.11/26.71 (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 (in__Cong => 182.11/26.71 (exuE3u => 182.11/26.71 (exu__Cong => 182.11/26.71 (setadjoin__Cong => 182.11/26.71 (powerset__Cong => 182.11/26.71 (setunion__Cong => 182.11/26.71 (omega__Cong => 182.11/26.71 (exuEu => 182.11/26.71 (descr__Cong => 182.11/26.71 (dsetconstr__Cong => 182.11/26.71 (subsetI1 => 182.11/26.71 (eqimpsubset2 => 182.11/26.71 (eqimpsubset1 => 182.11/26.71 (subsetI2 => 182.11/26.71 ( 182.11/26.71 emptysetsubset => 182.11/26.71 ( 182.11/26.71 subsetE => 182.11/26.71 ( 182.11/26.71 subsetE2 => 182.11/26.71 ( 182.11/26.71 notsubsetI => 182.11/26.71 ( 182.11/26.71 notequalI1 => 182.11/26.71 ( 182.11/26.71 notequalI2 => 182.11/26.71 ( 182.11/26.71 subsetRefl => 182.11/26.71 ( 182.11/26.71 subsetTrans => 182.11/26.71 ( 182.11/26.71 setadjoinSub => 182.11/26.71 ( 182.11/26.71 setadjoinSub2 => 182.11/26.71 ( 182.11/26.71 subset2powerset => 182.11/26.71 ( 182.11/26.71 !!(( 182.11/26.71 ^[Y0 : $i]: 182.11/26.71 (!!(( 182.11/26.71 ^[Y1 : $i]: 182.11/26.71 (subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 (subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 (Y0 = Y1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['33'])). 182.11/26.71 tff('35', plain, 182.11/26.71 ~ (emptysetE => 182.11/26.71 (emptysetimpfalse => 182.11/26.71 (notinemptyset => 182.11/26.71 (exuE3e => 182.11/26.71 (setext => 182.11/26.71 (emptyI => 182.11/26.71 (noeltsimpempty => 182.11/26.71 (setbeta => 182.11/26.71 (nonemptyE1 => 182.11/26.71 (nonemptyI => 182.11/26.71 (nonemptyI1 => 182.11/26.71 (setadjoinIL => 182.11/26.71 (in(emptyset, setadjoin(emptyset, emptyset)) => 182.11/26.71 (setadjoinIR => 182.11/26.71 (setadjoinE => 182.11/26.71 (setadjoinOr => 182.11/26.71 (setoftrueEq => 182.11/26.71 (powersetI => 182.11/26.71 (emptyinPowerset => 182.11/26.71 (emptyInPowerset => 182.11/26.71 (powersetE => 182.11/26.71 (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 (in__Cong => 182.11/26.71 (exuE3u => 182.11/26.71 (exu__Cong => 182.11/26.71 (setadjoin__Cong => 182.11/26.71 (powerset__Cong => 182.11/26.71 (setunion__Cong => 182.11/26.71 (omega__Cong => 182.11/26.71 (exuEu => 182.11/26.71 (descr__Cong => 182.11/26.71 (dsetconstr__Cong => 182.11/26.71 (subsetI1 => 182.11/26.71 (eqimpsubset2 => 182.11/26.71 (eqimpsubset1 => 182.11/26.71 (subsetI2 => 182.11/26.71 (emptysetsubset => 182.11/26.71 ( 182.11/26.71 subsetE => 182.11/26.71 ( 182.11/26.71 subsetE2 => 182.11/26.71 ( 182.11/26.71 notsubsetI => 182.11/26.71 ( 182.11/26.71 notequalI1 => 182.11/26.71 ( 182.11/26.71 notequalI2 => 182.11/26.71 ( 182.11/26.71 subsetRefl => 182.11/26.71 ( 182.11/26.71 subsetTrans => 182.11/26.71 ( 182.11/26.71 setadjoinSub => 182.11/26.71 ( 182.11/26.71 setadjoinSub2 => 182.11/26.71 ( 182.11/26.71 subset2powerset => 182.11/26.71 ( 182.11/26.71 !!(( 182.11/26.71 ^[Y0 : $i]: 182.11/26.71 (!!(( 182.11/26.71 ^[Y1 : $i]: 182.11/26.71 (subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 (subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 (Y0 = Y1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['34'])). 182.11/26.71 tff('36', plain, 182.11/26.71 ~ (emptysetimpfalse => 182.11/26.71 (notinemptyset => 182.11/26.71 (exuE3e => 182.11/26.71 (setext => 182.11/26.71 (emptyI => 182.11/26.71 (noeltsimpempty => 182.11/26.71 (setbeta => 182.11/26.71 (nonemptyE1 => 182.11/26.71 (nonemptyI => 182.11/26.71 (nonemptyI1 => 182.11/26.71 (setadjoinIL => 182.11/26.71 (in(emptyset, setadjoin(emptyset, emptyset)) => 182.11/26.71 (setadjoinIR => 182.11/26.71 (setadjoinE => 182.11/26.71 (setadjoinOr => 182.11/26.71 (setoftrueEq => 182.11/26.71 (powersetI => 182.11/26.71 (emptyinPowerset => 182.11/26.71 (emptyInPowerset => 182.11/26.71 (powersetE => 182.11/26.71 (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 (in__Cong => 182.11/26.71 (exuE3u => 182.11/26.71 (exu__Cong => 182.11/26.71 (setadjoin__Cong => 182.11/26.71 (powerset__Cong => 182.11/26.71 (setunion__Cong => 182.11/26.71 (omega__Cong => 182.11/26.71 (exuEu => 182.11/26.71 (descr__Cong => 182.11/26.71 (dsetconstr__Cong => 182.11/26.71 (subsetI1 => 182.11/26.71 (eqimpsubset2 => 182.11/26.71 (eqimpsubset1 => 182.11/26.71 (subsetI2 => 182.11/26.71 (emptysetsubset => 182.11/26.71 (subsetE => 182.11/26.71 ( 182.11/26.71 subsetE2 => 182.11/26.71 ( 182.11/26.71 notsubsetI => 182.11/26.71 ( 182.11/26.71 notequalI1 => 182.11/26.71 ( 182.11/26.71 notequalI2 => 182.11/26.71 ( 182.11/26.71 subsetRefl => 182.11/26.71 ( 182.11/26.71 subsetTrans => 182.11/26.71 ( 182.11/26.71 setadjoinSub => 182.11/26.71 ( 182.11/26.71 setadjoinSub2 => 182.11/26.71 ( 182.11/26.71 subset2powerset => 182.11/26.71 ( 182.11/26.71 !!(( 182.11/26.71 ^[Y0 : $i]: 182.11/26.71 (!!(( 182.11/26.71 ^[Y1 : $i]: 182.11/26.71 (subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 (subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 (Y0 = Y1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['35'])). 182.11/26.71 tff('37', plain, 182.11/26.71 ~ (notinemptyset => 182.11/26.71 (exuE3e => 182.11/26.71 (setext => 182.11/26.71 (emptyI => 182.11/26.71 (noeltsimpempty => 182.11/26.71 (setbeta => 182.11/26.71 (nonemptyE1 => 182.11/26.71 (nonemptyI => 182.11/26.71 (nonemptyI1 => 182.11/26.71 (setadjoinIL => 182.11/26.71 (in(emptyset, setadjoin(emptyset, emptyset)) => 182.11/26.71 (setadjoinIR => 182.11/26.71 (setadjoinE => 182.11/26.71 (setadjoinOr => 182.11/26.71 (setoftrueEq => 182.11/26.71 (powersetI => 182.11/26.71 (emptyinPowerset => 182.11/26.71 (emptyInPowerset => 182.11/26.71 (powersetE => 182.11/26.71 (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 (in__Cong => 182.11/26.71 (exuE3u => 182.11/26.71 (exu__Cong => 182.11/26.71 (setadjoin__Cong => 182.11/26.71 (powerset__Cong => 182.11/26.71 (setunion__Cong => 182.11/26.71 (omega__Cong => 182.11/26.71 (exuEu => 182.11/26.71 (descr__Cong => 182.11/26.71 (dsetconstr__Cong => 182.11/26.71 (subsetI1 => 182.11/26.71 (eqimpsubset2 => 182.11/26.71 (eqimpsubset1 => 182.11/26.71 (subsetI2 => 182.11/26.71 (emptysetsubset => 182.11/26.71 (subsetE => 182.11/26.71 (subsetE2 => 182.11/26.71 ( 182.11/26.71 notsubsetI => 182.11/26.71 ( 182.11/26.71 notequalI1 => 182.11/26.71 ( 182.11/26.71 notequalI2 => 182.11/26.71 ( 182.11/26.71 subsetRefl => 182.11/26.71 ( 182.11/26.71 subsetTrans => 182.11/26.71 ( 182.11/26.71 setadjoinSub => 182.11/26.71 ( 182.11/26.71 setadjoinSub2 => 182.11/26.71 ( 182.11/26.71 subset2powerset => 182.11/26.71 ( 182.11/26.71 !!(( 182.11/26.71 ^[Y0 : $i]: 182.11/26.71 (!!(( 182.11/26.71 ^[Y1 : $i]: 182.11/26.71 (subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 (subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 (Y0 = Y1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['36'])). 182.11/26.71 tff('38', plain, 182.11/26.71 ~ (exuE3e => 182.11/26.71 (setext => 182.11/26.71 (emptyI => 182.11/26.71 (noeltsimpempty => 182.11/26.71 (setbeta => 182.11/26.71 (nonemptyE1 => 182.11/26.71 (nonemptyI => 182.11/26.71 (nonemptyI1 => 182.11/26.71 (setadjoinIL => 182.11/26.71 (in(emptyset, setadjoin(emptyset, emptyset)) => 182.11/26.71 (setadjoinIR => 182.11/26.71 (setadjoinE => 182.11/26.71 (setadjoinOr => 182.11/26.71 (setoftrueEq => 182.11/26.71 (powersetI => 182.11/26.71 (emptyinPowerset => 182.11/26.71 (emptyInPowerset => 182.11/26.71 (powersetE => 182.11/26.71 (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 (in__Cong => 182.11/26.71 (exuE3u => 182.11/26.71 (exu__Cong => 182.11/26.71 (setadjoin__Cong => 182.11/26.71 (powerset__Cong => 182.11/26.71 (setunion__Cong => 182.11/26.71 (omega__Cong => 182.11/26.71 (exuEu => 182.11/26.71 (descr__Cong => 182.11/26.71 (dsetconstr__Cong => 182.11/26.71 (subsetI1 => 182.11/26.71 (eqimpsubset2 => 182.11/26.71 (eqimpsubset1 => 182.11/26.71 (subsetI2 => 182.11/26.71 (emptysetsubset => 182.11/26.71 (subsetE => 182.11/26.71 (subsetE2 => 182.11/26.71 (notsubsetI => 182.11/26.71 ( 182.11/26.71 notequalI1 => 182.11/26.71 ( 182.11/26.71 notequalI2 => 182.11/26.71 ( 182.11/26.71 subsetRefl => 182.11/26.71 ( 182.11/26.71 subsetTrans => 182.11/26.71 ( 182.11/26.71 setadjoinSub => 182.11/26.71 ( 182.11/26.71 setadjoinSub2 => 182.11/26.71 ( 182.11/26.71 subset2powerset => 182.11/26.71 ( 182.11/26.71 !!(( 182.11/26.71 ^[Y0 : $i]: 182.11/26.71 (!!(( 182.11/26.71 ^[Y1 : $i]: 182.11/26.71 (subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 (subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 (Y0 = Y1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['37'])). 182.11/26.71 tff('39', plain, 182.11/26.71 ~ (setext => 182.11/26.71 (emptyI => 182.11/26.71 (noeltsimpempty => 182.11/26.71 (setbeta => 182.11/26.71 (nonemptyE1 => 182.11/26.71 (nonemptyI => 182.11/26.71 (nonemptyI1 => 182.11/26.71 (setadjoinIL => 182.11/26.71 (in(emptyset, setadjoin(emptyset, emptyset)) => 182.11/26.71 (setadjoinIR => 182.11/26.71 (setadjoinE => 182.11/26.71 (setadjoinOr => 182.11/26.71 (setoftrueEq => 182.11/26.71 (powersetI => 182.11/26.71 (emptyinPowerset => 182.11/26.71 (emptyInPowerset => 182.11/26.71 (powersetE => 182.11/26.71 (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 (in__Cong => 182.11/26.71 (exuE3u => 182.11/26.71 (exu__Cong => 182.11/26.71 (setadjoin__Cong => 182.11/26.71 (powerset__Cong => 182.11/26.71 (setunion__Cong => 182.11/26.71 (omega__Cong => 182.11/26.71 (exuEu => 182.11/26.71 (descr__Cong => 182.11/26.71 (dsetconstr__Cong => 182.11/26.71 (subsetI1 => 182.11/26.71 (eqimpsubset2 => 182.11/26.71 (eqimpsubset1 => 182.11/26.71 (subsetI2 => 182.11/26.71 (emptysetsubset => 182.11/26.71 (subsetE => 182.11/26.71 (subsetE2 => 182.11/26.71 (notsubsetI => 182.11/26.71 (notequalI1 => 182.11/26.71 ( 182.11/26.71 notequalI2 => 182.11/26.71 ( 182.11/26.71 subsetRefl => 182.11/26.71 ( 182.11/26.71 subsetTrans => 182.11/26.71 ( 182.11/26.71 setadjoinSub => 182.11/26.71 ( 182.11/26.71 setadjoinSub2 => 182.11/26.71 ( 182.11/26.71 subset2powerset => 182.11/26.71 ( 182.11/26.71 !!(( 182.11/26.71 ^[Y0 : $i]: 182.11/26.71 (!!(( 182.11/26.71 ^[Y1 : $i]: 182.11/26.71 (subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 (subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 (Y0 = Y1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['38'])). 