0.11/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.13 % Command : run_portfolio.sh /export/starexec/sandbox/benchmark/theBenchmark.p /export/starexec/sandbox/tmp/tmp.ZFNhrMt1kj 0.14/0.34 % Computer : n008.cluster.edu 0.14/0.34 % Model : x86_64 x86_64 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.34 % Memory : 8042.1875MB 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.34 % CPULimit : 180 0.14/0.34 % DateTime : Thu Aug 29 17:39:38 EDT 2019 0.14/0.34 % CPUTime : 109.58/110.28 % Running portfolio for 180 s 109.58/110.28 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 109.58/110.28 % TempDir : /export/starexec/sandbox/tmp/tmp.ZFNhrMt1kj 109.58/110.28 % Recognized as monomorphic HO. 109.58/110.28 % Running /export/starexec/sandbox/solver/bin/competitive.sh for 18 109.58/110.28 % Running /export/starexec/sandbox/solver/bin/competitive.2.sh for 13 109.58/110.28 % Running /export/starexec/sandbox/solver/bin/competitive.3.sh for 3 109.58/110.28 % Running /export/starexec/sandbox/solver/bin/pragmatic.rudimentary.sh for 28 109.58/110.28 % Running /export/starexec/sandbox/solver/bin/pragmatic.rudimentary.1.sh for 12 109.58/110.28 % Running /export/starexec/sandbox/solver/bin/pragmatic.rudimentary.2.sh for 7 109.58/110.28 % Running /export/starexec/sandbox/solver/bin/pragmatic.shallow.sh for 3 109.58/110.28 % Running /export/starexec/sandbox/solver/bin/pragmatic.shallow.1.sh for 14 109.58/110.28 % Running /export/starexec/sandbox/solver/bin/pragmatic.shallow.2.sh for 12 109.58/110.28 % Running /export/starexec/sandbox/solver/bin/pragmatic.ll.e.sh for 19 109.58/110.28 % Solved by: pragmatic.ll.e.sh 109.58/110.28 % Running : timeout 16 /export/starexec/sandbox/solver/bin/eprover-ho /export/starexec/sandbox/tmp/tmp.ZFNhrMt1kj/e_input5d6dda --cpu-limit=14 --auto-schedule -s -p. 109.58/110.28 % done 468 iterations in 11.460s 109.58/110.28 % hashcons stats for terms: size 4096, num 19824, sum length 39663, buckets: small 3, median 7, big 22 109.58/110.28 % proof state stats: {active 208, passive 6226, simpl 0} 109.58/110.28 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 109.58/110.28 % SZS output start Refutation 109.58/110.28 tff(brelnall2, axiom, brelnall2 <=> 109.58/110.28 (![A,B,R]: 109.58/110.28 (breln(A,B,R) => 109.58/110.28 (![Xphi:($i > $o)]: 109.58/110.28 ((![Xx]: 109.58/110.28 (in(Xx,A) => 109.58/110.28 (![Xy]: 109.58/110.28 (in(Xy,B) => (in(kpair(Xx,Xy),R) => Xphi(kpair(Xx,Xy))))))) => 109.58/110.28 (![Xx]: (in(Xx,R) => Xphi(Xx)))))))). 109.58/110.28 tff('0', plain, 109.58/110.28 brelnall2 = 109.58/110.28 (![X2,X3,X4]: 109.58/110.28 (breln(X2,X3,X4) => 109.58/110.28 (![X5:($i > $o)]: 109.58/110.28 ((![X6]: 109.58/110.28 (in(X6,X2) => 109.58/110.28 (![X7]: 109.58/110.28 (in(X7,X3) => (in(kpair(X6,X7),X4) => X5(kpair(X6,X7))))))) => 109.58/110.28 (![X8]: (in(X8,X4) => X5(X8))))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(brelnall1, axiom, brelnall1 <=> 109.58/110.28 (![A,B,R]: 109.58/110.28 (breln(A,B,R) => 109.58/110.28 (![Xphi:($i > $o)]: 109.58/110.28 ((![Xx]: 109.58/110.28 (in(Xx,A) => 109.58/110.28 (![Xy]: 109.58/110.28 (in(Xy,B) => (in(kpair(Xx,Xy),R) => Xphi(kpair(Xx,Xy))))))) => 109.58/110.28 (![Xx]: (in(Xx,R) => Xphi(Xx)))))))). 109.58/110.28 tff('1', plain, 109.58/110.28 brelnall1 = 109.58/110.28 (![X2,X3,X4]: 109.58/110.28 (breln(X2,X3,X4) => 109.58/110.28 (![X5:($i > $o)]: 109.58/110.28 ((![X6]: 109.58/110.28 (in(X6,X2) => 109.58/110.28 (![X7]: 109.58/110.28 (in(X7,X3) => (in(kpair(X6,X7),X4) => X5(kpair(X6,X7))))))) => 109.58/110.28 (![X8]: (in(X8,X4) => X5(X8))))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(lam2p, axiom, lam2p <=> 109.58/110.28 (![A,B,Xf:($i > $i)]: 109.58/110.28 ((![Xx]: (in(Xx,A) => in(Xf(Xx),B))) => 109.58/110.28 in(lam(A,B,^[Xx]: Xf(Xx)),funcSet(A,B))))). 109.58/110.28 tff('2', plain, 109.58/110.28 lam2p = 109.58/110.28 (![X2,X3,X4:($i > $i)]: 109.58/110.28 ((![X5]: (in(X5,X2) => in(X4(X5),X3))) => 109.58/110.28 in(lam(X2,X3,^[V_1]: X4(V_1)),funcSet(X2,X3)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(lamp, axiom, lamp <=> 109.58/110.28 (![A,B,Xf:($i > $i)]: 109.58/110.28 ((![Xx]: (in(Xx,A) => in(Xf(Xx),B))) => func(A,B,lam(A,B,^[Xx]: Xf(Xx)))))). 109.58/110.28 tff('3', plain, 109.58/110.28 lamp = 109.58/110.28 (![X2,X3,X4:($i > $i)]: 109.58/110.28 ((![X5]: (in(X5,X2) => in(X4(X5),X3))) => 109.58/110.28 func(X2,X3,lam(X2,X3,^[V_1]: X4(V_1))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(lam, axiom, lam() = 109.58/110.28 ^[A,B,Xf:($i > $i)]: dpsetconstr(A,B,^[Xx,Xy]: (Xf(Xx) = Xy))). 109.58/110.28 tff('4', plain, 109.58/110.28 lam = 109.58/110.28 (^[V_1,V_2,V_3:($i > $i)]: 109.58/110.28 dpsetconstr(V_1,V_2,^[V_4,V_5]: (V_3(V_4) = V_5))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(lamProp, axiom, lamProp <=> 109.58/110.28 (![A,B,Xf:($i > $i)]: 109.58/110.28 ((![Xx]: (in(Xx,A) => in(Xf(Xx),B))) => 109.58/110.28 func(A,B,dpsetconstr(A,B,^[Xx,Xy]: (Xf(Xx) = Xy)))))). 109.58/110.28 tff('5', plain, 109.58/110.28 lamProp = 109.58/110.28 (![X2,X3,X4:($i > $i)]: 109.58/110.28 ((![X5]: (in(X5,X2) => in(X4(X5),X3))) => 109.58/110.28 func(X2,X3,dpsetconstr(X2,X3,^[V_1,V_2]: (X4(V_1) = V_2))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(funcinfuncset, axiom, funcinfuncset <=> 109.58/110.28 (![A,B,Xf]: (func(A,B,Xf) => in(Xf,funcSet(A,B))))). 109.58/110.28 tff('6', plain, 109.58/110.28 funcinfuncset = (![X2,X3,X4]: (func(X2,X3,X4) => in(X4,funcSet(X2,X3)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(ap2p, axiom, ap2p <=> 109.58/110.28 (![A,B,Xf]: 109.58/110.28 (in(Xf,funcSet(A,B)) => (![Xx]: (in(Xx,A) => in(ap(A,B,Xf,Xx),B)))))). 109.58/110.28 tff('7', plain, 109.58/110.28 ap2p = 109.58/110.28 (![X2,X3,X4]: 109.58/110.28 (in(X4,funcSet(X2,X3)) => 109.58/110.28 (![X5]: (in(X5,X2) => in(ap(X2,X3,X4,X5),X3))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(infuncsetfunc, axiom, infuncsetfunc <=> 109.58/110.28 (![A,B,Xf]: (in(Xf,funcSet(A,B)) => func(A,B,Xf)))). 109.58/110.28 tff('8', plain, 109.58/110.28 infuncsetfunc = (![X2,X3,X4]: (in(X4,funcSet(X2,X3)) => func(X2,X3,X4))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(app, axiom, app <=> 109.58/110.28 (![A,B,Xf]: (func(A,B,Xf) => (![Xx]: (in(Xx,A) => in(ap(A,B,Xf,Xx),B)))))). 109.58/110.28 tff('9', plain, 109.58/110.28 app = 109.58/110.28 (![X2,X3,X4]: 109.58/110.28 (func(X2,X3,X4) => (![X5]: (in(X5,X2) => in(ap(X2,X3,X4,X5),X3))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(ap, axiom, ap() = 109.58/110.28 ^[A,B,Xf,Xx]: setunion(dsetconstr(B,^[Xy]: in(kpair(Xx,Xy),Xf)))). 109.58/110.28 tff('10', plain, 109.58/110.28 ap = 109.58/110.28 (^[V_1,V_2,V_3,V_4]: 109.58/110.28 setunion(dsetconstr(V_2,^[V_5]: in(kpair(V_4,V_5),V_3)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(apProp, axiom, apProp <=> 109.58/110.28 (![A,B,Xf]: 109.58/110.28 (func(A,B,Xf) => 109.58/110.28 (![Xx]: 109.58/110.28 (in(Xx,A) => 109.58/110.28 in(setunion(dsetconstr(B,^[Xy]: in(kpair(Xx,Xy),Xf))),B)))))). 109.58/110.28 tff('11', plain, 109.58/110.28 apProp = 109.58/110.28 (![X2,X3,X4]: 109.58/110.28 (func(X2,X3,X4) => 109.58/110.28 (![X5]: 109.58/110.28 (in(X5,X2) => 109.58/110.28 in(setunion(dsetconstr(X3,^[V_1]: in(kpair(X5,V_1),X4))),X3))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(funcImageSingleton, axiom, funcImageSingleton <=> 109.58/110.28 (![A,B,Xf]: 109.58/110.28 (func(A,B,Xf) => 109.58/110.28 (![Xx]: 109.58/110.28 (in(Xx,A) => singleton(dsetconstr(B,^[Xy]: in(kpair(Xx,Xy),Xf)))))))). 109.58/110.28 tff('12', plain, 109.58/110.28 funcImageSingleton = 109.58/110.28 (![X2,X3,X4]: 109.58/110.28 (func(X2,X3,X4) => 109.58/110.28 (![X5]: 109.58/110.28 (in(X5,X2) => 109.58/110.28 singleton(dsetconstr(X3,^[V_1]: in(kpair(X5,V_1),X4))))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(func, axiom, func() = 109.58/110.28 ^[A,B,R]: 109.58/110.28 ((![Xx]: (in(Xx,A) => ex1(B,^[Xy]: in(kpair(Xx,Xy),R)))) & breln(A,B,R))). 109.58/110.28 tff('13', plain, 109.58/110.28 func = 109.58/110.28 (^[V_1,V_2,V_3]: 109.58/110.28 ((![X2]: (in(X2,V_1) => ex1(V_2,^[V_4]: in(kpair(X2,V_4),V_3)))) & 109.58/110.28 breln(V_1,V_2,V_3))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(dpsetconstrER, axiom, dpsetconstrER <=> 109.58/110.28 (![A,B,Xphi:(($i * $i) > $o),Xx,Xy]: 109.58/110.28 (in(kpair(Xx,Xy),dpsetconstr(A,B,^[Xz,Xu]: Xphi(Xz,Xu))) => Xphi(Xx,Xy)))). 109.58/110.28 tff('14', plain, 109.58/110.28 dpsetconstrER = 109.58/110.28 (![X2,X3,X4:(($i * $i) > $o),X5,X6]: 109.58/110.28 (in(kpair(X5,X6),dpsetconstr(X2,X3,^[V_1,V_2]: X4(V_1,V_2))) => 109.58/110.28 X4(X5,X6))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(dpsetconstrEL2, axiom, dpsetconstrEL2 <=> 109.58/110.28 (![A,B,Xphi:(($i * $i) > $o),Xx,Xy]: 109.58/110.28 (in(kpair(Xx,Xy),dpsetconstr(A,B,^[Xz,Xu]: Xphi(Xz,Xu))) => in(Xy,B)))). 109.58/110.28 tff('15', plain, 109.58/110.28 dpsetconstrEL2 = 109.58/110.28 (![X2,X3,X4:(($i * $i) > $o),X5,X6]: 109.58/110.28 (in(kpair(X5,X6),dpsetconstr(X2,X3,^[V_1,V_2]: X4(V_1,V_2))) => 109.58/110.28 in(X6,X3))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(dpsetconstrEL1, axiom, dpsetconstrEL1 <=> 109.58/110.28 (![A,B,Xphi:(($i * $i) > $o),Xx,Xy]: 109.58/110.28 (in(kpair(Xx,Xy),dpsetconstr(A,B,^[Xz,Xu]: Xphi(Xz,Xu))) => in(Xx,A)))). 109.58/110.28 tff('16', plain, 109.58/110.28 dpsetconstrEL1 = 109.58/110.28 (![X2,X3,X4:(($i * $i) > $o),X5,X6]: 109.58/110.28 (in(kpair(X5,X6),dpsetconstr(X2,X3,^[V_1,V_2]: X4(V_1,V_2))) => 109.58/110.28 in(X5,X2))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(dpsetconstrERa, axiom, dpsetconstrERa <=> 109.58/110.28 (![A,B,Xphi:(($i * $i) > $o),Xx]: 109.58/110.28 (in(Xx,A) => 109.58/110.28 (![Xy]: 109.58/110.28 (in(Xy,B) => 109.58/110.28 (in(kpair(Xx,Xy),dpsetconstr(A,B,^[Xz,Xu]: Xphi(Xz,Xu))) => 109.58/110.28 Xphi(Xx,Xy))))))). 109.58/110.28 tff('17', plain, 109.58/110.28 dpsetconstrERa = 109.58/110.28 (![X2,X3,X4:(($i * $i) > $o),X5]: 109.58/110.28 (in(X5,X2) => 109.58/110.28 (![X6]: 109.58/110.28 (in(X6,X3) => 109.58/110.28 (in(kpair(X5,X6),dpsetconstr(X2,X3,^[V_1,V_2]: X4(V_1,V_2))) => 109.58/110.28 X4(X5,X6)))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(setOfPairsIsBReln, axiom, setOfPairsIsBReln <=> 109.58/110.28 (![A,B,Xphi:(($i * $i) > $o)]: 109.58/110.28 breln(A,B,dpsetconstr(A,B,^[Xx,Xy]: Xphi(Xx,Xy))))). 109.58/110.28 tff('18', plain, 109.58/110.28 setOfPairsIsBReln = 109.58/110.28 (![X2,X3,X4:(($i * $i) > $o)]: 109.58/110.28 breln(X2,X3,dpsetconstr(X2,X3,^[V_1,V_2]: X4(V_1,V_2)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(dpsetconstrSub, axiom, dpsetconstrSub <=> 109.58/110.28 (![A,B,Xphi:(($i * $i) > $o)]: 109.58/110.28 subset(dpsetconstr(A,B,^[Xx,Xy]: Xphi(Xx,Xy)),cartprod(A,B)))). 109.58/110.28 tff('19', plain, 109.58/110.28 dpsetconstrSub = 109.58/110.28 (![X2,X3,X4:(($i * $i) > $o)]: 109.58/110.28 subset(dpsetconstr(X2,X3,^[V_1,V_2]: X4(V_1,V_2)),cartprod(X2,X3))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(dpsetconstrI, axiom, dpsetconstrI <=> 109.58/110.28 (![A,B,Xphi:(($i * $i) > $o),Xx]: 109.58/110.28 (in(Xx,A) => 109.58/110.28 (![Xy]: 109.58/110.28 (in(Xy,B) => 109.58/110.28 (Xphi(Xx,Xy) => 109.58/110.28 in(kpair(Xx,Xy),dpsetconstr(A,B,^[Xz,Xu]: Xphi(Xz,Xu))))))))). 109.58/110.28 tff('20', plain, 109.58/110.28 dpsetconstrI = 109.58/110.28 (![X2,X3,X4:(($i * $i) > $o),X5]: 109.58/110.28 (in(X5,X2) => 109.58/110.28 (![X6]: 109.58/110.28 (in(X6,X3) => 109.58/110.28 (X4(X5,X6) => 109.58/110.28 in(kpair(X5,X6),dpsetconstr(X2,X3,^[V_1,V_2]: X4(V_1,V_2)))))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(breln, axiom, breln() = ^[A,B,C]: subset(C,cartprod(A,B))). 109.58/110.28 tff('21', plain, breln = (^[V_1,V_2,V_3]: subset(V_3,cartprod(V_1,V_2))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(cartprodpairsurjEq, axiom, cartprodpairsurjEq <=> 109.58/110.28 (![A,B,Xu]: (in(Xu,cartprod(A,B)) => (kpair(kfst(Xu),ksnd(Xu)) = Xu)))). 109.58/110.28 tff('22', plain, 109.58/110.28 cartprodpairsurjEq = 109.58/110.28 (![X2,X3,X4]: (in(X4,cartprod(X2,X3)) => (kpair(kfst(X4),ksnd(X4)) = X4))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(cartprodsndpairEq, axiom, cartprodsndpairEq <=> 109.58/110.28 (![A,B,Xx]: (in(Xx,A) => (![Xy]: (in(Xy,B) => (ksnd(kpair(Xx,Xy)) = Xy)))))). 109.58/110.28 tff('23', plain, 109.58/110.28 cartprodsndpairEq = 109.58/110.28 (![X2,X3,X4]: 109.58/110.28 (in(X4,X2) => (![X5]: (in(X5,X3) => (ksnd(kpair(X4,X5)) = X5))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(cartprodfstpairEq, axiom, cartprodfstpairEq <=> 109.58/110.28 (![A,B,Xx]: (in(Xx,A) => (![Xy]: (in(Xy,B) => (kfst(kpair(Xx,Xy)) = Xx)))))). 109.58/110.28 tff('24', plain, 109.58/110.28 cartprodfstpairEq = 109.58/110.28 (![X2,X3,X4]: 109.58/110.28 (in(X4,X2) => (![X5]: (in(X5,X3) => (kfst(kpair(X4,X5)) = X4))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(cartprodmempaircEq, axiom, cartprodmempaircEq <=> 109.58/110.28 (![A,B,Xx]: 109.58/110.28 (in(Xx,A) => (![Xy]: (in(Xy,B) => (kpair(Xx,Xy) = kpair(Xx,Xy))))))). 109.58/110.28 tff('25', plain, 109.58/110.28 cartprodmempaircEq = 109.58/110.28 (![X2,X3,X4]: 109.58/110.28 (in(X4,X2) => (![X5]: (in(X5,X3) => (kpair(X4,X5) = kpair(X4,X5)))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(cartprodpairmemER, axiom, cartprodpairmemER <=> 109.58/110.28 (![A,B,Xx,Xy]: (in(kpair(Xx,Xy),cartprod(A,B)) => in(Xy,B)))). 109.58/110.28 tff('26', plain, 109.58/110.28 cartprodpairmemER = 109.58/110.28 (![X2,X3,X4,X5]: (in(kpair(X4,X5),cartprod(X2,X3)) => in(X5,X3))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(cartprodpairmemEL, axiom, cartprodpairmemEL <=> 109.58/110.28 (![A,B,Xx,Xy]: (in(kpair(Xx,Xy),cartprod(A,B)) => in(Xx,A)))). 109.58/110.28 tff('27', plain, 109.58/110.28 cartprodpairmemEL = 109.58/110.28 (![X2,X3,X4,X5]: (in(kpair(X4,X5),cartprod(X2,X3)) => in(X4,X2))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(cartprodsndin, axiom, cartprodsndin <=> 109.58/110.28 (![A,B,Xu]: (in(Xu,cartprod(A,B)) => in(ksnd(Xu),B)))). 109.58/110.28 tff('28', plain, 109.58/110.28 cartprodsndin = 109.58/110.28 (![X2,X3,X4]: (in(X4,cartprod(X2,X3)) => in(ksnd(X4),X3))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(kpairsurjEq, axiom, kpairsurjEq <=> 109.58/110.28 (![Xu]: (iskpair(Xu) => (kpair(kfst(Xu),ksnd(Xu)) = Xu)))). 109.58/110.28 tff('29', plain, 109.58/110.28 kpairsurjEq = (![X2]: (iskpair(X2) => (kpair(kfst(X2),ksnd(X2)) = X2))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(ksndpairEq, axiom, ksndpairEq <=> (![Xx,Xy]: (ksnd(kpair(Xx,Xy)) = Xy))). 109.58/110.28 tff('30', plain, ksndpairEq = (![X2,X3]: (ksnd(kpair(X2,X3)) = X3)), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(ksndsingleton, axiom, ksndsingleton <=> 109.58/110.28 (![Xu]: 109.58/110.28 (iskpair(Xu) => 109.58/110.28 singleton(dsetconstr(setunion(Xu),^[Xx]: (Xu = kpair(kfst(Xu),Xx))))))). 109.58/110.28 tff('31', plain, 109.58/110.28 ksndsingleton = 109.58/110.28 (![X2]: 109.58/110.28 (iskpair(X2) => 109.58/110.28 singleton(dsetconstr(setunion(X2),^[V_1]: (X2 = kpair(kfst(X2),V_1)))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(setukpairinjR, axiom, setukpairinjR <=> 109.58/110.28 (![Xx,Xy,Xz,Xu]: ((kpair(Xx,Xy) = kpair(Xz,Xu)) => (Xy = Xu)))). 109.58/110.28 tff('32', plain, 109.58/110.28 setukpairinjR = 109.58/110.28 (![X2,X3,X4,X5]: ((kpair(X2,X3) = kpair(X4,X5)) => (X3 = X5))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(setukpairinjR2, axiom, setukpairinjR2 <=> 109.58/110.28 (![Xx,Xy,Xz,Xu]: 109.58/110.28 ((setadjoin(setadjoin(Xx,emptyset), 109.58/110.28 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)),emptyset)) = 109.58/110.28 setadjoin(setadjoin(Xz,emptyset), 109.58/110.28 setadjoin(setadjoin(Xz,setadjoin(Xu,emptyset)),emptyset))) => 109.58/110.28 (Xy = Xu)))). 109.58/110.28 tff('33', plain, 109.58/110.28 setukpairinjR2 = 109.58/110.28 (![X2,X3,X4,X5]: 109.58/110.28 ((setadjoin(setadjoin(X2,emptyset), 109.58/110.28 setadjoin(setadjoin(X2,setadjoin(X3,emptyset)),emptyset)) = 109.58/110.28 setadjoin(setadjoin(X4,emptyset), 109.58/110.28 setadjoin(setadjoin(X4,setadjoin(X5,emptyset)),emptyset))) => 109.58/110.28 (X3 = X5))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(upairequniteq, axiom, upairequniteq <=> 109.58/110.28 (![Xx,Xy,Xz]: 109.58/110.28 ((setadjoin(Xx,setadjoin(Xy,emptyset)) = setadjoin(Xz,emptyset)) => 109.58/110.28 (Xx = Xy)))). 109.58/110.28 tff('34', plain, 109.58/110.28 upairequniteq = 109.58/110.28 (![X2,X3,X4]: 109.58/110.28 ((setadjoin(X2,setadjoin(X3,emptyset)) = setadjoin(X4,emptyset)) => 109.58/110.28 (X2 = X3))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(setukpairinjR1, axiom, setukpairinjR1 <=> 109.58/110.28 (![Xx,Xy,Xz,Xu]: 109.58/110.28 ((setadjoin(setadjoin(Xx,emptyset), 109.58/110.28 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)),emptyset)) = 109.58/110.28 setadjoin(setadjoin(Xz,emptyset), 109.58/110.28 setadjoin(setadjoin(Xz,setadjoin(Xu,emptyset)),emptyset))) => 109.58/110.28 ((Xz = Xu) => (Xy = Xu))))). 109.58/110.28 tff('35', plain, 109.58/110.28 setukpairinjR1 = 109.58/110.28 (![X2,X3,X4,X5]: 109.58/110.28 ((setadjoin(setadjoin(X2,emptyset), 109.58/110.28 setadjoin(setadjoin(X2,setadjoin(X3,emptyset)),emptyset)) = 109.58/110.28 setadjoin(setadjoin(X4,emptyset), 109.58/110.28 setadjoin(setadjoin(X4,setadjoin(X5,emptyset)),emptyset))) => 109.58/110.28 ((X4 = X5) => (X3 = X5)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(setukpairinjR12, axiom, setukpairinjR12 <=> 109.58/110.28 (![Xx,Xy]: 109.58/110.28 ((Xx = Xy) => 109.58/110.28 (setadjoin(setadjoin(Xx,emptyset), 109.58/110.28 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)),emptyset)) = 109.58/110.28 setadjoin(setadjoin(Xx,emptyset),emptyset))))). 109.58/110.28 tff('36', plain, 109.58/110.28 setukpairinjR12 = 109.58/110.28 (![X2,X3]: 109.58/110.28 ((X2 = X3) => 109.58/110.28 (setadjoin(setadjoin(X2,emptyset), 109.58/110.28 setadjoin(setadjoin(X2,setadjoin(X3,emptyset)),emptyset)) = 109.58/110.28 setadjoin(setadjoin(X2,emptyset),emptyset)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(setukpairinjR11, axiom, setukpairinjR11 <=> 109.58/110.28 (![Xx,Xy]: 109.58/110.28 ((Xx = Xy) => 109.58/110.28 (setadjoin(Xx,setadjoin(Xy,emptyset)) = setadjoin(Xx,emptyset))))). 109.58/110.28 tff('37', plain, 109.58/110.28 setukpairinjR11 = 109.58/110.28 (![X2,X3]: 109.58/110.28 ((X2 = X3) => 109.58/110.28 (setadjoin(X2,setadjoin(X3,emptyset)) = setadjoin(X2,emptyset)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(setukpairinjL, axiom, setukpairinjL <=> 109.58/110.28 (![Xx,Xy,Xz,Xu]: ((kpair(Xx,Xy) = kpair(Xz,Xu)) => (Xx = Xz)))). 109.58/110.28 tff('38', plain, 109.58/110.28 setukpairinjL = 109.58/110.28 (![X2,X3,X4,X5]: ((kpair(X2,X3) = kpair(X4,X5)) => (X2 = X4))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(setukpairinjL2, axiom, setukpairinjL2 <=> 109.58/110.28 (![Xx,Xy,Xz,Xu]: 109.58/110.28 ((setadjoin(setadjoin(Xx,emptyset), 109.58/110.28 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)),emptyset)) = 109.58/110.28 setadjoin(setadjoin(Xz,emptyset), 109.58/110.28 setadjoin(setadjoin(Xz,setadjoin(Xu,emptyset)),emptyset))) => 109.58/110.28 (Xx = Xz)))). 109.58/110.28 tff('39', plain, 109.58/110.28 setukpairinjL2 = 109.58/110.28 (![X2,X3,X4,X5]: 109.58/110.28 ((setadjoin(setadjoin(X2,emptyset), 109.58/110.28 setadjoin(setadjoin(X2,setadjoin(X3,emptyset)),emptyset)) = 109.58/110.28 setadjoin(setadjoin(X4,emptyset), 109.58/110.28 setadjoin(setadjoin(X4,setadjoin(X5,emptyset)),emptyset))) => 109.58/110.28 (X2 = X4))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(cartprodfstin, axiom, cartprodfstin <=> 109.58/110.28 (![A,B,Xu]: (in(Xu,cartprod(A,B)) => in(kfst(Xu),A)))). 109.58/110.28 tff('40', plain, 109.58/110.28 cartprodfstin = 109.58/110.28 (![X2,X3,X4]: (in(X4,cartprod(X2,X3)) => in(kfst(X4),X2))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(kfstpairEq, axiom, kfstpairEq <=> (![Xx,Xy]: (kfst(kpair(Xx,Xy)) = Xx))). 