0.06/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.14/0.15 % Command : run_portfolio.sh /export/starexec/sandbox2/benchmark/theBenchmark.p /export/starexec/sandbox2/tmp/tmp.Dq5EngrY06 0.14/0.35 % Computer : n010.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 11:31:06 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 0.41/0.60 % Estimated wc time : 1286 0.41/0.60 % Estimated cpu time (7 cpus) : 183.71428571428572 0.51/0.68 % /export/starexec/sandbox2/solver/bin/lams/s6.sh running for 21s 0.51/0.69 % /export/starexec/sandbox2/solver/bin/lams/new_b3.2.norw.sh running for 15s 0.51/0.70 % /export/starexec/sandbox2/solver/bin/lams/b.rpo.sh running for 21s 0.51/0.71 % /export/starexec/sandbox2/solver/bin/lams/c.s.2.sh running for 68s 0.51/0.71 % /export/starexec/sandbox2/solver/bin/lams/s6.ds.sh running for 10s 0.51/0.73 % /export/starexec/sandbox2/solver/bin/lams/c.easy.sh running for 26s 0.51/0.74 % /export/starexec/sandbox2/solver/bin/lams/old_b3.avatar.sh running for 15s 67.48/10.74 % /export/starexec/sandbox2/solver/bin/lams/old_sp2.sh running for 17s 102.42/15.86 % /export/starexec/sandbox2/solver/bin/lams/b.sh running for 31s 102.67/15.95 % /export/starexec/sandbox2/solver/bin/lams/sh1.sh running for 26s 142.31/21.90 % /export/starexec/sandbox2/solver/bin/lams/b.lsimp.sh running for 17s 142.83/22.01 % /export/starexec/sandbox2/solver/bin/lams/b.split.sh running for 31s 177.60/27.08 % /export/starexec/sandbox2/solver/bin/lams/s4.sh running for 15s 182.22/27.78 % /export/starexec/sandbox2/solver/bin/lams/b.rw.sh running for 26s 188.24/28.63 % /export/starexec/sandbox2/solver/bin/lams/c_ic.sh running for 42s 259.45/38.95 % /export/starexec/sandbox2/solver/bin/lams/s1.f.sh running for 15s 282.22/42.31 % /export/starexec/sandbox2/solver/bin/lams/c.preprocess2.sh running for 21s 294.74/44.19 % Solved by lams/c_ic.sh. 294.74/44.19 % Running : timeout 32 /export/starexec/sandbox2/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox2/tmp/tmp.Dq5EngrY06/e_input274f95 --cpu-limit=30 --auto-schedule -s -p. 294.74/44.19 % done 2940 iterations in 15.473s 294.74/44.19 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 294.74/44.19 % SZS output start Refutation 294.74/44.19 tff(ubforcartprodlem3, axiom, ubforcartprodlem3 <=> 294.74/44.19 (![A,B,Xx]: 294.74/44.19 (in(Xx,A) => 294.74/44.19 (![Xy]: 294.74/44.19 (in(Xy,B) => in(kpair(Xx,Xy),powerset(powerset(binunion(A,B))))))))). 294.74/44.19 tff('0', plain, 294.74/44.19 ubforcartprodlem3 = 294.74/44.19 (![X4,X6,X8]: 294.74/44.19 (in(X8,X4) => 294.74/44.19 (![X10]: 294.74/44.19 (in(X10,X6) => 294.74/44.19 in(kpair(X8,X10),powerset(powerset(binunion(X4,X6)))))))), 294.74/44.19 define([status(thm)])). 294.74/44.19 tff(ubforcartprodlem2, axiom, ubforcartprodlem2 <=> 294.74/44.19 (![A,B,Xx]: 294.74/44.19 (in(Xx,A) => 294.74/44.19 (![Xy]: 294.74/44.19 (in(Xy,B) => 294.74/44.19 in(setadjoin(setadjoin(Xx,emptyset), 294.74/44.19 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 294.74/44.19 emptyset)), 294.74/44.19 powerset(powerset(binunion(A,B))))))))). 294.74/44.19 tff('1', plain, 294.74/44.19 ubforcartprodlem2 = 294.74/44.19 (![X4,X6,X8]: 294.74/44.19 (in(X8,X4) => 294.74/44.19 (![X10]: 294.74/44.19 (in(X10,X6) => 294.74/44.19 in(setadjoin(setadjoin(X8,emptyset), 294.74/44.19 setadjoin(setadjoin(X8,setadjoin(X10,emptyset)), 294.74/44.19 emptyset)), 294.74/44.19 powerset(powerset(binunion(X4,X6)))))))), 294.74/44.19 define([status(thm)])). 294.74/44.19 tff(ubforcartprodlem1, axiom, ubforcartprodlem1 <=> 294.74/44.19 (![A,B,Xx]: 294.74/44.19 (in(Xx,A) => 294.74/44.19 (![Xy]: 294.74/44.19 (in(Xy,B) => 294.74/44.19 subset(setadjoin(setadjoin(Xx,emptyset), 294.74/44.19 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 294.74/44.19 emptyset)), 294.74/44.19 powerset(binunion(A,B)))))))). 294.74/44.19 tff('2', plain, 294.74/44.19 ubforcartprodlem1 = 294.74/44.19 (![X4,X6,X8]: 294.74/44.19 (in(X8,X4) => 294.74/44.19 (![X10]: 294.74/44.19 (in(X10,X6) => 294.74/44.19 subset(setadjoin(setadjoin(X8,emptyset), 294.74/44.19 setadjoin(setadjoin(X8,setadjoin(X10,emptyset)), 294.74/44.19 emptyset)), 294.74/44.19 powerset(binunion(X4,X6))))))), 294.74/44.19 define([status(thm)])). 294.74/44.19 tff(upairinpowunion, axiom, upairinpowunion <=> 294.74/44.19 (![A,B,Xx]: 294.74/44.19 (in(Xx,A) => 294.74/44.19 (![Xy]: 294.74/44.19 (in(Xy,B) => 294.74/44.19 in(setadjoin(Xx,setadjoin(Xy,emptyset)),powerset(binunion(A,B)))))))). 294.74/44.19 tff('3', plain, 294.74/44.19 upairinpowunion = 294.74/44.19 (![X4,X6,X8]: 294.74/44.19 (in(X8,X4) => 294.74/44.19 (![X10]: 294.74/44.19 (in(X10,X6) => 294.74/44.19 in(setadjoin(X8,setadjoin(X10,emptyset)), 294.74/44.19 powerset(binunion(X4,X6))))))), 294.74/44.19 define([status(thm)])). 294.74/44.19 tff(upairsubunion, axiom, upairsubunion <=> 294.74/44.19 (![A,B,Xx]: 294.74/44.19 (in(Xx,A) => 294.74/44.19 (![Xy]: 294.74/44.19 (in(Xy,B) => 294.74/44.19 subset(setadjoin(Xx,setadjoin(Xy,emptyset)),binunion(A,B))))))). 294.74/44.19 tff('4', plain, 294.74/44.19 upairsubunion = 294.74/44.19 (![X4,X6,X8]: 294.74/44.19 (in(X8,X4) => 294.74/44.19 (![X10]: 294.74/44.19 (in(X10,X6) => 294.74/44.19 subset(setadjoin(X8,setadjoin(X10,emptyset)),binunion(X4,X6)))))), 294.74/44.19 define([status(thm)])). 294.74/44.19 tff(singletoninpowunion, axiom, singletoninpowunion <=> 294.74/44.19 (![A,B,Xx]: 294.74/44.19 (in(Xx,A) => in(setadjoin(Xx,emptyset),powerset(binunion(A,B)))))). 294.74/44.19 tff('5', plain, 294.74/44.19 singletoninpowunion = 294.74/44.19 (![X4,X6,X8]: 294.74/44.19 (in(X8,X4) => in(setadjoin(X8,emptyset),powerset(binunion(X4,X6))))), 294.74/44.19 define([status(thm)])). 294.74/44.19 tff(singletoninpowerset, axiom, singletoninpowerset <=> 294.74/44.19 (![A,Xx]: (in(Xx,A) => in(setadjoin(Xx,emptyset),powerset(A))))). 294.74/44.19 tff('6', plain, 294.74/44.19 singletoninpowerset = 294.74/44.19 (![X4,X6]: (in(X6,X4) => in(setadjoin(X6,emptyset),powerset(X4)))), 294.74/44.19 define([status(thm)])). 294.74/44.19 tff(bs114d, axiom, bs114d <=> 294.74/44.19 (![A,B,C]: 294.74/44.19 (binintersect(A,binunion(B,C)) = 294.74/44.19 binunion(binintersect(A,B),binintersect(A,C))))). 294.74/44.19 tff('7', plain, 294.74/44.19 bs114d = 294.74/44.19 (![X4,X6,X8]: 294.74/44.19 (binintersect(X4,binunion(X6,X8)) = 294.74/44.19 binunion(binintersect(X4,X6),binintersect(X4,X8)))), 294.74/44.19 define([status(thm)])). 294.74/44.19 tff(binunionRsub, axiom, binunionRsub <=> (![A,B]: subset(B,binunion(A,B)))). 294.74/44.19 tff('8', plain, binunionRsub = (![X4,X6]: subset(X6,binunion(X4,X6))), 294.74/44.19 define([status(thm)])). 294.74/44.19 tff(binunionLsub, axiom, binunionLsub <=> (![A,B]: subset(A,binunion(A,B)))). 294.74/44.19 tff('9', plain, binunionLsub = (![X4,X6]: subset(X4,binunion(X4,X6))), 294.74/44.19 define([status(thm)])). 294.74/44.19 tff(binunionE, axiom, binunionE <=> 294.74/44.19 (![A,B,Xx]: (in(Xx,binunion(A,B)) => (in(Xx,A) | in(Xx,B))))). 294.74/44.19 tff('10', plain, 294.74/44.19 binunionE = 294.74/44.19 (![X4,X6,X8]: (in(X8,binunion(X4,X6)) => (in(X8,X4) | in(X8,X6)))), 294.74/44.19 define([status(thm)])). 294.74/44.19 tff(binunionEcases, axiom, binunionEcases <=> 294.74/44.19 (![A,B,Xx,Xphi:$o]: 294.74/44.19 (in(Xx,binunion(A,B)) => 294.74/44.19 ((in(Xx,A) => Xphi) => ((in(Xx,B) => Xphi) => Xphi))))). 294.74/44.19 tff('11', plain, 294.74/44.19 binunionEcases = 294.74/44.19 (![X4,X6,X8,X10:$o]: 294.74/44.19 (in(X8,binunion(X4,X6)) => 294.74/44.19 ((in(X8,X4) => X10) => ((in(X8,X6) => X10) => X10)))), 294.74/44.19 define([status(thm)])). 294.74/44.19 tff(binunionIR, axiom, binunionIR <=> 294.74/44.19 (![A,B,Xx]: (in(Xx,B) => in(Xx,binunion(A,B))))). 294.74/44.19 tff('12', plain, 294.74/44.19 binunionIR = (![X4,X6,X8]: (in(X8,X6) => in(X8,binunion(X4,X6)))), 294.74/44.19 define([status(thm)])). 294.74/44.19 tff(binunionIL, axiom, binunionIL <=> 294.74/44.19 (![A,B,Xx]: (in(Xx,A) => in(Xx,binunion(A,B))))). 294.74/44.19 tff('13', plain, 294.74/44.19 binunionIL = (![X4,X6,X8]: (in(X8,X4) => in(X8,binunion(X4,X6)))), 294.74/44.19 define([status(thm)])). 294.74/44.19 tff(sepInPowerset, axiom, sepInPowerset <=> 294.74/44.19 (![A,Xphi:(($i > $o))]: in(dsetconstr(A,^[Xx]: Xphi(Xx)),powerset(A)))). 294.74/44.19 tff('14', plain, 294.74/44.19 sepInPowerset = 294.74/44.19 (![X4,X6:(($i > $o))]: in(dsetconstr(X4,^[V_1]: X6(V_1)),powerset(X4))), 294.74/44.19 define([status(thm)])). 