182.11/26.71 tff('40', plain, 182.11/26.71 ~ (emptyI => 182.11/26.71 (noeltsimpempty => 182.11/26.71 (setbeta => 182.11/26.71 (nonemptyE1 => 182.11/26.71 (nonemptyI => 182.11/26.71 (nonemptyI1 => 182.11/26.71 (setadjoinIL => 182.11/26.71 (in(emptyset, setadjoin(emptyset, emptyset)) => 182.11/26.71 (setadjoinIR => 182.11/26.71 (setadjoinE => 182.11/26.71 (setadjoinOr => 182.11/26.71 (setoftrueEq => 182.11/26.71 (powersetI => 182.11/26.71 (emptyinPowerset => 182.11/26.71 (emptyInPowerset => 182.11/26.71 (powersetE => 182.11/26.71 (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 (in__Cong => 182.11/26.71 (exuE3u => 182.11/26.71 (exu__Cong => 182.11/26.71 (setadjoin__Cong => 182.11/26.71 (powerset__Cong => 182.11/26.71 (setunion__Cong => 182.11/26.71 (omega__Cong => 182.11/26.71 (exuEu => 182.11/26.71 (descr__Cong => 182.11/26.71 (dsetconstr__Cong => 182.11/26.71 (subsetI1 => 182.11/26.71 (eqimpsubset2 => 182.11/26.71 (eqimpsubset1 => 182.11/26.71 (subsetI2 => 182.11/26.71 (emptysetsubset => 182.11/26.71 (subsetE => 182.11/26.71 (subsetE2 => 182.11/26.71 (notsubsetI => 182.11/26.71 (notequalI1 => 182.11/26.71 (notequalI2 => 182.11/26.71 ( 182.11/26.71 subsetRefl => 182.11/26.71 ( 182.11/26.71 subsetTrans => 182.11/26.71 ( 182.11/26.71 setadjoinSub => 182.11/26.71 ( 182.11/26.71 setadjoinSub2 => 182.11/26.71 ( 182.11/26.71 subset2powerset => 182.11/26.71 ( 182.11/26.71 !!(( 182.11/26.71 ^[Y0 : $i]: 182.11/26.71 (!!(( 182.11/26.71 ^[Y1 : $i]: 182.11/26.71 (subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 (subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 (Y0 = Y1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['39'])). 182.11/26.71 tff('41', plain, 182.11/26.71 ~ (noeltsimpempty => 182.11/26.71 (setbeta => 182.11/26.71 (nonemptyE1 => 182.11/26.71 (nonemptyI => 182.11/26.71 (nonemptyI1 => 182.11/26.71 (setadjoinIL => 182.11/26.71 (in(emptyset, setadjoin(emptyset, emptyset)) => 182.11/26.71 (setadjoinIR => 182.11/26.71 (setadjoinE => 182.11/26.71 (setadjoinOr => 182.11/26.71 (setoftrueEq => 182.11/26.71 (powersetI => 182.11/26.71 (emptyinPowerset => 182.11/26.71 (emptyInPowerset => 182.11/26.71 (powersetE => 182.11/26.71 (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 (in__Cong => 182.11/26.71 (exuE3u => 182.11/26.71 (exu__Cong => 182.11/26.71 (setadjoin__Cong => 182.11/26.71 (powerset__Cong => 182.11/26.71 (setunion__Cong => 182.11/26.71 (omega__Cong => 182.11/26.71 (exuEu => 182.11/26.71 (descr__Cong => 182.11/26.71 (dsetconstr__Cong => 182.11/26.71 (subsetI1 => 182.11/26.71 (eqimpsubset2 => 182.11/26.71 (eqimpsubset1 => 182.11/26.71 (subsetI2 => 182.11/26.71 (emptysetsubset => 182.11/26.71 (subsetE => 182.11/26.71 (subsetE2 => 182.11/26.71 (notsubsetI => 182.11/26.71 (notequalI1 => 182.11/26.71 (notequalI2 => 182.11/26.71 (subsetRefl => 182.11/26.71 ( 182.11/26.71 subsetTrans => 182.11/26.71 ( 182.11/26.71 setadjoinSub => 182.11/26.71 ( 182.11/26.71 setadjoinSub2 => 182.11/26.71 ( 182.11/26.71 subset2powerset => 182.11/26.71 ( 182.11/26.71 !!(( 182.11/26.71 ^[Y0 : $i]: 182.11/26.71 (!!(( 182.11/26.71 ^[Y1 : $i]: 182.11/26.71 (subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 (subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 (Y0 = Y1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['40'])). 182.11/26.71 tff('42', plain, 182.11/26.71 ~ (setbeta => 182.11/26.71 (nonemptyE1 => 182.11/26.71 (nonemptyI => 182.11/26.71 (nonemptyI1 => 182.11/26.71 (setadjoinIL => 182.11/26.71 (in(emptyset, setadjoin(emptyset, emptyset)) => 182.11/26.71 (setadjoinIR => 182.11/26.71 (setadjoinE => 182.11/26.71 (setadjoinOr => 182.11/26.71 (setoftrueEq => 182.11/26.71 (powersetI => 182.11/26.71 (emptyinPowerset => 182.11/26.71 (emptyInPowerset => 182.11/26.71 (powersetE => 182.11/26.71 (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 (in__Cong => 182.11/26.71 (exuE3u => 182.11/26.71 (exu__Cong => 182.11/26.71 (setadjoin__Cong => 182.11/26.71 (powerset__Cong => 182.11/26.71 (setunion__Cong => 182.11/26.71 (omega__Cong => 182.11/26.71 (exuEu => 182.11/26.71 (descr__Cong => 182.11/26.71 (dsetconstr__Cong => 182.11/26.71 (subsetI1 => 182.11/26.71 (eqimpsubset2 => 182.11/26.71 (eqimpsubset1 => 182.11/26.71 (subsetI2 => 182.11/26.71 (emptysetsubset => 182.11/26.71 (subsetE => 182.11/26.71 (subsetE2 => 182.11/26.71 (notsubsetI => 182.11/26.71 (notequalI1 => 182.11/26.71 (notequalI2 => 182.11/26.71 (subsetRefl => 182.11/26.71 (subsetTrans => 182.11/26.71 ( 182.11/26.71 setadjoinSub => 182.11/26.71 ( 182.11/26.71 setadjoinSub2 => 182.11/26.71 ( 182.11/26.71 subset2powerset => 182.11/26.71 ( 182.11/26.71 !!(( 182.11/26.71 ^[Y0 : $i]: 182.11/26.71 (!!(( 182.11/26.71 ^[Y1 : $i]: 182.11/26.71 (subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 (subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 (Y0 = Y1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['41'])). 182.11/26.71 tff('43', plain, 182.11/26.71 ~ (nonemptyE1 => 182.11/26.71 (nonemptyI => 182.11/26.71 (nonemptyI1 => 182.11/26.71 (setadjoinIL => 182.11/26.71 (in(emptyset, setadjoin(emptyset, emptyset)) => 182.11/26.71 (setadjoinIR => 182.11/26.71 (setadjoinE => 182.11/26.71 (setadjoinOr => 182.11/26.71 (setoftrueEq => 182.11/26.71 (powersetI => 182.11/26.71 (emptyinPowerset => 182.11/26.71 (emptyInPowerset => 182.11/26.71 (powersetE => 182.11/26.71 (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 (in__Cong => 182.11/26.71 (exuE3u => 182.11/26.71 (exu__Cong => 182.11/26.71 (setadjoin__Cong => 182.11/26.71 (powerset__Cong => 182.11/26.71 (setunion__Cong => 182.11/26.71 (omega__Cong => 182.11/26.71 (exuEu => 182.11/26.71 (descr__Cong => 182.11/26.71 (dsetconstr__Cong => 182.11/26.71 (subsetI1 => 182.11/26.71 (eqimpsubset2 => 182.11/26.71 (eqimpsubset1 => 182.11/26.71 (subsetI2 => 182.11/26.71 (emptysetsubset => 182.11/26.71 (subsetE => 182.11/26.71 (subsetE2 => 182.11/26.71 (notsubsetI => 182.11/26.71 (notequalI1 => 182.11/26.71 (notequalI2 => 182.11/26.71 (subsetRefl => 182.11/26.71 (subsetTrans => 182.11/26.71 (setadjoinSub => 182.11/26.71 ( 182.11/26.71 setadjoinSub2 => 182.11/26.71 ( 182.11/26.71 subset2powerset => 182.11/26.71 ( 182.11/26.71 !!(( 182.11/26.71 ^[Y0 : $i]: 182.11/26.71 (!!(( 182.11/26.71 ^[Y1 : $i]: 182.11/26.71 (subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 (subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 (Y0 = Y1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['42'])). 182.11/26.71 tff('44', plain, 182.11/26.71 ~ (nonemptyI => 182.11/26.71 (nonemptyI1 => 182.11/26.71 (setadjoinIL => 182.11/26.71 (in(emptyset, setadjoin(emptyset, emptyset)) => 182.11/26.71 (setadjoinIR => 182.11/26.71 (setadjoinE => 182.11/26.71 (setadjoinOr => 182.11/26.71 (setoftrueEq => 182.11/26.71 (powersetI => 182.11/26.71 (emptyinPowerset => 182.11/26.71 (emptyInPowerset => 182.11/26.71 (powersetE => 182.11/26.71 (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 (in__Cong => 182.11/26.71 (exuE3u => 182.11/26.71 (exu__Cong => 182.11/26.71 (setadjoin__Cong => 182.11/26.71 (powerset__Cong => 182.11/26.71 (setunion__Cong => 182.11/26.71 (omega__Cong => 182.11/26.71 (exuEu => 182.11/26.71 (descr__Cong => 182.11/26.71 (dsetconstr__Cong => 182.11/26.71 (subsetI1 => 182.11/26.71 (eqimpsubset2 => 182.11/26.71 (eqimpsubset1 => 182.11/26.71 (subsetI2 => 182.11/26.71 (emptysetsubset => 182.11/26.71 (subsetE => 182.11/26.71 (subsetE2 => 182.11/26.71 (notsubsetI => 182.11/26.71 (notequalI1 => 182.11/26.71 (notequalI2 => 182.11/26.71 (subsetRefl => 182.11/26.71 (subsetTrans => 182.11/26.71 (setadjoinSub => 182.11/26.71 (setadjoinSub2 => 182.11/26.71 ( 182.11/26.71 subset2powerset => 182.11/26.71 ( 182.11/26.71 !!(( 182.11/26.71 ^[Y0 : $i]: 182.11/26.71 (!!(( 182.11/26.71 ^[Y1 : $i]: 182.11/26.71 (subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 (subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 (Y0 = Y1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['43'])). 182.11/26.71 tff('45', plain, 182.11/26.71 ~ (nonemptyI1 => 182.11/26.71 (setadjoinIL => 182.11/26.71 (in(emptyset, setadjoin(emptyset, emptyset)) => 182.11/26.71 (setadjoinIR => 182.11/26.71 (setadjoinE => 182.11/26.71 (setadjoinOr => 182.11/26.71 (setoftrueEq => 182.11/26.71 (powersetI => 182.11/26.71 (emptyinPowerset => 182.11/26.71 (emptyInPowerset => 182.11/26.71 (powersetE => 182.11/26.71 (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 (in__Cong => 182.11/26.71 (exuE3u => 182.11/26.71 (exu__Cong => 182.11/26.71 (setadjoin__Cong => 182.11/26.71 (powerset__Cong => 182.11/26.71 (setunion__Cong => 182.11/26.71 (omega__Cong => 182.11/26.71 (exuEu => 182.11/26.71 (descr__Cong => 182.11/26.71 (dsetconstr__Cong => 182.11/26.71 (subsetI1 => 182.11/26.71 (eqimpsubset2 => 182.11/26.71 (eqimpsubset1 => 182.11/26.71 (subsetI2 => 182.11/26.71 (emptysetsubset => 182.11/26.71 (subsetE => 182.11/26.71 (subsetE2 => 182.11/26.71 (notsubsetI => 182.11/26.71 (notequalI1 => 182.11/26.71 (notequalI2 => 182.11/26.71 (subsetRefl => 182.11/26.71 (subsetTrans => 182.11/26.71 (setadjoinSub => 182.11/26.71 (setadjoinSub2 => 182.11/26.71 (subset2powerset => 182.11/26.71 ( 182.11/26.71 !!(( 182.11/26.71 ^[Y0 : $i]: 182.11/26.71 (!!(( 182.11/26.71 ^[Y1 : $i]: 182.11/26.71 (subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 (subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 (Y0 = Y1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['44'])). 182.11/26.71 tff('46', plain, 182.11/26.71 ~ (setadjoinIL => 182.11/26.71 (in(emptyset, setadjoin(emptyset, emptyset)) => 182.11/26.71 (setadjoinIR => 182.11/26.71 (setadjoinE => 182.11/26.71 (setadjoinOr => 182.11/26.71 (setoftrueEq => 182.11/26.71 (powersetI => 182.11/26.71 (emptyinPowerset => 182.11/26.71 (emptyInPowerset => 182.11/26.71 (powersetE => 182.11/26.71 (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 (in__Cong => 182.11/26.71 (exuE3u => 182.11/26.71 (exu__Cong => 182.11/26.71 (setadjoin__Cong => 182.11/26.71 (powerset__Cong => 182.11/26.71 (setunion__Cong => 182.11/26.71 (omega__Cong => 182.11/26.71 (exuEu => 182.11/26.71 (descr__Cong => 182.11/26.71 (dsetconstr__Cong => 182.11/26.71 (subsetI1 => 182.11/26.71 (eqimpsubset2 => 182.11/26.71 (eqimpsubset1 => 182.11/26.71 (subsetI2 => 182.11/26.71 (emptysetsubset => 182.11/26.71 (subsetE => 182.11/26.71 (subsetE2 => 182.11/26.71 (notsubsetI => 182.11/26.71 (notequalI1 => 182.11/26.71 (notequalI2 => 182.11/26.71 (subsetRefl => 182.11/26.71 (subsetTrans => 182.11/26.71 (setadjoinSub => 182.11/26.71 (setadjoinSub2 => 182.11/26.71 (subset2powerset => 182.11/26.71 (!!