109.58/110.28 tff('41', plain, kfstpairEq = (![X2,X3]: (kfst(kpair(X2,X3)) = X2)), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(theprop, axiom, theprop <=> (![X]: (singleton(X) => in(setunion(X),X)))). 109.58/110.28 tff('42', plain, theprop = (![X2]: (singleton(X2) => in(setunion(X2),X2))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(kfstsingleton, axiom, kfstsingleton <=> 109.58/110.28 (![Xu]: 109.58/110.28 (iskpair(Xu) => 109.58/110.28 singleton(dsetconstr(setunion(Xu),^[Xx]: in(setadjoin(Xx,emptyset),Xu)))))). 109.58/110.28 tff('43', plain, 109.58/110.28 kfstsingleton = 109.58/110.28 (![X2]: 109.58/110.28 (iskpair(X2) => 109.58/110.28 singleton(dsetconstr(setunion(X2), 109.58/110.28 ^[V_1]: in(setadjoin(V_1,emptyset),X2))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(setukpairinjL1, axiom, setukpairinjL1 <=> 109.58/110.28 (![Xx,Xy,Xz]: 109.58/110.28 (in(setadjoin(Xz,emptyset), 109.58/110.28 setadjoin(setadjoin(Xx,emptyset), 109.58/110.28 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)),emptyset))) => 109.58/110.28 (Xx = Xz)))). 109.58/110.28 tff('44', plain, 109.58/110.28 setukpairinjL1 = 109.58/110.28 (![X2,X3,X4]: 109.58/110.28 (in(setadjoin(X4,emptyset), 109.58/110.28 setadjoin(setadjoin(X2,emptyset), 109.58/110.28 setadjoin(setadjoin(X2,setadjoin(X3,emptyset)),emptyset))) => 109.58/110.28 (X2 = X4))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(singletonsuniq, axiom, singletonsuniq <=> 109.58/110.28 (![Xx,Xy]: ((setadjoin(Xx,emptyset) = setadjoin(Xy,emptyset)) => (Xx = Xy)))). 109.58/110.28 tff('45', plain, 109.58/110.28 singletonsuniq = 109.58/110.28 (![X2,X3]: 109.58/110.28 ((setadjoin(X2,emptyset) = setadjoin(X3,emptyset)) => (X2 = X3))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(ex1I2, axiom, ex1I2 <=> 109.58/110.28 (![A,Xphi:($i > $o)]: 109.58/110.28 ((![Xx]: 109.58/110.28 (in(Xx,A) => 109.58/110.28 (![Xy]: (in(Xy,A) => (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))) => 109.58/110.28 ((?[Xx]: (Xphi(Xx) & in(Xx,A))) => ex1(A,^[Xx]: Xphi(Xx)))))). 109.58/110.28 tff('46', plain, 109.58/110.28 ex1I2 = 109.58/110.28 (![X2,X3:($i > $o)]: 109.58/110.28 ((![X4]: 109.58/110.28 (in(X4,X2) => 109.58/110.28 (![X5]: (in(X5,X2) => (X3(X4) => (X3(X5) => (X4 = X5))))))) => 109.58/110.28 ((?[X6]: (X3(X6) & in(X6,X2))) => ex1(X2,^[V_1]: X3(V_1))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(ex1I, axiom, ex1I <=> 109.58/110.28 (![A,Xphi:($i > $o),Xx]: 109.58/110.28 (in(Xx,A) => 109.58/110.28 (Xphi(Xx) => 109.58/110.28 ((![Xy]: (in(Xy,A) => (Xphi(Xy) => (Xy = Xx)))) => 109.58/110.28 ex1(A,^[Xy]: Xphi(Xy))))))). 109.58/110.28 tff('47', plain, 109.58/110.28 ex1I = 109.58/110.28 (![X2,X3:($i > $o),X4]: 109.58/110.28 (in(X4,X2) => 109.58/110.28 (X3(X4) => 109.58/110.28 ((![X5]: (in(X5,X2) => (X3(X5) => (X5 = X4)))) => 109.58/110.28 ex1(X2,^[V_1]: X3(V_1)))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(ex1E1, axiom, ex1E1 <=> 109.58/110.28 (![A,Xphi:($i > $o)]: 109.58/110.28 (ex1(A,^[Xx]: Xphi(Xx)) => (?[Xx]: (Xphi(Xx) & in(Xx,A)))))). 109.58/110.28 tff('48', plain, 109.58/110.28 ex1E1 = 109.58/110.28 (![X2,X3:($i > $o)]: 109.58/110.28 (ex1(X2,^[V_1]: X3(V_1)) => (?[X4]: (X3(X4) & in(X4,X2))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(ex1, axiom, ex1() = 109.58/110.28 ^[A,Xphi:($i > $o)]: singleton(dsetconstr(A,^[Xx]: Xphi(Xx)))). 109.58/110.28 tff('49', plain, 109.58/110.28 ex1 = (^[V_1,V_2:($i > $o)]: singleton(dsetconstr(V_1,^[V_3]: V_2(V_3)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(singletonprop, axiom, singletonprop <=> 109.58/110.28 (![A,Xphi:($i > $o)]: 109.58/110.28 ((![Xx]: 109.58/110.28 (in(Xx,A) => 109.58/110.28 (![Xy]: (in(Xy,A) => (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))) => 109.58/110.28 ((?[Xx]: (Xphi(Xx) & in(Xx,A))) => 109.58/110.28 singleton(dsetconstr(A,^[Xx]: Xphi(Xx))))))). 109.58/110.28 tff('50', plain, 109.58/110.28 singletonprop = 109.58/110.28 (![X2,X3:($i > $o)]: 109.58/110.28 ((![X4]: 109.58/110.28 (in(X4,X2) => 109.58/110.28 (![X5]: (in(X5,X2) => (X3(X4) => (X3(X5) => (X4 = X5))))))) => 109.58/110.28 ((?[X6]: (X3(X6) & in(X6,X2))) => 109.58/110.28 singleton(dsetconstr(X2,^[V_1]: X3(V_1)))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(singleton, axiom, singleton() = 109.58/110.28 ^[A]: (?[Xx]: ((A = setadjoin(Xx,emptyset)) & in(Xx,A)))). 109.58/110.28 tff('51', plain, 109.58/110.28 singleton = 109.58/110.28 (^[V_1]: (?[X2]: ((V_1 = setadjoin(X2,emptyset)) & in(X2,V_1)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(setunionsingleton, axiom, setunionsingleton <=> 109.58/110.28 (![Xx]: (setunion(setadjoin(Xx,emptyset)) = Xx))). 109.58/110.28 tff('52', plain, 109.58/110.28 setunionsingleton = (![X2]: (setunion(setadjoin(X2,emptyset)) = X2)), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(setunionsingleton2, axiom, setunionsingleton2 <=> 109.58/110.28 (![A]: subset(A,setunion(setadjoin(A,emptyset))))). 109.58/110.28 tff('53', plain, 109.58/110.28 setunionsingleton2 = (![X2]: subset(X2,setunion(setadjoin(X2,emptyset)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(setunionsingleton1, axiom, setunionsingleton1 <=> 109.58/110.28 (![A]: subset(setunion(setadjoin(A,emptyset)),A))). 109.58/110.28 tff('54', plain, 109.58/110.28 setunionsingleton1 = (![X2]: subset(setunion(setadjoin(X2,emptyset)),X2)), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(setunionE2, axiom, setunionE2 <=> 109.58/110.28 (![A,Xx]: (in(Xx,setunion(A)) => (?[X]: (in(Xx,X) & in(X,A)))))). 109.58/110.28 tff('55', plain, 109.58/110.28 setunionE2 = 109.58/110.28 (![X2,X3]: (in(X3,setunion(X2)) => (?[X4]: (in(X3,X4) & in(X4,X2))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(cartprodmempair, axiom, cartprodmempair <=> 109.58/110.28 (![A,B,Xu]: (in(Xu,cartprod(A,B)) => iskpair(Xu)))). 109.58/110.28 tff('56', plain, 109.58/110.28 cartprodmempair = (![X2,X3,X4]: (in(X4,cartprod(X2,X3)) => iskpair(X4))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(cartprodmempair1, axiom, cartprodmempair1 <=> 109.58/110.28 (![A,B,Xu]: 109.58/110.28 (in(Xu,cartprod(A,B)) => 109.58/110.28 (?[Xx]: ((?[Xy]: ((Xu = kpair(Xx,Xy)) & in(Xy,B))) & in(Xx,A)))))). 109.58/110.28 tff('57', plain, 109.58/110.28 cartprodmempair1 = 109.58/110.28 (![X2,X3,X4]: 109.58/110.28 (in(X4,cartprod(X2,X3)) => 109.58/110.28 (?[X5]: ((?[X6]: ((X4 = kpair(X5,X6)) & in(X6,X3))) & in(X5,X2))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(cartprodpairin, axiom, cartprodpairin <=> 109.58/110.28 (![A,B,Xx]: 109.58/110.28 (in(Xx,A) => (![Xy]: (in(Xy,B) => in(kpair(Xx,Xy),cartprod(A,B))))))). 109.58/110.28 tff('58', plain, 109.58/110.28 cartprodpairin = 109.58/110.28 (![X2,X3,X4]: 109.58/110.28 (in(X4,X2) => (![X5]: (in(X5,X3) => in(kpair(X4,X5),cartprod(X2,X3)))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(ubforcartprodlem3, axiom, ubforcartprodlem3 <=> 109.58/110.28 (![A,B,Xx]: 109.58/110.28 (in(Xx,A) => 109.58/110.28 (![Xy]: 109.58/110.28 (in(Xy,B) => in(kpair(Xx,Xy),powerset(powerset(binunion(A,B))))))))). 109.58/110.28 tff('59', plain, 109.58/110.28 ubforcartprodlem3 = 109.58/110.28 (![X2,X3,X4]: 109.58/110.28 (in(X4,X2) => 109.58/110.28 (![X5]: 109.58/110.28 (in(X5,X3) => in(kpair(X4,X5),powerset(powerset(binunion(X2,X3)))))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(ubforcartprodlem2, axiom, ubforcartprodlem2 <=> 109.58/110.28 (![A,B,Xx]: 109.58/110.28 (in(Xx,A) => 109.58/110.28 (![Xy]: 109.58/110.28 (in(Xy,B) => 109.58/110.28 in(setadjoin(setadjoin(Xx,emptyset), 109.58/110.28 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 109.58/110.28 emptyset)), 109.58/110.28 powerset(powerset(binunion(A,B))))))))). 109.58/110.28 tff('60', plain, 109.58/110.28 ubforcartprodlem2 = 109.58/110.28 (![X2,X3,X4]: 109.58/110.28 (in(X4,X2) => 109.58/110.28 (![X5]: 109.58/110.28 (in(X5,X3) => 109.58/110.28 in(setadjoin(setadjoin(X4,emptyset), 109.58/110.28 setadjoin(setadjoin(X4,setadjoin(X5,emptyset)), 109.58/110.28 emptyset)), 109.58/110.28 powerset(powerset(binunion(X2,X3)))))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(ubforcartprodlem1, axiom, ubforcartprodlem1 <=> 109.58/110.28 (![A,B,Xx]: 109.58/110.28 (in(Xx,A) => 109.58/110.28 (![Xy]: 109.58/110.28 (in(Xy,B) => 109.58/110.28 subset(setadjoin(setadjoin(Xx,emptyset), 109.58/110.28 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 109.58/110.28 emptyset)), 109.58/110.28 powerset(binunion(A,B)))))))). 109.58/110.28 tff('61', plain, 109.58/110.28 ubforcartprodlem1 = 109.58/110.28 (![X2,X3,X4]: 109.58/110.28 (in(X4,X2) => 109.58/110.28 (![X5]: 109.58/110.28 (in(X5,X3) => 109.58/110.28 subset(setadjoin(setadjoin(X4,emptyset), 109.58/110.28 setadjoin(setadjoin(X4,setadjoin(X5,emptyset)), 109.58/110.28 emptyset)), 109.58/110.28 powerset(binunion(X2,X3))))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(upairinpowunion, axiom, upairinpowunion <=> 109.58/110.28 (![A,B,Xx]: 109.58/110.28 (in(Xx,A) => 109.58/110.28 (![Xy]: 109.58/110.28 (in(Xy,B) => 109.58/110.28 in(setadjoin(Xx,setadjoin(Xy,emptyset)),powerset(binunion(A,B)))))))). 109.58/110.28 tff('62', plain, 109.58/110.28 upairinpowunion = 109.58/110.28 (![X2,X3,X4]: 109.58/110.28 (in(X4,X2) => 109.58/110.28 (![X5]: 109.58/110.28 (in(X5,X3) => 109.58/110.28 in(setadjoin(X4,setadjoin(X5,emptyset)),powerset(binunion(X2,X3))))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(upairsubunion, axiom, upairsubunion <=> 109.58/110.28 (![A,B,Xx]: 109.58/110.28 (in(Xx,A) => 109.58/110.28 (![Xy]: 109.58/110.28 (in(Xy,B) => 109.58/110.28 subset(setadjoin(Xx,setadjoin(Xy,emptyset)),binunion(A,B))))))). 109.58/110.28 tff('63', plain, 109.58/110.28 upairsubunion = 109.58/110.28 (![X2,X3,X4]: 109.58/110.28 (in(X4,X2) => 109.58/110.28 (![X5]: 109.58/110.28 (in(X5,X3) => 109.58/110.28 subset(setadjoin(X4,setadjoin(X5,emptyset)),binunion(X2,X3)))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(upairset2E, axiom, upairset2E <=> 109.58/110.28 (![Xx,Xy,Xz]: 109.58/110.28 (in(Xz,setadjoin(Xx,setadjoin(Xy,emptyset))) => ((Xz = Xy) | (Xz = Xx))))). 109.58/110.28 tff('64', plain, 109.58/110.28 upairset2E = 109.58/110.28 (![X2,X3,X4]: 109.58/110.28 (in(X4,setadjoin(X2,setadjoin(X3,emptyset))) => 109.58/110.28 ((X4 = X3) | (X4 = X2)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(singletoninpowunion, axiom, singletoninpowunion <=> 109.58/110.28 (![A,B,Xx]: 109.58/110.28 (in(Xx,A) => in(setadjoin(Xx,emptyset),powerset(binunion(A,B)))))). 109.58/110.28 tff('65', plain, 109.58/110.28 singletoninpowunion = 109.58/110.28 (![X2,X3,X4]: 109.58/110.28 (in(X4,X2) => in(setadjoin(X4,emptyset),powerset(binunion(X2,X3))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(singletoninpowerset, axiom, singletoninpowerset <=> 109.58/110.28 (![A,Xx]: (in(Xx,A) => in(setadjoin(Xx,emptyset),powerset(A))))). 109.58/110.28 tff('66', plain, 109.58/110.28 singletoninpowerset = 109.58/110.28 (![X2,X3]: (in(X3,X2) => in(setadjoin(X3,emptyset),powerset(X2)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(singletonsubset, axiom, singletonsubset <=> 109.58/110.28 (![A,Xx]: (in(Xx,A) => subset(setadjoin(Xx,emptyset),A)))). 109.58/110.28 tff('67', plain, 109.58/110.28 singletonsubset = 109.58/110.28 (![X2,X3]: (in(X3,X2) => subset(setadjoin(X3,emptyset),X2))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(kpairp, axiom, kpairp <=> (![Xx,Xy]: iskpair(kpair(Xx,Xy)))). 109.58/110.28 tff('68', plain, kpairp = (![X2,X3]: iskpair(kpair(X2,X3))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(kpairiskpair, axiom, kpairiskpair <=> 109.58/110.28 (![Xx,Xy]: 109.58/110.28 iskpair(setadjoin(setadjoin(Xx,emptyset), 109.58/110.28 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 109.58/110.28 emptyset))))). 109.58/110.28 tff('69', plain, 109.58/110.28 kpairiskpair = 109.58/110.28 (![X2,X3]: 109.58/110.28 iskpair(setadjoin(setadjoin(X2,emptyset), 109.58/110.28 setadjoin(setadjoin(X2,setadjoin(X3,emptyset)), 109.58/110.28 emptyset)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(setukpairIR, axiom, setukpairIR <=> 109.58/110.28 (![Xx,Xy]: 109.58/110.28 in(Xy, 109.58/110.28 setunion(setadjoin(setadjoin(Xx,emptyset), 109.58/110.28 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 109.58/110.28 emptyset)))))). 109.58/110.28 tff('70', plain, 109.58/110.28 setukpairIR = 109.58/110.28 (![X2,X3]: 109.58/110.28 in(X3, 109.58/110.28 setunion(setadjoin(setadjoin(X2,emptyset), 109.58/110.28 setadjoin(setadjoin(X2,setadjoin(X3,emptyset)), 109.58/110.28 emptyset))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(setukpairIL, axiom, setukpairIL <=> 109.58/110.28 (![Xx,Xy]: 109.58/110.28 in(Xx, 109.58/110.28 setunion(setadjoin(setadjoin(Xx,emptyset), 109.58/110.28 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 109.58/110.28 emptyset)))))). 109.58/110.28 tff('71', plain, 109.58/110.28 setukpairIL = 109.58/110.28 (![X2,X3]: 109.58/110.28 in(X2, 109.58/110.28 setunion(setadjoin(setadjoin(X2,emptyset), 109.58/110.28 setadjoin(setadjoin(X2,setadjoin(X3,emptyset)), 109.58/110.28 emptyset))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(secondinupair, axiom, secondinupair <=> 109.58/110.28 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 109.58/110.28 tff('72', plain, 109.58/110.28 secondinupair = (![X2,X3]: in(X3,setadjoin(X2,setadjoin(X3,emptyset)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(symdiffIneg2, axiom, symdiffIneg2 <=> 109.58/110.28 (![A,B,Xx]: ((~in(Xx,A)) => ((~in(Xx,B)) => (~in(Xx,symdiff(A,B))))))). 109.58/110.28 tff('73', plain, 109.58/110.28 symdiffIneg2 = 109.58/110.28 (![X2,X3,X4]: 109.58/110.28 ((~in(X4,X2)) => ((~in(X4,X3)) => (~in(X4,symdiff(X2,X3)))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(symdiffIneg1, axiom, symdiffIneg1 <=> 109.58/110.28 (![A,B,Xx]: (in(Xx,A) => (in(Xx,B) => (~in(Xx,symdiff(A,B))))))). 109.58/110.28 tff('74', plain, 109.58/110.28 symdiffIneg1 = 109.58/110.28 (![X2,X3,X4]: (in(X4,X2) => (in(X4,X3) => (~in(X4,symdiff(X2,X3)))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(symdiffI2, axiom, symdiffI2 <=> 109.58/110.28 (![A,B,Xx]: ((~in(Xx,A)) => (in(Xx,B) => in(Xx,symdiff(A,B)))))). 109.58/110.28 tff('75', plain, 109.58/110.28 symdiffI2 = 109.58/110.28 (![X2,X3,X4]: ((~in(X4,X2)) => (in(X4,X3) => in(X4,symdiff(X2,X3))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(symdiffI1, axiom, symdiffI1 <=> 109.58/110.28 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => in(Xx,symdiff(A,B)))))). 109.58/110.28 tff('76', plain, 109.58/110.28 symdiffI1 = 109.58/110.28 (![X2,X3,X4]: (in(X4,X2) => ((~in(X4,X3)) => in(X4,symdiff(X2,X3))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(symdiffE, axiom, symdiffE <=> 109.58/110.28 (![A,B,Xx]: 109.58/110.28 (in(Xx,symdiff(A,B)) => 109.58/110.28 (![Xphi:$o]: 109.58/110.28 ((in(Xx,A) => ((~in(Xx,B)) => Xphi)) => 109.58/110.28 (((~in(Xx,A)) => (in(Xx,B) => Xphi)) => Xphi)))))). 109.58/110.28 tff('77', plain, 109.58/110.28 symdiffE = 109.58/110.28 (![X2,X3,X4]: 109.58/110.28 (in(X4,symdiff(X2,X3)) => 109.58/110.28 (![X5:$o]: 109.58/110.28 ((in(X4,X2) => ((~in(X4,X3)) => X5)) => 109.58/110.28 (((~in(X4,X2)) => (in(X4,X3) => X5)) => X5))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(setminusSubset1, axiom, setminusSubset1 <=> 109.58/110.28 (![A,B]: ((setminus(A,B) = emptyset) => subset(A,B)))). 109.58/110.28 tff('78', plain, 109.58/110.28 setminusSubset1 = 109.58/110.28 (![X2,X3]: ((setminus(X2,X3) = emptyset) => subset(X2,X3))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(setminusLsub, axiom, setminusLsub <=> (![A,B]: subset(setminus(A,B),A))). 109.58/110.28 tff('79', plain, setminusLsub = (![X2,X3]: subset(setminus(X2,X3),X2)), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(setminusIRneg, axiom, setminusIRneg <=> 109.58/110.28 (![A,B,Xx]: (in(Xx,B) => (~in(Xx,setminus(A,B)))))). 109.58/110.28 tff('80', plain, 109.58/110.28 setminusIRneg = (![X2,X3,X4]: (in(X4,X3) => (~in(X4,setminus(X2,X3))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(setminusILneg, axiom, setminusILneg <=> 109.58/110.28 (![A,B,Xx]: ((~in(Xx,A)) => (~in(Xx,setminus(A,B)))))). 109.58/110.28 tff('81', plain, 109.58/110.28 setminusILneg = 109.58/110.28 (![X2,X3,X4]: ((~in(X4,X2)) => (~in(X4,setminus(X2,X3))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(setminusELneg, axiom, setminusELneg <=> 109.58/110.28 (![A,B,Xx]: ((~in(Xx,setminus(A,B))) => ((~in(Xx,B)) => (~in(Xx,A)))))). 109.58/110.28 tff('82', plain, 109.58/110.28 setminusELneg = 109.58/110.28 (![X2,X3,X4]: 109.58/110.28 ((~in(X4,setminus(X2,X3))) => ((~in(X4,X3)) => (~in(X4,X2))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(setminusERneg, axiom, setminusERneg <=> 109.58/110.28 (![A,B,Xx]: ((~in(Xx,setminus(A,B))) => (in(Xx,A) => in(Xx,B))))). 109.58/110.28 tff('83', plain, 109.58/110.28 setminusERneg = 109.58/110.28 (![X2,X3,X4]: ((~in(X4,setminus(X2,X3))) => (in(X4,X2) => in(X4,X3)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(setminusSubset2, axiom, setminusSubset2 <=> 109.58/110.28 (![A,B]: (subset(A,B) => (setminus(A,B) = emptyset)))). 109.58/110.28 tff('84', plain, 109.58/110.28 setminusSubset2 = 109.58/110.28 (![X2,X3]: (subset(X2,X3) => (setminus(X2,X3) = emptyset))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(setminusER, axiom, setminusER <=> 109.58/110.28 (![A,B,Xx]: (in(Xx,setminus(A,B)) => (~in(Xx,B))))). 109.58/110.28 tff('85', plain, 109.58/110.28 setminusER = (![X2,X3,X4]: (in(X4,setminus(X2,X3)) => (~in(X4,X3)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(setminusEL, axiom, setminusEL <=> 109.58/110.28 (![A,B,Xx]: (in(Xx,setminus(A,B)) => in(Xx,A)))). 109.58/110.28 tff('86', plain, 109.58/110.28 setminusEL = (![X2,X3,X4]: (in(X4,setminus(X2,X3)) => in(X4,X2))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(setminusI, axiom, setminusI <=> 109.58/110.28 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => in(Xx,setminus(A,B)))))). 109.58/110.28 tff('87', plain, 109.58/110.28 setminusI = 109.58/110.28 (![X2,X3,X4]: (in(X4,X2) => ((~in(X4,X3)) => in(X4,setminus(X2,X3))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(bs114d, axiom, bs114d <=> 109.58/110.28 (![A,B,C]: 109.58/110.28 (binintersect(A,binunion(B,C)) = 109.58/110.28 binunion(binintersect(A,B),binintersect(A,C))))). 109.58/110.28 tff('88', plain, 109.58/110.28 bs114d = 109.58/110.28 (![X2,X3,X4]: 109.58/110.28 (binintersect(X2,binunion(X3,X4)) = 109.58/110.28 binunion(binintersect(X2,X3),binintersect(X2,X4)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(binintersectSubset1, axiom, binintersectSubset1 <=> 109.58/110.28 (![A,B]: ((binintersect(A,B) = A) => subset(A,B)))). 109.58/110.28 tff('89', plain, 109.58/110.28 binintersectSubset1 = 109.58/110.28 (![X2,X3]: ((binintersect(X2,X3) = X2) => subset(X2,X3))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(binintersectSubset4, axiom, binintersectSubset4 <=> 109.58/110.28 (![A,B]: (subset(B,A) => (binintersect(A,B) = B)))). 109.58/110.28 tff('90', plain, 109.58/110.28 binintersectSubset4 = 109.58/110.28 (![X2,X3]: (subset(X3,X2) => (binintersect(X2,X3) = X3))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(binintersectRsub, axiom, binintersectRsub <=> 109.58/110.28 (![A,B]: subset(binintersect(A,B),B))). 109.58/110.28 tff('91', plain, 109.58/110.28 binintersectRsub = (![X2,X3]: subset(binintersect(X2,X3),X3)), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(disjointsetsI1, axiom, disjointsetsI1 <=> 109.58/110.28 (![A,B]: 109.58/110.28 ((~(?[Xx]: (in(Xx,B) & in(Xx,A)))) => (binintersect(A,B) = emptyset)))). 109.58/110.28 tff('92', plain, 109.58/110.28 disjointsetsI1 = 109.58/110.28 (![X2,X3]: 109.58/110.28 ((~(?[X4]: (in(X4,X3) & in(X4,X2)))) => 109.58/110.28 (binintersect(X2,X3) = emptyset))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(binintersectER, axiom, binintersectER <=> 109.58/110.28 (![A,B,Xx]: (in(Xx,binintersect(A,B)) => in(Xx,B)))). 