0.12/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.15 % Command : run_portfolio.sh /export/starexec/sandbox/benchmark/theBenchmark.p /export/starexec/sandbox/tmp/tmp.4JF7LiOopL 0.14/0.35 % Computer : n004.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 : 960 0.14/0.35 % DateTime : Thu Jul 2 08:57:58 EDT 2020 0.14/0.35 % CPUTime : 0.14/0.35 % Running portfolio for 120 s 0.14/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.14/0.35 % Number of cores: 8 0.14/0.35 % Python version: Python 3.6.8 0.14/0.35 % Running in HO mode 0.56/0.66 % Estimated wc time : 1286 0.56/0.66 % Estimated cpu time (7 cpus) : 183.71428571428572 0.56/0.72 % /export/starexec/sandbox/solver/bin/lams/s6.sh running for 21s 0.56/0.72 % /export/starexec/sandbox/solver/bin/lams/new_b3.2.norw.sh running for 15s 0.56/0.72 % /export/starexec/sandbox/solver/bin/lams/b.rpo.sh running for 21s 0.56/0.72 % /export/starexec/sandbox/solver/bin/lams/s6.ds.sh running for 10s 0.56/0.76 % /export/starexec/sandbox/solver/bin/lams/c.s.2.sh running for 68s 0.56/0.76 % /export/starexec/sandbox/solver/bin/lams/c.easy.sh running for 26s 0.56/0.77 % /export/starexec/sandbox/solver/bin/lams/old_b3.avatar.sh running for 15s 70.73/10.74 % /export/starexec/sandbox/solver/bin/lams/old_sp2.sh running for 17s 98.17/14.77 % Solved by lams/old_sp2.sh. 98.17/14.77 % done 307 iterations in 3.630s 98.17/14.77 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 98.17/14.77 % SZS output start Refutation 98.17/14.77 tff(cartprodpairin, axiom, cartprodpairin <=> 98.17/14.77 (![A,B,Xx]: 98.17/14.77 (in(Xx,A) => (![Xy]: (in(Xy,B) => in(kpair(Xx,Xy),cartprod(A,B))))))). 98.17/14.77 tff('0', plain, 98.17/14.77 cartprodpairin = 98.17/14.77 (![X4,X6,X8]: 98.17/14.77 (in(X8,X4) => 98.17/14.77 (![X10]: (in(X10,X6) => in(kpair(X8,X10),cartprod(X4,X6)))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(ubforcartprodlem3, axiom, ubforcartprodlem3 <=> 98.17/14.77 (![A,B,Xx]: 98.17/14.77 (in(Xx,A) => 98.17/14.77 (![Xy]: 98.17/14.77 (in(Xy,B) => in(kpair(Xx,Xy),powerset(powerset(binunion(A,B))))))))). 98.17/14.77 tff('1', plain, 98.17/14.77 ubforcartprodlem3 = 98.17/14.77 (![X4,X6,X8]: 98.17/14.77 (in(X8,X4) => 98.17/14.77 (![X10]: 98.17/14.77 (in(X10,X6) => 98.17/14.77 in(kpair(X8,X10),powerset(powerset(binunion(X4,X6)))))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(ubforcartprodlem2, axiom, ubforcartprodlem2 <=> 98.17/14.77 (![A,B,Xx]: 98.17/14.77 (in(Xx,A) => 98.17/14.77 (![Xy]: 98.17/14.77 (in(Xy,B) => 98.17/14.77 in(setadjoin(setadjoin(Xx,emptyset), 98.17/14.77 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 98.17/14.77 emptyset)), 98.17/14.77 powerset(powerset(binunion(A,B))))))))). 98.17/14.77 tff('2', plain, 98.17/14.77 ubforcartprodlem2 = 98.17/14.77 (![X4,X6,X8]: 98.17/14.77 (in(X8,X4) => 98.17/14.77 (![X10]: 98.17/14.77 (in(X10,X6) => 98.17/14.77 in(setadjoin(setadjoin(X8,emptyset), 98.17/14.77 setadjoin(setadjoin(X8,setadjoin(X10,emptyset)), 98.17/14.77 emptyset)), 98.17/14.77 powerset(powerset(binunion(X4,X6)))))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(ubforcartprodlem1, axiom, ubforcartprodlem1 <=> 98.17/14.77 (![A,B,Xx]: 98.17/14.77 (in(Xx,A) => 98.17/14.77 (![Xy]: 98.17/14.77 (in(Xy,B) => 98.17/14.77 subset(setadjoin(setadjoin(Xx,emptyset), 98.17/14.77 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 98.17/14.77 emptyset)), 98.17/14.77 powerset(binunion(A,B)))))))). 98.17/14.77 tff('3', plain, 98.17/14.77 ubforcartprodlem1 = 98.17/14.77 (![X4,X6,X8]: 98.17/14.77 (in(X8,X4) => 98.17/14.77 (![X10]: 98.17/14.77 (in(X10,X6) => 98.17/14.77 subset(setadjoin(setadjoin(X8,emptyset), 98.17/14.77 setadjoin(setadjoin(X8,setadjoin(X10,emptyset)), 98.17/14.77 emptyset)), 98.17/14.77 powerset(binunion(X4,X6))))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(upairinpowunion, axiom, upairinpowunion <=> 98.17/14.77 (![A,B,Xx]: 98.17/14.77 (in(Xx,A) => 98.17/14.77 (![Xy]: 98.17/14.77 (in(Xy,B) => 98.17/14.77 in(setadjoin(Xx,setadjoin(Xy,emptyset)),powerset(binunion(A,B)))))))). 98.17/14.77 tff('4', plain, 98.17/14.77 upairinpowunion = 98.17/14.77 (![X4,X6,X8]: 98.17/14.77 (in(X8,X4) => 98.17/14.77 (![X10]: 98.17/14.77 (in(X10,X6) => 98.17/14.77 in(setadjoin(X8,setadjoin(X10,emptyset)), 98.17/14.77 powerset(binunion(X4,X6))))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(upairsubunion, axiom, upairsubunion <=> 98.17/14.77 (![A,B,Xx]: 98.17/14.77 (in(Xx,A) => 98.17/14.77 (![Xy]: 98.17/14.77 (in(Xy,B) => 98.17/14.77 subset(setadjoin(Xx,setadjoin(Xy,emptyset)),binunion(A,B))))))). 98.17/14.77 tff('5', plain, 98.17/14.77 upairsubunion = 98.17/14.77 (![X4,X6,X8]: 98.17/14.77 (in(X8,X4) => 98.17/14.77 (![X10]: 98.17/14.77 (in(X10,X6) => 98.17/14.77 subset(setadjoin(X8,setadjoin(X10,emptyset)),binunion(X4,X6)))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(upairset2E, axiom, upairset2E <=> 98.17/14.77 (![Xx,Xy,Xz]: 98.17/14.77 (in(Xz,setadjoin(Xx,setadjoin(Xy,emptyset))) => ((Xz = Xx) | (Xz = Xy))))). 98.17/14.77 tff('6', plain, 98.17/14.77 upairset2E = 98.17/14.77 (![X4,X6,X8]: 98.17/14.77 (in(X8,setadjoin(X4,setadjoin(X6,emptyset))) => 98.17/14.77 ((X8 = X4) | (X8 = X6)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(singletoninpowunion, axiom, singletoninpowunion <=> 98.17/14.77 (![A,B,Xx]: 98.17/14.77 (in(Xx,A) => in(setadjoin(Xx,emptyset),powerset(binunion(A,B)))))). 98.17/14.77 tff('7', plain, 98.17/14.77 singletoninpowunion = 98.17/14.77 (![X4,X6,X8]: 98.17/14.77 (in(X8,X4) => in(setadjoin(X8,emptyset),powerset(binunion(X4,X6))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(singletoninpowerset, axiom, singletoninpowerset <=> 98.17/14.77 (![A,Xx]: (in(Xx,A) => in(setadjoin(Xx,emptyset),powerset(A))))). 98.17/14.77 tff('8', plain, 98.17/14.77 singletoninpowerset = 98.17/14.77 (![X4,X6]: (in(X6,X4) => in(setadjoin(X6,emptyset),powerset(X4)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(singletonsubset, axiom, singletonsubset <=> 98.17/14.77 (![A,Xx]: (in(Xx,A) => subset(setadjoin(Xx,emptyset),A)))). 98.17/14.77 tff('9', plain, 98.17/14.77 singletonsubset = 98.17/14.77 (![X4,X6]: (in(X6,X4) => subset(setadjoin(X6,emptyset),X4))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(cartprod, axiom, cartprod() = 98.17/14.77 ^[A,B]: 98.17/14.77 dsetconstr(powerset(powerset(binunion(A,B))), 98.17/14.77 ^[Xx]: 98.17/14.77 (?[Xy]: 98.17/14.77 ((?[Xz]: ((Xx = kpair(Xy,Xz)) & in(Xz,B))) & in(Xy,A))))). 98.17/14.77 tff(kpair, axiom, kpair() = 98.17/14.77 ^[Xx,Xy]: 98.17/14.77 setadjoin(setadjoin(Xx,emptyset), 98.17/14.77 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)),emptyset))). 98.17/14.77 tff('10', plain, 98.17/14.77 kpair = 98.17/14.77 (^[Xx,Xy]: 98.17/14.77 setadjoin(setadjoin(Xx,emptyset), 98.17/14.77 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)),emptyset))), 98.17/14.77 inference('simplify_rw_rule', [status(thm)], [kpair])). 98.17/14.77 tff('11', plain, 98.17/14.77 kpair = 98.17/14.77 (^[V_1,V_2]: 98.17/14.77 setadjoin(setadjoin(V_1,emptyset), 98.17/14.77 setadjoin(setadjoin(V_1,setadjoin(V_2,emptyset)),emptyset))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff('12', plain, 98.17/14.77 cartprod = 98.17/14.77 (^[A,B]: 98.17/14.77 dsetconstr(powerset(powerset(binunion(A,B))), 98.17/14.77 ^[Xx]: 98.17/14.77 (?[Xy]: 98.17/14.77 ((?[Xz]: ((Xx = kpair(Xy,Xz)) & in(Xz,B))) & in(Xy,A))))), 98.17/14.77 inference('simplify_rw_rule', [status(thm)], [cartprod, '11'])). 98.17/14.77 tff('13', plain, 98.17/14.77 cartprod = 98.17/14.77 (^[V_1,V_2]: 98.17/14.77 dsetconstr(powerset(powerset(binunion(V_1,V_2))), 98.17/14.77 ^[V_3]: 98.17/14.77 (?[X4]: 98.17/14.77 ((?[X6]: ((V_3 = kpair(X4,X6)) & in(X6,V_2))) & 98.17/14.77 in(X4,V_1))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(kpairp, axiom, kpairp <=> (![Xx,Xy]: iskpair(kpair(Xx,Xy)))). 98.17/14.77 tff('14', plain, kpairp = (![X4,X6]: iskpair(kpair(X4,X6))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(kpairiskpair, axiom, kpairiskpair <=> 98.17/14.77 (![Xx,Xy]: 98.17/14.77 iskpair(setadjoin(setadjoin(Xx,emptyset), 98.17/14.77 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 98.17/14.77 emptyset))))). 98.17/14.77 tff('15', plain, 98.17/14.77 kpairiskpair = 98.17/14.77 (![X4,X6]: 98.17/14.77 iskpair(setadjoin(setadjoin(X4,emptyset), 98.17/14.77 setadjoin(setadjoin(X4,setadjoin(X6,emptyset)), 98.17/14.77 emptyset)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(setukpairIR, axiom, setukpairIR <=> 98.17/14.77 (![Xx,Xy]: 98.17/14.77 in(Xy, 98.17/14.77 setunion(setadjoin(setadjoin(Xx,emptyset), 98.17/14.77 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 98.17/14.77 emptyset)))))). 98.17/14.77 tff('16', plain, 98.17/14.77 setukpairIR = 98.17/14.77 (![X4,X6]: 98.17/14.77 in(X6, 98.17/14.77 setunion(setadjoin(setadjoin(X4,emptyset), 98.17/14.77 setadjoin(setadjoin(X4,setadjoin(X6,emptyset)), 98.17/14.77 emptyset))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(setukpairIL, axiom, setukpairIL <=> 98.17/14.77 (![Xx,Xy]: 98.17/14.77 in(Xx, 98.17/14.77 setunion(setadjoin(setadjoin(Xx,emptyset), 98.17/14.77 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 98.17/14.77 emptyset)))))). 98.17/14.77 tff('17', plain, 98.17/14.77 setukpairIL = 98.17/14.77 (![X4,X6]: 98.17/14.77 in(X4, 98.17/14.77 setunion(setadjoin(setadjoin(X4,emptyset), 98.17/14.77 setadjoin(setadjoin(X4,setadjoin(X6,emptyset)), 98.17/14.77 emptyset))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(secondinupair, axiom, secondinupair <=> 98.17/14.77 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 98.17/14.77 tff('18', plain, 98.17/14.77 secondinupair = (![X4,X6]: in(X6,setadjoin(X4,setadjoin(X6,emptyset)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(iskpair, axiom, iskpair() = 98.17/14.77 ^[A]: 98.17/14.77 (?[Xx]: 98.17/14.77 ((?[Xy]: 98.17/14.77 ((A = 98.17/14.77 setadjoin(setadjoin(Xx,emptyset), 98.17/14.77 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 98.17/14.77 emptyset))) & 98.17/14.77 in(Xy,setunion(A)))) & 98.17/14.77 in(Xx,setunion(A))))). 98.17/14.77 tff('19', plain, 98.17/14.77 iskpair = 98.17/14.77 (^[A]: 98.17/14.77 (?[Xx]: 98.17/14.77 ((?[Xy]: 98.17/14.77 ((A = 98.17/14.77 setadjoin(setadjoin(Xx,emptyset), 98.17/14.77 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 98.17/14.77 emptyset))) & 98.17/14.77 in(Xy,setunion(A)))) & 98.17/14.77 in(Xx,setunion(A))))), 98.17/14.77 inference('simplify_rw_rule', [status(thm)], [iskpair])). 98.17/14.77 tff('20', plain, 98.17/14.77 iskpair = 98.17/14.77 (^[V_1]: 98.17/14.77 (?[X4]: 98.17/14.77 ((?[X6]: 98.17/14.77 ((V_1 = 98.17/14.77 setadjoin(setadjoin(X4,emptyset), 98.17/14.77 setadjoin(setadjoin(X4,setadjoin(X6,emptyset)), 98.17/14.77 emptyset))) & 98.17/14.77 in(X6,setunion(V_1)))) & 98.17/14.77 in(X4,setunion(V_1))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(symdiffIneg2, axiom, symdiffIneg2 <=> 98.17/14.77 (![A,B,Xx]: ((~in(Xx,A)) => ((~in(Xx,B)) => (~in(Xx,symdiff(A,B))))))). 98.17/14.77 tff('21', plain, 98.17/14.77 symdiffIneg2 = 98.17/14.77 (![X4,X6,X8]: 98.17/14.77 ((~in(X8,X4)) => ((~in(X8,X6)) => (~in(X8,symdiff(X4,X6)))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(symdiffIneg1, axiom, symdiffIneg1 <=> 98.17/14.77 (![A,B,Xx]: (in(Xx,A) => (in(Xx,B) => (~in(Xx,symdiff(A,B))))))). 98.17/14.77 tff('22', plain, 98.17/14.77 symdiffIneg1 = 98.17/14.77 (![X4,X6,X8]: (in(X8,X4) => (in(X8,X6) => (~in(X8,symdiff(X4,X6)))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(symdiffI2, axiom, symdiffI2 <=> 98.17/14.77 (![A,B,Xx]: ((~in(Xx,A)) => (in(Xx,B) => in(Xx,symdiff(A,B)))))). 98.17/14.77 tff('23', plain, 98.17/14.77 symdiffI2 = 98.17/14.77 (![X4,X6,X8]: ((~in(X8,X4)) => (in(X8,X6) => in(X8,symdiff(X4,X6))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(symdiffI1, axiom, symdiffI1 <=> 98.17/14.77 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => in(Xx,symdiff(A,B)))))). 98.17/14.77 tff('24', plain, 98.17/14.77 symdiffI1 = 98.17/14.77 (![X4,X6,X8]: (in(X8,X4) => ((~in(X8,X6)) => in(X8,symdiff(X4,X6))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(symdiffE, axiom, symdiffE <=> 98.17/14.77 (![A,B,Xx]: 98.17/14.77 (in(Xx,symdiff(A,B)) => 98.17/14.77 (![Xphi:$o]: 98.17/14.77 ((in(Xx,A) => ((~in(Xx,B)) => Xphi)) => 98.17/14.77 (((~in(Xx,A)) => (in(Xx,B) => Xphi)) => Xphi)))))). 98.17/14.77 tff('25', plain, 98.17/14.77 symdiffE = 98.17/14.77 (![X4,X6,X8]: 98.17/14.77 (in(X8,symdiff(X4,X6)) => 98.17/14.77 (![X10:$o]: 98.17/14.77 ((in(X8,X4) => ((~in(X8,X6)) => X10)) => 98.17/14.77 (((~in(X8,X4)) => (in(X8,X6) => X10)) => X10))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(setminusSubset1, axiom, setminusSubset1 <=> 98.17/14.77 (![A,B]: ((setminus(A,B) = emptyset) => subset(A,B)))). 98.17/14.77 tff('26', plain, 98.17/14.77 setminusSubset1 = 98.17/14.77 (![X4,X6]: ((setminus(X4,X6) = emptyset) => subset(X4,X6))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(setminusLsub, axiom, setminusLsub <=> (![A,B]: subset(setminus(A,B),A))). 98.17/14.77 tff('27', plain, setminusLsub = (![X4,X6]: subset(setminus(X4,X6),X4)), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(setminusIRneg, axiom, setminusIRneg <=> 98.17/14.77 (![A,B,Xx]: (in(Xx,B) => (~in(Xx,setminus(A,B)))))). 98.17/14.77 tff('28', plain, 98.17/14.77 setminusIRneg = (![X4,X6,X8]: (in(X8,X6) => (~in(X8,setminus(X4,X6))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(setminusILneg, axiom, setminusILneg <=> 98.17/14.77 (![A,B,Xx]: ((~in(Xx,A)) => (~in(Xx,setminus(A,B)))))). 98.17/14.77 tff('29', plain, 98.17/14.77 setminusILneg = 98.17/14.77 (![X4,X6,X8]: ((~in(X8,X4)) => (~in(X8,setminus(X4,X6))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(setminusELneg, axiom, setminusELneg <=> 98.17/14.77 (![A,B,Xx]: ((~in(Xx,setminus(A,B))) => ((~in(Xx,B)) => (~in(Xx,A)))))). 98.17/14.77 tff('30', plain, 98.17/14.77 setminusELneg = 98.17/14.77 (![X4,X6,X8]: 98.17/14.77 ((~in(X8,setminus(X4,X6))) => ((~in(X8,X6)) => (~in(X8,X4))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(setminusERneg, axiom, setminusERneg <=> 98.17/14.77 (![A,B,Xx]: ((~in(Xx,setminus(A,B))) => (in(Xx,A) => in(Xx,B))))). 98.17/14.77 tff('31', plain, 98.17/14.77 setminusERneg = 98.17/14.77 (![X4,X6,X8]: ((~in(X8,setminus(X4,X6))) => (in(X8,X4) => in(X8,X6)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(setminusSubset2, axiom, setminusSubset2 <=> 98.17/14.77 (![A,B]: (subset(A,B) => (setminus(A,B) = emptyset)))). 98.17/14.77 tff('32', plain, 98.17/14.77 setminusSubset2 = 98.17/14.77 (![X4,X6]: (subset(X4,X6) => (setminus(X4,X6) = emptyset))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(setminusER, axiom, setminusER <=> 98.17/14.77 (![A,B,Xx]: (in(Xx,setminus(A,B)) => (~in(Xx,B))))). 98.17/14.77 tff('33', plain, 98.17/14.77 setminusER = (![X4,X6,X8]: (in(X8,setminus(X4,X6)) => (~in(X8,X6)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(setminusEL, axiom, setminusEL <=> 98.17/14.77 (![A,B,Xx]: (in(Xx,setminus(A,B)) => in(Xx,A)))). 98.17/14.77 tff('34', plain, 98.17/14.77 setminusEL = (![X4,X6,X8]: (in(X8,setminus(X4,X6)) => in(X8,X4))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(setminusI, axiom, setminusI <=> 98.17/14.77 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => in(Xx,setminus(A,B)))))). 98.17/14.77 tff('35', plain, 98.17/14.77 setminusI = 98.17/14.77 (![X4,X6,X8]: (in(X8,X4) => ((~in(X8,X6)) => in(X8,setminus(X4,X6))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(bs114d, axiom, bs114d <=> 98.17/14.77 (![A,B,C]: 98.17/14.77 (binintersect(A,binunion(B,C)) = 98.17/14.77 binunion(binintersect(A,B),binintersect(A,C))))). 98.17/14.77 tff('36', plain, 98.17/14.77 bs114d = 98.17/14.77 (![X4,X6,X8]: 98.17/14.77 (binintersect(X4,binunion(X6,X8)) = 98.17/14.77 binunion(binintersect(X4,X6),binintersect(X4,X8)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(binintersectSubset1, axiom, binintersectSubset1 <=> 98.17/14.77 (![A,B]: ((binintersect(A,B) = A) => subset(A,B)))). 98.17/14.77 tff('37', plain, 98.17/14.77 binintersectSubset1 = 98.17/14.77 (![X4,X6]: ((binintersect(X4,X6) = X4) => subset(X4,X6))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(binintersectSubset4, axiom, binintersectSubset4 <=> 98.17/14.77 (![A,B]: (subset(B,A) => (binintersect(A,B) = B)))). 98.17/14.77 tff('38', plain, 98.17/14.77 binintersectSubset4 = 98.17/14.77 (![X4,X6]: (subset(X6,X4) => (binintersect(X4,X6) = X6))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(binintersectRsub, axiom, binintersectRsub <=> 98.17/14.77 (![A,B]: subset(binintersect(A,B),B))). 98.17/14.77 tff('39', plain, 98.17/14.77 binintersectRsub = (![X4,X6]: subset(binintersect(X4,X6),X6)), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(disjointsetsI1, axiom, disjointsetsI1 <=> 98.17/14.77 (![A,B]: 98.17/14.77 ((~(?[Xx]: (in(Xx,B) & in(Xx,A)))) => (binintersect(A,B) = emptyset)))). 98.17/14.77 tff('40', plain, 98.17/14.77 disjointsetsI1 = 98.17/14.77 (![X4,X6]: 98.17/14.77 ((~(?[X8]: (in(X8,X6) & in(X8,X4)))) => 98.17/14.77 (binintersect(X4,X6) = emptyset))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(binintersectER, axiom, binintersectER <=> 98.17/14.77 (![A,B,Xx]: (in(Xx,binintersect(A,B)) => in(Xx,B)))). 98.17/14.77 tff('41', plain, 98.17/14.77 binintersectER = (![X4,X6,X8]: (in(X8,binintersect(X4,X6)) => in(X8,X6))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(binintersectSubset3, axiom, binintersectSubset3 <=> 98.17/14.77 (![A,B]: ((binintersect(A,B) = B) => subset(B,A)))). 98.17/14.77 tff('42', plain, 98.17/14.77 binintersectSubset3 = 98.17/14.77 (![X4,X6]: ((binintersect(X4,X6) = X6) => subset(X6,X4))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(binintersectSubset2, axiom, binintersectSubset2 <=> 98.17/14.77 (![A,B]: (subset(A,B) => (binintersect(A,B) = A)))). 98.17/14.77 tff('43', plain, 98.17/14.77 binintersectSubset2 = 98.17/14.77 (![X4,X6]: (subset(X4,X6) => (binintersect(X4,X6) = X4))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(binintersectLsub, axiom, binintersectLsub <=> 98.17/14.77 (![A,B]: subset(binintersect(A,B),A))). 98.17/14.77 tff('44', plain, 98.17/14.77 binintersectLsub = (![X4,X6]: subset(binintersect(X4,X6),X4)), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(binintersectEL, axiom, binintersectEL <=> 98.17/14.77 (![A,B,Xx]: (in(Xx,binintersect(A,B)) => in(Xx,A)))). 98.17/14.77 tff('45', plain, 98.17/14.77 binintersectEL = (![X4,X6,X8]: (in(X8,binintersect(X4,X6)) => in(X8,X4))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(binintersectSubset5, axiom, binintersectSubset5 <=> 98.17/14.77 (![A,B,C]: (subset(C,A) => (subset(C,B) => subset(C,binintersect(A,B)))))). 98.17/14.77 tff('46', plain, 98.17/14.77 binintersectSubset5 = 98.17/14.77 (![X4,X6,X8]: 98.17/14.77 (subset(X8,X4) => (subset(X8,X6) => subset(X8,binintersect(X4,X6))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(binintersectI, axiom, binintersectI <=> 98.17/14.77 (![A,B,Xx]: (in(Xx,A) => (in(Xx,B) => in(Xx,binintersect(A,B)))))). 98.17/14.77 tff('47', plain, 98.17/14.77 binintersectI = 98.17/14.77 (![X4,X6,X8]: (in(X8,X4) => (in(X8,X6) => in(X8,binintersect(X4,X6))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(binunionRsub, axiom, binunionRsub <=> (![A,B]: subset(B,binunion(A,B)))). 98.17/14.77 tff('48', plain, binunionRsub = (![X4,X6]: subset(X6,binunion(X4,X6))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(binunionLsub, axiom, binunionLsub <=> (![A,B]: subset(A,binunion(A,B)))). 98.17/14.77 tff('49', plain, binunionLsub = (![X4,X6]: subset(X4,binunion(X4,X6))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(binunionE, axiom, binunionE <=> 98.17/14.77 (![A,B,Xx]: (in(Xx,binunion(A,B)) => (in(Xx,A) | in(Xx,B))))). 98.17/14.77 tff('50', plain, 98.17/14.77 binunionE = 98.17/14.77 (![X4,X6,X8]: (in(X8,binunion(X4,X6)) => (in(X8,X4) | in(X8,X6)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(binunionEcases, axiom, binunionEcases <=> 98.17/14.77 (![A,B,Xx,Xphi:$o]: 98.17/14.77 (in(Xx,binunion(A,B)) => 98.17/14.77 ((in(Xx,A) => Xphi) => ((in(Xx,B) => Xphi) => Xphi))))). 98.17/14.77 tff('51', plain, 98.17/14.77 binunionEcases = 98.17/14.77 (![X4,X6,X8,X10:$o]: 98.17/14.77 (in(X8,binunion(X4,X6)) => 98.17/14.77 ((in(X8,X4) => X10) => ((in(X8,X6) => X10) => X10)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(binunionIR, axiom, binunionIR <=> 98.17/14.77 (![A,B,Xx]: (in(Xx,B) => in(Xx,binunion(A,B))))). 98.17/14.77 tff('52', plain, 98.17/14.77 binunionIR = (![X4,X6,X8]: (in(X8,X6) => in(X8,binunion(X4,X6)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(upairset2IR, axiom, upairset2IR <=> 98.17/14.77 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 98.17/14.77 tff('53', plain, 98.17/14.77 upairset2IR = (![X4,X6]: in(X6,setadjoin(X4,setadjoin(X6,emptyset)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(binunionIL, axiom, binunionIL <=> 98.17/14.77 (![A,B,Xx]: (in(Xx,A) => in(Xx,binunion(A,B))))). 98.17/14.77 tff('54', plain, 98.17/14.77 binunionIL = (![X4,X6,X8]: (in(X8,X4) => in(X8,binunion(X4,X6)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(sepSubset, axiom, sepSubset <=> 98.17/14.77 (![A,Xphi:(($i > $o))]: subset(dsetconstr(A,^[Xx]: Xphi(Xx)),A))). 98.17/14.77 tff('55', plain, 98.17/14.77 sepSubset = 98.17/14.77 (![X4,X6:(($i > $o))]: subset(dsetconstr(X4,^[V_1]: X6(V_1)),X4)), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(sepInPowerset, axiom, sepInPowerset <=> 98.17/14.77 (![A,Xphi:(($i > $o))]: in(dsetconstr(A,^[Xx]: Xphi(Xx)),powerset(A)))). 98.17/14.77 tff('56', plain, 98.17/14.77 sepInPowerset = 98.17/14.77 (![X4,X6:(($i > $o))]: in(dsetconstr(X4,^[V_1]: X6(V_1)),powerset(X4))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(powersetsubset, axiom, powersetsubset <=> 98.17/14.77 (![A,B]: (subset(A,B) => subset(powerset(A),powerset(B))))). 98.17/14.77 tff('57', plain, 98.17/14.77 powersetsubset = 98.17/14.77 (![X4,X6]: (subset(X4,X6) => subset(powerset(X4),powerset(X6)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(inPowerset, axiom, inPowerset <=> (![A]: in(A,powerset(A)))). 98.17/14.77 tff('58', plain, inPowerset = (![X4]: in(X4,powerset(X4))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(powersetE1, axiom, powersetE1 <=> 98.17/14.77 (![A,B]: (in(B,powerset(A)) => subset(B,A)))). 98.17/14.77 tff('59', plain, 98.17/14.77 powersetE1 = (![X4,X6]: (in(X6,powerset(X4)) => subset(X6,X4))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(powersetI1, axiom, powersetI1 <=> 98.17/14.77 (![A,B]: (subset(B,A) => in(B,powerset(A))))). 98.17/14.77 tff('60', plain, 98.17/14.77 powersetI1 = (![X4,X6]: (subset(X6,X4) => in(X6,powerset(X4)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(subsetemptysetimpeq, axiom, subsetemptysetimpeq <=> 98.17/14.77 (![A]: (subset(A,emptyset) => (A = emptyset)))). 98.17/14.77 tff('61', plain, 98.17/14.77 subsetemptysetimpeq = (![X4]: (subset(X4,emptyset) => (X4 = emptyset))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(setextsub, axiom, setextsub <=> 98.17/14.77 (![A,B]: (subset(A,B) => (subset(B,A) => (A = B))))). 98.17/14.77 tff('62', plain, 98.17/14.77 setextsub = (![X4,X6]: (subset(X4,X6) => (subset(X6,X4) => (X4 = X6)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(subset2powerset, axiom, subset2powerset <=> 98.17/14.77 (![A,B]: (subset(A,B) => in(A,powerset(B))))). 98.17/14.77 tff('63', plain, 98.17/14.77 subset2powerset = (![X4,X6]: (subset(X4,X6) => in(X4,powerset(X6)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(setadjoinSub2, axiom, setadjoinSub2 <=> 98.17/14.77 (![A,Xx,B]: (subset(A,B) => subset(A,setadjoin(Xx,B))))). 98.17/14.77 tff('64', plain, 98.17/14.77 setadjoinSub2 = 98.17/14.77 (![X4,X6,X8]: (subset(X4,X8) => subset(X4,setadjoin(X6,X8)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(setadjoinSub, axiom, setadjoinSub <=> 98.17/14.77 (![Xx,A]: subset(A,setadjoin(Xx,A)))). 98.17/14.77 tff('65', plain, setadjoinSub = (![X4,X6]: subset(X6,setadjoin(X4,X6))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(subsetTrans, axiom, subsetTrans <=> 98.17/14.77 (![A,B,C]: (subset(A,B) => (subset(B,C) => subset(A,C))))). 98.17/14.77 tff('66', plain, 98.17/14.77 subsetTrans = 98.17/14.77 (![X4,X6,X8]: (subset(X4,X6) => (subset(X6,X8) => subset(X4,X8)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(subsetRefl, axiom, subsetRefl <=> (![A]: subset(A,A))). 98.17/14.77 tff('67', plain, subsetRefl = (![X4]: subset(X4,X4)), define([status(thm)])). 98.17/14.77 tff(notequalI2, axiom, notequalI2 <=> 98.17/14.77 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => (A != B))))). 98.17/14.77 tff('68', plain, 98.17/14.77 notequalI2 = (![X4,X6,X8]: (in(X8,X4) => ((~in(X8,X6)) => (X4 != X6)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(notequalI1, axiom, notequalI1 <=> (![A,B]: ((~subset(A,B)) => (A != B)))). 98.17/14.77 tff('69', plain, notequalI1 = (![X4,X6]: ((~subset(X4,X6)) => (X4 != X6))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(notsubsetI, axiom, notsubsetI <=> 98.17/14.77 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => (~subset(A,B)))))). 98.17/14.77 tff('70', plain, 98.17/14.77 notsubsetI = 98.17/14.77 (![X4,X6,X8]: (in(X8,X4) => ((~in(X8,X6)) => (~subset(X4,X6))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(subsetE2, axiom, subsetE2 <=> 98.17/14.77 (![A,B,Xx]: (subset(A,B) => ((~in(Xx,B)) => (~in(Xx,A)))))). 98.17/14.77 tff('71', plain, 98.17/14.77 subsetE2 = 98.17/14.77 (![X4,X6,X8]: (subset(X4,X6) => ((~in(X8,X6)) => (~in(X8,X4))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(subsetE, axiom, subsetE <=> 98.17/14.77 (![A,B,Xx]: (subset(A,B) => (in(Xx,A) => in(Xx,B))))). 98.17/14.77 tff('72', plain, 98.17/14.77 subsetE = (![X4,X6,X8]: (subset(X4,X6) => (in(X8,X4) => in(X8,X6)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(emptysetsubset, axiom, emptysetsubset <=> (![A]: subset(emptyset,A))). 98.17/14.77 tff('73', plain, emptysetsubset = (![X4]: subset(emptyset,X4)), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(subsetI2, axiom, subsetI2 <=> 98.17/14.77 (![A,B]: ((![Xx]: (in(Xx,A) => in(Xx,B))) => subset(A,B)))). 98.17/14.77 tff('74', plain, 98.17/14.77 subsetI2 = 98.17/14.77 (![X4,X6]: ((![X8]: (in(X8,X4) => in(X8,X6))) => subset(X4,X6))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(eqimpsubset1, axiom, eqimpsubset1 <=> (![A,B]: ((A = B) => subset(A,B)))). 98.17/14.77 tff('75', plain, eqimpsubset1 = (![X4,X6]: ((X4 = X6) => subset(X4,X6))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(eqimpsubset2, axiom, eqimpsubset2 <=> (![A,B]: ((A = B) => subset(B,A)))). 98.17/14.77 tff('76', plain, eqimpsubset2 = (![X4,X6]: ((X4 = X6) => subset(X6,X4))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(subsetI1, axiom, subsetI1 <=> 98.17/14.77 (![A,B]: ((![Xx]: (in(Xx,A) => in(Xx,B))) => subset(A,B)))). 98.17/14.77 tff('77', plain, 98.17/14.77 subsetI1 = 98.17/14.77 (![X4,X6]: ((![X8]: (in(X8,X4) => in(X8,X6))) => subset(X4,X6))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(dsetconstr__Cong, axiom, dsetconstr__Cong <=> 98.17/14.77 (![A,B]: 98.17/14.77 ((A = B) => 98.17/14.77 (![Xphi:(($i > $o)),Xpsi:(($i > $o))]: 98.17/14.77 ((![Xx]: 98.17/14.77 (in(Xx,A) => 98.17/14.77 (![Xy]: (in(Xy,B) => ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy))))))) => 98.17/14.77 (dsetconstr(A,^[Xx]: Xphi(Xx)) = dsetconstr(B,^[Xx]: Xpsi(Xx)))))))). 98.17/14.77 tff('78', plain, 98.17/14.77 dsetconstr__Cong = 98.17/14.77 (![X4,X6]: 98.17/14.77 ((X4 = X6) => 98.17/14.77 (![X8:(($i > $o)),X10:(($i > $o))]: 98.17/14.77 ((![X12]: 98.17/14.77 (in(X12,X4) => 98.17/14.77 (![X14]: 98.17/14.77 (in(X14,X6) => ((X12 = X14) => (X8(X12) <=> X10(X14))))))) => 98.17/14.77 (dsetconstr(X4,^[V_1]: X8(V_1)) = dsetconstr(X6,^[V_2]: X10(V_2))))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(descr__Cong, axiom, descr__Cong <=> 98.17/14.77 (![Xphi:(($i > $o)),Xpsi:(($i > $o))]: 98.17/14.77 ((![Xx,Xy]: ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy)))) => 98.17/14.77 (exu(^[Xx]: Xphi(Xx)) => 98.17/14.77 (exu(^[Xx]: Xpsi(Xx)) => 98.17/14.77 (descr(^[Xx]: Xphi(Xx)) = descr(^[Xx]: Xpsi(Xx)))))))). 98.17/14.77 tff('79', plain, 98.17/14.77 descr__Cong = 98.17/14.77 (![X4:(($i > $o)),X6:(($i > $o))]: 98.17/14.77 ((![X8,X10]: ((X8 = X10) => (X4(X8) <=> X6(X10)))) => 98.17/14.77 (exu(^[V_1]: X4(V_1)) => 98.17/14.77 (exu(^[V_2]: X6(V_2)) => 98.17/14.77 (descr(^[V_3]: X4(V_3)) = descr(^[V_4]: X6(V_4))))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(exuEu, axiom, exuEu <=> 98.17/14.77 (![Xphi:(($i > $o))]: 98.17/14.77 (exu(^[Xx]: Xphi(Xx)) => 98.17/14.77 (![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))). 98.17/14.77 tff('80', plain, 98.17/14.77 exuEu = 98.17/14.77 (![X4:(($i > $o))]: 98.17/14.77 (exu(^[V_1]: X4(V_1)) => (![X6,X8]: (X4(X6) => (X4(X8) => (X6 = X8)))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(omega__Cong, axiom, omega__Cong <=> (omega = omega)). 98.17/14.77 tff('81', plain, omega__Cong = (omega = omega), define([status(thm)])). 98.17/14.77 tff(setunion__Cong, axiom, setunion__Cong <=> 98.17/14.77 (![A,B]: ((A = B) => (setunion(A) = setunion(B))))). 98.17/14.77 tff('82', plain, 98.17/14.77 setunion__Cong = (![X4,X6]: ((X4 = X6) => (setunion(X4) = setunion(X6)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(powerset__Cong, axiom, powerset__Cong <=> 98.17/14.77 (![A,B]: ((A = B) => (powerset(A) = powerset(B))))). 98.17/14.77 tff('83', plain, 98.17/14.77 powerset__Cong = (![X4,X6]: ((X4 = X6) => (powerset(X4) = powerset(X6)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(setadjoin__Cong, axiom, setadjoin__Cong <=> 98.17/14.77 (![Xx,Xy]: 98.17/14.77 ((Xx = Xy) => 98.17/14.77 (![Xz,Xu]: ((Xz = Xu) => (setadjoin(Xx,Xz) = setadjoin(Xy,Xu))))))). 98.17/14.77 tff('84', plain, 98.17/14.77 setadjoin__Cong = 98.17/14.77 (![X4,X6]: 98.17/14.77 ((X4 = X6) => 98.17/14.77 (![X8,X10]: ((X8 = X10) => (setadjoin(X4,X8) = setadjoin(X6,X10)))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(emptyset__Cong, axiom, emptyset__Cong <=> (emptyset = emptyset)). 98.17/14.77 tff('85', plain, emptyset__Cong = (emptyset = emptyset), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(exu__Cong, axiom, exu__Cong <=> 98.17/14.77 (![Xphi:(($i > $o)),Xpsi:(($i > $o))]: 98.17/14.77 ((![Xx,Xy]: ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy)))) => 98.17/14.77 (exu(^[Xx]: Xphi(Xx)) <=> exu(^[Xx]: Xpsi(Xx)))))). 98.17/14.77 tff('86', plain, 98.17/14.77 exu__Cong = 98.17/14.77 (![X4:(($i > $o)),X6:(($i > $o))]: 98.17/14.77 ((![X8,X10]: ((X8 = X10) => (X4(X8) <=> X6(X10)))) => 98.17/14.77 (exu(^[V_1]: X4(V_1)) <=> exu(^[V_2]: X6(V_2))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(exuE3u, axiom, exuE3u <=> 98.17/14.77 (![Xphi:(($i > $o))]: 98.17/14.77 (exu(^[Xx]: Xphi(Xx)) => 98.17/14.77 (![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))). 98.17/14.77 tff('87', plain, 98.17/14.77 exuE3u = 98.17/14.77 (![X4:(($i > $o))]: 98.17/14.77 (exu(^[V_1]: X4(V_1)) => (![X6,X8]: (X4(X6) => (X4(X8) => (X6 = X8)))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(in__Cong, axiom, in__Cong <=> 98.17/14.77 (![A,B]: ((A = B) => (![Xx,Xy]: ((Xx = Xy) => (in(Xx,A) <=> in(Xy,B))))))). 98.17/14.77 tff('88', plain, 98.17/14.77 in__Cong = 98.17/14.77 (![X4,X6]: 98.17/14.77 ((X4 = X6) => (![X8,X10]: ((X8 = X10) => (in(X8,X4) <=> in(X10,X6)))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(inCongP, axiom, inCongP <=> 98.17/14.77 (![A,B]: ((A = B) => (![Xx,Xy]: ((Xx = Xy) => (in(Xx,A) => in(Xy,B))))))). 98.17/14.77 tff('89', plain, 98.17/14.77 inCongP = 98.17/14.77 (![X4,X6]: 98.17/14.77 ((X4 = X6) => (![X8,X10]: ((X8 = X10) => (in(X8,X4) => in(X10,X6)))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(exuI2, axiom, exuI2 <=> 98.17/14.77 (![Xphi:(($i > $o))]: 98.17/14.77 ((?[Xx]: (![Xy]: (Xphi(Xy) <=> (Xy = Xx)))) => exu(^[Xx]: Xphi(Xx))))). 98.17/14.77 tff('90', plain, 98.17/14.77 exuI2 = 98.17/14.77 (![X4:(($i > $o))]: 98.17/14.77 ((?[X6]: (![X8]: (X4(X8) <=> (X8 = X6)))) => exu(^[V_1]: X4(V_1)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(exuI3, axiom, exuI3 <=> 98.17/14.77 (![Xphi:(($i > $o))]: 98.17/14.77 ((?[Xx]: Xphi(Xx)) => 98.17/14.77 ((![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy)))) => 98.17/14.77 exu(^[Xx]: Xphi(Xx)))))). 98.17/14.77 tff('91', plain, 98.17/14.77 exuI3 = 98.17/14.77 (![X4:(($i > $o))]: 98.17/14.77 ((?[X6]: X4(X6)) => 98.17/14.77 ((![X8,X10]: (X4(X8) => (X4(X10) => (X8 = X10)))) => 98.17/14.77 exu(^[V_1]: X4(V_1))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(exuI1, axiom, exuI1 <=> 98.17/14.77 (![Xphi:(($i > $o))]: 98.17/14.77 ((?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx))) => 98.17/14.77 exu(^[Xx]: Xphi(Xx))))). 98.17/14.77 tff('92', plain, 98.17/14.77 exuI1 = 98.17/14.77 (![X4:(($i > $o))]: 98.17/14.77 ((?[X6]: ((![X8]: (X4(X8) => (X6 = X8))) & X4(X6))) => 98.17/14.77 exu(^[V_1]: X4(V_1)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(notdallE, axiom, notdallE <=> 98.17/14.77 (![A,Xphi:(($i > $o))]: 98.17/14.77 ((~(![Xx]: (in(Xx,A) => Xphi(Xx)))) => (?[Xx]: ((~Xphi(Xx)) & in(Xx,A)))))). 98.17/14.77 tff('93', plain, 98.17/14.77 notdallE = 98.17/14.77 (![X4,X6:(($i > $o))]: 98.17/14.77 ((~(![X8]: (in(X8,X4) => X6(X8)))) => 98.17/14.77 (?[X10]: ((~X6(X10)) & in(X10,X4))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(notdexE, axiom, notdexE <=> 98.17/14.77 (![A,Xphi:(($i > $o))]: 98.17/14.77 ((~(?[Xx]: (Xphi(Xx) & in(Xx,A)))) => (![Xx]: (in(Xx,A) => (~Xphi(Xx))))))). 98.17/14.77 tff('94', plain, 98.17/14.77 notdexE = 98.17/14.77 (![X4,X6:(($i > $o))]: 98.17/14.77 ((~(?[X8]: (X6(X8) & in(X8,X4)))) => 98.17/14.77 (![X10]: (in(X10,X4) => (~X6(X10)))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(prop2set2propI, axiom, prop2set2propI <=> 98.17/14.77 (![Xphi:$o]: (Xphi => set2prop(prop2set(Xphi))))). 98.17/14.77 tff('95', plain, prop2set2propI = (![X4:$o]: (X4 => set2prop(prop2set(X4)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(prop2setI, axiom, prop2setI <=> 98.17/14.77 (![Xphi:$o]: (Xphi => in(emptyset,prop2set(Xphi))))). 98.17/14.77 tff('96', plain, prop2setI = (![X4:$o]: (X4 => in(emptyset,prop2set(X4)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(quantDeMorgan4, axiom, quantDeMorgan4 <=> 98.17/14.77 (![A,Xphi:(($i > $o))]: 98.17/14.77 ((?[Xx]: ((~Xphi(Xx)) & in(Xx,A))) => (~(![Xx]: (in(Xx,A) => Xphi(Xx))))))). 98.17/14.77 tff('97', plain, 98.17/14.77 quantDeMorgan4 = 98.17/14.77 (![X4,X6:(($i > $o))]: 98.17/14.77 ((?[X8]: ((~X6(X8)) & in(X8,X4))) => 98.17/14.77 (~(![X10]: (in(X10,X4) => X6(X10)))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(quantDeMorgan3, axiom, quantDeMorgan3 <=> 98.17/14.77 (![A,Xphi:(($i > $o))]: 98.17/14.77 ((~(?[Xx]: (Xphi(Xx) & in(Xx,A)))) => (![Xx]: (in(Xx,A) => (~Xphi(Xx))))))). 98.17/14.77 tff('98', plain, 98.17/14.77 quantDeMorgan3 = 98.17/14.77 (![X4,X6:(($i > $o))]: 98.17/14.77 ((~(?[X8]: (X6(X8) & in(X8,X4)))) => 98.17/14.77 (![X10]: (in(X10,X4) => (~X6(X10)))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(quantDeMorgan2, axiom, quantDeMorgan2 <=> 98.17/14.77 (![A,Xphi:(($i > $o))]: 98.17/14.77 ((![Xx]: (in(Xx,A) => (~Xphi(Xx)))) => (~(?[Xx]: (Xphi(Xx) & in(Xx,A))))))). 98.17/14.77 tff('99', plain, 98.17/14.77 quantDeMorgan2 = 98.17/14.77 (![X4,X6:(($i > $o))]: 98.17/14.77 ((![X8]: (in(X8,X4) => (~X6(X8)))) => 98.17/14.77 (~(?[X10]: (X6(X10) & in(X10,X4)))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(quantDeMorgan1, axiom, quantDeMorgan1 <=> 98.17/14.77 (![A,Xphi:(($i > $o))]: 98.17/14.77 ((~(![Xx]: (in(Xx,A) => Xphi(Xx)))) => (?[Xx]: ((~Xphi(Xx)) & in(Xx,A)))))). 98.17/14.77 tff('100', plain, 98.17/14.77 quantDeMorgan1 = 98.17/14.77 (![X4,X6:(($i > $o))]: 98.17/14.77 ((~(![X8]: (in(X8,X4) => X6(X8)))) => 98.17/14.77 (?[X10]: ((~X6(X10)) & in(X10,X4))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(vacuousDall, axiom, vacuousDall <=> 98.17/14.77 (![Xphi:(($i > $o)),Xx]: (in(Xx,emptyset) => Xphi(Xx)))). 98.17/14.77 tff('101', plain, 98.17/14.77 vacuousDall = (![X4:(($i > $o)),X6]: (in(X6,emptyset) => X4(X6))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(emptyE1, axiom, emptyE1 <=> 98.17/14.77 (![A,Xphi:(($i > $o))]: 98.17/14.77 ((?[Xx]: (Xphi(Xx) & in(Xx,A))) => 98.17/14.77 ((dsetconstr(A,^[Xx]: Xphi(Xx)) = emptyset) => $false)))). 98.17/14.77 tff('102', plain, 98.17/14.77 emptyE1 = 98.17/14.77 (![X4,X6:(($i > $o))]: 98.17/14.77 ((?[X8]: (X6(X8) & in(X8,X4))) => 98.17/14.77 ((dsetconstr(X4,^[V_1]: X6(V_1)) = emptyset) => $false))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(upairsetIR, axiom, upairsetIR <=> 98.17/14.77 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 98.17/14.77 tff('103', plain, 98.17/14.77 upairsetIR = (![X4,X6]: in(X6,setadjoin(X4,setadjoin(X6,emptyset)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(upairsetIL, axiom, upairsetIL <=> 98.17/14.77 (![Xx,Xy]: in(Xx,setadjoin(Xx,setadjoin(Xy,emptyset))))). 98.17/14.77 tff('104', plain, 98.17/14.77 upairsetIL = (![X4,X6]: in(X4,setadjoin(X4,setadjoin(X6,emptyset)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(upairsetE, axiom, upairsetE <=> 98.17/14.77 (![Xx,Xy,Xz]: 98.17/14.77 (in(Xz,setadjoin(Xx,setadjoin(Xy,emptyset))) => ((Xz = Xx) | (Xz = Xy))))). 98.17/14.77 tff('105', plain, 98.17/14.77 upairsetE = 98.17/14.77 (![X4,X6,X8]: 98.17/14.77 (in(X8,setadjoin(X4,setadjoin(X6,emptyset))) => 98.17/14.77 ((X8 = X4) | (X8 = X6)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(singletonsswitch, axiom, singletonsswitch <=> 98.17/14.77 (![Xx,Xy]: (in(Xx,setadjoin(Xy,emptyset)) => in(Xy,setadjoin(Xx,emptyset))))). 98.17/14.77 tff('106', plain, 98.17/14.77 singletonsswitch = 98.17/14.77 (![X4,X6]: 98.17/14.77 (in(X4,setadjoin(X6,emptyset)) => in(X6,setadjoin(X4,emptyset)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(eqinunit, axiom, eqinunit <=> 98.17/14.77 (![Xx,Xy]: ((Xx = Xy) => in(Xx,setadjoin(Xy,emptyset))))). 98.17/14.77 tff('107', plain, 98.17/14.77 eqinunit = (![X4,X6]: ((X4 = X6) => in(X4,setadjoin(X6,emptyset)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(notinsingleton, axiom, notinsingleton <=> 98.17/14.77 (![Xx,Xy]: ((Xx != Xy) => (~in(Xy,setadjoin(Xx,emptyset)))))). 98.17/14.77 tff('108', plain, 98.17/14.77 notinsingleton = 98.17/14.77 (![X4,X6]: ((X4 != X6) => (~in(X6,setadjoin(X4,emptyset))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(uniqinunit, axiom, uniqinunit <=> 98.17/14.77 (![Xx,Xy]: (in(Xx,setadjoin(Xy,emptyset)) => (Xx = Xy)))). 98.17/14.77 tff('109', plain, 98.17/14.77 uniqinunit = (![X4,X6]: (in(X4,setadjoin(X6,emptyset)) => (X4 = X6))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(nonemptyImpWitness, axiom, nonemptyImpWitness <=> 98.17/14.77 (![A]: (nonempty(A) => (?[Xx]: in(Xx,A))))). 98.17/14.77 tff('110', plain, 98.17/14.77 nonemptyImpWitness = (![X4]: (nonempty(X4) => (?[X6]: in(X6,X4)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(exuE2, axiom, exuE2 <=> 98.17/14.77 (![Xphi:(($i > $o))]: 98.17/14.77 (exu(^[Xx]: Xphi(Xx)) => (?[Xx]: (![Xy]: (Xphi(Xy) <=> (Xy = Xx))))))). 98.17/14.77 tff('111', plain, 98.17/14.77 exuE2 = 98.17/14.77 (![X4:(($i > $o))]: 98.17/14.77 (exu(^[V_1]: X4(V_1)) => (?[X6]: (![X8]: (X4(X8) <=> (X8 = X6)))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(subPowSU, axiom, subPowSU <=> 98.17/14.77 (![A,Xx]: (in(Xx,A) => in(Xx,powerset(setunion(A)))))). 98.17/14.77 tff('112', plain, 98.17/14.77 subPowSU = (![X4,X6]: (in(X6,X4) => in(X6,powerset(setunion(X4))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(setunionE, axiom, setunionE <=> 98.17/14.77 (![A,Xx]: 98.17/14.77 (in(Xx,setunion(A)) => 98.17/14.77 (![Xphi:$o]: ((![B]: (in(Xx,B) => (in(B,A) => Xphi))) => Xphi))))). 98.17/14.77 tff('113', plain, 98.17/14.77 setunionE = 98.17/14.77 (![X4,X6]: 98.17/14.77 (in(X6,setunion(X4)) => 98.17/14.77 (![X8:$o]: ((![X10]: (in(X6,X10) => (in(X10,X4) => X8))) => X8)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(setunionI, axiom, setunionI <=> 98.17/14.77 (![A,Xx,B]: (in(Xx,B) => (in(B,A) => in(Xx,setunion(A)))))). 98.17/14.77 tff('114', plain, 98.17/14.77 setunionI = 98.17/14.77 (![X4,X6,X8]: (in(X6,X8) => (in(X8,X4) => in(X6,setunion(X4))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(powersetE, axiom, powersetE <=> 98.17/14.77 (![A,B,Xx]: (in(B,powerset(A)) => (in(Xx,B) => in(Xx,A))))). 98.17/14.77 tff('115', plain, 98.17/14.77 powersetE = 98.17/14.77 (![X4,X6,X8]: (in(X6,powerset(X4)) => (in(X8,X6) => in(X8,X4)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(emptyInPowerset, axiom, emptyInPowerset <=> 98.17/14.77 (![A]: in(emptyset,powerset(A)))). 98.17/14.77 tff('116', plain, emptyInPowerset = (![X4]: in(emptyset,powerset(X4))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(emptyinPowerset, axiom, emptyinPowerset <=> 98.17/14.77 (![A]: in(emptyset,powerset(A)))). 98.17/14.77 tff('117', plain, emptyinPowerset = (![X4]: in(emptyset,powerset(X4))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(powersetI, axiom, powersetI <=> 98.17/14.77 (![A,B]: ((![Xx]: (in(Xx,B) => in(Xx,A))) => in(B,powerset(A))))). 98.17/14.77 tff('118', plain, 98.17/14.77 powersetI = 98.17/14.77 (![X4,X6]: ((![X8]: (in(X8,X6) => in(X8,X4))) => in(X6,powerset(X4)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(setoftrueEq, axiom, setoftrueEq <=> 98.17/14.77 (![A]: (dsetconstr(A,^[Xx]: $true) = A))). 98.17/14.77 tff('119', plain, setoftrueEq = (![X4]: (dsetconstr(X4,^[V_1]: $true) = X4)), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(setadjoinOr, axiom, setadjoinOr <=> 98.17/14.77 (![Xx,A,Xy]: (in(Xy,setadjoin(Xx,A)) => ((Xy = Xx) | in(Xy,A))))). 98.17/14.77 tff('120', plain, 98.17/14.77 setadjoinOr = 98.17/14.77 (![X4,X6,X8]: (in(X8,setadjoin(X4,X6)) => ((X8 = X4) | in(X8,X6)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(setadjoinE, axiom, setadjoinE <=> 98.17/14.77 (![Xx,A,Xy]: 98.17/14.77 (in(Xy,setadjoin(Xx,A)) => 98.17/14.77 (![Xphi:$o]: (((Xy = Xx) => Xphi) => ((in(Xy,A) => Xphi) => Xphi)))))). 98.17/14.77 tff('121', plain, 98.17/14.77 setadjoinE = 98.17/14.77 (![X4,X6,X8]: 98.17/14.77 (in(X8,setadjoin(X4,X6)) => 98.17/14.77 (![X10:$o]: (((X8 = X4) => X10) => ((in(X8,X6) => X10) => X10))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(setadjoinIR, axiom, setadjoinIR <=> 98.17/14.77 (![Xx,A,Xy]: (in(Xy,A) => in(Xy,setadjoin(Xx,A))))). 98.17/14.77 tff('122', plain, 98.17/14.77 setadjoinIR = (![X4,X6,X8]: (in(X8,X6) => in(X8,setadjoin(X4,X6)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(emptyinunitempty, axiom, emptyinunitempty() = 98.17/14.77 in(emptyset,setadjoin(emptyset,emptyset))). 98.17/14.77 tff('123', plain, 98.17/14.77 emptyinunitempty = in(emptyset,setadjoin(emptyset,emptyset)), 98.17/14.77 inference('simplify_rw_rule', [status(thm)], [emptyinunitempty])). 98.17/14.77 tff('124', plain, 98.17/14.77 emptyinunitempty = in(emptyset,setadjoin(emptyset,emptyset)), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(setadjoinIL, axiom, setadjoinIL <=> (![Xx,Xy]: in(Xx,setadjoin(Xx,Xy)))). 98.17/14.77 tff('125', plain, setadjoinIL = (![X4,X6]: in(X4,setadjoin(X4,X6))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(nonemptyI1, axiom, nonemptyI1 <=> 98.17/14.77 (![A]: ((?[Xx]: in(Xx,A)) => nonempty(A)))). 98.17/14.77 tff('126', plain, nonemptyI1 = (![X4]: ((?[X6]: in(X6,X4)) => nonempty(X4))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(nonemptyI, axiom, nonemptyI <=> 98.17/14.77 (![A,Xphi:(($i > $o)),Xx]: 98.17/14.77 (in(Xx,A) => (Xphi(Xx) => nonempty(dsetconstr(A,^[Xy]: Xphi(Xy))))))). 98.17/14.77 tff('127', plain, 98.17/14.77 nonemptyI = 98.17/14.77 (![X4,X6:(($i > $o)),X8]: 98.17/14.77 (in(X8,X4) => (X6(X8) => nonempty(dsetconstr(X4,^[V_1]: X6(V_1)))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(nonemptyE1, axiom, nonemptyE1 <=> 98.17/14.77 (![A]: (nonempty(A) => (?[Xx]: in(Xx,A))))). 98.17/14.77 tff('128', plain, nonemptyE1 = (![X4]: (nonempty(X4) => (?[X6]: in(X6,X4)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(nonempty, axiom, nonempty() = ^[Xx]: (Xx != emptyset)). 98.17/14.77 tff('129', plain, nonempty = (^[Xx]: (Xx != emptyset)), 98.17/14.77 inference('simplify_rw_rule', [status(thm)], [nonempty])). 98.17/14.77 tff('130', plain, nonempty = (^[V_1]: (V_1 != emptyset)), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(setbeta, axiom, setbeta <=> 98.17/14.77 (![A,Xphi:(($i > $o)),Xx]: 98.17/14.77 (in(Xx,A) => (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) <=> Xphi(Xx))))). 98.17/14.77 tff('131', plain, 98.17/14.77 setbeta = 98.17/14.77 (![X4,X6:(($i > $o)),X8]: 98.17/14.77 (in(X8,X4) => (in(X8,dsetconstr(X4,^[V_1]: X6(V_1))) <=> X6(X8)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(noeltsimpempty, axiom, noeltsimpempty <=> 98.17/14.77 (![A]: ((![Xx]: (~in(Xx,A))) => (A = emptyset)))). 98.17/14.77 tff('132', plain, 98.17/14.77 noeltsimpempty = (![X4]: ((![X6]: (~in(X6,X4))) => (X4 = emptyset))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(emptyI, axiom, emptyI <=> 98.17/14.77 (![A]: ((![Xx]: (~in(Xx,A))) => (A = emptyset)))). 98.17/14.77 tff('133', plain, 98.17/14.77 emptyI = (![X4]: ((![X6]: (~in(X6,X4))) => (X4 = emptyset))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(setext, axiom, setext <=> 98.17/14.77 (![A,B]: 98.17/14.77 ((![Xx]: (in(Xx,A) => in(Xx,B))) => 98.17/14.77 ((![Xx]: (in(Xx,B) => in(Xx,A))) => (A = B))))). 98.17/14.77 tff('134', plain, 98.17/14.77 setext = 98.17/14.77 (![X4,X6]: 98.17/14.77 ((![X8]: (in(X8,X4) => in(X8,X6))) => 98.17/14.77 ((![X10]: (in(X10,X6) => in(X10,X4))) => (X4 = X6)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(exuE3e, axiom, exuE3e <=> 98.17/14.77 (![Xphi:(($i > $o))]: (exu(^[Xx]: Xphi(Xx)) => (?[Xx]: Xphi(Xx))))). 98.17/14.77 tff('135', plain, 98.17/14.77 exuE3e = (![X4:(($i > $o))]: (exu(^[V_1]: X4(V_1)) => (?[X6]: X4(X6)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(notinemptyset, axiom, notinemptyset <=> (![Xx]: (~in(Xx,emptyset)))). 98.17/14.77 tff('136', plain, notinemptyset = (![X4]: (~in(X4,emptyset))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(emptysetimpfalse, axiom, emptysetimpfalse <=> 98.17/14.77 (![Xx]: (in(Xx,emptyset) => $false))). 98.17/14.77 tff('137', plain, emptysetimpfalse = (![X4]: (in(X4,emptyset) => $false)), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(emptysetE, axiom, emptysetE <=> 98.17/14.77 (![Xx]: (in(Xx,emptyset) => (![Xphi:$o]: Xphi)))). 98.17/14.77 tff('138', plain, emptysetE = (![X4]: (in(X4,emptyset) => (![X6:$o]: X6))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(prop2setE, axiom, prop2setE <=> 98.17/14.77 (![Xphi:$o,Xx]: (in(Xx,prop2set(Xphi)) => Xphi))). 98.17/14.77 tff('139', plain, prop2setE = (![X4:$o,X6]: (in(X6,prop2set(X4)) => X4)), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(exuE1, axiom, exuE1 <=> 98.17/14.77 (![Xphi:(($i > $o))]: 98.17/14.77 (exu(^[Xx]: Xphi(Xx)) => 98.17/14.77 (?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx)))))). 98.17/14.77 tff('140', plain, 98.17/14.77 exuE1 = 98.17/14.77 (![X4:(($i > $o))]: 98.17/14.77 (exu(^[V_1]: X4(V_1)) => 98.17/14.77 (?[X6]: ((![X8]: (X4(X8) => (X6 = X8))) & X4(X6))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(dsetconstrER, axiom, dsetconstrER <=> 98.17/14.77 (![A,Xphi:(($i > $o)),Xx]: 98.17/14.77 (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) => Xphi(Xx)))). 98.17/14.77 tff('141', plain, 98.17/14.77 dsetconstrER = 98.17/14.77 (![X4,X6:(($i > $o)),X8]: 98.17/14.77 (in(X8,dsetconstr(X4,^[V_1]: X6(V_1))) => X6(X8))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(dsetconstrEL, axiom, dsetconstrEL <=> 98.17/14.77 (![A,Xphi:(($i > $o)),Xx]: 98.17/14.77 (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) => in(Xx,A)))). 98.17/14.77 tff('142', plain, 98.17/14.77 dsetconstrEL = 98.17/14.77 (![X4,X6:(($i > $o)),X8]: 98.17/14.77 (in(X8,dsetconstr(X4,^[V_1]: X6(V_1))) => in(X8,X4))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(dsetconstrI, axiom, dsetconstrI <=> 98.17/14.77 (![A,Xphi:(($i > $o)),Xx]: 98.17/14.77 (in(Xx,A) => (Xphi(Xx) => in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))))))). 98.17/14.77 tff('143', plain, 98.17/14.77 dsetconstrI = 98.17/14.77 (![X4,X6:(($i > $o)),X8]: 98.17/14.77 (in(X8,X4) => (X6(X8) => in(X8,dsetconstr(X4,^[V_1]: X6(V_1)))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(descrp, axiom, descrp <=> 98.17/14.77 (![Xphi:(($i > $o))]: 98.17/14.77 (exu(^[Xx]: Xphi(Xx)) => Xphi(descr(^[Xx]: Xphi(Xx)))))). 98.17/14.77 tff('144', plain, 98.17/14.77 descrp = 98.17/14.77 (![X4:(($i > $o))]: (exu(^[V_1]: X4(V_1)) => X4(descr(^[V_2]: X4(V_2))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(wellorderingAx, axiom, wellorderingAx <=> 98.17/14.77 (![A]: 98.17/14.77 (?[B]: 98.17/14.77 ((![C]: 98.17/14.77 (((![Xx]: (in(Xx,C) => in(Xx,A))) & (?[Xx]: in(Xx,C))) => 98.17/14.77 (?[D,Xx]: 98.17/14.77 ((![E]: 98.17/14.77 (in(E,B) => ((![Xy]: (in(Xy,E) => in(Xy,D))) | in(Xx,E)))) & 98.17/14.77 (~(?[Xy]: (in(Xy,C) & in(Xy,D)))) & in(Xx,C) & in(D,B))))) & 98.17/14.77 (![C,D]: 98.17/14.77 ((in(C,B) & in(D,B)) => 98.17/14.77 ((![Xx]: (in(Xx,C) => in(Xx,D))) | 98.17/14.77 (![Xx]: (in(Xx,D) => in(Xx,C)))))) & 98.17/14.77 (![Xx,Xy]: 98.17/14.77 ((in(Xx,A) & in(Xy,A)) => 98.17/14.77 ((![C]: (in(C,B) => (in(Xx,C) <=> in(Xy,C)))) => (Xx = Xy)))) & 98.17/14.77 (![C]: (in(C,B) => (![Xx]: (in(Xx,C) => in(Xx,A))))))))). 98.17/14.77 tff('145', plain, 98.17/14.77 wellorderingAx = 98.17/14.77 (![X4]: 98.17/14.77 (?[X6]: 98.17/14.77 ((![X8]: 98.17/14.77 (((![X10]: (in(X10,X8) => in(X10,X4))) & (?[X12]: in(X12,X8))) => 98.17/14.77 (?[X14,X16]: 98.17/14.77 ((![X18]: 98.17/14.77 (in(X18,X6) => 98.17/14.77 ((![X20]: (in(X20,X18) => in(X20,X14))) | in(X16,X18)))) & 98.17/14.77 (~(?[X22]: (in(X22,X8) & in(X22,X14)))) & in(X16,X8) & 98.17/14.77 in(X14,X6))))) & 98.17/14.77 (![X24,X26]: 98.17/14.77 ((in(X24,X6) & in(X26,X6)) => 98.17/14.77 ((![X28]: (in(X28,X24) => in(X28,X26))) | 98.17/14.77 (![X30]: (in(X30,X26) => in(X30,X24)))))) & 98.17/14.77 (![X32,X34]: 98.17/14.77 ((in(X32,X4) & in(X34,X4)) => 98.17/14.77 ((![X36]: (in(X36,X6) => (in(X32,X36) <=> in(X34,X36)))) => 98.17/14.77 (X32 = X34)))) & 98.17/14.77 (![X38]: (in(X38,X6) => (![X40]: (in(X40,X38) => in(X40,X4)))))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(foundationAx, axiom, foundationAx <=> 98.17/14.77 (![A]: 98.17/14.77 ((?[Xx]: in(Xx,A)) => 98.17/14.77 (?[B]: ((~(?[Xx]: (in(Xx,A) & in(Xx,B)))) & in(B,A)))))). 98.17/14.77 tff('146', plain, 98.17/14.77 foundationAx = 98.17/14.77 (![X4]: 98.17/14.77 ((?[X6]: in(X6,X4)) => 98.17/14.77 (?[X8]: ((~(?[X10]: (in(X10,X4) & in(X10,X8)))) & in(X8,X4))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(replAx, axiom, replAx <=> 98.17/14.77 (![Xphi:(($i * $i) > $o),A]: 98.17/14.77 ((![Xx]: (in(Xx,A) => exu(^[Xy]: Xphi(Xx,Xy)))) => 98.17/14.77 (?[B]: (![Xx]: (in(Xx,B) <=> (?[Xy]: (Xphi(Xy,Xx) & in(Xy,A))))))))). 98.17/14.77 tff('147', plain, 98.17/14.77 replAx = 98.17/14.77 (![X4:(($i * $i) > $o),X6]: 98.17/14.77 ((![X8]: (in(X8,X6) => exu(^[V_1]: X4(X8,V_1)))) => 98.17/14.77 (?[X10]: 98.17/14.77 (![X12]: (in(X12,X10) <=> (?[X14]: (X4(X14,X12) & in(X14,X6)))))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(omegaIndAx, axiom, omegaIndAx <=> 98.17/14.77 (![A]: 98.17/14.77 ((in(emptyset,A) & 98.17/14.77 (![Xx]: ((in(Xx,omega) & in(Xx,A)) => in(setadjoin(Xx,Xx),A)))) => 98.17/14.77 (![Xx]: (in(Xx,omega) => in(Xx,A)))))). 98.17/14.77 tff('148', plain, 98.17/14.77 omegaIndAx = 98.17/14.77 (![X4]: 98.17/14.77 ((in(emptyset,X4) & 98.17/14.77 (![X6]: ((in(X6,omega) & in(X6,X4)) => in(setadjoin(X6,X6),X4)))) => 98.17/14.77 (![X8]: (in(X8,omega) => in(X8,X4))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(omegaSAx, axiom, omegaSAx <=> 98.17/14.77 (![Xx]: (in(Xx,omega) => in(setadjoin(Xx,Xx),omega)))). 98.17/14.77 tff('149', plain, 98.17/14.77 omegaSAx = (![X4]: (in(X4,omega) => in(setadjoin(X4,X4),omega))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(omega0Ax, axiom, omega0Ax() = in(emptyset,omega)). 98.17/14.77 tff('150', plain, omega0Ax = in(emptyset,omega), 98.17/14.77 inference('simplify_rw_rule', [status(thm)], [omega0Ax])). 98.17/14.77 tff('151', plain, omega0Ax = in(emptyset,omega), define([status(thm)])). 98.17/14.77 tff(setunionAx, axiom, setunionAx <=> 98.17/14.77 (![A,Xx]: (in(Xx,setunion(A)) <=> (?[B]: (in(B,A) & in(Xx,B)))))). 98.17/14.77 tff('152', plain, 98.17/14.77 setunionAx = 98.17/14.77 (![X4,X6]: (in(X6,setunion(X4)) <=> (?[X8]: (in(X8,X4) & in(X6,X8))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(powersetAx, axiom, powersetAx <=> 98.17/14.77 (![A,B]: (in(B,powerset(A)) <=> (![Xx]: (in(Xx,B) => in(Xx,A)))))). 98.17/14.77 tff('153', plain, 98.17/14.77 powersetAx = 98.17/14.77 (![X4,X6]: (in(X6,powerset(X4)) <=> (![X8]: (in(X8,X6) => in(X8,X4))))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(setadjoinAx, axiom, setadjoinAx <=> 98.17/14.77 (![Xx,A,Xy]: (in(Xy,setadjoin(Xx,A)) <=> ((Xy = Xx) | in(Xy,A))))). 98.17/14.77 tff('154', plain, 98.17/14.77 setadjoinAx = 98.17/14.77 (![X4,X6,X8]: (in(X8,setadjoin(X4,X6)) <=> ((X8 = X4) | in(X8,X6)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(emptysetAx, axiom, emptysetAx <=> (![Xx]: (~in(Xx,emptyset)))). 98.17/14.77 tff('155', plain, emptysetAx = (![X4]: (~in(X4,emptyset))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(setextAx, axiom, setextAx <=> 98.17/14.77 (![A,B]: ((![Xx]: (in(Xx,A) <=> in(Xx,B))) => (A = B)))). 98.17/14.77 tff('156', plain, 98.17/14.77 setextAx = (![X4,X6]: ((![X8]: (in(X8,X4) <=> in(X8,X6))) => (X4 = X6))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(exu, axiom, exu() = 98.17/14.77 ^[Xphi:(($i > $o))]: (?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx)))). 98.17/14.77 tff('157', plain, 98.17/14.77 exu = 98.17/14.77 (^[Xphi:(($i > $o))]: 98.17/14.77 (?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx)))), 98.17/14.77 inference('simplify_rw_rule', [status(thm)], [exu])). 98.17/14.77 tff('158', plain, 98.17/14.77 exu = 98.17/14.77 (^[V_1:(($i > $o))]: (?[X4]: ((![X6]: (V_1(X6) => (X4 = X6))) & V_1(X4)))), 98.17/14.77 define([status(thm)])). 98.17/14.77 tff(cartprodmempair1, conjecture, 98.17/14.77 (setextAx => 98.17/14.77 (emptysetAx => 98.17/14.77 (setadjoinAx => 98.17/14.77 (powersetAx => 98.17/14.77 (setunionAx => 98.17/14.77 (omega0Ax => 98.17/14.77 (omegaSAx => 98.17/14.77 (omegaIndAx => 98.17/14.77 (replAx => 98.17/14.77 (foundationAx => 98.17/14.77 (wellorderingAx => 98.17/14.77 (descrp => 98.17/14.77 (dsetconstrI => 98.17/14.77 (dsetconstrEL => 98.17/14.77 (dsetconstrER => 98.17/14.77 (exuE1 => 98.17/14.77 (prop2setE => 98.17/14.77 (emptysetE => 98.17/14.77 (emptysetimpfalse => 98.17/14.77 (notinemptyset => 98.17/14.77 (exuE3e => 98.17/14.77 (setext => 98.17/14.77 (emptyI => 98.17/14.77 (noeltsimpempty => 98.17/14.77 (setbeta => 98.17/14.77 (nonemptyE1 => 98.17/14.77 (nonemptyI => 98.17/14.77 (nonemptyI1 => 98.17/14.77 (setadjoinIL => 98.17/14.77 (emptyinunitempty => 98.17/14.77 (setadjoinIR => 98.17/14.77 (setadjoinE => 98.17/14.77 (setadjoinOr => 98.17/14.77 (setoftrueEq => 98.17/14.77 (powersetI => 98.17/14.77 (emptyinPowerset => 98.17/14.77 (emptyInPowerset => 98.17/14.77 (powersetE => 98.17/14.77 (setunionI => 98.17/14.77 (setunionE => 98.17/14.77 (subPowSU => 98.17/14.77 (exuE2 => 98.17/14.77 (nonemptyImpWitness => 98.17/14.77 (uniqinunit => 98.17/14.77 (notinsingleton => 98.17/14.77 (eqinunit => 98.17/14.77 (singletonsswitch => 98.17/14.77 (upairsetE => 98.17/14.77 (upairsetIL => 98.17/14.77 (upairsetIR => 98.17/14.77 (emptyE1 => 98.17/14.77 (vacuousDall => 98.17/14.77 (quantDeMorgan1 => 98.17/14.77 (quantDeMorgan2 => 98.17/14.77 (quantDeMorgan3 => 98.17/14.77 (quantDeMorgan4 => 98.17/14.77 (prop2setI => 98.17/14.77 (prop2set2propI => 98.17/14.77 (notdexE => 98.17/14.77 (notdallE => 98.17/14.77 (exuI1 => 98.17/14.77 (exuI3 => 98.17/14.77 (exuI2 => 98.17/14.77 (inCongP => 98.17/14.77 (in__Cong => 98.17/14.77 (exuE3u => 98.17/14.77 ( 98.17/14.77 exu__Cong => 98.17/14.77 ( 98.17/14.77 emptyset__Cong => 98.17/14.77 ( 98.17/14.77 setadjoin__Cong => 98.17/14.77 ( 98.17/14.77 powerset__Cong => 98.17/14.77 ( 98.17/14.77 setunion__Cong => 98.17/14.77 ( 98.17/14.77 omega__Cong => 98.17/14.77 ( 98.17/14.77 exuEu => 98.17/14.77 ( 98.17/14.77 descr__Cong => 98.17/14.77 ( 98.17/14.77 dsetconstr__Cong => 98.17/14.77 ( 98.17/14.77 subsetI1 => 98.17/14.77 ( 98.17/14.77 eqimpsubset2 => 98.17/14.77 ( 98.17/14.77 eqimpsubset1 => 98.17/14.77 ( 98.17/14.77 subsetI2 => 98.17/14.77 ( 98.17/14.77 emptysetsubset => 98.17/14.77 ( 98.17/14.77 subsetE => 98.17/14.77 ( 98.17/14.77 subsetE2 => 98.17/14.77 ( 98.17/14.77 notsubsetI => 98.17/14.77 ( 98.17/14.77 notequalI1 => 98.17/14.77 ( 98.17/14.77 notequalI2 => 98.17/14.77 ( 98.17/14.77 subsetRefl => 98.17/14.77 ( 98.17/14.77 subsetTrans => 98.17/14.77 ( 98.17/14.77 setadjoinSub => 98.17/14.77 ( 98.17/14.77 setadjoinSub2 => 98.17/14.77 ( 98.17/14.77 subset2powerset => 98.17/14.77 ( 98.17/14.77 setextsub => 98.17/14.77 ( 98.17/14.77 subsetemptysetimpeq => 98.17/14.77 ( 98.17/14.77 powersetI1 => 98.17/14.77 ( 98.17/14.77 powersetE1 => 98.17/14.77 ( 98.17/14.77 inPowerset => 98.17/14.77 ( 98.17/14.77 powersetsubset => 98.17/14.77 ( 98.17/14.77 sepInPowerset => 98.17/14.77 ( 98.17/14.77 sepSubset => 98.17/14.77 ( 98.17/14.77 binunionIL => 98.17/14.77 ( 98.17/14.77 upairset2IR => 98.17/14.77 ( 98.17/14.77 binunionIR => 98.17/14.77 ( 98.17/14.77 binunionEcases => 98.17/14.77 ( 98.17/14.77 binunionE => 98.17/14.77 ( 98.17/14.77 binunionLsub => 98.17/14.77 ( 98.17/14.77 binunionRsub => 98.17/14.77 ( 98.17/14.77 binintersectI => 98.17/14.77 ( 98.17/14.77 binintersectSubset5 => 98.17/14.77 ( 98.17/14.77 binintersectEL => 98.17/14.77 ( 98.17/14.77 binintersectLsub => 98.17/14.77 ( 98.17/14.77 binintersectSubset2 => 98.17/14.77 ( 98.17/14.77 binintersectSubset3 => 98.17/14.77 ( 98.17/14.77 binintersectER => 98.17/14.77 ( 98.17/14.77 disjointsetsI1 => 98.17/14.77 ( 98.17/14.77 binintersectRsub => 98.17/14.77 ( 98.17/14.77 binintersectSubset4 => 98.17/14.77 ( 98.17/14.77 binintersectSubset1 => 98.17/14.77 ( 98.17/14.77 bs114d => 98.17/14.77 ( 98.17/14.77 setminusI => 98.17/14.77 ( 98.17/14.77 setminusEL => 98.17/14.77 ( 98.17/14.77 setminusER => 98.17/14.77 ( 98.17/14.77 setminusSubset2 => 98.17/14.77 ( 98.17/14.77 setminusERneg => 98.17/14.77 ( 98.17/14.77 setminusELneg => 98.17/14.77 ( 98.17/14.77 setminusILneg => 98.17/14.77 ( 98.17/14.77 setminusIRneg => 98.17/14.77 ( 98.17/14.77 setminusLsub => 98.17/14.77 ( 98.17/14.77 setminusSubset1 => 98.17/14.77 ( 98.17/14.77 symdiffE => 98.17/14.77 ( 98.17/14.77 symdiffI1 => 98.17/14.77 ( 98.17/14.77 symdiffI2 => 98.17/14.77 ( 98.17/14.77 symdiffIneg1 => 98.17/14.77 ( 98.17/14.77 symdiffIneg2 => 98.17/14.77 ( 98.17/14.77 secondinupair => 98.17/14.77 ( 98.17/14.77 setukpairIL => 98.17/14.77 ( 98.17/14.77 setukpairIR => 98.17/14.77 ( 98.17/14.77 kpairiskpair => 98.17/14.77 ( 98.17/14.77 kpairp => 98.17/14.77 ( 98.17/14.77 singletonsubset => 98.17/14.77 ( 98.17/14.77 singletoninpowerset => 98.17/14.77 ( 98.17/14.77 singletoninpowunion => 98.17/14.77 ( 98.17/14.77 upairset2E => 98.17/14.77 ( 98.17/14.77 upairsubunion => 98.17/14.77 ( 98.17/14.77 upairinpowunion => 98.17/14.77 ( 98.17/14.77 ubforcartprodlem1 => 98.17/14.77 ( 98.17/14.77 ubforcartprodlem2 => 98.17/14.77 ( 98.17/14.77 ubforcartprodlem3 => 98.17/14.77 ( 98.17/14.77 cartprodpairin => 98.17/14.77 ( 98.17/14.77 ![A,B,Xu]: 98.17/14.77 (in( 98.17/14.77 Xu, 98.17/14.77 cartprod( 98.17/14.77 A,B)) => 98.17/14.77 (?[Xx]: 98.17/14.77 (in(Xx,A) & 98.17/14.77 (?[Xy]: 98.17/14.77 (( 98.17/14.77 Xu = 98.17/14.77 kpair( 98.17/14.77 Xx,Xy)) & 98.17/14.77 in(Xy,B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 98.17/14.77 tff(zf_stmt_0, conjecture, 98.17/14.77 ((![X4,X6]: ((![X8]: (in(X8,X4) <=> in(X8,X6))) => (X4 = X6))) => 98.17/14.77 ((![X10]: (~in(X10,emptyset))) => 98.17/14.77 ((![X12,X14,X16]: 98.17/14.77 (in(X16,setadjoin(X12,X14)) <=> (in(X16,X14) | (X16 = X12)))) => 98.17/14.77 ((![X18,X20]: 98.17/14.77 (in(X20,powerset(X18)) <=> (![X22]: (in(X22,X20) => in(X22,X18))))) => 98.17/14.77 ((![X24,X26]: 98.17/14.77 (in(X26,setunion(X24)) <=> (?[X28]: (in(X26,X28) & in(X28,X24))))) => 98.17/14.77 (in(emptyset,omega) => 98.17/14.77 ((![X30]: (in(X30,omega) => in(setadjoin(X30,X30),omega))) => 98.17/14.77 ((![X32]: 98.17/14.77 (((![X34]: 98.17/14.77 ((in(X34,X32) & in(X34,omega)) => 98.17/14.77 in(setadjoin(X34,X34),X32))) & 98.17/14.77 in(emptyset,X32)) => 98.17/14.77 (![X36]: (in(X36,omega) => in(X36,X32))))) => 98.17/14.77 ((![X38:(($i * $i) > $o),X40]: 98.17/14.77 ((![X42]: 98.17/14.77 (in(X42,X40) => 98.17/14.77 (?[X44]: 98.17/14.77 (X38(X42,X44) & (![X46]: (X38(X42,X46) => (X44 = X46))))))) => 98.17/14.77 (?[X48]: 98.17/14.77 (![X50]: 98.17/14.77 (in(X50,X48) <=> (?[X52]: (in(X52,X40) & X38(X52,X50)))))))) => 98.17/14.77 ((![X54]: 98.17/14.77 ((?[X56]: in(X56,X54)) => 98.17/14.77 (?[X58]: 98.17/14.77 (in(X58,X54) & (~(?[X60]: (in(X60,X58) & in(X60,X54)))))))) => 98.17/14.77 ((![X62]: 98.17/14.77 (?[X64]: 98.17/14.77 ((![X96]: 98.17/14.77 (in(X96,X64) => (![X98]: (in(X98,X96) => in(X98,X62))))) & 98.17/14.77 (![X90,X92]: 98.17/14.77 ((in(X92,X62) & in(X90,X62)) => 98.17/14.77 ((![X94]: 98.17/14.77 (in(X94,X64) => (in(X90,X94) <=> in(X92,X94)))) => 98.17/14.77 (X90 = X92)))) & 98.17/14.77 (![X82,X84]: 98.17/14.77 ((in(X84,X64) & in(X82,X64)) => 98.17/14.77 ((![X88]: (in(X88,X84) => in(X88,X82))) | 98.17/14.77 (![X86]: (in(X86,X82) => in(X86,X84)))))) & 98.17/14.77 (![X66]: 98.17/14.77 (((?[X70]: in(X70,X66)) & 98.17/14.77 (![X68]: (in(X68,X66) => in(X68,X62)))) => 98.17/14.77 (?[X72,X74]: 98.17/14.77 (in(X72,X64) & in(X74,X66) & 98.17/14.77 (~(?[X80]: (in(X80,X72) & in(X80,X66)))) & 98.17/14.77 (![X76]: 98.17/14.77 (in(X76,X64) => 98.17/14.77 (in(X74,X76) | 98.17/14.77 (![X78]: (in(X78,X76) => in(X78,X72))))))))))))) => 98.17/14.77 ((![X100:(($i > $o))]: 98.17/14.77 ((?[X102]: 98.17/14.77 (X100(X102) & (![X104]: (X100(X104) => (X102 = X104))))) => 98.17/14.77 X100(descr(^[V_1]: X100(V_1))))) => 98.17/14.77 ((![X106,X108:(($i > $o)),X110]: 98.17/14.77 (in(X110,X106) => 98.17/14.77 (X108(X110) => in(X110,dsetconstr(X106,^[V_2]: X108(V_2)))))) => 98.17/14.77 ((![X112,X114:(($i > $o)),X116]: 98.17/14.77 (in(X116,dsetconstr(X112,^[V_3]: X114(V_3))) => 98.17/14.77 in(X116,X112))) => 98.17/14.77 ((![X118,X120:(($i > $o)),X122]: 98.17/14.77 (in(X122,dsetconstr(X118,^[V_4]: X120(V_4))) => 98.17/14.77 X120(X122))) => 98.17/14.77 ((![X124:(($i > $o))]: 98.17/14.77 ((?[X126]: 98.17/14.77 (X124(X126) & 98.17/14.77 (![X128]: (X124(X128) => (X126 = X128))))) => 98.17/14.77 (?[X130]: 98.17/14.77 (X124(X130) & 98.17/14.77 (![X132]: (X124(X132) => (X130 = X132))))))) => 98.17/14.77 ((![X134:$o,X136]: (in(X136,prop2set(X134)) => X134)) => 98.17/14.77 ((![X138]: (in(X138,emptyset) => (![X140:$o]: X140))) => 98.17/14.77 ((![X142]: (~in(X142,emptyset))) => 98.17/14.77 ((![X144]: (~in(X144,emptyset))) => 98.17/14.77 ((![X146:(($i > $o))]: 98.17/14.77 ((?[X148]: 98.17/14.77 (X146(X148) & 98.17/14.77 (![X150]: (X146(X150) => (X148 = X150))))) => 98.17/14.77 (?[X152]: X146(X152)))) => 98.17/14.77 ((![X154,X156]: 98.17/14.77 ((![X158]: (in(X158,X154) => in(X158,X156))) => 98.17/14.77 ((![X160]: (in(X160,X156) => in(X160,X154))) => 98.17/14.77 (X154 = X156)))) => 98.17/14.77 ((![X162]: 98.17/14.77 ((![X164]: (~in(X164,X162))) => (X162 = emptyset))) => 98.17/14.77 ((![X166]: 98.17/14.77 ((![X168]: (~in(X168,X166))) => 98.17/14.77 (X166 = emptyset))) => 98.17/14.77 ((![X170,X172:(($i > $o)),X174]: 98.17/14.77 (in(X174,X170) => 98.17/14.77 (in(X174,dsetconstr(X170,^[V_5]: X172(V_5))) <=> 98.17/14.77 X172(X174)))) => 98.17/14.77 ((![X176]: 98.17/14.77 ((X176 != emptyset) => 98.17/14.77 (?[X178]: in(X178,X176)))) => 98.17/14.77 ((![X180,X182:(($i > $o)),X184]: 98.17/14.77 (in(X184,X180) => 98.17/14.77 (X182(X184) => 98.17/14.77 (dsetconstr(X180,^[V_6]: X182(V_6)) != 98.17/14.77 emptyset)))) => 98.17/14.77 ((![X186]: 98.17/14.77 ((?[X188]: in(X188,X186)) => 98.17/14.77 (X186 != emptyset))) => 98.17/14.77 ((![X190,X192]: in(X190,setadjoin(X190,X192))) => 98.17/14.77 (in(emptyset,setadjoin(emptyset,emptyset)) => 98.17/14.77 ((![X194,X196,X198]: 98.17/14.77 (in(X198,X196) => 98.17/14.77 in(X198,setadjoin(X194,X196)))) => 98.17/14.77 ((![X200,X202,X204]: 98.17/14.77 (in(X204,setadjoin(X200,X202)) => 98.17/14.77 (![X206:$o]: 98.17/14.77 (((X204 = X200) => X206) => 98.17/14.77 ((in(X204,X202) => X206) => X206))))) => 98.17/14.77 ((![X208,X210,X212]: 98.17/14.77 (in(X212,setadjoin(X208,X210)) => 98.17/14.77 (in(X212,X210) | (X212 = X208)))) => 98.17/14.77 ((![X214]: 98.17/14.77 (dsetconstr(X214,^[V_7]: $true) = X214)) => 98.17/14.77 ((![X216,X218]: 98.17/14.77 ((![X220]: 98.17/14.77 (in(X220,X218) => in(X220,X216))) => 98.17/14.77 in(X218,powerset(X216)))) => 98.17/14.77 ((![X222]: in(emptyset,powerset(X222))) => 98.17/14.77 ((![X224]: in(emptyset,powerset(X224))) => 98.17/14.77 ((![X226,X228,X230]: 98.17/14.77 (in(X228,powerset(X226)) => 98.17/14.77 (in(X230,X228) => in(X230,X226)))) => 98.17/14.77 ((![X232,X234,X236]: 98.17/14.77 (in(X234,X236) => 98.17/14.77 (in(X236,X232) => 98.17/14.77 in(X234,setunion(X232))))) => 98.17/14.77 ((![X238,X240]: 98.17/14.77 (in(X240,setunion(X238)) => 98.17/14.77 (![X242:$o]: 98.17/14.77 ((![X244]: 98.17/14.77 (in(X240,X244) => 98.17/14.77 (in(X244,X238) => X242))) => 98.17/14.77 X242)))) => 98.17/14.77 ((![X246,X248]: 98.17/14.77 (in(X248,X246) => 98.17/14.77 in(X248, 98.17/14.77 powerset(setunion(X246))))) => 98.17/14.77 ((![X250:(($i > $o))]: 98.17/14.77 ((?[X252]: 98.17/14.77 (X250(X252) & 98.17/14.77 (![X254]: 98.17/14.77 (X250(X254) => 98.17/14.77 (X252 = X254))))) => 98.17/14.77 (?[X256]: 98.17/14.77 (![X258]: 98.17/14.77 (X250(X258) <=> 98.17/14.77 (X258 = X256)))))) => 98.17/14.77 ((![X260]: 98.17/14.77 ((X260 != emptyset) => 98.17/14.77 (?[X262]: in(X262,X260)))) => 98.17/14.77 ((![X264,X266]: 98.17/14.77 (in(X264, 98.17/14.77 setadjoin(X266,emptyset)) => 98.17/14.77 (X264 = X266))) => 98.17/14.77 ((![X268,X270]: 98.17/14.77 ((X268 != X270) => 98.17/14.77 (~ 98.17/14.77 in(X270, 98.17/14.77 setadjoin(X268, 98.17/14.77 emptyset))))) => 98.17/14.77 ((![X272,X274]: 98.17/14.77 ((X272 = X274) => 98.17/14.77 in(X272, 98.17/14.77 setadjoin(X274, 98.17/14.77 emptyset)))) => 98.17/14.77 ((![X276,X278]: 98.17/14.77 (in(X276, 98.17/14.77 setadjoin(X278, 98.17/14.77 emptyset)) => 98.17/14.77 in(X278, 98.17/14.77 setadjoin(X276, 98.17/14.77 emptyset)))) => 98.17/14.77 ((![X280,X282,X284]: 98.17/14.77 (in(X284, 98.17/14.77 setadjoin(X280, 98.17/14.77 setadjoin( 98.17/14.77 X282, 98.17/14.77 emptyset))) => 98.17/14.77 ((X284 = X282) | 98.17/14.77 (X284 = X280)))) => 98.17/14.77 ((![X286,X288]: 98.17/14.77 in(X286, 98.17/14.77 setadjoin(X286, 98.17/14.77 setadjoin( 98.17/14.77 X288, 98.17/14.77 emptyset)))) => 98.17/14.77 ((![X290,X292]: 98.17/14.77 in(X292, 98.17/14.77 setadjoin(X290, 98.17/14.77 setadjoin( 98.17/14.77 X292, 98.17/14.77 emptyset)))) => 98.17/14.77 ((![X294,X296:(($i > $o))]: 98.17/14.77 ((?[X298]: 98.17/14.77 (in(X298,X294) & 98.17/14.77 X296(X298))) => 98.17/14.77 (dsetconstr( 98.17/14.77 X294, 98.17/14.77 ^[V_8]: X296(V_8)) != 98.17/14.77 emptyset))) => 98.17/14.77 ((![X300:(($i > $o)), 98.17/14.77 X302]: 98.17/14.77 (in(X302,emptyset) => 98.17/14.77 X300(X302))) => 98.17/14.77 ((![X304, 98.17/14.77 X306:(($i > $o))]: 98.17/14.77 ((~ 98.17/14.77 (![X308]: 98.17/14.77 (in(X308,X304) => 98.17/14.77 X306(X308)))) => 98.17/14.77 (?[X310]: 98.17/14.77 (in(X310,X304) & 98.17/14.77 (~X306(X310)))))) => 98.17/14.77 ((![X312, 98.17/14.77 X314:(($i > $o))]: 98.17/14.77 ((![X316]: 98.17/14.77 (in(X316,X312) => 98.17/14.77 (~X314(X316)))) => 98.17/14.77 (~ 98.17/14.77 (?[X318]: 98.17/14.77 (in( 98.17/14.77 X318,X312) & 98.17/14.77 X314(X318)))))) => 98.17/14.77 ((![X320, 98.17/14.77 X322:(($i > $o))]: 98.17/14.77 ((~ 98.17/14.77 (?[X324]: 98.17/14.77 (in( 98.17/14.77 X324,X320) & 98.17/14.77 X322(X324)))) => 98.17/14.77 (![X326]: 98.17/14.77 (in(X326,X320) => 98.17/14.77 (~X322(X326)))))) => 98.17/14.77 ((![X328, 98.17/14.77 X330:(($i > $o))]: 98.17/14.77 ((?[X332]: 98.17/14.77 (in( 98.17/14.77 X332,X328) & 98.17/14.77 (~ 98.17/14.77 X330( 98.17/14.77 X332)))) => 98.17/14.77 (~ 98.17/14.77 (![X334]: 98.17/14.77 (in( 98.17/14.77 X334,X328) => 98.17/14.77 X330( 98.17/14.77 X334)))))) => 98.17/14.77 ((![X336:$o]: 98.17/14.77 (X336 => 98.17/14.77 in(emptyset, 98.17/14.77 prop2set( 98.17/14.77 X336)))) => 98.17/14.77 ((![X338:$o]: 98.17/14.77 (X338 => 98.17/14.77 set2prop( 98.17/14.77 prop2set( 98.17/14.77 X338)))) => 98.17/14.77 ((![X340, 98.17/14.77 X342:( 98.17/14.77 ($i > $o))]: 98.17/14.77 ((~ 98.17/14.77 (?[X344]: 98.17/14.77 (in( 98.17/14.77 X344,X340) & 98.17/14.77 X342( 98.17/14.77 X344)))) => 98.17/14.77 (![X346]: 98.17/14.77 ( 98.17/14.77 in( 98.17/14.77 X346,X340) => 98.17/14.77 ( 98.17/14.77 ~ 98.17/14.77 X342( 98.17/14.77 X346)))))) => 98.17/14.77 ((![X348, 98.17/14.77 X350:( 98.17/14.77 ($i > $o))]: 98.17/14.77 ((~ 98.17/14.77 ( 98.17/14.77 ![X352]: 98.17/14.77 (in( 98.17/14.77 X352,X348) => 98.17/14.77 X350( 98.17/14.77 X352)))) => 98.17/14.77 (?[X354]: 98.17/14.77 (in( 98.17/14.77 X354,X348) & 98.17/14.77 (~ 98.17/14.77 X350( 98.17/14.77 X354)))))) => 98.17/14.77 ((![X356:( 98.17/14.77 ($i > $o))]: 98.17/14.77 ((?[X358]: 98.17/14.77 (X356( 98.17/14.77 X358) & 98.17/14.77 (![X360]: 98.17/14.77 (X356( 98.17/14.77 X360) => 98.17/14.77 (X358 = 98.17/14.77 X360))))) => 98.17/14.77 (?[X362]: 98.17/14.77 (X356( 98.17/14.77 X362) & 98.17/14.77 (![X364]: 98.17/14.77 (X356( 98.17/14.77 X364) => 98.17/14.77 (X362 = 98.17/14.77 X364))))))) => 98.17/14.77 ((![X366:( 98.17/14.77 ($i > $o))]: 98.17/14.77 (( 98.17/14.77 ?[X368]: 98.17/14.77 X366( 98.17/14.77 X368)) => 98.17/14.77 ( 98.17/14.77 ( 98.17/14.77 ![X370, 98.17/14.77 X372]: 98.17/14.77 (X366( 98.17/14.77 X370) => 98.17/14.77 (X366( 98.17/14.77 X372) => 98.17/14.77 (X370 = 98.17/14.77 X372)))) => 98.17/14.77 ( 98.17/14.77 ?[X374]: 98.17/14.77 (X366( 98.17/14.77 X374) & 98.17/14.77 (![X376]: 98.17/14.77 (X366( 98.17/14.77 X376) => 98.17/14.77 (X374 = 98.17/14.77 X376)))))))) => 98.17/14.77 ((![X378:( 98.17/14.77 ( 98.17/14.77 $i > $o))]: 98.17/14.77 ( 98.17/14.77 ( 98.17/14.77 ?[X380]: 98.17/14.77 (![X382]: 98.17/14.77 (X378( 98.17/14.77 X382) <=> 98.17/14.77 (X382 = 98.17/14.77 X380)))) => 98.17/14.77 ( 98.17/14.77 ?[X384]: 98.17/14.77 (X378( 98.17/14.77 X384) & 98.17/14.77 (![X386]: 98.17/14.77 (X378( 98.17/14.77 X386) => 98.17/14.77 (X384 = 98.17/14.77 X386))))))) => 98.17/14.77 ((![X388, 98.17/14.77 X390]: 98.17/14.77 (( 98.17/14.77 X388 = 98.17/14.77 X390) => 98.17/14.77 (![X392, 98.17/14.77 X394]: 98.17/14.77 (( 98.17/14.77 X392 = 98.17/14.77 X394) => 98.17/14.77 (in( 98.17/14.77 X392,X388) => 98.17/14.77 in( 98.17/14.77 X394,X390)))))) => 98.17/14.77 ((![X396, 98.17/14.77 X398]: 98.17/14.77 (( 98.17/14.77 X396 = 98.17/14.77 X398) => 98.17/14.77 (![X400, 98.17/14.77 X402]: 98.17/14.77 (( 98.17/14.77 X400 = 98.17/14.77 X402) => 98.17/14.77 (in( 98.17/14.77 X400,X396) <=> 98.17/14.77 in( 98.17/14.77 X402,X398)))))) => 98.17/14.77 (( 98.17/14.77 ![X404:( 98.17/14.77 ( 98.17/14.77 $i > $o))]: 98.17/14.77 (( 98.17/14.77 ?[X406]: 98.17/14.77 (X404( 98.17/14.77 X406) & 98.17/14.77 (![X408]: 98.17/14.77 (X404( 98.17/14.77 X408) => 98.17/14.77 (X406 = 98.17/14.77 X408))))) => 98.17/14.77 (![X410, 98.17/14.77 X412]: 98.17/14.77 (X404( 98.17/14.77 X410) => 98.17/14.77 (X404( 98.17/14.77 X412) => 98.17/14.77 (X410 = 98.17/14.77 X412)))))) => 98.17/14.77 ( 98.17/14.77 ( 98.17/14.77 ![X414:( 98.17/14.77 ( 98.17/14.77 $i > $o)), 98.17/14.77 X416:( 98.17/14.77 ( 98.17/14.77 $i > $o))]: 98.17/14.77 (( 98.17/14.77 ![X418, 98.17/14.77 X420]: 98.17/14.77 (( 98.17/14.77 X418 = 98.17/14.77 X420) => 98.17/14.77 (X414( 98.17/14.77 X418) <=> 98.17/14.77 X416( 98.17/14.77 X420)))) => 98.17/14.77 (( 98.17/14.77 ?[X422]: 98.17/14.77 (X414( 98.17/14.77 X422) & 98.17/14.77 (![X424]: 98.17/14.77 (X414( 98.17/14.77 X424) => 98.17/14.77 (X422 = 98.17/14.77 X424))))) <=> 98.17/14.77 (?[X426]: 98.17/14.77 (X416( 98.17/14.77 X426) & 98.17/14.77 (![X428]: 98.17/14.77 (X416( 98.17/14.77 X428) => 98.17/14.77 (X426 = 98.17/14.77 X428)))))))) => 98.17/14.77 ( 98.17/14.77 ( 98.17/14.77 emptyset = 98.17/14.77 emptyset) => 98.17/14.77 ( 98.17/14.77 ( 98.17/14.77 ![X430, 98.17/14.77 X432]: 98.17/14.77 (( 98.17/14.77 X430 = 98.17/14.77 X432) => 98.17/14.77 (![X434, 98.17/14.77 X436]: 98.17/14.77 (( 98.17/14.77 X434 = 98.17/14.77 X436) => 98.17/14.77 (setadjoin( 98.17/14.77 X430,X434) = 98.17/14.77 setadjoin( 98.17/14.77 X432,X436)))))) => 98.17/14.77 ( 98.17/14.77 ( 98.17/14.77 ![X438, 98.17/14.77 X440]: 98.17/14.77 (( 98.17/14.77 X438 = 98.17/14.77 X440) => 98.17/14.77 (powerset( 98.17/14.77 X438) = 98.17/14.77 powerset( 98.17/14.77 X440)))) => 98.17/14.77 ( 98.17/14.77 ( 98.17/14.77 ![X442, 98.17/14.77 X444]: 98.17/14.77 (( 98.17/14.77 X442 = 98.17/14.77 X444) => 98.17/14.77 (setunion( 98.17/14.77 X442) = 98.17/14.77 setunion( 98.17/14.77 X444)))) => 98.17/14.77 ( 98.17/14.77 ( 98.17/14.77 omega = 98.17/14.77 omega) => 98.17/14.77 ( 98.17/14.77 ( 98.17/14.77 ![X446:( 98.17/14.77 ( 98.17/14.77 $i > $o))]: 98.17/14.77 (( 98.17/14.77 ?[X448]: 98.17/14.77 (X446( 98.17/14.77 X448) & 98.17/14.77 (![X450]: 98.17/14.77 (X446( 98.17/14.77 X450) => 98.17/14.77 (X448 = 98.17/14.77 X450))))) => 98.17/14.77 (![X452, 98.17/14.77 X454]: 98.17/14.77 (X446( 98.17/14.77 X452) => 98.17/14.77 (X446( 98.17/14.77 X454) => 98.17/14.77 (X452 = 98.17/14.77 X454)))))) => 98.17/14.77 ( 98.17/14.77 ( 98.17/14.77 ![X456:( 98.17/14.77 ( 98.17/14.77 $i > $o)), 98.17/14.77 X458:( 98.17/14.77 ( 98.17/14.77 $i > $o))]: 98.17/14.77 (( 98.17/14.77 ![X460, 98.17/14.77 X462]: 98.17/14.77 (( 98.17/14.77 X460 = 98.17/14.77 X462) => 98.17/14.77 (X456( 98.17/14.77 X460) <=> 98.17/14.77 X458( 98.17/14.77 X462)))) => 98.17/14.77 (( 98.17/14.77 ?[X464]: 98.17/14.77 (X456( 98.17/14.77 X464) & 98.17/14.77 (![X466]: 98.17/14.77 (X456( 98.17/14.77 X466) => 98.17/14.77 (X464 = 98.17/14.77 X466))))) => 98.17/14.77 (( 98.17/14.77 ?[X468]: 98.17/14.77 (X458( 98.17/14.77 X468) & 98.17/14.77 (![X470]: 98.17/14.77 (X458( 98.17/14.77 X470) => 98.17/14.77 (X468 = 98.17/14.77 X470))))) => 98.17/14.77 (descr( 98.17/14.77 ^[V_9]: 98.17/14.77 X456(V_9)) = 98.17/14.77 descr( 98.17/14.77 ^[V_10]: 98.17/14.77 X458( 98.17/14.77 V_10))))))) => 98.17/14.77 ( 98.17/14.77 ( 98.17/14.77 ![X472, 98.17/14.77 X474]: 98.17/14.77 (( 98.17/14.77 X472 = 98.17/14.77 X474) => 98.17/14.77 (![X476:( 98.17/14.77 ( 98.17/14.77 $i > $o)), 98.17/14.77 X478:( 98.17/14.77 ( 98.17/14.77 $i > $o))]: 98.17/14.77 (( 98.17/14.77 ![X480]: 98.17/14.77 (in( 98.17/14.77 X480,X472) => 98.17/14.77 (![X482]: 98.17/14.77 (in( 98.17/14.77 X482,X474) => 98.17/14.77 (( 98.17/14.77 X480 = 98.17/14.77 X482) => 98.17/14.77 (X476( 98.17/14.77 X480) <=> 98.17/14.77 X478( 98.17/14.77 X482))))))) => 98.17/14.77 (dsetconstr( 98.17/14.77 X472, 98.17/14.77 ^[V_11]: 98.17/14.77 X476( 98.17/14.77 V_11)) = 98.17/14.77 dsetconstr( 98.17/14.78 X474, 98.17/14.78 ^[V_12]: 98.17/14.78 X478( 98.17/14.78 V_12))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X484, 98.17/14.78 X486]: 98.17/14.78 (( 98.17/14.78 ![X488]: 98.17/14.78 (in( 98.17/14.78 X488,X484) => 98.17/14.78 in( 98.17/14.78 X488,X486))) => 98.17/14.78 subset( 98.17/14.78 X484,X486))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X490, 98.17/14.78 X492]: 98.17/14.78 (( 98.17/14.78 X490 = 98.17/14.78 X492) => 98.17/14.78 subset( 98.17/14.78 X492,X490))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X494, 98.17/14.78 X496]: 98.17/14.78 (( 98.17/14.78 X494 = 98.17/14.78 X496) => 98.17/14.78 subset( 98.17/14.78 X494,X496))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X498, 98.17/14.78 X500]: 98.17/14.78 (( 98.17/14.78 ![X502]: 98.17/14.78 (in( 98.17/14.78 X502,X498) => 98.17/14.78 in( 98.17/14.78 X502,X500))) => 98.17/14.78 subset( 98.17/14.78 X498,X500))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X504]: 98.17/14.78 subset( 98.17/14.78 emptyset, 98.17/14.78 X504)) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X506, 98.17/14.78 X508,X510]: 98.17/14.78 (subset( 98.17/14.78 X506,X508) => 98.17/14.78 (in( 98.17/14.78 X510,X506) => 98.17/14.78 in( 98.17/14.78 X510,X508)))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X512, 98.17/14.78 X514,X516]: 98.17/14.78 (subset( 98.17/14.78 X512,X514) => 98.17/14.78 (( 98.17/14.78 ~ 98.17/14.78 in( 98.17/14.78 X516,X514)) => 98.17/14.78 (~ 98.17/14.78 in( 98.17/14.78 X516,X512))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X518, 98.17/14.78 X520,X522]: 98.17/14.78 (in( 98.17/14.78 X522,X518) => 98.17/14.78 (( 98.17/14.78 ~ 98.17/14.78 in( 98.17/14.78 X522,X520)) => 98.17/14.78 (~ 98.17/14.78 subset( 98.17/14.78 X518,X520))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X524, 98.17/14.78 X526]: 98.17/14.78 (( 98.17/14.78 ~ 98.17/14.78 subset( 98.17/14.78 X524,X526)) => 98.17/14.78 (X524 != 98.17/14.78 X526))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X528, 98.17/14.78 X530,X532]: 98.17/14.78 (in( 98.17/14.78 X532,X528) => 98.17/14.78 (( 98.17/14.78 ~ 98.17/14.78 in( 98.17/14.78 X532,X530)) => 98.17/14.78 (X528 != 98.17/14.78 X530)))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X534]: 98.17/14.78 subset( 98.17/14.78 X534,X534)) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X536, 98.17/14.78 X538,X540]: 98.17/14.78 (subset( 98.17/14.78 X536,X538) => 98.17/14.78 (subset( 98.17/14.78 X538,X540) => 98.17/14.78 subset( 98.17/14.78 X536,X540)))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X542, 98.17/14.78 X544]: 98.17/14.78 subset( 98.17/14.78 X544, 98.17/14.78 setadjoin( 98.17/14.78 X542,X544))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X546, 98.17/14.78 X548,X550]: 98.17/14.78 (subset( 98.17/14.78 X546,X550) => 98.17/14.78 subset( 98.17/14.78 X546, 98.17/14.78 setadjoin( 98.17/14.78 X548,X550)))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X552, 98.17/14.78 X554]: 98.17/14.78 (subset( 98.17/14.78 X552,X554) => 98.17/14.78 in( 98.17/14.78 X552, 98.17/14.78 powerset( 98.17/14.78 X554)))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X556, 98.17/14.78 X558]: 98.17/14.78 (subset( 98.17/14.78 X556,X558) => 98.17/14.78 (subset( 98.17/14.78 X558,X556) => 98.17/14.78 (X556 = 98.17/14.78 X558)))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X560]: 98.17/14.78 (subset( 98.17/14.78 X560, 98.17/14.78 emptyset) => 98.17/14.78 (X560 = 98.17/14.78 emptyset))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X562, 98.17/14.78 X564]: 98.17/14.78 (subset( 98.17/14.78 X564,X562) => 98.17/14.78 in( 98.17/14.78 X564, 98.17/14.78 powerset( 98.17/14.78 X562)))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X566, 98.17/14.78 X568]: 98.17/14.78 (in( 98.17/14.78 X568, 98.17/14.78 powerset( 98.17/14.78 X566)) => 98.17/14.78 subset( 98.17/14.78 X568,X566))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X570]: 98.17/14.78 in( 98.17/14.78 X570, 98.17/14.78 powerset( 98.17/14.78 X570))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X572, 98.17/14.78 X574]: 98.17/14.78 (subset( 98.17/14.78 X572,X574) => 98.17/14.78 subset( 98.17/14.78 powerset( 98.17/14.78 X572), 98.17/14.78 powerset( 98.17/14.78 X574)))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X576, 98.17/14.78 X578:( 98.17/14.78 ( 98.17/14.78 $i > $o))]: 98.17/14.78 in( 98.17/14.78 dsetconstr( 98.17/14.78 X576, 98.17/14.78 ^[V_13]: 98.17/14.78 X578( 98.17/14.78 V_13)), 98.17/14.78 powerset( 98.17/14.78 X576))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X580, 98.17/14.78 X582:( 98.17/14.78 ( 98.17/14.78 $i > $o))]: 98.17/14.78 subset( 98.17/14.78 dsetconstr( 98.17/14.78 X580, 98.17/14.78 ^[V_14]: 98.17/14.78 X582( 98.17/14.78 V_14)), 98.17/14.78 X580)) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X584, 98.17/14.78 X586,X588]: 98.17/14.78 (in( 98.17/14.78 X588,X584) => 98.17/14.78 in( 98.17/14.78 X588, 98.17/14.78 binunion( 98.17/14.78 X584,X586)))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X590, 98.17/14.78 X592]: 98.17/14.78 in( 98.17/14.78 X592, 98.17/14.78 setadjoin( 98.17/14.78 X590, 98.17/14.78 setadjoin( 98.17/14.78 X592, 98.17/14.78 emptyset)))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X594, 98.17/14.78 X596,X598]: 98.17/14.78 (in( 98.17/14.78 X598,X596) => 98.17/14.78 in( 98.17/14.78 X598, 98.17/14.78 binunion( 98.17/14.78 X594,X596)))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X600, 98.17/14.78 X602, 98.17/14.78 X604, 98.17/14.78 X606:$o]: 98.17/14.78 (in( 98.17/14.78 X604, 98.17/14.78 binunion( 98.17/14.78 X600,X602)) => 98.17/14.78 (( 98.17/14.78 in( 98.17/14.78 X604,X600) => 98.17/14.78 X606) => 98.17/14.78 (( 98.17/14.78 in( 98.17/14.78 X604,X602) => 98.17/14.78 X606) => 98.17/14.78 X606)))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X608, 98.17/14.78 X610,X612]: 98.17/14.78 (in( 98.17/14.78 X612, 98.17/14.78 binunion( 98.17/14.78 X608,X610)) => 98.17/14.78 (in( 98.17/14.78 X612,X610) | 98.17/14.78 in( 98.17/14.78 X612,X608)))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X614, 98.17/14.78 X616]: 98.17/14.78 subset( 98.17/14.78 X614, 98.17/14.78 binunion( 98.17/14.78 X614,X616))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X618, 98.17/14.78 X620]: 98.17/14.78 subset( 98.17/14.78 X620, 98.17/14.78 binunion( 98.17/14.78 X618,X620))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X622, 98.17/14.78 X624,X626]: 98.17/14.78 (in( 98.17/14.78 X626,X622) => 98.17/14.78 (in( 98.17/14.78 X626,X624) => 98.17/14.78 in( 98.17/14.78 X626, 98.17/14.78 binintersect( 98.17/14.78 X622,X624))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X628, 98.17/14.78 X630,X632]: 98.17/14.78 (subset( 98.17/14.78 X632,X628) => 98.17/14.78 (subset( 98.17/14.78 X632,X630) => 98.17/14.78 subset( 98.17/14.78 X632, 98.17/14.78 binintersect( 98.17/14.78 X628,X630))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X634, 98.17/14.78 X636,X638]: 98.17/14.78 (in( 98.17/14.78 X638, 98.17/14.78 binintersect( 98.17/14.78 X634,X636)) => 98.17/14.78 in( 98.17/14.78 X638,X634))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X640, 98.17/14.78 X642]: 98.17/14.78 subset( 98.17/14.78 binintersect( 98.17/14.78 X640,X642), 98.17/14.78 X640)) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X644, 98.17/14.78 X646]: 98.17/14.78 (subset( 98.17/14.78 X644,X646) => 98.17/14.78 (binintersect( 98.17/14.78 X644,X646) = 98.17/14.78 X644))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X648, 98.17/14.78 X650]: 98.17/14.78 (( 98.17/14.78 binintersect( 98.17/14.78 X648,X650) = 98.17/14.78 X650) => 98.17/14.78 subset( 98.17/14.78 X650,X648))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X652, 98.17/14.78 X654,X656]: 98.17/14.78 (in( 98.17/14.78 X656, 98.17/14.78 binintersect( 98.17/14.78 X652,X654)) => 98.17/14.78 in( 98.17/14.78 X656,X654))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X658, 98.17/14.78 X660]: 98.17/14.78 (( 98.17/14.78 ~ 98.17/14.78 ( 98.17/14.78 ?[X662]: 98.17/14.78 (in( 98.17/14.78 X662,X658) & 98.17/14.78 in( 98.17/14.78 X662,X660)))) => 98.17/14.78 (binintersect( 98.17/14.78 X658,X660) = 98.17/14.78 emptyset))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X664, 98.17/14.78 X666]: 98.17/14.78 subset( 98.17/14.78 binintersect( 98.17/14.78 X664,X666), 98.17/14.78 X666)) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X668, 98.17/14.78 X670]: 98.17/14.78 (subset( 98.17/14.78 X670,X668) => 98.17/14.78 (binintersect( 98.17/14.78 X668,X670) = 98.17/14.78 X670))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X672, 98.17/14.78 X674]: 98.17/14.78 (( 98.17/14.78 binintersect( 98.17/14.78 X672,X674) = 98.17/14.78 X672) => 98.17/14.78 subset( 98.17/14.78 X672,X674))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X676, 98.17/14.78 X678,X680]: 98.17/14.78 (binintersect( 98.17/14.78 X676, 98.17/14.78 binunion( 98.17/14.78 X678,X680)) = 98.17/14.78 binunion( 98.17/14.78 binintersect( 98.17/14.78 X676,X678), 98.17/14.78 binintersect( 98.17/14.78 X676,X680)))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X682, 98.17/14.78 X684,X686]: 98.17/14.78 (in( 98.17/14.78 X686,X682) => 98.17/14.78 (( 98.17/14.78 ~ 98.17/14.78 in( 98.17/14.78 X686,X684)) => 98.17/14.78 in( 98.17/14.78 X686, 98.17/14.78 setminus( 98.17/14.78 X682,X684))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X688, 98.17/14.78 X690,X692]: 98.17/14.78 (in( 98.17/14.78 X692, 98.17/14.78 setminus( 98.17/14.78 X688,X690)) => 98.17/14.78 in( 98.17/14.78 X692,X688))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X694, 98.17/14.78 X696,X698]: 98.17/14.78 (in( 98.17/14.78 X698, 98.17/14.78 setminus( 98.17/14.78 X694,X696)) => 98.17/14.78 (~ 98.17/14.78 in( 98.17/14.78 X698,X696)))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X700, 98.17/14.78 X702]: 98.17/14.78 (subset( 98.17/14.78 X700,X702) => 98.17/14.78 (setminus( 98.17/14.78 X700,X702) = 98.17/14.78 emptyset))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X704, 98.17/14.78 X706,X708]: 98.17/14.78 (( 98.17/14.78 ~ 98.17/14.78 in( 98.17/14.78 X708, 98.17/14.78 setminus( 98.17/14.78 X704,X706))) => 98.17/14.78 (in( 98.17/14.78 X708,X704) => 98.17/14.78 in( 98.17/14.78 X708,X706)))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X710, 98.17/14.78 X712,X714]: 98.17/14.78 (( 98.17/14.78 ~ 98.17/14.78 in( 98.17/14.78 X714, 98.17/14.78 setminus( 98.17/14.78 X710,X712))) => 98.17/14.78 (( 98.17/14.78 ~ 98.17/14.78 in( 98.17/14.78 X714,X712)) => 98.17/14.78 (~ 98.17/14.78 in( 98.17/14.78 X714,X710))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X716, 98.17/14.78 X718,X720]: 98.17/14.78 (( 98.17/14.78 ~ 98.17/14.78 in( 98.17/14.78 X720,X716)) => 98.17/14.78 (~ 98.17/14.78 in( 98.17/14.78 X720, 98.17/14.78 setminus( 98.17/14.78 X716,X718))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X722, 98.17/14.78 X724,X726]: 98.17/14.78 (in( 98.17/14.78 X726,X724) => 98.17/14.78 (~ 98.17/14.78 in( 98.17/14.78 X726, 98.17/14.78 setminus( 98.17/14.78 X722,X724))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X728, 98.17/14.78 X730]: 98.17/14.78 subset( 98.17/14.78 setminus( 98.17/14.78 X728,X730), 98.17/14.78 X728)) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X732, 98.17/14.78 X734]: 98.17/14.78 (( 98.17/14.78 setminus( 98.17/14.78 X732,X734) = 98.17/14.78 emptyset) => 98.17/14.78 subset( 98.17/14.78 X732,X734))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X736, 98.17/14.78 X738,X740]: 98.17/14.78 (in( 98.17/14.78 X740, 98.17/14.78 symdiff( 98.17/14.78 X736,X738)) => 98.17/14.78 (![X742:$o]: 98.17/14.78 (( 98.17/14.78 in( 98.17/14.78 X740,X736) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ~ 98.17/14.78 in( 98.17/14.78 X740,X738)) => 98.17/14.78 X742)) => 98.17/14.78 (( 98.17/14.78 ( 98.17/14.78 ~ 98.17/14.78 in( 98.17/14.78 X740,X736)) => 98.17/14.78 ( 98.17/14.78 in( 98.17/14.78 X740,X738) => 98.17/14.78 X742)) => 98.17/14.78 X742))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X744, 98.17/14.78 X746,X748]: 98.17/14.78 (in( 98.17/14.78 X748,X744) => 98.17/14.78 (( 98.17/14.78 ~ 98.17/14.78 in( 98.17/14.78 X748,X746)) => 98.17/14.78 in( 98.17/14.78 X748, 98.17/14.78 symdiff( 98.17/14.78 X744,X746))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X750, 98.17/14.78 X752,X754]: 98.17/14.78 (( 98.17/14.78 ~ 98.17/14.78 in( 98.17/14.78 X754,X750)) => 98.17/14.78 (in( 98.17/14.78 X754,X752) => 98.17/14.78 in( 98.17/14.78 X754, 98.17/14.78 symdiff( 98.17/14.78 X750,X752))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X756, 98.17/14.78 X758,X760]: 98.17/14.78 (in( 98.17/14.78 X760,X756) => 98.17/14.78 (in( 98.17/14.78 X760,X758) => 98.17/14.78 (~ 98.17/14.78 in( 98.17/14.78 X760, 98.17/14.78 symdiff( 98.17/14.78 X756,X758)))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X762, 98.17/14.78 X764,X766]: 98.17/14.78 (( 98.17/14.78 ~ 98.17/14.78 in( 98.17/14.78 X766,X762)) => 98.17/14.78 (( 98.17/14.78 ~ 98.17/14.78 in( 98.17/14.78 X766,X764)) => 98.17/14.78 (~ 98.17/14.78 in( 98.17/14.78 X766, 98.17/14.78 symdiff( 98.17/14.78 X762,X764)))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X768, 98.17/14.78 X770]: 98.17/14.78 in( 98.17/14.78 X770, 98.17/14.78 setadjoin( 98.17/14.78 X768, 98.17/14.78 setadjoin( 98.17/14.78 X770, 98.17/14.78 emptyset)))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X772, 98.17/14.78 X774]: 98.17/14.78 in( 98.17/14.78 X772, 98.17/14.78 setunion( 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X772, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X772, 98.17/14.78 setadjoin( 98.17/14.78 X774, 98.17/14.78 emptyset)), 98.17/14.78 emptyset))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X776, 98.17/14.78 X778]: 98.17/14.78 in( 98.17/14.78 X778, 98.17/14.78 setunion( 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X776, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X776, 98.17/14.78 setadjoin( 98.17/14.78 X778, 98.17/14.78 emptyset)), 98.17/14.78 emptyset))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X780, 98.17/14.78 X782]: 98.17/14.78 (?[X784]: 98.17/14.78 (in( 98.17/14.78 X784, 98.17/14.78 setunion( 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X780, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X780, 98.17/14.78 setadjoin( 98.17/14.78 X782, 98.17/14.78 emptyset)), 98.17/14.78 emptyset)))) & 98.17/14.78 (?[X786]: 98.17/14.78 (in( 98.17/14.78 X786, 98.17/14.78 setunion( 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X780, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X780, 98.17/14.78 setadjoin( 98.17/14.78 X782, 98.17/14.78 emptyset)), 98.17/14.78 emptyset)))) & 98.17/14.78 (setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X780, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X780, 98.17/14.78 setadjoin( 98.17/14.78 X782, 98.17/14.78 emptyset)), 98.17/14.78 emptyset)) = 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X784, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X784, 98.17/14.78 setadjoin( 98.17/14.78 X786, 98.17/14.78 emptyset)), 98.17/14.78 emptyset)))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X788, 98.17/14.78 X790]: 98.17/14.78 (?[X792]: 98.17/14.78 (in( 98.17/14.78 X792, 98.17/14.78 setunion( 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X788, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X788, 98.17/14.78 setadjoin( 98.17/14.78 X790, 98.17/14.78 emptyset)), 98.17/14.78 emptyset)))) & 98.17/14.78 (?[X794]: 98.17/14.78 (in( 98.17/14.78 X794, 98.17/14.78 setunion( 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X788, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X788, 98.17/14.78 setadjoin( 98.17/14.78 X790, 98.17/14.78 emptyset)), 98.17/14.78 emptyset)))) & 98.17/14.78 (setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X788, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X788, 98.17/14.78 setadjoin( 98.17/14.78 X790, 98.17/14.78 emptyset)), 98.17/14.78 emptyset)) = 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X792, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X792, 98.17/14.78 setadjoin( 98.17/14.78 X794, 98.17/14.78 emptyset)), 98.17/14.78 emptyset)))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X796, 98.17/14.78 X798]: 98.17/14.78 (in( 98.17/14.78 X798,X796) => 98.17/14.78 subset( 98.17/14.78 setadjoin( 98.17/14.78 X798, 98.17/14.78 emptyset), 98.17/14.78 X796))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X800, 98.17/14.78 X802]: 98.17/14.78 (in( 98.17/14.78 X802,X800) => 98.17/14.78 in( 98.17/14.78 setadjoin( 98.17/14.78 X802, 98.17/14.78 emptyset), 98.17/14.78 powerset( 98.17/14.78 X800)))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X804, 98.17/14.78 X806,X808]: 98.17/14.78 (in( 98.17/14.78 X808,X804) => 98.17/14.78 in( 98.17/14.78 setadjoin( 98.17/14.78 X808, 98.17/14.78 emptyset), 98.17/14.78 powerset( 98.17/14.78 binunion( 98.17/14.78 X804,X806))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X810, 98.17/14.78 X812,X814]: 98.17/14.78 (in( 98.17/14.78 X814, 98.17/14.78 setadjoin( 98.17/14.78 X810, 98.17/14.78 setadjoin( 98.17/14.78 X812, 98.17/14.78 emptyset))) => 98.17/14.78 (( 98.17/14.78 X814 = 98.17/14.78 X812) | 98.17/14.78 (X814 = 98.17/14.78 X810)))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X816, 98.17/14.78 X818,X820]: 98.17/14.78 (in( 98.17/14.78 X820,X816) => 98.17/14.78 (![X822]: 98.17/14.78 (in( 98.17/14.78 X822,X818) => 98.17/14.78 subset( 98.17/14.78 setadjoin( 98.17/14.78 X820, 98.17/14.78 setadjoin( 98.17/14.78 X822, 98.17/14.78 emptyset)), 98.17/14.78 binunion( 98.17/14.78 X816,X818)))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X824, 98.17/14.78 X826,X828]: 98.17/14.78 (in( 98.17/14.78 X828,X824) => 98.17/14.78 (![X830]: 98.17/14.78 (in( 98.17/14.78 X830,X826) => 98.17/14.78 in( 98.17/14.78 setadjoin( 98.17/14.78 X828, 98.17/14.78 setadjoin( 98.17/14.78 X830, 98.17/14.78 emptyset)), 98.17/14.78 powerset( 98.17/14.78 binunion( 98.17/14.78 X824,X826))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X832, 98.17/14.78 X834,X836]: 98.17/14.78 (in( 98.17/14.78 X836,X832) => 98.17/14.78 (![X838]: 98.17/14.78 (in( 98.17/14.78 X838,X834) => 98.17/14.78 subset( 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X836, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X836, 98.17/14.78 setadjoin( 98.17/14.78 X838, 98.17/14.78 emptyset)), 98.17/14.78 emptyset)), 98.17/14.78 powerset( 98.17/14.78 binunion( 98.17/14.78 X832,X834))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X840, 98.17/14.78 X842,X844]: 98.17/14.78 (in( 98.17/14.78 X844,X840) => 98.17/14.78 (![X846]: 98.17/14.78 (in( 98.17/14.78 X846,X842) => 98.17/14.78 in( 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X844, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X844, 98.17/14.78 setadjoin( 98.17/14.78 X846, 98.17/14.78 emptyset)), 98.17/14.78 emptyset)), 98.17/14.78 powerset( 98.17/14.78 powerset( 98.17/14.78 binunion( 98.17/14.78 X840,X842)))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X848, 98.17/14.78 X850,X852]: 98.17/14.78 (in( 98.17/14.78 X852,X848) => 98.17/14.78 (![X854]: 98.17/14.78 (in( 98.17/14.78 X854,X850) => 98.17/14.78 in( 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X852, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X852, 98.17/14.78 setadjoin( 98.17/14.78 X854, 98.17/14.78 emptyset)), 98.17/14.78 emptyset)), 98.17/14.78 powerset( 98.17/14.78 powerset( 98.17/14.78 binunion( 98.17/14.78 X848,X850)))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X856, 98.17/14.78 X858,X860]: 98.17/14.78 (in( 98.17/14.78 X860,X856) => 98.17/14.78 (![X862]: 98.17/14.78 (in( 98.17/14.78 X862,X858) => 98.17/14.78 in( 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X860, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X860, 98.17/14.78 setadjoin( 98.17/14.78 X862, 98.17/14.78 emptyset)), 98.17/14.78 emptyset)), 98.17/14.78 dsetconstr( 98.17/14.78 powerset( 98.17/14.78 powerset( 98.17/14.78 binunion( 98.17/14.78 X856,X858))), 98.17/14.78 ^[V_15]: 98.17/14.78 (?[X864]: 98.17/14.78 (in( 98.17/14.78 X864,X856) & 98.17/14.78 (?[X866]: 98.17/14.78 (in( 98.17/14.78 X866,X858) & 98.17/14.78 (V_15 = 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X864, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X864, 98.17/14.78 setadjoin( 98.17/14.78 X866, 98.17/14.78 emptyset)), 98.17/14.78 emptyset))))))))))))) => 98.17/14.78 ( 98.17/14.78 ![X868, 98.17/14.78 X870,X872]: 98.17/14.78 (in( 98.17/14.78 X872, 98.17/14.78 dsetconstr( 98.17/14.78 powerset( 98.17/14.78 powerset( 98.17/14.78 binunion( 98.17/14.78 X868,X870))), 98.17/14.78 ^[V_16]: 98.17/14.78 (?[X874]: 98.17/14.78 (in( 98.17/14.78 X874,X868) & 98.17/14.78 (?[X876]: 98.17/14.78 (in( 98.17/14.78 X876,X870) & 98.17/14.78 (V_16 = 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X874, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X874, 98.17/14.78 setadjoin( 98.17/14.78 X876, 98.17/14.78 emptyset)), 98.17/14.78 emptyset))))))))) => 98.17/14.78 (?[X878]: 98.17/14.78 (( 98.17/14.78 ?[X880]: 98.17/14.78 (in( 98.17/14.78 X880,X870) & 98.17/14.78 (X872 = 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X878, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X878, 98.17/14.78 setadjoin( 98.17/14.78 X880, 98.17/14.78 emptyset)), 98.17/14.78 emptyset))))) & 98.17/14.78 in( 98.17/14.78 X878,X868))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 98.17/14.78 tff(zf_stmt_1, negated_conjecture, 98.17/14.78 (~ 98.17/14.78 ((![X4,X6]: ((![X8]: (in(X8,X4) <=> in(X8,X6))) => (X4 = X6))) => 98.17/14.78 ((![X10]: (~in(X10,emptyset))) => 98.17/14.78 ((![X12,X14,X16]: 98.17/14.78 (in(X16,setadjoin(X12,X14)) <=> (in(X16,X14) | (X16 = X12)))) => 98.17/14.78 ((![X18,X20]: 98.17/14.78 (in(X20,powerset(X18)) <=> (![X22]: (in(X22,X20) => in(X22,X18))))) => 98.17/14.78 ((![X24,X26]: 98.17/14.78 (in(X26,setunion(X24)) <=> (?[X28]: (in(X26,X28) & in(X28,X24))))) => 98.17/14.78 (in(emptyset,omega) => 98.17/14.78 ((![X30]: (in(X30,omega) => in(setadjoin(X30,X30),omega))) => 98.17/14.78 ((![X32]: 98.17/14.78 (((![X34]: 98.17/14.78 ((in(X34,X32) & in(X34,omega)) => 98.17/14.78 in(setadjoin(X34,X34),X32))) & 98.17/14.78 in(emptyset,X32)) => 98.17/14.78 (![X36]: (in(X36,omega) => in(X36,X32))))) => 98.17/14.78 ((![X38:(($i * $i) > $o),X40]: 98.17/14.78 ((![X42]: 98.17/14.78 (in(X42,X40) => 98.17/14.78 (?[X44]: 98.17/14.78 (X38(X42,X44) & 98.17/14.78 (![X46]: (X38(X42,X46) => (X44 = X46))))))) => 98.17/14.78 (?[X48]: 98.17/14.78 (![X50]: 98.17/14.78 (in(X50,X48) <=> 98.17/14.78 (?[X52]: (in(X52,X40) & X38(X52,X50)))))))) => 98.17/14.78 ((![X54]: 98.17/14.78 ((?[X56]: in(X56,X54)) => 98.17/14.78 (?[X58]: 98.17/14.78 (in(X58,X54) & (~(?[X60]: (in(X60,X58) & in(X60,X54)))))))) => 98.17/14.78 ((![X62]: 98.17/14.78 (?[X64]: 98.17/14.78 ((![X96]: 98.17/14.78 (in(X96,X64) => 98.17/14.78 (![X98]: (in(X98,X96) => in(X98,X62))))) & 98.17/14.78 (![X90,X92]: 98.17/14.78 ((in(X92,X62) & in(X90,X62)) => 98.17/14.78 ((![X94]: 98.17/14.78 (in(X94,X64) => (in(X90,X94) <=> in(X92,X94)))) => 98.17/14.78 (X90 = X92)))) & 98.17/14.78 (![X82,X84]: 98.17/14.78 ((in(X84,X64) & in(X82,X64)) => 98.17/14.78 ((![X88]: (in(X88,X84) => in(X88,X82))) | 98.17/14.78 (![X86]: (in(X86,X82) => in(X86,X84)))))) & 98.17/14.78 (![X66]: 98.17/14.78 (((?[X70]: in(X70,X66)) & 98.17/14.78 (![X68]: (in(X68,X66) => in(X68,X62)))) => 98.17/14.78 (?[X72,X74]: 98.17/14.78 (in(X72,X64) & in(X74,X66) & 98.17/14.78 (~(?[X80]: (in(X80,X72) & in(X80,X66)))) & 98.17/14.78 (![X76]: 98.17/14.78 (in(X76,X64) => 98.17/14.78 (in(X74,X76) | 98.17/14.78 (![X78]: (in(X78,X76) => in(X78,X72))))))))))))) => 98.17/14.78 ((![X100:(($i > $o))]: 98.17/14.78 ((?[X102]: 98.17/14.78 (X100(X102) & (![X104]: (X100(X104) => (X102 = X104))))) => 98.17/14.78 X100(descr(^[V_1]: X100(V_1))))) => 98.17/14.78 ((![X106,X108:(($i > $o)),X110]: 98.17/14.78 (in(X110,X106) => 98.17/14.78 (X108(X110) => 98.17/14.78 in(X110,dsetconstr(X106,^[V_2]: X108(V_2)))))) => 98.17/14.78 ((![X112,X114:(($i > $o)),X116]: 98.17/14.78 (in(X116,dsetconstr(X112,^[V_3]: X114(V_3))) => 98.17/14.78 in(X116,X112))) => 98.17/14.78 ((![X118,X120:(($i > $o)),X122]: 98.17/14.78 (in(X122,dsetconstr(X118,^[V_4]: X120(V_4))) => 98.17/14.78 X120(X122))) => 98.17/14.78 ((![X124:(($i > $o))]: 98.17/14.78 ((?[X126]: 98.17/14.78 (X124(X126) & 98.17/14.78 (![X128]: (X124(X128) => (X126 = X128))))) => 98.17/14.78 (?[X130]: 98.17/14.78 (X124(X130) & 98.17/14.78 (![X132]: (X124(X132) => (X130 = X132))))))) => 98.17/14.78 ((![X134:$o,X136]: (in(X136,prop2set(X134)) => X134)) => 98.17/14.78 ((![X138]: (in(X138,emptyset) => (![X140:$o]: X140))) => 98.17/14.78 ((![X142]: (~in(X142,emptyset))) => 98.17/14.78 ((![X144]: (~in(X144,emptyset))) => 98.17/14.78 ((![X146:(($i > $o))]: 98.17/14.78 ((?[X148]: 98.17/14.78 (X146(X148) & 98.17/14.78 (![X150]: (X146(X150) => (X148 = X150))))) => 98.17/14.78 (?[X152]: X146(X152)))) => 98.17/14.78 ((![X154,X156]: 98.17/14.78 ((![X158]: (in(X158,X154) => in(X158,X156))) => 98.17/14.78 ((![X160]: (in(X160,X156) => in(X160,X154))) => 98.17/14.78 (X154 = X156)))) => 98.17/14.78 ((![X162]: 98.17/14.78 ((![X164]: (~in(X164,X162))) => 98.17/14.78 (X162 = emptyset))) => 98.17/14.78 ((![X166]: 98.17/14.78 ((![X168]: (~in(X168,X166))) => 98.17/14.78 (X166 = emptyset))) => 98.17/14.78 ((![X170,X172:(($i > $o)),X174]: 98.17/14.78 (in(X174,X170) => 98.17/14.78 (in(X174,dsetconstr(X170,^[V_5]: X172(V_5))) <=> 98.17/14.78 X172(X174)))) => 98.17/14.78 ((![X176]: 98.17/14.78 ((X176 != emptyset) => 98.17/14.78 (?[X178]: in(X178,X176)))) => 98.17/14.78 ((![X180,X182:(($i > $o)),X184]: 98.17/14.78 (in(X184,X180) => 98.17/14.78 (X182(X184) => 98.17/14.78 (dsetconstr(X180,^[V_6]: X182(V_6)) != 98.17/14.78 emptyset)))) => 98.17/14.78 ((![X186]: 98.17/14.78 ((?[X188]: in(X188,X186)) => 98.17/14.78 (X186 != emptyset))) => 98.17/14.78 ((![X190,X192]: in(X190,setadjoin(X190,X192))) => 98.17/14.78 (in(emptyset,setadjoin(emptyset,emptyset)) => 98.17/14.78 ((![X194,X196,X198]: 98.17/14.78 (in(X198,X196) => 98.17/14.78 in(X198,setadjoin(X194,X196)))) => 98.17/14.78 ((![X200,X202,X204]: 98.17/14.78 (in(X204,setadjoin(X200,X202)) => 98.17/14.78 (![X206:$o]: 98.17/14.78 (((X204 = X200) => X206) => 98.17/14.78 ((in(X204,X202) => X206) => X206))))) => 98.17/14.78 ((![X208,X210,X212]: 98.17/14.78 (in(X212,setadjoin(X208,X210)) => 98.17/14.78 (in(X212,X210) | (X212 = X208)))) => 98.17/14.78 ((![X214]: 98.17/14.78 (dsetconstr(X214,^[V_7]: $true) = 98.17/14.78 X214)) => 98.17/14.78 ((![X216,X218]: 98.17/14.78 ((![X220]: 98.17/14.78 (in(X220,X218) => in(X220,X216))) => 98.17/14.78 in(X218,powerset(X216)))) => 98.17/14.78 ((![X222]: in(emptyset,powerset(X222))) => 98.17/14.78 ((![X224]: 98.17/14.78 in(emptyset,powerset(X224))) => 98.17/14.78 ((![X226,X228,X230]: 98.17/14.78 (in(X228,powerset(X226)) => 98.17/14.78 (in(X230,X228) => in(X230,X226)))) => 98.17/14.78 ((![X232,X234,X236]: 98.17/14.78 (in(X234,X236) => 98.17/14.78 (in(X236,X232) => 98.17/14.78 in(X234,setunion(X232))))) => 98.17/14.78 ((![X238,X240]: 98.17/14.78 (in(X240,setunion(X238)) => 98.17/14.78 (![X242:$o]: 98.17/14.78 ((![X244]: 98.17/14.78 (in(X240,X244) => 98.17/14.78 (in(X244,X238) => 98.17/14.78 X242))) => 98.17/14.78 X242)))) => 98.17/14.78 ((![X246,X248]: 98.17/14.78 (in(X248,X246) => 98.17/14.78 in(X248, 98.17/14.78 powerset(setunion(X246))))) => 98.17/14.78 ((![X250:(($i > $o))]: 98.17/14.78 ((?[X252]: 98.17/14.78 (X250(X252) & 98.17/14.78 (![X254]: 98.17/14.78 (X250(X254) => 98.17/14.78 (X252 = X254))))) => 98.17/14.78 (?[X256]: 98.17/14.78 (![X258]: 98.17/14.78 (X250(X258) <=> 98.17/14.78 (X258 = X256)))))) => 98.17/14.78 ((![X260]: 98.17/14.78 ((X260 != emptyset) => 98.17/14.78 (?[X262]: in(X262,X260)))) => 98.17/14.78 ((![X264,X266]: 98.17/14.78 (in(X264, 98.17/14.78 setadjoin(X266, 98.17/14.78 emptyset)) => 98.17/14.78 (X264 = X266))) => 98.17/14.78 ((![X268,X270]: 98.17/14.78 ((X268 != X270) => 98.17/14.78 (~ 98.17/14.78 in(X270, 98.17/14.78 setadjoin(X268, 98.17/14.78 emptyset))))) => 98.17/14.78 ((![X272,X274]: 98.17/14.78 ((X272 = X274) => 98.17/14.78 in(X272, 98.17/14.78 setadjoin(X274, 98.17/14.78 emptyset)))) => 98.17/14.78 ((![X276,X278]: 98.17/14.78 (in(X276, 98.17/14.78 setadjoin(X278, 98.17/14.78 emptyset)) => 98.17/14.78 in(X278, 98.17/14.78 setadjoin(X276, 98.17/14.78 emptyset)))) => 98.17/14.78 ((![X280,X282,X284]: 98.17/14.78 (in(X284, 98.17/14.78 setadjoin( 98.17/14.78 X280, 98.17/14.78 setadjoin( 98.17/14.78 X282,emptyset))) => 98.17/14.78 ((X284 = X282) | 98.17/14.78 (X284 = X280)))) => 98.17/14.78 ((![X286,X288]: 98.17/14.78 in(X286, 98.17/14.78 setadjoin( 98.17/14.78 X286, 98.17/14.78 setadjoin( 98.17/14.78 X288,emptyset)))) => 98.17/14.78 ((![X290,X292]: 98.17/14.78 in(X292, 98.17/14.78 setadjoin( 98.17/14.78 X290, 98.17/14.78 setadjoin( 98.17/14.78 X292,emptyset)))) => 98.17/14.78 ((![X294, 98.17/14.78 X296:(($i > $o))]: 98.17/14.78 ((?[X298]: 98.17/14.78 (in(X298,X294) & 98.17/14.78 X296(X298))) => 98.17/14.78 (dsetconstr( 98.17/14.78 X294, 98.17/14.78 ^[V_8]: X296(V_8)) != 98.17/14.78 emptyset))) => 98.17/14.78 ((![X300:(($i > $o)), 98.17/14.78 X302]: 98.17/14.78 (in(X302,emptyset) => 98.17/14.78 X300(X302))) => 98.17/14.78 ((![X304, 98.17/14.78 X306:(($i > $o))]: 98.17/14.78 ((~ 98.17/14.78 (![X308]: 98.17/14.78 (in( 98.17/14.78 X308,X304) => 98.17/14.78 X306(X308)))) => 98.17/14.78 (?[X310]: 98.17/14.78 (in(X310,X304) & 98.17/14.78 (~X306(X310)))))) => 98.17/14.78 ((![X312, 98.17/14.78 X314:(($i > $o))]: 98.17/14.78 ((![X316]: 98.17/14.78 (in( 98.17/14.78 X316,X312) => 98.17/14.78 (~ 98.17/14.78 X314( 98.17/14.78 X316)))) => 98.17/14.78 (~ 98.17/14.78 (?[X318]: 98.17/14.78 (in( 98.17/14.78 X318,X312) & 98.17/14.78 X314( 98.17/14.78 X318)))))) => 98.17/14.78 ((![X320, 98.17/14.78 X322:(($i > $o))]: 98.17/14.78 ((~ 98.17/14.78 (?[X324]: 98.17/14.78 ( 98.17/14.78 in( 98.17/14.78 X324,X320) & 98.17/14.78 X322( 98.17/14.78 X324)))) => 98.17/14.78 (![X326]: 98.17/14.78 (in( 98.17/14.78 X326,X320) => 98.17/14.78 (~ 98.17/14.78 X322( 98.17/14.78 X326)))))) => 98.17/14.78 ((![X328, 98.17/14.78 X330:( 98.17/14.78 ($i > $o))]: 98.17/14.78 ((?[X332]: 98.17/14.78 (in( 98.17/14.78 X332,X328) & 98.17/14.78 ( 98.17/14.78 ~ 98.17/14.78 X330( 98.17/14.78 X332)))) => 98.17/14.78 (~ 98.17/14.78 (![X334]: 98.17/14.78 (in( 98.17/14.78 X334,X328) => 98.17/14.78 X330( 98.17/14.78 X334)))))) => 98.17/14.78 ((![X336:$o]: 98.17/14.78 (X336 => 98.17/14.78 in(emptyset, 98.17/14.78 prop2set( 98.17/14.78 X336)))) => 98.17/14.78 ((![X338:$o]: 98.17/14.78 (X338 => 98.17/14.78 set2prop( 98.17/14.78 prop2set( 98.17/14.78 X338)))) => 98.17/14.78 ((![X340, 98.17/14.78 X342:( 98.17/14.78 ($i > $o))]: 98.17/14.78 ((~ 98.17/14.78 ( 98.17/14.78 ?[X344]: 98.17/14.78 (in( 98.17/14.78 X344,X340) & 98.17/14.78 X342( 98.17/14.78 X344)))) => 98.17/14.78 (![X346]: 98.17/14.78 (in( 98.17/14.78 X346,X340) => 98.17/14.78 (~ 98.17/14.78 X342( 98.17/14.78 X346)))))) => 98.17/14.78 ((![X348, 98.17/14.78 X350:( 98.17/14.78 ($i > $o))]: 98.17/14.78 (( 98.17/14.78 ~ 98.17/14.78 ( 98.17/14.78 ![X352]: 98.17/14.78 (in( 98.17/14.78 X352,X348) => 98.17/14.78 X350( 98.17/14.78 X352)))) => 98.17/14.78 ( 98.17/14.78 ?[X354]: 98.17/14.78 (in( 98.17/14.78 X354,X348) & 98.17/14.78 (~ 98.17/14.78 X350( 98.17/14.78 X354)))))) => 98.17/14.78 ((![X356:( 98.17/14.78 ( 98.17/14.78 $i > $o))]: 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ?[X358]: 98.17/14.78 (X356( 98.17/14.78 X358) & 98.17/14.78 (![X360]: 98.17/14.78 (X356( 98.17/14.78 X360) => 98.17/14.78 (X358 = 98.17/14.78 X360))))) => 98.17/14.78 ( 98.17/14.78 ?[X362]: 98.17/14.78 (X356( 98.17/14.78 X362) & 98.17/14.78 (![X364]: 98.17/14.78 (X356( 98.17/14.78 X364) => 98.17/14.78 (X362 = 98.17/14.78 X364))))))) => 98.17/14.78 ((![X366:( 98.17/14.78 ( 98.17/14.78 $i > $o))]: 98.17/14.78 (( 98.17/14.78 ?[X368]: 98.17/14.78 X366( 98.17/14.78 X368)) => 98.17/14.78 (( 98.17/14.78 ![X370, 98.17/14.78 X372]: 98.17/14.78 (X366( 98.17/14.78 X370) => 98.17/14.78 (X366( 98.17/14.78 X372) => 98.17/14.78 (X370 = 98.17/14.78 X372)))) => 98.17/14.78 (?[X374]: 98.17/14.78 (X366( 98.17/14.78 X374) & 98.17/14.78 (![X376]: 98.17/14.78 (X366( 98.17/14.78 X376) => 98.17/14.78 (X374 = 98.17/14.78 X376)))))))) => 98.17/14.78 ((![X378:( 98.17/14.78 ( 98.17/14.78 $i > $o))]: 98.17/14.78 (( 98.17/14.78 ?[X380]: 98.17/14.78 (![X382]: 98.17/14.78 (X378( 98.17/14.78 X382) <=> 98.17/14.78 (X382 = 98.17/14.78 X380)))) => 98.17/14.78 (?[X384]: 98.17/14.78 (X378( 98.17/14.78 X384) & 98.17/14.78 (![X386]: 98.17/14.78 (X378( 98.17/14.78 X386) => 98.17/14.78 (X384 = 98.17/14.78 X386))))))) => 98.17/14.78 (( 98.17/14.78 ![X388, 98.17/14.78 X390]: 98.17/14.78 (( 98.17/14.78 X388 = 98.17/14.78 X390) => 98.17/14.78 (![X392, 98.17/14.78 X394]: 98.17/14.78 (( 98.17/14.78 X392 = 98.17/14.78 X394) => 98.17/14.78 (in( 98.17/14.78 X392,X388) => 98.17/14.78 in( 98.17/14.78 X394,X390)))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X396, 98.17/14.78 X398]: 98.17/14.78 (( 98.17/14.78 X396 = 98.17/14.78 X398) => 98.17/14.78 (![X400, 98.17/14.78 X402]: 98.17/14.78 (( 98.17/14.78 X400 = 98.17/14.78 X402) => 98.17/14.78 (in( 98.17/14.78 X400,X396) <=> 98.17/14.78 in( 98.17/14.78 X402,X398)))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X404:( 98.17/14.78 ( 98.17/14.78 $i > $o))]: 98.17/14.78 (( 98.17/14.78 ?[X406]: 98.17/14.78 (X404( 98.17/14.78 X406) & 98.17/14.78 (![X408]: 98.17/14.78 (X404( 98.17/14.78 X408) => 98.17/14.78 (X406 = 98.17/14.78 X408))))) => 98.17/14.78 (![X410, 98.17/14.78 X412]: 98.17/14.78 (X404( 98.17/14.78 X410) => 98.17/14.78 (X404( 98.17/14.78 X412) => 98.17/14.78 (X410 = 98.17/14.78 X412)))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X414:( 98.17/14.78 ( 98.17/14.78 $i > $o)), 98.17/14.78 X416:( 98.17/14.78 ( 98.17/14.78 $i > $o))]: 98.17/14.78 (( 98.17/14.78 ![X418, 98.17/14.78 X420]: 98.17/14.78 (( 98.17/14.78 X418 = 98.17/14.78 X420) => 98.17/14.78 (X414( 98.17/14.78 X418) <=> 98.17/14.78 X416( 98.17/14.78 X420)))) => 98.17/14.78 (( 98.17/14.78 ?[X422]: 98.17/14.78 (X414( 98.17/14.78 X422) & 98.17/14.78 (![X424]: 98.17/14.78 (X414( 98.17/14.78 X424) => 98.17/14.78 (X422 = 98.17/14.78 X424))))) <=> 98.17/14.78 (?[X426]: 98.17/14.78 (X416( 98.17/14.78 X426) & 98.17/14.78 (![X428]: 98.17/14.78 (X416( 98.17/14.78 X428) => 98.17/14.78 (X426 = 98.17/14.78 X428)))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 emptyset = 98.17/14.78 emptyset) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X430, 98.17/14.78 X432]: 98.17/14.78 (( 98.17/14.78 X430 = 98.17/14.78 X432) => 98.17/14.78 (![X434, 98.17/14.78 X436]: 98.17/14.78 (( 98.17/14.78 X434 = 98.17/14.78 X436) => 98.17/14.78 (setadjoin( 98.17/14.78 X430,X434) = 98.17/14.78 setadjoin( 98.17/14.78 X432,X436)))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X438, 98.17/14.78 X440]: 98.17/14.78 (( 98.17/14.78 X438 = 98.17/14.78 X440) => 98.17/14.78 (powerset( 98.17/14.78 X438) = 98.17/14.78 powerset( 98.17/14.78 X440)))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X442, 98.17/14.78 X444]: 98.17/14.78 (( 98.17/14.78 X442 = 98.17/14.78 X444) => 98.17/14.78 (setunion( 98.17/14.78 X442) = 98.17/14.78 setunion( 98.17/14.78 X444)))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 omega = 98.17/14.78 omega) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X446:( 98.17/14.78 ( 98.17/14.78 $i > $o))]: 98.17/14.78 (( 98.17/14.78 ?[X448]: 98.17/14.78 (X446( 98.17/14.78 X448) & 98.17/14.78 (![X450]: 98.17/14.78 (X446( 98.17/14.78 X450) => 98.17/14.78 (X448 = 98.17/14.78 X450))))) => 98.17/14.78 (![X452, 98.17/14.78 X454]: 98.17/14.78 (X446( 98.17/14.78 X452) => 98.17/14.78 (X446( 98.17/14.78 X454) => 98.17/14.78 (X452 = 98.17/14.78 X454)))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X456:( 98.17/14.78 ( 98.17/14.78 $i > $o)), 98.17/14.78 X458:( 98.17/14.78 ( 98.17/14.78 $i > $o))]: 98.17/14.78 (( 98.17/14.78 ![X460, 98.17/14.78 X462]: 98.17/14.78 (( 98.17/14.78 X460 = 98.17/14.78 X462) => 98.17/14.78 (X456( 98.17/14.78 X460) <=> 98.17/14.78 X458( 98.17/14.78 X462)))) => 98.17/14.78 (( 98.17/14.78 ?[X464]: 98.17/14.78 (X456( 98.17/14.78 X464) & 98.17/14.78 (![X466]: 98.17/14.78 (X456( 98.17/14.78 X466) => 98.17/14.78 (X464 = 98.17/14.78 X466))))) => 98.17/14.78 (( 98.17/14.78 ?[X468]: 98.17/14.78 (X458( 98.17/14.78 X468) & 98.17/14.78 (![X470]: 98.17/14.78 (X458( 98.17/14.78 X470) => 98.17/14.78 (X468 = 98.17/14.78 X470))))) => 98.17/14.78 (descr( 98.17/14.78 ^[V_9]: 98.17/14.78 X456(V_9)) = 98.17/14.78 descr( 98.17/14.78 ^[V_10]: 98.17/14.78 X458( 98.17/14.78 V_10))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X472, 98.17/14.78 X474]: 98.17/14.78 (( 98.17/14.78 X472 = 98.17/14.78 X474) => 98.17/14.78 (![X476:( 98.17/14.78 ( 98.17/14.78 $i > $o)), 98.17/14.78 X478:( 98.17/14.78 ( 98.17/14.78 $i > $o))]: 98.17/14.78 (( 98.17/14.78 ![X480]: 98.17/14.78 (in( 98.17/14.78 X480,X472) => 98.17/14.78 (![X482]: 98.17/14.78 (in( 98.17/14.78 X482,X474) => 98.17/14.78 (( 98.17/14.78 X480 = 98.17/14.78 X482) => 98.17/14.78 (X476( 98.17/14.78 X480) <=> 98.17/14.78 X478( 98.17/14.78 X482))))))) => 98.17/14.78 (dsetconstr( 98.17/14.78 X472, 98.17/14.78 ^[V_11]: 98.17/14.78 X476( 98.17/14.78 V_11)) = 98.17/14.78 dsetconstr( 98.17/14.78 X474, 98.17/14.78 ^[V_12]: 98.17/14.78 X478( 98.17/14.78 V_12))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X484, 98.17/14.78 X486]: 98.17/14.78 (( 98.17/14.78 ![X488]: 98.17/14.78 (in( 98.17/14.78 X488,X484) => 98.17/14.78 in( 98.17/14.78 X488,X486))) => 98.17/14.78 subset( 98.17/14.78 X484,X486))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X490, 98.17/14.78 X492]: 98.17/14.78 (( 98.17/14.78 X490 = 98.17/14.78 X492) => 98.17/14.78 subset( 98.17/14.78 X492,X490))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X494, 98.17/14.78 X496]: 98.17/14.78 (( 98.17/14.78 X494 = 98.17/14.78 X496) => 98.17/14.78 subset( 98.17/14.78 X494,X496))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X498, 98.17/14.78 X500]: 98.17/14.78 (( 98.17/14.78 ![X502]: 98.17/14.78 (in( 98.17/14.78 X502,X498) => 98.17/14.78 in( 98.17/14.78 X502,X500))) => 98.17/14.78 subset( 98.17/14.78 X498,X500))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X504]: 98.17/14.78 subset( 98.17/14.78 emptyset, 98.17/14.78 X504)) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X506, 98.17/14.78 X508,X510]: 98.17/14.78 (subset( 98.17/14.78 X506,X508) => 98.17/14.78 (in( 98.17/14.78 X510,X506) => 98.17/14.78 in( 98.17/14.78 X510,X508)))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X512, 98.17/14.78 X514,X516]: 98.17/14.78 (subset( 98.17/14.78 X512,X514) => 98.17/14.78 (( 98.17/14.78 ~ 98.17/14.78 in( 98.17/14.78 X516,X514)) => 98.17/14.78 (~ 98.17/14.78 in( 98.17/14.78 X516,X512))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X518, 98.17/14.78 X520,X522]: 98.17/14.78 (in( 98.17/14.78 X522,X518) => 98.17/14.78 (( 98.17/14.78 ~ 98.17/14.78 in( 98.17/14.78 X522,X520)) => 98.17/14.78 (~ 98.17/14.78 subset( 98.17/14.78 X518,X520))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X524, 98.17/14.78 X526]: 98.17/14.78 (( 98.17/14.78 ~ 98.17/14.78 subset( 98.17/14.78 X524,X526)) => 98.17/14.78 (X524 != 98.17/14.78 X526))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X528, 98.17/14.78 X530,X532]: 98.17/14.78 (in( 98.17/14.78 X532,X528) => 98.17/14.78 (( 98.17/14.78 ~ 98.17/14.78 in( 98.17/14.78 X532,X530)) => 98.17/14.78 (X528 != 98.17/14.78 X530)))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X534]: 98.17/14.78 subset( 98.17/14.78 X534,X534)) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X536, 98.17/14.78 X538,X540]: 98.17/14.78 (subset( 98.17/14.78 X536,X538) => 98.17/14.78 (subset( 98.17/14.78 X538,X540) => 98.17/14.78 subset( 98.17/14.78 X536,X540)))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X542, 98.17/14.78 X544]: 98.17/14.78 subset( 98.17/14.78 X544, 98.17/14.78 setadjoin( 98.17/14.78 X542,X544))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X546, 98.17/14.78 X548,X550]: 98.17/14.78 (subset( 98.17/14.78 X546,X550) => 98.17/14.78 subset( 98.17/14.78 X546, 98.17/14.78 setadjoin( 98.17/14.78 X548,X550)))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X552, 98.17/14.78 X554]: 98.17/14.78 (subset( 98.17/14.78 X552,X554) => 98.17/14.78 in( 98.17/14.78 X552, 98.17/14.78 powerset( 98.17/14.78 X554)))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X556, 98.17/14.78 X558]: 98.17/14.78 (subset( 98.17/14.78 X556,X558) => 98.17/14.78 (subset( 98.17/14.78 X558,X556) => 98.17/14.78 (X556 = 98.17/14.78 X558)))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X560]: 98.17/14.78 (subset( 98.17/14.78 X560, 98.17/14.78 emptyset) => 98.17/14.78 (X560 = 98.17/14.78 emptyset))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X562, 98.17/14.78 X564]: 98.17/14.78 (subset( 98.17/14.78 X564,X562) => 98.17/14.78 in( 98.17/14.78 X564, 98.17/14.78 powerset( 98.17/14.78 X562)))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X566, 98.17/14.78 X568]: 98.17/14.78 (in( 98.17/14.78 X568, 98.17/14.78 powerset( 98.17/14.78 X566)) => 98.17/14.78 subset( 98.17/14.78 X568,X566))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X570]: 98.17/14.78 in( 98.17/14.78 X570, 98.17/14.78 powerset( 98.17/14.78 X570))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X572, 98.17/14.78 X574]: 98.17/14.78 (subset( 98.17/14.78 X572,X574) => 98.17/14.78 subset( 98.17/14.78 powerset( 98.17/14.78 X572), 98.17/14.78 powerset( 98.17/14.78 X574)))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X576, 98.17/14.78 X578:( 98.17/14.78 ( 98.17/14.78 $i > $o))]: 98.17/14.78 in( 98.17/14.78 dsetconstr( 98.17/14.78 X576, 98.17/14.78 ^[V_13]: 98.17/14.78 X578( 98.17/14.78 V_13)), 98.17/14.78 powerset( 98.17/14.78 X576))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X580, 98.17/14.78 X582:( 98.17/14.78 ( 98.17/14.78 $i > $o))]: 98.17/14.78 subset( 98.17/14.78 dsetconstr( 98.17/14.78 X580, 98.17/14.78 ^[V_14]: 98.17/14.78 X582( 98.17/14.78 V_14)), 98.17/14.78 X580)) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X584, 98.17/14.78 X586,X588]: 98.17/14.78 (in( 98.17/14.78 X588,X584) => 98.17/14.78 in( 98.17/14.78 X588, 98.17/14.78 binunion( 98.17/14.78 X584,X586)))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X590, 98.17/14.78 X592]: 98.17/14.78 in( 98.17/14.78 X592, 98.17/14.78 setadjoin( 98.17/14.78 X590, 98.17/14.78 setadjoin( 98.17/14.78 X592, 98.17/14.78 emptyset)))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X594, 98.17/14.78 X596,X598]: 98.17/14.78 (in( 98.17/14.78 X598,X596) => 98.17/14.78 in( 98.17/14.78 X598, 98.17/14.78 binunion( 98.17/14.78 X594,X596)))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X600, 98.17/14.78 X602, 98.17/14.78 X604, 98.17/14.78 X606:$o]: 98.17/14.78 (in( 98.17/14.78 X604, 98.17/14.78 binunion( 98.17/14.78 X600,X602)) => 98.17/14.78 (( 98.17/14.78 in( 98.17/14.78 X604,X600) => 98.17/14.78 X606) => 98.17/14.78 (( 98.17/14.78 in( 98.17/14.78 X604,X602) => 98.17/14.78 X606) => 98.17/14.78 X606)))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X608, 98.17/14.78 X610,X612]: 98.17/14.78 (in( 98.17/14.78 X612, 98.17/14.78 binunion( 98.17/14.78 X608,X610)) => 98.17/14.78 (in( 98.17/14.78 X612,X610) | 98.17/14.78 in( 98.17/14.78 X612,X608)))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X614, 98.17/14.78 X616]: 98.17/14.78 subset( 98.17/14.78 X614, 98.17/14.78 binunion( 98.17/14.78 X614,X616))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X618, 98.17/14.78 X620]: 98.17/14.78 subset( 98.17/14.78 X620, 98.17/14.78 binunion( 98.17/14.78 X618,X620))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X622, 98.17/14.78 X624,X626]: 98.17/14.78 (in( 98.17/14.78 X626,X622) => 98.17/14.78 (in( 98.17/14.78 X626,X624) => 98.17/14.78 in( 98.17/14.78 X626, 98.17/14.78 binintersect( 98.17/14.78 X622,X624))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X628, 98.17/14.78 X630,X632]: 98.17/14.78 (subset( 98.17/14.78 X632,X628) => 98.17/14.78 (subset( 98.17/14.78 X632,X630) => 98.17/14.78 subset( 98.17/14.78 X632, 98.17/14.78 binintersect( 98.17/14.78 X628,X630))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X634, 98.17/14.78 X636,X638]: 98.17/14.78 (in( 98.17/14.78 X638, 98.17/14.78 binintersect( 98.17/14.78 X634,X636)) => 98.17/14.78 in( 98.17/14.78 X638,X634))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X640, 98.17/14.78 X642]: 98.17/14.78 subset( 98.17/14.78 binintersect( 98.17/14.78 X640,X642), 98.17/14.78 X640)) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X644, 98.17/14.78 X646]: 98.17/14.78 (subset( 98.17/14.78 X644,X646) => 98.17/14.78 (binintersect( 98.17/14.78 X644,X646) = 98.17/14.78 X644))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X648, 98.17/14.78 X650]: 98.17/14.78 (( 98.17/14.78 binintersect( 98.17/14.78 X648,X650) = 98.17/14.78 X650) => 98.17/14.78 subset( 98.17/14.78 X650,X648))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X652, 98.17/14.78 X654,X656]: 98.17/14.78 (in( 98.17/14.78 X656, 98.17/14.78 binintersect( 98.17/14.78 X652,X654)) => 98.17/14.78 in( 98.17/14.78 X656,X654))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X658, 98.17/14.78 X660]: 98.17/14.78 (( 98.17/14.78 ~ 98.17/14.78 ( 98.17/14.78 ?[X662]: 98.17/14.78 (in( 98.17/14.78 X662,X658) & 98.17/14.78 in( 98.17/14.78 X662,X660)))) => 98.17/14.78 (binintersect( 98.17/14.78 X658,X660) = 98.17/14.78 emptyset))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X664, 98.17/14.78 X666]: 98.17/14.78 subset( 98.17/14.78 binintersect( 98.17/14.78 X664,X666), 98.17/14.78 X666)) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X668, 98.17/14.78 X670]: 98.17/14.78 (subset( 98.17/14.78 X670,X668) => 98.17/14.78 (binintersect( 98.17/14.78 X668,X670) = 98.17/14.78 X670))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X672, 98.17/14.78 X674]: 98.17/14.78 (( 98.17/14.78 binintersect( 98.17/14.78 X672,X674) = 98.17/14.78 X672) => 98.17/14.78 subset( 98.17/14.78 X672,X674))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X676, 98.17/14.78 X678,X680]: 98.17/14.78 (binintersect( 98.17/14.78 X676, 98.17/14.78 binunion( 98.17/14.78 X678,X680)) = 98.17/14.78 binunion( 98.17/14.78 binintersect( 98.17/14.78 X676,X678), 98.17/14.78 binintersect( 98.17/14.78 X676,X680)))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X682, 98.17/14.78 X684,X686]: 98.17/14.78 (in( 98.17/14.78 X686,X682) => 98.17/14.78 (( 98.17/14.78 ~ 98.17/14.78 in( 98.17/14.78 X686,X684)) => 98.17/14.78 in( 98.17/14.78 X686, 98.17/14.78 setminus( 98.17/14.78 X682,X684))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X688, 98.17/14.78 X690,X692]: 98.17/14.78 (in( 98.17/14.78 X692, 98.17/14.78 setminus( 98.17/14.78 X688,X690)) => 98.17/14.78 in( 98.17/14.78 X692,X688))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X694, 98.17/14.78 X696,X698]: 98.17/14.78 (in( 98.17/14.78 X698, 98.17/14.78 setminus( 98.17/14.78 X694,X696)) => 98.17/14.78 (~ 98.17/14.78 in( 98.17/14.78 X698,X696)))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X700, 98.17/14.78 X702]: 98.17/14.78 (subset( 98.17/14.78 X700,X702) => 98.17/14.78 (setminus( 98.17/14.78 X700,X702) = 98.17/14.78 emptyset))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X704, 98.17/14.78 X706,X708]: 98.17/14.78 (( 98.17/14.78 ~ 98.17/14.78 in( 98.17/14.78 X708, 98.17/14.78 setminus( 98.17/14.78 X704,X706))) => 98.17/14.78 (in( 98.17/14.78 X708,X704) => 98.17/14.78 in( 98.17/14.78 X708,X706)))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X710, 98.17/14.78 X712,X714]: 98.17/14.78 (( 98.17/14.78 ~ 98.17/14.78 in( 98.17/14.78 X714, 98.17/14.78 setminus( 98.17/14.78 X710,X712))) => 98.17/14.78 (( 98.17/14.78 ~ 98.17/14.78 in( 98.17/14.78 X714,X712)) => 98.17/14.78 (~ 98.17/14.78 in( 98.17/14.78 X714,X710))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X716, 98.17/14.78 X718,X720]: 98.17/14.78 (( 98.17/14.78 ~ 98.17/14.78 in( 98.17/14.78 X720,X716)) => 98.17/14.78 (~ 98.17/14.78 in( 98.17/14.78 X720, 98.17/14.78 setminus( 98.17/14.78 X716,X718))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X722, 98.17/14.78 X724,X726]: 98.17/14.78 (in( 98.17/14.78 X726,X724) => 98.17/14.78 (~ 98.17/14.78 in( 98.17/14.78 X726, 98.17/14.78 setminus( 98.17/14.78 X722,X724))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X728, 98.17/14.78 X730]: 98.17/14.78 subset( 98.17/14.78 setminus( 98.17/14.78 X728,X730), 98.17/14.78 X728)) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X732, 98.17/14.78 X734]: 98.17/14.78 (( 98.17/14.78 setminus( 98.17/14.78 X732,X734) = 98.17/14.78 emptyset) => 98.17/14.78 subset( 98.17/14.78 X732,X734))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X736, 98.17/14.78 X738,X740]: 98.17/14.78 (in( 98.17/14.78 X740, 98.17/14.78 symdiff( 98.17/14.78 X736,X738)) => 98.17/14.78 (![X742:$o]: 98.17/14.78 (( 98.17/14.78 in( 98.17/14.78 X740,X736) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ~ 98.17/14.78 in( 98.17/14.78 X740,X738)) => 98.17/14.78 X742)) => 98.17/14.78 (( 98.17/14.78 ( 98.17/14.78 ~ 98.17/14.78 in( 98.17/14.78 X740,X736)) => 98.17/14.78 ( 98.17/14.78 in( 98.17/14.78 X740,X738) => 98.17/14.78 X742)) => 98.17/14.78 X742))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X744, 98.17/14.78 X746,X748]: 98.17/14.78 (in( 98.17/14.78 X748,X744) => 98.17/14.78 (( 98.17/14.78 ~ 98.17/14.78 in( 98.17/14.78 X748,X746)) => 98.17/14.78 in( 98.17/14.78 X748, 98.17/14.78 symdiff( 98.17/14.78 X744,X746))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X750, 98.17/14.78 X752,X754]: 98.17/14.78 (( 98.17/14.78 ~ 98.17/14.78 in( 98.17/14.78 X754,X750)) => 98.17/14.78 (in( 98.17/14.78 X754,X752) => 98.17/14.78 in( 98.17/14.78 X754, 98.17/14.78 symdiff( 98.17/14.78 X750,X752))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X756, 98.17/14.78 X758,X760]: 98.17/14.78 (in( 98.17/14.78 X760,X756) => 98.17/14.78 (in( 98.17/14.78 X760,X758) => 98.17/14.78 (~ 98.17/14.78 in( 98.17/14.78 X760, 98.17/14.78 symdiff( 98.17/14.78 X756,X758)))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X762, 98.17/14.78 X764,X766]: 98.17/14.78 (( 98.17/14.78 ~ 98.17/14.78 in( 98.17/14.78 X766,X762)) => 98.17/14.78 (( 98.17/14.78 ~ 98.17/14.78 in( 98.17/14.78 X766,X764)) => 98.17/14.78 (~ 98.17/14.78 in( 98.17/14.78 X766, 98.17/14.78 symdiff( 98.17/14.78 X762,X764)))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X768, 98.17/14.78 X770]: 98.17/14.78 in( 98.17/14.78 X770, 98.17/14.78 setadjoin( 98.17/14.78 X768, 98.17/14.78 setadjoin( 98.17/14.78 X770, 98.17/14.78 emptyset)))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X772, 98.17/14.78 X774]: 98.17/14.78 in( 98.17/14.78 X772, 98.17/14.78 setunion( 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X772, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X772, 98.17/14.78 setadjoin( 98.17/14.78 X774, 98.17/14.78 emptyset)), 98.17/14.78 emptyset))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X776, 98.17/14.78 X778]: 98.17/14.78 in( 98.17/14.78 X778, 98.17/14.78 setunion( 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X776, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X776, 98.17/14.78 setadjoin( 98.17/14.78 X778, 98.17/14.78 emptyset)), 98.17/14.78 emptyset))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X780, 98.17/14.78 X782]: 98.17/14.78 (?[X784]: 98.17/14.78 (in( 98.17/14.78 X784, 98.17/14.78 setunion( 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X780, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X780, 98.17/14.78 setadjoin( 98.17/14.78 X782, 98.17/14.78 emptyset)), 98.17/14.78 emptyset)))) & 98.17/14.78 (?[X786]: 98.17/14.78 (in( 98.17/14.78 X786, 98.17/14.78 setunion( 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X780, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X780, 98.17/14.78 setadjoin( 98.17/14.78 X782, 98.17/14.78 emptyset)), 98.17/14.78 emptyset)))) & 98.17/14.78 (setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X780, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X780, 98.17/14.78 setadjoin( 98.17/14.78 X782, 98.17/14.78 emptyset)), 98.17/14.78 emptyset)) = 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X784, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X784, 98.17/14.78 setadjoin( 98.17/14.78 X786, 98.17/14.78 emptyset)), 98.17/14.78 emptyset)))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X788, 98.17/14.78 X790]: 98.17/14.78 (?[X792]: 98.17/14.78 (in( 98.17/14.78 X792, 98.17/14.78 setunion( 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X788, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X788, 98.17/14.78 setadjoin( 98.17/14.78 X790, 98.17/14.78 emptyset)), 98.17/14.78 emptyset)))) & 98.17/14.78 (?[X794]: 98.17/14.78 (in( 98.17/14.78 X794, 98.17/14.78 setunion( 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X788, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X788, 98.17/14.78 setadjoin( 98.17/14.78 X790, 98.17/14.78 emptyset)), 98.17/14.78 emptyset)))) & 98.17/14.78 (setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X788, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X788, 98.17/14.78 setadjoin( 98.17/14.78 X790, 98.17/14.78 emptyset)), 98.17/14.78 emptyset)) = 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X792, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X792, 98.17/14.78 setadjoin( 98.17/14.78 X794, 98.17/14.78 emptyset)), 98.17/14.78 emptyset)))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X796, 98.17/14.78 X798]: 98.17/14.78 (in( 98.17/14.78 X798,X796) => 98.17/14.78 subset( 98.17/14.78 setadjoin( 98.17/14.78 X798, 98.17/14.78 emptyset), 98.17/14.78 X796))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X800, 98.17/14.78 X802]: 98.17/14.78 (in( 98.17/14.78 X802,X800) => 98.17/14.78 in( 98.17/14.78 setadjoin( 98.17/14.78 X802, 98.17/14.78 emptyset), 98.17/14.78 powerset( 98.17/14.78 X800)))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X804, 98.17/14.78 X806,X808]: 98.17/14.78 (in( 98.17/14.78 X808,X804) => 98.17/14.78 in( 98.17/14.78 setadjoin( 98.17/14.78 X808, 98.17/14.78 emptyset), 98.17/14.78 powerset( 98.17/14.78 binunion( 98.17/14.78 X804,X806))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X810, 98.17/14.78 X812,X814]: 98.17/14.78 (in( 98.17/14.78 X814, 98.17/14.78 setadjoin( 98.17/14.78 X810, 98.17/14.78 setadjoin( 98.17/14.78 X812, 98.17/14.78 emptyset))) => 98.17/14.78 (( 98.17/14.78 X814 = 98.17/14.78 X812) | 98.17/14.78 (X814 = 98.17/14.78 X810)))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X816, 98.17/14.78 X818,X820]: 98.17/14.78 (in( 98.17/14.78 X820,X816) => 98.17/14.78 (![X822]: 98.17/14.78 (in( 98.17/14.78 X822,X818) => 98.17/14.78 subset( 98.17/14.78 setadjoin( 98.17/14.78 X820, 98.17/14.78 setadjoin( 98.17/14.78 X822, 98.17/14.78 emptyset)), 98.17/14.78 binunion( 98.17/14.78 X816,X818)))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X824, 98.17/14.78 X826,X828]: 98.17/14.78 (in( 98.17/14.78 X828,X824) => 98.17/14.78 (![X830]: 98.17/14.78 (in( 98.17/14.78 X830,X826) => 98.17/14.78 in( 98.17/14.78 setadjoin( 98.17/14.78 X828, 98.17/14.78 setadjoin( 98.17/14.78 X830, 98.17/14.78 emptyset)), 98.17/14.78 powerset( 98.17/14.78 binunion( 98.17/14.78 X824,X826))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X832, 98.17/14.78 X834,X836]: 98.17/14.78 (in( 98.17/14.78 X836,X832) => 98.17/14.78 (![X838]: 98.17/14.78 (in( 98.17/14.78 X838,X834) => 98.17/14.78 subset( 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X836, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X836, 98.17/14.78 setadjoin( 98.17/14.78 X838, 98.17/14.78 emptyset)), 98.17/14.78 emptyset)), 98.17/14.78 powerset( 98.17/14.78 binunion( 98.17/14.78 X832,X834))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X840, 98.17/14.78 X842,X844]: 98.17/14.78 (in( 98.17/14.78 X844,X840) => 98.17/14.78 (![X846]: 98.17/14.78 (in( 98.17/14.78 X846,X842) => 98.17/14.78 in( 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X844, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X844, 98.17/14.78 setadjoin( 98.17/14.78 X846, 98.17/14.78 emptyset)), 98.17/14.78 emptyset)), 98.17/14.78 powerset( 98.17/14.78 powerset( 98.17/14.78 binunion( 98.17/14.78 X840,X842)))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X848, 98.17/14.78 X850,X852]: 98.17/14.78 (in( 98.17/14.78 X852,X848) => 98.17/14.78 (![X854]: 98.17/14.78 (in( 98.17/14.78 X854,X850) => 98.17/14.78 in( 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X852, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X852, 98.17/14.78 setadjoin( 98.17/14.78 X854, 98.17/14.78 emptyset)), 98.17/14.78 emptyset)), 98.17/14.78 powerset( 98.17/14.78 powerset( 98.17/14.78 binunion( 98.17/14.78 X848,X850)))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ![X856, 98.17/14.78 X858,X860]: 98.17/14.78 (in( 98.17/14.78 X860,X856) => 98.17/14.78 (![X862]: 98.17/14.78 (in( 98.17/14.78 X862,X858) => 98.17/14.78 in( 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X860, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X860, 98.17/14.78 setadjoin( 98.17/14.78 X862, 98.17/14.78 emptyset)), 98.17/14.78 emptyset)), 98.17/14.78 dsetconstr( 98.17/14.78 powerset( 98.17/14.78 powerset( 98.17/14.78 binunion( 98.17/14.78 X856,X858))), 98.17/14.78 ^[V_15]: 98.17/14.78 (?[X864]: 98.17/14.78 (in( 98.17/14.78 X864,X856) & 98.17/14.78 (?[X866]: 98.17/14.78 (in( 98.17/14.78 X866,X858) & 98.17/14.78 (V_15 = 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X864, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X864, 98.17/14.78 setadjoin( 98.17/14.78 X866, 98.17/14.78 emptyset)), 98.17/14.78 emptyset))))))))))))) => 98.17/14.78 ( 98.17/14.78 ![X868, 98.17/14.78 X870,X872]: 98.17/14.78 (in( 98.17/14.78 X872, 98.17/14.78 dsetconstr( 98.17/14.78 powerset( 98.17/14.78 powerset( 98.17/14.78 binunion( 98.17/14.78 X868,X870))), 98.17/14.78 ^[V_16]: 98.17/14.78 (?[X874]: 98.17/14.78 (in( 98.17/14.78 X874,X868) & 98.17/14.78 (?[X876]: 98.17/14.78 (in( 98.17/14.78 X876,X870) & 98.17/14.78 (V_16 = 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X874, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X874, 98.17/14.78 setadjoin( 98.17/14.78 X876, 98.17/14.78 emptyset)), 98.17/14.78 emptyset))))))))) => 98.17/14.78 (?[X878]: 98.17/14.78 (( 98.17/14.78 ?[X880]: 98.17/14.78 (in( 98.17/14.78 X880,X870) & 98.17/14.78 (X872 = 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X878, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 X878, 98.17/14.78 setadjoin( 98.17/14.78 X880, 98.17/14.78 emptyset)), 98.17/14.78 emptyset))))) & 98.17/14.78 in( 98.17/14.78 X878,X868)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 98.17/14.78 tff('159', plain, 98.17/14.78 ~ ((!!((^[Y0 : $i]: 98.17/14.78 (!!((^[Y1 : $i]: 98.17/14.78 ((!!((^[Y2 : $i]: (in(Y2, Y0) <=> in(Y2, Y1))))) => 98.17/14.78 (Y0 = Y1)))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 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98.17/14.78 (!!((^[Y2 : $i]: 98.17/14.78 (in(Y2, Y0) => 98.17/14.78 (in(Y2, 98.17/14.78 dsetconstr(Y0, 98.17/14.78 (^[Y3 : $i]: Y1(Y3)))) <=> 98.17/14.78 Y1(Y2)))))))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 ((Y0 != emptyset) => 98.17/14.78 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (!!((^[Y1 : $i > $o]: 98.17/14.78 (!!((^[Y2 : $i]: 98.17/14.78 (in(Y2, Y0) => 98.17/14.78 (Y1(Y2) => 98.17/14.78 (dsetconstr(Y0, 98.17/14.78 (^[Y3 : $i]: 98.17/14.78 Y1(Y3))) != 98.17/14.78 emptyset)))))))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 98.17/14.78 (Y0 != emptyset))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (!!((^[Y1 : $i]: 98.17/14.78 in(Y0, setadjoin(Y0, Y1)))))))) => 98.17/14.78 (in(emptyset, 98.17/14.78 setadjoin(emptyset, emptyset)) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (!!((^[Y1 : $i]: 98.17/14.78 (!!((^[Y2 : $i]: 98.17/14.78 (in(Y2, Y1) => 98.17/14.78 in(Y2, 98.17/14.78 setadjoin(Y0, 98.17/14.78 Y1)))))))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (!!((^[Y1 : $i]: 98.17/14.78 (!!((^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 setadjoin(Y0, 98.17/14.78 Y1)) => 98.17/14.78 (!!((^[Y3 : $o]: 98.17/14.78 (( 98.17/14.78 ( 98.17/14.78 Y2 = Y0) => 98.17/14.78 Y3) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 in(Y2, 98.17/14.78 Y1) => Y3) => 98.17/14.78 Y3))))))))))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (!!((^[Y1 : $i]: 98.17/14.78 (!!((^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 setadjoin(Y0, 98.17/14.78 Y1)) => 98.17/14.78 (in(Y2, Y1) | 98.17/14.78 (Y2 = Y0)))))))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (dsetconstr(Y0, 98.17/14.78 (^[Y1 : $i]: $true)) = 98.17/14.78 Y0)))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (!!((^[Y1 : $i]: 98.17/14.78 ((!!((^[Y2 : $i]: 98.17/14.78 (in(Y2, Y1) => 98.17/14.78 in(Y2, Y0))))) => 98.17/14.78 in(Y1, powerset(Y0))))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 in(emptyset, powerset(Y0))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 in(emptyset, powerset(Y0))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (!!((^[Y1 : $i]: 98.17/14.78 (!!((^[Y2 : $i]: 98.17/14.78 (in(Y1, 98.17/14.78 powerset( 98.17/14.78 Y0)) => 98.17/14.78 (in(Y2, Y1) => 98.17/14.78 in(Y2, Y0)))))))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (!!((^[Y1 : $i]: 98.17/14.78 (!!((^[Y2 : $i]: 98.17/14.78 (in(Y1, Y2) => 98.17/14.78 (in(Y2, 98.17/14.78 Y0) => 98.17/14.78 in(Y1, 98.17/14.78 setunion( 98.17/14.78 Y0))))))))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (!!((^[Y1 : $i]: 98.17/14.78 (in(Y1, 98.17/14.78 setunion(Y0)) => 98.17/14.78 (!!((^[Y2 : $o]: 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y3 : $i]: 98.17/14.78 (in(Y1, 98.17/14.78 Y3) => 98.17/14.78 (in(Y3, 98.17/14.78 Y0) => Y2))))) => 98.17/14.78 Y2))))))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (!!((^[Y1 : $i]: 98.17/14.78 (in(Y1, Y0) => 98.17/14.78 in(Y1, 98.17/14.78 powerset( 98.17/14.78 setunion( 98.17/14.78 Y0)))))))))) 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$o]: 98.17/14.78 (( 98.17/14.78 ??(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) & 98.17/14.78 Y1(Y2))))) => 98.17/14.78 ( 98.17/14.78 dsetconstr( 98.17/14.78 Y0, 98.17/14.78 (^[Y2 : $i]: 98.17/14.78 Y1(Y2))) != 98.17/14.78 emptyset)))))))) => 98.17/14.78 ((!!((^[Y0 : $i > $o]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 ( 98.17/14.78 in(Y1, 98.17/14.78 emptyset) => 98.17/14.78 Y0(Y1)))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i > $o]: 98.17/14.78 (( 98.17/14.78 ~(( 98.17/14.78 !!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) => 98.17/14.78 Y1(Y2))))))) => 98.17/14.78 (??(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) & 98.17/14.78 (~( 98.17/14.78 Y1(Y2)))))))))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i > $o]: 98.17/14.78 (( 98.17/14.78 !!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) => 98.17/14.78 (~( 98.17/14.78 Y1(Y2))))))) => 98.17/14.78 (~(( 98.17/14.78 ??(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) & 98.17/14.78 Y1(Y2)))))))))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y1 : $i > $o]: 98.17/14.78 (( 98.17/14.78 ~(( 98.17/14.78 ??(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) & 98.17/14.78 Y1(Y2))))))) => 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) => 98.17/14.78 (~( 98.17/14.78 Y1(Y2)))))))))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i > $o]: 98.17/14.78 (( 98.17/14.78 ??(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) & 98.17/14.78 (~( 98.17/14.78 Y1(Y2))))))) => 98.17/14.78 (~(( 98.17/14.78 !!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) => 98.17/14.78 Y1(Y2)))))))))))))) => 98.17/14.78 ((!!((^[Y0 : $o]: 98.17/14.78 (Y0 => 98.17/14.78 in( 98.17/14.78 emptyset, 98.17/14.78 prop2set( 98.17/14.78 Y0)))))) => 98.17/14.78 ((!!(( 98.17/14.78 ^[Y0 : $o]: 98.17/14.78 (Y0 => 98.17/14.78 set2prop( 98.17/14.78 prop2set( 98.17/14.78 Y0)))))) => 98.17/14.78 ((!!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y1 : $i > $o]: 98.17/14.78 (( 98.17/14.78 ~(( 98.17/14.78 ??(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) & 98.17/14.78 Y1(Y2))))))) => 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) => 98.17/14.78 (~( 98.17/14.78 Y1(Y2)))))))))))))) => 98.17/14.78 ((!!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i > $o]: 98.17/14.78 (( 98.17/14.78 ~(( 98.17/14.78 !!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) => 98.17/14.78 Y1(Y2))))))) => 98.17/14.78 (??(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) & 98.17/14.78 (~( 98.17/14.78 Y1(Y2)))))))))))))) => 98.17/14.78 ((!!(( 98.17/14.78 ^[Y0 : $i > $o]: 98.17/14.78 (( 98.17/14.78 ??(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (Y0(Y1) & 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (Y0(Y2) => 98.17/14.78 (Y1 = Y2))))))))) => 98.17/14.78 (??(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (Y0(Y1) & 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (Y0(Y2) => 98.17/14.78 (Y1 = Y2))))))))))))) => 98.17/14.78 (( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i > $o]: 98.17/14.78 (( 98.17/14.78 ??(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 Y0(Y1)))) => 98.17/14.78 (( 98.17/14.78 !!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (Y0(Y1) => 98.17/14.78 (Y0(Y2) => 98.17/14.78 (Y1 = Y2))))))))) => 98.17/14.78 (??(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (Y0(Y1) & 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (Y0(Y2) => 98.17/14.78 (Y1 = Y2)))))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i > $o]: 98.17/14.78 (( 98.17/14.78 ??(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (Y0(Y2) <=> 98.17/14.78 (Y2 = Y1)))))))) => 98.17/14.78 (??(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (Y0(Y1) & 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (Y0(Y2) => 98.17/14.78 (Y1 = Y2))))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (( 98.17/14.78 Y0 = Y1) => 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y3 : $i]: 98.17/14.78 (( 98.17/14.78 Y2 = Y3) => 98.17/14.78 (in(Y2, 98.17/14.78 Y0) => 98.17/14.78 in(Y3, 98.17/14.78 Y1)))))))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (( 98.17/14.78 Y0 = Y1) => 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y3 : $i]: 98.17/14.78 (( 98.17/14.78 Y2 = Y3) => 98.17/14.78 (in(Y2, 98.17/14.78 Y0) <=> 98.17/14.78 in(Y3, 98.17/14.78 Y1)))))))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i > $o]: 98.17/14.78 (( 98.17/14.78 ??(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (Y0(Y1) & 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (Y0(Y2) => 98.17/14.78 (Y1 = Y2))))))))) => 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (Y0(Y1) => 98.17/14.78 (Y0(Y2) => 98.17/14.78 (Y1 = Y2))))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i > $o]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i > $o]: 98.17/14.78 (( 98.17/14.78 !!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y3 : $i]: 98.17/14.78 (( 98.17/14.78 Y2 = Y3) => 98.17/14.78 (Y0(Y2) <=> 98.17/14.78 Y1(Y3))))))))) => 98.17/14.78 (( 98.17/14.78 ??(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (Y0(Y2) & 98.17/14.78 (!!(( 98.17/14.78 ^[Y3 : $i]: 98.17/14.78 (Y0(Y3) => 98.17/14.78 (Y2 = Y3))))))))) <=> 98.17/14.78 (??(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (Y1(Y2) & 98.17/14.78 (!!(( 98.17/14.78 ^[Y3 : $i]: 98.17/14.78 (Y1(Y3) => 98.17/14.78 (Y2 = Y3))))))))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 emptyset = 98.17/14.78 emptyset) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (( 98.17/14.78 Y0 = Y1) => 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y3 : $i]: 98.17/14.78 (( 98.17/14.78 Y2 = Y3) => 98.17/14.78 (setadjoin( 98.17/14.78 Y0, Y2) = 98.17/14.78 setadjoin( 98.17/14.78 Y1, Y3)))))))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (( 98.17/14.78 Y0 = Y1) => 98.17/14.78 (powerset( 98.17/14.78 Y0) = 98.17/14.78 powerset( 98.17/14.78 Y1))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (( 98.17/14.78 Y0 = Y1) => 98.17/14.78 (setunion( 98.17/14.78 Y0) = 98.17/14.78 setunion( 98.17/14.78 Y1))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 omega = 98.17/14.78 omega) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i > $o]: 98.17/14.78 (( 98.17/14.78 ??(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (Y0(Y1) & 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (Y0(Y2) => 98.17/14.78 (Y1 = Y2))))))))) => 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (Y0(Y1) => 98.17/14.78 (Y0(Y2) => 98.17/14.78 (Y1 = Y2))))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i > $o]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i > $o]: 98.17/14.78 (( 98.17/14.78 !!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y3 : $i]: 98.17/14.78 (( 98.17/14.78 Y2 = Y3) => 98.17/14.78 (Y0(Y2) <=> 98.17/14.78 Y1(Y3))))))))) => 98.17/14.78 (( 98.17/14.78 ??(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (Y0(Y2) & 98.17/14.78 (!!(( 98.17/14.78 ^[Y3 : $i]: 98.17/14.78 (Y0(Y3) => 98.17/14.78 (Y2 = Y3))))))))) => 98.17/14.78 (( 98.17/14.78 ??(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (Y1(Y2) & 98.17/14.78 (!!(( 98.17/14.78 ^[Y3 : $i]: 98.17/14.78 (Y1(Y3) => 98.17/14.78 (Y2 = Y3))))))))) => 98.17/14.78 (descr( 98.17/14.78 (^[Y2 : $i]: 98.17/14.78 Y0(Y2))) = 98.17/14.78 descr( 98.17/14.78 (^[Y2 : $i]: 98.17/14.78 Y1(Y2))))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (( 98.17/14.78 Y0 = Y1) => 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i > $o]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y3 : $i > $o]: 98.17/14.78 (( 98.17/14.78 !!(( 98.17/14.78 ^[Y4 : $i]: 98.17/14.78 (in(Y4, 98.17/14.78 Y0) => 98.17/14.78 (!!(( 98.17/14.78 ^[Y5 : $i]: 98.17/14.78 (in(Y5, 98.17/14.78 Y1) => 98.17/14.78 (( 98.17/14.78 Y4 = Y5) => 98.17/14.78 (Y2(Y4) <=> 98.17/14.78 Y3(Y5))))))))))) => 98.17/14.78 (dsetconstr( 98.17/14.78 Y0, 98.17/14.78 (^[Y4 : $i]: 98.17/14.78 Y2(Y4))) = 98.17/14.78 dsetconstr( 98.17/14.78 Y1, 98.17/14.78 (^[Y4 : $i]: 98.17/14.78 Y3(Y4)))))))))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (( 98.17/14.78 !!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) => 98.17/14.78 in(Y2, 98.17/14.78 Y1))))) => 98.17/14.78 subset( 98.17/14.78 Y0, Y1)))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (( 98.17/14.78 Y0 = Y1) => 98.17/14.78 subset( 98.17/14.78 Y1, Y0)))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (( 98.17/14.78 Y0 = Y1) => 98.17/14.78 subset( 98.17/14.78 Y0, Y1)))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (( 98.17/14.78 !!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) => 98.17/14.78 in(Y2, 98.17/14.78 Y1))))) => 98.17/14.78 subset( 98.17/14.78 Y0, Y1)))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 subset( 98.17/14.78 emptyset, 98.17/14.78 Y0)))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (subset( 98.17/14.78 Y0, Y1) => 98.17/14.78 (in(Y2, 98.17/14.78 Y0) => 98.17/14.78 in(Y2, 98.17/14.78 Y1)))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (subset( 98.17/14.78 Y0, Y1) => 98.17/14.78 (( 98.17/14.78 ~( 98.17/14.78 in(Y2, 98.17/14.78 Y1))) => 98.17/14.78 (~( 98.17/14.78 in(Y2, 98.17/14.78 Y0)))))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) => 98.17/14.78 (( 98.17/14.78 ~( 98.17/14.78 in(Y2, 98.17/14.78 Y1))) => 98.17/14.78 (~( 98.17/14.78 subset( 98.17/14.78 Y0, Y1)))))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (( 98.17/14.78 ~( 98.17/14.78 subset( 98.17/14.78 Y0, Y1))) => 98.17/14.78 (Y0 != Y1)))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) => 98.17/14.78 (( 98.17/14.78 ~( 98.17/14.78 in(Y2, 98.17/14.78 Y1))) => 98.17/14.78 (Y0 != Y1)))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 subset( 98.17/14.78 Y0, Y0)))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (subset( 98.17/14.78 Y0, Y1) => 98.17/14.78 (subset( 98.17/14.78 Y1, Y2) => 98.17/14.78 subset( 98.17/14.78 Y0, Y2)))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 subset( 98.17/14.78 Y1, 98.17/14.78 setadjoin( 98.17/14.78 Y0, Y1)))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (subset( 98.17/14.78 Y0, Y2) => 98.17/14.78 subset( 98.17/14.78 Y0, 98.17/14.78 setadjoin( 98.17/14.78 Y1, Y2)))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (subset( 98.17/14.78 Y0, Y1) => 98.17/14.78 in(Y0, 98.17/14.78 powerset( 98.17/14.78 Y1))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (subset( 98.17/14.78 Y0, Y1) => 98.17/14.78 (subset( 98.17/14.78 Y1, Y0) => 98.17/14.78 (Y0 = Y1))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (subset( 98.17/14.78 Y0, 98.17/14.78 emptyset) => 98.17/14.78 (Y0 = 98.17/14.78 emptyset))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (subset( 98.17/14.78 Y1, Y0) => 98.17/14.78 in(Y1, 98.17/14.78 powerset( 98.17/14.78 Y0))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (in(Y1, 98.17/14.78 powerset( 98.17/14.78 Y0)) => 98.17/14.78 subset( 98.17/14.78 Y1, Y0)))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 in(Y0, 98.17/14.78 powerset( 98.17/14.78 Y0))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (subset( 98.17/14.78 Y0, Y1) => 98.17/14.78 subset( 98.17/14.78 powerset( 98.17/14.78 Y0), 98.17/14.78 powerset( 98.17/14.78 Y1))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i > $o]: 98.17/14.78 in( 98.17/14.78 dsetconstr( 98.17/14.78 Y0, 98.17/14.78 (^[Y2 : $i]: 98.17/14.78 Y1(Y2))), 98.17/14.78 powerset( 98.17/14.78 Y0)))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i > $o]: 98.17/14.78 subset( 98.17/14.78 dsetconstr( 98.17/14.78 Y0, 98.17/14.78 (^[Y2 : $i]: 98.17/14.78 Y1(Y2))), 98.17/14.78 Y0))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) => 98.17/14.78 in(Y2, 98.17/14.78 binunion( 98.17/14.78 Y0, Y1)))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 in(Y1, 98.17/14.78 setadjoin( 98.17/14.78 Y0, 98.17/14.78 setadjoin( 98.17/14.78 Y1, 98.17/14.78 emptyset))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y1) => 98.17/14.78 in(Y2, 98.17/14.78 binunion( 98.17/14.78 Y0, Y1)))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y3 : $o]: 98.17/14.78 (in(Y2, 98.17/14.78 binunion( 98.17/14.78 Y0, Y1)) => 98.17/14.78 (( 98.17/14.78 in(Y2, 98.17/14.78 Y0) => Y3) => 98.17/14.78 (( 98.17/14.78 in(Y2, 98.17/14.78 Y1) => Y3) => 98.17/14.78 Y3))))))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 binunion( 98.17/14.78 Y0, Y1)) => 98.17/14.78 (in(Y2, 98.17/14.78 Y1) | 98.17/14.78 in(Y2, 98.17/14.78 Y0)))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 subset( 98.17/14.78 Y0, 98.17/14.78 binunion( 98.17/14.78 Y0, Y1)))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 subset( 98.17/14.78 Y1, 98.17/14.78 binunion( 98.17/14.78 Y0, Y1)))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) => 98.17/14.78 (in(Y2, 98.17/14.78 Y1) => 98.17/14.78 in(Y2, 98.17/14.78 binintersect( 98.17/14.78 Y0, Y1))))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (subset( 98.17/14.78 Y2, Y0) => 98.17/14.78 (subset( 98.17/14.78 Y2, Y1) => 98.17/14.78 subset( 98.17/14.78 Y2, 98.17/14.78 binintersect( 98.17/14.78 Y0, Y1))))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 binintersect( 98.17/14.78 Y0, Y1)) => 98.17/14.78 in(Y2, 98.17/14.78 Y0))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 subset( 98.17/14.78 binintersect( 98.17/14.78 Y0, Y1), 98.17/14.78 Y0))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (subset( 98.17/14.78 Y0, Y1) => 98.17/14.78 (binintersect( 98.17/14.78 Y0, Y1) = 98.17/14.78 Y0)))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (( 98.17/14.78 binintersect( 98.17/14.78 Y0, Y1) = 98.17/14.78 Y1) => 98.17/14.78 subset( 98.17/14.78 Y1, Y0)))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 binintersect( 98.17/14.78 Y0, Y1)) => 98.17/14.78 in(Y2, 98.17/14.78 Y1))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (( 98.17/14.78 ~(( 98.17/14.78 ??(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) & 98.17/14.78 in(Y2, 98.17/14.78 Y1))))))) => 98.17/14.78 (binintersect( 98.17/14.78 Y0, Y1) = 98.17/14.78 emptyset)))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 subset( 98.17/14.78 binintersect( 98.17/14.78 Y0, Y1), 98.17/14.78 Y1))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (subset( 98.17/14.78 Y1, Y0) => 98.17/14.78 (binintersect( 98.17/14.78 Y0, Y1) = 98.17/14.78 Y1)))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (( 98.17/14.78 binintersect( 98.17/14.78 Y0, Y1) = 98.17/14.78 Y0) => 98.17/14.78 subset( 98.17/14.78 Y0, Y1)))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (binintersect( 98.17/14.78 Y0, 98.17/14.78 binunion( 98.17/14.78 Y1, Y2)) = 98.17/14.78 binunion( 98.17/14.78 binintersect( 98.17/14.78 Y0, Y1), 98.17/14.78 binintersect( 98.17/14.78 Y0, Y2)))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) => 98.17/14.78 (( 98.17/14.78 ~( 98.17/14.78 in(Y2, 98.17/14.78 Y1))) => 98.17/14.78 in(Y2, 98.17/14.78 setminus( 98.17/14.78 Y0, Y1))))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 setminus( 98.17/14.78 Y0, Y1)) => 98.17/14.78 in(Y2, 98.17/14.78 Y0))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 setminus( 98.17/14.78 Y0, Y1)) => 98.17/14.78 (~( 98.17/14.78 in(Y2, 98.17/14.78 Y1))))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (subset( 98.17/14.78 Y0, Y1) => 98.17/14.78 (setminus( 98.17/14.78 Y0, Y1) = 98.17/14.78 emptyset)))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (( 98.17/14.78 ~( 98.17/14.78 in(Y2, 98.17/14.78 setminus( 98.17/14.78 Y0, Y1)))) => 98.17/14.78 (in(Y2, 98.17/14.78 Y0) => 98.17/14.78 in(Y2, 98.17/14.78 Y1)))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (( 98.17/14.78 ~( 98.17/14.78 in(Y2, 98.17/14.78 setminus( 98.17/14.78 Y0, Y1)))) => 98.17/14.78 (( 98.17/14.78 ~( 98.17/14.78 in(Y2, 98.17/14.78 Y1))) => 98.17/14.78 (~( 98.17/14.78 in(Y2, 98.17/14.78 Y0)))))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (( 98.17/14.78 ~( 98.17/14.78 in(Y2, 98.17/14.78 Y0))) => 98.17/14.78 (~( 98.17/14.78 in(Y2, 98.17/14.78 setminus( 98.17/14.78 Y0, Y1)))))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y1) => 98.17/14.78 (~( 98.17/14.78 in(Y2, 98.17/14.78 setminus( 98.17/14.78 Y0, Y1)))))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 subset( 98.17/14.78 setminus( 98.17/14.78 Y0, Y1), 98.17/14.78 Y0))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (( 98.17/14.78 setminus( 98.17/14.78 Y0, Y1) = 98.17/14.78 emptyset) => 98.17/14.78 subset( 98.17/14.78 Y0, Y1)))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 symdiff( 98.17/14.78 Y0, Y1)) => 98.17/14.78 (!!(( 98.17/14.78 ^[Y3 : $o]: 98.17/14.78 (( 98.17/14.78 in(Y2, 98.17/14.78 Y0) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ~( 98.17/14.78 in(Y2, 98.17/14.78 Y1))) => 98.17/14.78 Y3)) => 98.17/14.78 (( 98.17/14.78 ( 98.17/14.78 ~( 98.17/14.78 in(Y2, 98.17/14.78 Y0))) => 98.17/14.78 ( 98.17/14.78 in(Y2, 98.17/14.78 Y1) => Y3)) => 98.17/14.78 Y3))))))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) => 98.17/14.78 (( 98.17/14.78 ~( 98.17/14.78 in(Y2, 98.17/14.78 Y1))) => 98.17/14.78 in(Y2, 98.17/14.78 symdiff( 98.17/14.78 Y0, Y1))))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (( 98.17/14.78 ~( 98.17/14.78 in(Y2, 98.17/14.78 Y0))) => 98.17/14.78 (in(Y2, 98.17/14.78 Y1) => 98.17/14.78 in(Y2, 98.17/14.78 symdiff( 98.17/14.78 Y0, Y1))))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) => 98.17/14.78 (in(Y2, 98.17/14.78 Y1) => 98.17/14.78 (~( 98.17/14.78 in(Y2, 98.17/14.78 symdiff( 98.17/14.78 Y0, Y1))))))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (( 98.17/14.78 ~( 98.17/14.78 in(Y2, 98.17/14.78 Y0))) => 98.17/14.78 (( 98.17/14.78 ~( 98.17/14.78 in(Y2, 98.17/14.78 Y1))) => 98.17/14.78 (~( 98.17/14.78 in(Y2, 98.17/14.78 symdiff( 98.17/14.78 Y0, Y1))))))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 in(Y1, 98.17/14.78 setadjoin( 98.17/14.78 Y0, 98.17/14.78 setadjoin( 98.17/14.78 Y1, 98.17/14.78 emptyset))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 in(Y0, 98.17/14.78 setunion( 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 Y0, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 Y0, 98.17/14.78 setadjoin( 98.17/14.78 Y1, 98.17/14.78 emptyset)), 98.17/14.78 emptyset)))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 in(Y1, 98.17/14.78 setunion( 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 Y0, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 Y0, 98.17/14.78 setadjoin( 98.17/14.78 Y1, 98.17/14.78 emptyset)), 98.17/14.78 emptyset)))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (??(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 setunion( 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 Y0, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 Y0, 98.17/14.78 setadjoin( 98.17/14.78 Y1, 98.17/14.78 emptyset)), 98.17/14.78 emptyset)))) & 98.17/14.78 (??(( 98.17/14.78 ^[Y3 : $i]: 98.17/14.78 (in(Y3, 98.17/14.78 setunion( 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 Y0, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 Y0, 98.17/14.78 setadjoin( 98.17/14.78 Y1, 98.17/14.78 emptyset)), 98.17/14.78 emptyset)))) & 98.17/14.78 (setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 Y0, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 Y0, 98.17/14.78 setadjoin( 98.17/14.78 Y1, 98.17/14.78 emptyset)), 98.17/14.78 emptyset)) = 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 Y2, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 Y2, 98.17/14.78 setadjoin( 98.17/14.78 Y3, 98.17/14.78 emptyset)), 98.17/14.78 emptyset))))))))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (??(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 setunion( 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 Y0, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 Y0, 98.17/14.78 setadjoin( 98.17/14.78 Y1, 98.17/14.78 emptyset)), 98.17/14.78 emptyset)))) & 98.17/14.78 (??(( 98.17/14.78 ^[Y3 : $i]: 98.17/14.78 (in(Y3, 98.17/14.78 setunion( 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 Y0, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 Y0, 98.17/14.78 setadjoin( 98.17/14.78 Y1, 98.17/14.78 emptyset)), 98.17/14.78 emptyset)))) & 98.17/14.78 (setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 Y0, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 Y0, 98.17/14.78 setadjoin( 98.17/14.78 Y1, 98.17/14.78 emptyset)), 98.17/14.78 emptyset)) = 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 Y2, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 Y2, 98.17/14.78 setadjoin( 98.17/14.78 Y3, 98.17/14.78 emptyset)), 98.17/14.78 emptyset))))))))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (in(Y1, 98.17/14.78 Y0) => 98.17/14.78 subset( 98.17/14.78 setadjoin( 98.17/14.78 Y1, 98.17/14.78 emptyset), 98.17/14.78 Y0)))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (in(Y1, 98.17/14.78 Y0) => 98.17/14.78 in( 98.17/14.78 setadjoin( 98.17/14.78 Y1, 98.17/14.78 emptyset), 98.17/14.78 powerset( 98.17/14.78 Y0))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) => 98.17/14.78 in( 98.17/14.78 setadjoin( 98.17/14.78 Y2, 98.17/14.78 emptyset), 98.17/14.78 powerset( 98.17/14.78 binunion( 98.17/14.78 Y0, Y1))))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 setadjoin( 98.17/14.78 Y0, 98.17/14.78 setadjoin( 98.17/14.78 Y1, 98.17/14.78 emptyset))) => 98.17/14.78 (( 98.17/14.78 Y2 = Y1) | 98.17/14.78 (Y2 = Y0)))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) => 98.17/14.78 (!!(( 98.17/14.78 ^[Y3 : $i]: 98.17/14.78 (in(Y3, 98.17/14.78 Y1) => 98.17/14.78 subset( 98.17/14.78 setadjoin( 98.17/14.78 Y2, 98.17/14.78 setadjoin( 98.17/14.78 Y3, 98.17/14.78 emptyset)), 98.17/14.78 binunion( 98.17/14.78 Y0, Y1)))))))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) => 98.17/14.78 (!!(( 98.17/14.78 ^[Y3 : $i]: 98.17/14.78 (in(Y3, 98.17/14.78 Y1) => 98.17/14.78 in( 98.17/14.78 setadjoin( 98.17/14.78 Y2, 98.17/14.78 setadjoin( 98.17/14.78 Y3, 98.17/14.78 emptyset)), 98.17/14.78 powerset( 98.17/14.78 binunion( 98.17/14.78 Y0, Y1))))))))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) => 98.17/14.78 (!!(( 98.17/14.78 ^[Y3 : $i]: 98.17/14.78 (in(Y3, 98.17/14.78 Y1) => 98.17/14.78 subset( 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 Y2, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 Y2, 98.17/14.78 setadjoin( 98.17/14.78 Y3, 98.17/14.78 emptyset)), 98.17/14.78 emptyset)), 98.17/14.78 powerset( 98.17/14.78 binunion( 98.17/14.78 Y0, Y1))))))))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) => 98.17/14.78 (!!(( 98.17/14.78 ^[Y3 : $i]: 98.17/14.78 (in(Y3, 98.17/14.78 Y1) => 98.17/14.78 in( 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 Y2, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 Y2, 98.17/14.78 setadjoin( 98.17/14.78 Y3, 98.17/14.78 emptyset)), 98.17/14.78 emptyset)), 98.17/14.78 powerset( 98.17/14.78 powerset( 98.17/14.78 binunion( 98.17/14.78 Y0, Y1)))))))))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) => 98.17/14.78 (!!(( 98.17/14.78 ^[Y3 : $i]: 98.17/14.78 (in(Y3, 98.17/14.78 Y1) => 98.17/14.78 in( 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 Y2, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 Y2, 98.17/14.78 setadjoin( 98.17/14.78 Y3, 98.17/14.78 emptyset)), 98.17/14.78 emptyset)), 98.17/14.78 powerset( 98.17/14.78 powerset( 98.17/14.78 binunion( 98.17/14.78 Y0, Y1)))))))))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) => 98.17/14.78 (!!(( 98.17/14.78 ^[Y3 : $i]: 98.17/14.78 (in(Y3, 98.17/14.78 Y1) => 98.17/14.78 in( 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 Y2, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 Y2, 98.17/14.78 setadjoin( 98.17/14.78 Y3, 98.17/14.78 emptyset)), 98.17/14.78 emptyset)), 98.17/14.78 dsetconstr( 98.17/14.78 powerset( 98.17/14.78 powerset( 98.17/14.78 binunion( 98.17/14.78 Y0, Y1))), 98.17/14.78 (^[Y4 : $i]: 98.17/14.78 (??(( 98.17/14.78 ^[Y5 : $i]: 98.17/14.78 (in(Y5, 98.17/14.78 Y0) & 98.17/14.78 (??(( 98.17/14.78 ^[Y6 : $i]: 98.17/14.78 (in(Y6, 98.17/14.78 Y1) & 98.17/14.78 (Y4 = 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 Y5, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 Y5, 98.17/14.78 setadjoin( 98.17/14.78 Y6, 98.17/14.78 emptyset)), 98.17/14.78 emptyset)))))))))))))))))))))))))))) => 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 dsetconstr( 98.17/14.78 powerset( 98.17/14.78 powerset( 98.17/14.78 binunion( 98.17/14.78 Y0, Y1))), 98.17/14.78 (^[Y3 : $i]: 98.17/14.78 (??(( 98.17/14.78 ^[Y4 : $i]: 98.17/14.78 (in(Y4, 98.17/14.78 Y0) & 98.17/14.78 (??(( 98.17/14.78 ^[Y5 : $i]: 98.17/14.78 (in(Y5, 98.17/14.78 Y1) & 98.17/14.78 (Y3 = 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 Y4, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 Y4, 98.17/14.78 setadjoin( 98.17/14.78 Y5, 98.17/14.78 emptyset)), 98.17/14.78 emptyset)))))))))))))) => 98.17/14.78 (??(( 98.17/14.78 ^[Y3 : $i]: 98.17/14.78 (( 98.17/14.78 ??(( 98.17/14.78 ^[Y4 : $i]: 98.17/14.78 (in(Y4, 98.17/14.78 Y1) & 98.17/14.78 (Y2 = 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 Y3, 98.17/14.78 emptyset), 98.17/14.78 setadjoin( 98.17/14.78 setadjoin( 98.17/14.78 Y3, 98.17/14.78 setadjoin( 98.17/14.78 Y4, 98.17/14.78 emptyset)), 98.17/14.78 emptyset))))))) & 98.17/14.78 in(Y3, 98.17/14.78 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 98.17/14.78 inference('cnf', [status(esa)], [zf_stmt_1])). 98.17/14.78 tff('160', plain, 98.17/14.78 ~ ((!!((^[Y0 : $i]: 98.17/14.78 (!!((^[Y1 : $i]: 98.17/14.78 ((!!((^[Y2 : $i]: (in(Y2, Y0) <=> in(Y2, Y1))))) => 98.17/14.78 (Y0 = Y1)))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (!!((^[Y1 : $i]: 98.17/14.78 (!!((^[Y2 : $i]: 98.17/14.78 (in(Y2, setadjoin(Y0, Y1)) <=> 98.17/14.78 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (!!((^[Y1 : $i]: 98.17/14.78 (in(Y1, powerset(Y0)) <=> 98.17/14.78 (!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (!!((^[Y1 : $i]: 98.17/14.78 (in(Y1, setunion(Y0)) <=> 98.17/14.78 (??((^[Y2 : $i]: (in(Y1, Y2) & in(Y2, Y0)))))))))))) => 98.17/14.78 (in(emptyset, omega) => 98.17/14.78 ((!!((^[Y0 : $i]: (in(Y0, omega) => in(setadjoin(Y0, Y0), omega))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (((!!((^[Y1 : $i]: 98.17/14.78 ((in(Y1, Y0) & in(Y1, omega)) => 98.17/14.78 in(setadjoin(Y1, Y1), Y0))))) & 98.17/14.78 in(emptyset, Y0)) => 98.17/14.78 (!!((^[Y1 : $i]: (in(Y1, omega) => in(Y1, Y0))))))))) => 98.17/14.78 ((!!((^[Y0 : ($i * $i) > $o]: 98.17/14.78 (!!((^[Y1 : $i]: 98.17/14.78 ((!!((^[Y2 : $i]: 98.17/14.78 (in(Y2, Y1) => 98.17/14.78 (??((^[Y3 : $i]: 98.17/14.78 (Y0(Y2, Y3) & 98.17/14.78 (!!((^[Y4 : $i]: 98.17/14.78 (Y0(Y2, Y4) => (Y3 = Y4))))))))))))) => 98.17/14.78 (??((^[Y2 : $i]: 98.17/14.78 (!!((^[Y3 : $i]: 98.17/14.78 (in(Y3, Y2) <=> 98.17/14.78 (??((^[Y4 : $i]: 98.17/14.78 (in(Y4, Y1) & Y0(Y4, Y3))))))))))))))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 98.17/14.78 (??((^[Y1 : $i]: 98.17/14.78 (in(Y1, Y0) & 98.17/14.78 (~((??((^[Y2 : $i]: (in(Y2, Y1) & in(Y2, Y0))))))))))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (??((^[Y1 : $i]: 98.17/14.78 ((!!((^[Y2 : $i]: 98.17/14.78 (in(Y2, Y1) => 98.17/14.78 (!!((^[Y3 : $i]: 98.17/14.78 (in(Y3, Y2) => in(Y3, Y0)))))))))& 98.17/14.78 (!!((^[Y2 : $i]: 98.17/14.78 (!!((^[Y3 : $i]: 98.17/14.78 ((in(Y3, Y0) & in(Y2, Y0)) => 98.17/14.78 ((!!((^[Y4 : $i]: 98.17/14.78 (in(Y4, Y1) => 98.17/14.78 (in(Y2, Y4) <=> 98.17/14.78 in(Y3, Y4)))))) => 98.17/14.78 (Y2 = Y3)))))))))& 98.17/14.78 (!!((^[Y2 : $i]: 98.17/14.78 (!!((^[Y3 : $i]: 98.17/14.78 ((in(Y3, Y1) & in(Y2, Y1)) => 98.17/14.78 ((!!((^[Y4 : $i]: 98.17/14.78 (in(Y4, Y3) => 98.17/14.78 in(Y4, Y2))))) | 98.17/14.78 (!!((^[Y4 : $i]: 98.17/14.78 (in(Y4, Y2) => 98.17/14.78 in(Y4, Y3)))))))))))))& 98.17/14.78 (!!((^[Y2 : $i]: 98.17/14.78 (((??((^[Y3 : $i]: in(Y3, Y2)))) & 98.17/14.78 (!!((^[Y3 : $i]: 98.17/14.78 (in(Y3, Y2) => in(Y3, Y0)))))) => 98.17/14.78 (??((^[Y3 : $i]: 98.17/14.78 (??((^[Y4 : $i]: 98.17/14.78 (in(Y3, Y1)&in(Y4, Y2)& 98.17/14.78 (~((??((^[Y5 : $i]: 98.17/14.78 (in(Y5, Y3) & 98.17/14.78 in(Y5, Y2)))))))& 98.17/14.78 (!!((^[Y5 : $i]: 98.17/14.78 (in(Y5, Y1) => 98.17/14.78 (in(Y4, Y5) | 98.17/14.78 (!!(( 98.17/14.78 ^[Y6 : $i]: 98.17/14.78 (in(Y6, 98.17/14.78 Y5) => 98.17/14.78 in(Y6, 98.17/14.78 Y3)))))))))))))))))))))))))))) => 98.17/14.78 ((!!((^[Y0 : $i > $o]: 98.17/14.78 ((??((^[Y1 : $i]: 98.17/14.78 (Y0(Y1) & 98.17/14.78 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 98.17/14.78 Y0(descr((^[Y1 : $i]: Y0(Y1)))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (!!((^[Y1 : $i > $o]: 98.17/14.78 (!!((^[Y2 : $i]: 98.17/14.78 (in(Y2, Y0) => 98.17/14.78 (Y1(Y2) => 98.17/14.78 in(Y2, 98.17/14.78 dsetconstr(Y0, 98.17/14.78 (^[Y3 : $i]: Y1(Y3))))))))))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (!!((^[Y1 : $i > $o]: 98.17/14.78 (!!((^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 dsetconstr(Y0, 98.17/14.78 (^[Y3 : $i]: Y1(Y3)))) => 98.17/14.78 in(Y2, Y0))))))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (!!((^[Y1 : $i > $o]: 98.17/14.78 (!!((^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 dsetconstr(Y0, 98.17/14.78 (^[Y3 : $i]: Y1(Y3)))) => 98.17/14.78 Y1(Y2))))))))))) => 98.17/14.78 ((!!((^[Y0 : $o]: 98.17/14.78 (!!((^[Y1 : $i]: (in(Y1, prop2set(Y0)) => Y0))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (in(Y0, emptyset) => (!!((^[Y1 : $o]: Y1))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 98.17/14.78 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 98.17/14.78 ((!!((^[Y0 : $i > $o]: 98.17/14.78 ((??((^[Y1 : $i]: 98.17/14.78 (Y0(Y1) & 98.17/14.78 (!!((^[Y2 : $i]: 98.17/14.78 (Y0(Y2) => (Y1 = Y2))))))))) => 98.17/14.78 (??((^[Y1 : $i]: Y0(Y1)))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (!!((^[Y1 : $i]: 98.17/14.78 ((!!((^[Y2 : $i]: 98.17/14.78 (in(Y2, Y0) => in(Y2, Y1))))) => 98.17/14.78 ((!!((^[Y2 : $i]: 98.17/14.78 (in(Y2, Y1) => in(Y2, Y0))))) => 98.17/14.78 (Y0 = Y1))))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 98.17/14.78 (Y0 = emptyset))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 98.17/14.78 (Y0 = emptyset))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (!!((^[Y1 : $i > $o]: 98.17/14.78 (!!((^[Y2 : $i]: 98.17/14.78 (in(Y2, Y0) => 98.17/14.78 (in(Y2, 98.17/14.78 dsetconstr(Y0, 98.17/14.78 (^[Y3 : $i]: Y1(Y3)))) <=> 98.17/14.78 Y1(Y2)))))))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 ((Y0 != emptyset) => 98.17/14.78 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (!!((^[Y1 : $i > $o]: 98.17/14.78 (!!((^[Y2 : $i]: 98.17/14.78 (in(Y2, Y0) => 98.17/14.78 (Y1(Y2) => 98.17/14.78 (dsetconstr(Y0, 98.17/14.78 (^[Y3 : $i]: Y1(Y3))) != 98.17/14.78 emptyset)))))))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 98.17/14.78 (Y0 != emptyset))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (!!((^[Y1 : $i]: 98.17/14.78 in(Y0, setadjoin(Y0, Y1)))))))) => 98.17/14.78 (in(emptyset, 98.17/14.78 setadjoin(emptyset, emptyset)) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (!!((^[Y1 : $i]: 98.17/14.78 (!!((^[Y2 : $i]: 98.17/14.78 (in(Y2, Y1) => 98.17/14.78 in(Y2, 98.17/14.78 setadjoin(Y0, Y1)))))))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (!!((^[Y1 : $i]: 98.17/14.78 (!!((^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 setadjoin(Y0, 98.17/14.78 Y1)) => 98.17/14.78 (!!((^[Y3 : $o]: 98.17/14.78 ((( 98.17/14.78 Y2 = Y0) => 98.17/14.78 Y3) => 98.17/14.78 (( 98.17/14.78 in(Y2, 98.17/14.78 Y1) => Y3) => 98.17/14.78 Y3))))))))))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (!!((^[Y1 : $i]: 98.17/14.78 (!!((^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 setadjoin(Y0, 98.17/14.78 Y1)) => 98.17/14.78 (in(Y2, Y1) | 98.17/14.78 (Y2 = Y0)))))))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (dsetconstr(Y0, 98.17/14.78 (^[Y1 : $i]: $true)) = 98.17/14.78 Y0)))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (!!((^[Y1 : $i]: 98.17/14.78 ((!!((^[Y2 : $i]: 98.17/14.78 (in(Y2, Y1) => 98.17/14.78 in(Y2, Y0))))) => 98.17/14.78 in(Y1, powerset(Y0))))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 in(emptyset, powerset(Y0))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 in(emptyset, powerset(Y0))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (!!((^[Y1 : $i]: 98.17/14.78 (!!((^[Y2 : $i]: 98.17/14.78 (in(Y1, 98.17/14.78 powerset( 98.17/14.78 Y0)) => 98.17/14.78 (in(Y2, Y1) => 98.17/14.78 in(Y2, Y0)))))))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (!!((^[Y1 : $i]: 98.17/14.78 (!!((^[Y2 : $i]: 98.17/14.78 (in(Y1, Y2) => 98.17/14.78 (in(Y2, Y0) => 98.17/14.78 in(Y1, 98.17/14.78 setunion( 98.17/14.78 Y0))))))))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (!!((^[Y1 : $i]: 98.17/14.78 (in(Y1, 98.17/14.78 setunion(Y0)) => 98.17/14.78 (!!((^[Y2 : $o]: 98.17/14.78 (( 98.17/14.78 !!(( 98.17/14.78 ^[Y3 : $i]: 98.17/14.78 (in(Y1, 98.17/14.78 Y3) => 98.17/14.78 (in(Y3, 98.17/14.78 Y0) => Y2))))) => 98.17/14.78 Y2))))))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (!!((^[Y1 : $i]: 98.17/14.78 (in(Y1, Y0) => 98.17/14.78 in(Y1, 98.17/14.78 powerset( 98.17/14.78 setunion(Y0)))))))))) => 98.17/14.78 ((!!((^[Y0 : $i > $o]: 98.17/14.78 ((??((^[Y1 : $i]: 98.17/14.78 (Y0(Y1) & 98.17/14.78 (!!((^[Y2 : $i]: 98.17/14.78 (Y0(Y2) => 98.17/14.78 (Y1 = Y2))))))))) => 98.17/14.78 (??((^[Y1 : $i]: 98.17/14.78 (!!((^[Y2 : $i]: 98.17/14.78 (Y0(Y2) <=> 98.17/14.78 (Y2 = Y1)))))))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 ((Y0 != emptyset) => 98.17/14.78 (??((^[Y1 : $i]: 98.17/14.78 in(Y1, Y0)))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (!!((^[Y1 : $i]: 98.17/14.78 (in(Y0, 98.17/14.78 setadjoin( 98.17/14.78 Y1, 98.17/14.78 emptyset)) => 98.17/14.78 (Y0 = Y1)))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (!!((^[Y1 : $i]: 98.17/14.78 ((Y0 != Y1) => 98.17/14.78 (~(in(Y1, 98.17/14.78 setadjoin( 98.17/14.78 Y0, 98.17/14.78 emptyset))))))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (!!((^[Y1 : $i]: 98.17/14.78 ((Y0 = Y1) => 98.17/14.78 in(Y0, 98.17/14.78 setadjoin( 98.17/14.78 Y1, 98.17/14.78 emptyset))))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (!!((^[Y1 : $i]: 98.17/14.78 (in(Y0, 98.17/14.78 setadjoin( 98.17/14.78 Y1, 98.17/14.78 emptyset)) => 98.17/14.78 in(Y1, 98.17/14.78 setadjoin( 98.17/14.78 Y0, 98.17/14.78 emptyset))))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (!!((^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 setadjoin( 98.17/14.78 Y0, 98.17/14.78 setadjoin( 98.17/14.78 Y1, 98.17/14.78 emptyset))) => 98.17/14.78 (( 98.17/14.78 Y2 = Y1) | 98.17/14.78 (Y2 = Y0)))))))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (!!((^[Y1 : $i]: 98.17/14.78 in(Y0, 98.17/14.78 setadjoin( 98.17/14.78 Y0, 98.17/14.78 setadjoin( 98.17/14.78 Y1, 98.17/14.78 emptyset))))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (!!((^[Y1 : $i]: 98.17/14.78 in(Y1, 98.17/14.78 setadjoin( 98.17/14.78 Y0, 98.17/14.78 setadjoin( 98.17/14.78 Y1, 98.17/14.78 emptyset))))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (!!((^[Y1 : $i > $o]: 98.17/14.78 (( 98.17/14.78 ??(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) & 98.17/14.78 Y1(Y2))))) => 98.17/14.78 (dsetconstr( 98.17/14.78 Y0, 98.17/14.78 (^[Y2 : $i]: 98.17/14.78 Y1(Y2))) != 98.17/14.78 emptyset)))))))) => 98.17/14.78 ((!!((^[Y0 : $i > $o]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (in(Y1, 98.17/14.78 emptyset) => 98.17/14.78 Y0(Y1)))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i > $o]: 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 ~(( 98.17/14.78 !!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) => 98.17/14.78 Y1(Y2))))))) => 98.17/14.78 ( 98.17/14.78 ??(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) & 98.17/14.78 (~( 98.17/14.78 Y1(Y2)))))))))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i > $o]: 98.17/14.78 (( 98.17/14.78 !!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) => 98.17/14.78 (~( 98.17/14.78 Y1(Y2))))))) => 98.17/14.78 (~(( 98.17/14.78 ??(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) & 98.17/14.78 Y1(Y2)))))))))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i > $o]: 98.17/14.78 (( 98.17/14.78 ~(( 98.17/14.78 ??(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) & 98.17/14.78 Y1(Y2))))))) => 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) => 98.17/14.78 (~( 98.17/14.78 Y1(Y2)))))))))))))) => 98.17/14.78 ((!!((^[Y0 : $i]: 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y1 : $i > $o]: 98.17/14.78 (( 98.17/14.78 ??(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) & 98.17/14.78 (~( 98.17/14.78 Y1(Y2))))))) => 98.17/14.78 (~(( 98.17/14.78 !!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) => 98.17/14.78 Y1(Y2)))))))))))))) => 98.17/14.78 ((!!((^[Y0 : $o]: 98.17/14.78 (Y0 => 98.17/14.78 in( 98.17/14.78 emptyset, 98.17/14.78 prop2set( 98.17/14.78 Y0)))))) => 98.17/14.78 ((!!((^[Y0 : $o]: 98.17/14.78 (Y0 => 98.17/14.78 set2prop( 98.17/14.78 prop2set( 98.17/14.78 Y0)))))) => 98.17/14.78 ((!!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i > $o]: 98.17/14.78 (( 98.17/14.78 ~(( 98.17/14.78 ??(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) & 98.17/14.78 Y1(Y2))))))) => 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) => 98.17/14.78 (~( 98.17/14.78 Y1(Y2)))))))))))))) => 98.17/14.78 ((!!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y1 : $i > $o]: 98.17/14.78 (( 98.17/14.78 ~(( 98.17/14.78 !!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) => 98.17/14.78 Y1(Y2))))))) => 98.17/14.78 (??(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (in(Y2, 98.17/14.78 Y0) & 98.17/14.78 (~( 98.17/14.78 Y1(Y2)))))))))))))) => 98.17/14.78 ((!!(( 98.17/14.78 ^[Y0 : $i > $o]: 98.17/14.78 (( 98.17/14.78 ??(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 Y0(Y1)))) => 98.17/14.78 (( 98.17/14.78 !!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (Y0(Y1) => 98.17/14.78 (Y0(Y2) => 98.17/14.78 (Y1 = Y2))))))))) => 98.17/14.78 (??(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (Y0(Y1) & 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (Y0(Y2) => 98.17/14.78 (Y1 = Y2)))))))))))))) => 98.17/14.78 ((!!(( 98.17/14.78 ^[Y0 : $i > $o]: 98.17/14.78 (( 98.17/14.78 ??(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (Y0(Y2) <=> 98.17/14.78 (Y2 = Y1)))))))) => 98.17/14.78 (??(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (Y0(Y1) & 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (Y0(Y2) => 98.17/14.78 (Y1 = Y2))))))))))))) => 98.17/14.78 (( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (( 98.17/14.78 Y0 = Y1) => 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y3 : $i]: 98.17/14.78 (( 98.17/14.78 Y2 = Y3) => 98.17/14.78 (in(Y2, 98.17/14.78 Y0) => 98.17/14.78 in(Y3, 98.17/14.78 Y1)))))))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (( 98.17/14.78 Y0 = Y1) => 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y3 : $i]: 98.17/14.78 (( 98.17/14.78 Y2 = Y3) => 98.17/14.78 (in(Y2, 98.17/14.78 Y0) <=> 98.17/14.78 in(Y3, 98.17/14.78 Y1)))))))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i > $o]: 98.17/14.78 (( 98.17/14.78 ??(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (Y0(Y1) & 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (Y0(Y2) => 98.17/14.78 (Y1 = Y2))))))))) => 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (Y0(Y1) => 98.17/14.78 (Y0(Y2) => 98.17/14.78 (Y1 = Y2))))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i > $o]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i > $o]: 98.17/14.78 (( 98.17/14.78 !!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y3 : $i]: 98.17/14.78 (( 98.17/14.78 Y2 = Y3) => 98.17/14.78 (Y0(Y2) <=> 98.17/14.78 Y1(Y3))))))))) => 98.17/14.78 (( 98.17/14.78 ??(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (Y0(Y2) & 98.17/14.78 (!!(( 98.17/14.78 ^[Y3 : $i]: 98.17/14.78 (Y0(Y3) => 98.17/14.78 (Y2 = Y3))))))))) <=> 98.17/14.78 (??(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (Y1(Y2) & 98.17/14.78 (!!(( 98.17/14.78 ^[Y3 : $i]: 98.17/14.78 (Y1(Y3) => 98.17/14.78 (Y2 = Y3))))))))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (( 98.17/14.78 Y0 = Y1) => 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y3 : $i]: 98.17/14.78 (( 98.17/14.78 Y2 = Y3) => 98.17/14.78 (setadjoin( 98.17/14.78 Y0, Y2) = 98.17/14.78 setadjoin( 98.17/14.78 Y1, Y3)))))))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (( 98.17/14.78 Y0 = Y1) => 98.17/14.78 (powerset( 98.17/14.78 Y0) = 98.17/14.78 powerset( 98.17/14.78 Y1))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (( 98.17/14.78 Y0 = Y1) => 98.17/14.78 (setunion( 98.17/14.78 Y0) = 98.17/14.78 setunion( 98.17/14.78 Y1))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i > $o]: 98.17/14.78 (( 98.17/14.78 ??(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (Y0(Y1) & 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (Y0(Y2) => 98.17/14.78 (Y1 = Y2))))))))) => 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (Y0(Y1) => 98.17/14.78 (Y0(Y2) => 98.17/14.78 (Y1 = Y2))))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i > $o]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i > $o]: 98.17/14.78 (( 98.17/14.78 !!(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y3 : $i]: 98.17/14.78 (( 98.17/14.78 Y2 = Y3) => 98.17/14.78 (Y0(Y2) <=> 98.17/14.78 Y1(Y3))))))))) => 98.17/14.78 (( 98.17/14.78 ??(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (Y0(Y2) & 98.17/14.78 (!!(( 98.17/14.78 ^[Y3 : $i]: 98.17/14.78 (Y0(Y3) => 98.17/14.78 (Y2 = Y3))))))))) => 98.17/14.78 (( 98.17/14.78 ??(( 98.17/14.78 ^[Y2 : $i]: 98.17/14.78 (Y1(Y2) & 98.17/14.78 (!!(( 98.17/14.78 ^[Y3 : $i]: 98.17/14.78 (Y1(Y3) => 98.17/14.78 (Y2 = Y3))))))))) => 98.17/14.78 (descr( 98.17/14.78 (^[Y2 : $i]: 98.17/14.78 Y0(Y2))) = 98.17/14.78 descr( 98.17/14.78 (^[Y2 : $i]: 98.17/14.78 Y1(Y2))))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y1 : $i]: 98.17/14.78 (( 98.17/14.78 Y0 = Y1) => 98.17/14.78 (!!(( 98.17/14.78 ^[Y2 : $i > $o]: 98.17/14.78 (!!(( 98.17/14.78 ^[Y3 : $i > $o]: 98.17/14.78 (( 98.17/14.78 !!(( 98.17/14.78 ^[Y4 : $i]: 98.17/14.78 (in(Y4, 98.17/14.78 Y0) => 98.17/14.78 (!!(( 98.17/14.78 ^[Y5 : $i]: 98.17/14.78 (in(Y5, 98.17/14.78 Y1) => 98.17/14.78 (( 98.17/14.78 Y4 = Y5) => 98.17/14.78 (Y2(Y4) <=> 98.17/14.78 Y3(Y5))))))))))) => 98.17/14.78 (dsetconstr( 98.17/14.78 Y0, 98.17/14.78 (^[Y4 : $i]: 98.17/14.78 Y2(Y4))) = 98.17/14.78 dsetconstr( 98.17/14.78 Y1, 98.17/14.78 (^[Y4 : $i]: 98.17/14.78 Y3(Y4)))))))))))))))))) => 98.17/14.78 ( 98.17/14.78 ( 98.17/14.78 !!(( 98.17/14.78 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (( 98.17/14.79 !!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 in(Y2, 98.17/14.79 Y1))))) => 98.17/14.79 subset( 98.17/14.79 Y0, Y1)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (( 98.17/14.79 Y0 = Y1) => 98.17/14.79 subset( 98.17/14.79 Y1, Y0)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (( 98.17/14.79 Y0 = Y1) => 98.17/14.79 subset( 98.17/14.79 Y0, Y1)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (( 98.17/14.79 !!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 in(Y2, 98.17/14.79 Y1))))) => 98.17/14.79 subset( 98.17/14.79 Y0, Y1)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 subset( 98.17/14.79 emptyset, 98.17/14.79 Y0)))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (subset( 98.17/14.79 Y0, Y1) => 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 in(Y2, 98.17/14.79 Y1)))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (subset( 98.17/14.79 Y0, Y1) => 98.17/14.79 (( 98.17/14.79 ~( 98.17/14.79 in(Y2, 98.17/14.79 Y1))) => 98.17/14.79 (~( 98.17/14.79 in(Y2, 98.17/14.79 Y0)))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 (( 98.17/14.79 ~( 98.17/14.79 in(Y2, 98.17/14.79 Y1))) => 98.17/14.79 (~( 98.17/14.79 subset( 98.17/14.79 Y0, Y1)))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (( 98.17/14.79 ~( 98.17/14.79 subset( 98.17/14.79 Y0, Y1))) => 98.17/14.79 (Y0 != Y1)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 (( 98.17/14.79 ~( 98.17/14.79 in(Y2, 98.17/14.79 Y1))) => 98.17/14.79 (Y0 != Y1)))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 subset( 98.17/14.79 Y0, Y0)))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (subset( 98.17/14.79 Y0, Y1) => 98.17/14.79 (subset( 98.17/14.79 Y1, Y2) => 98.17/14.79 subset( 98.17/14.79 Y0, Y2)))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 subset( 98.17/14.79 Y1, 98.17/14.79 setadjoin( 98.17/14.79 Y0, Y1)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (subset( 98.17/14.79 Y0, Y2) => 98.17/14.79 subset( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, Y2)))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (subset( 98.17/14.79 Y0, Y1) => 98.17/14.79 in(Y0, 98.17/14.79 powerset( 98.17/14.79 Y1))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (subset( 98.17/14.79 Y0, Y1) => 98.17/14.79 (subset( 98.17/14.79 Y1, Y0) => 98.17/14.79 (Y0 = Y1))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (subset( 98.17/14.79 Y0, 98.17/14.79 emptyset) => 98.17/14.79 (Y0 = 98.17/14.79 emptyset))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (subset( 98.17/14.79 Y1, Y0) => 98.17/14.79 in(Y1, 98.17/14.79 powerset( 98.17/14.79 Y0))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (in(Y1, 98.17/14.79 powerset( 98.17/14.79 Y0)) => 98.17/14.79 subset( 98.17/14.79 Y1, Y0)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 in(Y0, 98.17/14.79 powerset( 98.17/14.79 Y0))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (subset( 98.17/14.79 Y0, Y1) => 98.17/14.79 subset( 98.17/14.79 powerset( 98.17/14.79 Y0), 98.17/14.79 powerset( 98.17/14.79 Y1))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i > $o]: 98.17/14.79 in( 98.17/14.79 dsetconstr( 98.17/14.79 Y0, 98.17/14.79 (^[Y2 : $i]: 98.17/14.79 Y1(Y2))), 98.17/14.79 powerset( 98.17/14.79 Y0)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i > $o]: 98.17/14.79 subset( 98.17/14.79 dsetconstr( 98.17/14.79 Y0, 98.17/14.79 (^[Y2 : $i]: 98.17/14.79 Y1(Y2))), 98.17/14.79 Y0))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 in(Y2, 98.17/14.79 binunion( 98.17/14.79 Y0, Y1)))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 in(Y1, 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y1) => 98.17/14.79 in(Y2, 98.17/14.79 binunion( 98.17/14.79 Y0, Y1)))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $o]: 98.17/14.79 (in(Y2, 98.17/14.79 binunion( 98.17/14.79 Y0, Y1)) => 98.17/14.79 (( 98.17/14.79 in(Y2, 98.17/14.79 Y0) => Y3) => 98.17/14.79 (( 98.17/14.79 in(Y2, 98.17/14.79 Y1) => Y3) => 98.17/14.79 Y3))))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 binunion( 98.17/14.79 Y0, Y1)) => 98.17/14.79 (in(Y2, 98.17/14.79 Y1) | 98.17/14.79 in(Y2, 98.17/14.79 Y0)))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 subset( 98.17/14.79 Y0, 98.17/14.79 binunion( 98.17/14.79 Y0, Y1)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 subset( 98.17/14.79 Y1, 98.17/14.79 binunion( 98.17/14.79 Y0, Y1)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 (in(Y2, 98.17/14.79 Y1) => 98.17/14.79 in(Y2, 98.17/14.79 binintersect( 98.17/14.79 Y0, Y1))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (subset( 98.17/14.79 Y2, Y0) => 98.17/14.79 (subset( 98.17/14.79 Y2, Y1) => 98.17/14.79 subset( 98.17/14.79 Y2, 98.17/14.79 binintersect( 98.17/14.79 Y0, Y1))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 binintersect( 98.17/14.79 Y0, Y1)) => 98.17/14.79 in(Y2, 98.17/14.79 Y0))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 subset( 98.17/14.79 binintersect( 98.17/14.79 Y0, Y1), 98.17/14.79 Y0))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (subset( 98.17/14.79 Y0, Y1) => 98.17/14.79 (binintersect( 98.17/14.79 Y0, Y1) = 98.17/14.79 Y0)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (( 98.17/14.79 binintersect( 98.17/14.79 Y0, Y1) = 98.17/14.79 Y1) => 98.17/14.79 subset( 98.17/14.79 Y1, Y0)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 binintersect( 98.17/14.79 Y0, Y1)) => 98.17/14.79 in(Y2, 98.17/14.79 Y1))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (( 98.17/14.79 ~(( 98.17/14.79 ??(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) & 98.17/14.79 in(Y2, 98.17/14.79 Y1))))))) => 98.17/14.79 (binintersect( 98.17/14.79 Y0, Y1) = 98.17/14.79 emptyset)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 subset( 98.17/14.79 binintersect( 98.17/14.79 Y0, Y1), 98.17/14.79 Y1))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (subset( 98.17/14.79 Y1, Y0) => 98.17/14.79 (binintersect( 98.17/14.79 Y0, Y1) = 98.17/14.79 Y1)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (( 98.17/14.79 binintersect( 98.17/14.79 Y0, Y1) = 98.17/14.79 Y0) => 98.17/14.79 subset( 98.17/14.79 Y0, Y1)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (binintersect( 98.17/14.79 Y0, 98.17/14.79 binunion( 98.17/14.79 Y1, Y2)) = 98.17/14.79 binunion( 98.17/14.79 binintersect( 98.17/14.79 Y0, Y1), 98.17/14.79 binintersect( 98.17/14.79 Y0, Y2)))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 (( 98.17/14.79 ~( 98.17/14.79 in(Y2, 98.17/14.79 Y1))) => 98.17/14.79 in(Y2, 98.17/14.79 setminus( 98.17/14.79 Y0, Y1))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 setminus( 98.17/14.79 Y0, Y1)) => 98.17/14.79 in(Y2, 98.17/14.79 Y0))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 setminus( 98.17/14.79 Y0, Y1)) => 98.17/14.79 (~( 98.17/14.79 in(Y2, 98.17/14.79 Y1))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (subset( 98.17/14.79 Y0, Y1) => 98.17/14.79 (setminus( 98.17/14.79 Y0, Y1) = 98.17/14.79 emptyset)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (( 98.17/14.79 ~( 98.17/14.79 in(Y2, 98.17/14.79 setminus( 98.17/14.79 Y0, Y1)))) => 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 in(Y2, 98.17/14.79 Y1)))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (( 98.17/14.79 ~( 98.17/14.79 in(Y2, 98.17/14.79 setminus( 98.17/14.79 Y0, Y1)))) => 98.17/14.79 (( 98.17/14.79 ~( 98.17/14.79 in(Y2, 98.17/14.79 Y1))) => 98.17/14.79 (~( 98.17/14.79 in(Y2, 98.17/14.79 Y0)))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (( 98.17/14.79 ~( 98.17/14.79 in(Y2, 98.17/14.79 Y0))) => 98.17/14.79 (~( 98.17/14.79 in(Y2, 98.17/14.79 setminus( 98.17/14.79 Y0, Y1)))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y1) => 98.17/14.79 (~( 98.17/14.79 in(Y2, 98.17/14.79 setminus( 98.17/14.79 Y0, Y1)))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 subset( 98.17/14.79 setminus( 98.17/14.79 Y0, Y1), 98.17/14.79 Y0))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (( 98.17/14.79 setminus( 98.17/14.79 Y0, Y1) = 98.17/14.79 emptyset) => 98.17/14.79 subset( 98.17/14.79 Y0, Y1)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 symdiff( 98.17/14.79 Y0, Y1)) => 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $o]: 98.17/14.79 (( 98.17/14.79 in(Y2, 98.17/14.79 Y0) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 ~( 98.17/14.79 in(Y2, 98.17/14.79 Y1))) => 98.17/14.79 Y3)) => 98.17/14.79 (( 98.17/14.79 ( 98.17/14.79 ~( 98.17/14.79 in(Y2, 98.17/14.79 Y0))) => 98.17/14.79 ( 98.17/14.79 in(Y2, 98.17/14.79 Y1) => Y3)) => 98.17/14.79 Y3))))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 (( 98.17/14.79 ~( 98.17/14.79 in(Y2, 98.17/14.79 Y1))) => 98.17/14.79 in(Y2, 98.17/14.79 symdiff( 98.17/14.79 Y0, Y1))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (( 98.17/14.79 ~( 98.17/14.79 in(Y2, 98.17/14.79 Y0))) => 98.17/14.79 (in(Y2, 98.17/14.79 Y1) => 98.17/14.79 in(Y2, 98.17/14.79 symdiff( 98.17/14.79 Y0, Y1))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 (in(Y2, 98.17/14.79 Y1) => 98.17/14.79 (~( 98.17/14.79 in(Y2, 98.17/14.79 symdiff( 98.17/14.79 Y0, Y1))))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (( 98.17/14.79 ~( 98.17/14.79 in(Y2, 98.17/14.79 Y0))) => 98.17/14.79 (( 98.17/14.79 ~( 98.17/14.79 in(Y2, 98.17/14.79 Y1))) => 98.17/14.79 (~( 98.17/14.79 in(Y2, 98.17/14.79 symdiff( 98.17/14.79 Y0, Y1))))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 in(Y1, 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 in(Y0, 98.17/14.79 setunion( 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset)), 98.17/14.79 emptyset)))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 in(Y1, 98.17/14.79 setunion( 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset)), 98.17/14.79 emptyset)))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (??(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 setunion( 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset)), 98.17/14.79 emptyset)))) & 98.17/14.79 (??(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (in(Y3, 98.17/14.79 setunion( 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset)), 98.17/14.79 emptyset)))) & 98.17/14.79 (setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset)), 98.17/14.79 emptyset)) = 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 setadjoin( 98.17/14.79 Y3, 98.17/14.79 emptyset)), 98.17/14.79 emptyset))))))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (??(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 setunion( 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset)), 98.17/14.79 emptyset)))) & 98.17/14.79 (??(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (in(Y3, 98.17/14.79 setunion( 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset)), 98.17/14.79 emptyset)))) & 98.17/14.79 (setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset)), 98.17/14.79 emptyset)) = 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 setadjoin( 98.17/14.79 Y3, 98.17/14.79 emptyset)), 98.17/14.79 emptyset))))))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (in(Y1, 98.17/14.79 Y0) => 98.17/14.79 subset( 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset), 98.17/14.79 Y0)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (in(Y1, 98.17/14.79 Y0) => 98.17/14.79 in( 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset), 98.17/14.79 powerset( 98.17/14.79 Y0))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 in( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 emptyset), 98.17/14.79 powerset( 98.17/14.79 binunion( 98.17/14.79 Y0, Y1))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset))) => 98.17/14.79 (( 98.17/14.79 Y2 = Y1) | 98.17/14.79 (Y2 = Y0)))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (in(Y3, 98.17/14.79 Y1) => 98.17/14.79 subset( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 setadjoin( 98.17/14.79 Y3, 98.17/14.79 emptyset)), 98.17/14.79 binunion( 98.17/14.79 Y0, Y1)))))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (in(Y3, 98.17/14.79 Y1) => 98.17/14.79 in( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 setadjoin( 98.17/14.79 Y3, 98.17/14.79 emptyset)), 98.17/14.79 powerset( 98.17/14.79 binunion( 98.17/14.79 Y0, Y1))))))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (in(Y3, 98.17/14.79 Y1) => 98.17/14.79 subset( 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 setadjoin( 98.17/14.79 Y3, 98.17/14.79 emptyset)), 98.17/14.79 emptyset)), 98.17/14.79 powerset( 98.17/14.79 binunion( 98.17/14.79 Y0, Y1))))))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (in(Y3, 98.17/14.79 Y1) => 98.17/14.79 in( 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 setadjoin( 98.17/14.79 Y3, 98.17/14.79 emptyset)), 98.17/14.79 emptyset)), 98.17/14.79 powerset( 98.17/14.79 powerset( 98.17/14.79 binunion( 98.17/14.79 Y0, Y1)))))))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (in(Y3, 98.17/14.79 Y1) => 98.17/14.79 in( 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 setadjoin( 98.17/14.79 Y3, 98.17/14.79 emptyset)), 98.17/14.79 emptyset)), 98.17/14.79 powerset( 98.17/14.79 powerset( 98.17/14.79 binunion( 98.17/14.79 Y0, Y1)))))))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (in(Y3, 98.17/14.79 Y1) => 98.17/14.79 in( 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 setadjoin( 98.17/14.79 Y3, 98.17/14.79 emptyset)), 98.17/14.79 emptyset)), 98.17/14.79 dsetconstr( 98.17/14.79 powerset( 98.17/14.79 powerset( 98.17/14.79 binunion( 98.17/14.79 Y0, Y1))), 98.17/14.79 (^[Y4 : $i]: 98.17/14.79 (??(( 98.17/14.79 ^[Y5 : $i]: 98.17/14.79 (in(Y5, 98.17/14.79 Y0) & 98.17/14.79 (??(( 98.17/14.79 ^[Y6 : $i]: 98.17/14.79 (in(Y6, 98.17/14.79 Y1) & 98.17/14.79 (Y4 = 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y5, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y5, 98.17/14.79 setadjoin( 98.17/14.79 Y6, 98.17/14.79 emptyset)), 98.17/14.79 emptyset)))))))))))))))))))))))))))) => 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 dsetconstr( 98.17/14.79 powerset( 98.17/14.79 powerset( 98.17/14.79 binunion( 98.17/14.79 Y0, Y1))), 98.17/14.79 (^[Y3 : $i]: 98.17/14.79 (??(( 98.17/14.79 ^[Y4 : $i]: 98.17/14.79 (in(Y4, 98.17/14.79 Y0) & 98.17/14.79 (??(( 98.17/14.79 ^[Y5 : $i]: 98.17/14.79 (in(Y5, 98.17/14.79 Y1) & 98.17/14.79 (Y3 = 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y4, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y4, 98.17/14.79 setadjoin( 98.17/14.79 Y5, 98.17/14.79 emptyset)), 98.17/14.79 emptyset)))))))))))))) => 98.17/14.79 (??(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (( 98.17/14.79 ??(( 98.17/14.79 ^[Y4 : $i]: 98.17/14.79 (in(Y4, 98.17/14.79 Y1) & 98.17/14.79 (Y2 = 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y3, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y3, 98.17/14.79 setadjoin( 98.17/14.79 Y4, 98.17/14.79 emptyset)), 98.17/14.79 emptyset))))))) & 98.17/14.79 in(Y3, 98.17/14.79 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 98.17/14.79 inference('simplify boolean subterms', [status(thm)], ['159'])). 98.17/14.79 tff('161', plain, 98.17/14.79 ~ ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 ((!!((^[Y2 : $i]: (in(Y2, Y0) <=> in(Y2, Y1))))) => 98.17/14.79 (Y0 = Y1)))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (in(Y2, setadjoin(Y0, Y1)) <=> 98.17/14.79 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 (in(Y1, powerset(Y0)) <=> 98.17/14.79 (!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 (in(Y1, setunion(Y0)) <=> 98.17/14.79 (??((^[Y2 : $i]: (in(Y1, Y2) & in(Y2, Y0)))))))))))) => 98.17/14.79 (in(emptyset, omega) => 98.17/14.79 ((!!((^[Y0 : $i]: (in(Y0, omega) => in(setadjoin(Y0, Y0), omega))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (((!!((^[Y1 : $i]: 98.17/14.79 ((in(Y1, Y0) & in(Y1, omega)) => 98.17/14.79 in(setadjoin(Y1, Y1), Y0))))) & 98.17/14.79 in(emptyset, Y0)) => 98.17/14.79 (!!((^[Y1 : $i]: (in(Y1, omega) => in(Y1, Y0))))))))) => 98.17/14.79 ((!!((^[Y0 : ($i * $i) > $o]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 ((!!((^[Y2 : $i]: 98.17/14.79 (in(Y2, Y1) => 98.17/14.79 (??((^[Y3 : $i]: 98.17/14.79 (Y0(Y2, Y3) & 98.17/14.79 (!!((^[Y4 : $i]: 98.17/14.79 (Y0(Y2, Y4) => (Y3 = Y4))))))))))))) => 98.17/14.79 (??((^[Y2 : $i]: 98.17/14.79 (!!((^[Y3 : $i]: 98.17/14.79 (in(Y3, Y2) <=> 98.17/14.79 (??((^[Y4 : $i]: 98.17/14.79 (in(Y4, Y1) & Y0(Y4, Y3))))))))))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 98.17/14.79 (??((^[Y1 : $i]: 98.17/14.79 (in(Y1, Y0) & 98.17/14.79 (~((??((^[Y2 : $i]: (in(Y2, Y1) & in(Y2, Y0))))))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (??((^[Y1 : $i]: 98.17/14.79 ((!!((^[Y2 : $i]: 98.17/14.79 (in(Y2, Y1) => 98.17/14.79 (!!((^[Y3 : $i]: 98.17/14.79 (in(Y3, Y2) => in(Y3, Y0)))))))))& 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (!!((^[Y3 : $i]: 98.17/14.79 ((in(Y3, Y0) & in(Y2, Y0)) => 98.17/14.79 ((!!((^[Y4 : $i]: 98.17/14.79 (in(Y4, Y1) => 98.17/14.79 (in(Y2, Y4) <=> 98.17/14.79 in(Y3, Y4)))))) => 98.17/14.79 (Y2 = Y3)))))))))& 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (!!((^[Y3 : $i]: 98.17/14.79 ((in(Y3, Y1) & in(Y2, Y1)) => 98.17/14.79 ((!!((^[Y4 : $i]: 98.17/14.79 (in(Y4, Y3) => 98.17/14.79 in(Y4, Y2))))) | 98.17/14.79 (!!((^[Y4 : $i]: 98.17/14.79 (in(Y4, Y2) => 98.17/14.79 in(Y4, Y3)))))))))))))& 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (((??((^[Y3 : $i]: in(Y3, Y2)))) & 98.17/14.79 (!!((^[Y3 : $i]: 98.17/14.79 (in(Y3, Y2) => in(Y3, Y0)))))) => 98.17/14.79 (??((^[Y3 : $i]: 98.17/14.79 (??((^[Y4 : $i]: 98.17/14.79 (in(Y3, Y1)&in(Y4, Y2)& 98.17/14.79 (~((??((^[Y5 : $i]: 98.17/14.79 (in(Y5, Y3) & 98.17/14.79 in(Y5, Y2)))))))& 98.17/14.79 (!!((^[Y5 : $i]: 98.17/14.79 (in(Y5, Y1) => 98.17/14.79 (in(Y4, Y5) | 98.17/14.79 (!!(( 98.17/14.79 ^[Y6 : $i]: 98.17/14.79 (in(Y6, 98.17/14.79 Y5) => 98.17/14.79 in(Y6, 98.17/14.79 Y3)))))))))))))))))))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i > $o]: 98.17/14.79 ((??((^[Y1 : $i]: 98.17/14.79 (Y0(Y1) & 98.17/14.79 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 98.17/14.79 Y0(descr(Y0)))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i > $o]: 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (in(Y2, Y0) => 98.17/14.79 (Y1(Y2) => 98.17/14.79 in(Y2, dsetconstr(Y0, Y1))))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i > $o]: 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (in(Y2, dsetconstr(Y0, Y1)) => 98.17/14.79 in(Y2, Y0))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i > $o]: 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (in(Y2, dsetconstr(Y0, Y1)) => 98.17/14.79 Y1(Y2))))))))))) => 98.17/14.79 ((!!((^[Y0 : $o]: 98.17/14.79 (!!((^[Y1 : $i]: (in(Y1, prop2set(Y0)) => Y0))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (in(Y0, emptyset) => (!!((^[Y1 : $o]: Y1))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 98.17/14.79 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 98.17/14.79 ((!!((^[Y0 : $i > $o]: 98.17/14.79 ((??((^[Y1 : $i]: 98.17/14.79 (Y0(Y1) & 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (Y0(Y2) => (Y1 = Y2))))))))) => 98.17/14.79 (??(Y0)))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 ((!!((^[Y2 : $i]: 98.17/14.79 (in(Y2, Y0) => in(Y2, Y1))))) => 98.17/14.79 ((!!((^[Y2 : $i]: 98.17/14.79 (in(Y2, Y1) => in(Y2, Y0))))) => 98.17/14.79 (Y0 = Y1))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 98.17/14.79 (Y0 = emptyset))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 98.17/14.79 (Y0 = emptyset))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i > $o]: 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (in(Y2, Y0) => 98.17/14.79 (in(Y2, 98.17/14.79 dsetconstr(Y0, Y1)) <=> 98.17/14.79 Y1(Y2)))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 ((Y0 != emptyset) => 98.17/14.79 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i > $o]: 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (in(Y2, Y0) => 98.17/14.79 (Y1(Y2) => 98.17/14.79 (dsetconstr(Y0, Y1) != 98.17/14.79 emptyset)))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 98.17/14.79 (Y0 != emptyset))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 in(Y0, setadjoin(Y0, Y1)))))))) => 98.17/14.79 (in(emptyset, 98.17/14.79 setadjoin(emptyset, emptyset)) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (in(Y2, Y1) => 98.17/14.79 in(Y2, 98.17/14.79 setadjoin(Y0, Y1)))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 setadjoin(Y0, 98.17/14.79 Y1)) => 98.17/14.79 (!!((^[Y3 : $o]: 98.17/14.79 ((( 98.17/14.79 Y2 = Y0) => 98.17/14.79 Y3) => 98.17/14.79 (( 98.17/14.79 in(Y2, 98.17/14.79 Y1) => Y3) => 98.17/14.79 Y3))))))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 setadjoin(Y0, 98.17/14.79 Y1)) => 98.17/14.79 (in(Y2, Y1) | 98.17/14.79 (Y2 = Y0)))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (dsetconstr(Y0, 98.17/14.79 (^[Y1 : $i]: $true)) = 98.17/14.79 Y0)))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 ((!!((^[Y2 : $i]: 98.17/14.79 (in(Y2, Y1) => 98.17/14.79 in(Y2, Y0))))) => 98.17/14.79 in(Y1, powerset(Y0))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 in(emptyset, powerset(Y0))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 in(emptyset, powerset(Y0))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (in(Y1, 98.17/14.79 powerset( 98.17/14.79 Y0)) => 98.17/14.79 (in(Y2, Y1) => 98.17/14.79 in(Y2, Y0)))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (in(Y1, Y2) => 98.17/14.79 (in(Y2, Y0) => 98.17/14.79 in(Y1, 98.17/14.79 setunion( 98.17/14.79 Y0))))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 (in(Y1, 98.17/14.79 setunion(Y0)) => 98.17/14.79 (!!((^[Y2 : $o]: 98.17/14.79 (( 98.17/14.79 !!(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (in(Y1, 98.17/14.79 Y3) => 98.17/14.79 (in(Y3, 98.17/14.79 Y0) => Y2))))) => 98.17/14.79 Y2))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 (in(Y1, Y0) => 98.17/14.79 in(Y1, 98.17/14.79 powerset( 98.17/14.79 setunion(Y0)))))))))) => 98.17/14.79 ((!!((^[Y0 : $i > $o]: 98.17/14.79 ((??((^[Y1 : $i]: 98.17/14.79 (Y0(Y1) & 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (Y0(Y2) => 98.17/14.79 (Y1 = Y2))))))))) => 98.17/14.79 (??((^[Y1 : $i]: 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (Y0(Y2) <=> 98.17/14.79 (Y2 = Y1)))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 ((Y0 != emptyset) => 98.17/14.79 (??((^[Y1 : $i]: 98.17/14.79 in(Y1, Y0)))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 (in(Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset)) => 98.17/14.79 (Y0 = Y1)))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 ((Y0 != Y1) => 98.17/14.79 (~(in(Y1, 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 emptyset))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 ((Y0 = Y1) => 98.17/14.79 in(Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 (in(Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset)) => 98.17/14.79 in(Y1, 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 emptyset))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset))) => 98.17/14.79 (( 98.17/14.79 Y2 = Y1) | 98.17/14.79 (Y2 = Y0)))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 in(Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 in(Y1, 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i > $o]: 98.17/14.79 (( 98.17/14.79 ??(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) & 98.17/14.79 Y1(Y2))))) => 98.17/14.79 (dsetconstr( 98.17/14.79 Y0, Y1) != 98.17/14.79 emptyset)))))))) => 98.17/14.79 ((!!((^[Y0 : $i > $o]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (in(Y1, 98.17/14.79 emptyset) => 98.17/14.79 Y0(Y1)))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i > $o]: 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 ~(( 98.17/14.79 !!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 Y1(Y2))))))) => 98.17/14.79 ( 98.17/14.79 ??(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) & 98.17/14.79 (~( 98.17/14.79 Y1(Y2)))))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i > $o]: 98.17/14.79 (( 98.17/14.79 !!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 (~( 98.17/14.79 Y1(Y2))))))) => 98.17/14.79 (~(( 98.17/14.79 ??(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) & 98.17/14.79 Y1(Y2)))))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i > $o]: 98.17/14.79 (( 98.17/14.79 ~(( 98.17/14.79 ??(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) & 98.17/14.79 Y1(Y2))))))) => 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 (~( 98.17/14.79 Y1(Y2)))))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y1 : $i > $o]: 98.17/14.79 (( 98.17/14.79 ??(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) & 98.17/14.79 (~( 98.17/14.79 Y1(Y2))))))) => 98.17/14.79 (~(( 98.17/14.79 !!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 Y1(Y2)))))))))))))) => 98.17/14.79 ((!!((^[Y0 : $o]: 98.17/14.79 (Y0 => 98.17/14.79 in( 98.17/14.79 emptyset, 98.17/14.79 prop2set( 98.17/14.79 Y0)))))) => 98.17/14.79 ((!!((^[Y0 : $o]: 98.17/14.79 (Y0 => 98.17/14.79 set2prop( 98.17/14.79 prop2set( 98.17/14.79 Y0)))))) => 98.17/14.79 ((!!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i > $o]: 98.17/14.79 (( 98.17/14.79 ~(( 98.17/14.79 ??(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) & 98.17/14.79 Y1(Y2))))))) => 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 (~( 98.17/14.79 Y1(Y2)))))))))))))) => 98.17/14.79 ((!!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y1 : $i > $o]: 98.17/14.79 (( 98.17/14.79 ~(( 98.17/14.79 !!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 Y1(Y2))))))) => 98.17/14.79 (??(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) & 98.17/14.79 (~( 98.17/14.79 Y1(Y2)))))))))))))) => 98.17/14.79 ((!!(( 98.17/14.79 ^[Y0 : $i > $o]: 98.17/14.79 (( 98.17/14.79 ??(Y0)) => 98.17/14.79 (( 98.17/14.79 !!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (Y0(Y1) => 98.17/14.79 (Y0(Y2) => 98.17/14.79 (Y1 = Y2))))))))) => 98.17/14.79 (??(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (Y0(Y1) & 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (Y0(Y2) => 98.17/14.79 (Y1 = Y2)))))))))))))) => 98.17/14.79 ((!!(( 98.17/14.79 ^[Y0 : $i > $o]: 98.17/14.79 (( 98.17/14.79 ??(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (Y0(Y2) <=> 98.17/14.79 (Y2 = Y1)))))))) => 98.17/14.79 (??(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (Y0(Y1) & 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (Y0(Y2) => 98.17/14.79 (Y1 = Y2))))))))))))) => 98.17/14.79 (( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (( 98.17/14.79 Y0 = Y1) => 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (( 98.17/14.79 Y2 = Y3) => 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 in(Y3, 98.17/14.79 Y1)))))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (( 98.17/14.79 Y0 = Y1) => 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (( 98.17/14.79 Y2 = Y3) => 98.17/14.79 (in(Y2, 98.17/14.79 Y0) <=> 98.17/14.79 in(Y3, 98.17/14.79 Y1)))))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i > $o]: 98.17/14.79 (( 98.17/14.79 ??(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (Y0(Y1) & 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (Y0(Y2) => 98.17/14.79 (Y1 = Y2))))))))) => 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (Y0(Y1) => 98.17/14.79 (Y0(Y2) => 98.17/14.79 (Y1 = Y2))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i > $o]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i > $o]: 98.17/14.79 (( 98.17/14.79 !!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (( 98.17/14.79 Y2 = Y3) => 98.17/14.79 (Y0(Y2) <=> 98.17/14.79 Y1(Y3))))))))) => 98.17/14.79 (( 98.17/14.79 ??(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (Y0(Y2) & 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (Y0(Y3) => 98.17/14.79 (Y2 = Y3))))))))) <=> 98.17/14.79 (??(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (Y1(Y2) & 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (Y1(Y3) => 98.17/14.79 (Y2 = Y3))))))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (( 98.17/14.79 Y0 = Y1) => 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (( 98.17/14.79 Y2 = Y3) => 98.17/14.79 (setadjoin( 98.17/14.79 Y0, Y2) = 98.17/14.79 setadjoin( 98.17/14.79 Y1, Y3)))))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (( 98.17/14.79 Y0 = Y1) => 98.17/14.79 (powerset( 98.17/14.79 Y0) = 98.17/14.79 powerset( 98.17/14.79 Y1))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (( 98.17/14.79 Y0 = Y1) => 98.17/14.79 (setunion( 98.17/14.79 Y0) = 98.17/14.79 setunion( 98.17/14.79 Y1))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i > $o]: 98.17/14.79 (( 98.17/14.79 ??(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (Y0(Y1) & 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (Y0(Y2) => 98.17/14.79 (Y1 = Y2))))))))) => 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (Y0(Y1) => 98.17/14.79 (Y0(Y2) => 98.17/14.79 (Y1 = Y2))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i > $o]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i > $o]: 98.17/14.79 (( 98.17/14.79 !!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (( 98.17/14.79 Y2 = Y3) => 98.17/14.79 (Y0(Y2) <=> 98.17/14.79 Y1(Y3))))))))) => 98.17/14.79 (( 98.17/14.79 ??(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (Y0(Y2) & 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (Y0(Y3) => 98.17/14.79 (Y2 = Y3))))))))) => 98.17/14.79 (( 98.17/14.79 ??(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (Y1(Y2) & 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (Y1(Y3) => 98.17/14.79 (Y2 = Y3))))))))) => 98.17/14.79 (descr( 98.17/14.79 Y0) = 98.17/14.79 descr(Y1))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (( 98.17/14.79 Y0 = Y1) => 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i > $o]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $i > $o]: 98.17/14.79 (( 98.17/14.79 !!(( 98.17/14.79 ^[Y4 : $i]: 98.17/14.79 (in(Y4, 98.17/14.79 Y0) => 98.17/14.79 (!!(( 98.17/14.79 ^[Y5 : $i]: 98.17/14.79 (in(Y5, 98.17/14.79 Y1) => 98.17/14.79 (( 98.17/14.79 Y4 = Y5) => 98.17/14.79 (Y2(Y4) <=> 98.17/14.79 Y3(Y5))))))))))) => 98.17/14.79 (dsetconstr( 98.17/14.79 Y0, Y2) = 98.17/14.79 dsetconstr( 98.17/14.79 Y1, Y3)))))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (( 98.17/14.79 !!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 in(Y2, 98.17/14.79 Y1))))) => 98.17/14.79 subset( 98.17/14.79 Y0, Y1)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (( 98.17/14.79 Y0 = Y1) => 98.17/14.79 subset( 98.17/14.79 Y1, Y0)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (( 98.17/14.79 Y0 = Y1) => 98.17/14.79 subset( 98.17/14.79 Y0, Y1)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (( 98.17/14.79 !!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 in(Y2, 98.17/14.79 Y1))))) => 98.17/14.79 subset( 98.17/14.79 Y0, Y1)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!( 98.17/14.79 subset( 98.17/14.79 emptyset))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (subset( 98.17/14.79 Y0, Y1) => 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 in(Y2, 98.17/14.79 Y1)))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (subset( 98.17/14.79 Y0, Y1) => 98.17/14.79 (( 98.17/14.79 ~( 98.17/14.79 in(Y2, 98.17/14.79 Y1))) => 98.17/14.79 (~( 98.17/14.79 in(Y2, 98.17/14.79 Y0)))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 (( 98.17/14.79 ~( 98.17/14.79 in(Y2, 98.17/14.79 Y1))) => 98.17/14.79 (~( 98.17/14.79 subset( 98.17/14.79 Y0, Y1)))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (( 98.17/14.79 ~( 98.17/14.79 subset( 98.17/14.79 Y0, Y1))) => 98.17/14.79 (Y0 != Y1)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 (( 98.17/14.79 ~( 98.17/14.79 in(Y2, 98.17/14.79 Y1))) => 98.17/14.79 (Y0 != Y1)))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 subset( 98.17/14.79 Y0, Y0)))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (subset( 98.17/14.79 Y0, Y1) => 98.17/14.79 (subset( 98.17/14.79 Y1, Y2) => 98.17/14.79 subset( 98.17/14.79 Y0, Y2)))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 subset( 98.17/14.79 Y1, 98.17/14.79 setadjoin( 98.17/14.79 Y0, Y1)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (subset( 98.17/14.79 Y0, Y2) => 98.17/14.79 subset( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, Y2)))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (subset( 98.17/14.79 Y0, Y1) => 98.17/14.79 in(Y0, 98.17/14.79 powerset( 98.17/14.79 Y1))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (subset( 98.17/14.79 Y0, Y1) => 98.17/14.79 (subset( 98.17/14.79 Y1, Y0) => 98.17/14.79 (Y0 = Y1))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (subset( 98.17/14.79 Y0, 98.17/14.79 emptyset) => 98.17/14.79 (Y0 = 98.17/14.79 emptyset))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (subset( 98.17/14.79 Y1, Y0) => 98.17/14.79 in(Y1, 98.17/14.79 powerset( 98.17/14.79 Y0))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (in(Y1, 98.17/14.79 powerset( 98.17/14.79 Y0)) => 98.17/14.79 subset( 98.17/14.79 Y1, Y0)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 in(Y0, 98.17/14.79 powerset( 98.17/14.79 Y0))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (subset( 98.17/14.79 Y0, Y1) => 98.17/14.79 subset( 98.17/14.79 powerset( 98.17/14.79 Y0), 98.17/14.79 powerset( 98.17/14.79 Y1))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i > $o]: 98.17/14.79 in( 98.17/14.79 dsetconstr( 98.17/14.79 Y0, Y1), 98.17/14.79 powerset( 98.17/14.79 Y0)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i > $o]: 98.17/14.79 subset( 98.17/14.79 dsetconstr( 98.17/14.79 Y0, Y1), 98.17/14.79 Y0))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 in(Y2, 98.17/14.79 binunion( 98.17/14.79 Y0, Y1)))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 in(Y1, 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y1) => 98.17/14.79 in(Y2, 98.17/14.79 binunion( 98.17/14.79 Y0, Y1)))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $o]: 98.17/14.79 (in(Y2, 98.17/14.79 binunion( 98.17/14.79 Y0, Y1)) => 98.17/14.79 (( 98.17/14.79 in(Y2, 98.17/14.79 Y0) => Y3) => 98.17/14.79 (( 98.17/14.79 in(Y2, 98.17/14.79 Y1) => Y3) => 98.17/14.79 Y3))))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 binunion( 98.17/14.79 Y0, Y1)) => 98.17/14.79 (in(Y2, 98.17/14.79 Y1) | 98.17/14.79 in(Y2, 98.17/14.79 Y0)))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 subset( 98.17/14.79 Y0, 98.17/14.79 binunion( 98.17/14.79 Y0, Y1)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 subset( 98.17/14.79 Y1, 98.17/14.79 binunion( 98.17/14.79 Y0, Y1)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 (in(Y2, 98.17/14.79 Y1) => 98.17/14.79 in(Y2, 98.17/14.79 binintersect( 98.17/14.79 Y0, Y1))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (subset( 98.17/14.79 Y2, Y0) => 98.17/14.79 (subset( 98.17/14.79 Y2, Y1) => 98.17/14.79 subset( 98.17/14.79 Y2, 98.17/14.79 binintersect( 98.17/14.79 Y0, Y1))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 binintersect( 98.17/14.79 Y0, Y1)) => 98.17/14.79 in(Y2, 98.17/14.79 Y0))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 subset( 98.17/14.79 binintersect( 98.17/14.79 Y0, Y1), 98.17/14.79 Y0))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (subset( 98.17/14.79 Y0, Y1) => 98.17/14.79 (binintersect( 98.17/14.79 Y0, Y1) = 98.17/14.79 Y0)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (( 98.17/14.79 binintersect( 98.17/14.79 Y0, Y1) = 98.17/14.79 Y1) => 98.17/14.79 subset( 98.17/14.79 Y1, Y0)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 binintersect( 98.17/14.79 Y0, Y1)) => 98.17/14.79 in(Y2, 98.17/14.79 Y1))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (( 98.17/14.79 ~(( 98.17/14.79 ??(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) & 98.17/14.79 in(Y2, 98.17/14.79 Y1))))))) => 98.17/14.79 (binintersect( 98.17/14.79 Y0, Y1) = 98.17/14.79 emptyset)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 subset( 98.17/14.79 binintersect( 98.17/14.79 Y0, Y1), 98.17/14.79 Y1))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (subset( 98.17/14.79 Y1, Y0) => 98.17/14.79 (binintersect( 98.17/14.79 Y0, Y1) = 98.17/14.79 Y1)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (( 98.17/14.79 binintersect( 98.17/14.79 Y0, Y1) = 98.17/14.79 Y0) => 98.17/14.79 subset( 98.17/14.79 Y0, Y1)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (binintersect( 98.17/14.79 Y0, 98.17/14.79 binunion( 98.17/14.79 Y1, Y2)) = 98.17/14.79 binunion( 98.17/14.79 binintersect( 98.17/14.79 Y0, Y1), 98.17/14.79 binintersect( 98.17/14.79 Y0, Y2)))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 (( 98.17/14.79 ~( 98.17/14.79 in(Y2, 98.17/14.79 Y1))) => 98.17/14.79 in(Y2, 98.17/14.79 setminus( 98.17/14.79 Y0, Y1))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 setminus( 98.17/14.79 Y0, Y1)) => 98.17/14.79 in(Y2, 98.17/14.79 Y0))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 setminus( 98.17/14.79 Y0, Y1)) => 98.17/14.79 (~( 98.17/14.79 in(Y2, 98.17/14.79 Y1))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (subset( 98.17/14.79 Y0, Y1) => 98.17/14.79 (setminus( 98.17/14.79 Y0, Y1) = 98.17/14.79 emptyset)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (( 98.17/14.79 ~( 98.17/14.79 in(Y2, 98.17/14.79 setminus( 98.17/14.79 Y0, Y1)))) => 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 in(Y2, 98.17/14.79 Y1)))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (( 98.17/14.79 ~( 98.17/14.79 in(Y2, 98.17/14.79 setminus( 98.17/14.79 Y0, Y1)))) => 98.17/14.79 (( 98.17/14.79 ~( 98.17/14.79 in(Y2, 98.17/14.79 Y1))) => 98.17/14.79 (~( 98.17/14.79 in(Y2, 98.17/14.79 Y0)))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (( 98.17/14.79 ~( 98.17/14.79 in(Y2, 98.17/14.79 Y0))) => 98.17/14.79 (~( 98.17/14.79 in(Y2, 98.17/14.79 setminus( 98.17/14.79 Y0, Y1)))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y1) => 98.17/14.79 (~( 98.17/14.79 in(Y2, 98.17/14.79 setminus( 98.17/14.79 Y0, Y1)))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 subset( 98.17/14.79 setminus( 98.17/14.79 Y0, Y1), 98.17/14.79 Y0))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (( 98.17/14.79 setminus( 98.17/14.79 Y0, Y1) = 98.17/14.79 emptyset) => 98.17/14.79 subset( 98.17/14.79 Y0, Y1)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 symdiff( 98.17/14.79 Y0, Y1)) => 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $o]: 98.17/14.79 (( 98.17/14.79 in(Y2, 98.17/14.79 Y0) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 ~( 98.17/14.79 in(Y2, 98.17/14.79 Y1))) => 98.17/14.79 Y3)) => 98.17/14.79 (( 98.17/14.79 ( 98.17/14.79 ~( 98.17/14.79 in(Y2, 98.17/14.79 Y0))) => 98.17/14.79 ( 98.17/14.79 in(Y2, 98.17/14.79 Y1) => Y3)) => 98.17/14.79 Y3))))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 (( 98.17/14.79 ~( 98.17/14.79 in(Y2, 98.17/14.79 Y1))) => 98.17/14.79 in(Y2, 98.17/14.79 symdiff( 98.17/14.79 Y0, Y1))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (( 98.17/14.79 ~( 98.17/14.79 in(Y2, 98.17/14.79 Y0))) => 98.17/14.79 (in(Y2, 98.17/14.79 Y1) => 98.17/14.79 in(Y2, 98.17/14.79 symdiff( 98.17/14.79 Y0, Y1))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 (in(Y2, 98.17/14.79 Y1) => 98.17/14.79 (~( 98.17/14.79 in(Y2, 98.17/14.79 symdiff( 98.17/14.79 Y0, Y1))))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (( 98.17/14.79 ~( 98.17/14.79 in(Y2, 98.17/14.79 Y0))) => 98.17/14.79 (( 98.17/14.79 ~( 98.17/14.79 in(Y2, 98.17/14.79 Y1))) => 98.17/14.79 (~( 98.17/14.79 in(Y2, 98.17/14.79 symdiff( 98.17/14.79 Y0, Y1))))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 in(Y1, 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 in(Y0, 98.17/14.79 setunion( 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset)), 98.17/14.79 emptyset)))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 in(Y1, 98.17/14.79 setunion( 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset)), 98.17/14.79 emptyset)))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (??(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 setunion( 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset)), 98.17/14.79 emptyset)))) & 98.17/14.79 (??(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (in(Y3, 98.17/14.79 setunion( 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset)), 98.17/14.79 emptyset)))) & 98.17/14.79 (setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset)), 98.17/14.79 emptyset)) = 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 setadjoin( 98.17/14.79 Y3, 98.17/14.79 emptyset)), 98.17/14.79 emptyset))))))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (??(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 setunion( 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset)), 98.17/14.79 emptyset)))) & 98.17/14.79 (??(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (in(Y3, 98.17/14.79 setunion( 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset)), 98.17/14.79 emptyset)))) & 98.17/14.79 (setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset)), 98.17/14.79 emptyset)) = 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 setadjoin( 98.17/14.79 Y3, 98.17/14.79 emptyset)), 98.17/14.79 emptyset))))))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (in(Y1, 98.17/14.79 Y0) => 98.17/14.79 subset( 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset), 98.17/14.79 Y0)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (in(Y1, 98.17/14.79 Y0) => 98.17/14.79 in( 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset), 98.17/14.79 powerset( 98.17/14.79 Y0))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 in( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 emptyset), 98.17/14.79 powerset( 98.17/14.79 binunion( 98.17/14.79 Y0, Y1))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset))) => 98.17/14.79 (( 98.17/14.79 Y2 = Y1) | 98.17/14.79 (Y2 = Y0)))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (in(Y3, 98.17/14.79 Y1) => 98.17/14.79 subset( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 setadjoin( 98.17/14.79 Y3, 98.17/14.79 emptyset)), 98.17/14.79 binunion( 98.17/14.79 Y0, Y1)))))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (in(Y3, 98.17/14.79 Y1) => 98.17/14.79 in( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 setadjoin( 98.17/14.79 Y3, 98.17/14.79 emptyset)), 98.17/14.79 powerset( 98.17/14.79 binunion( 98.17/14.79 Y0, Y1))))))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (in(Y3, 98.17/14.79 Y1) => 98.17/14.79 subset( 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 setadjoin( 98.17/14.79 Y3, 98.17/14.79 emptyset)), 98.17/14.79 emptyset)), 98.17/14.79 powerset( 98.17/14.79 binunion( 98.17/14.79 Y0, Y1))))))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (in(Y3, 98.17/14.79 Y1) => 98.17/14.79 in( 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 setadjoin( 98.17/14.79 Y3, 98.17/14.79 emptyset)), 98.17/14.79 emptyset)), 98.17/14.79 powerset( 98.17/14.79 powerset( 98.17/14.79 binunion( 98.17/14.79 Y0, Y1)))))))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (in(Y3, 98.17/14.79 Y1) => 98.17/14.79 in( 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 setadjoin( 98.17/14.79 Y3, 98.17/14.79 emptyset)), 98.17/14.79 emptyset)), 98.17/14.79 powerset( 98.17/14.79 powerset( 98.17/14.79 binunion( 98.17/14.79 Y0, Y1)))))))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (in(Y3, 98.17/14.79 Y1) => 98.17/14.79 in( 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 setadjoin( 98.17/14.79 Y3, 98.17/14.79 emptyset)), 98.17/14.79 emptyset)), 98.17/14.79 dsetconstr( 98.17/14.79 powerset( 98.17/14.79 powerset( 98.17/14.79 binunion( 98.17/14.79 Y0, Y1))), 98.17/14.79 (^[Y4 : $i]: 98.17/14.79 (??(( 98.17/14.79 ^[Y5 : $i]: 98.17/14.79 (in(Y5, 98.17/14.79 Y0) & 98.17/14.79 (??(( 98.17/14.79 ^[Y6 : $i]: 98.17/14.79 (in(Y6, 98.17/14.79 Y1) & 98.17/14.79 (Y4 = 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y5, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y5, 98.17/14.79 setadjoin( 98.17/14.79 Y6, 98.17/14.79 emptyset)), 98.17/14.79 emptyset)))))))))))))))))))))))))))) => 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 dsetconstr( 98.17/14.79 powerset( 98.17/14.79 powerset( 98.17/14.79 binunion( 98.17/14.79 Y0, Y1))), 98.17/14.79 (^[Y3 : $i]: 98.17/14.79 (??(( 98.17/14.79 ^[Y4 : $i]: 98.17/14.79 (in(Y4, 98.17/14.79 Y0) & 98.17/14.79 (??(( 98.17/14.79 ^[Y5 : $i]: 98.17/14.79 (in(Y5, 98.17/14.79 Y1) & 98.17/14.79 (Y3 = 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y4, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y4, 98.17/14.79 setadjoin( 98.17/14.79 Y5, 98.17/14.79 emptyset)), 98.17/14.79 emptyset)))))))))))))) => 98.17/14.79 (??(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (( 98.17/14.79 ??(( 98.17/14.79 ^[Y4 : $i]: 98.17/14.79 (in(Y4, 98.17/14.79 Y1) & 98.17/14.79 (Y2 = 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y3, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y3, 98.17/14.79 setadjoin( 98.17/14.79 Y4, 98.17/14.79 emptyset)), 98.17/14.79 emptyset))))))) & 98.17/14.79 in(Y3, 98.17/14.79 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 98.17/14.79 inference('ho_norm', [status(thm)], ['160'])). 98.17/14.79 tff('162', plain, 98.17/14.79 ~ ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (in(Y2, setadjoin(Y0, Y1)) <=> 98.17/14.79 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 (in(Y1, powerset(Y0)) <=> 98.17/14.79 (!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 (in(Y1, setunion(Y0)) <=> 98.17/14.79 (??((^[Y2 : $i]: (in(Y1, Y2) & in(Y2, Y0)))))))))))) => 98.17/14.79 (in(emptyset, omega) => 98.17/14.79 ((!!((^[Y0 : $i]: (in(Y0, omega) => in(setadjoin(Y0, Y0), omega))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (((!!((^[Y1 : $i]: 98.17/14.79 ((in(Y1, Y0) & in(Y1, omega)) => 98.17/14.79 in(setadjoin(Y1, Y1), Y0))))) & 98.17/14.79 in(emptyset, Y0)) => 98.17/14.79 (!!((^[Y1 : $i]: (in(Y1, omega) => in(Y1, Y0))))))))) => 98.17/14.79 ((!!((^[Y0 : ($i * $i) > $o]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 ((!!((^[Y2 : $i]: 98.17/14.79 (in(Y2, Y1) => 98.17/14.79 (??((^[Y3 : $i]: 98.17/14.79 (Y0(Y2, Y3) & 98.17/14.79 (!!((^[Y4 : $i]: 98.17/14.79 (Y0(Y2, Y4) => (Y3 = Y4))))))))))))) => 98.17/14.79 (??((^[Y2 : $i]: 98.17/14.79 (!!((^[Y3 : $i]: 98.17/14.79 (in(Y3, Y2) <=> 98.17/14.79 (??((^[Y4 : $i]: 98.17/14.79 (in(Y4, Y1) & Y0(Y4, Y3))))))))))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 98.17/14.79 (??((^[Y1 : $i]: 98.17/14.79 (in(Y1, Y0) & 98.17/14.79 (~((??((^[Y2 : $i]: (in(Y2, Y1) & in(Y2, Y0))))))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (??((^[Y1 : $i]: 98.17/14.79 ((!!((^[Y2 : $i]: 98.17/14.79 (in(Y2, Y1) => 98.17/14.79 (!!((^[Y3 : $i]: 98.17/14.79 (in(Y3, Y2) => in(Y3, Y0)))))))))& 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (!!((^[Y3 : $i]: 98.17/14.79 ((in(Y3, Y0) & in(Y2, Y0)) => 98.17/14.79 ((!!((^[Y4 : $i]: 98.17/14.79 (in(Y4, Y1) => 98.17/14.79 (in(Y2, Y4) <=> 98.17/14.79 in(Y3, Y4)))))) => 98.17/14.79 (Y2 = Y3)))))))))& 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (!!((^[Y3 : $i]: 98.17/14.79 ((in(Y3, Y1) & in(Y2, Y1)) => 98.17/14.79 ((!!((^[Y4 : $i]: 98.17/14.79 (in(Y4, Y3) => 98.17/14.79 in(Y4, Y2))))) | 98.17/14.79 (!!((^[Y4 : $i]: 98.17/14.79 (in(Y4, Y2) => 98.17/14.79 in(Y4, Y3)))))))))))))& 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (((??((^[Y3 : $i]: in(Y3, Y2)))) & 98.17/14.79 (!!((^[Y3 : $i]: 98.17/14.79 (in(Y3, Y2) => in(Y3, Y0)))))) => 98.17/14.79 (??((^[Y3 : $i]: 98.17/14.79 (??((^[Y4 : $i]: 98.17/14.79 (in(Y3, Y1)&in(Y4, Y2)& 98.17/14.79 (~((??((^[Y5 : $i]: 98.17/14.79 (in(Y5, Y3) & 98.17/14.79 in(Y5, Y2)))))))& 98.17/14.79 (!!((^[Y5 : $i]: 98.17/14.79 (in(Y5, Y1) => 98.17/14.79 (in(Y4, Y5) | 98.17/14.79 (!!((^[Y6 : $i]: 98.17/14.79 (in(Y6, 98.17/14.79 Y5) => 98.17/14.79 in(Y6, 98.17/14.79 Y3)))))))))))))))))))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i > $o]: 98.17/14.79 ((??((^[Y1 : $i]: 98.17/14.79 (Y0(Y1) & 98.17/14.79 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 98.17/14.79 Y0(descr(Y0)))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i > $o]: 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (in(Y2, Y0) => 98.17/14.79 (Y1(Y2) => in(Y2, dsetconstr(Y0, Y1))))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i > $o]: 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (in(Y2, dsetconstr(Y0, Y1)) => 98.17/14.79 in(Y2, Y0))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i > $o]: 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (in(Y2, dsetconstr(Y0, Y1)) => 98.17/14.79 Y1(Y2))))))))))) => 98.17/14.79 ((!!((^[Y0 : $o]: 98.17/14.79 (!!((^[Y1 : $i]: (in(Y1, prop2set(Y0)) => Y0))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (in(Y0, emptyset) => (!!((^[Y1 : $o]: Y1))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 98.17/14.79 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 98.17/14.79 ((!!((^[Y0 : $i > $o]: 98.17/14.79 ((??((^[Y1 : $i]: 98.17/14.79 (Y0(Y1) & 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (Y0(Y2) => (Y1 = Y2))))))))) => 98.17/14.79 (??(Y0)))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 ((!!((^[Y2 : $i]: 98.17/14.79 (in(Y2, Y0) => in(Y2, Y1))))) => 98.17/14.79 ((!!((^[Y2 : $i]: 98.17/14.79 (in(Y2, Y1) => in(Y2, Y0))))) => 98.17/14.79 (Y0 = Y1))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 98.17/14.79 (Y0 = emptyset))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 98.17/14.79 (Y0 = emptyset))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i > $o]: 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (in(Y2, Y0) => 98.17/14.79 (in(Y2, 98.17/14.79 dsetconstr(Y0, Y1)) <=> 98.17/14.79 Y1(Y2)))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 ((Y0 != emptyset) => 98.17/14.79 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i > $o]: 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (in(Y2, Y0) => 98.17/14.79 (Y1(Y2) => 98.17/14.79 (dsetconstr(Y0, Y1) != 98.17/14.79 emptyset)))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 98.17/14.79 (Y0 != emptyset))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 in(Y0, setadjoin(Y0, Y1)))))))) => 98.17/14.79 (in(emptyset, setadjoin(emptyset, emptyset)) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (in(Y2, Y1) => 98.17/14.79 in(Y2, 98.17/14.79 setadjoin(Y0, Y1)))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 setadjoin(Y0, Y1)) => 98.17/14.79 (!!((^[Y3 : $o]: 98.17/14.79 (((Y2 = Y0) => 98.17/14.79 Y3) => 98.17/14.79 ((in(Y2, 98.17/14.79 Y1) => Y3) => 98.17/14.79 Y3))))))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 setadjoin(Y0, 98.17/14.79 Y1)) => 98.17/14.79 (in(Y2, Y1) | 98.17/14.79 (Y2 = Y0)))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (dsetconstr(Y0, 98.17/14.79 (^[Y1 : $i]: $true)) = 98.17/14.79 Y0)))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 ((!!((^[Y2 : $i]: 98.17/14.79 (in(Y2, Y1) => 98.17/14.79 in(Y2, Y0))))) => 98.17/14.79 in(Y1, powerset(Y0))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 in(emptyset, powerset(Y0))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 in(emptyset, powerset(Y0))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (in(Y1, 98.17/14.79 powerset( 98.17/14.79 Y0)) => 98.17/14.79 (in(Y2, Y1) => 98.17/14.79 in(Y2, Y0)))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (in(Y1, Y2) => 98.17/14.79 (in(Y2, Y0) => 98.17/14.79 in(Y1, 98.17/14.79 setunion( 98.17/14.79 Y0))))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 (in(Y1, 98.17/14.79 setunion(Y0)) => 98.17/14.79 (!!((^[Y2 : $o]: 98.17/14.79 ((!!(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (in(Y1, 98.17/14.79 Y3) => 98.17/14.79 (in(Y3, 98.17/14.79 Y0) => Y2))))) => 98.17/14.79 Y2))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 (in(Y1, Y0) => 98.17/14.79 in(Y1, 98.17/14.79 powerset( 98.17/14.79 setunion(Y0)))))))))) => 98.17/14.79 ((!!((^[Y0 : $i > $o]: 98.17/14.79 ((??((^[Y1 : $i]: 98.17/14.79 (Y0(Y1) & 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (Y0(Y2) => 98.17/14.79 (Y1 = Y2))))))))) => 98.17/14.79 (??((^[Y1 : $i]: 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 ( 98.17/14.79 Y0(Y2) <=> 98.17/14.79 ( 98.17/14.79 Y2 = Y1)))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 ((Y0 != emptyset) => 98.17/14.79 (??((^[Y1 : $i]: 98.17/14.79 in(Y1, Y0)))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 (in(Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset)) => 98.17/14.79 (Y0 = Y1)))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 ((Y0 != Y1) => 98.17/14.79 (~(in(Y1, 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 emptyset))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 ((Y0 = Y1) => 98.17/14.79 in(Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 (in(Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset)) => 98.17/14.79 in(Y1, 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 emptyset))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset))) => 98.17/14.79 (( 98.17/14.79 Y2 = Y1) | 98.17/14.79 (Y2 = Y0)))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 in(Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 in(Y1, 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i > $o]: 98.17/14.79 (( 98.17/14.79 ??(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) & 98.17/14.79 Y1(Y2))))) => 98.17/14.79 (dsetconstr( 98.17/14.79 Y0, Y1) != 98.17/14.79 emptyset)))))))) => 98.17/14.79 ((!!((^[Y0 : $i > $o]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 (in(Y1, 98.17/14.79 emptyset) => 98.17/14.79 Y0(Y1)))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i > $o]: 98.17/14.79 (( 98.17/14.79 ~(( 98.17/14.79 !!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 Y1(Y2))))))) => 98.17/14.79 ( 98.17/14.79 ??(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) & 98.17/14.79 (~( 98.17/14.79 Y1(Y2)))))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i > $o]: 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 (~( 98.17/14.79 Y1(Y2))))))) => 98.17/14.79 ( 98.17/14.79 ~(( 98.17/14.79 ??(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) & 98.17/14.79 Y1(Y2)))))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i > $o]: 98.17/14.79 (( 98.17/14.79 ~(( 98.17/14.79 ??(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) & 98.17/14.79 Y1(Y2))))))) => 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 (~( 98.17/14.79 Y1(Y2)))))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i > $o]: 98.17/14.79 (( 98.17/14.79 ??(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) & 98.17/14.79 (~( 98.17/14.79 Y1(Y2))))))) => 98.17/14.79 (~(( 98.17/14.79 !!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 Y1(Y2)))))))))))))) => 98.17/14.79 ((!!((^[Y0 : $o]: 98.17/14.79 ( 98.17/14.79 Y0 => 98.17/14.79 in( 98.17/14.79 emptyset, 98.17/14.79 prop2set( 98.17/14.79 Y0)))))) => 98.17/14.79 ((!!((^[Y0 : $o]: 98.17/14.79 (Y0 => 98.17/14.79 set2prop( 98.17/14.79 prop2set( 98.17/14.79 Y0)))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i > $o]: 98.17/14.79 (( 98.17/14.79 ~(( 98.17/14.79 ??(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) & 98.17/14.79 Y1(Y2))))))) => 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 (~( 98.17/14.79 Y1(Y2)))))))))))))) => 98.17/14.79 ((!!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i > $o]: 98.17/14.79 (( 98.17/14.79 ~(( 98.17/14.79 !!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 Y1(Y2))))))) => 98.17/14.79 (??(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) & 98.17/14.79 (~( 98.17/14.79 Y1(Y2)))))))))))))) => 98.17/14.79 ((!!(( 98.17/14.79 ^[Y0 : $i > $o]: 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 ??(Y0)) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (Y0(Y1) => 98.17/14.79 (Y0(Y2) => 98.17/14.79 (Y1 = Y2))))))))) => 98.17/14.79 ( 98.17/14.79 ??(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (Y0(Y1) & 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (Y0(Y2) => 98.17/14.79 (Y1 = Y2)))))))))))))) => 98.17/14.79 ((!!(( 98.17/14.79 ^[Y0 : $i > $o]: 98.17/14.79 (( 98.17/14.79 ??(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (Y0(Y2) <=> 98.17/14.79 (Y2 = Y1)))))))) => 98.17/14.79 (??(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (Y0(Y1) & 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (Y0(Y2) => 98.17/14.79 (Y1 = Y2))))))))))))) => 98.17/14.79 ((!!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (( 98.17/14.79 Y0 = Y1) => 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (( 98.17/14.79 Y2 = Y3) => 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 in(Y3, 98.17/14.79 Y1)))))))))))))))) => 98.17/14.79 (( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (( 98.17/14.79 Y0 = Y1) => 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (( 98.17/14.79 Y2 = Y3) => 98.17/14.79 (in(Y2, 98.17/14.79 Y0) <=> 98.17/14.79 in(Y3, 98.17/14.79 Y1)))))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i > $o]: 98.17/14.79 (( 98.17/14.79 ??(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (Y0(Y1) & 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (Y0(Y2) => 98.17/14.79 (Y1 = Y2))))))))) => 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (Y0(Y1) => 98.17/14.79 (Y0(Y2) => 98.17/14.79 (Y1 = Y2))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i > $o]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i > $o]: 98.17/14.79 (( 98.17/14.79 !!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (( 98.17/14.79 Y2 = Y3) => 98.17/14.79 (Y0(Y2) <=> 98.17/14.79 Y1(Y3))))))))) => 98.17/14.79 (( 98.17/14.79 ??(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (Y0(Y2) & 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (Y0(Y3) => 98.17/14.79 (Y2 = Y3))))))))) <=> 98.17/14.79 (??(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (Y1(Y2) & 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (Y1(Y3) => 98.17/14.79 (Y2 = Y3))))))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (( 98.17/14.79 Y0 = Y1) => 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (( 98.17/14.79 Y2 = Y3) => 98.17/14.79 (setadjoin( 98.17/14.79 Y0, Y2) = 98.17/14.79 setadjoin( 98.17/14.79 Y1, Y3)))))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (( 98.17/14.79 Y0 = Y1) => 98.17/14.79 (powerset( 98.17/14.79 Y0) = 98.17/14.79 powerset( 98.17/14.79 Y1))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (( 98.17/14.79 Y0 = Y1) => 98.17/14.79 (setunion( 98.17/14.79 Y0) = 98.17/14.79 setunion( 98.17/14.79 Y1))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i > $o]: 98.17/14.79 (( 98.17/14.79 ??(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (Y0(Y1) & 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (Y0(Y2) => 98.17/14.79 (Y1 = Y2))))))))) => 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (Y0(Y1) => 98.17/14.79 (Y0(Y2) => 98.17/14.79 (Y1 = Y2))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i > $o]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i > $o]: 98.17/14.79 (( 98.17/14.79 !!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (( 98.17/14.79 Y2 = Y3) => 98.17/14.79 (Y0(Y2) <=> 98.17/14.79 Y1(Y3))))))))) => 98.17/14.79 (( 98.17/14.79 ??(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (Y0(Y2) & 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (Y0(Y3) => 98.17/14.79 (Y2 = Y3))))))))) => 98.17/14.79 (( 98.17/14.79 ??(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (Y1(Y2) & 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (Y1(Y3) => 98.17/14.79 (Y2 = Y3))))))))) => 98.17/14.79 (descr( 98.17/14.79 Y0) = 98.17/14.79 descr(Y1))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (( 98.17/14.79 Y0 = Y1) => 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i > $o]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $i > $o]: 98.17/14.79 (( 98.17/14.79 !!(( 98.17/14.79 ^[Y4 : $i]: 98.17/14.79 (in(Y4, 98.17/14.79 Y0) => 98.17/14.79 (!!(( 98.17/14.79 ^[Y5 : $i]: 98.17/14.79 (in(Y5, 98.17/14.79 Y1) => 98.17/14.79 (( 98.17/14.79 Y4 = Y5) => 98.17/14.79 (Y2(Y4) <=> 98.17/14.79 Y3(Y5))))))))))) => 98.17/14.79 (dsetconstr( 98.17/14.79 Y0, Y2) = 98.17/14.79 dsetconstr( 98.17/14.79 Y1, Y3)))))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (( 98.17/14.79 !!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 in(Y2, 98.17/14.79 Y1))))) => 98.17/14.79 subset( 98.17/14.79 Y0, Y1)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (( 98.17/14.79 Y0 = Y1) => 98.17/14.79 subset( 98.17/14.79 Y1, Y0)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (( 98.17/14.79 Y0 = Y1) => 98.17/14.79 subset( 98.17/14.79 Y0, Y1)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (( 98.17/14.79 !!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 in(Y2, 98.17/14.79 Y1))))) => 98.17/14.79 subset( 98.17/14.79 Y0, Y1)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!( 98.17/14.79 subset( 98.17/14.79 emptyset))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (subset( 98.17/14.79 Y0, Y1) => 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 in(Y2, 98.17/14.79 Y1)))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (subset( 98.17/14.79 Y0, Y1) => 98.17/14.79 (( 98.17/14.79 ~( 98.17/14.79 in(Y2, 98.17/14.79 Y1))) => 98.17/14.79 (~( 98.17/14.79 in(Y2, 98.17/14.79 Y0)))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 (( 98.17/14.79 ~( 98.17/14.79 in(Y2, 98.17/14.79 Y1))) => 98.17/14.79 (~( 98.17/14.79 subset( 98.17/14.79 Y0, Y1)))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (( 98.17/14.79 ~( 98.17/14.79 subset( 98.17/14.79 Y0, Y1))) => 98.17/14.79 (Y0 != Y1)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 (( 98.17/14.79 ~( 98.17/14.79 in(Y2, 98.17/14.79 Y1))) => 98.17/14.79 (Y0 != Y1)))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 subset( 98.17/14.79 Y0, Y0)))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (subset( 98.17/14.79 Y0, Y1) => 98.17/14.79 (subset( 98.17/14.79 Y1, Y2) => 98.17/14.79 subset( 98.17/14.79 Y0, Y2)))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 subset( 98.17/14.79 Y1, 98.17/14.79 setadjoin( 98.17/14.79 Y0, Y1)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (subset( 98.17/14.79 Y0, Y2) => 98.17/14.79 subset( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, Y2)))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (subset( 98.17/14.79 Y0, Y1) => 98.17/14.79 in(Y0, 98.17/14.79 powerset( 98.17/14.79 Y1))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (subset( 98.17/14.79 Y0, Y1) => 98.17/14.79 (subset( 98.17/14.79 Y1, Y0) => 98.17/14.79 (Y0 = Y1))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (subset( 98.17/14.79 Y0, 98.17/14.79 emptyset) => 98.17/14.79 (Y0 = 98.17/14.79 emptyset))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (subset( 98.17/14.79 Y1, Y0) => 98.17/14.79 in(Y1, 98.17/14.79 powerset( 98.17/14.79 Y0))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (in(Y1, 98.17/14.79 powerset( 98.17/14.79 Y0)) => 98.17/14.79 subset( 98.17/14.79 Y1, Y0)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 in(Y0, 98.17/14.79 powerset( 98.17/14.79 Y0))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (subset( 98.17/14.79 Y0, Y1) => 98.17/14.79 subset( 98.17/14.79 powerset( 98.17/14.79 Y0), 98.17/14.79 powerset( 98.17/14.79 Y1))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i > $o]: 98.17/14.79 in( 98.17/14.79 dsetconstr( 98.17/14.79 Y0, Y1), 98.17/14.79 powerset( 98.17/14.79 Y0)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i > $o]: 98.17/14.79 subset( 98.17/14.79 dsetconstr( 98.17/14.79 Y0, Y1), 98.17/14.79 Y0))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 in(Y2, 98.17/14.79 binunion( 98.17/14.79 Y0, Y1)))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 in(Y1, 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y1) => 98.17/14.79 in(Y2, 98.17/14.79 binunion( 98.17/14.79 Y0, Y1)))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $o]: 98.17/14.79 (in(Y2, 98.17/14.79 binunion( 98.17/14.79 Y0, Y1)) => 98.17/14.79 (( 98.17/14.79 in(Y2, 98.17/14.79 Y0) => Y3) => 98.17/14.79 (( 98.17/14.79 in(Y2, 98.17/14.79 Y1) => Y3) => 98.17/14.79 Y3))))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 binunion( 98.17/14.79 Y0, Y1)) => 98.17/14.79 (in(Y2, 98.17/14.79 Y1) | 98.17/14.79 in(Y2, 98.17/14.79 Y0)))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 subset( 98.17/14.79 Y0, 98.17/14.79 binunion( 98.17/14.79 Y0, Y1)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 subset( 98.17/14.79 Y1, 98.17/14.79 binunion( 98.17/14.79 Y0, Y1)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 (in(Y2, 98.17/14.79 Y1) => 98.17/14.79 in(Y2, 98.17/14.79 binintersect( 98.17/14.79 Y0, Y1))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (subset( 98.17/14.79 Y2, Y0) => 98.17/14.79 (subset( 98.17/14.79 Y2, Y1) => 98.17/14.79 subset( 98.17/14.79 Y2, 98.17/14.79 binintersect( 98.17/14.79 Y0, Y1))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 binintersect( 98.17/14.79 Y0, Y1)) => 98.17/14.79 in(Y2, 98.17/14.79 Y0))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 subset( 98.17/14.79 binintersect( 98.17/14.79 Y0, Y1), 98.17/14.79 Y0))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (subset( 98.17/14.79 Y0, Y1) => 98.17/14.79 (binintersect( 98.17/14.79 Y0, Y1) = 98.17/14.79 Y0)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (( 98.17/14.79 binintersect( 98.17/14.79 Y0, Y1) = 98.17/14.79 Y1) => 98.17/14.79 subset( 98.17/14.79 Y1, Y0)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 binintersect( 98.17/14.79 Y0, Y1)) => 98.17/14.79 in(Y2, 98.17/14.79 Y1))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (( 98.17/14.79 ~(( 98.17/14.79 ??(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) & 98.17/14.79 in(Y2, 98.17/14.79 Y1))))))) => 98.17/14.79 (binintersect( 98.17/14.79 Y0, Y1) = 98.17/14.79 emptyset)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 subset( 98.17/14.79 binintersect( 98.17/14.79 Y0, Y1), 98.17/14.79 Y1))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (subset( 98.17/14.79 Y1, Y0) => 98.17/14.79 (binintersect( 98.17/14.79 Y0, Y1) = 98.17/14.79 Y1)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (( 98.17/14.79 binintersect( 98.17/14.79 Y0, Y1) = 98.17/14.79 Y0) => 98.17/14.79 subset( 98.17/14.79 Y0, Y1)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (binintersect( 98.17/14.79 Y0, 98.17/14.79 binunion( 98.17/14.79 Y1, Y2)) = 98.17/14.79 binunion( 98.17/14.79 binintersect( 98.17/14.79 Y0, Y1), 98.17/14.79 binintersect( 98.17/14.79 Y0, Y2)))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 (( 98.17/14.79 ~( 98.17/14.79 in(Y2, 98.17/14.79 Y1))) => 98.17/14.79 in(Y2, 98.17/14.79 setminus( 98.17/14.79 Y0, Y1))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 setminus( 98.17/14.79 Y0, Y1)) => 98.17/14.79 in(Y2, 98.17/14.79 Y0))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 setminus( 98.17/14.79 Y0, Y1)) => 98.17/14.79 (~( 98.17/14.79 in(Y2, 98.17/14.79 Y1))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (subset( 98.17/14.79 Y0, Y1) => 98.17/14.79 (setminus( 98.17/14.79 Y0, Y1) = 98.17/14.79 emptyset)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (( 98.17/14.79 ~( 98.17/14.79 in(Y2, 98.17/14.79 setminus( 98.17/14.79 Y0, Y1)))) => 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 in(Y2, 98.17/14.79 Y1)))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (( 98.17/14.79 ~( 98.17/14.79 in(Y2, 98.17/14.79 setminus( 98.17/14.79 Y0, Y1)))) => 98.17/14.79 (( 98.17/14.79 ~( 98.17/14.79 in(Y2, 98.17/14.79 Y1))) => 98.17/14.79 (~( 98.17/14.79 in(Y2, 98.17/14.79 Y0)))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (( 98.17/14.79 ~( 98.17/14.79 in(Y2, 98.17/14.79 Y0))) => 98.17/14.79 (~( 98.17/14.79 in(Y2, 98.17/14.79 setminus( 98.17/14.79 Y0, Y1)))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y1) => 98.17/14.79 (~( 98.17/14.79 in(Y2, 98.17/14.79 setminus( 98.17/14.79 Y0, Y1)))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 subset( 98.17/14.79 setminus( 98.17/14.79 Y0, Y1), 98.17/14.79 Y0))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (( 98.17/14.79 setminus( 98.17/14.79 Y0, Y1) = 98.17/14.79 emptyset) => 98.17/14.79 subset( 98.17/14.79 Y0, Y1)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 symdiff( 98.17/14.79 Y0, Y1)) => 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $o]: 98.17/14.79 (( 98.17/14.79 in(Y2, 98.17/14.79 Y0) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 ~( 98.17/14.79 in(Y2, 98.17/14.79 Y1))) => 98.17/14.79 Y3)) => 98.17/14.79 (( 98.17/14.79 ( 98.17/14.79 ~( 98.17/14.79 in(Y2, 98.17/14.79 Y0))) => 98.17/14.79 ( 98.17/14.79 in(Y2, 98.17/14.79 Y1) => Y3)) => 98.17/14.79 Y3))))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 (( 98.17/14.79 ~( 98.17/14.79 in(Y2, 98.17/14.79 Y1))) => 98.17/14.79 in(Y2, 98.17/14.79 symdiff( 98.17/14.79 Y0, Y1))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (( 98.17/14.79 ~( 98.17/14.79 in(Y2, 98.17/14.79 Y0))) => 98.17/14.79 (in(Y2, 98.17/14.79 Y1) => 98.17/14.79 in(Y2, 98.17/14.79 symdiff( 98.17/14.79 Y0, Y1))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 (in(Y2, 98.17/14.79 Y1) => 98.17/14.79 (~( 98.17/14.79 in(Y2, 98.17/14.79 symdiff( 98.17/14.79 Y0, Y1))))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (( 98.17/14.79 ~( 98.17/14.79 in(Y2, 98.17/14.79 Y0))) => 98.17/14.79 (( 98.17/14.79 ~( 98.17/14.79 in(Y2, 98.17/14.79 Y1))) => 98.17/14.79 (~( 98.17/14.79 in(Y2, 98.17/14.79 symdiff( 98.17/14.79 Y0, Y1))))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 in(Y1, 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 in(Y0, 98.17/14.79 setunion( 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset)), 98.17/14.79 emptyset)))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 in(Y1, 98.17/14.79 setunion( 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset)), 98.17/14.79 emptyset)))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (??(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 setunion( 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset)), 98.17/14.79 emptyset)))) & 98.17/14.79 (??(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (in(Y3, 98.17/14.79 setunion( 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset)), 98.17/14.79 emptyset)))) & 98.17/14.79 (setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset)), 98.17/14.79 emptyset)) = 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 setadjoin( 98.17/14.79 Y3, 98.17/14.79 emptyset)), 98.17/14.79 emptyset))))))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (??(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 setunion( 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset)), 98.17/14.79 emptyset)))) & 98.17/14.79 (??(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (in(Y3, 98.17/14.79 setunion( 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset)), 98.17/14.79 emptyset)))) & 98.17/14.79 (setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset)), 98.17/14.79 emptyset)) = 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 setadjoin( 98.17/14.79 Y3, 98.17/14.79 emptyset)), 98.17/14.79 emptyset))))))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (in(Y1, 98.17/14.79 Y0) => 98.17/14.79 subset( 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset), 98.17/14.79 Y0)))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (in(Y1, 98.17/14.79 Y0) => 98.17/14.79 in( 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset), 98.17/14.79 powerset( 98.17/14.79 Y0))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 in( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 emptyset), 98.17/14.79 powerset( 98.17/14.79 binunion( 98.17/14.79 Y0, Y1))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset))) => 98.17/14.79 (( 98.17/14.79 Y2 = Y1) | 98.17/14.79 (Y2 = Y0)))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (in(Y3, 98.17/14.79 Y1) => 98.17/14.79 subset( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 setadjoin( 98.17/14.79 Y3, 98.17/14.79 emptyset)), 98.17/14.79 binunion( 98.17/14.79 Y0, Y1)))))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (in(Y3, 98.17/14.79 Y1) => 98.17/14.79 in( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 setadjoin( 98.17/14.79 Y3, 98.17/14.79 emptyset)), 98.17/14.79 powerset( 98.17/14.79 binunion( 98.17/14.79 Y0, Y1))))))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (in(Y3, 98.17/14.79 Y1) => 98.17/14.79 subset( 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 setadjoin( 98.17/14.79 Y3, 98.17/14.79 emptyset)), 98.17/14.79 emptyset)), 98.17/14.79 powerset( 98.17/14.79 binunion( 98.17/14.79 Y0, Y1))))))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (in(Y3, 98.17/14.79 Y1) => 98.17/14.79 in( 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 setadjoin( 98.17/14.79 Y3, 98.17/14.79 emptyset)), 98.17/14.79 emptyset)), 98.17/14.79 powerset( 98.17/14.79 powerset( 98.17/14.79 binunion( 98.17/14.79 Y0, Y1)))))))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (in(Y3, 98.17/14.79 Y1) => 98.17/14.79 in( 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 setadjoin( 98.17/14.79 Y3, 98.17/14.79 emptyset)), 98.17/14.79 emptyset)), 98.17/14.79 powerset( 98.17/14.79 powerset( 98.17/14.79 binunion( 98.17/14.79 Y0, Y1)))))))))))))))))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 (!!(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (in(Y3, 98.17/14.79 Y1) => 98.17/14.79 in( 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y2, 98.17/14.79 setadjoin( 98.17/14.79 Y3, 98.17/14.79 emptyset)), 98.17/14.79 emptyset)), 98.17/14.79 dsetconstr( 98.17/14.79 powerset( 98.17/14.79 powerset( 98.17/14.79 binunion( 98.17/14.79 Y0, Y1))), 98.17/14.79 (^[Y4 : $i]: 98.17/14.79 (??(( 98.17/14.79 ^[Y5 : $i]: 98.17/14.79 (in(Y5, 98.17/14.79 Y0) & 98.17/14.79 (??(( 98.17/14.79 ^[Y6 : $i]: 98.17/14.79 (in(Y6, 98.17/14.79 Y1) & 98.17/14.79 (Y4 = 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y5, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y5, 98.17/14.79 setadjoin( 98.17/14.79 Y6, 98.17/14.79 emptyset)), 98.17/14.79 emptyset)))))))))))))))))))))))))))) => 98.17/14.79 ( 98.17/14.79 !!(( 98.17/14.79 ^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 dsetconstr( 98.17/14.79 powerset( 98.17/14.79 powerset( 98.17/14.79 binunion( 98.17/14.79 Y0, Y1))), 98.17/14.79 (^[Y3 : $i]: 98.17/14.79 (??(( 98.17/14.79 ^[Y4 : $i]: 98.17/14.79 (in(Y4, 98.17/14.79 Y0) & 98.17/14.79 (??(( 98.17/14.79 ^[Y5 : $i]: 98.17/14.79 (in(Y5, 98.17/14.79 Y1) & 98.17/14.79 (Y3 = 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y4, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y4, 98.17/14.79 setadjoin( 98.17/14.79 Y5, 98.17/14.79 emptyset)), 98.17/14.79 emptyset)))))))))))))) => 98.17/14.79 (??(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (( 98.17/14.79 ??(( 98.17/14.79 ^[Y4 : $i]: 98.17/14.79 (in(Y4, 98.17/14.79 Y1) & 98.17/14.79 (Y2 = 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y3, 98.17/14.79 emptyset), 98.17/14.79 setadjoin( 98.17/14.79 setadjoin( 98.17/14.79 Y3, 98.17/14.79 setadjoin( 98.17/14.79 Y4, 98.17/14.79 emptyset)), 98.17/14.79 emptyset))))))) & 98.17/14.79 in(Y3, 98.17/14.79 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 98.17/14.79 inference('lazy_cnf_imply', [status(thm)], ['161'])). 98.17/14.79 tff('163', plain, 98.17/14.79 ~ ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (in(Y2, setadjoin(Y0, Y1)) <=> 98.17/14.79 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 (in(Y1, powerset(Y0)) <=> 98.17/14.79 (!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 (in(Y1, setunion(Y0)) <=> 98.17/14.79 (??((^[Y2 : $i]: (in(Y1, Y2) & in(Y2, Y0)))))))))))) => 98.17/14.79 (in(emptyset, omega) => 98.17/14.79 ((!!((^[Y0 : $i]: (in(Y0, omega) => in(setadjoin(Y0, Y0), omega))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (((!!((^[Y1 : $i]: 98.17/14.79 ((in(Y1, Y0) & in(Y1, omega)) => 98.17/14.79 in(setadjoin(Y1, Y1), Y0))))) & 98.17/14.79 in(emptyset, Y0)) => 98.17/14.79 (!!((^[Y1 : $i]: (in(Y1, omega) => in(Y1, Y0))))))))) => 98.17/14.79 ((!!((^[Y0 : ($i * $i) > $o]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 ((!!((^[Y2 : $i]: 98.17/14.79 (in(Y2, Y1) => 98.17/14.79 (??((^[Y3 : $i]: 98.17/14.79 (Y0(Y2, Y3) & 98.17/14.79 (!!((^[Y4 : $i]: 98.17/14.79 (Y0(Y2, Y4) => (Y3 = Y4))))))))))))) => 98.17/14.79 (??((^[Y2 : $i]: 98.17/14.79 (!!((^[Y3 : $i]: 98.17/14.79 (in(Y3, Y2) <=> 98.17/14.79 (??((^[Y4 : $i]: 98.17/14.79 (in(Y4, Y1) & Y0(Y4, Y3))))))))))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 98.17/14.79 (??((^[Y1 : $i]: 98.17/14.79 (in(Y1, Y0) & 98.17/14.79 (~((??((^[Y2 : $i]: (in(Y2, Y1) & in(Y2, Y0))))))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (??((^[Y1 : $i]: 98.17/14.79 ((!!((^[Y2 : $i]: 98.17/14.79 (in(Y2, Y1) => 98.17/14.79 (!!((^[Y3 : $i]: 98.17/14.79 (in(Y3, Y2) => in(Y3, Y0)))))))))& 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (!!((^[Y3 : $i]: 98.17/14.79 ((in(Y3, Y0) & in(Y2, Y0)) => 98.17/14.79 ((!!((^[Y4 : $i]: 98.17/14.79 (in(Y4, Y1) => 98.17/14.79 (in(Y2, Y4) <=> 98.17/14.79 in(Y3, Y4)))))) => 98.17/14.79 (Y2 = Y3)))))))))& 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (!!((^[Y3 : $i]: 98.17/14.79 ((in(Y3, Y1) & in(Y2, Y1)) => 98.17/14.79 ((!!((^[Y4 : $i]: 98.17/14.79 (in(Y4, Y3) => 98.17/14.79 in(Y4, Y2))))) | 98.17/14.79 (!!((^[Y4 : $i]: 98.17/14.79 (in(Y4, Y2) => 98.17/14.79 in(Y4, Y3)))))))))))))& 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (((??((^[Y3 : $i]: in(Y3, Y2)))) & 98.17/14.79 (!!((^[Y3 : $i]: 98.17/14.79 (in(Y3, Y2) => in(Y3, Y0)))))) => 98.17/14.79 (??((^[Y3 : $i]: 98.17/14.79 (??((^[Y4 : $i]: 98.17/14.79 (in(Y3, Y1)&in(Y4, Y2)& 98.17/14.79 (~((??((^[Y5 : $i]: 98.17/14.79 (in(Y5, Y3) & 98.17/14.79 in(Y5, Y2)))))))& 98.17/14.79 (!!((^[Y5 : $i]: 98.17/14.79 (in(Y5, Y1) => 98.17/14.79 (in(Y4, Y5) | 98.17/14.79 (!!((^[Y6 : $i]: 98.17/14.79 (in(Y6, 98.17/14.79 Y5) => 98.17/14.79 in(Y6, 98.17/14.79 Y3)))))))))))))))))))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i > $o]: 98.17/14.79 ((??((^[Y1 : $i]: 98.17/14.79 (Y0(Y1) & 98.17/14.79 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 98.17/14.79 Y0(descr(Y0)))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i > $o]: 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (in(Y2, Y0) => 98.17/14.79 (Y1(Y2) => in(Y2, dsetconstr(Y0, Y1))))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i > $o]: 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (in(Y2, dsetconstr(Y0, Y1)) => 98.17/14.79 in(Y2, Y0))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i > $o]: 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (in(Y2, dsetconstr(Y0, Y1)) => Y1(Y2))))))))))) => 98.17/14.79 ((!!((^[Y0 : $o]: 98.17/14.79 (!!((^[Y1 : $i]: (in(Y1, prop2set(Y0)) => Y0))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (in(Y0, emptyset) => (!!((^[Y1 : $o]: Y1))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 98.17/14.79 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 98.17/14.79 ((!!((^[Y0 : $i > $o]: 98.17/14.79 ((??((^[Y1 : $i]: 98.17/14.79 (Y0(Y1) & 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (Y0(Y2) => (Y1 = Y2))))))))) => 98.17/14.79 (??(Y0)))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 ((!!((^[Y2 : $i]: 98.17/14.79 (in(Y2, Y0) => in(Y2, Y1))))) => 98.17/14.79 ((!!((^[Y2 : $i]: 98.17/14.79 (in(Y2, Y1) => in(Y2, Y0))))) => 98.17/14.79 (Y0 = Y1))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 98.17/14.79 (Y0 = emptyset))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 98.17/14.79 (Y0 = emptyset))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i > $o]: 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (in(Y2, Y0) => 98.17/14.79 (in(Y2, dsetconstr(Y0, Y1)) <=> 98.17/14.79 Y1(Y2)))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 ((Y0 != emptyset) => 98.17/14.79 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i > $o]: 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (in(Y2, Y0) => 98.17/14.79 (Y1(Y2) => 98.17/14.79 (dsetconstr(Y0, Y1) != 98.17/14.79 emptyset)))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 98.17/14.79 (Y0 != emptyset))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 in(Y0, setadjoin(Y0, Y1)))))))) => 98.17/14.79 (in(emptyset, setadjoin(emptyset, emptyset)) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (in(Y2, Y1) => 98.17/14.79 in(Y2, 98.17/14.79 setadjoin(Y0, Y1)))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 setadjoin(Y0, Y1)) => 98.17/14.79 (!!((^[Y3 : $o]: 98.17/14.79 (((Y2 = Y0) => 98.17/14.79 Y3) => 98.17/14.79 ((in(Y2, Y1) => 98.17/14.79 Y3) => 98.17/14.79 Y3))))))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 setadjoin(Y0, Y1)) => 98.17/14.79 (in(Y2, Y1) | 98.17/14.79 (Y2 = Y0)))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (dsetconstr(Y0, 98.17/14.79 (^[Y1 : $i]: $true)) = 98.17/14.79 Y0)))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 ((!!((^[Y2 : $i]: 98.17/14.79 (in(Y2, Y1) => 98.17/14.79 in(Y2, Y0))))) => 98.17/14.79 in(Y1, powerset(Y0))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 in(emptyset, powerset(Y0))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 in(emptyset, powerset(Y0))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (in(Y1, 98.17/14.79 powerset(Y0)) => 98.17/14.79 (in(Y2, Y1) => 98.17/14.79 in(Y2, Y0)))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (in(Y1, Y2) => 98.17/14.79 (in(Y2, Y0) => 98.17/14.79 in(Y1, 98.17/14.79 setunion( 98.17/14.79 Y0))))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 (in(Y1, 98.17/14.79 setunion(Y0)) => 98.17/14.79 (!!((^[Y2 : $o]: 98.17/14.79 ((!!(( 98.17/14.79 ^[Y3 : $i]: 98.17/14.79 (in(Y1, 98.17/14.79 Y3) => 98.17/14.79 (in(Y3, 98.17/14.79 Y0) => Y2))))) => 98.17/14.79 Y2))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 (in(Y1, Y0) => 98.17/14.79 in(Y1, 98.17/14.79 powerset( 98.17/14.79 setunion(Y0)))))))))) => 98.17/14.79 ((!!((^[Y0 : $i > $o]: 98.17/14.79 ((??((^[Y1 : $i]: 98.17/14.79 (Y0(Y1) & 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 ( 98.17/14.79 Y0(Y2) => 98.17/14.79 ( 98.17/14.79 Y1 = Y2))))))))) => 98.17/14.79 (??((^[Y1 : $i]: 98.17/14.79 (!!((^[Y2 : $i]: 98.17/14.79 (Y0(Y2) <=> 98.17/14.79 ( 98.17/14.79 Y2 = Y1)))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 ((Y0 != emptyset) => 98.17/14.79 (??((^[Y1 : $i]: 98.17/14.79 in(Y1, Y0)))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 (in(Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset)) => 98.17/14.79 (Y0 = Y1)))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 ((Y0 != Y1) => 98.17/14.79 (~(in(Y1, 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 emptyset))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 ((Y0 = Y1) => 98.17/14.79 in(Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 (in(Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset)) => 98.17/14.79 in(Y1, 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 emptyset))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 (!!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 ( 98.17/14.79 in(Y2, 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset))) => 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 Y2 = Y1) | 98.17/14.79 ( 98.17/14.79 Y2 = Y0)))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 in(Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 in(Y1, 98.17/14.79 setadjoin( 98.17/14.79 Y0, 98.17/14.79 setadjoin( 98.17/14.79 Y1, 98.17/14.79 emptyset))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i > $o]: 98.17/14.79 ( 98.17/14.79 ( 98.17/14.79 ??(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) & 98.17/14.79 Y1(Y2))))) => 98.17/14.79 ( 98.17/14.79 dsetconstr( 98.17/14.79 Y0, Y1) != 98.17/14.79 emptyset)))))))) => 98.17/14.79 ((!!((^[Y0 : $i > $o]: 98.17/14.79 (!!((^[Y1 : $i]: 98.17/14.79 (in(Y1, 98.17/14.79 emptyset) => 98.17/14.79 Y0(Y1)))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!((^[Y1 : $i > $o]: 98.17/14.79 (( 98.17/14.79 ~(( 98.17/14.79 !!(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) => 98.17/14.79 Y1(Y2))))))) => 98.17/14.79 (??(( 98.17/14.79 ^[Y2 : $i]: 98.17/14.79 (in(Y2, 98.17/14.79 Y0) & 98.17/14.79 (~( 98.17/14.79 Y1(Y2)))))))))))))) => 98.17/14.79 ((!!((^[Y0 : $i]: 98.17/14.79 (!!(( 98.17/14.80 ^[Y1 : $i > $o]: 98.17/14.80 (( 98.17/14.80 !!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (~( 98.17/14.80 Y1(Y2))))))) => 98.17/14.80 ( 98.17/14.80 ~(( 98.17/14.80 ??(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) & 98.17/14.80 Y1(Y2)))))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i > $o]: 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 ~(( 98.17/14.80 ??(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) & 98.17/14.80 Y1(Y2))))))) => 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (~( 98.17/14.80 Y1(Y2)))))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i > $o]: 98.17/14.80 (( 98.17/14.80 ??(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) & 98.17/14.80 (~( 98.17/14.80 Y1(Y2))))))) => 98.17/14.80 (~(( 98.17/14.80 !!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 Y1(Y2)))))))))))))) => 98.17/14.80 ((!!((^[Y0 : $o]: 98.17/14.80 (Y0 => 98.17/14.80 in( 98.17/14.80 emptyset, 98.17/14.80 prop2set( 98.17/14.80 Y0)))))) => 98.17/14.80 ((!!((^[Y0 : $o]: 98.17/14.80 ( 98.17/14.80 Y0 => 98.17/14.80 set2prop( 98.17/14.80 prop2set( 98.17/14.80 Y0)))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i > $o]: 98.17/14.80 (( 98.17/14.80 ~(( 98.17/14.80 ??(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) & 98.17/14.80 Y1(Y2))))))) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (~( 98.17/14.80 Y1(Y2)))))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i > $o]: 98.17/14.80 (( 98.17/14.80 ~(( 98.17/14.80 !!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 Y1(Y2))))))) => 98.17/14.80 (??(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) & 98.17/14.80 (~( 98.17/14.80 Y1(Y2)))))))))))))) => 98.17/14.80 ((!!(( 98.17/14.80 ^[Y0 : $i > $o]: 98.17/14.80 (( 98.17/14.80 ??(Y0)) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (Y0(Y1) => 98.17/14.80 (Y0(Y2) => 98.17/14.80 (Y1 = Y2))))))))) => 98.17/14.80 ( 98.17/14.80 ??(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (Y0(Y1) & 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (Y0(Y2) => 98.17/14.80 (Y1 = Y2)))))))))))))) => 98.17/14.80 ((!!(( 98.17/14.80 ^[Y0 : $i > $o]: 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 ??(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (Y0(Y2) <=> 98.17/14.80 (Y2 = Y1)))))))) => 98.17/14.80 ( 98.17/14.80 ??(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (Y0(Y1) & 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (Y0(Y2) => 98.17/14.80 (Y1 = Y2))))))))))))) => 98.17/14.80 ((!!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 Y0 = Y1) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (( 98.17/14.80 Y2 = Y3) => 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 in(Y3, 98.17/14.80 Y1)))))))))))))))) => 98.17/14.80 ((!!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 Y0 = Y1) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (( 98.17/14.80 Y2 = Y3) => 98.17/14.80 (in(Y2, 98.17/14.80 Y0) <=> 98.17/14.80 in(Y3, 98.17/14.80 Y1)))))))))))))))) => 98.17/14.80 (( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i > $o]: 98.17/14.80 (( 98.17/14.80 ??(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (Y0(Y1) & 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (Y0(Y2) => 98.17/14.80 (Y1 = Y2))))))))) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (Y0(Y1) => 98.17/14.80 (Y0(Y2) => 98.17/14.80 (Y1 = Y2))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i > $o]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i > $o]: 98.17/14.80 (( 98.17/14.80 !!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (( 98.17/14.80 Y2 = Y3) => 98.17/14.80 (Y0(Y2) <=> 98.17/14.80 Y1(Y3))))))))) => 98.17/14.80 (( 98.17/14.80 ??(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (Y0(Y2) & 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (Y0(Y3) => 98.17/14.80 (Y2 = Y3))))))))) <=> 98.17/14.80 (??(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (Y1(Y2) & 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (Y1(Y3) => 98.17/14.80 (Y2 = Y3))))))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 Y0 = Y1) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (( 98.17/14.80 Y2 = Y3) => 98.17/14.80 (setadjoin( 98.17/14.80 Y0, Y2) = 98.17/14.80 setadjoin( 98.17/14.80 Y1, Y3)))))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 Y0 = Y1) => 98.17/14.80 (powerset( 98.17/14.80 Y0) = 98.17/14.80 powerset( 98.17/14.80 Y1))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 Y0 = Y1) => 98.17/14.80 (setunion( 98.17/14.80 Y0) = 98.17/14.80 setunion( 98.17/14.80 Y1))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i > $o]: 98.17/14.80 (( 98.17/14.80 ??(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (Y0(Y1) & 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (Y0(Y2) => 98.17/14.80 (Y1 = Y2))))))))) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (Y0(Y1) => 98.17/14.80 (Y0(Y2) => 98.17/14.80 (Y1 = Y2))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i > $o]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i > $o]: 98.17/14.80 (( 98.17/14.80 !!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (( 98.17/14.80 Y2 = Y3) => 98.17/14.80 (Y0(Y2) <=> 98.17/14.80 Y1(Y3))))))))) => 98.17/14.80 (( 98.17/14.80 ??(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (Y0(Y2) & 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (Y0(Y3) => 98.17/14.80 (Y2 = Y3))))))))) => 98.17/14.80 (( 98.17/14.80 ??(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (Y1(Y2) & 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (Y1(Y3) => 98.17/14.80 (Y2 = Y3))))))))) => 98.17/14.80 (descr( 98.17/14.80 Y0) = 98.17/14.80 descr(Y1))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 Y0 = Y1) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i > $o]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i > $o]: 98.17/14.80 (( 98.17/14.80 !!(( 98.17/14.80 ^[Y4 : $i]: 98.17/14.80 (in(Y4, 98.17/14.80 Y0) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y5 : $i]: 98.17/14.80 (in(Y5, 98.17/14.80 Y1) => 98.17/14.80 (( 98.17/14.80 Y4 = Y5) => 98.17/14.80 (Y2(Y4) <=> 98.17/14.80 Y3(Y5))))))))))) => 98.17/14.80 (dsetconstr( 98.17/14.80 Y0, Y2) = 98.17/14.80 dsetconstr( 98.17/14.80 Y1, Y3)))))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 !!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 in(Y2, 98.17/14.80 Y1))))) => 98.17/14.80 subset( 98.17/14.80 Y0, Y1)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 Y0 = Y1) => 98.17/14.80 subset( 98.17/14.80 Y1, Y0)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 Y0 = Y1) => 98.17/14.80 subset( 98.17/14.80 Y0, Y1)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 !!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 in(Y2, 98.17/14.80 Y1))))) => 98.17/14.80 subset( 98.17/14.80 Y0, Y1)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!( 98.17/14.80 subset( 98.17/14.80 emptyset))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (subset( 98.17/14.80 Y0, Y1) => 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 in(Y2, 98.17/14.80 Y1)))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (subset( 98.17/14.80 Y0, Y1) => 98.17/14.80 (( 98.17/14.80 ~( 98.17/14.80 in(Y2, 98.17/14.80 Y1))) => 98.17/14.80 (~( 98.17/14.80 in(Y2, 98.17/14.80 Y0)))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (( 98.17/14.80 ~( 98.17/14.80 in(Y2, 98.17/14.80 Y1))) => 98.17/14.80 (~( 98.17/14.80 subset( 98.17/14.80 Y0, Y1)))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 ~( 98.17/14.80 subset( 98.17/14.80 Y0, Y1))) => 98.17/14.80 (Y0 != Y1)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (( 98.17/14.80 ~( 98.17/14.80 in(Y2, 98.17/14.80 Y1))) => 98.17/14.80 (Y0 != Y1)))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 subset( 98.17/14.80 Y0, Y0)))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (subset( 98.17/14.80 Y0, Y1) => 98.17/14.80 (subset( 98.17/14.80 Y1, Y2) => 98.17/14.80 subset( 98.17/14.80 Y0, Y2)))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 subset( 98.17/14.80 Y1, 98.17/14.80 setadjoin( 98.17/14.80 Y0, Y1)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (subset( 98.17/14.80 Y0, Y2) => 98.17/14.80 subset( 98.17/14.80 Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, Y2)))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (subset( 98.17/14.80 Y0, Y1) => 98.17/14.80 in(Y0, 98.17/14.80 powerset( 98.17/14.80 Y1))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (subset( 98.17/14.80 Y0, Y1) => 98.17/14.80 (subset( 98.17/14.80 Y1, Y0) => 98.17/14.80 (Y0 = Y1))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (subset( 98.17/14.80 Y0, 98.17/14.80 emptyset) => 98.17/14.80 (Y0 = 98.17/14.80 emptyset))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (subset( 98.17/14.80 Y1, Y0) => 98.17/14.80 in(Y1, 98.17/14.80 powerset( 98.17/14.80 Y0))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (in(Y1, 98.17/14.80 powerset( 98.17/14.80 Y0)) => 98.17/14.80 subset( 98.17/14.80 Y1, Y0)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 in(Y0, 98.17/14.80 powerset( 98.17/14.80 Y0))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (subset( 98.17/14.80 Y0, Y1) => 98.17/14.80 subset( 98.17/14.80 powerset( 98.17/14.80 Y0), 98.17/14.80 powerset( 98.17/14.80 Y1))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i > $o]: 98.17/14.80 in( 98.17/14.80 dsetconstr( 98.17/14.80 Y0, Y1), 98.17/14.80 powerset( 98.17/14.80 Y0)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i > $o]: 98.17/14.80 subset( 98.17/14.80 dsetconstr( 98.17/14.80 Y0, Y1), 98.17/14.80 Y0))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 in(Y2, 98.17/14.80 binunion( 98.17/14.80 Y0, Y1)))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 in(Y1, 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y1) => 98.17/14.80 in(Y2, 98.17/14.80 binunion( 98.17/14.80 Y0, Y1)))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $o]: 98.17/14.80 (in(Y2, 98.17/14.80 binunion( 98.17/14.80 Y0, Y1)) => 98.17/14.80 (( 98.17/14.80 in(Y2, 98.17/14.80 Y0) => Y3) => 98.17/14.80 (( 98.17/14.80 in(Y2, 98.17/14.80 Y1) => Y3) => 98.17/14.80 Y3))))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 binunion( 98.17/14.80 Y0, Y1)) => 98.17/14.80 (in(Y2, 98.17/14.80 Y1) | 98.17/14.80 in(Y2, 98.17/14.80 Y0)))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 subset( 98.17/14.80 Y0, 98.17/14.80 binunion( 98.17/14.80 Y0, Y1)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 subset( 98.17/14.80 Y1, 98.17/14.80 binunion( 98.17/14.80 Y0, Y1)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (in(Y2, 98.17/14.80 Y1) => 98.17/14.80 in(Y2, 98.17/14.80 binintersect( 98.17/14.80 Y0, Y1))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (subset( 98.17/14.80 Y2, Y0) => 98.17/14.80 (subset( 98.17/14.80 Y2, Y1) => 98.17/14.80 subset( 98.17/14.80 Y2, 98.17/14.80 binintersect( 98.17/14.80 Y0, Y1))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 binintersect( 98.17/14.80 Y0, Y1)) => 98.17/14.80 in(Y2, 98.17/14.80 Y0))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 subset( 98.17/14.80 binintersect( 98.17/14.80 Y0, Y1), 98.17/14.80 Y0))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (subset( 98.17/14.80 Y0, Y1) => 98.17/14.80 (binintersect( 98.17/14.80 Y0, Y1) = 98.17/14.80 Y0)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 binintersect( 98.17/14.80 Y0, Y1) = 98.17/14.80 Y1) => 98.17/14.80 subset( 98.17/14.80 Y1, Y0)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 binintersect( 98.17/14.80 Y0, Y1)) => 98.17/14.80 in(Y2, 98.17/14.80 Y1))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 ~(( 98.17/14.80 ??