(( 182.11/26.71 ^[Y0 : $i]: 182.11/26.71 (!!(( 182.11/26.71 ^[Y1 : $i]: 182.11/26.71 (subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 (subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 (Y0 = Y1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['45'])). 182.11/26.71 tff('47', plain, 182.11/26.71 ~ (in(emptyset, setadjoin(emptyset, emptyset)) => 182.11/26.71 (setadjoinIR => 182.11/26.71 (setadjoinE => 182.11/26.71 (setadjoinOr => 182.11/26.71 (setoftrueEq => 182.11/26.71 (powersetI => 182.11/26.71 (emptyinPowerset => 182.11/26.71 (emptyInPowerset => 182.11/26.71 (powersetE => 182.11/26.71 (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 (in__Cong => 182.11/26.71 (exuE3u => 182.11/26.71 (exu__Cong => 182.11/26.71 (setadjoin__Cong => 182.11/26.71 (powerset__Cong => 182.11/26.71 (setunion__Cong => 182.11/26.71 (omega__Cong => 182.11/26.71 (exuEu => 182.11/26.71 (descr__Cong => 182.11/26.71 (dsetconstr__Cong => 182.11/26.71 (subsetI1 => 182.11/26.71 (eqimpsubset2 => 182.11/26.71 (eqimpsubset1 => 182.11/26.71 (subsetI2 => 182.11/26.71 (emptysetsubset => 182.11/26.71 (subsetE => 182.11/26.71 (subsetE2 => 182.11/26.71 (notsubsetI => 182.11/26.71 (notequalI1 => 182.11/26.71 (notequalI2 => 182.11/26.71 (subsetRefl => 182.11/26.71 (subsetTrans => 182.11/26.71 (setadjoinSub => 182.11/26.71 (setadjoinSub2 => 182.11/26.71 (subset2powerset => 182.11/26.71 (!!(( 182.11/26.71 ^[Y0 : $i]: 182.11/26.71 (!!(( 182.11/26.71 ^[Y1 : $i]: 182.11/26.71 (subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 (subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 (Y0 = Y1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['46'])). 182.11/26.71 tff('48', plain, 182.11/26.71 ~ (setadjoinIR => 182.11/26.71 (setadjoinE => 182.11/26.71 (setadjoinOr => 182.11/26.71 (setoftrueEq => 182.11/26.71 (powersetI => 182.11/26.71 (emptyinPowerset => 182.11/26.71 (emptyInPowerset => 182.11/26.71 (powersetE => 182.11/26.71 (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 (in__Cong => 182.11/26.71 (exuE3u => 182.11/26.71 (exu__Cong => 182.11/26.71 (setadjoin__Cong => 182.11/26.71 (powerset__Cong => 182.11/26.71 (setunion__Cong => 182.11/26.71 (omega__Cong => 182.11/26.71 (exuEu => 182.11/26.71 (descr__Cong => 182.11/26.71 (dsetconstr__Cong => 182.11/26.71 (subsetI1 => 182.11/26.71 (eqimpsubset2 => 182.11/26.71 (eqimpsubset1 => 182.11/26.71 (subsetI2 => 182.11/26.71 (emptysetsubset => 182.11/26.71 (subsetE => 182.11/26.71 (subsetE2 => 182.11/26.71 (notsubsetI => 182.11/26.71 (notequalI1 => 182.11/26.71 (notequalI2 => 182.11/26.71 (subsetRefl => 182.11/26.71 (subsetTrans => 182.11/26.71 (setadjoinSub => 182.11/26.71 (setadjoinSub2 => 182.11/26.71 (subset2powerset => 182.11/26.71 (!!(( 182.11/26.71 ^[Y0 : $i]: 182.11/26.71 ( 182.11/26.71 !!(( 182.11/26.71 ^[Y1 : $i]: 182.11/26.71 (subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 (subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 (Y0 = Y1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['47'])). 182.11/26.71 tff('49', plain, 182.11/26.71 ~ (setadjoinE => 182.11/26.71 (setadjoinOr => 182.11/26.71 (setoftrueEq => 182.11/26.71 (powersetI => 182.11/26.71 (emptyinPowerset => 182.11/26.71 (emptyInPowerset => 182.11/26.71 (powersetE => 182.11/26.71 (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 (in__Cong => 182.11/26.71 (exuE3u => 182.11/26.71 (exu__Cong => 182.11/26.71 (setadjoin__Cong => 182.11/26.71 (powerset__Cong => 182.11/26.71 (setunion__Cong => 182.11/26.71 (omega__Cong => 182.11/26.71 (exuEu => 182.11/26.71 (descr__Cong => 182.11/26.71 (dsetconstr__Cong => 182.11/26.71 (subsetI1 => 182.11/26.71 (eqimpsubset2 => 182.11/26.71 (eqimpsubset1 => 182.11/26.71 (subsetI2 => 182.11/26.71 (emptysetsubset => 182.11/26.71 (subsetE => 182.11/26.71 (subsetE2 => 182.11/26.71 (notsubsetI => 182.11/26.71 (notequalI1 => 182.11/26.71 (notequalI2 => 182.11/26.71 (subsetRefl => 182.11/26.71 (subsetTrans => 182.11/26.71 (setadjoinSub => 182.11/26.71 (setadjoinSub2 => 182.11/26.71 (subset2powerset => 182.11/26.71 (!!(( 182.11/26.71 ^[Y0 : $i]: 182.11/26.71 (!!(( 182.11/26.71 ^[Y1 : $i]: 182.11/26.71 (subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 (subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 (Y0 = Y1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['48'])). 182.11/26.71 tff('50', plain, 182.11/26.71 ~ (setadjoinOr => 182.11/26.71 (setoftrueEq => 182.11/26.71 (powersetI => 182.11/26.71 (emptyinPowerset => 182.11/26.71 (emptyInPowerset => 182.11/26.71 (powersetE => 182.11/26.71 (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 (in__Cong => 182.11/26.71 (exuE3u => 182.11/26.71 (exu__Cong => 182.11/26.71 (setadjoin__Cong => 182.11/26.71 (powerset__Cong => 182.11/26.71 (setunion__Cong => 182.11/26.71 (omega__Cong => 182.11/26.71 (exuEu => 182.11/26.71 (descr__Cong => 182.11/26.71 (dsetconstr__Cong => 182.11/26.71 (subsetI1 => 182.11/26.71 (eqimpsubset2 => 182.11/26.71 (eqimpsubset1 => 182.11/26.71 (subsetI2 => 182.11/26.71 (emptysetsubset => 182.11/26.71 (subsetE => 182.11/26.71 (subsetE2 => 182.11/26.71 (notsubsetI => 182.11/26.71 (notequalI1 => 182.11/26.71 (notequalI2 => 182.11/26.71 (subsetRefl => 182.11/26.71 (subsetTrans => 182.11/26.71 (setadjoinSub => 182.11/26.71 (setadjoinSub2 => 182.11/26.71 (subset2powerset => 182.11/26.71 (!!((^[Y0 : $i]: 182.11/26.71 (!!(( 182.11/26.71 ^[Y1 : $i]: 182.11/26.71 (subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 (subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 (Y0 = Y1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['49'])). 182.11/26.71 tff('51', plain, 182.11/26.71 ~ (setoftrueEq => 182.11/26.71 (powersetI => 182.11/26.71 (emptyinPowerset => 182.11/26.71 (emptyInPowerset => 182.11/26.71 (powersetE => 182.11/26.71 (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 (in__Cong => 182.11/26.71 (exuE3u => 182.11/26.71 (exu__Cong => 182.11/26.71 (setadjoin__Cong => 182.11/26.71 (powerset__Cong => 182.11/26.71 (setunion__Cong => 182.11/26.71 (omega__Cong => 182.11/26.71 (exuEu => 182.11/26.71 (descr__Cong => 182.11/26.71 (dsetconstr__Cong => 182.11/26.71 (subsetI1 => 182.11/26.71 (eqimpsubset2 => 182.11/26.71 (eqimpsubset1 => 182.11/26.71 (subsetI2 => 182.11/26.71 (emptysetsubset => 182.11/26.71 (subsetE => 182.11/26.71 (subsetE2 => 182.11/26.71 (notsubsetI => 182.11/26.71 (notequalI1 => 182.11/26.71 (notequalI2 => 182.11/26.71 (subsetRefl => 182.11/26.71 (subsetTrans => 182.11/26.71 (setadjoinSub => 182.11/26.71 (setadjoinSub2 => 182.11/26.71 (subset2powerset => 182.11/26.71 (!!((^[Y0 : $i]: 182.11/26.71 (!!(( 182.11/26.71 ^[Y1 : $i]: 182.11/26.71 (subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 (subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 (Y0 = Y1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['50'])). 182.11/26.71 tff('52', plain, 182.11/26.71 ~ (powersetI => 182.11/26.71 (emptyinPowerset => 182.11/26.71 (emptyInPowerset => 182.11/26.71 (powersetE => 182.11/26.71 (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 (in__Cong => 182.11/26.71 (exuE3u => 182.11/26.71 (exu__Cong => 182.11/26.71 (setadjoin__Cong => 182.11/26.71 (powerset__Cong => 182.11/26.71 (setunion__Cong => 182.11/26.71 (omega__Cong => 182.11/26.71 (exuEu => 182.11/26.71 (descr__Cong => 182.11/26.71 (dsetconstr__Cong => 182.11/26.71 (subsetI1 => 182.11/26.71 (eqimpsubset2 => 182.11/26.71 (eqimpsubset1 => 182.11/26.71 (subsetI2 => 182.11/26.71 (emptysetsubset => 182.11/26.71 (subsetE => 182.11/26.71 (subsetE2 => 182.11/26.71 (notsubsetI => 182.11/26.71 (notequalI1 => 182.11/26.71 (notequalI2 => 182.11/26.71 (subsetRefl => 182.11/26.71 (subsetTrans => 182.11/26.71 (setadjoinSub => 182.11/26.71 (setadjoinSub2 => 182.11/26.71 (subset2powerset => 182.11/26.71 (!!((^[Y0 : $i]: 182.11/26.71 ( 182.11/26.71 !!(( 182.11/26.71 ^[Y1 : $i]: 182.11/26.71 (subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 (subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 (Y0 = Y1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['51'])). 182.11/26.71 tff('53', plain, 182.11/26.71 ~ (emptyinPowerset => 182.11/26.71 (emptyInPowerset => 182.11/26.71 (powersetE => 182.11/26.71 (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 (in__Cong => 182.11/26.71 (exuE3u => 182.11/26.71 (exu__Cong => 182.11/26.71 (setadjoin__Cong => 182.11/26.71 (powerset__Cong => 182.11/26.71 (setunion__Cong => 182.11/26.71 (omega__Cong => 182.11/26.71 (exuEu => 182.11/26.71 (descr__Cong => 182.11/26.71 (dsetconstr__Cong => 182.11/26.71 (subsetI1 => 182.11/26.71 (eqimpsubset2 => 182.11/26.71 (eqimpsubset1 => 182.11/26.71 (subsetI2 => 182.11/26.71 (emptysetsubset => 182.11/26.71 (subsetE => 182.11/26.71 (subsetE2 => 182.11/26.71 (notsubsetI => 182.11/26.71 (notequalI1 => 182.11/26.71 (notequalI2 => 182.11/26.71 (subsetRefl => 182.11/26.71 (subsetTrans => 182.11/26.71 (setadjoinSub => 182.11/26.71 (setadjoinSub2 => 182.11/26.71 (subset2powerset => 182.11/26.71 (!!((^[Y0 : $i]: 182.11/26.71 (!!(( 182.11/26.71 ^[Y1 : $i]: 182.11/26.71 (subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 (subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 (Y0 = Y1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['52'])). 182.11/26.71 tff('54', plain, 182.11/26.71 ~ (emptyInPowerset => 182.11/26.71 (powersetE => 182.11/26.71 (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 (in__Cong => 182.11/26.71 (exuE3u => 182.11/26.71 (exu__Cong => 182.11/26.71 (setadjoin__Cong => 182.11/26.71 (powerset__Cong => 182.11/26.71 (setunion__Cong => 182.11/26.71 (omega__Cong => 182.11/26.71 (exuEu => 182.11/26.71 (descr__Cong => 182.11/26.71 (dsetconstr__Cong => 182.11/26.71 (subsetI1 => 182.11/26.71 (eqimpsubset2 => 182.11/26.71 (eqimpsubset1 => 182.11/26.71 (subsetI2 => 182.11/26.71 (emptysetsubset => 182.11/26.71 (subsetE => 182.11/26.71 (subsetE2 => 182.11/26.71 (notsubsetI => 182.11/26.71 (notequalI1 => 182.11/26.71 (notequalI2 => 182.11/26.71 (subsetRefl => 182.11/26.71 (subsetTrans => 182.11/26.71 (setadjoinSub => 182.11/26.71 (setadjoinSub2 => 182.11/26.71 (subset2powerset => 182.11/26.71 (!!