109.58/110.28 tff('93', plain, 109.58/110.28 binintersectER = (![X2,X3,X4]: (in(X4,binintersect(X2,X3)) => in(X4,X3))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(binintersectSubset3, axiom, binintersectSubset3 <=> 109.58/110.28 (![A,B]: ((binintersect(A,B) = B) => subset(B,A)))). 109.58/110.28 tff('94', plain, 109.58/110.28 binintersectSubset3 = 109.58/110.28 (![X2,X3]: ((binintersect(X2,X3) = X3) => subset(X3,X2))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(binintersectSubset2, axiom, binintersectSubset2 <=> 109.58/110.28 (![A,B]: (subset(A,B) => (binintersect(A,B) = A)))). 109.58/110.28 tff('95', plain, 109.58/110.28 binintersectSubset2 = 109.58/110.28 (![X2,X3]: (subset(X2,X3) => (binintersect(X2,X3) = X2))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(binintersectLsub, axiom, binintersectLsub <=> 109.58/110.28 (![A,B]: subset(binintersect(A,B),A))). 109.58/110.28 tff('96', plain, 109.58/110.28 binintersectLsub = (![X2,X3]: subset(binintersect(X2,X3),X2)), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(binintersectEL, axiom, binintersectEL <=> 109.58/110.28 (![A,B,Xx]: (in(Xx,binintersect(A,B)) => in(Xx,A)))). 109.58/110.28 tff('97', plain, 109.58/110.28 binintersectEL = (![X2,X3,X4]: (in(X4,binintersect(X2,X3)) => in(X4,X2))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(binintersectSubset5, axiom, binintersectSubset5 <=> 109.58/110.28 (![A,B,C]: (subset(C,A) => (subset(C,B) => subset(C,binintersect(A,B)))))). 109.58/110.28 tff('98', plain, 109.58/110.28 binintersectSubset5 = 109.58/110.28 (![X2,X3,X4]: 109.58/110.28 (subset(X4,X2) => (subset(X4,X3) => subset(X4,binintersect(X2,X3))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(binintersectI, axiom, binintersectI <=> 109.58/110.28 (![A,B,Xx]: (in(Xx,A) => (in(Xx,B) => in(Xx,binintersect(A,B)))))). 109.58/110.28 tff('99', plain, 109.58/110.28 binintersectI = 109.58/110.28 (![X2,X3,X4]: (in(X4,X2) => (in(X4,X3) => in(X4,binintersect(X2,X3))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(binunionRsub, axiom, binunionRsub <=> (![A,B]: subset(B,binunion(A,B)))). 109.58/110.28 tff('100', plain, binunionRsub = (![X2,X3]: subset(X3,binunion(X2,X3))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(binunionLsub, axiom, binunionLsub <=> (![A,B]: subset(A,binunion(A,B)))). 109.58/110.28 tff('101', plain, binunionLsub = (![X2,X3]: subset(X2,binunion(X2,X3))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(binunionE, axiom, binunionE <=> 109.58/110.28 (![A,B,Xx]: (in(Xx,binunion(A,B)) => (in(Xx,B) | in(Xx,A))))). 109.58/110.28 tff('102', plain, 109.58/110.28 binunionE = 109.58/110.28 (![X2,X3,X4]: (in(X4,binunion(X2,X3)) => (in(X4,X3) | in(X4,X2)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(binunionEcases, axiom, binunionEcases <=> 109.58/110.28 (![A,B,Xx,Xphi:$o]: 109.58/110.28 (in(Xx,binunion(A,B)) => 109.58/110.28 ((in(Xx,A) => Xphi) => ((in(Xx,B) => Xphi) => Xphi))))). 109.58/110.28 tff('103', plain, 109.58/110.28 binunionEcases = 109.58/110.28 (![X2,X3,X4,X5:$o]: 109.58/110.28 (in(X4,binunion(X2,X3)) => 109.58/110.28 ((in(X4,X2) => X5) => ((in(X4,X3) => X5) => X5)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(binunionIR, axiom, binunionIR <=> 109.58/110.28 (![A,B,Xx]: (in(Xx,B) => in(Xx,binunion(A,B))))). 109.58/110.28 tff('104', plain, 109.58/110.28 binunionIR = (![X2,X3,X4]: (in(X4,X3) => in(X4,binunion(X2,X3)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(upairset2IR, axiom, upairset2IR <=> 109.58/110.28 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 109.58/110.28 tff('105', plain, 109.58/110.28 upairset2IR = (![X2,X3]: in(X3,setadjoin(X2,setadjoin(X3,emptyset)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(binunionIL, axiom, binunionIL <=> 109.58/110.28 (![A,B,Xx]: (in(Xx,A) => in(Xx,binunion(A,B))))). 109.58/110.28 tff('106', plain, 109.58/110.28 binunionIL = (![X2,X3,X4]: (in(X4,X2) => in(X4,binunion(X2,X3)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(sepSubset, axiom, sepSubset <=> 109.58/110.28 (![A,Xphi:($i > $o)]: subset(dsetconstr(A,^[Xx]: Xphi(Xx)),A))). 109.58/110.28 tff('107', plain, 109.58/110.28 sepSubset = 109.58/110.28 (![X2,X3:($i > $o)]: subset(dsetconstr(X2,^[V_1]: X3(V_1)),X2)), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(sepInPowerset, axiom, sepInPowerset <=> 109.58/110.28 (![A,Xphi:($i > $o)]: in(dsetconstr(A,^[Xx]: Xphi(Xx)),powerset(A)))). 109.58/110.28 tff('108', plain, 109.58/110.28 sepInPowerset = 109.58/110.28 (![X2,X3:($i > $o)]: in(dsetconstr(X2,^[V_1]: X3(V_1)),powerset(X2))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(powersetsubset, axiom, powersetsubset <=> 109.58/110.28 (![A,B]: (subset(A,B) => subset(powerset(A),powerset(B))))). 109.58/110.28 tff('109', plain, 109.58/110.28 powersetsubset = 109.58/110.28 (![X2,X3]: (subset(X2,X3) => subset(powerset(X2),powerset(X3)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(inPowerset, axiom, inPowerset <=> (![A]: in(A,powerset(A)))). 109.58/110.28 tff('110', plain, inPowerset = (![X2]: in(X2,powerset(X2))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(powersetE1, axiom, powersetE1 <=> 109.58/110.28 (![A,B]: (in(B,powerset(A)) => subset(B,A)))). 109.58/110.28 tff('111', plain, 109.58/110.28 powersetE1 = (![X2,X3]: (in(X3,powerset(X2)) => subset(X3,X2))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(powersetI1, axiom, powersetI1 <=> 109.58/110.28 (![A,B]: (subset(B,A) => in(B,powerset(A))))). 109.58/110.28 tff('112', plain, 109.58/110.28 powersetI1 = (![X2,X3]: (subset(X3,X2) => in(X3,powerset(X2)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(subsetemptysetimpeq, axiom, subsetemptysetimpeq <=> 109.58/110.28 (![A]: (subset(A,emptyset) => (A = emptyset)))). 109.58/110.28 tff('113', plain, 109.58/110.28 subsetemptysetimpeq = (![X2]: (subset(X2,emptyset) => (X2 = emptyset))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(setextsub, axiom, setextsub <=> 109.58/110.28 (![A,B]: (subset(A,B) => (subset(B,A) => (A = B))))). 109.58/110.28 tff('114', plain, 109.58/110.28 setextsub = (![X2,X3]: (subset(X2,X3) => (subset(X3,X2) => (X2 = X3)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(subset2powerset, axiom, subset2powerset <=> 109.58/110.28 (![A,B]: (subset(A,B) => in(A,powerset(B))))). 109.58/110.28 tff('115', plain, 109.58/110.28 subset2powerset = (![X2,X3]: (subset(X2,X3) => in(X2,powerset(X3)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(setadjoinSub2, axiom, setadjoinSub2 <=> 109.58/110.28 (![A,Xx,B]: (subset(A,B) => subset(A,setadjoin(Xx,B))))). 109.58/110.28 tff('116', plain, 109.58/110.28 setadjoinSub2 = 109.58/110.28 (![X2,X3,X4]: (subset(X2,X4) => subset(X2,setadjoin(X3,X4)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(setadjoinSub, axiom, setadjoinSub <=> 109.58/110.28 (![Xx,A]: subset(A,setadjoin(Xx,A)))). 109.58/110.28 tff('117', plain, setadjoinSub = (![X2,X3]: subset(X3,setadjoin(X2,X3))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(subsetTrans, axiom, subsetTrans <=> 109.58/110.28 (![A,B,C]: (subset(A,B) => (subset(B,C) => subset(A,C))))). 109.58/110.28 tff('118', plain, 109.58/110.28 subsetTrans = 109.58/110.28 (![X2,X3,X4]: (subset(X2,X3) => (subset(X3,X4) => subset(X2,X4)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(subsetRefl, axiom, subsetRefl <=> (![A]: subset(A,A))). 109.58/110.28 tff('119', plain, subsetRefl = (![X2]: subset(X2,X2)), define([status(thm)])). 109.58/110.28 tff(notequalI2, axiom, notequalI2 <=> 109.58/110.28 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => (A != B))))). 109.58/110.28 tff('120', plain, 109.58/110.28 notequalI2 = (![X2,X3,X4]: (in(X4,X2) => ((~in(X4,X3)) => (X2 != X3)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(notequalI1, axiom, notequalI1 <=> (![A,B]: ((~subset(A,B)) => (A != B)))). 109.58/110.28 tff('121', plain, notequalI1 = (![X2,X3]: ((~subset(X2,X3)) => (X2 != X3))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(notsubsetI, axiom, notsubsetI <=> 109.58/110.28 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => (~subset(A,B)))))). 109.58/110.28 tff('122', plain, 109.58/110.28 notsubsetI = 109.58/110.28 (![X2,X3,X4]: (in(X4,X2) => ((~in(X4,X3)) => (~subset(X2,X3))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(subsetE2, axiom, subsetE2 <=> 109.58/110.28 (![A,B,Xx]: (subset(A,B) => ((~in(Xx,B)) => (~in(Xx,A)))))). 109.58/110.28 tff('123', plain, 109.58/110.28 subsetE2 = 109.58/110.28 (![X2,X3,X4]: (subset(X2,X3) => ((~in(X4,X3)) => (~in(X4,X2))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(subsetE, axiom, subsetE <=> 109.58/110.28 (![A,B,Xx]: (subset(A,B) => (in(Xx,A) => in(Xx,B))))). 109.58/110.28 tff('124', plain, 109.58/110.28 subsetE = (![X2,X3,X4]: (subset(X2,X3) => (in(X4,X2) => in(X4,X3)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(emptysetsubset, axiom, emptysetsubset <=> (![A]: subset(emptyset,A))). 109.58/110.28 tff('125', plain, emptysetsubset = (![X2]: subset(emptyset,X2)), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(subsetI2, axiom, subsetI2 <=> 109.58/110.28 (![A,B]: ((![Xx]: (in(Xx,A) => in(Xx,B))) => subset(A,B)))). 109.58/110.28 tff('126', plain, 109.58/110.28 subsetI2 = 109.58/110.28 (![X2,X3]: ((![X4]: (in(X4,X2) => in(X4,X3))) => subset(X2,X3))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(eqimpsubset1, axiom, eqimpsubset1 <=> (![A,B]: ((A = B) => subset(A,B)))). 109.58/110.28 tff('127', plain, eqimpsubset1 = (![X2,X3]: ((X2 = X3) => subset(X2,X3))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(eqimpsubset2, axiom, eqimpsubset2 <=> (![A,B]: ((A = B) => subset(B,A)))). 109.58/110.28 tff('128', plain, eqimpsubset2 = (![X2,X3]: ((X2 = X3) => subset(X3,X2))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(subsetI1, axiom, subsetI1 <=> 109.58/110.28 (![A,B]: ((![Xx]: (in(Xx,A) => in(Xx,B))) => subset(A,B)))). 109.58/110.28 tff('129', plain, 109.58/110.28 subsetI1 = 109.58/110.28 (![X2,X3]: ((![X4]: (in(X4,X2) => in(X4,X3))) => subset(X2,X3))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(dsetconstr__Cong, axiom, dsetconstr__Cong <=> 109.58/110.28 (![A,B]: 109.58/110.28 ((A = B) => 109.58/110.28 (![Xphi:($i > $o),Xpsi:($i > $o)]: 109.58/110.28 ((![Xx]: 109.58/110.28 (in(Xx,A) => 109.58/110.28 (![Xy]: (in(Xy,B) => ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy))))))) => 109.58/110.28 (dsetconstr(A,^[Xx]: Xphi(Xx)) = dsetconstr(B,^[Xx]: Xpsi(Xx)))))))). 109.58/110.28 tff('130', plain, 109.58/110.28 dsetconstr__Cong = 109.58/110.28 (![X2,X3]: 109.58/110.28 ((X2 = X3) => 109.58/110.28 (![X4:($i > $o),X5:($i > $o)]: 109.58/110.28 ((![X6]: 109.58/110.28 (in(X6,X2) => 109.58/110.28 (![X7]: (in(X7,X3) => ((X6 = X7) => (X4(X6) <=> X5(X7))))))) => 109.58/110.28 (dsetconstr(X2,^[V_1]: X4(V_1)) = dsetconstr(X3,^[V_2]: X5(V_2))))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(descr__Cong, axiom, descr__Cong <=> 109.58/110.28 (![Xphi:($i > $o),Xpsi:($i > $o)]: 109.58/110.28 ((![Xx,Xy]: ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy)))) => 109.58/110.28 (exu(^[Xx]: Xphi(Xx)) => 109.58/110.28 (exu(^[Xx]: Xpsi(Xx)) => 109.58/110.28 (descr(^[Xx]: Xphi(Xx)) = descr(^[Xx]: Xpsi(Xx)))))))). 109.58/110.28 tff('131', plain, 109.58/110.28 descr__Cong = 109.58/110.28 (![X2:($i > $o),X3:($i > $o)]: 109.58/110.28 ((![X4,X5]: ((X4 = X5) => (X2(X4) <=> X3(X5)))) => 109.58/110.28 (exu(^[V_1]: X2(V_1)) => 109.58/110.28 (exu(^[V_2]: X3(V_2)) => 109.58/110.28 (descr(^[V_3]: X2(V_3)) = descr(^[V_4]: X3(V_4))))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(exuEu, axiom, exuEu <=> 109.58/110.28 (![Xphi:($i > $o)]: 109.58/110.28 (exu(^[Xx]: Xphi(Xx)) => 109.58/110.28 (![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))). 109.58/110.28 tff('132', plain, 109.58/110.28 exuEu = 109.58/110.28 (![X2:($i > $o)]: 109.58/110.28 (exu(^[V_1]: X2(V_1)) => (![X3,X4]: (X2(X3) => (X2(X4) => (X3 = X4)))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(omega__Cong, axiom, omega__Cong <=> (omega = omega)). 109.58/110.28 tff('133', plain, omega__Cong = (omega = omega), define([status(thm)])). 109.58/110.28 tff(setunion__Cong, axiom, setunion__Cong <=> 109.58/110.28 (![A,B]: ((A = B) => (setunion(A) = setunion(B))))). 109.58/110.28 tff('134', plain, 109.58/110.28 setunion__Cong = (![X2,X3]: ((X2 = X3) => (setunion(X2) = setunion(X3)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(powerset__Cong, axiom, powerset__Cong <=> 109.58/110.28 (![A,B]: ((A = B) => (powerset(A) = powerset(B))))). 109.58/110.28 tff('135', plain, 109.58/110.28 powerset__Cong = (![X2,X3]: ((X2 = X3) => (powerset(X2) = powerset(X3)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(setadjoin__Cong, axiom, setadjoin__Cong <=> 109.58/110.28 (![Xx,Xy]: 109.58/110.28 ((Xx = Xy) => 109.58/110.28 (![Xz,Xu]: ((Xz = Xu) => (setadjoin(Xx,Xz) = setadjoin(Xy,Xu))))))). 109.58/110.28 tff('136', plain, 109.58/110.28 setadjoin__Cong = 109.58/110.28 (![X2,X3]: 109.58/110.28 ((X2 = X3) => 109.58/110.28 (![X4,X5]: ((X4 = X5) => (setadjoin(X2,X4) = setadjoin(X3,X5)))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(emptyset__Cong, axiom, emptyset__Cong <=> (emptyset = emptyset)). 109.58/110.28 tff('137', plain, emptyset__Cong = (emptyset = emptyset), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(exu__Cong, axiom, exu__Cong <=> 109.58/110.28 (![Xphi:($i > $o),Xpsi:($i > $o)]: 109.58/110.28 ((![Xx,Xy]: ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy)))) => 109.58/110.28 (exu(^[Xx]: Xphi(Xx)) <=> exu(^[Xx]: Xpsi(Xx)))))). 109.58/110.28 tff('138', plain, 109.58/110.28 exu__Cong = 109.58/110.28 (![X2:($i > $o),X3:($i > $o)]: 109.58/110.28 ((![X4,X5]: ((X4 = X5) => (X2(X4) <=> X3(X5)))) => 109.58/110.28 (exu(^[V_1]: X2(V_1)) <=> exu(^[V_2]: X3(V_2))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(exuE3u, axiom, exuE3u <=> 109.58/110.28 (![Xphi:($i > $o)]: 109.58/110.28 (exu(^[Xx]: Xphi(Xx)) => 109.58/110.28 (![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))). 109.58/110.28 tff('139', plain, 109.58/110.28 exuE3u = 109.58/110.28 (![X2:($i > $o)]: 109.58/110.28 (exu(^[V_1]: X2(V_1)) => (![X3,X4]: (X2(X3) => (X2(X4) => (X3 = X4)))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(in__Cong, axiom, in__Cong <=> 109.58/110.28 (![A,B]: ((A = B) => (![Xx,Xy]: ((Xx = Xy) => (in(Xx,A) <=> in(Xy,B))))))). 109.58/110.28 tff('140', plain, 109.58/110.28 in__Cong = 109.58/110.28 (![X2,X3]: 109.58/110.28 ((X2 = X3) => (![X4,X5]: ((X4 = X5) => (in(X4,X2) <=> in(X5,X3)))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(inCongP, axiom, inCongP <=> 109.58/110.28 (![A,B]: ((A = B) => (![Xx,Xy]: ((Xx = Xy) => (in(Xx,A) => in(Xy,B))))))). 109.58/110.28 tff('141', plain, 109.58/110.28 inCongP = 109.58/110.28 (![X2,X3]: 109.58/110.28 ((X2 = X3) => (![X4,X5]: ((X4 = X5) => (in(X4,X2) => in(X5,X3)))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(exuI2, axiom, exuI2 <=> 109.58/110.28 (![Xphi:($i > $o)]: 109.58/110.28 ((?[Xx]: (![Xy]: (Xphi(Xy) <=> (Xy = Xx)))) => exu(^[Xx]: Xphi(Xx))))). 109.58/110.28 tff('142', plain, 109.58/110.28 exuI2 = 109.58/110.28 (![X2:($i > $o)]: 109.58/110.28 ((?[X3]: (![X4]: (X2(X4) <=> (X4 = X3)))) => exu(^[V_1]: X2(V_1)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(exuI3, axiom, exuI3 <=> 109.58/110.28 (![Xphi:($i > $o)]: 109.58/110.28 ((?[Xx]: Xphi(Xx)) => 109.58/110.28 ((![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy)))) => 109.58/110.28 exu(^[Xx]: Xphi(Xx)))))). 109.58/110.28 tff('143', plain, 109.58/110.28 exuI3 = 109.58/110.28 (![X2:($i > $o)]: 109.58/110.28 ((?[X3]: X2(X3)) => 109.58/110.28 ((![X4,X5]: (X2(X4) => (X2(X5) => (X4 = X5)))) => 109.58/110.28 exu(^[V_1]: X2(V_1))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(exuI1, axiom, exuI1 <=> 109.58/110.28 (![Xphi:($i > $o)]: 109.58/110.28 ((?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx))) => 109.58/110.28 exu(^[Xx]: Xphi(Xx))))). 109.58/110.28 tff('144', plain, 109.58/110.28 exuI1 = 109.58/110.28 (![X2:($i > $o)]: 109.58/110.28 ((?[X3]: ((![X4]: (X2(X4) => (X3 = X4))) & X2(X3))) => 109.58/110.28 exu(^[V_1]: X2(V_1)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(notdallE, axiom, notdallE <=> 109.58/110.28 (![A,Xphi:($i > $o)]: 109.58/110.28 ((~(![Xx]: (in(Xx,A) => Xphi(Xx)))) => (?[Xx]: ((~Xphi(Xx)) & in(Xx,A)))))). 109.58/110.28 tff('145', plain, 109.58/110.28 notdallE = 109.58/110.28 (![X2,X3:($i > $o)]: 109.58/110.28 ((~(![X4]: (in(X4,X2) => X3(X4)))) => (?[X5]: ((~X3(X5)) & in(X5,X2))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(notdexE, axiom, notdexE <=> 109.58/110.28 (![A,Xphi:($i > $o)]: 109.58/110.28 ((~(?[Xx]: (Xphi(Xx) & in(Xx,A)))) => (![Xx]: (in(Xx,A) => (~Xphi(Xx))))))). 109.58/110.28 tff('146', plain, 109.58/110.28 notdexE = 109.58/110.28 (![X2,X3:($i > $o)]: 109.58/110.28 ((~(?[X4]: (X3(X4) & in(X4,X2)))) => (![X5]: (in(X5,X2) => (~X3(X5)))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(prop2set2propI, axiom, prop2set2propI <=> 109.58/110.28 (![Xphi:$o]: (Xphi => set2prop(prop2set(Xphi))))). 109.58/110.28 tff('147', plain, 109.58/110.28 prop2set2propI = (![X2:$o]: (X2 => set2prop(prop2set(X2)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(prop2setI, axiom, prop2setI <=> 109.58/110.28 (![Xphi:$o]: (Xphi => in(emptyset,prop2set(Xphi))))). 109.58/110.28 tff('148', plain, prop2setI = (![X2:$o]: (X2 => in(emptyset,prop2set(X2)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(quantDeMorgan4, axiom, quantDeMorgan4 <=> 109.58/110.28 (![A,Xphi:($i > $o)]: 109.58/110.28 ((?[Xx]: ((~Xphi(Xx)) & in(Xx,A))) => (~(![Xx]: (in(Xx,A) => Xphi(Xx))))))). 109.58/110.28 tff('149', plain, 109.58/110.28 quantDeMorgan4 = 109.58/110.28 (![X2,X3:($i > $o)]: 109.58/110.28 ((?[X4]: ((~X3(X4)) & in(X4,X2))) => (~(![X5]: (in(X5,X2) => X3(X5)))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(quantDeMorgan3, axiom, quantDeMorgan3 <=> 109.58/110.28 (![A,Xphi:($i > $o)]: 109.58/110.28 ((~(?[Xx]: (Xphi(Xx) & in(Xx,A)))) => (![Xx]: (in(Xx,A) => (~Xphi(Xx))))))). 109.58/110.28 tff('150', plain, 109.58/110.28 quantDeMorgan3 = 109.58/110.28 (![X2,X3:($i > $o)]: 109.58/110.28 ((~(?[X4]: (X3(X4) & in(X4,X2)))) => (![X5]: (in(X5,X2) => (~X3(X5)))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(quantDeMorgan2, axiom, quantDeMorgan2 <=> 109.58/110.28 (![A,Xphi:($i > $o)]: 109.58/110.28 ((![Xx]: (in(Xx,A) => (~Xphi(Xx)))) => (~(?[Xx]: (Xphi(Xx) & in(Xx,A))))))). 109.58/110.28 tff('151', plain, 109.58/110.28 quantDeMorgan2 = 109.58/110.28 (![X2,X3:($i > $o)]: 109.58/110.28 ((![X4]: (in(X4,X2) => (~X3(X4)))) => (~(?[X5]: (X3(X5) & in(X5,X2)))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(quantDeMorgan1, axiom, quantDeMorgan1 <=> 109.58/110.28 (![A,Xphi:($i > $o)]: 109.58/110.28 ((~(![Xx]: (in(Xx,A) => Xphi(Xx)))) => (?[Xx]: ((~Xphi(Xx)) & in(Xx,A)))))). 109.58/110.28 tff('152', plain, 109.58/110.28 quantDeMorgan1 = 109.58/110.28 (![X2,X3:($i > $o)]: 109.58/110.28 ((~(![X4]: (in(X4,X2) => X3(X4)))) => (?[X5]: ((~X3(X5)) & in(X5,X2))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(vacuousDall, axiom, vacuousDall <=> 109.58/110.28 (![Xphi:($i > $o),Xx]: (in(Xx,emptyset) => Xphi(Xx)))). 109.58/110.28 tff('153', plain, 109.58/110.28 vacuousDall = (![X2:($i > $o),X3]: (in(X3,emptyset) => X2(X3))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(emptyE1, axiom, emptyE1 <=> 109.58/110.28 (![A,Xphi:($i > $o)]: 109.58/110.28 ((?[Xx]: (Xphi(Xx) & in(Xx,A))) => 109.58/110.28 ((dsetconstr(A,^[Xx]: Xphi(Xx)) = emptyset) => $false)))). 109.58/110.28 tff('154', plain, 109.58/110.28 emptyE1 = 109.58/110.28 (![X2,X3:($i > $o)]: 109.58/110.28 ((?