(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) & 98.17/14.80 in(Y2, 98.17/14.80 Y1))))))) => 98.17/14.80 (binintersect( 98.17/14.80 Y0, Y1) = 98.17/14.80 emptyset)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 subset( 98.17/14.80 binintersect( 98.17/14.80 Y0, Y1), 98.17/14.80 Y1))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (subset( 98.17/14.80 Y1, Y0) => 98.17/14.80 (binintersect( 98.17/14.80 Y0, Y1) = 98.17/14.80 Y1)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 binintersect( 98.17/14.80 Y0, Y1) = 98.17/14.80 Y0) => 98.17/14.80 subset( 98.17/14.80 Y0, Y1)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (binintersect( 98.17/14.80 Y0, 98.17/14.80 binunion( 98.17/14.80 Y1, Y2)) = 98.17/14.80 binunion( 98.17/14.80 binintersect( 98.17/14.80 Y0, Y1), 98.17/14.80 binintersect( 98.17/14.80 Y0, Y2)))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (( 98.17/14.80 ~( 98.17/14.80 in(Y2, 98.17/14.80 Y1))) => 98.17/14.80 in(Y2, 98.17/14.80 setminus( 98.17/14.80 Y0, Y1))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 setminus( 98.17/14.80 Y0, Y1)) => 98.17/14.80 in(Y2, 98.17/14.80 Y0))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 setminus( 98.17/14.80 Y0, Y1)) => 98.17/14.80 (~( 98.17/14.80 in(Y2, 98.17/14.80 Y1))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (subset( 98.17/14.80 Y0, Y1) => 98.17/14.80 (setminus( 98.17/14.80 Y0, Y1) = 98.17/14.80 emptyset)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (( 98.17/14.80 ~( 98.17/14.80 in(Y2, 98.17/14.80 setminus( 98.17/14.80 Y0, Y1)))) => 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 in(Y2, 98.17/14.80 Y1)))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (( 98.17/14.80 ~( 98.17/14.80 in(Y2, 98.17/14.80 setminus( 98.17/14.80 Y0, Y1)))) => 98.17/14.80 (( 98.17/14.80 ~( 98.17/14.80 in(Y2, 98.17/14.80 Y1))) => 98.17/14.80 (~( 98.17/14.80 in(Y2, 98.17/14.80 Y0)))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (( 98.17/14.80 ~( 98.17/14.80 in(Y2, 98.17/14.80 Y0))) => 98.17/14.80 (~( 98.17/14.80 in(Y2, 98.17/14.80 setminus( 98.17/14.80 Y0, Y1)))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y1) => 98.17/14.80 (~( 98.17/14.80 in(Y2, 98.17/14.80 setminus( 98.17/14.80 Y0, Y1)))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 subset( 98.17/14.80 setminus( 98.17/14.80 Y0, Y1), 98.17/14.80 Y0))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 setminus( 98.17/14.80 Y0, Y1) = 98.17/14.80 emptyset) => 98.17/14.80 subset( 98.17/14.80 Y0, Y1)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 symdiff( 98.17/14.80 Y0, Y1)) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $o]: 98.17/14.80 (( 98.17/14.80 in(Y2, 98.17/14.80 Y0) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 ~( 98.17/14.80 in(Y2, 98.17/14.80 Y1))) => 98.17/14.80 Y3)) => 98.17/14.80 (( 98.17/14.80 ( 98.17/14.80 ~( 98.17/14.80 in(Y2, 98.17/14.80 Y0))) => 98.17/14.80 ( 98.17/14.80 in(Y2, 98.17/14.80 Y1) => Y3)) => 98.17/14.80 Y3))))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (( 98.17/14.80 ~( 98.17/14.80 in(Y2, 98.17/14.80 Y1))) => 98.17/14.80 in(Y2, 98.17/14.80 symdiff( 98.17/14.80 Y0, Y1))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (( 98.17/14.80 ~( 98.17/14.80 in(Y2, 98.17/14.80 Y0))) => 98.17/14.80 (in(Y2, 98.17/14.80 Y1) => 98.17/14.80 in(Y2, 98.17/14.80 symdiff( 98.17/14.80 Y0, Y1))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (in(Y2, 98.17/14.80 Y1) => 98.17/14.80 (~( 98.17/14.80 in(Y2, 98.17/14.80 symdiff( 98.17/14.80 Y0, Y1))))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (( 98.17/14.80 ~( 98.17/14.80 in(Y2, 98.17/14.80 Y0))) => 98.17/14.80 (( 98.17/14.80 ~( 98.17/14.80 in(Y2, 98.17/14.80 Y1))) => 98.17/14.80 (~( 98.17/14.80 in(Y2, 98.17/14.80 symdiff( 98.17/14.80 Y0, Y1))))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 in(Y1, 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 in(Y0, 98.17/14.80 setunion( 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset)), 98.17/14.80 emptyset)))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 in(Y1, 98.17/14.80 setunion( 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset)), 98.17/14.80 emptyset)))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (??(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 setunion( 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset)), 98.17/14.80 emptyset)))) & 98.17/14.80 (??(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (in(Y3, 98.17/14.80 setunion( 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset)), 98.17/14.80 emptyset)))) & 98.17/14.80 (setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset)), 98.17/14.80 emptyset)) = 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 setadjoin( 98.17/14.80 Y3, 98.17/14.80 emptyset)), 98.17/14.80 emptyset))))))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (??(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 setunion( 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset)), 98.17/14.80 emptyset)))) & 98.17/14.80 (??(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (in(Y3, 98.17/14.80 setunion( 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset)), 98.17/14.80 emptyset)))) & 98.17/14.80 (setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset)), 98.17/14.80 emptyset)) = 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 setadjoin( 98.17/14.80 Y3, 98.17/14.80 emptyset)), 98.17/14.80 emptyset))))))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (in(Y1, 98.17/14.80 Y0) => 98.17/14.80 subset( 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset), 98.17/14.80 Y0)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (in(Y1, 98.17/14.80 Y0) => 98.17/14.80 in( 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset), 98.17/14.80 powerset( 98.17/14.80 Y0))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 in( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 emptyset), 98.17/14.80 powerset( 98.17/14.80 binunion( 98.17/14.80 Y0, Y1))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset))) => 98.17/14.80 (( 98.17/14.80 Y2 = Y1) | 98.17/14.80 (Y2 = Y0)))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (in(Y3, 98.17/14.80 Y1) => 98.17/14.80 subset( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 setadjoin( 98.17/14.80 Y3, 98.17/14.80 emptyset)), 98.17/14.80 binunion( 98.17/14.80 Y0, Y1)))))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (in(Y3, 98.17/14.80 Y1) => 98.17/14.80 in( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 setadjoin( 98.17/14.80 Y3, 98.17/14.80 emptyset)), 98.17/14.80 powerset( 98.17/14.80 binunion( 98.17/14.80 Y0, Y1))))))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (in(Y3, 98.17/14.80 Y1) => 98.17/14.80 subset( 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 setadjoin( 98.17/14.80 Y3, 98.17/14.80 emptyset)), 98.17/14.80 emptyset)), 98.17/14.80 powerset( 98.17/14.80 binunion( 98.17/14.80 Y0, Y1))))))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (in(Y3, 98.17/14.80 Y1) => 98.17/14.80 in( 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 setadjoin( 98.17/14.80 Y3, 98.17/14.80 emptyset)), 98.17/14.80 emptyset)), 98.17/14.80 powerset( 98.17/14.80 powerset( 98.17/14.80 binunion( 98.17/14.80 Y0, Y1)))))))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (in(Y3, 98.17/14.80 Y1) => 98.17/14.80 in( 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 setadjoin( 98.17/14.80 Y3, 98.17/14.80 emptyset)), 98.17/14.80 emptyset)), 98.17/14.80 powerset( 98.17/14.80 powerset( 98.17/14.80 binunion( 98.17/14.80 Y0, Y1)))))))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (in(Y3, 98.17/14.80 Y1) => 98.17/14.80 in( 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 setadjoin( 98.17/14.80 Y3, 98.17/14.80 emptyset)), 98.17/14.80 emptyset)), 98.17/14.80 dsetconstr( 98.17/14.80 powerset( 98.17/14.80 powerset( 98.17/14.80 binunion( 98.17/14.80 Y0, Y1))), 98.17/14.80 (^[Y4 : $i]: 98.17/14.80 (??(( 98.17/14.80 ^[Y5 : $i]: 98.17/14.80 (in(Y5, 98.17/14.80 Y0) & 98.17/14.80 (??(( 98.17/14.80 ^[Y6 : $i]: 98.17/14.80 (in(Y6, 98.17/14.80 Y1) & 98.17/14.80 (Y4 = 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y5, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y5, 98.17/14.80 setadjoin( 98.17/14.80 Y6, 98.17/14.80 emptyset)), 98.17/14.80 emptyset)))))))))))))))))))))))))))) => 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 dsetconstr( 98.17/14.80 powerset( 98.17/14.80 powerset( 98.17/14.80 binunion( 98.17/14.80 Y0, Y1))), 98.17/14.80 (^[Y3 : $i]: 98.17/14.80 (??(( 98.17/14.80 ^[Y4 : $i]: 98.17/14.80 (in(Y4, 98.17/14.80 Y0) & 98.17/14.80 (??(( 98.17/14.80 ^[Y5 : $i]: 98.17/14.80 (in(Y5, 98.17/14.80 Y1) & 98.17/14.80 (Y3 = 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y4, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y4, 98.17/14.80 setadjoin( 98.17/14.80 Y5, 98.17/14.80 emptyset)), 98.17/14.80 emptyset)))))))))))))) => 98.17/14.80 (??(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (( 98.17/14.80 ??(( 98.17/14.80 ^[Y4 : $i]: 98.17/14.80 (in(Y4, 98.17/14.80 Y1) & 98.17/14.80 (Y2 = 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y3, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y3, 98.17/14.80 setadjoin( 98.17/14.80 Y4, 98.17/14.80 emptyset)), 98.17/14.80 emptyset))))))) & 98.17/14.80 in(Y3, 98.17/14.80 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 98.17/14.80 inference('lazy_cnf_imply', [status(thm)], ['162'])). 98.17/14.80 tff('164', plain, 98.17/14.80 ~ ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i]: 98.17/14.80 (in(Y1, powerset(Y0)) <=> 98.17/14.80 (!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i]: 98.17/14.80 (in(Y1, setunion(Y0)) <=> 98.17/14.80 (??((^[Y2 : $i]: (in(Y1, Y2) & in(Y2, Y0)))))))))))) => 98.17/14.80 (in(emptyset, omega) => 98.17/14.80 ((!!((^[Y0 : $i]: (in(Y0, omega) => in(setadjoin(Y0, Y0), omega))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (((!!((^[Y1 : $i]: 98.17/14.80 ((in(Y1, Y0) & in(Y1, omega)) => 98.17/14.80 in(setadjoin(Y1, Y1), Y0))))) & 98.17/14.80 in(emptyset, Y0)) => 98.17/14.80 (!!((^[Y1 : $i]: (in(Y1, omega) => in(Y1, Y0))))))))) => 98.17/14.80 ((!!((^[Y0 : ($i * $i) > $o]: 98.17/14.80 (!!((^[Y1 : $i]: 98.17/14.80 ((!!((^[Y2 : $i]: 98.17/14.80 (in(Y2, Y1) => 98.17/14.80 (??((^[Y3 : $i]: 98.17/14.80 (Y0(Y2, Y3) & 98.17/14.80 (!!((^[Y4 : $i]: 98.17/14.80 (Y0(Y2, Y4) => (Y3 = Y4))))))))))))) => 98.17/14.80 (??((^[Y2 : $i]: 98.17/14.80 (!!((^[Y3 : $i]: 98.17/14.80 (in(Y3, Y2) <=> 98.17/14.80 (??((^[Y4 : $i]: 98.17/14.80 (in(Y4, Y1) & Y0(Y4, Y3))))))))))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 98.17/14.80 (??((^[Y1 : $i]: 98.17/14.80 (in(Y1, Y0) & 98.17/14.80 (~((??((^[Y2 : $i]: (in(Y2, Y1) & in(Y2, Y0))))))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (??((^[Y1 : $i]: 98.17/14.80 ((!!((^[Y2 : $i]: 98.17/14.80 (in(Y2, Y1) => 98.17/14.80 (!!((^[Y3 : $i]: 98.17/14.80 (in(Y3, Y2) => in(Y3, Y0)))))))))& 98.17/14.80 (!!((^[Y2 : $i]: 98.17/14.80 (!!((^[Y3 : $i]: 98.17/14.80 ((in(Y3, Y0) & in(Y2, Y0)) => 98.17/14.80 ((!!((^[Y4 : $i]: 98.17/14.80 (in(Y4, Y1) => 98.17/14.80 (in(Y2, Y4) <=> 98.17/14.80 in(Y3, Y4)))))) => 98.17/14.80 (Y2 = Y3)))))))))& 98.17/14.80 (!!((^[Y2 : $i]: 98.17/14.80 (!!((^[Y3 : $i]: 98.17/14.80 ((in(Y3, Y1) & in(Y2, Y1)) => 98.17/14.80 ((!!((^[Y4 : $i]: 98.17/14.80 (in(Y4, Y3) => in(Y4, Y2))))) | 98.17/14.80 (!!((^[Y4 : $i]: 98.17/14.80 (in(Y4, Y2) => in(Y4, Y3)))))))))))))& 98.17/14.80 (!!((^[Y2 : $i]: 98.17/14.80 (((??((^[Y3 : $i]: in(Y3, Y2)))) & 98.17/14.80 (!!((^[Y3 : $i]: 98.17/14.80 (in(Y3, Y2) => in(Y3, Y0)))))) => 98.17/14.80 (??((^[Y3 : $i]: 98.17/14.80 (??((^[Y4 : $i]: 98.17/14.80 (in(Y3, Y1)&in(Y4, Y2)& 98.17/14.80 (~((??((^[Y5 : $i]: 98.17/14.80 (in(Y5, Y3) & 98.17/14.80 in(Y5, Y2)))))))& 98.17/14.80 (!!((^[Y5 : $i]: 98.17/14.80 (in(Y5, Y1) => 98.17/14.80 (in(Y4, Y5) | 98.17/14.80 (!!((^[Y6 : $i]: 98.17/14.80 ( 98.17/14.80 in(Y6, 98.17/14.80 Y5) => 98.17/14.80 in(Y6, 98.17/14.80 Y3)))))))))))))))))))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i > $o]: 98.17/14.80 ((??((^[Y1 : $i]: 98.17/14.80 (Y0(Y1) & 98.17/14.80 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 98.17/14.80 Y0(descr(Y0)))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i > $o]: 98.17/14.80 (!!((^[Y2 : $i]: 98.17/14.80 (in(Y2, Y0) => 98.17/14.80 (Y1(Y2) => in(Y2, dsetconstr(Y0, Y1))))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i > $o]: 98.17/14.80 (!!((^[Y2 : $i]: 98.17/14.80 (in(Y2, dsetconstr(Y0, Y1)) => 98.17/14.80 in(Y2, Y0))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i > $o]: 98.17/14.80 (!!((^[Y2 : $i]: 98.17/14.80 (in(Y2, dsetconstr(Y0, Y1)) => Y1(Y2))))))))))) => 98.17/14.80 ((!!((^[Y0 : $o]: 98.17/14.80 (!!((^[Y1 : $i]: (in(Y1, prop2set(Y0)) => Y0))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (in(Y0, emptyset) => (!!((^[Y1 : $o]: Y1))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 98.17/14.80 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 98.17/14.80 ((!!((^[Y0 : $i > $o]: 98.17/14.80 ((??((^[Y1 : $i]: 98.17/14.80 (Y0(Y1) & 98.17/14.80 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 98.17/14.80 (??(Y0)))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i]: 98.17/14.80 ((!!((^[Y2 : $i]: 98.17/14.80 (in(Y2, Y0) => in(Y2, Y1))))) => 98.17/14.80 ((!!((^[Y2 : $i]: 98.17/14.80 (in(Y2, Y1) => in(Y2, Y0))))) => 98.17/14.80 (Y0 = Y1))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 98.17/14.80 (Y0 = emptyset))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 98.17/14.80 (Y0 = emptyset))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i > $o]: 98.17/14.80 (!!((^[Y2 : $i]: 98.17/14.80 (in(Y2, Y0) => 98.17/14.80 (in(Y2, dsetconstr(Y0, Y1)) <=> 98.17/14.80 Y1(Y2)))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 ((Y0 != emptyset) => 98.17/14.80 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i > $o]: 98.17/14.80 (!!((^[Y2 : $i]: 98.17/14.80 (in(Y2, Y0) => 98.17/14.80 (Y1(Y2) => 98.17/14.80 (dsetconstr(Y0, Y1) != 98.17/14.80 emptyset)))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 98.17/14.80 (Y0 != emptyset))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i]: 98.17/14.80 in(Y0, setadjoin(Y0, Y1)))))))) => 98.17/14.80 (in(emptyset, setadjoin(emptyset, emptyset)) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i]: 98.17/14.80 (!!((^[Y2 : $i]: 98.17/14.80 (in(Y2, Y1) => 98.17/14.80 in(Y2, 98.17/14.80 setadjoin(Y0, Y1)))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i]: 98.17/14.80 (!!((^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 setadjoin(Y0, Y1)) => 98.17/14.80 (!!((^[Y3 : $o]: 98.17/14.80 (((Y2 = Y0) => 98.17/14.80 Y3) => 98.17/14.80 ((in(Y2, Y1) => 98.17/14.80 Y3) => 98.17/14.80 Y3))))))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i]: 98.17/14.80 (!!((^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 setadjoin(Y0, Y1)) => 98.17/14.80 (in(Y2, Y1) | 98.17/14.80 (Y2 = Y0)))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (dsetconstr(Y0, 98.17/14.80 (^[Y1 : $i]: $true)) = 98.17/14.80 Y0)))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i]: 98.17/14.80 ((!!((^[Y2 : $i]: 98.17/14.80 (in(Y2, Y1) => 98.17/14.80 in(Y2, Y0))))) => 98.17/14.80 in(Y1, powerset(Y0))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 in(emptyset, powerset(Y0))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 in(emptyset, powerset(Y0))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i]: 98.17/14.80 (!!((^[Y2 : $i]: 98.17/14.80 (in(Y1, 98.17/14.80 powerset(Y0)) => 98.17/14.80 (in(Y2, Y1) => 98.17/14.80 in(Y2, Y0)))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i]: 98.17/14.80 (!!((^[Y2 : $i]: 98.17/14.80 (in(Y1, Y2) => 98.17/14.80 (in(Y2, Y0) => 98.17/14.80 in(Y1, 98.17/14.80 setunion( 98.17/14.80 Y0))))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i]: 98.17/14.80 (in(Y1, setunion(Y0)) => 98.17/14.80 (!!((^[Y2 : $o]: 98.17/14.80 ((!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 ( 98.17/14.80 in(Y1, 98.17/14.80 Y3) => 98.17/14.80 ( 98.17/14.80 in(Y3, 98.17/14.80 Y0) => Y2))))) => 98.17/14.80 Y2))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i]: 98.17/14.80 (in(Y1, Y0) => 98.17/14.80 in(Y1, 98.17/14.80 powerset( 98.17/14.80 setunion(Y0)))))))))) => 98.17/14.80 ((!!((^[Y0 : $i > $o]: 98.17/14.80 ((??((^[Y1 : $i]: 98.17/14.80 (Y0(Y1) & 98.17/14.80 (!!((^[Y2 : $i]: 98.17/14.80 (Y0(Y2) => 98.17/14.80 ( 98.17/14.80 Y1 = Y2))))))))) => 98.17/14.80 (??((^[Y1 : $i]: 98.17/14.80 (!!((^[Y2 : $i]: 98.17/14.80 (Y0(Y2) <=> 98.17/14.80 (Y2 = Y1)))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 ((Y0 != emptyset) => 98.17/14.80 (??((^[Y1 : $i]: 98.17/14.80 in(Y1, Y0)))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i]: 98.17/14.80 (in(Y0, 98.17/14.80 setadjoin(Y1, 98.17/14.80 emptyset)) => 98.17/14.80 (Y0 = Y1)))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i]: 98.17/14.80 ((Y0 != Y1) => 98.17/14.80 (~(in(Y1, 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 emptyset))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i]: 98.17/14.80 ((Y0 = Y1) => 98.17/14.80 in(Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i]: 98.17/14.80 (in(Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset)) => 98.17/14.80 in(Y1, 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 emptyset))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 Y2 = Y1) | 98.17/14.80 ( 98.17/14.80 Y2 = Y0)))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i]: 98.17/14.80 in(Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i]: 98.17/14.80 in(Y1, 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i > $o]: 98.17/14.80 (( 98.17/14.80 ??(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) & 98.17/14.80 Y1(Y2))))) => 98.17/14.80 ( 98.17/14.80 dsetconstr( 98.17/14.80 Y0, Y1) != 98.17/14.80 emptyset)))))))) => 98.17/14.80 ((!!((^[Y0 : $i > $o]: 98.17/14.80 (!!((^[Y1 : $i]: 98.17/14.80 ( 98.17/14.80 in(Y1, 98.17/14.80 emptyset) => 98.17/14.80 Y0(Y1)))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i > $o]: 98.17/14.80 (( 98.17/14.80 ~(( 98.17/14.80 !!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 Y1(Y2))))))) => 98.17/14.80 (??(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) & 98.17/14.80 (~( 98.17/14.80 Y1(Y2)))))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i > $o]: 98.17/14.80 (( 98.17/14.80 !!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (~( 98.17/14.80 Y1(Y2))))))) => 98.17/14.80 (~(( 98.17/14.80 ??(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) & 98.17/14.80 Y1(Y2)))))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i > $o]: 98.17/14.80 (( 98.17/14.80 ~(( 98.17/14.80 ??(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) & 98.17/14.80 Y1(Y2))))))) => 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (~( 98.17/14.80 Y1(Y2)))))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i > $o]: 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 ??(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) & 98.17/14.80 (~( 98.17/14.80 Y1(Y2))))))) => 98.17/14.80 ( 98.17/14.80 ~(( 98.17/14.80 !!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 Y1(Y2)))))))))))))) => 98.17/14.80 ((!!((^[Y0 : $o]: 98.17/14.80 (Y0 => 98.17/14.80 in( 98.17/14.80 emptyset, 98.17/14.80 prop2set( 98.17/14.80 Y0)))))) => 98.17/14.80 ((!!((^[Y0 : $o]: 98.17/14.80 (Y0 => 98.17/14.80 set2prop( 98.17/14.80 prop2set( 98.17/14.80 Y0)))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y1 : $i > $o]: 98.17/14.80 (( 98.17/14.80 ~(( 98.17/14.80 ??(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) & 98.17/14.80 Y1(Y2))))))) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (~( 98.17/14.80 Y1(Y2)))))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i > $o]: 98.17/14.80 (( 98.17/14.80 ~(( 98.17/14.80 !!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 Y1(Y2))))))) => 98.17/14.80 (??(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) & 98.17/14.80 (~( 98.17/14.80 Y1(Y2)))))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i > $o]: 98.17/14.80 (( 98.17/14.80 ??(Y0)) => 98.17/14.80 (( 98.17/14.80 !!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (Y0(Y1) => 98.17/14.80 (Y0(Y2) => 98.17/14.80 (Y1 = Y2))))))))) => 98.17/14.80 (??(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (Y0(Y1) & 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (Y0(Y2) => 98.17/14.80 (Y1 = Y2)))))))))))))) => 98.17/14.80 ((!!(( 98.17/14.80 ^[Y0 : $i > $o]: 98.17/14.80 (( 98.17/14.80 ??(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (Y0(Y2) <=> 98.17/14.80 (Y2 = Y1)))))))) => 98.17/14.80 ( 98.17/14.80 ??(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (Y0(Y1) & 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (Y0(Y2) => 98.17/14.80 (Y1 = Y2))))))))))))) => 98.17/14.80 ((!!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 Y0 = Y1) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (( 98.17/14.80 Y2 = Y3) => 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 in(Y3, 98.17/14.80 Y1)))))))))))))))) => 98.17/14.80 ((!!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 Y0 = Y1) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (( 98.17/14.80 Y2 = Y3) => 98.17/14.80 (in(Y2, 98.17/14.80 Y0) <=> 98.17/14.80 in(Y3, 98.17/14.80 Y1)))))))))))))))) => 98.17/14.80 ((!!(( 98.17/14.80 ^[Y0 : $i > $o]: 98.17/14.80 (( 98.17/14.80 ??(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (Y0(Y1) & 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (Y0(Y2) => 98.17/14.80 (Y1 = Y2))))))))) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (Y0(Y1) => 98.17/14.80 (Y0(Y2) => 98.17/14.80 (Y1 = Y2))))))))))))) => 98.17/14.80 (( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i > $o]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i > $o]: 98.17/14.80 (( 98.17/14.80 !!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (( 98.17/14.80 Y2 = Y3) => 98.17/14.80 (Y0(Y2) <=> 98.17/14.80 Y1(Y3))))))))) => 98.17/14.80 (( 98.17/14.80 ??(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (Y0(Y2) & 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (Y0(Y3) => 98.17/14.80 (Y2 = Y3))))))))) <=> 98.17/14.80 (??(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (Y1(Y2) & 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (Y1(Y3) => 98.17/14.80 (Y2 = Y3))))))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 Y0 = Y1) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (( 98.17/14.80 Y2 = Y3) => 98.17/14.80 (setadjoin( 98.17/14.80 Y0, Y2) = 98.17/14.80 setadjoin( 98.17/14.80 Y1, Y3)))))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 Y0 = Y1) => 98.17/14.80 (powerset( 98.17/14.80 Y0) = 98.17/14.80 powerset( 98.17/14.80 Y1))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 Y0 = Y1) => 98.17/14.80 (setunion( 98.17/14.80 Y0) = 98.17/14.80 setunion( 98.17/14.80 Y1))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i > $o]: 98.17/14.80 (( 98.17/14.80 ??(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (Y0(Y1) & 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (Y0(Y2) => 98.17/14.80 (Y1 = Y2))))))))) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (Y0(Y1) => 98.17/14.80 (Y0(Y2) => 98.17/14.80 (Y1 = Y2))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i > $o]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i > $o]: 98.17/14.80 (( 98.17/14.80 !!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (( 98.17/14.80 Y2 = Y3) => 98.17/14.80 (Y0(Y2) <=> 98.17/14.80 Y1(Y3))))))))) => 98.17/14.80 (( 98.17/14.80 ??(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (Y0(Y2) & 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (Y0(Y3) => 98.17/14.80 (Y2 = Y3))))))))) => 98.17/14.80 (( 98.17/14.80 ??(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (Y1(Y2) & 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (Y1(Y3) => 98.17/14.80 (Y2 = Y3))))))))) => 98.17/14.80 (descr( 98.17/14.80 Y0) = 98.17/14.80 descr(Y1))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 Y0 = Y1) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i > $o]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i > $o]: 98.17/14.80 (( 98.17/14.80 !!(( 98.17/14.80 ^[Y4 : $i]: 98.17/14.80 (in(Y4, 98.17/14.80 Y0) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y5 : $i]: 98.17/14.80 (in(Y5, 98.17/14.80 Y1) => 98.17/14.80 (( 98.17/14.80 Y4 = Y5) => 98.17/14.80 (Y2(Y4) <=> 98.17/14.80 Y3(Y5))))))))))) => 98.17/14.80 (dsetconstr( 98.17/14.80 Y0, Y2) = 98.17/14.80 dsetconstr( 98.17/14.80 Y1, Y3)))))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 !!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 in(Y2, 98.17/14.80 Y1))))) => 98.17/14.80 subset( 98.17/14.80 Y0, Y1)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 Y0 = Y1) => 98.17/14.80 subset( 98.17/14.80 Y1, Y0)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 Y0 = Y1) => 98.17/14.80 subset( 98.17/14.80 Y0, Y1)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 !!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 in(Y2, 98.17/14.80 Y1))))) => 98.17/14.80 subset( 98.17/14.80 Y0, Y1)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!( 98.17/14.80 subset( 98.17/14.80 emptyset))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (subset( 98.17/14.80 Y0, Y1) => 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 in(Y2, 98.17/14.80 Y1)))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (subset( 98.17/14.80 Y0, Y1) => 98.17/14.80 (( 98.17/14.80 ~( 98.17/14.80 in(Y2, 98.17/14.80 Y1))) => 98.17/14.80 (~( 98.17/14.80 in(Y2, 98.17/14.80 Y0)))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (( 98.17/14.80 ~( 98.17/14.80 in(Y2, 98.17/14.80 Y1))) => 98.17/14.80 (~( 98.17/14.80 subset( 98.17/14.80 Y0, Y1)))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 ~( 98.17/14.80 subset( 98.17/14.80 Y0, Y1))) => 98.17/14.80 (Y0 != Y1)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (( 98.17/14.80 ~( 98.17/14.80 in(Y2, 98.17/14.80 Y1))) => 98.17/14.80 (Y0 != Y1)))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 subset( 98.17/14.80 Y0, Y0)))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (subset( 98.17/14.80 Y0, Y1) => 98.17/14.80 (subset( 98.17/14.80 Y1, Y2) => 98.17/14.80 subset( 98.17/14.80 Y0, Y2)))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 subset( 98.17/14.80 Y1, 98.17/14.80 setadjoin( 98.17/14.80 Y0, Y1)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (subset( 98.17/14.80 Y0, Y2) => 98.17/14.80 subset( 98.17/14.80 Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, Y2)))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (subset( 98.17/14.80 Y0, Y1) => 98.17/14.80 in(Y0, 98.17/14.80 powerset( 98.17/14.80 Y1))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (subset( 98.17/14.80 Y0, Y1) => 98.17/14.80 (subset( 98.17/14.80 Y1, Y0) => 98.17/14.80 (Y0 = Y1))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (subset( 98.17/14.80 Y0, 98.17/14.80 emptyset) => 98.17/14.80 (Y0 = 98.17/14.80 emptyset))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (subset( 98.17/14.80 Y1, Y0) => 98.17/14.80 in(Y1, 98.17/14.80 powerset( 98.17/14.80 Y0))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (in(Y1, 98.17/14.80 powerset( 98.17/14.80 Y0)) => 98.17/14.80 subset( 98.17/14.80 Y1, Y0)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 in(Y0, 98.17/14.80 powerset( 98.17/14.80 Y0))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (subset( 98.17/14.80 Y0, Y1) => 98.17/14.80 subset( 98.17/14.80 powerset( 98.17/14.80 Y0), 98.17/14.80 powerset( 98.17/14.80 Y1))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i > $o]: 98.17/14.80 in( 98.17/14.80 dsetconstr( 98.17/14.80 Y0, Y1), 98.17/14.80 powerset( 98.17/14.80 Y0)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i > $o]: 98.17/14.80 subset( 98.17/14.80 dsetconstr( 98.17/14.80 Y0, Y1), 98.17/14.80 Y0))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 in(Y2, 98.17/14.80 binunion( 98.17/14.80 Y0, Y1)))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 in(Y1, 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y1) => 98.17/14.80 in(Y2, 98.17/14.80 binunion( 98.17/14.80 Y0, Y1)))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $o]: 98.17/14.80 (in(Y2, 98.17/14.80 binunion( 98.17/14.80 Y0, Y1)) => 98.17/14.80 (( 98.17/14.80 in(Y2, 98.17/14.80 Y0) => Y3) => 98.17/14.80 (( 98.17/14.80 in(Y2, 98.17/14.80 Y1) => Y3) => 98.17/14.80 Y3))))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 binunion( 98.17/14.80 Y0, Y1)) => 98.17/14.80 (in(Y2, 98.17/14.80 Y1) | 98.17/14.80 in(Y2, 98.17/14.80 Y0)))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 subset( 98.17/14.80 Y0, 98.17/14.80 binunion( 98.17/14.80 Y0, Y1)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 subset( 98.17/14.80 Y1, 98.17/14.80 binunion( 98.17/14.80 Y0, Y1)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (in(Y2, 98.17/14.80 Y1) => 98.17/14.80 in(Y2, 98.17/14.80 binintersect( 98.17/14.80 Y0, Y1))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (subset( 98.17/14.80 Y2, Y0) => 98.17/14.80 (subset( 98.17/14.80 Y2, Y1) => 98.17/14.80 subset( 98.17/14.80 Y2, 98.17/14.80 binintersect( 98.17/14.80 Y0, Y1))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 binintersect( 98.17/14.80 Y0, Y1)) => 98.17/14.80 in(Y2, 98.17/14.80 Y0))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 subset( 98.17/14.80 binintersect( 98.17/14.80 Y0, Y1), 98.17/14.80 Y0))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (subset( 98.17/14.80 Y0, Y1) => 98.17/14.80 (binintersect( 98.17/14.80 Y0, Y1) = 98.17/14.80 Y0)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 binintersect( 98.17/14.80 Y0, Y1) = 98.17/14.80 Y1) => 98.17/14.80 subset( 98.17/14.80 Y1, Y0)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 binintersect( 98.17/14.80 Y0, Y1)) => 98.17/14.80 in(Y2, 98.17/14.80 Y1))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 ~(( 98.17/14.80 ??(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) & 98.17/14.80 in(Y2, 98.17/14.80 Y1))))))) => 98.17/14.80 (binintersect( 98.17/14.80 Y0, Y1) = 98.17/14.80 emptyset)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 subset( 98.17/14.80 binintersect( 98.17/14.80 Y0, Y1), 98.17/14.80 Y1))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (subset( 98.17/14.80 Y1, Y0) => 98.17/14.80 (binintersect( 98.17/14.80 Y0, Y1) = 98.17/14.80 Y1)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 binintersect( 98.17/14.80 Y0, Y1) = 98.17/14.80 Y0) => 98.17/14.80 subset( 98.17/14.80 Y0, Y1)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (binintersect( 98.17/14.80 Y0, 98.17/14.80 binunion( 98.17/14.80 Y1, Y2)) = 98.17/14.80 binunion( 98.17/14.80 binintersect( 98.17/14.80 Y0, Y1), 98.17/14.80 binintersect( 98.17/14.80 Y0, Y2)))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (( 98.17/14.80 ~( 98.17/14.80 in(Y2, 98.17/14.80 Y1))) => 98.17/14.80 in(Y2, 98.17/14.80 setminus( 98.17/14.80 Y0, Y1))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 setminus( 98.17/14.80 Y0, Y1)) => 98.17/14.80 in(Y2, 98.17/14.80 Y0))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 setminus( 98.17/14.80 Y0, Y1)) => 98.17/14.80 (~( 98.17/14.80 in(Y2, 98.17/14.80 Y1))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (subset( 98.17/14.80 Y0, Y1) => 98.17/14.80 (setminus( 98.17/14.80 Y0, Y1) = 98.17/14.80 emptyset)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (( 98.17/14.80 ~( 98.17/14.80 in(Y2, 98.17/14.80 setminus( 98.17/14.80 Y0, Y1)))) => 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 in(Y2, 98.17/14.80 Y1)))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (( 98.17/14.80 ~( 98.17/14.80 in(Y2, 98.17/14.80 setminus( 98.17/14.80 Y0, Y1)))) => 98.17/14.80 (( 98.17/14.80 ~( 98.17/14.80 in(Y2, 98.17/14.80 Y1))) => 98.17/14.80 (~( 98.17/14.80 in(Y2, 98.17/14.80 Y0)))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (( 98.17/14.80 ~( 98.17/14.80 in(Y2, 98.17/14.80 Y0))) => 98.17/14.80 (~( 98.17/14.80 in(Y2, 98.17/14.80 setminus( 98.17/14.80 Y0, Y1)))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y1) => 98.17/14.80 (~( 98.17/14.80 in(Y2, 98.17/14.80 setminus( 98.17/14.80 Y0, Y1)))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 subset( 98.17/14.80 setminus( 98.17/14.80 Y0, Y1), 98.17/14.80 Y0))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 setminus( 98.17/14.80 Y0, Y1) = 98.17/14.80 emptyset) => 98.17/14.80 subset( 98.17/14.80 Y0, Y1)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 symdiff( 98.17/14.80 Y0, Y1)) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $o]: 98.17/14.80 (( 98.17/14.80 in(Y2, 98.17/14.80 Y0) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 ~( 98.17/14.80 in(Y2, 98.17/14.80 Y1))) => 98.17/14.80 Y3)) => 98.17/14.80 (( 98.17/14.80 ( 98.17/14.80 ~( 98.17/14.80 in(Y2, 98.17/14.80 Y0))) => 98.17/14.80 ( 98.17/14.80 in(Y2, 98.17/14.80 Y1) => Y3)) => 98.17/14.80 Y3))))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (( 98.17/14.80 ~( 98.17/14.80 in(Y2, 98.17/14.80 Y1))) => 98.17/14.80 in(Y2, 98.17/14.80 symdiff( 98.17/14.80 Y0, Y1))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (( 98.17/14.80 ~( 98.17/14.80 in(Y2, 98.17/14.80 Y0))) => 98.17/14.80 (in(Y2, 98.17/14.80 Y1) => 98.17/14.80 in(Y2, 98.17/14.80 symdiff( 98.17/14.80 Y0, Y1))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (in(Y2, 98.17/14.80 Y1) => 98.17/14.80 (~( 98.17/14.80 in(Y2, 98.17/14.80 symdiff( 98.17/14.80 Y0, Y1))))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (( 98.17/14.80 ~( 98.17/14.80 in(Y2, 98.17/14.80 Y0))) => 98.17/14.80 (( 98.17/14.80 ~( 98.17/14.80 in(Y2, 98.17/14.80 Y1))) => 98.17/14.80 (~( 98.17/14.80 in(Y2, 98.17/14.80 symdiff( 98.17/14.80 Y0, Y1))))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 in(Y1, 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 in(Y0, 98.17/14.80 setunion( 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset)), 98.17/14.80 emptyset)))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 in(Y1, 98.17/14.80 setunion( 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset)), 98.17/14.80 emptyset)))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (??(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 setunion( 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset)), 98.17/14.80 emptyset)))) & 98.17/14.80 (??(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (in(Y3, 98.17/14.80 setunion( 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset)), 98.17/14.80 emptyset)))) & 98.17/14.80 (setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset)), 98.17/14.80 emptyset)) = 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 setadjoin( 98.17/14.80 Y3, 98.17/14.80 emptyset)), 98.17/14.80 emptyset))))))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (??(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 setunion( 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset)), 98.17/14.80 emptyset)))) & 98.17/14.80 (??(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (in(Y3, 98.17/14.80 setunion( 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset)), 98.17/14.80 emptyset)))) & 98.17/14.80 (setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset)), 98.17/14.80 emptyset)) = 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 setadjoin( 98.17/14.80 Y3, 98.17/14.80 emptyset)), 98.17/14.80 emptyset))))))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (in(Y1, 98.17/14.80 Y0) => 98.17/14.80 subset( 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset), 98.17/14.80 Y0)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (in(Y1, 98.17/14.80 Y0) => 98.17/14.80 in( 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset), 98.17/14.80 powerset( 98.17/14.80 Y0))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 in( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 emptyset), 98.17/14.80 powerset( 98.17/14.80 binunion( 98.17/14.80 Y0, Y1))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset))) => 98.17/14.80 (( 98.17/14.80 Y2 = Y1) | 98.17/14.80 (Y2 = Y0)))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (in(Y3, 98.17/14.80 Y1) => 98.17/14.80 subset( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 setadjoin( 98.17/14.80 Y3, 98.17/14.80 emptyset)), 98.17/14.80 binunion( 98.17/14.80 Y0, Y1)))))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (in(Y3, 98.17/14.80 Y1) => 98.17/14.80 in( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 setadjoin( 98.17/14.80 Y3, 98.17/14.80 emptyset)), 98.17/14.80 powerset( 98.17/14.80 binunion( 98.17/14.80 Y0, Y1))))))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (in(Y3, 98.17/14.80 Y1) => 98.17/14.80 subset( 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 setadjoin( 98.17/14.80 Y3, 98.17/14.80 emptyset)), 98.17/14.80 emptyset)), 98.17/14.80 powerset( 98.17/14.80 binunion( 98.17/14.80 Y0, Y1))))))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (in(Y3, 98.17/14.80 Y1) => 98.17/14.80 in( 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 setadjoin( 98.17/14.80 Y3, 98.17/14.80 emptyset)), 98.17/14.80 emptyset)), 98.17/14.80 powerset( 98.17/14.80 powerset( 98.17/14.80 binunion( 98.17/14.80 Y0, Y1)))))))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (in(Y3, 98.17/14.80 Y1) => 98.17/14.80 in( 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 setadjoin( 98.17/14.80 Y3, 98.17/14.80 emptyset)), 98.17/14.80 emptyset)), 98.17/14.80 powerset( 98.17/14.80 powerset( 98.17/14.80 binunion( 98.17/14.80 Y0, Y1)))))))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (in(Y3, 98.17/14.80 Y1) => 98.17/14.80 in( 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 setadjoin( 98.17/14.80 Y3, 98.17/14.80 emptyset)), 98.17/14.80 emptyset)), 98.17/14.80 dsetconstr( 98.17/14.80 powerset( 98.17/14.80 powerset( 98.17/14.80 binunion( 98.17/14.80 Y0, Y1))), 98.17/14.80 (^[Y4 : $i]: 98.17/14.80 (??(( 98.17/14.80 ^[Y5 : $i]: 98.17/14.80 (in(Y5, 98.17/14.80 Y0) & 98.17/14.80 (??(( 98.17/14.80 ^[Y6 : $i]: 98.17/14.80 (in(Y6, 98.17/14.80 Y1) & 98.17/14.80 (Y4 = 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y5, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y5, 98.17/14.80 setadjoin( 98.17/14.80 Y6, 98.17/14.80 emptyset)), 98.17/14.80 emptyset)))))))))))))))))))))))))))) => 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 dsetconstr( 98.17/14.80 powerset( 98.17/14.80 powerset( 98.17/14.80 binunion( 98.17/14.80 Y0, Y1))), 98.17/14.80 (^[Y3 : $i]: 98.17/14.80 (??(( 98.17/14.80 ^[Y4 : $i]: 98.17/14.80 (in(Y4, 98.17/14.80 Y0) & 98.17/14.80 (??(( 98.17/14.80 ^[Y5 : $i]: 98.17/14.80 (in(Y5, 98.17/14.80 Y1) & 98.17/14.80 (Y3 = 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y4, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y4, 98.17/14.80 setadjoin( 98.17/14.80 Y5, 98.17/14.80 emptyset)), 98.17/14.80 emptyset)))))))))))))) => 98.17/14.80 (??(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (( 98.17/14.80 ??(( 98.17/14.80 ^[Y4 : $i]: 98.17/14.80 (in(Y4, 98.17/14.80 Y1) & 98.17/14.80 (Y2 = 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y3, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y3, 98.17/14.80 setadjoin( 98.17/14.80 Y4, 98.17/14.80 emptyset)), 98.17/14.80 emptyset))))))) & 98.17/14.80 in(Y3, 98.17/14.80 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 98.17/14.80 inference('lazy_cnf_imply', [status(thm)], ['163'])). 98.17/14.80 tff('165', plain, 98.17/14.80 ~ ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i]: 98.17/14.80 (in(Y1, setunion(Y0)) <=> 98.17/14.80 (??((^[Y2 : $i]: (in(Y1, Y2) & in(Y2, Y0)))))))))))) => 98.17/14.80 (in(emptyset, omega) => 98.17/14.80 ((!!((^[Y0 : $i]: (in(Y0, omega) => in(setadjoin(Y0, Y0), omega))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (((!!((^[Y1 : $i]: 98.17/14.80 ((in(Y1, Y0) & in(Y1, omega)) => 98.17/14.80 in(setadjoin(Y1, Y1), Y0))))) & 98.17/14.80 in(emptyset, Y0)) => 98.17/14.80 (!!((^[Y1 : $i]: (in(Y1, omega) => in(Y1, Y0))))))))) => 98.17/14.80 ((!!((^[Y0 : ($i * $i) > $o]: 98.17/14.80 (!!((^[Y1 : $i]: 98.17/14.80 ((!!((^[Y2 : $i]: 98.17/14.80 (in(Y2, Y1) => 98.17/14.80 (??((^[Y3 : $i]: 98.17/14.80 (Y0(Y2, Y3) & 98.17/14.80 (!!((^[Y4 : $i]: 98.17/14.80 (Y0(Y2, Y4) => (Y3 = Y4))))))))))))) => 98.17/14.80 (??((^[Y2 : $i]: 98.17/14.80 (!!((^[Y3 : $i]: 98.17/14.80 (in(Y3, Y2) <=> 98.17/14.80 (??((^[Y4 : $i]: 98.17/14.80 (in(Y4, Y1) & Y0(Y4, Y3))))))))))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 98.17/14.80 (??((^[Y1 : $i]: 98.17/14.80 (in(Y1, Y0) & 98.17/14.80 (~((??((^[Y2 : $i]: (in(Y2, Y1) & in(Y2, Y0))))))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (??((^[Y1 : $i]: 98.17/14.80 ((!!((^[Y2 : $i]: 98.17/14.80 (in(Y2, Y1) => 98.17/14.80 (!!((^[Y3 : $i]: 98.17/14.80 (in(Y3, Y2) => in(Y3, Y0)))))))))& 98.17/14.80 (!!((^[Y2 : $i]: 98.17/14.80 (!!((^[Y3 : $i]: 98.17/14.80 ((in(Y3, Y0) & in(Y2, Y0)) => 98.17/14.80 ((!!((^[Y4 : $i]: 98.17/14.80 (in(Y4, Y1) => 98.17/14.80 (in(Y2, Y4) <=> 98.17/14.80 in(Y3, Y4)))))) => 98.17/14.80 (Y2 = Y3)))))))))& 98.17/14.80 (!!((^[Y2 : $i]: 98.17/14.80 (!!((^[Y3 : $i]: 98.17/14.80 ((in(Y3, Y1) & in(Y2, Y1)) => 98.17/14.80 ((!!((^[Y4 : $i]: 98.17/14.80 (in(Y4, Y3) => in(Y4, Y2))))) | 98.17/14.80 (!!((^[Y4 : $i]: 98.17/14.80 (in(Y4, Y2) => in(Y4, Y3)))))))))))))& 98.17/14.80 (!!((^[Y2 : $i]: 98.17/14.80 (((??((^[Y3 : $i]: in(Y3, Y2)))) & 98.17/14.80 (!!((^[Y3 : $i]: 98.17/14.80 (in(Y3, Y2) => in(Y3, Y0)))))) => 98.17/14.80 (??((^[Y3 : $i]: 98.17/14.80 (??((^[Y4 : $i]: 98.17/14.80 (in(Y3, Y1)&in(Y4, Y2)& 98.17/14.80 (~((??((^[Y5 : $i]: 98.17/14.80 (in(Y5, Y3) & 98.17/14.80 in(Y5, Y2)))))))& 98.17/14.80 (!!((^[Y5 : $i]: 98.17/14.80 (in(Y5, Y1) => 98.17/14.80 (in(Y4, Y5) | 98.17/14.80 (!!((^[Y6 : $i]: 98.17/14.80 (in(Y6, 98.17/14.80 Y5) => 98.17/14.80 in(Y6, 98.17/14.80 Y3)))))))))))))))))))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i > $o]: 98.17/14.80 ((??((^[Y1 : $i]: 98.17/14.80 (Y0(Y1) & 98.17/14.80 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 98.17/14.80 Y0(descr(Y0)))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i > $o]: 98.17/14.80 (!!((^[Y2 : $i]: 98.17/14.80 (in(Y2, Y0) => 98.17/14.80 (Y1(Y2) => in(Y2, dsetconstr(Y0, Y1))))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i > $o]: 98.17/14.80 (!!((^[Y2 : $i]: 98.17/14.80 (in(Y2, dsetconstr(Y0, Y1)) => 98.17/14.80 in(Y2, Y0))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i > $o]: 98.17/14.80 (!!((^[Y2 : $i]: 98.17/14.80 (in(Y2, dsetconstr(Y0, Y1)) => Y1(Y2))))))))))) => 98.17/14.80 ((!!((^[Y0 : $o]: 98.17/14.80 (!!((^[Y1 : $i]: (in(Y1, prop2set(Y0)) => Y0))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (in(Y0, emptyset) => (!!((^[Y1 : $o]: Y1))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 98.17/14.80 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 98.17/14.80 ((!!((^[Y0 : $i > $o]: 98.17/14.80 ((??((^[Y1 : $i]: 98.17/14.80 (Y0(Y1) & 98.17/14.80 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 98.17/14.80 (??(Y0)))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i]: 98.17/14.80 ((!!((^[Y2 : $i]: 98.17/14.80 (in(Y2, Y0) => in(Y2, Y1))))) => 98.17/14.80 ((!!((^[Y2 : $i]: 98.17/14.80 (in(Y2, Y1) => in(Y2, Y0))))) => 98.17/14.80 (Y0 = Y1))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 98.17/14.80 (Y0 = emptyset))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 98.17/14.80 (Y0 = emptyset))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i > $o]: 98.17/14.80 (!!((^[Y2 : $i]: 98.17/14.80 (in(Y2, Y0) => 98.17/14.80 (in(Y2, dsetconstr(Y0, Y1)) <=> 98.17/14.80 Y1(Y2)))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 ((Y0 != emptyset) => 98.17/14.80 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i > $o]: 98.17/14.80 (!!((^[Y2 : $i]: 98.17/14.80 (in(Y2, Y0) => 98.17/14.80 (Y1(Y2) => 98.17/14.80 (dsetconstr(Y0, Y1) != 98.17/14.80 emptyset)))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 98.17/14.80 (Y0 != emptyset))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i]: 98.17/14.80 in(Y0, setadjoin(Y0, Y1)))))))) => 98.17/14.80 (in(emptyset, setadjoin(emptyset, emptyset)) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i]: 98.17/14.80 (!!((^[Y2 : $i]: 98.17/14.80 (in(Y2, Y1) => 98.17/14.80 in(Y2, 98.17/14.80 setadjoin(Y0, Y1)))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i]: 98.17/14.80 (!!((^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 setadjoin(Y0, Y1)) => 98.17/14.80 (!!((^[Y3 : $o]: 98.17/14.80 (((Y2 = Y0) => 98.17/14.80 Y3) => 98.17/14.80 ((in(Y2, Y1) => 98.17/14.80 Y3) => 98.17/14.80 Y3))))))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i]: 98.17/14.80 (!!((^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 setadjoin(Y0, Y1)) => 98.17/14.80 (in(Y2, Y1) | 98.17/14.80 (Y2 = Y0)))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (dsetconstr(Y0, 98.17/14.80 (^[Y1 : $i]: $true)) = 98.17/14.80 Y0)))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i]: 98.17/14.80 ((!!((^[Y2 : $i]: 98.17/14.80 (in(Y2, Y1) => 98.17/14.80 in(Y2, Y0))))) => 98.17/14.80 in(Y1, powerset(Y0))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 in(emptyset, powerset(Y0))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 in(emptyset, powerset(Y0))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i]: 98.17/14.80 (!!((^[Y2 : $i]: 98.17/14.80 (in(Y1, 98.17/14.80 powerset(Y0)) => 98.17/14.80 (in(Y2, Y1) => 98.17/14.80 in(Y2, Y0)))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i]: 98.17/14.80 (!!((^[Y2 : $i]: 98.17/14.80 (in(Y1, Y2) => 98.17/14.80 (in(Y2, Y0) => 98.17/14.80 in(Y1, 98.17/14.80 setunion(Y0))))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i]: 98.17/14.80 (in(Y1, setunion(Y0)) => 98.17/14.80 (!!((^[Y2 : $o]: 98.17/14.80 ((!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (in(Y1, 98.17/14.80 Y3) => 98.17/14.80 ( 98.17/14.80 in(Y3, 98.17/14.80 Y0) => Y2))))) => 98.17/14.80 Y2))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i]: 98.17/14.80 (in(Y1, Y0) => 98.17/14.80 in(Y1, 98.17/14.80 powerset( 98.17/14.80 setunion(Y0)))))))))) => 98.17/14.80 ((!!((^[Y0 : $i > $o]: 98.17/14.80 ((??((^[Y1 : $i]: 98.17/14.80 (Y0(Y1) & 98.17/14.80 (!!((^[Y2 : $i]: 98.17/14.80 (Y0(Y2) => 98.17/14.80 (Y1 = Y2))))))))) => 98.17/14.80 (??((^[Y1 : $i]: 98.17/14.80 (!!((^[Y2 : $i]: 98.17/14.80 (Y0(Y2) <=> 98.17/14.80 (Y2 = Y1)))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 ((Y0 != emptyset) => 98.17/14.80 (??((^[Y1 : $i]: 98.17/14.80 in(Y1, Y0)))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i]: 98.17/14.80 (in(Y0, 98.17/14.80 setadjoin(Y1, 98.17/14.80 emptyset)) => 98.17/14.80 (Y0 = Y1)))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i]: 98.17/14.80 ((Y0 != Y1) => 98.17/14.80 (~(in(Y1, 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 emptyset))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i]: 98.17/14.80 ((Y0 = Y1) => 98.17/14.80 in(Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i]: 98.17/14.80 (in(Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset)) => 98.17/14.80 in(Y1, 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 emptyset))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i]: 98.17/14.80 (!!((^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset))) => 98.17/14.80 (( 98.17/14.80 Y2 = Y1) | 98.17/14.80 (Y2 = Y0)))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i]: 98.17/14.80 in(Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i]: 98.17/14.80 in(Y1, 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i > $o]: 98.17/14.80 ((??(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) & 98.17/14.80 Y1(Y2))))) => 98.17/14.80 (dsetconstr( 98.17/14.80 Y0, Y1) != 98.17/14.80 emptyset)))))))) => 98.17/14.80 ((!!((^[Y0 : $i > $o]: 98.17/14.80 (!!((^[Y1 : $i]: 98.17/14.80 (in(Y1, 98.17/14.80 emptyset) => 98.17/14.80 Y0(Y1)))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i > $o]: 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 ~(( 98.17/14.80 !!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 Y1(Y2))))))) => 98.17/14.80 ( 98.17/14.80 ??(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) & 98.17/14.80 (~( 98.17/14.80 Y1(Y2)))))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i > $o]: 98.17/14.80 (( 98.17/14.80 !!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (~( 98.17/14.80 Y1(Y2))))))) => 98.17/14.80 (~(( 98.17/14.80 ??(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) & 98.17/14.80 Y1(Y2)))))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i > $o]: 98.17/14.80 (( 98.17/14.80 ~(( 98.17/14.80 ??(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) & 98.17/14.80 Y1(Y2))))))) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (~( 98.17/14.80 Y1(Y2)))))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i > $o]: 98.17/14.80 (( 98.17/14.80 ??(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) & 98.17/14.80 (~( 98.17/14.80 Y1(Y2))))))) => 98.17/14.80 ( 98.17/14.80 ~(( 98.17/14.80 !!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 Y1(Y2)))))))))))))) => 98.17/14.80 ((!!((^[Y0 : $o]: 98.17/14.80 (Y0 => 98.17/14.80 in( 98.17/14.80 emptyset, 98.17/14.80 prop2set( 98.17/14.80 Y0)))))) => 98.17/14.80 ((!!((^[Y0 : $o]: 98.17/14.80 (Y0 => 98.17/14.80 set2prop( 98.17/14.80 prop2set( 98.17/14.80 Y0)))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i > $o]: 98.17/14.80 (( 98.17/14.80 ~(( 98.17/14.80 ??(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) & 98.17/14.80 Y1(Y2))))))) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (~( 98.17/14.80 Y1(Y2)))))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y1 : $i > $o]: 98.17/14.80 (( 98.17/14.80 ~(( 98.17/14.80 !!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 Y1(Y2))))))) => 98.17/14.80 (??(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) & 98.17/14.80 (~( 98.17/14.80 Y1(Y2)))))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i > $o]: 98.17/14.80 (( 98.17/14.80 ??(Y0)) => 98.17/14.80 (( 98.17/14.80 !!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (Y0(Y1) => 98.17/14.80 (Y0(Y2) => 98.17/14.80 (Y1 = Y2))))))))) => 98.17/14.80 (??(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (Y0(Y1) & 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (Y0(Y2) => 98.17/14.80 (Y1 = Y2)))))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i > $o]: 98.17/14.80 (( 98.17/14.80 ??(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (Y0(Y2) <=> 98.17/14.80 (Y2 = Y1)))))))) => 98.17/14.80 (??(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (Y0(Y1) & 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (Y0(Y2) => 98.17/14.80 (Y1 = Y2))))))))))))) => 98.17/14.80 ((!!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 Y0 = Y1) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (( 98.17/14.80 Y2 = Y3) => 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 in(Y3, 98.17/14.80 Y1)))))))))))))))) => 98.17/14.80 ((!!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 Y0 = Y1) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (( 98.17/14.80 Y2 = Y3) => 98.17/14.80 (in(Y2, 98.17/14.80 Y0) <=> 98.17/14.80 in(Y3, 98.17/14.80 Y1)))))))))))))))) => 98.17/14.80 ((!!(( 98.17/14.80 ^[Y0 : $i > $o]: 98.17/14.80 (( 98.17/14.80 ??(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (Y0(Y1) & 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (Y0(Y2) => 98.17/14.80 (Y1 = Y2))))))))) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (Y0(Y1) => 98.17/14.80 (Y0(Y2) => 98.17/14.80 (Y1 = Y2))))))))))))) => 98.17/14.80 ((!!(( 98.17/14.80 ^[Y0 : $i > $o]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i > $o]: 98.17/14.80 (( 98.17/14.80 !!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (( 98.17/14.80 Y2 = Y3) => 98.17/14.80 (Y0(Y2) <=> 98.17/14.80 Y1(Y3))))))))) => 98.17/14.80 (( 98.17/14.80 ??(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (Y0(Y2) & 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (Y0(Y3) => 98.17/14.80 (Y2 = Y3))))))))) <=> 98.17/14.80 (??(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (Y1(Y2) & 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (Y1(Y3) => 98.17/14.80 (Y2 = Y3))))))))))))))))) => 98.17/14.80 (( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 Y0 = Y1) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (( 98.17/14.80 Y2 = Y3) => 98.17/14.80 (setadjoin( 98.17/14.80 Y0, Y2) = 98.17/14.80 setadjoin( 98.17/14.80 Y1, Y3)))))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 Y0 = Y1) => 98.17/14.80 (powerset( 98.17/14.80 Y0) = 98.17/14.80 powerset( 98.17/14.80 Y1))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 Y0 = Y1) => 98.17/14.80 (setunion( 98.17/14.80 Y0) = 98.17/14.80 setunion( 98.17/14.80 Y1))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i > $o]: 98.17/14.80 (( 98.17/14.80 ??(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (Y0(Y1) & 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (Y0(Y2) => 98.17/14.80 (Y1 = Y2))))))))) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (Y0(Y1) => 98.17/14.80 (Y0(Y2) => 98.17/14.80 (Y1 = Y2))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i > $o]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i > $o]: 98.17/14.80 (( 98.17/14.80 !!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (( 98.17/14.80 Y2 = Y3) => 98.17/14.80 (Y0(Y2) <=> 98.17/14.80 Y1(Y3))))))))) => 98.17/14.80 (( 98.17/14.80 ??(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (Y0(Y2) & 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (Y0(Y3) => 98.17/14.80 (Y2 = Y3))))))))) => 98.17/14.80 (( 98.17/14.80 ??(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (Y1(Y2) & 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (Y1(Y3) => 98.17/14.80 (Y2 = Y3))))))))) => 98.17/14.80 (descr( 98.17/14.80 Y0) = 98.17/14.80 descr(Y1))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 Y0 = Y1) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i > $o]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i > $o]: 98.17/14.80 (( 98.17/14.80 !!(( 98.17/14.80 ^[Y4 : $i]: 98.17/14.80 (in(Y4, 98.17/14.80 Y0) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y5 : $i]: 98.17/14.80 (in(Y5, 98.17/14.80 Y1) => 98.17/14.80 (( 98.17/14.80 Y4 = Y5) => 98.17/14.80 (Y2(Y4) <=> 98.17/14.80 Y3(Y5))))))))))) => 98.17/14.80 (dsetconstr( 98.17/14.80 Y0, Y2) = 98.17/14.80 dsetconstr( 98.17/14.80 Y1, Y3)))))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 !!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 in(Y2, 98.17/14.80 Y1))))) => 98.17/14.80 subset( 98.17/14.80 Y0, Y1)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 Y0 = Y1) => 98.17/14.80 subset( 98.17/14.80 Y1, Y0)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 Y0 = Y1) => 98.17/14.80 subset( 98.17/14.80 Y0, Y1)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 !!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 in(Y2, 98.17/14.80 Y1))))) => 98.17/14.80 subset( 98.17/14.80 Y0, Y1)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!( 98.17/14.80 subset( 98.17/14.80 emptyset))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (subset( 98.17/14.80 Y0, Y1) => 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 in(Y2, 98.17/14.80 Y1)))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (subset( 98.17/14.80 Y0, Y1) => 98.17/14.80 (( 98.17/14.80 ~( 98.17/14.80 in(Y2, 98.17/14.80 Y1))) => 98.17/14.80 (~( 98.17/14.80 in(Y2, 98.17/14.80 Y0)))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (( 98.17/14.80 ~( 98.17/14.80 in(Y2, 98.17/14.80 Y1))) => 98.17/14.80 (~( 98.17/14.80 subset( 98.17/14.80 Y0, Y1)))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 ~( 98.17/14.80 subset( 98.17/14.80 Y0, Y1))) => 98.17/14.80 (Y0 != Y1)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (( 98.17/14.80 ~( 98.17/14.80 in(Y2, 98.17/14.80 Y1))) => 98.17/14.80 (Y0 != Y1)))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 subset( 98.17/14.80 Y0, Y0)))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (subset( 98.17/14.80 Y0, Y1) => 98.17/14.80 (subset( 98.17/14.80 Y1, Y2) => 98.17/14.80 subset( 98.17/14.80 Y0, Y2)))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 subset( 98.17/14.80 Y1, 98.17/14.80 setadjoin( 98.17/14.80 Y0, Y1)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (subset( 98.17/14.80 Y0, Y2) => 98.17/14.80 subset( 98.17/14.80 Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, Y2)))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (subset( 98.17/14.80 Y0, Y1) => 98.17/14.80 in(Y0, 98.17/14.80 powerset( 98.17/14.80 Y1))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (subset( 98.17/14.80 Y0, Y1) => 98.17/14.80 (subset( 98.17/14.80 Y1, Y0) => 98.17/14.80 (Y0 = Y1))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (subset( 98.17/14.80 Y0, 98.17/14.80 emptyset) => 98.17/14.80 (Y0 = 98.17/14.80 emptyset))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (subset( 98.17/14.80 Y1, Y0) => 98.17/14.80 in(Y1, 98.17/14.80 powerset( 98.17/14.80 Y0))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (in(Y1, 98.17/14.80 powerset( 98.17/14.80 Y0)) => 98.17/14.80 subset( 98.17/14.80 Y1, Y0)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 in(Y0, 98.17/14.80 powerset( 98.17/14.80 Y0))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (subset( 98.17/14.80 Y0, Y1) => 98.17/14.80 subset( 98.17/14.80 powerset( 98.17/14.80 Y0), 98.17/14.80 powerset( 98.17/14.80 Y1))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i > $o]: 98.17/14.80 in( 98.17/14.80 dsetconstr( 98.17/14.80 Y0, Y1), 98.17/14.80 powerset( 98.17/14.80 Y0)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i > $o]: 98.17/14.80 subset( 98.17/14.80 dsetconstr( 98.17/14.80 Y0, Y1), 98.17/14.80 Y0))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 in(Y2, 98.17/14.80 binunion( 98.17/14.80 Y0, Y1)))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 in(Y1, 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y1) => 98.17/14.80 in(Y2, 98.17/14.80 binunion( 98.17/14.80 Y0, Y1)))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $o]: 98.17/14.80 (in(Y2, 98.17/14.80 binunion( 98.17/14.80 Y0, Y1)) => 98.17/14.80 (( 98.17/14.80 in(Y2, 98.17/14.80 Y0) => Y3) => 98.17/14.80 (( 98.17/14.80 in(Y2, 98.17/14.80 Y1) => Y3) => 98.17/14.80 Y3))))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 binunion( 98.17/14.80 Y0, Y1)) => 98.17/14.80 (in(Y2, 98.17/14.80 Y1) | 98.17/14.80 in(Y2, 98.17/14.80 Y0)))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 subset( 98.17/14.80 Y0, 98.17/14.80 binunion( 98.17/14.80 Y0, Y1)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 subset( 98.17/14.80 Y1, 98.17/14.80 binunion( 98.17/14.80 Y0, Y1)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (in(Y2, 98.17/14.80 Y1) => 98.17/14.80 in(Y2, 98.17/14.80 binintersect( 98.17/14.80 Y0, Y1))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (subset( 98.17/14.80 Y2, Y0) => 98.17/14.80 (subset( 98.17/14.80 Y2, Y1) => 98.17/14.80 subset( 98.17/14.80 Y2, 98.17/14.80 binintersect( 98.17/14.80 Y0, Y1))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 binintersect( 98.17/14.80 Y0, Y1)) => 98.17/14.80 in(Y2, 98.17/14.80 Y0))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 subset( 98.17/14.80 binintersect( 98.17/14.80 Y0, Y1), 98.17/14.80 Y0))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (subset( 98.17/14.80 Y0, Y1) => 98.17/14.80 (binintersect( 98.17/14.80 Y0, Y1) = 98.17/14.80 Y0)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 binintersect( 98.17/14.80 Y0, Y1) = 98.17/14.80 Y1) => 98.17/14.80 subset( 98.17/14.80 Y1, Y0)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 binintersect( 98.17/14.80 Y0, Y1)) => 98.17/14.80 in(Y2, 98.17/14.80 Y1))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 ~(( 98.17/14.80 ??(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) & 98.17/14.80 in(Y2, 98.17/14.80 Y1))))))) => 98.17/14.80 (binintersect( 98.17/14.80 Y0, Y1) = 98.17/14.80 emptyset)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 subset( 98.17/14.80 binintersect( 98.17/14.80 Y0, Y1), 98.17/14.80 Y1))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (subset( 98.17/14.80 Y1, Y0) => 98.17/14.80 (binintersect( 98.17/14.80 Y0, Y1) = 98.17/14.80 Y1)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 binintersect( 98.17/14.80 Y0, Y1) = 98.17/14.80 Y0) => 98.17/14.80 subset( 98.17/14.80 Y0, Y1)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (binintersect( 98.17/14.80 Y0, 98.17/14.80 binunion( 98.17/14.80 Y1, Y2)) = 98.17/14.80 binunion( 98.17/14.80 binintersect( 98.17/14.80 Y0, Y1), 98.17/14.80 binintersect( 98.17/14.80 Y0, Y2)))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (( 98.17/14.80 ~( 98.17/14.80 in(Y2, 98.17/14.80 Y1))) => 98.17/14.80 in(Y2, 98.17/14.80 setminus( 98.17/14.80 Y0, Y1))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 setminus( 98.17/14.80 Y0, Y1)) => 98.17/14.80 in(Y2, 98.17/14.80 Y0))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 setminus( 98.17/14.80 Y0, Y1)) => 98.17/14.80 (~( 98.17/14.80 in(Y2, 98.17/14.80 Y1))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (subset( 98.17/14.80 Y0, Y1) => 98.17/14.80 (setminus( 98.17/14.80 Y0, Y1) = 98.17/14.80 emptyset)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (( 98.17/14.80 ~( 98.17/14.80 in(Y2, 98.17/14.80 setminus( 98.17/14.80 Y0, Y1)))) => 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 in(Y2, 98.17/14.80 Y1)))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (( 98.17/14.80 ~( 98.17/14.80 in(Y2, 98.17/14.80 setminus( 98.17/14.80 Y0, Y1)))) => 98.17/14.80 (( 98.17/14.80 ~( 98.17/14.80 in(Y2, 98.17/14.80 Y1))) => 98.17/14.80 (~( 98.17/14.80 in(Y2, 98.17/14.80 Y0)))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (( 98.17/14.80 ~( 98.17/14.80 in(Y2, 98.17/14.80 Y0))) => 98.17/14.80 (~( 98.17/14.80 in(Y2, 98.17/14.80 setminus( 98.17/14.80 Y0, Y1)))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y1) => 98.17/14.80 (~( 98.17/14.80 in(Y2, 98.17/14.80 setminus( 98.17/14.80 Y0, Y1)))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 subset( 98.17/14.80 setminus( 98.17/14.80 Y0, Y1), 98.17/14.80 Y0))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (( 98.17/14.80 setminus( 98.17/14.80 Y0, Y1) = 98.17/14.80 emptyset) => 98.17/14.80 subset( 98.17/14.80 Y0, Y1)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 symdiff( 98.17/14.80 Y0, Y1)) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $o]: 98.17/14.80 (( 98.17/14.80 in(Y2, 98.17/14.80 Y0) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 ~( 98.17/14.80 in(Y2, 98.17/14.80 Y1))) => 98.17/14.80 Y3)) => 98.17/14.80 (( 98.17/14.80 ( 98.17/14.80 ~( 98.17/14.80 in(Y2, 98.17/14.80 Y0))) => 98.17/14.80 ( 98.17/14.80 in(Y2, 98.17/14.80 Y1) => Y3)) => 98.17/14.80 Y3))))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (( 98.17/14.80 ~( 98.17/14.80 in(Y2, 98.17/14.80 Y1))) => 98.17/14.80 in(Y2, 98.17/14.80 symdiff( 98.17/14.80 Y0, Y1))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (( 98.17/14.80 ~( 98.17/14.80 in(Y2, 98.17/14.80 Y0))) => 98.17/14.80 (in(Y2, 98.17/14.80 Y1) => 98.17/14.80 in(Y2, 98.17/14.80 symdiff( 98.17/14.80 Y0, Y1))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (in(Y2, 98.17/14.80 Y1) => 98.17/14.80 (~( 98.17/14.80 in(Y2, 98.17/14.80 symdiff( 98.17/14.80 Y0, Y1))))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (( 98.17/14.80 ~( 98.17/14.80 in(Y2, 98.17/14.80 Y0))) => 98.17/14.80 (( 98.17/14.80 ~( 98.17/14.80 in(Y2, 98.17/14.80 Y1))) => 98.17/14.80 (~( 98.17/14.80 in(Y2, 98.17/14.80 symdiff( 98.17/14.80 Y0, Y1))))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 in(Y1, 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 in(Y0, 98.17/14.80 setunion( 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset)), 98.17/14.80 emptyset)))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 in(Y1, 98.17/14.80 setunion( 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset)), 98.17/14.80 emptyset)))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (??(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 setunion( 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset)), 98.17/14.80 emptyset)))) & 98.17/14.80 (??(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (in(Y3, 98.17/14.80 setunion( 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset)), 98.17/14.80 emptyset)))) & 98.17/14.80 (setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset)), 98.17/14.80 emptyset)) = 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 setadjoin( 98.17/14.80 Y3, 98.17/14.80 emptyset)), 98.17/14.80 emptyset))))))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (??(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 setunion( 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset)), 98.17/14.80 emptyset)))) & 98.17/14.80 (??(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (in(Y3, 98.17/14.80 setunion( 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset)), 98.17/14.80 emptyset)))) & 98.17/14.80 (setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset)), 98.17/14.80 emptyset)) = 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 setadjoin( 98.17/14.80 Y3, 98.17/14.80 emptyset)), 98.17/14.80 emptyset))))))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (in(Y1, 98.17/14.80 Y0) => 98.17/14.80 subset( 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset), 98.17/14.80 Y0)))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (in(Y1, 98.17/14.80 Y0) => 98.17/14.80 in( 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset), 98.17/14.80 powerset( 98.17/14.80 Y0))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 in( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 emptyset), 98.17/14.80 powerset( 98.17/14.80 binunion( 98.17/14.80 Y0, Y1))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 setadjoin( 98.17/14.80 Y0, 98.17/14.80 setadjoin( 98.17/14.80 Y1, 98.17/14.80 emptyset))) => 98.17/14.80 (( 98.17/14.80 Y2 = Y1) | 98.17/14.80 (Y2 = Y0)))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (in(Y3, 98.17/14.80 Y1) => 98.17/14.80 subset( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 setadjoin( 98.17/14.80 Y3, 98.17/14.80 emptyset)), 98.17/14.80 binunion( 98.17/14.80 Y0, Y1)))))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (in(Y3, 98.17/14.80 Y1) => 98.17/14.80 in( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 setadjoin( 98.17/14.80 Y3, 98.17/14.80 emptyset)), 98.17/14.80 powerset( 98.17/14.80 binunion( 98.17/14.80 Y0, Y1))))))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (in(Y3, 98.17/14.80 Y1) => 98.17/14.80 subset( 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 setadjoin( 98.17/14.80 Y3, 98.17/14.80 emptyset)), 98.17/14.80 emptyset)), 98.17/14.80 powerset( 98.17/14.80 binunion( 98.17/14.80 Y0, Y1))))))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (in(Y3, 98.17/14.80 Y1) => 98.17/14.80 in( 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 setadjoin( 98.17/14.80 Y3, 98.17/14.80 emptyset)), 98.17/14.80 emptyset)), 98.17/14.80 powerset( 98.17/14.80 powerset( 98.17/14.80 binunion( 98.17/14.80 Y0, Y1)))))))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (in(Y3, 98.17/14.80 Y1) => 98.17/14.80 in( 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 setadjoin( 98.17/14.80 Y3, 98.17/14.80 emptyset)), 98.17/14.80 emptyset)), 98.17/14.80 powerset( 98.17/14.80 powerset( 98.17/14.80 binunion( 98.17/14.80 Y0, Y1)))))))))))))))))) => 98.17/14.80 ( 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 Y0) => 98.17/14.80 (!!(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (in(Y3, 98.17/14.80 Y1) => 98.17/14.80 in( 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y2, 98.17/14.80 setadjoin( 98.17/14.80 Y3, 98.17/14.80 emptyset)), 98.17/14.80 emptyset)), 98.17/14.80 dsetconstr( 98.17/14.80 powerset( 98.17/14.80 powerset( 98.17/14.80 binunion( 98.17/14.80 Y0, Y1))), 98.17/14.80 (^[Y4 : $i]: 98.17/14.80 (??(( 98.17/14.80 ^[Y5 : $i]: 98.17/14.80 (in(Y5, 98.17/14.80 Y0) & 98.17/14.80 (??(( 98.17/14.80 ^[Y6 : $i]: 98.17/14.80 (in(Y6, 98.17/14.80 Y1) & 98.17/14.80 (Y4 = 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y5, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y5, 98.17/14.80 setadjoin( 98.17/14.80 Y6, 98.17/14.80 emptyset)), 98.17/14.80 emptyset)))))))))))))))))))))))))))) => 98.17/14.80 ( 98.17/14.80 !!(( 98.17/14.80 ^[Y0 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y1 : $i]: 98.17/14.80 (!!(( 98.17/14.80 ^[Y2 : $i]: 98.17/14.80 (in(Y2, 98.17/14.80 dsetconstr( 98.17/14.80 powerset( 98.17/14.80 powerset( 98.17/14.80 binunion( 98.17/14.80 Y0, Y1))), 98.17/14.80 (^[Y3 : $i]: 98.17/14.80 (??(( 98.17/14.80 ^[Y4 : $i]: 98.17/14.80 (in(Y4, 98.17/14.80 Y0) & 98.17/14.80 (??(( 98.17/14.80 ^[Y5 : $i]: 98.17/14.80 (in(Y5, 98.17/14.80 Y1) & 98.17/14.80 (Y3 = 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y4, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y4, 98.17/14.80 setadjoin( 98.17/14.80 Y5, 98.17/14.80 emptyset)), 98.17/14.80 emptyset)))))))))))))) => 98.17/14.80 (??(( 98.17/14.80 ^[Y3 : $i]: 98.17/14.80 (( 98.17/14.80 ??(( 98.17/14.80 ^[Y4 : $i]: 98.17/14.80 (in(Y4, 98.17/14.80 Y1) & 98.17/14.80 (Y2 = 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y3, 98.17/14.80 emptyset), 98.17/14.80 setadjoin( 98.17/14.80 setadjoin( 98.17/14.80 Y3, 98.17/14.80 setadjoin( 98.17/14.80 Y4, 98.17/14.80 emptyset)), 98.17/14.80 emptyset))))))) & 98.17/14.80 in(Y3, 98.17/14.80 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 98.17/14.80 inference('lazy_cnf_imply', [status(thm)], ['164'])). 98.17/14.80 tff('166', plain, 98.17/14.80 ~ (in(emptyset, omega) => 98.17/14.80 ((!!((^[Y0 : $i]: (in(Y0, omega) => in(setadjoin(Y0, Y0), omega))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (((!!((^[Y1 : $i]: 98.17/14.80 ((in(Y1, Y0) & in(Y1, omega)) => 98.17/14.80 in(setadjoin(Y1, Y1), Y0))))) & 98.17/14.80 in(emptyset, Y0)) => 98.17/14.80 (!!((^[Y1 : $i]: (in(Y1, omega) => in(Y1, Y0))))))))) => 98.17/14.80 ((!!((^[Y0 : ($i * $i) > $o]: 98.17/14.80 (!!((^[Y1 : $i]: 98.17/14.80 ((!!((^[Y2 : $i]: 98.17/14.80 (in(Y2, Y1) => 98.17/14.80 (??((^[Y3 : $i]: 98.17/14.80 (Y0(Y2, Y3) & 98.17/14.80 (!!((^[Y4 : $i]: 98.17/14.80 (Y0(Y2, Y4) => (Y3 = Y4))))))))))))) => 98.17/14.80 (??((^[Y2 : $i]: 98.17/14.80 (!!((^[Y3 : $i]: 98.17/14.80 (in(Y3, Y2) <=> 98.17/14.80 (??((^[Y4 : $i]: 98.17/14.80 (in(Y4, Y1) & Y0(Y4, Y3))))))))))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 98.17/14.80 (??((^[Y1 : $i]: 98.17/14.80 (in(Y1, Y0) & 98.17/14.80 (~((??((^[Y2 : $i]: (in(Y2, Y1) & in(Y2, Y0))))))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (??((^[Y1 : $i]: 98.17/14.80 ((!!((^[Y2 : $i]: 98.17/14.80 (in(Y2, Y1) => 98.17/14.80 (!!((^[Y3 : $i]: 98.17/14.80 (in(Y3, Y2) => in(Y3, Y0)))))))))& 98.17/14.80 (!!((^[Y2 : $i]: 98.17/14.80 (!!((^[Y3 : $i]: 98.17/14.80 ((in(Y3, Y0) & in(Y2, Y0)) => 98.17/14.80 ((!!((^[Y4 : $i]: 98.17/14.80 (in(Y4, Y1) => 98.17/14.80 (in(Y2, Y4) <=> in(Y3, Y4)))))) => 98.17/14.80 (Y2 = Y3)))))))))& 98.17/14.80 (!!((^[Y2 : $i]: 98.17/14.80 (!!((^[Y3 : $i]: 98.17/14.80 ((in(Y3, Y1) & in(Y2, Y1)) => 98.17/14.80 ((!!((^[Y4 : $i]: 98.17/14.80 (in(Y4, Y3) => in(Y4, Y2))))) | 98.17/14.80 (!!((^[Y4 : $i]: 98.17/14.80 (in(Y4, Y2) => in(Y4, Y3)))))))))))))& 98.17/14.80 (!!((^[Y2 : $i]: 98.17/14.80 (((??((^[Y3 : $i]: in(Y3, Y2)))) & 98.17/14.80 (!!((^[Y3 : $i]: 98.17/14.80 (in(Y3, Y2) => in(Y3, Y0)))))) => 98.17/14.80 (??((^[Y3 : $i]: 98.17/14.80 (??((^[Y4 : $i]: 98.17/14.80 (in(Y3, Y1)&in(Y4, Y2)& 98.17/14.80 (~((??((^[Y5 : $i]: 98.17/14.80 (in(Y5, Y3) & 98.17/14.80 in(Y5, Y2)))))))& 98.17/14.80 (!!((^[Y5 : $i]: 98.17/14.80 (in(Y5, Y1) => 98.17/14.80 (in(Y4, Y5) | 98.17/14.80 (!!((^[Y6 : $i]: 98.17/14.80 (in(Y6, Y5) => 98.17/14.80 in(Y6, Y3)))))))))))))))))))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i > $o]: 98.17/14.80 ((??((^[Y1 : $i]: 98.17/14.80 (Y0(Y1) & 98.17/14.80 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 98.17/14.80 Y0(descr(Y0)))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i > $o]: 98.17/14.80 (!!((^[Y2 : $i]: 98.17/14.80 (in(Y2, Y0) => 98.17/14.80 (Y1(Y2) => in(Y2, dsetconstr(Y0, Y1))))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i > $o]: 98.17/14.80 (!!((^[Y2 : $i]: 98.17/14.80 (in(Y2, dsetconstr(Y0, Y1)) => in(Y2, Y0))))))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (!!((^[Y1 : $i > $o]: 98.17/14.80 (!!((^[Y2 : $i]: 98.17/14.80 (in(Y2, dsetconstr(Y0, Y1)) => Y1(Y2))))))))))) => 98.17/14.80 ((!!((^[Y0 : $o]: 98.17/14.80 (!!((^[Y1 : $i]: (in(Y1, prop2set(Y0)) => Y0))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: 98.17/14.80 (in(Y0, emptyset) => (!!((^[Y1 : $o]: Y1))))))) => 98.17/14.80 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 98.17/14.80 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 98.17/14.80 ((!!((^[Y0 : $i > $o]: 98.17/14.80 ((??((^[Y1 : $i]: 98.17/14.81 (Y0(Y1) & 98.17/14.81 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 98.17/14.81 (??(Y0)))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 ((!!((^[Y2 : $i]: 98.17/14.81 (in(Y2, Y0) => in(Y2, Y1))))) => 98.17/14.81 ((!!((^[Y2 : $i]: 98.17/14.81 (in(Y2, Y1) => in(Y2, Y0))))) => 98.17/14.81 (Y0 = Y1))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 98.17/14.81 (Y0 = emptyset))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 98.17/14.81 (Y0 = emptyset))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i > $o]: 98.17/14.81 (!!((^[Y2 : $i]: 98.17/14.81 (in(Y2, Y0) => 98.17/14.81 (in(Y2, dsetconstr(Y0, Y1)) <=> 98.17/14.81 Y1(Y2)))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 ((Y0 != emptyset) => 98.17/14.81 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i > $o]: 98.17/14.81 (!!((^[Y2 : $i]: 98.17/14.81 (in(Y2, Y0) => 98.17/14.81 (Y1(Y2) => 98.17/14.81 (dsetconstr(Y0, Y1) != 98.17/14.81 emptyset)))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 98.17/14.81 (Y0 != emptyset))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 in(Y0, setadjoin(Y0, Y1)))))))) => 98.17/14.81 (in(emptyset, setadjoin(emptyset, emptyset)) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 (!!((^[Y2 : $i]: 98.17/14.81 (in(Y2, Y1) => 98.17/14.81 in(Y2, 98.17/14.81 setadjoin(Y0, Y1)))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 (!!((^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 setadjoin(Y0, Y1)) => 98.17/14.81 (!!((^[Y3 : $o]: 98.17/14.81 (((Y2 = Y0) => 98.17/14.81 Y3) => 98.17/14.81 ((in(Y2, Y1) => 98.17/14.81 Y3) => 98.17/14.81 Y3))))))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 (!!((^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 setadjoin(Y0, Y1)) => 98.17/14.81 (in(Y2, Y1) | 98.17/14.81 (Y2 = Y0)))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (dsetconstr(Y0, (^[Y1 : $i]: $true)) = 98.17/14.81 Y0)))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 ((!!((^[Y2 : $i]: 98.17/14.81 (in(Y2, Y1) => 98.17/14.81 in(Y2, Y0))))) => 98.17/14.81 in(Y1, powerset(Y0))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 in(emptyset, powerset(Y0))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 in(emptyset, powerset(Y0))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 (!!((^[Y2 : $i]: 98.17/14.81 (in(Y1, 98.17/14.81 powerset(Y0)) => 98.17/14.81 (in(Y2, Y1) => 98.17/14.81 in(Y2, Y0)))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 (!!((^[Y2 : $i]: 98.17/14.81 (in(Y1, Y2) => 98.17/14.81 (in(Y2, Y0) => 98.17/14.81 in(Y1, 98.17/14.81 setunion(Y0))))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 (in(Y1, setunion(Y0)) => 98.17/14.81 (!!((^[Y2 : $o]: 98.17/14.81 ((!!((^[Y3 : $i]: 98.17/14.81 (in(Y1, 98.17/14.81 Y3) => 98.17/14.81 (in(Y3, 98.17/14.81 Y0) => Y2))))) => 98.17/14.81 Y2))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 (in(Y1, Y0) => 98.17/14.81 in(Y1, 98.17/14.81 powerset( 98.17/14.81 setunion(Y0)))))))))) => 98.17/14.81 ((!!((^[Y0 : $i > $o]: 98.17/14.81 ((??((^[Y1 : $i]: 98.17/14.81 (Y0(Y1) & 98.17/14.81 (!!((^[Y2 : $i]: 98.17/14.81 (Y0(Y2) => 98.17/14.81 (Y1 = Y2))))))))) => 98.17/14.81 (??((^[Y1 : $i]: 98.17/14.81 (!!((^[Y2 : $i]: 98.17/14.81 (Y0(Y2) <=> 98.17/14.81 (Y2 = Y1)))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 ((Y0 != emptyset) => 98.17/14.81 (??((^[Y1 : $i]: 98.17/14.81 in(Y1, Y0)))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 (in(Y0, 98.17/14.81 setadjoin(Y1, 98.17/14.81 emptyset)) => 98.17/14.81 (Y0 = Y1)))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 ((Y0 != Y1) => 98.17/14.81 (~(in(Y1, 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 emptyset))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 ((Y0 = Y1) => 98.17/14.81 in(Y0, 98.17/14.81 setadjoin(Y1, 98.17/14.81 emptyset))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 (in(Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset)) => 98.17/14.81 in(Y1, 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 emptyset))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 (!!((^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset))) => 98.17/14.81 (( 98.17/14.81 Y2 = Y1) | 98.17/14.81 (Y2 = Y0)))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 in(Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 in(Y1, 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i > $o]: 98.17/14.81 ((??(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) & 98.17/14.81 Y1(Y2))))) => 98.17/14.81 (dsetconstr( 98.17/14.81 Y0, Y1) != 98.17/14.81 emptyset)))))))) => 98.17/14.81 ((!!((^[Y0 : $i > $o]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 (in(Y1, 98.17/14.81 emptyset) => 98.17/14.81 Y0(Y1)))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i > $o]: 98.17/14.81 (( 98.17/14.81 ~(( 98.17/14.81 !!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 Y1(Y2))))))) => 98.17/14.81 ( 98.17/14.81 ??(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) & 98.17/14.81 (~( 98.17/14.81 Y1(Y2)))))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i > $o]: 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (~( 98.17/14.81 Y1(Y2))))))) => 98.17/14.81 ( 98.17/14.81 ~(( 98.17/14.81 ??(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) & 98.17/14.81 Y1(Y2)))))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i > $o]: 98.17/14.81 (( 98.17/14.81 ~(( 98.17/14.81 ??(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) & 98.17/14.81 Y1(Y2))))))) => 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (~( 98.17/14.81 Y1(Y2)))))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i > $o]: 98.17/14.81 (( 98.17/14.81 ??(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) & 98.17/14.81 (~( 98.17/14.81 Y1(Y2))))))) => 98.17/14.81 (~(( 98.17/14.81 !!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 Y1(Y2)))))))))))))) => 98.17/14.81 ((!!((^[Y0 : $o]: 98.17/14.81 (Y0 => 98.17/14.81 in( 98.17/14.81 emptyset, 98.17/14.81 prop2set( 98.17/14.81 Y0)))))) => 98.17/14.81 ((!!((^[Y0 : $o]: 98.17/14.81 (Y0 => 98.17/14.81 set2prop( 98.17/14.81 prop2set( 98.17/14.81 Y0)))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i > $o]: 98.17/14.81 (( 98.17/14.81 ~(( 98.17/14.81 ??(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) & 98.17/14.81 Y1(Y2))))))) => 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (~( 98.17/14.81 Y1(Y2)))))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i > $o]: 98.17/14.81 (( 98.17/14.81 ~(( 98.17/14.81 !!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 Y1(Y2))))))) => 98.17/14.81 (??(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) & 98.17/14.81 (~( 98.17/14.81 Y1(Y2)))))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i > $o]: 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 ??(Y0)) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (Y0(Y1) => 98.17/14.81 (Y0(Y2) => 98.17/14.81 (Y1 = Y2))))))))) => 98.17/14.81 ( 98.17/14.81 ??(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (Y0(Y1) & 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (Y0(Y2) => 98.17/14.81 (Y1 = Y2)))))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i > $o]: 98.17/14.81 (( 98.17/14.81 ??(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (Y0(Y2) <=> 98.17/14.81 (Y2 = Y1)))))))) => 98.17/14.81 (??(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (Y0(Y1) & 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (Y0(Y2) => 98.17/14.81 (Y1 = Y2))))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 Y0 = Y1) => 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (( 98.17/14.81 Y2 = Y3) => 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 in(Y3, 98.17/14.81 Y1)))))))))))))))) => 98.17/14.81 ((!!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 Y0 = Y1) => 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (( 98.17/14.81 Y2 = Y3) => 98.17/14.81 (in(Y2, 98.17/14.81 Y0) <=> 98.17/14.81 in(Y3, 98.17/14.81 Y1)))))))))))))))) => 98.17/14.81 ((!!(( 98.17/14.81 ^[Y0 : $i > $o]: 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 ??(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (Y0(Y1) & 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (Y0(Y2) => 98.17/14.81 (Y1 = Y2))))))))) => 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (Y0(Y1) => 98.17/14.81 (Y0(Y2) => 98.17/14.81 (Y1 = Y2))))))))))))) => 98.17/14.81 ((!!(( 98.17/14.81 ^[Y0 : $i > $o]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i > $o]: 98.17/14.81 (( 98.17/14.81 !!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (( 98.17/14.81 Y2 = Y3) => 98.17/14.81 (Y0(Y2) <=> 98.17/14.81 Y1(Y3))))))))) => 98.17/14.81 (( 98.17/14.81 ??(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (Y0(Y2) & 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (Y0(Y3) => 98.17/14.81 (Y2 = Y3))))))))) <=> 98.17/14.81 (??(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (Y1(Y2) & 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (Y1(Y3) => 98.17/14.81 (Y2 = Y3))))))))))))))))) => 98.17/14.81 ((!!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 Y0 = Y1) => 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (( 98.17/14.81 Y2 = Y3) => 98.17/14.81 (setadjoin( 98.17/14.81 Y0, Y2) = 98.17/14.81 setadjoin( 98.17/14.81 Y1, Y3)))))))))))))))) => 98.17/14.81 (( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 Y0 = Y1) => 98.17/14.81 (powerset( 98.17/14.81 Y0) = 98.17/14.81 powerset( 98.17/14.81 Y1))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 Y0 = Y1) => 98.17/14.81 (setunion( 98.17/14.81 Y0) = 98.17/14.81 setunion( 98.17/14.81 Y1))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i > $o]: 98.17/14.81 (( 98.17/14.81 ??(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (Y0(Y1) & 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (Y0(Y2) => 98.17/14.81 (Y1 = Y2))))))))) => 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (Y0(Y1) => 98.17/14.81 (Y0(Y2) => 98.17/14.81 (Y1 = Y2))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i > $o]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i > $o]: 98.17/14.81 (( 98.17/14.81 !!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (( 98.17/14.81 Y2 = Y3) => 98.17/14.81 (Y0(Y2) <=> 98.17/14.81 Y1(Y3))))))))) => 98.17/14.81 (( 98.17/14.81 ??(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (Y0(Y2) & 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (Y0(Y3) => 98.17/14.81 (Y2 = Y3))))))))) => 98.17/14.81 (( 98.17/14.81 ??(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (Y1(Y2) & 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (Y1(Y3) => 98.17/14.81 (Y2 = Y3))))))))) => 98.17/14.81 (descr( 98.17/14.81 Y0) = 98.17/14.81 descr(Y1))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 Y0 = Y1) => 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i > $o]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i > $o]: 98.17/14.81 (( 98.17/14.81 !!(( 98.17/14.81 ^[Y4 : $i]: 98.17/14.81 (in(Y4, 98.17/14.81 Y0) => 98.17/14.81 (!!(( 98.17/14.81 ^[Y5 : $i]: 98.17/14.81 (in(Y5, 98.17/14.81 Y1) => 98.17/14.81 (( 98.17/14.81 Y4 = Y5) => 98.17/14.81 (Y2(Y4) <=> 98.17/14.81 Y3(Y5))))))))))) => 98.17/14.81 (dsetconstr( 98.17/14.81 Y0, Y2) = 98.17/14.81 dsetconstr( 98.17/14.81 Y1, Y3)))))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 !!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 in(Y2, 98.17/14.81 Y1))))) => 98.17/14.81 subset( 98.17/14.81 Y0, Y1)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 Y0 = Y1) => 98.17/14.81 subset( 98.17/14.81 Y1, Y0)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 Y0 = Y1) => 98.17/14.81 subset( 98.17/14.81 Y0, Y1)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 !!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 in(Y2, 98.17/14.81 Y1))))) => 98.17/14.81 subset( 98.17/14.81 Y0, Y1)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!( 98.17/14.81 subset( 98.17/14.81 emptyset))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (subset( 98.17/14.81 Y0, Y1) => 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 in(Y2, 98.17/14.81 Y1)))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (subset( 98.17/14.81 Y0, Y1) => 98.17/14.81 (( 98.17/14.81 ~( 98.17/14.81 in(Y2, 98.17/14.81 Y1))) => 98.17/14.81 (~( 98.17/14.81 in(Y2, 98.17/14.81 Y0)))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (( 98.17/14.81 ~( 98.17/14.81 in(Y2, 98.17/14.81 Y1))) => 98.17/14.81 (~( 98.17/14.81 subset( 98.17/14.81 Y0, Y1)))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 ~( 98.17/14.81 subset( 98.17/14.81 Y0, Y1))) => 98.17/14.81 (Y0 != Y1)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (( 98.17/14.81 ~( 98.17/14.81 in(Y2, 98.17/14.81 Y1))) => 98.17/14.81 (Y0 != Y1)))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 subset( 98.17/14.81 Y0, Y0)))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (subset( 98.17/14.81 Y0, Y1) => 98.17/14.81 (subset( 98.17/14.81 Y1, Y2) => 98.17/14.81 subset( 98.17/14.81 Y0, Y2)))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 subset( 98.17/14.81 Y1, 98.17/14.81 setadjoin( 98.17/14.81 Y0, Y1)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (subset( 98.17/14.81 Y0, Y2) => 98.17/14.81 subset( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, Y2)))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (subset( 98.17/14.81 Y0, Y1) => 98.17/14.81 in(Y0, 98.17/14.81 powerset( 98.17/14.81 Y1))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (subset( 98.17/14.81 Y0, Y1) => 98.17/14.81 (subset( 98.17/14.81 Y1, Y0) => 98.17/14.81 (Y0 = Y1))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (subset( 98.17/14.81 Y0, 98.17/14.81 emptyset) => 98.17/14.81 (Y0 = 98.17/14.81 emptyset))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (subset( 98.17/14.81 Y1, Y0) => 98.17/14.81 in(Y1, 98.17/14.81 powerset( 98.17/14.81 Y0))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (in(Y1, 98.17/14.81 powerset( 98.17/14.81 Y0)) => 98.17/14.81 subset( 98.17/14.81 Y1, Y0)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 in(Y0, 98.17/14.81 powerset( 98.17/14.81 Y0))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (subset( 98.17/14.81 Y0, Y1) => 98.17/14.81 subset( 98.17/14.81 powerset( 98.17/14.81 Y0), 98.17/14.81 powerset( 98.17/14.81 Y1))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i > $o]: 98.17/14.81 in( 98.17/14.81 dsetconstr( 98.17/14.81 Y0, Y1), 98.17/14.81 powerset( 98.17/14.81 Y0)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i > $o]: 98.17/14.81 subset( 98.17/14.81 dsetconstr( 98.17/14.81 Y0, Y1), 98.17/14.81 Y0))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 in(Y2, 98.17/14.81 binunion( 98.17/14.81 Y0, Y1)))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 in(Y1, 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y1) => 98.17/14.81 in(Y2, 98.17/14.81 binunion( 98.17/14.81 Y0, Y1)))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $o]: 98.17/14.81 (in(Y2, 98.17/14.81 binunion( 98.17/14.81 Y0, Y1)) => 98.17/14.81 (( 98.17/14.81 in(Y2, 98.17/14.81 Y0) => Y3) => 98.17/14.81 (( 98.17/14.81 in(Y2, 98.17/14.81 Y1) => Y3) => 98.17/14.81 Y3))))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 binunion( 98.17/14.81 Y0, Y1)) => 98.17/14.81 (in(Y2, 98.17/14.81 Y1) | 98.17/14.81 in(Y2, 98.17/14.81 Y0)))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 subset( 98.17/14.81 Y0, 98.17/14.81 binunion( 98.17/14.81 Y0, Y1)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 subset( 98.17/14.81 Y1, 98.17/14.81 binunion( 98.17/14.81 Y0, Y1)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (in(Y2, 98.17/14.81 Y1) => 98.17/14.81 in(Y2, 98.17/14.81 binintersect( 98.17/14.81 Y0, Y1))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (subset( 98.17/14.81 Y2, Y0) => 98.17/14.81 (subset( 98.17/14.81 Y2, Y1) => 98.17/14.81 subset( 98.17/14.81 Y2, 98.17/14.81 binintersect( 98.17/14.81 Y0, Y1))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 binintersect( 98.17/14.81 Y0, Y1)) => 98.17/14.81 in(Y2, 98.17/14.81 Y0))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 subset( 98.17/14.81 binintersect( 98.17/14.81 Y0, Y1), 98.17/14.81 Y0))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (subset( 98.17/14.81 Y0, Y1) => 98.17/14.81 (binintersect( 98.17/14.81 Y0, Y1) = 98.17/14.81 Y0)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 binintersect( 98.17/14.81 Y0, Y1) = 98.17/14.81 Y1) => 98.17/14.81 subset( 98.17/14.81 Y1, Y0)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 binintersect( 98.17/14.81 Y0, Y1)) => 98.17/14.81 in(Y2, 98.17/14.81 Y1))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 ~(( 98.17/14.81 ??(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) & 98.17/14.81 in(Y2, 98.17/14.81 Y1))))))) => 98.17/14.81 (binintersect( 98.17/14.81 Y0, Y1) = 98.17/14.81 emptyset)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 subset( 98.17/14.81 binintersect( 98.17/14.81 Y0, Y1), 98.17/14.81 Y1))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (subset( 98.17/14.81 Y1, Y0) => 98.17/14.81 (binintersect( 98.17/14.81 Y0, Y1) = 98.17/14.81 Y1)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 binintersect( 98.17/14.81 Y0, Y1) = 98.17/14.81 Y0) => 98.17/14.81 subset( 98.17/14.81 Y0, Y1)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (binintersect( 98.17/14.81 Y0, 98.17/14.81 binunion( 98.17/14.81 Y1, Y2)) = 98.17/14.81 binunion( 98.17/14.81 binintersect( 98.17/14.81 Y0, Y1), 98.17/14.81 binintersect( 98.17/14.81 Y0, Y2)))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (( 98.17/14.81 ~( 98.17/14.81 in(Y2, 98.17/14.81 Y1))) => 98.17/14.81 in(Y2, 98.17/14.81 setminus( 98.17/14.81 Y0, Y1))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 setminus( 98.17/14.81 Y0, Y1)) => 98.17/14.81 in(Y2, 98.17/14.81 Y0))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 setminus( 98.17/14.81 Y0, Y1)) => 98.17/14.81 (~( 98.17/14.81 in(Y2, 98.17/14.81 Y1))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (subset( 98.17/14.81 Y0, Y1) => 98.17/14.81 (setminus( 98.17/14.81 Y0, Y1) = 98.17/14.81 emptyset)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (( 98.17/14.81 ~( 98.17/14.81 in(Y2, 98.17/14.81 setminus( 98.17/14.81 Y0, Y1)))) => 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 in(Y2, 98.17/14.81 Y1)))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (( 98.17/14.81 ~( 98.17/14.81 in(Y2, 98.17/14.81 setminus( 98.17/14.81 Y0, Y1)))) => 98.17/14.81 (( 98.17/14.81 ~( 98.17/14.81 in(Y2, 98.17/14.81 Y1))) => 98.17/14.81 (~( 98.17/14.81 in(Y2, 98.17/14.81 Y0)))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (( 98.17/14.81 ~( 98.17/14.81 in(Y2, 98.17/14.81 Y0))) => 98.17/14.81 (~( 98.17/14.81 in(Y2, 98.17/14.81 setminus( 98.17/14.81 Y0, Y1)))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y1) => 98.17/14.81 (~( 98.17/14.81 in(Y2, 98.17/14.81 setminus( 98.17/14.81 Y0, Y1)))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 subset( 98.17/14.81 setminus( 98.17/14.81 Y0, Y1), 98.17/14.81 Y0))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 setminus( 98.17/14.81 Y0, Y1) = 98.17/14.81 emptyset) => 98.17/14.81 subset( 98.17/14.81 Y0, Y1)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 symdiff( 98.17/14.81 Y0, Y1)) => 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $o]: 98.17/14.81 (( 98.17/14.81 in(Y2, 98.17/14.81 Y0) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 ~( 98.17/14.81 in(Y2, 98.17/14.81 Y1))) => 98.17/14.81 Y3)) => 98.17/14.81 (( 98.17/14.81 ( 98.17/14.81 ~( 98.17/14.81 in(Y2, 98.17/14.81 Y0))) => 98.17/14.81 ( 98.17/14.81 in(Y2, 98.17/14.81 Y1) => Y3)) => 98.17/14.81 Y3))))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (( 98.17/14.81 ~( 98.17/14.81 in(Y2, 98.17/14.81 Y1))) => 98.17/14.81 in(Y2, 98.17/14.81 symdiff( 98.17/14.81 Y0, Y1))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (( 98.17/14.81 ~( 98.17/14.81 in(Y2, 98.17/14.81 Y0))) => 98.17/14.81 (in(Y2, 98.17/14.81 Y1) => 98.17/14.81 in(Y2, 98.17/14.81 symdiff( 98.17/14.81 Y0, Y1))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (in(Y2, 98.17/14.81 Y1) => 98.17/14.81 (~( 98.17/14.81 in(Y2, 98.17/14.81 symdiff( 98.17/14.81 Y0, Y1))))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (( 98.17/14.81 ~( 98.17/14.81 in(Y2, 98.17/14.81 Y0))) => 98.17/14.81 (( 98.17/14.81 ~( 98.17/14.81 in(Y2, 98.17/14.81 Y1))) => 98.17/14.81 (~( 98.17/14.81 in(Y2, 98.17/14.81 symdiff( 98.17/14.81 Y0, Y1))))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 in(Y1, 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 in(Y0, 98.17/14.81 setunion( 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset)), 98.17/14.81 emptyset)))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 in(Y1, 98.17/14.81 setunion( 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset)), 98.17/14.81 emptyset)))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (??(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 setunion( 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset)), 98.17/14.81 emptyset)))) & 98.17/14.81 (??(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (in(Y3, 98.17/14.81 setunion( 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset)), 98.17/14.81 emptyset)))) & 98.17/14.81 (setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset)), 98.17/14.81 emptyset)) = 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 setadjoin( 98.17/14.81 Y3, 98.17/14.81 emptyset)), 98.17/14.81 emptyset))))))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (??(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 setunion( 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset)), 98.17/14.81 emptyset)))) & 98.17/14.81 (??(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (in(Y3, 98.17/14.81 setunion( 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset)), 98.17/14.81 emptyset)))) & 98.17/14.81 (setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset)), 98.17/14.81 emptyset)) = 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 setadjoin( 98.17/14.81 Y3, 98.17/14.81 emptyset)), 98.17/14.81 emptyset))))))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (in(Y1, 98.17/14.81 Y0) => 98.17/14.81 subset( 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset), 98.17/14.81 Y0)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (in(Y1, 98.17/14.81 Y0) => 98.17/14.81 in( 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset), 98.17/14.81 powerset( 98.17/14.81 Y0))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 in( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 emptyset), 98.17/14.81 powerset( 98.17/14.81 binunion( 98.17/14.81 Y0, Y1))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset))) => 98.17/14.81 (( 98.17/14.81 Y2 = Y1) | 98.17/14.81 (Y2 = Y0)))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (in(Y3, 98.17/14.81 Y1) => 98.17/14.81 subset( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 setadjoin( 98.17/14.81 Y3, 98.17/14.81 emptyset)), 98.17/14.81 binunion( 98.17/14.81 Y0, Y1)))))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (in(Y3, 98.17/14.81 Y1) => 98.17/14.81 in( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 setadjoin( 98.17/14.81 Y3, 98.17/14.81 emptyset)), 98.17/14.81 powerset( 98.17/14.81 binunion( 98.17/14.81 Y0, Y1))))))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (in(Y3, 98.17/14.81 Y1) => 98.17/14.81 subset( 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 setadjoin( 98.17/14.81 Y3, 98.17/14.81 emptyset)), 98.17/14.81 emptyset)), 98.17/14.81 powerset( 98.17/14.81 binunion( 98.17/14.81 Y0, Y1))))))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (in(Y3, 98.17/14.81 Y1) => 98.17/14.81 in( 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 setadjoin( 98.17/14.81 Y3, 98.17/14.81 emptyset)), 98.17/14.81 emptyset)), 98.17/14.81 powerset( 98.17/14.81 powerset( 98.17/14.81 binunion( 98.17/14.81 Y0, Y1)))))))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (in(Y3, 98.17/14.81 Y1) => 98.17/14.81 in( 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 setadjoin( 98.17/14.81 Y3, 98.17/14.81 emptyset)), 98.17/14.81 emptyset)), 98.17/14.81 powerset( 98.17/14.81 powerset( 98.17/14.81 binunion( 98.17/14.81 Y0, Y1)))))))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (in(Y3, 98.17/14.81 Y1) => 98.17/14.81 in( 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 setadjoin( 98.17/14.81 Y3, 98.17/14.81 emptyset)), 98.17/14.81 emptyset)), 98.17/14.81 dsetconstr( 98.17/14.81 powerset( 98.17/14.81 powerset( 98.17/14.81 binunion( 98.17/14.81 Y0, Y1))), 98.17/14.81 (^[Y4 : $i]: 98.17/14.81 (??(( 98.17/14.81 ^[Y5 : $i]: 98.17/14.81 (in(Y5, 98.17/14.81 Y0) & 98.17/14.81 (??(( 98.17/14.81 ^[Y6 : $i]: 98.17/14.81 (in(Y6, 98.17/14.81 Y1) & 98.17/14.81 (Y4 = 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y5, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y5, 98.17/14.81 setadjoin( 98.17/14.81 Y6, 98.17/14.81 emptyset)), 98.17/14.81 emptyset)))))))))))))))))))))))))))) => 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 dsetconstr( 98.17/14.81 powerset( 98.17/14.81 powerset( 98.17/14.81 binunion( 98.17/14.81 Y0, Y1))), 98.17/14.81 (^[Y3 : $i]: 98.17/14.81 (??(( 98.17/14.81 ^[Y4 : $i]: 98.17/14.81 (in(Y4, 98.17/14.81 Y0) & 98.17/14.81 (??(( 98.17/14.81 ^[Y5 : $i]: 98.17/14.81 (in(Y5, 98.17/14.81 Y1) & 98.17/14.81 (Y3 = 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y4, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y4, 98.17/14.81 setadjoin( 98.17/14.81 Y5, 98.17/14.81 emptyset)), 98.17/14.81 emptyset)))))))))))))) => 98.17/14.81 (??(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (( 98.17/14.81 ??(( 98.17/14.81 ^[Y4 : $i]: 98.17/14.81 (in(Y4, 98.17/14.81 Y1) & 98.17/14.81 (Y2 = 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y3, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y3, 98.17/14.81 setadjoin( 98.17/14.81 Y4, 98.17/14.81 emptyset)), 98.17/14.81 emptyset))))))) & 98.17/14.81 in(Y3, 98.17/14.81 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 98.17/14.81 inference('lazy_cnf_imply', [status(thm)], ['165'])). 98.17/14.81 tff('167', plain, 98.17/14.81 ~ ((!!((^[Y0 : $i]: (in(Y0, omega) => in(setadjoin(Y0, Y0), omega))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (((!!((^[Y1 : $i]: 98.17/14.81 ((in(Y1, Y0) & in(Y1, omega)) => 98.17/14.81 in(setadjoin(Y1, Y1), Y0))))) & 98.17/14.81 in(emptyset, Y0)) => 98.17/14.81 (!!((^[Y1 : $i]: (in(Y1, omega) => in(Y1, Y0))))))))) => 98.17/14.81 ((!!((^[Y0 : ($i * $i) > $o]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 ((!!((^[Y2 : $i]: 98.17/14.81 (in(Y2, Y1) => 98.17/14.81 (??((^[Y3 : $i]: 98.17/14.81 (Y0(Y2, Y3) & 98.17/14.81 (!!((^[Y4 : $i]: 98.17/14.81 (Y0(Y2, Y4) => (Y3 = Y4))))))))))))) => 98.17/14.81 (??((^[Y2 : $i]: 98.17/14.81 (!!((^[Y3 : $i]: 98.17/14.81 (in(Y3, Y2) <=> 98.17/14.81 (??((^[Y4 : $i]: 98.17/14.81 (in(Y4, Y1) & Y0(Y4, Y3))))))))))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 98.17/14.81 (??((^[Y1 : $i]: 98.17/14.81 (in(Y1, Y0) & 98.17/14.81 (~((??((^[Y2 : $i]: (in(Y2, Y1) & in(Y2, Y0))))))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (??((^[Y1 : $i]: 98.17/14.81 ((!!((^[Y2 : $i]: 98.17/14.81 (in(Y2, Y1) => 98.17/14.81 (!!((^[Y3 : $i]: (in(Y3, Y2) => in(Y3, Y0)))))))))& 98.17/14.81 (!!((^[Y2 : $i]: 98.17/14.81 (!!((^[Y3 : $i]: 98.17/14.81 ((in(Y3, Y0) & in(Y2, Y0)) => 98.17/14.81 ((!!((^[Y4 : $i]: 98.17/14.81 (in(Y4, Y1) => 98.17/14.81 (in(Y2, Y4) <=> in(Y3, Y4)))))) => 98.17/14.81 (Y2 = Y3)))))))))& 98.17/14.81 (!!((^[Y2 : $i]: 98.17/14.81 (!!((^[Y3 : $i]: 98.17/14.81 ((in(Y3, Y1) & in(Y2, Y1)) => 98.17/14.81 ((!!((^[Y4 : $i]: 98.17/14.81 (in(Y4, Y3) => in(Y4, Y2))))) | 98.17/14.81 (!!((^[Y4 : $i]: 98.17/14.81 (in(Y4, Y2) => in(Y4, Y3)))))))))))))& 98.17/14.81 (!!((^[Y2 : $i]: 98.17/14.81 (((??((^[Y3 : $i]: in(Y3, Y2)))) & 98.17/14.81 (!!((^[Y3 : $i]: 98.17/14.81 (in(Y3, Y2) => in(Y3, Y0)))))) => 98.17/14.81 (??((^[Y3 : $i]: 98.17/14.81 (??((^[Y4 : $i]: 98.17/14.81 (in(Y3, Y1)&in(Y4, Y2)& 98.17/14.81 (~((??((^[Y5 : $i]: 98.17/14.81 (in(Y5, Y3) & 98.17/14.81 in(Y5, Y2)))))))& 98.17/14.81 (!!((^[Y5 : $i]: 98.17/14.81 (in(Y5, Y1) => 98.17/14.81 (in(Y4, Y5) | 98.17/14.81 (!!((^[Y6 : $i]: 98.17/14.81 (in(Y6, Y5) => 98.17/14.81 in(Y6, Y3)))))))))))))))))))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i > $o]: 98.17/14.81 ((??((^[Y1 : $i]: 98.17/14.81 (Y0(Y1) & 98.17/14.81 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 98.17/14.81 Y0(descr(Y0)))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i > $o]: 98.17/14.81 (!!((^[Y2 : $i]: 98.17/14.81 (in(Y2, Y0) => 98.17/14.81 (Y1(Y2) => in(Y2, dsetconstr(Y0, Y1))))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i > $o]: 98.17/14.81 (!!((^[Y2 : $i]: 98.17/14.81 (in(Y2, dsetconstr(Y0, Y1)) => in(Y2, Y0))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i > $o]: 98.17/14.81 (!!((^[Y2 : $i]: 98.17/14.81 (in(Y2, dsetconstr(Y0, Y1)) => Y1(Y2))))))))))) => 98.17/14.81 ((!!((^[Y0 : $o]: 98.17/14.81 (!!((^[Y1 : $i]: (in(Y1, prop2set(Y0)) => Y0))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (in(Y0, emptyset) => (!!((^[Y1 : $o]: Y1))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 98.17/14.81 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 98.17/14.81 ((!!((^[Y0 : $i > $o]: 98.17/14.81 ((??((^[Y1 : $i]: 98.17/14.81 (Y0(Y1) & 98.17/14.81 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 98.17/14.81 (??(Y0)))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 ((!!((^[Y2 : $i]: 98.17/14.81 (in(Y2, Y0) => in(Y2, Y1))))) => 98.17/14.81 ((!!((^[Y2 : $i]: 98.17/14.81 (in(Y2, Y1) => in(Y2, Y0))))) => 98.17/14.81 (Y0 = Y1))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 98.17/14.81 (Y0 = emptyset))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 98.17/14.81 (Y0 = emptyset))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i > $o]: 98.17/14.81 (!!((^[Y2 : $i]: 98.17/14.81 (in(Y2, Y0) => 98.17/14.81 (in(Y2, dsetconstr(Y0, Y1)) <=> 98.17/14.81 Y1(Y2)))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 ((Y0 != emptyset) => 98.17/14.81 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i > $o]: 98.17/14.81 (!!((^[Y2 : $i]: 98.17/14.81 (in(Y2, Y0) => 98.17/14.81 (Y1(Y2) => 98.17/14.81 (dsetconstr(Y0, Y1) != 98.17/14.81 emptyset)))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 98.17/14.81 (Y0 != emptyset))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 98.17/14.81 (in(emptyset, setadjoin(emptyset, emptyset)) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 (!!((^[Y2 : $i]: 98.17/14.81 (in(Y2, Y1) => 98.17/14.81 in(Y2, setadjoin(Y0, Y1)))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 (!!((^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 setadjoin(Y0, Y1)) => 98.17/14.81 (!!((^[Y3 : $o]: 98.17/14.81 (((Y2 = Y0) => Y3) => 98.17/14.81 ((in(Y2, Y1) => 98.17/14.81 Y3) => 98.17/14.81 Y3))))))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 (!!((^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 setadjoin(Y0, Y1)) => 98.17/14.81 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (dsetconstr(Y0, (^[Y1 : $i]: $true)) = 98.17/14.81 Y0)))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 ((!!((^[Y2 : $i]: 98.17/14.81 (in(Y2, Y1) => 98.17/14.81 in(Y2, Y0))))) => 98.17/14.81 in(Y1, powerset(Y0))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 in(emptyset, powerset(Y0))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 in(emptyset, powerset(Y0))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 (!!((^[Y2 : $i]: 98.17/14.81 (in(Y1, 98.17/14.81 powerset(Y0)) => 98.17/14.81 (in(Y2, Y1) => 98.17/14.81 in(Y2, Y0)))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 (!!((^[Y2 : $i]: 98.17/14.81 (in(Y1, Y2) => 98.17/14.81 (in(Y2, Y0) => 98.17/14.81 in(Y1, 98.17/14.81 setunion(Y0))))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 (in(Y1, setunion(Y0)) => 98.17/14.81 (!!((^[Y2 : $o]: 98.17/14.81 ((!!((^[Y3 : $i]: 98.17/14.81 (in(Y1, 98.17/14.81 Y3) => 98.17/14.81 (in(Y3, 98.17/14.81 Y0) => Y2))))) => 98.17/14.81 Y2))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 (in(Y1, Y0) => 98.17/14.81 in(Y1, 98.17/14.81 powerset( 98.17/14.81 setunion(Y0)))))))))) => 98.17/14.81 ((!!((^[Y0 : $i > $o]: 98.17/14.81 ((??((^[Y1 : $i]: 98.17/14.81 (Y0(Y1) & 98.17/14.81 (!!((^[Y2 : $i]: 98.17/14.81 (Y0(Y2) => 98.17/14.81 (Y1 = Y2))))))))) => 98.17/14.81 (??((^[Y1 : $i]: 98.17/14.81 (!!((^[Y2 : $i]: 98.17/14.81 (Y0(Y2) <=> 98.17/14.81 (Y2 = Y1)))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 ((Y0 != emptyset) => 98.17/14.81 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 (in(Y0, 98.17/14.81 setadjoin(Y1, 98.17/14.81 emptyset)) => 98.17/14.81 (Y0 = Y1)))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 ((Y0 != Y1) => 98.17/14.81 (~(in(Y1, 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 emptyset))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 ((Y0 = Y1) => 98.17/14.81 in(Y0, 98.17/14.81 setadjoin(Y1, 98.17/14.81 emptyset))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 (in(Y0, 98.17/14.81 setadjoin(Y1, 98.17/14.81 emptyset)) => 98.17/14.81 in(Y1, 98.17/14.81 setadjoin(Y0, 98.17/14.81 emptyset))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 (!!((^[Y2 : $i]: 98.17/14.81 ( 98.17/14.81 in(Y2, 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 Y2 = Y1) | 98.17/14.81 ( 98.17/14.81 Y2 = Y0)))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 in(Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 in(Y1, 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i > $o]: 98.17/14.81 ((??(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 ( 98.17/14.81 in(Y2, 98.17/14.81 Y0) & 98.17/14.81 Y1(Y2))))) => 98.17/14.81 (dsetconstr( 98.17/14.81 Y0, Y1) != 98.17/14.81 emptyset)))))))) => 98.17/14.81 ((!!((^[Y0 : $i > $o]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 (in(Y1, 98.17/14.81 emptyset) => 98.17/14.81 Y0(Y1)))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i > $o]: 98.17/14.81 ((~(( 98.17/14.81 !!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 Y1(Y2))))))) => 98.17/14.81 (??(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) & 98.17/14.81 (~( 98.17/14.81 Y1(Y2)))))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i > $o]: 98.17/14.81 (( 98.17/14.81 !!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (~( 98.17/14.81 Y1(Y2))))))) => 98.17/14.81 ( 98.17/14.81 ~(( 98.17/14.81 ??(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) & 98.17/14.81 Y1(Y2)))))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i > $o]: 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 ~(( 98.17/14.81 ??(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) & 98.17/14.81 Y1(Y2))))))) => 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (~( 98.17/14.81 Y1(Y2)))))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i > $o]: 98.17/14.81 (( 98.17/14.81 ??(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) & 98.17/14.81 (~( 98.17/14.81 Y1(Y2))))))) => 98.17/14.81 (~(( 98.17/14.81 !!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 Y1(Y2)))))))))))))) => 98.17/14.81 ((!!((^[Y0 : $o]: 98.17/14.81 (Y0 => 98.17/14.81 in(emptyset, 98.17/14.81 prop2set( 98.17/14.81 Y0)))))) => 98.17/14.81 ((!!((^[Y0 : $o]: 98.17/14.81 (Y0 => 98.17/14.81 set2prop( 98.17/14.81 prop2set( 98.17/14.81 Y0)))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i > $o]: 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 ~(( 98.17/14.81 ??(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) & 98.17/14.81 Y1(Y2))))))) => 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (~( 98.17/14.81 Y1(Y2)))))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i > $o]: 98.17/14.81 (( 98.17/14.81 ~(( 98.17/14.81 !!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 Y1(Y2))))))) => 98.17/14.81 (??(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) & 98.17/14.81 (~( 98.17/14.81 Y1(Y2)))))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i > $o]: 98.17/14.81 (( 98.17/14.81 ??(Y0)) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (Y0(Y1) => 98.17/14.81 (Y0(Y2) => 98.17/14.81 (Y1 = Y2))))))))) => 98.17/14.81 ( 98.17/14.81 ??(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (Y0(Y1) & 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (Y0(Y2) => 98.17/14.81 (Y1 = Y2)))))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i > $o]: 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 ??(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (Y0(Y2) <=> 98.17/14.81 (Y2 = Y1)))))))) => 98.17/14.81 ( 98.17/14.81 ??(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (Y0(Y1) & 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (Y0(Y2) => 98.17/14.81 (Y1 = Y2))))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 Y0 = Y1) => 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (( 98.17/14.81 Y2 = Y3) => 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 in(Y3, 98.17/14.81 Y1)))))))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 Y0 = Y1) => 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (( 98.17/14.81 Y2 = Y3) => 98.17/14.81 (in(Y2, 98.17/14.81 Y0) <=> 98.17/14.81 in(Y3, 98.17/14.81 Y1)))))))))))))))) => 98.17/14.81 ((!!(( 98.17/14.81 ^[Y0 : $i > $o]: 98.17/14.81 (( 98.17/14.81 ??(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (Y0(Y1) & 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (Y0(Y2) => 98.17/14.81 (Y1 = Y2))))))))) => 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (Y0(Y1) => 98.17/14.81 (Y0(Y2) => 98.17/14.81 (Y1 = Y2))))))))))))) => 98.17/14.81 ((!!(( 98.17/14.81 ^[Y0 : $i > $o]: 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y1 : $i > $o]: 98.17/14.81 (( 98.17/14.81 !!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (( 98.17/14.81 Y2 = Y3) => 98.17/14.81 (Y0(Y2) <=> 98.17/14.81 Y1(Y3))))))))) => 98.17/14.81 (( 98.17/14.81 ??(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (Y0(Y2) & 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (Y0(Y3) => 98.17/14.81 (Y2 = Y3))))))))) <=> 98.17/14.81 (??(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (Y1(Y2) & 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (Y1(Y3) => 98.17/14.81 (Y2 = Y3))))))))))))))))) => 98.17/14.81 ((!!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 Y0 = Y1) => 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (( 98.17/14.81 Y2 = Y3) => 98.17/14.81 (setadjoin( 98.17/14.81 Y0, Y2) = 98.17/14.81 setadjoin( 98.17/14.81 Y1, Y3)))))))))))))))) => 98.17/14.81 ((!!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 Y0 = Y1) => 98.17/14.81 (powerset( 98.17/14.81 Y0) = 98.17/14.81 powerset( 98.17/14.81 Y1))))))))) => 98.17/14.81 (( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 Y0 = Y1) => 98.17/14.81 (setunion( 98.17/14.81 Y0) = 98.17/14.81 setunion( 98.17/14.81 Y1))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i > $o]: 98.17/14.81 (( 98.17/14.81 ??(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (Y0(Y1) & 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (Y0(Y2) => 98.17/14.81 (Y1 = Y2))))))))) => 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (Y0(Y1) => 98.17/14.81 (Y0(Y2) => 98.17/14.81 (Y1 = Y2))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i > $o]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i > $o]: 98.17/14.81 (( 98.17/14.81 !!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (( 98.17/14.81 Y2 = Y3) => 98.17/14.81 (Y0(Y2) <=> 98.17/14.81 Y1(Y3))))))))) => 98.17/14.81 (( 98.17/14.81 ??(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (Y0(Y2) & 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (Y0(Y3) => 98.17/14.81 (Y2 = Y3))))))))) => 98.17/14.81 (( 98.17/14.81 ??(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (Y1(Y2) & 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (Y1(Y3) => 98.17/14.81 (Y2 = Y3))))))))) => 98.17/14.81 (descr( 98.17/14.81 Y0) = 98.17/14.81 descr(Y1))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 Y0 = Y1) => 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i > $o]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i > $o]: 98.17/14.81 (( 98.17/14.81 !!(( 98.17/14.81 ^[Y4 : $i]: 98.17/14.81 (in(Y4, 98.17/14.81 Y0) => 98.17/14.81 (!!(( 98.17/14.81 ^[Y5 : $i]: 98.17/14.81 (in(Y5, 98.17/14.81 Y1) => 98.17/14.81 (( 98.17/14.81 Y4 = Y5) => 98.17/14.81 (Y2(Y4) <=> 98.17/14.81 Y3(Y5))))))))))) => 98.17/14.81 (dsetconstr( 98.17/14.81 Y0, Y2) = 98.17/14.81 dsetconstr( 98.17/14.81 Y1, Y3)))))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 !!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 in(Y2, 98.17/14.81 Y1))))) => 98.17/14.81 subset( 98.17/14.81 Y0, Y1)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 Y0 = Y1) => 98.17/14.81 subset( 98.17/14.81 Y1, Y0)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 Y0 = Y1) => 98.17/14.81 subset( 98.17/14.81 Y0, Y1)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 !!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 in(Y2, 98.17/14.81 Y1))))) => 98.17/14.81 subset( 98.17/14.81 Y0, Y1)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!( 98.17/14.81 subset( 98.17/14.81 emptyset))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (subset( 98.17/14.81 Y0, Y1) => 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 in(Y2, 98.17/14.81 Y1)))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (subset( 98.17/14.81 Y0, Y1) => 98.17/14.81 (( 98.17/14.81 ~( 98.17/14.81 in(Y2, 98.17/14.81 Y1))) => 98.17/14.81 (~( 98.17/14.81 in(Y2, 98.17/14.81 Y0)))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (( 98.17/14.81 ~( 98.17/14.81 in(Y2, 98.17/14.81 Y1))) => 98.17/14.81 (~( 98.17/14.81 subset( 98.17/14.81 Y0, Y1)))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 ~( 98.17/14.81 subset( 98.17/14.81 Y0, Y1))) => 98.17/14.81 (Y0 != Y1)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (( 98.17/14.81 ~( 98.17/14.81 in(Y2, 98.17/14.81 Y1))) => 98.17/14.81 (Y0 != Y1)))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 subset( 98.17/14.81 Y0, Y0)))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (subset( 98.17/14.81 Y0, Y1) => 98.17/14.81 (subset( 98.17/14.81 Y1, Y2) => 98.17/14.81 subset( 98.17/14.81 Y0, Y2)))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 subset( 98.17/14.81 Y1, 98.17/14.81 setadjoin( 98.17/14.81 Y0, Y1)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (subset( 98.17/14.81 Y0, Y2) => 98.17/14.81 subset( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, Y2)))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (subset( 98.17/14.81 Y0, Y1) => 98.17/14.81 in(Y0, 98.17/14.81 powerset( 98.17/14.81 Y1))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (subset( 98.17/14.81 Y0, Y1) => 98.17/14.81 (subset( 98.17/14.81 Y1, Y0) => 98.17/14.81 (Y0 = Y1))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (subset( 98.17/14.81 Y0, 98.17/14.81 emptyset) => 98.17/14.81 (Y0 = 98.17/14.81 emptyset))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (subset( 98.17/14.81 Y1, Y0) => 98.17/14.81 in(Y1, 98.17/14.81 powerset( 98.17/14.81 Y0))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (in(Y1, 98.17/14.81 powerset( 98.17/14.81 Y0)) => 98.17/14.81 subset( 98.17/14.81 Y1, Y0)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 in(Y0, 98.17/14.81 powerset( 98.17/14.81 Y0))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (subset( 98.17/14.81 Y0, Y1) => 98.17/14.81 subset( 98.17/14.81 powerset( 98.17/14.81 Y0), 98.17/14.81 powerset( 98.17/14.81 Y1))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i > $o]: 98.17/14.81 in( 98.17/14.81 dsetconstr( 98.17/14.81 Y0, Y1), 98.17/14.81 powerset( 98.17/14.81 Y0)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i > $o]: 98.17/14.81 subset( 98.17/14.81 dsetconstr( 98.17/14.81 Y0, Y1), 98.17/14.81 Y0))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 in(Y2, 98.17/14.81 binunion( 98.17/14.81 Y0, Y1)))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 in(Y1, 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y1) => 98.17/14.81 in(Y2, 98.17/14.81 binunion( 98.17/14.81 Y0, Y1)))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $o]: 98.17/14.81 (in(Y2, 98.17/14.81 binunion( 98.17/14.81 Y0, Y1)) => 98.17/14.81 (( 98.17/14.81 in(Y2, 98.17/14.81 Y0) => Y3) => 98.17/14.81 (( 98.17/14.81 in(Y2, 98.17/14.81 Y1) => Y3) => 98.17/14.81 Y3))))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 binunion( 98.17/14.81 Y0, Y1)) => 98.17/14.81 (in(Y2, 98.17/14.81 Y1) | 98.17/14.81 in(Y2, 98.17/14.81 Y0)))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 subset( 98.17/14.81 Y0, 98.17/14.81 binunion( 98.17/14.81 Y0, Y1)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 subset( 98.17/14.81 Y1, 98.17/14.81 binunion( 98.17/14.81 Y0, Y1)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (in(Y2, 98.17/14.81 Y1) => 98.17/14.81 in(Y2, 98.17/14.81 binintersect( 98.17/14.81 Y0, Y1))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (subset( 98.17/14.81 Y2, Y0) => 98.17/14.81 (subset( 98.17/14.81 Y2, Y1) => 98.17/14.81 subset( 98.17/14.81 Y2, 98.17/14.81 binintersect( 98.17/14.81 Y0, Y1))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 binintersect( 98.17/14.81 Y0, Y1)) => 98.17/14.81 in(Y2, 98.17/14.81 Y0))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 subset( 98.17/14.81 binintersect( 98.17/14.81 Y0, Y1), 98.17/14.81 Y0))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (subset( 98.17/14.81 Y0, Y1) => 98.17/14.81 (binintersect( 98.17/14.81 Y0, Y1) = 98.17/14.81 Y0)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 binintersect( 98.17/14.81 Y0, Y1) = 98.17/14.81 Y1) => 98.17/14.81 subset( 98.17/14.81 Y1, Y0)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 binintersect( 98.17/14.81 Y0, Y1)) => 98.17/14.81 in(Y2, 98.17/14.81 Y1))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 ~(( 98.17/14.81 ??(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) & 98.17/14.81 in(Y2, 98.17/14.81 Y1))))))) => 98.17/14.81 (binintersect( 98.17/14.81 Y0, Y1) = 98.17/14.81 emptyset)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 subset( 98.17/14.81 binintersect( 98.17/14.81 Y0, Y1), 98.17/14.81 Y1))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (subset( 98.17/14.81 Y1, Y0) => 98.17/14.81 (binintersect( 98.17/14.81 Y0, Y1) = 98.17/14.81 Y1)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 binintersect( 98.17/14.81 Y0, Y1) = 98.17/14.81 Y0) => 98.17/14.81 subset( 98.17/14.81 Y0, Y1)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (binintersect( 98.17/14.81 Y0, 98.17/14.81 binunion( 98.17/14.81 Y1, Y2)) = 98.17/14.81 binunion( 98.17/14.81 binintersect( 98.17/14.81 Y0, Y1), 98.17/14.81 binintersect( 98.17/14.81 Y0, Y2)))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (( 98.17/14.81 ~( 98.17/14.81 in(Y2, 98.17/14.81 Y1))) => 98.17/14.81 in(Y2, 98.17/14.81 setminus( 98.17/14.81 Y0, Y1))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 setminus( 98.17/14.81 Y0, Y1)) => 98.17/14.81 in(Y2, 98.17/14.81 Y0))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 setminus( 98.17/14.81 Y0, Y1)) => 98.17/14.81 (~( 98.17/14.81 in(Y2, 98.17/14.81 Y1))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (subset( 98.17/14.81 Y0, Y1) => 98.17/14.81 (setminus( 98.17/14.81 Y0, Y1) = 98.17/14.81 emptyset)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (( 98.17/14.81 ~( 98.17/14.81 in(Y2, 98.17/14.81 setminus( 98.17/14.81 Y0, Y1)))) => 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 in(Y2, 98.17/14.81 Y1)))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (( 98.17/14.81 ~( 98.17/14.81 in(Y2, 98.17/14.81 setminus( 98.17/14.81 Y0, Y1)))) => 98.17/14.81 (( 98.17/14.81 ~( 98.17/14.81 in(Y2, 98.17/14.81 Y1))) => 98.17/14.81 (~( 98.17/14.81 in(Y2, 98.17/14.81 Y0)))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (( 98.17/14.81 ~( 98.17/14.81 in(Y2, 98.17/14.81 Y0))) => 98.17/14.81 (~( 98.17/14.81 in(Y2, 98.17/14.81 setminus( 98.17/14.81 Y0, Y1)))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y1) => 98.17/14.81 (~( 98.17/14.81 in(Y2, 98.17/14.81 setminus( 98.17/14.81 Y0, Y1)))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 subset( 98.17/14.81 setminus( 98.17/14.81 Y0, Y1), 98.17/14.81 Y0))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 setminus( 98.17/14.81 Y0, Y1) = 98.17/14.81 emptyset) => 98.17/14.81 subset( 98.17/14.81 Y0, Y1)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 symdiff( 98.17/14.81 Y0, Y1)) => 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $o]: 98.17/14.81 (( 98.17/14.81 in(Y2, 98.17/14.81 Y0) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 ~( 98.17/14.81 in(Y2, 98.17/14.81 Y1))) => 98.17/14.81 Y3)) => 98.17/14.81 (( 98.17/14.81 ( 98.17/14.81 ~( 98.17/14.81 in(Y2, 98.17/14.81 Y0))) => 98.17/14.81 ( 98.17/14.81 in(Y2, 98.17/14.81 Y1) => Y3)) => 98.17/14.81 Y3))))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (( 98.17/14.81 ~( 98.17/14.81 in(Y2, 98.17/14.81 Y1))) => 98.17/14.81 in(Y2, 98.17/14.81 symdiff( 98.17/14.81 Y0, Y1))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (( 98.17/14.81 ~( 98.17/14.81 in(Y2, 98.17/14.81 Y0))) => 98.17/14.81 (in(Y2, 98.17/14.81 Y1) => 98.17/14.81 in(Y2, 98.17/14.81 symdiff( 98.17/14.81 Y0, Y1))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (in(Y2, 98.17/14.81 Y1) => 98.17/14.81 (~( 98.17/14.81 in(Y2, 98.17/14.81 symdiff( 98.17/14.81 Y0, Y1))))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (( 98.17/14.81 ~( 98.17/14.81 in(Y2, 98.17/14.81 Y0))) => 98.17/14.81 (( 98.17/14.81 ~( 98.17/14.81 in(Y2, 98.17/14.81 Y1))) => 98.17/14.81 (~( 98.17/14.81 in(Y2, 98.17/14.81 symdiff( 98.17/14.81 Y0, Y1))))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 in(Y1, 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 in(Y0, 98.17/14.81 setunion( 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset)), 98.17/14.81 emptyset)))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 in(Y1, 98.17/14.81 setunion( 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset)), 98.17/14.81 emptyset)))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (??(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 setunion( 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset)), 98.17/14.81 emptyset)))) & 98.17/14.81 (??(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (in(Y3, 98.17/14.81 setunion( 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset)), 98.17/14.81 emptyset)))) & 98.17/14.81 (setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset)), 98.17/14.81 emptyset)) = 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 setadjoin( 98.17/14.81 Y3, 98.17/14.81 emptyset)), 98.17/14.81 emptyset))))))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (??(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 setunion( 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset)), 98.17/14.81 emptyset)))) & 98.17/14.81 (??(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (in(Y3, 98.17/14.81 setunion( 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset)), 98.17/14.81 emptyset)))) & 98.17/14.81 (setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset)), 98.17/14.81 emptyset)) = 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 setadjoin( 98.17/14.81 Y3, 98.17/14.81 emptyset)), 98.17/14.81 emptyset))))))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (in(Y1, 98.17/14.81 Y0) => 98.17/14.81 subset( 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset), 98.17/14.81 Y0)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (in(Y1, 98.17/14.81 Y0) => 98.17/14.81 in( 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset), 98.17/14.81 powerset( 98.17/14.81 Y0))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 in( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 emptyset), 98.17/14.81 powerset( 98.17/14.81 binunion( 98.17/14.81 Y0, Y1))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset))) => 98.17/14.81 (( 98.17/14.81 Y2 = Y1) | 98.17/14.81 (Y2 = Y0)))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (in(Y3, 98.17/14.81 Y1) => 98.17/14.81 subset( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 setadjoin( 98.17/14.81 Y3, 98.17/14.81 emptyset)), 98.17/14.81 binunion( 98.17/14.81 Y0, Y1)))))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (in(Y3, 98.17/14.81 Y1) => 98.17/14.81 in( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 setadjoin( 98.17/14.81 Y3, 98.17/14.81 emptyset)), 98.17/14.81 powerset( 98.17/14.81 binunion( 98.17/14.81 Y0, Y1))))))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (in(Y3, 98.17/14.81 Y1) => 98.17/14.81 subset( 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 setadjoin( 98.17/14.81 Y3, 98.17/14.81 emptyset)), 98.17/14.81 emptyset)), 98.17/14.81 powerset( 98.17/14.81 binunion( 98.17/14.81 Y0, Y1))))))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (in(Y3, 98.17/14.81 Y1) => 98.17/14.81 in( 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 setadjoin( 98.17/14.81 Y3, 98.17/14.81 emptyset)), 98.17/14.81 emptyset)), 98.17/14.81 powerset( 98.17/14.81 powerset( 98.17/14.81 binunion( 98.17/14.81 Y0, Y1)))))))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (in(Y3, 98.17/14.81 Y1) => 98.17/14.81 in( 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 setadjoin( 98.17/14.81 Y3, 98.17/14.81 emptyset)), 98.17/14.81 emptyset)), 98.17/14.81 powerset( 98.17/14.81 powerset( 98.17/14.81 binunion( 98.17/14.81 Y0, Y1)))))))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (in(Y3, 98.17/14.81 Y1) => 98.17/14.81 in( 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 setadjoin( 98.17/14.81 Y3, 98.17/14.81 emptyset)), 98.17/14.81 emptyset)), 98.17/14.81 dsetconstr( 98.17/14.81 powerset( 98.17/14.81 powerset( 98.17/14.81 binunion( 98.17/14.81 Y0, Y1))), 98.17/14.81 (^[Y4 : $i]: 98.17/14.81 (??(( 98.17/14.81 ^[Y5 : $i]: 98.17/14.81 (in(Y5, 98.17/14.81 Y0) & 98.17/14.81 (??(( 98.17/14.81 ^[Y6 : $i]: 98.17/14.81 (in(Y6, 98.17/14.81 Y1) & 98.17/14.81 (Y4 = 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y5, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y5, 98.17/14.81 setadjoin( 98.17/14.81 Y6, 98.17/14.81 emptyset)), 98.17/14.81 emptyset)))))))))))))))))))))))))))) => 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 dsetconstr( 98.17/14.81 powerset( 98.17/14.81 powerset( 98.17/14.81 binunion( 98.17/14.81 Y0, Y1))), 98.17/14.81 (^[Y3 : $i]: 98.17/14.81 (??(( 98.17/14.81 ^[Y4 : $i]: 98.17/14.81 (in(Y4, 98.17/14.81 Y0) & 98.17/14.81 (??(( 98.17/14.81 ^[Y5 : $i]: 98.17/14.81 (in(Y5, 98.17/14.81 Y1) & 98.17/14.81 (Y3 = 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y4, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y4, 98.17/14.81 setadjoin( 98.17/14.81 Y5, 98.17/14.81 emptyset)), 98.17/14.81 emptyset)))))))))))))) => 98.17/14.81 (??(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (( 98.17/14.81 ??(( 98.17/14.81 ^[Y4 : $i]: 98.17/14.81 (in(Y4, 98.17/14.81 Y1) & 98.17/14.81 (Y2 = 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y3, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y3, 98.17/14.81 setadjoin( 98.17/14.81 Y4, 98.17/14.81 emptyset)), 98.17/14.81 emptyset))))))) & 98.17/14.81 in(Y3, 98.17/14.81 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 98.17/14.81 inference('lazy_cnf_imply', [status(thm)], ['166'])). 98.17/14.81 tff('168', plain, 98.17/14.81 ~ ((!!((^[Y0 : $i]: 98.17/14.81 (((!!((^[Y1 : $i]: 98.17/14.81 ((in(Y1, Y0) & in(Y1, omega)) => 98.17/14.81 in(setadjoin(Y1, Y1), Y0))))) & 98.17/14.81 in(emptyset, Y0)) => 98.17/14.81 (!!((^[Y1 : $i]: (in(Y1, omega) => in(Y1, Y0))))))))) => 98.17/14.81 ((!!((^[Y0 : ($i * $i) > $o]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 ((!!((^[Y2 : $i]: 98.17/14.81 (in(Y2, Y1) => 98.17/14.81 (??((^[Y3 : $i]: 98.17/14.81 (Y0(Y2, Y3) & 98.17/14.81 (!!((^[Y4 : $i]: 98.17/14.81 (Y0(Y2, Y4) => (Y3 = Y4))))))))))))) => 98.17/14.81 (??((^[Y2 : $i]: 98.17/14.81 (!!((^[Y3 : $i]: 98.17/14.81 (in(Y3, Y2) <=> 98.17/14.81 (??((^[Y4 : $i]: 98.17/14.81 (in(Y4, Y1) & Y0(Y4, Y3))))))))))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 98.17/14.81 (??((^[Y1 : $i]: 98.17/14.81 (in(Y1, Y0) & 98.17/14.81 (~((??((^[Y2 : $i]: (in(Y2, Y1) & in(Y2, Y0))))))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (??((^[Y1 : $i]: 98.17/14.81 ((!!((^[Y2 : $i]: 98.17/14.81 (in(Y2, Y1) => 98.17/14.81 (!!((^[Y3 : $i]: (in(Y3, Y2) => in(Y3, Y0)))))))))& 98.17/14.81 (!!((^[Y2 : $i]: 98.17/14.81 (!!((^[Y3 : $i]: 98.17/14.81 ((in(Y3, Y0) & in(Y2, Y0)) => 98.17/14.81 ((!!((^[Y4 : $i]: 98.17/14.81 (in(Y4, Y1) => 98.17/14.81 (in(Y2, Y4) <=> in(Y3, Y4)))))) => 98.17/14.81 (Y2 = Y3)))))))))& 98.17/14.81 (!!((^[Y2 : $i]: 98.17/14.81 (!!((^[Y3 : $i]: 98.17/14.81 ((in(Y3, Y1) & in(Y2, Y1)) => 98.17/14.81 ((!!((^[Y4 : $i]: 98.17/14.81 (in(Y4, Y3) => in(Y4, Y2))))) | 98.17/14.81 (!!((^[Y4 : $i]: 98.17/14.81 (in(Y4, Y2) => in(Y4, Y3)))))))))))))& 98.17/14.81 (!!((^[Y2 : $i]: 98.17/14.81 (((??((^[Y3 : $i]: in(Y3, Y2)))) & 98.17/14.81 (!!((^[Y3 : $i]: (in(Y3, Y2) => in(Y3, Y0)))))) => 98.17/14.81 (??((^[Y3 : $i]: 98.17/14.81 (??((^[Y4 : $i]: 98.17/14.81 (in(Y3, Y1)&in(Y4, Y2)& 98.17/14.81 (~((??((^[Y5 : $i]: 98.17/14.81 (in(Y5, Y3) & 98.17/14.81 in(Y5, Y2)))))))& 98.17/14.81 (!!((^[Y5 : $i]: 98.17/14.81 (in(Y5, Y1) => 98.17/14.81 (in(Y4, Y5) | 98.17/14.81 (!!((^[Y6 : $i]: 98.17/14.81 (in(Y6, Y5) => 98.17/14.81 in(Y6, Y3)))))))))))))))))))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i > $o]: 98.17/14.81 ((??((^[Y1 : $i]: 98.17/14.81 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 98.17/14.81 Y0(descr(Y0)))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i > $o]: 98.17/14.81 (!!((^[Y2 : $i]: 98.17/14.81 (in(Y2, Y0) => 98.17/14.81 (Y1(Y2) => in(Y2, dsetconstr(Y0, Y1))))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i > $o]: 98.17/14.81 (!!((^[Y2 : $i]: 98.17/14.81 (in(Y2, dsetconstr(Y0, Y1)) => in(Y2, Y0))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i > $o]: 98.17/14.81 (!!((^[Y2 : $i]: 98.17/14.81 (in(Y2, dsetconstr(Y0, Y1)) => Y1(Y2))))))))))) => 98.17/14.81 ((!!((^[Y0 : $o]: 98.17/14.81 (!!((^[Y1 : $i]: (in(Y1, prop2set(Y0)) => Y0))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: (in(Y0, emptyset) => (!!((^[Y1 : $o]: Y1))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 98.17/14.81 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 98.17/14.81 ((!!((^[Y0 : $i > $o]: 98.17/14.81 ((??((^[Y1 : $i]: 98.17/14.81 (Y0(Y1) & 98.17/14.81 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 98.17/14.81 (??(Y0)))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 ((!!((^[Y2 : $i]: 98.17/14.81 (in(Y2, Y0) => in(Y2, Y1))))) => 98.17/14.81 ((!!((^[Y2 : $i]: 98.17/14.81 (in(Y2, Y1) => in(Y2, Y0))))) => 98.17/14.81 (Y0 = Y1))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 98.17/14.81 (Y0 = emptyset))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 98.17/14.81 (Y0 = emptyset))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i > $o]: 98.17/14.81 (!!((^[Y2 : $i]: 98.17/14.81 (in(Y2, Y0) => 98.17/14.81 (in(Y2, dsetconstr(Y0, Y1)) <=> 98.17/14.81 Y1(Y2)))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 ((Y0 != emptyset) => 98.17/14.81 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i > $o]: 98.17/14.81 (!!((^[Y2 : $i]: 98.17/14.81 (in(Y2, Y0) => 98.17/14.81 (Y1(Y2) => 98.17/14.81 (dsetconstr(Y0, Y1) != 98.17/14.81 emptyset)))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 98.17/14.81 (Y0 != emptyset))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 98.17/14.81 (in(emptyset, setadjoin(emptyset, emptyset)) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 (!!((^[Y2 : $i]: 98.17/14.81 (in(Y2, Y1) => 98.17/14.81 in(Y2, setadjoin(Y0, Y1)))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 (!!((^[Y2 : $i]: 98.17/14.81 (in(Y2, setadjoin(Y0, Y1)) => 98.17/14.81 (!!((^[Y3 : $o]: 98.17/14.81 (((Y2 = Y0) => Y3) => 98.17/14.81 ((in(Y2, Y1) => 98.17/14.81 Y3) => 98.17/14.81 Y3))))))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 (!!((^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 setadjoin(Y0, Y1)) => 98.17/14.81 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (dsetconstr(Y0, (^[Y1 : $i]: $true)) = 98.17/14.81 Y0)))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 ((!!((^[Y2 : $i]: 98.17/14.81 (in(Y2, Y1) => 98.17/14.81 in(Y2, Y0))))) => 98.17/14.81 in(Y1, powerset(Y0))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 in(emptyset, powerset(Y0))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 (!!((^[Y2 : $i]: 98.17/14.81 (in(Y1, 98.17/14.81 powerset(Y0)) => 98.17/14.81 (in(Y2, Y1) => 98.17/14.81 in(Y2, Y0)))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 (!!((^[Y2 : $i]: 98.17/14.81 (in(Y1, Y2) => 98.17/14.81 (in(Y2, Y0) => 98.17/14.81 in(Y1, 98.17/14.81 setunion(Y0))))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 (in(Y1, setunion(Y0)) => 98.17/14.81 (!!((^[Y2 : $o]: 98.17/14.81 ((!!((^[Y3 : $i]: 98.17/14.81 ( 98.17/14.81 in(Y1, 98.17/14.81 Y3) => 98.17/14.81 ( 98.17/14.81 in(Y3, 98.17/14.81 Y0) => Y2))))) => 98.17/14.81 Y2))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 (in(Y1, Y0) => 98.17/14.81 in(Y1, 98.17/14.81 powerset( 98.17/14.81 setunion(Y0)))))))))) => 98.17/14.81 ((!!((^[Y0 : $i > $o]: 98.17/14.81 ((??((^[Y1 : $i]: 98.17/14.81 (Y0(Y1) & 98.17/14.81 (!!((^[Y2 : $i]: 98.17/14.81 (Y0(Y2) => 98.17/14.81 (Y1 = Y2))))))))) => 98.17/14.81 (??((^[Y1 : $i]: 98.17/14.81 (!!((^[Y2 : $i]: 98.17/14.81 (Y0(Y2) <=> 98.17/14.81 (Y2 = Y1)))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 ((Y0 != emptyset) => 98.17/14.81 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 (in(Y0, 98.17/14.81 setadjoin(Y1, 98.17/14.81 emptyset)) => 98.17/14.81 (Y0 = Y1)))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 ((Y0 != Y1) => 98.17/14.81 (~(in(Y1, 98.17/14.81 setadjoin(Y0, 98.17/14.81 emptyset))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 ((Y0 = Y1) => 98.17/14.81 in(Y0, 98.17/14.81 setadjoin(Y1, 98.17/14.81 emptyset))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 (in(Y0, 98.17/14.81 setadjoin(Y1, 98.17/14.81 emptyset)) => 98.17/14.81 in(Y1, 98.17/14.81 setadjoin(Y0, 98.17/14.81 emptyset))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 (!!((^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 Y2 = Y1) | 98.17/14.81 ( 98.17/14.81 Y2 = Y0)))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 in(Y0, 98.17/14.81 setadjoin(Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 in(Y1, 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i > $o]: 98.17/14.81 ((??(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) & 98.17/14.81 Y1(Y2))))) => 98.17/14.81 (dsetconstr( 98.17/14.81 Y0, Y1) != 98.17/14.81 emptyset)))))))) => 98.17/14.81 ((!!((^[Y0 : $i > $o]: 98.17/14.81 (!!((^[Y1 : $i]: 98.17/14.81 (in(Y1, 98.17/14.81 emptyset) => 98.17/14.81 Y0(Y1)))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i > $o]: 98.17/14.81 ((~(( 98.17/14.81 !!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 Y1(Y2))))))) => 98.17/14.81 (??(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) & 98.17/14.81 (~( 98.17/14.81 Y1(Y2)))))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i > $o]: 98.17/14.81 ((!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (~( 98.17/14.81 Y1(Y2))))))) => 98.17/14.81 (~(( 98.17/14.81 ??(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) & 98.17/14.81 Y1(Y2)))))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i > $o]: 98.17/14.81 (( 98.17/14.81 ~(( 98.17/14.81 ??(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) & 98.17/14.81 Y1(Y2))))))) => 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (~( 98.17/14.81 Y1(Y2)))))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!((^[Y1 : $i > $o]: 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 ??(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) & 98.17/14.81 (~( 98.17/14.81 Y1(Y2))))))) => 98.17/14.81 ( 98.17/14.81 ~(( 98.17/14.81 !!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 Y1(Y2)))))))))))))) => 98.17/14.81 ((!!((^[Y0 : $o]: 98.17/14.81 (Y0 => 98.17/14.81 in(emptyset, 98.17/14.81 prop2set(Y0)))))) => 98.17/14.81 ((!!((^[Y0 : $o]: 98.17/14.81 (Y0 => 98.17/14.81 set2prop( 98.17/14.81 prop2set( 98.17/14.81 Y0)))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i > $o]: 98.17/14.81 (( 98.17/14.81 ~(( 98.17/14.81 ??(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) & 98.17/14.81 Y1(Y2))))))) => 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (~( 98.17/14.81 Y1(Y2)))))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i > $o]: 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 ~(( 98.17/14.81 !!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 Y1(Y2))))))) => 98.17/14.81 ( 98.17/14.81 ??(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) & 98.17/14.81 (~( 98.17/14.81 Y1(Y2)))))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i > $o]: 98.17/14.81 ((??(Y0)) => 98.17/14.81 (( 98.17/14.81 !!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (Y0(Y1) => 98.17/14.81 (Y0(Y2) => 98.17/14.81 (Y1 = Y2))))))))) => 98.17/14.81 ( 98.17/14.81 ??(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (Y0(Y1) & 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (Y0(Y2) => 98.17/14.81 (Y1 = Y2)))))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i > $o]: 98.17/14.81 (( 98.17/14.81 ??(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (Y0(Y2) <=> 98.17/14.81 (Y2 = Y1)))))))) => 98.17/14.81 ( 98.17/14.81 ??(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (Y0(Y1) & 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (Y0(Y2) => 98.17/14.81 (Y1 = Y2))))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 Y0 = Y1) => 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (( 98.17/14.81 Y2 = Y3) => 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 in(Y3, 98.17/14.81 Y1)))))))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 Y0 = Y1) => 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (( 98.17/14.81 Y2 = Y3) => 98.17/14.81 (in(Y2, 98.17/14.81 Y0) <=> 98.17/14.81 in(Y3, 98.17/14.81 Y1)))))))))))))))) => 98.17/14.81 ((!!((^[Y0 : $i > $o]: 98.17/14.81 (( 98.17/14.81 ??(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (Y0(Y1) & 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (Y0(Y2) => 98.17/14.81 (Y1 = Y2))))))))) => 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (Y0(Y1) => 98.17/14.81 (Y0(Y2) => 98.17/14.81 (Y1 = Y2))))))))))))) => 98.17/14.81 ((!!(( 98.17/14.81 ^[Y0 : $i > $o]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i > $o]: 98.17/14.81 (( 98.17/14.81 !!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (( 98.17/14.81 Y2 = Y3) => 98.17/14.81 (Y0(Y2) <=> 98.17/14.81 Y1(Y3))))))))) => 98.17/14.81 (( 98.17/14.81 ??(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (Y0(Y2) & 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (Y0(Y3) => 98.17/14.81 (Y2 = Y3))))))))) <=> 98.17/14.81 (??(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (Y1(Y2) & 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (Y1(Y3) => 98.17/14.81 (Y2 = Y3))))))))))))))))) => 98.17/14.81 ((!!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 Y0 = Y1) => 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (( 98.17/14.81 Y2 = Y3) => 98.17/14.81 (setadjoin( 98.17/14.81 Y0, Y2) = 98.17/14.81 setadjoin( 98.17/14.81 Y1, Y3)))))))))))))))) => 98.17/14.81 ((!!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 Y0 = Y1) => 98.17/14.81 (powerset( 98.17/14.81 Y0) = 98.17/14.81 powerset( 98.17/14.81 Y1))))))))) => 98.17/14.81 ((!!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 Y0 = Y1) => 98.17/14.81 (setunion( 98.17/14.81 Y0) = 98.17/14.81 setunion( 98.17/14.81 Y1))))))))) => 98.17/14.81 (( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i > $o]: 98.17/14.81 (( 98.17/14.81 ??(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (Y0(Y1) & 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (Y0(Y2) => 98.17/14.81 (Y1 = Y2))))))))) => 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (Y0(Y1) => 98.17/14.81 (Y0(Y2) => 98.17/14.81 (Y1 = Y2))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i > $o]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i > $o]: 98.17/14.81 (( 98.17/14.81 !!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (( 98.17/14.81 Y2 = Y3) => 98.17/14.81 (Y0(Y2) <=> 98.17/14.81 Y1(Y3))))))))) => 98.17/14.81 (( 98.17/14.81 ??(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (Y0(Y2) & 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (Y0(Y3) => 98.17/14.81 (Y2 = Y3))))))))) => 98.17/14.81 (( 98.17/14.81 ??(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (Y1(Y2) & 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (Y1(Y3) => 98.17/14.81 (Y2 = Y3))))))))) => 98.17/14.81 (descr( 98.17/14.81 Y0) = 98.17/14.81 descr(Y1))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 Y0 = Y1) => 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i > $o]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i > $o]: 98.17/14.81 (( 98.17/14.81 !!(( 98.17/14.81 ^[Y4 : $i]: 98.17/14.81 (in(Y4, 98.17/14.81 Y0) => 98.17/14.81 (!!(( 98.17/14.81 ^[Y5 : $i]: 98.17/14.81 (in(Y5, 98.17/14.81 Y1) => 98.17/14.81 (( 98.17/14.81 Y4 = Y5) => 98.17/14.81 (Y2(Y4) <=> 98.17/14.81 Y3(Y5))))))))))) => 98.17/14.81 (dsetconstr( 98.17/14.81 Y0, Y2) = 98.17/14.81 dsetconstr( 98.17/14.81 Y1, Y3)))))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 !!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 in(Y2, 98.17/14.81 Y1))))) => 98.17/14.81 subset( 98.17/14.81 Y0, Y1)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 Y0 = Y1) => 98.17/14.81 subset( 98.17/14.81 Y1, Y0)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 Y0 = Y1) => 98.17/14.81 subset( 98.17/14.81 Y0, Y1)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 !!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 in(Y2, 98.17/14.81 Y1))))) => 98.17/14.81 subset( 98.17/14.81 Y0, Y1)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!( 98.17/14.81 subset( 98.17/14.81 emptyset))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (subset( 98.17/14.81 Y0, Y1) => 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 in(Y2, 98.17/14.81 Y1)))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (subset( 98.17/14.81 Y0, Y1) => 98.17/14.81 (( 98.17/14.81 ~( 98.17/14.81 in(Y2, 98.17/14.81 Y1))) => 98.17/14.81 (~( 98.17/14.81 in(Y2, 98.17/14.81 Y0)))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (( 98.17/14.81 ~( 98.17/14.81 in(Y2, 98.17/14.81 Y1))) => 98.17/14.81 (~( 98.17/14.81 subset( 98.17/14.81 Y0, Y1)))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 ~( 98.17/14.81 subset( 98.17/14.81 Y0, Y1))) => 98.17/14.81 (Y0 != Y1)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (( 98.17/14.81 ~( 98.17/14.81 in(Y2, 98.17/14.81 Y1))) => 98.17/14.81 (Y0 != Y1)))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 subset( 98.17/14.81 Y0, Y0)))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (subset( 98.17/14.81 Y0, Y1) => 98.17/14.81 (subset( 98.17/14.81 Y1, Y2) => 98.17/14.81 subset( 98.17/14.81 Y0, Y2)))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 subset( 98.17/14.81 Y1, 98.17/14.81 setadjoin( 98.17/14.81 Y0, Y1)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (subset( 98.17/14.81 Y0, Y2) => 98.17/14.81 subset( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, Y2)))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (subset( 98.17/14.81 Y0, Y1) => 98.17/14.81 in(Y0, 98.17/14.81 powerset( 98.17/14.81 Y1))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (subset( 98.17/14.81 Y0, Y1) => 98.17/14.81 (subset( 98.17/14.81 Y1, Y0) => 98.17/14.81 (Y0 = Y1))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (subset( 98.17/14.81 Y0, 98.17/14.81 emptyset) => 98.17/14.81 (Y0 = 98.17/14.81 emptyset))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (subset( 98.17/14.81 Y1, Y0) => 98.17/14.81 in(Y1, 98.17/14.81 powerset( 98.17/14.81 Y0))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (in(Y1, 98.17/14.81 powerset( 98.17/14.81 Y0)) => 98.17/14.81 subset( 98.17/14.81 Y1, Y0)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 in(Y0, 98.17/14.81 powerset( 98.17/14.81 Y0))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (subset( 98.17/14.81 Y0, Y1) => 98.17/14.81 subset( 98.17/14.81 powerset( 98.17/14.81 Y0), 98.17/14.81 powerset( 98.17/14.81 Y1))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i > $o]: 98.17/14.81 in( 98.17/14.81 dsetconstr( 98.17/14.81 Y0, Y1), 98.17/14.81 powerset( 98.17/14.81 Y0)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i > $o]: 98.17/14.81 subset( 98.17/14.81 dsetconstr( 98.17/14.81 Y0, Y1), 98.17/14.81 Y0))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 in(Y2, 98.17/14.81 binunion( 98.17/14.81 Y0, Y1)))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 in(Y1, 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y1) => 98.17/14.81 in(Y2, 98.17/14.81 binunion( 98.17/14.81 Y0, Y1)))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $o]: 98.17/14.81 (in(Y2, 98.17/14.81 binunion( 98.17/14.81 Y0, Y1)) => 98.17/14.81 (( 98.17/14.81 in(Y2, 98.17/14.81 Y0) => Y3) => 98.17/14.81 (( 98.17/14.81 in(Y2, 98.17/14.81 Y1) => Y3) => 98.17/14.81 Y3))))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 binunion( 98.17/14.81 Y0, Y1)) => 98.17/14.81 (in(Y2, 98.17/14.81 Y1) | 98.17/14.81 in(Y2, 98.17/14.81 Y0)))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 subset( 98.17/14.81 Y0, 98.17/14.81 binunion( 98.17/14.81 Y0, Y1)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 subset( 98.17/14.81 Y1, 98.17/14.81 binunion( 98.17/14.81 Y0, Y1)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (in(Y2, 98.17/14.81 Y1) => 98.17/14.81 in(Y2, 98.17/14.81 binintersect( 98.17/14.81 Y0, Y1))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (subset( 98.17/14.81 Y2, Y0) => 98.17/14.81 (subset( 98.17/14.81 Y2, Y1) => 98.17/14.81 subset( 98.17/14.81 Y2, 98.17/14.81 binintersect( 98.17/14.81 Y0, Y1))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 binintersect( 98.17/14.81 Y0, Y1)) => 98.17/14.81 in(Y2, 98.17/14.81 Y0))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 subset( 98.17/14.81 binintersect( 98.17/14.81 Y0, Y1), 98.17/14.81 Y0))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (subset( 98.17/14.81 Y0, Y1) => 98.17/14.81 (binintersect( 98.17/14.81 Y0, Y1) = 98.17/14.81 Y0)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 binintersect( 98.17/14.81 Y0, Y1) = 98.17/14.81 Y1) => 98.17/14.81 subset( 98.17/14.81 Y1, Y0)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 binintersect( 98.17/14.81 Y0, Y1)) => 98.17/14.81 in(Y2, 98.17/14.81 Y1))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 ~(( 98.17/14.81 ??(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) & 98.17/14.81 in(Y2, 98.17/14.81 Y1))))))) => 98.17/14.81 (binintersect( 98.17/14.81 Y0, Y1) = 98.17/14.81 emptyset)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 subset( 98.17/14.81 binintersect( 98.17/14.81 Y0, Y1), 98.17/14.81 Y1))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (subset( 98.17/14.81 Y1, Y0) => 98.17/14.81 (binintersect( 98.17/14.81 Y0, Y1) = 98.17/14.81 Y1)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 binintersect( 98.17/14.81 Y0, Y1) = 98.17/14.81 Y0) => 98.17/14.81 subset( 98.17/14.81 Y0, Y1)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (binintersect( 98.17/14.81 Y0, 98.17/14.81 binunion( 98.17/14.81 Y1, Y2)) = 98.17/14.81 binunion( 98.17/14.81 binintersect( 98.17/14.81 Y0, Y1), 98.17/14.81 binintersect( 98.17/14.81 Y0, Y2)))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (( 98.17/14.81 ~( 98.17/14.81 in(Y2, 98.17/14.81 Y1))) => 98.17/14.81 in(Y2, 98.17/14.81 setminus( 98.17/14.81 Y0, Y1))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 setminus( 98.17/14.81 Y0, Y1)) => 98.17/14.81 in(Y2, 98.17/14.81 Y0))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 setminus( 98.17/14.81 Y0, Y1)) => 98.17/14.81 (~( 98.17/14.81 in(Y2, 98.17/14.81 Y1))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (subset( 98.17/14.81 Y0, Y1) => 98.17/14.81 (setminus( 98.17/14.81 Y0, Y1) = 98.17/14.81 emptyset)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (( 98.17/14.81 ~( 98.17/14.81 in(Y2, 98.17/14.81 setminus( 98.17/14.81 Y0, Y1)))) => 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 in(Y2, 98.17/14.81 Y1)))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (( 98.17/14.81 ~( 98.17/14.81 in(Y2, 98.17/14.81 setminus( 98.17/14.81 Y0, Y1)))) => 98.17/14.81 (( 98.17/14.81 ~( 98.17/14.81 in(Y2, 98.17/14.81 Y1))) => 98.17/14.81 (~( 98.17/14.81 in(Y2, 98.17/14.81 Y0)))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (( 98.17/14.81 ~( 98.17/14.81 in(Y2, 98.17/14.81 Y0))) => 98.17/14.81 (~( 98.17/14.81 in(Y2, 98.17/14.81 setminus( 98.17/14.81 Y0, Y1)))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y1) => 98.17/14.81 (~( 98.17/14.81 in(Y2, 98.17/14.81 setminus( 98.17/14.81 Y0, Y1)))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 subset( 98.17/14.81 setminus( 98.17/14.81 Y0, Y1), 98.17/14.81 Y0))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (( 98.17/14.81 setminus( 98.17/14.81 Y0, Y1) = 98.17/14.81 emptyset) => 98.17/14.81 subset( 98.17/14.81 Y0, Y1)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 symdiff( 98.17/14.81 Y0, Y1)) => 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $o]: 98.17/14.81 (( 98.17/14.81 in(Y2, 98.17/14.81 Y0) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 ~( 98.17/14.81 in(Y2, 98.17/14.81 Y1))) => 98.17/14.81 Y3)) => 98.17/14.81 (( 98.17/14.81 ( 98.17/14.81 ~( 98.17/14.81 in(Y2, 98.17/14.81 Y0))) => 98.17/14.81 ( 98.17/14.81 in(Y2, 98.17/14.81 Y1) => Y3)) => 98.17/14.81 Y3))))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (( 98.17/14.81 ~( 98.17/14.81 in(Y2, 98.17/14.81 Y1))) => 98.17/14.81 in(Y2, 98.17/14.81 symdiff( 98.17/14.81 Y0, Y1))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (( 98.17/14.81 ~( 98.17/14.81 in(Y2, 98.17/14.81 Y0))) => 98.17/14.81 (in(Y2, 98.17/14.81 Y1) => 98.17/14.81 in(Y2, 98.17/14.81 symdiff( 98.17/14.81 Y0, Y1))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (in(Y2, 98.17/14.81 Y1) => 98.17/14.81 (~( 98.17/14.81 in(Y2, 98.17/14.81 symdiff( 98.17/14.81 Y0, Y1))))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (( 98.17/14.81 ~( 98.17/14.81 in(Y2, 98.17/14.81 Y0))) => 98.17/14.81 (( 98.17/14.81 ~( 98.17/14.81 in(Y2, 98.17/14.81 Y1))) => 98.17/14.81 (~( 98.17/14.81 in(Y2, 98.17/14.81 symdiff( 98.17/14.81 Y0, Y1))))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 in(Y1, 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 in(Y0, 98.17/14.81 setunion( 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset)), 98.17/14.81 emptyset)))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 in(Y1, 98.17/14.81 setunion( 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset)), 98.17/14.81 emptyset)))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (??(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 setunion( 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset)), 98.17/14.81 emptyset)))) & 98.17/14.81 (??(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (in(Y3, 98.17/14.81 setunion( 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset)), 98.17/14.81 emptyset)))) & 98.17/14.81 (setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset)), 98.17/14.81 emptyset)) = 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 setadjoin( 98.17/14.81 Y3, 98.17/14.81 emptyset)), 98.17/14.81 emptyset))))))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (??(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 setunion( 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset)), 98.17/14.81 emptyset)))) & 98.17/14.81 (??(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (in(Y3, 98.17/14.81 setunion( 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset)), 98.17/14.81 emptyset)))) & 98.17/14.81 (setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset)), 98.17/14.81 emptyset)) = 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 setadjoin( 98.17/14.81 Y3, 98.17/14.81 emptyset)), 98.17/14.81 emptyset))))))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (in(Y1, 98.17/14.81 Y0) => 98.17/14.81 subset( 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset), 98.17/14.81 Y0)))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (in(Y1, 98.17/14.81 Y0) => 98.17/14.81 in( 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset), 98.17/14.81 powerset( 98.17/14.81 Y0))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 in( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 emptyset), 98.17/14.81 powerset( 98.17/14.81 binunion( 98.17/14.81 Y0, Y1))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 setadjoin( 98.17/14.81 Y0, 98.17/14.81 setadjoin( 98.17/14.81 Y1, 98.17/14.81 emptyset))) => 98.17/14.81 (( 98.17/14.81 Y2 = Y1) | 98.17/14.81 (Y2 = Y0)))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (in(Y3, 98.17/14.81 Y1) => 98.17/14.81 subset( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 setadjoin( 98.17/14.81 Y3, 98.17/14.81 emptyset)), 98.17/14.81 binunion( 98.17/14.81 Y0, Y1)))))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (in(Y3, 98.17/14.81 Y1) => 98.17/14.81 in( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 setadjoin( 98.17/14.81 Y3, 98.17/14.81 emptyset)), 98.17/14.81 powerset( 98.17/14.81 binunion( 98.17/14.81 Y0, Y1))))))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (in(Y3, 98.17/14.81 Y1) => 98.17/14.81 subset( 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 setadjoin( 98.17/14.81 Y3, 98.17/14.81 emptyset)), 98.17/14.81 emptyset)), 98.17/14.81 powerset( 98.17/14.81 binunion( 98.17/14.81 Y0, Y1))))))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (in(Y3, 98.17/14.81 Y1) => 98.17/14.81 in( 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 setadjoin( 98.17/14.81 Y3, 98.17/14.81 emptyset)), 98.17/14.81 emptyset)), 98.17/14.81 powerset( 98.17/14.81 powerset( 98.17/14.81 binunion( 98.17/14.81 Y0, Y1)))))))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (in(Y3, 98.17/14.81 Y1) => 98.17/14.81 in( 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 setadjoin( 98.17/14.81 Y3, 98.17/14.81 emptyset)), 98.17/14.81 emptyset)), 98.17/14.81 powerset( 98.17/14.81 powerset( 98.17/14.81 binunion( 98.17/14.81 Y0, Y1)))))))))))))))))) => 98.17/14.81 ( 98.17/14.81 ( 98.17/14.81 !!(( 98.17/14.81 ^[Y0 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y1 : $i]: 98.17/14.81 (!!(( 98.17/14.81 ^[Y2 : $i]: 98.17/14.81 (in(Y2, 98.17/14.81 Y0) => 98.17/14.81 (!!(( 98.17/14.81 ^[Y3 : $i]: 98.17/14.81 (in(Y3, 98.17/14.81 Y1) => 98.17/14.81 in( 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 emptyset), 98.17/14.81 setadjoin( 98.17/14.81 setadjoin( 98.17/14.81 Y2, 98.17/14.81 setadjoin( 98.17/14.81 Y3, 98.17/14.81 emptyset)), 98.17/14.81 emptyset)), 98.17/14.81 dsetconstr( 98.17/14.81 powerset( 98.17/14.81 powerset( 98.17/14.81 binunion( 98.17/14.81 Y0, Y1))), 98.17/14.81 (^[Y4 : $i]: 98.17/14.81 (??(( 98.17/14.81 ^[Y5 : $i]: 98.17/14.81 (in(Y5, 98.17/14.81 Y0) & 98.17/14.82 (??(( 98.17/14.82 ^[Y6 : $i]: 98.17/14.82 (in(Y6, 98.17/14.82 Y1) & 98.17/14.82 (Y4 = 98.17/14.82 setadjoin( 98.17/14.82 setadjoin( 98.17/14.82 Y5, 98.17/14.82 emptyset), 98.17/14.82 setadjoin( 98.17/14.82 setadjoin( 98.17/14.82 Y5, 98.17/14.82 setadjoin( 98.17/14.82 Y6, 98.17/14.82 emptyset)), 98.17/14.82 emptyset)))))))))))))))))))))))))))) => 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 dsetconstr( 98.17/14.82 powerset( 98.17/14.82 powerset( 98.17/14.82 binunion( 98.17/14.82 Y0, Y1))), 98.17/14.82 (^[Y3 : $i]: 98.17/14.82 (??(( 98.17/14.82 ^[Y4 : $i]: 98.17/14.82 (in(Y4, 98.17/14.82 Y0) & 98.17/14.82 (??(( 98.17/14.82 ^[Y5 : $i]: 98.17/14.82 (in(Y5, 98.17/14.82 Y1) & 98.17/14.82 (Y3 = 98.17/14.82 setadjoin( 98.17/14.82 setadjoin( 98.17/14.82 Y4, 98.17/14.82 emptyset), 98.17/14.82 setadjoin( 98.17/14.82 setadjoin( 98.17/14.82 Y4, 98.17/14.82 setadjoin( 98.17/14.82 Y5, 98.17/14.82 emptyset)), 98.17/14.82 emptyset)))))))))))))) => 98.17/14.82 (??(( 98.17/14.82 ^[Y3 : $i]: 98.17/14.82 (( 98.17/14.82 ??(( 98.17/14.82 ^[Y4 : $i]: 98.17/14.82 (in(Y4, 98.17/14.82 Y1) & 98.17/14.82 (Y2 = 98.17/14.82 setadjoin( 98.17/14.82 setadjoin( 98.17/14.82 Y3, 98.17/14.82 emptyset), 98.17/14.82 setadjoin( 98.17/14.82 setadjoin( 98.17/14.82 Y3, 98.17/14.82 setadjoin( 98.17/14.82 Y4, 98.17/14.82 emptyset)), 98.17/14.82 emptyset))))))) & 98.17/14.82 in(Y3, 98.17/14.82 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 98.17/14.82 inference('lazy_cnf_imply', [status(thm)], ['167'])). 98.17/14.82 tff('169', plain, 98.17/14.82 ~ ((!!((^[Y0 : ($i * $i) > $o]: 98.17/14.82 (!!((^[Y1 : $i]: 98.17/14.82 ((!!((^[Y2 : $i]: 98.17/14.82 (in(Y2, Y1) => 98.17/14.82 (??((^[Y3 : $i]: 98.17/14.82 (Y0(Y2, Y3) & 98.17/14.82 (!!((^[Y4 : $i]: 98.17/14.82 (Y0(Y2, Y4) => (Y3 = Y4))))))))))))) => 98.17/14.82 (??((^[Y2 : $i]: 98.17/14.82 (!!((^[Y3 : $i]: 98.17/14.82 (in(Y3, Y2) <=> 98.17/14.82 (??((^[Y4 : $i]: 98.17/14.82 (in(Y4, Y1) & Y0(Y4, Y3))))))))))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 98.17/14.82 (??((^[Y1 : $i]: 98.17/14.82 (in(Y1, Y0) & 98.17/14.82 (~((??((^[Y2 : $i]: (in(Y2, Y1) & in(Y2, Y0))))))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (??((^[Y1 : $i]: 98.17/14.82 ((!!((^[Y2 : $i]: 98.17/14.82 (in(Y2, Y1) => 98.17/14.82 (!!((^[Y3 : $i]: (in(Y3, Y2) => in(Y3, Y0)))))))))& 98.17/14.82 (!!((^[Y2 : $i]: 98.17/14.82 (!!((^[Y3 : $i]: 98.17/14.82 ((in(Y3, Y0) & in(Y2, Y0)) => 98.17/14.82 ((!!((^[Y4 : $i]: 98.17/14.82 (in(Y4, Y1) => 98.17/14.82 (in(Y2, Y4) <=> in(Y3, Y4)))))) => 98.17/14.82 (Y2 = Y3)))))))))& 98.17/14.82 (!!((^[Y2 : $i]: 98.17/14.82 (!!((^[Y3 : $i]: 98.17/14.82 ((in(Y3, Y1) & in(Y2, Y1)) => 98.17/14.82 ((!!((^[Y4 : $i]: 98.17/14.82 (in(Y4, Y3) => in(Y4, Y2))))) | 98.17/14.82 (!!((^[Y4 : $i]: 98.17/14.82 (in(Y4, Y2) => in(Y4, Y3)))))))))))))& 98.17/14.82 (!!((^[Y2 : $i]: 98.17/14.82 (((??((^[Y3 : $i]: in(Y3, Y2)))) & 98.17/14.82 (!!((^[Y3 : $i]: (in(Y3, Y2) => in(Y3, Y0)))))) => 98.17/14.82 (??((^[Y3 : $i]: 98.17/14.82 (??((^[Y4 : $i]: 98.17/14.82 (in(Y3, Y1)&in(Y4, Y2)& 98.17/14.82 (~((??((^[Y5 : $i]: 98.17/14.82 (in(Y5, Y3) & 98.17/14.82 in(Y5, Y2)))))))& 98.17/14.82 (!!((^[Y5 : $i]: 98.17/14.82 (in(Y5, Y1) => 98.17/14.82 (in(Y4, Y5) | 98.17/14.82 (!!((^[Y6 : $i]: 98.17/14.82 (in(Y6, Y5) => 98.17/14.82 in(Y6, Y3)))))))))))))))))))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i > $o]: 98.17/14.82 ((??((^[Y1 : $i]: 98.17/14.82 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 98.17/14.82 Y0(descr(Y0)))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i > $o]: 98.17/14.82 (!!((^[Y2 : $i]: 98.17/14.82 (in(Y2, Y0) => 98.17/14.82 (Y1(Y2) => in(Y2, dsetconstr(Y0, Y1))))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i > $o]: 98.17/14.82 (!!((^[Y2 : $i]: 98.17/14.82 (in(Y2, dsetconstr(Y0, Y1)) => in(Y2, Y0))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i > $o]: 98.17/14.82 (!!((^[Y2 : $i]: 98.17/14.82 (in(Y2, dsetconstr(Y0, Y1)) => Y1(Y2))))))))))) => 98.17/14.82 ((!!((^[Y0 : $o]: 98.17/14.82 (!!((^[Y1 : $i]: (in(Y1, prop2set(Y0)) => Y0))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: (in(Y0, emptyset) => (!!((^[Y1 : $o]: Y1))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 98.17/14.82 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 98.17/14.82 ((!!((^[Y0 : $i > $o]: 98.17/14.82 ((??((^[Y1 : $i]: 98.17/14.82 (Y0(Y1) & 98.17/14.82 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 98.17/14.82 (??(Y0)))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i]: 98.17/14.82 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 98.17/14.82 ((!!((^[Y2 : $i]: 98.17/14.82 (in(Y2, Y1) => in(Y2, Y0))))) => 98.17/14.82 (Y0 = Y1))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 98.17/14.82 (Y0 = emptyset))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 98.17/14.82 (Y0 = emptyset))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i > $o]: 98.17/14.82 (!!((^[Y2 : $i]: 98.17/14.82 (in(Y2, Y0) => 98.17/14.82 (in(Y2, dsetconstr(Y0, Y1)) <=> 98.17/14.82 Y1(Y2)))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 ((Y0 != emptyset) => 98.17/14.82 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i > $o]: 98.17/14.82 (!!((^[Y2 : $i]: 98.17/14.82 (in(Y2, Y0) => 98.17/14.82 (Y1(Y2) => 98.17/14.82 (dsetconstr(Y0, Y1) != 98.17/14.82 emptyset)))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 98.17/14.82 (Y0 != emptyset))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 98.17/14.82 (in(emptyset, setadjoin(emptyset, emptyset)) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i]: 98.17/14.82 (!!((^[Y2 : $i]: 98.17/14.82 (in(Y2, Y1) => 98.17/14.82 in(Y2, setadjoin(Y0, Y1)))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i]: 98.17/14.82 (!!((^[Y2 : $i]: 98.17/14.82 (in(Y2, setadjoin(Y0, Y1)) => 98.17/14.82 (!!((^[Y3 : $o]: 98.17/14.82 (((Y2 = Y0) => Y3) => 98.17/14.82 ((in(Y2, Y1) => Y3) => 98.17/14.82 Y3))))))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i]: 98.17/14.82 (!!((^[Y2 : $i]: 98.17/14.82 (in(Y2, setadjoin(Y0, Y1)) => 98.17/14.82 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (dsetconstr(Y0, (^[Y1 : $i]: $true)) = 98.17/14.82 Y0)))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i]: 98.17/14.82 ((!!((^[Y2 : $i]: 98.17/14.82 (in(Y2, Y1) => 98.17/14.82 in(Y2, Y0))))) => 98.17/14.82 in(Y1, powerset(Y0))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.17/14.82 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i]: 98.17/14.82 (!!((^[Y2 : $i]: 98.17/14.82 (in(Y1, powerset(Y0)) => 98.17/14.82 (in(Y2, Y1) => 98.17/14.82 in(Y2, Y0)))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i]: 98.17/14.82 (!!((^[Y2 : $i]: 98.17/14.82 (in(Y1, Y2) => 98.17/14.82 (in(Y2, Y0) => 98.17/14.82 in(Y1, 98.17/14.82 setunion(Y0))))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i]: 98.17/14.82 (in(Y1, setunion(Y0)) => 98.17/14.82 (!!((^[Y2 : $o]: 98.17/14.82 ((!!((^[Y3 : $i]: 98.17/14.82 (in(Y1, 98.17/14.82 Y3) => 98.17/14.82 ( 98.17/14.82 in(Y3, 98.17/14.82 Y0) => Y2))))) => 98.17/14.82 Y2))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i]: 98.17/14.82 (in(Y1, Y0) => 98.17/14.82 in(Y1, 98.17/14.82 powerset(setunion(Y0)))))))))) => 98.17/14.82 ((!!((^[Y0 : $i > $o]: 98.17/14.82 ((??((^[Y1 : $i]: 98.17/14.82 (Y0(Y1) & 98.17/14.82 (!!((^[Y2 : $i]: 98.17/14.82 (Y0(Y2) => 98.17/14.82 (Y1 = Y2))))))))) => 98.17/14.82 (??((^[Y1 : $i]: 98.17/14.82 (!!((^[Y2 : $i]: 98.17/14.82 (Y0(Y2) <=> 98.17/14.82 (Y2 = Y1)))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 ((Y0 != emptyset) => 98.17/14.82 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i]: 98.17/14.82 (in(Y0, 98.17/14.82 setadjoin(Y1, 98.17/14.82 emptyset)) => 98.17/14.82 (Y0 = Y1)))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i]: 98.17/14.82 ((Y0 != Y1) => 98.17/14.82 (~(in(Y1, 98.17/14.82 setadjoin(Y0, 98.17/14.82 emptyset))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i]: 98.17/14.82 ((Y0 = Y1) => 98.17/14.82 in(Y0, 98.17/14.82 setadjoin(Y1, 98.17/14.82 emptyset))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i]: 98.17/14.82 (in(Y0, 98.17/14.82 setadjoin(Y1, 98.17/14.82 emptyset)) => 98.17/14.82 in(Y1, 98.17/14.82 setadjoin(Y0, 98.17/14.82 emptyset))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i]: 98.17/14.82 (!!((^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 setadjoin( 98.17/14.82 Y0, 98.17/14.82 setadjoin( 98.17/14.82 Y1, 98.17/14.82 emptyset))) => 98.17/14.82 (( 98.17/14.82 Y2 = Y1) | 98.17/14.82 ( 98.17/14.82 Y2 = Y0)))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i]: 98.17/14.82 in(Y0, 98.17/14.82 setadjoin(Y0, 98.17/14.82 setadjoin( 98.17/14.82 Y1, 98.17/14.82 emptyset))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i]: 98.17/14.82 in(Y1, 98.17/14.82 setadjoin(Y0, 98.17/14.82 setadjoin( 98.17/14.82 Y1, 98.17/14.82 emptyset))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i > $o]: 98.17/14.82 ((??((^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) & 98.17/14.82 Y1(Y2))))) => 98.17/14.82 (dsetconstr( 98.17/14.82 Y0, Y1) != 98.17/14.82 emptyset)))))))) => 98.17/14.82 ((!!((^[Y0 : $i > $o]: 98.17/14.82 (!!((^[Y1 : $i]: 98.17/14.82 (in(Y1, 98.17/14.82 emptyset) => 98.17/14.82 Y0(Y1)))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i > $o]: 98.17/14.82 ((~(( 98.17/14.82 !!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 ( 98.17/14.82 in(Y2, 98.17/14.82 Y0) => 98.17/14.82 Y1(Y2))))))) => 98.17/14.82 (??(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 ( 98.17/14.82 in(Y2, 98.17/14.82 Y0) & 98.17/14.82 ( 98.17/14.82 ~( 98.17/14.82 Y1(Y2)))))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i > $o]: 98.17/14.82 ((!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) => 98.17/14.82 (~( 98.17/14.82 Y1(Y2))))))) => 98.17/14.82 (~(( 98.17/14.82 ??(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) & 98.17/14.82 Y1(Y2)))))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i > $o]: 98.17/14.82 ((~(( 98.17/14.82 ??(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) & 98.17/14.82 Y1(Y2))))))) => 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) => 98.17/14.82 (~( 98.17/14.82 Y1(Y2)))))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i > $o]: 98.17/14.82 (( 98.17/14.82 ??(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) & 98.17/14.82 (~( 98.17/14.82 Y1(Y2))))))) => 98.17/14.82 ( 98.17/14.82 ~(( 98.17/14.82 !!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) => 98.17/14.82 Y1(Y2)))))))))))))) => 98.17/14.82 ((!!((^[Y0 : $o]: 98.17/14.82 (Y0 => 98.17/14.82 in(emptyset, 98.17/14.82 prop2set(Y0)))))) => 98.17/14.82 ((!!((^[Y0 : $o]: 98.17/14.82 (Y0 => 98.17/14.82 set2prop( 98.17/14.82 prop2set(Y0)))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i > $o]: 98.17/14.82 (( 98.17/14.82 ~(( 98.17/14.82 ??(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) & 98.17/14.82 Y1(Y2))))))) => 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) => 98.17/14.82 (~( 98.17/14.82 Y1(Y2)))))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i > $o]: 98.17/14.82 (( 98.17/14.82 ~(( 98.17/14.82 !!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) => 98.17/14.82 Y1(Y2))))))) => 98.17/14.82 ( 98.17/14.82 ??(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) & 98.17/14.82 (~( 98.17/14.82 Y1(Y2)))))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i > $o]: 98.17/14.82 ((??(Y0)) => 98.17/14.82 ((!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (Y0(Y1) => 98.17/14.82 (Y0(Y2) => 98.17/14.82 (Y1 = Y2))))))))) => 98.17/14.82 (??(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (Y0(Y1) & 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (Y0(Y2) => 98.17/14.82 (Y1 = Y2)))))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i > $o]: 98.17/14.82 ((??(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (Y0(Y2) <=> 98.17/14.82 (Y2 = Y1)))))))) => 98.17/14.82 (??(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (Y0(Y1) & 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (Y0(Y2) => 98.17/14.82 (Y1 = Y2))))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (( 98.17/14.82 Y0 = Y1) => 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y3 : $i]: 98.17/14.82 (( 98.17/14.82 Y2 = Y3) => 98.17/14.82 (in(Y2, 98.17/14.82 Y0) => 98.17/14.82 in(Y3, 98.17/14.82 Y1)))))))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (( 98.17/14.82 Y0 = Y1) => 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y3 : $i]: 98.17/14.82 (( 98.17/14.82 Y2 = Y3) => 98.17/14.82 (in(Y2, 98.17/14.82 Y0) <=> 98.17/14.82 in(Y3, 98.17/14.82 Y1)))))))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i > $o]: 98.17/14.82 (( 98.17/14.82 ??(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (Y0(Y1) & 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (Y0(Y2) => 98.17/14.82 (Y1 = Y2))))))))) => 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (Y0(Y1) => 98.17/14.82 (Y0(Y2) => 98.17/14.82 (Y1 = Y2))))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i > $o]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i > $o]: 98.17/14.82 (( 98.17/14.82 !!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y3 : $i]: 98.17/14.82 (( 98.17/14.82 Y2 = Y3) => 98.17/14.82 (Y0(Y2) <=> 98.17/14.82 Y1(Y3))))))))) => 98.17/14.82 (( 98.17/14.82 ??(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (Y0(Y2) & 98.17/14.82 (!!(( 98.17/14.82 ^[Y3 : $i]: 98.17/14.82 (Y0(Y3) => 98.17/14.82 (Y2 = Y3))))))))) <=> 98.17/14.82 (??(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (Y1(Y2) & 98.17/14.82 (!!(( 98.17/14.82 ^[Y3 : $i]: 98.17/14.82 (Y1(Y3) => 98.17/14.82 (Y2 = Y3))))))))))))))))) => 98.17/14.82 ((!!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (( 98.17/14.82 Y0 = Y1) => 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y3 : $i]: 98.17/14.82 (( 98.17/14.82 Y2 = Y3) => 98.17/14.82 (setadjoin( 98.17/14.82 Y0, Y2) = 98.17/14.82 setadjoin( 98.17/14.82 Y1, Y3)))))))))))))))) => 98.17/14.82 ((!!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (( 98.17/14.82 Y0 = Y1) => 98.17/14.82 (powerset( 98.17/14.82 Y0) = 98.17/14.82 powerset( 98.17/14.82 Y1))))))))) => 98.17/14.82 ((!!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (( 98.17/14.82 Y0 = Y1) => 98.17/14.82 (setunion( 98.17/14.82 Y0) = 98.17/14.82 setunion( 98.17/14.82 Y1))))))))) => 98.17/14.82 ((!!(( 98.17/14.82 ^[Y0 : $i > $o]: 98.17/14.82 (( 98.17/14.82 ??(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (Y0(Y1) & 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (Y0(Y2) => 98.17/14.82 (Y1 = Y2))))))))) => 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (Y0(Y1) => 98.17/14.82 (Y0(Y2) => 98.17/14.82 (Y1 = Y2))))))))))))) => 98.17/14.82 (( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i > $o]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i > $o]: 98.17/14.82 (( 98.17/14.82 !!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y3 : $i]: 98.17/14.82 (( 98.17/14.82 Y2 = Y3) => 98.17/14.82 (Y0(Y2) <=> 98.17/14.82 Y1(Y3))))))))) => 98.17/14.82 (( 98.17/14.82 ??(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (Y0(Y2) & 98.17/14.82 (!!(( 98.17/14.82 ^[Y3 : $i]: 98.17/14.82 (Y0(Y3) => 98.17/14.82 (Y2 = Y3))))))))) => 98.17/14.82 (( 98.17/14.82 ??(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (Y1(Y2) & 98.17/14.82 (!!(( 98.17/14.82 ^[Y3 : $i]: 98.17/14.82 (Y1(Y3) => 98.17/14.82 (Y2 = Y3))))))))) => 98.17/14.82 (descr( 98.17/14.82 Y0) = 98.17/14.82 descr(Y1))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (( 98.17/14.82 Y0 = Y1) => 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i > $o]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y3 : $i > $o]: 98.17/14.82 (( 98.17/14.82 !!(( 98.17/14.82 ^[Y4 : $i]: 98.17/14.82 (in(Y4, 98.17/14.82 Y0) => 98.17/14.82 (!!(( 98.17/14.82 ^[Y5 : $i]: 98.17/14.82 (in(Y5, 98.17/14.82 Y1) => 98.17/14.82 (( 98.17/14.82 Y4 = Y5) => 98.17/14.82 (Y2(Y4) <=> 98.17/14.82 Y3(Y5))))))))))) => 98.17/14.82 (dsetconstr( 98.17/14.82 Y0, Y2) = 98.17/14.82 dsetconstr( 98.17/14.82 Y1, Y3)))))))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (( 98.17/14.82 !!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) => 98.17/14.82 in(Y2, 98.17/14.82 Y1))))) => 98.17/14.82 subset( 98.17/14.82 Y0, Y1)))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (( 98.17/14.82 Y0 = Y1) => 98.17/14.82 subset( 98.17/14.82 Y1, Y0)))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (( 98.17/14.82 Y0 = Y1) => 98.17/14.82 subset( 98.17/14.82 Y0, Y1)))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (( 98.17/14.82 !!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) => 98.17/14.82 in(Y2, 98.17/14.82 Y1))))) => 98.17/14.82 subset( 98.17/14.82 Y0, Y1)))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!( 98.17/14.82 subset( 98.17/14.82 emptyset))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (subset( 98.17/14.82 Y0, Y1) => 98.17/14.82 (in(Y2, 98.17/14.82 Y0) => 98.17/14.82 in(Y2, 98.17/14.82 Y1)))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (subset( 98.17/14.82 Y0, Y1) => 98.17/14.82 (( 98.17/14.82 ~( 98.17/14.82 in(Y2, 98.17/14.82 Y1))) => 98.17/14.82 (~( 98.17/14.82 in(Y2, 98.17/14.82 Y0)))))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) => 98.17/14.82 (( 98.17/14.82 ~( 98.17/14.82 in(Y2, 98.17/14.82 Y1))) => 98.17/14.82 (~( 98.17/14.82 subset( 98.17/14.82 Y0, Y1)))))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (( 98.17/14.82 ~( 98.17/14.82 subset( 98.17/14.82 Y0, Y1))) => 98.17/14.82 (Y0 != Y1)))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) => 98.17/14.82 (( 98.17/14.82 ~( 98.17/14.82 in(Y2, 98.17/14.82 Y1))) => 98.17/14.82 (Y0 != Y1)))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 subset( 98.17/14.82 Y0, Y0)))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (subset( 98.17/14.82 Y0, Y1) => 98.17/14.82 (subset( 98.17/14.82 Y1, Y2) => 98.17/14.82 subset( 98.17/14.82 Y0, Y2)))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 subset( 98.17/14.82 Y1, 98.17/14.82 setadjoin( 98.17/14.82 Y0, Y1)))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (subset( 98.17/14.82 Y0, Y2) => 98.17/14.82 subset( 98.17/14.82 Y0, 98.17/14.82 setadjoin( 98.17/14.82 Y1, Y2)))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (subset( 98.17/14.82 Y0, Y1) => 98.17/14.82 in(Y0, 98.17/14.82 powerset( 98.17/14.82 Y1))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (subset( 98.17/14.82 Y0, Y1) => 98.17/14.82 (subset( 98.17/14.82 Y1, Y0) => 98.17/14.82 (Y0 = Y1))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (subset( 98.17/14.82 Y0, 98.17/14.82 emptyset) => 98.17/14.82 (Y0 = 98.17/14.82 emptyset))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (subset( 98.17/14.82 Y1, Y0) => 98.17/14.82 in(Y1, 98.17/14.82 powerset( 98.17/14.82 Y0))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (in(Y1, 98.17/14.82 powerset( 98.17/14.82 Y0)) => 98.17/14.82 subset( 98.17/14.82 Y1, Y0)))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 in(Y0, 98.17/14.82 powerset( 98.17/14.82 Y0))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (subset( 98.17/14.82 Y0, Y1) => 98.17/14.82 subset( 98.17/14.82 powerset( 98.17/14.82 Y0), 98.17/14.82 powerset( 98.17/14.82 Y1))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i > $o]: 98.17/14.82 in( 98.17/14.82 dsetconstr( 98.17/14.82 Y0, Y1), 98.17/14.82 powerset( 98.17/14.82 Y0)))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i > $o]: 98.17/14.82 subset( 98.17/14.82 dsetconstr( 98.17/14.82 Y0, Y1), 98.17/14.82 Y0))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) => 98.17/14.82 in(Y2, 98.17/14.82 binunion( 98.17/14.82 Y0, Y1)))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 in(Y1, 98.17/14.82 setadjoin( 98.17/14.82 Y0, 98.17/14.82 setadjoin( 98.17/14.82 Y1, 98.17/14.82 emptyset))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y1) => 98.17/14.82 in(Y2, 98.17/14.82 binunion( 98.17/14.82 Y0, Y1)))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y3 : $o]: 98.17/14.82 (in(Y2, 98.17/14.82 binunion( 98.17/14.82 Y0, Y1)) => 98.17/14.82 (( 98.17/14.82 in(Y2, 98.17/14.82 Y0) => Y3) => 98.17/14.82 (( 98.17/14.82 in(Y2, 98.17/14.82 Y1) => Y3) => 98.17/14.82 Y3))))))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 binunion( 98.17/14.82 Y0, Y1)) => 98.17/14.82 (in(Y2, 98.17/14.82 Y1) | 98.17/14.82 in(Y2, 98.17/14.82 Y0)))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 subset( 98.17/14.82 Y0, 98.17/14.82 binunion( 98.17/14.82 Y0, Y1)))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 subset( 98.17/14.82 Y1, 98.17/14.82 binunion( 98.17/14.82 Y0, Y1)))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) => 98.17/14.82 (in(Y2, 98.17/14.82 Y1) => 98.17/14.82 in(Y2, 98.17/14.82 binintersect( 98.17/14.82 Y0, Y1))))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (subset( 98.17/14.82 Y2, Y0) => 98.17/14.82 (subset( 98.17/14.82 Y2, Y1) => 98.17/14.82 subset( 98.17/14.82 Y2, 98.17/14.82 binintersect( 98.17/14.82 Y0, Y1))))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 binintersect( 98.17/14.82 Y0, Y1)) => 98.17/14.82 in(Y2, 98.17/14.82 Y0))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 subset( 98.17/14.82 binintersect( 98.17/14.82 Y0, Y1), 98.17/14.82 Y0))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (subset( 98.17/14.82 Y0, Y1) => 98.17/14.82 (binintersect( 98.17/14.82 Y0, Y1) = 98.17/14.82 Y0)))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (( 98.17/14.82 binintersect( 98.17/14.82 Y0, Y1) = 98.17/14.82 Y1) => 98.17/14.82 subset( 98.17/14.82 Y1, Y0)))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 binintersect( 98.17/14.82 Y0, Y1)) => 98.17/14.82 in(Y2, 98.17/14.82 Y1))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (( 98.17/14.82 ~(( 98.17/14.82 ??(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) & 98.17/14.82 in(Y2, 98.17/14.82 Y1))))))) => 98.17/14.82 (binintersect( 98.17/14.82 Y0, Y1) = 98.17/14.82 emptyset)))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 subset( 98.17/14.82 binintersect( 98.17/14.82 Y0, Y1), 98.17/14.82 Y1))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (subset( 98.17/14.82 Y1, Y0) => 98.17/14.82 (binintersect( 98.17/14.82 Y0, Y1) = 98.17/14.82 Y1)))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (( 98.17/14.82 binintersect( 98.17/14.82 Y0, Y1) = 98.17/14.82 Y0) => 98.17/14.82 subset( 98.17/14.82 Y0, Y1)))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (binintersect( 98.17/14.82 Y0, 98.17/14.82 binunion( 98.17/14.82 Y1, Y2)) = 98.17/14.82 binunion( 98.17/14.82 binintersect( 98.17/14.82 Y0, Y1), 98.17/14.82 binintersect( 98.17/14.82 Y0, Y2)))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) => 98.17/14.82 (( 98.17/14.82 ~( 98.17/14.82 in(Y2, 98.17/14.82 Y1))) => 98.17/14.82 in(Y2, 98.17/14.82 setminus( 98.17/14.82 Y0, Y1))))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 setminus( 98.17/14.82 Y0, Y1)) => 98.17/14.82 in(Y2, 98.17/14.82 Y0))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 setminus( 98.17/14.82 Y0, Y1)) => 98.17/14.82 (~( 98.17/14.82 in(Y2, 98.17/14.82 Y1))))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (subset( 98.17/14.82 Y0, Y1) => 98.17/14.82 (setminus( 98.17/14.82 Y0, Y1) = 98.17/14.82 emptyset)))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (( 98.17/14.82 ~( 98.17/14.82 in(Y2, 98.17/14.82 setminus( 98.17/14.82 Y0, Y1)))) => 98.17/14.82 (in(Y2, 98.17/14.82 Y0) => 98.17/14.82 in(Y2, 98.17/14.82 Y1)))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (( 98.17/14.82 ~( 98.17/14.82 in(Y2, 98.17/14.82 setminus( 98.17/14.82 Y0, Y1)))) => 98.17/14.82 (( 98.17/14.82 ~( 98.17/14.82 in(Y2, 98.17/14.82 Y1))) => 98.17/14.82 (~( 98.17/14.82 in(Y2, 98.17/14.82 Y0)))))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (( 98.17/14.82 ~( 98.17/14.82 in(Y2, 98.17/14.82 Y0))) => 98.17/14.82 (~( 98.17/14.82 in(Y2, 98.17/14.82 setminus( 98.17/14.82 Y0, Y1)))))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y1) => 98.17/14.82 (~( 98.17/14.82 in(Y2, 98.17/14.82 setminus( 98.17/14.82 Y0, Y1)))))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 subset( 98.17/14.82 setminus( 98.17/14.82 Y0, Y1), 98.17/14.82 Y0))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (( 98.17/14.82 setminus( 98.17/14.82 Y0, Y1) = 98.17/14.82 emptyset) => 98.17/14.82 subset( 98.17/14.82 Y0, Y1)))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 symdiff( 98.17/14.82 Y0, Y1)) => 98.17/14.82 (!!(( 98.17/14.82 ^[Y3 : $o]: 98.17/14.82 (( 98.17/14.82 in(Y2, 98.17/14.82 Y0) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 ~( 98.17/14.82 in(Y2, 98.17/14.82 Y1))) => 98.17/14.82 Y3)) => 98.17/14.82 (( 98.17/14.82 ( 98.17/14.82 ~( 98.17/14.82 in(Y2, 98.17/14.82 Y0))) => 98.17/14.82 ( 98.17/14.82 in(Y2, 98.17/14.82 Y1) => Y3)) => 98.17/14.82 Y3))))))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) => 98.17/14.82 (( 98.17/14.82 ~( 98.17/14.82 in(Y2, 98.17/14.82 Y1))) => 98.17/14.82 in(Y2, 98.17/14.82 symdiff( 98.17/14.82 Y0, Y1))))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (( 98.17/14.82 ~( 98.17/14.82 in(Y2, 98.17/14.82 Y0))) => 98.17/14.82 (in(Y2, 98.17/14.82 Y1) => 98.17/14.82 in(Y2, 98.17/14.82 symdiff( 98.17/14.82 Y0, Y1))))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) => 98.17/14.82 (in(Y2, 98.17/14.82 Y1) => 98.17/14.82 (~( 98.17/14.82 in(Y2, 98.17/14.82 symdiff( 98.17/14.82 Y0, Y1))))))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (( 98.17/14.82 ~( 98.17/14.82 in(Y2, 98.17/14.82 Y0))) => 98.17/14.82 (( 98.17/14.82 ~( 98.17/14.82 in(Y2, 98.17/14.82 Y1))) => 98.17/14.82 (~( 98.17/14.82 in(Y2, 98.17/14.82 symdiff( 98.17/14.82 Y0, Y1))))))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 in(Y1, 98.17/14.82 setadjoin( 98.17/14.82 Y0, 98.17/14.82 setadjoin( 98.17/14.82 Y1, 98.17/14.82 emptyset))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 in(Y0, 98.17/14.82 setunion( 98.17/14.82 setadjoin( 98.17/14.82 setadjoin( 98.17/14.82 Y0, 98.17/14.82 emptyset), 98.17/14.82 setadjoin( 98.17/14.82 setadjoin( 98.17/14.82 Y0, 98.17/14.82 setadjoin( 98.17/14.82 Y1, 98.17/14.82 emptyset)), 98.17/14.82 emptyset)))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 in(Y1, 98.17/14.82 setunion( 98.17/14.82 setadjoin( 98.17/14.82 setadjoin( 98.17/14.82 Y0, 98.17/14.82 emptyset), 98.17/14.82 setadjoin( 98.17/14.82 setadjoin( 98.17/14.82 Y0, 98.17/14.82 setadjoin( 98.17/14.82 Y1, 98.17/14.82 emptyset)), 98.17/14.82 emptyset)))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (??(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 setunion( 98.17/14.82 setadjoin( 98.17/14.82 setadjoin( 98.17/14.82 Y0, 98.17/14.82 emptyset), 98.17/14.82 setadjoin( 98.17/14.82 setadjoin( 98.17/14.82 Y0, 98.17/14.82 setadjoin( 98.17/14.82 Y1, 98.17/14.82 emptyset)), 98.17/14.82 emptyset)))) & 98.17/14.82 (??(( 98.17/14.82 ^[Y3 : $i]: 98.17/14.82 (in(Y3, 98.17/14.82 setunion( 98.17/14.82 setadjoin( 98.17/14.82 setadjoin( 98.17/14.82 Y0, 98.17/14.82 emptyset), 98.17/14.82 setadjoin( 98.17/14.82 setadjoin( 98.17/14.82 Y0, 98.17/14.82 setadjoin( 98.17/14.82 Y1, 98.17/14.82 emptyset)), 98.17/14.82 emptyset)))) & 98.17/14.82 (setadjoin( 98.17/14.82 setadjoin( 98.17/14.82 Y0, 98.17/14.82 emptyset), 98.17/14.82 setadjoin( 98.17/14.82 setadjoin( 98.17/14.82 Y0, 98.17/14.82 setadjoin( 98.17/14.82 Y1, 98.17/14.82 emptyset)), 98.17/14.82 emptyset)) = 98.17/14.82 setadjoin( 98.17/14.82 setadjoin( 98.17/14.82 Y2, 98.17/14.82 emptyset), 98.17/14.82 setadjoin( 98.17/14.82 setadjoin( 98.17/14.82 Y2, 98.17/14.82 setadjoin( 98.17/14.82 Y3, 98.17/14.82 emptyset)), 98.17/14.82 emptyset))))))))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (??(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 setunion( 98.17/14.82 setadjoin( 98.17/14.82 setadjoin( 98.17/14.82 Y0, 98.17/14.82 emptyset), 98.17/14.82 setadjoin( 98.17/14.82 setadjoin( 98.17/14.82 Y0, 98.17/14.82 setadjoin( 98.17/14.82 Y1, 98.17/14.82 emptyset)), 98.17/14.82 emptyset)))) & 98.17/14.82 (??(( 98.17/14.82 ^[Y3 : $i]: 98.17/14.82 (in(Y3, 98.17/14.82 setunion( 98.17/14.82 setadjoin( 98.17/14.82 setadjoin( 98.17/14.82 Y0, 98.17/14.82 emptyset), 98.17/14.82 setadjoin( 98.17/14.82 setadjoin( 98.17/14.82 Y0, 98.17/14.82 setadjoin( 98.17/14.82 Y1, 98.17/14.82 emptyset)), 98.17/14.82 emptyset)))) & 98.17/14.82 (setadjoin( 98.17/14.82 setadjoin( 98.17/14.82 Y0, 98.17/14.82 emptyset), 98.17/14.82 setadjoin( 98.17/14.82 setadjoin( 98.17/14.82 Y0, 98.17/14.82 setadjoin( 98.17/14.82 Y1, 98.17/14.82 emptyset)), 98.17/14.82 emptyset)) = 98.17/14.82 setadjoin( 98.17/14.82 setadjoin( 98.17/14.82 Y2, 98.17/14.82 emptyset), 98.17/14.82 setadjoin( 98.17/14.82 setadjoin( 98.17/14.82 Y2, 98.17/14.82 setadjoin( 98.17/14.82 Y3, 98.17/14.82 emptyset)), 98.17/14.82 emptyset))))))))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (in(Y1, 98.17/14.82 Y0) => 98.17/14.82 subset( 98.17/14.82 setadjoin( 98.17/14.82 Y1, 98.17/14.82 emptyset), 98.17/14.82 Y0)))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (in(Y1, 98.17/14.82 Y0) => 98.17/14.82 in( 98.17/14.82 setadjoin( 98.17/14.82 Y1, 98.17/14.82 emptyset), 98.17/14.82 powerset( 98.17/14.82 Y0))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) => 98.17/14.82 in( 98.17/14.82 setadjoin( 98.17/14.82 Y2, 98.17/14.82 emptyset), 98.17/14.82 powerset( 98.17/14.82 binunion( 98.17/14.82 Y0, Y1))))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 setadjoin( 98.17/14.82 Y0, 98.17/14.82 setadjoin( 98.17/14.82 Y1, 98.17/14.82 emptyset))) => 98.17/14.82 (( 98.17/14.82 Y2 = Y1) | 98.17/14.82 (Y2 = Y0)))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) => 98.17/14.82 (!!(( 98.17/14.82 ^[Y3 : $i]: 98.17/14.82 (in(Y3, 98.17/14.82 Y1) => 98.17/14.82 subset( 98.17/14.82 setadjoin( 98.17/14.82 Y2, 98.17/14.82 setadjoin( 98.17/14.82 Y3, 98.17/14.82 emptyset)), 98.17/14.82 binunion( 98.17/14.82 Y0, Y1)))))))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) => 98.17/14.82 (!!(( 98.17/14.82 ^[Y3 : $i]: 98.17/14.82 (in(Y3, 98.17/14.82 Y1) => 98.17/14.82 in( 98.17/14.82 setadjoin( 98.17/14.82 Y2, 98.17/14.82 setadjoin( 98.17/14.82 Y3, 98.17/14.82 emptyset)), 98.17/14.82 powerset( 98.17/14.82 binunion( 98.17/14.82 Y0, Y1))))))))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) => 98.17/14.82 (!!(( 98.17/14.82 ^[Y3 : $i]: 98.17/14.82 (in(Y3, 98.17/14.82 Y1) => 98.17/14.82 subset( 98.17/14.82 setadjoin( 98.17/14.82 setadjoin( 98.17/14.82 Y2, 98.17/14.82 emptyset), 98.17/14.82 setadjoin( 98.17/14.82 setadjoin( 98.17/14.82 Y2, 98.17/14.82 setadjoin( 98.17/14.82 Y3, 98.17/14.82 emptyset)), 98.17/14.82 emptyset)), 98.17/14.82 powerset( 98.17/14.82 binunion( 98.17/14.82 Y0, Y1))))))))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) => 98.17/14.82 (!!(( 98.17/14.82 ^[Y3 : $i]: 98.17/14.82 (in(Y3, 98.17/14.82 Y1) => 98.17/14.82 in( 98.17/14.82 setadjoin( 98.17/14.82 setadjoin( 98.17/14.82 Y2, 98.17/14.82 emptyset), 98.17/14.82 setadjoin( 98.17/14.82 setadjoin( 98.17/14.82 Y2, 98.17/14.82 setadjoin( 98.17/14.82 Y3, 98.17/14.82 emptyset)), 98.17/14.82 emptyset)), 98.17/14.82 powerset( 98.17/14.82 powerset( 98.17/14.82 binunion( 98.17/14.82 Y0, Y1)))))))))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) => 98.17/14.82 (!!(( 98.17/14.82 ^[Y3 : $i]: 98.17/14.82 (in(Y3, 98.17/14.82 Y1) => 98.17/14.82 in( 98.17/14.82 setadjoin( 98.17/14.82 setadjoin( 98.17/14.82 Y2, 98.17/14.82 emptyset), 98.17/14.82 setadjoin( 98.17/14.82 setadjoin( 98.17/14.82 Y2, 98.17/14.82 setadjoin( 98.17/14.82 Y3, 98.17/14.82 emptyset)), 98.17/14.82 emptyset)), 98.17/14.82 powerset( 98.17/14.82 powerset( 98.17/14.82 binunion( 98.17/14.82 Y0, Y1)))))))))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) => 98.17/14.82 (!!(( 98.17/14.82 ^[Y3 : $i]: 98.17/14.82 (in(Y3, 98.17/14.82 Y1) => 98.17/14.82 in( 98.17/14.82 setadjoin( 98.17/14.82 setadjoin( 98.17/14.82 Y2, 98.17/14.82 emptyset), 98.17/14.82 setadjoin( 98.17/14.82 setadjoin( 98.17/14.82 Y2, 98.17/14.82 setadjoin( 98.17/14.82 Y3, 98.17/14.82 emptyset)), 98.17/14.82 emptyset)), 98.17/14.82 dsetconstr( 98.17/14.82 powerset( 98.17/14.82 powerset( 98.17/14.82 binunion( 98.17/14.82 Y0, Y1))), 98.17/14.82 (^[Y4 : $i]: 98.17/14.82 (??(( 98.17/14.82 ^[Y5 : $i]: 98.17/14.82 (in(Y5, 98.17/14.82 Y0) & 98.17/14.82 (??(( 98.17/14.82 ^[Y6 : $i]: 98.17/14.82 (in(Y6, 98.17/14.82 Y1) & 98.17/14.82 (Y4 = 98.17/14.82 setadjoin( 98.17/14.82 setadjoin( 98.17/14.82 Y5, 98.17/14.82 emptyset), 98.17/14.82 setadjoin( 98.17/14.82 setadjoin( 98.17/14.82 Y5, 98.17/14.82 setadjoin( 98.17/14.82 Y6, 98.17/14.82 emptyset)), 98.17/14.82 emptyset)))))))))))))))))))))))))))) => 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 dsetconstr( 98.17/14.82 powerset( 98.17/14.82 powerset( 98.17/14.82 binunion( 98.17/14.82 Y0, Y1))), 98.17/14.82 (^[Y3 : $i]: 98.17/14.82 (??(( 98.17/14.82 ^[Y4 : $i]: 98.17/14.82 (in(Y4, 98.17/14.82 Y0) & 98.17/14.82 (??(( 98.17/14.82 ^[Y5 : $i]: 98.17/14.82 (in(Y5, 98.17/14.82 Y1) & 98.17/14.82 (Y3 = 98.17/14.82 setadjoin( 98.17/14.82 setadjoin( 98.17/14.82 Y4, 98.17/14.82 emptyset), 98.17/14.82 setadjoin( 98.17/14.82 setadjoin( 98.17/14.82 Y4, 98.17/14.82 setadjoin( 98.17/14.82 Y5, 98.17/14.82 emptyset)), 98.17/14.82 emptyset)))))))))))))) => 98.17/14.82 (??(( 98.17/14.82 ^[Y3 : $i]: 98.17/14.82 (( 98.17/14.82 ??(( 98.17/14.82 ^[Y4 : $i]: 98.17/14.82 (in(Y4, 98.17/14.82 Y1) & 98.17/14.82 (Y2 = 98.17/14.82 setadjoin( 98.17/14.82 setadjoin( 98.17/14.82 Y3, 98.17/14.82 emptyset), 98.17/14.82 setadjoin( 98.17/14.82 setadjoin( 98.17/14.82 Y3, 98.17/14.82 setadjoin( 98.17/14.82 Y4, 98.17/14.82 emptyset)), 98.17/14.82 emptyset))))))) & 98.17/14.82 in(Y3, 98.17/14.82 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 98.17/14.82 inference('lazy_cnf_imply', [status(thm)], ['168'])). 98.17/14.82 tff('170', plain, 98.17/14.82 ~ ((!!((^[Y0 : $i]: 98.17/14.82 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 98.17/14.82 (??((^[Y1 : $i]: 98.17/14.82 (in(Y1, Y0) & 98.17/14.82 (~((??((^[Y2 : $i]: (in(Y2, Y1) & in(Y2, Y0))))))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (??((^[Y1 : $i]: 98.17/14.82 ((!!((^[Y2 : $i]: 98.17/14.82 (in(Y2, Y1) => 98.17/14.82 (!!((^[Y3 : $i]: (in(Y3, Y2) => in(Y3, Y0)))))))))& 98.17/14.82 (!!((^[Y2 : $i]: 98.17/14.82 (!!((^[Y3 : $i]: 98.17/14.82 ((in(Y3, Y0) & in(Y2, Y0)) => 98.17/14.82 ((!!((^[Y4 : $i]: 98.17/14.82 (in(Y4, Y1) => 98.17/14.82 (in(Y2, Y4) <=> in(Y3, Y4)))))) => 98.17/14.82 (Y2 = Y3)))))))))& 98.17/14.82 (!!((^[Y2 : $i]: 98.17/14.82 (!!((^[Y3 : $i]: 98.17/14.82 ((in(Y3, Y1) & in(Y2, Y1)) => 98.17/14.82 ((!!((^[Y4 : $i]: 98.17/14.82 (in(Y4, Y3) => in(Y4, Y2))))) | 98.17/14.82 (!!((^[Y4 : $i]: 98.17/14.82 (in(Y4, Y2) => in(Y4, Y3)))))))))))))& 98.17/14.82 (!!((^[Y2 : $i]: 98.17/14.82 (((??((^[Y3 : $i]: in(Y3, Y2)))) & 98.17/14.82 (!!((^[Y3 : $i]: (in(Y3, Y2) => in(Y3, Y0)))))) => 98.17/14.82 (??((^[Y3 : $i]: 98.17/14.82 (??((^[Y4 : $i]: 98.17/14.82 (in(Y3, Y1)&in(Y4, Y2)& 98.17/14.82 (~((??((^[Y5 : $i]: 98.17/14.82 (in(Y5, Y3) & 98.17/14.82 in(Y5, Y2)))))))& 98.17/14.82 (!!((^[Y5 : $i]: 98.17/14.82 (in(Y5, Y1) => 98.17/14.82 (in(Y4, Y5) | 98.17/14.82 (!!((^[Y6 : $i]: 98.17/14.82 (in(Y6, Y5) => 98.17/14.82 in(Y6, Y3)))))))))))))))))))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i > $o]: 98.17/14.82 ((??((^[Y1 : $i]: 98.17/14.82 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 98.17/14.82 Y0(descr(Y0)))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i > $o]: 98.17/14.82 (!!((^[Y2 : $i]: 98.17/14.82 (in(Y2, Y0) => 98.17/14.82 (Y1(Y2) => in(Y2, dsetconstr(Y0, Y1))))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i > $o]: 98.17/14.82 (!!((^[Y2 : $i]: 98.17/14.82 (in(Y2, dsetconstr(Y0, Y1)) => in(Y2, Y0))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i > $o]: 98.17/14.82 (!!((^[Y2 : $i]: 98.17/14.82 (in(Y2, dsetconstr(Y0, Y1)) => Y1(Y2))))))))))) => 98.17/14.82 ((!!((^[Y0 : $o]: 98.17/14.82 (!!((^[Y1 : $i]: (in(Y1, prop2set(Y0)) => Y0))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: (in(Y0, emptyset) => (!!((^[Y1 : $o]: Y1))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 98.17/14.82 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 98.17/14.82 ((!!((^[Y0 : $i > $o]: 98.17/14.82 ((??((^[Y1 : $i]: 98.17/14.82 (Y0(Y1) & 98.17/14.82 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 98.17/14.82 (??(Y0)))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i]: 98.17/14.82 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 98.17/14.82 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 98.17/14.82 (Y0 = Y1))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 98.17/14.82 (Y0 = emptyset))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 98.17/14.82 (Y0 = emptyset))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i > $o]: 98.17/14.82 (!!((^[Y2 : $i]: 98.17/14.82 (in(Y2, Y0) => 98.17/14.82 (in(Y2, dsetconstr(Y0, Y1)) <=> 98.17/14.82 Y1(Y2)))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 ((Y0 != emptyset) => 98.17/14.82 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i > $o]: 98.17/14.82 (!!((^[Y2 : $i]: 98.17/14.82 (in(Y2, Y0) => 98.17/14.82 (Y1(Y2) => 98.17/14.82 (dsetconstr(Y0, Y1) != emptyset)))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 98.17/14.82 (Y0 != emptyset))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 98.17/14.82 (in(emptyset, setadjoin(emptyset, emptyset)) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i]: 98.17/14.82 (!!((^[Y2 : $i]: 98.17/14.82 (in(Y2, Y1) => 98.17/14.82 in(Y2, setadjoin(Y0, Y1)))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i]: 98.17/14.82 (!!((^[Y2 : $i]: 98.17/14.82 (in(Y2, setadjoin(Y0, Y1)) => 98.17/14.82 (!!((^[Y3 : $o]: 98.17/14.82 (((Y2 = Y0) => Y3) => 98.17/14.82 ((in(Y2, Y1) => Y3) => 98.17/14.82 Y3))))))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i]: 98.17/14.82 (!!((^[Y2 : $i]: 98.17/14.82 (in(Y2, setadjoin(Y0, Y1)) => 98.17/14.82 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (dsetconstr(Y0, (^[Y1 : $i]: $true)) = 98.17/14.82 Y0)))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i]: 98.17/14.82 ((!!((^[Y2 : $i]: 98.17/14.82 (in(Y2, Y1) => 98.17/14.82 in(Y2, Y0))))) => 98.17/14.82 in(Y1, powerset(Y0))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.17/14.82 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i]: 98.17/14.82 (!!((^[Y2 : $i]: 98.17/14.82 (in(Y1, powerset(Y0)) => 98.17/14.82 (in(Y2, Y1) => 98.17/14.82 in(Y2, Y0)))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i]: 98.17/14.82 (!!((^[Y2 : $i]: 98.17/14.82 (in(Y1, Y2) => 98.17/14.82 (in(Y2, Y0) => 98.17/14.82 in(Y1, 98.17/14.82 setunion(Y0))))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i]: 98.17/14.82 (in(Y1, setunion(Y0)) => 98.17/14.82 (!!((^[Y2 : $o]: 98.17/14.82 ((!!((^[Y3 : $i]: 98.17/14.82 (in(Y1, Y3) => 98.17/14.82 (in(Y3, 98.17/14.82 Y0) => Y2))))) => 98.17/14.82 Y2))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i]: 98.17/14.82 (in(Y1, Y0) => 98.17/14.82 in(Y1, 98.17/14.82 powerset(setunion(Y0)))))))))) => 98.17/14.82 ((!!((^[Y0 : $i > $o]: 98.17/14.82 ((??((^[Y1 : $i]: 98.17/14.82 (Y0(Y1) & 98.17/14.82 (!!((^[Y2 : $i]: 98.17/14.82 (Y0(Y2) => 98.17/14.82 (Y1 = Y2))))))))) => 98.17/14.82 (??((^[Y1 : $i]: 98.17/14.82 (!!((^[Y2 : $i]: 98.17/14.82 (Y0(Y2) <=> 98.17/14.82 (Y2 = Y1)))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 ((Y0 != emptyset) => 98.17/14.82 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i]: 98.17/14.82 (in(Y0, 98.17/14.82 setadjoin(Y1, 98.17/14.82 emptyset)) => 98.17/14.82 (Y0 = Y1)))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i]: 98.17/14.82 ((Y0 != Y1) => 98.17/14.82 (~(in(Y1, 98.17/14.82 setadjoin(Y0, 98.17/14.82 emptyset))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i]: 98.17/14.82 ((Y0 = Y1) => 98.17/14.82 in(Y0, 98.17/14.82 setadjoin(Y1, 98.17/14.82 emptyset))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i]: 98.17/14.82 (in(Y0, 98.17/14.82 setadjoin(Y1, 98.17/14.82 emptyset)) => 98.17/14.82 in(Y1, 98.17/14.82 setadjoin(Y0, 98.17/14.82 emptyset))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i]: 98.17/14.82 (!!((^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 setadjoin( 98.17/14.82 Y0, 98.17/14.82 setadjoin( 98.17/14.82 Y1, 98.17/14.82 emptyset))) => 98.17/14.82 ((Y2 = Y1) | 98.17/14.82 (Y2 = Y0)))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i]: 98.17/14.82 in(Y0, 98.17/14.82 setadjoin(Y0, 98.17/14.82 setadjoin(Y1, 98.17/14.82 emptyset))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i]: 98.17/14.82 in(Y1, 98.17/14.82 setadjoin(Y0, 98.17/14.82 setadjoin( 98.17/14.82 Y1, 98.17/14.82 emptyset))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i > $o]: 98.17/14.82 ((??((^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) & 98.17/14.82 Y1(Y2))))) => 98.17/14.82 (dsetconstr( 98.17/14.82 Y0, Y1) != 98.17/14.82 emptyset)))))))) => 98.17/14.82 ((!!((^[Y0 : $i > $o]: 98.17/14.82 (!!((^[Y1 : $i]: 98.17/14.82 (in(Y1, 98.17/14.82 emptyset) => 98.17/14.82 Y0(Y1)))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i > $o]: 98.17/14.82 ((~((!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) => 98.17/14.82 Y1(Y2))))))) => 98.17/14.82 (??(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) & 98.17/14.82 ( 98.17/14.82 ~( 98.17/14.82 Y1(Y2)))))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i > $o]: 98.17/14.82 ((!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 ( 98.17/14.82 in(Y2, 98.17/14.82 Y0) => 98.17/14.82 ( 98.17/14.82 ~( 98.17/14.82 Y1(Y2))))))) => 98.17/14.82 (~(( 98.17/14.82 ??(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 ( 98.17/14.82 in(Y2, 98.17/14.82 Y0) & 98.17/14.82 Y1(Y2)))))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i > $o]: 98.17/14.82 ((~(( 98.17/14.82 ??(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) & 98.17/14.82 Y1(Y2))))))) => 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) => 98.17/14.82 (~( 98.17/14.82 Y1(Y2)))))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i > $o]: 98.17/14.82 ((??(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) & 98.17/14.82 (~( 98.17/14.82 Y1(Y2))))))) => 98.17/14.82 (~(( 98.17/14.82 !!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) => 98.17/14.82 Y1(Y2)))))))))))))) => 98.17/14.82 ((!!((^[Y0 : $o]: 98.17/14.82 (Y0 => 98.17/14.82 in(emptyset, 98.17/14.82 prop2set(Y0)))))) => 98.17/14.82 ((!!((^[Y0 : $o]: 98.17/14.82 (Y0 => 98.17/14.82 set2prop( 98.17/14.82 prop2set(Y0)))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i > $o]: 98.17/14.82 (( 98.17/14.82 ~(( 98.17/14.82 ??(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) & 98.17/14.82 Y1(Y2))))))) => 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) => 98.17/14.82 (~( 98.17/14.82 Y1(Y2)))))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!((^[Y1 : $i > $o]: 98.17/14.82 (( 98.17/14.82 ~(( 98.17/14.82 !!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) => 98.17/14.82 Y1(Y2))))))) => 98.17/14.82 (??(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) & 98.17/14.82 (~( 98.17/14.82 Y1(Y2)))))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i > $o]: 98.17/14.82 ((??(Y0)) => 98.17/14.82 ((!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (Y0(Y1) => 98.17/14.82 (Y0(Y2) => 98.17/14.82 (Y1 = Y2))))))))) => 98.17/14.82 (??(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (Y0(Y1) & 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (Y0(Y2) => 98.17/14.82 (Y1 = Y2)))))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i > $o]: 98.17/14.82 ((??(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (Y0(Y2) <=> 98.17/14.82 (Y2 = Y1)))))))) => 98.17/14.82 (??(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (Y0(Y1) & 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (Y0(Y2) => 98.17/14.82 (Y1 = Y2))))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (( 98.17/14.82 Y0 = Y1) => 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y3 : $i]: 98.17/14.82 (( 98.17/14.82 Y2 = Y3) => 98.17/14.82 (in(Y2, 98.17/14.82 Y0) => 98.17/14.82 in(Y3, 98.17/14.82 Y1)))))))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (( 98.17/14.82 Y0 = Y1) => 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y3 : $i]: 98.17/14.82 (( 98.17/14.82 Y2 = Y3) => 98.17/14.82 (in(Y2, 98.17/14.82 Y0) <=> 98.17/14.82 in(Y3, 98.17/14.82 Y1)))))))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i > $o]: 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 ??(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (Y0(Y1) & 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (Y0(Y2) => 98.17/14.82 (Y1 = Y2))))))))) => 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (Y0(Y1) => 98.17/14.82 (Y0(Y2) => 98.17/14.82 (Y1 = Y2))))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i > $o]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i > $o]: 98.17/14.82 (( 98.17/14.82 !!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y3 : $i]: 98.17/14.82 (( 98.17/14.82 Y2 = Y3) => 98.17/14.82 (Y0(Y2) <=> 98.17/14.82 Y1(Y3))))))))) => 98.17/14.82 (( 98.17/14.82 ??(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (Y0(Y2) & 98.17/14.82 (!!(( 98.17/14.82 ^[Y3 : $i]: 98.17/14.82 (Y0(Y3) => 98.17/14.82 (Y2 = Y3))))))))) <=> 98.17/14.82 (??(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (Y1(Y2) & 98.17/14.82 (!!(( 98.17/14.82 ^[Y3 : $i]: 98.17/14.82 (Y1(Y3) => 98.17/14.82 (Y2 = Y3))))))))))))))))) => 98.17/14.82 ((!!((^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (( 98.17/14.82 Y0 = Y1) => 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y3 : $i]: 98.17/14.82 (( 98.17/14.82 Y2 = Y3) => 98.17/14.82 (setadjoin( 98.17/14.82 Y0, Y2) = 98.17/14.82 setadjoin( 98.17/14.82 Y1, Y3)))))))))))))))) => 98.17/14.82 ((!!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (( 98.17/14.82 Y0 = Y1) => 98.17/14.82 (powerset( 98.17/14.82 Y0) = 98.17/14.82 powerset( 98.17/14.82 Y1))))))))) => 98.17/14.82 ((!!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (( 98.17/14.82 Y0 = Y1) => 98.17/14.82 (setunion( 98.17/14.82 Y0) = 98.17/14.82 setunion( 98.17/14.82 Y1))))))))) => 98.17/14.82 ((!!(( 98.17/14.82 ^[Y0 : $i > $o]: 98.17/14.82 (( 98.17/14.82 ??(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (Y0(Y1) & 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (Y0(Y2) => 98.17/14.82 (Y1 = Y2))))))))) => 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (Y0(Y1) => 98.17/14.82 (Y0(Y2) => 98.17/14.82 (Y1 = Y2))))))))))))) => 98.17/14.82 ((!!(( 98.17/14.82 ^[Y0 : $i > $o]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i > $o]: 98.17/14.82 (( 98.17/14.82 !!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y3 : $i]: 98.17/14.82 (( 98.17/14.82 Y2 = Y3) => 98.17/14.82 (Y0(Y2) <=> 98.17/14.82 Y1(Y3))))))))) => 98.17/14.82 (( 98.17/14.82 ??(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (Y0(Y2) & 98.17/14.82 (!!(( 98.17/14.82 ^[Y3 : $i]: 98.17/14.82 (Y0(Y3) => 98.17/14.82 (Y2 = Y3))))))))) => 98.17/14.82 (( 98.17/14.82 ??(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (Y1(Y2) & 98.17/14.82 (!!(( 98.17/14.82 ^[Y3 : $i]: 98.17/14.82 (Y1(Y3) => 98.17/14.82 (Y2 = Y3))))))))) => 98.17/14.82 (descr( 98.17/14.82 Y0) = 98.17/14.82 descr(Y1))))))))))) => 98.17/14.82 (( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (( 98.17/14.82 Y0 = Y1) => 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i > $o]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y3 : $i > $o]: 98.17/14.82 (( 98.17/14.82 !!(( 98.17/14.82 ^[Y4 : $i]: 98.17/14.82 (in(Y4, 98.17/14.82 Y0) => 98.17/14.82 (!!(( 98.17/14.82 ^[Y5 : $i]: 98.17/14.82 (in(Y5, 98.17/14.82 Y1) => 98.17/14.82 (( 98.17/14.82 Y4 = Y5) => 98.17/14.82 (Y2(Y4) <=> 98.17/14.82 Y3(Y5))))))))))) => 98.17/14.82 (dsetconstr( 98.17/14.82 Y0, Y2) = 98.17/14.82 dsetconstr( 98.17/14.82 Y1, Y3)))))))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (( 98.17/14.82 !!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) => 98.17/14.82 in(Y2, 98.17/14.82 Y1))))) => 98.17/14.82 subset( 98.17/14.82 Y0, Y1)))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (( 98.17/14.82 Y0 = Y1) => 98.17/14.82 subset( 98.17/14.82 Y1, Y0)))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (( 98.17/14.82 Y0 = Y1) => 98.17/14.82 subset( 98.17/14.82 Y0, Y1)))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (( 98.17/14.82 !!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) => 98.17/14.82 in(Y2, 98.17/14.82 Y1))))) => 98.17/14.82 subset( 98.17/14.82 Y0, Y1)))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!( 98.17/14.82 subset( 98.17/14.82 emptyset))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (subset( 98.17/14.82 Y0, Y1) => 98.17/14.82 (in(Y2, 98.17/14.82 Y0) => 98.17/14.82 in(Y2, 98.17/14.82 Y1)))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (subset( 98.17/14.82 Y0, Y1) => 98.17/14.82 (( 98.17/14.82 ~( 98.17/14.82 in(Y2, 98.17/14.82 Y1))) => 98.17/14.82 (~( 98.17/14.82 in(Y2, 98.17/14.82 Y0)))))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) => 98.17/14.82 (( 98.17/14.82 ~( 98.17/14.82 in(Y2, 98.17/14.82 Y1))) => 98.17/14.82 (~( 98.17/14.82 subset( 98.17/14.82 Y0, Y1)))))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (( 98.17/14.82 ~( 98.17/14.82 subset( 98.17/14.82 Y0, Y1))) => 98.17/14.82 (Y0 != Y1)))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) => 98.17/14.82 (( 98.17/14.82 ~( 98.17/14.82 in(Y2, 98.17/14.82 Y1))) => 98.17/14.82 (Y0 != Y1)))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 subset( 98.17/14.82 Y0, Y0)))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (subset( 98.17/14.82 Y0, Y1) => 98.17/14.82 (subset( 98.17/14.82 Y1, Y2) => 98.17/14.82 subset( 98.17/14.82 Y0, Y2)))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 subset( 98.17/14.82 Y1, 98.17/14.82 setadjoin( 98.17/14.82 Y0, Y1)))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (subset( 98.17/14.82 Y0, Y2) => 98.17/14.82 subset( 98.17/14.82 Y0, 98.17/14.82 setadjoin( 98.17/14.82 Y1, Y2)))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (subset( 98.17/14.82 Y0, Y1) => 98.17/14.82 in(Y0, 98.17/14.82 powerset( 98.17/14.82 Y1))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (subset( 98.17/14.82 Y0, Y1) => 98.17/14.82 (subset( 98.17/14.82 Y1, Y0) => 98.17/14.82 (Y0 = Y1))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (subset( 98.17/14.82 Y0, 98.17/14.82 emptyset) => 98.17/14.82 (Y0 = 98.17/14.82 emptyset))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (subset( 98.17/14.82 Y1, Y0) => 98.17/14.82 in(Y1, 98.17/14.82 powerset( 98.17/14.82 Y0))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (in(Y1, 98.17/14.82 powerset( 98.17/14.82 Y0)) => 98.17/14.82 subset( 98.17/14.82 Y1, Y0)))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 in(Y0, 98.17/14.82 powerset( 98.17/14.82 Y0))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (subset( 98.17/14.82 Y0, Y1) => 98.17/14.82 subset( 98.17/14.82 powerset( 98.17/14.82 Y0), 98.17/14.82 powerset( 98.17/14.82 Y1))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i > $o]: 98.17/14.82 in( 98.17/14.82 dsetconstr( 98.17/14.82 Y0, Y1), 98.17/14.82 powerset( 98.17/14.82 Y0)))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i > $o]: 98.17/14.82 subset( 98.17/14.82 dsetconstr( 98.17/14.82 Y0, Y1), 98.17/14.82 Y0))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) => 98.17/14.82 in(Y2, 98.17/14.82 binunion( 98.17/14.82 Y0, Y1)))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 in(Y1, 98.17/14.82 setadjoin( 98.17/14.82 Y0, 98.17/14.82 setadjoin( 98.17/14.82 Y1, 98.17/14.82 emptyset))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y1) => 98.17/14.82 in(Y2, 98.17/14.82 binunion( 98.17/14.82 Y0, Y1)))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y3 : $o]: 98.17/14.82 (in(Y2, 98.17/14.82 binunion( 98.17/14.82 Y0, Y1)) => 98.17/14.82 (( 98.17/14.82 in(Y2, 98.17/14.82 Y0) => Y3) => 98.17/14.82 (( 98.17/14.82 in(Y2, 98.17/14.82 Y1) => Y3) => 98.17/14.82 Y3))))))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 binunion( 98.17/14.82 Y0, Y1)) => 98.17/14.82 (in(Y2, 98.17/14.82 Y1) | 98.17/14.82 in(Y2, 98.17/14.82 Y0)))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 subset( 98.17/14.82 Y0, 98.17/14.82 binunion( 98.17/14.82 Y0, Y1)))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 subset( 98.17/14.82 Y1, 98.17/14.82 binunion( 98.17/14.82 Y0, Y1)))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) => 98.17/14.82 (in(Y2, 98.17/14.82 Y1) => 98.17/14.82 in(Y2, 98.17/14.82 binintersect( 98.17/14.82 Y0, Y1))))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (subset( 98.17/14.82 Y2, Y0) => 98.17/14.82 (subset( 98.17/14.82 Y2, Y1) => 98.17/14.82 subset( 98.17/14.82 Y2, 98.17/14.82 binintersect( 98.17/14.82 Y0, Y1))))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 binintersect( 98.17/14.82 Y0, Y1)) => 98.17/14.82 in(Y2, 98.17/14.82 Y0))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 subset( 98.17/14.82 binintersect( 98.17/14.82 Y0, Y1), 98.17/14.82 Y0))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (subset( 98.17/14.82 Y0, Y1) => 98.17/14.82 (binintersect( 98.17/14.82 Y0, Y1) = 98.17/14.82 Y0)))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (( 98.17/14.82 binintersect( 98.17/14.82 Y0, Y1) = 98.17/14.82 Y1) => 98.17/14.82 subset( 98.17/14.82 Y1, Y0)))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 binintersect( 98.17/14.82 Y0, Y1)) => 98.17/14.82 in(Y2, 98.17/14.82 Y1))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (( 98.17/14.82 ~(( 98.17/14.82 ??(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) & 98.17/14.82 in(Y2, 98.17/14.82 Y1))))))) => 98.17/14.82 (binintersect( 98.17/14.82 Y0, Y1) = 98.17/14.82 emptyset)))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 subset( 98.17/14.82 binintersect( 98.17/14.82 Y0, Y1), 98.17/14.82 Y1))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (subset( 98.17/14.82 Y1, Y0) => 98.17/14.82 (binintersect( 98.17/14.82 Y0, Y1) = 98.17/14.82 Y1)))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (( 98.17/14.82 binintersect( 98.17/14.82 Y0, Y1) = 98.17/14.82 Y0) => 98.17/14.82 subset( 98.17/14.82 Y0, Y1)))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (binintersect( 98.17/14.82 Y0, 98.17/14.82 binunion( 98.17/14.82 Y1, Y2)) = 98.17/14.82 binunion( 98.17/14.82 binintersect( 98.17/14.82 Y0, Y1), 98.17/14.82 binintersect( 98.17/14.82 Y0, Y2)))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) => 98.17/14.82 (( 98.17/14.82 ~( 98.17/14.82 in(Y2, 98.17/14.82 Y1))) => 98.17/14.82 in(Y2, 98.17/14.82 setminus( 98.17/14.82 Y0, Y1))))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 setminus( 98.17/14.82 Y0, Y1)) => 98.17/14.82 in(Y2, 98.17/14.82 Y0))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 setminus( 98.17/14.82 Y0, Y1)) => 98.17/14.82 (~( 98.17/14.82 in(Y2, 98.17/14.82 Y1))))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (subset( 98.17/14.82 Y0, Y1) => 98.17/14.82 (setminus( 98.17/14.82 Y0, Y1) = 98.17/14.82 emptyset)))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (( 98.17/14.82 ~( 98.17/14.82 in(Y2, 98.17/14.82 setminus( 98.17/14.82 Y0, Y1)))) => 98.17/14.82 (in(Y2, 98.17/14.82 Y0) => 98.17/14.82 in(Y2, 98.17/14.82 Y1)))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (( 98.17/14.82 ~( 98.17/14.82 in(Y2, 98.17/14.82 setminus( 98.17/14.82 Y0, Y1)))) => 98.17/14.82 (( 98.17/14.82 ~( 98.17/14.82 in(Y2, 98.17/14.82 Y1))) => 98.17/14.82 (~( 98.17/14.82 in(Y2, 98.17/14.82 Y0)))))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (( 98.17/14.82 ~( 98.17/14.82 in(Y2, 98.17/14.82 Y0))) => 98.17/14.82 (~( 98.17/14.82 in(Y2, 98.17/14.82 setminus( 98.17/14.82 Y0, Y1)))))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y1) => 98.17/14.82 (~( 98.17/14.82 in(Y2, 98.17/14.82 setminus( 98.17/14.82 Y0, Y1)))))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 subset( 98.17/14.82 setminus( 98.17/14.82 Y0, Y1), 98.17/14.82 Y0))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (( 98.17/14.82 setminus( 98.17/14.82 Y0, Y1) = 98.17/14.82 emptyset) => 98.17/14.82 subset( 98.17/14.82 Y0, Y1)))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 symdiff( 98.17/14.82 Y0, Y1)) => 98.17/14.82 (!!(( 98.17/14.82 ^[Y3 : $o]: 98.17/14.82 (( 98.17/14.82 in(Y2, 98.17/14.82 Y0) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 ~( 98.17/14.82 in(Y2, 98.17/14.82 Y1))) => 98.17/14.82 Y3)) => 98.17/14.82 (( 98.17/14.82 ( 98.17/14.82 ~( 98.17/14.82 in(Y2, 98.17/14.82 Y0))) => 98.17/14.82 ( 98.17/14.82 in(Y2, 98.17/14.82 Y1) => Y3)) => 98.17/14.82 Y3))))))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.17/14.82 Y0) => 98.17/14.82 (( 98.17/14.82 ~( 98.17/14.82 in(Y2, 98.17/14.82 Y1))) => 98.17/14.82 in(Y2, 98.17/14.82 symdiff( 98.17/14.82 Y0, Y1))))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (( 98.17/14.82 ~( 98.17/14.82 in(Y2, 98.17/14.82 Y0))) => 98.17/14.82 (in(Y2, 98.17/14.82 Y1) => 98.17/14.82 in(Y2, 98.17/14.82 symdiff( 98.17/14.82 Y0, Y1))))))))))))) => 98.17/14.82 ( 98.17/14.82 ( 98.17/14.82 !!(( 98.17/14.82 ^[Y0 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y1 : $i]: 98.17/14.82 (!!(( 98.17/14.82 ^[Y2 : $i]: 98.17/14.82 (in(Y2, 98.71/14.82 Y0) => 98.71/14.82 (in(Y2, 98.71/14.82 Y1) => 98.71/14.82 (~( 98.71/14.82 in(Y2, 98.71/14.82 symdiff( 98.71/14.82 Y0, Y1))))))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (( 98.71/14.82 ~( 98.71/14.82 in(Y2, 98.71/14.82 Y0))) => 98.71/14.82 (( 98.71/14.82 ~( 98.71/14.82 in(Y2, 98.71/14.82 Y1))) => 98.71/14.82 (~( 98.71/14.82 in(Y2, 98.71/14.82 symdiff( 98.71/14.82 Y0, Y1))))))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 in(Y1, 98.71/14.82 setadjoin( 98.71/14.82 Y0, 98.71/14.82 setadjoin( 98.71/14.82 Y1, 98.71/14.82 emptyset))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 in(Y0, 98.71/14.82 setunion( 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y0, 98.71/14.82 emptyset), 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y0, 98.71/14.82 setadjoin( 98.71/14.82 Y1, 98.71/14.82 emptyset)), 98.71/14.82 emptyset)))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 in(Y1, 98.71/14.82 setunion( 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y0, 98.71/14.82 emptyset), 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y0, 98.71/14.82 setadjoin( 98.71/14.82 Y1, 98.71/14.82 emptyset)), 98.71/14.82 emptyset)))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (??(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 setunion( 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y0, 98.71/14.82 emptyset), 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y0, 98.71/14.82 setadjoin( 98.71/14.82 Y1, 98.71/14.82 emptyset)), 98.71/14.82 emptyset)))) & 98.71/14.82 (??(( 98.71/14.82 ^[Y3 : $i]: 98.71/14.82 (in(Y3, 98.71/14.82 setunion( 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y0, 98.71/14.82 emptyset), 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y0, 98.71/14.82 setadjoin( 98.71/14.82 Y1, 98.71/14.82 emptyset)), 98.71/14.82 emptyset)))) & 98.71/14.82 (setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y0, 98.71/14.82 emptyset), 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y0, 98.71/14.82 setadjoin( 98.71/14.82 Y1, 98.71/14.82 emptyset)), 98.71/14.82 emptyset)) = 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y2, 98.71/14.82 emptyset), 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y2, 98.71/14.82 setadjoin( 98.71/14.82 Y3, 98.71/14.82 emptyset)), 98.71/14.82 emptyset))))))))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (??(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 setunion( 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y0, 98.71/14.82 emptyset), 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y0, 98.71/14.82 setadjoin( 98.71/14.82 Y1, 98.71/14.82 emptyset)), 98.71/14.82 emptyset)))) & 98.71/14.82 (??(( 98.71/14.82 ^[Y3 : $i]: 98.71/14.82 (in(Y3, 98.71/14.82 setunion( 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y0, 98.71/14.82 emptyset), 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y0, 98.71/14.82 setadjoin( 98.71/14.82 Y1, 98.71/14.82 emptyset)), 98.71/14.82 emptyset)))) & 98.71/14.82 (setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y0, 98.71/14.82 emptyset), 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y0, 98.71/14.82 setadjoin( 98.71/14.82 Y1, 98.71/14.82 emptyset)), 98.71/14.82 emptyset)) = 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y2, 98.71/14.82 emptyset), 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y2, 98.71/14.82 setadjoin( 98.71/14.82 Y3, 98.71/14.82 emptyset)), 98.71/14.82 emptyset))))))))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (in(Y1, 98.71/14.82 Y0) => 98.71/14.82 subset( 98.71/14.82 setadjoin( 98.71/14.82 Y1, 98.71/14.82 emptyset), 98.71/14.82 Y0)))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (in(Y1, 98.71/14.82 Y0) => 98.71/14.82 in( 98.71/14.82 setadjoin( 98.71/14.82 Y1, 98.71/14.82 emptyset), 98.71/14.82 powerset( 98.71/14.82 Y0))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 Y0) => 98.71/14.82 in( 98.71/14.82 setadjoin( 98.71/14.82 Y2, 98.71/14.82 emptyset), 98.71/14.82 powerset( 98.71/14.82 binunion( 98.71/14.82 Y0, Y1))))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 setadjoin( 98.71/14.82 Y0, 98.71/14.82 setadjoin( 98.71/14.82 Y1, 98.71/14.82 emptyset))) => 98.71/14.82 (( 98.71/14.82 Y2 = Y1) | 98.71/14.82 (Y2 = Y0)))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 Y0) => 98.71/14.82 (!!(( 98.71/14.82 ^[Y3 : $i]: 98.71/14.82 (in(Y3, 98.71/14.82 Y1) => 98.71/14.82 subset( 98.71/14.82 setadjoin( 98.71/14.82 Y2, 98.71/14.82 setadjoin( 98.71/14.82 Y3, 98.71/14.82 emptyset)), 98.71/14.82 binunion( 98.71/14.82 Y0, Y1)))))))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 Y0) => 98.71/14.82 (!!(( 98.71/14.82 ^[Y3 : $i]: 98.71/14.82 (in(Y3, 98.71/14.82 Y1) => 98.71/14.82 in( 98.71/14.82 setadjoin( 98.71/14.82 Y2, 98.71/14.82 setadjoin( 98.71/14.82 Y3, 98.71/14.82 emptyset)), 98.71/14.82 powerset( 98.71/14.82 binunion( 98.71/14.82 Y0, Y1))))))))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 Y0) => 98.71/14.82 (!!(( 98.71/14.82 ^[Y3 : $i]: 98.71/14.82 (in(Y3, 98.71/14.82 Y1) => 98.71/14.82 subset( 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y2, 98.71/14.82 emptyset), 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y2, 98.71/14.82 setadjoin( 98.71/14.82 Y3, 98.71/14.82 emptyset)), 98.71/14.82 emptyset)), 98.71/14.82 powerset( 98.71/14.82 binunion( 98.71/14.82 Y0, Y1))))))))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 Y0) => 98.71/14.82 (!!(( 98.71/14.82 ^[Y3 : $i]: 98.71/14.82 (in(Y3, 98.71/14.82 Y1) => 98.71/14.82 in( 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y2, 98.71/14.82 emptyset), 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y2, 98.71/14.82 setadjoin( 98.71/14.82 Y3, 98.71/14.82 emptyset)), 98.71/14.82 emptyset)), 98.71/14.82 powerset( 98.71/14.82 powerset( 98.71/14.82 binunion( 98.71/14.82 Y0, Y1)))))))))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 Y0) => 98.71/14.82 (!!(( 98.71/14.82 ^[Y3 : $i]: 98.71/14.82 (in(Y3, 98.71/14.82 Y1) => 98.71/14.82 in( 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y2, 98.71/14.82 emptyset), 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y2, 98.71/14.82 setadjoin( 98.71/14.82 Y3, 98.71/14.82 emptyset)), 98.71/14.82 emptyset)), 98.71/14.82 powerset( 98.71/14.82 powerset( 98.71/14.82 binunion( 98.71/14.82 Y0, Y1)))))))))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 Y0) => 98.71/14.82 (!!(( 98.71/14.82 ^[Y3 : $i]: 98.71/14.82 (in(Y3, 98.71/14.82 Y1) => 98.71/14.82 in( 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y2, 98.71/14.82 emptyset), 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y2, 98.71/14.82 setadjoin( 98.71/14.82 Y3, 98.71/14.82 emptyset)), 98.71/14.82 emptyset)), 98.71/14.82 dsetconstr( 98.71/14.82 powerset( 98.71/14.82 powerset( 98.71/14.82 binunion( 98.71/14.82 Y0, Y1))), 98.71/14.82 (^[Y4 : $i]: 98.71/14.82 (??(( 98.71/14.82 ^[Y5 : $i]: 98.71/14.82 (in(Y5, 98.71/14.82 Y0) & 98.71/14.82 (??(( 98.71/14.82 ^[Y6 : $i]: 98.71/14.82 (in(Y6, 98.71/14.82 Y1) & 98.71/14.82 (Y4 = 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y5, 98.71/14.82 emptyset), 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y5, 98.71/14.82 setadjoin( 98.71/14.82 Y6, 98.71/14.82 emptyset)), 98.71/14.82 emptyset)))))))))))))))))))))))))))) => 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 dsetconstr( 98.71/14.82 powerset( 98.71/14.82 powerset( 98.71/14.82 binunion( 98.71/14.82 Y0, Y1))), 98.71/14.82 (^[Y3 : $i]: 98.71/14.82 (??(( 98.71/14.82 ^[Y4 : $i]: 98.71/14.82 (in(Y4, 98.71/14.82 Y0) & 98.71/14.82 (??(( 98.71/14.82 ^[Y5 : $i]: 98.71/14.82 (in(Y5, 98.71/14.82 Y1) & 98.71/14.82 (Y3 = 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y4, 98.71/14.82 emptyset), 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y4, 98.71/14.82 setadjoin( 98.71/14.82 Y5, 98.71/14.82 emptyset)), 98.71/14.82 emptyset)))))))))))))) => 98.71/14.82 (??(( 98.71/14.82 ^[Y3 : $i]: 98.71/14.82 (( 98.71/14.82 ??(( 98.71/14.82 ^[Y4 : $i]: 98.71/14.82 (in(Y4, 98.71/14.82 Y1) & 98.71/14.82 (Y2 = 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y3, 98.71/14.82 emptyset), 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y3, 98.71/14.82 setadjoin( 98.71/14.82 Y4, 98.71/14.82 emptyset)), 98.71/14.82 emptyset))))))) & 98.71/14.82 in(Y3, 98.71/14.82 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 98.71/14.82 inference('lazy_cnf_imply', [status(thm)], ['169'])). 98.71/14.82 tff('171', plain, 98.71/14.82 ~ ((!!((^[Y0 : $i]: 98.71/14.82 (??((^[Y1 : $i]: 98.71/14.82 ((!!((^[Y2 : $i]: 98.71/14.82 (in(Y2, Y1) => 98.71/14.82 (!!((^[Y3 : $i]: (in(Y3, Y2) => in(Y3, Y0)))))))))& 98.71/14.82 (!!((^[Y2 : $i]: 98.71/14.82 (!!((^[Y3 : $i]: 98.71/14.82 ((in(Y3, Y0) & in(Y2, Y0)) => 98.71/14.82 ((!!((^[Y4 : $i]: 98.71/14.82 (in(Y4, Y1) => 98.71/14.82 (in(Y2, Y4) <=> in(Y3, Y4)))))) => 98.71/14.82 (Y2 = Y3)))))))))& 98.71/14.82 (!!((^[Y2 : $i]: 98.71/14.82 (!!((^[Y3 : $i]: 98.71/14.82 ((in(Y3, Y1) & in(Y2, Y1)) => 98.71/14.82 ((!!((^[Y4 : $i]: 98.71/14.82 (in(Y4, Y3) => in(Y4, Y2))))) | 98.71/14.82 (!!((^[Y4 : $i]: 98.71/14.82 (in(Y4, Y2) => in(Y4, Y3)))))))))))))& 98.71/14.82 (!!((^[Y2 : $i]: 98.71/14.82 (((??((^[Y3 : $i]: in(Y3, Y2)))) & 98.71/14.82 (!!((^[Y3 : $i]: (in(Y3, Y2) => in(Y3, Y0)))))) => 98.71/14.82 (??((^[Y3 : $i]: 98.71/14.82 (??((^[Y4 : $i]: 98.71/14.82 (in(Y3, Y1)&in(Y4, Y2)& 98.71/14.82 (~((??((^[Y5 : $i]: 98.71/14.82 (in(Y5, Y3) & 98.71/14.82 in(Y5, Y2)))))))& 98.71/14.82 (!!((^[Y5 : $i]: 98.71/14.82 (in(Y5, Y1) => 98.71/14.82 (in(Y4, Y5) | 98.71/14.82 (!!((^[Y6 : $i]: 98.71/14.82 (in(Y6, Y5) => 98.71/14.82 in(Y6, Y3)))))))))))))))))))))))))))) => 98.71/14.82 ((!!((^[Y0 : $i > $o]: 98.71/14.82 ((??((^[Y1 : $i]: 98.71/14.82 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 98.71/14.82 Y0(descr(Y0)))))) => 98.71/14.82 ((!!((^[Y0 : $i]: 98.71/14.82 (!!((^[Y1 : $i > $o]: 98.71/14.82 (!!((^[Y2 : $i]: 98.71/14.82 (in(Y2, Y0) => 98.71/14.82 (Y1(Y2) => in(Y2, dsetconstr(Y0, Y1))))))))))))) => 98.71/14.82 ((!!((^[Y0 : $i]: 98.71/14.82 (!!((^[Y1 : $i > $o]: 98.71/14.82 (!!((^[Y2 : $i]: 98.71/14.82 (in(Y2, dsetconstr(Y0, Y1)) => in(Y2, Y0))))))))))) => 98.71/14.82 ((!!((^[Y0 : $i]: 98.71/14.82 (!!((^[Y1 : $i > $o]: 98.71/14.82 (!!((^[Y2 : $i]: 98.71/14.82 (in(Y2, dsetconstr(Y0, Y1)) => Y1(Y2))))))))))) => 98.71/14.82 ((!!((^[Y0 : $o]: (!!((^[Y1 : $i]: (in(Y1, prop2set(Y0)) => Y0))))))) => 98.71/14.82 ((!!((^[Y0 : $i]: (in(Y0, emptyset) => (!!((^[Y1 : $o]: Y1))))))) => 98.71/14.82 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 98.71/14.82 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 98.71/14.82 ((!!((^[Y0 : $i > $o]: 98.71/14.82 ((??((^[Y1 : $i]: 98.71/14.82 (Y0(Y1) & 98.71/14.82 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 98.71/14.82 (??(Y0)))))) => 98.71/14.82 ((!!((^[Y0 : $i]: 98.71/14.82 (!!((^[Y1 : $i]: 98.71/14.82 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 98.71/14.82 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 98.71/14.82 (Y0 = Y1))))))))) => 98.71/14.82 ((!!((^[Y0 : $i]: 98.71/14.82 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 98.71/14.82 (Y0 = emptyset))))) => 98.71/14.82 ((!!((^[Y0 : $i]: 98.71/14.82 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 98.71/14.82 (Y0 = emptyset))))) => 98.71/14.82 ((!!((^[Y0 : $i]: 98.71/14.82 (!!((^[Y1 : $i > $o]: 98.71/14.82 (!!((^[Y2 : $i]: 98.71/14.82 (in(Y2, Y0) => 98.71/14.82 (in(Y2, dsetconstr(Y0, Y1)) <=> 98.71/14.82 Y1(Y2)))))))))))) => 98.71/14.82 ((!!((^[Y0 : $i]: 98.71/14.82 ((Y0 != emptyset) => 98.71/14.82 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.71/14.82 ((!!((^[Y0 : $i]: 98.71/14.82 (!!((^[Y1 : $i > $o]: 98.71/14.82 (!!((^[Y2 : $i]: 98.71/14.82 (in(Y2, Y0) => 98.71/14.82 (Y1(Y2) => 98.71/14.82 (dsetconstr(Y0, Y1) != emptyset)))))))))))) => 98.71/14.82 ((!!((^[Y0 : $i]: 98.71/14.82 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 98.71/14.82 (Y0 != emptyset))))) => 98.71/14.82 ((!!((^[Y0 : $i]: 98.71/14.82 (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 98.71/14.82 (in(emptyset, setadjoin(emptyset, emptyset)) => 98.71/14.82 ((!!((^[Y0 : $i]: 98.71/14.82 (!!((^[Y1 : $i]: 98.71/14.82 (!!((^[Y2 : $i]: 98.71/14.82 (in(Y2, Y1) => 98.71/14.82 in(Y2, setadjoin(Y0, Y1)))))))))))) => 98.71/14.82 ((!!((^[Y0 : $i]: 98.71/14.82 (!!((^[Y1 : $i]: 98.71/14.82 (!!((^[Y2 : $i]: 98.71/14.82 (in(Y2, setadjoin(Y0, Y1)) => 98.71/14.82 (!!((^[Y3 : $o]: 98.71/14.82 (((Y2 = Y0) => Y3) => 98.71/14.82 ((in(Y2, Y1) => Y3) => 98.71/14.82 Y3))))))))))))))) => 98.71/14.82 ((!!((^[Y0 : $i]: 98.71/14.82 (!!((^[Y1 : $i]: 98.71/14.82 (!!((^[Y2 : $i]: 98.71/14.82 (in(Y2, setadjoin(Y0, Y1)) => 98.71/14.82 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 98.71/14.82 ((!!((^[Y0 : $i]: 98.71/14.82 (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 98.71/14.82 ((!!((^[Y0 : $i]: 98.71/14.82 (!!((^[Y1 : $i]: 98.71/14.82 ((!!((^[Y2 : $i]: 98.71/14.82 (in(Y2, Y1) => in(Y2, Y0))))) => 98.71/14.82 in(Y1, powerset(Y0))))))))) => 98.71/14.82 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.71/14.82 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.71/14.82 ((!!((^[Y0 : $i]: 98.71/14.82 (!!((^[Y1 : $i]: 98.71/14.82 (!!((^[Y2 : $i]: 98.71/14.82 (in(Y1, powerset(Y0)) => 98.71/14.82 (in(Y2, Y1) => 98.71/14.82 in(Y2, Y0)))))))))))) => 98.71/14.82 ((!!((^[Y0 : $i]: 98.71/14.82 (!!((^[Y1 : $i]: 98.71/14.82 (!!((^[Y2 : $i]: 98.71/14.82 (in(Y1, Y2) => 98.71/14.82 (in(Y2, Y0) => 98.71/14.82 in(Y1, setunion(Y0))))))))))))) => 98.71/14.82 ((!!((^[Y0 : $i]: 98.71/14.82 (!!((^[Y1 : $i]: 98.71/14.82 (in(Y1, setunion(Y0)) => 98.71/14.82 (!!((^[Y2 : $o]: 98.71/14.82 ((!!((^[Y3 : $i]: 98.71/14.82 (in(Y1, Y3) => 98.71/14.82 (in(Y3, Y0) => 98.71/14.82 Y2))))) => 98.71/14.82 Y2))))))))))) => 98.71/14.82 ((!!((^[Y0 : $i]: 98.71/14.82 (!!((^[Y1 : $i]: 98.71/14.82 (in(Y1, Y0) => 98.71/14.82 in(Y1, 98.71/14.82 powerset(setunion(Y0)))))))))) => 98.71/14.82 ((!!((^[Y0 : $i > $o]: 98.71/14.82 ((??((^[Y1 : $i]: 98.71/14.82 (Y0(Y1) & 98.71/14.82 (!!((^[Y2 : $i]: 98.71/14.82 (Y0(Y2) => 98.71/14.82 (Y1 = Y2))))))))) => 98.71/14.82 (??((^[Y1 : $i]: 98.71/14.82 (!!((^[Y2 : $i]: 98.71/14.82 (Y0(Y2) <=> 98.71/14.82 (Y2 = Y1)))))))))))) => 98.71/14.82 ((!!((^[Y0 : $i]: 98.71/14.82 ((Y0 != emptyset) => 98.71/14.82 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.71/14.82 ((!!((^[Y0 : $i]: 98.71/14.82 (!!((^[Y1 : $i]: 98.71/14.82 (in(Y0, 98.71/14.82 setadjoin(Y1, 98.71/14.82 emptyset)) => 98.71/14.82 (Y0 = Y1)))))))) => 98.71/14.82 ((!!((^[Y0 : $i]: 98.71/14.82 (!!((^[Y1 : $i]: 98.71/14.82 ((Y0 != Y1) => 98.71/14.82 (~(in(Y1, 98.71/14.82 setadjoin(Y0, 98.71/14.82 emptyset))))))))))) => 98.71/14.82 ((!!((^[Y0 : $i]: 98.71/14.82 (!!((^[Y1 : $i]: 98.71/14.82 ((Y0 = Y1) => 98.71/14.82 in(Y0, 98.71/14.82 setadjoin(Y1, 98.71/14.82 emptyset))))))))) => 98.71/14.82 ((!!((^[Y0 : $i]: 98.71/14.82 (!!((^[Y1 : $i]: 98.71/14.82 (in(Y0, 98.71/14.82 setadjoin(Y1, 98.71/14.82 emptyset)) => 98.71/14.82 in(Y1, 98.71/14.82 setadjoin(Y0, 98.71/14.82 emptyset))))))))) => 98.71/14.82 ((!!((^[Y0 : $i]: 98.71/14.82 (!!((^[Y1 : $i]: 98.71/14.82 (!!((^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 setadjoin( 98.71/14.82 Y0, 98.71/14.82 setadjoin( 98.71/14.82 Y1, 98.71/14.82 emptyset))) => 98.71/14.82 ((Y2 = Y1) | 98.71/14.82 (Y2 = Y0)))))))))))) => 98.71/14.82 ((!!((^[Y0 : $i]: 98.71/14.82 (!!((^[Y1 : $i]: 98.71/14.82 in(Y0, 98.71/14.82 setadjoin(Y0, 98.71/14.82 setadjoin(Y1, 98.71/14.82 emptyset))))))))) => 98.71/14.82 ((!!((^[Y0 : $i]: 98.71/14.82 (!!((^[Y1 : $i]: 98.71/14.82 in(Y1, 98.71/14.82 setadjoin(Y0, 98.71/14.82 setadjoin(Y1, 98.71/14.82 emptyset))))))))) => 98.71/14.82 ((!!((^[Y0 : $i]: 98.71/14.82 (!!((^[Y1 : $i > $o]: 98.71/14.82 ((??((^[Y2 : $i]: 98.71/14.82 ( 98.71/14.82 in(Y2, 98.71/14.82 Y0) & 98.71/14.82 Y1(Y2))))) => 98.71/14.82 (dsetconstr(Y0, 98.71/14.82 Y1) != 98.71/14.82 emptyset)))))))) => 98.71/14.82 ((!!((^[Y0 : $i > $o]: 98.71/14.82 (!!((^[Y1 : $i]: 98.71/14.82 (in(Y1, 98.71/14.82 emptyset) => 98.71/14.82 Y0(Y1)))))))) => 98.71/14.82 ((!!((^[Y0 : $i]: 98.71/14.82 (!!((^[Y1 : $i > $o]: 98.71/14.82 ((~((!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 Y0) => 98.71/14.82 Y1(Y2))))))) => 98.71/14.82 (??((^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 Y0) & 98.71/14.82 (~( 98.71/14.82 Y1(Y2)))))))))))))) => 98.71/14.82 ((!!((^[Y0 : $i]: 98.71/14.82 (!!((^[Y1 : $i > $o]: 98.71/14.82 ((!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 Y0) => 98.71/14.82 ( 98.71/14.82 ~( 98.71/14.82 Y1(Y2))))))) => 98.71/14.82 (~((??(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 Y0) & 98.71/14.82 Y1(Y2)))))))))))))) => 98.71/14.82 ((!!((^[Y0 : $i]: 98.71/14.82 (!!((^[Y1 : $i > $o]: 98.71/14.82 ((~(( 98.71/14.82 ??(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 ( 98.71/14.82 in(Y2, 98.71/14.82 Y0) & 98.71/14.82 Y1(Y2))))))) => 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 ( 98.71/14.82 in(Y2, 98.71/14.82 Y0) => 98.71/14.82 ( 98.71/14.82 ~( 98.71/14.82 Y1(Y2)))))))))))))) => 98.71/14.82 ((!!((^[Y0 : $i]: 98.71/14.82 (!!((^[Y1 : $i > $o]: 98.71/14.82 ((??(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 Y0) & 98.71/14.82 (~( 98.71/14.82 Y1(Y2))))))) => 98.71/14.82 (~(( 98.71/14.82 !!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 Y0) => 98.71/14.82 Y1(Y2)))))))))))))) => 98.71/14.82 ((!!((^[Y0 : $o]: 98.71/14.82 (Y0 => 98.71/14.82 in(emptyset, 98.71/14.82 prop2set(Y0)))))) => 98.71/14.82 ((!!((^[Y0 : $o]: 98.71/14.82 (Y0 => 98.71/14.82 set2prop( 98.71/14.82 prop2set(Y0)))))) => 98.71/14.82 ((!!((^[Y0 : $i]: 98.71/14.82 (!!((^[Y1 : $i > $o]: 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 ~(( 98.71/14.82 ??(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 Y0) & 98.71/14.82 Y1(Y2))))))) => 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 Y0) => 98.71/14.82 (~( 98.71/14.82 Y1(Y2)))))))))))))) => 98.71/14.82 ((!!((^[Y0 : $i]: 98.71/14.82 (!!((^[Y1 : $i > $o]: 98.71/14.82 (( 98.71/14.82 ~(( 98.71/14.82 !!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 Y0) => 98.71/14.82 Y1(Y2))))))) => 98.71/14.82 (??(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 Y0) & 98.71/14.82 (~( 98.71/14.82 Y1(Y2)))))))))))))) => 98.71/14.82 ((!!((^[Y0 : $i > $o]: 98.71/14.82 ((??(Y0)) => 98.71/14.82 ((!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (Y0(Y1) => 98.71/14.82 (Y0(Y2) => 98.71/14.82 (Y1 = Y2))))))))) => 98.71/14.82 (??(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 ( 98.71/14.82 Y0(Y1) & 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (Y0(Y2) => 98.71/14.82 (Y1 = Y2)))))))))))))) => 98.71/14.82 ((!!((^[Y0 : $i > $o]: 98.71/14.82 ((??(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (Y0(Y2) <=> 98.71/14.82 (Y2 = Y1)))))))) => 98.71/14.82 (??(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 ( 98.71/14.82 Y0(Y1) & 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (Y0(Y2) => 98.71/14.82 (Y1 = Y2))))))))))))) => 98.71/14.82 ((!!((^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 Y0 = Y1) => 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y3 : $i]: 98.71/14.82 (( 98.71/14.82 Y2 = Y3) => 98.71/14.82 (in(Y2, 98.71/14.82 Y0) => 98.71/14.82 in(Y3, 98.71/14.82 Y1)))))))))))))))) => 98.71/14.82 ((!!((^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (( 98.71/14.82 Y0 = Y1) => 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y3 : $i]: 98.71/14.82 (( 98.71/14.82 Y2 = Y3) => 98.71/14.82 (in(Y2, 98.71/14.82 Y0) <=> 98.71/14.82 in(Y3, 98.71/14.82 Y1)))))))))))))))) => 98.71/14.82 ((!!((^[Y0 : $i > $o]: 98.71/14.82 (( 98.71/14.82 ??(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (Y0(Y1) & 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (Y0(Y2) => 98.71/14.82 (Y1 = Y2))))))))) => 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (Y0(Y1) => 98.71/14.82 (Y0(Y2) => 98.71/14.82 (Y1 = Y2))))))))))))) => 98.71/14.82 ((!!((^[Y0 : $i > $o]: 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y1 : $i > $o]: 98.71/14.82 (( 98.71/14.82 !!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y3 : $i]: 98.71/14.82 (( 98.71/14.82 Y2 = Y3) => 98.71/14.82 (Y0(Y2) <=> 98.71/14.82 Y1(Y3))))))))) => 98.71/14.82 (( 98.71/14.82 ??(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (Y0(Y2) & 98.71/14.82 (!!(( 98.71/14.82 ^[Y3 : $i]: 98.71/14.82 (Y0(Y3) => 98.71/14.82 (Y2 = Y3))))))))) <=> 98.71/14.82 (??(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (Y1(Y2) & 98.71/14.82 (!!(( 98.71/14.82 ^[Y3 : $i]: 98.71/14.82 (Y1(Y3) => 98.71/14.82 (Y2 = Y3))))))))))))))))) => 98.71/14.82 ((!!((^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (( 98.71/14.82 Y0 = Y1) => 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y3 : $i]: 98.71/14.82 (( 98.71/14.82 Y2 = Y3) => 98.71/14.82 (setadjoin( 98.71/14.82 Y0, Y2) = 98.71/14.82 setadjoin( 98.71/14.82 Y1, Y3)))))))))))))))) => 98.71/14.82 ((!!((^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (( 98.71/14.82 Y0 = Y1) => 98.71/14.82 (powerset( 98.71/14.82 Y0) = 98.71/14.82 powerset( 98.71/14.82 Y1))))))))) => 98.71/14.82 ((!!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (( 98.71/14.82 Y0 = Y1) => 98.71/14.82 (setunion( 98.71/14.82 Y0) = 98.71/14.82 setunion( 98.71/14.82 Y1))))))))) => 98.71/14.82 ((!!(( 98.71/14.82 ^[Y0 : $i > $o]: 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 ??(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (Y0(Y1) & 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (Y0(Y2) => 98.71/14.82 (Y1 = Y2))))))))) => 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (Y0(Y1) => 98.71/14.82 (Y0(Y2) => 98.71/14.82 (Y1 = Y2))))))))))))) => 98.71/14.82 ((!!(( 98.71/14.82 ^[Y0 : $i > $o]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i > $o]: 98.71/14.82 (( 98.71/14.82 !!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y3 : $i]: 98.71/14.82 (( 98.71/14.82 Y2 = Y3) => 98.71/14.82 (Y0(Y2) <=> 98.71/14.82 Y1(Y3))))))))) => 98.71/14.82 (( 98.71/14.82 ??(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (Y0(Y2) & 98.71/14.82 (!!(( 98.71/14.82 ^[Y3 : $i]: 98.71/14.82 (Y0(Y3) => 98.71/14.82 (Y2 = Y3))))))))) => 98.71/14.82 (( 98.71/14.82 ??(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (Y1(Y2) & 98.71/14.82 (!!(( 98.71/14.82 ^[Y3 : $i]: 98.71/14.82 (Y1(Y3) => 98.71/14.82 (Y2 = Y3))))))))) => 98.71/14.82 (descr( 98.71/14.82 Y0) = 98.71/14.82 descr(Y1))))))))))) => 98.71/14.82 ((!!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (( 98.71/14.82 Y0 = Y1) => 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i > $o]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y3 : $i > $o]: 98.71/14.82 (( 98.71/14.82 !!(( 98.71/14.82 ^[Y4 : $i]: 98.71/14.82 (in(Y4, 98.71/14.82 Y0) => 98.71/14.82 (!!(( 98.71/14.82 ^[Y5 : $i]: 98.71/14.82 (in(Y5, 98.71/14.82 Y1) => 98.71/14.82 (( 98.71/14.82 Y4 = Y5) => 98.71/14.82 (Y2(Y4) <=> 98.71/14.82 Y3(Y5))))))))))) => 98.71/14.82 (dsetconstr( 98.71/14.82 Y0, Y2) = 98.71/14.82 dsetconstr( 98.71/14.82 Y1, Y3)))))))))))))))) => 98.71/14.82 (( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (( 98.71/14.82 !!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 Y0) => 98.71/14.82 in(Y2, 98.71/14.82 Y1))))) => 98.71/14.82 subset( 98.71/14.82 Y0, Y1)))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (( 98.71/14.82 Y0 = Y1) => 98.71/14.82 subset( 98.71/14.82 Y1, Y0)))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (( 98.71/14.82 Y0 = Y1) => 98.71/14.82 subset( 98.71/14.82 Y0, Y1)))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (( 98.71/14.82 !!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 Y0) => 98.71/14.82 in(Y2, 98.71/14.82 Y1))))) => 98.71/14.82 subset( 98.71/14.82 Y0, Y1)))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!( 98.71/14.82 subset( 98.71/14.82 emptyset))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (subset( 98.71/14.82 Y0, Y1) => 98.71/14.82 (in(Y2, 98.71/14.82 Y0) => 98.71/14.82 in(Y2, 98.71/14.82 Y1)))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (subset( 98.71/14.82 Y0, Y1) => 98.71/14.82 (( 98.71/14.82 ~( 98.71/14.82 in(Y2, 98.71/14.82 Y1))) => 98.71/14.82 (~( 98.71/14.82 in(Y2, 98.71/14.82 Y0)))))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 Y0) => 98.71/14.82 (( 98.71/14.82 ~( 98.71/14.82 in(Y2, 98.71/14.82 Y1))) => 98.71/14.82 (~( 98.71/14.82 subset( 98.71/14.82 Y0, Y1)))))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (( 98.71/14.82 ~( 98.71/14.82 subset( 98.71/14.82 Y0, Y1))) => 98.71/14.82 (Y0 != Y1)))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 Y0) => 98.71/14.82 (( 98.71/14.82 ~( 98.71/14.82 in(Y2, 98.71/14.82 Y1))) => 98.71/14.82 (Y0 != Y1)))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 subset( 98.71/14.82 Y0, Y0)))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (subset( 98.71/14.82 Y0, Y1) => 98.71/14.82 (subset( 98.71/14.82 Y1, Y2) => 98.71/14.82 subset( 98.71/14.82 Y0, Y2)))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 subset( 98.71/14.82 Y1, 98.71/14.82 setadjoin( 98.71/14.82 Y0, Y1)))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (subset( 98.71/14.82 Y0, Y2) => 98.71/14.82 subset( 98.71/14.82 Y0, 98.71/14.82 setadjoin( 98.71/14.82 Y1, Y2)))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (subset( 98.71/14.82 Y0, Y1) => 98.71/14.82 in(Y0, 98.71/14.82 powerset( 98.71/14.82 Y1))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (subset( 98.71/14.82 Y0, Y1) => 98.71/14.82 (subset( 98.71/14.82 Y1, Y0) => 98.71/14.82 (Y0 = Y1))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (subset( 98.71/14.82 Y0, 98.71/14.82 emptyset) => 98.71/14.82 (Y0 = 98.71/14.82 emptyset))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (subset( 98.71/14.82 Y1, Y0) => 98.71/14.82 in(Y1, 98.71/14.82 powerset( 98.71/14.82 Y0))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (in(Y1, 98.71/14.82 powerset( 98.71/14.82 Y0)) => 98.71/14.82 subset( 98.71/14.82 Y1, Y0)))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 in(Y0, 98.71/14.82 powerset( 98.71/14.82 Y0))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (subset( 98.71/14.82 Y0, Y1) => 98.71/14.82 subset( 98.71/14.82 powerset( 98.71/14.82 Y0), 98.71/14.82 powerset( 98.71/14.82 Y1))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i > $o]: 98.71/14.82 in( 98.71/14.82 dsetconstr( 98.71/14.82 Y0, Y1), 98.71/14.82 powerset( 98.71/14.82 Y0)))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i > $o]: 98.71/14.82 subset( 98.71/14.82 dsetconstr( 98.71/14.82 Y0, Y1), 98.71/14.82 Y0))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 Y0) => 98.71/14.82 in(Y2, 98.71/14.82 binunion( 98.71/14.82 Y0, Y1)))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 in(Y1, 98.71/14.82 setadjoin( 98.71/14.82 Y0, 98.71/14.82 setadjoin( 98.71/14.82 Y1, 98.71/14.82 emptyset))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 Y1) => 98.71/14.82 in(Y2, 98.71/14.82 binunion( 98.71/14.82 Y0, Y1)))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y3 : $o]: 98.71/14.82 (in(Y2, 98.71/14.82 binunion( 98.71/14.82 Y0, Y1)) => 98.71/14.82 (( 98.71/14.82 in(Y2, 98.71/14.82 Y0) => Y3) => 98.71/14.82 (( 98.71/14.82 in(Y2, 98.71/14.82 Y1) => Y3) => 98.71/14.82 Y3))))))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 binunion( 98.71/14.82 Y0, Y1)) => 98.71/14.82 (in(Y2, 98.71/14.82 Y1) | 98.71/14.82 in(Y2, 98.71/14.82 Y0)))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 subset( 98.71/14.82 Y0, 98.71/14.82 binunion( 98.71/14.82 Y0, Y1)))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 subset( 98.71/14.82 Y1, 98.71/14.82 binunion( 98.71/14.82 Y0, Y1)))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 Y0) => 98.71/14.82 (in(Y2, 98.71/14.82 Y1) => 98.71/14.82 in(Y2, 98.71/14.82 binintersect( 98.71/14.82 Y0, Y1))))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (subset( 98.71/14.82 Y2, Y0) => 98.71/14.82 (subset( 98.71/14.82 Y2, Y1) => 98.71/14.82 subset( 98.71/14.82 Y2, 98.71/14.82 binintersect( 98.71/14.82 Y0, Y1))))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 binintersect( 98.71/14.82 Y0, Y1)) => 98.71/14.82 in(Y2, 98.71/14.82 Y0))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 subset( 98.71/14.82 binintersect( 98.71/14.82 Y0, Y1), 98.71/14.82 Y0))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (subset( 98.71/14.82 Y0, Y1) => 98.71/14.82 (binintersect( 98.71/14.82 Y0, Y1) = 98.71/14.82 Y0)))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (( 98.71/14.82 binintersect( 98.71/14.82 Y0, Y1) = 98.71/14.82 Y1) => 98.71/14.82 subset( 98.71/14.82 Y1, Y0)))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 binintersect( 98.71/14.82 Y0, Y1)) => 98.71/14.82 in(Y2, 98.71/14.82 Y1))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (( 98.71/14.82 ~(( 98.71/14.82 ??(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 Y0) & 98.71/14.82 in(Y2, 98.71/14.82 Y1))))))) => 98.71/14.82 (binintersect( 98.71/14.82 Y0, Y1) = 98.71/14.82 emptyset)))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 subset( 98.71/14.82 binintersect( 98.71/14.82 Y0, Y1), 98.71/14.82 Y1))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (subset( 98.71/14.82 Y1, Y0) => 98.71/14.82 (binintersect( 98.71/14.82 Y0, Y1) = 98.71/14.82 Y1)))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (( 98.71/14.82 binintersect( 98.71/14.82 Y0, Y1) = 98.71/14.82 Y0) => 98.71/14.82 subset( 98.71/14.82 Y0, Y1)))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (binintersect( 98.71/14.82 Y0, 98.71/14.82 binunion( 98.71/14.82 Y1, Y2)) = 98.71/14.82 binunion( 98.71/14.82 binintersect( 98.71/14.82 Y0, Y1), 98.71/14.82 binintersect( 98.71/14.82 Y0, Y2)))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 Y0) => 98.71/14.82 (( 98.71/14.82 ~( 98.71/14.82 in(Y2, 98.71/14.82 Y1))) => 98.71/14.82 in(Y2, 98.71/14.82 setminus( 98.71/14.82 Y0, Y1))))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 setminus( 98.71/14.82 Y0, Y1)) => 98.71/14.82 in(Y2, 98.71/14.82 Y0))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 setminus( 98.71/14.82 Y0, Y1)) => 98.71/14.82 (~( 98.71/14.82 in(Y2, 98.71/14.82 Y1))))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (subset( 98.71/14.82 Y0, Y1) => 98.71/14.82 (setminus( 98.71/14.82 Y0, Y1) = 98.71/14.82 emptyset)))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (( 98.71/14.82 ~( 98.71/14.82 in(Y2, 98.71/14.82 setminus( 98.71/14.82 Y0, Y1)))) => 98.71/14.82 (in(Y2, 98.71/14.82 Y0) => 98.71/14.82 in(Y2, 98.71/14.82 Y1)))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (( 98.71/14.82 ~( 98.71/14.82 in(Y2, 98.71/14.82 setminus( 98.71/14.82 Y0, Y1)))) => 98.71/14.82 (( 98.71/14.82 ~( 98.71/14.82 in(Y2, 98.71/14.82 Y1))) => 98.71/14.82 (~( 98.71/14.82 in(Y2, 98.71/14.82 Y0)))))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (( 98.71/14.82 ~( 98.71/14.82 in(Y2, 98.71/14.82 Y0))) => 98.71/14.82 (~( 98.71/14.82 in(Y2, 98.71/14.82 setminus( 98.71/14.82 Y0, Y1)))))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 Y1) => 98.71/14.82 (~( 98.71/14.82 in(Y2, 98.71/14.82 setminus( 98.71/14.82 Y0, Y1)))))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 subset( 98.71/14.82 setminus( 98.71/14.82 Y0, Y1), 98.71/14.82 Y0))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (( 98.71/14.82 setminus( 98.71/14.82 Y0, Y1) = 98.71/14.82 emptyset) => 98.71/14.82 subset( 98.71/14.82 Y0, Y1)))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 symdiff( 98.71/14.82 Y0, Y1)) => 98.71/14.82 (!!(( 98.71/14.82 ^[Y3 : $o]: 98.71/14.82 (( 98.71/14.82 in(Y2, 98.71/14.82 Y0) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 ~( 98.71/14.82 in(Y2, 98.71/14.82 Y1))) => 98.71/14.82 Y3)) => 98.71/14.82 (( 98.71/14.82 ( 98.71/14.82 ~( 98.71/14.82 in(Y2, 98.71/14.82 Y0))) => 98.71/14.82 ( 98.71/14.82 in(Y2, 98.71/14.82 Y1) => Y3)) => 98.71/14.82 Y3))))))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 Y0) => 98.71/14.82 (( 98.71/14.82 ~( 98.71/14.82 in(Y2, 98.71/14.82 Y1))) => 98.71/14.82 in(Y2, 98.71/14.82 symdiff( 98.71/14.82 Y0, Y1))))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (( 98.71/14.82 ~( 98.71/14.82 in(Y2, 98.71/14.82 Y0))) => 98.71/14.82 (in(Y2, 98.71/14.82 Y1) => 98.71/14.82 in(Y2, 98.71/14.82 symdiff( 98.71/14.82 Y0, Y1))))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 Y0) => 98.71/14.82 (in(Y2, 98.71/14.82 Y1) => 98.71/14.82 (~( 98.71/14.82 in(Y2, 98.71/14.82 symdiff( 98.71/14.82 Y0, Y1))))))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (( 98.71/14.82 ~( 98.71/14.82 in(Y2, 98.71/14.82 Y0))) => 98.71/14.82 (( 98.71/14.82 ~( 98.71/14.82 in(Y2, 98.71/14.82 Y1))) => 98.71/14.82 (~( 98.71/14.82 in(Y2, 98.71/14.82 symdiff( 98.71/14.82 Y0, Y1))))))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 in(Y1, 98.71/14.82 setadjoin( 98.71/14.82 Y0, 98.71/14.82 setadjoin( 98.71/14.82 Y1, 98.71/14.82 emptyset))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 in(Y0, 98.71/14.82 setunion( 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y0, 98.71/14.82 emptyset), 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y0, 98.71/14.82 setadjoin( 98.71/14.82 Y1, 98.71/14.82 emptyset)), 98.71/14.82 emptyset)))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 in(Y1, 98.71/14.82 setunion( 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y0, 98.71/14.82 emptyset), 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y0, 98.71/14.82 setadjoin( 98.71/14.82 Y1, 98.71/14.82 emptyset)), 98.71/14.82 emptyset)))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (??(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 setunion( 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y0, 98.71/14.82 emptyset), 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y0, 98.71/14.82 setadjoin( 98.71/14.82 Y1, 98.71/14.82 emptyset)), 98.71/14.82 emptyset)))) & 98.71/14.82 (??(( 98.71/14.82 ^[Y3 : $i]: 98.71/14.82 (in(Y3, 98.71/14.82 setunion( 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y0, 98.71/14.82 emptyset), 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y0, 98.71/14.82 setadjoin( 98.71/14.82 Y1, 98.71/14.82 emptyset)), 98.71/14.82 emptyset)))) & 98.71/14.82 (setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y0, 98.71/14.82 emptyset), 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y0, 98.71/14.82 setadjoin( 98.71/14.82 Y1, 98.71/14.82 emptyset)), 98.71/14.82 emptyset)) = 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y2, 98.71/14.82 emptyset), 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y2, 98.71/14.82 setadjoin( 98.71/14.82 Y3, 98.71/14.82 emptyset)), 98.71/14.82 emptyset))))))))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (??(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 setunion( 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y0, 98.71/14.82 emptyset), 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y0, 98.71/14.82 setadjoin( 98.71/14.82 Y1, 98.71/14.82 emptyset)), 98.71/14.82 emptyset)))) & 98.71/14.82 (??(( 98.71/14.82 ^[Y3 : $i]: 98.71/14.82 (in(Y3, 98.71/14.82 setunion( 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y0, 98.71/14.82 emptyset), 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y0, 98.71/14.82 setadjoin( 98.71/14.82 Y1, 98.71/14.82 emptyset)), 98.71/14.82 emptyset)))) & 98.71/14.82 (setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y0, 98.71/14.82 emptyset), 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y0, 98.71/14.82 setadjoin( 98.71/14.82 Y1, 98.71/14.82 emptyset)), 98.71/14.82 emptyset)) = 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y2, 98.71/14.82 emptyset), 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y2, 98.71/14.82 setadjoin( 98.71/14.82 Y3, 98.71/14.82 emptyset)), 98.71/14.82 emptyset))))))))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (in(Y1, 98.71/14.82 Y0) => 98.71/14.82 subset( 98.71/14.82 setadjoin( 98.71/14.82 Y1, 98.71/14.82 emptyset), 98.71/14.82 Y0)))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (in(Y1, 98.71/14.82 Y0) => 98.71/14.82 in( 98.71/14.82 setadjoin( 98.71/14.82 Y1, 98.71/14.82 emptyset), 98.71/14.82 powerset( 98.71/14.82 Y0))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 Y0) => 98.71/14.82 in( 98.71/14.82 setadjoin( 98.71/14.82 Y2, 98.71/14.82 emptyset), 98.71/14.82 powerset( 98.71/14.82 binunion( 98.71/14.82 Y0, Y1))))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 setadjoin( 98.71/14.82 Y0, 98.71/14.82 setadjoin( 98.71/14.82 Y1, 98.71/14.82 emptyset))) => 98.71/14.82 (( 98.71/14.82 Y2 = Y1) | 98.71/14.82 (Y2 = Y0)))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 Y0) => 98.71/14.82 (!!(( 98.71/14.82 ^[Y3 : $i]: 98.71/14.82 (in(Y3, 98.71/14.82 Y1) => 98.71/14.82 subset( 98.71/14.82 setadjoin( 98.71/14.82 Y2, 98.71/14.82 setadjoin( 98.71/14.82 Y3, 98.71/14.82 emptyset)), 98.71/14.82 binunion( 98.71/14.82 Y0, Y1)))))))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 Y0) => 98.71/14.82 (!!(( 98.71/14.82 ^[Y3 : $i]: 98.71/14.82 (in(Y3, 98.71/14.82 Y1) => 98.71/14.82 in( 98.71/14.82 setadjoin( 98.71/14.82 Y2, 98.71/14.82 setadjoin( 98.71/14.82 Y3, 98.71/14.82 emptyset)), 98.71/14.82 powerset( 98.71/14.82 binunion( 98.71/14.82 Y0, Y1))))))))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 Y0) => 98.71/14.82 (!!(( 98.71/14.82 ^[Y3 : $i]: 98.71/14.82 (in(Y3, 98.71/14.82 Y1) => 98.71/14.82 subset( 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y2, 98.71/14.82 emptyset), 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y2, 98.71/14.82 setadjoin( 98.71/14.82 Y3, 98.71/14.82 emptyset)), 98.71/14.82 emptyset)), 98.71/14.82 powerset( 98.71/14.82 binunion( 98.71/14.82 Y0, Y1))))))))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 Y0) => 98.71/14.82 (!!(( 98.71/14.82 ^[Y3 : $i]: 98.71/14.82 (in(Y3, 98.71/14.82 Y1) => 98.71/14.82 in( 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y2, 98.71/14.82 emptyset), 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y2, 98.71/14.82 setadjoin( 98.71/14.82 Y3, 98.71/14.82 emptyset)), 98.71/14.82 emptyset)), 98.71/14.82 powerset( 98.71/14.82 powerset( 98.71/14.82 binunion( 98.71/14.82 Y0, Y1)))))))))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 Y0) => 98.71/14.82 (!!(( 98.71/14.82 ^[Y3 : $i]: 98.71/14.82 (in(Y3, 98.71/14.82 Y1) => 98.71/14.82 in( 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y2, 98.71/14.82 emptyset), 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y2, 98.71/14.82 setadjoin( 98.71/14.82 Y3, 98.71/14.82 emptyset)), 98.71/14.82 emptyset)), 98.71/14.82 powerset( 98.71/14.82 powerset( 98.71/14.82 binunion( 98.71/14.82 Y0, Y1)))))))))))))))))) => 98.71/14.82 ( 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 Y0) => 98.71/14.82 (!!(( 98.71/14.82 ^[Y3 : $i]: 98.71/14.82 (in(Y3, 98.71/14.82 Y1) => 98.71/14.82 in( 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y2, 98.71/14.82 emptyset), 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y2, 98.71/14.82 setadjoin( 98.71/14.82 Y3, 98.71/14.82 emptyset)), 98.71/14.82 emptyset)), 98.71/14.82 dsetconstr( 98.71/14.82 powerset( 98.71/14.82 powerset( 98.71/14.82 binunion( 98.71/14.82 Y0, Y1))), 98.71/14.82 (^[Y4 : $i]: 98.71/14.82 (??(( 98.71/14.82 ^[Y5 : $i]: 98.71/14.82 (in(Y5, 98.71/14.82 Y0) & 98.71/14.82 (??(( 98.71/14.82 ^[Y6 : $i]: 98.71/14.82 (in(Y6, 98.71/14.82 Y1) & 98.71/14.82 (Y4 = 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y5, 98.71/14.82 emptyset), 98.71/14.82 setadjoin( 98.71/14.82 setadjoin( 98.71/14.82 Y5, 98.71/14.82 setadjoin( 98.71/14.82 Y6, 98.71/14.82 emptyset)), 98.71/14.82 emptyset)))))))))))))))))))))))))))) => 98.71/14.82 ( 98.71/14.82 !!(( 98.71/14.82 ^[Y0 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y1 : $i]: 98.71/14.82 (!!(( 98.71/14.82 ^[Y2 : $i]: 98.71/14.82 (in(Y2, 98.71/14.82 dsetconstr( 98.71/14.82 powerset( 98.71/14.82 powerset( 98.71/14.82 binunion( 98.71/14.82 Y0, Y1))), 98.71/14.82 (^[Y3 : $i]: 98.71/14.82 (??(( 98.71/14.82 ^[Y4 : $i]: 98.71/14.82 (in(Y4, 98.71/14.82 Y0) & 98.71/14.82 (??(( 98.71/14.82 ^[Y5 : $i]: 98.71/14.83 (in(Y5, 98.71/14.83 Y1) & 98.71/14.83 (Y3 = 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y4, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y4, 98.71/14.83 setadjoin( 98.71/14.83 Y5, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)))))))))))))) => 98.71/14.83 (??(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (( 98.71/14.83 ??(( 98.71/14.83 ^[Y4 : $i]: 98.71/14.83 (in(Y4, 98.71/14.83 Y1) & 98.71/14.83 (Y2 = 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y3, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y3, 98.71/14.83 setadjoin( 98.71/14.83 Y4, 98.71/14.83 emptyset)), 98.71/14.83 emptyset))))))) & 98.71/14.83 in(Y3, 98.71/14.83 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 98.71/14.83 inference('lazy_cnf_imply', [status(thm)], ['170'])). 98.71/14.83 tff('172', plain, 98.71/14.83 ~ ((!!((^[Y0 : $i > $o]: 98.71/14.83 ((??((^[Y1 : $i]: 98.71/14.83 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 98.71/14.83 Y0(descr(Y0)))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (in(Y2, Y0) => 98.71/14.83 (Y1(Y2) => in(Y2, dsetconstr(Y0, Y1))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (in(Y2, dsetconstr(Y0, Y1)) => in(Y2, Y0))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (in(Y2, dsetconstr(Y0, Y1)) => Y1(Y2))))))))))) => 98.71/14.83 ((!!((^[Y0 : $o]: (!!((^[Y1 : $i]: (in(Y1, prop2set(Y0)) => Y0))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: (in(Y0, emptyset) => (!!((^[Y1 : $o]: Y1))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 98.71/14.83 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 98.71/14.83 ((!!((^[Y0 : $i > $o]: 98.71/14.83 ((??((^[Y1 : $i]: 98.71/14.83 (Y0(Y1) & 98.71/14.83 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 98.71/14.83 (??(Y0)))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 98.71/14.83 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 98.71/14.83 (Y0 = Y1))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 98.71/14.83 (Y0 = emptyset))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 98.71/14.83 (Y0 = emptyset))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (in(Y2, Y0) => 98.71/14.83 (in(Y2, dsetconstr(Y0, Y1)) <=> 98.71/14.83 Y1(Y2)))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 ((Y0 != emptyset) => 98.71/14.83 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (in(Y2, Y0) => 98.71/14.83 (Y1(Y2) => 98.71/14.83 (dsetconstr(Y0, Y1) != emptyset)))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 98.71/14.83 (Y0 != emptyset))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 98.71/14.83 (in(emptyset, setadjoin(emptyset, emptyset)) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (in(Y2, Y1) => 98.71/14.83 in(Y2, setadjoin(Y0, Y1)))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (in(Y2, setadjoin(Y0, Y1)) => 98.71/14.83 (!!((^[Y3 : $o]: 98.71/14.83 (((Y2 = Y0) => Y3) => 98.71/14.83 ((in(Y2, Y1) => Y3) => 98.71/14.83 Y3))))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (in(Y2, setadjoin(Y0, Y1)) => 98.71/14.83 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 ((!!((^[Y2 : $i]: 98.71/14.83 (in(Y2, Y1) => in(Y2, Y0))))) => 98.71/14.83 in(Y1, powerset(Y0))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.71/14.83 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (in(Y1, powerset(Y0)) => 98.71/14.83 (in(Y2, Y1) => 98.71/14.83 in(Y2, Y0)))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (in(Y1, Y2) => 98.71/14.83 (in(Y2, Y0) => 98.71/14.83 in(Y1, setunion(Y0))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (in(Y1, setunion(Y0)) => 98.71/14.83 (!!((^[Y2 : $o]: 98.71/14.83 ((!!((^[Y3 : $i]: 98.71/14.83 (in(Y1, Y3) => 98.71/14.83 (in(Y3, Y0) => 98.71/14.83 Y2))))) => 98.71/14.83 Y2))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (in(Y1, Y0) => 98.71/14.83 in(Y1, 98.71/14.83 powerset(setunion(Y0)))))))))) => 98.71/14.83 ((!!((^[Y0 : $i > $o]: 98.71/14.83 ((??((^[Y1 : $i]: 98.71/14.83 (Y0(Y1) & 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (Y0(Y2) => 98.71/14.83 (Y1 = Y2))))))))) => 98.71/14.83 (??((^[Y1 : $i]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (Y0(Y2) <=> 98.71/14.83 (Y2 = Y1)))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 ((Y0 != emptyset) => 98.71/14.83 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (in(Y0, 98.71/14.83 setadjoin(Y1, 98.71/14.83 emptyset)) => 98.71/14.83 (Y0 = Y1)))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 ((Y0 != Y1) => 98.71/14.83 (~(in(Y1, 98.71/14.83 setadjoin(Y0, 98.71/14.83 emptyset))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 ((Y0 = Y1) => 98.71/14.83 in(Y0, 98.71/14.83 setadjoin(Y1, 98.71/14.83 emptyset))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (in(Y0, 98.71/14.83 setadjoin(Y1, 98.71/14.83 emptyset)) => 98.71/14.83 in(Y1, 98.71/14.83 setadjoin(Y0, 98.71/14.83 emptyset))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset))) => 98.71/14.83 ((Y2 = Y1) | 98.71/14.83 (Y2 = Y0)))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 in(Y0, 98.71/14.83 setadjoin(Y0, 98.71/14.83 setadjoin(Y1, 98.71/14.83 emptyset))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 in(Y1, 98.71/14.83 setadjoin(Y0, 98.71/14.83 setadjoin(Y1, 98.71/14.83 emptyset))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 ((??((^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) & 98.71/14.83 Y1(Y2))))) => 98.71/14.83 (dsetconstr(Y0, 98.71/14.83 Y1) != 98.71/14.83 emptyset)))))))) => 98.71/14.83 ((!!((^[Y0 : $i > $o]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (in(Y1, emptyset) => 98.71/14.83 Y0(Y1)))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 ((~((!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 ( 98.71/14.83 in(Y2, 98.71/14.83 Y0) => 98.71/14.83 Y1(Y2))))))) => 98.71/14.83 (??((^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) & 98.71/14.83 (~( 98.71/14.83 Y1(Y2)))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 ((!!((^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (~( 98.71/14.83 Y1(Y2))))))) => 98.71/14.83 (~((??(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) & 98.71/14.83 Y1(Y2)))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 ((~((??(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) & 98.71/14.83 Y1(Y2))))))) => 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 ( 98.71/14.83 ~( 98.71/14.83 Y1(Y2)))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 ((??(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 ( 98.71/14.83 in(Y2, 98.71/14.83 Y0) & 98.71/14.83 ( 98.71/14.83 ~( 98.71/14.83 Y1(Y2))))))) => 98.71/14.83 (~(( 98.71/14.83 !!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 ( 98.71/14.83 in(Y2, 98.71/14.83 Y0) => 98.71/14.83 Y1(Y2)))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $o]: 98.71/14.83 (Y0 => 98.71/14.83 in(emptyset, 98.71/14.83 prop2set(Y0)))))) => 98.71/14.83 ((!!((^[Y0 : $o]: 98.71/14.83 (Y0 => 98.71/14.83 set2prop( 98.71/14.83 prop2set(Y0)))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 (( 98.71/14.83 ~(( 98.71/14.83 ??(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) & 98.71/14.83 Y1(Y2))))))) => 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (~( 98.71/14.83 Y1(Y2)))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 ~(( 98.71/14.83 !!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 Y1(Y2))))))) => 98.71/14.83 ( 98.71/14.83 ??(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) & 98.71/14.83 (~( 98.71/14.83 Y1(Y2)))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i > $o]: 98.71/14.83 ((??(Y0)) => 98.71/14.83 ((!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (Y0(Y1) => 98.71/14.83 (Y0(Y2) => 98.71/14.83 (Y1 = Y2))))))))) => 98.71/14.83 (??(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (Y0(Y1) & 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (Y0(Y2) => 98.71/14.83 (Y1 = Y2)))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i > $o]: 98.71/14.83 ((??(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (Y0(Y2) <=> 98.71/14.83 (Y2 = Y1)))))))) => 98.71/14.83 (??(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (Y0(Y1) & 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (Y0(Y2) => 98.71/14.83 (Y1 = Y2))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 Y0 = Y1) => 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (( 98.71/14.83 Y2 = Y3) => 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 in(Y3, 98.71/14.83 Y1)))))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 Y0 = Y1) => 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (( 98.71/14.83 Y2 = Y3) => 98.71/14.83 (in(Y2, 98.71/14.83 Y0) <=> 98.71/14.83 in(Y3, 98.71/14.83 Y1)))))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i > $o]: 98.71/14.83 ((??(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (Y0(Y1) & 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (Y0(Y2) => 98.71/14.83 (Y1 = Y2))))))))) => 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (Y0(Y1) => 98.71/14.83 (Y0(Y2) => 98.71/14.83 (Y1 = Y2))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i > $o]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i > $o]: 98.71/14.83 (( 98.71/14.83 !!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (( 98.71/14.83 Y2 = Y3) => 98.71/14.83 (Y0(Y2) <=> 98.71/14.83 Y1(Y3))))))))) => 98.71/14.83 (( 98.71/14.83 ??(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (Y0(Y2) & 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (Y0(Y3) => 98.71/14.83 (Y2 = Y3))))))))) <=> 98.71/14.83 (??(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (Y1(Y2) & 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (Y1(Y3) => 98.71/14.83 (Y2 = Y3))))))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 Y0 = Y1) => 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (( 98.71/14.83 Y2 = Y3) => 98.71/14.83 (setadjoin( 98.71/14.83 Y0, Y2) = 98.71/14.83 setadjoin( 98.71/14.83 Y1, Y3)))))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 Y0 = Y1) => 98.71/14.83 (powerset( 98.71/14.83 Y0) = 98.71/14.83 powerset( 98.71/14.83 Y1))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 Y0 = Y1) => 98.71/14.83 (setunion( 98.71/14.83 Y0) = 98.71/14.83 setunion( 98.71/14.83 Y1))))))))) => 98.71/14.83 ((!!(( 98.71/14.83 ^[Y0 : $i > $o]: 98.71/14.83 (( 98.71/14.83 ??(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (Y0(Y1) & 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (Y0(Y2) => 98.71/14.83 (Y1 = Y2))))))))) => 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (Y0(Y1) => 98.71/14.83 (Y0(Y2) => 98.71/14.83 (Y1 = Y2))))))))))))) => 98.71/14.83 ((!!(( 98.71/14.83 ^[Y0 : $i > $o]: 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y1 : $i > $o]: 98.71/14.83 (( 98.71/14.83 !!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (( 98.71/14.83 Y2 = Y3) => 98.71/14.83 (Y0(Y2) <=> 98.71/14.83 Y1(Y3))))))))) => 98.71/14.83 (( 98.71/14.83 ??(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (Y0(Y2) & 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (Y0(Y3) => 98.71/14.83 (Y2 = Y3))))))))) => 98.71/14.83 (( 98.71/14.83 ??(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (Y1(Y2) & 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (Y1(Y3) => 98.71/14.83 (Y2 = Y3))))))))) => 98.71/14.83 (descr( 98.71/14.83 Y0) = 98.71/14.83 descr(Y1))))))))))) => 98.71/14.83 ((!!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 Y0 = Y1) => 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i > $o]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i > $o]: 98.71/14.83 (( 98.71/14.83 !!(( 98.71/14.83 ^[Y4 : $i]: 98.71/14.83 (in(Y4, 98.71/14.83 Y0) => 98.71/14.83 (!!(( 98.71/14.83 ^[Y5 : $i]: 98.71/14.83 (in(Y5, 98.71/14.83 Y1) => 98.71/14.83 (( 98.71/14.83 Y4 = Y5) => 98.71/14.83 (Y2(Y4) <=> 98.71/14.83 Y3(Y5))))))))))) => 98.71/14.83 (dsetconstr( 98.71/14.83 Y0, Y2) = 98.71/14.83 dsetconstr( 98.71/14.83 Y1, Y3)))))))))))))))) => 98.71/14.83 ((!!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 !!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 in(Y2, 98.71/14.83 Y1))))) => 98.71/14.83 subset( 98.71/14.83 Y0, Y1)))))))) => 98.71/14.83 (( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 Y0 = Y1) => 98.71/14.83 subset( 98.71/14.83 Y1, Y0)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 Y0 = Y1) => 98.71/14.83 subset( 98.71/14.83 Y0, Y1)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 !!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 in(Y2, 98.71/14.83 Y1))))) => 98.71/14.83 subset( 98.71/14.83 Y0, Y1)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!( 98.71/14.83 subset( 98.71/14.83 emptyset))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (subset( 98.71/14.83 Y0, Y1) => 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 in(Y2, 98.71/14.83 Y1)))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (subset( 98.71/14.83 Y0, Y1) => 98.71/14.83 (( 98.71/14.83 ~( 98.71/14.83 in(Y2, 98.71/14.83 Y1))) => 98.71/14.83 (~( 98.71/14.83 in(Y2, 98.71/14.83 Y0)))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (( 98.71/14.83 ~( 98.71/14.83 in(Y2, 98.71/14.83 Y1))) => 98.71/14.83 (~( 98.71/14.83 subset( 98.71/14.83 Y0, Y1)))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 ~( 98.71/14.83 subset( 98.71/14.83 Y0, Y1))) => 98.71/14.83 (Y0 != Y1)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (( 98.71/14.83 ~( 98.71/14.83 in(Y2, 98.71/14.83 Y1))) => 98.71/14.83 (Y0 != Y1)))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 subset( 98.71/14.83 Y0, Y0)))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (subset( 98.71/14.83 Y0, Y1) => 98.71/14.83 (subset( 98.71/14.83 Y1, Y2) => 98.71/14.83 subset( 98.71/14.83 Y0, Y2)))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 subset( 98.71/14.83 Y1, 98.71/14.83 setadjoin( 98.71/14.83 Y0, Y1)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (subset( 98.71/14.83 Y0, Y2) => 98.71/14.83 subset( 98.71/14.83 Y0, 98.71/14.83 setadjoin( 98.71/14.83 Y1, Y2)))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (subset( 98.71/14.83 Y0, Y1) => 98.71/14.83 in(Y0, 98.71/14.83 powerset( 98.71/14.83 Y1))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (subset( 98.71/14.83 Y0, Y1) => 98.71/14.83 (subset( 98.71/14.83 Y1, Y0) => 98.71/14.83 (Y0 = Y1))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (subset( 98.71/14.83 Y0, 98.71/14.83 emptyset) => 98.71/14.83 (Y0 = 98.71/14.83 emptyset))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (subset( 98.71/14.83 Y1, Y0) => 98.71/14.83 in(Y1, 98.71/14.83 powerset( 98.71/14.83 Y0))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (in(Y1, 98.71/14.83 powerset( 98.71/14.83 Y0)) => 98.71/14.83 subset( 98.71/14.83 Y1, Y0)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 in(Y0, 98.71/14.83 powerset( 98.71/14.83 Y0))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (subset( 98.71/14.83 Y0, Y1) => 98.71/14.83 subset( 98.71/14.83 powerset( 98.71/14.83 Y0), 98.71/14.83 powerset( 98.71/14.83 Y1))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i > $o]: 98.71/14.83 in( 98.71/14.83 dsetconstr( 98.71/14.83 Y0, Y1), 98.71/14.83 powerset( 98.71/14.83 Y0)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i > $o]: 98.71/14.83 subset( 98.71/14.83 dsetconstr( 98.71/14.83 Y0, Y1), 98.71/14.83 Y0))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 in(Y2, 98.71/14.83 binunion( 98.71/14.83 Y0, Y1)))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 in(Y1, 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y1) => 98.71/14.83 in(Y2, 98.71/14.83 binunion( 98.71/14.83 Y0, Y1)))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $o]: 98.71/14.83 (in(Y2, 98.71/14.83 binunion( 98.71/14.83 Y0, Y1)) => 98.71/14.83 (( 98.71/14.83 in(Y2, 98.71/14.83 Y0) => Y3) => 98.71/14.83 (( 98.71/14.83 in(Y2, 98.71/14.83 Y1) => Y3) => 98.71/14.83 Y3))))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 binunion( 98.71/14.83 Y0, Y1)) => 98.71/14.83 (in(Y2, 98.71/14.83 Y1) | 98.71/14.83 in(Y2, 98.71/14.83 Y0)))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 subset( 98.71/14.83 Y0, 98.71/14.83 binunion( 98.71/14.83 Y0, Y1)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 subset( 98.71/14.83 Y1, 98.71/14.83 binunion( 98.71/14.83 Y0, Y1)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (in(Y2, 98.71/14.83 Y1) => 98.71/14.83 in(Y2, 98.71/14.83 binintersect( 98.71/14.83 Y0, Y1))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (subset( 98.71/14.83 Y2, Y0) => 98.71/14.83 (subset( 98.71/14.83 Y2, Y1) => 98.71/14.83 subset( 98.71/14.83 Y2, 98.71/14.83 binintersect( 98.71/14.83 Y0, Y1))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 binintersect( 98.71/14.83 Y0, Y1)) => 98.71/14.83 in(Y2, 98.71/14.83 Y0))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 subset( 98.71/14.83 binintersect( 98.71/14.83 Y0, Y1), 98.71/14.83 Y0))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (subset( 98.71/14.83 Y0, Y1) => 98.71/14.83 (binintersect( 98.71/14.83 Y0, Y1) = 98.71/14.83 Y0)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 binintersect( 98.71/14.83 Y0, Y1) = 98.71/14.83 Y1) => 98.71/14.83 subset( 98.71/14.83 Y1, Y0)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 binintersect( 98.71/14.83 Y0, Y1)) => 98.71/14.83 in(Y2, 98.71/14.83 Y1))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 ~(( 98.71/14.83 ??(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) & 98.71/14.83 in(Y2, 98.71/14.83 Y1))))))) => 98.71/14.83 (binintersect( 98.71/14.83 Y0, Y1) = 98.71/14.83 emptyset)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 subset( 98.71/14.83 binintersect( 98.71/14.83 Y0, Y1), 98.71/14.83 Y1))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (subset( 98.71/14.83 Y1, Y0) => 98.71/14.83 (binintersect( 98.71/14.83 Y0, Y1) = 98.71/14.83 Y1)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 binintersect( 98.71/14.83 Y0, Y1) = 98.71/14.83 Y0) => 98.71/14.83 subset( 98.71/14.83 Y0, Y1)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (binintersect( 98.71/14.83 Y0, 98.71/14.83 binunion( 98.71/14.83 Y1, Y2)) = 98.71/14.83 binunion( 98.71/14.83 binintersect( 98.71/14.83 Y0, Y1), 98.71/14.83 binintersect( 98.71/14.83 Y0, Y2)))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (( 98.71/14.83 ~( 98.71/14.83 in(Y2, 98.71/14.83 Y1))) => 98.71/14.83 in(Y2, 98.71/14.83 setminus( 98.71/14.83 Y0, Y1))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 setminus( 98.71/14.83 Y0, Y1)) => 98.71/14.83 in(Y2, 98.71/14.83 Y0))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 setminus( 98.71/14.83 Y0, Y1)) => 98.71/14.83 (~( 98.71/14.83 in(Y2, 98.71/14.83 Y1))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (subset( 98.71/14.83 Y0, Y1) => 98.71/14.83 (setminus( 98.71/14.83 Y0, Y1) = 98.71/14.83 emptyset)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (( 98.71/14.83 ~( 98.71/14.83 in(Y2, 98.71/14.83 setminus( 98.71/14.83 Y0, Y1)))) => 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 in(Y2, 98.71/14.83 Y1)))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (( 98.71/14.83 ~( 98.71/14.83 in(Y2, 98.71/14.83 setminus( 98.71/14.83 Y0, Y1)))) => 98.71/14.83 (( 98.71/14.83 ~( 98.71/14.83 in(Y2, 98.71/14.83 Y1))) => 98.71/14.83 (~( 98.71/14.83 in(Y2, 98.71/14.83 Y0)))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (( 98.71/14.83 ~( 98.71/14.83 in(Y2, 98.71/14.83 Y0))) => 98.71/14.83 (~( 98.71/14.83 in(Y2, 98.71/14.83 setminus( 98.71/14.83 Y0, Y1)))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y1) => 98.71/14.83 (~( 98.71/14.83 in(Y2, 98.71/14.83 setminus( 98.71/14.83 Y0, Y1)))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 subset( 98.71/14.83 setminus( 98.71/14.83 Y0, Y1), 98.71/14.83 Y0))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 setminus( 98.71/14.83 Y0, Y1) = 98.71/14.83 emptyset) => 98.71/14.83 subset( 98.71/14.83 Y0, Y1)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 symdiff( 98.71/14.83 Y0, Y1)) => 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $o]: 98.71/14.83 (( 98.71/14.83 in(Y2, 98.71/14.83 Y0) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 ~( 98.71/14.83 in(Y2, 98.71/14.83 Y1))) => 98.71/14.83 Y3)) => 98.71/14.83 (( 98.71/14.83 ( 98.71/14.83 ~( 98.71/14.83 in(Y2, 98.71/14.83 Y0))) => 98.71/14.83 ( 98.71/14.83 in(Y2, 98.71/14.83 Y1) => Y3)) => 98.71/14.83 Y3))))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (( 98.71/14.83 ~( 98.71/14.83 in(Y2, 98.71/14.83 Y1))) => 98.71/14.83 in(Y2, 98.71/14.83 symdiff( 98.71/14.83 Y0, Y1))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (( 98.71/14.83 ~( 98.71/14.83 in(Y2, 98.71/14.83 Y0))) => 98.71/14.83 (in(Y2, 98.71/14.83 Y1) => 98.71/14.83 in(Y2, 98.71/14.83 symdiff( 98.71/14.83 Y0, Y1))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (in(Y2, 98.71/14.83 Y1) => 98.71/14.83 (~( 98.71/14.83 in(Y2, 98.71/14.83 symdiff( 98.71/14.83 Y0, Y1))))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (( 98.71/14.83 ~( 98.71/14.83 in(Y2, 98.71/14.83 Y0))) => 98.71/14.83 (( 98.71/14.83 ~( 98.71/14.83 in(Y2, 98.71/14.83 Y1))) => 98.71/14.83 (~( 98.71/14.83 in(Y2, 98.71/14.83 symdiff( 98.71/14.83 Y0, Y1))))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 in(Y1, 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 in(Y0, 98.71/14.83 setunion( 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 in(Y1, 98.71/14.83 setunion( 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (??(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 setunion( 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)))) & 98.71/14.83 (??(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (in(Y3, 98.71/14.83 setunion( 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)))) & 98.71/14.83 (setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)) = 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 setadjoin( 98.71/14.83 Y3, 98.71/14.83 emptyset)), 98.71/14.83 emptyset))))))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (??(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 setunion( 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)))) & 98.71/14.83 (??(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (in(Y3, 98.71/14.83 setunion( 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)))) & 98.71/14.83 (setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)) = 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 setadjoin( 98.71/14.83 Y3, 98.71/14.83 emptyset)), 98.71/14.83 emptyset))))))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (in(Y1, 98.71/14.83 Y0) => 98.71/14.83 subset( 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset), 98.71/14.83 Y0)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (in(Y1, 98.71/14.83 Y0) => 98.71/14.83 in( 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset), 98.71/14.83 powerset( 98.71/14.83 Y0))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 in( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 emptyset), 98.71/14.83 powerset( 98.71/14.83 binunion( 98.71/14.83 Y0, Y1))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset))) => 98.71/14.83 (( 98.71/14.83 Y2 = Y1) | 98.71/14.83 (Y2 = Y0)))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (in(Y3, 98.71/14.83 Y1) => 98.71/14.83 subset( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 setadjoin( 98.71/14.83 Y3, 98.71/14.83 emptyset)), 98.71/14.83 binunion( 98.71/14.83 Y0, Y1)))))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (in(Y3, 98.71/14.83 Y1) => 98.71/14.83 in( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 setadjoin( 98.71/14.83 Y3, 98.71/14.83 emptyset)), 98.71/14.83 powerset( 98.71/14.83 binunion( 98.71/14.83 Y0, Y1))))))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (in(Y3, 98.71/14.83 Y1) => 98.71/14.83 subset( 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 setadjoin( 98.71/14.83 Y3, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)), 98.71/14.83 powerset( 98.71/14.83 binunion( 98.71/14.83 Y0, Y1))))))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (in(Y3, 98.71/14.83 Y1) => 98.71/14.83 in( 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 setadjoin( 98.71/14.83 Y3, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)), 98.71/14.83 powerset( 98.71/14.83 powerset( 98.71/14.83 binunion( 98.71/14.83 Y0, Y1)))))))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (in(Y3, 98.71/14.83 Y1) => 98.71/14.83 in( 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 setadjoin( 98.71/14.83 Y3, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)), 98.71/14.83 powerset( 98.71/14.83 powerset( 98.71/14.83 binunion( 98.71/14.83 Y0, Y1)))))))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (in(Y3, 98.71/14.83 Y1) => 98.71/14.83 in( 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 setadjoin( 98.71/14.83 Y3, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)), 98.71/14.83 dsetconstr( 98.71/14.83 powerset( 98.71/14.83 powerset( 98.71/14.83 binunion( 98.71/14.83 Y0, Y1))), 98.71/14.83 (^[Y4 : $i]: 98.71/14.83 (??(( 98.71/14.83 ^[Y5 : $i]: 98.71/14.83 (in(Y5, 98.71/14.83 Y0) & 98.71/14.83 (??(( 98.71/14.83 ^[Y6 : $i]: 98.71/14.83 (in(Y6, 98.71/14.83 Y1) & 98.71/14.83 (Y4 = 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y5, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y5, 98.71/14.83 setadjoin( 98.71/14.83 Y6, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)))))))))))))))))))))))))))) => 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 dsetconstr( 98.71/14.83 powerset( 98.71/14.83 powerset( 98.71/14.83 binunion( 98.71/14.83 Y0, Y1))), 98.71/14.83 (^[Y3 : $i]: 98.71/14.83 (??(( 98.71/14.83 ^[Y4 : $i]: 98.71/14.83 (in(Y4, 98.71/14.83 Y0) & 98.71/14.83 (??(( 98.71/14.83 ^[Y5 : $i]: 98.71/14.83 (in(Y5, 98.71/14.83 Y1) & 98.71/14.83 (Y3 = 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y4, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y4, 98.71/14.83 setadjoin( 98.71/14.83 Y5, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)))))))))))))) => 98.71/14.83 (??(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (( 98.71/14.83 ??(( 98.71/14.83 ^[Y4 : $i]: 98.71/14.83 (in(Y4, 98.71/14.83 Y1) & 98.71/14.83 (Y2 = 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y3, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y3, 98.71/14.83 setadjoin( 98.71/14.83 Y4, 98.71/14.83 emptyset)), 98.71/14.83 emptyset))))))) & 98.71/14.83 in(Y3, 98.71/14.83 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 98.71/14.83 inference('lazy_cnf_imply', [status(thm)], ['171'])). 98.71/14.83 tff('173', plain, 98.71/14.83 ~ ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (in(Y2, Y0) => 98.71/14.83 (Y1(Y2) => in(Y2, dsetconstr(Y0, Y1))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (in(Y2, dsetconstr(Y0, Y1)) => in(Y2, Y0))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (in(Y2, dsetconstr(Y0, Y1)) => Y1(Y2))))))))))) => 98.71/14.83 ((!!