((^[Y0 : $i]: 182.11/26.71 (!!(( 182.11/26.71 ^[Y1 : $i]: 182.11/26.71 (subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 (subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 (Y0 = Y1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['53'])). 182.11/26.71 tff('55', plain, 182.11/26.71 ~ (powersetE => 182.11/26.71 (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 (in__Cong => 182.11/26.71 (exuE3u => 182.11/26.71 (exu__Cong => 182.11/26.71 (setadjoin__Cong => 182.11/26.71 (powerset__Cong => 182.11/26.71 (setunion__Cong => 182.11/26.71 (omega__Cong => 182.11/26.71 (exuEu => 182.11/26.71 (descr__Cong => 182.11/26.71 (dsetconstr__Cong => 182.11/26.71 (subsetI1 => 182.11/26.71 (eqimpsubset2 => 182.11/26.71 (eqimpsubset1 => 182.11/26.71 (subsetI2 => 182.11/26.71 (emptysetsubset => 182.11/26.71 (subsetE => 182.11/26.71 (subsetE2 => 182.11/26.71 (notsubsetI => 182.11/26.71 (notequalI1 => 182.11/26.71 (notequalI2 => 182.11/26.71 (subsetRefl => 182.11/26.71 (subsetTrans => 182.11/26.71 (setadjoinSub => 182.11/26.71 (setadjoinSub2 => 182.11/26.71 (subset2powerset => 182.11/26.71 (!!((^[Y0 : $i]: 182.11/26.71 (!!(( 182.11/26.71 ^[Y1 : $i]: 182.11/26.71 ( 182.11/26.71 subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 ( 182.11/26.71 subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 ( 182.11/26.71 Y0 = Y1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['54'])). 182.11/26.71 tff('56', plain, 182.11/26.71 ~ (setunionI => 182.11/26.71 (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 (in__Cong => 182.11/26.71 (exuE3u => 182.11/26.71 (exu__Cong => 182.11/26.71 (setadjoin__Cong => 182.11/26.71 (powerset__Cong => 182.11/26.71 (setunion__Cong => 182.11/26.71 (omega__Cong => 182.11/26.71 (exuEu => 182.11/26.71 (descr__Cong => 182.11/26.71 (dsetconstr__Cong => 182.11/26.71 (subsetI1 => 182.11/26.71 (eqimpsubset2 => 182.11/26.71 (eqimpsubset1 => 182.11/26.71 (subsetI2 => 182.11/26.71 (emptysetsubset => 182.11/26.71 (subsetE => 182.11/26.71 (subsetE2 => 182.11/26.71 (notsubsetI => 182.11/26.71 (notequalI1 => 182.11/26.71 (notequalI2 => 182.11/26.71 (subsetRefl => 182.11/26.71 (subsetTrans => 182.11/26.71 (setadjoinSub => 182.11/26.71 (setadjoinSub2 => 182.11/26.71 (subset2powerset => 182.11/26.71 (!!((^[Y0 : $i]: 182.11/26.71 (!!(( 182.11/26.71 ^[Y1 : $i]: 182.11/26.71 (subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 ( 182.11/26.71 subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 ( 182.11/26.71 Y0 = Y1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['55'])). 182.11/26.71 tff('57', plain, 182.11/26.71 ~ (setunionE => 182.11/26.71 (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 (in__Cong => 182.11/26.71 (exuE3u => 182.11/26.71 (exu__Cong => 182.11/26.71 (setadjoin__Cong => 182.11/26.71 (powerset__Cong => 182.11/26.71 (setunion__Cong => 182.11/26.71 (omega__Cong => 182.11/26.71 (exuEu => 182.11/26.71 (descr__Cong => 182.11/26.71 (dsetconstr__Cong => 182.11/26.71 (subsetI1 => 182.11/26.71 (eqimpsubset2 => 182.11/26.71 (eqimpsubset1 => 182.11/26.71 (subsetI2 => 182.11/26.71 (emptysetsubset => 182.11/26.71 (subsetE => 182.11/26.71 (subsetE2 => 182.11/26.71 (notsubsetI => 182.11/26.71 (notequalI1 => 182.11/26.71 (notequalI2 => 182.11/26.71 (subsetRefl => 182.11/26.71 (subsetTrans => 182.11/26.71 (setadjoinSub => 182.11/26.71 (setadjoinSub2 => 182.11/26.71 (subset2powerset => 182.11/26.71 (!!((^[Y0 : $i]: 182.11/26.71 (!!((^[Y1 : $i]: 182.11/26.71 (subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 (subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 (Y0 = Y1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['56'])). 182.11/26.71 tff('58', plain, 182.11/26.71 ~ (subPowSU => 182.11/26.71 (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 (in__Cong => 182.11/26.71 (exuE3u => 182.11/26.71 (exu__Cong => 182.11/26.71 (setadjoin__Cong => 182.11/26.71 (powerset__Cong => 182.11/26.71 (setunion__Cong => 182.11/26.71 (omega__Cong => 182.11/26.71 (exuEu => 182.11/26.71 (descr__Cong => 182.11/26.71 (dsetconstr__Cong => 182.11/26.71 (subsetI1 => 182.11/26.71 (eqimpsubset2 => 182.11/26.71 (eqimpsubset1 => 182.11/26.71 (subsetI2 => 182.11/26.71 (emptysetsubset => 182.11/26.71 (subsetE => 182.11/26.71 (subsetE2 => 182.11/26.71 (notsubsetI => 182.11/26.71 (notequalI1 => 182.11/26.71 (notequalI2 => 182.11/26.71 (subsetRefl => 182.11/26.71 (subsetTrans => 182.11/26.71 (setadjoinSub => 182.11/26.71 (setadjoinSub2 => 182.11/26.71 (subset2powerset => 182.11/26.71 (!!((^[Y0 : $i]: 182.11/26.71 (!!((^[Y1 : $i]: 182.11/26.71 (subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 (subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 (Y0 = Y1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['57'])). 182.11/26.71 tff('59', plain, 182.11/26.71 ~ (exuE2 => 182.11/26.71 (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 (in__Cong => 182.11/26.71 (exuE3u => 182.11/26.71 (exu__Cong => 182.11/26.71 (setadjoin__Cong => 182.11/26.71 (powerset__Cong => 182.11/26.71 (setunion__Cong => 182.11/26.71 (omega__Cong => 182.11/26.71 (exuEu => 182.11/26.71 (descr__Cong => 182.11/26.71 (dsetconstr__Cong => 182.11/26.71 (subsetI1 => 182.11/26.71 (eqimpsubset2 => 182.11/26.71 (eqimpsubset1 => 182.11/26.71 (subsetI2 => 182.11/26.71 (emptysetsubset => 182.11/26.71 (subsetE => 182.11/26.71 (subsetE2 => 182.11/26.71 (notsubsetI => 182.11/26.71 (notequalI1 => 182.11/26.71 (notequalI2 => 182.11/26.71 (subsetRefl => 182.11/26.71 (subsetTrans => 182.11/26.71 (setadjoinSub => 182.11/26.71 (setadjoinSub2 => 182.11/26.71 (subset2powerset => 182.11/26.71 (!!((^[Y0 : $i]: 182.11/26.71 (!!((^[Y1 : $i]: 182.11/26.71 ( 182.11/26.71 subset( 182.11/26.71 Y0, Y1) => 182.11/26.71 ( 182.11/26.71 subset( 182.11/26.71 Y1, Y0) => 182.11/26.71 ( 182.11/26.71 Y0 = Y1))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.11/26.71 inference('lazy_cnf_imply', [status(thm)], ['58'])). 182.11/26.71 tff('60', plain, 182.11/26.71 ~ (nonemptyImpWitness => 182.11/26.71 (uniqinunit => 182.11/26.71 (notinsingleton => 182.11/26.71 (eqinunit => 182.11/26.71 (singletonsswitch => 182.11/26.71 (upairsetE => 182.11/26.71 (upairsetIL => 182.11/26.71 (upairsetIR => 182.11/26.71 (emptyE1 => 182.11/26.71 (vacuousDall => 182.11/26.71 (quantDeMorgan1 => 182.11/26.71 (quantDeMorgan2 => 182.11/26.71 (quantDeMorgan3 => 182.11/26.71 (quantDeMorgan4 => 182.11/26.71 (prop2setI => 182.11/26.71 (prop2set2propI => 182.11/26.71 (notdexE => 182.11/26.71 (notdallE => 182.11/26.71 (exuI1 => 182.11/26.71 (exuI3 => 182.11/26.71 (exuI2 => 182.11/26.71 (inCongP => 182.11/26.71 (in__Cong => 182.11/26.71 (exuE3u => 182.11/26.71 (exu__Cong => 182.11/26.71 (setadjoin__Cong => 182.11/26.71 (powerset__Cong => 182.11/26.71 (setunion__Cong => 182.11/26.71 (omega__Cong => 182.11/26.71 (exuEu => 182.11/26.71 (descr__Cong => 182.11/26.71 (dsetconstr__Cong => 182.30/26.72 (subsetI1 => 182.30/26.72 (eqimpsubset2 => 182.30/26.72 (eqimpsubset1 => 182.30/26.72 (subsetI2 => 182.30/26.72 (emptysetsubset => 182.30/26.72 (subsetE => 182.30/26.72 (subsetE2 => 182.30/26.72 (notsubsetI => 182.30/26.72 (notequalI1 => 182.30/26.72 (notequalI2 => 182.30/26.72 (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset( 182.30/26.72 Y0, Y1) => 182.30/26.72 ( 182.30/26.72 subset( 182.30/26.72 Y1, Y0) => 182.30/26.72 ( 182.30/26.72 Y0 = Y1)))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['59'])). 182.30/26.72 tff('61', plain, 182.30/26.72 ~ (uniqinunit => 182.30/26.72 (notinsingleton => 182.30/26.72 (eqinunit => 182.30/26.72 (singletonsswitch => 182.30/26.72 (upairsetE => 182.30/26.72 (upairsetIL => 182.30/26.72 (upairsetIR => 182.30/26.72 (emptyE1 => 182.30/26.72 (vacuousDall => 182.30/26.72 (quantDeMorgan1 => 182.30/26.72 (quantDeMorgan2 => 182.30/26.72 (quantDeMorgan3 => 182.30/26.72 (quantDeMorgan4 => 182.30/26.72 (prop2setI => 182.30/26.72 (prop2set2propI => 182.30/26.72 (notdexE => 182.30/26.72 (notdallE => 182.30/26.72 (exuI1 => 182.30/26.72 (exuI3 => 182.30/26.72 (exuI2 => 182.30/26.72 (inCongP => 182.30/26.72 (in__Cong => 182.30/26.72 (exuE3u => 182.30/26.72 (exu__Cong => 182.30/26.72 (setadjoin__Cong => 182.30/26.72 (powerset__Cong => 182.30/26.72 (setunion__Cong => 182.30/26.72 (omega__Cong => 182.30/26.72 (exuEu => 182.30/26.72 (descr__Cong => 182.30/26.72 (dsetconstr__Cong => 182.30/26.72 (subsetI1 => 182.30/26.72 (eqimpsubset2 => 182.30/26.72 (eqimpsubset1 => 182.30/26.72 (subsetI2 => 182.30/26.72 (emptysetsubset => 182.30/26.72 (subsetE => 182.30/26.72 (subsetE2 => 182.30/26.72 (notsubsetI => 182.30/26.72 (notequalI1 => 182.30/26.72 (notequalI2 => 182.30/26.72 (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset( 182.30/26.72 Y0, Y1) => 182.30/26.72 (subset( 182.30/26.72 Y1, Y0) => 182.30/26.72 ( 182.30/26.72 Y0 = Y1))))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['60'])). 182.30/26.72 tff('62', plain, 182.30/26.72 ~ (notinsingleton => 182.30/26.72 (eqinunit => 182.30/26.72 (singletonsswitch => 182.30/26.72 (upairsetE => 182.30/26.72 (upairsetIL => 182.30/26.72 (upairsetIR => 182.30/26.72 (emptyE1 => 182.30/26.72 (vacuousDall => 182.30/26.72 (quantDeMorgan1 => 182.30/26.72 (quantDeMorgan2 => 182.30/26.72 (quantDeMorgan3 => 182.30/26.72 (quantDeMorgan4 => 182.30/26.72 (prop2setI => 182.30/26.72 (prop2set2propI => 182.30/26.72 (notdexE => 182.30/26.72 (notdallE => 182.30/26.72 (exuI1 => 182.30/26.72 (exuI3 => 182.30/26.72 (exuI2 => 182.30/26.72 (inCongP => 182.30/26.72 (in__Cong => 182.30/26.72 (exuE3u => 182.30/26.72 (exu__Cong => 182.30/26.72 (setadjoin__Cong => 182.30/26.72 (powerset__Cong => 182.30/26.72 (setunion__Cong => 182.30/26.72 (omega__Cong => 182.30/26.72 (exuEu => 182.30/26.72 (descr__Cong => 182.30/26.72 (dsetconstr__Cong => 182.30/26.72 (subsetI1 => 182.30/26.72 (eqimpsubset2 => 182.30/26.72 (eqimpsubset1 => 182.30/26.72 (subsetI2 => 182.30/26.72 (emptysetsubset => 182.30/26.72 (subsetE => 182.30/26.72 (subsetE2 => 182.30/26.72 (notsubsetI => 182.30/26.72 (notequalI1 => 182.30/26.72 (notequalI2 => 182.30/26.72 (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, 182.30/26.72 Y1) => 182.30/26.72 (subset( 182.30/26.72 Y1, Y0) => 182.30/26.72 (Y0 = Y1)))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['61'])). 