294.74/44.19 tff(powersetsubset, axiom, powersetsubset <=> 294.74/44.19 (![A,B]: (subset(A,B) => subset(powerset(A),powerset(B))))). 294.74/44.19 tff('15', plain, 294.74/44.19 powersetsubset = 294.74/44.19 (![X4,X6]: (subset(X4,X6) => subset(powerset(X4),powerset(X6)))), 294.74/44.19 define([status(thm)])). 294.74/44.19 tff(inPowerset, axiom, inPowerset <=> (![A]: in(A,powerset(A)))). 294.74/44.19 tff('16', plain, inPowerset = (![X4]: in(X4,powerset(X4))), 294.74/44.19 define([status(thm)])). 294.74/44.19 tff(powersetE1, axiom, powersetE1 <=> 294.74/44.19 (![A,B]: (in(B,powerset(A)) => subset(B,A)))). 294.74/44.19 tff('17', plain, 294.74/44.19 powersetE1 = (![X4,X6]: (in(X6,powerset(X4)) => subset(X6,X4))), 294.74/44.19 define([status(thm)])). 294.74/44.19 tff(powersetI1, axiom, powersetI1 <=> 294.74/44.19 (![A,B]: (subset(B,A) => in(B,powerset(A))))). 294.74/44.19 tff('18', plain, 294.74/44.19 powersetI1 = (![X4,X6]: (subset(X6,X4) => in(X6,powerset(X4)))), 294.74/44.19 define([status(thm)])). 294.74/44.19 tff(subset2powerset, axiom, subset2powerset <=> 294.74/44.19 (![A,B]: (subset(A,B) => in(A,powerset(B))))). 294.74/44.19 tff('19', plain, 294.74/44.19 subset2powerset = (![X4,X6]: (subset(X4,X6) => in(X4,powerset(X6)))), 294.74/44.19 define([status(thm)])). 294.74/44.19 tff(powerset__Cong, axiom, powerset__Cong <=> 294.74/44.19 (![A,B]: ((A = B) => (powerset(A) = powerset(B))))). 294.74/44.19 tff('20', plain, 294.74/44.19 powerset__Cong = (![X4,X6]: ((X4 = X6) => (powerset(X4) = powerset(X6)))), 294.74/44.19 define([status(thm)])). 294.74/44.19 tff(powersetE, axiom, powersetE <=> 294.74/44.19 (![A,B,Xx]: (in(B,powerset(A)) => (in(Xx,B) => in(Xx,A))))). 294.74/44.19 tff('21', plain, 294.74/44.19 powersetE = 294.74/44.19 (![X4,X6,X8]: (in(X6,powerset(X4)) => (in(X8,X6) => in(X8,X4)))), 294.74/44.19 define([status(thm)])). 294.74/44.19 tff(emptyInPowerset, axiom, emptyInPowerset <=> 294.74/44.19 (![A]: in(emptyset,powerset(A)))). 294.74/44.19 tff('22', plain, emptyInPowerset = (![X4]: in(emptyset,powerset(X4))), 294.74/44.19 define([status(thm)])). 294.74/44.19 tff(emptyinPowerset, axiom, emptyinPowerset <=> 294.74/44.19 (![A]: in(emptyset,powerset(A)))). 294.74/44.19 tff('23', plain, emptyinPowerset = (![X4]: in(emptyset,powerset(X4))), 294.74/44.19 define([status(thm)])). 294.74/44.19 tff(powersetI, axiom, powersetI <=> 294.74/44.19 (![A,B]: ((![Xx]: (in(Xx,B) => in(Xx,A))) => in(B,powerset(A))))). 294.74/44.19 tff('24', plain, 294.74/44.19 powersetI = 294.74/44.19 (![X4,X6]: ((![X8]: (in(X8,X6) => in(X8,X4))) => in(X6,powerset(X4)))), 294.74/44.19 define([status(thm)])). 294.74/44.19 tff(powersetAx, axiom, powersetAx <=> 294.74/44.19 (![A,B]: (in(B,powerset(A)) <=> (![Xx]: (in(Xx,B) => in(Xx,A)))))). 294.74/44.19 tff('25', plain, 294.74/44.19 powersetAx = 294.74/44.19 (![X4,X6]: (in(X6,powerset(X4)) <=> (![X8]: (in(X8,X6) => in(X8,X4))))), 294.74/44.19 define([status(thm)])). 294.74/44.19 tff(binunionT_lem, conjecture, 294.74/44.19 (setextAx => 294.74/44.19 (emptysetAx => 294.74/44.19 (setadjoinAx => 294.74/44.19 (powersetAx => 294.74/44.19 (setunionAx => 294.74/44.19 (omega0Ax => 294.74/44.19 (omegaSAx => 294.74/44.19 (omegaIndAx => 294.74/44.19 (replAx => 294.74/44.19 (foundationAx => 294.74/44.19 (wellorderingAx => 294.74/44.19 (descrp => 294.74/44.19 (dsetconstrI => 294.74/44.19 (dsetconstrEL => 294.74/44.19 (dsetconstrER => 294.74/44.19 (exuE1 => 294.74/44.19 (prop2setE => 294.74/44.19 (emptysetE => 294.74/44.19 (emptysetimpfalse => 294.74/44.19 (notinemptyset => 294.74/44.19 (exuE3e => 294.74/44.19 (setext => 294.74/44.19 (emptyI => 294.74/44.19 (noeltsimpempty => 294.74/44.19 (setbeta => 294.74/44.19 (nonemptyE1 => 294.74/44.19 (nonemptyI => 294.74/44.19 (nonemptyI1 => 294.74/44.19 (setadjoinIL => 294.74/44.19 (emptyinunitempty => 294.74/44.19 (setadjoinIR => 294.74/44.19 (setadjoinE => 294.74/44.19 (setadjoinOr => 294.74/44.19 (setoftrueEq => 294.74/44.19 (powersetI => 294.74/44.19 (emptyinPowerset => 294.74/44.19 (emptyInPowerset => 294.74/44.19 (powersetE => 294.74/44.19 (setunionI => 294.74/44.19 (setunionE => 294.74/44.19 (subPowSU => 294.74/44.19 (exuE2 => 294.74/44.19 (nonemptyImpWitness => 294.74/44.19 (uniqinunit => 294.74/44.19 (notinsingleton => 294.74/44.19 (eqinunit => 294.74/44.19 (singletonsswitch => 294.74/44.19 (upairsetE => 294.74/44.19 (upairsetIL => 294.74/44.19 (upairsetIR => 294.74/44.19 (emptyE1 => 294.74/44.19 (vacuousDall => 294.74/44.19 (quantDeMorgan1 => 294.74/44.19 (quantDeMorgan2 => 294.74/44.19 (quantDeMorgan3 => 294.74/44.19 (quantDeMorgan4 => 294.74/44.19 (prop2setI => 294.74/44.19 (prop2set2propI => 294.74/44.19 (notdexE => 294.74/44.19 (notdallE => 294.74/44.19 (exuI1 => 294.74/44.19 (exuI3 => 294.74/44.19 (exuI2 => 294.74/44.19 (inCongP => 294.74/44.19 (in__Cong => 294.74/44.19 (exuE3u => 294.74/44.19 ( 294.74/44.19 exu__Cong => 294.74/44.19 ( 294.74/44.19 emptyset__Cong => 294.74/44.19 ( 294.74/44.19 setadjoin__Cong => 294.74/44.19 ( 294.74/44.19 powerset__Cong => 294.74/44.19 ( 294.74/44.19 setunion__Cong => 294.74/44.19 ( 294.74/44.19 omega__Cong => 294.74/44.19 ( 294.74/44.19 exuEu => 294.74/44.19 ( 294.74/44.19 descr__Cong => 294.74/44.19 ( 294.74/44.19 dsetconstr__Cong => 294.74/44.19 ( 294.74/44.19 subsetI1 => 294.74/44.19 ( 294.74/44.19 eqimpsubset2 => 294.74/44.19 ( 294.74/44.19 eqimpsubset1 => 294.74/44.19 ( 294.74/44.19 subsetI2 => 294.74/44.19 ( 294.74/44.19 emptysetsubset => 294.74/44.19 ( 294.74/44.19 subsetE => 294.74/44.19 ( 294.74/44.19 subsetE2 => 294.74/44.19 ( 294.74/44.19 notsubsetI => 294.74/44.19 ( 294.74/44.19 notequalI1 => 294.74/44.19 ( 294.74/44.19 notequalI2 => 294.74/44.19 ( 294.74/44.19 subsetRefl => 294.74/44.19 ( 294.74/44.19 subsetTrans => 294.74/44.19 ( 294.74/44.19 setadjoinSub => 294.74/44.19 ( 294.74/44.19 setadjoinSub2 => 294.74/44.19 ( 294.74/44.19 subset2powerset => 294.74/44.19 ( 294.74/44.19 setextsub => 294.74/44.19 ( 294.74/44.19 subsetemptysetimpeq => 294.74/44.19 ( 294.74/44.19 powersetI1 => 294.74/44.19 ( 294.74/44.19 powersetE1 => 294.74/44.19 ( 294.74/44.19 inPowerset => 294.74/44.19 ( 294.74/44.19 powersetsubset => 294.74/44.19 ( 294.74/44.19 sepInPowerset => 294.74/44.19 ( 294.74/44.19 sepSubset => 294.74/44.19 ( 294.74/44.19 binunionIL => 294.74/44.19 ( 294.74/44.19 upairset2IR => 294.74/44.19 ( 294.74/44.19 binunionIR => 294.74/44.19 ( 294.74/44.19 binunionEcases => 294.74/44.19 ( 294.74/44.19 binunionE => 294.74/44.19 ( 294.74/44.19 binunionLsub => 294.74/44.19 ( 294.74/44.19 binunionRsub => 294.74/44.19 ( 294.74/44.19 binintersectI => 294.74/44.19 ( 294.74/44.19 binintersectSubset5 => 294.74/44.19 ( 294.74/44.19 binintersectEL => 294.74/44.19 ( 294.74/44.19 binintersectLsub => 294.74/44.19 ( 294.74/44.19 binintersectSubset2 => 294.74/44.19 ( 294.74/44.19 binintersectSubset3 => 294.74/44.19 ( 294.74/44.19 binintersectER => 294.74/44.19 ( 294.74/44.19 disjointsetsI1 => 294.74/44.19 ( 294.74/44.19 binintersectRsub => 294.74/44.19 ( 294.74/44.19 binintersectSubset4 => 294.74/44.19 ( 294.74/44.19 binintersectSubset1 => 294.74/44.19 ( 294.74/44.19 bs114d => 294.74/44.19 ( 294.74/44.19 setminusI => 294.74/44.19 ( 294.74/44.19 setminusEL => 294.74/44.19 ( 294.74/44.19 setminusER => 294.74/44.19 ( 294.74/44.19 setminusSubset2 => 294.74/44.19 ( 294.74/44.19 setminusERneg => 294.74/44.19 ( 294.74/44.19 setminusELneg => 294.74/44.19 ( 294.74/44.19 setminusILneg => 294.74/44.19 ( 294.74/44.19 setminusIRneg => 294.74/44.19 ( 294.74/44.19 setminusLsub => 294.74/44.19 ( 294.74/44.19 setminusSubset1 => 294.74/44.19 ( 294.74/44.19 symdiffE => 294.74/44.19 ( 294.74/44.19 symdiffI1 => 294.74/44.19 ( 294.74/44.19 symdiffI2 => 294.74/44.19 ( 294.74/44.19 symdiffIneg1 => 294.74/44.19 ( 294.74/44.19 symdiffIneg2 => 294.74/44.19 ( 294.74/44.19 secondinupair => 294.74/44.19 ( 294.74/44.19 setukpairIL => 294.74/44.19 ( 294.74/44.19 setukpairIR => 294.74/44.19 ( 294.74/44.19 kpairiskpair => 294.74/44.19 ( 294.74/44.19 kpairp => 294.74/44.19 ( 294.74/44.19 singletonsubset => 294.74/44.19 ( 294.74/44.19 singletoninpowerset => 294.74/44.19 ( 294.74/44.19 singletoninpowunion => 294.74/44.20 ( 294.74/44.20 upairset2E => 294.74/44.20 ( 294.74/44.20 upairsubunion => 294.74/44.20 ( 294.74/44.20 upairinpowunion => 294.74/44.20 ( 294.74/44.20 ubforcartprodlem1 => 294.74/44.20 ( 294.74/44.20 ubforcartprodlem2 => 294.74/44.20 ( 294.74/44.20 