[X4]: (X3(X4) & in(X4,X2))) => 109.58/110.28 ((dsetconstr(X2,^[V_1]: X3(V_1)) = emptyset) => $false))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(upairsetIR, axiom, upairsetIR <=> 109.58/110.28 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 109.58/110.28 tff('155', plain, 109.58/110.28 upairsetIR = (![X2,X3]: in(X3,setadjoin(X2,setadjoin(X3,emptyset)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(upairsetIL, axiom, upairsetIL <=> 109.58/110.28 (![Xx,Xy]: in(Xx,setadjoin(Xx,setadjoin(Xy,emptyset))))). 109.58/110.28 tff('156', plain, 109.58/110.28 upairsetIL = (![X2,X3]: in(X2,setadjoin(X2,setadjoin(X3,emptyset)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(upairsetE, axiom, upairsetE <=> 109.58/110.28 (![Xx,Xy,Xz]: 109.58/110.28 (in(Xz,setadjoin(Xx,setadjoin(Xy,emptyset))) => ((Xz = Xy) | (Xz = Xx))))). 109.58/110.28 tff('157', plain, 109.58/110.28 upairsetE = 109.58/110.28 (![X2,X3,X4]: 109.58/110.28 (in(X4,setadjoin(X2,setadjoin(X3,emptyset))) => 109.58/110.28 ((X4 = X3) | (X4 = X2)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(singletonsswitch, axiom, singletonsswitch <=> 109.58/110.28 (![Xx,Xy]: (in(Xx,setadjoin(Xy,emptyset)) => in(Xy,setadjoin(Xx,emptyset))))). 109.58/110.28 tff('158', plain, 109.58/110.28 singletonsswitch = 109.58/110.28 (![X2,X3]: 109.58/110.28 (in(X2,setadjoin(X3,emptyset)) => in(X3,setadjoin(X2,emptyset)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(eqinunit, axiom, eqinunit <=> 109.58/110.28 (![Xx,Xy]: ((Xx = Xy) => in(Xx,setadjoin(Xy,emptyset))))). 109.58/110.28 tff('159', plain, 109.58/110.28 eqinunit = (![X2,X3]: ((X2 = X3) => in(X2,setadjoin(X3,emptyset)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(notinsingleton, axiom, notinsingleton <=> 109.58/110.28 (![Xx,Xy]: ((Xx != Xy) => (~in(Xy,setadjoin(Xx,emptyset)))))). 109.58/110.28 tff('160', plain, 109.58/110.28 notinsingleton = 109.58/110.28 (![X2,X3]: ((X2 != X3) => (~in(X3,setadjoin(X2,emptyset))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(uniqinunit, axiom, uniqinunit <=> 109.58/110.28 (![Xx,Xy]: (in(Xx,setadjoin(Xy,emptyset)) => (Xx = Xy)))). 109.58/110.28 tff('161', plain, 109.58/110.28 uniqinunit = (![X2,X3]: (in(X2,setadjoin(X3,emptyset)) => (X2 = X3))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(nonemptyImpWitness, axiom, nonemptyImpWitness <=> 109.58/110.28 (![A]: (nonempty(A) => (?[Xx]: (in(Xx,A)))))). 109.58/110.28 tff('162', plain, 109.58/110.28 nonemptyImpWitness = (![X2]: (nonempty(X2) => (?[X3]: (in(X3,X2))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(exuE2, axiom, exuE2 <=> 109.58/110.28 (![Xphi:($i > $o)]: 109.58/110.28 (exu(^[Xx]: Xphi(Xx)) => (?[Xx]: (![Xy]: (Xphi(Xy) <=> (Xy = Xx))))))). 109.58/110.28 tff('163', plain, 109.58/110.28 exuE2 = 109.58/110.28 (![X2:($i > $o)]: 109.58/110.28 (exu(^[V_1]: X2(V_1)) => (?[X3]: (![X4]: (X2(X4) <=> (X4 = X3)))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(subPowSU, axiom, subPowSU <=> 109.58/110.28 (![A,Xx]: (in(Xx,A) => in(Xx,powerset(setunion(A)))))). 109.58/110.28 tff('164', plain, 109.58/110.28 subPowSU = (![X2,X3]: (in(X3,X2) => in(X3,powerset(setunion(X2))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(setunionE, axiom, setunionE <=> 109.58/110.28 (![A,Xx]: 109.58/110.28 (in(Xx,setunion(A)) => 109.58/110.28 (![Xphi:$o]: ((![B]: (in(Xx,B) => (in(B,A) => Xphi))) => Xphi))))). 109.58/110.28 tff('165', plain, 109.58/110.28 setunionE = 109.58/110.28 (![X2,X3]: 109.58/110.28 (in(X3,setunion(X2)) => 109.58/110.28 (![X4:$o]: ((![X5]: (in(X3,X5) => (in(X5,X2) => X4))) => X4)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(setunionI, axiom, setunionI <=> 109.58/110.28 (![A,Xx,B]: (in(Xx,B) => (in(B,A) => in(Xx,setunion(A)))))). 109.58/110.28 tff('166', plain, 109.58/110.28 setunionI = 109.58/110.28 (![X2,X3,X4]: (in(X3,X4) => (in(X4,X2) => in(X3,setunion(X2))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(powersetE, axiom, powersetE <=> 109.58/110.28 (![A,B,Xx]: (in(B,powerset(A)) => (in(Xx,B) => in(Xx,A))))). 109.58/110.28 tff('167', plain, 109.58/110.28 powersetE = 109.58/110.28 (![X2,X3,X4]: (in(X3,powerset(X2)) => (in(X4,X3) => in(X4,X2)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(emptyInPowerset, axiom, emptyInPowerset <=> 109.58/110.28 (![A]: in(emptyset,powerset(A)))). 109.58/110.28 tff('168', plain, emptyInPowerset = (![X2]: in(emptyset,powerset(X2))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(emptyinPowerset, axiom, emptyinPowerset <=> 109.58/110.28 (![A]: in(emptyset,powerset(A)))). 109.58/110.28 tff('169', plain, emptyinPowerset = (![X2]: in(emptyset,powerset(X2))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(powersetI, axiom, powersetI <=> 109.58/110.28 (![A,B]: ((![Xx]: (in(Xx,B) => in(Xx,A))) => in(B,powerset(A))))). 109.58/110.28 tff('170', plain, 109.58/110.28 powersetI = 109.58/110.28 (![X2,X3]: ((![X4]: (in(X4,X3) => in(X4,X2))) => in(X3,powerset(X2)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(setoftrueEq, axiom, setoftrueEq <=> 109.58/110.28 (![A]: (dsetconstr(A,^[Xx]: $true) = A))). 109.58/110.28 tff('171', plain, setoftrueEq = (![X2]: (dsetconstr(X2,^[V_1]: $true) = X2)), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(setadjoinOr, axiom, setadjoinOr <=> 109.58/110.28 (![Xx,A,Xy]: (in(Xy,setadjoin(Xx,A)) => (in(Xy,A) | (Xy = Xx))))). 109.58/110.28 tff('172', plain, 109.58/110.28 setadjoinOr = 109.58/110.28 (![X2,X3,X4]: (in(X4,setadjoin(X2,X3)) => (in(X4,X3) | (X4 = X2)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(setadjoinE, axiom, setadjoinE <=> 109.58/110.28 (![Xx,A,Xy]: 109.58/110.28 (in(Xy,setadjoin(Xx,A)) => 109.58/110.28 (![Xphi:$o]: (((Xy = Xx) => Xphi) => ((in(Xy,A) => Xphi) => Xphi)))))). 109.58/110.28 tff('173', plain, 109.58/110.28 setadjoinE = 109.58/110.28 (![X2,X3,X4]: 109.58/110.28 (in(X4,setadjoin(X2,X3)) => 109.58/110.28 (![X5:$o]: (((X4 = X2) => X5) => ((in(X4,X3) => X5) => X5))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(setadjoinIR, axiom, setadjoinIR <=> 109.58/110.28 (![Xx,A,Xy]: (in(Xy,A) => in(Xy,setadjoin(Xx,A))))). 109.58/110.28 tff('174', plain, 109.58/110.28 setadjoinIR = (![X2,X3,X4]: (in(X4,X3) => in(X4,setadjoin(X2,X3)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(emptyinunitempty, axiom, emptyinunitempty() = 109.58/110.28 in(emptyset,setadjoin(emptyset,emptyset))). 109.58/110.28 tff('175', plain, 109.58/110.28 emptyinunitempty = in(emptyset,setadjoin(emptyset,emptyset)), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(setadjoinIL, axiom, setadjoinIL <=> (![Xx,Xy]: in(Xx,setadjoin(Xx,Xy)))). 109.58/110.28 tff('176', plain, setadjoinIL = (![X2,X3]: in(X2,setadjoin(X2,X3))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(nonemptyI1, axiom, nonemptyI1 <=> 109.58/110.28 (![A]: ((?[Xx]: in(Xx,A)) => nonempty(A)))). 109.58/110.28 tff('177', plain, nonemptyI1 = (![X2]: ((?[X3]: in(X3,X2)) => nonempty(X2))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(nonemptyI, axiom, nonemptyI <=> 109.58/110.28 (![A,Xphi:($i > $o),Xx]: 109.58/110.28 (in(Xx,A) => (Xphi(Xx) => nonempty(dsetconstr(A,^[Xy]: Xphi(Xy))))))). 109.58/110.28 tff('178', plain, 109.58/110.28 nonemptyI = 109.58/110.28 (![X2,X3:($i > $o),X4]: 109.58/110.28 (in(X4,X2) => (X3(X4) => nonempty(dsetconstr(X2,^[V_1]: X3(V_1)))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(nonemptyE1, axiom, nonemptyE1 <=> 109.58/110.28 (![A]: (nonempty(A) => (?[Xx]: in(Xx,A))))). 109.58/110.28 tff('179', plain, nonemptyE1 = (![X2]: (nonempty(X2) => (?[X3]: in(X3,X2)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(nonempty, axiom, nonempty() = ^[Xx]: (Xx != emptyset)). 109.58/110.28 tff('180', plain, nonempty = (^[V_1]: (V_1 != emptyset)), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(setbeta, axiom, setbeta <=> 109.58/110.28 (![A,Xphi:($i > $o),Xx]: 109.58/110.28 (in(Xx,A) => (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) <=> Xphi(Xx))))). 109.58/110.28 tff('181', plain, 109.58/110.28 setbeta = 109.58/110.28 (![X2,X3:($i > $o),X4]: 109.58/110.28 (in(X4,X2) => (in(X4,dsetconstr(X2,^[V_1]: X3(V_1))) <=> X3(X4)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(noeltsimpempty, axiom, noeltsimpempty <=> 109.58/110.28 (![A]: ((![Xx]: (~in(Xx,A))) => (A = emptyset)))). 109.58/110.28 tff('182', plain, 109.58/110.28 noeltsimpempty = (![X2]: ((![X3]: (~in(X3,X2))) => (X2 = emptyset))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(emptyI, axiom, emptyI <=> 109.58/110.28 (![A]: ((![Xx]: (~in(Xx,A))) => (A = emptyset)))). 109.58/110.28 tff('183', plain, 109.58/110.28 emptyI = (![X2]: ((![X3]: (~in(X3,X2))) => (X2 = emptyset))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(setext, axiom, setext <=> 109.58/110.28 (![A,B]: 109.58/110.28 ((![Xx]: (in(Xx,A) => in(Xx,B))) => 109.58/110.28 ((![Xx]: (in(Xx,B) => in(Xx,A))) => (A = B))))). 109.58/110.28 tff('184', plain, 109.58/110.28 setext = 109.58/110.28 (![X2,X3]: 109.58/110.28 ((![X4]: (in(X4,X2) => in(X4,X3))) => 109.58/110.28 ((![X5]: (in(X5,X3) => in(X5,X2))) => (X2 = X3)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(exuE3e, axiom, exuE3e <=> 109.58/110.28 (![Xphi:($i > $o)]: (exu(^[Xx]: Xphi(Xx)) => (?[Xx]: Xphi(Xx))))). 109.58/110.28 tff('185', plain, 109.58/110.28 exuE3e = (![X2:($i > $o)]: (exu(^[V_1]: X2(V_1)) => (?[X3]: X2(X3)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(notinemptyset, axiom, notinemptyset <=> (![Xx]: (~in(Xx,emptyset)))). 109.58/110.28 tff('186', plain, notinemptyset = (![X2]: (~in(X2,emptyset))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(emptysetimpfalse, axiom, emptysetimpfalse <=> 109.58/110.28 (![Xx]: (in(Xx,emptyset) => $false))). 109.58/110.28 tff('187', plain, emptysetimpfalse = (![X2]: (in(X2,emptyset) => $false)), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(emptysetE, axiom, emptysetE <=> 109.58/110.28 (![Xx]: (in(Xx,emptyset) => (![Xphi:$o]: Xphi)))). 109.58/110.28 tff('188', plain, emptysetE = (![X2]: (in(X2,emptyset) => (![X3:$o]: X3))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(prop2setE, axiom, prop2setE <=> 109.58/110.28 (![Xphi:$o,Xx]: (in(Xx,prop2set(Xphi)) => Xphi))). 109.58/110.28 tff('189', plain, prop2setE = (![X2:$o,X3]: (in(X3,prop2set(X2)) => X2)), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(exuE1, axiom, exuE1 <=> 109.58/110.28 (![Xphi:($i > $o)]: 109.58/110.28 (exu(^[Xx]: Xphi(Xx)) => 109.58/110.28 (?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx)))))). 109.58/110.28 tff('190', plain, 109.58/110.28 exuE1 = 109.58/110.28 (![X2:($i > $o)]: 109.58/110.28 (exu(^[V_1]: X2(V_1)) => 109.58/110.28 (?[X3]: ((![X4]: (X2(X4) => (X3 = X4))) & X2(X3))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(dsetconstrER, axiom, dsetconstrER <=> 109.58/110.28 (![A,Xphi:($i > $o),Xx]: (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) => Xphi(Xx)))). 109.58/110.28 tff('191', plain, 109.58/110.28 dsetconstrER = 109.58/110.28 (![X2,X3:($i > $o),X4]: (in(X4,dsetconstr(X2,^[V_1]: X3(V_1))) => X3(X4))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(dsetconstrEL, axiom, dsetconstrEL <=> 109.58/110.28 (![A,Xphi:($i > $o),Xx]: (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) => in(Xx,A)))). 109.58/110.28 tff('192', plain, 109.58/110.28 dsetconstrEL = 109.58/110.28 (![X2,X3:($i > $o),X4]: 109.58/110.28 (in(X4,dsetconstr(X2,^[V_1]: X3(V_1))) => in(X4,X2))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(dsetconstrI, axiom, dsetconstrI <=> 109.58/110.28 (![A,Xphi:($i > $o),Xx]: 109.58/110.28 (in(Xx,A) => (Xphi(Xx) => in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))))))). 109.58/110.28 tff('193', plain, 109.58/110.28 dsetconstrI = 109.58/110.28 (![X2,X3:($i > $o),X4]: 109.58/110.28 (in(X4,X2) => (X3(X4) => in(X4,dsetconstr(X2,^[V_1]: X3(V_1)))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(descrp, axiom, descrp <=> 109.58/110.28 (![Xphi:($i > $o)]: (exu(^[Xx]: Xphi(Xx)) => Xphi(descr(^[Xx]: Xphi(Xx)))))). 109.58/110.28 tff('194', plain, 109.58/110.28 descrp = 109.58/110.28 (![X2:($i > $o)]: (exu(^[V_1]: X2(V_1)) => X2(descr(^[V_2]: X2(V_2))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(wellorderingAx, axiom, wellorderingAx <=> 109.58/110.28 (![A]: 109.58/110.28 (?[B]: 109.58/110.28 ((![C]: 109.58/110.28 (((?[Xx]: in(Xx,C)) & (![Xx]: (in(Xx,C) => in(Xx,A)))) => 109.58/110.28 (?[D,Xx]: 109.58/110.28 ((![E]: 109.58/110.28 (in(E,B) => (in(Xx,E) | (![Xy]: (in(Xy,E) => in(Xy,D)))))) & 109.58/110.28 (~(?[Xy]: (in(Xy,C) & in(Xy,D)))) & in(Xx,C) & in(D,B))))) & 109.58/110.28 (![C,D]: 109.58/110.28 ((in(D,B) & in(C,B)) => 109.58/110.28 ((![Xx]: (in(Xx,D) => in(Xx,C))) | 109.58/110.28 (![Xx]: (in(Xx,C) => in(Xx,D)))))) & 109.58/110.28 (![Xx,Xy]: 109.58/110.28 ((in(Xy,A) & in(Xx,A)) => 109.58/110.28 ((![C]: (in(C,B) => (in(Xx,C) <=> in(Xy,C)))) => (Xx = Xy)))) & 109.58/110.28 (![C]: (in(C,B) => (![Xx]: (in(Xx,C) => in(Xx,A))))))))). 109.58/110.28 tff('195', plain, 109.58/110.28 wellorderingAx = 109.58/110.28 (![X2]: 109.58/110.28 (?[X3]: 109.58/110.28 ((![X4]: 109.58/110.28 (((?[X5]: in(X5,X4)) & (![X6]: (in(X6,X4) => in(X6,X2)))) => 109.58/110.28 (?[X7,X8]: 109.58/110.28 ((![X9]: 109.58/110.28 (in(X9,X3) => 109.58/110.28 (in(X8,X9) | (![X10]: (in(X10,X9) => in(X10,X7)))))) & 109.58/110.28 (~(?[X11]: (in(X11,X4) & in(X11,X7)))) & in(X8,X4) & 109.58/110.28 in(X7,X3))))) & 109.58/110.28 (![X12,X13]: 109.58/110.28 ((in(X13,X3) & in(X12,X3)) => 109.58/110.28 ((![X14]: (in(X14,X13) => in(X14,X12))) | 109.58/110.28 (![X15]: (in(X15,X12) => in(X15,X13)))))) & 109.58/110.28 (![X16,X17]: 109.58/110.28 ((in(X17,X2) & in(X16,X2)) => 109.58/110.28 ((![X18]: (in(X18,X3) => (in(X16,X18) <=> in(X17,X18)))) => 109.58/110.28 (X16 = X17)))) & 109.58/110.28 (![X19]: (in(X19,X3) => (![X20]: (in(X20,X19) => in(X20,X2)))))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(foundationAx, axiom, foundationAx <=> 109.58/110.28 (![A]: 109.58/110.28 ((?[Xx]: in(Xx,A)) => 109.58/110.28 (?[B]: ((~(?[Xx]: (in(Xx,A) & in(Xx,B)))) & in(B,A)))))). 109.58/110.28 tff('196', plain, 109.58/110.28 foundationAx = 109.58/110.28 (![X2]: 109.58/110.28 ((?[X3]: in(X3,X2)) => 109.58/110.28 (?[X4]: ((~(?[X5]: (in(X5,X2) & in(X5,X4)))) & in(X4,X2))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(replAx, axiom, replAx <=> 109.58/110.28 (![Xphi:(($i * $i) > $o),A]: 109.58/110.28 ((![Xx]: (in(Xx,A) => exu(^[Xy]: Xphi(Xx,Xy)))) => 109.58/110.28 (?[B]: (![Xx]: (in(Xx,B) <=> (?[Xy]: (Xphi(Xy,Xx) & in(Xy,A))))))))). 109.58/110.28 tff('197', plain, 109.58/110.28 replAx = 109.58/110.28 (![X2:(($i * $i) > $o),X3]: 109.58/110.28 ((![X4]: (in(X4,X3) => exu(^[V_1]: X2(X4,V_1)))) => 109.58/110.28 (?[X5]: (![X6]: (in(X6,X5) <=> (?[X7]: (X2(X7,X6) & in(X7,X3)))))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(omegaIndAx, axiom, omegaIndAx <=> 109.58/110.28 (![A]: 109.58/110.28 (((![Xx]: ((in(Xx,A) & in(Xx,omega)) => in(setadjoin(Xx,Xx),A))) & 109.58/110.28 in(emptyset,A)) => 109.58/110.28 (![Xx]: (in(Xx,omega) => in(Xx,A)))))). 109.58/110.28 tff('198', plain, 109.58/110.28 omegaIndAx = 109.58/110.28 (![X2]: 109.58/110.28 (((![X3]: ((in(X3,X2) & in(X3,omega)) => in(setadjoin(X3,X3),X2))) & 109.58/110.28 in(emptyset,X2)) => 109.58/110.28 (![X4]: (in(X4,omega) => in(X4,X2))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(omegaSAx, axiom, omegaSAx <=> 109.58/110.28 (![Xx]: (in(Xx,omega) => in(setadjoin(Xx,Xx),omega)))). 109.58/110.28 tff('199', plain, 109.58/110.28 omegaSAx = (![X2]: (in(X2,omega) => in(setadjoin(X2,X2),omega))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(omega0Ax, axiom, omega0Ax() = in(emptyset,omega)). 109.58/110.28 tff('200', plain, omega0Ax = in(emptyset,omega), define([status(thm)])). 109.58/110.28 tff(setunionAx, axiom, setunionAx <=> 109.58/110.28 (![A,Xx]: (in(Xx,setunion(A)) <=> (?[B]: (in(B,A) & in(Xx,B)))))). 109.58/110.28 tff('201', plain, 109.58/110.28 setunionAx = 109.58/110.28 (![X2,X3]: (in(X3,setunion(X2)) <=> (?[X4]: (in(X4,X2) & in(X3,X4))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(powersetAx, axiom, powersetAx <=> 109.58/110.28 (![A,B]: (in(B,powerset(A)) <=> (![Xx]: (in(Xx,B) => in(Xx,A)))))). 109.58/110.28 tff('202', plain, 109.58/110.28 powersetAx = 109.58/110.28 (![X2,X3]: (in(X3,powerset(X2)) <=> (![X4]: (in(X4,X3) => in(X4,X2))))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(setadjoinAx, axiom, setadjoinAx <=> 109.58/110.28 (![Xx,A,Xy]: (in(Xy,setadjoin(Xx,A)) <=> (in(Xy,A) | (Xy = Xx))))). 109.58/110.28 tff('203', plain, 109.58/110.28 setadjoinAx = 109.58/110.28 (![X2,X3,X4]: (in(X4,setadjoin(X2,X3)) <=> (in(X4,X3) | (X4 = X2)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(emptysetAx, axiom, emptysetAx <=> (![Xx]: (~in(Xx,emptyset)))). 109.58/110.28 tff('204', plain, emptysetAx = (![X2]: (~in(X2,emptyset))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(setextAx, axiom, setextAx <=> 109.58/110.28 (![A,B]: ((![Xx]: (in(Xx,A) <=> in(Xx,B))) => (A = B)))). 109.58/110.28 tff('205', plain, 109.58/110.28 setextAx = (![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(exu, axiom, exu() = 109.58/110.28 ^[Xphi:($i > $o)]: (?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx)))). 109.58/110.28 tff('206', plain, 109.58/110.28 exu = 109.58/110.28 (^[V_1:($i > $o)]: (?[X2]: ((![X3]: (V_1(X3) => (X2 = X3))) & V_1(X2)))), 109.58/110.28 define([status(thm)])). 