182.30/26.72 tff('63', plain, 182.30/26.72 ~ (eqinunit => 182.30/26.72 (singletonsswitch => 182.30/26.72 (upairsetE => 182.30/26.72 (upairsetIL => 182.30/26.72 (upairsetIR => 182.30/26.72 (emptyE1 => 182.30/26.72 (vacuousDall => 182.30/26.72 (quantDeMorgan1 => 182.30/26.72 (quantDeMorgan2 => 182.30/26.72 (quantDeMorgan3 => 182.30/26.72 (quantDeMorgan4 => 182.30/26.72 (prop2setI => 182.30/26.72 (prop2set2propI => 182.30/26.72 (notdexE => 182.30/26.72 (notdallE => 182.30/26.72 (exuI1 => 182.30/26.72 (exuI3 => 182.30/26.72 (exuI2 => 182.30/26.72 (inCongP => 182.30/26.72 (in__Cong => 182.30/26.72 (exuE3u => 182.30/26.72 (exu__Cong => 182.30/26.72 (setadjoin__Cong => 182.30/26.72 (powerset__Cong => 182.30/26.72 (setunion__Cong => 182.30/26.72 (omega__Cong => 182.30/26.72 (exuEu => 182.30/26.72 (descr__Cong => 182.30/26.72 (dsetconstr__Cong => 182.30/26.72 (subsetI1 => 182.30/26.72 (eqimpsubset2 => 182.30/26.72 (eqimpsubset1 => 182.30/26.72 (subsetI2 => 182.30/26.72 (emptysetsubset => 182.30/26.72 (subsetE => 182.30/26.72 (subsetE2 => 182.30/26.72 (notsubsetI => 182.30/26.72 (notequalI1 => 182.30/26.72 (notequalI2 => 182.30/26.72 (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, 182.30/26.72 Y1) => 182.30/26.72 (subset(Y1, 182.30/26.72 Y0) => 182.30/26.72 (Y0 = Y1))))))))))))))))))))))))))))))))))))))))))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['62'])). 182.30/26.72 tff('64', plain, 182.30/26.72 ~ (singletonsswitch => 182.30/26.72 (upairsetE => 182.30/26.72 (upairsetIL => 182.30/26.72 (upairsetIR => 182.30/26.72 (emptyE1 => 182.30/26.72 (vacuousDall => 182.30/26.72 (quantDeMorgan1 => 182.30/26.72 (quantDeMorgan2 => 182.30/26.72 (quantDeMorgan3 => 182.30/26.72 (quantDeMorgan4 => 182.30/26.72 (prop2setI => 182.30/26.72 (prop2set2propI => 182.30/26.72 (notdexE => 182.30/26.72 (notdallE => 182.30/26.72 (exuI1 => 182.30/26.72 (exuI3 => 182.30/26.72 (exuI2 => 182.30/26.72 (inCongP => 182.30/26.72 (in__Cong => 182.30/26.72 (exuE3u => 182.30/26.72 (exu__Cong => 182.30/26.72 (setadjoin__Cong => 182.30/26.72 (powerset__Cong => 182.30/26.72 (setunion__Cong => 182.30/26.72 (omega__Cong => 182.30/26.72 (exuEu => 182.30/26.72 (descr__Cong => 182.30/26.72 (dsetconstr__Cong => 182.30/26.72 (subsetI1 => 182.30/26.72 (eqimpsubset2 => 182.30/26.72 (eqimpsubset1 => 182.30/26.72 (subsetI2 => 182.30/26.72 (emptysetsubset => 182.30/26.72 (subsetE => 182.30/26.72 (subsetE2 => 182.30/26.72 (notsubsetI => 182.30/26.72 (notequalI1 => 182.30/26.72 (notequalI2 => 182.30/26.72 (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, 182.30/26.72 Y1) => 182.30/26.72 (subset(Y1, 182.30/26.72 Y0) => 182.30/26.72 (Y0 = Y1)))))))))))))))))))))))))))))))))))))))))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['63'])). 182.30/26.72 tff('65', plain, 182.30/26.72 ~ (upairsetE => 182.30/26.72 (upairsetIL => 182.30/26.72 (upairsetIR => 182.30/26.72 (emptyE1 => 182.30/26.72 (vacuousDall => 182.30/26.72 (quantDeMorgan1 => 182.30/26.72 (quantDeMorgan2 => 182.30/26.72 (quantDeMorgan3 => 182.30/26.72 (quantDeMorgan4 => 182.30/26.72 (prop2setI => 182.30/26.72 (prop2set2propI => 182.30/26.72 (notdexE => 182.30/26.72 (notdallE => 182.30/26.72 (exuI1 => 182.30/26.72 (exuI3 => 182.30/26.72 (exuI2 => 182.30/26.72 (inCongP => 182.30/26.72 (in__Cong => 182.30/26.72 (exuE3u => 182.30/26.72 (exu__Cong => 182.30/26.72 (setadjoin__Cong => 182.30/26.72 (powerset__Cong => 182.30/26.72 (setunion__Cong => 182.30/26.72 (omega__Cong => 182.30/26.72 (exuEu => 182.30/26.72 (descr__Cong => 182.30/26.72 (dsetconstr__Cong => 182.30/26.72 (subsetI1 => 182.30/26.72 (eqimpsubset2 => 182.30/26.72 (eqimpsubset1 => 182.30/26.72 (subsetI2 => 182.30/26.72 (emptysetsubset => 182.30/26.72 (subsetE => 182.30/26.72 (subsetE2 => 182.30/26.72 (notsubsetI => 182.30/26.72 (notequalI1 => 182.30/26.72 (notequalI2 => 182.30/26.72 (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => 182.30/26.72 (subset(Y1, 182.30/26.72 Y0) => 182.30/26.72 (Y0 = Y1))))))))))))))))))))))))))))))))))))))))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['64'])). 182.30/26.72 tff('66', plain, 182.30/26.72 ~ (upairsetIL => 182.30/26.72 (upairsetIR => 182.30/26.72 (emptyE1 => 182.30/26.72 (vacuousDall => 182.30/26.72 (quantDeMorgan1 => 182.30/26.72 (quantDeMorgan2 => 182.30/26.72 (quantDeMorgan3 => 182.30/26.72 (quantDeMorgan4 => 182.30/26.72 (prop2setI => 182.30/26.72 (prop2set2propI => 182.30/26.72 (notdexE => 182.30/26.72 (notdallE => 182.30/26.72 (exuI1 => 182.30/26.72 (exuI3 => 182.30/26.72 (exuI2 => 182.30/26.72 (inCongP => 182.30/26.72 (in__Cong => 182.30/26.72 (exuE3u => 182.30/26.72 (exu__Cong => 182.30/26.72 (setadjoin__Cong => 182.30/26.72 (powerset__Cong => 182.30/26.72 (setunion__Cong => 182.30/26.72 (omega__Cong => 182.30/26.72 (exuEu => 182.30/26.72 (descr__Cong => 182.30/26.72 (dsetconstr__Cong => 182.30/26.72 (subsetI1 => 182.30/26.72 (eqimpsubset2 => 182.30/26.72 (eqimpsubset1 => 182.30/26.72 (subsetI2 => 182.30/26.72 (emptysetsubset => 182.30/26.72 (subsetE => 182.30/26.72 (subsetE2 => 182.30/26.72 (notsubsetI => 182.30/26.72 (notequalI1 => 182.30/26.72 (notequalI2 => 182.30/26.72 (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => 182.30/26.72 (subset(Y1, Y0) => 182.30/26.72 (Y0 = Y1)))))))))))))))))))))))))))))))))))))))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['65'])). 182.30/26.72 tff('67', plain, 182.30/26.72 ~ (upairsetIR => 182.30/26.72 (emptyE1 => 182.30/26.72 (vacuousDall => 182.30/26.72 (quantDeMorgan1 => 182.30/26.72 (quantDeMorgan2 => 182.30/26.72 (quantDeMorgan3 => 182.30/26.72 (quantDeMorgan4 => 182.30/26.72 (prop2setI => 182.30/26.72 (prop2set2propI => 182.30/26.72 (notdexE => 182.30/26.72 (notdallE => 182.30/26.72 (exuI1 => 182.30/26.72 (exuI3 => 182.30/26.72 (exuI2 => 182.30/26.72 (inCongP => 182.30/26.72 (in__Cong => 182.30/26.72 (exuE3u => 182.30/26.72 (exu__Cong => 182.30/26.72 (setadjoin__Cong => 182.30/26.72 (powerset__Cong => 182.30/26.72 (setunion__Cong => 182.30/26.72 (omega__Cong => 182.30/26.72 (exuEu => 182.30/26.72 (descr__Cong => 182.30/26.72 (dsetconstr__Cong => 182.30/26.72 (subsetI1 => 182.30/26.72 (eqimpsubset2 => 182.30/26.72 (eqimpsubset1 => 182.30/26.72 (subsetI2 => 182.30/26.72 (emptysetsubset => 182.30/26.72 (subsetE => 182.30/26.72 (subsetE2 => 182.30/26.72 (notsubsetI => 182.30/26.72 (notequalI1 => 182.30/26.72 (notequalI2 => 182.30/26.72 (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => 182.30/26.72 (subset(Y1, Y0) => 182.30/26.72 (Y0 = Y1))))))))))))))))))))))))))))))))))))))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['66'])). 182.30/26.72 tff('68', plain, 182.30/26.72 ~ (emptyE1 => 182.30/26.72 (vacuousDall => 182.30/26.72 (quantDeMorgan1 => 182.30/26.72 (quantDeMorgan2 => 182.30/26.72 (quantDeMorgan3 => 182.30/26.72 (quantDeMorgan4 => 182.30/26.72 (prop2setI => 182.30/26.72 (prop2set2propI => 182.30/26.72 (notdexE => 182.30/26.72 (notdallE => 182.30/26.72 (exuI1 => 182.30/26.72 (exuI3 => 182.30/26.72 (exuI2 => 182.30/26.72 (inCongP => 182.30/26.72 (in__Cong => 182.30/26.72 (exuE3u => 182.30/26.72 (exu__Cong => 182.30/26.72 (setadjoin__Cong => 182.30/26.72 (powerset__Cong => 182.30/26.72 (setunion__Cong => 182.30/26.72 (omega__Cong => 182.30/26.72 (exuEu => 182.30/26.72 (descr__Cong => 182.30/26.72 (dsetconstr__Cong => 182.30/26.72 (subsetI1 => 182.30/26.72 (eqimpsubset2 => 182.30/26.72 (eqimpsubset1 => 182.30/26.72 (subsetI2 => 182.30/26.72 (emptysetsubset => 182.30/26.72 (subsetE => 182.30/26.72 (subsetE2 => 182.30/26.72 (notsubsetI => 182.30/26.72 (notequalI1 => 182.30/26.72 (notequalI2 => 182.30/26.72 (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => 182.30/26.72 (subset(Y1, Y0) => 182.30/26.72 (Y0 = Y1)))))))))))))))))))))))))))))))))))))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['67'])). 182.30/26.72 tff('69', plain, 182.30/26.72 ~ (vacuousDall => 182.30/26.72 (quantDeMorgan1 => 182.30/26.72 (quantDeMorgan2 => 182.30/26.72 (quantDeMorgan3 => 182.30/26.72 (quantDeMorgan4 => 182.30/26.72 (prop2setI => 182.30/26.72 (prop2set2propI => 182.30/26.72 (notdexE => 182.30/26.72 (notdallE => 182.30/26.72 (exuI1 => 182.30/26.72 (exuI3 => 182.30/26.72 (exuI2 => 182.30/26.72 (inCongP => 182.30/26.72 (in__Cong => 182.30/26.72 (exuE3u => 182.30/26.72 (exu__Cong => 182.30/26.72 (setadjoin__Cong => 182.30/26.72 (powerset__Cong => 182.30/26.72 (setunion__Cong => 182.30/26.72 (omega__Cong => 182.30/26.72 (exuEu => 182.30/26.72 (descr__Cong => 182.30/26.72 (dsetconstr__Cong => 182.30/26.72 (subsetI1 => 182.30/26.72 (eqimpsubset2 => 182.30/26.72 (eqimpsubset1 => 182.30/26.72 (subsetI2 => 182.30/26.72 (emptysetsubset => 182.30/26.72 (subsetE => 182.30/26.72 (subsetE2 => 182.30/26.72 (notsubsetI => 182.30/26.72 (notequalI1 => 182.30/26.72 (notequalI2 => 182.30/26.72 (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => 182.30/26.72 (subset(Y1, Y0) => 182.30/26.72 (Y0 = Y1))))))))))))))))))))))))))))))))))))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['68'])). 182.30/26.72 tff('70', plain, 182.30/26.72 ~ (quantDeMorgan1 => 182.30/26.72 (quantDeMorgan2 => 182.30/26.72 (quantDeMorgan3 => 182.30/26.72 (quantDeMorgan4 => 182.30/26.72 (prop2setI => 182.30/26.72 (prop2set2propI => 182.30/26.72 (notdexE => 182.30/26.72 (notdallE => 182.30/26.72 (exuI1 => 182.30/26.72 (exuI3 => 182.30/26.72 (exuI2 => 182.30/26.72 (inCongP => 182.30/26.72 (in__Cong => 182.30/26.72 (exuE3u => 182.30/26.72 (exu__Cong => 182.30/26.72 (setadjoin__Cong => 182.30/26.72 (powerset__Cong => 182.30/26.72 (setunion__Cong => 182.30/26.72 (omega__Cong => 182.30/26.72 (exuEu => 182.30/26.72 (descr__Cong => 182.30/26.72 (dsetconstr__Cong => 182.30/26.72 (subsetI1 => 182.30/26.72 (eqimpsubset2 => 182.30/26.72 (eqimpsubset1 => 182.30/26.72 (subsetI2 => 182.30/26.72 (emptysetsubset => 182.30/26.72 (subsetE => 182.30/26.72 (subsetE2 => 182.30/26.72 (notsubsetI => 182.30/26.72 (notequalI1 => 182.30/26.72 (notequalI2 => 182.30/26.72 (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => 182.30/26.72 (subset(Y1, Y0) => 182.30/26.72 (Y0 = Y1)))))))))))))))))))))))))))))))))))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['69'])). 