ubforcartprodlem3 => 294.74/44.20 ( 294.74/44.20 cartprodpairin => 294.74/44.20 ( 294.74/44.20 cartprodmempair1 => 294.74/44.20 ( 294.74/44.20 cartprodmempair => 294.74/44.20 ( 294.74/44.20 setunionE2 => 294.74/44.20 ( 294.74/44.20 setunionsingleton1 => 294.74/44.20 ( 294.74/44.20 setunionsingleton2 => 294.74/44.20 ( 294.74/44.20 setunionsingleton => 294.74/44.20 ( 294.74/44.20 singletonprop => 294.74/44.20 ( 294.74/44.20 ex1E1 => 294.74/44.20 ( 294.74/44.20 ex1I => 294.74/44.20 ( 294.74/44.20 ex1I2 => 294.74/44.20 ( 294.74/44.20 singletonsuniq => 294.74/44.20 ( 294.74/44.20 setukpairinjL1 => 294.74/44.20 ( 294.74/44.20 kfstsingleton => 294.74/44.20 ( 294.74/44.20 theprop => 294.74/44.20 ( 294.74/44.20 kfstpairEq => 294.74/44.20 ( 294.74/44.20 cartprodfstin => 294.74/44.20 ( 294.74/44.20 setukpairinjL2 => 294.74/44.20 ( 294.74/44.20 setukpairinjL => 294.74/44.20 ( 294.74/44.20 setukpairinjR11 => 294.74/44.20 ( 294.74/44.20 setukpairinjR12 => 294.74/44.20 ( 294.74/44.20 setukpairinjR1 => 294.74/44.20 ( 294.74/44.20 upairequniteq => 294.74/44.20 ( 294.74/44.20 setukpairinjR2 => 294.74/44.20 ( 294.74/44.20 setukpairinjR => 294.74/44.20 ( 294.74/44.20 ksndsingleton => 294.74/44.20 ( 294.74/44.20 ksndpairEq => 294.74/44.20 ( 294.74/44.20 kpairsurjEq => 294.74/44.20 ( 294.74/44.20 cartprodsndin => 294.74/44.20 ( 294.74/44.20 cartprodpairmemEL => 294.74/44.20 ( 294.74/44.20 cartprodpairmemER => 294.74/44.20 ( 294.74/44.20 cartprodmempaircEq => 294.74/44.20 ( 294.74/44.20 cartprodfstpairEq => 294.74/44.20 ( 294.74/44.20 cartprodsndpairEq => 294.74/44.20 ( 294.74/44.20 cartprodpairsurjEq => 294.74/44.20 ( 294.74/44.20 dpsetconstrI => 294.74/44.20 ( 294.74/44.20 dpsetconstrSub => 294.74/44.20 ( 294.74/44.20 setOfPairsIsBReln => 294.74/44.20 ( 294.74/44.20 dpsetconstrERa => 294.74/44.20 ( 294.74/44.20 dpsetconstrEL1 => 294.74/44.20 ( 294.74/44.20 dpsetconstrEL2 => 294.74/44.20 ( 294.74/44.20 dpsetconstrER => 294.74/44.20 ( 294.74/44.20 funcImageSingleton => 294.74/44.20 ( 294.74/44.20 apProp => 294.74/44.20 ( 294.74/44.20 app => 294.74/44.20 ( 294.74/44.20 infuncsetfunc => 294.74/44.20 ( 294.74/44.20 ap2p => 294.74/44.20 ( 294.74/44.20 funcinfuncset => 294.74/44.20 ( 294.74/44.20 lamProp => 294.74/44.20 ( 294.74/44.20 lamp => 294.74/44.20 ( 294.74/44.20 lam2p => 294.74/44.20 ( 294.74/44.20 brelnall1 => 294.74/44.20 ( 294.74/44.20 brelnall2 => 294.74/44.20 ( 294.74/44.20 ex1E2 => 294.74/44.20 ( 294.74/44.20 funcGraphProp1 => 294.74/44.20 ( 294.74/44.20 funcGraphProp3 => 294.74/44.20 ( 294.74/44.20 funcGraphProp2 => 294.74/44.20 ( 294.74/44.20 funcextLem => 294.74/44.20 ( 294.74/44.20 funcGraphProp4 => 294.74/44.20 ( 294.74/44.20 subbreln => 294.74/44.20 ( 294.74/44.20 eqbreln => 294.74/44.20 ( 294.74/44.20 funcext => 294.74/44.20 ( 294.74/44.20 funcext2 => 294.74/44.20 ( 294.74/44.20 ap2apEq1 => 294.74/44.20 ( 294.74/44.20 ap2apEq2 => 294.74/44.20 ( 294.74/44.20 beta1 => 294.74/44.20 ( 294.74/44.20 eta1 => 294.74/44.20 ( 294.74/44.20 lam2lamEq => 294.74/44.20 ( 294.74/44.20 beta2 => 294.74/44.20 ( 294.74/44.20 eta2 => 294.74/44.20 ( 294.74/44.20 iffalseProp1 => 294.74/44.20 ( 294.74/44.20 iffalseProp2 => 294.74/44.20 ( 294.74/44.20 iftrueProp1 => 294.74/44.20 ( 294.74/44.20 iftrueProp2 => 294.74/44.20 ( 294.74/44.20 ifSingleton => 294.74/44.20 ( 294.74/44.20 ifp => 294.74/44.20 ( 294.74/44.20 theeq => 294.74/44.20 ( 294.74/44.20 iftrue => 294.74/44.20 ( 294.74/44.20 iffalse => 294.74/44.20 ( 294.74/44.20 iftrueorfalse => 294.74/44.20 ( 294.74/44.20 binintersectT_lem => 294.74/44.20 ( 294.74/44.20 ![A,X]: 294.74/44.20 (in( 294.74/44.20 X, 294.74/44.20 powerset( 294.74/44.20 A)) => 294.74/44.20 (![Y]: 294.74/44.20 (in( 294.74/44.20 Y, 294.74/44.20 powerset( 294.74/44.20 A)) => 294.74/44.20 in( 294.74/44.20 binunion( 294.74/44.20 X,Y), 294.74/44.20 powerset( 294.74/44.20 A)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 294.74/44.20 tff(zf_stmt_0, conjecture, 294.74/44.20 (setextAx => 294.74/44.20 (emptysetAx => 294.74/44.20 (setadjoinAx => 294.74/44.20 ((![X4,X6]: (in(X6,powerset(X4)) <=> (![X8]: (in(X8,X6) => in(X8,X4))))) => 294.74/44.20 (setunionAx => 294.74/44.20 (omega0Ax => 294.74/44.20 (omegaSAx => 294.74/44.20 (omegaIndAx => 294.74/44.20 (replAx => 294.74/44.20 (foundationAx => 294.74/44.20 (wellorderingAx => 294.74/44.20 (descrp => 294.74/44.20 (dsetconstrI => 294.74/44.20 (dsetconstrEL => 294.74/44.20 (dsetconstrER => 294.74/44.20 (exuE1 => 294.74/44.20 (prop2setE => 294.74/44.20 (emptysetE => 294.74/44.20 (emptysetimpfalse => 294.74/44.20 (notinemptyset => 294.74/44.20 (exuE3e => 294.74/44.20 (setext => 294.74/44.20 (emptyI => 294.74/44.20 (noeltsimpempty => 294.74/44.20 (setbeta => 294.74/44.20 (nonemptyE1 => 294.74/44.20 (nonemptyI => 294.74/44.20 (nonemptyI1 => 294.74/44.20 (setadjoinIL => 294.74/44.20 (emptyinunitempty => 294.74/44.20 (setadjoinIR => 294.74/44.20 (setadjoinE => 294.74/44.20 (setadjoinOr => 294.74/44.20 (setoftrueEq => 294.74/44.20 ((![X10,X12]: 294.74/44.20 ((![X14]: 294.74/44.20 (in(X14,X12) => in(X14,X10))) => 294.74/44.20 in(X12,powerset(X10)))) => 294.74/44.20 ((![X16]: in(emptyset,powerset(X16))) => 294.74/44.20 ((![X18]: in(emptyset,powerset(X18))) => 294.74/44.20 ((![X20,X22,X24]: 294.74/44.20 (in(X22,powerset(X20)) => 294.74/44.20 (in(X24,X22) => in(X24,X20)))) => 294.74/44.20 (setunionI => 294.74/44.20 (setunionE => 294.74/44.20 (subPowSU => 294.74/44.20 (exuE2 => 294.74/44.20 (nonemptyImpWitness => 294.74/44.20 (uniqinunit => 294.74/44.20 (notinsingleton => 294.74/44.20 (eqinunit => 294.74/44.20 (singletonsswitch => 294.74/44.20 (upairsetE => 294.74/44.20 (upairsetIL => 294.74/44.20 (upairsetIR => 294.74/44.20 (emptyE1 => 294.74/44.20 (vacuousDall => 294.74/44.20 (quantDeMorgan1 => 294.74/44.20 (quantDeMorgan2 => 294.74/44.20 (quantDeMorgan3 => 294.74/44.20 (quantDeMorgan4 => 294.74/44.20 (prop2setI => 294.74/44.20 (prop2set2propI => 294.74/44.20 (notdexE => 294.74/44.20 (notdallE => 294.74/44.20 (exuI1 => 294.74/44.20 (exuI3 => 294.74/44.20 (exuI2 => 294.74/44.20 (inCongP => 294.74/44.20 (in__Cong => 294.74/44.20 (exuE3u => 294.74/44.20 ( 294.74/44.20 exu__Cong => 294.74/44.20 ( 294.74/44.20 emptyset__Cong => 294.74/44.20 ( 294.74/44.20 setadjoin__Cong => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X26,X28]: 294.74/44.20 (( 294.74/44.20 X26 = X28) => 294.74/44.20 (powerset( 294.74/44.20 X26) = 294.74/44.20 powerset( 294.74/44.20 X28)))) => 294.74/44.20 ( 294.74/44.20 setunion__Cong => 294.74/44.20 ( 294.74/44.20 omega__Cong => 294.74/44.20 ( 294.74/44.20 exuEu => 294.74/44.20 ( 294.74/44.20 descr__Cong => 294.74/44.20 ( 294.74/44.20 dsetconstr__Cong => 294.74/44.20 ( 294.74/44.20 subsetI1 => 294.74/44.20 ( 294.74/44.20 eqimpsubset2 => 294.74/44.20 ( 294.74/44.20 eqimpsubset1 => 294.74/44.20 ( 294.74/44.20 subsetI2 => 294.74/44.20 ( 294.74/44.20 emptysetsubset => 294.74/44.20 ( 294.74/44.20 subsetE => 294.74/44.20 ( 294.74/44.20 subsetE2 => 294.74/44.20 ( 294.74/44.20 notsubsetI => 294.74/44.20 ( 294.74/44.20 notequalI1 => 294.74/44.20 ( 294.74/44.20 notequalI2 => 294.74/44.20 ( 294.74/44.20 subsetRefl => 294.74/44.20 ( 294.74/44.20 subsetTrans => 294.74/44.20 ( 294.74/44.20 setadjoinSub => 294.74/44.20 ( 294.74/44.20 setadjoinSub2 => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X30,X32]: 294.74/44.20 (subset( 294.74/44.20 X30,X32) => 294.74/44.20 in( 294.74/44.20 X30, 294.74/44.20 powerset( 294.74/44.20 X32)))) => 294.74/44.20 ( 294.74/44.20 setextsub => 294.74/44.20 ( 294.74/44.20 subsetemptysetimpeq => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X34,X36]: 294.74/44.20 (subset( 294.74/44.20 X36,X34) => 294.74/44.20 in( 294.74/44.20 X36, 294.74/44.20 powerset( 294.74/44.20 X34)))) => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X38,X40]: 294.74/44.20 (in( 294.74/44.20 X40, 294.74/44.20 powerset( 294.74/44.20 X38)) => 294.74/44.20 subset( 294.74/44.20 X40,X38))) => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X42]: 294.74/44.20 in( 294.74/44.20 X42, 294.74/44.20 powerset( 294.74/44.20 X42))) => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X44,X46]: 294.74/44.20 (subset( 294.74/44.20 X44,X46) => 294.74/44.20 subset( 294.74/44.20 powerset( 294.74/44.20 X44), 294.74/44.20 powerset( 294.74/44.20 X46)))) => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X48, 294.74/44.20 X50:( 294.74/44.20 ( 294.74/44.20 $i > $o))]: 294.74/44.20 in( 