((^[Y0 : $o]: (!!((^[Y1 : $i]: (in(Y1, prop2set(Y0)) => Y0))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: (in(Y0, emptyset) => (!!((^[Y1 : $o]: Y1))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 98.71/14.83 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 98.71/14.83 ((!!((^[Y0 : $i > $o]: 98.71/14.83 ((??((^[Y1 : $i]: 98.71/14.83 (Y0(Y1) & 98.71/14.83 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 98.71/14.83 (??(Y0)))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 98.71/14.83 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 98.71/14.83 (Y0 = Y1))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 98.71/14.83 (Y0 = emptyset))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 98.71/14.83 (Y0 = emptyset))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (in(Y2, Y0) => 98.71/14.83 (in(Y2, dsetconstr(Y0, Y1)) <=> 98.71/14.83 Y1(Y2)))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (in(Y2, Y0) => 98.71/14.83 (Y1(Y2) => 98.71/14.83 (dsetconstr(Y0, Y1) != emptyset)))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 98.71/14.83 (Y0 != emptyset))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 98.71/14.83 (in(emptyset, setadjoin(emptyset, emptyset)) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (in(Y2, Y1) => 98.71/14.83 in(Y2, setadjoin(Y0, Y1)))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (in(Y2, setadjoin(Y0, Y1)) => 98.71/14.83 (!!((^[Y3 : $o]: 98.71/14.83 (((Y2 = Y0) => Y3) => 98.71/14.83 ((in(Y2, Y1) => Y3) => 98.71/14.83 Y3))))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (in(Y2, setadjoin(Y0, Y1)) => 98.71/14.83 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 ((!!((^[Y2 : $i]: 98.71/14.83 (in(Y2, Y1) => in(Y2, Y0))))) => 98.71/14.83 in(Y1, powerset(Y0))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.71/14.83 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (in(Y1, powerset(Y0)) => 98.71/14.83 (in(Y2, Y1) => 98.71/14.83 in(Y2, Y0)))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (in(Y1, Y2) => 98.71/14.83 (in(Y2, Y0) => 98.71/14.83 in(Y1, setunion(Y0))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (in(Y1, setunion(Y0)) => 98.71/14.83 (!!((^[Y2 : $o]: 98.71/14.83 ((!!((^[Y3 : $i]: 98.71/14.83 (in(Y1, Y3) => 98.71/14.83 (in(Y3, Y0) => 98.71/14.83 Y2))))) => 98.71/14.83 Y2))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (in(Y1, Y0) => 98.71/14.83 in(Y1, 98.71/14.83 powerset(setunion(Y0)))))))))) => 98.71/14.83 ((!!((^[Y0 : $i > $o]: 98.71/14.83 ((??((^[Y1 : $i]: 98.71/14.83 (Y0(Y1) & 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (Y0(Y2) => 98.71/14.83 (Y1 = Y2))))))))) => 98.71/14.83 (??((^[Y1 : $i]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (Y0(Y2) <=> 98.71/14.83 (Y2 = Y1)))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 ((Y0 != emptyset) => 98.71/14.83 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (in(Y0, 98.71/14.83 setadjoin(Y1, emptyset)) => 98.71/14.83 (Y0 = Y1)))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 ((Y0 != Y1) => 98.71/14.83 (~(in(Y1, 98.71/14.83 setadjoin(Y0, 98.71/14.83 emptyset))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 ((Y0 = Y1) => 98.71/14.83 in(Y0, 98.71/14.83 setadjoin(Y1, 98.71/14.83 emptyset))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (in(Y0, 98.71/14.83 setadjoin(Y1, 98.71/14.83 emptyset)) => 98.71/14.83 in(Y1, 98.71/14.83 setadjoin(Y0, 98.71/14.83 emptyset))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset))) => 98.71/14.83 ((Y2 = Y1) | 98.71/14.83 (Y2 = Y0)))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 in(Y0, 98.71/14.83 setadjoin(Y0, 98.71/14.83 setadjoin(Y1, 98.71/14.83 emptyset))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 in(Y1, 98.71/14.83 setadjoin(Y0, 98.71/14.83 setadjoin(Y1, 98.71/14.83 emptyset))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 ((??((^[Y2 : $i]: 98.71/14.83 (in(Y2, Y0) & 98.71/14.83 Y1(Y2))))) => 98.71/14.83 (dsetconstr(Y0, 98.71/14.83 Y1) != 98.71/14.83 emptyset)))))))) => 98.71/14.83 ((!!((^[Y0 : $i > $o]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (in(Y1, emptyset) => 98.71/14.83 Y0(Y1)))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 ((~((!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 Y1(Y2))))))) => 98.71/14.83 (??((^[Y2 : $i]: 98.71/14.83 ( 98.71/14.83 in(Y2, 98.71/14.83 Y0) & 98.71/14.83 ( 98.71/14.83 ~( 98.71/14.83 Y1(Y2)))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 ((!!((^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (~( 98.71/14.83 Y1(Y2))))))) => 98.71/14.83 (~((??(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 ( 98.71/14.83 in(Y2, 98.71/14.83 Y0) & 98.71/14.83 Y1(Y2)))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 ((~((??(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) & 98.71/14.83 Y1(Y2))))))) => 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (~( 98.71/14.83 Y1(Y2)))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 ((??(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) & 98.71/14.83 ( 98.71/14.83 ~( 98.71/14.83 Y1(Y2))))))) => 98.71/14.83 (~((!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 Y1(Y2)))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $o]: 98.71/14.83 (Y0 => 98.71/14.83 in(emptyset, 98.71/14.83 prop2set(Y0)))))) => 98.71/14.83 ((!!((^[Y0 : $o]: 98.71/14.83 (Y0 => 98.71/14.83 set2prop( 98.71/14.83 prop2set(Y0)))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 ((~(( 98.71/14.83 ??(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) & 98.71/14.83 Y1(Y2))))))) => 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (~( 98.71/14.83 Y1(Y2)))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 (( 98.71/14.83 ~(( 98.71/14.83 !!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 Y1(Y2))))))) => 98.71/14.83 ( 98.71/14.83 ??(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) & 98.71/14.83 (~( 98.71/14.83 Y1(Y2)))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i > $o]: 98.71/14.83 ((??(Y0)) => 98.71/14.83 ((!!((^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (Y0(Y1) => 98.71/14.83 (Y0(Y2) => 98.71/14.83 (Y1 = Y2))))))))) => 98.71/14.83 (??((^[Y1 : $i]: 98.71/14.83 (Y0(Y1) & 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (Y0(Y2) => 98.71/14.83 (Y1 = Y2)))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i > $o]: 98.71/14.83 ((??((^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (Y0(Y2) <=> 98.71/14.83 (Y2 = Y1)))))))) => 98.71/14.83 (??((^[Y1 : $i]: 98.71/14.83 (Y0(Y1) & 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (Y0(Y2) => 98.71/14.83 (Y1 = Y2))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 Y0 = Y1) => 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (( 98.71/14.83 Y2 = Y3) => 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 in(Y3, 98.71/14.83 Y1)))))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 Y0 = Y1) => 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (( 98.71/14.83 Y2 = Y3) => 98.71/14.83 (in(Y2, 98.71/14.83 Y0) <=> 98.71/14.83 in(Y3, 98.71/14.83 Y1)))))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i > $o]: 98.71/14.83 ((??(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (Y0(Y1) & 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (Y0(Y2) => 98.71/14.83 (Y1 = Y2))))))))) => 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (Y0(Y1) => 98.71/14.83 (Y0(Y2) => 98.71/14.83 (Y1 = Y2))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i > $o]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i > $o]: 98.71/14.83 (( 98.71/14.83 !!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (( 98.71/14.83 Y2 = Y3) => 98.71/14.83 (Y0(Y2) <=> 98.71/14.83 Y1(Y3))))))))) => 98.71/14.83 (( 98.71/14.83 ??(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (Y0(Y2) & 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (Y0(Y3) => 98.71/14.83 (Y2 = Y3))))))))) <=> 98.71/14.83 (??(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (Y1(Y2) & 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (Y1(Y3) => 98.71/14.83 (Y2 = Y3))))))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 Y0 = Y1) => 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (( 98.71/14.83 Y2 = Y3) => 98.71/14.83 (setadjoin( 98.71/14.83 Y0, Y2) = 98.71/14.83 setadjoin( 98.71/14.83 Y1, Y3)))))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 Y0 = Y1) => 98.71/14.83 (powerset( 98.71/14.83 Y0) = 98.71/14.83 powerset( 98.71/14.83 Y1))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 Y0 = Y1) => 98.71/14.83 (setunion( 98.71/14.83 Y0) = 98.71/14.83 setunion( 98.71/14.83 Y1))))))))) => 98.71/14.83 ((!!((^[Y0 : $i > $o]: 98.71/14.83 (( 98.71/14.83 ??(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (Y0(Y1) & 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (Y0(Y2) => 98.71/14.83 (Y1 = Y2))))))))) => 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (Y0(Y1) => 98.71/14.83 (Y0(Y2) => 98.71/14.83 (Y1 = Y2))))))))))))) => 98.71/14.83 ((!!(( 98.71/14.83 ^[Y0 : $i > $o]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i > $o]: 98.71/14.83 (( 98.71/14.83 !!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (( 98.71/14.83 Y2 = Y3) => 98.71/14.83 (Y0(Y2) <=> 98.71/14.83 Y1(Y3))))))))) => 98.71/14.83 (( 98.71/14.83 ??(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (Y0(Y2) & 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (Y0(Y3) => 98.71/14.83 (Y2 = Y3))))))))) => 98.71/14.83 (( 98.71/14.83 ??(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (Y1(Y2) & 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (Y1(Y3) => 98.71/14.83 (Y2 = Y3))))))))) => 98.71/14.83 (descr( 98.71/14.83 Y0) = 98.71/14.83 descr(Y1))))))))))) => 98.71/14.83 ((!!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 Y0 = Y1) => 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i > $o]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i > $o]: 98.71/14.83 (( 98.71/14.83 !!(( 98.71/14.83 ^[Y4 : $i]: 98.71/14.83 (in(Y4, 98.71/14.83 Y0) => 98.71/14.83 (!!(( 98.71/14.83 ^[Y5 : $i]: 98.71/14.83 (in(Y5, 98.71/14.83 Y1) => 98.71/14.83 (( 98.71/14.83 Y4 = Y5) => 98.71/14.83 (Y2(Y4) <=> 98.71/14.83 Y3(Y5))))))))))) => 98.71/14.83 (dsetconstr( 98.71/14.83 Y0, Y2) = 98.71/14.83 dsetconstr( 98.71/14.83 Y1, Y3)))))))))))))))) => 98.71/14.83 ((!!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 !!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 in(Y2, 98.71/14.83 Y1))))) => 98.71/14.83 subset( 98.71/14.83 Y0, Y1)))))))) => 98.71/14.83 ((!!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 Y0 = Y1) => 98.71/14.83 subset( 98.71/14.83 Y1, Y0)))))))) => 98.71/14.83 (( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 Y0 = Y1) => 98.71/14.83 subset( 98.71/14.83 Y0, Y1)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 !!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 in(Y2, 98.71/14.83 Y1))))) => 98.71/14.83 subset( 98.71/14.83 Y0, Y1)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!( 98.71/14.83 subset( 98.71/14.83 emptyset))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (subset( 98.71/14.83 Y0, Y1) => 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 in(Y2, 98.71/14.83 Y1)))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (subset( 98.71/14.83 Y0, Y1) => 98.71/14.83 (( 98.71/14.83 ~( 98.71/14.83 in(Y2, 98.71/14.83 Y1))) => 98.71/14.83 (~( 98.71/14.83 in(Y2, 98.71/14.83 Y0)))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (( 98.71/14.83 ~( 98.71/14.83 in(Y2, 98.71/14.83 Y1))) => 98.71/14.83 (~( 98.71/14.83 subset( 98.71/14.83 Y0, Y1)))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 ~( 98.71/14.83 subset( 98.71/14.83 Y0, Y1))) => 98.71/14.83 (Y0 != Y1)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (( 98.71/14.83 ~( 98.71/14.83 in(Y2, 98.71/14.83 Y1))) => 98.71/14.83 (Y0 != Y1)))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 subset( 98.71/14.83 Y0, Y0)))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (subset( 98.71/14.83 Y0, Y1) => 98.71/14.83 (subset( 98.71/14.83 Y1, Y2) => 98.71/14.83 subset( 98.71/14.83 Y0, Y2)))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 subset( 98.71/14.83 Y1, 98.71/14.83 setadjoin( 98.71/14.83 Y0, Y1)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (subset( 98.71/14.83 Y0, Y2) => 98.71/14.83 subset( 98.71/14.83 Y0, 98.71/14.83 setadjoin( 98.71/14.83 Y1, Y2)))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (subset( 98.71/14.83 Y0, Y1) => 98.71/14.83 in(Y0, 98.71/14.83 powerset( 98.71/14.83 Y1))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (subset( 98.71/14.83 Y0, Y1) => 98.71/14.83 (subset( 98.71/14.83 Y1, Y0) => 98.71/14.83 (Y0 = Y1))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (subset( 98.71/14.83 Y0, 98.71/14.83 emptyset) => 98.71/14.83 (Y0 = 98.71/14.83 emptyset))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (subset( 98.71/14.83 Y1, Y0) => 98.71/14.83 in(Y1, 98.71/14.83 powerset( 98.71/14.83 Y0))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (in(Y1, 98.71/14.83 powerset( 98.71/14.83 Y0)) => 98.71/14.83 subset( 98.71/14.83 Y1, Y0)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 in(Y0, 98.71/14.83 powerset( 98.71/14.83 Y0))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (subset( 98.71/14.83 Y0, Y1) => 98.71/14.83 subset( 98.71/14.83 powerset( 98.71/14.83 Y0), 98.71/14.83 powerset( 98.71/14.83 Y1))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i > $o]: 98.71/14.83 in( 98.71/14.83 dsetconstr( 98.71/14.83 Y0, Y1), 98.71/14.83 powerset( 98.71/14.83 Y0)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i > $o]: 98.71/14.83 subset( 98.71/14.83 dsetconstr( 98.71/14.83 Y0, Y1), 98.71/14.83 Y0))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 in(Y2, 98.71/14.83 binunion( 98.71/14.83 Y0, Y1)))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 in(Y1, 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y1) => 98.71/14.83 in(Y2, 98.71/14.83 binunion( 98.71/14.83 Y0, Y1)))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $o]: 98.71/14.83 (in(Y2, 98.71/14.83 binunion( 98.71/14.83 Y0, Y1)) => 98.71/14.83 (( 98.71/14.83 in(Y2, 98.71/14.83 Y0) => Y3) => 98.71/14.83 (( 98.71/14.83 in(Y2, 98.71/14.83 Y1) => Y3) => 98.71/14.83 Y3))))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 binunion( 98.71/14.83 Y0, Y1)) => 98.71/14.83 (in(Y2, 98.71/14.83 Y1) | 98.71/14.83 in(Y2, 98.71/14.83 Y0)))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 subset( 98.71/14.83 Y0, 98.71/14.83 binunion( 98.71/14.83 Y0, Y1)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 subset( 98.71/14.83 Y1, 98.71/14.83 binunion( 98.71/14.83 Y0, Y1)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (in(Y2, 98.71/14.83 Y1) => 98.71/14.83 in(Y2, 98.71/14.83 binintersect( 98.71/14.83 Y0, Y1))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (subset( 98.71/14.83 Y2, Y0) => 98.71/14.83 (subset( 98.71/14.83 Y2, Y1) => 98.71/14.83 subset( 98.71/14.83 Y2, 98.71/14.83 binintersect( 98.71/14.83 Y0, Y1))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 binintersect( 98.71/14.83 Y0, Y1)) => 98.71/14.83 in(Y2, 98.71/14.83 Y0))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 subset( 98.71/14.83 binintersect( 98.71/14.83 Y0, Y1), 98.71/14.83 Y0))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (subset( 98.71/14.83 Y0, Y1) => 98.71/14.83 (binintersect( 98.71/14.83 Y0, Y1) = 98.71/14.83 Y0)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 binintersect( 98.71/14.83 Y0, Y1) = 98.71/14.83 Y1) => 98.71/14.83 subset( 98.71/14.83 Y1, Y0)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 binintersect( 98.71/14.83 Y0, Y1)) => 98.71/14.83 in(Y2, 98.71/14.83 Y1))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 ~(( 98.71/14.83 ??(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) & 98.71/14.83 in(Y2, 98.71/14.83 Y1))))))) => 98.71/14.83 (binintersect( 98.71/14.83 Y0, Y1) = 98.71/14.83 emptyset)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 subset( 98.71/14.83 binintersect( 98.71/14.83 Y0, Y1), 98.71/14.83 Y1))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (subset( 98.71/14.83 Y1, Y0) => 98.71/14.83 (binintersect( 98.71/14.83 Y0, Y1) = 98.71/14.83 Y1)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 binintersect( 98.71/14.83 Y0, Y1) = 98.71/14.83 Y0) => 98.71/14.83 subset( 98.71/14.83 Y0, Y1)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (binintersect( 98.71/14.83 Y0, 98.71/14.83 binunion( 98.71/14.83 Y1, Y2)) = 98.71/14.83 binunion( 98.71/14.83 binintersect( 98.71/14.83 Y0, Y1), 98.71/14.83 binintersect( 98.71/14.83 Y0, Y2)))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (( 98.71/14.83 ~( 98.71/14.83 in(Y2, 98.71/14.83 Y1))) => 98.71/14.83 in(Y2, 98.71/14.83 setminus( 98.71/14.83 Y0, Y1))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 setminus( 98.71/14.83 Y0, Y1)) => 98.71/14.83 in(Y2, 98.71/14.83 Y0))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 setminus( 98.71/14.83 Y0, Y1)) => 98.71/14.83 (~( 98.71/14.83 in(Y2, 98.71/14.83 Y1))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (subset( 98.71/14.83 Y0, Y1) => 98.71/14.83 (setminus( 98.71/14.83 Y0, Y1) = 98.71/14.83 emptyset)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (( 98.71/14.83 ~( 98.71/14.83 in(Y2, 98.71/14.83 setminus( 98.71/14.83 Y0, Y1)))) => 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 in(Y2, 98.71/14.83 Y1)))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (( 98.71/14.83 ~( 98.71/14.83 in(Y2, 98.71/14.83 setminus( 98.71/14.83 Y0, Y1)))) => 98.71/14.83 (( 98.71/14.83 ~( 98.71/14.83 in(Y2, 98.71/14.83 Y1))) => 98.71/14.83 (~( 98.71/14.83 in(Y2, 98.71/14.83 Y0)))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (( 98.71/14.83 ~( 98.71/14.83 in(Y2, 98.71/14.83 Y0))) => 98.71/14.83 (~( 98.71/14.83 in(Y2, 98.71/14.83 setminus( 98.71/14.83 Y0, Y1)))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y1) => 98.71/14.83 (~( 98.71/14.83 in(Y2, 98.71/14.83 setminus( 98.71/14.83 Y0, Y1)))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 subset( 98.71/14.83 setminus( 98.71/14.83 Y0, Y1), 98.71/14.83 Y0))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 setminus( 98.71/14.83 Y0, Y1) = 98.71/14.83 emptyset) => 98.71/14.83 subset( 98.71/14.83 Y0, Y1)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 symdiff( 98.71/14.83 Y0, Y1)) => 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $o]: 98.71/14.83 (( 98.71/14.83 in(Y2, 98.71/14.83 Y0) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 ~( 98.71/14.83 in(Y2, 98.71/14.83 Y1))) => 98.71/14.83 Y3)) => 98.71/14.83 (( 98.71/14.83 ( 98.71/14.83 ~( 98.71/14.83 in(Y2, 98.71/14.83 Y0))) => 98.71/14.83 ( 98.71/14.83 in(Y2, 98.71/14.83 Y1) => Y3)) => 98.71/14.83 Y3))))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (( 98.71/14.83 ~( 98.71/14.83 in(Y2, 98.71/14.83 Y1))) => 98.71/14.83 in(Y2, 98.71/14.83 symdiff( 98.71/14.83 Y0, Y1))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (( 98.71/14.83 ~( 98.71/14.83 in(Y2, 98.71/14.83 Y0))) => 98.71/14.83 (in(Y2, 98.71/14.83 Y1) => 98.71/14.83 in(Y2, 98.71/14.83 symdiff( 98.71/14.83 Y0, Y1))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (in(Y2, 98.71/14.83 Y1) => 98.71/14.83 (~( 98.71/14.83 in(Y2, 98.71/14.83 symdiff( 98.71/14.83 Y0, Y1))))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (( 98.71/14.83 ~( 98.71/14.83 in(Y2, 98.71/14.83 Y0))) => 98.71/14.83 (( 98.71/14.83 ~( 98.71/14.83 in(Y2, 98.71/14.83 Y1))) => 98.71/14.83 (~( 98.71/14.83 in(Y2, 98.71/14.83 symdiff( 98.71/14.83 Y0, Y1))))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 in(Y1, 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 in(Y0, 98.71/14.83 setunion( 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 in(Y1, 98.71/14.83 setunion( 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (??(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 setunion( 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)))) & 98.71/14.83 (??(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (in(Y3, 98.71/14.83 setunion( 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)))) & 98.71/14.83 (setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)) = 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 setadjoin( 98.71/14.83 Y3, 98.71/14.83 emptyset)), 98.71/14.83 emptyset))))))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (??(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 setunion( 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)))) & 98.71/14.83 (??(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (in(Y3, 98.71/14.83 setunion( 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)))) & 98.71/14.83 (setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)) = 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 setadjoin( 98.71/14.83 Y3, 98.71/14.83 emptyset)), 98.71/14.83 emptyset))))))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (in(Y1, 98.71/14.83 Y0) => 98.71/14.83 subset( 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset), 98.71/14.83 Y0)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (in(Y1, 98.71/14.83 Y0) => 98.71/14.83 in( 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset), 98.71/14.83 powerset( 98.71/14.83 Y0))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 in( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 emptyset), 98.71/14.83 powerset( 98.71/14.83 binunion( 98.71/14.83 Y0, Y1))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset))) => 98.71/14.83 (( 98.71/14.83 Y2 = Y1) | 98.71/14.83 (Y2 = Y0)))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (in(Y3, 98.71/14.83 Y1) => 98.71/14.83 subset( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 setadjoin( 98.71/14.83 Y3, 98.71/14.83 emptyset)), 98.71/14.83 binunion( 98.71/14.83 Y0, Y1)))))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (in(Y3, 98.71/14.83 Y1) => 98.71/14.83 in( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 setadjoin( 98.71/14.83 Y3, 98.71/14.83 emptyset)), 98.71/14.83 powerset( 98.71/14.83 binunion( 98.71/14.83 Y0, Y1))))))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (in(Y3, 98.71/14.83 Y1) => 98.71/14.83 subset( 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 setadjoin( 98.71/14.83 Y3, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)), 98.71/14.83 powerset( 98.71/14.83 binunion( 98.71/14.83 Y0, Y1))))))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (in(Y3, 98.71/14.83 Y1) => 98.71/14.83 in( 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 setadjoin( 98.71/14.83 Y3, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)), 98.71/14.83 powerset( 98.71/14.83 powerset( 98.71/14.83 binunion( 98.71/14.83 Y0, Y1)))))))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (in(Y3, 98.71/14.83 Y1) => 98.71/14.83 in( 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 setadjoin( 98.71/14.83 Y3, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)), 98.71/14.83 powerset( 98.71/14.83 powerset( 98.71/14.83 binunion( 98.71/14.83 Y0, Y1)))))))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (in(Y3, 98.71/14.83 Y1) => 98.71/14.83 in( 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 setadjoin( 98.71/14.83 Y3, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)), 98.71/14.83 dsetconstr( 98.71/14.83 powerset( 98.71/14.83 powerset( 98.71/14.83 binunion( 98.71/14.83 Y0, Y1))), 98.71/14.83 (^[Y4 : $i]: 98.71/14.83 (??(( 98.71/14.83 ^[Y5 : $i]: 98.71/14.83 (in(Y5, 98.71/14.83 Y0) & 98.71/14.83 (??(( 98.71/14.83 ^[Y6 : $i]: 98.71/14.83 (in(Y6, 98.71/14.83 Y1) & 98.71/14.83 (Y4 = 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y5, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y5, 98.71/14.83 setadjoin( 98.71/14.83 Y6, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)))))))))))))))))))))))))))) => 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 dsetconstr( 98.71/14.83 powerset( 98.71/14.83 powerset( 98.71/14.83 binunion( 98.71/14.83 Y0, Y1))), 98.71/14.83 (^[Y3 : $i]: 98.71/14.83 (??(( 98.71/14.83 ^[Y4 : $i]: 98.71/14.83 (in(Y4, 98.71/14.83 Y0) & 98.71/14.83 (??(( 98.71/14.83 ^[Y5 : $i]: 98.71/14.83 (in(Y5, 98.71/14.83 Y1) & 98.71/14.83 (Y3 = 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y4, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y4, 98.71/14.83 setadjoin( 98.71/14.83 Y5, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)))))))))))))) => 98.71/14.83 (??(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (( 98.71/14.83 ??(( 98.71/14.83 ^[Y4 : $i]: 98.71/14.83 (in(Y4, 98.71/14.83 Y1) & 98.71/14.83 (Y2 = 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y3, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y3, 98.71/14.83 setadjoin( 98.71/14.83 Y4, 98.71/14.83 emptyset)), 98.71/14.83 emptyset))))))) & 98.71/14.83 in(Y3, 98.71/14.83 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 98.71/14.83 inference('lazy_cnf_imply', [status(thm)], ['172'])). 98.71/14.83 tff('174', plain, 98.71/14.83 ~ ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (in(Y2, dsetconstr(Y0, Y1)) => in(Y2, Y0))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 (!!((^[Y2 : $i]: (in(Y2, dsetconstr(Y0, Y1)) => Y1(Y2))))))))))) => 98.71/14.83 ((!!((^[Y0 : $o]: (!!((^[Y1 : $i]: (in(Y1, prop2set(Y0)) => Y0))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: (in(Y0, emptyset) => (!!((^[Y1 : $o]: Y1))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 98.71/14.83 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 98.71/14.83 ((!!((^[Y0 : $i > $o]: 98.71/14.83 ((??((^[Y1 : $i]: 98.71/14.83 (Y0(Y1) & 98.71/14.83 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 98.71/14.83 (??(Y0)))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 98.71/14.83 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 98.71/14.83 (Y0 = Y1))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => (Y0 = emptyset))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 98.71/14.83 (Y0 = emptyset))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (in(Y2, Y0) => 98.71/14.83 (in(Y2, dsetconstr(Y0, Y1)) <=> Y1(Y2)))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (in(Y2, Y0) => 98.71/14.83 (Y1(Y2) => 98.71/14.83 (dsetconstr(Y0, Y1) != emptyset)))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 98.71/14.83 (Y0 != emptyset))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 98.71/14.83 (in(emptyset, setadjoin(emptyset, emptyset)) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (in(Y2, Y1) => 98.71/14.83 in(Y2, setadjoin(Y0, Y1)))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (in(Y2, setadjoin(Y0, Y1)) => 98.71/14.83 (!!((^[Y3 : $o]: 98.71/14.83 (((Y2 = Y0) => Y3) => 98.71/14.83 ((in(Y2, Y1) => Y3) => 98.71/14.83 Y3))))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (in(Y2, setadjoin(Y0, Y1)) => 98.71/14.83 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 ((!!((^[Y2 : $i]: 98.71/14.83 (in(Y2, Y1) => in(Y2, Y0))))) => 98.71/14.83 in(Y1, powerset(Y0))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.71/14.83 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (in(Y1, powerset(Y0)) => 98.71/14.83 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (in(Y1, Y2) => 98.71/14.83 (in(Y2, Y0) => 98.71/14.83 in(Y1, setunion(Y0))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (in(Y1, setunion(Y0)) => 98.71/14.83 (!!((^[Y2 : $o]: 98.71/14.83 ((!!((^[Y3 : $i]: 98.71/14.83 (in(Y1, Y3) => 98.71/14.83 (in(Y3, Y0) => 98.71/14.83 Y2))))) => 98.71/14.83 Y2))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (in(Y1, Y0) => 98.71/14.83 in(Y1, 98.71/14.83 powerset(setunion(Y0)))))))))) => 98.71/14.83 ((!!((^[Y0 : $i > $o]: 98.71/14.83 ((??((^[Y1 : $i]: 98.71/14.83 (Y0(Y1) & 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (Y0(Y2) => (Y1 = Y2))))))))) => 98.71/14.83 (??((^[Y1 : $i]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 ((Y0 != emptyset) => 98.71/14.83 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (in(Y0, 98.71/14.83 setadjoin(Y1, emptyset)) => 98.71/14.83 (Y0 = Y1)))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 ((Y0 != Y1) => 98.71/14.83 (~(in(Y1, 98.71/14.83 setadjoin(Y0, 98.71/14.83 emptyset))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 ((Y0 = Y1) => 98.71/14.83 in(Y0, 98.71/14.83 setadjoin(Y1, 98.71/14.83 emptyset))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (in(Y0, 98.71/14.83 setadjoin(Y1, 98.71/14.83 emptyset)) => 98.71/14.83 in(Y1, 98.71/14.83 setadjoin(Y0, 98.71/14.83 emptyset))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset))) => 98.71/14.83 ((Y2 = Y1) | 98.71/14.83 (Y2 = Y0)))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 in(Y0, 98.71/14.83 setadjoin(Y0, 98.71/14.83 setadjoin(Y1, 98.71/14.83 emptyset))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 in(Y1, 98.71/14.83 setadjoin(Y0, 98.71/14.83 setadjoin(Y1, 98.71/14.83 emptyset))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 ((??((^[Y2 : $i]: 98.71/14.83 (in(Y2, Y0) & 98.71/14.83 Y1(Y2))))) => 98.71/14.83 (dsetconstr(Y0, Y1) != 98.71/14.83 emptyset)))))))) => 98.71/14.83 ((!!((^[Y0 : $i > $o]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (in(Y1, emptyset) => 98.71/14.83 Y0(Y1)))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 ((~((!!((^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 Y1(Y2))))))) => 98.71/14.83 (??((^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) & 98.71/14.83 ( 98.71/14.83 ~( 98.71/14.83 Y1(Y2)))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 ((!!((^[Y2 : $i]: 98.71/14.83 ( 98.71/14.83 in(Y2, 98.71/14.83 Y0) => 98.71/14.83 ( 98.71/14.83 ~( 98.71/14.83 Y1(Y2))))))) => 98.71/14.83 (~((??(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) & 98.71/14.83 Y1(Y2)))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 ((~((??(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 ( 98.71/14.83 in(Y2, 98.71/14.83 Y0) & 98.71/14.83 Y1(Y2))))))) => 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (~( 98.71/14.83 Y1(Y2)))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 ((??((^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) & 98.71/14.83 (~( 98.71/14.83 Y1(Y2))))))) => 98.71/14.83 (~((!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 Y1(Y2)))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $o]: 98.71/14.83 (Y0 => 98.71/14.83 in(emptyset, 98.71/14.83 prop2set(Y0)))))) => 98.71/14.83 ((!!((^[Y0 : $o]: 98.71/14.83 (Y0 => 98.71/14.83 set2prop( 98.71/14.83 prop2set(Y0)))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 ((~(( 98.71/14.83 ??(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) & 98.71/14.83 Y1(Y2))))))) => 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (~( 98.71/14.83 Y1(Y2)))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 ((~(( 98.71/14.83 !!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 Y1(Y2))))))) => 98.71/14.83 (??(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) & 98.71/14.83 (~( 98.71/14.83 Y1(Y2)))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i > $o]: 98.71/14.83 ((??(Y0)) => 98.71/14.83 ((!!((^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (Y0(Y1) => 98.71/14.83 (Y0(Y2) => 98.71/14.83 (Y1 = Y2))))))))) => 98.71/14.83 (??((^[Y1 : $i]: 98.71/14.83 (Y0(Y1) & 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (Y0(Y2) => 98.71/14.83 (Y1 = Y2)))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i > $o]: 98.71/14.83 ((??((^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (Y0(Y2) <=> 98.71/14.83 (Y2 = Y1)))))))) => 98.71/14.83 (??((^[Y1 : $i]: 98.71/14.83 (Y0(Y1) & 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (Y0(Y2) => 98.71/14.83 (Y1 = Y2))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 Y0 = Y1) => 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (( 98.71/14.83 Y2 = Y3) => 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 in(Y3, 98.71/14.83 Y1)))))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 Y0 = Y1) => 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (( 98.71/14.83 Y2 = Y3) => 98.71/14.83 (in(Y2, 98.71/14.83 Y0) <=> 98.71/14.83 in(Y3, 98.71/14.83 Y1)))))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i > $o]: 98.71/14.83 ((??(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 ( 98.71/14.83 Y0(Y1) & 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (Y0(Y2) => 98.71/14.83 (Y1 = Y2))))))))) => 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (Y0(Y1) => 98.71/14.83 (Y0(Y2) => 98.71/14.83 (Y1 = Y2))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i > $o]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i > $o]: 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (( 98.71/14.83 Y2 = Y3) => 98.71/14.83 (Y0(Y2) <=> 98.71/14.83 Y1(Y3))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 ??(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (Y0(Y2) & 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (Y0(Y3) => 98.71/14.83 (Y2 = Y3))))))))) <=> 98.71/14.83 ( 98.71/14.83 ??(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (Y1(Y2) & 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (Y1(Y3) => 98.71/14.83 (Y2 = Y3))))))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 Y0 = Y1) => 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (( 98.71/14.83 Y2 = Y3) => 98.71/14.83 (setadjoin( 98.71/14.83 Y0, Y2) = 98.71/14.83 setadjoin( 98.71/14.83 Y1, Y3)))))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 Y0 = Y1) => 98.71/14.83 (powerset( 98.71/14.83 Y0) = 98.71/14.83 powerset( 98.71/14.83 Y1))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 Y0 = Y1) => 98.71/14.83 (setunion( 98.71/14.83 Y0) = 98.71/14.83 setunion( 98.71/14.83 Y1))))))))) => 98.71/14.83 ((!!((^[Y0 : $i > $o]: 98.71/14.83 (( 98.71/14.83 ??(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (Y0(Y1) & 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (Y0(Y2) => 98.71/14.83 (Y1 = Y2))))))))) => 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (Y0(Y1) => 98.71/14.83 (Y0(Y2) => 98.71/14.83 (Y1 = Y2))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i > $o]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i > $o]: 98.71/14.83 (( 98.71/14.83 !!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (( 98.71/14.83 Y2 = Y3) => 98.71/14.83 (Y0(Y2) <=> 98.71/14.83 Y1(Y3))))))))) => 98.71/14.83 (( 98.71/14.83 ??(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (Y0(Y2) & 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (Y0(Y3) => 98.71/14.83 (Y2 = Y3))))))))) => 98.71/14.83 (( 98.71/14.83 ??(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (Y1(Y2) & 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (Y1(Y3) => 98.71/14.83 (Y2 = Y3))))))))) => 98.71/14.83 (descr( 98.71/14.83 Y0) = 98.71/14.83 descr(Y1))))))))))) => 98.71/14.83 ((!!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 Y0 = Y1) => 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i > $o]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i > $o]: 98.71/14.83 (( 98.71/14.83 !!(( 98.71/14.83 ^[Y4 : $i]: 98.71/14.83 (in(Y4, 98.71/14.83 Y0) => 98.71/14.83 (!!(( 98.71/14.83 ^[Y5 : $i]: 98.71/14.83 (in(Y5, 98.71/14.83 Y1) => 98.71/14.83 (( 98.71/14.83 Y4 = Y5) => 98.71/14.83 (Y2(Y4) <=> 98.71/14.83 Y3(Y5))))))))))) => 98.71/14.83 (dsetconstr( 98.71/14.83 Y0, Y2) = 98.71/14.83 dsetconstr( 98.71/14.83 Y1, Y3)))))))))))))))) => 98.71/14.83 ((!!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 !!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 in(Y2, 98.71/14.83 Y1))))) => 98.71/14.83 subset( 98.71/14.83 Y0, Y1)))))))) => 98.71/14.83 ((!!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 Y0 = Y1) => 98.71/14.83 subset( 98.71/14.83 Y1, Y0)))))))) => 98.71/14.83 ((!!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 Y0 = Y1) => 98.71/14.83 subset( 98.71/14.83 Y0, Y1)))))))) => 98.71/14.83 (( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 !!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 in(Y2, 98.71/14.83 Y1))))) => 98.71/14.83 subset( 98.71/14.83 Y0, Y1)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!( 98.71/14.83 subset( 98.71/14.83 emptyset))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (subset( 98.71/14.83 Y0, Y1) => 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 in(Y2, 98.71/14.83 Y1)))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (subset( 98.71/14.83 Y0, Y1) => 98.71/14.83 (( 98.71/14.83 ~( 98.71/14.83 in(Y2, 98.71/14.83 Y1))) => 98.71/14.83 (~( 98.71/14.83 in(Y2, 98.71/14.83 Y0)))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (( 98.71/14.83 ~( 98.71/14.83 in(Y2, 98.71/14.83 Y1))) => 98.71/14.83 (~( 98.71/14.83 subset( 98.71/14.83 Y0, Y1)))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 ~( 98.71/14.83 subset( 98.71/14.83 Y0, Y1))) => 98.71/14.83 (Y0 != Y1)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (( 98.71/14.83 ~( 98.71/14.83 in(Y2, 98.71/14.83 Y1))) => 98.71/14.83 (Y0 != Y1)))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 subset( 98.71/14.83 Y0, Y0)))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (subset( 98.71/14.83 Y0, Y1) => 98.71/14.83 (subset( 98.71/14.83 Y1, Y2) => 98.71/14.83 subset( 98.71/14.83 Y0, Y2)))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 subset( 98.71/14.83 Y1, 98.71/14.83 setadjoin( 98.71/14.83 Y0, Y1)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (subset( 98.71/14.83 Y0, Y2) => 98.71/14.83 subset( 98.71/14.83 Y0, 98.71/14.83 setadjoin( 98.71/14.83 Y1, Y2)))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (subset( 98.71/14.83 Y0, Y1) => 98.71/14.83 in(Y0, 98.71/14.83 powerset( 98.71/14.83 Y1))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (subset( 98.71/14.83 Y0, Y1) => 98.71/14.83 (subset( 98.71/14.83 Y1, Y0) => 98.71/14.83 (Y0 = Y1))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (subset( 98.71/14.83 Y0, 98.71/14.83 emptyset) => 98.71/14.83 (Y0 = 98.71/14.83 emptyset))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (subset( 98.71/14.83 Y1, Y0) => 98.71/14.83 in(Y1, 98.71/14.83 powerset( 98.71/14.83 Y0))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (in(Y1, 98.71/14.83 powerset( 98.71/14.83 Y0)) => 98.71/14.83 subset( 98.71/14.83 Y1, Y0)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 in(Y0, 98.71/14.83 powerset( 98.71/14.83 Y0))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (subset( 98.71/14.83 Y0, Y1) => 98.71/14.83 subset( 98.71/14.83 powerset( 98.71/14.83 Y0), 98.71/14.83 powerset( 98.71/14.83 Y1))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i > $o]: 98.71/14.83 in( 98.71/14.83 dsetconstr( 98.71/14.83 Y0, Y1), 98.71/14.83 powerset( 98.71/14.83 Y0)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i > $o]: 98.71/14.83 subset( 98.71/14.83 dsetconstr( 98.71/14.83 Y0, Y1), 98.71/14.83 Y0))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 in(Y2, 98.71/14.83 binunion( 98.71/14.83 Y0, Y1)))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 in(Y1, 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y1) => 98.71/14.83 in(Y2, 98.71/14.83 binunion( 98.71/14.83 Y0, Y1)))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $o]: 98.71/14.83 (in(Y2, 98.71/14.83 binunion( 98.71/14.83 Y0, Y1)) => 98.71/14.83 (( 98.71/14.83 in(Y2, 98.71/14.83 Y0) => Y3) => 98.71/14.83 (( 98.71/14.83 in(Y2, 98.71/14.83 Y1) => Y3) => 98.71/14.83 Y3))))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 binunion( 98.71/14.83 Y0, Y1)) => 98.71/14.83 (in(Y2, 98.71/14.83 Y1) | 98.71/14.83 in(Y2, 98.71/14.83 Y0)))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 subset( 98.71/14.83 Y0, 98.71/14.83 binunion( 98.71/14.83 Y0, Y1)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 subset( 98.71/14.83 Y1, 98.71/14.83 binunion( 98.71/14.83 Y0, Y1)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (in(Y2, 98.71/14.83 Y1) => 98.71/14.83 in(Y2, 98.71/14.83 binintersect( 98.71/14.83 Y0, Y1))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (subset( 98.71/14.83 Y2, Y0) => 98.71/14.83 (subset( 98.71/14.83 Y2, Y1) => 98.71/14.83 subset( 98.71/14.83 Y2, 98.71/14.83 binintersect( 98.71/14.83 Y0, Y1))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 binintersect( 98.71/14.83 Y0, Y1)) => 98.71/14.83 in(Y2, 98.71/14.83 Y0))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 subset( 98.71/14.83 binintersect( 98.71/14.83 Y0, Y1), 98.71/14.83 Y0))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (subset( 98.71/14.83 Y0, Y1) => 98.71/14.83 (binintersect( 98.71/14.83 Y0, Y1) = 98.71/14.83 Y0)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 binintersect( 98.71/14.83 Y0, Y1) = 98.71/14.83 Y1) => 98.71/14.83 subset( 98.71/14.83 Y1, Y0)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 binintersect( 98.71/14.83 Y0, Y1)) => 98.71/14.83 in(Y2, 98.71/14.83 Y1))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 ~(( 98.71/14.83 ??(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) & 98.71/14.83 in(Y2, 98.71/14.83 Y1))))))) => 98.71/14.83 (binintersect( 98.71/14.83 Y0, Y1) = 98.71/14.83 emptyset)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 subset( 98.71/14.83 binintersect( 98.71/14.83 Y0, Y1), 98.71/14.83 Y1))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (subset( 98.71/14.83 Y1, Y0) => 98.71/14.83 (binintersect( 98.71/14.83 Y0, Y1) = 98.71/14.83 Y1)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 binintersect( 98.71/14.83 Y0, Y1) = 98.71/14.83 Y0) => 98.71/14.83 subset( 98.71/14.83 Y0, Y1)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (binintersect( 98.71/14.83 Y0, 98.71/14.83 binunion( 98.71/14.83 Y1, Y2)) = 98.71/14.83 binunion( 98.71/14.83 binintersect( 98.71/14.83 Y0, Y1), 98.71/14.83 binintersect( 98.71/14.83 Y0, Y2)))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (( 98.71/14.83 ~( 98.71/14.83 in(Y2, 98.71/14.83 Y1))) => 98.71/14.83 in(Y2, 98.71/14.83 setminus( 98.71/14.83 Y0, Y1))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 setminus( 98.71/14.83 Y0, Y1)) => 98.71/14.83 in(Y2, 98.71/14.83 Y0))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 setminus( 98.71/14.83 Y0, Y1)) => 98.71/14.83 (~( 98.71/14.83 in(Y2, 98.71/14.83 Y1))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (subset( 98.71/14.83 Y0, Y1) => 98.71/14.83 (setminus( 98.71/14.83 Y0, Y1) = 98.71/14.83 emptyset)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (( 98.71/14.83 ~( 98.71/14.83 in(Y2, 98.71/14.83 setminus( 98.71/14.83 Y0, Y1)))) => 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 in(Y2, 98.71/14.83 Y1)))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (( 98.71/14.83 ~( 98.71/14.83 in(Y2, 98.71/14.83 setminus( 98.71/14.83 Y0, Y1)))) => 98.71/14.83 (( 98.71/14.83 ~( 98.71/14.83 in(Y2, 98.71/14.83 Y1))) => 98.71/14.83 (~( 98.71/14.83 in(Y2, 98.71/14.83 Y0)))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (( 98.71/14.83 ~( 98.71/14.83 in(Y2, 98.71/14.83 Y0))) => 98.71/14.83 (~( 98.71/14.83 in(Y2, 98.71/14.83 setminus( 98.71/14.83 Y0, Y1)))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y1) => 98.71/14.83 (~( 98.71/14.83 in(Y2, 98.71/14.83 setminus( 98.71/14.83 Y0, Y1)))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 subset( 98.71/14.83 setminus( 98.71/14.83 Y0, Y1), 98.71/14.83 Y0))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (( 98.71/14.83 setminus( 98.71/14.83 Y0, Y1) = 98.71/14.83 emptyset) => 98.71/14.83 subset( 98.71/14.83 Y0, Y1)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 symdiff( 98.71/14.83 Y0, Y1)) => 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $o]: 98.71/14.83 (( 98.71/14.83 in(Y2, 98.71/14.83 Y0) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 ~( 98.71/14.83 in(Y2, 98.71/14.83 Y1))) => 98.71/14.83 Y3)) => 98.71/14.83 (( 98.71/14.83 ( 98.71/14.83 ~( 98.71/14.83 in(Y2, 98.71/14.83 Y0))) => 98.71/14.83 ( 98.71/14.83 in(Y2, 98.71/14.83 Y1) => Y3)) => 98.71/14.83 Y3))))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (( 98.71/14.83 ~( 98.71/14.83 in(Y2, 98.71/14.83 Y1))) => 98.71/14.83 in(Y2, 98.71/14.83 symdiff( 98.71/14.83 Y0, Y1))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (( 98.71/14.83 ~( 98.71/14.83 in(Y2, 98.71/14.83 Y0))) => 98.71/14.83 (in(Y2, 98.71/14.83 Y1) => 98.71/14.83 in(Y2, 98.71/14.83 symdiff( 98.71/14.83 Y0, Y1))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (in(Y2, 98.71/14.83 Y1) => 98.71/14.83 (~( 98.71/14.83 in(Y2, 98.71/14.83 symdiff( 98.71/14.83 Y0, Y1))))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (( 98.71/14.83 ~( 98.71/14.83 in(Y2, 98.71/14.83 Y0))) => 98.71/14.83 (( 98.71/14.83 ~( 98.71/14.83 in(Y2, 98.71/14.83 Y1))) => 98.71/14.83 (~( 98.71/14.83 in(Y2, 98.71/14.83 symdiff( 98.71/14.83 Y0, Y1))))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 in(Y1, 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 in(Y0, 98.71/14.83 setunion( 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 in(Y1, 98.71/14.83 setunion( 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (??(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 setunion( 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)))) & 98.71/14.83 (??(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (in(Y3, 98.71/14.83 setunion( 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)))) & 98.71/14.83 (setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)) = 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 setadjoin( 98.71/14.83 Y3, 98.71/14.83 emptyset)), 98.71/14.83 emptyset))))))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (??(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 setunion( 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)))) & 98.71/14.83 (??(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (in(Y3, 98.71/14.83 setunion( 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)))) & 98.71/14.83 (setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)) = 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 setadjoin( 98.71/14.83 Y3, 98.71/14.83 emptyset)), 98.71/14.83 emptyset))))))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (in(Y1, 98.71/14.83 Y0) => 98.71/14.83 subset( 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset), 98.71/14.83 Y0)))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (in(Y1, 98.71/14.83 Y0) => 98.71/14.83 in( 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset), 98.71/14.83 powerset( 98.71/14.83 Y0))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 in( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 emptyset), 98.71/14.83 powerset( 98.71/14.83 binunion( 98.71/14.83 Y0, Y1))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 setadjoin( 98.71/14.83 Y0, 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset))) => 98.71/14.83 (( 98.71/14.83 Y2 = Y1) | 98.71/14.83 (Y2 = Y0)))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (in(Y3, 98.71/14.83 Y1) => 98.71/14.83 subset( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 setadjoin( 98.71/14.83 Y3, 98.71/14.83 emptyset)), 98.71/14.83 binunion( 98.71/14.83 Y0, Y1)))))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (in(Y3, 98.71/14.83 Y1) => 98.71/14.83 in( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 setadjoin( 98.71/14.83 Y3, 98.71/14.83 emptyset)), 98.71/14.83 powerset( 98.71/14.83 binunion( 98.71/14.83 Y0, Y1))))))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (in(Y3, 98.71/14.83 Y1) => 98.71/14.83 subset( 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 setadjoin( 98.71/14.83 Y3, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)), 98.71/14.83 powerset( 98.71/14.83 binunion( 98.71/14.83 Y0, Y1))))))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (in(Y3, 98.71/14.83 Y1) => 98.71/14.83 in( 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 setadjoin( 98.71/14.83 Y3, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)), 98.71/14.83 powerset( 98.71/14.83 powerset( 98.71/14.83 binunion( 98.71/14.83 Y0, Y1)))))))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (in(Y3, 98.71/14.83 Y1) => 98.71/14.83 in( 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 setadjoin( 98.71/14.83 Y3, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)), 98.71/14.83 powerset( 98.71/14.83 powerset( 98.71/14.83 binunion( 98.71/14.83 Y0, Y1)))))))))))))))))) => 98.71/14.83 ( 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 (!!(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (in(Y3, 98.71/14.83 Y1) => 98.71/14.83 in( 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y2, 98.71/14.83 setadjoin( 98.71/14.83 Y3, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)), 98.71/14.83 dsetconstr( 98.71/14.83 powerset( 98.71/14.83 powerset( 98.71/14.83 binunion( 98.71/14.83 Y0, Y1))), 98.71/14.83 (^[Y4 : $i]: 98.71/14.83 (??(( 98.71/14.83 ^[Y5 : $i]: 98.71/14.83 (in(Y5, 98.71/14.83 Y0) & 98.71/14.83 (??(( 98.71/14.83 ^[Y6 : $i]: 98.71/14.83 (in(Y6, 98.71/14.83 Y1) & 98.71/14.83 (Y4 = 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y5, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y5, 98.71/14.83 setadjoin( 98.71/14.83 Y6, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)))))))))))))))))))))))))))) => 98.71/14.83 ( 98.71/14.83 !!(( 98.71/14.83 ^[Y0 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y1 : $i]: 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 dsetconstr( 98.71/14.83 powerset( 98.71/14.83 powerset( 98.71/14.83 binunion( 98.71/14.83 Y0, Y1))), 98.71/14.83 (^[Y3 : $i]: 98.71/14.83 (??(( 98.71/14.83 ^[Y4 : $i]: 98.71/14.83 (in(Y4, 98.71/14.83 Y0) & 98.71/14.83 (??(( 98.71/14.83 ^[Y5 : $i]: 98.71/14.83 (in(Y5, 98.71/14.83 Y1) & 98.71/14.83 (Y3 = 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y4, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y4, 98.71/14.83 setadjoin( 98.71/14.83 Y5, 98.71/14.83 emptyset)), 98.71/14.83 emptyset)))))))))))))) => 98.71/14.83 (??(( 98.71/14.83 ^[Y3 : $i]: 98.71/14.83 (( 98.71/14.83 ??(( 98.71/14.83 ^[Y4 : $i]: 98.71/14.83 (in(Y4, 98.71/14.83 Y1) & 98.71/14.83 (Y2 = 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y3, 98.71/14.83 emptyset), 98.71/14.83 setadjoin( 98.71/14.83 setadjoin( 98.71/14.83 Y3, 98.71/14.83 setadjoin( 98.71/14.83 Y4, 98.71/14.83 emptyset)), 98.71/14.83 emptyset))))))) & 98.71/14.83 in(Y3, 98.71/14.83 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 98.71/14.83 inference('lazy_cnf_imply', [status(thm)], ['173'])). 98.71/14.83 tff('175', plain, 98.71/14.83 ~ ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 (!!((^[Y2 : $i]: (in(Y2, dsetconstr(Y0, Y1)) => Y1(Y2))))))))))) => 98.71/14.83 ((!!((^[Y0 : $o]: (!!((^[Y1 : $i]: (in(Y1, prop2set(Y0)) => Y0))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: (in(Y0, emptyset) => (!!((^[Y1 : $o]: Y1))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 98.71/14.83 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 98.71/14.83 ((!!((^[Y0 : $i > $o]: 98.71/14.83 ((??((^[Y1 : $i]: 98.71/14.83 (Y0(Y1) & 98.71/14.83 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 98.71/14.83 (??(Y0)))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 98.71/14.83 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 98.71/14.83 (Y0 = Y1))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => (Y0 = emptyset))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => (Y0 = emptyset))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (in(Y2, Y0) => 98.71/14.83 (in(Y2, dsetconstr(Y0, Y1)) <=> Y1(Y2)))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (in(Y2, Y0) => 98.71/14.83 (Y1(Y2) => 98.71/14.83 (dsetconstr(Y0, Y1) != emptyset)))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 ((??((^[Y1 : $i]: in(Y1, Y0)))) => (Y0 != emptyset))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 98.71/14.83 (in(emptyset, setadjoin(emptyset, emptyset)) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (in(Y2, Y1) => 98.71/14.83 in(Y2, setadjoin(Y0, Y1)))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (in(Y2, setadjoin(Y0, Y1)) => 98.71/14.83 (!!((^[Y3 : $o]: 98.71/14.83 (((Y2 = Y0) => Y3) => 98.71/14.83 ((in(Y2, Y1) => Y3) => 98.71/14.83 Y3))))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (in(Y2, setadjoin(Y0, Y1)) => 98.71/14.83 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 ((!!((^[Y2 : $i]: 98.71/14.83 (in(Y2, Y1) => in(Y2, Y0))))) => 98.71/14.83 in(Y1, powerset(Y0))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.71/14.83 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (in(Y1, powerset(Y0)) => 98.71/14.83 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (in(Y1, Y2) => 98.71/14.83 (in(Y2, Y0) => 98.71/14.83 in(Y1, setunion(Y0))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (in(Y1, setunion(Y0)) => 98.71/14.83 (!!((^[Y2 : $o]: 98.71/14.83 ((!!((^[Y3 : $i]: 98.71/14.83 (in(Y1, Y3) => 98.71/14.83 (in(Y3, Y0) => 98.71/14.83 Y2))))) => 98.71/14.83 Y2))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (in(Y1, Y0) => 98.71/14.83 in(Y1, powerset(setunion(Y0)))))))))) => 98.71/14.83 ((!!((^[Y0 : $i > $o]: 98.71/14.83 ((??((^[Y1 : $i]: 98.71/14.83 (Y0(Y1) & 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (Y0(Y2) => (Y1 = Y2))))))))) => 98.71/14.83 (??((^[Y1 : $i]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 ((Y0 != emptyset) => 98.71/14.83 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (in(Y0, 98.71/14.83 setadjoin(Y1, emptyset)) => 98.71/14.83 (Y0 = Y1)))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 ((Y0 != Y1) => 98.71/14.83 (~(in(Y1, 98.71/14.83 setadjoin(Y0, 98.71/14.83 emptyset))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 ((Y0 = Y1) => 98.71/14.83 in(Y0, 98.71/14.83 setadjoin(Y1, emptyset))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (in(Y0, 98.71/14.83 setadjoin(Y1, 98.71/14.83 emptyset)) => 98.71/14.83 in(Y1, 98.71/14.83 setadjoin(Y0, 98.71/14.83 emptyset))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 setadjoin(Y0, 98.71/14.83 setadjoin( 98.71/14.83 Y1, 98.71/14.83 emptyset))) => 98.71/14.83 ((Y2 = Y1) | 98.71/14.83 (Y2 = Y0)))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 in(Y0, 98.71/14.83 setadjoin(Y0, 98.71/14.83 setadjoin(Y1, 98.71/14.83 emptyset))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 in(Y1, 98.71/14.83 setadjoin(Y0, 98.71/14.83 setadjoin(Y1, 98.71/14.83 emptyset))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 ((??((^[Y2 : $i]: 98.71/14.83 (in(Y2, Y0) & 98.71/14.83 Y1(Y2))))) => 98.71/14.83 (dsetconstr(Y0, Y1) != 98.71/14.83 emptyset)))))))) => 98.71/14.83 ((!!((^[Y0 : $i > $o]: 98.71/14.83 (!!((^[Y1 : $i]: 98.71/14.83 (in(Y1, emptyset) => 98.71/14.83 Y0(Y1)))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 ((~((!!((^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 Y1(Y2))))))) => 98.71/14.83 (??((^[Y2 : $i]: 98.71/14.83 (in(Y2, Y0) & 98.71/14.83 (~(Y1(Y2)))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 ((!!((^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) => 98.71/14.83 ( 98.71/14.83 ~( 98.71/14.83 Y1(Y2))))))) => 98.71/14.83 (~((??((^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) & 98.71/14.83 Y1(Y2)))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 ((~((??(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) & 98.71/14.83 Y1(Y2))))))) => 98.71/14.83 (!!((^[Y2 : $i]: 98.71/14.83 ( 98.71/14.83 in(Y2, 98.71/14.83 Y0) => 98.71/14.83 ( 98.71/14.83 ~( 98.71/14.83 Y1(Y2)))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 ((??((^[Y2 : $i]: 98.71/14.83 (in(Y2, 98.71/14.83 Y0) & 98.71/14.83 (~( 98.71/14.83 Y1(Y2))))))) => 98.71/14.83 (~((!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 ( 98.71/14.83 in(Y2, 98.71/14.83 Y0) => 98.71/14.83 Y1(Y2)))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $o]: 98.71/14.83 (Y0 => 98.71/14.83 in(emptyset, 98.71/14.83 prop2set(Y0)))))) => 98.71/14.83 ((!!((^[Y0 : $o]: 98.71/14.83 (Y0 => 98.71/14.83 set2prop( 98.71/14.83 prop2set(Y0)))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 ((~(( 98.71/14.83 ??(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 ( 98.71/14.83 in(Y2, 98.71/14.83 Y0) & 98.71/14.83 Y1(Y2))))))) => 98.71/14.83 (!!(( 98.71/14.83 ^[Y2 : $i]: 98.71/14.83 ( 98.71/14.83 in(Y2, 98.71/14.83 Y0) => 98.71/14.83 ( 98.71/14.83 ~( 98.71/14.83 Y1(Y2)))))))))))))) => 98.71/14.83 ((!!((^[Y0 : $i]: 98.71/14.83 (!!((^[Y1 : $i > $o]: 98.71/14.83 ((~(( 98.71/14.83 !!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 Y1(Y2))))))) => 98.71/14.84 (??(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) & 98.71/14.84 (~( 98.71/14.84 Y1(Y2)))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i > $o]: 98.71/14.84 ((??(Y0)) => 98.71/14.84 ((!!((^[Y1 : $i]: 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y0(Y1) => 98.71/14.84 (Y0(Y2) => 98.71/14.84 (Y1 = Y2))))))))) => 98.71/14.84 (??((^[Y1 : $i]: 98.71/14.84 ( 98.71/14.84 Y0(Y1) & 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y0(Y2) => 98.71/14.84 (Y1 = Y2)))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i > $o]: 98.71/14.84 ((??((^[Y1 : $i]: 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y0(Y2) <=> 98.71/14.84 (Y2 = Y1)))))))) => 98.71/14.84 (??((^[Y1 : $i]: 98.71/14.84 ( 98.71/14.84 Y0(Y1) & 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y0(Y2) => 98.71/14.84 (Y1 = Y2))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 Y0 = Y1) => 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (( 98.71/14.84 Y2 = Y3) => 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 in(Y3, 98.71/14.84 Y1)))))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 Y0 = Y1) => 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (( 98.71/14.84 Y2 = Y3) => 98.71/14.84 (in(Y2, 98.71/14.84 Y0) <=> 98.71/14.84 in(Y3, 98.71/14.84 Y1)))))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i > $o]: 98.71/14.84 ((??(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (Y0(Y1) & 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y0(Y2) => 98.71/14.84 (Y1 = Y2))))))))) => 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y0(Y1) => 98.71/14.84 (Y0(Y2) => 98.71/14.84 (Y1 = Y2))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i > $o]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i > $o]: 98.71/14.84 (( 98.71/14.84 !!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (( 98.71/14.84 Y2 = Y3) => 98.71/14.84 (Y0(Y2) <=> 98.71/14.84 Y1(Y3))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 ??(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y0(Y2) & 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (Y0(Y3) => 98.71/14.84 (Y2 = Y3))))))))) <=> 98.71/14.84 ( 98.71/14.84 ??(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y1(Y2) & 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (Y1(Y3) => 98.71/14.84 (Y2 = Y3))))))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 Y0 = Y1) => 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (( 98.71/14.84 Y2 = Y3) => 98.71/14.84 (setadjoin( 98.71/14.84 Y0, Y2) = 98.71/14.84 setadjoin( 98.71/14.84 Y1, Y3)))))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 Y0 = Y1) => 98.71/14.84 (powerset( 98.71/14.84 Y0) = 98.71/14.84 powerset( 98.71/14.84 Y1))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 Y0 = Y1) => 98.71/14.84 (setunion( 98.71/14.84 Y0) = 98.71/14.84 setunion( 98.71/14.84 Y1))))))))) => 98.71/14.84 ((!!((^[Y0 : $i > $o]: 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 ??(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (Y0(Y1) & 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y0(Y2) => 98.71/14.84 (Y1 = Y2))))))))) => 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y0(Y1) => 98.71/14.84 (Y0(Y2) => 98.71/14.84 (Y1 = Y2))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i > $o]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i > $o]: 98.71/14.84 (( 98.71/14.84 !!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (( 98.71/14.84 Y2 = Y3) => 98.71/14.84 (Y0(Y2) <=> 98.71/14.84 Y1(Y3))))))))) => 98.71/14.84 (( 98.71/14.84 ??(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y0(Y2) & 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (Y0(Y3) => 98.71/14.84 (Y2 = Y3))))))))) => 98.71/14.84 (( 98.71/14.84 ??(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y1(Y2) & 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (Y1(Y3) => 98.71/14.84 (Y2 = Y3))))))))) => 98.71/14.84 (descr( 98.71/14.84 Y0) = 98.71/14.84 descr(Y1))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 Y0 = Y1) => 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i > $o]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i > $o]: 98.71/14.84 (( 98.71/14.84 !!(( 98.71/14.84 ^[Y4 : $i]: 98.71/14.84 (in(Y4, 98.71/14.84 Y0) => 98.71/14.84 (!!(( 98.71/14.84 ^[Y5 : $i]: 98.71/14.84 (in(Y5, 98.71/14.84 Y1) => 98.71/14.84 (( 98.71/14.84 Y4 = Y5) => 98.71/14.84 (Y2(Y4) <=> 98.71/14.84 Y3(Y5))))))))))) => 98.71/14.84 (dsetconstr( 98.71/14.84 Y0, Y2) = 98.71/14.84 dsetconstr( 98.71/14.84 Y1, Y3)))))))))))))))) => 98.71/14.84 ((!!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 !!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 in(Y2, 98.71/14.84 Y1))))) => 98.71/14.84 subset( 98.71/14.84 Y0, Y1)))))))) => 98.71/14.84 ((!!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 Y0 = Y1) => 98.71/14.84 subset( 98.71/14.84 Y1, Y0)))))))) => 98.71/14.84 ((!!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 Y0 = Y1) => 98.71/14.84 subset( 98.71/14.84 Y0, Y1)))))))) => 98.71/14.84 ((!!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 !!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 in(Y2, 98.71/14.84 Y1))))) => 98.71/14.84 subset( 98.71/14.84 Y0, Y1)))))))) => 98.71/14.84 (( 98.71/14.84 !!( 98.71/14.84 subset( 98.71/14.84 emptyset))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y0, Y1) => 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 in(Y2, 98.71/14.84 Y1)))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y0, Y1) => 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 Y1))) => 98.71/14.84 (~( 98.71/14.84 in(Y2, 98.71/14.84 Y0)))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 Y1))) => 98.71/14.84 (~( 98.71/14.84 subset( 98.71/14.84 Y0, Y1)))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 subset( 98.71/14.84 Y0, Y1))) => 98.71/14.84 (Y0 != Y1)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 Y1))) => 98.71/14.84 (Y0 != Y1)))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 subset( 98.71/14.84 Y0, Y0)))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y0, Y1) => 98.71/14.84 (subset( 98.71/14.84 Y1, Y2) => 98.71/14.84 subset( 98.71/14.84 Y0, Y2)))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 subset( 98.71/14.84 Y1, 98.71/14.84 setadjoin( 98.71/14.84 Y0, Y1)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y0, Y2) => 98.71/14.84 subset( 98.71/14.84 Y0, 98.71/14.84 setadjoin( 98.71/14.84 Y1, Y2)))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y0, Y1) => 98.71/14.84 in(Y0, 98.71/14.84 powerset( 98.71/14.84 Y1))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y0, Y1) => 98.71/14.84 (subset( 98.71/14.84 Y1, Y0) => 98.71/14.84 (Y0 = Y1))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y0, 98.71/14.84 emptyset) => 98.71/14.84 (Y0 = 98.71/14.84 emptyset))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y1, Y0) => 98.71/14.84 in(Y1, 98.71/14.84 powerset( 98.71/14.84 Y0))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (in(Y1, 98.71/14.84 powerset( 98.71/14.84 Y0)) => 98.71/14.84 subset( 98.71/14.84 Y1, Y0)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 in(Y0, 98.71/14.84 powerset( 98.71/14.84 Y0))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y0, Y1) => 98.71/14.84 subset( 98.71/14.84 powerset( 98.71/14.84 Y0), 98.71/14.84 powerset( 98.71/14.84 Y1))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i > $o]: 98.71/14.84 in( 98.71/14.84 dsetconstr( 98.71/14.84 Y0, Y1), 98.71/14.84 powerset( 98.71/14.84 Y0)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i > $o]: 98.71/14.84 subset( 98.71/14.84 dsetconstr( 98.71/14.84 Y0, Y1), 98.71/14.84 Y0))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 in(Y2, 98.71/14.84 binunion( 98.71/14.84 Y0, Y1)))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 in(Y1, 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 setadjoin( 98.71/14.84 Y1, 98.71/14.84 emptyset))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y1) => 98.71/14.84 in(Y2, 98.71/14.84 binunion( 98.71/14.84 Y0, Y1)))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $o]: 98.71/14.84 (in(Y2, 98.71/14.84 binunion( 98.71/14.84 Y0, Y1)) => 98.71/14.84 (( 98.71/14.84 in(Y2, 98.71/14.84 Y0) => Y3) => 98.71/14.84 (( 98.71/14.84 in(Y2, 98.71/14.84 Y1) => Y3) => 98.71/14.84 Y3))))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 binunion( 98.71/14.84 Y0, Y1)) => 98.71/14.84 (in(Y2, 98.71/14.84 Y1) | 98.71/14.84 in(Y2, 98.71/14.84 Y0)))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 subset( 98.71/14.84 Y0, 98.71/14.84 binunion( 98.71/14.84 Y0, Y1)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 subset( 98.71/14.84 Y1, 98.71/14.84 binunion( 98.71/14.84 Y0, Y1)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 (in(Y2, 98.71/14.84 Y1) => 98.71/14.84 in(Y2, 98.71/14.84 binintersect( 98.71/14.84 Y0, Y1))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y2, Y0) => 98.71/14.84 (subset( 98.71/14.84 Y2, Y1) => 98.71/14.84 subset( 98.71/14.84 Y2, 98.71/14.84 binintersect( 98.71/14.84 Y0, Y1))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 binintersect( 98.71/14.84 Y0, Y1)) => 98.71/14.84 in(Y2, 98.71/14.84 Y0))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 subset( 98.71/14.84 binintersect( 98.71/14.84 Y0, Y1), 98.71/14.84 Y0))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y0, Y1) => 98.71/14.84 (binintersect( 98.71/14.84 Y0, Y1) = 98.71/14.84 Y0)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 binintersect( 98.71/14.84 Y0, Y1) = 98.71/14.84 Y1) => 98.71/14.84 subset( 98.71/14.84 Y1, Y0)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 binintersect( 98.71/14.84 Y0, Y1)) => 98.71/14.84 in(Y2, 98.71/14.84 Y1))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 ~(( 98.71/14.84 ??(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) & 98.71/14.84 in(Y2, 98.71/14.84 Y1))))))) => 98.71/14.84 (binintersect( 98.71/14.84 Y0, Y1) = 98.71/14.84 emptyset)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 subset( 98.71/14.84 binintersect( 98.71/14.84 Y0, Y1), 98.71/14.84 Y1))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y1, Y0) => 98.71/14.84 (binintersect( 98.71/14.84 Y0, Y1) = 98.71/14.84 Y1)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 binintersect( 98.71/14.84 Y0, Y1) = 98.71/14.84 Y0) => 98.71/14.84 subset( 98.71/14.84 Y0, Y1)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (binintersect( 98.71/14.84 Y0, 98.71/14.84 binunion( 98.71/14.84 Y1, Y2)) = 98.71/14.84 binunion( 98.71/14.84 binintersect( 98.71/14.84 Y0, Y1), 98.71/14.84 binintersect( 98.71/14.84 Y0, Y2)))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 Y1))) => 98.71/14.84 in(Y2, 98.71/14.84 setminus( 98.71/14.84 Y0, Y1))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 setminus( 98.71/14.84 Y0, Y1)) => 98.71/14.84 in(Y2, 98.71/14.84 Y0))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 setminus( 98.71/14.84 Y0, Y1)) => 98.71/14.84 (~( 98.71/14.84 in(Y2, 98.71/14.84 Y1))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y0, Y1) => 98.71/14.84 (setminus( 98.71/14.84 Y0, Y1) = 98.71/14.84 emptyset)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 setminus( 98.71/14.84 Y0, Y1)))) => 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 in(Y2, 98.71/14.84 Y1)))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 setminus( 98.71/14.84 Y0, Y1)))) => 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 Y1))) => 98.71/14.84 (~( 98.71/14.84 in(Y2, 98.71/14.84 Y0)))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 Y0))) => 98.71/14.84 (~( 98.71/14.84 in(Y2, 98.71/14.84 setminus( 98.71/14.84 Y0, Y1)))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y1) => 98.71/14.84 (~( 98.71/14.84 in(Y2, 98.71/14.84 setminus( 98.71/14.84 Y0, Y1)))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 subset( 98.71/14.84 setminus( 98.71/14.84 Y0, Y1), 98.71/14.84 Y0))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 setminus( 98.71/14.84 Y0, Y1) = 98.71/14.84 emptyset) => 98.71/14.84 subset( 98.71/14.84 Y0, Y1)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 symdiff( 98.71/14.84 Y0, Y1)) => 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $o]: 98.71/14.84 (( 98.71/14.84 in(Y2, 98.71/14.84 Y0) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 Y1))) => 98.71/14.84 Y3)) => 98.71/14.84 (( 98.71/14.84 ( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 Y0))) => 98.71/14.84 ( 98.71/14.84 in(Y2, 98.71/14.84 Y1) => Y3)) => 98.71/14.84 Y3))))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 Y1))) => 98.71/14.84 in(Y2, 98.71/14.84 symdiff( 98.71/14.84 Y0, Y1))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 Y0))) => 98.71/14.84 (in(Y2, 98.71/14.84 Y1) => 98.71/14.84 in(Y2, 98.71/14.84 symdiff( 98.71/14.84 Y0, Y1))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 (in(Y2, 98.71/14.84 Y1) => 98.71/14.84 (~( 98.71/14.84 in(Y2, 98.71/14.84 symdiff( 98.71/14.84 Y0, Y1))))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 Y0))) => 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 Y1))) => 98.71/14.84 (~( 98.71/14.84 in(Y2, 98.71/14.84 symdiff( 98.71/14.84 Y0, Y1))))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 in(Y1, 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 setadjoin( 98.71/14.84 Y1, 98.71/14.84 emptyset))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 in(Y0, 98.71/14.84 setunion( 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 setadjoin( 98.71/14.84 Y1, 98.71/14.84 emptyset)), 98.71/14.84 emptyset)))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 in(Y1, 98.71/14.84 setunion( 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 setadjoin( 98.71/14.84 Y1, 98.71/14.84 emptyset)), 98.71/14.84 emptyset)))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (??(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 setunion( 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 setadjoin( 98.71/14.84 Y1, 98.71/14.84 emptyset)), 98.71/14.84 emptyset)))) & 98.71/14.84 (??(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (in(Y3, 98.71/14.84 setunion( 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 setadjoin( 98.71/14.84 Y1, 98.71/14.84 emptyset)), 98.71/14.84 emptyset)))) & 98.71/14.84 (setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 setadjoin( 98.71/14.84 Y1, 98.71/14.84 emptyset)), 98.71/14.84 emptyset)) = 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 setadjoin( 98.71/14.84 Y3, 98.71/14.84 emptyset)), 98.71/14.84 emptyset))))))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (??(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 setunion( 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 setadjoin( 98.71/14.84 Y1, 98.71/14.84 emptyset)), 98.71/14.84 emptyset)))) & 98.71/14.84 (??(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (in(Y3, 98.71/14.84 setunion( 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 setadjoin( 98.71/14.84 Y1, 98.71/14.84 emptyset)), 98.71/14.84 emptyset)))) & 98.71/14.84 (setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 setadjoin( 98.71/14.84 Y1, 98.71/14.84 emptyset)), 98.71/14.84 emptyset)) = 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 setadjoin( 98.71/14.84 Y3, 98.71/14.84 emptyset)), 98.71/14.84 emptyset))))))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (in(Y1, 98.71/14.84 Y0) => 98.71/14.84 subset( 98.71/14.84 setadjoin( 98.71/14.84 Y1, 98.71/14.84 emptyset), 98.71/14.84 Y0)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (in(Y1, 98.71/14.84 Y0) => 98.71/14.84 in( 98.71/14.84 setadjoin( 98.71/14.84 Y1, 98.71/14.84 emptyset), 98.71/14.84 powerset( 98.71/14.84 Y0))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 in( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 emptyset), 98.71/14.84 powerset( 98.71/14.84 binunion( 98.71/14.84 Y0, Y1))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 setadjoin( 98.71/14.84 Y1, 98.71/14.84 emptyset))) => 98.71/14.84 (( 98.71/14.84 Y2 = Y1) | 98.71/14.84 (Y2 = Y0)))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (in(Y3, 98.71/14.84 Y1) => 98.71/14.84 subset( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 setadjoin( 98.71/14.84 Y3, 98.71/14.84 emptyset)), 98.71/14.84 binunion( 98.71/14.84 Y0, Y1)))))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (in(Y3, 98.71/14.84 Y1) => 98.71/14.84 in( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 setadjoin( 98.71/14.84 Y3, 98.71/14.84 emptyset)), 98.71/14.84 powerset( 98.71/14.84 binunion( 98.71/14.84 Y0, Y1))))))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (in(Y3, 98.71/14.84 Y1) => 98.71/14.84 subset( 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 setadjoin( 98.71/14.84 Y3, 98.71/14.84 emptyset)), 98.71/14.84 emptyset)), 98.71/14.84 powerset( 98.71/14.84 binunion( 98.71/14.84 Y0, Y1))))))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (in(Y3, 98.71/14.84 Y1) => 98.71/14.84 in( 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 setadjoin( 98.71/14.84 Y3, 98.71/14.84 emptyset)), 98.71/14.84 emptyset)), 98.71/14.84 powerset( 98.71/14.84 powerset( 98.71/14.84 binunion( 98.71/14.84 Y0, Y1)))))))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (in(Y3, 98.71/14.84 Y1) => 98.71/14.84 in( 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 setadjoin( 98.71/14.84 Y3, 98.71/14.84 emptyset)), 98.71/14.84 emptyset)), 98.71/14.84 powerset( 98.71/14.84 powerset( 98.71/14.84 binunion( 98.71/14.84 Y0, Y1)))))))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (in(Y3, 98.71/14.84 Y1) => 98.71/14.84 in( 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 setadjoin( 98.71/14.84 Y3, 98.71/14.84 emptyset)), 98.71/14.84 emptyset)), 98.71/14.84 dsetconstr( 98.71/14.84 powerset( 98.71/14.84 powerset( 98.71/14.84 binunion( 98.71/14.84 Y0, Y1))), 98.71/14.84 (^[Y4 : $i]: 98.71/14.84 (??(( 98.71/14.84 ^[Y5 : $i]: 98.71/14.84 (in(Y5, 98.71/14.84 Y0) & 98.71/14.84 (??(( 98.71/14.84 ^[Y6 : $i]: 98.71/14.84 (in(Y6, 98.71/14.84 Y1) & 98.71/14.84 (Y4 = 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y5, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y5, 98.71/14.84 setadjoin( 98.71/14.84 Y6, 98.71/14.84 emptyset)), 98.71/14.84 emptyset)))))))))))))))))))))))))))) => 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 dsetconstr( 98.71/14.84 powerset( 98.71/14.84 powerset( 98.71/14.84 binunion( 98.71/14.84 Y0, Y1))), 98.71/14.84 (^[Y3 : $i]: 98.71/14.84 (??(( 98.71/14.84 ^[Y4 : $i]: 98.71/14.84 (in(Y4, 98.71/14.84 Y0) & 98.71/14.84 (??(( 98.71/14.84 ^[Y5 : $i]: 98.71/14.84 (in(Y5, 98.71/14.84 Y1) & 98.71/14.84 (Y3 = 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y4, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y4, 98.71/14.84 setadjoin( 98.71/14.84 Y5, 98.71/14.84 emptyset)), 98.71/14.84 emptyset)))))))))))))) => 98.71/14.84 (??(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (( 98.71/14.84 ??(( 98.71/14.84 ^[Y4 : $i]: 98.71/14.84 (in(Y4, 98.71/14.84 Y1) & 98.71/14.84 (Y2 = 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y3, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y3, 98.71/14.84 setadjoin( 98.71/14.84 Y4, 98.71/14.84 emptyset)), 98.71/14.84 emptyset))))))) & 98.71/14.84 in(Y3, 98.71/14.84 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 98.71/14.84 inference('lazy_cnf_imply', [status(thm)], ['174'])). 98.71/14.84 tff('176', plain, 98.71/14.84 ~ ((!!((^[Y0 : $o]: (!!((^[Y1 : $i]: (in(Y1, prop2set(Y0)) => Y0))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: (in(Y0, emptyset) => (!!((^[Y1 : $o]: Y1))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 98.71/14.84 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 98.71/14.84 ((!!((^[Y0 : $i > $o]: 98.71/14.84 ((??((^[Y1 : $i]: 98.71/14.84 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 98.71/14.84 (??(Y0)))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 98.71/14.84 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 98.71/14.84 (Y0 = Y1))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => (Y0 = emptyset))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => (Y0 = emptyset))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i > $o]: 98.71/14.84 (!!((^[Y2 : $i]: 98.71/14.84 (in(Y2, Y0) => 98.71/14.84 (in(Y2, dsetconstr(Y0, Y1)) <=> Y1(Y2)))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i > $o]: 98.71/14.84 (!!((^[Y2 : $i]: 98.71/14.84 (in(Y2, Y0) => 98.71/14.84 (Y1(Y2) => 98.71/14.84 (dsetconstr(Y0, Y1) != emptyset)))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 ((??((^[Y1 : $i]: in(Y1, Y0)))) => (Y0 != emptyset))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 98.71/14.84 (in(emptyset, setadjoin(emptyset, emptyset)) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 (!!((^[Y2 : $i]: 98.71/14.84 (in(Y2, Y1) => 98.71/14.84 in(Y2, setadjoin(Y0, Y1)))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 (!!((^[Y2 : $i]: 98.71/14.84 (in(Y2, setadjoin(Y0, Y1)) => 98.71/14.84 (!!((^[Y3 : $o]: 98.71/14.84 (((Y2 = Y0) => Y3) => 98.71/14.84 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 (!!((^[Y2 : $i]: 98.71/14.84 (in(Y2, setadjoin(Y0, Y1)) => 98.71/14.84 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 ((!!((^[Y2 : $i]: 98.71/14.84 (in(Y2, Y1) => in(Y2, Y0))))) => 98.71/14.84 in(Y1, powerset(Y0))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.71/14.84 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 (!!((^[Y2 : $i]: 98.71/14.84 (in(Y1, powerset(Y0)) => 98.71/14.84 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 (!!((^[Y2 : $i]: 98.71/14.84 (in(Y1, Y2) => 98.71/14.84 (in(Y2, Y0) => 98.71/14.84 in(Y1, setunion(Y0))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 (in(Y1, setunion(Y0)) => 98.71/14.84 (!!((^[Y2 : $o]: 98.71/14.84 ((!!((^[Y3 : $i]: 98.71/14.84 (in(Y1, Y3) => 98.71/14.84 (in(Y3, Y0) => 98.71/14.84 Y2))))) => 98.71/14.84 Y2))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 (in(Y1, Y0) => 98.71/14.84 in(Y1, powerset(setunion(Y0)))))))))) => 98.71/14.84 ((!!((^[Y0 : $i > $o]: 98.71/14.84 ((??((^[Y1 : $i]: 98.71/14.84 (Y0(Y1) & 98.71/14.84 (!!((^[Y2 : $i]: 98.71/14.84 (Y0(Y2) => (Y1 = Y2))))))))) => 98.71/14.84 (??((^[Y1 : $i]: 98.71/14.84 (!!((^[Y2 : $i]: 98.71/14.84 (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 ((Y0 != emptyset) => 98.71/14.84 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 (in(Y0, 98.71/14.84 setadjoin(Y1, emptyset)) => 98.71/14.84 (Y0 = Y1)))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 ((Y0 != Y1) => 98.71/14.84 (~(in(Y1, 98.71/14.84 setadjoin(Y0, 98.71/14.84 emptyset))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 ((Y0 = Y1) => 98.71/14.84 in(Y0, 98.71/14.84 setadjoin(Y1, emptyset))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 (in(Y0, 98.71/14.84 setadjoin(Y1, emptyset)) => 98.71/14.84 in(Y1, 98.71/14.84 setadjoin(Y0, emptyset))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 (!!((^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 setadjoin(Y0, 98.71/14.84 setadjoin( 98.71/14.84 Y1, 98.71/14.84 emptyset))) => 98.71/14.84 ((Y2 = Y1) | 98.71/14.84 (Y2 = Y0)))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 in(Y0, 98.71/14.84 setadjoin(Y0, 98.71/14.84 setadjoin(Y1, 98.71/14.84 emptyset))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 in(Y1, 98.71/14.84 setadjoin(Y0, 98.71/14.84 setadjoin(Y1, 98.71/14.84 emptyset))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i > $o]: 98.71/14.84 ((??((^[Y2 : $i]: 98.71/14.84 (in(Y2, Y0) & 98.71/14.84 Y1(Y2))))) => 98.71/14.84 (dsetconstr(Y0, Y1) != 98.71/14.84 emptyset)))))))) => 98.71/14.84 ((!!((^[Y0 : $i > $o]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 (in(Y1, emptyset) => 98.71/14.84 Y0(Y1)))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i > $o]: 98.71/14.84 ((~((!!((^[Y2 : $i]: 98.71/14.84 ( 98.71/14.84 in(Y2, 98.71/14.84 Y0) => 98.71/14.84 Y1(Y2))))))) => 98.71/14.84 (??((^[Y2 : $i]: 98.71/14.84 (in(Y2, Y0) & 98.71/14.84 (~(Y1(Y2)))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i > $o]: 98.71/14.84 ((!!((^[Y2 : $i]: 98.71/14.84 (in(Y2, Y0) => 98.71/14.84 (~(Y1(Y2))))))) => 98.71/14.84 (~((??((^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) & 98.71/14.84 Y1(Y2)))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i > $o]: 98.71/14.84 ((~((??((^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) & 98.71/14.84 Y1(Y2))))))) => 98.71/14.84 (!!((^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 ( 98.71/14.84 ~( 98.71/14.84 Y1(Y2)))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i > $o]: 98.71/14.84 ((??((^[Y2 : $i]: 98.71/14.84 ( 98.71/14.84 in(Y2, 98.71/14.84 Y0) & 98.71/14.84 ( 98.71/14.84 ~( 98.71/14.84 Y1(Y2))))))) => 98.71/14.84 (~((!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 Y1(Y2)))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $o]: 98.71/14.84 (Y0 => 98.71/14.84 in(emptyset, 98.71/14.84 prop2set(Y0)))))) => 98.71/14.84 ((!!((^[Y0 : $o]: 98.71/14.84 (Y0 => 98.71/14.84 set2prop( 98.71/14.84 prop2set(Y0)))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i > $o]: 98.71/14.84 ((~((??(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) & 98.71/14.84 Y1(Y2))))))) => 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 ( 98.71/14.84 ~( 98.71/14.84 Y1(Y2)))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i > $o]: 98.71/14.84 ((~(( 98.71/14.84 !!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 ( 98.71/14.84 in(Y2, 98.71/14.84 Y0) => 98.71/14.84 Y1(Y2))))))) => 98.71/14.84 (??(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 ( 98.71/14.84 in(Y2, 98.71/14.84 Y0) & 98.71/14.84 ( 98.71/14.84 ~( 98.71/14.84 Y1(Y2)))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i > $o]: 98.71/14.84 ((??(Y0)) => 98.71/14.84 ((!!((^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y0(Y1) => 98.71/14.84 (Y0(Y2) => 98.71/14.84 (Y1 = Y2))))))))) => 98.71/14.84 (??((^[Y1 : $i]: 98.71/14.84 (Y0(Y1) & 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y0(Y2) => 98.71/14.84 (Y1 = Y2)))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i > $o]: 98.71/14.84 ((??((^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y0(Y2) <=> 98.71/14.84 (Y2 = Y1)))))))) => 98.71/14.84 (??((^[Y1 : $i]: 98.71/14.84 (Y0(Y1) & 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y0(Y2) => 98.71/14.84 (Y1 = Y2))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 Y0 = Y1) => 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (( 98.71/14.84 Y2 = Y3) => 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 in(Y3, 98.71/14.84 Y1)))))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 Y0 = Y1) => 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (( 98.71/14.84 Y2 = Y3) => 98.71/14.84 (in(Y2, 98.71/14.84 Y0) <=> 98.71/14.84 in(Y3, 98.71/14.84 Y1)))))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i > $o]: 98.71/14.84 ((??((^[Y1 : $i]: 98.71/14.84 (Y0(Y1) & 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y0(Y2) => 98.71/14.84 (Y1 = Y2))))))))) => 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y0(Y1) => 98.71/14.84 (Y0(Y2) => 98.71/14.84 (Y1 = Y2))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i > $o]: 98.71/14.84 (!!((^[Y1 : $i > $o]: 98.71/14.84 (( 98.71/14.84 !!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (( 98.71/14.84 Y2 = Y3) => 98.71/14.84 (Y0(Y2) <=> 98.71/14.84 Y1(Y3))))))))) => 98.71/14.84 (( 98.71/14.84 ??(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y0(Y2) & 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (Y0(Y3) => 98.71/14.84 (Y2 = Y3))))))))) <=> 98.71/14.84 (??(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y1(Y2) & 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (Y1(Y3) => 98.71/14.84 (Y2 = Y3))))))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 Y0 = Y1) => 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (( 98.71/14.84 Y2 = Y3) => 98.71/14.84 (setadjoin( 98.71/14.84 Y0, Y2) = 98.71/14.84 setadjoin( 98.71/14.84 Y1, Y3)))))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 Y0 = Y1) => 98.71/14.84 ( 98.71/14.84 powerset( 98.71/14.84 Y0) = 98.71/14.84 powerset( 98.71/14.84 Y1))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 Y0 = Y1) => 98.71/14.84 (setunion( 98.71/14.84 Y0) = 98.71/14.84 setunion( 98.71/14.84 Y1))))))))) => 98.71/14.84 ((!!((^[Y0 : $i > $o]: 98.71/14.84 (( 98.71/14.84 ??(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (Y0(Y1) & 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y0(Y2) => 98.71/14.84 (Y1 = Y2))))))))) => 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y0(Y1) => 98.71/14.84 (Y0(Y2) => 98.71/14.84 (Y1 = Y2))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i > $o]: 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y1 : $i > $o]: 98.71/14.84 (( 98.71/14.84 !!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (( 98.71/14.84 Y2 = Y3) => 98.71/14.84 (Y0(Y2) <=> 98.71/14.84 Y1(Y3))))))))) => 98.71/14.84 (( 98.71/14.84 ??(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y0(Y2) & 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (Y0(Y3) => 98.71/14.84 (Y2 = Y3))))))))) => 98.71/14.84 (( 98.71/14.84 ??(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y1(Y2) & 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (Y1(Y3) => 98.71/14.84 (Y2 = Y3))))))))) => 98.71/14.84 (descr( 98.71/14.84 Y0) = 98.71/14.84 descr(Y1))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 Y0 = Y1) => 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i > $o]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i > $o]: 98.71/14.84 (( 98.71/14.84 !!(( 98.71/14.84 ^[Y4 : $i]: 98.71/14.84 (in(Y4, 98.71/14.84 Y0) => 98.71/14.84 (!!(( 98.71/14.84 ^[Y5 : $i]: 98.71/14.84 (in(Y5, 98.71/14.84 Y1) => 98.71/14.84 (( 98.71/14.84 Y4 = Y5) => 98.71/14.84 (Y2(Y4) <=> 98.71/14.84 Y3(Y5))))))))))) => 98.71/14.84 (dsetconstr( 98.71/14.84 Y0, Y2) = 98.71/14.84 dsetconstr( 98.71/14.84 Y1, Y3)))))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 !!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 in(Y2, 98.71/14.84 Y1))))) => 98.71/14.84 subset( 98.71/14.84 Y0, Y1)))))))) => 98.71/14.84 ((!!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 Y0 = Y1) => 98.71/14.84 subset( 98.71/14.84 Y1, Y0)))))))) => 98.71/14.84 ((!!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 Y0 = Y1) => 98.71/14.84 subset( 98.71/14.84 Y0, Y1)))))))) => 98.71/14.84 ((!!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 !!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 in(Y2, 98.71/14.84 Y1))))) => 98.71/14.84 subset( 98.71/14.84 Y0, Y1)))))))) => 98.71/14.84 ((!!( 98.71/14.84 subset( 98.71/14.84 emptyset))) => 98.71/14.84 (( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y0, Y1) => 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 in(Y2, 98.71/14.84 Y1)))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y0, Y1) => 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 Y1))) => 98.71/14.84 (~( 98.71/14.84 in(Y2, 98.71/14.84 Y0)))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 Y1))) => 98.71/14.84 (~( 98.71/14.84 subset( 98.71/14.84 Y0, Y1)))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 subset( 98.71/14.84 Y0, Y1))) => 98.71/14.84 (Y0 != Y1)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 Y1))) => 98.71/14.84 (Y0 != Y1)))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 subset( 98.71/14.84 Y0, Y0)))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y0, Y1) => 98.71/14.84 (subset( 98.71/14.84 Y1, Y2) => 98.71/14.84 subset( 98.71/14.84 Y0, Y2)))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 subset( 98.71/14.84 Y1, 98.71/14.84 setadjoin( 98.71/14.84 Y0, Y1)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y0, Y2) => 98.71/14.84 subset( 98.71/14.84 Y0, 98.71/14.84 setadjoin( 98.71/14.84 Y1, Y2)))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y0, Y1) => 98.71/14.84 in(Y0, 98.71/14.84 powerset( 98.71/14.84 Y1))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y0, Y1) => 98.71/14.84 (subset( 98.71/14.84 Y1, Y0) => 98.71/14.84 (Y0 = Y1))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y0, 98.71/14.84 emptyset) => 98.71/14.84 (Y0 = 98.71/14.84 emptyset))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y1, Y0) => 98.71/14.84 in(Y1, 98.71/14.84 powerset( 98.71/14.84 Y0))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (in(Y1, 98.71/14.84 powerset( 98.71/14.84 Y0)) => 98.71/14.84 subset( 98.71/14.84 Y1, Y0)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 in(Y0, 98.71/14.84 powerset( 98.71/14.84 Y0))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y0, Y1) => 98.71/14.84 subset( 98.71/14.84 powerset( 98.71/14.84 Y0), 98.71/14.84 powerset( 98.71/14.84 Y1))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i > $o]: 98.71/14.84 in( 98.71/14.84 dsetconstr( 98.71/14.84 Y0, Y1), 98.71/14.84 powerset( 98.71/14.84 Y0)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i > $o]: 98.71/14.84 subset( 98.71/14.84 dsetconstr( 98.71/14.84 Y0, Y1), 98.71/14.84 Y0))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 in(Y2, 98.71/14.84 binunion( 98.71/14.84 Y0, Y1)))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 in(Y1, 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 setadjoin( 98.71/14.84 Y1, 98.71/14.84 emptyset))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y1) => 98.71/14.84 in(Y2, 98.71/14.84 binunion( 98.71/14.84 Y0, Y1)))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $o]: 98.71/14.84 (in(Y2, 98.71/14.84 binunion( 98.71/14.84 Y0, Y1)) => 98.71/14.84 (( 98.71/14.84 in(Y2, 98.71/14.84 Y0) => Y3) => 98.71/14.84 (( 98.71/14.84 in(Y2, 98.71/14.84 Y1) => Y3) => 98.71/14.84 Y3))))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 binunion( 98.71/14.84 Y0, Y1)) => 98.71/14.84 (in(Y2, 98.71/14.84 Y1) | 98.71/14.84 in(Y2, 98.71/14.84 Y0)))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 subset( 98.71/14.84 Y0, 98.71/14.84 binunion( 98.71/14.84 Y0, Y1)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 subset( 98.71/14.84 Y1, 98.71/14.84 binunion( 98.71/14.84 Y0, Y1)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 (in(Y2, 98.71/14.84 Y1) => 98.71/14.84 in(Y2, 98.71/14.84 binintersect( 98.71/14.84 Y0, Y1))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y2, Y0) => 98.71/14.84 (subset( 98.71/14.84 Y2, Y1) => 98.71/14.84 subset( 98.71/14.84 Y2, 98.71/14.84 binintersect( 98.71/14.84 Y0, Y1))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 binintersect( 98.71/14.84 Y0, Y1)) => 98.71/14.84 in(Y2, 98.71/14.84 Y0))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 subset( 98.71/14.84 binintersect( 98.71/14.84 Y0, Y1), 98.71/14.84 Y0))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y0, Y1) => 98.71/14.84 (binintersect( 98.71/14.84 Y0, Y1) = 98.71/14.84 Y0)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 binintersect( 98.71/14.84 Y0, Y1) = 98.71/14.84 Y1) => 98.71/14.84 subset( 98.71/14.84 Y1, Y0)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 binintersect( 98.71/14.84 Y0, Y1)) => 98.71/14.84 in(Y2, 98.71/14.84 Y1))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 ~(( 98.71/14.84 ??(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) & 98.71/14.84 in(Y2, 98.71/14.84 Y1))))))) => 98.71/14.84 (binintersect( 98.71/14.84 Y0, Y1) = 98.71/14.84 emptyset)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 subset( 98.71/14.84 binintersect( 98.71/14.84 Y0, Y1), 98.71/14.84 Y1))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y1, Y0) => 98.71/14.84 (binintersect( 98.71/14.84 Y0, Y1) = 98.71/14.84 Y1)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 binintersect( 98.71/14.84 Y0, Y1) = 98.71/14.84 Y0) => 98.71/14.84 subset( 98.71/14.84 Y0, Y1)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (binintersect( 98.71/14.84 Y0, 98.71/14.84 binunion( 98.71/14.84 Y1, Y2)) = 98.71/14.84 binunion( 98.71/14.84 binintersect( 98.71/14.84 Y0, Y1), 98.71/14.84 binintersect( 98.71/14.84 Y0, Y2)))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 Y1))) => 98.71/14.84 in(Y2, 98.71/14.84 setminus( 98.71/14.84 Y0, Y1))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 setminus( 98.71/14.84 Y0, Y1)) => 98.71/14.84 in(Y2, 98.71/14.84 Y0))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 setminus( 98.71/14.84 Y0, Y1)) => 98.71/14.84 (~( 98.71/14.84 in(Y2, 98.71/14.84 Y1))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y0, Y1) => 98.71/14.84 (setminus( 98.71/14.84 Y0, Y1) = 98.71/14.84 emptyset)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 setminus( 98.71/14.84 Y0, Y1)))) => 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 in(Y2, 98.71/14.84 Y1)))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 setminus( 98.71/14.84 Y0, Y1)))) => 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 Y1))) => 98.71/14.84 (~( 98.71/14.84 in(Y2, 98.71/14.84 Y0)))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 Y0))) => 98.71/14.84 (~( 98.71/14.84 in(Y2, 98.71/14.84 setminus( 98.71/14.84 Y0, Y1)))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y1) => 98.71/14.84 (~( 98.71/14.84 in(Y2, 98.71/14.84 setminus( 98.71/14.84 Y0, Y1)))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 subset( 98.71/14.84 setminus( 98.71/14.84 Y0, Y1), 98.71/14.84 Y0))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 setminus( 98.71/14.84 Y0, Y1) = 98.71/14.84 emptyset) => 98.71/14.84 subset( 98.71/14.84 Y0, Y1)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 symdiff( 98.71/14.84 Y0, Y1)) => 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $o]: 98.71/14.84 (( 98.71/14.84 in(Y2, 98.71/14.84 Y0) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 Y1))) => 98.71/14.84 Y3)) => 98.71/14.84 (( 98.71/14.84 ( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 Y0))) => 98.71/14.84 ( 98.71/14.84 in(Y2, 98.71/14.84 Y1) => Y3)) => 98.71/14.84 Y3))))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 Y1))) => 98.71/14.84 in(Y2, 98.71/14.84 symdiff( 98.71/14.84 Y0, Y1))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 Y0))) => 98.71/14.84 (in(Y2, 98.71/14.84 Y1) => 98.71/14.84 in(Y2, 98.71/14.84 symdiff( 98.71/14.84 Y0, Y1))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 (in(Y2, 98.71/14.84 Y1) => 98.71/14.84 (~( 98.71/14.84 in(Y2, 98.71/14.84 symdiff( 98.71/14.84 Y0, Y1))))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 Y0))) => 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 Y1))) => 98.71/14.84 (~( 98.71/14.84 in(Y2, 98.71/14.84 symdiff( 98.71/14.84 Y0, Y1))))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 in(Y1, 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 setadjoin( 98.71/14.84 Y1, 98.71/14.84 emptyset))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 in(Y0, 98.71/14.84 setunion( 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 setadjoin( 98.71/14.84 Y1, 98.71/14.84 emptyset)), 98.71/14.84 emptyset)))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 in(Y1, 98.71/14.84 setunion( 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 setadjoin( 98.71/14.84 Y1, 98.71/14.84 emptyset)), 98.71/14.84 emptyset)))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (??(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 setunion( 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 setadjoin( 98.71/14.84 Y1, 98.71/14.84 emptyset)), 98.71/14.84 emptyset)))) & 98.71/14.84 (??(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (in(Y3, 98.71/14.84 setunion( 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 setadjoin( 98.71/14.84 Y1, 98.71/14.84 emptyset)), 98.71/14.84 emptyset)))) & 98.71/14.84 (setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 setadjoin( 98.71/14.84 Y1, 98.71/14.84 emptyset)), 98.71/14.84 emptyset)) = 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 setadjoin( 98.71/14.84 Y3, 98.71/14.84 emptyset)), 98.71/14.84 emptyset))))))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (??(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 setunion( 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 setadjoin( 98.71/14.84 Y1, 98.71/14.84 emptyset)), 98.71/14.84 emptyset)))) & 98.71/14.84 (??(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (in(Y3, 98.71/14.84 setunion( 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 setadjoin( 98.71/14.84 Y1, 98.71/14.84 emptyset)), 98.71/14.84 emptyset)))) & 98.71/14.84 (setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 setadjoin( 98.71/14.84 Y1, 98.71/14.84 emptyset)), 98.71/14.84 emptyset)) = 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 setadjoin( 98.71/14.84 Y3, 98.71/14.84 emptyset)), 98.71/14.84 emptyset))))))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (in(Y1, 98.71/14.84 Y0) => 98.71/14.84 subset( 98.71/14.84 setadjoin( 98.71/14.84 Y1, 98.71/14.84 emptyset), 98.71/14.84 Y0)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (in(Y1, 98.71/14.84 Y0) => 98.71/14.84 in( 98.71/14.84 setadjoin( 98.71/14.84 Y1, 98.71/14.84 emptyset), 98.71/14.84 powerset( 98.71/14.84 Y0))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 in( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 emptyset), 98.71/14.84 powerset( 98.71/14.84 binunion( 98.71/14.84 Y0, Y1))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 setadjoin( 98.71/14.84 Y1, 98.71/14.84 emptyset))) => 98.71/14.84 (( 98.71/14.84 Y2 = Y1) | 98.71/14.84 (Y2 = Y0)))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (in(Y3, 98.71/14.84 Y1) => 98.71/14.84 subset( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 setadjoin( 98.71/14.84 Y3, 98.71/14.84 emptyset)), 98.71/14.84 binunion( 98.71/14.84 Y0, Y1)))))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (in(Y3, 98.71/14.84 Y1) => 98.71/14.84 in( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 setadjoin( 98.71/14.84 Y3, 98.71/14.84 emptyset)), 98.71/14.84 powerset( 98.71/14.84 binunion( 98.71/14.84 Y0, Y1))))))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (in(Y3, 98.71/14.84 Y1) => 98.71/14.84 subset( 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 setadjoin( 98.71/14.84 Y3, 98.71/14.84 emptyset)), 98.71/14.84 emptyset)), 98.71/14.84 powerset( 98.71/14.84 binunion( 98.71/14.84 Y0, Y1))))))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (in(Y3, 98.71/14.84 Y1) => 98.71/14.84 in( 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 setadjoin( 98.71/14.84 Y3, 98.71/14.84 emptyset)), 98.71/14.84 emptyset)), 98.71/14.84 powerset( 98.71/14.84 powerset( 98.71/14.84 binunion( 98.71/14.84 Y0, Y1)))))))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (in(Y3, 98.71/14.84 Y1) => 98.71/14.84 in( 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 setadjoin( 98.71/14.84 Y3, 98.71/14.84 emptyset)), 98.71/14.84 emptyset)), 98.71/14.84 powerset( 98.71/14.84 powerset( 98.71/14.84 binunion( 98.71/14.84 Y0, Y1)))))))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (in(Y3, 98.71/14.84 Y1) => 98.71/14.84 in( 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 setadjoin( 98.71/14.84 Y3, 98.71/14.84 emptyset)), 98.71/14.84 emptyset)), 98.71/14.84 dsetconstr( 98.71/14.84 powerset( 98.71/14.84 powerset( 98.71/14.84 binunion( 98.71/14.84 Y0, Y1))), 98.71/14.84 (^[Y4 : $i]: 98.71/14.84 (??(( 98.71/14.84 ^[Y5 : $i]: 98.71/14.84 (in(Y5, 98.71/14.84 Y0) & 98.71/14.84 (??(( 98.71/14.84 ^[Y6 : $i]: 98.71/14.84 (in(Y6, 98.71/14.84 Y1) & 98.71/14.84 (Y4 = 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y5, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y5, 98.71/14.84 setadjoin( 98.71/14.84 Y6, 98.71/14.84 emptyset)), 98.71/14.84 emptyset)))))))))))))))))))))))))))) => 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 dsetconstr( 98.71/14.84 powerset( 98.71/14.84 powerset( 98.71/14.84 binunion( 98.71/14.84 Y0, Y1))), 98.71/14.84 (^[Y3 : $i]: 98.71/14.84 (??(( 98.71/14.84 ^[Y4 : $i]: 98.71/14.84 (in(Y4, 98.71/14.84 Y0) & 98.71/14.84 (??(( 98.71/14.84 ^[Y5 : $i]: 98.71/14.84 (in(Y5, 98.71/14.84 Y1) & 98.71/14.84 (Y3 = 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y4, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y4, 98.71/14.84 setadjoin( 98.71/14.84 Y5, 98.71/14.84 emptyset)), 98.71/14.84 emptyset)))))))))))))) => 98.71/14.84 (??(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (( 98.71/14.84 ??(( 98.71/14.84 ^[Y4 : $i]: 98.71/14.84 (in(Y4, 98.71/14.84 Y1) & 98.71/14.84 (Y2 = 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y3, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y3, 98.71/14.84 setadjoin( 98.71/14.84 Y4, 98.71/14.84 emptyset)), 98.71/14.84 emptyset))))))) & 98.71/14.84 in(Y3, 98.71/14.84 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 98.71/14.84 inference('lazy_cnf_imply', [status(thm)], ['175'])). 98.71/14.84 tff('177', plain, 98.71/14.84 ~ ((!!((^[Y0 : $i]: (in(Y0, emptyset) => (!!((^[Y1 : $o]: Y1))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 98.71/14.84 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 98.71/14.84 ((!!((^[Y0 : $i > $o]: 98.71/14.84 ((??((^[Y1 : $i]: 98.71/14.84 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 98.71/14.84 (??(Y0)))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 98.71/14.84 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 98.71/14.84 (Y0 = Y1))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => (Y0 = emptyset))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => (Y0 = emptyset))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i > $o]: 98.71/14.84 (!!((^[Y2 : $i]: 98.71/14.84 (in(Y2, Y0) => 98.71/14.84 (in(Y2, dsetconstr(Y0, Y1)) <=> Y1(Y2)))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i > $o]: 98.71/14.84 (!!((^[Y2 : $i]: 98.71/14.84 (in(Y2, Y0) => 98.71/14.84 (Y1(Y2) => 98.71/14.84 (dsetconstr(Y0, Y1) != emptyset)))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 ((??((^[Y1 : $i]: in(Y1, Y0)))) => (Y0 != emptyset))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 98.71/14.84 (in(emptyset, setadjoin(emptyset, emptyset)) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 (!!((^[Y2 : $i]: 98.71/14.84 (in(Y2, Y1) => 98.71/14.84 in(Y2, setadjoin(Y0, Y1)))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 (!!((^[Y2 : $i]: 98.71/14.84 (in(Y2, setadjoin(Y0, Y1)) => 98.71/14.84 (!!((^[Y3 : $o]: 98.71/14.84 (((Y2 = Y0) => Y3) => 98.71/14.84 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 (!!((^[Y2 : $i]: 98.71/14.84 (in(Y2, setadjoin(Y0, Y1)) => 98.71/14.84 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 ((!!((^[Y2 : $i]: 98.71/14.84 (in(Y2, Y1) => in(Y2, Y0))))) => 98.71/14.84 in(Y1, powerset(Y0))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.71/14.84 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 (!!((^[Y2 : $i]: 98.71/14.84 (in(Y1, powerset(Y0)) => 98.71/14.84 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 (!!((^[Y2 : $i]: 98.71/14.84 (in(Y1, Y2) => 98.71/14.84 (in(Y2, Y0) => 98.71/14.84 in(Y1, setunion(Y0))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 (in(Y1, setunion(Y0)) => 98.71/14.84 (!!((^[Y2 : $o]: 98.71/14.84 ((!!((^[Y3 : $i]: 98.71/14.84 (in(Y1, Y3) => 98.71/14.84 (in(Y3, Y0) => Y2))))) => 98.71/14.84 Y2))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 (in(Y1, Y0) => 98.71/14.84 in(Y1, powerset(setunion(Y0)))))))))) => 98.71/14.84 ((!!((^[Y0 : $i > $o]: 98.71/14.84 ((??((^[Y1 : $i]: 98.71/14.84 (Y0(Y1) & 98.71/14.84 (!!((^[Y2 : $i]: 98.71/14.84 (Y0(Y2) => (Y1 = Y2))))))))) => 98.71/14.84 (??((^[Y1 : $i]: 98.71/14.84 (!!((^[Y2 : $i]: 98.71/14.84 (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 ((Y0 != emptyset) => 98.71/14.84 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 (in(Y0, 98.71/14.84 setadjoin(Y1, emptyset)) => 98.71/14.84 (Y0 = Y1)))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 ((Y0 != Y1) => 98.71/14.84 (~(in(Y1, 98.71/14.84 setadjoin(Y0, emptyset))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 ((Y0 = Y1) => 98.71/14.84 in(Y0, 98.71/14.84 setadjoin(Y1, emptyset))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 (in(Y0, 98.71/14.84 setadjoin(Y1, emptyset)) => 98.71/14.84 in(Y1, 98.71/14.84 setadjoin(Y0, emptyset))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 (!!((^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 setadjoin(Y0, 98.71/14.84 setadjoin(Y1, 98.71/14.84 emptyset))) => 98.71/14.84 ((Y2 = Y1) | 98.71/14.84 (Y2 = Y0)))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 in(Y0, 98.71/14.84 setadjoin(Y0, 98.71/14.84 setadjoin(Y1, 98.71/14.84 emptyset))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 in(Y1, 98.71/14.84 setadjoin(Y0, 98.71/14.84 setadjoin(Y1, 98.71/14.84 emptyset))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i > $o]: 98.71/14.84 ((??((^[Y2 : $i]: 98.71/14.84 (in(Y2, Y0) & 98.71/14.84 Y1(Y2))))) => 98.71/14.84 (dsetconstr(Y0, Y1) != 98.71/14.84 emptyset)))))))) => 98.71/14.84 ((!!((^[Y0 : $i > $o]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 (in(Y1, emptyset) => 98.71/14.84 Y0(Y1)))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i > $o]: 98.71/14.84 ((~((!!((^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 Y1(Y2))))))) => 98.71/14.84 (??((^[Y2 : $i]: 98.71/14.84 (in(Y2, Y0) & 98.71/14.84 (~(Y1(Y2)))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i > $o]: 98.71/14.84 ((!!((^[Y2 : $i]: 98.71/14.84 (in(Y2, Y0) => 98.71/14.84 (~(Y1(Y2))))))) => 98.71/14.84 (~((??((^[Y2 : $i]: 98.71/14.84 ( 98.71/14.84 in(Y2, 98.71/14.84 Y0) & 98.71/14.84 Y1(Y2)))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i > $o]: 98.71/14.84 ((~((??((^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) & 98.71/14.84 Y1(Y2))))))) => 98.71/14.84 (!!((^[Y2 : $i]: 98.71/14.84 (in(Y2, Y0) => 98.71/14.84 (~(Y1(Y2)))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i > $o]: 98.71/14.84 ((??((^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) & 98.71/14.84 ( 98.71/14.84 ~( 98.71/14.84 Y1(Y2))))))) => 98.71/14.84 (~((!!((^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 Y1(Y2)))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $o]: 98.71/14.84 (Y0 => 98.71/14.84 in(emptyset, 98.71/14.84 prop2set(Y0)))))) => 98.71/14.84 ((!!((^[Y0 : $o]: 98.71/14.84 (Y0 => 98.71/14.84 set2prop(prop2set(Y0)))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i > $o]: 98.71/14.84 ((~((??(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) & 98.71/14.84 Y1(Y2))))))) => 98.71/14.84 (!!((^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 (~( 98.71/14.84 Y1(Y2)))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i > $o]: 98.71/14.84 ((~((!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 Y1(Y2))))))) => 98.71/14.84 (??(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) & 98.71/14.84 ( 98.71/14.84 ~( 98.71/14.84 Y1(Y2)))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i > $o]: 98.71/14.84 ((??(Y0)) => 98.71/14.84 ((!!((^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y0(Y1) => 98.71/14.84 (Y0(Y2) => 98.71/14.84 (Y1 = Y2))))))))) => 98.71/14.84 (??((^[Y1 : $i]: 98.71/14.84 (Y0(Y1) & 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y0(Y2) => 98.71/14.84 (Y1 = Y2)))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i > $o]: 98.71/14.84 ((??((^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y0(Y2) <=> 98.71/14.84 (Y2 = Y1)))))))) => 98.71/14.84 (??((^[Y1 : $i]: 98.71/14.84 (Y0(Y1) & 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y0(Y2) => 98.71/14.84 (Y1 = Y2))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 ((Y0 = Y1) => 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (( 98.71/14.84 Y2 = Y3) => 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 in(Y3, 98.71/14.84 Y1)))))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 Y0 = Y1) => 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (( 98.71/14.84 Y2 = Y3) => 98.71/14.84 (in(Y2, 98.71/14.84 Y0) <=> 98.71/14.84 in(Y3, 98.71/14.84 Y1)))))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i > $o]: 98.71/14.84 ((??((^[Y1 : $i]: 98.71/14.84 (Y0(Y1) & 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y0(Y2) => 98.71/14.84 (Y1 = Y2))))))))) => 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y0(Y1) => 98.71/14.84 (Y0(Y2) => 98.71/14.84 (Y1 = Y2))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i > $o]: 98.71/14.84 (!!((^[Y1 : $i > $o]: 98.71/14.84 (( 98.71/14.84 !!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (( 98.71/14.84 Y2 = Y3) => 98.71/14.84 (Y0(Y2) <=> 98.71/14.84 Y1(Y3))))))))) => 98.71/14.84 (( 98.71/14.84 ??(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y0(Y2) & 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (Y0(Y3) => 98.71/14.84 (Y2 = Y3))))))))) <=> 98.71/14.84 (??(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y1(Y2) & 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (Y1(Y3) => 98.71/14.84 (Y2 = Y3))))))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 Y0 = Y1) => 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (( 98.71/14.84 Y2 = Y3) => 98.71/14.84 (setadjoin( 98.71/14.84 Y0, Y2) = 98.71/14.84 setadjoin( 98.71/14.84 Y1, Y3)))))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 Y0 = Y1) => 98.71/14.84 ( 98.71/14.84 powerset( 98.71/14.84 Y0) = 98.71/14.84 powerset( 98.71/14.84 Y1))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 Y0 = Y1) => 98.71/14.84 ( 98.71/14.84 setunion( 98.71/14.84 Y0) = 98.71/14.84 setunion( 98.71/14.84 Y1))))))))) => 98.71/14.84 ((!!((^[Y0 : $i > $o]: 98.71/14.84 ((??(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (Y0(Y1) & 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y0(Y2) => 98.71/14.84 (Y1 = Y2))))))))) => 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y0(Y1) => 98.71/14.84 (Y0(Y2) => 98.71/14.84 (Y1 = Y2))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i > $o]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i > $o]: 98.71/14.84 (( 98.71/14.84 !!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (( 98.71/14.84 Y2 = Y3) => 98.71/14.84 (Y0(Y2) <=> 98.71/14.84 Y1(Y3))))))))) => 98.71/14.84 (( 98.71/14.84 ??(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y0(Y2) & 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (Y0(Y3) => 98.71/14.84 (Y2 = Y3))))))))) => 98.71/14.84 (( 98.71/14.84 ??(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y1(Y2) & 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (Y1(Y3) => 98.71/14.84 (Y2 = Y3))))))))) => 98.71/14.84 (descr( 98.71/14.84 Y0) = 98.71/14.84 descr(Y1))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 Y0 = Y1) => 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i > $o]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i > $o]: 98.71/14.84 (( 98.71/14.84 !!(( 98.71/14.84 ^[Y4 : $i]: 98.71/14.84 (in(Y4, 98.71/14.84 Y0) => 98.71/14.84 (!!(( 98.71/14.84 ^[Y5 : $i]: 98.71/14.84 (in(Y5, 98.71/14.84 Y1) => 98.71/14.84 (( 98.71/14.84 Y4 = Y5) => 98.71/14.84 (Y2(Y4) <=> 98.71/14.84 Y3(Y5))))))))))) => 98.71/14.84 (dsetconstr( 98.71/14.84 Y0, Y2) = 98.71/14.84 dsetconstr( 98.71/14.84 Y1, Y3)))))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 !!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 in(Y2, 98.71/14.84 Y1))))) => 98.71/14.84 subset( 98.71/14.84 Y0, Y1)))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 Y0 = Y1) => 98.71/14.84 subset( 98.71/14.84 Y1, Y0)))))))) => 98.71/14.84 ((!!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 Y0 = Y1) => 98.71/14.84 subset( 98.71/14.84 Y0, Y1)))))))) => 98.71/14.84 ((!!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 !!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 in(Y2, 98.71/14.84 Y1))))) => 98.71/14.84 subset( 98.71/14.84 Y0, Y1)))))))) => 98.71/14.84 ((!!( 98.71/14.84 subset( 98.71/14.84 emptyset))) => 98.71/14.84 ((!!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y0, Y1) => 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 in(Y2, 98.71/14.84 Y1)))))))))))) => 98.71/14.84 (( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y0, Y1) => 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 Y1))) => 98.71/14.84 (~( 98.71/14.84 in(Y2, 98.71/14.84 Y0)))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 Y1))) => 98.71/14.84 (~( 98.71/14.84 subset( 98.71/14.84 Y0, Y1)))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 subset( 98.71/14.84 Y0, Y1))) => 98.71/14.84 (Y0 != Y1)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 Y1))) => 98.71/14.84 (Y0 != Y1)))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 subset( 98.71/14.84 Y0, Y0)))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y0, Y1) => 98.71/14.84 (subset( 98.71/14.84 Y1, Y2) => 98.71/14.84 subset( 98.71/14.84 Y0, Y2)))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 subset( 98.71/14.84 Y1, 98.71/14.84 setadjoin( 98.71/14.84 Y0, Y1)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y0, Y2) => 98.71/14.84 subset( 98.71/14.84 Y0, 98.71/14.84 setadjoin( 98.71/14.84 Y1, Y2)))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y0, Y1) => 98.71/14.84 in(Y0, 98.71/14.84 powerset( 98.71/14.84 Y1))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y0, Y1) => 98.71/14.84 (subset( 98.71/14.84 Y1, Y0) => 98.71/14.84 (Y0 = Y1))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y0, 98.71/14.84 emptyset) => 98.71/14.84 (Y0 = 98.71/14.84 emptyset))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y1, Y0) => 98.71/14.84 in(Y1, 98.71/14.84 powerset( 98.71/14.84 Y0))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (in(Y1, 98.71/14.84 powerset( 98.71/14.84 Y0)) => 98.71/14.84 subset( 98.71/14.84 Y1, Y0)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 in(Y0, 98.71/14.84 powerset( 98.71/14.84 Y0))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y0, Y1) => 98.71/14.84 subset( 98.71/14.84 powerset( 98.71/14.84 Y0), 98.71/14.84 powerset( 98.71/14.84 Y1))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i > $o]: 98.71/14.84 in( 98.71/14.84 dsetconstr( 98.71/14.84 Y0, Y1), 98.71/14.84 powerset( 98.71/14.84 Y0)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i > $o]: 98.71/14.84 subset( 98.71/14.84 dsetconstr( 98.71/14.84 Y0, Y1), 98.71/14.84 Y0))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 in(Y2, 98.71/14.84 binunion( 98.71/14.84 Y0, Y1)))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 in(Y1, 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 setadjoin( 98.71/14.84 Y1, 98.71/14.84 emptyset))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y1) => 98.71/14.84 in(Y2, 98.71/14.84 binunion( 98.71/14.84 Y0, Y1)))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $o]: 98.71/14.84 (in(Y2, 98.71/14.84 binunion( 98.71/14.84 Y0, Y1)) => 98.71/14.84 (( 98.71/14.84 in(Y2, 98.71/14.84 Y0) => Y3) => 98.71/14.84 (( 98.71/14.84 in(Y2, 98.71/14.84 Y1) => Y3) => 98.71/14.84 Y3))))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 binunion( 98.71/14.84 Y0, Y1)) => 98.71/14.84 (in(Y2, 98.71/14.84 Y1) | 98.71/14.84 in(Y2, 98.71/14.84 Y0)))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 subset( 98.71/14.84 Y0, 98.71/14.84 binunion( 98.71/14.84 Y0, Y1)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 subset( 98.71/14.84 Y1, 98.71/14.84 binunion( 98.71/14.84 Y0, Y1)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 (in(Y2, 98.71/14.84 Y1) => 98.71/14.84 in(Y2, 98.71/14.84 binintersect( 98.71/14.84 Y0, Y1))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y2, Y0) => 98.71/14.84 (subset( 98.71/14.84 Y2, Y1) => 98.71/14.84 subset( 98.71/14.84 Y2, 98.71/14.84 binintersect( 98.71/14.84 Y0, Y1))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 binintersect( 98.71/14.84 Y0, Y1)) => 98.71/14.84 in(Y2, 98.71/14.84 Y0))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 subset( 98.71/14.84 binintersect( 98.71/14.84 Y0, Y1), 98.71/14.84 Y0))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y0, Y1) => 98.71/14.84 (binintersect( 98.71/14.84 Y0, Y1) = 98.71/14.84 Y0)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 binintersect( 98.71/14.84 Y0, Y1) = 98.71/14.84 Y1) => 98.71/14.84 subset( 98.71/14.84 Y1, Y0)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 binintersect( 98.71/14.84 Y0, Y1)) => 98.71/14.84 in(Y2, 98.71/14.84 Y1))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 ~(( 98.71/14.84 ??(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) & 98.71/14.84 in(Y2, 98.71/14.84 Y1))))))) => 98.71/14.84 (binintersect( 98.71/14.84 Y0, Y1) = 98.71/14.84 emptyset)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 subset( 98.71/14.84 binintersect( 98.71/14.84 Y0, Y1), 98.71/14.84 Y1))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y1, Y0) => 98.71/14.84 (binintersect( 98.71/14.84 Y0, Y1) = 98.71/14.84 Y1)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 binintersect( 98.71/14.84 Y0, Y1) = 98.71/14.84 Y0) => 98.71/14.84 subset( 98.71/14.84 Y0, Y1)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (binintersect( 98.71/14.84 Y0, 98.71/14.84 binunion( 98.71/14.84 Y1, Y2)) = 98.71/14.84 binunion( 98.71/14.84 binintersect( 98.71/14.84 Y0, Y1), 98.71/14.84 binintersect( 98.71/14.84 Y0, Y2)))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 Y1))) => 98.71/14.84 in(Y2, 98.71/14.84 setminus( 98.71/14.84 Y0, Y1))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 setminus( 98.71/14.84 Y0, Y1)) => 98.71/14.84 in(Y2, 98.71/14.84 Y0))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 setminus( 98.71/14.84 Y0, Y1)) => 98.71/14.84 (~( 98.71/14.84 in(Y2, 98.71/14.84 Y1))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y0, Y1) => 98.71/14.84 (setminus( 98.71/14.84 Y0, Y1) = 98.71/14.84 emptyset)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 setminus( 98.71/14.84 Y0, Y1)))) => 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 in(Y2, 98.71/14.84 Y1)))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 setminus( 98.71/14.84 Y0, Y1)))) => 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 Y1))) => 98.71/14.84 (~( 98.71/14.84 in(Y2, 98.71/14.84 Y0)))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 Y0))) => 98.71/14.84 (~( 98.71/14.84 in(Y2, 98.71/14.84 setminus( 98.71/14.84 Y0, Y1)))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y1) => 98.71/14.84 (~( 98.71/14.84 in(Y2, 98.71/14.84 setminus( 98.71/14.84 Y0, Y1)))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 subset( 98.71/14.84 setminus( 98.71/14.84 Y0, Y1), 98.71/14.84 Y0))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 setminus( 98.71/14.84 Y0, Y1) = 98.71/14.84 emptyset) => 98.71/14.84 subset( 98.71/14.84 Y0, Y1)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 symdiff( 98.71/14.84 Y0, Y1)) => 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $o]: 98.71/14.84 (( 98.71/14.84 in(Y2, 98.71/14.84 Y0) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 Y1))) => 98.71/14.84 Y3)) => 98.71/14.84 (( 98.71/14.84 ( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 Y0))) => 98.71/14.84 ( 98.71/14.84 in(Y2, 98.71/14.84 Y1) => Y3)) => 98.71/14.84 Y3))))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 Y1))) => 98.71/14.84 in(Y2, 98.71/14.84 symdiff( 98.71/14.84 Y0, Y1))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 Y0))) => 98.71/14.84 (in(Y2, 98.71/14.84 Y1) => 98.71/14.84 in(Y2, 98.71/14.84 symdiff( 98.71/14.84 Y0, Y1))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 (in(Y2, 98.71/14.84 Y1) => 98.71/14.84 (~( 98.71/14.84 in(Y2, 98.71/14.84 symdiff( 98.71/14.84 Y0, Y1))))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 Y0))) => 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 Y1))) => 98.71/14.84 (~( 98.71/14.84 in(Y2, 98.71/14.84 symdiff( 98.71/14.84 Y0, Y1))))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 in(Y1, 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 setadjoin( 98.71/14.84 Y1, 98.71/14.84 emptyset))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 in(Y0, 98.71/14.84 setunion( 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 setadjoin( 98.71/14.84 Y1, 98.71/14.84 emptyset)), 98.71/14.84 emptyset)))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 in(Y1, 98.71/14.84 setunion( 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 setadjoin( 98.71/14.84 Y1, 98.71/14.84 emptyset)), 98.71/14.84 emptyset)))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (??(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 setunion( 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 setadjoin( 98.71/14.84 Y1, 98.71/14.84 emptyset)), 98.71/14.84 emptyset)))) & 98.71/14.84 (??(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (in(Y3, 98.71/14.84 setunion( 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 setadjoin( 98.71/14.84 Y1, 98.71/14.84 emptyset)), 98.71/14.84 emptyset)))) & 98.71/14.84 (setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 setadjoin( 98.71/14.84 Y1, 98.71/14.84 emptyset)), 98.71/14.84 emptyset)) = 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 setadjoin( 98.71/14.84 Y3, 98.71/14.84 emptyset)), 98.71/14.84 emptyset))))))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (??(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 setunion( 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 setadjoin( 98.71/14.84 Y1, 98.71/14.84 emptyset)), 98.71/14.84 emptyset)))) & 98.71/14.84 (??(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (in(Y3, 98.71/14.84 setunion( 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 setadjoin( 98.71/14.84 Y1, 98.71/14.84 emptyset)), 98.71/14.84 emptyset)))) & 98.71/14.84 (setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 setadjoin( 98.71/14.84 Y1, 98.71/14.84 emptyset)), 98.71/14.84 emptyset)) = 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 setadjoin( 98.71/14.84 Y3, 98.71/14.84 emptyset)), 98.71/14.84 emptyset))))))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (in(Y1, 98.71/14.84 Y0) => 98.71/14.84 subset( 98.71/14.84 setadjoin( 98.71/14.84 Y1, 98.71/14.84 emptyset), 98.71/14.84 Y0)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (in(Y1, 98.71/14.84 Y0) => 98.71/14.84 in( 98.71/14.84 setadjoin( 98.71/14.84 Y1, 98.71/14.84 emptyset), 98.71/14.84 powerset( 98.71/14.84 Y0))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 in( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 emptyset), 98.71/14.84 powerset( 98.71/14.84 binunion( 98.71/14.84 Y0, Y1))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 setadjoin( 98.71/14.84 Y0, 98.71/14.84 setadjoin( 98.71/14.84 Y1, 98.71/14.84 emptyset))) => 98.71/14.84 (( 98.71/14.84 Y2 = Y1) | 98.71/14.84 (Y2 = Y0)))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (in(Y3, 98.71/14.84 Y1) => 98.71/14.84 subset( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 setadjoin( 98.71/14.84 Y3, 98.71/14.84 emptyset)), 98.71/14.84 binunion( 98.71/14.84 Y0, Y1)))))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (in(Y3, 98.71/14.84 Y1) => 98.71/14.84 in( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 setadjoin( 98.71/14.84 Y3, 98.71/14.84 emptyset)), 98.71/14.84 powerset( 98.71/14.84 binunion( 98.71/14.84 Y0, Y1))))))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (in(Y3, 98.71/14.84 Y1) => 98.71/14.84 subset( 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 setadjoin( 98.71/14.84 Y3, 98.71/14.84 emptyset)), 98.71/14.84 emptyset)), 98.71/14.84 powerset( 98.71/14.84 binunion( 98.71/14.84 Y0, Y1))))))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (in(Y3, 98.71/14.84 Y1) => 98.71/14.84 in( 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 setadjoin( 98.71/14.84 Y3, 98.71/14.84 emptyset)), 98.71/14.84 emptyset)), 98.71/14.84 powerset( 98.71/14.84 powerset( 98.71/14.84 binunion( 98.71/14.84 Y0, Y1)))))))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (in(Y3, 98.71/14.84 Y1) => 98.71/14.84 in( 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 setadjoin( 98.71/14.84 Y3, 98.71/14.84 emptyset)), 98.71/14.84 emptyset)), 98.71/14.84 powerset( 98.71/14.84 powerset( 98.71/14.84 binunion( 98.71/14.84 Y0, Y1)))))))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (in(Y3, 98.71/14.84 Y1) => 98.71/14.84 in( 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y2, 98.71/14.84 setadjoin( 98.71/14.84 Y3, 98.71/14.84 emptyset)), 98.71/14.84 emptyset)), 98.71/14.84 dsetconstr( 98.71/14.84 powerset( 98.71/14.84 powerset( 98.71/14.84 binunion( 98.71/14.84 Y0, Y1))), 98.71/14.84 (^[Y4 : $i]: 98.71/14.84 (??(( 98.71/14.84 ^[Y5 : $i]: 98.71/14.84 (in(Y5, 98.71/14.84 Y0) & 98.71/14.84 (??(( 98.71/14.84 ^[Y6 : $i]: 98.71/14.84 (in(Y6, 98.71/14.84 Y1) & 98.71/14.84 (Y4 = 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y5, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y5, 98.71/14.84 setadjoin( 98.71/14.84 Y6, 98.71/14.84 emptyset)), 98.71/14.84 emptyset)))))))))))))))))))))))))))) => 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 dsetconstr( 98.71/14.84 powerset( 98.71/14.84 powerset( 98.71/14.84 binunion( 98.71/14.84 Y0, Y1))), 98.71/14.84 (^[Y3 : $i]: 98.71/14.84 (??(( 98.71/14.84 ^[Y4 : $i]: 98.71/14.84 (in(Y4, 98.71/14.84 Y0) & 98.71/14.84 (??(( 98.71/14.84 ^[Y5 : $i]: 98.71/14.84 (in(Y5, 98.71/14.84 Y1) & 98.71/14.84 (Y3 = 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y4, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y4, 98.71/14.84 setadjoin( 98.71/14.84 Y5, 98.71/14.84 emptyset)), 98.71/14.84 emptyset)))))))))))))) => 98.71/14.84 (??(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (( 98.71/14.84 ??(( 98.71/14.84 ^[Y4 : $i]: 98.71/14.84 (in(Y4, 98.71/14.84 Y1) & 98.71/14.84 (Y2 = 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y3, 98.71/14.84 emptyset), 98.71/14.84 setadjoin( 98.71/14.84 setadjoin( 98.71/14.84 Y3, 98.71/14.84 setadjoin( 98.71/14.84 Y4, 98.71/14.84 emptyset)), 98.71/14.84 emptyset))))))) & 98.71/14.84 in(Y3, 98.71/14.84 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 98.71/14.84 inference('lazy_cnf_imply', [status(thm)], ['176'])). 98.71/14.84 tff('178', plain, 98.71/14.84 ~ ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 98.71/14.84 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 98.71/14.84 ((!!((^[Y0 : $i > $o]: 98.71/14.84 ((??((^[Y1 : $i]: 98.71/14.84 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 98.71/14.84 (??(Y0)))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 98.71/14.84 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 98.71/14.84 (Y0 = Y1))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => (Y0 = emptyset))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => (Y0 = emptyset))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i > $o]: 98.71/14.84 (!!((^[Y2 : $i]: 98.71/14.84 (in(Y2, Y0) => 98.71/14.84 (in(Y2, dsetconstr(Y0, Y1)) <=> Y1(Y2)))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i > $o]: 98.71/14.84 (!!((^[Y2 : $i]: 98.71/14.84 (in(Y2, Y0) => 98.71/14.84 (Y1(Y2) => 98.71/14.84 (dsetconstr(Y0, Y1) != emptyset)))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 ((??((^[Y1 : $i]: in(Y1, Y0)))) => (Y0 != emptyset))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 98.71/14.84 (in(emptyset, setadjoin(emptyset, emptyset)) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 (!!((^[Y2 : $i]: 98.71/14.84 (in(Y2, Y1) => 98.71/14.84 in(Y2, setadjoin(Y0, Y1)))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 (!!((^[Y2 : $i]: 98.71/14.84 (in(Y2, setadjoin(Y0, Y1)) => 98.71/14.84 (!!((^[Y3 : $o]: 98.71/14.84 (((Y2 = Y0) => Y3) => 98.71/14.84 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 (!!((^[Y2 : $i]: 98.71/14.84 (in(Y2, setadjoin(Y0, Y1)) => 98.71/14.84 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 ((!!((^[Y2 : $i]: 98.71/14.84 (in(Y2, Y1) => in(Y2, Y0))))) => 98.71/14.84 in(Y1, powerset(Y0))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.71/14.84 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 (!!((^[Y2 : $i]: 98.71/14.84 (in(Y1, powerset(Y0)) => 98.71/14.84 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 (!!((^[Y2 : $i]: 98.71/14.84 (in(Y1, Y2) => 98.71/14.84 (in(Y2, Y0) => 98.71/14.84 in(Y1, setunion(Y0))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 (in(Y1, setunion(Y0)) => 98.71/14.84 (!!((^[Y2 : $o]: 98.71/14.84 ((!!((^[Y3 : $i]: 98.71/14.84 (in(Y1, Y3) => 98.71/14.84 (in(Y3, Y0) => Y2))))) => 98.71/14.84 Y2))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 (in(Y1, Y0) => 98.71/14.84 in(Y1, powerset(setunion(Y0)))))))))) => 98.71/14.84 ((!!((^[Y0 : $i > $o]: 98.71/14.84 ((??((^[Y1 : $i]: 98.71/14.84 (Y0(Y1) & 98.71/14.84 (!!((^[Y2 : $i]: 98.71/14.84 (Y0(Y2) => (Y1 = Y2))))))))) => 98.71/14.84 (??((^[Y1 : $i]: 98.71/14.84 (!!((^[Y2 : $i]: 98.71/14.84 (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 ((Y0 != emptyset) => 98.71/14.84 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 (in(Y0, 98.71/14.84 setadjoin(Y1, emptyset)) => 98.71/14.84 (Y0 = Y1)))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 ((Y0 != Y1) => 98.71/14.84 (~(in(Y1, 98.71/14.84 setadjoin(Y0, emptyset))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 ((Y0 = Y1) => 98.71/14.84 in(Y0, 98.71/14.84 setadjoin(Y1, emptyset))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 (in(Y0, 98.71/14.84 setadjoin(Y1, emptyset)) => 98.71/14.84 in(Y1, 98.71/14.84 setadjoin(Y0, emptyset))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 (!!((^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 setadjoin(Y0, 98.71/14.84 setadjoin(Y1, 98.71/14.84 emptyset))) => 98.71/14.84 ((Y2 = Y1) | 98.71/14.84 (Y2 = Y0)))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 in(Y0, 98.71/14.84 setadjoin(Y0, 98.71/14.84 setadjoin(Y1, 98.71/14.84 emptyset))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 in(Y1, 98.71/14.84 setadjoin(Y0, 98.71/14.84 setadjoin(Y1, 98.71/14.84 emptyset))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i > $o]: 98.71/14.84 ((??((^[Y2 : $i]: 98.71/14.84 (in(Y2, Y0) & 98.71/14.84 Y1(Y2))))) => 98.71/14.84 (dsetconstr(Y0, Y1) != 98.71/14.84 emptyset)))))))) => 98.71/14.84 ((!!((^[Y0 : $i > $o]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 (in(Y1, emptyset) => 98.71/14.84 Y0(Y1)))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i > $o]: 98.71/14.84 ((~((!!((^[Y2 : $i]: 98.71/14.84 (in(Y2, Y0) => 98.71/14.84 Y1(Y2))))))) => 98.71/14.84 (??((^[Y2 : $i]: 98.71/14.84 (in(Y2, Y0) & 98.71/14.84 (~(Y1(Y2)))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i > $o]: 98.71/14.84 ((!!((^[Y2 : $i]: 98.71/14.84 (in(Y2, Y0) => 98.71/14.84 (~(Y1(Y2))))))) => 98.71/14.84 (~((??((^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) & 98.71/14.84 Y1(Y2)))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i > $o]: 98.71/14.84 ((~((??((^[Y2 : $i]: 98.71/14.84 ( 98.71/14.84 in(Y2, 98.71/14.84 Y0) & 98.71/14.84 Y1(Y2))))))) => 98.71/14.84 (!!((^[Y2 : $i]: 98.71/14.84 (in(Y2, Y0) => 98.71/14.84 (~(Y1(Y2)))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i > $o]: 98.71/14.84 ((??((^[Y2 : $i]: 98.71/14.84 (in(Y2, Y0) & 98.71/14.84 (~(Y1(Y2))))))) => 98.71/14.84 (~((!!((^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 Y1(Y2)))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $o]: 98.71/14.84 (Y0 => 98.71/14.84 in(emptyset, 98.71/14.84 prop2set(Y0)))))) => 98.71/14.84 ((!!((^[Y0 : $o]: 98.71/14.84 (Y0 => 98.71/14.84 set2prop(prop2set(Y0)))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i > $o]: 98.71/14.84 ((~((??(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 ( 98.71/14.84 in(Y2, 98.71/14.84 Y0) & 98.71/14.84 Y1(Y2))))))) => 98.71/14.84 (!!((^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 (~( 98.71/14.84 Y1(Y2)))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i > $o]: 98.71/14.84 ((~((!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 Y1(Y2))))))) => 98.71/14.84 (??((^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) & 98.71/14.84 (~( 98.71/14.84 Y1(Y2)))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i > $o]: 98.71/14.84 ((??(Y0)) => 98.71/14.84 ((!!((^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 ( 98.71/14.84 Y0(Y1) => 98.71/14.84 ( 98.71/14.84 Y0(Y2) => 98.71/14.84 ( 98.71/14.84 Y1 = Y2))))))))) => 98.71/14.84 (??((^[Y1 : $i]: 98.71/14.84 (Y0(Y1) & 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y0(Y2) => 98.71/14.84 (Y1 = Y2)))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i > $o]: 98.71/14.84 ((??((^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 ( 98.71/14.84 Y0(Y2) <=> 98.71/14.84 ( 98.71/14.84 Y2 = Y1)))))))) => 98.71/14.84 (??((^[Y1 : $i]: 98.71/14.84 (Y0(Y1) & 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y0(Y2) => 98.71/14.84 (Y1 = Y2))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 ((Y0 = Y1) => 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (( 98.71/14.84 Y2 = Y3) => 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 in(Y3, 98.71/14.84 Y1)))))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 ((Y0 = Y1) => 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (( 98.71/14.84 Y2 = Y3) => 98.71/14.84 (in(Y2, 98.71/14.84 Y0) <=> 98.71/14.84 in(Y3, 98.71/14.84 Y1)))))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i > $o]: 98.71/14.84 ((??((^[Y1 : $i]: 98.71/14.84 ( 98.71/14.84 Y0(Y1) & 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y0(Y2) => 98.71/14.84 (Y1 = Y2))))))))) => 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y0(Y1) => 98.71/14.84 (Y0(Y2) => 98.71/14.84 (Y1 = Y2))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i > $o]: 98.71/14.84 (!!((^[Y1 : $i > $o]: 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (( 98.71/14.84 Y2 = Y3) => 98.71/14.84 (Y0(Y2) <=> 98.71/14.84 Y1(Y3))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 ??(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y0(Y2) & 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (Y0(Y3) => 98.71/14.84 (Y2 = Y3))))))))) <=> 98.71/14.84 ( 98.71/14.84 ??(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y1(Y2) & 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (Y1(Y3) => 98.71/14.84 (Y2 = Y3))))))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 Y0 = Y1) => 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (( 98.71/14.84 Y2 = Y3) => 98.71/14.84 (setadjoin( 98.71/14.84 Y0, Y2) = 98.71/14.84 setadjoin( 98.71/14.84 Y1, Y3)))))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!((^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 Y0 = Y1) => 98.71/14.84 (powerset( 98.71/14.84 Y0) = 98.71/14.84 powerset( 98.71/14.84 Y1))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 Y0 = Y1) => 98.71/14.84 ( 98.71/14.84 setunion( 98.71/14.84 Y0) = 98.71/14.84 setunion( 98.71/14.84 Y1))))))))) => 98.71/14.84 ((!!((^[Y0 : $i > $o]: 98.71/14.84 ((??(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (Y0(Y1) & 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y0(Y2) => 98.71/14.84 (Y1 = Y2))))))))) => 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y0(Y1) => 98.71/14.84 (Y0(Y2) => 98.71/14.84 (Y1 = Y2))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i > $o]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i > $o]: 98.71/14.84 (( 98.71/14.84 !!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (( 98.71/14.84 Y2 = Y3) => 98.71/14.84 (Y0(Y2) <=> 98.71/14.84 Y1(Y3))))))))) => 98.71/14.84 (( 98.71/14.84 ??(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y0(Y2) & 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (Y0(Y3) => 98.71/14.84 (Y2 = Y3))))))))) => 98.71/14.84 (( 98.71/14.84 ??(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (Y1(Y2) & 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i]: 98.71/14.84 (Y1(Y3) => 98.71/14.84 (Y2 = Y3))))))))) => 98.71/14.84 (descr( 98.71/14.84 Y0) = 98.71/14.84 descr(Y1))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 Y0 = Y1) => 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i > $o]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y3 : $i > $o]: 98.71/14.84 (( 98.71/14.84 !!(( 98.71/14.84 ^[Y4 : $i]: 98.71/14.84 (in(Y4, 98.71/14.84 Y0) => 98.71/14.84 (!!(( 98.71/14.84 ^[Y5 : $i]: 98.71/14.84 (in(Y5, 98.71/14.84 Y1) => 98.71/14.84 (( 98.71/14.84 Y4 = Y5) => 98.71/14.84 (Y2(Y4) <=> 98.71/14.84 Y3(Y5))))))))))) => 98.71/14.84 (dsetconstr( 98.71/14.84 Y0, Y2) = 98.71/14.84 dsetconstr( 98.71/14.84 Y1, Y3)))))))))))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 !!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 in(Y2, 98.71/14.84 Y1))))) => 98.71/14.84 subset( 98.71/14.84 Y0, Y1)))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 Y0 = Y1) => 98.71/14.84 subset( 98.71/14.84 Y1, Y0)))))))) => 98.71/14.84 ((!!((^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 Y0 = Y1) => 98.71/14.84 subset( 98.71/14.84 Y0, Y1)))))))) => 98.71/14.84 ((!!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 !!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 in(Y2, 98.71/14.84 Y1))))) => 98.71/14.84 subset( 98.71/14.84 Y0, Y1)))))))) => 98.71/14.84 ((!!( 98.71/14.84 subset( 98.71/14.84 emptyset))) => 98.71/14.84 ((!!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y0, Y1) => 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 in(Y2, 98.71/14.84 Y1)))))))))))) => 98.71/14.84 ((!!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y0, Y1) => 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 Y1))) => 98.71/14.84 (~( 98.71/14.84 in(Y2, 98.71/14.84 Y0)))))))))))))) => 98.71/14.84 (( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 Y1))) => 98.71/14.84 (~( 98.71/14.84 subset( 98.71/14.84 Y0, Y1)))))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 subset( 98.71/14.84 Y0, Y1))) => 98.71/14.84 (Y0 != Y1)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (in(Y2, 98.71/14.84 Y0) => 98.71/14.84 (( 98.71/14.84 ~( 98.71/14.84 in(Y2, 98.71/14.84 Y1))) => 98.71/14.84 (Y0 != Y1)))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 subset( 98.71/14.84 Y0, Y0)))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y0, Y1) => 98.71/14.84 (subset( 98.71/14.84 Y1, Y2) => 98.71/14.84 subset( 98.71/14.84 Y0, Y2)))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 subset( 98.71/14.84 Y1, 98.71/14.84 setadjoin( 98.71/14.84 Y0, Y1)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y2 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y0, Y2) => 98.71/14.84 subset( 98.71/14.84 Y0, 98.71/14.84 setadjoin( 98.71/14.84 Y1, Y2)))))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y0, Y1) => 98.71/14.84 in(Y0, 98.71/14.84 powerset( 98.71/14.84 Y1))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y0, Y1) => 98.71/14.84 (subset( 98.71/14.84 Y1, Y0) => 98.71/14.84 (Y0 = Y1))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y0, 98.71/14.84 emptyset) => 98.71/14.84 (Y0 = 98.71/14.84 emptyset))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (subset( 98.71/14.84 Y1, Y0) => 98.71/14.84 in(Y1, 98.71/14.84 powerset( 98.71/14.84 Y0))))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 (!!(( 98.71/14.84 ^[Y1 : $i]: 98.71/14.84 (in(Y1, 98.71/14.84 powerset( 98.71/14.84 Y0)) => 98.71/14.84 subset( 98.71/14.84 Y1, Y0)))))))) => 98.71/14.84 ( 98.71/14.84 ( 98.71/14.84 !!(( 98.71/14.84 ^[Y0 : $i]: 98.71/14.84 in(Y0, 98.71/14.85 powerset( 98.71/14.85 Y0))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y0, Y1) => 98.71/14.85 subset( 98.71/14.85 powerset( 98.71/14.85 Y0), 98.71/14.85 powerset( 98.71/14.85 Y1))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i > $o]: 98.71/14.85 in( 98.71/14.85 dsetconstr( 98.71/14.85 Y0, Y1), 98.71/14.85 powerset( 98.71/14.85 Y0)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i > $o]: 98.71/14.85 subset( 98.71/14.85 dsetconstr( 98.71/14.85 Y0, Y1), 98.71/14.85 Y0))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 in(Y2, 98.71/14.85 binunion( 98.71/14.85 Y0, Y1)))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 in(Y1, 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 setadjoin( 98.71/14.85 Y1, 98.71/14.85 emptyset))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y1) => 98.71/14.85 in(Y2, 98.71/14.85 binunion( 98.71/14.85 Y0, Y1)))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $o]: 98.71/14.85 (in(Y2, 98.71/14.85 binunion( 98.71/14.85 Y0, Y1)) => 98.71/14.85 (( 98.71/14.85 in(Y2, 98.71/14.85 Y0) => Y3) => 98.71/14.85 (( 98.71/14.85 in(Y2, 98.71/14.85 Y1) => Y3) => 98.71/14.85 Y3))))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 binunion( 98.71/14.85 Y0, Y1)) => 98.71/14.85 (in(Y2, 98.71/14.85 Y1) | 98.71/14.85 in(Y2, 98.71/14.85 Y0)))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 subset( 98.71/14.85 Y0, 98.71/14.85 binunion( 98.71/14.85 Y0, Y1)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 subset( 98.71/14.85 Y1, 98.71/14.85 binunion( 98.71/14.85 Y0, Y1)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 (in(Y2, 98.71/14.85 Y1) => 98.71/14.85 in(Y2, 98.71/14.85 binintersect( 98.71/14.85 Y0, Y1))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y2, Y0) => 98.71/14.85 (subset( 98.71/14.85 Y2, Y1) => 98.71/14.85 subset( 98.71/14.85 Y2, 98.71/14.85 binintersect( 98.71/14.85 Y0, Y1))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 binintersect( 98.71/14.85 Y0, Y1)) => 98.71/14.85 in(Y2, 98.71/14.85 Y0))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 subset( 98.71/14.85 binintersect( 98.71/14.85 Y0, Y1), 98.71/14.85 Y0))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y0, Y1) => 98.71/14.85 (binintersect( 98.71/14.85 Y0, Y1) = 98.71/14.85 Y0)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (( 98.71/14.85 binintersect( 98.71/14.85 Y0, Y1) = 98.71/14.85 Y1) => 98.71/14.85 subset( 98.71/14.85 Y1, Y0)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 binintersect( 98.71/14.85 Y0, Y1)) => 98.71/14.85 in(Y2, 98.71/14.85 Y1))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (( 98.71/14.85 ~(( 98.71/14.85 ??(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) & 98.71/14.85 in(Y2, 98.71/14.85 Y1))))))) => 98.71/14.85 (binintersect( 98.71/14.85 Y0, Y1) = 98.71/14.85 emptyset)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 subset( 98.71/14.85 binintersect( 98.71/14.85 Y0, Y1), 98.71/14.85 Y1))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y1, Y0) => 98.71/14.85 (binintersect( 98.71/14.85 Y0, Y1) = 98.71/14.85 Y1)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (( 98.71/14.85 binintersect( 98.71/14.85 Y0, Y1) = 98.71/14.85 Y0) => 98.71/14.85 subset( 98.71/14.85 Y0, Y1)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (binintersect( 98.71/14.85 Y0, 98.71/14.85 binunion( 98.71/14.85 Y1, Y2)) = 98.71/14.85 binunion( 98.71/14.85 binintersect( 98.71/14.85 Y0, Y1), 98.71/14.85 binintersect( 98.71/14.85 Y0, Y2)))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y1))) => 98.71/14.85 in(Y2, 98.71/14.85 setminus( 98.71/14.85 Y0, Y1))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 setminus( 98.71/14.85 Y0, Y1)) => 98.71/14.85 in(Y2, 98.71/14.85 Y0))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 setminus( 98.71/14.85 Y0, Y1)) => 98.71/14.85 (~( 98.71/14.85 in(Y2, 98.71/14.85 Y1))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y0, Y1) => 98.71/14.85 (setminus( 98.71/14.85 Y0, Y1) = 98.71/14.85 emptyset)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 setminus( 98.71/14.85 Y0, Y1)))) => 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 in(Y2, 98.71/14.85 Y1)))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 setminus( 98.71/14.85 Y0, Y1)))) => 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y1))) => 98.71/14.85 (~( 98.71/14.85 in(Y2, 98.71/14.85 Y0)))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y0))) => 98.71/14.85 (~( 98.71/14.85 in(Y2, 98.71/14.85 setminus( 98.71/14.85 Y0, Y1)))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y1) => 98.71/14.85 (~( 98.71/14.85 in(Y2, 98.71/14.85 setminus( 98.71/14.85 Y0, Y1)))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 subset( 98.71/14.85 setminus( 98.71/14.85 Y0, Y1), 98.71/14.85 Y0))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (( 98.71/14.85 setminus( 98.71/14.85 Y0, Y1) = 98.71/14.85 emptyset) => 98.71/14.85 subset( 98.71/14.85 Y0, Y1)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 symdiff( 98.71/14.85 Y0, Y1)) => 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $o]: 98.71/14.85 (( 98.71/14.85 in(Y2, 98.71/14.85 Y0) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y1))) => 98.71/14.85 Y3)) => 98.71/14.85 (( 98.71/14.85 ( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y0))) => 98.71/14.85 ( 98.71/14.85 in(Y2, 98.71/14.85 Y1) => Y3)) => 98.71/14.85 Y3))))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y1))) => 98.71/14.85 in(Y2, 98.71/14.85 symdiff( 98.71/14.85 Y0, Y1))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y0))) => 98.71/14.85 (in(Y2, 98.71/14.85 Y1) => 98.71/14.85 in(Y2, 98.71/14.85 symdiff( 98.71/14.85 Y0, Y1))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 (in(Y2, 98.71/14.85 Y1) => 98.71/14.85 (~( 98.71/14.85 in(Y2, 98.71/14.85 symdiff( 98.71/14.85 Y0, Y1))))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y0))) => 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y1))) => 98.71/14.85 (~( 98.71/14.85 in(Y2, 98.71/14.85 symdiff( 98.71/14.85 Y0, Y1))))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 in(Y1, 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 setadjoin( 98.71/14.85 Y1, 98.71/14.85 emptyset))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 in(Y0, 98.71/14.85 setunion( 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 setadjoin( 98.71/14.85 Y1, 98.71/14.85 emptyset)), 98.71/14.85 emptyset)))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 in(Y1, 98.71/14.85 setunion( 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 setadjoin( 98.71/14.85 Y1, 98.71/14.85 emptyset)), 98.71/14.85 emptyset)))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (??(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 setunion( 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 setadjoin( 98.71/14.85 Y1, 98.71/14.85 emptyset)), 98.71/14.85 emptyset)))) & 98.71/14.85 (??(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (in(Y3, 98.71/14.85 setunion( 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 setadjoin( 98.71/14.85 Y1, 98.71/14.85 emptyset)), 98.71/14.85 emptyset)))) & 98.71/14.85 (setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 setadjoin( 98.71/14.85 Y1, 98.71/14.85 emptyset)), 98.71/14.85 emptyset)) = 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 setadjoin( 98.71/14.85 Y3, 98.71/14.85 emptyset)), 98.71/14.85 emptyset))))))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (??(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 setunion( 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 setadjoin( 98.71/14.85 Y1, 98.71/14.85 emptyset)), 98.71/14.85 emptyset)))) & 98.71/14.85 (??(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (in(Y3, 98.71/14.85 setunion( 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 setadjoin( 98.71/14.85 Y1, 98.71/14.85 emptyset)), 98.71/14.85 emptyset)))) & 98.71/14.85 (setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 setadjoin( 98.71/14.85 Y1, 98.71/14.85 emptyset)), 98.71/14.85 emptyset)) = 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 setadjoin( 98.71/14.85 Y3, 98.71/14.85 emptyset)), 98.71/14.85 emptyset))))))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (in(Y1, 98.71/14.85 Y0) => 98.71/14.85 subset( 98.71/14.85 setadjoin( 98.71/14.85 Y1, 98.71/14.85 emptyset), 98.71/14.85 Y0)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (in(Y1, 98.71/14.85 Y0) => 98.71/14.85 in( 98.71/14.85 setadjoin( 98.71/14.85 Y1, 98.71/14.85 emptyset), 98.71/14.85 powerset( 98.71/14.85 Y0))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 in( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 emptyset), 98.71/14.85 powerset( 98.71/14.85 binunion( 98.71/14.85 Y0, Y1))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 setadjoin( 98.71/14.85 Y1, 98.71/14.85 emptyset))) => 98.71/14.85 (( 98.71/14.85 Y2 = Y1) | 98.71/14.85 (Y2 = Y0)))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (in(Y3, 98.71/14.85 Y1) => 98.71/14.85 subset( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 setadjoin( 98.71/14.85 Y3, 98.71/14.85 emptyset)), 98.71/14.85 binunion( 98.71/14.85 Y0, Y1)))))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (in(Y3, 98.71/14.85 Y1) => 98.71/14.85 in( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 setadjoin( 98.71/14.85 Y3, 98.71/14.85 emptyset)), 98.71/14.85 powerset( 98.71/14.85 binunion( 98.71/14.85 Y0, Y1))))))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (in(Y3, 98.71/14.85 Y1) => 98.71/14.85 subset( 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 setadjoin( 98.71/14.85 Y3, 98.71/14.85 emptyset)), 98.71/14.85 emptyset)), 98.71/14.85 powerset( 98.71/14.85 binunion( 98.71/14.85 Y0, Y1))))))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (in(Y3, 98.71/14.85 Y1) => 98.71/14.85 in( 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 setadjoin( 98.71/14.85 Y3, 98.71/14.85 emptyset)), 98.71/14.85 emptyset)), 98.71/14.85 powerset( 98.71/14.85 powerset( 98.71/14.85 binunion( 98.71/14.85 Y0, Y1)))))))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (in(Y3, 98.71/14.85 Y1) => 98.71/14.85 in( 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 setadjoin( 98.71/14.85 Y3, 98.71/14.85 emptyset)), 98.71/14.85 emptyset)), 98.71/14.85 powerset( 98.71/14.85 powerset( 98.71/14.85 binunion( 98.71/14.85 Y0, Y1)))))))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (in(Y3, 98.71/14.85 Y1) => 98.71/14.85 in( 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 setadjoin( 98.71/14.85 Y3, 98.71/14.85 emptyset)), 98.71/14.85 emptyset)), 98.71/14.85 dsetconstr( 98.71/14.85 powerset( 98.71/14.85 powerset( 98.71/14.85 binunion( 98.71/14.85 Y0, Y1))), 98.71/14.85 (^[Y4 : $i]: 98.71/14.85 (??(( 98.71/14.85 ^[Y5 : $i]: 98.71/14.85 (in(Y5, 98.71/14.85 Y0) & 98.71/14.85 (??(( 98.71/14.85 ^[Y6 : $i]: 98.71/14.85 (in(Y6, 98.71/14.85 Y1) & 98.71/14.85 (Y4 = 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y5, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y5, 98.71/14.85 setadjoin( 98.71/14.85 Y6, 98.71/14.85 emptyset)), 98.71/14.85 emptyset)))))))))))))))))))))))))))) => 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 dsetconstr( 98.71/14.85 powerset( 98.71/14.85 powerset( 98.71/14.85 binunion( 98.71/14.85 Y0, Y1))), 98.71/14.85 (^[Y3 : $i]: 98.71/14.85 (??(( 98.71/14.85 ^[Y4 : $i]: 98.71/14.85 (in(Y4, 98.71/14.85 Y0) & 98.71/14.85 (??(( 98.71/14.85 ^[Y5 : $i]: 98.71/14.85 (in(Y5, 98.71/14.85 Y1) & 98.71/14.85 (Y3 = 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y4, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y4, 98.71/14.85 setadjoin( 98.71/14.85 Y5, 98.71/14.85 emptyset)), 98.71/14.85 emptyset)))))))))))))) => 98.71/14.85 (??(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (( 98.71/14.85 ??(( 98.71/14.85 ^[Y4 : $i]: 98.71/14.85 (in(Y4, 98.71/14.85 Y1) & 98.71/14.85 (Y2 = 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y3, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y3, 98.71/14.85 setadjoin( 98.71/14.85 Y4, 98.71/14.85 emptyset)), 98.71/14.85 emptyset))))))) & 98.71/14.85 in(Y3, 98.71/14.85 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 98.71/14.85 inference('lazy_cnf_imply', [status(thm)], ['177'])). 98.71/14.85 tff('179', plain, 98.71/14.85 ~ ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 98.71/14.85 ((!!((^[Y0 : $i > $o]: 98.71/14.85 ((??((^[Y1 : $i]: 98.71/14.85 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 98.71/14.85 (??(Y0)))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 98.71/14.85 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 98.71/14.85 (Y0 = Y1))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => (Y0 = emptyset))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => (Y0 = emptyset))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i > $o]: 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 (in(Y2, Y0) => 98.71/14.85 (in(Y2, dsetconstr(Y0, Y1)) <=> Y1(Y2)))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i > $o]: 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 (in(Y2, Y0) => 98.71/14.85 (Y1(Y2) => 98.71/14.85 (dsetconstr(Y0, Y1) != emptyset)))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 ((??((^[Y1 : $i]: in(Y1, Y0)))) => (Y0 != emptyset))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 98.71/14.85 (in(emptyset, setadjoin(emptyset, emptyset)) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 (in(Y2, Y1) => 98.71/14.85 in(Y2, setadjoin(Y0, Y1)))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 (in(Y2, setadjoin(Y0, Y1)) => 98.71/14.85 (!!((^[Y3 : $o]: 98.71/14.85 (((Y2 = Y0) => Y3) => 98.71/14.85 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 (in(Y2, setadjoin(Y0, Y1)) => 98.71/14.85 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 ((!!((^[Y2 : $i]: 98.71/14.85 (in(Y2, Y1) => in(Y2, Y0))))) => 98.71/14.85 in(Y1, powerset(Y0))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.71/14.85 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 (in(Y1, powerset(Y0)) => 98.71/14.85 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 (in(Y1, Y2) => 98.71/14.85 (in(Y2, Y0) => 98.71/14.85 in(Y1, setunion(Y0))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 (in(Y1, setunion(Y0)) => 98.71/14.85 (!!((^[Y2 : $o]: 98.71/14.85 ((!!((^[Y3 : $i]: 98.71/14.85 (in(Y1, Y3) => 98.71/14.85 (in(Y3, Y0) => Y2))))) => 98.71/14.85 Y2))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 (in(Y1, Y0) => 98.71/14.85 in(Y1, powerset(setunion(Y0)))))))))) => 98.71/14.85 ((!!((^[Y0 : $i > $o]: 98.71/14.85 ((??((^[Y1 : $i]: 98.71/14.85 (Y0(Y1) & 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 (Y0(Y2) => (Y1 = Y2))))))))) => 98.71/14.85 (??((^[Y1 : $i]: 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 ((Y0 != emptyset) => 98.71/14.85 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 (in(Y0, setadjoin(Y1, emptyset)) => 98.71/14.85 (Y0 = Y1)))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 ((Y0 != Y1) => 98.71/14.85 (~(in(Y1, 98.71/14.85 setadjoin(Y0, emptyset))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 ((Y0 = Y1) => 98.71/14.85 in(Y0, 98.71/14.85 setadjoin(Y1, emptyset))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 (in(Y0, 98.71/14.85 setadjoin(Y1, emptyset)) => 98.71/14.85 in(Y1, 98.71/14.85 setadjoin(Y0, emptyset))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 setadjoin(Y0, 98.71/14.85 setadjoin(Y1, 98.71/14.85 emptyset))) => 98.71/14.85 ((Y2 = Y1) | 98.71/14.85 (Y2 = Y0)))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 in(Y0, 98.71/14.85 setadjoin(Y0, 98.71/14.85 setadjoin(Y1, emptyset))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 in(Y1, 98.71/14.85 setadjoin(Y0, 98.71/14.85 setadjoin(Y1, 98.71/14.85 emptyset))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i > $o]: 98.71/14.85 ((??((^[Y2 : $i]: 98.71/14.85 (in(Y2, Y0) & 98.71/14.85 Y1(Y2))))) => 98.71/14.85 (dsetconstr(Y0, Y1) != 98.71/14.85 emptyset)))))))) => 98.71/14.85 ((!!((^[Y0 : $i > $o]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 (in(Y1, emptyset) => 98.71/14.85 Y0(Y1)))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i > $o]: 98.71/14.85 ((~((!!((^[Y2 : $i]: 98.71/14.85 (in(Y2, Y0) => 98.71/14.85 Y1(Y2))))))) => 98.71/14.85 (??((^[Y2 : $i]: 98.71/14.85 (in(Y2, Y0) & 98.71/14.85 (~(Y1(Y2)))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i > $o]: 98.71/14.85 ((!!((^[Y2 : $i]: 98.71/14.85 (in(Y2, Y0) => 98.71/14.85 (~(Y1(Y2))))))) => 98.71/14.85 (~((??((^[Y2 : $i]: 98.71/14.85 (in(Y2, Y0) & 98.71/14.85 Y1(Y2)))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i > $o]: 98.71/14.85 ((~((??((^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) & 98.71/14.85 Y1(Y2))))))) => 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 (in(Y2, Y0) => 98.71/14.85 (~(Y1(Y2)))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i > $o]: 98.71/14.85 ((??((^[Y2 : $i]: 98.71/14.85 (in(Y2, Y0) & 98.71/14.85 (~(Y1(Y2))))))) => 98.71/14.85 (~((!!((^[Y2 : $i]: 98.71/14.85 ( 98.71/14.85 in(Y2, 98.71/14.85 Y0) => 98.71/14.85 Y1(Y2)))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $o]: 98.71/14.85 (Y0 => 98.71/14.85 in(emptyset, 98.71/14.85 prop2set(Y0)))))) => 98.71/14.85 ((!!((^[Y0 : $o]: 98.71/14.85 (Y0 => 98.71/14.85 set2prop(prop2set(Y0)))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i > $o]: 98.71/14.85 ((~((??(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) & 98.71/14.85 Y1(Y2))))))) => 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 ( 98.71/14.85 in(Y2, 98.71/14.85 Y0) => 98.71/14.85 ( 98.71/14.85 ~( 98.71/14.85 Y1(Y2)))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i > $o]: 98.71/14.85 ((~((!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 ( 98.71/14.85 in(Y2, 98.71/14.85 Y0) => 98.71/14.85 Y1(Y2))))))) => 98.71/14.85 (??((^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) & 98.71/14.85 (~( 98.71/14.85 Y1(Y2)))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i > $o]: 98.71/14.85 ((??(Y0)) => 98.71/14.85 ((!!((^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (Y0(Y1) => 98.71/14.85 ( 98.71/14.85 Y0(Y2) => 98.71/14.85 ( 98.71/14.85 Y1 = Y2))))))))) => 98.71/14.85 (??((^[Y1 : $i]: 98.71/14.85 (Y0(Y1) & 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 ( 98.71/14.85 Y0(Y2) => 98.71/14.85 ( 98.71/14.85 Y1 = Y2)))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i > $o]: 98.71/14.85 ((??((^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (Y0(Y2) <=> 98.71/14.85 ( 98.71/14.85 Y2 = Y1)))))))) => 98.71/14.85 (??((^[Y1 : $i]: 98.71/14.85 (Y0(Y1) & 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 ( 98.71/14.85 Y0(Y2) => 98.71/14.85 ( 98.71/14.85 Y1 = Y2))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 ((Y0 = Y1) => 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (( 98.71/14.85 Y2 = Y3) => 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 in(Y3, 98.71/14.85 Y1)))))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 ((Y0 = Y1) => 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (( 98.71/14.85 Y2 = Y3) => 98.71/14.85 (in(Y2, 98.71/14.85 Y0) <=> 98.71/14.85 in(Y3, 98.71/14.85 Y1)))))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i > $o]: 98.71/14.85 ((??((^[Y1 : $i]: 98.71/14.85 (Y0(Y1) & 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (Y0(Y2) => 98.71/14.85 (Y1 = Y2))))))))) => 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (Y0(Y1) => 98.71/14.85 (Y0(Y2) => 98.71/14.85 (Y1 = Y2))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i > $o]: 98.71/14.85 (!!((^[Y1 : $i > $o]: 98.71/14.85 (( 98.71/14.85 !!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (( 98.71/14.85 Y2 = Y3) => 98.71/14.85 (Y0(Y2) <=> 98.71/14.85 Y1(Y3))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 ??(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (Y0(Y2) & 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (Y0(Y3) => 98.71/14.85 (Y2 = Y3))))))))) <=> 98.71/14.85 ( 98.71/14.85 ??(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (Y1(Y2) & 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (Y1(Y3) => 98.71/14.85 (Y2 = Y3))))))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 Y0 = Y1) => 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (( 98.71/14.85 Y2 = Y3) => 98.71/14.85 (setadjoin( 98.71/14.85 Y0, Y2) = 98.71/14.85 setadjoin( 98.71/14.85 Y1, Y3)))))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 (( 98.71/14.85 Y0 = Y1) => 98.71/14.85 (powerset( 98.71/14.85 Y0) = 98.71/14.85 powerset( 98.71/14.85 Y1))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 (( 98.71/14.85 Y0 = Y1) => 98.71/14.85 (setunion( 98.71/14.85 Y0) = 98.71/14.85 setunion( 98.71/14.85 Y1))))))))) => 98.71/14.85 ((!!((^[Y0 : $i > $o]: 98.71/14.85 ((??(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 ( 98.71/14.85 Y0(Y1) & 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (Y0(Y2) => 98.71/14.85 (Y1 = Y2))))))))) => 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (Y0(Y1) => 98.71/14.85 (Y0(Y2) => 98.71/14.85 (Y1 = Y2))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i > $o]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i > $o]: 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (( 98.71/14.85 Y2 = Y3) => 98.71/14.85 (Y0(Y2) <=> 98.71/14.85 Y1(Y3))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 ??(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (Y0(Y2) & 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (Y0(Y3) => 98.71/14.85 (Y2 = Y3))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 ??(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (Y1(Y2) & 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (Y1(Y3) => 98.71/14.85 (Y2 = Y3))))))))) => 98.71/14.85 ( 98.71/14.85 descr(Y0) = 98.71/14.85 descr(Y1))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (( 98.71/14.85 Y0 = Y1) => 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i > $o]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i > $o]: 98.71/14.85 (( 98.71/14.85 !!(( 98.71/14.85 ^[Y4 : $i]: 98.71/14.85 (in(Y4, 98.71/14.85 Y0) => 98.71/14.85 (!!(( 98.71/14.85 ^[Y5 : $i]: 98.71/14.85 (in(Y5, 98.71/14.85 Y1) => 98.71/14.85 (( 98.71/14.85 Y4 = Y5) => 98.71/14.85 (Y2(Y4) <=> 98.71/14.85 Y3(Y5))))))))))) => 98.71/14.85 (dsetconstr( 98.71/14.85 Y0, Y2) = 98.71/14.85 dsetconstr( 98.71/14.85 Y1, Y3)))))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (( 98.71/14.85 !!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 in(Y2, 98.71/14.85 Y1))))) => 98.71/14.85 subset( 98.71/14.85 Y0, Y1)))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (( 98.71/14.85 Y0 = Y1) => 98.71/14.85 subset( 98.71/14.85 Y1, Y0)))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (( 98.71/14.85 Y0 = Y1) => 98.71/14.85 subset( 98.71/14.85 Y0, Y1)))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (( 98.71/14.85 !!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 in(Y2, 98.71/14.85 Y1))))) => 98.71/14.85 subset( 98.71/14.85 Y0, Y1)))))))) => 98.71/14.85 ((!!(subset( 98.71/14.85 emptyset))) => 98.71/14.85 ((!!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y0, Y1) => 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 in(Y2, 98.71/14.85 Y1)))))))))))) => 98.71/14.85 ((!!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y0, Y1) => 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y1))) => 98.71/14.85 (~( 98.71/14.85 in(Y2, 98.71/14.85 Y0)))))))))))))) => 98.71/14.85 ((!!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y1))) => 98.71/14.85 (~( 98.71/14.85 subset( 98.71/14.85 Y0, Y1)))))))))))))) => 98.71/14.85 (( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 subset( 98.71/14.85 Y0, Y1))) => 98.71/14.85 (Y0 != Y1)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y1))) => 98.71/14.85 (Y0 != Y1)))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 subset( 98.71/14.85 Y0, Y0)))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y0, Y1) => 98.71/14.85 (subset( 98.71/14.85 Y1, Y2) => 98.71/14.85 subset( 98.71/14.85 Y0, Y2)))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 subset( 98.71/14.85 Y1, 98.71/14.85 setadjoin( 98.71/14.85 Y0, Y1)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y0, Y2) => 98.71/14.85 subset( 98.71/14.85 Y0, 98.71/14.85 setadjoin( 98.71/14.85 Y1, Y2)))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y0, Y1) => 98.71/14.85 in(Y0, 98.71/14.85 powerset( 98.71/14.85 Y1))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y0, Y1) => 98.71/14.85 (subset( 98.71/14.85 Y1, Y0) => 98.71/14.85 (Y0 = Y1))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y0, 98.71/14.85 emptyset) => 98.71/14.85 (Y0 = 98.71/14.85 emptyset))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y1, Y0) => 98.71/14.85 in(Y1, 98.71/14.85 powerset( 98.71/14.85 Y0))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (in(Y1, 98.71/14.85 powerset( 98.71/14.85 Y0)) => 98.71/14.85 subset( 98.71/14.85 Y1, Y0)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 in(Y0, 98.71/14.85 powerset( 98.71/14.85 Y0))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y0, Y1) => 98.71/14.85 subset( 98.71/14.85 powerset( 98.71/14.85 Y0), 98.71/14.85 powerset( 98.71/14.85 Y1))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i > $o]: 98.71/14.85 in( 98.71/14.85 dsetconstr( 98.71/14.85 Y0, Y1), 98.71/14.85 powerset( 98.71/14.85 Y0)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i > $o]: 98.71/14.85 subset( 98.71/14.85 dsetconstr( 98.71/14.85 Y0, Y1), 98.71/14.85 Y0))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 in(Y2, 98.71/14.85 binunion( 98.71/14.85 Y0, Y1)))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 in(Y1, 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 setadjoin( 98.71/14.85 Y1, 98.71/14.85 emptyset))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y1) => 98.71/14.85 in(Y2, 98.71/14.85 binunion( 98.71/14.85 Y0, Y1)))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $o]: 98.71/14.85 (in(Y2, 98.71/14.85 binunion( 98.71/14.85 Y0, Y1)) => 98.71/14.85 (( 98.71/14.85 in(Y2, 98.71/14.85 Y0) => Y3) => 98.71/14.85 (( 98.71/14.85 in(Y2, 98.71/14.85 Y1) => Y3) => 98.71/14.85 Y3))))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 binunion( 98.71/14.85 Y0, Y1)) => 98.71/14.85 (in(Y2, 98.71/14.85 Y1) | 98.71/14.85 in(Y2, 98.71/14.85 Y0)))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 subset( 98.71/14.85 Y0, 98.71/14.85 binunion( 98.71/14.85 Y0, Y1)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 subset( 98.71/14.85 Y1, 98.71/14.85 binunion( 98.71/14.85 Y0, Y1)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 (in(Y2, 98.71/14.85 Y1) => 98.71/14.85 in(Y2, 98.71/14.85 binintersect( 98.71/14.85 Y0, Y1))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y2, Y0) => 98.71/14.85 (subset( 98.71/14.85 Y2, Y1) => 98.71/14.85 subset( 98.71/14.85 Y2, 98.71/14.85 binintersect( 98.71/14.85 Y0, Y1))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 binintersect( 98.71/14.85 Y0, Y1)) => 98.71/14.85 in(Y2, 98.71/14.85 Y0))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 subset( 98.71/14.85 binintersect( 98.71/14.85 Y0, Y1), 98.71/14.85 Y0))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y0, Y1) => 98.71/14.85 (binintersect( 98.71/14.85 Y0, Y1) = 98.71/14.85 Y0)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (( 98.71/14.85 binintersect( 98.71/14.85 Y0, Y1) = 98.71/14.85 Y1) => 98.71/14.85 subset( 98.71/14.85 Y1, Y0)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 binintersect( 98.71/14.85 Y0, Y1)) => 98.71/14.85 in(Y2, 98.71/14.85 Y1))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (( 98.71/14.85 ~(( 98.71/14.85 ??(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) & 98.71/14.85 in(Y2, 98.71/14.85 Y1))))))) => 98.71/14.85 (binintersect( 98.71/14.85 Y0, Y1) = 98.71/14.85 emptyset)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 subset( 98.71/14.85 binintersect( 98.71/14.85 Y0, Y1), 98.71/14.85 Y1))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y1, Y0) => 98.71/14.85 (binintersect( 98.71/14.85 Y0, Y1) = 98.71/14.85 Y1)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (( 98.71/14.85 binintersect( 98.71/14.85 Y0, Y1) = 98.71/14.85 Y0) => 98.71/14.85 subset( 98.71/14.85 Y0, Y1)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (binintersect( 98.71/14.85 Y0, 98.71/14.85 binunion( 98.71/14.85 Y1, Y2)) = 98.71/14.85 binunion( 98.71/14.85 binintersect( 98.71/14.85 Y0, Y1), 98.71/14.85 binintersect( 98.71/14.85 Y0, Y2)))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y1))) => 98.71/14.85 in(Y2, 98.71/14.85 setminus( 98.71/14.85 Y0, Y1))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 setminus( 98.71/14.85 Y0, Y1)) => 98.71/14.85 in(Y2, 98.71/14.85 Y0))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 setminus( 98.71/14.85 Y0, Y1)) => 98.71/14.85 (~( 98.71/14.85 in(Y2, 98.71/14.85 Y1))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y0, Y1) => 98.71/14.85 (setminus( 98.71/14.85 Y0, Y1) = 98.71/14.85 emptyset)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 setminus( 98.71/14.85 Y0, Y1)))) => 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 in(Y2, 98.71/14.85 Y1)))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 setminus( 98.71/14.85 Y0, Y1)))) => 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y1))) => 98.71/14.85 (~( 98.71/14.85 in(Y2, 98.71/14.85 Y0)))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y0))) => 98.71/14.85 (~( 98.71/14.85 in(Y2, 98.71/14.85 setminus( 98.71/14.85 Y0, Y1)))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y1) => 98.71/14.85 (~( 98.71/14.85 in(Y2, 98.71/14.85 setminus( 98.71/14.85 Y0, Y1)))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 subset( 98.71/14.85 setminus( 98.71/14.85 Y0, Y1), 98.71/14.85 Y0))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (( 98.71/14.85 setminus( 98.71/14.85 Y0, Y1) = 98.71/14.85 emptyset) => 98.71/14.85 subset( 98.71/14.85 Y0, Y1)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 symdiff( 98.71/14.85 Y0, Y1)) => 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $o]: 98.71/14.85 (( 98.71/14.85 in(Y2, 98.71/14.85 Y0) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y1))) => 98.71/14.85 Y3)) => 98.71/14.85 (( 98.71/14.85 ( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y0))) => 98.71/14.85 ( 98.71/14.85 in(Y2, 98.71/14.85 Y1) => Y3)) => 98.71/14.85 Y3))))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y1))) => 98.71/14.85 in(Y2, 98.71/14.85 symdiff( 98.71/14.85 Y0, Y1))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y0))) => 98.71/14.85 (in(Y2, 98.71/14.85 Y1) => 98.71/14.85 in(Y2, 98.71/14.85 symdiff( 98.71/14.85 Y0, Y1))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 (in(Y2, 98.71/14.85 Y1) => 98.71/14.85 (~( 98.71/14.85 in(Y2, 98.71/14.85 symdiff( 98.71/14.85 Y0, Y1))))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y0))) => 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y1))) => 98.71/14.85 (~( 98.71/14.85 in(Y2, 98.71/14.85 symdiff( 98.71/14.85 Y0, Y1))))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 in(Y1, 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 setadjoin( 98.71/14.85 Y1, 98.71/14.85 emptyset))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 in(Y0, 98.71/14.85 setunion( 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 setadjoin( 98.71/14.85 Y1, 98.71/14.85 emptyset)), 98.71/14.85 emptyset)))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 in(Y1, 98.71/14.85 setunion( 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 setadjoin( 98.71/14.85 Y1, 98.71/14.85 emptyset)), 98.71/14.85 emptyset)))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (??(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 setunion( 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 setadjoin( 98.71/14.85 Y1, 98.71/14.85 emptyset)), 98.71/14.85 emptyset)))) & 98.71/14.85 (??(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (in(Y3, 98.71/14.85 setunion( 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 setadjoin( 98.71/14.85 Y1, 98.71/14.85 emptyset)), 98.71/14.85 emptyset)))) & 98.71/14.85 (setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 setadjoin( 98.71/14.85 Y1, 98.71/14.85 emptyset)), 98.71/14.85 emptyset)) = 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 setadjoin( 98.71/14.85 Y3, 98.71/14.85 emptyset)), 98.71/14.85 emptyset))))))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (??(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 setunion( 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 setadjoin( 98.71/14.85 Y1, 98.71/14.85 emptyset)), 98.71/14.85 emptyset)))) & 98.71/14.85 (??(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (in(Y3, 98.71/14.85 setunion( 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 setadjoin( 98.71/14.85 Y1, 98.71/14.85 emptyset)), 98.71/14.85 emptyset)))) & 98.71/14.85 (setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 setadjoin( 98.71/14.85 Y1, 98.71/14.85 emptyset)), 98.71/14.85 emptyset)) = 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 setadjoin( 98.71/14.85 Y3, 98.71/14.85 emptyset)), 98.71/14.85 emptyset))))))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (in(Y1, 98.71/14.85 Y0) => 98.71/14.85 subset( 98.71/14.85 setadjoin( 98.71/14.85 Y1, 98.71/14.85 emptyset), 98.71/14.85 Y0)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (in(Y1, 98.71/14.85 Y0) => 98.71/14.85 in( 98.71/14.85 setadjoin( 98.71/14.85 Y1, 98.71/14.85 emptyset), 98.71/14.85 powerset( 98.71/14.85 Y0))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 in( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 emptyset), 98.71/14.85 powerset( 98.71/14.85 binunion( 98.71/14.85 Y0, Y1))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 setadjoin( 98.71/14.85 Y1, 98.71/14.85 emptyset))) => 98.71/14.85 (( 98.71/14.85 Y2 = Y1) | 98.71/14.85 (Y2 = Y0)))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (in(Y3, 98.71/14.85 Y1) => 98.71/14.85 subset( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 setadjoin( 98.71/14.85 Y3, 98.71/14.85 emptyset)), 98.71/14.85 binunion( 98.71/14.85 Y0, Y1)))))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (in(Y3, 98.71/14.85 Y1) => 98.71/14.85 in( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 setadjoin( 98.71/14.85 Y3, 98.71/14.85 emptyset)), 98.71/14.85 powerset( 98.71/14.85 binunion( 98.71/14.85 Y0, Y1))))))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (in(Y3, 98.71/14.85 Y1) => 98.71/14.85 subset( 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 setadjoin( 98.71/14.85 Y3, 98.71/14.85 emptyset)), 98.71/14.85 emptyset)), 98.71/14.85 powerset( 98.71/14.85 binunion( 98.71/14.85 Y0, Y1))))))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (in(Y3, 98.71/14.85 Y1) => 98.71/14.85 in( 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 setadjoin( 98.71/14.85 Y3, 98.71/14.85 emptyset)), 98.71/14.85 emptyset)), 98.71/14.85 powerset( 98.71/14.85 powerset( 98.71/14.85 binunion( 98.71/14.85 Y0, Y1)))))))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (in(Y3, 98.71/14.85 Y1) => 98.71/14.85 in( 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 setadjoin( 98.71/14.85 Y3, 98.71/14.85 emptyset)), 98.71/14.85 emptyset)), 98.71/14.85 powerset( 98.71/14.85 powerset( 98.71/14.85 binunion( 98.71/14.85 Y0, Y1)))))))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (in(Y3, 98.71/14.85 Y1) => 98.71/14.85 in( 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 setadjoin( 98.71/14.85 Y3, 98.71/14.85 emptyset)), 98.71/14.85 emptyset)), 98.71/14.85 dsetconstr( 98.71/14.85 powerset( 98.71/14.85 powerset( 98.71/14.85 binunion( 98.71/14.85 Y0, Y1))), 98.71/14.85 (^[Y4 : $i]: 98.71/14.85 (??(( 98.71/14.85 ^[Y5 : $i]: 98.71/14.85 (in(Y5, 98.71/14.85 Y0) & 98.71/14.85 (??(( 98.71/14.85 ^[Y6 : $i]: 98.71/14.85 (in(Y6, 98.71/14.85 Y1) & 98.71/14.85 (Y4 = 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y5, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y5, 98.71/14.85 setadjoin( 98.71/14.85 Y6, 98.71/14.85 emptyset)), 98.71/14.85 emptyset)))))))))))))))))))))))))))) => 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 dsetconstr( 98.71/14.85 powerset( 98.71/14.85 powerset( 98.71/14.85 binunion( 98.71/14.85 Y0, Y1))), 98.71/14.85 (^[Y3 : $i]: 98.71/14.85 (??(( 98.71/14.85 ^[Y4 : $i]: 98.71/14.85 (in(Y4, 98.71/14.85 Y0) & 98.71/14.85 (??(( 98.71/14.85 ^[Y5 : $i]: 98.71/14.85 (in(Y5, 98.71/14.85 Y1) & 98.71/14.85 (Y3 = 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y4, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y4, 98.71/14.85 setadjoin( 98.71/14.85 Y5, 98.71/14.85 emptyset)), 98.71/14.85 emptyset)))))))))))))) => 98.71/14.85 (??(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (( 98.71/14.85 ??(( 98.71/14.85 ^[Y4 : $i]: 98.71/14.85 (in(Y4, 98.71/14.85 Y1) & 98.71/14.85 (Y2 = 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y3, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y3, 98.71/14.85 setadjoin( 98.71/14.85 Y4, 98.71/14.85 emptyset)), 98.71/14.85 emptyset))))))) & 98.71/14.85 in(Y3, 98.71/14.85 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 98.71/14.85 inference('lazy_cnf_imply', [status(thm)], ['178'])). 98.71/14.85 tff('180', plain, 98.71/14.85 ~ ((!!((^[Y0 : $i > $o]: 98.71/14.85 ((??((^[Y1 : $i]: 98.71/14.85 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 98.71/14.85 (??(Y0)))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 98.71/14.85 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 98.71/14.85 (Y0 = Y1))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => (Y0 = emptyset))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => (Y0 = emptyset))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i > $o]: 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 (in(Y2, Y0) => 98.71/14.85 (in(Y2, dsetconstr(Y0, Y1)) <=> Y1(Y2)))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i > $o]: 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 (in(Y2, Y0) => 98.71/14.85 (Y1(Y2) => 98.71/14.85 (dsetconstr(Y0, Y1) != emptyset)))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 ((??((^[Y1 : $i]: in(Y1, Y0)))) => (Y0 != emptyset))))) => 98.71/14.85 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 98.71/14.85 (in(emptyset, setadjoin(emptyset, emptyset)) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 (in(Y2, Y1) => 98.71/14.85 in(Y2, setadjoin(Y0, Y1)))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 (in(Y2, setadjoin(Y0, Y1)) => 98.71/14.85 (!!((^[Y3 : $o]: 98.71/14.85 (((Y2 = Y0) => Y3) => 98.71/14.85 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 (in(Y2, setadjoin(Y0, Y1)) => 98.71/14.85 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 ((!!((^[Y2 : $i]: 98.71/14.85 (in(Y2, Y1) => in(Y2, Y0))))) => 98.71/14.85 in(Y1, powerset(Y0))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.71/14.85 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 (in(Y1, powerset(Y0)) => 98.71/14.85 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 (in(Y1, Y2) => 98.71/14.85 (in(Y2, Y0) => 98.71/14.85 in(Y1, setunion(Y0))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 (in(Y1, setunion(Y0)) => 98.71/14.85 (!!((^[Y2 : $o]: 98.71/14.85 ((!!((^[Y3 : $i]: 98.71/14.85 (in(Y1, Y3) => 98.71/14.85 (in(Y3, Y0) => Y2))))) => 98.71/14.85 Y2))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 (in(Y1, Y0) => 98.71/14.85 in(Y1, powerset(setunion(Y0)))))))))) => 98.71/14.85 ((!!((^[Y0 : $i > $o]: 98.71/14.85 ((??((^[Y1 : $i]: 98.71/14.85 (Y0(Y1) & 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 (Y0(Y2) => (Y1 = Y2))))))))) => 98.71/14.85 (??((^[Y1 : $i]: 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 ((Y0 != emptyset) => 98.71/14.85 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 (in(Y0, setadjoin(Y1, emptyset)) => 98.71/14.85 (Y0 = Y1)))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 ((Y0 != Y1) => 98.71/14.85 (~(in(Y1, 98.71/14.85 setadjoin(Y0, emptyset))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 ((Y0 = Y1) => 98.71/14.85 in(Y0, 98.71/14.85 setadjoin(Y1, emptyset))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 (in(Y0, 98.71/14.85 setadjoin(Y1, emptyset)) => 98.71/14.85 in(Y1, 98.71/14.85 setadjoin(Y0, emptyset))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 setadjoin(Y0, 98.71/14.85 setadjoin(Y1, 98.71/14.85 emptyset))) => 98.71/14.85 ((Y2 = Y1) | 98.71/14.85 (Y2 = Y0)))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 in(Y0, 98.71/14.85 setadjoin(Y0, 98.71/14.85 setadjoin(Y1, emptyset))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 in(Y1, 98.71/14.85 setadjoin(Y0, 98.71/14.85 setadjoin(Y1, emptyset))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i > $o]: 98.71/14.85 ((??((^[Y2 : $i]: 98.71/14.85 (in(Y2, Y0) & 98.71/14.85 Y1(Y2))))) => 98.71/14.85 (dsetconstr(Y0, Y1) != 98.71/14.85 emptyset)))))))) => 98.71/14.85 ((!!((^[Y0 : $i > $o]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 (in(Y1, emptyset) => 98.71/14.85 Y0(Y1)))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i > $o]: 98.71/14.85 ((~((!!((^[Y2 : $i]: 98.71/14.85 (in(Y2, Y0) => 98.71/14.85 Y1(Y2))))))) => 98.71/14.85 (??((^[Y2 : $i]: 98.71/14.85 (in(Y2, Y0) & 98.71/14.85 (~(Y1(Y2)))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i > $o]: 98.71/14.85 ((!!((^[Y2 : $i]: 98.71/14.85 (in(Y2, Y0) => 98.71/14.85 (~(Y1(Y2))))))) => 98.71/14.85 (~((??((^[Y2 : $i]: 98.71/14.85 (in(Y2, Y0) & 98.71/14.85 Y1(Y2)))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i > $o]: 98.71/14.85 ((~((??((^[Y2 : $i]: 98.71/14.85 (in(Y2, Y0) & 98.71/14.85 Y1(Y2))))))) => 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 (in(Y2, Y0) => 98.71/14.85 (~(Y1(Y2)))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i > $o]: 98.71/14.85 ((??((^[Y2 : $i]: 98.71/14.85 (in(Y2, Y0) & 98.71/14.85 (~(Y1(Y2))))))) => 98.71/14.85 (~((!!((^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 Y1(Y2)))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $o]: 98.71/14.85 (Y0 => 98.71/14.85 in(emptyset, prop2set(Y0)))))) => 98.71/14.85 ((!!((^[Y0 : $o]: 98.71/14.85 (Y0 => 98.71/14.85 set2prop(prop2set(Y0)))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i > $o]: 98.71/14.85 ((~((??((^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) & 98.71/14.85 Y1(Y2))))))) => 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 ( 98.71/14.85 ~( 98.71/14.85 Y1(Y2)))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i > $o]: 98.71/14.85 ((~((!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 Y1(Y2))))))) => 98.71/14.85 (??((^[Y2 : $i]: 98.71/14.85 ( 98.71/14.85 in(Y2, 98.71/14.85 Y0) & 98.71/14.85 ( 98.71/14.85 ~( 98.71/14.85 Y1(Y2)))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i > $o]: 98.71/14.85 ((??(Y0)) => 98.71/14.85 ((!!((^[Y1 : $i]: 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 (Y0(Y1) => 98.71/14.85 (Y0(Y2) => 98.71/14.85 (Y1 = Y2))))))))) => 98.71/14.85 (??((^[Y1 : $i]: 98.71/14.85 (Y0(Y1) & 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (Y0(Y2) => 98.71/14.85 ( 98.71/14.85 Y1 = Y2)))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i > $o]: 98.71/14.85 ((??((^[Y1 : $i]: 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 (Y0(Y2) <=> 98.71/14.85 (Y2 = Y1)))))))) => 98.71/14.85 (??((^[Y1 : $i]: 98.71/14.85 (Y0(Y1) & 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (Y0(Y2) => 98.71/14.85 ( 98.71/14.85 Y1 = Y2))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 ((Y0 = Y1) => 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (( 98.71/14.85 Y2 = Y3) => 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 in(Y3, 98.71/14.85 Y1)))))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 ((Y0 = Y1) => 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (( 98.71/14.85 Y2 = Y3) => 98.71/14.85 (in(Y2, 98.71/14.85 Y0) <=> 98.71/14.85 in(Y3, 98.71/14.85 Y1)))))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i > $o]: 98.71/14.85 ((??((^[Y1 : $i]: 98.71/14.85 (Y0(Y1) & 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (Y0(Y2) => 98.71/14.85 (Y1 = Y2))))))))) => 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (Y0(Y1) => 98.71/14.85 (Y0(Y2) => 98.71/14.85 (Y1 = Y2))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i > $o]: 98.71/14.85 (!!((^[Y1 : $i > $o]: 98.71/14.85 ((!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (( 98.71/14.85 Y2 = Y3) => 98.71/14.85 (Y0(Y2) <=> 98.71/14.85 Y1(Y3))))))))) => 98.71/14.85 (( 98.71/14.85 ??(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (Y0(Y2) & 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (Y0(Y3) => 98.71/14.85 (Y2 = Y3))))))))) <=> 98.71/14.85 ( 98.71/14.85 ??(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (Y1(Y2) & 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (Y1(Y3) => 98.71/14.85 (Y2 = Y3))))))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 (( 98.71/14.85 Y0 = Y1) => 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (( 98.71/14.85 Y2 = Y3) => 98.71/14.85 (setadjoin( 98.71/14.85 Y0, Y2) = 98.71/14.85 setadjoin( 98.71/14.85 Y1, Y3)))))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 Y0 = Y1) => 98.71/14.85 ( 98.71/14.85 powerset( 98.71/14.85 Y0) = 98.71/14.85 powerset( 98.71/14.85 Y1))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 (( 98.71/14.85 Y0 = Y1) => 98.71/14.85 (setunion( 98.71/14.85 Y0) = 98.71/14.85 setunion( 98.71/14.85 Y1))))))))) => 98.71/14.85 ((!!((^[Y0 : $i > $o]: 98.71/14.85 ((??(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (Y0(Y1) & 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (Y0(Y2) => 98.71/14.85 (Y1 = Y2))))))))) => 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (Y0(Y1) => 98.71/14.85 (Y0(Y2) => 98.71/14.85 (Y1 = Y2))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i > $o]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i > $o]: 98.71/14.85 (( 98.71/14.85 !!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (( 98.71/14.85 Y2 = Y3) => 98.71/14.85 (Y0(Y2) <=> 98.71/14.85 Y1(Y3))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 ??(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (Y0(Y2) & 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (Y0(Y3) => 98.71/14.85 (Y2 = Y3))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 ??(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (Y1(Y2) & 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (Y1(Y3) => 98.71/14.85 (Y2 = Y3))))))))) => 98.71/14.85 ( 98.71/14.85 descr(Y0) = 98.71/14.85 descr(Y1))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 Y0 = Y1) => 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y2 : $i > $o]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i > $o]: 98.71/14.85 (( 98.71/14.85 !!(( 98.71/14.85 ^[Y4 : $i]: 98.71/14.85 (in(Y4, 98.71/14.85 Y0) => 98.71/14.85 (!!(( 98.71/14.85 ^[Y5 : $i]: 98.71/14.85 (in(Y5, 98.71/14.85 Y1) => 98.71/14.85 (( 98.71/14.85 Y4 = Y5) => 98.71/14.85 (Y2(Y4) <=> 98.71/14.85 Y3(Y5))))))))))) => 98.71/14.85 (dsetconstr( 98.71/14.85 Y0, Y2) = 98.71/14.85 dsetconstr( 98.71/14.85 Y1, Y3)))))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (( 98.71/14.85 !!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 in(Y2, 98.71/14.85 Y1))))) => 98.71/14.85 subset( 98.71/14.85 Y0, Y1)))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (( 98.71/14.85 Y0 = Y1) => 98.71/14.85 subset( 98.71/14.85 Y1, Y0)))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (( 98.71/14.85 Y0 = Y1) => 98.71/14.85 subset( 98.71/14.85 Y0, Y1)))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (( 98.71/14.85 !!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 in(Y2, 98.71/14.85 Y1))))) => 98.71/14.85 subset( 98.71/14.85 Y0, Y1)))))))) => 98.71/14.85 ((!!(subset( 98.71/14.85 emptyset))) => 98.71/14.85 ((!!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y0, Y1) => 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 in(Y2, 98.71/14.85 Y1)))))))))))) => 98.71/14.85 ((!!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y0, Y1) => 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y1))) => 98.71/14.85 (~( 98.71/14.85 in(Y2, 98.71/14.85 Y0)))))))))))))) => 98.71/14.85 ((!!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y1))) => 98.71/14.85 (~( 98.71/14.85 subset( 98.71/14.85 Y0, Y1)))))))))))))) => 98.71/14.85 ((!!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 subset( 98.71/14.85 Y0, Y1))) => 98.71/14.85 (Y0 != Y1)))))))) => 98.71/14.85 (( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y1))) => 98.71/14.85 (Y0 != Y1)))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 subset( 98.71/14.85 Y0, Y0)))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y0, Y1) => 98.71/14.85 (subset( 98.71/14.85 Y1, Y2) => 98.71/14.85 subset( 98.71/14.85 Y0, Y2)))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 subset( 98.71/14.85 Y1, 98.71/14.85 setadjoin( 98.71/14.85 Y0, Y1)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y0, Y2) => 98.71/14.85 subset( 98.71/14.85 Y0, 98.71/14.85 setadjoin( 98.71/14.85 Y1, Y2)))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y0, Y1) => 98.71/14.85 in(Y0, 98.71/14.85 powerset( 98.71/14.85 Y1))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y0, Y1) => 98.71/14.85 (subset( 98.71/14.85 Y1, Y0) => 98.71/14.85 (Y0 = Y1))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y0, 98.71/14.85 emptyset) => 98.71/14.85 (Y0 = 98.71/14.85 emptyset))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y1, Y0) => 98.71/14.85 in(Y1, 98.71/14.85 powerset( 98.71/14.85 Y0))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (in(Y1, 98.71/14.85 powerset( 98.71/14.85 Y0)) => 98.71/14.85 subset( 98.71/14.85 Y1, Y0)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 in(Y0, 98.71/14.85 powerset( 98.71/14.85 Y0))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y0, Y1) => 98.71/14.85 subset( 98.71/14.85 powerset( 98.71/14.85 Y0), 98.71/14.85 powerset( 98.71/14.85 Y1))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i > $o]: 98.71/14.85 in( 98.71/14.85 dsetconstr( 98.71/14.85 Y0, Y1), 98.71/14.85 powerset( 98.71/14.85 Y0)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i > $o]: 98.71/14.85 subset( 98.71/14.85 dsetconstr( 98.71/14.85 Y0, Y1), 98.71/14.85 Y0))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 in(Y2, 98.71/14.85 binunion( 98.71/14.85 Y0, Y1)))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 in(Y1, 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 setadjoin( 98.71/14.85 Y1, 98.71/14.85 emptyset))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y1) => 98.71/14.85 in(Y2, 98.71/14.85 binunion( 98.71/14.85 Y0, Y1)))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $o]: 98.71/14.85 (in(Y2, 98.71/14.85 binunion( 98.71/14.85 Y0, Y1)) => 98.71/14.85 (( 98.71/14.85 in(Y2, 98.71/14.85 Y0) => Y3) => 98.71/14.85 (( 98.71/14.85 in(Y2, 98.71/14.85 Y1) => Y3) => 98.71/14.85 Y3))))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 binunion( 98.71/14.85 Y0, Y1)) => 98.71/14.85 (in(Y2, 98.71/14.85 Y1) | 98.71/14.85 in(Y2, 98.71/14.85 Y0)))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 subset( 98.71/14.85 Y0, 98.71/14.85 binunion( 98.71/14.85 Y0, Y1)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 subset( 98.71/14.85 Y1, 98.71/14.85 binunion( 98.71/14.85 Y0, Y1)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 (in(Y2, 98.71/14.85 Y1) => 98.71/14.85 in(Y2, 98.71/14.85 binintersect( 98.71/14.85 Y0, Y1))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y2, Y0) => 98.71/14.85 (subset( 98.71/14.85 Y2, Y1) => 98.71/14.85 subset( 98.71/14.85 Y2, 98.71/14.85 binintersect( 98.71/14.85 Y0, Y1))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 binintersect( 98.71/14.85 Y0, Y1)) => 98.71/14.85 in(Y2, 98.71/14.85 Y0))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 subset( 98.71/14.85 binintersect( 98.71/14.85 Y0, Y1), 98.71/14.85 Y0))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y0, Y1) => 98.71/14.85 (binintersect( 98.71/14.85 Y0, Y1) = 98.71/14.85 Y0)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (( 98.71/14.85 binintersect( 98.71/14.85 Y0, Y1) = 98.71/14.85 Y1) => 98.71/14.85 subset( 98.71/14.85 Y1, Y0)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 binintersect( 98.71/14.85 Y0, Y1)) => 98.71/14.85 in(Y2, 98.71/14.85 Y1))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (( 98.71/14.85 ~(( 98.71/14.85 ??(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) & 98.71/14.85 in(Y2, 98.71/14.85 Y1))))))) => 98.71/14.85 (binintersect( 98.71/14.85 Y0, Y1) = 98.71/14.85 emptyset)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 subset( 98.71/14.85 binintersect( 98.71/14.85 Y0, Y1), 98.71/14.85 Y1))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y1, Y0) => 98.71/14.85 (binintersect( 98.71/14.85 Y0, Y1) = 98.71/14.85 Y1)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (( 98.71/14.85 binintersect( 98.71/14.85 Y0, Y1) = 98.71/14.85 Y0) => 98.71/14.85 subset( 98.71/14.85 Y0, Y1)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (binintersect( 98.71/14.85 Y0, 98.71/14.85 binunion( 98.71/14.85 Y1, Y2)) = 98.71/14.85 binunion( 98.71/14.85 binintersect( 98.71/14.85 Y0, Y1), 98.71/14.85 binintersect( 98.71/14.85 Y0, Y2)))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y1))) => 98.71/14.85 in(Y2, 98.71/14.85 setminus( 98.71/14.85 Y0, Y1))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 setminus( 98.71/14.85 Y0, Y1)) => 98.71/14.85 in(Y2, 98.71/14.85 Y0))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 setminus( 98.71/14.85 Y0, Y1)) => 98.71/14.85 (~( 98.71/14.85 in(Y2, 98.71/14.85 Y1))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y0, Y1) => 98.71/14.85 (setminus( 98.71/14.85 Y0, Y1) = 98.71/14.85 emptyset)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 setminus( 98.71/14.85 Y0, Y1)))) => 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 in(Y2, 98.71/14.85 Y1)))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 setminus( 98.71/14.85 Y0, Y1)))) => 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y1))) => 98.71/14.85 (~( 98.71/14.85 in(Y2, 98.71/14.85 Y0)))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y0))) => 98.71/14.85 (~( 98.71/14.85 in(Y2, 98.71/14.85 setminus( 98.71/14.85 Y0, Y1)))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y1) => 98.71/14.85 (~( 98.71/14.85 in(Y2, 98.71/14.85 setminus( 98.71/14.85 Y0, Y1)))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 subset( 98.71/14.85 setminus( 98.71/14.85 Y0, Y1), 98.71/14.85 Y0))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (( 98.71/14.85 setminus( 98.71/14.85 Y0, Y1) = 98.71/14.85 emptyset) => 98.71/14.85 subset( 98.71/14.85 Y0, Y1)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 symdiff( 98.71/14.85 Y0, Y1)) => 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $o]: 98.71/14.85 (( 98.71/14.85 in(Y2, 98.71/14.85 Y0) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y1))) => 98.71/14.85 Y3)) => 98.71/14.85 (( 98.71/14.85 ( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y0))) => 98.71/14.85 ( 98.71/14.85 in(Y2, 98.71/14.85 Y1) => Y3)) => 98.71/14.85 Y3))))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y1))) => 98.71/14.85 in(Y2, 98.71/14.85 symdiff( 98.71/14.85 Y0, Y1))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y0))) => 98.71/14.85 (in(Y2, 98.71/14.85 Y1) => 98.71/14.85 in(Y2, 98.71/14.85 symdiff( 98.71/14.85 Y0, Y1))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 (in(Y2, 98.71/14.85 Y1) => 98.71/14.85 (~( 98.71/14.85 in(Y2, 98.71/14.85 symdiff( 98.71/14.85 Y0, Y1))))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y0))) => 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y1))) => 98.71/14.85 (~( 98.71/14.85 in(Y2, 98.71/14.85 symdiff( 98.71/14.85 Y0, Y1))))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 in(Y1, 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 setadjoin( 98.71/14.85 Y1, 98.71/14.85 emptyset))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 in(Y0, 98.71/14.85 setunion( 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 setadjoin( 98.71/14.85 Y1, 98.71/14.85 emptyset)), 98.71/14.85 emptyset)))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 in(Y1, 98.71/14.85 setunion( 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 setadjoin( 98.71/14.85 Y1, 98.71/14.85 emptyset)), 98.71/14.85 emptyset)))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (??(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 setunion( 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 setadjoin( 98.71/14.85 Y1, 98.71/14.85 emptyset)), 98.71/14.85 emptyset)))) & 98.71/14.85 (??(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (in(Y3, 98.71/14.85 setunion( 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 setadjoin( 98.71/14.85 Y1, 98.71/14.85 emptyset)), 98.71/14.85 emptyset)))) & 98.71/14.85 (setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 setadjoin( 98.71/14.85 Y1, 98.71/14.85 emptyset)), 98.71/14.85 emptyset)) = 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 setadjoin( 98.71/14.85 Y3, 98.71/14.85 emptyset)), 98.71/14.85 emptyset))))))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (??(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 setunion( 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 setadjoin( 98.71/14.85 Y1, 98.71/14.85 emptyset)), 98.71/14.85 emptyset)))) & 98.71/14.85 (??(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (in(Y3, 98.71/14.85 setunion( 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 setadjoin( 98.71/14.85 Y1, 98.71/14.85 emptyset)), 98.71/14.85 emptyset)))) & 98.71/14.85 (setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 setadjoin( 98.71/14.85 Y1, 98.71/14.85 emptyset)), 98.71/14.85 emptyset)) = 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 setadjoin( 98.71/14.85 Y3, 98.71/14.85 emptyset)), 98.71/14.85 emptyset))))))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (in(Y1, 98.71/14.85 Y0) => 98.71/14.85 subset( 98.71/14.85 setadjoin( 98.71/14.85 Y1, 98.71/14.85 emptyset), 98.71/14.85 Y0)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (in(Y1, 98.71/14.85 Y0) => 98.71/14.85 in( 98.71/14.85 setadjoin( 98.71/14.85 Y1, 98.71/14.85 emptyset), 98.71/14.85 powerset( 98.71/14.85 Y0))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 in( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 emptyset), 98.71/14.85 powerset( 98.71/14.85 binunion( 98.71/14.85 Y0, Y1))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 setadjoin( 98.71/14.85 Y1, 98.71/14.85 emptyset))) => 98.71/14.85 (( 98.71/14.85 Y2 = Y1) | 98.71/14.85 (Y2 = Y0)))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (in(Y3, 98.71/14.85 Y1) => 98.71/14.85 subset( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 setadjoin( 98.71/14.85 Y3, 98.71/14.85 emptyset)), 98.71/14.85 binunion( 98.71/14.85 Y0, Y1)))))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (in(Y3, 98.71/14.85 Y1) => 98.71/14.85 in( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 setadjoin( 98.71/14.85 Y3, 98.71/14.85 emptyset)), 98.71/14.85 powerset( 98.71/14.85 binunion( 98.71/14.85 Y0, Y1))))))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (in(Y3, 98.71/14.85 Y1) => 98.71/14.85 subset( 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 setadjoin( 98.71/14.85 Y3, 98.71/14.85 emptyset)), 98.71/14.85 emptyset)), 98.71/14.85 powerset( 98.71/14.85 binunion( 98.71/14.85 Y0, Y1))))))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (in(Y3, 98.71/14.85 Y1) => 98.71/14.85 in( 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 setadjoin( 98.71/14.85 Y3, 98.71/14.85 emptyset)), 98.71/14.85 emptyset)), 98.71/14.85 powerset( 98.71/14.85 powerset( 98.71/14.85 binunion( 98.71/14.85 Y0, Y1)))))))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (in(Y3, 98.71/14.85 Y1) => 98.71/14.85 in( 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 setadjoin( 98.71/14.85 Y3, 98.71/14.85 emptyset)), 98.71/14.85 emptyset)), 98.71/14.85 powerset( 98.71/14.85 powerset( 98.71/14.85 binunion( 98.71/14.85 Y0, Y1)))))))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (in(Y3, 98.71/14.85 Y1) => 98.71/14.85 in( 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y2, 98.71/14.85 setadjoin( 98.71/14.85 Y3, 98.71/14.85 emptyset)), 98.71/14.85 emptyset)), 98.71/14.85 dsetconstr( 98.71/14.85 powerset( 98.71/14.85 powerset( 98.71/14.85 binunion( 98.71/14.85 Y0, Y1))), 98.71/14.85 (^[Y4 : $i]: 98.71/14.85 (??(( 98.71/14.85 ^[Y5 : $i]: 98.71/14.85 (in(Y5, 98.71/14.85 Y0) & 98.71/14.85 (??(( 98.71/14.85 ^[Y6 : $i]: 98.71/14.85 (in(Y6, 98.71/14.85 Y1) & 98.71/14.85 (Y4 = 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y5, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y5, 98.71/14.85 setadjoin( 98.71/14.85 Y6, 98.71/14.85 emptyset)), 98.71/14.85 emptyset)))))))))))))))))))))))))))) => 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 dsetconstr( 98.71/14.85 powerset( 98.71/14.85 powerset( 98.71/14.85 binunion( 98.71/14.85 Y0, Y1))), 98.71/14.85 (^[Y3 : $i]: 98.71/14.85 (??(( 98.71/14.85 ^[Y4 : $i]: 98.71/14.85 (in(Y4, 98.71/14.85 Y0) & 98.71/14.85 (??(( 98.71/14.85 ^[Y5 : $i]: 98.71/14.85 (in(Y5, 98.71/14.85 Y1) & 98.71/14.85 (Y3 = 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y4, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y4, 98.71/14.85 setadjoin( 98.71/14.85 Y5, 98.71/14.85 emptyset)), 98.71/14.85 emptyset)))))))))))))) => 98.71/14.85 (??(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (( 98.71/14.85 ??(( 98.71/14.85 ^[Y4 : $i]: 98.71/14.85 (in(Y4, 98.71/14.85 Y1) & 98.71/14.85 (Y2 = 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y3, 98.71/14.85 emptyset), 98.71/14.85 setadjoin( 98.71/14.85 setadjoin( 98.71/14.85 Y3, 98.71/14.85 setadjoin( 98.71/14.85 Y4, 98.71/14.85 emptyset)), 98.71/14.85 emptyset))))))) & 98.71/14.85 in(Y3, 98.71/14.85 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 98.71/14.85 inference('lazy_cnf_imply', [status(thm)], ['179'])). 98.71/14.85 tff('181', plain, 98.71/14.85 ~ ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 98.71/14.85 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 98.71/14.85 (Y0 = Y1))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => (Y0 = emptyset))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => (Y0 = emptyset))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i > $o]: 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 (in(Y2, Y0) => 98.71/14.85 (in(Y2, dsetconstr(Y0, Y1)) <=> Y1(Y2)))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i > $o]: 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 (in(Y2, Y0) => 98.71/14.85 (Y1(Y2) => (dsetconstr(Y0, Y1) != emptyset)))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 ((??((^[Y1 : $i]: in(Y1, Y0)))) => (Y0 != emptyset))))) => 98.71/14.85 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 98.71/14.85 (in(emptyset, setadjoin(emptyset, emptyset)) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 (in(Y2, Y1) => in(Y2, setadjoin(Y0, Y1)))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 (in(Y2, setadjoin(Y0, Y1)) => 98.71/14.85 (!!((^[Y3 : $o]: 98.71/14.85 (((Y2 = Y0) => Y3) => 98.71/14.85 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 (in(Y2, setadjoin(Y0, Y1)) => 98.71/14.85 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 ((!!((^[Y2 : $i]: 98.71/14.85 (in(Y2, Y1) => in(Y2, Y0))))) => 98.71/14.85 in(Y1, powerset(Y0))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.71/14.85 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 (in(Y1, powerset(Y0)) => 98.71/14.85 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 (in(Y1, Y2) => 98.71/14.85 (in(Y2, Y0) => 98.71/14.85 in(Y1, setunion(Y0))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 (in(Y1, setunion(Y0)) => 98.71/14.85 (!!((^[Y2 : $o]: 98.71/14.85 ((!!((^[Y3 : $i]: 98.71/14.85 (in(Y1, Y3) => 98.71/14.85 (in(Y3, Y0) => Y2))))) => 98.71/14.85 Y2))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 (in(Y1, Y0) => 98.71/14.85 in(Y1, powerset(setunion(Y0)))))))))) => 98.71/14.85 ((!!((^[Y0 : $i > $o]: 98.71/14.85 ((??((^[Y1 : $i]: 98.71/14.85 (Y0(Y1) & 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 (Y0(Y2) => (Y1 = Y2))))))))) => 98.71/14.85 (??((^[Y1 : $i]: 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 ((Y0 != emptyset) => 98.71/14.85 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 (in(Y0, setadjoin(Y1, emptyset)) => 98.71/14.85 (Y0 = Y1)))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 ((Y0 != Y1) => 98.71/14.85 (~(in(Y1, 98.71/14.85 setadjoin(Y0, emptyset))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 ((Y0 = Y1) => 98.71/14.85 in(Y0, setadjoin(Y1, emptyset))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 (in(Y0, 98.71/14.85 setadjoin(Y1, emptyset)) => 98.71/14.85 in(Y1, 98.71/14.85 setadjoin(Y0, emptyset))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 setadjoin(Y0, 98.71/14.85 setadjoin(Y1, 98.71/14.85 emptyset))) => 98.71/14.85 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 in(Y0, 98.71/14.85 setadjoin(Y0, 98.71/14.85 setadjoin(Y1, emptyset))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 in(Y1, 98.71/14.85 setadjoin(Y0, 98.71/14.85 setadjoin(Y1, emptyset))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i > $o]: 98.71/14.85 ((??((^[Y2 : $i]: 98.71/14.85 (in(Y2, Y0) & 98.71/14.85 Y1(Y2))))) => 98.71/14.85 (dsetconstr(Y0, Y1) != 98.71/14.85 emptyset)))))))) => 98.71/14.85 ((!!((^[Y0 : $i > $o]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 (in(Y1, emptyset) => 98.71/14.85 Y0(Y1)))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i > $o]: 98.71/14.85 ((~((!!((^[Y2 : $i]: 98.71/14.85 (in(Y2, Y0) => 98.71/14.85 Y1(Y2))))))) => 98.71/14.85 (??((^[Y2 : $i]: 98.71/14.85 (in(Y2, Y0) & 98.71/14.85 (~(Y1(Y2)))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i > $o]: 98.71/14.85 ((!!((^[Y2 : $i]: 98.71/14.85 (in(Y2, Y0) => 98.71/14.85 (~(Y1(Y2))))))) => 98.71/14.85 (~((??((^[Y2 : $i]: 98.71/14.85 (in(Y2, Y0) & 98.71/14.85 Y1(Y2)))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i > $o]: 98.71/14.85 ((~((??((^[Y2 : $i]: 98.71/14.85 (in(Y2, Y0) & 98.71/14.85 Y1(Y2))))))) => 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 (in(Y2, Y0) => 98.71/14.85 (~(Y1(Y2)))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i > $o]: 98.71/14.85 ((??((^[Y2 : $i]: 98.71/14.85 (in(Y2, Y0) & 98.71/14.85 (~(Y1(Y2))))))) => 98.71/14.85 (~((!!((^[Y2 : $i]: 98.71/14.85 (in(Y2, Y0) => 98.71/14.85 Y1(Y2)))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $o]: 98.71/14.85 (Y0 => 98.71/14.85 in(emptyset, prop2set(Y0)))))) => 98.71/14.85 ((!!((^[Y0 : $o]: 98.71/14.85 (Y0 => 98.71/14.85 set2prop(prop2set(Y0)))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i > $o]: 98.71/14.85 ((~((??((^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) & 98.71/14.85 Y1(Y2))))))) => 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 (in(Y2, Y0) => 98.71/14.85 (~(Y1(Y2)))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i > $o]: 98.71/14.85 ((~((!!((^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 Y1(Y2))))))) => 98.71/14.85 (??((^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) & 98.71/14.85 ( 98.71/14.85 ~( 98.71/14.85 Y1(Y2)))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i > $o]: 98.71/14.85 ((??(Y0)) => 98.71/14.85 ((!!((^[Y1 : $i]: 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 (Y0(Y1) => 98.71/14.85 (Y0(Y2) => 98.71/14.85 (Y1 = Y2))))))))) => 98.71/14.85 (??((^[Y1 : $i]: 98.71/14.85 (Y0(Y1) & 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 (Y0(Y2) => 98.71/14.85 (Y1 = Y2)))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i > $o]: 98.71/14.85 ((??((^[Y1 : $i]: 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 (Y0(Y2) <=> 98.71/14.85 (Y2 = Y1)))))))) => 98.71/14.85 (??((^[Y1 : $i]: 98.71/14.85 (Y0(Y1) & 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 (Y0(Y2) => 98.71/14.85 (Y1 = Y2))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 ((Y0 = Y1) => 98.71/14.85 (!!((^[Y2 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (( 98.71/14.85 Y2 = Y3) => 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 in(Y3, 98.71/14.85 Y1)))))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 ((Y0 = Y1) => 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (( 98.71/14.85 Y2 = Y3) => 98.71/14.85 (in(Y2, 98.71/14.85 Y0) <=> 98.71/14.85 in(Y3, 98.71/14.85 Y1)))))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i > $o]: 98.71/14.85 ((??((^[Y1 : $i]: 98.71/14.85 (Y0(Y1) & 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (Y0(Y2) => 98.71/14.85 (Y1 = Y2))))))))) => 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 ( 98.71/14.85 Y0(Y1) => 98.71/14.85 ( 98.71/14.85 Y0(Y2) => 98.71/14.85 ( 98.71/14.85 Y1 = Y2))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i > $o]: 98.71/14.85 (!!((^[Y1 : $i > $o]: 98.71/14.85 ((!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (( 98.71/14.85 Y2 = Y3) => 98.71/14.85 (Y0(Y2) <=> 98.71/14.85 Y1(Y3))))))))) => 98.71/14.85 ((??(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (Y0(Y2) & 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (Y0(Y3) => 98.71/14.85 (Y2 = Y3))))))))) <=> 98.71/14.85 (??(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (Y1(Y2) & 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (Y1(Y3) => 98.71/14.85 (Y2 = Y3))))))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 ((Y0 = Y1) => 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (( 98.71/14.85 Y2 = Y3) => 98.71/14.85 (setadjoin( 98.71/14.85 Y0, Y2) = 98.71/14.85 setadjoin( 98.71/14.85 Y1, Y3)))))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 (( 98.71/14.85 Y0 = Y1) => 98.71/14.85 ( 98.71/14.85 powerset( 98.71/14.85 Y0) = 98.71/14.85 powerset( 98.71/14.85 Y1))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 Y0 = Y1) => 98.71/14.85 ( 98.71/14.85 setunion( 98.71/14.85 Y0) = 98.71/14.85 setunion( 98.71/14.85 Y1))))))))) => 98.71/14.85 ((!!((^[Y0 : $i > $o]: 98.71/14.85 ((??((^[Y1 : $i]: 98.71/14.85 (Y0(Y1) & 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (Y0(Y2) => 98.71/14.85 (Y1 = Y2))))))))) => 98.71/14.85 (!!((^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (Y0(Y1) => 98.71/14.85 (Y0(Y2) => 98.71/14.85 (Y1 = Y2))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i > $o]: 98.71/14.85 (!!((^[Y1 : $i > $o]: 98.71/14.85 (( 98.71/14.85 !!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (( 98.71/14.85 Y2 = Y3) => 98.71/14.85 (Y0(Y2) <=> 98.71/14.85 Y1(Y3))))))))) => 98.71/14.85 (( 98.71/14.85 ??(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (Y0(Y2) & 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (Y0(Y3) => 98.71/14.85 (Y2 = Y3))))))))) => 98.71/14.85 (( 98.71/14.85 ??(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (Y1(Y2) & 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i]: 98.71/14.85 (Y1(Y3) => 98.71/14.85 (Y2 = Y3))))))))) => 98.71/14.85 (descr( 98.71/14.85 Y0) = 98.71/14.85 descr(Y1))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (( 98.71/14.85 Y0 = Y1) => 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y2 : $i > $o]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $i > $o]: 98.71/14.85 (( 98.71/14.85 !!(( 98.71/14.85 ^[Y4 : $i]: 98.71/14.85 (in(Y4, 98.71/14.85 Y0) => 98.71/14.85 (!!(( 98.71/14.85 ^[Y5 : $i]: 98.71/14.85 (in(Y5, 98.71/14.85 Y1) => 98.71/14.85 (( 98.71/14.85 Y4 = Y5) => 98.71/14.85 (Y2(Y4) <=> 98.71/14.85 Y3(Y5))))))))))) => 98.71/14.85 (dsetconstr( 98.71/14.85 Y0, Y2) = 98.71/14.85 dsetconstr( 98.71/14.85 Y1, Y3)))))))))))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 in(Y2, 98.71/14.85 Y1))))) => 98.71/14.85 subset( 98.71/14.85 Y0, Y1)))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (( 98.71/14.85 Y0 = Y1) => 98.71/14.85 subset( 98.71/14.85 Y1, Y0)))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (( 98.71/14.85 Y0 = Y1) => 98.71/14.85 subset( 98.71/14.85 Y0, Y1)))))))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (( 98.71/14.85 !!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 in(Y2, 98.71/14.85 Y1))))) => 98.71/14.85 subset( 98.71/14.85 Y0, Y1)))))))) => 98.71/14.85 ((!!(subset( 98.71/14.85 emptyset))) => 98.71/14.85 ((!!((^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y0, Y1) => 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 in(Y2, 98.71/14.85 Y1)))))))))))) => 98.71/14.85 ((!!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y0, Y1) => 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y1))) => 98.71/14.85 (~( 98.71/14.85 in(Y2, 98.71/14.85 Y0)))))))))))))) => 98.71/14.85 ((!!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y1))) => 98.71/14.85 (~( 98.71/14.85 subset( 98.71/14.85 Y0, Y1)))))))))))))) => 98.71/14.85 ((!!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 subset( 98.71/14.85 Y0, Y1))) => 98.71/14.85 (Y0 != Y1)))))))) => 98.71/14.85 ((!!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y1))) => 98.71/14.85 (Y0 != Y1)))))))))))) => 98.71/14.85 (( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 subset( 98.71/14.85 Y0, Y0)))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y0, Y1) => 98.71/14.85 (subset( 98.71/14.85 Y1, Y2) => 98.71/14.85 subset( 98.71/14.85 Y0, Y2)))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 subset( 98.71/14.85 Y1, 98.71/14.85 setadjoin( 98.71/14.85 Y0, Y1)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y0, Y2) => 98.71/14.85 subset( 98.71/14.85 Y0, 98.71/14.85 setadjoin( 98.71/14.85 Y1, Y2)))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y0, Y1) => 98.71/14.85 in(Y0, 98.71/14.85 powerset( 98.71/14.85 Y1))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y0, Y1) => 98.71/14.85 (subset( 98.71/14.85 Y1, Y0) => 98.71/14.85 (Y0 = Y1))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y0, 98.71/14.85 emptyset) => 98.71/14.85 (Y0 = 98.71/14.85 emptyset))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y1, Y0) => 98.71/14.85 in(Y1, 98.71/14.85 powerset( 98.71/14.85 Y0))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (in(Y1, 98.71/14.85 powerset( 98.71/14.85 Y0)) => 98.71/14.85 subset( 98.71/14.85 Y1, Y0)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 in(Y0, 98.71/14.85 powerset( 98.71/14.85 Y0))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y0, Y1) => 98.71/14.85 subset( 98.71/14.85 powerset( 98.71/14.85 Y0), 98.71/14.85 powerset( 98.71/14.85 Y1))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i > $o]: 98.71/14.85 in( 98.71/14.85 dsetconstr( 98.71/14.85 Y0, Y1), 98.71/14.85 powerset( 98.71/14.85 Y0)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i > $o]: 98.71/14.85 subset( 98.71/14.85 dsetconstr( 98.71/14.85 Y0, Y1), 98.71/14.85 Y0))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 in(Y2, 98.71/14.85 binunion( 98.71/14.85 Y0, Y1)))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 in(Y1, 98.71/14.85 setadjoin( 98.71/14.85 Y0, 98.71/14.85 setadjoin( 98.71/14.85 Y1, 98.71/14.85 emptyset))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y1) => 98.71/14.85 in(Y2, 98.71/14.85 binunion( 98.71/14.85 Y0, Y1)))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $o]: 98.71/14.85 (in(Y2, 98.71/14.85 binunion( 98.71/14.85 Y0, Y1)) => 98.71/14.85 (( 98.71/14.85 in(Y2, 98.71/14.85 Y0) => Y3) => 98.71/14.85 (( 98.71/14.85 in(Y2, 98.71/14.85 Y1) => Y3) => 98.71/14.85 Y3))))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 binunion( 98.71/14.85 Y0, Y1)) => 98.71/14.85 (in(Y2, 98.71/14.85 Y1) | 98.71/14.85 in(Y2, 98.71/14.85 Y0)))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 subset( 98.71/14.85 Y0, 98.71/14.85 binunion( 98.71/14.85 Y0, Y1)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 subset( 98.71/14.85 Y1, 98.71/14.85 binunion( 98.71/14.85 Y0, Y1)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 (in(Y2, 98.71/14.85 Y1) => 98.71/14.85 in(Y2, 98.71/14.85 binintersect( 98.71/14.85 Y0, Y1))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y2, Y0) => 98.71/14.85 (subset( 98.71/14.85 Y2, Y1) => 98.71/14.85 subset( 98.71/14.85 Y2, 98.71/14.85 binintersect( 98.71/14.85 Y0, Y1))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 binintersect( 98.71/14.85 Y0, Y1)) => 98.71/14.85 in(Y2, 98.71/14.85 Y0))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 subset( 98.71/14.85 binintersect( 98.71/14.85 Y0, Y1), 98.71/14.85 Y0))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y0, Y1) => 98.71/14.85 (binintersect( 98.71/14.85 Y0, Y1) = 98.71/14.85 Y0)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (( 98.71/14.85 binintersect( 98.71/14.85 Y0, Y1) = 98.71/14.85 Y1) => 98.71/14.85 subset( 98.71/14.85 Y1, Y0)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 binintersect( 98.71/14.85 Y0, Y1)) => 98.71/14.85 in(Y2, 98.71/14.85 Y1))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (( 98.71/14.85 ~(( 98.71/14.85 ??(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) & 98.71/14.85 in(Y2, 98.71/14.85 Y1))))))) => 98.71/14.85 (binintersect( 98.71/14.85 Y0, Y1) = 98.71/14.85 emptyset)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 subset( 98.71/14.85 binintersect( 98.71/14.85 Y0, Y1), 98.71/14.85 Y1))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y1, Y0) => 98.71/14.85 (binintersect( 98.71/14.85 Y0, Y1) = 98.71/14.85 Y1)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (( 98.71/14.85 binintersect( 98.71/14.85 Y0, Y1) = 98.71/14.85 Y0) => 98.71/14.85 subset( 98.71/14.85 Y0, Y1)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (binintersect( 98.71/14.85 Y0, 98.71/14.85 binunion( 98.71/14.85 Y1, Y2)) = 98.71/14.85 binunion( 98.71/14.85 binintersect( 98.71/14.85 Y0, Y1), 98.71/14.85 binintersect( 98.71/14.85 Y0, Y2)))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y1))) => 98.71/14.85 in(Y2, 98.71/14.85 setminus( 98.71/14.85 Y0, Y1))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 setminus( 98.71/14.85 Y0, Y1)) => 98.71/14.85 in(Y2, 98.71/14.85 Y0))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 setminus( 98.71/14.85 Y0, Y1)) => 98.71/14.85 (~( 98.71/14.85 in(Y2, 98.71/14.85 Y1))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (subset( 98.71/14.85 Y0, Y1) => 98.71/14.85 (setminus( 98.71/14.85 Y0, Y1) = 98.71/14.85 emptyset)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 setminus( 98.71/14.85 Y0, Y1)))) => 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 in(Y2, 98.71/14.85 Y1)))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 setminus( 98.71/14.85 Y0, Y1)))) => 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y1))) => 98.71/14.85 (~( 98.71/14.85 in(Y2, 98.71/14.85 Y0)))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y0))) => 98.71/14.85 (~( 98.71/14.85 in(Y2, 98.71/14.85 setminus( 98.71/14.85 Y0, Y1)))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y1) => 98.71/14.85 (~( 98.71/14.85 in(Y2, 98.71/14.85 setminus( 98.71/14.85 Y0, Y1)))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 subset( 98.71/14.85 setminus( 98.71/14.85 Y0, Y1), 98.71/14.85 Y0))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (( 98.71/14.85 setminus( 98.71/14.85 Y0, Y1) = 98.71/14.85 emptyset) => 98.71/14.85 subset( 98.71/14.85 Y0, Y1)))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 symdiff( 98.71/14.85 Y0, Y1)) => 98.71/14.85 (!!(( 98.71/14.85 ^[Y3 : $o]: 98.71/14.85 (( 98.71/14.85 in(Y2, 98.71/14.85 Y0) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y1))) => 98.71/14.85 Y3)) => 98.71/14.85 (( 98.71/14.85 ( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y0))) => 98.71/14.85 ( 98.71/14.85 in(Y2, 98.71/14.85 Y1) => Y3)) => 98.71/14.85 Y3))))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y1))) => 98.71/14.85 in(Y2, 98.71/14.85 symdiff( 98.71/14.85 Y0, Y1))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y0))) => 98.71/14.85 (in(Y2, 98.71/14.85 Y1) => 98.71/14.85 in(Y2, 98.71/14.85 symdiff( 98.71/14.85 Y0, Y1))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (in(Y2, 98.71/14.85 Y0) => 98.71/14.85 (in(Y2, 98.71/14.85 Y1) => 98.71/14.85 (~( 98.71/14.85 in(Y2, 98.71/14.85 symdiff( 98.71/14.85 Y0, Y1))))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y2 : $i]: 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y0))) => 98.71/14.85 (( 98.71/14.85 ~( 98.71/14.85 in(Y2, 98.71/14.85 Y1))) => 98.71/14.85 (~( 98.71/14.85 in(Y2, 98.71/14.85 symdiff( 98.71/14.85 Y0, Y1))))))))))))))) => 98.71/14.85 ( 98.71/14.85 ( 98.71/14.85 !!(( 98.71/14.85 ^[Y0 : $i]: 98.71/14.85 (!!(( 98.71/14.85 ^[Y1 : $i]: 98.71/14.86 in(Y1, 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 in(Y0, 98.71/14.86 setunion( 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 in(Y1, 98.71/14.86 setunion( 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (??(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 setunion( 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)))) & 98.71/14.86 (??(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (in(Y3, 98.71/14.86 setunion( 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)))) & 98.71/14.86 (setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)) = 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 setadjoin( 98.71/14.86 Y3, 98.71/14.86 emptyset)), 98.71/14.86 emptyset))))))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (??(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 setunion( 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)))) & 98.71/14.86 (??(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (in(Y3, 98.71/14.86 setunion( 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)))) & 98.71/14.86 (setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)) = 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 setadjoin( 98.71/14.86 Y3, 98.71/14.86 emptyset)), 98.71/14.86 emptyset))))))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (in(Y1, 98.71/14.86 Y0) => 98.71/14.86 subset( 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset), 98.71/14.86 Y0)))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (in(Y1, 98.71/14.86 Y0) => 98.71/14.86 in( 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset), 98.71/14.86 powerset( 98.71/14.86 Y0))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 in( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 emptyset), 98.71/14.86 powerset( 98.71/14.86 binunion( 98.71/14.86 Y0, Y1))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset))) => 98.71/14.86 (( 98.71/14.86 Y2 = Y1) | 98.71/14.86 (Y2 = Y0)))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (in(Y3, 98.71/14.86 Y1) => 98.71/14.86 subset( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 setadjoin( 98.71/14.86 Y3, 98.71/14.86 emptyset)), 98.71/14.86 binunion( 98.71/14.86 Y0, Y1)))))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (in(Y3, 98.71/14.86 Y1) => 98.71/14.86 in( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 setadjoin( 98.71/14.86 Y3, 98.71/14.86 emptyset)), 98.71/14.86 powerset( 98.71/14.86 binunion( 98.71/14.86 Y0, Y1))))))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (in(Y3, 98.71/14.86 Y1) => 98.71/14.86 subset( 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 setadjoin( 98.71/14.86 Y3, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)), 98.71/14.86 powerset( 98.71/14.86 binunion( 98.71/14.86 Y0, Y1))))))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (in(Y3, 98.71/14.86 Y1) => 98.71/14.86 in( 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 setadjoin( 98.71/14.86 Y3, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)), 98.71/14.86 powerset( 98.71/14.86 powerset( 98.71/14.86 binunion( 98.71/14.86 Y0, Y1)))))))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (in(Y3, 98.71/14.86 Y1) => 98.71/14.86 in( 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 setadjoin( 98.71/14.86 Y3, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)), 98.71/14.86 powerset( 98.71/14.86 powerset( 98.71/14.86 binunion( 98.71/14.86 Y0, Y1)))))))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (in(Y3, 98.71/14.86 Y1) => 98.71/14.86 in( 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 setadjoin( 98.71/14.86 Y3, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)), 98.71/14.86 dsetconstr( 98.71/14.86 powerset( 98.71/14.86 powerset( 98.71/14.86 binunion( 98.71/14.86 Y0, Y1))), 98.71/14.86 (^[Y4 : $i]: 98.71/14.86 (??(( 98.71/14.86 ^[Y5 : $i]: 98.71/14.86 (in(Y5, 98.71/14.86 Y0) & 98.71/14.86 (??(( 98.71/14.86 ^[Y6 : $i]: 98.71/14.86 (in(Y6, 98.71/14.86 Y1) & 98.71/14.86 (Y4 = 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y5, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y5, 98.71/14.86 setadjoin( 98.71/14.86 Y6, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)))))))))))))))))))))))))))) => 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 dsetconstr( 98.71/14.86 powerset( 98.71/14.86 powerset( 98.71/14.86 binunion( 98.71/14.86 Y0, Y1))), 98.71/14.86 (^[Y3 : $i]: 98.71/14.86 (??(( 98.71/14.86 ^[Y4 : $i]: 98.71/14.86 (in(Y4, 98.71/14.86 Y0) & 98.71/14.86 (??(( 98.71/14.86 ^[Y5 : $i]: 98.71/14.86 (in(Y5, 98.71/14.86 Y1) & 98.71/14.86 (Y3 = 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y4, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y4, 98.71/14.86 setadjoin( 98.71/14.86 Y5, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)))))))))))))) => 98.71/14.86 (??(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (( 98.71/14.86 ??(( 98.71/14.86 ^[Y4 : $i]: 98.71/14.86 (in(Y4, 98.71/14.86 Y1) & 98.71/14.86 (Y2 = 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y3, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y3, 98.71/14.86 setadjoin( 98.71/14.86 Y4, 98.71/14.86 emptyset)), 98.71/14.86 emptyset))))))) & 98.71/14.86 in(Y3, 98.71/14.86 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 98.71/14.86 inference('lazy_cnf_imply', [status(thm)], ['180'])). 98.71/14.86 tff('182', plain, 98.71/14.86 ~ ((!!((^[Y0 : $i]: 98.71/14.86 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => (Y0 = emptyset))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => (Y0 = emptyset))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i > $o]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) => 98.71/14.86 (in(Y2, dsetconstr(Y0, Y1)) <=> Y1(Y2)))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i > $o]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) => 98.71/14.86 (Y1(Y2) => (dsetconstr(Y0, Y1) != emptyset)))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 ((??((^[Y1 : $i]: in(Y1, Y0)))) => (Y0 != emptyset))))) => 98.71/14.86 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 98.71/14.86 (in(emptyset, setadjoin(emptyset, emptyset)) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y1) => in(Y2, setadjoin(Y0, Y1)))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, setadjoin(Y0, Y1)) => 98.71/14.86 (!!((^[Y3 : $o]: 98.71/14.86 (((Y2 = Y0) => Y3) => 98.71/14.86 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, setadjoin(Y0, Y1)) => 98.71/14.86 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 98.71/14.86 in(Y1, powerset(Y0))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.71/14.86 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (in(Y1, powerset(Y0)) => 98.71/14.86 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (in(Y1, Y2) => 98.71/14.86 (in(Y2, Y0) => 98.71/14.86 in(Y1, setunion(Y0))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (in(Y1, setunion(Y0)) => 98.71/14.86 (!!((^[Y2 : $o]: 98.71/14.86 ((!!((^[Y3 : $i]: 98.71/14.86 (in(Y1, Y3) => 98.71/14.86 (in(Y3, Y0) => Y2))))) => 98.71/14.86 Y2))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (in(Y1, Y0) => 98.71/14.86 in(Y1, powerset(setunion(Y0)))))))))) => 98.71/14.86 ((!!((^[Y0 : $i > $o]: 98.71/14.86 ((??((^[Y1 : $i]: 98.71/14.86 (Y0(Y1) & 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (Y0(Y2) => (Y1 = Y2))))))))) => 98.71/14.86 (??((^[Y1 : $i]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 ((Y0 != emptyset) => 98.71/14.86 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (in(Y0, setadjoin(Y1, emptyset)) => 98.71/14.86 (Y0 = Y1)))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 ((Y0 != Y1) => 98.71/14.86 (~(in(Y1, 98.71/14.86 setadjoin(Y0, emptyset))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 ((Y0 = Y1) => 98.71/14.86 in(Y0, setadjoin(Y1, emptyset))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (in(Y0, setadjoin(Y1, emptyset)) => 98.71/14.86 in(Y1, setadjoin(Y0, emptyset))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 setadjoin(Y0, 98.71/14.86 setadjoin(Y1, 98.71/14.86 emptyset))) => 98.71/14.86 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 in(Y0, 98.71/14.86 setadjoin(Y0, 98.71/14.86 setadjoin(Y1, emptyset))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 in(Y1, 98.71/14.86 setadjoin(Y0, 98.71/14.86 setadjoin(Y1, emptyset))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i > $o]: 98.71/14.86 ((??((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) & Y1(Y2))))) => 98.71/14.86 (dsetconstr(Y0, Y1) != 98.71/14.86 emptyset)))))))) => 98.71/14.86 ((!!((^[Y0 : $i > $o]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (in(Y1, emptyset) => Y0(Y1)))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i > $o]: 98.71/14.86 ((~((!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) => 98.71/14.86 Y1(Y2))))))) => 98.71/14.86 (??((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) & 98.71/14.86 (~(Y1(Y2)))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i > $o]: 98.71/14.86 ((!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) => 98.71/14.86 (~(Y1(Y2))))))) => 98.71/14.86 (~((??((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) & 98.71/14.86 Y1(Y2)))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i > $o]: 98.71/14.86 ((~((??((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) & 98.71/14.86 Y1(Y2))))))) => 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) => 98.71/14.86 (~(Y1(Y2)))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i > $o]: 98.71/14.86 ((??((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) & 98.71/14.86 (~(Y1(Y2))))))) => 98.71/14.86 (~((!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) => 98.71/14.86 Y1(Y2)))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $o]: 98.71/14.86 (Y0 => 98.71/14.86 in(emptyset, prop2set(Y0)))))) => 98.71/14.86 ((!!((^[Y0 : $o]: 98.71/14.86 (Y0 => 98.71/14.86 set2prop(prop2set(Y0)))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i > $o]: 98.71/14.86 ((~((??((^[Y2 : $i]: 98.71/14.86 ( 98.71/14.86 in(Y2, 98.71/14.86 Y0) & 98.71/14.86 Y1(Y2))))))) => 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) => 98.71/14.86 (~(Y1(Y2)))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i > $o]: 98.71/14.86 ((~((!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 Y1(Y2))))))) => 98.71/14.86 (??((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) & 98.71/14.86 (~(Y1(Y2)))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i > $o]: 98.71/14.86 ((??(Y0)) => 98.71/14.86 ((!!((^[Y1 : $i]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 ( 98.71/14.86 Y0(Y1) => 98.71/14.86 ( 98.71/14.86 Y0(Y2) => 98.71/14.86 ( 98.71/14.86 Y1 = Y2))))))))) => 98.71/14.86 (??((^[Y1 : $i]: 98.71/14.86 (Y0(Y1) & 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (Y0(Y2) => 98.71/14.86 (Y1 = Y2)))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i > $o]: 98.71/14.86 ((??((^[Y1 : $i]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 ( 98.71/14.86 Y0(Y2) <=> 98.71/14.86 ( 98.71/14.86 Y2 = Y1)))))))) => 98.71/14.86 (??((^[Y1 : $i]: 98.71/14.86 (Y0(Y1) & 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (Y0(Y2) => 98.71/14.86 (Y1 = Y2))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 ((Y0 = Y1) => 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (( 98.71/14.86 Y2 = Y3) => 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 in(Y3, 98.71/14.86 Y1)))))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 ((Y0 = Y1) => 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (( 98.71/14.86 Y2 = Y3) => 98.71/14.86 (in(Y2, 98.71/14.86 Y0) <=> 98.71/14.86 in(Y3, 98.71/14.86 Y1)))))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i > $o]: 98.71/14.86 ((??((^[Y1 : $i]: 98.71/14.86 (Y0(Y1) & 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 ( 98.71/14.86 Y0(Y2) => 98.71/14.86 ( 98.71/14.86 Y1 = Y2))))))))) => 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (Y0(Y1) => 98.71/14.86 ( 98.71/14.86 Y0(Y2) => 98.71/14.86 ( 98.71/14.86 Y1 = Y2))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i > $o]: 98.71/14.86 (!!((^[Y1 : $i > $o]: 98.71/14.86 ((!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (( 98.71/14.86 Y2 = Y3) => 98.71/14.86 (Y0(Y2) <=> 98.71/14.86 Y1(Y3))))))))) => 98.71/14.86 ((??(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (Y0(Y2) & 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (Y0(Y3) => 98.71/14.86 (Y2 = Y3))))))))) <=> 98.71/14.86 (??(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (Y1(Y2) & 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (Y1(Y3) => 98.71/14.86 (Y2 = Y3))))))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 ((Y0 = Y1) => 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (( 98.71/14.86 Y2 = Y3) => 98.71/14.86 (setadjoin( 98.71/14.86 Y0, Y2) = 98.71/14.86 setadjoin( 98.71/14.86 Y1, Y3)))))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 ((Y0 = Y1) => 98.71/14.86 (powerset( 98.71/14.86 Y0) = 98.71/14.86 powerset( 98.71/14.86 Y1))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (( 98.71/14.86 Y0 = Y1) => 98.71/14.86 ( 98.71/14.86 setunion( 98.71/14.86 Y0) = 98.71/14.86 setunion( 98.71/14.86 Y1))))))))) => 98.71/14.86 ((!!((^[Y0 : $i > $o]: 98.71/14.86 ((??((^[Y1 : $i]: 98.71/14.86 (Y0(Y1) & 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (Y0(Y2) => 98.71/14.86 (Y1 = Y2))))))))) => 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (Y0(Y1) => 98.71/14.86 (Y0(Y2) => 98.71/14.86 (Y1 = Y2))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i > $o]: 98.71/14.86 (!!((^[Y1 : $i > $o]: 98.71/14.86 (( 98.71/14.86 !!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (( 98.71/14.86 Y2 = Y3) => 98.71/14.86 (Y0(Y2) <=> 98.71/14.86 Y1(Y3))))))))) => 98.71/14.86 (( 98.71/14.86 ??(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (Y0(Y2) & 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (Y0(Y3) => 98.71/14.86 (Y2 = Y3))))))))) => 98.71/14.86 (( 98.71/14.86 ??(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (Y1(Y2) & 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (Y1(Y3) => 98.71/14.86 (Y2 = Y3))))))))) => 98.71/14.86 (descr( 98.71/14.86 Y0) = 98.71/14.86 descr(Y1))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (( 98.71/14.86 Y0 = Y1) => 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i > $o]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i > $o]: 98.71/14.86 (( 98.71/14.86 !!(( 98.71/14.86 ^[Y4 : $i]: 98.71/14.86 (in(Y4, 98.71/14.86 Y0) => 98.71/14.86 (!!(( 98.71/14.86 ^[Y5 : $i]: 98.71/14.86 (in(Y5, 98.71/14.86 Y1) => 98.71/14.86 (( 98.71/14.86 Y4 = Y5) => 98.71/14.86 (Y2(Y4) <=> 98.71/14.86 Y3(Y5))))))))))) => 98.71/14.86 (dsetconstr( 98.71/14.86 Y0, Y2) = 98.71/14.86 dsetconstr( 98.71/14.86 Y1, Y3)))))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (( 98.71/14.86 !!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 in(Y2, 98.71/14.86 Y1))))) => 98.71/14.86 subset( 98.71/14.86 Y0, Y1)))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 Y0 = Y1) => 98.71/14.86 subset( 98.71/14.86 Y1, Y0)))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (( 98.71/14.86 Y0 = Y1) => 98.71/14.86 subset( 98.71/14.86 Y0, Y1)))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (( 98.71/14.86 !!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 in(Y2, 98.71/14.86 Y1))))) => 98.71/14.86 subset( 98.71/14.86 Y0, Y1)))))))) => 98.71/14.86 ((!!(subset( 98.71/14.86 emptyset))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (subset( 98.71/14.86 Y0, Y1) => 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 in(Y2, 98.71/14.86 Y1)))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (subset( 98.71/14.86 Y0, Y1) => 98.71/14.86 (( 98.71/14.86 ~( 98.71/14.86 in(Y2, 98.71/14.86 Y1))) => 98.71/14.86 (~( 98.71/14.86 in(Y2, 98.71/14.86 Y0)))))))))))))) => 98.71/14.86 ((!!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 (( 98.71/14.86 ~( 98.71/14.86 in(Y2, 98.71/14.86 Y1))) => 98.71/14.86 (~( 98.71/14.86 subset( 98.71/14.86 Y0, Y1)))))))))))))) => 98.71/14.86 ((!!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (( 98.71/14.86 ~( 98.71/14.86 subset( 98.71/14.86 Y0, Y1))) => 98.71/14.86 (Y0 != Y1)))))))) => 98.71/14.86 ((!!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 (( 98.71/14.86 ~( 98.71/14.86 in(Y2, 98.71/14.86 Y1))) => 98.71/14.86 (Y0 != Y1)))))))))))) => 98.71/14.86 ((!!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 subset( 98.71/14.86 Y0, Y0)))) => 98.71/14.86 (( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (subset( 98.71/14.86 Y0, Y1) => 98.71/14.86 (subset( 98.71/14.86 Y1, Y2) => 98.71/14.86 subset( 98.71/14.86 Y0, Y2)))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 subset( 98.71/14.86 Y1, 98.71/14.86 setadjoin( 98.71/14.86 Y0, Y1)))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (subset( 98.71/14.86 Y0, Y2) => 98.71/14.86 subset( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, Y2)))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (subset( 98.71/14.86 Y0, Y1) => 98.71/14.86 in(Y0, 98.71/14.86 powerset( 98.71/14.86 Y1))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (subset( 98.71/14.86 Y0, Y1) => 98.71/14.86 (subset( 98.71/14.86 Y1, Y0) => 98.71/14.86 (Y0 = Y1))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (subset( 98.71/14.86 Y0, 98.71/14.86 emptyset) => 98.71/14.86 (Y0 = 98.71/14.86 emptyset))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (subset( 98.71/14.86 Y1, Y0) => 98.71/14.86 in(Y1, 98.71/14.86 powerset( 98.71/14.86 Y0))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (in(Y1, 98.71/14.86 powerset( 98.71/14.86 Y0)) => 98.71/14.86 subset( 98.71/14.86 Y1, Y0)))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 in(Y0, 98.71/14.86 powerset( 98.71/14.86 Y0))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (subset( 98.71/14.86 Y0, Y1) => 98.71/14.86 subset( 98.71/14.86 powerset( 98.71/14.86 Y0), 98.71/14.86 powerset( 98.71/14.86 Y1))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i > $o]: 98.71/14.86 in( 98.71/14.86 dsetconstr( 98.71/14.86 Y0, Y1), 98.71/14.86 powerset( 98.71/14.86 Y0)))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i > $o]: 98.71/14.86 subset( 98.71/14.86 dsetconstr( 98.71/14.86 Y0, Y1), 98.71/14.86 Y0))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 in(Y2, 98.71/14.86 binunion( 98.71/14.86 Y0, Y1)))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 in(Y1, 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y1) => 98.71/14.86 in(Y2, 98.71/14.86 binunion( 98.71/14.86 Y0, Y1)))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $o]: 98.71/14.86 (in(Y2, 98.71/14.86 binunion( 98.71/14.86 Y0, Y1)) => 98.71/14.86 (( 98.71/14.86 in(Y2, 98.71/14.86 Y0) => Y3) => 98.71/14.86 (( 98.71/14.86 in(Y2, 98.71/14.86 Y1) => Y3) => 98.71/14.86 Y3))))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 binunion( 98.71/14.86 Y0, Y1)) => 98.71/14.86 (in(Y2, 98.71/14.86 Y1) | 98.71/14.86 in(Y2, 98.71/14.86 Y0)))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 subset( 98.71/14.86 Y0, 98.71/14.86 binunion( 98.71/14.86 Y0, Y1)))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 subset( 98.71/14.86 Y1, 98.71/14.86 binunion( 98.71/14.86 Y0, Y1)))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 (in(Y2, 98.71/14.86 Y1) => 98.71/14.86 in(Y2, 98.71/14.86 binintersect( 98.71/14.86 Y0, Y1))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (subset( 98.71/14.86 Y2, Y0) => 98.71/14.86 (subset( 98.71/14.86 Y2, Y1) => 98.71/14.86 subset( 98.71/14.86 Y2, 98.71/14.86 binintersect( 98.71/14.86 Y0, Y1))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 binintersect( 98.71/14.86 Y0, Y1)) => 98.71/14.86 in(Y2, 98.71/14.86 Y0))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 subset( 98.71/14.86 binintersect( 98.71/14.86 Y0, Y1), 98.71/14.86 Y0))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (subset( 98.71/14.86 Y0, Y1) => 98.71/14.86 (binintersect( 98.71/14.86 Y0, Y1) = 98.71/14.86 Y0)))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (( 98.71/14.86 binintersect( 98.71/14.86 Y0, Y1) = 98.71/14.86 Y1) => 98.71/14.86 subset( 98.71/14.86 Y1, Y0)))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 binintersect( 98.71/14.86 Y0, Y1)) => 98.71/14.86 in(Y2, 98.71/14.86 Y1))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (( 98.71/14.86 ~(( 98.71/14.86 ??(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) & 98.71/14.86 in(Y2, 98.71/14.86 Y1))))))) => 98.71/14.86 (binintersect( 98.71/14.86 Y0, Y1) = 98.71/14.86 emptyset)))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 subset( 98.71/14.86 binintersect( 98.71/14.86 Y0, Y1), 98.71/14.86 Y1))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (subset( 98.71/14.86 Y1, Y0) => 98.71/14.86 (binintersect( 98.71/14.86 Y0, Y1) = 98.71/14.86 Y1)))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (( 98.71/14.86 binintersect( 98.71/14.86 Y0, Y1) = 98.71/14.86 Y0) => 98.71/14.86 subset( 98.71/14.86 Y0, Y1)))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (binintersect( 98.71/14.86 Y0, 98.71/14.86 binunion( 98.71/14.86 Y1, Y2)) = 98.71/14.86 binunion( 98.71/14.86 binintersect( 98.71/14.86 Y0, Y1), 98.71/14.86 binintersect( 98.71/14.86 Y0, Y2)))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 (( 98.71/14.86 ~( 98.71/14.86 in(Y2, 98.71/14.86 Y1))) => 98.71/14.86 in(Y2, 98.71/14.86 setminus( 98.71/14.86 Y0, Y1))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 setminus( 98.71/14.86 Y0, Y1)) => 98.71/14.86 in(Y2, 98.71/14.86 Y0))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 setminus( 98.71/14.86 Y0, Y1)) => 98.71/14.86 (~( 98.71/14.86 in(Y2, 98.71/14.86 Y1))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (subset( 98.71/14.86 Y0, Y1) => 98.71/14.86 (setminus( 98.71/14.86 Y0, Y1) = 98.71/14.86 emptyset)))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (( 98.71/14.86 ~( 98.71/14.86 in(Y2, 98.71/14.86 setminus( 98.71/14.86 Y0, Y1)))) => 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 in(Y2, 98.71/14.86 Y1)))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (( 98.71/14.86 ~( 98.71/14.86 in(Y2, 98.71/14.86 setminus( 98.71/14.86 Y0, Y1)))) => 98.71/14.86 (( 98.71/14.86 ~( 98.71/14.86 in(Y2, 98.71/14.86 Y1))) => 98.71/14.86 (~( 98.71/14.86 in(Y2, 98.71/14.86 Y0)))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (( 98.71/14.86 ~( 98.71/14.86 in(Y2, 98.71/14.86 Y0))) => 98.71/14.86 (~( 98.71/14.86 in(Y2, 98.71/14.86 setminus( 98.71/14.86 Y0, Y1)))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y1) => 98.71/14.86 (~( 98.71/14.86 in(Y2, 98.71/14.86 setminus( 98.71/14.86 Y0, Y1)))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 subset( 98.71/14.86 setminus( 98.71/14.86 Y0, Y1), 98.71/14.86 Y0))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (( 98.71/14.86 setminus( 98.71/14.86 Y0, Y1) = 98.71/14.86 emptyset) => 98.71/14.86 subset( 98.71/14.86 Y0, Y1)))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 symdiff( 98.71/14.86 Y0, Y1)) => 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $o]: 98.71/14.86 (( 98.71/14.86 in(Y2, 98.71/14.86 Y0) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 ~( 98.71/14.86 in(Y2, 98.71/14.86 Y1))) => 98.71/14.86 Y3)) => 98.71/14.86 (( 98.71/14.86 ( 98.71/14.86 ~( 98.71/14.86 in(Y2, 98.71/14.86 Y0))) => 98.71/14.86 ( 98.71/14.86 in(Y2, 98.71/14.86 Y1) => Y3)) => 98.71/14.86 Y3))))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 (( 98.71/14.86 ~( 98.71/14.86 in(Y2, 98.71/14.86 Y1))) => 98.71/14.86 in(Y2, 98.71/14.86 symdiff( 98.71/14.86 Y0, Y1))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (( 98.71/14.86 ~( 98.71/14.86 in(Y2, 98.71/14.86 Y0))) => 98.71/14.86 (in(Y2, 98.71/14.86 Y1) => 98.71/14.86 in(Y2, 98.71/14.86 symdiff( 98.71/14.86 Y0, Y1))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 (in(Y2, 98.71/14.86 Y1) => 98.71/14.86 (~( 98.71/14.86 in(Y2, 98.71/14.86 symdiff( 98.71/14.86 Y0, Y1))))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (( 98.71/14.86 ~( 98.71/14.86 in(Y2, 98.71/14.86 Y0))) => 98.71/14.86 (( 98.71/14.86 ~( 98.71/14.86 in(Y2, 98.71/14.86 Y1))) => 98.71/14.86 (~( 98.71/14.86 in(Y2, 98.71/14.86 symdiff( 98.71/14.86 Y0, Y1))))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 in(Y1, 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 in(Y0, 98.71/14.86 setunion( 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 in(Y1, 98.71/14.86 setunion( 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (??(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 setunion( 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)))) & 98.71/14.86 (??(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (in(Y3, 98.71/14.86 setunion( 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)))) & 98.71/14.86 (setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)) = 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 setadjoin( 98.71/14.86 Y3, 98.71/14.86 emptyset)), 98.71/14.86 emptyset))))))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (??(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 setunion( 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)))) & 98.71/14.86 (??(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (in(Y3, 98.71/14.86 setunion( 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)))) & 98.71/14.86 (setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)) = 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 setadjoin( 98.71/14.86 Y3, 98.71/14.86 emptyset)), 98.71/14.86 emptyset))))))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (in(Y1, 98.71/14.86 Y0) => 98.71/14.86 subset( 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset), 98.71/14.86 Y0)))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (in(Y1, 98.71/14.86 Y0) => 98.71/14.86 in( 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset), 98.71/14.86 powerset( 98.71/14.86 Y0))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 in( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 emptyset), 98.71/14.86 powerset( 98.71/14.86 binunion( 98.71/14.86 Y0, Y1))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset))) => 98.71/14.86 (( 98.71/14.86 Y2 = Y1) | 98.71/14.86 (Y2 = Y0)))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (in(Y3, 98.71/14.86 Y1) => 98.71/14.86 subset( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 setadjoin( 98.71/14.86 Y3, 98.71/14.86 emptyset)), 98.71/14.86 binunion( 98.71/14.86 Y0, Y1)))))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (in(Y3, 98.71/14.86 Y1) => 98.71/14.86 in( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 setadjoin( 98.71/14.86 Y3, 98.71/14.86 emptyset)), 98.71/14.86 powerset( 98.71/14.86 binunion( 98.71/14.86 Y0, Y1))))))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (in(Y3, 98.71/14.86 Y1) => 98.71/14.86 subset( 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 setadjoin( 98.71/14.86 Y3, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)), 98.71/14.86 powerset( 98.71/14.86 binunion( 98.71/14.86 Y0, Y1))))))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (in(Y3, 98.71/14.86 Y1) => 98.71/14.86 in( 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 setadjoin( 98.71/14.86 Y3, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)), 98.71/14.86 powerset( 98.71/14.86 powerset( 98.71/14.86 binunion( 98.71/14.86 Y0, Y1)))))))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (in(Y3, 98.71/14.86 Y1) => 98.71/14.86 in( 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 setadjoin( 98.71/14.86 Y3, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)), 98.71/14.86 powerset( 98.71/14.86 powerset( 98.71/14.86 binunion( 98.71/14.86 Y0, Y1)))))))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (in(Y3, 98.71/14.86 Y1) => 98.71/14.86 in( 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 setadjoin( 98.71/14.86 Y3, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)), 98.71/14.86 dsetconstr( 98.71/14.86 powerset( 98.71/14.86 powerset( 98.71/14.86 binunion( 98.71/14.86 Y0, Y1))), 98.71/14.86 (^[Y4 : $i]: 98.71/14.86 (??(( 98.71/14.86 ^[Y5 : $i]: 98.71/14.86 (in(Y5, 98.71/14.86 Y0) & 98.71/14.86 (??(( 98.71/14.86 ^[Y6 : $i]: 98.71/14.86 (in(Y6, 98.71/14.86 Y1) & 98.71/14.86 (Y4 = 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y5, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y5, 98.71/14.86 setadjoin( 98.71/14.86 Y6, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)))))))))))))))))))))))))))) => 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 dsetconstr( 98.71/14.86 powerset( 98.71/14.86 powerset( 98.71/14.86 binunion( 98.71/14.86 Y0, Y1))), 98.71/14.86 (^[Y3 : $i]: 98.71/14.86 (??(( 98.71/14.86 ^[Y4 : $i]: 98.71/14.86 (in(Y4, 98.71/14.86 Y0) & 98.71/14.86 (??(( 98.71/14.86 ^[Y5 : $i]: 98.71/14.86 (in(Y5, 98.71/14.86 Y1) & 98.71/14.86 (Y3 = 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y4, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y4, 98.71/14.86 setadjoin( 98.71/14.86 Y5, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)))))))))))))) => 98.71/14.86 (??(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (( 98.71/14.86 ??(( 98.71/14.86 ^[Y4 : $i]: 98.71/14.86 (in(Y4, 98.71/14.86 Y1) & 98.71/14.86 (Y2 = 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y3, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y3, 98.71/14.86 setadjoin( 98.71/14.86 Y4, 98.71/14.86 emptyset)), 98.71/14.86 emptyset))))))) & 98.71/14.86 in(Y3, 98.71/14.86 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 98.71/14.86 inference('lazy_cnf_imply', [status(thm)], ['181'])). 98.71/14.86 tff('183', plain, 98.71/14.86 ~ ((!!((^[Y0 : $i]: 98.71/14.86 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => (Y0 = emptyset))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i > $o]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) => 98.71/14.86 (in(Y2, dsetconstr(Y0, Y1)) <=> Y1(Y2)))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i > $o]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) => 98.71/14.86 (Y1(Y2) => (dsetconstr(Y0, Y1) != emptyset)))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 ((??((^[Y1 : $i]: in(Y1, Y0)))) => (Y0 != emptyset))))) => 98.71/14.86 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 98.71/14.86 (in(emptyset, setadjoin(emptyset, emptyset)) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y1) => in(Y2, setadjoin(Y0, Y1)))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, setadjoin(Y0, Y1)) => 98.71/14.86 (!!((^[Y3 : $o]: 98.71/14.86 (((Y2 = Y0) => Y3) => 98.71/14.86 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, setadjoin(Y0, Y1)) => 98.71/14.86 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 98.71/14.86 in(Y1, powerset(Y0))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.71/14.86 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (in(Y1, powerset(Y0)) => 98.71/14.86 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (in(Y1, Y2) => 98.71/14.86 (in(Y2, Y0) => 98.71/14.86 in(Y1, setunion(Y0))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (in(Y1, setunion(Y0)) => 98.71/14.86 (!!((^[Y2 : $o]: 98.71/14.86 ((!!((^[Y3 : $i]: 98.71/14.86 (in(Y1, Y3) => 98.71/14.86 (in(Y3, Y0) => Y2))))) => 98.71/14.86 Y2))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (in(Y1, Y0) => 98.71/14.86 in(Y1, powerset(setunion(Y0)))))))))) => 98.71/14.86 ((!!((^[Y0 : $i > $o]: 98.71/14.86 ((??((^[Y1 : $i]: 98.71/14.86 (Y0(Y1) & 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (Y0(Y2) => (Y1 = Y2))))))))) => 98.71/14.86 (??((^[Y1 : $i]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 ((Y0 != emptyset) => 98.71/14.86 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (in(Y0, setadjoin(Y1, emptyset)) => 98.71/14.86 (Y0 = Y1)))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 ((Y0 != Y1) => 98.71/14.86 (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 ((Y0 = Y1) => 98.71/14.86 in(Y0, setadjoin(Y1, emptyset))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (in(Y0, setadjoin(Y1, emptyset)) => 98.71/14.86 in(Y1, setadjoin(Y0, emptyset))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 setadjoin(Y0, 98.71/14.86 setadjoin(Y1, 98.71/14.86 emptyset))) => 98.71/14.86 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 in(Y0, 98.71/14.86 setadjoin(Y0, 98.71/14.86 setadjoin(Y1, emptyset))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 in(Y1, 98.71/14.86 setadjoin(Y0, 98.71/14.86 setadjoin(Y1, emptyset))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i > $o]: 98.71/14.86 ((??((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) & Y1(Y2))))) => 98.71/14.86 (dsetconstr(Y0, Y1) != 98.71/14.86 emptyset)))))))) => 98.71/14.86 ((!!((^[Y0 : $i > $o]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (in(Y1, emptyset) => Y0(Y1)))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i > $o]: 98.71/14.86 ((~((!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) => 98.71/14.86 Y1(Y2))))))) => 98.71/14.86 (??((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) & 98.71/14.86 (~(Y1(Y2)))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i > $o]: 98.71/14.86 ((!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) => 98.71/14.86 (~(Y1(Y2))))))) => 98.71/14.86 (~((??((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) & 98.71/14.86 Y1(Y2)))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i > $o]: 98.71/14.86 ((~((??((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) & 98.71/14.86 Y1(Y2))))))) => 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) => 98.71/14.86 (~(Y1(Y2)))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i > $o]: 98.71/14.86 ((??((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) & 98.71/14.86 (~(Y1(Y2))))))) => 98.71/14.86 (~((!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) => 98.71/14.86 Y1(Y2)))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $o]: 98.71/14.86 (Y0 => 98.71/14.86 in(emptyset, prop2set(Y0)))))) => 98.71/14.86 ((!!((^[Y0 : $o]: 98.71/14.86 (Y0 => set2prop(prop2set(Y0)))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i > $o]: 98.71/14.86 ((~((??((^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) & 98.71/14.86 Y1(Y2))))))) => 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) => 98.71/14.86 (~(Y1(Y2)))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i > $o]: 98.71/14.86 ((~((!!((^[Y2 : $i]: 98.71/14.86 ( 98.71/14.86 in(Y2, 98.71/14.86 Y0) => 98.71/14.86 Y1(Y2))))))) => 98.71/14.86 (??((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) & 98.71/14.86 (~(Y1(Y2)))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i > $o]: 98.71/14.86 ((??(Y0)) => 98.71/14.86 ((!!((^[Y1 : $i]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (Y0(Y1) => 98.71/14.86 ( 98.71/14.86 Y0(Y2) => 98.71/14.86 ( 98.71/14.86 Y1 = Y2))))))))) => 98.71/14.86 (??((^[Y1 : $i]: 98.71/14.86 (Y0(Y1) & 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 ( 98.71/14.86 Y0(Y2) => 98.71/14.86 ( 98.71/14.86 Y1 = Y2)))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i > $o]: 98.71/14.86 ((??((^[Y1 : $i]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (Y0(Y2) <=> 98.71/14.86 ( 98.71/14.86 Y2 = Y1)))))))) => 98.71/14.86 (??((^[Y1 : $i]: 98.71/14.86 (Y0(Y1) & 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 ( 98.71/14.86 Y0(Y2) => 98.71/14.86 ( 98.71/14.86 Y1 = Y2))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 ((Y0 = Y1) => 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (( 98.71/14.86 Y2 = Y3) => 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 in(Y3, 98.71/14.86 Y1)))))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 ((Y0 = Y1) => 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (( 98.71/14.86 Y2 = Y3) => 98.71/14.86 (in(Y2, 98.71/14.86 Y0) <=> 98.71/14.86 in(Y3, 98.71/14.86 Y1)))))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i > $o]: 98.71/14.86 ((??((^[Y1 : $i]: 98.71/14.86 (Y0(Y1) & 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (Y0(Y2) => 98.71/14.86 ( 98.71/14.86 Y1 = Y2))))))))) => 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (Y0(Y1) => 98.71/14.86 (Y0(Y2) => 98.71/14.86 (Y1 = Y2))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i > $o]: 98.71/14.86 (!!((^[Y1 : $i > $o]: 98.71/14.86 ((!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (( 98.71/14.86 Y2 = Y3) => 98.71/14.86 (Y0(Y2) <=> 98.71/14.86 Y1(Y3))))))))) => 98.71/14.86 ((??(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 ( 98.71/14.86 Y0(Y2) & 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (Y0(Y3) => 98.71/14.86 (Y2 = Y3))))))))) <=> 98.71/14.86 (??(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 ( 98.71/14.86 Y1(Y2) & 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (Y1(Y3) => 98.71/14.86 (Y2 = Y3))))))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 ((Y0 = Y1) => 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (( 98.71/14.86 Y2 = Y3) => 98.71/14.86 (setadjoin( 98.71/14.86 Y0, Y2) = 98.71/14.86 setadjoin( 98.71/14.86 Y1, Y3)))))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 ((Y0 = Y1) => 98.71/14.86 (powerset( 98.71/14.86 Y0) = 98.71/14.86 powerset( 98.71/14.86 Y1))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 ((Y0 = Y1) => 98.71/14.86 (setunion( 98.71/14.86 Y0) = 98.71/14.86 setunion( 98.71/14.86 Y1))))))))) => 98.71/14.86 ((!!((^[Y0 : $i > $o]: 98.71/14.86 ((??((^[Y1 : $i]: 98.71/14.86 ( 98.71/14.86 Y0(Y1) & 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (Y0(Y2) => 98.71/14.86 (Y1 = Y2))))))))) => 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (Y0(Y1) => 98.71/14.86 (Y0(Y2) => 98.71/14.86 (Y1 = Y2))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i > $o]: 98.71/14.86 (!!((^[Y1 : $i > $o]: 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (( 98.71/14.86 Y2 = Y3) => 98.71/14.86 (Y0(Y2) <=> 98.71/14.86 Y1(Y3))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 ??(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (Y0(Y2) & 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (Y0(Y3) => 98.71/14.86 (Y2 = Y3))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 ??(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (Y1(Y2) & 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (Y1(Y3) => 98.71/14.86 (Y2 = Y3))))))))) => 98.71/14.86 ( 98.71/14.86 descr(Y0) = 98.71/14.86 descr(Y1))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (( 98.71/14.86 Y0 = Y1) => 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i > $o]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i > $o]: 98.71/14.86 (( 98.71/14.86 !!(( 98.71/14.86 ^[Y4 : $i]: 98.71/14.86 (in(Y4, 98.71/14.86 Y0) => 98.71/14.86 (!!(( 98.71/14.86 ^[Y5 : $i]: 98.71/14.86 (in(Y5, 98.71/14.86 Y1) => 98.71/14.86 (( 98.71/14.86 Y4 = Y5) => 98.71/14.86 (Y2(Y4) <=> 98.71/14.86 Y3(Y5))))))))))) => 98.71/14.86 (dsetconstr( 98.71/14.86 Y0, Y2) = 98.71/14.86 dsetconstr( 98.71/14.86 Y1, Y3)))))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (( 98.71/14.86 !!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 in(Y2, 98.71/14.86 Y1))))) => 98.71/14.86 subset( 98.71/14.86 Y0, Y1)))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (( 98.71/14.86 Y0 = Y1) => 98.71/14.86 subset( 98.71/14.86 Y1, Y0)))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 Y0 = Y1) => 98.71/14.86 subset( 98.71/14.86 Y0, Y1)))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (( 98.71/14.86 !!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 in(Y2, 98.71/14.86 Y1))))) => 98.71/14.86 subset( 98.71/14.86 Y0, Y1)))))))) => 98.71/14.86 ((!!(subset( 98.71/14.86 emptyset))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (subset( 98.71/14.86 Y0, Y1) => 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 in(Y2, 98.71/14.86 Y1)))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (subset( 98.71/14.86 Y0, Y1) => 98.71/14.86 (( 98.71/14.86 ~( 98.71/14.86 in(Y2, 98.71/14.86 Y1))) => 98.71/14.86 (~( 98.71/14.86 in(Y2, 98.71/14.86 Y0)))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 (( 98.71/14.86 ~( 98.71/14.86 in(Y2, 98.71/14.86 Y1))) => 98.71/14.86 (~( 98.71/14.86 subset( 98.71/14.86 Y0, Y1)))))))))))))) => 98.71/14.86 ((!!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (( 98.71/14.86 ~( 98.71/14.86 subset( 98.71/14.86 Y0, Y1))) => 98.71/14.86 (Y0 != Y1)))))))) => 98.71/14.86 ((!!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 (( 98.71/14.86 ~( 98.71/14.86 in(Y2, 98.71/14.86 Y1))) => 98.71/14.86 (Y0 != Y1)))))))))))) => 98.71/14.86 ((!!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 subset( 98.71/14.86 Y0, Y0)))) => 98.71/14.86 ((!!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (subset( 98.71/14.86 Y0, Y1) => 98.71/14.86 (subset( 98.71/14.86 Y1, Y2) => 98.71/14.86 subset( 98.71/14.86 Y0, Y2)))))))))))) => 98.71/14.86 (( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 subset( 98.71/14.86 Y1, 98.71/14.86 setadjoin( 98.71/14.86 Y0, Y1)))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (subset( 98.71/14.86 Y0, Y2) => 98.71/14.86 subset( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, Y2)))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (subset( 98.71/14.86 Y0, Y1) => 98.71/14.86 in(Y0, 98.71/14.86 powerset( 98.71/14.86 Y1))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (subset( 98.71/14.86 Y0, Y1) => 98.71/14.86 (subset( 98.71/14.86 Y1, Y0) => 98.71/14.86 (Y0 = Y1))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (subset( 98.71/14.86 Y0, 98.71/14.86 emptyset) => 98.71/14.86 (Y0 = 98.71/14.86 emptyset))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (subset( 98.71/14.86 Y1, Y0) => 98.71/14.86 in(Y1, 98.71/14.86 powerset( 98.71/14.86 Y0))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (in(Y1, 98.71/14.86 powerset( 98.71/14.86 Y0)) => 98.71/14.86 subset( 98.71/14.86 Y1, Y0)))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 in(Y0, 98.71/14.86 powerset( 98.71/14.86 Y0))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (subset( 98.71/14.86 Y0, Y1) => 98.71/14.86 subset( 98.71/14.86 powerset( 98.71/14.86 Y0), 98.71/14.86 powerset( 98.71/14.86 Y1))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i > $o]: 98.71/14.86 in( 98.71/14.86 dsetconstr( 98.71/14.86 Y0, Y1), 98.71/14.86 powerset( 98.71/14.86 Y0)))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i > $o]: 98.71/14.86 subset( 98.71/14.86 dsetconstr( 98.71/14.86 Y0, Y1), 98.71/14.86 Y0))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 in(Y2, 98.71/14.86 binunion( 98.71/14.86 Y0, Y1)))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 in(Y1, 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y1) => 98.71/14.86 in(Y2, 98.71/14.86 binunion( 98.71/14.86 Y0, Y1)))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $o]: 98.71/14.86 (in(Y2, 98.71/14.86 binunion( 98.71/14.86 Y0, Y1)) => 98.71/14.86 (( 98.71/14.86 in(Y2, 98.71/14.86 Y0) => Y3) => 98.71/14.86 (( 98.71/14.86 in(Y2, 98.71/14.86 Y1) => Y3) => 98.71/14.86 Y3))))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 binunion( 98.71/14.86 Y0, Y1)) => 98.71/14.86 (in(Y2, 98.71/14.86 Y1) | 98.71/14.86 in(Y2, 98.71/14.86 Y0)))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 subset( 98.71/14.86 Y0, 98.71/14.86 binunion( 98.71/14.86 Y0, Y1)))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 subset( 98.71/14.86 Y1, 98.71/14.86 binunion( 98.71/14.86 Y0, Y1)))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 (in(Y2, 98.71/14.86 Y1) => 98.71/14.86 in(Y2, 98.71/14.86 binintersect( 98.71/14.86 Y0, Y1))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (subset( 98.71/14.86 Y2, Y0) => 98.71/14.86 (subset( 98.71/14.86 Y2, Y1) => 98.71/14.86 subset( 98.71/14.86 Y2, 98.71/14.86 binintersect( 98.71/14.86 Y0, Y1))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 binintersect( 98.71/14.86 Y0, Y1)) => 98.71/14.86 in(Y2, 98.71/14.86 Y0))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 subset( 98.71/14.86 binintersect( 98.71/14.86 Y0, Y1), 98.71/14.86 Y0))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (subset( 98.71/14.86 Y0, Y1) => 98.71/14.86 (binintersect( 98.71/14.86 Y0, Y1) = 98.71/14.86 Y0)))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (( 98.71/14.86 binintersect( 98.71/14.86 Y0, Y1) = 98.71/14.86 Y1) => 98.71/14.86 subset( 98.71/14.86 Y1, Y0)))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 binintersect( 98.71/14.86 Y0, Y1)) => 98.71/14.86 in(Y2, 98.71/14.86 Y1))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (( 98.71/14.86 ~(( 98.71/14.86 ??(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) & 98.71/14.86 in(Y2, 98.71/14.86 Y1))))))) => 98.71/14.86 (binintersect( 98.71/14.86 Y0, Y1) = 98.71/14.86 emptyset)))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 subset( 98.71/14.86 binintersect( 98.71/14.86 Y0, Y1), 98.71/14.86 Y1))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (subset( 98.71/14.86 Y1, Y0) => 98.71/14.86 (binintersect( 98.71/14.86 Y0, Y1) = 98.71/14.86 Y1)))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (( 98.71/14.86 binintersect( 98.71/14.86 Y0, Y1) = 98.71/14.86 Y0) => 98.71/14.86 subset( 98.71/14.86 Y0, Y1)))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (binintersect( 98.71/14.86 Y0, 98.71/14.86 binunion( 98.71/14.86 Y1, Y2)) = 98.71/14.86 binunion( 98.71/14.86 binintersect( 98.71/14.86 Y0, Y1), 98.71/14.86 binintersect( 98.71/14.86 Y0, Y2)))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 (( 98.71/14.86 ~( 98.71/14.86 in(Y2, 98.71/14.86 Y1))) => 98.71/14.86 in(Y2, 98.71/14.86 setminus( 98.71/14.86 Y0, Y1))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 setminus( 98.71/14.86 Y0, Y1)) => 98.71/14.86 in(Y2, 98.71/14.86 Y0))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 setminus( 98.71/14.86 Y0, Y1)) => 98.71/14.86 (~( 98.71/14.86 in(Y2, 98.71/14.86 Y1))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (subset( 98.71/14.86 Y0, Y1) => 98.71/14.86 (setminus( 98.71/14.86 Y0, Y1) = 98.71/14.86 emptyset)))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (( 98.71/14.86 ~( 98.71/14.86 in(Y2, 98.71/14.86 setminus( 98.71/14.86 Y0, Y1)))) => 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 in(Y2, 98.71/14.86 Y1)))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (( 98.71/14.86 ~( 98.71/14.86 in(Y2, 98.71/14.86 setminus( 98.71/14.86 Y0, Y1)))) => 98.71/14.86 (( 98.71/14.86 ~( 98.71/14.86 in(Y2, 98.71/14.86 Y1))) => 98.71/14.86 (~( 98.71/14.86 in(Y2, 98.71/14.86 Y0)))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (( 98.71/14.86 ~( 98.71/14.86 in(Y2, 98.71/14.86 Y0))) => 98.71/14.86 (~( 98.71/14.86 in(Y2, 98.71/14.86 setminus( 98.71/14.86 Y0, Y1)))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y1) => 98.71/14.86 (~( 98.71/14.86 in(Y2, 98.71/14.86 setminus( 98.71/14.86 Y0, Y1)))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 subset( 98.71/14.86 setminus( 98.71/14.86 Y0, Y1), 98.71/14.86 Y0))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (( 98.71/14.86 setminus( 98.71/14.86 Y0, Y1) = 98.71/14.86 emptyset) => 98.71/14.86 subset( 98.71/14.86 Y0, Y1)))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 symdiff( 98.71/14.86 Y0, Y1)) => 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $o]: 98.71/14.86 (( 98.71/14.86 in(Y2, 98.71/14.86 Y0) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 ~( 98.71/14.86 in(Y2, 98.71/14.86 Y1))) => 98.71/14.86 Y3)) => 98.71/14.86 (( 98.71/14.86 ( 98.71/14.86 ~( 98.71/14.86 in(Y2, 98.71/14.86 Y0))) => 98.71/14.86 ( 98.71/14.86 in(Y2, 98.71/14.86 Y1) => Y3)) => 98.71/14.86 Y3))))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 (( 98.71/14.86 ~( 98.71/14.86 in(Y2, 98.71/14.86 Y1))) => 98.71/14.86 in(Y2, 98.71/14.86 symdiff( 98.71/14.86 Y0, Y1))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (( 98.71/14.86 ~( 98.71/14.86 in(Y2, 98.71/14.86 Y0))) => 98.71/14.86 (in(Y2, 98.71/14.86 Y1) => 98.71/14.86 in(Y2, 98.71/14.86 symdiff( 98.71/14.86 Y0, Y1))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 (in(Y2, 98.71/14.86 Y1) => 98.71/14.86 (~( 98.71/14.86 in(Y2, 98.71/14.86 symdiff( 98.71/14.86 Y0, Y1))))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (( 98.71/14.86 ~( 98.71/14.86 in(Y2, 98.71/14.86 Y0))) => 98.71/14.86 (( 98.71/14.86 ~( 98.71/14.86 in(Y2, 98.71/14.86 Y1))) => 98.71/14.86 (~( 98.71/14.86 in(Y2, 98.71/14.86 symdiff( 98.71/14.86 Y0, Y1))))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 in(Y1, 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 in(Y0, 98.71/14.86 setunion( 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 in(Y1, 98.71/14.86 setunion( 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (??(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 setunion( 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)))) & 98.71/14.86 (??(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (in(Y3, 98.71/14.86 setunion( 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)))) & 98.71/14.86 (setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)) = 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 setadjoin( 98.71/14.86 Y3, 98.71/14.86 emptyset)), 98.71/14.86 emptyset))))))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (??(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 setunion( 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)))) & 98.71/14.86 (??(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (in(Y3, 98.71/14.86 setunion( 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)))) & 98.71/14.86 (setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)) = 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 setadjoin( 98.71/14.86 Y3, 98.71/14.86 emptyset)), 98.71/14.86 emptyset))))))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (in(Y1, 98.71/14.86 Y0) => 98.71/14.86 subset( 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset), 98.71/14.86 Y0)))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (in(Y1, 98.71/14.86 Y0) => 98.71/14.86 in( 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset), 98.71/14.86 powerset( 98.71/14.86 Y0))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 in( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 emptyset), 98.71/14.86 powerset( 98.71/14.86 binunion( 98.71/14.86 Y0, Y1))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset))) => 98.71/14.86 (( 98.71/14.86 Y2 = Y1) | 98.71/14.86 (Y2 = Y0)))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (in(Y3, 98.71/14.86 Y1) => 98.71/14.86 subset( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 setadjoin( 98.71/14.86 Y3, 98.71/14.86 emptyset)), 98.71/14.86 binunion( 98.71/14.86 Y0, Y1)))))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (in(Y3, 98.71/14.86 Y1) => 98.71/14.86 in( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 setadjoin( 98.71/14.86 Y3, 98.71/14.86 emptyset)), 98.71/14.86 powerset( 98.71/14.86 binunion( 98.71/14.86 Y0, Y1))))))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (in(Y3, 98.71/14.86 Y1) => 98.71/14.86 subset( 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 setadjoin( 98.71/14.86 Y3, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)), 98.71/14.86 powerset( 98.71/14.86 binunion( 98.71/14.86 Y0, Y1))))))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (in(Y3, 98.71/14.86 Y1) => 98.71/14.86 in( 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 setadjoin( 98.71/14.86 Y3, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)), 98.71/14.86 powerset( 98.71/14.86 powerset( 98.71/14.86 binunion( 98.71/14.86 Y0, Y1)))))))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (in(Y3, 98.71/14.86 Y1) => 98.71/14.86 in( 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 setadjoin( 98.71/14.86 Y3, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)), 98.71/14.86 powerset( 98.71/14.86 powerset( 98.71/14.86 binunion( 98.71/14.86 Y0, Y1)))))))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (in(Y3, 98.71/14.86 Y1) => 98.71/14.86 in( 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 setadjoin( 98.71/14.86 Y3, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)), 98.71/14.86 dsetconstr( 98.71/14.86 powerset( 98.71/14.86 powerset( 98.71/14.86 binunion( 98.71/14.86 Y0, Y1))), 98.71/14.86 (^[Y4 : $i]: 98.71/14.86 (??(( 98.71/14.86 ^[Y5 : $i]: 98.71/14.86 (in(Y5, 98.71/14.86 Y0) & 98.71/14.86 (??(( 98.71/14.86 ^[Y6 : $i]: 98.71/14.86 (in(Y6, 98.71/14.86 Y1) & 98.71/14.86 (Y4 = 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y5, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y5, 98.71/14.86 setadjoin( 98.71/14.86 Y6, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)))))))))))))))))))))))))))) => 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 dsetconstr( 98.71/14.86 powerset( 98.71/14.86 powerset( 98.71/14.86 binunion( 98.71/14.86 Y0, Y1))), 98.71/14.86 (^[Y3 : $i]: 98.71/14.86 (??(( 98.71/14.86 ^[Y4 : $i]: 98.71/14.86 (in(Y4, 98.71/14.86 Y0) & 98.71/14.86 (??(( 98.71/14.86 ^[Y5 : $i]: 98.71/14.86 (in(Y5, 98.71/14.86 Y1) & 98.71/14.86 (Y3 = 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y4, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y4, 98.71/14.86 setadjoin( 98.71/14.86 Y5, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)))))))))))))) => 98.71/14.86 (??(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (( 98.71/14.86 ??(( 98.71/14.86 ^[Y4 : $i]: 98.71/14.86 (in(Y4, 98.71/14.86 Y1) & 98.71/14.86 (Y2 = 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y3, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y3, 98.71/14.86 setadjoin( 98.71/14.86 Y4, 98.71/14.86 emptyset)), 98.71/14.86 emptyset))))))) & 98.71/14.86 in(Y3, 98.71/14.86 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 98.71/14.86 inference('lazy_cnf_imply', [status(thm)], ['182'])). 98.71/14.86 tff('184', plain, 98.71/14.86 ~ ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i > $o]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) => 98.71/14.86 (in(Y2, dsetconstr(Y0, Y1)) <=> Y1(Y2)))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i > $o]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) => 98.71/14.86 (Y1(Y2) => (dsetconstr(Y0, Y1) != emptyset)))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 ((??((^[Y1 : $i]: in(Y1, Y0)))) => (Y0 != emptyset))))) => 98.71/14.86 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 98.71/14.86 (in(emptyset, setadjoin(emptyset, emptyset)) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y1) => in(Y2, setadjoin(Y0, Y1)))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, setadjoin(Y0, Y1)) => 98.71/14.86 (!!((^[Y3 : $o]: 98.71/14.86 (((Y2 = Y0) => Y3) => 98.71/14.86 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, setadjoin(Y0, Y1)) => 98.71/14.86 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 98.71/14.86 in(Y1, powerset(Y0))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.71/14.86 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (in(Y1, powerset(Y0)) => 98.71/14.86 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (in(Y1, Y2) => 98.71/14.86 (in(Y2, Y0) => 98.71/14.86 in(Y1, setunion(Y0))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (in(Y1, setunion(Y0)) => 98.71/14.86 (!!((^[Y2 : $o]: 98.71/14.86 ((!!((^[Y3 : $i]: 98.71/14.86 (in(Y1, Y3) => 98.71/14.86 (in(Y3, Y0) => Y2))))) => 98.71/14.86 Y2))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (in(Y1, Y0) => 98.71/14.86 in(Y1, powerset(setunion(Y0)))))))))) => 98.71/14.86 ((!!((^[Y0 : $i > $o]: 98.71/14.86 ((??((^[Y1 : $i]: 98.71/14.86 (Y0(Y1) & 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (Y0(Y2) => (Y1 = Y2))))))))) => 98.71/14.86 (??((^[Y1 : $i]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 ((Y0 != emptyset) => 98.71/14.86 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (in(Y0, setadjoin(Y1, emptyset)) => 98.71/14.86 (Y0 = Y1)))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 ((Y0 != Y1) => 98.71/14.86 (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 ((Y0 = Y1) => 98.71/14.86 in(Y0, setadjoin(Y1, emptyset))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (in(Y0, setadjoin(Y1, emptyset)) => 98.71/14.86 in(Y1, setadjoin(Y0, emptyset))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 setadjoin(Y0, 98.71/14.86 setadjoin(Y1, 98.71/14.86 emptyset))) => 98.71/14.86 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 in(Y0, 98.71/14.86 setadjoin(Y0, 98.71/14.86 setadjoin(Y1, emptyset))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 in(Y1, 98.71/14.86 setadjoin(Y0, 98.71/14.86 setadjoin(Y1, emptyset))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i > $o]: 98.71/14.86 ((??((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) & Y1(Y2))))) => 98.71/14.86 (dsetconstr(Y0, Y1) != 98.71/14.86 emptyset)))))))) => 98.71/14.86 ((!!((^[Y0 : $i > $o]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (in(Y1, emptyset) => Y0(Y1)))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i > $o]: 98.71/14.86 ((~((!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) => 98.71/14.86 Y1(Y2))))))) => 98.71/14.86 (??((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) & 98.71/14.86 (~(Y1(Y2)))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i > $o]: 98.71/14.86 ((!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) => 98.71/14.86 (~(Y1(Y2))))))) => 98.71/14.86 (~((??((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) & 98.71/14.86 Y1(Y2)))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i > $o]: 98.71/14.86 ((~((??((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) & 98.71/14.86 Y1(Y2))))))) => 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) => 98.71/14.86 (~(Y1(Y2)))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i > $o]: 98.71/14.86 ((??((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) & 98.71/14.86 (~(Y1(Y2))))))) => 98.71/14.86 (~((!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) => 98.71/14.86 Y1(Y2)))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $o]: 98.71/14.86 (Y0 => 98.71/14.86 in(emptyset, prop2set(Y0)))))) => 98.71/14.86 ((!!((^[Y0 : $o]: 98.71/14.86 (Y0 => set2prop(prop2set(Y0)))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i > $o]: 98.71/14.86 ((~((??