109.58/110.28 tff(ex1E2, conjecture, 109.58/110.28 (setextAx => 109.58/110.28 (emptysetAx => 109.58/110.28 (setadjoinAx => 109.58/110.28 (powersetAx => 109.58/110.28 (setunionAx => 109.58/110.28 (omega0Ax => 109.58/110.28 (omegaSAx => 109.58/110.28 (omegaIndAx => 109.58/110.28 (replAx => 109.58/110.28 (foundationAx => 109.58/110.28 (wellorderingAx => 109.58/110.28 (descrp => 109.58/110.28 (dsetconstrI => 109.58/110.28 (dsetconstrEL => 109.58/110.28 (dsetconstrER => 109.58/110.28 (exuE1 => 109.58/110.28 (prop2setE => 109.58/110.28 (emptysetE => 109.58/110.28 (emptysetimpfalse => 109.58/110.28 (notinemptyset => 109.58/110.28 (exuE3e => 109.58/110.28 (setext => 109.58/110.28 (emptyI => 109.58/110.28 (noeltsimpempty => 109.58/110.28 (setbeta => 109.58/110.28 (nonemptyE1 => 109.58/110.28 (nonemptyI => 109.58/110.28 (nonemptyI1 => 109.58/110.28 (setadjoinIL => 109.58/110.28 (emptyinunitempty => 109.58/110.28 (setadjoinIR => 109.58/110.28 (setadjoinE => 109.58/110.28 (setadjoinOr => 109.58/110.28 (setoftrueEq => 109.58/110.28 (powersetI => 109.58/110.28 (emptyinPowerset => 109.58/110.28 (emptyInPowerset => 109.58/110.28 (powersetE => 109.58/110.28 (setunionI => 109.58/110.28 (setunionE => 109.58/110.28 (subPowSU => 109.58/110.28 (exuE2 => 109.58/110.28 (nonemptyImpWitness => 109.58/110.28 (uniqinunit => 109.58/110.28 (notinsingleton => 109.58/110.28 (eqinunit => 109.58/110.28 (singletonsswitch => 109.58/110.28 (upairsetE => 109.58/110.28 (upairsetIL => 109.58/110.28 (upairsetIR => 109.58/110.28 (emptyE1 => 109.58/110.28 (vacuousDall => 109.58/110.28 (quantDeMorgan1 => 109.58/110.28 (quantDeMorgan2 => 109.58/110.28 (quantDeMorgan3 => 109.58/110.28 (quantDeMorgan4 => 109.58/110.28 (prop2setI => 109.58/110.28 (prop2set2propI => 109.58/110.28 (notdexE => 109.58/110.28 (notdallE => 109.58/110.28 (exuI1 => 109.58/110.28 (exuI3 => 109.58/110.28 (exuI2 => 109.58/110.28 (inCongP => 109.58/110.28 (in__Cong => 109.58/110.28 (exuE3u => 109.58/110.28 ( 109.58/110.28 exu__Cong => 109.58/110.28 ( 109.58/110.28 emptyset__Cong => 109.58/110.28 ( 109.58/110.28 setadjoin__Cong => 109.58/110.28 ( 109.58/110.28 powerset__Cong => 109.58/110.28 ( 109.58/110.28 setunion__Cong => 109.58/110.28 ( 109.58/110.28 omega__Cong => 109.58/110.28 ( 109.58/110.28 exuEu => 109.58/110.28 ( 109.58/110.28 descr__Cong => 109.58/110.28 ( 109.58/110.28 dsetconstr__Cong => 109.58/110.28 ( 109.58/110.28 subsetI1 => 109.58/110.28 ( 109.58/110.28 eqimpsubset2 => 109.58/110.28 ( 109.58/110.28 eqimpsubset1 => 109.58/110.28 ( 109.58/110.28 subsetI2 => 109.58/110.28 ( 109.58/110.28 emptysetsubset => 109.58/110.28 ( 109.58/110.28 subsetE => 109.58/110.28 ( 109.58/110.28 subsetE2 => 109.58/110.28 ( 109.58/110.28 notsubsetI => 109.58/110.28 ( 109.58/110.28 notequalI1 => 109.58/110.28 ( 109.58/110.28 notequalI2 => 109.58/110.28 ( 109.58/110.28 subsetRefl => 109.58/110.28 ( 109.58/110.28 subsetTrans => 109.58/110.28 ( 109.58/110.28 setadjoinSub => 109.58/110.28 ( 109.58/110.28 setadjoinSub2 => 109.58/110.28 ( 109.58/110.28 subset2powerset => 109.58/110.28 ( 109.58/110.28 setextsub => 109.58/110.28 ( 109.58/110.28 subsetemptysetimpeq => 109.58/110.28 ( 109.58/110.28 powersetI1 => 109.58/110.28 ( 109.58/110.28 powersetE1 => 109.58/110.28 ( 109.58/110.28 inPowerset => 109.58/110.28 ( 109.58/110.28 powersetsubset => 109.58/110.28 ( 109.58/110.28 sepInPowerset => 109.58/110.28 ( 109.58/110.28 sepSubset => 109.58/110.28 ( 109.58/110.28 binunionIL => 109.58/110.28 ( 109.58/110.28 upairset2IR => 109.58/110.28 ( 109.58/110.28 binunionIR => 109.58/110.28 ( 109.58/110.28 binunionEcases => 109.58/110.28 ( 109.58/110.28 binunionE => 109.58/110.28 ( 109.58/110.28 binunionLsub => 109.58/110.28 ( 109.58/110.28 binunionRsub => 109.58/110.28 ( 109.58/110.28 binintersectI => 109.58/110.28 ( 109.58/110.28 binintersectSubset5 => 109.58/110.28 ( 109.58/110.28 binintersectEL => 109.58/110.28 ( 109.58/110.28 binintersectLsub => 109.58/110.28 ( 109.58/110.28 binintersectSubset2 => 109.58/110.28 ( 109.58/110.28 binintersectSubset3 => 109.58/110.28 ( 109.58/110.28 binintersectER => 109.58/110.28 ( 109.58/110.28 disjointsetsI1 => 109.58/110.28 ( 109.58/110.28 binintersectRsub => 109.58/110.28 ( 109.58/110.28 binintersectSubset4 => 109.58/110.28 ( 109.58/110.28 binintersectSubset1 => 109.58/110.28 ( 109.58/110.28 bs114d => 109.58/110.28 ( 109.58/110.28 setminusI => 109.58/110.28 ( 109.58/110.28 setminusEL => 109.58/110.28 ( 109.58/110.28 setminusER => 109.58/110.28 ( 109.58/110.28 setminusSubset2 => 109.58/110.28 ( 109.58/110.28 setminusERneg => 109.58/110.28 ( 109.58/110.29 setminusELneg => 109.58/110.29 ( 109.58/110.29 setminusILneg => 109.58/110.29 ( 109.58/110.29 setminusIRneg => 109.58/110.29 ( 109.58/110.29 setminusLsub => 109.58/110.29 ( 109.58/110.29 setminusSubset1 => 109.58/110.29 ( 109.58/110.29 symdiffE => 109.58/110.29 ( 109.58/110.29 symdiffI1 => 109.58/110.29 ( 109.58/110.29 symdiffI2 => 109.58/110.29 ( 109.58/110.29 symdiffIneg1 => 109.58/110.29 ( 109.58/110.29 symdiffIneg2 => 109.58/110.29 ( 109.58/110.29 secondinupair => 109.58/110.29 ( 109.58/110.29 setukpairIL => 109.58/110.29 ( 109.58/110.29 setukpairIR => 109.58/110.29 ( 109.58/110.29 kpairiskpair => 109.58/110.29 ( 109.58/110.29 kpairp => 109.58/110.29 ( 109.58/110.29 singletonsubset => 109.58/110.29 ( 109.58/110.29 singletoninpowerset => 109.58/110.29 ( 109.58/110.29 singletoninpowunion => 109.58/110.29 ( 109.58/110.29 upairset2E => 109.58/110.29 ( 109.58/110.29 upairsubunion => 109.58/110.29 ( 109.58/110.29 upairinpowunion => 109.58/110.29 ( 109.58/110.29 ubforcartprodlem1 => 109.58/110.29 ( 109.58/110.29 ubforcartprodlem2 => 109.58/110.29 ( 109.58/110.29 ubforcartprodlem3 => 109.58/110.29 ( 109.58/110.29 cartprodpairin => 109.58/110.29 ( 109.58/110.29 cartprodmempair1 => 109.58/110.29 ( 109.58/110.29 cartprodmempair => 109.58/110.29 ( 109.58/110.29 setunionE2 => 109.58/110.29 ( 109.58/110.29 setunionsingleton1 => 109.58/110.29 ( 109.58/110.29 setunionsingleton2 => 109.58/110.29 ( 109.58/110.29 setunionsingleton => 109.58/110.29 ( 109.58/110.29 singletonprop => 109.58/110.29 ( 109.58/110.29 ex1E1 => 109.58/110.29 ( 109.58/110.29 ex1I => 109.58/110.29 ( 109.58/110.29 ex1I2 => 109.58/110.29 ( 109.58/110.29 singletonsuniq => 109.58/110.29 ( 109.58/110.29 setukpairinjL1 => 109.58/110.29 ( 109.58/110.29 kfstsingleton => 109.58/110.29 ( 109.58/110.29 theprop => 109.58/110.29 ( 109.58/110.29 kfstpairEq => 109.58/110.29 ( 109.58/110.29 cartprodfstin => 109.58/110.29 ( 109.58/110.29 setukpairinjL2 => 109.58/110.29 ( 109.58/110.29 setukpairinjL => 109.58/110.29 ( 109.58/110.29 setukpairinjR11 => 109.58/110.29 ( 109.58/110.29 setukpairinjR12 => 109.58/110.29 ( 109.58/110.29 setukpairinjR1 => 109.58/110.29 ( 109.58/110.29 upairequniteq => 109.58/110.29 ( 109.58/110.29 setukpairinjR2 => 109.58/110.29 ( 109.58/110.29 setukpairinjR => 109.58/110.29 ( 109.58/110.29 ksndsingleton => 109.58/110.29 ( 109.58/110.29 ksndpairEq => 109.58/110.29 ( 109.58/110.29 kpairsurjEq => 109.58/110.29 ( 109.58/110.29 cartprodsndin => 109.58/110.29 ( 109.58/110.29 cartprodpairmemEL => 109.58/110.29 ( 109.58/110.29 cartprodpairmemER => 109.58/110.29 ( 109.58/110.29 cartprodmempaircEq => 109.58/110.29 ( 109.58/110.29 cartprodfstpairEq => 109.58/110.29 ( 109.58/110.29 cartprodsndpairEq => 109.58/110.29 ( 109.58/110.29 cartprodpairsurjEq => 109.58/110.29 ( 109.58/110.29 dpsetconstrI => 109.58/110.29 ( 109.58/110.29 dpsetconstrSub => 109.58/110.29 ( 109.58/110.29 setOfPairsIsBReln => 109.58/110.29 ( 109.58/110.29 dpsetconstrERa => 109.58/110.29 ( 109.58/110.29 dpsetconstrEL1 => 109.58/110.29 ( 109.58/110.29 dpsetconstrEL2 => 109.58/110.29 ( 109.58/110.29 dpsetconstrER => 109.58/110.29 ( 109.58/110.29 funcImageSingleton => 109.58/110.29 ( 109.58/110.29 apProp => 109.58/110.29 ( 109.58/110.29 app => 109.58/110.29 ( 109.58/110.29 infuncsetfunc => 109.58/110.29 ( 109.58/110.29 ap2p => 109.58/110.29 ( 109.58/110.29 funcinfuncset => 109.58/110.29 ( 109.58/110.29 lamProp => 109.58/110.29 ( 109.58/110.29 lamp => 109.58/110.29 ( 109.58/110.29 lam2p => 109.58/110.29 ( 109.58/110.29 brelnall1 => 109.58/110.29 ( 109.58/110.29 brelnall2 => 109.58/110.29 ( 109.58/110.29 ![A, 109.58/110.29 Xphi:( 109.58/110.29 $i > $o)]: 109.58/110.29 (ex1( 109.58/110.29 A, 109.58/110.29 ^[Xx]: 109.58/110.29 Xphi(Xx)) => 109.58/110.29 (![Xx]: 109.58/110.29 (in(Xx,A) => 109.58/110.29 (![Xy]: 109.58/110.29 (in(Xy,A) => 109.58/110.29 (Xphi(Xx) => 109.58/110.29 (Xphi(Xy) => 109.58/110.29 (Xx = Xy))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 109.58/110.29 tff(zf_stmt_0, conjecture, 109.58/110.29 ((![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))) => 109.58/110.29 ((![X5]: (~in(X5,emptyset))) => 109.58/110.29 ((![X6,X7,X8]: (in(X8,setadjoin(X6,X7)) <=> ((X8 = X6) | in(X8,X7)))) => 109.58/110.29 ((![X9,X10]: 109.58/110.29 (in(X10,powerset(X9)) <=> (![X11]: (in(X11,X10) => in(X11,X9))))) => 109.58/110.29 ((![X12,X13]: 109.58/110.29 (in(X13,setunion(X12)) <=> (?[X14]: (in(X13,X14) & in(X14,X12))))) => 109.58/110.29 (in(emptyset,omega) => 109.58/110.29 ((![X15]: (in(X15,omega) => in(setadjoin(X15,X15),omega))) => 109.58/110.29 ((![X16]: 109.58/110.29 ((in(emptyset,X16) & 109.58/110.29 (![X17]: 109.58/110.29 ((in(X17,omega) & in(X17,X16)) => 109.58/110.29 in(setadjoin(X17,X17),X16)))) => 109.58/110.29 (![X18]: (in(X18,omega) => in(X18,X16))))) => 109.58/110.29 ((![X19:(($i * $i) > $o),X20]: 109.58/110.29 ((![X21]: 109.58/110.29 (in(X21,X20) => 109.58/110.29 (?[X22]: 109.58/110.29 (X19(X21,X22) & (![X23]: (X19(X21,X23) => (X22 = X23))))))) => 109.58/110.29 (?[X24]: 109.58/110.29 (![X25]: 109.58/110.29 (in(X25,X24) <=> (?[X26]: (in(X26,X20) & X19(X26,X25)))))))) => 109.58/110.29 ((![X27]: 109.58/110.29 ((?[X28]: in(X28,X27)) => 109.58/110.29 (?[X29]: 109.58/110.29 (in(X29,X27) & (~(?[X30]: (in(X30,X29) & in(X30,X27)))))))) => 109.58/110.29 ((![X31]: 109.58/110.29 (?[X32]: 109.58/110.29 ((![X48]: 109.58/110.29 (in(X48,X32) => (![X49]: (in(X49,X48) => in(X49,X31))))) & 109.58/110.29 (![X45,X46]: 109.58/110.29 ((in(X45,X31) & in(X46,X31)) => 109.58/110.29 ((![X47]: 109.58/110.29 (in(X47,X32) => (in(X45,X47) <=> in(X46,X47)))) => 109.58/110.29 (X45 = X46)))) & 109.58/110.29 (![X41,X42]: 109.58/110.29 ((in(X41,X32) & in(X42,X32)) => 109.58/110.29 ((![X44]: (in(X44,X41) => in(X44,X42))) | 109.58/110.29 (![X43]: (in(X43,X42) => in(X43,X41)))))) & 109.58/110.29 (![X33]: 109.58/110.29 (((![X35]: (in(X35,X33) => in(X35,X31))) & 109.58/110.29 (?[X34]: in(X34,X33))) => 109.58/110.29 (?[X36,X37]: 109.58/110.29 (in(X36,X32) & in(X37,X33) & 109.58/110.29 (~(?[X40]: (in(X40,X36) & in(X40,X33)))) & 109.58/110.29 (![X38]: 109.58/110.29 (in(X38,X32) => 109.58/110.29 ((![X39]: (in(X39,X38) => in(X39,X36))) | 109.58/110.29 in(X37,X38))))))))))) => 109.58/110.29 ((![X50:($i > $o)]: 109.58/110.29 ((?[X51]: (X50(X51) & (![X52]: (X50(X52) => (X51 = X52))))) => 109.58/110.29 X50(descr('#ll_0'(X50))))) => 109.58/110.29 ((![X53,X54:($i > $o),X55]: 109.58/110.29 (in(X55,X53) => 109.58/110.29 (X54(X55) => in(X55,dsetconstr(X53,'#ll_0'(X54)))))) => 109.58/110.29 ((![X56,X57:($i > $o),X58]: 109.58/110.29 (in(X58,dsetconstr(X56,'#ll_0'(X57))) => in(X58,X56))) => 109.58/110.29 ((![X59,X60:($i > $o),X61]: 109.58/110.29 (in(X61,dsetconstr(X59,'#ll_0'(X60))) => X60(X61))) => 109.58/110.29 ((![X62:($i > $o)]: 109.58/110.29 ((?[X63]: 109.58/110.29 (X62(X63) & (![X64]: (X62(X64) => (X63 = X64))))) => 109.58/110.29 (?[X65]: 109.58/110.29 (X62(X65) & (![X66]: (X62(X66) => (X65 = X66))))))) => 109.58/110.29 ((![X67:$o,X68]: (in(X68,prop2set(X67)) => X67)) => 109.58/110.29 ((![X69]: (in(X69,emptyset) => (![X70:$o]: X70))) => 109.58/110.29 ((![X71]: (in(X71,emptyset) => $false)) => 109.58/110.29 ((![X72]: (~in(X72,emptyset))) => 109.58/110.29 ((![X73:($i > $o)]: 109.58/110.29 ((?[X74]: 109.58/110.29 (X73(X74) & (![X75]: (X73(X75) => (X74 = X75))))) => 109.58/110.29 (?[X76]: X73(X76)))) => 109.58/110.29 ((![X77,X78]: 109.58/110.29 ((![X79]: (in(X79,X77) => in(X79,X78))) => 109.58/110.29 ((![X80]: (in(X80,X78) => in(X80,X77))) => 109.58/110.29 (X77 = X78)))) => 109.58/110.29 ((![X81]: 109.58/110.29 ((![X82]: (~in(X82,X81))) => (X81 = emptyset))) => 109.58/110.29 ((![X83]: 109.58/110.29 ((![X84]: (~in(X84,X83))) => (X83 = emptyset))) => 109.58/110.29 ((![X85,X86:($i > $o),X87]: 109.58/110.29 (in(X87,X85) => 109.58/110.29 (in(X87,dsetconstr(X85,'#ll_0'(X86))) <=> 109.58/110.29 X86(X87)))) => 109.58/110.29 ((![X88]: 109.58/110.29 ((X88 != emptyset) => (?[X89]: in(X89,X88)))) => 109.58/110.29 ((![X90,X91:($i > $o),X92]: 109.58/110.29 (in(X92,X90) => 109.58/110.29 (X91(X92) => 109.58/110.29 (dsetconstr(X90,'#ll_0'(X91)) != emptyset)))) => 109.58/110.29 ((![X93]: 109.58/110.29 ((?[X94]: in(X94,X93)) => (X93 != emptyset))) => 109.58/110.29 ((![X95,X96]: in(X95,setadjoin(X95,X96))) => 109.58/110.29 (in(emptyset,setadjoin(emptyset,emptyset)) => 109.58/110.29 ((![X97,X98,X99]: 109.58/110.29 (in(X99,X98) => 109.58/110.29 in(X99,setadjoin(X97,X98)))) => 109.58/110.29 ((![X100,X101,X102]: 109.58/110.29 (in(X102,setadjoin(X100,X101)) => 109.58/110.29 (![X103:$o]: 109.58/110.29 (((X102 = X100) => X103) => 109.58/110.29 ((in(X102,X101) => X103) => X103))))) => 109.58/110.29 ((![X104,X105,X106]: 109.58/110.29 (in(X106,setadjoin(X104,X105)) => 109.58/110.29 ((X106 = X104) | in(X106,X105)))) => 109.58/110.29 ((![X107]: 109.58/110.29 (dsetconstr(X107,'#ll_7') = X107)) => 109.58/110.29 ((![X108,X109]: 109.58/110.29 ((![X110]: 109.58/110.29 (in(X110,X109) => in(X110,X108))) => 109.58/110.29 in(X109,powerset(X108)))) => 109.58/110.29 ((![X111]: in(emptyset,powerset(X111))) => 109.58/110.29 ((![X112]: in(emptyset,powerset(X112))) => 109.58/110.29 ((![X113,X114,X115]: 109.58/110.29 (in(X114,powerset(X113)) => 109.58/110.29 (in(X115,X114) => in(X115,X113)))) => 109.58/110.29 ((![X116,X117,X118]: 109.58/110.29 (in(X117,X118) => 109.58/110.29 (in(X118,X116) => 109.58/110.29 in(X117,setunion(X116))))) => 109.58/110.29 ((![X119,X120]: 109.58/110.29 (in(X120,setunion(X119)) => 109.58/110.29 (![X121:$o]: 109.58/110.29 ((![X122]: 109.58/110.29 (in(X120,X122) => 109.58/110.29 (in(X122,X119) => X121))) => 109.58/110.29 X121)))) => 109.58/110.29 ((![X123,X124]: 109.58/110.29 (in(X124,X123) => 109.58/110.29 in(X124, 109.58/110.29 powerset(setunion(X123))))) => 109.58/110.29 ((![X125:($i > $o)]: 109.58/110.29 ((?[X126]: 109.58/110.29 (X125(X126) & 109.58/110.29 (![X127]: 109.58/110.29 (X125(X127) => 109.58/110.29 (X126 = X127))))) => 109.58/110.29 (?[X128]: 109.58/110.29 (![X129]: 109.58/110.29 (X125(X129) <=> 109.58/110.29 (X129 = X128)))))) => 109.58/110.29 ((![X130]: 109.58/110.29 ((X130 != emptyset) => 109.58/110.29 (?[X131]: in(X131,X130)))) => 109.58/110.29 ((![X132,X133]: 109.58/110.29 (in(X132, 109.58/110.29 setadjoin(X133,emptyset)) => 109.58/110.29 (X132 = X133))) => 109.58/110.29 ((![X134,X135]: 109.58/110.29 ((X134 != X135) => 109.58/110.29 (~ 109.58/110.29 in(X135, 109.58/110.29 setadjoin(X134, 109.58/110.29 emptyset))))) => 109.58/110.29 ((![X136,X137]: 109.58/110.29 ((X136 = X137) => 109.58/110.29 in(X136, 109.58/110.29 setadjoin(X137, 109.58/110.29 emptyset)))) => 109.58/110.29 ((![X138,X139]: 109.58/110.29 (in(X138, 109.58/110.29 setadjoin(X139, 109.58/110.29 emptyset)) => 109.58/110.29 in(X139, 109.58/110.29 setadjoin(X138, 109.58/110.29 emptyset)))) => 109.58/110.29 ((![X140,X141,X142]: 109.58/110.29 (in(X142, 109.58/110.29 setadjoin(X140, 109.58/110.29 setadjoin( 109.58/110.29 X141, 109.58/110.29 emptyset))) => 109.58/110.29 ((X142 = X140) | 109.58/110.29 (X142 = X141)))) => 109.58/110.29 ((![X143,X144]: 109.58/110.29 in(X143, 109.58/110.29 setadjoin(X143, 109.58/110.29 setadjoin( 109.58/110.29 X144, 109.58/110.29 emptyset)))) => 109.58/110.29 ((![X145,X146]: 109.58/110.29 in(X146, 109.58/110.29 setadjoin(X145, 109.58/110.29 setadjoin( 109.58/110.29 X146, 109.58/110.29 emptyset)))) => 109.58/110.29 ((![X147,X148:($i > $o)]: 109.58/110.29 ((?[X149]: 109.58/110.29 (in(X149,X147) & 109.58/110.29 X148(X149))) => 109.58/110.29 ((dsetconstr( 109.58/110.29 X147,'#ll_0'(X148)) = 109.58/110.29 emptyset) => 109.58/110.29 $false))) => 109.58/110.29 ((![X150:($i > $o),X151]: 109.58/110.29 (in(X151,emptyset) => 109.58/110.29 X150(X151))) => 109.58/110.29 ((![X152,X153:($i > $o)]: 109.58/110.29 ((~ 109.58/110.29 (![X154]: 109.58/110.29 (in(X154,X152) => 109.58/110.29 X153(X154)))) => 109.58/110.29 (?[X155]: 109.58/110.29 (in(X155,X152) & 109.58/110.29 (~X153(X155)))))) => 109.58/110.29 ((![X156, 109.58/110.29 X157:($i > $o)]: 109.58/110.29 ((![X158]: 109.58/110.29 (in(X158,X156) => 109.58/110.29 (~X157(X158)))) => 109.58/110.29 (~ 109.58/110.29 (?[X159]: 109.58/110.29 (in( 109.58/110.29 X159,X156) & 109.58/110.29 X157(X159)))))) => 109.58/110.29 ((![X160, 109.58/110.29 X161:($i > $o)]: 109.58/110.29 ((~ 109.58/110.29 (?[X162]: 109.58/110.29 (in( 109.58/110.29 X162,X160) & 109.58/110.29 X161(X162)))) => 109.58/110.29 (![X163]: 109.58/110.29 (in(X163,X160) => 109.58/110.29 (~X161(X163)))))) => 109.58/110.29 ((![X164, 109.58/110.29 X165:($i > $o)]: 109.58/110.29 ((?[X166]: 109.58/110.29 (in( 109.58/110.29 X166,X164) & 109.58/110.29 (~ 109.58/110.29 X165( 109.58/110.29 X166)))) => 109.58/110.29 (~ 109.58/110.29 (![X167]: 109.58/110.29 (in( 109.58/110.29 X167,X164) => 109.58/110.29 X165( 109.58/110.29 X167)))))) => 109.58/110.29 ((![X168:$o]: 109.58/110.29 (X168 => 109.58/110.29 in(emptyset, 109.58/110.29 prop2set( 109.58/110.29 X168)))) => 109.58/110.29 ((![X169:$o]: 109.58/110.29 (X169 => 109.58/110.29 set2prop( 109.58/110.29 prop2set( 109.58/110.29 X169)))) => 109.58/110.29 ((![X170, 109.58/110.29 X171:( 109.58/110.29 $i > $o)]: 109.58/110.29 ((~ 109.58/110.29 (?[X172]: 109.58/110.29 (in( 109.58/110.29 X172,X170) & 109.58/110.29 X171( 109.58/110.29 X172)))) => 109.58/110.29 (![X173]: 109.58/110.29 ( 109.58/110.29 in( 109.58/110.29 X173,X170) => 109.58/110.29 ( 109.58/110.29 ~ 109.58/110.29 X171( 109.58/110.29 X173)))))) => 109.58/110.29 ((![X174, 109.58/110.29 X175:( 109.58/110.29 $i > $o)]: 109.58/110.29 ((~ 109.58/110.29 ( 109.58/110.29 ![X176]: 109.58/110.29 (in( 109.58/110.29 X176,X174) => 109.58/110.29 X175( 109.58/110.29 X176)))) => 109.58/110.29 (?[X177]: 109.58/110.29 (in( 109.58/110.29 X177,X174) & 109.58/110.29 (~ 109.58/110.29 X175( 109.58/110.29 X177)))))) => 109.58/110.29 ((![X178:( 109.58/110.29 $i > $o)]: 109.58/110.29 ((?[X179]: 109.58/110.29 (X178( 109.58/110.29 X179) & 109.58/110.29 (![X180]: 109.58/110.29 (X178( 109.58/110.29 X180) => 109.58/110.29 (X179 = 109.58/110.29 X180))))) => 109.58/110.29 (?[X181]: 109.58/110.29 (X178( 109.58/110.29 X181) & 109.58/110.29 (![X182]: 109.58/110.29 (X178( 109.58/110.29 X182) => 109.58/110.29 (X181 = 109.58/110.29 X182))))))) => 109.58/110.29 ((![X183:( 109.58/110.29 $i > $o)]: 109.58/110.29 (( 109.58/110.29 ?[X184]: 109.58/110.29 X183( 109.58/110.29 X184)) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X185, 109.58/110.29 X186]: 109.58/110.29 (X183( 109.58/110.29 X185) => 109.58/110.29 (X183( 109.58/110.29 X186) => 109.58/110.29 (X185 = 109.58/110.29 X186)))) => 109.58/110.29 ( 109.58/110.29 ?[X187]: 109.58/110.29 (X183( 109.58/110.29 X187) & 109.58/110.29 (![X188]: 109.58/110.29 (X183( 109.58/110.29 X188) => 109.58/110.29 (X187 = 109.58/110.29 X188)))))))) => 109.58/110.29 ((![X189:( 109.58/110.29 $i > $o)]: 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ?[X190]: 109.58/110.29 (![X191]: 109.58/110.29 (X189( 109.58/110.29 X191) <=> 109.58/110.29 (X191 = 109.58/110.29 X190)))) => 109.58/110.29 ( 109.58/110.29 ?[X192]: 109.58/110.29 (X189( 109.58/110.29 X192) & 109.58/110.29 (![X193]: 109.58/110.29 (X189( 109.58/110.29 X193) => 109.58/110.29 (X192 = 109.58/110.29 X193))))))) => 109.58/110.29 ((![X194, 109.58/110.29 X195]: 109.58/110.29 (( 109.58/110.29 X194 = 109.58/110.29 X195) => 109.58/110.29 (![X196, 109.58/110.29 X197]: 109.58/110.29 (( 109.58/110.29 X196 = 109.58/110.29 X197) => 109.58/110.29 (in( 109.58/110.29 X196,X194) => 109.58/110.29 in( 109.58/110.29 X197,X195)))))) => 109.58/110.29 ((![X198, 109.58/110.29 X199]: 109.58/110.29 (( 109.58/110.29 X198 = 109.58/110.29 X199) => 109.58/110.29 (![X200, 109.58/110.29 X201]: 109.58/110.29 (( 109.58/110.29 X200 = 109.58/110.29 X201) => 109.58/110.29 (in( 109.58/110.29 X200,X198) <=> 109.58/110.29 in( 109.58/110.29 X201,X199)))))) => 109.58/110.29 (( 109.58/110.29 ![X202:( 109.58/110.29 $i > $o)]: 109.58/110.29 (( 109.58/110.29 ?[X203]: 109.58/110.29 (X202( 109.58/110.29 X203) & 109.58/110.29 (![X204]: 109.58/110.29 (X202( 109.58/110.29 X204) => 109.58/110.29 (X203 = 109.58/110.29 X204))))) => 109.58/110.29 (![X205, 109.58/110.29 X206]: 109.58/110.29 (X202( 109.58/110.29 X205) => 109.58/110.29 (X202( 109.58/110.29 X206) => 109.58/110.29 (X205 = 109.58/110.29 X206)))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X207:( 109.58/110.29 $i > $o), 109.58/110.29 X208:( 109.58/110.29 $i > $o)]: 109.58/110.29 (( 109.58/110.29 ![X209, 109.58/110.29 X210]: 109.58/110.29 (( 109.58/110.29 X209 = 109.58/110.29 X210) => 109.58/110.29 (X207( 109.58/110.29 X209) <=> 109.58/110.29 X208( 109.58/110.29 X210)))) => 109.58/110.29 (( 109.58/110.29 ?[X211]: 109.58/110.29 (X207( 109.58/110.29 X211) & 109.58/110.29 (![X212]: 109.58/110.29 (X207( 109.58/110.29 X212) => 109.58/110.29 (X211 = 109.58/110.29 X212))))) <=> 109.58/110.29 (?[X213]: 109.58/110.29 (X208( 109.58/110.29 X213) & 109.58/110.29 (![X214]: 109.58/110.29 (X208( 109.58/110.29 X214) => 109.58/110.29 (X213 = 109.58/110.29 X214)))))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 emptyset = 109.58/110.29 emptyset) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X215, 109.58/110.29 X216]: 109.58/110.29 (( 109.58/110.29 X215 = 109.58/110.29 X216) => 109.58/110.29 (![X217, 109.58/110.29 X218]: 109.58/110.29 (( 109.58/110.29 X217 = 109.58/110.29 X218) => 109.58/110.29 (setadjoin( 109.58/110.29 X215,X217) = 109.58/110.29 setadjoin( 109.58/110.29 X216,X218)))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X219, 109.58/110.29 X220]: 109.58/110.29 (( 109.58/110.29 X219 = 109.58/110.29 X220) => 109.58/110.29 (powerset( 109.58/110.29 X219) = 109.58/110.29 powerset( 109.58/110.29 X220)))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X221, 109.58/110.29 X222]: 109.58/110.29 (( 109.58/110.29 X221 = 109.58/110.29 X222) => 109.58/110.29 (setunion( 109.58/110.29 X221) = 109.58/110.29 setunion( 109.58/110.29 X222)))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 omega = 109.58/110.29 omega) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X223:( 109.58/110.29 $i > $o)]: 109.58/110.29 (( 109.58/110.29 ?