294.74/44.20 dsetconstr( 294.74/44.20 X48, 294.74/44.20 ^[V_1]: 294.74/44.20 X50(V_1)), 294.74/44.20 powerset( 294.74/44.20 X48))) => 294.74/44.20 ( 294.74/44.20 sepSubset => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X52, 294.74/44.20 X54,X56]: 294.74/44.20 (in( 294.74/44.20 X56,X52) => 294.74/44.20 in( 294.74/44.20 X56, 294.74/44.20 binunion( 294.74/44.20 X52,X54)))) => 294.74/44.20 ( 294.74/44.20 upairset2IR => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X58, 294.74/44.20 X60,X62]: 294.74/44.20 (in( 294.74/44.20 X62,X60) => 294.74/44.20 in( 294.74/44.20 X62, 294.74/44.20 binunion( 294.74/44.20 X58,X60)))) => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X64, 294.74/44.20 X66,X68, 294.74/44.20 X70:$o]: 294.74/44.20 (in( 294.74/44.20 X68, 294.74/44.20 binunion( 294.74/44.20 X64,X66)) => 294.74/44.20 (( 294.74/44.20 in( 294.74/44.20 X68,X64) => 294.74/44.20 X70) => 294.74/44.20 (( 294.74/44.20 in( 294.74/44.20 X68,X66) => 294.74/44.20 X70) => 294.74/44.20 X70)))) => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X72, 294.74/44.20 X74,X76]: 294.74/44.20 (in( 294.74/44.20 X76, 294.74/44.20 binunion( 294.74/44.20 X72,X74)) => 294.74/44.20 (in( 294.74/44.20 X76,X74) | 294.74/44.20 in( 294.74/44.20 X76,X72)))) => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X78,X80]: 294.74/44.20 subset( 294.74/44.20 X78, 294.74/44.20 binunion( 294.74/44.20 X78,X80))) => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X82,X84]: 294.74/44.20 subset( 294.74/44.20 X84, 294.74/44.20 binunion( 294.74/44.20 X82,X84))) => 294.74/44.20 ( 294.74/44.20 binintersectI => 294.74/44.20 ( 294.74/44.20 binintersectSubset5 => 294.74/44.20 ( 294.74/44.20 binintersectEL => 294.74/44.20 ( 294.74/44.20 binintersectLsub => 294.74/44.20 ( 294.74/44.20 binintersectSubset2 => 294.74/44.20 ( 294.74/44.20 binintersectSubset3 => 294.74/44.20 ( 294.74/44.20 binintersectER => 294.74/44.20 ( 294.74/44.20 disjointsetsI1 => 294.74/44.20 ( 294.74/44.20 binintersectRsub => 294.74/44.20 ( 294.74/44.20 binintersectSubset4 => 294.74/44.20 ( 294.74/44.20 binintersectSubset1 => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X86, 294.74/44.20 X88,X90]: 294.74/44.20 (binintersect( 294.74/44.20 X86, 294.74/44.20 binunion( 294.74/44.20 X88,X90)) = 294.74/44.20 binunion( 294.74/44.20 binintersect( 294.74/44.20 X86,X88), 294.74/44.20 binintersect( 294.74/44.20 X86,X90)))) => 294.74/44.20 ( 294.74/44.20 setminusI => 294.74/44.20 ( 294.74/44.20 setminusEL => 294.74/44.20 ( 294.74/44.20 setminusER => 294.74/44.20 ( 294.74/44.20 setminusSubset2 => 294.74/44.20 ( 294.74/44.20 setminusERneg => 294.74/44.20 ( 294.74/44.20 setminusELneg => 294.74/44.20 ( 294.74/44.20 setminusILneg => 294.74/44.20 ( 294.74/44.20 setminusIRneg => 294.74/44.20 ( 294.74/44.20 setminusLsub => 294.74/44.20 ( 294.74/44.20 setminusSubset1 => 294.74/44.20 ( 294.74/44.20 symdiffE => 294.74/44.20 ( 294.74/44.20 symdiffI1 => 294.74/44.20 ( 294.74/44.20 symdiffI2 => 294.74/44.20 ( 294.74/44.20 symdiffIneg1 => 294.74/44.20 ( 294.74/44.20 symdiffIneg2 => 294.74/44.20 ( 294.74/44.20 secondinupair => 294.74/44.20 ( 294.74/44.20 setukpairIL => 294.74/44.20 ( 294.74/44.20 setukpairIR => 294.74/44.20 ( 294.74/44.20 kpairiskpair => 294.74/44.20 ( 294.74/44.20 kpairp => 294.74/44.20 ( 294.74/44.20 singletonsubset => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X92,X94]: 294.74/44.20 (in( 294.74/44.20 X94,X92) => 294.74/44.20 in( 294.74/44.20 setadjoin( 294.74/44.20 X94, 294.74/44.20 emptyset), 294.74/44.20 powerset( 294.74/44.20 X92)))) => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X96, 294.74/44.20 X98,X100]: 294.74/44.20 (in( 294.74/44.20 X100,X96) => 294.74/44.20 in( 294.74/44.20 setadjoin( 294.74/44.20 X100, 294.74/44.20 emptyset), 294.74/44.20 powerset( 294.74/44.20 binunion( 294.74/44.20 X96,X98))))) => 294.74/44.20 ( 294.74/44.20 upairset2E => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X102, 294.74/44.20 X104,X106]: 294.74/44.20 (in( 294.74/44.20 X106,X102) => 294.74/44.20 (![X108]: 294.74/44.20 (in( 294.74/44.20 X108,X104) => 294.74/44.20 subset( 294.74/44.20 setadjoin( 294.74/44.20 X106, 294.74/44.20 setadjoin( 294.74/44.20 X108, 294.74/44.20 emptyset)), 294.74/44.20 binunion( 294.74/44.20 X102,X104)))))) => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X110, 294.74/44.20 X112,X114]: 294.74/44.20 (in( 294.74/44.20 X114,X110) => 294.74/44.20 (![X116]: 294.74/44.20 (in( 294.74/44.20 X116,X112) => 294.74/44.20 in( 294.74/44.20 setadjoin( 294.74/44.20 X114, 294.74/44.20 setadjoin( 294.74/44.20 X116, 294.74/44.20 emptyset)), 294.74/44.20 powerset( 294.74/44.20 binunion( 294.74/44.20 X110,X112))))))) => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X118, 294.74/44.20 X120,X122]: 294.74/44.20 (in( 294.74/44.20 X122,X118) => 294.74/44.20 (![X124]: 294.74/44.20 (in( 294.74/44.20 X124,X120) => 294.74/44.20 subset( 294.74/44.20 setadjoin( 294.74/44.20 setadjoin( 294.74/44.20 X122, 294.74/44.20 emptyset), 294.74/44.20 setadjoin( 294.74/44.20 setadjoin( 294.74/44.20 X122, 294.74/44.20 setadjoin( 294.74/44.20 X124, 294.74/44.20 emptyset)), 294.74/44.20 emptyset)), 294.74/44.20 powerset( 294.74/44.20 binunion( 294.74/44.20 X118,X120))))))) => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X126, 294.74/44.20 X128,X130]: 294.74/44.20 (in( 294.74/44.20 X130,X126) => 294.74/44.20 (![X132]: 294.74/44.20 (in( 294.74/44.20 X132,X128) => 294.74/44.20 in( 294.74/44.20 setadjoin( 294.74/44.20 setadjoin( 294.74/44.20 X130, 294.74/44.20 emptyset), 294.74/44.20 setadjoin( 294.74/44.20 setadjoin( 294.74/44.20 X130, 294.74/44.20 setadjoin( 294.74/44.20 X132, 294.74/44.20 emptyset)), 294.74/44.20 emptyset)), 294.74/44.20 powerset( 294.74/44.20 powerset( 294.74/44.20 binunion( 294.74/44.20 X126,X128)))))))) => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X134, 294.74/44.20 X136,X138]: 294.74/44.20 (in( 294.74/44.20 X138,X134) => 294.74/44.20 (![X140]: 294.74/44.20 (in( 294.74/44.20 X140,X136) => 294.74/44.20 in( 294.74/44.20 kpair( 294.74/44.20 X138,X140), 294.74/44.20 powerset( 294.74/44.20 powerset( 294.74/44.20 binunion( 294.74/44.20 X134,X136)))))))) => 294.74/44.20 ( 294.74/44.20 cartprodpairin => 294.74/44.20 ( 294.74/44.20 cartprodmempair1 => 294.74/44.20 ( 294.74/44.20 cartprodmempair => 294.74/44.20 ( 294.74/44.20 setunionE2 => 294.74/44.20 ( 294.74/44.20 setunionsingleton1 => 294.74/44.20 ( 294.74/44.20 setunionsingleton2 => 294.74/44.20 ( 294.74/44.20 setunionsingleton => 294.74/44.20 ( 294.74/44.20 singletonprop => 294.74/44.20 ( 294.74/44.20 ex1E1 => 294.74/44.20 ( 294.74/44.20 ex1I => 294.74/44.20 ( 294.74/44.20 ex1I2 => 294.74/44.20 ( 294.74/44.20 singletonsuniq => 294.74/44.20 ( 294.74/44.20 setukpairinjL1 => 294.74/44.20 ( 294.74/44.20 kfstsingleton => 294.74/44.20 ( 294.74/44.20 theprop => 294.74/44.20 ( 294.74/44.20 kfstpairEq => 294.74/44.20 ( 294.74/44.20 cartprodfstin => 294.74/44.20 ( 294.74/44.20 setukpairinjL2 => 294.74/44.20 ( 294.74/44.20 setukpairinjL => 294.74/44.20 ( 294.74/44.20 setukpairinjR11 => 294.74/44.20 ( 294.74/44.20 setukpairinjR12 => 294.74/44.20 ( 294.74/44.20 setukpairinjR1 => 294.74/44.20 ( 294.74/44.20 upairequniteq => 294.74/44.20 ( 294.74/44.20 setukpairinjR2 => 294.74/44.20 ( 294.74/44.20 setukpairinjR => 294.74/44.20 ( 294.74/44.20 ksndsingleton => 294.74/44.20 ( 294.74/44.20 ksndpairEq => 294.74/44.20 ( 294.74/44.20 kpairsurjEq => 294.74/44.20 ( 294.74/44.20 cartprodsndin => 294.74/44.20 ( 294.74/44.20 cartprodpairmemEL => 294.74/44.20 ( 294.74/44.20 cartprodpairmemER => 294.74/44.20 ( 294.74/44.20 cartprodmempaircEq => 294.74/44.20 ( 294.74/44.20 cartprodfstpairEq => 294.74/44.20 ( 294.74/44.20 cartprodsndpairEq => 294.74/44.20 ( 294.74/44.20 cartprodpairsurjEq => 294.74/44.20 ( 294.74/44.20 dpsetconstrI => 294.74/44.20 ( 294.74/44.20 dpsetconstrSub => 294.74/44.20 ( 294.74/44.20 setOfPairsIsBReln => 294.74/44.20 ( 294.74/44.20 dpsetconstrERa => 294.74/44.20 ( 294.74/44.20 dpsetconstrEL1 => 294.74/44.20 ( 294.74/44.20 dpsetconstrEL2 => 294.74/44.20 ( 294.74/44.20 dpsetconstrER => 294.74/44.20 ( 294.74/44.20 funcImageSingleton => 294.74/44.20 ( 294.74/44.20 apProp => 294.74/44.20 ( 294.74/44.20 app => 294.74/44.20 ( 294.74/44.20 infuncsetfunc => 294.74/44.20 ( 294.74/44.20 ap2p => 294.74/44.20 ( 294.74/44.20 funcinfuncset => 294.74/44.20 ( 294.74/44.20 lamProp => 294.74/44.20 ( 294.74/44.20 lamp => 294.74/44.20 ( 294.74/44.20 lam2p => 294.74/44.20 ( 294.74/44.20 brelnall1 => 294.74/44.20 ( 294.74/44.20 brelnall2 => 294.74/44.20 ( 294.74/44.20 ex1E2 => 294.74/44.20 ( 294.74/44.20 funcGraphProp1 => 294.74/44.20 ( 294.74/44.20 funcGraphProp3 => 294.74/44.20 ( 294.74/44.20 funcGraphProp2 => 294.74/44.20 ( 294.74/44.20 funcextLem => 294.74/44.20 ( 294.74/44.20 funcGraphProp4 => 294.74/44.20 ( 294.74/44.20 subbreln => 294.74/44.20 ( 294.74/44.20 eqbreln => 294.74/44.20 ( 294.74/44.20 funcext => 294.74/44.20 ( 294.74/44.20 funcext2 => 294.74/44.20 ( 294.74/44.20 ap2apEq1 => 294.74/44.20 ( 294.74/44.20 ap2apEq2 => 294.74/44.20 ( 294.74/44.20 beta1 => 294.74/44.20 ( 294.74/44.20 eta1 => 294.74/44.20 ( 294.74/44.20 lam2lamEq => 294.74/44.20 ( 294.74/44.20 beta2 => 294.74/44.20 ( 294.74/44.20 eta2 => 294.74/44.20 ( 294.74/44.20 iffalseProp1 => 294.74/44.20 ( 294.74/44.20 iffalseProp2 => 294.74/44.20 ( 294.74/44.20 iftrueProp1 => 294.74/44.20 ( 294.74/44.20 iftrueProp2 => 294.74/44.20 ( 294.74/44.20 ifSingleton => 294.74/44.20 ( 294.74/44.20 ifp => 294.74/44.20 ( 294.74/44.20 theeq => 294.74/44.20 ( 294.74/44.20 iftrue => 294.74/44.20 ( 294.74/44.20 iffalse => 294.74/44.20 ( 294.74/44.20 iftrueorfalse => 294.74/44.20 ( 294.74/44.20 binintersectT_lem => 294.74/44.20 ( 294.74/44.20 ![X142, 294.74/44.20 X144]: 294.74/44.20 (in( 294.74/44.20 X144, 294.74/44.20 powerset( 294.74/44.20 X142)) => 294.74/44.20 (![X146]: 294.74/44.20 (in( 294.74/44.20 X146, 294.74/44.20 powerset( 294.74/44.20 X142)) => 294.74/44.20 in( 294.74/44.20 binunion( 294.74/44.20 X144,X146), 294.74/44.20 powerset( 294.74/44.20 X142)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 294.74/44.20 tff(zf_stmt_1, type, zip_tseitin_0 : ($i * $i * $i) > $o). 294.74/44.20 tff(zf_stmt_2, axiom, (zip_tseitin_0(X8,X6,X4) <=> (in(X8,X6) => in(X8,X4)))). 294.74/44.20 tff(zf_stmt_3, conjecture, 294.74/44.20 (setextAx => 294.74/44.20 (emptysetAx => 294.74/44.20 (setadjoinAx => 294.74/44.20 ((![X4,X6]: (in(X6,powerset(X4)) <=> (![X8]: zip_tseitin_0(X8,X6,X4)))) => 294.74/44.20 (setunionAx => 294.74/44.20 (omega0Ax => 294.74/44.20 (omegaSAx => 294.74/44.20 (omegaIndAx => 294.74/44.20 (replAx => 294.74/44.20 (foundationAx => 294.74/44.20 (wellorderingAx => 294.74/44.20 (descrp => 294.74/44.20 (dsetconstrI => 294.74/44.20 (dsetconstrEL => 294.74/44.20 (dsetconstrER => 294.74/44.20 (exuE1 => 294.74/44.20 (prop2setE => 294.74/44.20 (emptysetE => 294.74/44.20 (emptysetimpfalse => 294.74/44.20 (notinemptyset => 294.74/44.20 (exuE3e => 294.74/44.20 (setext => 294.74/44.20 (emptyI => 294.74/44.20 (noeltsimpempty => 294.74/44.20 (setbeta => 294.74/44.20 (nonemptyE1 => 294.74/44.20 (nonemptyI => 294.74/44.20 (nonemptyI1 => 294.74/44.20 (setadjoinIL => 294.74/44.20 (emptyinunitempty => 294.74/44.20 (setadjoinIR => 294.74/44.20 (setadjoinE => 294.74/44.20 (setadjoinOr => 294.74/44.20 (setoftrueEq => 294.74/44.20 ((![X10,X12]: 294.74/44.20 ((![X14]: 294.74/44.20 (in(X14,X12) => in(X14,X10))) => 294.74/44.20 in(X12,powerset(X10)))) => 294.74/44.20 ((![X16]: in(emptyset,powerset(X16))) => 294.74/44.20 ((![X18]: in(emptyset,powerset(X18))) => 294.74/44.20 ((![X20,X22,X24]: 294.74/44.20 (in(X22,powerset(X20)) => 294.74/44.20 (in(X24,X22) => in(X24,X20)))) => 294.74/44.20 (setunionI => 294.74/44.20 (setunionE => 294.74/44.20 (subPowSU => 294.74/44.20 (exuE2 => 294.74/44.20 (nonemptyImpWitness => 294.74/44.20 (uniqinunit => 294.74/44.20 (notinsingleton => 294.74/44.20 (eqinunit => 294.74/44.20 (singletonsswitch => 294.74/44.20 (upairsetE => 294.74/44.20 (upairsetIL => 294.74/44.20 (upairsetIR => 294.74/44.20 (emptyE1 => 294.74/44.20 (vacuousDall => 294.74/44.20 (quantDeMorgan1 => 294.74/44.20 (quantDeMorgan2 => 294.74/44.20 (quantDeMorgan3 => 294.74/44.20 (quantDeMorgan4 => 294.74/44.20 (prop2setI => 294.74/44.20 (prop2set2propI => 294.74/44.20 (notdexE => 294.74/44.20 (notdallE => 294.74/44.20 (exuI1 => 294.74/44.20 (exuI3 => 294.74/44.20 (exuI2 => 294.74/44.20 (inCongP => 294.74/44.20 (in__Cong => 294.74/44.20 (exuE3u => 294.74/44.20 ( 294.74/44.20 exu__Cong => 294.74/44.20 ( 294.74/44.20 emptyset__Cong => 294.74/44.20 ( 294.74/44.20 setadjoin__Cong => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X26,X28]: 294.74/44.20 (( 294.74/44.20 X26 = X28) => 294.74/44.20 (powerset( 294.74/44.20 X26) = 294.74/44.20 powerset( 294.74/44.20 X28)))) => 294.74/44.20 ( 294.74/44.20 setunion__Cong => 294.74/44.20 ( 294.74/44.20 omega__Cong => 294.74/44.20 ( 294.74/44.20 exuEu => 294.74/44.20 ( 294.74/44.20 descr__Cong => 294.74/44.20 ( 294.74/44.20 dsetconstr__Cong => 294.74/44.20 ( 294.74/44.20 subsetI1 => 294.74/44.20 ( 294.74/44.20 eqimpsubset2 => 294.74/44.20 ( 294.74/44.20 eqimpsubset1 => 294.74/44.20 ( 294.74/44.20 subsetI2 => 294.74/44.20 ( 294.74/44.20 emptysetsubset => 294.74/44.20 ( 294.74/44.20 subsetE => 294.74/44.20 ( 294.74/44.20 subsetE2 => 294.74/44.20 ( 294.74/44.20 notsubsetI => 294.74/44.20 ( 294.74/44.20 notequalI1 => 294.74/44.20 ( 294.74/44.20 notequalI2 => 294.74/44.20 ( 294.74/44.20 subsetRefl => 294.74/44.20 ( 294.74/44.20 subsetTrans => 294.74/44.20 ( 294.74/44.20 setadjoinSub => 294.74/44.20 ( 294.74/44.20 setadjoinSub2 => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X30,X32]: 294.74/44.20 (subset( 294.74/44.20 X30,X32) => 294.74/44.20 in( 294.74/44.20 X30, 294.74/44.20 powerset( 294.74/44.20 X32)))) => 294.74/44.20 ( 294.74/44.20 setextsub => 294.74/44.20 ( 294.74/44.20 subsetemptysetimpeq => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X34,X36]: 294.74/44.20 (subset( 294.74/44.20 X36,X34) => 294.74/44.20 in( 294.74/44.20 X36, 294.74/44.20 powerset( 294.74/44.20 X34)))) => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X38,X40]: 294.74/44.20 (in( 294.74/44.20 X40, 294.74/44.20 powerset( 294.74/44.20 X38)) => 294.74/44.20 subset( 294.74/44.20 X40,X38))) => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X42]: 294.74/44.20 in( 294.74/44.20 X42, 294.74/44.20 powerset( 294.74/44.20 X42))) => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X44,X46]: 294.74/44.20 (subset( 294.74/44.20 X44,X46) => 294.74/44.20 subset( 294.74/44.20 powerset( 294.74/44.20 X44), 294.74/44.20 powerset( 294.74/44.20 X46)))) => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X48, 294.74/44.20 X50:( 294.74/44.20 ( 294.74/44.20 $i > $o))]: 294.74/44.20 in( 294.74/44.20 dsetconstr( 294.74/44.20 X48, 294.74/44.20 ^[V_1]: 294.74/44.20 X50(V_1)), 294.74/44.20 powerset( 294.74/44.20 X48))) => 294.74/44.20 ( 294.74/44.20 sepSubset => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X52, 294.74/44.20 X54,X56]: 294.74/44.20 (in( 294.74/44.20 X56,X52) => 294.74/44.20 in( 294.74/44.20 X56, 294.74/44.20 binunion( 294.74/44.20 X52,X54)))) => 294.74/44.20 ( 294.74/44.20 upairset2IR => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X58, 294.74/44.20 X60,X62]: 294.74/44.20 (in( 294.74/44.20 X62,X60) => 294.74/44.20 in( 294.74/44.20 X62, 294.74/44.20 binunion( 294.74/44.20 X58,X60)))) => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X64, 294.74/44.20 X66,X68, 294.74/44.20 X70:$o]: 294.74/44.20 (in( 294.74/44.20 X68, 294.74/44.20 binunion( 294.74/44.20 X64,X66)) => 294.74/44.20 (( 294.74/44.20 in( 294.74/44.20 X68,X64) => 294.74/44.20 X70) => 294.74/44.20 (( 294.74/44.20 in( 294.74/44.20 X68,X66) => 294.74/44.20 X70) => 294.74/44.20 X70)))) => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X72, 294.74/44.20 X74,X76]: 294.74/44.20 (in( 294.74/44.20 X76, 294.74/44.20 binunion( 294.74/44.20 X72,X74)) => 294.74/44.20 (in( 294.74/44.20 X76,X72) | 294.74/44.20 in( 294.74/44.20 X76,X74)))) => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X78,X80]: 294.74/44.20 subset( 294.74/44.20 X78, 294.74/44.20 binunion( 294.74/44.20 X78,X80))) => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X82,X84]: 294.74/44.20 subset( 294.74/44.20 X84, 294.74/44.20 binunion( 294.74/44.20 X82,X84))) => 294.74/44.20 ( 294.74/44.20 binintersectI => 294.74/44.20 ( 294.74/44.20 binintersectSubset5 => 294.74/44.20 ( 294.74/44.20 binintersectEL => 294.74/44.20 ( 294.74/44.20 binintersectLsub => 294.74/44.20 ( 294.74/44.20 binintersectSubset2 => 294.74/44.20 ( 294.74/44.20 binintersectSubset3 => 294.74/44.20 ( 294.74/44.20 binintersectER => 294.74/44.20 ( 294.74/44.20 disjointsetsI1 => 294.74/44.20 ( 294.74/44.20 binintersectRsub => 294.74/44.20 ( 294.74/44.20 binintersectSubset4 => 294.74/44.20 ( 