((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) & 98.71/14.86 Y1(Y2))))))) => 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) => 98.71/14.86 (~(Y1(Y2)))))))))))))) => 98.71/14.86 ((!!((^[Y0 : 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(!!((^[Y2 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (( 98.71/14.86 Y2 = Y3) => 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 in(Y3, 98.71/14.86 Y1)))))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 ((Y0 = Y1) => 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (( 98.71/14.86 Y2 = Y3) => 98.71/14.86 (in(Y2, 98.71/14.86 Y0) <=> 98.71/14.86 in(Y3, 98.71/14.86 Y1)))))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i > $o]: 98.71/14.86 ((??((^[Y1 : $i]: 98.71/14.86 (Y0(Y1) & 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (Y0(Y2) => 98.71/14.86 (Y1 = Y2))))))))) => 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (Y0(Y1) => 98.71/14.86 (Y0(Y2) => 98.71/14.86 (Y1 = Y2))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i > $o]: 98.71/14.86 (!!((^[Y1 : $i > $o]: 98.71/14.86 ((!!((^[Y2 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (( 98.71/14.86 Y2 = Y3) => 98.71/14.86 (Y0(Y2) <=> 98.71/14.86 Y1(Y3))))))))) => 98.71/14.86 ((??(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (Y0(Y2) & 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (Y0(Y3) => 98.71/14.86 (Y2 = Y3))))))))) <=> 98.71/14.86 (??(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (Y1(Y2) & 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (Y1(Y3) => 98.71/14.86 (Y2 = Y3))))))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 ((Y0 = Y1) => 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (( 98.71/14.86 Y2 = Y3) => 98.71/14.86 (setadjoin( 98.71/14.86 Y0, Y2) = 98.71/14.86 setadjoin( 98.71/14.86 Y1, Y3)))))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 ((Y0 = Y1) => 98.71/14.86 (powerset( 98.71/14.86 Y0) = 98.71/14.86 powerset( 98.71/14.86 Y1))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 ((Y0 = Y1) => 98.71/14.86 (setunion( 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98.71/14.86 (Y1(Y3) => 98.71/14.86 (Y2 = Y3))))))))) => 98.71/14.86 ( 98.71/14.86 descr(Y0) = 98.71/14.86 descr(Y1))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 Y0 = Y1) => 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y2 : $i > $o]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i > $o]: 98.71/14.86 (( 98.71/14.86 !!(( 98.71/14.86 ^[Y4 : $i]: 98.71/14.86 (in(Y4, 98.71/14.86 Y0) => 98.71/14.86 (!!(( 98.71/14.86 ^[Y5 : $i]: 98.71/14.86 (in(Y5, 98.71/14.86 Y1) => 98.71/14.86 (( 98.71/14.86 Y4 = Y5) => 98.71/14.86 (Y2(Y4) <=> 98.71/14.86 Y3(Y5))))))))))) => 98.71/14.86 (dsetconstr( 98.71/14.86 Y0, Y2) = 98.71/14.86 dsetconstr( 98.71/14.86 Y1, Y3)))))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (( 98.71/14.86 !!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 in(Y2, 98.71/14.86 Y1))))) => 98.71/14.86 subset( 98.71/14.86 Y0, Y1)))))))) => 98.71/14.86 ((!!((^[Y0 : 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(subset( 98.71/14.86 Y0, Y1) => 98.71/14.86 (( 98.71/14.86 ~( 98.71/14.86 in(Y2, 98.71/14.86 Y1))) => 98.71/14.86 (~( 98.71/14.86 in(Y2, 98.71/14.86 Y0)))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 (( 98.71/14.86 ~( 98.71/14.86 in(Y2, 98.71/14.86 Y1))) => 98.71/14.86 (~( 98.71/14.86 subset( 98.71/14.86 Y0, Y1)))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (( 98.71/14.86 ~( 98.71/14.86 subset( 98.71/14.86 Y0, Y1))) => 98.71/14.86 (Y0 != Y1)))))))) => 98.71/14.86 ((!!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 (( 98.71/14.86 ~( 98.71/14.86 in(Y2, 98.71/14.86 Y1))) => 98.71/14.86 (Y0 != Y1)))))))))))) => 98.71/14.86 ((!!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 subset( 98.71/14.86 Y0, Y0)))) => 98.71/14.86 ((!!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (subset( 98.71/14.86 Y0, Y1) => 98.71/14.86 (subset( 98.71/14.86 Y1, Y2) => 98.71/14.86 subset( 98.71/14.86 Y0, Y2)))))))))))) => 98.71/14.86 ((!!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 subset( 98.71/14.86 Y1, 98.71/14.86 setadjoin( 98.71/14.86 Y0, Y1)))))))) => 98.71/14.86 (( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (subset( 98.71/14.86 Y0, Y2) => 98.71/14.86 subset( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, Y2)))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (subset( 98.71/14.86 Y0, Y1) => 98.71/14.86 in(Y0, 98.71/14.86 powerset( 98.71/14.86 Y1))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (subset( 98.71/14.86 Y0, Y1) => 98.71/14.86 (subset( 98.71/14.86 Y1, Y0) => 98.71/14.86 (Y0 = Y1))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (subset( 98.71/14.86 Y0, 98.71/14.86 emptyset) => 98.71/14.86 (Y0 = 98.71/14.86 emptyset))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (subset( 98.71/14.86 Y1, Y0) => 98.71/14.86 in(Y1, 98.71/14.86 powerset( 98.71/14.86 Y0))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (in(Y1, 98.71/14.86 powerset( 98.71/14.86 Y0)) => 98.71/14.86 subset( 98.71/14.86 Y1, Y0)))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 in(Y0, 98.71/14.86 powerset( 98.71/14.86 Y0))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (subset( 98.71/14.86 Y0, Y1) => 98.71/14.86 subset( 98.71/14.86 powerset( 98.71/14.86 Y0), 98.71/14.86 powerset( 98.71/14.86 Y1))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i > $o]: 98.71/14.86 in( 98.71/14.86 dsetconstr( 98.71/14.86 Y0, Y1), 98.71/14.86 powerset( 98.71/14.86 Y0)))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i > $o]: 98.71/14.86 subset( 98.71/14.86 dsetconstr( 98.71/14.86 Y0, Y1), 98.71/14.86 Y0))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 in(Y2, 98.71/14.86 binunion( 98.71/14.86 Y0, Y1)))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 in(Y1, 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y1) => 98.71/14.86 in(Y2, 98.71/14.86 binunion( 98.71/14.86 Y0, Y1)))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $o]: 98.71/14.86 (in(Y2, 98.71/14.86 binunion( 98.71/14.86 Y0, Y1)) => 98.71/14.86 (( 98.71/14.86 in(Y2, 98.71/14.86 Y0) => Y3) => 98.71/14.86 (( 98.71/14.86 in(Y2, 98.71/14.86 Y1) => Y3) => 98.71/14.86 Y3))))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 binunion( 98.71/14.86 Y0, Y1)) => 98.71/14.86 (in(Y2, 98.71/14.86 Y1) | 98.71/14.86 in(Y2, 98.71/14.86 Y0)))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 subset( 98.71/14.86 Y0, 98.71/14.86 binunion( 98.71/14.86 Y0, Y1)))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 subset( 98.71/14.86 Y1, 98.71/14.86 binunion( 98.71/14.86 Y0, Y1)))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 (in(Y2, 98.71/14.86 Y1) => 98.71/14.86 in(Y2, 98.71/14.86 binintersect( 98.71/14.86 Y0, Y1))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (subset( 98.71/14.86 Y2, Y0) => 98.71/14.86 (subset( 98.71/14.86 Y2, Y1) => 98.71/14.86 subset( 98.71/14.86 Y2, 98.71/14.86 binintersect( 98.71/14.86 Y0, Y1))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 binintersect( 98.71/14.86 Y0, Y1)) => 98.71/14.86 in(Y2, 98.71/14.86 Y0))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 subset( 98.71/14.86 binintersect( 98.71/14.86 Y0, Y1), 98.71/14.86 Y0))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (subset( 98.71/14.86 Y0, Y1) => 98.71/14.86 (binintersect( 98.71/14.86 Y0, Y1) = 98.71/14.86 Y0)))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (( 98.71/14.86 binintersect( 98.71/14.86 Y0, Y1) = 98.71/14.86 Y1) => 98.71/14.86 subset( 98.71/14.86 Y1, Y0)))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 binintersect( 98.71/14.86 Y0, Y1)) => 98.71/14.86 in(Y2, 98.71/14.86 Y1))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (( 98.71/14.86 ~(( 98.71/14.86 ??(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) & 98.71/14.86 in(Y2, 98.71/14.86 Y1))))))) => 98.71/14.86 (binintersect( 98.71/14.86 Y0, Y1) = 98.71/14.86 emptyset)))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 subset( 98.71/14.86 binintersect( 98.71/14.86 Y0, Y1), 98.71/14.86 Y1))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (subset( 98.71/14.86 Y1, Y0) => 98.71/14.86 (binintersect( 98.71/14.86 Y0, Y1) = 98.71/14.86 Y1)))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (( 98.71/14.86 binintersect( 98.71/14.86 Y0, Y1) = 98.71/14.86 Y0) => 98.71/14.86 subset( 98.71/14.86 Y0, Y1)))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (binintersect( 98.71/14.86 Y0, 98.71/14.86 binunion( 98.71/14.86 Y1, Y2)) = 98.71/14.86 binunion( 98.71/14.86 binintersect( 98.71/14.86 Y0, Y1), 98.71/14.86 binintersect( 98.71/14.86 Y0, Y2)))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 (( 98.71/14.86 ~( 98.71/14.86 in(Y2, 98.71/14.86 Y1))) => 98.71/14.86 in(Y2, 98.71/14.86 setminus( 98.71/14.86 Y0, Y1))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 setminus( 98.71/14.86 Y0, Y1)) => 98.71/14.86 in(Y2, 98.71/14.86 Y0))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 setminus( 98.71/14.86 Y0, Y1)) => 98.71/14.86 (~( 98.71/14.86 in(Y2, 98.71/14.86 Y1))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (subset( 98.71/14.86 Y0, Y1) => 98.71/14.86 (setminus( 98.71/14.86 Y0, Y1) = 98.71/14.86 emptyset)))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (( 98.71/14.86 ~( 98.71/14.86 in(Y2, 98.71/14.86 setminus( 98.71/14.86 Y0, Y1)))) => 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 in(Y2, 98.71/14.86 Y1)))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (( 98.71/14.86 ~( 98.71/14.86 in(Y2, 98.71/14.86 setminus( 98.71/14.86 Y0, Y1)))) => 98.71/14.86 (( 98.71/14.86 ~( 98.71/14.86 in(Y2, 98.71/14.86 Y1))) => 98.71/14.86 (~( 98.71/14.86 in(Y2, 98.71/14.86 Y0)))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (( 98.71/14.86 ~( 98.71/14.86 in(Y2, 98.71/14.86 Y0))) => 98.71/14.86 (~( 98.71/14.86 in(Y2, 98.71/14.86 setminus( 98.71/14.86 Y0, Y1)))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y1) => 98.71/14.86 (~( 98.71/14.86 in(Y2, 98.71/14.86 setminus( 98.71/14.86 Y0, Y1)))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 subset( 98.71/14.86 setminus( 98.71/14.86 Y0, Y1), 98.71/14.86 Y0))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (( 98.71/14.86 setminus( 98.71/14.86 Y0, Y1) = 98.71/14.86 emptyset) => 98.71/14.86 subset( 98.71/14.86 Y0, Y1)))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 symdiff( 98.71/14.86 Y0, Y1)) => 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $o]: 98.71/14.86 (( 98.71/14.86 in(Y2, 98.71/14.86 Y0) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 ~( 98.71/14.86 in(Y2, 98.71/14.86 Y1))) => 98.71/14.86 Y3)) => 98.71/14.86 (( 98.71/14.86 ( 98.71/14.86 ~( 98.71/14.86 in(Y2, 98.71/14.86 Y0))) => 98.71/14.86 ( 98.71/14.86 in(Y2, 98.71/14.86 Y1) => Y3)) => 98.71/14.86 Y3))))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 (( 98.71/14.86 ~( 98.71/14.86 in(Y2, 98.71/14.86 Y1))) => 98.71/14.86 in(Y2, 98.71/14.86 symdiff( 98.71/14.86 Y0, Y1))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (( 98.71/14.86 ~( 98.71/14.86 in(Y2, 98.71/14.86 Y0))) => 98.71/14.86 (in(Y2, 98.71/14.86 Y1) => 98.71/14.86 in(Y2, 98.71/14.86 symdiff( 98.71/14.86 Y0, Y1))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 (in(Y2, 98.71/14.86 Y1) => 98.71/14.86 (~( 98.71/14.86 in(Y2, 98.71/14.86 symdiff( 98.71/14.86 Y0, Y1))))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (( 98.71/14.86 ~( 98.71/14.86 in(Y2, 98.71/14.86 Y0))) => 98.71/14.86 (( 98.71/14.86 ~( 98.71/14.86 in(Y2, 98.71/14.86 Y1))) => 98.71/14.86 (~( 98.71/14.86 in(Y2, 98.71/14.86 symdiff( 98.71/14.86 Y0, Y1))))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 in(Y1, 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 in(Y0, 98.71/14.86 setunion( 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 in(Y1, 98.71/14.86 setunion( 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (??(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 setunion( 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)))) & 98.71/14.86 (??(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (in(Y3, 98.71/14.86 setunion( 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)))) & 98.71/14.86 (setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)) = 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 setadjoin( 98.71/14.86 Y3, 98.71/14.86 emptyset)), 98.71/14.86 emptyset))))))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (??(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 setunion( 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)))) & 98.71/14.86 (??(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (in(Y3, 98.71/14.86 setunion( 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)))) & 98.71/14.86 (setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)) = 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 setadjoin( 98.71/14.86 Y3, 98.71/14.86 emptyset)), 98.71/14.86 emptyset))))))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (in(Y1, 98.71/14.86 Y0) => 98.71/14.86 subset( 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset), 98.71/14.86 Y0)))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (in(Y1, 98.71/14.86 Y0) => 98.71/14.86 in( 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset), 98.71/14.86 powerset( 98.71/14.86 Y0))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 in( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 emptyset), 98.71/14.86 powerset( 98.71/14.86 binunion( 98.71/14.86 Y0, Y1))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 setadjoin( 98.71/14.86 Y0, 98.71/14.86 setadjoin( 98.71/14.86 Y1, 98.71/14.86 emptyset))) => 98.71/14.86 (( 98.71/14.86 Y2 = Y1) | 98.71/14.86 (Y2 = Y0)))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (in(Y3, 98.71/14.86 Y1) => 98.71/14.86 subset( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 setadjoin( 98.71/14.86 Y3, 98.71/14.86 emptyset)), 98.71/14.86 binunion( 98.71/14.86 Y0, Y1)))))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (in(Y3, 98.71/14.86 Y1) => 98.71/14.86 in( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 setadjoin( 98.71/14.86 Y3, 98.71/14.86 emptyset)), 98.71/14.86 powerset( 98.71/14.86 binunion( 98.71/14.86 Y0, Y1))))))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (in(Y3, 98.71/14.86 Y1) => 98.71/14.86 subset( 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 setadjoin( 98.71/14.86 Y3, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)), 98.71/14.86 powerset( 98.71/14.86 binunion( 98.71/14.86 Y0, Y1))))))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (in(Y3, 98.71/14.86 Y1) => 98.71/14.86 in( 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 setadjoin( 98.71/14.86 Y3, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)), 98.71/14.86 powerset( 98.71/14.86 powerset( 98.71/14.86 binunion( 98.71/14.86 Y0, Y1)))))))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (in(Y3, 98.71/14.86 Y1) => 98.71/14.86 in( 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 setadjoin( 98.71/14.86 Y3, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)), 98.71/14.86 powerset( 98.71/14.86 powerset( 98.71/14.86 binunion( 98.71/14.86 Y0, Y1)))))))))))))))))) => 98.71/14.86 ( 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (in(Y3, 98.71/14.86 Y1) => 98.71/14.86 in( 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y2, 98.71/14.86 setadjoin( 98.71/14.86 Y3, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)), 98.71/14.86 dsetconstr( 98.71/14.86 powerset( 98.71/14.86 powerset( 98.71/14.86 binunion( 98.71/14.86 Y0, Y1))), 98.71/14.86 (^[Y4 : $i]: 98.71/14.86 (??(( 98.71/14.86 ^[Y5 : $i]: 98.71/14.86 (in(Y5, 98.71/14.86 Y0) & 98.71/14.86 (??(( 98.71/14.86 ^[Y6 : $i]: 98.71/14.86 (in(Y6, 98.71/14.86 Y1) & 98.71/14.86 (Y4 = 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y5, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y5, 98.71/14.86 setadjoin( 98.71/14.86 Y6, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)))))))))))))))))))))))))))) => 98.71/14.86 ( 98.71/14.86 !!(( 98.71/14.86 ^[Y0 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y1 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 dsetconstr( 98.71/14.86 powerset( 98.71/14.86 powerset( 98.71/14.86 binunion( 98.71/14.86 Y0, Y1))), 98.71/14.86 (^[Y3 : $i]: 98.71/14.86 (??(( 98.71/14.86 ^[Y4 : $i]: 98.71/14.86 (in(Y4, 98.71/14.86 Y0) & 98.71/14.86 (??(( 98.71/14.86 ^[Y5 : $i]: 98.71/14.86 (in(Y5, 98.71/14.86 Y1) & 98.71/14.86 (Y3 = 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y4, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y4, 98.71/14.86 setadjoin( 98.71/14.86 Y5, 98.71/14.86 emptyset)), 98.71/14.86 emptyset)))))))))))))) => 98.71/14.86 (??(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (( 98.71/14.86 ??(( 98.71/14.86 ^[Y4 : $i]: 98.71/14.86 (in(Y4, 98.71/14.86 Y1) & 98.71/14.86 (Y2 = 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y3, 98.71/14.86 emptyset), 98.71/14.86 setadjoin( 98.71/14.86 setadjoin( 98.71/14.86 Y3, 98.71/14.86 setadjoin( 98.71/14.86 Y4, 98.71/14.86 emptyset)), 98.71/14.86 emptyset))))))) & 98.71/14.86 in(Y3, 98.71/14.86 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 98.71/14.86 inference('lazy_cnf_imply', [status(thm)], ['183'])). 98.71/14.86 tff('185', plain, 98.71/14.86 ~ ((!!((^[Y0 : $i]: ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i > $o]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) => 98.71/14.86 (Y1(Y2) => (dsetconstr(Y0, Y1) != emptyset)))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 ((??((^[Y1 : $i]: in(Y1, Y0)))) => (Y0 != emptyset))))) => 98.71/14.86 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 98.71/14.86 (in(emptyset, setadjoin(emptyset, emptyset)) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y1) => in(Y2, setadjoin(Y0, Y1)))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, setadjoin(Y0, Y1)) => 98.71/14.86 (!!((^[Y3 : $o]: 98.71/14.86 (((Y2 = Y0) => Y3) => 98.71/14.86 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, setadjoin(Y0, Y1)) => 98.71/14.86 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 98.71/14.86 in(Y1, powerset(Y0))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.71/14.86 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (in(Y1, powerset(Y0)) => 98.71/14.86 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (in(Y1, Y2) => 98.71/14.86 (in(Y2, Y0) => in(Y1, setunion(Y0))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (in(Y1, setunion(Y0)) => 98.71/14.86 (!!((^[Y2 : $o]: 98.71/14.86 ((!!((^[Y3 : $i]: 98.71/14.86 (in(Y1, Y3) => 98.71/14.86 (in(Y3, Y0) => Y2))))) => 98.71/14.86 Y2))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (in(Y1, Y0) => 98.71/14.86 in(Y1, powerset(setunion(Y0)))))))))) => 98.71/14.86 ((!!((^[Y0 : $i > $o]: 98.71/14.86 ((??((^[Y1 : $i]: 98.71/14.86 (Y0(Y1) & 98.71/14.86 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 98.71/14.86 (??((^[Y1 : $i]: 98.71/14.86 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 ((Y0 != emptyset) => 98.71/14.86 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (in(Y0, setadjoin(Y1, emptyset)) => 98.71/14.86 (Y0 = Y1)))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 ((Y0 != Y1) => 98.71/14.86 (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 ((Y0 = Y1) => 98.71/14.86 in(Y0, setadjoin(Y1, emptyset))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (in(Y0, setadjoin(Y1, emptyset)) => 98.71/14.86 in(Y1, setadjoin(Y0, emptyset))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, 98.71/14.86 setadjoin(Y0, 98.71/14.86 setadjoin(Y1, 98.71/14.86 emptyset))) => 98.71/14.86 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 in(Y0, 98.71/14.86 setadjoin(Y0, 98.71/14.86 setadjoin(Y1, emptyset))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 in(Y1, 98.71/14.86 setadjoin(Y0, 98.71/14.86 setadjoin(Y1, emptyset))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i > $o]: 98.71/14.86 ((??((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) & Y1(Y2))))) => 98.71/14.86 (dsetconstr(Y0, Y1) != 98.71/14.86 emptyset)))))))) => 98.71/14.86 ((!!((^[Y0 : $i > $o]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (in(Y1, emptyset) => Y0(Y1)))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i > $o]: 98.71/14.86 ((~((!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) => 98.71/14.86 Y1(Y2))))))) => 98.71/14.86 (??((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) & 98.71/14.86 (~(Y1(Y2)))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i > $o]: 98.71/14.86 ((!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) => 98.71/14.86 (~(Y1(Y2))))))) => 98.71/14.86 (~((??((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) & 98.71/14.86 Y1(Y2)))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i > $o]: 98.71/14.86 ((~((??((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) & 98.71/14.86 Y1(Y2))))))) => 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) => 98.71/14.86 (~(Y1(Y2)))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i > $o]: 98.71/14.86 ((??((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) & 98.71/14.86 (~(Y1(Y2))))))) => 98.71/14.86 (~((!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) => 98.71/14.86 Y1(Y2)))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $o]: 98.71/14.86 (Y0 => 98.71/14.86 in(emptyset, prop2set(Y0)))))) => 98.71/14.86 ((!!((^[Y0 : $o]: 98.71/14.86 (Y0 => set2prop(prop2set(Y0)))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i > $o]: 98.71/14.86 ((~((??((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) & 98.71/14.86 Y1(Y2))))))) => 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) => 98.71/14.86 (~(Y1(Y2)))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i > $o]: 98.71/14.86 ((~((!!((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) => 98.71/14.86 Y1(Y2))))))) => 98.71/14.86 (??((^[Y2 : $i]: 98.71/14.86 (in(Y2, Y0) & 98.71/14.86 (~(Y1(Y2)))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i > $o]: 98.71/14.86 ((??(Y0)) => 98.71/14.86 ((!!((^[Y1 : $i]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (Y0(Y1) => 98.71/14.86 (Y0(Y2) => 98.71/14.86 (Y1 = Y2))))))))) => 98.71/14.86 (??((^[Y1 : $i]: 98.71/14.86 (Y0(Y1) & 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (Y0(Y2) => 98.71/14.86 (Y1 = Y2)))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i > $o]: 98.71/14.86 ((??((^[Y1 : $i]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (Y0(Y2) <=> 98.71/14.86 (Y2 = Y1)))))))) => 98.71/14.86 (??((^[Y1 : $i]: 98.71/14.86 (Y0(Y1) & 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (Y0(Y2) => 98.71/14.86 (Y1 = Y2))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 ((Y0 = Y1) => 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (( 98.71/14.86 Y2 = Y3) => 98.71/14.86 (in(Y2, 98.71/14.86 Y0) => 98.71/14.86 in(Y3, 98.71/14.86 Y1)))))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i]: 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 ((Y0 = Y1) => 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (!!(( 98.71/14.86 ^[Y3 : $i]: 98.71/14.86 (( 98.71/14.86 Y2 = Y3) => 98.71/14.86 (in(Y2, 98.71/14.86 Y0) <=> 98.71/14.86 in(Y3, 98.71/14.86 Y1)))))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i > $o]: 98.71/14.86 ((??((^[Y1 : $i]: 98.71/14.86 (Y0(Y1) & 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 (Y0(Y2) => 98.71/14.86 (Y1 = Y2))))))))) => 98.71/14.86 (!!((^[Y1 : $i]: 98.71/14.86 (!!((^[Y2 : $i]: 98.71/14.86 ( 98.71/14.86 Y0(Y1) => 98.71/14.86 ( 98.71/14.86 Y0(Y2) => 98.71/14.86 ( 98.71/14.86 Y1 = Y2))))))))))))) => 98.71/14.86 ((!!((^[Y0 : $i > $o]: 98.71/14.86 (!!((^[Y1 : $i > $o]: 98.71/14.86 ((!!((^[Y2 : $i]: 98.71/14.86 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (( 98.71/14.87 Y2 = Y3) => 98.71/14.87 (Y0(Y2) <=> 98.71/14.87 Y1(Y3))))))))) => 98.71/14.87 ((??((^[Y2 : $i]: 98.71/14.87 (Y0(Y2) & 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (Y0(Y3) => 98.71/14.87 (Y2 = Y3))))))))) <=> 98.71/14.87 (??((^[Y2 : $i]: 98.71/14.87 (Y1(Y2) & 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (Y1(Y3) => 98.71/14.87 (Y2 = Y3))))))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 ((Y0 = Y1) => 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (( 98.71/14.87 Y2 = Y3) => 98.71/14.87 (setadjoin( 98.71/14.87 Y0, Y2) = 98.71/14.87 setadjoin( 98.71/14.87 Y1, Y3)))))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 ((Y0 = Y1) => 98.71/14.87 (powerset(Y0) = 98.71/14.87 powerset(Y1))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 ((Y0 = Y1) => 98.71/14.87 (setunion( 98.71/14.87 Y0) = 98.71/14.87 setunion( 98.71/14.87 Y1))))))))) => 98.71/14.87 ((!!((^[Y0 : $i > $o]: 98.71/14.87 ((??((^[Y1 : $i]: 98.71/14.87 (Y0(Y1) & 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (Y0(Y2) => 98.71/14.87 (Y1 = Y2))))))))) => 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (Y0(Y1) => 98.71/14.87 (Y0(Y2) => 98.71/14.87 (Y1 = Y2))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i > $o]: 98.71/14.87 (!!((^[Y1 : $i > $o]: 98.71/14.87 ((!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (( 98.71/14.87 Y2 = Y3) => 98.71/14.87 (Y0(Y2) <=> 98.71/14.87 Y1(Y3))))))))) => 98.71/14.87 (( 98.71/14.87 ??(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (Y0(Y2) & 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (Y0(Y3) => 98.71/14.87 (Y2 = Y3))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 ??(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (Y1(Y2) & 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (Y1(Y3) => 98.71/14.87 (Y2 = Y3))))))))) => 98.71/14.87 ( 98.71/14.87 descr(Y0) = 98.71/14.87 descr(Y1))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (( 98.71/14.87 Y0 = Y1) => 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y2 : $i > $o]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i > $o]: 98.71/14.87 (( 98.71/14.87 !!(( 98.71/14.87 ^[Y4 : $i]: 98.71/14.87 (in(Y4, 98.71/14.87 Y0) => 98.71/14.87 (!!(( 98.71/14.87 ^[Y5 : $i]: 98.71/14.87 (in(Y5, 98.71/14.87 Y1) => 98.71/14.87 (( 98.71/14.87 Y4 = Y5) => 98.71/14.87 (Y2(Y4) <=> 98.71/14.87 Y3(Y5))))))))))) => 98.71/14.87 (dsetconstr( 98.71/14.87 Y0, Y2) = 98.71/14.87 dsetconstr( 98.71/14.87 Y1, Y3)))))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 in(Y2, 98.71/14.87 Y1))))) => 98.71/14.87 subset( 98.71/14.87 Y0, Y1)))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (( 98.71/14.87 Y0 = Y1) => 98.71/14.87 subset( 98.71/14.87 Y1, Y0)))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (( 98.71/14.87 Y0 = Y1) => 98.71/14.87 subset( 98.71/14.87 Y0, Y1)))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (( 98.71/14.87 !!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 in(Y2, 98.71/14.87 Y1))))) => 98.71/14.87 subset( 98.71/14.87 Y0, Y1)))))))) => 98.71/14.87 ((!!(subset( 98.71/14.87 emptyset))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y0, Y1) => 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 in(Y2, 98.71/14.87 Y1)))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y0, Y1) => 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y1))) => 98.71/14.87 (~( 98.71/14.87 in(Y2, 98.71/14.87 Y0)))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y1))) => 98.71/14.87 (~( 98.71/14.87 subset( 98.71/14.87 Y0, Y1)))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 subset( 98.71/14.87 Y0, Y1))) => 98.71/14.87 (Y0 != Y1)))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y1))) => 98.71/14.87 (Y0 != Y1)))))))))))) => 98.71/14.87 ((!!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 subset( 98.71/14.87 Y0, Y0)))) => 98.71/14.87 ((!!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y0, Y1) => 98.71/14.87 (subset( 98.71/14.87 Y1, Y2) => 98.71/14.87 subset( 98.71/14.87 Y0, Y2)))))))))))) => 98.71/14.87 ((!!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 subset( 98.71/14.87 Y1, 98.71/14.87 setadjoin( 98.71/14.87 Y0, Y1)))))))) => 98.71/14.87 ((!!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y0, Y2) => 98.71/14.87 subset( 98.71/14.87 Y0, 98.71/14.87 setadjoin( 98.71/14.87 Y1, Y2)))))))))))) => 98.71/14.87 (( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y0, Y1) => 98.71/14.87 in(Y0, 98.71/14.87 powerset( 98.71/14.87 Y1))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y0, Y1) => 98.71/14.87 (subset( 98.71/14.87 Y1, Y0) => 98.71/14.87 (Y0 = Y1))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y0, 98.71/14.87 emptyset) => 98.71/14.87 (Y0 = 98.71/14.87 emptyset))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y1, Y0) => 98.71/14.87 in(Y1, 98.71/14.87 powerset( 98.71/14.87 Y0))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (in(Y1, 98.71/14.87 powerset( 98.71/14.87 Y0)) => 98.71/14.87 subset( 98.71/14.87 Y1, Y0)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 in(Y0, 98.71/14.87 powerset( 98.71/14.87 Y0))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y0, Y1) => 98.71/14.87 subset( 98.71/14.87 powerset( 98.71/14.87 Y0), 98.71/14.87 powerset( 98.71/14.87 Y1))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i > $o]: 98.71/14.87 in( 98.71/14.87 dsetconstr( 98.71/14.87 Y0, Y1), 98.71/14.87 powerset( 98.71/14.87 Y0)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i > $o]: 98.71/14.87 subset( 98.71/14.87 dsetconstr( 98.71/14.87 Y0, Y1), 98.71/14.87 Y0))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 in(Y2, 98.71/14.87 binunion( 98.71/14.87 Y0, Y1)))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 in(Y1, 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 setadjoin( 98.71/14.87 Y1, 98.71/14.87 emptyset))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y1) => 98.71/14.87 in(Y2, 98.71/14.87 binunion( 98.71/14.87 Y0, Y1)))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $o]: 98.71/14.87 (in(Y2, 98.71/14.87 binunion( 98.71/14.87 Y0, Y1)) => 98.71/14.87 (( 98.71/14.87 in(Y2, 98.71/14.87 Y0) => Y3) => 98.71/14.87 (( 98.71/14.87 in(Y2, 98.71/14.87 Y1) => Y3) => 98.71/14.87 Y3))))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 binunion( 98.71/14.87 Y0, Y1)) => 98.71/14.87 (in(Y2, 98.71/14.87 Y1) | 98.71/14.87 in(Y2, 98.71/14.87 Y0)))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 subset( 98.71/14.87 Y0, 98.71/14.87 binunion( 98.71/14.87 Y0, Y1)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 subset( 98.71/14.87 Y1, 98.71/14.87 binunion( 98.71/14.87 Y0, Y1)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 (in(Y2, 98.71/14.87 Y1) => 98.71/14.87 in(Y2, 98.71/14.87 binintersect( 98.71/14.87 Y0, Y1))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y2, Y0) => 98.71/14.87 (subset( 98.71/14.87 Y2, Y1) => 98.71/14.87 subset( 98.71/14.87 Y2, 98.71/14.87 binintersect( 98.71/14.87 Y0, Y1))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 binintersect( 98.71/14.87 Y0, Y1)) => 98.71/14.87 in(Y2, 98.71/14.87 Y0))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 subset( 98.71/14.87 binintersect( 98.71/14.87 Y0, Y1), 98.71/14.87 Y0))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y0, Y1) => 98.71/14.87 (binintersect( 98.71/14.87 Y0, Y1) = 98.71/14.87 Y0)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (( 98.71/14.87 binintersect( 98.71/14.87 Y0, Y1) = 98.71/14.87 Y1) => 98.71/14.87 subset( 98.71/14.87 Y1, Y0)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 binintersect( 98.71/14.87 Y0, Y1)) => 98.71/14.87 in(Y2, 98.71/14.87 Y1))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (( 98.71/14.87 ~(( 98.71/14.87 ??(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) & 98.71/14.87 in(Y2, 98.71/14.87 Y1))))))) => 98.71/14.87 (binintersect( 98.71/14.87 Y0, Y1) = 98.71/14.87 emptyset)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 subset( 98.71/14.87 binintersect( 98.71/14.87 Y0, Y1), 98.71/14.87 Y1))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y1, Y0) => 98.71/14.87 (binintersect( 98.71/14.87 Y0, Y1) = 98.71/14.87 Y1)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (( 98.71/14.87 binintersect( 98.71/14.87 Y0, Y1) = 98.71/14.87 Y0) => 98.71/14.87 subset( 98.71/14.87 Y0, Y1)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (binintersect( 98.71/14.87 Y0, 98.71/14.87 binunion( 98.71/14.87 Y1, Y2)) = 98.71/14.87 binunion( 98.71/14.87 binintersect( 98.71/14.87 Y0, Y1), 98.71/14.87 binintersect( 98.71/14.87 Y0, Y2)))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y1))) => 98.71/14.87 in(Y2, 98.71/14.87 setminus( 98.71/14.87 Y0, Y1))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 setminus( 98.71/14.87 Y0, Y1)) => 98.71/14.87 in(Y2, 98.71/14.87 Y0))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 setminus( 98.71/14.87 Y0, Y1)) => 98.71/14.87 (~( 98.71/14.87 in(Y2, 98.71/14.87 Y1))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y0, Y1) => 98.71/14.87 (setminus( 98.71/14.87 Y0, Y1) = 98.71/14.87 emptyset)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 setminus( 98.71/14.87 Y0, Y1)))) => 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 in(Y2, 98.71/14.87 Y1)))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 setminus( 98.71/14.87 Y0, Y1)))) => 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y1))) => 98.71/14.87 (~( 98.71/14.87 in(Y2, 98.71/14.87 Y0)))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y0))) => 98.71/14.87 (~( 98.71/14.87 in(Y2, 98.71/14.87 setminus( 98.71/14.87 Y0, Y1)))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y1) => 98.71/14.87 (~( 98.71/14.87 in(Y2, 98.71/14.87 setminus( 98.71/14.87 Y0, Y1)))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 subset( 98.71/14.87 setminus( 98.71/14.87 Y0, Y1), 98.71/14.87 Y0))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (( 98.71/14.87 setminus( 98.71/14.87 Y0, Y1) = 98.71/14.87 emptyset) => 98.71/14.87 subset( 98.71/14.87 Y0, Y1)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 symdiff( 98.71/14.87 Y0, Y1)) => 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $o]: 98.71/14.87 (( 98.71/14.87 in(Y2, 98.71/14.87 Y0) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y1))) => 98.71/14.87 Y3)) => 98.71/14.87 (( 98.71/14.87 ( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y0))) => 98.71/14.87 ( 98.71/14.87 in(Y2, 98.71/14.87 Y1) => Y3)) => 98.71/14.87 Y3))))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y1))) => 98.71/14.87 in(Y2, 98.71/14.87 symdiff( 98.71/14.87 Y0, Y1))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y0))) => 98.71/14.87 (in(Y2, 98.71/14.87 Y1) => 98.71/14.87 in(Y2, 98.71/14.87 symdiff( 98.71/14.87 Y0, Y1))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 (in(Y2, 98.71/14.87 Y1) => 98.71/14.87 (~( 98.71/14.87 in(Y2, 98.71/14.87 symdiff( 98.71/14.87 Y0, Y1))))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y0))) => 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y1))) => 98.71/14.87 (~( 98.71/14.87 in(Y2, 98.71/14.87 symdiff( 98.71/14.87 Y0, Y1))))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 in(Y1, 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 setadjoin( 98.71/14.87 Y1, 98.71/14.87 emptyset))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 in(Y0, 98.71/14.87 setunion( 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 setadjoin( 98.71/14.87 Y1, 98.71/14.87 emptyset)), 98.71/14.87 emptyset)))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 in(Y1, 98.71/14.87 setunion( 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 setadjoin( 98.71/14.87 Y1, 98.71/14.87 emptyset)), 98.71/14.87 emptyset)))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (??(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 setunion( 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 setadjoin( 98.71/14.87 Y1, 98.71/14.87 emptyset)), 98.71/14.87 emptyset)))) & 98.71/14.87 (??(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (in(Y3, 98.71/14.87 setunion( 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 setadjoin( 98.71/14.87 Y1, 98.71/14.87 emptyset)), 98.71/14.87 emptyset)))) & 98.71/14.87 (setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 setadjoin( 98.71/14.87 Y1, 98.71/14.87 emptyset)), 98.71/14.87 emptyset)) = 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 setadjoin( 98.71/14.87 Y3, 98.71/14.87 emptyset)), 98.71/14.87 emptyset))))))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (??(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 setunion( 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 setadjoin( 98.71/14.87 Y1, 98.71/14.87 emptyset)), 98.71/14.87 emptyset)))) & 98.71/14.87 (??(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (in(Y3, 98.71/14.87 setunion( 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 setadjoin( 98.71/14.87 Y1, 98.71/14.87 emptyset)), 98.71/14.87 emptyset)))) & 98.71/14.87 (setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 setadjoin( 98.71/14.87 Y1, 98.71/14.87 emptyset)), 98.71/14.87 emptyset)) = 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 setadjoin( 98.71/14.87 Y3, 98.71/14.87 emptyset)), 98.71/14.87 emptyset))))))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (in(Y1, 98.71/14.87 Y0) => 98.71/14.87 subset( 98.71/14.87 setadjoin( 98.71/14.87 Y1, 98.71/14.87 emptyset), 98.71/14.87 Y0)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (in(Y1, 98.71/14.87 Y0) => 98.71/14.87 in( 98.71/14.87 setadjoin( 98.71/14.87 Y1, 98.71/14.87 emptyset), 98.71/14.87 powerset( 98.71/14.87 Y0))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 in( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 emptyset), 98.71/14.87 powerset( 98.71/14.87 binunion( 98.71/14.87 Y0, Y1))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 setadjoin( 98.71/14.87 Y1, 98.71/14.87 emptyset))) => 98.71/14.87 (( 98.71/14.87 Y2 = Y1) | 98.71/14.87 (Y2 = Y0)))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (in(Y3, 98.71/14.87 Y1) => 98.71/14.87 subset( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 setadjoin( 98.71/14.87 Y3, 98.71/14.87 emptyset)), 98.71/14.87 binunion( 98.71/14.87 Y0, Y1)))))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (in(Y3, 98.71/14.87 Y1) => 98.71/14.87 in( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 setadjoin( 98.71/14.87 Y3, 98.71/14.87 emptyset)), 98.71/14.87 powerset( 98.71/14.87 binunion( 98.71/14.87 Y0, Y1))))))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (in(Y3, 98.71/14.87 Y1) => 98.71/14.87 subset( 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 setadjoin( 98.71/14.87 Y3, 98.71/14.87 emptyset)), 98.71/14.87 emptyset)), 98.71/14.87 powerset( 98.71/14.87 binunion( 98.71/14.87 Y0, Y1))))))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (in(Y3, 98.71/14.87 Y1) => 98.71/14.87 in( 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 setadjoin( 98.71/14.87 Y3, 98.71/14.87 emptyset)), 98.71/14.87 emptyset)), 98.71/14.87 powerset( 98.71/14.87 powerset( 98.71/14.87 binunion( 98.71/14.87 Y0, Y1)))))))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (in(Y3, 98.71/14.87 Y1) => 98.71/14.87 in( 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 setadjoin( 98.71/14.87 Y3, 98.71/14.87 emptyset)), 98.71/14.87 emptyset)), 98.71/14.87 powerset( 98.71/14.87 powerset( 98.71/14.87 binunion( 98.71/14.87 Y0, Y1)))))))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (in(Y3, 98.71/14.87 Y1) => 98.71/14.87 in( 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 setadjoin( 98.71/14.87 Y3, 98.71/14.87 emptyset)), 98.71/14.87 emptyset)), 98.71/14.87 dsetconstr( 98.71/14.87 powerset( 98.71/14.87 powerset( 98.71/14.87 binunion( 98.71/14.87 Y0, Y1))), 98.71/14.87 (^[Y4 : $i]: 98.71/14.87 (??(( 98.71/14.87 ^[Y5 : $i]: 98.71/14.87 (in(Y5, 98.71/14.87 Y0) & 98.71/14.87 (??(( 98.71/14.87 ^[Y6 : $i]: 98.71/14.87 (in(Y6, 98.71/14.87 Y1) & 98.71/14.87 (Y4 = 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y5, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y5, 98.71/14.87 setadjoin( 98.71/14.87 Y6, 98.71/14.87 emptyset)), 98.71/14.87 emptyset)))))))))))))))))))))))))))) => 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 dsetconstr( 98.71/14.87 powerset( 98.71/14.87 powerset( 98.71/14.87 binunion( 98.71/14.87 Y0, Y1))), 98.71/14.87 (^[Y3 : $i]: 98.71/14.87 (??(( 98.71/14.87 ^[Y4 : $i]: 98.71/14.87 (in(Y4, 98.71/14.87 Y0) & 98.71/14.87 (??(( 98.71/14.87 ^[Y5 : $i]: 98.71/14.87 (in(Y5, 98.71/14.87 Y1) & 98.71/14.87 (Y3 = 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y4, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y4, 98.71/14.87 setadjoin( 98.71/14.87 Y5, 98.71/14.87 emptyset)), 98.71/14.87 emptyset)))))))))))))) => 98.71/14.87 (??(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (( 98.71/14.87 ??(( 98.71/14.87 ^[Y4 : $i]: 98.71/14.87 (in(Y4, 98.71/14.87 Y1) & 98.71/14.87 (Y2 = 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y3, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y3, 98.71/14.87 setadjoin( 98.71/14.87 Y4, 98.71/14.87 emptyset)), 98.71/14.87 emptyset))))))) & 98.71/14.87 in(Y3, 98.71/14.87 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 98.71/14.87 inference('lazy_cnf_imply', [status(thm)], ['184'])). 98.71/14.87 tff('186', plain, 98.71/14.87 ~ ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i > $o]: 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y0) => 98.71/14.87 (Y1(Y2) => (dsetconstr(Y0, Y1) != emptyset)))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: ((??((^[Y1 : $i]: in(Y1, Y0)))) => (Y0 != emptyset))))) => 98.71/14.87 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 98.71/14.87 (in(emptyset, setadjoin(emptyset, emptyset)) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y1) => in(Y2, setadjoin(Y0, Y1)))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (in(Y2, setadjoin(Y0, Y1)) => 98.71/14.87 (!!((^[Y3 : $o]: 98.71/14.87 (((Y2 = Y0) => Y3) => 98.71/14.87 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (in(Y2, setadjoin(Y0, Y1)) => 98.71/14.87 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 98.71/14.87 in(Y1, powerset(Y0))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.71/14.87 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (in(Y1, powerset(Y0)) => 98.71/14.87 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (in(Y1, Y2) => 98.71/14.87 (in(Y2, Y0) => in(Y1, setunion(Y0))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (in(Y1, setunion(Y0)) => 98.71/14.87 (!!((^[Y2 : $o]: 98.71/14.87 ((!!((^[Y3 : $i]: 98.71/14.87 (in(Y1, Y3) => 98.71/14.87 (in(Y3, Y0) => Y2))))) => 98.71/14.87 Y2))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (in(Y1, Y0) => 98.71/14.87 in(Y1, powerset(setunion(Y0)))))))))) => 98.71/14.87 ((!!((^[Y0 : $i > $o]: 98.71/14.87 ((??((^[Y1 : $i]: 98.71/14.87 (Y0(Y1) & 98.71/14.87 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 98.71/14.87 (??((^[Y1 : $i]: 98.71/14.87 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 ((Y0 != emptyset) => 98.71/14.87 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (in(Y0, setadjoin(Y1, emptyset)) => 98.71/14.87 (Y0 = Y1)))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 ((Y0 != Y1) => 98.71/14.87 (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 ((Y0 = Y1) => 98.71/14.87 in(Y0, setadjoin(Y1, emptyset))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (in(Y0, setadjoin(Y1, emptyset)) => 98.71/14.87 in(Y1, setadjoin(Y0, emptyset))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 setadjoin(Y0, 98.71/14.87 setadjoin(Y1, emptyset))) => 98.71/14.87 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 in(Y0, 98.71/14.87 setadjoin(Y0, 98.71/14.87 setadjoin(Y1, emptyset))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 in(Y1, 98.71/14.87 setadjoin(Y0, 98.71/14.87 setadjoin(Y1, emptyset))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i > $o]: 98.71/14.87 ((??((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y0) & Y1(Y2))))) => 98.71/14.87 (dsetconstr(Y0, Y1) != emptyset)))))))) => 98.71/14.87 ((!!((^[Y0 : $i > $o]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (in(Y1, emptyset) => Y0(Y1)))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i > $o]: 98.71/14.87 ((~((!!((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y0) => 98.71/14.87 Y1(Y2))))))) => 98.71/14.87 (??((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y0) & 98.71/14.87 (~(Y1(Y2)))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i > $o]: 98.71/14.87 ((!!((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y0) => 98.71/14.87 (~(Y1(Y2))))))) => 98.71/14.87 (~((??((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y0) & 98.71/14.87 Y1(Y2)))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i > $o]: 98.71/14.87 ((~((??((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y0) & 98.71/14.87 Y1(Y2))))))) => 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y0) => 98.71/14.87 (~(Y1(Y2)))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i > $o]: 98.71/14.87 ((??((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y0) & 98.71/14.87 (~(Y1(Y2))))))) => 98.71/14.87 (~((!!((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y0) => 98.71/14.87 Y1(Y2)))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $o]: 98.71/14.87 (Y0 => in(emptyset, prop2set(Y0)))))) => 98.71/14.87 ((!!((^[Y0 : $o]: 98.71/14.87 (Y0 => set2prop(prop2set(Y0)))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i > $o]: 98.71/14.87 ((~((??((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y0) & 98.71/14.87 Y1(Y2))))))) => 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y0) => 98.71/14.87 (~(Y1(Y2)))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i > $o]: 98.71/14.87 ((~((!!((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y0) => 98.71/14.87 Y1(Y2))))))) => 98.71/14.87 (??((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y0) & 98.71/14.87 (~(Y1(Y2)))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i > $o]: 98.71/14.87 ((??(Y0)) => 98.71/14.87 ((!!((^[Y1 : $i]: 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (Y0(Y1) => 98.71/14.87 (Y0(Y2) => 98.71/14.87 (Y1 = Y2))))))))) => 98.71/14.87 (??((^[Y1 : $i]: 98.71/14.87 (Y0(Y1) & 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (Y0(Y2) => 98.71/14.87 (Y1 = Y2)))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i > $o]: 98.71/14.87 ((??((^[Y1 : $i]: 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (Y0(Y2) <=> 98.71/14.87 (Y2 = Y1)))))))) => 98.71/14.87 (??((^[Y1 : $i]: 98.71/14.87 (Y0(Y1) & 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (Y0(Y2) => 98.71/14.87 (Y1 = Y2))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 ((Y0 = Y1) => 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 Y2 = Y3) => 98.71/14.87 ( 98.71/14.87 in(Y2, 98.71/14.87 Y0) => 98.71/14.87 in(Y3, 98.71/14.87 Y1)))))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 ((Y0 = Y1) => 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (( 98.71/14.87 Y2 = Y3) => 98.71/14.87 (in(Y2, 98.71/14.87 Y0) <=> 98.71/14.87 in(Y3, 98.71/14.87 Y1)))))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i > $o]: 98.71/14.87 ((??((^[Y1 : $i]: 98.71/14.87 (Y0(Y1) & 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 ( 98.71/14.87 Y0(Y2) => 98.71/14.87 ( 98.71/14.87 Y1 = Y2))))))))) => 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (Y0(Y1) => 98.71/14.87 ( 98.71/14.87 Y0(Y2) => 98.71/14.87 ( 98.71/14.87 Y1 = Y2))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i > $o]: 98.71/14.87 (!!((^[Y1 : $i > $o]: 98.71/14.87 ((!!((^[Y2 : $i]: 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (( 98.71/14.87 Y2 = Y3) => 98.71/14.87 (Y0(Y2) <=> 98.71/14.87 Y1(Y3))))))))) => 98.71/14.87 ((??((^[Y2 : $i]: 98.71/14.87 (Y0(Y2) & 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (Y0(Y3) => 98.71/14.87 (Y2 = Y3))))))))) <=> 98.71/14.87 (??((^[Y2 : $i]: 98.71/14.87 (Y1(Y2) & 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (Y1(Y3) => 98.71/14.87 (Y2 = Y3))))))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 ((Y0 = Y1) => 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (( 98.71/14.87 Y2 = Y3) => 98.71/14.87 (setadjoin( 98.71/14.87 Y0, Y2) = 98.71/14.87 setadjoin( 98.71/14.87 Y1, Y3)))))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 ((Y0 = Y1) => 98.71/14.87 (powerset(Y0) = 98.71/14.87 powerset(Y1))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 ((Y0 = Y1) => 98.71/14.87 (setunion(Y0) = 98.71/14.87 setunion(Y1))))))))) => 98.71/14.87 ((!!((^[Y0 : $i > $o]: 98.71/14.87 ((??((^[Y1 : $i]: 98.71/14.87 (Y0(Y1) & 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (Y0(Y2) => 98.71/14.87 (Y1 = Y2))))))))) => 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 ( 98.71/14.87 Y0(Y1) => 98.71/14.87 ( 98.71/14.87 Y0(Y2) => 98.71/14.87 ( 98.71/14.87 Y1 = Y2))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i > $o]: 98.71/14.87 (!!((^[Y1 : $i > $o]: 98.71/14.87 ((!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (( 98.71/14.87 Y2 = Y3) => 98.71/14.87 (Y0(Y2) <=> 98.71/14.87 Y1(Y3))))))))) => 98.71/14.87 ((??(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (Y0(Y2) & 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (Y0(Y3) => 98.71/14.87 (Y2 = Y3))))))))) => 98.71/14.87 (( 98.71/14.87 ??(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (Y1(Y2) & 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (Y1(Y3) => 98.71/14.87 (Y2 = Y3))))))))) => 98.71/14.87 ( 98.71/14.87 descr(Y0) = 98.71/14.87 descr(Y1))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 ((Y0 = Y1) => 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i > $o]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i > $o]: 98.71/14.87 (( 98.71/14.87 !!(( 98.71/14.87 ^[Y4 : $i]: 98.71/14.87 (in(Y4, 98.71/14.87 Y0) => 98.71/14.87 (!!(( 98.71/14.87 ^[Y5 : $i]: 98.71/14.87 (in(Y5, 98.71/14.87 Y1) => 98.71/14.87 (( 98.71/14.87 Y4 = Y5) => 98.71/14.87 (Y2(Y4) <=> 98.71/14.87 Y3(Y5))))))))))) => 98.71/14.87 (dsetconstr( 98.71/14.87 Y0, Y2) = 98.71/14.87 dsetconstr( 98.71/14.87 Y1, Y3)))))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (( 98.71/14.87 !!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 in(Y2, 98.71/14.87 Y1))))) => 98.71/14.87 subset( 98.71/14.87 Y0, Y1)))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 Y0 = Y1) => 98.71/14.87 subset( 98.71/14.87 Y1, Y0)))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (( 98.71/14.87 Y0 = Y1) => 98.71/14.87 subset( 98.71/14.87 Y0, Y1)))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (( 98.71/14.87 !!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 in(Y2, 98.71/14.87 Y1))))) => 98.71/14.87 subset( 98.71/14.87 Y0, Y1)))))))) => 98.71/14.87 ((!!(subset(emptyset))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y0, Y1) => 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 in(Y2, 98.71/14.87 Y1)))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y0, Y1) => 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y1))) => 98.71/14.87 (~( 98.71/14.87 in(Y2, 98.71/14.87 Y0)))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y1))) => 98.71/14.87 (~( 98.71/14.87 subset( 98.71/14.87 Y0, Y1)))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 subset( 98.71/14.87 Y0, Y1))) => 98.71/14.87 (Y0 != Y1)))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y1))) => 98.71/14.87 (Y0 != Y1)))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 subset( 98.71/14.87 Y0, Y0)))) => 98.71/14.87 ((!!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y0, Y1) => 98.71/14.87 (subset( 98.71/14.87 Y1, Y2) => 98.71/14.87 subset( 98.71/14.87 Y0, Y2)))))))))))) => 98.71/14.87 ((!!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 subset( 98.71/14.87 Y1, 98.71/14.87 setadjoin( 98.71/14.87 Y0, Y1)))))))) => 98.71/14.87 ((!!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y0, Y2) => 98.71/14.87 subset( 98.71/14.87 Y0, 98.71/14.87 setadjoin( 98.71/14.87 Y1, Y2)))))))))))) => 98.71/14.87 ((!!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y0, Y1) => 98.71/14.87 in(Y0, 98.71/14.87 powerset( 98.71/14.87 Y1))))))))) => 98.71/14.87 (( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y0, Y1) => 98.71/14.87 (subset( 98.71/14.87 Y1, Y0) => 98.71/14.87 (Y0 = Y1))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y0, 98.71/14.87 emptyset) => 98.71/14.87 (Y0 = 98.71/14.87 emptyset))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y1, Y0) => 98.71/14.87 in(Y1, 98.71/14.87 powerset( 98.71/14.87 Y0))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (in(Y1, 98.71/14.87 powerset( 98.71/14.87 Y0)) => 98.71/14.87 subset( 98.71/14.87 Y1, Y0)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 in(Y0, 98.71/14.87 powerset( 98.71/14.87 Y0))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y0, Y1) => 98.71/14.87 subset( 98.71/14.87 powerset( 98.71/14.87 Y0), 98.71/14.87 powerset( 98.71/14.87 Y1))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i > $o]: 98.71/14.87 in( 98.71/14.87 dsetconstr( 98.71/14.87 Y0, Y1), 98.71/14.87 powerset( 98.71/14.87 Y0)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i > $o]: 98.71/14.87 subset( 98.71/14.87 dsetconstr( 98.71/14.87 Y0, Y1), 98.71/14.87 Y0))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 in(Y2, 98.71/14.87 binunion( 98.71/14.87 Y0, Y1)))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 in(Y1, 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 setadjoin( 98.71/14.87 Y1, 98.71/14.87 emptyset))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y1) => 98.71/14.87 in(Y2, 98.71/14.87 binunion( 98.71/14.87 Y0, Y1)))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $o]: 98.71/14.87 (in(Y2, 98.71/14.87 binunion( 98.71/14.87 Y0, Y1)) => 98.71/14.87 (( 98.71/14.87 in(Y2, 98.71/14.87 Y0) => Y3) => 98.71/14.87 (( 98.71/14.87 in(Y2, 98.71/14.87 Y1) => Y3) => 98.71/14.87 Y3))))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 binunion( 98.71/14.87 Y0, Y1)) => 98.71/14.87 (in(Y2, 98.71/14.87 Y1) | 98.71/14.87 in(Y2, 98.71/14.87 Y0)))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 subset( 98.71/14.87 Y0, 98.71/14.87 binunion( 98.71/14.87 Y0, Y1)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 subset( 98.71/14.87 Y1, 98.71/14.87 binunion( 98.71/14.87 Y0, Y1)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 (in(Y2, 98.71/14.87 Y1) => 98.71/14.87 in(Y2, 98.71/14.87 binintersect( 98.71/14.87 Y0, Y1))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y2, Y0) => 98.71/14.87 (subset( 98.71/14.87 Y2, Y1) => 98.71/14.87 subset( 98.71/14.87 Y2, 98.71/14.87 binintersect( 98.71/14.87 Y0, Y1))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 binintersect( 98.71/14.87 Y0, Y1)) => 98.71/14.87 in(Y2, 98.71/14.87 Y0))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 subset( 98.71/14.87 binintersect( 98.71/14.87 Y0, Y1), 98.71/14.87 Y0))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y0, Y1) => 98.71/14.87 (binintersect( 98.71/14.87 Y0, Y1) = 98.71/14.87 Y0)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (( 98.71/14.87 binintersect( 98.71/14.87 Y0, Y1) = 98.71/14.87 Y1) => 98.71/14.87 subset( 98.71/14.87 Y1, Y0)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 binintersect( 98.71/14.87 Y0, Y1)) => 98.71/14.87 in(Y2, 98.71/14.87 Y1))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (( 98.71/14.87 ~(( 98.71/14.87 ??(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) & 98.71/14.87 in(Y2, 98.71/14.87 Y1))))))) => 98.71/14.87 (binintersect( 98.71/14.87 Y0, Y1) = 98.71/14.87 emptyset)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 subset( 98.71/14.87 binintersect( 98.71/14.87 Y0, Y1), 98.71/14.87 Y1))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y1, Y0) => 98.71/14.87 (binintersect( 98.71/14.87 Y0, Y1) = 98.71/14.87 Y1)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (( 98.71/14.87 binintersect( 98.71/14.87 Y0, Y1) = 98.71/14.87 Y0) => 98.71/14.87 subset( 98.71/14.87 Y0, Y1)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (binintersect( 98.71/14.87 Y0, 98.71/14.87 binunion( 98.71/14.87 Y1, Y2)) = 98.71/14.87 binunion( 98.71/14.87 binintersect( 98.71/14.87 Y0, Y1), 98.71/14.87 binintersect( 98.71/14.87 Y0, Y2)))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y1))) => 98.71/14.87 in(Y2, 98.71/14.87 setminus( 98.71/14.87 Y0, Y1))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 setminus( 98.71/14.87 Y0, Y1)) => 98.71/14.87 in(Y2, 98.71/14.87 Y0))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 setminus( 98.71/14.87 Y0, Y1)) => 98.71/14.87 (~( 98.71/14.87 in(Y2, 98.71/14.87 Y1))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y0, Y1) => 98.71/14.87 (setminus( 98.71/14.87 Y0, Y1) = 98.71/14.87 emptyset)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 setminus( 98.71/14.87 Y0, Y1)))) => 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 in(Y2, 98.71/14.87 Y1)))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 setminus( 98.71/14.87 Y0, Y1)))) => 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y1))) => 98.71/14.87 (~( 98.71/14.87 in(Y2, 98.71/14.87 Y0)))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y0))) => 98.71/14.87 (~( 98.71/14.87 in(Y2, 98.71/14.87 setminus( 98.71/14.87 Y0, Y1)))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y1) => 98.71/14.87 (~( 98.71/14.87 in(Y2, 98.71/14.87 setminus( 98.71/14.87 Y0, Y1)))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 subset( 98.71/14.87 setminus( 98.71/14.87 Y0, Y1), 98.71/14.87 Y0))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (( 98.71/14.87 setminus( 98.71/14.87 Y0, Y1) = 98.71/14.87 emptyset) => 98.71/14.87 subset( 98.71/14.87 Y0, Y1)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 symdiff( 98.71/14.87 Y0, Y1)) => 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $o]: 98.71/14.87 (( 98.71/14.87 in(Y2, 98.71/14.87 Y0) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y1))) => 98.71/14.87 Y3)) => 98.71/14.87 (( 98.71/14.87 ( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y0))) => 98.71/14.87 ( 98.71/14.87 in(Y2, 98.71/14.87 Y1) => Y3)) => 98.71/14.87 Y3))))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y1))) => 98.71/14.87 in(Y2, 98.71/14.87 symdiff( 98.71/14.87 Y0, Y1))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y0))) => 98.71/14.87 (in(Y2, 98.71/14.87 Y1) => 98.71/14.87 in(Y2, 98.71/14.87 symdiff( 98.71/14.87 Y0, Y1))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 (in(Y2, 98.71/14.87 Y1) => 98.71/14.87 (~( 98.71/14.87 in(Y2, 98.71/14.87 symdiff( 98.71/14.87 Y0, Y1))))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y0))) => 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y1))) => 98.71/14.87 (~( 98.71/14.87 in(Y2, 98.71/14.87 symdiff( 98.71/14.87 Y0, Y1))))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 in(Y1, 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 setadjoin( 98.71/14.87 Y1, 98.71/14.87 emptyset))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 in(Y0, 98.71/14.87 setunion( 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 setadjoin( 98.71/14.87 Y1, 98.71/14.87 emptyset)), 98.71/14.87 emptyset)))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 in(Y1, 98.71/14.87 setunion( 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 setadjoin( 98.71/14.87 Y1, 98.71/14.87 emptyset)), 98.71/14.87 emptyset)))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (??(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 setunion( 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 setadjoin( 98.71/14.87 Y1, 98.71/14.87 emptyset)), 98.71/14.87 emptyset)))) & 98.71/14.87 (??(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (in(Y3, 98.71/14.87 setunion( 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 setadjoin( 98.71/14.87 Y1, 98.71/14.87 emptyset)), 98.71/14.87 emptyset)))) & 98.71/14.87 (setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 setadjoin( 98.71/14.87 Y1, 98.71/14.87 emptyset)), 98.71/14.87 emptyset)) = 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 setadjoin( 98.71/14.87 Y3, 98.71/14.87 emptyset)), 98.71/14.87 emptyset))))))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (??(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 setunion( 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 setadjoin( 98.71/14.87 Y1, 98.71/14.87 emptyset)), 98.71/14.87 emptyset)))) & 98.71/14.87 (??(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (in(Y3, 98.71/14.87 setunion( 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 setadjoin( 98.71/14.87 Y1, 98.71/14.87 emptyset)), 98.71/14.87 emptyset)))) & 98.71/14.87 (setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 setadjoin( 98.71/14.87 Y1, 98.71/14.87 emptyset)), 98.71/14.87 emptyset)) = 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 setadjoin( 98.71/14.87 Y3, 98.71/14.87 emptyset)), 98.71/14.87 emptyset))))))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (in(Y1, 98.71/14.87 Y0) => 98.71/14.87 subset( 98.71/14.87 setadjoin( 98.71/14.87 Y1, 98.71/14.87 emptyset), 98.71/14.87 Y0)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (in(Y1, 98.71/14.87 Y0) => 98.71/14.87 in( 98.71/14.87 setadjoin( 98.71/14.87 Y1, 98.71/14.87 emptyset), 98.71/14.87 powerset( 98.71/14.87 Y0))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 in( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 emptyset), 98.71/14.87 powerset( 98.71/14.87 binunion( 98.71/14.87 Y0, Y1))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 setadjoin( 98.71/14.87 Y1, 98.71/14.87 emptyset))) => 98.71/14.87 (( 98.71/14.87 Y2 = Y1) | 98.71/14.87 (Y2 = Y0)))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (in(Y3, 98.71/14.87 Y1) => 98.71/14.87 subset( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 setadjoin( 98.71/14.87 Y3, 98.71/14.87 emptyset)), 98.71/14.87 binunion( 98.71/14.87 Y0, Y1)))))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (in(Y3, 98.71/14.87 Y1) => 98.71/14.87 in( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 setadjoin( 98.71/14.87 Y3, 98.71/14.87 emptyset)), 98.71/14.87 powerset( 98.71/14.87 binunion( 98.71/14.87 Y0, Y1))))))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (in(Y3, 98.71/14.87 Y1) => 98.71/14.87 subset( 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 setadjoin( 98.71/14.87 Y3, 98.71/14.87 emptyset)), 98.71/14.87 emptyset)), 98.71/14.87 powerset( 98.71/14.87 binunion( 98.71/14.87 Y0, Y1))))))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (in(Y3, 98.71/14.87 Y1) => 98.71/14.87 in( 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 setadjoin( 98.71/14.87 Y3, 98.71/14.87 emptyset)), 98.71/14.87 emptyset)), 98.71/14.87 powerset( 98.71/14.87 powerset( 98.71/14.87 binunion( 98.71/14.87 Y0, Y1)))))))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (in(Y3, 98.71/14.87 Y1) => 98.71/14.87 in( 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 setadjoin( 98.71/14.87 Y3, 98.71/14.87 emptyset)), 98.71/14.87 emptyset)), 98.71/14.87 powerset( 98.71/14.87 powerset( 98.71/14.87 binunion( 98.71/14.87 Y0, Y1)))))))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (in(Y3, 98.71/14.87 Y1) => 98.71/14.87 in( 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 setadjoin( 98.71/14.87 Y3, 98.71/14.87 emptyset)), 98.71/14.87 emptyset)), 98.71/14.87 dsetconstr( 98.71/14.87 powerset( 98.71/14.87 powerset( 98.71/14.87 binunion( 98.71/14.87 Y0, Y1))), 98.71/14.87 (^[Y4 : $i]: 98.71/14.87 (??(( 98.71/14.87 ^[Y5 : $i]: 98.71/14.87 (in(Y5, 98.71/14.87 Y0) & 98.71/14.87 (??(( 98.71/14.87 ^[Y6 : $i]: 98.71/14.87 (in(Y6, 98.71/14.87 Y1) & 98.71/14.87 (Y4 = 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y5, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y5, 98.71/14.87 setadjoin( 98.71/14.87 Y6, 98.71/14.87 emptyset)), 98.71/14.87 emptyset)))))))))))))))))))))))))))) => 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 dsetconstr( 98.71/14.87 powerset( 98.71/14.87 powerset( 98.71/14.87 binunion( 98.71/14.87 Y0, Y1))), 98.71/14.87 (^[Y3 : $i]: 98.71/14.87 (??(( 98.71/14.87 ^[Y4 : $i]: 98.71/14.87 (in(Y4, 98.71/14.87 Y0) & 98.71/14.87 (??(( 98.71/14.87 ^[Y5 : $i]: 98.71/14.87 (in(Y5, 98.71/14.87 Y1) & 98.71/14.87 (Y3 = 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y4, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y4, 98.71/14.87 setadjoin( 98.71/14.87 Y5, 98.71/14.87 emptyset)), 98.71/14.87 emptyset)))))))))))))) => 98.71/14.87 (??(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (( 98.71/14.87 ??(( 98.71/14.87 ^[Y4 : $i]: 98.71/14.87 (in(Y4, 98.71/14.87 Y1) & 98.71/14.87 (Y2 = 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y3, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y3, 98.71/14.87 setadjoin( 98.71/14.87 Y4, 98.71/14.87 emptyset)), 98.71/14.87 emptyset))))))) & 98.71/14.87 in(Y3, 98.71/14.87 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 98.71/14.87 inference('lazy_cnf_imply', [status(thm)], ['185'])). 98.71/14.87 tff('187', plain, 98.71/14.87 ~ ((!!((^[Y0 : $i]: ((??((^[Y1 : $i]: in(Y1, Y0)))) => (Y0 != emptyset))))) => 98.71/14.87 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 98.71/14.87 (in(emptyset, setadjoin(emptyset, emptyset)) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y1) => in(Y2, setadjoin(Y0, Y1)))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (in(Y2, setadjoin(Y0, Y1)) => 98.71/14.87 (!!((^[Y3 : $o]: 98.71/14.87 (((Y2 = Y0) => Y3) => 98.71/14.87 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (in(Y2, setadjoin(Y0, Y1)) => 98.71/14.87 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 98.71/14.87 in(Y1, powerset(Y0))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.71/14.87 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (in(Y1, powerset(Y0)) => 98.71/14.87 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (in(Y1, Y2) => 98.71/14.87 (in(Y2, Y0) => in(Y1, setunion(Y0))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (in(Y1, setunion(Y0)) => 98.71/14.87 (!!((^[Y2 : $o]: 98.71/14.87 ((!!((^[Y3 : $i]: 98.71/14.87 (in(Y1, Y3) => 98.71/14.87 (in(Y3, Y0) => Y2))))) => 98.71/14.87 Y2))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (in(Y1, Y0) => 98.71/14.87 in(Y1, powerset(setunion(Y0)))))))))) => 98.71/14.87 ((!!((^[Y0 : $i > $o]: 98.71/14.87 ((??((^[Y1 : $i]: 98.71/14.87 (Y0(Y1) & 98.71/14.87 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 98.71/14.87 (??((^[Y1 : $i]: 98.71/14.87 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 ((Y0 != emptyset) => 98.71/14.87 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (in(Y0, setadjoin(Y1, emptyset)) => 98.71/14.87 (Y0 = Y1)))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 ((Y0 != Y1) => 98.71/14.87 (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 ((Y0 = Y1) => 98.71/14.87 in(Y0, setadjoin(Y1, emptyset))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (in(Y0, setadjoin(Y1, emptyset)) => 98.71/14.87 in(Y1, setadjoin(Y0, emptyset))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 setadjoin(Y0, 98.71/14.87 setadjoin(Y1, emptyset))) => 98.71/14.87 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 in(Y0, 98.71/14.87 setadjoin(Y0, 98.71/14.87 setadjoin(Y1, emptyset))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 in(Y1, 98.71/14.87 setadjoin(Y0, 98.71/14.87 setadjoin(Y1, emptyset))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i > $o]: 98.71/14.87 ((??((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y0) & Y1(Y2))))) => 98.71/14.87 (dsetconstr(Y0, Y1) != emptyset)))))))) => 98.71/14.87 ((!!((^[Y0 : $i > $o]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (in(Y1, emptyset) => Y0(Y1)))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i > $o]: 98.71/14.87 ((~((!!((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y0) => 98.71/14.87 Y1(Y2))))))) => 98.71/14.87 (??((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y0) & 98.71/14.87 (~(Y1(Y2)))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i > $o]: 98.71/14.87 ((!!((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y0) => 98.71/14.87 (~(Y1(Y2))))))) => 98.71/14.87 (~((??((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y0) & 98.71/14.87 Y1(Y2)))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i > $o]: 98.71/14.87 ((~((??((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y0) & 98.71/14.87 Y1(Y2))))))) => 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y0) => 98.71/14.87 (~(Y1(Y2)))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i > $o]: 98.71/14.87 ((??((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y0) & 98.71/14.87 (~(Y1(Y2))))))) => 98.71/14.87 (~((!!((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y0) => 98.71/14.87 Y1(Y2)))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $o]: 98.71/14.87 (Y0 => in(emptyset, prop2set(Y0)))))) => 98.71/14.87 ((!!((^[Y0 : $o]: 98.71/14.87 (Y0 => set2prop(prop2set(Y0)))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i > $o]: 98.71/14.87 ((~((??((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y0) & 98.71/14.87 Y1(Y2))))))) => 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y0) => 98.71/14.87 (~(Y1(Y2)))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i > $o]: 98.71/14.87 ((~((!!((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y0) => 98.71/14.87 Y1(Y2))))))) => 98.71/14.87 (??((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y0) & 98.71/14.87 (~(Y1(Y2)))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i > $o]: 98.71/14.87 ((??(Y0)) => 98.71/14.87 ((!!((^[Y1 : $i]: 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (Y0(Y1) => 98.71/14.87 (Y0(Y2) => 98.71/14.87 (Y1 = Y2))))))))) => 98.71/14.87 (??((^[Y1 : $i]: 98.71/14.87 (Y0(Y1) & 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (Y0(Y2) => 98.71/14.87 (Y1 = Y2)))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i > $o]: 98.71/14.87 ((??((^[Y1 : $i]: 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (Y0(Y2) <=> 98.71/14.87 (Y2 = Y1)))))))) => 98.71/14.87 (??((^[Y1 : $i]: 98.71/14.87 (Y0(Y1) & 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (Y0(Y2) => 98.71/14.87 (Y1 = Y2))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 ((Y0 = Y1) => 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (( 98.71/14.87 Y2 = Y3) => 98.71/14.87 ( 98.71/14.87 in(Y2, 98.71/14.87 Y0) => 98.71/14.87 in(Y3, 98.71/14.87 Y1)))))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 ((Y0 = Y1) => 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 Y2 = Y3) => 98.71/14.87 ( 98.71/14.87 in(Y2, 98.71/14.87 Y0) <=> 98.71/14.87 in(Y3, 98.71/14.87 Y1)))))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i > $o]: 98.71/14.87 ((??((^[Y1 : $i]: 98.71/14.87 (Y0(Y1) & 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (Y0(Y2) => 98.71/14.87 ( 98.71/14.87 Y1 = Y2))))))))) => 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (Y0(Y1) => 98.71/14.87 (Y0(Y2) => 98.71/14.87 ( 98.71/14.87 Y1 = Y2))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i > $o]: 98.71/14.87 (!!((^[Y1 : $i > $o]: 98.71/14.87 ((!!((^[Y2 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (( 98.71/14.87 Y2 = Y3) => 98.71/14.87 (Y0(Y2) <=> 98.71/14.87 Y1(Y3))))))))) => 98.71/14.87 ((??((^[Y2 : $i]: 98.71/14.87 ( 98.71/14.87 Y0(Y2) & 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (Y0(Y3) => 98.71/14.87 (Y2 = Y3))))))))) <=> 98.71/14.87 (??((^[Y2 : $i]: 98.71/14.87 ( 98.71/14.87 Y1(Y2) & 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (Y1(Y3) => 98.71/14.87 (Y2 = Y3))))))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 ((Y0 = Y1) => 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (( 98.71/14.87 Y2 = Y3) => 98.71/14.87 (setadjoin( 98.71/14.87 Y0, Y2) = 98.71/14.87 setadjoin( 98.71/14.87 Y1, Y3)))))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 ((Y0 = Y1) => 98.71/14.87 (powerset(Y0) = 98.71/14.87 powerset(Y1))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 ((Y0 = Y1) => 98.71/14.87 (setunion(Y0) = 98.71/14.87 setunion(Y1))))))))) => 98.71/14.87 ((!!((^[Y0 : $i > $o]: 98.71/14.87 ((??((^[Y1 : $i]: 98.71/14.87 (Y0(Y1) & 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 ( 98.71/14.87 Y0(Y2) => 98.71/14.87 ( 98.71/14.87 Y1 = Y2))))))))) => 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (Y0(Y1) => 98.71/14.87 ( 98.71/14.87 Y0(Y2) => 98.71/14.87 ( 98.71/14.87 Y1 = Y2))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i > $o]: 98.71/14.87 (!!((^[Y1 : $i > $o]: 98.71/14.87 ((!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (( 98.71/14.87 Y2 = Y3) => 98.71/14.87 (Y0(Y2) <=> 98.71/14.87 Y1(Y3))))))))) => 98.71/14.87 ((??(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (Y0(Y2) & 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (Y0(Y3) => 98.71/14.87 (Y2 = Y3))))))))) => 98.71/14.87 ((??(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (Y1(Y2) & 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (Y1(Y3) => 98.71/14.87 (Y2 = Y3))))))))) => 98.71/14.87 (descr(Y0) = 98.71/14.87 descr(Y1))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 ((Y0 = Y1) => 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i > $o]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i > $o]: 98.71/14.87 (( 98.71/14.87 !!(( 98.71/14.87 ^[Y4 : $i]: 98.71/14.87 (in(Y4, 98.71/14.87 Y0) => 98.71/14.87 (!!(( 98.71/14.87 ^[Y5 : $i]: 98.71/14.87 (in(Y5, 98.71/14.87 Y1) => 98.71/14.87 (( 98.71/14.87 Y4 = Y5) => 98.71/14.87 (Y2(Y4) <=> 98.71/14.87 Y3(Y5))))))))))) => 98.71/14.87 (dsetconstr( 98.71/14.87 Y0, Y2) = 98.71/14.87 dsetconstr( 98.71/14.87 Y1, Y3)))))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 ((!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 in(Y2, 98.71/14.87 Y1))))) => 98.71/14.87 subset( 98.71/14.87 Y0, Y1)))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (( 98.71/14.87 Y0 = Y1) => 98.71/14.87 subset( 98.71/14.87 Y1, Y0)))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 Y0 = Y1) => 98.71/14.87 subset( 98.71/14.87 Y0, Y1)))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (( 98.71/14.87 !!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 in(Y2, 98.71/14.87 Y1))))) => 98.71/14.87 subset( 98.71/14.87 Y0, Y1)))))))) => 98.71/14.87 ((!!(subset(emptyset))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y0, Y1) => 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 in(Y2, 98.71/14.87 Y1)))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y0, Y1) => 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y1))) => 98.71/14.87 (~( 98.71/14.87 in(Y2, 98.71/14.87 Y0)))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y1))) => 98.71/14.87 (~( 98.71/14.87 subset( 98.71/14.87 Y0, Y1)))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 subset( 98.71/14.87 Y0, Y1))) => 98.71/14.87 (Y0 != Y1)))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y1))) => 98.71/14.87 (Y0 != Y1)))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 subset( 98.71/14.87 Y0, Y0)))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y0, Y1) => 98.71/14.87 (subset( 98.71/14.87 Y1, Y2) => 98.71/14.87 subset( 98.71/14.87 Y0, Y2)))))))))))) => 98.71/14.87 ((!!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 subset( 98.71/14.87 Y1, 98.71/14.87 setadjoin( 98.71/14.87 Y0, Y1)))))))) => 98.71/14.87 ((!!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y0, Y2) => 98.71/14.87 subset( 98.71/14.87 Y0, 98.71/14.87 setadjoin( 98.71/14.87 Y1, Y2)))))))))))) => 98.71/14.87 ((!!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y0, Y1) => 98.71/14.87 in(Y0, 98.71/14.87 powerset( 98.71/14.87 Y1))))))))) => 98.71/14.87 ((!!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y0, Y1) => 98.71/14.87 (subset( 98.71/14.87 Y1, Y0) => 98.71/14.87 (Y0 = Y1))))))))) => 98.71/14.87 (( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y0, 98.71/14.87 emptyset) => 98.71/14.87 (Y0 = 98.71/14.87 emptyset))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y1, Y0) => 98.71/14.87 in(Y1, 98.71/14.87 powerset( 98.71/14.87 Y0))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (in(Y1, 98.71/14.87 powerset( 98.71/14.87 Y0)) => 98.71/14.87 subset( 98.71/14.87 Y1, Y0)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 in(Y0, 98.71/14.87 powerset( 98.71/14.87 Y0))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y0, Y1) => 98.71/14.87 subset( 98.71/14.87 powerset( 98.71/14.87 Y0), 98.71/14.87 powerset( 98.71/14.87 Y1))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i > $o]: 98.71/14.87 in( 98.71/14.87 dsetconstr( 98.71/14.87 Y0, Y1), 98.71/14.87 powerset( 98.71/14.87 Y0)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i > $o]: 98.71/14.87 subset( 98.71/14.87 dsetconstr( 98.71/14.87 Y0, Y1), 98.71/14.87 Y0))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 in(Y2, 98.71/14.87 binunion( 98.71/14.87 Y0, Y1)))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 in(Y1, 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 setadjoin( 98.71/14.87 Y1, 98.71/14.87 emptyset))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y1) => 98.71/14.87 in(Y2, 98.71/14.87 binunion( 98.71/14.87 Y0, Y1)))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $o]: 98.71/14.87 (in(Y2, 98.71/14.87 binunion( 98.71/14.87 Y0, Y1)) => 98.71/14.87 (( 98.71/14.87 in(Y2, 98.71/14.87 Y0) => Y3) => 98.71/14.87 (( 98.71/14.87 in(Y2, 98.71/14.87 Y1) => Y3) => 98.71/14.87 Y3))))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 binunion( 98.71/14.87 Y0, Y1)) => 98.71/14.87 (in(Y2, 98.71/14.87 Y1) | 98.71/14.87 in(Y2, 98.71/14.87 Y0)))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 subset( 98.71/14.87 Y0, 98.71/14.87 binunion( 98.71/14.87 Y0, Y1)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 subset( 98.71/14.87 Y1, 98.71/14.87 binunion( 98.71/14.87 Y0, Y1)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 (in(Y2, 98.71/14.87 Y1) => 98.71/14.87 in(Y2, 98.71/14.87 binintersect( 98.71/14.87 Y0, Y1))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y2, Y0) => 98.71/14.87 (subset( 98.71/14.87 Y2, Y1) => 98.71/14.87 subset( 98.71/14.87 Y2, 98.71/14.87 binintersect( 98.71/14.87 Y0, Y1))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 binintersect( 98.71/14.87 Y0, Y1)) => 98.71/14.87 in(Y2, 98.71/14.87 Y0))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 subset( 98.71/14.87 binintersect( 98.71/14.87 Y0, Y1), 98.71/14.87 Y0))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y0, Y1) => 98.71/14.87 (binintersect( 98.71/14.87 Y0, Y1) = 98.71/14.87 Y0)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (( 98.71/14.87 binintersect( 98.71/14.87 Y0, Y1) = 98.71/14.87 Y1) => 98.71/14.87 subset( 98.71/14.87 Y1, Y0)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 binintersect( 98.71/14.87 Y0, Y1)) => 98.71/14.87 in(Y2, 98.71/14.87 Y1))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (( 98.71/14.87 ~(( 98.71/14.87 ??(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) & 98.71/14.87 in(Y2, 98.71/14.87 Y1))))))) => 98.71/14.87 (binintersect( 98.71/14.87 Y0, Y1) = 98.71/14.87 emptyset)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 subset( 98.71/14.87 binintersect( 98.71/14.87 Y0, Y1), 98.71/14.87 Y1))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y1, Y0) => 98.71/14.87 (binintersect( 98.71/14.87 Y0, Y1) = 98.71/14.87 Y1)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (( 98.71/14.87 binintersect( 98.71/14.87 Y0, Y1) = 98.71/14.87 Y0) => 98.71/14.87 subset( 98.71/14.87 Y0, Y1)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (binintersect( 98.71/14.87 Y0, 98.71/14.87 binunion( 98.71/14.87 Y1, Y2)) = 98.71/14.87 binunion( 98.71/14.87 binintersect( 98.71/14.87 Y0, Y1), 98.71/14.87 binintersect( 98.71/14.87 Y0, Y2)))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y1))) => 98.71/14.87 in(Y2, 98.71/14.87 setminus( 98.71/14.87 Y0, Y1))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 setminus( 98.71/14.87 Y0, Y1)) => 98.71/14.87 in(Y2, 98.71/14.87 Y0))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 setminus( 98.71/14.87 Y0, Y1)) => 98.71/14.87 (~( 98.71/14.87 in(Y2, 98.71/14.87 Y1))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y0, Y1) => 98.71/14.87 (setminus( 98.71/14.87 Y0, Y1) = 98.71/14.87 emptyset)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 setminus( 98.71/14.87 Y0, Y1)))) => 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 in(Y2, 98.71/14.87 Y1)))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 setminus( 98.71/14.87 Y0, Y1)))) => 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y1))) => 98.71/14.87 (~( 98.71/14.87 in(Y2, 98.71/14.87 Y0)))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y0))) => 98.71/14.87 (~( 98.71/14.87 in(Y2, 98.71/14.87 setminus( 98.71/14.87 Y0, Y1)))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y1) => 98.71/14.87 (~( 98.71/14.87 in(Y2, 98.71/14.87 setminus( 98.71/14.87 Y0, Y1)))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 subset( 98.71/14.87 setminus( 98.71/14.87 Y0, Y1), 98.71/14.87 Y0))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (( 98.71/14.87 setminus( 98.71/14.87 Y0, Y1) = 98.71/14.87 emptyset) => 98.71/14.87 subset( 98.71/14.87 Y0, Y1)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 symdiff( 98.71/14.87 Y0, Y1)) => 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $o]: 98.71/14.87 (( 98.71/14.87 in(Y2, 98.71/14.87 Y0) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y1))) => 98.71/14.87 Y3)) => 98.71/14.87 (( 98.71/14.87 ( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y0))) => 98.71/14.87 ( 98.71/14.87 in(Y2, 98.71/14.87 Y1) => Y3)) => 98.71/14.87 Y3))))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y1))) => 98.71/14.87 in(Y2, 98.71/14.87 symdiff( 98.71/14.87 Y0, Y1))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y0))) => 98.71/14.87 (in(Y2, 98.71/14.87 Y1) => 98.71/14.87 in(Y2, 98.71/14.87 symdiff( 98.71/14.87 Y0, Y1))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 (in(Y2, 98.71/14.87 Y1) => 98.71/14.87 (~( 98.71/14.87 in(Y2, 98.71/14.87 symdiff( 98.71/14.87 Y0, Y1))))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y0))) => 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y1))) => 98.71/14.87 (~( 98.71/14.87 in(Y2, 98.71/14.87 symdiff( 98.71/14.87 Y0, Y1))))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 in(Y1, 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 setadjoin( 98.71/14.87 Y1, 98.71/14.87 emptyset))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 in(Y0, 98.71/14.87 setunion( 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 setadjoin( 98.71/14.87 Y1, 98.71/14.87 emptyset)), 98.71/14.87 emptyset)))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 in(Y1, 98.71/14.87 setunion( 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 setadjoin( 98.71/14.87 Y1, 98.71/14.87 emptyset)), 98.71/14.87 emptyset)))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (??(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 setunion( 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 setadjoin( 98.71/14.87 Y1, 98.71/14.87 emptyset)), 98.71/14.87 emptyset)))) & 98.71/14.87 (??(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (in(Y3, 98.71/14.87 setunion( 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 setadjoin( 98.71/14.87 Y1, 98.71/14.87 emptyset)), 98.71/14.87 emptyset)))) & 98.71/14.87 (setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 setadjoin( 98.71/14.87 Y1, 98.71/14.87 emptyset)), 98.71/14.87 emptyset)) = 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 setadjoin( 98.71/14.87 Y3, 98.71/14.87 emptyset)), 98.71/14.87 emptyset))))))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (??(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 setunion( 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 setadjoin( 98.71/14.87 Y1, 98.71/14.87 emptyset)), 98.71/14.87 emptyset)))) & 98.71/14.87 (??(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (in(Y3, 98.71/14.87 setunion( 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 setadjoin( 98.71/14.87 Y1, 98.71/14.87 emptyset)), 98.71/14.87 emptyset)))) & 98.71/14.87 (setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 setadjoin( 98.71/14.87 Y1, 98.71/14.87 emptyset)), 98.71/14.87 emptyset)) = 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 setadjoin( 98.71/14.87 Y3, 98.71/14.87 emptyset)), 98.71/14.87 emptyset))))))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (in(Y1, 98.71/14.87 Y0) => 98.71/14.87 subset( 98.71/14.87 setadjoin( 98.71/14.87 Y1, 98.71/14.87 emptyset), 98.71/14.87 Y0)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (in(Y1, 98.71/14.87 Y0) => 98.71/14.87 in( 98.71/14.87 setadjoin( 98.71/14.87 Y1, 98.71/14.87 emptyset), 98.71/14.87 powerset( 98.71/14.87 Y0))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 in( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 emptyset), 98.71/14.87 powerset( 98.71/14.87 binunion( 98.71/14.87 Y0, Y1))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 setadjoin( 98.71/14.87 Y1, 98.71/14.87 emptyset))) => 98.71/14.87 (( 98.71/14.87 Y2 = Y1) | 98.71/14.87 (Y2 = Y0)))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (in(Y3, 98.71/14.87 Y1) => 98.71/14.87 subset( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 setadjoin( 98.71/14.87 Y3, 98.71/14.87 emptyset)), 98.71/14.87 binunion( 98.71/14.87 Y0, Y1)))))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (in(Y3, 98.71/14.87 Y1) => 98.71/14.87 in( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 setadjoin( 98.71/14.87 Y3, 98.71/14.87 emptyset)), 98.71/14.87 powerset( 98.71/14.87 binunion( 98.71/14.87 Y0, Y1))))))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (in(Y3, 98.71/14.87 Y1) => 98.71/14.87 subset( 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 setadjoin( 98.71/14.87 Y3, 98.71/14.87 emptyset)), 98.71/14.87 emptyset)), 98.71/14.87 powerset( 98.71/14.87 binunion( 98.71/14.87 Y0, Y1))))))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (in(Y3, 98.71/14.87 Y1) => 98.71/14.87 in( 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 setadjoin( 98.71/14.87 Y3, 98.71/14.87 emptyset)), 98.71/14.87 emptyset)), 98.71/14.87 powerset( 98.71/14.87 powerset( 98.71/14.87 binunion( 98.71/14.87 Y0, Y1)))))))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (in(Y3, 98.71/14.87 Y1) => 98.71/14.87 in( 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 setadjoin( 98.71/14.87 Y3, 98.71/14.87 emptyset)), 98.71/14.87 emptyset)), 98.71/14.87 powerset( 98.71/14.87 powerset( 98.71/14.87 binunion( 98.71/14.87 Y0, Y1)))))))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (in(Y3, 98.71/14.87 Y1) => 98.71/14.87 in( 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y2, 98.71/14.87 setadjoin( 98.71/14.87 Y3, 98.71/14.87 emptyset)), 98.71/14.87 emptyset)), 98.71/14.87 dsetconstr( 98.71/14.87 powerset( 98.71/14.87 powerset( 98.71/14.87 binunion( 98.71/14.87 Y0, Y1))), 98.71/14.87 (^[Y4 : $i]: 98.71/14.87 (??(( 98.71/14.87 ^[Y5 : $i]: 98.71/14.87 (in(Y5, 98.71/14.87 Y0) & 98.71/14.87 (??(( 98.71/14.87 ^[Y6 : $i]: 98.71/14.87 (in(Y6, 98.71/14.87 Y1) & 98.71/14.87 (Y4 = 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y5, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y5, 98.71/14.87 setadjoin( 98.71/14.87 Y6, 98.71/14.87 emptyset)), 98.71/14.87 emptyset)))))))))))))))))))))))))))) => 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 dsetconstr( 98.71/14.87 powerset( 98.71/14.87 powerset( 98.71/14.87 binunion( 98.71/14.87 Y0, Y1))), 98.71/14.87 (^[Y3 : $i]: 98.71/14.87 (??(( 98.71/14.87 ^[Y4 : $i]: 98.71/14.87 (in(Y4, 98.71/14.87 Y0) & 98.71/14.87 (??(( 98.71/14.87 ^[Y5 : $i]: 98.71/14.87 (in(Y5, 98.71/14.87 Y1) & 98.71/14.87 (Y3 = 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y4, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y4, 98.71/14.87 setadjoin( 98.71/14.87 Y5, 98.71/14.87 emptyset)), 98.71/14.87 emptyset)))))))))))))) => 98.71/14.87 (??(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (( 98.71/14.87 ??(( 98.71/14.87 ^[Y4 : $i]: 98.71/14.87 (in(Y4, 98.71/14.87 Y1) & 98.71/14.87 (Y2 = 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y3, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y3, 98.71/14.87 setadjoin( 98.71/14.87 Y4, 98.71/14.87 emptyset)), 98.71/14.87 emptyset))))))) & 98.71/14.87 in(Y3, 98.71/14.87 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 98.71/14.87 inference('lazy_cnf_imply', [status(thm)], ['186'])). 98.71/14.87 tff('188', plain, 98.71/14.87 ~ ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 98.71/14.87 (in(emptyset, setadjoin(emptyset, emptyset)) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y1) => in(Y2, setadjoin(Y0, Y1)))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (in(Y2, setadjoin(Y0, Y1)) => 98.71/14.87 (!!((^[Y3 : $o]: 98.71/14.87 (((Y2 = Y0) => Y3) => 98.71/14.87 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (in(Y2, setadjoin(Y0, Y1)) => 98.71/14.87 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 98.71/14.87 in(Y1, powerset(Y0))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.71/14.87 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (in(Y1, powerset(Y0)) => 98.71/14.87 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (in(Y1, Y2) => 98.71/14.87 (in(Y2, Y0) => in(Y1, setunion(Y0))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (in(Y1, setunion(Y0)) => 98.71/14.87 (!!((^[Y2 : $o]: 98.71/14.87 ((!!((^[Y3 : $i]: 98.71/14.87 (in(Y1, Y3) => 98.71/14.87 (in(Y3, Y0) => Y2))))) => 98.71/14.87 Y2))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (in(Y1, Y0) => 98.71/14.87 in(Y1, powerset(setunion(Y0)))))))))) => 98.71/14.87 ((!!((^[Y0 : $i > $o]: 98.71/14.87 ((??((^[Y1 : $i]: 98.71/14.87 (Y0(Y1) & 98.71/14.87 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 98.71/14.87 (??((^[Y1 : $i]: 98.71/14.87 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 ((Y0 != emptyset) => 98.71/14.87 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (in(Y0, setadjoin(Y1, emptyset)) => 98.71/14.87 (Y0 = Y1)))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 ((Y0 != Y1) => 98.71/14.87 (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 ((Y0 = Y1) => 98.71/14.87 in(Y0, setadjoin(Y1, emptyset))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (in(Y0, setadjoin(Y1, emptyset)) => 98.71/14.87 in(Y1, setadjoin(Y0, emptyset))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 setadjoin(Y0, 98.71/14.87 setadjoin(Y1, emptyset))) => 98.71/14.87 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 in(Y0, 98.71/14.87 setadjoin(Y0, 98.71/14.87 setadjoin(Y1, emptyset))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 in(Y1, 98.71/14.87 setadjoin(Y0, 98.71/14.87 setadjoin(Y1, emptyset))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i > $o]: 98.71/14.87 ((??((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y0) & Y1(Y2))))) => 98.71/14.87 (dsetconstr(Y0, Y1) != emptyset)))))))) => 98.71/14.87 ((!!((^[Y0 : $i > $o]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (in(Y1, emptyset) => Y0(Y1)))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i > $o]: 98.71/14.87 ((~((!!((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y0) => Y1(Y2))))))) => 98.71/14.87 (??((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y0) & 98.71/14.87 (~(Y1(Y2)))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i > $o]: 98.71/14.87 ((!!((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y0) => 98.71/14.87 (~(Y1(Y2))))))) => 98.71/14.87 (~((??((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y0) & Y1(Y2)))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i > $o]: 98.71/14.87 ((~((??((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y0) & 98.71/14.87 Y1(Y2))))))) => 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y0) => 98.71/14.87 (~(Y1(Y2)))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i > $o]: 98.71/14.87 ((??((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y0) & 98.71/14.87 (~(Y1(Y2))))))) => 98.71/14.87 (~((!!((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y0) => 98.71/14.87 Y1(Y2)))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $o]: 98.71/14.87 (Y0 => in(emptyset, prop2set(Y0)))))) => 98.71/14.87 ((!!((^[Y0 : $o]: 98.71/14.87 (Y0 => set2prop(prop2set(Y0)))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i > $o]: 98.71/14.87 ((~((??((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y0) & 98.71/14.87 Y1(Y2))))))) => 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y0) => 98.71/14.87 (~(Y1(Y2)))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i > $o]: 98.71/14.87 ((~((!!((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y0) => 98.71/14.87 Y1(Y2))))))) => 98.71/14.87 (??((^[Y2 : $i]: 98.71/14.87 (in(Y2, Y0) & 98.71/14.87 (~(Y1(Y2)))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i > $o]: 98.71/14.87 ((??(Y0)) => 98.71/14.87 ((!!((^[Y1 : $i]: 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (Y0(Y1) => 98.71/14.87 (Y0(Y2) => 98.71/14.87 (Y1 = Y2))))))))) => 98.71/14.87 (??((^[Y1 : $i]: 98.71/14.87 (Y0(Y1) & 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (Y0(Y2) => 98.71/14.87 (Y1 = Y2)))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i > $o]: 98.71/14.87 ((??((^[Y1 : $i]: 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (Y0(Y2) <=> 98.71/14.87 (Y2 = Y1)))))))) => 98.71/14.87 (??((^[Y1 : $i]: 98.71/14.87 (Y0(Y1) & 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (Y0(Y2) => 98.71/14.87 (Y1 = Y2))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 ((Y0 = Y1) => 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (!!((^[Y3 : $i]: 98.71/14.87 (( 98.71/14.87 Y2 = Y3) => 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 in(Y3, 98.71/14.87 Y1)))))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 ((Y0 = Y1) => 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (( 98.71/14.87 Y2 = Y3) => 98.71/14.87 ( 98.71/14.87 in(Y2, 98.71/14.87 Y0) <=> 98.71/14.87 in(Y3, 98.71/14.87 Y1)))))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i > $o]: 98.71/14.87 ((??((^[Y1 : $i]: 98.71/14.87 (Y0(Y1) & 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (Y0(Y2) => 98.71/14.87 (Y1 = Y2))))))))) => 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (Y0(Y1) => 98.71/14.87 (Y0(Y2) => 98.71/14.87 (Y1 = Y2))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i > $o]: 98.71/14.87 (!!((^[Y1 : $i > $o]: 98.71/14.87 ((!!((^[Y2 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (( 98.71/14.87 Y2 = Y3) => 98.71/14.87 (Y0(Y2) <=> 98.71/14.87 Y1(Y3))))))))) => 98.71/14.87 ((??((^[Y2 : $i]: 98.71/14.87 (Y0(Y2) & 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (Y0(Y3) => 98.71/14.87 (Y2 = Y3))))))))) <=> 98.71/14.87 (??((^[Y2 : $i]: 98.71/14.87 (Y1(Y2) & 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (Y1(Y3) => 98.71/14.87 (Y2 = Y3))))))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 ((Y0 = Y1) => 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (( 98.71/14.87 Y2 = Y3) => 98.71/14.87 (setadjoin( 98.71/14.87 Y0, Y2) = 98.71/14.87 setadjoin( 98.71/14.87 Y1, Y3)))))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 ((Y0 = Y1) => 98.71/14.87 (powerset(Y0) = 98.71/14.87 powerset(Y1))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 ((Y0 = Y1) => 98.71/14.87 (setunion(Y0) = 98.71/14.87 setunion(Y1))))))))) => 98.71/14.87 ((!!((^[Y0 : $i > $o]: 98.71/14.87 ((??((^[Y1 : $i]: 98.71/14.87 (Y0(Y1) & 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (Y0(Y2) => 98.71/14.87 ( 98.71/14.87 Y1 = Y2))))))))) => 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (!!((^[Y2 : $i]: 98.71/14.87 (Y0(Y1) => 98.71/14.87 (Y0(Y2) => 98.71/14.87 (Y1 = Y2))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i > $o]: 98.71/14.87 (!!((^[Y1 : $i > $o]: 98.71/14.87 ((!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (( 98.71/14.87 Y2 = Y3) => 98.71/14.87 (Y0(Y2) <=> 98.71/14.87 Y1(Y3))))))))) => 98.71/14.87 ((??(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 ( 98.71/14.87 Y0(Y2) & 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (Y0(Y3) => 98.71/14.87 (Y2 = Y3))))))))) => 98.71/14.87 ((??(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (Y1(Y2) & 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $i]: 98.71/14.87 (Y1(Y3) => 98.71/14.87 (Y2 = Y3))))))))) => 98.71/14.87 (descr(Y0) = 98.71/14.87 descr(Y1))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 ((Y0 = Y1) => 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i > $o]: 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y3 : $i > $o]: 98.71/14.87 (( 98.71/14.87 !!(( 98.71/14.87 ^[Y4 : $i]: 98.71/14.87 (in(Y4, 98.71/14.87 Y0) => 98.71/14.87 (!!(( 98.71/14.87 ^[Y5 : $i]: 98.71/14.87 (in(Y5, 98.71/14.87 Y1) => 98.71/14.87 (( 98.71/14.87 Y4 = Y5) => 98.71/14.87 (Y2(Y4) <=> 98.71/14.87 Y3(Y5))))))))))) => 98.71/14.87 (dsetconstr( 98.71/14.87 Y0, Y2) = 98.71/14.87 dsetconstr( 98.71/14.87 Y1, Y3)))))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 ((!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 in(Y2, 98.71/14.87 Y1))))) => 98.71/14.87 subset(Y0, 98.71/14.87 Y1)))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 ((Y0 = Y1) => 98.71/14.87 subset( 98.71/14.87 Y1, Y0)))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (( 98.71/14.87 Y0 = Y1) => 98.71/14.87 subset( 98.71/14.87 Y0, Y1)))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 in(Y2, 98.71/14.87 Y1))))) => 98.71/14.87 subset( 98.71/14.87 Y0, Y1)))))))) => 98.71/14.87 ((!!(subset(emptyset))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!((^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y0, Y1) => 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 in(Y2, 98.71/14.87 Y1)))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y0, Y1) => 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y1))) => 98.71/14.87 (~( 98.71/14.87 in(Y2, 98.71/14.87 Y0)))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y1))) => 98.71/14.87 (~( 98.71/14.87 subset( 98.71/14.87 Y0, Y1)))))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 subset( 98.71/14.87 Y0, Y1))) => 98.71/14.87 (Y0 != Y1)))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y1))) => 98.71/14.87 (Y0 != Y1)))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 subset( 98.71/14.87 Y0, Y0)))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y0, Y1) => 98.71/14.87 (subset( 98.71/14.87 Y1, Y2) => 98.71/14.87 subset( 98.71/14.87 Y0, Y2)))))))))))) => 98.71/14.87 ((!!((^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 subset( 98.71/14.87 Y1, 98.71/14.87 setadjoin( 98.71/14.87 Y0, Y1)))))))) => 98.71/14.87 ((!!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y0, Y2) => 98.71/14.87 subset( 98.71/14.87 Y0, 98.71/14.87 setadjoin( 98.71/14.87 Y1, Y2)))))))))))) => 98.71/14.87 ((!!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y0, Y1) => 98.71/14.87 in(Y0, 98.71/14.87 powerset( 98.71/14.87 Y1))))))))) => 98.71/14.87 ((!!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y0, Y1) => 98.71/14.87 (subset( 98.71/14.87 Y1, Y0) => 98.71/14.87 (Y0 = Y1))))))))) => 98.71/14.87 ((!!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y0, 98.71/14.87 emptyset) => 98.71/14.87 (Y0 = 98.71/14.87 emptyset))))) => 98.71/14.87 (( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y1, Y0) => 98.71/14.87 in(Y1, 98.71/14.87 powerset( 98.71/14.87 Y0))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (in(Y1, 98.71/14.87 powerset( 98.71/14.87 Y0)) => 98.71/14.87 subset( 98.71/14.87 Y1, Y0)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 in(Y0, 98.71/14.87 powerset( 98.71/14.87 Y0))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y0, Y1) => 98.71/14.87 subset( 98.71/14.87 powerset( 98.71/14.87 Y0), 98.71/14.87 powerset( 98.71/14.87 Y1))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i > $o]: 98.71/14.87 in( 98.71/14.87 dsetconstr( 98.71/14.87 Y0, Y1), 98.71/14.87 powerset( 98.71/14.87 Y0)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i > $o]: 98.71/14.87 subset( 98.71/14.87 dsetconstr( 98.71/14.87 Y0, Y1), 98.71/14.87 Y0))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 in(Y2, 98.71/14.87 binunion( 98.71/14.87 Y0, Y1)))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 in(Y1, 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 setadjoin( 98.71/14.87 Y1, 98.71/14.87 emptyset))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y1) => 98.71/14.87 in(Y2, 98.71/14.87 binunion( 98.71/14.87 Y0, Y1)))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $o]: 98.71/14.87 (in(Y2, 98.71/14.87 binunion( 98.71/14.87 Y0, Y1)) => 98.71/14.87 (( 98.71/14.87 in(Y2, 98.71/14.87 Y0) => Y3) => 98.71/14.87 (( 98.71/14.87 in(Y2, 98.71/14.87 Y1) => Y3) => 98.71/14.87 Y3))))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 binunion( 98.71/14.87 Y0, Y1)) => 98.71/14.87 (in(Y2, 98.71/14.87 Y1) | 98.71/14.87 in(Y2, 98.71/14.87 Y0)))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 subset( 98.71/14.87 Y0, 98.71/14.87 binunion( 98.71/14.87 Y0, Y1)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 subset( 98.71/14.87 Y1, 98.71/14.87 binunion( 98.71/14.87 Y0, Y1)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 (in(Y2, 98.71/14.87 Y1) => 98.71/14.87 in(Y2, 98.71/14.87 binintersect( 98.71/14.87 Y0, Y1))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y2, Y0) => 98.71/14.87 (subset( 98.71/14.87 Y2, Y1) => 98.71/14.87 subset( 98.71/14.87 Y2, 98.71/14.87 binintersect( 98.71/14.87 Y0, Y1))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 binintersect( 98.71/14.87 Y0, Y1)) => 98.71/14.87 in(Y2, 98.71/14.87 Y0))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 subset( 98.71/14.87 binintersect( 98.71/14.87 Y0, Y1), 98.71/14.87 Y0))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y0, Y1) => 98.71/14.87 (binintersect( 98.71/14.87 Y0, Y1) = 98.71/14.87 Y0)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (( 98.71/14.87 binintersect( 98.71/14.87 Y0, Y1) = 98.71/14.87 Y1) => 98.71/14.87 subset( 98.71/14.87 Y1, Y0)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 binintersect( 98.71/14.87 Y0, Y1)) => 98.71/14.87 in(Y2, 98.71/14.87 Y1))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (( 98.71/14.87 ~(( 98.71/14.87 ??(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) & 98.71/14.87 in(Y2, 98.71/14.87 Y1))))))) => 98.71/14.87 (binintersect( 98.71/14.87 Y0, Y1) = 98.71/14.87 emptyset)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 subset( 98.71/14.87 binintersect( 98.71/14.87 Y0, Y1), 98.71/14.87 Y1))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y1, Y0) => 98.71/14.87 (binintersect( 98.71/14.87 Y0, Y1) = 98.71/14.87 Y1)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (( 98.71/14.87 binintersect( 98.71/14.87 Y0, Y1) = 98.71/14.87 Y0) => 98.71/14.87 subset( 98.71/14.87 Y0, Y1)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (binintersect( 98.71/14.87 Y0, 98.71/14.87 binunion( 98.71/14.87 Y1, Y2)) = 98.71/14.87 binunion( 98.71/14.87 binintersect( 98.71/14.87 Y0, Y1), 98.71/14.87 binintersect( 98.71/14.87 Y0, Y2)))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y1))) => 98.71/14.87 in(Y2, 98.71/14.87 setminus( 98.71/14.87 Y0, Y1))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 setminus( 98.71/14.87 Y0, Y1)) => 98.71/14.87 in(Y2, 98.71/14.87 Y0))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 setminus( 98.71/14.87 Y0, Y1)) => 98.71/14.87 (~( 98.71/14.87 in(Y2, 98.71/14.87 Y1))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (subset( 98.71/14.87 Y0, Y1) => 98.71/14.87 (setminus( 98.71/14.87 Y0, Y1) = 98.71/14.87 emptyset)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 setminus( 98.71/14.87 Y0, Y1)))) => 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 in(Y2, 98.71/14.87 Y1)))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 setminus( 98.71/14.87 Y0, Y1)))) => 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y1))) => 98.71/14.87 (~( 98.71/14.87 in(Y2, 98.71/14.87 Y0)))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y0))) => 98.71/14.87 (~( 98.71/14.87 in(Y2, 98.71/14.87 setminus( 98.71/14.87 Y0, Y1)))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y1) => 98.71/14.87 (~( 98.71/14.87 in(Y2, 98.71/14.87 setminus( 98.71/14.87 Y0, Y1)))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 subset( 98.71/14.87 setminus( 98.71/14.87 Y0, Y1), 98.71/14.87 Y0))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (( 98.71/14.87 setminus( 98.71/14.87 Y0, Y1) = 98.71/14.87 emptyset) => 98.71/14.87 subset( 98.71/14.87 Y0, Y1)))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 symdiff( 98.71/14.87 Y0, Y1)) => 98.71/14.87 (!!(( 98.71/14.87 ^[Y3 : $o]: 98.71/14.87 (( 98.71/14.87 in(Y2, 98.71/14.87 Y0) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y1))) => 98.71/14.87 Y3)) => 98.71/14.87 (( 98.71/14.87 ( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y0))) => 98.71/14.87 ( 98.71/14.87 in(Y2, 98.71/14.87 Y1) => Y3)) => 98.71/14.87 Y3))))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y1))) => 98.71/14.87 in(Y2, 98.71/14.87 symdiff( 98.71/14.87 Y0, Y1))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y0))) => 98.71/14.87 (in(Y2, 98.71/14.87 Y1) => 98.71/14.87 in(Y2, 98.71/14.87 symdiff( 98.71/14.87 Y0, Y1))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (in(Y2, 98.71/14.87 Y0) => 98.71/14.87 (in(Y2, 98.71/14.87 Y1) => 98.71/14.87 (~( 98.71/14.87 in(Y2, 98.71/14.87 symdiff( 98.71/14.87 Y0, Y1))))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y2 : $i]: 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y0))) => 98.71/14.87 (( 98.71/14.87 ~( 98.71/14.87 in(Y2, 98.71/14.87 Y1))) => 98.71/14.87 (~( 98.71/14.87 in(Y2, 98.71/14.87 symdiff( 98.71/14.87 Y0, Y1))))))))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 in(Y1, 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 setadjoin( 98.71/14.87 Y1, 98.71/14.87 emptyset))))))))) => 98.71/14.87 ( 98.71/14.87 ( 98.71/14.87 !!(( 98.71/14.87 ^[Y0 : $i]: 98.71/14.87 (!!(( 98.71/14.87 ^[Y1 : $i]: 98.71/14.87 in(Y0, 98.71/14.87 setunion( 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 emptyset), 98.71/14.87 setadjoin( 98.71/14.87 setadjoin( 98.71/14.87 Y0, 98.71/14.87 setadjoin( 98.71/14.87 Y1, 98.71/14.87 emptyset)), 98.71/14.88 emptyset)))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 in(Y1, 98.71/14.88 setunion( 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y0, 98.71/14.88 emptyset), 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y0, 98.71/14.88 setadjoin( 98.71/14.88 Y1, 98.71/14.88 emptyset)), 98.71/14.88 emptyset)))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (??(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 setunion( 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y0, 98.71/14.88 emptyset), 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y0, 98.71/14.88 setadjoin( 98.71/14.88 Y1, 98.71/14.88 emptyset)), 98.71/14.88 emptyset)))) & 98.71/14.88 (??(( 98.71/14.88 ^[Y3 : $i]: 98.71/14.88 (in(Y3, 98.71/14.88 setunion( 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y0, 98.71/14.88 emptyset), 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y0, 98.71/14.88 setadjoin( 98.71/14.88 Y1, 98.71/14.88 emptyset)), 98.71/14.88 emptyset)))) & 98.71/14.88 (setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y0, 98.71/14.88 emptyset), 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y0, 98.71/14.88 setadjoin( 98.71/14.88 Y1, 98.71/14.88 emptyset)), 98.71/14.88 emptyset)) = 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y2, 98.71/14.88 emptyset), 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y2, 98.71/14.88 setadjoin( 98.71/14.88 Y3, 98.71/14.88 emptyset)), 98.71/14.88 emptyset))))))))))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (??(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 setunion( 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y0, 98.71/14.88 emptyset), 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y0, 98.71/14.88 setadjoin( 98.71/14.88 Y1, 98.71/14.88 emptyset)), 98.71/14.88 emptyset)))) & 98.71/14.88 (??(( 98.71/14.88 ^[Y3 : $i]: 98.71/14.88 (in(Y3, 98.71/14.88 setunion( 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y0, 98.71/14.88 emptyset), 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y0, 98.71/14.88 setadjoin( 98.71/14.88 Y1, 98.71/14.88 emptyset)), 98.71/14.88 emptyset)))) & 98.71/14.88 (setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y0, 98.71/14.88 emptyset), 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y0, 98.71/14.88 setadjoin( 98.71/14.88 Y1, 98.71/14.88 emptyset)), 98.71/14.88 emptyset)) = 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y2, 98.71/14.88 emptyset), 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y2, 98.71/14.88 setadjoin( 98.71/14.88 Y3, 98.71/14.88 emptyset)), 98.71/14.88 emptyset))))))))))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (in(Y1, 98.71/14.88 Y0) => 98.71/14.88 subset( 98.71/14.88 setadjoin( 98.71/14.88 Y1, 98.71/14.88 emptyset), 98.71/14.88 Y0)))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (in(Y1, 98.71/14.88 Y0) => 98.71/14.88 in( 98.71/14.88 setadjoin( 98.71/14.88 Y1, 98.71/14.88 emptyset), 98.71/14.88 powerset( 98.71/14.88 Y0))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 Y0) => 98.71/14.88 in( 98.71/14.88 setadjoin( 98.71/14.88 Y2, 98.71/14.88 emptyset), 98.71/14.88 powerset( 98.71/14.88 binunion( 98.71/14.88 Y0, Y1))))))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 setadjoin( 98.71/14.88 Y0, 98.71/14.88 setadjoin( 98.71/14.88 Y1, 98.71/14.88 emptyset))) => 98.71/14.88 (( 98.71/14.88 Y2 = Y1) | 98.71/14.88 (Y2 = Y0)))))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 Y0) => 98.71/14.88 (!!(( 98.71/14.88 ^[Y3 : $i]: 98.71/14.88 (in(Y3, 98.71/14.88 Y1) => 98.71/14.88 subset( 98.71/14.88 setadjoin( 98.71/14.88 Y2, 98.71/14.88 setadjoin( 98.71/14.88 Y3, 98.71/14.88 emptyset)), 98.71/14.88 binunion( 98.71/14.88 Y0, Y1)))))))))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 Y0) => 98.71/14.88 (!!(( 98.71/14.88 ^[Y3 : $i]: 98.71/14.88 (in(Y3, 98.71/14.88 Y1) => 98.71/14.88 in( 98.71/14.88 setadjoin( 98.71/14.88 Y2, 98.71/14.88 setadjoin( 98.71/14.88 Y3, 98.71/14.88 emptyset)), 98.71/14.88 powerset( 98.71/14.88 binunion( 98.71/14.88 Y0, Y1))))))))))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 Y0) => 98.71/14.88 (!!(( 98.71/14.88 ^[Y3 : $i]: 98.71/14.88 (in(Y3, 98.71/14.88 Y1) => 98.71/14.88 subset( 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y2, 98.71/14.88 emptyset), 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y2, 98.71/14.88 setadjoin( 98.71/14.88 Y3, 98.71/14.88 emptyset)), 98.71/14.88 emptyset)), 98.71/14.88 powerset( 98.71/14.88 binunion( 98.71/14.88 Y0, Y1))))))))))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 Y0) => 98.71/14.88 (!!(( 98.71/14.88 ^[Y3 : $i]: 98.71/14.88 (in(Y3, 98.71/14.88 Y1) => 98.71/14.88 in( 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y2, 98.71/14.88 emptyset), 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y2, 98.71/14.88 setadjoin( 98.71/14.88 Y3, 98.71/14.88 emptyset)), 98.71/14.88 emptyset)), 98.71/14.88 powerset( 98.71/14.88 powerset( 98.71/14.88 binunion( 98.71/14.88 Y0, Y1)))))))))))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 Y0) => 98.71/14.88 (!!(( 98.71/14.88 ^[Y3 : $i]: 98.71/14.88 (in(Y3, 98.71/14.88 Y1) => 98.71/14.88 in( 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y2, 98.71/14.88 emptyset), 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y2, 98.71/14.88 setadjoin( 98.71/14.88 Y3, 98.71/14.88 emptyset)), 98.71/14.88 emptyset)), 98.71/14.88 powerset( 98.71/14.88 powerset( 98.71/14.88 binunion( 98.71/14.88 Y0, Y1)))))))))))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 Y0) => 98.71/14.88 (!!(( 98.71/14.88 ^[Y3 : $i]: 98.71/14.88 (in(Y3, 98.71/14.88 Y1) => 98.71/14.88 in( 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y2, 98.71/14.88 emptyset), 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y2, 98.71/14.88 setadjoin( 98.71/14.88 Y3, 98.71/14.88 emptyset)), 98.71/14.88 emptyset)), 98.71/14.88 dsetconstr( 98.71/14.88 powerset( 98.71/14.88 powerset( 98.71/14.88 binunion( 98.71/14.88 Y0, Y1))), 98.71/14.88 (^[Y4 : $i]: 98.71/14.88 (??(( 98.71/14.88 ^[Y5 : $i]: 98.71/14.88 (in(Y5, 98.71/14.88 Y0) & 98.71/14.88 (??(( 98.71/14.88 ^[Y6 : $i]: 98.71/14.88 (in(Y6, 98.71/14.88 Y1) & 98.71/14.88 (Y4 = 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y5, 98.71/14.88 emptyset), 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y5, 98.71/14.88 setadjoin( 98.71/14.88 Y6, 98.71/14.88 emptyset)), 98.71/14.88 emptyset)))))))))))))))))))))))))))) => 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 dsetconstr( 98.71/14.88 powerset( 98.71/14.88 powerset( 98.71/14.88 binunion( 98.71/14.88 Y0, Y1))), 98.71/14.88 (^[Y3 : $i]: 98.71/14.88 (??(( 98.71/14.88 ^[Y4 : $i]: 98.71/14.88 (in(Y4, 98.71/14.88 Y0) & 98.71/14.88 (??(( 98.71/14.88 ^[Y5 : $i]: 98.71/14.88 (in(Y5, 98.71/14.88 Y1) & 98.71/14.88 (Y3 = 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y4, 98.71/14.88 emptyset), 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y4, 98.71/14.88 setadjoin( 98.71/14.88 Y5, 98.71/14.88 emptyset)), 98.71/14.88 emptyset)))))))))))))) => 98.71/14.88 (??(( 98.71/14.88 ^[Y3 : $i]: 98.71/14.88 (( 98.71/14.88 ??(( 98.71/14.88 ^[Y4 : $i]: 98.71/14.88 (in(Y4, 98.71/14.88 Y1) & 98.71/14.88 (Y2 = 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y3, 98.71/14.88 emptyset), 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y3, 98.71/14.88 setadjoin( 98.71/14.88 Y4, 98.71/14.88 emptyset)), 98.71/14.88 emptyset))))))) & 98.71/14.88 in(Y3, 98.71/14.88 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 98.71/14.88 inference('lazy_cnf_imply', [status(thm)], ['187'])). 98.71/14.88 tff('189', plain, 98.71/14.88 ~ (in(emptyset, setadjoin(emptyset, emptyset)) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 (!!((^[Y2 : $i]: 98.71/14.88 (in(Y2, Y1) => in(Y2, setadjoin(Y0, Y1)))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 (!!((^[Y2 : $i]: 98.71/14.88 (in(Y2, setadjoin(Y0, Y1)) => 98.71/14.88 (!!((^[Y3 : $o]: 98.71/14.88 (((Y2 = Y0) => Y3) => 98.71/14.88 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 (!!((^[Y2 : $i]: 98.71/14.88 (in(Y2, setadjoin(Y0, Y1)) => 98.71/14.88 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 98.71/14.88 in(Y1, powerset(Y0))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.71/14.88 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 (!!((^[Y2 : $i]: 98.71/14.88 (in(Y1, powerset(Y0)) => 98.71/14.88 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 (!!((^[Y2 : $i]: 98.71/14.88 (in(Y1, Y2) => 98.71/14.88 (in(Y2, Y0) => in(Y1, setunion(Y0))))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 (in(Y1, setunion(Y0)) => 98.71/14.88 (!!((^[Y2 : $o]: 98.71/14.88 ((!!((^[Y3 : $i]: 98.71/14.88 (in(Y1, Y3) => 98.71/14.88 (in(Y3, Y0) => Y2))))) => 98.71/14.88 Y2))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 (in(Y1, Y0) => in(Y1, powerset(setunion(Y0)))))))))) => 98.71/14.88 ((!!((^[Y0 : $i > $o]: 98.71/14.88 ((??((^[Y1 : $i]: 98.71/14.88 (Y0(Y1) & 98.71/14.88 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 98.71/14.88 (??((^[Y1 : $i]: 98.71/14.88 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 ((Y0 != emptyset) => 98.71/14.88 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 (in(Y0, setadjoin(Y1, emptyset)) => 98.71/14.88 (Y0 = Y1)))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 ((Y0 != Y1) => 98.71/14.88 (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 ((Y0 = Y1) => 98.71/14.88 in(Y0, setadjoin(Y1, emptyset))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 (in(Y0, setadjoin(Y1, emptyset)) => 98.71/14.88 in(Y1, setadjoin(Y0, emptyset))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 (!!((^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 setadjoin(Y0, 98.71/14.88 setadjoin(Y1, emptyset))) => 98.71/14.88 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 in(Y0, 98.71/14.88 setadjoin(Y0, 98.71/14.88 setadjoin(Y1, emptyset))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 in(Y1, 98.71/14.88 setadjoin(Y0, 98.71/14.88 setadjoin(Y1, emptyset))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i > $o]: 98.71/14.88 ((??((^[Y2 : $i]: 98.71/14.88 (in(Y2, Y0) & Y1(Y2))))) => 98.71/14.88 (dsetconstr(Y0, Y1) != emptyset)))))))) => 98.71/14.88 ((!!((^[Y0 : $i > $o]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 (in(Y1, emptyset) => Y0(Y1)))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i > $o]: 98.71/14.88 ((~((!!((^[Y2 : $i]: 98.71/14.88 (in(Y2, Y0) => Y1(Y2))))))) => 98.71/14.88 (??((^[Y2 : $i]: 98.71/14.88 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i > $o]: 98.71/14.88 ((!!((^[Y2 : $i]: 98.71/14.88 (in(Y2, Y0) => 98.71/14.88 (~(Y1(Y2))))))) => 98.71/14.88 (~((??((^[Y2 : $i]: 98.71/14.88 (in(Y2, Y0) & Y1(Y2)))))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i > $o]: 98.71/14.88 ((~((??((^[Y2 : $i]: 98.71/14.88 (in(Y2, Y0) & Y1(Y2))))))) => 98.71/14.88 (!!((^[Y2 : $i]: 98.71/14.88 (in(Y2, Y0) => 98.71/14.88 (~(Y1(Y2)))))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i > $o]: 98.71/14.88 ((??((^[Y2 : $i]: 98.71/14.88 (in(Y2, Y0) & 98.71/14.88 (~(Y1(Y2))))))) => 98.71/14.88 (~((!!((^[Y2 : $i]: 98.71/14.88 (in(Y2, Y0) => 98.71/14.88 Y1(Y2)))))))))))))) => 98.71/14.88 ((!!((^[Y0 : $o]: 98.71/14.88 (Y0 => in(emptyset, prop2set(Y0)))))) => 98.71/14.88 ((!!((^[Y0 : $o]: 98.71/14.88 (Y0 => set2prop(prop2set(Y0)))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i > $o]: 98.71/14.88 ((~((??((^[Y2 : $i]: 98.71/14.88 (in(Y2, Y0) & 98.71/14.88 Y1(Y2))))))) => 98.71/14.88 (!!((^[Y2 : $i]: 98.71/14.88 (in(Y2, Y0) => 98.71/14.88 (~(Y1(Y2)))))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i > $o]: 98.71/14.88 ((~((!!((^[Y2 : $i]: 98.71/14.88 (in(Y2, Y0) => 98.71/14.88 Y1(Y2))))))) => 98.71/14.88 (??((^[Y2 : $i]: 98.71/14.88 (in(Y2, Y0) & 98.71/14.88 (~(Y1(Y2)))))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i > $o]: 98.71/14.88 ((??(Y0)) => 98.71/14.88 ((!!((^[Y1 : $i]: 98.71/14.88 (!!((^[Y2 : $i]: 98.71/14.88 (Y0(Y1) => 98.71/14.88 (Y0(Y2) => 98.71/14.88 (Y1 = Y2))))))))) => 98.71/14.88 (??((^[Y1 : $i]: 98.71/14.88 (Y0(Y1) & 98.71/14.88 (!!((^[Y2 : $i]: 98.71/14.88 (Y0(Y2) => 98.71/14.88 (Y1 = Y2)))))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i > $o]: 98.71/14.88 ((??((^[Y1 : $i]: 98.71/14.88 (!!((^[Y2 : $i]: 98.71/14.88 (Y0(Y2) <=> 98.71/14.88 (Y2 = Y1)))))))) => 98.71/14.88 (??((^[Y1 : $i]: 98.71/14.88 (Y0(Y1) & 98.71/14.88 (!!((^[Y2 : $i]: 98.71/14.88 (Y0(Y2) => 98.71/14.88 (Y1 = Y2))))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 ((Y0 = Y1) => 98.71/14.88 (!!((^[Y2 : $i]: 98.71/14.88 (!!((^[Y3 : $i]: 98.71/14.88 (( 98.71/14.88 Y2 = Y3) => 98.71/14.88 (in(Y2, 98.71/14.88 Y0) => 98.71/14.88 in(Y3, 98.71/14.88 Y1)))))))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 ((Y0 = Y1) => 98.71/14.88 (!!((^[Y2 : $i]: 98.71/14.88 (!!((^[Y3 : $i]: 98.71/14.88 (( 98.71/14.88 Y2 = Y3) => 98.71/14.88 (in(Y2, 98.71/14.88 Y0) <=> 98.71/14.88 in(Y3, 98.71/14.88 Y1)))))))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i > $o]: 98.71/14.88 ((??((^[Y1 : $i]: 98.71/14.88 (Y0(Y1) & 98.71/14.88 (!!((^[Y2 : $i]: 98.71/14.88 (Y0(Y2) => 98.71/14.88 (Y1 = Y2))))))))) => 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 (!!((^[Y2 : $i]: 98.71/14.88 (Y0(Y1) => 98.71/14.88 (Y0(Y2) => 98.71/14.88 (Y1 = Y2))))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i > $o]: 98.71/14.88 (!!((^[Y1 : $i > $o]: 98.71/14.88 ((!!((^[Y2 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y3 : $i]: 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 Y2 = Y3) => 98.71/14.88 ( 98.71/14.88 Y0(Y2) <=> 98.71/14.88 Y1(Y3))))))))) => 98.71/14.88 ((??((^[Y2 : $i]: 98.71/14.88 (Y0(Y2) & 98.71/14.88 (!!(( 98.71/14.88 ^[Y3 : $i]: 98.71/14.88 (Y0(Y3) => 98.71/14.88 (Y2 = Y3))))))))) <=> 98.71/14.88 (??((^[Y2 : $i]: 98.71/14.88 (Y1(Y2) & 98.71/14.88 (!!(( 98.71/14.88 ^[Y3 : $i]: 98.71/14.88 (Y1(Y3) => 98.71/14.88 (Y2 = Y3))))))))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 ((Y0 = Y1) => 98.71/14.88 (!!((^[Y2 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y3 : $i]: 98.71/14.88 (( 98.71/14.88 Y2 = Y3) => 98.71/14.88 (setadjoin( 98.71/14.88 Y0, Y2) = 98.71/14.88 setadjoin( 98.71/14.88 Y1, Y3)))))))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 ((Y0 = Y1) => 98.71/14.88 (powerset(Y0) = 98.71/14.88 powerset(Y1))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 ((Y0 = Y1) => 98.71/14.88 (setunion(Y0) = 98.71/14.88 setunion(Y1))))))))) => 98.71/14.88 ((!!((^[Y0 : $i > $o]: 98.71/14.88 ((??((^[Y1 : $i]: 98.71/14.88 (Y0(Y1) & 98.71/14.88 (!!((^[Y2 : $i]: 98.71/14.88 (Y0(Y2) => 98.71/14.88 (Y1 = Y2))))))))) => 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 (!!((^[Y2 : $i]: 98.71/14.88 (Y0(Y1) => 98.71/14.88 (Y0(Y2) => 98.71/14.88 (Y1 = Y2))))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i > $o]: 98.71/14.88 (!!((^[Y1 : $i > $o]: 98.71/14.88 ((!!((^[Y2 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y3 : $i]: 98.71/14.88 (( 98.71/14.88 Y2 = Y3) => 98.71/14.88 (Y0(Y2) <=> 98.71/14.88 Y1(Y3))))))))) => 98.71/14.88 ((??(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (Y0(Y2) & 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y3 : $i]: 98.71/14.88 (Y0(Y3) => 98.71/14.88 (Y2 = Y3))))))))) => 98.71/14.88 ((??(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 ( 98.71/14.88 Y1(Y2) & 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y3 : $i]: 98.71/14.88 (Y1(Y3) => 98.71/14.88 (Y2 = Y3))))))))) => 98.71/14.88 (descr(Y0) = 98.71/14.88 descr(Y1))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 ((Y0 = Y1) => 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i > $o]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y3 : $i > $o]: 98.71/14.88 (( 98.71/14.88 !!(( 98.71/14.88 ^[Y4 : $i]: 98.71/14.88 (in(Y4, 98.71/14.88 Y0) => 98.71/14.88 (!!(( 98.71/14.88 ^[Y5 : $i]: 98.71/14.88 (in(Y5, 98.71/14.88 Y1) => 98.71/14.88 (( 98.71/14.88 Y4 = Y5) => 98.71/14.88 (Y2(Y4) <=> 98.71/14.88 Y3(Y5))))))))))) => 98.71/14.88 (dsetconstr( 98.71/14.88 Y0, Y2) = 98.71/14.88 dsetconstr( 98.71/14.88 Y1, Y3)))))))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 ((!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 ( 98.71/14.88 in(Y2, 98.71/14.88 Y0) => 98.71/14.88 in(Y2, 98.71/14.88 Y1))))) => 98.71/14.88 subset(Y0, 98.71/14.88 Y1)))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 ((Y0 = Y1) => 98.71/14.88 subset(Y1, 98.71/14.88 Y0)))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 ((Y0 = Y1) => 98.71/14.88 subset( 98.71/14.88 Y0, Y1)))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 (( 98.71/14.88 !!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 Y0) => 98.71/14.88 in(Y2, 98.71/14.88 Y1))))) => 98.71/14.88 subset( 98.71/14.88 Y0, Y1)))))))) => 98.71/14.88 ((!!(subset(emptyset))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (subset( 98.71/14.88 Y0, Y1) => 98.71/14.88 (in(Y2, 98.71/14.88 Y0) => 98.71/14.88 in(Y2, 98.71/14.88 Y1)))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (subset( 98.71/14.88 Y0, Y1) => 98.71/14.88 (( 98.71/14.88 ~( 98.71/14.88 in(Y2, 98.71/14.88 Y1))) => 98.71/14.88 (~( 98.71/14.88 in(Y2, 98.71/14.88 Y0)))))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 Y0) => 98.71/14.88 (( 98.71/14.88 ~( 98.71/14.88 in(Y2, 98.71/14.88 Y1))) => 98.71/14.88 (~( 98.71/14.88 subset( 98.71/14.88 Y0, Y1)))))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 ~( 98.71/14.88 subset( 98.71/14.88 Y0, Y1))) => 98.71/14.88 ( 98.71/14.88 Y0 != Y1)))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 Y0) => 98.71/14.88 (( 98.71/14.88 ~( 98.71/14.88 in(Y2, 98.71/14.88 Y1))) => 98.71/14.88 (Y0 != Y1)))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 subset( 98.71/14.88 Y0, Y0)))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (subset( 98.71/14.88 Y0, Y1) => 98.71/14.88 (subset( 98.71/14.88 Y1, Y2) => 98.71/14.88 subset( 98.71/14.88 Y0, Y2)))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 subset( 98.71/14.88 Y1, 98.71/14.88 setadjoin( 98.71/14.88 Y0, Y1)))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (subset( 98.71/14.88 Y0, Y2) => 98.71/14.88 subset( 98.71/14.88 Y0, 98.71/14.88 setadjoin( 98.71/14.88 Y1, Y2)))))))))))) => 98.71/14.88 ((!!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (subset( 98.71/14.88 Y0, Y1) => 98.71/14.88 in(Y0, 98.71/14.88 powerset( 98.71/14.88 Y1))))))))) => 98.71/14.88 ((!!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (subset( 98.71/14.88 Y0, Y1) => 98.71/14.88 (subset( 98.71/14.88 Y1, Y0) => 98.71/14.88 (Y0 = Y1))))))))) => 98.71/14.88 ((!!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (subset( 98.71/14.88 Y0, 98.71/14.88 emptyset) => 98.71/14.88 (Y0 = 98.71/14.88 emptyset))))) => 98.71/14.88 ((!!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (subset( 98.71/14.88 Y1, Y0) => 98.71/14.88 in(Y1, 98.71/14.88 powerset( 98.71/14.88 Y0))))))))) => 98.71/14.88 (( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (in(Y1, 98.71/14.88 powerset( 98.71/14.88 Y0)) => 98.71/14.88 subset( 98.71/14.88 Y1, Y0)))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 in(Y0, 98.71/14.88 powerset( 98.71/14.88 Y0))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (subset( 98.71/14.88 Y0, Y1) => 98.71/14.88 subset( 98.71/14.88 powerset( 98.71/14.88 Y0), 98.71/14.88 powerset( 98.71/14.88 Y1))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i > $o]: 98.71/14.88 in( 98.71/14.88 dsetconstr( 98.71/14.88 Y0, Y1), 98.71/14.88 powerset( 98.71/14.88 Y0)))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i > $o]: 98.71/14.88 subset( 98.71/14.88 dsetconstr( 98.71/14.88 Y0, Y1), 98.71/14.88 Y0))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 Y0) => 98.71/14.88 in(Y2, 98.71/14.88 binunion( 98.71/14.88 Y0, Y1)))))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 in(Y1, 98.71/14.88 setadjoin( 98.71/14.88 Y0, 98.71/14.88 setadjoin( 98.71/14.88 Y1, 98.71/14.88 emptyset))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 Y1) => 98.71/14.88 in(Y2, 98.71/14.88 binunion( 98.71/14.88 Y0, Y1)))))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y3 : $o]: 98.71/14.88 (in(Y2, 98.71/14.88 binunion( 98.71/14.88 Y0, Y1)) => 98.71/14.88 (( 98.71/14.88 in(Y2, 98.71/14.88 Y0) => Y3) => 98.71/14.88 (( 98.71/14.88 in(Y2, 98.71/14.88 Y1) => Y3) => 98.71/14.88 Y3))))))))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 binunion( 98.71/14.88 Y0, Y1)) => 98.71/14.88 (in(Y2, 98.71/14.88 Y1) | 98.71/14.88 in(Y2, 98.71/14.88 Y0)))))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 subset( 98.71/14.88 Y0, 98.71/14.88 binunion( 98.71/14.88 Y0, Y1)))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 subset( 98.71/14.88 Y1, 98.71/14.88 binunion( 98.71/14.88 Y0, Y1)))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 Y0) => 98.71/14.88 (in(Y2, 98.71/14.88 Y1) => 98.71/14.88 in(Y2, 98.71/14.88 binintersect( 98.71/14.88 Y0, Y1))))))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (subset( 98.71/14.88 Y2, Y0) => 98.71/14.88 (subset( 98.71/14.88 Y2, Y1) => 98.71/14.88 subset( 98.71/14.88 Y2, 98.71/14.88 binintersect( 98.71/14.88 Y0, Y1))))))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 binintersect( 98.71/14.88 Y0, Y1)) => 98.71/14.88 in(Y2, 98.71/14.88 Y0))))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 subset( 98.71/14.88 binintersect( 98.71/14.88 Y0, Y1), 98.71/14.88 Y0))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (subset( 98.71/14.88 Y0, Y1) => 98.71/14.88 (binintersect( 98.71/14.88 Y0, Y1) = 98.71/14.88 Y0)))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (( 98.71/14.88 binintersect( 98.71/14.88 Y0, Y1) = 98.71/14.88 Y1) => 98.71/14.88 subset( 98.71/14.88 Y1, Y0)))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 binintersect( 98.71/14.88 Y0, Y1)) => 98.71/14.88 in(Y2, 98.71/14.88 Y1))))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (( 98.71/14.88 ~(( 98.71/14.88 ??(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 Y0) & 98.71/14.88 in(Y2, 98.71/14.88 Y1))))))) => 98.71/14.88 (binintersect( 98.71/14.88 Y0, Y1) = 98.71/14.88 emptyset)))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 subset( 98.71/14.88 binintersect( 98.71/14.88 Y0, Y1), 98.71/14.88 Y1))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (subset( 98.71/14.88 Y1, Y0) => 98.71/14.88 (binintersect( 98.71/14.88 Y0, Y1) = 98.71/14.88 Y1)))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (( 98.71/14.88 binintersect( 98.71/14.88 Y0, Y1) = 98.71/14.88 Y0) => 98.71/14.88 subset( 98.71/14.88 Y0, Y1)))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (binintersect( 98.71/14.88 Y0, 98.71/14.88 binunion( 98.71/14.88 Y1, Y2)) = 98.71/14.88 binunion( 98.71/14.88 binintersect( 98.71/14.88 Y0, Y1), 98.71/14.88 binintersect( 98.71/14.88 Y0, Y2)))))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 Y0) => 98.71/14.88 (( 98.71/14.88 ~( 98.71/14.88 in(Y2, 98.71/14.88 Y1))) => 98.71/14.88 in(Y2, 98.71/14.88 setminus( 98.71/14.88 Y0, Y1))))))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 setminus( 98.71/14.88 Y0, Y1)) => 98.71/14.88 in(Y2, 98.71/14.88 Y0))))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 setminus( 98.71/14.88 Y0, Y1)) => 98.71/14.88 (~( 98.71/14.88 in(Y2, 98.71/14.88 Y1))))))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (subset( 98.71/14.88 Y0, Y1) => 98.71/14.88 (setminus( 98.71/14.88 Y0, Y1) = 98.71/14.88 emptyset)))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (( 98.71/14.88 ~( 98.71/14.88 in(Y2, 98.71/14.88 setminus( 98.71/14.88 Y0, Y1)))) => 98.71/14.88 (in(Y2, 98.71/14.88 Y0) => 98.71/14.88 in(Y2, 98.71/14.88 Y1)))))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (( 98.71/14.88 ~( 98.71/14.88 in(Y2, 98.71/14.88 setminus( 98.71/14.88 Y0, Y1)))) => 98.71/14.88 (( 98.71/14.88 ~( 98.71/14.88 in(Y2, 98.71/14.88 Y1))) => 98.71/14.88 (~( 98.71/14.88 in(Y2, 98.71/14.88 Y0)))))))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (( 98.71/14.88 ~( 98.71/14.88 in(Y2, 98.71/14.88 Y0))) => 98.71/14.88 (~( 98.71/14.88 in(Y2, 98.71/14.88 setminus( 98.71/14.88 Y0, Y1)))))))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 Y1) => 98.71/14.88 (~( 98.71/14.88 in(Y2, 98.71/14.88 setminus( 98.71/14.88 Y0, Y1)))))))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 subset( 98.71/14.88 setminus( 98.71/14.88 Y0, Y1), 98.71/14.88 Y0))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (( 98.71/14.88 setminus( 98.71/14.88 Y0, Y1) = 98.71/14.88 emptyset) => 98.71/14.88 subset( 98.71/14.88 Y0, Y1)))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 symdiff( 98.71/14.88 Y0, Y1)) => 98.71/14.88 (!!(( 98.71/14.88 ^[Y3 : $o]: 98.71/14.88 (( 98.71/14.88 in(Y2, 98.71/14.88 Y0) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 ~( 98.71/14.88 in(Y2, 98.71/14.88 Y1))) => 98.71/14.88 Y3)) => 98.71/14.88 (( 98.71/14.88 ( 98.71/14.88 ~( 98.71/14.88 in(Y2, 98.71/14.88 Y0))) => 98.71/14.88 ( 98.71/14.88 in(Y2, 98.71/14.88 Y1) => Y3)) => 98.71/14.88 Y3))))))))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 Y0) => 98.71/14.88 (( 98.71/14.88 ~( 98.71/14.88 in(Y2, 98.71/14.88 Y1))) => 98.71/14.88 in(Y2, 98.71/14.88 symdiff( 98.71/14.88 Y0, Y1))))))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (( 98.71/14.88 ~( 98.71/14.88 in(Y2, 98.71/14.88 Y0))) => 98.71/14.88 (in(Y2, 98.71/14.88 Y1) => 98.71/14.88 in(Y2, 98.71/14.88 symdiff( 98.71/14.88 Y0, Y1))))))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 Y0) => 98.71/14.88 (in(Y2, 98.71/14.88 Y1) => 98.71/14.88 (~( 98.71/14.88 in(Y2, 98.71/14.88 symdiff( 98.71/14.88 Y0, Y1))))))))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (( 98.71/14.88 ~( 98.71/14.88 in(Y2, 98.71/14.88 Y0))) => 98.71/14.88 (( 98.71/14.88 ~( 98.71/14.88 in(Y2, 98.71/14.88 Y1))) => 98.71/14.88 (~( 98.71/14.88 in(Y2, 98.71/14.88 symdiff( 98.71/14.88 Y0, Y1))))))))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 in(Y1, 98.71/14.88 setadjoin( 98.71/14.88 Y0, 98.71/14.88 setadjoin( 98.71/14.88 Y1, 98.71/14.88 emptyset))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 in(Y0, 98.71/14.88 setunion( 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y0, 98.71/14.88 emptyset), 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y0, 98.71/14.88 setadjoin( 98.71/14.88 Y1, 98.71/14.88 emptyset)), 98.71/14.88 emptyset)))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 in(Y1, 98.71/14.88 setunion( 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y0, 98.71/14.88 emptyset), 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y0, 98.71/14.88 setadjoin( 98.71/14.88 Y1, 98.71/14.88 emptyset)), 98.71/14.88 emptyset)))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (??(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 setunion( 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y0, 98.71/14.88 emptyset), 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y0, 98.71/14.88 setadjoin( 98.71/14.88 Y1, 98.71/14.88 emptyset)), 98.71/14.88 emptyset)))) & 98.71/14.88 (??(( 98.71/14.88 ^[Y3 : $i]: 98.71/14.88 (in(Y3, 98.71/14.88 setunion( 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y0, 98.71/14.88 emptyset), 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y0, 98.71/14.88 setadjoin( 98.71/14.88 Y1, 98.71/14.88 emptyset)), 98.71/14.88 emptyset)))) & 98.71/14.88 (setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y0, 98.71/14.88 emptyset), 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y0, 98.71/14.88 setadjoin( 98.71/14.88 Y1, 98.71/14.88 emptyset)), 98.71/14.88 emptyset)) = 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y2, 98.71/14.88 emptyset), 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y2, 98.71/14.88 setadjoin( 98.71/14.88 Y3, 98.71/14.88 emptyset)), 98.71/14.88 emptyset))))))))))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (??(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 setunion( 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y0, 98.71/14.88 emptyset), 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y0, 98.71/14.88 setadjoin( 98.71/14.88 Y1, 98.71/14.88 emptyset)), 98.71/14.88 emptyset)))) & 98.71/14.88 (??(( 98.71/14.88 ^[Y3 : $i]: 98.71/14.88 (in(Y3, 98.71/14.88 setunion( 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y0, 98.71/14.88 emptyset), 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y0, 98.71/14.88 setadjoin( 98.71/14.88 Y1, 98.71/14.88 emptyset)), 98.71/14.88 emptyset)))) & 98.71/14.88 (setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y0, 98.71/14.88 emptyset), 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y0, 98.71/14.88 setadjoin( 98.71/14.88 Y1, 98.71/14.88 emptyset)), 98.71/14.88 emptyset)) = 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y2, 98.71/14.88 emptyset), 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y2, 98.71/14.88 setadjoin( 98.71/14.88 Y3, 98.71/14.88 emptyset)), 98.71/14.88 emptyset))))))))))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (in(Y1, 98.71/14.88 Y0) => 98.71/14.88 subset( 98.71/14.88 setadjoin( 98.71/14.88 Y1, 98.71/14.88 emptyset), 98.71/14.88 Y0)))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (in(Y1, 98.71/14.88 Y0) => 98.71/14.88 in( 98.71/14.88 setadjoin( 98.71/14.88 Y1, 98.71/14.88 emptyset), 98.71/14.88 powerset( 98.71/14.88 Y0))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 Y0) => 98.71/14.88 in( 98.71/14.88 setadjoin( 98.71/14.88 Y2, 98.71/14.88 emptyset), 98.71/14.88 powerset( 98.71/14.88 binunion( 98.71/14.88 Y0, Y1))))))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 setadjoin( 98.71/14.88 Y0, 98.71/14.88 setadjoin( 98.71/14.88 Y1, 98.71/14.88 emptyset))) => 98.71/14.88 (( 98.71/14.88 Y2 = Y1) | 98.71/14.88 (Y2 = Y0)))))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 Y0) => 98.71/14.88 (!!(( 98.71/14.88 ^[Y3 : $i]: 98.71/14.88 (in(Y3, 98.71/14.88 Y1) => 98.71/14.88 subset( 98.71/14.88 setadjoin( 98.71/14.88 Y2, 98.71/14.88 setadjoin( 98.71/14.88 Y3, 98.71/14.88 emptyset)), 98.71/14.88 binunion( 98.71/14.88 Y0, Y1)))))))))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 Y0) => 98.71/14.88 (!!(( 98.71/14.88 ^[Y3 : $i]: 98.71/14.88 (in(Y3, 98.71/14.88 Y1) => 98.71/14.88 in( 98.71/14.88 setadjoin( 98.71/14.88 Y2, 98.71/14.88 setadjoin( 98.71/14.88 Y3, 98.71/14.88 emptyset)), 98.71/14.88 powerset( 98.71/14.88 binunion( 98.71/14.88 Y0, Y1))))))))))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 Y0) => 98.71/14.88 (!!(( 98.71/14.88 ^[Y3 : $i]: 98.71/14.88 (in(Y3, 98.71/14.88 Y1) => 98.71/14.88 subset( 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y2, 98.71/14.88 emptyset), 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y2, 98.71/14.88 setadjoin( 98.71/14.88 Y3, 98.71/14.88 emptyset)), 98.71/14.88 emptyset)), 98.71/14.88 powerset( 98.71/14.88 binunion( 98.71/14.88 Y0, Y1))))))))))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 Y0) => 98.71/14.88 (!!(( 98.71/14.88 ^[Y3 : $i]: 98.71/14.88 (in(Y3, 98.71/14.88 Y1) => 98.71/14.88 in( 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y2, 98.71/14.88 emptyset), 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y2, 98.71/14.88 setadjoin( 98.71/14.88 Y3, 98.71/14.88 emptyset)), 98.71/14.88 emptyset)), 98.71/14.88 powerset( 98.71/14.88 powerset( 98.71/14.88 binunion( 98.71/14.88 Y0, Y1)))))))))))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 Y0) => 98.71/14.88 (!!(( 98.71/14.88 ^[Y3 : $i]: 98.71/14.88 (in(Y3, 98.71/14.88 Y1) => 98.71/14.88 in( 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y2, 98.71/14.88 emptyset), 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y2, 98.71/14.88 setadjoin( 98.71/14.88 Y3, 98.71/14.88 emptyset)), 98.71/14.88 emptyset)), 98.71/14.88 powerset( 98.71/14.88 powerset( 98.71/14.88 binunion( 98.71/14.88 Y0, Y1)))))))))))))))))) => 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 Y0) => 98.71/14.88 (!!(( 98.71/14.88 ^[Y3 : $i]: 98.71/14.88 (in(Y3, 98.71/14.88 Y1) => 98.71/14.88 in( 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y2, 98.71/14.88 emptyset), 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y2, 98.71/14.88 setadjoin( 98.71/14.88 Y3, 98.71/14.88 emptyset)), 98.71/14.88 emptyset)), 98.71/14.88 dsetconstr( 98.71/14.88 powerset( 98.71/14.88 powerset( 98.71/14.88 binunion( 98.71/14.88 Y0, Y1))), 98.71/14.88 (^[Y4 : $i]: 98.71/14.88 (??(( 98.71/14.88 ^[Y5 : $i]: 98.71/14.88 (in(Y5, 98.71/14.88 Y0) & 98.71/14.88 (??(( 98.71/14.88 ^[Y6 : $i]: 98.71/14.88 (in(Y6, 98.71/14.88 Y1) & 98.71/14.88 (Y4 = 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y5, 98.71/14.88 emptyset), 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y5, 98.71/14.88 setadjoin( 98.71/14.88 Y6, 98.71/14.88 emptyset)), 98.71/14.88 emptyset)))))))))))))))))))))))))))) => 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 dsetconstr( 98.71/14.88 powerset( 98.71/14.88 powerset( 98.71/14.88 binunion( 98.71/14.88 Y0, Y1))), 98.71/14.88 (^[Y3 : $i]: 98.71/14.88 (??(( 98.71/14.88 ^[Y4 : $i]: 98.71/14.88 (in(Y4, 98.71/14.88 Y0) & 98.71/14.88 (??(( 98.71/14.88 ^[Y5 : $i]: 98.71/14.88 (in(Y5, 98.71/14.88 Y1) & 98.71/14.88 (Y3 = 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y4, 98.71/14.88 emptyset), 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y4, 98.71/14.88 setadjoin( 98.71/14.88 Y5, 98.71/14.88 emptyset)), 98.71/14.88 emptyset)))))))))))))) => 98.71/14.88 (??(( 98.71/14.88 ^[Y3 : $i]: 98.71/14.88 (( 98.71/14.88 ??(( 98.71/14.88 ^[Y4 : $i]: 98.71/14.88 (in(Y4, 98.71/14.88 Y1) & 98.71/14.88 (Y2 = 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y3, 98.71/14.88 emptyset), 98.71/14.88 setadjoin( 98.71/14.88 setadjoin( 98.71/14.88 Y3, 98.71/14.88 setadjoin( 98.71/14.88 Y4, 98.71/14.88 emptyset)), 98.71/14.88 emptyset))))))) & 98.71/14.88 in(Y3, 98.71/14.88 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 98.71/14.88 inference('lazy_cnf_imply', [status(thm)], ['188'])). 98.71/14.88 tff('190', plain, 98.71/14.88 ~ ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 (!!((^[Y2 : $i]: 98.71/14.88 (in(Y2, Y1) => in(Y2, setadjoin(Y0, Y1)))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 (!!((^[Y2 : $i]: 98.71/14.88 (in(Y2, setadjoin(Y0, Y1)) => 98.71/14.88 (!!((^[Y3 : $o]: 98.71/14.88 (((Y2 = Y0) => Y3) => 98.71/14.88 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 (!!((^[Y2 : $i]: 98.71/14.88 (in(Y2, setadjoin(Y0, Y1)) => 98.71/14.88 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 98.71/14.88 in(Y1, powerset(Y0))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.71/14.88 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 (!!((^[Y2 : $i]: 98.71/14.88 (in(Y1, powerset(Y0)) => 98.71/14.88 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 (!!((^[Y2 : $i]: 98.71/14.88 (in(Y1, Y2) => 98.71/14.88 (in(Y2, Y0) => in(Y1, setunion(Y0))))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 (in(Y1, setunion(Y0)) => 98.71/14.88 (!!((^[Y2 : $o]: 98.71/14.88 ((!!((^[Y3 : $i]: 98.71/14.88 (in(Y1, Y3) => 98.71/14.88 (in(Y3, Y0) => Y2))))) => 98.71/14.88 Y2))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 (in(Y1, Y0) => in(Y1, powerset(setunion(Y0)))))))))) => 98.71/14.88 ((!!((^[Y0 : $i > $o]: 98.71/14.88 ((??((^[Y1 : $i]: 98.71/14.88 (Y0(Y1) & 98.71/14.88 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 98.71/14.88 (??((^[Y1 : $i]: 98.71/14.88 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 (in(Y0, setadjoin(Y1, emptyset)) => 98.71/14.88 (Y0 = Y1)))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 ((Y0 != Y1) => 98.71/14.88 (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 ((Y0 = Y1) => 98.71/14.88 in(Y0, setadjoin(Y1, emptyset))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 (in(Y0, setadjoin(Y1, emptyset)) => 98.71/14.88 in(Y1, setadjoin(Y0, emptyset))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 (!!((^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 setadjoin(Y0, 98.71/14.88 setadjoin(Y1, emptyset))) => 98.71/14.88 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 in(Y0, 98.71/14.88 setadjoin(Y0, 98.71/14.88 setadjoin(Y1, emptyset))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 in(Y1, 98.71/14.88 setadjoin(Y0, 98.71/14.88 setadjoin(Y1, emptyset))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i > $o]: 98.71/14.88 ((??((^[Y2 : $i]: 98.71/14.88 (in(Y2, Y0) & Y1(Y2))))) => 98.71/14.88 (dsetconstr(Y0, Y1) != emptyset)))))))) => 98.71/14.88 ((!!((^[Y0 : $i > $o]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 (in(Y1, emptyset) => Y0(Y1)))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i > $o]: 98.71/14.88 ((~((!!((^[Y2 : $i]: 98.71/14.88 (in(Y2, Y0) => Y1(Y2))))))) => 98.71/14.88 (??((^[Y2 : $i]: 98.71/14.88 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i > $o]: 98.71/14.88 ((!!((^[Y2 : $i]: 98.71/14.88 (in(Y2, Y0) => 98.71/14.88 (~(Y1(Y2))))))) => 98.71/14.88 (~((??((^[Y2 : $i]: 98.71/14.88 (in(Y2, Y0) & Y1(Y2)))))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i > $o]: 98.71/14.88 ((~((??((^[Y2 : $i]: 98.71/14.88 (in(Y2, Y0) & Y1(Y2))))))) => 98.71/14.88 (!!((^[Y2 : $i]: 98.71/14.88 (in(Y2, Y0) => 98.71/14.88 (~(Y1(Y2)))))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i > $o]: 98.71/14.88 ((??((^[Y2 : $i]: 98.71/14.88 (in(Y2, Y0) & 98.71/14.88 (~(Y1(Y2))))))) => 98.71/14.88 (~((!!((^[Y2 : $i]: 98.71/14.88 (in(Y2, Y0) => 98.71/14.88 Y1(Y2)))))))))))))) => 98.71/14.88 ((!!((^[Y0 : $o]: 98.71/14.88 (Y0 => in(emptyset, prop2set(Y0)))))) => 98.71/14.88 ((!!((^[Y0 : $o]: 98.71/14.88 (Y0 => set2prop(prop2set(Y0)))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i > $o]: 98.71/14.88 ((~((??((^[Y2 : $i]: 98.71/14.88 (in(Y2, Y0) & 98.71/14.88 Y1(Y2))))))) => 98.71/14.88 (!!((^[Y2 : $i]: 98.71/14.88 (in(Y2, Y0) => 98.71/14.88 (~(Y1(Y2)))))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i > $o]: 98.71/14.88 ((~((!!((^[Y2 : $i]: 98.71/14.88 (in(Y2, Y0) => 98.71/14.88 Y1(Y2))))))) => 98.71/14.88 (??((^[Y2 : $i]: 98.71/14.88 (in(Y2, Y0) & 98.71/14.88 (~(Y1(Y2)))))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i > $o]: 98.71/14.88 ((??(Y0)) => 98.71/14.88 ((!!((^[Y1 : $i]: 98.71/14.88 (!!((^[Y2 : $i]: 98.71/14.88 (Y0(Y1) => 98.71/14.88 (Y0(Y2) => 98.71/14.88 (Y1 = Y2))))))))) => 98.71/14.88 (??((^[Y1 : $i]: 98.71/14.88 (Y0(Y1) & 98.71/14.88 (!!((^[Y2 : $i]: 98.71/14.88 (Y0(Y2) => 98.71/14.88 (Y1 = Y2)))))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i > $o]: 98.71/14.88 ((??((^[Y1 : $i]: 98.71/14.88 (!!((^[Y2 : $i]: 98.71/14.88 (Y0(Y2) <=> 98.71/14.88 (Y2 = Y1)))))))) => 98.71/14.88 (??((^[Y1 : $i]: 98.71/14.88 (Y0(Y1) & 98.71/14.88 (!!((^[Y2 : $i]: 98.71/14.88 (Y0(Y2) => 98.71/14.88 (Y1 = Y2))))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 ((Y0 = Y1) => 98.71/14.88 (!!((^[Y2 : $i]: 98.71/14.88 (!!((^[Y3 : $i]: 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 Y2 = Y3) => 98.71/14.88 ( 98.71/14.88 in(Y2, 98.71/14.88 Y0) => 98.71/14.88 in(Y3, 98.71/14.88 Y1)))))))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 ((Y0 = Y1) => 98.71/14.88 (!!((^[Y2 : $i]: 98.71/14.88 (!!((^[Y3 : $i]: 98.71/14.88 (( 98.71/14.88 Y2 = Y3) => 98.71/14.88 (in(Y2, 98.71/14.88 Y0) <=> 98.71/14.88 in(Y3, 98.71/14.88 Y1)))))))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i > $o]: 98.71/14.88 ((??((^[Y1 : $i]: 98.71/14.88 (Y0(Y1) & 98.71/14.88 (!!((^[Y2 : $i]: 98.71/14.88 (Y0(Y2) => 98.71/14.88 (Y1 = Y2))))))))) => 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 (!!((^[Y2 : $i]: 98.71/14.88 (Y0(Y1) => 98.71/14.88 (Y0(Y2) => 98.71/14.88 (Y1 = Y2))))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i > $o]: 98.71/14.88 (!!((^[Y1 : $i > $o]: 98.71/14.88 ((!!((^[Y2 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y3 : $i]: 98.71/14.88 (( 98.71/14.88 Y2 = Y3) => 98.71/14.88 ( 98.71/14.88 Y0(Y2) <=> 98.71/14.88 Y1(Y3))))))))) => 98.71/14.88 ((??((^[Y2 : $i]: 98.71/14.88 (Y0(Y2) & 98.71/14.88 (!!(( 98.71/14.88 ^[Y3 : $i]: 98.71/14.88 (Y0(Y3) => 98.71/14.88 (Y2 = Y3))))))))) <=> 98.71/14.88 (??((^[Y2 : $i]: 98.71/14.88 (Y1(Y2) & 98.71/14.88 (!!(( 98.71/14.88 ^[Y3 : $i]: 98.71/14.88 (Y1(Y3) => 98.71/14.88 (Y2 = Y3))))))))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 ((Y0 = Y1) => 98.71/14.88 (!!((^[Y2 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y3 : $i]: 98.71/14.88 ( 98.71/14.88 ( 98.71/14.88 Y2 = Y3) => 98.71/14.88 ( 98.71/14.88 setadjoin( 98.71/14.88 Y0, Y2) = 98.71/14.88 setadjoin( 98.71/14.88 Y1, Y3)))))))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 ((Y0 = Y1) => 98.71/14.88 (powerset(Y0) = 98.71/14.88 powerset(Y1))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 ((Y0 = Y1) => 98.71/14.88 (setunion(Y0) = 98.71/14.88 setunion(Y1))))))))) => 98.71/14.88 ((!!((^[Y0 : $i > $o]: 98.71/14.88 ((??((^[Y1 : $i]: 98.71/14.88 (Y0(Y1) & 98.71/14.88 (!!((^[Y2 : $i]: 98.71/14.88 (Y0(Y2) => 98.71/14.88 (Y1 = Y2))))))))) => 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 (!!((^[Y2 : $i]: 98.71/14.88 ( 98.71/14.88 Y0(Y1) => 98.71/14.88 ( 98.71/14.88 Y0(Y2) => 98.71/14.88 ( 98.71/14.88 Y1 = Y2))))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i > $o]: 98.71/14.88 (!!((^[Y1 : $i > $o]: 98.71/14.88 ((!!((^[Y2 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y3 : $i]: 98.71/14.88 (( 98.71/14.88 Y2 = Y3) => 98.71/14.88 (Y0(Y2) <=> 98.71/14.88 Y1(Y3))))))))) => 98.71/14.88 ((??((^[Y2 : $i]: 98.71/14.88 (Y0(Y2) & 98.71/14.88 (!!(( 98.71/14.88 ^[Y3 : $i]: 98.71/14.88 (Y0(Y3) => 98.71/14.88 (Y2 = Y3))))))))) => 98.71/14.88 ((??(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (Y1(Y2) & 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y3 : $i]: 98.71/14.88 (Y1(Y3) => 98.71/14.88 (Y2 = Y3))))))))) => 98.71/14.88 (descr(Y0) = 98.71/14.88 descr(Y1))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 ((Y0 = Y1) => 98.71/14.88 (!!((^[Y2 : $i > $o]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y3 : $i > $o]: 98.71/14.88 (( 98.71/14.88 !!(( 98.71/14.88 ^[Y4 : $i]: 98.71/14.88 (in(Y4, 98.71/14.88 Y0) => 98.71/14.88 (!!(( 98.71/14.88 ^[Y5 : $i]: 98.71/14.88 (in(Y5, 98.71/14.88 Y1) => 98.71/14.88 (( 98.71/14.88 Y4 = Y5) => 98.71/14.88 (Y2(Y4) <=> 98.71/14.88 Y3(Y5))))))))))) => 98.71/14.88 (dsetconstr( 98.71/14.88 Y0, Y2) = 98.71/14.88 dsetconstr( 98.71/14.88 Y1, Y3)))))))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 ((!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 Y0) => 98.71/14.88 in(Y2, 98.71/14.88 Y1))))) => 98.71/14.88 subset(Y0, 98.71/14.88 Y1)))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 ((Y0 = Y1) => 98.71/14.88 subset(Y1, 98.71/14.88 Y0)))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 ((Y0 = Y1) => 98.71/14.88 subset(Y0, 98.71/14.88 Y1)))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 ((!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 Y0) => 98.71/14.88 in(Y2, 98.71/14.88 Y1))))) => 98.71/14.88 subset( 98.71/14.88 Y0, Y1)))))))) => 98.71/14.88 ((!!(subset(emptyset))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (subset( 98.71/14.88 Y0, Y1) => 98.71/14.88 (in(Y2, 98.71/14.88 Y0) => 98.71/14.88 in(Y2, 98.71/14.88 Y1)))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (subset( 98.71/14.88 Y0, Y1) => 98.71/14.88 (( 98.71/14.88 ~( 98.71/14.88 in(Y2, 98.71/14.88 Y1))) => 98.71/14.88 (~( 98.71/14.88 in(Y2, 98.71/14.88 Y0)))))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!((^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 Y0) => 98.71/14.88 (( 98.71/14.88 ~( 98.71/14.88 in(Y2, 98.71/14.88 Y1))) => 98.71/14.88 (~( 98.71/14.88 subset( 98.71/14.88 Y0, Y1)))))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (( 98.71/14.88 ~( 98.71/14.88 subset( 98.71/14.88 Y0, Y1))) => 98.71/14.88 ( 98.71/14.88 Y0 != Y1)))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (in(Y2, 98.71/14.88 Y0) => 98.71/14.88 (( 98.71/14.88 ~( 98.71/14.88 in(Y2, 98.71/14.88 Y1))) => 98.71/14.88 (Y0 != Y1)))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 subset(Y0, 98.71/14.88 Y0)))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (subset( 98.71/14.88 Y0, Y1) => 98.71/14.88 (subset( 98.71/14.88 Y1, Y2) => 98.71/14.88 subset( 98.71/14.88 Y0, Y2)))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 ( 98.71/14.88 !!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 subset( 98.71/14.88 Y1, 98.71/14.88 setadjoin( 98.71/14.88 Y0, Y1)))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y2 : $i]: 98.71/14.88 (subset( 98.71/14.88 Y0, Y2) => 98.71/14.88 subset( 98.71/14.88 Y0, 98.71/14.88 setadjoin( 98.71/14.88 Y1, Y2)))))))))))) => 98.71/14.88 ((!!((^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (subset( 98.71/14.88 Y0, Y1) => 98.71/14.88 in(Y0, 98.71/14.88 powerset( 98.71/14.88 Y1))))))))) => 98.71/14.88 ((!!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (subset( 98.71/14.88 Y0, Y1) => 98.71/14.88 (subset( 98.71/14.88 Y1, Y0) => 98.71/14.88 (Y0 = Y1))))))))) => 98.71/14.88 ((!!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 ( 98.71/14.88 subset( 98.71/14.88 Y0, 98.71/14.88 emptyset) => 98.71/14.88 ( 98.71/14.88 Y0 = 98.71/14.88 emptyset))))) => 98.71/14.88 ((!!(( 98.71/14.88 ^[Y0 : $i]: 98.71/14.88 (!!(( 98.71/14.88 ^[Y1 : $i]: 98.71/14.88 (subset( 98.71/14.88 Y1, Y0) => 98.71/14.88 in(Y1, 98.71/14.88 powerset( 98.71/14.88 Y0))))))))) => 98.71/14.88 ((!!(( 98.71/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (in(Y1, 99.05/14.88 powerset( 99.05/14.88 Y0)) => 99.05/14.88 subset( 99.05/14.88 Y1, Y0)))))))) => 99.05/14.88 (( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 in(Y0, 99.05/14.88 powerset( 99.05/14.88 Y0))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (subset( 99.05/14.88 Y0, Y1) => 99.05/14.88 subset( 99.05/14.88 powerset( 99.05/14.88 Y0), 99.05/14.88 powerset( 99.05/14.88 Y1))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i > $o]: 99.05/14.88 in( 99.05/14.88 dsetconstr( 99.05/14.88 Y0, Y1), 99.05/14.88 powerset( 99.05/14.88 Y0)))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i > $o]: 99.05/14.88 subset( 99.05/14.88 dsetconstr( 99.05/14.88 Y0, Y1), 99.05/14.88 Y0))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 Y0) => 99.05/14.88 in(Y2, 99.05/14.88 binunion( 99.05/14.88 Y0, Y1)))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 in(Y1, 99.05/14.88 setadjoin( 99.05/14.88 Y0, 99.05/14.88 setadjoin( 99.05/14.88 Y1, 99.05/14.88 emptyset))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 Y1) => 99.05/14.88 in(Y2, 99.05/14.88 binunion( 99.05/14.88 Y0, Y1)))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y3 : $o]: 99.05/14.88 (in(Y2, 99.05/14.88 binunion( 99.05/14.88 Y0, Y1)) => 99.05/14.88 (( 99.05/14.88 in(Y2, 99.05/14.88 Y0) => Y3) => 99.05/14.88 (( 99.05/14.88 in(Y2, 99.05/14.88 Y1) => Y3) => 99.05/14.88 Y3))))))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 binunion( 99.05/14.88 Y0, Y1)) => 99.05/14.88 (in(Y2, 99.05/14.88 Y1) | 99.05/14.88 in(Y2, 99.05/14.88 Y0)))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 subset( 99.05/14.88 Y0, 99.05/14.88 binunion( 99.05/14.88 Y0, Y1)))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 subset( 99.05/14.88 Y1, 99.05/14.88 binunion( 99.05/14.88 Y0, Y1)))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 Y0) => 99.05/14.88 (in(Y2, 99.05/14.88 Y1) => 99.05/14.88 in(Y2, 99.05/14.88 binintersect( 99.05/14.88 Y0, Y1))))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (subset( 99.05/14.88 Y2, Y0) => 99.05/14.88 (subset( 99.05/14.88 Y2, Y1) => 99.05/14.88 subset( 99.05/14.88 Y2, 99.05/14.88 binintersect( 99.05/14.88 Y0, Y1))))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 binintersect( 99.05/14.88 Y0, Y1)) => 99.05/14.88 in(Y2, 99.05/14.88 Y0))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 subset( 99.05/14.88 binintersect( 99.05/14.88 Y0, Y1), 99.05/14.88 Y0))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (subset( 99.05/14.88 Y0, Y1) => 99.05/14.88 (binintersect( 99.05/14.88 Y0, Y1) = 99.05/14.88 Y0)))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (( 99.05/14.88 binintersect( 99.05/14.88 Y0, Y1) = 99.05/14.88 Y1) => 99.05/14.88 subset( 99.05/14.88 Y1, Y0)))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 binintersect( 99.05/14.88 Y0, Y1)) => 99.05/14.88 in(Y2, 99.05/14.88 Y1))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (( 99.05/14.88 ~(( 99.05/14.88 ??(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 Y0) & 99.05/14.88 in(Y2, 99.05/14.88 Y1))))))) => 99.05/14.88 (binintersect( 99.05/14.88 Y0, Y1) = 99.05/14.88 emptyset)))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 subset( 99.05/14.88 binintersect( 99.05/14.88 Y0, Y1), 99.05/14.88 Y1))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (subset( 99.05/14.88 Y1, Y0) => 99.05/14.88 (binintersect( 99.05/14.88 Y0, Y1) = 99.05/14.88 Y1)))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (( 99.05/14.88 binintersect( 99.05/14.88 Y0, Y1) = 99.05/14.88 Y0) => 99.05/14.88 subset( 99.05/14.88 Y0, Y1)))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (binintersect( 99.05/14.88 Y0, 99.05/14.88 binunion( 99.05/14.88 Y1, Y2)) = 99.05/14.88 binunion( 99.05/14.88 binintersect( 99.05/14.88 Y0, Y1), 99.05/14.88 binintersect( 99.05/14.88 Y0, Y2)))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 Y0) => 99.05/14.88 (( 99.05/14.88 ~( 99.05/14.88 in(Y2, 99.05/14.88 Y1))) => 99.05/14.88 in(Y2, 99.05/14.88 setminus( 99.05/14.88 Y0, Y1))))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 setminus( 99.05/14.88 Y0, Y1)) => 99.05/14.88 in(Y2, 99.05/14.88 Y0))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 setminus( 99.05/14.88 Y0, Y1)) => 99.05/14.88 (~( 99.05/14.88 in(Y2, 99.05/14.88 Y1))))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (subset( 99.05/14.88 Y0, Y1) => 99.05/14.88 (setminus( 99.05/14.88 Y0, Y1) = 99.05/14.88 emptyset)))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (( 99.05/14.88 ~( 99.05/14.88 in(Y2, 99.05/14.88 setminus( 99.05/14.88 Y0, Y1)))) => 99.05/14.88 (in(Y2, 99.05/14.88 Y0) => 99.05/14.88 in(Y2, 99.05/14.88 Y1)))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (( 99.05/14.88 ~( 99.05/14.88 in(Y2, 99.05/14.88 setminus( 99.05/14.88 Y0, Y1)))) => 99.05/14.88 (( 99.05/14.88 ~( 99.05/14.88 in(Y2, 99.05/14.88 Y1))) => 99.05/14.88 (~( 99.05/14.88 in(Y2, 99.05/14.88 Y0)))))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (( 99.05/14.88 ~( 99.05/14.88 in(Y2, 99.05/14.88 Y0))) => 99.05/14.88 (~( 99.05/14.88 in(Y2, 99.05/14.88 setminus( 99.05/14.88 Y0, Y1)))))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 Y1) => 99.05/14.88 (~( 99.05/14.88 in(Y2, 99.05/14.88 setminus( 99.05/14.88 Y0, Y1)))))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 subset( 99.05/14.88 setminus( 99.05/14.88 Y0, Y1), 99.05/14.88 Y0))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (( 99.05/14.88 setminus( 99.05/14.88 Y0, Y1) = 99.05/14.88 emptyset) => 99.05/14.88 subset( 99.05/14.88 Y0, Y1)))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 symdiff( 99.05/14.88 Y0, Y1)) => 99.05/14.88 (!!(( 99.05/14.88 ^[Y3 : $o]: 99.05/14.88 (( 99.05/14.88 in(Y2, 99.05/14.88 Y0) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 ~( 99.05/14.88 in(Y2, 99.05/14.88 Y1))) => 99.05/14.88 Y3)) => 99.05/14.88 (( 99.05/14.88 ( 99.05/14.88 ~( 99.05/14.88 in(Y2, 99.05/14.88 Y0))) => 99.05/14.88 ( 99.05/14.88 in(Y2, 99.05/14.88 Y1) => Y3)) => 99.05/14.88 Y3))))))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 Y0) => 99.05/14.88 (( 99.05/14.88 ~( 99.05/14.88 in(Y2, 99.05/14.88 Y1))) => 99.05/14.88 in(Y2, 99.05/14.88 symdiff( 99.05/14.88 Y0, Y1))))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (( 99.05/14.88 ~( 99.05/14.88 in(Y2, 99.05/14.88 Y0))) => 99.05/14.88 (in(Y2, 99.05/14.88 Y1) => 99.05/14.88 in(Y2, 99.05/14.88 symdiff( 99.05/14.88 Y0, Y1))))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 Y0) => 99.05/14.88 (in(Y2, 99.05/14.88 Y1) => 99.05/14.88 (~( 99.05/14.88 in(Y2, 99.05/14.88 symdiff( 99.05/14.88 Y0, Y1))))))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (( 99.05/14.88 ~( 99.05/14.88 in(Y2, 99.05/14.88 Y0))) => 99.05/14.88 (( 99.05/14.88 ~( 99.05/14.88 in(Y2, 99.05/14.88 Y1))) => 99.05/14.88 (~( 99.05/14.88 in(Y2, 99.05/14.88 symdiff( 99.05/14.88 Y0, Y1))))))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 in(Y1, 99.05/14.88 setadjoin( 99.05/14.88 Y0, 99.05/14.88 setadjoin( 99.05/14.88 Y1, 99.05/14.88 emptyset))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 in(Y0, 99.05/14.88 setunion( 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y0, 99.05/14.88 emptyset), 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y0, 99.05/14.88 setadjoin( 99.05/14.88 Y1, 99.05/14.88 emptyset)), 99.05/14.88 emptyset)))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 in(Y1, 99.05/14.88 setunion( 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y0, 99.05/14.88 emptyset), 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y0, 99.05/14.88 setadjoin( 99.05/14.88 Y1, 99.05/14.88 emptyset)), 99.05/14.88 emptyset)))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (??(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 setunion( 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y0, 99.05/14.88 emptyset), 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y0, 99.05/14.88 setadjoin( 99.05/14.88 Y1, 99.05/14.88 emptyset)), 99.05/14.88 emptyset)))) & 99.05/14.88 (??(( 99.05/14.88 ^[Y3 : $i]: 99.05/14.88 (in(Y3, 99.05/14.88 setunion( 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y0, 99.05/14.88 emptyset), 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y0, 99.05/14.88 setadjoin( 99.05/14.88 Y1, 99.05/14.88 emptyset)), 99.05/14.88 emptyset)))) & 99.05/14.88 (setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y0, 99.05/14.88 emptyset), 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y0, 99.05/14.88 setadjoin( 99.05/14.88 Y1, 99.05/14.88 emptyset)), 99.05/14.88 emptyset)) = 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y2, 99.05/14.88 emptyset), 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y2, 99.05/14.88 setadjoin( 99.05/14.88 Y3, 99.05/14.88 emptyset)), 99.05/14.88 emptyset))))))))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (??(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 setunion( 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y0, 99.05/14.88 emptyset), 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y0, 99.05/14.88 setadjoin( 99.05/14.88 Y1, 99.05/14.88 emptyset)), 99.05/14.88 emptyset)))) & 99.05/14.88 (??(( 99.05/14.88 ^[Y3 : $i]: 99.05/14.88 (in(Y3, 99.05/14.88 setunion( 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y0, 99.05/14.88 emptyset), 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y0, 99.05/14.88 setadjoin( 99.05/14.88 Y1, 99.05/14.88 emptyset)), 99.05/14.88 emptyset)))) & 99.05/14.88 (setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y0, 99.05/14.88 emptyset), 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y0, 99.05/14.88 setadjoin( 99.05/14.88 Y1, 99.05/14.88 emptyset)), 99.05/14.88 emptyset)) = 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y2, 99.05/14.88 emptyset), 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y2, 99.05/14.88 setadjoin( 99.05/14.88 Y3, 99.05/14.88 emptyset)), 99.05/14.88 emptyset))))))))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (in(Y1, 99.05/14.88 Y0) => 99.05/14.88 subset( 99.05/14.88 setadjoin( 99.05/14.88 Y1, 99.05/14.88 emptyset), 99.05/14.88 Y0)))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (in(Y1, 99.05/14.88 Y0) => 99.05/14.88 in( 99.05/14.88 setadjoin( 99.05/14.88 Y1, 99.05/14.88 emptyset), 99.05/14.88 powerset( 99.05/14.88 Y0))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 Y0) => 99.05/14.88 in( 99.05/14.88 setadjoin( 99.05/14.88 Y2, 99.05/14.88 emptyset), 99.05/14.88 powerset( 99.05/14.88 binunion( 99.05/14.88 Y0, Y1))))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 setadjoin( 99.05/14.88 Y0, 99.05/14.88 setadjoin( 99.05/14.88 Y1, 99.05/14.88 emptyset))) => 99.05/14.88 (( 99.05/14.88 Y2 = Y1) | 99.05/14.88 (Y2 = Y0)))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 Y0) => 99.05/14.88 (!!(( 99.05/14.88 ^[Y3 : $i]: 99.05/14.88 (in(Y3, 99.05/14.88 Y1) => 99.05/14.88 subset( 99.05/14.88 setadjoin( 99.05/14.88 Y2, 99.05/14.88 setadjoin( 99.05/14.88 Y3, 99.05/14.88 emptyset)), 99.05/14.88 binunion( 99.05/14.88 Y0, Y1)))))))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 Y0) => 99.05/14.88 (!!(( 99.05/14.88 ^[Y3 : $i]: 99.05/14.88 (in(Y3, 99.05/14.88 Y1) => 99.05/14.88 in( 99.05/14.88 setadjoin( 99.05/14.88 Y2, 99.05/14.88 setadjoin( 99.05/14.88 Y3, 99.05/14.88 emptyset)), 99.05/14.88 powerset( 99.05/14.88 binunion( 99.05/14.88 Y0, Y1))))))))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 Y0) => 99.05/14.88 (!!(( 99.05/14.88 ^[Y3 : $i]: 99.05/14.88 (in(Y3, 99.05/14.88 Y1) => 99.05/14.88 subset( 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y2, 99.05/14.88 emptyset), 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y2, 99.05/14.88 setadjoin( 99.05/14.88 Y3, 99.05/14.88 emptyset)), 99.05/14.88 emptyset)), 99.05/14.88 powerset( 99.05/14.88 binunion( 99.05/14.88 Y0, Y1))))))))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 Y0) => 99.05/14.88 (!!(( 99.05/14.88 ^[Y3 : $i]: 99.05/14.88 (in(Y3, 99.05/14.88 Y1) => 99.05/14.88 in( 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y2, 99.05/14.88 emptyset), 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y2, 99.05/14.88 setadjoin( 99.05/14.88 Y3, 99.05/14.88 emptyset)), 99.05/14.88 emptyset)), 99.05/14.88 powerset( 99.05/14.88 powerset( 99.05/14.88 binunion( 99.05/14.88 Y0, Y1)))))))))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 Y0) => 99.05/14.88 (!!(( 99.05/14.88 ^[Y3 : $i]: 99.05/14.88 (in(Y3, 99.05/14.88 Y1) => 99.05/14.88 in( 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y2, 99.05/14.88 emptyset), 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y2, 99.05/14.88 setadjoin( 99.05/14.88 Y3, 99.05/14.88 emptyset)), 99.05/14.88 emptyset)), 99.05/14.88 powerset( 99.05/14.88 powerset( 99.05/14.88 binunion( 99.05/14.88 Y0, Y1)))))))))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 Y0) => 99.05/14.88 (!!(( 99.05/14.88 ^[Y3 : $i]: 99.05/14.88 (in(Y3, 99.05/14.88 Y1) => 99.05/14.88 in( 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y2, 99.05/14.88 emptyset), 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y2, 99.05/14.88 setadjoin( 99.05/14.88 Y3, 99.05/14.88 emptyset)), 99.05/14.88 emptyset)), 99.05/14.88 dsetconstr( 99.05/14.88 powerset( 99.05/14.88 powerset( 99.05/14.88 binunion( 99.05/14.88 Y0, Y1))), 99.05/14.88 (^[Y4 : $i]: 99.05/14.88 (??(( 99.05/14.88 ^[Y5 : $i]: 99.05/14.88 (in(Y5, 99.05/14.88 Y0) & 99.05/14.88 (??(( 99.05/14.88 ^[Y6 : $i]: 99.05/14.88 (in(Y6, 99.05/14.88 Y1) & 99.05/14.88 (Y4 = 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y5, 99.05/14.88 emptyset), 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y5, 99.05/14.88 setadjoin( 99.05/14.88 Y6, 99.05/14.88 emptyset)), 99.05/14.88 emptyset)))))))))))))))))))))))))))) => 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 dsetconstr( 99.05/14.88 powerset( 99.05/14.88 powerset( 99.05/14.88 binunion( 99.05/14.88 Y0, Y1))), 99.05/14.88 (^[Y3 : $i]: 99.05/14.88 (??(( 99.05/14.88 ^[Y4 : $i]: 99.05/14.88 (in(Y4, 99.05/14.88 Y0) & 99.05/14.88 (??(( 99.05/14.88 ^[Y5 : $i]: 99.05/14.88 (in(Y5, 99.05/14.88 Y1) & 99.05/14.88 (Y3 = 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y4, 99.05/14.88 emptyset), 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y4, 99.05/14.88 setadjoin( 99.05/14.88 Y5, 99.05/14.88 emptyset)), 99.05/14.88 emptyset)))))))))))))) => 99.05/14.88 (??(( 99.05/14.88 ^[Y3 : $i]: 99.05/14.88 (( 99.05/14.88 ??(( 99.05/14.88 ^[Y4 : $i]: 99.05/14.88 (in(Y4, 99.05/14.88 Y1) & 99.05/14.88 (Y2 = 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y3, 99.05/14.88 emptyset), 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y3, 99.05/14.88 setadjoin( 99.05/14.88 Y4, 99.05/14.88 emptyset)), 99.05/14.88 emptyset))))))) & 99.05/14.88 in(Y3, 99.05/14.88 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.05/14.88 inference('lazy_cnf_imply', [status(thm)], ['189'])). 99.05/14.88 tff('191', plain, 99.05/14.88 ~ ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 (!!((^[Y2 : $i]: 99.05/14.88 (in(Y2, setadjoin(Y0, Y1)) => 99.05/14.88 (!!((^[Y3 : $o]: 99.05/14.88 (((Y2 = Y0) => Y3) => 99.05/14.88 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 (!!((^[Y2 : $i]: 99.05/14.88 (in(Y2, setadjoin(Y0, Y1)) => 99.05/14.88 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 99.05/14.88 in(Y1, powerset(Y0))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 99.05/14.88 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 (!!((^[Y2 : $i]: 99.05/14.88 (in(Y1, powerset(Y0)) => 99.05/14.88 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 (!!((^[Y2 : $i]: 99.05/14.88 (in(Y1, Y2) => 99.05/14.88 (in(Y2, Y0) => in(Y1, setunion(Y0))))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 (in(Y1, setunion(Y0)) => 99.05/14.88 (!!((^[Y2 : $o]: 99.05/14.88 ((!!((^[Y3 : $i]: 99.05/14.88 (in(Y1, Y3) => 99.05/14.88 (in(Y3, Y0) => Y2))))) => 99.05/14.88 Y2))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 (in(Y1, Y0) => in(Y1, powerset(setunion(Y0)))))))))) => 99.05/14.88 ((!!((^[Y0 : $i > $o]: 99.05/14.88 ((??((^[Y1 : $i]: 99.05/14.88 (Y0(Y1) & 99.05/14.88 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.88 (??((^[Y1 : $i]: 99.05/14.88 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 (in(Y0, setadjoin(Y1, emptyset)) => 99.05/14.88 (Y0 = Y1)))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 ((Y0 != Y1) => 99.05/14.88 (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 ((Y0 = Y1) => 99.05/14.88 in(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 (in(Y0, setadjoin(Y1, emptyset)) => 99.05/14.88 in(Y1, setadjoin(Y0, emptyset))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 (!!((^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 setadjoin(Y0, 99.05/14.88 setadjoin(Y1, emptyset))) => 99.05/14.88 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 in(Y0, 99.05/14.88 setadjoin(Y0, 99.05/14.88 setadjoin(Y1, emptyset))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 in(Y1, 99.05/14.88 setadjoin(Y0, 99.05/14.88 setadjoin(Y1, emptyset))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i > $o]: 99.05/14.88 ((??((^[Y2 : $i]: 99.05/14.88 (in(Y2, Y0) & Y1(Y2))))) => 99.05/14.88 (dsetconstr(Y0, Y1) != emptyset)))))))) => 99.05/14.88 ((!!((^[Y0 : $i > $o]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 (in(Y1, emptyset) => Y0(Y1)))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i > $o]: 99.05/14.88 ((~((!!((^[Y2 : $i]: 99.05/14.88 (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.88 (??((^[Y2 : $i]: 99.05/14.88 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i > $o]: 99.05/14.88 ((!!((^[Y2 : $i]: 99.05/14.88 (in(Y2, Y0) => (~(Y1(Y2))))))) => 99.05/14.88 (~((??((^[Y2 : $i]: 99.05/14.88 (in(Y2, Y0) & Y1(Y2)))))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i > $o]: 99.05/14.88 ((~((??((^[Y2 : $i]: 99.05/14.88 (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.88 (!!((^[Y2 : $i]: 99.05/14.88 (in(Y2, Y0) => 99.05/14.88 (~(Y1(Y2)))))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i > $o]: 99.05/14.88 ((??((^[Y2 : $i]: 99.05/14.88 (in(Y2, Y0) & 99.05/14.88 (~(Y1(Y2))))))) => 99.05/14.88 (~((!!((^[Y2 : $i]: 99.05/14.88 (in(Y2, Y0) => Y1(Y2)))))))))))))) => 99.05/14.88 ((!!((^[Y0 : $o]: 99.05/14.88 (Y0 => in(emptyset, prop2set(Y0)))))) => 99.05/14.88 ((!!((^[Y0 : $o]: 99.05/14.88 (Y0 => set2prop(prop2set(Y0)))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i > $o]: 99.05/14.88 ((~((??((^[Y2 : $i]: 99.05/14.88 (in(Y2, Y0) & 99.05/14.88 Y1(Y2))))))) => 99.05/14.88 (!!((^[Y2 : $i]: 99.05/14.88 (in(Y2, Y0) => 99.05/14.88 (~(Y1(Y2)))))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i > $o]: 99.05/14.88 ((~((!!((^[Y2 : $i]: 99.05/14.88 (in(Y2, Y0) => 99.05/14.88 Y1(Y2))))))) => 99.05/14.88 (??((^[Y2 : $i]: 99.05/14.88 (in(Y2, Y0) & 99.05/14.88 (~(Y1(Y2)))))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i > $o]: 99.05/14.88 ((??(Y0)) => 99.05/14.88 ((!!((^[Y1 : $i]: 99.05/14.88 (!!((^[Y2 : $i]: 99.05/14.88 (Y0(Y1) => 99.05/14.88 (Y0(Y2) => 99.05/14.88 (Y1 = Y2))))))))) => 99.05/14.88 (??((^[Y1 : $i]: 99.05/14.88 (Y0(Y1) & 99.05/14.88 (!!((^[Y2 : $i]: 99.05/14.88 (Y0(Y2) => 99.05/14.88 (Y1 = Y2)))))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i > $o]: 99.05/14.88 ((??((^[Y1 : $i]: 99.05/14.88 (!!((^[Y2 : $i]: 99.05/14.88 (Y0(Y2) <=> 99.05/14.88 (Y2 = Y1)))))))) => 99.05/14.88 (??((^[Y1 : $i]: 99.05/14.88 (Y0(Y1) & 99.05/14.88 (!!((^[Y2 : $i]: 99.05/14.88 (Y0(Y2) => 99.05/14.88 (Y1 = Y2))))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 ((Y0 = Y1) => 99.05/14.88 (!!((^[Y2 : $i]: 99.05/14.88 (!!((^[Y3 : $i]: 99.05/14.88 (( 99.05/14.88 Y2 = Y3) => 99.05/14.88 ( 99.05/14.88 in(Y2, 99.05/14.88 Y0) => 99.05/14.88 in(Y3, 99.05/14.88 Y1)))))))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 ((Y0 = Y1) => 99.05/14.88 (!!((^[Y2 : $i]: 99.05/14.88 (!!((^[Y3 : $i]: 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 Y2 = Y3) => 99.05/14.88 ( 99.05/14.88 in(Y2, 99.05/14.88 Y0) <=> 99.05/14.88 in(Y3, 99.05/14.88 Y1)))))))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i > $o]: 99.05/14.88 ((??((^[Y1 : $i]: 99.05/14.88 (Y0(Y1) & 99.05/14.88 (!!((^[Y2 : $i]: 99.05/14.88 (Y0(Y2) => 99.05/14.88 (Y1 = Y2))))))))) => 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 (!!((^[Y2 : $i]: 99.05/14.88 (Y0(Y1) => 99.05/14.88 (Y0(Y2) => 99.05/14.88 (Y1 = Y2))))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i > $o]: 99.05/14.88 (!!((^[Y1 : $i > $o]: 99.05/14.88 ((!!((^[Y2 : $i]: 99.05/14.88 (!!((^[Y3 : $i]: 99.05/14.88 (( 99.05/14.88 Y2 = Y3) => 99.05/14.88 (Y0(Y2) <=> 99.05/14.88 Y1(Y3))))))))) => 99.05/14.88 ((??((^[Y2 : $i]: 99.05/14.88 (Y0(Y2) & 99.05/14.88 (!!(( 99.05/14.88 ^[Y3 : $i]: 99.05/14.88 ( 99.05/14.88 Y0(Y3) => 99.05/14.88 ( 99.05/14.88 Y2 = Y3))))))))) <=> 99.05/14.88 (??((^[Y2 : $i]: 99.05/14.88 (Y1(Y2) & 99.05/14.88 (!!(( 99.05/14.88 ^[Y3 : $i]: 99.05/14.88 ( 99.05/14.88 Y1(Y3) => 99.05/14.88 ( 99.05/14.88 Y2 = Y3))))))))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 ((Y0 = Y1) => 99.05/14.88 (!!((^[Y2 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y3 : $i]: 99.05/14.88 (( 99.05/14.88 Y2 = Y3) => 99.05/14.88 ( 99.05/14.88 setadjoin( 99.05/14.88 Y0, Y2) = 99.05/14.88 setadjoin( 99.05/14.88 Y1, Y3)))))))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 ((Y0 = Y1) => 99.05/14.88 (powerset(Y0) = 99.05/14.88 powerset(Y1))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 ((Y0 = Y1) => 99.05/14.88 (setunion(Y0) = 99.05/14.88 setunion(Y1))))))))) => 99.05/14.88 ((!!((^[Y0 : $i > $o]: 99.05/14.88 ((??((^[Y1 : $i]: 99.05/14.88 (Y0(Y1) & 99.05/14.88 (!!((^[Y2 : $i]: 99.05/14.88 ( 99.05/14.88 Y0(Y2) => 99.05/14.88 ( 99.05/14.88 Y1 = Y2))))))))) => 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 (!!((^[Y2 : $i]: 99.05/14.88 (Y0(Y1) => 99.05/14.88 ( 99.05/14.88 Y0(Y2) => 99.05/14.88 ( 99.05/14.88 Y1 = Y2))))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i > $o]: 99.05/14.88 (!!((^[Y1 : $i > $o]: 99.05/14.88 ((!!((^[Y2 : $i]: 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y3 : $i]: 99.05/14.88 (( 99.05/14.88 Y2 = Y3) => 99.05/14.88 (Y0(Y2) <=> 99.05/14.88 Y1(Y3))))))))) => 99.05/14.88 ((??((^[Y2 : $i]: 99.05/14.88 (Y0(Y2) & 99.05/14.88 (!!(( 99.05/14.88 ^[Y3 : $i]: 99.05/14.88 (Y0(Y3) => 99.05/14.88 (Y2 = Y3))))))))) => 99.05/14.88 ((??((^[Y2 : $i]: 99.05/14.88 (Y1(Y2) & 99.05/14.88 (!!(( 99.05/14.88 ^[Y3 : $i]: 99.05/14.88 (Y1(Y3) => 99.05/14.88 (Y2 = Y3))))))))) => 99.05/14.88 (descr(Y0) = 99.05/14.88 descr(Y1))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 ((Y0 = Y1) => 99.05/14.88 (!!((^[Y2 : $i > $o]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y3 : $i > $o]: 99.05/14.88 (( 99.05/14.88 !!(( 99.05/14.88 ^[Y4 : $i]: 99.05/14.88 (in(Y4, 99.05/14.88 Y0) => 99.05/14.88 (!!(( 99.05/14.88 ^[Y5 : $i]: 99.05/14.88 (in(Y5, 99.05/14.88 Y1) => 99.05/14.88 (( 99.05/14.88 Y4 = Y5) => 99.05/14.88 (Y2(Y4) <=> 99.05/14.88 Y3(Y5))))))))))) => 99.05/14.88 (dsetconstr( 99.05/14.88 Y0, Y2) = 99.05/14.88 dsetconstr( 99.05/14.88 Y1, Y3)))))))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 ((!!((^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 Y0) => 99.05/14.88 in(Y2, 99.05/14.88 Y1))))) => 99.05/14.88 subset(Y0, Y1)))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 ((Y0 = Y1) => 99.05/14.88 subset(Y1, 99.05/14.88 Y0)))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 ((Y0 = Y1) => 99.05/14.88 subset(Y0, 99.05/14.88 Y1)))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 ((!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 Y0) => 99.05/14.88 in(Y2, 99.05/14.88 Y1))))) => 99.05/14.88 subset(Y0, 99.05/14.88 Y1)))))))) => 99.05/14.88 ((!!(subset(emptyset))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (subset( 99.05/14.88 Y0, Y1) => 99.05/14.88 (in(Y2, 99.05/14.88 Y0) => 99.05/14.88 in(Y2, 99.05/14.88 Y1)))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (subset( 99.05/14.88 Y0, Y1) => 99.05/14.88 (( 99.05/14.88 ~( 99.05/14.88 in(Y2, 99.05/14.88 Y1))) => 99.05/14.88 (~( 99.05/14.88 in(Y2, 99.05/14.88 Y0)))))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 Y0) => 99.05/14.88 (( 99.05/14.88 ~( 99.05/14.88 in(Y2, 99.05/14.88 Y1))) => 99.05/14.88 (~( 99.05/14.88 subset( 99.05/14.88 Y0, Y1)))))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 (( 99.05/14.88 ~( 99.05/14.88 subset( 99.05/14.88 Y0, Y1))) => 99.05/14.88 (Y0 != Y1)))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 Y0) => 99.05/14.88 (( 99.05/14.88 ~( 99.05/14.88 in(Y2, 99.05/14.88 Y1))) => 99.05/14.88 (Y0 != Y1)))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 subset(Y0, 99.05/14.88 Y0)))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (subset( 99.05/14.88 Y0, Y1) => 99.05/14.88 (subset( 99.05/14.88 Y1, Y2) => 99.05/14.88 subset( 99.05/14.88 Y0, Y2)))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 subset( 99.05/14.88 Y1, 99.05/14.88 setadjoin( 99.05/14.88 Y0, Y1)))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (subset( 99.05/14.88 Y0, Y2) => 99.05/14.88 subset( 99.05/14.88 Y0, 99.05/14.88 setadjoin( 99.05/14.88 Y1, Y2)))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (subset( 99.05/14.88 Y0, Y1) => 99.05/14.88 in(Y0, 99.05/14.88 powerset( 99.05/14.88 Y1))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (subset( 99.05/14.88 Y0, Y1) => 99.05/14.88 (subset( 99.05/14.88 Y1, Y0) => 99.05/14.88 (Y0 = Y1))))))))) => 99.05/14.88 ((!!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (subset( 99.05/14.88 Y0, 99.05/14.88 emptyset) => 99.05/14.88 ( 99.05/14.88 Y0 = 99.05/14.88 emptyset))))) => 99.05/14.88 ((!!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (subset( 99.05/14.88 Y1, Y0) => 99.05/14.88 in(Y1, 99.05/14.88 powerset( 99.05/14.88 Y0))))))))) => 99.05/14.88 ((!!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (in(Y1, 99.05/14.88 powerset( 99.05/14.88 Y0)) => 99.05/14.88 subset( 99.05/14.88 Y1, Y0)))))))) => 99.05/14.88 ((!!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 in(Y0, 99.05/14.88 powerset( 99.05/14.88 Y0))))) => 99.05/14.88 (( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (subset( 99.05/14.88 Y0, Y1) => 99.05/14.88 subset( 99.05/14.88 powerset( 99.05/14.88 Y0), 99.05/14.88 powerset( 99.05/14.88 Y1))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i > $o]: 99.05/14.88 in( 99.05/14.88 dsetconstr( 99.05/14.88 Y0, Y1), 99.05/14.88 powerset( 99.05/14.88 Y0)))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i > $o]: 99.05/14.88 subset( 99.05/14.88 dsetconstr( 99.05/14.88 Y0, Y1), 99.05/14.88 Y0))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 Y0) => 99.05/14.88 in(Y2, 99.05/14.88 binunion( 99.05/14.88 Y0, Y1)))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 in(Y1, 99.05/14.88 setadjoin( 99.05/14.88 Y0, 99.05/14.88 setadjoin( 99.05/14.88 Y1, 99.05/14.88 emptyset))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 Y1) => 99.05/14.88 in(Y2, 99.05/14.88 binunion( 99.05/14.88 Y0, Y1)))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y3 : $o]: 99.05/14.88 (in(Y2, 99.05/14.88 binunion( 99.05/14.88 Y0, Y1)) => 99.05/14.88 (( 99.05/14.88 in(Y2, 99.05/14.88 Y0) => Y3) => 99.05/14.88 (( 99.05/14.88 in(Y2, 99.05/14.88 Y1) => Y3) => 99.05/14.88 Y3))))))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 binunion( 99.05/14.88 Y0, Y1)) => 99.05/14.88 (in(Y2, 99.05/14.88 Y1) | 99.05/14.88 in(Y2, 99.05/14.88 Y0)))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 subset( 99.05/14.88 Y0, 99.05/14.88 binunion( 99.05/14.88 Y0, Y1)))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 subset( 99.05/14.88 Y1, 99.05/14.88 binunion( 99.05/14.88 Y0, Y1)))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 Y0) => 99.05/14.88 (in(Y2, 99.05/14.88 Y1) => 99.05/14.88 in(Y2, 99.05/14.88 binintersect( 99.05/14.88 Y0, Y1))))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (subset( 99.05/14.88 Y2, Y0) => 99.05/14.88 (subset( 99.05/14.88 Y2, Y1) => 99.05/14.88 subset( 99.05/14.88 Y2, 99.05/14.88 binintersect( 99.05/14.88 Y0, Y1))))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 binintersect( 99.05/14.88 Y0, Y1)) => 99.05/14.88 in(Y2, 99.05/14.88 Y0))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 subset( 99.05/14.88 binintersect( 99.05/14.88 Y0, Y1), 99.05/14.88 Y0))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (subset( 99.05/14.88 Y0, Y1) => 99.05/14.88 (binintersect( 99.05/14.88 Y0, Y1) = 99.05/14.88 Y0)))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (( 99.05/14.88 binintersect( 99.05/14.88 Y0, Y1) = 99.05/14.88 Y1) => 99.05/14.88 subset( 99.05/14.88 Y1, Y0)))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 binintersect( 99.05/14.88 Y0, Y1)) => 99.05/14.88 in(Y2, 99.05/14.88 Y1))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (( 99.05/14.88 ~(( 99.05/14.88 ??(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 Y0) & 99.05/14.88 in(Y2, 99.05/14.88 Y1))))))) => 99.05/14.88 (binintersect( 99.05/14.88 Y0, Y1) = 99.05/14.88 emptyset)))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 subset( 99.05/14.88 binintersect( 99.05/14.88 Y0, Y1), 99.05/14.88 Y1))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (subset( 99.05/14.88 Y1, Y0) => 99.05/14.88 (binintersect( 99.05/14.88 Y0, Y1) = 99.05/14.88 Y1)))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (( 99.05/14.88 binintersect( 99.05/14.88 Y0, Y1) = 99.05/14.88 Y0) => 99.05/14.88 subset( 99.05/14.88 Y0, Y1)))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (binintersect( 99.05/14.88 Y0, 99.05/14.88 binunion( 99.05/14.88 Y1, Y2)) = 99.05/14.88 binunion( 99.05/14.88 binintersect( 99.05/14.88 Y0, Y1), 99.05/14.88 binintersect( 99.05/14.88 Y0, Y2)))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 Y0) => 99.05/14.88 (( 99.05/14.88 ~( 99.05/14.88 in(Y2, 99.05/14.88 Y1))) => 99.05/14.88 in(Y2, 99.05/14.88 setminus( 99.05/14.88 Y0, Y1))))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 setminus( 99.05/14.88 Y0, Y1)) => 99.05/14.88 in(Y2, 99.05/14.88 Y0))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 setminus( 99.05/14.88 Y0, Y1)) => 99.05/14.88 (~( 99.05/14.88 in(Y2, 99.05/14.88 Y1))))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (subset( 99.05/14.88 Y0, Y1) => 99.05/14.88 (setminus( 99.05/14.88 Y0, Y1) = 99.05/14.88 emptyset)))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (( 99.05/14.88 ~( 99.05/14.88 in(Y2, 99.05/14.88 setminus( 99.05/14.88 Y0, Y1)))) => 99.05/14.88 (in(Y2, 99.05/14.88 Y0) => 99.05/14.88 in(Y2, 99.05/14.88 Y1)))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (( 99.05/14.88 ~( 99.05/14.88 in(Y2, 99.05/14.88 setminus( 99.05/14.88 Y0, Y1)))) => 99.05/14.88 (( 99.05/14.88 ~( 99.05/14.88 in(Y2, 99.05/14.88 Y1))) => 99.05/14.88 (~( 99.05/14.88 in(Y2, 99.05/14.88 Y0)))))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (( 99.05/14.88 ~( 99.05/14.88 in(Y2, 99.05/14.88 Y0))) => 99.05/14.88 (~( 99.05/14.88 in(Y2, 99.05/14.88 setminus( 99.05/14.88 Y0, Y1)))))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 Y1) => 99.05/14.88 (~( 99.05/14.88 in(Y2, 99.05/14.88 setminus( 99.05/14.88 Y0, Y1)))))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 subset( 99.05/14.88 setminus( 99.05/14.88 Y0, Y1), 99.05/14.88 Y0))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (( 99.05/14.88 setminus( 99.05/14.88 Y0, Y1) = 99.05/14.88 emptyset) => 99.05/14.88 subset( 99.05/14.88 Y0, Y1)))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 symdiff( 99.05/14.88 Y0, Y1)) => 99.05/14.88 (!!(( 99.05/14.88 ^[Y3 : $o]: 99.05/14.88 (( 99.05/14.88 in(Y2, 99.05/14.88 Y0) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 ~( 99.05/14.88 in(Y2, 99.05/14.88 Y1))) => 99.05/14.88 Y3)) => 99.05/14.88 (( 99.05/14.88 ( 99.05/14.88 ~( 99.05/14.88 in(Y2, 99.05/14.88 Y0))) => 99.05/14.88 ( 99.05/14.88 in(Y2, 99.05/14.88 Y1) => Y3)) => 99.05/14.88 Y3))))))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 Y0) => 99.05/14.88 (( 99.05/14.88 ~( 99.05/14.88 in(Y2, 99.05/14.88 Y1))) => 99.05/14.88 in(Y2, 99.05/14.88 symdiff( 99.05/14.88 Y0, Y1))))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (( 99.05/14.88 ~( 99.05/14.88 in(Y2, 99.05/14.88 Y0))) => 99.05/14.88 (in(Y2, 99.05/14.88 Y1) => 99.05/14.88 in(Y2, 99.05/14.88 symdiff( 99.05/14.88 Y0, Y1))))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 Y0) => 99.05/14.88 (in(Y2, 99.05/14.88 Y1) => 99.05/14.88 (~( 99.05/14.88 in(Y2, 99.05/14.88 symdiff( 99.05/14.88 Y0, Y1))))))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (( 99.05/14.88 ~( 99.05/14.88 in(Y2, 99.05/14.88 Y0))) => 99.05/14.88 (( 99.05/14.88 ~( 99.05/14.88 in(Y2, 99.05/14.88 Y1))) => 99.05/14.88 (~( 99.05/14.88 in(Y2, 99.05/14.88 symdiff( 99.05/14.88 Y0, Y1))))))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 in(Y1, 99.05/14.88 setadjoin( 99.05/14.88 Y0, 99.05/14.88 setadjoin( 99.05/14.88 Y1, 99.05/14.88 emptyset))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 in(Y0, 99.05/14.88 setunion( 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y0, 99.05/14.88 emptyset), 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y0, 99.05/14.88 setadjoin( 99.05/14.88 Y1, 99.05/14.88 emptyset)), 99.05/14.88 emptyset)))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 in(Y1, 99.05/14.88 setunion( 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y0, 99.05/14.88 emptyset), 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y0, 99.05/14.88 setadjoin( 99.05/14.88 Y1, 99.05/14.88 emptyset)), 99.05/14.88 emptyset)))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (??(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 setunion( 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y0, 99.05/14.88 emptyset), 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y0, 99.05/14.88 setadjoin( 99.05/14.88 Y1, 99.05/14.88 emptyset)), 99.05/14.88 emptyset)))) & 99.05/14.88 (??(( 99.05/14.88 ^[Y3 : $i]: 99.05/14.88 (in(Y3, 99.05/14.88 setunion( 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y0, 99.05/14.88 emptyset), 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y0, 99.05/14.88 setadjoin( 99.05/14.88 Y1, 99.05/14.88 emptyset)), 99.05/14.88 emptyset)))) & 99.05/14.88 (setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y0, 99.05/14.88 emptyset), 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y0, 99.05/14.88 setadjoin( 99.05/14.88 Y1, 99.05/14.88 emptyset)), 99.05/14.88 emptyset)) = 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y2, 99.05/14.88 emptyset), 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y2, 99.05/14.88 setadjoin( 99.05/14.88 Y3, 99.05/14.88 emptyset)), 99.05/14.88 emptyset))))))))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (??(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 setunion( 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y0, 99.05/14.88 emptyset), 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y0, 99.05/14.88 setadjoin( 99.05/14.88 Y1, 99.05/14.88 emptyset)), 99.05/14.88 emptyset)))) & 99.05/14.88 (??(( 99.05/14.88 ^[Y3 : $i]: 99.05/14.88 (in(Y3, 99.05/14.88 setunion( 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y0, 99.05/14.88 emptyset), 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y0, 99.05/14.88 setadjoin( 99.05/14.88 Y1, 99.05/14.88 emptyset)), 99.05/14.88 emptyset)))) & 99.05/14.88 (setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y0, 99.05/14.88 emptyset), 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y0, 99.05/14.88 setadjoin( 99.05/14.88 Y1, 99.05/14.88 emptyset)), 99.05/14.88 emptyset)) = 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y2, 99.05/14.88 emptyset), 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y2, 99.05/14.88 setadjoin( 99.05/14.88 Y3, 99.05/14.88 emptyset)), 99.05/14.88 emptyset))))))))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (in(Y1, 99.05/14.88 Y0) => 99.05/14.88 subset( 99.05/14.88 setadjoin( 99.05/14.88 Y1, 99.05/14.88 emptyset), 99.05/14.88 Y0)))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (in(Y1, 99.05/14.88 Y0) => 99.05/14.88 in( 99.05/14.88 setadjoin( 99.05/14.88 Y1, 99.05/14.88 emptyset), 99.05/14.88 powerset( 99.05/14.88 Y0))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 Y0) => 99.05/14.88 in( 99.05/14.88 setadjoin( 99.05/14.88 Y2, 99.05/14.88 emptyset), 99.05/14.88 powerset( 99.05/14.88 binunion( 99.05/14.88 Y0, Y1))))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 setadjoin( 99.05/14.88 Y0, 99.05/14.88 setadjoin( 99.05/14.88 Y1, 99.05/14.88 emptyset))) => 99.05/14.88 (( 99.05/14.88 Y2 = Y1) | 99.05/14.88 (Y2 = Y0)))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 Y0) => 99.05/14.88 (!!(( 99.05/14.88 ^[Y3 : $i]: 99.05/14.88 (in(Y3, 99.05/14.88 Y1) => 99.05/14.88 subset( 99.05/14.88 setadjoin( 99.05/14.88 Y2, 99.05/14.88 setadjoin( 99.05/14.88 Y3, 99.05/14.88 emptyset)), 99.05/14.88 binunion( 99.05/14.88 Y0, Y1)))))))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 Y0) => 99.05/14.88 (!!(( 99.05/14.88 ^[Y3 : $i]: 99.05/14.88 (in(Y3, 99.05/14.88 Y1) => 99.05/14.88 in( 99.05/14.88 setadjoin( 99.05/14.88 Y2, 99.05/14.88 setadjoin( 99.05/14.88 Y3, 99.05/14.88 emptyset)), 99.05/14.88 powerset( 99.05/14.88 binunion( 99.05/14.88 Y0, Y1))))))))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 Y0) => 99.05/14.88 (!!(( 99.05/14.88 ^[Y3 : $i]: 99.05/14.88 (in(Y3, 99.05/14.88 Y1) => 99.05/14.88 subset( 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y2, 99.05/14.88 emptyset), 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y2, 99.05/14.88 setadjoin( 99.05/14.88 Y3, 99.05/14.88 emptyset)), 99.05/14.88 emptyset)), 99.05/14.88 powerset( 99.05/14.88 binunion( 99.05/14.88 Y0, Y1))))))))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 Y0) => 99.05/14.88 (!!(( 99.05/14.88 ^[Y3 : $i]: 99.05/14.88 (in(Y3, 99.05/14.88 Y1) => 99.05/14.88 in( 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y2, 99.05/14.88 emptyset), 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y2, 99.05/14.88 setadjoin( 99.05/14.88 Y3, 99.05/14.88 emptyset)), 99.05/14.88 emptyset)), 99.05/14.88 powerset( 99.05/14.88 powerset( 99.05/14.88 binunion( 99.05/14.88 Y0, Y1)))))))))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 Y0) => 99.05/14.88 (!!(( 99.05/14.88 ^[Y3 : $i]: 99.05/14.88 (in(Y3, 99.05/14.88 Y1) => 99.05/14.88 in( 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y2, 99.05/14.88 emptyset), 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y2, 99.05/14.88 setadjoin( 99.05/14.88 Y3, 99.05/14.88 emptyset)), 99.05/14.88 emptyset)), 99.05/14.88 powerset( 99.05/14.88 powerset( 99.05/14.88 binunion( 99.05/14.88 Y0, Y1)))))))))))))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 Y0) => 99.05/14.88 (!!(( 99.05/14.88 ^[Y3 : $i]: 99.05/14.88 (in(Y3, 99.05/14.88 Y1) => 99.05/14.88 in( 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y2, 99.05/14.88 emptyset), 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y2, 99.05/14.88 setadjoin( 99.05/14.88 Y3, 99.05/14.88 emptyset)), 99.05/14.88 emptyset)), 99.05/14.88 dsetconstr( 99.05/14.88 powerset( 99.05/14.88 powerset( 99.05/14.88 binunion( 99.05/14.88 Y0, Y1))), 99.05/14.88 (^[Y4 : $i]: 99.05/14.88 (??(( 99.05/14.88 ^[Y5 : $i]: 99.05/14.88 (in(Y5, 99.05/14.88 Y0) & 99.05/14.88 (??(( 99.05/14.88 ^[Y6 : $i]: 99.05/14.88 (in(Y6, 99.05/14.88 Y1) & 99.05/14.88 (Y4 = 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y5, 99.05/14.88 emptyset), 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y5, 99.05/14.88 setadjoin( 99.05/14.88 Y6, 99.05/14.88 emptyset)), 99.05/14.88 emptyset)))))))))))))))))))))))))))) => 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 dsetconstr( 99.05/14.88 powerset( 99.05/14.88 powerset( 99.05/14.88 binunion( 99.05/14.88 Y0, Y1))), 99.05/14.88 (^[Y3 : $i]: 99.05/14.88 (??(( 99.05/14.88 ^[Y4 : $i]: 99.05/14.88 (in(Y4, 99.05/14.88 Y0) & 99.05/14.88 (??(( 99.05/14.88 ^[Y5 : $i]: 99.05/14.88 (in(Y5, 99.05/14.88 Y1) & 99.05/14.88 (Y3 = 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y4, 99.05/14.88 emptyset), 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y4, 99.05/14.88 setadjoin( 99.05/14.88 Y5, 99.05/14.88 emptyset)), 99.05/14.88 emptyset)))))))))))))) => 99.05/14.88 (??(( 99.05/14.88 ^[Y3 : $i]: 99.05/14.88 (( 99.05/14.88 ??(( 99.05/14.88 ^[Y4 : $i]: 99.05/14.88 (in(Y4, 99.05/14.88 Y1) & 99.05/14.88 (Y2 = 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y3, 99.05/14.88 emptyset), 99.05/14.88 setadjoin( 99.05/14.88 setadjoin( 99.05/14.88 Y3, 99.05/14.88 setadjoin( 99.05/14.88 Y4, 99.05/14.88 emptyset)), 99.05/14.88 emptyset))))))) & 99.05/14.88 in(Y3, 99.05/14.88 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.05/14.88 inference('lazy_cnf_imply', [status(thm)], ['190'])). 99.05/14.88 tff('192', plain, 99.05/14.88 ~ ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 (!!((^[Y2 : $i]: 99.05/14.88 (in(Y2, setadjoin(Y0, Y1)) => 99.05/14.88 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 99.05/14.88 in(Y1, powerset(Y0))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 99.05/14.88 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 (!!((^[Y2 : $i]: 99.05/14.88 (in(Y1, powerset(Y0)) => 99.05/14.88 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 (!!((^[Y2 : $i]: 99.05/14.88 (in(Y1, Y2) => 99.05/14.88 (in(Y2, Y0) => in(Y1, setunion(Y0))))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 (in(Y1, setunion(Y0)) => 99.05/14.88 (!!((^[Y2 : $o]: 99.05/14.88 ((!!((^[Y3 : $i]: 99.05/14.88 (in(Y1, Y3) => (in(Y3, Y0) => Y2))))) => 99.05/14.88 Y2))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 (in(Y1, Y0) => in(Y1, powerset(setunion(Y0)))))))))) => 99.05/14.88 ((!!((^[Y0 : $i > $o]: 99.05/14.88 ((??((^[Y1 : $i]: 99.05/14.88 (Y0(Y1) & 99.05/14.88 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.88 (??((^[Y1 : $i]: 99.05/14.88 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 (in(Y0, setadjoin(Y1, emptyset)) => (Y0 = Y1)))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 ((Y0 != Y1) => 99.05/14.88 (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 ((Y0 = Y1) => 99.05/14.88 in(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 (in(Y0, setadjoin(Y1, emptyset)) => 99.05/14.88 in(Y1, setadjoin(Y0, emptyset))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 (!!((^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 setadjoin(Y0, 99.05/14.88 setadjoin(Y1, emptyset))) => 99.05/14.88 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 in(Y0, 99.05/14.88 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 in(Y1, 99.05/14.88 setadjoin(Y0, 99.05/14.88 setadjoin(Y1, emptyset))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i > $o]: 99.05/14.88 ((??((^[Y2 : $i]: 99.05/14.88 (in(Y2, Y0) & Y1(Y2))))) => 99.05/14.88 (dsetconstr(Y0, Y1) != emptyset)))))))) => 99.05/14.88 ((!!((^[Y0 : $i > $o]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 (in(Y1, emptyset) => Y0(Y1)))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i > $o]: 99.05/14.88 ((~((!!((^[Y2 : $i]: 99.05/14.88 (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.88 (??((^[Y2 : $i]: 99.05/14.88 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i > $o]: 99.05/14.88 ((!!((^[Y2 : $i]: 99.05/14.88 (in(Y2, Y0) => (~(Y1(Y2))))))) => 99.05/14.88 (~((??((^[Y2 : $i]: 99.05/14.88 (in(Y2, Y0) & Y1(Y2)))))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i > $o]: 99.05/14.88 ((~((??((^[Y2 : $i]: 99.05/14.88 (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.88 (!!((^[Y2 : $i]: 99.05/14.88 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i > $o]: 99.05/14.88 ((??((^[Y2 : $i]: 99.05/14.88 (in(Y2, Y0) & (~(Y1(Y2))))))) => 99.05/14.88 (~((!!((^[Y2 : $i]: 99.05/14.88 (in(Y2, Y0) => Y1(Y2)))))))))))))) => 99.05/14.88 ((!!((^[Y0 : $o]: 99.05/14.88 (Y0 => in(emptyset, prop2set(Y0)))))) => 99.05/14.88 ((!!((^[Y0 : $o]: 99.05/14.88 (Y0 => set2prop(prop2set(Y0)))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i > $o]: 99.05/14.88 ((~((??((^[Y2 : $i]: 99.05/14.88 (in(Y2, Y0) & 99.05/14.88 Y1(Y2))))))) => 99.05/14.88 (!!((^[Y2 : $i]: 99.05/14.88 (in(Y2, Y0) => 99.05/14.88 (~(Y1(Y2)))))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i > $o]: 99.05/14.88 ((~((!!((^[Y2 : $i]: 99.05/14.88 (in(Y2, Y0) => 99.05/14.88 Y1(Y2))))))) => 99.05/14.88 (??((^[Y2 : $i]: 99.05/14.88 (in(Y2, Y0) & 99.05/14.88 (~(Y1(Y2)))))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i > $o]: 99.05/14.88 ((??(Y0)) => 99.05/14.88 ((!!((^[Y1 : $i]: 99.05/14.88 (!!((^[Y2 : $i]: 99.05/14.88 (Y0(Y1) => 99.05/14.88 (Y0(Y2) => 99.05/14.88 (Y1 = Y2))))))))) => 99.05/14.88 (??((^[Y1 : $i]: 99.05/14.88 (Y0(Y1) & 99.05/14.88 (!!((^[Y2 : $i]: 99.05/14.88 (Y0(Y2) => 99.05/14.88 (Y1 = Y2)))))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i > $o]: 99.05/14.88 ((??((^[Y1 : $i]: 99.05/14.88 (!!((^[Y2 : $i]: 99.05/14.88 (Y0(Y2) <=> 99.05/14.88 (Y2 = Y1)))))))) => 99.05/14.88 (??((^[Y1 : $i]: 99.05/14.88 (Y0(Y1) & 99.05/14.88 (!!((^[Y2 : $i]: 99.05/14.88 (Y0(Y2) => 99.05/14.88 (Y1 = Y2))))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 ((Y0 = Y1) => 99.05/14.88 (!!((^[Y2 : $i]: 99.05/14.88 (!!((^[Y3 : $i]: 99.05/14.88 ((Y2 = Y3) => 99.05/14.88 (in(Y2, 99.05/14.88 Y0) => 99.05/14.88 in(Y3, 99.05/14.88 Y1)))))))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 ((Y0 = Y1) => 99.05/14.88 (!!((^[Y2 : $i]: 99.05/14.88 (!!((^[Y3 : $i]: 99.05/14.88 (( 99.05/14.88 Y2 = Y3) => 99.05/14.88 ( 99.05/14.88 in(Y2, 99.05/14.88 Y0) <=> 99.05/14.88 in(Y3, 99.05/14.88 Y1)))))))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i > $o]: 99.05/14.88 ((??((^[Y1 : $i]: 99.05/14.88 (Y0(Y1) & 99.05/14.88 (!!((^[Y2 : $i]: 99.05/14.88 (Y0(Y2) => 99.05/14.88 (Y1 = Y2))))))))) => 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 (!!((^[Y2 : $i]: 99.05/14.88 (Y0(Y1) => 99.05/14.88 (Y0(Y2) => 99.05/14.88 (Y1 = Y2))))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i > $o]: 99.05/14.88 (!!((^[Y1 : $i > $o]: 99.05/14.88 ((!!((^[Y2 : $i]: 99.05/14.88 (!!((^[Y3 : $i]: 99.05/14.88 (( 99.05/14.88 Y2 = Y3) => 99.05/14.88 (Y0(Y2) <=> 99.05/14.88 Y1(Y3))))))))) => 99.05/14.88 ((??((^[Y2 : $i]: 99.05/14.88 (Y0(Y2) & 99.05/14.88 (!!(( 99.05/14.88 ^[Y3 : $i]: 99.05/14.88 (Y0(Y3) => 99.05/14.88 ( 99.05/14.88 Y2 = Y3))))))))) <=> 99.05/14.88 (??((^[Y2 : $i]: 99.05/14.88 (Y1(Y2) & 99.05/14.88 (!!(( 99.05/14.88 ^[Y3 : $i]: 99.05/14.88 (Y1(Y3) => 99.05/14.88 ( 99.05/14.88 Y2 = Y3))))))))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 ((Y0 = Y1) => 99.05/14.88 (!!((^[Y2 : $i]: 99.05/14.88 (!!((^[Y3 : $i]: 99.05/14.88 (( 99.05/14.88 Y2 = Y3) => 99.05/14.88 (setadjoin( 99.05/14.88 Y0, Y2) = 99.05/14.88 setadjoin( 99.05/14.88 Y1, Y3)))))))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 ((Y0 = Y1) => 99.05/14.88 (powerset(Y0) = 99.05/14.88 powerset(Y1))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 ((Y0 = Y1) => 99.05/14.88 (setunion(Y0) = 99.05/14.88 setunion(Y1))))))))) => 99.05/14.88 ((!!((^[Y0 : $i > $o]: 99.05/14.88 ((??((^[Y1 : $i]: 99.05/14.88 (Y0(Y1) & 99.05/14.88 (!!((^[Y2 : $i]: 99.05/14.88 (Y0(Y2) => 99.05/14.88 ( 99.05/14.88 Y1 = Y2))))))))) => 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 (!!((^[Y2 : $i]: 99.05/14.88 (Y0(Y1) => 99.05/14.88 (Y0(Y2) => 99.05/14.88 ( 99.05/14.88 Y1 = Y2))))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i > $o]: 99.05/14.88 (!!((^[Y1 : $i > $o]: 99.05/14.88 ((!!((^[Y2 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y3 : $i]: 99.05/14.88 (( 99.05/14.88 Y2 = Y3) => 99.05/14.88 (Y0(Y2) <=> 99.05/14.88 Y1(Y3))))))))) => 99.05/14.88 ((??((^[Y2 : $i]: 99.05/14.88 ( 99.05/14.88 Y0(Y2) & 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y3 : $i]: 99.05/14.88 (Y0(Y3) => 99.05/14.88 (Y2 = Y3))))))))) => 99.05/14.88 ((??((^[Y2 : $i]: 99.05/14.88 (Y1(Y2) & 99.05/14.88 (!!(( 99.05/14.88 ^[Y3 : $i]: 99.05/14.88 (Y1(Y3) => 99.05/14.88 (Y2 = Y3))))))))) => 99.05/14.88 (descr(Y0) = 99.05/14.88 descr(Y1))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 ((Y0 = Y1) => 99.05/14.88 (!!((^[Y2 : $i > $o]: 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y3 : $i > $o]: 99.05/14.88 (( 99.05/14.88 !!(( 99.05/14.88 ^[Y4 : $i]: 99.05/14.88 (in(Y4, 99.05/14.88 Y0) => 99.05/14.88 (!!(( 99.05/14.88 ^[Y5 : $i]: 99.05/14.88 (in(Y5, 99.05/14.88 Y1) => 99.05/14.88 (( 99.05/14.88 Y4 = Y5) => 99.05/14.88 (Y2(Y4) <=> 99.05/14.88 Y3(Y5))))))))))) => 99.05/14.88 (dsetconstr( 99.05/14.88 Y0, Y2) = 99.05/14.88 dsetconstr( 99.05/14.88 Y1, Y3)))))))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 ((!!((^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 Y0) => 99.05/14.88 in(Y2, 99.05/14.88 Y1))))) => 99.05/14.88 subset(Y0, Y1)))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 ((Y0 = Y1) => 99.05/14.88 subset(Y1, Y0)))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 ((Y0 = Y1) => 99.05/14.88 subset(Y0, 99.05/14.88 Y1)))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 ((!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 ( 99.05/14.88 in(Y2, 99.05/14.88 Y0) => 99.05/14.88 in(Y2, 99.05/14.88 Y1))))) => 99.05/14.88 subset(Y0, 99.05/14.88 Y1)))))))) => 99.05/14.88 ((!!(subset(emptyset))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (subset( 99.05/14.88 Y0, Y1) => 99.05/14.88 (in(Y2, 99.05/14.88 Y0) => 99.05/14.88 in(Y2, 99.05/14.88 Y1)))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (subset( 99.05/14.88 Y0, Y1) => 99.05/14.88 (( 99.05/14.88 ~( 99.05/14.88 in(Y2, 99.05/14.88 Y1))) => 99.05/14.88 (~( 99.05/14.88 in(Y2, 99.05/14.88 Y0)))))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 Y0) => 99.05/14.88 (( 99.05/14.88 ~( 99.05/14.88 in(Y2, 99.05/14.88 Y1))) => 99.05/14.88 (~( 99.05/14.88 subset( 99.05/14.88 Y0, Y1)))))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 (( 99.05/14.88 ~( 99.05/14.88 subset( 99.05/14.88 Y0, Y1))) => 99.05/14.88 (Y0 != Y1)))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!((^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 Y0) => 99.05/14.88 (( 99.05/14.88 ~( 99.05/14.88 in(Y2, 99.05/14.88 Y1))) => 99.05/14.88 (Y0 != Y1)))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 subset(Y0, 99.05/14.88 Y0)))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (subset( 99.05/14.88 Y0, Y1) => 99.05/14.88 (subset( 99.05/14.88 Y1, Y2) => 99.05/14.88 subset( 99.05/14.88 Y0, Y2)))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 subset( 99.05/14.88 Y1, 99.05/14.88 setadjoin( 99.05/14.88 Y0, Y1)))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (subset( 99.05/14.88 Y0, Y2) => 99.05/14.88 subset( 99.05/14.88 Y0, 99.05/14.88 setadjoin( 99.05/14.88 Y1, Y2)))))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (subset( 99.05/14.88 Y0, Y1) => 99.05/14.88 in(Y0, 99.05/14.88 powerset( 99.05/14.88 Y1))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (subset( 99.05/14.88 Y0, Y1) => 99.05/14.88 (subset( 99.05/14.88 Y1, Y0) => 99.05/14.88 (Y0 = Y1))))))))) => 99.05/14.88 ((!!((^[Y0 : $i]: 99.05/14.88 (subset( 99.05/14.88 Y0, 99.05/14.88 emptyset) => 99.05/14.88 (Y0 = 99.05/14.88 emptyset))))) => 99.05/14.88 ((!!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (subset( 99.05/14.88 Y1, Y0) => 99.05/14.88 in(Y1, 99.05/14.88 powerset( 99.05/14.88 Y0))))))))) => 99.05/14.88 ((!!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (in(Y1, 99.05/14.88 powerset( 99.05/14.88 Y0)) => 99.05/14.88 subset( 99.05/14.88 Y1, Y0)))))))) => 99.05/14.88 ((!!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 in(Y0, 99.05/14.88 powerset( 99.05/14.88 Y0))))) => 99.05/14.88 ((!!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (subset( 99.05/14.88 Y0, Y1) => 99.05/14.88 subset( 99.05/14.88 powerset( 99.05/14.88 Y0), 99.05/14.88 powerset( 99.05/14.88 Y1))))))))) => 99.05/14.88 (( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i > $o]: 99.05/14.88 in( 99.05/14.88 dsetconstr( 99.05/14.88 Y0, Y1), 99.05/14.88 powerset( 99.05/14.88 Y0)))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i > $o]: 99.05/14.88 subset( 99.05/14.88 dsetconstr( 99.05/14.88 Y0, Y1), 99.05/14.88 Y0))))))) => 99.05/14.88 ( 99.05/14.88 ( 99.05/14.88 !!(( 99.05/14.88 ^[Y0 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y1 : $i]: 99.05/14.88 (!!(( 99.05/14.88 ^[Y2 : $i]: 99.05/14.88 (in(Y2, 99.05/14.88 Y0) => 99.05/14.89 in(Y2, 99.05/14.89 binunion( 99.05/14.89 Y0, Y1)))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 in(Y1, 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y1) => 99.05/14.89 in(Y2, 99.05/14.89 binunion( 99.05/14.89 Y0, Y1)))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y3 : $o]: 99.05/14.89 (in(Y2, 99.05/14.89 binunion( 99.05/14.89 Y0, Y1)) => 99.05/14.89 (( 99.05/14.89 in(Y2, 99.05/14.89 Y0) => Y3) => 99.05/14.89 (( 99.05/14.89 in(Y2, 99.05/14.89 Y1) => Y3) => 99.05/14.89 Y3))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 binunion( 99.05/14.89 Y0, Y1)) => 99.05/14.89 (in(Y2, 99.05/14.89 Y1) | 99.05/14.89 in(Y2, 99.05/14.89 Y0)))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 subset( 99.05/14.89 Y0, 99.05/14.89 binunion( 99.05/14.89 Y0, Y1)))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 subset( 99.05/14.89 Y1, 99.05/14.89 binunion( 99.05/14.89 Y0, Y1)))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (in(Y2, 99.05/14.89 Y1) => 99.05/14.89 in(Y2, 99.05/14.89 binintersect( 99.05/14.89 Y0, Y1))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (subset( 99.05/14.89 Y2, Y0) => 99.05/14.89 (subset( 99.05/14.89 Y2, Y1) => 99.05/14.89 subset( 99.05/14.89 Y2, 99.05/14.89 binintersect( 99.05/14.89 Y0, Y1))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 binintersect( 99.05/14.89 Y0, Y1)) => 99.05/14.89 in(Y2, 99.05/14.89 Y0))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 subset( 99.05/14.89 binintersect( 99.05/14.89 Y0, Y1), 99.05/14.89 Y0))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (subset( 99.05/14.89 Y0, Y1) => 99.05/14.89 (binintersect( 99.05/14.89 Y0, Y1) = 99.05/14.89 Y0)))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (( 99.05/14.89 binintersect( 99.05/14.89 Y0, Y1) = 99.05/14.89 Y1) => 99.05/14.89 subset( 99.05/14.89 Y1, Y0)))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 binintersect( 99.05/14.89 Y0, Y1)) => 99.05/14.89 in(Y2, 99.05/14.89 Y1))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (( 99.05/14.89 ~(( 99.05/14.89 ??(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) & 99.05/14.89 in(Y2, 99.05/14.89 Y1))))))) => 99.05/14.89 (binintersect( 99.05/14.89 Y0, Y1) = 99.05/14.89 emptyset)))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 subset( 99.05/14.89 binintersect( 99.05/14.89 Y0, Y1), 99.05/14.89 Y1))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (subset( 99.05/14.89 Y1, Y0) => 99.05/14.89 (binintersect( 99.05/14.89 Y0, Y1) = 99.05/14.89 Y1)))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (( 99.05/14.89 binintersect( 99.05/14.89 Y0, Y1) = 99.05/14.89 Y0) => 99.05/14.89 subset( 99.05/14.89 Y0, Y1)))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (binintersect( 99.05/14.89 Y0, 99.05/14.89 binunion( 99.05/14.89 Y1, Y2)) = 99.05/14.89 binunion( 99.05/14.89 binintersect( 99.05/14.89 Y0, Y1), 99.05/14.89 binintersect( 99.05/14.89 Y0, Y2)))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y1))) => 99.05/14.89 in(Y2, 99.05/14.89 setminus( 99.05/14.89 Y0, Y1))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 setminus( 99.05/14.89 Y0, Y1)) => 99.05/14.89 in(Y2, 99.05/14.89 Y0))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 setminus( 99.05/14.89 Y0, Y1)) => 99.05/14.89 (~( 99.05/14.89 in(Y2, 99.05/14.89 Y1))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (subset( 99.05/14.89 Y0, Y1) => 99.05/14.89 (setminus( 99.05/14.89 Y0, Y1) = 99.05/14.89 emptyset)))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 setminus( 99.05/14.89 Y0, Y1)))) => 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 in(Y2, 99.05/14.89 Y1)))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 setminus( 99.05/14.89 Y0, Y1)))) => 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y1))) => 99.05/14.89 (~( 99.05/14.89 in(Y2, 99.05/14.89 Y0)))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y0))) => 99.05/14.89 (~( 99.05/14.89 in(Y2, 99.05/14.89 setminus( 99.05/14.89 Y0, Y1)))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y1) => 99.05/14.89 (~( 99.05/14.89 in(Y2, 99.05/14.89 setminus( 99.05/14.89 Y0, Y1)))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 subset( 99.05/14.89 setminus( 99.05/14.89 Y0, Y1), 99.05/14.89 Y0))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (( 99.05/14.89 setminus( 99.05/14.89 Y0, Y1) = 99.05/14.89 emptyset) => 99.05/14.89 subset( 99.05/14.89 Y0, Y1)))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 symdiff( 99.05/14.89 Y0, Y1)) => 99.05/14.89 (!!(( 99.05/14.89 ^[Y3 : $o]: 99.05/14.89 (( 99.05/14.89 in(Y2, 99.05/14.89 Y0) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y1))) => 99.05/14.89 Y3)) => 99.05/14.89 (( 99.05/14.89 ( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y0))) => 99.05/14.89 ( 99.05/14.89 in(Y2, 99.05/14.89 Y1) => Y3)) => 99.05/14.89 Y3))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y1))) => 99.05/14.89 in(Y2, 99.05/14.89 symdiff( 99.05/14.89 Y0, Y1))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y0))) => 99.05/14.89 (in(Y2, 99.05/14.89 Y1) => 99.05/14.89 in(Y2, 99.05/14.89 symdiff( 99.05/14.89 Y0, Y1))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (in(Y2, 99.05/14.89 Y1) => 99.05/14.89 (~( 99.05/14.89 in(Y2, 99.05/14.89 symdiff( 99.05/14.89 Y0, Y1))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y0))) => 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y1))) => 99.05/14.89 (~( 99.05/14.89 in(Y2, 99.05/14.89 symdiff( 99.05/14.89 Y0, Y1))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 in(Y1, 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 in(Y0, 99.05/14.89 setunion( 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 in(Y1, 99.05/14.89 setunion( 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (??(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 setunion( 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)))) & 99.05/14.89 (??(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (in(Y3, 99.05/14.89 setunion( 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)))) & 99.05/14.89 (setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)) = 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 setadjoin( 99.05/14.89 Y3, 99.05/14.89 emptyset)), 99.05/14.89 emptyset))))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (??(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 setunion( 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)))) & 99.05/14.89 (??(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (in(Y3, 99.05/14.89 setunion( 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)))) & 99.05/14.89 (setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)) = 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 setadjoin( 99.05/14.89 Y3, 99.05/14.89 emptyset)), 99.05/14.89 emptyset))))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (in(Y1, 99.05/14.89 Y0) => 99.05/14.89 subset( 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset), 99.05/14.89 Y0)))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (in(Y1, 99.05/14.89 Y0) => 99.05/14.89 in( 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset), 99.05/14.89 powerset( 99.05/14.89 Y0))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 in( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 emptyset), 99.05/14.89 powerset( 99.05/14.89 binunion( 99.05/14.89 Y0, Y1))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset))) => 99.05/14.89 (( 99.05/14.89 Y2 = Y1) | 99.05/14.89 (Y2 = Y0)))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (!!(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (in(Y3, 99.05/14.89 Y1) => 99.05/14.89 subset( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 setadjoin( 99.05/14.89 Y3, 99.05/14.89 emptyset)), 99.05/14.89 binunion( 99.05/14.89 Y0, Y1)))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (!!(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (in(Y3, 99.05/14.89 Y1) => 99.05/14.89 in( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 setadjoin( 99.05/14.89 Y3, 99.05/14.89 emptyset)), 99.05/14.89 powerset( 99.05/14.89 binunion( 99.05/14.89 Y0, Y1))))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (!!(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (in(Y3, 99.05/14.89 Y1) => 99.05/14.89 subset( 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 setadjoin( 99.05/14.89 Y3, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)), 99.05/14.89 powerset( 99.05/14.89 binunion( 99.05/14.89 Y0, Y1))))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (!!(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (in(Y3, 99.05/14.89 Y1) => 99.05/14.89 in( 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 setadjoin( 99.05/14.89 Y3, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)), 99.05/14.89 powerset( 99.05/14.89 powerset( 99.05/14.89 binunion( 99.05/14.89 Y0, Y1)))))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (!!(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (in(Y3, 99.05/14.89 Y1) => 99.05/14.89 in( 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 setadjoin( 99.05/14.89 Y3, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)), 99.05/14.89 powerset( 99.05/14.89 powerset( 99.05/14.89 binunion( 99.05/14.89 Y0, Y1)))))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (!!(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (in(Y3, 99.05/14.89 Y1) => 99.05/14.89 in( 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 setadjoin( 99.05/14.89 Y3, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)), 99.05/14.89 dsetconstr( 99.05/14.89 powerset( 99.05/14.89 powerset( 99.05/14.89 binunion( 99.05/14.89 Y0, Y1))), 99.05/14.89 (^[Y4 : $i]: 99.05/14.89 (??(( 99.05/14.89 ^[Y5 : $i]: 99.05/14.89 (in(Y5, 99.05/14.89 Y0) & 99.05/14.89 (??(( 99.05/14.89 ^[Y6 : $i]: 99.05/14.89 (in(Y6, 99.05/14.89 Y1) & 99.05/14.89 (Y4 = 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y5, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y5, 99.05/14.89 setadjoin( 99.05/14.89 Y6, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)))))))))))))))))))))))))))) => 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 dsetconstr( 99.05/14.89 powerset( 99.05/14.89 powerset( 99.05/14.89 binunion( 99.05/14.89 Y0, Y1))), 99.05/14.89 (^[Y3 : $i]: 99.05/14.89 (??(( 99.05/14.89 ^[Y4 : $i]: 99.05/14.89 (in(Y4, 99.05/14.89 Y0) & 99.05/14.89 (??(( 99.05/14.89 ^[Y5 : $i]: 99.05/14.89 (in(Y5, 99.05/14.89 Y1) & 99.05/14.89 (Y3 = 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y4, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y4, 99.05/14.89 setadjoin( 99.05/14.89 Y5, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)))))))))))))) => 99.05/14.89 (??(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (( 99.05/14.89 ??(( 99.05/14.89 ^[Y4 : $i]: 99.05/14.89 (in(Y4, 99.05/14.89 Y1) & 99.05/14.89 (Y2 = 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y3, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y3, 99.05/14.89 setadjoin( 99.05/14.89 Y4, 99.05/14.89 emptyset)), 99.05/14.89 emptyset))))))) & 99.05/14.89 in(Y3, 99.05/14.89 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.05/14.89 inference('lazy_cnf_imply', [status(thm)], ['191'])). 99.05/14.89 tff('193', plain, 99.05/14.89 ~ ((!!((^[Y0 : $i]: (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 99.05/14.89 in(Y1, powerset(Y0))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 99.05/14.89 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (in(Y1, powerset(Y0)) => 99.05/14.89 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (in(Y1, Y2) => 99.05/14.89 (in(Y2, Y0) => in(Y1, setunion(Y0))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (in(Y1, setunion(Y0)) => 99.05/14.89 (!!((^[Y2 : $o]: 99.05/14.89 ((!!((^[Y3 : $i]: 99.05/14.89 (in(Y1, Y3) => (in(Y3, Y0) => Y2))))) => 99.05/14.89 Y2))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (in(Y1, Y0) => in(Y1, powerset(setunion(Y0)))))))))) => 99.05/14.89 ((!!((^[Y0 : $i > $o]: 99.05/14.89 ((??((^[Y1 : $i]: 99.05/14.89 (Y0(Y1) & 99.05/14.89 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.89 (??((^[Y1 : $i]: 99.05/14.89 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (in(Y0, setadjoin(Y1, emptyset)) => (Y0 = Y1)))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((Y0 != Y1) => 99.05/14.89 (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((Y0 = Y1) => 99.05/14.89 in(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (in(Y0, setadjoin(Y1, emptyset)) => 99.05/14.89 in(Y1, setadjoin(Y0, emptyset))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 setadjoin(Y0, 99.05/14.89 setadjoin(Y1, emptyset))) => 99.05/14.89 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 in(Y0, 99.05/14.89 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 in(Y1, 99.05/14.89 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i > $o]: 99.05/14.89 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 99.05/14.89 (dsetconstr(Y0, Y1) != emptyset)))))))) => 99.05/14.89 ((!!((^[Y0 : $i > $o]: 99.05/14.89 (!!((^[Y1 : $i]: (in(Y1, emptyset) => Y0(Y1)))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i > $o]: 99.05/14.89 ((~((!!((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.89 (??((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i > $o]: 99.05/14.89 ((!!((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) => (~(Y1(Y2))))))) => 99.05/14.89 (~((??((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) & Y1(Y2)))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i > $o]: 99.05/14.89 ((~((??((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i > $o]: 99.05/14.89 ((??((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) & (~(Y1(Y2))))))) => 99.05/14.89 (~((!!((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) => Y1(Y2)))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $o]: 99.05/14.89 (Y0 => in(emptyset, prop2set(Y0)))))) => 99.05/14.89 ((!!((^[Y0 : $o]: 99.05/14.89 (Y0 => set2prop(prop2set(Y0)))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i > $o]: 99.05/14.89 ((~((??((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) => 99.05/14.89 (~(Y1(Y2)))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i > $o]: 99.05/14.89 ((~((!!((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) => 99.05/14.89 Y1(Y2))))))) => 99.05/14.89 (??((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) & 99.05/14.89 (~(Y1(Y2)))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i > $o]: 99.05/14.89 ((??(Y0)) => 99.05/14.89 ((!!((^[Y1 : $i]: 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (Y0(Y1) => 99.05/14.89 (Y0(Y2) => 99.05/14.89 (Y1 = Y2))))))))) => 99.05/14.89 (??((^[Y1 : $i]: 99.05/14.89 (Y0(Y1) & 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (Y0(Y2) => 99.05/14.89 (Y1 = Y2)))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i > $o]: 99.05/14.89 ((??((^[Y1 : $i]: 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (Y0(Y2) <=> 99.05/14.89 (Y2 = Y1)))))))) => 99.05/14.89 (??((^[Y1 : $i]: 99.05/14.89 (Y0(Y1) & 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (Y0(Y2) => 99.05/14.89 (Y1 = Y2))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((Y0 = Y1) => 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (!!((^[Y3 : $i]: 99.05/14.89 ((Y2 = Y3) => 99.05/14.89 (in(Y2, Y0) => 99.05/14.89 in(Y3, Y1)))))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((Y0 = Y1) => 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (!!((^[Y3 : $i]: 99.05/14.89 ((Y2 = Y3) => 99.05/14.89 (in(Y2, 99.05/14.89 Y0) <=> 99.05/14.89 in(Y3, 99.05/14.89 Y1)))))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i > $o]: 99.05/14.89 ((??((^[Y1 : $i]: 99.05/14.89 (Y0(Y1) & 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (Y0(Y2) => 99.05/14.89 (Y1 = Y2))))))))) => 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (Y0(Y1) => 99.05/14.89 (Y0(Y2) => 99.05/14.89 (Y1 = Y2))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i > $o]: 99.05/14.89 (!!((^[Y1 : $i > $o]: 99.05/14.89 ((!!((^[Y2 : $i]: 99.05/14.89 (!!((^[Y3 : $i]: 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 Y2 = Y3) => 99.05/14.89 ( 99.05/14.89 Y0(Y2) <=> 99.05/14.89 Y1(Y3))))))))) => 99.05/14.89 ((??((^[Y2 : $i]: 99.05/14.89 (Y0(Y2) & 99.05/14.89 (!!((^[Y3 : $i]: 99.05/14.89 (Y0(Y3) => 99.05/14.89 (Y2 = Y3))))))))) <=> 99.05/14.89 (??((^[Y2 : $i]: 99.05/14.89 (Y1(Y2) & 99.05/14.89 (!!((^[Y3 : $i]: 99.05/14.89 (Y1(Y3) => 99.05/14.89 (Y2 = Y3))))))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((Y0 = Y1) => 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (!!((^[Y3 : $i]: 99.05/14.89 (( 99.05/14.89 Y2 = Y3) => 99.05/14.89 (setadjoin( 99.05/14.89 Y0, Y2) = 99.05/14.89 setadjoin( 99.05/14.89 Y1, Y3)))))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((Y0 = Y1) => 99.05/14.89 (powerset(Y0) = 99.05/14.89 powerset(Y1))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((Y0 = Y1) => 99.05/14.89 (setunion(Y0) = 99.05/14.89 setunion(Y1))))))))) => 99.05/14.89 ((!!((^[Y0 : $i > $o]: 99.05/14.89 ((??((^[Y1 : $i]: 99.05/14.89 (Y0(Y1) & 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (Y0(Y2) => 99.05/14.89 (Y1 = Y2))))))))) => 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (Y0(Y1) => 99.05/14.89 (Y0(Y2) => 99.05/14.89 (Y1 = Y2))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i > $o]: 99.05/14.89 (!!((^[Y1 : $i > $o]: 99.05/14.89 ((!!((^[Y2 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (( 99.05/14.89 Y2 = Y3) => 99.05/14.89 (Y0(Y2) <=> 99.05/14.89 Y1(Y3))))))))) => 99.05/14.89 ((??((^[Y2 : $i]: 99.05/14.89 (Y0(Y2) & 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (Y0(Y3) => 99.05/14.89 (Y2 = Y3))))))))) => 99.05/14.89 ((??((^[Y2 : $i]: 99.05/14.89 ( 99.05/14.89 Y1(Y2) & 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (Y1(Y3) => 99.05/14.89 (Y2 = Y3))))))))) => 99.05/14.89 (descr(Y0) = 99.05/14.89 descr(Y1))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((Y0 = Y1) => 99.05/14.89 (!!((^[Y2 : $i > $o]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y3 : $i > $o]: 99.05/14.89 (( 99.05/14.89 !!(( 99.05/14.89 ^[Y4 : $i]: 99.05/14.89 (in(Y4, 99.05/14.89 Y0) => 99.05/14.89 (!!(( 99.05/14.89 ^[Y5 : $i]: 99.05/14.89 (in(Y5, 99.05/14.89 Y1) => 99.05/14.89 (( 99.05/14.89 Y4 = Y5) => 99.05/14.89 (Y2(Y4) <=> 99.05/14.89 Y3(Y5))))))))))) => 99.05/14.89 (dsetconstr( 99.05/14.89 Y0, Y2) = 99.05/14.89 dsetconstr( 99.05/14.89 Y1, Y3)))))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((!!((^[Y2 : $i]: 99.05/14.89 ( 99.05/14.89 in(Y2, 99.05/14.89 Y0) => 99.05/14.89 in(Y2, 99.05/14.89 Y1))))) => 99.05/14.89 subset(Y0, Y1)))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((Y0 = Y1) => 99.05/14.89 subset(Y1, Y0)))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((Y0 = Y1) => 99.05/14.89 subset(Y0, Y1)))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 in(Y2, 99.05/14.89 Y1))))) => 99.05/14.89 subset(Y0, 99.05/14.89 Y1)))))))) => 99.05/14.89 ((!!(subset(emptyset))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 ( 99.05/14.89 subset( 99.05/14.89 Y0, Y1) => 99.05/14.89 ( 99.05/14.89 in(Y2, 99.05/14.89 Y0) => 99.05/14.89 in(Y2, 99.05/14.89 Y1)))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (subset( 99.05/14.89 Y0, Y1) => 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y1))) => 99.05/14.89 (~( 99.05/14.89 in(Y2, 99.05/14.89 Y0)))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y1))) => 99.05/14.89 (~( 99.05/14.89 subset( 99.05/14.89 Y0, Y1)))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 ~( 99.05/14.89 subset( 99.05/14.89 Y0, Y1))) => 99.05/14.89 ( 99.05/14.89 Y0 != Y1)))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y1))) => 99.05/14.89 (Y0 != Y1)))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 subset(Y0, Y0)))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (subset( 99.05/14.89 Y0, Y1) => 99.05/14.89 (subset( 99.05/14.89 Y1, Y2) => 99.05/14.89 subset( 99.05/14.89 Y0, Y2)))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 subset( 99.05/14.89 Y1, 99.05/14.89 setadjoin( 99.05/14.89 Y0, Y1)))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (subset( 99.05/14.89 Y0, Y2) => 99.05/14.89 subset( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, Y2)))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (subset( 99.05/14.89 Y0, Y1) => 99.05/14.89 in(Y0, 99.05/14.89 powerset( 99.05/14.89 Y1))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (subset( 99.05/14.89 Y0, Y1) => 99.05/14.89 (subset( 99.05/14.89 Y1, Y0) => 99.05/14.89 (Y0 = Y1))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (subset( 99.05/14.89 Y0, 99.05/14.89 emptyset) => 99.05/14.89 (Y0 = 99.05/14.89 emptyset))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (subset( 99.05/14.89 Y1, Y0) => 99.05/14.89 in(Y1, 99.05/14.89 powerset( 99.05/14.89 Y0))))))))) => 99.05/14.89 ((!!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (in(Y1, 99.05/14.89 powerset( 99.05/14.89 Y0)) => 99.05/14.89 subset( 99.05/14.89 Y1, Y0)))))))) => 99.05/14.89 ((!!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 in(Y0, 99.05/14.89 powerset( 99.05/14.89 Y0))))) => 99.05/14.89 ((!!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (subset( 99.05/14.89 Y0, Y1) => 99.05/14.89 subset( 99.05/14.89 powerset( 99.05/14.89 Y0), 99.05/14.89 powerset( 99.05/14.89 Y1))))))))) => 99.05/14.89 ((!!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i > $o]: 99.05/14.89 in( 99.05/14.89 dsetconstr( 99.05/14.89 Y0, Y1), 99.05/14.89 powerset( 99.05/14.89 Y0)))))))) => 99.05/14.89 (( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i > $o]: 99.05/14.89 subset( 99.05/14.89 dsetconstr( 99.05/14.89 Y0, Y1), 99.05/14.89 Y0))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 in(Y2, 99.05/14.89 binunion( 99.05/14.89 Y0, Y1)))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 in(Y1, 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y1) => 99.05/14.89 in(Y2, 99.05/14.89 binunion( 99.05/14.89 Y0, Y1)))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y3 : $o]: 99.05/14.89 (in(Y2, 99.05/14.89 binunion( 99.05/14.89 Y0, Y1)) => 99.05/14.89 (( 99.05/14.89 in(Y2, 99.05/14.89 Y0) => Y3) => 99.05/14.89 (( 99.05/14.89 in(Y2, 99.05/14.89 Y1) => Y3) => 99.05/14.89 Y3))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 binunion( 99.05/14.89 Y0, Y1)) => 99.05/14.89 (in(Y2, 99.05/14.89 Y1) | 99.05/14.89 in(Y2, 99.05/14.89 Y0)))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 subset( 99.05/14.89 Y0, 99.05/14.89 binunion( 99.05/14.89 Y0, Y1)))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 subset( 99.05/14.89 Y1, 99.05/14.89 binunion( 99.05/14.89 Y0, Y1)))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (in(Y2, 99.05/14.89 Y1) => 99.05/14.89 in(Y2, 99.05/14.89 binintersect( 99.05/14.89 Y0, Y1))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (subset( 99.05/14.89 Y2, Y0) => 99.05/14.89 (subset( 99.05/14.89 Y2, Y1) => 99.05/14.89 subset( 99.05/14.89 Y2, 99.05/14.89 binintersect( 99.05/14.89 Y0, Y1))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 binintersect( 99.05/14.89 Y0, Y1)) => 99.05/14.89 in(Y2, 99.05/14.89 Y0))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 subset( 99.05/14.89 binintersect( 99.05/14.89 Y0, Y1), 99.05/14.89 Y0))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (subset( 99.05/14.89 Y0, Y1) => 99.05/14.89 (binintersect( 99.05/14.89 Y0, Y1) = 99.05/14.89 Y0)))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (( 99.05/14.89 binintersect( 99.05/14.89 Y0, Y1) = 99.05/14.89 Y1) => 99.05/14.89 subset( 99.05/14.89 Y1, Y0)))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 binintersect( 99.05/14.89 Y0, Y1)) => 99.05/14.89 in(Y2, 99.05/14.89 Y1))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (( 99.05/14.89 ~(( 99.05/14.89 ??(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) & 99.05/14.89 in(Y2, 99.05/14.89 Y1))))))) => 99.05/14.89 (binintersect( 99.05/14.89 Y0, Y1) = 99.05/14.89 emptyset)))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 subset( 99.05/14.89 binintersect( 99.05/14.89 Y0, Y1), 99.05/14.89 Y1))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (subset( 99.05/14.89 Y1, Y0) => 99.05/14.89 (binintersect( 99.05/14.89 Y0, Y1) = 99.05/14.89 Y1)))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (( 99.05/14.89 binintersect( 99.05/14.89 Y0, Y1) = 99.05/14.89 Y0) => 99.05/14.89 subset( 99.05/14.89 Y0, Y1)))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (binintersect( 99.05/14.89 Y0, 99.05/14.89 binunion( 99.05/14.89 Y1, Y2)) = 99.05/14.89 binunion( 99.05/14.89 binintersect( 99.05/14.89 Y0, Y1), 99.05/14.89 binintersect( 99.05/14.89 Y0, Y2)))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y1))) => 99.05/14.89 in(Y2, 99.05/14.89 setminus( 99.05/14.89 Y0, Y1))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 setminus( 99.05/14.89 Y0, Y1)) => 99.05/14.89 in(Y2, 99.05/14.89 Y0))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 setminus( 99.05/14.89 Y0, Y1)) => 99.05/14.89 (~( 99.05/14.89 in(Y2, 99.05/14.89 Y1))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (subset( 99.05/14.89 Y0, Y1) => 99.05/14.89 (setminus( 99.05/14.89 Y0, Y1) = 99.05/14.89 emptyset)))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 setminus( 99.05/14.89 Y0, Y1)))) => 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 in(Y2, 99.05/14.89 Y1)))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 setminus( 99.05/14.89 Y0, Y1)))) => 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y1))) => 99.05/14.89 (~( 99.05/14.89 in(Y2, 99.05/14.89 Y0)))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y0))) => 99.05/14.89 (~( 99.05/14.89 in(Y2, 99.05/14.89 setminus( 99.05/14.89 Y0, Y1)))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y1) => 99.05/14.89 (~( 99.05/14.89 in(Y2, 99.05/14.89 setminus( 99.05/14.89 Y0, Y1)))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 subset( 99.05/14.89 setminus( 99.05/14.89 Y0, Y1), 99.05/14.89 Y0))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (( 99.05/14.89 setminus( 99.05/14.89 Y0, Y1) = 99.05/14.89 emptyset) => 99.05/14.89 subset( 99.05/14.89 Y0, Y1)))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 symdiff( 99.05/14.89 Y0, Y1)) => 99.05/14.89 (!!(( 99.05/14.89 ^[Y3 : $o]: 99.05/14.89 (( 99.05/14.89 in(Y2, 99.05/14.89 Y0) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y1))) => 99.05/14.89 Y3)) => 99.05/14.89 (( 99.05/14.89 ( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y0))) => 99.05/14.89 ( 99.05/14.89 in(Y2, 99.05/14.89 Y1) => Y3)) => 99.05/14.89 Y3))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y1))) => 99.05/14.89 in(Y2, 99.05/14.89 symdiff( 99.05/14.89 Y0, Y1))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y0))) => 99.05/14.89 (in(Y2, 99.05/14.89 Y1) => 99.05/14.89 in(Y2, 99.05/14.89 symdiff( 99.05/14.89 Y0, Y1))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (in(Y2, 99.05/14.89 Y1) => 99.05/14.89 (~( 99.05/14.89 in(Y2, 99.05/14.89 symdiff( 99.05/14.89 Y0, Y1))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y0))) => 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y1))) => 99.05/14.89 (~( 99.05/14.89 in(Y2, 99.05/14.89 symdiff( 99.05/14.89 Y0, Y1))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 in(Y1, 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 in(Y0, 99.05/14.89 setunion( 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 in(Y1, 99.05/14.89 setunion( 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (??(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 setunion( 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)))) & 99.05/14.89 (??(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (in(Y3, 99.05/14.89 setunion( 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)))) & 99.05/14.89 (setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)) = 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 setadjoin( 99.05/14.89 Y3, 99.05/14.89 emptyset)), 99.05/14.89 emptyset))))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (??(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 setunion( 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)))) & 99.05/14.89 (??(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (in(Y3, 99.05/14.89 setunion( 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)))) & 99.05/14.89 (setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)) = 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 setadjoin( 99.05/14.89 Y3, 99.05/14.89 emptyset)), 99.05/14.89 emptyset))))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (in(Y1, 99.05/14.89 Y0) => 99.05/14.89 subset( 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset), 99.05/14.89 Y0)))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (in(Y1, 99.05/14.89 Y0) => 99.05/14.89 in( 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset), 99.05/14.89 powerset( 99.05/14.89 Y0))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 in( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 emptyset), 99.05/14.89 powerset( 99.05/14.89 binunion( 99.05/14.89 Y0, Y1))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset))) => 99.05/14.89 (( 99.05/14.89 Y2 = Y1) | 99.05/14.89 (Y2 = Y0)))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (!!(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (in(Y3, 99.05/14.89 Y1) => 99.05/14.89 subset( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 setadjoin( 99.05/14.89 Y3, 99.05/14.89 emptyset)), 99.05/14.89 binunion( 99.05/14.89 Y0, Y1)))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (!!(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (in(Y3, 99.05/14.89 Y1) => 99.05/14.89 in( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 setadjoin( 99.05/14.89 Y3, 99.05/14.89 emptyset)), 99.05/14.89 powerset( 99.05/14.89 binunion( 99.05/14.89 Y0, Y1))))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (!!(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (in(Y3, 99.05/14.89 Y1) => 99.05/14.89 subset( 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 setadjoin( 99.05/14.89 Y3, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)), 99.05/14.89 powerset( 99.05/14.89 binunion( 99.05/14.89 Y0, Y1))))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (!!(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (in(Y3, 99.05/14.89 Y1) => 99.05/14.89 in( 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 setadjoin( 99.05/14.89 Y3, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)), 99.05/14.89 powerset( 99.05/14.89 powerset( 99.05/14.89 binunion( 99.05/14.89 Y0, Y1)))))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (!!(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (in(Y3, 99.05/14.89 Y1) => 99.05/14.89 in( 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 setadjoin( 99.05/14.89 Y3, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)), 99.05/14.89 powerset( 99.05/14.89 powerset( 99.05/14.89 binunion( 99.05/14.89 Y0, Y1)))))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (!!(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (in(Y3, 99.05/14.89 Y1) => 99.05/14.89 in( 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 setadjoin( 99.05/14.89 Y3, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)), 99.05/14.89 dsetconstr( 99.05/14.89 powerset( 99.05/14.89 powerset( 99.05/14.89 binunion( 99.05/14.89 Y0, Y1))), 99.05/14.89 (^[Y4 : $i]: 99.05/14.89 (??(( 99.05/14.89 ^[Y5 : $i]: 99.05/14.89 (in(Y5, 99.05/14.89 Y0) & 99.05/14.89 (??(( 99.05/14.89 ^[Y6 : $i]: 99.05/14.89 (in(Y6, 99.05/14.89 Y1) & 99.05/14.89 (Y4 = 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y5, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y5, 99.05/14.89 setadjoin( 99.05/14.89 Y6, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)))))))))))))))))))))))))))) => 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 dsetconstr( 99.05/14.89 powerset( 99.05/14.89 powerset( 99.05/14.89 binunion( 99.05/14.89 Y0, Y1))), 99.05/14.89 (^[Y3 : $i]: 99.05/14.89 (??(( 99.05/14.89 ^[Y4 : $i]: 99.05/14.89 (in(Y4, 99.05/14.89 Y0) & 99.05/14.89 (??(( 99.05/14.89 ^[Y5 : $i]: 99.05/14.89 (in(Y5, 99.05/14.89 Y1) & 99.05/14.89 (Y3 = 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y4, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y4, 99.05/14.89 setadjoin( 99.05/14.89 Y5, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)))))))))))))) => 99.05/14.89 (??(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (( 99.05/14.89 ??(( 99.05/14.89 ^[Y4 : $i]: 99.05/14.89 (in(Y4, 99.05/14.89 Y1) & 99.05/14.89 (Y2 = 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y3, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y3, 99.05/14.89 setadjoin( 99.05/14.89 Y4, 99.05/14.89 emptyset)), 99.05/14.89 emptyset))))))) & 99.05/14.89 in(Y3, 99.05/14.89 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.05/14.89 inference('lazy_cnf_imply', [status(thm)], ['192'])). 99.05/14.89 tff('194', plain, 99.05/14.89 ~ ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 99.05/14.89 in(Y1, powerset(Y0))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 99.05/14.89 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (in(Y1, powerset(Y0)) => 99.05/14.89 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (in(Y1, Y2) => 99.05/14.89 (in(Y2, Y0) => in(Y1, setunion(Y0))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (in(Y1, setunion(Y0)) => 99.05/14.89 (!!((^[Y2 : $o]: 99.05/14.89 ((!!((^[Y3 : $i]: 99.05/14.89 (in(Y1, Y3) => (in(Y3, Y0) => Y2))))) => 99.05/14.89 Y2))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (in(Y1, Y0) => in(Y1, powerset(setunion(Y0)))))))))) => 99.05/14.89 ((!!((^[Y0 : $i > $o]: 99.05/14.89 ((??((^[Y1 : $i]: 99.05/14.89 (Y0(Y1) & 99.05/14.89 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.89 (??((^[Y1 : $i]: 99.05/14.89 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (in(Y0, setadjoin(Y1, emptyset)) => (Y0 = Y1)))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((Y0 != Y1) => 99.05/14.89 (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((Y0 = Y1) => in(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (in(Y0, setadjoin(Y1, emptyset)) => 99.05/14.89 in(Y1, setadjoin(Y0, emptyset))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 setadjoin(Y0, 99.05/14.89 setadjoin(Y1, emptyset))) => 99.05/14.89 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 in(Y0, 99.05/14.89 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 in(Y1, 99.05/14.89 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i > $o]: 99.05/14.89 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 99.05/14.89 (dsetconstr(Y0, Y1) != emptyset)))))))) => 99.05/14.89 ((!!((^[Y0 : $i > $o]: 99.05/14.89 (!!((^[Y1 : $i]: (in(Y1, emptyset) => Y0(Y1)))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i > $o]: 99.05/14.89 ((~((!!((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.89 (??((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i > $o]: 99.05/14.89 ((!!((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) => (~(Y1(Y2))))))) => 99.05/14.89 (~((??((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) & Y1(Y2)))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i > $o]: 99.05/14.89 ((~((??((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i > $o]: 99.05/14.89 ((??((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) & (~(Y1(Y2))))))) => 99.05/14.89 (~((!!((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) => Y1(Y2)))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $o]: 99.05/14.89 (Y0 => in(emptyset, prop2set(Y0)))))) => 99.05/14.89 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i > $o]: 99.05/14.89 ((~((??((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) => 99.05/14.89 (~(Y1(Y2)))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i > $o]: 99.05/14.89 ((~((!!((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) => 99.05/14.89 Y1(Y2))))))) => 99.05/14.89 (??((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) & 99.05/14.89 (~(Y1(Y2)))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i > $o]: 99.05/14.89 ((??(Y0)) => 99.05/14.89 ((!!((^[Y1 : $i]: 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (Y0(Y1) => 99.05/14.89 (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.89 (??((^[Y1 : $i]: 99.05/14.89 (Y0(Y1) & 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (Y0(Y2) => (Y1 = Y2)))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i > $o]: 99.05/14.89 ((??((^[Y1 : $i]: 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (Y0(Y2) <=> (Y2 = Y1)))))))) => 99.05/14.89 (??((^[Y1 : $i]: 99.05/14.89 (Y0(Y1) & 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((Y0 = Y1) => 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (!!((^[Y3 : $i]: 99.05/14.89 ((Y2 = Y3) => 99.05/14.89 (in(Y2, Y0) => 99.05/14.89 in(Y3, Y1)))))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((Y0 = Y1) => 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (!!((^[Y3 : $i]: 99.05/14.89 ((Y2 = Y3) => 99.05/14.89 (in(Y2, Y0) <=> 99.05/14.89 in(Y3, Y1)))))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i > $o]: 99.05/14.89 ((??((^[Y1 : $i]: 99.05/14.89 (Y0(Y1) & 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (Y0(Y2) => 99.05/14.89 (Y1 = Y2))))))))) => 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (Y0(Y1) => 99.05/14.89 (Y0(Y2) => 99.05/14.89 (Y1 = Y2))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i > $o]: 99.05/14.89 (!!((^[Y1 : $i > $o]: 99.05/14.89 ((!!((^[Y2 : $i]: 99.05/14.89 (!!((^[Y3 : $i]: 99.05/14.89 (( 99.05/14.89 Y2 = Y3) => 99.05/14.89 ( 99.05/14.89 Y0(Y2) <=> 99.05/14.89 Y1(Y3))))))))) => 99.05/14.89 ((??((^[Y2 : $i]: 99.05/14.89 (Y0(Y2) & 99.05/14.89 (!!((^[Y3 : $i]: 99.05/14.89 (Y0(Y3) => 99.05/14.89 (Y2 = Y3))))))))) <=> 99.05/14.89 (??((^[Y2 : $i]: 99.05/14.89 (Y1(Y2) & 99.05/14.89 (!!((^[Y3 : $i]: 99.05/14.89 (Y1(Y3) => 99.05/14.89 (Y2 = Y3))))))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((Y0 = Y1) => 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (!!((^[Y3 : $i]: 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 Y2 = Y3) => 99.05/14.89 ( 99.05/14.89 setadjoin( 99.05/14.89 Y0, Y2) = 99.05/14.89 setadjoin( 99.05/14.89 Y1, Y3)))))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((Y0 = Y1) => 99.05/14.89 (powerset(Y0) = 99.05/14.89 powerset(Y1))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((Y0 = Y1) => 99.05/14.89 (setunion(Y0) = 99.05/14.89 setunion(Y1))))))))) => 99.05/14.89 ((!!((^[Y0 : $i > $o]: 99.05/14.89 ((??((^[Y1 : $i]: 99.05/14.89 (Y0(Y1) & 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (Y0(Y2) => 99.05/14.89 (Y1 = Y2))))))))) => 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (Y0(Y1) => 99.05/14.89 (Y0(Y2) => 99.05/14.89 (Y1 = Y2))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i > $o]: 99.05/14.89 (!!((^[Y1 : $i > $o]: 99.05/14.89 ((!!((^[Y2 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 Y2 = Y3) => 99.05/14.89 ( 99.05/14.89 Y0(Y2) <=> 99.05/14.89 Y1(Y3))))))))) => 99.05/14.89 ((??((^[Y2 : $i]: 99.05/14.89 (Y0(Y2) & 99.05/14.89 (!!(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (Y0(Y3) => 99.05/14.89 (Y2 = Y3))))))))) => 99.05/14.89 ((??((^[Y2 : $i]: 99.05/14.89 (Y1(Y2) & 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (Y1(Y3) => 99.05/14.89 (Y2 = Y3))))))))) => 99.05/14.89 (descr(Y0) = 99.05/14.89 descr(Y1))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((Y0 = Y1) => 99.05/14.89 (!!((^[Y2 : $i > $o]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y3 : $i > $o]: 99.05/14.89 (( 99.05/14.89 !!(( 99.05/14.89 ^[Y4 : $i]: 99.05/14.89 (in(Y4, 99.05/14.89 Y0) => 99.05/14.89 (!!(( 99.05/14.89 ^[Y5 : $i]: 99.05/14.89 (in(Y5, 99.05/14.89 Y1) => 99.05/14.89 (( 99.05/14.89 Y4 = Y5) => 99.05/14.89 (Y2(Y4) <=> 99.05/14.89 Y3(Y5))))))))))) => 99.05/14.89 (dsetconstr( 99.05/14.89 Y0, Y2) = 99.05/14.89 dsetconstr( 99.05/14.89 Y1, Y3)))))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((!!((^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 in(Y2, 99.05/14.89 Y1))))) => 99.05/14.89 subset(Y0, Y1)))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((Y0 = Y1) => 99.05/14.89 subset(Y1, Y0)))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((Y0 = Y1) => 99.05/14.89 subset(Y0, Y1)))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((!!((^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 in(Y2, 99.05/14.89 Y1))))) => 99.05/14.89 subset(Y0, Y1)))))))) => 99.05/14.89 ((!!(subset(emptyset))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (subset( 99.05/14.89 Y0, Y1) => 99.05/14.89 ( 99.05/14.89 in(Y2, 99.05/14.89 Y0) => 99.05/14.89 in(Y2, 99.05/14.89 Y1)))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 ( 99.05/14.89 subset( 99.05/14.89 Y0, Y1) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y1))) => 99.05/14.89 ( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y0)))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y1))) => 99.05/14.89 (~( 99.05/14.89 subset( 99.05/14.89 Y0, Y1)))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 subset( 99.05/14.89 Y0, Y1))) => 99.05/14.89 ( 99.05/14.89 Y0 != Y1)))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y1))) => 99.05/14.89 (Y0 != Y1)))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 subset(Y0, Y0)))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (subset( 99.05/14.89 Y0, Y1) => 99.05/14.89 (subset( 99.05/14.89 Y1, Y2) => 99.05/14.89 subset( 99.05/14.89 Y0, Y2)))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 subset( 99.05/14.89 Y1, 99.05/14.89 setadjoin( 99.05/14.89 Y0, Y1)))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (subset( 99.05/14.89 Y0, Y2) => 99.05/14.89 subset( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, Y2)))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (subset( 99.05/14.89 Y0, Y1) => 99.05/14.89 in(Y0, 99.05/14.89 powerset( 99.05/14.89 Y1))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (subset( 99.05/14.89 Y0, Y1) => 99.05/14.89 (subset( 99.05/14.89 Y1, Y0) => 99.05/14.89 (Y0 = Y1))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 ( 99.05/14.89 subset( 99.05/14.89 Y0, 99.05/14.89 emptyset) => 99.05/14.89 ( 99.05/14.89 Y0 = 99.05/14.89 emptyset))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (subset( 99.05/14.89 Y1, Y0) => 99.05/14.89 in(Y1, 99.05/14.89 powerset( 99.05/14.89 Y0))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (in(Y1, 99.05/14.89 powerset( 99.05/14.89 Y0)) => 99.05/14.89 subset( 99.05/14.89 Y1, Y0)))))))) => 99.05/14.89 ((!!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 in(Y0, 99.05/14.89 powerset( 99.05/14.89 Y0))))) => 99.05/14.89 ((!!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (subset( 99.05/14.89 Y0, Y1) => 99.05/14.89 subset( 99.05/14.89 powerset( 99.05/14.89 Y0), 99.05/14.89 powerset( 99.05/14.89 Y1))))))))) => 99.05/14.89 ((!!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i > $o]: 99.05/14.89 in( 99.05/14.89 dsetconstr( 99.05/14.89 Y0, Y1), 99.05/14.89 powerset( 99.05/14.89 Y0)))))))) => 99.05/14.89 ((!!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i > $o]: 99.05/14.89 subset( 99.05/14.89 dsetconstr( 99.05/14.89 Y0, Y1), 99.05/14.89 Y0))))))) => 99.05/14.89 (( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 in(Y2, 99.05/14.89 binunion( 99.05/14.89 Y0, Y1)))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 in(Y1, 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y1) => 99.05/14.89 in(Y2, 99.05/14.89 binunion( 99.05/14.89 Y0, Y1)))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y3 : $o]: 99.05/14.89 (in(Y2, 99.05/14.89 binunion( 99.05/14.89 Y0, Y1)) => 99.05/14.89 (( 99.05/14.89 in(Y2, 99.05/14.89 Y0) => Y3) => 99.05/14.89 (( 99.05/14.89 in(Y2, 99.05/14.89 Y1) => Y3) => 99.05/14.89 Y3))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 binunion( 99.05/14.89 Y0, Y1)) => 99.05/14.89 (in(Y2, 99.05/14.89 Y1) | 99.05/14.89 in(Y2, 99.05/14.89 Y0)))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 subset( 99.05/14.89 Y0, 99.05/14.89 binunion( 99.05/14.89 Y0, Y1)))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 subset( 99.05/14.89 Y1, 99.05/14.89 binunion( 99.05/14.89 Y0, Y1)))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (in(Y2, 99.05/14.89 Y1) => 99.05/14.89 in(Y2, 99.05/14.89 binintersect( 99.05/14.89 Y0, Y1))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (subset( 99.05/14.89 Y2, Y0) => 99.05/14.89 (subset( 99.05/14.89 Y2, Y1) => 99.05/14.89 subset( 99.05/14.89 Y2, 99.05/14.89 binintersect( 99.05/14.89 Y0, Y1))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 binintersect( 99.05/14.89 Y0, Y1)) => 99.05/14.89 in(Y2, 99.05/14.89 Y0))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 subset( 99.05/14.89 binintersect( 99.05/14.89 Y0, Y1), 99.05/14.89 Y0))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (subset( 99.05/14.89 Y0, Y1) => 99.05/14.89 (binintersect( 99.05/14.89 Y0, Y1) = 99.05/14.89 Y0)))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (( 99.05/14.89 binintersect( 99.05/14.89 Y0, Y1) = 99.05/14.89 Y1) => 99.05/14.89 subset( 99.05/14.89 Y1, Y0)))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 binintersect( 99.05/14.89 Y0, Y1)) => 99.05/14.89 in(Y2, 99.05/14.89 Y1))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (( 99.05/14.89 ~(( 99.05/14.89 ??(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) & 99.05/14.89 in(Y2, 99.05/14.89 Y1))))))) => 99.05/14.89 (binintersect( 99.05/14.89 Y0, Y1) = 99.05/14.89 emptyset)))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 subset( 99.05/14.89 binintersect( 99.05/14.89 Y0, Y1), 99.05/14.89 Y1))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (subset( 99.05/14.89 Y1, Y0) => 99.05/14.89 (binintersect( 99.05/14.89 Y0, Y1) = 99.05/14.89 Y1)))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (( 99.05/14.89 binintersect( 99.05/14.89 Y0, Y1) = 99.05/14.89 Y0) => 99.05/14.89 subset( 99.05/14.89 Y0, Y1)))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (binintersect( 99.05/14.89 Y0, 99.05/14.89 binunion( 99.05/14.89 Y1, Y2)) = 99.05/14.89 binunion( 99.05/14.89 binintersect( 99.05/14.89 Y0, Y1), 99.05/14.89 binintersect( 99.05/14.89 Y0, Y2)))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y1))) => 99.05/14.89 in(Y2, 99.05/14.89 setminus( 99.05/14.89 Y0, Y1))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 setminus( 99.05/14.89 Y0, Y1)) => 99.05/14.89 in(Y2, 99.05/14.89 Y0))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 setminus( 99.05/14.89 Y0, Y1)) => 99.05/14.89 (~( 99.05/14.89 in(Y2, 99.05/14.89 Y1))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (subset( 99.05/14.89 Y0, Y1) => 99.05/14.89 (setminus( 99.05/14.89 Y0, Y1) = 99.05/14.89 emptyset)))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 setminus( 99.05/14.89 Y0, Y1)))) => 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 in(Y2, 99.05/14.89 Y1)))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 setminus( 99.05/14.89 Y0, Y1)))) => 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y1))) => 99.05/14.89 (~( 99.05/14.89 in(Y2, 99.05/14.89 Y0)))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y0))) => 99.05/14.89 (~( 99.05/14.89 in(Y2, 99.05/14.89 setminus( 99.05/14.89 Y0, Y1)))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y1) => 99.05/14.89 (~( 99.05/14.89 in(Y2, 99.05/14.89 setminus( 99.05/14.89 Y0, Y1)))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 subset( 99.05/14.89 setminus( 99.05/14.89 Y0, Y1), 99.05/14.89 Y0))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (( 99.05/14.89 setminus( 99.05/14.89 Y0, Y1) = 99.05/14.89 emptyset) => 99.05/14.89 subset( 99.05/14.89 Y0, Y1)))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 symdiff( 99.05/14.89 Y0, Y1)) => 99.05/14.89 (!!(( 99.05/14.89 ^[Y3 : $o]: 99.05/14.89 (( 99.05/14.89 in(Y2, 99.05/14.89 Y0) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y1))) => 99.05/14.89 Y3)) => 99.05/14.89 (( 99.05/14.89 ( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y0))) => 99.05/14.89 ( 99.05/14.89 in(Y2, 99.05/14.89 Y1) => Y3)) => 99.05/14.89 Y3))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y1))) => 99.05/14.89 in(Y2, 99.05/14.89 symdiff( 99.05/14.89 Y0, Y1))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y0))) => 99.05/14.89 (in(Y2, 99.05/14.89 Y1) => 99.05/14.89 in(Y2, 99.05/14.89 symdiff( 99.05/14.89 Y0, Y1))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (in(Y2, 99.05/14.89 Y1) => 99.05/14.89 (~( 99.05/14.89 in(Y2, 99.05/14.89 symdiff( 99.05/14.89 Y0, Y1))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y0))) => 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y1))) => 99.05/14.89 (~( 99.05/14.89 in(Y2, 99.05/14.89 symdiff( 99.05/14.89 Y0, Y1))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 in(Y1, 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 in(Y0, 99.05/14.89 setunion( 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 in(Y1, 99.05/14.89 setunion( 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (??(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 setunion( 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)))) & 99.05/14.89 (??(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (in(Y3, 99.05/14.89 setunion( 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)))) & 99.05/14.89 (setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)) = 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 setadjoin( 99.05/14.89 Y3, 99.05/14.89 emptyset)), 99.05/14.89 emptyset))))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (??(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 setunion( 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)))) & 99.05/14.89 (??(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (in(Y3, 99.05/14.89 setunion( 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)))) & 99.05/14.89 (setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)) = 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 setadjoin( 99.05/14.89 Y3, 99.05/14.89 emptyset)), 99.05/14.89 emptyset))))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (in(Y1, 99.05/14.89 Y0) => 99.05/14.89 subset( 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset), 99.05/14.89 Y0)))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (in(Y1, 99.05/14.89 Y0) => 99.05/14.89 in( 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset), 99.05/14.89 powerset( 99.05/14.89 Y0))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 in( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 emptyset), 99.05/14.89 powerset( 99.05/14.89 binunion( 99.05/14.89 Y0, Y1))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset))) => 99.05/14.89 (( 99.05/14.89 Y2 = Y1) | 99.05/14.89 (Y2 = Y0)))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (!!(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (in(Y3, 99.05/14.89 Y1) => 99.05/14.89 subset( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 setadjoin( 99.05/14.89 Y3, 99.05/14.89 emptyset)), 99.05/14.89 binunion( 99.05/14.89 Y0, Y1)))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (!!(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (in(Y3, 99.05/14.89 Y1) => 99.05/14.89 in( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 setadjoin( 99.05/14.89 Y3, 99.05/14.89 emptyset)), 99.05/14.89 powerset( 99.05/14.89 binunion( 99.05/14.89 Y0, Y1))))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (!!(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (in(Y3, 99.05/14.89 Y1) => 99.05/14.89 subset( 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 setadjoin( 99.05/14.89 Y3, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)), 99.05/14.89 powerset( 99.05/14.89 binunion( 99.05/14.89 Y0, Y1))))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (!!(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (in(Y3, 99.05/14.89 Y1) => 99.05/14.89 in( 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 setadjoin( 99.05/14.89 Y3, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)), 99.05/14.89 powerset( 99.05/14.89 powerset( 99.05/14.89 binunion( 99.05/14.89 Y0, Y1)))))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (!!(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (in(Y3, 99.05/14.89 Y1) => 99.05/14.89 in( 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 setadjoin( 99.05/14.89 Y3, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)), 99.05/14.89 powerset( 99.05/14.89 powerset( 99.05/14.89 binunion( 99.05/14.89 Y0, Y1)))))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (!!(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (in(Y3, 99.05/14.89 Y1) => 99.05/14.89 in( 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 setadjoin( 99.05/14.89 Y3, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)), 99.05/14.89 dsetconstr( 99.05/14.89 powerset( 99.05/14.89 powerset( 99.05/14.89 binunion( 99.05/14.89 Y0, Y1))), 99.05/14.89 (^[Y4 : $i]: 99.05/14.89 (??(( 99.05/14.89 ^[Y5 : $i]: 99.05/14.89 (in(Y5, 99.05/14.89 Y0) & 99.05/14.89 (??(( 99.05/14.89 ^[Y6 : $i]: 99.05/14.89 (in(Y6, 99.05/14.89 Y1) & 99.05/14.89 (Y4 = 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y5, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y5, 99.05/14.89 setadjoin( 99.05/14.89 Y6, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)))))))))))))))))))))))))))) => 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 dsetconstr( 99.05/14.89 powerset( 99.05/14.89 powerset( 99.05/14.89 binunion( 99.05/14.89 Y0, Y1))), 99.05/14.89 (^[Y3 : $i]: 99.05/14.89 (??(( 99.05/14.89 ^[Y4 : $i]: 99.05/14.89 (in(Y4, 99.05/14.89 Y0) & 99.05/14.89 (??(( 99.05/14.89 ^[Y5 : $i]: 99.05/14.89 (in(Y5, 99.05/14.89 Y1) & 99.05/14.89 (Y3 = 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y4, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y4, 99.05/14.89 setadjoin( 99.05/14.89 Y5, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)))))))))))))) => 99.05/14.89 (??(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (( 99.05/14.89 ??(( 99.05/14.89 ^[Y4 : $i]: 99.05/14.89 (in(Y4, 99.05/14.89 Y1) & 99.05/14.89 (Y2 = 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y3, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y3, 99.05/14.89 setadjoin( 99.05/14.89 Y4, 99.05/14.89 emptyset)), 99.05/14.89 emptyset))))))) & 99.05/14.89 in(Y3, 99.05/14.89 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.05/14.89 inference('lazy_cnf_imply', [status(thm)], ['193'])). 99.05/14.89 tff('195', plain, 99.05/14.89 ~ ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 99.05/14.89 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (in(Y1, powerset(Y0)) => 99.05/14.89 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (in(Y1, Y2) => 99.05/14.89 (in(Y2, Y0) => in(Y1, setunion(Y0))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (in(Y1, setunion(Y0)) => 99.05/14.89 (!!((^[Y2 : $o]: 99.05/14.89 ((!!((^[Y3 : $i]: 99.05/14.89 (in(Y1, Y3) => (in(Y3, Y0) => Y2))))) => 99.05/14.89 Y2))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (in(Y1, Y0) => in(Y1, powerset(setunion(Y0)))))))))) => 99.05/14.89 ((!!((^[Y0 : $i > $o]: 99.05/14.89 ((??((^[Y1 : $i]: 99.05/14.89 (Y0(Y1) & 99.05/14.89 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.89 (??((^[Y1 : $i]: 99.05/14.89 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (in(Y0, setadjoin(Y1, emptyset)) => (Y0 = Y1)))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((Y0 != Y1) => 99.05/14.89 (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((Y0 = Y1) => in(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (in(Y0, setadjoin(Y1, emptyset)) => 99.05/14.89 in(Y1, setadjoin(Y0, emptyset))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 setadjoin(Y0, 99.05/14.89 setadjoin(Y1, emptyset))) => 99.05/14.89 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 in(Y0, 99.05/14.89 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 in(Y1, 99.05/14.89 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i > $o]: 99.05/14.89 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 99.05/14.89 (dsetconstr(Y0, Y1) != emptyset)))))))) => 99.05/14.89 ((!!((^[Y0 : $i > $o]: 99.05/14.89 (!!((^[Y1 : $i]: (in(Y1, emptyset) => Y0(Y1)))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i > $o]: 99.05/14.89 ((~((!!((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.89 (??((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i > $o]: 99.05/14.89 ((!!((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) => (~(Y1(Y2))))))) => 99.05/14.89 (~((??((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) & Y1(Y2)))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i > $o]: 99.05/14.89 ((~((??((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i > $o]: 99.05/14.89 ((??((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) & (~(Y1(Y2))))))) => 99.05/14.89 (~((!!((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) => Y1(Y2)))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $o]: 99.05/14.89 (Y0 => in(emptyset, prop2set(Y0)))))) => 99.05/14.89 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i > $o]: 99.05/14.89 ((~((??((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) => 99.05/14.89 (~(Y1(Y2)))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i > $o]: 99.05/14.89 ((~((!!((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.89 (??((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) & 99.05/14.89 (~(Y1(Y2)))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i > $o]: 99.05/14.89 ((??(Y0)) => 99.05/14.89 ((!!((^[Y1 : $i]: 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (Y0(Y1) => 99.05/14.89 (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.89 (??((^[Y1 : $i]: 99.05/14.89 (Y0(Y1) & 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (Y0(Y2) => (Y1 = Y2)))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i > $o]: 99.05/14.89 ((??((^[Y1 : $i]: 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (Y0(Y2) <=> (Y2 = Y1)))))))) => 99.05/14.89 (??((^[Y1 : $i]: 99.05/14.89 (Y0(Y1) & 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((Y0 = Y1) => 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (!!((^[Y3 : $i]: 99.05/14.89 ((Y2 = Y3) => 99.05/14.89 (in(Y2, Y0) => 99.05/14.89 in(Y3, Y1)))))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((Y0 = Y1) => 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (!!((^[Y3 : $i]: 99.05/14.89 ((Y2 = Y3) => 99.05/14.89 (in(Y2, Y0) <=> 99.05/14.89 in(Y3, Y1)))))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i > $o]: 99.05/14.89 ((??((^[Y1 : $i]: 99.05/14.89 (Y0(Y1) & 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (Y0(Y2) => 99.05/14.89 (Y1 = Y2))))))))) => 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (Y0(Y1) => 99.05/14.89 (Y0(Y2) => 99.05/14.89 (Y1 = Y2))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i > $o]: 99.05/14.89 (!!((^[Y1 : $i > $o]: 99.05/14.89 ((!!((^[Y2 : $i]: 99.05/14.89 (!!((^[Y3 : $i]: 99.05/14.89 ((Y2 = Y3) => 99.05/14.89 (Y0(Y2) <=> 99.05/14.89 Y1(Y3))))))))) => 99.05/14.89 ((??((^[Y2 : $i]: 99.05/14.89 (Y0(Y2) & 99.05/14.89 (!!((^[Y3 : $i]: 99.05/14.89 ( 99.05/14.89 Y0(Y3) => 99.05/14.89 ( 99.05/14.89 Y2 = Y3))))))))) <=> 99.05/14.89 (??((^[Y2 : $i]: 99.05/14.89 (Y1(Y2) & 99.05/14.89 (!!((^[Y3 : $i]: 99.05/14.89 ( 99.05/14.89 Y1(Y3) => 99.05/14.89 ( 99.05/14.89 Y2 = Y3))))))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((Y0 = Y1) => 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (!!((^[Y3 : $i]: 99.05/14.89 (( 99.05/14.89 Y2 = Y3) => 99.05/14.89 ( 99.05/14.89 setadjoin( 99.05/14.89 Y0, Y2) = 99.05/14.89 setadjoin( 99.05/14.89 Y1, Y3)))))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((Y0 = Y1) => 99.05/14.89 (powerset(Y0) = 99.05/14.89 powerset(Y1))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((Y0 = Y1) => 99.05/14.89 (setunion(Y0) = 99.05/14.89 setunion(Y1))))))))) => 99.05/14.89 ((!!((^[Y0 : $i > $o]: 99.05/14.89 ((??((^[Y1 : $i]: 99.05/14.89 (Y0(Y1) & 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (Y0(Y2) => 99.05/14.89 (Y1 = Y2))))))))) => 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (Y0(Y1) => 99.05/14.89 (Y0(Y2) => 99.05/14.89 (Y1 = Y2))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i > $o]: 99.05/14.89 (!!((^[Y1 : $i > $o]: 99.05/14.89 ((!!((^[Y2 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (( 99.05/14.89 Y2 = Y3) => 99.05/14.89 ( 99.05/14.89 Y0(Y2) <=> 99.05/14.89 Y1(Y3))))))))) => 99.05/14.89 ((??((^[Y2 : $i]: 99.05/14.89 (Y0(Y2) & 99.05/14.89 (!!(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (Y0(Y3) => 99.05/14.89 (Y2 = Y3))))))))) => 99.05/14.89 ((??((^[Y2 : $i]: 99.05/14.89 (Y1(Y2) & 99.05/14.89 (!!(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (Y1(Y3) => 99.05/14.89 (Y2 = Y3))))))))) => 99.05/14.89 (descr(Y0) = 99.05/14.89 descr(Y1))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((Y0 = Y1) => 99.05/14.89 (!!((^[Y2 : $i > $o]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y3 : $i > $o]: 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y4 : $i]: 99.05/14.89 (in(Y4, 99.05/14.89 Y0) => 99.05/14.89 (!!(( 99.05/14.89 ^[Y5 : $i]: 99.05/14.89 (in(Y5, 99.05/14.89 Y1) => 99.05/14.89 (( 99.05/14.89 Y4 = Y5) => 99.05/14.89 (Y2(Y4) <=> 99.05/14.89 Y3(Y5))))))))))) => 99.05/14.89 ( 99.05/14.89 dsetconstr( 99.05/14.89 Y0, Y2) = 99.05/14.89 dsetconstr( 99.05/14.89 Y1, Y3)))))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((!!((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) => 99.05/14.89 in(Y2, Y1))))) => 99.05/14.89 subset(Y0, Y1)))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((Y0 = Y1) => 99.05/14.89 subset(Y1, Y0)))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((Y0 = Y1) => 99.05/14.89 subset(Y0, Y1)))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((!!((^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 in(Y2, 99.05/14.89 Y1))))) => 99.05/14.89 subset(Y0, Y1)))))))) => 99.05/14.89 ((!!(subset(emptyset))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (subset( 99.05/14.89 Y0, Y1) => 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 in(Y2, 99.05/14.89 Y1)))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (subset( 99.05/14.89 Y0, Y1) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y1))) => 99.05/14.89 ( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y0)))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 ( 99.05/14.89 in(Y2, 99.05/14.89 Y0) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y1))) => 99.05/14.89 ( 99.05/14.89 ~( 99.05/14.89 subset( 99.05/14.89 Y0, Y1)))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((~( 99.05/14.89 subset( 99.05/14.89 Y0, Y1))) => 99.05/14.89 (Y0 != Y1)))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y1))) => 99.05/14.89 (Y0 != Y1)))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 subset(Y0, Y0)))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (subset( 99.05/14.89 Y0, Y1) => 99.05/14.89 (subset( 99.05/14.89 Y1, Y2) => 99.05/14.89 subset( 99.05/14.89 Y0, Y2)))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 subset( 99.05/14.89 Y1, 99.05/14.89 setadjoin( 99.05/14.89 Y0, Y1)))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (subset( 99.05/14.89 Y0, Y2) => 99.05/14.89 subset( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, Y2)))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 ( 99.05/14.89 subset( 99.05/14.89 Y0, Y1) => 99.05/14.89 in(Y0, 99.05/14.89 powerset( 99.05/14.89 Y1))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (subset( 99.05/14.89 Y0, Y1) => 99.05/14.89 (subset( 99.05/14.89 Y1, Y0) => 99.05/14.89 (Y0 = Y1))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (subset( 99.05/14.89 Y0, 99.05/14.89 emptyset) => 99.05/14.89 ( 99.05/14.89 Y0 = 99.05/14.89 emptyset))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (subset( 99.05/14.89 Y1, Y0) => 99.05/14.89 in(Y1, 99.05/14.89 powerset( 99.05/14.89 Y0))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (in(Y1, 99.05/14.89 powerset( 99.05/14.89 Y0)) => 99.05/14.89 subset( 99.05/14.89 Y1, Y0)))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 in(Y0, 99.05/14.89 powerset( 99.05/14.89 Y0))))) => 99.05/14.89 ((!!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (subset( 99.05/14.89 Y0, Y1) => 99.05/14.89 subset( 99.05/14.89 powerset( 99.05/14.89 Y0), 99.05/14.89 powerset( 99.05/14.89 Y1))))))))) => 99.05/14.89 ((!!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y1 : $i > $o]: 99.05/14.89 in( 99.05/14.89 dsetconstr( 99.05/14.89 Y0, Y1), 99.05/14.89 powerset( 99.05/14.89 Y0)))))))) => 99.05/14.89 ((!!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i > $o]: 99.05/14.89 subset( 99.05/14.89 dsetconstr( 99.05/14.89 Y0, Y1), 99.05/14.89 Y0))))))) => 99.05/14.89 ((!!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 in(Y2, 99.05/14.89 binunion( 99.05/14.89 Y0, Y1)))))))))))) => 99.05/14.89 (( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 in(Y1, 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y1) => 99.05/14.89 in(Y2, 99.05/14.89 binunion( 99.05/14.89 Y0, Y1)))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y3 : $o]: 99.05/14.89 (in(Y2, 99.05/14.89 binunion( 99.05/14.89 Y0, Y1)) => 99.05/14.89 (( 99.05/14.89 in(Y2, 99.05/14.89 Y0) => Y3) => 99.05/14.89 (( 99.05/14.89 in(Y2, 99.05/14.89 Y1) => Y3) => 99.05/14.89 Y3))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 binunion( 99.05/14.89 Y0, Y1)) => 99.05/14.89 (in(Y2, 99.05/14.89 Y1) | 99.05/14.89 in(Y2, 99.05/14.89 Y0)))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 subset( 99.05/14.89 Y0, 99.05/14.89 binunion( 99.05/14.89 Y0, Y1)))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 subset( 99.05/14.89 Y1, 99.05/14.89 binunion( 99.05/14.89 Y0, Y1)))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (in(Y2, 99.05/14.89 Y1) => 99.05/14.89 in(Y2, 99.05/14.89 binintersect( 99.05/14.89 Y0, Y1))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (subset( 99.05/14.89 Y2, Y0) => 99.05/14.89 (subset( 99.05/14.89 Y2, Y1) => 99.05/14.89 subset( 99.05/14.89 Y2, 99.05/14.89 binintersect( 99.05/14.89 Y0, Y1))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 binintersect( 99.05/14.89 Y0, Y1)) => 99.05/14.89 in(Y2, 99.05/14.89 Y0))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 subset( 99.05/14.89 binintersect( 99.05/14.89 Y0, Y1), 99.05/14.89 Y0))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (subset( 99.05/14.89 Y0, Y1) => 99.05/14.89 (binintersect( 99.05/14.89 Y0, Y1) = 99.05/14.89 Y0)))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (( 99.05/14.89 binintersect( 99.05/14.89 Y0, Y1) = 99.05/14.89 Y1) => 99.05/14.89 subset( 99.05/14.89 Y1, Y0)))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 binintersect( 99.05/14.89 Y0, Y1)) => 99.05/14.89 in(Y2, 99.05/14.89 Y1))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (( 99.05/14.89 ~(( 99.05/14.89 ??(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) & 99.05/14.89 in(Y2, 99.05/14.89 Y1))))))) => 99.05/14.89 (binintersect( 99.05/14.89 Y0, Y1) = 99.05/14.89 emptyset)))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 subset( 99.05/14.89 binintersect( 99.05/14.89 Y0, Y1), 99.05/14.89 Y1))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (subset( 99.05/14.89 Y1, Y0) => 99.05/14.89 (binintersect( 99.05/14.89 Y0, Y1) = 99.05/14.89 Y1)))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (( 99.05/14.89 binintersect( 99.05/14.89 Y0, Y1) = 99.05/14.89 Y0) => 99.05/14.89 subset( 99.05/14.89 Y0, Y1)))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (binintersect( 99.05/14.89 Y0, 99.05/14.89 binunion( 99.05/14.89 Y1, Y2)) = 99.05/14.89 binunion( 99.05/14.89 binintersect( 99.05/14.89 Y0, Y1), 99.05/14.89 binintersect( 99.05/14.89 Y0, Y2)))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y1))) => 99.05/14.89 in(Y2, 99.05/14.89 setminus( 99.05/14.89 Y0, Y1))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 setminus( 99.05/14.89 Y0, Y1)) => 99.05/14.89 in(Y2, 99.05/14.89 Y0))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 setminus( 99.05/14.89 Y0, Y1)) => 99.05/14.89 (~( 99.05/14.89 in(Y2, 99.05/14.89 Y1))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (subset( 99.05/14.89 Y0, Y1) => 99.05/14.89 (setminus( 99.05/14.89 Y0, Y1) = 99.05/14.89 emptyset)))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 setminus( 99.05/14.89 Y0, Y1)))) => 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 in(Y2, 99.05/14.89 Y1)))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 setminus( 99.05/14.89 Y0, Y1)))) => 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y1))) => 99.05/14.89 (~( 99.05/14.89 in(Y2, 99.05/14.89 Y0)))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y0))) => 99.05/14.89 (~( 99.05/14.89 in(Y2, 99.05/14.89 setminus( 99.05/14.89 Y0, Y1)))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y1) => 99.05/14.89 (~( 99.05/14.89 in(Y2, 99.05/14.89 setminus( 99.05/14.89 Y0, Y1)))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 subset( 99.05/14.89 setminus( 99.05/14.89 Y0, Y1), 99.05/14.89 Y0))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (( 99.05/14.89 setminus( 99.05/14.89 Y0, Y1) = 99.05/14.89 emptyset) => 99.05/14.89 subset( 99.05/14.89 Y0, Y1)))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 symdiff( 99.05/14.89 Y0, Y1)) => 99.05/14.89 (!!(( 99.05/14.89 ^[Y3 : $o]: 99.05/14.89 (( 99.05/14.89 in(Y2, 99.05/14.89 Y0) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y1))) => 99.05/14.89 Y3)) => 99.05/14.89 (( 99.05/14.89 ( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y0))) => 99.05/14.89 ( 99.05/14.89 in(Y2, 99.05/14.89 Y1) => Y3)) => 99.05/14.89 Y3))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y1))) => 99.05/14.89 in(Y2, 99.05/14.89 symdiff( 99.05/14.89 Y0, Y1))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y0))) => 99.05/14.89 (in(Y2, 99.05/14.89 Y1) => 99.05/14.89 in(Y2, 99.05/14.89 symdiff( 99.05/14.89 Y0, Y1))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (in(Y2, 99.05/14.89 Y1) => 99.05/14.89 (~( 99.05/14.89 in(Y2, 99.05/14.89 symdiff( 99.05/14.89 Y0, Y1))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y0))) => 99.05/14.89 (( 99.05/14.89 ~( 99.05/14.89 in(Y2, 99.05/14.89 Y1))) => 99.05/14.89 (~( 99.05/14.89 in(Y2, 99.05/14.89 symdiff( 99.05/14.89 Y0, Y1))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 in(Y1, 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 in(Y0, 99.05/14.89 setunion( 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 in(Y1, 99.05/14.89 setunion( 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (??(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 setunion( 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)))) & 99.05/14.89 (??(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (in(Y3, 99.05/14.89 setunion( 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)))) & 99.05/14.89 (setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)) = 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 setadjoin( 99.05/14.89 Y3, 99.05/14.89 emptyset)), 99.05/14.89 emptyset))))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (??(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 setunion( 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)))) & 99.05/14.89 (??(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (in(Y3, 99.05/14.89 setunion( 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)))) & 99.05/14.89 (setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)) = 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 setadjoin( 99.05/14.89 Y3, 99.05/14.89 emptyset)), 99.05/14.89 emptyset))))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (in(Y1, 99.05/14.89 Y0) => 99.05/14.89 subset( 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset), 99.05/14.89 Y0)))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (in(Y1, 99.05/14.89 Y0) => 99.05/14.89 in( 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset), 99.05/14.89 powerset( 99.05/14.89 Y0))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 in( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 emptyset), 99.05/14.89 powerset( 99.05/14.89 binunion( 99.05/14.89 Y0, Y1))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 setadjoin( 99.05/14.89 Y0, 99.05/14.89 setadjoin( 99.05/14.89 Y1, 99.05/14.89 emptyset))) => 99.05/14.89 (( 99.05/14.89 Y2 = Y1) | 99.05/14.89 (Y2 = Y0)))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (!!(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (in(Y3, 99.05/14.89 Y1) => 99.05/14.89 subset( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 setadjoin( 99.05/14.89 Y3, 99.05/14.89 emptyset)), 99.05/14.89 binunion( 99.05/14.89 Y0, Y1)))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (!!(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (in(Y3, 99.05/14.89 Y1) => 99.05/14.89 in( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 setadjoin( 99.05/14.89 Y3, 99.05/14.89 emptyset)), 99.05/14.89 powerset( 99.05/14.89 binunion( 99.05/14.89 Y0, Y1))))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (!!(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (in(Y3, 99.05/14.89 Y1) => 99.05/14.89 subset( 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 setadjoin( 99.05/14.89 Y3, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)), 99.05/14.89 powerset( 99.05/14.89 binunion( 99.05/14.89 Y0, Y1))))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (!!(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (in(Y3, 99.05/14.89 Y1) => 99.05/14.89 in( 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 setadjoin( 99.05/14.89 Y3, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)), 99.05/14.89 powerset( 99.05/14.89 powerset( 99.05/14.89 binunion( 99.05/14.89 Y0, Y1)))))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (!!(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (in(Y3, 99.05/14.89 Y1) => 99.05/14.89 in( 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 setadjoin( 99.05/14.89 Y3, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)), 99.05/14.89 powerset( 99.05/14.89 powerset( 99.05/14.89 binunion( 99.05/14.89 Y0, Y1)))))))))))))))))) => 99.05/14.89 ( 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 Y0) => 99.05/14.89 (!!