[X224]: 109.58/110.29 (X223( 109.58/110.29 X224) & 109.58/110.29 (![X225]: 109.58/110.29 (X223( 109.58/110.29 X225) => 109.58/110.29 (X224 = 109.58/110.29 X225))))) => 109.58/110.29 (![X226, 109.58/110.29 X227]: 109.58/110.29 (X223( 109.58/110.29 X226) => 109.58/110.29 (X223( 109.58/110.29 X227) => 109.58/110.29 (X226 = 109.58/110.29 X227)))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X228:( 109.58/110.29 $i > $o), 109.58/110.29 X229:( 109.58/110.29 $i > $o)]: 109.58/110.29 (( 109.58/110.29 ![X230, 109.58/110.29 X231]: 109.58/110.29 (( 109.58/110.29 X230 = 109.58/110.29 X231) => 109.58/110.29 (X228( 109.58/110.29 X230) <=> 109.58/110.29 X229( 109.58/110.29 X231)))) => 109.58/110.29 (( 109.58/110.29 ?[X232]: 109.58/110.29 (X228( 109.58/110.29 X232) & 109.58/110.29 (![X233]: 109.58/110.29 (X228( 109.58/110.29 X233) => 109.58/110.29 (X232 = 109.58/110.29 X233))))) => 109.58/110.29 (( 109.58/110.29 ?[X234]: 109.58/110.29 (X229( 109.58/110.29 X234) & 109.58/110.29 (![X235]: 109.58/110.29 (X229( 109.58/110.29 X235) => 109.58/110.29 (X234 = 109.58/110.29 X235))))) => 109.58/110.29 (descr( 109.58/110.29 '#ll_0'( 109.58/110.29 X228)) = 109.58/110.29 descr( 109.58/110.29 '#ll_0'( 109.58/110.29 X229))))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X236, 109.58/110.29 X237]: 109.58/110.29 (( 109.58/110.29 X236 = 109.58/110.29 X237) => 109.58/110.29 (![X238:( 109.58/110.29 $i > $o), 109.58/110.29 X239:( 109.58/110.29 $i > $o)]: 109.58/110.29 (( 109.58/110.29 ![X240]: 109.58/110.29 (in( 109.58/110.29 X240,X236) => 109.58/110.29 (![X241]: 109.58/110.29 (in( 109.58/110.29 X241,X237) => 109.58/110.29 (( 109.58/110.29 X240 = 109.58/110.29 X241) => 109.58/110.29 (X238( 109.58/110.29 X240) <=> 109.58/110.29 X239( 109.58/110.29 X241))))))) => 109.58/110.29 (dsetconstr( 109.58/110.29 X236, 109.58/110.29 '#ll_0'( 109.58/110.29 X238)) = 109.58/110.29 dsetconstr( 109.58/110.29 X237, 109.58/110.29 '#ll_0'( 109.58/110.29 X239))))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X242, 109.58/110.29 X243]: 109.58/110.29 (( 109.58/110.29 ![X244]: 109.58/110.29 (in( 109.58/110.29 X244,X242) => 109.58/110.29 in( 109.58/110.29 X244,X243))) => 109.58/110.29 subset( 109.58/110.29 X242,X243))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X245, 109.58/110.29 X246]: 109.58/110.29 (( 109.58/110.29 X245 = 109.58/110.29 X246) => 109.58/110.29 subset( 109.58/110.29 X246,X245))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X247, 109.58/110.29 X248]: 109.58/110.29 (( 109.58/110.29 X247 = 109.58/110.29 X248) => 109.58/110.29 subset( 109.58/110.29 X247,X248))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X249, 109.58/110.29 X250]: 109.58/110.29 (( 109.58/110.29 ![X251]: 109.58/110.29 (in( 109.58/110.29 X251,X249) => 109.58/110.29 in( 109.58/110.29 X251,X250))) => 109.58/110.29 subset( 109.58/110.29 X249,X250))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X252]: 109.58/110.29 subset( 109.58/110.29 emptyset, 109.58/110.29 X252)) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X253, 109.58/110.29 X254,X255]: 109.58/110.29 (subset( 109.58/110.29 X253,X254) => 109.58/110.29 (in( 109.58/110.29 X255,X253) => 109.58/110.29 in( 109.58/110.29 X255,X254)))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X256, 109.58/110.29 X257,X258]: 109.58/110.29 (subset( 109.58/110.29 X256,X257) => 109.58/110.29 (( 109.58/110.29 ~ 109.58/110.29 in( 109.58/110.29 X258,X257)) => 109.58/110.29 (~ 109.58/110.29 in( 109.58/110.29 X258,X256))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X259, 109.58/110.29 X260,X261]: 109.58/110.29 (in( 109.58/110.29 X261,X259) => 109.58/110.29 (( 109.58/110.29 ~ 109.58/110.29 in( 109.58/110.29 X261,X260)) => 109.58/110.29 (~ 109.58/110.29 subset( 109.58/110.29 X259,X260))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X262, 109.58/110.29 X263]: 109.58/110.29 (( 109.58/110.29 ~ 109.58/110.29 subset( 109.58/110.29 X262,X263)) => 109.58/110.29 (X262 != 109.58/110.29 X263))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X264, 109.58/110.29 X265,X266]: 109.58/110.29 (in( 109.58/110.29 X266,X264) => 109.58/110.29 (( 109.58/110.29 ~ 109.58/110.29 in( 109.58/110.29 X266,X265)) => 109.58/110.29 (X264 != 109.58/110.29 X265)))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X267]: 109.58/110.29 subset( 109.58/110.29 X267,X267)) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X268, 109.58/110.29 X269,X270]: 109.58/110.29 (subset( 109.58/110.29 X268,X269) => 109.58/110.29 (subset( 109.58/110.29 X269,X270) => 109.58/110.29 subset( 109.58/110.29 X268,X270)))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X271, 109.58/110.29 X272]: 109.58/110.29 subset( 109.58/110.29 X272, 109.58/110.29 setadjoin( 109.58/110.29 X271,X272))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X273, 109.58/110.29 X274,X275]: 109.58/110.29 (subset( 109.58/110.29 X273,X275) => 109.58/110.29 subset( 109.58/110.29 X273, 109.58/110.29 setadjoin( 109.58/110.29 X274,X275)))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X276, 109.58/110.29 X277]: 109.58/110.29 (subset( 109.58/110.29 X276,X277) => 109.58/110.29 in( 109.58/110.29 X276, 109.58/110.29 powerset( 109.58/110.29 X277)))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X278, 109.58/110.29 X279]: 109.58/110.29 (subset( 109.58/110.29 X278,X279) => 109.58/110.29 (subset( 109.58/110.29 X279,X278) => 109.58/110.29 (X278 = 109.58/110.29 X279)))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X280]: 109.58/110.29 (subset( 109.58/110.29 X280, 109.58/110.29 emptyset) => 109.58/110.29 (X280 = 109.58/110.29 emptyset))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X281, 109.58/110.29 X282]: 109.58/110.29 (subset( 109.58/110.29 X282,X281) => 109.58/110.29 in( 109.58/110.29 X282, 109.58/110.29 powerset( 109.58/110.29 X281)))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X283, 109.58/110.29 X284]: 109.58/110.29 (in( 109.58/110.29 X284, 109.58/110.29 powerset( 109.58/110.29 X283)) => 109.58/110.29 subset( 109.58/110.29 X284,X283))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X285]: 109.58/110.29 in( 109.58/110.29 X285, 109.58/110.29 powerset( 109.58/110.29 X285))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X286, 109.58/110.29 X287]: 109.58/110.29 (subset( 109.58/110.29 X286,X287) => 109.58/110.29 subset( 109.58/110.29 powerset( 109.58/110.29 X286), 109.58/110.29 powerset( 109.58/110.29 X287)))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X288, 109.58/110.29 X289:( 109.58/110.29 $i > $o)]: 109.58/110.29 in( 109.58/110.29 dsetconstr( 109.58/110.29 X288, 109.58/110.29 '#ll_0'( 109.58/110.29 X289)), 109.58/110.29 powerset( 109.58/110.29 X288))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X290, 109.58/110.29 X291:( 109.58/110.29 $i > $o)]: 109.58/110.29 subset( 109.58/110.29 dsetconstr( 109.58/110.29 X290, 109.58/110.29 '#ll_0'( 109.58/110.29 X291)), 109.58/110.29 X290)) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X292, 109.58/110.29 X293,X294]: 109.58/110.29 (in( 109.58/110.29 X294,X292) => 109.58/110.29 in( 109.58/110.29 X294, 109.58/110.29 binunion( 109.58/110.29 X292,X293)))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X295, 109.58/110.29 X296]: 109.58/110.29 in( 109.58/110.29 X296, 109.58/110.29 setadjoin( 109.58/110.29 X295, 109.58/110.29 setadjoin( 109.58/110.29 X296, 109.58/110.29 emptyset)))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X297, 109.58/110.29 X298,X299]: 109.58/110.29 (in( 109.58/110.29 X299,X298) => 109.58/110.29 in( 109.58/110.29 X299, 109.58/110.29 binunion( 109.58/110.29 X297,X298)))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X300, 109.58/110.29 X301, 109.58/110.29 X302, 109.58/110.29 X303:$o]: 109.58/110.29 (in( 109.58/110.29 X302, 109.58/110.29 binunion( 109.58/110.29 X300,X301)) => 109.58/110.29 (( 109.58/110.29 in( 109.58/110.29 X302,X300) => 109.58/110.29 X303) => 109.58/110.29 (( 109.58/110.29 in( 109.58/110.29 X302,X301) => 109.58/110.29 X303) => 109.58/110.29 X303)))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X304, 109.58/110.29 X305,X306]: 109.58/110.29 (in( 109.58/110.29 X306, 109.58/110.29 binunion( 109.58/110.29 X304,X305)) => 109.58/110.29 (in( 109.58/110.29 X306,X304) | 109.58/110.29 in( 109.58/110.29 X306,X305)))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X307, 109.58/110.29 X308]: 109.58/110.29 subset( 109.58/110.29 X307, 109.58/110.29 binunion( 109.58/110.29 X307,X308))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X309, 109.58/110.29 X310]: 109.58/110.29 subset( 109.58/110.29 X310, 109.58/110.29 binunion( 109.58/110.29 X309,X310))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X311, 109.58/110.29 X312,X313]: 109.58/110.29 (in( 109.58/110.29 X313,X311) => 109.58/110.29 (in( 109.58/110.29 X313,X312) => 109.58/110.29 in( 109.58/110.29 X313, 109.58/110.29 binintersect( 109.58/110.29 X311,X312))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X314, 109.58/110.29 X315,X316]: 109.58/110.29 (subset( 109.58/110.29 X316,X314) => 109.58/110.29 (subset( 109.58/110.29 X316,X315) => 109.58/110.29 subset( 109.58/110.29 X316, 109.58/110.29 binintersect( 109.58/110.29 X314,X315))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X317, 109.58/110.29 X318,X319]: 109.58/110.29 (in( 109.58/110.29 X319, 109.58/110.29 binintersect( 109.58/110.29 X317,X318)) => 109.58/110.29 in( 109.58/110.29 X319,X317))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X320, 109.58/110.29 X321]: 109.58/110.29 subset( 109.58/110.29 binintersect( 109.58/110.29 X320,X321), 109.58/110.29 X320)) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X322, 109.58/110.29 X323]: 109.58/110.29 (subset( 109.58/110.29 X322,X323) => 109.58/110.29 (binintersect( 109.58/110.29 X322,X323) = 109.58/110.29 X322))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X324, 109.58/110.29 X325]: 109.58/110.29 (( 109.58/110.29 binintersect( 109.58/110.29 X324,X325) = 109.58/110.29 X325) => 109.58/110.29 subset( 109.58/110.29 X325,X324))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X326, 109.58/110.29 X327,X328]: 109.58/110.29 (in( 109.58/110.29 X328, 109.58/110.29 binintersect( 109.58/110.29 X326,X327)) => 109.58/110.29 in( 109.58/110.29 X328,X327))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X329, 109.58/110.29 X330]: 109.58/110.29 (( 109.58/110.29 ~ 109.58/110.29 ( 109.58/110.29 ?[X331]: 109.58/110.29 (in( 109.58/110.29 X331,X329) & 109.58/110.29 in( 109.58/110.29 X331,X330)))) => 109.58/110.29 (binintersect( 109.58/110.29 X329,X330) = 109.58/110.29 emptyset))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X332, 109.58/110.29 X333]: 109.58/110.29 subset( 109.58/110.29 binintersect( 109.58/110.29 X332,X333), 109.58/110.29 X333)) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X334, 109.58/110.29 X335]: 109.58/110.29 (subset( 109.58/110.29 X335,X334) => 109.58/110.29 (binintersect( 109.58/110.29 X334,X335) = 109.58/110.29 X335))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X336, 109.58/110.29 X337]: 109.58/110.29 (( 109.58/110.29 binintersect( 109.58/110.29 X336,X337) = 109.58/110.29 X336) => 109.58/110.29 subset( 109.58/110.29 X336,X337))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X338, 109.58/110.29 X339,X340]: 109.58/110.29 (binintersect( 109.58/110.29 X338, 109.58/110.29 binunion( 109.58/110.29 X339,X340)) = 109.58/110.29 binunion( 109.58/110.29 binintersect( 109.58/110.29 X338,X339), 109.58/110.29 binintersect( 109.58/110.29 X338,X340)))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X341, 109.58/110.29 X342,X343]: 109.58/110.29 (in( 109.58/110.29 X343,X341) => 109.58/110.29 (( 109.58/110.29 ~ 109.58/110.29 in( 109.58/110.29 X343,X342)) => 109.58/110.29 in( 109.58/110.29 X343, 109.58/110.29 setminus( 109.58/110.29 X341,X342))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X344, 109.58/110.29 X345,X346]: 109.58/110.29 (in( 109.58/110.29 X346, 109.58/110.29 setminus( 109.58/110.29 X344,X345)) => 109.58/110.29 in( 109.58/110.29 X346,X344))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X347, 109.58/110.29 X348,X349]: 109.58/110.29 (in( 109.58/110.29 X349, 109.58/110.29 setminus( 109.58/110.29 X347,X348)) => 109.58/110.29 (~ 109.58/110.29 in( 109.58/110.29 X349,X348)))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X350, 109.58/110.29 X351]: 109.58/110.29 (subset( 109.58/110.29 X350,X351) => 109.58/110.29 (setminus( 109.58/110.29 X350,X351) = 109.58/110.29 emptyset))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X352, 109.58/110.29 X353,X354]: 109.58/110.29 (( 109.58/110.29 ~ 109.58/110.29 in( 109.58/110.29 X354, 109.58/110.29 setminus( 109.58/110.29 X352,X353))) => 109.58/110.29 (in( 109.58/110.29 X354,X352) => 109.58/110.29 in( 109.58/110.29 X354,X353)))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X355, 109.58/110.29 X356,X357]: 109.58/110.29 (( 109.58/110.29 ~ 109.58/110.29 in( 109.58/110.29 X357, 109.58/110.29 setminus( 109.58/110.29 X355,X356))) => 109.58/110.29 (( 109.58/110.29 ~ 109.58/110.29 in( 109.58/110.29 X357,X356)) => 109.58/110.29 (~ 109.58/110.29 in( 109.58/110.29 X357,X355))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X358, 109.58/110.29 X359,X360]: 109.58/110.29 (( 109.58/110.29 ~ 109.58/110.29 in( 109.58/110.29 X360,X358)) => 109.58/110.29 (~ 109.58/110.29 in( 109.58/110.29 X360, 109.58/110.29 setminus( 109.58/110.29 X358,X359))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X361, 109.58/110.29 X362,X363]: 109.58/110.29 (in( 109.58/110.29 X363,X362) => 109.58/110.29 (~ 109.58/110.29 in( 109.58/110.29 X363, 109.58/110.29 setminus( 109.58/110.29 X361,X362))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X364, 109.58/110.29 X365]: 109.58/110.29 subset( 109.58/110.29 setminus( 109.58/110.29 X364,X365), 109.58/110.29 X364)) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X366, 109.58/110.29 X367]: 109.58/110.29 (( 109.58/110.29 setminus( 109.58/110.29 X366,X367) = 109.58/110.29 emptyset) => 109.58/110.29 subset( 109.58/110.29 X366,X367))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X368, 109.58/110.29 X369,X370]: 109.58/110.29 (in( 109.58/110.29 X370, 109.58/110.29 symdiff( 109.58/110.29 X368,X369)) => 109.58/110.29 (![X371:$o]: 109.58/110.29 (( 109.58/110.29 in( 109.58/110.29 X370,X368) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ~ 109.58/110.29 in( 109.58/110.29 X370,X369)) => 109.58/110.29 X371)) => 109.58/110.29 (( 109.58/110.29 ( 109.58/110.29 ~ 109.58/110.29 in( 109.58/110.29 X370,X368)) => 109.58/110.29 ( 109.58/110.29 in( 109.58/110.29 X370,X369) => 109.58/110.29 X371)) => 109.58/110.29 X371))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X372, 109.58/110.29 X373,X374]: 109.58/110.29 (in( 109.58/110.29 X374,X372) => 109.58/110.29 (( 109.58/110.29 ~ 109.58/110.29 in( 109.58/110.29 X374,X373)) => 109.58/110.29 in( 109.58/110.29 X374, 109.58/110.29 symdiff( 109.58/110.29 X372,X373))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X375, 109.58/110.29 X376,X377]: 109.58/110.29 (( 109.58/110.29 ~ 109.58/110.29 in( 109.58/110.29 X377,X375)) => 109.58/110.29 (in( 109.58/110.29 X377,X376) => 109.58/110.29 in( 109.58/110.29 X377, 109.58/110.29 symdiff( 109.58/110.29 X375,X376))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X378, 109.58/110.29 X379,X380]: 109.58/110.29 (in( 109.58/110.29 X380,X378) => 109.58/110.29 (in( 109.58/110.29 X380,X379) => 109.58/110.29 (~ 109.58/110.29 in( 109.58/110.29 X380, 109.58/110.29 symdiff( 109.58/110.29 X378,X379)))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X381, 109.58/110.29 X382,X383]: 109.58/110.29 (( 109.58/110.29 ~ 109.58/110.29 in( 109.58/110.29 X383,X381)) => 109.58/110.29 (( 109.58/110.29 ~ 109.58/110.29 in( 109.58/110.29 X383,X382)) => 109.58/110.29 (~ 109.58/110.29 in( 109.58/110.29 X383, 109.58/110.29 symdiff( 109.58/110.29 X381,X382)))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X384, 109.58/110.29 X385]: 109.58/110.29 in( 109.58/110.29 X385, 109.58/110.29 setadjoin( 109.58/110.29 X384, 109.58/110.29 setadjoin( 109.58/110.29 X385, 109.58/110.29 emptyset)))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X386, 109.58/110.29 X387]: 109.58/110.29 in( 109.58/110.29 X386, 109.58/110.29 setunion( 109.58/110.29 setadjoin( 109.58/110.29 setadjoin( 109.58/110.29 X386, 109.58/110.29 emptyset), 109.58/110.29 setadjoin( 109.58/110.29 setadjoin( 109.58/110.29 X386, 109.58/110.29 setadjoin( 109.58/110.29 X387, 109.58/110.29 emptyset)), 109.58/110.29 emptyset))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X388, 109.58/110.29 X389]: 109.58/110.29 in( 109.58/110.29 X389, 109.58/110.29 setunion( 109.58/110.29 setadjoin( 109.58/110.29 setadjoin( 109.58/110.29 X388, 109.58/110.29 emptyset), 109.58/110.29 setadjoin( 109.58/110.29 setadjoin( 109.58/110.29 X388, 109.58/110.29 setadjoin( 109.58/110.29 X389, 109.58/110.29 emptyset)), 109.58/110.29 emptyset))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X390, 109.58/110.29 X391]: 109.58/110.29 iskpair( 109.58/110.29 setadjoin( 109.58/110.29 setadjoin( 109.58/110.29 X390, 109.58/110.29 emptyset), 109.58/110.29 setadjoin( 109.58/110.29 setadjoin( 109.58/110.29 X390, 109.58/110.29 setadjoin( 109.58/110.29 X391, 109.58/110.29 emptyset)), 109.58/110.29 emptyset)))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X392, 109.58/110.29 X393]: 109.58/110.29 iskpair( 109.58/110.29 kpair( 109.58/110.29 X392,X393))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X394, 109.58/110.29 X395]: 109.58/110.29 (in( 109.58/110.29 X395,X394) => 109.58/110.29 subset( 109.58/110.29 setadjoin( 109.58/110.29 X395, 109.58/110.29 emptyset), 109.58/110.29 X394))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X396, 109.58/110.29 X397]: 109.58/110.29 (in( 109.58/110.29 X397,X396) => 109.58/110.29 in( 109.58/110.29 setadjoin( 109.58/110.29 X397, 109.58/110.29 emptyset), 109.58/110.29 powerset( 109.58/110.29 X396)))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X398, 109.58/110.29 X399,X400]: 109.58/110.29 (in( 109.58/110.29 X400,X398) => 109.58/110.29 in( 109.58/110.29 setadjoin( 109.58/110.29 X400, 109.58/110.29 emptyset), 109.58/110.29 powerset( 109.58/110.29 binunion( 109.58/110.29 X398,X399))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X401, 109.58/110.29 X402,X403]: 109.58/110.29 (in( 109.58/110.29 X403, 109.58/110.29 setadjoin( 109.58/110.29 X401, 109.58/110.29 setadjoin( 109.58/110.29 X402, 109.58/110.29 emptyset))) => 109.58/110.29 (( 109.58/110.29 X403 = 109.58/110.29 X401) | 109.58/110.29 (X403 = 109.58/110.29 X402)))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X404, 109.58/110.29 X405,X406]: 109.58/110.29 (in( 109.58/110.29 X406,X404) => 109.58/110.29 (![X407]: 109.58/110.29 (in( 109.58/110.29 X407,X405) => 109.58/110.29 subset( 109.58/110.29 setadjoin( 109.58/110.29 X406, 109.58/110.29 setadjoin( 109.58/110.29 X407, 109.58/110.29 emptyset)), 109.58/110.29 binunion( 109.58/110.29 X404,X405)))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X408, 109.58/110.29 X409,X410]: 109.58/110.29 (in( 109.58/110.29 X410,X408) => 109.58/110.29 (![X411]: 109.58/110.29 (in( 109.58/110.29 X411,X409) => 109.58/110.29 in( 109.58/110.29 setadjoin( 109.58/110.29 X410, 109.58/110.29 setadjoin( 109.58/110.29 X411, 109.58/110.29 emptyset)), 109.58/110.29 powerset( 109.58/110.29 binunion( 109.58/110.29 X408,X409))))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X412, 109.58/110.29 X413,X414]: 109.58/110.29 (in( 109.58/110.29 X414,X412) => 109.58/110.29 (![X415]: 109.58/110.29 (in( 109.58/110.29 X415,X413) => 109.58/110.29 subset( 109.58/110.29 setadjoin( 109.58/110.29 setadjoin( 109.58/110.29 X414, 109.58/110.29 emptyset), 109.58/110.29 setadjoin( 109.58/110.29 setadjoin( 109.58/110.29 X414, 109.58/110.29 setadjoin( 109.58/110.29 X415, 109.58/110.29 emptyset)), 109.58/110.29 emptyset)), 109.58/110.29 powerset( 109.58/110.29 binunion( 109.58/110.29 X412,X413))))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X416, 109.58/110.29 X417,X418]: 109.58/110.29 (in( 109.58/110.29 X418,X416) => 109.58/110.29 (![X419]: 109.58/110.29 (in( 109.58/110.29 X419,X417) => 109.58/110.29 in( 109.58/110.29 setadjoin( 109.58/110.29 setadjoin( 109.58/110.29 X418, 109.58/110.29 emptyset), 109.58/110.29 setadjoin( 109.58/110.29 setadjoin( 109.58/110.29 X418, 109.58/110.29 setadjoin( 109.58/110.29 X419, 109.58/110.29 emptyset)), 109.58/110.29 emptyset)), 109.58/110.29 powerset( 109.58/110.29 powerset( 109.58/110.29 binunion( 109.58/110.29 X416,X417)))))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X420, 109.58/110.29 X421,X422]: 109.58/110.29 (in( 109.58/110.29 X422,X420) => 109.58/110.29 (![X423]: 109.58/110.29 (in( 109.58/110.29 X423,X421) => 109.58/110.29 in( 109.58/110.29 kpair( 109.58/110.29 X422,X423), 109.58/110.29 powerset( 109.58/110.29 powerset( 109.58/110.29 binunion( 109.58/110.29 X420,X421)))))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X424, 109.58/110.29 X425,X426]: 109.58/110.29 (in( 109.58/110.29 X426,X424) => 109.58/110.29 (![X427]: 109.58/110.29 (in( 109.58/110.29 X427,X425) => 109.58/110.29 in( 109.58/110.29 kpair( 109.58/110.29 X426,X427), 109.58/110.29 cartprod( 109.58/110.29 X424,X425)))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X428, 109.58/110.29 X429,X430]: 109.58/110.29 (in( 109.58/110.29 X430, 109.58/110.29 cartprod( 109.58/110.29 X428,X429)) => 109.58/110.29 (?