294.74/44.20 binintersectSubset1 => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X86, 294.74/44.20 X88,X90]: 294.74/44.20 (binintersect( 294.74/44.20 X86, 294.74/44.20 binunion( 294.74/44.20 X88,X90)) = 294.74/44.20 binunion( 294.74/44.20 binintersect( 294.74/44.20 X86,X88), 294.74/44.20 binintersect( 294.74/44.20 X86,X90)))) => 294.74/44.20 ( 294.74/44.20 setminusI => 294.74/44.20 ( 294.74/44.20 setminusEL => 294.74/44.20 ( 294.74/44.20 setminusER => 294.74/44.20 ( 294.74/44.20 setminusSubset2 => 294.74/44.20 ( 294.74/44.20 setminusERneg => 294.74/44.20 ( 294.74/44.20 setminusELneg => 294.74/44.20 ( 294.74/44.20 setminusILneg => 294.74/44.20 ( 294.74/44.20 setminusIRneg => 294.74/44.20 ( 294.74/44.20 setminusLsub => 294.74/44.20 ( 294.74/44.20 setminusSubset1 => 294.74/44.20 ( 294.74/44.20 symdiffE => 294.74/44.20 ( 294.74/44.20 symdiffI1 => 294.74/44.20 ( 294.74/44.20 symdiffI2 => 294.74/44.20 ( 294.74/44.20 symdiffIneg1 => 294.74/44.20 ( 294.74/44.20 symdiffIneg2 => 294.74/44.20 ( 294.74/44.20 secondinupair => 294.74/44.20 ( 294.74/44.20 setukpairIL => 294.74/44.20 ( 294.74/44.20 setukpairIR => 294.74/44.20 ( 294.74/44.20 kpairiskpair => 294.74/44.20 ( 294.74/44.20 kpairp => 294.74/44.20 ( 294.74/44.20 singletonsubset => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X92,X94]: 294.74/44.20 (in( 294.74/44.20 X94,X92) => 294.74/44.20 in( 294.74/44.20 setadjoin( 294.74/44.20 X94, 294.74/44.20 emptyset), 294.74/44.20 powerset( 294.74/44.20 X92)))) => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X96, 294.74/44.20 X98,X100]: 294.74/44.20 (in( 294.74/44.20 X100,X96) => 294.74/44.20 in( 294.74/44.20 setadjoin( 294.74/44.20 X100, 294.74/44.20 emptyset), 294.74/44.20 powerset( 294.74/44.20 binunion( 294.74/44.20 X96,X98))))) => 294.74/44.20 ( 294.74/44.20 upairset2E => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X102, 294.74/44.20 X104,X106]: 294.74/44.20 (in( 294.74/44.20 X106,X102) => 294.74/44.20 (![X108]: 294.74/44.20 (in( 294.74/44.20 X108,X104) => 294.74/44.20 subset( 294.74/44.20 setadjoin( 294.74/44.20 X106, 294.74/44.20 setadjoin( 294.74/44.20 X108, 294.74/44.20 emptyset)), 294.74/44.20 binunion( 294.74/44.20 X102,X104)))))) => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X110, 294.74/44.20 X112,X114]: 294.74/44.20 (in( 294.74/44.20 X114,X110) => 294.74/44.20 (![X116]: 294.74/44.20 (in( 294.74/44.20 X116,X112) => 294.74/44.20 in( 294.74/44.20 setadjoin( 294.74/44.20 X114, 294.74/44.20 setadjoin( 294.74/44.20 X116, 294.74/44.20 emptyset)), 294.74/44.20 powerset( 294.74/44.20 binunion( 294.74/44.20 X110,X112))))))) => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X118, 294.74/44.20 X120,X122]: 294.74/44.20 (in( 294.74/44.20 X122,X118) => 294.74/44.20 (![X124]: 294.74/44.20 (in( 294.74/44.20 X124,X120) => 294.74/44.20 subset( 294.74/44.20 setadjoin( 294.74/44.20 setadjoin( 294.74/44.20 X122, 294.74/44.20 emptyset), 294.74/44.20 setadjoin( 294.74/44.20 setadjoin( 294.74/44.20 X122, 294.74/44.20 setadjoin( 294.74/44.20 X124, 294.74/44.20 emptyset)), 294.74/44.20 emptyset)), 294.74/44.20 powerset( 294.74/44.20 binunion( 294.74/44.20 X118,X120))))))) => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X126, 294.74/44.20 X128,X130]: 294.74/44.20 (in( 294.74/44.20 X130,X126) => 294.74/44.20 (![X132]: 294.74/44.20 (in( 294.74/44.20 X132,X128) => 294.74/44.20 in( 294.74/44.20 setadjoin( 294.74/44.20 setadjoin( 294.74/44.20 X130, 294.74/44.20 emptyset), 294.74/44.20 setadjoin( 294.74/44.20 setadjoin( 294.74/44.20 X130, 294.74/44.20 setadjoin( 294.74/44.20 X132, 294.74/44.20 emptyset)), 294.74/44.20 emptyset)), 294.74/44.20 powerset( 294.74/44.20 powerset( 294.74/44.20 binunion( 294.74/44.20 X126,X128)))))))) => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X134, 294.74/44.20 X136,X138]: 294.74/44.20 (in( 294.74/44.20 X138,X134) => 294.74/44.20 (![X140]: 294.74/44.20 (in( 294.74/44.20 X140,X136) => 294.74/44.20 in( 294.74/44.20 kpair( 294.74/44.20 X138,X140), 294.74/44.20 powerset( 294.74/44.20 powerset( 294.74/44.20 binunion( 294.74/44.20 X134,X136)))))))) => 294.74/44.20 ( 294.74/44.20 cartprodpairin => 294.74/44.20 ( 294.74/44.20 cartprodmempair1 => 294.74/44.20 ( 294.74/44.20 cartprodmempair => 294.74/44.20 ( 294.74/44.20 setunionE2 => 294.74/44.20 ( 294.74/44.20 setunionsingleton1 => 294.74/44.20 ( 294.74/44.20 setunionsingleton2 => 294.74/44.20 ( 294.74/44.20 setunionsingleton => 294.74/44.20 ( 294.74/44.20 singletonprop => 294.74/44.20 ( 294.74/44.20 ex1E1 => 294.74/44.20 ( 294.74/44.20 ex1I => 294.74/44.20 ( 294.74/44.20 ex1I2 => 294.74/44.20 ( 294.74/44.20 singletonsuniq => 294.74/44.20 ( 294.74/44.20 setukpairinjL1 => 294.74/44.20 ( 294.74/44.20 kfstsingleton => 294.74/44.20 ( 294.74/44.20 theprop => 294.74/44.20 ( 294.74/44.20 kfstpairEq => 294.74/44.20 ( 294.74/44.20 cartprodfstin => 294.74/44.20 ( 294.74/44.20 setukpairinjL2 => 294.74/44.20 ( 294.74/44.20 setukpairinjL => 294.74/44.20 ( 294.74/44.20 setukpairinjR11 => 294.74/44.20 ( 294.74/44.20 setukpairinjR12 => 294.74/44.20 ( 294.74/44.20 setukpairinjR1 => 294.74/44.20 ( 294.74/44.20 upairequniteq => 294.74/44.20 ( 294.74/44.20 setukpairinjR2 => 294.74/44.20 ( 294.74/44.20 setukpairinjR => 294.74/44.20 ( 294.74/44.20 ksndsingleton => 294.74/44.20 ( 294.74/44.20 ksndpairEq => 294.74/44.20 ( 294.74/44.20 kpairsurjEq => 294.74/44.20 ( 294.74/44.20 cartprodsndin => 294.74/44.20 ( 294.74/44.20 cartprodpairmemEL => 294.74/44.20 ( 294.74/44.20 cartprodpairmemER => 294.74/44.20 ( 294.74/44.20 cartprodmempaircEq => 294.74/44.20 ( 294.74/44.20 cartprodfstpairEq => 294.74/44.20 ( 294.74/44.20 cartprodsndpairEq => 294.74/44.20 ( 294.74/44.20 cartprodpairsurjEq => 294.74/44.20 ( 294.74/44.20 dpsetconstrI => 294.74/44.20 ( 294.74/44.20 dpsetconstrSub => 294.74/44.20 ( 294.74/44.20 setOfPairsIsBReln => 294.74/44.20 ( 294.74/44.20 dpsetconstrERa => 294.74/44.20 ( 294.74/44.20 dpsetconstrEL1 => 294.74/44.20 ( 294.74/44.20 dpsetconstrEL2 => 294.74/44.20 ( 294.74/44.20 dpsetconstrER => 294.74/44.20 ( 294.74/44.20 funcImageSingleton => 294.74/44.20 ( 294.74/44.20 apProp => 294.74/44.20 ( 294.74/44.20 app => 294.74/44.20 ( 294.74/44.20 infuncsetfunc => 294.74/44.20 ( 294.74/44.20 ap2p => 294.74/44.20 ( 294.74/44.20 funcinfuncset => 294.74/44.20 ( 294.74/44.20 lamProp => 294.74/44.20 ( 294.74/44.20 lamp => 294.74/44.20 ( 294.74/44.20 lam2p => 294.74/44.20 ( 294.74/44.20 brelnall1 => 294.74/44.20 ( 294.74/44.20 brelnall2 => 294.74/44.20 ( 294.74/44.20 ex1E2 => 294.74/44.20 ( 294.74/44.20 funcGraphProp1 => 294.74/44.20 ( 294.74/44.20 funcGraphProp3 => 294.74/44.20 ( 294.74/44.20 funcGraphProp2 => 294.74/44.20 ( 294.74/44.20 funcextLem => 294.74/44.20 ( 294.74/44.20 funcGraphProp4 => 294.74/44.20 ( 294.74/44.20 subbreln => 294.74/44.20 ( 294.74/44.20 eqbreln => 294.74/44.20 ( 294.74/44.20 funcext => 294.74/44.20 ( 294.74/44.20 funcext2 => 294.74/44.20 ( 294.74/44.20 ap2apEq1 => 294.74/44.20 ( 294.74/44.20 ap2apEq2 => 294.74/44.20 ( 294.74/44.20 beta1 => 294.74/44.20 ( 294.74/44.20 eta1 => 294.74/44.20 ( 294.74/44.20 lam2lamEq => 294.74/44.20 ( 294.74/44.20 beta2 => 294.74/44.20 ( 294.74/44.20 eta2 => 294.74/44.20 ( 294.74/44.20 iffalseProp1 => 294.74/44.20 ( 294.74/44.20 iffalseProp2 => 294.74/44.20 ( 294.74/44.20 iftrueProp1 => 294.74/44.20 ( 294.74/44.20 iftrueProp2 => 294.74/44.20 ( 294.74/44.20 ifSingleton => 294.74/44.20 ( 294.74/44.20 ifp => 294.74/44.20 ( 294.74/44.20 theeq => 294.74/44.20 ( 294.74/44.20 iftrue => 294.74/44.20 ( 294.74/44.20 iffalse => 294.74/44.20 ( 294.74/44.20 iftrueorfalse => 294.74/44.20 ( 294.74/44.20 binintersectT_lem => 294.74/44.20 ( 294.74/44.20 ![X142, 294.74/44.20 X144]: 294.74/44.20 (in( 294.74/44.20 X144, 294.74/44.20 powerset( 294.74/44.20 X142)) => 294.74/44.20 (![X146]: 294.74/44.20 (in( 294.74/44.20 X146, 294.74/44.20 powerset( 294.74/44.20 X142)) => 294.74/44.20 in( 294.74/44.20 binunion( 294.74/44.20 X144,X146), 294.74/44.20 powerset( 294.74/44.20 X142)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 294.74/44.20 tff(zf_stmt_4, negated_conjecture, 294.74/44.20 (~ 294.74/44.20 (setextAx => 294.74/44.20 (emptysetAx => 294.74/44.20 (setadjoinAx => 294.74/44.20 ((![X4,X6]: (in(X6,powerset(X4)) <=> (![X8]: zip_tseitin_0(X8,X6,X4)))) => 294.74/44.20 (setunionAx => 294.74/44.20 (omega0Ax => 294.74/44.20 (omegaSAx => 294.74/44.20 (omegaIndAx => 294.74/44.20 (replAx => 294.74/44.20 (foundationAx => 294.74/44.20 (wellorderingAx => 294.74/44.20 (descrp => 294.74/44.20 (dsetconstrI => 294.74/44.20 (dsetconstrEL => 294.74/44.20 (dsetconstrER => 294.74/44.20 (exuE1 => 294.74/44.20 (prop2setE => 294.74/44.20 (emptysetE => 294.74/44.20 (emptysetimpfalse => 294.74/44.20 (notinemptyset => 294.74/44.20 (exuE3e => 294.74/44.20 (setext => 294.74/44.20 (emptyI => 294.74/44.20 (noeltsimpempty => 294.74/44.20 (setbeta => 294.74/44.20 (nonemptyE1 => 294.74/44.20 (nonemptyI => 294.74/44.20 (nonemptyI1 => 294.74/44.20 (setadjoinIL => 294.74/44.20 (emptyinunitempty => 294.74/44.20 (setadjoinIR => 294.74/44.20 (setadjoinE => 294.74/44.20 (setadjoinOr => 294.74/44.20 (setoftrueEq => 294.74/44.20 ((![X10,X12]: 294.74/44.20 ((![X14]: 294.74/44.20 (in(X14,X12) => in(X14,X10))) => 294.74/44.20 in(X12,powerset(X10)))) => 294.74/44.20 ((![X16]: in(emptyset,powerset(X16))) => 294.74/44.20 ((![X18]: in(emptyset,powerset(X18))) => 294.74/44.20 ((![X20,X22,X24]: 294.74/44.20 (in(X22,powerset(X20)) => 294.74/44.20 (in(X24,X22) => in(X24,X20)))) => 294.74/44.20 (setunionI => 294.74/44.20 (setunionE => 294.74/44.20 (subPowSU => 294.74/44.20 (exuE2 => 294.74/44.20 (nonemptyImpWitness => 294.74/44.20 (uniqinunit => 294.74/44.20 (notinsingleton => 294.74/44.20 (eqinunit => 294.74/44.20 (singletonsswitch => 294.74/44.20 (upairsetE => 294.74/44.20 (upairsetIL => 294.74/44.20 (upairsetIR => 294.74/44.20 (emptyE1 => 294.74/44.20 (vacuousDall => 294.74/44.20 (quantDeMorgan1 => 294.74/44.20 (quantDeMorgan2 => 294.74/44.20 (quantDeMorgan3 => 294.74/44.20 (quantDeMorgan4 => 294.74/44.20 (prop2setI => 294.74/44.20 (prop2set2propI => 294.74/44.20 (notdexE => 294.74/44.20 (notdallE => 294.74/44.20 (exuI1 => 294.74/44.20 (exuI3 => 294.74/44.20 (exuI2 => 294.74/44.20 (inCongP => 294.74/44.20 ( 294.74/44.20 in__Cong => 294.74/44.20 ( 294.74/44.20 exuE3u => 294.74/44.20 ( 294.74/44.20 exu__Cong => 294.74/44.20 ( 294.74/44.20 emptyset__Cong => 294.74/44.20 ( 294.74/44.20 setadjoin__Cong => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X26,X28]: 294.74/44.20 (( 294.74/44.20 X26 = X28) => 294.74/44.20 (powerset( 294.74/44.20 X26) = 294.74/44.20 powerset( 294.74/44.20 X28)))) => 294.74/44.20 ( 294.74/44.20 setunion__Cong => 294.74/44.20 ( 294.74/44.20 omega__Cong => 294.74/44.20 ( 294.74/44.20 exuEu => 294.74/44.20 ( 294.74/44.20 descr__Cong => 294.74/44.20 ( 294.74/44.20 dsetconstr__Cong => 294.74/44.20 ( 294.74/44.20 subsetI1 => 294.74/44.20 ( 294.74/44.20 eqimpsubset2 => 294.74/44.20 ( 294.74/44.20 eqimpsubset1 => 294.74/44.20 ( 294.74/44.20 subsetI2 => 294.74/44.20 ( 294.74/44.20 emptysetsubset => 294.74/44.20 ( 294.74/44.20 subsetE => 294.74/44.20 ( 294.74/44.20 subsetE2 => 294.74/44.20 ( 294.74/44.20 notsubsetI => 294.74/44.20 ( 294.74/44.20 notequalI1 => 294.74/44.20 ( 294.74/44.20 notequalI2 => 294.74/44.20 ( 294.74/44.20 subsetRefl => 294.74/44.20 ( 294.74/44.20 subsetTrans => 294.74/44.20 ( 294.74/44.20 setadjoinSub => 294.74/44.20 ( 294.74/44.20 setadjoinSub2 => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X30,X32]: 294.74/44.20 (subset( 294.74/44.20 X30,X32) => 294.74/44.20 in( 294.74/44.20 X30, 294.74/44.20 powerset( 294.74/44.20 X32)))) => 294.74/44.20 ( 294.74/44.20 setextsub => 294.74/44.20 ( 294.74/44.20 subsetemptysetimpeq => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X34,X36]: 294.74/44.20 (subset( 294.74/44.20 X36,X34) => 294.74/44.20 in( 294.74/44.20 X36, 294.74/44.20 powerset( 294.74/44.20 X34)))) => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X38,X40]: 294.74/44.20 (in( 294.74/44.20 X40, 294.74/44.20 powerset( 294.74/44.20 X38)) => 294.74/44.20 subset( 294.74/44.20 X40,X38))) => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X42]: 294.74/44.20 in( 294.74/44.20 X42, 294.74/44.20 powerset( 294.74/44.20 X42))) => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X44,X46]: 294.74/44.20 (subset( 294.74/44.20 X44,X46) => 294.74/44.20 subset( 294.74/44.20 powerset( 294.74/44.20 X44), 294.74/44.20 powerset( 294.74/44.20 X46)))) => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X48, 294.74/44.20 X50:( 294.74/44.20 ( 294.74/44.20 $i > $o))]: 294.74/44.20 in( 294.74/44.20 dsetconstr( 294.74/44.20 X48, 294.74/44.20 ^[V_1]: 294.74/44.20 X50(V_1)), 294.74/44.20 powerset( 294.74/44.20 X48))) => 294.74/44.20 ( 294.74/44.20 sepSubset => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X52, 294.74/44.20 X54,X56]: 294.74/44.20 (in( 294.74/44.20 X56,X52) => 294.74/44.20 in( 294.74/44.20 X56, 294.74/44.20 binunion( 294.74/44.20 X52,X54)))) => 294.74/44.20 ( 294.74/44.20 upairset2IR => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X58, 294.74/44.20 X60,X62]: 294.74/44.20 (in( 294.74/44.20 X62,X60) => 294.74/44.20 in( 294.74/44.20 X62, 294.74/44.20 binunion( 294.74/44.20 X58,X60)))) => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X64, 294.74/44.20 X66,X68, 294.74/44.20 X70:$o]: 294.74/44.20 (in( 294.74/44.20 X68, 294.74/44.20 binunion( 294.74/44.20 X64,X66)) => 294.74/44.20 (( 294.74/44.20 in( 294.74/44.20 X68,X64) => 294.74/44.20 X70) => 294.74/44.20 (( 294.74/44.20 in( 294.74/44.20 X68,X66) => 294.74/44.20 X70) => 294.74/44.20 X70)))) => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X72, 294.74/44.20 X74,X76]: 294.74/44.20 (in( 294.74/44.20 X76, 294.74/44.20 binunion( 294.74/44.20 X72,X74)) => 294.74/44.20 (in( 294.74/44.20 X76,X72) | 294.74/44.20 in( 294.74/44.20 X76,X74)))) => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X78,X80]: 294.74/44.20 subset( 294.74/44.20 X78, 294.74/44.20 binunion( 294.74/44.20 X78,X80))) => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X82,X84]: 294.74/44.20 subset( 294.74/44.20 X84, 294.74/44.20 binunion( 294.74/44.20 X82,X84))) => 294.74/44.20 ( 294.74/44.20 binintersectI => 294.74/44.20 ( 294.74/44.20 binintersectSubset5 => 294.74/44.20 ( 294.74/44.20 binintersectEL => 294.74/44.20 ( 294.74/44.20 binintersectLsub => 294.74/44.20 ( 294.74/44.20 binintersectSubset2 => 294.74/44.20 ( 294.74/44.20 binintersectSubset3 => 294.74/44.20 ( 294.74/44.20 binintersectER => 294.74/44.20 ( 294.74/44.20 disjointsetsI1 => 294.74/44.20 ( 294.74/44.20 binintersectRsub => 294.74/44.20 ( 294.74/44.20 binintersectSubset4 => 294.74/44.20 ( 294.74/44.20 binintersectSubset1 => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X86, 294.74/44.20 X88,X90]: 294.74/44.20 (binintersect( 294.74/44.20 X86, 294.74/44.20 binunion( 294.74/44.20 X88,X90)) = 294.74/44.20 binunion( 294.74/44.20 binintersect( 294.74/44.20 X86,X88), 294.74/44.20 binintersect( 294.74/44.20 X86,X90)))) => 294.74/44.20 ( 294.74/44.20 setminusI => 294.74/44.20 ( 294.74/44.20 setminusEL => 294.74/44.20 ( 294.74/44.20 setminusER => 294.74/44.20 ( 294.74/44.20 setminusSubset2 => 294.74/44.20 ( 294.74/44.20 setminusERneg => 294.74/44.20 ( 294.74/44.20 setminusELneg => 294.74/44.20 ( 294.74/44.20 setminusILneg => 294.74/44.20 ( 294.74/44.20 setminusIRneg => 294.74/44.20 ( 294.74/44.20 setminusLsub => 294.74/44.20 ( 294.74/44.20 setminusSubset1 => 294.74/44.20 ( 294.74/44.20 symdiffE => 294.74/44.20 ( 294.74/44.20 symdiffI1 => 294.74/44.20 ( 294.74/44.20 symdiffI2 => 294.74/44.20 ( 294.74/44.20 symdiffIneg1 => 294.74/44.20 ( 294.74/44.20 symdiffIneg2 => 294.74/44.20 ( 294.74/44.20 secondinupair => 294.74/44.20 ( 294.74/44.20 setukpairIL => 294.74/44.20 ( 294.74/44.20 setukpairIR => 294.74/44.20 ( 294.74/44.20 kpairiskpair => 294.74/44.20 ( 294.74/44.20 kpairp => 294.74/44.20 ( 294.74/44.20 singletonsubset => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X92,X94]: 294.74/44.20 (in( 294.74/44.20 X94,X92) => 294.74/44.20 in( 294.74/44.20 setadjoin( 294.74/44.20 X94, 294.74/44.20 emptyset), 294.74/44.20 powerset( 294.74/44.20 X92)))) => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X96, 294.74/44.20 X98,X100]: 294.74/44.20 (in( 294.74/44.20 X100,X96) => 294.74/44.20 in( 294.74/44.20 setadjoin( 294.74/44.20 X100, 294.74/44.20 emptyset), 294.74/44.20 powerset( 294.74/44.20 binunion( 294.74/44.20 X96,X98))))) => 294.74/44.20 ( 294.74/44.20 upairset2E => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X102, 294.74/44.20 X104,X106]: 294.74/44.20 (in( 294.74/44.20 X106,X102) => 294.74/44.20 (![X108]: 294.74/44.20 (in( 294.74/44.20 X108,X104) => 294.74/44.20 subset( 294.74/44.20 setadjoin( 294.74/44.20 X106, 294.74/44.20 setadjoin( 294.74/44.20 X108, 294.74/44.20 emptyset)), 294.74/44.20 binunion( 294.74/44.20 