(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (in(Y3, 99.05/14.89 Y1) => 99.05/14.89 in( 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y2, 99.05/14.89 setadjoin( 99.05/14.89 Y3, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)), 99.05/14.89 dsetconstr( 99.05/14.89 powerset( 99.05/14.89 powerset( 99.05/14.89 binunion( 99.05/14.89 Y0, Y1))), 99.05/14.89 (^[Y4 : $i]: 99.05/14.89 (??(( 99.05/14.89 ^[Y5 : $i]: 99.05/14.89 (in(Y5, 99.05/14.89 Y0) & 99.05/14.89 (??(( 99.05/14.89 ^[Y6 : $i]: 99.05/14.89 (in(Y6, 99.05/14.89 Y1) & 99.05/14.89 (Y4 = 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y5, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y5, 99.05/14.89 setadjoin( 99.05/14.89 Y6, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)))))))))))))))))))))))))))) => 99.05/14.89 ( 99.05/14.89 !!(( 99.05/14.89 ^[Y0 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y1 : $i]: 99.05/14.89 (!!(( 99.05/14.89 ^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 dsetconstr( 99.05/14.89 powerset( 99.05/14.89 powerset( 99.05/14.89 binunion( 99.05/14.89 Y0, Y1))), 99.05/14.89 (^[Y3 : $i]: 99.05/14.89 (??(( 99.05/14.89 ^[Y4 : $i]: 99.05/14.89 (in(Y4, 99.05/14.89 Y0) & 99.05/14.89 (??(( 99.05/14.89 ^[Y5 : $i]: 99.05/14.89 (in(Y5, 99.05/14.89 Y1) & 99.05/14.89 (Y3 = 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y4, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y4, 99.05/14.89 setadjoin( 99.05/14.89 Y5, 99.05/14.89 emptyset)), 99.05/14.89 emptyset)))))))))))))) => 99.05/14.89 (??(( 99.05/14.89 ^[Y3 : $i]: 99.05/14.89 (( 99.05/14.89 ??(( 99.05/14.89 ^[Y4 : $i]: 99.05/14.89 (in(Y4, 99.05/14.89 Y1) & 99.05/14.89 (Y2 = 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y3, 99.05/14.89 emptyset), 99.05/14.89 setadjoin( 99.05/14.89 setadjoin( 99.05/14.89 Y3, 99.05/14.89 setadjoin( 99.05/14.89 Y4, 99.05/14.89 emptyset)), 99.05/14.89 emptyset))))))) & 99.05/14.89 in(Y3, 99.05/14.89 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.05/14.89 inference('lazy_cnf_imply', [status(thm)], ['194'])). 99.05/14.89 tff('196', plain, 99.05/14.89 ~ ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (in(Y1, powerset(Y0)) => 99.05/14.89 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (in(Y1, Y2) => 99.05/14.89 (in(Y2, Y0) => in(Y1, setunion(Y0))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (in(Y1, setunion(Y0)) => 99.05/14.89 (!!((^[Y2 : $o]: 99.05/14.89 ((!!((^[Y3 : $i]: 99.05/14.89 (in(Y1, Y3) => (in(Y3, Y0) => Y2))))) => 99.05/14.89 Y2))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (in(Y1, Y0) => in(Y1, powerset(setunion(Y0)))))))))) => 99.05/14.89 ((!!((^[Y0 : $i > $o]: 99.05/14.89 ((??((^[Y1 : $i]: 99.05/14.89 (Y0(Y1) & 99.05/14.89 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.89 (??((^[Y1 : $i]: 99.05/14.89 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (in(Y0, setadjoin(Y1, emptyset)) => (Y0 = Y1)))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((Y0 != Y1) => 99.05/14.89 (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((Y0 = Y1) => in(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (in(Y0, setadjoin(Y1, emptyset)) => 99.05/14.89 in(Y1, setadjoin(Y0, emptyset))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (in(Y2, 99.05/14.89 setadjoin(Y0, 99.05/14.89 setadjoin(Y1, emptyset))) => 99.05/14.89 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 in(Y0, 99.05/14.89 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 in(Y1, 99.05/14.89 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i > $o]: 99.05/14.89 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 99.05/14.89 (dsetconstr(Y0, Y1) != emptyset)))))))) => 99.05/14.89 ((!!((^[Y0 : $i > $o]: 99.05/14.89 (!!((^[Y1 : $i]: (in(Y1, emptyset) => Y0(Y1)))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i > $o]: 99.05/14.89 ((~((!!((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.89 (??((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i > $o]: 99.05/14.89 ((!!((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) => (~(Y1(Y2))))))) => 99.05/14.89 (~((??((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) & Y1(Y2)))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i > $o]: 99.05/14.89 ((~((??((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i > $o]: 99.05/14.89 ((??((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) & (~(Y1(Y2))))))) => 99.05/14.89 (~((!!((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) => Y1(Y2)))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $o]: 99.05/14.89 (Y0 => in(emptyset, prop2set(Y0)))))) => 99.05/14.89 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i > $o]: 99.05/14.89 ((~((??((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i > $o]: 99.05/14.89 ((~((!!((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.89 (??((^[Y2 : $i]: 99.05/14.89 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i > $o]: 99.05/14.89 ((??(Y0)) => 99.05/14.89 ((!!((^[Y1 : $i]: 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (Y0(Y1) => 99.05/14.89 (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.89 (??((^[Y1 : $i]: 99.05/14.89 (Y0(Y1) & 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (Y0(Y2) => (Y1 = Y2)))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i > $o]: 99.05/14.89 ((??((^[Y1 : $i]: 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (Y0(Y2) <=> (Y2 = Y1)))))))) => 99.05/14.89 (??((^[Y1 : $i]: 99.05/14.89 (Y0(Y1) & 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((Y0 = Y1) => 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (!!((^[Y3 : $i]: 99.05/14.89 ((Y2 = Y3) => 99.05/14.89 (in(Y2, Y0) => 99.05/14.89 in(Y3, Y1)))))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i]: 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 ((Y0 = Y1) => 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (!!((^[Y3 : $i]: 99.05/14.89 ((Y2 = Y3) => 99.05/14.89 (in(Y2, Y0) <=> 99.05/14.89 in(Y3, Y1)))))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i > $o]: 99.05/14.89 ((??((^[Y1 : $i]: 99.05/14.89 (Y0(Y1) & 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (Y0(Y2) => 99.05/14.89 (Y1 = Y2))))))))) => 99.05/14.89 (!!((^[Y1 : $i]: 99.05/14.89 (!!((^[Y2 : $i]: 99.05/14.89 (Y0(Y1) => 99.05/14.89 (Y0(Y2) => 99.05/14.89 (Y1 = Y2))))))))))))) => 99.05/14.89 ((!!((^[Y0 : $i > $o]: 99.05/14.89 (!!((^[Y1 : $i > $o]: 99.05/14.89 ((!!((^[Y2 : $i]: 99.05/14.89 (!!((^[Y3 : $i]: 99.05/14.89 ((Y2 = Y3) => 99.05/14.89 (Y0(Y2) <=> 99.05/14.89 Y1(Y3))))))))) => 99.05/14.89 ((??((^[Y2 : $i]: 99.05/14.89 (Y0(Y2) & 99.05/14.89 (!!((^[Y3 : $i]: 99.05/14.89 (Y0(Y3) => 99.05/14.89 ( 99.05/14.89 Y2 = Y3))))))))) <=> 99.05/14.90 (??((^[Y2 : $i]: 99.05/14.90 (Y1(Y2) & 99.05/14.90 (!!((^[Y3 : $i]: 99.05/14.90 (Y1(Y3) => 99.05/14.90 ( 99.05/14.90 Y2 = Y3))))))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((Y0 = Y1) => 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (!!((^[Y3 : $i]: 99.05/14.90 ((Y2 = Y3) => 99.05/14.90 (setadjoin( 99.05/14.90 Y0, Y2) = 99.05/14.90 setadjoin( 99.05/14.90 Y1, Y3)))))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((Y0 = Y1) => 99.05/14.90 (powerset(Y0) = 99.05/14.90 powerset(Y1))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((Y0 = Y1) => 99.05/14.90 (setunion(Y0) = 99.05/14.90 setunion(Y1))))))))) => 99.05/14.90 ((!!((^[Y0 : $i > $o]: 99.05/14.90 ((??((^[Y1 : $i]: 99.05/14.90 (Y0(Y1) & 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (Y0(Y2) => 99.05/14.90 (Y1 = Y2))))))))) => 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (Y0(Y1) => 99.05/14.90 (Y0(Y2) => 99.05/14.90 (Y1 = Y2))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i > $o]: 99.05/14.90 (!!((^[Y1 : $i > $o]: 99.05/14.90 ((!!((^[Y2 : $i]: 99.05/14.90 (!!((^[Y3 : $i]: 99.05/14.90 (( 99.05/14.90 Y2 = Y3) => 99.05/14.90 (Y0(Y2) <=> 99.05/14.90 Y1(Y3))))))))) => 99.05/14.90 ((??((^[Y2 : $i]: 99.05/14.90 (Y0(Y2) & 99.05/14.90 (!!(( 99.05/14.90 ^[Y3 : $i]: 99.05/14.90 ( 99.05/14.90 Y0(Y3) => 99.05/14.90 ( 99.05/14.90 Y2 = Y3))))))))) => 99.05/14.90 ((??((^[Y2 : $i]: 99.05/14.90 (Y1(Y2) & 99.05/14.90 (!!(( 99.05/14.90 ^[Y3 : $i]: 99.05/14.90 (Y1(Y3) => 99.05/14.90 (Y2 = Y3))))))))) => 99.05/14.90 (descr(Y0) = 99.05/14.90 descr(Y1))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((Y0 = Y1) => 99.05/14.90 (!!((^[Y2 : $i > $o]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y3 : $i > $o]: 99.05/14.90 (( 99.05/14.90 !!(( 99.05/14.90 ^[Y4 : $i]: 99.05/14.90 (in(Y4, 99.05/14.90 Y0) => 99.05/14.90 (!!(( 99.05/14.90 ^[Y5 : $i]: 99.05/14.90 (in(Y5, 99.05/14.90 Y1) => 99.05/14.90 (( 99.05/14.90 Y4 = Y5) => 99.05/14.90 (Y2(Y4) <=> 99.05/14.90 Y3(Y5))))))))))) => 99.05/14.90 ( 99.05/14.90 dsetconstr( 99.05/14.90 Y0, Y2) = 99.05/14.90 dsetconstr( 99.05/14.90 Y1, Y3)))))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((!!((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) => 99.05/14.90 in(Y2, Y1))))) => 99.05/14.90 subset(Y0, Y1)))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((Y0 = Y1) => 99.05/14.90 subset(Y1, Y0)))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((Y0 = Y1) => 99.05/14.90 subset(Y0, Y1)))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((!!((^[Y2 : $i]: 99.05/14.90 ( 99.05/14.90 in(Y2, 99.05/14.90 Y0) => 99.05/14.90 in(Y2, 99.05/14.90 Y1))))) => 99.05/14.90 subset(Y0, Y1)))))))) => 99.05/14.90 ((!!(subset(emptyset))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y0, Y1) => 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 in(Y2, 99.05/14.90 Y1)))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y0, Y1) => 99.05/14.90 (( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y1))) => 99.05/14.90 (~( 99.05/14.90 in(Y2, 99.05/14.90 Y0)))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y1))) => 99.05/14.90 ( 99.05/14.90 ~( 99.05/14.90 subset( 99.05/14.90 Y0, Y1)))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((~( 99.05/14.90 subset( 99.05/14.90 Y0, Y1))) => 99.05/14.90 (Y0 != Y1)))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y1))) => 99.05/14.90 (Y0 != Y1)))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 subset(Y0, Y0)))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y0, Y1) => 99.05/14.90 (subset( 99.05/14.90 Y1, Y2) => 99.05/14.90 subset( 99.05/14.90 Y0, Y2)))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 subset( 99.05/14.90 Y1, 99.05/14.90 setadjoin( 99.05/14.90 Y0, Y1)))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y0, Y2) => 99.05/14.90 subset( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, Y2)))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y0, Y1) => 99.05/14.90 in(Y0, 99.05/14.90 powerset( 99.05/14.90 Y1))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 ( 99.05/14.90 subset( 99.05/14.90 Y0, Y1) => 99.05/14.90 ( 99.05/14.90 subset( 99.05/14.90 Y1, Y0) => 99.05/14.90 ( 99.05/14.90 Y0 = Y1))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y0, 99.05/14.90 emptyset) => 99.05/14.90 (Y0 = 99.05/14.90 emptyset))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y1, Y0) => 99.05/14.90 in(Y1, 99.05/14.90 powerset( 99.05/14.90 Y0))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (in(Y1, 99.05/14.90 powerset( 99.05/14.90 Y0)) => 99.05/14.90 subset( 99.05/14.90 Y1, Y0)))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 in(Y0, 99.05/14.90 powerset( 99.05/14.90 Y0))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y0, Y1) => 99.05/14.90 subset( 99.05/14.90 powerset( 99.05/14.90 Y0), 99.05/14.90 powerset( 99.05/14.90 Y1))))))))) => 99.05/14.90 ((!!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i > $o]: 99.05/14.90 in( 99.05/14.90 dsetconstr( 99.05/14.90 Y0, Y1), 99.05/14.90 powerset( 99.05/14.90 Y0)))))))) => 99.05/14.90 ((!!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y1 : $i > $o]: 99.05/14.90 subset( 99.05/14.90 dsetconstr( 99.05/14.90 Y0, Y1), 99.05/14.90 Y0))))))) => 99.05/14.90 ((!!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 in(Y2, 99.05/14.90 binunion( 99.05/14.90 Y0, Y1)))))))))))) => 99.05/14.90 ((!!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 in(Y1, 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset))))))))) => 99.05/14.90 (( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y1) => 99.05/14.90 in(Y2, 99.05/14.90 binunion( 99.05/14.90 Y0, Y1)))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y3 : $o]: 99.05/14.90 (in(Y2, 99.05/14.90 binunion( 99.05/14.90 Y0, Y1)) => 99.05/14.90 (( 99.05/14.90 in(Y2, 99.05/14.90 Y0) => Y3) => 99.05/14.90 (( 99.05/14.90 in(Y2, 99.05/14.90 Y1) => Y3) => 99.05/14.90 Y3))))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 binunion( 99.05/14.90 Y0, Y1)) => 99.05/14.90 (in(Y2, 99.05/14.90 Y1) | 99.05/14.90 in(Y2, 99.05/14.90 Y0)))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 subset( 99.05/14.90 Y0, 99.05/14.90 binunion( 99.05/14.90 Y0, Y1)))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 subset( 99.05/14.90 Y1, 99.05/14.90 binunion( 99.05/14.90 Y0, Y1)))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (in(Y2, 99.05/14.90 Y1) => 99.05/14.90 in(Y2, 99.05/14.90 binintersect( 99.05/14.90 Y0, Y1))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y2, Y0) => 99.05/14.90 (subset( 99.05/14.90 Y2, Y1) => 99.05/14.90 subset( 99.05/14.90 Y2, 99.05/14.90 binintersect( 99.05/14.90 Y0, Y1))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 binintersect( 99.05/14.90 Y0, Y1)) => 99.05/14.90 in(Y2, 99.05/14.90 Y0))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 subset( 99.05/14.90 binintersect( 99.05/14.90 Y0, Y1), 99.05/14.90 Y0))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y0, Y1) => 99.05/14.90 (binintersect( 99.05/14.90 Y0, Y1) = 99.05/14.90 Y0)))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (( 99.05/14.90 binintersect( 99.05/14.90 Y0, Y1) = 99.05/14.90 Y1) => 99.05/14.90 subset( 99.05/14.90 Y1, Y0)))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 binintersect( 99.05/14.90 Y0, Y1)) => 99.05/14.90 in(Y2, 99.05/14.90 Y1))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (( 99.05/14.90 ~(( 99.05/14.90 ??(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) & 99.05/14.90 in(Y2, 99.05/14.90 Y1))))))) => 99.05/14.90 (binintersect( 99.05/14.90 Y0, Y1) = 99.05/14.90 emptyset)))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 subset( 99.05/14.90 binintersect( 99.05/14.90 Y0, Y1), 99.05/14.90 Y1))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y1, Y0) => 99.05/14.90 (binintersect( 99.05/14.90 Y0, Y1) = 99.05/14.90 Y1)))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (( 99.05/14.90 binintersect( 99.05/14.90 Y0, Y1) = 99.05/14.90 Y0) => 99.05/14.90 subset( 99.05/14.90 Y0, Y1)))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (binintersect( 99.05/14.90 Y0, 99.05/14.90 binunion( 99.05/14.90 Y1, Y2)) = 99.05/14.90 binunion( 99.05/14.90 binintersect( 99.05/14.90 Y0, Y1), 99.05/14.90 binintersect( 99.05/14.90 Y0, Y2)))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y1))) => 99.05/14.90 in(Y2, 99.05/14.90 setminus( 99.05/14.90 Y0, Y1))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 setminus( 99.05/14.90 Y0, Y1)) => 99.05/14.90 in(Y2, 99.05/14.90 Y0))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 setminus( 99.05/14.90 Y0, Y1)) => 99.05/14.90 (~( 99.05/14.90 in(Y2, 99.05/14.90 Y1))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y0, Y1) => 99.05/14.90 (setminus( 99.05/14.90 Y0, Y1) = 99.05/14.90 emptyset)))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 setminus( 99.05/14.90 Y0, Y1)))) => 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 in(Y2, 99.05/14.90 Y1)))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 setminus( 99.05/14.90 Y0, Y1)))) => 99.05/14.90 (( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y1))) => 99.05/14.90 (~( 99.05/14.90 in(Y2, 99.05/14.90 Y0)))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y0))) => 99.05/14.90 (~( 99.05/14.90 in(Y2, 99.05/14.90 setminus( 99.05/14.90 Y0, Y1)))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y1) => 99.05/14.90 (~( 99.05/14.90 in(Y2, 99.05/14.90 setminus( 99.05/14.90 Y0, Y1)))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 subset( 99.05/14.90 setminus( 99.05/14.90 Y0, Y1), 99.05/14.90 Y0))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (( 99.05/14.90 setminus( 99.05/14.90 Y0, Y1) = 99.05/14.90 emptyset) => 99.05/14.90 subset( 99.05/14.90 Y0, Y1)))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 symdiff( 99.05/14.90 Y0, Y1)) => 99.05/14.90 (!!(( 99.05/14.90 ^[Y3 : $o]: 99.05/14.90 (( 99.05/14.90 in(Y2, 99.05/14.90 Y0) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y1))) => 99.05/14.90 Y3)) => 99.05/14.90 (( 99.05/14.90 ( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y0))) => 99.05/14.90 ( 99.05/14.90 in(Y2, 99.05/14.90 Y1) => Y3)) => 99.05/14.90 Y3))))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y1))) => 99.05/14.90 in(Y2, 99.05/14.90 symdiff( 99.05/14.90 Y0, Y1))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y0))) => 99.05/14.90 (in(Y2, 99.05/14.90 Y1) => 99.05/14.90 in(Y2, 99.05/14.90 symdiff( 99.05/14.90 Y0, Y1))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (in(Y2, 99.05/14.90 Y1) => 99.05/14.90 (~( 99.05/14.90 in(Y2, 99.05/14.90 symdiff( 99.05/14.90 Y0, Y1))))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y0))) => 99.05/14.90 (( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y1))) => 99.05/14.90 (~( 99.05/14.90 in(Y2, 99.05/14.90 symdiff( 99.05/14.90 Y0, Y1))))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 in(Y1, 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 in(Y0, 99.05/14.90 setunion( 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 in(Y1, 99.05/14.90 setunion( 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (??(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 setunion( 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)))) & 99.05/14.90 (??(( 99.05/14.90 ^[Y3 : $i]: 99.05/14.90 (in(Y3, 99.05/14.90 setunion( 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)))) & 99.05/14.90 (setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)) = 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 setadjoin( 99.05/14.90 Y3, 99.05/14.90 emptyset)), 99.05/14.90 emptyset))))))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (??(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 setunion( 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)))) & 99.05/14.90 (??(( 99.05/14.90 ^[Y3 : $i]: 99.05/14.90 (in(Y3, 99.05/14.90 setunion( 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)))) & 99.05/14.90 (setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)) = 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 setadjoin( 99.05/14.90 Y3, 99.05/14.90 emptyset)), 99.05/14.90 emptyset))))))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (in(Y1, 99.05/14.90 Y0) => 99.05/14.90 subset( 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset), 99.05/14.90 Y0)))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (in(Y1, 99.05/14.90 Y0) => 99.05/14.90 in( 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset), 99.05/14.90 powerset( 99.05/14.90 Y0))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 in( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 emptyset), 99.05/14.90 powerset( 99.05/14.90 binunion( 99.05/14.90 Y0, Y1))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset))) => 99.05/14.90 (( 99.05/14.90 Y2 = Y1) | 99.05/14.90 (Y2 = Y0)))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (!!(( 99.05/14.90 ^[Y3 : $i]: 99.05/14.90 (in(Y3, 99.05/14.90 Y1) => 99.05/14.90 subset( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 setadjoin( 99.05/14.90 Y3, 99.05/14.90 emptyset)), 99.05/14.90 binunion( 99.05/14.90 Y0, Y1)))))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (!!(( 99.05/14.90 ^[Y3 : $i]: 99.05/14.90 (in(Y3, 99.05/14.90 Y1) => 99.05/14.90 in( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 setadjoin( 99.05/14.90 Y3, 99.05/14.90 emptyset)), 99.05/14.90 powerset( 99.05/14.90 binunion( 99.05/14.90 Y0, Y1))))))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (!!(( 99.05/14.90 ^[Y3 : $i]: 99.05/14.90 (in(Y3, 99.05/14.90 Y1) => 99.05/14.90 subset( 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 setadjoin( 99.05/14.90 Y3, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)), 99.05/14.90 powerset( 99.05/14.90 binunion( 99.05/14.90 Y0, Y1))))))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (!!(( 99.05/14.90 ^[Y3 : $i]: 99.05/14.90 (in(Y3, 99.05/14.90 Y1) => 99.05/14.90 in( 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 setadjoin( 99.05/14.90 Y3, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)), 99.05/14.90 powerset( 99.05/14.90 powerset( 99.05/14.90 binunion( 99.05/14.90 Y0, Y1)))))))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (!!(( 99.05/14.90 ^[Y3 : $i]: 99.05/14.90 (in(Y3, 99.05/14.90 Y1) => 99.05/14.90 in( 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 setadjoin( 99.05/14.90 Y3, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)), 99.05/14.90 powerset( 99.05/14.90 powerset( 99.05/14.90 binunion( 99.05/14.90 Y0, Y1)))))))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (!!(( 99.05/14.90 ^[Y3 : $i]: 99.05/14.90 (in(Y3, 99.05/14.90 Y1) => 99.05/14.90 in( 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 setadjoin( 99.05/14.90 Y3, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)), 99.05/14.90 dsetconstr( 99.05/14.90 powerset( 99.05/14.90 powerset( 99.05/14.90 binunion( 99.05/14.90 Y0, Y1))), 99.05/14.90 (^[Y4 : $i]: 99.05/14.90 (??(( 99.05/14.90 ^[Y5 : $i]: 99.05/14.90 (in(Y5, 99.05/14.90 Y0) & 99.05/14.90 (??(( 99.05/14.90 ^[Y6 : $i]: 99.05/14.90 (in(Y6, 99.05/14.90 Y1) & 99.05/14.90 (Y4 = 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y5, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y5, 99.05/14.90 setadjoin( 99.05/14.90 Y6, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)))))))))))))))))))))))))))) => 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 dsetconstr( 99.05/14.90 powerset( 99.05/14.90 powerset( 99.05/14.90 binunion( 99.05/14.90 Y0, Y1))), 99.05/14.90 (^[Y3 : $i]: 99.05/14.90 (??(( 99.05/14.90 ^[Y4 : $i]: 99.05/14.90 (in(Y4, 99.05/14.90 Y0) & 99.05/14.90 (??(( 99.05/14.90 ^[Y5 : $i]: 99.05/14.90 (in(Y5, 99.05/14.90 Y1) & 99.05/14.90 (Y3 = 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y4, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y4, 99.05/14.90 setadjoin( 99.05/14.90 Y5, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)))))))))))))) => 99.05/14.90 (??(( 99.05/14.90 ^[Y3 : $i]: 99.05/14.90 (( 99.05/14.90 ??(( 99.05/14.90 ^[Y4 : $i]: 99.05/14.90 (in(Y4, 99.05/14.90 Y1) & 99.05/14.90 (Y2 = 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y3, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y3, 99.05/14.90 setadjoin( 99.05/14.90 Y4, 99.05/14.90 emptyset)), 99.05/14.90 emptyset))))))) & 99.05/14.90 in(Y3, 99.05/14.90 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.05/14.90 inference('lazy_cnf_imply', [status(thm)], ['195'])). 99.05/14.90 tff('197', plain, 99.05/14.90 ~ ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (in(Y1, powerset(Y0)) => 99.05/14.90 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (in(Y1, Y2) => 99.05/14.90 (in(Y2, Y0) => in(Y1, setunion(Y0))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (in(Y1, setunion(Y0)) => 99.05/14.90 (!!((^[Y2 : $o]: 99.05/14.90 ((!!((^[Y3 : $i]: 99.05/14.90 (in(Y1, Y3) => (in(Y3, Y0) => Y2))))) => 99.05/14.90 Y2))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (in(Y1, Y0) => in(Y1, powerset(setunion(Y0)))))))))) => 99.05/14.90 ((!!((^[Y0 : $i > $o]: 99.05/14.90 ((??((^[Y1 : $i]: 99.05/14.90 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.90 (??((^[Y1 : $i]: 99.05/14.90 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (in(Y0, setadjoin(Y1, emptyset)) => (Y0 = Y1)))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((Y0 != Y1) => 99.05/14.90 (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((Y0 = Y1) => in(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (in(Y0, setadjoin(Y1, emptyset)) => 99.05/14.90 in(Y1, setadjoin(Y0, emptyset))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 setadjoin(Y0, 99.05/14.90 setadjoin(Y1, emptyset))) => 99.05/14.90 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 in(Y0, 99.05/14.90 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 in(Y1, 99.05/14.90 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i > $o]: 99.05/14.90 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 99.05/14.90 (dsetconstr(Y0, Y1) != emptyset)))))))) => 99.05/14.90 ((!!((^[Y0 : $i > $o]: 99.05/14.90 (!!((^[Y1 : $i]: (in(Y1, emptyset) => Y0(Y1)))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i > $o]: 99.05/14.90 ((~((!!((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.90 (??((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i > $o]: 99.05/14.90 ((!!((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) => (~(Y1(Y2))))))) => 99.05/14.90 (~((??((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) & Y1(Y2)))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i > $o]: 99.05/14.90 ((~((??((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i > $o]: 99.05/14.90 ((??((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) & (~(Y1(Y2))))))) => 99.05/14.90 (~((!!((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) => Y1(Y2)))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $o]: (Y0 => in(emptyset, prop2set(Y0)))))) => 99.05/14.90 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i > $o]: 99.05/14.90 ((~((??((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i > $o]: 99.05/14.90 ((~((!!((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.90 (??((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i > $o]: 99.05/14.90 ((??(Y0)) => 99.05/14.90 ((!!((^[Y1 : $i]: 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (Y0(Y1) => 99.05/14.90 (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.90 (??((^[Y1 : $i]: 99.05/14.90 (Y0(Y1) & 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (Y0(Y2) => (Y1 = Y2)))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i > $o]: 99.05/14.90 ((??((^[Y1 : $i]: 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (Y0(Y2) <=> (Y2 = Y1)))))))) => 99.05/14.90 (??((^[Y1 : $i]: 99.05/14.90 (Y0(Y1) & 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((Y0 = Y1) => 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (!!((^[Y3 : $i]: 99.05/14.90 ((Y2 = Y3) => 99.05/14.90 (in(Y2, Y0) => 99.05/14.90 in(Y3, Y1)))))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((Y0 = Y1) => 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (!!((^[Y3 : $i]: 99.05/14.90 ((Y2 = Y3) => 99.05/14.90 (in(Y2, Y0) <=> 99.05/14.90 in(Y3, Y1)))))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i > $o]: 99.05/14.90 ((??((^[Y1 : $i]: 99.05/14.90 (Y0(Y1) & 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (Y0(Y1) => 99.05/14.90 (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i > $o]: 99.05/14.90 (!!((^[Y1 : $i > $o]: 99.05/14.90 ((!!((^[Y2 : $i]: 99.05/14.90 (!!((^[Y3 : $i]: 99.05/14.90 ((Y2 = Y3) => 99.05/14.90 (Y0(Y2) <=> 99.05/14.90 Y1(Y3))))))))) => 99.05/14.90 ((??((^[Y2 : $i]: 99.05/14.90 (Y0(Y2) & 99.05/14.90 (!!((^[Y3 : $i]: 99.05/14.90 (Y0(Y3) => 99.05/14.90 (Y2 = Y3))))))))) <=> 99.05/14.90 (??((^[Y2 : $i]: 99.05/14.90 (Y1(Y2) & 99.05/14.90 (!!((^[Y3 : $i]: 99.05/14.90 (Y1(Y3) => 99.05/14.90 (Y2 = Y3))))))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((Y0 = Y1) => 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (!!((^[Y3 : $i]: 99.05/14.90 ((Y2 = Y3) => 99.05/14.90 (setadjoin( 99.05/14.90 Y0, Y2) = 99.05/14.90 setadjoin( 99.05/14.90 Y1, Y3)))))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((Y0 = Y1) => 99.05/14.90 (powerset(Y0) = 99.05/14.90 powerset(Y1))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((Y0 = Y1) => 99.05/14.90 (setunion(Y0) = 99.05/14.90 setunion(Y1))))))))) => 99.05/14.90 ((!!((^[Y0 : $i > $o]: 99.05/14.90 ((??((^[Y1 : $i]: 99.05/14.90 (Y0(Y1) & 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (Y0(Y2) => 99.05/14.90 (Y1 = Y2))))))))) => 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (Y0(Y1) => 99.05/14.90 (Y0(Y2) => 99.05/14.90 (Y1 = Y2))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i > $o]: 99.05/14.90 (!!((^[Y1 : $i > $o]: 99.05/14.90 ((!!((^[Y2 : $i]: 99.05/14.90 (!!((^[Y3 : $i]: 99.05/14.90 (( 99.05/14.90 Y2 = Y3) => 99.05/14.90 (Y0(Y2) <=> 99.05/14.90 Y1(Y3))))))))) => 99.05/14.90 ((??((^[Y2 : $i]: 99.05/14.90 (Y0(Y2) & 99.05/14.90 (!!(( 99.05/14.90 ^[Y3 : $i]: 99.05/14.90 (Y0(Y3) => 99.05/14.90 ( 99.05/14.90 Y2 = Y3))))))))) => 99.05/14.90 ((??((^[Y2 : $i]: 99.05/14.90 (Y1(Y2) & 99.05/14.90 (!!(( 99.05/14.90 ^[Y3 : $i]: 99.05/14.90 ( 99.05/14.90 Y1(Y3) => 99.05/14.90 ( 99.05/14.90 Y2 = Y3))))))))) => 99.05/14.90 (descr(Y0) = 99.05/14.90 descr(Y1))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((Y0 = Y1) => 99.05/14.90 (!!((^[Y2 : $i > $o]: 99.05/14.90 (!!((^[Y3 : $i > $o]: 99.05/14.90 (( 99.05/14.90 !!(( 99.05/14.90 ^[Y4 : $i]: 99.05/14.90 (in(Y4, 99.05/14.90 Y0) => 99.05/14.90 (!!(( 99.05/14.90 ^[Y5 : $i]: 99.05/14.90 (in(Y5, 99.05/14.90 Y1) => 99.05/14.90 (( 99.05/14.90 Y4 = Y5) => 99.05/14.90 (Y2(Y4) <=> 99.05/14.90 Y3(Y5))))))))))) => 99.05/14.90 (dsetconstr( 99.05/14.90 Y0, Y2) = 99.05/14.90 dsetconstr( 99.05/14.90 Y1, Y3)))))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((!!((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) => 99.05/14.90 in(Y2, Y1))))) => 99.05/14.90 subset(Y0, Y1)))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((Y0 = Y1) => 99.05/14.90 subset(Y1, Y0)))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((Y0 = Y1) => 99.05/14.90 subset(Y0, Y1)))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((!!((^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 in(Y2, 99.05/14.90 Y1))))) => 99.05/14.90 subset(Y0, Y1)))))))) => 99.05/14.90 ((!!(subset(emptyset))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 ( 99.05/14.90 subset( 99.05/14.90 Y0, Y1) => 99.05/14.90 ( 99.05/14.90 in(Y2, 99.05/14.90 Y0) => 99.05/14.90 in(Y2, 99.05/14.90 Y1)))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y0, Y1) => 99.05/14.90 (( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y1))) => 99.05/14.90 (~( 99.05/14.90 in(Y2, 99.05/14.90 Y0)))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y1))) => 99.05/14.90 (~( 99.05/14.90 subset( 99.05/14.90 Y0, Y1)))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((~(subset( 99.05/14.90 Y0, Y1))) => 99.05/14.90 (Y0 != Y1)))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 ( 99.05/14.90 in(Y2, 99.05/14.90 Y0) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y1))) => 99.05/14.90 ( 99.05/14.90 Y0 != Y1)))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 subset(Y0, Y0)))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y0, Y1) => 99.05/14.90 (subset( 99.05/14.90 Y1, Y2) => 99.05/14.90 subset( 99.05/14.90 Y0, Y2)))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 subset( 99.05/14.90 Y1, 99.05/14.90 setadjoin( 99.05/14.90 Y0, Y1)))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y0, Y2) => 99.05/14.90 subset( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, Y2)))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y0, Y1) => 99.05/14.90 in(Y0, 99.05/14.90 powerset( 99.05/14.90 Y1))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y0, Y1) => 99.05/14.90 ( 99.05/14.90 subset( 99.05/14.90 Y1, Y0) => 99.05/14.90 ( 99.05/14.90 Y0 = Y1))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (subset(Y0, 99.05/14.90 emptyset) => 99.05/14.90 (Y0 = 99.05/14.90 emptyset))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y1, Y0) => 99.05/14.90 in(Y1, 99.05/14.90 powerset( 99.05/14.90 Y0))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (in(Y1, 99.05/14.90 powerset( 99.05/14.90 Y0)) => 99.05/14.90 subset( 99.05/14.90 Y1, Y0)))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 in(Y0, 99.05/14.90 powerset( 99.05/14.90 Y0))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y0, Y1) => 99.05/14.90 subset( 99.05/14.90 powerset( 99.05/14.90 Y0), 99.05/14.90 powerset( 99.05/14.90 Y1))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i > $o]: 99.05/14.90 in( 99.05/14.90 dsetconstr( 99.05/14.90 Y0, Y1), 99.05/14.90 powerset( 99.05/14.90 Y0)))))))) => 99.05/14.90 ((!!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i > $o]: 99.05/14.90 subset( 99.05/14.90 dsetconstr( 99.05/14.90 Y0, Y1), 99.05/14.90 Y0))))))) => 99.05/14.90 ((!!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 in(Y2, 99.05/14.90 binunion( 99.05/14.90 Y0, Y1)))))))))))) => 99.05/14.90 ((!!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 in(Y1, 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset))))))))) => 99.05/14.90 ((!!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y1) => 99.05/14.90 in(Y2, 99.05/14.90 binunion( 99.05/14.90 Y0, Y1)))))))))))) => 99.05/14.90 (( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y3 : $o]: 99.05/14.90 (in(Y2, 99.05/14.90 binunion( 99.05/14.90 Y0, Y1)) => 99.05/14.90 (( 99.05/14.90 in(Y2, 99.05/14.90 Y0) => Y3) => 99.05/14.90 (( 99.05/14.90 in(Y2, 99.05/14.90 Y1) => Y3) => 99.05/14.90 Y3))))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 binunion( 99.05/14.90 Y0, Y1)) => 99.05/14.90 (in(Y2, 99.05/14.90 Y1) | 99.05/14.90 in(Y2, 99.05/14.90 Y0)))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 subset( 99.05/14.90 Y0, 99.05/14.90 binunion( 99.05/14.90 Y0, Y1)))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 subset( 99.05/14.90 Y1, 99.05/14.90 binunion( 99.05/14.90 Y0, Y1)))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (in(Y2, 99.05/14.90 Y1) => 99.05/14.90 in(Y2, 99.05/14.90 binintersect( 99.05/14.90 Y0, Y1))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y2, Y0) => 99.05/14.90 (subset( 99.05/14.90 Y2, Y1) => 99.05/14.90 subset( 99.05/14.90 Y2, 99.05/14.90 binintersect( 99.05/14.90 Y0, Y1))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 binintersect( 99.05/14.90 Y0, Y1)) => 99.05/14.90 in(Y2, 99.05/14.90 Y0))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 subset( 99.05/14.90 binintersect( 99.05/14.90 Y0, Y1), 99.05/14.90 Y0))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y0, Y1) => 99.05/14.90 (binintersect( 99.05/14.90 Y0, Y1) = 99.05/14.90 Y0)))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (( 99.05/14.90 binintersect( 99.05/14.90 Y0, Y1) = 99.05/14.90 Y1) => 99.05/14.90 subset( 99.05/14.90 Y1, Y0)))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 binintersect( 99.05/14.90 Y0, Y1)) => 99.05/14.90 in(Y2, 99.05/14.90 Y1))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (( 99.05/14.90 ~(( 99.05/14.90 ??(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) & 99.05/14.90 in(Y2, 99.05/14.90 Y1))))))) => 99.05/14.90 (binintersect( 99.05/14.90 Y0, Y1) = 99.05/14.90 emptyset)))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 subset( 99.05/14.90 binintersect( 99.05/14.90 Y0, Y1), 99.05/14.90 Y1))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y1, Y0) => 99.05/14.90 (binintersect( 99.05/14.90 Y0, Y1) = 99.05/14.90 Y1)))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (( 99.05/14.90 binintersect( 99.05/14.90 Y0, Y1) = 99.05/14.90 Y0) => 99.05/14.90 subset( 99.05/14.90 Y0, Y1)))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (binintersect( 99.05/14.90 Y0, 99.05/14.90 binunion( 99.05/14.90 Y1, Y2)) = 99.05/14.90 binunion( 99.05/14.90 binintersect( 99.05/14.90 Y0, Y1), 99.05/14.90 binintersect( 99.05/14.90 Y0, Y2)))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y1))) => 99.05/14.90 in(Y2, 99.05/14.90 setminus( 99.05/14.90 Y0, Y1))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 setminus( 99.05/14.90 Y0, Y1)) => 99.05/14.90 in(Y2, 99.05/14.90 Y0))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 setminus( 99.05/14.90 Y0, Y1)) => 99.05/14.90 (~( 99.05/14.90 in(Y2, 99.05/14.90 Y1))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y0, Y1) => 99.05/14.90 (setminus( 99.05/14.90 Y0, Y1) = 99.05/14.90 emptyset)))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 setminus( 99.05/14.90 Y0, Y1)))) => 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 in(Y2, 99.05/14.90 Y1)))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 setminus( 99.05/14.90 Y0, Y1)))) => 99.05/14.90 (( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y1))) => 99.05/14.90 (~( 99.05/14.90 in(Y2, 99.05/14.90 Y0)))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y0))) => 99.05/14.90 (~( 99.05/14.90 in(Y2, 99.05/14.90 setminus( 99.05/14.90 Y0, Y1)))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y1) => 99.05/14.90 (~( 99.05/14.90 in(Y2, 99.05/14.90 setminus( 99.05/14.90 Y0, Y1)))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 subset( 99.05/14.90 setminus( 99.05/14.90 Y0, Y1), 99.05/14.90 Y0))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (( 99.05/14.90 setminus( 99.05/14.90 Y0, Y1) = 99.05/14.90 emptyset) => 99.05/14.90 subset( 99.05/14.90 Y0, Y1)))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 symdiff( 99.05/14.90 Y0, Y1)) => 99.05/14.90 (!!(( 99.05/14.90 ^[Y3 : $o]: 99.05/14.90 (( 99.05/14.90 in(Y2, 99.05/14.90 Y0) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y1))) => 99.05/14.90 Y3)) => 99.05/14.90 (( 99.05/14.90 ( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y0))) => 99.05/14.90 ( 99.05/14.90 in(Y2, 99.05/14.90 Y1) => Y3)) => 99.05/14.90 Y3))))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y1))) => 99.05/14.90 in(Y2, 99.05/14.90 symdiff( 99.05/14.90 Y0, Y1))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y0))) => 99.05/14.90 (in(Y2, 99.05/14.90 Y1) => 99.05/14.90 in(Y2, 99.05/14.90 symdiff( 99.05/14.90 Y0, Y1))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (in(Y2, 99.05/14.90 Y1) => 99.05/14.90 (~( 99.05/14.90 in(Y2, 99.05/14.90 symdiff( 99.05/14.90 Y0, Y1))))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y0))) => 99.05/14.90 (( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y1))) => 99.05/14.90 (~( 99.05/14.90 in(Y2, 99.05/14.90 symdiff( 99.05/14.90 Y0, Y1))))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 in(Y1, 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 in(Y0, 99.05/14.90 setunion( 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 in(Y1, 99.05/14.90 setunion( 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (??(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 setunion( 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)))) & 99.05/14.90 (??(( 99.05/14.90 ^[Y3 : $i]: 99.05/14.90 (in(Y3, 99.05/14.90 setunion( 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)))) & 99.05/14.90 (setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)) = 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 setadjoin( 99.05/14.90 Y3, 99.05/14.90 emptyset)), 99.05/14.90 emptyset))))))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (??(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 setunion( 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)))) & 99.05/14.90 (??(( 99.05/14.90 ^[Y3 : $i]: 99.05/14.90 (in(Y3, 99.05/14.90 setunion( 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)))) & 99.05/14.90 (setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)) = 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 setadjoin( 99.05/14.90 Y3, 99.05/14.90 emptyset)), 99.05/14.90 emptyset))))))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (in(Y1, 99.05/14.90 Y0) => 99.05/14.90 subset( 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset), 99.05/14.90 Y0)))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (in(Y1, 99.05/14.90 Y0) => 99.05/14.90 in( 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset), 99.05/14.90 powerset( 99.05/14.90 Y0))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 in( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 emptyset), 99.05/14.90 powerset( 99.05/14.90 binunion( 99.05/14.90 Y0, Y1))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset))) => 99.05/14.90 (( 99.05/14.90 Y2 = Y1) | 99.05/14.90 (Y2 = Y0)))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (!!(( 99.05/14.90 ^[Y3 : $i]: 99.05/14.90 (in(Y3, 99.05/14.90 Y1) => 99.05/14.90 subset( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 setadjoin( 99.05/14.90 Y3, 99.05/14.90 emptyset)), 99.05/14.90 binunion( 99.05/14.90 Y0, Y1)))))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (!!(( 99.05/14.90 ^[Y3 : $i]: 99.05/14.90 (in(Y3, 99.05/14.90 Y1) => 99.05/14.90 in( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 setadjoin( 99.05/14.90 Y3, 99.05/14.90 emptyset)), 99.05/14.90 powerset( 99.05/14.90 binunion( 99.05/14.90 Y0, Y1))))))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (!!(( 99.05/14.90 ^[Y3 : $i]: 99.05/14.90 (in(Y3, 99.05/14.90 Y1) => 99.05/14.90 subset( 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 setadjoin( 99.05/14.90 Y3, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)), 99.05/14.90 powerset( 99.05/14.90 binunion( 99.05/14.90 Y0, Y1))))))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (!!(( 99.05/14.90 ^[Y3 : $i]: 99.05/14.90 (in(Y3, 99.05/14.90 Y1) => 99.05/14.90 in( 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 setadjoin( 99.05/14.90 Y3, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)), 99.05/14.90 powerset( 99.05/14.90 powerset( 99.05/14.90 binunion( 99.05/14.90 Y0, Y1)))))))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (!!(( 99.05/14.90 ^[Y3 : $i]: 99.05/14.90 (in(Y3, 99.05/14.90 Y1) => 99.05/14.90 in( 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 setadjoin( 99.05/14.90 Y3, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)), 99.05/14.90 powerset( 99.05/14.90 powerset( 99.05/14.90 binunion( 99.05/14.90 Y0, Y1)))))))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (!!(( 99.05/14.90 ^[Y3 : $i]: 99.05/14.90 (in(Y3, 99.05/14.90 Y1) => 99.05/14.90 in( 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 setadjoin( 99.05/14.90 Y3, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)), 99.05/14.90 dsetconstr( 99.05/14.90 powerset( 99.05/14.90 powerset( 99.05/14.90 binunion( 99.05/14.90 Y0, Y1))), 99.05/14.90 (^[Y4 : $i]: 99.05/14.90 (??(( 99.05/14.90 ^[Y5 : $i]: 99.05/14.90 (in(Y5, 99.05/14.90 Y0) & 99.05/14.90 (??(( 99.05/14.90 ^[Y6 : $i]: 99.05/14.90 (in(Y6, 99.05/14.90 Y1) & 99.05/14.90 (Y4 = 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y5, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y5, 99.05/14.90 setadjoin( 99.05/14.90 Y6, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)))))))))))))))))))))))))))) => 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 dsetconstr( 99.05/14.90 powerset( 99.05/14.90 powerset( 99.05/14.90 binunion( 99.05/14.90 Y0, Y1))), 99.05/14.90 (^[Y3 : $i]: 99.05/14.90 (??(( 99.05/14.90 ^[Y4 : $i]: 99.05/14.90 (in(Y4, 99.05/14.90 Y0) & 99.05/14.90 (??(( 99.05/14.90 ^[Y5 : $i]: 99.05/14.90 (in(Y5, 99.05/14.90 Y1) & 99.05/14.90 (Y3 = 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y4, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y4, 99.05/14.90 setadjoin( 99.05/14.90 Y5, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)))))))))))))) => 99.05/14.90 (??(( 99.05/14.90 ^[Y3 : $i]: 99.05/14.90 (( 99.05/14.90 ??(( 99.05/14.90 ^[Y4 : $i]: 99.05/14.90 (in(Y4, 99.05/14.90 Y1) & 99.05/14.90 (Y2 = 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y3, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y3, 99.05/14.90 setadjoin( 99.05/14.90 Y4, 99.05/14.90 emptyset)), 99.05/14.90 emptyset))))))) & 99.05/14.90 in(Y3, 99.05/14.90 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.05/14.90 inference('lazy_cnf_imply', [status(thm)], ['196'])). 99.05/14.90 tff('198', plain, 99.05/14.90 ~ ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (in(Y1, Y2) => 99.05/14.90 (in(Y2, Y0) => in(Y1, setunion(Y0))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (in(Y1, setunion(Y0)) => 99.05/14.90 (!!((^[Y2 : $o]: 99.05/14.90 ((!!((^[Y3 : $i]: 99.05/14.90 (in(Y1, Y3) => (in(Y3, Y0) => Y2))))) => 99.05/14.90 Y2))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (in(Y1, Y0) => in(Y1, powerset(setunion(Y0)))))))))) => 99.05/14.90 ((!!((^[Y0 : $i > $o]: 99.05/14.90 ((??((^[Y1 : $i]: 99.05/14.90 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.90 (??((^[Y1 : $i]: (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (in(Y0, setadjoin(Y1, emptyset)) => (Y0 = Y1)))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((Y0 != Y1) => 99.05/14.90 (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((Y0 = Y1) => in(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (in(Y0, setadjoin(Y1, emptyset)) => 99.05/14.90 in(Y1, setadjoin(Y0, emptyset))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 setadjoin(Y0, 99.05/14.90 setadjoin(Y1, emptyset))) => 99.05/14.90 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 in(Y0, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 in(Y1, 99.05/14.90 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i > $o]: 99.05/14.90 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 99.05/14.90 (dsetconstr(Y0, Y1) != emptyset)))))))) => 99.05/14.90 ((!!((^[Y0 : $i > $o]: 99.05/14.90 (!!((^[Y1 : $i]: (in(Y1, emptyset) => Y0(Y1)))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i > $o]: 99.05/14.90 ((~((!!((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.90 (??((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i > $o]: 99.05/14.90 ((!!((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) => (~(Y1(Y2))))))) => 99.05/14.90 (~((??((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) & Y1(Y2)))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i > $o]: 99.05/14.90 ((~((??((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i > $o]: 99.05/14.90 ((??((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) & (~(Y1(Y2))))))) => 99.05/14.90 (~((!!((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) => Y1(Y2)))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $o]: (Y0 => in(emptyset, prop2set(Y0)))))) => 99.05/14.90 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i > $o]: 99.05/14.90 ((~((??((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i > $o]: 99.05/14.90 ((~((!!((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.90 (??((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i > $o]: 99.05/14.90 ((??(Y0)) => 99.05/14.90 ((!!((^[Y1 : $i]: 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (Y0(Y1) => 99.05/14.90 (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.90 (??((^[Y1 : $i]: 99.05/14.90 (Y0(Y1) & 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (Y0(Y2) => (Y1 = Y2)))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i > $o]: 99.05/14.90 ((??((^[Y1 : $i]: 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (Y0(Y2) <=> (Y2 = Y1)))))))) => 99.05/14.90 (??((^[Y1 : $i]: 99.05/14.90 (Y0(Y1) & 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((Y0 = Y1) => 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (!!((^[Y3 : $i]: 99.05/14.90 ((Y2 = Y3) => 99.05/14.90 (in(Y2, Y0) => 99.05/14.90 in(Y3, Y1)))))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((Y0 = Y1) => 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (!!((^[Y3 : $i]: 99.05/14.90 ((Y2 = Y3) => 99.05/14.90 (in(Y2, Y0) <=> 99.05/14.90 in(Y3, Y1)))))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i > $o]: 99.05/14.90 ((??((^[Y1 : $i]: 99.05/14.90 (Y0(Y1) & 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (Y0(Y1) => 99.05/14.90 (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i > $o]: 99.05/14.90 (!!((^[Y1 : $i > $o]: 99.05/14.90 ((!!((^[Y2 : $i]: 99.05/14.90 (!!((^[Y3 : $i]: 99.05/14.90 ((Y2 = Y3) => 99.05/14.90 (Y0(Y2) <=> 99.05/14.90 Y1(Y3))))))))) => 99.05/14.90 ((??((^[Y2 : $i]: 99.05/14.90 (Y0(Y2) & 99.05/14.90 (!!((^[Y3 : $i]: 99.05/14.90 (Y0(Y3) => 99.05/14.90 (Y2 = Y3))))))))) <=> 99.05/14.90 (??((^[Y2 : $i]: 99.05/14.90 (Y1(Y2) & 99.05/14.90 (!!((^[Y3 : $i]: 99.05/14.90 (Y1(Y3) => 99.05/14.90 (Y2 = Y3))))))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((Y0 = Y1) => 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (!!((^[Y3 : $i]: 99.05/14.90 ((Y2 = Y3) => 99.05/14.90 (setadjoin( 99.05/14.90 Y0, Y2) = 99.05/14.90 setadjoin( 99.05/14.90 Y1, Y3)))))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((Y0 = Y1) => 99.05/14.90 (powerset(Y0) = 99.05/14.90 powerset(Y1))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((Y0 = Y1) => 99.05/14.90 (setunion(Y0) = 99.05/14.90 setunion(Y1))))))))) => 99.05/14.90 ((!!((^[Y0 : $i > $o]: 99.05/14.90 ((??((^[Y1 : $i]: 99.05/14.90 (Y0(Y1) & 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (Y0(Y2) => 99.05/14.90 (Y1 = Y2))))))))) => 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (Y0(Y1) => 99.05/14.90 (Y0(Y2) => 99.05/14.90 (Y1 = Y2))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i > $o]: 99.05/14.90 (!!((^[Y1 : $i > $o]: 99.05/14.90 ((!!((^[Y2 : $i]: 99.05/14.90 (!!((^[Y3 : $i]: 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 Y2 = Y3) => 99.05/14.90 ( 99.05/14.90 Y0(Y2) <=> 99.05/14.90 Y1(Y3))))))))) => 99.05/14.90 ((??((^[Y2 : $i]: 99.05/14.90 (Y0(Y2) & 99.05/14.90 (!!((^[Y3 : $i]: 99.05/14.90 (Y0(Y3) => 99.05/14.90 (Y2 = Y3))))))))) => 99.05/14.90 ((??((^[Y2 : $i]: 99.05/14.90 (Y1(Y2) & 99.05/14.90 (!!(( 99.05/14.90 ^[Y3 : $i]: 99.05/14.90 (Y1(Y3) => 99.05/14.90 ( 99.05/14.90 Y2 = Y3))))))))) => 99.05/14.90 (descr(Y0) = 99.05/14.90 descr(Y1))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((Y0 = Y1) => 99.05/14.90 (!!((^[Y2 : $i > $o]: 99.05/14.90 (!!((^[Y3 : $i > $o]: 99.05/14.90 (( 99.05/14.90 !!(( 99.05/14.90 ^[Y4 : $i]: 99.05/14.90 (in(Y4, 99.05/14.90 Y0) => 99.05/14.90 (!!(( 99.05/14.90 ^[Y5 : $i]: 99.05/14.90 (in(Y5, 99.05/14.90 Y1) => 99.05/14.90 (( 99.05/14.90 Y4 = Y5) => 99.05/14.90 (Y2(Y4) <=> 99.05/14.90 Y3(Y5))))))))))) => 99.05/14.90 (dsetconstr( 99.05/14.90 Y0, Y2) = 99.05/14.90 dsetconstr( 99.05/14.90 Y1, Y3)))))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((!!((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) => 99.05/14.90 in(Y2, Y1))))) => 99.05/14.90 subset(Y0, Y1)))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((Y0 = Y1) => 99.05/14.90 subset(Y1, Y0)))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((Y0 = Y1) => 99.05/14.90 subset(Y0, Y1)))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((!!((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) => 99.05/14.90 in(Y2, Y1))))) => 99.05/14.90 subset(Y0, Y1)))))))) => 99.05/14.90 ((!!(subset(emptyset))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y0, Y1) => 99.05/14.90 ( 99.05/14.90 in(Y2, 99.05/14.90 Y0) => 99.05/14.90 in(Y2, 99.05/14.90 Y1)))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 ( 99.05/14.90 subset( 99.05/14.90 Y0, Y1) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y1))) => 99.05/14.90 ( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y0)))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y1))) => 99.05/14.90 (~( 99.05/14.90 subset( 99.05/14.90 Y0, Y1)))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((~(subset( 99.05/14.90 Y0, Y1))) => 99.05/14.90 (Y0 != Y1)))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y1))) => 99.05/14.90 ( 99.05/14.90 Y0 != Y1)))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 subset(Y0, Y0)))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y0, Y1) => 99.05/14.90 (subset( 99.05/14.90 Y1, Y2) => 99.05/14.90 subset( 99.05/14.90 Y0, Y2)))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 subset( 99.05/14.90 Y1, 99.05/14.90 setadjoin( 99.05/14.90 Y0, Y1)))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y0, Y2) => 99.05/14.90 subset( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, Y2)))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y0, Y1) => 99.05/14.90 in(Y0, 99.05/14.90 powerset( 99.05/14.90 Y1))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y0, Y1) => 99.05/14.90 (subset( 99.05/14.90 Y1, Y0) => 99.05/14.90 (Y0 = Y1))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (subset(Y0, 99.05/14.90 emptyset) => 99.05/14.90 (Y0 = 99.05/14.90 emptyset))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 ( 99.05/14.90 subset( 99.05/14.90 Y1, Y0) => 99.05/14.90 in(Y1, 99.05/14.90 powerset( 99.05/14.90 Y0))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (in(Y1, 99.05/14.90 powerset( 99.05/14.90 Y0)) => 99.05/14.90 subset( 99.05/14.90 Y1, Y0)))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 in(Y0, 99.05/14.90 powerset( 99.05/14.90 Y0))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y0, Y1) => 99.05/14.90 subset( 99.05/14.90 powerset( 99.05/14.90 Y0), 99.05/14.90 powerset( 99.05/14.90 Y1))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i > $o]: 99.05/14.90 in( 99.05/14.90 dsetconstr( 99.05/14.90 Y0, Y1), 99.05/14.90 powerset( 99.05/14.90 Y0)))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i > $o]: 99.05/14.90 subset( 99.05/14.90 dsetconstr( 99.05/14.90 Y0, Y1), 99.05/14.90 Y0))))))) => 99.05/14.90 ((!!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 in(Y2, 99.05/14.90 binunion( 99.05/14.90 Y0, Y1)))))))))))) => 99.05/14.90 ((!!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 in(Y1, 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset))))))))) => 99.05/14.90 ((!!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y1) => 99.05/14.90 in(Y2, 99.05/14.90 binunion( 99.05/14.90 Y0, Y1)))))))))))) => 99.05/14.90 ((!!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y3 : $o]: 99.05/14.90 (in(Y2, 99.05/14.90 binunion( 99.05/14.90 Y0, Y1)) => 99.05/14.90 (( 99.05/14.90 in(Y2, 99.05/14.90 Y0) => Y3) => 99.05/14.90 (( 99.05/14.90 in(Y2, 99.05/14.90 Y1) => Y3) => 99.05/14.90 Y3))))))))))))))) => 99.05/14.90 (( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 binunion( 99.05/14.90 Y0, Y1)) => 99.05/14.90 (in(Y2, 99.05/14.90 Y1) | 99.05/14.90 in(Y2, 99.05/14.90 Y0)))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 subset( 99.05/14.90 Y0, 99.05/14.90 binunion( 99.05/14.90 Y0, Y1)))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 subset( 99.05/14.90 Y1, 99.05/14.90 binunion( 99.05/14.90 Y0, Y1)))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (in(Y2, 99.05/14.90 Y1) => 99.05/14.90 in(Y2, 99.05/14.90 binintersect( 99.05/14.90 Y0, Y1))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y2, Y0) => 99.05/14.90 (subset( 99.05/14.90 Y2, Y1) => 99.05/14.90 subset( 99.05/14.90 Y2, 99.05/14.90 binintersect( 99.05/14.90 Y0, Y1))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 binintersect( 99.05/14.90 Y0, Y1)) => 99.05/14.90 in(Y2, 99.05/14.90 Y0))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 subset( 99.05/14.90 binintersect( 99.05/14.90 Y0, Y1), 99.05/14.90 Y0))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y0, Y1) => 99.05/14.90 (binintersect( 99.05/14.90 Y0, Y1) = 99.05/14.90 Y0)))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (( 99.05/14.90 binintersect( 99.05/14.90 Y0, Y1) = 99.05/14.90 Y1) => 99.05/14.90 subset( 99.05/14.90 Y1, Y0)))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 binintersect( 99.05/14.90 Y0, Y1)) => 99.05/14.90 in(Y2, 99.05/14.90 Y1))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (( 99.05/14.90 ~(( 99.05/14.90 ??(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) & 99.05/14.90 in(Y2, 99.05/14.90 Y1))))))) => 99.05/14.90 (binintersect( 99.05/14.90 Y0, Y1) = 99.05/14.90 emptyset)))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 subset( 99.05/14.90 binintersect( 99.05/14.90 Y0, Y1), 99.05/14.90 Y1))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y1, Y0) => 99.05/14.90 (binintersect( 99.05/14.90 Y0, Y1) = 99.05/14.90 Y1)))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (( 99.05/14.90 binintersect( 99.05/14.90 Y0, Y1) = 99.05/14.90 Y0) => 99.05/14.90 subset( 99.05/14.90 Y0, Y1)))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (binintersect( 99.05/14.90 Y0, 99.05/14.90 binunion( 99.05/14.90 Y1, Y2)) = 99.05/14.90 binunion( 99.05/14.90 binintersect( 99.05/14.90 Y0, Y1), 99.05/14.90 binintersect( 99.05/14.90 Y0, Y2)))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y1))) => 99.05/14.90 in(Y2, 99.05/14.90 setminus( 99.05/14.90 Y0, Y1))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 setminus( 99.05/14.90 Y0, Y1)) => 99.05/14.90 in(Y2, 99.05/14.90 Y0))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 setminus( 99.05/14.90 Y0, Y1)) => 99.05/14.90 (~( 99.05/14.90 in(Y2, 99.05/14.90 Y1))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y0, Y1) => 99.05/14.90 (setminus( 99.05/14.90 Y0, Y1) = 99.05/14.90 emptyset)))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 setminus( 99.05/14.90 Y0, Y1)))) => 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 in(Y2, 99.05/14.90 Y1)))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 setminus( 99.05/14.90 Y0, Y1)))) => 99.05/14.90 (( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y1))) => 99.05/14.90 (~( 99.05/14.90 in(Y2, 99.05/14.90 Y0)))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y0))) => 99.05/14.90 (~( 99.05/14.90 in(Y2, 99.05/14.90 setminus( 99.05/14.90 Y0, Y1)))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y1) => 99.05/14.90 (~( 99.05/14.90 in(Y2, 99.05/14.90 setminus( 99.05/14.90 Y0, Y1)))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 subset( 99.05/14.90 setminus( 99.05/14.90 Y0, Y1), 99.05/14.90 Y0))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (( 99.05/14.90 setminus( 99.05/14.90 Y0, Y1) = 99.05/14.90 emptyset) => 99.05/14.90 subset( 99.05/14.90 Y0, Y1)))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 symdiff( 99.05/14.90 Y0, Y1)) => 99.05/14.90 (!!(( 99.05/14.90 ^[Y3 : $o]: 99.05/14.90 (( 99.05/14.90 in(Y2, 99.05/14.90 Y0) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y1))) => 99.05/14.90 Y3)) => 99.05/14.90 (( 99.05/14.90 ( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y0))) => 99.05/14.90 ( 99.05/14.90 in(Y2, 99.05/14.90 Y1) => Y3)) => 99.05/14.90 Y3))))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y1))) => 99.05/14.90 in(Y2, 99.05/14.90 symdiff( 99.05/14.90 Y0, Y1))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y0))) => 99.05/14.90 (in(Y2, 99.05/14.90 Y1) => 99.05/14.90 in(Y2, 99.05/14.90 symdiff( 99.05/14.90 Y0, Y1))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (in(Y2, 99.05/14.90 Y1) => 99.05/14.90 (~( 99.05/14.90 in(Y2, 99.05/14.90 symdiff( 99.05/14.90 Y0, Y1))))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y0))) => 99.05/14.90 (( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y1))) => 99.05/14.90 (~( 99.05/14.90 in(Y2, 99.05/14.90 symdiff( 99.05/14.90 Y0, Y1))))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 in(Y1, 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 in(Y0, 99.05/14.90 setunion( 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 in(Y1, 99.05/14.90 setunion( 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (??(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 setunion( 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)))) & 99.05/14.90 (??(( 99.05/14.90 ^[Y3 : $i]: 99.05/14.90 (in(Y3, 99.05/14.90 setunion( 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)))) & 99.05/14.90 (setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)) = 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 setadjoin( 99.05/14.90 Y3, 99.05/14.90 emptyset)), 99.05/14.90 emptyset))))))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (??(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 setunion( 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)))) & 99.05/14.90 (??(( 99.05/14.90 ^[Y3 : $i]: 99.05/14.90 (in(Y3, 99.05/14.90 setunion( 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)))) & 99.05/14.90 (setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)) = 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 setadjoin( 99.05/14.90 Y3, 99.05/14.90 emptyset)), 99.05/14.90 emptyset))))))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (in(Y1, 99.05/14.90 Y0) => 99.05/14.90 subset( 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset), 99.05/14.90 Y0)))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (in(Y1, 99.05/14.90 Y0) => 99.05/14.90 in( 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset), 99.05/14.90 powerset( 99.05/14.90 Y0))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 in( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 emptyset), 99.05/14.90 powerset( 99.05/14.90 binunion( 99.05/14.90 Y0, Y1))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset))) => 99.05/14.90 (( 99.05/14.90 Y2 = Y1) | 99.05/14.90 (Y2 = Y0)))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (!!(( 99.05/14.90 ^[Y3 : $i]: 99.05/14.90 (in(Y3, 99.05/14.90 Y1) => 99.05/14.90 subset( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 setadjoin( 99.05/14.90 Y3, 99.05/14.90 emptyset)), 99.05/14.90 binunion( 99.05/14.90 Y0, Y1)))))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (!!(( 99.05/14.90 ^[Y3 : $i]: 99.05/14.90 (in(Y3, 99.05/14.90 Y1) => 99.05/14.90 in( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 setadjoin( 99.05/14.90 Y3, 99.05/14.90 emptyset)), 99.05/14.90 powerset( 99.05/14.90 binunion( 99.05/14.90 Y0, Y1))))))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (!!(( 99.05/14.90 ^[Y3 : $i]: 99.05/14.90 (in(Y3, 99.05/14.90 Y1) => 99.05/14.90 subset( 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 setadjoin( 99.05/14.90 Y3, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)), 99.05/14.90 powerset( 99.05/14.90 binunion( 99.05/14.90 Y0, Y1))))))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (!!(( 99.05/14.90 ^[Y3 : $i]: 99.05/14.90 (in(Y3, 99.05/14.90 Y1) => 99.05/14.90 in( 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 setadjoin( 99.05/14.90 Y3, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)), 99.05/14.90 powerset( 99.05/14.90 powerset( 99.05/14.90 binunion( 99.05/14.90 Y0, Y1)))))))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (!!(( 99.05/14.90 ^[Y3 : $i]: 99.05/14.90 (in(Y3, 99.05/14.90 Y1) => 99.05/14.90 in( 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 setadjoin( 99.05/14.90 Y3, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)), 99.05/14.90 powerset( 99.05/14.90 powerset( 99.05/14.90 binunion( 99.05/14.90 Y0, Y1)))))))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (!!(( 99.05/14.90 ^[Y3 : $i]: 99.05/14.90 (in(Y3, 99.05/14.90 Y1) => 99.05/14.90 in( 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 setadjoin( 99.05/14.90 Y3, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)), 99.05/14.90 dsetconstr( 99.05/14.90 powerset( 99.05/14.90 powerset( 99.05/14.90 binunion( 99.05/14.90 Y0, Y1))), 99.05/14.90 (^[Y4 : $i]: 99.05/14.90 (??(( 99.05/14.90 ^[Y5 : $i]: 99.05/14.90 (in(Y5, 99.05/14.90 Y0) & 99.05/14.90 (??(( 99.05/14.90 ^[Y6 : $i]: 99.05/14.90 (in(Y6, 99.05/14.90 Y1) & 99.05/14.90 (Y4 = 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y5, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y5, 99.05/14.90 setadjoin( 99.05/14.90 Y6, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)))))))))))))))))))))))))))) => 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 dsetconstr( 99.05/14.90 powerset( 99.05/14.90 powerset( 99.05/14.90 binunion( 99.05/14.90 Y0, Y1))), 99.05/14.90 (^[Y3 : $i]: 99.05/14.90 (??(( 99.05/14.90 ^[Y4 : $i]: 99.05/14.90 (in(Y4, 99.05/14.90 Y0) & 99.05/14.90 (??(( 99.05/14.90 ^[Y5 : $i]: 99.05/14.90 (in(Y5, 99.05/14.90 Y1) & 99.05/14.90 (Y3 = 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y4, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y4, 99.05/14.90 setadjoin( 99.05/14.90 Y5, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)))))))))))))) => 99.05/14.90 (??(( 99.05/14.90 ^[Y3 : $i]: 99.05/14.90 (( 99.05/14.90 ??(( 99.05/14.90 ^[Y4 : $i]: 99.05/14.90 (in(Y4, 99.05/14.90 Y1) & 99.05/14.90 (Y2 = 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y3, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y3, 99.05/14.90 setadjoin( 99.05/14.90 Y4, 99.05/14.90 emptyset)), 99.05/14.90 emptyset))))))) & 99.05/14.90 in(Y3, 99.05/14.90 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.05/14.90 inference('lazy_cnf_imply', [status(thm)], ['197'])). 99.05/14.90 tff('199', plain, 99.05/14.90 ~ ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (in(Y1, setunion(Y0)) => 99.05/14.90 (!!((^[Y2 : $o]: 99.05/14.90 ((!!((^[Y3 : $i]: 99.05/14.90 (in(Y1, Y3) => (in(Y3, Y0) => Y2))))) => 99.05/14.90 Y2))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (in(Y1, Y0) => in(Y1, powerset(setunion(Y0)))))))))) => 99.05/14.90 ((!!((^[Y0 : $i > $o]: 99.05/14.90 ((??((^[Y1 : $i]: 99.05/14.90 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.90 (??((^[Y1 : $i]: (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (in(Y0, setadjoin(Y1, emptyset)) => (Y0 = Y1)))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((Y0 != Y1) => (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((Y0 = Y1) => in(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (in(Y0, setadjoin(Y1, emptyset)) => 99.05/14.90 in(Y1, setadjoin(Y0, emptyset))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 setadjoin(Y0, setadjoin(Y1, emptyset))) => 99.05/14.90 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 in(Y0, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i > $o]: 99.05/14.90 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 99.05/14.90 (dsetconstr(Y0, Y1) != emptyset)))))))) => 99.05/14.90 ((!!((^[Y0 : $i > $o]: 99.05/14.90 (!!((^[Y1 : $i]: (in(Y1, emptyset) => Y0(Y1)))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i > $o]: 99.05/14.90 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.90 (??((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i > $o]: 99.05/14.90 ((!!((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) => (~(Y1(Y2))))))) => 99.05/14.90 (~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i > $o]: 99.05/14.90 ((~((??((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i > $o]: 99.05/14.90 ((??((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) & (~(Y1(Y2))))))) => 99.05/14.90 (~((!!((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) => Y1(Y2)))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $o]: (Y0 => in(emptyset, prop2set(Y0)))))) => 99.05/14.90 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i > $o]: 99.05/14.90 ((~((??((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i > $o]: 99.05/14.90 ((~((!!((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.90 (??((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i > $o]: 99.05/14.90 ((??(Y0)) => 99.05/14.90 ((!!((^[Y1 : $i]: 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (Y0(Y1) => 99.05/14.90 (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.90 (??((^[Y1 : $i]: 99.05/14.90 (Y0(Y1) & 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (Y0(Y2) => (Y1 = Y2)))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i > $o]: 99.05/14.90 ((??((^[Y1 : $i]: 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (Y0(Y2) <=> (Y2 = Y1)))))))) => 99.05/14.90 (??((^[Y1 : $i]: 99.05/14.90 (Y0(Y1) & 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((Y0 = Y1) => 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (!!((^[Y3 : $i]: 99.05/14.90 ((Y2 = Y3) => 99.05/14.90 (in(Y2, Y0) => 99.05/14.90 in(Y3, Y1)))))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((Y0 = Y1) => 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (!!((^[Y3 : $i]: 99.05/14.90 ((Y2 = Y3) => 99.05/14.90 (in(Y2, Y0) <=> 99.05/14.90 in(Y3, Y1)))))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i > $o]: 99.05/14.90 ((??((^[Y1 : $i]: 99.05/14.90 (Y0(Y1) & 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (Y0(Y1) => 99.05/14.90 (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i > $o]: 99.05/14.90 (!!((^[Y1 : $i > $o]: 99.05/14.90 ((!!((^[Y2 : $i]: 99.05/14.90 (!!((^[Y3 : $i]: 99.05/14.90 ((Y2 = Y3) => 99.05/14.90 (Y0(Y2) <=> 99.05/14.90 Y1(Y3))))))))) => 99.05/14.90 ((??((^[Y2 : $i]: 99.05/14.90 (Y0(Y2) & 99.05/14.90 (!!((^[Y3 : $i]: 99.05/14.90 (Y0(Y3) => 99.05/14.90 (Y2 = Y3))))))))) <=> 99.05/14.90 (??((^[Y2 : $i]: 99.05/14.90 (Y1(Y2) & 99.05/14.90 (!!((^[Y3 : $i]: 99.05/14.90 (Y1(Y3) => 99.05/14.90 (Y2 = Y3))))))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((Y0 = Y1) => 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (!!((^[Y3 : $i]: 99.05/14.90 ((Y2 = Y3) => 99.05/14.90 (setadjoin( 99.05/14.90 Y0, Y2) = 99.05/14.90 setadjoin( 99.05/14.90 Y1, Y3)))))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((Y0 = Y1) => 99.05/14.90 (powerset(Y0) = 99.05/14.90 powerset(Y1))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((Y0 = Y1) => 99.05/14.90 (setunion(Y0) = 99.05/14.90 setunion(Y1))))))))) => 99.05/14.90 ((!!((^[Y0 : $i > $o]: 99.05/14.90 ((??((^[Y1 : $i]: 99.05/14.90 (Y0(Y1) & 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (Y0(Y2) => 99.05/14.90 (Y1 = Y2))))))))) => 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (Y0(Y1) => 99.05/14.90 (Y0(Y2) => 99.05/14.90 (Y1 = Y2))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i > $o]: 99.05/14.90 (!!((^[Y1 : $i > $o]: 99.05/14.90 ((!!((^[Y2 : $i]: 99.05/14.90 (!!((^[Y3 : $i]: 99.05/14.90 (( 99.05/14.90 Y2 = Y3) => 99.05/14.90 ( 99.05/14.90 Y0(Y2) <=> 99.05/14.90 Y1(Y3))))))))) => 99.05/14.90 ((??((^[Y2 : $i]: 99.05/14.90 (Y0(Y2) & 99.05/14.90 (!!((^[Y3 : $i]: 99.05/14.90 (Y0(Y3) => 99.05/14.90 (Y2 = Y3))))))))) => 99.05/14.90 ((??((^[Y2 : $i]: 99.05/14.90 (Y1(Y2) & 99.05/14.90 (!!((^[Y3 : $i]: 99.05/14.90 (Y1(Y3) => 99.05/14.90 (Y2 = Y3))))))))) => 99.05/14.90 (descr(Y0) = descr(Y1))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((Y0 = Y1) => 99.05/14.90 (!!((^[Y2 : $i > $o]: 99.05/14.90 (!!((^[Y3 : $i > $o]: 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y4 : $i]: 99.05/14.90 (in(Y4, 99.05/14.90 Y0) => 99.05/14.90 (!!(( 99.05/14.90 ^[Y5 : $i]: 99.05/14.90 (in(Y5, 99.05/14.90 Y1) => 99.05/14.90 (( 99.05/14.90 Y4 = Y5) => 99.05/14.90 (Y2(Y4) <=> 99.05/14.90 Y3(Y5))))))))))) => 99.05/14.90 ( 99.05/14.90 dsetconstr( 99.05/14.90 Y0, Y2) = 99.05/14.90 dsetconstr( 99.05/14.90 Y1, Y3)))))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((!!((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) => 99.05/14.90 in(Y2, Y1))))) => 99.05/14.90 subset(Y0, Y1)))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((Y0 = Y1) => 99.05/14.90 subset(Y1, Y0)))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((Y0 = Y1) => 99.05/14.90 subset(Y0, Y1)))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((!!((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) => 99.05/14.90 in(Y2, Y1))))) => 99.05/14.90 subset(Y0, Y1)))))))) => 99.05/14.90 ((!!(subset(emptyset))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y0, Y1) => 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 in(Y2, 99.05/14.90 Y1)))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y0, Y1) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y1))) => 99.05/14.90 ( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y0)))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 ( 99.05/14.90 in(Y2, 99.05/14.90 Y0) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y1))) => 99.05/14.90 ( 99.05/14.90 ~( 99.05/14.90 subset( 99.05/14.90 Y0, Y1)))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((~(subset(Y0, 99.05/14.90 Y1))) => 99.05/14.90 (Y0 != Y1)))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y1))) => 99.05/14.90 (Y0 != Y1)))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 subset(Y0, Y0)))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 ( 99.05/14.90 subset( 99.05/14.90 Y0, Y1) => 99.05/14.90 ( 99.05/14.90 subset( 99.05/14.90 Y1, Y2) => 99.05/14.90 subset( 99.05/14.90 Y0, Y2)))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 subset(Y1, 99.05/14.90 setadjoin( 99.05/14.90 Y0, Y1)))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y0, Y2) => 99.05/14.90 subset( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, Y2)))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ( 99.05/14.90 subset( 99.05/14.90 Y0, Y1) => 99.05/14.90 in(Y0, 99.05/14.90 powerset( 99.05/14.90 Y1))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y0, Y1) => 99.05/14.90 (subset( 99.05/14.90 Y1, Y0) => 99.05/14.90 (Y0 = Y1))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (subset(Y0, 99.05/14.90 emptyset) => 99.05/14.90 (Y0 = 99.05/14.90 emptyset))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y1, Y0) => 99.05/14.90 in(Y1, 99.05/14.90 powerset( 99.05/14.90 Y0))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 ( 99.05/14.90 in(Y1, 99.05/14.90 powerset( 99.05/14.90 Y0)) => 99.05/14.90 subset( 99.05/14.90 Y1, Y0)))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 in(Y0, 99.05/14.90 powerset( 99.05/14.90 Y0))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y0, Y1) => 99.05/14.90 subset( 99.05/14.90 powerset( 99.05/14.90 Y0), 99.05/14.90 powerset( 99.05/14.90 Y1))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y1 : $i > $o]: 99.05/14.90 in( 99.05/14.90 dsetconstr( 99.05/14.90 Y0, Y1), 99.05/14.90 powerset( 99.05/14.90 Y0)))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i > $o]: 99.05/14.90 subset( 99.05/14.90 dsetconstr( 99.05/14.90 Y0, Y1), 99.05/14.90 Y0))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 in(Y2, 99.05/14.90 binunion( 99.05/14.90 Y0, Y1)))))))))))) => 99.05/14.90 ((!!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 in(Y1, 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset))))))))) => 99.05/14.90 ((!!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y1) => 99.05/14.90 in(Y2, 99.05/14.90 binunion( 99.05/14.90 Y0, Y1)))))))))))) => 99.05/14.90 ((!!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y3 : $o]: 99.05/14.90 (in(Y2, 99.05/14.90 binunion( 99.05/14.90 Y0, Y1)) => 99.05/14.90 (( 99.05/14.90 in(Y2, 99.05/14.90 Y0) => Y3) => 99.05/14.90 (( 99.05/14.90 in(Y2, 99.05/14.90 Y1) => Y3) => 99.05/14.90 Y3))))))))))))))) => 99.05/14.90 ((!!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 binunion( 99.05/14.90 Y0, Y1)) => 99.05/14.90 (in(Y2, 99.05/14.90 Y1) | 99.05/14.90 in(Y2, 99.05/14.90 Y0)))))))))))) => 99.05/14.90 (( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 subset( 99.05/14.90 Y0, 99.05/14.90 binunion( 99.05/14.90 Y0, Y1)))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 subset( 99.05/14.90 Y1, 99.05/14.90 binunion( 99.05/14.90 Y0, Y1)))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (in(Y2, 99.05/14.90 Y1) => 99.05/14.90 in(Y2, 99.05/14.90 binintersect( 99.05/14.90 Y0, Y1))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y2, Y0) => 99.05/14.90 (subset( 99.05/14.90 Y2, Y1) => 99.05/14.90 subset( 99.05/14.90 Y2, 99.05/14.90 binintersect( 99.05/14.90 Y0, Y1))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 binintersect( 99.05/14.90 Y0, Y1)) => 99.05/14.90 in(Y2, 99.05/14.90 Y0))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 subset( 99.05/14.90 binintersect( 99.05/14.90 Y0, Y1), 99.05/14.90 Y0))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y0, Y1) => 99.05/14.90 (binintersect( 99.05/14.90 Y0, Y1) = 99.05/14.90 Y0)))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (( 99.05/14.90 binintersect( 99.05/14.90 Y0, Y1) = 99.05/14.90 Y1) => 99.05/14.90 subset( 99.05/14.90 Y1, Y0)))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 binintersect( 99.05/14.90 Y0, Y1)) => 99.05/14.90 in(Y2, 99.05/14.90 Y1))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (( 99.05/14.90 ~(( 99.05/14.90 ??(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) & 99.05/14.90 in(Y2, 99.05/14.90 Y1))))))) => 99.05/14.90 (binintersect( 99.05/14.90 Y0, Y1) = 99.05/14.90 emptyset)))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 subset( 99.05/14.90 binintersect( 99.05/14.90 Y0, Y1), 99.05/14.90 Y1))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y1, Y0) => 99.05/14.90 (binintersect( 99.05/14.90 Y0, Y1) = 99.05/14.90 Y1)))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (( 99.05/14.90 binintersect( 99.05/14.90 Y0, Y1) = 99.05/14.90 Y0) => 99.05/14.90 subset( 99.05/14.90 Y0, Y1)))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (binintersect( 99.05/14.90 Y0, 99.05/14.90 binunion( 99.05/14.90 Y1, Y2)) = 99.05/14.90 binunion( 99.05/14.90 binintersect( 99.05/14.90 Y0, Y1), 99.05/14.90 binintersect( 99.05/14.90 Y0, Y2)))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y1))) => 99.05/14.90 in(Y2, 99.05/14.90 setminus( 99.05/14.90 Y0, Y1))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 setminus( 99.05/14.90 Y0, Y1)) => 99.05/14.90 in(Y2, 99.05/14.90 Y0))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 setminus( 99.05/14.90 Y0, Y1)) => 99.05/14.90 (~( 99.05/14.90 in(Y2, 99.05/14.90 Y1))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (subset( 99.05/14.90 Y0, Y1) => 99.05/14.90 (setminus( 99.05/14.90 Y0, Y1) = 99.05/14.90 emptyset)))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 setminus( 99.05/14.90 Y0, Y1)))) => 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 in(Y2, 99.05/14.90 Y1)))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 setminus( 99.05/14.90 Y0, Y1)))) => 99.05/14.90 (( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y1))) => 99.05/14.90 (~( 99.05/14.90 in(Y2, 99.05/14.90 Y0)))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y0))) => 99.05/14.90 (~( 99.05/14.90 in(Y2, 99.05/14.90 setminus( 99.05/14.90 Y0, Y1)))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y1) => 99.05/14.90 (~( 99.05/14.90 in(Y2, 99.05/14.90 setminus( 99.05/14.90 Y0, Y1)))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 subset( 99.05/14.90 setminus( 99.05/14.90 Y0, Y1), 99.05/14.90 Y0))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (( 99.05/14.90 setminus( 99.05/14.90 Y0, Y1) = 99.05/14.90 emptyset) => 99.05/14.90 subset( 99.05/14.90 Y0, Y1)))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 symdiff( 99.05/14.90 Y0, Y1)) => 99.05/14.90 (!!(( 99.05/14.90 ^[Y3 : $o]: 99.05/14.90 (( 99.05/14.90 in(Y2, 99.05/14.90 Y0) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y1))) => 99.05/14.90 Y3)) => 99.05/14.90 (( 99.05/14.90 ( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y0))) => 99.05/14.90 ( 99.05/14.90 in(Y2, 99.05/14.90 Y1) => Y3)) => 99.05/14.90 Y3))))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y1))) => 99.05/14.90 in(Y2, 99.05/14.90 symdiff( 99.05/14.90 Y0, Y1))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y0))) => 99.05/14.90 (in(Y2, 99.05/14.90 Y1) => 99.05/14.90 in(Y2, 99.05/14.90 symdiff( 99.05/14.90 Y0, Y1))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (in(Y2, 99.05/14.90 Y1) => 99.05/14.90 (~( 99.05/14.90 in(Y2, 99.05/14.90 symdiff( 99.05/14.90 Y0, Y1))))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y0))) => 99.05/14.90 (( 99.05/14.90 ~( 99.05/14.90 in(Y2, 99.05/14.90 Y1))) => 99.05/14.90 (~( 99.05/14.90 in(Y2, 99.05/14.90 symdiff( 99.05/14.90 Y0, Y1))))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 in(Y1, 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 in(Y0, 99.05/14.90 setunion( 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 in(Y1, 99.05/14.90 setunion( 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (??(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 setunion( 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)))) & 99.05/14.90 (??(( 99.05/14.90 ^[Y3 : $i]: 99.05/14.90 (in(Y3, 99.05/14.90 setunion( 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)))) & 99.05/14.90 (setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)) = 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 setadjoin( 99.05/14.90 Y3, 99.05/14.90 emptyset)), 99.05/14.90 emptyset))))))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (??(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 setunion( 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)))) & 99.05/14.90 (??(( 99.05/14.90 ^[Y3 : $i]: 99.05/14.90 (in(Y3, 99.05/14.90 setunion( 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)))) & 99.05/14.90 (setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)) = 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 setadjoin( 99.05/14.90 Y3, 99.05/14.90 emptyset)), 99.05/14.90 emptyset))))))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (in(Y1, 99.05/14.90 Y0) => 99.05/14.90 subset( 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset), 99.05/14.90 Y0)))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (in(Y1, 99.05/14.90 Y0) => 99.05/14.90 in( 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset), 99.05/14.90 powerset( 99.05/14.90 Y0))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 in( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 emptyset), 99.05/14.90 powerset( 99.05/14.90 binunion( 99.05/14.90 Y0, Y1))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 setadjoin( 99.05/14.90 Y0, 99.05/14.90 setadjoin( 99.05/14.90 Y1, 99.05/14.90 emptyset))) => 99.05/14.90 (( 99.05/14.90 Y2 = Y1) | 99.05/14.90 (Y2 = Y0)))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (!!(( 99.05/14.90 ^[Y3 : $i]: 99.05/14.90 (in(Y3, 99.05/14.90 Y1) => 99.05/14.90 subset( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 setadjoin( 99.05/14.90 Y3, 99.05/14.90 emptyset)), 99.05/14.90 binunion( 99.05/14.90 Y0, Y1)))))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (!!(( 99.05/14.90 ^[Y3 : $i]: 99.05/14.90 (in(Y3, 99.05/14.90 Y1) => 99.05/14.90 in( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 setadjoin( 99.05/14.90 Y3, 99.05/14.90 emptyset)), 99.05/14.90 powerset( 99.05/14.90 binunion( 99.05/14.90 Y0, Y1))))))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (!!(( 99.05/14.90 ^[Y3 : $i]: 99.05/14.90 (in(Y3, 99.05/14.90 Y1) => 99.05/14.90 subset( 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 setadjoin( 99.05/14.90 Y3, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)), 99.05/14.90 powerset( 99.05/14.90 binunion( 99.05/14.90 Y0, Y1))))))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (!!(( 99.05/14.90 ^[Y3 : $i]: 99.05/14.90 (in(Y3, 99.05/14.90 Y1) => 99.05/14.90 in( 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 setadjoin( 99.05/14.90 Y3, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)), 99.05/14.90 powerset( 99.05/14.90 powerset( 99.05/14.90 binunion( 99.05/14.90 Y0, Y1)))))))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (!!(( 99.05/14.90 ^[Y3 : $i]: 99.05/14.90 (in(Y3, 99.05/14.90 Y1) => 99.05/14.90 in( 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 setadjoin( 99.05/14.90 Y3, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)), 99.05/14.90 powerset( 99.05/14.90 powerset( 99.05/14.90 binunion( 99.05/14.90 Y0, Y1)))))))))))))))))) => 99.05/14.90 ( 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 Y0) => 99.05/14.90 (!!(( 99.05/14.90 ^[Y3 : $i]: 99.05/14.90 (in(Y3, 99.05/14.90 Y1) => 99.05/14.90 in( 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y2, 99.05/14.90 setadjoin( 99.05/14.90 Y3, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)), 99.05/14.90 dsetconstr( 99.05/14.90 powerset( 99.05/14.90 powerset( 99.05/14.90 binunion( 99.05/14.90 Y0, Y1))), 99.05/14.90 (^[Y4 : $i]: 99.05/14.90 (??(( 99.05/14.90 ^[Y5 : $i]: 99.05/14.90 (in(Y5, 99.05/14.90 Y0) & 99.05/14.90 (??(( 99.05/14.90 ^[Y6 : $i]: 99.05/14.90 (in(Y6, 99.05/14.90 Y1) & 99.05/14.90 (Y4 = 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y5, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y5, 99.05/14.90 setadjoin( 99.05/14.90 Y6, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)))))))))))))))))))))))))))) => 99.05/14.90 ( 99.05/14.90 !!(( 99.05/14.90 ^[Y0 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y1 : $i]: 99.05/14.90 (!!(( 99.05/14.90 ^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 dsetconstr( 99.05/14.90 powerset( 99.05/14.90 powerset( 99.05/14.90 binunion( 99.05/14.90 Y0, Y1))), 99.05/14.90 (^[Y3 : $i]: 99.05/14.90 (??(( 99.05/14.90 ^[Y4 : $i]: 99.05/14.90 (in(Y4, 99.05/14.90 Y0) & 99.05/14.90 (??(( 99.05/14.90 ^[Y5 : $i]: 99.05/14.90 (in(Y5, 99.05/14.90 Y1) & 99.05/14.90 (Y3 = 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y4, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y4, 99.05/14.90 setadjoin( 99.05/14.90 Y5, 99.05/14.90 emptyset)), 99.05/14.90 emptyset)))))))))))))) => 99.05/14.90 (??(( 99.05/14.90 ^[Y3 : $i]: 99.05/14.90 (( 99.05/14.90 ??(( 99.05/14.90 ^[Y4 : $i]: 99.05/14.90 (in(Y4, 99.05/14.90 Y1) & 99.05/14.90 (Y2 = 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y3, 99.05/14.90 emptyset), 99.05/14.90 setadjoin( 99.05/14.90 setadjoin( 99.05/14.90 Y3, 99.05/14.90 setadjoin( 99.05/14.90 Y4, 99.05/14.90 emptyset)), 99.05/14.90 emptyset))))))) & 99.05/14.90 in(Y3, 99.05/14.90 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.05/14.90 inference('lazy_cnf_imply', [status(thm)], ['198'])). 99.05/14.90 tff('200', plain, 99.05/14.90 ~ ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: (in(Y1, Y0) => in(Y1, powerset(setunion(Y0)))))))))) => 99.05/14.90 ((!!((^[Y0 : $i > $o]: 99.05/14.90 ((??((^[Y1 : $i]: 99.05/14.90 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.90 (??((^[Y1 : $i]: (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (in(Y0, setadjoin(Y1, emptyset)) => (Y0 = Y1)))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((Y0 != Y1) => (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 ((Y0 = Y1) => in(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (in(Y0, setadjoin(Y1, emptyset)) => 99.05/14.90 in(Y1, setadjoin(Y0, emptyset))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (in(Y2, 99.05/14.90 setadjoin(Y0, setadjoin(Y1, emptyset))) => 99.05/14.90 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 in(Y0, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i]: 99.05/14.90 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i > $o]: 99.05/14.90 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 99.05/14.90 (dsetconstr(Y0, Y1) != emptyset)))))))) => 99.05/14.90 ((!!((^[Y0 : $i > $o]: 99.05/14.90 (!!((^[Y1 : $i]: (in(Y1, emptyset) => Y0(Y1)))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i > $o]: 99.05/14.90 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.90 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i > $o]: 99.05/14.90 ((!!((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) => (~(Y1(Y2))))))) => 99.05/14.90 (~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i > $o]: 99.05/14.90 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i > $o]: 99.05/14.90 ((??((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) & (~(Y1(Y2))))))) => 99.05/14.90 (~((!!((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) => Y1(Y2)))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $o]: (Y0 => in(emptyset, prop2set(Y0)))))) => 99.05/14.90 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i > $o]: 99.05/14.90 ((~((??((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.90 (!!((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i]: 99.05/14.90 (!!((^[Y1 : $i > $o]: 99.05/14.90 ((~((!!((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.90 (??((^[Y2 : $i]: 99.05/14.90 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.90 ((!!((^[Y0 : $i > $o]: 99.05/14.90 ((??(Y0)) => 99.05/14.91 ((!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (Y0(Y1) => 99.05/14.91 (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.91 (??((^[Y1 : $i]: 99.05/14.91 (Y0(Y1) & 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (Y0(Y2) => (Y1 = Y2)))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i > $o]: 99.05/14.91 ((??((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (Y0(Y2) <=> (Y2 = Y1)))))))) => 99.05/14.91 (??((^[Y1 : $i]: 99.05/14.91 (Y0(Y1) & 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 ((Y2 = Y3) => 99.05/14.91 (in(Y2, Y0) => 99.05/14.91 in(Y3, Y1)))))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 ((Y2 = Y3) => 99.05/14.91 (in(Y2, Y0) <=> 99.05/14.91 in(Y3, Y1)))))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i > $o]: 99.05/14.91 ((??((^[Y1 : $i]: 99.05/14.91 (Y0(Y1) & 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (Y0(Y1) => 99.05/14.91 (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i > $o]: 99.05/14.91 (!!((^[Y1 : $i > $o]: 99.05/14.91 ((!!((^[Y2 : $i]: 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 ((Y2 = Y3) => 99.05/14.91 (Y0(Y2) <=> 99.05/14.91 Y1(Y3))))))))) => 99.05/14.91 ((??((^[Y2 : $i]: 99.05/14.91 (Y0(Y2) & 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 (Y0(Y3) => 99.05/14.91 (Y2 = Y3))))))))) <=> 99.05/14.91 (??((^[Y2 : $i]: 99.05/14.91 (Y1(Y2) & 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 (Y1(Y3) => 99.05/14.91 (Y2 = Y3))))))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 ((Y2 = Y3) => 99.05/14.91 (setadjoin( 99.05/14.91 Y0, Y2) = 99.05/14.91 setadjoin( 99.05/14.91 Y1, Y3)))))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => 99.05/14.91 (powerset(Y0) = powerset(Y1))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => 99.05/14.91 (setunion(Y0) = 99.05/14.91 setunion(Y1))))))))) => 99.05/14.91 ((!!((^[Y0 : $i > $o]: 99.05/14.91 ((??((^[Y1 : $i]: 99.05/14.91 (Y0(Y1) & 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (Y0(Y2) => 99.05/14.91 (Y1 = Y2))))))))) => 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (Y0(Y1) => 99.05/14.91 (Y0(Y2) => 99.05/14.91 (Y1 = Y2))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i > $o]: 99.05/14.91 (!!((^[Y1 : $i > $o]: 99.05/14.91 ((!!((^[Y2 : $i]: 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 ((Y2 = Y3) => 99.05/14.91 (Y0(Y2) <=> 99.05/14.91 Y1(Y3))))))))) => 99.05/14.91 ((??((^[Y2 : $i]: 99.05/14.91 (Y0(Y2) & 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 ( 99.05/14.91 Y0(Y3) => 99.05/14.91 ( 99.05/14.91 Y2 = Y3))))))))) => 99.05/14.91 ((??((^[Y2 : $i]: 99.05/14.91 (Y1(Y2) & 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 (Y1(Y3) => 99.05/14.91 (Y2 = Y3))))))))) => 99.05/14.91 (descr(Y0) = descr(Y1))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => 99.05/14.91 (!!((^[Y2 : $i > $o]: 99.05/14.91 (!!((^[Y3 : $i > $o]: 99.05/14.91 (( 99.05/14.91 !!(( 99.05/14.91 ^[Y4 : $i]: 99.05/14.91 (in(Y4, 99.05/14.91 Y0) => 99.05/14.91 (!!(( 99.05/14.91 ^[Y5 : $i]: 99.05/14.91 (in(Y5, 99.05/14.91 Y1) => 99.05/14.91 (( 99.05/14.91 Y4 = Y5) => 99.05/14.91 (Y2(Y4) <=> 99.05/14.91 Y3(Y5))))))))))) => 99.05/14.91 ( 99.05/14.91 dsetconstr( 99.05/14.91 Y0, Y2) = 99.05/14.91 dsetconstr( 99.05/14.91 Y1, Y3)))))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((!!((^[Y2 : $i]: 99.05/14.91 (in(Y2, Y0) => 99.05/14.91 in(Y2, Y1))))) => 99.05/14.91 subset(Y0, Y1)))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => 99.05/14.91 subset(Y1, Y0)))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => 99.05/14.91 subset(Y0, Y1)))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((!!((^[Y2 : $i]: 99.05/14.91 (in(Y2, Y0) => 99.05/14.91 in(Y2, Y1))))) => 99.05/14.91 subset(Y0, Y1)))))))) => 99.05/14.91 ((!!(subset(emptyset))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (subset(Y0, 99.05/14.91 Y1) => 99.05/14.91 (in(Y2, Y0) => 99.05/14.91 in(Y2, Y1)))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (subset( 99.05/14.91 Y0, Y1) => 99.05/14.91 (( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y1))) => 99.05/14.91 ( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y0)))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y1))) => 99.05/14.91 ( 99.05/14.91 ~( 99.05/14.91 subset( 99.05/14.91 Y0, Y1)))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((~(subset(Y0, 99.05/14.91 Y1))) => 99.05/14.91 (Y0 != Y1)))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 (( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y1))) => 99.05/14.91 (Y0 != Y1)))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 subset(Y0, Y0)))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (subset( 99.05/14.91 Y0, Y1) => 99.05/14.91 ( 99.05/14.91 subset( 99.05/14.91 Y1, Y2) => 99.05/14.91 subset( 99.05/14.91 Y0, Y2)))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 subset(Y1, 99.05/14.91 setadjoin( 99.05/14.91 Y0, Y1)))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (subset( 99.05/14.91 Y0, Y2) => 99.05/14.91 subset( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, Y2)))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (subset( 99.05/14.91 Y0, Y1) => 99.05/14.91 in(Y0, 99.05/14.91 powerset( 99.05/14.91 Y1))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ( 99.05/14.91 subset( 99.05/14.91 Y0, Y1) => 99.05/14.91 ( 99.05/14.91 subset( 99.05/14.91 Y1, Y0) => 99.05/14.91 ( 99.05/14.91 Y0 = Y1))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (subset(Y0, 99.05/14.91 emptyset) => 99.05/14.91 (Y0 = emptyset))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (subset( 99.05/14.91 Y1, Y0) => 99.05/14.91 in(Y1, 99.05/14.91 powerset( 99.05/14.91 Y0))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (in(Y1, 99.05/14.91 powerset( 99.05/14.91 Y0)) => 99.05/14.91 subset( 99.05/14.91 Y1, Y0)))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 in(Y0, 99.05/14.91 powerset( 99.05/14.91 Y0))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (subset( 99.05/14.91 Y0, Y1) => 99.05/14.91 subset( 99.05/14.91 powerset( 99.05/14.91 Y0), 99.05/14.91 powerset( 99.05/14.91 Y1))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i > $o]: 99.05/14.91 in( 99.05/14.91 dsetconstr( 99.05/14.91 Y0, Y1), 99.05/14.91 powerset( 99.05/14.91 Y0)))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y1 : $i > $o]: 99.05/14.91 subset( 99.05/14.91 dsetconstr( 99.05/14.91 Y0, Y1), 99.05/14.91 Y0))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 in(Y2, 99.05/14.91 binunion( 99.05/14.91 Y0, Y1)))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 in(Y1, 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset))))))))) => 99.05/14.91 ((!!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y1) => 99.05/14.91 in(Y2, 99.05/14.91 binunion( 99.05/14.91 Y0, Y1)))))))))))) => 99.05/14.91 ((!!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y3 : $o]: 99.05/14.91 (in(Y2, 99.05/14.91 binunion( 99.05/14.91 Y0, Y1)) => 99.05/14.91 (( 99.05/14.91 in(Y2, 99.05/14.91 Y0) => Y3) => 99.05/14.91 (( 99.05/14.91 in(Y2, 99.05/14.91 Y1) => Y3) => 99.05/14.91 Y3))))))))))))))) => 99.05/14.91 ((!!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 binunion( 99.05/14.91 Y0, Y1)) => 99.05/14.91 (in(Y2, 99.05/14.91 Y1) | 99.05/14.91 in(Y2, 99.05/14.91 Y0)))))))))))) => 99.05/14.91 ((!!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 subset( 99.05/14.91 Y0, 99.05/14.91 binunion( 99.05/14.91 Y0, Y1)))))))) => 99.05/14.91 (( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 subset( 99.05/14.91 Y1, 99.05/14.91 binunion( 99.05/14.91 Y0, Y1)))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 (in(Y2, 99.05/14.91 Y1) => 99.05/14.91 in(Y2, 99.05/14.91 binintersect( 99.05/14.91 Y0, Y1))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (subset( 99.05/14.91 Y2, Y0) => 99.05/14.91 (subset( 99.05/14.91 Y2, Y1) => 99.05/14.91 subset( 99.05/14.91 Y2, 99.05/14.91 binintersect( 99.05/14.91 Y0, Y1))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 binintersect( 99.05/14.91 Y0, Y1)) => 99.05/14.91 in(Y2, 99.05/14.91 Y0))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 subset( 99.05/14.91 binintersect( 99.05/14.91 Y0, Y1), 99.05/14.91 Y0))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (subset( 99.05/14.91 Y0, Y1) => 99.05/14.91 (binintersect( 99.05/14.91 Y0, Y1) = 99.05/14.91 Y0)))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (( 99.05/14.91 binintersect( 99.05/14.91 Y0, Y1) = 99.05/14.91 Y1) => 99.05/14.91 subset( 99.05/14.91 Y1, Y0)))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 binintersect( 99.05/14.91 Y0, Y1)) => 99.05/14.91 in(Y2, 99.05/14.91 Y1))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (( 99.05/14.91 ~(( 99.05/14.91 ??(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) & 99.05/14.91 in(Y2, 99.05/14.91 Y1))))))) => 99.05/14.91 (binintersect( 99.05/14.91 Y0, Y1) = 99.05/14.91 emptyset)))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 subset( 99.05/14.91 binintersect( 99.05/14.91 Y0, Y1), 99.05/14.91 Y1))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (subset( 99.05/14.91 Y1, Y0) => 99.05/14.91 (binintersect( 99.05/14.91 Y0, Y1) = 99.05/14.91 Y1)))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (( 99.05/14.91 binintersect( 99.05/14.91 Y0, Y1) = 99.05/14.91 Y0) => 99.05/14.91 subset( 99.05/14.91 Y0, Y1)))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (binintersect( 99.05/14.91 Y0, 99.05/14.91 binunion( 99.05/14.91 Y1, Y2)) = 99.05/14.91 binunion( 99.05/14.91 binintersect( 99.05/14.91 Y0, Y1), 99.05/14.91 binintersect( 99.05/14.91 Y0, Y2)))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 (( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y1))) => 99.05/14.91 in(Y2, 99.05/14.91 setminus( 99.05/14.91 Y0, Y1))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 setminus( 99.05/14.91 Y0, Y1)) => 99.05/14.91 in(Y2, 99.05/14.91 Y0))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 setminus( 99.05/14.91 Y0, Y1)) => 99.05/14.91 (~( 99.05/14.91 in(Y2, 99.05/14.91 Y1))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (subset( 99.05/14.91 Y0, Y1) => 99.05/14.91 (setminus( 99.05/14.91 Y0, Y1) = 99.05/14.91 emptyset)))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 setminus( 99.05/14.91 Y0, Y1)))) => 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 in(Y2, 99.05/14.91 Y1)))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 setminus( 99.05/14.91 Y0, Y1)))) => 99.05/14.91 (( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y1))) => 99.05/14.91 (~( 99.05/14.91 in(Y2, 99.05/14.91 Y0)))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y0))) => 99.05/14.91 (~( 99.05/14.91 in(Y2, 99.05/14.91 setminus( 99.05/14.91 Y0, Y1)))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y1) => 99.05/14.91 (~( 99.05/14.91 in(Y2, 99.05/14.91 setminus( 99.05/14.91 Y0, Y1)))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 subset( 99.05/14.91 setminus( 99.05/14.91 Y0, Y1), 99.05/14.91 Y0))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (( 99.05/14.91 setminus( 99.05/14.91 Y0, Y1) = 99.05/14.91 emptyset) => 99.05/14.91 subset( 99.05/14.91 Y0, Y1)))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 symdiff( 99.05/14.91 Y0, Y1)) => 99.05/14.91 (!!(( 99.05/14.91 ^[Y3 : $o]: 99.05/14.91 (( 99.05/14.91 in(Y2, 99.05/14.91 Y0) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y1))) => 99.05/14.91 Y3)) => 99.05/14.91 (( 99.05/14.91 ( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y0))) => 99.05/14.91 ( 99.05/14.91 in(Y2, 99.05/14.91 Y1) => Y3)) => 99.05/14.91 Y3))))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 (( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y1))) => 99.05/14.91 in(Y2, 99.05/14.91 symdiff( 99.05/14.91 Y0, Y1))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y0))) => 99.05/14.91 (in(Y2, 99.05/14.91 Y1) => 99.05/14.91 in(Y2, 99.05/14.91 symdiff( 99.05/14.91 Y0, Y1))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 (in(Y2, 99.05/14.91 Y1) => 99.05/14.91 (~( 99.05/14.91 in(Y2, 99.05/14.91 symdiff( 99.05/14.91 Y0, Y1))))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y0))) => 99.05/14.91 (( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y1))) => 99.05/14.91 (~( 99.05/14.91 in(Y2, 99.05/14.91 symdiff( 99.05/14.91 Y0, Y1))))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 in(Y1, 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 in(Y0, 99.05/14.91 setunion( 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 in(Y1, 99.05/14.91 setunion( 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (??(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 setunion( 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)))) & 99.05/14.91 (??(( 99.05/14.91 ^[Y3 : $i]: 99.05/14.91 (in(Y3, 99.05/14.91 setunion( 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)))) & 99.05/14.91 (setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)) = 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 setadjoin( 99.05/14.91 Y3, 99.05/14.91 emptyset)), 99.05/14.91 emptyset))))))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (??(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 setunion( 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)))) & 99.05/14.91 (??(( 99.05/14.91 ^[Y3 : $i]: 99.05/14.91 (in(Y3, 99.05/14.91 setunion( 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)))) & 99.05/14.91 (setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)) = 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 setadjoin( 99.05/14.91 Y3, 99.05/14.91 emptyset)), 99.05/14.91 emptyset))))))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (in(Y1, 99.05/14.91 Y0) => 99.05/14.91 subset( 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset), 99.05/14.91 Y0)))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (in(Y1, 99.05/14.91 Y0) => 99.05/14.91 in( 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset), 99.05/14.91 powerset( 99.05/14.91 Y0))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 in( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 emptyset), 99.05/14.91 powerset( 99.05/14.91 binunion( 99.05/14.91 Y0, Y1))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset))) => 99.05/14.91 (( 99.05/14.91 Y2 = Y1) | 99.05/14.91 (Y2 = Y0)))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 (!!(( 99.05/14.91 ^[Y3 : $i]: 99.05/14.91 (in(Y3, 99.05/14.91 Y1) => 99.05/14.91 subset( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 setadjoin( 99.05/14.91 Y3, 99.05/14.91 emptyset)), 99.05/14.91 binunion( 99.05/14.91 Y0, Y1)))))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 (!!(( 99.05/14.91 ^[Y3 : $i]: 99.05/14.91 (in(Y3, 99.05/14.91 Y1) => 99.05/14.91 in( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 setadjoin( 99.05/14.91 Y3, 99.05/14.91 emptyset)), 99.05/14.91 powerset( 99.05/14.91 binunion( 99.05/14.91 Y0, Y1))))))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 (!!(( 99.05/14.91 ^[Y3 : $i]: 99.05/14.91 (in(Y3, 99.05/14.91 Y1) => 99.05/14.91 subset( 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 setadjoin( 99.05/14.91 Y3, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)), 99.05/14.91 powerset( 99.05/14.91 binunion( 99.05/14.91 Y0, Y1))))))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 (!!(( 99.05/14.91 ^[Y3 : $i]: 99.05/14.91 (in(Y3, 99.05/14.91 Y1) => 99.05/14.91 in( 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 setadjoin( 99.05/14.91 Y3, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)), 99.05/14.91 powerset( 99.05/14.91 powerset( 99.05/14.91 binunion( 99.05/14.91 Y0, Y1)))))))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 (!!(( 99.05/14.91 ^[Y3 : $i]: 99.05/14.91 (in(Y3, 99.05/14.91 Y1) => 99.05/14.91 in( 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 setadjoin( 99.05/14.91 Y3, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)), 99.05/14.91 powerset( 99.05/14.91 powerset( 99.05/14.91 binunion( 99.05/14.91 Y0, Y1)))))))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 (!!(( 99.05/14.91 ^[Y3 : $i]: 99.05/14.91 (in(Y3, 99.05/14.91 Y1) => 99.05/14.91 in( 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 setadjoin( 99.05/14.91 Y3, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)), 99.05/14.91 dsetconstr( 99.05/14.91 powerset( 99.05/14.91 powerset( 99.05/14.91 binunion( 99.05/14.91 Y0, Y1))), 99.05/14.91 (^[Y4 : $i]: 99.05/14.91 (??(( 99.05/14.91 ^[Y5 : $i]: 99.05/14.91 (in(Y5, 99.05/14.91 Y0) & 99.05/14.91 (??(( 99.05/14.91 ^[Y6 : $i]: 99.05/14.91 (in(Y6, 99.05/14.91 Y1) & 99.05/14.91 (Y4 = 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y5, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y5, 99.05/14.91 setadjoin( 99.05/14.91 Y6, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)))))))))))))))))))))))))))) => 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 dsetconstr( 99.05/14.91 powerset( 99.05/14.91 powerset( 99.05/14.91 binunion( 99.05/14.91 Y0, Y1))), 99.05/14.91 (^[Y3 : $i]: 99.05/14.91 (??(( 99.05/14.91 ^[Y4 : $i]: 99.05/14.91 (in(Y4, 99.05/14.91 Y0) & 99.05/14.91 (??(( 99.05/14.91 ^[Y5 : $i]: 99.05/14.91 (in(Y5, 99.05/14.91 Y1) & 99.05/14.91 (Y3 = 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y4, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y4, 99.05/14.91 setadjoin( 99.05/14.91 Y5, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)))))))))))))) => 99.05/14.91 (??(( 99.05/14.91 ^[Y3 : $i]: 99.05/14.91 (( 99.05/14.91 ??(( 99.05/14.91 ^[Y4 : $i]: 99.05/14.91 (in(Y4, 99.05/14.91 Y1) & 99.05/14.91 (Y2 = 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y3, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y3, 99.05/14.91 setadjoin( 99.05/14.91 Y4, 99.05/14.91 emptyset)), 99.05/14.91 emptyset))))))) & 99.05/14.91 in(Y3, 99.05/14.91 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.05/14.91 inference('lazy_cnf_imply', [status(thm)], ['199'])). 99.05/14.91 tff('201', plain, 99.05/14.91 ~ ((!!((^[Y0 : $i > $o]: 99.05/14.91 ((??((^[Y1 : $i]: 99.05/14.91 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.91 (??((^[Y1 : $i]: (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (in(Y0, setadjoin(Y1, emptyset)) => (Y0 = Y1)))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 != Y1) => (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => in(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (in(Y0, setadjoin(Y1, emptyset)) => 99.05/14.91 in(Y1, setadjoin(Y0, emptyset))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 setadjoin(Y0, setadjoin(Y1, emptyset))) => 99.05/14.91 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 in(Y0, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i > $o]: 99.05/14.91 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 99.05/14.91 (dsetconstr(Y0, Y1) != emptyset)))))))) => 99.05/14.91 ((!!((^[Y0 : $i > $o]: 99.05/14.91 (!!((^[Y1 : $i]: (in(Y1, emptyset) => Y0(Y1)))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i > $o]: 99.05/14.91 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.91 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i > $o]: 99.05/14.91 ((!!((^[Y2 : $i]: 99.05/14.91 (in(Y2, Y0) => (~(Y1(Y2))))))) => 99.05/14.91 (~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i > $o]: 99.05/14.91 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i > $o]: 99.05/14.91 ((??((^[Y2 : $i]: 99.05/14.91 (in(Y2, Y0) & (~(Y1(Y2))))))) => 99.05/14.91 (~((!!((^[Y2 : $i]: 99.05/14.91 (in(Y2, Y0) => Y1(Y2)))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $o]: (Y0 => in(emptyset, prop2set(Y0)))))) => 99.05/14.91 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i > $o]: 99.05/14.91 ((~((??((^[Y2 : $i]: 99.05/14.91 (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i > $o]: 99.05/14.91 ((~((!!((^[Y2 : $i]: 99.05/14.91 (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.91 (??((^[Y2 : $i]: 99.05/14.91 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i > $o]: 99.05/14.91 ((??(Y0)) => 99.05/14.91 ((!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (Y0(Y1) => 99.05/14.91 (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.91 (??((^[Y1 : $i]: 99.05/14.91 (Y0(Y1) & 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (Y0(Y2) => (Y1 = Y2)))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i > $o]: 99.05/14.91 ((??((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (Y0(Y2) <=> (Y2 = Y1)))))))) => 99.05/14.91 (??((^[Y1 : $i]: 99.05/14.91 (Y0(Y1) & 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 ((Y2 = Y3) => 99.05/14.91 (in(Y2, Y0) => 99.05/14.91 in(Y3, Y1)))))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 ((Y2 = Y3) => 99.05/14.91 (in(Y2, Y0) <=> 99.05/14.91 in(Y3, Y1)))))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i > $o]: 99.05/14.91 ((??((^[Y1 : $i]: 99.05/14.91 (Y0(Y1) & 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (Y0(Y1) => 99.05/14.91 (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i > $o]: 99.05/14.91 (!!((^[Y1 : $i > $o]: 99.05/14.91 ((!!((^[Y2 : $i]: 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 ((Y2 = Y3) => 99.05/14.91 (Y0(Y2) <=> 99.05/14.91 Y1(Y3))))))))) => 99.05/14.91 ((??((^[Y2 : $i]: 99.05/14.91 (Y0(Y2) & 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 (Y0(Y3) => 99.05/14.91 (Y2 = Y3))))))))) <=> 99.05/14.91 (??((^[Y2 : $i]: 99.05/14.91 (Y1(Y2) & 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 (Y1(Y3) => 99.05/14.91 (Y2 = Y3))))))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 ((Y2 = Y3) => 99.05/14.91 (setadjoin(Y0, 99.05/14.91 Y2) = 99.05/14.91 setadjoin(Y1, 99.05/14.91 Y3)))))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => 99.05/14.91 (powerset(Y0) = powerset(Y1))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => 99.05/14.91 (setunion(Y0) = setunion(Y1))))))))) => 99.05/14.91 ((!!((^[Y0 : $i > $o]: 99.05/14.91 ((??((^[Y1 : $i]: 99.05/14.91 (Y0(Y1) & 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (Y0(Y2) => 99.05/14.91 (Y1 = Y2))))))))) => 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (Y0(Y1) => 99.05/14.91 (Y0(Y2) => 99.05/14.91 (Y1 = Y2))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i > $o]: 99.05/14.91 (!!((^[Y1 : $i > $o]: 99.05/14.91 ((!!((^[Y2 : $i]: 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 ((Y2 = Y3) => 99.05/14.91 (Y0(Y2) <=> 99.05/14.91 Y1(Y3))))))))) => 99.05/14.91 ((??((^[Y2 : $i]: 99.05/14.91 (Y0(Y2) & 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 (Y0(Y3) => 99.05/14.91 ( 99.05/14.91 Y2 = Y3))))))))) => 99.05/14.91 ((??((^[Y2 : $i]: 99.05/14.91 (Y1(Y2) & 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 ( 99.05/14.91 Y1(Y3) => 99.05/14.91 ( 99.05/14.91 Y2 = Y3))))))))) => 99.05/14.91 (descr(Y0) = descr(Y1))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => 99.05/14.91 (!!((^[Y2 : $i > $o]: 99.05/14.91 (!!((^[Y3 : $i > $o]: 99.05/14.91 ((!!(( 99.05/14.91 ^[Y4 : $i]: 99.05/14.91 (in(Y4, 99.05/14.91 Y0) => 99.05/14.91 (!!(( 99.05/14.91 ^[Y5 : $i]: 99.05/14.91 (in(Y5, 99.05/14.91 Y1) => 99.05/14.91 (( 99.05/14.91 Y4 = Y5) => 99.05/14.91 (Y2(Y4) <=> 99.05/14.91 Y3(Y5))))))))))) => 99.05/14.91 (dsetconstr( 99.05/14.91 Y0, Y2) = 99.05/14.91 dsetconstr( 99.05/14.91 Y1, Y3)))))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((!!((^[Y2 : $i]: 99.05/14.91 (in(Y2, Y0) => 99.05/14.91 in(Y2, Y1))))) => 99.05/14.91 subset(Y0, Y1)))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => 99.05/14.91 subset(Y1, Y0)))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => 99.05/14.91 subset(Y0, Y1)))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((!!((^[Y2 : $i]: 99.05/14.91 (in(Y2, Y0) => 99.05/14.91 in(Y2, Y1))))) => 99.05/14.91 subset(Y0, Y1)))))))) => 99.05/14.91 ((!!(subset(emptyset))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (subset(Y0, 99.05/14.91 Y1) => 99.05/14.91 (in(Y2, Y0) => 99.05/14.91 in(Y2, Y1)))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (subset(Y0, 99.05/14.91 Y1) => 99.05/14.91 ((~( 99.05/14.91 in(Y2, 99.05/14.91 Y1))) => 99.05/14.91 (~( 99.05/14.91 in(Y2, 99.05/14.91 Y0)))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (in(Y2, Y0) => 99.05/14.91 (( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y1))) => 99.05/14.91 ( 99.05/14.91 ~( 99.05/14.91 subset( 99.05/14.91 Y0, Y1)))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((~(subset(Y0, 99.05/14.91 Y1))) => 99.05/14.91 (Y0 != Y1)))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 ( 99.05/14.91 in(Y2, 99.05/14.91 Y0) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y1))) => 99.05/14.91 ( 99.05/14.91 Y0 != Y1)))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 subset(Y0, Y0)))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (subset( 99.05/14.91 Y0, Y1) => 99.05/14.91 (subset( 99.05/14.91 Y1, Y2) => 99.05/14.91 subset( 99.05/14.91 Y0, Y2)))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 subset(Y1, 99.05/14.91 setadjoin( 99.05/14.91 Y0, Y1)))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 ( 99.05/14.91 subset( 99.05/14.91 Y0, Y2) => 99.05/14.91 subset( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, Y2)))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (subset( 99.05/14.91 Y0, Y1) => 99.05/14.91 in(Y0, 99.05/14.91 powerset( 99.05/14.91 Y1))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (subset( 99.05/14.91 Y0, Y1) => 99.05/14.91 ( 99.05/14.91 subset( 99.05/14.91 Y1, Y0) => 99.05/14.91 ( 99.05/14.91 Y0 = Y1))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (subset(Y0, 99.05/14.91 emptyset) => 99.05/14.91 (Y0 = emptyset))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (subset( 99.05/14.91 Y1, Y0) => 99.05/14.91 in(Y1, 99.05/14.91 powerset( 99.05/14.91 Y0))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (in(Y1, 99.05/14.91 powerset( 99.05/14.91 Y0)) => 99.05/14.91 subset( 99.05/14.91 Y1, Y0)))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 in(Y0, 99.05/14.91 powerset( 99.05/14.91 Y0))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 ( 99.05/14.91 subset( 99.05/14.91 Y0, Y1) => 99.05/14.91 subset( 99.05/14.91 powerset( 99.05/14.91 Y0), 99.05/14.91 powerset( 99.05/14.91 Y1))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i > $o]: 99.05/14.91 in( 99.05/14.91 dsetconstr( 99.05/14.91 Y0, Y1), 99.05/14.91 powerset( 99.05/14.91 Y0)))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i > $o]: 99.05/14.91 subset( 99.05/14.91 dsetconstr( 99.05/14.91 Y0, Y1), 99.05/14.91 Y0))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 in(Y2, 99.05/14.91 binunion( 99.05/14.91 Y0, Y1)))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 in(Y1, 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y1) => 99.05/14.91 in(Y2, 99.05/14.91 binunion( 99.05/14.91 Y0, Y1)))))))))))) => 99.05/14.91 ((!!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y3 : $o]: 99.05/14.91 (in(Y2, 99.05/14.91 binunion( 99.05/14.91 Y0, Y1)) => 99.05/14.91 (( 99.05/14.91 in(Y2, 99.05/14.91 Y0) => Y3) => 99.05/14.91 (( 99.05/14.91 in(Y2, 99.05/14.91 Y1) => Y3) => 99.05/14.91 Y3))))))))))))))) => 99.05/14.91 ((!!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 binunion( 99.05/14.91 Y0, Y1)) => 99.05/14.91 (in(Y2, 99.05/14.91 Y1) | 99.05/14.91 in(Y2, 99.05/14.91 Y0)))))))))))) => 99.05/14.91 ((!!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 subset( 99.05/14.91 Y0, 99.05/14.91 binunion( 99.05/14.91 Y0, Y1)))))))) => 99.05/14.91 ((!!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 subset( 99.05/14.91 Y1, 99.05/14.91 binunion( 99.05/14.91 Y0, Y1)))))))) => 99.05/14.91 (( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 (in(Y2, 99.05/14.91 Y1) => 99.05/14.91 in(Y2, 99.05/14.91 binintersect( 99.05/14.91 Y0, Y1))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (subset( 99.05/14.91 Y2, Y0) => 99.05/14.91 (subset( 99.05/14.91 Y2, Y1) => 99.05/14.91 subset( 99.05/14.91 Y2, 99.05/14.91 binintersect( 99.05/14.91 Y0, Y1))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 binintersect( 99.05/14.91 Y0, Y1)) => 99.05/14.91 in(Y2, 99.05/14.91 Y0))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 subset( 99.05/14.91 binintersect( 99.05/14.91 Y0, Y1), 99.05/14.91 Y0))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (subset( 99.05/14.91 Y0, Y1) => 99.05/14.91 (binintersect( 99.05/14.91 Y0, Y1) = 99.05/14.91 Y0)))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (( 99.05/14.91 binintersect( 99.05/14.91 Y0, Y1) = 99.05/14.91 Y1) => 99.05/14.91 subset( 99.05/14.91 Y1, Y0)))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 binintersect( 99.05/14.91 Y0, Y1)) => 99.05/14.91 in(Y2, 99.05/14.91 Y1))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (( 99.05/14.91 ~(( 99.05/14.91 ??(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) & 99.05/14.91 in(Y2, 99.05/14.91 Y1))))))) => 99.05/14.91 (binintersect( 99.05/14.91 Y0, Y1) = 99.05/14.91 emptyset)))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 subset( 99.05/14.91 binintersect( 99.05/14.91 Y0, Y1), 99.05/14.91 Y1))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (subset( 99.05/14.91 Y1, Y0) => 99.05/14.91 (binintersect( 99.05/14.91 Y0, Y1) = 99.05/14.91 Y1)))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (( 99.05/14.91 binintersect( 99.05/14.91 Y0, Y1) = 99.05/14.91 Y0) => 99.05/14.91 subset( 99.05/14.91 Y0, Y1)))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (binintersect( 99.05/14.91 Y0, 99.05/14.91 binunion( 99.05/14.91 Y1, Y2)) = 99.05/14.91 binunion( 99.05/14.91 binintersect( 99.05/14.91 Y0, Y1), 99.05/14.91 binintersect( 99.05/14.91 Y0, Y2)))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 (( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y1))) => 99.05/14.91 in(Y2, 99.05/14.91 setminus( 99.05/14.91 Y0, Y1))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 setminus( 99.05/14.91 Y0, Y1)) => 99.05/14.91 in(Y2, 99.05/14.91 Y0))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 setminus( 99.05/14.91 Y0, Y1)) => 99.05/14.91 (~( 99.05/14.91 in(Y2, 99.05/14.91 Y1))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (subset( 99.05/14.91 Y0, Y1) => 99.05/14.91 (setminus( 99.05/14.91 Y0, Y1) = 99.05/14.91 emptyset)))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 setminus( 99.05/14.91 Y0, Y1)))) => 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 in(Y2, 99.05/14.91 Y1)))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 setminus( 99.05/14.91 Y0, Y1)))) => 99.05/14.91 (( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y1))) => 99.05/14.91 (~( 99.05/14.91 in(Y2, 99.05/14.91 Y0)))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y0))) => 99.05/14.91 (~( 99.05/14.91 in(Y2, 99.05/14.91 setminus( 99.05/14.91 Y0, Y1)))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y1) => 99.05/14.91 (~( 99.05/14.91 in(Y2, 99.05/14.91 setminus( 99.05/14.91 Y0, Y1)))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 subset( 99.05/14.91 setminus( 99.05/14.91 Y0, Y1), 99.05/14.91 Y0))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (( 99.05/14.91 setminus( 99.05/14.91 Y0, Y1) = 99.05/14.91 emptyset) => 99.05/14.91 subset( 99.05/14.91 Y0, Y1)))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 symdiff( 99.05/14.91 Y0, Y1)) => 99.05/14.91 (!!(( 99.05/14.91 ^[Y3 : $o]: 99.05/14.91 (( 99.05/14.91 in(Y2, 99.05/14.91 Y0) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y1))) => 99.05/14.91 Y3)) => 99.05/14.91 (( 99.05/14.91 ( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y0))) => 99.05/14.91 ( 99.05/14.91 in(Y2, 99.05/14.91 Y1) => Y3)) => 99.05/14.91 Y3))))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 (( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y1))) => 99.05/14.91 in(Y2, 99.05/14.91 symdiff( 99.05/14.91 Y0, Y1))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y0))) => 99.05/14.91 (in(Y2, 99.05/14.91 Y1) => 99.05/14.91 in(Y2, 99.05/14.91 symdiff( 99.05/14.91 Y0, Y1))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 (in(Y2, 99.05/14.91 Y1) => 99.05/14.91 (~( 99.05/14.91 in(Y2, 99.05/14.91 symdiff( 99.05/14.91 Y0, Y1))))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y0))) => 99.05/14.91 (( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y1))) => 99.05/14.91 (~( 99.05/14.91 in(Y2, 99.05/14.91 symdiff( 99.05/14.91 Y0, Y1))))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 in(Y1, 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 in(Y0, 99.05/14.91 setunion( 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 in(Y1, 99.05/14.91 setunion( 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (??(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 setunion( 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)))) & 99.05/14.91 (??(( 99.05/14.91 ^[Y3 : $i]: 99.05/14.91 (in(Y3, 99.05/14.91 setunion( 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)))) & 99.05/14.91 (setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)) = 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 setadjoin( 99.05/14.91 Y3, 99.05/14.91 emptyset)), 99.05/14.91 emptyset))))))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (??(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 setunion( 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)))) & 99.05/14.91 (??(( 99.05/14.91 ^[Y3 : $i]: 99.05/14.91 (in(Y3, 99.05/14.91 setunion( 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)))) & 99.05/14.91 (setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)) = 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 setadjoin( 99.05/14.91 Y3, 99.05/14.91 emptyset)), 99.05/14.91 emptyset))))))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (in(Y1, 99.05/14.91 Y0) => 99.05/14.91 subset( 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset), 99.05/14.91 Y0)))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (in(Y1, 99.05/14.91 Y0) => 99.05/14.91 in( 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset), 99.05/14.91 powerset( 99.05/14.91 Y0))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 in( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 emptyset), 99.05/14.91 powerset( 99.05/14.91 binunion( 99.05/14.91 Y0, Y1))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset))) => 99.05/14.91 (( 99.05/14.91 Y2 = Y1) | 99.05/14.91 (Y2 = Y0)))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 (!!(( 99.05/14.91 ^[Y3 : $i]: 99.05/14.91 (in(Y3, 99.05/14.91 Y1) => 99.05/14.91 subset( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 setadjoin( 99.05/14.91 Y3, 99.05/14.91 emptyset)), 99.05/14.91 binunion( 99.05/14.91 Y0, Y1)))))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 (!!(( 99.05/14.91 ^[Y3 : $i]: 99.05/14.91 (in(Y3, 99.05/14.91 Y1) => 99.05/14.91 in( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 setadjoin( 99.05/14.91 Y3, 99.05/14.91 emptyset)), 99.05/14.91 powerset( 99.05/14.91 binunion( 99.05/14.91 Y0, Y1))))))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 (!!(( 99.05/14.91 ^[Y3 : $i]: 99.05/14.91 (in(Y3, 99.05/14.91 Y1) => 99.05/14.91 subset( 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 setadjoin( 99.05/14.91 Y3, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)), 99.05/14.91 powerset( 99.05/14.91 binunion( 99.05/14.91 Y0, Y1))))))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 (!!(( 99.05/14.91 ^[Y3 : $i]: 99.05/14.91 (in(Y3, 99.05/14.91 Y1) => 99.05/14.91 in( 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 setadjoin( 99.05/14.91 Y3, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)), 99.05/14.91 powerset( 99.05/14.91 powerset( 99.05/14.91 binunion( 99.05/14.91 Y0, Y1)))))))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 (!!(( 99.05/14.91 ^[Y3 : $i]: 99.05/14.91 (in(Y3, 99.05/14.91 Y1) => 99.05/14.91 in( 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 setadjoin( 99.05/14.91 Y3, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)), 99.05/14.91 powerset( 99.05/14.91 powerset( 99.05/14.91 binunion( 99.05/14.91 Y0, Y1)))))))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 (!!(( 99.05/14.91 ^[Y3 : $i]: 99.05/14.91 (in(Y3, 99.05/14.91 Y1) => 99.05/14.91 in( 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 setadjoin( 99.05/14.91 Y3, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)), 99.05/14.91 dsetconstr( 99.05/14.91 powerset( 99.05/14.91 powerset( 99.05/14.91 binunion( 99.05/14.91 Y0, Y1))), 99.05/14.91 (^[Y4 : $i]: 99.05/14.91 (??(( 99.05/14.91 ^[Y5 : $i]: 99.05/14.91 (in(Y5, 99.05/14.91 Y0) & 99.05/14.91 (??(( 99.05/14.91 ^[Y6 : $i]: 99.05/14.91 (in(Y6, 99.05/14.91 Y1) & 99.05/14.91 (Y4 = 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y5, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y5, 99.05/14.91 setadjoin( 99.05/14.91 Y6, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)))))))))))))))))))))))))))) => 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 dsetconstr( 99.05/14.91 powerset( 99.05/14.91 powerset( 99.05/14.91 binunion( 99.05/14.91 Y0, Y1))), 99.05/14.91 (^[Y3 : $i]: 99.05/14.91 (??(( 99.05/14.91 ^[Y4 : $i]: 99.05/14.91 (in(Y4, 99.05/14.91 Y0) & 99.05/14.91 (??(( 99.05/14.91 ^[Y5 : $i]: 99.05/14.91 (in(Y5, 99.05/14.91 Y1) & 99.05/14.91 (Y3 = 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y4, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y4, 99.05/14.91 setadjoin( 99.05/14.91 Y5, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)))))))))))))) => 99.05/14.91 (??(( 99.05/14.91 ^[Y3 : $i]: 99.05/14.91 (( 99.05/14.91 ??(( 99.05/14.91 ^[Y4 : $i]: 99.05/14.91 (in(Y4, 99.05/14.91 Y1) & 99.05/14.91 (Y2 = 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y3, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y3, 99.05/14.91 setadjoin( 99.05/14.91 Y4, 99.05/14.91 emptyset)), 99.05/14.91 emptyset))))))) & 99.05/14.91 in(Y3, 99.05/14.91 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.05/14.91 inference('lazy_cnf_imply', [status(thm)], ['200'])). 99.05/14.91 tff('202', plain, 99.05/14.91 ~ ((!!((^[Y0 : $i]: ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (in(Y0, setadjoin(Y1, emptyset)) => (Y0 = Y1)))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 != Y1) => (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => in(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (in(Y0, setadjoin(Y1, emptyset)) => 99.05/14.91 in(Y1, setadjoin(Y0, emptyset))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 setadjoin(Y0, setadjoin(Y1, emptyset))) => 99.05/14.91 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 in(Y0, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i > $o]: 99.05/14.91 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 99.05/14.91 (dsetconstr(Y0, Y1) != emptyset)))))))) => 99.05/14.91 ((!!((^[Y0 : $i > $o]: 99.05/14.91 (!!((^[Y1 : $i]: (in(Y1, emptyset) => Y0(Y1)))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i > $o]: 99.05/14.91 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.91 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i > $o]: 99.05/14.91 ((!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2))))))) => 99.05/14.91 (~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i > $o]: 99.05/14.91 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i > $o]: 99.05/14.91 ((??((^[Y2 : $i]: 99.05/14.91 (in(Y2, Y0) & (~(Y1(Y2))))))) => 99.05/14.91 (~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2)))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $o]: (Y0 => in(emptyset, prop2set(Y0)))))) => 99.05/14.91 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i > $o]: 99.05/14.91 ((~((??((^[Y2 : $i]: 99.05/14.91 (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i > $o]: 99.05/14.91 ((~((!!((^[Y2 : $i]: 99.05/14.91 (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.91 (??((^[Y2 : $i]: 99.05/14.91 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i > $o]: 99.05/14.91 ((??(Y0)) => 99.05/14.91 ((!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (Y0(Y1) => 99.05/14.91 (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.91 (??((^[Y1 : $i]: 99.05/14.91 (Y0(Y1) & 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (Y0(Y2) => (Y1 = Y2)))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i > $o]: 99.05/14.91 ((??((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (Y0(Y2) <=> (Y2 = Y1)))))))) => 99.05/14.91 (??((^[Y1 : $i]: 99.05/14.91 (Y0(Y1) & 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 ((Y2 = Y3) => 99.05/14.91 (in(Y2, Y0) => 99.05/14.91 in(Y3, Y1)))))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 ((Y2 = Y3) => 99.05/14.91 (in(Y2, Y0) <=> 99.05/14.91 in(Y3, Y1)))))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i > $o]: 99.05/14.91 ((??((^[Y1 : $i]: 99.05/14.91 (Y0(Y1) & 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (Y0(Y1) => 99.05/14.91 (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i > $o]: 99.05/14.91 (!!((^[Y1 : $i > $o]: 99.05/14.91 ((!!((^[Y2 : $i]: 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 ((Y2 = Y3) => 99.05/14.91 (Y0(Y2) <=> 99.05/14.91 Y1(Y3))))))))) => 99.05/14.91 ((??((^[Y2 : $i]: 99.05/14.91 (Y0(Y2) & 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 (Y0(Y3) => 99.05/14.91 (Y2 = Y3))))))))) <=> 99.05/14.91 (??((^[Y2 : $i]: 99.05/14.91 (Y1(Y2) & 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 (Y1(Y3) => 99.05/14.91 (Y2 = Y3))))))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 ((Y2 = Y3) => 99.05/14.91 (setadjoin(Y0, 99.05/14.91 Y2) = 99.05/14.91 setadjoin(Y1, 99.05/14.91 Y3)))))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => 99.05/14.91 (powerset(Y0) = powerset(Y1))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => 99.05/14.91 (setunion(Y0) = setunion(Y1))))))))) => 99.05/14.91 ((!!((^[Y0 : $i > $o]: 99.05/14.91 ((??((^[Y1 : $i]: 99.05/14.91 (Y0(Y1) & 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (Y0(Y1) => 99.05/14.91 (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i > $o]: 99.05/14.91 (!!((^[Y1 : $i > $o]: 99.05/14.91 ((!!((^[Y2 : $i]: 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 ((Y2 = Y3) => 99.05/14.91 (Y0(Y2) <=> 99.05/14.91 Y1(Y3))))))))) => 99.05/14.91 ((??((^[Y2 : $i]: 99.05/14.91 (Y0(Y2) & 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 (Y0(Y3) => 99.05/14.91 (Y2 = Y3))))))))) => 99.05/14.91 ((??((^[Y2 : $i]: 99.05/14.91 (Y1(Y2) & 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 (Y1(Y3) => 99.05/14.91 ( 99.05/14.91 Y2 = Y3))))))))) => 99.05/14.91 (descr(Y0) = descr(Y1))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => 99.05/14.91 (!!((^[Y2 : $i > $o]: 99.05/14.91 (!!((^[Y3 : $i > $o]: 99.05/14.91 ((!!(( 99.05/14.91 ^[Y4 : $i]: 99.05/14.91 (in(Y4, 99.05/14.91 Y0) => 99.05/14.91 (!!(( 99.05/14.91 ^[Y5 : $i]: 99.05/14.91 (in(Y5, 99.05/14.91 Y1) => 99.05/14.91 (( 99.05/14.91 Y4 = Y5) => 99.05/14.91 (Y2(Y4) <=> 99.05/14.91 Y3(Y5))))))))))) => 99.05/14.91 (dsetconstr( 99.05/14.91 Y0, Y2) = 99.05/14.91 dsetconstr( 99.05/14.91 Y1, Y3)))))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((!!((^[Y2 : $i]: 99.05/14.91 (in(Y2, Y0) => 99.05/14.91 in(Y2, Y1))))) => 99.05/14.91 subset(Y0, Y1)))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => 99.05/14.91 subset(Y1, Y0)))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => 99.05/14.91 subset(Y0, Y1)))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((!!((^[Y2 : $i]: 99.05/14.91 (in(Y2, Y0) => 99.05/14.91 in(Y2, Y1))))) => 99.05/14.91 subset(Y0, Y1)))))))) => 99.05/14.91 ((!!(subset(emptyset))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (subset(Y0, 99.05/14.91 Y1) => 99.05/14.91 (in(Y2, Y0) => 99.05/14.91 in(Y2, Y1)))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (subset(Y0, 99.05/14.91 Y1) => 99.05/14.91 ((~( 99.05/14.91 in(Y2, Y1))) => 99.05/14.91 (~( 99.05/14.91 in(Y2, Y0)))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (in(Y2, Y0) => 99.05/14.91 ((~( 99.05/14.91 in(Y2, 99.05/14.91 Y1))) => 99.05/14.91 (~( 99.05/14.91 subset( 99.05/14.91 Y0, Y1)))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((~(subset(Y0, Y1))) => 99.05/14.91 (Y0 != Y1)))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y1))) => 99.05/14.91 ( 99.05/14.91 Y0 != Y1)))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 subset(Y0, Y0)))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (subset( 99.05/14.91 Y0, Y1) => 99.05/14.91 (subset( 99.05/14.91 Y1, Y2) => 99.05/14.91 subset( 99.05/14.91 Y0, Y2)))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 subset(Y1, 99.05/14.91 setadjoin( 99.05/14.91 Y0, Y1)))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (subset( 99.05/14.91 Y0, Y2) => 99.05/14.91 subset( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, Y2)))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (subset(Y0, 99.05/14.91 Y1) => 99.05/14.91 in(Y0, 99.05/14.91 powerset( 99.05/14.91 Y1))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (subset( 99.05/14.91 Y0, Y1) => 99.05/14.91 (subset( 99.05/14.91 Y1, Y0) => 99.05/14.91 ( 99.05/14.91 Y0 = Y1))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (subset(Y0, 99.05/14.91 emptyset) => 99.05/14.91 (Y0 = emptyset))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ( 99.05/14.91 subset( 99.05/14.91 Y1, Y0) => 99.05/14.91 in(Y1, 99.05/14.91 powerset( 99.05/14.91 Y0))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (in(Y1, 99.05/14.91 powerset( 99.05/14.91 Y0)) => 99.05/14.91 subset( 99.05/14.91 Y1, Y0)))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 in(Y0, 99.05/14.91 powerset(Y0))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (subset( 99.05/14.91 Y0, Y1) => 99.05/14.91 subset( 99.05/14.91 powerset( 99.05/14.91 Y0), 99.05/14.91 powerset( 99.05/14.91 Y1))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i > $o]: 99.05/14.91 in( 99.05/14.91 dsetconstr( 99.05/14.91 Y0, Y1), 99.05/14.91 powerset( 99.05/14.91 Y0)))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i > $o]: 99.05/14.91 subset( 99.05/14.91 dsetconstr( 99.05/14.91 Y0, Y1), 99.05/14.91 Y0))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 in(Y2, 99.05/14.91 binunion( 99.05/14.91 Y0, Y1)))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 in(Y1, 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y1) => 99.05/14.91 in(Y2, 99.05/14.91 binunion( 99.05/14.91 Y0, Y1)))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y3 : $o]: 99.05/14.91 (in(Y2, 99.05/14.91 binunion( 99.05/14.91 Y0, Y1)) => 99.05/14.91 (( 99.05/14.91 in(Y2, 99.05/14.91 Y0) => Y3) => 99.05/14.91 (( 99.05/14.91 in(Y2, 99.05/14.91 Y1) => Y3) => 99.05/14.91 Y3))))))))))))))) => 99.05/14.91 ((!!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 binunion( 99.05/14.91 Y0, Y1)) => 99.05/14.91 (in(Y2, 99.05/14.91 Y1) | 99.05/14.91 in(Y2, 99.05/14.91 Y0)))))))))))) => 99.05/14.91 ((!!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 subset( 99.05/14.91 Y0, 99.05/14.91 binunion( 99.05/14.91 Y0, Y1)))))))) => 99.05/14.91 ((!!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 subset( 99.05/14.91 Y1, 99.05/14.91 binunion( 99.05/14.91 Y0, Y1)))))))) => 99.05/14.91 ((!!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 (in(Y2, 99.05/14.91 Y1) => 99.05/14.91 in(Y2, 99.05/14.91 binintersect( 99.05/14.91 Y0, Y1))))))))))))) => 99.05/14.91 (( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (subset( 99.05/14.91 Y2, Y0) => 99.05/14.91 (subset( 99.05/14.91 Y2, Y1) => 99.05/14.91 subset( 99.05/14.91 Y2, 99.05/14.91 binintersect( 99.05/14.91 Y0, Y1))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 binintersect( 99.05/14.91 Y0, Y1)) => 99.05/14.91 in(Y2, 99.05/14.91 Y0))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 subset( 99.05/14.91 binintersect( 99.05/14.91 Y0, Y1), 99.05/14.91 Y0))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (subset( 99.05/14.91 Y0, Y1) => 99.05/14.91 (binintersect( 99.05/14.91 Y0, Y1) = 99.05/14.91 Y0)))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (( 99.05/14.91 binintersect( 99.05/14.91 Y0, Y1) = 99.05/14.91 Y1) => 99.05/14.91 subset( 99.05/14.91 Y1, Y0)))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 binintersect( 99.05/14.91 Y0, Y1)) => 99.05/14.91 in(Y2, 99.05/14.91 Y1))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (( 99.05/14.91 ~(( 99.05/14.91 ??(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) & 99.05/14.91 in(Y2, 99.05/14.91 Y1))))))) => 99.05/14.91 (binintersect( 99.05/14.91 Y0, Y1) = 99.05/14.91 emptyset)))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 subset( 99.05/14.91 binintersect( 99.05/14.91 Y0, Y1), 99.05/14.91 Y1))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (subset( 99.05/14.91 Y1, Y0) => 99.05/14.91 (binintersect( 99.05/14.91 Y0, Y1) = 99.05/14.91 Y1)))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (( 99.05/14.91 binintersect( 99.05/14.91 Y0, Y1) = 99.05/14.91 Y0) => 99.05/14.91 subset( 99.05/14.91 Y0, Y1)))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (binintersect( 99.05/14.91 Y0, 99.05/14.91 binunion( 99.05/14.91 Y1, Y2)) = 99.05/14.91 binunion( 99.05/14.91 binintersect( 99.05/14.91 Y0, Y1), 99.05/14.91 binintersect( 99.05/14.91 Y0, Y2)))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 (( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y1))) => 99.05/14.91 in(Y2, 99.05/14.91 setminus( 99.05/14.91 Y0, Y1))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 setminus( 99.05/14.91 Y0, Y1)) => 99.05/14.91 in(Y2, 99.05/14.91 Y0))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 setminus( 99.05/14.91 Y0, Y1)) => 99.05/14.91 (~( 99.05/14.91 in(Y2, 99.05/14.91 Y1))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (subset( 99.05/14.91 Y0, Y1) => 99.05/14.91 (setminus( 99.05/14.91 Y0, Y1) = 99.05/14.91 emptyset)))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 setminus( 99.05/14.91 Y0, Y1)))) => 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 in(Y2, 99.05/14.91 Y1)))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 setminus( 99.05/14.91 Y0, Y1)))) => 99.05/14.91 (( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y1))) => 99.05/14.91 (~( 99.05/14.91 in(Y2, 99.05/14.91 Y0)))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y0))) => 99.05/14.91 (~( 99.05/14.91 in(Y2, 99.05/14.91 setminus( 99.05/14.91 Y0, Y1)))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y1) => 99.05/14.91 (~( 99.05/14.91 in(Y2, 99.05/14.91 setminus( 99.05/14.91 Y0, Y1)))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 subset( 99.05/14.91 setminus( 99.05/14.91 Y0, Y1), 99.05/14.91 Y0))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (( 99.05/14.91 setminus( 99.05/14.91 Y0, Y1) = 99.05/14.91 emptyset) => 99.05/14.91 subset( 99.05/14.91 Y0, Y1)))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 symdiff( 99.05/14.91 Y0, Y1)) => 99.05/14.91 (!!(( 99.05/14.91 ^[Y3 : $o]: 99.05/14.91 (( 99.05/14.91 in(Y2, 99.05/14.91 Y0) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y1))) => 99.05/14.91 Y3)) => 99.05/14.91 (( 99.05/14.91 ( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y0))) => 99.05/14.91 ( 99.05/14.91 in(Y2, 99.05/14.91 Y1) => Y3)) => 99.05/14.91 Y3))))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 (( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y1))) => 99.05/14.91 in(Y2, 99.05/14.91 symdiff( 99.05/14.91 Y0, Y1))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y0))) => 99.05/14.91 (in(Y2, 99.05/14.91 Y1) => 99.05/14.91 in(Y2, 99.05/14.91 symdiff( 99.05/14.91 Y0, Y1))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 (in(Y2, 99.05/14.91 Y1) => 99.05/14.91 (~( 99.05/14.91 in(Y2, 99.05/14.91 symdiff( 99.05/14.91 Y0, Y1))))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y0))) => 99.05/14.91 (( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y1))) => 99.05/14.91 (~( 99.05/14.91 in(Y2, 99.05/14.91 symdiff( 99.05/14.91 Y0, Y1))))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 in(Y1, 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 in(Y0, 99.05/14.91 setunion( 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 in(Y1, 99.05/14.91 setunion( 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (??(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 setunion( 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)))) & 99.05/14.91 (??(( 99.05/14.91 ^[Y3 : $i]: 99.05/14.91 (in(Y3, 99.05/14.91 setunion( 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)))) & 99.05/14.91 (setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)) = 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 setadjoin( 99.05/14.91 Y3, 99.05/14.91 emptyset)), 99.05/14.91 emptyset))))))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (??(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 setunion( 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)))) & 99.05/14.91 (??(( 99.05/14.91 ^[Y3 : $i]: 99.05/14.91 (in(Y3, 99.05/14.91 setunion( 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)))) & 99.05/14.91 (setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)) = 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 setadjoin( 99.05/14.91 Y3, 99.05/14.91 emptyset)), 99.05/14.91 emptyset))))))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (in(Y1, 99.05/14.91 Y0) => 99.05/14.91 subset( 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset), 99.05/14.91 Y0)))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (in(Y1, 99.05/14.91 Y0) => 99.05/14.91 in( 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset), 99.05/14.91 powerset( 99.05/14.91 Y0))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 in( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 emptyset), 99.05/14.91 powerset( 99.05/14.91 binunion( 99.05/14.91 Y0, Y1))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset))) => 99.05/14.91 (( 99.05/14.91 Y2 = Y1) | 99.05/14.91 (Y2 = Y0)))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 (!!(( 99.05/14.91 ^[Y3 : $i]: 99.05/14.91 (in(Y3, 99.05/14.91 Y1) => 99.05/14.91 subset( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 setadjoin( 99.05/14.91 Y3, 99.05/14.91 emptyset)), 99.05/14.91 binunion( 99.05/14.91 Y0, Y1)))))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 (!!(( 99.05/14.91 ^[Y3 : $i]: 99.05/14.91 (in(Y3, 99.05/14.91 Y1) => 99.05/14.91 in( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 setadjoin( 99.05/14.91 Y3, 99.05/14.91 emptyset)), 99.05/14.91 powerset( 99.05/14.91 binunion( 99.05/14.91 Y0, Y1))))))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 (!!(( 99.05/14.91 ^[Y3 : $i]: 99.05/14.91 (in(Y3, 99.05/14.91 Y1) => 99.05/14.91 subset( 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 setadjoin( 99.05/14.91 Y3, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)), 99.05/14.91 powerset( 99.05/14.91 binunion( 99.05/14.91 Y0, Y1))))))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 (!!(( 99.05/14.91 ^[Y3 : $i]: 99.05/14.91 (in(Y3, 99.05/14.91 Y1) => 99.05/14.91 in( 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 setadjoin( 99.05/14.91 Y3, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)), 99.05/14.91 powerset( 99.05/14.91 powerset( 99.05/14.91 binunion( 99.05/14.91 Y0, Y1)))))))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 (!!(( 99.05/14.91 ^[Y3 : $i]: 99.05/14.91 (in(Y3, 99.05/14.91 Y1) => 99.05/14.91 in( 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 setadjoin( 99.05/14.91 Y3, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)), 99.05/14.91 powerset( 99.05/14.91 powerset( 99.05/14.91 binunion( 99.05/14.91 Y0, Y1)))))))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 (!!(( 99.05/14.91 ^[Y3 : $i]: 99.05/14.91 (in(Y3, 99.05/14.91 Y1) => 99.05/14.91 in( 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 setadjoin( 99.05/14.91 Y3, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)), 99.05/14.91 dsetconstr( 99.05/14.91 powerset( 99.05/14.91 powerset( 99.05/14.91 binunion( 99.05/14.91 Y0, Y1))), 99.05/14.91 (^[Y4 : $i]: 99.05/14.91 (??(( 99.05/14.91 ^[Y5 : $i]: 99.05/14.91 (in(Y5, 99.05/14.91 Y0) & 99.05/14.91 (??(( 99.05/14.91 ^[Y6 : $i]: 99.05/14.91 (in(Y6, 99.05/14.91 Y1) & 99.05/14.91 (Y4 = 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y5, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y5, 99.05/14.91 setadjoin( 99.05/14.91 Y6, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)))))))))))))))))))))))))))) => 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 dsetconstr( 99.05/14.91 powerset( 99.05/14.91 powerset( 99.05/14.91 binunion( 99.05/14.91 Y0, Y1))), 99.05/14.91 (^[Y3 : $i]: 99.05/14.91 (??(( 99.05/14.91 ^[Y4 : $i]: 99.05/14.91 (in(Y4, 99.05/14.91 Y0) & 99.05/14.91 (??(( 99.05/14.91 ^[Y5 : $i]: 99.05/14.91 (in(Y5, 99.05/14.91 Y1) & 99.05/14.91 (Y3 = 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y4, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y4, 99.05/14.91 setadjoin( 99.05/14.91 Y5, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)))))))))))))) => 99.05/14.91 (??(( 99.05/14.91 ^[Y3 : $i]: 99.05/14.91 (( 99.05/14.91 ??(( 99.05/14.91 ^[Y4 : $i]: 99.05/14.91 (in(Y4, 99.05/14.91 Y1) & 99.05/14.91 (Y2 = 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y3, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y3, 99.05/14.91 setadjoin( 99.05/14.91 Y4, 99.05/14.91 emptyset)), 99.05/14.91 emptyset))))))) & 99.05/14.91 in(Y3, 99.05/14.91 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.05/14.91 inference('lazy_cnf_imply', [status(thm)], ['201'])). 99.05/14.91 tff('203', plain, 99.05/14.91 ~ ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: (in(Y0, setadjoin(Y1, emptyset)) => (Y0 = Y1)))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 != Y1) => (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => in(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (in(Y0, setadjoin(Y1, emptyset)) => 99.05/14.91 in(Y1, setadjoin(Y0, emptyset))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 setadjoin(Y0, setadjoin(Y1, emptyset))) => 99.05/14.91 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 in(Y0, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i > $o]: 99.05/14.91 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 99.05/14.91 (dsetconstr(Y0, Y1) != emptyset)))))))) => 99.05/14.91 ((!!((^[Y0 : $i > $o]: 99.05/14.91 (!!((^[Y1 : $i]: (in(Y1, emptyset) => Y0(Y1)))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i > $o]: 99.05/14.91 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.91 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i > $o]: 99.05/14.91 ((!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2))))))) => 99.05/14.91 (~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i > $o]: 99.05/14.91 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.91 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i > $o]: 99.05/14.91 ((??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2))))))) => 99.05/14.91 (~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2)))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $o]: (Y0 => in(emptyset, prop2set(Y0)))))) => 99.05/14.91 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i > $o]: 99.05/14.91 ((~((??((^[Y2 : $i]: 99.05/14.91 (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i > $o]: 99.05/14.91 ((~((!!((^[Y2 : $i]: 99.05/14.91 (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.91 (??((^[Y2 : $i]: 99.05/14.91 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i > $o]: 99.05/14.91 ((??(Y0)) => 99.05/14.91 ((!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (Y0(Y1) => 99.05/14.91 (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.91 (??((^[Y1 : $i]: 99.05/14.91 (Y0(Y1) & 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (Y0(Y2) => (Y1 = Y2)))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i > $o]: 99.05/14.91 ((??((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (Y0(Y2) <=> (Y2 = Y1)))))))) => 99.05/14.91 (??((^[Y1 : $i]: 99.05/14.91 (Y0(Y1) & 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 ((Y2 = Y3) => 99.05/14.91 (in(Y2, Y0) => 99.05/14.91 in(Y3, Y1)))))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 ((Y2 = Y3) => 99.05/14.91 (in(Y2, Y0) <=> 99.05/14.91 in(Y3, Y1)))))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i > $o]: 99.05/14.91 ((??((^[Y1 : $i]: 99.05/14.91 (Y0(Y1) & 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (Y0(Y1) => 99.05/14.91 (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i > $o]: 99.05/14.91 (!!((^[Y1 : $i > $o]: 99.05/14.91 ((!!((^[Y2 : $i]: 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 ((Y2 = Y3) => 99.05/14.91 (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.91 ((??((^[Y2 : $i]: 99.05/14.91 (Y0(Y2) & 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 (Y0(Y3) => 99.05/14.91 (Y2 = Y3))))))))) <=> 99.05/14.91 (??((^[Y2 : $i]: 99.05/14.91 (Y1(Y2) & 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 (Y1(Y3) => 99.05/14.91 (Y2 = Y3))))))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 ((Y2 = Y3) => 99.05/14.91 (setadjoin(Y0, 99.05/14.91 Y2) = 99.05/14.91 setadjoin(Y1, 99.05/14.91 Y3)))))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => 99.05/14.91 (powerset(Y0) = powerset(Y1))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => 99.05/14.91 (setunion(Y0) = setunion(Y1))))))))) => 99.05/14.91 ((!!((^[Y0 : $i > $o]: 99.05/14.91 ((??((^[Y1 : $i]: 99.05/14.91 (Y0(Y1) & 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (Y0(Y1) => 99.05/14.91 (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i > $o]: 99.05/14.91 (!!((^[Y1 : $i > $o]: 99.05/14.91 ((!!((^[Y2 : $i]: 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 ((Y2 = Y3) => 99.05/14.91 (Y0(Y2) <=> 99.05/14.91 Y1(Y3))))))))) => 99.05/14.91 ((??((^[Y2 : $i]: 99.05/14.91 (Y0(Y2) & 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 (Y0(Y3) => 99.05/14.91 (Y2 = Y3))))))))) => 99.05/14.91 ((??((^[Y2 : $i]: 99.05/14.91 (Y1(Y2) & 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 (Y1(Y3) => 99.05/14.91 (Y2 = Y3))))))))) => 99.05/14.91 (descr(Y0) = descr(Y1))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => 99.05/14.91 (!!((^[Y2 : $i > $o]: 99.05/14.91 (!!((^[Y3 : $i > $o]: 99.05/14.91 ((!!(( 99.05/14.91 ^[Y4 : $i]: 99.05/14.91 ( 99.05/14.91 in(Y4, 99.05/14.91 Y0) => 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y5 : $i]: 99.05/14.91 (in(Y5, 99.05/14.91 Y1) => 99.05/14.91 (( 99.05/14.91 Y4 = Y5) => 99.05/14.91 (Y2(Y4) <=> 99.05/14.91 Y3(Y5))))))))))) => 99.05/14.91 (dsetconstr( 99.05/14.91 Y0, Y2) = 99.05/14.91 dsetconstr( 99.05/14.91 Y1, Y3)))))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((!!((^[Y2 : $i]: 99.05/14.91 (in(Y2, Y0) => 99.05/14.91 in(Y2, Y1))))) => 99.05/14.91 subset(Y0, Y1)))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => 99.05/14.91 subset(Y1, Y0)))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => 99.05/14.91 subset(Y0, Y1)))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((!!((^[Y2 : $i]: 99.05/14.91 (in(Y2, Y0) => 99.05/14.91 in(Y2, Y1))))) => 99.05/14.91 subset(Y0, Y1)))))))) => 99.05/14.91 ((!!(subset(emptyset))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (subset(Y0, Y1) => 99.05/14.91 (in(Y2, Y0) => 99.05/14.91 in(Y2, Y1)))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (subset(Y0, 99.05/14.91 Y1) => 99.05/14.91 ((~(in(Y2, 99.05/14.91 Y1))) => 99.05/14.91 (~(in(Y2, 99.05/14.91 Y0)))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (in(Y2, Y0) => 99.05/14.91 ((~( 99.05/14.91 in(Y2, Y1))) => 99.05/14.91 (~( 99.05/14.91 subset( 99.05/14.91 Y0, Y1)))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((~(subset(Y0, Y1))) => 99.05/14.91 (Y0 != Y1)))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (in(Y2, Y0) => 99.05/14.91 (( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y1))) => 99.05/14.91 ( 99.05/14.91 Y0 != Y1)))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 ( 99.05/14.91 subset( 99.05/14.91 Y0, Y1) => 99.05/14.91 ( 99.05/14.91 subset( 99.05/14.91 Y1, Y2) => 99.05/14.91 subset( 99.05/14.91 Y0, Y2)))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 subset(Y1, 99.05/14.91 setadjoin( 99.05/14.91 Y0, Y1)))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (subset( 99.05/14.91 Y0, Y2) => 99.05/14.91 subset( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, Y2)))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (subset(Y0, 99.05/14.91 Y1) => 99.05/14.91 in(Y0, 99.05/14.91 powerset( 99.05/14.91 Y1))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (subset(Y0, 99.05/14.91 Y1) => 99.05/14.91 (subset( 99.05/14.91 Y1, Y0) => 99.05/14.91 (Y0 = Y1))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (subset(Y0, 99.05/14.91 emptyset) => 99.05/14.91 (Y0 = emptyset))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (subset( 99.05/14.91 Y1, Y0) => 99.05/14.91 in(Y1, 99.05/14.91 powerset( 99.05/14.91 Y0))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ( 99.05/14.91 in(Y1, 99.05/14.91 powerset( 99.05/14.91 Y0)) => 99.05/14.91 subset( 99.05/14.91 Y1, Y0)))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 in(Y0, 99.05/14.91 powerset(Y0))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (subset( 99.05/14.91 Y0, Y1) => 99.05/14.91 subset( 99.05/14.91 powerset( 99.05/14.91 Y0), 99.05/14.91 powerset( 99.05/14.91 Y1))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i > $o]: 99.05/14.91 in( 99.05/14.91 dsetconstr( 99.05/14.91 Y0, Y1), 99.05/14.91 powerset( 99.05/14.91 Y0)))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i > $o]: 99.05/14.91 subset( 99.05/14.91 dsetconstr( 99.05/14.91 Y0, Y1), 99.05/14.91 Y0))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 in(Y2, 99.05/14.91 binunion( 99.05/14.91 Y0, Y1)))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 in(Y1, 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y1) => 99.05/14.91 in(Y2, 99.05/14.91 binunion( 99.05/14.91 Y0, Y1)))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y3 : $o]: 99.05/14.91 (in(Y2, 99.05/14.91 binunion( 99.05/14.91 Y0, Y1)) => 99.05/14.91 (( 99.05/14.91 in(Y2, 99.05/14.91 Y0) => Y3) => 99.05/14.91 (( 99.05/14.91 in(Y2, 99.05/14.91 Y1) => Y3) => 99.05/14.91 Y3))))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 binunion( 99.05/14.91 Y0, Y1)) => 99.05/14.91 (in(Y2, 99.05/14.91 Y1) | 99.05/14.91 in(Y2, 99.05/14.91 Y0)))))))))))) => 99.05/14.91 ((!!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 subset( 99.05/14.91 Y0, 99.05/14.91 binunion( 99.05/14.91 Y0, Y1)))))))) => 99.05/14.91 ((!!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 subset( 99.05/14.91 Y1, 99.05/14.91 binunion( 99.05/14.91 Y0, Y1)))))))) => 99.05/14.91 ((!!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 (in(Y2, 99.05/14.91 Y1) => 99.05/14.91 in(Y2, 99.05/14.91 binintersect( 99.05/14.91 Y0, Y1))))))))))))) => 99.05/14.91 ((!!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (subset( 99.05/14.91 Y2, Y0) => 99.05/14.91 (subset( 99.05/14.91 Y2, Y1) => 99.05/14.91 subset( 99.05/14.91 Y2, 99.05/14.91 binintersect( 99.05/14.91 Y0, Y1))))))))))))) => 99.05/14.91 (( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 binintersect( 99.05/14.91 Y0, Y1)) => 99.05/14.91 in(Y2, 99.05/14.91 Y0))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 subset( 99.05/14.91 binintersect( 99.05/14.91 Y0, Y1), 99.05/14.91 Y0))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (subset( 99.05/14.91 Y0, Y1) => 99.05/14.91 (binintersect( 99.05/14.91 Y0, Y1) = 99.05/14.91 Y0)))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (( 99.05/14.91 binintersect( 99.05/14.91 Y0, Y1) = 99.05/14.91 Y1) => 99.05/14.91 subset( 99.05/14.91 Y1, Y0)))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 binintersect( 99.05/14.91 Y0, Y1)) => 99.05/14.91 in(Y2, 99.05/14.91 Y1))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (( 99.05/14.91 ~(( 99.05/14.91 ??(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) & 99.05/14.91 in(Y2, 99.05/14.91 Y1))))))) => 99.05/14.91 (binintersect( 99.05/14.91 Y0, Y1) = 99.05/14.91 emptyset)))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 subset( 99.05/14.91 binintersect( 99.05/14.91 Y0, Y1), 99.05/14.91 Y1))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (subset( 99.05/14.91 Y1, Y0) => 99.05/14.91 (binintersect( 99.05/14.91 Y0, Y1) = 99.05/14.91 Y1)))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (( 99.05/14.91 binintersect( 99.05/14.91 Y0, Y1) = 99.05/14.91 Y0) => 99.05/14.91 subset( 99.05/14.91 Y0, Y1)))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (binintersect( 99.05/14.91 Y0, 99.05/14.91 binunion( 99.05/14.91 Y1, Y2)) = 99.05/14.91 binunion( 99.05/14.91 binintersect( 99.05/14.91 Y0, Y1), 99.05/14.91 binintersect( 99.05/14.91 Y0, Y2)))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 (( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y1))) => 99.05/14.91 in(Y2, 99.05/14.91 setminus( 99.05/14.91 Y0, Y1))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 setminus( 99.05/14.91 Y0, Y1)) => 99.05/14.91 in(Y2, 99.05/14.91 Y0))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 setminus( 99.05/14.91 Y0, Y1)) => 99.05/14.91 (~( 99.05/14.91 in(Y2, 99.05/14.91 Y1))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (subset( 99.05/14.91 Y0, Y1) => 99.05/14.91 (setminus( 99.05/14.91 Y0, Y1) = 99.05/14.91 emptyset)))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 setminus( 99.05/14.91 Y0, Y1)))) => 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 in(Y2, 99.05/14.91 Y1)))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 setminus( 99.05/14.91 Y0, Y1)))) => 99.05/14.91 (( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y1))) => 99.05/14.91 (~( 99.05/14.91 in(Y2, 99.05/14.91 Y0)))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y0))) => 99.05/14.91 (~( 99.05/14.91 in(Y2, 99.05/14.91 setminus( 99.05/14.91 Y0, Y1)))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y1) => 99.05/14.91 (~( 99.05/14.91 in(Y2, 99.05/14.91 setminus( 99.05/14.91 Y0, Y1)))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 subset( 99.05/14.91 setminus( 99.05/14.91 Y0, Y1), 99.05/14.91 Y0))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (( 99.05/14.91 setminus( 99.05/14.91 Y0, Y1) = 99.05/14.91 emptyset) => 99.05/14.91 subset( 99.05/14.91 Y0, Y1)))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 symdiff( 99.05/14.91 Y0, Y1)) => 99.05/14.91 (!!(( 99.05/14.91 ^[Y3 : $o]: 99.05/14.91 (( 99.05/14.91 in(Y2, 99.05/14.91 Y0) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y1))) => 99.05/14.91 Y3)) => 99.05/14.91 (( 99.05/14.91 ( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y0))) => 99.05/14.91 ( 99.05/14.91 in(Y2, 99.05/14.91 Y1) => Y3)) => 99.05/14.91 Y3))))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 (( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y1))) => 99.05/14.91 in(Y2, 99.05/14.91 symdiff( 99.05/14.91 Y0, Y1))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y0))) => 99.05/14.91 (in(Y2, 99.05/14.91 Y1) => 99.05/14.91 in(Y2, 99.05/14.91 symdiff( 99.05/14.91 Y0, Y1))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 (in(Y2, 99.05/14.91 Y1) => 99.05/14.91 (~( 99.05/14.91 in(Y2, 99.05/14.91 symdiff( 99.05/14.91 Y0, Y1))))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y0))) => 99.05/14.91 (( 99.05/14.91 ~( 99.05/14.91 in(Y2, 99.05/14.91 Y1))) => 99.05/14.91 (~( 99.05/14.91 in(Y2, 99.05/14.91 symdiff( 99.05/14.91 Y0, Y1))))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 in(Y1, 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 in(Y0, 99.05/14.91 setunion( 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 in(Y1, 99.05/14.91 setunion( 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (??(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 setunion( 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)))) & 99.05/14.91 (??(( 99.05/14.91 ^[Y3 : $i]: 99.05/14.91 (in(Y3, 99.05/14.91 setunion( 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)))) & 99.05/14.91 (setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)) = 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 setadjoin( 99.05/14.91 Y3, 99.05/14.91 emptyset)), 99.05/14.91 emptyset))))))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (??(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 setunion( 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)))) & 99.05/14.91 (??(( 99.05/14.91 ^[Y3 : $i]: 99.05/14.91 (in(Y3, 99.05/14.91 setunion( 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)))) & 99.05/14.91 (setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)) = 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 setadjoin( 99.05/14.91 Y3, 99.05/14.91 emptyset)), 99.05/14.91 emptyset))))))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (in(Y1, 99.05/14.91 Y0) => 99.05/14.91 subset( 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset), 99.05/14.91 Y0)))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (in(Y1, 99.05/14.91 Y0) => 99.05/14.91 in( 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset), 99.05/14.91 powerset( 99.05/14.91 Y0))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 in( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 emptyset), 99.05/14.91 powerset( 99.05/14.91 binunion( 99.05/14.91 Y0, Y1))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 setadjoin( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, 99.05/14.91 emptyset))) => 99.05/14.91 (( 99.05/14.91 Y2 = Y1) | 99.05/14.91 (Y2 = Y0)))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 (!!(( 99.05/14.91 ^[Y3 : $i]: 99.05/14.91 (in(Y3, 99.05/14.91 Y1) => 99.05/14.91 subset( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 setadjoin( 99.05/14.91 Y3, 99.05/14.91 emptyset)), 99.05/14.91 binunion( 99.05/14.91 Y0, Y1)))))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 (!!(( 99.05/14.91 ^[Y3 : $i]: 99.05/14.91 (in(Y3, 99.05/14.91 Y1) => 99.05/14.91 in( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 setadjoin( 99.05/14.91 Y3, 99.05/14.91 emptyset)), 99.05/14.91 powerset( 99.05/14.91 binunion( 99.05/14.91 Y0, Y1))))))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 (!!(( 99.05/14.91 ^[Y3 : $i]: 99.05/14.91 (in(Y3, 99.05/14.91 Y1) => 99.05/14.91 subset( 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 setadjoin( 99.05/14.91 Y3, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)), 99.05/14.91 powerset( 99.05/14.91 binunion( 99.05/14.91 Y0, Y1))))))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 (!!(( 99.05/14.91 ^[Y3 : $i]: 99.05/14.91 (in(Y3, 99.05/14.91 Y1) => 99.05/14.91 in( 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 setadjoin( 99.05/14.91 Y3, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)), 99.05/14.91 powerset( 99.05/14.91 powerset( 99.05/14.91 binunion( 99.05/14.91 Y0, Y1)))))))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 (!!(( 99.05/14.91 ^[Y3 : $i]: 99.05/14.91 (in(Y3, 99.05/14.91 Y1) => 99.05/14.91 in( 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 setadjoin( 99.05/14.91 Y3, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)), 99.05/14.91 powerset( 99.05/14.91 powerset( 99.05/14.91 binunion( 99.05/14.91 Y0, Y1)))))))))))))))))) => 99.05/14.91 ( 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 Y0) => 99.05/14.91 (!!(( 99.05/14.91 ^[Y3 : $i]: 99.05/14.91 (in(Y3, 99.05/14.91 Y1) => 99.05/14.91 in( 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y2, 99.05/14.91 setadjoin( 99.05/14.91 Y3, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)), 99.05/14.91 dsetconstr( 99.05/14.91 powerset( 99.05/14.91 powerset( 99.05/14.91 binunion( 99.05/14.91 Y0, Y1))), 99.05/14.91 (^[Y4 : $i]: 99.05/14.91 (??(( 99.05/14.91 ^[Y5 : $i]: 99.05/14.91 (in(Y5, 99.05/14.91 Y0) & 99.05/14.91 (??(( 99.05/14.91 ^[Y6 : $i]: 99.05/14.91 (in(Y6, 99.05/14.91 Y1) & 99.05/14.91 (Y4 = 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y5, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y5, 99.05/14.91 setadjoin( 99.05/14.91 Y6, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)))))))))))))))))))))))))))) => 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y0 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y1 : $i]: 99.05/14.91 (!!(( 99.05/14.91 ^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 dsetconstr( 99.05/14.91 powerset( 99.05/14.91 powerset( 99.05/14.91 binunion( 99.05/14.91 Y0, Y1))), 99.05/14.91 (^[Y3 : $i]: 99.05/14.91 (??(( 99.05/14.91 ^[Y4 : $i]: 99.05/14.91 (in(Y4, 99.05/14.91 Y0) & 99.05/14.91 (??(( 99.05/14.91 ^[Y5 : $i]: 99.05/14.91 (in(Y5, 99.05/14.91 Y1) & 99.05/14.91 (Y3 = 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y4, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y4, 99.05/14.91 setadjoin( 99.05/14.91 Y5, 99.05/14.91 emptyset)), 99.05/14.91 emptyset)))))))))))))) => 99.05/14.91 (??(( 99.05/14.91 ^[Y3 : $i]: 99.05/14.91 (( 99.05/14.91 ??(( 99.05/14.91 ^[Y4 : $i]: 99.05/14.91 (in(Y4, 99.05/14.91 Y1) & 99.05/14.91 (Y2 = 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y3, 99.05/14.91 emptyset), 99.05/14.91 setadjoin( 99.05/14.91 setadjoin( 99.05/14.91 Y3, 99.05/14.91 setadjoin( 99.05/14.91 Y4, 99.05/14.91 emptyset)), 99.05/14.91 emptyset))))))) & 99.05/14.91 in(Y3, 99.05/14.91 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.05/14.91 inference('lazy_cnf_imply', [status(thm)], ['202'])). 99.05/14.91 tff('204', plain, 99.05/14.91 ~ ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 != Y1) => (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => in(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (in(Y0, setadjoin(Y1, emptyset)) => 99.05/14.91 in(Y1, setadjoin(Y0, emptyset))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (in(Y2, 99.05/14.91 setadjoin(Y0, setadjoin(Y1, emptyset))) => 99.05/14.91 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 in(Y0, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i > $o]: 99.05/14.91 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 99.05/14.91 (dsetconstr(Y0, Y1) != emptyset)))))))) => 99.05/14.91 ((!!((^[Y0 : $i > $o]: 99.05/14.91 (!!((^[Y1 : $i]: (in(Y1, emptyset) => Y0(Y1)))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i > $o]: 99.05/14.91 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.91 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i > $o]: 99.05/14.91 ((!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2))))))) => 99.05/14.91 (~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i > $o]: 99.05/14.91 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.91 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i > $o]: 99.05/14.91 ((??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2))))))) => 99.05/14.91 (~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2)))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $o]: (Y0 => in(emptyset, prop2set(Y0)))))) => 99.05/14.91 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i > $o]: 99.05/14.91 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i > $o]: 99.05/14.91 ((~((!!((^[Y2 : $i]: 99.05/14.91 (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.91 (??((^[Y2 : $i]: 99.05/14.91 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i > $o]: 99.05/14.91 ((??(Y0)) => 99.05/14.91 ((!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (Y0(Y1) => 99.05/14.91 (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.91 (??((^[Y1 : $i]: 99.05/14.91 (Y0(Y1) & 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (Y0(Y2) => (Y1 = Y2)))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i > $o]: 99.05/14.91 ((??((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (Y0(Y2) <=> (Y2 = Y1)))))))) => 99.05/14.91 (??((^[Y1 : $i]: 99.05/14.91 (Y0(Y1) & 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 ((Y2 = Y3) => 99.05/14.91 (in(Y2, Y0) => 99.05/14.91 in(Y3, Y1)))))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 ((Y2 = Y3) => 99.05/14.91 (in(Y2, Y0) <=> 99.05/14.91 in(Y3, Y1)))))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i > $o]: 99.05/14.91 ((??((^[Y1 : $i]: 99.05/14.91 (Y0(Y1) & 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (Y0(Y1) => 99.05/14.91 (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i > $o]: 99.05/14.91 (!!((^[Y1 : $i > $o]: 99.05/14.91 ((!!((^[Y2 : $i]: 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 ((Y2 = Y3) => 99.05/14.91 (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.91 ((??((^[Y2 : $i]: 99.05/14.91 (Y0(Y2) & 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 (Y0(Y3) => 99.05/14.91 (Y2 = Y3))))))))) <=> 99.05/14.91 (??((^[Y2 : $i]: 99.05/14.91 (Y1(Y2) & 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 (Y1(Y3) => 99.05/14.91 (Y2 = Y3))))))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 ((Y2 = Y3) => 99.05/14.91 (setadjoin(Y0, Y2) = 99.05/14.91 setadjoin(Y1, Y3)))))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => 99.05/14.91 (powerset(Y0) = powerset(Y1))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => 99.05/14.91 (setunion(Y0) = setunion(Y1))))))))) => 99.05/14.91 ((!!((^[Y0 : $i > $o]: 99.05/14.91 ((??((^[Y1 : $i]: 99.05/14.91 (Y0(Y1) & 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (Y0(Y1) => 99.05/14.91 (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i > $o]: 99.05/14.91 (!!((^[Y1 : $i > $o]: 99.05/14.91 ((!!((^[Y2 : $i]: 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 ((Y2 = Y3) => 99.05/14.91 (Y0(Y2) <=> 99.05/14.91 Y1(Y3))))))))) => 99.05/14.91 ((??((^[Y2 : $i]: 99.05/14.91 (Y0(Y2) & 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 (Y0(Y3) => 99.05/14.91 (Y2 = Y3))))))))) => 99.05/14.91 ((??((^[Y2 : $i]: 99.05/14.91 (Y1(Y2) & 99.05/14.91 (!!((^[Y3 : $i]: 99.05/14.91 (Y1(Y3) => 99.05/14.91 (Y2 = Y3))))))))) => 99.05/14.91 (descr(Y0) = descr(Y1))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => 99.05/14.91 (!!((^[Y2 : $i > $o]: 99.05/14.91 (!!((^[Y3 : $i > $o]: 99.05/14.91 ((!!(( 99.05/14.91 ^[Y4 : $i]: 99.05/14.91 (in(Y4, 99.05/14.91 Y0) => 99.05/14.91 ( 99.05/14.91 !!(( 99.05/14.91 ^[Y5 : $i]: 99.05/14.91 (in(Y5, 99.05/14.91 Y1) => 99.05/14.91 (( 99.05/14.91 Y4 = Y5) => 99.05/14.91 (Y2(Y4) <=> 99.05/14.91 Y3(Y5))))))))))) => 99.05/14.91 (dsetconstr( 99.05/14.91 Y0, Y2) = 99.05/14.91 dsetconstr( 99.05/14.91 Y1, Y3)))))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((!!((^[Y2 : $i]: 99.05/14.91 (in(Y2, Y0) => 99.05/14.91 in(Y2, Y1))))) => 99.05/14.91 subset(Y0, Y1)))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => 99.05/14.91 subset(Y1, Y0)))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((Y0 = Y1) => 99.05/14.91 subset(Y0, Y1)))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((!!((^[Y2 : $i]: 99.05/14.91 (in(Y2, Y0) => 99.05/14.91 in(Y2, Y1))))) => 99.05/14.91 subset(Y0, Y1)))))))) => 99.05/14.91 ((!!(subset(emptyset))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (subset(Y0, Y1) => 99.05/14.91 (in(Y2, Y0) => 99.05/14.91 in(Y2, Y1)))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (subset(Y0, Y1) => 99.05/14.91 ((~(in(Y2, Y1))) => 99.05/14.91 (~(in(Y2, Y0)))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (in(Y2, Y0) => 99.05/14.91 ((~(in(Y2, 99.05/14.91 Y1))) => 99.05/14.91 (~(subset( 99.05/14.91 Y0, Y1)))))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 ((~(subset(Y0, Y1))) => 99.05/14.91 (Y0 != Y1)))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (in(Y2, Y0) => 99.05/14.91 ((~( 99.05/14.91 in(Y2, 99.05/14.91 Y1))) => 99.05/14.91 (Y0 != Y1)))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (subset( 99.05/14.91 Y0, Y1) => 99.05/14.91 ( 99.05/14.91 subset( 99.05/14.91 Y1, Y2) => 99.05/14.91 subset( 99.05/14.91 Y0, Y2)))))))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 subset(Y1, 99.05/14.91 setadjoin(Y0, 99.05/14.91 Y1)))))))) => 99.05/14.91 ((!!((^[Y0 : $i]: 99.05/14.91 (!!((^[Y1 : $i]: 99.05/14.91 (!!((^[Y2 : $i]: 99.05/14.91 (subset( 99.05/14.91 Y0, Y2) => 99.05/14.91 subset( 99.05/14.91 Y0, 99.05/14.91 setadjoin( 99.05/14.91 Y1, Y2)))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (subset(Y0, 99.05/14.92 Y1) => 99.05/14.92 in(Y0, 99.05/14.92 powerset( 99.05/14.92 Y1))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (subset(Y0, 99.05/14.92 Y1) => 99.05/14.92 (subset(Y1, 99.05/14.92 Y0) => 99.05/14.92 (Y0 = Y1))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (subset(Y0, 99.05/14.92 emptyset) => 99.05/14.92 (Y0 = emptyset))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (subset( 99.05/14.92 Y1, Y0) => 99.05/14.92 in(Y1, 99.05/14.92 powerset( 99.05/14.92 Y0))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (in(Y1, 99.05/14.92 powerset( 99.05/14.92 Y0)) => 99.05/14.92 subset( 99.05/14.92 Y1, Y0)))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 in(Y0, 99.05/14.92 powerset(Y0))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (subset( 99.05/14.92 Y0, Y1) => 99.05/14.92 subset( 99.05/14.92 powerset( 99.05/14.92 Y0), 99.05/14.92 powerset( 99.05/14.92 Y1))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 in( 99.05/14.92 dsetconstr( 99.05/14.92 Y0, Y1), 99.05/14.92 powerset( 99.05/14.92 Y0)))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i > $o]: 99.05/14.92 subset( 99.05/14.92 dsetconstr( 99.05/14.92 Y0, Y1), 99.05/14.92 Y0))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 in(Y2, 99.05/14.92 binunion( 99.05/14.92 Y0, Y1)))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 in(Y1, 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y1) => 99.05/14.92 in(Y2, 99.05/14.92 binunion( 99.05/14.92 Y0, Y1)))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y3 : $o]: 99.05/14.92 (in(Y2, 99.05/14.92 binunion( 99.05/14.92 Y0, Y1)) => 99.05/14.92 (( 99.05/14.92 in(Y2, 99.05/14.92 Y0) => Y3) => 99.05/14.92 (( 99.05/14.92 in(Y2, 99.05/14.92 Y1) => Y3) => 99.05/14.92 Y3))))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 binunion( 99.05/14.92 Y0, Y1)) => 99.05/14.92 (in(Y2, 99.05/14.92 Y1) | 99.05/14.92 in(Y2, 99.05/14.92 Y0)))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 subset( 99.05/14.92 Y0, 99.05/14.92 binunion( 99.05/14.92 Y0, Y1)))))))) => 99.05/14.92 ((!!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 subset( 99.05/14.92 Y1, 99.05/14.92 binunion( 99.05/14.92 Y0, Y1)))))))) => 99.05/14.92 ((!!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (in(Y2, 99.05/14.92 Y1) => 99.05/14.92 in(Y2, 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1))))))))))))) => 99.05/14.92 ((!!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (subset( 99.05/14.92 Y2, Y0) => 99.05/14.92 (subset( 99.05/14.92 Y2, Y1) => 99.05/14.92 subset( 99.05/14.92 Y2, 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1))))))))))))) => 99.05/14.92 ((!!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1)) => 99.05/14.92 in(Y2, 99.05/14.92 Y0))))))))))) => 99.05/14.92 (( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 subset( 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1), 99.05/14.92 Y0))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (subset( 99.05/14.92 Y0, Y1) => 99.05/14.92 (binintersect( 99.05/14.92 Y0, Y1) = 99.05/14.92 Y0)))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (( 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1) = 99.05/14.92 Y1) => 99.05/14.92 subset( 99.05/14.92 Y1, Y0)))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1)) => 99.05/14.92 in(Y2, 99.05/14.92 Y1))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (( 99.05/14.92 ~(( 99.05/14.92 ??(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) & 99.05/14.92 in(Y2, 99.05/14.92 Y1))))))) => 99.05/14.92 (binintersect( 99.05/14.92 Y0, Y1) = 99.05/14.92 emptyset)))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 subset( 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1), 99.05/14.92 Y1))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (subset( 99.05/14.92 Y1, Y0) => 99.05/14.92 (binintersect( 99.05/14.92 Y0, Y1) = 99.05/14.92 Y1)))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (( 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1) = 99.05/14.92 Y0) => 99.05/14.92 subset( 99.05/14.92 Y0, Y1)))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (binintersect( 99.05/14.92 Y0, 99.05/14.92 binunion( 99.05/14.92 Y1, Y2)) = 99.05/14.92 binunion( 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1), 99.05/14.92 binintersect( 99.05/14.92 Y0, Y2)))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y1))) => 99.05/14.92 in(Y2, 99.05/14.92 setminus( 99.05/14.92 Y0, Y1))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 setminus( 99.05/14.92 Y0, Y1)) => 99.05/14.92 in(Y2, 99.05/14.92 Y0))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 setminus( 99.05/14.92 Y0, Y1)) => 99.05/14.92 (~( 99.05/14.92 in(Y2, 99.05/14.92 Y1))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (subset( 99.05/14.92 Y0, Y1) => 99.05/14.92 (setminus( 99.05/14.92 Y0, Y1) = 99.05/14.92 emptyset)))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 setminus( 99.05/14.92 Y0, Y1)))) => 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 in(Y2, 99.05/14.92 Y1)))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 setminus( 99.05/14.92 Y0, Y1)))) => 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y1))) => 99.05/14.92 (~( 99.05/14.92 in(Y2, 99.05/14.92 Y0)))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y0))) => 99.05/14.92 (~( 99.05/14.92 in(Y2, 99.05/14.92 setminus( 99.05/14.92 Y0, Y1)))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y1) => 99.05/14.92 (~( 99.05/14.92 in(Y2, 99.05/14.92 setminus( 99.05/14.92 Y0, Y1)))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 subset( 99.05/14.92 setminus( 99.05/14.92 Y0, Y1), 99.05/14.92 Y0))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (( 99.05/14.92 setminus( 99.05/14.92 Y0, Y1) = 99.05/14.92 emptyset) => 99.05/14.92 subset( 99.05/14.92 Y0, Y1)))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 symdiff( 99.05/14.92 Y0, Y1)) => 99.05/14.92 (!!(( 99.05/14.92 ^[Y3 : $o]: 99.05/14.92 (( 99.05/14.92 in(Y2, 99.05/14.92 Y0) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y1))) => 99.05/14.92 Y3)) => 99.05/14.92 (( 99.05/14.92 ( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y0))) => 99.05/14.92 ( 99.05/14.92 in(Y2, 99.05/14.92 Y1) => Y3)) => 99.05/14.92 Y3))))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y1))) => 99.05/14.92 in(Y2, 99.05/14.92 symdiff( 99.05/14.92 Y0, Y1))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y0))) => 99.05/14.92 (in(Y2, 99.05/14.92 Y1) => 99.05/14.92 in(Y2, 99.05/14.92 symdiff( 99.05/14.92 Y0, Y1))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (in(Y2, 99.05/14.92 Y1) => 99.05/14.92 (~( 99.05/14.92 in(Y2, 99.05/14.92 symdiff( 99.05/14.92 Y0, Y1))))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y0))) => 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y1))) => 99.05/14.92 (~( 99.05/14.92 in(Y2, 99.05/14.92 symdiff( 99.05/14.92 Y0, Y1))))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 in(Y1, 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 in(Y0, 99.05/14.92 setunion( 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 in(Y1, 99.05/14.92 setunion( 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (??(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 setunion( 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)))) & 99.05/14.92 (??(( 99.05/14.92 ^[Y3 : $i]: 99.05/14.92 (in(Y3, 99.05/14.92 setunion( 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)))) & 99.05/14.92 (setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)) = 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 setadjoin( 99.05/14.92 Y3, 99.05/14.92 emptyset)), 99.05/14.92 emptyset))))))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (??(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 setunion( 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)))) & 99.05/14.92 (??(( 99.05/14.92 ^[Y3 : $i]: 99.05/14.92 (in(Y3, 99.05/14.92 setunion( 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)))) & 99.05/14.92 (setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)) = 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 setadjoin( 99.05/14.92 Y3, 99.05/14.92 emptyset)), 99.05/14.92 emptyset))))))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (in(Y1, 99.05/14.92 Y0) => 99.05/14.92 subset( 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset), 99.05/14.92 Y0)))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (in(Y1, 99.05/14.92 Y0) => 99.05/14.92 in( 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset), 99.05/14.92 powerset( 99.05/14.92 Y0))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 in( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 emptyset), 99.05/14.92 powerset( 99.05/14.92 binunion( 99.05/14.92 Y0, Y1))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset))) => 99.05/14.92 (( 99.05/14.92 Y2 = Y1) | 99.05/14.92 (Y2 = Y0)))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (!!(( 99.05/14.92 ^[Y3 : $i]: 99.05/14.92 (in(Y3, 99.05/14.92 Y1) => 99.05/14.92 subset( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 setadjoin( 99.05/14.92 Y3, 99.05/14.92 emptyset)), 99.05/14.92 binunion( 99.05/14.92 Y0, Y1)))))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (!!(( 99.05/14.92 ^[Y3 : $i]: 99.05/14.92 (in(Y3, 99.05/14.92 Y1) => 99.05/14.92 in( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 setadjoin( 99.05/14.92 Y3, 99.05/14.92 emptyset)), 99.05/14.92 powerset( 99.05/14.92 binunion( 99.05/14.92 Y0, Y1))))))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (!!(( 99.05/14.92 ^[Y3 : $i]: 99.05/14.92 (in(Y3, 99.05/14.92 Y1) => 99.05/14.92 subset( 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 setadjoin( 99.05/14.92 Y3, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)), 99.05/14.92 powerset( 99.05/14.92 binunion( 99.05/14.92 Y0, Y1))))))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (!!(( 99.05/14.92 ^[Y3 : $i]: 99.05/14.92 (in(Y3, 99.05/14.92 Y1) => 99.05/14.92 in( 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 setadjoin( 99.05/14.92 Y3, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)), 99.05/14.92 powerset( 99.05/14.92 powerset( 99.05/14.92 binunion( 99.05/14.92 Y0, Y1)))))))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (!!(( 99.05/14.92 ^[Y3 : $i]: 99.05/14.92 (in(Y3, 99.05/14.92 Y1) => 99.05/14.92 in( 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 setadjoin( 99.05/14.92 Y3, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)), 99.05/14.92 powerset( 99.05/14.92 powerset( 99.05/14.92 binunion( 99.05/14.92 Y0, Y1)))))))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (!!(( 99.05/14.92 ^[Y3 : $i]: 99.05/14.92 (in(Y3, 99.05/14.92 Y1) => 99.05/14.92 in( 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 setadjoin( 99.05/14.92 Y3, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)), 99.05/14.92 dsetconstr( 99.05/14.92 powerset( 99.05/14.92 powerset( 99.05/14.92 binunion( 99.05/14.92 Y0, Y1))), 99.05/14.92 (^[Y4 : $i]: 99.05/14.92 (??(( 99.05/14.92 ^[Y5 : $i]: 99.05/14.92 (in(Y5, 99.05/14.92 Y0) & 99.05/14.92 (??(( 99.05/14.92 ^[Y6 : $i]: 99.05/14.92 (in(Y6, 99.05/14.92 Y1) & 99.05/14.92 (Y4 = 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y5, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y5, 99.05/14.92 setadjoin( 99.05/14.92 Y6, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)))))))))))))))))))))))))))) => 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 dsetconstr( 99.05/14.92 powerset( 99.05/14.92 powerset( 99.05/14.92 binunion( 99.05/14.92 Y0, Y1))), 99.05/14.92 (^[Y3 : $i]: 99.05/14.92 (??(( 99.05/14.92 ^[Y4 : $i]: 99.05/14.92 (in(Y4, 99.05/14.92 Y0) & 99.05/14.92 (??(( 99.05/14.92 ^[Y5 : $i]: 99.05/14.92 (in(Y5, 99.05/14.92 Y1) & 99.05/14.92 (Y3 = 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y4, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y4, 99.05/14.92 setadjoin( 99.05/14.92 Y5, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)))))))))))))) => 99.05/14.92 (??(( 99.05/14.92 ^[Y3 : $i]: 99.05/14.92 (( 99.05/14.92 ??(( 99.05/14.92 ^[Y4 : $i]: 99.05/14.92 (in(Y4, 99.05/14.92 Y1) & 99.05/14.92 (Y2 = 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y3, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y3, 99.05/14.92 setadjoin( 99.05/14.92 Y4, 99.05/14.92 emptyset)), 99.05/14.92 emptyset))))))) & 99.05/14.92 in(Y3, 99.05/14.92 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.05/14.92 inference('lazy_cnf_imply', [status(thm)], ['203'])). 99.05/14.92 tff('205', plain, 99.05/14.92 ~ ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: ((Y0 = Y1) => in(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (in(Y0, setadjoin(Y1, emptyset)) => 99.05/14.92 in(Y1, setadjoin(Y0, emptyset))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (in(Y2, setadjoin(Y0, setadjoin(Y1, emptyset))) => 99.05/14.92 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 in(Y0, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 99.05/14.92 (dsetconstr(Y0, Y1) != emptyset)))))))) => 99.05/14.92 ((!!((^[Y0 : $i > $o]: 99.05/14.92 (!!((^[Y1 : $i]: (in(Y1, emptyset) => Y0(Y1)))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.92 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 ((!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2))))))) => 99.05/14.92 (~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.92 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 ((??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2))))))) => 99.05/14.92 (~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2)))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $o]: (Y0 => in(emptyset, prop2set(Y0)))))) => 99.05/14.92 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 ((~((!!((^[Y2 : $i]: 99.05/14.92 (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.92 (??((^[Y2 : $i]: 99.05/14.92 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i > $o]: 99.05/14.92 ((??(Y0)) => 99.05/14.92 ((!!((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.92 (??((^[Y1 : $i]: 99.05/14.92 (Y0(Y1) & 99.05/14.92 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2)))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i > $o]: 99.05/14.92 ((??((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))) => 99.05/14.92 (??((^[Y1 : $i]: 99.05/14.92 (Y0(Y1) & 99.05/14.92 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((Y0 = Y1) => 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (!!((^[Y3 : $i]: 99.05/14.92 ((Y2 = Y3) => 99.05/14.92 (in(Y2, Y0) => 99.05/14.92 in(Y3, Y1)))))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((Y0 = Y1) => 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (!!((^[Y3 : $i]: 99.05/14.92 ((Y2 = Y3) => 99.05/14.92 (in(Y2, Y0) <=> 99.05/14.92 in(Y3, Y1)))))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i > $o]: 99.05/14.92 ((??((^[Y1 : $i]: 99.05/14.92 (Y0(Y1) & 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (Y0(Y1) => 99.05/14.92 (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i > $o]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 ((!!((^[Y2 : $i]: 99.05/14.92 (!!((^[Y3 : $i]: 99.05/14.92 ((Y2 = Y3) => 99.05/14.92 (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.92 ((??((^[Y2 : $i]: 99.05/14.92 (Y0(Y2) & 99.05/14.92 (!!((^[Y3 : $i]: 99.05/14.92 (Y0(Y3) => 99.05/14.92 (Y2 = Y3))))))))) <=> 99.05/14.92 (??((^[Y2 : $i]: 99.05/14.92 (Y1(Y2) & 99.05/14.92 (!!((^[Y3 : $i]: 99.05/14.92 (Y1(Y3) => 99.05/14.92 (Y2 = Y3))))))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((Y0 = Y1) => 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (!!((^[Y3 : $i]: 99.05/14.92 ((Y2 = Y3) => 99.05/14.92 (setadjoin(Y0, Y2) = 99.05/14.92 setadjoin(Y1, Y3)))))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((Y0 = Y1) => 99.05/14.92 (powerset(Y0) = powerset(Y1))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((Y0 = Y1) => 99.05/14.92 (setunion(Y0) = setunion(Y1))))))))) => 99.05/14.92 ((!!((^[Y0 : $i > $o]: 99.05/14.92 ((??((^[Y1 : $i]: 99.05/14.92 (Y0(Y1) & 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (Y0(Y1) => 99.05/14.92 (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i > $o]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 ((!!((^[Y2 : $i]: 99.05/14.92 (!!((^[Y3 : $i]: 99.05/14.92 ((Y2 = Y3) => 99.05/14.92 (Y0(Y2) <=> 99.05/14.92 Y1(Y3))))))))) => 99.05/14.92 ((??((^[Y2 : $i]: 99.05/14.92 (Y0(Y2) & 99.05/14.92 (!!((^[Y3 : $i]: 99.05/14.92 (Y0(Y3) => 99.05/14.92 (Y2 = Y3))))))))) => 99.05/14.92 ((??((^[Y2 : $i]: 99.05/14.92 (Y1(Y2) & 99.05/14.92 (!!((^[Y3 : $i]: 99.05/14.92 (Y1(Y3) => 99.05/14.92 (Y2 = Y3))))))))) => 99.05/14.92 (descr(Y0) = descr(Y1))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((Y0 = Y1) => 99.05/14.92 (!!((^[Y2 : $i > $o]: 99.05/14.92 (!!((^[Y3 : $i > $o]: 99.05/14.92 ((!!((^[Y4 : $i]: 99.05/14.92 (in(Y4, 99.05/14.92 Y0) => 99.05/14.92 (!!(( 99.05/14.92 ^[Y5 : $i]: 99.05/14.92 (in(Y5, 99.05/14.92 Y1) => 99.05/14.92 (( 99.05/14.92 Y4 = Y5) => 99.05/14.92 (Y2(Y4) <=> 99.05/14.92 Y3(Y5))))))))))) => 99.05/14.92 (dsetconstr( 99.05/14.92 Y0, Y2) = 99.05/14.92 dsetconstr( 99.05/14.92 Y1, Y3)))))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((!!((^[Y2 : $i]: 99.05/14.92 (in(Y2, Y0) => 99.05/14.92 in(Y2, Y1))))) => 99.05/14.92 subset(Y0, Y1)))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((Y0 = Y1) => subset(Y1, Y0)))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((Y0 = Y1) => 99.05/14.92 subset(Y0, Y1)))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((!!((^[Y2 : $i]: 99.05/14.92 (in(Y2, Y0) => 99.05/14.92 in(Y2, Y1))))) => 99.05/14.92 subset(Y0, Y1)))))))) => 99.05/14.92 ((!!(subset(emptyset))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (subset(Y0, Y1) => 99.05/14.92 (in(Y2, Y0) => 99.05/14.92 in(Y2, Y1)))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (subset(Y0, Y1) => 99.05/14.92 ((~(in(Y2, Y1))) => 99.05/14.92 (~(in(Y2, Y0)))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (in(Y2, Y0) => 99.05/14.92 ((~(in(Y2, Y1))) => 99.05/14.92 (~(subset( 99.05/14.92 Y0, Y1)))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((~(subset(Y0, Y1))) => 99.05/14.92 (Y0 != Y1)))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (in(Y2, Y0) => 99.05/14.92 ((~( 99.05/14.92 in(Y2, Y1))) => 99.05/14.92 (Y0 != Y1)))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (subset( 99.05/14.92 Y0, Y1) => 99.05/14.92 (subset( 99.05/14.92 Y1, Y2) => 99.05/14.92 subset( 99.05/14.92 Y0, Y2)))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 subset(Y1, 99.05/14.92 setadjoin(Y0, 99.05/14.92 Y1)))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 ( 99.05/14.92 subset( 99.05/14.92 Y0, Y2) => 99.05/14.92 subset( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, Y2)))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (subset(Y0, Y1) => 99.05/14.92 in(Y0, 99.05/14.92 powerset(Y1))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (subset(Y0, 99.05/14.92 Y1) => 99.05/14.92 (subset(Y1, 99.05/14.92 Y0) => 99.05/14.92 (Y0 = Y1))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (subset(Y0, 99.05/14.92 emptyset) => 99.05/14.92 (Y0 = emptyset))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (subset(Y1, 99.05/14.92 Y0) => 99.05/14.92 in(Y1, 99.05/14.92 powerset( 99.05/14.92 Y0))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (in(Y1, 99.05/14.92 powerset( 99.05/14.92 Y0)) => 99.05/14.92 subset( 99.05/14.92 Y1, Y0)))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 in(Y0, 99.05/14.92 powerset(Y0))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ( 99.05/14.92 subset( 99.05/14.92 Y0, Y1) => 99.05/14.92 subset( 99.05/14.92 powerset( 99.05/14.92 Y0), 99.05/14.92 powerset( 99.05/14.92 Y1))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 in( 99.05/14.92 dsetconstr( 99.05/14.92 Y0, Y1), 99.05/14.92 powerset( 99.05/14.92 Y0)))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 subset( 99.05/14.92 dsetconstr( 99.05/14.92 Y0, Y1), 99.05/14.92 Y0))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 in(Y2, 99.05/14.92 binunion( 99.05/14.92 Y0, Y1)))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 in(Y1, 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y1) => 99.05/14.92 in(Y2, 99.05/14.92 binunion( 99.05/14.92 Y0, Y1)))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y3 : $o]: 99.05/14.92 (in(Y2, 99.05/14.92 binunion( 99.05/14.92 Y0, Y1)) => 99.05/14.92 (( 99.05/14.92 in(Y2, 99.05/14.92 Y0) => Y3) => 99.05/14.92 (( 99.05/14.92 in(Y2, 99.05/14.92 Y1) => Y3) => 99.05/14.92 Y3))))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 binunion( 99.05/14.92 Y0, Y1)) => 99.05/14.92 (in(Y2, 99.05/14.92 Y1) | 99.05/14.92 in(Y2, 99.05/14.92 Y0)))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 subset( 99.05/14.92 Y0, 99.05/14.92 binunion( 99.05/14.92 Y0, Y1)))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 subset( 99.05/14.92 Y1, 99.05/14.92 binunion( 99.05/14.92 Y0, Y1)))))))) => 99.05/14.92 ((!!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (in(Y2, 99.05/14.92 Y1) => 99.05/14.92 in(Y2, 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1))))))))))))) => 99.05/14.92 ((!!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (subset( 99.05/14.92 Y2, Y0) => 99.05/14.92 (subset( 99.05/14.92 Y2, Y1) => 99.05/14.92 subset( 99.05/14.92 Y2, 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1))))))))))))) => 99.05/14.92 ((!!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1)) => 99.05/14.92 in(Y2, 99.05/14.92 Y0))))))))))) => 99.05/14.92 ((!!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 subset( 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1), 99.05/14.92 Y0))))))) => 99.05/14.92 (( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (subset( 99.05/14.92 Y0, Y1) => 99.05/14.92 (binintersect( 99.05/14.92 Y0, Y1) = 99.05/14.92 Y0)))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (( 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1) = 99.05/14.92 Y1) => 99.05/14.92 subset( 99.05/14.92 Y1, Y0)))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1)) => 99.05/14.92 in(Y2, 99.05/14.92 Y1))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (( 99.05/14.92 ~(( 99.05/14.92 ??(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) & 99.05/14.92 in(Y2, 99.05/14.92 Y1))))))) => 99.05/14.92 (binintersect( 99.05/14.92 Y0, Y1) = 99.05/14.92 emptyset)))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 subset( 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1), 99.05/14.92 Y1))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (subset( 99.05/14.92 Y1, Y0) => 99.05/14.92 (binintersect( 99.05/14.92 Y0, Y1) = 99.05/14.92 Y1)))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (( 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1) = 99.05/14.92 Y0) => 99.05/14.92 subset( 99.05/14.92 Y0, Y1)))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (binintersect( 99.05/14.92 Y0, 99.05/14.92 binunion( 99.05/14.92 Y1, Y2)) = 99.05/14.92 binunion( 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1), 99.05/14.92 binintersect( 99.05/14.92 Y0, Y2)))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y1))) => 99.05/14.92 in(Y2, 99.05/14.92 setminus( 99.05/14.92 Y0, Y1))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 setminus( 99.05/14.92 Y0, Y1)) => 99.05/14.92 in(Y2, 99.05/14.92 Y0))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 setminus( 99.05/14.92 Y0, Y1)) => 99.05/14.92 (~( 99.05/14.92 in(Y2, 99.05/14.92 Y1))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (subset( 99.05/14.92 Y0, Y1) => 99.05/14.92 (setminus( 99.05/14.92 Y0, Y1) = 99.05/14.92 emptyset)))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 setminus( 99.05/14.92 Y0, Y1)))) => 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 in(Y2, 99.05/14.92 Y1)))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 setminus( 99.05/14.92 Y0, Y1)))) => 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y1))) => 99.05/14.92 (~( 99.05/14.92 in(Y2, 99.05/14.92 Y0)))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y0))) => 99.05/14.92 (~( 99.05/14.92 in(Y2, 99.05/14.92 setminus( 99.05/14.92 Y0, Y1)))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y1) => 99.05/14.92 (~( 99.05/14.92 in(Y2, 99.05/14.92 setminus( 99.05/14.92 Y0, Y1)))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 subset( 99.05/14.92 setminus( 99.05/14.92 Y0, Y1), 99.05/14.92 Y0))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (( 99.05/14.92 setminus( 99.05/14.92 Y0, Y1) = 99.05/14.92 emptyset) => 99.05/14.92 subset( 99.05/14.92 Y0, Y1)))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 symdiff( 99.05/14.92 Y0, Y1)) => 99.05/14.92 (!!(( 99.05/14.92 ^[Y3 : $o]: 99.05/14.92 (( 99.05/14.92 in(Y2, 99.05/14.92 Y0) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y1))) => 99.05/14.92 Y3)) => 99.05/14.92 (( 99.05/14.92 ( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y0))) => 99.05/14.92 ( 99.05/14.92 in(Y2, 99.05/14.92 Y1) => Y3)) => 99.05/14.92 Y3))))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y1))) => 99.05/14.92 in(Y2, 99.05/14.92 symdiff( 99.05/14.92 Y0, Y1))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y0))) => 99.05/14.92 (in(Y2, 99.05/14.92 Y1) => 99.05/14.92 in(Y2, 99.05/14.92 symdiff( 99.05/14.92 Y0, Y1))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (in(Y2, 99.05/14.92 Y1) => 99.05/14.92 (~( 99.05/14.92 in(Y2, 99.05/14.92 symdiff( 99.05/14.92 Y0, Y1))))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y0))) => 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y1))) => 99.05/14.92 (~( 99.05/14.92 in(Y2, 99.05/14.92 symdiff( 99.05/14.92 Y0, Y1))))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 in(Y1, 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 in(Y0, 99.05/14.92 setunion( 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 in(Y1, 99.05/14.92 setunion( 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (??(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 setunion( 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)))) & 99.05/14.92 (??(( 99.05/14.92 ^[Y3 : $i]: 99.05/14.92 (in(Y3, 99.05/14.92 setunion( 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)))) & 99.05/14.92 (setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)) = 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 setadjoin( 99.05/14.92 Y3, 99.05/14.92 emptyset)), 99.05/14.92 emptyset))))))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (??(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 setunion( 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)))) & 99.05/14.92 (??(( 99.05/14.92 ^[Y3 : $i]: 99.05/14.92 (in(Y3, 99.05/14.92 setunion( 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)))) & 99.05/14.92 (setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)) = 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 setadjoin( 99.05/14.92 Y3, 99.05/14.92 emptyset)), 99.05/14.92 emptyset))))))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (in(Y1, 99.05/14.92 Y0) => 99.05/14.92 subset( 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset), 99.05/14.92 Y0)))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (in(Y1, 99.05/14.92 Y0) => 99.05/14.92 in( 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset), 99.05/14.92 powerset( 99.05/14.92 Y0))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 in( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 emptyset), 99.05/14.92 powerset( 99.05/14.92 binunion( 99.05/14.92 Y0, Y1))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset))) => 99.05/14.92 (( 99.05/14.92 Y2 = Y1) | 99.05/14.92 (Y2 = Y0)))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (!!(( 99.05/14.92 ^[Y3 : $i]: 99.05/14.92 (in(Y3, 99.05/14.92 Y1) => 99.05/14.92 subset( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 setadjoin( 99.05/14.92 Y3, 99.05/14.92 emptyset)), 99.05/14.92 binunion( 99.05/14.92 Y0, Y1)))))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (!!(( 99.05/14.92 ^[Y3 : $i]: 99.05/14.92 (in(Y3, 99.05/14.92 Y1) => 99.05/14.92 in( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 setadjoin( 99.05/14.92 Y3, 99.05/14.92 emptyset)), 99.05/14.92 powerset( 99.05/14.92 binunion( 99.05/14.92 Y0, Y1))))))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (!!(( 99.05/14.92 ^[Y3 : $i]: 99.05/14.92 (in(Y3, 99.05/14.92 Y1) => 99.05/14.92 subset( 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 setadjoin( 99.05/14.92 Y3, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)), 99.05/14.92 powerset( 99.05/14.92 binunion( 99.05/14.92 Y0, Y1))))))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (!!(( 99.05/14.92 ^[Y3 : $i]: 99.05/14.92 (in(Y3, 99.05/14.92 Y1) => 99.05/14.92 in( 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 setadjoin( 99.05/14.92 Y3, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)), 99.05/14.92 powerset( 99.05/14.92 powerset( 99.05/14.92 binunion( 99.05/14.92 Y0, Y1)))))))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (!!(( 99.05/14.92 ^[Y3 : $i]: 99.05/14.92 (in(Y3, 99.05/14.92 Y1) => 99.05/14.92 in( 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 setadjoin( 99.05/14.92 Y3, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)), 99.05/14.92 powerset( 99.05/14.92 powerset( 99.05/14.92 binunion( 99.05/14.92 Y0, Y1)))))))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (!!(( 99.05/14.92 ^[Y3 : $i]: 99.05/14.92 (in(Y3, 99.05/14.92 Y1) => 99.05/14.92 in( 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 setadjoin( 99.05/14.92 Y3, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)), 99.05/14.92 dsetconstr( 99.05/14.92 powerset( 99.05/14.92 powerset( 99.05/14.92 binunion( 99.05/14.92 Y0, Y1))), 99.05/14.92 (^[Y4 : $i]: 99.05/14.92 (??(( 99.05/14.92 ^[Y5 : $i]: 99.05/14.92 (in(Y5, 99.05/14.92 Y0) & 99.05/14.92 (??(( 99.05/14.92 ^[Y6 : $i]: 99.05/14.92 (in(Y6, 99.05/14.92 Y1) & 99.05/14.92 (Y4 = 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y5, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y5, 99.05/14.92 setadjoin( 99.05/14.92 Y6, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)))))))))))))))))))))))))))) => 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 dsetconstr( 99.05/14.92 powerset( 99.05/14.92 powerset( 99.05/14.92 binunion( 99.05/14.92 Y0, Y1))), 99.05/14.92 (^[Y3 : $i]: 99.05/14.92 (??(( 99.05/14.92 ^[Y4 : $i]: 99.05/14.92 (in(Y4, 99.05/14.92 Y0) & 99.05/14.92 (??(( 99.05/14.92 ^[Y5 : $i]: 99.05/14.92 (in(Y5, 99.05/14.92 Y1) & 99.05/14.92 (Y3 = 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y4, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y4, 99.05/14.92 setadjoin( 99.05/14.92 Y5, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)))))))))))))) => 99.05/14.92 (??(( 99.05/14.92 ^[Y3 : $i]: 99.05/14.92 (( 99.05/14.92 ??(( 99.05/14.92 ^[Y4 : $i]: 99.05/14.92 (in(Y4, 99.05/14.92 Y1) & 99.05/14.92 (Y2 = 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y3, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y3, 99.05/14.92 setadjoin( 99.05/14.92 Y4, 99.05/14.92 emptyset)), 99.05/14.92 emptyset))))))) & 99.05/14.92 in(Y3, 99.05/14.92 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.05/14.92 inference('lazy_cnf_imply', [status(thm)], ['204'])). 99.05/14.92 tff('206', plain, 99.05/14.92 ~ ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (in(Y0, setadjoin(Y1, emptyset)) => 99.05/14.92 in(Y1, setadjoin(Y0, emptyset))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (in(Y2, setadjoin(Y0, setadjoin(Y1, emptyset))) => 99.05/14.92 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 in(Y0, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 99.05/14.92 (dsetconstr(Y0, Y1) != emptyset)))))))) => 99.05/14.92 ((!!((^[Y0 : $i > $o]: 99.05/14.92 (!!((^[Y1 : $i]: (in(Y1, emptyset) => Y0(Y1)))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.92 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 ((!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2))))))) => 99.05/14.92 (~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.92 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 ((??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2))))))) => 99.05/14.92 (~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2)))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $o]: (Y0 => in(emptyset, prop2set(Y0)))))) => 99.05/14.92 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.92 (??((^[Y2 : $i]: 99.05/14.92 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i > $o]: 99.05/14.92 ((??(Y0)) => 99.05/14.92 ((!!((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.92 (??((^[Y1 : $i]: 99.05/14.92 (Y0(Y1) & 99.05/14.92 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2)))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i > $o]: 99.05/14.92 ((??((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))) => 99.05/14.92 (??((^[Y1 : $i]: 99.05/14.92 (Y0(Y1) & 99.05/14.92 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((Y0 = Y1) => 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (!!((^[Y3 : $i]: 99.05/14.92 ((Y2 = Y3) => 99.05/14.92 (in(Y2, Y0) => 99.05/14.92 in(Y3, Y1)))))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((Y0 = Y1) => 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (!!((^[Y3 : $i]: 99.05/14.92 ((Y2 = Y3) => 99.05/14.92 (in(Y2, Y0) <=> 99.05/14.92 in(Y3, Y1)))))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i > $o]: 99.05/14.92 ((??((^[Y1 : $i]: 99.05/14.92 (Y0(Y1) & 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (Y0(Y1) => 99.05/14.92 (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i > $o]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 ((!!((^[Y2 : $i]: 99.05/14.92 (!!((^[Y3 : $i]: 99.05/14.92 ((Y2 = Y3) => 99.05/14.92 (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.92 ((??((^[Y2 : $i]: 99.05/14.92 (Y0(Y2) & 99.05/14.92 (!!((^[Y3 : $i]: 99.05/14.92 (Y0(Y3) => (Y2 = Y3))))))))) <=> 99.05/14.92 (??((^[Y2 : $i]: 99.05/14.92 (Y1(Y2) & 99.05/14.92 (!!((^[Y3 : $i]: 99.05/14.92 (Y1(Y3) => (Y2 = Y3))))))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((Y0 = Y1) => 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (!!((^[Y3 : $i]: 99.05/14.92 ((Y2 = Y3) => 99.05/14.92 (setadjoin(Y0, Y2) = 99.05/14.92 setadjoin(Y1, Y3)))))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((Y0 = Y1) => 99.05/14.92 (powerset(Y0) = powerset(Y1))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((Y0 = Y1) => 99.05/14.92 (setunion(Y0) = setunion(Y1))))))))) => 99.05/14.92 ((!!((^[Y0 : $i > $o]: 99.05/14.92 ((??((^[Y1 : $i]: 99.05/14.92 (Y0(Y1) & 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (Y0(Y1) => 99.05/14.92 (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i > $o]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 ((!!((^[Y2 : $i]: 99.05/14.92 (!!((^[Y3 : $i]: 99.05/14.92 ((Y2 = Y3) => 99.05/14.92 (Y0(Y2) <=> 99.05/14.92 Y1(Y3))))))))) => 99.05/14.92 ((??((^[Y2 : $i]: 99.05/14.92 (Y0(Y2) & 99.05/14.92 (!!((^[Y3 : $i]: 99.05/14.92 (Y0(Y3) => 99.05/14.92 (Y2 = Y3))))))))) => 99.05/14.92 ((??((^[Y2 : $i]: 99.05/14.92 (Y1(Y2) & 99.05/14.92 (!!((^[Y3 : $i]: 99.05/14.92 (Y1(Y3) => 99.05/14.92 (Y2 = Y3))))))))) => 99.05/14.92 (descr(Y0) = descr(Y1))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((Y0 = Y1) => 99.05/14.92 (!!((^[Y2 : $i > $o]: 99.05/14.92 (!!((^[Y3 : $i > $o]: 99.05/14.92 ((!!((^[Y4 : $i]: 99.05/14.92 (in(Y4, 99.05/14.92 Y0) => 99.05/14.92 (!!(( 99.05/14.92 ^[Y5 : $i]: 99.05/14.92 (in(Y5, 99.05/14.92 Y1) => 99.05/14.92 (( 99.05/14.92 Y4 = Y5) => 99.05/14.92 (Y2(Y4) <=> 99.05/14.92 Y3(Y5))))))))))) => 99.05/14.92 (dsetconstr( 99.05/14.92 Y0, Y2) = 99.05/14.92 dsetconstr( 99.05/14.92 Y1, Y3)))))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((!!((^[Y2 : $i]: 99.05/14.92 (in(Y2, Y0) => 99.05/14.92 in(Y2, Y1))))) => 99.05/14.92 subset(Y0, Y1)))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((Y0 = Y1) => subset(Y1, Y0)))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((Y0 = Y1) => subset(Y0, Y1)))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((!!((^[Y2 : $i]: 99.05/14.92 (in(Y2, Y0) => 99.05/14.92 in(Y2, Y1))))) => 99.05/14.92 subset(Y0, Y1)))))))) => 99.05/14.92 ((!!(subset(emptyset))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (subset(Y0, Y1) => 99.05/14.92 (in(Y2, Y0) => 99.05/14.92 in(Y2, Y1)))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (subset(Y0, Y1) => 99.05/14.92 ((~(in(Y2, Y1))) => 99.05/14.92 (~(in(Y2, Y0)))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (in(Y2, Y0) => 99.05/14.92 ((~(in(Y2, Y1))) => 99.05/14.92 (~(subset(Y0, 99.05/14.92 Y1)))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((~(subset(Y0, Y1))) => 99.05/14.92 (Y0 != Y1)))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (in(Y2, Y0) => 99.05/14.92 ((~(in(Y2, 99.05/14.92 Y1))) => 99.05/14.92 (Y0 != Y1)))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (subset(Y0, 99.05/14.92 Y1) => 99.05/14.92 (subset( 99.05/14.92 Y1, Y2) => 99.05/14.92 subset( 99.05/14.92 Y0, Y2)))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 subset(Y1, 99.05/14.92 setadjoin(Y0, 99.05/14.92 Y1)))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (subset( 99.05/14.92 Y0, Y2) => 99.05/14.92 subset( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, Y2)))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (subset(Y0, Y1) => 99.05/14.92 in(Y0, 99.05/14.92 powerset(Y1))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (subset(Y0, Y1) => 99.05/14.92 (subset(Y1, 99.05/14.92 Y0) => 99.05/14.92 (Y0 = Y1))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (subset(Y0, emptyset) => 99.05/14.92 (Y0 = emptyset))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (subset(Y1, 99.05/14.92 Y0) => 99.05/14.92 in(Y1, 99.05/14.92 powerset( 99.05/14.92 Y0))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (in(Y1, 99.05/14.92 powerset( 99.05/14.92 Y0)) => 99.05/14.92 subset(Y1, 99.05/14.92 Y0)))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 in(Y0, 99.05/14.92 powerset(Y0))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (subset( 99.05/14.92 Y0, Y1) => 99.05/14.92 subset( 99.05/14.92 powerset( 99.05/14.92 Y0), 99.05/14.92 powerset( 99.05/14.92 Y1))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 in( 99.05/14.92 dsetconstr( 99.05/14.92 Y0, Y1), 99.05/14.92 powerset( 99.05/14.92 Y0)))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 subset( 99.05/14.92 dsetconstr( 99.05/14.92 Y0, Y1), 99.05/14.92 Y0))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 in(Y2, 99.05/14.92 binunion( 99.05/14.92 Y0, Y1)))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 in(Y1, 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y1) => 99.05/14.92 in(Y2, 99.05/14.92 binunion( 99.05/14.92 Y0, Y1)))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y3 : $o]: 99.05/14.92 (in(Y2, 99.05/14.92 binunion( 99.05/14.92 Y0, Y1)) => 99.05/14.92 (( 99.05/14.92 in(Y2, 99.05/14.92 Y0) => Y3) => 99.05/14.92 (( 99.05/14.92 in(Y2, 99.05/14.92 Y1) => Y3) => 99.05/14.92 Y3))))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 binunion( 99.05/14.92 Y0, Y1)) => 99.05/14.92 (in(Y2, 99.05/14.92 Y1) | 99.05/14.92 in(Y2, 99.05/14.92 Y0)))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 subset( 99.05/14.92 Y0, 99.05/14.92 binunion( 99.05/14.92 Y0, Y1)))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 subset( 99.05/14.92 Y1, 99.05/14.92 binunion( 99.05/14.92 Y0, Y1)))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (in(Y2, 99.05/14.92 Y1) => 99.05/14.92 in(Y2, 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1))))))))))))) => 99.05/14.92 ((!!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (subset( 99.05/14.92 Y2, Y0) => 99.05/14.92 (subset( 99.05/14.92 Y2, Y1) => 99.05/14.92 subset( 99.05/14.92 Y2, 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1))))))))))))) => 99.05/14.92 ((!!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1)) => 99.05/14.92 in(Y2, 99.05/14.92 Y0))))))))))) => 99.05/14.92 ((!!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 subset( 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1), 99.05/14.92 Y0))))))) => 99.05/14.92 ((!!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (subset( 99.05/14.92 Y0, Y1) => 99.05/14.92 (binintersect( 99.05/14.92 Y0, Y1) = 99.05/14.92 Y0)))))))) => 99.05/14.92 (( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (( 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1) = 99.05/14.92 Y1) => 99.05/14.92 subset( 99.05/14.92 Y1, Y0)))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1)) => 99.05/14.92 in(Y2, 99.05/14.92 Y1))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (( 99.05/14.92 ~(( 99.05/14.92 ??(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) & 99.05/14.92 in(Y2, 99.05/14.92 Y1))))))) => 99.05/14.92 (binintersect( 99.05/14.92 Y0, Y1) = 99.05/14.92 emptyset)))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 subset( 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1), 99.05/14.92 Y1))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (subset( 99.05/14.92 Y1, Y0) => 99.05/14.92 (binintersect( 99.05/14.92 Y0, Y1) = 99.05/14.92 Y1)))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (( 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1) = 99.05/14.92 Y0) => 99.05/14.92 subset( 99.05/14.92 Y0, Y1)))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (binintersect( 99.05/14.92 Y0, 99.05/14.92 binunion( 99.05/14.92 Y1, Y2)) = 99.05/14.92 binunion( 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1), 99.05/14.92 binintersect( 99.05/14.92 Y0, Y2)))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y1))) => 99.05/14.92 in(Y2, 99.05/14.92 setminus( 99.05/14.92 Y0, Y1))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 setminus( 99.05/14.92 Y0, Y1)) => 99.05/14.92 in(Y2, 99.05/14.92 Y0))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 setminus( 99.05/14.92 Y0, Y1)) => 99.05/14.92 (~( 99.05/14.92 in(Y2, 99.05/14.92 Y1))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (subset( 99.05/14.92 Y0, Y1) => 99.05/14.92 (setminus( 99.05/14.92 Y0, Y1) = 99.05/14.92 emptyset)))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 setminus( 99.05/14.92 Y0, Y1)))) => 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 in(Y2, 99.05/14.92 Y1)))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 setminus( 99.05/14.92 Y0, Y1)))) => 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y1))) => 99.05/14.92 (~( 99.05/14.92 in(Y2, 99.05/14.92 Y0)))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y0))) => 99.05/14.92 (~( 99.05/14.92 in(Y2, 99.05/14.92 setminus( 99.05/14.92 Y0, Y1)))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y1) => 99.05/14.92 (~( 99.05/14.92 in(Y2, 99.05/14.92 setminus( 99.05/14.92 Y0, Y1)))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 subset( 99.05/14.92 setminus( 99.05/14.92 Y0, Y1), 99.05/14.92 Y0))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (( 99.05/14.92 setminus( 99.05/14.92 Y0, Y1) = 99.05/14.92 emptyset) => 99.05/14.92 subset( 99.05/14.92 Y0, Y1)))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 symdiff( 99.05/14.92 Y0, Y1)) => 99.05/14.92 (!!(( 99.05/14.92 ^[Y3 : $o]: 99.05/14.92 (( 99.05/14.92 in(Y2, 99.05/14.92 Y0) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y1))) => 99.05/14.92 Y3)) => 99.05/14.92 (( 99.05/14.92 ( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y0))) => 99.05/14.92 ( 99.05/14.92 in(Y2, 99.05/14.92 Y1) => Y3)) => 99.05/14.92 Y3))))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y1))) => 99.05/14.92 in(Y2, 99.05/14.92 symdiff( 99.05/14.92 Y0, Y1))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y0))) => 99.05/14.92 (in(Y2, 99.05/14.92 Y1) => 99.05/14.92 in(Y2, 99.05/14.92 symdiff( 99.05/14.92 Y0, Y1))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (in(Y2, 99.05/14.92 Y1) => 99.05/14.92 (~( 99.05/14.92 in(Y2, 99.05/14.92 symdiff( 99.05/14.92 Y0, Y1))))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y0))) => 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y1))) => 99.05/14.92 (~( 99.05/14.92 in(Y2, 99.05/14.92 symdiff( 99.05/14.92 Y0, Y1))))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 in(Y1, 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 in(Y0, 99.05/14.92 setunion( 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 in(Y1, 99.05/14.92 setunion( 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (??(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 setunion( 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)))) & 99.05/14.92 (??(( 99.05/14.92 ^[Y3 : $i]: 99.05/14.92 (in(Y3, 99.05/14.92 setunion( 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)))) & 99.05/14.92 (setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)) = 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 setadjoin( 99.05/14.92 Y3, 99.05/14.92 emptyset)), 99.05/14.92 emptyset))))))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (??(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 setunion( 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)))) & 99.05/14.92 (??(( 99.05/14.92 ^[Y3 : $i]: 99.05/14.92 (in(Y3, 99.05/14.92 setunion( 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)))) & 99.05/14.92 (setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)) = 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 setadjoin( 99.05/14.92 Y3, 99.05/14.92 emptyset)), 99.05/14.92 emptyset))))))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (in(Y1, 99.05/14.92 Y0) => 99.05/14.92 subset( 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset), 99.05/14.92 Y0)))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (in(Y1, 99.05/14.92 Y0) => 99.05/14.92 in( 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset), 99.05/14.92 powerset( 99.05/14.92 Y0))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 in( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 emptyset), 99.05/14.92 powerset( 99.05/14.92 binunion( 99.05/14.92 Y0, Y1))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset))) => 99.05/14.92 (( 99.05/14.92 Y2 = Y1) | 99.05/14.92 (Y2 = Y0)))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (!!(( 99.05/14.92 ^[Y3 : $i]: 99.05/14.92 (in(Y3, 99.05/14.92 Y1) => 99.05/14.92 subset( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 setadjoin( 99.05/14.92 Y3, 99.05/14.92 emptyset)), 99.05/14.92 binunion( 99.05/14.92 Y0, Y1)))))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (!!(( 99.05/14.92 ^[Y3 : $i]: 99.05/14.92 (in(Y3, 99.05/14.92 Y1) => 99.05/14.92 in( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 setadjoin( 99.05/14.92 Y3, 99.05/14.92 emptyset)), 99.05/14.92 powerset( 99.05/14.92 binunion( 99.05/14.92 Y0, Y1))))))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (!!(( 99.05/14.92 ^[Y3 : $i]: 99.05/14.92 (in(Y3, 99.05/14.92 Y1) => 99.05/14.92 subset( 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 setadjoin( 99.05/14.92 Y3, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)), 99.05/14.92 powerset( 99.05/14.92 binunion( 99.05/14.92 Y0, Y1))))))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (!!(( 99.05/14.92 ^[Y3 : $i]: 99.05/14.92 (in(Y3, 99.05/14.92 Y1) => 99.05/14.92 in( 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 setadjoin( 99.05/14.92 Y3, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)), 99.05/14.92 powerset( 99.05/14.92 powerset( 99.05/14.92 binunion( 99.05/14.92 Y0, Y1)))))))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (!!(( 99.05/14.92 ^[Y3 : $i]: 99.05/14.92 (in(Y3, 99.05/14.92 Y1) => 99.05/14.92 in( 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 setadjoin( 99.05/14.92 Y3, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)), 99.05/14.92 powerset( 99.05/14.92 powerset( 99.05/14.92 binunion( 99.05/14.92 Y0, Y1)))))))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (!!(( 99.05/14.92 ^[Y3 : $i]: 99.05/14.92 (in(Y3, 99.05/14.92 Y1) => 99.05/14.92 in( 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 setadjoin( 99.05/14.92 Y3, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)), 99.05/14.92 dsetconstr( 99.05/14.92 powerset( 99.05/14.92 powerset( 99.05/14.92 binunion( 99.05/14.92 Y0, Y1))), 99.05/14.92 (^[Y4 : $i]: 99.05/14.92 (??(( 99.05/14.92 ^[Y5 : $i]: 99.05/14.92 (in(Y5, 99.05/14.92 Y0) & 99.05/14.92 (??(( 99.05/14.92 ^[Y6 : $i]: 99.05/14.92 (in(Y6, 99.05/14.92 Y1) & 99.05/14.92 (Y4 = 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y5, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y5, 99.05/14.92 setadjoin( 99.05/14.92 Y6, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)))))))))))))))))))))))))))) => 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 dsetconstr( 99.05/14.92 powerset( 99.05/14.92 powerset( 99.05/14.92 binunion( 99.05/14.92 Y0, Y1))), 99.05/14.92 (^[Y3 : $i]: 99.05/14.92 (??(( 99.05/14.92 ^[Y4 : $i]: 99.05/14.92 (in(Y4, 99.05/14.92 Y0) & 99.05/14.92 (??(( 99.05/14.92 ^[Y5 : $i]: 99.05/14.92 (in(Y5, 99.05/14.92 Y1) & 99.05/14.92 (Y3 = 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y4, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y4, 99.05/14.92 setadjoin( 99.05/14.92 Y5, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)))))))))))))) => 99.05/14.92 (??(( 99.05/14.92 ^[Y3 : $i]: 99.05/14.92 (( 99.05/14.92 ??(( 99.05/14.92 ^[Y4 : $i]: 99.05/14.92 (in(Y4, 99.05/14.92 Y1) & 99.05/14.92 (Y2 = 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y3, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y3, 99.05/14.92 setadjoin( 99.05/14.92 Y4, 99.05/14.92 emptyset)), 99.05/14.92 emptyset))))))) & 99.05/14.92 in(Y3, 99.05/14.92 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.05/14.92 inference('lazy_cnf_imply', [status(thm)], ['205'])). 99.05/14.92 tff('207', plain, 99.05/14.92 ~ ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (in(Y2, setadjoin(Y0, setadjoin(Y1, emptyset))) => 99.05/14.92 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 in(Y0, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 99.05/14.92 (dsetconstr(Y0, Y1) != emptyset)))))))) => 99.05/14.92 ((!!((^[Y0 : $i > $o]: 99.05/14.92 (!!((^[Y1 : $i]: (in(Y1, emptyset) => Y0(Y1)))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.92 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 ((!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2))))))) => 99.05/14.92 (~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.92 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 ((??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2))))))) => 99.05/14.92 (~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2)))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $o]: (Y0 => in(emptyset, prop2set(Y0)))))) => 99.05/14.92 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.92 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.92 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i > $o]: 99.05/14.92 ((??(Y0)) => 99.05/14.92 ((!!((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.92 (??((^[Y1 : $i]: 99.05/14.92 (Y0(Y1) & 99.05/14.92 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2)))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i > $o]: 99.05/14.92 ((??((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))) => 99.05/14.92 (??((^[Y1 : $i]: 99.05/14.92 (Y0(Y1) & 99.05/14.92 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((Y0 = Y1) => 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (!!((^[Y3 : $i]: 99.05/14.92 ((Y2 = Y3) => 99.05/14.92 (in(Y2, Y0) => in(Y3, Y1)))))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((Y0 = Y1) => 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (!!((^[Y3 : $i]: 99.05/14.92 ((Y2 = Y3) => 99.05/14.92 (in(Y2, Y0) <=> 99.05/14.92 in(Y3, Y1)))))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i > $o]: 99.05/14.92 ((??((^[Y1 : $i]: 99.05/14.92 (Y0(Y1) & 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (Y0(Y1) => 99.05/14.92 (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i > $o]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 ((!!((^[Y2 : $i]: 99.05/14.92 (!!((^[Y3 : $i]: 99.05/14.92 ((Y2 = Y3) => 99.05/14.92 (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.92 ((??((^[Y2 : $i]: 99.05/14.92 (Y0(Y2) & 99.05/14.92 (!!((^[Y3 : $i]: 99.05/14.92 (Y0(Y3) => (Y2 = Y3))))))))) <=> 99.05/14.92 (??((^[Y2 : $i]: 99.05/14.92 (Y1(Y2) & 99.05/14.92 (!!((^[Y3 : $i]: 99.05/14.92 (Y1(Y3) => (Y2 = Y3))))))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((Y0 = Y1) => 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (!!((^[Y3 : $i]: 99.05/14.92 ((Y2 = Y3) => 99.05/14.92 (setadjoin(Y0, Y2) = 99.05/14.92 setadjoin(Y1, Y3)))))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((Y0 = Y1) => 99.05/14.92 (powerset(Y0) = powerset(Y1))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((Y0 = Y1) => 99.05/14.92 (setunion(Y0) = setunion(Y1))))))))) => 99.05/14.92 ((!!((^[Y0 : $i > $o]: 99.05/14.92 ((??((^[Y1 : $i]: 99.05/14.92 (Y0(Y1) & 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (Y0(Y1) => 99.05/14.92 (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i > $o]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 ((!!((^[Y2 : $i]: 99.05/14.92 (!!((^[Y3 : $i]: 99.05/14.92 ((Y2 = Y3) => 99.05/14.92 (Y0(Y2) <=> 99.05/14.92 Y1(Y3))))))))) => 99.05/14.92 ((??((^[Y2 : $i]: 99.05/14.92 (Y0(Y2) & 99.05/14.92 (!!((^[Y3 : $i]: 99.05/14.92 (Y0(Y3) => 99.05/14.92 (Y2 = Y3))))))))) => 99.05/14.92 ((??((^[Y2 : $i]: 99.05/14.92 (Y1(Y2) & 99.05/14.92 (!!((^[Y3 : $i]: 99.05/14.92 (Y1(Y3) => 99.05/14.92 (Y2 = Y3))))))))) => 99.05/14.92 (descr(Y0) = descr(Y1))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((Y0 = Y1) => 99.05/14.92 (!!((^[Y2 : $i > $o]: 99.05/14.92 (!!((^[Y3 : $i > $o]: 99.05/14.92 ((!!((^[Y4 : $i]: 99.05/14.92 ( 99.05/14.92 in(Y4, 99.05/14.92 Y0) => 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y5 : $i]: 99.05/14.92 (in(Y5, 99.05/14.92 Y1) => 99.05/14.92 (( 99.05/14.92 Y4 = Y5) => 99.05/14.92 (Y2(Y4) <=> 99.05/14.92 Y3(Y5))))))))))) => 99.05/14.92 (dsetconstr(Y0, 99.05/14.92 Y2) = 99.05/14.92 dsetconstr(Y1, 99.05/14.92 Y3)))))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((!!((^[Y2 : $i]: 99.05/14.92 (in(Y2, Y0) => 99.05/14.92 in(Y2, Y1))))) => 99.05/14.92 subset(Y0, Y1)))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((Y0 = Y1) => subset(Y1, Y0)))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((Y0 = Y1) => subset(Y0, Y1)))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((!!((^[Y2 : $i]: 99.05/14.92 (in(Y2, Y0) => 99.05/14.92 in(Y2, Y1))))) => 99.05/14.92 subset(Y0, Y1)))))))) => 99.05/14.92 ((!!(subset(emptyset))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (subset(Y0, Y1) => 99.05/14.92 (in(Y2, Y0) => 99.05/14.92 in(Y2, Y1)))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (subset(Y0, Y1) => 99.05/14.92 ((~(in(Y2, Y1))) => 99.05/14.92 (~(in(Y2, Y0)))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (in(Y2, Y0) => 99.05/14.92 ((~(in(Y2, Y1))) => 99.05/14.92 (~(subset(Y0, 99.05/14.92 Y1)))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((~(subset(Y0, Y1))) => 99.05/14.92 (Y0 != Y1)))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (in(Y2, Y0) => 99.05/14.92 ((~(in(Y2, Y1))) => 99.05/14.92 (Y0 != Y1)))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (subset(Y0, 99.05/14.92 Y1) => 99.05/14.92 (subset(Y1, 99.05/14.92 Y2) => 99.05/14.92 subset(Y0, 99.05/14.92 Y2)))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 subset(Y1, 99.05/14.92 setadjoin(Y0, Y1)))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (subset( 99.05/14.92 Y0, Y2) => 99.05/14.92 subset( 99.05/14.92 Y0, 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subset( 99.05/14.92 powerset( 99.05/14.92 Y0), 99.05/14.92 powerset( 99.05/14.92 Y1))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 in( 99.05/14.92 dsetconstr( 99.05/14.92 Y0, Y1), 99.05/14.92 powerset( 99.05/14.92 Y0)))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 subset( 99.05/14.92 dsetconstr( 99.05/14.92 Y0, Y1), 99.05/14.92 Y0))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 in(Y2, 99.05/14.92 binunion( 99.05/14.92 Y0, Y1)))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 in(Y1, 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y1) => 99.05/14.92 in(Y2, 99.05/14.92 binunion( 99.05/14.92 Y0, Y1)))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y3 : $o]: 99.05/14.92 (in(Y2, 99.05/14.92 binunion( 99.05/14.92 Y0, Y1)) => 99.05/14.92 (( 99.05/14.92 in(Y2, 99.05/14.92 Y0) => Y3) => 99.05/14.92 (( 99.05/14.92 in(Y2, 99.05/14.92 Y1) => Y3) => 99.05/14.92 Y3))))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 binunion( 99.05/14.92 Y0, Y1)) => 99.05/14.92 (in(Y2, 99.05/14.92 Y1) | 99.05/14.92 in(Y2, 99.05/14.92 Y0)))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 subset( 99.05/14.92 Y0, 99.05/14.92 binunion( 99.05/14.92 Y0, Y1)))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 subset( 99.05/14.92 Y1, 99.05/14.92 binunion( 99.05/14.92 Y0, Y1)))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (in(Y2, 99.05/14.92 Y1) => 99.05/14.92 in(Y2, 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (subset( 99.05/14.92 Y2, Y0) => 99.05/14.92 (subset( 99.05/14.92 Y2, Y1) => 99.05/14.92 subset( 99.05/14.92 Y2, 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1))))))))))))) => 99.05/14.92 ((!!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1)) => 99.05/14.92 in(Y2, 99.05/14.92 Y0))))))))))) => 99.05/14.92 ((!!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 subset( 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1), 99.05/14.92 Y0))))))) => 99.05/14.92 ((!!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (subset( 99.05/14.92 Y0, Y1) => 99.05/14.92 (binintersect( 99.05/14.92 Y0, Y1) = 99.05/14.92 Y0)))))))) => 99.05/14.92 ((!!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (( 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1) = 99.05/14.92 Y1) => 99.05/14.92 subset( 99.05/14.92 Y1, Y0)))))))) => 99.05/14.92 (( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1)) => 99.05/14.92 in(Y2, 99.05/14.92 Y1))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (( 99.05/14.92 ~(( 99.05/14.92 ??(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) & 99.05/14.92 in(Y2, 99.05/14.92 Y1))))))) => 99.05/14.92 (binintersect( 99.05/14.92 Y0, Y1) = 99.05/14.92 emptyset)))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 subset( 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1), 99.05/14.92 Y1))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (subset( 99.05/14.92 Y1, Y0) => 99.05/14.92 (binintersect( 99.05/14.92 Y0, Y1) = 99.05/14.92 Y1)))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (( 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1) = 99.05/14.92 Y0) => 99.05/14.92 subset( 99.05/14.92 Y0, Y1)))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (binintersect( 99.05/14.92 Y0, 99.05/14.92 binunion( 99.05/14.92 Y1, Y2)) = 99.05/14.92 binunion( 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1), 99.05/14.92 binintersect( 99.05/14.92 Y0, Y2)))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y1))) => 99.05/14.92 in(Y2, 99.05/14.92 setminus( 99.05/14.92 Y0, Y1))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 setminus( 99.05/14.92 Y0, Y1)) => 99.05/14.92 in(Y2, 99.05/14.92 Y0))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 setminus( 99.05/14.92 Y0, Y1)) => 99.05/14.92 (~( 99.05/14.92 in(Y2, 99.05/14.92 Y1))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (subset( 99.05/14.92 Y0, Y1) => 99.05/14.92 (setminus( 99.05/14.92 Y0, Y1) = 99.05/14.92 emptyset)))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 setminus( 99.05/14.92 Y0, Y1)))) => 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 in(Y2, 99.05/14.92 Y1)))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 setminus( 99.05/14.92 Y0, Y1)))) => 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y1))) => 99.05/14.92 (~( 99.05/14.92 in(Y2, 99.05/14.92 Y0)))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y0))) => 99.05/14.92 (~( 99.05/14.92 in(Y2, 99.05/14.92 setminus( 99.05/14.92 Y0, Y1)))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y1) => 99.05/14.92 (~( 99.05/14.92 in(Y2, 99.05/14.92 setminus( 99.05/14.92 Y0, Y1)))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 subset( 99.05/14.92 setminus( 99.05/14.92 Y0, Y1), 99.05/14.92 Y0))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (( 99.05/14.92 setminus( 99.05/14.92 Y0, Y1) = 99.05/14.92 emptyset) => 99.05/14.92 subset( 99.05/14.92 Y0, Y1)))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 symdiff( 99.05/14.92 Y0, Y1)) => 99.05/14.92 (!!(( 99.05/14.92 ^[Y3 : $o]: 99.05/14.92 (( 99.05/14.92 in(Y2, 99.05/14.92 Y0) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y1))) => 99.05/14.92 Y3)) => 99.05/14.92 (( 99.05/14.92 ( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y0))) => 99.05/14.92 ( 99.05/14.92 in(Y2, 99.05/14.92 Y1) => Y3)) => 99.05/14.92 Y3))))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y1))) => 99.05/14.92 in(Y2, 99.05/14.92 symdiff( 99.05/14.92 Y0, Y1))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y0))) => 99.05/14.92 (in(Y2, 99.05/14.92 Y1) => 99.05/14.92 in(Y2, 99.05/14.92 symdiff( 99.05/14.92 Y0, Y1))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (in(Y2, 99.05/14.92 Y1) => 99.05/14.92 (~( 99.05/14.92 in(Y2, 99.05/14.92 symdiff( 99.05/14.92 Y0, Y1))))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y0))) => 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y1))) => 99.05/14.92 (~( 99.05/14.92 in(Y2, 99.05/14.92 symdiff( 99.05/14.92 Y0, Y1))))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 in(Y1, 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 in(Y0, 99.05/14.92 setunion( 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 in(Y1, 99.05/14.92 setunion( 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (??(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 setunion( 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)))) & 99.05/14.92 (??(( 99.05/14.92 ^[Y3 : $i]: 99.05/14.92 (in(Y3, 99.05/14.92 setunion( 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)))) & 99.05/14.92 (setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)) = 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 setadjoin( 99.05/14.92 Y3, 99.05/14.92 emptyset)), 99.05/14.92 emptyset))))))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (??(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 setunion( 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)))) & 99.05/14.92 (??(( 99.05/14.92 ^[Y3 : $i]: 99.05/14.92 (in(Y3, 99.05/14.92 setunion( 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)))) & 99.05/14.92 (setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)) = 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 setadjoin( 99.05/14.92 Y3, 99.05/14.92 emptyset)), 99.05/14.92 emptyset))))))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (in(Y1, 99.05/14.92 Y0) => 99.05/14.92 subset( 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset), 99.05/14.92 Y0)))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (in(Y1, 99.05/14.92 Y0) => 99.05/14.92 in( 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset), 99.05/14.92 powerset( 99.05/14.92 Y0))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 in( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 emptyset), 99.05/14.92 powerset( 99.05/14.92 binunion( 99.05/14.92 Y0, Y1))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset))) => 99.05/14.92 (( 99.05/14.92 Y2 = Y1) | 99.05/14.92 (Y2 = Y0)))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (!!(( 99.05/14.92 ^[Y3 : $i]: 99.05/14.92 (in(Y3, 99.05/14.92 Y1) => 99.05/14.92 subset( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 setadjoin( 99.05/14.92 Y3, 99.05/14.92 emptyset)), 99.05/14.92 binunion( 99.05/14.92 Y0, Y1)))))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (!!(( 99.05/14.92 ^[Y3 : $i]: 99.05/14.92 (in(Y3, 99.05/14.92 Y1) => 99.05/14.92 in( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 setadjoin( 99.05/14.92 Y3, 99.05/14.92 emptyset)), 99.05/14.92 powerset( 99.05/14.92 binunion( 99.05/14.92 Y0, Y1))))))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (!!(( 99.05/14.92 ^[Y3 : $i]: 99.05/14.92 (in(Y3, 99.05/14.92 Y1) => 99.05/14.92 subset( 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 setadjoin( 99.05/14.92 Y3, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)), 99.05/14.92 powerset( 99.05/14.92 binunion( 99.05/14.92 Y0, Y1))))))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (!!(( 99.05/14.92 ^[Y3 : $i]: 99.05/14.92 (in(Y3, 99.05/14.92 Y1) => 99.05/14.92 in( 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 setadjoin( 99.05/14.92 Y3, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)), 99.05/14.92 powerset( 99.05/14.92 powerset( 99.05/14.92 binunion( 99.05/14.92 Y0, Y1)))))))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (!!(( 99.05/14.92 ^[Y3 : $i]: 99.05/14.92 (in(Y3, 99.05/14.92 Y1) => 99.05/14.92 in( 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 setadjoin( 99.05/14.92 Y3, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)), 99.05/14.92 powerset( 99.05/14.92 powerset( 99.05/14.92 binunion( 99.05/14.92 Y0, Y1)))))))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (!!(( 99.05/14.92 ^[Y3 : $i]: 99.05/14.92 (in(Y3, 99.05/14.92 Y1) => 99.05/14.92 in( 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y2, 99.05/14.92 setadjoin( 99.05/14.92 Y3, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)), 99.05/14.92 dsetconstr( 99.05/14.92 powerset( 99.05/14.92 powerset( 99.05/14.92 binunion( 99.05/14.92 Y0, Y1))), 99.05/14.92 (^[Y4 : $i]: 99.05/14.92 (??(( 99.05/14.92 ^[Y5 : $i]: 99.05/14.92 (in(Y5, 99.05/14.92 Y0) & 99.05/14.92 (??(( 99.05/14.92 ^[Y6 : $i]: 99.05/14.92 (in(Y6, 99.05/14.92 Y1) & 99.05/14.92 (Y4 = 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y5, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y5, 99.05/14.92 setadjoin( 99.05/14.92 Y6, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)))))))))))))))))))))))))))) => 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 dsetconstr( 99.05/14.92 powerset( 99.05/14.92 powerset( 99.05/14.92 binunion( 99.05/14.92 Y0, Y1))), 99.05/14.92 (^[Y3 : $i]: 99.05/14.92 (??(( 99.05/14.92 ^[Y4 : $i]: 99.05/14.92 (in(Y4, 99.05/14.92 Y0) & 99.05/14.92 (??(( 99.05/14.92 ^[Y5 : $i]: 99.05/14.92 (in(Y5, 99.05/14.92 Y1) & 99.05/14.92 (Y3 = 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y4, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y4, 99.05/14.92 setadjoin( 99.05/14.92 Y5, 99.05/14.92 emptyset)), 99.05/14.92 emptyset)))))))))))))) => 99.05/14.92 (??(( 99.05/14.92 ^[Y3 : $i]: 99.05/14.92 (( 99.05/14.92 ??(( 99.05/14.92 ^[Y4 : $i]: 99.05/14.92 (in(Y4, 99.05/14.92 Y1) & 99.05/14.92 (Y2 = 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y3, 99.05/14.92 emptyset), 99.05/14.92 setadjoin( 99.05/14.92 setadjoin( 99.05/14.92 Y3, 99.05/14.92 setadjoin( 99.05/14.92 Y4, 99.05/14.92 emptyset)), 99.05/14.92 emptyset))))))) & 99.05/14.92 in(Y3, 99.05/14.92 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.05/14.92 inference('lazy_cnf_imply', [status(thm)], ['206'])). 99.05/14.92 tff('208', plain, 99.05/14.92 ~ ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 99.05/14.92 (dsetconstr(Y0, Y1) != emptyset)))))))) => 99.05/14.92 ((!!((^[Y0 : $i > $o]: 99.05/14.92 (!!((^[Y1 : $i]: (in(Y1, emptyset) => Y0(Y1)))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.92 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 ((!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2))))))) => 99.05/14.92 (~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.92 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 ((??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2))))))) => 99.05/14.92 (~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2)))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $o]: (Y0 => in(emptyset, prop2set(Y0)))))) => 99.05/14.92 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.92 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.92 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i > $o]: 99.05/14.92 ((??(Y0)) => 99.05/14.92 ((!!((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.92 (??((^[Y1 : $i]: 99.05/14.92 (Y0(Y1) & 99.05/14.92 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2)))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i > $o]: 99.05/14.92 ((??((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))) => 99.05/14.92 (??((^[Y1 : $i]: 99.05/14.92 (Y0(Y1) & 99.05/14.92 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((Y0 = Y1) => 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (!!((^[Y3 : $i]: 99.05/14.92 ((Y2 = Y3) => 99.05/14.92 (in(Y2, Y0) => in(Y3, Y1)))))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((Y0 = Y1) => 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (!!((^[Y3 : $i]: 99.05/14.92 ((Y2 = Y3) => 99.05/14.92 (in(Y2, Y0) <=> 99.05/14.92 in(Y3, Y1)))))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i > $o]: 99.05/14.92 ((??((^[Y1 : $i]: 99.05/14.92 (Y0(Y1) & 99.05/14.92 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i > $o]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 ((!!((^[Y2 : $i]: 99.05/14.92 (!!((^[Y3 : $i]: 99.05/14.92 ((Y2 = Y3) => 99.05/14.92 (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.92 ((??((^[Y2 : $i]: 99.05/14.92 (Y0(Y2) & 99.05/14.92 (!!((^[Y3 : $i]: 99.05/14.92 (Y0(Y3) => (Y2 = Y3))))))))) <=> 99.05/14.92 (??((^[Y2 : $i]: 99.05/14.92 (Y1(Y2) & 99.05/14.92 (!!((^[Y3 : $i]: 99.05/14.92 (Y1(Y3) => (Y2 = Y3))))))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((Y0 = Y1) => 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (!!((^[Y3 : $i]: 99.05/14.92 ((Y2 = Y3) => 99.05/14.92 (setadjoin(Y0, Y2) = 99.05/14.92 setadjoin(Y1, Y3)))))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((Y0 = Y1) => 99.05/14.92 (powerset(Y0) = powerset(Y1))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((Y0 = Y1) => 99.05/14.92 (setunion(Y0) = setunion(Y1))))))))) => 99.05/14.92 ((!!((^[Y0 : $i > $o]: 99.05/14.92 ((??((^[Y1 : $i]: 99.05/14.92 (Y0(Y1) & 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (Y0(Y1) => 99.05/14.92 (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i > $o]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 ((!!((^[Y2 : $i]: 99.05/14.92 (!!((^[Y3 : $i]: 99.05/14.92 ((Y2 = Y3) => 99.05/14.92 (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.92 ((??((^[Y2 : $i]: 99.05/14.92 (Y0(Y2) & 99.05/14.92 (!!((^[Y3 : $i]: 99.05/14.92 (Y0(Y3) => 99.05/14.92 (Y2 = Y3))))))))) => 99.05/14.92 ((??((^[Y2 : $i]: 99.05/14.92 (Y1(Y2) & 99.05/14.92 (!!((^[Y3 : $i]: 99.05/14.92 (Y1(Y3) => 99.05/14.92 (Y2 = Y3))))))))) => 99.05/14.92 (descr(Y0) = descr(Y1))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((Y0 = Y1) => 99.05/14.92 (!!((^[Y2 : $i > $o]: 99.05/14.92 (!!((^[Y3 : $i > $o]: 99.05/14.92 ((!!((^[Y4 : $i]: 99.05/14.92 (in(Y4, 99.05/14.92 Y0) => 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y5 : $i]: 99.05/14.92 (in(Y5, 99.05/14.92 Y1) => 99.05/14.92 (( 99.05/14.92 Y4 = Y5) => 99.05/14.92 (Y2(Y4) <=> 99.05/14.92 Y3(Y5))))))))))) => 99.05/14.92 (dsetconstr(Y0, 99.05/14.92 Y2) = 99.05/14.92 dsetconstr(Y1, 99.05/14.92 Y3)))))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((!!((^[Y2 : $i]: 99.05/14.92 (in(Y2, Y0) => 99.05/14.92 in(Y2, Y1))))) => 99.05/14.92 subset(Y0, Y1)))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((Y0 = Y1) => subset(Y1, Y0)))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((Y0 = Y1) => subset(Y0, Y1)))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((!!((^[Y2 : $i]: 99.05/14.92 (in(Y2, Y0) => 99.05/14.92 in(Y2, Y1))))) => 99.05/14.92 subset(Y0, Y1)))))))) => 99.05/14.92 ((!!(subset(emptyset))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (subset(Y0, Y1) => 99.05/14.92 (in(Y2, Y0) => 99.05/14.92 in(Y2, Y1)))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (subset(Y0, Y1) => 99.05/14.92 ((~(in(Y2, Y1))) => 99.05/14.92 (~(in(Y2, Y0)))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (in(Y2, Y0) => 99.05/14.92 ((~(in(Y2, Y1))) => 99.05/14.92 (~(subset(Y0, 99.05/14.92 Y1)))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ((~(subset(Y0, Y1))) => 99.05/14.92 (Y0 != Y1)))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (in(Y2, Y0) => 99.05/14.92 ((~(in(Y2, Y1))) => 99.05/14.92 (Y0 != Y1)))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (subset(Y0, 99.05/14.92 Y1) => 99.05/14.92 (subset(Y1, 99.05/14.92 Y2) => 99.05/14.92 subset(Y0, 99.05/14.92 Y2)))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 subset(Y1, 99.05/14.92 setadjoin(Y0, Y1)))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (!!((^[Y2 : $i]: 99.05/14.92 (subset(Y0, 99.05/14.92 Y2) => 99.05/14.92 subset(Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, Y2)))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (subset(Y0, Y1) => 99.05/14.92 in(Y0, 99.05/14.92 powerset(Y1))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (subset(Y0, Y1) => 99.05/14.92 (subset(Y1, Y0) => 99.05/14.92 (Y0 = Y1))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (subset(Y0, emptyset) => 99.05/14.92 (Y0 = emptyset))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (subset(Y1, Y0) => 99.05/14.92 in(Y1, 99.05/14.92 powerset(Y0))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (in(Y1, 99.05/14.92 powerset( 99.05/14.92 Y0)) => 99.05/14.92 subset(Y1, 99.05/14.92 Y0)))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 in(Y0, powerset(Y0))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (subset(Y0, 99.05/14.92 Y1) => 99.05/14.92 subset( 99.05/14.92 powerset( 99.05/14.92 Y0), 99.05/14.92 powerset( 99.05/14.92 Y1))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 in( 99.05/14.92 dsetconstr( 99.05/14.92 Y0, Y1), 99.05/14.92 powerset( 99.05/14.92 Y0)))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i > $o]: 99.05/14.92 subset( 99.05/14.92 dsetconstr( 99.05/14.92 Y0, Y1), 99.05/14.92 Y0))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 in(Y2, 99.05/14.92 binunion( 99.05/14.92 Y0, Y1)))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 in(Y1, 99.05/14.92 setadjoin( 99.05/14.92 Y0, 99.05/14.92 setadjoin( 99.05/14.92 Y1, 99.05/14.92 emptyset))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!((^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y1) => 99.05/14.92 in(Y2, 99.05/14.92 binunion( 99.05/14.92 Y0, Y1)))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y3 : $o]: 99.05/14.92 (in(Y2, 99.05/14.92 binunion( 99.05/14.92 Y0, Y1)) => 99.05/14.92 (( 99.05/14.92 in(Y2, 99.05/14.92 Y0) => Y3) => 99.05/14.92 (( 99.05/14.92 in(Y2, 99.05/14.92 Y1) => Y3) => 99.05/14.92 Y3))))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 binunion( 99.05/14.92 Y0, Y1)) => 99.05/14.92 (in(Y2, 99.05/14.92 Y1) | 99.05/14.92 in(Y2, 99.05/14.92 Y0)))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 subset( 99.05/14.92 Y0, 99.05/14.92 binunion( 99.05/14.92 Y0, Y1)))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 subset( 99.05/14.92 Y1, 99.05/14.92 binunion( 99.05/14.92 Y0, Y1)))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (in(Y2, 99.05/14.92 Y1) => 99.05/14.92 in(Y2, 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (subset( 99.05/14.92 Y2, Y0) => 99.05/14.92 (subset( 99.05/14.92 Y2, Y1) => 99.05/14.92 subset( 99.05/14.92 Y2, 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1))))))))))))) => 99.05/14.92 ((!!((^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1)) => 99.05/14.92 in(Y2, 99.05/14.92 Y0))))))))))) => 99.05/14.92 ((!!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 subset( 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1), 99.05/14.92 Y0))))))) => 99.05/14.92 ((!!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (subset( 99.05/14.92 Y0, Y1) => 99.05/14.92 (binintersect( 99.05/14.92 Y0, Y1) = 99.05/14.92 Y0)))))))) => 99.05/14.92 ((!!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (( 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1) = 99.05/14.92 Y1) => 99.05/14.92 subset( 99.05/14.92 Y1, Y0)))))))) => 99.05/14.92 ((!!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1)) => 99.05/14.92 in(Y2, 99.05/14.92 Y1))))))))))) => 99.05/14.92 (( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (( 99.05/14.92 ~(( 99.05/14.92 ??(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) & 99.05/14.92 in(Y2, 99.05/14.92 Y1))))))) => 99.05/14.92 (binintersect( 99.05/14.92 Y0, Y1) = 99.05/14.92 emptyset)))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 subset( 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1), 99.05/14.92 Y1))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (subset( 99.05/14.92 Y1, Y0) => 99.05/14.92 (binintersect( 99.05/14.92 Y0, Y1) = 99.05/14.92 Y1)))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (( 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1) = 99.05/14.92 Y0) => 99.05/14.92 subset( 99.05/14.92 Y0, Y1)))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (binintersect( 99.05/14.92 Y0, 99.05/14.92 binunion( 99.05/14.92 Y1, Y2)) = 99.05/14.92 binunion( 99.05/14.92 binintersect( 99.05/14.92 Y0, Y1), 99.05/14.92 binintersect( 99.05/14.92 Y0, Y2)))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y1))) => 99.05/14.92 in(Y2, 99.05/14.92 setminus( 99.05/14.92 Y0, Y1))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 setminus( 99.05/14.92 Y0, Y1)) => 99.05/14.92 in(Y2, 99.05/14.92 Y0))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 setminus( 99.05/14.92 Y0, Y1)) => 99.05/14.92 (~( 99.05/14.92 in(Y2, 99.05/14.92 Y1))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (subset( 99.05/14.92 Y0, Y1) => 99.05/14.92 (setminus( 99.05/14.92 Y0, Y1) = 99.05/14.92 emptyset)))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 setminus( 99.05/14.92 Y0, Y1)))) => 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 in(Y2, 99.05/14.92 Y1)))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 setminus( 99.05/14.92 Y0, Y1)))) => 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y1))) => 99.05/14.92 (~( 99.05/14.92 in(Y2, 99.05/14.92 Y0)))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y0))) => 99.05/14.92 (~( 99.05/14.92 in(Y2, 99.05/14.92 setminus( 99.05/14.92 Y0, Y1)))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y1) => 99.05/14.92 (~( 99.05/14.92 in(Y2, 99.05/14.92 setminus( 99.05/14.92 Y0, Y1)))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 subset( 99.05/14.92 setminus( 99.05/14.92 Y0, Y1), 99.05/14.92 Y0))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (( 99.05/14.92 setminus( 99.05/14.92 Y0, Y1) = 99.05/14.92 emptyset) => 99.05/14.92 subset( 99.05/14.92 Y0, Y1)))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 symdiff( 99.05/14.92 Y0, Y1)) => 99.05/14.92 (!!(( 99.05/14.92 ^[Y3 : $o]: 99.05/14.92 (( 99.05/14.92 in(Y2, 99.05/14.92 Y0) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y1))) => 99.05/14.92 Y3)) => 99.05/14.92 (( 99.05/14.92 ( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y0))) => 99.05/14.92 ( 99.05/14.92 in(Y2, 99.05/14.92 Y1) => Y3)) => 99.05/14.92 Y3))))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y1))) => 99.05/14.92 in(Y2, 99.05/14.92 symdiff( 99.05/14.92 Y0, Y1))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (( 99.05/14.92 ~( 99.05/14.92 in(Y2, 99.05/14.92 Y0))) => 99.05/14.92 (in(Y2, 99.05/14.92 Y1) => 99.05/14.92 in(Y2, 99.05/14.92 symdiff( 99.05/14.92 Y0, Y1))))))))))))) => 99.05/14.92 ( 99.05/14.92 ( 99.05/14.92 !!(( 99.05/14.92 ^[Y0 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y1 : $i]: 99.05/14.92 (!!(( 99.05/14.92 ^[Y2 : $i]: 99.05/14.92 (in(Y2, 99.05/14.92 Y0) => 99.05/14.92 (in(Y2, 99.05/14.92 Y1) => 99.05/14.93 (~( 99.05/14.93 in(Y2, 99.05/14.93 symdiff( 99.05/14.93 Y0, Y1))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 Y0))) => 99.05/14.93 (( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 Y1))) => 99.05/14.93 (~( 99.05/14.93 in(Y2, 99.05/14.93 symdiff( 99.05/14.93 Y0, Y1))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 in(Y1, 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 in(Y0, 99.05/14.93 setunion( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 in(Y1, 99.05/14.93 setunion( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (??(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 setunion( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)))) & 99.05/14.93 (??(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (in(Y3, 99.05/14.93 setunion( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)))) & 99.05/14.93 (setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)) = 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset)), 99.05/14.93 emptyset))))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (??(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 setunion( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)))) & 99.05/14.93 (??(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (in(Y3, 99.05/14.93 setunion( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)))) & 99.05/14.93 (setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)) = 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset)), 99.05/14.93 emptyset))))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (in(Y1, 99.05/14.93 Y0) => 99.05/14.93 subset( 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset), 99.05/14.93 Y0)))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (in(Y1, 99.05/14.93 Y0) => 99.05/14.93 in( 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset), 99.05/14.93 powerset( 99.05/14.93 Y0))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 in( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 emptyset), 99.05/14.93 powerset( 99.05/14.93 binunion( 99.05/14.93 Y0, Y1))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset))) => 99.05/14.93 (( 99.05/14.93 Y2 = Y1) | 99.05/14.93 (Y2 = Y0)))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (!!(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (in(Y3, 99.05/14.93 Y1) => 99.05/14.93 subset( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset)), 99.05/14.93 binunion( 99.05/14.93 Y0, Y1)))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (!!(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (in(Y3, 99.05/14.93 Y1) => 99.05/14.93 in( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset)), 99.05/14.93 powerset( 99.05/14.93 binunion( 99.05/14.93 Y0, Y1))))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (!!(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (in(Y3, 99.05/14.93 Y1) => 99.05/14.93 subset( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)), 99.05/14.93 powerset( 99.05/14.93 binunion( 99.05/14.93 Y0, Y1))))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (!!(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (in(Y3, 99.05/14.93 Y1) => 99.05/14.93 in( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)), 99.05/14.93 powerset( 99.05/14.93 powerset( 99.05/14.93 binunion( 99.05/14.93 Y0, Y1)))))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (!!(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (in(Y3, 99.05/14.93 Y1) => 99.05/14.93 in( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)), 99.05/14.93 powerset( 99.05/14.93 powerset( 99.05/14.93 binunion( 99.05/14.93 Y0, Y1)))))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (!!(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (in(Y3, 99.05/14.93 Y1) => 99.05/14.93 in( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)), 99.05/14.93 dsetconstr( 99.05/14.93 powerset( 99.05/14.93 powerset( 99.05/14.93 binunion( 99.05/14.93 Y0, Y1))), 99.05/14.93 (^[Y4 : $i]: 99.05/14.93 (??(( 99.05/14.93 ^[Y5 : $i]: 99.05/14.93 (in(Y5, 99.05/14.93 Y0) & 99.05/14.93 (??(( 99.05/14.93 ^[Y6 : $i]: 99.05/14.93 (in(Y6, 99.05/14.93 Y1) & 99.05/14.93 (Y4 = 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y5, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y5, 99.05/14.93 setadjoin( 99.05/14.93 Y6, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)))))))))))))))))))))))))))) => 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 dsetconstr( 99.05/14.93 powerset( 99.05/14.93 powerset( 99.05/14.93 binunion( 99.05/14.93 Y0, Y1))), 99.05/14.93 (^[Y3 : $i]: 99.05/14.93 (??(( 99.05/14.93 ^[Y4 : $i]: 99.05/14.93 (in(Y4, 99.05/14.93 Y0) & 99.05/14.93 (??(( 99.05/14.93 ^[Y5 : $i]: 99.05/14.93 (in(Y5, 99.05/14.93 Y1) & 99.05/14.93 (Y3 = 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y4, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y4, 99.05/14.93 setadjoin( 99.05/14.93 Y5, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)))))))))))))) => 99.05/14.93 (??(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (( 99.05/14.93 ??(( 99.05/14.93 ^[Y4 : $i]: 99.05/14.93 (in(Y4, 99.05/14.93 Y1) & 99.05/14.93 (Y2 = 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 setadjoin( 99.05/14.93 Y4, 99.05/14.93 emptyset)), 99.05/14.93 emptyset))))))) & 99.05/14.93 in(Y3, 99.05/14.93 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.05/14.93 inference('lazy_cnf_imply', [status(thm)], ['207'])). 99.05/14.93 tff('209', plain, 99.05/14.93 ~ ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 99.05/14.93 (dsetconstr(Y0, Y1) != emptyset)))))))) => 99.05/14.93 ((!!((^[Y0 : $i > $o]: 99.05/14.93 (!!((^[Y1 : $i]: (in(Y1, emptyset) => Y0(Y1)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.93 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 ((!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2))))))) => 99.05/14.93 (~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.93 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 ((??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2))))))) => 99.05/14.93 (~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $o]: (Y0 => in(emptyset, prop2set(Y0)))))) => 99.05/14.93 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.93 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.93 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i > $o]: 99.05/14.93 ((??(Y0)) => 99.05/14.93 ((!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.93 (??((^[Y1 : $i]: 99.05/14.93 (Y0(Y1) & 99.05/14.93 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i > $o]: 99.05/14.93 ((??((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))) => 99.05/14.93 (??((^[Y1 : $i]: 99.05/14.93 (Y0(Y1) & 99.05/14.93 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((Y0 = Y1) => 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 ((Y2 = Y3) => 99.05/14.93 (in(Y2, Y0) => in(Y3, Y1)))))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((Y0 = Y1) => 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 ((Y2 = Y3) => 99.05/14.93 (in(Y2, Y0) <=> in(Y3, Y1)))))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i > $o]: 99.05/14.93 ((??((^[Y1 : $i]: 99.05/14.93 (Y0(Y1) & 99.05/14.93 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i > $o]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 ((!!((^[Y2 : $i]: 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 ((Y2 = Y3) => 99.05/14.93 (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.93 ((??((^[Y2 : $i]: 99.05/14.93 (Y0(Y2) & 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 (Y0(Y3) => (Y2 = Y3))))))))) <=> 99.05/14.93 (??((^[Y2 : $i]: 99.05/14.93 (Y1(Y2) & 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 (Y1(Y3) => (Y2 = Y3))))))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((Y0 = Y1) => 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 ((Y2 = Y3) => 99.05/14.93 (setadjoin(Y0, Y2) = 99.05/14.93 setadjoin(Y1, Y3)))))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((Y0 = Y1) => 99.05/14.93 (powerset(Y0) = powerset(Y1))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((Y0 = Y1) => 99.05/14.93 (setunion(Y0) = setunion(Y1))))))))) => 99.05/14.93 ((!!((^[Y0 : $i > $o]: 99.05/14.93 ((??((^[Y1 : $i]: 99.05/14.93 (Y0(Y1) & 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (Y0(Y1) => 99.05/14.93 (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i > $o]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 ((!!((^[Y2 : $i]: 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 ((Y2 = Y3) => 99.05/14.93 (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.93 ((??((^[Y2 : $i]: 99.05/14.93 (Y0(Y2) & 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 (Y0(Y3) => 99.05/14.93 (Y2 = Y3))))))))) => 99.05/14.93 ((??((^[Y2 : $i]: 99.05/14.93 (Y1(Y2) & 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 (Y1(Y3) => 99.05/14.93 (Y2 = Y3))))))))) => 99.05/14.93 (descr(Y0) = descr(Y1))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((Y0 = Y1) => 99.05/14.93 (!!((^[Y2 : $i > $o]: 99.05/14.93 (!!((^[Y3 : $i > $o]: 99.05/14.93 ((!!((^[Y4 : $i]: 99.05/14.93 (in(Y4, Y0) => 99.05/14.93 (!!(( 99.05/14.93 ^[Y5 : $i]: 99.05/14.93 (in(Y5, 99.05/14.93 Y1) => 99.05/14.93 (( 99.05/14.93 Y4 = Y5) => 99.05/14.93 (Y2(Y4) <=> 99.05/14.93 Y3(Y5))))))))))) => 99.05/14.93 (dsetconstr(Y0, 99.05/14.93 Y2) = 99.05/14.93 dsetconstr(Y1, 99.05/14.93 Y3)))))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((!!((^[Y2 : $i]: 99.05/14.93 (in(Y2, Y0) => in(Y2, Y1))))) => 99.05/14.93 subset(Y0, Y1)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((Y0 = Y1) => subset(Y1, Y0)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((Y0 = Y1) => subset(Y0, Y1)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((!!((^[Y2 : $i]: 99.05/14.93 (in(Y2, Y0) => 99.05/14.93 in(Y2, Y1))))) => 99.05/14.93 subset(Y0, Y1)))))))) => 99.05/14.93 ((!!(subset(emptyset))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (subset(Y0, Y1) => 99.05/14.93 (in(Y2, Y0) => 99.05/14.93 in(Y2, Y1)))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (subset(Y0, Y1) => 99.05/14.93 ((~(in(Y2, Y1))) => 99.05/14.93 (~(in(Y2, Y0)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (in(Y2, Y0) => 99.05/14.93 ((~(in(Y2, Y1))) => 99.05/14.93 (~(subset(Y0, Y1)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((~(subset(Y0, Y1))) => 99.05/14.93 (Y0 != Y1)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (in(Y2, Y0) => 99.05/14.93 ((~(in(Y2, Y1))) => 99.05/14.93 (Y0 != Y1)))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (subset(Y0, Y1) => 99.05/14.93 (subset(Y1, 99.05/14.93 Y2) => 99.05/14.93 subset(Y0, 99.05/14.93 Y2)))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 subset(Y1, 99.05/14.93 setadjoin(Y0, Y1)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (subset(Y0, 99.05/14.93 Y2) => 99.05/14.93 subset(Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, Y2)))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (subset(Y0, Y1) => 99.05/14.93 in(Y0, 99.05/14.93 powerset(Y1))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (subset(Y0, Y1) => 99.05/14.93 (subset(Y1, Y0) => 99.05/14.93 (Y0 = Y1))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (subset(Y0, emptyset) => 99.05/14.93 (Y0 = emptyset))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (subset(Y1, Y0) => 99.05/14.93 in(Y1, 99.05/14.93 powerset(Y0))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (in(Y1, 99.05/14.93 powerset(Y0)) => 99.05/14.93 subset(Y1, Y0)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 in(Y0, powerset(Y0))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (subset(Y0, 99.05/14.93 Y1) => 99.05/14.93 subset( 99.05/14.93 powerset( 99.05/14.93 Y0), 99.05/14.93 powerset( 99.05/14.93 Y1))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 in( 99.05/14.93 dsetconstr( 99.05/14.93 Y0, Y1), 99.05/14.93 powerset( 99.05/14.93 Y0)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 subset( 99.05/14.93 dsetconstr( 99.05/14.93 Y0, Y1), 99.05/14.93 Y0))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 in(Y2, 99.05/14.93 binunion( 99.05/14.93 Y0, Y1)))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 in(Y1, 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y1) => 99.05/14.93 in(Y2, 99.05/14.93 binunion( 99.05/14.93 Y0, Y1)))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y3 : $o]: 99.05/14.93 (in(Y2, 99.05/14.93 binunion( 99.05/14.93 Y0, Y1)) => 99.05/14.93 (( 99.05/14.93 in(Y2, 99.05/14.93 Y0) => Y3) => 99.05/14.93 (( 99.05/14.93 in(Y2, 99.05/14.93 Y1) => Y3) => 99.05/14.93 Y3))))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 binunion( 99.05/14.93 Y0, Y1)) => 99.05/14.93 (in(Y2, 99.05/14.93 Y1) | 99.05/14.93 in(Y2, 99.05/14.93 Y0)))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 subset( 99.05/14.93 Y0, 99.05/14.93 binunion( 99.05/14.93 Y0, Y1)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 subset( 99.05/14.93 Y1, 99.05/14.93 binunion( 99.05/14.93 Y0, Y1)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (in(Y2, 99.05/14.93 Y1) => 99.05/14.93 in(Y2, 99.05/14.93 binintersect( 99.05/14.93 Y0, Y1))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (subset( 99.05/14.93 Y2, Y0) => 99.05/14.93 (subset( 99.05/14.93 Y2, Y1) => 99.05/14.93 subset( 99.05/14.93 Y2, 99.05/14.93 binintersect( 99.05/14.93 Y0, Y1))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 binintersect( 99.05/14.93 Y0, Y1)) => 99.05/14.93 in(Y2, 99.05/14.93 Y0))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 subset( 99.05/14.93 binintersect( 99.05/14.93 Y0, Y1), 99.05/14.93 Y0))))))) => 99.05/14.93 ((!!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (subset( 99.05/14.93 Y0, Y1) => 99.05/14.93 (binintersect( 99.05/14.93 Y0, Y1) = 99.05/14.93 Y0)))))))) => 99.05/14.93 ((!!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (( 99.05/14.93 binintersect( 99.05/14.93 Y0, Y1) = 99.05/14.93 Y1) => 99.05/14.93 subset( 99.05/14.93 Y1, Y0)))))))) => 99.05/14.93 ((!!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 binintersect( 99.05/14.93 Y0, Y1)) => 99.05/14.93 in(Y2, 99.05/14.93 Y1))))))))))) => 99.05/14.93 ((!!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (( 99.05/14.93 ~(( 99.05/14.93 ??(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) & 99.05/14.93 in(Y2, 99.05/14.93 Y1))))))) => 99.05/14.93 (binintersect( 99.05/14.93 Y0, Y1) = 99.05/14.93 emptyset)))))))) => 99.05/14.93 (( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 subset( 99.05/14.93 binintersect( 99.05/14.93 Y0, Y1), 99.05/14.93 Y1))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (subset( 99.05/14.93 Y1, Y0) => 99.05/14.93 (binintersect( 99.05/14.93 Y0, Y1) = 99.05/14.93 Y1)))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (( 99.05/14.93 binintersect( 99.05/14.93 Y0, Y1) = 99.05/14.93 Y0) => 99.05/14.93 subset( 99.05/14.93 Y0, Y1)))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (binintersect( 99.05/14.93 Y0, 99.05/14.93 binunion( 99.05/14.93 Y1, Y2)) = 99.05/14.93 binunion( 99.05/14.93 binintersect( 99.05/14.93 Y0, Y1), 99.05/14.93 binintersect( 99.05/14.93 Y0, Y2)))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 Y1))) => 99.05/14.93 in(Y2, 99.05/14.93 setminus( 99.05/14.93 Y0, Y1))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 setminus( 99.05/14.93 Y0, Y1)) => 99.05/14.93 in(Y2, 99.05/14.93 Y0))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 setminus( 99.05/14.93 Y0, Y1)) => 99.05/14.93 (~( 99.05/14.93 in(Y2, 99.05/14.93 Y1))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (subset( 99.05/14.93 Y0, Y1) => 99.05/14.93 (setminus( 99.05/14.93 Y0, Y1) = 99.05/14.93 emptyset)))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 setminus( 99.05/14.93 Y0, Y1)))) => 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 in(Y2, 99.05/14.93 Y1)))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 setminus( 99.05/14.93 Y0, Y1)))) => 99.05/14.93 (( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 Y1))) => 99.05/14.93 (~( 99.05/14.93 in(Y2, 99.05/14.93 Y0)))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 Y0))) => 99.05/14.93 (~( 99.05/14.93 in(Y2, 99.05/14.93 setminus( 99.05/14.93 Y0, Y1)))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y1) => 99.05/14.93 (~( 99.05/14.93 in(Y2, 99.05/14.93 setminus( 99.05/14.93 Y0, Y1)))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 subset( 99.05/14.93 setminus( 99.05/14.93 Y0, Y1), 99.05/14.93 Y0))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (( 99.05/14.93 setminus( 99.05/14.93 Y0, Y1) = 99.05/14.93 emptyset) => 99.05/14.93 subset( 99.05/14.93 Y0, Y1)))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 symdiff( 99.05/14.93 Y0, Y1)) => 99.05/14.93 (!!(( 99.05/14.93 ^[Y3 : $o]: 99.05/14.93 (( 99.05/14.93 in(Y2, 99.05/14.93 Y0) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 Y1))) => 99.05/14.93 Y3)) => 99.05/14.93 (( 99.05/14.93 ( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 Y0))) => 99.05/14.93 ( 99.05/14.93 in(Y2, 99.05/14.93 Y1) => Y3)) => 99.05/14.93 Y3))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 Y1))) => 99.05/14.93 in(Y2, 99.05/14.93 symdiff( 99.05/14.93 Y0, Y1))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 Y0))) => 99.05/14.93 (in(Y2, 99.05/14.93 Y1) => 99.05/14.93 in(Y2, 99.05/14.93 symdiff( 99.05/14.93 Y0, Y1))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (in(Y2, 99.05/14.93 Y1) => 99.05/14.93 (~( 99.05/14.93 in(Y2, 99.05/14.93 symdiff( 99.05/14.93 Y0, Y1))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 Y0))) => 99.05/14.93 (( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 Y1))) => 99.05/14.93 (~( 99.05/14.93 in(Y2, 99.05/14.93 symdiff( 99.05/14.93 Y0, Y1))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 in(Y1, 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 in(Y0, 99.05/14.93 setunion( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 in(Y1, 99.05/14.93 setunion( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (??(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 setunion( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)))) & 99.05/14.93 (??(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (in(Y3, 99.05/14.93 setunion( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)))) & 99.05/14.93 (setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)) = 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset)), 99.05/14.93 emptyset))))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (??(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 setunion( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)))) & 99.05/14.93 (??(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (in(Y3, 99.05/14.93 setunion( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)))) & 99.05/14.93 (setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)) = 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset)), 99.05/14.93 emptyset))))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (in(Y1, 99.05/14.93 Y0) => 99.05/14.93 subset( 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset), 99.05/14.93 Y0)))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (in(Y1, 99.05/14.93 Y0) => 99.05/14.93 in( 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset), 99.05/14.93 powerset( 99.05/14.93 Y0))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 in( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 emptyset), 99.05/14.93 powerset( 99.05/14.93 binunion( 99.05/14.93 Y0, Y1))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset))) => 99.05/14.93 (( 99.05/14.93 Y2 = Y1) | 99.05/14.93 (Y2 = Y0)))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (!!(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (in(Y3, 99.05/14.93 Y1) => 99.05/14.93 subset( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset)), 99.05/14.93 binunion( 99.05/14.93 Y0, Y1)))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (!!(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (in(Y3, 99.05/14.93 Y1) => 99.05/14.93 in( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset)), 99.05/14.93 powerset( 99.05/14.93 binunion( 99.05/14.93 Y0, Y1))))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (!!(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (in(Y3, 99.05/14.93 Y1) => 99.05/14.93 subset( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)), 99.05/14.93 powerset( 99.05/14.93 binunion( 99.05/14.93 Y0, Y1))))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (!!(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (in(Y3, 99.05/14.93 Y1) => 99.05/14.93 in( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)), 99.05/14.93 powerset( 99.05/14.93 powerset( 99.05/14.93 binunion( 99.05/14.93 Y0, Y1)))))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (!!(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (in(Y3, 99.05/14.93 Y1) => 99.05/14.93 in( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)), 99.05/14.93 powerset( 99.05/14.93 powerset( 99.05/14.93 binunion( 99.05/14.93 Y0, Y1)))))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (!!(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (in(Y3, 99.05/14.93 Y1) => 99.05/14.93 in( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)), 99.05/14.93 dsetconstr( 99.05/14.93 powerset( 99.05/14.93 powerset( 99.05/14.93 binunion( 99.05/14.93 Y0, Y1))), 99.05/14.93 (^[Y4 : $i]: 99.05/14.93 (??(( 99.05/14.93 ^[Y5 : $i]: 99.05/14.93 (in(Y5, 99.05/14.93 Y0) & 99.05/14.93 (??(( 99.05/14.93 ^[Y6 : $i]: 99.05/14.93 (in(Y6, 99.05/14.93 Y1) & 99.05/14.93 (Y4 = 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y5, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y5, 99.05/14.93 setadjoin( 99.05/14.93 Y6, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)))))))))))))))))))))))))))) => 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 dsetconstr( 99.05/14.93 powerset( 99.05/14.93 powerset( 99.05/14.93 binunion( 99.05/14.93 Y0, Y1))), 99.05/14.93 (^[Y3 : $i]: 99.05/14.93 (??(( 99.05/14.93 ^[Y4 : $i]: 99.05/14.93 (in(Y4, 99.05/14.93 Y0) & 99.05/14.93 (??(( 99.05/14.93 ^[Y5 : $i]: 99.05/14.93 (in(Y5, 99.05/14.93 Y1) & 99.05/14.93 (Y3 = 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y4, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y4, 99.05/14.93 setadjoin( 99.05/14.93 Y5, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)))))))))))))) => 99.05/14.93 (??(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (( 99.05/14.93 ??(( 99.05/14.93 ^[Y4 : $i]: 99.05/14.93 (in(Y4, 99.05/14.93 Y1) & 99.05/14.93 (Y2 = 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 setadjoin( 99.05/14.93 Y4, 99.05/14.93 emptyset)), 99.05/14.93 emptyset))))))) & 99.05/14.93 in(Y3, 99.05/14.93 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.05/14.93 inference('lazy_cnf_imply', [status(thm)], ['208'])). 99.05/14.93 tff('210', plain, 99.05/14.93 ~ ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 99.05/14.93 (dsetconstr(Y0, Y1) != emptyset)))))))) => 99.05/14.93 ((!!((^[Y0 : $i > $o]: 99.05/14.93 (!!((^[Y1 : $i]: (in(Y1, emptyset) => Y0(Y1)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.93 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 ((!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2))))))) => 99.05/14.93 (~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.93 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 ((??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2))))))) => 99.05/14.93 (~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $o]: (Y0 => in(emptyset, prop2set(Y0)))))) => 99.05/14.93 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.93 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.93 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i > $o]: 99.05/14.93 ((??(Y0)) => 99.05/14.93 ((!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.93 (??((^[Y1 : $i]: 99.05/14.93 (Y0(Y1) & 99.05/14.93 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i > $o]: 99.05/14.93 ((??((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))) => 99.05/14.93 (??((^[Y1 : $i]: 99.05/14.93 (Y0(Y1) & 99.05/14.93 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((Y0 = Y1) => 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 ((Y2 = Y3) => 99.05/14.93 (in(Y2, Y0) => in(Y3, Y1)))))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((Y0 = Y1) => 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 ((Y2 = Y3) => 99.05/14.93 (in(Y2, Y0) <=> in(Y3, Y1)))))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i > $o]: 99.05/14.93 ((??((^[Y1 : $i]: 99.05/14.93 (Y0(Y1) & 99.05/14.93 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i > $o]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 ((!!((^[Y2 : $i]: 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 ((Y2 = Y3) => 99.05/14.93 (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.93 ((??((^[Y2 : $i]: 99.05/14.93 (Y0(Y2) & 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 (Y0(Y3) => (Y2 = Y3))))))))) <=> 99.05/14.93 (??((^[Y2 : $i]: 99.05/14.93 (Y1(Y2) & 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 (Y1(Y3) => (Y2 = Y3))))))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((Y0 = Y1) => 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 ((Y2 = Y3) => 99.05/14.93 (setadjoin(Y0, Y2) = 99.05/14.93 setadjoin(Y1, Y3)))))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((Y0 = Y1) => 99.05/14.93 (powerset(Y0) = powerset(Y1))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((Y0 = Y1) => 99.05/14.93 (setunion(Y0) = setunion(Y1))))))))) => 99.05/14.93 ((!!((^[Y0 : $i > $o]: 99.05/14.93 ((??((^[Y1 : $i]: 99.05/14.93 (Y0(Y1) & 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (Y0(Y1) => 99.05/14.93 (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i > $o]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 ((!!((^[Y2 : $i]: 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 ((Y2 = Y3) => 99.05/14.93 (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.93 ((??((^[Y2 : $i]: 99.05/14.93 (Y0(Y2) & 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 (Y0(Y3) => 99.05/14.93 (Y2 = Y3))))))))) => 99.05/14.93 ((??((^[Y2 : $i]: 99.05/14.93 (Y1(Y2) & 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 (Y1(Y3) => 99.05/14.93 (Y2 = Y3))))))))) => 99.05/14.93 (descr(Y0) = descr(Y1))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((Y0 = Y1) => 99.05/14.93 (!!((^[Y2 : $i > $o]: 99.05/14.93 (!!((^[Y3 : $i > $o]: 99.05/14.93 ((!!((^[Y4 : $i]: 99.05/14.93 (in(Y4, Y0) => 99.05/14.93 (!!(( 99.05/14.93 ^[Y5 : $i]: 99.05/14.93 (in(Y5, 99.05/14.93 Y1) => 99.05/14.93 (( 99.05/14.93 Y4 = Y5) => 99.05/14.93 (Y2(Y4) <=> 99.05/14.93 Y3(Y5))))))))))) => 99.05/14.93 (dsetconstr(Y0, Y2) = 99.05/14.93 dsetconstr(Y1, Y3)))))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((!!