[X431]: 109.58/110.29 (in( 109.58/110.29 X431,X428) & 109.58/110.29 (?[X432]: 109.58/110.29 (in( 109.58/110.29 X432,X429) & 109.58/110.29 (X430 = 109.58/110.29 kpair( 109.58/110.29 X431,X432)))))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X433, 109.58/110.29 X434,X435]: 109.58/110.29 (in( 109.58/110.29 X435, 109.58/110.29 cartprod( 109.58/110.29 X433,X434)) => 109.58/110.29 iskpair( 109.58/110.29 X435))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X436, 109.58/110.29 X437]: 109.58/110.29 (in( 109.58/110.29 X437, 109.58/110.29 setunion( 109.58/110.29 X436)) => 109.58/110.29 (?[X438]: 109.58/110.29 (in( 109.58/110.29 X438,X436) & 109.58/110.29 in( 109.58/110.29 X437,X438))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X439]: 109.58/110.29 subset( 109.58/110.29 setunion( 109.58/110.29 setadjoin( 109.58/110.29 X439, 109.58/110.29 emptyset)), 109.58/110.29 X439)) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X440]: 109.58/110.29 subset( 109.58/110.29 X440, 109.58/110.29 setunion( 109.58/110.29 setadjoin( 109.58/110.29 X440, 109.58/110.29 emptyset)))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X441]: 109.58/110.29 (setunion( 109.58/110.29 setadjoin( 109.58/110.29 X441, 109.58/110.29 emptyset)) = 109.58/110.29 X441)) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X442, 109.58/110.29 X443:( 109.58/110.29 $i > $o)]: 109.58/110.29 (( 109.58/110.29 ![X444]: 109.58/110.29 (in( 109.58/110.29 X444,X442) => 109.58/110.29 (![X445]: 109.58/110.29 (in( 109.58/110.29 X445,X442) => 109.58/110.29 (X443( 109.58/110.29 X444) => 109.58/110.29 (X443( 109.58/110.29 X445) => 109.58/110.29 (X444 = 109.58/110.29 X445))))))) => 109.58/110.29 (( 109.58/110.29 ?[X446]: 109.58/110.29 (in( 109.58/110.29 X446,X442) & 109.58/110.29 X443( 109.58/110.29 X446))) => 109.58/110.29 (?[X447]: 109.58/110.29 (in( 109.58/110.29 X447, 109.58/110.29 dsetconstr( 109.58/110.29 X442, 109.58/110.29 '#ll_0'( 109.58/110.29 X443))) & 109.58/110.29 (dsetconstr( 109.58/110.29 X442, 109.58/110.29 '#ll_0'( 109.58/110.29 X443)) = 109.58/110.29 setadjoin( 109.58/110.29 X447, 109.58/110.29 emptyset))))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X448, 109.58/110.29 X449:( 109.58/110.29 $i > $o)]: 109.58/110.29 (( 109.58/110.29 ?[X450]: 109.58/110.29 (in( 109.58/110.29 X450, 109.58/110.29 dsetconstr( 109.58/110.29 X448, 109.58/110.29 '#ll_0'( 109.58/110.29 X449))) & 109.58/110.29 (dsetconstr( 109.58/110.29 X448, 109.58/110.29 '#ll_0'( 109.58/110.29 X449)) = 109.58/110.29 setadjoin( 109.58/110.29 X450, 109.58/110.29 emptyset)))) => 109.58/110.29 (?[X451]: 109.58/110.29 (in( 109.58/110.29 X451,X448) & 109.58/110.29 X449( 109.58/110.29 X451))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X452, 109.58/110.29 X453:( 109.58/110.29 $i > $o), 109.58/110.29 X454]: 109.58/110.29 (in( 109.58/110.29 X454,X452) => 109.58/110.29 (X453( 109.58/110.29 X454) => 109.58/110.29 (( 109.58/110.29 ![X455]: 109.58/110.29 (in( 109.58/110.29 X455,X452) => 109.58/110.29 (X453( 109.58/110.29 X455) => 109.58/110.29 (X455 = 109.58/110.29 X454)))) => 109.58/110.29 (?[X456]: 109.58/110.29 (in( 109.58/110.29 X456, 109.58/110.29 dsetconstr( 109.58/110.29 X452, 109.58/110.29 '#ll_0'( 109.58/110.29 X453))) & 109.58/110.29 (dsetconstr( 109.58/110.29 X452, 109.58/110.29 '#ll_0'( 109.58/110.29 X453)) = 109.58/110.29 setadjoin( 109.58/110.29 X456, 109.58/110.29 emptyset)))))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X457, 109.58/110.29 X458:( 109.58/110.29 $i > $o)]: 109.58/110.29 (( 109.58/110.29 ![X459]: 109.58/110.29 (in( 109.58/110.29 X459,X457) => 109.58/110.29 (![X460]: 109.58/110.29 (in( 109.58/110.29 X460,X457) => 109.58/110.29 (X458( 109.58/110.29 X459) => 109.58/110.29 (X458( 109.58/110.29 X460) => 109.58/110.29 (X459 = 109.58/110.29 X460))))))) => 109.58/110.29 (( 109.58/110.29 ?[X461]: 109.58/110.29 (in( 109.58/110.29 X461,X457) & 109.58/110.29 X458( 109.58/110.29 X461))) => 109.58/110.29 (?[X462]: 109.58/110.29 (in( 109.58/110.29 X462, 109.58/110.29 dsetconstr( 109.58/110.29 X457, 109.58/110.29 '#ll_0'( 109.58/110.29 X458))) & 109.58/110.29 (dsetconstr( 109.58/110.29 X457, 109.58/110.29 '#ll_0'( 109.58/110.29 X458)) = 109.58/110.29 setadjoin( 109.58/110.29 X462, 109.58/110.29 emptyset))))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X463, 109.58/110.29 X464]: 109.58/110.29 (( 109.58/110.29 setadjoin( 109.58/110.29 X463, 109.58/110.29 emptyset) = 109.58/110.29 setadjoin( 109.58/110.29 X464, 109.58/110.29 emptyset)) => 109.58/110.29 (X463 = 109.58/110.29 X464))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X465, 109.58/110.29 X466,X467]: 109.58/110.29 (in( 109.58/110.29 setadjoin( 109.58/110.29 X467, 109.58/110.29 emptyset), 109.58/110.29 setadjoin( 109.58/110.29 setadjoin( 109.58/110.29 X465, 109.58/110.29 emptyset), 109.58/110.29 setadjoin( 109.58/110.29 setadjoin( 109.58/110.29 X465, 109.58/110.29 setadjoin( 109.58/110.29 X466, 109.58/110.29 emptyset)), 109.58/110.29 emptyset))) => 109.58/110.29 (X465 = 109.58/110.29 X467))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X468]: 109.58/110.29 (iskpair( 109.58/110.29 X468) => 109.58/110.29 (?[X469]: 109.58/110.29 (in( 109.58/110.29 X469, 109.58/110.29 dsetconstr( 109.58/110.29 setunion( 109.58/110.29 X468), 109.58/110.29 '#ll_6'( 109.58/110.29 X468))) & 109.58/110.29 (dsetconstr( 109.58/110.29 setunion( 109.58/110.29 X468), 109.58/110.29 '#ll_6'( 109.58/110.29 X468)) = 109.58/110.29 setadjoin( 109.58/110.29 X469, 109.58/110.29 emptyset)))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X470]: 109.58/110.29 (( 109.58/110.29 ?[X471]: 109.58/110.29 (in( 109.58/110.29 X471,X470) & 109.58/110.29 (X470 = 109.58/110.29 setadjoin( 109.58/110.29 X471, 109.58/110.29 emptyset)))) => 109.58/110.29 in( 109.58/110.29 setunion( 109.58/110.29 X470), 109.58/110.29 X470))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X472, 109.58/110.29 X473]: 109.58/110.29 (kfst( 109.58/110.29 kpair( 109.58/110.29 X472,X473)) = 109.58/110.29 X472)) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X474, 109.58/110.29 X475,X476]: 109.58/110.29 (in( 109.58/110.29 X476, 109.58/110.29 cartprod( 109.58/110.29 X474,X475)) => 109.58/110.29 in( 109.58/110.29 kfst( 109.58/110.29 X476), 109.58/110.29 X474))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X477, 109.58/110.29 X478, 109.58/110.29 X479,X480]: 109.58/110.29 (( 109.58/110.29 setadjoin( 109.58/110.29 setadjoin( 109.58/110.29 X477, 109.58/110.29 emptyset), 109.58/110.29 setadjoin( 109.58/110.29 setadjoin( 109.58/110.29 X477, 109.58/110.29 setadjoin( 109.58/110.29 X478, 109.58/110.29 emptyset)), 109.58/110.29 emptyset)) = 109.58/110.29 setadjoin( 109.58/110.29 setadjoin( 109.58/110.29 X479, 109.58/110.29 emptyset), 109.58/110.29 setadjoin( 109.58/110.29 setadjoin( 109.58/110.29 X479, 109.58/110.29 setadjoin( 109.58/110.29 X480, 109.58/110.29 emptyset)), 109.58/110.29 emptyset))) => 109.58/110.29 (X477 = 109.58/110.29 X479))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X481, 109.58/110.29 X482, 109.58/110.29 X483,X484]: 109.58/110.29 (( 109.58/110.29 kpair( 109.58/110.29 X481,X482) = 109.58/110.29 kpair( 109.58/110.29 X483,X484)) => 109.58/110.29 (X481 = 109.58/110.29 X483))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X485, 109.58/110.29 X486]: 109.58/110.29 (( 109.58/110.29 X485 = 109.58/110.29 X486) => 109.58/110.29 (setadjoin( 109.58/110.29 X485, 109.58/110.29 setadjoin( 109.58/110.29 X486, 109.58/110.29 emptyset)) = 109.58/110.29 setadjoin( 109.58/110.29 X485, 109.58/110.29 emptyset)))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X487, 109.58/110.29 X488]: 109.58/110.29 (( 109.58/110.29 X487 = 109.58/110.29 X488) => 109.58/110.29 (setadjoin( 109.58/110.29 setadjoin( 109.58/110.29 X487, 109.58/110.29 emptyset), 109.58/110.29 setadjoin( 109.58/110.29 setadjoin( 109.58/110.29 X487, 109.58/110.29 setadjoin( 109.58/110.29 X488, 109.58/110.29 emptyset)), 109.58/110.29 emptyset)) = 109.58/110.29 setadjoin( 109.58/110.29 setadjoin( 109.58/110.29 X487, 109.58/110.29 emptyset), 109.58/110.29 emptyset)))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X489, 109.58/110.29 X490, 109.58/110.29 X491,X492]: 109.58/110.29 (( 109.58/110.29 setadjoin( 109.58/110.29 setadjoin( 109.58/110.29 X489, 109.58/110.29 emptyset), 109.58/110.29 setadjoin( 109.58/110.29 setadjoin( 109.58/110.29 X489, 109.58/110.29 setadjoin( 109.58/110.29 X490, 109.58/110.29 emptyset)), 109.58/110.29 emptyset)) = 109.58/110.29 setadjoin( 109.58/110.29 setadjoin( 109.58/110.29 X491, 109.58/110.29 emptyset), 109.58/110.29 setadjoin( 109.58/110.29 setadjoin( 109.58/110.29 X491, 109.58/110.29 setadjoin( 109.58/110.29 X492, 109.58/110.29 emptyset)), 109.58/110.29 emptyset))) => 109.58/110.29 (( 109.58/110.29 X491 = 109.58/110.29 X492) => 109.58/110.29 (X490 = 109.58/110.29 X492)))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X493, 109.58/110.29 X494,X495]: 109.58/110.29 (( 109.58/110.29 setadjoin( 109.58/110.29 X493, 109.58/110.29 setadjoin( 109.58/110.29 X494, 109.58/110.29 emptyset)) = 109.58/110.29 setadjoin( 109.58/110.29 X495, 109.58/110.29 emptyset)) => 109.58/110.29 (X493 = 109.58/110.29 X494))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X496, 109.58/110.29 X497, 109.58/110.29 X498,X499]: 109.58/110.29 (( 109.58/110.29 setadjoin( 109.58/110.29 setadjoin( 109.58/110.29 X496, 109.58/110.29 emptyset), 109.58/110.29 setadjoin( 109.58/110.29 setadjoin( 109.58/110.29 X496, 109.58/110.29 setadjoin( 109.58/110.29 X497, 109.58/110.29 emptyset)), 109.58/110.29 emptyset)) = 109.58/110.29 setadjoin( 109.58/110.29 setadjoin( 109.58/110.29 X498, 109.58/110.29 emptyset), 109.58/110.29 setadjoin( 109.58/110.29 setadjoin( 109.58/110.29 X498, 109.58/110.29 setadjoin( 109.58/110.29 X499, 109.58/110.29 emptyset)), 109.58/110.29 emptyset))) => 109.58/110.29 (X497 = 109.58/110.29 X499))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X500, 109.58/110.29 X501, 109.58/110.29 X502,X503]: 109.58/110.29 (( 109.58/110.29 kpair( 109.58/110.29 X500,X501) = 109.58/110.29 kpair( 109.58/110.29 X502,X503)) => 109.58/110.29 (X501 = 109.58/110.29 X503))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X504]: 109.58/110.29 (iskpair( 109.58/110.29 X504) => 109.58/110.29 (?[X505]: 109.58/110.29 (in( 109.58/110.29 X505, 109.58/110.29 dsetconstr( 109.58/110.29 setunion( 109.58/110.29 X504), 109.58/110.29 '#ll_5'( 109.58/110.29 X504))) & 109.58/110.29 (dsetconstr( 109.58/110.29 setunion( 109.58/110.29 X504), 109.58/110.29 '#ll_5'( 109.58/110.29 X504)) = 109.58/110.29 setadjoin( 109.58/110.29 X505, 109.58/110.29 emptyset)))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X506, 109.58/110.29 X507]: 109.58/110.29 (ksnd( 109.58/110.29 kpair( 109.58/110.29 X506,X507)) = 109.58/110.29 X507)) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X508]: 109.58/110.29 (iskpair( 109.58/110.29 X508) => 109.58/110.29 (kpair( 109.58/110.29 kfst( 109.58/110.29 X508), 109.58/110.29 ksnd( 109.58/110.29 X508)) = 109.58/110.29 X508))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X509, 109.58/110.29 X510,X511]: 109.58/110.29 (in( 109.58/110.29 X511, 109.58/110.29 cartprod( 109.58/110.29 X509,X510)) => 109.58/110.29 in( 109.58/110.29 ksnd( 109.58/110.29 X511), 109.58/110.29 X510))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X512, 109.58/110.29 X513, 109.58/110.29 X514,X515]: 109.58/110.29 (in( 109.58/110.29 kpair( 109.58/110.29 X514,X515), 109.58/110.29 cartprod( 109.58/110.29 X512,X513)) => 109.58/110.29 in( 109.58/110.29 X514,X512))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X516, 109.58/110.29 X517, 109.58/110.29 X518,X519]: 109.58/110.29 (in( 109.58/110.29 kpair( 109.58/110.29 X518,X519), 109.58/110.29 cartprod( 109.58/110.29 X516,X517)) => 109.58/110.29 in( 109.58/110.29 X519,X517))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X520, 109.58/110.29 X521,X522]: 109.58/110.29 (in( 109.58/110.29 X522,X520) => 109.58/110.29 (![X523]: 109.58/110.29 (in( 109.58/110.29 X523,X521) => 109.58/110.29 (kpair( 109.58/110.29 X522,X523) = 109.58/110.29 kpair( 109.58/110.29 X522,X523)))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X524, 109.58/110.29 X525,X526]: 109.58/110.29 (in( 109.58/110.29 X526,X524) => 109.58/110.29 (![X527]: 109.58/110.29 (in( 109.58/110.29 X527,X525) => 109.58/110.29 (kfst( 109.58/110.29 kpair( 109.58/110.29 X526,X527)) = 109.58/110.29 X526))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X528, 109.58/110.29 X529,X530]: 109.58/110.29 (in( 109.58/110.29 X530,X528) => 109.58/110.29 (![X531]: 109.58/110.29 (in( 109.58/110.29 X531,X529) => 109.58/110.29 (ksnd( 109.58/110.29 kpair( 109.58/110.29 X530,X531)) = 109.58/110.29 X531))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X532, 109.58/110.29 X533,X534]: 109.58/110.29 (in( 109.58/110.29 X534, 109.58/110.29 cartprod( 109.58/110.29 X532,X533)) => 109.58/110.29 (kpair( 109.58/110.29 kfst( 109.58/110.29 X534), 109.58/110.29 ksnd( 109.58/110.29 X534)) = 109.58/110.29 X534))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X535, 109.58/110.29 X536, 109.58/110.29 X537:( 109.58/110.29 ($i * $i) > 109.58/110.29 $o),X538]: 109.58/110.29 (in( 109.58/110.29 X538,X535) => 109.58/110.29 (![X539]: 109.58/110.29 (in( 109.58/110.29 X539,X536) => 109.58/110.29 (X537( 109.58/110.29 X538,X539) => 109.58/110.29 in( 109.58/110.29 kpair( 109.58/110.29 X538,X539), 109.58/110.29 dpsetconstr( 109.58/110.29 X535, 109.58/110.29 X536, 109.58/110.29 '#ll_4'( 109.58/110.29 X537)))))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X540, 109.58/110.29 X541, 109.58/110.29 X542:( 109.58/110.29 ($i * $i) > 109.58/110.29 $o)]: 109.58/110.29 subset( 109.58/110.29 dpsetconstr( 109.58/110.29 X540, 109.58/110.29 X541, 109.58/110.29 '#ll_4'( 109.58/110.29 X542)), 109.58/110.29 cartprod( 109.58/110.29 X540,X541))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X543, 109.58/110.29 X544, 109.58/110.29 X545:( 109.58/110.29 ($i * $i) > 109.58/110.29 $o)]: 109.58/110.29 subset( 109.58/110.29 dpsetconstr( 109.58/110.29 X543, 109.58/110.29 X544, 109.58/110.29 '#ll_4'( 109.58/110.29 X545)), 109.58/110.29 cartprod( 109.58/110.29 X543,X544))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X546, 109.58/110.29 X547, 109.58/110.29 X548:( 109.58/110.29 ($i * $i) > 109.58/110.29 $o),X549]: 109.58/110.29 (in( 109.58/110.29 X549,X546) => 109.58/110.29 (![X550]: 109.58/110.29 (in( 109.58/110.29 X550,X547) => 109.58/110.29 (in( 109.58/110.29 kpair( 109.58/110.29 X549,X550), 109.58/110.29 dpsetconstr( 109.58/110.29 X546, 109.58/110.29 X547, 109.58/110.29 '#ll_4'( 109.58/110.29 X548))) => 109.58/110.29 X548( 109.58/110.29 X549,X550)))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X551, 109.58/110.29 X552, 109.58/110.29 X553:( 109.58/110.29 ($i * $i) > 109.58/110.29 $o),X554, 109.58/110.29 X555]: 109.58/110.29 (in( 109.58/110.29 kpair( 109.58/110.29 X554,X555), 109.58/110.29 dpsetconstr( 109.58/110.29 X551, 109.58/110.29 X552, 109.58/110.29 '#ll_4'( 109.58/110.29 X553))) => 109.58/110.29 in( 109.58/110.29 X554,X551))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X556, 109.58/110.29 X557, 109.58/110.29 X558:( 109.58/110.29 ($i * $i) > 109.58/110.29 $o),X559, 109.58/110.29 X560]: 109.58/110.29 (in( 109.58/110.29 kpair( 109.58/110.29 X559,X560), 109.58/110.29 dpsetconstr( 109.58/110.29 X556, 109.58/110.29 X557, 109.58/110.29 '#ll_4'( 109.58/110.29 X558))) => 109.58/110.29 in( 109.58/110.29 X560,X557))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X561, 109.58/110.29 X562, 109.58/110.29 X563:( 109.58/110.29 ($i * $i) > 109.58/110.29 $o),X564, 109.58/110.29 X565]: 109.58/110.29 (in( 109.58/110.29 kpair( 109.58/110.29 X564,X565), 109.58/110.29 dpsetconstr( 109.58/110.29 X561, 109.58/110.29 X562, 109.58/110.29 '#ll_4'( 109.58/110.29 X563))) => 109.58/110.29 X563( 109.58/110.29 X564,X565))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X566, 109.58/110.29 X567,X568]: 109.58/110.29 (( 109.58/110.29 subset( 109.58/110.29 X568, 109.58/110.29 cartprod( 109.58/110.29 X566,X567)) & 109.58/110.29 ( 109.58/110.29 ![X569]: 109.58/110.29 (in( 109.58/110.29 X569,X566) => 109.58/110.29 (?[X570]: 109.58/110.29 (in( 109.58/110.29 X570, 109.58/110.29 dsetconstr( 109.58/110.29 X567, 109.58/110.29 '#ll_3'( 109.58/110.29 X569,X568))) & 109.58/110.29 (dsetconstr( 109.58/110.29 X567, 109.58/110.29 '#ll_3'( 109.58/110.29 X569,X568)) = 109.58/110.29 setadjoin( 109.58/110.29 X570, 109.58/110.29 emptyset))))))) => 109.58/110.29 (![X571]: 109.58/110.29 (in( 109.58/110.29 X571,X566) => 109.58/110.29 (?[X572]: 109.58/110.29 (in( 109.58/110.29 X572, 109.58/110.29 dsetconstr( 109.58/110.29 X567, 109.58/110.29 '#ll_3'( 109.58/110.29 X571,X568))) & 109.58/110.29 (dsetconstr( 109.58/110.29 X567, 109.58/110.29 '#ll_3'( 109.58/110.29 X571,X568)) = 109.58/110.29 setadjoin( 109.58/110.29 X572, 109.58/110.29 emptyset)))))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X573, 109.58/110.29 X574,X575]: 109.58/110.29 (( 109.58/110.29 subset( 109.58/110.29 X575, 109.58/110.29 cartprod( 109.58/110.29 X573,X574)) & 109.58/110.29 ( 109.58/110.29 ![X576]: 109.58/110.29 (in( 109.58/110.29 X576,X573) => 109.58/110.29 (?[X577]: 109.58/110.29 (in( 109.58/110.29 X577, 109.58/110.29 dsetconstr( 109.58/110.29 X574, 109.58/110.29 '#ll_3'( 109.58/110.29 X576,X575))) & 109.58/110.29 (dsetconstr( 109.58/110.29 X574, 109.58/110.29 '#ll_3'( 109.58/110.29 X576,X575)) = 109.58/110.29 setadjoin( 109.58/110.29 X577, 109.58/110.29 emptyset))))))) => 109.58/110.29 (![X578]: 109.58/110.29 (in( 109.58/110.29 X578,X573) => 109.58/110.29 in( 109.58/110.29 setunion( 109.58/110.29 dsetconstr( 109.58/110.29 X574, 109.58/110.29 '#ll_3'( 109.58/110.29 X578,X575))), 109.58/110.29 X574))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X579, 109.58/110.29 X580,X581]: 109.58/110.29 (( 109.58/110.29 subset( 109.58/110.29 X581, 109.58/110.29 cartprod( 109.58/110.29 X579,X580)) & 109.58/110.29 ( 109.58/110.29 ![X582]: 109.58/110.29 (in( 109.58/110.29 X582,X579) => 109.58/110.29 (?