X102,X104)))))) => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X110, 294.74/44.20 X112,X114]: 294.74/44.20 (in( 294.74/44.20 X114,X110) => 294.74/44.20 (![X116]: 294.74/44.20 (in( 294.74/44.20 X116,X112) => 294.74/44.20 in( 294.74/44.20 setadjoin( 294.74/44.20 X114, 294.74/44.20 setadjoin( 294.74/44.20 X116, 294.74/44.20 emptyset)), 294.74/44.20 powerset( 294.74/44.20 binunion( 294.74/44.20 X110,X112))))))) => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X118, 294.74/44.20 X120,X122]: 294.74/44.20 (in( 294.74/44.20 X122,X118) => 294.74/44.20 (![X124]: 294.74/44.20 (in( 294.74/44.20 X124,X120) => 294.74/44.20 subset( 294.74/44.20 setadjoin( 294.74/44.20 setadjoin( 294.74/44.20 X122, 294.74/44.20 emptyset), 294.74/44.20 setadjoin( 294.74/44.20 setadjoin( 294.74/44.20 X122, 294.74/44.20 setadjoin( 294.74/44.20 X124, 294.74/44.20 emptyset)), 294.74/44.20 emptyset)), 294.74/44.20 powerset( 294.74/44.20 binunion( 294.74/44.20 X118,X120))))))) => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X126, 294.74/44.20 X128,X130]: 294.74/44.20 (in( 294.74/44.20 X130,X126) => 294.74/44.20 (![X132]: 294.74/44.20 (in( 294.74/44.20 X132,X128) => 294.74/44.20 in( 294.74/44.20 setadjoin( 294.74/44.20 setadjoin( 294.74/44.20 X130, 294.74/44.20 emptyset), 294.74/44.20 setadjoin( 294.74/44.20 setadjoin( 294.74/44.20 X130, 294.74/44.20 setadjoin( 294.74/44.20 X132, 294.74/44.20 emptyset)), 294.74/44.20 emptyset)), 294.74/44.20 powerset( 294.74/44.20 powerset( 294.74/44.20 binunion( 294.74/44.20 X126,X128)))))))) => 294.74/44.20 ( 294.74/44.20 ( 294.74/44.20 ![X134, 294.74/44.20 X136,X138]: 294.74/44.20 (in( 294.74/44.20 X138,X134) => 294.74/44.20 (![X140]: 294.74/44.20 (in( 294.74/44.20 X140,X136) => 294.74/44.20 in( 294.74/44.20 kpair( 294.74/44.20 X138,X140), 294.74/44.20 powerset( 294.74/44.20 powerset( 294.74/44.20 binunion( 294.74/44.20 X134,X136)))))))) => 294.74/44.20 ( 294.74/44.20 cartprodpairin => 294.74/44.20 ( 294.74/44.20 cartprodmempair1 => 294.74/44.20 ( 294.74/44.20 cartprodmempair => 294.74/44.20 ( 294.74/44.20 setunionE2 => 294.74/44.20 ( 294.74/44.20 setunionsingleton1 => 294.74/44.20 ( 294.74/44.20 setunionsingleton2 => 294.74/44.20 ( 294.74/44.20 setunionsingleton => 294.74/44.20 ( 294.74/44.20 singletonprop => 294.74/44.20 ( 294.74/44.20 ex1E1 => 294.74/44.20 ( 294.74/44.20 ex1I => 294.74/44.20 ( 294.74/44.20 ex1I2 => 294.74/44.20 ( 294.74/44.20 singletonsuniq => 294.74/44.20 ( 294.74/44.20 setukpairinjL1 => 294.74/44.20 ( 294.74/44.20 kfstsingleton => 294.74/44.20 ( 294.74/44.20 theprop => 294.74/44.20 ( 294.74/44.20 kfstpairEq => 294.74/44.20 ( 294.74/44.20 cartprodfstin => 294.74/44.20 ( 294.74/44.20 setukpairinjL2 => 294.74/44.20 ( 294.74/44.20 setukpairinjL => 294.74/44.20 ( 294.74/44.20 setukpairinjR11 => 294.74/44.20 ( 294.74/44.20 setukpairinjR12 => 294.74/44.20 ( 294.74/44.20 setukpairinjR1 => 294.74/44.20 ( 294.74/44.20 upairequniteq => 294.74/44.20 ( 294.74/44.20 setukpairinjR2 => 294.74/44.20 ( 294.74/44.20 setukpairinjR => 294.74/44.20 ( 294.74/44.20 ksndsingleton => 294.74/44.20 ( 294.74/44.20 ksndpairEq => 294.74/44.20 ( 294.74/44.20 kpairsurjEq => 294.74/44.20 ( 294.74/44.20 cartprodsndin => 294.74/44.20 ( 294.74/44.20 cartprodpairmemEL => 294.74/44.20 ( 294.74/44.20 cartprodpairmemER => 294.74/44.20 ( 294.74/44.20 cartprodmempaircEq => 294.74/44.20 ( 294.74/44.20 cartprodfstpairEq => 294.74/44.20 ( 294.74/44.20 cartprodsndpairEq => 294.74/44.20 ( 294.74/44.20 cartprodpairsurjEq => 294.74/44.20 ( 294.74/44.20 dpsetconstrI => 294.74/44.20 ( 294.74/44.20 dpsetconstrSub => 294.74/44.20 ( 294.74/44.20 setOfPairsIsBReln => 294.74/44.20 ( 294.74/44.20 dpsetconstrERa => 294.74/44.20 ( 294.74/44.20 dpsetconstrEL1 => 294.74/44.20 ( 294.74/44.20 dpsetconstrEL2 => 294.74/44.20 ( 294.74/44.20 dpsetconstrER => 294.74/44.20 ( 294.74/44.20 funcImageSingleton => 294.74/44.20 ( 294.74/44.20 apProp => 294.74/44.20 ( 294.74/44.20 app => 294.74/44.20 ( 294.74/44.20 infuncsetfunc => 294.74/44.20 ( 294.74/44.20 ap2p => 294.74/44.20 ( 294.74/44.20 funcinfuncset => 294.74/44.20 ( 294.74/44.20 lamProp => 294.74/44.20 ( 294.74/44.20 lamp => 294.74/44.20 ( 294.74/44.20 lam2p => 294.74/44.20 ( 294.74/44.20 brelnall1 => 294.74/44.20 ( 294.74/44.20 brelnall2 => 294.74/44.20 ( 294.74/44.20 ex1E2 => 294.74/44.20 ( 294.74/44.20 funcGraphProp1 => 294.74/44.20 ( 294.74/44.20 funcGraphProp3 => 294.74/44.20 ( 294.74/44.20 funcGraphProp2 => 294.74/44.20 ( 294.74/44.20 funcextLem => 294.74/44.20 ( 294.74/44.20 funcGraphProp4 => 294.74/44.20 ( 294.74/44.20 subbreln => 294.74/44.20 ( 294.74/44.20 eqbreln => 294.74/44.20 ( 294.74/44.20 funcext => 294.74/44.20 ( 294.74/44.20 funcext2 => 294.74/44.20 ( 294.74/44.20 ap2apEq1 => 294.74/44.20 ( 294.74/44.20 ap2apEq2 => 294.74/44.20 ( 294.74/44.20 beta1 => 294.74/44.20 ( 294.74/44.20 eta1 => 294.74/44.20 ( 294.74/44.20 lam2lamEq => 294.74/44.20 ( 294.74/44.20 beta2 => 294.74/44.20 ( 294.74/44.20 eta2 => 294.74/44.20 ( 294.74/44.20 iffalseProp1 => 294.74/44.20 ( 294.74/44.20 iffalseProp2 => 294.74/44.20 ( 294.74/44.20 iftrueProp1 => 294.74/44.20 ( 294.74/44.20 iftrueProp2 => 294.74/44.20 ( 294.74/44.20 ifSingleton => 294.74/44.20 ( 294.74/44.20 ifp => 294.74/44.20 ( 294.74/44.20 theeq => 294.74/44.20 ( 294.74/44.20 iftrue => 294.96/44.20 ( 294.96/44.20 iffalse => 294.96/44.20 ( 294.96/44.20 iftrueorfalse => 294.96/44.20 ( 294.96/44.20 binintersectT_lem => 294.96/44.20 ( 294.96/44.20 ![X142, 294.96/44.20 X144]: 294.96/44.20 (in( 294.96/44.20 X144, 294.96/44.20 powerset( 294.96/44.20 X142)) => 294.96/44.20 (![X146]: 294.96/44.20 (in( 294.96/44.20 X146, 294.96/44.20 powerset( 294.96/44.20 X142)) => 294.96/44.20 in( 294.96/44.20 binunion( 294.96/44.20 X144,X146), 294.96/44.20 powerset( 294.96/44.20 X142))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 294.96/44.20 tff('26', plain, ~ in(binunion(sk_X144, sk_X146), powerset(sk_X142)), 294.96/44.20 inference('cnf', [status(esa)], [zf_stmt_4])). 294.96/44.20 tff('27', plain, ![X121, X122]: subset(X121, binunion(X121, X122)), 294.96/44.20 inference('cnf', [status(esa)], [zf_stmt_4])). 294.96/44.20 tff('28', plain, 294.96/44.20 ![X129, X130]: ( subset(X129, X130) | ~ in(X129, powerset(X130))), 294.96/44.20 inference('cnf', [status(esa)], [zf_stmt_4])). 294.96/44.20 tff('29', plain, in(sk_X144, powerset(sk_X142)), 294.96/44.20 inference('cnf', [status(esa)], [zf_stmt_4])). 294.96/44.20 tff('30', plain, 294.96/44.20 ![X85, X86, X87]: ( in(X85, binunion(X86, X87)) | ~ in(X85, X87)), 294.96/44.20 inference('cnf', [status(esa)], [zf_stmt_4])). 294.96/44.20 tff('31', plain, 294.96/44.20 ![X74, X75]: ( in(X74, powerset(X75)) | ~ in(sk_X14(X74, X75), X75)), 294.96/44.20 inference('cnf', [status(esa)], [zf_stmt_4])). 294.96/44.20 tff('32', plain, ![X91, X92]: subset(X91, binunion(X92, X91)), 294.96/44.20 inference('cnf', [status(esa)], [zf_stmt_4])). 294.96/44.20 tff('33', plain, in(sk_X146, powerset(sk_X142)), 294.96/44.20 inference('cnf', [status(esa)], [zf_stmt_4])). 294.96/44.20 tff('34', plain, 294.96/44.20 ![X74, X75]: ( in(X74, powerset(X75)) | in(sk_X14(X74, X75), X74)), 294.96/44.20 inference('cnf', [status(esa)], [zf_stmt_4])). 294.96/44.20 tff('35', plain, 294.96/44.20 ![X88, X89, X90]: 294.96/44.20 ( in(X88, X89) | in(X88, X90) | ~ in(X88, binunion(X90, X89))), 294.96/44.20 inference('cnf', [status(esa)], [zf_stmt_4])). 294.96/44.20 tff('36', plain, 294.96/44.20 ![X127, X128]: 294.96/44.20 ( subset(powerset(X127), powerset(X128)) | ~ subset(X127, X128)), 294.96/44.20 inference('cnf', [status(esa)], [zf_stmt_4])). 294.96/44.20 tff('37', plain, ![X77, X78]: ( in(X77, powerset(X78)) | ~ subset(X77, X78)), 294.96/44.20 inference('cnf', [status(esa)], [zf_stmt_4])). 294.96/44.20 tff('38', plain, 294.96/44.20 ![X135, X136, X137]: 294.96/44.20 (~ in(X135, powerset(X136)) | in(X137, X136) | ~ in(X137, X135)), 294.96/44.20 inference('cnf', [status(esa)], [zf_stmt_4])). 294.96/44.20 tff('39', plain, $false, 294.96/44.20 inference('eprover', [status(thm)], 294.96/44.20 ['26', '27', '28', '29', '30', '31', '32', '33', '34', '35', 294.96/44.20 '36', '37', '38'])). 294.96/44.20 294.96/44.20 % SZS output end Refutation 294.96/44.20 294.96/44.20 294.96/44.20 % Terminating... 294.96/44.20 % /export/starexec/sandbox2/solver/bin/lams/sh.or.sh running for 26s 295.13/44.32 % Runner terminated. 295.13/44.33 % Zipperpin 1.5 exiting 295.13/44.33 EOF