((^[Y2 : $i]: 99.05/14.93 (in(Y2, Y0) => in(Y2, Y1))))) => 99.05/14.93 subset(Y0, Y1)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((Y0 = Y1) => subset(Y1, Y0)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((Y0 = Y1) => subset(Y0, Y1)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((!!((^[Y2 : $i]: 99.05/14.93 (in(Y2, Y0) => 99.05/14.93 in(Y2, Y1))))) => 99.05/14.93 subset(Y0, Y1)))))))) => 99.05/14.93 ((!!(subset(emptyset))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (subset(Y0, Y1) => 99.05/14.93 (in(Y2, Y0) => 99.05/14.93 in(Y2, Y1)))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (subset(Y0, Y1) => 99.05/14.93 ((~(in(Y2, Y1))) => 99.05/14.93 (~(in(Y2, Y0)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (in(Y2, Y0) => 99.05/14.93 ((~(in(Y2, Y1))) => 99.05/14.93 (~(subset(Y0, Y1)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((~(subset(Y0, Y1))) => 99.05/14.93 (Y0 != Y1)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (in(Y2, Y0) => 99.05/14.93 ((~(in(Y2, Y1))) => 99.05/14.93 (Y0 != Y1)))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (subset(Y0, Y1) => 99.05/14.93 (subset(Y1, Y2) => 99.05/14.93 subset(Y0, Y2)))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 subset(Y1, 99.05/14.93 setadjoin(Y0, Y1)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (subset(Y0, 99.05/14.93 Y2) => 99.05/14.93 subset(Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, Y2)))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (subset(Y0, Y1) => 99.05/14.93 in(Y0, 99.05/14.93 powerset(Y1))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (subset(Y0, Y1) => 99.05/14.93 (subset(Y1, Y0) => 99.05/14.93 (Y0 = Y1))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (subset(Y0, emptyset) => 99.05/14.93 (Y0 = emptyset))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (subset(Y1, Y0) => 99.05/14.93 in(Y1, 99.05/14.93 powerset(Y0))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (in(Y1, 99.05/14.93 powerset(Y0)) => 99.05/14.93 subset(Y1, Y0)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 in(Y0, powerset(Y0))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (subset(Y0, 99.05/14.93 Y1) => 99.05/14.93 subset( 99.05/14.93 powerset( 99.05/14.93 Y0), 99.05/14.93 powerset( 99.05/14.93 Y1))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 in( 99.05/14.93 dsetconstr( 99.05/14.93 Y0, Y1), 99.05/14.93 powerset( 99.05/14.93 Y0)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 subset( 99.05/14.93 dsetconstr( 99.05/14.93 Y0, Y1), 99.05/14.93 Y0))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 in(Y2, 99.05/14.93 binunion( 99.05/14.93 Y0, Y1)))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 in(Y1, 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y1) => 99.05/14.93 in(Y2, 99.05/14.93 binunion( 99.05/14.93 Y0, Y1)))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y3 : $o]: 99.05/14.93 (in(Y2, 99.05/14.93 binunion( 99.05/14.93 Y0, Y1)) => 99.05/14.93 (( 99.05/14.93 in(Y2, 99.05/14.93 Y0) => Y3) => 99.05/14.93 (( 99.05/14.93 in(Y2, 99.05/14.93 Y1) => Y3) => 99.05/14.93 Y3))))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 binunion( 99.05/14.93 Y0, Y1)) => 99.05/14.93 (in(Y2, 99.05/14.93 Y1) | 99.05/14.93 in(Y2, 99.05/14.93 Y0)))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 subset( 99.05/14.93 Y0, 99.05/14.93 binunion( 99.05/14.93 Y0, Y1)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 subset( 99.05/14.93 Y1, 99.05/14.93 binunion( 99.05/14.93 Y0, Y1)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (in(Y2, 99.05/14.93 Y1) => 99.05/14.93 in(Y2, 99.05/14.93 binintersect( 99.05/14.93 Y0, Y1))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (subset( 99.05/14.93 Y2, Y0) => 99.05/14.93 (subset( 99.05/14.93 Y2, Y1) => 99.05/14.93 subset( 99.05/14.93 Y2, 99.05/14.93 binintersect( 99.05/14.93 Y0, Y1))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 binintersect( 99.05/14.93 Y0, Y1)) => 99.05/14.93 in(Y2, 99.05/14.93 Y0))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 subset( 99.05/14.93 binintersect( 99.05/14.93 Y0, Y1), 99.05/14.93 Y0))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (subset( 99.05/14.93 Y0, Y1) => 99.05/14.93 (binintersect( 99.05/14.93 Y0, Y1) = 99.05/14.93 Y0)))))))) => 99.05/14.93 ((!!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (( 99.05/14.93 binintersect( 99.05/14.93 Y0, Y1) = 99.05/14.93 Y1) => 99.05/14.93 subset( 99.05/14.93 Y1, Y0)))))))) => 99.05/14.93 ((!!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 binintersect( 99.05/14.93 Y0, Y1)) => 99.05/14.93 in(Y2, 99.05/14.93 Y1))))))))))) => 99.05/14.93 ((!!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (( 99.05/14.93 ~(( 99.05/14.93 ??(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) & 99.05/14.93 in(Y2, 99.05/14.93 Y1))))))) => 99.05/14.93 (binintersect( 99.05/14.93 Y0, Y1) = 99.05/14.93 emptyset)))))))) => 99.05/14.93 ((!!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 subset( 99.05/14.93 binintersect( 99.05/14.93 Y0, Y1), 99.05/14.93 Y1))))))) => 99.05/14.93 (( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (subset( 99.05/14.93 Y1, Y0) => 99.05/14.93 (binintersect( 99.05/14.93 Y0, Y1) = 99.05/14.93 Y1)))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (( 99.05/14.93 binintersect( 99.05/14.93 Y0, Y1) = 99.05/14.93 Y0) => 99.05/14.93 subset( 99.05/14.93 Y0, Y1)))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (binintersect( 99.05/14.93 Y0, 99.05/14.93 binunion( 99.05/14.93 Y1, Y2)) = 99.05/14.93 binunion( 99.05/14.93 binintersect( 99.05/14.93 Y0, Y1), 99.05/14.93 binintersect( 99.05/14.93 Y0, Y2)))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 Y1))) => 99.05/14.93 in(Y2, 99.05/14.93 setminus( 99.05/14.93 Y0, Y1))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 setminus( 99.05/14.93 Y0, Y1)) => 99.05/14.93 in(Y2, 99.05/14.93 Y0))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 setminus( 99.05/14.93 Y0, Y1)) => 99.05/14.93 (~( 99.05/14.93 in(Y2, 99.05/14.93 Y1))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (subset( 99.05/14.93 Y0, Y1) => 99.05/14.93 (setminus( 99.05/14.93 Y0, Y1) = 99.05/14.93 emptyset)))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 setminus( 99.05/14.93 Y0, Y1)))) => 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 in(Y2, 99.05/14.93 Y1)))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 setminus( 99.05/14.93 Y0, Y1)))) => 99.05/14.93 (( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 Y1))) => 99.05/14.93 (~( 99.05/14.93 in(Y2, 99.05/14.93 Y0)))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 Y0))) => 99.05/14.93 (~( 99.05/14.93 in(Y2, 99.05/14.93 setminus( 99.05/14.93 Y0, Y1)))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y1) => 99.05/14.93 (~( 99.05/14.93 in(Y2, 99.05/14.93 setminus( 99.05/14.93 Y0, Y1)))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 subset( 99.05/14.93 setminus( 99.05/14.93 Y0, Y1), 99.05/14.93 Y0))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (( 99.05/14.93 setminus( 99.05/14.93 Y0, Y1) = 99.05/14.93 emptyset) => 99.05/14.93 subset( 99.05/14.93 Y0, Y1)))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 symdiff( 99.05/14.93 Y0, Y1)) => 99.05/14.93 (!!(( 99.05/14.93 ^[Y3 : $o]: 99.05/14.93 (( 99.05/14.93 in(Y2, 99.05/14.93 Y0) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 Y1))) => 99.05/14.93 Y3)) => 99.05/14.93 (( 99.05/14.93 ( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 Y0))) => 99.05/14.93 ( 99.05/14.93 in(Y2, 99.05/14.93 Y1) => Y3)) => 99.05/14.93 Y3))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 Y1))) => 99.05/14.93 in(Y2, 99.05/14.93 symdiff( 99.05/14.93 Y0, Y1))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 Y0))) => 99.05/14.93 (in(Y2, 99.05/14.93 Y1) => 99.05/14.93 in(Y2, 99.05/14.93 symdiff( 99.05/14.93 Y0, Y1))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (in(Y2, 99.05/14.93 Y1) => 99.05/14.93 (~( 99.05/14.93 in(Y2, 99.05/14.93 symdiff( 99.05/14.93 Y0, Y1))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 Y0))) => 99.05/14.93 (( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 Y1))) => 99.05/14.93 (~( 99.05/14.93 in(Y2, 99.05/14.93 symdiff( 99.05/14.93 Y0, Y1))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 in(Y1, 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 in(Y0, 99.05/14.93 setunion( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 in(Y1, 99.05/14.93 setunion( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (??(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 setunion( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)))) & 99.05/14.93 (??(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (in(Y3, 99.05/14.93 setunion( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)))) & 99.05/14.93 (setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)) = 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset)), 99.05/14.93 emptyset))))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (??(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 setunion( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)))) & 99.05/14.93 (??(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (in(Y3, 99.05/14.93 setunion( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)))) & 99.05/14.93 (setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)) = 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset)), 99.05/14.93 emptyset))))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (in(Y1, 99.05/14.93 Y0) => 99.05/14.93 subset( 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset), 99.05/14.93 Y0)))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (in(Y1, 99.05/14.93 Y0) => 99.05/14.93 in( 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset), 99.05/14.93 powerset( 99.05/14.93 Y0))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 in( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 emptyset), 99.05/14.93 powerset( 99.05/14.93 binunion( 99.05/14.93 Y0, Y1))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset))) => 99.05/14.93 (( 99.05/14.93 Y2 = Y1) | 99.05/14.93 (Y2 = Y0)))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (!!(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (in(Y3, 99.05/14.93 Y1) => 99.05/14.93 subset( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset)), 99.05/14.93 binunion( 99.05/14.93 Y0, Y1)))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (!!(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (in(Y3, 99.05/14.93 Y1) => 99.05/14.93 in( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset)), 99.05/14.93 powerset( 99.05/14.93 binunion( 99.05/14.93 Y0, Y1))))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (!!(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (in(Y3, 99.05/14.93 Y1) => 99.05/14.93 subset( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)), 99.05/14.93 powerset( 99.05/14.93 binunion( 99.05/14.93 Y0, Y1))))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (!!(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (in(Y3, 99.05/14.93 Y1) => 99.05/14.93 in( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)), 99.05/14.93 powerset( 99.05/14.93 powerset( 99.05/14.93 binunion( 99.05/14.93 Y0, Y1)))))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (!!(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (in(Y3, 99.05/14.93 Y1) => 99.05/14.93 in( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)), 99.05/14.93 powerset( 99.05/14.93 powerset( 99.05/14.93 binunion( 99.05/14.93 Y0, Y1)))))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (!!(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (in(Y3, 99.05/14.93 Y1) => 99.05/14.93 in( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)), 99.05/14.93 dsetconstr( 99.05/14.93 powerset( 99.05/14.93 powerset( 99.05/14.93 binunion( 99.05/14.93 Y0, Y1))), 99.05/14.93 (^[Y4 : $i]: 99.05/14.93 (??(( 99.05/14.93 ^[Y5 : $i]: 99.05/14.93 (in(Y5, 99.05/14.93 Y0) & 99.05/14.93 (??(( 99.05/14.93 ^[Y6 : $i]: 99.05/14.93 (in(Y6, 99.05/14.93 Y1) & 99.05/14.93 (Y4 = 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y5, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y5, 99.05/14.93 setadjoin( 99.05/14.93 Y6, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)))))))))))))))))))))))))))) => 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 dsetconstr( 99.05/14.93 powerset( 99.05/14.93 powerset( 99.05/14.93 binunion( 99.05/14.93 Y0, Y1))), 99.05/14.93 (^[Y3 : $i]: 99.05/14.93 (??(( 99.05/14.93 ^[Y4 : $i]: 99.05/14.93 (in(Y4, 99.05/14.93 Y0) & 99.05/14.93 (??(( 99.05/14.93 ^[Y5 : $i]: 99.05/14.93 (in(Y5, 99.05/14.93 Y1) & 99.05/14.93 (Y3 = 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y4, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y4, 99.05/14.93 setadjoin( 99.05/14.93 Y5, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)))))))))))))) => 99.05/14.93 (??(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (( 99.05/14.93 ??(( 99.05/14.93 ^[Y4 : $i]: 99.05/14.93 (in(Y4, 99.05/14.93 Y1) & 99.05/14.93 (Y2 = 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 setadjoin( 99.05/14.93 Y4, 99.05/14.93 emptyset)), 99.05/14.93 emptyset))))))) & 99.05/14.93 in(Y3, 99.05/14.93 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.05/14.93 inference('lazy_cnf_imply', [status(thm)], ['209'])). 99.05/14.93 tff('211', plain, 99.05/14.93 ~ ((!!((^[Y0 : $i > $o]: (!!((^[Y1 : $i]: (in(Y1, emptyset) => Y0(Y1)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.93 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 ((!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2))))))) => 99.05/14.93 (~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.93 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 ((??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2))))))) => 99.05/14.93 (~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $o]: (Y0 => in(emptyset, prop2set(Y0)))))) => 99.05/14.93 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.93 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.93 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i > $o]: 99.05/14.93 ((??(Y0)) => 99.05/14.93 ((!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.93 (??((^[Y1 : $i]: 99.05/14.93 (Y0(Y1) & 99.05/14.93 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i > $o]: 99.05/14.93 ((??((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))) => 99.05/14.93 (??((^[Y1 : $i]: 99.05/14.93 (Y0(Y1) & 99.05/14.93 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((Y0 = Y1) => 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 ((Y2 = Y3) => 99.05/14.93 (in(Y2, Y0) => in(Y3, Y1)))))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((Y0 = Y1) => 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 ((Y2 = Y3) => 99.05/14.93 (in(Y2, Y0) <=> in(Y3, Y1)))))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i > $o]: 99.05/14.93 ((??((^[Y1 : $i]: 99.05/14.93 (Y0(Y1) & 99.05/14.93 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i > $o]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 ((!!((^[Y2 : $i]: 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 ((Y2 = Y3) => 99.05/14.93 (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.93 ((??((^[Y2 : $i]: 99.05/14.93 (Y0(Y2) & 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 (Y0(Y3) => (Y2 = Y3))))))))) <=> 99.05/14.93 (??((^[Y2 : $i]: 99.05/14.93 (Y1(Y2) & 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 (Y1(Y3) => (Y2 = Y3))))))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((Y0 = Y1) => 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 ((Y2 = Y3) => 99.05/14.93 (setadjoin(Y0, Y2) = 99.05/14.93 setadjoin(Y1, Y3)))))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((Y0 = Y1) => 99.05/14.93 (powerset(Y0) = powerset(Y1))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((Y0 = Y1) => 99.05/14.93 (setunion(Y0) = setunion(Y1))))))))) => 99.05/14.93 ((!!((^[Y0 : $i > $o]: 99.05/14.93 ((??((^[Y1 : $i]: 99.05/14.93 (Y0(Y1) & 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (Y0(Y1) => 99.05/14.93 (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i > $o]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 ((!!((^[Y2 : $i]: 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 ((Y2 = Y3) => 99.05/14.93 (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.93 ((??((^[Y2 : $i]: 99.05/14.93 (Y0(Y2) & 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 (Y0(Y3) => (Y2 = Y3))))))))) => 99.05/14.93 ((??((^[Y2 : $i]: 99.05/14.93 (Y1(Y2) & 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 (Y1(Y3) => 99.05/14.93 (Y2 = Y3))))))))) => 99.05/14.93 (descr(Y0) = descr(Y1))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((Y0 = Y1) => 99.05/14.93 (!!((^[Y2 : $i > $o]: 99.05/14.93 (!!((^[Y3 : $i > $o]: 99.05/14.93 ((!!((^[Y4 : $i]: 99.05/14.93 (in(Y4, Y0) => 99.05/14.93 (!!(( 99.05/14.93 ^[Y5 : $i]: 99.05/14.93 ( 99.05/14.93 in(Y5, 99.05/14.93 Y1) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 Y4 = Y5) => 99.05/14.93 ( 99.05/14.93 Y2(Y4) <=> 99.05/14.93 Y3(Y5))))))))))) => 99.05/14.93 (dsetconstr(Y0, Y2) = 99.05/14.93 dsetconstr(Y1, Y3)))))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((!!((^[Y2 : $i]: 99.05/14.93 (in(Y2, Y0) => in(Y2, Y1))))) => 99.05/14.93 subset(Y0, Y1)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((Y0 = Y1) => subset(Y1, Y0)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((Y0 = Y1) => subset(Y0, Y1)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((!!((^[Y2 : $i]: 99.05/14.93 (in(Y2, Y0) => 99.05/14.93 in(Y2, Y1))))) => 99.05/14.93 subset(Y0, Y1)))))))) => 99.05/14.93 ((!!(subset(emptyset))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (subset(Y0, Y1) => 99.05/14.93 (in(Y2, Y0) => 99.05/14.93 in(Y2, Y1)))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (subset(Y0, Y1) => 99.05/14.93 ((~(in(Y2, Y1))) => 99.05/14.93 (~(in(Y2, Y0)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (in(Y2, Y0) => 99.05/14.93 ((~(in(Y2, Y1))) => 99.05/14.93 (~(subset(Y0, Y1)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((~(subset(Y0, Y1))) => 99.05/14.93 (Y0 != Y1)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (in(Y2, Y0) => 99.05/14.93 ((~(in(Y2, Y1))) => 99.05/14.93 (Y0 != Y1)))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (subset(Y0, Y1) => 99.05/14.93 (subset(Y1, Y2) => 99.05/14.93 subset(Y0, Y2)))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 subset(Y1, 99.05/14.93 setadjoin(Y0, Y1)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (subset(Y0, Y2) => 99.05/14.93 subset(Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, Y2)))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (subset(Y0, Y1) => 99.05/14.93 in(Y0, powerset(Y1))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (subset(Y0, Y1) => 99.05/14.93 (subset(Y1, Y0) => 99.05/14.93 (Y0 = Y1))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (subset(Y0, emptyset) => 99.05/14.93 (Y0 = emptyset))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (subset(Y1, Y0) => 99.05/14.93 in(Y1, 99.05/14.93 powerset(Y0))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (in(Y1, 99.05/14.93 powerset(Y0)) => 99.05/14.93 subset(Y1, Y0)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 in(Y0, powerset(Y0))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (subset(Y0, Y1) => 99.05/14.93 subset( 99.05/14.93 powerset(Y0), 99.05/14.93 powerset(Y1))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 in( 99.05/14.93 dsetconstr( 99.05/14.93 Y0, Y1), 99.05/14.93 powerset(Y0)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 subset( 99.05/14.93 dsetconstr( 99.05/14.93 Y0, Y1), 99.05/14.93 Y0))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 ( 99.05/14.93 in(Y2, 99.05/14.93 Y0) => 99.05/14.93 in(Y2, 99.05/14.93 binunion( 99.05/14.93 Y0, Y1)))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 in(Y1, 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y1) => 99.05/14.93 in(Y2, 99.05/14.93 binunion( 99.05/14.93 Y0, Y1)))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y3 : $o]: 99.05/14.93 (in(Y2, 99.05/14.93 binunion( 99.05/14.93 Y0, Y1)) => 99.05/14.93 (( 99.05/14.93 in(Y2, 99.05/14.93 Y0) => Y3) => 99.05/14.93 (( 99.05/14.93 in(Y2, 99.05/14.93 Y1) => Y3) => 99.05/14.93 Y3))))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 binunion( 99.05/14.93 Y0, Y1)) => 99.05/14.93 (in(Y2, 99.05/14.93 Y1) | 99.05/14.93 in(Y2, 99.05/14.93 Y0)))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 subset( 99.05/14.93 Y0, 99.05/14.93 binunion( 99.05/14.93 Y0, Y1)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 subset( 99.05/14.93 Y1, 99.05/14.93 binunion( 99.05/14.93 Y0, Y1)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (in(Y2, 99.05/14.93 Y1) => 99.05/14.93 in(Y2, 99.05/14.93 binintersect( 99.05/14.93 Y0, Y1))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (subset( 99.05/14.93 Y2, Y0) => 99.05/14.93 (subset( 99.05/14.93 Y2, Y1) => 99.05/14.93 subset( 99.05/14.93 Y2, 99.05/14.93 binintersect( 99.05/14.93 Y0, Y1))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 binintersect( 99.05/14.93 Y0, Y1)) => 99.05/14.93 in(Y2, 99.05/14.93 Y0))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 subset( 99.05/14.93 binintersect( 99.05/14.93 Y0, Y1), 99.05/14.93 Y0))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (subset( 99.05/14.93 Y0, Y1) => 99.05/14.93 (binintersect( 99.05/14.93 Y0, Y1) = 99.05/14.93 Y0)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (( 99.05/14.93 binintersect( 99.05/14.93 Y0, Y1) = 99.05/14.93 Y1) => 99.05/14.93 subset( 99.05/14.93 Y1, Y0)))))))) => 99.05/14.93 ((!!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 binintersect( 99.05/14.93 Y0, Y1)) => 99.05/14.93 in(Y2, 99.05/14.93 Y1))))))))))) => 99.05/14.93 ((!!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (( 99.05/14.93 ~(( 99.05/14.93 ??(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) & 99.05/14.93 in(Y2, 99.05/14.93 Y1))))))) => 99.05/14.93 (binintersect( 99.05/14.93 Y0, Y1) = 99.05/14.93 emptyset)))))))) => 99.05/14.93 ((!!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 subset( 99.05/14.93 binintersect( 99.05/14.93 Y0, Y1), 99.05/14.93 Y1))))))) => 99.05/14.93 ((!!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (subset( 99.05/14.93 Y1, Y0) => 99.05/14.93 (binintersect( 99.05/14.93 Y0, Y1) = 99.05/14.93 Y1)))))))) => 99.05/14.93 (( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (( 99.05/14.93 binintersect( 99.05/14.93 Y0, Y1) = 99.05/14.93 Y0) => 99.05/14.93 subset( 99.05/14.93 Y0, Y1)))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (binintersect( 99.05/14.93 Y0, 99.05/14.93 binunion( 99.05/14.93 Y1, Y2)) = 99.05/14.93 binunion( 99.05/14.93 binintersect( 99.05/14.93 Y0, Y1), 99.05/14.93 binintersect( 99.05/14.93 Y0, Y2)))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 Y1))) => 99.05/14.93 in(Y2, 99.05/14.93 setminus( 99.05/14.93 Y0, Y1))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 setminus( 99.05/14.93 Y0, Y1)) => 99.05/14.93 in(Y2, 99.05/14.93 Y0))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 setminus( 99.05/14.93 Y0, Y1)) => 99.05/14.93 (~( 99.05/14.93 in(Y2, 99.05/14.93 Y1))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (subset( 99.05/14.93 Y0, Y1) => 99.05/14.93 (setminus( 99.05/14.93 Y0, Y1) = 99.05/14.93 emptyset)))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 setminus( 99.05/14.93 Y0, Y1)))) => 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 in(Y2, 99.05/14.93 Y1)))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 setminus( 99.05/14.93 Y0, Y1)))) => 99.05/14.93 (( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 Y1))) => 99.05/14.93 (~( 99.05/14.93 in(Y2, 99.05/14.93 Y0)))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 Y0))) => 99.05/14.93 (~( 99.05/14.93 in(Y2, 99.05/14.93 setminus( 99.05/14.93 Y0, Y1)))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y1) => 99.05/14.93 (~( 99.05/14.93 in(Y2, 99.05/14.93 setminus( 99.05/14.93 Y0, Y1)))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 subset( 99.05/14.93 setminus( 99.05/14.93 Y0, Y1), 99.05/14.93 Y0))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (( 99.05/14.93 setminus( 99.05/14.93 Y0, Y1) = 99.05/14.93 emptyset) => 99.05/14.93 subset( 99.05/14.93 Y0, Y1)))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 symdiff( 99.05/14.93 Y0, Y1)) => 99.05/14.93 (!!(( 99.05/14.93 ^[Y3 : $o]: 99.05/14.93 (( 99.05/14.93 in(Y2, 99.05/14.93 Y0) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 Y1))) => 99.05/14.93 Y3)) => 99.05/14.93 (( 99.05/14.93 ( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 Y0))) => 99.05/14.93 ( 99.05/14.93 in(Y2, 99.05/14.93 Y1) => Y3)) => 99.05/14.93 Y3))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 Y1))) => 99.05/14.93 in(Y2, 99.05/14.93 symdiff( 99.05/14.93 Y0, Y1))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 Y0))) => 99.05/14.93 (in(Y2, 99.05/14.93 Y1) => 99.05/14.93 in(Y2, 99.05/14.93 symdiff( 99.05/14.93 Y0, Y1))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (in(Y2, 99.05/14.93 Y1) => 99.05/14.93 (~( 99.05/14.93 in(Y2, 99.05/14.93 symdiff( 99.05/14.93 Y0, Y1))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 Y0))) => 99.05/14.93 (( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 Y1))) => 99.05/14.93 (~( 99.05/14.93 in(Y2, 99.05/14.93 symdiff( 99.05/14.93 Y0, Y1))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 in(Y1, 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 in(Y0, 99.05/14.93 setunion( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 in(Y1, 99.05/14.93 setunion( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (??(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 setunion( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)))) & 99.05/14.93 (??(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (in(Y3, 99.05/14.93 setunion( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)))) & 99.05/14.93 (setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)) = 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset)), 99.05/14.93 emptyset))))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (??(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 setunion( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)))) & 99.05/14.93 (??(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (in(Y3, 99.05/14.93 setunion( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)))) & 99.05/14.93 (setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)) = 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset)), 99.05/14.93 emptyset))))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (in(Y1, 99.05/14.93 Y0) => 99.05/14.93 subset( 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset), 99.05/14.93 Y0)))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (in(Y1, 99.05/14.93 Y0) => 99.05/14.93 in( 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset), 99.05/14.93 powerset( 99.05/14.93 Y0))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 in( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 emptyset), 99.05/14.93 powerset( 99.05/14.93 binunion( 99.05/14.93 Y0, Y1))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset))) => 99.05/14.93 (( 99.05/14.93 Y2 = Y1) | 99.05/14.93 (Y2 = Y0)))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (!!(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (in(Y3, 99.05/14.93 Y1) => 99.05/14.93 subset( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset)), 99.05/14.93 binunion( 99.05/14.93 Y0, Y1)))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (!!(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (in(Y3, 99.05/14.93 Y1) => 99.05/14.93 in( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset)), 99.05/14.93 powerset( 99.05/14.93 binunion( 99.05/14.93 Y0, Y1))))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (!!(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (in(Y3, 99.05/14.93 Y1) => 99.05/14.93 subset( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)), 99.05/14.93 powerset( 99.05/14.93 binunion( 99.05/14.93 Y0, Y1))))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (!!(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (in(Y3, 99.05/14.93 Y1) => 99.05/14.93 in( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)), 99.05/14.93 powerset( 99.05/14.93 powerset( 99.05/14.93 binunion( 99.05/14.93 Y0, Y1)))))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (!!(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (in(Y3, 99.05/14.93 Y1) => 99.05/14.93 in( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)), 99.05/14.93 powerset( 99.05/14.93 powerset( 99.05/14.93 binunion( 99.05/14.93 Y0, Y1)))))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (!!(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (in(Y3, 99.05/14.93 Y1) => 99.05/14.93 in( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)), 99.05/14.93 dsetconstr( 99.05/14.93 powerset( 99.05/14.93 powerset( 99.05/14.93 binunion( 99.05/14.93 Y0, Y1))), 99.05/14.93 (^[Y4 : $i]: 99.05/14.93 (??(( 99.05/14.93 ^[Y5 : $i]: 99.05/14.93 (in(Y5, 99.05/14.93 Y0) & 99.05/14.93 (??(( 99.05/14.93 ^[Y6 : $i]: 99.05/14.93 (in(Y6, 99.05/14.93 Y1) & 99.05/14.93 (Y4 = 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y5, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y5, 99.05/14.93 setadjoin( 99.05/14.93 Y6, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)))))))))))))))))))))))))))) => 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 dsetconstr( 99.05/14.93 powerset( 99.05/14.93 powerset( 99.05/14.93 binunion( 99.05/14.93 Y0, Y1))), 99.05/14.93 (^[Y3 : $i]: 99.05/14.93 (??(( 99.05/14.93 ^[Y4 : $i]: 99.05/14.93 (in(Y4, 99.05/14.93 Y0) & 99.05/14.93 (??(( 99.05/14.93 ^[Y5 : $i]: 99.05/14.93 (in(Y5, 99.05/14.93 Y1) & 99.05/14.93 (Y3 = 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y4, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y4, 99.05/14.93 setadjoin( 99.05/14.93 Y5, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)))))))))))))) => 99.05/14.93 (??(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (( 99.05/14.93 ??(( 99.05/14.93 ^[Y4 : $i]: 99.05/14.93 (in(Y4, 99.05/14.93 Y1) & 99.05/14.93 (Y2 = 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 setadjoin( 99.05/14.93 Y4, 99.05/14.93 emptyset)), 99.05/14.93 emptyset))))))) & 99.05/14.93 in(Y3, 99.05/14.93 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.05/14.93 inference('lazy_cnf_imply', [status(thm)], ['210'])). 99.05/14.93 tff('212', plain, 99.05/14.93 ~ ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.93 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 ((!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2))))))) => 99.05/14.93 (~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.93 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 ((??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2))))))) => 99.05/14.93 (~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $o]: (Y0 => in(emptyset, prop2set(Y0)))))) => 99.05/14.93 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.93 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.93 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i > $o]: 99.05/14.93 ((??(Y0)) => 99.05/14.93 ((!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.93 (??((^[Y1 : $i]: 99.05/14.93 (Y0(Y1) & 99.05/14.93 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i > $o]: 99.05/14.93 ((??((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))) => 99.05/14.93 (??((^[Y1 : $i]: 99.05/14.93 (Y0(Y1) & 99.05/14.93 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((Y0 = Y1) => 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 ((Y2 = Y3) => 99.05/14.93 (in(Y2, Y0) => in(Y3, Y1)))))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((Y0 = Y1) => 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 ((Y2 = Y3) => 99.05/14.93 (in(Y2, Y0) <=> in(Y3, Y1)))))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i > $o]: 99.05/14.93 ((??((^[Y1 : $i]: 99.05/14.93 (Y0(Y1) & 99.05/14.93 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i > $o]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 ((!!((^[Y2 : $i]: 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 ((Y2 = Y3) => 99.05/14.93 (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.93 ((??((^[Y2 : $i]: 99.05/14.93 (Y0(Y2) & 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 (Y0(Y3) => (Y2 = Y3))))))))) <=> 99.05/14.93 (??((^[Y2 : $i]: 99.05/14.93 (Y1(Y2) & 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 (Y1(Y3) => (Y2 = Y3))))))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((Y0 = Y1) => 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 ((Y2 = Y3) => 99.05/14.93 (setadjoin(Y0, Y2) = 99.05/14.93 setadjoin(Y1, Y3)))))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((Y0 = Y1) => 99.05/14.93 (powerset(Y0) = powerset(Y1))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((Y0 = Y1) => 99.05/14.93 (setunion(Y0) = setunion(Y1))))))))) => 99.05/14.93 ((!!((^[Y0 : $i > $o]: 99.05/14.93 ((??((^[Y1 : $i]: 99.05/14.93 (Y0(Y1) & 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (Y0(Y1) => 99.05/14.93 (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i > $o]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 ((!!((^[Y2 : $i]: 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 ((Y2 = Y3) => 99.05/14.93 (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.93 ((??((^[Y2 : $i]: 99.05/14.93 (Y0(Y2) & 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 (Y0(Y3) => (Y2 = Y3))))))))) => 99.05/14.93 ((??((^[Y2 : $i]: 99.05/14.93 (Y1(Y2) & 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 (Y1(Y3) => (Y2 = Y3))))))))) => 99.05/14.93 (descr(Y0) = descr(Y1))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((Y0 = Y1) => 99.05/14.93 (!!((^[Y2 : $i > $o]: 99.05/14.93 (!!((^[Y3 : $i > $o]: 99.05/14.93 ((!!((^[Y4 : $i]: 99.05/14.93 (in(Y4, Y0) => 99.05/14.93 (!!(( 99.05/14.93 ^[Y5 : $i]: 99.05/14.93 (in(Y5, 99.05/14.93 Y1) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 Y4 = Y5) => 99.05/14.93 ( 99.05/14.93 Y2(Y4) <=> 99.05/14.93 Y3(Y5))))))))))) => 99.05/14.93 (dsetconstr(Y0, Y2) = 99.05/14.93 dsetconstr(Y1, Y3)))))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((!!((^[Y2 : $i]: 99.05/14.93 (in(Y2, Y0) => in(Y2, Y1))))) => 99.05/14.93 subset(Y0, Y1)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((Y0 = Y1) => subset(Y1, Y0)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((Y0 = Y1) => subset(Y0, Y1)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((!!((^[Y2 : $i]: 99.05/14.93 (in(Y2, Y0) => in(Y2, Y1))))) => 99.05/14.93 subset(Y0, Y1)))))))) => 99.05/14.93 ((!!(subset(emptyset))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (subset(Y0, Y1) => 99.05/14.93 (in(Y2, Y0) => 99.05/14.93 in(Y2, Y1)))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (subset(Y0, Y1) => 99.05/14.93 ((~(in(Y2, Y1))) => 99.05/14.93 (~(in(Y2, Y0)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (in(Y2, Y0) => 99.05/14.93 ((~(in(Y2, Y1))) => 99.05/14.93 (~(subset(Y0, Y1)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((~(subset(Y0, Y1))) => 99.05/14.93 (Y0 != Y1)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (in(Y2, Y0) => 99.05/14.93 ((~(in(Y2, Y1))) => 99.05/14.93 (Y0 != Y1)))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (subset(Y0, Y1) => 99.05/14.93 (subset(Y1, Y2) => 99.05/14.93 subset(Y0, Y2)))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 subset(Y1, 99.05/14.93 setadjoin(Y0, Y1)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (subset(Y0, Y2) => 99.05/14.93 subset(Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, Y2)))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (subset(Y0, Y1) => 99.05/14.93 in(Y0, powerset(Y1))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (subset(Y0, Y1) => 99.05/14.93 (subset(Y1, Y0) => 99.05/14.93 (Y0 = Y1))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (subset(Y0, emptyset) => 99.05/14.93 (Y0 = emptyset))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (subset(Y1, Y0) => 99.05/14.93 in(Y1, 99.05/14.93 powerset(Y0))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (in(Y1, 99.05/14.93 powerset(Y0)) => 99.05/14.93 subset(Y1, Y0)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 in(Y0, powerset(Y0))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (subset(Y0, Y1) => 99.05/14.93 subset( 99.05/14.93 powerset(Y0), 99.05/14.93 powerset(Y1))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 in( 99.05/14.93 dsetconstr( 99.05/14.93 Y0, Y1), 99.05/14.93 powerset(Y0)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 subset( 99.05/14.93 dsetconstr( 99.05/14.93 Y0, Y1), 99.05/14.93 Y0))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 in(Y2, 99.05/14.93 binunion( 99.05/14.93 Y0, Y1)))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 in(Y1, 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y1) => 99.05/14.93 in(Y2, 99.05/14.93 binunion( 99.05/14.93 Y0, Y1)))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y3 : $o]: 99.05/14.93 (in(Y2, 99.05/14.93 binunion( 99.05/14.93 Y0, Y1)) => 99.05/14.93 (( 99.05/14.93 in(Y2, 99.05/14.93 Y0) => Y3) => 99.05/14.93 (( 99.05/14.93 in(Y2, 99.05/14.93 Y1) => Y3) => 99.05/14.93 Y3))))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 binunion( 99.05/14.93 Y0, Y1)) => 99.05/14.93 (in(Y2, 99.05/14.93 Y1) | 99.05/14.93 in(Y2, 99.05/14.93 Y0)))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 subset( 99.05/14.93 Y0, 99.05/14.93 binunion( 99.05/14.93 Y0, Y1)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 subset( 99.05/14.93 Y1, 99.05/14.93 binunion( 99.05/14.93 Y0, Y1)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (in(Y2, 99.05/14.93 Y1) => 99.05/14.93 in(Y2, 99.05/14.93 binintersect( 99.05/14.93 Y0, Y1))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (subset( 99.05/14.93 Y2, Y0) => 99.05/14.93 (subset( 99.05/14.93 Y2, Y1) => 99.05/14.93 subset( 99.05/14.93 Y2, 99.05/14.93 binintersect( 99.05/14.93 Y0, Y1))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 binintersect( 99.05/14.93 Y0, Y1)) => 99.05/14.93 in(Y2, 99.05/14.93 Y0))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 subset( 99.05/14.93 binintersect( 99.05/14.93 Y0, Y1), 99.05/14.93 Y0))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (subset( 99.05/14.93 Y0, Y1) => 99.05/14.93 (binintersect( 99.05/14.93 Y0, Y1) = 99.05/14.93 Y0)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (( 99.05/14.93 binintersect( 99.05/14.93 Y0, Y1) = 99.05/14.93 Y1) => 99.05/14.93 subset( 99.05/14.93 Y1, Y0)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 binintersect( 99.05/14.93 Y0, Y1)) => 99.05/14.93 in(Y2, 99.05/14.93 Y1))))))))))) => 99.05/14.93 ((!!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (( 99.05/14.93 ~(( 99.05/14.93 ??(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) & 99.05/14.93 in(Y2, 99.05/14.93 Y1))))))) => 99.05/14.93 (binintersect( 99.05/14.93 Y0, Y1) = 99.05/14.93 emptyset)))))))) => 99.05/14.93 ((!!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 subset( 99.05/14.93 binintersect( 99.05/14.93 Y0, Y1), 99.05/14.93 Y1))))))) => 99.05/14.93 ((!!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (subset( 99.05/14.93 Y1, Y0) => 99.05/14.93 (binintersect( 99.05/14.93 Y0, Y1) = 99.05/14.93 Y1)))))))) => 99.05/14.93 ((!!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (( 99.05/14.93 binintersect( 99.05/14.93 Y0, Y1) = 99.05/14.93 Y0) => 99.05/14.93 subset( 99.05/14.93 Y0, Y1)))))))) => 99.05/14.93 (( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (binintersect( 99.05/14.93 Y0, 99.05/14.93 binunion( 99.05/14.93 Y1, Y2)) = 99.05/14.93 binunion( 99.05/14.93 binintersect( 99.05/14.93 Y0, Y1), 99.05/14.93 binintersect( 99.05/14.93 Y0, Y2)))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 Y1))) => 99.05/14.93 in(Y2, 99.05/14.93 setminus( 99.05/14.93 Y0, Y1))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 setminus( 99.05/14.93 Y0, Y1)) => 99.05/14.93 in(Y2, 99.05/14.93 Y0))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 setminus( 99.05/14.93 Y0, Y1)) => 99.05/14.93 (~( 99.05/14.93 in(Y2, 99.05/14.93 Y1))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (subset( 99.05/14.93 Y0, Y1) => 99.05/14.93 (setminus( 99.05/14.93 Y0, Y1) = 99.05/14.93 emptyset)))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 setminus( 99.05/14.93 Y0, Y1)))) => 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 in(Y2, 99.05/14.93 Y1)))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 setminus( 99.05/14.93 Y0, Y1)))) => 99.05/14.93 (( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 Y1))) => 99.05/14.93 (~( 99.05/14.93 in(Y2, 99.05/14.93 Y0)))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 Y0))) => 99.05/14.93 (~( 99.05/14.93 in(Y2, 99.05/14.93 setminus( 99.05/14.93 Y0, Y1)))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y1) => 99.05/14.93 (~( 99.05/14.93 in(Y2, 99.05/14.93 setminus( 99.05/14.93 Y0, Y1)))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 subset( 99.05/14.93 setminus( 99.05/14.93 Y0, Y1), 99.05/14.93 Y0))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (( 99.05/14.93 setminus( 99.05/14.93 Y0, Y1) = 99.05/14.93 emptyset) => 99.05/14.93 subset( 99.05/14.93 Y0, Y1)))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 symdiff( 99.05/14.93 Y0, Y1)) => 99.05/14.93 (!!(( 99.05/14.93 ^[Y3 : $o]: 99.05/14.93 (( 99.05/14.93 in(Y2, 99.05/14.93 Y0) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 Y1))) => 99.05/14.93 Y3)) => 99.05/14.93 (( 99.05/14.93 ( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 Y0))) => 99.05/14.93 ( 99.05/14.93 in(Y2, 99.05/14.93 Y1) => Y3)) => 99.05/14.93 Y3))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 Y1))) => 99.05/14.93 in(Y2, 99.05/14.93 symdiff( 99.05/14.93 Y0, Y1))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 Y0))) => 99.05/14.93 (in(Y2, 99.05/14.93 Y1) => 99.05/14.93 in(Y2, 99.05/14.93 symdiff( 99.05/14.93 Y0, Y1))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (in(Y2, 99.05/14.93 Y1) => 99.05/14.93 (~( 99.05/14.93 in(Y2, 99.05/14.93 symdiff( 99.05/14.93 Y0, Y1))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 Y0))) => 99.05/14.93 (( 99.05/14.93 ~( 99.05/14.93 in(Y2, 99.05/14.93 Y1))) => 99.05/14.93 (~( 99.05/14.93 in(Y2, 99.05/14.93 symdiff( 99.05/14.93 Y0, Y1))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 in(Y1, 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 in(Y0, 99.05/14.93 setunion( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 in(Y1, 99.05/14.93 setunion( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (??(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 setunion( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)))) & 99.05/14.93 (??(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (in(Y3, 99.05/14.93 setunion( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)))) & 99.05/14.93 (setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)) = 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset)), 99.05/14.93 emptyset))))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (??(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 setunion( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)))) & 99.05/14.93 (??(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (in(Y3, 99.05/14.93 setunion( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)))) & 99.05/14.93 (setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)) = 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset)), 99.05/14.93 emptyset))))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (in(Y1, 99.05/14.93 Y0) => 99.05/14.93 subset( 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset), 99.05/14.93 Y0)))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (in(Y1, 99.05/14.93 Y0) => 99.05/14.93 in( 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset), 99.05/14.93 powerset( 99.05/14.93 Y0))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 in( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 emptyset), 99.05/14.93 powerset( 99.05/14.93 binunion( 99.05/14.93 Y0, Y1))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y0, 99.05/14.93 setadjoin( 99.05/14.93 Y1, 99.05/14.93 emptyset))) => 99.05/14.93 (( 99.05/14.93 Y2 = Y1) | 99.05/14.93 (Y2 = Y0)))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (!!(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (in(Y3, 99.05/14.93 Y1) => 99.05/14.93 subset( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset)), 99.05/14.93 binunion( 99.05/14.93 Y0, Y1)))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (!!(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (in(Y3, 99.05/14.93 Y1) => 99.05/14.93 in( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset)), 99.05/14.93 powerset( 99.05/14.93 binunion( 99.05/14.93 Y0, Y1))))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (!!(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (in(Y3, 99.05/14.93 Y1) => 99.05/14.93 subset( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)), 99.05/14.93 powerset( 99.05/14.93 binunion( 99.05/14.93 Y0, Y1))))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (!!(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (in(Y3, 99.05/14.93 Y1) => 99.05/14.93 in( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)), 99.05/14.93 powerset( 99.05/14.93 powerset( 99.05/14.93 binunion( 99.05/14.93 Y0, Y1)))))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (!!(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (in(Y3, 99.05/14.93 Y1) => 99.05/14.93 in( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)), 99.05/14.93 powerset( 99.05/14.93 powerset( 99.05/14.93 binunion( 99.05/14.93 Y0, Y1)))))))))))))))))) => 99.05/14.93 ( 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 Y0) => 99.05/14.93 (!!(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (in(Y3, 99.05/14.93 Y1) => 99.05/14.93 in( 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y2, 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)), 99.05/14.93 dsetconstr( 99.05/14.93 powerset( 99.05/14.93 powerset( 99.05/14.93 binunion( 99.05/14.93 Y0, Y1))), 99.05/14.93 (^[Y4 : $i]: 99.05/14.93 (??(( 99.05/14.93 ^[Y5 : $i]: 99.05/14.93 (in(Y5, 99.05/14.93 Y0) & 99.05/14.93 (??(( 99.05/14.93 ^[Y6 : $i]: 99.05/14.93 (in(Y6, 99.05/14.93 Y1) & 99.05/14.93 (Y4 = 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y5, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y5, 99.05/14.93 setadjoin( 99.05/14.93 Y6, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)))))))))))))))))))))))))))) => 99.05/14.93 ( 99.05/14.93 !!(( 99.05/14.93 ^[Y0 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y1 : $i]: 99.05/14.93 (!!(( 99.05/14.93 ^[Y2 : $i]: 99.05/14.93 (in(Y2, 99.05/14.93 dsetconstr( 99.05/14.93 powerset( 99.05/14.93 powerset( 99.05/14.93 binunion( 99.05/14.93 Y0, Y1))), 99.05/14.93 (^[Y3 : $i]: 99.05/14.93 (??(( 99.05/14.93 ^[Y4 : $i]: 99.05/14.93 (in(Y4, 99.05/14.93 Y0) & 99.05/14.93 (??(( 99.05/14.93 ^[Y5 : $i]: 99.05/14.93 (in(Y5, 99.05/14.93 Y1) & 99.05/14.93 (Y3 = 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y4, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y4, 99.05/14.93 setadjoin( 99.05/14.93 Y5, 99.05/14.93 emptyset)), 99.05/14.93 emptyset)))))))))))))) => 99.05/14.93 (??(( 99.05/14.93 ^[Y3 : $i]: 99.05/14.93 (( 99.05/14.93 ??(( 99.05/14.93 ^[Y4 : $i]: 99.05/14.93 (in(Y4, 99.05/14.93 Y1) & 99.05/14.93 (Y2 = 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 emptyset), 99.05/14.93 setadjoin( 99.05/14.93 setadjoin( 99.05/14.93 Y3, 99.05/14.93 setadjoin( 99.05/14.93 Y4, 99.05/14.93 emptyset)), 99.05/14.93 emptyset))))))) & 99.05/14.93 in(Y3, 99.05/14.93 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.05/14.93 inference('lazy_cnf_imply', [status(thm)], ['211'])). 99.05/14.93 tff('213', plain, 99.05/14.93 ~ ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 ((!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2))))))) => 99.05/14.93 (~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.93 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 ((??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2))))))) => 99.05/14.93 (~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $o]: (Y0 => in(emptyset, prop2set(Y0)))))) => 99.05/14.93 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.93 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.93 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i > $o]: 99.05/14.93 ((??(Y0)) => 99.05/14.93 ((!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.93 (??((^[Y1 : $i]: 99.05/14.93 (Y0(Y1) & 99.05/14.93 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i > $o]: 99.05/14.93 ((??((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))) => 99.05/14.93 (??((^[Y1 : $i]: 99.05/14.93 (Y0(Y1) & 99.05/14.93 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((Y0 = Y1) => 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 ((Y2 = Y3) => 99.05/14.93 (in(Y2, Y0) => in(Y3, Y1)))))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((Y0 = Y1) => 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 ((Y2 = Y3) => 99.05/14.93 (in(Y2, Y0) <=> in(Y3, Y1)))))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i > $o]: 99.05/14.93 ((??((^[Y1 : $i]: 99.05/14.93 (Y0(Y1) & 99.05/14.93 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i > $o]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 ((!!((^[Y2 : $i]: 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 ((Y2 = Y3) => 99.05/14.93 (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.93 ((??((^[Y2 : $i]: 99.05/14.93 (Y0(Y2) & 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 (Y0(Y3) => (Y2 = Y3))))))))) <=> 99.05/14.93 (??((^[Y2 : $i]: 99.05/14.93 (Y1(Y2) & 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 (Y1(Y3) => (Y2 = Y3))))))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((Y0 = Y1) => 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 ((Y2 = Y3) => 99.05/14.93 (setadjoin(Y0, Y2) = 99.05/14.93 setadjoin(Y1, Y3)))))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((Y0 = Y1) => 99.05/14.93 (powerset(Y0) = powerset(Y1))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((Y0 = Y1) => 99.05/14.93 (setunion(Y0) = setunion(Y1))))))))) => 99.05/14.93 ((!!((^[Y0 : $i > $o]: 99.05/14.93 ((??((^[Y1 : $i]: 99.05/14.93 (Y0(Y1) & 99.05/14.93 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i > $o]: 99.05/14.93 (!!((^[Y1 : $i > $o]: 99.05/14.93 ((!!((^[Y2 : $i]: 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 ((Y2 = Y3) => 99.05/14.93 (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.93 ((??((^[Y2 : $i]: 99.05/14.93 (Y0(Y2) & 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 (Y0(Y3) => (Y2 = Y3))))))))) => 99.05/14.93 ((??((^[Y2 : $i]: 99.05/14.93 (Y1(Y2) & 99.05/14.93 (!!((^[Y3 : $i]: 99.05/14.93 (Y1(Y3) => (Y2 = Y3))))))))) => 99.05/14.93 (descr(Y0) = descr(Y1))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((Y0 = Y1) => 99.05/14.93 (!!((^[Y2 : $i > $o]: 99.05/14.93 (!!((^[Y3 : $i > $o]: 99.05/14.93 ((!!((^[Y4 : $i]: 99.05/14.93 (in(Y4, Y0) => 99.05/14.93 (!!((^[Y5 : $i]: 99.05/14.93 (in(Y5, 99.05/14.93 Y1) => 99.05/14.93 (( 99.05/14.93 Y4 = Y5) => 99.05/14.93 (Y2(Y4) <=> 99.05/14.93 Y3(Y5))))))))))) => 99.05/14.93 (dsetconstr(Y0, Y2) = 99.05/14.93 dsetconstr(Y1, Y3)))))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((!!((^[Y2 : $i]: 99.05/14.93 (in(Y2, Y0) => in(Y2, Y1))))) => 99.05/14.93 subset(Y0, Y1)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((Y0 = Y1) => subset(Y1, Y0)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((Y0 = Y1) => subset(Y0, Y1)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((!!((^[Y2 : $i]: 99.05/14.93 (in(Y2, Y0) => in(Y2, Y1))))) => 99.05/14.93 subset(Y0, Y1)))))))) => 99.05/14.93 ((!!(subset(emptyset))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (subset(Y0, Y1) => 99.05/14.93 (in(Y2, Y0) => 99.05/14.93 in(Y2, Y1)))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (subset(Y0, Y1) => 99.05/14.93 ((~(in(Y2, Y1))) => 99.05/14.93 (~(in(Y2, Y0)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (in(Y2, Y0) => 99.05/14.93 ((~(in(Y2, Y1))) => 99.05/14.93 (~(subset(Y0, Y1)))))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 ((~(subset(Y0, Y1))) => 99.05/14.93 (Y0 != Y1)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (in(Y2, Y0) => 99.05/14.93 ((~(in(Y2, Y1))) => 99.05/14.93 (Y0 != Y1)))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (subset(Y0, Y1) => 99.05/14.93 (subset(Y1, Y2) => 99.05/14.93 subset(Y0, Y2)))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 subset(Y1, 99.05/14.93 setadjoin(Y0, Y1)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (!!((^[Y2 : $i]: 99.05/14.93 (subset(Y0, Y2) => 99.05/14.93 subset(Y0, 99.05/14.93 setadjoin(Y1, 99.05/14.93 Y2)))))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (subset(Y0, Y1) => 99.05/14.93 in(Y0, powerset(Y1))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (subset(Y0, Y1) => 99.05/14.93 (subset(Y1, Y0) => 99.05/14.93 (Y0 = Y1))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (subset(Y0, emptyset) => 99.05/14.93 (Y0 = emptyset))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (subset(Y1, Y0) => 99.05/14.93 in(Y1, 99.05/14.93 powerset(Y0))))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (in(Y1, 99.05/14.93 powerset(Y0)) => 99.05/14.93 subset(Y1, Y0)))))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 in(Y0, powerset(Y0))))) => 99.05/14.93 ((!!((^[Y0 : $i]: 99.05/14.93 (!!((^[Y1 : $i]: 99.05/14.93 (subset(Y0, Y1) => 99.05/14.94 subset( 99.05/14.94 powerset(Y0), 99.05/14.94 powerset(Y1))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i > $o]: 99.05/14.94 in( 99.05/14.94 dsetconstr( 99.05/14.94 Y0, Y1), 99.05/14.94 powerset(Y0)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i > $o]: 99.05/14.94 subset( 99.05/14.94 dsetconstr( 99.05/14.94 Y0, Y1), 99.05/14.94 Y0))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 in(Y2, 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 in(Y1, 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 ( 99.05/14.94 in(Y2, 99.05/14.94 Y1) => 99.05/14.94 in(Y2, 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y3 : $o]: 99.05/14.94 (in(Y2, 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)) => 99.05/14.94 (( 99.05/14.94 in(Y2, 99.05/14.94 Y0) => Y3) => 99.05/14.94 (( 99.05/14.94 in(Y2, 99.05/14.94 Y1) => Y3) => 99.05/14.94 Y3))))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)) => 99.05/14.94 (in(Y2, 99.05/14.94 Y1) | 99.05/14.94 in(Y2, 99.05/14.94 Y0)))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 subset( 99.05/14.94 Y0, 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 subset( 99.05/14.94 Y1, 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (in(Y2, 99.05/14.94 Y1) => 99.05/14.94 in(Y2, 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (subset( 99.05/14.94 Y2, Y0) => 99.05/14.94 (subset( 99.05/14.94 Y2, Y1) => 99.05/14.94 subset( 99.05/14.94 Y2, 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1)) => 99.05/14.94 in(Y2, 99.05/14.94 Y0))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 subset( 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1), 99.05/14.94 Y0))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (subset( 99.05/14.94 Y0, Y1) => 99.05/14.94 (binintersect( 99.05/14.94 Y0, Y1) = 99.05/14.94 Y0)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (( 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1) = 99.05/14.94 Y1) => 99.05/14.94 subset( 99.05/14.94 Y1, Y0)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1)) => 99.05/14.94 in(Y2, 99.05/14.94 Y1))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (( 99.05/14.94 ~(( 99.05/14.94 ??(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) & 99.05/14.94 in(Y2, 99.05/14.94 Y1))))))) => 99.05/14.94 (binintersect( 99.05/14.94 Y0, Y1) = 99.05/14.94 emptyset)))))))) => 99.05/14.94 ((!!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 subset( 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1), 99.05/14.94 Y1))))))) => 99.05/14.94 ((!!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (subset( 99.05/14.94 Y1, Y0) => 99.05/14.94 (binintersect( 99.05/14.94 Y0, Y1) = 99.05/14.94 Y1)))))))) => 99.05/14.94 ((!!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (( 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1) = 99.05/14.94 Y0) => 99.05/14.94 subset( 99.05/14.94 Y0, Y1)))))))) => 99.05/14.94 ((!!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (binintersect( 99.05/14.94 Y0, 99.05/14.94 binunion( 99.05/14.94 Y1, Y2)) = 99.05/14.94 binunion( 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1), 99.05/14.94 binintersect( 99.05/14.94 Y0, Y2)))))))))))) => 99.05/14.94 (( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y1))) => 99.05/14.94 in(Y2, 99.05/14.94 setminus( 99.05/14.94 Y0, Y1))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 setminus( 99.05/14.94 Y0, Y1)) => 99.05/14.94 in(Y2, 99.05/14.94 Y0))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 setminus( 99.05/14.94 Y0, Y1)) => 99.05/14.94 (~( 99.05/14.94 in(Y2, 99.05/14.94 Y1))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (subset( 99.05/14.94 Y0, Y1) => 99.05/14.94 (setminus( 99.05/14.94 Y0, Y1) = 99.05/14.94 emptyset)))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 setminus( 99.05/14.94 Y0, Y1)))) => 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 in(Y2, 99.05/14.94 Y1)))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 setminus( 99.05/14.94 Y0, Y1)))) => 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y1))) => 99.05/14.94 (~( 99.05/14.94 in(Y2, 99.05/14.94 Y0)))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y0))) => 99.05/14.94 (~( 99.05/14.94 in(Y2, 99.05/14.94 setminus( 99.05/14.94 Y0, Y1)))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y1) => 99.05/14.94 (~( 99.05/14.94 in(Y2, 99.05/14.94 setminus( 99.05/14.94 Y0, Y1)))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 subset( 99.05/14.94 setminus( 99.05/14.94 Y0, Y1), 99.05/14.94 Y0))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (( 99.05/14.94 setminus( 99.05/14.94 Y0, Y1) = 99.05/14.94 emptyset) => 99.05/14.94 subset( 99.05/14.94 Y0, Y1)))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 symdiff( 99.05/14.94 Y0, Y1)) => 99.05/14.94 (!!(( 99.05/14.94 ^[Y3 : $o]: 99.05/14.94 (( 99.05/14.94 in(Y2, 99.05/14.94 Y0) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y1))) => 99.05/14.94 Y3)) => 99.05/14.94 (( 99.05/14.94 ( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y0))) => 99.05/14.94 ( 99.05/14.94 in(Y2, 99.05/14.94 Y1) => Y3)) => 99.05/14.94 Y3))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y1))) => 99.05/14.94 in(Y2, 99.05/14.94 symdiff( 99.05/14.94 Y0, Y1))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y0))) => 99.05/14.94 (in(Y2, 99.05/14.94 Y1) => 99.05/14.94 in(Y2, 99.05/14.94 symdiff( 99.05/14.94 Y0, Y1))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (in(Y2, 99.05/14.94 Y1) => 99.05/14.94 (~( 99.05/14.94 in(Y2, 99.05/14.94 symdiff( 99.05/14.94 Y0, Y1))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y0))) => 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y1))) => 99.05/14.94 (~( 99.05/14.94 in(Y2, 99.05/14.94 symdiff( 99.05/14.94 Y0, Y1))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 in(Y1, 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 in(Y0, 99.05/14.94 setunion( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 in(Y1, 99.05/14.94 setunion( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (??(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 setunion( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)))) & 99.05/14.94 (??(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (in(Y3, 99.05/14.94 setunion( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)))) & 99.05/14.94 (setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)) = 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset)), 99.05/14.94 emptyset))))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (??(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 setunion( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)))) & 99.05/14.94 (??(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (in(Y3, 99.05/14.94 setunion( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)))) & 99.05/14.94 (setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)) = 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset)), 99.05/14.94 emptyset))))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (in(Y1, 99.05/14.94 Y0) => 99.05/14.94 subset( 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset), 99.05/14.94 Y0)))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (in(Y1, 99.05/14.94 Y0) => 99.05/14.94 in( 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset), 99.05/14.94 powerset( 99.05/14.94 Y0))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 in( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 emptyset), 99.05/14.94 powerset( 99.05/14.94 binunion( 99.05/14.94 Y0, Y1))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset))) => 99.05/14.94 (( 99.05/14.94 Y2 = Y1) | 99.05/14.94 (Y2 = Y0)))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (!!(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (in(Y3, 99.05/14.94 Y1) => 99.05/14.94 subset( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset)), 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (!!(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (in(Y3, 99.05/14.94 Y1) => 99.05/14.94 in( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset)), 99.05/14.94 powerset( 99.05/14.94 binunion( 99.05/14.94 Y0, Y1))))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (!!(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (in(Y3, 99.05/14.94 Y1) => 99.05/14.94 subset( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)), 99.05/14.94 powerset( 99.05/14.94 binunion( 99.05/14.94 Y0, Y1))))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (!!(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (in(Y3, 99.05/14.94 Y1) => 99.05/14.94 in( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)), 99.05/14.94 powerset( 99.05/14.94 powerset( 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)))))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (!!(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (in(Y3, 99.05/14.94 Y1) => 99.05/14.94 in( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)), 99.05/14.94 powerset( 99.05/14.94 powerset( 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)))))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (!!(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (in(Y3, 99.05/14.94 Y1) => 99.05/14.94 in( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)), 99.05/14.94 dsetconstr( 99.05/14.94 powerset( 99.05/14.94 powerset( 99.05/14.94 binunion( 99.05/14.94 Y0, Y1))), 99.05/14.94 (^[Y4 : $i]: 99.05/14.94 (??(( 99.05/14.94 ^[Y5 : $i]: 99.05/14.94 (in(Y5, 99.05/14.94 Y0) & 99.05/14.94 (??(( 99.05/14.94 ^[Y6 : $i]: 99.05/14.94 (in(Y6, 99.05/14.94 Y1) & 99.05/14.94 (Y4 = 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y5, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y5, 99.05/14.94 setadjoin( 99.05/14.94 Y6, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)))))))))))))))))))))))))))) => 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 dsetconstr( 99.05/14.94 powerset( 99.05/14.94 powerset( 99.05/14.94 binunion( 99.05/14.94 Y0, Y1))), 99.05/14.94 (^[Y3 : $i]: 99.05/14.94 (??(( 99.05/14.94 ^[Y4 : $i]: 99.05/14.94 (in(Y4, 99.05/14.94 Y0) & 99.05/14.94 (??(( 99.05/14.94 ^[Y5 : $i]: 99.05/14.94 (in(Y5, 99.05/14.94 Y1) & 99.05/14.94 (Y3 = 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y4, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y4, 99.05/14.94 setadjoin( 99.05/14.94 Y5, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)))))))))))))) => 99.05/14.94 (??(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (( 99.05/14.94 ??(( 99.05/14.94 ^[Y4 : $i]: 99.05/14.94 (in(Y4, 99.05/14.94 Y1) & 99.05/14.94 (Y2 = 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 setadjoin( 99.05/14.94 Y4, 99.05/14.94 emptyset)), 99.05/14.94 emptyset))))))) & 99.05/14.94 in(Y3, 99.05/14.94 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.05/14.94 inference('lazy_cnf_imply', [status(thm)], ['212'])). 99.05/14.94 tff('214', plain, 99.05/14.94 ~ ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i > $o]: 99.05/14.94 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.94 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i > $o]: 99.05/14.94 ((??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2))))))) => 99.05/14.94 (~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2)))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $o]: (Y0 => in(emptyset, prop2set(Y0)))))) => 99.05/14.94 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i > $o]: 99.05/14.94 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.94 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i > $o]: 99.05/14.94 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.94 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i > $o]: 99.05/14.94 ((??(Y0)) => 99.05/14.94 ((!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.94 (??((^[Y1 : $i]: 99.05/14.94 (Y0(Y1) & 99.05/14.94 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2)))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i > $o]: 99.05/14.94 ((??((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))) => 99.05/14.94 (??((^[Y1 : $i]: 99.05/14.94 (Y0(Y1) & 99.05/14.94 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((Y0 = Y1) => 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (!!((^[Y3 : $i]: 99.05/14.94 ((Y2 = Y3) => 99.05/14.94 (in(Y2, Y0) => in(Y3, Y1)))))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((Y0 = Y1) => 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (!!((^[Y3 : $i]: 99.05/14.94 ((Y2 = Y3) => 99.05/14.94 (in(Y2, Y0) <=> in(Y3, Y1)))))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i > $o]: 99.05/14.94 ((??((^[Y1 : $i]: 99.05/14.94 (Y0(Y1) & 99.05/14.94 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i > $o]: 99.05/14.94 (!!((^[Y1 : $i > $o]: 99.05/14.94 ((!!((^[Y2 : $i]: 99.05/14.94 (!!((^[Y3 : $i]: 99.05/14.94 ((Y2 = Y3) => 99.05/14.94 (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.94 ((??((^[Y2 : $i]: 99.05/14.94 (Y0(Y2) & 99.05/14.94 (!!((^[Y3 : $i]: 99.05/14.94 (Y0(Y3) => (Y2 = Y3))))))))) <=> 99.05/14.94 (??((^[Y2 : $i]: 99.05/14.94 (Y1(Y2) & 99.05/14.94 (!!((^[Y3 : $i]: 99.05/14.94 (Y1(Y3) => (Y2 = Y3))))))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((Y0 = Y1) => 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (!!((^[Y3 : $i]: 99.05/14.94 ((Y2 = Y3) => 99.05/14.94 (setadjoin(Y0, Y2) = 99.05/14.94 setadjoin(Y1, Y3)))))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((Y0 = Y1) => (powerset(Y0) = powerset(Y1))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((Y0 = Y1) => 99.05/14.94 (setunion(Y0) = setunion(Y1))))))))) => 99.05/14.94 ((!!((^[Y0 : $i > $o]: 99.05/14.94 ((??((^[Y1 : $i]: 99.05/14.94 (Y0(Y1) & 99.05/14.94 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i > $o]: 99.05/14.94 (!!((^[Y1 : $i > $o]: 99.05/14.94 ((!!((^[Y2 : $i]: 99.05/14.94 (!!((^[Y3 : $i]: 99.05/14.94 ((Y2 = Y3) => 99.05/14.94 (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.94 ((??((^[Y2 : $i]: 99.05/14.94 (Y0(Y2) & 99.05/14.94 (!!((^[Y3 : $i]: 99.05/14.94 (Y0(Y3) => (Y2 = Y3))))))))) => 99.05/14.94 ((??((^[Y2 : $i]: 99.05/14.94 (Y1(Y2) & 99.05/14.94 (!!((^[Y3 : $i]: 99.05/14.94 (Y1(Y3) => (Y2 = Y3))))))))) => 99.05/14.94 (descr(Y0) = descr(Y1))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((Y0 = Y1) => 99.05/14.94 (!!((^[Y2 : $i > $o]: 99.05/14.94 (!!((^[Y3 : $i > $o]: 99.05/14.94 ((!!((^[Y4 : $i]: 99.05/14.94 (in(Y4, Y0) => 99.05/14.94 (!!((^[Y5 : $i]: 99.05/14.94 (in(Y5, 99.05/14.94 Y1) => 99.05/14.94 (( 99.05/14.94 Y4 = Y5) => 99.05/14.94 (Y2(Y4) <=> 99.05/14.94 Y3(Y5))))))))))) => 99.05/14.94 (dsetconstr(Y0, Y2) = 99.05/14.94 dsetconstr(Y1, Y3)))))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((!!((^[Y2 : $i]: 99.05/14.94 (in(Y2, Y0) => in(Y2, Y1))))) => 99.05/14.94 subset(Y0, Y1)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((Y0 = Y1) => subset(Y1, Y0)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((Y0 = Y1) => subset(Y0, Y1)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((!!((^[Y2 : $i]: 99.05/14.94 (in(Y2, Y0) => in(Y2, Y1))))) => 99.05/14.94 subset(Y0, Y1)))))))) => 99.05/14.94 ((!!(subset(emptyset))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (subset(Y0, Y1) => 99.05/14.94 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (subset(Y0, Y1) => 99.05/14.94 ((~(in(Y2, Y1))) => 99.05/14.94 (~(in(Y2, Y0)))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (in(Y2, Y0) => 99.05/14.94 ((~(in(Y2, Y1))) => 99.05/14.94 (~(subset(Y0, Y1)))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((~(subset(Y0, Y1))) => 99.05/14.94 (Y0 != Y1)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (in(Y2, Y0) => 99.05/14.94 ((~(in(Y2, Y1))) => 99.05/14.94 (Y0 != Y1)))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (subset(Y0, Y1) => 99.05/14.94 (subset(Y1, Y2) => 99.05/14.94 subset(Y0, Y2)))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 subset(Y1, 99.05/14.94 setadjoin(Y0, Y1)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (subset(Y0, Y2) => 99.05/14.94 subset(Y0, 99.05/14.94 setadjoin(Y1, 99.05/14.94 Y2)))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (subset(Y0, Y1) => 99.05/14.94 in(Y0, powerset(Y1))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (subset(Y0, Y1) => 99.05/14.94 (subset(Y1, Y0) => 99.05/14.94 (Y0 = Y1))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (subset(Y0, emptyset) => 99.05/14.94 (Y0 = emptyset))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (subset(Y1, Y0) => 99.05/14.94 in(Y1, powerset(Y0))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (in(Y1, 99.05/14.94 powerset(Y0)) => 99.05/14.94 subset(Y1, Y0)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 in(Y0, powerset(Y0))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (subset(Y0, Y1) => 99.05/14.94 subset( 99.05/14.94 powerset(Y0), 99.05/14.94 powerset(Y1))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i > $o]: 99.05/14.94 in( 99.05/14.94 dsetconstr(Y0, 99.05/14.94 Y1), 99.05/14.94 powerset(Y0)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i > $o]: 99.05/14.94 subset( 99.05/14.94 dsetconstr( 99.05/14.94 Y0, Y1), Y0))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 in(Y2, 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 in(Y1, 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y1) => 99.05/14.94 in(Y2, 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y3 : $o]: 99.05/14.94 (in(Y2, 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)) => 99.05/14.94 (( 99.05/14.94 in(Y2, 99.05/14.94 Y0) => Y3) => 99.05/14.94 (( 99.05/14.94 in(Y2, 99.05/14.94 Y1) => Y3) => 99.05/14.94 Y3))))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)) => 99.05/14.94 (in(Y2, 99.05/14.94 Y1) | 99.05/14.94 in(Y2, 99.05/14.94 Y0)))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 subset( 99.05/14.94 Y0, 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 subset( 99.05/14.94 Y1, 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (in(Y2, 99.05/14.94 Y1) => 99.05/14.94 in(Y2, 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (subset( 99.05/14.94 Y2, Y0) => 99.05/14.94 (subset( 99.05/14.94 Y2, Y1) => 99.05/14.94 subset( 99.05/14.94 Y2, 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1)) => 99.05/14.94 in(Y2, 99.05/14.94 Y0))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 subset( 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1), 99.05/14.94 Y0))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (subset( 99.05/14.94 Y0, Y1) => 99.05/14.94 (binintersect( 99.05/14.94 Y0, Y1) = 99.05/14.94 Y0)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (( 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1) = 99.05/14.94 Y1) => 99.05/14.94 subset( 99.05/14.94 Y1, Y0)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1)) => 99.05/14.94 in(Y2, 99.05/14.94 Y1))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (( 99.05/14.94 ~(( 99.05/14.94 ??(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) & 99.05/14.94 in(Y2, 99.05/14.94 Y1))))))) => 99.05/14.94 (binintersect( 99.05/14.94 Y0, Y1) = 99.05/14.94 emptyset)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 subset( 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1), 99.05/14.94 Y1))))))) => 99.05/14.94 ((!!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (subset( 99.05/14.94 Y1, Y0) => 99.05/14.94 (binintersect( 99.05/14.94 Y0, Y1) = 99.05/14.94 Y1)))))))) => 99.05/14.94 ((!!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (( 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1) = 99.05/14.94 Y0) => 99.05/14.94 subset( 99.05/14.94 Y0, Y1)))))))) => 99.05/14.94 ((!!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (binintersect( 99.05/14.94 Y0, 99.05/14.94 binunion( 99.05/14.94 Y1, Y2)) = 99.05/14.94 binunion( 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1), 99.05/14.94 binintersect( 99.05/14.94 Y0, Y2)))))))))))) => 99.05/14.94 ((!!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y1))) => 99.05/14.94 in(Y2, 99.05/14.94 setminus( 99.05/14.94 Y0, Y1))))))))))))) => 99.05/14.94 (( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 setminus( 99.05/14.94 Y0, Y1)) => 99.05/14.94 in(Y2, 99.05/14.94 Y0))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 setminus( 99.05/14.94 Y0, Y1)) => 99.05/14.94 (~( 99.05/14.94 in(Y2, 99.05/14.94 Y1))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (subset( 99.05/14.94 Y0, Y1) => 99.05/14.94 (setminus( 99.05/14.94 Y0, Y1) = 99.05/14.94 emptyset)))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 setminus( 99.05/14.94 Y0, Y1)))) => 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 in(Y2, 99.05/14.94 Y1)))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 setminus( 99.05/14.94 Y0, Y1)))) => 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y1))) => 99.05/14.94 (~( 99.05/14.94 in(Y2, 99.05/14.94 Y0)))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y0))) => 99.05/14.94 (~( 99.05/14.94 in(Y2, 99.05/14.94 setminus( 99.05/14.94 Y0, Y1)))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y1) => 99.05/14.94 (~( 99.05/14.94 in(Y2, 99.05/14.94 setminus( 99.05/14.94 Y0, Y1)))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 subset( 99.05/14.94 setminus( 99.05/14.94 Y0, Y1), 99.05/14.94 Y0))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (( 99.05/14.94 setminus( 99.05/14.94 Y0, Y1) = 99.05/14.94 emptyset) => 99.05/14.94 subset( 99.05/14.94 Y0, Y1)))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 symdiff( 99.05/14.94 Y0, Y1)) => 99.05/14.94 (!!(( 99.05/14.94 ^[Y3 : $o]: 99.05/14.94 (( 99.05/14.94 in(Y2, 99.05/14.94 Y0) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y1))) => 99.05/14.94 Y3)) => 99.05/14.94 (( 99.05/14.94 ( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y0))) => 99.05/14.94 ( 99.05/14.94 in(Y2, 99.05/14.94 Y1) => Y3)) => 99.05/14.94 Y3))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y1))) => 99.05/14.94 in(Y2, 99.05/14.94 symdiff( 99.05/14.94 Y0, Y1))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y0))) => 99.05/14.94 (in(Y2, 99.05/14.94 Y1) => 99.05/14.94 in(Y2, 99.05/14.94 symdiff( 99.05/14.94 Y0, Y1))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (in(Y2, 99.05/14.94 Y1) => 99.05/14.94 (~( 99.05/14.94 in(Y2, 99.05/14.94 symdiff( 99.05/14.94 Y0, Y1))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y0))) => 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y1))) => 99.05/14.94 (~( 99.05/14.94 in(Y2, 99.05/14.94 symdiff( 99.05/14.94 Y0, Y1))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 in(Y1, 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 in(Y0, 99.05/14.94 setunion( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 in(Y1, 99.05/14.94 setunion( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (??(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 setunion( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)))) & 99.05/14.94 (??(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (in(Y3, 99.05/14.94 setunion( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)))) & 99.05/14.94 (setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)) = 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset)), 99.05/14.94 emptyset))))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (??(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 setunion( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)))) & 99.05/14.94 (??(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (in(Y3, 99.05/14.94 setunion( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)))) & 99.05/14.94 (setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)) = 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset)), 99.05/14.94 emptyset))))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (in(Y1, 99.05/14.94 Y0) => 99.05/14.94 subset( 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset), 99.05/14.94 Y0)))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (in(Y1, 99.05/14.94 Y0) => 99.05/14.94 in( 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset), 99.05/14.94 powerset( 99.05/14.94 Y0))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 in( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 emptyset), 99.05/14.94 powerset( 99.05/14.94 binunion( 99.05/14.94 Y0, Y1))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset))) => 99.05/14.94 (( 99.05/14.94 Y2 = Y1) | 99.05/14.94 (Y2 = Y0)))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (!!(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (in(Y3, 99.05/14.94 Y1) => 99.05/14.94 subset( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset)), 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (!!(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (in(Y3, 99.05/14.94 Y1) => 99.05/14.94 in( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset)), 99.05/14.94 powerset( 99.05/14.94 binunion( 99.05/14.94 Y0, Y1))))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (!!(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (in(Y3, 99.05/14.94 Y1) => 99.05/14.94 subset( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)), 99.05/14.94 powerset( 99.05/14.94 binunion( 99.05/14.94 Y0, Y1))))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (!!(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (in(Y3, 99.05/14.94 Y1) => 99.05/14.94 in( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)), 99.05/14.94 powerset( 99.05/14.94 powerset( 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)))))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (!!(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (in(Y3, 99.05/14.94 Y1) => 99.05/14.94 in( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)), 99.05/14.94 powerset( 99.05/14.94 powerset( 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)))))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (!!(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (in(Y3, 99.05/14.94 Y1) => 99.05/14.94 in( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)), 99.05/14.94 dsetconstr( 99.05/14.94 powerset( 99.05/14.94 powerset( 99.05/14.94 binunion( 99.05/14.94 Y0, Y1))), 99.05/14.94 (^[Y4 : $i]: 99.05/14.94 (??(( 99.05/14.94 ^[Y5 : $i]: 99.05/14.94 (in(Y5, 99.05/14.94 Y0) & 99.05/14.94 (??(( 99.05/14.94 ^[Y6 : $i]: 99.05/14.94 (in(Y6, 99.05/14.94 Y1) & 99.05/14.94 (Y4 = 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y5, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y5, 99.05/14.94 setadjoin( 99.05/14.94 Y6, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)))))))))))))))))))))))))))) => 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 dsetconstr( 99.05/14.94 powerset( 99.05/14.94 powerset( 99.05/14.94 binunion( 99.05/14.94 Y0, Y1))), 99.05/14.94 (^[Y3 : $i]: 99.05/14.94 (??(( 99.05/14.94 ^[Y4 : $i]: 99.05/14.94 (in(Y4, 99.05/14.94 Y0) & 99.05/14.94 (??(( 99.05/14.94 ^[Y5 : $i]: 99.05/14.94 (in(Y5, 99.05/14.94 Y1) & 99.05/14.94 (Y3 = 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y4, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y4, 99.05/14.94 setadjoin( 99.05/14.94 Y5, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)))))))))))))) => 99.05/14.94 (??(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (( 99.05/14.94 ??(( 99.05/14.94 ^[Y4 : $i]: 99.05/14.94 (in(Y4, 99.05/14.94 Y1) & 99.05/14.94 (Y2 = 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 setadjoin( 99.05/14.94 Y4, 99.05/14.94 emptyset)), 99.05/14.94 emptyset))))))) & 99.05/14.94 in(Y3, 99.05/14.94 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.05/14.94 inference('lazy_cnf_imply', [status(thm)], ['213'])). 99.05/14.94 tff('215', plain, 99.05/14.94 ~ ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i > $o]: 99.05/14.94 ((??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2))))))) => 99.05/14.94 (~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2)))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $o]: (Y0 => in(emptyset, prop2set(Y0)))))) => 99.05/14.94 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i > $o]: 99.05/14.94 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.94 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i > $o]: 99.05/14.94 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.94 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i > $o]: 99.05/14.94 ((??(Y0)) => 99.05/14.94 ((!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.94 (??((^[Y1 : $i]: 99.05/14.94 (Y0(Y1) & 99.05/14.94 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2)))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i > $o]: 99.05/14.94 ((??((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))) => 99.05/14.94 (??((^[Y1 : $i]: 99.05/14.94 (Y0(Y1) & 99.05/14.94 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((Y0 = Y1) => 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (!!((^[Y3 : $i]: 99.05/14.94 ((Y2 = Y3) => 99.05/14.94 (in(Y2, Y0) => in(Y3, Y1)))))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((Y0 = Y1) => 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (!!((^[Y3 : $i]: 99.05/14.94 ((Y2 = Y3) => 99.05/14.94 (in(Y2, Y0) <=> in(Y3, Y1)))))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i > $o]: 99.05/14.94 ((??((^[Y1 : $i]: 99.05/14.94 (Y0(Y1) & 99.05/14.94 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i > $o]: 99.05/14.94 (!!((^[Y1 : $i > $o]: 99.05/14.94 ((!!((^[Y2 : $i]: 99.05/14.94 (!!((^[Y3 : $i]: 99.05/14.94 ((Y2 = Y3) => 99.05/14.94 (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.94 ((??((^[Y2 : $i]: 99.05/14.94 (Y0(Y2) & 99.05/14.94 (!!((^[Y3 : $i]: 99.05/14.94 (Y0(Y3) => (Y2 = Y3))))))))) <=> 99.05/14.94 (??((^[Y2 : $i]: 99.05/14.94 (Y1(Y2) & 99.05/14.94 (!!((^[Y3 : $i]: 99.05/14.94 (Y1(Y3) => (Y2 = Y3))))))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((Y0 = Y1) => 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (!!((^[Y3 : $i]: 99.05/14.94 ((Y2 = Y3) => 99.05/14.94 (setadjoin(Y0, Y2) = 99.05/14.94 setadjoin(Y1, Y3)))))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((Y0 = Y1) => (powerset(Y0) = powerset(Y1))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((Y0 = Y1) => (setunion(Y0) = setunion(Y1))))))))) => 99.05/14.94 ((!!((^[Y0 : $i > $o]: 99.05/14.94 ((??((^[Y1 : $i]: 99.05/14.94 (Y0(Y1) & 99.05/14.94 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i > $o]: 99.05/14.94 (!!((^[Y1 : $i > $o]: 99.05/14.94 ((!!((^[Y2 : $i]: 99.05/14.94 (!!((^[Y3 : $i]: 99.05/14.94 ((Y2 = Y3) => 99.05/14.94 (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.94 ((??((^[Y2 : $i]: 99.05/14.94 (Y0(Y2) & 99.05/14.94 (!!((^[Y3 : $i]: 99.05/14.94 (Y0(Y3) => (Y2 = Y3))))))))) => 99.05/14.94 ((??((^[Y2 : $i]: 99.05/14.94 (Y1(Y2) & 99.05/14.94 (!!((^[Y3 : $i]: 99.05/14.94 (Y1(Y3) => (Y2 = Y3))))))))) => 99.05/14.94 (descr(Y0) = descr(Y1))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((Y0 = Y1) => 99.05/14.94 (!!((^[Y2 : $i > $o]: 99.05/14.94 (!!((^[Y3 : $i > $o]: 99.05/14.94 ((!!((^[Y4 : $i]: 99.05/14.94 (in(Y4, Y0) => 99.05/14.94 (!!((^[Y5 : $i]: 99.05/14.94 ( 99.05/14.94 in(Y5, 99.05/14.94 Y1) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 Y4 = Y5) => 99.05/14.94 ( 99.05/14.94 Y2(Y4) <=> 99.05/14.94 Y3(Y5))))))))))) => 99.05/14.94 (dsetconstr(Y0, Y2) = 99.05/14.94 dsetconstr(Y1, Y3)))))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((!!((^[Y2 : $i]: 99.05/14.94 (in(Y2, Y0) => in(Y2, Y1))))) => 99.05/14.94 subset(Y0, Y1)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((Y0 = Y1) => subset(Y1, Y0)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((Y0 = Y1) => subset(Y0, Y1)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((!!((^[Y2 : $i]: 99.05/14.94 (in(Y2, Y0) => in(Y2, Y1))))) => 99.05/14.94 subset(Y0, Y1)))))))) => 99.05/14.94 ((!!(subset(emptyset))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (subset(Y0, Y1) => 99.05/14.94 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (subset(Y0, Y1) => 99.05/14.94 ((~(in(Y2, Y1))) => 99.05/14.94 (~(in(Y2, Y0)))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (in(Y2, Y0) => 99.05/14.94 ((~(in(Y2, Y1))) => 99.05/14.94 (~(subset(Y0, Y1)))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((~(subset(Y0, Y1))) => 99.05/14.94 (Y0 != Y1)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (in(Y2, Y0) => 99.05/14.94 ((~(in(Y2, Y1))) => 99.05/14.94 (Y0 != Y1)))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (subset(Y0, Y1) => 99.05/14.94 (subset(Y1, Y2) => 99.05/14.94 subset(Y0, Y2)))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 subset(Y1, 99.05/14.94 setadjoin(Y0, Y1)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (subset(Y0, Y2) => 99.05/14.94 subset(Y0, 99.05/14.94 setadjoin(Y1, 99.05/14.94 Y2)))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (subset(Y0, Y1) => 99.05/14.94 in(Y0, powerset(Y1))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (subset(Y0, Y1) => 99.05/14.94 (subset(Y1, Y0) => 99.05/14.94 (Y0 = Y1))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (subset(Y0, emptyset) => 99.05/14.94 (Y0 = emptyset))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (subset(Y1, Y0) => 99.05/14.94 in(Y1, powerset(Y0))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (in(Y1, powerset(Y0)) => 99.05/14.94 subset(Y1, Y0)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 in(Y0, powerset(Y0))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (subset(Y0, Y1) => 99.05/14.94 subset( 99.05/14.94 powerset(Y0), 99.05/14.94 powerset(Y1))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i > $o]: 99.05/14.94 in( 99.05/14.94 dsetconstr(Y0, 99.05/14.94 Y1), 99.05/14.94 powerset(Y0)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i > $o]: 99.05/14.94 subset( 99.05/14.94 dsetconstr(Y0, 99.05/14.94 Y1), Y0))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 ( 99.05/14.94 in(Y2, 99.05/14.94 Y0) => 99.05/14.94 in(Y2, 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 in(Y1, 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y1) => 99.05/14.94 in(Y2, 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y3 : $o]: 99.05/14.94 (in(Y2, 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)) => 99.05/14.94 (( 99.05/14.94 in(Y2, 99.05/14.94 Y0) => Y3) => 99.05/14.94 (( 99.05/14.94 in(Y2, 99.05/14.94 Y1) => Y3) => 99.05/14.94 Y3))))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 ( 99.05/14.94 in(Y2, 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)) => 99.05/14.94 ( 99.05/14.94 in(Y2, 99.05/14.94 Y1) | 99.05/14.94 in(Y2, 99.05/14.94 Y0)))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 subset(Y0, 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 subset( 99.05/14.94 Y1, 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (in(Y2, 99.05/14.94 Y1) => 99.05/14.94 in(Y2, 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (subset( 99.05/14.94 Y2, Y0) => 99.05/14.94 (subset( 99.05/14.94 Y2, Y1) => 99.05/14.94 subset( 99.05/14.94 Y2, 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1)) => 99.05/14.94 in(Y2, 99.05/14.94 Y0))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 subset( 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1), 99.05/14.94 Y0))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 ( 99.05/14.94 subset( 99.05/14.94 Y0, Y1) => 99.05/14.94 ( 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1) = 99.05/14.94 Y0)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (( 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1) = 99.05/14.94 Y1) => 99.05/14.94 subset( 99.05/14.94 Y1, Y0)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1)) => 99.05/14.94 in(Y2, 99.05/14.94 Y1))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (( 99.05/14.94 ~(( 99.05/14.94 ??(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) & 99.05/14.94 in(Y2, 99.05/14.94 Y1))))))) => 99.05/14.94 (binintersect( 99.05/14.94 Y0, Y1) = 99.05/14.94 emptyset)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 subset( 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1), 99.05/14.94 Y1))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (subset( 99.05/14.94 Y1, Y0) => 99.05/14.94 (binintersect( 99.05/14.94 Y0, Y1) = 99.05/14.94 Y1)))))))) => 99.05/14.94 ((!!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (( 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1) = 99.05/14.94 Y0) => 99.05/14.94 subset( 99.05/14.94 Y0, Y1)))))))) => 99.05/14.94 ((!!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (binintersect( 99.05/14.94 Y0, 99.05/14.94 binunion( 99.05/14.94 Y1, Y2)) = 99.05/14.94 binunion( 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1), 99.05/14.94 binintersect( 99.05/14.94 Y0, Y2)))))))))))) => 99.05/14.94 ((!!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y1))) => 99.05/14.94 in(Y2, 99.05/14.94 setminus( 99.05/14.94 Y0, Y1))))))))))))) => 99.05/14.94 ((!!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 setminus( 99.05/14.94 Y0, Y1)) => 99.05/14.94 in(Y2, 99.05/14.94 Y0))))))))))) => 99.05/14.94 (( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 setminus( 99.05/14.94 Y0, Y1)) => 99.05/14.94 (~( 99.05/14.94 in(Y2, 99.05/14.94 Y1))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (subset( 99.05/14.94 Y0, Y1) => 99.05/14.94 (setminus( 99.05/14.94 Y0, Y1) = 99.05/14.94 emptyset)))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 setminus( 99.05/14.94 Y0, Y1)))) => 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 in(Y2, 99.05/14.94 Y1)))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 setminus( 99.05/14.94 Y0, Y1)))) => 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y1))) => 99.05/14.94 (~( 99.05/14.94 in(Y2, 99.05/14.94 Y0)))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y0))) => 99.05/14.94 (~( 99.05/14.94 in(Y2, 99.05/14.94 setminus( 99.05/14.94 Y0, Y1)))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y1) => 99.05/14.94 (~( 99.05/14.94 in(Y2, 99.05/14.94 setminus( 99.05/14.94 Y0, Y1)))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 subset( 99.05/14.94 setminus( 99.05/14.94 Y0, Y1), 99.05/14.94 Y0))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (( 99.05/14.94 setminus( 99.05/14.94 Y0, Y1) = 99.05/14.94 emptyset) => 99.05/14.94 subset( 99.05/14.94 Y0, Y1)))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 symdiff( 99.05/14.94 Y0, Y1)) => 99.05/14.94 (!!(( 99.05/14.94 ^[Y3 : $o]: 99.05/14.94 (( 99.05/14.94 in(Y2, 99.05/14.94 Y0) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y1))) => 99.05/14.94 Y3)) => 99.05/14.94 (( 99.05/14.94 ( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y0))) => 99.05/14.94 ( 99.05/14.94 in(Y2, 99.05/14.94 Y1) => Y3)) => 99.05/14.94 Y3))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y1))) => 99.05/14.94 in(Y2, 99.05/14.94 symdiff( 99.05/14.94 Y0, Y1))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y0))) => 99.05/14.94 (in(Y2, 99.05/14.94 Y1) => 99.05/14.94 in(Y2, 99.05/14.94 symdiff( 99.05/14.94 Y0, Y1))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (in(Y2, 99.05/14.94 Y1) => 99.05/14.94 (~( 99.05/14.94 in(Y2, 99.05/14.94 symdiff( 99.05/14.94 Y0, Y1))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y0))) => 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y1))) => 99.05/14.94 (~( 99.05/14.94 in(Y2, 99.05/14.94 symdiff( 99.05/14.94 Y0, Y1))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 in(Y1, 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 in(Y0, 99.05/14.94 setunion( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 in(Y1, 99.05/14.94 setunion( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (??(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 setunion( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)))) & 99.05/14.94 (??(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (in(Y3, 99.05/14.94 setunion( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)))) & 99.05/14.94 (setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)) = 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset)), 99.05/14.94 emptyset))))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (??(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 setunion( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)))) & 99.05/14.94 (??(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (in(Y3, 99.05/14.94 setunion( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)))) & 99.05/14.94 (setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)) = 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset)), 99.05/14.94 emptyset))))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (in(Y1, 99.05/14.94 Y0) => 99.05/14.94 subset( 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset), 99.05/14.94 Y0)))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (in(Y1, 99.05/14.94 Y0) => 99.05/14.94 in( 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset), 99.05/14.94 powerset( 99.05/14.94 Y0))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 in( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 emptyset), 99.05/14.94 powerset( 99.05/14.94 binunion( 99.05/14.94 Y0, Y1))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset))) => 99.05/14.94 (( 99.05/14.94 Y2 = Y1) | 99.05/14.94 (Y2 = Y0)))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (!!(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (in(Y3, 99.05/14.94 Y1) => 99.05/14.94 subset( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset)), 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (!!(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (in(Y3, 99.05/14.94 Y1) => 99.05/14.94 in( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset)), 99.05/14.94 powerset( 99.05/14.94 binunion( 99.05/14.94 Y0, Y1))))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (!!(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (in(Y3, 99.05/14.94 Y1) => 99.05/14.94 subset( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)), 99.05/14.94 powerset( 99.05/14.94 binunion( 99.05/14.94 Y0, Y1))))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (!!(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (in(Y3, 99.05/14.94 Y1) => 99.05/14.94 in( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)), 99.05/14.94 powerset( 99.05/14.94 powerset( 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)))))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (!!(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (in(Y3, 99.05/14.94 Y1) => 99.05/14.94 in( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)), 99.05/14.94 powerset( 99.05/14.94 powerset( 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)))))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (!!(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (in(Y3, 99.05/14.94 Y1) => 99.05/14.94 in( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)), 99.05/14.94 dsetconstr( 99.05/14.94 powerset( 99.05/14.94 powerset( 99.05/14.94 binunion( 99.05/14.94 Y0, Y1))), 99.05/14.94 (^[Y4 : $i]: 99.05/14.94 (??(( 99.05/14.94 ^[Y5 : $i]: 99.05/14.94 (in(Y5, 99.05/14.94 Y0) & 99.05/14.94 (??(( 99.05/14.94 ^[Y6 : $i]: 99.05/14.94 (in(Y6, 99.05/14.94 Y1) & 99.05/14.94 (Y4 = 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y5, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y5, 99.05/14.94 setadjoin( 99.05/14.94 Y6, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)))))))))))))))))))))))))))) => 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 dsetconstr( 99.05/14.94 powerset( 99.05/14.94 powerset( 99.05/14.94 binunion( 99.05/14.94 Y0, Y1))), 99.05/14.94 (^[Y3 : $i]: 99.05/14.94 (??(( 99.05/14.94 ^[Y4 : $i]: 99.05/14.94 (in(Y4, 99.05/14.94 Y0) & 99.05/14.94 (??(( 99.05/14.94 ^[Y5 : $i]: 99.05/14.94 (in(Y5, 99.05/14.94 Y1) & 99.05/14.94 (Y3 = 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y4, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y4, 99.05/14.94 setadjoin( 99.05/14.94 Y5, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)))))))))))))) => 99.05/14.94 (??(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (( 99.05/14.94 ??(( 99.05/14.94 ^[Y4 : $i]: 99.05/14.94 (in(Y4, 99.05/14.94 Y1) & 99.05/14.94 (Y2 = 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 setadjoin( 99.05/14.94 Y4, 99.05/14.94 emptyset)), 99.05/14.94 emptyset))))))) & 99.05/14.94 in(Y3, 99.05/14.94 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.05/14.94 inference('lazy_cnf_imply', [status(thm)], ['214'])). 99.05/14.94 tff('216', plain, 99.05/14.94 ~ ((!!((^[Y0 : $o]: (Y0 => in(emptyset, prop2set(Y0)))))) => 99.05/14.94 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i > $o]: 99.05/14.94 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.94 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i > $o]: 99.05/14.94 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.94 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i > $o]: 99.05/14.94 ((??(Y0)) => 99.05/14.94 ((!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.94 (??((^[Y1 : $i]: 99.05/14.94 (Y0(Y1) & 99.05/14.94 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2)))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i > $o]: 99.05/14.94 ((??((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))) => 99.05/14.94 (??((^[Y1 : $i]: 99.05/14.94 (Y0(Y1) & 99.05/14.94 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((Y0 = Y1) => 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (!!((^[Y3 : $i]: 99.05/14.94 ((Y2 = Y3) => 99.05/14.94 (in(Y2, Y0) => in(Y3, Y1)))))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((Y0 = Y1) => 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (!!((^[Y3 : $i]: 99.05/14.94 ((Y2 = Y3) => 99.05/14.94 (in(Y2, Y0) <=> in(Y3, Y1)))))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i > $o]: 99.05/14.94 ((??((^[Y1 : $i]: 99.05/14.94 (Y0(Y1) & 99.05/14.94 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i > $o]: 99.05/14.94 (!!((^[Y1 : $i > $o]: 99.05/14.94 ((!!((^[Y2 : $i]: 99.05/14.94 (!!((^[Y3 : $i]: 99.05/14.94 ((Y2 = Y3) => 99.05/14.94 (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.94 ((??((^[Y2 : $i]: 99.05/14.94 (Y0(Y2) & 99.05/14.94 (!!((^[Y3 : $i]: 99.05/14.94 (Y0(Y3) => (Y2 = Y3))))))))) <=> 99.05/14.94 (??((^[Y2 : $i]: 99.05/14.94 (Y1(Y2) & 99.05/14.94 (!!((^[Y3 : $i]: 99.05/14.94 (Y1(Y3) => (Y2 = Y3))))))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((Y0 = Y1) => 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (!!((^[Y3 : $i]: 99.05/14.94 ((Y2 = Y3) => 99.05/14.94 (setadjoin(Y0, Y2) = 99.05/14.94 setadjoin(Y1, Y3)))))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((Y0 = Y1) => (powerset(Y0) = powerset(Y1))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((Y0 = Y1) => (setunion(Y0) = setunion(Y1))))))))) => 99.05/14.94 ((!!((^[Y0 : $i > $o]: 99.05/14.94 ((??((^[Y1 : $i]: 99.05/14.94 (Y0(Y1) & 99.05/14.94 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i > $o]: 99.05/14.94 (!!((^[Y1 : $i > $o]: 99.05/14.94 ((!!((^[Y2 : $i]: 99.05/14.94 (!!((^[Y3 : $i]: 99.05/14.94 ((Y2 = Y3) => 99.05/14.94 (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.94 ((??((^[Y2 : $i]: 99.05/14.94 (Y0(Y2) & 99.05/14.94 (!!((^[Y3 : $i]: 99.05/14.94 (Y0(Y3) => (Y2 = Y3))))))))) => 99.05/14.94 ((??((^[Y2 : $i]: 99.05/14.94 (Y1(Y2) & 99.05/14.94 (!!((^[Y3 : $i]: 99.05/14.94 (Y1(Y3) => (Y2 = Y3))))))))) => 99.05/14.94 (descr(Y0) = descr(Y1))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((Y0 = Y1) => 99.05/14.94 (!!((^[Y2 : $i > $o]: 99.05/14.94 (!!((^[Y3 : $i > $o]: 99.05/14.94 ((!!((^[Y4 : $i]: 99.05/14.94 (in(Y4, Y0) => 99.05/14.94 (!!((^[Y5 : $i]: 99.05/14.94 (in(Y5, 99.05/14.94 Y1) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 Y4 = Y5) => 99.05/14.94 ( 99.05/14.94 Y2(Y4) <=> 99.05/14.94 Y3(Y5))))))))))) => 99.05/14.94 (dsetconstr(Y0, Y2) = 99.05/14.94 dsetconstr(Y1, Y3)))))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((!!((^[Y2 : $i]: 99.05/14.94 (in(Y2, Y0) => in(Y2, Y1))))) => 99.05/14.94 subset(Y0, Y1)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y1, Y0)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((Y0 = Y1) => subset(Y0, Y1)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((!!((^[Y2 : $i]: 99.05/14.94 (in(Y2, Y0) => in(Y2, Y1))))) => 99.05/14.94 subset(Y0, Y1)))))))) => 99.05/14.94 ((!!(subset(emptyset))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (subset(Y0, Y1) => 99.05/14.94 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (subset(Y0, Y1) => 99.05/14.94 ((~(in(Y2, Y1))) => 99.05/14.94 (~(in(Y2, Y0)))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (in(Y2, Y0) => 99.05/14.94 ((~(in(Y2, Y1))) => 99.05/14.94 (~(subset(Y0, Y1)))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((~(subset(Y0, Y1))) => 99.05/14.94 (Y0 != Y1)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (in(Y2, Y0) => 99.05/14.94 ((~(in(Y2, Y1))) => 99.05/14.94 (Y0 != Y1)))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (subset(Y0, Y1) => 99.05/14.94 (subset(Y1, Y2) => 99.05/14.94 subset(Y0, Y2)))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 subset(Y1, 99.05/14.94 setadjoin(Y0, Y1)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (subset(Y0, Y2) => 99.05/14.94 subset(Y0, 99.05/14.94 setadjoin(Y1, Y2)))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (subset(Y0, Y1) => 99.05/14.94 in(Y0, powerset(Y1))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (subset(Y0, Y1) => 99.05/14.94 (subset(Y1, Y0) => 99.05/14.94 (Y0 = Y1))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (subset(Y0, emptyset) => 99.05/14.94 (Y0 = emptyset))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (subset(Y1, Y0) => 99.05/14.94 in(Y1, powerset(Y0))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (in(Y1, powerset(Y0)) => 99.05/14.94 subset(Y1, Y0)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 in(Y0, powerset(Y0))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (subset(Y0, Y1) => 99.05/14.94 subset( 99.05/14.94 powerset(Y0), 99.05/14.94 powerset(Y1))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i > $o]: 99.05/14.94 in( 99.05/14.94 dsetconstr(Y0, 99.05/14.94 Y1), 99.05/14.94 powerset(Y0)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i > $o]: 99.05/14.94 subset( 99.05/14.94 dsetconstr(Y0, 99.05/14.94 Y1), Y0))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 in(Y2, 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 in(Y1, 99.05/14.94 setadjoin(Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y1) => 99.05/14.94 in(Y2, 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y3 : $o]: 99.05/14.94 (in(Y2, 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)) => 99.05/14.94 (( 99.05/14.94 in(Y2, 99.05/14.94 Y0) => Y3) => 99.05/14.94 (( 99.05/14.94 in(Y2, 99.05/14.94 Y1) => Y3) => 99.05/14.94 Y3))))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)) => 99.05/14.94 ( 99.05/14.94 in(Y2, 99.05/14.94 Y1) | 99.05/14.94 in(Y2, 99.05/14.94 Y0)))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 subset(Y0, 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 subset(Y1, 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (in(Y2, 99.05/14.94 Y1) => 99.05/14.94 in(Y2, 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (subset( 99.05/14.94 Y2, Y0) => 99.05/14.94 (subset( 99.05/14.94 Y2, Y1) => 99.05/14.94 subset( 99.05/14.94 Y2, 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1)) => 99.05/14.94 in(Y2, 99.05/14.94 Y0))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 subset( 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1), 99.05/14.94 Y0))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (subset( 99.05/14.94 Y0, Y1) => 99.05/14.94 ( 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1) = 99.05/14.94 Y0)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1) = 99.05/14.94 Y1) => 99.05/14.94 subset( 99.05/14.94 Y1, Y0)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1)) => 99.05/14.94 in(Y2, 99.05/14.94 Y1))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (( 99.05/14.94 ~(( 99.05/14.94 ??(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) & 99.05/14.94 in(Y2, 99.05/14.94 Y1))))))) => 99.05/14.94 (binintersect( 99.05/14.94 Y0, Y1) = 99.05/14.94 emptyset)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 subset( 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1), 99.05/14.94 Y1))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (subset( 99.05/14.94 Y1, Y0) => 99.05/14.94 (binintersect( 99.05/14.94 Y0, Y1) = 99.05/14.94 Y1)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (( 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1) = 99.05/14.94 Y0) => 99.05/14.94 subset( 99.05/14.94 Y0, Y1)))))))) => 99.05/14.94 ((!!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (binintersect( 99.05/14.94 Y0, 99.05/14.94 binunion( 99.05/14.94 Y1, Y2)) = 99.05/14.94 binunion( 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1), 99.05/14.94 binintersect( 99.05/14.94 Y0, Y2)))))))))))) => 99.05/14.94 ((!!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y1))) => 99.05/14.94 in(Y2, 99.05/14.94 setminus( 99.05/14.94 Y0, Y1))))))))))))) => 99.05/14.94 ((!!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 setminus( 99.05/14.94 Y0, Y1)) => 99.05/14.94 in(Y2, 99.05/14.94 Y0))))))))))) => 99.05/14.94 ((!!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 setminus( 99.05/14.94 Y0, Y1)) => 99.05/14.94 (~( 99.05/14.94 in(Y2, 99.05/14.94 Y1))))))))))))) => 99.05/14.94 (( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (subset( 99.05/14.94 Y0, Y1) => 99.05/14.94 (setminus( 99.05/14.94 Y0, Y1) = 99.05/14.94 emptyset)))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 setminus( 99.05/14.94 Y0, Y1)))) => 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 in(Y2, 99.05/14.94 Y1)))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 setminus( 99.05/14.94 Y0, Y1)))) => 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y1))) => 99.05/14.94 (~( 99.05/14.94 in(Y2, 99.05/14.94 Y0)))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y0))) => 99.05/14.94 (~( 99.05/14.94 in(Y2, 99.05/14.94 setminus( 99.05/14.94 Y0, Y1)))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y1) => 99.05/14.94 (~( 99.05/14.94 in(Y2, 99.05/14.94 setminus( 99.05/14.94 Y0, Y1)))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 subset( 99.05/14.94 setminus( 99.05/14.94 Y0, Y1), 99.05/14.94 Y0))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (( 99.05/14.94 setminus( 99.05/14.94 Y0, Y1) = 99.05/14.94 emptyset) => 99.05/14.94 subset( 99.05/14.94 Y0, Y1)))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 symdiff( 99.05/14.94 Y0, Y1)) => 99.05/14.94 (!!(( 99.05/14.94 ^[Y3 : $o]: 99.05/14.94 (( 99.05/14.94 in(Y2, 99.05/14.94 Y0) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y1))) => 99.05/14.94 Y3)) => 99.05/14.94 (( 99.05/14.94 ( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y0))) => 99.05/14.94 ( 99.05/14.94 in(Y2, 99.05/14.94 Y1) => Y3)) => 99.05/14.94 Y3))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y1))) => 99.05/14.94 in(Y2, 99.05/14.94 symdiff( 99.05/14.94 Y0, Y1))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y0))) => 99.05/14.94 (in(Y2, 99.05/14.94 Y1) => 99.05/14.94 in(Y2, 99.05/14.94 symdiff( 99.05/14.94 Y0, Y1))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (in(Y2, 99.05/14.94 Y1) => 99.05/14.94 (~( 99.05/14.94 in(Y2, 99.05/14.94 symdiff( 99.05/14.94 Y0, Y1))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y0))) => 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y1))) => 99.05/14.94 (~( 99.05/14.94 in(Y2, 99.05/14.94 symdiff( 99.05/14.94 Y0, Y1))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 in(Y1, 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 in(Y0, 99.05/14.94 setunion( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 in(Y1, 99.05/14.94 setunion( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (??(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 setunion( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)))) & 99.05/14.94 (??(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (in(Y3, 99.05/14.94 setunion( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)))) & 99.05/14.94 (setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)) = 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset)), 99.05/14.94 emptyset))))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (??(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 setunion( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)))) & 99.05/14.94 (??(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (in(Y3, 99.05/14.94 setunion( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)))) & 99.05/14.94 (setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)) = 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset)), 99.05/14.94 emptyset))))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (in(Y1, 99.05/14.94 Y0) => 99.05/14.94 subset( 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset), 99.05/14.94 Y0)))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (in(Y1, 99.05/14.94 Y0) => 99.05/14.94 in( 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset), 99.05/14.94 powerset( 99.05/14.94 Y0))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 in( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 emptyset), 99.05/14.94 powerset( 99.05/14.94 binunion( 99.05/14.94 Y0, Y1))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset))) => 99.05/14.94 (( 99.05/14.94 Y2 = Y1) | 99.05/14.94 (Y2 = Y0)))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (!!(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (in(Y3, 99.05/14.94 Y1) => 99.05/14.94 subset( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset)), 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (!!(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (in(Y3, 99.05/14.94 Y1) => 99.05/14.94 in( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset)), 99.05/14.94 powerset( 99.05/14.94 binunion( 99.05/14.94 Y0, Y1))))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (!!(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (in(Y3, 99.05/14.94 Y1) => 99.05/14.94 subset( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)), 99.05/14.94 powerset( 99.05/14.94 binunion( 99.05/14.94 Y0, Y1))))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (!!(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (in(Y3, 99.05/14.94 Y1) => 99.05/14.94 in( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)), 99.05/14.94 powerset( 99.05/14.94 powerset( 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)))))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (!!(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (in(Y3, 99.05/14.94 Y1) => 99.05/14.94 in( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)), 99.05/14.94 powerset( 99.05/14.94 powerset( 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)))))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (!!(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (in(Y3, 99.05/14.94 Y1) => 99.05/14.94 in( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)), 99.05/14.94 dsetconstr( 99.05/14.94 powerset( 99.05/14.94 powerset( 99.05/14.94 binunion( 99.05/14.94 Y0, Y1))), 99.05/14.94 (^[Y4 : $i]: 99.05/14.94 (??(( 99.05/14.94 ^[Y5 : $i]: 99.05/14.94 (in(Y5, 99.05/14.94 Y0) & 99.05/14.94 (??(( 99.05/14.94 ^[Y6 : $i]: 99.05/14.94 (in(Y6, 99.05/14.94 Y1) & 99.05/14.94 (Y4 = 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y5, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y5, 99.05/14.94 setadjoin( 99.05/14.94 Y6, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)))))))))))))))))))))))))))) => 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 dsetconstr( 99.05/14.94 powerset( 99.05/14.94 powerset( 99.05/14.94 binunion( 99.05/14.94 Y0, Y1))), 99.05/14.94 (^[Y3 : $i]: 99.05/14.94 (??(( 99.05/14.94 ^[Y4 : $i]: 99.05/14.94 (in(Y4, 99.05/14.94 Y0) & 99.05/14.94 (??(( 99.05/14.94 ^[Y5 : $i]: 99.05/14.94 (in(Y5, 99.05/14.94 Y1) & 99.05/14.94 (Y3 = 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y4, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y4, 99.05/14.94 setadjoin( 99.05/14.94 Y5, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)))))))))))))) => 99.05/14.94 (??(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (( 99.05/14.94 ??(( 99.05/14.94 ^[Y4 : $i]: 99.05/14.94 (in(Y4, 99.05/14.94 Y1) & 99.05/14.94 (Y2 = 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 setadjoin( 99.05/14.94 Y4, 99.05/14.94 emptyset)), 99.05/14.94 emptyset))))))) & 99.05/14.94 in(Y3, 99.05/14.94 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.05/14.94 inference('lazy_cnf_imply', [status(thm)], ['215'])). 99.05/14.94 tff('217', plain, 99.05/14.94 ~ ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i > $o]: 99.05/14.94 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.94 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i > $o]: 99.05/14.94 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.94 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i > $o]: 99.05/14.94 ((??(Y0)) => 99.05/14.94 ((!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.94 (??((^[Y1 : $i]: 99.05/14.94 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2)))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i > $o]: 99.05/14.94 ((??((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))) => 99.05/14.94 (??((^[Y1 : $i]: 99.05/14.94 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((Y0 = Y1) => 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (!!((^[Y3 : $i]: 99.05/14.94 ((Y2 = Y3) => 99.05/14.94 (in(Y2, Y0) => in(Y3, Y1)))))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((Y0 = Y1) => 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (!!((^[Y3 : $i]: 99.05/14.94 ((Y2 = Y3) => 99.05/14.94 (in(Y2, Y0) <=> in(Y3, Y1)))))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i > $o]: 99.05/14.94 ((??((^[Y1 : $i]: 99.05/14.94 (Y0(Y1) & 99.05/14.94 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i > $o]: 99.05/14.94 (!!((^[Y1 : $i > $o]: 99.05/14.94 ((!!((^[Y2 : $i]: 99.05/14.94 (!!((^[Y3 : $i]: 99.05/14.94 ((Y2 = Y3) => (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.94 ((??((^[Y2 : $i]: 99.05/14.94 (Y0(Y2) & 99.05/14.94 (!!((^[Y3 : $i]: (Y0(Y3) => (Y2 = Y3))))))))) <=> 99.05/14.94 (??((^[Y2 : $i]: 99.05/14.94 (Y1(Y2) & 99.05/14.94 (!!((^[Y3 : $i]: (Y1(Y3) => (Y2 = Y3))))))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((Y0 = Y1) => 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (!!((^[Y3 : $i]: 99.05/14.94 ((Y2 = Y3) => 99.05/14.94 (setadjoin(Y0, Y2) = 99.05/14.94 setadjoin(Y1, Y3)))))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((Y0 = Y1) => (powerset(Y0) = powerset(Y1))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((Y0 = Y1) => (setunion(Y0) = setunion(Y1))))))))) => 99.05/14.94 ((!!((^[Y0 : $i > $o]: 99.05/14.94 ((??((^[Y1 : $i]: 99.05/14.94 (Y0(Y1) & 99.05/14.94 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i > $o]: 99.05/14.94 (!!((^[Y1 : $i > $o]: 99.05/14.94 ((!!((^[Y2 : $i]: 99.05/14.94 (!!((^[Y3 : $i]: 99.05/14.94 ((Y2 = Y3) => 99.05/14.94 (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.94 ((??((^[Y2 : $i]: 99.05/14.94 (Y0(Y2) & 99.05/14.94 (!!((^[Y3 : $i]: 99.05/14.94 (Y0(Y3) => (Y2 = Y3))))))))) => 99.05/14.94 ((??((^[Y2 : $i]: 99.05/14.94 (Y1(Y2) & 99.05/14.94 (!!((^[Y3 : $i]: 99.05/14.94 (Y1(Y3) => (Y2 = Y3))))))))) => 99.05/14.94 (descr(Y0) = descr(Y1))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((Y0 = Y1) => 99.05/14.94 (!!((^[Y2 : $i > $o]: 99.05/14.94 (!!((^[Y3 : $i > $o]: 99.05/14.94 ((!!((^[Y4 : $i]: 99.05/14.94 (in(Y4, Y0) => 99.05/14.94 (!!((^[Y5 : $i]: 99.05/14.94 (in(Y5, Y1) => 99.05/14.94 (( 99.05/14.94 Y4 = Y5) => 99.05/14.94 ( 99.05/14.94 Y2(Y4) <=> 99.05/14.94 Y3(Y5))))))))))) => 99.05/14.94 (dsetconstr(Y0, Y2) = 99.05/14.94 dsetconstr(Y1, Y3)))))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((!!((^[Y2 : $i]: 99.05/14.94 (in(Y2, Y0) => in(Y2, Y1))))) => 99.05/14.94 subset(Y0, Y1)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y1, Y0)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y0, Y1)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((!!((^[Y2 : $i]: 99.05/14.94 (in(Y2, Y0) => in(Y2, Y1))))) => 99.05/14.94 subset(Y0, Y1)))))))) => 99.05/14.94 ((!!(subset(emptyset))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (subset(Y0, Y1) => 99.05/14.94 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (subset(Y0, Y1) => 99.05/14.94 ((~(in(Y2, Y1))) => 99.05/14.94 (~(in(Y2, Y0)))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (in(Y2, Y0) => 99.05/14.94 ((~(in(Y2, Y1))) => 99.05/14.94 (~(subset(Y0, Y1)))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((~(subset(Y0, Y1))) => 99.05/14.94 (Y0 != Y1)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (in(Y2, Y0) => 99.05/14.94 ((~(in(Y2, Y1))) => 99.05/14.94 (Y0 != Y1)))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (subset(Y0, Y1) => 99.05/14.94 (subset(Y1, Y2) => 99.05/14.94 subset(Y0, Y2)))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 subset(Y1, setadjoin(Y0, Y1)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (subset(Y0, Y2) => 99.05/14.94 subset(Y0, 99.05/14.94 setadjoin(Y1, Y2)))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (subset(Y0, Y1) => 99.05/14.94 in(Y0, powerset(Y1))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (subset(Y0, Y1) => 99.05/14.94 (subset(Y1, Y0) => 99.05/14.94 (Y0 = Y1))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (subset(Y0, emptyset) => 99.05/14.94 (Y0 = emptyset))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (subset(Y1, Y0) => 99.05/14.94 in(Y1, powerset(Y0))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (in(Y1, powerset(Y0)) => 99.05/14.94 subset(Y1, Y0)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 in(Y0, powerset(Y0))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (subset(Y0, Y1) => 99.05/14.94 subset( 99.05/14.94 powerset(Y0), 99.05/14.94 powerset(Y1))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i > $o]: 99.05/14.94 in( 99.05/14.94 dsetconstr(Y0, Y1), 99.05/14.94 powerset(Y0)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i > $o]: 99.05/14.94 subset( 99.05/14.94 dsetconstr(Y0, 99.05/14.94 Y1), Y0))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (in(Y2, Y0) => 99.05/14.94 in(Y2, 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 in(Y1, 99.05/14.94 setadjoin(Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 ( 99.05/14.94 in(Y2, 99.05/14.94 Y1) => 99.05/14.94 in(Y2, 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y3 : $o]: 99.05/14.94 (in(Y2, 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)) => 99.05/14.94 (( 99.05/14.94 in(Y2, 99.05/14.94 Y0) => Y3) => 99.05/14.94 (( 99.05/14.94 in(Y2, 99.05/14.94 Y1) => Y3) => 99.05/14.94 Y3))))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)) => 99.05/14.94 (in(Y2, 99.05/14.94 Y1) | 99.05/14.94 in(Y2, 99.05/14.94 Y0)))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 subset(Y0, 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 subset(Y1, 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (in(Y2, 99.05/14.94 Y1) => 99.05/14.94 in(Y2, 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (subset( 99.05/14.94 Y2, Y0) => 99.05/14.94 (subset( 99.05/14.94 Y2, Y1) => 99.05/14.94 subset( 99.05/14.94 Y2, 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1)) => 99.05/14.94 in(Y2, 99.05/14.94 Y0))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 subset( 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1), 99.05/14.94 Y0))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (subset( 99.05/14.94 Y0, Y1) => 99.05/14.94 (binintersect( 99.05/14.94 Y0, Y1) = 99.05/14.94 Y0)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (( 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1) = 99.05/14.94 Y1) => 99.05/14.94 subset( 99.05/14.94 Y1, Y0)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1)) => 99.05/14.94 in(Y2, 99.05/14.94 Y1))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (( 99.05/14.94 ~(( 99.05/14.94 ??(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) & 99.05/14.94 in(Y2, 99.05/14.94 Y1))))))) => 99.05/14.94 (binintersect( 99.05/14.94 Y0, Y1) = 99.05/14.94 emptyset)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 subset( 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1), 99.05/14.94 Y1))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (subset( 99.05/14.94 Y1, Y0) => 99.05/14.94 (binintersect( 99.05/14.94 Y0, Y1) = 99.05/14.94 Y1)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (( 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1) = 99.05/14.94 Y0) => 99.05/14.94 subset( 99.05/14.94 Y0, Y1)))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (binintersect( 99.05/14.94 Y0, 99.05/14.94 binunion( 99.05/14.94 Y1, Y2)) = 99.05/14.94 binunion( 99.05/14.94 binintersect( 99.05/14.94 Y0, Y1), 99.05/14.94 binintersect( 99.05/14.94 Y0, Y2)))))))))))) => 99.05/14.94 ((!!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y1))) => 99.05/14.94 in(Y2, 99.05/14.94 setminus( 99.05/14.94 Y0, Y1))))))))))))) => 99.05/14.94 ((!!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 setminus( 99.05/14.94 Y0, Y1)) => 99.05/14.94 in(Y2, 99.05/14.94 Y0))))))))))) => 99.05/14.94 ((!!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 setminus( 99.05/14.94 Y0, Y1)) => 99.05/14.94 (~( 99.05/14.94 in(Y2, 99.05/14.94 Y1))))))))))))) => 99.05/14.94 ((!!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (subset( 99.05/14.94 Y0, Y1) => 99.05/14.94 (setminus( 99.05/14.94 Y0, Y1) = 99.05/14.94 emptyset)))))))) => 99.05/14.94 (( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 setminus( 99.05/14.94 Y0, Y1)))) => 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 in(Y2, 99.05/14.94 Y1)))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 setminus( 99.05/14.94 Y0, Y1)))) => 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y1))) => 99.05/14.94 (~( 99.05/14.94 in(Y2, 99.05/14.94 Y0)))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y0))) => 99.05/14.94 (~( 99.05/14.94 in(Y2, 99.05/14.94 setminus( 99.05/14.94 Y0, Y1)))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y1) => 99.05/14.94 (~( 99.05/14.94 in(Y2, 99.05/14.94 setminus( 99.05/14.94 Y0, Y1)))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 subset( 99.05/14.94 setminus( 99.05/14.94 Y0, Y1), 99.05/14.94 Y0))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (( 99.05/14.94 setminus( 99.05/14.94 Y0, Y1) = 99.05/14.94 emptyset) => 99.05/14.94 subset( 99.05/14.94 Y0, Y1)))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 symdiff( 99.05/14.94 Y0, Y1)) => 99.05/14.94 (!!(( 99.05/14.94 ^[Y3 : $o]: 99.05/14.94 (( 99.05/14.94 in(Y2, 99.05/14.94 Y0) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y1))) => 99.05/14.94 Y3)) => 99.05/14.94 (( 99.05/14.94 ( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y0))) => 99.05/14.94 ( 99.05/14.94 in(Y2, 99.05/14.94 Y1) => Y3)) => 99.05/14.94 Y3))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y1))) => 99.05/14.94 in(Y2, 99.05/14.94 symdiff( 99.05/14.94 Y0, Y1))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y0))) => 99.05/14.94 (in(Y2, 99.05/14.94 Y1) => 99.05/14.94 in(Y2, 99.05/14.94 symdiff( 99.05/14.94 Y0, Y1))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (in(Y2, 99.05/14.94 Y1) => 99.05/14.94 (~( 99.05/14.94 in(Y2, 99.05/14.94 symdiff( 99.05/14.94 Y0, Y1))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y0))) => 99.05/14.94 (( 99.05/14.94 ~( 99.05/14.94 in(Y2, 99.05/14.94 Y1))) => 99.05/14.94 (~( 99.05/14.94 in(Y2, 99.05/14.94 symdiff( 99.05/14.94 Y0, Y1))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 in(Y1, 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 in(Y0, 99.05/14.94 setunion( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 in(Y1, 99.05/14.94 setunion( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (??(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 setunion( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)))) & 99.05/14.94 (??(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (in(Y3, 99.05/14.94 setunion( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)))) & 99.05/14.94 (setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)) = 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset)), 99.05/14.94 emptyset))))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (??(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 setunion( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)))) & 99.05/14.94 (??(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (in(Y3, 99.05/14.94 setunion( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)))) & 99.05/14.94 (setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)) = 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset)), 99.05/14.94 emptyset))))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (in(Y1, 99.05/14.94 Y0) => 99.05/14.94 subset( 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset), 99.05/14.94 Y0)))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (in(Y1, 99.05/14.94 Y0) => 99.05/14.94 in( 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset), 99.05/14.94 powerset( 99.05/14.94 Y0))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 in( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 emptyset), 99.05/14.94 powerset( 99.05/14.94 binunion( 99.05/14.94 Y0, Y1))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y0, 99.05/14.94 setadjoin( 99.05/14.94 Y1, 99.05/14.94 emptyset))) => 99.05/14.94 (( 99.05/14.94 Y2 = Y1) | 99.05/14.94 (Y2 = Y0)))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (!!(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (in(Y3, 99.05/14.94 Y1) => 99.05/14.94 subset( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset)), 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (!!(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (in(Y3, 99.05/14.94 Y1) => 99.05/14.94 in( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset)), 99.05/14.94 powerset( 99.05/14.94 binunion( 99.05/14.94 Y0, Y1))))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (!!(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (in(Y3, 99.05/14.94 Y1) => 99.05/14.94 subset( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)), 99.05/14.94 powerset( 99.05/14.94 binunion( 99.05/14.94 Y0, Y1))))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (!!(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (in(Y3, 99.05/14.94 Y1) => 99.05/14.94 in( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)), 99.05/14.94 powerset( 99.05/14.94 powerset( 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)))))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (!!(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (in(Y3, 99.05/14.94 Y1) => 99.05/14.94 in( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)), 99.05/14.94 powerset( 99.05/14.94 powerset( 99.05/14.94 binunion( 99.05/14.94 Y0, Y1)))))))))))))))))) => 99.05/14.94 ( 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 Y0) => 99.05/14.94 (!!(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (in(Y3, 99.05/14.94 Y1) => 99.05/14.94 in( 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y2, 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)), 99.05/14.94 dsetconstr( 99.05/14.94 powerset( 99.05/14.94 powerset( 99.05/14.94 binunion( 99.05/14.94 Y0, Y1))), 99.05/14.94 (^[Y4 : $i]: 99.05/14.94 (??(( 99.05/14.94 ^[Y5 : $i]: 99.05/14.94 (in(Y5, 99.05/14.94 Y0) & 99.05/14.94 (??(( 99.05/14.94 ^[Y6 : $i]: 99.05/14.94 (in(Y6, 99.05/14.94 Y1) & 99.05/14.94 (Y4 = 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y5, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y5, 99.05/14.94 setadjoin( 99.05/14.94 Y6, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)))))))))))))))))))))))))))) => 99.05/14.94 ( 99.05/14.94 !!(( 99.05/14.94 ^[Y0 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y1 : $i]: 99.05/14.94 (!!(( 99.05/14.94 ^[Y2 : $i]: 99.05/14.94 (in(Y2, 99.05/14.94 dsetconstr( 99.05/14.94 powerset( 99.05/14.94 powerset( 99.05/14.94 binunion( 99.05/14.94 Y0, Y1))), 99.05/14.94 (^[Y3 : $i]: 99.05/14.94 (??(( 99.05/14.94 ^[Y4 : $i]: 99.05/14.94 (in(Y4, 99.05/14.94 Y0) & 99.05/14.94 (??(( 99.05/14.94 ^[Y5 : $i]: 99.05/14.94 (in(Y5, 99.05/14.94 Y1) & 99.05/14.94 (Y3 = 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y4, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y4, 99.05/14.94 setadjoin( 99.05/14.94 Y5, 99.05/14.94 emptyset)), 99.05/14.94 emptyset)))))))))))))) => 99.05/14.94 (??(( 99.05/14.94 ^[Y3 : $i]: 99.05/14.94 (( 99.05/14.94 ??(( 99.05/14.94 ^[Y4 : $i]: 99.05/14.94 (in(Y4, 99.05/14.94 Y1) & 99.05/14.94 (Y2 = 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 emptyset), 99.05/14.94 setadjoin( 99.05/14.94 setadjoin( 99.05/14.94 Y3, 99.05/14.94 setadjoin( 99.05/14.94 Y4, 99.05/14.94 emptyset)), 99.05/14.94 emptyset))))))) & 99.05/14.94 in(Y3, 99.05/14.94 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.05/14.94 inference('lazy_cnf_imply', [status(thm)], ['216'])). 99.05/14.94 tff('218', plain, 99.05/14.94 ~ ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i > $o]: 99.05/14.94 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 99.05/14.94 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i > $o]: 99.05/14.94 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.94 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i > $o]: 99.05/14.94 ((??(Y0)) => 99.05/14.94 ((!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.94 (??((^[Y1 : $i]: 99.05/14.94 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2)))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i > $o]: 99.05/14.94 ((??((^[Y1 : $i]: (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))) => 99.05/14.94 (??((^[Y1 : $i]: 99.05/14.94 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((Y0 = Y1) => 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (!!((^[Y3 : $i]: 99.05/14.94 ((Y2 = Y3) => 99.05/14.94 (in(Y2, Y0) => in(Y3, Y1)))))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((Y0 = Y1) => 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (!!((^[Y3 : $i]: 99.05/14.94 ((Y2 = Y3) => 99.05/14.94 (in(Y2, Y0) <=> in(Y3, Y1)))))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i > $o]: 99.05/14.94 ((??((^[Y1 : $i]: 99.05/14.94 (Y0(Y1) & 99.05/14.94 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.94 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i > $o]: 99.05/14.94 (!!((^[Y1 : $i > $o]: 99.05/14.94 ((!!((^[Y2 : $i]: 99.05/14.94 (!!((^[Y3 : $i]: 99.05/14.94 ((Y2 = Y3) => (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.94 ((??((^[Y2 : $i]: 99.05/14.94 (Y0(Y2) & 99.05/14.94 (!!((^[Y3 : $i]: (Y0(Y3) => (Y2 = Y3))))))))) <=> 99.05/14.94 (??((^[Y2 : $i]: 99.05/14.94 (Y1(Y2) & 99.05/14.94 (!!((^[Y3 : $i]: (Y1(Y3) => (Y2 = Y3))))))))))))))))) => 99.05/14.94 ((!!((^[Y0 : $i]: 99.05/14.94 (!!((^[Y1 : $i]: 99.05/14.94 ((Y0 = Y1) => 99.05/14.94 (!!((^[Y2 : $i]: 99.05/14.95 (!!((^[Y3 : $i]: 99.05/14.95 ((Y2 = Y3) => 99.05/14.95 (setadjoin(Y0, Y2) = 99.05/14.95 setadjoin(Y1, Y3)))))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((Y0 = Y1) => (powerset(Y0) = powerset(Y1))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((Y0 = Y1) => (setunion(Y0) = setunion(Y1))))))))) => 99.05/14.95 ((!!((^[Y0 : $i > $o]: 99.05/14.95 ((??((^[Y1 : $i]: 99.05/14.95 (Y0(Y1) & 99.05/14.95 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i > $o]: 99.05/14.95 (!!((^[Y1 : $i > $o]: 99.05/14.95 ((!!((^[Y2 : $i]: 99.05/14.95 (!!((^[Y3 : $i]: 99.05/14.95 ((Y2 = Y3) => 99.05/14.95 (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.95 ((??((^[Y2 : $i]: 99.05/14.95 (Y0(Y2) & 99.05/14.95 (!!((^[Y3 : $i]: 99.05/14.95 (Y0(Y3) => (Y2 = Y3))))))))) => 99.05/14.95 ((??((^[Y2 : $i]: 99.05/14.95 (Y1(Y2) & 99.05/14.95 (!!((^[Y3 : $i]: 99.05/14.95 (Y1(Y3) => (Y2 = Y3))))))))) => 99.05/14.95 (descr(Y0) = descr(Y1))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((Y0 = Y1) => 99.05/14.95 (!!((^[Y2 : $i > $o]: 99.05/14.95 (!!((^[Y3 : $i > $o]: 99.05/14.95 ((!!((^[Y4 : $i]: 99.05/14.95 (in(Y4, Y0) => 99.05/14.95 (!!((^[Y5 : $i]: 99.05/14.95 (in(Y5, Y1) => 99.05/14.95 ((Y4 = Y5) => 99.05/14.95 (Y2(Y4) <=> 99.05/14.95 Y3(Y5))))))))))) => 99.05/14.95 (dsetconstr(Y0, Y2) = 99.05/14.95 dsetconstr(Y1, Y3)))))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((!!((^[Y2 : $i]: 99.05/14.95 (in(Y2, Y0) => in(Y2, Y1))))) => 99.05/14.95 subset(Y0, Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y1, Y0)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y0, Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((!!((^[Y2 : $i]: 99.05/14.95 (in(Y2, Y0) => in(Y2, Y1))))) => 99.05/14.95 subset(Y0, Y1)))))))) => 99.05/14.95 ((!!(subset(emptyset))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (subset(Y0, Y1) => 99.05/14.95 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (subset(Y0, Y1) => 99.05/14.95 ((~(in(Y2, Y1))) => 99.05/14.95 (~(in(Y2, Y0)))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (in(Y2, Y0) => 99.05/14.95 ((~(in(Y2, Y1))) => 99.05/14.95 (~(subset(Y0, Y1)))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (in(Y2, Y0) => 99.05/14.95 ((~(in(Y2, Y1))) => 99.05/14.95 (Y0 != Y1)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (subset(Y0, Y1) => 99.05/14.95 (subset(Y1, Y2) => 99.05/14.95 subset(Y0, Y2)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 subset(Y1, setadjoin(Y0, Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (subset(Y0, Y2) => 99.05/14.95 subset(Y0, 99.05/14.95 setadjoin(Y1, Y2)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (subset(Y0, Y1) => 99.05/14.95 in(Y0, powerset(Y1))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (subset(Y0, Y1) => 99.05/14.95 (subset(Y1, Y0) => 99.05/14.95 (Y0 = Y1))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (subset(Y0, emptyset) => 99.05/14.95 (Y0 = emptyset))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (subset(Y1, Y0) => 99.05/14.95 in(Y1, powerset(Y0))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (in(Y1, powerset(Y0)) => 99.05/14.95 subset(Y1, Y0)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (subset(Y0, Y1) => 99.05/14.95 subset(powerset(Y0), 99.05/14.95 powerset(Y1))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i > $o]: 99.05/14.95 in( 99.05/14.95 dsetconstr(Y0, Y1), 99.05/14.95 powerset(Y0)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i > $o]: 99.05/14.95 subset( 99.05/14.95 dsetconstr(Y0, Y1), 99.05/14.95 Y0))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (in(Y2, Y0) => 99.05/14.95 in(Y2, 99.05/14.95 binunion( 99.05/14.95 Y0, Y1)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 in(Y1, 99.05/14.95 setadjoin(Y0, 99.05/14.95 setadjoin(Y1, 99.05/14.95 emptyset))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y1) => 99.05/14.95 in(Y2, 99.05/14.95 binunion( 99.05/14.95 Y0, Y1)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y3 : $o]: 99.05/14.95 (in(Y2, 99.05/14.95 binunion( 99.05/14.95 Y0, Y1)) => 99.05/14.95 (( 99.05/14.95 in(Y2, 99.05/14.95 Y0) => Y3) => 99.05/14.95 (( 99.05/14.95 in(Y2, 99.05/14.95 Y1) => Y3) => 99.05/14.95 Y3))))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 binunion( 99.05/14.95 Y0, Y1)) => 99.05/14.95 (in(Y2, 99.05/14.95 Y1) | 99.05/14.95 in(Y2, 99.05/14.95 Y0)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 subset(Y0, 99.05/14.95 binunion( 99.05/14.95 Y0, Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 subset(Y1, 99.05/14.95 binunion( 99.05/14.95 Y0, Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 ( 99.05/14.95 in(Y2, 99.05/14.95 Y0) => 99.05/14.95 ( 99.05/14.95 in(Y2, 99.05/14.95 Y1) => 99.05/14.95 in(Y2, 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (subset( 99.05/14.95 Y2, Y0) => 99.05/14.95 (subset( 99.05/14.95 Y2, Y1) => 99.05/14.95 subset( 99.05/14.95 Y2, 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1)) => 99.05/14.95 in(Y2, 99.05/14.95 Y0))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 subset( 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1), 99.05/14.95 Y0))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (subset( 99.05/14.95 Y0, Y1) => 99.05/14.95 (binintersect( 99.05/14.95 Y0, Y1) = 99.05/14.95 Y0)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (( 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1) = 99.05/14.95 Y1) => 99.05/14.95 subset( 99.05/14.95 Y1, Y0)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1)) => 99.05/14.95 in(Y2, 99.05/14.95 Y1))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 ~(( 99.05/14.95 ??(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) & 99.05/14.95 in(Y2, 99.05/14.95 Y1))))))) => 99.05/14.95 ( 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1) = 99.05/14.95 emptyset)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 subset( 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1), 99.05/14.95 Y1))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (subset( 99.05/14.95 Y1, Y0) => 99.05/14.95 (binintersect( 99.05/14.95 Y0, Y1) = 99.05/14.95 Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (( 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1) = 99.05/14.95 Y0) => 99.05/14.95 subset( 99.05/14.95 Y0, Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (binintersect( 99.05/14.95 Y0, 99.05/14.95 binunion( 99.05/14.95 Y1, Y2)) = 99.05/14.95 binunion( 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1), 99.05/14.95 binintersect( 99.05/14.95 Y0, Y2)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y1))) => 99.05/14.95 in(Y2, 99.05/14.95 setminus( 99.05/14.95 Y0, Y1))))))))))))) => 99.05/14.95 ((!!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 setminus( 99.05/14.95 Y0, Y1)) => 99.05/14.95 in(Y2, 99.05/14.95 Y0))))))))))) => 99.05/14.95 ((!!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 setminus( 99.05/14.95 Y0, Y1)) => 99.05/14.95 (~( 99.05/14.95 in(Y2, 99.05/14.95 Y1))))))))))))) => 99.05/14.95 ((!!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (subset( 99.05/14.95 Y0, Y1) => 99.05/14.95 (setminus( 99.05/14.95 Y0, Y1) = 99.05/14.95 emptyset)))))))) => 99.05/14.95 ((!!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 setminus( 99.05/14.95 Y0, Y1)))) => 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 in(Y2, 99.05/14.95 Y1)))))))))))) => 99.05/14.95 (( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 setminus( 99.05/14.95 Y0, Y1)))) => 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y1))) => 99.05/14.95 (~( 99.05/14.95 in(Y2, 99.05/14.95 Y0)))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y0))) => 99.05/14.95 (~( 99.05/14.95 in(Y2, 99.05/14.95 setminus( 99.05/14.95 Y0, Y1)))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y1) => 99.05/14.95 (~( 99.05/14.95 in(Y2, 99.05/14.95 setminus( 99.05/14.95 Y0, Y1)))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 subset( 99.05/14.95 setminus( 99.05/14.95 Y0, Y1), 99.05/14.95 Y0))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (( 99.05/14.95 setminus( 99.05/14.95 Y0, Y1) = 99.05/14.95 emptyset) => 99.05/14.95 subset( 99.05/14.95 Y0, Y1)))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 symdiff( 99.05/14.95 Y0, Y1)) => 99.05/14.95 (!!(( 99.05/14.95 ^[Y3 : $o]: 99.05/14.95 (( 99.05/14.95 in(Y2, 99.05/14.95 Y0) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y1))) => 99.05/14.95 Y3)) => 99.05/14.95 (( 99.05/14.95 ( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y0))) => 99.05/14.95 ( 99.05/14.95 in(Y2, 99.05/14.95 Y1) => Y3)) => 99.05/14.95 Y3))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y1))) => 99.05/14.95 in(Y2, 99.05/14.95 symdiff( 99.05/14.95 Y0, Y1))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y0))) => 99.05/14.95 (in(Y2, 99.05/14.95 Y1) => 99.05/14.95 in(Y2, 99.05/14.95 symdiff( 99.05/14.95 Y0, Y1))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (in(Y2, 99.05/14.95 Y1) => 99.05/14.95 (~( 99.05/14.95 in(Y2, 99.05/14.95 symdiff( 99.05/14.95 Y0, Y1))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y0))) => 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y1))) => 99.05/14.95 (~( 99.05/14.95 in(Y2, 99.05/14.95 symdiff( 99.05/14.95 Y0, Y1))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 in(Y1, 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 in(Y0, 99.05/14.95 setunion( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 in(Y1, 99.05/14.95 setunion( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (??(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 setunion( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)))) & 99.05/14.95 (??(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (in(Y3, 99.05/14.95 setunion( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)))) & 99.05/14.95 (setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)) = 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset)), 99.05/14.95 emptyset))))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (??(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 setunion( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)))) & 99.05/14.95 (??(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (in(Y3, 99.05/14.95 setunion( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)))) & 99.05/14.95 (setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)) = 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset)), 99.05/14.95 emptyset))))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (in(Y1, 99.05/14.95 Y0) => 99.05/14.95 subset( 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset), 99.05/14.95 Y0)))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (in(Y1, 99.05/14.95 Y0) => 99.05/14.95 in( 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset), 99.05/14.95 powerset( 99.05/14.95 Y0))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 in( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 emptyset), 99.05/14.95 powerset( 99.05/14.95 binunion( 99.05/14.95 Y0, Y1))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset))) => 99.05/14.95 (( 99.05/14.95 Y2 = Y1) | 99.05/14.95 (Y2 = Y0)))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (!!(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (in(Y3, 99.05/14.95 Y1) => 99.05/14.95 subset( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset)), 99.05/14.95 binunion( 99.05/14.95 Y0, Y1)))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (!!(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (in(Y3, 99.05/14.95 Y1) => 99.05/14.95 in( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset)), 99.05/14.95 powerset( 99.05/14.95 binunion( 99.05/14.95 Y0, Y1))))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (!!(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (in(Y3, 99.05/14.95 Y1) => 99.05/14.95 subset( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)), 99.05/14.95 powerset( 99.05/14.95 binunion( 99.05/14.95 Y0, Y1))))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (!!(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (in(Y3, 99.05/14.95 Y1) => 99.05/14.95 in( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)), 99.05/14.95 powerset( 99.05/14.95 powerset( 99.05/14.95 binunion( 99.05/14.95 Y0, Y1)))))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (!!(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (in(Y3, 99.05/14.95 Y1) => 99.05/14.95 in( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)), 99.05/14.95 powerset( 99.05/14.95 powerset( 99.05/14.95 binunion( 99.05/14.95 Y0, Y1)))))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (!!(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (in(Y3, 99.05/14.95 Y1) => 99.05/14.95 in( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)), 99.05/14.95 dsetconstr( 99.05/14.95 powerset( 99.05/14.95 powerset( 99.05/14.95 binunion( 99.05/14.95 Y0, Y1))), 99.05/14.95 (^[Y4 : $i]: 99.05/14.95 (??(( 99.05/14.95 ^[Y5 : $i]: 99.05/14.95 (in(Y5, 99.05/14.95 Y0) & 99.05/14.95 (??(( 99.05/14.95 ^[Y6 : $i]: 99.05/14.95 (in(Y6, 99.05/14.95 Y1) & 99.05/14.95 (Y4 = 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y5, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y5, 99.05/14.95 setadjoin( 99.05/14.95 Y6, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)))))))))))))))))))))))))))) => 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 dsetconstr( 99.05/14.95 powerset( 99.05/14.95 powerset( 99.05/14.95 binunion( 99.05/14.95 Y0, Y1))), 99.05/14.95 (^[Y3 : $i]: 99.05/14.95 (??(( 99.05/14.95 ^[Y4 : $i]: 99.05/14.95 (in(Y4, 99.05/14.95 Y0) & 99.05/14.95 (??(( 99.05/14.95 ^[Y5 : $i]: 99.05/14.95 (in(Y5, 99.05/14.95 Y1) & 99.05/14.95 (Y3 = 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y4, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y4, 99.05/14.95 setadjoin( 99.05/14.95 Y5, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)))))))))))))) => 99.05/14.95 (??(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (( 99.05/14.95 ??(( 99.05/14.95 ^[Y4 : $i]: 99.05/14.95 (in(Y4, 99.05/14.95 Y1) & 99.05/14.95 (Y2 = 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 setadjoin( 99.05/14.95 Y4, 99.05/14.95 emptyset)), 99.05/14.95 emptyset))))))) & 99.05/14.95 in(Y3, 99.05/14.95 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.05/14.95 inference('lazy_cnf_imply', [status(thm)], ['217'])). 99.05/14.95 tff('219', plain, 99.05/14.95 ~ ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i > $o]: 99.05/14.95 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 99.05/14.95 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i > $o]: 99.05/14.95 ((??(Y0)) => 99.05/14.95 ((!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.95 (??((^[Y1 : $i]: 99.05/14.95 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2)))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i > $o]: 99.05/14.95 ((??((^[Y1 : $i]: (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))) => 99.05/14.95 (??((^[Y1 : $i]: 99.05/14.95 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((Y0 = Y1) => 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (!!((^[Y3 : $i]: 99.05/14.95 ((Y2 = Y3) => 99.05/14.95 (in(Y2, Y0) => in(Y3, Y1)))))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((Y0 = Y1) => 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (!!((^[Y3 : $i]: 99.05/14.95 ((Y2 = Y3) => 99.05/14.95 (in(Y2, Y0) <=> in(Y3, Y1)))))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i > $o]: 99.05/14.95 ((??((^[Y1 : $i]: 99.05/14.95 (Y0(Y1) & 99.05/14.95 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i > $o]: 99.05/14.95 (!!((^[Y1 : $i > $o]: 99.05/14.95 ((!!((^[Y2 : $i]: 99.05/14.95 (!!((^[Y3 : $i]: 99.05/14.95 ((Y2 = Y3) => (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.95 ((??((^[Y2 : $i]: 99.05/14.95 (Y0(Y2) & 99.05/14.95 (!!((^[Y3 : $i]: (Y0(Y3) => (Y2 = Y3))))))))) <=> 99.05/14.95 (??((^[Y2 : $i]: 99.05/14.95 (Y1(Y2) & 99.05/14.95 (!!((^[Y3 : $i]: (Y1(Y3) => (Y2 = Y3))))))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((Y0 = Y1) => 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (!!((^[Y3 : $i]: 99.05/14.95 ((Y2 = Y3) => 99.05/14.95 (setadjoin(Y0, Y2) = 99.05/14.95 setadjoin(Y1, Y3)))))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((Y0 = Y1) => (powerset(Y0) = powerset(Y1))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((Y0 = Y1) => (setunion(Y0) = setunion(Y1))))))))) => 99.05/14.95 ((!!((^[Y0 : $i > $o]: 99.05/14.95 ((??((^[Y1 : $i]: 99.05/14.95 (Y0(Y1) & 99.05/14.95 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i > $o]: 99.05/14.95 (!!((^[Y1 : $i > $o]: 99.05/14.95 ((!!((^[Y2 : $i]: 99.05/14.95 (!!((^[Y3 : $i]: 99.05/14.95 ((Y2 = Y3) => 99.05/14.95 (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.95 ((??((^[Y2 : $i]: 99.05/14.95 (Y0(Y2) & 99.05/14.95 (!!((^[Y3 : $i]: 99.05/14.95 (Y0(Y3) => (Y2 = Y3))))))))) => 99.05/14.95 ((??((^[Y2 : $i]: 99.05/14.95 (Y1(Y2) & 99.05/14.95 (!!((^[Y3 : $i]: 99.05/14.95 (Y1(Y3) => (Y2 = Y3))))))))) => 99.05/14.95 (descr(Y0) = descr(Y1))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((Y0 = Y1) => 99.05/14.95 (!!((^[Y2 : $i > $o]: 99.05/14.95 (!!((^[Y3 : $i > $o]: 99.05/14.95 ((!!((^[Y4 : $i]: 99.05/14.95 (in(Y4, Y0) => 99.05/14.95 (!!((^[Y5 : $i]: 99.05/14.95 (in(Y5, Y1) => 99.05/14.95 ((Y4 = Y5) => 99.05/14.95 (Y2(Y4) <=> 99.05/14.95 Y3(Y5))))))))))) => 99.05/14.95 (dsetconstr(Y0, Y2) = 99.05/14.95 dsetconstr(Y1, Y3)))))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((!!((^[Y2 : $i]: 99.05/14.95 (in(Y2, Y0) => in(Y2, Y1))))) => 99.05/14.95 subset(Y0, Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y1, Y0)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y0, Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((!!((^[Y2 : $i]: 99.05/14.95 (in(Y2, Y0) => in(Y2, Y1))))) => 99.05/14.95 subset(Y0, Y1)))))))) => 99.05/14.95 ((!!(subset(emptyset))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (subset(Y0, Y1) => 99.05/14.95 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (subset(Y0, Y1) => 99.05/14.95 ((~(in(Y2, Y1))) => 99.05/14.95 (~(in(Y2, Y0)))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (in(Y2, Y0) => 99.05/14.95 ((~(in(Y2, Y1))) => 99.05/14.95 (~(subset(Y0, Y1)))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (in(Y2, Y0) => 99.05/14.95 ((~(in(Y2, Y1))) => 99.05/14.95 (Y0 != Y1)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (subset(Y0, Y1) => 99.05/14.95 (subset(Y1, Y2) => 99.05/14.95 subset(Y0, Y2)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 subset(Y1, setadjoin(Y0, Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (subset(Y0, Y2) => 99.05/14.95 subset(Y0, 99.05/14.95 setadjoin(Y1, Y2)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (subset(Y0, Y1) => 99.05/14.95 in(Y0, powerset(Y1))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (subset(Y0, Y1) => 99.05/14.95 (subset(Y1, Y0) => 99.05/14.95 (Y0 = Y1))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (subset(Y0, emptyset) => 99.05/14.95 (Y0 = emptyset))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (subset(Y1, Y0) => 99.05/14.95 in(Y1, powerset(Y0))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (in(Y1, powerset(Y0)) => 99.05/14.95 subset(Y1, Y0)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (subset(Y0, Y1) => 99.05/14.95 subset(powerset(Y0), 99.05/14.95 powerset(Y1))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i > $o]: 99.05/14.95 in( 99.05/14.95 dsetconstr(Y0, Y1), 99.05/14.95 powerset(Y0)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i > $o]: 99.05/14.95 subset( 99.05/14.95 dsetconstr(Y0, Y1), 99.05/14.95 Y0))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (in(Y2, Y0) => 99.05/14.95 in(Y2, 99.05/14.95 binunion( 99.05/14.95 Y0, Y1)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 in(Y1, 99.05/14.95 setadjoin(Y0, 99.05/14.95 setadjoin(Y1, 99.05/14.95 emptyset))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (in(Y2, Y1) => 99.05/14.95 in(Y2, 99.05/14.95 binunion( 99.05/14.95 Y0, Y1)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y3 : $o]: 99.05/14.95 (in(Y2, 99.05/14.95 binunion( 99.05/14.95 Y0, Y1)) => 99.05/14.95 (( 99.05/14.95 in(Y2, 99.05/14.95 Y0) => Y3) => 99.05/14.95 (( 99.05/14.95 in(Y2, 99.05/14.95 Y1) => Y3) => 99.05/14.95 Y3))))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 ( 99.05/14.95 in(Y2, 99.05/14.95 binunion( 99.05/14.95 Y0, Y1)) => 99.05/14.95 ( 99.05/14.95 in(Y2, 99.05/14.95 Y1) | 99.05/14.95 in(Y2, 99.05/14.95 Y0)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 subset(Y0, 99.05/14.95 binunion(Y0, 99.05/14.95 Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 subset(Y1, 99.05/14.95 binunion( 99.05/14.95 Y0, Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 ( 99.05/14.95 in(Y2, 99.05/14.95 Y1) => 99.05/14.95 in(Y2, 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 ( 99.05/14.95 subset( 99.05/14.95 Y2, Y0) => 99.05/14.95 ( 99.05/14.95 subset( 99.05/14.95 Y2, Y1) => 99.05/14.95 subset( 99.05/14.95 Y2, 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1)) => 99.05/14.95 in(Y2, 99.05/14.95 Y0))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 subset( 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1), 99.05/14.95 Y0))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ( 99.05/14.95 subset( 99.05/14.95 Y0, Y1) => 99.05/14.95 ( 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1) = 99.05/14.95 Y0)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (( 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1) = 99.05/14.95 Y1) => 99.05/14.95 subset( 99.05/14.95 Y1, Y0)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1)) => 99.05/14.95 in(Y2, 99.05/14.95 Y1))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (( 99.05/14.95 ~(( 99.05/14.95 ??(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) & 99.05/14.95 in(Y2, 99.05/14.95 Y1))))))) => 99.05/14.95 ( 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1) = 99.05/14.95 emptyset)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 subset( 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1), 99.05/14.95 Y1))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (subset( 99.05/14.95 Y1, Y0) => 99.05/14.95 (binintersect( 99.05/14.95 Y0, Y1) = 99.05/14.95 Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (( 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1) = 99.05/14.95 Y0) => 99.05/14.95 subset( 99.05/14.95 Y0, Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (binintersect( 99.05/14.95 Y0, 99.05/14.95 binunion( 99.05/14.95 Y1, Y2)) = 99.05/14.95 binunion( 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1), 99.05/14.95 binintersect( 99.05/14.95 Y0, Y2)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y1))) => 99.05/14.95 in(Y2, 99.05/14.95 setminus( 99.05/14.95 Y0, Y1))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 setminus( 99.05/14.95 Y0, Y1)) => 99.05/14.95 in(Y2, 99.05/14.95 Y0))))))))))) => 99.05/14.95 ((!!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 setminus( 99.05/14.95 Y0, Y1)) => 99.05/14.95 (~( 99.05/14.95 in(Y2, 99.05/14.95 Y1))))))))))))) => 99.05/14.95 ((!!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (subset( 99.05/14.95 Y0, Y1) => 99.05/14.95 (setminus( 99.05/14.95 Y0, Y1) = 99.05/14.95 emptyset)))))))) => 99.05/14.95 ((!!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 setminus( 99.05/14.95 Y0, Y1)))) => 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 in(Y2, 99.05/14.95 Y1)))))))))))) => 99.05/14.95 ((!!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 setminus( 99.05/14.95 Y0, Y1)))) => 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y1))) => 99.05/14.95 (~( 99.05/14.95 in(Y2, 99.05/14.95 Y0)))))))))))))) => 99.05/14.95 (( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y0))) => 99.05/14.95 (~( 99.05/14.95 in(Y2, 99.05/14.95 setminus( 99.05/14.95 Y0, Y1)))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y1) => 99.05/14.95 (~( 99.05/14.95 in(Y2, 99.05/14.95 setminus( 99.05/14.95 Y0, Y1)))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 subset( 99.05/14.95 setminus( 99.05/14.95 Y0, Y1), 99.05/14.95 Y0))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (( 99.05/14.95 setminus( 99.05/14.95 Y0, Y1) = 99.05/14.95 emptyset) => 99.05/14.95 subset( 99.05/14.95 Y0, Y1)))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 symdiff( 99.05/14.95 Y0, Y1)) => 99.05/14.95 (!!(( 99.05/14.95 ^[Y3 : $o]: 99.05/14.95 (( 99.05/14.95 in(Y2, 99.05/14.95 Y0) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y1))) => 99.05/14.95 Y3)) => 99.05/14.95 (( 99.05/14.95 ( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y0))) => 99.05/14.95 ( 99.05/14.95 in(Y2, 99.05/14.95 Y1) => Y3)) => 99.05/14.95 Y3))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y1))) => 99.05/14.95 in(Y2, 99.05/14.95 symdiff( 99.05/14.95 Y0, Y1))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y0))) => 99.05/14.95 (in(Y2, 99.05/14.95 Y1) => 99.05/14.95 in(Y2, 99.05/14.95 symdiff( 99.05/14.95 Y0, Y1))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (in(Y2, 99.05/14.95 Y1) => 99.05/14.95 (~( 99.05/14.95 in(Y2, 99.05/14.95 symdiff( 99.05/14.95 Y0, Y1))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y0))) => 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y1))) => 99.05/14.95 (~( 99.05/14.95 in(Y2, 99.05/14.95 symdiff( 99.05/14.95 Y0, Y1))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 in(Y1, 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 in(Y0, 99.05/14.95 setunion( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 in(Y1, 99.05/14.95 setunion( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (??(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 setunion( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)))) & 99.05/14.95 (??(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (in(Y3, 99.05/14.95 setunion( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)))) & 99.05/14.95 (setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)) = 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset)), 99.05/14.95 emptyset))))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (??(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 setunion( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)))) & 99.05/14.95 (??(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (in(Y3, 99.05/14.95 setunion( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)))) & 99.05/14.95 (setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)) = 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset)), 99.05/14.95 emptyset))))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (in(Y1, 99.05/14.95 Y0) => 99.05/14.95 subset( 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset), 99.05/14.95 Y0)))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (in(Y1, 99.05/14.95 Y0) => 99.05/14.95 in( 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset), 99.05/14.95 powerset( 99.05/14.95 Y0))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 in( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 emptyset), 99.05/14.95 powerset( 99.05/14.95 binunion( 99.05/14.95 Y0, Y1))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset))) => 99.05/14.95 (( 99.05/14.95 Y2 = Y1) | 99.05/14.95 (Y2 = Y0)))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (!!(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (in(Y3, 99.05/14.95 Y1) => 99.05/14.95 subset( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset)), 99.05/14.95 binunion( 99.05/14.95 Y0, Y1)))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (!!(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (in(Y3, 99.05/14.95 Y1) => 99.05/14.95 in( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset)), 99.05/14.95 powerset( 99.05/14.95 binunion( 99.05/14.95 Y0, Y1))))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (!!(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (in(Y3, 99.05/14.95 Y1) => 99.05/14.95 subset( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)), 99.05/14.95 powerset( 99.05/14.95 binunion( 99.05/14.95 Y0, Y1))))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (!!(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (in(Y3, 99.05/14.95 Y1) => 99.05/14.95 in( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)), 99.05/14.95 powerset( 99.05/14.95 powerset( 99.05/14.95 binunion( 99.05/14.95 Y0, Y1)))))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (!!(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (in(Y3, 99.05/14.95 Y1) => 99.05/14.95 in( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)), 99.05/14.95 powerset( 99.05/14.95 powerset( 99.05/14.95 binunion( 99.05/14.95 Y0, Y1)))))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (!!(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (in(Y3, 99.05/14.95 Y1) => 99.05/14.95 in( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)), 99.05/14.95 dsetconstr( 99.05/14.95 powerset( 99.05/14.95 powerset( 99.05/14.95 binunion( 99.05/14.95 Y0, Y1))), 99.05/14.95 (^[Y4 : $i]: 99.05/14.95 (??(( 99.05/14.95 ^[Y5 : $i]: 99.05/14.95 (in(Y5, 99.05/14.95 Y0) & 99.05/14.95 (??(( 99.05/14.95 ^[Y6 : $i]: 99.05/14.95 (in(Y6, 99.05/14.95 Y1) & 99.05/14.95 (Y4 = 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y5, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y5, 99.05/14.95 setadjoin( 99.05/14.95 Y6, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)))))))))))))))))))))))))))) => 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 dsetconstr( 99.05/14.95 powerset( 99.05/14.95 powerset( 99.05/14.95 binunion( 99.05/14.95 Y0, Y1))), 99.05/14.95 (^[Y3 : $i]: 99.05/14.95 (??(( 99.05/14.95 ^[Y4 : $i]: 99.05/14.95 (in(Y4, 99.05/14.95 Y0) & 99.05/14.95 (??(( 99.05/14.95 ^[Y5 : $i]: 99.05/14.95 (in(Y5, 99.05/14.95 Y1) & 99.05/14.95 (Y3 = 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y4, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y4, 99.05/14.95 setadjoin( 99.05/14.95 Y5, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)))))))))))))) => 99.05/14.95 (??(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (( 99.05/14.95 ??(( 99.05/14.95 ^[Y4 : $i]: 99.05/14.95 (in(Y4, 99.05/14.95 Y1) & 99.05/14.95 (Y2 = 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 setadjoin( 99.05/14.95 Y4, 99.05/14.95 emptyset)), 99.05/14.95 emptyset))))))) & 99.05/14.95 in(Y3, 99.05/14.95 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.05/14.95 inference('lazy_cnf_imply', [status(thm)], ['218'])). 99.05/14.95 tff('220', plain, 99.05/14.95 ~ ((!!((^[Y0 : $i > $o]: 99.05/14.95 ((??(Y0)) => 99.05/14.95 ((!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.95 (??((^[Y1 : $i]: 99.05/14.95 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2)))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i > $o]: 99.05/14.95 ((??((^[Y1 : $i]: (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))) => 99.05/14.95 (??((^[Y1 : $i]: 99.05/14.95 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((Y0 = Y1) => 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (!!((^[Y3 : $i]: 99.05/14.95 ((Y2 = Y3) => 99.05/14.95 (in(Y2, Y0) => in(Y3, Y1)))))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((Y0 = Y1) => 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (!!((^[Y3 : $i]: 99.05/14.95 ((Y2 = Y3) => 99.05/14.95 (in(Y2, Y0) <=> in(Y3, Y1)))))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i > $o]: 99.05/14.95 ((??((^[Y1 : $i]: 99.05/14.95 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i > $o]: 99.05/14.95 (!!((^[Y1 : $i > $o]: 99.05/14.95 ((!!((^[Y2 : $i]: 99.05/14.95 (!!((^[Y3 : $i]: 99.05/14.95 ((Y2 = Y3) => (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.95 ((??((^[Y2 : $i]: 99.05/14.95 (Y0(Y2) & 99.05/14.95 (!!((^[Y3 : $i]: (Y0(Y3) => (Y2 = Y3))))))))) <=> 99.05/14.95 (??((^[Y2 : $i]: 99.05/14.95 (Y1(Y2) & 99.05/14.95 (!!((^[Y3 : $i]: (Y1(Y3) => (Y2 = Y3))))))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((Y0 = Y1) => 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (!!((^[Y3 : $i]: 99.05/14.95 ((Y2 = Y3) => 99.05/14.95 (setadjoin(Y0, Y2) = 99.05/14.95 setadjoin(Y1, Y3)))))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((Y0 = Y1) => (powerset(Y0) = powerset(Y1))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((Y0 = Y1) => (setunion(Y0) = setunion(Y1))))))))) => 99.05/14.95 ((!!((^[Y0 : $i > $o]: 99.05/14.95 ((??((^[Y1 : $i]: 99.05/14.95 (Y0(Y1) & 99.05/14.95 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i > $o]: 99.05/14.95 (!!((^[Y1 : $i > $o]: 99.05/14.95 ((!!((^[Y2 : $i]: 99.05/14.95 (!!((^[Y3 : $i]: 99.05/14.95 ((Y2 = Y3) => 99.05/14.95 (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.95 ((??((^[Y2 : $i]: 99.05/14.95 (Y0(Y2) & 99.05/14.95 (!!((^[Y3 : $i]: 99.05/14.95 (Y0(Y3) => (Y2 = Y3))))))))) => 99.05/14.95 ((??((^[Y2 : $i]: 99.05/14.95 (Y1(Y2) & 99.05/14.95 (!!((^[Y3 : $i]: 99.05/14.95 (Y1(Y3) => (Y2 = Y3))))))))) => 99.05/14.95 (descr(Y0) = descr(Y1))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((Y0 = Y1) => 99.05/14.95 (!!((^[Y2 : $i > $o]: 99.05/14.95 (!!((^[Y3 : $i > $o]: 99.05/14.95 ((!!((^[Y4 : $i]: 99.05/14.95 (in(Y4, Y0) => 99.05/14.95 (!!((^[Y5 : $i]: 99.05/14.95 (in(Y5, Y1) => 99.05/14.95 ((Y4 = Y5) => 99.05/14.95 (Y2(Y4) <=> 99.05/14.95 Y3(Y5))))))))))) => 99.05/14.95 (dsetconstr(Y0, Y2) = 99.05/14.95 dsetconstr(Y1, Y3)))))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 99.05/14.95 subset(Y0, Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y1, Y0)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y0, Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((!!((^[Y2 : $i]: 99.05/14.95 (in(Y2, Y0) => in(Y2, Y1))))) => 99.05/14.95 subset(Y0, Y1)))))))) => 99.05/14.95 ((!!(subset(emptyset))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (subset(Y0, Y1) => 99.05/14.95 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (subset(Y0, Y1) => 99.05/14.95 ((~(in(Y2, Y1))) => 99.05/14.95 (~(in(Y2, Y0)))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (in(Y2, Y0) => 99.05/14.95 ((~(in(Y2, Y1))) => 99.05/14.95 (~(subset(Y0, Y1)))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (in(Y2, Y0) => 99.05/14.95 ((~(in(Y2, Y1))) => 99.05/14.95 (Y0 != Y1)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (subset(Y0, Y1) => 99.05/14.95 (subset(Y1, Y2) => 99.05/14.95 subset(Y0, Y2)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 subset(Y1, setadjoin(Y0, Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (subset(Y0, Y2) => 99.05/14.95 subset(Y0, 99.05/14.95 setadjoin(Y1, Y2)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (subset(Y0, Y1) => 99.05/14.95 in(Y0, powerset(Y1))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (subset(Y0, Y1) => 99.05/14.95 (subset(Y1, Y0) => (Y0 = Y1))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (subset(Y0, emptyset) => 99.05/14.95 (Y0 = emptyset))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (subset(Y1, Y0) => 99.05/14.95 in(Y1, powerset(Y0))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (in(Y1, powerset(Y0)) => 99.05/14.95 subset(Y1, Y0)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (subset(Y0, Y1) => 99.05/14.95 subset(powerset(Y0), 99.05/14.95 powerset(Y1))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i > $o]: 99.05/14.95 in(dsetconstr(Y0, Y1), 99.05/14.95 powerset(Y0)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i > $o]: 99.05/14.95 subset( 99.05/14.95 dsetconstr(Y0, Y1), 99.05/14.95 Y0))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (in(Y2, Y0) => 99.05/14.95 in(Y2, 99.05/14.95 binunion( 99.05/14.95 Y0, Y1)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 in(Y1, 99.05/14.95 setadjoin(Y0, 99.05/14.95 setadjoin(Y1, 99.05/14.95 emptyset))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (in(Y2, Y1) => 99.05/14.95 in(Y2, 99.05/14.95 binunion( 99.05/14.95 Y0, Y1)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y3 : $o]: 99.05/14.95 (in(Y2, 99.05/14.95 binunion( 99.05/14.95 Y0, Y1)) => 99.05/14.95 (( 99.05/14.95 in(Y2, 99.05/14.95 Y0) => Y3) => 99.05/14.95 (( 99.05/14.95 in(Y2, 99.05/14.95 Y1) => Y3) => 99.05/14.95 Y3))))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 binunion( 99.05/14.95 Y0, Y1)) => 99.05/14.95 ( 99.05/14.95 in(Y2, 99.05/14.95 Y1) | 99.05/14.95 in(Y2, 99.05/14.95 Y0)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 subset(Y0, 99.05/14.95 binunion(Y0, 99.05/14.95 Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 subset(Y1, 99.05/14.95 binunion(Y0, 99.05/14.95 Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (in(Y2, 99.05/14.95 Y1) => 99.05/14.95 in(Y2, 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (subset( 99.05/14.95 Y2, Y0) => 99.05/14.95 ( 99.05/14.95 subset( 99.05/14.95 Y2, Y1) => 99.05/14.95 subset( 99.05/14.95 Y2, 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 ( 99.05/14.95 in(Y2, 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1)) => 99.05/14.95 in(Y2, 99.05/14.95 Y0))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 subset( 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1), 99.05/14.95 Y0))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (subset( 99.05/14.95 Y0, Y1) => 99.05/14.95 ( 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1) = 99.05/14.95 Y0)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1) = 99.05/14.95 Y1) => 99.05/14.95 subset( 99.05/14.95 Y1, Y0)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1)) => 99.05/14.95 in(Y2, 99.05/14.95 Y1))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (( 99.05/14.95 ~(( 99.05/14.95 ??(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) & 99.05/14.95 in(Y2, 99.05/14.95 Y1))))))) => 99.05/14.95 (binintersect( 99.05/14.95 Y0, Y1) = 99.05/14.95 emptyset)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 subset( 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1), 99.05/14.95 Y1))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 ( 99.05/14.95 subset( 99.05/14.95 Y1, Y0) => 99.05/14.95 ( 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1) = 99.05/14.95 Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (( 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1) = 99.05/14.95 Y0) => 99.05/14.95 subset( 99.05/14.95 Y0, Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (binintersect( 99.05/14.95 Y0, 99.05/14.95 binunion( 99.05/14.95 Y1, Y2)) = 99.05/14.95 binunion( 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1), 99.05/14.95 binintersect( 99.05/14.95 Y0, Y2)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y1))) => 99.05/14.95 in(Y2, 99.05/14.95 setminus( 99.05/14.95 Y0, Y1))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 setminus( 99.05/14.95 Y0, Y1)) => 99.05/14.95 in(Y2, 99.05/14.95 Y0))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 setminus( 99.05/14.95 Y0, Y1)) => 99.05/14.95 (~( 99.05/14.95 in(Y2, 99.05/14.95 Y1))))))))))))) => 99.05/14.95 ((!!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (subset( 99.05/14.95 Y0, Y1) => 99.05/14.95 (setminus( 99.05/14.95 Y0, Y1) = 99.05/14.95 emptyset)))))))) => 99.05/14.95 ((!!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 setminus( 99.05/14.95 Y0, Y1)))) => 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 in(Y2, 99.05/14.95 Y1)))))))))))) => 99.05/14.95 ((!!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 setminus( 99.05/14.95 Y0, Y1)))) => 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y1))) => 99.05/14.95 (~( 99.05/14.95 in(Y2, 99.05/14.95 Y0)))))))))))))) => 99.05/14.95 ((!!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y0))) => 99.05/14.95 (~( 99.05/14.95 in(Y2, 99.05/14.95 setminus( 99.05/14.95 Y0, Y1)))))))))))))) => 99.05/14.95 (( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y1) => 99.05/14.95 (~( 99.05/14.95 in(Y2, 99.05/14.95 setminus( 99.05/14.95 Y0, Y1)))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 subset( 99.05/14.95 setminus( 99.05/14.95 Y0, Y1), 99.05/14.95 Y0))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (( 99.05/14.95 setminus( 99.05/14.95 Y0, Y1) = 99.05/14.95 emptyset) => 99.05/14.95 subset( 99.05/14.95 Y0, Y1)))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 symdiff( 99.05/14.95 Y0, Y1)) => 99.05/14.95 (!!(( 99.05/14.95 ^[Y3 : $o]: 99.05/14.95 (( 99.05/14.95 in(Y2, 99.05/14.95 Y0) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y1))) => 99.05/14.95 Y3)) => 99.05/14.95 (( 99.05/14.95 ( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y0))) => 99.05/14.95 ( 99.05/14.95 in(Y2, 99.05/14.95 Y1) => Y3)) => 99.05/14.95 Y3))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y1))) => 99.05/14.95 in(Y2, 99.05/14.95 symdiff( 99.05/14.95 Y0, Y1))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y0))) => 99.05/14.95 (in(Y2, 99.05/14.95 Y1) => 99.05/14.95 in(Y2, 99.05/14.95 symdiff( 99.05/14.95 Y0, Y1))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (in(Y2, 99.05/14.95 Y1) => 99.05/14.95 (~( 99.05/14.95 in(Y2, 99.05/14.95 symdiff( 99.05/14.95 Y0, Y1))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y0))) => 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y1))) => 99.05/14.95 (~( 99.05/14.95 in(Y2, 99.05/14.95 symdiff( 99.05/14.95 Y0, Y1))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 in(Y1, 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 in(Y0, 99.05/14.95 setunion( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 in(Y1, 99.05/14.95 setunion( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (??(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 setunion( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)))) & 99.05/14.95 (??(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (in(Y3, 99.05/14.95 setunion( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)))) & 99.05/14.95 (setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)) = 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset)), 99.05/14.95 emptyset))))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (??(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 setunion( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)))) & 99.05/14.95 (??(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (in(Y3, 99.05/14.95 setunion( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)))) & 99.05/14.95 (setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)) = 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset)), 99.05/14.95 emptyset))))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (in(Y1, 99.05/14.95 Y0) => 99.05/14.95 subset( 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset), 99.05/14.95 Y0)))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (in(Y1, 99.05/14.95 Y0) => 99.05/14.95 in( 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset), 99.05/14.95 powerset( 99.05/14.95 Y0))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 in( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 emptyset), 99.05/14.95 powerset( 99.05/14.95 binunion( 99.05/14.95 Y0, Y1))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset))) => 99.05/14.95 (( 99.05/14.95 Y2 = Y1) | 99.05/14.95 (Y2 = Y0)))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (!!(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (in(Y3, 99.05/14.95 Y1) => 99.05/14.95 subset( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset)), 99.05/14.95 binunion( 99.05/14.95 Y0, Y1)))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (!!(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (in(Y3, 99.05/14.95 Y1) => 99.05/14.95 in( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset)), 99.05/14.95 powerset( 99.05/14.95 binunion( 99.05/14.95 Y0, Y1))))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (!!(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (in(Y3, 99.05/14.95 Y1) => 99.05/14.95 subset( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)), 99.05/14.95 powerset( 99.05/14.95 binunion( 99.05/14.95 Y0, Y1))))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (!!(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (in(Y3, 99.05/14.95 Y1) => 99.05/14.95 in( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)), 99.05/14.95 powerset( 99.05/14.95 powerset( 99.05/14.95 binunion( 99.05/14.95 Y0, Y1)))))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (!!(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (in(Y3, 99.05/14.95 Y1) => 99.05/14.95 in( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)), 99.05/14.95 powerset( 99.05/14.95 powerset( 99.05/14.95 binunion( 99.05/14.95 Y0, Y1)))))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (!!(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (in(Y3, 99.05/14.95 Y1) => 99.05/14.95 in( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)), 99.05/14.95 dsetconstr( 99.05/14.95 powerset( 99.05/14.95 powerset( 99.05/14.95 binunion( 99.05/14.95 Y0, Y1))), 99.05/14.95 (^[Y4 : $i]: 99.05/14.95 (??(( 99.05/14.95 ^[Y5 : $i]: 99.05/14.95 (in(Y5, 99.05/14.95 Y0) & 99.05/14.95 (??(( 99.05/14.95 ^[Y6 : $i]: 99.05/14.95 (in(Y6, 99.05/14.95 Y1) & 99.05/14.95 (Y4 = 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y5, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y5, 99.05/14.95 setadjoin( 99.05/14.95 Y6, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)))))))))))))))))))))))))))) => 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 dsetconstr( 99.05/14.95 powerset( 99.05/14.95 powerset( 99.05/14.95 binunion( 99.05/14.95 Y0, Y1))), 99.05/14.95 (^[Y3 : $i]: 99.05/14.95 (??(( 99.05/14.95 ^[Y4 : $i]: 99.05/14.95 (in(Y4, 99.05/14.95 Y0) & 99.05/14.95 (??(( 99.05/14.95 ^[Y5 : $i]: 99.05/14.95 (in(Y5, 99.05/14.95 Y1) & 99.05/14.95 (Y3 = 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y4, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y4, 99.05/14.95 setadjoin( 99.05/14.95 Y5, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)))))))))))))) => 99.05/14.95 (??(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (( 99.05/14.95 ??(( 99.05/14.95 ^[Y4 : $i]: 99.05/14.95 (in(Y4, 99.05/14.95 Y1) & 99.05/14.95 (Y2 = 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 setadjoin( 99.05/14.95 Y4, 99.05/14.95 emptyset)), 99.05/14.95 emptyset))))))) & 99.05/14.95 in(Y3, 99.05/14.95 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.05/14.95 inference('lazy_cnf_imply', [status(thm)], ['219'])). 99.05/14.95 tff('221', plain, 99.05/14.95 ~ ((!!((^[Y0 : $i > $o]: 99.05/14.95 ((??((^[Y1 : $i]: (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))) => 99.05/14.95 (??((^[Y1 : $i]: 99.05/14.95 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((Y0 = Y1) => 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (!!((^[Y3 : $i]: 99.05/14.95 ((Y2 = Y3) => (in(Y2, Y0) => in(Y3, Y1)))))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((Y0 = Y1) => 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (!!((^[Y3 : $i]: 99.05/14.95 ((Y2 = Y3) => 99.05/14.95 (in(Y2, Y0) <=> in(Y3, Y1)))))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i > $o]: 99.05/14.95 ((??((^[Y1 : $i]: 99.05/14.95 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i > $o]: 99.05/14.95 (!!((^[Y1 : $i > $o]: 99.05/14.95 ((!!((^[Y2 : $i]: 99.05/14.95 (!!((^[Y3 : $i]: 99.05/14.95 ((Y2 = Y3) => (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.95 ((??((^[Y2 : $i]: 99.05/14.95 (Y0(Y2) & 99.05/14.95 (!!((^[Y3 : $i]: (Y0(Y3) => (Y2 = Y3))))))))) <=> 99.05/14.95 (??((^[Y2 : $i]: 99.05/14.95 (Y1(Y2) & 99.05/14.95 (!!((^[Y3 : $i]: (Y1(Y3) => (Y2 = Y3))))))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((Y0 = Y1) => 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (!!((^[Y3 : $i]: 99.05/14.95 ((Y2 = Y3) => 99.05/14.95 (setadjoin(Y0, Y2) = 99.05/14.95 setadjoin(Y1, Y3)))))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((Y0 = Y1) => (powerset(Y0) = powerset(Y1))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((Y0 = Y1) => (setunion(Y0) = setunion(Y1))))))))) => 99.05/14.95 ((!!((^[Y0 : $i > $o]: 99.05/14.95 ((??((^[Y1 : $i]: 99.05/14.95 (Y0(Y1) & 99.05/14.95 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i > $o]: 99.05/14.95 (!!((^[Y1 : $i > $o]: 99.05/14.95 ((!!((^[Y2 : $i]: 99.05/14.95 (!!((^[Y3 : $i]: 99.05/14.95 ((Y2 = Y3) => 99.05/14.95 (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.95 ((??((^[Y2 : $i]: 99.05/14.95 (Y0(Y2) & 99.05/14.95 (!!((^[Y3 : $i]: 99.05/14.95 (Y0(Y3) => (Y2 = Y3))))))))) => 99.05/14.95 ((??((^[Y2 : $i]: 99.05/14.95 (Y1(Y2) & 99.05/14.95 (!!((^[Y3 : $i]: 99.05/14.95 (Y1(Y3) => (Y2 = Y3))))))))) => 99.05/14.95 (descr(Y0) = descr(Y1))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((Y0 = Y1) => 99.05/14.95 (!!((^[Y2 : $i > $o]: 99.05/14.95 (!!((^[Y3 : $i > $o]: 99.05/14.95 ((!!((^[Y4 : $i]: 99.05/14.95 (in(Y4, Y0) => 99.05/14.95 (!!((^[Y5 : $i]: 99.05/14.95 (in(Y5, Y1) => 99.05/14.95 ((Y4 = Y5) => 99.05/14.95 (Y2(Y4) <=> 99.05/14.95 Y3(Y5))))))))))) => 99.05/14.95 (dsetconstr(Y0, Y2) = 99.05/14.95 dsetconstr(Y1, Y3)))))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 99.05/14.95 subset(Y0, Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y1, Y0)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y0, Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((!!((^[Y2 : $i]: 99.05/14.95 (in(Y2, Y0) => in(Y2, Y1))))) => 99.05/14.95 subset(Y0, Y1)))))))) => 99.05/14.95 ((!!(subset(emptyset))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (subset(Y0, Y1) => 99.05/14.95 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (subset(Y0, Y1) => 99.05/14.95 ((~(in(Y2, Y1))) => 99.05/14.95 (~(in(Y2, Y0)))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (in(Y2, Y0) => 99.05/14.95 ((~(in(Y2, Y1))) => 99.05/14.95 (~(subset(Y0, Y1)))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (in(Y2, Y0) => 99.05/14.95 ((~(in(Y2, Y1))) => 99.05/14.95 (Y0 != Y1)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (subset(Y0, Y1) => 99.05/14.95 (subset(Y1, Y2) => 99.05/14.95 subset(Y0, Y2)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 subset(Y1, setadjoin(Y0, Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (subset(Y0, Y2) => 99.05/14.95 subset(Y0, 99.05/14.95 setadjoin(Y1, Y2)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (subset(Y0, Y1) => 99.05/14.95 in(Y0, powerset(Y1))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (subset(Y0, Y1) => 99.05/14.95 (subset(Y1, Y0) => (Y0 = Y1))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (subset(Y0, emptyset) => 99.05/14.95 (Y0 = emptyset))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (subset(Y1, Y0) => 99.05/14.95 in(Y1, powerset(Y0))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (in(Y1, powerset(Y0)) => 99.05/14.95 subset(Y1, Y0)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (subset(Y0, Y1) => 99.05/14.95 subset(powerset(Y0), 99.05/14.95 powerset(Y1))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i > $o]: 99.05/14.95 in(dsetconstr(Y0, Y1), 99.05/14.95 powerset(Y0)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i > $o]: 99.05/14.95 subset( 99.05/14.95 dsetconstr(Y0, Y1), 99.05/14.95 Y0))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (in(Y2, Y0) => 99.05/14.95 in(Y2, 99.05/14.95 binunion( 99.05/14.95 Y0, Y1)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 in(Y1, 99.05/14.95 setadjoin(Y0, 99.05/14.95 setadjoin(Y1, 99.05/14.95 emptyset))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (in(Y2, Y1) => 99.05/14.95 in(Y2, 99.05/14.95 binunion( 99.05/14.95 Y0, Y1)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y3 : $o]: 99.05/14.95 ( 99.05/14.95 in(Y2, 99.05/14.95 binunion( 99.05/14.95 Y0, Y1)) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 in(Y2, 99.05/14.95 Y0) => Y3) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 in(Y2, 99.05/14.95 Y1) => Y3) => 99.05/14.95 Y3))))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 binunion( 99.05/14.95 Y0, Y1)) => 99.05/14.95 (in(Y2, 99.05/14.95 Y1) | 99.05/14.95 in(Y2, 99.05/14.95 Y0)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 subset(Y0, 99.05/14.95 binunion(Y0, 99.05/14.95 Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 subset(Y1, 99.05/14.95 binunion(Y0, 99.05/14.95 Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (in(Y2, 99.05/14.95 Y1) => 99.05/14.95 in(Y2, 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (subset( 99.05/14.95 Y2, Y0) => 99.05/14.95 (subset( 99.05/14.95 Y2, Y1) => 99.05/14.95 subset( 99.05/14.95 Y2, 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1)) => 99.05/14.95 in(Y2, 99.05/14.95 Y0))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 subset( 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1), 99.05/14.95 Y0))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (subset( 99.05/14.95 Y0, Y1) => 99.05/14.95 (binintersect( 99.05/14.95 Y0, Y1) = 99.05/14.95 Y0)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (( 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1) = 99.05/14.95 Y1) => 99.05/14.95 subset( 99.05/14.95 Y1, Y0)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1)) => 99.05/14.95 in(Y2, 99.05/14.95 Y1))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (( 99.05/14.95 ~(( 99.05/14.95 ??(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) & 99.05/14.95 in(Y2, 99.05/14.95 Y1))))))) => 99.05/14.95 (binintersect( 99.05/14.95 Y0, Y1) = 99.05/14.95 emptyset)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 subset( 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1), 99.05/14.95 Y1))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (subset( 99.05/14.95 Y1, Y0) => 99.05/14.95 ( 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1) = 99.05/14.95 Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1) = 99.05/14.95 Y0) => 99.05/14.95 subset( 99.05/14.95 Y0, Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (binintersect( 99.05/14.95 Y0, 99.05/14.95 binunion( 99.05/14.95 Y1, Y2)) = 99.05/14.95 binunion( 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1), 99.05/14.95 binintersect( 99.05/14.95 Y0, Y2)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y1))) => 99.05/14.95 in(Y2, 99.05/14.95 setminus( 99.05/14.95 Y0, Y1))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 setminus( 99.05/14.95 Y0, Y1)) => 99.05/14.95 in(Y2, 99.05/14.95 Y0))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 setminus( 99.05/14.95 Y0, Y1)) => 99.05/14.95 (~( 99.05/14.95 in(Y2, 99.05/14.95 Y1))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (subset( 99.05/14.95 Y0, Y1) => 99.05/14.95 (setminus( 99.05/14.95 Y0, Y1) = 99.05/14.95 emptyset)))))))) => 99.05/14.95 ((!!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 setminus( 99.05/14.95 Y0, Y1)))) => 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 in(Y2, 99.05/14.95 Y1)))))))))))) => 99.05/14.95 ((!!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 setminus( 99.05/14.95 Y0, Y1)))) => 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y1))) => 99.05/14.95 (~( 99.05/14.95 in(Y2, 99.05/14.95 Y0)))))))))))))) => 99.05/14.95 ((!!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y0))) => 99.05/14.95 (~( 99.05/14.95 in(Y2, 99.05/14.95 setminus( 99.05/14.95 Y0, Y1)))))))))))))) => 99.05/14.95 ((!!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y1) => 99.05/14.95 (~( 99.05/14.95 in(Y2, 99.05/14.95 setminus( 99.05/14.95 Y0, Y1)))))))))))))) => 99.05/14.95 (( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 subset( 99.05/14.95 setminus( 99.05/14.95 Y0, Y1), 99.05/14.95 Y0))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (( 99.05/14.95 setminus( 99.05/14.95 Y0, Y1) = 99.05/14.95 emptyset) => 99.05/14.95 subset( 99.05/14.95 Y0, Y1)))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 symdiff( 99.05/14.95 Y0, Y1)) => 99.05/14.95 (!!(( 99.05/14.95 ^[Y3 : $o]: 99.05/14.95 (( 99.05/14.95 in(Y2, 99.05/14.95 Y0) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y1))) => 99.05/14.95 Y3)) => 99.05/14.95 (( 99.05/14.95 ( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y0))) => 99.05/14.95 ( 99.05/14.95 in(Y2, 99.05/14.95 Y1) => Y3)) => 99.05/14.95 Y3))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y1))) => 99.05/14.95 in(Y2, 99.05/14.95 symdiff( 99.05/14.95 Y0, Y1))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y0))) => 99.05/14.95 (in(Y2, 99.05/14.95 Y1) => 99.05/14.95 in(Y2, 99.05/14.95 symdiff( 99.05/14.95 Y0, Y1))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (in(Y2, 99.05/14.95 Y1) => 99.05/14.95 (~( 99.05/14.95 in(Y2, 99.05/14.95 symdiff( 99.05/14.95 Y0, Y1))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y0))) => 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y1))) => 99.05/14.95 (~( 99.05/14.95 in(Y2, 99.05/14.95 symdiff( 99.05/14.95 Y0, Y1))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 in(Y1, 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 in(Y0, 99.05/14.95 setunion( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 in(Y1, 99.05/14.95 setunion( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (??(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 setunion( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)))) & 99.05/14.95 (??(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (in(Y3, 99.05/14.95 setunion( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)))) & 99.05/14.95 (setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)) = 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset)), 99.05/14.95 emptyset))))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (??(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 setunion( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)))) & 99.05/14.95 (??(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (in(Y3, 99.05/14.95 setunion( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)))) & 99.05/14.95 (setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)) = 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset)), 99.05/14.95 emptyset))))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (in(Y1, 99.05/14.95 Y0) => 99.05/14.95 subset( 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset), 99.05/14.95 Y0)))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (in(Y1, 99.05/14.95 Y0) => 99.05/14.95 in( 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset), 99.05/14.95 powerset( 99.05/14.95 Y0))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 in( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 emptyset), 99.05/14.95 powerset( 99.05/14.95 binunion( 99.05/14.95 Y0, Y1))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset))) => 99.05/14.95 (( 99.05/14.95 Y2 = Y1) | 99.05/14.95 (Y2 = Y0)))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (!!(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (in(Y3, 99.05/14.95 Y1) => 99.05/14.95 subset( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset)), 99.05/14.95 binunion( 99.05/14.95 Y0, Y1)))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (!!(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (in(Y3, 99.05/14.95 Y1) => 99.05/14.95 in( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset)), 99.05/14.95 powerset( 99.05/14.95 binunion( 99.05/14.95 Y0, Y1))))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (!!(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (in(Y3, 99.05/14.95 Y1) => 99.05/14.95 subset( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)), 99.05/14.95 powerset( 99.05/14.95 binunion( 99.05/14.95 Y0, Y1))))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (!!(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (in(Y3, 99.05/14.95 Y1) => 99.05/14.95 in( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)), 99.05/14.95 powerset( 99.05/14.95 powerset( 99.05/14.95 binunion( 99.05/14.95 Y0, Y1)))))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (!!(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (in(Y3, 99.05/14.95 Y1) => 99.05/14.95 in( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)), 99.05/14.95 powerset( 99.05/14.95 powerset( 99.05/14.95 binunion( 99.05/14.95 Y0, Y1)))))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (!!(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (in(Y3, 99.05/14.95 Y1) => 99.05/14.95 in( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)), 99.05/14.95 dsetconstr( 99.05/14.95 powerset( 99.05/14.95 powerset( 99.05/14.95 binunion( 99.05/14.95 Y0, Y1))), 99.05/14.95 (^[Y4 : $i]: 99.05/14.95 (??(( 99.05/14.95 ^[Y5 : $i]: 99.05/14.95 (in(Y5, 99.05/14.95 Y0) & 99.05/14.95 (??(( 99.05/14.95 ^[Y6 : $i]: 99.05/14.95 (in(Y6, 99.05/14.95 Y1) & 99.05/14.95 (Y4 = 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y5, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y5, 99.05/14.95 setadjoin( 99.05/14.95 Y6, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)))))))))))))))))))))))))))) => 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 dsetconstr( 99.05/14.95 powerset( 99.05/14.95 powerset( 99.05/14.95 binunion( 99.05/14.95 Y0, Y1))), 99.05/14.95 (^[Y3 : $i]: 99.05/14.95 (??(( 99.05/14.95 ^[Y4 : $i]: 99.05/14.95 (in(Y4, 99.05/14.95 Y0) & 99.05/14.95 (??(( 99.05/14.95 ^[Y5 : $i]: 99.05/14.95 (in(Y5, 99.05/14.95 Y1) & 99.05/14.95 (Y3 = 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y4, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y4, 99.05/14.95 setadjoin( 99.05/14.95 Y5, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)))))))))))))) => 99.05/14.95 (??(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (( 99.05/14.95 ??(( 99.05/14.95 ^[Y4 : $i]: 99.05/14.95 (in(Y4, 99.05/14.95 Y1) & 99.05/14.95 (Y2 = 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 setadjoin( 99.05/14.95 Y4, 99.05/14.95 emptyset)), 99.05/14.95 emptyset))))))) & 99.05/14.95 in(Y3, 99.05/14.95 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.05/14.95 inference('lazy_cnf_imply', [status(thm)], ['220'])). 99.05/14.95 tff('222', plain, 99.05/14.95 ~ ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((Y0 = Y1) => 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (!!((^[Y3 : $i]: 99.05/14.95 ((Y2 = Y3) => (in(Y2, Y0) => in(Y3, Y1)))))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((Y0 = Y1) => 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (!!((^[Y3 : $i]: 99.05/14.95 ((Y2 = Y3) => 99.05/14.95 (in(Y2, Y0) <=> in(Y3, Y1)))))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i > $o]: 99.05/14.95 ((??((^[Y1 : $i]: 99.05/14.95 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i > $o]: 99.05/14.95 (!!((^[Y1 : $i > $o]: 99.05/14.95 ((!!((^[Y2 : $i]: 99.05/14.95 (!!((^[Y3 : $i]: 99.05/14.95 ((Y2 = Y3) => (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.95 ((??((^[Y2 : $i]: 99.05/14.95 (Y0(Y2) & 99.05/14.95 (!!((^[Y3 : $i]: (Y0(Y3) => (Y2 = Y3))))))))) <=> 99.05/14.95 (??((^[Y2 : $i]: 99.05/14.95 (Y1(Y2) & 99.05/14.95 (!!((^[Y3 : $i]: (Y1(Y3) => (Y2 = Y3))))))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((Y0 = Y1) => 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (!!((^[Y3 : $i]: 99.05/14.95 ((Y2 = Y3) => 99.05/14.95 (setadjoin(Y0, Y2) = 99.05/14.95 setadjoin(Y1, Y3)))))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((Y0 = Y1) => (powerset(Y0) = powerset(Y1))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((Y0 = Y1) => (setunion(Y0) = setunion(Y1))))))))) => 99.05/14.95 ((!!((^[Y0 : $i > $o]: 99.05/14.95 ((??((^[Y1 : $i]: 99.05/14.95 (Y0(Y1) & 99.05/14.95 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i > $o]: 99.05/14.95 (!!((^[Y1 : $i > $o]: 99.05/14.95 ((!!((^[Y2 : $i]: 99.05/14.95 (!!((^[Y3 : $i]: 99.05/14.95 ((Y2 = Y3) => (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.95 ((??((^[Y2 : $i]: 99.05/14.95 (Y0(Y2) & 99.05/14.95 (!!((^[Y3 : $i]: (Y0(Y3) => (Y2 = Y3))))))))) => 99.05/14.95 ((??((^[Y2 : $i]: 99.05/14.95 (Y1(Y2) & 99.05/14.95 (!!((^[Y3 : $i]: 99.05/14.95 (Y1(Y3) => (Y2 = Y3))))))))) => 99.05/14.95 (descr(Y0) = descr(Y1))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((Y0 = Y1) => 99.05/14.95 (!!((^[Y2 : $i > $o]: 99.05/14.95 (!!((^[Y3 : $i > $o]: 99.05/14.95 ((!!((^[Y4 : $i]: 99.05/14.95 (in(Y4, Y0) => 99.05/14.95 (!!((^[Y5 : $i]: 99.05/14.95 (in(Y5, Y1) => 99.05/14.95 ((Y4 = Y5) => 99.05/14.95 (Y2(Y4) <=> 99.05/14.95 Y3(Y5))))))))))) => 99.05/14.95 (dsetconstr(Y0, Y2) = 99.05/14.95 dsetconstr(Y1, Y3)))))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 99.05/14.95 subset(Y0, Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y1, Y0)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y0, Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((!!((^[Y2 : $i]: 99.05/14.95 (in(Y2, Y0) => in(Y2, Y1))))) => 99.05/14.95 subset(Y0, Y1)))))))) => 99.05/14.95 ((!!(subset(emptyset))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (subset(Y0, Y1) => 99.05/14.95 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (subset(Y0, Y1) => 99.05/14.95 ((~(in(Y2, Y1))) => 99.05/14.95 (~(in(Y2, Y0)))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (in(Y2, Y0) => 99.05/14.95 ((~(in(Y2, Y1))) => 99.05/14.95 (~(subset(Y0, Y1)))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (in(Y2, Y0) => 99.05/14.95 ((~(in(Y2, Y1))) => 99.05/14.95 (Y0 != Y1)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (subset(Y0, Y1) => 99.05/14.95 (subset(Y1, Y2) => 99.05/14.95 subset(Y0, Y2)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 subset(Y1, setadjoin(Y0, Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (subset(Y0, Y2) => 99.05/14.95 subset(Y0, 99.05/14.95 setadjoin(Y1, Y2)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (subset(Y0, Y1) => 99.05/14.95 in(Y0, powerset(Y1))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (subset(Y0, Y1) => 99.05/14.95 (subset(Y1, Y0) => (Y0 = Y1))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (subset(Y0, emptyset) => 99.05/14.95 (Y0 = emptyset))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (subset(Y1, Y0) => 99.05/14.95 in(Y1, powerset(Y0))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (in(Y1, powerset(Y0)) => 99.05/14.95 subset(Y1, Y0)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (subset(Y0, Y1) => 99.05/14.95 subset(powerset(Y0), 99.05/14.95 powerset(Y1))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i > $o]: 99.05/14.95 in(dsetconstr(Y0, Y1), 99.05/14.95 powerset(Y0)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i > $o]: 99.05/14.95 subset( 99.05/14.95 dsetconstr(Y0, Y1), 99.05/14.95 Y0))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (in(Y2, Y0) => 99.05/14.95 in(Y2, 99.05/14.95 binunion(Y0, 99.05/14.95 Y1)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 in(Y1, 99.05/14.95 setadjoin(Y0, 99.05/14.95 setadjoin(Y1, 99.05/14.95 emptyset))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (in(Y2, Y1) => 99.05/14.95 in(Y2, 99.05/14.95 binunion( 99.05/14.95 Y0, Y1)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y3 : $o]: 99.05/14.95 (in(Y2, 99.05/14.95 binunion( 99.05/14.95 Y0, Y1)) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 in(Y2, 99.05/14.95 Y0) => Y3) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 in(Y2, 99.05/14.95 Y1) => Y3) => 99.05/14.95 Y3))))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 binunion( 99.05/14.95 Y0, Y1)) => 99.05/14.95 (in(Y2, Y1) | 99.05/14.95 in(Y2, Y0)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 subset(Y0, 99.05/14.95 binunion(Y0, Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 subset(Y1, 99.05/14.95 binunion(Y0, 99.05/14.95 Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 ( 99.05/14.95 in(Y2, 99.05/14.95 Y0) => 99.05/14.95 ( 99.05/14.95 in(Y2, 99.05/14.95 Y1) => 99.05/14.95 in(Y2, 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (subset( 99.05/14.95 Y2, Y0) => 99.05/14.95 (subset( 99.05/14.95 Y2, Y1) => 99.05/14.95 subset( 99.05/14.95 Y2, 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1)) => 99.05/14.95 in(Y2, 99.05/14.95 Y0))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 subset( 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1), 99.05/14.95 Y0))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (subset(Y0, 99.05/14.95 Y1) => 99.05/14.95 (binintersect( 99.05/14.95 Y0, Y1) = 99.05/14.95 Y0)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((binintersect( 99.05/14.95 Y0, Y1) = 99.05/14.95 Y1) => 99.05/14.95 subset( 99.05/14.95 Y1, Y0)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1)) => 99.05/14.95 in(Y2, 99.05/14.95 Y1))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 ~(( 99.05/14.95 ??(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) & 99.05/14.95 in(Y2, 99.05/14.95 Y1))))))) => 99.05/14.95 ( 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1) = 99.05/14.95 emptyset)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 subset( 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1), 99.05/14.95 Y1))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (subset( 99.05/14.95 Y1, Y0) => 99.05/14.95 (binintersect( 99.05/14.95 Y0, Y1) = 99.05/14.95 Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (( 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1) = 99.05/14.95 Y0) => 99.05/14.95 subset( 99.05/14.95 Y0, Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (binintersect( 99.05/14.95 Y0, 99.05/14.95 binunion( 99.05/14.95 Y1, Y2)) = 99.05/14.95 binunion( 99.05/14.95 binintersect( 99.05/14.95 Y0, Y1), 99.05/14.95 binintersect( 99.05/14.95 Y0, Y2)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y1))) => 99.05/14.95 in(Y2, 99.05/14.95 setminus( 99.05/14.95 Y0, Y1))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 setminus( 99.05/14.95 Y0, Y1)) => 99.05/14.95 in(Y2, 99.05/14.95 Y0))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 setminus( 99.05/14.95 Y0, Y1)) => 99.05/14.95 (~( 99.05/14.95 in(Y2, 99.05/14.95 Y1))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (subset( 99.05/14.95 Y0, Y1) => 99.05/14.95 (setminus( 99.05/14.95 Y0, Y1) = 99.05/14.95 emptyset)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 setminus( 99.05/14.95 Y0, Y1)))) => 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 in(Y2, 99.05/14.95 Y1)))))))))))) => 99.05/14.95 ((!!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 setminus( 99.05/14.95 Y0, Y1)))) => 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y1))) => 99.05/14.95 (~( 99.05/14.95 in(Y2, 99.05/14.95 Y0)))))))))))))) => 99.05/14.95 ((!!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y0))) => 99.05/14.95 (~( 99.05/14.95 in(Y2, 99.05/14.95 setminus( 99.05/14.95 Y0, Y1)))))))))))))) => 99.05/14.95 ((!!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y1) => 99.05/14.95 (~( 99.05/14.95 in(Y2, 99.05/14.95 setminus( 99.05/14.95 Y0, Y1)))))))))))))) => 99.05/14.95 ((!!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 subset( 99.05/14.95 setminus( 99.05/14.95 Y0, Y1), 99.05/14.95 Y0))))))) => 99.05/14.95 (( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (( 99.05/14.95 setminus( 99.05/14.95 Y0, Y1) = 99.05/14.95 emptyset) => 99.05/14.95 subset( 99.05/14.95 Y0, Y1)))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 symdiff( 99.05/14.95 Y0, Y1)) => 99.05/14.95 (!!(( 99.05/14.95 ^[Y3 : $o]: 99.05/14.95 (( 99.05/14.95 in(Y2, 99.05/14.95 Y0) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y1))) => 99.05/14.95 Y3)) => 99.05/14.95 (( 99.05/14.95 ( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y0))) => 99.05/14.95 ( 99.05/14.95 in(Y2, 99.05/14.95 Y1) => Y3)) => 99.05/14.95 Y3))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y1))) => 99.05/14.95 in(Y2, 99.05/14.95 symdiff( 99.05/14.95 Y0, Y1))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y0))) => 99.05/14.95 (in(Y2, 99.05/14.95 Y1) => 99.05/14.95 in(Y2, 99.05/14.95 symdiff( 99.05/14.95 Y0, Y1))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (in(Y2, 99.05/14.95 Y1) => 99.05/14.95 (~( 99.05/14.95 in(Y2, 99.05/14.95 symdiff( 99.05/14.95 Y0, Y1))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y0))) => 99.05/14.95 (( 99.05/14.95 ~( 99.05/14.95 in(Y2, 99.05/14.95 Y1))) => 99.05/14.95 (~( 99.05/14.95 in(Y2, 99.05/14.95 symdiff( 99.05/14.95 Y0, Y1))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 in(Y1, 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 in(Y0, 99.05/14.95 setunion( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 in(Y1, 99.05/14.95 setunion( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (??(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 setunion( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)))) & 99.05/14.95 (??(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (in(Y3, 99.05/14.95 setunion( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)))) & 99.05/14.95 (setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)) = 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset)), 99.05/14.95 emptyset))))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (??(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 setunion( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)))) & 99.05/14.95 (??(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (in(Y3, 99.05/14.95 setunion( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)))) & 99.05/14.95 (setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)) = 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset)), 99.05/14.95 emptyset))))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (in(Y1, 99.05/14.95 Y0) => 99.05/14.95 subset( 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset), 99.05/14.95 Y0)))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (in(Y1, 99.05/14.95 Y0) => 99.05/14.95 in( 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset), 99.05/14.95 powerset( 99.05/14.95 Y0))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 in( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 emptyset), 99.05/14.95 powerset( 99.05/14.95 binunion( 99.05/14.95 Y0, Y1))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y0, 99.05/14.95 setadjoin( 99.05/14.95 Y1, 99.05/14.95 emptyset))) => 99.05/14.95 (( 99.05/14.95 Y2 = Y1) | 99.05/14.95 (Y2 = Y0)))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (!!(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (in(Y3, 99.05/14.95 Y1) => 99.05/14.95 subset( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset)), 99.05/14.95 binunion( 99.05/14.95 Y0, Y1)))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (!!(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (in(Y3, 99.05/14.95 Y1) => 99.05/14.95 in( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset)), 99.05/14.95 powerset( 99.05/14.95 binunion( 99.05/14.95 Y0, Y1))))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (!!(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (in(Y3, 99.05/14.95 Y1) => 99.05/14.95 subset( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)), 99.05/14.95 powerset( 99.05/14.95 binunion( 99.05/14.95 Y0, Y1))))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (!!(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (in(Y3, 99.05/14.95 Y1) => 99.05/14.95 in( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)), 99.05/14.95 powerset( 99.05/14.95 powerset( 99.05/14.95 binunion( 99.05/14.95 Y0, Y1)))))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (!!(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (in(Y3, 99.05/14.95 Y1) => 99.05/14.95 in( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)), 99.05/14.95 powerset( 99.05/14.95 powerset( 99.05/14.95 binunion( 99.05/14.95 Y0, Y1)))))))))))))))))) => 99.05/14.95 ( 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 Y0) => 99.05/14.95 (!!(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (in(Y3, 99.05/14.95 Y1) => 99.05/14.95 in( 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y2, 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)), 99.05/14.95 dsetconstr( 99.05/14.95 powerset( 99.05/14.95 powerset( 99.05/14.95 binunion( 99.05/14.95 Y0, Y1))), 99.05/14.95 (^[Y4 : $i]: 99.05/14.95 (??(( 99.05/14.95 ^[Y5 : $i]: 99.05/14.95 (in(Y5, 99.05/14.95 Y0) & 99.05/14.95 (??(( 99.05/14.95 ^[Y6 : $i]: 99.05/14.95 (in(Y6, 99.05/14.95 Y1) & 99.05/14.95 (Y4 = 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y5, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y5, 99.05/14.95 setadjoin( 99.05/14.95 Y6, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)))))))))))))))))))))))))))) => 99.05/14.95 ( 99.05/14.95 !!(( 99.05/14.95 ^[Y0 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y1 : $i]: 99.05/14.95 (!!(( 99.05/14.95 ^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 dsetconstr( 99.05/14.95 powerset( 99.05/14.95 powerset( 99.05/14.95 binunion( 99.05/14.95 Y0, Y1))), 99.05/14.95 (^[Y3 : $i]: 99.05/14.95 (??(( 99.05/14.95 ^[Y4 : $i]: 99.05/14.95 (in(Y4, 99.05/14.95 Y0) & 99.05/14.95 (??(( 99.05/14.95 ^[Y5 : $i]: 99.05/14.95 (in(Y5, 99.05/14.95 Y1) & 99.05/14.95 (Y3 = 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y4, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y4, 99.05/14.95 setadjoin( 99.05/14.95 Y5, 99.05/14.95 emptyset)), 99.05/14.95 emptyset)))))))))))))) => 99.05/14.95 (??(( 99.05/14.95 ^[Y3 : $i]: 99.05/14.95 (( 99.05/14.95 ??(( 99.05/14.95 ^[Y4 : $i]: 99.05/14.95 (in(Y4, 99.05/14.95 Y1) & 99.05/14.95 (Y2 = 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 emptyset), 99.05/14.95 setadjoin( 99.05/14.95 setadjoin( 99.05/14.95 Y3, 99.05/14.95 setadjoin( 99.05/14.95 Y4, 99.05/14.95 emptyset)), 99.05/14.95 emptyset))))))) & 99.05/14.95 in(Y3, 99.05/14.95 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.05/14.95 inference('lazy_cnf_imply', [status(thm)], ['221'])). 99.05/14.95 tff('223', plain, 99.05/14.95 ~ ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((Y0 = Y1) => 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (!!((^[Y3 : $i]: 99.05/14.95 ((Y2 = Y3) => (in(Y2, Y0) <=> in(Y3, Y1)))))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i > $o]: 99.05/14.95 ((??((^[Y1 : $i]: 99.05/14.95 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i > $o]: 99.05/14.95 (!!((^[Y1 : $i > $o]: 99.05/14.95 ((!!((^[Y2 : $i]: 99.05/14.95 (!!((^[Y3 : $i]: 99.05/14.95 ((Y2 = Y3) => (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.95 ((??((^[Y2 : $i]: 99.05/14.95 (Y0(Y2) & 99.05/14.95 (!!((^[Y3 : $i]: (Y0(Y3) => (Y2 = Y3))))))))) <=> 99.05/14.95 (??((^[Y2 : $i]: 99.05/14.95 (Y1(Y2) & 99.05/14.95 (!!((^[Y3 : $i]: (Y1(Y3) => (Y2 = Y3))))))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((Y0 = Y1) => 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (!!((^[Y3 : $i]: 99.05/14.95 ((Y2 = Y3) => 99.05/14.95 (setadjoin(Y0, Y2) = 99.05/14.95 setadjoin(Y1, Y3)))))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((Y0 = Y1) => (powerset(Y0) = powerset(Y1))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((Y0 = Y1) => (setunion(Y0) = setunion(Y1))))))))) => 99.05/14.95 ((!!((^[Y0 : $i > $o]: 99.05/14.95 ((??((^[Y1 : $i]: 99.05/14.95 (Y0(Y1) & 99.05/14.95 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i > $o]: 99.05/14.95 (!!((^[Y1 : $i > $o]: 99.05/14.95 ((!!((^[Y2 : $i]: 99.05/14.95 (!!((^[Y3 : $i]: 99.05/14.95 ((Y2 = Y3) => (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.95 ((??((^[Y2 : $i]: 99.05/14.95 (Y0(Y2) & 99.05/14.95 (!!((^[Y3 : $i]: (Y0(Y3) => (Y2 = Y3))))))))) => 99.05/14.95 ((??((^[Y2 : $i]: 99.05/14.95 (Y1(Y2) & 99.05/14.95 (!!((^[Y3 : $i]: (Y1(Y3) => (Y2 = Y3))))))))) => 99.05/14.95 (descr(Y0) = descr(Y1))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((Y0 = Y1) => 99.05/14.95 (!!((^[Y2 : $i > $o]: 99.05/14.95 (!!((^[Y3 : $i > $o]: 99.05/14.95 ((!!((^[Y4 : $i]: 99.05/14.95 (in(Y4, Y0) => 99.05/14.95 (!!((^[Y5 : $i]: 99.05/14.95 (in(Y5, Y1) => 99.05/14.95 ((Y4 = Y5) => 99.05/14.95 (Y2(Y4) <=> 99.05/14.95 Y3(Y5))))))))))) => 99.05/14.95 (dsetconstr(Y0, Y2) = 99.05/14.95 dsetconstr(Y1, Y3)))))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 99.05/14.95 subset(Y0, Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y1, Y0)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y0, Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 99.05/14.95 subset(Y0, Y1)))))))) => 99.05/14.95 ((!!(subset(emptyset))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (subset(Y0, Y1) => 99.05/14.95 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (subset(Y0, Y1) => 99.05/14.95 ((~(in(Y2, Y1))) => 99.05/14.95 (~(in(Y2, Y0)))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (in(Y2, Y0) => 99.05/14.95 ((~(in(Y2, Y1))) => 99.05/14.95 (~(subset(Y0, Y1)))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (in(Y2, Y0) => 99.05/14.95 ((~(in(Y2, Y1))) => (Y0 != Y1)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (subset(Y0, Y1) => 99.05/14.95 (subset(Y1, Y2) => 99.05/14.95 subset(Y0, Y2)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 subset(Y1, setadjoin(Y0, Y1)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (subset(Y0, Y2) => 99.05/14.95 subset(Y0, 99.05/14.95 setadjoin(Y1, Y2)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (subset(Y0, Y1) => 99.05/14.95 in(Y0, powerset(Y1))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (subset(Y0, Y1) => 99.05/14.95 (subset(Y1, Y0) => (Y0 = Y1))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (subset(Y0, emptyset) => 99.05/14.95 (Y0 = emptyset))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (subset(Y1, Y0) => 99.05/14.95 in(Y1, powerset(Y0))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (in(Y1, powerset(Y0)) => 99.05/14.95 subset(Y1, Y0)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (subset(Y0, Y1) => 99.05/14.95 subset(powerset(Y0), 99.05/14.95 powerset(Y1))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i > $o]: 99.05/14.95 in(dsetconstr(Y0, Y1), 99.05/14.95 powerset(Y0)))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i > $o]: 99.05/14.95 subset( 99.05/14.95 dsetconstr(Y0, Y1), Y0))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (in(Y2, Y0) => 99.05/14.95 in(Y2, 99.05/14.95 binunion(Y0, 99.05/14.95 Y1)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 in(Y1, 99.05/14.95 setadjoin(Y0, 99.05/14.95 setadjoin(Y1, 99.05/14.95 emptyset))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (in(Y2, Y1) => 99.05/14.95 in(Y2, 99.05/14.95 binunion( 99.05/14.95 Y0, Y1)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (!!((^[Y3 : $o]: 99.05/14.95 (in(Y2, 99.05/14.95 binunion( 99.05/14.95 Y0, Y1)) => 99.05/14.95 (( 99.05/14.95 in(Y2, 99.05/14.95 Y0) => Y3) => 99.05/14.95 (( 99.05/14.95 in(Y2, 99.05/14.95 Y1) => Y3) => 99.05/14.95 Y3))))))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.95 (!!((^[Y1 : $i]: 99.05/14.95 (!!((^[Y2 : $i]: 99.05/14.95 (in(Y2, 99.05/14.95 binunion( 99.05/14.95 Y0, Y1)) => 99.05/14.95 (in(Y2, Y1) | 99.05/14.95 in(Y2, Y0)))))))))))) => 99.05/14.95 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 subset(Y0, 99.05/14.96 binunion(Y0, Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 subset(Y1, 99.05/14.96 binunion(Y0, Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 ( 99.05/14.96 in(Y2, 99.05/14.96 Y1) => 99.05/14.96 in(Y2, 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 ( 99.05/14.96 subset( 99.05/14.96 Y2, Y0) => 99.05/14.96 ( 99.05/14.96 subset( 99.05/14.96 Y2, Y1) => 99.05/14.96 subset( 99.05/14.96 Y2, 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1)) => 99.05/14.96 in(Y2, 99.05/14.96 Y0))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 subset( 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1), 99.05/14.96 Y0))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (subset(Y0, 99.05/14.96 Y1) => 99.05/14.96 (binintersect( 99.05/14.96 Y0, Y1) = 99.05/14.96 Y0)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ((binintersect( 99.05/14.96 Y0, Y1) = 99.05/14.96 Y1) => 99.05/14.96 subset(Y1, 99.05/14.96 Y0)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1)) => 99.05/14.96 in(Y2, 99.05/14.96 Y1))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (( 99.05/14.96 ~(( 99.05/14.96 ??(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) & 99.05/14.96 in(Y2, 99.05/14.96 Y1))))))) => 99.05/14.96 ( 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1) = 99.05/14.96 emptyset)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 subset( 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1), 99.05/14.96 Y1))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (subset( 99.05/14.96 Y1, Y0) => 99.05/14.96 (binintersect( 99.05/14.96 Y0, Y1) = 99.05/14.96 Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (( 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1) = 99.05/14.96 Y0) => 99.05/14.96 subset( 99.05/14.96 Y0, Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (binintersect( 99.05/14.96 Y0, 99.05/14.96 binunion( 99.05/14.96 Y1, Y2)) = 99.05/14.96 binunion( 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1), 99.05/14.96 binintersect( 99.05/14.96 Y0, Y2)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y1))) => 99.05/14.96 in(Y2, 99.05/14.96 setminus( 99.05/14.96 Y0, Y1))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 setminus( 99.05/14.96 Y0, Y1)) => 99.05/14.96 in(Y2, 99.05/14.96 Y0))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 setminus( 99.05/14.96 Y0, Y1)) => 99.05/14.96 (~( 99.05/14.96 in(Y2, 99.05/14.96 Y1))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (subset( 99.05/14.96 Y0, Y1) => 99.05/14.96 (setminus( 99.05/14.96 Y0, Y1) = 99.05/14.96 emptyset)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 setminus( 99.05/14.96 Y0, Y1)))) => 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 in(Y2, 99.05/14.96 Y1)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 setminus( 99.05/14.96 Y0, Y1)))) => 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y1))) => 99.05/14.96 (~( 99.05/14.96 in(Y2, 99.05/14.96 Y0)))))))))))))) => 99.05/14.96 ((!!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y0))) => 99.05/14.96 (~( 99.05/14.96 in(Y2, 99.05/14.96 setminus( 99.05/14.96 Y0, Y1)))))))))))))) => 99.05/14.96 ((!!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y1) => 99.05/14.96 (~( 99.05/14.96 in(Y2, 99.05/14.96 setminus( 99.05/14.96 Y0, Y1)))))))))))))) => 99.05/14.96 ((!!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 subset( 99.05/14.96 setminus( 99.05/14.96 Y0, Y1), 99.05/14.96 Y0))))))) => 99.05/14.96 ((!!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (( 99.05/14.96 setminus( 99.05/14.96 Y0, Y1) = 99.05/14.96 emptyset) => 99.05/14.96 subset( 99.05/14.96 Y0, Y1)))))))) => 99.05/14.96 (( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 symdiff( 99.05/14.96 Y0, Y1)) => 99.05/14.96 (!!(( 99.05/14.96 ^[Y3 : $o]: 99.05/14.96 (( 99.05/14.96 in(Y2, 99.05/14.96 Y0) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y1))) => 99.05/14.96 Y3)) => 99.05/14.96 (( 99.05/14.96 ( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y0))) => 99.05/14.96 ( 99.05/14.96 in(Y2, 99.05/14.96 Y1) => Y3)) => 99.05/14.96 Y3))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y1))) => 99.05/14.96 in(Y2, 99.05/14.96 symdiff( 99.05/14.96 Y0, Y1))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y0))) => 99.05/14.96 (in(Y2, 99.05/14.96 Y1) => 99.05/14.96 in(Y2, 99.05/14.96 symdiff( 99.05/14.96 Y0, Y1))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (in(Y2, 99.05/14.96 Y1) => 99.05/14.96 (~( 99.05/14.96 in(Y2, 99.05/14.96 symdiff( 99.05/14.96 Y0, Y1))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y0))) => 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y1))) => 99.05/14.96 (~( 99.05/14.96 in(Y2, 99.05/14.96 symdiff( 99.05/14.96 Y0, Y1))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 in(Y1, 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 in(Y0, 99.05/14.96 setunion( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 in(Y1, 99.05/14.96 setunion( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (??(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 setunion( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)))) & 99.05/14.96 (??(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (in(Y3, 99.05/14.96 setunion( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)))) & 99.05/14.96 (setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)) = 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset)), 99.05/14.96 emptyset))))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (??(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 setunion( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)))) & 99.05/14.96 (??(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (in(Y3, 99.05/14.96 setunion( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)))) & 99.05/14.96 (setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)) = 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset)), 99.05/14.96 emptyset))))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (in(Y1, 99.05/14.96 Y0) => 99.05/14.96 subset( 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset), 99.05/14.96 Y0)))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (in(Y1, 99.05/14.96 Y0) => 99.05/14.96 in( 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset), 99.05/14.96 powerset( 99.05/14.96 Y0))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 in( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 emptyset), 99.05/14.96 powerset( 99.05/14.96 binunion( 99.05/14.96 Y0, Y1))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset))) => 99.05/14.96 (( 99.05/14.96 Y2 = Y1) | 99.05/14.96 (Y2 = Y0)))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (!!(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (in(Y3, 99.05/14.96 Y1) => 99.05/14.96 subset( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset)), 99.05/14.96 binunion( 99.05/14.96 Y0, Y1)))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (!!(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (in(Y3, 99.05/14.96 Y1) => 99.05/14.96 in( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset)), 99.05/14.96 powerset( 99.05/14.96 binunion( 99.05/14.96 Y0, Y1))))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (!!(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (in(Y3, 99.05/14.96 Y1) => 99.05/14.96 subset( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)), 99.05/14.96 powerset( 99.05/14.96 binunion( 99.05/14.96 Y0, Y1))))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (!!(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (in(Y3, 99.05/14.96 Y1) => 99.05/14.96 in( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)), 99.05/14.96 powerset( 99.05/14.96 powerset( 99.05/14.96 binunion( 99.05/14.96 Y0, Y1)))))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (!!(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (in(Y3, 99.05/14.96 Y1) => 99.05/14.96 in( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)), 99.05/14.96 powerset( 99.05/14.96 powerset( 99.05/14.96 binunion( 99.05/14.96 Y0, Y1)))))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (!!(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (in(Y3, 99.05/14.96 Y1) => 99.05/14.96 in( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)), 99.05/14.96 dsetconstr( 99.05/14.96 powerset( 99.05/14.96 powerset( 99.05/14.96 binunion( 99.05/14.96 Y0, Y1))), 99.05/14.96 (^[Y4 : $i]: 99.05/14.96 (??(( 99.05/14.96 ^[Y5 : $i]: 99.05/14.96 (in(Y5, 99.05/14.96 Y0) & 99.05/14.96 (??(( 99.05/14.96 ^[Y6 : $i]: 99.05/14.96 (in(Y6, 99.05/14.96 Y1) & 99.05/14.96 (Y4 = 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y5, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y5, 99.05/14.96 setadjoin( 99.05/14.96 Y6, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)))))))))))))))))))))))))))) => 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 dsetconstr( 99.05/14.96 powerset( 99.05/14.96 powerset( 99.05/14.96 binunion( 99.05/14.96 Y0, Y1))), 99.05/14.96 (^[Y3 : $i]: 99.05/14.96 (??(( 99.05/14.96 ^[Y4 : $i]: 99.05/14.96 (in(Y4, 99.05/14.96 Y0) & 99.05/14.96 (??(( 99.05/14.96 ^[Y5 : $i]: 99.05/14.96 (in(Y5, 99.05/14.96 Y1) & 99.05/14.96 (Y3 = 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y4, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y4, 99.05/14.96 setadjoin( 99.05/14.96 Y5, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)))))))))))))) => 99.05/14.96 (??(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (( 99.05/14.96 ??(( 99.05/14.96 ^[Y4 : $i]: 99.05/14.96 (in(Y4, 99.05/14.96 Y1) & 99.05/14.96 (Y2 = 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 setadjoin( 99.05/14.96 Y4, 99.05/14.96 emptyset)), 99.05/14.96 emptyset))))))) & 99.05/14.96 in(Y3, 99.05/14.96 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.05/14.96 inference('lazy_cnf_imply', [status(thm)], ['222'])). 99.05/14.96 tff('224', plain, 99.05/14.96 ~ ((!!((^[Y0 : $i > $o]: 99.05/14.96 ((??((^[Y1 : $i]: 99.05/14.96 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i > $o]: 99.05/14.96 (!!((^[Y1 : $i > $o]: 99.05/14.96 ((!!((^[Y2 : $i]: 99.05/14.96 (!!((^[Y3 : $i]: 99.05/14.96 ((Y2 = Y3) => (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.96 ((??((^[Y2 : $i]: 99.05/14.96 (Y0(Y2) & 99.05/14.96 (!!((^[Y3 : $i]: (Y0(Y3) => (Y2 = Y3))))))))) <=> 99.05/14.96 (??((^[Y2 : $i]: 99.05/14.96 (Y1(Y2) & 99.05/14.96 (!!((^[Y3 : $i]: (Y1(Y3) => (Y2 = Y3))))))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ((Y0 = Y1) => 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (!!((^[Y3 : $i]: 99.05/14.96 ((Y2 = Y3) => 99.05/14.96 (setadjoin(Y0, Y2) = setadjoin(Y1, Y3)))))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ((Y0 = Y1) => (powerset(Y0) = powerset(Y1))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ((Y0 = Y1) => (setunion(Y0) = setunion(Y1))))))))) => 99.05/14.96 ((!!((^[Y0 : $i > $o]: 99.05/14.96 ((??((^[Y1 : $i]: 99.05/14.96 (Y0(Y1) & 99.05/14.96 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i > $o]: 99.05/14.96 (!!((^[Y1 : $i > $o]: 99.05/14.96 ((!!((^[Y2 : $i]: 99.05/14.96 (!!((^[Y3 : $i]: 99.05/14.96 ((Y2 = Y3) => (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.96 ((??((^[Y2 : $i]: 99.05/14.96 (Y0(Y2) & 99.05/14.96 (!!((^[Y3 : $i]: (Y0(Y3) => (Y2 = Y3))))))))) => 99.05/14.96 ((??((^[Y2 : $i]: 99.05/14.96 (Y1(Y2) & 99.05/14.96 (!!((^[Y3 : $i]: (Y1(Y3) => (Y2 = Y3))))))))) => 99.05/14.96 (descr(Y0) = descr(Y1))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ((Y0 = Y1) => 99.05/14.96 (!!((^[Y2 : $i > $o]: 99.05/14.96 (!!((^[Y3 : $i > $o]: 99.05/14.96 ((!!((^[Y4 : $i]: 99.05/14.96 (in(Y4, Y0) => 99.05/14.96 (!!((^[Y5 : $i]: 99.05/14.96 (in(Y5, Y1) => 99.05/14.96 ((Y4 = Y5) => 99.05/14.96 (Y2(Y4) <=> 99.05/14.96 Y3(Y5))))))))))) => 99.05/14.96 (dsetconstr(Y0, Y2) = 99.05/14.96 dsetconstr(Y1, Y3)))))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 99.05/14.96 subset(Y0, Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y1, Y0)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y0, Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 99.05/14.96 subset(Y0, Y1)))))))) => 99.05/14.96 ((!!(subset(emptyset))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (subset(Y0, 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$i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 subset(Y1, setadjoin(Y0, Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (subset(Y0, Y2) => 99.05/14.96 subset(Y0, 99.05/14.96 setadjoin(Y1, Y2)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (subset(Y0, Y1) => 99.05/14.96 in(Y0, powerset(Y1))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (subset(Y0, Y1) => 99.05/14.96 (subset(Y1, Y0) => (Y0 = Y1))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (subset(Y0, emptyset) => 99.05/14.96 (Y0 = emptyset))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (subset(Y1, Y0) => 99.05/14.96 in(Y1, powerset(Y0))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (in(Y1, powerset(Y0)) => 99.05/14.96 subset(Y1, Y0)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (subset(Y0, Y1) => 99.05/14.96 subset(powerset(Y0), 99.05/14.96 powerset(Y1))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i > $o]: 99.05/14.96 in(dsetconstr(Y0, Y1), 99.05/14.96 powerset(Y0)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i > $o]: 99.05/14.96 subset( 99.05/14.96 dsetconstr(Y0, Y1), Y0))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (in(Y2, Y0) => 99.05/14.96 in(Y2, 99.05/14.96 binunion(Y0, 99.05/14.96 Y1)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 in(Y1, 99.05/14.96 setadjoin(Y0, 99.05/14.96 setadjoin(Y1, 99.05/14.96 emptyset))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (in(Y2, Y1) => 99.05/14.96 in(Y2, 99.05/14.96 binunion(Y0, 99.05/14.96 Y1)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (!!((^[Y3 : $o]: 99.05/14.96 (in(Y2, 99.05/14.96 binunion( 99.05/14.96 Y0, Y1)) => 99.05/14.96 (( 99.05/14.96 in(Y2, 99.05/14.96 Y0) => Y3) => 99.05/14.96 (( 99.05/14.96 in(Y2, 99.05/14.96 Y1) => Y3) => 99.05/14.96 Y3))))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 binunion( 99.05/14.96 Y0, Y1)) => 99.05/14.96 (in(Y2, Y1) | 99.05/14.96 in(Y2, Y0)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 subset(Y0, 99.05/14.96 binunion(Y0, Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 subset(Y1, 99.05/14.96 binunion(Y0, Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (in(Y2, Y0) => 99.05/14.96 (in(Y2, 99.05/14.96 Y1) => 99.05/14.96 in(Y2, 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (subset( 99.05/14.96 Y2, Y0) => 99.05/14.96 ( 99.05/14.96 subset( 99.05/14.96 Y2, Y1) => 99.05/14.96 subset( 99.05/14.96 Y2, 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 ( 99.05/14.96 in(Y2, 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1)) => 99.05/14.96 in(Y2, 99.05/14.96 Y0))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 subset( 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1), 99.05/14.96 Y0))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (subset(Y0, 99.05/14.96 Y1) => 99.05/14.96 (binintersect( 99.05/14.96 Y0, Y1) = 99.05/14.96 Y0)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ((binintersect( 99.05/14.96 Y0, Y1) = 99.05/14.96 Y1) => 99.05/14.96 subset(Y1, 99.05/14.96 Y0)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 ( 99.05/14.96 in(Y2, 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1)) => 99.05/14.96 in(Y2, 99.05/14.96 Y1))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ((~(( 99.05/14.96 ??(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) & 99.05/14.96 in(Y2, 99.05/14.96 Y1))))))) => 99.05/14.96 (binintersect( 99.05/14.96 Y0, Y1) = 99.05/14.96 emptyset)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 subset( 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1), 99.05/14.96 Y1))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ( 99.05/14.96 subset( 99.05/14.96 Y1, Y0) => 99.05/14.96 ( 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1) = 99.05/14.96 Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (( 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1) = 99.05/14.96 Y0) => 99.05/14.96 subset( 99.05/14.96 Y0, Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (binintersect( 99.05/14.96 Y0, 99.05/14.96 binunion( 99.05/14.96 Y1, Y2)) = 99.05/14.96 binunion( 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1), 99.05/14.96 binintersect( 99.05/14.96 Y0, Y2)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y1))) => 99.05/14.96 in(Y2, 99.05/14.96 setminus( 99.05/14.96 Y0, Y1))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 setminus( 99.05/14.96 Y0, Y1)) => 99.05/14.96 in(Y2, 99.05/14.96 Y0))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 setminus( 99.05/14.96 Y0, Y1)) => 99.05/14.96 (~( 99.05/14.96 in(Y2, 99.05/14.96 Y1))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (subset( 99.05/14.96 Y0, Y1) => 99.05/14.96 (setminus( 99.05/14.96 Y0, Y1) = 99.05/14.96 emptyset)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 setminus( 99.05/14.96 Y0, Y1)))) => 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 in(Y2, 99.05/14.96 Y1)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 setminus( 99.05/14.96 Y0, Y1)))) => 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y1))) => 99.05/14.96 (~( 99.05/14.96 in(Y2, 99.05/14.96 Y0)))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y0))) => 99.05/14.96 (~( 99.05/14.96 in(Y2, 99.05/14.96 setminus( 99.05/14.96 Y0, Y1)))))))))))))) => 99.05/14.96 ((!!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y1) => 99.05/14.96 (~( 99.05/14.96 in(Y2, 99.05/14.96 setminus( 99.05/14.96 Y0, Y1)))))))))))))) => 99.05/14.96 ((!!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 subset( 99.05/14.96 setminus( 99.05/14.96 Y0, Y1), 99.05/14.96 Y0))))))) => 99.05/14.96 ((!!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (( 99.05/14.96 setminus( 99.05/14.96 Y0, Y1) = 99.05/14.96 emptyset) => 99.05/14.96 subset( 99.05/14.96 Y0, Y1)))))))) => 99.05/14.96 ((!!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 symdiff( 99.05/14.96 Y0, Y1)) => 99.05/14.96 (!!(( 99.05/14.96 ^[Y3 : $o]: 99.05/14.96 (( 99.05/14.96 in(Y2, 99.05/14.96 Y0) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y1))) => 99.05/14.96 Y3)) => 99.05/14.96 (( 99.05/14.96 ( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y0))) => 99.05/14.96 ( 99.05/14.96 in(Y2, 99.05/14.96 Y1) => Y3)) => 99.05/14.96 Y3))))))))))))))) => 99.05/14.96 (( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y1))) => 99.05/14.96 in(Y2, 99.05/14.96 symdiff( 99.05/14.96 Y0, Y1))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y0))) => 99.05/14.96 (in(Y2, 99.05/14.96 Y1) => 99.05/14.96 in(Y2, 99.05/14.96 symdiff( 99.05/14.96 Y0, Y1))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (in(Y2, 99.05/14.96 Y1) => 99.05/14.96 (~( 99.05/14.96 in(Y2, 99.05/14.96 symdiff( 99.05/14.96 Y0, Y1))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y0))) => 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y1))) => 99.05/14.96 (~( 99.05/14.96 in(Y2, 99.05/14.96 symdiff( 99.05/14.96 Y0, Y1))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 in(Y1, 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 in(Y0, 99.05/14.96 setunion( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 in(Y1, 99.05/14.96 setunion( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (??(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 setunion( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)))) & 99.05/14.96 (??(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (in(Y3, 99.05/14.96 setunion( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)))) & 99.05/14.96 (setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)) = 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset)), 99.05/14.96 emptyset))))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (??(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 setunion( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)))) & 99.05/14.96 (??(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (in(Y3, 99.05/14.96 setunion( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)))) & 99.05/14.96 (setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)) = 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset)), 99.05/14.96 emptyset))))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (in(Y1, 99.05/14.96 Y0) => 99.05/14.96 subset( 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset), 99.05/14.96 Y0)))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (in(Y1, 99.05/14.96 Y0) => 99.05/14.96 in( 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset), 99.05/14.96 powerset( 99.05/14.96 Y0))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 in( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 emptyset), 99.05/14.96 powerset( 99.05/14.96 binunion( 99.05/14.96 Y0, Y1))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset))) => 99.05/14.96 (( 99.05/14.96 Y2 = Y1) | 99.05/14.96 (Y2 = Y0)))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (!!(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (in(Y3, 99.05/14.96 Y1) => 99.05/14.96 subset( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset)), 99.05/14.96 binunion( 99.05/14.96 Y0, Y1)))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (!!(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (in(Y3, 99.05/14.96 Y1) => 99.05/14.96 in( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset)), 99.05/14.96 powerset( 99.05/14.96 binunion( 99.05/14.96 Y0, Y1))))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (!!(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (in(Y3, 99.05/14.96 Y1) => 99.05/14.96 subset( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)), 99.05/14.96 powerset( 99.05/14.96 binunion( 99.05/14.96 Y0, Y1))))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (!!(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (in(Y3, 99.05/14.96 Y1) => 99.05/14.96 in( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)), 99.05/14.96 powerset( 99.05/14.96 powerset( 99.05/14.96 binunion( 99.05/14.96 Y0, Y1)))))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (!!(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (in(Y3, 99.05/14.96 Y1) => 99.05/14.96 in( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)), 99.05/14.96 powerset( 99.05/14.96 powerset( 99.05/14.96 binunion( 99.05/14.96 Y0, Y1)))))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (!!(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (in(Y3, 99.05/14.96 Y1) => 99.05/14.96 in( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)), 99.05/14.96 dsetconstr( 99.05/14.96 powerset( 99.05/14.96 powerset( 99.05/14.96 binunion( 99.05/14.96 Y0, Y1))), 99.05/14.96 (^[Y4 : $i]: 99.05/14.96 (??(( 99.05/14.96 ^[Y5 : $i]: 99.05/14.96 (in(Y5, 99.05/14.96 Y0) & 99.05/14.96 (??(( 99.05/14.96 ^[Y6 : $i]: 99.05/14.96 (in(Y6, 99.05/14.96 Y1) & 99.05/14.96 (Y4 = 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y5, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y5, 99.05/14.96 setadjoin( 99.05/14.96 Y6, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)))))))))))))))))))))))))))) => 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 dsetconstr( 99.05/14.96 powerset( 99.05/14.96 powerset( 99.05/14.96 binunion( 99.05/14.96 Y0, Y1))), 99.05/14.96 (^[Y3 : $i]: 99.05/14.96 (??(( 99.05/14.96 ^[Y4 : $i]: 99.05/14.96 (in(Y4, 99.05/14.96 Y0) & 99.05/14.96 (??(( 99.05/14.96 ^[Y5 : $i]: 99.05/14.96 (in(Y5, 99.05/14.96 Y1) & 99.05/14.96 (Y3 = 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y4, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y4, 99.05/14.96 setadjoin( 99.05/14.96 Y5, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)))))))))))))) => 99.05/14.96 (??(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (( 99.05/14.96 ??(( 99.05/14.96 ^[Y4 : $i]: 99.05/14.96 (in(Y4, 99.05/14.96 Y1) & 99.05/14.96 (Y2 = 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 setadjoin( 99.05/14.96 Y4, 99.05/14.96 emptyset)), 99.05/14.96 emptyset))))))) & 99.05/14.96 in(Y3, 99.05/14.96 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.05/14.96 inference('lazy_cnf_imply', [status(thm)], ['223'])). 99.05/14.96 tff('225', plain, 99.05/14.96 ~ ((!!((^[Y0 : $i > $o]: 99.05/14.96 (!!((^[Y1 : $i > $o]: 99.05/14.96 ((!!((^[Y2 : $i]: 99.05/14.96 (!!((^[Y3 : $i]: 99.05/14.96 ((Y2 = Y3) => (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.96 ((??((^[Y2 : $i]: 99.05/14.96 (Y0(Y2) & 99.05/14.96 (!!((^[Y3 : $i]: (Y0(Y3) => (Y2 = Y3))))))))) <=> 99.05/14.96 (??((^[Y2 : $i]: 99.05/14.96 (Y1(Y2) & 99.05/14.96 (!!((^[Y3 : $i]: (Y1(Y3) => (Y2 = Y3))))))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ((Y0 = Y1) => 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (!!((^[Y3 : $i]: 99.05/14.96 ((Y2 = Y3) => 99.05/14.96 (setadjoin(Y0, Y2) = setadjoin(Y1, Y3)))))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: ((Y0 = Y1) => (powerset(Y0) = powerset(Y1))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ((Y0 = Y1) => (setunion(Y0) = setunion(Y1))))))))) => 99.05/14.96 ((!!((^[Y0 : $i > $o]: 99.05/14.96 ((??((^[Y1 : $i]: 99.05/14.96 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i > $o]: 99.05/14.96 (!!((^[Y1 : $i > $o]: 99.05/14.96 ((!!((^[Y2 : $i]: 99.05/14.96 (!!((^[Y3 : $i]: 99.05/14.96 ((Y2 = Y3) => (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.96 ((??((^[Y2 : $i]: 99.05/14.96 (Y0(Y2) & 99.05/14.96 (!!((^[Y3 : $i]: (Y0(Y3) => (Y2 = Y3))))))))) => 99.05/14.96 ((??((^[Y2 : $i]: 99.05/14.96 (Y1(Y2) & 99.05/14.96 (!!((^[Y3 : $i]: (Y1(Y3) => (Y2 = Y3))))))))) => 99.05/14.96 (descr(Y0) = descr(Y1))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ((Y0 = Y1) => 99.05/14.96 (!!((^[Y2 : $i > $o]: 99.05/14.96 (!!((^[Y3 : $i > $o]: 99.05/14.96 ((!!((^[Y4 : $i]: 99.05/14.96 (in(Y4, Y0) => 99.05/14.96 (!!((^[Y5 : $i]: 99.05/14.96 (in(Y5, Y1) => 99.05/14.96 ((Y4 = Y5) => 99.05/14.96 (Y2(Y4) <=> 99.05/14.96 Y3(Y5))))))))))) => 99.05/14.96 (dsetconstr(Y0, Y2) = 99.05/14.96 dsetconstr(Y1, Y3)))))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 99.05/14.96 subset(Y0, Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y1, Y0)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y0, Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 99.05/14.96 subset(Y0, Y1)))))))) => 99.05/14.96 ((!!(subset(emptyset))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (subset(Y0, Y1) => 99.05/14.96 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (subset(Y0, Y1) => 99.05/14.96 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (in(Y2, Y0) => 99.05/14.96 ((~(in(Y2, Y1))) => 99.05/14.96 (~(subset(Y0, Y1)))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (in(Y2, Y0) => 99.05/14.96 ((~(in(Y2, Y1))) => (Y0 != Y1)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (subset(Y0, Y1) => 99.05/14.96 (subset(Y1, Y2) => 99.05/14.96 subset(Y0, Y2)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 subset(Y1, setadjoin(Y0, Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (subset(Y0, Y2) => 99.05/14.96 subset(Y0, 99.05/14.96 setadjoin(Y1, Y2)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (subset(Y0, Y1) => 99.05/14.96 in(Y0, powerset(Y1))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (subset(Y0, Y1) => 99.05/14.96 (subset(Y1, Y0) => (Y0 = Y1))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (subset(Y0, emptyset) => (Y0 = emptyset))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (subset(Y1, Y0) => 99.05/14.96 in(Y1, powerset(Y0))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (in(Y1, powerset(Y0)) => 99.05/14.96 subset(Y1, Y0)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (subset(Y0, Y1) => 99.05/14.96 subset(powerset(Y0), 99.05/14.96 powerset(Y1))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i > $o]: 99.05/14.96 in(dsetconstr(Y0, Y1), 99.05/14.96 powerset(Y0)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i > $o]: 99.05/14.96 subset(dsetconstr(Y0, Y1), 99.05/14.96 Y0))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (in(Y2, Y0) => 99.05/14.96 in(Y2, 99.05/14.96 binunion(Y0, Y1)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 in(Y1, 99.05/14.96 setadjoin(Y0, 99.05/14.96 setadjoin(Y1, 99.05/14.96 emptyset))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (in(Y2, Y1) => 99.05/14.96 in(Y2, 99.05/14.96 binunion(Y0, 99.05/14.96 Y1)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (!!((^[Y3 : $o]: 99.05/14.96 ( 99.05/14.96 in(Y2, 99.05/14.96 binunion( 99.05/14.96 Y0, Y1)) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 in(Y2, 99.05/14.96 Y0) => Y3) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 in(Y2, 99.05/14.96 Y1) => Y3) => 99.05/14.96 Y3))))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 binunion( 99.05/14.96 Y0, Y1)) => 99.05/14.96 (in(Y2, Y1) | 99.05/14.96 in(Y2, Y0)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 subset(Y0, 99.05/14.96 binunion(Y0, Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 subset(Y1, 99.05/14.96 binunion(Y0, Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (in(Y2, Y0) => 99.05/14.96 (in(Y2, Y1) => 99.05/14.96 in(Y2, 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (subset( 99.05/14.96 Y2, Y0) => 99.05/14.96 (subset( 99.05/14.96 Y2, Y1) => 99.05/14.96 subset( 99.05/14.96 Y2, 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1)) => 99.05/14.96 in(Y2, 99.05/14.96 Y0))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 subset( 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1), Y0))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (subset(Y0, Y1) => 99.05/14.96 (binintersect( 99.05/14.96 Y0, Y1) = 99.05/14.96 Y0)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ((binintersect( 99.05/14.96 Y0, Y1) = 99.05/14.96 Y1) => 99.05/14.96 subset(Y1, 99.05/14.96 Y0)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1)) => 99.05/14.96 in(Y2, 99.05/14.96 Y1))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ((~(( 99.05/14.96 ??(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) & 99.05/14.96 in(Y2, 99.05/14.96 Y1))))))) => 99.05/14.96 (binintersect( 99.05/14.96 Y0, Y1) = 99.05/14.96 emptyset)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 subset( 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1), 99.05/14.96 Y1))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (subset( 99.05/14.96 Y1, Y0) => 99.05/14.96 ( 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1) = 99.05/14.96 Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1) = 99.05/14.96 Y0) => 99.05/14.96 subset( 99.05/14.96 Y0, Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (binintersect( 99.05/14.96 Y0, 99.05/14.96 binunion( 99.05/14.96 Y1, Y2)) = 99.05/14.96 binunion( 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1), 99.05/14.96 binintersect( 99.05/14.96 Y0, Y2)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y1))) => 99.05/14.96 in(Y2, 99.05/14.96 setminus( 99.05/14.96 Y0, Y1))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 setminus( 99.05/14.96 Y0, Y1)) => 99.05/14.96 in(Y2, 99.05/14.96 Y0))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 setminus( 99.05/14.96 Y0, Y1)) => 99.05/14.96 (~( 99.05/14.96 in(Y2, 99.05/14.96 Y1))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (subset( 99.05/14.96 Y0, Y1) => 99.05/14.96 (setminus( 99.05/14.96 Y0, Y1) = 99.05/14.96 emptyset)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 setminus( 99.05/14.96 Y0, Y1)))) => 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 in(Y2, 99.05/14.96 Y1)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 setminus( 99.05/14.96 Y0, Y1)))) => 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y1))) => 99.05/14.96 (~( 99.05/14.96 in(Y2, 99.05/14.96 Y0)))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y0))) => 99.05/14.96 (~( 99.05/14.96 in(Y2, 99.05/14.96 setminus( 99.05/14.96 Y0, Y1)))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y1) => 99.05/14.96 (~( 99.05/14.96 in(Y2, 99.05/14.96 setminus( 99.05/14.96 Y0, Y1)))))))))))))) => 99.05/14.96 ((!!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 subset( 99.05/14.96 setminus( 99.05/14.96 Y0, Y1), 99.05/14.96 Y0))))))) => 99.05/14.96 ((!!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (( 99.05/14.96 setminus( 99.05/14.96 Y0, Y1) = 99.05/14.96 emptyset) => 99.05/14.96 subset( 99.05/14.96 Y0, Y1)))))))) => 99.05/14.96 ((!!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 symdiff( 99.05/14.96 Y0, Y1)) => 99.05/14.96 (!!(( 99.05/14.96 ^[Y3 : $o]: 99.05/14.96 (( 99.05/14.96 in(Y2, 99.05/14.96 Y0) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y1))) => 99.05/14.96 Y3)) => 99.05/14.96 (( 99.05/14.96 ( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y0))) => 99.05/14.96 ( 99.05/14.96 in(Y2, 99.05/14.96 Y1) => Y3)) => 99.05/14.96 Y3))))))))))))))) => 99.05/14.96 ((!!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y1))) => 99.05/14.96 in(Y2, 99.05/14.96 symdiff( 99.05/14.96 Y0, Y1))))))))))))) => 99.05/14.96 (( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y0))) => 99.05/14.96 (in(Y2, 99.05/14.96 Y1) => 99.05/14.96 in(Y2, 99.05/14.96 symdiff( 99.05/14.96 Y0, Y1))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (in(Y2, 99.05/14.96 Y1) => 99.05/14.96 (~( 99.05/14.96 in(Y2, 99.05/14.96 symdiff( 99.05/14.96 Y0, Y1))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y0))) => 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y1))) => 99.05/14.96 (~( 99.05/14.96 in(Y2, 99.05/14.96 symdiff( 99.05/14.96 Y0, Y1))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 in(Y1, 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 in(Y0, 99.05/14.96 setunion( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 in(Y1, 99.05/14.96 setunion( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (??(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 setunion( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)))) & 99.05/14.96 (??(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (in(Y3, 99.05/14.96 setunion( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)))) & 99.05/14.96 (setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)) = 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset)), 99.05/14.96 emptyset))))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (??(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 setunion( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)))) & 99.05/14.96 (??(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (in(Y3, 99.05/14.96 setunion( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)))) & 99.05/14.96 (setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)) = 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset)), 99.05/14.96 emptyset))))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (in(Y1, 99.05/14.96 Y0) => 99.05/14.96 subset( 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset), 99.05/14.96 Y0)))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (in(Y1, 99.05/14.96 Y0) => 99.05/14.96 in( 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset), 99.05/14.96 powerset( 99.05/14.96 Y0))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 in( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 emptyset), 99.05/14.96 powerset( 99.05/14.96 binunion( 99.05/14.96 Y0, Y1))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset))) => 99.05/14.96 (( 99.05/14.96 Y2 = Y1) | 99.05/14.96 (Y2 = Y0)))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (!!(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (in(Y3, 99.05/14.96 Y1) => 99.05/14.96 subset( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset)), 99.05/14.96 binunion( 99.05/14.96 Y0, Y1)))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (!!(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (in(Y3, 99.05/14.96 Y1) => 99.05/14.96 in( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset)), 99.05/14.96 powerset( 99.05/14.96 binunion( 99.05/14.96 Y0, Y1))))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (!!(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (in(Y3, 99.05/14.96 Y1) => 99.05/14.96 subset( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)), 99.05/14.96 powerset( 99.05/14.96 binunion( 99.05/14.96 Y0, Y1))))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (!!(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (in(Y3, 99.05/14.96 Y1) => 99.05/14.96 in( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)), 99.05/14.96 powerset( 99.05/14.96 powerset( 99.05/14.96 binunion( 99.05/14.96 Y0, Y1)))))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (!!(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (in(Y3, 99.05/14.96 Y1) => 99.05/14.96 in( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)), 99.05/14.96 powerset( 99.05/14.96 powerset( 99.05/14.96 binunion( 99.05/14.96 Y0, Y1)))))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (!!(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (in(Y3, 99.05/14.96 Y1) => 99.05/14.96 in( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)), 99.05/14.96 dsetconstr( 99.05/14.96 powerset( 99.05/14.96 powerset( 99.05/14.96 binunion( 99.05/14.96 Y0, Y1))), 99.05/14.96 (^[Y4 : $i]: 99.05/14.96 (??(( 99.05/14.96 ^[Y5 : $i]: 99.05/14.96 (in(Y5, 99.05/14.96 Y0) & 99.05/14.96 (??(( 99.05/14.96 ^[Y6 : $i]: 99.05/14.96 (in(Y6, 99.05/14.96 Y1) & 99.05/14.96 (Y4 = 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y5, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y5, 99.05/14.96 setadjoin( 99.05/14.96 Y6, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)))))))))))))))))))))))))))) => 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 dsetconstr( 99.05/14.96 powerset( 99.05/14.96 powerset( 99.05/14.96 binunion( 99.05/14.96 Y0, Y1))), 99.05/14.96 (^[Y3 : $i]: 99.05/14.96 (??(( 99.05/14.96 ^[Y4 : $i]: 99.05/14.96 (in(Y4, 99.05/14.96 Y0) & 99.05/14.96 (??(( 99.05/14.96 ^[Y5 : $i]: 99.05/14.96 (in(Y5, 99.05/14.96 Y1) & 99.05/14.96 (Y3 = 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y4, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y4, 99.05/14.96 setadjoin( 99.05/14.96 Y5, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)))))))))))))) => 99.05/14.96 (??(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (( 99.05/14.96 ??(( 99.05/14.96 ^[Y4 : $i]: 99.05/14.96 (in(Y4, 99.05/14.96 Y1) & 99.05/14.96 (Y2 = 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 setadjoin( 99.05/14.96 Y4, 99.05/14.96 emptyset)), 99.05/14.96 emptyset))))))) & 99.05/14.96 in(Y3, 99.05/14.96 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.05/14.96 inference('lazy_cnf_imply', [status(thm)], ['224'])). 99.05/14.96 tff('226', plain, 99.05/14.96 ~ ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ((Y0 = Y1) => 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (!!((^[Y3 : $i]: 99.05/14.96 ((Y2 = Y3) => 99.05/14.96 (setadjoin(Y0, Y2) = setadjoin(Y1, Y3)))))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: ((Y0 = Y1) => (powerset(Y0) = powerset(Y1))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: ((Y0 = Y1) => (setunion(Y0) = setunion(Y1))))))))) => 99.05/14.96 ((!!((^[Y0 : $i > $o]: 99.05/14.96 ((??((^[Y1 : $i]: 99.05/14.96 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i > $o]: 99.05/14.96 (!!((^[Y1 : $i > $o]: 99.05/14.96 ((!!((^[Y2 : $i]: 99.05/14.96 (!!((^[Y3 : $i]: 99.05/14.96 ((Y2 = Y3) => (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.96 ((??((^[Y2 : $i]: 99.05/14.96 (Y0(Y2) & 99.05/14.96 (!!((^[Y3 : $i]: (Y0(Y3) => (Y2 = Y3))))))))) => 99.05/14.96 ((??((^[Y2 : $i]: 99.05/14.96 (Y1(Y2) & 99.05/14.96 (!!((^[Y3 : $i]: (Y1(Y3) => (Y2 = Y3))))))))) => 99.05/14.96 (descr(Y0) = descr(Y1))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ((Y0 = Y1) => 99.05/14.96 (!!((^[Y2 : $i > $o]: 99.05/14.96 (!!((^[Y3 : $i > $o]: 99.05/14.96 ((!!((^[Y4 : $i]: 99.05/14.96 (in(Y4, Y0) => 99.05/14.96 (!!((^[Y5 : $i]: 99.05/14.96 (in(Y5, Y1) => 99.05/14.96 ((Y4 = Y5) => 99.05/14.96 (Y2(Y4) <=> Y3(Y5))))))))))) => 99.05/14.96 (dsetconstr(Y0, Y2) = 99.05/14.96 dsetconstr(Y1, Y3)))))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 99.05/14.96 subset(Y0, Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y1, Y0)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y0, Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 99.05/14.96 subset(Y0, Y1)))))))) => 99.05/14.96 ((!!(subset(emptyset))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (subset(Y0, Y1) => 99.05/14.96 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (subset(Y0, Y1) => 99.05/14.96 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (in(Y2, Y0) => 99.05/14.96 ((~(in(Y2, Y1))) => 99.05/14.96 (~(subset(Y0, Y1)))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (in(Y2, Y0) => 99.05/14.96 ((~(in(Y2, Y1))) => (Y0 != Y1)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (subset(Y0, Y1) => 99.05/14.96 (subset(Y1, Y2) => 99.05/14.96 subset(Y0, Y2)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 subset(Y1, setadjoin(Y0, Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (subset(Y0, Y2) => 99.05/14.96 subset(Y0, setadjoin(Y1, Y2)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (subset(Y0, Y1) => 99.05/14.96 in(Y0, powerset(Y1))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (subset(Y0, Y1) => 99.05/14.96 (subset(Y1, Y0) => (Y0 = Y1))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (subset(Y0, emptyset) => (Y0 = emptyset))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (subset(Y1, Y0) => 99.05/14.96 in(Y1, powerset(Y0))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (in(Y1, powerset(Y0)) => 99.05/14.96 subset(Y1, Y0)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (subset(Y0, Y1) => 99.05/14.96 subset(powerset(Y0), 99.05/14.96 powerset(Y1))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i > $o]: 99.05/14.96 in(dsetconstr(Y0, Y1), 99.05/14.96 powerset(Y0)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i > $o]: 99.05/14.96 subset(dsetconstr(Y0, Y1), 99.05/14.96 Y0))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (in(Y2, Y0) => 99.05/14.96 in(Y2, 99.05/14.96 binunion(Y0, Y1)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 in(Y1, 99.05/14.96 setadjoin(Y0, 99.05/14.96 setadjoin(Y1, 99.05/14.96 emptyset))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (in(Y2, Y1) => 99.05/14.96 in(Y2, 99.05/14.96 binunion(Y0, 99.05/14.96 Y1)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (!!((^[Y3 : $o]: 99.05/14.96 (in(Y2, 99.05/14.96 binunion( 99.05/14.96 Y0, Y1)) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 in(Y2, 99.05/14.96 Y0) => Y3) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 in(Y2, 99.05/14.96 Y1) => Y3) => 99.05/14.96 Y3))))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 binunion(Y0, 99.05/14.96 Y1)) => 99.05/14.96 (in(Y2, Y1) | 99.05/14.96 in(Y2, Y0)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 subset(Y0, 99.05/14.96 binunion(Y0, Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 subset(Y1, 99.05/14.96 binunion(Y0, Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (in(Y2, Y0) => 99.05/14.96 (in(Y2, Y1) => 99.05/14.96 in(Y2, 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (subset(Y2, 99.05/14.96 Y0) => 99.05/14.96 (subset( 99.05/14.96 Y2, Y1) => 99.05/14.96 subset( 99.05/14.96 Y2, 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1)) => 99.05/14.96 in(Y2, Y0))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 subset( 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1), Y0))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (subset(Y0, Y1) => 99.05/14.96 (binintersect( 99.05/14.96 Y0, Y1) = 99.05/14.96 Y0)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ((binintersect( 99.05/14.96 Y0, Y1) = 99.05/14.96 Y1) => 99.05/14.96 subset(Y1, Y0)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1)) => 99.05/14.96 in(Y2, 99.05/14.96 Y1))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ((~(( 99.05/14.96 ??(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 ( 99.05/14.96 in(Y2, 99.05/14.96 Y0) & 99.05/14.96 in(Y2, 99.05/14.96 Y1))))))) => 99.05/14.96 (binintersect( 99.05/14.96 Y0, Y1) = 99.05/14.96 emptyset)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 subset( 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1), 99.05/14.96 Y1))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (subset( 99.05/14.96 Y1, Y0) => 99.05/14.96 (binintersect( 99.05/14.96 Y0, Y1) = 99.05/14.96 Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (( 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1) = 99.05/14.96 Y0) => 99.05/14.96 subset( 99.05/14.96 Y0, Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (binintersect( 99.05/14.96 Y0, 99.05/14.96 binunion( 99.05/14.96 Y1, Y2)) = 99.05/14.96 binunion( 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1), 99.05/14.96 binintersect( 99.05/14.96 Y0, Y2)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y1))) => 99.05/14.96 in(Y2, 99.05/14.96 setminus( 99.05/14.96 Y0, Y1))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 setminus( 99.05/14.96 Y0, Y1)) => 99.05/14.96 in(Y2, 99.05/14.96 Y0))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 setminus( 99.05/14.96 Y0, Y1)) => 99.05/14.96 (~( 99.05/14.96 in(Y2, 99.05/14.96 Y1))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 ( 99.05/14.96 subset( 99.05/14.96 Y0, Y1) => 99.05/14.96 ( 99.05/14.96 setminus( 99.05/14.96 Y0, Y1) = 99.05/14.96 emptyset)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 setminus( 99.05/14.96 Y0, Y1)))) => 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 in(Y2, 99.05/14.96 Y1)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 setminus( 99.05/14.96 Y0, Y1)))) => 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y1))) => 99.05/14.96 (~( 99.05/14.96 in(Y2, 99.05/14.96 Y0)))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y0))) => 99.05/14.96 (~( 99.05/14.96 in(Y2, 99.05/14.96 setminus( 99.05/14.96 Y0, Y1)))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y1) => 99.05/14.96 (~( 99.05/14.96 in(Y2, 99.05/14.96 setminus( 99.05/14.96 Y0, Y1)))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 subset( 99.05/14.96 setminus( 99.05/14.96 Y0, Y1), 99.05/14.96 Y0))))))) => 99.05/14.96 ((!!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (( 99.05/14.96 setminus( 99.05/14.96 Y0, Y1) = 99.05/14.96 emptyset) => 99.05/14.96 subset( 99.05/14.96 Y0, Y1)))))))) => 99.05/14.96 ((!!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 symdiff( 99.05/14.96 Y0, Y1)) => 99.05/14.96 (!!(( 99.05/14.96 ^[Y3 : $o]: 99.05/14.96 (( 99.05/14.96 in(Y2, 99.05/14.96 Y0) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y1))) => 99.05/14.96 Y3)) => 99.05/14.96 (( 99.05/14.96 ( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y0))) => 99.05/14.96 ( 99.05/14.96 in(Y2, 99.05/14.96 Y1) => Y3)) => 99.05/14.96 Y3))))))))))))))) => 99.05/14.96 ((!!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y1))) => 99.05/14.96 in(Y2, 99.05/14.96 symdiff( 99.05/14.96 Y0, Y1))))))))))))) => 99.05/14.96 ((!!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y0))) => 99.05/14.96 (in(Y2, 99.05/14.96 Y1) => 99.05/14.96 in(Y2, 99.05/14.96 symdiff( 99.05/14.96 Y0, Y1))))))))))))) => 99.05/14.96 (( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (in(Y2, 99.05/14.96 Y1) => 99.05/14.96 (~( 99.05/14.96 in(Y2, 99.05/14.96 symdiff( 99.05/14.96 Y0, Y1))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y0))) => 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y1))) => 99.05/14.96 (~( 99.05/14.96 in(Y2, 99.05/14.96 symdiff( 99.05/14.96 Y0, Y1))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 in(Y1, 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 in(Y0, 99.05/14.96 setunion( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 in(Y1, 99.05/14.96 setunion( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (??(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 setunion( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)))) & 99.05/14.96 (??(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (in(Y3, 99.05/14.96 setunion( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)))) & 99.05/14.96 (setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)) = 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset)), 99.05/14.96 emptyset))))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (??(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 setunion( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)))) & 99.05/14.96 (??(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (in(Y3, 99.05/14.96 setunion( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)))) & 99.05/14.96 (setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)) = 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset)), 99.05/14.96 emptyset))))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (in(Y1, 99.05/14.96 Y0) => 99.05/14.96 subset( 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset), 99.05/14.96 Y0)))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (in(Y1, 99.05/14.96 Y0) => 99.05/14.96 in( 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset), 99.05/14.96 powerset( 99.05/14.96 Y0))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 in( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 emptyset), 99.05/14.96 powerset( 99.05/14.96 binunion( 99.05/14.96 Y0, Y1))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset))) => 99.05/14.96 (( 99.05/14.96 Y2 = Y1) | 99.05/14.96 (Y2 = Y0)))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (!!(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (in(Y3, 99.05/14.96 Y1) => 99.05/14.96 subset( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset)), 99.05/14.96 binunion( 99.05/14.96 Y0, Y1)))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (!!(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (in(Y3, 99.05/14.96 Y1) => 99.05/14.96 in( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset)), 99.05/14.96 powerset( 99.05/14.96 binunion( 99.05/14.96 Y0, Y1))))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (!!(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (in(Y3, 99.05/14.96 Y1) => 99.05/14.96 subset( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)), 99.05/14.96 powerset( 99.05/14.96 binunion( 99.05/14.96 Y0, Y1))))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (!!(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (in(Y3, 99.05/14.96 Y1) => 99.05/14.96 in( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)), 99.05/14.96 powerset( 99.05/14.96 powerset( 99.05/14.96 binunion( 99.05/14.96 Y0, Y1)))))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (!!(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (in(Y3, 99.05/14.96 Y1) => 99.05/14.96 in( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)), 99.05/14.96 powerset( 99.05/14.96 powerset( 99.05/14.96 binunion( 99.05/14.96 Y0, Y1)))))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (!!(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (in(Y3, 99.05/14.96 Y1) => 99.05/14.96 in( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)), 99.05/14.96 dsetconstr( 99.05/14.96 powerset( 99.05/14.96 powerset( 99.05/14.96 binunion( 99.05/14.96 Y0, Y1))), 99.05/14.96 (^[Y4 : $i]: 99.05/14.96 (??(( 99.05/14.96 ^[Y5 : $i]: 99.05/14.96 (in(Y5, 99.05/14.96 Y0) & 99.05/14.96 (??(( 99.05/14.96 ^[Y6 : $i]: 99.05/14.96 (in(Y6, 99.05/14.96 Y1) & 99.05/14.96 (Y4 = 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y5, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y5, 99.05/14.96 setadjoin( 99.05/14.96 Y6, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)))))))))))))))))))))))))))) => 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 dsetconstr( 99.05/14.96 powerset( 99.05/14.96 powerset( 99.05/14.96 binunion( 99.05/14.96 Y0, Y1))), 99.05/14.96 (^[Y3 : $i]: 99.05/14.96 (??(( 99.05/14.96 ^[Y4 : $i]: 99.05/14.96 (in(Y4, 99.05/14.96 Y0) & 99.05/14.96 (??(( 99.05/14.96 ^[Y5 : $i]: 99.05/14.96 (in(Y5, 99.05/14.96 Y1) & 99.05/14.96 (Y3 = 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y4, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y4, 99.05/14.96 setadjoin( 99.05/14.96 Y5, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)))))))))))))) => 99.05/14.96 (??(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (( 99.05/14.96 ??(( 99.05/14.96 ^[Y4 : $i]: 99.05/14.96 (in(Y4, 99.05/14.96 Y1) & 99.05/14.96 (Y2 = 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 setadjoin( 99.05/14.96 Y4, 99.05/14.96 emptyset)), 99.05/14.96 emptyset))))))) & 99.05/14.96 in(Y3, 99.05/14.96 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.05/14.96 inference('lazy_cnf_imply', [status(thm)], ['225'])). 99.05/14.96 tff('227', plain, 99.05/14.96 ~ ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: ((Y0 = Y1) => (powerset(Y0) = powerset(Y1))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: ((Y0 = Y1) => (setunion(Y0) = setunion(Y1))))))))) => 99.05/14.96 ((!!((^[Y0 : $i > $o]: 99.05/14.96 ((??((^[Y1 : $i]: 99.05/14.96 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i > $o]: 99.05/14.96 (!!((^[Y1 : $i > $o]: 99.05/14.96 ((!!((^[Y2 : $i]: 99.05/14.96 (!!((^[Y3 : $i]: 99.05/14.96 ((Y2 = Y3) => (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.96 ((??((^[Y2 : $i]: 99.05/14.96 (Y0(Y2) & 99.05/14.96 (!!((^[Y3 : $i]: (Y0(Y3) => (Y2 = Y3))))))))) => 99.05/14.96 ((??((^[Y2 : $i]: 99.05/14.96 (Y1(Y2) & 99.05/14.96 (!!((^[Y3 : $i]: (Y1(Y3) => (Y2 = Y3))))))))) => 99.05/14.96 (descr(Y0) = descr(Y1))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ((Y0 = Y1) => 99.05/14.96 (!!((^[Y2 : $i > $o]: 99.05/14.96 (!!((^[Y3 : $i > $o]: 99.05/14.96 ((!!((^[Y4 : $i]: 99.05/14.96 (in(Y4, Y0) => 99.05/14.96 (!!((^[Y5 : $i]: 99.05/14.96 (in(Y5, Y1) => 99.05/14.96 ((Y4 = Y5) => 99.05/14.96 (Y2(Y4) <=> Y3(Y5))))))))))) => 99.05/14.96 (dsetconstr(Y0, Y2) = 99.05/14.96 dsetconstr(Y1, Y3)))))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 99.05/14.96 subset(Y0, Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y1, Y0)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y0, Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 99.05/14.96 subset(Y0, Y1)))))))) => 99.05/14.96 ((!!(subset(emptyset))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (subset(Y0, Y1) => 99.05/14.96 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (subset(Y0, Y1) => 99.05/14.96 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (in(Y2, Y0) => 99.05/14.96 ((~(in(Y2, Y1))) => 99.05/14.96 (~(subset(Y0, Y1)))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (in(Y2, Y0) => 99.05/14.96 ((~(in(Y2, Y1))) => (Y0 != Y1)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (subset(Y0, Y1) => 99.05/14.96 (subset(Y1, Y2) => 99.05/14.96 subset(Y0, Y2)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: subset(Y1, setadjoin(Y0, Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (subset(Y0, Y2) => 99.05/14.96 subset(Y0, setadjoin(Y1, Y2)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (subset(Y0, Y1) => 99.05/14.96 in(Y0, powerset(Y1))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (subset(Y0, Y1) => 99.05/14.96 (subset(Y1, Y0) => (Y0 = Y1))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (subset(Y0, emptyset) => (Y0 = emptyset))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (subset(Y1, Y0) => 99.05/14.96 in(Y1, powerset(Y0))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (in(Y1, powerset(Y0)) => 99.05/14.96 subset(Y1, Y0)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (subset(Y0, Y1) => 99.05/14.96 subset(powerset(Y0), 99.05/14.96 powerset(Y1))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i > $o]: 99.05/14.96 in(dsetconstr(Y0, Y1), 99.05/14.96 powerset(Y0)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i > $o]: 99.05/14.96 subset(dsetconstr(Y0, Y1), 99.05/14.96 Y0))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (in(Y2, Y0) => 99.05/14.96 in(Y2, 99.05/14.96 binunion(Y0, Y1)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 in(Y1, 99.05/14.96 setadjoin(Y0, 99.05/14.96 setadjoin(Y1, emptyset))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (in(Y2, Y1) => 99.05/14.96 in(Y2, 99.05/14.96 binunion(Y0, Y1)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (!!((^[Y3 : $o]: 99.05/14.96 (in(Y2, 99.05/14.96 binunion( 99.05/14.96 Y0, Y1)) => 99.05/14.96 (( 99.05/14.96 in(Y2, 99.05/14.96 Y0) => Y3) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 in(Y2, 99.05/14.96 Y1) => Y3) => 99.05/14.96 Y3))))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 binunion(Y0, 99.05/14.96 Y1)) => 99.05/14.96 (in(Y2, Y1) | 99.05/14.96 in(Y2, Y0)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 subset(Y0, 99.05/14.96 binunion(Y0, Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 subset(Y1, 99.05/14.96 binunion(Y0, Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (in(Y2, Y0) => 99.05/14.96 (in(Y2, Y1) => 99.05/14.96 in(Y2, 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (subset(Y2, 99.05/14.96 Y0) => 99.05/14.96 (subset(Y2, 99.05/14.96 Y1) => 99.05/14.96 subset(Y2, 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1)) => 99.05/14.96 in(Y2, Y0))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 subset( 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1), Y0))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (subset(Y0, Y1) => 99.05/14.96 (binintersect( 99.05/14.96 Y0, Y1) = 99.05/14.96 Y0)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ((binintersect( 99.05/14.96 Y0, Y1) = 99.05/14.96 Y1) => 99.05/14.96 subset(Y1, Y0)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1)) => 99.05/14.96 in(Y2, 99.05/14.96 Y1))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ((~((??(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) & 99.05/14.96 in(Y2, 99.05/14.96 Y1))))))) => 99.05/14.96 (binintersect( 99.05/14.96 Y0, Y1) = 99.05/14.96 emptyset)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 subset( 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1), 99.05/14.96 Y1))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (subset(Y1, 99.05/14.96 Y0) => 99.05/14.96 (binintersect( 99.05/14.96 Y0, Y1) = 99.05/14.96 Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ((binintersect( 99.05/14.96 Y0, Y1) = 99.05/14.96 Y0) => 99.05/14.96 subset( 99.05/14.96 Y0, Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (binintersect( 99.05/14.96 Y0, 99.05/14.96 binunion( 99.05/14.96 Y1, Y2)) = 99.05/14.96 binunion( 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1), 99.05/14.96 binintersect( 99.05/14.96 Y0, Y2)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y1))) => 99.05/14.96 in(Y2, 99.05/14.96 setminus( 99.05/14.96 Y0, Y1))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 setminus( 99.05/14.96 Y0, Y1)) => 99.05/14.96 in(Y2, 99.05/14.96 Y0))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 setminus( 99.05/14.96 Y0, Y1)) => 99.05/14.96 (~( 99.05/14.96 in(Y2, 99.05/14.96 Y1))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (subset( 99.05/14.96 Y0, Y1) => 99.05/14.96 ( 99.05/14.96 setminus( 99.05/14.96 Y0, Y1) = 99.05/14.96 emptyset)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 setminus( 99.05/14.96 Y0, Y1)))) => 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 in(Y2, 99.05/14.96 Y1)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 setminus( 99.05/14.96 Y0, Y1)))) => 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y1))) => 99.05/14.96 (~( 99.05/14.96 in(Y2, 99.05/14.96 Y0)))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y0))) => 99.05/14.96 (~( 99.05/14.96 in(Y2, 99.05/14.96 setminus( 99.05/14.96 Y0, Y1)))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y1) => 99.05/14.96 (~( 99.05/14.96 in(Y2, 99.05/14.96 setminus( 99.05/14.96 Y0, Y1)))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 subset( 99.05/14.96 setminus( 99.05/14.96 Y0, Y1), 99.05/14.96 Y0))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (( 99.05/14.96 setminus( 99.05/14.96 Y0, Y1) = 99.05/14.96 emptyset) => 99.05/14.96 subset( 99.05/14.96 Y0, Y1)))))))) => 99.05/14.96 ((!!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 symdiff( 99.05/14.96 Y0, Y1)) => 99.05/14.96 (!!(( 99.05/14.96 ^[Y3 : $o]: 99.05/14.96 (( 99.05/14.96 in(Y2, 99.05/14.96 Y0) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y1))) => 99.05/14.96 Y3)) => 99.05/14.96 (( 99.05/14.96 ( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y0))) => 99.05/14.96 ( 99.05/14.96 in(Y2, 99.05/14.96 Y1) => Y3)) => 99.05/14.96 Y3))))))))))))))) => 99.05/14.96 ((!!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y1))) => 99.05/14.96 in(Y2, 99.05/14.96 symdiff( 99.05/14.96 Y0, Y1))))))))))))) => 99.05/14.96 ((!!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y0))) => 99.05/14.96 (in(Y2, 99.05/14.96 Y1) => 99.05/14.96 in(Y2, 99.05/14.96 symdiff( 99.05/14.96 Y0, Y1))))))))))))) => 99.05/14.96 ((!!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (in(Y2, 99.05/14.96 Y1) => 99.05/14.96 (~( 99.05/14.96 in(Y2, 99.05/14.96 symdiff( 99.05/14.96 Y0, Y1))))))))))))))) => 99.05/14.96 (( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y0))) => 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y1))) => 99.05/14.96 (~( 99.05/14.96 in(Y2, 99.05/14.96 symdiff( 99.05/14.96 Y0, Y1))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 in(Y1, 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 in(Y0, 99.05/14.96 setunion( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 in(Y1, 99.05/14.96 setunion( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (??(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 setunion( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)))) & 99.05/14.96 (??(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (in(Y3, 99.05/14.96 setunion( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)))) & 99.05/14.96 (setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)) = 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset)), 99.05/14.96 emptyset))))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (??(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 setunion( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)))) & 99.05/14.96 (??