182.30/26.72 tff('71', plain, 182.30/26.72 ~ (quantDeMorgan2 => 182.30/26.72 (quantDeMorgan3 => 182.30/26.72 (quantDeMorgan4 => 182.30/26.72 (prop2setI => 182.30/26.72 (prop2set2propI => 182.30/26.72 (notdexE => 182.30/26.72 (notdallE => 182.30/26.72 (exuI1 => 182.30/26.72 (exuI3 => 182.30/26.72 (exuI2 => 182.30/26.72 (inCongP => 182.30/26.72 (in__Cong => 182.30/26.72 (exuE3u => 182.30/26.72 (exu__Cong => 182.30/26.72 (setadjoin__Cong => 182.30/26.72 (powerset__Cong => 182.30/26.72 (setunion__Cong => 182.30/26.72 (omega__Cong => 182.30/26.72 (exuEu => 182.30/26.72 (descr__Cong => 182.30/26.72 (dsetconstr__Cong => 182.30/26.72 (subsetI1 => 182.30/26.72 (eqimpsubset2 => 182.30/26.72 (eqimpsubset1 => 182.30/26.72 (subsetI2 => 182.30/26.72 (emptysetsubset => 182.30/26.72 (subsetE => 182.30/26.72 (subsetE2 => 182.30/26.72 (notsubsetI => 182.30/26.72 (notequalI1 => 182.30/26.72 (notequalI2 => 182.30/26.72 (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => 182.30/26.72 (subset(Y1, Y0) => 182.30/26.72 (Y0 = Y1))))))))))))))))))))))))))))))))))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['70'])). 182.30/26.72 tff('72', plain, 182.30/26.72 ~ (quantDeMorgan3 => 182.30/26.72 (quantDeMorgan4 => 182.30/26.72 (prop2setI => 182.30/26.72 (prop2set2propI => 182.30/26.72 (notdexE => 182.30/26.72 (notdallE => 182.30/26.72 (exuI1 => 182.30/26.72 (exuI3 => 182.30/26.72 (exuI2 => 182.30/26.72 (inCongP => 182.30/26.72 (in__Cong => 182.30/26.72 (exuE3u => 182.30/26.72 (exu__Cong => 182.30/26.72 (setadjoin__Cong => 182.30/26.72 (powerset__Cong => 182.30/26.72 (setunion__Cong => 182.30/26.72 (omega__Cong => 182.30/26.72 (exuEu => 182.30/26.72 (descr__Cong => 182.30/26.72 (dsetconstr__Cong => 182.30/26.72 (subsetI1 => 182.30/26.72 (eqimpsubset2 => 182.30/26.72 (eqimpsubset1 => 182.30/26.72 (subsetI2 => 182.30/26.72 (emptysetsubset => 182.30/26.72 (subsetE => 182.30/26.72 (subsetE2 => 182.30/26.72 (notsubsetI => 182.30/26.72 (notequalI1 => 182.30/26.72 (notequalI2 => 182.30/26.72 (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => 182.30/26.72 (subset(Y1, Y0) => 182.30/26.72 (Y0 = Y1)))))))))))))))))))))))))))))))))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['71'])). 182.30/26.72 tff('73', plain, 182.30/26.72 ~ (quantDeMorgan4 => 182.30/26.72 (prop2setI => 182.30/26.72 (prop2set2propI => 182.30/26.72 (notdexE => 182.30/26.72 (notdallE => 182.30/26.72 (exuI1 => 182.30/26.72 (exuI3 => 182.30/26.72 (exuI2 => 182.30/26.72 (inCongP => 182.30/26.72 (in__Cong => 182.30/26.72 (exuE3u => 182.30/26.72 (exu__Cong => 182.30/26.72 (setadjoin__Cong => 182.30/26.72 (powerset__Cong => 182.30/26.72 (setunion__Cong => 182.30/26.72 (omega__Cong => 182.30/26.72 (exuEu => 182.30/26.72 (descr__Cong => 182.30/26.72 (dsetconstr__Cong => 182.30/26.72 (subsetI1 => 182.30/26.72 (eqimpsubset2 => 182.30/26.72 (eqimpsubset1 => 182.30/26.72 (subsetI2 => 182.30/26.72 (emptysetsubset => 182.30/26.72 (subsetE => 182.30/26.72 (subsetE2 => 182.30/26.72 (notsubsetI => 182.30/26.72 (notequalI1 => 182.30/26.72 (notequalI2 => 182.30/26.72 (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => 182.30/26.72 (subset(Y1, Y0) => 182.30/26.72 (Y0 = Y1))))))))))))))))))))))))))))))))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['72'])). 182.30/26.72 tff('74', plain, 182.30/26.72 ~ (prop2setI => 182.30/26.72 (prop2set2propI => 182.30/26.72 (notdexE => 182.30/26.72 (notdallE => 182.30/26.72 (exuI1 => 182.30/26.72 (exuI3 => 182.30/26.72 (exuI2 => 182.30/26.72 (inCongP => 182.30/26.72 (in__Cong => 182.30/26.72 (exuE3u => 182.30/26.72 (exu__Cong => 182.30/26.72 (setadjoin__Cong => 182.30/26.72 (powerset__Cong => 182.30/26.72 (setunion__Cong => 182.30/26.72 (omega__Cong => 182.30/26.72 (exuEu => 182.30/26.72 (descr__Cong => 182.30/26.72 (dsetconstr__Cong => 182.30/26.72 (subsetI1 => 182.30/26.72 (eqimpsubset2 => 182.30/26.72 (eqimpsubset1 => 182.30/26.72 (subsetI2 => 182.30/26.72 (emptysetsubset => 182.30/26.72 (subsetE => 182.30/26.72 (subsetE2 => 182.30/26.72 (notsubsetI => 182.30/26.72 (notequalI1 => 182.30/26.72 (notequalI2 => 182.30/26.72 (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => 182.30/26.72 (subset(Y1, Y0) => 182.30/26.72 (Y0 = Y1)))))))))))))))))))))))))))))))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['73'])). 182.30/26.72 tff('75', plain, 182.30/26.72 ~ (prop2set2propI => 182.30/26.72 (notdexE => 182.30/26.72 (notdallE => 182.30/26.72 (exuI1 => 182.30/26.72 (exuI3 => 182.30/26.72 (exuI2 => 182.30/26.72 (inCongP => 182.30/26.72 (in__Cong => 182.30/26.72 (exuE3u => 182.30/26.72 (exu__Cong => 182.30/26.72 (setadjoin__Cong => 182.30/26.72 (powerset__Cong => 182.30/26.72 (setunion__Cong => 182.30/26.72 (omega__Cong => 182.30/26.72 (exuEu => 182.30/26.72 (descr__Cong => 182.30/26.72 (dsetconstr__Cong => 182.30/26.72 (subsetI1 => 182.30/26.72 (eqimpsubset2 => 182.30/26.72 (eqimpsubset1 => 182.30/26.72 (subsetI2 => 182.30/26.72 (emptysetsubset => 182.30/26.72 (subsetE => 182.30/26.72 (subsetE2 => 182.30/26.72 (notsubsetI => 182.30/26.72 (notequalI1 => 182.30/26.72 (notequalI2 => 182.30/26.72 (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => 182.30/26.72 (subset(Y1, Y0) => 182.30/26.72 (Y0 = Y1))))))))))))))))))))))))))))))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['74'])). 182.30/26.72 tff('76', plain, 182.30/26.72 ~ (notdexE => 182.30/26.72 (notdallE => 182.30/26.72 (exuI1 => 182.30/26.72 (exuI3 => 182.30/26.72 (exuI2 => 182.30/26.72 (inCongP => 182.30/26.72 (in__Cong => 182.30/26.72 (exuE3u => 182.30/26.72 (exu__Cong => 182.30/26.72 (setadjoin__Cong => 182.30/26.72 (powerset__Cong => 182.30/26.72 (setunion__Cong => 182.30/26.72 (omega__Cong => 182.30/26.72 (exuEu => 182.30/26.72 (descr__Cong => 182.30/26.72 (dsetconstr__Cong => 182.30/26.72 (subsetI1 => 182.30/26.72 (eqimpsubset2 => 182.30/26.72 (eqimpsubset1 => 182.30/26.72 (subsetI2 => 182.30/26.72 (emptysetsubset => 182.30/26.72 (subsetE => 182.30/26.72 (subsetE2 => 182.30/26.72 (notsubsetI => 182.30/26.72 (notequalI1 => 182.30/26.72 (notequalI2 => 182.30/26.72 (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => 182.30/26.72 (subset(Y1, Y0) => 182.30/26.72 (Y0 = Y1)))))))))))))))))))))))))))))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['75'])). 182.30/26.72 tff('77', plain, 182.30/26.72 ~ (notdallE => 182.30/26.72 (exuI1 => 182.30/26.72 (exuI3 => 182.30/26.72 (exuI2 => 182.30/26.72 (inCongP => 182.30/26.72 (in__Cong => 182.30/26.72 (exuE3u => 182.30/26.72 (exu__Cong => 182.30/26.72 (setadjoin__Cong => 182.30/26.72 (powerset__Cong => 182.30/26.72 (setunion__Cong => 182.30/26.72 (omega__Cong => 182.30/26.72 (exuEu => 182.30/26.72 (descr__Cong => 182.30/26.72 (dsetconstr__Cong => 182.30/26.72 (subsetI1 => 182.30/26.72 (eqimpsubset2 => 182.30/26.72 (eqimpsubset1 => 182.30/26.72 (subsetI2 => 182.30/26.72 (emptysetsubset => 182.30/26.72 (subsetE => 182.30/26.72 (subsetE2 => 182.30/26.72 (notsubsetI => 182.30/26.72 (notequalI1 => 182.30/26.72 (notequalI2 => 182.30/26.72 (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => 182.30/26.72 (subset(Y1, Y0) => 182.30/26.72 (Y0 = Y1))))))))))))))))))))))))))))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['76'])). 182.30/26.72 tff('78', plain, 182.30/26.72 ~ (exuI1 => 182.30/26.72 (exuI3 => 182.30/26.72 (exuI2 => 182.30/26.72 (inCongP => 182.30/26.72 (in__Cong => 182.30/26.72 (exuE3u => 182.30/26.72 (exu__Cong => 182.30/26.72 (setadjoin__Cong => 182.30/26.72 (powerset__Cong => 182.30/26.72 (setunion__Cong => 182.30/26.72 (omega__Cong => 182.30/26.72 (exuEu => 182.30/26.72 (descr__Cong => 182.30/26.72 (dsetconstr__Cong => 182.30/26.72 (subsetI1 => 182.30/26.72 (eqimpsubset2 => 182.30/26.72 (eqimpsubset1 => 182.30/26.72 (subsetI2 => 182.30/26.72 (emptysetsubset => 182.30/26.72 (subsetE => 182.30/26.72 (subsetE2 => 182.30/26.72 (notsubsetI => 182.30/26.72 (notequalI1 => 182.30/26.72 (notequalI2 => 182.30/26.72 (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => 182.30/26.72 (subset(Y1, Y0) => 182.30/26.72 (Y0 = Y1)))))))))))))))))))))))))))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['77'])). 182.30/26.72 tff('79', plain, 182.30/26.72 ~ (exuI3 => 182.30/26.72 (exuI2 => 182.30/26.72 (inCongP => 182.30/26.72 (in__Cong => 182.30/26.72 (exuE3u => 182.30/26.72 (exu__Cong => 182.30/26.72 (setadjoin__Cong => 182.30/26.72 (powerset__Cong => 182.30/26.72 (setunion__Cong => 182.30/26.72 (omega__Cong => 182.30/26.72 (exuEu => 182.30/26.72 (descr__Cong => 182.30/26.72 (dsetconstr__Cong => 182.30/26.72 (subsetI1 => 182.30/26.72 (eqimpsubset2 => 182.30/26.72 (eqimpsubset1 => 182.30/26.72 (subsetI2 => 182.30/26.72 (emptysetsubset => 182.30/26.72 (subsetE => 182.30/26.72 (subsetE2 => 182.30/26.72 (notsubsetI => 182.30/26.72 (notequalI1 => 182.30/26.72 (notequalI2 => 182.30/26.72 (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => 182.30/26.72 (subset(Y1, Y0) => (Y0 = Y1))))))))))))))))))))))))))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['78'])). 182.30/26.72 tff('80', plain, 182.30/26.72 ~ (exuI2 => 182.30/26.72 (inCongP => 182.30/26.72 (in__Cong => 182.30/26.72 (exuE3u => 182.30/26.72 (exu__Cong => 182.30/26.72 (setadjoin__Cong => 182.30/26.72 (powerset__Cong => 182.30/26.72 (setunion__Cong => 182.30/26.72 (omega__Cong => 182.30/26.72 (exuEu => 182.30/26.72 (descr__Cong => 182.30/26.72 (dsetconstr__Cong => 182.30/26.72 (subsetI1 => 182.30/26.72 (eqimpsubset2 => 182.30/26.72 (eqimpsubset1 => 182.30/26.72 (subsetI2 => 182.30/26.72 (emptysetsubset => 182.30/26.72 (subsetE => 182.30/26.72 (subsetE2 => 182.30/26.72 (notsubsetI => 182.30/26.72 (notequalI1 => 182.30/26.72 (notequalI2 => 182.30/26.72 (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => 182.30/26.72 (subset(Y1, Y0) => (Y0 = Y1)))))))))))))))))))))))))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['79'])). 