(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (in(Y3, 99.05/14.96 setunion( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)))) & 99.05/14.96 (setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)) = 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset)), 99.05/14.96 emptyset))))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (in(Y1, 99.05/14.96 Y0) => 99.05/14.96 subset( 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset), 99.05/14.96 Y0)))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (in(Y1, 99.05/14.96 Y0) => 99.05/14.96 in( 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset), 99.05/14.96 powerset( 99.05/14.96 Y0))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 in( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 emptyset), 99.05/14.96 powerset( 99.05/14.96 binunion( 99.05/14.96 Y0, Y1))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset))) => 99.05/14.96 (( 99.05/14.96 Y2 = Y1) | 99.05/14.96 (Y2 = Y0)))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (!!(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (in(Y3, 99.05/14.96 Y1) => 99.05/14.96 subset( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset)), 99.05/14.96 binunion( 99.05/14.96 Y0, Y1)))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (!!(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (in(Y3, 99.05/14.96 Y1) => 99.05/14.96 in( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset)), 99.05/14.96 powerset( 99.05/14.96 binunion( 99.05/14.96 Y0, Y1))))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (!!(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (in(Y3, 99.05/14.96 Y1) => 99.05/14.96 subset( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)), 99.05/14.96 powerset( 99.05/14.96 binunion( 99.05/14.96 Y0, Y1))))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (!!(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (in(Y3, 99.05/14.96 Y1) => 99.05/14.96 in( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)), 99.05/14.96 powerset( 99.05/14.96 powerset( 99.05/14.96 binunion( 99.05/14.96 Y0, Y1)))))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (!!(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (in(Y3, 99.05/14.96 Y1) => 99.05/14.96 in( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)), 99.05/14.96 powerset( 99.05/14.96 powerset( 99.05/14.96 binunion( 99.05/14.96 Y0, Y1)))))))))))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (!!(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (in(Y3, 99.05/14.96 Y1) => 99.05/14.96 in( 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y2, 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)), 99.05/14.96 dsetconstr( 99.05/14.96 powerset( 99.05/14.96 powerset( 99.05/14.96 binunion( 99.05/14.96 Y0, Y1))), 99.05/14.96 (^[Y4 : $i]: 99.05/14.96 (??(( 99.05/14.96 ^[Y5 : $i]: 99.05/14.96 (in(Y5, 99.05/14.96 Y0) & 99.05/14.96 (??(( 99.05/14.96 ^[Y6 : $i]: 99.05/14.96 (in(Y6, 99.05/14.96 Y1) & 99.05/14.96 (Y4 = 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y5, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y5, 99.05/14.96 setadjoin( 99.05/14.96 Y6, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)))))))))))))))))))))))))))) => 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 dsetconstr( 99.05/14.96 powerset( 99.05/14.96 powerset( 99.05/14.96 binunion( 99.05/14.96 Y0, Y1))), 99.05/14.96 (^[Y3 : $i]: 99.05/14.96 (??(( 99.05/14.96 ^[Y4 : $i]: 99.05/14.96 (in(Y4, 99.05/14.96 Y0) & 99.05/14.96 (??(( 99.05/14.96 ^[Y5 : $i]: 99.05/14.96 (in(Y5, 99.05/14.96 Y1) & 99.05/14.96 (Y3 = 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y4, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y4, 99.05/14.96 setadjoin( 99.05/14.96 Y5, 99.05/14.96 emptyset)), 99.05/14.96 emptyset)))))))))))))) => 99.05/14.96 (??(( 99.05/14.96 ^[Y3 : $i]: 99.05/14.96 (( 99.05/14.96 ??(( 99.05/14.96 ^[Y4 : $i]: 99.05/14.96 (in(Y4, 99.05/14.96 Y1) & 99.05/14.96 (Y2 = 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 emptyset), 99.05/14.96 setadjoin( 99.05/14.96 setadjoin( 99.05/14.96 Y3, 99.05/14.96 setadjoin( 99.05/14.96 Y4, 99.05/14.96 emptyset)), 99.05/14.96 emptyset))))))) & 99.05/14.96 in(Y3, 99.05/14.96 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.05/14.96 inference('lazy_cnf_imply', [status(thm)], ['226'])). 99.05/14.96 tff('228', plain, 99.05/14.96 ~ ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: ((Y0 = Y1) => (setunion(Y0) = setunion(Y1))))))))) => 99.05/14.96 ((!!((^[Y0 : $i > $o]: 99.05/14.96 ((??((^[Y1 : $i]: 99.05/14.96 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i > $o]: 99.05/14.96 (!!((^[Y1 : $i > $o]: 99.05/14.96 ((!!((^[Y2 : $i]: 99.05/14.96 (!!((^[Y3 : $i]: 99.05/14.96 ((Y2 = Y3) => (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.96 ((??((^[Y2 : $i]: 99.05/14.96 (Y0(Y2) & 99.05/14.96 (!!((^[Y3 : $i]: (Y0(Y3) => (Y2 = Y3))))))))) => 99.05/14.96 ((??((^[Y2 : $i]: 99.05/14.96 (Y1(Y2) & 99.05/14.96 (!!((^[Y3 : $i]: (Y1(Y3) => (Y2 = Y3))))))))) => 99.05/14.96 (descr(Y0) = descr(Y1))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ((Y0 = Y1) => 99.05/14.96 (!!((^[Y2 : $i > $o]: 99.05/14.96 (!!((^[Y3 : $i > $o]: 99.05/14.96 ((!!((^[Y4 : $i]: 99.05/14.96 (in(Y4, Y0) => 99.05/14.96 (!!((^[Y5 : $i]: 99.05/14.96 (in(Y5, Y1) => 99.05/14.96 ((Y4 = Y5) => 99.05/14.96 (Y2(Y4) <=> Y3(Y5))))))))))) => 99.05/14.96 (dsetconstr(Y0, Y2) = 99.05/14.96 dsetconstr(Y1, Y3)))))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 99.05/14.96 subset(Y0, Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y1, Y0)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y0, Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 99.05/14.96 subset(Y0, Y1)))))))) => 99.05/14.96 ((!!(subset(emptyset))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (subset(Y0, Y1) => 99.05/14.96 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (subset(Y0, Y1) => 99.05/14.96 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (in(Y2, Y0) => 99.05/14.96 ((~(in(Y2, Y1))) => 99.05/14.96 (~(subset(Y0, Y1)))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (in(Y2, Y0) => 99.05/14.96 ((~(in(Y2, Y1))) => (Y0 != Y1)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (subset(Y0, Y1) => 99.05/14.96 (subset(Y1, Y2) => subset(Y0, Y2)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: subset(Y1, setadjoin(Y0, Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (subset(Y0, Y2) => 99.05/14.96 subset(Y0, setadjoin(Y1, Y2)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (subset(Y0, Y1) => 99.05/14.96 in(Y0, powerset(Y1))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (subset(Y0, Y1) => 99.05/14.96 (subset(Y1, Y0) => (Y0 = Y1))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (subset(Y0, emptyset) => (Y0 = emptyset))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (subset(Y1, Y0) => 99.05/14.96 in(Y1, powerset(Y0))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (in(Y1, powerset(Y0)) => 99.05/14.96 subset(Y1, Y0)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (subset(Y0, Y1) => 99.05/14.96 subset(powerset(Y0), 99.05/14.96 powerset(Y1))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i > $o]: 99.05/14.96 in(dsetconstr(Y0, Y1), 99.05/14.96 powerset(Y0)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i > $o]: 99.05/14.96 subset(dsetconstr(Y0, Y1), Y0))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (in(Y2, Y0) => 99.05/14.96 in(Y2, 99.05/14.96 binunion(Y0, Y1)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 in(Y1, 99.05/14.96 setadjoin(Y0, 99.05/14.96 setadjoin(Y1, emptyset))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (in(Y2, Y1) => 99.05/14.96 in(Y2, 99.05/14.96 binunion(Y0, Y1)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (!!((^[Y3 : $o]: 99.05/14.96 (in(Y2, 99.05/14.96 binunion( 99.05/14.96 Y0, Y1)) => 99.05/14.96 ((in(Y2, 99.05/14.96 Y0) => Y3) => 99.05/14.96 (( 99.05/14.96 in(Y2, 99.05/14.96 Y1) => Y3) => 99.05/14.96 Y3))))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 binunion(Y0, 99.05/14.96 Y1)) => 99.05/14.96 (in(Y2, Y1) | 99.05/14.96 in(Y2, Y0)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 subset(Y0, 99.05/14.96 binunion(Y0, Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 subset(Y1, 99.05/14.96 binunion(Y0, Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (in(Y2, Y0) => 99.05/14.96 (in(Y2, Y1) => 99.05/14.96 in(Y2, 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (subset(Y2, 99.05/14.96 Y0) => 99.05/14.96 (subset(Y2, 99.05/14.96 Y1) => 99.05/14.96 subset(Y2, 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1)) => 99.05/14.96 in(Y2, Y0))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 subset( 99.05/14.96 binintersect(Y0, 99.05/14.96 Y1), Y0))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (subset(Y0, Y1) => 99.05/14.96 (binintersect( 99.05/14.96 Y0, Y1) = 99.05/14.96 Y0)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ((binintersect( 99.05/14.96 Y0, Y1) = 99.05/14.96 Y1) => 99.05/14.96 subset(Y1, Y0)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!((^[Y2 : $i]: 99.05/14.96 ( 99.05/14.96 in(Y2, 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1)) => 99.05/14.96 in(Y2, 99.05/14.96 Y1))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ((~((??(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) & 99.05/14.96 in(Y2, 99.05/14.96 Y1))))))) => 99.05/14.96 (binintersect( 99.05/14.96 Y0, Y1) = 99.05/14.96 emptyset)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 subset( 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1), 99.05/14.96 Y1))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (subset(Y1, 99.05/14.96 Y0) => 99.05/14.96 (binintersect( 99.05/14.96 Y0, Y1) = 99.05/14.96 Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ((binintersect( 99.05/14.96 Y0, Y1) = 99.05/14.96 Y0) => 99.05/14.96 subset(Y0, 99.05/14.96 Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (binintersect( 99.05/14.96 Y0, 99.05/14.96 binunion( 99.05/14.96 Y1, Y2)) = 99.05/14.96 binunion( 99.05/14.96 binintersect( 99.05/14.96 Y0, Y1), 99.05/14.96 binintersect( 99.05/14.96 Y0, Y2)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y1))) => 99.05/14.96 in(Y2, 99.05/14.96 setminus( 99.05/14.96 Y0, Y1))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 setminus( 99.05/14.96 Y0, Y1)) => 99.05/14.96 in(Y2, 99.05/14.96 Y0))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 setminus( 99.05/14.96 Y0, Y1)) => 99.05/14.96 (~( 99.05/14.96 in(Y2, 99.05/14.96 Y1))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!((^[Y1 : $i]: 99.05/14.96 (subset( 99.05/14.96 Y0, Y1) => 99.05/14.96 (setminus( 99.05/14.96 Y0, Y1) = 99.05/14.96 emptyset)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 setminus( 99.05/14.96 Y0, Y1)))) => 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 in(Y2, 99.05/14.96 Y1)))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 setminus( 99.05/14.96 Y0, Y1)))) => 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y1))) => 99.05/14.96 (~( 99.05/14.96 in(Y2, 99.05/14.96 Y0)))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y0))) => 99.05/14.96 (~( 99.05/14.96 in(Y2, 99.05/14.96 setminus( 99.05/14.96 Y0, Y1)))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y1) => 99.05/14.96 (~( 99.05/14.96 in(Y2, 99.05/14.96 setminus( 99.05/14.96 Y0, Y1)))))))))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 subset( 99.05/14.96 setminus( 99.05/14.96 Y0, Y1), 99.05/14.96 Y0))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (( 99.05/14.96 setminus( 99.05/14.96 Y0, Y1) = 99.05/14.96 emptyset) => 99.05/14.96 subset( 99.05/14.96 Y0, Y1)))))))) => 99.05/14.96 ((!!((^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 symdiff( 99.05/14.96 Y0, Y1)) => 99.05/14.96 (!!(( 99.05/14.96 ^[Y3 : $o]: 99.05/14.96 (( 99.05/14.96 in(Y2, 99.05/14.96 Y0) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y1))) => 99.05/14.96 Y3)) => 99.05/14.96 (( 99.05/14.96 ( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y0))) => 99.05/14.96 ( 99.05/14.96 in(Y2, 99.05/14.96 Y1) => Y3)) => 99.05/14.96 Y3))))))))))))))) => 99.05/14.96 ((!!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y1))) => 99.05/14.96 in(Y2, 99.05/14.96 symdiff( 99.05/14.96 Y0, Y1))))))))))))) => 99.05/14.96 ((!!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 ( 99.05/14.96 !!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y0))) => 99.05/14.96 (in(Y2, 99.05/14.96 Y1) => 99.05/14.96 in(Y2, 99.05/14.96 symdiff( 99.05/14.96 Y0, Y1))))))))))))) => 99.05/14.96 ((!!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (in(Y2, 99.05/14.96 Y0) => 99.05/14.96 (in(Y2, 99.05/14.96 Y1) => 99.05/14.96 (~( 99.05/14.96 in(Y2, 99.05/14.96 symdiff( 99.05/14.96 Y0, Y1))))))))))))))) => 99.05/14.96 ((!!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y2 : $i]: 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y0))) => 99.05/14.96 (( 99.05/14.96 ~( 99.05/14.96 in(Y2, 99.05/14.96 Y1))) => 99.05/14.96 (~( 99.05/14.96 in(Y2, 99.05/14.96 symdiff( 99.05/14.96 Y0, Y1))))))))))))))) => 99.05/14.96 (( 99.05/14.96 !!(( 99.05/14.96 ^[Y0 : $i]: 99.05/14.96 (!!(( 99.05/14.96 ^[Y1 : $i]: 99.05/14.96 in(Y1, 99.05/14.96 setadjoin( 99.05/14.96 Y0, 99.05/14.96 setadjoin( 99.05/14.96 Y1, 99.05/14.96 emptyset))))))))) => 99.05/14.96 ( 99.05/14.96 ( 99.05/14.97 !!(( 99.05/14.97 ^[Y0 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y1 : $i]: 99.05/14.97 in(Y0, 99.05/14.97 setunion( 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y0, 99.05/14.97 emptyset), 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y0, 99.05/14.97 setadjoin( 99.05/14.97 Y1, 99.05/14.97 emptyset)), 99.05/14.97 emptyset)))))))))) => 99.05/14.97 ( 99.05/14.97 ( 99.05/14.97 !!(( 99.05/14.97 ^[Y0 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y1 : $i]: 99.05/14.97 in(Y1, 99.05/14.97 setunion( 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y0, 99.05/14.97 emptyset), 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y0, 99.05/14.97 setadjoin( 99.05/14.97 Y1, 99.05/14.97 emptyset)), 99.05/14.97 emptyset)))))))))) => 99.05/14.97 ( 99.05/14.97 ( 99.05/14.97 !!(( 99.05/14.97 ^[Y0 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y1 : $i]: 99.05/14.97 (??(( 99.05/14.97 ^[Y2 : $i]: 99.05/14.97 (in(Y2, 99.05/14.97 setunion( 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y0, 99.05/14.97 emptyset), 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y0, 99.05/14.97 setadjoin( 99.05/14.97 Y1, 99.05/14.97 emptyset)), 99.05/14.97 emptyset)))) & 99.05/14.97 (??(( 99.05/14.97 ^[Y3 : $i]: 99.05/14.97 (in(Y3, 99.05/14.97 setunion( 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y0, 99.05/14.97 emptyset), 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y0, 99.05/14.97 setadjoin( 99.05/14.97 Y1, 99.05/14.97 emptyset)), 99.05/14.97 emptyset)))) & 99.05/14.97 (setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y0, 99.05/14.97 emptyset), 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y0, 99.05/14.97 setadjoin( 99.05/14.97 Y1, 99.05/14.97 emptyset)), 99.05/14.97 emptyset)) = 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y2, 99.05/14.97 emptyset), 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y2, 99.05/14.97 setadjoin( 99.05/14.97 Y3, 99.05/14.97 emptyset)), 99.05/14.97 emptyset))))))))))))))))) => 99.05/14.97 ( 99.05/14.97 ( 99.05/14.97 !!(( 99.05/14.97 ^[Y0 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y1 : $i]: 99.05/14.97 (??(( 99.05/14.97 ^[Y2 : $i]: 99.05/14.97 (in(Y2, 99.05/14.97 setunion( 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y0, 99.05/14.97 emptyset), 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y0, 99.05/14.97 setadjoin( 99.05/14.97 Y1, 99.05/14.97 emptyset)), 99.05/14.97 emptyset)))) & 99.05/14.97 (??(( 99.05/14.97 ^[Y3 : $i]: 99.05/14.97 (in(Y3, 99.05/14.97 setunion( 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y0, 99.05/14.97 emptyset), 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y0, 99.05/14.97 setadjoin( 99.05/14.97 Y1, 99.05/14.97 emptyset)), 99.05/14.97 emptyset)))) & 99.05/14.97 (setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y0, 99.05/14.97 emptyset), 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y0, 99.05/14.97 setadjoin( 99.05/14.97 Y1, 99.05/14.97 emptyset)), 99.05/14.97 emptyset)) = 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y2, 99.05/14.97 emptyset), 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y2, 99.05/14.97 setadjoin( 99.05/14.97 Y3, 99.05/14.97 emptyset)), 99.05/14.97 emptyset))))))))))))))))) => 99.05/14.97 ( 99.05/14.97 ( 99.05/14.97 !!(( 99.05/14.97 ^[Y0 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y1 : $i]: 99.05/14.97 (in(Y1, 99.05/14.97 Y0) => 99.05/14.97 subset( 99.05/14.97 setadjoin( 99.05/14.97 Y1, 99.05/14.97 emptyset), 99.05/14.97 Y0)))))))) => 99.05/14.97 ( 99.05/14.97 ( 99.05/14.97 !!(( 99.05/14.97 ^[Y0 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y1 : $i]: 99.05/14.97 (in(Y1, 99.05/14.97 Y0) => 99.05/14.97 in( 99.05/14.97 setadjoin( 99.05/14.97 Y1, 99.05/14.97 emptyset), 99.05/14.97 powerset( 99.05/14.97 Y0))))))))) => 99.05/14.97 ( 99.05/14.97 ( 99.05/14.97 !!(( 99.05/14.97 ^[Y0 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y1 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y2 : $i]: 99.05/14.97 (in(Y2, 99.05/14.97 Y0) => 99.05/14.97 in( 99.05/14.97 setadjoin( 99.05/14.97 Y2, 99.05/14.97 emptyset), 99.05/14.97 powerset( 99.05/14.97 binunion( 99.05/14.97 Y0, Y1))))))))))))) => 99.05/14.97 ( 99.05/14.97 ( 99.05/14.97 !!(( 99.05/14.97 ^[Y0 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y1 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y2 : $i]: 99.05/14.97 (in(Y2, 99.05/14.97 setadjoin( 99.05/14.97 Y0, 99.05/14.97 setadjoin( 99.05/14.97 Y1, 99.05/14.97 emptyset))) => 99.05/14.97 (( 99.05/14.97 Y2 = Y1) | 99.05/14.97 (Y2 = Y0)))))))))))) => 99.05/14.97 ( 99.05/14.97 ( 99.05/14.97 !!(( 99.05/14.97 ^[Y0 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y1 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y2 : $i]: 99.05/14.97 (in(Y2, 99.05/14.97 Y0) => 99.05/14.97 (!!(( 99.05/14.97 ^[Y3 : $i]: 99.05/14.97 (in(Y3, 99.05/14.97 Y1) => 99.05/14.97 subset( 99.05/14.97 setadjoin( 99.05/14.97 Y2, 99.05/14.97 setadjoin( 99.05/14.97 Y3, 99.05/14.97 emptyset)), 99.05/14.97 binunion( 99.05/14.97 Y0, Y1)))))))))))))))) => 99.05/14.97 ( 99.05/14.97 ( 99.05/14.97 !!(( 99.05/14.97 ^[Y0 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y1 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y2 : $i]: 99.05/14.97 (in(Y2, 99.05/14.97 Y0) => 99.05/14.97 (!!(( 99.05/14.97 ^[Y3 : $i]: 99.05/14.97 (in(Y3, 99.05/14.97 Y1) => 99.05/14.97 in( 99.05/14.97 setadjoin( 99.05/14.97 Y2, 99.05/14.97 setadjoin( 99.05/14.97 Y3, 99.05/14.97 emptyset)), 99.05/14.97 powerset( 99.05/14.97 binunion( 99.05/14.97 Y0, Y1))))))))))))))))) => 99.05/14.97 ( 99.05/14.97 ( 99.05/14.97 !!(( 99.05/14.97 ^[Y0 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y1 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y2 : $i]: 99.05/14.97 (in(Y2, 99.05/14.97 Y0) => 99.05/14.97 (!!(( 99.05/14.97 ^[Y3 : $i]: 99.05/14.97 (in(Y3, 99.05/14.97 Y1) => 99.05/14.97 subset( 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y2, 99.05/14.97 emptyset), 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y2, 99.05/14.97 setadjoin( 99.05/14.97 Y3, 99.05/14.97 emptyset)), 99.05/14.97 emptyset)), 99.05/14.97 powerset( 99.05/14.97 binunion( 99.05/14.97 Y0, Y1))))))))))))))))) => 99.05/14.97 ( 99.05/14.97 ( 99.05/14.97 !!(( 99.05/14.97 ^[Y0 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y1 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y2 : $i]: 99.05/14.97 (in(Y2, 99.05/14.97 Y0) => 99.05/14.97 (!!(( 99.05/14.97 ^[Y3 : $i]: 99.05/14.97 (in(Y3, 99.05/14.97 Y1) => 99.05/14.97 in( 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y2, 99.05/14.97 emptyset), 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y2, 99.05/14.97 setadjoin( 99.05/14.97 Y3, 99.05/14.97 emptyset)), 99.05/14.97 emptyset)), 99.05/14.97 powerset( 99.05/14.97 powerset( 99.05/14.97 binunion( 99.05/14.97 Y0, Y1)))))))))))))))))) => 99.05/14.97 ( 99.05/14.97 ( 99.05/14.97 !!(( 99.05/14.97 ^[Y0 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y1 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y2 : $i]: 99.05/14.97 (in(Y2, 99.05/14.97 Y0) => 99.05/14.97 (!!(( 99.05/14.97 ^[Y3 : $i]: 99.05/14.97 (in(Y3, 99.05/14.97 Y1) => 99.05/14.97 in( 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y2, 99.05/14.97 emptyset), 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y2, 99.05/14.97 setadjoin( 99.05/14.97 Y3, 99.05/14.97 emptyset)), 99.05/14.97 emptyset)), 99.05/14.97 powerset( 99.05/14.97 powerset( 99.05/14.97 binunion( 99.05/14.97 Y0, Y1)))))))))))))))))) => 99.05/14.97 ( 99.05/14.97 ( 99.05/14.97 !!(( 99.05/14.97 ^[Y0 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y1 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y2 : $i]: 99.05/14.97 (in(Y2, 99.05/14.97 Y0) => 99.05/14.97 (!!(( 99.05/14.97 ^[Y3 : $i]: 99.05/14.97 (in(Y3, 99.05/14.97 Y1) => 99.05/14.97 in( 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y2, 99.05/14.97 emptyset), 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y2, 99.05/14.97 setadjoin( 99.05/14.97 Y3, 99.05/14.97 emptyset)), 99.05/14.97 emptyset)), 99.05/14.97 dsetconstr( 99.05/14.97 powerset( 99.05/14.97 powerset( 99.05/14.97 binunion( 99.05/14.97 Y0, Y1))), 99.05/14.97 (^[Y4 : $i]: 99.05/14.97 (??(( 99.05/14.97 ^[Y5 : $i]: 99.05/14.97 (in(Y5, 99.05/14.97 Y0) & 99.05/14.97 (??(( 99.05/14.97 ^[Y6 : $i]: 99.05/14.97 (in(Y6, 99.05/14.97 Y1) & 99.05/14.97 (Y4 = 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y5, 99.05/14.97 emptyset), 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y5, 99.05/14.97 setadjoin( 99.05/14.97 Y6, 99.05/14.97 emptyset)), 99.05/14.97 emptyset)))))))))))))))))))))))))))) => 99.05/14.97 ( 99.05/14.97 !!(( 99.05/14.97 ^[Y0 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y1 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y2 : $i]: 99.05/14.97 (in(Y2, 99.05/14.97 dsetconstr( 99.05/14.97 powerset( 99.05/14.97 powerset( 99.05/14.97 binunion( 99.05/14.97 Y0, Y1))), 99.05/14.97 (^[Y3 : $i]: 99.05/14.97 (??(( 99.05/14.97 ^[Y4 : $i]: 99.05/14.97 (in(Y4, 99.05/14.97 Y0) & 99.05/14.97 (??(( 99.05/14.97 ^[Y5 : $i]: 99.05/14.97 (in(Y5, 99.05/14.97 Y1) & 99.05/14.97 (Y3 = 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y4, 99.05/14.97 emptyset), 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y4, 99.05/14.97 setadjoin( 99.05/14.97 Y5, 99.05/14.97 emptyset)), 99.05/14.97 emptyset)))))))))))))) => 99.05/14.97 (??(( 99.05/14.97 ^[Y3 : $i]: 99.05/14.97 (( 99.05/14.97 ??(( 99.05/14.97 ^[Y4 : $i]: 99.05/14.97 (in(Y4, 99.05/14.97 Y1) & 99.05/14.97 (Y2 = 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y3, 99.05/14.97 emptyset), 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y3, 99.05/14.97 setadjoin( 99.05/14.97 Y4, 99.05/14.97 emptyset)), 99.05/14.97 emptyset))))))) & 99.05/14.97 in(Y3, 99.05/14.97 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.05/14.97 inference('lazy_cnf_imply', [status(thm)], ['227'])). 99.05/14.97 tff('229', plain, 99.05/14.97 ~ ((!!((^[Y0 : $i > $o]: 99.05/14.97 ((??((^[Y1 : $i]: 99.05/14.97 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.05/14.97 (!!((^[Y1 : $i]: 99.05/14.97 (!!((^[Y2 : $i]: (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 99.05/14.97 ((!!((^[Y0 : $i > $o]: 99.05/14.97 (!!((^[Y1 : $i > $o]: 99.05/14.97 ((!!((^[Y2 : $i]: 99.05/14.97 (!!((^[Y3 : $i]: 99.05/14.97 ((Y2 = Y3) => (Y0(Y2) <=> Y1(Y3))))))))) => 99.05/14.97 ((??((^[Y2 : $i]: 99.05/14.97 (Y0(Y2) & 99.05/14.97 (!!((^[Y3 : $i]: (Y0(Y3) => (Y2 = Y3))))))))) => 99.05/14.97 ((??((^[Y2 : $i]: 99.05/14.97 (Y1(Y2) & 99.05/14.97 (!!((^[Y3 : $i]: (Y1(Y3) => (Y2 = Y3))))))))) => 99.05/14.97 (descr(Y0) = descr(Y1))))))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i]: 99.05/14.97 ((Y0 = Y1) => 99.05/14.97 (!!((^[Y2 : $i > $o]: 99.05/14.97 (!!((^[Y3 : $i > $o]: 99.05/14.97 ((!!((^[Y4 : $i]: 99.05/14.97 (in(Y4, Y0) => 99.05/14.97 (!!((^[Y5 : $i]: 99.05/14.97 (in(Y5, Y1) => 99.05/14.97 ((Y4 = Y5) => 99.05/14.97 (Y2(Y4) <=> Y3(Y5))))))))))) => 99.05/14.97 (dsetconstr(Y0, Y2) = 99.05/14.97 dsetconstr(Y1, Y3)))))))))))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i]: 99.05/14.97 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 99.05/14.97 subset(Y0, Y1)))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y1, Y0)))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y0, Y1)))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i]: 99.05/14.97 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 99.05/14.97 subset(Y0, Y1)))))))) => 99.05/14.97 ((!!(subset(emptyset))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i]: 99.05/14.97 (!!((^[Y2 : $i]: 99.05/14.97 (subset(Y0, Y1) => 99.05/14.97 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i]: 99.05/14.97 (!!((^[Y2 : $i]: 99.05/14.97 (subset(Y0, Y1) => 99.05/14.97 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i]: 99.05/14.97 (!!((^[Y2 : $i]: 99.05/14.97 (in(Y2, Y0) => 99.05/14.97 ((~(in(Y2, Y1))) => 99.05/14.97 (~(subset(Y0, Y1)))))))))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i]: ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i]: 99.05/14.97 (!!((^[Y2 : $i]: 99.05/14.97 (in(Y2, Y0) => 99.05/14.97 ((~(in(Y2, Y1))) => (Y0 != Y1)))))))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i]: 99.05/14.97 (!!((^[Y2 : $i]: 99.05/14.97 (subset(Y0, Y1) => 99.05/14.97 (subset(Y1, Y2) => subset(Y0, Y2)))))))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i]: subset(Y1, setadjoin(Y0, Y1)))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i]: 99.05/14.97 (!!((^[Y2 : $i]: 99.05/14.97 (subset(Y0, Y2) => 99.05/14.97 subset(Y0, setadjoin(Y1, Y2)))))))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i]: 99.05/14.97 (subset(Y0, Y1) => in(Y0, powerset(Y1))))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i]: 99.05/14.97 (subset(Y0, Y1) => 99.05/14.97 (subset(Y1, Y0) => (Y0 = Y1))))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (subset(Y0, emptyset) => (Y0 = emptyset))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i]: 99.05/14.97 (subset(Y1, Y0) => 99.05/14.97 in(Y1, powerset(Y0))))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i]: 99.05/14.97 (in(Y1, powerset(Y0)) => 99.05/14.97 subset(Y1, Y0)))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i]: 99.05/14.97 (subset(Y0, Y1) => 99.05/14.97 subset(powerset(Y0), 99.05/14.97 powerset(Y1))))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i > $o]: 99.05/14.97 in(dsetconstr(Y0, Y1), 99.05/14.97 powerset(Y0)))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i > $o]: 99.05/14.97 subset(dsetconstr(Y0, Y1), Y0))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i]: 99.05/14.97 (!!((^[Y2 : $i]: 99.05/14.97 (in(Y2, Y0) => 99.05/14.97 in(Y2, 99.05/14.97 binunion(Y0, Y1)))))))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i]: 99.05/14.97 in(Y1, 99.05/14.97 setadjoin(Y0, 99.05/14.97 setadjoin(Y1, emptyset))))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i]: 99.05/14.97 (!!((^[Y2 : $i]: 99.05/14.97 (in(Y2, Y1) => 99.05/14.97 in(Y2, 99.05/14.97 binunion(Y0, Y1)))))))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i]: 99.05/14.97 (!!((^[Y2 : $i]: 99.05/14.97 (!!((^[Y3 : $o]: 99.05/14.97 (in(Y2, 99.05/14.97 binunion( 99.05/14.97 Y0, Y1)) => 99.05/14.97 ((in(Y2, Y0) => 99.05/14.97 Y3) => 99.05/14.97 ((in(Y2, 99.05/14.97 Y1) => Y3) => 99.05/14.97 Y3))))))))))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i]: 99.05/14.97 (!!((^[Y2 : $i]: 99.05/14.97 (in(Y2, 99.05/14.97 binunion(Y0, Y1)) => 99.05/14.97 (in(Y2, Y1) | 99.05/14.97 in(Y2, Y0)))))))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i]: 99.05/14.97 subset(Y0, 99.05/14.97 binunion(Y0, Y1)))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i]: 99.05/14.97 subset(Y1, 99.05/14.97 binunion(Y0, Y1)))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i]: 99.05/14.97 (!!((^[Y2 : $i]: 99.05/14.97 (in(Y2, Y0) => 99.05/14.97 (in(Y2, Y1) => 99.05/14.97 in(Y2, 99.05/14.97 binintersect( 99.05/14.97 Y0, Y1))))))))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i]: 99.05/14.97 (!!((^[Y2 : $i]: 99.05/14.97 (subset(Y2, Y0) => 99.05/14.97 (subset(Y2, 99.05/14.97 Y1) => 99.05/14.97 subset(Y2, 99.05/14.97 binintersect( 99.05/14.97 Y0, Y1))))))))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i]: 99.05/14.97 (!!((^[Y2 : $i]: 99.05/14.97 (in(Y2, 99.05/14.97 binintersect( 99.05/14.97 Y0, Y1)) => 99.05/14.97 in(Y2, Y0))))))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i]: 99.05/14.97 subset( 99.05/14.97 binintersect(Y0, 99.05/14.97 Y1), Y0))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i]: 99.05/14.97 (subset(Y0, Y1) => 99.05/14.97 (binintersect(Y0, 99.05/14.97 Y1) = 99.05/14.97 Y0)))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i]: 99.05/14.97 ((binintersect( 99.05/14.97 Y0, Y1) = 99.05/14.97 Y1) => 99.05/14.97 subset(Y1, Y0)))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i]: 99.05/14.97 (!!((^[Y2 : $i]: 99.05/14.97 (in(Y2, 99.05/14.97 binintersect( 99.05/14.97 Y0, Y1)) => 99.05/14.97 in(Y2, 99.05/14.97 Y1))))))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i]: 99.05/14.97 ((~((??(( 99.05/14.97 ^[Y2 : $i]: 99.05/14.97 ( 99.05/14.97 in(Y2, 99.05/14.97 Y0) & 99.05/14.97 in(Y2, 99.05/14.97 Y1))))))) => 99.05/14.97 (binintersect( 99.05/14.97 Y0, Y1) = 99.05/14.97 emptyset)))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i]: 99.05/14.97 subset( 99.05/14.97 binintersect( 99.05/14.97 Y0, Y1), 99.05/14.97 Y1))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i]: 99.05/14.97 (subset(Y1, 99.05/14.97 Y0) => 99.05/14.97 (binintersect( 99.05/14.97 Y0, Y1) = 99.05/14.97 Y1)))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i]: 99.05/14.97 ((binintersect( 99.05/14.97 Y0, Y1) = 99.05/14.97 Y0) => 99.05/14.97 subset(Y0, 99.05/14.97 Y1)))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y2 : $i]: 99.05/14.97 ( 99.05/14.97 binintersect( 99.05/14.97 Y0, 99.05/14.97 binunion( 99.05/14.97 Y1, Y2)) = 99.05/14.97 binunion( 99.05/14.97 binintersect( 99.05/14.97 Y0, Y1), 99.05/14.97 binintersect( 99.05/14.97 Y0, Y2)))))))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y2 : $i]: 99.05/14.97 (in(Y2, 99.05/14.97 Y0) => 99.05/14.97 (( 99.05/14.97 ~( 99.05/14.97 in(Y2, 99.05/14.97 Y1))) => 99.05/14.97 in(Y2, 99.05/14.97 setminus( 99.05/14.97 Y0, Y1))))))))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y2 : $i]: 99.05/14.97 (in(Y2, 99.05/14.97 setminus( 99.05/14.97 Y0, Y1)) => 99.05/14.97 in(Y2, 99.05/14.97 Y0))))))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i]: 99.05/14.97 ( 99.05/14.97 !!(( 99.05/14.97 ^[Y2 : $i]: 99.05/14.97 (in(Y2, 99.05/14.97 setminus( 99.05/14.97 Y0, Y1)) => 99.05/14.97 (~( 99.05/14.97 in(Y2, 99.05/14.97 Y1))))))))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i]: 99.05/14.97 (subset( 99.05/14.97 Y0, Y1) => 99.05/14.97 (setminus( 99.05/14.97 Y0, Y1) = 99.05/14.97 emptyset)))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!((^[Y1 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y2 : $i]: 99.05/14.97 (( 99.05/14.97 ~( 99.05/14.97 in(Y2, 99.05/14.97 setminus( 99.05/14.97 Y0, Y1)))) => 99.05/14.97 (in(Y2, 99.05/14.97 Y0) => 99.05/14.97 in(Y2, 99.05/14.97 Y1)))))))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y1 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y2 : $i]: 99.05/14.97 (( 99.05/14.97 ~( 99.05/14.97 in(Y2, 99.05/14.97 setminus( 99.05/14.97 Y0, Y1)))) => 99.05/14.97 (( 99.05/14.97 ~( 99.05/14.97 in(Y2, 99.05/14.97 Y1))) => 99.05/14.97 (~( 99.05/14.97 in(Y2, 99.05/14.97 Y0)))))))))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y1 : $i]: 99.05/14.97 ( 99.05/14.97 !!(( 99.05/14.97 ^[Y2 : $i]: 99.05/14.97 (( 99.05/14.97 ~( 99.05/14.97 in(Y2, 99.05/14.97 Y0))) => 99.05/14.97 (~( 99.05/14.97 in(Y2, 99.05/14.97 setminus( 99.05/14.97 Y0, Y1)))))))))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y1 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y2 : $i]: 99.05/14.97 (in(Y2, 99.05/14.97 Y1) => 99.05/14.97 (~( 99.05/14.97 in(Y2, 99.05/14.97 setminus( 99.05/14.97 Y0, Y1)))))))))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y1 : $i]: 99.05/14.97 subset( 99.05/14.97 setminus( 99.05/14.97 Y0, Y1), 99.05/14.97 Y0))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 ( 99.05/14.97 !!(( 99.05/14.97 ^[Y1 : $i]: 99.05/14.97 (( 99.05/14.97 setminus( 99.05/14.97 Y0, Y1) = 99.05/14.97 emptyset) => 99.05/14.97 subset( 99.05/14.97 Y0, Y1)))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y1 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y2 : $i]: 99.05/14.97 (in(Y2, 99.05/14.97 symdiff( 99.05/14.97 Y0, Y1)) => 99.05/14.97 (!!(( 99.05/14.97 ^[Y3 : $o]: 99.05/14.97 (( 99.05/14.97 in(Y2, 99.05/14.97 Y0) => 99.05/14.97 ( 99.05/14.97 ( 99.05/14.97 ~( 99.05/14.97 in(Y2, 99.05/14.97 Y1))) => 99.05/14.97 Y3)) => 99.05/14.97 (( 99.05/14.97 ( 99.05/14.97 ~( 99.05/14.97 in(Y2, 99.05/14.97 Y0))) => 99.05/14.97 ( 99.05/14.97 in(Y2, 99.05/14.97 Y1) => Y3)) => 99.05/14.97 Y3))))))))))))))) => 99.05/14.97 ((!!((^[Y0 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y1 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y2 : $i]: 99.05/14.97 (in(Y2, 99.05/14.97 Y0) => 99.05/14.97 (( 99.05/14.97 ~( 99.05/14.97 in(Y2, 99.05/14.97 Y1))) => 99.05/14.97 in(Y2, 99.05/14.97 symdiff( 99.05/14.97 Y0, Y1))))))))))))) => 99.05/14.97 ((!!(( 99.05/14.97 ^[Y0 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y1 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y2 : $i]: 99.05/14.97 (( 99.05/14.97 ~( 99.05/14.97 in(Y2, 99.05/14.97 Y0))) => 99.05/14.97 (in(Y2, 99.05/14.97 Y1) => 99.05/14.97 in(Y2, 99.05/14.97 symdiff( 99.05/14.97 Y0, Y1))))))))))))) => 99.05/14.97 ((!!(( 99.05/14.97 ^[Y0 : $i]: 99.05/14.97 ( 99.05/14.97 !!(( 99.05/14.97 ^[Y1 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y2 : $i]: 99.05/14.97 (in(Y2, 99.05/14.97 Y0) => 99.05/14.97 (in(Y2, 99.05/14.97 Y1) => 99.05/14.97 (~( 99.05/14.97 in(Y2, 99.05/14.97 symdiff( 99.05/14.97 Y0, Y1))))))))))))))) => 99.05/14.97 ((!!(( 99.05/14.97 ^[Y0 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y1 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y2 : $i]: 99.05/14.97 (( 99.05/14.97 ~( 99.05/14.97 in(Y2, 99.05/14.97 Y0))) => 99.05/14.97 (( 99.05/14.97 ~( 99.05/14.97 in(Y2, 99.05/14.97 Y1))) => 99.05/14.97 (~( 99.05/14.97 in(Y2, 99.05/14.97 symdiff( 99.05/14.97 Y0, Y1))))))))))))))) => 99.05/14.97 ((!!(( 99.05/14.97 ^[Y0 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y1 : $i]: 99.05/14.97 in(Y1, 99.05/14.97 setadjoin( 99.05/14.97 Y0, 99.05/14.97 setadjoin( 99.05/14.97 Y1, 99.05/14.97 emptyset))))))))) => 99.05/14.97 (( 99.05/14.97 !!(( 99.05/14.97 ^[Y0 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y1 : $i]: 99.05/14.97 in(Y0, 99.05/14.97 setunion( 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y0, 99.05/14.97 emptyset), 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y0, 99.05/14.97 setadjoin( 99.05/14.97 Y1, 99.05/14.97 emptyset)), 99.05/14.97 emptyset)))))))))) => 99.05/14.97 ( 99.05/14.97 ( 99.05/14.97 !!(( 99.05/14.97 ^[Y0 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y1 : $i]: 99.05/14.97 in(Y1, 99.05/14.97 setunion( 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y0, 99.05/14.97 emptyset), 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y0, 99.05/14.97 setadjoin( 99.05/14.97 Y1, 99.05/14.97 emptyset)), 99.05/14.97 emptyset)))))))))) => 99.05/14.97 ( 99.05/14.97 ( 99.05/14.97 !!(( 99.05/14.97 ^[Y0 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y1 : $i]: 99.05/14.97 (??(( 99.05/14.97 ^[Y2 : $i]: 99.05/14.97 (in(Y2, 99.05/14.97 setunion( 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y0, 99.05/14.97 emptyset), 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y0, 99.05/14.97 setadjoin( 99.05/14.97 Y1, 99.05/14.97 emptyset)), 99.05/14.97 emptyset)))) & 99.05/14.97 (??(( 99.05/14.97 ^[Y3 : $i]: 99.05/14.97 (in(Y3, 99.05/14.97 setunion( 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y0, 99.05/14.97 emptyset), 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y0, 99.05/14.97 setadjoin( 99.05/14.97 Y1, 99.05/14.97 emptyset)), 99.05/14.97 emptyset)))) & 99.05/14.97 (setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y0, 99.05/14.97 emptyset), 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y0, 99.05/14.97 setadjoin( 99.05/14.97 Y1, 99.05/14.97 emptyset)), 99.05/14.97 emptyset)) = 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y2, 99.05/14.97 emptyset), 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y2, 99.05/14.97 setadjoin( 99.05/14.97 Y3, 99.05/14.97 emptyset)), 99.05/14.97 emptyset))))))))))))))))) => 99.05/14.97 ( 99.05/14.97 ( 99.05/14.97 !!(( 99.05/14.97 ^[Y0 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y1 : $i]: 99.05/14.97 (??(( 99.05/14.97 ^[Y2 : $i]: 99.05/14.97 (in(Y2, 99.05/14.97 setunion( 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y0, 99.05/14.97 emptyset), 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y0, 99.05/14.97 setadjoin( 99.05/14.97 Y1, 99.05/14.97 emptyset)), 99.05/14.97 emptyset)))) & 99.05/14.97 (??(( 99.05/14.97 ^[Y3 : $i]: 99.05/14.97 (in(Y3, 99.05/14.97 setunion( 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y0, 99.05/14.97 emptyset), 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y0, 99.05/14.97 setadjoin( 99.05/14.97 Y1, 99.05/14.97 emptyset)), 99.05/14.97 emptyset)))) & 99.05/14.97 (setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y0, 99.05/14.97 emptyset), 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y0, 99.05/14.97 setadjoin( 99.05/14.97 Y1, 99.05/14.97 emptyset)), 99.05/14.97 emptyset)) = 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y2, 99.05/14.97 emptyset), 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y2, 99.05/14.97 setadjoin( 99.05/14.97 Y3, 99.05/14.97 emptyset)), 99.05/14.97 emptyset))))))))))))))))) => 99.05/14.97 ( 99.05/14.97 ( 99.05/14.97 !!(( 99.05/14.97 ^[Y0 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y1 : $i]: 99.05/14.97 (in(Y1, 99.05/14.97 Y0) => 99.05/14.97 subset( 99.05/14.97 setadjoin( 99.05/14.97 Y1, 99.05/14.97 emptyset), 99.05/14.97 Y0)))))))) => 99.05/14.97 ( 99.05/14.97 ( 99.05/14.97 !!(( 99.05/14.97 ^[Y0 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y1 : $i]: 99.05/14.97 (in(Y1, 99.05/14.97 Y0) => 99.05/14.97 in( 99.05/14.97 setadjoin( 99.05/14.97 Y1, 99.05/14.97 emptyset), 99.05/14.97 powerset( 99.05/14.97 Y0))))))))) => 99.05/14.97 ( 99.05/14.97 ( 99.05/14.97 !!(( 99.05/14.97 ^[Y0 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y1 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y2 : $i]: 99.05/14.97 (in(Y2, 99.05/14.97 Y0) => 99.05/14.97 in( 99.05/14.97 setadjoin( 99.05/14.97 Y2, 99.05/14.97 emptyset), 99.05/14.97 powerset( 99.05/14.97 binunion( 99.05/14.97 Y0, Y1))))))))))))) => 99.05/14.97 ( 99.05/14.97 ( 99.05/14.97 !!(( 99.05/14.97 ^[Y0 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y1 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y2 : $i]: 99.05/14.97 (in(Y2, 99.05/14.97 setadjoin( 99.05/14.97 Y0, 99.05/14.97 setadjoin( 99.05/14.97 Y1, 99.05/14.97 emptyset))) => 99.05/14.97 (( 99.05/14.97 Y2 = Y1) | 99.05/14.97 (Y2 = Y0)))))))))))) => 99.05/14.97 ( 99.05/14.97 ( 99.05/14.97 !!(( 99.05/14.97 ^[Y0 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y1 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y2 : $i]: 99.05/14.97 (in(Y2, 99.05/14.97 Y0) => 99.05/14.97 (!!(( 99.05/14.97 ^[Y3 : $i]: 99.05/14.97 (in(Y3, 99.05/14.97 Y1) => 99.05/14.97 subset( 99.05/14.97 setadjoin( 99.05/14.97 Y2, 99.05/14.97 setadjoin( 99.05/14.97 Y3, 99.05/14.97 emptyset)), 99.05/14.97 binunion( 99.05/14.97 Y0, Y1)))))))))))))))) => 99.05/14.97 ( 99.05/14.97 ( 99.05/14.97 !!(( 99.05/14.97 ^[Y0 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y1 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y2 : $i]: 99.05/14.97 (in(Y2, 99.05/14.97 Y0) => 99.05/14.97 (!!(( 99.05/14.97 ^[Y3 : $i]: 99.05/14.97 (in(Y3, 99.05/14.97 Y1) => 99.05/14.97 in( 99.05/14.97 setadjoin( 99.05/14.97 Y2, 99.05/14.97 setadjoin( 99.05/14.97 Y3, 99.05/14.97 emptyset)), 99.05/14.97 powerset( 99.05/14.97 binunion( 99.05/14.97 Y0, Y1))))))))))))))))) => 99.05/14.97 ( 99.05/14.97 ( 99.05/14.97 !!(( 99.05/14.97 ^[Y0 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y1 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y2 : $i]: 99.05/14.97 (in(Y2, 99.05/14.97 Y0) => 99.05/14.97 (!!(( 99.05/14.97 ^[Y3 : $i]: 99.05/14.97 (in(Y3, 99.05/14.97 Y1) => 99.05/14.97 subset( 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y2, 99.05/14.97 emptyset), 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y2, 99.05/14.97 setadjoin( 99.05/14.97 Y3, 99.05/14.97 emptyset)), 99.05/14.97 emptyset)), 99.05/14.97 powerset( 99.05/14.97 binunion( 99.05/14.97 Y0, Y1))))))))))))))))) => 99.05/14.97 ( 99.05/14.97 ( 99.05/14.97 !!(( 99.05/14.97 ^[Y0 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y1 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y2 : $i]: 99.05/14.97 (in(Y2, 99.05/14.97 Y0) => 99.05/14.97 (!!(( 99.05/14.97 ^[Y3 : $i]: 99.05/14.97 (in(Y3, 99.05/14.97 Y1) => 99.05/14.97 in( 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y2, 99.05/14.97 emptyset), 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y2, 99.05/14.97 setadjoin( 99.05/14.97 Y3, 99.05/14.97 emptyset)), 99.05/14.97 emptyset)), 99.05/14.97 powerset( 99.05/14.97 powerset( 99.05/14.97 binunion( 99.05/14.97 Y0, Y1)))))))))))))))))) => 99.05/14.97 ( 99.05/14.97 ( 99.05/14.97 !!(( 99.05/14.97 ^[Y0 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y1 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y2 : $i]: 99.05/14.97 (in(Y2, 99.05/14.97 Y0) => 99.05/14.97 (!!(( 99.05/14.97 ^[Y3 : $i]: 99.05/14.97 (in(Y3, 99.05/14.97 Y1) => 99.05/14.97 in( 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y2, 99.05/14.97 emptyset), 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y2, 99.05/14.97 setadjoin( 99.05/14.97 Y3, 99.05/14.97 emptyset)), 99.05/14.97 emptyset)), 99.05/14.97 powerset( 99.05/14.97 powerset( 99.05/14.97 binunion( 99.05/14.97 Y0, Y1)))))))))))))))))) => 99.05/14.97 ( 99.05/14.97 ( 99.05/14.97 !!(( 99.05/14.97 ^[Y0 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y1 : $i]: 99.05/14.97 (!!(( 99.05/14.97 ^[Y2 : $i]: 99.05/14.97 (in(Y2, 99.05/14.97 Y0) => 99.05/14.97 (!!(( 99.05/14.97 ^[Y3 : $i]: 99.05/14.97 (in(Y3, 99.05/14.97 Y1) => 99.05/14.97 in( 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y2, 99.05/14.97 emptyset), 99.05/14.97 setadjoin( 99.05/14.97 setadjoin( 99.05/14.97 Y2, 99.05/14.97 setadjoin( 99.05/14.97 Y3, 99.05/14.97 emptyset)), 99.05/14.97 emptyset)), 99.05/14.97 dsetconstr( 99.05/14.97 powerset( 99.05/14.97 powerset( 99.05/14.97 binunion( 99.05/14.97 Y0, Y1))), 99.05/14.97 (^[Y4 : $i]: 99.05/14.97 (??(( 99.05/14.97 ^[Y5 : $i]: 99.05/14.97 (in(Y5, 99.05/14.97 Y0) & 99.05/14.97 (??(( 99.56/14.97 ^[Y6 : $i]: 99.56/14.97 (in(Y6, 99.56/14.97 Y1) & 99.56/14.97 (Y4 = 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y5, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y5, 99.56/14.97 setadjoin( 99.56/14.97 Y6, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)))))))))))))))))))))))))))) => 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 dsetconstr( 99.56/14.97 powerset( 99.56/14.97 powerset( 99.56/14.97 binunion( 99.56/14.97 Y0, Y1))), 99.56/14.97 (^[Y3 : $i]: 99.56/14.97 (??(( 99.56/14.97 ^[Y4 : $i]: 99.56/14.97 (in(Y4, 99.56/14.97 Y0) & 99.56/14.97 (??(( 99.56/14.97 ^[Y5 : $i]: 99.56/14.97 (in(Y5, 99.56/14.97 Y1) & 99.56/14.97 (Y3 = 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y4, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y4, 99.56/14.97 setadjoin( 99.56/14.97 Y5, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)))))))))))))) => 99.56/14.97 (??(( 99.56/14.97 ^[Y3 : $i]: 99.56/14.97 (( 99.56/14.97 ??(( 99.56/14.97 ^[Y4 : $i]: 99.56/14.97 (in(Y4, 99.56/14.97 Y1) & 99.56/14.97 (Y2 = 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y3, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y3, 99.56/14.97 setadjoin( 99.56/14.97 Y4, 99.56/14.97 emptyset)), 99.56/14.97 emptyset))))))) & 99.56/14.97 in(Y3, 99.56/14.97 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.56/14.97 inference('lazy_cnf_imply', [status(thm)], ['228'])). 99.56/14.97 tff('230', plain, 99.56/14.97 ~ ((!!((^[Y0 : $i > $o]: 99.56/14.97 (!!((^[Y1 : $i > $o]: 99.56/14.97 ((!!((^[Y2 : $i]: 99.56/14.97 (!!((^[Y3 : $i]: 99.56/14.97 ((Y2 = Y3) => (Y0(Y2) <=> Y1(Y3))))))))) => 99.56/14.97 ((??((^[Y2 : $i]: 99.56/14.97 (Y0(Y2) & 99.56/14.97 (!!((^[Y3 : $i]: (Y0(Y3) => (Y2 = Y3))))))))) => 99.56/14.97 ((??((^[Y2 : $i]: 99.56/14.97 (Y1(Y2) & 99.56/14.97 (!!((^[Y3 : $i]: (Y1(Y3) => (Y2 = Y3))))))))) => 99.56/14.97 (descr(Y0) = descr(Y1))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 ((Y0 = Y1) => 99.56/14.97 (!!((^[Y2 : $i > $o]: 99.56/14.97 (!!((^[Y3 : $i > $o]: 99.56/14.97 ((!!((^[Y4 : $i]: 99.56/14.97 (in(Y4, Y0) => 99.56/14.97 (!!((^[Y5 : $i]: 99.56/14.97 (in(Y5, Y1) => 99.56/14.97 ((Y4 = Y5) => 99.56/14.97 (Y2(Y4) <=> Y3(Y5))))))))))) => 99.56/14.97 (dsetconstr(Y0, Y2) = 99.56/14.97 dsetconstr(Y1, Y3)))))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 99.56/14.97 subset(Y0, Y1)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y1, Y0)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y0, Y1)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 99.56/14.97 subset(Y0, Y1)))))))) => 99.56/14.97 ((!!(subset(emptyset))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (subset(Y0, Y1) => 99.56/14.97 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (subset(Y0, Y1) => 99.56/14.97 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, Y0) => 99.56/14.97 ((~(in(Y2, Y1))) => (~(subset(Y0, Y1)))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, Y0) => 99.56/14.97 ((~(in(Y2, Y1))) => (Y0 != Y1)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (subset(Y0, Y1) => 99.56/14.97 (subset(Y1, Y2) => subset(Y0, Y2)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: subset(Y1, setadjoin(Y0, Y1)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (subset(Y0, Y2) => 99.56/14.97 subset(Y0, setadjoin(Y1, Y2)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (subset(Y0, Y1) => in(Y0, powerset(Y1))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (subset(Y0, Y1) => 99.56/14.97 (subset(Y1, Y0) => (Y0 = Y1))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (subset(Y0, emptyset) => (Y0 = emptyset))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (subset(Y1, Y0) => 99.56/14.97 in(Y1, powerset(Y0))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (in(Y1, powerset(Y0)) => 99.56/14.97 subset(Y1, Y0)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (subset(Y0, Y1) => 99.56/14.97 subset(powerset(Y0), 99.56/14.97 powerset(Y1))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i > $o]: 99.56/14.97 in(dsetconstr(Y0, Y1), 99.56/14.97 powerset(Y0)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i > $o]: 99.56/14.97 subset(dsetconstr(Y0, Y1), Y0))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, Y0) => 99.56/14.97 in(Y2, 99.56/14.97 binunion(Y0, Y1)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 in(Y1, 99.56/14.97 setadjoin(Y0, 99.56/14.97 setadjoin(Y1, emptyset))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, Y1) => 99.56/14.97 in(Y2, 99.56/14.97 binunion(Y0, Y1)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (!!((^[Y3 : $o]: 99.56/14.97 (in(Y2, 99.56/14.97 binunion( 99.56/14.97 Y0, Y1)) => 99.56/14.97 ((in(Y2, Y0) => 99.56/14.97 Y3) => 99.56/14.97 ((in(Y2, Y1) => 99.56/14.97 Y3) => 99.56/14.97 Y3))))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 binunion(Y0, Y1)) => 99.56/14.97 (in(Y2, Y1) | 99.56/14.97 in(Y2, Y0)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 subset(Y0, 99.56/14.97 binunion(Y0, Y1)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 subset(Y1, 99.56/14.97 binunion(Y0, Y1)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, Y0) => 99.56/14.97 (in(Y2, Y1) => 99.56/14.97 in(Y2, 99.56/14.97 binintersect( 99.56/14.97 Y0, Y1))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (subset(Y2, Y0) => 99.56/14.97 (subset(Y2, Y1) => 99.56/14.97 subset(Y2, 99.56/14.97 binintersect( 99.56/14.97 Y0, Y1))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 binintersect( 99.56/14.97 Y0, Y1)) => 99.56/14.97 in(Y2, Y0))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 subset( 99.56/14.97 binintersect(Y0, 99.56/14.97 Y1), Y0))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (subset(Y0, Y1) => 99.56/14.97 (binintersect(Y0, 99.56/14.97 Y1) = 99.56/14.97 Y0)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 ((binintersect(Y0, 99.56/14.97 Y1) = 99.56/14.97 Y1) => 99.56/14.97 subset(Y1, Y0)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 binintersect( 99.56/14.97 Y0, Y1)) => 99.56/14.97 in(Y2, Y1))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 ((~((??(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) & 99.56/14.97 in(Y2, 99.56/14.97 Y1))))))) => 99.56/14.97 (binintersect( 99.56/14.97 Y0, Y1) = 99.56/14.97 emptyset)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 subset( 99.56/14.97 binintersect( 99.56/14.97 Y0, Y1), Y1))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (subset(Y1, Y0) => 99.56/14.97 (binintersect( 99.56/14.97 Y0, Y1) = 99.56/14.97 Y1)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 ((binintersect( 99.56/14.97 Y0, Y1) = 99.56/14.97 Y0) => 99.56/14.97 subset(Y0, 99.56/14.97 Y1)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (binintersect( 99.56/14.97 Y0, 99.56/14.97 binunion( 99.56/14.97 Y1, Y2)) = 99.56/14.97 binunion( 99.56/14.97 binintersect( 99.56/14.97 Y0, Y1), 99.56/14.97 binintersect( 99.56/14.97 Y0, Y2)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 ( 99.56/14.97 in(Y2, 99.56/14.97 Y0) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 Y1))) => 99.56/14.97 in(Y2, 99.56/14.97 setminus( 99.56/14.97 Y0, Y1))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 setminus( 99.56/14.97 Y0, Y1)) => 99.56/14.97 in(Y2, 99.56/14.97 Y0))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 setminus( 99.56/14.97 Y0, Y1)) => 99.56/14.97 (~( 99.56/14.97 in(Y2, 99.56/14.97 Y1))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 ( 99.56/14.97 subset( 99.56/14.97 Y0, Y1) => 99.56/14.97 ( 99.56/14.97 setminus( 99.56/14.97 Y0, Y1) = 99.56/14.97 emptyset)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 setminus( 99.56/14.97 Y0, Y1)))) => 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 in(Y2, 99.56/14.97 Y1)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 setminus( 99.56/14.97 Y0, Y1)))) => 99.56/14.97 (( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 Y1))) => 99.56/14.97 (~( 99.56/14.97 in(Y2, 99.56/14.97 Y0)))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 Y0))) => 99.56/14.97 (~( 99.56/14.97 in(Y2, 99.56/14.97 setminus( 99.56/14.97 Y0, Y1)))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y1) => 99.56/14.97 (~( 99.56/14.97 in(Y2, 99.56/14.97 setminus( 99.56/14.97 Y0, Y1)))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 subset( 99.56/14.97 setminus( 99.56/14.97 Y0, Y1), 99.56/14.97 Y0))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (( 99.56/14.97 setminus( 99.56/14.97 Y0, Y1) = 99.56/14.97 emptyset) => 99.56/14.97 subset( 99.56/14.97 Y0, Y1)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 symdiff( 99.56/14.97 Y0, Y1)) => 99.56/14.97 (!!(( 99.56/14.97 ^[Y3 : $o]: 99.56/14.97 (( 99.56/14.97 in(Y2, 99.56/14.97 Y0) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 Y1))) => 99.56/14.97 Y3)) => 99.56/14.97 (( 99.56/14.97 ( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 Y0))) => 99.56/14.97 ( 99.56/14.97 in(Y2, 99.56/14.97 Y1) => Y3)) => 99.56/14.97 Y3))))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 (( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 Y1))) => 99.56/14.97 in(Y2, 99.56/14.97 symdiff( 99.56/14.97 Y0, Y1))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 Y0))) => 99.56/14.97 (in(Y2, 99.56/14.97 Y1) => 99.56/14.97 in(Y2, 99.56/14.97 symdiff( 99.56/14.97 Y0, Y1))))))))))))) => 99.56/14.97 ((!!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 (in(Y2, 99.56/14.97 Y1) => 99.56/14.97 (~( 99.56/14.97 in(Y2, 99.56/14.97 symdiff( 99.56/14.97 Y0, Y1))))))))))))))) => 99.56/14.97 ((!!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 Y0))) => 99.56/14.97 (( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 Y1))) => 99.56/14.97 (~( 99.56/14.97 in(Y2, 99.56/14.97 symdiff( 99.56/14.97 Y0, Y1))))))))))))))) => 99.56/14.97 ((!!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 in(Y1, 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset))))))))) => 99.56/14.97 ((!!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 in(Y0, 99.56/14.97 setunion( 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)))))))))) => 99.56/14.97 (( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 in(Y1, 99.56/14.97 setunion( 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)))))))))) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (??(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 setunion( 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)))) & 99.56/14.97 (??(( 99.56/14.97 ^[Y3 : $i]: 99.56/14.97 (in(Y3, 99.56/14.97 setunion( 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)))) & 99.56/14.97 (setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)) = 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 setadjoin( 99.56/14.97 Y3, 99.56/14.97 emptyset)), 99.56/14.97 emptyset))))))))))))))))) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (??(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 setunion( 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)))) & 99.56/14.97 (??(( 99.56/14.97 ^[Y3 : $i]: 99.56/14.97 (in(Y3, 99.56/14.97 setunion( 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)))) & 99.56/14.97 (setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)) = 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 setadjoin( 99.56/14.97 Y3, 99.56/14.97 emptyset)), 99.56/14.97 emptyset))))))))))))))))) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (in(Y1, 99.56/14.97 Y0) => 99.56/14.97 subset( 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset), 99.56/14.97 Y0)))))))) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (in(Y1, 99.56/14.97 Y0) => 99.56/14.97 in( 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset), 99.56/14.97 powerset( 99.56/14.97 Y0))))))))) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 in( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 emptyset), 99.56/14.97 powerset( 99.56/14.97 binunion( 99.56/14.97 Y0, Y1))))))))))))) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset))) => 99.56/14.97 (( 99.56/14.97 Y2 = Y1) | 99.56/14.97 (Y2 = Y0)))))))))))) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 (!!(( 99.56/14.97 ^[Y3 : $i]: 99.56/14.97 (in(Y3, 99.56/14.97 Y1) => 99.56/14.97 subset( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 setadjoin( 99.56/14.97 Y3, 99.56/14.97 emptyset)), 99.56/14.97 binunion( 99.56/14.97 Y0, Y1)))))))))))))))) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 (!!(( 99.56/14.97 ^[Y3 : $i]: 99.56/14.97 (in(Y3, 99.56/14.97 Y1) => 99.56/14.97 in( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 setadjoin( 99.56/14.97 Y3, 99.56/14.97 emptyset)), 99.56/14.97 powerset( 99.56/14.97 binunion( 99.56/14.97 Y0, Y1))))))))))))))))) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 (!!(( 99.56/14.97 ^[Y3 : $i]: 99.56/14.97 (in(Y3, 99.56/14.97 Y1) => 99.56/14.97 subset( 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 setadjoin( 99.56/14.97 Y3, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)), 99.56/14.97 powerset( 99.56/14.97 binunion( 99.56/14.97 Y0, Y1))))))))))))))))) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 (!!(( 99.56/14.97 ^[Y3 : $i]: 99.56/14.97 (in(Y3, 99.56/14.97 Y1) => 99.56/14.97 in( 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 setadjoin( 99.56/14.97 Y3, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)), 99.56/14.97 powerset( 99.56/14.97 powerset( 99.56/14.97 binunion( 99.56/14.97 Y0, Y1)))))))))))))))))) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 (!!(( 99.56/14.97 ^[Y3 : $i]: 99.56/14.97 (in(Y3, 99.56/14.97 Y1) => 99.56/14.97 in( 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 setadjoin( 99.56/14.97 Y3, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)), 99.56/14.97 powerset( 99.56/14.97 powerset( 99.56/14.97 binunion( 99.56/14.97 Y0, Y1)))))))))))))))))) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 (!!(( 99.56/14.97 ^[Y3 : $i]: 99.56/14.97 (in(Y3, 99.56/14.97 Y1) => 99.56/14.97 in( 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 setadjoin( 99.56/14.97 Y3, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)), 99.56/14.97 dsetconstr( 99.56/14.97 powerset( 99.56/14.97 powerset( 99.56/14.97 binunion( 99.56/14.97 Y0, Y1))), 99.56/14.97 (^[Y4 : $i]: 99.56/14.97 (??(( 99.56/14.97 ^[Y5 : $i]: 99.56/14.97 (in(Y5, 99.56/14.97 Y0) & 99.56/14.97 (??(( 99.56/14.97 ^[Y6 : $i]: 99.56/14.97 (in(Y6, 99.56/14.97 Y1) & 99.56/14.97 (Y4 = 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y5, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y5, 99.56/14.97 setadjoin( 99.56/14.97 Y6, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)))))))))))))))))))))))))))) => 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 dsetconstr( 99.56/14.97 powerset( 99.56/14.97 powerset( 99.56/14.97 binunion( 99.56/14.97 Y0, Y1))), 99.56/14.97 (^[Y3 : $i]: 99.56/14.97 (??(( 99.56/14.97 ^[Y4 : $i]: 99.56/14.97 (in(Y4, 99.56/14.97 Y0) & 99.56/14.97 (??(( 99.56/14.97 ^[Y5 : $i]: 99.56/14.97 (in(Y5, 99.56/14.97 Y1) & 99.56/14.97 (Y3 = 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y4, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y4, 99.56/14.97 setadjoin( 99.56/14.97 Y5, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)))))))))))))) => 99.56/14.97 (??(( 99.56/14.97 ^[Y3 : $i]: 99.56/14.97 (( 99.56/14.97 ??(( 99.56/14.97 ^[Y4 : $i]: 99.56/14.97 (in(Y4, 99.56/14.97 Y1) & 99.56/14.97 (Y2 = 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y3, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y3, 99.56/14.97 setadjoin( 99.56/14.97 Y4, 99.56/14.97 emptyset)), 99.56/14.97 emptyset))))))) & 99.56/14.97 in(Y3, 99.56/14.97 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.56/14.97 inference('lazy_cnf_imply', [status(thm)], ['229'])). 99.56/14.97 tff('231', plain, 99.56/14.97 ~ ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 ((Y0 = Y1) => 99.56/14.97 (!!((^[Y2 : $i > $o]: 99.56/14.97 (!!((^[Y3 : $i > $o]: 99.56/14.97 ((!!((^[Y4 : $i]: 99.56/14.97 (in(Y4, Y0) => 99.56/14.97 (!!((^[Y5 : $i]: 99.56/14.97 (in(Y5, Y1) => 99.56/14.97 ((Y4 = Y5) => 99.56/14.97 (Y2(Y4) <=> Y3(Y5))))))))))) => 99.56/14.97 (dsetconstr(Y0, Y2) = dsetconstr(Y1, Y3)))))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 99.56/14.97 subset(Y0, Y1)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y1, Y0)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y0, Y1)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 99.56/14.97 subset(Y0, Y1)))))))) => 99.56/14.97 ((!!(subset(emptyset))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (subset(Y0, Y1) => 99.56/14.97 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (subset(Y0, Y1) => 99.56/14.97 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, Y0) => 99.56/14.97 ((~(in(Y2, Y1))) => (~(subset(Y0, Y1)))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, Y0) => 99.56/14.97 ((~(in(Y2, Y1))) => (Y0 != Y1)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (subset(Y0, Y1) => 99.56/14.97 (subset(Y1, Y2) => subset(Y0, Y2)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: subset(Y1, setadjoin(Y0, Y1)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (subset(Y0, Y2) => 99.56/14.97 subset(Y0, setadjoin(Y1, Y2)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (subset(Y0, Y1) => in(Y0, powerset(Y1))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (subset(Y0, Y1) => 99.56/14.97 (subset(Y1, Y0) => (Y0 = Y1))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (subset(Y0, emptyset) => (Y0 = emptyset))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (subset(Y1, Y0) => 99.56/14.97 in(Y1, powerset(Y0))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (in(Y1, powerset(Y0)) => 99.56/14.97 subset(Y1, Y0)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (subset(Y0, Y1) => 99.56/14.97 subset(powerset(Y0), powerset(Y1))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i > $o]: 99.56/14.97 in(dsetconstr(Y0, Y1), 99.56/14.97 powerset(Y0)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i > $o]: 99.56/14.97 subset(dsetconstr(Y0, Y1), Y0))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, Y0) => 99.56/14.97 in(Y2, binunion(Y0, Y1)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 in(Y1, 99.56/14.97 setadjoin(Y0, 99.56/14.97 setadjoin(Y1, emptyset))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, Y1) => 99.56/14.97 in(Y2, 99.56/14.97 binunion(Y0, Y1)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (!!((^[Y3 : $o]: 99.56/14.97 (in(Y2, 99.56/14.97 binunion( 99.56/14.97 Y0, Y1)) => 99.56/14.97 ((in(Y2, Y0) => 99.56/14.97 Y3) => 99.56/14.97 ((in(Y2, Y1) => 99.56/14.97 Y3) => 99.56/14.97 Y3))))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 binunion(Y0, Y1)) => 99.56/14.97 (in(Y2, Y1) | 99.56/14.97 in(Y2, Y0)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 subset(Y0, 99.56/14.97 binunion(Y0, Y1)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 subset(Y1, 99.56/14.97 binunion(Y0, Y1)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, Y0) => 99.56/14.97 (in(Y2, Y1) => 99.56/14.97 in(Y2, 99.56/14.97 binintersect( 99.56/14.97 Y0, Y1))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (subset(Y2, Y0) => 99.56/14.97 (subset(Y2, Y1) => 99.56/14.97 subset(Y2, 99.56/14.97 binintersect( 99.56/14.97 Y0, Y1))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 binintersect( 99.56/14.97 Y0, Y1)) => 99.56/14.97 in(Y2, Y0))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 subset( 99.56/14.97 binintersect(Y0, Y1), 99.56/14.97 Y0))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (subset(Y0, Y1) => 99.56/14.97 (binintersect(Y0, 99.56/14.97 Y1) = 99.56/14.97 Y0)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 ((binintersect(Y0, 99.56/14.97 Y1) = 99.56/14.97 Y1) => 99.56/14.97 subset(Y1, Y0)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 binintersect( 99.56/14.97 Y0, Y1)) => 99.56/14.97 in(Y2, Y1))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 ((~((??((^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) & 99.56/14.97 in(Y2, 99.56/14.97 Y1))))))) => 99.56/14.97 (binintersect( 99.56/14.97 Y0, Y1) = 99.56/14.97 emptyset)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 subset( 99.56/14.97 binintersect( 99.56/14.97 Y0, Y1), Y1))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (subset(Y1, Y0) => 99.56/14.97 (binintersect( 99.56/14.97 Y0, Y1) = 99.56/14.97 Y1)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 ((binintersect( 99.56/14.97 Y0, Y1) = 99.56/14.97 Y0) => 99.56/14.97 subset(Y0, Y1)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (binintersect( 99.56/14.97 Y0, 99.56/14.97 binunion( 99.56/14.97 Y1, Y2)) = 99.56/14.97 binunion( 99.56/14.97 binintersect( 99.56/14.97 Y0, Y1), 99.56/14.97 binintersect( 99.56/14.97 Y0, Y2)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 Y1))) => 99.56/14.97 in(Y2, 99.56/14.97 setminus( 99.56/14.97 Y0, Y1))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 ( 99.56/14.97 in(Y2, 99.56/14.97 setminus( 99.56/14.97 Y0, Y1)) => 99.56/14.97 in(Y2, 99.56/14.97 Y0))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 setminus( 99.56/14.97 Y0, Y1)) => 99.56/14.97 (~( 99.56/14.97 in(Y2, 99.56/14.97 Y1))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (subset( 99.56/14.97 Y0, Y1) => 99.56/14.97 ( 99.56/14.97 setminus( 99.56/14.97 Y0, Y1) = 99.56/14.97 emptyset)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 setminus( 99.56/14.97 Y0, Y1)))) => 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 in(Y2, 99.56/14.97 Y1)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 setminus( 99.56/14.97 Y0, Y1)))) => 99.56/14.97 (( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 Y1))) => 99.56/14.97 (~( 99.56/14.97 in(Y2, 99.56/14.97 Y0)))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 Y0))) => 99.56/14.97 (~( 99.56/14.97 in(Y2, 99.56/14.97 setminus( 99.56/14.97 Y0, Y1)))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y1) => 99.56/14.97 (~( 99.56/14.97 in(Y2, 99.56/14.97 setminus( 99.56/14.97 Y0, Y1)))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 subset( 99.56/14.97 setminus( 99.56/14.97 Y0, Y1), 99.56/14.97 Y0))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (( 99.56/14.97 setminus( 99.56/14.97 Y0, Y1) = 99.56/14.97 emptyset) => 99.56/14.97 subset( 99.56/14.97 Y0, Y1)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 symdiff( 99.56/14.97 Y0, Y1)) => 99.56/14.97 (!!(( 99.56/14.97 ^[Y3 : $o]: 99.56/14.97 (( 99.56/14.97 in(Y2, 99.56/14.97 Y0) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 Y1))) => 99.56/14.97 Y3)) => 99.56/14.97 (( 99.56/14.97 ( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 Y0))) => 99.56/14.97 ( 99.56/14.97 in(Y2, 99.56/14.97 Y1) => Y3)) => 99.56/14.97 Y3))))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 (( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 Y1))) => 99.56/14.97 in(Y2, 99.56/14.97 symdiff( 99.56/14.97 Y0, Y1))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 Y0))) => 99.56/14.97 (in(Y2, 99.56/14.97 Y1) => 99.56/14.97 in(Y2, 99.56/14.97 symdiff( 99.56/14.97 Y0, Y1))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 (in(Y2, 99.56/14.97 Y1) => 99.56/14.97 (~( 99.56/14.97 in(Y2, 99.56/14.97 symdiff( 99.56/14.97 Y0, Y1))))))))))))))) => 99.56/14.97 ((!!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 Y0))) => 99.56/14.97 (( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 Y1))) => 99.56/14.97 (~( 99.56/14.97 in(Y2, 99.56/14.97 symdiff( 99.56/14.97 Y0, Y1))))))))))))))) => 99.56/14.97 ((!!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 in(Y1, 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset))))))))) => 99.56/14.97 ((!!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 in(Y0, 99.56/14.97 setunion( 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)))))))))) => 99.56/14.97 ((!!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 in(Y1, 99.56/14.97 setunion( 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)))))))))) => 99.56/14.97 (( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (??(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 setunion( 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)))) & 99.56/14.97 (??(( 99.56/14.97 ^[Y3 : $i]: 99.56/14.97 (in(Y3, 99.56/14.97 setunion( 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)))) & 99.56/14.97 (setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)) = 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 setadjoin( 99.56/14.97 Y3, 99.56/14.97 emptyset)), 99.56/14.97 emptyset))))))))))))))))) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (??(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 setunion( 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)))) & 99.56/14.97 (??(( 99.56/14.97 ^[Y3 : $i]: 99.56/14.97 (in(Y3, 99.56/14.97 setunion( 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)))) & 99.56/14.97 (setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)) = 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 setadjoin( 99.56/14.97 Y3, 99.56/14.97 emptyset)), 99.56/14.97 emptyset))))))))))))))))) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (in(Y1, 99.56/14.97 Y0) => 99.56/14.97 subset( 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset), 99.56/14.97 Y0)))))))) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (in(Y1, 99.56/14.97 Y0) => 99.56/14.97 in( 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset), 99.56/14.97 powerset( 99.56/14.97 Y0))))))))) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 in( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 emptyset), 99.56/14.97 powerset( 99.56/14.97 binunion( 99.56/14.97 Y0, Y1))))))))))))) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset))) => 99.56/14.97 (( 99.56/14.97 Y2 = Y1) | 99.56/14.97 (Y2 = Y0)))))))))))) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 (!!(( 99.56/14.97 ^[Y3 : $i]: 99.56/14.97 (in(Y3, 99.56/14.97 Y1) => 99.56/14.97 subset( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 setadjoin( 99.56/14.97 Y3, 99.56/14.97 emptyset)), 99.56/14.97 binunion( 99.56/14.97 Y0, Y1)))))))))))))))) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 (!!(( 99.56/14.97 ^[Y3 : $i]: 99.56/14.97 (in(Y3, 99.56/14.97 Y1) => 99.56/14.97 in( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 setadjoin( 99.56/14.97 Y3, 99.56/14.97 emptyset)), 99.56/14.97 powerset( 99.56/14.97 binunion( 99.56/14.97 Y0, Y1))))))))))))))))) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 (!!(( 99.56/14.97 ^[Y3 : $i]: 99.56/14.97 (in(Y3, 99.56/14.97 Y1) => 99.56/14.97 subset( 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 setadjoin( 99.56/14.97 Y3, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)), 99.56/14.97 powerset( 99.56/14.97 binunion( 99.56/14.97 Y0, Y1))))))))))))))))) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 (!!(( 99.56/14.97 ^[Y3 : $i]: 99.56/14.97 (in(Y3, 99.56/14.97 Y1) => 99.56/14.97 in( 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 setadjoin( 99.56/14.97 Y3, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)), 99.56/14.97 powerset( 99.56/14.97 powerset( 99.56/14.97 binunion( 99.56/14.97 Y0, Y1)))))))))))))))))) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 (!!(( 99.56/14.97 ^[Y3 : $i]: 99.56/14.97 (in(Y3, 99.56/14.97 Y1) => 99.56/14.97 in( 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 setadjoin( 99.56/14.97 Y3, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)), 99.56/14.97 powerset( 99.56/14.97 powerset( 99.56/14.97 binunion( 99.56/14.97 Y0, Y1)))))))))))))))))) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 (!!(( 99.56/14.97 ^[Y3 : $i]: 99.56/14.97 (in(Y3, 99.56/14.97 Y1) => 99.56/14.97 in( 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 setadjoin( 99.56/14.97 Y3, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)), 99.56/14.97 dsetconstr( 99.56/14.97 powerset( 99.56/14.97 powerset( 99.56/14.97 binunion( 99.56/14.97 Y0, Y1))), 99.56/14.97 (^[Y4 : $i]: 99.56/14.97 (??(( 99.56/14.97 ^[Y5 : $i]: 99.56/14.97 (in(Y5, 99.56/14.97 Y0) & 99.56/14.97 (??(( 99.56/14.97 ^[Y6 : $i]: 99.56/14.97 (in(Y6, 99.56/14.97 Y1) & 99.56/14.97 (Y4 = 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y5, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y5, 99.56/14.97 setadjoin( 99.56/14.97 Y6, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)))))))))))))))))))))))))))) => 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 dsetconstr( 99.56/14.97 powerset( 99.56/14.97 powerset( 99.56/14.97 binunion( 99.56/14.97 Y0, Y1))), 99.56/14.97 (^[Y3 : $i]: 99.56/14.97 (??(( 99.56/14.97 ^[Y4 : $i]: 99.56/14.97 (in(Y4, 99.56/14.97 Y0) & 99.56/14.97 (??(( 99.56/14.97 ^[Y5 : $i]: 99.56/14.97 (in(Y5, 99.56/14.97 Y1) & 99.56/14.97 (Y3 = 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y4, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y4, 99.56/14.97 setadjoin( 99.56/14.97 Y5, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)))))))))))))) => 99.56/14.97 (??(( 99.56/14.97 ^[Y3 : $i]: 99.56/14.97 (( 99.56/14.97 ??(( 99.56/14.97 ^[Y4 : $i]: 99.56/14.97 (in(Y4, 99.56/14.97 Y1) & 99.56/14.97 (Y2 = 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y3, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y3, 99.56/14.97 setadjoin( 99.56/14.97 Y4, 99.56/14.97 emptyset)), 99.56/14.97 emptyset))))))) & 99.56/14.97 in(Y3, 99.56/14.97 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.56/14.97 inference('lazy_cnf_imply', [status(thm)], ['230'])). 99.56/14.97 tff('232', plain, 99.56/14.97 ~ ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 99.56/14.97 subset(Y0, Y1)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y1, Y0)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y0, Y1)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 99.56/14.97 subset(Y0, Y1)))))))) => 99.56/14.97 ((!!(subset(emptyset))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (subset(Y0, Y1) => 99.56/14.97 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (subset(Y0, Y1) => 99.56/14.97 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, Y0) => 99.56/14.97 ((~(in(Y2, Y1))) => (~(subset(Y0, Y1)))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, Y0) => 99.56/14.97 ((~(in(Y2, Y1))) => (Y0 != Y1)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (subset(Y0, Y1) => 99.56/14.97 (subset(Y1, Y2) => subset(Y0, Y2)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: subset(Y1, setadjoin(Y0, Y1)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (subset(Y0, Y2) => 99.56/14.97 subset(Y0, setadjoin(Y1, Y2)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (subset(Y0, Y1) => in(Y0, powerset(Y1))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (subset(Y0, Y1) => 99.56/14.97 (subset(Y1, Y0) => (Y0 = Y1))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (subset(Y0, emptyset) => (Y0 = emptyset))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (subset(Y1, Y0) => in(Y1, powerset(Y0))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (in(Y1, powerset(Y0)) => 99.56/14.97 subset(Y1, Y0)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (subset(Y0, Y1) => 99.56/14.97 subset(powerset(Y0), powerset(Y1))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i > $o]: 99.56/14.97 in(dsetconstr(Y0, Y1), 99.56/14.97 powerset(Y0)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i > $o]: 99.56/14.97 subset(dsetconstr(Y0, Y1), Y0))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, Y0) => 99.56/14.97 in(Y2, binunion(Y0, Y1)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 in(Y1, 99.56/14.97 setadjoin(Y0, 99.56/14.97 setadjoin(Y1, emptyset))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, Y1) => 99.56/14.97 in(Y2, 99.56/14.97 binunion(Y0, Y1)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (!!((^[Y3 : $o]: 99.56/14.97 (in(Y2, 99.56/14.97 binunion(Y0, 99.56/14.97 Y1)) => 99.56/14.97 ((in(Y2, Y0) => 99.56/14.97 Y3) => 99.56/14.97 ((in(Y2, Y1) => 99.56/14.97 Y3) => 99.56/14.97 Y3))))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 binunion(Y0, Y1)) => 99.56/14.97 (in(Y2, Y1) | 99.56/14.97 in(Y2, Y0)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 subset(Y0, binunion(Y0, Y1)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 subset(Y1, 99.56/14.97 binunion(Y0, Y1)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, Y0) => 99.56/14.97 (in(Y2, Y1) => 99.56/14.97 in(Y2, 99.56/14.97 binintersect( 99.56/14.97 Y0, Y1))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (subset(Y2, Y0) => 99.56/14.97 (subset(Y2, Y1) => 99.56/14.97 subset(Y2, 99.56/14.97 binintersect( 99.56/14.97 Y0, Y1))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 binintersect( 99.56/14.97 Y0, Y1)) => 99.56/14.97 in(Y2, Y0))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 subset( 99.56/14.97 binintersect(Y0, Y1), 99.56/14.97 Y0))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (subset(Y0, Y1) => 99.56/14.97 (binintersect(Y0, Y1) = 99.56/14.97 Y0)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 ((binintersect(Y0, 99.56/14.97 Y1) = 99.56/14.97 Y1) => 99.56/14.97 subset(Y1, Y0)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 binintersect( 99.56/14.97 Y0, Y1)) => 99.56/14.97 in(Y2, Y1))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 ((~((??((^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) & 99.56/14.97 in(Y2, 99.56/14.97 Y1))))))) => 99.56/14.97 (binintersect(Y0, 99.56/14.97 Y1) = 99.56/14.97 emptyset)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 subset( 99.56/14.97 binintersect( 99.56/14.97 Y0, Y1), Y1))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (subset(Y1, Y0) => 99.56/14.97 (binintersect( 99.56/14.97 Y0, Y1) = 99.56/14.97 Y1)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 ((binintersect( 99.56/14.97 Y0, Y1) = 99.56/14.97 Y0) => 99.56/14.97 subset(Y0, Y1)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (binintersect( 99.56/14.97 Y0, 99.56/14.97 binunion( 99.56/14.97 Y1, Y2)) = 99.56/14.97 binunion( 99.56/14.97 binintersect( 99.56/14.97 Y0, Y1), 99.56/14.97 binintersect( 99.56/14.97 Y0, Y2)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 (( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 Y1))) => 99.56/14.97 in(Y2, 99.56/14.97 setminus( 99.56/14.97 Y0, Y1))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 setminus( 99.56/14.97 Y0, Y1)) => 99.56/14.97 in(Y2, 99.56/14.97 Y0))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 ( 99.56/14.97 in(Y2, 99.56/14.97 setminus( 99.56/14.97 Y0, Y1)) => 99.56/14.97 ( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 Y1))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (subset( 99.56/14.97 Y0, Y1) => 99.56/14.97 (setminus( 99.56/14.97 Y0, Y1) = 99.56/14.97 emptyset)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 setminus( 99.56/14.97 Y0, Y1)))) => 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 in(Y2, 99.56/14.97 Y1)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 setminus( 99.56/14.97 Y0, Y1)))) => 99.56/14.97 (( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 Y1))) => 99.56/14.97 (~( 99.56/14.97 in(Y2, 99.56/14.97 Y0)))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 Y0))) => 99.56/14.97 (~( 99.56/14.97 in(Y2, 99.56/14.97 setminus( 99.56/14.97 Y0, Y1)))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y1) => 99.56/14.97 (~( 99.56/14.97 in(Y2, 99.56/14.97 setminus( 99.56/14.97 Y0, Y1)))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 subset( 99.56/14.97 setminus( 99.56/14.97 Y0, Y1), 99.56/14.97 Y0))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 setminus( 99.56/14.97 Y0, Y1) = 99.56/14.97 emptyset) => 99.56/14.97 subset( 99.56/14.97 Y0, Y1)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 symdiff( 99.56/14.97 Y0, Y1)) => 99.56/14.97 (!!(( 99.56/14.97 ^[Y3 : $o]: 99.56/14.97 (( 99.56/14.97 in(Y2, 99.56/14.97 Y0) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 Y1))) => 99.56/14.97 Y3)) => 99.56/14.97 (( 99.56/14.97 ( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 Y0))) => 99.56/14.97 ( 99.56/14.97 in(Y2, 99.56/14.97 Y1) => Y3)) => 99.56/14.97 Y3))))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 (( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 Y1))) => 99.56/14.97 in(Y2, 99.56/14.97 symdiff( 99.56/14.97 Y0, Y1))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 Y0))) => 99.56/14.97 (in(Y2, 99.56/14.97 Y1) => 99.56/14.97 in(Y2, 99.56/14.97 symdiff( 99.56/14.97 Y0, Y1))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 (in(Y2, 99.56/14.97 Y1) => 99.56/14.97 (~( 99.56/14.97 in(Y2, 99.56/14.97 symdiff( 99.56/14.97 Y0, Y1))))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 Y0))) => 99.56/14.97 (( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 Y1))) => 99.56/14.97 (~( 99.56/14.97 in(Y2, 99.56/14.97 symdiff( 99.56/14.97 Y0, Y1))))))))))))))) => 99.56/14.97 ((!!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 in(Y1, 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset))))))))) => 99.56/14.97 ((!!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 in(Y0, 99.56/14.97 setunion( 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)))))))))) => 99.56/14.97 ((!!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 in(Y1, 99.56/14.97 setunion( 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)))))))))) => 99.56/14.97 ((!!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (??(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 setunion( 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)))) & 99.56/14.97 (??(( 99.56/14.97 ^[Y3 : $i]: 99.56/14.97 (in(Y3, 99.56/14.97 setunion( 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)))) & 99.56/14.97 (setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)) = 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 setadjoin( 99.56/14.97 Y3, 99.56/14.97 emptyset)), 99.56/14.97 emptyset))))))))))))))))) => 99.56/14.97 (( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (??(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 setunion( 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)))) & 99.56/14.97 (??(( 99.56/14.97 ^[Y3 : $i]: 99.56/14.97 (in(Y3, 99.56/14.97 setunion( 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)))) & 99.56/14.97 (setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)) = 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 setadjoin( 99.56/14.97 Y3, 99.56/14.97 emptyset)), 99.56/14.97 emptyset))))))))))))))))) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (in(Y1, 99.56/14.97 Y0) => 99.56/14.97 subset( 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset), 99.56/14.97 Y0)))))))) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (in(Y1, 99.56/14.97 Y0) => 99.56/14.97 in( 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset), 99.56/14.97 powerset( 99.56/14.97 Y0))))))))) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 in( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 emptyset), 99.56/14.97 powerset( 99.56/14.97 binunion( 99.56/14.97 Y0, Y1))))))))))))) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset))) => 99.56/14.97 (( 99.56/14.97 Y2 = Y1) | 99.56/14.97 (Y2 = Y0)))))))))))) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 (!!(( 99.56/14.97 ^[Y3 : $i]: 99.56/14.97 (in(Y3, 99.56/14.97 Y1) => 99.56/14.97 subset( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 setadjoin( 99.56/14.97 Y3, 99.56/14.97 emptyset)), 99.56/14.97 binunion( 99.56/14.97 Y0, Y1)))))))))))))))) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 (!!(( 99.56/14.97 ^[Y3 : $i]: 99.56/14.97 (in(Y3, 99.56/14.97 Y1) => 99.56/14.97 in( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 setadjoin( 99.56/14.97 Y3, 99.56/14.97 emptyset)), 99.56/14.97 powerset( 99.56/14.97 binunion( 99.56/14.97 Y0, Y1))))))))))))))))) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 (!!(( 99.56/14.97 ^[Y3 : $i]: 99.56/14.97 (in(Y3, 99.56/14.97 Y1) => 99.56/14.97 subset( 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 setadjoin( 99.56/14.97 Y3, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)), 99.56/14.97 powerset( 99.56/14.97 binunion( 99.56/14.97 Y0, Y1))))))))))))))))) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 (!!(( 99.56/14.97 ^[Y3 : $i]: 99.56/14.97 (in(Y3, 99.56/14.97 Y1) => 99.56/14.97 in( 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 setadjoin( 99.56/14.97 Y3, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)), 99.56/14.97 powerset( 99.56/14.97 powerset( 99.56/14.97 binunion( 99.56/14.97 Y0, Y1)))))))))))))))))) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 (!!(( 99.56/14.97 ^[Y3 : $i]: 99.56/14.97 (in(Y3, 99.56/14.97 Y1) => 99.56/14.97 in( 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 setadjoin( 99.56/14.97 Y3, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)), 99.56/14.97 powerset( 99.56/14.97 powerset( 99.56/14.97 binunion( 99.56/14.97 Y0, Y1)))))))))))))))))) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 (!!(( 99.56/14.97 ^[Y3 : $i]: 99.56/14.97 (in(Y3, 99.56/14.97 Y1) => 99.56/14.97 in( 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 setadjoin( 99.56/14.97 Y3, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)), 99.56/14.97 dsetconstr( 99.56/14.97 powerset( 99.56/14.97 powerset( 99.56/14.97 binunion( 99.56/14.97 Y0, Y1))), 99.56/14.97 (^[Y4 : $i]: 99.56/14.97 (??(( 99.56/14.97 ^[Y5 : $i]: 99.56/14.97 (in(Y5, 99.56/14.97 Y0) & 99.56/14.97 (??(( 99.56/14.97 ^[Y6 : $i]: 99.56/14.97 (in(Y6, 99.56/14.97 Y1) & 99.56/14.97 (Y4 = 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y5, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y5, 99.56/14.97 setadjoin( 99.56/14.97 Y6, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)))))))))))))))))))))))))))) => 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 dsetconstr( 99.56/14.97 powerset( 99.56/14.97 powerset( 99.56/14.97 binunion( 99.56/14.97 Y0, Y1))), 99.56/14.97 (^[Y3 : $i]: 99.56/14.97 (??(( 99.56/14.97 ^[Y4 : $i]: 99.56/14.97 (in(Y4, 99.56/14.97 Y0) & 99.56/14.97 (??(( 99.56/14.97 ^[Y5 : $i]: 99.56/14.97 (in(Y5, 99.56/14.97 Y1) & 99.56/14.97 (Y3 = 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y4, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y4, 99.56/14.97 setadjoin( 99.56/14.97 Y5, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)))))))))))))) => 99.56/14.97 (??(( 99.56/14.97 ^[Y3 : $i]: 99.56/14.97 (( 99.56/14.97 ??(( 99.56/14.97 ^[Y4 : $i]: 99.56/14.97 (in(Y4, 99.56/14.97 Y1) & 99.56/14.97 (Y2 = 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y3, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y3, 99.56/14.97 setadjoin( 99.56/14.97 Y4, 99.56/14.97 emptyset)), 99.56/14.97 emptyset))))))) & 99.56/14.97 in(Y3, 99.56/14.97 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.56/14.97 inference('lazy_cnf_imply', [status(thm)], ['231'])). 99.56/14.97 tff('233', plain, 99.56/14.97 ~ ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y1, Y0)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y0, Y1)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 99.56/14.97 subset(Y0, Y1)))))))) => 99.56/14.97 ((!!(subset(emptyset))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (subset(Y0, Y1) => (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (subset(Y0, Y1) => 99.56/14.97 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, Y0) => 99.56/14.97 ((~(in(Y2, Y1))) => (~(subset(Y0, Y1)))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, Y0) => 99.56/14.97 ((~(in(Y2, Y1))) => (Y0 != Y1)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (subset(Y0, Y1) => 99.56/14.97 (subset(Y1, Y2) => subset(Y0, Y2)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: subset(Y1, setadjoin(Y0, Y1)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (subset(Y0, Y2) => 99.56/14.97 subset(Y0, setadjoin(Y1, Y2)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (subset(Y0, Y1) => in(Y0, powerset(Y1))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (subset(Y0, Y1) => 99.56/14.97 (subset(Y1, Y0) => (Y0 = Y1))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (subset(Y0, emptyset) => (Y0 = emptyset))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (subset(Y1, Y0) => in(Y1, powerset(Y0))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (in(Y1, powerset(Y0)) => subset(Y1, Y0)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (subset(Y0, Y1) => 99.56/14.97 subset(powerset(Y0), powerset(Y1))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i > $o]: 99.56/14.97 in(dsetconstr(Y0, Y1), powerset(Y0)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i > $o]: 99.56/14.97 subset(dsetconstr(Y0, Y1), Y0))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, Y0) => 99.56/14.97 in(Y2, binunion(Y0, Y1)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 in(Y1, 99.56/14.97 setadjoin(Y0, 99.56/14.97 setadjoin(Y1, emptyset))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, Y1) => 99.56/14.97 in(Y2, binunion(Y0, Y1)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (!!((^[Y3 : $o]: 99.56/14.97 (in(Y2, 99.56/14.97 binunion(Y0, 99.56/14.97 Y1)) => 99.56/14.97 ((in(Y2, Y0) => 99.56/14.97 Y3) => 99.56/14.97 ((in(Y2, Y1) => 99.56/14.97 Y3) => 99.56/14.97 Y3))))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 binunion(Y0, Y1)) => 99.56/14.97 (in(Y2, Y1) | 99.56/14.97 in(Y2, Y0)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 subset(Y0, binunion(Y0, Y1)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 subset(Y1, binunion(Y0, Y1)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, Y0) => 99.56/14.97 (in(Y2, Y1) => 99.56/14.97 in(Y2, 99.56/14.97 binintersect( 99.56/14.97 Y0, Y1))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (subset(Y2, Y0) => 99.56/14.97 (subset(Y2, Y1) => 99.56/14.97 subset(Y2, 99.56/14.97 binintersect( 99.56/14.97 Y0, Y1))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 binintersect( 99.56/14.97 Y0, Y1)) => 99.56/14.97 in(Y2, Y0))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 subset( 99.56/14.97 binintersect(Y0, Y1), 99.56/14.97 Y0))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (subset(Y0, Y1) => 99.56/14.97 (binintersect(Y0, Y1) = 99.56/14.97 Y0)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 ((binintersect(Y0, Y1) = 99.56/14.97 Y1) => 99.56/14.97 subset(Y1, Y0)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 binintersect( 99.56/14.97 Y0, Y1)) => 99.56/14.97 in(Y2, Y1))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 ((~((??((^[Y2 : $i]: 99.56/14.97 ( 99.56/14.97 in(Y2, 99.56/14.97 Y0) & 99.56/14.97 in(Y2, 99.56/14.97 Y1))))))) => 99.56/14.97 (binintersect(Y0, 99.56/14.97 Y1) = 99.56/14.97 emptyset)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 subset( 99.56/14.97 binintersect(Y0, 99.56/14.97 Y1), Y1))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (subset(Y1, Y0) => 99.56/14.97 (binintersect( 99.56/14.97 Y0, Y1) = 99.56/14.97 Y1)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 ((binintersect( 99.56/14.97 Y0, Y1) = 99.56/14.97 Y0) => 99.56/14.97 subset(Y0, Y1)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 ( 99.56/14.97 binintersect( 99.56/14.97 Y0, 99.56/14.97 binunion( 99.56/14.97 Y1, Y2)) = 99.56/14.97 binunion( 99.56/14.97 binintersect( 99.56/14.97 Y0, Y1), 99.56/14.97 binintersect( 99.56/14.97 Y0, Y2)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 (( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 Y1))) => 99.56/14.97 in(Y2, 99.56/14.97 setminus( 99.56/14.97 Y0, Y1))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 setminus( 99.56/14.97 Y0, Y1)) => 99.56/14.97 in(Y2, 99.56/14.97 Y0))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 setminus( 99.56/14.97 Y0, Y1)) => 99.56/14.97 ( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 Y1))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (subset(Y0, 99.56/14.97 Y1) => 99.56/14.97 (setminus( 99.56/14.97 Y0, Y1) = 99.56/14.97 emptyset)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 setminus( 99.56/14.97 Y0, Y1)))) => 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 in(Y2, 99.56/14.97 Y1)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 setminus( 99.56/14.97 Y0, Y1)))) => 99.56/14.97 (( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 Y1))) => 99.56/14.97 (~( 99.56/14.97 in(Y2, 99.56/14.97 Y0)))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 Y0))) => 99.56/14.97 (~( 99.56/14.97 in(Y2, 99.56/14.97 setminus( 99.56/14.97 Y0, Y1)))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y1) => 99.56/14.97 (~( 99.56/14.97 in(Y2, 99.56/14.97 setminus( 99.56/14.97 Y0, Y1)))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 subset( 99.56/14.97 setminus( 99.56/14.97 Y0, Y1), 99.56/14.97 Y0))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (( 99.56/14.97 setminus( 99.56/14.97 Y0, Y1) = 99.56/14.97 emptyset) => 99.56/14.97 subset( 99.56/14.97 Y0, Y1)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 symdiff( 99.56/14.97 Y0, Y1)) => 99.56/14.97 (!!(( 99.56/14.97 ^[Y3 : $o]: 99.56/14.97 (( 99.56/14.97 in(Y2, 99.56/14.97 Y0) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 Y1))) => 99.56/14.97 Y3)) => 99.56/14.97 (( 99.56/14.97 ( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 Y0))) => 99.56/14.97 ( 99.56/14.97 in(Y2, 99.56/14.97 Y1) => Y3)) => 99.56/14.97 Y3))))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 (( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 Y1))) => 99.56/14.97 in(Y2, 99.56/14.97 symdiff( 99.56/14.97 Y0, Y1))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 Y0))) => 99.56/14.97 (in(Y2, 99.56/14.97 Y1) => 99.56/14.97 in(Y2, 99.56/14.97 symdiff( 99.56/14.97 Y0, Y1))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 (in(Y2, 99.56/14.97 Y1) => 99.56/14.97 (~( 99.56/14.97 in(Y2, 99.56/14.97 symdiff( 99.56/14.97 Y0, Y1))))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 Y0))) => 99.56/14.97 (( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 Y1))) => 99.56/14.97 (~( 99.56/14.97 in(Y2, 99.56/14.97 symdiff( 99.56/14.97 Y0, Y1))))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 in(Y1, 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset))))))))) => 99.56/14.97 ((!!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 in(Y0, 99.56/14.97 setunion( 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)))))))))) => 99.56/14.97 ((!!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 in(Y1, 99.56/14.97 setunion( 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)))))))))) => 99.56/14.97 ((!!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (??(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 setunion( 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)))) & 99.56/14.97 (??(( 99.56/14.97 ^[Y3 : $i]: 99.56/14.97 (in(Y3, 99.56/14.97 setunion( 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)))) & 99.56/14.97 (setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)) = 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 setadjoin( 99.56/14.97 Y3, 99.56/14.97 emptyset)), 99.56/14.97 emptyset))))))))))))))))) => 99.56/14.97 ((!!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (??(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 setunion( 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)))) & 99.56/14.97 (??(( 99.56/14.97 ^[Y3 : $i]: 99.56/14.97 (in(Y3, 99.56/14.97 setunion( 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)))) & 99.56/14.97 (setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)) = 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 setadjoin( 99.56/14.97 Y3, 99.56/14.97 emptyset)), 99.56/14.97 emptyset))))))))))))))))) => 99.56/14.97 (( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (in(Y1, 99.56/14.97 Y0) => 99.56/14.97 subset( 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset), 99.56/14.97 Y0)))))))) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (in(Y1, 99.56/14.97 Y0) => 99.56/14.97 in( 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset), 99.56/14.97 powerset( 99.56/14.97 Y0))))))))) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 in( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 emptyset), 99.56/14.97 powerset( 99.56/14.97 binunion( 99.56/14.97 Y0, Y1))))))))))))) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 setadjoin( 99.56/14.97 Y0, 99.56/14.97 setadjoin( 99.56/14.97 Y1, 99.56/14.97 emptyset))) => 99.56/14.97 (( 99.56/14.97 Y2 = Y1) | 99.56/14.97 (Y2 = Y0)))))))))))) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 (!!(( 99.56/14.97 ^[Y3 : $i]: 99.56/14.97 (in(Y3, 99.56/14.97 Y1) => 99.56/14.97 subset( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 setadjoin( 99.56/14.97 Y3, 99.56/14.97 emptyset)), 99.56/14.97 binunion( 99.56/14.97 Y0, Y1)))))))))))))))) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 (!!(( 99.56/14.97 ^[Y3 : $i]: 99.56/14.97 (in(Y3, 99.56/14.97 Y1) => 99.56/14.97 in( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 setadjoin( 99.56/14.97 Y3, 99.56/14.97 emptyset)), 99.56/14.97 powerset( 99.56/14.97 binunion( 99.56/14.97 Y0, Y1))))))))))))))))) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 (!!(( 99.56/14.97 ^[Y3 : $i]: 99.56/14.97 (in(Y3, 99.56/14.97 Y1) => 99.56/14.97 subset( 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 setadjoin( 99.56/14.97 Y3, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)), 99.56/14.97 powerset( 99.56/14.97 binunion( 99.56/14.97 Y0, Y1))))))))))))))))) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 (!!(( 99.56/14.97 ^[Y3 : $i]: 99.56/14.97 (in(Y3, 99.56/14.97 Y1) => 99.56/14.97 in( 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 setadjoin( 99.56/14.97 Y3, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)), 99.56/14.97 powerset( 99.56/14.97 powerset( 99.56/14.97 binunion( 99.56/14.97 Y0, Y1)))))))))))))))))) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 (!!(( 99.56/14.97 ^[Y3 : $i]: 99.56/14.97 (in(Y3, 99.56/14.97 Y1) => 99.56/14.97 in( 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 setadjoin( 99.56/14.97 Y3, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)), 99.56/14.97 powerset( 99.56/14.97 powerset( 99.56/14.97 binunion( 99.56/14.97 Y0, Y1)))))))))))))))))) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) => 99.56/14.97 (!!(( 99.56/14.97 ^[Y3 : $i]: 99.56/14.97 (in(Y3, 99.56/14.97 Y1) => 99.56/14.97 in( 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y2, 99.56/14.97 setadjoin( 99.56/14.97 Y3, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)), 99.56/14.97 dsetconstr( 99.56/14.97 powerset( 99.56/14.97 powerset( 99.56/14.97 binunion( 99.56/14.97 Y0, Y1))), 99.56/14.97 (^[Y4 : $i]: 99.56/14.97 (??(( 99.56/14.97 ^[Y5 : $i]: 99.56/14.97 (in(Y5, 99.56/14.97 Y0) & 99.56/14.97 (??(( 99.56/14.97 ^[Y6 : $i]: 99.56/14.97 (in(Y6, 99.56/14.97 Y1) & 99.56/14.97 (Y4 = 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y5, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y5, 99.56/14.97 setadjoin( 99.56/14.97 Y6, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)))))))))))))))))))))))))))) => 99.56/14.97 ( 99.56/14.97 !!(( 99.56/14.97 ^[Y0 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y1 : $i]: 99.56/14.97 (!!(( 99.56/14.97 ^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 dsetconstr( 99.56/14.97 powerset( 99.56/14.97 powerset( 99.56/14.97 binunion( 99.56/14.97 Y0, Y1))), 99.56/14.97 (^[Y3 : $i]: 99.56/14.97 (??(( 99.56/14.97 ^[Y4 : $i]: 99.56/14.97 (in(Y4, 99.56/14.97 Y0) & 99.56/14.97 (??(( 99.56/14.97 ^[Y5 : $i]: 99.56/14.97 (in(Y5, 99.56/14.97 Y1) & 99.56/14.97 (Y3 = 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y4, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y4, 99.56/14.97 setadjoin( 99.56/14.97 Y5, 99.56/14.97 emptyset)), 99.56/14.97 emptyset)))))))))))))) => 99.56/14.97 (??(( 99.56/14.97 ^[Y3 : $i]: 99.56/14.97 (( 99.56/14.97 ??(( 99.56/14.97 ^[Y4 : $i]: 99.56/14.97 (in(Y4, 99.56/14.97 Y1) & 99.56/14.97 (Y2 = 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y3, 99.56/14.97 emptyset), 99.56/14.97 setadjoin( 99.56/14.97 setadjoin( 99.56/14.97 Y3, 99.56/14.97 setadjoin( 99.56/14.97 Y4, 99.56/14.97 emptyset)), 99.56/14.97 emptyset))))))) & 99.56/14.97 in(Y3, 99.56/14.97 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.56/14.97 inference('lazy_cnf_imply', [status(thm)], ['232'])). 99.56/14.97 tff('234', plain, 99.56/14.97 ~ ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y0, Y1)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 99.56/14.97 subset(Y0, Y1)))))))) => 99.56/14.97 ((!!(subset(emptyset))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (subset(Y0, Y1) => (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (subset(Y0, Y1) => 99.56/14.97 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, Y0) => 99.56/14.97 ((~(in(Y2, Y1))) => (~(subset(Y0, Y1)))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, Y0) => 99.56/14.97 ((~(in(Y2, Y1))) => (Y0 != Y1)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (subset(Y0, Y1) => 99.56/14.97 (subset(Y1, Y2) => subset(Y0, Y2)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: subset(Y1, setadjoin(Y0, Y1)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (subset(Y0, Y2) => 99.56/14.97 subset(Y0, setadjoin(Y1, Y2)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (subset(Y0, Y1) => in(Y0, powerset(Y1))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (subset(Y0, Y1) => 99.56/14.97 (subset(Y1, Y0) => (Y0 = Y1))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (subset(Y0, emptyset) => (Y0 = emptyset))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (subset(Y1, Y0) => in(Y1, powerset(Y0))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (in(Y1, powerset(Y0)) => subset(Y1, Y0)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (subset(Y0, Y1) => 99.56/14.97 subset(powerset(Y0), powerset(Y1))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i > $o]: 99.56/14.97 in(dsetconstr(Y0, Y1), powerset(Y0)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i > $o]: 99.56/14.97 subset(dsetconstr(Y0, Y1), Y0))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, Y0) => 99.56/14.97 in(Y2, binunion(Y0, Y1)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 in(Y1, 99.56/14.97 setadjoin(Y0, 99.56/14.97 setadjoin(Y1, emptyset))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, Y1) => 99.56/14.97 in(Y2, binunion(Y0, Y1)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (!!((^[Y3 : $o]: 99.56/14.97 (in(Y2, 99.56/14.97 binunion(Y0, 99.56/14.97 Y1)) => 99.56/14.97 ((in(Y2, Y0) => 99.56/14.97 Y3) => 99.56/14.97 ((in(Y2, Y1) => 99.56/14.97 Y3) => 99.56/14.97 Y3))))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 binunion(Y0, Y1)) => 99.56/14.97 (in(Y2, Y1) | 99.56/14.97 in(Y2, Y0)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 subset(Y0, binunion(Y0, Y1)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 subset(Y1, binunion(Y0, Y1)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, Y0) => 99.56/14.97 (in(Y2, Y1) => 99.56/14.97 in(Y2, 99.56/14.97 binintersect(Y0, 99.56/14.97 Y1))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (subset(Y2, Y0) => 99.56/14.97 (subset(Y2, Y1) => 99.56/14.97 subset(Y2, 99.56/14.97 binintersect( 99.56/14.97 Y0, Y1))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 binintersect( 99.56/14.97 Y0, Y1)) => 99.56/14.97 in(Y2, Y0))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 subset( 99.56/14.97 binintersect(Y0, Y1), 99.56/14.97 Y0))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (subset(Y0, Y1) => 99.56/14.97 (binintersect(Y0, Y1) = 99.56/14.97 Y0)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 ((binintersect(Y0, Y1) = 99.56/14.97 Y1) => 99.56/14.97 subset(Y1, Y0)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 binintersect( 99.56/14.97 Y0, Y1)) => 99.56/14.97 in(Y2, Y1))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 ((~((??((^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 Y0) & 99.56/14.97 in(Y2, 99.56/14.97 Y1))))))) => 99.56/14.97 (binintersect(Y0, 99.56/14.97 Y1) = 99.56/14.97 emptyset)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 subset( 99.56/14.97 binintersect(Y0, 99.56/14.97 Y1), Y1))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (subset(Y1, Y0) => 99.56/14.97 (binintersect(Y0, 99.56/14.97 Y1) = 99.56/14.97 Y1)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 ((binintersect( 99.56/14.97 Y0, Y1) = 99.56/14.97 Y0) => 99.56/14.97 subset(Y0, Y1)))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (binintersect( 99.56/14.97 Y0, 99.56/14.97 binunion( 99.56/14.97 Y1, Y2)) = 99.56/14.97 binunion( 99.56/14.97 binintersect( 99.56/14.97 Y0, Y1), 99.56/14.97 binintersect( 99.56/14.97 Y0, Y2)))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 ( 99.56/14.97 in(Y2, 99.56/14.97 Y0) => 99.56/14.97 ( 99.56/14.97 ( 99.56/14.97 ~( 99.56/14.97 in(Y2, 99.56/14.97 Y1))) => 99.56/14.97 in(Y2, 99.56/14.97 setminus( 99.56/14.97 Y0, Y1))))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.97 (!!((^[Y2 : $i]: 99.56/14.97 (in(Y2, 99.56/14.97 setminus( 99.56/14.97 Y0, Y1)) => 99.56/14.97 in(Y2, 99.56/14.97 Y0))))))))))) => 99.56/14.97 ((!!((^[Y0 : $i]: 99.56/14.97 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1)) => 99.56/14.98 (~( 99.56/14.98 in(Y2, 99.56/14.98 Y1))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (subset(Y0, 99.56/14.98 Y1) => 99.56/14.98 (setminus( 99.56/14.98 Y0, Y1) = 99.56/14.98 emptyset)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1)))) => 99.56/14.98 ( 99.56/14.98 in(Y2, 99.56/14.98 Y0) => 99.56/14.98 in(Y2, 99.56/14.98 Y1)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1)))) => 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y1))) => 99.56/14.98 (~( 99.56/14.98 in(Y2, 99.56/14.98 Y0)))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y0))) => 99.56/14.98 (~( 99.56/14.98 in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1)))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y1) => 99.56/14.98 (~( 99.56/14.98 in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1)))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 subset( 99.56/14.98 setminus( 99.56/14.98 Y0, Y1), 99.56/14.98 Y0))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (( 99.56/14.98 setminus( 99.56/14.98 Y0, Y1) = 99.56/14.98 emptyset) => 99.56/14.98 subset( 99.56/14.98 Y0, Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 symdiff( 99.56/14.98 Y0, Y1)) => 99.56/14.98 (!!(( 99.56/14.98 ^[Y3 : $o]: 99.56/14.98 (( 99.56/14.98 in(Y2, 99.56/14.98 Y0) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y1))) => 99.56/14.98 Y3)) => 99.56/14.98 (( 99.56/14.98 ( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y0))) => 99.56/14.98 ( 99.56/14.98 in(Y2, 99.56/14.98 Y1) => Y3)) => 99.56/14.98 Y3))))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y1))) => 99.56/14.98 in(Y2, 99.56/14.98 symdiff( 99.56/14.98 Y0, Y1))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y0))) => 99.56/14.98 (in(Y2, 99.56/14.98 Y1) => 99.56/14.98 in(Y2, 99.56/14.98 symdiff( 99.56/14.98 Y0, Y1))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (in(Y2, 99.56/14.98 Y1) => 99.56/14.98 (~( 99.56/14.98 in(Y2, 99.56/14.98 symdiff( 99.56/14.98 Y0, Y1))))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y0))) => 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y1))) => 99.56/14.98 (~( 99.56/14.98 in(Y2, 99.56/14.98 symdiff( 99.56/14.98 Y0, Y1))))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 in(Y1, 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 in(Y0, 99.56/14.98 setunion( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))))))))) => 99.56/14.98 ((!!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 in(Y1, 99.56/14.98 setunion( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))))))))) => 99.56/14.98 ((!!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (??(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 setunion( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))) & 99.56/14.98 (??(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 setunion( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))) & 99.56/14.98 (setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)) = 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 emptyset))))))))))))))))) => 99.56/14.98 ((!!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (??(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 setunion( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))) & 99.56/14.98 (??(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 setunion( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))) & 99.56/14.98 (setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)) = 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 emptyset))))))))))))))))) => 99.56/14.98 ((!!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (in(Y1, 99.56/14.98 Y0) => 99.56/14.98 subset( 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset), 99.56/14.98 Y0)))))))) => 99.56/14.98 (( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (in(Y1, 99.56/14.98 Y0) => 99.56/14.98 in( 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset), 99.56/14.98 powerset( 99.56/14.98 Y0))))))))) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 in( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 powerset( 99.56/14.98 binunion( 99.56/14.98 Y0, Y1))))))))))))) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset))) => 99.56/14.98 (( 99.56/14.98 Y2 = Y1) | 99.56/14.98 (Y2 = Y0)))))))))))) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (!!(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 Y1) => 99.56/14.98 subset( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 binunion( 99.56/14.98 Y0, Y1)))))))))))))))) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (!!(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 Y1) => 99.56/14.98 in( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 powerset( 99.56/14.98 binunion( 99.56/14.98 Y0, Y1))))))))))))))))) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (!!(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 Y1) => 99.56/14.98 subset( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)), 99.56/14.98 powerset( 99.56/14.98 binunion( 99.56/14.98 Y0, Y1))))))))))))))))) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (!!(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 Y1) => 99.56/14.98 in( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)), 99.56/14.98 powerset( 99.56/14.98 powerset( 99.56/14.98 binunion( 99.56/14.98 Y0, Y1)))))))))))))))))) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (!!(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 Y1) => 99.56/14.98 in( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)), 99.56/14.98 powerset( 99.56/14.98 powerset( 99.56/14.98 binunion( 99.56/14.98 Y0, Y1)))))))))))))))))) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (!!(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 Y1) => 99.56/14.98 in( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)), 99.56/14.98 dsetconstr( 99.56/14.98 powerset( 99.56/14.98 powerset( 99.56/14.98 binunion( 99.56/14.98 Y0, Y1))), 99.56/14.98 (^[Y4 : $i]: 99.56/14.98 (??(( 99.56/14.98 ^[Y5 : $i]: 99.56/14.98 (in(Y5, 99.56/14.98 Y0) & 99.56/14.98 (??(( 99.56/14.98 ^[Y6 : $i]: 99.56/14.98 (in(Y6, 99.56/14.98 Y1) & 99.56/14.98 (Y4 = 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y5, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y5, 99.56/14.98 setadjoin( 99.56/14.98 Y6, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))))))))))))))))))))))))))) => 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 dsetconstr( 99.56/14.98 powerset( 99.56/14.98 powerset( 99.56/14.98 binunion( 99.56/14.98 Y0, Y1))), 99.56/14.98 (^[Y3 : $i]: 99.56/14.98 (??(( 99.56/14.98 ^[Y4 : $i]: 99.56/14.98 (in(Y4, 99.56/14.98 Y0) & 99.56/14.98 (??(( 99.56/14.98 ^[Y5 : $i]: 99.56/14.98 (in(Y5, 99.56/14.98 Y1) & 99.56/14.98 (Y3 = 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y4, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y4, 99.56/14.98 setadjoin( 99.56/14.98 Y5, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))))))))))))) => 99.56/14.98 (??(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (( 99.56/14.98 ??(( 99.56/14.98 ^[Y4 : $i]: 99.56/14.98 (in(Y4, 99.56/14.98 Y1) & 99.56/14.98 (Y2 = 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 setadjoin( 99.56/14.98 Y4, 99.56/14.98 emptyset)), 99.56/14.98 emptyset))))))) & 99.56/14.98 in(Y3, 99.56/14.98 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.56/14.98 inference('lazy_cnf_imply', [status(thm)], ['233'])). 99.56/14.98 tff('235', plain, 99.56/14.98 ~ ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 99.56/14.98 subset(Y0, Y1)))))))) => 99.56/14.98 ((!!(subset(emptyset))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (subset(Y0, Y1) => (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (subset(Y0, Y1) => 99.56/14.98 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, Y0) => 99.56/14.98 ((~(in(Y2, Y1))) => (~(subset(Y0, Y1)))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, Y0) => 99.56/14.98 ((~(in(Y2, Y1))) => (Y0 != Y1)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (subset(Y0, Y1) => 99.56/14.98 (subset(Y1, Y2) => subset(Y0, Y2)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: subset(Y1, setadjoin(Y0, Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (subset(Y0, Y2) => 99.56/14.98 subset(Y0, setadjoin(Y1, Y2)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (subset(Y0, Y1) => in(Y0, powerset(Y1))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (subset(Y0, Y1) => 99.56/14.98 (subset(Y1, Y0) => (Y0 = Y1))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (subset(Y0, emptyset) => (Y0 = emptyset))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (subset(Y1, Y0) => in(Y1, powerset(Y0))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (in(Y1, powerset(Y0)) => subset(Y1, Y0)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (subset(Y0, Y1) => 99.56/14.98 subset(powerset(Y0), powerset(Y1))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i > $o]: 99.56/14.98 in(dsetconstr(Y0, Y1), powerset(Y0)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i > $o]: 99.56/14.98 subset(dsetconstr(Y0, Y1), Y0))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, Y0) => 99.56/14.98 in(Y2, binunion(Y0, Y1)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 in(Y1, 99.56/14.98 setadjoin(Y0, 99.56/14.98 setadjoin(Y1, emptyset))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, Y1) => 99.56/14.98 in(Y2, binunion(Y0, Y1)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (!!((^[Y3 : $o]: 99.56/14.98 (in(Y2, 99.56/14.98 binunion(Y0, Y1)) => 99.56/14.98 ((in(Y2, Y0) => Y3) => 99.56/14.98 ((in(Y2, Y1) => 99.56/14.98 Y3) => 99.56/14.98 Y3))))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, binunion(Y0, Y1)) => 99.56/14.98 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 subset(Y0, binunion(Y0, Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 subset(Y1, binunion(Y0, Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, Y0) => 99.56/14.98 (in(Y2, Y1) => 99.56/14.98 in(Y2, 99.56/14.98 binintersect(Y0, 99.56/14.98 Y1))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (subset(Y2, Y0) => 99.56/14.98 (subset(Y2, Y1) => 99.56/14.98 subset(Y2, 99.56/14.98 binintersect(Y0, 99.56/14.98 Y1))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 binintersect(Y0, 99.56/14.98 Y1)) => 99.56/14.98 in(Y2, Y0))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 subset( 99.56/14.98 binintersect(Y0, Y1), 99.56/14.98 Y0))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (subset(Y0, Y1) => 99.56/14.98 (binintersect(Y0, Y1) = 99.56/14.98 Y0)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 ((binintersect(Y0, Y1) = 99.56/14.98 Y1) => 99.56/14.98 subset(Y1, Y0)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 binintersect( 99.56/14.98 Y0, Y1)) => 99.56/14.98 in(Y2, Y1))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 ((~((??((^[Y2 : $i]: 99.56/14.98 (in(Y2, Y0) & 99.56/14.98 in(Y2, Y1))))))) => 99.56/14.98 (binintersect(Y0, Y1) = 99.56/14.98 emptyset)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 subset( 99.56/14.98 binintersect(Y0, 99.56/14.98 Y1), Y1))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (subset(Y1, Y0) => 99.56/14.98 (binintersect(Y0, 99.56/14.98 Y1) = 99.56/14.98 Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 ((binintersect(Y0, 99.56/14.98 Y1) = 99.56/14.98 Y0) => 99.56/14.98 subset(Y0, Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (binintersect( 99.56/14.98 Y0, 99.56/14.98 binunion( 99.56/14.98 Y1, Y2)) = 99.56/14.98 binunion( 99.56/14.98 binintersect( 99.56/14.98 Y0, Y1), 99.56/14.98 binintersect( 99.56/14.98 Y0, Y2)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y1))) => 99.56/14.98 in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 ( 99.56/14.98 in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1)) => 99.56/14.98 in(Y2, 99.56/14.98 Y0))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1)) => 99.56/14.98 (~( 99.56/14.98 in(Y2, 99.56/14.98 Y1))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (subset(Y0, 99.56/14.98 Y1) => 99.56/14.98 (setminus( 99.56/14.98 Y0, Y1) = 99.56/14.98 emptyset)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1)))) => 99.56/14.98 ( 99.56/14.98 in(Y2, 99.56/14.98 Y0) => 99.56/14.98 in(Y2, 99.56/14.98 Y1)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1)))) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y1))) => 99.56/14.98 ( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y0)))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y0))) => 99.56/14.98 (~( 99.56/14.98 in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1)))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y1) => 99.56/14.98 (~( 99.56/14.98 in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1)))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 subset( 99.56/14.98 setminus( 99.56/14.98 Y0, Y1), 99.56/14.98 Y0))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (( 99.56/14.98 setminus( 99.56/14.98 Y0, Y1) = 99.56/14.98 emptyset) => 99.56/14.98 subset( 99.56/14.98 Y0, Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 symdiff( 99.56/14.98 Y0, Y1)) => 99.56/14.98 (!!(( 99.56/14.98 ^[Y3 : $o]: 99.56/14.98 (( 99.56/14.98 in(Y2, 99.56/14.98 Y0) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y1))) => 99.56/14.98 Y3)) => 99.56/14.98 (( 99.56/14.98 ( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y0))) => 99.56/14.98 ( 99.56/14.98 in(Y2, 99.56/14.98 Y1) => Y3)) => 99.56/14.98 Y3))))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y1))) => 99.56/14.98 in(Y2, 99.56/14.98 symdiff( 99.56/14.98 Y0, Y1))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y0))) => 99.56/14.98 (in(Y2, 99.56/14.98 Y1) => 99.56/14.98 in(Y2, 99.56/14.98 symdiff( 99.56/14.98 Y0, Y1))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (in(Y2, 99.56/14.98 Y1) => 99.56/14.98 (~( 99.56/14.98 in(Y2, 99.56/14.98 symdiff( 99.56/14.98 Y0, Y1))))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y0))) => 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y1))) => 99.56/14.98 (~( 99.56/14.98 in(Y2, 99.56/14.98 symdiff( 99.56/14.98 Y0, Y1))))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 in(Y1, 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 in(Y0, 99.56/14.98 setunion( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 in(Y1, 99.56/14.98 setunion( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))))))))) => 99.56/14.98 ((!!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (??(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 setunion( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))) & 99.56/14.98 (??(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 setunion( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))) & 99.56/14.98 (setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)) = 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 emptyset))))))))))))))))) => 99.56/14.98 ((!!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (??(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 setunion( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))) & 99.56/14.98 (??(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 setunion( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))) & 99.56/14.98 (setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)) = 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 emptyset))))))))))))))))) => 99.56/14.98 ((!!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (in(Y1, 99.56/14.98 Y0) => 99.56/14.98 subset( 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset), 99.56/14.98 Y0)))))))) => 99.56/14.98 ((!!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (in(Y1, 99.56/14.98 Y0) => 99.56/14.98 in( 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset), 99.56/14.98 powerset( 99.56/14.98 Y0))))))))) => 99.56/14.98 (( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 in( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 powerset( 99.56/14.98 binunion( 99.56/14.98 Y0, Y1))))))))))))) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset))) => 99.56/14.98 (( 99.56/14.98 Y2 = Y1) | 99.56/14.98 (Y2 = Y0)))))))))))) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (!!(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 Y1) => 99.56/14.98 subset( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 binunion( 99.56/14.98 Y0, Y1)))))))))))))))) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (!!(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 Y1) => 99.56/14.98 in( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 powerset( 99.56/14.98 binunion( 99.56/14.98 Y0, Y1))))))))))))))))) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (!!(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 Y1) => 99.56/14.98 subset( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)), 99.56/14.98 powerset( 99.56/14.98 binunion( 99.56/14.98 Y0, Y1))))))))))))))))) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (!!(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 Y1) => 99.56/14.98 in( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)), 99.56/14.98 powerset( 99.56/14.98 powerset( 99.56/14.98 binunion( 99.56/14.98 Y0, Y1)))))))))))))))))) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (!!(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 Y1) => 99.56/14.98 in( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)), 99.56/14.98 powerset( 99.56/14.98 powerset( 99.56/14.98 binunion( 99.56/14.98 Y0, Y1)))))))))))))))))) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (!!(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 Y1) => 99.56/14.98 in( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)), 99.56/14.98 dsetconstr( 99.56/14.98 powerset( 99.56/14.98 powerset( 99.56/14.98 binunion( 99.56/14.98 Y0, Y1))), 99.56/14.98 (^[Y4 : $i]: 99.56/14.98 (??(( 99.56/14.98 ^[Y5 : $i]: 99.56/14.98 (in(Y5, 99.56/14.98 Y0) & 99.56/14.98 (??(( 99.56/14.98 ^[Y6 : $i]: 99.56/14.98 (in(Y6, 99.56/14.98 Y1) & 99.56/14.98 (Y4 = 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y5, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y5, 99.56/14.98 setadjoin( 99.56/14.98 Y6, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))))))))))))))))))))))))))) => 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 dsetconstr( 99.56/14.98 powerset( 99.56/14.98 powerset( 99.56/14.98 binunion( 99.56/14.98 Y0, Y1))), 99.56/14.98 (^[Y3 : $i]: 99.56/14.98 (??(( 99.56/14.98 ^[Y4 : $i]: 99.56/14.98 (in(Y4, 99.56/14.98 Y0) & 99.56/14.98 (??(( 99.56/14.98 ^[Y5 : $i]: 99.56/14.98 (in(Y5, 99.56/14.98 Y1) & 99.56/14.98 (Y3 = 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y4, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y4, 99.56/14.98 setadjoin( 99.56/14.98 Y5, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))))))))))))) => 99.56/14.98 (??(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (( 99.56/14.98 ??(( 99.56/14.98 ^[Y4 : $i]: 99.56/14.98 (in(Y4, 99.56/14.98 Y1) & 99.56/14.98 (Y2 = 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 setadjoin( 99.56/14.98 Y4, 99.56/14.98 emptyset)), 99.56/14.98 emptyset))))))) & 99.56/14.98 in(Y3, 99.56/14.98 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.56/14.98 inference('lazy_cnf_imply', [status(thm)], ['234'])). 99.56/14.98 tff('236', plain, 99.56/14.98 ~ ((!!(subset(emptyset))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (subset(Y0, Y1) => (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (subset(Y0, Y1) => 99.56/14.98 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, Y0) => 99.56/14.98 ((~(in(Y2, Y1))) => (~(subset(Y0, Y1)))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, Y0) => 99.56/14.98 ((~(in(Y2, Y1))) => (Y0 != Y1)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (subset(Y0, Y1) => 99.56/14.98 (subset(Y1, Y2) => subset(Y0, Y2)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: subset(Y1, setadjoin(Y0, Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (subset(Y0, Y2) => 99.56/14.98 subset(Y0, setadjoin(Y1, Y2)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (subset(Y0, Y1) => in(Y0, powerset(Y1))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (subset(Y0, Y1) => 99.56/14.98 (subset(Y1, Y0) => (Y0 = Y1))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: (subset(Y0, emptyset) => (Y0 = emptyset))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (subset(Y1, Y0) => in(Y1, powerset(Y0))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (in(Y1, powerset(Y0)) => subset(Y1, Y0)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (subset(Y0, Y1) => 99.56/14.98 subset(powerset(Y0), powerset(Y1))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i > $o]: 99.56/14.98 in(dsetconstr(Y0, Y1), powerset(Y0)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i > $o]: 99.56/14.98 subset(dsetconstr(Y0, Y1), Y0))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, Y0) => 99.56/14.98 in(Y2, binunion(Y0, Y1)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 in(Y1, 99.56/14.98 setadjoin(Y0, 99.56/14.98 setadjoin(Y1, emptyset))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, Y1) => 99.56/14.98 in(Y2, binunion(Y0, Y1)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (!!((^[Y3 : $o]: 99.56/14.98 (in(Y2, 99.56/14.98 binunion(Y0, Y1)) => 99.56/14.98 ((in(Y2, Y0) => Y3) => 99.56/14.98 ((in(Y2, Y1) => Y3) => 99.56/14.98 Y3))))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, binunion(Y0, Y1)) => 99.56/14.98 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 subset(Y0, binunion(Y0, Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 subset(Y1, binunion(Y0, Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, Y0) => 99.56/14.98 (in(Y2, Y1) => 99.56/14.98 in(Y2, 99.56/14.98 binintersect(Y0, 99.56/14.98 Y1))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (subset(Y2, Y0) => 99.56/14.98 (subset(Y2, Y1) => 99.56/14.98 subset(Y2, 99.56/14.98 binintersect(Y0, 99.56/14.98 Y1))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 binintersect(Y0, 99.56/14.98 Y1)) => 99.56/14.98 in(Y2, Y0))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 subset( 99.56/14.98 binintersect(Y0, Y1), Y0))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (subset(Y0, Y1) => 99.56/14.98 (binintersect(Y0, Y1) = 99.56/14.98 Y0)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 ((binintersect(Y0, Y1) = 99.56/14.98 Y1) => 99.56/14.98 subset(Y1, Y0)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 binintersect( 99.56/14.98 Y0, Y1)) => 99.56/14.98 in(Y2, Y1))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 ((~((??((^[Y2 : $i]: 99.56/14.98 (in(Y2, Y0) & 99.56/14.98 in(Y2, Y1))))))) => 99.56/14.98 (binintersect(Y0, Y1) = 99.56/14.98 emptyset)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 subset( 99.56/14.98 binintersect(Y0, Y1), 99.56/14.98 Y1))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (subset(Y1, Y0) => 99.56/14.98 (binintersect(Y0, 99.56/14.98 Y1) = 99.56/14.98 Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 ((binintersect(Y0, 99.56/14.98 Y1) = 99.56/14.98 Y0) => 99.56/14.98 subset(Y0, Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (binintersect( 99.56/14.98 Y0, 99.56/14.98 binunion( 99.56/14.98 Y1, Y2)) = 99.56/14.98 binunion( 99.56/14.98 binintersect( 99.56/14.98 Y0, Y1), 99.56/14.98 binintersect( 99.56/14.98 Y0, Y2)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, Y0) => 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y1))) => 99.56/14.98 in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1)) => 99.56/14.98 in(Y2, 99.56/14.98 Y0))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 ( 99.56/14.98 in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1)) => 99.56/14.98 ( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y1))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (subset(Y0, Y1) => 99.56/14.98 (setminus(Y0, 99.56/14.98 Y1) = 99.56/14.98 emptyset)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1)))) => 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 in(Y2, 99.56/14.98 Y1)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1)))) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y1))) => 99.56/14.98 ( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y0)))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y0))) => 99.56/14.98 ( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1)))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y1) => 99.56/14.98 (~( 99.56/14.98 in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1)))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 subset( 99.56/14.98 setminus( 99.56/14.98 Y0, Y1), 99.56/14.98 Y0))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 setminus( 99.56/14.98 Y0, Y1) = 99.56/14.98 emptyset) => 99.56/14.98 subset( 99.56/14.98 Y0, Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 symdiff( 99.56/14.98 Y0, Y1)) => 99.56/14.98 (!!(( 99.56/14.98 ^[Y3 : $o]: 99.56/14.98 (( 99.56/14.98 in(Y2, 99.56/14.98 Y0) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y1))) => 99.56/14.98 Y3)) => 99.56/14.98 (( 99.56/14.98 ( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y0))) => 99.56/14.98 ( 99.56/14.98 in(Y2, 99.56/14.98 Y1) => Y3)) => 99.56/14.98 Y3))))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y1))) => 99.56/14.98 in(Y2, 99.56/14.98 symdiff( 99.56/14.98 Y0, Y1))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y0))) => 99.56/14.98 (in(Y2, 99.56/14.98 Y1) => 99.56/14.98 in(Y2, 99.56/14.98 symdiff( 99.56/14.98 Y0, Y1))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (in(Y2, 99.56/14.98 Y1) => 99.56/14.98 (~( 99.56/14.98 in(Y2, 99.56/14.98 symdiff( 99.56/14.98 Y0, Y1))))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y0))) => 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y1))) => 99.56/14.98 (~( 99.56/14.98 in(Y2, 99.56/14.98 symdiff( 99.56/14.98 Y0, Y1))))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 in(Y1, 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 in(Y0, 99.56/14.98 setunion( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 in(Y1, 99.56/14.98 setunion( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (??(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 setunion( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))) & 99.56/14.98 (??(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 setunion( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))) & 99.56/14.98 (setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)) = 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 emptyset))))))))))))))))) => 99.56/14.98 ((!!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (??(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 setunion( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))) & 99.56/14.98 (??(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 setunion( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))) & 99.56/14.98 (setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)) = 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 emptyset))))))))))))))))) => 99.56/14.98 ((!!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (in(Y1, 99.56/14.98 Y0) => 99.56/14.98 subset( 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset), 99.56/14.98 Y0)))))))) => 99.56/14.98 ((!!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (in(Y1, 99.56/14.98 Y0) => 99.56/14.98 in( 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset), 99.56/14.98 powerset( 99.56/14.98 Y0))))))))) => 99.56/14.98 ((!!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 in( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 powerset( 99.56/14.98 binunion( 99.56/14.98 Y0, Y1))))))))))))) => 99.56/14.98 (( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset))) => 99.56/14.98 (( 99.56/14.98 Y2 = Y1) | 99.56/14.98 (Y2 = Y0)))))))))))) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (!!(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 Y1) => 99.56/14.98 subset( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 binunion( 99.56/14.98 Y0, Y1)))))))))))))))) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (!!(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 Y1) => 99.56/14.98 in( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 powerset( 99.56/14.98 binunion( 99.56/14.98 Y0, Y1))))))))))))))))) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (!!(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 Y1) => 99.56/14.98 subset( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)), 99.56/14.98 powerset( 99.56/14.98 binunion( 99.56/14.98 Y0, Y1))))))))))))))))) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (!!(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 Y1) => 99.56/14.98 in( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)), 99.56/14.98 powerset( 99.56/14.98 powerset( 99.56/14.98 binunion( 99.56/14.98 Y0, Y1)))))))))))))))))) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (!!(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 Y1) => 99.56/14.98 in( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)), 99.56/14.98 powerset( 99.56/14.98 powerset( 99.56/14.98 binunion( 99.56/14.98 Y0, Y1)))))))))))))))))) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (!!(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 Y1) => 99.56/14.98 in( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)), 99.56/14.98 dsetconstr( 99.56/14.98 powerset( 99.56/14.98 powerset( 99.56/14.98 binunion( 99.56/14.98 Y0, Y1))), 99.56/14.98 (^[Y4 : $i]: 99.56/14.98 (??(( 99.56/14.98 ^[Y5 : $i]: 99.56/14.98 (in(Y5, 99.56/14.98 Y0) & 99.56/14.98 (??(( 99.56/14.98 ^[Y6 : $i]: 99.56/14.98 (in(Y6, 99.56/14.98 Y1) & 99.56/14.98 (Y4 = 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y5, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y5, 99.56/14.98 setadjoin( 99.56/14.98 Y6, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))))))))))))))))))))))))))) => 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 dsetconstr( 99.56/14.98 powerset( 99.56/14.98 powerset( 99.56/14.98 binunion( 99.56/14.98 Y0, Y1))), 99.56/14.98 (^[Y3 : $i]: 99.56/14.98 (??(( 99.56/14.98 ^[Y4 : $i]: 99.56/14.98 (in(Y4, 99.56/14.98 Y0) & 99.56/14.98 (??(( 99.56/14.98 ^[Y5 : $i]: 99.56/14.98 (in(Y5, 99.56/14.98 Y1) & 99.56/14.98 (Y3 = 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y4, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y4, 99.56/14.98 setadjoin( 99.56/14.98 Y5, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))))))))))))) => 99.56/14.98 (??(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (( 99.56/14.98 ??(( 99.56/14.98 ^[Y4 : $i]: 99.56/14.98 (in(Y4, 99.56/14.98 Y1) & 99.56/14.98 (Y2 = 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 setadjoin( 99.56/14.98 Y4, 99.56/14.98 emptyset)), 99.56/14.98 emptyset))))))) & 99.56/14.98 in(Y3, 99.56/14.98 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.56/14.98 inference('lazy_cnf_imply', [status(thm)], ['235'])). 99.56/14.98 tff('237', plain, 99.56/14.98 ~ ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (subset(Y0, Y1) => (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (subset(Y0, Y1) => 99.56/14.98 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, Y0) => 99.56/14.98 ((~(in(Y2, Y1))) => (~(subset(Y0, Y1)))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, Y0) => 99.56/14.98 ((~(in(Y2, Y1))) => (Y0 != Y1)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (subset(Y0, Y1) => 99.56/14.98 (subset(Y1, Y2) => subset(Y0, Y2)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: subset(Y1, setadjoin(Y0, Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (subset(Y0, Y2) => 99.56/14.98 subset(Y0, setadjoin(Y1, Y2)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (subset(Y0, Y1) => in(Y0, powerset(Y1))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (subset(Y0, Y1) => 99.56/14.98 (subset(Y1, Y0) => (Y0 = Y1))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: (subset(Y0, emptyset) => (Y0 = emptyset))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (subset(Y1, Y0) => in(Y1, powerset(Y0))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (in(Y1, powerset(Y0)) => subset(Y1, Y0)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (subset(Y0, Y1) => 99.56/14.98 subset(powerset(Y0), powerset(Y1))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i > $o]: 99.56/14.98 in(dsetconstr(Y0, Y1), powerset(Y0)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i > $o]: 99.56/14.98 subset(dsetconstr(Y0, Y1), Y0))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, Y0) => 99.56/14.98 in(Y2, binunion(Y0, Y1)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 in(Y1, 99.56/14.98 setadjoin(Y0, 99.56/14.98 setadjoin(Y1, emptyset))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, Y1) => 99.56/14.98 in(Y2, binunion(Y0, Y1)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (!!((^[Y3 : $o]: 99.56/14.98 (in(Y2, 99.56/14.98 binunion(Y0, Y1)) => 99.56/14.98 ((in(Y2, Y0) => Y3) => 99.56/14.98 ((in(Y2, Y1) => Y3) => 99.56/14.98 Y3))))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, binunion(Y0, Y1)) => 99.56/14.98 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 subset(Y0, binunion(Y0, Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 subset(Y1, binunion(Y0, Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, Y0) => 99.56/14.98 (in(Y2, Y1) => 99.56/14.98 in(Y2, 99.56/14.98 binintersect(Y0, Y1))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (subset(Y2, Y0) => 99.56/14.98 (subset(Y2, Y1) => 99.56/14.98 subset(Y2, 99.56/14.98 binintersect(Y0, 99.56/14.98 Y1))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 binintersect(Y0, 99.56/14.98 Y1)) => 99.56/14.98 in(Y2, Y0))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 subset( 99.56/14.98 binintersect(Y0, Y1), Y0))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (subset(Y0, Y1) => 99.56/14.98 (binintersect(Y0, Y1) = Y0)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 ((binintersect(Y0, Y1) = 99.56/14.98 Y1) => 99.56/14.98 subset(Y1, Y0)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 binintersect( 99.56/14.98 Y0, Y1)) => 99.56/14.98 in(Y2, Y1))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 ((~((??((^[Y2 : $i]: 99.56/14.98 (in(Y2, Y0) & 99.56/14.98 in(Y2, Y1))))))) => 99.56/14.98 (binintersect(Y0, Y1) = 99.56/14.98 emptyset)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 subset( 99.56/14.98 binintersect(Y0, Y1), 99.56/14.98 Y1))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (subset(Y1, Y0) => 99.56/14.98 (binintersect(Y0, Y1) = 99.56/14.98 Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 ((binintersect(Y0, 99.56/14.98 Y1) = 99.56/14.98 Y0) => 99.56/14.98 subset(Y0, Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (binintersect( 99.56/14.98 Y0, 99.56/14.98 binunion( 99.56/14.98 Y1, Y2)) = 99.56/14.98 binunion( 99.56/14.98 binintersect( 99.56/14.98 Y0, Y1), 99.56/14.98 binintersect( 99.56/14.98 Y0, Y2)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, Y0) => 99.56/14.98 ((~( 99.56/14.98 in(Y2, 99.56/14.98 Y1))) => 99.56/14.98 in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1)) => 99.56/14.98 in(Y2, Y0))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1)) => 99.56/14.98 ( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y1))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (subset(Y0, Y1) => 99.56/14.98 (setminus(Y0, 99.56/14.98 Y1) = 99.56/14.98 emptyset)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1)))) => 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 in(Y2, 99.56/14.98 Y1)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1)))) => 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y1))) => 99.56/14.98 (~( 99.56/14.98 in(Y2, 99.56/14.98 Y0)))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y0))) => 99.56/14.98 ( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1)))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 ( 99.56/14.98 in(Y2, 99.56/14.98 Y1) => 99.56/14.98 ( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1)))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 subset( 99.56/14.98 setminus( 99.56/14.98 Y0, Y1), 99.56/14.98 Y0))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (( 99.56/14.98 setminus( 99.56/14.98 Y0, Y1) = 99.56/14.98 emptyset) => 99.56/14.98 subset( 99.56/14.98 Y0, Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 symdiff( 99.56/14.98 Y0, Y1)) => 99.56/14.98 (!!(( 99.56/14.98 ^[Y3 : $o]: 99.56/14.98 (( 99.56/14.98 in(Y2, 99.56/14.98 Y0) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y1))) => 99.56/14.98 Y3)) => 99.56/14.98 (( 99.56/14.98 ( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y0))) => 99.56/14.98 ( 99.56/14.98 in(Y2, 99.56/14.98 Y1) => Y3)) => 99.56/14.98 Y3))))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y1))) => 99.56/14.98 in(Y2, 99.56/14.98 symdiff( 99.56/14.98 Y0, Y1))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y0))) => 99.56/14.98 (in(Y2, 99.56/14.98 Y1) => 99.56/14.98 in(Y2, 99.56/14.98 symdiff( 99.56/14.98 Y0, Y1))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (in(Y2, 99.56/14.98 Y1) => 99.56/14.98 (~( 99.56/14.98 in(Y2, 99.56/14.98 symdiff( 99.56/14.98 Y0, Y1))))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y0))) => 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y1))) => 99.56/14.98 (~( 99.56/14.98 in(Y2, 99.56/14.98 symdiff( 99.56/14.98 Y0, Y1))))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 in(Y1, 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 in(Y0, 99.56/14.98 setunion( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 in(Y1, 99.56/14.98 setunion( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (??(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 setunion( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))) & 99.56/14.98 (??(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 setunion( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))) & 99.56/14.98 (setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)) = 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 emptyset))))))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (??(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 setunion( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))) & 99.56/14.98 (??(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 setunion( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))) & 99.56/14.98 (setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)) = 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 emptyset))))))))))))))))) => 99.56/14.98 ((!!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (in(Y1, 99.56/14.98 Y0) => 99.56/14.98 subset( 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset), 99.56/14.98 Y0)))))))) => 99.56/14.98 ((!!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (in(Y1, 99.56/14.98 Y0) => 99.56/14.98 in( 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset), 99.56/14.98 powerset( 99.56/14.98 Y0))))))))) => 99.56/14.98 ((!!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 in( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 powerset( 99.56/14.98 binunion( 99.56/14.98 Y0, Y1))))))))))))) => 99.56/14.98 ((!!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset))) => 99.56/14.98 (( 99.56/14.98 Y2 = Y1) | 99.56/14.98 (Y2 = Y0)))))))))))) => 99.56/14.98 (( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (!!(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 Y1) => 99.56/14.98 subset( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 binunion( 99.56/14.98 Y0, Y1)))))))))))))))) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (!!(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 Y1) => 99.56/14.98 in( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 powerset( 99.56/14.98 binunion( 99.56/14.98 Y0, Y1))))))))))))))))) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (!!(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 Y1) => 99.56/14.98 subset( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)), 99.56/14.98 powerset( 99.56/14.98 binunion( 99.56/14.98 Y0, Y1))))))))))))))))) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (!!(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 Y1) => 99.56/14.98 in( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)), 99.56/14.98 powerset( 99.56/14.98 powerset( 99.56/14.98 binunion( 99.56/14.98 Y0, Y1)))))))))))))))))) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (!!(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 Y1) => 99.56/14.98 in( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)), 99.56/14.98 powerset( 99.56/14.98 powerset( 99.56/14.98 binunion( 99.56/14.98 Y0, Y1)))))))))))))))))) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (!!(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 Y1) => 99.56/14.98 in( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)), 99.56/14.98 dsetconstr( 99.56/14.98 powerset( 99.56/14.98 powerset( 99.56/14.98 binunion( 99.56/14.98 Y0, Y1))), 99.56/14.98 (^[Y4 : $i]: 99.56/14.98 (??(( 99.56/14.98 ^[Y5 : $i]: 99.56/14.98 (in(Y5, 99.56/14.98 Y0) & 99.56/14.98 (??(( 99.56/14.98 ^[Y6 : $i]: 99.56/14.98 (in(Y6, 99.56/14.98 Y1) & 99.56/14.98 (Y4 = 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y5, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y5, 99.56/14.98 setadjoin( 99.56/14.98 Y6, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))))))))))))))))))))))))))) => 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 dsetconstr( 99.56/14.98 powerset( 99.56/14.98 powerset( 99.56/14.98 binunion( 99.56/14.98 Y0, Y1))), 99.56/14.98 (^[Y3 : $i]: 99.56/14.98 (??(( 99.56/14.98 ^[Y4 : $i]: 99.56/14.98 (in(Y4, 99.56/14.98 Y0) & 99.56/14.98 (??(( 99.56/14.98 ^[Y5 : $i]: 99.56/14.98 (in(Y5, 99.56/14.98 Y1) & 99.56/14.98 (Y3 = 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y4, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y4, 99.56/14.98 setadjoin( 99.56/14.98 Y5, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))))))))))))) => 99.56/14.98 (??(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (( 99.56/14.98 ??(( 99.56/14.98 ^[Y4 : $i]: 99.56/14.98 (in(Y4, 99.56/14.98 Y1) & 99.56/14.98 (Y2 = 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 setadjoin( 99.56/14.98 Y4, 99.56/14.98 emptyset)), 99.56/14.98 emptyset))))))) & 99.56/14.98 in(Y3, 99.56/14.98 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.56/14.98 inference('lazy_cnf_imply', [status(thm)], ['236'])). 99.56/14.98 tff('238', plain, 99.56/14.98 ~ ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (subset(Y0, Y1) => 99.56/14.98 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, Y0) => 99.56/14.98 ((~(in(Y2, Y1))) => (~(subset(Y0, Y1)))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, Y0) => ((~(in(Y2, Y1))) => (Y0 != Y1)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (subset(Y0, Y1) => 99.56/14.98 (subset(Y1, Y2) => subset(Y0, Y2)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: subset(Y1, setadjoin(Y0, Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (subset(Y0, Y2) => 99.56/14.98 subset(Y0, setadjoin(Y1, Y2)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (subset(Y0, Y1) => in(Y0, powerset(Y1))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (subset(Y0, Y1) => 99.56/14.98 (subset(Y1, Y0) => (Y0 = Y1))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: (subset(Y0, emptyset) => (Y0 = emptyset))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (subset(Y1, Y0) => in(Y1, powerset(Y0))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (in(Y1, powerset(Y0)) => subset(Y1, Y0)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (subset(Y0, Y1) => 99.56/14.98 subset(powerset(Y0), powerset(Y1))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i > $o]: 99.56/14.98 in(dsetconstr(Y0, Y1), powerset(Y0)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i > $o]: 99.56/14.98 subset(dsetconstr(Y0, Y1), Y0))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, Y0) => 99.56/14.98 in(Y2, binunion(Y0, Y1)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 in(Y1, 99.56/14.98 setadjoin(Y0, 99.56/14.98 setadjoin(Y1, emptyset))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, Y1) => 99.56/14.98 in(Y2, binunion(Y0, Y1)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (!!((^[Y3 : $o]: 99.56/14.98 (in(Y2, 99.56/14.98 binunion(Y0, Y1)) => 99.56/14.98 ((in(Y2, Y0) => Y3) => 99.56/14.98 ((in(Y2, Y1) => Y3) => 99.56/14.98 Y3))))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, binunion(Y0, Y1)) => 99.56/14.98 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 subset(Y0, binunion(Y0, Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 subset(Y1, binunion(Y0, Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, Y0) => 99.56/14.98 (in(Y2, Y1) => 99.56/14.98 in(Y2, 99.56/14.98 binintersect(Y0, Y1))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (subset(Y2, Y0) => 99.56/14.98 (subset(Y2, Y1) => 99.56/14.98 subset(Y2, 99.56/14.98 binintersect(Y0, Y1))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 binintersect(Y0, Y1)) => 99.56/14.98 in(Y2, Y0))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 subset(binintersect(Y0, Y1), 99.56/14.98 Y0))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (subset(Y0, Y1) => 99.56/14.98 (binintersect(Y0, Y1) = Y0)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 ((binintersect(Y0, Y1) = Y1) => 99.56/14.98 subset(Y1, Y0)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 binintersect( 99.56/14.98 Y0, Y1)) => 99.56/14.98 in(Y2, Y1))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 ((~((??((^[Y2 : $i]: 99.56/14.98 (in(Y2, Y0) & 99.56/14.98 in(Y2, Y1))))))) => 99.56/14.98 (binintersect(Y0, Y1) = 99.56/14.98 emptyset)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 subset( 99.56/14.98 binintersect(Y0, Y1), 99.56/14.98 Y1))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (subset(Y1, Y0) => 99.56/14.98 (binintersect(Y0, Y1) = 99.56/14.98 Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 ((binintersect(Y0, Y1) = 99.56/14.98 Y0) => 99.56/14.98 subset(Y0, Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (binintersect( 99.56/14.98 Y0, 99.56/14.98 binunion( 99.56/14.98 Y1, Y2)) = 99.56/14.98 binunion( 99.56/14.98 binintersect( 99.56/14.98 Y0, Y1), 99.56/14.98 binintersect( 99.56/14.98 Y0, Y2)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, Y0) => 99.56/14.98 ((~( 99.56/14.98 in(Y2, Y1))) => 99.56/14.98 in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1)) => 99.56/14.98 in(Y2, Y0))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1)) => 99.56/14.98 (~( 99.56/14.98 in(Y2, 99.56/14.98 Y1))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (subset(Y0, Y1) => 99.56/14.98 (setminus(Y0, 99.56/14.98 Y1) = 99.56/14.98 emptyset)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1)))) => 99.56/14.98 ( 99.56/14.98 in(Y2, 99.56/14.98 Y0) => 99.56/14.98 in(Y2, 99.56/14.98 Y1)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1)))) => 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y1))) => 99.56/14.98 (~( 99.56/14.98 in(Y2, 99.56/14.98 Y0)))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y0))) => 99.56/14.98 (~( 99.56/14.98 in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1)))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y1) => 99.56/14.98 ( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1)))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 subset( 99.56/14.98 setminus( 99.56/14.98 Y0, Y1), 99.56/14.98 Y0))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 ((setminus( 99.56/14.98 Y0, Y1) = 99.56/14.98 emptyset) => 99.56/14.98 subset( 99.56/14.98 Y0, Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 symdiff( 99.56/14.98 Y0, Y1)) => 99.56/14.98 (!!(( 99.56/14.98 ^[Y3 : $o]: 99.56/14.98 (( 99.56/14.98 in(Y2, 99.56/14.98 Y0) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y1))) => 99.56/14.98 Y3)) => 99.56/14.98 (( 99.56/14.98 ( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y0))) => 99.56/14.98 ( 99.56/14.98 in(Y2, 99.56/14.98 Y1) => Y3)) => 99.56/14.98 Y3))))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y1))) => 99.56/14.98 in(Y2, 99.56/14.98 symdiff( 99.56/14.98 Y0, Y1))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y0))) => 99.56/14.98 (in(Y2, 99.56/14.98 Y1) => 99.56/14.98 in(Y2, 99.56/14.98 symdiff( 99.56/14.98 Y0, Y1))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (in(Y2, 99.56/14.98 Y1) => 99.56/14.98 (~( 99.56/14.98 in(Y2, 99.56/14.98 symdiff( 99.56/14.98 Y0, Y1))))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y0))) => 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y1))) => 99.56/14.98 (~( 99.56/14.98 in(Y2, 99.56/14.98 symdiff( 99.56/14.98 Y0, Y1))))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 in(Y1, 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 in(Y0, 99.56/14.98 setunion( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 in(Y1, 99.56/14.98 setunion( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (??(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 setunion( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))) & 99.56/14.98 (??(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 setunion( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))) & 99.56/14.98 (setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)) = 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 emptyset))))))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (??(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 setunion( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))) & 99.56/14.98 (??(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 setunion( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))) & 99.56/14.98 (setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)) = 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 emptyset))))))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (in(Y1, 99.56/14.98 Y0) => 99.56/14.98 subset( 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset), 99.56/14.98 Y0)))))))) => 99.56/14.98 ((!!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (in(Y1, 99.56/14.98 Y0) => 99.56/14.98 in( 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset), 99.56/14.98 powerset( 99.56/14.98 Y0))))))))) => 99.56/14.98 ((!!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 in( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 powerset( 99.56/14.98 binunion( 99.56/14.98 Y0, Y1))))))))))))) => 99.56/14.98 ((!!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset))) => 99.56/14.98 (( 99.56/14.98 Y2 = Y1) | 99.56/14.98 (Y2 = Y0)))))))))))) => 99.56/14.98 ((!!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (!!(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 Y1) => 99.56/14.98 subset( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 binunion( 99.56/14.98 Y0, Y1)))))))))))))))) => 99.56/14.98 (( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (!!(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 Y1) => 99.56/14.98 in( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 powerset( 99.56/14.98 binunion( 99.56/14.98 Y0, Y1))))))))))))))))) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (!!(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 Y1) => 99.56/14.98 subset( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)), 99.56/14.98 powerset( 99.56/14.98 binunion( 99.56/14.98 Y0, Y1))))))))))))))))) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (!!(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 Y1) => 99.56/14.98 in( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)), 99.56/14.98 powerset( 99.56/14.98 powerset( 99.56/14.98 binunion( 99.56/14.98 Y0, Y1)))))))))))))))))) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (!!(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 Y1) => 99.56/14.98 in( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)), 99.56/14.98 powerset( 99.56/14.98 powerset( 99.56/14.98 binunion( 99.56/14.98 Y0, Y1)))))))))))))))))) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (!!(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 Y1) => 99.56/14.98 in( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)), 99.56/14.98 dsetconstr( 99.56/14.98 powerset( 99.56/14.98 powerset( 99.56/14.98 binunion( 99.56/14.98 Y0, Y1))), 99.56/14.98 (^[Y4 : $i]: 99.56/14.98 (??(( 99.56/14.98 ^[Y5 : $i]: 99.56/14.98 (in(Y5, 99.56/14.98 Y0) & 99.56/14.98 (??(( 99.56/14.98 ^[Y6 : $i]: 99.56/14.98 (in(Y6, 99.56/14.98 Y1) & 99.56/14.98 (Y4 = 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y5, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y5, 99.56/14.98 setadjoin( 99.56/14.98 Y6, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))))))))))))))))))))))))))) => 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 dsetconstr( 99.56/14.98 powerset( 99.56/14.98 powerset( 99.56/14.98 binunion( 99.56/14.98 Y0, Y1))), 99.56/14.98 (^[Y3 : $i]: 99.56/14.98 (??(( 99.56/14.98 ^[Y4 : $i]: 99.56/14.98 (in(Y4, 99.56/14.98 Y0) & 99.56/14.98 (??(( 99.56/14.98 ^[Y5 : $i]: 99.56/14.98 (in(Y5, 99.56/14.98 Y1) & 99.56/14.98 (Y3 = 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y4, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y4, 99.56/14.98 setadjoin( 99.56/14.98 Y5, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))))))))))))) => 99.56/14.98 (??(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (( 99.56/14.98 ??(( 99.56/14.98 ^[Y4 : $i]: 99.56/14.98 (in(Y4, 99.56/14.98 Y1) & 99.56/14.98 (Y2 = 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 setadjoin( 99.56/14.98 Y4, 99.56/14.98 emptyset)), 99.56/14.98 emptyset))))))) & 99.56/14.98 in(Y3, 99.56/14.98 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.56/14.98 inference('lazy_cnf_imply', [status(thm)], ['237'])). 99.56/14.98 tff('239', plain, 99.56/14.98 ~ ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, Y0) => 99.56/14.98 ((~(in(Y2, Y1))) => (~(subset(Y0, Y1)))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, Y0) => ((~(in(Y2, Y1))) => (Y0 != Y1)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (subset(Y0, Y1) => 99.56/14.98 (subset(Y1, Y2) => subset(Y0, Y2)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: subset(Y1, setadjoin(Y0, Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (subset(Y0, Y2) => 99.56/14.98 subset(Y0, setadjoin(Y1, Y2)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (subset(Y0, Y1) => in(Y0, powerset(Y1))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (subset(Y0, Y1) => (subset(Y1, Y0) => (Y0 = Y1))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: (subset(Y0, emptyset) => (Y0 = emptyset))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (subset(Y1, Y0) => in(Y1, powerset(Y0))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (in(Y1, powerset(Y0)) => subset(Y1, Y0)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (subset(Y0, Y1) => 99.56/14.98 subset(powerset(Y0), powerset(Y1))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i > $o]: 99.56/14.98 in(dsetconstr(Y0, Y1), powerset(Y0)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i > $o]: 99.56/14.98 subset(dsetconstr(Y0, Y1), Y0))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, Y0) => 99.56/14.98 in(Y2, binunion(Y0, Y1)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 in(Y1, 99.56/14.98 setadjoin(Y0, 99.56/14.98 setadjoin(Y1, emptyset))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, Y1) => 99.56/14.98 in(Y2, binunion(Y0, Y1)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (!!((^[Y3 : $o]: 99.56/14.98 (in(Y2, 99.56/14.98 binunion(Y0, Y1)) => 99.56/14.98 ((in(Y2, Y0) => Y3) => 99.56/14.98 ((in(Y2, Y1) => Y3) => 99.56/14.98 Y3))))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, binunion(Y0, Y1)) => 99.56/14.98 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 subset(Y0, binunion(Y0, Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 subset(Y1, binunion(Y0, Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, Y0) => 99.56/14.98 (in(Y2, Y1) => 99.56/14.98 in(Y2, 99.56/14.98 binintersect(Y0, Y1))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (subset(Y2, Y0) => 99.56/14.98 (subset(Y2, Y1) => 99.56/14.98 subset(Y2, 99.56/14.98 binintersect(Y0, Y1))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 binintersect(Y0, Y1)) => 99.56/14.98 in(Y2, Y0))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 subset(binintersect(Y0, Y1), 99.56/14.98 Y0))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (subset(Y0, Y1) => 99.56/14.98 (binintersect(Y0, Y1) = Y0)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 ((binintersect(Y0, Y1) = Y1) => 99.56/14.98 subset(Y1, Y0)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 binintersect(Y0, 99.56/14.98 Y1)) => 99.56/14.98 in(Y2, Y1))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 ((~((??((^[Y2 : $i]: 99.56/14.98 (in(Y2, Y0) & 99.56/14.98 in(Y2, Y1))))))) => 99.56/14.98 (binintersect(Y0, Y1) = 99.56/14.98 emptyset)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 subset( 99.56/14.98 binintersect(Y0, Y1), 99.56/14.98 Y1))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (subset(Y1, Y0) => 99.56/14.98 (binintersect(Y0, Y1) = 99.56/14.98 Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 ((binintersect(Y0, Y1) = 99.56/14.98 Y0) => 99.56/14.98 subset(Y0, Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (binintersect( 99.56/14.98 Y0, 99.56/14.98 binunion( 99.56/14.98 Y1, Y2)) = 99.56/14.98 binunion( 99.56/14.98 binintersect( 99.56/14.98 Y0, Y1), 99.56/14.98 binintersect( 99.56/14.98 Y0, Y2)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, Y0) => 99.56/14.98 ((~(in(Y2, 99.56/14.98 Y1))) => 99.56/14.98 in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1)) => 99.56/14.98 in(Y2, Y0))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1)) => 99.56/14.98 (~( 99.56/14.98 in(Y2, Y1))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (subset(Y0, Y1) => 99.56/14.98 (setminus(Y0, Y1) = 99.56/14.98 emptyset)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1)))) => 99.56/14.98 ( 99.56/14.98 in(Y2, 99.56/14.98 Y0) => 99.56/14.98 in(Y2, 99.56/14.98 Y1)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1)))) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y1))) => 99.56/14.98 ( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y0)))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y0))) => 99.56/14.98 (~( 99.56/14.98 in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1)))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y1) => 99.56/14.98 (~( 99.56/14.98 in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1)))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 subset( 99.56/14.98 setminus( 99.56/14.98 Y0, Y1), 99.56/14.98 Y0))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 ((setminus( 99.56/14.98 Y0, Y1) = 99.56/14.98 emptyset) => 99.56/14.98 subset(Y0, 99.56/14.98 Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 symdiff( 99.56/14.98 Y0, Y1)) => 99.56/14.98 (!!(( 99.56/14.98 ^[Y3 : $o]: 99.56/14.98 (( 99.56/14.98 in(Y2, 99.56/14.98 Y0) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y1))) => 99.56/14.98 Y3)) => 99.56/14.98 (( 99.56/14.98 ( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y0))) => 99.56/14.98 ( 99.56/14.98 in(Y2, 99.56/14.98 Y1) => Y3)) => 99.56/14.98 Y3))))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y1))) => 99.56/14.98 in(Y2, 99.56/14.98 symdiff( 99.56/14.98 Y0, Y1))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y0))) => 99.56/14.98 (in(Y2, 99.56/14.98 Y1) => 99.56/14.98 in(Y2, 99.56/14.98 symdiff( 99.56/14.98 Y0, Y1))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (in(Y2, 99.56/14.98 Y1) => 99.56/14.98 (~( 99.56/14.98 in(Y2, 99.56/14.98 symdiff( 99.56/14.98 Y0, Y1))))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y0))) => 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y1))) => 99.56/14.98 (~( 99.56/14.98 in(Y2, 99.56/14.98 symdiff( 99.56/14.98 Y0, Y1))))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 in(Y1, 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 in(Y0, 99.56/14.98 setunion( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 in(Y1, 99.56/14.98 setunion( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (??(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 setunion( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))) & 99.56/14.98 (??(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 setunion( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))) & 99.56/14.98 (setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)) = 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 emptyset))))))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (??(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 setunion( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))) & 99.56/14.98 (??(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 setunion( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))) & 99.56/14.98 (setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)) = 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 emptyset))))))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (in(Y1, 99.56/14.98 Y0) => 99.56/14.98 subset( 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset), 99.56/14.98 Y0)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (in(Y1, 99.56/14.98 Y0) => 99.56/14.98 in( 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset), 99.56/14.98 powerset( 99.56/14.98 Y0))))))))) => 99.56/14.98 ((!!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 in( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 powerset( 99.56/14.98 binunion( 99.56/14.98 Y0, Y1))))))))))))) => 99.56/14.98 ((!!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset))) => 99.56/14.98 (( 99.56/14.98 Y2 = Y1) | 99.56/14.98 (Y2 = Y0)))))))))))) => 99.56/14.98 ((!!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (!!(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 Y1) => 99.56/14.98 subset( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 binunion( 99.56/14.98 Y0, Y1)))))))))))))))) => 99.56/14.98 ((!!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (!!(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 Y1) => 99.56/14.98 in( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 powerset( 99.56/14.98 binunion( 99.56/14.98 Y0, Y1))))))))))))))))) => 99.56/14.98 (( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (!!(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 Y1) => 99.56/14.98 subset( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)), 99.56/14.98 powerset( 99.56/14.98 binunion( 99.56/14.98 Y0, Y1))))))))))))))))) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (!!(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 Y1) => 99.56/14.98 in( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)), 99.56/14.98 powerset( 99.56/14.98 powerset( 99.56/14.98 binunion( 99.56/14.98 Y0, Y1)))))))))))))))))) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (!!(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 Y1) => 99.56/14.98 in( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)), 99.56/14.98 powerset( 99.56/14.98 powerset( 99.56/14.98 binunion( 99.56/14.98 Y0, Y1)))))))))))))))))) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (!!(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 Y1) => 99.56/14.98 in( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)), 99.56/14.98 dsetconstr( 99.56/14.98 powerset( 99.56/14.98 powerset( 99.56/14.98 binunion( 99.56/14.98 Y0, Y1))), 99.56/14.98 (^[Y4 : $i]: 99.56/14.98 (??(( 99.56/14.98 ^[Y5 : $i]: 99.56/14.98 (in(Y5, 99.56/14.98 Y0) & 99.56/14.98 (??(( 99.56/14.98 ^[Y6 : $i]: 99.56/14.98 (in(Y6, 99.56/14.98 Y1) & 99.56/14.98 (Y4 = 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y5, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y5, 99.56/14.98 setadjoin( 99.56/14.98 Y6, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))))))))))))))))))))))))))) => 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 dsetconstr( 99.56/14.98 powerset( 99.56/14.98 powerset( 99.56/14.98 binunion( 99.56/14.98 Y0, Y1))), 99.56/14.98 (^[Y3 : $i]: 99.56/14.98 (??(( 99.56/14.98 ^[Y4 : $i]: 99.56/14.98 (in(Y4, 99.56/14.98 Y0) & 99.56/14.98 (??(( 99.56/14.98 ^[Y5 : $i]: 99.56/14.98 (in(Y5, 99.56/14.98 Y1) & 99.56/14.98 (Y3 = 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y4, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y4, 99.56/14.98 setadjoin( 99.56/14.98 Y5, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))))))))))))) => 99.56/14.98 (??(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (( 99.56/14.98 ??(( 99.56/14.98 ^[Y4 : $i]: 99.56/14.98 (in(Y4, 99.56/14.98 Y1) & 99.56/14.98 (Y2 = 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 setadjoin( 99.56/14.98 Y4, 99.56/14.98 emptyset)), 99.56/14.98 emptyset))))))) & 99.56/14.98 in(Y3, 99.56/14.98 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.56/14.98 inference('lazy_cnf_imply', [status(thm)], ['238'])). 99.56/14.98 tff('240', plain, 99.56/14.98 ~ ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, Y0) => ((~(in(Y2, Y1))) => (Y0 != Y1)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (subset(Y0, Y1) => 99.56/14.98 (subset(Y1, Y2) => subset(Y0, Y2)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(Y1, setadjoin(Y0, Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (subset(Y0, Y2) => 99.56/14.98 subset(Y0, setadjoin(Y1, Y2)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: (subset(Y0, Y1) => in(Y0, powerset(Y1))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (subset(Y0, Y1) => (subset(Y1, Y0) => (Y0 = Y1))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: (subset(Y0, emptyset) => (Y0 = emptyset))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (subset(Y1, Y0) => in(Y1, powerset(Y0))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (in(Y1, powerset(Y0)) => subset(Y1, Y0)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (subset(Y0, Y1) => 99.56/14.98 subset(powerset(Y0), powerset(Y1))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i > $o]: 99.56/14.98 in(dsetconstr(Y0, Y1), powerset(Y0)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i > $o]: 99.56/14.98 subset(dsetconstr(Y0, Y1), Y0))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, Y0) => 99.56/14.98 in(Y2, binunion(Y0, Y1)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 in(Y1, 99.56/14.98 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, Y1) => 99.56/14.98 in(Y2, binunion(Y0, Y1)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (!!((^[Y3 : $o]: 99.56/14.98 (in(Y2, 99.56/14.98 binunion(Y0, Y1)) => 99.56/14.98 ((in(Y2, Y0) => Y3) => 99.56/14.98 ((in(Y2, Y1) => Y3) => 99.56/14.98 Y3))))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, binunion(Y0, Y1)) => 99.56/14.98 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 subset(Y0, binunion(Y0, Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 subset(Y1, binunion(Y0, Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, Y0) => 99.56/14.98 (in(Y2, Y1) => 99.56/14.98 in(Y2, 99.56/14.98 binintersect(Y0, Y1))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (subset(Y2, Y0) => 99.56/14.98 (subset(Y2, Y1) => 99.56/14.98 subset(Y2, 99.56/14.98 binintersect(Y0, Y1))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 binintersect(Y0, Y1)) => 99.56/14.98 in(Y2, Y0))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 subset(binintersect(Y0, Y1), 99.56/14.98 Y0))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (subset(Y0, Y1) => 99.56/14.98 (binintersect(Y0, Y1) = Y0)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 ((binintersect(Y0, Y1) = Y1) => 99.56/14.98 subset(Y1, Y0)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 binintersect(Y0, 99.56/14.98 Y1)) => 99.56/14.98 in(Y2, Y1))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 ((~((??((^[Y2 : $i]: 99.56/14.98 (in(Y2, Y0) & 99.56/14.98 in(Y2, Y1))))))) => 99.56/14.98 (binintersect(Y0, Y1) = 99.56/14.98 emptyset)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 subset( 99.56/14.98 binintersect(Y0, Y1), 99.56/14.98 Y1))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (subset(Y1, Y0) => 99.56/14.98 (binintersect(Y0, Y1) = 99.56/14.98 Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 ((binintersect(Y0, Y1) = 99.56/14.98 Y0) => 99.56/14.98 subset(Y0, Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (binintersect( 99.56/14.98 Y0, 99.56/14.98 binunion(Y1, 99.56/14.98 Y2)) = 99.56/14.98 binunion( 99.56/14.98 binintersect( 99.56/14.98 Y0, Y1), 99.56/14.98 binintersect( 99.56/14.98 Y0, Y2)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, Y0) => 99.56/14.98 ((~(in(Y2, Y1))) => 99.56/14.98 in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1)) => 99.56/14.98 in(Y2, Y0))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1)) => 99.56/14.98 (~(in(Y2, 99.56/14.98 Y1))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (subset(Y0, Y1) => 99.56/14.98 (setminus(Y0, Y1) = 99.56/14.98 emptyset)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 ((~( 99.56/14.98 in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1)))) => 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 in(Y2, 99.56/14.98 Y1)))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1)))) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y1))) => 99.56/14.98 ( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y0)))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y0))) => 99.56/14.98 ( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1)))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!((^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y1) => 99.56/14.98 (~( 99.56/14.98 in(Y2, 99.56/14.98 setminus( 99.56/14.98 Y0, Y1)))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 subset( 99.56/14.98 setminus( 99.56/14.98 Y0, Y1), 99.56/14.98 Y0))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 ((setminus( 99.56/14.98 Y0, Y1) = 99.56/14.98 emptyset) => 99.56/14.98 subset(Y0, 99.56/14.98 Y1)))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 ( 99.56/14.98 in(Y2, 99.56/14.98 symdiff( 99.56/14.98 Y0, Y1)) => 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y3 : $o]: 99.56/14.98 (( 99.56/14.98 in(Y2, 99.56/14.98 Y0) => 99.56/14.98 ( 99.56/14.98 ( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y1))) => 99.56/14.98 Y3)) => 99.56/14.98 (( 99.56/14.98 ( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y0))) => 99.56/14.98 ( 99.56/14.98 in(Y2, 99.56/14.98 Y1) => Y3)) => 99.56/14.98 Y3))))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y1))) => 99.56/14.98 in(Y2, 99.56/14.98 symdiff( 99.56/14.98 Y0, Y1))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y0))) => 99.56/14.98 (in(Y2, 99.56/14.98 Y1) => 99.56/14.98 in(Y2, 99.56/14.98 symdiff( 99.56/14.98 Y0, Y1))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 ( 99.56/14.98 !!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 Y0) => 99.56/14.98 (in(Y2, 99.56/14.98 Y1) => 99.56/14.98 (~( 99.56/14.98 in(Y2, 99.56/14.98 symdiff( 99.56/14.98 Y0, Y1))))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y0))) => 99.56/14.98 (( 99.56/14.98 ~( 99.56/14.98 in(Y2, 99.56/14.98 Y1))) => 99.56/14.98 (~( 99.56/14.98 in(Y2, 99.56/14.98 symdiff( 99.56/14.98 Y0, Y1))))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!((^[Y1 : $i]: 99.56/14.98 in(Y1, 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 in(Y0, 99.56/14.98 setunion( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 in(Y1, 99.56/14.98 setunion( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (??(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 setunion( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))) & 99.56/14.98 (??(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 setunion( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))) & 99.56/14.98 (setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)) = 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y2, 99.56/14.98 setadjoin( 99.56/14.98 Y3, 99.56/14.98 emptyset)), 99.56/14.98 emptyset))))))))))))))))) => 99.56/14.98 ((!!((^[Y0 : $i]: 99.56/14.98 (!!(( 99.56/14.98 ^[Y1 : $i]: 99.56/14.98 (??(( 99.56/14.98 ^[Y2 : $i]: 99.56/14.98 (in(Y2, 99.56/14.98 setunion( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))) & 99.56/14.98 (??(( 99.56/14.98 ^[Y3 : $i]: 99.56/14.98 (in(Y3, 99.56/14.98 setunion( 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 emptyset), 99.56/14.98 setadjoin( 99.56/14.98 setadjoin( 99.56/14.98 Y0, 99.56/14.98 setadjoin( 99.56/14.98 Y1, 99.56/14.98 emptyset)), 99.56/14.98 emptyset)))) & 99.56/14.98 (setadjoin( 99.56/14.98 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)) = 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset))))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 ( 99.67/14.99 !!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (in(Y1, 99.67/14.99 Y0) => 99.67/14.99 subset( 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset), 99.67/14.99 Y0)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (in(Y1, 99.67/14.99 Y0) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset), 99.67/14.99 powerset( 99.67/14.99 Y0))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1))))))))))))) => 99.67/14.99 ((!!(( 99.67/14.99 ^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset))) => 99.67/14.99 (( 99.67/14.99 Y2 = Y1) | 99.67/14.99 (Y2 = Y0)))))))))))) => 99.67/14.99 ((!!(( 99.67/14.99 ^[Y0 : $i]: 99.67/14.99 ( 99.67/14.99 !!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 subset( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 binunion( 99.67/14.99 Y0, Y1)))))))))))))))) => 99.67/14.99 ((!!(( 99.67/14.99 ^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1))))))))))))))))) => 99.67/14.99 ((!!(( 99.67/14.99 ^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 subset( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)), 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1))))))))))))))))) => 99.67/14.99 (( 99.67/14.99 !!(( 99.67/14.99 ^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)), 99.67/14.99 powerset( 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1)))))))))))))))))) => 99.67/14.99 ( 99.67/14.99 ( 99.67/14.99 !!(( 99.67/14.99 ^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)), 99.67/14.99 powerset( 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1)))))))))))))))))) => 99.67/14.99 ( 99.67/14.99 ( 99.67/14.99 !!(( 99.67/14.99 ^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)), 99.67/14.99 dsetconstr( 99.67/14.99 powerset( 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1))), 99.67/14.99 (^[Y4 : $i]: 99.67/14.99 (??(( 99.67/14.99 ^[Y5 : $i]: 99.67/14.99 (in(Y5, 99.67/14.99 Y0) & 99.67/14.99 (??(( 99.67/14.99 ^[Y6 : $i]: 99.67/14.99 (in(Y6, 99.67/14.99 Y1) & 99.67/14.99 (Y4 = 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y5, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y5, 99.67/14.99 setadjoin( 99.67/14.99 Y6, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))))))))))))))))))))))))))) => 99.67/14.99 ( 99.67/14.99 !!(( 99.67/14.99 ^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 dsetconstr( 99.67/14.99 powerset( 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1))), 99.67/14.99 (^[Y3 : $i]: 99.67/14.99 (??(( 99.67/14.99 ^[Y4 : $i]: 99.67/14.99 (in(Y4, 99.67/14.99 Y0) & 99.67/14.99 (??(( 99.67/14.99 ^[Y5 : $i]: 99.67/14.99 (in(Y5, 99.67/14.99 Y1) & 99.67/14.99 (Y3 = 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y4, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y4, 99.67/14.99 setadjoin( 99.67/14.99 Y5, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))))))))))))) => 99.67/14.99 (??(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (( 99.67/14.99 ??(( 99.67/14.99 ^[Y4 : $i]: 99.67/14.99 (in(Y4, 99.67/14.99 Y1) & 99.67/14.99 (Y2 = 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 setadjoin( 99.67/14.99 Y4, 99.67/14.99 emptyset)), 99.67/14.99 emptyset))))))) & 99.67/14.99 in(Y3, 99.67/14.99 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.67/14.99 inference('lazy_cnf_imply', [status(thm)], ['239'])). 99.67/14.99 tff('241', plain, 99.67/14.99 ~ ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, Y0) => ((~(in(Y2, Y1))) => (Y0 != Y1)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (subset(Y0, Y1) => 99.67/14.99 (subset(Y1, Y2) => subset(Y0, Y2)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(Y1, setadjoin(Y0, Y1)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (subset(Y0, Y2) => 99.67/14.99 subset(Y0, setadjoin(Y1, Y2)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: (subset(Y0, Y1) => in(Y0, powerset(Y1))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (subset(Y0, Y1) => (subset(Y1, Y0) => (Y0 = Y1))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: (subset(Y0, emptyset) => (Y0 = emptyset))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (subset(Y1, Y0) => in(Y1, powerset(Y0))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (in(Y1, powerset(Y0)) => subset(Y1, Y0)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (subset(Y0, Y1) => 99.67/14.99 subset(powerset(Y0), powerset(Y1))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i > $o]: 99.67/14.99 in(dsetconstr(Y0, Y1), powerset(Y0)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i > $o]: 99.67/14.99 subset(dsetconstr(Y0, Y1), Y0))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, Y0) => 99.67/14.99 in(Y2, binunion(Y0, Y1)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 in(Y1, 99.67/14.99 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, Y1) => 99.67/14.99 in(Y2, binunion(Y0, Y1)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (!!((^[Y3 : $o]: 99.67/14.99 (in(Y2, binunion(Y0, Y1)) => 99.67/14.99 ((in(Y2, Y0) => Y3) => 99.67/14.99 ((in(Y2, Y1) => Y3) => 99.67/14.99 Y3))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, binunion(Y0, Y1)) => 99.67/14.99 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 subset(Y0, binunion(Y0, Y1)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 subset(Y1, binunion(Y0, Y1)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, Y0) => 99.67/14.99 (in(Y2, Y1) => 99.67/14.99 in(Y2, 99.67/14.99 binintersect(Y0, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (subset(Y2, Y0) => 99.67/14.99 (subset(Y2, Y1) => 99.67/14.99 subset(Y2, 99.67/14.99 binintersect(Y0, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 binintersect(Y0, Y1)) => 99.67/14.99 in(Y2, Y0))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 subset(binintersect(Y0, Y1), Y0))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (subset(Y0, Y1) => 99.67/14.99 (binintersect(Y0, Y1) = Y0)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 ((binintersect(Y0, Y1) = Y1) => 99.67/14.99 subset(Y1, Y0)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 binintersect(Y0, 99.67/14.99 Y1)) => 99.67/14.99 in(Y2, Y1))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 ((~((??((^[Y2 : $i]: 99.67/14.99 (in(Y2, Y0) & 99.67/14.99 in(Y2, Y1))))))) => 99.67/14.99 (binintersect(Y0, Y1) = 99.67/14.99 emptyset)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 subset( 99.67/14.99 binintersect(Y0, Y1), Y1))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (subset(Y1, Y0) => 99.67/14.99 (binintersect(Y0, Y1) = 99.67/14.99 Y1)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 ((binintersect(Y0, Y1) = 99.67/14.99 Y0) => 99.67/14.99 subset(Y0, Y1)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (binintersect( 99.67/14.99 Y0, 99.67/14.99 binunion(Y1, 99.67/14.99 Y2)) = 99.67/14.99 binunion( 99.67/14.99 binintersect( 99.67/14.99 Y0, Y1), 99.67/14.99 binintersect( 99.67/14.99 Y0, Y2)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, Y0) => 99.67/14.99 ((~(in(Y2, Y1))) => 99.67/14.99 in(Y2, 99.67/14.99 setminus( 99.67/14.99 Y0, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 setminus( 99.67/14.99 Y0, Y1)) => 99.67/14.99 in(Y2, Y0))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 setminus( 99.67/14.99 Y0, Y1)) => 99.67/14.99 (~(in(Y2, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (subset(Y0, Y1) => 99.67/14.99 (setminus(Y0, Y1) = 99.67/14.99 emptyset)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 ((~( 99.67/14.99 in(Y2, 99.67/14.99 setminus( 99.67/14.99 Y0, Y1)))) => 99.67/14.99 (in(Y2, Y0) => 99.67/14.99 in(Y2, Y1)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 ((~( 99.67/14.99 in(Y2, 99.67/14.99 setminus( 99.67/14.99 Y0, Y1)))) => 99.67/14.99 (( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y1))) => 99.67/14.99 ( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y0)))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y0))) => 99.67/14.99 ( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 setminus( 99.67/14.99 Y0, Y1)))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 ( 99.67/14.99 in(Y2, 99.67/14.99 Y1) => 99.67/14.99 ( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 setminus( 99.67/14.99 Y0, Y1)))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 subset( 99.67/14.99 setminus(Y0, 99.67/14.99 Y1), Y0))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 ((setminus( 99.67/14.99 Y0, Y1) = 99.67/14.99 emptyset) => 99.67/14.99 subset(Y0, 99.67/14.99 Y1)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 symdiff( 99.67/14.99 Y0, Y1)) => 99.67/14.99 ( 99.67/14.99 !!(( 99.67/14.99 ^[Y3 : $o]: 99.67/14.99 (( 99.67/14.99 in(Y2, 99.67/14.99 Y0) => 99.67/14.99 ( 99.67/14.99 ( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y1))) => 99.67/14.99 Y3)) => 99.67/14.99 (( 99.67/14.99 ( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y0))) => 99.67/14.99 ( 99.67/14.99 in(Y2, 99.67/14.99 Y1) => Y3)) => 99.67/14.99 Y3))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 ( 99.67/14.99 in(Y2, 99.67/14.99 Y0) => 99.67/14.99 ( 99.67/14.99 ( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y1))) => 99.67/14.99 in(Y2, 99.67/14.99 symdiff( 99.67/14.99 Y0, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y0))) => 99.67/14.99 (in(Y2, 99.67/14.99 Y1) => 99.67/14.99 in(Y2, 99.67/14.99 symdiff( 99.67/14.99 Y0, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (in(Y2, 99.67/14.99 Y1) => 99.67/14.99 (~( 99.67/14.99 in(Y2, 99.67/14.99 symdiff( 99.67/14.99 Y0, Y1))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 ( 99.67/14.99 !!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y0))) => 99.67/14.99 (( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y1))) => 99.67/14.99 (~( 99.67/14.99 in(Y2, 99.67/14.99 symdiff( 99.67/14.99 Y0, Y1))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 in(Y1, 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 in(Y0, 99.67/14.99 setunion( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 in(Y1, 99.67/14.99 setunion( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 ( 99.67/14.99 ??(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 setunion( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))) & 99.67/14.99 (??(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 setunion( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))) & 99.67/14.99 (setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)) = 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset))))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (??(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 setunion( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))) & 99.67/14.99 (??(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 setunion( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))) & 99.67/14.99 (setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)) = 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset))))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (in(Y1, 99.67/14.99 Y0) => 99.67/14.99 subset( 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset), 99.67/14.99 Y0)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 ( 99.67/14.99 !!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (in(Y1, 99.67/14.99 Y0) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset), 99.67/14.99 powerset( 99.67/14.99 Y0))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset))) => 99.67/14.99 (( 99.67/14.99 Y2 = Y1) | 99.67/14.99 (Y2 = Y0)))))))))))) => 99.67/14.99 ((!!(( 99.67/14.99 ^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 subset( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 binunion( 99.67/14.99 Y0, Y1)))))))))))))))) => 99.67/14.99 ((!!(( 99.67/14.99 ^[Y0 : $i]: 99.67/14.99 ( 99.67/14.99 !!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1))))))))))))))))) => 99.67/14.99 ((!!(( 99.67/14.99 ^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 subset( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)), 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1))))))))))))))))) => 99.67/14.99 ((!!(( 99.67/14.99 ^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)), 99.67/14.99 powerset( 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1)))))))))))))))))) => 99.67/14.99 (( 99.67/14.99 !!(( 99.67/14.99 ^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)), 99.67/14.99 powerset( 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1)))))))))))))))))) => 99.67/14.99 ( 99.67/14.99 ( 99.67/14.99 !!(( 99.67/14.99 ^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)), 99.67/14.99 dsetconstr( 99.67/14.99 powerset( 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1))), 99.67/14.99 (^[Y4 : $i]: 99.67/14.99 (??(( 99.67/14.99 ^[Y5 : $i]: 99.67/14.99 (in(Y5, 99.67/14.99 Y0) & 99.67/14.99 (??(( 99.67/14.99 ^[Y6 : $i]: 99.67/14.99 (in(Y6, 99.67/14.99 Y1) & 99.67/14.99 (Y4 = 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y5, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y5, 99.67/14.99 setadjoin( 99.67/14.99 Y6, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))))))))))))))))))))))))))) => 99.67/14.99 ( 99.67/14.99 !!(( 99.67/14.99 ^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 dsetconstr( 99.67/14.99 powerset( 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1))), 99.67/14.99 (^[Y3 : $i]: 99.67/14.99 (??(( 99.67/14.99 ^[Y4 : $i]: 99.67/14.99 (in(Y4, 99.67/14.99 Y0) & 99.67/14.99 (??(( 99.67/14.99 ^[Y5 : $i]: 99.67/14.99 (in(Y5, 99.67/14.99 Y1) & 99.67/14.99 (Y3 = 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y4, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y4, 99.67/14.99 setadjoin( 99.67/14.99 Y5, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))))))))))))) => 99.67/14.99 (??(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (( 99.67/14.99 ??(( 99.67/14.99 ^[Y4 : $i]: 99.67/14.99 (in(Y4, 99.67/14.99 Y1) & 99.67/14.99 (Y2 = 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 setadjoin( 99.67/14.99 Y4, 99.67/14.99 emptyset)), 99.67/14.99 emptyset))))))) & 99.67/14.99 in(Y3, 99.67/14.99 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.67/14.99 inference('lazy_cnf_imply', [status(thm)], ['240'])). 99.67/14.99 tff('242', plain, 99.67/14.99 ~ ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (subset(Y0, Y1) => 99.67/14.99 (subset(Y1, Y2) => subset(Y0, Y2)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(Y1, setadjoin(Y0, Y1)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (subset(Y0, Y2) => 99.67/14.99 subset(Y0, setadjoin(Y1, Y2)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: (subset(Y0, Y1) => in(Y0, powerset(Y1))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (subset(Y0, Y1) => (subset(Y1, Y0) => (Y0 = Y1))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: (subset(Y0, emptyset) => (Y0 = emptyset))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (subset(Y1, Y0) => in(Y1, powerset(Y0))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (in(Y1, powerset(Y0)) => subset(Y1, Y0)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (subset(Y0, Y1) => 99.67/14.99 subset(powerset(Y0), powerset(Y1))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i > $o]: 99.67/14.99 in(dsetconstr(Y0, Y1), powerset(Y0)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i > $o]: 99.67/14.99 subset(dsetconstr(Y0, Y1), Y0))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, Y0) => 99.67/14.99 in(Y2, binunion(Y0, Y1)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 in(Y1, 99.67/14.99 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, Y1) => 99.67/14.99 in(Y2, binunion(Y0, Y1)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (!!((^[Y3 : $o]: 99.67/14.99 (in(Y2, binunion(Y0, Y1)) => 99.67/14.99 ((in(Y2, Y0) => Y3) => 99.67/14.99 ((in(Y2, Y1) => Y3) => 99.67/14.99 Y3))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, binunion(Y0, Y1)) => 99.67/14.99 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: subset(Y0, binunion(Y0, Y1)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 subset(Y1, binunion(Y0, Y1)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, Y0) => 99.67/14.99 (in(Y2, Y1) => 99.67/14.99 in(Y2, 99.67/14.99 binintersect(Y0, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (subset(Y2, Y0) => 99.67/14.99 (subset(Y2, Y1) => 99.67/14.99 subset(Y2, 99.67/14.99 binintersect(Y0, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 binintersect(Y0, Y1)) => 99.67/14.99 in(Y2, Y0))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 subset(binintersect(Y0, Y1), Y0))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (subset(Y0, Y1) => 99.67/14.99 (binintersect(Y0, Y1) = Y0)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 ((binintersect(Y0, Y1) = Y1) => 99.67/14.99 subset(Y1, Y0)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 binintersect(Y0, Y1)) => 99.67/14.99 in(Y2, Y1))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 ((~((??((^[Y2 : $i]: 99.67/14.99 (in(Y2, Y0) & 99.67/14.99 in(Y2, Y1))))))) => 99.67/14.99 (binintersect(Y0, Y1) = 99.67/14.99 emptyset)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 subset( 99.67/14.99 binintersect(Y0, Y1), Y1))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (subset(Y1, Y0) => 99.67/14.99 (binintersect(Y0, Y1) = Y1)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 ((binintersect(Y0, Y1) = 99.67/14.99 Y0) => 99.67/14.99 subset(Y0, Y1)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (binintersect(Y0, 99.67/14.99 binunion(Y1, 99.67/14.99 Y2)) = 99.67/14.99 binunion( 99.67/14.99 binintersect( 99.67/14.99 Y0, Y1), 99.67/14.99 binintersect( 99.67/14.99 Y0, Y2)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, Y0) => 99.67/14.99 ((~(in(Y2, Y1))) => 99.67/14.99 in(Y2, 99.67/14.99 setminus(Y0, 99.67/14.99 Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 setminus(Y0, 99.67/14.99 Y1)) => 99.67/14.99 in(Y2, Y0))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 setminus( 99.67/14.99 Y0, Y1)) => 99.67/14.99 (~(in(Y2, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (subset(Y0, Y1) => 99.67/14.99 (setminus(Y0, Y1) = 99.67/14.99 emptyset)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 ((~(in(Y2, 99.67/14.99 setminus( 99.67/14.99 Y0, Y1)))) => 99.67/14.99 (in(Y2, Y0) => 99.67/14.99 in(Y2, Y1)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 ((~( 99.67/14.99 in(Y2, 99.67/14.99 setminus( 99.67/14.99 Y0, Y1)))) => 99.67/14.99 ((~( 99.67/14.99 in(Y2, 99.67/14.99 Y1))) => 99.67/14.99 (~( 99.67/14.99 in(Y2, 99.67/14.99 Y0)))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 ((~( 99.67/14.99 in(Y2, 99.67/14.99 Y0))) => 99.67/14.99 (~( 99.67/14.99 in(Y2, 99.67/14.99 setminus( 99.67/14.99 Y0, Y1)))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y1) => 99.67/14.99 ( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 setminus( 99.67/14.99 Y0, Y1)))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 subset( 99.67/14.99 setminus(Y0, 99.67/14.99 Y1), Y0))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 ((setminus(Y0, 99.67/14.99 Y1) = 99.67/14.99 emptyset) => 99.67/14.99 subset(Y0, Y1)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 symdiff( 99.67/14.99 Y0, Y1)) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $o]: 99.67/14.99 (( 99.67/14.99 in(Y2, 99.67/14.99 Y0) => 99.67/14.99 ( 99.67/14.99 ( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y1))) => 99.67/14.99 Y3)) => 99.67/14.99 (( 99.67/14.99 ( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y0))) => 99.67/14.99 ( 99.67/14.99 in(Y2, 99.67/14.99 Y1) => Y3)) => 99.67/14.99 Y3))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 ( 99.67/14.99 ( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y1))) => 99.67/14.99 in(Y2, 99.67/14.99 symdiff( 99.67/14.99 Y0, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 ( 99.67/14.99 ( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y0))) => 99.67/14.99 ( 99.67/14.99 in(Y2, 99.67/14.99 Y1) => 99.67/14.99 in(Y2, 99.67/14.99 symdiff( 99.67/14.99 Y0, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (in(Y2, 99.67/14.99 Y1) => 99.67/14.99 (~( 99.67/14.99 in(Y2, 99.67/14.99 symdiff( 99.67/14.99 Y0, Y1))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y0))) => 99.67/14.99 (( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y1))) => 99.67/14.99 (~( 99.67/14.99 in(Y2, 99.67/14.99 symdiff( 99.67/14.99 Y0, Y1))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 in(Y1, 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 in(Y0, 99.67/14.99 setunion( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 in(Y1, 99.67/14.99 setunion( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (??(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 setunion( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))) & 99.67/14.99 (??(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 setunion( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))) & 99.67/14.99 (setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)) = 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset))))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 ( 99.67/14.99 ??(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 setunion( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))) & 99.67/14.99 (??(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 setunion( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))) & 99.67/14.99 (setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)) = 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset))))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (in(Y1, 99.67/14.99 Y0) => 99.67/14.99 subset( 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset), 99.67/14.99 Y0)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (in(Y1, 99.67/14.99 Y0) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset), 99.67/14.99 powerset( 99.67/14.99 Y0))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 ( 99.67/14.99 !!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset))) => 99.67/14.99 (( 99.67/14.99 Y2 = Y1) | 99.67/14.99 (Y2 = Y0)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 subset( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 binunion( 99.67/14.99 Y0, Y1)))))))))))))))) => 99.67/14.99 ((!!(( 99.67/14.99 ^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1))))))))))))))))) => 99.67/14.99 ((!!(( 99.67/14.99 ^[Y0 : $i]: 99.67/14.99 ( 99.67/14.99 !!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 subset( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)), 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1))))))))))))))))) => 99.67/14.99 ((!!(( 99.67/14.99 ^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)), 99.67/14.99 powerset( 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1)))))))))))))))))) => 99.67/14.99 ((!!(( 99.67/14.99 ^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)), 99.67/14.99 powerset( 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1)))))))))))))))))) => 99.67/14.99 (( 99.67/14.99 !!(( 99.67/14.99 ^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)), 99.67/14.99 dsetconstr( 99.67/14.99 powerset( 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1))), 99.67/14.99 (^[Y4 : $i]: 99.67/14.99 (??(( 99.67/14.99 ^[Y5 : $i]: 99.67/14.99 (in(Y5, 99.67/14.99 Y0) & 99.67/14.99 (??(( 99.67/14.99 ^[Y6 : $i]: 99.67/14.99 (in(Y6, 99.67/14.99 Y1) & 99.67/14.99 (Y4 = 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y5, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y5, 99.67/14.99 setadjoin( 99.67/14.99 Y6, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))))))))))))))))))))))))))) => 99.67/14.99 ( 99.67/14.99 !!(( 99.67/14.99 ^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 dsetconstr( 99.67/14.99 powerset( 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1))), 99.67/14.99 (^[Y3 : $i]: 99.67/14.99 (??(( 99.67/14.99 ^[Y4 : $i]: 99.67/14.99 (in(Y4, 99.67/14.99 Y0) & 99.67/14.99 (??(( 99.67/14.99 ^[Y5 : $i]: 99.67/14.99 (in(Y5, 99.67/14.99 Y1) & 99.67/14.99 (Y3 = 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y4, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y4, 99.67/14.99 setadjoin( 99.67/14.99 Y5, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))))))))))))) => 99.67/14.99 (??(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (( 99.67/14.99 ??(( 99.67/14.99 ^[Y4 : $i]: 99.67/14.99 (in(Y4, 99.67/14.99 Y1) & 99.67/14.99 (Y2 = 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 setadjoin( 99.67/14.99 Y4, 99.67/14.99 emptyset)), 99.67/14.99 emptyset))))))) & 99.67/14.99 in(Y3, 99.67/14.99 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.67/14.99 inference('lazy_cnf_imply', [status(thm)], ['241'])). 99.67/14.99 tff('243', plain, 99.67/14.99 ~ ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (subset(Y0, Y1) => 99.67/14.99 (subset(Y1, Y2) => subset(Y0, Y2)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(Y1, setadjoin(Y0, Y1)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (subset(Y0, Y2) => 99.67/14.99 subset(Y0, setadjoin(Y1, Y2)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: (subset(Y0, Y1) => in(Y0, powerset(Y1))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (subset(Y0, Y1) => (subset(Y1, Y0) => (Y0 = Y1))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: (subset(Y0, emptyset) => (Y0 = emptyset))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: (subset(Y1, Y0) => in(Y1, powerset(Y0))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (in(Y1, powerset(Y0)) => subset(Y1, Y0)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (subset(Y0, Y1) => 99.67/14.99 subset(powerset(Y0), powerset(Y1))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i > $o]: 99.67/14.99 in(dsetconstr(Y0, Y1), powerset(Y0)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i > $o]: subset(dsetconstr(Y0, Y1), Y0))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, Y0) => 99.67/14.99 in(Y2, binunion(Y0, Y1)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 in(Y1, 99.67/14.99 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, Y1) => 99.67/14.99 in(Y2, binunion(Y0, Y1)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (!!((^[Y3 : $o]: 99.67/14.99 (in(Y2, binunion(Y0, Y1)) => 99.67/14.99 ((in(Y2, Y0) => Y3) => 99.67/14.99 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, binunion(Y0, Y1)) => 99.67/14.99 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: subset(Y0, binunion(Y0, Y1)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: subset(Y1, binunion(Y0, Y1)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, Y0) => 99.67/14.99 (in(Y2, Y1) => 99.67/14.99 in(Y2, binintersect(Y0, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (subset(Y2, Y0) => 99.67/14.99 (subset(Y2, Y1) => 99.67/14.99 subset(Y2, 99.67/14.99 binintersect(Y0, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 binintersect(Y0, Y1)) => 99.67/14.99 in(Y2, Y0))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 subset(binintersect(Y0, Y1), Y0))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (subset(Y0, Y1) => 99.67/14.99 (binintersect(Y0, Y1) = Y0)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 ((binintersect(Y0, Y1) = Y1) => 99.67/14.99 subset(Y1, Y0)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 binintersect(Y0, Y1)) => 99.67/14.99 in(Y2, Y1))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 ((~((??((^[Y2 : $i]: 99.67/14.99 (in(Y2, Y0) & 99.67/14.99 in(Y2, Y1))))))) => 99.67/14.99 (binintersect(Y0, Y1) = 99.67/14.99 emptyset)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 subset(binintersect(Y0, Y1), 99.67/14.99 Y1))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (subset(Y1, Y0) => 99.67/14.99 (binintersect(Y0, Y1) = Y1)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 ((binintersect(Y0, Y1) = Y0) => 99.67/14.99 subset(Y0, Y1)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (binintersect(Y0, 99.67/14.99 binunion(Y1, Y2)) = 99.67/14.99 binunion( 99.67/14.99 binintersect( 99.67/14.99 Y0, Y1), 99.67/14.99 binintersect( 99.67/14.99 Y0, Y2)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, Y0) => 99.67/14.99 ((~(in(Y2, Y1))) => 99.67/14.99 in(Y2, 99.67/14.99 setminus(Y0, 99.67/14.99 Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 setminus(Y0, 99.67/14.99 Y1)) => 99.67/14.99 in(Y2, Y0))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 setminus(Y0, 99.67/14.99 Y1)) => 99.67/14.99 (~(in(Y2, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (subset(Y0, Y1) => 99.67/14.99 (setminus(Y0, Y1) = 99.67/14.99 emptyset)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 ((~(in(Y2, 99.67/14.99 setminus( 99.67/14.99 Y0, Y1)))) => 99.67/14.99 (in(Y2, Y0) => 99.67/14.99 in(Y2, Y1)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 ((~(in(Y2, 99.67/14.99 setminus( 99.67/14.99 Y0, Y1)))) => 99.67/14.99 ((~( 99.67/14.99 in(Y2, Y1))) => 99.67/14.99 (~( 99.67/14.99 in(Y2, Y0)))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 ((~( 99.67/14.99 in(Y2, Y0))) => 99.67/14.99 (~( 99.67/14.99 in(Y2, 99.67/14.99 setminus( 99.67/14.99 Y0, Y1)))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, Y1) => 99.67/14.99 (~( 99.67/14.99 in(Y2, 99.67/14.99 setminus( 99.67/14.99 Y0, Y1)))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 subset( 99.67/14.99 setminus(Y0, 99.67/14.99 Y1), Y0))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 ((setminus(Y0, 99.67/14.99 Y1) = 99.67/14.99 emptyset) => 99.67/14.99 subset(Y0, Y1)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 symdiff( 99.67/14.99 Y0, Y1)) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $o]: 99.67/14.99 (( 99.67/14.99 in(Y2, 99.67/14.99 Y0) => 99.67/14.99 ( 99.67/14.99 ( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y1))) => 99.67/14.99 Y3)) => 99.67/14.99 (( 99.67/14.99 ( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y0))) => 99.67/14.99 ( 99.67/14.99 in(Y2, 99.67/14.99 Y1) => Y3)) => 99.67/14.99 Y3))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y1))) => 99.67/14.99 in(Y2, 99.67/14.99 symdiff( 99.67/14.99 Y0, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y0))) => 99.67/14.99 ( 99.67/14.99 in(Y2, 99.67/14.99 Y1) => 99.67/14.99 in(Y2, 99.67/14.99 symdiff( 99.67/14.99 Y0, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 ( 99.67/14.99 in(Y2, 99.67/14.99 Y0) => 99.67/14.99 ( 99.67/14.99 in(Y2, 99.67/14.99 Y1) => 99.67/14.99 ( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 symdiff( 99.67/14.99 Y0, Y1))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y0))) => 99.67/14.99 (( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y1))) => 99.67/14.99 (~( 99.67/14.99 in(Y2, 99.67/14.99 symdiff( 99.67/14.99 Y0, Y1))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 in(Y1, 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 in(Y0, 99.67/14.99 setunion( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 in(Y1, 99.67/14.99 setunion( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (??(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 setunion( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))) & 99.67/14.99 (??(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 setunion( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))) & 99.67/14.99 (setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)) = 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset))))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (??(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 setunion( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))) & 99.67/14.99 (??(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 setunion( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))) & 99.67/14.99 (setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)) = 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset))))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 ( 99.67/14.99 in(Y1, 99.67/14.99 Y0) => 99.67/14.99 subset( 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset), 99.67/14.99 Y0)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (in(Y1, 99.67/14.99 Y0) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset), 99.67/14.99 powerset( 99.67/14.99 Y0))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 ( 99.67/14.99 !!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset))) => 99.67/14.99 (( 99.67/14.99 Y2 = Y1) | 99.67/14.99 (Y2 = Y0)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 subset( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 binunion( 99.67/14.99 Y0, Y1)))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1))))))))))))))))) => 99.67/14.99 ((!!(( 99.67/14.99 ^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 subset( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)), 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1))))))))))))))))) => 99.67/14.99 ((!!(( 99.67/14.99 ^[Y0 : $i]: 99.67/14.99 ( 99.67/14.99 !!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)), 99.67/14.99 powerset( 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1)))))))))))))))))) => 99.67/14.99 ((!!(( 99.67/14.99 ^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)), 99.67/14.99 powerset( 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1)))))))))))))))))) => 99.67/14.99 ((!!(( 99.67/14.99 ^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)), 99.67/14.99 dsetconstr( 99.67/14.99 powerset( 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1))), 99.67/14.99 (^[Y4 : $i]: 99.67/14.99 (??(( 99.67/14.99 ^[Y5 : $i]: 99.67/14.99 (in(Y5, 99.67/14.99 Y0) & 99.67/14.99 (??(( 99.67/14.99 ^[Y6 : $i]: 99.67/14.99 (in(Y6, 99.67/14.99 Y1) & 99.67/14.99 (Y4 = 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y5, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y5, 99.67/14.99 setadjoin( 99.67/14.99 Y6, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))))))))))))))))))))))))))) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 dsetconstr( 99.67/14.99 powerset( 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1))), 99.67/14.99 (^[Y3 : $i]: 99.67/14.99 (??(( 99.67/14.99 ^[Y4 : $i]: 99.67/14.99 (in(Y4, 99.67/14.99 Y0) & 99.67/14.99 (??(( 99.67/14.99 ^[Y5 : $i]: 99.67/14.99 (in(Y5, 99.67/14.99 Y1) & 99.67/14.99 (Y3 = 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y4, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y4, 99.67/14.99 setadjoin( 99.67/14.99 Y5, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))))))))))))) => 99.67/14.99 (??(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (( 99.67/14.99 ??(( 99.67/14.99 ^[Y4 : $i]: 99.67/14.99 (in(Y4, 99.67/14.99 Y1) & 99.67/14.99 (Y2 = 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 setadjoin( 99.67/14.99 Y4, 99.67/14.99 emptyset)), 99.67/14.99 emptyset))))))) & 99.67/14.99 in(Y3, 99.67/14.99 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.67/14.99 inference('lazy_cnf_imply', [status(thm)], ['242'])). 99.67/14.99 tff('244', plain, 99.67/14.99 ~ ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(Y1, setadjoin(Y0, Y1)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (subset(Y0, Y2) => subset(Y0, setadjoin(Y1, Y2)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: (subset(Y0, Y1) => in(Y0, powerset(Y1))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (subset(Y0, Y1) => (subset(Y1, Y0) => (Y0 = Y1))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: (subset(Y0, emptyset) => (Y0 = emptyset))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: (subset(Y1, Y0) => in(Y1, powerset(Y0))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: (in(Y1, powerset(Y0)) => subset(Y1, Y0)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (subset(Y0, Y1) => 99.67/14.99 subset(powerset(Y0), powerset(Y1))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i > $o]: 99.67/14.99 in(dsetconstr(Y0, Y1), powerset(Y0)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i > $o]: subset(dsetconstr(Y0, Y1), Y0))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, Y0) => 99.67/14.99 in(Y2, binunion(Y0, Y1)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 in(Y1, 99.67/14.99 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, Y1) => 99.67/14.99 in(Y2, binunion(Y0, Y1)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (!!((^[Y3 : $o]: 99.67/14.99 (in(Y2, binunion(Y0, Y1)) => 99.67/14.99 ((in(Y2, Y0) => Y3) => 99.67/14.99 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, binunion(Y0, Y1)) => 99.67/14.99 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: subset(Y0, binunion(Y0, Y1)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: subset(Y1, binunion(Y0, Y1)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, Y0) => 99.67/14.99 (in(Y2, Y1) => 99.67/14.99 in(Y2, binintersect(Y0, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (subset(Y2, Y0) => 99.67/14.99 (subset(Y2, Y1) => 99.67/14.99 subset(Y2, 99.67/14.99 binintersect(Y0, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, binintersect(Y0, Y1)) => 99.67/14.99 in(Y2, Y0))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 subset(binintersect(Y0, Y1), Y0))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (subset(Y0, Y1) => 99.67/14.99 (binintersect(Y0, Y1) = Y0)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 ((binintersect(Y0, Y1) = Y1) => 99.67/14.99 subset(Y1, Y0)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 binintersect(Y0, Y1)) => 99.67/14.99 in(Y2, Y1))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 ((~((??((^[Y2 : $i]: 99.67/14.99 (in(Y2, Y0) & 99.67/14.99 in(Y2, Y1))))))) => 99.67/14.99 (binintersect(Y0, Y1) = 99.67/14.99 emptyset)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 subset(binintersect(Y0, Y1), 99.67/14.99 Y1))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (subset(Y1, Y0) => 99.67/14.99 (binintersect(Y0, Y1) = Y1)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 ((binintersect(Y0, Y1) = Y0) => 99.67/14.99 subset(Y0, Y1)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (binintersect(Y0, 99.67/14.99 binunion(Y1, Y2)) = 99.67/14.99 binunion( 99.67/14.99 binintersect(Y0, 99.67/14.99 Y1), 99.67/14.99 binintersect(Y0, 99.67/14.99 Y2)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, Y0) => 99.67/14.99 ((~(in(Y2, Y1))) => 99.67/14.99 in(Y2, 99.67/14.99 setminus(Y0, 99.67/14.99 Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 setminus(Y0, 99.67/14.99 Y1)) => 99.67/14.99 in(Y2, Y0))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 setminus(Y0, 99.67/14.99 Y1)) => 99.67/14.99 (~(in(Y2, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (subset(Y0, Y1) => 99.67/14.99 (setminus(Y0, Y1) = 99.67/14.99 emptyset)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 ((~(in(Y2, 99.67/14.99 setminus( 99.67/14.99 Y0, Y1)))) => 99.67/14.99 (in(Y2, Y0) => 99.67/14.99 in(Y2, Y1)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 ((~(in(Y2, 99.67/14.99 setminus( 99.67/14.99 Y0, Y1)))) => 99.67/14.99 ((~(in(Y2, 99.67/14.99 Y1))) => 99.67/14.99 (~(in(Y2, 99.67/14.99 Y0)))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 ((~(in(Y2, 99.67/14.99 Y0))) => 99.67/14.99 (~(in(Y2, 99.67/14.99 setminus( 99.67/14.99 Y0, Y1)))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, Y1) => 99.67/14.99 (~( 99.67/14.99 in(Y2, 99.67/14.99 setminus( 99.67/14.99 Y0, Y1)))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 subset( 99.67/14.99 setminus(Y0, Y1), 99.67/14.99 Y0))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 ((setminus(Y0, 99.67/14.99 Y1) = 99.67/14.99 emptyset) => 99.67/14.99 subset(Y0, Y1)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 ( 99.67/14.99 in(Y2, 99.67/14.99 symdiff( 99.67/14.99 Y0, Y1)) => 99.67/14.99 ( 99.67/14.99 !!(( 99.67/14.99 ^[Y3 : $o]: 99.67/14.99 (( 99.67/14.99 in(Y2, 99.67/14.99 Y0) => 99.67/14.99 ( 99.67/14.99 ( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y1))) => 99.67/14.99 Y3)) => 99.67/14.99 (( 99.67/14.99 ( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y0))) => 99.67/14.99 ( 99.67/14.99 in(Y2, 99.67/14.99 Y1) => Y3)) => 99.67/14.99 Y3))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y1))) => 99.67/14.99 in(Y2, 99.67/14.99 symdiff( 99.67/14.99 Y0, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y0))) => 99.67/14.99 (in(Y2, 99.67/14.99 Y1) => 99.67/14.99 in(Y2, 99.67/14.99 symdiff( 99.67/14.99 Y0, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 ( 99.67/14.99 in(Y2, 99.67/14.99 Y1) => 99.67/14.99 ( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 symdiff( 99.67/14.99 Y0, Y1))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 ( 99.67/14.99 ( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y0))) => 99.67/14.99 ( 99.67/14.99 ( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y1))) => 99.67/14.99 ( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 symdiff( 99.67/14.99 Y0, Y1))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 in(Y1, 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 in(Y0, 99.67/14.99 setunion( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 in(Y1, 99.67/14.99 setunion( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (??(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 setunion( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))) & 99.67/14.99 (??(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 setunion( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))) & 99.67/14.99 (setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)) = 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset))))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (??(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 setunion( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))) & 99.67/14.99 (??(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 setunion( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))) & 99.67/14.99 (setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)) = 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset))))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (in(Y1, 99.67/14.99 Y0) => 99.67/14.99 subset( 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset), 99.67/14.99 Y0)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 ( 99.67/14.99 in(Y1, 99.67/14.99 Y0) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset), 99.67/14.99 powerset( 99.67/14.99 Y0))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset))) => 99.67/14.99 (( 99.67/14.99 Y2 = Y1) | 99.67/14.99 (Y2 = Y0)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 ( 99.67/14.99 !!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 subset( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 binunion( 99.67/14.99 Y0, Y1)))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1))))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 subset( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)), 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1))))))))))))))))) => 99.67/14.99 ((!!(( 99.67/14.99 ^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)), 99.67/14.99 powerset( 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1)))))))))))))))))) => 99.67/14.99 ((!!(( 99.67/14.99 ^[Y0 : $i]: 99.67/14.99 ( 99.67/14.99 !!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)), 99.67/14.99 powerset( 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1)))))))))))))))))) => 99.67/14.99 ((!!(( 99.67/14.99 ^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)), 99.67/14.99 dsetconstr( 99.67/14.99 powerset( 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1))), 99.67/14.99 (^[Y4 : $i]: 99.67/14.99 (??(( 99.67/14.99 ^[Y5 : $i]: 99.67/14.99 (in(Y5, 99.67/14.99 Y0) & 99.67/14.99 (??(( 99.67/14.99 ^[Y6 : $i]: 99.67/14.99 (in(Y6, 99.67/14.99 Y1) & 99.67/14.99 (Y4 = 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y5, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y5, 99.67/14.99 setadjoin( 99.67/14.99 Y6, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))))))))))))))))))))))))))) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 dsetconstr( 99.67/14.99 powerset( 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1))), 99.67/14.99 (^[Y3 : $i]: 99.67/14.99 (??(( 99.67/14.99 ^[Y4 : $i]: 99.67/14.99 (in(Y4, 99.67/14.99 Y0) & 99.67/14.99 (??(( 99.67/14.99 ^[Y5 : $i]: 99.67/14.99 (in(Y5, 99.67/14.99 Y1) & 99.67/14.99 (Y3 = 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y4, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y4, 99.67/14.99 setadjoin( 99.67/14.99 Y5, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))))))))))))) => 99.67/14.99 (??(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (( 99.67/14.99 ??(( 99.67/14.99 ^[Y4 : $i]: 99.67/14.99 (in(Y4, 99.67/14.99 Y1) & 99.67/14.99 (Y2 = 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 setadjoin( 99.67/14.99 Y4, 99.67/14.99 emptyset)), 99.67/14.99 emptyset))))))) & 99.67/14.99 in(Y3, 99.67/14.99 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.67/14.99 inference('lazy_cnf_imply', [status(thm)], ['243'])). 99.67/14.99 tff('245', plain, 99.67/14.99 ~ ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (subset(Y0, Y2) => subset(Y0, setadjoin(Y1, Y2)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: (subset(Y0, Y1) => in(Y0, powerset(Y1))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (subset(Y0, Y1) => (subset(Y1, Y0) => (Y0 = Y1))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: (subset(Y0, emptyset) => (Y0 = emptyset))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: (subset(Y1, Y0) => in(Y1, powerset(Y0))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: (in(Y1, powerset(Y0)) => subset(Y1, Y0)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (subset(Y0, Y1) => 99.67/14.99 subset(powerset(Y0), powerset(Y1))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i > $o]: 99.67/14.99 in(dsetconstr(Y0, Y1), powerset(Y0)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i > $o]: subset(dsetconstr(Y0, Y1), Y0))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, Y0) => in(Y2, binunion(Y0, Y1)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 in(Y1, 99.67/14.99 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, Y1) => 99.67/14.99 in(Y2, binunion(Y0, Y1)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (!!((^[Y3 : $o]: 99.67/14.99 (in(Y2, binunion(Y0, Y1)) => 99.67/14.99 ((in(Y2, Y0) => Y3) => 99.67/14.99 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, binunion(Y0, Y1)) => 99.67/14.99 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: subset(Y0, binunion(Y0, Y1)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: subset(Y1, binunion(Y0, Y1)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, Y0) => 99.67/14.99 (in(Y2, Y1) => 99.67/14.99 in(Y2, binintersect(Y0, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (subset(Y2, Y0) => 99.67/14.99 (subset(Y2, Y1) => 99.67/14.99 subset(Y2, 99.67/14.99 binintersect(Y0, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, binintersect(Y0, Y1)) => 99.67/14.99 in(Y2, Y0))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 subset(binintersect(Y0, Y1), Y0))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (subset(Y0, Y1) => 99.67/14.99 (binintersect(Y0, Y1) = Y0)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 ((binintersect(Y0, Y1) = Y1) => 99.67/14.99 subset(Y1, Y0)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 binintersect(Y0, Y1)) => 99.67/14.99 in(Y2, Y1))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 ((~((??((^[Y2 : $i]: 99.67/14.99 (in(Y2, Y0) & 99.67/14.99 in(Y2, Y1))))))) => 99.67/14.99 (binintersect(Y0, Y1) = 99.67/14.99 emptyset)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 subset(binintersect(Y0, Y1), 99.67/14.99 Y1))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (subset(Y1, Y0) => 99.67/14.99 (binintersect(Y0, Y1) = Y1)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 ((binintersect(Y0, Y1) = Y0) => 99.67/14.99 subset(Y0, Y1)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (binintersect(Y0, 99.67/14.99 binunion(Y1, Y2)) = 99.67/14.99 binunion( 99.67/14.99 binintersect(Y0, 99.67/14.99 Y1), 99.67/14.99 binintersect(Y0, 99.67/14.99 Y2)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, Y0) => 99.67/14.99 ((~(in(Y2, Y1))) => 99.67/14.99 in(Y2, 99.67/14.99 setminus(Y0, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 setminus(Y0, Y1)) => 99.67/14.99 in(Y2, Y0))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 setminus(Y0, 99.67/14.99 Y1)) => 99.67/14.99 (~(in(Y2, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (subset(Y0, Y1) => 99.67/14.99 (setminus(Y0, Y1) = 99.67/14.99 emptyset)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 ((~(in(Y2, 99.67/14.99 setminus( 99.67/14.99 Y0, Y1)))) => 99.67/14.99 (in(Y2, Y0) => 99.67/14.99 in(Y2, Y1)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 ((~(in(Y2, 99.67/14.99 setminus( 99.67/14.99 Y0, Y1)))) => 99.67/14.99 ((~(in(Y2, Y1))) => 99.67/14.99 (~(in(Y2, Y0)))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 ((~(in(Y2, Y0))) => 99.67/14.99 (~(in(Y2, 99.67/14.99 setminus( 99.67/14.99 Y0, Y1)))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, Y1) => 99.67/14.99 (~(in(Y2, 99.67/14.99 setminus( 99.67/14.99 Y0, Y1)))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 subset( 99.67/14.99 setminus(Y0, Y1), 99.67/14.99 Y0))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 ((setminus(Y0, Y1) = 99.67/14.99 emptyset) => 99.67/14.99 subset(Y0, Y1)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 symdiff( 99.67/14.99 Y0, Y1)) => 99.67/14.99 ( 99.67/14.99 !!(( 99.67/14.99 ^[Y3 : $o]: 99.67/14.99 (( 99.67/14.99 in(Y2, 99.67/14.99 Y0) => 99.67/14.99 ( 99.67/14.99 ( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y1))) => 99.67/14.99 Y3)) => 99.67/14.99 (( 99.67/14.99 ( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y0))) => 99.67/14.99 ( 99.67/14.99 in(Y2, 99.67/14.99 Y1) => Y3)) => 99.67/14.99 Y3))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 ( 99.67/14.99 in(Y2, 99.67/14.99 Y0) => 99.67/14.99 ( 99.67/14.99 ( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y1))) => 99.67/14.99 in(Y2, 99.67/14.99 symdiff( 99.67/14.99 Y0, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y0))) => 99.67/14.99 (in(Y2, 99.67/14.99 Y1) => 99.67/14.99 in(Y2, 99.67/14.99 symdiff( 99.67/14.99 Y0, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (in(Y2, 99.67/14.99 Y1) => 99.67/14.99 (~( 99.67/14.99 in(Y2, 99.67/14.99 symdiff( 99.67/14.99 Y0, Y1))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y0))) => 99.67/14.99 ( 99.67/14.99 ( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y1))) => 99.67/14.99 ( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 symdiff( 99.67/14.99 Y0, Y1))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 in(Y1, 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 in(Y0, 99.67/14.99 setunion( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 in(Y1, 99.67/14.99 setunion( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 ( 99.67/14.99 ??(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 setunion( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))) & 99.67/14.99 (??(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 setunion( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))) & 99.67/14.99 (setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)) = 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset))))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (??(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 setunion( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))) & 99.67/14.99 (??(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 setunion( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))) & 99.67/14.99 (setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)) = 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset))))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (in(Y1, 99.67/14.99 Y0) => 99.67/14.99 subset( 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset), 99.67/14.99 Y0)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (in(Y1, 99.67/14.99 Y0) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset), 99.67/14.99 powerset( 99.67/14.99 Y0))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 ( 99.67/14.99 !!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset))) => 99.67/14.99 (( 99.67/14.99 Y2 = Y1) | 99.67/14.99 (Y2 = Y0)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 subset( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 binunion( 99.67/14.99 Y0, Y1)))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 ( 99.67/14.99 !!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1))))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 subset( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)), 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1))))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)), 99.67/14.99 powerset( 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1)))))))))))))))))) => 99.67/14.99 ((!!(( 99.67/14.99 ^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)), 99.67/14.99 powerset( 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1)))))))))))))))))) => 99.67/14.99 ((!!(( 99.67/14.99 ^[Y0 : $i]: 99.67/14.99 ( 99.67/14.99 !!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)), 99.67/14.99 dsetconstr( 99.67/14.99 powerset( 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1))), 99.67/14.99 (^[Y4 : $i]: 99.67/14.99 (??(( 99.67/14.99 ^[Y5 : $i]: 99.67/14.99 (in(Y5, 99.67/14.99 Y0) & 99.67/14.99 (??(( 99.67/14.99 ^[Y6 : $i]: 99.67/14.99 (in(Y6, 99.67/14.99 Y1) & 99.67/14.99 (Y4 = 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y5, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y5, 99.67/14.99 setadjoin( 99.67/14.99 Y6, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))))))))))))))))))))))))))) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y0 : $i]: 99.67/14.99 ( 99.67/14.99 !!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 dsetconstr( 99.67/14.99 powerset( 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1))), 99.67/14.99 (^[Y3 : $i]: 99.67/14.99 (??(( 99.67/14.99 ^[Y4 : $i]: 99.67/14.99 (in(Y4, 99.67/14.99 Y0) & 99.67/14.99 (??(( 99.67/14.99 ^[Y5 : $i]: 99.67/14.99 (in(Y5, 99.67/14.99 Y1) & 99.67/14.99 (Y3 = 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y4, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y4, 99.67/14.99 setadjoin( 99.67/14.99 Y5, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))))))))))))) => 99.67/14.99 (??(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (( 99.67/14.99 ??(( 99.67/14.99 ^[Y4 : $i]: 99.67/14.99 (in(Y4, 99.67/14.99 Y1) & 99.67/14.99 (Y2 = 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 setadjoin( 99.67/14.99 Y4, 99.67/14.99 emptyset)), 99.67/14.99 emptyset))))))) & 99.67/14.99 in(Y3, 99.67/14.99 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.67/14.99 inference('lazy_cnf_imply', [status(thm)], ['244'])). 99.67/14.99 tff('246', plain, 99.67/14.99 ~ ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: (subset(Y0, Y1) => in(Y0, powerset(Y1))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (subset(Y0, Y1) => (subset(Y1, Y0) => (Y0 = Y1))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: (subset(Y0, emptyset) => (Y0 = emptyset))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: (subset(Y1, Y0) => in(Y1, powerset(Y0))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: (in(Y1, powerset(Y0)) => subset(Y1, Y0)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (subset(Y0, Y1) => 99.67/14.99 subset(powerset(Y0), powerset(Y1))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i > $o]: 99.67/14.99 in(dsetconstr(Y0, Y1), powerset(Y0)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i > $o]: subset(dsetconstr(Y0, Y1), Y0))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, Y0) => in(Y2, binunion(Y0, Y1)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, Y1) => 99.67/14.99 in(Y2, binunion(Y0, Y1)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (!!((^[Y3 : $o]: 99.67/14.99 (in(Y2, binunion(Y0, Y1)) => 99.67/14.99 ((in(Y2, Y0) => Y3) => 99.67/14.99 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, binunion(Y0, Y1)) => 99.67/14.99 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: subset(Y0, binunion(Y0, Y1)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: subset(Y1, binunion(Y0, Y1)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, Y0) => 99.67/14.99 (in(Y2, Y1) => 99.67/14.99 in(Y2, binintersect(Y0, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (subset(Y2, Y0) => 99.67/14.99 (subset(Y2, Y1) => 99.67/14.99 subset(Y2, 99.67/14.99 binintersect(Y0, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, binintersect(Y0, Y1)) => 99.67/14.99 in(Y2, Y0))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 subset(binintersect(Y0, Y1), Y0))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (subset(Y0, Y1) => 99.67/14.99 (binintersect(Y0, Y1) = Y0)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 ((binintersect(Y0, Y1) = Y1) => 99.67/14.99 subset(Y1, Y0)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 binintersect(Y0, Y1)) => 99.67/14.99 in(Y2, Y1))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 ((~((??((^[Y2 : $i]: 99.67/14.99 (in(Y2, Y0) & 99.67/14.99 in(Y2, Y1))))))) => 99.67/14.99 (binintersect(Y0, Y1) = emptyset)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 subset(binintersect(Y0, Y1), Y1))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (subset(Y1, Y0) => 99.67/14.99 (binintersect(Y0, Y1) = Y1)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 ((binintersect(Y0, Y1) = Y0) => 99.67/14.99 subset(Y0, Y1)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (binintersect(Y0, 99.67/14.99 binunion(Y1, Y2)) = 99.67/14.99 binunion( 99.67/14.99 binintersect(Y0, 99.67/14.99 Y1), 99.67/14.99 binintersect(Y0, 99.67/14.99 Y2)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, Y0) => 99.67/14.99 ((~(in(Y2, Y1))) => 99.67/14.99 in(Y2, 99.67/14.99 setminus(Y0, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 setminus(Y0, Y1)) => 99.67/14.99 in(Y2, Y0))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 setminus(Y0, Y1)) => 99.67/14.99 (~(in(Y2, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (subset(Y0, Y1) => 99.67/14.99 (setminus(Y0, Y1) = 99.67/14.99 emptyset)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 ((~(in(Y2, 99.67/14.99 setminus( 99.67/14.99 Y0, Y1)))) => 99.67/14.99 (in(Y2, Y0) => 99.67/14.99 in(Y2, Y1)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 ((~(in(Y2, 99.67/14.99 setminus( 99.67/14.99 Y0, Y1)))) => 99.67/14.99 ((~(in(Y2, Y1))) => 99.67/14.99 (~(in(Y2, Y0)))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 ((~(in(Y2, Y0))) => 99.67/14.99 (~(in(Y2, 99.67/14.99 setminus( 99.67/14.99 Y0, Y1)))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, Y1) => 99.67/14.99 (~(in(Y2, 99.67/14.99 setminus( 99.67/14.99 Y0, Y1)))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 subset( 99.67/14.99 setminus(Y0, Y1), 99.67/14.99 Y0))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 ((setminus(Y0, Y1) = 99.67/14.99 emptyset) => 99.67/14.99 subset(Y0, Y1)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 symdiff( 99.67/14.99 Y0, Y1)) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $o]: 99.67/14.99 (( 99.67/14.99 in(Y2, 99.67/14.99 Y0) => 99.67/14.99 ( 99.67/14.99 ( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y1))) => 99.67/14.99 Y3)) => 99.67/14.99 (( 99.67/14.99 ( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y0))) => 99.67/14.99 ( 99.67/14.99 in(Y2, 99.67/14.99 Y1) => Y3)) => 99.67/14.99 Y3))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 ( 99.67/14.99 ( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y1))) => 99.67/14.99 in(Y2, 99.67/14.99 symdiff( 99.67/14.99 Y0, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 ( 99.67/14.99 ( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y0))) => 99.67/14.99 ( 99.67/14.99 in(Y2, 99.67/14.99 Y1) => 99.67/14.99 in(Y2, 99.67/14.99 symdiff( 99.67/14.99 Y0, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (in(Y2, 99.67/14.99 Y1) => 99.67/14.99 (~( 99.67/14.99 in(Y2, 99.67/14.99 symdiff( 99.67/14.99 Y0, Y1))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y0))) => 99.67/14.99 (( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y1))) => 99.67/14.99 (~( 99.67/14.99 in(Y2, 99.67/14.99 symdiff( 99.67/14.99 Y0, Y1))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 in(Y1, 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 in(Y0, 99.67/14.99 setunion( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 in(Y1, 99.67/14.99 setunion( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (??(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 setunion( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))) & 99.67/14.99 (??(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 setunion( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))) & 99.67/14.99 (setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)) = 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset))))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 ( 99.67/14.99 ??(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 setunion( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))) & 99.67/14.99 (??(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 setunion( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))) & 99.67/14.99 (setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)) = 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset))))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (in(Y1, 99.67/14.99 Y0) => 99.67/14.99 subset( 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset), 99.67/14.99 Y0)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (in(Y1, 99.67/14.99 Y0) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset), 99.67/14.99 powerset( 99.67/14.99 Y0))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 ( 99.67/14.99 !!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset))) => 99.67/14.99 (( 99.67/14.99 Y2 = Y1) | 99.67/14.99 (Y2 = Y0)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 subset( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 binunion( 99.67/14.99 Y0, Y1)))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1))))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 ( 99.67/14.99 !!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 subset( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)), 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1))))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)), 99.67/14.99 powerset( 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1)))))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)), 99.67/14.99 powerset( 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1)))))))))))))))))) => 99.67/14.99 ((!!(( 99.67/14.99 ^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)), 99.67/14.99 dsetconstr( 99.67/14.99 powerset( 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1))), 99.67/14.99 (^[Y4 : $i]: 99.67/14.99 (??(( 99.67/14.99 ^[Y5 : $i]: 99.67/14.99 (in(Y5, 99.67/14.99 Y0) & 99.67/14.99 (??(( 99.67/14.99 ^[Y6 : $i]: 99.67/14.99 (in(Y6, 99.67/14.99 Y1) & 99.67/14.99 (Y4 = 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y5, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y5, 99.67/14.99 setadjoin( 99.67/14.99 Y6, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))))))))))))))))))))))))))) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 dsetconstr( 99.67/14.99 powerset( 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1))), 99.67/14.99 (^[Y3 : $i]: 99.67/14.99 (??(( 99.67/14.99 ^[Y4 : $i]: 99.67/14.99 (in(Y4, 99.67/14.99 Y0) & 99.67/14.99 (??(( 99.67/14.99 ^[Y5 : $i]: 99.67/14.99 (in(Y5, 99.67/14.99 Y1) & 99.67/14.99 (Y3 = 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y4, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y4, 99.67/14.99 setadjoin( 99.67/14.99 Y5, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))))))))))))) => 99.67/14.99 (??(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (( 99.67/14.99 ??(( 99.67/14.99 ^[Y4 : $i]: 99.67/14.99 (in(Y4, 99.67/14.99 Y1) & 99.67/14.99 (Y2 = 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 setadjoin( 99.67/14.99 Y4, 99.67/14.99 emptyset)), 99.67/14.99 emptyset))))))) & 99.67/14.99 in(Y3, 99.67/14.99 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.67/14.99 inference('lazy_cnf_imply', [status(thm)], ['245'])). 99.67/14.99 tff('247', plain, 99.67/14.99 ~ ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (subset(Y0, Y1) => (subset(Y1, Y0) => (Y0 = Y1))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: (subset(Y0, emptyset) => (Y0 = emptyset))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: (subset(Y1, Y0) => in(Y1, powerset(Y0))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: (in(Y1, powerset(Y0)) => subset(Y1, Y0)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (subset(Y0, Y1) => 99.67/14.99 subset(powerset(Y0), powerset(Y1))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i > $o]: 99.67/14.99 in(dsetconstr(Y0, Y1), powerset(Y0)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i > $o]: subset(dsetconstr(Y0, Y1), Y0))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, Y0) => in(Y2, binunion(Y0, Y1)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, Y1) => in(Y2, binunion(Y0, Y1)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (!!((^[Y3 : $o]: 99.67/14.99 (in(Y2, binunion(Y0, Y1)) => 99.67/14.99 ((in(Y2, Y0) => Y3) => 99.67/14.99 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, binunion(Y0, Y1)) => 99.67/14.99 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: subset(Y0, binunion(Y0, Y1)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: subset(Y1, binunion(Y0, Y1)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, Y0) => 99.67/14.99 (in(Y2, Y1) => 99.67/14.99 in(Y2, binintersect(Y0, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (subset(Y2, Y0) => 99.67/14.99 (subset(Y2, Y1) => 99.67/14.99 subset(Y2, 99.67/14.99 binintersect(Y0, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, binintersect(Y0, Y1)) => 99.67/14.99 in(Y2, Y0))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 subset(binintersect(Y0, Y1), Y0))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (subset(Y0, Y1) => 99.67/14.99 (binintersect(Y0, Y1) = Y0)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 ((binintersect(Y0, Y1) = Y1) => 99.67/14.99 subset(Y1, Y0)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 binintersect(Y0, Y1)) => 99.67/14.99 in(Y2, Y1))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 ((~((??((^[Y2 : $i]: 99.67/14.99 (in(Y2, Y0) & 99.67/14.99 in(Y2, Y1))))))) => 99.67/14.99 (binintersect(Y0, Y1) = emptyset)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 subset(binintersect(Y0, Y1), Y1))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (subset(Y1, Y0) => 99.67/14.99 (binintersect(Y0, Y1) = Y1)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 ((binintersect(Y0, Y1) = Y0) => 99.67/14.99 subset(Y0, Y1)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (binintersect(Y0, 99.67/14.99 binunion(Y1, Y2)) = 99.67/14.99 binunion( 99.67/14.99 binintersect(Y0, Y1), 99.67/14.99 binintersect(Y0, Y2)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, Y0) => 99.67/14.99 ((~(in(Y2, Y1))) => 99.67/14.99 in(Y2, 99.67/14.99 setminus(Y0, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 setminus(Y0, Y1)) => 99.67/14.99 in(Y2, Y0))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 setminus(Y0, Y1)) => 99.67/14.99 (~(in(Y2, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (subset(Y0, Y1) => 99.67/14.99 (setminus(Y0, Y1) = 99.67/14.99 emptyset)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 ((~(in(Y2, 99.67/14.99 setminus( 99.67/14.99 Y0, Y1)))) => 99.67/14.99 (in(Y2, Y0) => 99.67/14.99 in(Y2, Y1)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 ((~(in(Y2, 99.67/14.99 setminus( 99.67/14.99 Y0, Y1)))) => 99.67/14.99 ((~(in(Y2, Y1))) => 99.67/14.99 (~(in(Y2, Y0)))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 ((~(in(Y2, Y0))) => 99.67/14.99 (~(in(Y2, 99.67/14.99 setminus( 99.67/14.99 Y0, Y1)))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, Y1) => 99.67/14.99 (~(in(Y2, 99.67/14.99 setminus( 99.67/14.99 Y0, Y1)))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 subset( 99.67/14.99 setminus(Y0, Y1), 99.67/14.99 Y0))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 ((setminus(Y0, Y1) = 99.67/14.99 emptyset) => 99.67/14.99 subset(Y0, Y1)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 symdiff( 99.67/14.99 Y0, Y1)) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $o]: 99.67/14.99 (( 99.67/14.99 in(Y2, 99.67/14.99 Y0) => 99.67/14.99 ( 99.67/14.99 ( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y1))) => 99.67/14.99 Y3)) => 99.67/14.99 (( 99.67/14.99 ( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y0))) => 99.67/14.99 ( 99.67/14.99 in(Y2, 99.67/14.99 Y1) => Y3)) => 99.67/14.99 Y3))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (in(Y2, Y0) => 99.67/14.99 (( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y1))) => 99.67/14.99 in(Y2, 99.67/14.99 symdiff( 99.67/14.99 Y0, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y0))) => 99.67/14.99 ( 99.67/14.99 in(Y2, 99.67/14.99 Y1) => 99.67/14.99 in(Y2, 99.67/14.99 symdiff( 99.67/14.99 Y0, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 ( 99.67/14.99 in(Y2, 99.67/14.99 Y0) => 99.67/14.99 ( 99.67/14.99 in(Y2, 99.67/14.99 Y1) => 99.67/14.99 ( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 symdiff( 99.67/14.99 Y0, Y1))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!((^[Y2 : $i]: 99.67/14.99 (( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y0))) => 99.67/14.99 (( 99.67/14.99 ~( 99.67/14.99 in(Y2, 99.67/14.99 Y1))) => 99.67/14.99 (~( 99.67/14.99 in(Y2, 99.67/14.99 symdiff( 99.67/14.99 Y0, Y1))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 in(Y1, 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 in(Y0, 99.67/14.99 setunion( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 in(Y1, 99.67/14.99 setunion( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (??(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 setunion( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))) & 99.67/14.99 (??(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 setunion( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))) & 99.67/14.99 (setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)) = 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset))))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (??(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 setunion( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))) & 99.67/14.99 (??(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 setunion( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)))) & 99.67/14.99 (setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)) = 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset))))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 ( 99.67/14.99 in(Y1, 99.67/14.99 Y0) => 99.67/14.99 subset( 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset), 99.67/14.99 Y0)))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (in(Y1, 99.67/14.99 Y0) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset), 99.67/14.99 powerset( 99.67/14.99 Y0))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!((^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y0, 99.67/14.99 setadjoin( 99.67/14.99 Y1, 99.67/14.99 emptyset))) => 99.67/14.99 (( 99.67/14.99 Y2 = Y1) | 99.67/14.99 (Y2 = Y0)))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 ( 99.67/14.99 !!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 subset( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 binunion( 99.67/14.99 Y0, Y1)))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1))))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 subset( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)), 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1))))))))))))))))) => 99.67/14.99 ((!!((^[Y0 : $i]: 99.67/14.99 ( 99.67/14.99 !!(( 99.67/14.99 ^[Y1 : $i]: 99.67/14.99 (!!(( 99.67/14.99 ^[Y2 : $i]: 99.67/14.99 (in(Y2, 99.67/14.99 Y0) => 99.67/14.99 (!!(( 99.67/14.99 ^[Y3 : $i]: 99.67/14.99 (in(Y3, 99.67/14.99 Y1) => 99.67/14.99 in( 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 emptyset), 99.67/14.99 setadjoin( 99.67/14.99 setadjoin( 99.67/14.99 Y2, 99.67/14.99 setadjoin( 99.67/14.99 Y3, 99.67/14.99 emptyset)), 99.67/14.99 emptyset)), 99.67/14.99 powerset( 99.67/14.99 powerset( 99.67/14.99 binunion( 99.67/14.99 Y0, Y1)))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)), 99.67/15.00 powerset( 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1)))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)), 99.67/15.00 dsetconstr( 99.67/15.00 powerset( 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1))), 99.67/15.00 (^[Y4 : $i]: 99.67/15.00 (??(( 99.67/15.00 ^[Y5 : $i]: 99.67/15.00 (in(Y5, 99.67/15.00 Y0) & 99.67/15.00 (??(( 99.67/15.00 ^[Y6 : $i]: 99.67/15.00 (in(Y6, 99.67/15.00 Y1) & 99.67/15.00 (Y4 = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y5, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y5, 99.67/15.00 setadjoin( 99.67/15.00 Y6, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))))))))))))))))))))))))))) => 99.67/15.00 (!!((^[Y0 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 dsetconstr( 99.67/15.00 powerset( 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1))), 99.67/15.00 (^[Y3 : $i]: 99.67/15.00 (??(( 99.67/15.00 ^[Y4 : $i]: 99.67/15.00 (in(Y4, 99.67/15.00 Y0) & 99.67/15.00 (??(( 99.67/15.00 ^[Y5 : $i]: 99.67/15.00 (in(Y5, 99.67/15.00 Y1) & 99.67/15.00 (Y3 = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y4, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y4, 99.67/15.00 setadjoin( 99.67/15.00 Y5, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))))))))))))) => 99.67/15.00 (??(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (( 99.67/15.00 ??(( 99.67/15.00 ^[Y4 : $i]: 99.67/15.00 (in(Y4, 99.67/15.00 Y1) & 99.67/15.00 (Y2 = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 setadjoin( 99.67/15.00 Y4, 99.67/15.00 emptyset)), 99.67/15.00 emptyset))))))) & 99.67/15.00 in(Y3, 99.67/15.00 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.67/15.00 inference('lazy_cnf_imply', [status(thm)], ['246'])). 99.67/15.00 tff('248', plain, 99.67/15.00 ~ ((!!((^[Y0 : $i]: (subset(Y0, emptyset) => (Y0 = emptyset))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: (subset(Y1, Y0) => in(Y1, powerset(Y0))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: (in(Y1, powerset(Y0)) => subset(Y1, Y0)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (subset(Y0, Y1) => 99.67/15.00 subset(powerset(Y0), powerset(Y1))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i > $o]: in(dsetconstr(Y0, Y1), powerset(Y0)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i > $o]: subset(dsetconstr(Y0, Y1), Y0))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => in(Y2, binunion(Y0, Y1)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y1) => in(Y2, binunion(Y0, Y1)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (!!((^[Y3 : $o]: 99.67/15.00 (in(Y2, binunion(Y0, Y1)) => 99.67/15.00 ((in(Y2, Y0) => Y3) => 99.67/15.00 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, binunion(Y0, Y1)) => 99.67/15.00 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: subset(Y0, binunion(Y0, Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: subset(Y1, binunion(Y0, Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => 99.67/15.00 (in(Y2, Y1) => 99.67/15.00 in(Y2, binintersect(Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (subset(Y2, Y0) => 99.67/15.00 (subset(Y2, Y1) => 99.67/15.00 subset(Y2, binintersect(Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, binintersect(Y0, Y1)) => 99.67/15.00 in(Y2, Y0))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 subset(binintersect(Y0, Y1), Y0))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (subset(Y0, Y1) => 99.67/15.00 (binintersect(Y0, Y1) = Y0)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ((binintersect(Y0, Y1) = Y1) => 99.67/15.00 subset(Y1, Y0)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, binintersect(Y0, Y1)) => 99.67/15.00 in(Y2, Y1))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ((~((??((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) & in(Y2, Y1))))))) => 99.67/15.00 (binintersect(Y0, Y1) = emptyset)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 subset(binintersect(Y0, Y1), Y1))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (subset(Y1, Y0) => 99.67/15.00 (binintersect(Y0, Y1) = Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ((binintersect(Y0, Y1) = Y0) => 99.67/15.00 subset(Y0, Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (binintersect(Y0, 99.67/15.00 binunion(Y1, Y2)) = 99.67/15.00 binunion( 99.67/15.00 binintersect(Y0, Y1), 99.67/15.00 binintersect(Y0, Y2)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => 99.67/15.00 ((~(in(Y2, Y1))) => 99.67/15.00 in(Y2, 99.67/15.00 setminus(Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 setminus(Y0, Y1)) => 99.67/15.00 in(Y2, Y0))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 setminus(Y0, Y1)) => 99.67/15.00 (~(in(Y2, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (subset(Y0, Y1) => 99.67/15.00 (setminus(Y0, Y1) = 99.67/15.00 emptyset)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~(in(Y2, 99.67/15.00 setminus(Y0, 99.67/15.00 Y1)))) => 99.67/15.00 (in(Y2, Y0) => 99.67/15.00 in(Y2, Y1)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~(in(Y2, 99.67/15.00 setminus( 99.67/15.00 Y0, Y1)))) => 99.67/15.00 ((~(in(Y2, Y1))) => 99.67/15.00 (~(in(Y2, Y0)))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~(in(Y2, Y0))) => 99.67/15.00 (~(in(Y2, 99.67/15.00 setminus( 99.67/15.00 Y0, Y1)))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y1) => 99.67/15.00 (~(in(Y2, 99.67/15.00 setminus( 99.67/15.00 Y0, Y1)))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 subset( 99.67/15.00 setminus(Y0, Y1), 99.67/15.00 Y0))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ((setminus(Y0, Y1) = 99.67/15.00 emptyset) => 99.67/15.00 subset(Y0, Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 symdiff( 99.67/15.00 Y0, Y1)) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $o]: 99.67/15.00 ( 99.67/15.00 ( 99.67/15.00 in(Y2, 99.67/15.00 Y0) => 99.67/15.00 ( 99.67/15.00 ( 99.67/15.00 ~( 99.67/15.00 in(Y2, 99.67/15.00 Y1))) => 99.67/15.00 Y3)) => 99.67/15.00 ( 99.67/15.00 ( 99.67/15.00 ( 99.67/15.00 ~( 99.67/15.00 in(Y2, 99.67/15.00 Y0))) => 99.67/15.00 ( 99.67/15.00 in(Y2, 99.67/15.00 Y1) => Y3)) => 99.67/15.00 Y3))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => 99.67/15.00 ((~( 99.67/15.00 in(Y2, 99.67/15.00 Y1))) => 99.67/15.00 in(Y2, 99.67/15.00 symdiff( 99.67/15.00 Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~( 99.67/15.00 in(Y2, 99.67/15.00 Y0))) => 99.67/15.00 (in(Y2, 99.67/15.00 Y1) => 99.67/15.00 in(Y2, 99.67/15.00 symdiff( 99.67/15.00 Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 ( 99.67/15.00 in(Y2, 99.67/15.00 Y1) => 99.67/15.00 ( 99.67/15.00 ~( 99.67/15.00 in(Y2, 99.67/15.00 symdiff( 99.67/15.00 Y0, Y1))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ( 99.67/15.00 ( 99.67/15.00 ~( 99.67/15.00 in(Y2, 99.67/15.00 Y0))) => 99.67/15.00 ( 99.67/15.00 ( 99.67/15.00 ~( 99.67/15.00 in(Y2, 99.67/15.00 Y1))) => 99.67/15.00 ( 99.67/15.00 ~( 99.67/15.00 in(Y2, 99.67/15.00 symdiff( 99.67/15.00 Y0, Y1))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 in(Y1, 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 in(Y0, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 in(Y1, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (??(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 ( 99.67/15.00 in(Y2, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))) & 99.67/15.00 ( 99.67/15.00 ??(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))) & 99.67/15.00 (setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)) = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (??(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))) & 99.67/15.00 (??(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))) & 99.67/15.00 (setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)) = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (in(Y1, 99.67/15.00 Y0) => 99.67/15.00 subset( 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset), 99.67/15.00 Y0)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ( 99.67/15.00 in(Y1, 99.67/15.00 Y0) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset), 99.67/15.00 powerset( 99.67/15.00 Y0))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset))) => 99.67/15.00 (( 99.67/15.00 Y2 = Y1) | 99.67/15.00 (Y2 = Y0)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 subset( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 binunion( 99.67/15.00 Y0, Y1)))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y1 : $i]: 99.67/15.00 ( 99.67/15.00 !!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 subset( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)), 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)), 99.67/15.00 powerset( 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1)))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 ( 99.67/15.00 !!(( 99.67/15.00 ^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)), 99.67/15.00 powerset( 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1)))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)), 99.67/15.00 dsetconstr( 99.67/15.00 powerset( 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1))), 99.67/15.00 (^[Y4 : $i]: 99.67/15.00 (??(( 99.67/15.00 ^[Y5 : $i]: 99.67/15.00 (in(Y5, 99.67/15.00 Y0) & 99.67/15.00 (??(( 99.67/15.00 ^[Y6 : $i]: 99.67/15.00 (in(Y6, 99.67/15.00 Y1) & 99.67/15.00 (Y4 = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y5, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y5, 99.67/15.00 setadjoin( 99.67/15.00 Y6, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))))))))))))))))))))))))))) => 99.67/15.00 (!!((^[Y0 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 dsetconstr( 99.67/15.00 powerset( 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1))), 99.67/15.00 (^[Y3 : $i]: 99.67/15.00 (??(( 99.67/15.00 ^[Y4 : $i]: 99.67/15.00 (in(Y4, 99.67/15.00 Y0) & 99.67/15.00 (??(( 99.67/15.00 ^[Y5 : $i]: 99.67/15.00 (in(Y5, 99.67/15.00 Y1) & 99.67/15.00 (Y3 = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y4, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y4, 99.67/15.00 setadjoin( 99.67/15.00 Y5, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))))))))))))) => 99.67/15.00 (??(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (( 99.67/15.00 ??(( 99.67/15.00 ^[Y4 : $i]: 99.67/15.00 (in(Y4, 99.67/15.00 Y1) & 99.67/15.00 (Y2 = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 setadjoin( 99.67/15.00 Y4, 99.67/15.00 emptyset)), 99.67/15.00 emptyset))))))) & 99.67/15.00 in(Y3, 99.67/15.00 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.67/15.00 inference('lazy_cnf_imply', [status(thm)], ['247'])). 99.67/15.00 tff('249', plain, 99.67/15.00 ~ ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: (subset(Y1, Y0) => in(Y1, powerset(Y0))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: (in(Y1, powerset(Y0)) => subset(Y1, Y0)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (subset(Y0, Y1) => subset(powerset(Y0), powerset(Y1))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i > $o]: in(dsetconstr(Y0, Y1), powerset(Y0)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i > $o]: subset(dsetconstr(Y0, Y1), Y0))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => in(Y2, binunion(Y0, Y1)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y1) => in(Y2, binunion(Y0, Y1)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (!!((^[Y3 : $o]: 99.67/15.00 (in(Y2, binunion(Y0, Y1)) => 99.67/15.00 ((in(Y2, Y0) => Y3) => 99.67/15.00 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, binunion(Y0, Y1)) => 99.67/15.00 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: subset(Y0, binunion(Y0, Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: subset(Y1, binunion(Y0, Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => 99.67/15.00 (in(Y2, Y1) => 99.67/15.00 in(Y2, binintersect(Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (subset(Y2, Y0) => 99.67/15.00 (subset(Y2, Y1) => 99.67/15.00 subset(Y2, binintersect(Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, binintersect(Y0, Y1)) => 99.67/15.00 in(Y2, Y0))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 subset(binintersect(Y0, Y1), Y0))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (subset(Y0, Y1) => 99.67/15.00 (binintersect(Y0, Y1) = Y0)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ((binintersect(Y0, Y1) = Y1) => 99.67/15.00 subset(Y1, Y0)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, binintersect(Y0, Y1)) => 99.67/15.00 in(Y2, Y1))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ((~((??((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) & in(Y2, Y1))))))) => 99.67/15.00 (binintersect(Y0, Y1) = emptyset)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 subset(binintersect(Y0, Y1), Y1))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (subset(Y1, Y0) => 99.67/15.00 (binintersect(Y0, Y1) = Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ((binintersect(Y0, Y1) = Y0) => 99.67/15.00 subset(Y0, Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (binintersect(Y0, 99.67/15.00 binunion(Y1, Y2)) = 99.67/15.00 binunion( 99.67/15.00 binintersect(Y0, Y1), 99.67/15.00 binintersect(Y0, Y2)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => 99.67/15.00 ((~(in(Y2, Y1))) => 99.67/15.00 in(Y2, 99.67/15.00 setminus(Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 setminus(Y0, Y1)) => 99.67/15.00 in(Y2, Y0))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 setminus(Y0, Y1)) => 99.67/15.00 (~(in(Y2, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (subset(Y0, Y1) => 99.67/15.00 (setminus(Y0, Y1) = 99.67/15.00 emptyset)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~(in(Y2, 99.67/15.00 setminus(Y0, 99.67/15.00 Y1)))) => 99.67/15.00 (in(Y2, Y0) => 99.67/15.00 in(Y2, Y1)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~(in(Y2, 99.67/15.00 setminus(Y0, 99.67/15.00 Y1)))) => 99.67/15.00 ((~(in(Y2, Y1))) => 99.67/15.00 (~(in(Y2, Y0)))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~(in(Y2, Y0))) => 99.67/15.00 (~(in(Y2, 99.67/15.00 setminus( 99.67/15.00 Y0, Y1)))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y1) => 99.67/15.00 (~(in(Y2, 99.67/15.00 setminus( 99.67/15.00 Y0, Y1)))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 subset( 99.67/15.00 setminus(Y0, Y1), Y0))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ((setminus(Y0, Y1) = 99.67/15.00 emptyset) => 99.67/15.00 subset(Y0, Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 symdiff( 99.67/15.00 Y0, Y1)) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $o]: 99.67/15.00 (( 99.67/15.00 in(Y2, 99.67/15.00 Y0) => 99.67/15.00 ( 99.67/15.00 ( 99.67/15.00 ~( 99.67/15.00 in(Y2, 99.67/15.00 Y1))) => 99.67/15.00 Y3)) => 99.67/15.00 ( 99.67/15.00 ( 99.67/15.00 ( 99.67/15.00 ~( 99.67/15.00 in(Y2, 99.67/15.00 Y0))) => 99.67/15.00 ( 99.67/15.00 in(Y2, 99.67/15.00 Y1) => Y3)) => 99.67/15.00 Y3))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => 99.67/15.00 ((~( 99.67/15.00 in(Y2, Y1))) => 99.67/15.00 in(Y2, 99.67/15.00 symdiff( 99.67/15.00 Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~( 99.67/15.00 in(Y2, Y0))) => 99.67/15.00 (in(Y2, Y1) => 99.67/15.00 in(Y2, 99.67/15.00 symdiff( 99.67/15.00 Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => 99.67/15.00 (in(Y2, 99.67/15.00 Y1) => 99.67/15.00 ( 99.67/15.00 ~( 99.67/15.00 in(Y2, 99.67/15.00 symdiff( 99.67/15.00 Y0, Y1))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (( 99.67/15.00 ~( 99.67/15.00 in(Y2, 99.67/15.00 Y0))) => 99.67/15.00 ( 99.67/15.00 ( 99.67/15.00 ~( 99.67/15.00 in(Y2, 99.67/15.00 Y1))) => 99.67/15.00 ( 99.67/15.00 ~( 99.67/15.00 in(Y2, 99.67/15.00 symdiff( 99.67/15.00 Y0, Y1))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 in(Y1, 99.67/15.00 setadjoin(Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 in(Y0, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 in(Y1, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (??(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))) & 99.67/15.00 ( 99.67/15.00 ??(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))) & 99.67/15.00 (setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)) = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (??(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 ( 99.67/15.00 in(Y2, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))) & 99.67/15.00 ( 99.67/15.00 ??(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))) & 99.67/15.00 (setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)) = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (in(Y1, Y0) => 99.67/15.00 subset( 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset), 99.67/15.00 Y0)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (in(Y1, 99.67/15.00 Y0) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset), 99.67/15.00 powerset( 99.67/15.00 Y0))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ( 99.67/15.00 !!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset))) => 99.67/15.00 (( 99.67/15.00 Y2 = Y1) | 99.67/15.00 (Y2 = Y0)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 subset( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 binunion( 99.67/15.00 Y0, Y1)))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y1 : $i]: 99.67/15.00 ( 99.67/15.00 !!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 subset( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)), 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)), 99.67/15.00 powerset( 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1)))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)), 99.67/15.00 powerset( 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1)))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 ( 99.67/15.00 !!(( 99.67/15.00 ^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)), 99.67/15.00 dsetconstr( 99.67/15.00 powerset( 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1))), 99.67/15.00 (^[Y4 : $i]: 99.67/15.00 (??(( 99.67/15.00 ^[Y5 : $i]: 99.67/15.00 (in(Y5, 99.67/15.00 Y0) & 99.67/15.00 (??(( 99.67/15.00 ^[Y6 : $i]: 99.67/15.00 (in(Y6, 99.67/15.00 Y1) & 99.67/15.00 (Y4 = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y5, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y5, 99.67/15.00 setadjoin( 99.67/15.00 Y6, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))))))))))))))))))))))))))) => 99.67/15.00 (!!((^[Y0 : $i]: 99.67/15.00 ( 99.67/15.00 !!(( 99.67/15.00 ^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 dsetconstr( 99.67/15.00 powerset( 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1))), 99.67/15.00 (^[Y3 : $i]: 99.67/15.00 (??(( 99.67/15.00 ^[Y4 : $i]: 99.67/15.00 (in(Y4, 99.67/15.00 Y0) & 99.67/15.00 (??(( 99.67/15.00 ^[Y5 : $i]: 99.67/15.00 (in(Y5, 99.67/15.00 Y1) & 99.67/15.00 (Y3 = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y4, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y4, 99.67/15.00 setadjoin( 99.67/15.00 Y5, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))))))))))))) => 99.67/15.00 (??(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (( 99.67/15.00 ??(( 99.67/15.00 ^[Y4 : $i]: 99.67/15.00 (in(Y4, 99.67/15.00 Y1) & 99.67/15.00 (Y2 = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 setadjoin( 99.67/15.00 Y4, 99.67/15.00 emptyset)), 99.67/15.00 emptyset))))))) & 99.67/15.00 in(Y3, 99.67/15.00 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.67/15.00 inference('lazy_cnf_imply', [status(thm)], ['248'])). 99.67/15.00 tff('250', plain, 99.67/15.00 ~ ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: (in(Y1, powerset(Y0)) => subset(Y1, Y0)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (subset(Y0, Y1) => subset(powerset(Y0), powerset(Y1))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i > $o]: in(dsetconstr(Y0, Y1), powerset(Y0)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i > $o]: subset(dsetconstr(Y0, Y1), Y0))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => in(Y2, binunion(Y0, Y1)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y1) => in(Y2, binunion(Y0, Y1)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (!!((^[Y3 : $o]: 99.67/15.00 (in(Y2, binunion(Y0, Y1)) => 99.67/15.00 ((in(Y2, Y0) => Y3) => 99.67/15.00 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, binunion(Y0, Y1)) => 99.67/15.00 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: subset(Y0, binunion(Y0, Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: subset(Y1, binunion(Y0, Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => 99.67/15.00 (in(Y2, Y1) => 99.67/15.00 in(Y2, binintersect(Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (subset(Y2, Y0) => 99.67/15.00 (subset(Y2, Y1) => 99.67/15.00 subset(Y2, binintersect(Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, binintersect(Y0, Y1)) => 99.67/15.00 in(Y2, Y0))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 subset(binintersect(Y0, Y1), Y0))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (subset(Y0, Y1) => 99.67/15.00 (binintersect(Y0, Y1) = Y0)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ((binintersect(Y0, Y1) = Y1) => 99.67/15.00 subset(Y1, Y0)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, binintersect(Y0, Y1)) => 99.67/15.00 in(Y2, Y1))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ((~((??((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) & in(Y2, Y1))))))) => 99.67/15.00 (binintersect(Y0, Y1) = emptyset)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 subset(binintersect(Y0, Y1), Y1))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (subset(Y1, Y0) => 99.67/15.00 (binintersect(Y0, Y1) = Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ((binintersect(Y0, Y1) = Y0) => 99.67/15.00 subset(Y0, Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (binintersect(Y0, 99.67/15.00 binunion(Y1, Y2)) = 99.67/15.00 binunion( 99.67/15.00 binintersect(Y0, Y1), 99.67/15.00 binintersect(Y0, Y2)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => 99.67/15.00 ((~(in(Y2, Y1))) => 99.67/15.00 in(Y2, 99.67/15.00 setminus(Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 setminus(Y0, Y1)) => 99.67/15.00 in(Y2, Y0))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 setminus(Y0, Y1)) => 99.67/15.00 (~(in(Y2, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (subset(Y0, Y1) => 99.67/15.00 (setminus(Y0, Y1) = emptyset)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~(in(Y2, 99.67/15.00 setminus(Y0, 99.67/15.00 Y1)))) => 99.67/15.00 (in(Y2, Y0) => 99.67/15.00 in(Y2, Y1)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~(in(Y2, 99.67/15.00 setminus(Y0, 99.67/15.00 Y1)))) => 99.67/15.00 ((~(in(Y2, Y1))) => 99.67/15.00 (~(in(Y2, Y0)))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~(in(Y2, Y0))) => 99.67/15.00 (~(in(Y2, 99.67/15.00 setminus(Y0, 99.67/15.00 Y1)))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y1) => 99.67/15.00 (~(in(Y2, 99.67/15.00 setminus( 99.67/15.00 Y0, Y1)))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 subset( 99.67/15.00 setminus(Y0, Y1), Y0))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ((setminus(Y0, Y1) = 99.67/15.00 emptyset) => 99.67/15.00 subset(Y0, Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 symdiff(Y0, 99.67/15.00 Y1)) => 99.67/15.00 (!!((^[Y3 : $o]: 99.67/15.00 (( 99.67/15.00 in(Y2, 99.67/15.00 Y0) => 99.67/15.00 ( 99.67/15.00 ( 99.67/15.00 ~( 99.67/15.00 in(Y2, 99.67/15.00 Y1))) => 99.67/15.00 Y3)) => 99.67/15.00 (( 99.67/15.00 ( 99.67/15.00 ~( 99.67/15.00 in(Y2, 99.67/15.00 Y0))) => 99.67/15.00 ( 99.67/15.00 in(Y2, 99.67/15.00 Y1) => Y3)) => 99.67/15.00 Y3))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => 99.67/15.00 ((~(in(Y2, 99.67/15.00 Y1))) => 99.67/15.00 in(Y2, 99.67/15.00 symdiff( 99.67/15.00 Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~(in(Y2, 99.67/15.00 Y0))) => 99.67/15.00 (in(Y2, Y1) => 99.67/15.00 in(Y2, 99.67/15.00 symdiff( 99.67/15.00 Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => 99.67/15.00 (in(Y2, Y1) => 99.67/15.00 (~( 99.67/15.00 in(Y2, 99.67/15.00 symdiff( 99.67/15.00 Y0, Y1))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~( 99.67/15.00 in(Y2, 99.67/15.00 Y0))) => 99.67/15.00 (( 99.67/15.00 ~( 99.67/15.00 in(Y2, 99.67/15.00 Y1))) => 99.67/15.00 ( 99.67/15.00 ~( 99.67/15.00 in(Y2, 99.67/15.00 symdiff( 99.67/15.00 Y0, Y1))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 in(Y1, 99.67/15.00 setadjoin(Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 in(Y0, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 in(Y1, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (??((^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))) & 99.67/15.00 (??(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))) & 99.67/15.00 (setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)) = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (??(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))) & 99.67/15.00 ( 99.67/15.00 ??(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))) & 99.67/15.00 (setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)) = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (in(Y1, Y0) => 99.67/15.00 subset( 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset), 99.67/15.00 Y0)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (in(Y1, Y0) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset), 99.67/15.00 powerset( 99.67/15.00 Y0))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ( 99.67/15.00 !!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset))) => 99.67/15.00 (( 99.67/15.00 Y2 = Y1) | 99.67/15.00 (Y2 = Y0)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 subset( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 binunion( 99.67/15.00 Y0, Y1)))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 subset( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)), 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y1 : $i]: 99.67/15.00 ( 99.67/15.00 !!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)), 99.67/15.00 powerset( 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1)))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)), 99.67/15.00 powerset( 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1)))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)), 99.67/15.00 dsetconstr( 99.67/15.00 powerset( 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1))), 99.67/15.00 (^[Y4 : $i]: 99.67/15.00 (??(( 99.67/15.00 ^[Y5 : $i]: 99.67/15.00 (in(Y5, 99.67/15.00 Y0) & 99.67/15.00 (??(( 99.67/15.00 ^[Y6 : $i]: 99.67/15.00 (in(Y6, 99.67/15.00 Y1) & 99.67/15.00 (Y4 = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y5, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y5, 99.67/15.00 setadjoin( 99.67/15.00 Y6, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))))))))))))))))))))))))))) => 99.67/15.00 (!!((^[Y0 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 dsetconstr( 99.67/15.00 powerset( 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1))), 99.67/15.00 (^[Y3 : $i]: 99.67/15.00 (??(( 99.67/15.00 ^[Y4 : $i]: 99.67/15.00 (in(Y4, 99.67/15.00 Y0) & 99.67/15.00 (??(( 99.67/15.00 ^[Y5 : $i]: 99.67/15.00 (in(Y5, 99.67/15.00 Y1) & 99.67/15.00 (Y3 = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y4, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y4, 99.67/15.00 setadjoin( 99.67/15.00 Y5, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))))))))))))) => 99.67/15.00 (??(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (( 99.67/15.00 ??(( 99.67/15.00 ^[Y4 : $i]: 99.67/15.00 (in(Y4, 99.67/15.00 Y1) & 99.67/15.00 (Y2 = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 setadjoin( 99.67/15.00 Y4, 99.67/15.00 emptyset)), 99.67/15.00 emptyset))))))) & 99.67/15.00 in(Y3, 99.67/15.00 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.67/15.00 inference('lazy_cnf_imply', [status(thm)], ['249'])). 99.67/15.00 tff('251', plain, 99.67/15.00 ~ ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (subset(Y0, Y1) => subset(powerset(Y0), powerset(Y1))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i > $o]: in(dsetconstr(Y0, Y1), powerset(Y0)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i > $o]: subset(dsetconstr(Y0, Y1), Y0))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => in(Y2, binunion(Y0, Y1)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y1) => in(Y2, binunion(Y0, Y1)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (!!((^[Y3 : $o]: 99.67/15.00 (in(Y2, binunion(Y0, Y1)) => 99.67/15.00 ((in(Y2, Y0) => Y3) => 99.67/15.00 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, binunion(Y0, Y1)) => 99.67/15.00 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: subset(Y0, binunion(Y0, Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: subset(Y1, binunion(Y0, Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => 99.67/15.00 (in(Y2, Y1) => 99.67/15.00 in(Y2, binintersect(Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (subset(Y2, Y0) => 99.67/15.00 (subset(Y2, Y1) => 99.67/15.00 subset(Y2, binintersect(Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, binintersect(Y0, Y1)) => 99.67/15.00 in(Y2, Y0))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y0))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (subset(Y0, Y1) => 99.67/15.00 (binintersect(Y0, Y1) = Y0)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ((binintersect(Y0, Y1) = Y1) => 99.67/15.00 subset(Y1, Y0)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, binintersect(Y0, Y1)) => 99.67/15.00 in(Y2, Y1))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ((~((??((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) & in(Y2, Y1))))))) => 99.67/15.00 (binintersect(Y0, Y1) = emptyset)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 subset(binintersect(Y0, Y1), Y1))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (subset(Y1, Y0) => 99.67/15.00 (binintersect(Y0, Y1) = Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ((binintersect(Y0, Y1) = Y0) => 99.67/15.00 subset(Y0, Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (binintersect(Y0, 99.67/15.00 binunion(Y1, Y2)) = 99.67/15.00 binunion( 99.67/15.00 binintersect(Y0, Y1), 99.67/15.00 binintersect(Y0, Y2)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => 99.67/15.00 ((~(in(Y2, Y1))) => 99.67/15.00 in(Y2, setminus(Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, setminus(Y0, Y1)) => 99.67/15.00 in(Y2, Y0))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 setminus(Y0, Y1)) => 99.67/15.00 (~(in(Y2, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (subset(Y0, Y1) => 99.67/15.00 (setminus(Y0, Y1) = emptyset)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~(in(Y2, 99.67/15.00 setminus(Y0, Y1)))) => 99.67/15.00 (in(Y2, Y0) => 99.67/15.00 in(Y2, Y1)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~(in(Y2, 99.67/15.00 setminus(Y0, 99.67/15.00 Y1)))) => 99.67/15.00 ((~(in(Y2, Y1))) => 99.67/15.00 (~(in(Y2, Y0)))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~(in(Y2, Y0))) => 99.67/15.00 (~(in(Y2, 99.67/15.00 setminus(Y0, 99.67/15.00 Y1)))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y1) => 99.67/15.00 (~(in(Y2, 99.67/15.00 setminus(Y0, 99.67/15.00 Y1)))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 subset(setminus(Y0, Y1), 99.67/15.00 Y0))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ((setminus(Y0, Y1) = 99.67/15.00 emptyset) => 99.67/15.00 subset(Y0, Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 symdiff(Y0, 99.67/15.00 Y1)) => 99.67/15.00 (!!((^[Y3 : $o]: 99.67/15.00 (( 99.67/15.00 in(Y2, 99.67/15.00 Y0) => 99.67/15.00 ( 99.67/15.00 ( 99.67/15.00 ~( 99.67/15.00 in(Y2, 99.67/15.00 Y1))) => 99.67/15.00 Y3)) => 99.67/15.00 (( 99.67/15.00 ( 99.67/15.00 ~( 99.67/15.00 in(Y2, 99.67/15.00 Y0))) => 99.67/15.00 ( 99.67/15.00 in(Y2, 99.67/15.00 Y1) => Y3)) => 99.67/15.00 Y3))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => 99.67/15.00 ((~(in(Y2, Y1))) => 99.67/15.00 in(Y2, 99.67/15.00 symdiff( 99.67/15.00 Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~(in(Y2, Y0))) => 99.67/15.00 (in(Y2, Y1) => 99.67/15.00 in(Y2, 99.67/15.00 symdiff( 99.67/15.00 Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => 99.67/15.00 (in(Y2, Y1) => 99.67/15.00 (~( 99.67/15.00 in(Y2, 99.67/15.00 symdiff( 99.67/15.00 Y0, Y1))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~( 99.67/15.00 in(Y2, Y0))) => 99.67/15.00 ((~( 99.67/15.00 in(Y2, 99.67/15.00 Y1))) => 99.67/15.00 (~( 99.67/15.00 in(Y2, 99.67/15.00 symdiff( 99.67/15.00 Y0, Y1))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 in(Y1, 99.67/15.00 setadjoin(Y0, 99.67/15.00 setadjoin(Y1, 99.67/15.00 emptyset))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 in(Y0, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 in(Y1, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (??((^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))) & 99.67/15.00 (??(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))) & 99.67/15.00 (setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)) = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (??((^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))) & 99.67/15.00 (??(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))) & 99.67/15.00 (setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)) = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (in(Y1, Y0) => 99.67/15.00 subset( 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset), 99.67/15.00 Y0)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (in(Y1, Y0) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset), 99.67/15.00 powerset( 99.67/15.00 Y0))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset))) => 99.67/15.00 (( 99.67/15.00 Y2 = Y1) | 99.67/15.00 (Y2 = Y0)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ( 99.67/15.00 !!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 subset( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 binunion( 99.67/15.00 Y0, Y1)))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 subset( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)), 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)), 99.67/15.00 powerset( 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1)))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y1 : $i]: 99.67/15.00 ( 99.67/15.00 !!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)), 99.67/15.00 powerset( 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1)))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)), 99.67/15.00 dsetconstr( 99.67/15.00 powerset( 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1))), 99.67/15.00 (^[Y4 : $i]: 99.67/15.00 (??(( 99.67/15.00 ^[Y5 : $i]: 99.67/15.00 (in(Y5, 99.67/15.00 Y0) & 99.67/15.00 (??(( 99.67/15.00 ^[Y6 : $i]: 99.67/15.00 (in(Y6, 99.67/15.00 Y1) & 99.67/15.00 (Y4 = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y5, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y5, 99.67/15.00 setadjoin( 99.67/15.00 Y6, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))))))))))))))))))))))))))) => 99.67/15.00 (!!((^[Y0 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 dsetconstr( 99.67/15.00 powerset( 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1))), 99.67/15.00 (^[Y3 : $i]: 99.67/15.00 (??(( 99.67/15.00 ^[Y4 : $i]: 99.67/15.00 (in(Y4, 99.67/15.00 Y0) & 99.67/15.00 (??(( 99.67/15.00 ^[Y5 : $i]: 99.67/15.00 (in(Y5, 99.67/15.00 Y1) & 99.67/15.00 (Y3 = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y4, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y4, 99.67/15.00 setadjoin( 99.67/15.00 Y5, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))))))))))))) => 99.67/15.00 (??(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (( 99.67/15.00 ??(( 99.67/15.00 ^[Y4 : $i]: 99.67/15.00 (in(Y4, 99.67/15.00 Y1) & 99.67/15.00 (Y2 = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 setadjoin( 99.67/15.00 Y4, 99.67/15.00 emptyset)), 99.67/15.00 emptyset))))))) & 99.67/15.00 in(Y3, 99.67/15.00 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.67/15.00 inference('lazy_cnf_imply', [status(thm)], ['250'])). 99.67/15.00 tff('252', plain, 99.67/15.00 ~ ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (subset(Y0, Y1) => subset(powerset(Y0), powerset(Y1))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i > $o]: in(dsetconstr(Y0, Y1), powerset(Y0)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i > $o]: subset(dsetconstr(Y0, Y1), Y0))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => in(Y2, binunion(Y0, Y1)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y1) => in(Y2, binunion(Y0, Y1)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (!!((^[Y3 : $o]: 99.67/15.00 (in(Y2, binunion(Y0, Y1)) => 99.67/15.00 ((in(Y2, Y0) => Y3) => 99.67/15.00 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, binunion(Y0, Y1)) => 99.67/15.00 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: subset(Y0, binunion(Y0, Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: subset(Y1, binunion(Y0, Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => 99.67/15.00 (in(Y2, Y1) => 99.67/15.00 in(Y2, binintersect(Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (subset(Y2, Y0) => 99.67/15.00 (subset(Y2, Y1) => 99.67/15.00 subset(Y2, binintersect(Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, binintersect(Y0, Y1)) => 99.67/15.00 in(Y2, Y0))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y0))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (subset(Y0, Y1) => 99.67/15.00 (binintersect(Y0, Y1) = Y0)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ((binintersect(Y0, Y1) = Y1) => 99.67/15.00 subset(Y1, Y0)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, binintersect(Y0, Y1)) => 99.67/15.00 in(Y2, Y1))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ((~((??((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) & in(Y2, Y1))))))) => 99.67/15.00 (binintersect(Y0, Y1) = emptyset)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 subset(binintersect(Y0, Y1), Y1))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (subset(Y1, Y0) => 99.67/15.00 (binintersect(Y0, Y1) = Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ((binintersect(Y0, Y1) = Y0) => 99.67/15.00 subset(Y0, Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (binintersect(Y0, 99.67/15.00 binunion(Y1, Y2)) = 99.67/15.00 binunion( 99.67/15.00 binintersect(Y0, Y1), 99.67/15.00 binintersect(Y0, Y2)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => 99.67/15.00 ((~(in(Y2, Y1))) => 99.67/15.00 in(Y2, setminus(Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, setminus(Y0, Y1)) => 99.67/15.00 in(Y2, Y0))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, setminus(Y0, Y1)) => 99.67/15.00 (~(in(Y2, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (subset(Y0, Y1) => 99.67/15.00 (setminus(Y0, Y1) = emptyset)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~(in(Y2, 99.67/15.00 setminus(Y0, Y1)))) => 99.67/15.00 (in(Y2, Y0) => 99.67/15.00 in(Y2, Y1)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~(in(Y2, 99.67/15.00 setminus(Y0, Y1)))) => 99.67/15.00 ((~(in(Y2, Y1))) => 99.67/15.00 (~(in(Y2, Y0)))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~(in(Y2, Y0))) => 99.67/15.00 (~(in(Y2, 99.67/15.00 setminus(Y0, 99.67/15.00 Y1)))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y1) => 99.67/15.00 (~(in(Y2, 99.67/15.00 setminus(Y0, 99.67/15.00 Y1)))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 subset(setminus(Y0, Y1), 99.67/15.00 Y0))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ((setminus(Y0, Y1) = 99.67/15.00 emptyset) => 99.67/15.00 subset(Y0, Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 symdiff(Y0, 99.67/15.00 Y1)) => 99.67/15.00 (!!((^[Y3 : $o]: 99.67/15.00 ( 99.67/15.00 ( 99.67/15.00 in(Y2, 99.67/15.00 Y0) => 99.67/15.00 ( 99.67/15.00 ( 99.67/15.00 ~( 99.67/15.00 in(Y2, 99.67/15.00 Y1))) => 99.67/15.00 Y3)) => 99.67/15.00 ( 99.67/15.00 ( 99.67/15.00 ( 99.67/15.00 ~( 99.67/15.00 in(Y2, 99.67/15.00 Y0))) => 99.67/15.00 ( 99.67/15.00 in(Y2, 99.67/15.00 Y1) => Y3)) => 99.67/15.00 Y3))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => 99.67/15.00 ((~(in(Y2, Y1))) => 99.67/15.00 in(Y2, 99.67/15.00 symdiff(Y0, 99.67/15.00 Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~(in(Y2, Y0))) => 99.67/15.00 (in(Y2, Y1) => 99.67/15.00 in(Y2, 99.67/15.00 symdiff( 99.67/15.00 Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => 99.67/15.00 (in(Y2, Y1) => 99.67/15.00 (~(in(Y2, 99.67/15.00 symdiff( 99.67/15.00 Y0, Y1))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~(in(Y2, 99.67/15.00 Y0))) => 99.67/15.00 ((~( 99.67/15.00 in(Y2, Y1))) => 99.67/15.00 (~( 99.67/15.00 in(Y2, 99.67/15.00 symdiff( 99.67/15.00 Y0, Y1))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 in(Y1, 99.67/15.00 setadjoin(Y0, 99.67/15.00 setadjoin(Y1, 99.67/15.00 emptyset))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 in(Y0, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 in(Y1, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (??((^[Y2 : $i]: 99.67/15.00 ( 99.67/15.00 in(Y2, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))) & 99.67/15.00 ( 99.67/15.00 ??(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))) & 99.67/15.00 (setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)) = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (??((^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))) & 99.67/15.00 (??(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))) & 99.67/15.00 (setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)) = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (in(Y1, Y0) => 99.67/15.00 subset( 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset), 99.67/15.00 Y0)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (in(Y1, Y0) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset), 99.67/15.00 powerset( 99.67/15.00 Y0))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 ( 99.67/15.00 in(Y2, 99.67/15.00 Y0) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset))) => 99.67/15.00 (( 99.67/15.00 Y2 = Y1) | 99.67/15.00 (Y2 = Y0)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 subset( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 binunion( 99.67/15.00 Y0, Y1)))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ( 99.67/15.00 !!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 subset( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)), 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)), 99.67/15.00 powerset( 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1)))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)), 99.67/15.00 powerset( 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1)))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y1 : $i]: 99.67/15.00 ( 99.67/15.00 !!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)), 99.67/15.00 dsetconstr( 99.67/15.00 powerset( 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1))), 99.67/15.00 (^[Y4 : $i]: 99.67/15.00 (??(( 99.67/15.00 ^[Y5 : $i]: 99.67/15.00 (in(Y5, 99.67/15.00 Y0) & 99.67/15.00 (??(( 99.67/15.00 ^[Y6 : $i]: 99.67/15.00 (in(Y6, 99.67/15.00 Y1) & 99.67/15.00 (Y4 = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y5, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y5, 99.67/15.00 setadjoin( 99.67/15.00 Y6, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))))))))))))))))))))))))))) => 99.67/15.00 (!!((^[Y0 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y1 : $i]: 99.67/15.00 ( 99.67/15.00 !!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 dsetconstr( 99.67/15.00 powerset( 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1))), 99.67/15.00 (^[Y3 : $i]: 99.67/15.00 (??(( 99.67/15.00 ^[Y4 : $i]: 99.67/15.00 (in(Y4, 99.67/15.00 Y0) & 99.67/15.00 (??(( 99.67/15.00 ^[Y5 : $i]: 99.67/15.00 (in(Y5, 99.67/15.00 Y1) & 99.67/15.00 (Y3 = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y4, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y4, 99.67/15.00 setadjoin( 99.67/15.00 Y5, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))))))))))))) => 99.67/15.00 (??(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (( 99.67/15.00 ??(( 99.67/15.00 ^[Y4 : $i]: 99.67/15.00 (in(Y4, 99.67/15.00 Y1) & 99.67/15.00 (Y2 = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 setadjoin( 99.67/15.00 Y4, 99.67/15.00 emptyset)), 99.67/15.00 emptyset))))))) & 99.67/15.00 in(Y3, 99.67/15.00 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.67/15.00 inference('lazy_cnf_imply', [status(thm)], ['251'])). 99.67/15.00 tff('253', plain, 99.67/15.00 ~ ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i > $o]: in(dsetconstr(Y0, Y1), powerset(Y0)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i > $o]: subset(dsetconstr(Y0, Y1), Y0))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => in(Y2, binunion(Y0, Y1)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y1) => in(Y2, binunion(Y0, Y1)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (!!((^[Y3 : $o]: 99.67/15.00 (in(Y2, binunion(Y0, Y1)) => 99.67/15.00 ((in(Y2, Y0) => Y3) => 99.67/15.00 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, binunion(Y0, Y1)) => 99.67/15.00 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: subset(Y0, binunion(Y0, Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: subset(Y1, binunion(Y0, Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => 99.67/15.00 (in(Y2, Y1) => 99.67/15.00 in(Y2, binintersect(Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (subset(Y2, Y0) => 99.67/15.00 (subset(Y2, Y1) => 99.67/15.00 subset(Y2, binintersect(Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, binintersect(Y0, Y1)) => 99.67/15.00 in(Y2, Y0))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y0))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (subset(Y0, Y1) => 99.67/15.00 (binintersect(Y0, Y1) = Y0)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ((binintersect(Y0, Y1) = Y1) => 99.67/15.00 subset(Y1, Y0)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, binintersect(Y0, Y1)) => 99.67/15.00 in(Y2, Y1))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ((~((??((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) & in(Y2, Y1))))))) => 99.67/15.00 (binintersect(Y0, Y1) = emptyset)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 subset(binintersect(Y0, Y1), Y1))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (subset(Y1, Y0) => 99.67/15.00 (binintersect(Y0, Y1) = Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ((binintersect(Y0, Y1) = Y0) => 99.67/15.00 subset(Y0, Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (binintersect(Y0, 99.67/15.00 binunion(Y1, Y2)) = 99.67/15.00 binunion( 99.67/15.00 binintersect(Y0, Y1), 99.67/15.00 binintersect(Y0, Y2)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => 99.67/15.00 ((~(in(Y2, Y1))) => 99.67/15.00 in(Y2, setminus(Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, setminus(Y0, Y1)) => 99.67/15.00 in(Y2, Y0))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, setminus(Y0, Y1)) => 99.67/15.00 (~(in(Y2, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (subset(Y0, Y1) => 99.67/15.00 (setminus(Y0, Y1) = emptyset)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~(in(Y2, 99.67/15.00 setminus(Y0, Y1)))) => 99.67/15.00 (in(Y2, Y0) => 99.67/15.00 in(Y2, Y1)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~(in(Y2, 99.67/15.00 setminus(Y0, Y1)))) => 99.67/15.00 ((~(in(Y2, Y1))) => 99.67/15.00 (~(in(Y2, Y0)))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~(in(Y2, Y0))) => 99.67/15.00 (~(in(Y2, 99.67/15.00 setminus(Y0, Y1)))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y1) => 99.67/15.00 (~(in(Y2, 99.67/15.00 setminus(Y0, 99.67/15.00 Y1)))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 subset(setminus(Y0, Y1), 99.67/15.00 Y0))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ((setminus(Y0, Y1) = 99.67/15.00 emptyset) => 99.67/15.00 subset(Y0, Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 symdiff(Y0, Y1)) => 99.67/15.00 (!!((^[Y3 : $o]: 99.67/15.00 (( 99.67/15.00 in(Y2, 99.67/15.00 Y0) => 99.67/15.00 ( 99.67/15.00 ( 99.67/15.00 ~( 99.67/15.00 in(Y2, 99.67/15.00 Y1))) => 99.67/15.00 Y3)) => 99.67/15.00 ( 99.67/15.00 ( 99.67/15.00 ( 99.67/15.00 ~( 99.67/15.00 in(Y2, 99.67/15.00 Y0))) => 99.67/15.00 ( 99.67/15.00 in(Y2, 99.67/15.00 Y1) => Y3)) => 99.67/15.00 Y3))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => 99.67/15.00 ((~(in(Y2, Y1))) => 99.67/15.00 in(Y2, 99.67/15.00 symdiff(Y0, 99.67/15.00 Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~(in(Y2, Y0))) => 99.67/15.00 (in(Y2, Y1) => 99.67/15.00 in(Y2, 99.67/15.00 symdiff(Y0, 99.67/15.00 Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => 99.67/15.00 (in(Y2, Y1) => 99.67/15.00 (~(in(Y2, 99.67/15.00 symdiff( 99.67/15.00 Y0, Y1))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~(in(Y2, Y0))) => 99.67/15.00 ((~(in(Y2, 99.67/15.00 Y1))) => 99.67/15.00 (~(in(Y2, 99.67/15.00 symdiff( 99.67/15.00 Y0, Y1))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 in(Y1, 99.67/15.00 setadjoin(Y0, 99.67/15.00 setadjoin(Y1, 99.67/15.00 emptyset))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 in(Y0, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 in(Y1, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (??((^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))) & 99.67/15.00 ( 99.67/15.00 ??(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))) & 99.67/15.00 (setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)) = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (??((^[Y2 : $i]: 99.67/15.00 ( 99.67/15.00 in(Y2, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))) & 99.67/15.00 ( 99.67/15.00 ??(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))) & 99.67/15.00 (setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)) = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (in(Y1, Y0) => 99.67/15.00 subset( 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset), 99.67/15.00 Y0)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (in(Y1, Y0) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset), 99.67/15.00 powerset( 99.67/15.00 Y0))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 ( 99.67/15.00 in(Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset))) => 99.67/15.00 ( 99.67/15.00 ( 99.67/15.00 Y2 = Y1) | 99.67/15.00 ( 99.67/15.00 Y2 = Y0)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 subset( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 binunion( 99.67/15.00 Y0, Y1)))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ( 99.67/15.00 !!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 subset( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)), 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)), 99.67/15.00 powerset( 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1)))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)), 99.67/15.00 powerset( 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1)))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)), 99.67/15.00 dsetconstr( 99.67/15.00 powerset( 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1))), 99.67/15.00 (^[Y4 : $i]: 99.67/15.00 (??(( 99.67/15.00 ^[Y5 : $i]: 99.67/15.00 (in(Y5, 99.67/15.00 Y0) & 99.67/15.00 (??(( 99.67/15.00 ^[Y6 : $i]: 99.67/15.00 (in(Y6, 99.67/15.00 Y1) & 99.67/15.00 (Y4 = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y5, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y5, 99.67/15.00 setadjoin( 99.67/15.00 Y6, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))))))))))))))))))))))))))) => 99.67/15.00 (!!((^[Y0 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 dsetconstr( 99.67/15.00 powerset( 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1))), 99.67/15.00 (^[Y3 : $i]: 99.67/15.00 (??(( 99.67/15.00 ^[Y4 : $i]: 99.67/15.00 (in(Y4, 99.67/15.00 Y0) & 99.67/15.00 (??(( 99.67/15.00 ^[Y5 : $i]: 99.67/15.00 (in(Y5, 99.67/15.00 Y1) & 99.67/15.00 (Y3 = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y4, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y4, 99.67/15.00 setadjoin( 99.67/15.00 Y5, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))))))))))))) => 99.67/15.00 (??(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (( 99.67/15.00 ??(( 99.67/15.00 ^[Y4 : $i]: 99.67/15.00 (in(Y4, 99.67/15.00 Y1) & 99.67/15.00 (Y2 = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 setadjoin( 99.67/15.00 Y4, 99.67/15.00 emptyset)), 99.67/15.00 emptyset))))))) & 99.67/15.00 in(Y3, 99.67/15.00 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.67/15.00 inference('lazy_cnf_imply', [status(thm)], ['252'])). 99.67/15.00 tff('254', plain, 99.67/15.00 ~ ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i > $o]: subset(dsetconstr(Y0, Y1), Y0))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => in(Y2, binunion(Y0, Y1)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y1) => in(Y2, binunion(Y0, Y1)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (!!((^[Y3 : $o]: 99.67/15.00 (in(Y2, binunion(Y0, Y1)) => 99.67/15.00 ((in(Y2, Y0) => Y3) => 99.67/15.00 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, binunion(Y0, Y1)) => 99.67/15.00 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: subset(Y0, binunion(Y0, Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: subset(Y1, binunion(Y0, Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => 99.67/15.00 (in(Y2, Y1) => 99.67/15.00 in(Y2, binintersect(Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (subset(Y2, Y0) => 99.67/15.00 (subset(Y2, Y1) => 99.67/15.00 subset(Y2, binintersect(Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, binintersect(Y0, Y1)) => 99.67/15.00 in(Y2, Y0))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y0))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (subset(Y0, Y1) => 99.67/15.00 (binintersect(Y0, Y1) = Y0)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ((binintersect(Y0, Y1) = Y1) => 99.67/15.00 subset(Y1, Y0)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, binintersect(Y0, Y1)) => 99.67/15.00 in(Y2, Y1))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ((~((??((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) & in(Y2, Y1))))))) => 99.67/15.00 (binintersect(Y0, Y1) = emptyset)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 subset(binintersect(Y0, Y1), Y1))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (subset(Y1, Y0) => 99.67/15.00 (binintersect(Y0, Y1) = Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ((binintersect(Y0, Y1) = Y0) => 99.67/15.00 subset(Y0, Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (binintersect(Y0, 99.67/15.00 binunion(Y1, Y2)) = 99.67/15.00 binunion( 99.67/15.00 binintersect(Y0, Y1), 99.67/15.00 binintersect(Y0, Y2)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => 99.67/15.00 ((~(in(Y2, Y1))) => 99.67/15.00 in(Y2, setminus(Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, setminus(Y0, Y1)) => 99.67/15.00 in(Y2, Y0))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, setminus(Y0, Y1)) => 99.67/15.00 (~(in(Y2, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (subset(Y0, Y1) => 99.67/15.00 (setminus(Y0, Y1) = emptyset)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~(in(Y2, 99.67/15.00 setminus(Y0, Y1)))) => 99.67/15.00 (in(Y2, Y0) => 99.67/15.00 in(Y2, Y1)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~(in(Y2, 99.67/15.00 setminus(Y0, Y1)))) => 99.67/15.00 ((~(in(Y2, Y1))) => 99.67/15.00 (~(in(Y2, Y0)))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~(in(Y2, Y0))) => 99.67/15.00 (~(in(Y2, 99.67/15.00 setminus(Y0, Y1)))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y1) => 99.67/15.00 (~(in(Y2, 99.67/15.00 setminus(Y0, Y1)))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 subset(setminus(Y0, Y1), Y0))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ((setminus(Y0, Y1) = 99.67/15.00 emptyset) => 99.67/15.00 subset(Y0, Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 symdiff(Y0, Y1)) => 99.67/15.00 (!!((^[Y3 : $o]: 99.67/15.00 ((in(Y2, 99.67/15.00 Y0) => 99.67/15.00 ( 99.67/15.00 ( 99.67/15.00 ~( 99.67/15.00 in(Y2, 99.67/15.00 Y1))) => 99.67/15.00 Y3)) => 99.67/15.00 (( 99.67/15.00 ( 99.67/15.00 ~( 99.67/15.00 in(Y2, 99.67/15.00 Y0))) => 99.67/15.00 ( 99.67/15.00 in(Y2, 99.67/15.00 Y1) => Y3)) => 99.67/15.00 Y3))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => 99.67/15.00 ((~(in(Y2, Y1))) => 99.67/15.00 in(Y2, 99.67/15.00 symdiff(Y0, 99.67/15.00 Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~(in(Y2, Y0))) => 99.67/15.00 (in(Y2, Y1) => 99.67/15.00 in(Y2, 99.67/15.00 symdiff(Y0, 99.67/15.00 Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => 99.67/15.00 (in(Y2, Y1) => 99.67/15.00 (~(in(Y2, 99.67/15.00 symdiff( 99.67/15.00 Y0, Y1))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~(in(Y2, Y0))) => 99.67/15.00 ((~(in(Y2, Y1))) => 99.67/15.00 (~(in(Y2, 99.67/15.00 symdiff( 99.67/15.00 Y0, Y1))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 in(Y1, 99.67/15.00 setadjoin(Y0, 99.67/15.00 setadjoin(Y1, 99.67/15.00 emptyset))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 in(Y0, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin(Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 in(Y1, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (??((^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))) & 99.67/15.00 (??(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))) & 99.67/15.00 (setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)) = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (??((^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))) & 99.67/15.00 ( 99.67/15.00 ??(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))) & 99.67/15.00 (setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)) = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (in(Y1, Y0) => 99.67/15.00 subset( 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset), 99.67/15.00 Y0)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (in(Y1, Y0) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset), 99.67/15.00 powerset(Y0))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset))) => 99.67/15.00 ( 99.67/15.00 ( 99.67/15.00 Y2 = Y1) | 99.67/15.00 ( 99.67/15.00 Y2 = Y0)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 ( 99.67/15.00 in(Y2, 99.67/15.00 Y0) => 99.67/15.00 ( 99.67/15.00 !!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 subset( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 binunion( 99.67/15.00 Y0, Y1)))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 subset( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)), 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ( 99.67/15.00 !!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)), 99.67/15.00 powerset( 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1)))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)), 99.67/15.00 powerset( 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1)))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)), 99.67/15.00 dsetconstr( 99.67/15.00 powerset( 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1))), 99.67/15.00 (^[Y4 : $i]: 99.67/15.00 (??(( 99.67/15.00 ^[Y5 : $i]: 99.67/15.00 (in(Y5, 99.67/15.00 Y0) & 99.67/15.00 (??(( 99.67/15.00 ^[Y6 : $i]: 99.67/15.00 (in(Y6, 99.67/15.00 Y1) & 99.67/15.00 (Y4 = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y5, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y5, 99.67/15.00 setadjoin( 99.67/15.00 Y6, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))))))))))))))))))))))))))) => 99.67/15.00 (!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 dsetconstr( 99.67/15.00 powerset( 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1))), 99.67/15.00 (^[Y3 : $i]: 99.67/15.00 (??(( 99.67/15.00 ^[Y4 : $i]: 99.67/15.00 (in(Y4, 99.67/15.00 Y0) & 99.67/15.00 (??(( 99.67/15.00 ^[Y5 : $i]: 99.67/15.00 (in(Y5, 99.67/15.00 Y1) & 99.67/15.00 (Y3 = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y4, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y4, 99.67/15.00 setadjoin( 99.67/15.00 Y5, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))))))))))))) => 99.67/15.00 (??(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (( 99.67/15.00 ??(( 99.67/15.00 ^[Y4 : $i]: 99.67/15.00 (in(Y4, 99.67/15.00 Y1) & 99.67/15.00 (Y2 = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 setadjoin( 99.67/15.00 Y4, 99.67/15.00 emptyset)), 99.67/15.00 emptyset))))))) & 99.67/15.00 in(Y3, 99.67/15.00 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.67/15.00 inference('lazy_cnf_imply', [status(thm)], ['253'])). 99.67/15.00 tff('255', plain, 99.67/15.00 ~ ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => in(Y2, binunion(Y0, Y1)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y1) => in(Y2, binunion(Y0, Y1)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (!!((^[Y3 : $o]: 99.67/15.00 (in(Y2, binunion(Y0, Y1)) => 99.67/15.00 ((in(Y2, Y0) => Y3) => 99.67/15.00 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, binunion(Y0, Y1)) => 99.67/15.00 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(Y0, binunion(Y0, Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: subset(Y1, binunion(Y0, Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => 99.67/15.00 (in(Y2, Y1) => 99.67/15.00 in(Y2, binintersect(Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (subset(Y2, Y0) => 99.67/15.00 (subset(Y2, Y1) => 99.67/15.00 subset(Y2, binintersect(Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, binintersect(Y0, Y1)) => 99.67/15.00 in(Y2, Y0))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y0))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (subset(Y0, Y1) => 99.67/15.00 (binintersect(Y0, Y1) = Y0)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ((binintersect(Y0, Y1) = Y1) => 99.67/15.00 subset(Y1, Y0)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, binintersect(Y0, Y1)) => 99.67/15.00 in(Y2, Y1))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ((~((??((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) & in(Y2, Y1))))))) => 99.67/15.00 (binintersect(Y0, Y1) = emptyset)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 subset(binintersect(Y0, Y1), Y1))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (subset(Y1, Y0) => 99.67/15.00 (binintersect(Y0, Y1) = Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ((binintersect(Y0, Y1) = Y0) => 99.67/15.00 subset(Y0, Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (binintersect(Y0, 99.67/15.00 binunion(Y1, Y2)) = 99.67/15.00 binunion( 99.67/15.00 binintersect(Y0, Y1), 99.67/15.00 binintersect(Y0, Y2)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => 99.67/15.00 ((~(in(Y2, Y1))) => 99.67/15.00 in(Y2, setminus(Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, setminus(Y0, Y1)) => 99.67/15.00 in(Y2, Y0))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, setminus(Y0, Y1)) => 99.67/15.00 (~(in(Y2, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (subset(Y0, Y1) => 99.67/15.00 (setminus(Y0, Y1) = emptyset)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~(in(Y2, 99.67/15.00 setminus(Y0, Y1)))) => 99.67/15.00 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~(in(Y2, 99.67/15.00 setminus(Y0, Y1)))) => 99.67/15.00 ((~(in(Y2, Y1))) => 99.67/15.00 (~(in(Y2, Y0)))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~(in(Y2, Y0))) => 99.67/15.00 (~(in(Y2, 99.67/15.00 setminus(Y0, Y1)))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y1) => 99.67/15.00 (~(in(Y2, 99.67/15.00 setminus(Y0, Y1)))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 subset(setminus(Y0, Y1), Y0))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ((setminus(Y0, Y1) = 99.67/15.00 emptyset) => 99.67/15.00 subset(Y0, Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 symdiff(Y0, Y1)) => 99.67/15.00 (!!((^[Y3 : $o]: 99.67/15.00 ((in(Y2, Y0) => 99.67/15.00 (( 99.67/15.00 ~( 99.67/15.00 in(Y2, 99.67/15.00 Y1))) => 99.67/15.00 Y3)) => 99.67/15.00 ((( 99.67/15.00 ~( 99.67/15.00 in(Y2, 99.67/15.00 Y0))) => 99.67/15.00 ( 99.67/15.00 in(Y2, 99.67/15.00 Y1) => Y3)) => 99.67/15.00 Y3))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => 99.67/15.00 ((~(in(Y2, Y1))) => 99.67/15.00 in(Y2, 99.67/15.00 symdiff(Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~(in(Y2, Y0))) => 99.67/15.00 (in(Y2, Y1) => 99.67/15.00 in(Y2, 99.67/15.00 symdiff(Y0, 99.67/15.00 Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => 99.67/15.00 (in(Y2, Y1) => 99.67/15.00 (~(in(Y2, 99.67/15.00 symdiff( 99.67/15.00 Y0, Y1))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~(in(Y2, Y0))) => 99.67/15.00 ((~(in(Y2, Y1))) => 99.67/15.00 (~(in(Y2, 99.67/15.00 symdiff( 99.67/15.00 Y0, Y1))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 in(Y1, 99.67/15.00 setadjoin(Y0, 99.67/15.00 setadjoin(Y1, 99.67/15.00 emptyset))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 in(Y0, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin(Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 in(Y1, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin(Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (??((^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))) & 99.67/15.00 (??(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))) & 99.67/15.00 (setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)) = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (??((^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))) & 99.67/15.00 (??(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))) & 99.67/15.00 (setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)) = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (in(Y1, Y0) => 99.67/15.00 subset( 99.67/15.00 setadjoin(Y1, 99.67/15.00 emptyset), 99.67/15.00 Y0)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (in(Y1, Y0) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset), 99.67/15.00 powerset(Y0))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset))) => 99.67/15.00 (( 99.67/15.00 Y2 = Y1) | 99.67/15.00 (Y2 = Y0)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 ( 99.67/15.00 !!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 subset( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 binunion( 99.67/15.00 Y0, Y1)))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 ( 99.67/15.00 in(Y2, 99.67/15.00 Y0) => 99.67/15.00 ( 99.67/15.00 !!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 subset( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)), 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)), 99.67/15.00 powerset( 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1)))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ( 99.67/15.00 !!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)), 99.67/15.00 powerset( 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1)))))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 Y0) => 99.67/15.00 (!!(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (in(Y3, 99.67/15.00 Y1) => 99.67/15.00 in( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)), 99.67/15.00 dsetconstr( 99.67/15.00 powerset( 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1))), 99.67/15.00 (^[Y4 : $i]: 99.67/15.00 (??(( 99.67/15.00 ^[Y5 : $i]: 99.67/15.00 (in(Y5, 99.67/15.00 Y0) & 99.67/15.00 (??(( 99.67/15.00 ^[Y6 : $i]: 99.67/15.00 (in(Y6, 99.67/15.00 Y1) & 99.67/15.00 (Y4 = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y5, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y5, 99.67/15.00 setadjoin( 99.67/15.00 Y6, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))))))))))))))))))))))))))) => 99.67/15.00 (!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!(( 99.67/15.00 ^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 dsetconstr( 99.67/15.00 powerset( 99.67/15.00 powerset( 99.67/15.00 binunion( 99.67/15.00 Y0, Y1))), 99.67/15.00 (^[Y3 : $i]: 99.67/15.00 (??(( 99.67/15.00 ^[Y4 : $i]: 99.67/15.00 (in(Y4, 99.67/15.00 Y0) & 99.67/15.00 (??(( 99.67/15.00 ^[Y5 : $i]: 99.67/15.00 (in(Y5, 99.67/15.00 Y1) & 99.67/15.00 (Y3 = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y4, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y4, 99.67/15.00 setadjoin( 99.67/15.00 Y5, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))))))))))))) => 99.67/15.00 (??(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 (( 99.67/15.00 ??(( 99.67/15.00 ^[Y4 : $i]: 99.67/15.00 (in(Y4, 99.67/15.00 Y1) & 99.67/15.00 (Y2 = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 setadjoin( 99.67/15.00 Y4, 99.67/15.00 emptyset)), 99.67/15.00 emptyset))))))) & 99.67/15.00 in(Y3, 99.67/15.00 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.67/15.00 inference('lazy_cnf_imply', [status(thm)], ['254'])). 99.67/15.00 tff('256', plain, 99.67/15.00 ~ ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y1) => in(Y2, binunion(Y0, Y1)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (!!((^[Y3 : $o]: 99.67/15.00 (in(Y2, binunion(Y0, Y1)) => 99.67/15.00 ((in(Y2, Y0) => Y3) => 99.67/15.00 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, binunion(Y0, Y1)) => 99.67/15.00 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(Y0, binunion(Y0, Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(Y1, binunion(Y0, Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => 99.67/15.00 (in(Y2, Y1) => 99.67/15.00 in(Y2, binintersect(Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (subset(Y2, Y0) => 99.67/15.00 (subset(Y2, Y1) => 99.67/15.00 subset(Y2, binintersect(Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, binintersect(Y0, Y1)) => 99.67/15.00 in(Y2, Y0))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y0))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (subset(Y0, Y1) => (binintersect(Y0, Y1) = Y0)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ((binintersect(Y0, Y1) = Y1) => 99.67/15.00 subset(Y1, Y0)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, binintersect(Y0, Y1)) => 99.67/15.00 in(Y2, Y1))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ((~((??((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) & in(Y2, Y1))))))) => 99.67/15.00 (binintersect(Y0, Y1) = emptyset)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y1))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (subset(Y1, Y0) => 99.67/15.00 (binintersect(Y0, Y1) = Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ((binintersect(Y0, Y1) = Y0) => 99.67/15.00 subset(Y0, Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (binintersect(Y0, 99.67/15.00 binunion(Y1, Y2)) = 99.67/15.00 binunion(binintersect(Y0, Y1), 99.67/15.00 binintersect(Y0, Y2)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => 99.67/15.00 ((~(in(Y2, Y1))) => 99.67/15.00 in(Y2, setminus(Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, setminus(Y0, Y1)) => 99.67/15.00 in(Y2, Y0))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, setminus(Y0, Y1)) => 99.67/15.00 (~(in(Y2, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (subset(Y0, Y1) => 99.67/15.00 (setminus(Y0, Y1) = emptyset)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~(in(Y2, 99.67/15.00 setminus(Y0, Y1)))) => 99.67/15.00 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~(in(Y2, 99.67/15.00 setminus(Y0, Y1)))) => 99.67/15.00 ((~(in(Y2, Y1))) => 99.67/15.00 (~(in(Y2, Y0)))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~(in(Y2, Y0))) => 99.67/15.00 (~(in(Y2, 99.67/15.00 setminus(Y0, Y1)))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y1) => 99.67/15.00 (~(in(Y2, 99.67/15.00 setminus(Y0, Y1)))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 subset(setminus(Y0, Y1), Y0))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 ((setminus(Y0, Y1) = emptyset) => 99.67/15.00 subset(Y0, Y1)))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 symdiff(Y0, Y1)) => 99.67/15.00 (!!((^[Y3 : $o]: 99.67/15.00 ((in(Y2, Y0) => 99.67/15.00 ((~( 99.67/15.00 in(Y2, 99.67/15.00 Y1))) => 99.67/15.00 Y3)) => 99.67/15.00 (((~( 99.67/15.00 in(Y2, 99.67/15.00 Y0))) => 99.67/15.00 (in(Y2, 99.67/15.00 Y1) => Y3)) => 99.67/15.00 Y3))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => 99.67/15.00 ((~(in(Y2, Y1))) => 99.67/15.00 in(Y2, 99.67/15.00 symdiff(Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~(in(Y2, Y0))) => 99.67/15.00 (in(Y2, Y1) => 99.67/15.00 in(Y2, 99.67/15.00 symdiff(Y0, Y1))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 (in(Y2, Y0) => 99.67/15.00 (in(Y2, Y1) => 99.67/15.00 (~(in(Y2, 99.67/15.00 symdiff( 99.67/15.00 Y0, Y1))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (!!((^[Y2 : $i]: 99.67/15.00 ((~(in(Y2, Y0))) => 99.67/15.00 ((~(in(Y2, Y1))) => 99.67/15.00 (~(in(Y2, 99.67/15.00 symdiff( 99.67/15.00 Y0, Y1))))))))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 in(Y1, 99.67/15.00 setadjoin(Y0, 99.67/15.00 setadjoin(Y1, 99.67/15.00 emptyset))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 in(Y0, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin(Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin(Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 in(Y1, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin(Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))))))))) => 99.67/15.00 ((!!((^[Y0 : $i]: 99.67/15.00 (!!((^[Y1 : $i]: 99.67/15.00 (??((^[Y2 : $i]: 99.67/15.00 (in(Y2, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))) & 99.67/15.00 (??(( 99.67/15.00 ^[Y3 : $i]: 99.67/15.00 ( 99.67/15.00 in(Y3, 99.67/15.00 setunion( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)))) & 99.67/15.00 ( 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y0, 99.67/15.00 setadjoin( 99.67/15.00 Y1, 99.67/15.00 emptyset)), 99.67/15.00 emptyset)) = 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 emptyset), 99.67/15.00 setadjoin( 99.67/15.00 setadjoin( 99.67/15.00 Y2, 99.67/15.00 setadjoin( 99.67/15.00 Y3, 99.67/15.00 emptyset)), 99.67/15.00 emptyset))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (??((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))) & 99.67/15.01 (??(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))) & 99.67/15.01 (setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)) = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (in(Y1, Y0) => 99.67/15.01 subset( 99.67/15.01 setadjoin(Y1, 99.67/15.01 emptyset), 99.67/15.01 Y0)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (in(Y1, Y0) => 99.67/15.01 in( 99.67/15.01 setadjoin(Y1, 99.67/15.01 emptyset), 99.67/15.01 powerset(Y0))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ( 99.67/15.01 in(Y2, 99.67/15.01 Y0) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset))) => 99.67/15.01 (( 99.67/15.01 Y2 = Y1) | 99.67/15.01 (Y2 = Y0)))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 Y0) => 99.67/15.01 (!!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 subset( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 binunion( 99.67/15.01 Y0, Y1)))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!(( 99.67/15.01 ^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 Y0) => 99.67/15.01 ( 99.67/15.01 !!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!(( 99.67/15.01 ^[Y2 : $i]: 99.67/15.01 ( 99.67/15.01 in(Y2, 99.67/15.01 Y0) => 99.67/15.01 ( 99.67/15.01 !!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 subset( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!(( 99.67/15.01 ^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 Y0) => 99.67/15.01 (!!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1)))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!(( 99.67/15.01 ^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 Y0) => 99.67/15.01 (!!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1)))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 ( 99.67/15.01 !!(( 99.67/15.01 ^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 Y0) => 99.67/15.01 (!!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 dsetconstr( 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))), 99.67/15.01 (^[Y4 : $i]: 99.67/15.01 (??(( 99.67/15.01 ^[Y5 : $i]: 99.67/15.01 (in(Y5, 99.67/15.01 Y0) & 99.67/15.01 (??(( 99.67/15.01 ^[Y6 : $i]: 99.67/15.01 (in(Y6, 99.67/15.01 Y1) & 99.67/15.01 (Y4 = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y5, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y5, 99.67/15.01 setadjoin( 99.67/15.01 Y6, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))))))))))))))))))))))))))) => 99.67/15.01 (!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 ( 99.67/15.01 !!(( 99.67/15.01 ^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 dsetconstr( 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))), 99.67/15.01 (^[Y3 : $i]: 99.67/15.01 (??(( 99.67/15.01 ^[Y4 : $i]: 99.67/15.01 (in(Y4, 99.67/15.01 Y0) & 99.67/15.01 (??(( 99.67/15.01 ^[Y5 : $i]: 99.67/15.01 (in(Y5, 99.67/15.01 Y1) & 99.67/15.01 (Y3 = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y4, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y4, 99.67/15.01 setadjoin( 99.67/15.01 Y5, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))))))))))))) => 99.67/15.01 (??(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (( 99.67/15.01 ??(( 99.67/15.01 ^[Y4 : $i]: 99.67/15.01 (in(Y4, 99.67/15.01 Y1) & 99.67/15.01 (Y2 = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 setadjoin( 99.67/15.01 Y4, 99.67/15.01 emptyset)), 99.67/15.01 emptyset))))))) & 99.67/15.01 in(Y3, 99.67/15.01 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.67/15.01 inference('lazy_cnf_imply', [status(thm)], ['255'])). 99.67/15.01 tff('257', plain, 99.67/15.01 ~ ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y1) => in(Y2, binunion(Y0, Y1)))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (!!((^[Y3 : $o]: 99.67/15.01 (in(Y2, binunion(Y0, Y1)) => 99.67/15.01 ((in(Y2, Y0) => Y3) => 99.67/15.01 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, binunion(Y0, Y1)) => 99.67/15.01 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(Y0, binunion(Y0, Y1)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(Y1, binunion(Y0, Y1)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (in(Y2, Y1) => in(Y2, binintersect(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (subset(Y2, Y0) => 99.67/15.01 (subset(Y2, Y1) => 99.67/15.01 subset(Y2, binintersect(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, binintersect(Y0, Y1)) => 99.67/15.01 in(Y2, Y0))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y0))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (subset(Y0, Y1) => (binintersect(Y0, Y1) = Y0)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 ((binintersect(Y0, Y1) = Y1) => subset(Y1, Y0)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, binintersect(Y0, Y1)) => 99.67/15.01 in(Y2, Y1))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 ((~((??((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) & in(Y2, Y1))))))) => 99.67/15.01 (binintersect(Y0, Y1) = emptyset)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y1))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (subset(Y1, Y0) => 99.67/15.01 (binintersect(Y0, Y1) = Y1)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 ((binintersect(Y0, Y1) = Y0) => 99.67/15.01 subset(Y0, Y1)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (binintersect(Y0, 99.67/15.01 binunion(Y1, Y2)) = 99.67/15.01 binunion(binintersect(Y0, Y1), 99.67/15.01 binintersect(Y0, Y2)))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 in(Y2, setminus(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, setminus(Y0, Y1)) => 99.67/15.01 in(Y2, Y0))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, setminus(Y0, Y1)) => 99.67/15.01 (~(in(Y2, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (subset(Y0, Y1) => 99.67/15.01 (setminus(Y0, Y1) = emptyset)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.01 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, 99.67/15.01 setminus(Y0, Y1)))) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 (~(in(Y2, Y0)))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, Y0))) => 99.67/15.01 (~(in(Y2, 99.67/15.01 setminus(Y0, Y1)))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y1) => 99.67/15.01 (~(in(Y2, 99.67/15.01 setminus(Y0, Y1)))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 subset(setminus(Y0, Y1), Y0))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 ((setminus(Y0, Y1) = emptyset) => 99.67/15.01 subset(Y0, Y1)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 symdiff(Y0, Y1)) => 99.67/15.01 (!!((^[Y3 : $o]: 99.67/15.01 ((in(Y2, Y0) => 99.67/15.01 ((~( 99.67/15.01 in(Y2, Y1))) => 99.67/15.01 Y3)) => 99.67/15.01 (((~( 99.67/15.01 in(Y2, Y0))) => 99.67/15.01 (in(Y2, Y1) => 99.67/15.01 Y3)) => 99.67/15.01 Y3))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 in(Y2, 99.67/15.01 symdiff(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, Y0))) => 99.67/15.01 (in(Y2, Y1) => 99.67/15.01 in(Y2, 99.67/15.01 symdiff(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (in(Y2, Y1) => 99.67/15.01 (~(in(Y2, 99.67/15.01 symdiff(Y0, 99.67/15.01 Y1))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, Y0))) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 (~(in(Y2, 99.67/15.01 symdiff( 99.67/15.01 Y0, Y1))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 in(Y1, 99.67/15.01 setadjoin(Y0, 99.67/15.01 setadjoin(Y1, 99.67/15.01 emptyset))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 in(Y0, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 in(Y1, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (??((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))) & 99.67/15.01 (??(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))) & 99.67/15.01 ( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)) = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (??((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))) & 99.67/15.01 (??(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 ( 99.67/15.01 in(Y3, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))) & 99.67/15.01 ( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)) = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (in(Y1, Y0) => 99.67/15.01 subset( 99.67/15.01 setadjoin(Y1, 99.67/15.01 emptyset), Y0)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (in(Y1, Y0) => 99.67/15.01 in( 99.67/15.01 setadjoin(Y1, 99.67/15.01 emptyset), 99.67/15.01 powerset(Y0))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 Y0) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ( 99.67/15.01 in(Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset))) => 99.67/15.01 ( 99.67/15.01 ( 99.67/15.01 Y2 = Y1) | 99.67/15.01 ( 99.67/15.01 Y2 = Y0)))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 Y0) => 99.67/15.01 (!!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 subset( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 binunion( 99.67/15.01 Y0, Y1)))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 Y0) => 99.67/15.01 (!!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!(( 99.67/15.01 ^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 Y0) => 99.67/15.01 ( 99.67/15.01 !!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 subset( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!(( 99.67/15.01 ^[Y2 : $i]: 99.67/15.01 ( 99.67/15.01 in(Y2, 99.67/15.01 Y0) => 99.67/15.01 ( 99.67/15.01 !!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1)))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!(( 99.67/15.01 ^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 Y0) => 99.67/15.01 (!!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1)))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!(( 99.67/15.01 ^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 Y0) => 99.67/15.01 (!!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 dsetconstr( 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))), 99.67/15.01 (^[Y4 : $i]: 99.67/15.01 (??(( 99.67/15.01 ^[Y5 : $i]: 99.67/15.01 (in(Y5, 99.67/15.01 Y0) & 99.67/15.01 (??(( 99.67/15.01 ^[Y6 : $i]: 99.67/15.01 (in(Y6, 99.67/15.01 Y1) & 99.67/15.01 (Y4 = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y5, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y5, 99.67/15.01 setadjoin( 99.67/15.01 Y6, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))))))))))))))))))))))))))) => 99.67/15.01 (!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!(( 99.67/15.01 ^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 dsetconstr( 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))), 99.67/15.01 (^[Y3 : $i]: 99.67/15.01 (??(( 99.67/15.01 ^[Y4 : $i]: 99.67/15.01 (in(Y4, 99.67/15.01 Y0) & 99.67/15.01 (??(( 99.67/15.01 ^[Y5 : $i]: 99.67/15.01 (in(Y5, 99.67/15.01 Y1) & 99.67/15.01 (Y3 = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y4, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y4, 99.67/15.01 setadjoin( 99.67/15.01 Y5, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))))))))))))) => 99.67/15.01 (??(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (( 99.67/15.01 ??(( 99.67/15.01 ^[Y4 : $i]: 99.67/15.01 (in(Y4, 99.67/15.01 Y1) & 99.67/15.01 (Y2 = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 setadjoin( 99.67/15.01 Y4, 99.67/15.01 emptyset)), 99.67/15.01 emptyset))))))) & 99.67/15.01 in(Y3, 99.67/15.01 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.67/15.01 inference('lazy_cnf_imply', [status(thm)], ['256'])). 99.67/15.01 tff('258', plain, 99.67/15.01 ~ ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (!!((^[Y3 : $o]: 99.67/15.01 (in(Y2, binunion(Y0, Y1)) => 99.67/15.01 ((in(Y2, Y0) => Y3) => 99.67/15.01 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, binunion(Y0, Y1)) => 99.67/15.01 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(Y0, binunion(Y0, Y1)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(Y1, binunion(Y0, Y1)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (in(Y2, Y1) => in(Y2, binintersect(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (subset(Y2, Y0) => 99.67/15.01 (subset(Y2, Y1) => 99.67/15.01 subset(Y2, binintersect(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, binintersect(Y0, Y1)) => in(Y2, Y0))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y0))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (subset(Y0, Y1) => (binintersect(Y0, Y1) = Y0)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 ((binintersect(Y0, Y1) = Y1) => subset(Y1, Y0)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, binintersect(Y0, Y1)) => 99.67/15.01 in(Y2, Y1))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 ((~((??((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) & in(Y2, Y1))))))) => 99.67/15.01 (binintersect(Y0, Y1) = emptyset)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y1))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (subset(Y1, Y0) => 99.67/15.01 (binintersect(Y0, Y1) = Y1)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 ((binintersect(Y0, Y1) = Y0) => 99.67/15.01 subset(Y0, Y1)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (binintersect(Y0, 99.67/15.01 binunion(Y1, Y2)) = 99.67/15.01 binunion(binintersect(Y0, Y1), 99.67/15.01 binintersect(Y0, Y2)))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 in(Y2, setminus(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, setminus(Y0, Y1)) => 99.67/15.01 in(Y2, Y0))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, setminus(Y0, Y1)) => 99.67/15.01 (~(in(Y2, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (subset(Y0, Y1) => 99.67/15.01 (setminus(Y0, Y1) = emptyset)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.01 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 (~(in(Y2, Y0)))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, Y0))) => 99.67/15.01 (~(in(Y2, 99.67/15.01 setminus(Y0, Y1)))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y1) => 99.67/15.01 (~(in(Y2, 99.67/15.01 setminus(Y0, Y1)))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 subset(setminus(Y0, Y1), Y0))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 ((setminus(Y0, Y1) = emptyset) => 99.67/15.01 subset(Y0, Y1)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 symdiff(Y0, Y1)) => 99.67/15.01 (!!((^[Y3 : $o]: 99.67/15.01 ((in(Y2, Y0) => 99.67/15.01 ((~(in(Y2, 99.67/15.01 Y1))) => 99.67/15.01 Y3)) => 99.67/15.01 (((~(in(Y2, 99.67/15.01 Y0))) => 99.67/15.01 (in(Y2, Y1) => 99.67/15.01 Y3)) => 99.67/15.01 Y3))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 in(Y2, 99.67/15.01 symdiff(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, Y0))) => 99.67/15.01 (in(Y2, Y1) => 99.67/15.01 in(Y2, 99.67/15.01 symdiff(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (in(Y2, Y1) => 99.67/15.01 (~(in(Y2, 99.67/15.01 symdiff(Y0, 99.67/15.01 Y1))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, Y0))) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 (~(in(Y2, 99.67/15.01 symdiff(Y0, 99.67/15.01 Y1))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 in(Y1, 99.67/15.01 setadjoin(Y0, 99.67/15.01 setadjoin(Y1, 99.67/15.01 emptyset))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 in(Y0, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, 99.67/15.01 setadjoin(Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 in(Y1, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (??((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))) & 99.67/15.01 (??((^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))) & 99.67/15.01 (setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)) = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (??((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))) & 99.67/15.01 (??(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))) & 99.67/15.01 ( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)) = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (in(Y1, Y0) => 99.67/15.01 subset( 99.67/15.01 setadjoin(Y1, 99.67/15.01 emptyset), Y0)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (in(Y1, Y0) => 99.67/15.01 in( 99.67/15.01 setadjoin(Y1, 99.67/15.01 emptyset), 99.67/15.01 powerset(Y0))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset))) => 99.67/15.01 ( 99.67/15.01 ( 99.67/15.01 Y2 = Y1) | 99.67/15.01 ( 99.67/15.01 Y2 = Y0)))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ( 99.67/15.01 in(Y2, 99.67/15.01 Y0) => 99.67/15.01 ( 99.67/15.01 !!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 subset( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 binunion( 99.67/15.01 Y0, Y1)))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 Y0) => 99.67/15.01 (!!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 Y0) => 99.67/15.01 (!!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 subset( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!(( 99.67/15.01 ^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 Y0) => 99.67/15.01 ( 99.67/15.01 !!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1)))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!(( 99.67/15.01 ^[Y2 : $i]: 99.67/15.01 ( 99.67/15.01 in(Y2, 99.67/15.01 Y0) => 99.67/15.01 ( 99.67/15.01 !!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1)))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!(( 99.67/15.01 ^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 Y0) => 99.67/15.01 (!!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 dsetconstr( 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))), 99.67/15.01 (^[Y4 : $i]: 99.67/15.01 (??(( 99.67/15.01 ^[Y5 : $i]: 99.67/15.01 (in(Y5, 99.67/15.01 Y0) & 99.67/15.01 (??(( 99.67/15.01 ^[Y6 : $i]: 99.67/15.01 (in(Y6, 99.67/15.01 Y1) & 99.67/15.01 (Y4 = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y5, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y5, 99.67/15.01 setadjoin( 99.67/15.01 Y6, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))))))))))))))))))))))))))) => 99.67/15.01 (!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!(( 99.67/15.01 ^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 dsetconstr( 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))), 99.67/15.01 (^[Y3 : $i]: 99.67/15.01 (??(( 99.67/15.01 ^[Y4 : $i]: 99.67/15.01 (in(Y4, 99.67/15.01 Y0) & 99.67/15.01 (??(( 99.67/15.01 ^[Y5 : $i]: 99.67/15.01 (in(Y5, 99.67/15.01 Y1) & 99.67/15.01 (Y3 = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y4, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y4, 99.67/15.01 setadjoin( 99.67/15.01 Y5, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))))))))))))) => 99.67/15.01 (??(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (( 99.67/15.01 ??(( 99.67/15.01 ^[Y4 : $i]: 99.67/15.01 (in(Y4, 99.67/15.01 Y1) & 99.67/15.01 (Y2 = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 setadjoin( 99.67/15.01 Y4, 99.67/15.01 emptyset)), 99.67/15.01 emptyset))))))) & 99.67/15.01 in(Y3, 99.67/15.01 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.67/15.01 inference('lazy_cnf_imply', [status(thm)], ['257'])). 99.67/15.01 tff('259', plain, 99.67/15.01 ~ ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, binunion(Y0, Y1)) => 99.67/15.01 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(Y0, binunion(Y0, Y1)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(Y1, binunion(Y0, Y1)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (in(Y2, Y1) => in(Y2, binintersect(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (subset(Y2, Y0) => 99.67/15.01 (subset(Y2, Y1) => 99.67/15.01 subset(Y2, binintersect(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, binintersect(Y0, Y1)) => in(Y2, Y0))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y0))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (subset(Y0, Y1) => (binintersect(Y0, Y1) = Y0)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 ((binintersect(Y0, Y1) = Y1) => subset(Y1, Y0)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, binintersect(Y0, Y1)) => 99.67/15.01 in(Y2, Y1))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & in(Y2, Y1))))))) => 99.67/15.01 (binintersect(Y0, Y1) = emptyset)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y1))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (subset(Y1, Y0) => 99.67/15.01 (binintersect(Y0, Y1) = Y1)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 ((binintersect(Y0, Y1) = Y0) => 99.67/15.01 subset(Y0, Y1)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (binintersect(Y0, binunion(Y1, Y2)) = 99.67/15.01 binunion(binintersect(Y0, Y1), 99.67/15.01 binintersect(Y0, Y2)))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 in(Y2, setminus(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, setminus(Y0, Y1)) => 99.67/15.01 in(Y2, Y0))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, setminus(Y0, Y1)) => 99.67/15.01 (~(in(Y2, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (subset(Y0, Y1) => 99.67/15.01 (setminus(Y0, Y1) = emptyset)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.01 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 (~(in(Y2, Y0)))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, Y0))) => 99.67/15.01 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y1) => 99.67/15.01 (~(in(Y2, 99.67/15.01 setminus(Y0, Y1)))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 subset(setminus(Y0, Y1), Y0))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 ((setminus(Y0, Y1) = emptyset) => 99.67/15.01 subset(Y0, Y1)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, symdiff(Y0, Y1)) => 99.67/15.01 (!!((^[Y3 : $o]: 99.67/15.01 ((in(Y2, Y0) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 Y3)) => 99.67/15.01 (((~(in(Y2, Y0))) => 99.67/15.01 (in(Y2, Y1) => 99.67/15.01 Y3)) => 99.67/15.01 Y3))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 in(Y2, 99.67/15.01 symdiff(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, Y0))) => 99.67/15.01 (in(Y2, Y1) => 99.67/15.01 in(Y2, 99.67/15.01 symdiff(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (in(Y2, Y1) => 99.67/15.01 (~(in(Y2, 99.67/15.01 symdiff(Y0, 99.67/15.01 Y1))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, Y0))) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 (~(in(Y2, 99.67/15.01 symdiff(Y0, 99.67/15.01 Y1))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 in(Y1, 99.67/15.01 setadjoin(Y0, 99.67/15.01 setadjoin(Y1, 99.67/15.01 emptyset))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 in(Y0, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, 99.67/15.01 setadjoin(Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 in(Y1, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, 99.67/15.01 setadjoin(Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (??((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))) & 99.67/15.01 (??((^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))) & 99.67/15.01 (setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)) = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (??((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))) & 99.67/15.01 (??((^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))) & 99.67/15.01 (setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)) = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (in(Y1, Y0) => 99.67/15.01 subset( 99.67/15.01 setadjoin(Y1, 99.67/15.01 emptyset), Y0)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (in(Y1, Y0) => 99.67/15.01 in( 99.67/15.01 setadjoin(Y1, 99.67/15.01 emptyset), 99.67/15.01 powerset(Y0))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset))) => 99.67/15.01 (( 99.67/15.01 Y2 = Y1) | 99.67/15.01 ( 99.67/15.01 Y2 = Y0)))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 Y0) => 99.67/15.01 ( 99.67/15.01 !!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 subset( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 binunion( 99.67/15.01 Y0, Y1)))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ( 99.67/15.01 in(Y2, 99.67/15.01 Y0) => 99.67/15.01 ( 99.67/15.01 !!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 Y0) => 99.67/15.01 (!!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 subset( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 Y0) => 99.67/15.01 (!!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1)))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!(( 99.67/15.01 ^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 Y0) => 99.67/15.01 ( 99.67/15.01 !!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1)))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!(( 99.67/15.01 ^[Y2 : $i]: 99.67/15.01 ( 99.67/15.01 in(Y2, 99.67/15.01 Y0) => 99.67/15.01 ( 99.67/15.01 !!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 dsetconstr( 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))), 99.67/15.01 (^[Y4 : $i]: 99.67/15.01 (??(( 99.67/15.01 ^[Y5 : $i]: 99.67/15.01 (in(Y5, 99.67/15.01 Y0) & 99.67/15.01 (??(( 99.67/15.01 ^[Y6 : $i]: 99.67/15.01 (in(Y6, 99.67/15.01 Y1) & 99.67/15.01 (Y4 = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y5, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y5, 99.67/15.01 setadjoin( 99.67/15.01 Y6, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))))))))))))))))))))))))))) => 99.67/15.01 (!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!(( 99.67/15.01 ^[Y2 : $i]: 99.67/15.01 ( 99.67/15.01 in(Y2, 99.67/15.01 dsetconstr( 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))), 99.67/15.01 (^[Y3 : $i]: 99.67/15.01 (??(( 99.67/15.01 ^[Y4 : $i]: 99.67/15.01 (in(Y4, 99.67/15.01 Y0) & 99.67/15.01 (??(( 99.67/15.01 ^[Y5 : $i]: 99.67/15.01 (in(Y5, 99.67/15.01 Y1) & 99.67/15.01 (Y3 = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y4, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y4, 99.67/15.01 setadjoin( 99.67/15.01 Y5, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))))))))))))) => 99.67/15.01 ( 99.67/15.01 ??(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (( 99.67/15.01 ??(( 99.67/15.01 ^[Y4 : $i]: 99.67/15.01 (in(Y4, 99.67/15.01 Y1) & 99.67/15.01 (Y2 = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 setadjoin( 99.67/15.01 Y4, 99.67/15.01 emptyset)), 99.67/15.01 emptyset))))))) & 99.67/15.01 in(Y3, 99.67/15.01 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.67/15.01 inference('lazy_cnf_imply', [status(thm)], ['258'])). 99.67/15.01 tff('260', plain, 99.67/15.01 ~ ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(Y0, binunion(Y0, Y1)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(Y1, binunion(Y0, Y1)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (in(Y2, Y1) => in(Y2, binintersect(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (subset(Y2, Y0) => 99.67/15.01 (subset(Y2, Y1) => 99.67/15.01 subset(Y2, binintersect(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, binintersect(Y0, Y1)) => in(Y2, Y0))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y0))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (subset(Y0, Y1) => (binintersect(Y0, Y1) = Y0)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 ((binintersect(Y0, Y1) = Y1) => subset(Y1, Y0)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, binintersect(Y0, Y1)) => 99.67/15.01 in(Y2, Y1))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & in(Y2, Y1))))))) => 99.67/15.01 (binintersect(Y0, Y1) = emptyset)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y1))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (subset(Y1, Y0) => 99.67/15.01 (binintersect(Y0, Y1) = Y1)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 ((binintersect(Y0, Y1) = Y0) => 99.67/15.01 subset(Y0, Y1)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (binintersect(Y0, binunion(Y1, Y2)) = 99.67/15.01 binunion(binintersect(Y0, Y1), 99.67/15.01 binintersect(Y0, Y2)))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 in(Y2, setminus(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, setminus(Y0, Y1)) => 99.67/15.01 in(Y2, Y0))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, setminus(Y0, Y1)) => 99.67/15.01 (~(in(Y2, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (subset(Y0, Y1) => 99.67/15.01 (setminus(Y0, Y1) = emptyset)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.01 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 (~(in(Y2, Y0)))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, Y0))) => 99.67/15.01 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y1) => 99.67/15.01 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 subset(setminus(Y0, Y1), Y0))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 ((setminus(Y0, Y1) = emptyset) => 99.67/15.01 subset(Y0, Y1)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, symdiff(Y0, Y1)) => 99.67/15.01 (!!((^[Y3 : $o]: 99.67/15.01 ((in(Y2, Y0) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 Y3)) => 99.67/15.01 (((~(in(Y2, Y0))) => 99.67/15.01 (in(Y2, Y1) => 99.67/15.01 Y3)) => 99.67/15.01 Y3))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 in(Y2, 99.67/15.01 symdiff(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, Y0))) => 99.67/15.01 (in(Y2, Y1) => 99.67/15.01 in(Y2, 99.67/15.01 symdiff(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (in(Y2, Y1) => 99.67/15.01 (~(in(Y2, 99.67/15.01 symdiff(Y0, Y1))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, Y0))) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 (~(in(Y2, 99.67/15.01 symdiff(Y0, 99.67/15.01 Y1))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 in(Y1, 99.67/15.01 setadjoin(Y0, 99.67/15.01 setadjoin(Y1, emptyset))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 in(Y0, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, 99.67/15.01 setadjoin(Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 in(Y1, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, 99.67/15.01 setadjoin(Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (??((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))) & 99.67/15.01 (??((^[Y3 : $i]: 99.67/15.01 ( 99.67/15.01 in(Y3, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))) & 99.67/15.01 ( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)) = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (??((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))) & 99.67/15.01 (??((^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))) & 99.67/15.01 (setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)) = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (in(Y1, Y0) => 99.67/15.01 subset( 99.67/15.01 setadjoin(Y1, 99.67/15.01 emptyset), Y0)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (in(Y1, Y0) => 99.67/15.01 in( 99.67/15.01 setadjoin(Y1, 99.67/15.01 emptyset), 99.67/15.01 powerset(Y0))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset))) => 99.67/15.01 ((Y2 = Y1) | 99.67/15.01 (Y2 = Y0)))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (!!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 subset( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 binunion( 99.67/15.01 Y0, Y1)))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 Y0) => 99.67/15.01 ( 99.67/15.01 !!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ( 99.67/15.01 in(Y2, 99.67/15.01 Y0) => 99.67/15.01 ( 99.67/15.01 !!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 subset( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 Y0) => 99.67/15.01 (!!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1)))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 Y0) => 99.67/15.01 (!!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1)))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!(( 99.67/15.01 ^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 Y0) => 99.67/15.01 ( 99.67/15.01 !!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 dsetconstr( 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))), 99.67/15.01 (^[Y4 : $i]: 99.67/15.01 (??(( 99.67/15.01 ^[Y5 : $i]: 99.67/15.01 (in(Y5, 99.67/15.01 Y0) & 99.67/15.01 (??(( 99.67/15.01 ^[Y6 : $i]: 99.67/15.01 (in(Y6, 99.67/15.01 Y1) & 99.67/15.01 (Y4 = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y5, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y5, 99.67/15.01 setadjoin( 99.67/15.01 Y6, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))))))))))))))))))))))))))) => 99.67/15.01 (!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!(( 99.67/15.01 ^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 dsetconstr( 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))), 99.67/15.01 (^[Y3 : $i]: 99.67/15.01 (??(( 99.67/15.01 ^[Y4 : $i]: 99.67/15.01 (in(Y4, 99.67/15.01 Y0) & 99.67/15.01 (??(( 99.67/15.01 ^[Y5 : $i]: 99.67/15.01 (in(Y5, 99.67/15.01 Y1) & 99.67/15.01 (Y3 = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y4, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y4, 99.67/15.01 setadjoin( 99.67/15.01 Y5, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))))))))))))) => 99.67/15.01 ( 99.67/15.01 ??(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (( 99.67/15.01 ??(( 99.67/15.01 ^[Y4 : $i]: 99.67/15.01 (in(Y4, 99.67/15.01 Y1) & 99.67/15.01 (Y2 = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 setadjoin( 99.67/15.01 Y4, 99.67/15.01 emptyset)), 99.67/15.01 emptyset))))))) & 99.67/15.01 in(Y3, 99.67/15.01 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.67/15.01 inference('lazy_cnf_imply', [status(thm)], ['259'])). 99.67/15.01 tff('261', plain, 99.67/15.01 ~ ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(Y1, binunion(Y0, Y1)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (in(Y2, Y1) => in(Y2, binintersect(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (subset(Y2, Y0) => 99.67/15.01 (subset(Y2, Y1) => 99.67/15.01 subset(Y2, binintersect(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, binintersect(Y0, Y1)) => in(Y2, Y0))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y0))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (subset(Y0, Y1) => (binintersect(Y0, Y1) = Y0)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 ((binintersect(Y0, Y1) = Y1) => subset(Y1, Y0)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, binintersect(Y0, Y1)) => 99.67/15.01 in(Y2, Y1))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & in(Y2, Y1))))))) => 99.67/15.01 (binintersect(Y0, Y1) = emptyset)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y1))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (subset(Y1, Y0) => (binintersect(Y0, Y1) = Y1)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 ((binintersect(Y0, Y1) = Y0) => 99.67/15.01 subset(Y0, Y1)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (binintersect(Y0, binunion(Y1, Y2)) = 99.67/15.01 binunion(binintersect(Y0, Y1), 99.67/15.01 binintersect(Y0, Y2)))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 in(Y2, setminus(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, setminus(Y0, Y1)) => 99.67/15.01 in(Y2, Y0))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, setminus(Y0, Y1)) => 99.67/15.01 (~(in(Y2, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (subset(Y0, Y1) => 99.67/15.01 (setminus(Y0, Y1) = emptyset)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.01 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 (~(in(Y2, Y0)))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, Y0))) => 99.67/15.01 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y1) => 99.67/15.01 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 subset(setminus(Y0, Y1), Y0))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 ((setminus(Y0, Y1) = emptyset) => 99.67/15.01 subset(Y0, Y1)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, symdiff(Y0, Y1)) => 99.67/15.01 (!!((^[Y3 : $o]: 99.67/15.01 ((in(Y2, Y0) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 Y3)) => 99.67/15.01 (((~(in(Y2, Y0))) => 99.67/15.01 (in(Y2, Y1) => 99.67/15.01 Y3)) => 99.67/15.01 Y3))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, Y0))) => 99.67/15.01 (in(Y2, Y1) => 99.67/15.01 in(Y2, 99.67/15.01 symdiff(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (in(Y2, Y1) => 99.67/15.01 (~(in(Y2, 99.67/15.01 symdiff(Y0, Y1))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, Y0))) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 (~(in(Y2, 99.67/15.01 symdiff(Y0, Y1))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 in(Y1, 99.67/15.01 setadjoin(Y0, 99.67/15.01 setadjoin(Y1, emptyset))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 in(Y0, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, 99.67/15.01 setadjoin(Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 in(Y1, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, 99.67/15.01 setadjoin(Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (??((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))) & 99.67/15.01 (??((^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))) & 99.67/15.01 ( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)) = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (??((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))) & 99.67/15.01 (??((^[Y3 : $i]: 99.67/15.01 ( 99.67/15.01 in(Y3, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))) & 99.67/15.01 ( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)) = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (in(Y1, Y0) => 99.67/15.01 subset( 99.67/15.01 setadjoin(Y1, 99.67/15.01 emptyset), Y0)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (in(Y1, Y0) => 99.67/15.01 in( 99.67/15.01 setadjoin(Y1, 99.67/15.01 emptyset), 99.67/15.01 powerset(Y0))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset))) => 99.67/15.01 ((Y2 = Y1) | 99.67/15.01 (Y2 = Y0)))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (!!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 subset( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 binunion( 99.67/15.01 Y0, Y1)))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (!!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 Y0) => 99.67/15.01 ( 99.67/15.01 !!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 subset( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ( 99.67/15.01 in(Y2, 99.67/15.01 Y0) => 99.67/15.01 ( 99.67/15.01 !!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1)))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 Y0) => 99.67/15.01 (!!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1)))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 Y0) => 99.67/15.01 (!!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 dsetconstr( 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))), 99.67/15.01 (^[Y4 : $i]: 99.67/15.01 (??(( 99.67/15.01 ^[Y5 : $i]: 99.67/15.01 (in(Y5, 99.67/15.01 Y0) & 99.67/15.01 (??(( 99.67/15.01 ^[Y6 : $i]: 99.67/15.01 (in(Y6, 99.67/15.01 Y1) & 99.67/15.01 (Y4 = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y5, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y5, 99.67/15.01 setadjoin( 99.67/15.01 Y6, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))))))))))))))))))))))))))) => 99.67/15.01 (!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 dsetconstr( 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))), 99.67/15.01 (^[Y3 : $i]: 99.67/15.01 (??(( 99.67/15.01 ^[Y4 : $i]: 99.67/15.01 (in(Y4, 99.67/15.01 Y0) & 99.67/15.01 (??(( 99.67/15.01 ^[Y5 : $i]: 99.67/15.01 (in(Y5, 99.67/15.01 Y1) & 99.67/15.01 (Y3 = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y4, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y4, 99.67/15.01 setadjoin( 99.67/15.01 Y5, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))))))))))))) => 99.67/15.01 (??(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (( 99.67/15.01 ??(( 99.67/15.01 ^[Y4 : $i]: 99.67/15.01 (in(Y4, 99.67/15.01 Y1) & 99.67/15.01 (Y2 = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 setadjoin( 99.67/15.01 Y4, 99.67/15.01 emptyset)), 99.67/15.01 emptyset))))))) & 99.67/15.01 in(Y3, 99.67/15.01 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.67/15.01 inference('lazy_cnf_imply', [status(thm)], ['260'])). 99.67/15.01 tff('262', plain, 99.67/15.01 ~ ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (in(Y2, Y1) => in(Y2, binintersect(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (subset(Y2, Y0) => 99.67/15.01 (subset(Y2, Y1) => 99.67/15.01 subset(Y2, binintersect(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, binintersect(Y0, Y1)) => in(Y2, Y0))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y0))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (subset(Y0, Y1) => (binintersect(Y0, Y1) = Y0)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 ((binintersect(Y0, Y1) = Y1) => subset(Y1, Y0)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, binintersect(Y0, Y1)) => in(Y2, Y1))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & in(Y2, Y1))))))) => 99.67/15.01 (binintersect(Y0, Y1) = emptyset)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y1))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (subset(Y1, Y0) => (binintersect(Y0, Y1) = Y1)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 ((binintersect(Y0, Y1) = Y0) => subset(Y0, Y1)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (binintersect(Y0, binunion(Y1, Y2)) = 99.67/15.01 binunion(binintersect(Y0, Y1), 99.67/15.01 binintersect(Y0, Y2)))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 in(Y2, setminus(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, setminus(Y0, Y1)) => 99.67/15.01 in(Y2, Y0))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, setminus(Y0, Y1)) => 99.67/15.01 (~(in(Y2, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (subset(Y0, Y1) => 99.67/15.01 (setminus(Y0, Y1) = emptyset)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.01 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 (~(in(Y2, Y0)))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, Y0))) => 99.67/15.01 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y1) => 99.67/15.01 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 subset(setminus(Y0, Y1), Y0))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 ((setminus(Y0, Y1) = emptyset) => 99.67/15.01 subset(Y0, Y1)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, symdiff(Y0, Y1)) => 99.67/15.01 (!!((^[Y3 : $o]: 99.67/15.01 ((in(Y2, Y0) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 Y3)) => 99.67/15.01 (((~(in(Y2, Y0))) => 99.67/15.01 (in(Y2, Y1) => 99.67/15.01 Y3)) => 99.67/15.01 Y3))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, Y0))) => 99.67/15.01 (in(Y2, Y1) => 99.67/15.01 in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (in(Y2, Y1) => 99.67/15.01 (~(in(Y2, 99.67/15.01 symdiff(Y0, Y1))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, Y0))) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 (~(in(Y2, 99.67/15.01 symdiff(Y0, Y1))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 in(Y1, 99.67/15.01 setadjoin(Y0, 99.67/15.01 setadjoin(Y1, emptyset))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 in(Y0, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, 99.67/15.01 setadjoin(Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 in(Y1, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, 99.67/15.01 setadjoin(Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (??((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))) & 99.67/15.01 (??((^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))) & 99.67/15.01 (setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)) = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (??((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))) & 99.67/15.01 (??((^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))) & 99.67/15.01 ( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)) = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (in(Y1, Y0) => 99.67/15.01 subset( 99.67/15.01 setadjoin(Y1, 99.67/15.01 emptyset), Y0)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (in(Y1, Y0) => 99.67/15.01 in( 99.67/15.01 setadjoin(Y1, 99.67/15.01 emptyset), 99.67/15.01 powerset(Y0))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset))) => 99.67/15.01 ((Y2 = Y1) | 99.67/15.01 (Y2 = Y0)))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (!!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 ( 99.67/15.01 in(Y3, 99.67/15.01 Y1) => 99.67/15.01 subset( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 binunion( 99.67/15.01 Y0, Y1)))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (!!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (!!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 subset( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 Y0) => 99.67/15.01 ( 99.67/15.01 !!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1)))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ( 99.67/15.01 in(Y2, 99.67/15.01 Y0) => 99.67/15.01 ( 99.67/15.01 !!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1)))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 Y0) => 99.67/15.01 (!!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 dsetconstr( 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))), 99.67/15.01 (^[Y4 : $i]: 99.67/15.01 (??(( 99.67/15.01 ^[Y5 : $i]: 99.67/15.01 (in(Y5, 99.67/15.01 Y0) & 99.67/15.01 (??(( 99.67/15.01 ^[Y6 : $i]: 99.67/15.01 (in(Y6, 99.67/15.01 Y1) & 99.67/15.01 (Y4 = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y5, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y5, 99.67/15.01 setadjoin( 99.67/15.01 Y6, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))))))))))))))))))))))))))) => 99.67/15.01 (!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 dsetconstr( 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))), 99.67/15.01 (^[Y3 : $i]: 99.67/15.01 (??(( 99.67/15.01 ^[Y4 : $i]: 99.67/15.01 (in(Y4, 99.67/15.01 Y0) & 99.67/15.01 (??(( 99.67/15.01 ^[Y5 : $i]: 99.67/15.01 (in(Y5, 99.67/15.01 Y1) & 99.67/15.01 (Y3 = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y4, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y4, 99.67/15.01 setadjoin( 99.67/15.01 Y5, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))))))))))))) => 99.67/15.01 (??(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (( 99.67/15.01 ??(( 99.67/15.01 ^[Y4 : $i]: 99.67/15.01 (in(Y4, 99.67/15.01 Y1) & 99.67/15.01 (Y2 = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 setadjoin( 99.67/15.01 Y4, 99.67/15.01 emptyset)), 99.67/15.01 emptyset))))))) & 99.67/15.01 in(Y3, 99.67/15.01 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.67/15.01 inference('lazy_cnf_imply', [status(thm)], ['261'])). 99.67/15.01 tff('263', plain, 99.67/15.01 ~ ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (subset(Y2, Y0) => 99.67/15.01 (subset(Y2, Y1) => 99.67/15.01 subset(Y2, binintersect(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, binintersect(Y0, Y1)) => in(Y2, Y0))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y0))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (subset(Y0, Y1) => (binintersect(Y0, Y1) = Y0)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 ((binintersect(Y0, Y1) = Y1) => subset(Y1, Y0)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, binintersect(Y0, Y1)) => in(Y2, Y1))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & in(Y2, Y1))))))) => 99.67/15.01 (binintersect(Y0, Y1) = emptyset)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y1))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (subset(Y1, Y0) => (binintersect(Y0, Y1) = Y1)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 ((binintersect(Y0, Y1) = Y0) => subset(Y0, Y1)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (binintersect(Y0, binunion(Y1, Y2)) = 99.67/15.01 binunion(binintersect(Y0, Y1), 99.67/15.01 binintersect(Y0, Y2)))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 in(Y2, setminus(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, setminus(Y0, Y1)) => 99.67/15.01 in(Y2, Y0))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, setminus(Y0, Y1)) => 99.67/15.01 (~(in(Y2, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (subset(Y0, Y1) => 99.67/15.01 (setminus(Y0, Y1) = emptyset)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.01 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 (~(in(Y2, Y0)))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, Y0))) => 99.67/15.01 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y1) => 99.67/15.01 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 subset(setminus(Y0, Y1), Y0))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 ((setminus(Y0, Y1) = emptyset) => 99.67/15.01 subset(Y0, Y1)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, symdiff(Y0, Y1)) => 99.67/15.01 (!!((^[Y3 : $o]: 99.67/15.01 ((in(Y2, Y0) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 Y3)) => 99.67/15.01 (((~(in(Y2, Y0))) => 99.67/15.01 (in(Y2, Y1) => Y3)) => 99.67/15.01 Y3))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, Y0))) => 99.67/15.01 (in(Y2, Y1) => 99.67/15.01 in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (in(Y2, Y1) => 99.67/15.01 (~(in(Y2, 99.67/15.01 symdiff(Y0, Y1))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, Y0))) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 (~(in(Y2, 99.67/15.01 symdiff(Y0, Y1))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 in(Y1, 99.67/15.01 setadjoin(Y0, 99.67/15.01 setadjoin(Y1, emptyset))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 in(Y0, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, 99.67/15.01 setadjoin(Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 in(Y1, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, 99.67/15.01 setadjoin(Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (??((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))) & 99.67/15.01 (??((^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))) & 99.67/15.01 (setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)) = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (??((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))) & 99.67/15.01 (??((^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))) & 99.67/15.01 (setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)) = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (in(Y1, Y0) => 99.67/15.01 subset( 99.67/15.01 setadjoin(Y1, 99.67/15.01 emptyset), Y0)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (in(Y1, Y0) => 99.67/15.01 in( 99.67/15.01 setadjoin(Y1, 99.67/15.01 emptyset), 99.67/15.01 powerset(Y0))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset))) => 99.67/15.01 ((Y2 = Y1) | 99.67/15.01 (Y2 = Y0)))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (!!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 subset( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 binunion( 99.67/15.01 Y0, Y1)))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (!!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 ( 99.67/15.01 in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (!!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 subset( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (!!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1)))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 Y0) => 99.67/15.01 ( 99.67/15.01 !!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1)))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ( 99.67/15.01 in(Y2, 99.67/15.01 Y0) => 99.67/15.01 ( 99.67/15.01 !!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 dsetconstr( 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))), 99.67/15.01 (^[Y4 : $i]: 99.67/15.01 (??(( 99.67/15.01 ^[Y5 : $i]: 99.67/15.01 (in(Y5, 99.67/15.01 Y0) & 99.67/15.01 (??(( 99.67/15.01 ^[Y6 : $i]: 99.67/15.01 (in(Y6, 99.67/15.01 Y1) & 99.67/15.01 (Y4 = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y5, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y5, 99.67/15.01 setadjoin( 99.67/15.01 Y6, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))))))))))))))))))))))))))) => 99.67/15.01 (!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ( 99.67/15.01 in(Y2, 99.67/15.01 dsetconstr( 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))), 99.67/15.01 (^[Y3 : $i]: 99.67/15.01 (??(( 99.67/15.01 ^[Y4 : $i]: 99.67/15.01 (in(Y4, 99.67/15.01 Y0) & 99.67/15.01 (??(( 99.67/15.01 ^[Y5 : $i]: 99.67/15.01 (in(Y5, 99.67/15.01 Y1) & 99.67/15.01 (Y3 = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y4, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y4, 99.67/15.01 setadjoin( 99.67/15.01 Y5, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))))))))))))) => 99.67/15.01 ( 99.67/15.01 ??(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (( 99.67/15.01 ??(( 99.67/15.01 ^[Y4 : $i]: 99.67/15.01 (in(Y4, 99.67/15.01 Y1) & 99.67/15.01 (Y2 = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 setadjoin( 99.67/15.01 Y4, 99.67/15.01 emptyset)), 99.67/15.01 emptyset))))))) & 99.67/15.01 in(Y3, 99.67/15.01 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.67/15.01 inference('lazy_cnf_imply', [status(thm)], ['262'])). 99.67/15.01 tff('264', plain, 99.67/15.01 ~ ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, binintersect(Y0, Y1)) => in(Y2, Y0))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y0))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (subset(Y0, Y1) => (binintersect(Y0, Y1) = Y0)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 ((binintersect(Y0, Y1) = Y1) => subset(Y1, Y0)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, binintersect(Y0, Y1)) => in(Y2, Y1))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & in(Y2, Y1))))))) => 99.67/15.01 (binintersect(Y0, Y1) = emptyset)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y1))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (subset(Y1, Y0) => (binintersect(Y0, Y1) = Y1)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 ((binintersect(Y0, Y1) = Y0) => subset(Y0, Y1)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (binintersect(Y0, binunion(Y1, Y2)) = 99.67/15.01 binunion(binintersect(Y0, Y1), 99.67/15.01 binintersect(Y0, Y2)))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 in(Y2, setminus(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, setminus(Y0, Y1)) => 99.67/15.01 in(Y2, Y0))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, setminus(Y0, Y1)) => 99.67/15.01 (~(in(Y2, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (subset(Y0, Y1) => 99.67/15.01 (setminus(Y0, Y1) = emptyset)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.01 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 (~(in(Y2, Y0)))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, Y0))) => 99.67/15.01 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y1) => 99.67/15.01 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: subset(setminus(Y0, Y1), Y0))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 ((setminus(Y0, Y1) = emptyset) => 99.67/15.01 subset(Y0, Y1)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, symdiff(Y0, Y1)) => 99.67/15.01 (!!((^[Y3 : $o]: 99.67/15.01 ((in(Y2, Y0) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 Y3)) => 99.67/15.01 (((~(in(Y2, Y0))) => 99.67/15.01 (in(Y2, Y1) => Y3)) => 99.67/15.01 Y3))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, Y0))) => 99.67/15.01 (in(Y2, Y1) => 99.67/15.01 in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (in(Y2, Y1) => 99.67/15.01 (~(in(Y2, 99.67/15.01 symdiff(Y0, Y1))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, Y0))) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 (~(in(Y2, 99.67/15.01 symdiff(Y0, Y1))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 in(Y1, 99.67/15.01 setadjoin(Y0, 99.67/15.01 setadjoin(Y1, emptyset))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 in(Y0, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, 99.67/15.01 setadjoin(Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 in(Y1, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, 99.67/15.01 setadjoin(Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (??((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))) & 99.67/15.01 (??((^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))) & 99.67/15.01 (setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)) = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (??((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))) & 99.67/15.01 (??((^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))) & 99.67/15.01 (setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)) = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (in(Y1, Y0) => 99.67/15.01 subset( 99.67/15.01 setadjoin(Y1, emptyset), 99.67/15.01 Y0)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (in(Y1, Y0) => 99.67/15.01 in( 99.67/15.01 setadjoin(Y1, 99.67/15.01 emptyset), 99.67/15.01 powerset(Y0))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 in( 99.67/15.01 setadjoin(Y2, 99.67/15.01 emptyset), 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset))) => 99.67/15.01 ((Y2 = Y1) | 99.67/15.01 (Y2 = Y0)))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (!!((^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 subset( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 binunion( 99.67/15.01 Y0, Y1)))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (!!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (!!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 ( 99.67/15.01 in(Y3, 99.67/15.01 Y1) => 99.67/15.01 subset( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (!!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1)))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (!!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1)))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 Y0) => 99.67/15.01 ( 99.67/15.01 !!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 dsetconstr( 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))), 99.67/15.01 (^[Y4 : $i]: 99.67/15.01 (??(( 99.67/15.01 ^[Y5 : $i]: 99.67/15.01 (in(Y5, 99.67/15.01 Y0) & 99.67/15.01 (??(( 99.67/15.01 ^[Y6 : $i]: 99.67/15.01 (in(Y6, 99.67/15.01 Y1) & 99.67/15.01 (Y4 = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y5, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y5, 99.67/15.01 setadjoin( 99.67/15.01 Y6, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))))))))))))))))))))))))))) => 99.67/15.01 (!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 dsetconstr( 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))), 99.67/15.01 (^[Y3 : $i]: 99.67/15.01 (??(( 99.67/15.01 ^[Y4 : $i]: 99.67/15.01 (in(Y4, 99.67/15.01 Y0) & 99.67/15.01 (??(( 99.67/15.01 ^[Y5 : $i]: 99.67/15.01 (in(Y5, 99.67/15.01 Y1) & 99.67/15.01 (Y3 = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y4, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y4, 99.67/15.01 setadjoin( 99.67/15.01 Y5, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))))))))))))) => 99.67/15.01 ( 99.67/15.01 ??(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (( 99.67/15.01 ??(( 99.67/15.01 ^[Y4 : $i]: 99.67/15.01 (in(Y4, 99.67/15.01 Y1) & 99.67/15.01 (Y2 = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 setadjoin( 99.67/15.01 Y4, 99.67/15.01 emptyset)), 99.67/15.01 emptyset))))))) & 99.67/15.01 in(Y3, 99.67/15.01 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.67/15.01 inference('lazy_cnf_imply', [status(thm)], ['263'])). 99.67/15.01 tff('265', plain, 99.67/15.01 ~ ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y0))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (subset(Y0, Y1) => (binintersect(Y0, Y1) = Y0)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 ((binintersect(Y0, Y1) = Y1) => subset(Y1, Y0)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, binintersect(Y0, Y1)) => in(Y2, Y1))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & in(Y2, Y1))))))) => 99.67/15.01 (binintersect(Y0, Y1) = emptyset)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y1))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (subset(Y1, Y0) => (binintersect(Y0, Y1) = Y1)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 ((binintersect(Y0, Y1) = Y0) => subset(Y0, Y1)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (binintersect(Y0, binunion(Y1, Y2)) = 99.67/15.01 binunion(binintersect(Y0, Y1), 99.67/15.01 binintersect(Y0, Y2)))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 in(Y2, setminus(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, setminus(Y0, Y1)) => in(Y2, Y0))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, setminus(Y0, Y1)) => 99.67/15.01 (~(in(Y2, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (subset(Y0, Y1) => 99.67/15.01 (setminus(Y0, Y1) = emptyset)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.01 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 (~(in(Y2, Y0)))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, Y0))) => 99.67/15.01 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y1) => 99.67/15.01 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: subset(setminus(Y0, Y1), Y0))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 ((setminus(Y0, Y1) = emptyset) => 99.67/15.01 subset(Y0, Y1)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, symdiff(Y0, Y1)) => 99.67/15.01 (!!((^[Y3 : $o]: 99.67/15.01 ((in(Y2, Y0) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 Y3)) => 99.67/15.01 (((~(in(Y2, Y0))) => 99.67/15.01 (in(Y2, Y1) => Y3)) => 99.67/15.01 Y3))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, Y0))) => 99.67/15.01 (in(Y2, Y1) => 99.67/15.01 in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (in(Y2, Y1) => 99.67/15.01 (~(in(Y2, 99.67/15.01 symdiff(Y0, Y1))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, Y0))) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 (~(in(Y2, 99.67/15.01 symdiff(Y0, Y1))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 in(Y1, 99.67/15.01 setadjoin(Y0, 99.67/15.01 setadjoin(Y1, emptyset))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 in(Y0, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, 99.67/15.01 setadjoin(Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 in(Y1, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, 99.67/15.01 setadjoin(Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (??((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))) & 99.67/15.01 (??((^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))) & 99.67/15.01 (setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)) = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (??((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))) & 99.67/15.01 (??((^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))) & 99.67/15.01 (setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)) = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (in(Y1, Y0) => 99.67/15.01 subset( 99.67/15.01 setadjoin(Y1, emptyset), 99.67/15.01 Y0)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (in(Y1, Y0) => 99.67/15.01 in( 99.67/15.01 setadjoin(Y1, emptyset), 99.67/15.01 powerset(Y0))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 in( 99.67/15.01 setadjoin(Y2, 99.67/15.01 emptyset), 99.67/15.01 powerset( 99.67/15.01 binunion(Y0, 99.67/15.01 Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 setadjoin(Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset))) => 99.67/15.01 ((Y2 = Y1) | 99.67/15.01 (Y2 = Y0)))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (!!((^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 subset( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 binunion( 99.67/15.01 Y0, Y1)))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (!!((^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (!!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 subset( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (!!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 ( 99.67/15.01 in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1)))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (!!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1)))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (!!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 dsetconstr( 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))), 99.67/15.01 (^[Y4 : $i]: 99.67/15.01 (??(( 99.67/15.01 ^[Y5 : $i]: 99.67/15.01 (in(Y5, 99.67/15.01 Y0) & 99.67/15.01 (??(( 99.67/15.01 ^[Y6 : $i]: 99.67/15.01 (in(Y6, 99.67/15.01 Y1) & 99.67/15.01 (Y4 = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y5, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y5, 99.67/15.01 setadjoin( 99.67/15.01 Y6, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))))))))))))))))))))))))))) => 99.67/15.01 (!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 dsetconstr( 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))), 99.67/15.01 (^[Y3 : $i]: 99.67/15.01 (??(( 99.67/15.01 ^[Y4 : $i]: 99.67/15.01 (in(Y4, 99.67/15.01 Y0) & 99.67/15.01 (??(( 99.67/15.01 ^[Y5 : $i]: 99.67/15.01 (in(Y5, 99.67/15.01 Y1) & 99.67/15.01 (Y3 = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y4, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y4, 99.67/15.01 setadjoin( 99.67/15.01 Y5, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))))))))))))) => 99.67/15.01 (??(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (( 99.67/15.01 ??(( 99.67/15.01 ^[Y4 : $i]: 99.67/15.01 (in(Y4, 99.67/15.01 Y1) & 99.67/15.01 (Y2 = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 setadjoin( 99.67/15.01 Y4, 99.67/15.01 emptyset)), 99.67/15.01 emptyset))))))) & 99.67/15.01 in(Y3, 99.67/15.01 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.67/15.01 inference('lazy_cnf_imply', [status(thm)], ['264'])). 99.67/15.01 tff('266', plain, 99.67/15.01 ~ ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (subset(Y0, Y1) => (binintersect(Y0, Y1) = Y0)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 ((binintersect(Y0, Y1) = Y1) => subset(Y1, Y0)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, binintersect(Y0, Y1)) => in(Y2, Y1))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & in(Y2, Y1))))))) => 99.67/15.01 (binintersect(Y0, Y1) = emptyset)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y1))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (subset(Y1, Y0) => (binintersect(Y0, Y1) = Y1)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 ((binintersect(Y0, Y1) = Y0) => subset(Y0, Y1)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (binintersect(Y0, binunion(Y1, Y2)) = 99.67/15.01 binunion(binintersect(Y0, Y1), 99.67/15.01 binintersect(Y0, Y2)))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 in(Y2, setminus(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, setminus(Y0, Y1)) => in(Y2, Y0))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, setminus(Y0, Y1)) => 99.67/15.01 (~(in(Y2, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (subset(Y0, Y1) => 99.67/15.01 (setminus(Y0, Y1) = emptyset)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.01 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.01 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, Y0))) => 99.67/15.01 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y1) => 99.67/15.01 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: subset(setminus(Y0, Y1), Y0))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 ((setminus(Y0, Y1) = emptyset) => 99.67/15.01 subset(Y0, Y1)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, symdiff(Y0, Y1)) => 99.67/15.01 (!!((^[Y3 : $o]: 99.67/15.01 ((in(Y2, Y0) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 Y3)) => 99.67/15.01 (((~(in(Y2, Y0))) => 99.67/15.01 (in(Y2, Y1) => Y3)) => 99.67/15.01 Y3))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, Y0))) => 99.67/15.01 (in(Y2, Y1) => 99.67/15.01 in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (in(Y2, Y1) => 99.67/15.01 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 ((~(in(Y2, Y0))) => 99.67/15.01 ((~(in(Y2, Y1))) => 99.67/15.01 (~(in(Y2, 99.67/15.01 symdiff(Y0, Y1))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 in(Y1, 99.67/15.01 setadjoin(Y0, 99.67/15.01 setadjoin(Y1, emptyset))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 in(Y0, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, 99.67/15.01 setadjoin(Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 in(Y1, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, 99.67/15.01 setadjoin(Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (??((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))) & 99.67/15.01 (??((^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))) & 99.67/15.01 (setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)) = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (??((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin(Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))) & 99.67/15.01 (??((^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 setunion( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))) & 99.67/15.01 (setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)) = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (in(Y1, Y0) => 99.67/15.01 subset( 99.67/15.01 setadjoin(Y1, emptyset), 99.67/15.01 Y0)))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (in(Y1, Y0) => 99.67/15.01 in( 99.67/15.01 setadjoin(Y1, emptyset), 99.67/15.01 powerset(Y0))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 in( 99.67/15.01 setadjoin(Y2, 99.67/15.01 emptyset), 99.67/15.01 powerset( 99.67/15.01 binunion(Y0, 99.67/15.01 Y1))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 setadjoin(Y0, 99.67/15.01 setadjoin( 99.67/15.01 Y1, 99.67/15.01 emptyset))) => 99.67/15.01 ((Y2 = Y1) | 99.67/15.01 (Y2 = Y0)))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (!!((^[Y3 : $i]: 99.67/15.01 ( 99.67/15.01 in(Y3, 99.67/15.01 Y1) => 99.67/15.01 subset( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 binunion( 99.67/15.01 Y0, Y1)))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (!!((^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (!!((^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 subset( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (!!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1)))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (!!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 ( 99.67/15.01 in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1)))))))))))))))))) => 99.67/15.01 ((!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, Y0) => 99.67/15.01 (!!(( 99.67/15.01 ^[Y3 : $i]: 99.67/15.01 (in(Y3, 99.67/15.01 Y1) => 99.67/15.01 in( 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y2, 99.67/15.01 setadjoin( 99.67/15.01 Y3, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)), 99.67/15.01 dsetconstr( 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))), 99.67/15.01 (^[Y4 : $i]: 99.67/15.01 (??(( 99.67/15.01 ^[Y5 : $i]: 99.67/15.01 (in(Y5, 99.67/15.01 Y0) & 99.67/15.01 (??(( 99.67/15.01 ^[Y6 : $i]: 99.67/15.01 (in(Y6, 99.67/15.01 Y1) & 99.67/15.01 (Y4 = 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y5, 99.67/15.01 emptyset), 99.67/15.01 setadjoin( 99.67/15.01 setadjoin( 99.67/15.01 Y5, 99.67/15.01 setadjoin( 99.67/15.01 Y6, 99.67/15.01 emptyset)), 99.67/15.01 emptyset)))))))))))))))))))))))))))) => 99.67/15.01 (!!((^[Y0 : $i]: 99.67/15.01 (!!((^[Y1 : $i]: 99.67/15.01 (!!((^[Y2 : $i]: 99.67/15.01 (in(Y2, 99.67/15.01 dsetconstr( 99.67/15.01 powerset( 99.67/15.01 powerset( 99.67/15.01 binunion( 99.67/15.01 Y0, Y1))), 99.67/15.01 (^[Y3 : $i]: 99.67/15.01 (??(( 99.67/15.01 ^[Y4 : $i]: 99.67/15.01 (in(Y4, 99.67/15.02 Y0) & 99.67/15.02 (??(( 99.67/15.02 ^[Y5 : $i]: 99.67/15.02 (in(Y5, 99.67/15.02 Y1) & 99.67/15.02 (Y3 = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y4, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y4, 99.67/15.02 setadjoin( 99.67/15.02 Y5, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))))))))))))) => 99.67/15.02 (??(( 99.67/15.02 ^[Y3 : $i]: 99.67/15.02 (( 99.67/15.02 ??(( 99.67/15.02 ^[Y4 : $i]: 99.67/15.02 (in(Y4, 99.67/15.02 Y1) & 99.67/15.02 (Y2 = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 setadjoin( 99.67/15.02 Y4, 99.67/15.02 emptyset)), 99.67/15.02 emptyset))))))) & 99.67/15.02 in(Y3, 99.67/15.02 Y0))))))))))))))))))))))))))))))))))))))))))))))))))))), 99.67/15.02 inference('lazy_cnf_imply', [status(thm)], ['265'])). 99.67/15.02 tff('267', plain, 99.67/15.02 ~ ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 ((binintersect(Y0, Y1) = Y1) => subset(Y1, Y0)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, binintersect(Y0, Y1)) => in(Y2, Y1))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & in(Y2, Y1))))))) => 99.67/15.02 (binintersect(Y0, Y1) = emptyset)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y1))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (subset(Y1, Y0) => (binintersect(Y0, Y1) = Y1)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 ((binintersect(Y0, Y1) = Y0) => subset(Y0, Y1)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (binintersect(Y0, binunion(Y1, Y2)) = 99.67/15.02 binunion(binintersect(Y0, Y1), 99.67/15.02 binintersect(Y0, Y2)))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 ((~(in(Y2, Y1))) => 99.67/15.02 in(Y2, setminus(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, setminus(Y0, Y1)) => in(Y2, Y0))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, setminus(Y0, Y1)) => 99.67/15.02 (~(in(Y2, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (subset(Y0, Y1) => 99.67/15.02 (setminus(Y0, Y1) = emptyset)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.02 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.02 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, Y0))) => 99.67/15.02 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y1) => 99.67/15.02 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: subset(setminus(Y0, Y1), Y0))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 ((setminus(Y0, Y1) = emptyset) => 99.67/15.02 subset(Y0, Y1)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, symdiff(Y0, Y1)) => 99.67/15.02 (!!((^[Y3 : $o]: 99.67/15.02 ((in(Y2, Y0) => 99.67/15.02 ((~(in(Y2, Y1))) => Y3)) => 99.67/15.02 (((~(in(Y2, Y0))) => 99.67/15.02 (in(Y2, Y1) => Y3)) => 99.67/15.02 Y3))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 ((~(in(Y2, Y1))) => 99.67/15.02 in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, Y0))) => 99.67/15.02 (in(Y2, Y1) => 99.67/15.02 in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (in(Y2, Y1) => 99.67/15.02 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, Y0))) => 99.67/15.02 ((~(in(Y2, Y1))) => 99.67/15.02 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 in(Y1, 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 in(Y0, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset)), 99.67/15.02 emptyset)))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 in(Y1, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (??((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin( 99.67/15.02 Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (??((^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y0, 99.67/15.02 setadjoin( 99.67/15.02 Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y0, 99.67/15.02 setadjoin( 99.67/15.02 Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)) = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (??((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin( 99.67/15.02 Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (??((^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y0, 99.67/15.02 setadjoin( 99.67/15.02 Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y0, 99.67/15.02 setadjoin( 99.67/15.02 Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)) = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (in(Y1, Y0) => 99.67/15.02 subset( 99.67/15.02 setadjoin(Y1, emptyset), 99.67/15.02 Y0)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (in(Y1, Y0) => 99.67/15.02 in( 99.67/15.02 setadjoin(Y1, emptyset), 99.67/15.02 powerset(Y0))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 in( 99.67/15.02 setadjoin(Y2, 99.67/15.02 emptyset), 99.67/15.02 powerset( 99.67/15.02 binunion(Y0, 99.67/15.02 Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset))) => 99.67/15.02 ((Y2 = Y1) | 99.67/15.02 (Y2 = Y0)))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 Y1) => 99.67/15.02 subset( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 binunion( 99.67/15.02 Y0, Y1)))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 ( 99.67/15.02 in(Y3, 99.67/15.02 Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 Y1) => 99.67/15.02 subset( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1)))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!(( 99.67/15.02 ^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1)))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!(( 99.67/15.02 ^[Y3 : $i]: 99.67/15.02 ( 99.67/15.02 in(Y3, 99.67/15.02 Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 dsetconstr( 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1))), 99.67/15.02 (^[Y4 : $i]: 99.67/15.02 (??(( 99.67/15.02 ^[Y5 : $i]: 99.67/15.02 (in(Y5, 99.67/15.02 Y0) & 99.67/15.02 (??(( 99.67/15.02 ^[Y6 : $i]: 99.67/15.02 (in(Y6, 99.67/15.02 Y1) & 99.67/15.02 (Y4 = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y5, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y5, 99.67/15.02 setadjoin( 99.67/15.02 Y6, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))))))))))))))))))))))))))) => 99.67/15.02 (!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 dsetconstr( 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1))), 99.67/15.02 (^[Y3 : $i]: 99.67/15.02 (??(( 99.67/15.02 ^[Y4 : $i]: 99.67/15.02 (in(Y4, 99.67/15.02 Y0) & 99.67/15.02 (??(( 99.67/15.02 ^[Y5 : $i]: 99.67/15.02 (in(Y5, 99.67/15.02 Y1) & 99.67/15.02 (Y3 = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y4, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y4, 99.67/15.02 setadjoin( 99.67/15.02 Y5, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))))))))))))) => 99.67/15.02 (??(( 99.67/15.02 ^[Y3 : $i]: 99.67/15.02 ( 99.67/15.02 ( 99.67/15.02 ??(( 99.67/15.02 ^[Y4 : $i]: 99.67/15.02 (in(Y4, 99.67/15.02 Y1) & 99.67/15.02 (Y2 = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 setadjoin( 99.67/15.02 Y4, 99.67/15.02 emptyset)), 99.67/15.02 emptyset))))))) & 99.67/15.02 in(Y3, 99.67/15.02 Y0)))))))))))))))))))))))))))))))))))))))))))))))))))), 99.67/15.02 inference('lazy_cnf_imply', [status(thm)], ['266'])). 99.67/15.02 tff('268', plain, 99.67/15.02 ~ ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, binintersect(Y0, Y1)) => in(Y2, Y1))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & in(Y2, Y1))))))) => 99.67/15.02 (binintersect(Y0, Y1) = emptyset)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y1))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (subset(Y1, Y0) => (binintersect(Y0, Y1) = Y1)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 ((binintersect(Y0, Y1) = Y0) => subset(Y0, Y1)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (binintersect(Y0, binunion(Y1, Y2)) = 99.67/15.02 binunion(binintersect(Y0, Y1), 99.67/15.02 binintersect(Y0, Y2)))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 ((~(in(Y2, Y1))) => 99.67/15.02 in(Y2, setminus(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, setminus(Y0, Y1)) => in(Y2, Y0))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, setminus(Y0, Y1)) => 99.67/15.02 (~(in(Y2, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (subset(Y0, Y1) => 99.67/15.02 (setminus(Y0, Y1) = emptyset)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.02 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.02 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, Y0))) => 99.67/15.02 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y1) => 99.67/15.02 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: subset(setminus(Y0, Y1), Y0))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 ((setminus(Y0, Y1) = emptyset) => 99.67/15.02 subset(Y0, Y1)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, symdiff(Y0, Y1)) => 99.67/15.02 (!!((^[Y3 : $o]: 99.67/15.02 ((in(Y2, Y0) => 99.67/15.02 ((~(in(Y2, Y1))) => Y3)) => 99.67/15.02 (((~(in(Y2, Y0))) => 99.67/15.02 (in(Y2, Y1) => Y3)) => 99.67/15.02 Y3))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 ((~(in(Y2, Y1))) => 99.67/15.02 in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, Y0))) => 99.67/15.02 (in(Y2, Y1) => 99.67/15.02 in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (in(Y2, Y1) => 99.67/15.02 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, Y0))) => 99.67/15.02 ((~(in(Y2, Y1))) => 99.67/15.02 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 in(Y1, 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 in(Y0, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset)), 99.67/15.02 emptyset)))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 in(Y1, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset)), 99.67/15.02 emptyset)))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (??((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (??((^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y0, 99.67/15.02 setadjoin( 99.67/15.02 Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y0, 99.67/15.02 setadjoin( 99.67/15.02 Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)) = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (??((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin( 99.67/15.02 Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (??((^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y0, 99.67/15.02 setadjoin( 99.67/15.02 Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y0, 99.67/15.02 setadjoin( 99.67/15.02 Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)) = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (in(Y1, Y0) => 99.67/15.02 subset( 99.67/15.02 setadjoin(Y1, emptyset), 99.67/15.02 Y0)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (in(Y1, Y0) => 99.67/15.02 in(setadjoin(Y1, emptyset), 99.67/15.02 powerset(Y0))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 in( 99.67/15.02 setadjoin(Y2, 99.67/15.02 emptyset), 99.67/15.02 powerset( 99.67/15.02 binunion(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset))) => 99.67/15.02 ((Y2 = Y1) | 99.67/15.02 (Y2 = Y0)))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 subset( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 binunion( 99.67/15.02 Y0, Y1)))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 ( 99.67/15.02 in(Y3, 99.67/15.02 Y1) => 99.67/15.02 subset( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1)))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1)))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!(( 99.67/15.02 ^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 dsetconstr( 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1))), 99.67/15.02 (^[Y4 : $i]: 99.67/15.02 (??(( 99.67/15.02 ^[Y5 : $i]: 99.67/15.02 (in(Y5, 99.67/15.02 Y0) & 99.67/15.02 (??(( 99.67/15.02 ^[Y6 : $i]: 99.67/15.02 (in(Y6, 99.67/15.02 Y1) & 99.67/15.02 (Y4 = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y5, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y5, 99.67/15.02 setadjoin( 99.67/15.02 Y6, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))))))))))))))))))))))))))) => 99.67/15.02 (!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 dsetconstr( 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1))), 99.67/15.02 ( 99.67/15.02 ^[Y3 : $i]: 99.67/15.02 (??(( 99.67/15.02 ^[Y4 : $i]: 99.67/15.02 (in(Y4, 99.67/15.02 Y0) & 99.67/15.02 (??(( 99.67/15.02 ^[Y5 : $i]: 99.67/15.02 (in(Y5, 99.67/15.02 Y1) & 99.67/15.02 (Y3 = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y4, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y4, 99.67/15.02 setadjoin( 99.67/15.02 Y5, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))))))))))))) => 99.67/15.02 (??(( 99.67/15.02 ^[Y3 : $i]: 99.67/15.02 (( 99.67/15.02 ??(( 99.67/15.02 ^[Y4 : $i]: 99.67/15.02 (in(Y4, 99.67/15.02 Y1) & 99.67/15.02 (Y2 = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 setadjoin( 99.67/15.02 Y4, 99.67/15.02 emptyset)), 99.67/15.02 emptyset))))))) & 99.67/15.02 in(Y3, 99.67/15.02 Y0))))))))))))))))))))))))))))))))))))))))))))))))))), 99.67/15.02 inference('lazy_cnf_imply', [status(thm)], ['267'])). 99.67/15.02 tff('269', plain, 99.67/15.02 ~ ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & in(Y2, Y1))))))) => 99.67/15.02 (binintersect(Y0, Y1) = emptyset)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y1))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (subset(Y1, Y0) => (binintersect(Y0, Y1) = Y1)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 ((binintersect(Y0, Y1) = Y0) => subset(Y0, Y1)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (binintersect(Y0, binunion(Y1, Y2)) = 99.67/15.02 binunion(binintersect(Y0, Y1), 99.67/15.02 binintersect(Y0, Y2)))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 ((~(in(Y2, Y1))) => 99.67/15.02 in(Y2, setminus(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, setminus(Y0, Y1)) => in(Y2, Y0))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, setminus(Y0, Y1)) => 99.67/15.02 (~(in(Y2, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (subset(Y0, Y1) => (setminus(Y0, Y1) = emptyset)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.02 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.02 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, Y0))) => 99.67/15.02 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y1) => 99.67/15.02 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: subset(setminus(Y0, Y1), Y0))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 ((setminus(Y0, Y1) = emptyset) => 99.67/15.02 subset(Y0, Y1)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, symdiff(Y0, Y1)) => 99.67/15.02 (!!((^[Y3 : $o]: 99.67/15.02 ((in(Y2, Y0) => 99.67/15.02 ((~(in(Y2, Y1))) => Y3)) => 99.67/15.02 (((~(in(Y2, Y0))) => 99.67/15.02 (in(Y2, Y1) => Y3)) => 99.67/15.02 Y3))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 ((~(in(Y2, Y1))) => 99.67/15.02 in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, Y0))) => 99.67/15.02 (in(Y2, Y1) => 99.67/15.02 in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (in(Y2, Y1) => 99.67/15.02 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, Y0))) => 99.67/15.02 ((~(in(Y2, Y1))) => 99.67/15.02 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 in(Y1, 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 in(Y0, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset)), 99.67/15.02 emptyset)))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 in(Y1, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset)), 99.67/15.02 emptyset)))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (??((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (??((^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y0, 99.67/15.02 setadjoin( 99.67/15.02 Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y0, 99.67/15.02 setadjoin( 99.67/15.02 Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)) = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (??((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (??((^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y0, 99.67/15.02 setadjoin( 99.67/15.02 Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y0, 99.67/15.02 setadjoin( 99.67/15.02 Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)) = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (in(Y1, Y0) => 99.67/15.02 subset( 99.67/15.02 setadjoin(Y1, emptyset), Y0)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (in(Y1, Y0) => 99.67/15.02 in(setadjoin(Y1, emptyset), 99.67/15.02 powerset(Y0))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 in( 99.67/15.02 setadjoin(Y2, 99.67/15.02 emptyset), 99.67/15.02 powerset( 99.67/15.02 binunion(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset))) => 99.67/15.02 ((Y2 = Y1) | 99.67/15.02 (Y2 = Y0)))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 subset( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 binunion( 99.67/15.02 Y0, Y1)))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 Y1) => 99.67/15.02 subset( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 ( 99.67/15.02 in(Y3, 99.67/15.02 Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1)))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1)))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 dsetconstr( 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1))), 99.67/15.02 (^[Y4 : $i]: 99.67/15.02 (??(( 99.67/15.02 ^[Y5 : $i]: 99.67/15.02 (in(Y5, 99.67/15.02 Y0) & 99.67/15.02 (??(( 99.67/15.02 ^[Y6 : $i]: 99.67/15.02 (in(Y6, 99.67/15.02 Y1) & 99.67/15.02 (Y4 = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y5, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y5, 99.67/15.02 setadjoin( 99.67/15.02 Y6, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))))))))))))))))))))))))))) => 99.67/15.02 (!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 dsetconstr( 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1))), 99.67/15.02 (^[Y3 : $i]: 99.67/15.02 (??(( 99.67/15.02 ^[Y4 : $i]: 99.67/15.02 (in(Y4, 99.67/15.02 Y0) & 99.67/15.02 (??(( 99.67/15.02 ^[Y5 : $i]: 99.67/15.02 (in(Y5, 99.67/15.02 Y1) & 99.67/15.02 (Y3 = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y4, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y4, 99.67/15.02 setadjoin( 99.67/15.02 Y5, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))))))))))))) => 99.67/15.02 (??((^[Y3 : $i]: 99.67/15.02 (( 99.67/15.02 ??(( 99.67/15.02 ^[Y4 : $i]: 99.67/15.02 (in(Y4, 99.67/15.02 Y1) & 99.67/15.02 (Y2 = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 setadjoin( 99.67/15.02 Y4, 99.67/15.02 emptyset)), 99.67/15.02 emptyset))))))) & 99.67/15.02 in(Y3, 99.67/15.02 Y0)))))))))))))))))))))))))))))))))))))))))))))))))), 99.67/15.02 inference('lazy_cnf_imply', [status(thm)], ['268'])). 99.67/15.02 tff('270', plain, 99.67/15.02 ~ ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y1))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (subset(Y1, Y0) => (binintersect(Y0, Y1) = Y1)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 ((binintersect(Y0, Y1) = Y0) => subset(Y0, Y1)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (binintersect(Y0, binunion(Y1, Y2)) = 99.67/15.02 binunion(binintersect(Y0, Y1), 99.67/15.02 binintersect(Y0, Y2)))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 ((~(in(Y2, Y1))) => in(Y2, setminus(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, setminus(Y0, Y1)) => in(Y2, Y0))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, setminus(Y0, Y1)) => 99.67/15.02 (~(in(Y2, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (subset(Y0, Y1) => (setminus(Y0, Y1) = emptyset)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.02 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.02 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, Y0))) => 99.67/15.02 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y1) => 99.67/15.02 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: subset(setminus(Y0, Y1), Y0))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 ((setminus(Y0, Y1) = emptyset) => 99.67/15.02 subset(Y0, Y1)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, symdiff(Y0, Y1)) => 99.67/15.02 (!!((^[Y3 : $o]: 99.67/15.02 ((in(Y2, Y0) => 99.67/15.02 ((~(in(Y2, Y1))) => Y3)) => 99.67/15.02 (((~(in(Y2, Y0))) => 99.67/15.02 (in(Y2, Y1) => Y3)) => 99.67/15.02 Y3))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 ((~(in(Y2, Y1))) => 99.67/15.02 in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, Y0))) => 99.67/15.02 (in(Y2, Y1) => 99.67/15.02 in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (in(Y2, Y1) => 99.67/15.02 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, Y0))) => 99.67/15.02 ((~(in(Y2, Y1))) => 99.67/15.02 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 in(Y1, 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 in(Y0, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset)), 99.67/15.02 emptyset)))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 in(Y1, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset)), 99.67/15.02 emptyset)))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (??((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (??((^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y0, 99.67/15.02 setadjoin( 99.67/15.02 Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y0, 99.67/15.02 setadjoin( 99.67/15.02 Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)) = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (??((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (??((^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y0, 99.67/15.02 setadjoin( 99.67/15.02 Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y0, 99.67/15.02 setadjoin( 99.67/15.02 Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)) = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (in(Y1, Y0) => 99.67/15.02 subset( 99.67/15.02 setadjoin(Y1, emptyset), Y0)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (in(Y1, Y0) => 99.67/15.02 in(setadjoin(Y1, emptyset), 99.67/15.02 powerset(Y0))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 in( 99.67/15.02 setadjoin(Y2, 99.67/15.02 emptyset), 99.67/15.02 powerset( 99.67/15.02 binunion(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset))) => 99.67/15.02 ((Y2 = Y1) | 99.67/15.02 (Y2 = Y0)))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 subset( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 binunion( 99.67/15.02 Y0, Y1)))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 subset( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1)))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 ( 99.67/15.02 in(Y3, 99.67/15.02 Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1)))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 dsetconstr( 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1))), 99.67/15.02 (^[Y4 : $i]: 99.67/15.02 (??(( 99.67/15.02 ^[Y5 : $i]: 99.67/15.02 (in(Y5, 99.67/15.02 Y0) & 99.67/15.02 (??(( 99.67/15.02 ^[Y6 : $i]: 99.67/15.02 (in(Y6, 99.67/15.02 Y1) & 99.67/15.02 (Y4 = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y5, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y5, 99.67/15.02 setadjoin( 99.67/15.02 Y6, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))))))))))))))))))))))))))) => 99.67/15.02 (!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 dsetconstr( 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1))), 99.67/15.02 (^[Y3 : $i]: 99.67/15.02 (??(( 99.67/15.02 ^[Y4 : $i]: 99.67/15.02 (in(Y4, 99.67/15.02 Y0) & 99.67/15.02 (??(( 99.67/15.02 ^[Y5 : $i]: 99.67/15.02 (in(Y5, 99.67/15.02 Y1) & 99.67/15.02 (Y3 = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y4, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y4, 99.67/15.02 setadjoin( 99.67/15.02 Y5, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))))))))))))) => 99.67/15.02 (??((^[Y3 : $i]: 99.67/15.02 (( 99.67/15.02 ??(( 99.67/15.02 ^[Y4 : $i]: 99.67/15.02 (in(Y4, 99.67/15.02 Y1) & 99.67/15.02 (Y2 = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 setadjoin( 99.67/15.02 Y4, 99.67/15.02 emptyset)), 99.67/15.02 emptyset))))))) & 99.67/15.02 in(Y3, 99.67/15.02 Y0))))))))))))))))))))))))))))))))))))))))))))))))), 99.67/15.02 inference('lazy_cnf_imply', [status(thm)], ['269'])). 99.67/15.02 tff('271', plain, 99.67/15.02 ~ ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (subset(Y1, Y0) => (binintersect(Y0, Y1) = Y1)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 ((binintersect(Y0, Y1) = Y0) => subset(Y0, Y1)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (binintersect(Y0, binunion(Y1, Y2)) = 99.67/15.02 binunion(binintersect(Y0, Y1), 99.67/15.02 binintersect(Y0, Y2)))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 ((~(in(Y2, Y1))) => in(Y2, setminus(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, setminus(Y0, Y1)) => in(Y2, Y0))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, setminus(Y0, Y1)) => (~(in(Y2, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (subset(Y0, Y1) => (setminus(Y0, Y1) = emptyset)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.02 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.02 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, Y0))) => 99.67/15.02 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y1) => 99.67/15.02 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: subset(setminus(Y0, Y1), Y0))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 ((setminus(Y0, Y1) = emptyset) => 99.67/15.02 subset(Y0, Y1)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, symdiff(Y0, Y1)) => 99.67/15.02 (!!((^[Y3 : $o]: 99.67/15.02 ((in(Y2, Y0) => 99.67/15.02 ((~(in(Y2, Y1))) => Y3)) => 99.67/15.02 (((~(in(Y2, Y0))) => 99.67/15.02 (in(Y2, Y1) => Y3)) => 99.67/15.02 Y3))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 ((~(in(Y2, Y1))) => 99.67/15.02 in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, Y0))) => 99.67/15.02 (in(Y2, Y1) => 99.67/15.02 in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (in(Y2, Y1) => 99.67/15.02 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, Y0))) => 99.67/15.02 ((~(in(Y2, Y1))) => 99.67/15.02 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 in(Y1, 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 in(Y0, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset)), 99.67/15.02 emptyset)))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 in(Y1, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset)), 99.67/15.02 emptyset)))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (??((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (??((^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y0, 99.67/15.02 setadjoin( 99.67/15.02 Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin( 99.67/15.02 Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)) = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (??((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (??((^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y0, 99.67/15.02 setadjoin( 99.67/15.02 Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y0, 99.67/15.02 setadjoin( 99.67/15.02 Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)) = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (in(Y1, Y0) => 99.67/15.02 subset(setadjoin(Y1, emptyset), 99.67/15.02 Y0)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (in(Y1, Y0) => 99.67/15.02 in(setadjoin(Y1, emptyset), 99.67/15.02 powerset(Y0))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 in( 99.67/15.02 setadjoin(Y2, 99.67/15.02 emptyset), 99.67/15.02 powerset( 99.67/15.02 binunion(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset))) => 99.67/15.02 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 subset( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 binunion( 99.67/15.02 Y0, Y1)))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 subset( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1)))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1)))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 ( 99.67/15.02 in(Y3, 99.67/15.02 Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 dsetconstr( 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1))), 99.67/15.02 (^[Y4 : $i]: 99.67/15.02 (??(( 99.67/15.02 ^[Y5 : $i]: 99.67/15.02 (in(Y5, 99.67/15.02 Y0) & 99.67/15.02 (??(( 99.67/15.02 ^[Y6 : $i]: 99.67/15.02 (in(Y6, 99.67/15.02 Y1) & 99.67/15.02 (Y4 = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y5, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y5, 99.67/15.02 setadjoin( 99.67/15.02 Y6, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))))))))))))))))))))))))))) => 99.67/15.02 (!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 dsetconstr( 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1))), 99.67/15.02 (^[Y3 : $i]: 99.67/15.02 ( 99.67/15.02 ??(( 99.67/15.02 ^[Y4 : $i]: 99.67/15.02 (in(Y4, 99.67/15.02 Y0) & 99.67/15.02 (??(( 99.67/15.02 ^[Y5 : $i]: 99.67/15.02 (in(Y5, 99.67/15.02 Y1) & 99.67/15.02 (Y3 = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y4, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y4, 99.67/15.02 setadjoin( 99.67/15.02 Y5, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))))))))))))) => 99.67/15.02 (??((^[Y3 : $i]: 99.67/15.02 ( 99.67/15.02 ( 99.67/15.02 ??(( 99.67/15.02 ^[Y4 : $i]: 99.67/15.02 (in(Y4, 99.67/15.02 Y1) & 99.67/15.02 (Y2 = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 setadjoin( 99.67/15.02 Y4, 99.67/15.02 emptyset)), 99.67/15.02 emptyset))))))) & 99.67/15.02 in(Y3, 99.67/15.02 Y0)))))))))))))))))))))))))))))))))))))))))))))))), 99.67/15.02 inference('lazy_cnf_imply', [status(thm)], ['270'])). 99.67/15.02 tff('272', plain, 99.67/15.02 ~ ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 ((binintersect(Y0, Y1) = Y0) => subset(Y0, Y1)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (binintersect(Y0, binunion(Y1, Y2)) = 99.67/15.02 binunion(binintersect(Y0, Y1), 99.67/15.02 binintersect(Y0, Y2)))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 ((~(in(Y2, Y1))) => in(Y2, setminus(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, setminus(Y0, Y1)) => in(Y2, Y0))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, setminus(Y0, Y1)) => (~(in(Y2, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (subset(Y0, Y1) => (setminus(Y0, Y1) = emptyset)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.02 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.02 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, Y0))) => 99.67/15.02 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y1) => 99.67/15.02 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: subset(setminus(Y0, Y1), Y0))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 ((setminus(Y0, Y1) = emptyset) => 99.67/15.02 subset(Y0, Y1)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, symdiff(Y0, Y1)) => 99.67/15.02 (!!((^[Y3 : $o]: 99.67/15.02 ((in(Y2, Y0) => 99.67/15.02 ((~(in(Y2, Y1))) => Y3)) => 99.67/15.02 (((~(in(Y2, Y0))) => 99.67/15.02 (in(Y2, Y1) => Y3)) => 99.67/15.02 Y3))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 ((~(in(Y2, Y1))) => 99.67/15.02 in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, Y0))) => 99.67/15.02 (in(Y2, Y1) => 99.67/15.02 in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (in(Y2, Y1) => 99.67/15.02 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, Y0))) => 99.67/15.02 ((~(in(Y2, Y1))) => 99.67/15.02 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 in(Y1, 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 in(Y0, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset)), 99.67/15.02 emptyset)))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 in(Y1, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset)), 99.67/15.02 emptyset)))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (??((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (??((^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y0, 99.67/15.02 setadjoin( 99.67/15.02 Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin( 99.67/15.02 Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)) = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (??((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (??((^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y0, 99.67/15.02 setadjoin( 99.67/15.02 Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin( 99.67/15.02 Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)) = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (in(Y1, Y0) => 99.67/15.02 subset(setadjoin(Y1, emptyset), 99.67/15.02 Y0)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (in(Y1, Y0) => 99.67/15.02 in(setadjoin(Y1, emptyset), 99.67/15.02 powerset(Y0))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 in( 99.67/15.02 setadjoin(Y2, 99.67/15.02 emptyset), 99.67/15.02 powerset( 99.67/15.02 binunion(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset))) => 99.67/15.02 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 subset( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 binunion( 99.67/15.02 Y0, Y1)))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 subset( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1)))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1)))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 dsetconstr( 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1))), 99.67/15.02 (^[Y4 : $i]: 99.67/15.02 (??(( 99.67/15.02 ^[Y5 : $i]: 99.67/15.02 (in(Y5, 99.67/15.02 Y0) & 99.67/15.02 (??(( 99.67/15.02 ^[Y6 : $i]: 99.67/15.02 (in(Y6, 99.67/15.02 Y1) & 99.67/15.02 (Y4 = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y5, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y5, 99.67/15.02 setadjoin( 99.67/15.02 Y6, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))))))))))))))))))))))))))) => 99.67/15.02 (!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 dsetconstr( 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1))), 99.67/15.02 (^[Y3 : $i]: 99.67/15.02 (??(( 99.67/15.02 ^[Y4 : $i]: 99.67/15.02 (in(Y4, 99.67/15.02 Y0) & 99.67/15.02 (??(( 99.67/15.02 ^[Y5 : $i]: 99.67/15.02 (in(Y5, 99.67/15.02 Y1) & 99.67/15.02 (Y3 = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y4, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y4, 99.67/15.02 setadjoin( 99.67/15.02 Y5, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))))))))))))) => 99.67/15.02 (??((^[Y3 : $i]: 99.67/15.02 (( 99.67/15.02 ??(( 99.67/15.02 ^[Y4 : $i]: 99.67/15.02 (in(Y4, 99.67/15.02 Y1) & 99.67/15.02 (Y2 = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 setadjoin( 99.67/15.02 Y4, 99.67/15.02 emptyset)), 99.67/15.02 emptyset))))))) & 99.67/15.02 in(Y3, 99.67/15.02 Y0))))))))))))))))))))))))))))))))))))))))))))))), 99.67/15.02 inference('lazy_cnf_imply', [status(thm)], ['271'])). 99.67/15.02 tff('273', plain, 99.67/15.02 ~ ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (binintersect(Y0, binunion(Y1, Y2)) = 99.67/15.02 binunion(binintersect(Y0, Y1), 99.67/15.02 binintersect(Y0, Y2)))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 ((~(in(Y2, Y1))) => in(Y2, setminus(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, setminus(Y0, Y1)) => in(Y2, Y0))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, setminus(Y0, Y1)) => (~(in(Y2, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (subset(Y0, Y1) => (setminus(Y0, Y1) = emptyset)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.02 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.02 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, Y0))) => 99.67/15.02 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y1) => 99.67/15.02 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: subset(setminus(Y0, Y1), Y0))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 ((setminus(Y0, Y1) = emptyset) => 99.67/15.02 subset(Y0, Y1)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, symdiff(Y0, Y1)) => 99.67/15.02 (!!((^[Y3 : $o]: 99.67/15.02 ((in(Y2, Y0) => 99.67/15.02 ((~(in(Y2, Y1))) => Y3)) => 99.67/15.02 (((~(in(Y2, Y0))) => 99.67/15.02 (in(Y2, Y1) => Y3)) => 99.67/15.02 Y3))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 ((~(in(Y2, Y1))) => 99.67/15.02 in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, Y0))) => 99.67/15.02 (in(Y2, Y1) => 99.67/15.02 in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (in(Y2, Y1) => 99.67/15.02 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, Y0))) => 99.67/15.02 ((~(in(Y2, Y1))) => 99.67/15.02 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 in(Y1, 99.67/15.02 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 in(Y0, 99.67/15.02 setunion( 99.67/15.02 setadjoin(setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset)), 99.67/15.02 emptyset)))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 in(Y1, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset)), 99.67/15.02 emptyset)))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (??((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (??((^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y0, 99.67/15.02 setadjoin( 99.67/15.02 Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)) = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, 99.67/15.02 setadjoin(Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (??((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (??((^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y0, 99.67/15.02 setadjoin( 99.67/15.02 Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin( 99.67/15.02 Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)) = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (in(Y1, Y0) => 99.67/15.02 subset(setadjoin(Y1, emptyset), 99.67/15.02 Y0)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (in(Y1, Y0) => 99.67/15.02 in(setadjoin(Y1, emptyset), 99.67/15.02 powerset(Y0))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 in( 99.67/15.02 setadjoin(Y2, emptyset), 99.67/15.02 powerset( 99.67/15.02 binunion(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset))) => 99.67/15.02 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 subset( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 binunion(Y0, 99.67/15.02 Y1)))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 subset( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1)))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1)))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 dsetconstr( 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1))), 99.67/15.02 (^[Y4 : $i]: 99.67/15.02 (??(( 99.67/15.02 ^[Y5 : $i]: 99.67/15.02 (in(Y5, 99.67/15.02 Y0) & 99.67/15.02 (??(( 99.67/15.02 ^[Y6 : $i]: 99.67/15.02 (in(Y6, 99.67/15.02 Y1) & 99.67/15.02 (Y4 = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y5, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y5, 99.67/15.02 setadjoin( 99.67/15.02 Y6, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))))))))))))))))))))))))))) => 99.67/15.02 (!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 dsetconstr( 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1))), 99.67/15.02 (^[Y3 : $i]: 99.67/15.02 (??(( 99.67/15.02 ^[Y4 : $i]: 99.67/15.02 (in(Y4, 99.67/15.02 Y0) & 99.67/15.02 (??(( 99.67/15.02 ^[Y5 : $i]: 99.67/15.02 (in(Y5, 99.67/15.02 Y1) & 99.67/15.02 (Y3 = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y4, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y4, 99.67/15.02 setadjoin( 99.67/15.02 Y5, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))))))))))))) => 99.67/15.02 (??((^[Y3 : $i]: 99.67/15.02 ((??(( 99.67/15.02 ^[Y4 : $i]: 99.67/15.02 (in(Y4, 99.67/15.02 Y1) & 99.67/15.02 (Y2 = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 setadjoin( 99.67/15.02 Y4, 99.67/15.02 emptyset)), 99.67/15.02 emptyset))))))) & 99.67/15.02 in(Y3, Y0)))))))))))))))))))))))))))))))))))))))))))))), 99.67/15.02 inference('lazy_cnf_imply', [status(thm)], ['272'])). 99.67/15.02 tff('274', plain, 99.67/15.02 ~ ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 ((~(in(Y2, Y1))) => in(Y2, setminus(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, setminus(Y0, Y1)) => in(Y2, Y0))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, setminus(Y0, Y1)) => (~(in(Y2, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (subset(Y0, Y1) => (setminus(Y0, Y1) = emptyset)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.02 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.02 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, Y0))) => 99.67/15.02 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y1) => 99.67/15.02 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: subset(setminus(Y0, Y1), Y0))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 ((setminus(Y0, Y1) = emptyset) => 99.67/15.02 subset(Y0, Y1)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, symdiff(Y0, Y1)) => 99.67/15.02 (!!((^[Y3 : $o]: 99.67/15.02 ((in(Y2, Y0) => 99.67/15.02 ((~(in(Y2, Y1))) => Y3)) => 99.67/15.02 (((~(in(Y2, Y0))) => 99.67/15.02 (in(Y2, Y1) => Y3)) => 99.67/15.02 Y3))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 ((~(in(Y2, Y1))) => 99.67/15.02 in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, Y0))) => 99.67/15.02 (in(Y2, Y1) => 99.67/15.02 in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (in(Y2, Y1) => 99.67/15.02 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, Y0))) => 99.67/15.02 ((~(in(Y2, Y1))) => 99.67/15.02 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 in(Y1, 99.67/15.02 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 in(Y0, 99.67/15.02 setunion( 99.67/15.02 setadjoin(setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset)), 99.67/15.02 emptyset)))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 in(Y1, 99.67/15.02 setunion( 99.67/15.02 setadjoin(setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset)), 99.67/15.02 emptyset)))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (??((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (??((^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin( 99.67/15.02 Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)) = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, 99.67/15.02 setadjoin(Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (??((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (??((^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y0, 99.67/15.02 setadjoin( 99.67/15.02 Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)) = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, 99.67/15.02 setadjoin(Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (in(Y1, Y0) => 99.67/15.02 subset(setadjoin(Y1, emptyset), Y0)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (in(Y1, Y0) => 99.67/15.02 in(setadjoin(Y1, emptyset), 99.67/15.02 powerset(Y0))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 in( 99.67/15.02 setadjoin(Y2, emptyset), 99.67/15.02 powerset( 99.67/15.02 binunion(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset))) => 99.67/15.02 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 subset( 99.67/15.02 setadjoin(Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 binunion(Y0, 99.67/15.02 Y1)))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 subset( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1)))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1)))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 dsetconstr( 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1))), 99.67/15.02 (^[Y4 : $i]: 99.67/15.02 (??(( 99.67/15.02 ^[Y5 : $i]: 99.67/15.02 (in(Y5, 99.67/15.02 Y0) & 99.67/15.02 (??(( 99.67/15.02 ^[Y6 : $i]: 99.67/15.02 (in(Y6, 99.67/15.02 Y1) & 99.67/15.02 (Y4 = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y5, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y5, 99.67/15.02 setadjoin( 99.67/15.02 Y6, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))))))))))))))))))))))))))) => 99.67/15.02 (!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 dsetconstr( 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1))), 99.67/15.02 (^[Y3 : $i]: 99.67/15.02 (??(( 99.67/15.02 ^[Y4 : $i]: 99.67/15.02 ( 99.67/15.02 in(Y4, 99.67/15.02 Y0) & 99.67/15.02 ( 99.67/15.02 ??(( 99.67/15.02 ^[Y5 : $i]: 99.67/15.02 (in(Y5, 99.67/15.02 Y1) & 99.67/15.02 (Y3 = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y4, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y4, 99.67/15.02 setadjoin( 99.67/15.02 Y5, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))))))))))))) => 99.67/15.02 (??((^[Y3 : $i]: 99.67/15.02 ((??(( 99.67/15.02 ^[Y4 : $i]: 99.67/15.02 (in(Y4, 99.67/15.02 Y1) & 99.67/15.02 (Y2 = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 setadjoin( 99.67/15.02 Y4, 99.67/15.02 emptyset)), 99.67/15.02 emptyset))))))) & 99.67/15.02 in(Y3, Y0))))))))))))))))))))))))))))))))))))))))))))), 99.67/15.02 inference('lazy_cnf_imply', [status(thm)], ['273'])). 99.67/15.02 tff('275', plain, 99.67/15.02 ~ ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, setminus(Y0, Y1)) => in(Y2, Y0))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, setminus(Y0, Y1)) => (~(in(Y2, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (subset(Y0, Y1) => (setminus(Y0, Y1) = emptyset)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.02 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.02 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, Y0))) => 99.67/15.02 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y1) => 99.67/15.02 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: subset(setminus(Y0, Y1), Y0))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 ((setminus(Y0, Y1) = emptyset) => subset(Y0, Y1)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, symdiff(Y0, Y1)) => 99.67/15.02 (!!((^[Y3 : $o]: 99.67/15.02 ((in(Y2, Y0) => 99.67/15.02 ((~(in(Y2, Y1))) => Y3)) => 99.67/15.02 (((~(in(Y2, Y0))) => 99.67/15.02 (in(Y2, Y1) => Y3)) => 99.67/15.02 Y3))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 ((~(in(Y2, Y1))) => 99.67/15.02 in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, Y0))) => 99.67/15.02 (in(Y2, Y1) => 99.67/15.02 in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (in(Y2, Y1) => 99.67/15.02 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, Y0))) => 99.67/15.02 ((~(in(Y2, Y1))) => 99.67/15.02 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 in(Y1, 99.67/15.02 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 in(Y0, 99.67/15.02 setunion( 99.67/15.02 setadjoin(setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset)), 99.67/15.02 emptyset)))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 in(Y1, 99.67/15.02 setunion( 99.67/15.02 setadjoin(setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset)), 99.67/15.02 emptyset)))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (??((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (??((^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin( 99.67/15.02 Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)) = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, 99.67/15.02 setadjoin(Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (??((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (??((^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin( 99.67/15.02 Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)) = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, 99.67/15.02 setadjoin(Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (in(Y1, Y0) => 99.67/15.02 subset(setadjoin(Y1, emptyset), Y0)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (in(Y1, Y0) => 99.67/15.02 in(setadjoin(Y1, emptyset), 99.67/15.02 powerset(Y0))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 in( 99.67/15.02 setadjoin(Y2, emptyset), 99.67/15.02 powerset( 99.67/15.02 binunion(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset))) => 99.67/15.02 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 subset( 99.67/15.02 setadjoin(Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 binunion(Y0, 99.67/15.02 Y1)))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin(Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 subset( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1)))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1)))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 dsetconstr( 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1))), 99.67/15.02 (^[Y4 : $i]: 99.67/15.02 (??(( 99.67/15.02 ^[Y5 : $i]: 99.67/15.02 (in(Y5, 99.67/15.02 Y0) & 99.67/15.02 (??(( 99.67/15.02 ^[Y6 : $i]: 99.67/15.02 (in(Y6, 99.67/15.02 Y1) & 99.67/15.02 (Y4 = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y5, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y5, 99.67/15.02 setadjoin( 99.67/15.02 Y6, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))))))))))))))))))))))))))) => 99.67/15.02 (!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 dsetconstr( 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1))), 99.67/15.02 (^[Y3 : $i]: 99.67/15.02 (??(( 99.67/15.02 ^[Y4 : $i]: 99.67/15.02 (in(Y4, 99.67/15.02 Y0) & 99.67/15.02 ( 99.67/15.02 ??(( 99.67/15.02 ^[Y5 : $i]: 99.67/15.02 (in(Y5, 99.67/15.02 Y1) & 99.67/15.02 (Y3 = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y4, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y4, 99.67/15.02 setadjoin( 99.67/15.02 Y5, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))))))))))))) => 99.67/15.02 (??((^[Y3 : $i]: 99.67/15.02 ((??(( 99.67/15.02 ^[Y4 : $i]: 99.67/15.02 ( 99.67/15.02 in(Y4, 99.67/15.02 Y1) & 99.67/15.02 ( 99.67/15.02 Y2 = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 setadjoin( 99.67/15.02 Y4, 99.67/15.02 emptyset)), 99.67/15.02 emptyset))))))) & 99.67/15.02 in(Y3, Y0)))))))))))))))))))))))))))))))))))))))))))), 99.67/15.02 inference('lazy_cnf_imply', [status(thm)], ['274'])). 99.67/15.02 tff('276', plain, 99.67/15.02 ~ ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, setminus(Y0, Y1)) => (~(in(Y2, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (subset(Y0, Y1) => (setminus(Y0, Y1) = emptyset)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.02 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.02 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, Y0))) => 99.67/15.02 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y1) => (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: subset(setminus(Y0, Y1), Y0))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 ((setminus(Y0, Y1) = emptyset) => subset(Y0, Y1)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, symdiff(Y0, Y1)) => 99.67/15.02 (!!((^[Y3 : $o]: 99.67/15.02 ((in(Y2, Y0) => 99.67/15.02 ((~(in(Y2, Y1))) => Y3)) => 99.67/15.02 (((~(in(Y2, Y0))) => 99.67/15.02 (in(Y2, Y1) => Y3)) => 99.67/15.02 Y3))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 ((~(in(Y2, Y1))) => 99.67/15.02 in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, Y0))) => 99.67/15.02 (in(Y2, Y1) => in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (in(Y2, Y1) => 99.67/15.02 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, Y0))) => 99.67/15.02 ((~(in(Y2, Y1))) => 99.67/15.02 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 in(Y1, 99.67/15.02 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 in(Y0, 99.67/15.02 setunion( 99.67/15.02 setadjoin(setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset)), 99.67/15.02 emptyset)))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 in(Y1, 99.67/15.02 setunion( 99.67/15.02 setadjoin(setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset)), 99.67/15.02 emptyset)))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (??((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (??((^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)) = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, 99.67/15.02 setadjoin(Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (??((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (??((^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin( 99.67/15.02 Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)) = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, 99.67/15.02 setadjoin(Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (in(Y1, Y0) => 99.67/15.02 subset(setadjoin(Y1, emptyset), Y0)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (in(Y1, Y0) => 99.67/15.02 in(setadjoin(Y1, emptyset), 99.67/15.02 powerset(Y0))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 in(setadjoin(Y2, emptyset), 99.67/15.02 powerset(binunion(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset))) => 99.67/15.02 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 subset( 99.67/15.02 setadjoin(Y2, 99.67/15.02 setadjoin(Y3, 99.67/15.02 emptyset)), 99.67/15.02 binunion(Y0, Y1)))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin(Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 binunion(Y0, 99.67/15.02 Y1))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 subset( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1)))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1)))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 dsetconstr( 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1))), 99.67/15.02 ( 99.67/15.02 ^[Y4 : $i]: 99.67/15.02 (??(( 99.67/15.02 ^[Y5 : $i]: 99.67/15.02 (in(Y5, 99.67/15.02 Y0) & 99.67/15.02 (??(( 99.67/15.02 ^[Y6 : $i]: 99.67/15.02 (in(Y6, 99.67/15.02 Y1) & 99.67/15.02 (Y4 = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y5, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y5, 99.67/15.02 setadjoin( 99.67/15.02 Y6, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))))))))))))))))))))))))))) => 99.67/15.02 (!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 dsetconstr( 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion(Y0, 99.67/15.02 Y1))), 99.67/15.02 (^[Y3 : $i]: 99.67/15.02 (??((^[Y4 : $i]: 99.67/15.02 (in(Y4, 99.67/15.02 Y0) & 99.67/15.02 (??(( 99.67/15.02 ^[Y5 : $i]: 99.67/15.02 (in(Y5, 99.67/15.02 Y1) & 99.67/15.02 (Y3 = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y4, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y4, 99.67/15.02 setadjoin( 99.67/15.02 Y5, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))))))))))))) => 99.67/15.02 (??((^[Y3 : $i]: 99.67/15.02 ((??(( 99.67/15.02 ^[Y4 : $i]: 99.67/15.02 (in(Y4, 99.67/15.02 Y1) & 99.67/15.02 ( 99.67/15.02 Y2 = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 setadjoin( 99.67/15.02 Y4, 99.67/15.02 emptyset)), 99.67/15.02 emptyset))))))) & 99.67/15.02 in(Y3, Y0))))))))))))))))))))))))))))))))))))))))))), 99.67/15.02 inference('lazy_cnf_imply', [status(thm)], ['275'])). 99.67/15.02 tff('277', plain, 99.67/15.02 ~ ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (subset(Y0, Y1) => (setminus(Y0, Y1) = emptyset)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.02 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.02 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, Y0))) => 99.67/15.02 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y1) => (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(setminus(Y0, Y1), Y0))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 ((setminus(Y0, Y1) = emptyset) => subset(Y0, Y1)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, symdiff(Y0, Y1)) => 99.67/15.02 (!!((^[Y3 : $o]: 99.67/15.02 ((in(Y2, Y0) => 99.67/15.02 ((~(in(Y2, Y1))) => Y3)) => 99.67/15.02 (((~(in(Y2, Y0))) => 99.67/15.02 (in(Y2, Y1) => Y3)) => 99.67/15.02 Y3))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 ((~(in(Y2, Y1))) => 99.67/15.02 in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, Y0))) => 99.67/15.02 (in(Y2, Y1) => in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (in(Y2, Y1) => 99.67/15.02 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, Y0))) => 99.67/15.02 ((~(in(Y2, Y1))) => 99.67/15.02 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 in(Y1, 99.67/15.02 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 in(Y0, 99.67/15.02 setunion( 99.67/15.02 setadjoin(setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset)), 99.67/15.02 emptyset)))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 in(Y1, 99.67/15.02 setunion( 99.67/15.02 setadjoin(setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset)), 99.67/15.02 emptyset)))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (??((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (??((^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)) = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, 99.67/15.02 setadjoin(Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (??((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (??((^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)) = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, 99.67/15.02 setadjoin(Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (in(Y1, Y0) => 99.67/15.02 subset(setadjoin(Y1, emptyset), Y0)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (in(Y1, Y0) => 99.67/15.02 in(setadjoin(Y1, emptyset), 99.67/15.02 powerset(Y0))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 in(setadjoin(Y2, emptyset), 99.67/15.02 powerset(binunion(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset))) => 99.67/15.02 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 subset( 99.67/15.02 setadjoin(Y2, 99.67/15.02 setadjoin(Y3, 99.67/15.02 emptyset)), 99.67/15.02 binunion(Y0, Y1)))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin(Y2, 99.67/15.02 setadjoin(Y3, 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 binunion(Y0, 99.67/15.02 Y1))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 subset( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 binunion(Y0, 99.67/15.02 Y1))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1)))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1)))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 dsetconstr( 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1))), 99.67/15.02 (^[Y4 : $i]: 99.67/15.02 (??(( 99.67/15.02 ^[Y5 : $i]: 99.67/15.02 (in(Y5, 99.67/15.02 Y0) & 99.67/15.02 (??(( 99.67/15.02 ^[Y6 : $i]: 99.67/15.02 (in(Y6, 99.67/15.02 Y1) & 99.67/15.02 (Y4 = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y5, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y5, 99.67/15.02 setadjoin( 99.67/15.02 Y6, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))))))))))))))))))))))))))) => 99.67/15.02 (!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 dsetconstr( 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion(Y0, 99.67/15.02 Y1))), 99.67/15.02 (^[Y3 : $i]: 99.67/15.02 (??((^[Y4 : $i]: 99.67/15.02 (in(Y4, 99.67/15.02 Y0) & 99.67/15.02 (??(( 99.67/15.02 ^[Y5 : $i]: 99.67/15.02 (in(Y5, 99.67/15.02 Y1) & 99.67/15.02 (Y3 = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y4, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y4, 99.67/15.02 setadjoin( 99.67/15.02 Y5, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))))))))))))) => 99.67/15.02 (??((^[Y3 : $i]: 99.67/15.02 ((??((^[Y4 : $i]: 99.67/15.02 (in(Y4, 99.67/15.02 Y1) & 99.67/15.02 (Y2 = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 setadjoin( 99.67/15.02 Y4, 99.67/15.02 emptyset)), 99.67/15.02 emptyset))))))) & 99.67/15.02 in(Y3, Y0)))))))))))))))))))))))))))))))))))))))))), 99.67/15.02 inference('lazy_cnf_imply', [status(thm)], ['276'])). 99.67/15.02 tff('278', plain, 99.67/15.02 ~ ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.02 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.02 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, Y0))) => 99.67/15.02 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y1) => (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(setminus(Y0, Y1), Y0))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 ((setminus(Y0, Y1) = emptyset) => subset(Y0, Y1)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, symdiff(Y0, Y1)) => 99.67/15.02 (!!((^[Y3 : $o]: 99.67/15.02 ((in(Y2, Y0) => 99.67/15.02 ((~(in(Y2, Y1))) => Y3)) => 99.67/15.02 (((~(in(Y2, Y0))) => 99.67/15.02 (in(Y2, Y1) => Y3)) => 99.67/15.02 Y3))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 ((~(in(Y2, Y1))) => 99.67/15.02 in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, Y0))) => 99.67/15.02 (in(Y2, Y1) => in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (in(Y2, Y1) => 99.67/15.02 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, Y0))) => 99.67/15.02 ((~(in(Y2, Y1))) => 99.67/15.02 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 in(Y1, 99.67/15.02 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 in(Y0, 99.67/15.02 setunion( 99.67/15.02 setadjoin(setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset)), 99.67/15.02 emptyset)))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 in(Y1, 99.67/15.02 setunion( 99.67/15.02 setadjoin(setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset)), 99.67/15.02 emptyset)))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (??((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (??((^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (setadjoin( 99.67/15.02 setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)) = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, 99.67/15.02 setadjoin(Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (??((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (??((^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)) = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, 99.67/15.02 setadjoin(Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (in(Y1, Y0) => 99.67/15.02 subset(setadjoin(Y1, emptyset), Y0)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (in(Y1, Y0) => 99.67/15.02 in(setadjoin(Y1, emptyset), 99.67/15.02 powerset(Y0))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 in(setadjoin(Y2, emptyset), 99.67/15.02 powerset(binunion(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset))) => 99.67/15.02 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 subset( 99.67/15.02 setadjoin(Y2, 99.67/15.02 setadjoin(Y3, 99.67/15.02 emptyset)), 99.67/15.02 binunion(Y0, Y1)))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin(Y2, 99.67/15.02 setadjoin(Y3, 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 binunion(Y0, 99.67/15.02 Y1))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 subset( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 binunion(Y0, 99.67/15.02 Y1))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1)))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1)))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 dsetconstr( 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1))), 99.67/15.02 (^[Y4 : $i]: 99.67/15.02 (??(( 99.67/15.02 ^[Y5 : $i]: 99.67/15.02 (in(Y5, 99.67/15.02 Y0) & 99.67/15.02 (??(( 99.67/15.02 ^[Y6 : $i]: 99.67/15.02 (in(Y6, 99.67/15.02 Y1) & 99.67/15.02 (Y4 = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y5, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y5, 99.67/15.02 setadjoin( 99.67/15.02 Y6, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))))))))))))))))))))))))))) => 99.67/15.02 (!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 dsetconstr( 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion(Y0, 99.67/15.02 Y1))), 99.67/15.02 (^[Y3 : $i]: 99.67/15.02 (??((^[Y4 : $i]: 99.67/15.02 ( 99.67/15.02 in(Y4, 99.67/15.02 Y0) & 99.67/15.02 ( 99.67/15.02 ??(( 99.67/15.02 ^[Y5 : $i]: 99.67/15.02 (in(Y5, 99.67/15.02 Y1) & 99.67/15.02 (Y3 = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y4, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y4, 99.67/15.02 setadjoin( 99.67/15.02 Y5, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))))))))))))) => 99.67/15.02 (??((^[Y3 : $i]: 99.67/15.02 ((??((^[Y4 : $i]: 99.67/15.02 (in(Y4, 99.67/15.02 Y1) & 99.67/15.02 (Y2 = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 setadjoin( 99.67/15.02 Y4, 99.67/15.02 emptyset)), 99.67/15.02 emptyset))))))) & 99.67/15.02 in(Y3, Y0))))))))))))))))))))))))))))))))))))))))), 99.67/15.02 inference('lazy_cnf_imply', [status(thm)], ['277'])). 99.67/15.02 tff('279', plain, 99.67/15.02 ~ ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, setminus(Y0, Y1)))) => 99.67/15.02 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, Y0))) => 99.67/15.02 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y1) => (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(setminus(Y0, Y1), Y0))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 ((setminus(Y0, Y1) = emptyset) => subset(Y0, Y1)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, symdiff(Y0, Y1)) => 99.67/15.02 (!!((^[Y3 : $o]: 99.67/15.02 ((in(Y2, Y0) => 99.67/15.02 ((~(in(Y2, Y1))) => Y3)) => 99.67/15.02 (((~(in(Y2, Y0))) => 99.67/15.02 (in(Y2, Y1) => Y3)) => 99.67/15.02 Y3))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 ((~(in(Y2, Y1))) => 99.67/15.02 in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, Y0))) => 99.67/15.02 (in(Y2, Y1) => in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (in(Y2, Y1) => 99.67/15.02 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, Y0))) => 99.67/15.02 ((~(in(Y2, Y1))) => 99.67/15.02 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 in(Y0, 99.67/15.02 setunion( 99.67/15.02 setadjoin(setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset)), emptyset)))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 in(Y1, 99.67/15.02 setunion( 99.67/15.02 setadjoin(setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset)), 99.67/15.02 emptyset)))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (??((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (??((^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (setadjoin( 99.67/15.02 setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)) = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, 99.67/15.02 setadjoin(Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (??((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (??((^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (setadjoin( 99.67/15.02 setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)) = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, 99.67/15.02 setadjoin(Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (in(Y1, Y0) => 99.67/15.02 subset(setadjoin(Y1, emptyset), Y0)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (in(Y1, Y0) => 99.67/15.02 in(setadjoin(Y1, emptyset), 99.67/15.02 powerset(Y0))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 in(setadjoin(Y2, emptyset), 99.67/15.02 powerset(binunion(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset))) => 99.67/15.02 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 subset( 99.67/15.02 setadjoin(Y2, 99.67/15.02 setadjoin(Y3, 99.67/15.02 emptyset)), 99.67/15.02 binunion(Y0, Y1)))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin(Y2, 99.67/15.02 setadjoin(Y3, 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 binunion(Y0, Y1))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 subset( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 binunion(Y0, 99.67/15.02 Y1))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1)))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1)))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 in( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y2, 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)), 99.67/15.02 dsetconstr( 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion( 99.67/15.02 Y0, Y1))), 99.67/15.02 (^[Y4 : $i]: 99.67/15.02 ( 99.67/15.02 ??(( 99.67/15.02 ^[Y5 : $i]: 99.67/15.02 (in(Y5, 99.67/15.02 Y0) & 99.67/15.02 (??(( 99.67/15.02 ^[Y6 : $i]: 99.67/15.02 (in(Y6, 99.67/15.02 Y1) & 99.67/15.02 (Y4 = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y5, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y5, 99.67/15.02 setadjoin( 99.67/15.02 Y6, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))))))))))))))))))))))))))) => 99.67/15.02 (!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 dsetconstr( 99.67/15.02 powerset( 99.67/15.02 powerset( 99.67/15.02 binunion(Y0, Y1))), 99.67/15.02 (^[Y3 : $i]: 99.67/15.02 (??((^[Y4 : $i]: 99.67/15.02 (in(Y4, 99.67/15.02 Y0) & 99.67/15.02 ( 99.67/15.02 ??(( 99.67/15.02 ^[Y5 : $i]: 99.67/15.02 (in(Y5, 99.67/15.02 Y1) & 99.67/15.02 (Y3 = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y4, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y4, 99.67/15.02 setadjoin( 99.67/15.02 Y5, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))))))))))))) => 99.67/15.02 (??((^[Y3 : $i]: 99.67/15.02 ((??((^[Y4 : $i]: 99.67/15.02 ( 99.67/15.02 in(Y4, 99.67/15.02 Y1) & 99.67/15.02 ( 99.67/15.02 Y2 = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin( 99.67/15.02 Y3, 99.67/15.02 setadjoin( 99.67/15.02 Y4, 99.67/15.02 emptyset)), 99.67/15.02 emptyset))))))) & 99.67/15.02 in(Y3, Y0)))))))))))))))))))))))))))))))))))))))), 99.67/15.02 inference('lazy_cnf_imply', [status(thm)], ['278'])). 99.67/15.02 tff('280', plain, 99.67/15.02 ~ ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, Y0))) => (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y1) => (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(setminus(Y0, Y1), Y0))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 ((setminus(Y0, Y1) = emptyset) => subset(Y0, Y1)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, symdiff(Y0, Y1)) => 99.67/15.02 (!!((^[Y3 : $o]: 99.67/15.02 ((in(Y2, Y0) => 99.67/15.02 ((~(in(Y2, Y1))) => Y3)) => 99.67/15.02 (((~(in(Y2, Y0))) => 99.67/15.02 (in(Y2, Y1) => Y3)) => 99.67/15.02 Y3))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 ((~(in(Y2, Y1))) => in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, Y0))) => 99.67/15.02 (in(Y2, Y1) => in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (in(Y2, Y1) => 99.67/15.02 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 ((~(in(Y2, Y0))) => 99.67/15.02 ((~(in(Y2, Y1))) => 99.67/15.02 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 in(Y0, 99.67/15.02 setunion( 99.67/15.02 setadjoin(setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, setadjoin(Y1, emptyset)), 99.67/15.02 emptyset)))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 in(Y1, 99.67/15.02 setunion( 99.67/15.02 setadjoin(setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset)), emptyset)))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (??((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (??((^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (setadjoin( 99.67/15.02 setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)) = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, 99.67/15.02 setadjoin(Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (??((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (??((^[Y3 : $i]: 99.67/15.02 (in(Y3, 99.67/15.02 setunion( 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)))) & 99.67/15.02 (setadjoin( 99.67/15.02 setadjoin(Y0, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, 99.67/15.02 emptyset)), 99.67/15.02 emptyset)) = 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, emptyset), 99.67/15.02 setadjoin( 99.67/15.02 setadjoin(Y2, 99.67/15.02 setadjoin(Y3, 99.67/15.02 emptyset)), 99.67/15.02 emptyset))))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (in(Y1, Y0) => 99.67/15.02 subset(setadjoin(Y1, emptyset), Y0)))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (in(Y1, Y0) => 99.67/15.02 in(setadjoin(Y1, emptyset), 99.67/15.02 powerset(Y0))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 in(setadjoin(Y2, emptyset), 99.67/15.02 powerset(binunion(Y0, Y1))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, 99.67/15.02 setadjoin(Y0, 99.67/15.02 setadjoin(Y1, emptyset))) => 99.67/15.02 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.02 (!!((^[Y3 : $i]: 99.67/15.02 (in(Y3, Y1) => 99.67/15.02 subset( 99.67/15.02 setadjoin(Y2, 99.67/15.02 setadjoin(Y3, 99.67/15.02 emptyset)), 99.67/15.02 binunion(Y0, Y1)))))))))))))))) => 99.67/15.02 ((!!((^[Y0 : $i]: 99.67/15.02 (!!((^[Y1 : $i]: 99.67/15.02 (!!((^[Y2 : $i]: 99.67/15.02 (in(Y2, Y0) => 99.67/15.03 (!!((^[Y3 : $i]: 99.67/15.03 (in(Y3, Y1) => 99.67/15.03 in( 99.67/15.03 setadjoin(Y2, 99.67/15.03 setadjoin(Y3, 99.67/15.03 emptyset)), 99.67/15.03 powerset( 99.67/15.03 binunion(Y0, Y1))))))))))))))))) => 99.67/15.03 ((!!((^[Y0 : $i]: 99.67/15.03 (!!((^[Y1 : $i]: 99.67/15.03 (!!((^[Y2 : $i]: 99.67/15.03 (in(Y2, Y0) => 99.67/15.03 (!!((^[Y3 : $i]: 99.67/15.03 (in(Y3, Y1) => 99.67/15.03 subset( 99.67/15.03 setadjoin( 99.67/15.03 setadjoin(Y2, 99.67/15.03 emptyset), 99.67/15.03 setadjoin( 99.67/15.03 setadjoin(Y2, 99.67/15.03 setadjoin( 99.67/15.03 Y3, 99.67/15.03 emptyset)), 99.67/15.03 emptyset)), 99.67/15.03 powerset( 99.67/15.03 binunion(Y0, Y1))))))))))))))))) => 99.67/15.03 ((!!((^[Y0 : $i]: 99.67/15.03 (!!((^[Y1 : $i]: 99.67/15.03 (!!((^[Y2 : $i]: 99.67/15.03 (in(Y2, Y0) => 99.67/15.03 (!!((^[Y3 : $i]: 99.67/15.03 (in(Y3, Y1) => 99.67/15.03 in( 99.67/15.03 setadjoin( 99.67/15.03 setadjoin(Y2, 99.67/15.03 emptyset), 99.67/15.03 setadjoin( 99.67/15.03 setadjoin( 99.67/15.03 Y2, 99.67/15.03 setadjoin( 99.67/15.03 Y3, 99.67/15.03 emptyset)), 99.67/15.03 emptyset)), 99.67/15.03 powerset( 99.67/15.03 powerset( 99.67/15.03 binunion(Y0, 99.67/15.03 Y1)))))))))))))))))) => 99.67/15.03 ((!!((^[Y0 : $i]: 99.67/15.03 (!!((^[Y1 : $i]: 99.67/15.03 (!!((^[Y2 : $i]: 99.67/15.03 (in(Y2, Y0) => 99.67/15.03 (!!((^[Y3 : $i]: 99.67/15.03 (in(Y3, Y1) => 99.67/15.03 in( 99.67/15.03 setadjoin( 99.67/15.03 setadjoin(Y2, 99.67/15.03 emptyset), 99.67/15.03 setadjoin( 99.67/15.03 setadjoin( 99.67/15.03 Y2, 99.67/15.03 setadjoin( 99.67/15.03 Y3, 99.67/15.03 emptyset)), 99.67/15.03 emptyset)), 99.67/15.03 powerset( 99.67/15.03 powerset( 99.67/15.03 binunion( 99.67/15.03 Y0, Y1)))))))))))))))))) => 99.67/15.03 ((!!((^[Y0 : $i]: 99.67/15.03 (!!((^[Y1 : $i]: 99.67/15.03 (!!((^[Y2 : $i]: 99.67/15.03 (in(Y2, Y0) => 99.67/15.03 (!!((^[Y3 : $i]: 99.67/15.03 (in(Y3, Y1) => 99.67/15.03 in( 99.67/15.03 setadjoin( 99.67/15.03 setadjoin( 99.67/15.03 Y2, 99.67/15.03 emptyset), 99.67/15.03 setadjoin( 99.67/15.03 setadjoin( 99.67/15.03 Y2, 99.67/15.03 setadjoin( 99.67/15.03 Y3, 99.67/15.03 emptyset)), 99.67/15.03 emptyset)), 99.67/15.03 dsetconstr( 99.67/15.03 powerset( 99.67/15.03 powerset( 99.67/15.03 binunion( 99.67/15.03 Y0, Y1))), 99.67/15.03 (^[Y4 : $i]: 99.67/15.03 (??(( 99.67/15.03 ^[Y5 : $i]: 99.67/15.03 (in(Y5, 99.67/15.03 Y0) & 99.67/15.03 (??(( 99.67/15.03 ^[Y6 : $i]: 99.67/15.03 (in(Y6, 99.67/15.03 Y1) & 99.67/15.03 (Y4 = 99.67/15.03 setadjoin( 99.67/15.03 setadjoin( 99.67/15.03 Y5, 99.67/15.03 emptyset), 99.67/15.03 setadjoin( 99.67/15.03 setadjoin( 99.67/15.03 Y5, 99.67/15.03 setadjoin( 99.67/15.03 Y6, 99.67/15.03 emptyset)), 99.67/15.03 emptyset)))))))))))))))))))))))))))) => 99.67/15.03 (!!((^[Y0 : $i]: 99.67/15.03 (!!((^[Y1 : $i]: 99.67/15.03 (!!((^[Y2 : $i]: 99.67/15.03 (in(Y2, 99.67/15.03 dsetconstr( 99.67/15.03 powerset( 99.67/15.03 powerset( 99.67/15.03 binunion(Y0, Y1))), 99.67/15.03 (^[Y3 : $i]: 99.67/15.03 (??((^[Y4 : $i]: 99.67/15.03 (in(Y4, Y0) & 99.67/15.03 (??(( 99.67/15.03 ^[Y5 : $i]: 99.67/15.03 (in(Y5, 99.67/15.03 Y1) & 99.67/15.03 (Y3 = 99.67/15.03 setadjoin( 99.67/15.03 setadjoin( 99.67/15.03 Y4, 99.67/15.03 emptyset), 99.67/15.03 setadjoin( 99.67/15.03 setadjoin( 99.67/15.03 Y4, 99.67/15.03 setadjoin( 99.67/15.03 Y5, 99.67/15.03 emptyset)), 99.67/15.03 emptyset)))))))))))))) => 99.67/15.03 (??((^[Y3 : $i]: 99.67/15.03 ((??((^[Y4 : $i]: 99.67/15.03 (in(Y4, 99.67/15.03 Y1) & 99.67/15.03 ( 99.67/15.03 Y2 = 99.67/15.03 setadjoin( 99.67/15.03 setadjoin( 99.67/15.03 Y3, 99.67/15.03 emptyset), 99.67/15.03 setadjoin( 99.67/15.03 setadjoin( 99.67/15.03 Y3, 99.67/15.03 setadjoin( 99.67/15.03 Y4, 99.67/15.03 emptyset)), 99.67/15.03 emptyset))))))) & 99.67/15.03 in(Y3, Y0))))))))))))))))))))))))))))))))))))))), 99.67/15.03 inference('lazy_cnf_imply', [status(thm)], ['279'])). 99.67/15.03 tff('281', plain, 99.67/15.03 ~ ((!!((^[Y0 : $i]: 99.67/15.03 (!!((^[Y1 : $i]: 99.67/15.03 (!!((^[Y2 : $i]: 99.67/15.03 (in(Y2, Y1) => (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 99.67/15.03 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(setminus(Y0, Y1), Y0))))))) => 99.67/15.03 ((!!((^[Y0 : $i]: 99.67/15.03 (!!((^[Y1 : $i]: 99.67/15.03 ((setminus(Y0, Y1) = emptyset) => subset(Y0, Y1)))))))) => 99.67/15.03 ((!!((^[Y0 : $i]: 99.67/15.03 (!!((^[Y1 : $i]: 99.67/15.03 (!!((^[Y2 : $i]: 99.67/15.03 (in(Y2, symdiff(Y0, Y1)) => 99.67/15.03 (!!((^[Y3 : $o]: 99.67/15.03 ((in(Y2, Y0) => 99.67/15.03 ((~(in(Y2, Y1))) => Y3)) => 99.67/15.03 (((~(in(Y2, Y0))) => 99.67/15.03 (in(Y2, Y1) => Y3)) => 99.67/15.03 Y3))))))))))))))) => 99.67/15.03 ((!!((^[Y0 : $i]: 99.67/15.03 (!!((^[Y1 : $i]: 99.67/15.03 (!!((^[Y2 : $i]: 99.67/15.03 (in(Y2, Y0) => 99.67/15.03 ((~(in(Y2, Y1))) => in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.03 ((!!((^[Y0 : $i]: 99.67/15.03 (!!((^[Y1 : $i]: 99.67/15.03 (!!((^[Y2 : $i]: 99.67/15.03 ((~(in(Y2, Y0))) => 99.67/15.03 (in(Y2, Y1) => in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.03 ((!!((^[Y0 : $i]: 99.67/15.03 (!!((^[Y1 : $i]: 99.67/15.03 (!!((^[Y2 : $i]: 99.67/15.03 (in(Y2, Y0) => 99.67/15.03 (in(Y2, Y1) => 99.67/15.03 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.67/15.03 ((!!((^[Y0 : $i]: 99.67/15.03 (!!((^[Y1 : $i]: 99.67/15.03 (!!((^[Y2 : $i]: 99.67/15.03 ((~(in(Y2, Y0))) => 99.67/15.03 ((~(in(Y2, Y1))) => 99.67/15.03 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.67/15.03 ((!!((^[Y0 : $i]: 99.67/15.03 (!!((^[Y1 : $i]: 99.67/15.03 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.67/15.03 ((!!((^[Y0 : $i]: 99.67/15.03 (!!((^[Y1 : $i]: 99.67/15.03 in(Y0, 99.67/15.03 setunion( 99.67/15.03 setadjoin(setadjoin(Y0, emptyset), 99.67/15.03 setadjoin( 99.67/15.03 setadjoin(Y0, setadjoin(Y1, emptyset)), 99.67/15.03 emptyset)))))))))) => 99.67/15.03 ((!!((^[Y0 : $i]: 99.67/15.03 (!!((^[Y1 : $i]: 99.67/15.03 in(Y1, 99.67/15.03 setunion( 99.67/15.03 setadjoin(setadjoin(Y0, emptyset), 99.67/15.03 setadjoin( 99.67/15.03 setadjoin(Y0, setadjoin(Y1, emptyset)), 99.67/15.03 emptyset)))))))))) => 99.67/15.03 ((!!((^[Y0 : $i]: 99.67/15.03 (!!((^[Y1 : $i]: 99.67/15.03 (??((^[Y2 : $i]: 99.67/15.03 (in(Y2, 99.67/15.03 setunion( 99.67/15.03 setadjoin( 99.67/15.03 setadjoin(Y0, emptyset), 99.67/15.03 setadjoin( 99.67/15.03 setadjoin(Y0, 99.67/15.03 setadjoin(Y1, emptyset)), 99.67/15.03 emptyset)))) & 99.67/15.03 (??((^[Y3 : $i]: 99.67/15.03 (in(Y3, 99.67/15.03 setunion( 99.67/15.03 setadjoin( 99.67/15.03 setadjoin(Y0, emptyset), 99.67/15.03 setadjoin( 99.67/15.03 setadjoin(Y0, 99.67/15.03 setadjoin(Y1, 99.67/15.03 emptyset)), 99.67/15.03 emptyset)))) & 99.67/15.03 (setadjoin( 99.67/15.03 setadjoin(Y0, emptyset), 99.67/15.03 setadjoin( 99.67/15.03 setadjoin(Y0, 99.67/15.03 setadjoin(Y1, 99.67/15.03 emptyset)), 99.67/15.03 emptyset)) = 99.67/15.03 setadjoin( 99.67/15.03 setadjoin(Y2, emptyset), 99.67/15.03 setadjoin( 99.67/15.03 setadjoin(Y2, 99.67/15.03 setadjoin(Y3, 99.67/15.03 emptyset)), 99.67/15.03 emptyset))))))))))))))))) => 99.67/15.03 ((!!((^[Y0 : $i]: 99.67/15.03 (!!((^[Y1 : $i]: 99.67/15.03 (??((^[Y2 : $i]: 99.67/15.03 (in(Y2, 99.67/15.03 setunion( 99.67/15.03 setadjoin( 99.67/15.03 setadjoin(Y0, emptyset), 99.67/15.03 setadjoin( 99.67/15.03 setadjoin(Y0, 99.67/15.03 setadjoin(Y1, emptyset)), 99.67/15.03 emptyset)))) & 99.67/15.03 (??((^[Y3 : $i]: 99.67/15.03 (in(Y3, 99.67/15.03 setunion( 99.67/15.03 setadjoin( 99.67/15.03 setadjoin(Y0, 99.67/15.03 emptyset), 99.67/15.03 setadjoin( 99.67/15.03 setadjoin(Y0, 99.67/15.03 setadjoin(Y1, 99.67/15.03 emptyset)), 99.67/15.03 emptyset)))) & 99.67/15.03 (setadjoin( 99.67/15.03 setadjoin(Y0, emptyset), 99.67/15.03 setadjoin( 99.67/15.03 setadjoin(Y0, 99.67/15.03 setadjoin(Y1, 99.67/15.03 emptyset)), 99.67/15.03 emptyset)) = 99.67/15.03 setadjoin( 99.67/15.03 setadjoin(Y2, emptyset), 99.67/15.03 setadjoin( 99.67/15.03 setadjoin(Y2, 99.67/15.03 setadjoin(Y3, 99.67/15.03 emptyset)), 99.67/15.03 emptyset))))))))))))))))) => 99.67/15.03 ((!!((^[Y0 : $i]: 99.67/15.03 (!!((^[Y1 : $i]: 99.67/15.03 (in(Y1, Y0) => 99.67/15.03 subset(setadjoin(Y1, emptyset), Y0)))))))) => 99.67/15.03 ((!!((^[Y0 : $i]: 99.67/15.03 (!!((^[Y1 : $i]: 99.67/15.03 (in(Y1, Y0) => 99.67/15.03 in(setadjoin(Y1, emptyset), powerset(Y0))))))))) => 99.67/15.03 ((!!((^[Y0 : $i]: 99.67/15.03 (!!((^[Y1 : $i]: 99.67/15.03 (!!((^[Y2 : $i]: 99.67/15.03 (in(Y2, Y0) => 99.67/15.03 in(setadjoin(Y2, emptyset), 99.67/15.03 powerset(binunion(Y0, Y1))))))))))))) => 99.67/15.03 ((!!((^[Y0 : $i]: 99.67/15.03 (!!((^[Y1 : $i]: 99.67/15.03 (!!((^[Y2 : $i]: 99.67/15.03 (in(Y2, 99.67/15.03 setadjoin(Y0, 99.67/15.03 setadjoin(Y1, emptyset))) => 99.67/15.03 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.67/15.03 ((!!((^[Y0 : $i]: 99.67/15.03 (!!((^[Y1 : $i]: 99.67/15.03 (!!((^[Y2 : $i]: 99.67/15.03 (in(Y2, Y0) => 99.67/15.03 (!!((^[Y3 : $i]: 99.67/15.03 (in(Y3, Y1) => 99.67/15.03 subset( 99.67/15.03 setadjoin(Y2, 99.67/15.03 setadjoin(Y3, 99.67/15.03 emptyset)), 99.67/15.03 binunion(Y0, Y1)))))))))))))))) => 99.67/15.03 ((!!((^[Y0 : $i]: 99.67/15.03 (!!((^[Y1 : $i]: 99.67/15.03 (!!((^[Y2 : $i]: 99.67/15.03 (in(Y2, Y0) => 99.67/15.03 (!!((^[Y3 : $i]: 99.67/15.03 (in(Y3, Y1) => 99.67/15.03 in( 99.67/15.03 setadjoin(Y2, 99.67/15.03 setadjoin(Y3, 99.67/15.03 emptyset)), 99.67/15.03 powerset( 99.67/15.03 binunion(Y0, Y1))))))))))))))))) => 99.67/15.03 ((!!((^[Y0 : $i]: 99.67/15.03 (!!((^[Y1 : $i]: 99.67/15.03 (!!((^[Y2 : $i]: 99.67/15.03 (in(Y2, Y0) => 99.67/15.03 (!!((^[Y3 : $i]: 99.67/15.03 (in(Y3, Y1) => 99.67/15.03 subset( 99.67/15.03 setadjoin( 99.67/15.03 setadjoin(Y2, 99.67/15.03 emptyset), 99.67/15.03 setadjoin( 99.67/15.03 setadjoin(Y2, 99.67/15.03 setadjoin( 99.67/15.03 Y3, 99.67/15.03 emptyset)), 99.67/15.03 emptyset)), 99.67/15.03 powerset( 99.67/15.03 binunion(Y0, Y1))))))))))))))))) => 99.67/15.03 ((!!((^[Y0 : $i]: 99.67/15.03 (!!((^[Y1 : $i]: 99.67/15.03 (!!((^[Y2 : $i]: 99.67/15.03 (in(Y2, Y0) => 99.67/15.03 (!!((^[Y3 : $i]: 99.67/15.03 (in(Y3, Y1) => 99.67/15.03 in( 99.67/15.03 setadjoin( 99.67/15.03 setadjoin(Y2, 99.67/15.03 emptyset), 99.67/15.03 setadjoin( 99.67/15.03 setadjoin(Y2, 99.67/15.03 setadjoin( 99.67/15.03 Y3, 99.67/15.03 emptyset)), 99.67/15.03 emptyset)), 99.67/15.03 powerset( 99.67/15.03 powerset( 99.67/15.03 binunion(Y0, 99.67/15.03 Y1)))))))))))))))))) => 99.67/15.03 ((!!((^[Y0 : $i]: 99.67/15.03 (!!((^[Y1 : $i]: 99.67/15.03 (!!((^[Y2 : $i]: 99.67/15.03 (in(Y2, Y0) => 99.67/15.03 (!!((^[Y3 : $i]: 99.67/15.03 (in(Y3, Y1) => 99.67/15.03 in( 99.67/15.03 setadjoin( 99.67/15.03 setadjoin(Y2, 99.67/15.03 emptyset), 99.67/15.03 setadjoin( 99.67/15.03 setadjoin( 99.67/15.03 Y2, 99.67/15.03 setadjoin( 99.67/15.03 Y3, 99.67/15.03 emptyset)), 99.67/15.03 emptyset)), 99.67/15.03 powerset( 99.67/15.03 powerset( 99.67/15.03 binunion(Y0, 99.67/15.03 Y1)))))))))))))))))) => 99.67/15.03 ((!!((^[Y0 : $i]: 99.67/15.03 (!!((^[Y1 : $i]: 99.67/15.03 (!!((^[Y2 : $i]: 99.67/15.03 (in(Y2, Y0) => 99.67/15.03 (!!((^[Y3 : $i]: 99.67/15.03 (in(Y3, Y1) => 99.67/15.03 in( 99.67/15.03 setadjoin( 99.67/15.03 setadjoin(Y2, 99.67/15.03 emptyset), 99.67/15.03 setadjoin( 99.67/15.03 setadjoin( 99.67/15.03 Y2, 99.67/15.03 setadjoin( 99.67/15.03 Y3, 99.67/15.03 emptyset)), 99.67/15.03 emptyset)), 99.67/15.03 dsetconstr( 99.67/15.03 powerset( 99.67/15.03 powerset( 99.67/15.03 binunion( 99.67/15.03 Y0, Y1))), 99.67/15.03 (^[Y4 : $i]: 99.67/15.03 (??(( 99.67/15.03 ^[Y5 : $i]: 99.67/15.03 (in(Y5, 99.67/15.03 Y0) & 99.67/15.03 (??(( 99.67/15.03 ^[Y6 : $i]: 99.67/15.03 (in(Y6, 99.67/15.03 Y1) & 99.67/15.03 (Y4 = 99.67/15.03 setadjoin( 99.67/15.03 setadjoin( 99.67/15.03 Y5, 99.67/15.03 emptyset), 99.67/15.03 setadjoin( 99.67/15.03 setadjoin( 99.67/15.03 Y5, 99.67/15.03 setadjoin( 99.67/15.03 Y6, 99.67/15.03 emptyset)), 99.67/15.03 emptyset)))))))))))))))))))))))))))) => 99.67/15.03 (!!((^[Y0 : $i]: 99.67/15.03 (!!((^[Y1 : $i]: 99.67/15.03 (!!((^[Y2 : $i]: 99.67/15.03 (in(Y2, 99.67/15.03 dsetconstr( 99.67/15.03 powerset( 99.67/15.03 powerset( 99.67/15.03 binunion(Y0, Y1))), 99.67/15.03 (^[Y3 : $i]: 99.67/15.03 (??((^[Y4 : $i]: 99.67/15.03 (in(Y4, Y0) & 99.67/15.03 (??(( 99.67/15.03 ^[Y5 : $i]: 99.67/15.03 (in(Y5, 99.67/15.03 Y1) & 99.67/15.03 (Y3 = 99.67/15.03 setadjoin( 99.67/15.03 setadjoin( 99.67/15.03 Y4, 99.67/15.03 emptyset), 99.67/15.03 setadjoin( 99.67/15.03 setadjoin( 99.67/15.03 Y4, 99.67/15.03 setadjoin( 99.67/15.03 Y5, 99.67/15.03 emptyset)), 99.67/15.03 emptyset)))))))))))))) => 99.67/15.03 (??((^[Y3 : $i]: 99.67/15.03 ((??((^[Y4 : $i]: 99.67/15.03 (in(Y4, Y1) & 99.67/15.03 (Y2 = 99.67/15.03 setadjoin( 99.67/15.03 setadjoin( 99.67/15.03 Y3, 99.67/15.03 emptyset), 99.67/15.03 setadjoin( 99.67/15.03 setadjoin( 99.67/15.03 Y3, 99.67/15.03 setadjoin( 99.67/15.03 Y4, 99.67/15.03 emptyset)), 99.67/15.03 emptyset))))))) & 99.67/15.03 in(Y3, Y0)))))))))))))))))))))))))))))))))))))), 99.67/15.03 inference('lazy_cnf_imply', [status(thm)], ['280'])). 99.67/15.03 tff('282', plain, 99.67/15.03 ~ ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(setminus(Y0, Y1), Y0))))))) => 99.67/15.03 ((!!((^[Y0 : $i]: 99.67/15.03 (!!((^[Y1 : $i]: 99.67/15.03 ((setminus(Y0, Y1) = emptyset) => subset(Y0, Y1)))))))) => 99.67/15.03 ((!!((^[Y0 : $i]: 99.67/15.03 (!!((^[Y1 : $i]: 99.67/15.03 (!!((^[Y2 : $i]: 99.67/15.03 (in(Y2, symdiff(Y0, Y1)) => 99.67/15.03 (!!((^[Y3 : $o]: 99.67/15.03 ((in(Y2, Y0) => ((~(in(Y2, Y1))) => Y3)) => 99.67/15.03 (((~(in(Y2, Y0))) => 99.67/15.03 (in(Y2, Y1) => Y3)) => 99.67/15.03 Y3))))))))))))))) => 99.67/15.03 ((!!((^[Y0 : $i]: 99.67/15.03 (!!((^[Y1 : $i]: 99.67/15.03 (!!((^[Y2 : $i]: 99.67/15.03 (in(Y2, Y0) => 99.67/15.03 ((~(in(Y2, Y1))) => in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.03 ((!!((^[Y0 : $i]: 99.67/15.03 (!!((^[Y1 : $i]: 99.67/15.03 (!!((^[Y2 : $i]: 99.67/15.03 ((~(in(Y2, Y0))) => 99.67/15.03 (in(Y2, Y1) => in(Y2, symdiff(Y0, Y1))))))))))))) => 99.67/15.03 ((!!((^[Y0 : $i]: 99.67/15.03 (!!((^[Y1 : $i]: 99.67/15.03 (!!((^[Y2 : $i]: 99.67/15.03 (in(Y2, Y0) => 99.67/15.03 (in(Y2, Y1) => (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.67/15.03 ((!!((^[Y0 : $i]: 99.67/15.03 (!!((^[Y1 : $i]: 99.67/15.03 (!!((^[Y2 : $i]: 99.67/15.03 ((~(in(Y2, Y0))) => 99.67/15.03 ((~(in(Y2, Y1))) => 99.67/15.03 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.67/15.03 ((!!((^[Y0 : $i]: 99.67/15.03 (!!((^[Y1 : $i]: 99.67/15.03 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.67/15.03 ((!!((^[Y0 : $i]: 99.67/15.03 (!!((^[Y1 : $i]: 99.67/15.03 in(Y0, 99.67/15.03 setunion( 99.67/15.03 setadjoin(setadjoin(Y0, emptyset), 99.67/15.03 setadjoin( 99.67/15.03 setadjoin(Y0, setadjoin(Y1, emptyset)), 99.67/15.03 emptyset)))))))))) => 99.67/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 in(Y1, 99.91/15.03 setunion( 99.91/15.03 setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (??((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 setunion( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (??((^[Y3 : $i]: 99.91/15.03 (in(Y3, 99.91/15.03 setunion( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (setadjoin( 99.91/15.03 setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)) = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (??((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 setunion( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (??((^[Y3 : $i]: 99.91/15.03 (in(Y3, 99.91/15.03 setunion( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (setadjoin( 99.91/15.03 setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)) = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (in(Y1, Y0) => 99.91/15.03 subset(setadjoin(Y1, emptyset), Y0)))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (in(Y1, Y0) => 99.91/15.03 in(setadjoin(Y1, emptyset), powerset(Y0))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 in(setadjoin(Y2, emptyset), 99.91/15.03 powerset(binunion(Y0, Y1))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset))) => 99.91/15.03 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 subset( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 binunion(Y0, Y1)))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, Y1))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 subset( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, Y1))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin( 99.91/15.03 Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, 99.91/15.03 Y1)))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin( 99.91/15.03 Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, 99.91/15.03 Y1)))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y2, 99.91/15.03 setadjoin( 99.91/15.03 Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 dsetconstr( 99.91/15.03 powerset( 99.91/15.03 powerset( 99.91/15.03 binunion( 99.91/15.03 Y0, Y1))), 99.91/15.03 (^[Y4 : $i]: 99.91/15.03 (??(( 99.91/15.03 ^[Y5 : $i]: 99.91/15.03 ( 99.91/15.03 in(Y5, 99.91/15.03 Y0) & 99.91/15.03 ( 99.91/15.03 ??(( 99.91/15.03 ^[Y6 : $i]: 99.91/15.03 (in(Y6, 99.91/15.03 Y1) & 99.91/15.03 (Y4 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 setadjoin( 99.91/15.03 Y6, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))))))))))))))))))))))))))) => 99.91/15.03 (!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 dsetconstr( 99.91/15.03 powerset( 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, Y1))), 99.91/15.03 (^[Y3 : $i]: 99.91/15.03 (??((^[Y4 : $i]: 99.91/15.03 (in(Y4, Y0) & 99.91/15.03 (??(( 99.91/15.03 ^[Y5 : $i]: 99.91/15.03 ( 99.91/15.03 in(Y5, 99.91/15.03 Y1) & 99.91/15.03 ( 99.91/15.03 Y3 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y4, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y4, 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))))))))))))) => 99.91/15.03 (??((^[Y3 : $i]: 99.91/15.03 ((??((^[Y4 : $i]: 99.91/15.03 (in(Y4, Y1) & 99.91/15.03 (Y2 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y3, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y3, 99.91/15.03 setadjoin( 99.91/15.03 Y4, 99.91/15.03 emptyset)), 99.91/15.03 emptyset))))))) & 99.91/15.03 in(Y3, Y0))))))))))))))))))))))))))))))))))))), 99.91/15.03 inference('lazy_cnf_imply', [status(thm)], ['281'])). 99.91/15.03 tff('283', plain, 99.91/15.03 ~ ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 ((setminus(Y0, Y1) = emptyset) => subset(Y0, Y1)))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, symdiff(Y0, Y1)) => 99.91/15.03 (!!((^[Y3 : $o]: 99.91/15.03 ((in(Y2, Y0) => ((~(in(Y2, Y1))) => Y3)) => 99.91/15.03 (((~(in(Y2, Y0))) => (in(Y2, Y1) => Y3)) => 99.91/15.03 Y3))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 ((~(in(Y2, Y1))) => in(Y2, symdiff(Y0, Y1))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 ((~(in(Y2, Y0))) => 99.91/15.03 (in(Y2, Y1) => in(Y2, symdiff(Y0, Y1))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (in(Y2, Y1) => (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 ((~(in(Y2, Y0))) => 99.91/15.03 ((~(in(Y2, Y1))) => 99.91/15.03 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 in(Y0, 99.91/15.03 setunion( 99.91/15.03 setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 in(Y1, 99.91/15.03 setunion( 99.91/15.03 setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (??((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 setunion( 99.91/15.03 setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (??((^[Y3 : $i]: 99.91/15.03 (in(Y3, 99.91/15.03 setunion( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (setadjoin( 99.91/15.03 setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)) = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (??((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 setunion( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (??((^[Y3 : $i]: 99.91/15.03 (in(Y3, 99.91/15.03 setunion( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (setadjoin( 99.91/15.03 setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)) = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (in(Y1, Y0) => 99.91/15.03 subset(setadjoin(Y1, emptyset), Y0)))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (in(Y1, Y0) => 99.91/15.03 in(setadjoin(Y1, emptyset), powerset(Y0))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 in(setadjoin(Y2, emptyset), 99.91/15.03 powerset(binunion(Y0, Y1))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset))) => 99.91/15.03 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 subset( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 binunion(Y0, Y1)))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, Y1))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 subset( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, Y1))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, Y1)))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin( 99.91/15.03 Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, 99.91/15.03 Y1)))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin( 99.91/15.03 Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 dsetconstr( 99.91/15.03 powerset( 99.91/15.03 powerset( 99.91/15.03 binunion( 99.91/15.03 Y0, Y1))), 99.91/15.03 (^[Y4 : $i]: 99.91/15.03 (??(( 99.91/15.03 ^[Y5 : $i]: 99.91/15.03 (in(Y5, 99.91/15.03 Y0) & 99.91/15.03 ( 99.91/15.03 ??(( 99.91/15.03 ^[Y6 : $i]: 99.91/15.03 (in(Y6, 99.91/15.03 Y1) & 99.91/15.03 (Y4 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 setadjoin( 99.91/15.03 Y6, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))))))))))))))))))))))))))) => 99.91/15.03 (!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 dsetconstr( 99.91/15.03 powerset( 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, Y1))), 99.91/15.03 (^[Y3 : $i]: 99.91/15.03 (??((^[Y4 : $i]: 99.91/15.03 (in(Y4, Y0) & 99.91/15.03 (??(( 99.91/15.03 ^[Y5 : $i]: 99.91/15.03 (in(Y5, 99.91/15.03 Y1) & 99.91/15.03 ( 99.91/15.03 Y3 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y4, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y4, 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))))))))))))) => 99.91/15.03 (??((^[Y3 : $i]: 99.91/15.03 ((??((^[Y4 : $i]: 99.91/15.03 (in(Y4, Y1) & 99.91/15.03 (Y2 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y3, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y3, 99.91/15.03 setadjoin( 99.91/15.03 Y4, 99.91/15.03 emptyset)), 99.91/15.03 emptyset))))))) & 99.91/15.03 in(Y3, Y0)))))))))))))))))))))))))))))))))))), 99.91/15.03 inference('lazy_cnf_imply', [status(thm)], ['282'])). 99.91/15.03 tff('284', plain, 99.91/15.03 ~ ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, symdiff(Y0, Y1)) => 99.91/15.03 (!!((^[Y3 : $o]: 99.91/15.03 ((in(Y2, Y0) => ((~(in(Y2, Y1))) => Y3)) => 99.91/15.03 (((~(in(Y2, Y0))) => (in(Y2, Y1) => Y3)) => 99.91/15.03 Y3))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 ((~(in(Y2, Y1))) => in(Y2, symdiff(Y0, Y1))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 ((~(in(Y2, Y0))) => 99.91/15.03 (in(Y2, Y1) => in(Y2, symdiff(Y0, Y1))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (in(Y2, Y1) => (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 ((~(in(Y2, Y0))) => 99.91/15.03 ((~(in(Y2, Y1))) => 99.91/15.03 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 in(Y0, 99.91/15.03 setunion( 99.91/15.03 setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 in(Y1, 99.91/15.03 setunion( 99.91/15.03 setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (??((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 setunion( 99.91/15.03 setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (??((^[Y3 : $i]: 99.91/15.03 (in(Y3, 99.91/15.03 setunion( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (setadjoin( 99.91/15.03 setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)) = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (??((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 setunion( 99.91/15.03 setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (??((^[Y3 : $i]: 99.91/15.03 (in(Y3, 99.91/15.03 setunion( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (setadjoin( 99.91/15.03 setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)) = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (in(Y1, Y0) => 99.91/15.03 subset(setadjoin(Y1, emptyset), Y0)))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (in(Y1, Y0) => 99.91/15.03 in(setadjoin(Y1, emptyset), powerset(Y0))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 in(setadjoin(Y2, emptyset), 99.91/15.03 powerset(binunion(Y0, Y1))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset))) => 99.91/15.03 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 subset( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 binunion(Y0, Y1)))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, Y1))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 subset( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, Y1))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, Y1)))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, Y1)))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin( 99.91/15.03 Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 dsetconstr( 99.91/15.03 powerset( 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, 99.91/15.03 Y1))), 99.91/15.03 (^[Y4 : $i]: 99.91/15.03 (??((^[Y5 : $i]: 99.91/15.03 (in(Y5, 99.91/15.03 Y0) & 99.91/15.03 (??(( 99.91/15.03 ^[Y6 : $i]: 99.91/15.03 (in(Y6, 99.91/15.03 Y1) & 99.91/15.03 (Y4 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 setadjoin( 99.91/15.03 Y6, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))))))))))))))))))))))))))) => 99.91/15.03 (!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 dsetconstr( 99.91/15.03 powerset( 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, Y1))), 99.91/15.03 (^[Y3 : $i]: 99.91/15.03 (??((^[Y4 : $i]: 99.91/15.03 (in(Y4, Y0) & 99.91/15.03 (??((^[Y5 : $i]: 99.91/15.03 (in(Y5, 99.91/15.03 Y1) & 99.91/15.03 (Y3 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y4, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y4, 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))))))))))))) => 99.91/15.03 (??((^[Y3 : $i]: 99.91/15.03 ((??((^[Y4 : $i]: 99.91/15.03 (in(Y4, Y1) & 99.91/15.03 (Y2 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y3, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y3, 99.91/15.03 setadjoin( 99.91/15.03 Y4, 99.91/15.03 emptyset)), 99.91/15.03 emptyset))))))) & 99.91/15.03 in(Y3, Y0))))))))))))))))))))))))))))))))))), 99.91/15.03 inference('lazy_cnf_imply', [status(thm)], ['283'])). 99.91/15.03 tff('285', plain, 99.91/15.03 ~ ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 ((~(in(Y2, Y1))) => in(Y2, symdiff(Y0, Y1))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 ((~(in(Y2, Y0))) => 99.91/15.03 (in(Y2, Y1) => in(Y2, symdiff(Y0, Y1))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (in(Y2, Y1) => (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 ((~(in(Y2, Y0))) => 99.91/15.03 ((~(in(Y2, Y1))) => 99.91/15.03 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 in(Y0, 99.91/15.03 setunion( 99.91/15.03 setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 in(Y1, 99.91/15.03 setunion( 99.91/15.03 setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (??((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 setunion( 99.91/15.03 setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (??((^[Y3 : $i]: 99.91/15.03 (in(Y3, 99.91/15.03 setunion( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (setadjoin( 99.91/15.03 setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)) = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (??((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 setunion( 99.91/15.03 setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (??((^[Y3 : $i]: 99.91/15.03 (in(Y3, 99.91/15.03 setunion( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (setadjoin( 99.91/15.03 setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)) = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (in(Y1, Y0) => 99.91/15.03 subset(setadjoin(Y1, emptyset), Y0)))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (in(Y1, Y0) => 99.91/15.03 in(setadjoin(Y1, emptyset), powerset(Y0))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 in(setadjoin(Y2, emptyset), 99.91/15.03 powerset(binunion(Y0, Y1))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset))) => 99.91/15.03 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 subset( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 binunion(Y0, Y1)))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, Y1))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 subset( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, Y1))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, Y1)))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, Y1)))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 dsetconstr( 99.91/15.03 powerset( 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, 99.91/15.03 Y1))), 99.91/15.03 (^[Y4 : $i]: 99.91/15.03 (??((^[Y5 : $i]: 99.91/15.03 (in(Y5, 99.91/15.03 Y0) & 99.91/15.03 (??(( 99.91/15.03 ^[Y6 : $i]: 99.91/15.03 (in(Y6, 99.91/15.03 Y1) & 99.91/15.03 (Y4 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 setadjoin( 99.91/15.03 Y6, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))))))))))))))))))))))))))) => 99.91/15.03 (!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 dsetconstr( 99.91/15.03 powerset( 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, Y1))), 99.91/15.03 (^[Y3 : $i]: 99.91/15.03 (??((^[Y4 : $i]: 99.91/15.03 (in(Y4, Y0) & 99.91/15.03 (??((^[Y5 : $i]: 99.91/15.03 (in(Y5, 99.91/15.03 Y1) & 99.91/15.03 (Y3 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y4, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y4, 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))))))))))))) => 99.91/15.03 (??((^[Y3 : $i]: 99.91/15.03 ((??((^[Y4 : $i]: 99.91/15.03 (in(Y4, Y1) & 99.91/15.03 (Y2 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y3, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y3, 99.91/15.03 setadjoin( 99.91/15.03 Y4, 99.91/15.03 emptyset)), 99.91/15.03 emptyset))))))) & 99.91/15.03 in(Y3, Y0)))))))))))))))))))))))))))))))))), 99.91/15.03 inference('lazy_cnf_imply', [status(thm)], ['284'])). 99.91/15.03 tff('286', plain, 99.91/15.03 ~ ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 ((~(in(Y2, Y0))) => 99.91/15.03 (in(Y2, Y1) => in(Y2, symdiff(Y0, Y1))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (in(Y2, Y1) => (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 ((~(in(Y2, Y0))) => 99.91/15.03 ((~(in(Y2, Y1))) => 99.91/15.03 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 in(Y0, 99.91/15.03 setunion( 99.91/15.03 setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 in(Y1, 99.91/15.03 setunion( 99.91/15.03 setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (??((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 setunion( 99.91/15.03 setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (??((^[Y3 : $i]: 99.91/15.03 (in(Y3, 99.91/15.03 setunion( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (setadjoin( 99.91/15.03 setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)) = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (??((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 setunion( 99.91/15.03 setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (??((^[Y3 : $i]: 99.91/15.03 (in(Y3, 99.91/15.03 setunion( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (setadjoin( 99.91/15.03 setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)) = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (in(Y1, Y0) => 99.91/15.03 subset(setadjoin(Y1, emptyset), Y0)))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (in(Y1, Y0) => 99.91/15.03 in(setadjoin(Y1, emptyset), powerset(Y0))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 in(setadjoin(Y2, emptyset), 99.91/15.03 powerset(binunion(Y0, Y1))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset))) => 99.91/15.03 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 subset( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 binunion(Y0, Y1)))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, Y1))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 subset( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, Y1))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, Y1)))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, Y1)))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 dsetconstr( 99.91/15.03 powerset( 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, 99.91/15.03 Y1))), 99.91/15.03 (^[Y4 : $i]: 99.91/15.03 (??((^[Y5 : $i]: 99.91/15.03 ( 99.91/15.03 in(Y5, 99.91/15.03 Y0) & 99.91/15.03 ( 99.91/15.03 ??(( 99.91/15.03 ^[Y6 : $i]: 99.91/15.03 (in(Y6, 99.91/15.03 Y1) & 99.91/15.03 (Y4 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 setadjoin( 99.91/15.03 Y6, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))))))))))))))))))))))))))) => 99.91/15.03 (!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 dsetconstr( 99.91/15.03 powerset( 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, Y1))), 99.91/15.03 (^[Y3 : $i]: 99.91/15.03 (??((^[Y4 : $i]: 99.91/15.03 (in(Y4, Y0) & 99.91/15.03 (??((^[Y5 : $i]: 99.91/15.03 ( 99.91/15.03 in(Y5, 99.91/15.03 Y1) & 99.91/15.03 ( 99.91/15.03 Y3 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y4, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y4, 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))))))))))))) => 99.91/15.03 (??((^[Y3 : $i]: 99.91/15.03 ((??((^[Y4 : $i]: 99.91/15.03 (in(Y4, Y1) & 99.91/15.03 (Y2 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y3, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y3, 99.91/15.03 setadjoin( 99.91/15.03 Y4, 99.91/15.03 emptyset)), 99.91/15.03 emptyset))))))) & 99.91/15.03 in(Y3, Y0))))))))))))))))))))))))))))))))), 99.91/15.03 inference('lazy_cnf_imply', [status(thm)], ['285'])). 99.91/15.03 tff('287', plain, 99.91/15.03 ~ ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (in(Y2, Y1) => (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 ((~(in(Y2, Y0))) => 99.91/15.03 ((~(in(Y2, Y1))) => 99.91/15.03 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 in(Y0, 99.91/15.03 setunion( 99.91/15.03 setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 in(Y1, 99.91/15.03 setunion( 99.91/15.03 setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (??((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 setunion( 99.91/15.03 setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (??((^[Y3 : $i]: 99.91/15.03 (in(Y3, 99.91/15.03 setunion( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (setadjoin( 99.91/15.03 setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)) = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (??((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 setunion( 99.91/15.03 setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (??((^[Y3 : $i]: 99.91/15.03 (in(Y3, 99.91/15.03 setunion( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (setadjoin( 99.91/15.03 setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)) = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (in(Y1, Y0) => 99.91/15.03 subset(setadjoin(Y1, emptyset), Y0)))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (in(Y1, Y0) => 99.91/15.03 in(setadjoin(Y1, emptyset), powerset(Y0))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 in(setadjoin(Y2, emptyset), 99.91/15.03 powerset(binunion(Y0, Y1))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset))) => 99.91/15.03 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 subset( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 binunion(Y0, Y1)))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 powerset(binunion(Y0, Y1))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 subset( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, Y1))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, Y1)))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, Y1)))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 dsetconstr( 99.91/15.03 powerset( 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, Y1))), 99.91/15.03 (^[Y4 : $i]: 99.91/15.03 (??((^[Y5 : $i]: 99.91/15.03 (in(Y5, 99.91/15.03 Y0) & 99.91/15.03 ( 99.91/15.03 ??(( 99.91/15.03 ^[Y6 : $i]: 99.91/15.03 (in(Y6, 99.91/15.03 Y1) & 99.91/15.03 (Y4 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 setadjoin( 99.91/15.03 Y6, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))))))))))))))))))))))))))) => 99.91/15.03 (!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 dsetconstr( 99.91/15.03 powerset( 99.91/15.03 powerset(binunion(Y0, Y1))), 99.91/15.03 (^[Y3 : $i]: 99.91/15.03 (??((^[Y4 : $i]: 99.91/15.03 (in(Y4, Y0) & 99.91/15.03 (??((^[Y5 : $i]: 99.91/15.03 (in(Y5, 99.91/15.03 Y1) & 99.91/15.03 ( 99.91/15.03 Y3 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y4, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y4, 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))))))))))))) => 99.91/15.03 (??((^[Y3 : $i]: 99.91/15.03 ((??((^[Y4 : $i]: 99.91/15.03 (in(Y4, Y1) & 99.91/15.03 (Y2 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y3, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y3, 99.91/15.03 setadjoin( 99.91/15.03 Y4, 99.91/15.03 emptyset)), 99.91/15.03 emptyset))))))) & 99.91/15.03 in(Y3, Y0)))))))))))))))))))))))))))))))), 99.91/15.03 inference('lazy_cnf_imply', [status(thm)], ['286'])). 99.91/15.03 tff('288', plain, 99.91/15.03 ~ ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 ((~(in(Y2, Y0))) => 99.91/15.03 ((~(in(Y2, Y1))) => (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 in(Y0, 99.91/15.03 setunion( 99.91/15.03 setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 in(Y1, 99.91/15.03 setunion( 99.91/15.03 setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (??((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 setunion( 99.91/15.03 setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (??((^[Y3 : $i]: 99.91/15.03 (in(Y3, 99.91/15.03 setunion( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)) = 99.91/15.03 setadjoin(setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (??((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 setunion( 99.91/15.03 setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (??((^[Y3 : $i]: 99.91/15.03 (in(Y3, 99.91/15.03 setunion( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (setadjoin( 99.91/15.03 setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)) = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (in(Y1, Y0) => subset(setadjoin(Y1, emptyset), Y0)))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (in(Y1, Y0) => 99.91/15.03 in(setadjoin(Y1, emptyset), powerset(Y0))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 in(setadjoin(Y2, emptyset), 99.91/15.03 powerset(binunion(Y0, Y1))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset))) => 99.91/15.03 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 subset( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 binunion(Y0, Y1)))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 powerset(binunion(Y0, Y1))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 subset( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset(binunion(Y0, Y1))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, Y1)))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, Y1)))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 dsetconstr( 99.91/15.03 powerset( 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, Y1))), 99.91/15.03 (^[Y4 : $i]: 99.91/15.03 (??((^[Y5 : $i]: 99.91/15.03 (in(Y5, Y0) & 99.91/15.03 (??(( 99.91/15.03 ^[Y6 : $i]: 99.91/15.03 (in(Y6, 99.91/15.03 Y1) & 99.91/15.03 (Y4 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 setadjoin( 99.91/15.03 Y6, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))))))))))))))))))))))))))) => 99.91/15.03 (!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 dsetconstr( 99.91/15.03 powerset( 99.91/15.03 powerset(binunion(Y0, Y1))), 99.91/15.03 (^[Y3 : $i]: 99.91/15.03 (??((^[Y4 : $i]: 99.91/15.03 (in(Y4, Y0) & 99.91/15.03 (??((^[Y5 : $i]: 99.91/15.03 (in(Y5, Y1) & 99.91/15.03 (Y3 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y4, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y4, 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))))))))))))) => 99.91/15.03 (??((^[Y3 : $i]: 99.91/15.03 ((??((^[Y4 : $i]: 99.91/15.03 (in(Y4, Y1) & 99.91/15.03 (Y2 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y3, 99.91/15.03 setadjoin( 99.91/15.03 Y4, 99.91/15.03 emptyset)), 99.91/15.03 emptyset))))))) & 99.91/15.03 in(Y3, Y0))))))))))))))))))))))))))))))), 99.91/15.03 inference('lazy_cnf_imply', [status(thm)], ['287'])). 99.91/15.03 tff('289', plain, 99.91/15.03 ~ ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 in(Y0, 99.91/15.03 setunion( 99.91/15.03 setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 in(Y1, 99.91/15.03 setunion( 99.91/15.03 setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (??((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 setunion( 99.91/15.03 setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), emptyset)))) & 99.91/15.03 (??((^[Y3 : $i]: 99.91/15.03 (in(Y3, 99.91/15.03 setunion( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)) = 99.91/15.03 setadjoin(setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (??((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 setunion( 99.91/15.03 setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (??((^[Y3 : $i]: 99.91/15.03 (in(Y3, 99.91/15.03 setunion( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)) = 99.91/15.03 setadjoin(setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (in(Y1, Y0) => subset(setadjoin(Y1, emptyset), Y0)))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (in(Y1, Y0) => 99.91/15.03 in(setadjoin(Y1, emptyset), powerset(Y0))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 in(setadjoin(Y2, emptyset), 99.91/15.03 powerset(binunion(Y0, Y1))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 setadjoin(Y0, setadjoin(Y1, emptyset))) => 99.91/15.03 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 subset( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 binunion(Y0, Y1)))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 powerset(binunion(Y0, Y1))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 subset( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset(binunion(Y0, Y1))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, Y1)))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, Y1)))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 dsetconstr( 99.91/15.03 powerset( 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, Y1))), 99.91/15.03 (^[Y4 : $i]: 99.91/15.03 (??((^[Y5 : $i]: 99.91/15.03 (in(Y5, Y0) & 99.91/15.03 (??(( 99.91/15.03 ^[Y6 : $i]: 99.91/15.03 (in(Y6, 99.91/15.03 Y1) & 99.91/15.03 (Y4 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 setadjoin( 99.91/15.03 Y6, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))))))))))))))))))))))))))) => 99.91/15.03 (!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 dsetconstr( 99.91/15.03 powerset( 99.91/15.03 powerset(binunion(Y0, Y1))), 99.91/15.03 (^[Y3 : $i]: 99.91/15.03 (??((^[Y4 : $i]: 99.91/15.03 (in(Y4, Y0) & 99.91/15.03 (??((^[Y5 : $i]: 99.91/15.03 (in(Y5, Y1) & 99.91/15.03 (Y3 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y4, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y4, 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))))))))))))) => 99.91/15.03 (??((^[Y3 : $i]: 99.91/15.03 ((??((^[Y4 : $i]: 99.91/15.03 (in(Y4, Y1) & 99.91/15.03 (Y2 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y3, 99.91/15.03 setadjoin( 99.91/15.03 Y4, 99.91/15.03 emptyset)), 99.91/15.03 emptyset))))))) & 99.91/15.03 in(Y3, Y0)))))))))))))))))))))))))))))), 99.91/15.03 inference('lazy_cnf_imply', [status(thm)], ['288'])). 99.91/15.03 tff('290', plain, 99.91/15.03 ~ ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 in(Y0, 99.91/15.03 setunion( 99.91/15.03 setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin(setadjoin(Y0, setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 in(Y1, 99.91/15.03 setunion( 99.91/15.03 setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (??((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 setunion( 99.91/15.03 setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (??((^[Y3 : $i]: 99.91/15.03 (in(Y3, 99.91/15.03 setunion( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)) = 99.91/15.03 setadjoin(setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (??((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 setunion( 99.91/15.03 setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), emptyset)))) & 99.91/15.03 (??((^[Y3 : $i]: 99.91/15.03 (in(Y3, 99.91/15.03 setunion( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)) = 99.91/15.03 setadjoin(setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (in(Y1, Y0) => subset(setadjoin(Y1, emptyset), Y0)))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (in(Y1, Y0) => 99.91/15.03 in(setadjoin(Y1, emptyset), powerset(Y0))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 in(setadjoin(Y2, emptyset), 99.91/15.03 powerset(binunion(Y0, Y1))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 setadjoin(Y0, setadjoin(Y1, emptyset))) => 99.91/15.03 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 subset( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 binunion(Y0, Y1)))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 powerset(binunion(Y0, Y1))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 subset( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset(binunion(Y0, Y1))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, Y1)))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, Y1)))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 dsetconstr( 99.91/15.03 powerset( 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, Y1))), 99.91/15.03 (^[Y4 : $i]: 99.91/15.03 (??((^[Y5 : $i]: 99.91/15.03 (in(Y5, Y0) & 99.91/15.03 (??(( 99.91/15.03 ^[Y6 : $i]: 99.91/15.03 ( 99.91/15.03 in(Y6, 99.91/15.03 Y1) & 99.91/15.03 ( 99.91/15.03 Y4 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 setadjoin( 99.91/15.03 Y6, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))))))))))))))))))))))))))) => 99.91/15.03 (!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 dsetconstr( 99.91/15.03 powerset( 99.91/15.03 powerset(binunion(Y0, Y1))), 99.91/15.03 (^[Y3 : $i]: 99.91/15.03 (??((^[Y4 : $i]: 99.91/15.03 (in(Y4, Y0) & 99.91/15.03 (??((^[Y5 : $i]: 99.91/15.03 (in(Y5, Y1) & 99.91/15.03 (Y3 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y4, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y4, 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))))))))))))) => 99.91/15.03 (??((^[Y3 : $i]: 99.91/15.03 ((??((^[Y4 : $i]: 99.91/15.03 (in(Y4, Y1) & 99.91/15.03 (Y2 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y3, 99.91/15.03 setadjoin( 99.91/15.03 Y4, 99.91/15.03 emptyset)), 99.91/15.03 emptyset))))))) & 99.91/15.03 in(Y3, Y0))))))))))))))))))))))))))))), 99.91/15.03 inference('lazy_cnf_imply', [status(thm)], ['289'])). 99.91/15.03 tff('291', plain, 99.91/15.03 ~ ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 in(Y1, 99.91/15.03 setunion( 99.91/15.03 setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin(setadjoin(Y0, setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (??((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 setunion( 99.91/15.03 setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (??((^[Y3 : $i]: 99.91/15.03 (in(Y3, 99.91/15.03 setunion( 99.91/15.03 setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)) = 99.91/15.03 setadjoin(setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (??((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 setunion( 99.91/15.03 setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (??((^[Y3 : $i]: 99.91/15.03 (in(Y3, 99.91/15.03 setunion( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)) = 99.91/15.03 setadjoin(setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (in(Y1, Y0) => subset(setadjoin(Y1, emptyset), Y0)))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (in(Y1, Y0) => 99.91/15.03 in(setadjoin(Y1, emptyset), powerset(Y0))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 in(setadjoin(Y2, emptyset), 99.91/15.03 powerset(binunion(Y0, Y1))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 setadjoin(Y0, setadjoin(Y1, emptyset))) => 99.91/15.03 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 subset( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 binunion(Y0, Y1)))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 powerset(binunion(Y0, Y1))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 subset( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset(binunion(Y0, Y1))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 powerset(binunion(Y0, Y1)))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, Y1)))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 dsetconstr( 99.91/15.03 powerset( 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, Y1))), 99.91/15.03 (^[Y4 : $i]: 99.91/15.03 (??((^[Y5 : $i]: 99.91/15.03 (in(Y5, Y0) & 99.91/15.03 (??(( 99.91/15.03 ^[Y6 : $i]: 99.91/15.03 (in(Y6, 99.91/15.03 Y1) & 99.91/15.03 ( 99.91/15.03 Y4 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 setadjoin( 99.91/15.03 Y6, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))))))))))))))))))))))))))) => 99.91/15.03 (!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 dsetconstr( 99.91/15.03 powerset( 99.91/15.03 powerset(binunion(Y0, Y1))), 99.91/15.03 (^[Y3 : $i]: 99.91/15.03 (??((^[Y4 : $i]: 99.91/15.03 (in(Y4, Y0) & 99.91/15.03 (??((^[Y5 : $i]: 99.91/15.03 (in(Y5, Y1) & 99.91/15.03 (Y3 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y4, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y4, 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))))))))))))) => 99.91/15.03 (??((^[Y3 : $i]: 99.91/15.03 ((??((^[Y4 : $i]: 99.91/15.03 (in(Y4, Y1) & 99.91/15.03 (Y2 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y3, 99.91/15.03 setadjoin( 99.91/15.03 Y4, 99.91/15.03 emptyset)), 99.91/15.03 emptyset))))))) & 99.91/15.03 in(Y3, Y0)))))))))))))))))))))))))))), 99.91/15.03 inference('lazy_cnf_imply', [status(thm)], ['290'])). 99.91/15.03 tff('292', plain, 99.91/15.03 ~ ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (??((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 setunion( 99.91/15.03 setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (??((^[Y3 : $i]: 99.91/15.03 (in(Y3, 99.91/15.03 setunion( 99.91/15.03 setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)) = 99.91/15.03 setadjoin(setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (??((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 setunion( 99.91/15.03 setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (??((^[Y3 : $i]: 99.91/15.03 (in(Y3, 99.91/15.03 setunion( 99.91/15.03 setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)) = 99.91/15.03 setadjoin(setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (in(Y1, Y0) => subset(setadjoin(Y1, emptyset), Y0)))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (in(Y1, Y0) => 99.91/15.03 in(setadjoin(Y1, emptyset), powerset(Y0))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 in(setadjoin(Y2, emptyset), 99.91/15.03 powerset(binunion(Y0, Y1))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 setadjoin(Y0, setadjoin(Y1, emptyset))) => 99.91/15.03 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 subset( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 binunion(Y0, Y1)))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 powerset(binunion(Y0, Y1))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 subset( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset(binunion(Y0, Y1))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 powerset(binunion(Y0, Y1)))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 powerset(binunion(Y0, Y1)))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 dsetconstr( 99.91/15.03 powerset( 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, Y1))), 99.91/15.03 (^[Y4 : $i]: 99.91/15.03 (??((^[Y5 : $i]: 99.91/15.03 (in(Y5, Y0) & 99.91/15.03 (??((^[Y6 : $i]: 99.91/15.03 (in(Y6, 99.91/15.03 Y1) & 99.91/15.03 (Y4 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 setadjoin( 99.91/15.03 Y6, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))))))))))))))))))))))))))) => 99.91/15.03 (!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 dsetconstr( 99.91/15.03 powerset( 99.91/15.03 powerset(binunion(Y0, Y1))), 99.91/15.03 (^[Y3 : $i]: 99.91/15.03 (??((^[Y4 : $i]: 99.91/15.03 (in(Y4, Y0) & 99.91/15.03 (??((^[Y5 : $i]: 99.91/15.03 (in(Y5, Y1) & 99.91/15.03 (Y3 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y4, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y4, 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))))))))))))) => 99.91/15.03 (??((^[Y3 : $i]: 99.91/15.03 ((??((^[Y4 : $i]: 99.91/15.03 (in(Y4, Y1) & 99.91/15.03 (Y2 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y3, 99.91/15.03 setadjoin(Y4, 99.91/15.03 emptyset)), 99.91/15.03 emptyset))))))) & 99.91/15.03 in(Y3, Y0))))))))))))))))))))))))))), 99.91/15.03 inference('lazy_cnf_imply', [status(thm)], ['291'])). 99.91/15.03 tff('293', plain, 99.91/15.03 ~ ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (??((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 setunion( 99.91/15.03 setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (??((^[Y3 : $i]: 99.91/15.03 (in(Y3, 99.91/15.03 setunion( 99.91/15.03 setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)))) & 99.91/15.03 (setadjoin(setadjoin(Y0, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y0, 99.91/15.03 setadjoin(Y1, emptyset)), 99.91/15.03 emptyset)) = 99.91/15.03 setadjoin(setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (in(Y1, Y0) => subset(setadjoin(Y1, emptyset), Y0)))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (in(Y1, Y0) => 99.91/15.03 in(setadjoin(Y1, emptyset), powerset(Y0))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 in(setadjoin(Y2, emptyset), 99.91/15.03 powerset(binunion(Y0, Y1))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 setadjoin(Y0, setadjoin(Y1, emptyset))) => 99.91/15.03 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 subset( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 binunion(Y0, Y1)))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 powerset(binunion(Y0, Y1))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 subset( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset(binunion(Y0, Y1))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 powerset(binunion(Y0, Y1)))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 powerset(binunion(Y0, Y1)))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 dsetconstr( 99.91/15.03 powerset( 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, Y1))), 99.91/15.03 (^[Y4 : $i]: 99.91/15.03 (??((^[Y5 : $i]: 99.91/15.03 (in(Y5, Y0) & 99.91/15.03 (??((^[Y6 : $i]: 99.91/15.03 (in(Y6, 99.91/15.03 Y1) & 99.91/15.03 (Y4 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 setadjoin( 99.91/15.03 Y6, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))))))))))))))))))))))))))) => 99.91/15.03 (!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 dsetconstr( 99.91/15.03 powerset( 99.91/15.03 powerset(binunion(Y0, Y1))), 99.91/15.03 (^[Y3 : $i]: 99.91/15.03 (??((^[Y4 : $i]: 99.91/15.03 (in(Y4, Y0) & 99.91/15.03 (??((^[Y5 : $i]: 99.91/15.03 (in(Y5, Y1) & 99.91/15.03 (Y3 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y4, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y4, 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))))))))))))) => 99.91/15.03 (??((^[Y3 : $i]: 99.91/15.03 ((??((^[Y4 : $i]: 99.91/15.03 (in(Y4, Y1) & 99.91/15.03 (Y2 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y3, 99.91/15.03 setadjoin(Y4, 99.91/15.03 emptyset)), 99.91/15.03 emptyset))))))) & 99.91/15.03 in(Y3, Y0)))))))))))))))))))))))))), 99.91/15.03 inference('lazy_cnf_imply', [status(thm)], ['292'])). 99.91/15.03 tff('294', plain, 99.91/15.03 ~ ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (in(Y1, Y0) => subset(setadjoin(Y1, emptyset), Y0)))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (in(Y1, Y0) => 99.91/15.03 in(setadjoin(Y1, emptyset), powerset(Y0))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 in(setadjoin(Y2, emptyset), 99.91/15.03 powerset(binunion(Y0, Y1))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 setadjoin(Y0, setadjoin(Y1, emptyset))) => 99.91/15.03 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 subset( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 binunion(Y0, Y1)))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 powerset(binunion(Y0, Y1))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 subset( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset(binunion(Y0, Y1))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 powerset(binunion(Y0, Y1)))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 powerset(binunion(Y0, Y1)))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 dsetconstr( 99.91/15.03 powerset( 99.91/15.03 powerset( 99.91/15.03 binunion(Y0, Y1))), 99.91/15.03 (^[Y4 : $i]: 99.91/15.03 (??((^[Y5 : $i]: 99.91/15.03 (in(Y5, Y0) & 99.91/15.03 (??((^[Y6 : $i]: 99.91/15.03 ( 99.91/15.03 in(Y6, 99.91/15.03 Y1) & 99.91/15.03 ( 99.91/15.03 Y4 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 setadjoin( 99.91/15.03 Y6, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))))))))))))))))))))))))))) => 99.91/15.03 (!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 dsetconstr( 99.91/15.03 powerset( 99.91/15.03 powerset(binunion(Y0, Y1))), 99.91/15.03 (^[Y3 : $i]: 99.91/15.03 (??((^[Y4 : $i]: 99.91/15.03 (in(Y4, Y0) & 99.91/15.03 (??((^[Y5 : $i]: 99.91/15.03 (in(Y5, Y1) & 99.91/15.03 (Y3 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y4, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y4, 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))))))))))))) => 99.91/15.03 (??((^[Y3 : $i]: 99.91/15.03 ((??((^[Y4 : $i]: 99.91/15.03 (in(Y4, Y1) & 99.91/15.03 (Y2 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y3, 99.91/15.03 setadjoin(Y4, 99.91/15.03 emptyset)), 99.91/15.03 emptyset))))))) & 99.91/15.03 in(Y3, Y0))))))))))))))))))))))))), 99.91/15.03 inference('lazy_cnf_imply', [status(thm)], ['293'])). 99.91/15.03 tff('295', plain, 99.91/15.03 ~ ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (in(Y1, Y0) => in(setadjoin(Y1, emptyset), powerset(Y0))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 in(setadjoin(Y2, emptyset), 99.91/15.03 powerset(binunion(Y0, Y1))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, setadjoin(Y0, setadjoin(Y1, emptyset))) => 99.91/15.03 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 subset( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 binunion(Y0, Y1)))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 powerset(binunion(Y0, Y1))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 subset( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset(binunion(Y0, Y1))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 powerset(binunion(Y0, Y1)))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 powerset(binunion(Y0, Y1)))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 dsetconstr( 99.91/15.03 powerset( 99.91/15.03 powerset(binunion(Y0, Y1))), 99.91/15.03 (^[Y4 : $i]: 99.91/15.03 (??((^[Y5 : $i]: 99.91/15.03 (in(Y5, Y0) & 99.91/15.03 (??((^[Y6 : $i]: 99.91/15.03 (in(Y6, 99.91/15.03 Y1) & 99.91/15.03 ( 99.91/15.03 Y4 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 setadjoin( 99.91/15.03 Y6, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))))))))))))))))))))))))))) => 99.91/15.03 (!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 dsetconstr( 99.91/15.03 powerset(powerset(binunion(Y0, Y1))), 99.91/15.03 (^[Y3 : $i]: 99.91/15.03 (??((^[Y4 : $i]: 99.91/15.03 (in(Y4, Y0) & 99.91/15.03 (??((^[Y5 : $i]: 99.91/15.03 (in(Y5, Y1) & 99.91/15.03 (Y3 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y4, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y4, 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))))))))))))) => 99.91/15.03 (??((^[Y3 : $i]: 99.91/15.03 ((??((^[Y4 : $i]: 99.91/15.03 (in(Y4, Y1) & 99.91/15.03 (Y2 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y3, 99.91/15.03 setadjoin(Y4, 99.91/15.03 emptyset)), 99.91/15.03 emptyset))))))) & 99.91/15.03 in(Y3, Y0)))))))))))))))))))))))), 99.91/15.03 inference('lazy_cnf_imply', [status(thm)], ['294'])). 99.91/15.03 tff('296', plain, 99.91/15.03 ~ ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 in(setadjoin(Y2, emptyset), 99.91/15.03 powerset(binunion(Y0, Y1))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, setadjoin(Y0, setadjoin(Y1, emptyset))) => 99.91/15.03 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 subset( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 binunion(Y0, Y1)))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 powerset(binunion(Y0, Y1))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 subset( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset(binunion(Y0, Y1))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 powerset(binunion(Y0, Y1)))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 powerset(binunion(Y0, Y1)))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 dsetconstr( 99.91/15.03 powerset( 99.91/15.03 powerset(binunion(Y0, Y1))), 99.91/15.03 (^[Y4 : $i]: 99.91/15.03 (??((^[Y5 : $i]: 99.91/15.03 (in(Y5, Y0) & 99.91/15.03 (??((^[Y6 : $i]: 99.91/15.03 (in(Y6, Y1) & 99.91/15.03 (Y4 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 setadjoin( 99.91/15.03 Y6, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))))))))))))))))))))))))))) => 99.91/15.03 (!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 dsetconstr( 99.91/15.03 powerset(powerset(binunion(Y0, Y1))), 99.91/15.03 (^[Y3 : $i]: 99.91/15.03 (??((^[Y4 : $i]: 99.91/15.03 (in(Y4, Y0) & 99.91/15.03 (??((^[Y5 : $i]: 99.91/15.03 (in(Y5, Y1) & 99.91/15.03 (Y3 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y4, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y4, 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))))))))))))) => 99.91/15.03 (??((^[Y3 : $i]: 99.91/15.03 ((??((^[Y4 : $i]: 99.91/15.03 (in(Y4, Y1) & 99.91/15.03 (Y2 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y3, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y3, 99.91/15.03 setadjoin(Y4, 99.91/15.03 emptyset)), 99.91/15.03 emptyset))))))) & 99.91/15.03 in(Y3, Y0))))))))))))))))))))))), 99.91/15.03 inference('lazy_cnf_imply', [status(thm)], ['295'])). 99.91/15.03 tff('297', plain, 99.91/15.03 ~ ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, setadjoin(Y0, setadjoin(Y1, emptyset))) => 99.91/15.03 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 subset( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 binunion(Y0, Y1)))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 powerset(binunion(Y0, Y1))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 subset( 99.91/15.03 setadjoin(setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset(binunion(Y0, Y1))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 powerset(binunion(Y0, Y1)))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 powerset(binunion(Y0, Y1)))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 dsetconstr( 99.91/15.03 powerset( 99.91/15.03 powerset(binunion(Y0, Y1))), 99.91/15.03 (^[Y4 : $i]: 99.91/15.03 (??((^[Y5 : $i]: 99.91/15.03 (in(Y5, Y0) & 99.91/15.03 (??((^[Y6 : $i]: 99.91/15.03 (in(Y6, Y1) & 99.91/15.03 (Y4 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 setadjoin( 99.91/15.03 Y6, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))))))))))))))))))))))))))) => 99.91/15.03 (!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 dsetconstr( 99.91/15.03 powerset(powerset(binunion(Y0, Y1))), 99.91/15.03 (^[Y3 : $i]: 99.91/15.03 (??((^[Y4 : $i]: 99.91/15.03 (in(Y4, Y0) & 99.91/15.03 (??((^[Y5 : $i]: 99.91/15.03 (in(Y5, Y1) & 99.91/15.03 (Y3 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y4, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y4, 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))))))))))))) => 99.91/15.03 (??((^[Y3 : $i]: 99.91/15.03 ((??((^[Y4 : $i]: 99.91/15.03 (in(Y4, Y1) & 99.91/15.03 (Y2 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y3, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y3, 99.91/15.03 setadjoin(Y4, 99.91/15.03 emptyset)), 99.91/15.03 emptyset))))))) & 99.91/15.03 in(Y3, Y0)))))))))))))))))))))), 99.91/15.03 inference('lazy_cnf_imply', [status(thm)], ['296'])). 99.91/15.03 tff('298', plain, 99.91/15.03 ~ ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 subset( 99.91/15.03 setadjoin(Y2, setadjoin(Y3, emptyset)), 99.91/15.03 binunion(Y0, Y1)))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 powerset(binunion(Y0, Y1))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 subset( 99.91/15.03 setadjoin(setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset(binunion(Y0, Y1))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin(setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 powerset(binunion(Y0, Y1)))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 powerset(binunion(Y0, Y1)))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 dsetconstr( 99.91/15.03 powerset( 99.91/15.03 powerset(binunion(Y0, Y1))), 99.91/15.03 (^[Y4 : $i]: 99.91/15.03 (??((^[Y5 : $i]: 99.91/15.03 (in(Y5, Y0) & 99.91/15.03 (??((^[Y6 : $i]: 99.91/15.03 (in(Y6, Y1) & 99.91/15.03 (Y4 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 setadjoin( 99.91/15.03 Y6, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))))))))))))))))))))))))))) => 99.91/15.03 (!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 dsetconstr( 99.91/15.03 powerset(powerset(binunion(Y0, Y1))), 99.91/15.03 (^[Y3 : $i]: 99.91/15.03 (??((^[Y4 : $i]: 99.91/15.03 (in(Y4, Y0) & 99.91/15.03 (??((^[Y5 : $i]: 99.91/15.03 (in(Y5, Y1) & 99.91/15.03 (Y3 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y4, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y4, 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))))))))))))) => 99.91/15.03 (??((^[Y3 : $i]: 99.91/15.03 ((??((^[Y4 : $i]: 99.91/15.03 (in(Y4, Y1) & 99.91/15.03 (Y2 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y3, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y3, 99.91/15.03 setadjoin(Y4, 99.91/15.03 emptyset)), 99.91/15.03 emptyset))))))) & 99.91/15.03 in(Y3, Y0))))))))))))))))))))), 99.91/15.03 inference('lazy_cnf_imply', [status(thm)], ['297'])). 99.91/15.03 tff('299', plain, 99.91/15.03 ~ ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin(Y2, setadjoin(Y3, emptyset)), 99.91/15.03 powerset(binunion(Y0, Y1))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 subset( 99.91/15.03 setadjoin(setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset(binunion(Y0, Y1))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin(setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset(powerset(binunion(Y0, Y1)))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin(setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset( 99.91/15.03 powerset(binunion(Y0, Y1)))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 dsetconstr( 99.91/15.03 powerset( 99.91/15.03 powerset(binunion(Y0, Y1))), 99.91/15.03 (^[Y4 : $i]: 99.91/15.03 (??((^[Y5 : $i]: 99.91/15.03 (in(Y5, Y0) & 99.91/15.03 (??((^[Y6 : $i]: 99.91/15.03 (in(Y6, Y1) & 99.91/15.03 (Y4 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin( 99.91/15.03 Y5, 99.91/15.03 setadjoin( 99.91/15.03 Y6, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))))))))))))))))))))))))))) => 99.91/15.03 (!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, 99.91/15.03 dsetconstr( 99.91/15.03 powerset(powerset(binunion(Y0, Y1))), 99.91/15.03 (^[Y3 : $i]: 99.91/15.03 (??((^[Y4 : $i]: 99.91/15.03 (in(Y4, Y0) & 99.91/15.03 (??((^[Y5 : $i]: 99.91/15.03 (in(Y5, Y1) & 99.91/15.03 (Y3 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y4, 99.91/15.03 emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y4, 99.91/15.03 setadjoin(Y5, 99.91/15.03 emptyset)), 99.91/15.03 emptyset)))))))))))))) => 99.91/15.03 (??((^[Y3 : $i]: 99.91/15.03 ((??((^[Y4 : $i]: 99.91/15.03 (in(Y4, Y1) & 99.91/15.03 (Y2 = 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y3, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y3, 99.91/15.03 setadjoin(Y4, 99.91/15.03 emptyset)), 99.91/15.03 emptyset))))))) & 99.91/15.03 in(Y3, Y0)))))))))))))))))))), 99.91/15.03 inference('lazy_cnf_imply', [status(thm)], ['298'])). 99.91/15.03 tff('300', plain, 99.91/15.03 ~ ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 subset( 99.91/15.03 setadjoin(setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset(binunion(Y0, Y1))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin(setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset(powerset(binunion(Y0, Y1)))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.03 (!!((^[Y3 : $i]: 99.91/15.03 (in(Y3, Y1) => 99.91/15.03 in( 99.91/15.03 setadjoin(setadjoin(Y2, emptyset), 99.91/15.03 setadjoin( 99.91/15.03 setadjoin(Y2, 99.91/15.03 setadjoin(Y3, emptyset)), 99.91/15.03 emptyset)), 99.91/15.03 powerset(powerset(binunion(Y0, Y1)))))))))))))))))) => 99.91/15.03 ((!!((^[Y0 : $i]: 99.91/15.03 (!!((^[Y1 : $i]: 99.91/15.03 (!!((^[Y2 : $i]: 99.91/15.03 (in(Y2, Y0) => 99.91/15.04 (!!((^[Y3 : $i]: 99.91/15.04 (in(Y3, Y1) => 99.91/15.04 in( 99.91/15.04 setadjoin(setadjoin(Y2, emptyset), 99.91/15.04 setadjoin( 99.91/15.04 setadjoin(Y2, 99.91/15.04 setadjoin(Y3, emptyset)), 99.91/15.04 emptyset)), 99.91/15.04 dsetconstr( 99.91/15.04 powerset( 99.91/15.04 powerset(binunion(Y0, Y1))), 99.91/15.04 (^[Y4 : $i]: 99.91/15.04 (??((^[Y5 : $i]: 99.91/15.04 (in(Y5, Y0) & 99.91/15.04 (??((^[Y6 : $i]: 99.91/15.04 (in(Y6, Y1) & 99.91/15.04 (Y4 = 99.91/15.04 setadjoin( 99.91/15.04 setadjoin( 99.91/15.04 Y5, 99.91/15.04 emptyset), 99.91/15.04 setadjoin( 99.91/15.04 setadjoin( 99.91/15.04 Y5, 99.91/15.04 setadjoin( 99.91/15.04 Y6, 99.91/15.04 emptyset)), 99.91/15.04 emptyset)))))))))))))))))))))))))))) => 99.91/15.04 (!!((^[Y0 : $i]: 99.91/15.04 (!!((^[Y1 : $i]: 99.91/15.04 (!!((^[Y2 : $i]: 99.91/15.04 (in(Y2, 99.91/15.04 dsetconstr( 99.91/15.04 powerset(powerset(binunion(Y0, Y1))), 99.91/15.04 (^[Y3 : $i]: 99.91/15.04 (??((^[Y4 : $i]: 99.91/15.04 (in(Y4, Y0) & 99.91/15.04 (??((^[Y5 : $i]: 99.91/15.04 (in(Y5, Y1) & 99.91/15.04 (Y3 = 99.91/15.04 setadjoin( 99.91/15.04 setadjoin(Y4, 99.91/15.04 emptyset), 99.91/15.04 setadjoin( 99.91/15.04 setadjoin(Y4, 99.91/15.04 setadjoin(Y5, 99.91/15.04 emptyset)), 99.91/15.04 emptyset)))))))))))))) => 99.91/15.04 (??((^[Y3 : $i]: 99.91/15.04 ((??((^[Y4 : $i]: 99.91/15.04 (in(Y4, Y1) & 99.91/15.04 (Y2 = 99.91/15.04 setadjoin( 99.91/15.04 setadjoin(Y3, emptyset), 99.91/15.04 setadjoin( 99.91/15.04 setadjoin(Y3, 99.91/15.04 setadjoin(Y4, 99.91/15.04 emptyset)), 99.91/15.04 emptyset))))))) & 99.91/15.04 in(Y3, Y0))))))))))))))))))), 99.91/15.04 inference('lazy_cnf_imply', [status(thm)], ['299'])). 99.91/15.04 tff('301', plain, 99.91/15.04 ~ ((!!((^[Y0 : $i]: 99.91/15.04 (!!((^[Y1 : $i]: 99.91/15.04 (!!((^[Y2 : $i]: 99.91/15.04 (in(Y2, Y0) => 99.91/15.04 (!!((^[Y3 : $i]: 99.91/15.04 (in(Y3, Y1) => 99.91/15.04 in( 99.91/15.04 setadjoin(setadjoin(Y2, emptyset), 99.91/15.04 setadjoin( 99.91/15.04 setadjoin(Y2, 99.91/15.04 setadjoin(Y3, emptyset)), 99.91/15.04 emptyset)), 99.91/15.04 powerset(powerset(binunion(Y0, Y1)))))))))))))))))) => 99.91/15.04 ((!!((^[Y0 : $i]: 99.91/15.04 (!!((^[Y1 : $i]: 99.91/15.04 (!!((^[Y2 : $i]: 99.91/15.04 (in(Y2, Y0) => 99.91/15.04 (!!((^[Y3 : $i]: 99.91/15.04 (in(Y3, Y1) => 99.91/15.04 in( 99.91/15.04 setadjoin(setadjoin(Y2, emptyset), 99.91/15.04 setadjoin( 99.91/15.04 setadjoin(Y2, 99.91/15.04 setadjoin(Y3, emptyset)), 99.91/15.04 emptyset)), 99.91/15.04 powerset(powerset(binunion(Y0, Y1)))))))))))))))))) => 99.91/15.04 ((!!((^[Y0 : $i]: 99.91/15.04 (!!((^[Y1 : $i]: 99.91/15.04 (!!((^[Y2 : $i]: 99.91/15.04 (in(Y2, Y0) => 99.91/15.04 (!!((^[Y3 : $i]: 99.91/15.04 (in(Y3, Y1) => 99.91/15.04 in( 99.91/15.04 setadjoin(setadjoin(Y2, emptyset), 99.91/15.04 setadjoin( 99.91/15.04 setadjoin(Y2, 99.91/15.04 setadjoin(Y3, emptyset)), 99.91/15.04 emptyset)), 99.91/15.04 dsetconstr( 99.91/15.04 powerset( 99.91/15.04 powerset(binunion(Y0, Y1))), 99.91/15.04 (^[Y4 : $i]: 99.91/15.04 (??((^[Y5 : $i]: 99.91/15.04 (in(Y5, Y0) & 99.91/15.04 (??((^[Y6 : $i]: 99.91/15.04 (in(Y6, Y1) & 99.91/15.04 (Y4 = 99.91/15.04 setadjoin( 99.91/15.04 setadjoin( 99.91/15.04 Y5, 99.91/15.04 emptyset), 99.91/15.04 setadjoin( 99.91/15.04 setadjoin( 99.91/15.04 Y5, 99.91/15.04 setadjoin( 99.91/15.04 Y6, 99.91/15.04 emptyset)), 99.91/15.04 emptyset)))))))))))))))))))))))))))) => 99.91/15.04 (!!((^[Y0 : $i]: 99.91/15.04 (!!((^[Y1 : $i]: 99.91/15.04 (!!((^[Y2 : $i]: 99.91/15.04 (in(Y2, 99.91/15.04 dsetconstr( 99.91/15.04 powerset(powerset(binunion(Y0, Y1))), 99.91/15.04 (^[Y3 : $i]: 99.91/15.04 (??((^[Y4 : $i]: 99.91/15.04 (in(Y4, Y0) & 99.91/15.04 (??((^[Y5 : $i]: 99.91/15.04 (in(Y5, Y1) & 99.91/15.04 (Y3 = 99.91/15.04 setadjoin( 99.91/15.04 setadjoin(Y4, 99.91/15.04 emptyset), 99.91/15.04 setadjoin( 99.91/15.04 setadjoin(Y4, 99.91/15.04 setadjoin(Y5, 99.91/15.04 emptyset)), 99.91/15.04 emptyset)))))))))))))) => 99.91/15.04 (??((^[Y3 : $i]: 99.91/15.04 ((??((^[Y4 : $i]: 99.91/15.04 (in(Y4, Y1) & 99.91/15.04 (Y2 = 99.91/15.04 setadjoin( 99.91/15.04 setadjoin(Y3, emptyset), 99.91/15.04 setadjoin( 99.91/15.04 setadjoin(Y3, 99.91/15.04 setadjoin(Y4, emptyset)), 99.91/15.04 emptyset))))))) & 99.91/15.04 in(Y3, Y0)))))))))))))))))), 99.91/15.04 inference('lazy_cnf_imply', [status(thm)], ['300'])). 99.91/15.04 tff('302', plain, 99.91/15.04 ~ ((!!((^[Y0 : $i]: 99.91/15.04 (!!((^[Y1 : $i]: 99.91/15.04 (!!((^[Y2 : $i]: 99.91/15.04 (in(Y2, Y0) => 99.91/15.04 (!!((^[Y3 : $i]: 99.91/15.04 (in(Y3, Y1) => 99.91/15.04 in( 99.91/15.04 setadjoin(setadjoin(Y2, emptyset), 99.91/15.04 setadjoin( 99.91/15.04 setadjoin(Y2, 99.91/15.04 setadjoin(Y3, emptyset)), 99.91/15.04 emptyset)), 99.91/15.04 powerset(powerset(binunion(Y0, Y1)))))))))))))))))) => 99.91/15.04 ((!!((^[Y0 : $i]: 99.91/15.04 (!!((^[Y1 : $i]: 99.91/15.04 (!!((^[Y2 : $i]: 99.91/15.04 (in(Y2, Y0) => 99.91/15.04 (!!((^[Y3 : $i]: 99.91/15.04 (in(Y3, Y1) => 99.91/15.04 in( 99.91/15.04 setadjoin(setadjoin(Y2, emptyset), 99.91/15.04 setadjoin( 99.91/15.04 setadjoin(Y2, 99.91/15.04 setadjoin(Y3, emptyset)), 99.91/15.04 emptyset)), 99.91/15.04 dsetconstr( 99.91/15.04 powerset( 99.91/15.04 powerset(binunion(Y0, Y1))), 99.91/15.04 (^[Y4 : $i]: 99.91/15.04 (??((^[Y5 : $i]: 99.91/15.04 (in(Y5, Y0) & 99.91/15.04 (??((^[Y6 : $i]: 99.91/15.04 (in(Y6, Y1) & 99.91/15.04 (Y4 = 99.91/15.04 setadjoin( 99.91/15.04 setadjoin( 99.91/15.04 Y5, 99.91/15.04 emptyset), 99.91/15.04 setadjoin( 99.91/15.04 setadjoin( 99.91/15.04 Y5, 99.91/15.04 setadjoin( 99.91/15.04 Y6, 99.91/15.04 emptyset)), 99.91/15.04 emptyset)))))))))))))))))))))))))))) => 99.91/15.04 (!!((^[Y0 : $i]: 99.91/15.04 (!!((^[Y1 : $i]: 99.91/15.04 (!!((^[Y2 : $i]: 99.91/15.04 (in(Y2, 99.91/15.04 dsetconstr( 99.91/15.04 powerset(powerset(binunion(Y0, Y1))), 99.91/15.04 (^[Y3 : $i]: 99.91/15.04 (??((^[Y4 : $i]: 99.91/15.04 (in(Y4, Y0) & 99.91/15.04 (??((^[Y5 : $i]: 99.91/15.04 (in(Y5, Y1) & 99.91/15.04 (Y3 = 99.91/15.04 setadjoin( 99.91/15.04 setadjoin(Y4, 99.91/15.04 emptyset), 99.91/15.04 setadjoin( 99.91/15.04 setadjoin(Y4, 99.91/15.04 setadjoin(Y5, 99.91/15.04 emptyset)), 99.91/15.04 emptyset)))))))))))))) => 99.91/15.04 (??((^[Y3 : $i]: 99.91/15.04 ((??((^[Y4 : $i]: 99.91/15.04 (in(Y4, Y1) & 99.91/15.04 (Y2 = 99.91/15.04 setadjoin( 99.91/15.04 setadjoin(Y3, emptyset), 99.91/15.04 setadjoin( 99.91/15.04 setadjoin(Y3, 99.91/15.04 setadjoin(Y4, emptyset)), 99.91/15.04 emptyset))))))) & 99.91/15.04 in(Y3, Y0))))))))))))))))), 99.91/15.04 inference('lazy_cnf_imply', [status(thm)], ['301'])). 99.91/15.04 tff('303', plain, 99.91/15.04 ~ ((!!((^[Y0 : $i]: 99.91/15.04 (!!((^[Y1 : $i]: 99.91/15.04 (!!((^[Y2 : $i]: 99.91/15.04 (in(Y2, Y0) => 99.91/15.04 (!!((^[Y3 : $i]: 99.91/15.04 (in(Y3, Y1) => 99.91/15.04 in( 99.91/15.04 setadjoin(setadjoin(Y2, emptyset), 99.91/15.04 setadjoin( 99.91/15.04 setadjoin(Y2, 99.91/15.04 setadjoin(Y3, emptyset)), 99.91/15.04 emptyset)), 99.91/15.04 dsetconstr( 99.91/15.04 powerset(powerset(binunion(Y0, Y1))), 99.91/15.04 (^[Y4 : $i]: 99.91/15.04 (??((^[Y5 : $i]: 99.91/15.04 (in(Y5, Y0) & 99.91/15.04 (??((^[Y6 : $i]: 99.91/15.04 (in(Y6, Y1) & 99.91/15.04 (Y4 = 99.91/15.04 setadjoin( 99.91/15.04 setadjoin(Y5, 99.91/15.04 emptyset), 99.91/15.04 setadjoin( 99.91/15.04 setadjoin( 99.91/15.04 Y5, 99.91/15.04 setadjoin( 99.91/15.04 Y6, 99.91/15.04 emptyset)), 99.91/15.04 emptyset)))))))))))))))))))))))))))) => 99.91/15.04 (!!((^[Y0 : $i]: 99.91/15.04 (!!((^[Y1 : $i]: 99.91/15.04 (!!((^[Y2 : $i]: 99.91/15.04 (in(Y2, 99.91/15.04 dsetconstr( 99.91/15.04 powerset(powerset(binunion(Y0, Y1))), 99.91/15.04 (^[Y3 : $i]: 99.91/15.04 (??((^[Y4 : $i]: 99.91/15.04 (in(Y4, Y0) & 99.91/15.04 (??((^[Y5 : $i]: 99.91/15.04 (in(Y5, Y1) & 99.91/15.04 (Y3 = 99.91/15.04 setadjoin( 99.91/15.04 setadjoin(Y4, 99.91/15.04 emptyset), 99.91/15.04 setadjoin( 99.91/15.04 setadjoin(Y4, 99.91/15.04 setadjoin(Y5, 99.91/15.04 emptyset)), 99.91/15.04 emptyset)))))))))))))) => 99.91/15.04 (??((^[Y3 : $i]: 99.91/15.04 ((??((^[Y4 : $i]: 99.91/15.04 (in(Y4, Y1) & 99.91/15.04 (Y2 = 99.91/15.04 setadjoin( 99.91/15.04 setadjoin(Y3, emptyset), 99.91/15.04 setadjoin( 99.91/15.04 setadjoin(Y3, 99.91/15.04 setadjoin(Y4, emptyset)), 99.91/15.04 emptyset))))))) & 99.91/15.04 in(Y3, Y0)))))))))))))))), 99.91/15.04 inference('lazy_cnf_imply', [status(thm)], ['302'])). 99.91/15.04 tff('304', plain, 99.91/15.04 ~ (!!((^[Y0 : $i]: 99.91/15.04 (!!((^[Y1 : $i]: 99.91/15.04 (!!((^[Y2 : $i]: 99.91/15.04 (in(Y2, 99.91/15.04 dsetconstr( 99.91/15.04 powerset(powerset(binunion(Y0, Y1))), 99.91/15.04 (^[Y3 : $i]: 99.91/15.04 (??((^[Y4 : $i]: 99.91/15.04 (in(Y4, Y0) & 99.91/15.04 (??((^[Y5 : $i]: 99.91/15.04 (in(Y5, Y1) & 99.91/15.04 (Y3 = 99.91/15.04 setadjoin( 99.91/15.04 setadjoin(Y4, emptyset), 99.91/15.04 setadjoin( 99.91/15.04 setadjoin(Y4, 99.91/15.04 setadjoin(Y5, 99.91/15.04 emptyset)), 99.91/15.04 emptyset)))))))))))))) => 99.91/15.04 (??((^[Y3 : $i]: 99.91/15.04 ((??((^[Y4 : $i]: 99.91/15.04 (in(Y4, Y1) & 99.91/15.04 (Y2 = 99.91/15.04 setadjoin( 99.91/15.04 setadjoin(Y3, emptyset), 99.91/15.04 setadjoin( 99.91/15.04 setadjoin(Y3, 99.91/15.04 setadjoin(Y4, emptyset)), 99.91/15.04 emptyset))))))) & 99.91/15.04 in(Y3, Y0))))))))))))))), 99.91/15.04 inference('lazy_cnf_imply', [status(thm)], ['303'])). 99.91/15.04 tff('305', plain, 99.91/15.04 ~ (!!((^[Y0 : $i]: 99.91/15.04 (!!((^[Y1 : $i]: 99.91/15.04 (in(Y1, 99.91/15.04 dsetconstr( 99.91/15.04 powerset(powerset(binunion('#sk710', Y0))), 99.91/15.04 (^[Y2 : $i]: 99.91/15.04 (??((^[Y3 : $i]: 99.91/15.04 (in(Y3, '#sk710') & 99.91/15.04 (??((^[Y4 : $i]: 99.91/15.04 (in(Y4, Y0) & 99.91/15.04 (Y2 = 99.91/15.04 setadjoin( 99.91/15.04 setadjoin(Y3, emptyset), 99.91/15.04 setadjoin( 99.91/15.04 setadjoin(Y3, 99.91/15.04 setadjoin(Y4, emptyset)), 99.91/15.04 emptyset)))))))))))))) => 99.91/15.04 (??((^[Y2 : $i]: 99.91/15.04 ((??((^[Y3 : $i]: 99.91/15.04 (in(Y3, Y0) & 99.91/15.04 (Y1 = 99.91/15.04 setadjoin(setadjoin(Y2, emptyset), 99.91/15.04 setadjoin( 99.91/15.04 setadjoin(Y2, 99.91/15.04 setadjoin(Y3, emptyset)), 99.91/15.04 emptyset))))))) & 99.91/15.04 in(Y2, '#sk710')))))))))))), 99.91/15.04 inference('lazy_cnf_exists', [status(thm)], ['304'])). 99.91/15.04 tff('306', plain, 99.91/15.04 ~ (!!((^[Y0 : $i]: 99.91/15.04 (in(Y0, 99.91/15.04 dsetconstr(powerset(powerset(binunion('#sk710', '#sk711'))), 99.91/15.04 (^[Y1 : $i]: 99.91/15.04 (??((^[Y2 : $i]: 99.91/15.04 (in(Y2, '#sk710') & 99.91/15.04 (??((^[Y3 : $i]: 99.91/15.04 (in(Y3, '#sk711') & 99.91/15.04 (Y1 = 99.91/15.04 setadjoin(setadjoin(Y2, emptyset), 99.91/15.04 setadjoin( 99.91/15.04 setadjoin(Y2, 99.91/15.04 setadjoin(Y3, emptyset)), 99.91/15.04 emptyset)))))))))))))) => 99.91/15.04 (??((^[Y1 : $i]: 99.91/15.04 ((??((^[Y2 : $i]: 99.91/15.04 (in(Y2, '#sk711') & 99.91/15.04 (Y0 = 99.91/15.04 setadjoin(setadjoin(Y1, emptyset), 99.91/15.04 setadjoin( 99.91/15.04 setadjoin(Y1, setadjoin(Y2, emptyset)), 99.91/15.04 emptyset))))))) & 99.91/15.04 in(Y1, '#sk710'))))))))), 99.91/15.04 inference('lazy_cnf_exists', [status(thm)], ['305'])). 99.91/15.04 tff('307', plain, 99.91/15.04 ~ (in('#sk712', 99.91/15.04 dsetconstr(powerset(powerset(binunion('#sk710', '#sk711'))), 99.91/15.04 (^[Y0 : $i]: 99.91/15.04 (??((^[Y1 : $i]: 99.91/15.04 (in(Y1, '#sk710') & 99.91/15.04 (??((^[Y2 : $i]: 99.91/15.04 (in(Y2, '#sk711') & 99.91/15.04 (Y0 = 99.91/15.04 setadjoin(setadjoin(Y1, emptyset), 99.91/15.04 setadjoin( 99.91/15.04 setadjoin(Y1, setadjoin(Y2, emptyset)), 99.91/15.04 emptyset)))))))))))))) => 99.91/15.04 (??((^[Y0 : $i]: 99.91/15.04 ((??((^[Y1 : $i]: 99.91/15.04 (in(Y1, '#sk711') & 99.91/15.04 ('#sk712' = 99.91/15.04 setadjoin(setadjoin(Y0, emptyset), 99.91/15.04 setadjoin(setadjoin(Y0, setadjoin(Y1, emptyset)), 99.91/15.04 emptyset))))))) & 99.91/15.04 in(Y0, '#sk710')))))), 99.91/15.04 inference('lazy_cnf_exists', [status(thm)], ['306'])). 99.91/15.04 tff('308', plain, 99.91/15.04 ~ (??((^[Y0 : $i]: 99.91/15.04 ((??((^[Y1 : $i]: 99.91/15.04 (in(Y1, '#sk711') & 99.91/15.04 ('#sk712' = 99.91/15.04 setadjoin(setadjoin(Y0, emptyset), 99.91/15.04 setadjoin(setadjoin(Y0, setadjoin(Y1, emptyset)), 99.91/15.04 emptyset))))))) & 99.91/15.04 in(Y0, '#sk710'))))), 99.91/15.04 inference('lazy_cnf_imply', [status(thm)], ['307'])). 99.91/15.04 tff('309', plain, 99.91/15.04 (!!((^[Y0 : $i]: ((??((^[Y1 : $i]: in(Y1, Y0)))) => (Y0 != emptyset))))), 99.91/15.04 inference('lazy_cnf_imply', [status(thm)], ['187'])). 99.91/15.04 tff('310', plain, 99.91/15.04 ![X1]: ((??((^[Y0 : $i]: in(Y0, X1)))) => (X1 != emptyset)), 99.91/15.04 inference('lazy_cnf_forall', [status(thm)], ['309'])). 99.91/15.04 tff('311', plain, ![X1]: (~ (??((^[Y0 : $i]: in(Y0, X1)))) | X1 != emptyset), 99.91/15.04 inference('lazy_cnf_imply', [status(thm)], ['310'])). 99.91/15.04 tff('312', plain, ~ (??((^[Y0 : $i]: in(Y0, emptyset)))), 99.91/15.04 inference('simplify', [status(thm)], ['311'])). 99.91/15.04 tff('313', plain, ![X1 : $i > $o]: ( '#form178'(X1) | ~ (??(X1))), 99.91/15.04 define([status(thm)])). 99.91/15.04 tff('314', plain, 99.91/15.04 ~ '#form178'( 99.91/15.04 (^[Y0 : $i]: 99.91/15.04 ((??((^[Y1 : $i]: 99.91/15.04 (in(Y1, '#sk711') & 99.91/15.04 ('#sk712' = 99.91/15.04 setadjoin(setadjoin(Y0, emptyset), 99.91/15.04 setadjoin(setadjoin(Y0, setadjoin(Y1, emptyset)), 99.91/15.04 emptyset))))))) & 99.91/15.04 in(Y0, '#sk710')))), 99.91/15.04 inference('renaming', [status(thm)], ['308', '313'])). 99.91/15.04 tff('315', plain, 99.91/15.04 in('#sk712', 99.91/15.04 dsetconstr(powerset(powerset(binunion('#sk710', '#sk711'))), 99.91/15.04 (^[Y0 : $i]: 99.91/15.04 (??((^[Y1 : $i]: 99.91/15.04 (in(Y1, '#sk710') & 99.91/15.04 (??((^[Y2 : $i]: 99.91/15.04 (in(Y2, '#sk711') & 99.91/15.04 (Y0 = 99.91/15.04 setadjoin(setadjoin(Y1, emptyset), 99.91/15.04 setadjoin( 99.91/15.04 setadjoin(Y1, setadjoin(Y2, emptyset)), 99.91/15.04 emptyset)))))))))))))), 99.91/15.04 inference('lazy_cnf_imply', [status(thm)], ['307'])). 99.91/15.04 tff('316', plain, 99.91/15.04 (!!((^[Y0 : $i]: 99.91/15.04 (!!((^[Y1 : $i > $o]: 99.91/15.04 (!!((^[Y2 : $i]: (in(Y2, dsetconstr(Y0, Y1)) => Y1(Y2))))))))))), 99.91/15.04 inference('lazy_cnf_imply', [status(thm)], ['175'])). 99.91/15.04 tff('317', plain, 99.91/15.04 ![X1]: 99.91/15.04 (!!((^[Y0 : $i > $o]: 99.91/15.04 (!!((^[Y1 : $i]: (in(Y1, dsetconstr(X1, Y0)) => Y0(Y1)))))))), 99.91/15.04 inference('lazy_cnf_forall', [status(thm)], ['316'])). 99.91/15.04 tff('318', plain, 99.91/15.04 ![X1, X2 : $i > $o]: 99.91/15.04 (!!((^[Y0 : $i]: (in(Y0, dsetconstr(X1, X2)) => X2(Y0))))), 99.91/15.04 inference('lazy_cnf_forall', [status(thm)], ['317'])). 99.91/15.04 tff('319', plain, 99.91/15.04 ![X1, X2 : $i > $o, X3]: (in(X3, dsetconstr(X1, X2)) => X2(X3)), 99.91/15.04 inference('lazy_cnf_forall', [status(thm)], ['318'])). 99.91/15.04 tff('320', plain, 99.91/15.04 ![X1, X2 : $i > $o, X3]: (~ in(X3, dsetconstr(X1, X2)) | X2(X3)), 99.91/15.04 inference('lazy_cnf_imply', [status(thm)], ['319'])). 99.91/15.04 tff('321', plain, 99.91/15.04 (^[Y0 : $i]: 99.91/15.04 (??((^[Y1 : $i]: 99.91/15.04 (in(Y1, '#sk710') & 99.91/15.04 (??((^[Y2 : $i]: 99.91/15.04 (in(Y2, '#sk711') & 99.91/15.04 (Y0 = 99.91/15.04 setadjoin(setadjoin(Y1, emptyset), 99.91/15.04 setadjoin(setadjoin(Y1, setadjoin(Y2, emptyset)), 99.91/15.04 emptyset))))))))))))('#sk712'), 99.91/15.04 inference('sup-', [status(thm)], ['315', '320'])). 99.91/15.04 tff('322', plain, 99.91/15.04 (??((^[Y0 : $i]: 99.91/15.04 (in(Y0, '#sk710') & 99.91/15.04 (??((^[Y1 : $i]: 99.91/15.04 (in(Y1, '#sk711') & 99.91/15.04 ('#sk712' = 99.91/15.04 setadjoin(setadjoin(Y0, emptyset), 99.91/15.04 setadjoin(setadjoin(Y0, setadjoin(Y1, emptyset)), 99.91/15.04 emptyset))))))))))), 99.91/15.04 inference('ho_norm', [status(thm)], ['321'])). 99.91/15.04 tff('323', plain, 99.91/15.04 (!!((^[Y0 : $i > $o]: 99.91/15.04 ((??((^[Y1 : $i]: 99.91/15.04 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 99.91/15.04 (??(Y0)))))), 99.91/15.04 inference('lazy_cnf_imply', [status(thm)], ['180'])). 99.91/15.04 tff('324', plain, 99.91/15.04 ![X1 : $i > $o]: 99.91/15.04 ((??((^[Y0 : $i]: (X1(Y0) & (!!((^[Y1 : $i]: (X1(Y1) => (Y0 = Y1))))))))) => 99.91/15.04 (??(X1))), 99.91/15.04 inference('lazy_cnf_forall', [status(thm)], ['323'])). 99.91/15.04 tff('325', plain, 99.91/15.04 ![X1 : $i > $o]: 99.91/15.04 (~ (??((^[Y0 : $i]: 99.91/15.04 (X1(Y0) & (!!((^[Y1 : $i]: (X1(Y1) => (Y0 = Y1))))))))) 99.91/15.04 | (??(X1))), 99.91/15.04 inference('lazy_cnf_imply', [status(thm)], ['324'])). 99.91/15.04 tff('326', plain, 99.91/15.04 ![X1 : $i > $o, X2]: 99.91/15.04 (~ (X1(X2) & (!!((^[Y0 : $i]: (X1(Y0) => (X2 = Y0)))))) | (??(X1))), 99.91/15.04 inference('lazy_cnf_forall', [status(thm)], ['325'])). 99.91/15.04 tff('327', plain, 99.91/15.04 ![X1 : $i > $o, X2]: 99.91/15.04 (~ X1(X2) | ~ (!!((^[Y0 : $i]: (X1(Y0) => (X2 = Y0))))) | (??(X1))), 99.91/15.04 inference('lazy_cnf_and', [status(thm)], ['326'])). 99.91/15.04 tff('328', plain, ![X1 : $i > $o]: (~ '#form178'(X1) | (??(X1))), 99.91/15.04 define([status(thm)])). 99.91/15.04 tff('329', plain, 99.91/15.04 '#form178'( 99.91/15.04 (^[Y0 : $i]: 99.91/15.04 (in(Y0, '#sk710') & 99.91/15.04 (??((^[Y1 : $i]: 99.91/15.04 (in(Y1, '#sk711') & 99.91/15.04 ('#sk712' = 99.91/15.04 setadjoin(setadjoin(Y0, emptyset), 99.91/15.04 setadjoin(setadjoin(Y0, setadjoin(Y1, emptyset)), 99.91/15.04 emptyset)))))))))), 99.91/15.04 inference('renaming', [status(thm)], ['322', '328'])). 99.91/15.04 tff('330', plain, $false, inference('demod', [status(thm)], ['314', '329'])). 99.91/15.04 99.91/15.04 % SZS output end Refutation 99.91/15.04 99.91/15.04 99.91/15.04 % /export/starexec/sandbox/solver/bin/lams/b.sh running for 31s 99.91/15.04 % Terminating... 99.98/15.16 % Runner terminated. 99.98/15.16 % Zipperpin 1.5 exiting 99.98/15.16 EOF