182.30/26.72 tff('81', plain, 182.30/26.72 ~ (inCongP => 182.30/26.72 (in__Cong => 182.30/26.72 (exuE3u => 182.30/26.72 (exu__Cong => 182.30/26.72 (setadjoin__Cong => 182.30/26.72 (powerset__Cong => 182.30/26.72 (setunion__Cong => 182.30/26.72 (omega__Cong => 182.30/26.72 (exuEu => 182.30/26.72 (descr__Cong => 182.30/26.72 (dsetconstr__Cong => 182.30/26.72 (subsetI1 => 182.30/26.72 (eqimpsubset2 => 182.30/26.72 (eqimpsubset1 => 182.30/26.72 (subsetI2 => 182.30/26.72 (emptysetsubset => 182.30/26.72 (subsetE => 182.30/26.72 (subsetE2 => 182.30/26.72 (notsubsetI => 182.30/26.72 (notequalI1 => 182.30/26.72 (notequalI2 => 182.30/26.72 (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => 182.30/26.72 (subset(Y1, Y0) => (Y0 = Y1))))))))))))))))))))))))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['80'])). 182.30/26.72 tff('82', plain, 182.30/26.72 ~ (in__Cong => 182.30/26.72 (exuE3u => 182.30/26.72 (exu__Cong => 182.30/26.72 (setadjoin__Cong => 182.30/26.72 (powerset__Cong => 182.30/26.72 (setunion__Cong => 182.30/26.72 (omega__Cong => 182.30/26.72 (exuEu => 182.30/26.72 (descr__Cong => 182.30/26.72 (dsetconstr__Cong => 182.30/26.72 (subsetI1 => 182.30/26.72 (eqimpsubset2 => 182.30/26.72 (eqimpsubset1 => 182.30/26.72 (subsetI2 => 182.30/26.72 (emptysetsubset => 182.30/26.72 (subsetE => 182.30/26.72 (subsetE2 => 182.30/26.72 (notsubsetI => 182.30/26.72 (notequalI1 => 182.30/26.72 (notequalI2 => 182.30/26.72 (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => 182.30/26.72 (subset(Y1, Y0) => (Y0 = Y1)))))))))))))))))))))))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['81'])). 182.30/26.72 tff('83', plain, 182.30/26.72 ~ (exuE3u => 182.30/26.72 (exu__Cong => 182.30/26.72 (setadjoin__Cong => 182.30/26.72 (powerset__Cong => 182.30/26.72 (setunion__Cong => 182.30/26.72 (omega__Cong => 182.30/26.72 (exuEu => 182.30/26.72 (descr__Cong => 182.30/26.72 (dsetconstr__Cong => 182.30/26.72 (subsetI1 => 182.30/26.72 (eqimpsubset2 => 182.30/26.72 (eqimpsubset1 => 182.30/26.72 (subsetI2 => 182.30/26.72 (emptysetsubset => 182.30/26.72 (subsetE => 182.30/26.72 (subsetE2 => 182.30/26.72 (notsubsetI => 182.30/26.72 (notequalI1 => 182.30/26.72 (notequalI2 => 182.30/26.72 (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => 182.30/26.72 (subset(Y1, Y0) => (Y0 = Y1))))))))))))))))))))))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['82'])). 182.30/26.72 tff('84', plain, 182.30/26.72 ~ (exu__Cong => 182.30/26.72 (setadjoin__Cong => 182.30/26.72 (powerset__Cong => 182.30/26.72 (setunion__Cong => 182.30/26.72 (omega__Cong => 182.30/26.72 (exuEu => 182.30/26.72 (descr__Cong => 182.30/26.72 (dsetconstr__Cong => 182.30/26.72 (subsetI1 => 182.30/26.72 (eqimpsubset2 => 182.30/26.72 (eqimpsubset1 => 182.30/26.72 (subsetI2 => 182.30/26.72 (emptysetsubset => 182.30/26.72 (subsetE => 182.30/26.72 (subsetE2 => 182.30/26.72 (notsubsetI => 182.30/26.72 (notequalI1 => 182.30/26.72 (notequalI2 => 182.30/26.72 (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => 182.30/26.72 (subset(Y1, Y0) => (Y0 = Y1)))))))))))))))))))))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['83'])). 182.30/26.72 tff('85', plain, 182.30/26.72 ~ (setadjoin__Cong => 182.30/26.72 (powerset__Cong => 182.30/26.72 (setunion__Cong => 182.30/26.72 (omega__Cong => 182.30/26.72 (exuEu => 182.30/26.72 (descr__Cong => 182.30/26.72 (dsetconstr__Cong => 182.30/26.72 (subsetI1 => 182.30/26.72 (eqimpsubset2 => 182.30/26.72 (eqimpsubset1 => 182.30/26.72 (subsetI2 => 182.30/26.72 (emptysetsubset => 182.30/26.72 (subsetE => 182.30/26.72 (subsetE2 => 182.30/26.72 (notsubsetI => 182.30/26.72 (notequalI1 => 182.30/26.72 (notequalI2 => 182.30/26.72 (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => 182.30/26.72 (subset(Y1, Y0) => (Y0 = Y1))))))))))))))))))))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['84'])). 182.30/26.72 tff('86', plain, 182.30/26.72 ~ (powerset__Cong => 182.30/26.72 (setunion__Cong => 182.30/26.72 (omega__Cong => 182.30/26.72 (exuEu => 182.30/26.72 (descr__Cong => 182.30/26.72 (dsetconstr__Cong => 182.30/26.72 (subsetI1 => 182.30/26.72 (eqimpsubset2 => 182.30/26.72 (eqimpsubset1 => 182.30/26.72 (subsetI2 => 182.30/26.72 (emptysetsubset => 182.30/26.72 (subsetE => 182.30/26.72 (subsetE2 => 182.30/26.72 (notsubsetI => 182.30/26.72 (notequalI1 => 182.30/26.72 (notequalI2 => 182.30/26.72 (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => 182.30/26.72 (subset(Y1, Y0) => (Y0 = Y1)))))))))))))))))))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['85'])). 182.30/26.72 tff('87', plain, 182.30/26.72 ~ (setunion__Cong => 182.30/26.72 (omega__Cong => 182.30/26.72 (exuEu => 182.30/26.72 (descr__Cong => 182.30/26.72 (dsetconstr__Cong => 182.30/26.72 (subsetI1 => 182.30/26.72 (eqimpsubset2 => 182.30/26.72 (eqimpsubset1 => 182.30/26.72 (subsetI2 => 182.30/26.72 (emptysetsubset => 182.30/26.72 (subsetE => 182.30/26.72 (subsetE2 => 182.30/26.72 (notsubsetI => 182.30/26.72 (notequalI1 => 182.30/26.72 (notequalI2 => 182.30/26.72 (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => 182.30/26.72 (subset(Y1, Y0) => (Y0 = Y1))))))))))))))))))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['86'])). 182.30/26.72 tff('88', plain, 182.30/26.72 ~ (omega__Cong => 182.30/26.72 (exuEu => 182.30/26.72 (descr__Cong => 182.30/26.72 (dsetconstr__Cong => 182.30/26.72 (subsetI1 => 182.30/26.72 (eqimpsubset2 => 182.30/26.72 (eqimpsubset1 => 182.30/26.72 (subsetI2 => 182.30/26.72 (emptysetsubset => 182.30/26.72 (subsetE => 182.30/26.72 (subsetE2 => 182.30/26.72 (notsubsetI => 182.30/26.72 (notequalI1 => 182.30/26.72 (notequalI2 => 182.30/26.72 (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => 182.30/26.72 (subset(Y1, Y0) => (Y0 = Y1)))))))))))))))))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['87'])). 182.30/26.72 tff('89', plain, 182.30/26.72 ~ (exuEu => 182.30/26.72 (descr__Cong => 182.30/26.72 (dsetconstr__Cong => 182.30/26.72 (subsetI1 => 182.30/26.72 (eqimpsubset2 => 182.30/26.72 (eqimpsubset1 => 182.30/26.72 (subsetI2 => 182.30/26.72 (emptysetsubset => 182.30/26.72 (subsetE => 182.30/26.72 (subsetE2 => 182.30/26.72 (notsubsetI => 182.30/26.72 (notequalI1 => 182.30/26.72 (notequalI2 => 182.30/26.72 (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => 182.30/26.72 (subset(Y1, Y0) => (Y0 = Y1))))))))))))))))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['88'])). 182.30/26.72 tff('90', plain, 182.30/26.72 ~ (descr__Cong => 182.30/26.72 (dsetconstr__Cong => 182.30/26.72 (subsetI1 => 182.30/26.72 (eqimpsubset2 => 182.30/26.72 (eqimpsubset1 => 182.30/26.72 (subsetI2 => 182.30/26.72 (emptysetsubset => 182.30/26.72 (subsetE => 182.30/26.72 (subsetE2 => 182.30/26.72 (notsubsetI => 182.30/26.72 (notequalI1 => 182.30/26.72 (notequalI2 => 182.30/26.72 (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => 182.30/26.72 (subset(Y1, Y0) => (Y0 = Y1)))))))))))))))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['89'])). 182.30/26.72 tff('91', plain, 182.30/26.72 ~ (dsetconstr__Cong => 182.30/26.72 (subsetI1 => 182.30/26.72 (eqimpsubset2 => 182.30/26.72 (eqimpsubset1 => 182.30/26.72 (subsetI2 => 182.30/26.72 (emptysetsubset => 182.30/26.72 (subsetE => 182.30/26.72 (subsetE2 => 182.30/26.72 (notsubsetI => 182.30/26.72 (notequalI1 => 182.30/26.72 (notequalI2 => 182.30/26.72 (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => 182.30/26.72 (subset(Y1, Y0) => (Y0 = Y1))))))))))))))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['90'])). 182.30/26.72 tff('92', plain, 182.30/26.72 ~ (subsetI1 => 182.30/26.72 (eqimpsubset2 => 182.30/26.72 (eqimpsubset1 => 182.30/26.72 (subsetI2 => 182.30/26.72 (emptysetsubset => 182.30/26.72 (subsetE => 182.30/26.72 (subsetE2 => 182.30/26.72 (notsubsetI => 182.30/26.72 (notequalI1 => 182.30/26.72 (notequalI2 => 182.30/26.72 (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => 182.30/26.72 (subset(Y1, Y0) => (Y0 = Y1)))))))))))))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['91'])). 182.30/26.72 tff('93', plain, 182.30/26.72 ~ (eqimpsubset2 => 182.30/26.72 (eqimpsubset1 => 182.30/26.72 (subsetI2 => 182.30/26.72 (emptysetsubset => 182.30/26.72 (subsetE => 182.30/26.72 (subsetE2 => 182.30/26.72 (notsubsetI => 182.30/26.72 (notequalI1 => 182.30/26.72 (notequalI2 => 182.30/26.72 (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => 182.30/26.72 (subset(Y1, Y0) => (Y0 = Y1))))))))))))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['92'])). 182.30/26.72 tff('94', plain, 182.30/26.72 ~ (eqimpsubset1 => 182.30/26.72 (subsetI2 => 182.30/26.72 (emptysetsubset => 182.30/26.72 (subsetE => 182.30/26.72 (subsetE2 => 182.30/26.72 (notsubsetI => 182.30/26.72 (notequalI1 => 182.30/26.72 (notequalI2 => 182.30/26.72 (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => 182.30/26.72 (subset(Y1, Y0) => (Y0 = Y1)))))))))))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['93'])). 182.30/26.72 tff('95', plain, 182.30/26.72 ~ (subsetI2 => 182.30/26.72 (emptysetsubset => 182.30/26.72 (subsetE => 182.30/26.72 (subsetE2 => 182.30/26.72 (notsubsetI => 182.30/26.72 (notequalI1 => 182.30/26.72 (notequalI2 => 182.30/26.72 (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => 182.30/26.72 (subset(Y1, Y0) => (Y0 = Y1))))))))))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['94'])). 182.30/26.72 tff('96', plain, 182.30/26.72 ~ (emptysetsubset => 182.30/26.72 (subsetE => 182.30/26.72 (subsetE2 => 182.30/26.72 (notsubsetI => 182.30/26.72 (notequalI1 => 182.30/26.72 (notequalI2 => 182.30/26.72 (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => 182.30/26.72 (subset(Y1, Y0) => (Y0 = Y1)))))))))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['95'])). 182.30/26.72 tff('97', plain, 182.30/26.72 ~ (subsetE => 182.30/26.72 (subsetE2 => 182.30/26.72 (notsubsetI => 182.30/26.72 (notequalI1 => 182.30/26.72 (notequalI2 => 182.30/26.72 (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => 182.30/26.72 (subset(Y1, Y0) => (Y0 = Y1))))))))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['96'])). 182.30/26.72 tff('98', plain, 182.30/26.72 ~ (subsetE2 => 182.30/26.72 (notsubsetI => 182.30/26.72 (notequalI1 => 182.30/26.72 (notequalI2 => 182.30/26.72 (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => (subset(Y1, Y0) => (Y0 = Y1)))))))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['97'])). 182.30/26.72 tff('99', plain, 182.30/26.72 ~ (notsubsetI => 182.30/26.72 (notequalI1 => 182.30/26.72 (notequalI2 => 182.30/26.72 (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => (subset(Y1, Y0) => (Y0 = Y1))))))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['98'])). 182.30/26.72 tff('100', plain, 182.30/26.72 ~ (notequalI1 => 182.30/26.72 (notequalI2 => 182.30/26.72 (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => (subset(Y1, Y0) => (Y0 = Y1)))))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['99'])). 182.30/26.72 tff('101', plain, 182.30/26.72 ~ (notequalI2 => 182.30/26.72 (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => (subset(Y1, Y0) => (Y0 = Y1))))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['100'])). 182.30/26.72 tff('102', plain, 182.30/26.72 ~ (subsetRefl => 182.30/26.72 (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => (subset(Y1, Y0) => (Y0 = Y1)))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['101'])). 182.30/26.72 tff('103', plain, 182.30/26.72 ~ (subsetTrans => 182.30/26.72 (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => (subset(Y1, Y0) => (Y0 = Y1))))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['102'])). 182.30/26.72 tff('104', plain, 182.30/26.72 ~ (setadjoinSub => 182.30/26.72 (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => (subset(Y1, Y0) => (Y0 = Y1)))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['103'])). 182.30/26.72 tff('105', plain, 182.30/26.72 ~ (setadjoinSub2 => 182.30/26.72 (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => (subset(Y1, Y0) => (Y0 = Y1))))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['104'])). 182.30/26.72 tff('106', plain, 182.30/26.72 ~ (subset2powerset => 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => (subset(Y1, Y0) => (Y0 = Y1)))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['105'])). 182.30/26.72 tff('107', plain, 182.30/26.72 ~ (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (subset(Y0, Y1) => (subset(Y1, Y0) => (Y0 = Y1))))))))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['106'])). 182.30/26.72 tff('108', plain, 182.30/26.72 ~ (!!((^[Y0 : $i]: 182.30/26.72 (subset('#sk113', Y0) => 182.30/26.72 (subset(Y0, '#sk113') => ('#sk113' = Y0)))))), 182.30/26.72 inference('lazy_cnf_exists', [status(thm)], ['107'])). 182.30/26.72 tff('109', plain, 182.30/26.72 ~ (subset('#sk113', '#sk114') => 182.30/26.72 (subset('#sk114', '#sk113') => ('#sk113' = '#sk114'))), 182.30/26.72 inference('lazy_cnf_exists', [status(thm)], ['108'])). 182.30/26.72 tff('110', plain, ~ (subset('#sk114', '#sk113') => ('#sk113' = '#sk114')), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['109'])). 182.30/26.72 tff('111', plain, subset('#sk114', '#sk113'), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['110'])). 182.30/26.72 tff('112', plain, subsetE, 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['97'])). 182.30/26.72 tff(subsetE, axiom, subsetE => 182.30/26.72 ((!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (!!((^[Y2 : $i]: 182.30/26.72 (subset(Y0, Y1) => (in(Y2, Y0) => in(Y2, Y1)))))))))))) 182.30/26.72 = $true)). 182.30/26.72 tff('113', plain, 182.30/26.72 subsetE <=> (![X5,X7,X9]: (subset(X5,X7) => (in(X9,X5) => in(X9,X7)))), 182.30/26.72 inference('rw.lit', [status(esa)], [subsetE])). 182.30/26.72 tff('114', plain, 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 (!!((^[Y2 : $i]: 182.30/26.72 (subset(Y0, Y1) => (in(Y2, Y0) => in(Y2, Y1)))))))))))), 182.30/26.72 inference('rw_clause', [status(thm)], ['112', '113'])). 182.30/26.72 tff('115', plain, 182.30/26.72 ![X1]: 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: (subset(X1, Y0) => (in(Y1, X1) => in(Y1, Y0))))))))), 182.30/26.72 inference('lazy_cnf_forall', [status(thm)], ['114'])). 182.30/26.72 tff('116', plain, 182.30/26.72 ![X1, X2]: 182.30/26.72 (!!((^[Y0 : $i]: (subset(X1, X2) => (in(Y0, X1) => in(Y0, X2)))))), 182.30/26.72 inference('lazy_cnf_forall', [status(thm)], ['115'])). 182.30/26.72 tff('117', plain, 182.30/26.72 ![X1, X2, X3]: (subset(X1, X2) => (in(X3, X1) => in(X3, X2))), 182.30/26.72 inference('lazy_cnf_forall', [status(thm)], ['116'])). 182.30/26.72 tff('118', plain, 182.30/26.72 ![X1, X2, X3]: (~ subset(X1, X2) | (in(X3, X1) => in(X3, X2))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['117'])). 182.30/26.72 tff('119', plain, 182.30/26.72 ![X1, X2, X3]: (~ in(X3, X1) | in(X3, X2) | ~ subset(X1, X2)), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['118'])). 182.30/26.72 tff('120', plain, ![X0]: ( in(X0, '#sk113') | ~ in(X0, '#sk114')), 182.30/26.72 inference('sup-', [status(thm)], ['111', '119'])). 182.30/26.72 tff('121', plain, 182.30/26.72 ![X0]: ( '#form6'(X0, '#sk114') | in('#sk8'(X0, '#sk114'), '#sk113')), 182.30/26.72 inference('sup-', [status(thm)], ['28', '120'])). 182.30/26.72 tff('122', plain, ![X1, X2]: (~ in('#sk8'(X1, X2), X1) | '#form6'(X1, X2)), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['27'])). 182.30/26.72 tff('123', plain, 182.30/26.72 ( '#form6'('#sk113', '#sk114') | '#form6'('#sk113', '#sk114')), 182.30/26.72 inference('sup-', [status(thm)], ['121', '122'])). 182.30/26.72 tff('124', plain, '#form6'('#sk113', '#sk114'), 182.30/26.72 inference('simplify', [status(thm)], ['123'])). 182.30/26.72 tff('125', plain, setext, inference('lazy_cnf_imply', [status(thm)], ['39'])). 182.30/26.72 tff(setext, axiom, setext => 182.30/26.72 ((!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 182.30/26.72 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 182.30/26.72 (Y0 = Y1))))))))) 182.30/26.72 = $true)). 182.30/26.72 tff('126', plain, 182.30/26.72 setext <=> 182.30/26.72 (![X5,X7]: 182.30/26.72 ((![X9]: (in(X9,X5) => in(X9,X7))) => 182.30/26.72 ((![X11]: (in(X11,X7) => in(X11,X5))) => (X5 = X7)))), 182.30/26.72 inference('rw.lit', [status(esa)], [setext])). 182.30/26.72 tff('127', plain, 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 (!!((^[Y1 : $i]: 182.30/26.72 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 182.30/26.72 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 182.30/26.72 (Y0 = Y1))))))))), 182.30/26.72 inference('rw_clause', [status(thm)], ['125', '126'])). 182.30/26.72 tff('128', plain, 182.30/26.72 ![X1]: 182.30/26.72 (!!((^[Y0 : $i]: 182.30/26.72 ((!!((^[Y1 : $i]: (in(Y1, X1) => in(Y1, Y0))))) => 182.30/26.72 ((!!((^[Y1 : $i]: (in(Y1, Y0) => in(Y1, X1))))) => (X1 = Y0)))))), 182.30/26.72 inference('lazy_cnf_forall', [status(thm)], ['127'])). 182.30/26.72 tff('129', plain, 182.30/26.72 ![X1, X2]: 182.30/26.72 ((!!((^[Y0 : $i]: (in(Y0, X1) => in(Y0, X2))))) => 182.30/26.72 ((!!((^[Y0 : $i]: (in(Y0, X2) => in(Y0, X1))))) => (X1 = X2))), 182.30/26.72 inference('lazy_cnf_forall', [status(thm)], ['128'])). 182.30/26.72 tff('130', plain, 182.30/26.72 ![X1, X2]: 182.30/26.72 (~ (!!((^[Y0 : $i]: (in(Y0, X1) => in(Y0, X2))))) 182.30/26.72 | ((!!((^[Y0 : $i]: (in(Y0, X2) => in(Y0, X1))))) => (X1 = X2))), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['129'])). 182.30/26.72 tff('131', plain, 182.30/26.72 ![X1, X2]: 182.30/26.72 ( '#form6'(X1, X2) | ~ (!!((^[Y0 : $i]: (in(Y0, X2) => in(Y0, X1)))))), 182.30/26.72 define([status(thm)])). 182.30/26.72 tff('132', plain, 182.30/26.72 ![X1, X2]: 182.30/26.72 (~ '#form6'(X2, X1) 182.30/26.72 | ((!!((^[Y0 : $i]: (in(Y0, X2) => in(Y0, X1))))) => (X1 = X2))), 182.30/26.72 inference('renaming', [status(thm)], ['130', '131'])). 182.30/26.72 tff('133', plain, 182.30/26.72 ![X1, X2]: 182.30/26.72 (~ (!!((^[Y0 : $i]: (in(Y0, X2) => in(Y0, X1))))) 182.30/26.72 | X1 = X2 182.30/26.72 | ~ '#form6'(X2, X1)), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['132'])). 182.30/26.72 tff('134', plain, 182.30/26.72 ![X1, X2]: 182.30/26.72 ( '#form6'(X1, X2) | ~ (!!((^[Y0 : $i]: (in(Y0, X2) => in(Y0, X1)))))), 182.30/26.72 define([status(thm)])). 182.30/26.72 tff('135', plain, 182.30/26.72 ![X1, X2]: (~ '#form6'(X1, X2) | ~ '#form6'(X2, X1) | X1 = X2), 182.30/26.72 inference('renaming', [status(thm)], ['133', '134'])). 182.30/26.72 tff('136', plain, ('#sk113' = '#sk114' | ~ '#form6'('#sk114', '#sk113')), 182.30/26.72 inference('sup-', [status(thm)], ['124', '135'])). 182.30/26.72 tff('137', plain, '#sk113' != '#sk114', 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['110'])). 182.30/26.72 tff('138', plain, ~ '#form6'('#sk114', '#sk113'), 182.30/26.72 inference('simplify_reflect-', [status(thm)], ['136', '137'])). 182.30/26.72 tff('139', plain, ![X1, X2]: ( in('#sk8'(X1, X2), X2) | '#form6'(X1, X2)), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['27'])). 182.30/26.72 tff('140', plain, subset('#sk113', '#sk114'), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['109'])). 182.30/26.72 tff('141', plain, 182.30/26.72 ![X1, X2, X3]: (~ in(X3, X1) | in(X3, X2) | ~ subset(X1, X2)), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['118'])). 182.30/26.72 tff('142', plain, ![X0]: ( in(X0, '#sk114') | ~ in(X0, '#sk113')), 182.30/26.72 inference('sup-', [status(thm)], ['140', '141'])). 182.30/26.72 tff('143', plain, 182.30/26.72 ![X0]: ( '#form6'(X0, '#sk113') | in('#sk8'(X0, '#sk113'), '#sk114')), 182.30/26.72 inference('sup-', [status(thm)], ['139', '142'])). 182.30/26.72 tff('144', plain, ![X1, X2]: (~ in('#sk8'(X1, X2), X1) | '#form6'(X1, X2)), 182.30/26.72 inference('lazy_cnf_imply', [status(thm)], ['27'])). 182.30/26.72 tff('145', plain, 182.30/26.72 ( '#form6'('#sk114', '#sk113') | '#form6'('#sk114', '#sk113')), 182.30/26.72 inference('sup-', [status(thm)], ['143', '144'])). 182.30/26.72 tff('146', plain, '#form6'('#sk114', '#sk113'), 182.30/26.72 inference('simplify', [status(thm)], ['145'])). 182.30/26.72 tff('147', plain, $false, inference('demod', [status(thm)], ['138', '146'])). 182.30/26.72 182.30/26.72 % SZS output end Refutation 182.30/26.72 182.30/26.72 182.30/26.72 % Terminating... 182.30/26.72 % /export/starexec/sandbox2/solver/bin/lams/b.rw.sh running for 26s 182.36/26.81 % Runner terminated. 182.36/26.83 % Zipperpin 1.5 exiting 182.36/26.83 EOF