[X583]: 109.58/110.29 (in( 109.58/110.29 X583, 109.58/110.29 dsetconstr( 109.58/110.29 X580, 109.58/110.29 '#ll_3'( 109.58/110.29 X582,X581))) & 109.58/110.29 (dsetconstr( 109.58/110.29 X580, 109.58/110.29 '#ll_3'( 109.58/110.29 X582,X581)) = 109.58/110.29 setadjoin( 109.58/110.29 X583, 109.58/110.29 emptyset))))))) => 109.58/110.29 (![X584]: 109.58/110.29 (in( 109.58/110.29 X584,X579) => 109.58/110.29 in( 109.58/110.29 setunion( 109.58/110.29 dsetconstr( 109.58/110.29 X580, 109.58/110.29 '#ll_3'( 109.58/110.29 X584,X581))), 109.58/110.29 X580))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X585, 109.58/110.29 X586,X587]: 109.58/110.29 (in( 109.58/110.29 X587, 109.58/110.29 funcSet( 109.58/110.29 X585,X586)) => 109.58/110.29 (subset( 109.58/110.29 X587, 109.58/110.29 cartprod( 109.58/110.29 X585,X586)) & 109.58/110.29 (![X588]: 109.58/110.29 (in( 109.58/110.29 X588,X585) => 109.58/110.29 (?[X589]: 109.58/110.29 (in( 109.58/110.29 X589, 109.58/110.29 dsetconstr( 109.58/110.29 X586, 109.58/110.29 '#ll_3'( 109.58/110.29 X588,X587))) & 109.58/110.29 (dsetconstr( 109.58/110.29 X586, 109.58/110.29 '#ll_3'( 109.58/110.29 X588,X587)) = 109.58/110.29 setadjoin( 109.58/110.29 X589, 109.58/110.29 emptyset))))))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X590, 109.58/110.29 X591,X592]: 109.58/110.29 (in( 109.58/110.29 X592, 109.58/110.29 funcSet( 109.58/110.29 X590,X591)) => 109.58/110.29 (![X593]: 109.58/110.29 (in( 109.58/110.29 X593,X590) => 109.58/110.29 in( 109.58/110.29 setunion( 109.58/110.29 dsetconstr( 109.58/110.29 X591, 109.58/110.29 '#ll_3'( 109.58/110.29 X593,X592))), 109.58/110.29 X591))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X594, 109.58/110.29 X595,X596]: 109.58/110.29 (( 109.58/110.29 subset( 109.58/110.29 X596, 109.58/110.29 cartprod( 109.58/110.29 X594,X595)) & 109.58/110.29 ( 109.58/110.29 ![X597]: 109.58/110.29 (in( 109.58/110.29 X597,X594) => 109.58/110.29 (?[X598]: 109.58/110.29 (in( 109.58/110.29 X598, 109.58/110.29 dsetconstr( 109.58/110.29 X595, 109.58/110.29 '#ll_3'( 109.58/110.29 X597,X596))) & 109.58/110.29 (dsetconstr( 109.58/110.29 X595, 109.58/110.29 '#ll_3'( 109.58/110.29 X597,X596)) = 109.58/110.29 setadjoin( 109.58/110.29 X598, 109.58/110.29 emptyset))))))) => 109.58/110.29 in( 109.58/110.29 X596, 109.58/110.29 funcSet( 109.58/110.29 X594,X595)))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X599, 109.58/110.29 X600, 109.58/110.29 X601:( 109.58/110.29 $i > $i)]: 109.58/110.29 (( 109.58/110.29 ![X602]: 109.58/110.29 (in( 109.58/110.29 X602,X599) => 109.58/110.29 in( 109.58/110.29 X601( 109.58/110.29 X602), 109.58/110.29 X600))) => 109.58/110.29 (subset( 109.58/110.29 dpsetconstr( 109.58/110.29 X599, 109.58/110.29 X600, 109.58/110.29 '#ll_1'( 109.58/110.29 X601)), 109.58/110.29 cartprod( 109.58/110.29 X599,X600)) & 109.58/110.29 (![X603]: 109.58/110.29 (in( 109.58/110.29 X603,X599) => 109.58/110.29 (?[X604]: 109.58/110.29 (in( 109.58/110.29 X604, 109.58/110.29 dsetconstr( 109.58/110.29 X600, 109.58/110.29 '#ll_2'( 109.58/110.29 X603, 109.58/110.29 X601, 109.58/110.29 X600,X599))) & 109.58/110.29 (dsetconstr( 109.58/110.29 X600, 109.58/110.29 '#ll_2'( 109.58/110.29 X603, 109.58/110.29 X601, 109.58/110.29 X600,X599)) = 109.58/110.29 setadjoin( 109.58/110.29 X604, 109.58/110.29 emptyset))))))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X605, 109.58/110.29 X606, 109.58/110.29 X607:( 109.58/110.29 $i > $i)]: 109.58/110.29 (( 109.58/110.29 ![X608]: 109.58/110.29 (in( 109.58/110.29 X608,X605) => 109.58/110.29 in( 109.58/110.29 X607( 109.58/110.29 X608), 109.58/110.29 X606))) => 109.58/110.29 (subset( 109.58/110.29 dpsetconstr( 109.58/110.29 X605, 109.58/110.29 X606, 109.58/110.29 '#ll_1'( 109.58/110.29 X607)), 109.58/110.29 cartprod( 109.58/110.29 X605,X606)) & 109.58/110.29 (![X609]: 109.58/110.29 (in( 109.58/110.29 X609,X605) => 109.58/110.29 (?[X610]: 109.58/110.29 (in( 109.58/110.29 X610, 109.58/110.29 dsetconstr( 109.58/110.29 X606, 109.58/110.29 '#ll_2'( 109.58/110.29 X609, 109.58/110.29 X607, 109.58/110.29 X606,X605))) & 109.58/110.29 (dsetconstr( 109.58/110.29 X606, 109.58/110.29 '#ll_2'( 109.58/110.29 X609, 109.58/110.29 X607, 109.58/110.29 X606,X605)) = 109.58/110.29 setadjoin( 109.58/110.29 X610, 109.58/110.29 emptyset))))))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X611, 109.58/110.29 X612, 109.58/110.29 X613:( 109.58/110.29 $i > $i)]: 109.58/110.29 (( 109.58/110.29 ![X614]: 109.58/110.29 (in( 109.58/110.29 X614,X611) => 109.58/110.29 in( 109.58/110.29 X613( 109.58/110.29 X614), 109.58/110.29 X612))) => 109.58/110.29 in( 109.58/110.29 dpsetconstr( 109.58/110.29 X611, 109.58/110.29 X612, 109.58/110.29 '#ll_1'( 109.58/110.29 X613)), 109.58/110.29 funcSet( 109.58/110.29 X611,X612)))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X615, 109.58/110.29 X616,X617]: 109.58/110.29 (subset( 109.58/110.29 X617, 109.58/110.29 cartprod( 109.58/110.29 X615,X616)) => 109.58/110.29 (![X618:( 109.58/110.29 $i > $o)]: 109.58/110.29 (( 109.58/110.29 ![X619]: 109.58/110.29 (in( 109.58/110.29 X619,X615) => 109.58/110.29 (![X620]: 109.58/110.29 (in( 109.58/110.29 X620,X616) => 109.58/110.29 (in( 109.58/110.29 kpair( 109.58/110.29 X619,X620), 109.58/110.29 X617) => 109.58/110.29 X618( 109.58/110.29 kpair( 109.58/110.29 X619,X620))))))) => 109.58/110.29 (![X621]: 109.58/110.29 (in( 109.58/110.29 X621,X617) => 109.58/110.29 X618( 109.58/110.29 X621))))))) => 109.58/110.29 ( 109.58/110.29 ( 109.58/110.29 ![X622, 109.58/110.29 X623,X624]: 109.58/110.29 (subset( 109.58/110.29 X624, 109.58/110.29 cartprod( 109.58/110.29 X622,X623)) => 109.58/110.29 (![X625:( 109.58/110.29 $i > $o)]: 109.58/110.29 (( 109.58/110.29 ![X626]: 109.58/110.29 (in( 109.58/110.29 X626,X622) => 109.58/110.29 (![X627]: 109.58/110.29 (in( 109.58/110.29 X627,X623) => 109.58/110.29 (in( 109.58/110.29 kpair( 109.58/110.29 X626,X627), 109.58/110.29 X624) => 109.58/110.29 X625( 109.58/110.29 kpair( 109.58/110.29 X626,X627))))))) => 109.58/110.29 (![X628]: 109.58/110.29 (in( 109.58/110.29 X628,X624) => 109.58/110.29 X625( 109.58/110.29 X628))))))) => 109.58/110.29 ( 109.58/110.29 ![X629, 109.58/110.29 X630:( 109.58/110.29 $i > $o)]: 109.58/110.29 (( 109.58/110.29 ?[X631]: 109.58/110.29 (in( 109.58/110.29 X631, 109.58/110.29 dsetconstr( 109.58/110.29 X629, 109.58/110.29 '#ll_0'( 109.58/110.29 X630))) & 109.58/110.29 (dsetconstr( 109.58/110.29 X629, 109.58/110.29 '#ll_0'( 109.58/110.29 X630)) = 109.58/110.29 setadjoin( 109.58/110.29 X631, 109.58/110.29 emptyset)))) => 109.58/110.29 (![X632]: 109.58/110.29 (in( 109.58/110.29 X632,X629) => 109.58/110.29 (![X633]: 109.58/110.29 (in( 109.58/110.29 X633,X629) => 109.58/110.29 (X630( 109.58/110.29 X632) => 109.58/110.29 (X630( 109.58/110.29 X633) => 109.58/110.29 (X632 = 109.58/110.29 X633))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 109.58/110.29 tff(zf_stmt_1, type, zip_tseitin5 : ($i * $i > $o) > $o). 109.58/110.29 tff(zf_stmt_2, axiom, 109.58/110.29 (zip_tseitin5(X211,X207) <=> 109.58/110.29 ((![X212]: zip_tseitin4(X212,X211,X207)) & X207(X211)))). 109.58/110.29 tff(zf_stmt_3, type, zip_tseitin4 : ($i * $i * $i > $o) > $o). 109.58/110.29 tff(zf_stmt_4, axiom, 109.58/110.29 (zip_tseitin4(X212,X211,X207) <=> (X207(X212) => (X211 = X212)))). 109.58/110.29 tff(zf_stmt_5, type, zip_tseitin3 : ($i * $i * $i * ($i * $i) > $o) > $o). 109.58/110.29 tff(zf_stmt_6, axiom, 109.58/110.29 (zip_tseitin3(X26,X25,X20,X19) <=> (X19(X26,X25) & in(X26,X20)))). 109.58/110.29 tff(zf_stmt_7, type, zip_tseitin2 : ($i * $i * $i) > $o). 109.58/110.29 tff(zf_stmt_8, axiom, 109.58/110.29 (zip_tseitin2(X14,X13,X12) <=> (in(X14,X12) & in(X13,X14)))). 109.58/110.29 tff(zf_stmt_9, type, zip_tseitin1 : ($i * $i * $i) > $o). 109.58/110.29 tff(zf_stmt_10, axiom, 109.58/110.29 (zip_tseitin1(X11,X10,X9) <=> (in(X11,X10) => in(X11,X9)))). 109.58/110.29 tff(zf_stmt_11, type, zip_tseitin0 : ($i * $i * $i) > $o). 109.58/110.29 tff(zf_stmt_12, axiom, (zip_tseitin0(X8,X7,X6) <=> (in(X8,X7) | (X8 = X6)))). 109.58/110.29 tff(zf_stmt_13, conjecture, 109.58/110.29 ((![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))) => 109.58/110.29 ((![X5]: (~in(X5,emptyset))) => 109.58/110.29 ((![X6,X7,X8]: (in(X8,setadjoin(X6,X7)) <=> zip_tseitin0(X8,X7,X6))) => 109.58/110.29 ((![X9,X10]: 109.58/110.29 (in(X10,powerset(X9)) <=> (![X11]: zip_tseitin1(X11,X10,X9)))) => 109.58/110.29 ((![X12,X13]: 109.58/110.29 (in(X13,setunion(X12)) <=> (?[X14]: zip_tseitin2(X14,X13,X12)))) => 109.58/110.29 (in(emptyset,omega) => 109.58/110.29 ((![X15]: (in(X15,omega) => in(setadjoin(X15,X15),omega))) => 109.58/110.29 ((![X16]: 109.58/110.29 (((![X17]: 109.58/110.29 ((in(X17,X16) & in(X17,omega)) => 109.58/110.29 in(setadjoin(X17,X17),X16))) & 109.58/110.29 in(emptyset,X16)) => 109.58/110.29 (![X18]: (in(X18,omega) => in(X18,X16))))) => 109.58/110.29 ((![X19:(($i * $i) > $o),X20]: 109.58/110.29 ((![X21]: 109.58/110.29 (in(X21,X20) => 109.58/110.29 (?[X22]: 109.58/110.29 ((![X23]: (X19(X21,X23) => (X22 = X23))) & X19(X21,X22))))) => 109.58/110.29 (?[X24]: 109.58/110.29 (![X25]: 109.58/110.29 (in(X25,X24) <=> (?[X26]: zip_tseitin3(X26,X25,X20,X19))))))) => 109.58/110.29 ((![X27]: 109.58/110.29 ((?[X28]: in(X28,X27)) => 109.58/110.29 (?[X29]: 109.58/110.29 ((~(?[X30]: (in(X30,X27) & in(X30,X29)))) & in(X29,X27))))) => 109.58/110.29 ((![X31]: 109.58/110.29 (?[X32]: 109.58/110.29 ((![X33]: 109.58/110.29 (((?[X34]: in(X34,X33)) & 109.58/110.29 (![X35]: (in(X35,X33) => in(X35,X31)))) => 109.58/110.29 (?[X36,X37]: 109.58/110.29 ((![X38]: 109.58/110.29 (in(X38,X32) => 109.58/110.29 (in(X37,X38) | 109.58/110.29 (![X39]: (in(X39,X38) => in(X39,X36)))))) & 109.58/110.29 (~(?[X40]: (in(X40,X33) & in(X40,X36)))) & 109.58/110.29 in(X37,X33) & in(X36,X32))))) & 109.58/110.29 (![X41,X42]: 109.58/110.29 ((in(X42,X32) & in(X41,X32)) => 109.58/110.29 ((![X43]: (in(X43,X42) => in(X43,X41))) | 109.58/110.29 (![X44]: (in(X44,X41) => in(X44,X42)))))) & 109.58/110.29 (![X45,X46]: 109.58/110.29 ((in(X46,X31) & in(X45,X31)) => 109.58/110.29 ((![X47]: 109.58/110.29 (in(X47,X32) => (in(X45,X47) <=> in(X46,X47)))) => 109.58/110.29 (X45 = X46)))) & 109.58/110.29 (![X48]: 109.58/110.29 (in(X48,X32) => (![X49]: (in(X49,X48) => in(X49,X31)))))))) => 109.58/110.29 ((![X50:($i > $o)]: 109.58/110.29 ((?[X51]: ((![X52]: (X50(X52) => (X51 = X52))) & X50(X51))) => 109.58/110.29 X50(descr('#ll_0'(X50))))) => 109.58/110.29 ((![X53,X54:($i > $o),X55]: 109.58/110.29 (in(X55,X53) => 109.58/110.29 (X54(X55) => in(X55,dsetconstr(X53,'#ll_0'(X54)))))) => 109.58/110.29 ((![X56,X57:($i > $o),X58]: 109.58/110.29 (in(X58,dsetconstr(X56,'#ll_0'(X57))) => in(X58,X56))) => 109.58/110.29 ((![X59,X60:($i > $o),X61]: 109.58/110.29 (in(X61,dsetconstr(X59,'#ll_0'(X60))) => X60(X61))) => 109.58/110.29 ((![X62:($i > $o)]: 109.58/110.29 ((?[X63]: 109.58/110.29 ((![X64]: (X62(X64) => (X63 = X64))) & X62(X63))) => 109.58/110.29 (?[X65]: 109.58/110.29 ((![X66]: (X62(X66) => (X65 = X66))) & X62(X65))))) => 109.58/110.29 ((![X67:$o,X68]: (in(X68,prop2set(X67)) => X67)) => 109.58/110.29 ((![X69]: (in(X69,emptyset) => (![X70:$o]: X70))) => 109.58/110.29 ((![X71]: (in(X71,emptyset) => $false)) => 109.58/110.29 ((![X72]: (~in(X72,emptyset))) => 109.58/110.29 ((![X73:($i > $o)]: 109.58/110.29 ((?[X74]: 109.58/110.29 ((![X75]: (X73(X75) => (X74 = X75))) & X73(X74))) => 109.58/110.29 (?[X76]: X73(X76)))) => 109.58/110.29 ((![X77,X78]: 109.58/110.29 ((![X79]: (in(X79,X77) => in(X79,X78))) => 109.58/110.29 ((![X80]: (in(X80,X78) => in(X80,X77))) => 109.58/110.29 (X77 = X78)))) => 109.58/110.29 ((![X81]: 109.58/110.29 ((![X82]: (~in(X82,X81))) => (X81 = emptyset))) => 109.58/110.29 ((![X83]: 109.58/110.29 ((![X84]: (~in(X84,X83))) => (X83 = emptyset))) => 109.58/110.29 ((![X85,X86:($i > $o),X87]: 109.58/110.29 (in(X87,X85) => 109.58/110.29 (in(X87,dsetconstr(X85,'#ll_0'(X86))) <=> 109.58/110.29 X86(X87)))) => 109.58/110.29 ((![X88]: 109.58/110.29 ((X88 != emptyset) => (?[X89]: in(X89,X88)))) => 109.58/110.29 ((![X90,X91:($i > $o),X92]: 109.58/110.29 (in(X92,X90) => 109.58/110.29 (X91(X92) => 109.58/110.29 (dsetconstr(X90,'#ll_0'(X91)) != emptyset)))) => 109.58/110.29 ((![X93]: 109.58/110.29 ((?[X94]: in(X94,X93)) => (X93 != emptyset))) => 109.58/110.29 ((![X95,X96]: in(X95,setadjoin(X95,X96))) => 109.58/110.29 (in(emptyset,setadjoin(emptyset,emptyset)) => 109.58/110.29 ((![X97,X98,X99]: 109.58/110.29 (in(X99,X98) => 109.58/110.29 in(X99,setadjoin(X97,X98)))) => 109.58/110.29 ((![X100,X101,X102]: 109.58/110.29 (in(X102,setadjoin(X100,X101)) => 109.58/110.29 (![X103:$o]: 109.58/110.29 (((X102 = X100) => X103) => 109.58/110.29 ((in(X102,X101) => X103) => X103))))) => 109.58/110.29 ((![X104,X105,X106]: 109.58/110.29 (in(X106,setadjoin(X104,X105)) => 109.58/110.29 (in(X106,X105) | (X106 = X104)))) => 109.58/110.29 ((![X107]: 109.58/110.29 (dsetconstr(X107,'#ll_7') = X107)) => 109.58/110.29 ((![X108,X109]: 109.58/110.29 ((![X110]: 109.58/110.29 (in(X110,X109) => in(X110,X108))) => 109.58/110.29 in(X109,powerset(X108)))) => 109.58/110.29 ((![X111]: in(emptyset,powerset(X111))) => 109.58/110.29 ((![X112]: in(emptyset,powerset(X112))) => 109.58/110.29 ((![X113,X114,X115]: 109.58/110.29 (in(X114,powerset(X113)) => 109.58/110.29 (in(X115,X114) => in(X115,X113)))) => 109.58/110.29 ((![X116,X117,X118]: 109.58/110.29 (in(X117,X118) => 109.58/110.29 (in(X118,X116) => 109.58/110.29 in(X117,setunion(X116))))) => 109.58/110.29 ((![X119,X120]: 109.58/110.29 (in(X120,setunion(X119)) => 109.58/110.29 (![X121:$o]: 109.58/110.29 ((![X122]: 109.58/110.29 (in(X120,X122) => 109.58/110.29 (in(X122,X119) => X121))) => 109.58/110.29 X121)))) => 109.58/110.29 ((![X123,X124]: 109.58/110.29 (in(X124,X123) => 109.58/110.29 in(X124, 109.58/110.29 powerset(setunion(X123))))) => 109.58/110.29 ((![X125:($i > $o)]: 109.58/110.29 ((?[X126]: 109.58/110.29 ((![X127]: 109.58/110.29 (X125(X127) => 109.58/110.29 (X126 = X127))) & 109.58/110.29 X125(X126))) => 109.58/110.29 (?[X128]: 109.58/110.29 (![X129]: 109.58/110.29 (X125(X129) <=> 109.58/110.29 (X129 = X128)))))) => 109.58/110.29 ((![X130]: 109.58/110.29 ((X130 != emptyset) => 109.58/110.29 (?[X131]: in(X131,X130)))) => 109.58/110.29 ((![X132,X133]: 109.58/110.29 (in(X132, 109.58/110.29 setadjoin(X133,emptyset)) => 109.58/110.29 (X132 = X133))) => 109.58/110.29 ((![X134,X135]: 109.58/110.30 ((X134 != X135) => 109.58/110.30 (~ 109.58/110.30 in(X135, 109.58/110.30 setadjoin(X134, 109.58/110.30 emptyset))))) => 109.58/110.30 ((![X136,X137]: 109.58/110.30 ((X136 = X137) => 109.58/110.30 in(X136, 109.58/110.30 setadjoin(X137, 109.58/110.30 emptyset)))) => 109.58/110.30 ((![X138,X139]: 109.58/110.30 (in(X138, 109.58/110.30 setadjoin(X139, 109.58/110.30 emptyset)) => 109.58/110.30 in(X139, 109.58/110.30 setadjoin(X138, 109.58/110.30 emptyset)))) => 109.58/110.30 ((![X140,X141,X142]: 109.58/110.30 (in(X142, 109.58/110.30 setadjoin(X140, 109.58/110.30 setadjoin( 109.58/110.30 X141, 109.58/110.30 emptyset))) => 109.58/110.30 ((X142 = X141) | 109.58/110.30 (X142 = X140)))) => 109.58/110.30 ((![X143,X144]: 109.58/110.30 in(X143, 109.58/110.30 setadjoin(X143, 109.58/110.30 setadjoin( 109.58/110.30 X144, 109.58/110.30 emptyset)))) => 109.58/110.30 ((![X145,X146]: 109.58/110.30 in(X146, 109.58/110.30 setadjoin(X145, 109.58/110.30 setadjoin( 109.58/110.30 X146, 109.58/110.30 emptyset)))) => 109.58/110.30 ((![X147,X148:($i > $o)]: 109.58/110.30 ((?[X149]: 109.58/110.30 (X148(X149) & 109.58/110.30 in(X149,X147))) => 109.58/110.30 ((dsetconstr( 109.58/110.30 X147,'#ll_0'(X148)) = 109.58/110.30 emptyset) => 109.58/110.30 $false))) => 109.58/110.30 ((![X150:($i > $o),X151]: 109.58/110.30 (in(X151,emptyset) => 109.58/110.30 X150(X151))) => 109.58/110.30 ((![X152,X153:($i > $o)]: 109.58/110.30 ((~ 109.58/110.30 (![X154]: 109.58/110.30 (in(X154,X152) => 109.58/110.30 X153(X154)))) => 109.58/110.30 (?[X155]: 109.58/110.30 ((~X153(X155)) & 109.58/110.30 in(X155,X152))))) => 109.58/110.30 ((![X156, 109.58/110.30 X157:($i > $o)]: 109.58/110.30 ((![X158]: 109.58/110.30 (in(X158,X156) => 109.58/110.30 (~X157(X158)))) => 109.58/110.30 (~ 109.58/110.30 (?[X159]: 109.58/110.30 (X157(X159) & 109.58/110.30 in( 109.58/110.30 X159,X156)))))) => 109.58/110.30 ((![X160, 109.58/110.30 X161:($i > $o)]: 109.58/110.30 ((~ 109.58/110.30 (?[X162]: 109.58/110.30 (X161(X162) & 109.58/110.30 in( 109.58/110.30 X162,X160)))) => 109.58/110.30 (![X163]: 109.58/110.30 (in(X163,X160) => 109.58/110.30 (~X161(X163)))))) => 109.58/110.30 ((![X164, 109.58/110.30 X165:($i > $o)]: 109.58/110.30 ((?[X166]: 109.58/110.30 ((~ 109.58/110.30 X165( 109.58/110.30 X166)) & 109.58/110.30 in( 109.58/110.30 X166,X164))) => 109.58/110.30 (~ 109.58/110.30 (![X167]: 109.58/110.30 (in( 109.58/110.30 X167,X164) => 109.58/110.30 X165( 109.58/110.30 X167)))))) => 109.58/110.30 ((![X168:$o]: 109.58/110.30 (X168 => 109.58/110.30 in(emptyset, 109.58/110.30 prop2set( 109.58/110.30 X168)))) => 109.58/110.30 ((![X169:$o]: 109.58/110.30 (X169 => 109.58/110.30 set2prop( 109.58/110.30 prop2set( 109.58/110.30 X169)))) => 109.58/110.30 ((![X170, 109.58/110.30 X171:( 109.58/110.30 $i > $o)]: 109.58/110.30 ((~ 109.58/110.30 (?[X172]: 109.58/110.30 (X171( 109.58/110.30 X172) & 109.58/110.30 in( 109.58/110.30 X172,X170)))) => 109.58/110.30 (![X173]: 109.58/110.30 ( 109.58/110.30 in( 109.58/110.30 X173,X170) => 109.58/110.30 ( 109.58/110.30 ~ 109.58/110.30 X171( 109.58/110.30 X173)))))) => 109.58/110.30 ((![X174, 109.58/110.30 X175:( 109.58/110.30 $i > $o)]: 109.58/110.30 ((~ 109.58/110.30 ( 109.58/110.30 ![X176]: 109.58/110.30 (in( 109.58/110.30 X176,X174) => 109.58/110.30 X175( 109.58/110.30 X176)))) => 109.58/110.30 (?[X177]: 109.58/110.30 (( 109.58/110.30 ~ 109.58/110.30 X175( 109.58/110.30 X177)) & 109.58/110.30 in( 109.58/110.30 X177,X174))))) => 109.58/110.30 ((![X178:( 109.58/110.30 $i > $o)]: 109.58/110.30 ((?[X179]: 109.58/110.30 (( 109.58/110.30 ![X180]: 109.58/110.30 (X178( 109.58/110.30 X180) => 109.58/110.30 (X179 = 109.58/110.30 X180))) & 109.58/110.30 X178( 109.58/110.30 X179))) => 109.58/110.30 (?[X181]: 109.58/110.30 (( 109.58/110.30 ![X182]: 109.58/110.30 (X178( 109.58/110.30 X182) => 109.58/110.30 (X181 = 109.58/110.30 X182))) & 109.58/110.30 X178( 109.58/110.30 X181))))) => 109.58/110.30 ((![X183:( 109.58/110.30 $i > $o)]: 109.58/110.30 (( 109.58/110.30 ?[X184]: 109.58/110.30 X183( 109.58/110.30 X184)) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X185, 109.58/110.30 X186]: 109.58/110.30 (X183( 109.58/110.30 X185) => 109.58/110.30 (X183( 109.58/110.30 X186) => 109.58/110.30 (X185 = 109.58/110.30 X186)))) => 109.58/110.30 ( 109.58/110.30 ?[X187]: 109.58/110.30 (( 109.58/110.30 ![X188]: 109.58/110.30 (X183( 109.58/110.30 X188) => 109.58/110.30 (X187 = 109.58/110.30 X188))) & 109.58/110.30 X183( 109.58/110.30 X187)))))) => 109.58/110.30 ((![X189:( 109.58/110.30 $i > $o)]: 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ?[X190]: 109.58/110.30 (![X191]: 109.58/110.30 (X189( 109.58/110.30 X191) <=> 109.58/110.30 (X191 = 109.58/110.30 X190)))) => 109.58/110.30 ( 109.58/110.30 ?[X192]: 109.58/110.30 (( 109.58/110.30 ![X193]: 109.58/110.30 (X189( 109.58/110.30 X193) => 109.58/110.30 (X192 = 109.58/110.30 X193))) & 109.58/110.30 X189( 109.58/110.30 X192))))) => 109.58/110.30 ((![X194, 109.58/110.30 X195]: 109.58/110.30 (( 109.58/110.30 X194 = 109.58/110.30 X195) => 109.58/110.30 (![X196, 109.58/110.30 X197]: 109.58/110.30 (( 109.58/110.30 X196 = 109.58/110.30 X197) => 109.58/110.30 (in( 109.58/110.30 X196,X194) => 109.58/110.30 in( 109.58/110.30 X197,X195)))))) => 109.58/110.30 ((![X198, 109.58/110.30 X199]: 109.58/110.30 (( 109.58/110.30 X198 = 109.58/110.30 X199) => 109.58/110.30 (![X200, 109.58/110.30 X201]: 109.58/110.30 (( 109.58/110.30 X200 = 109.58/110.30 X201) => 109.58/110.30 (in( 109.58/110.30 X200,X198) <=> 109.58/110.30 in( 109.58/110.30 X201,X199)))))) => 109.58/110.30 (( 109.58/110.30 ![X202:( 109.58/110.30 $i > $o)]: 109.58/110.30 (( 109.58/110.30 ?[X203]: 109.58/110.30 (( 109.58/110.30 ![X204]: 109.58/110.30 (X202( 109.58/110.30 X204) => 109.58/110.30 (X203 = 109.58/110.30 X204))) & 109.58/110.30 X202( 109.58/110.30 X203))) => 109.58/110.30 (![X205, 109.58/110.30 X206]: 109.58/110.30 (X202( 109.58/110.30 X205) => 109.58/110.30 (X202( 109.58/110.30 X206) => 109.58/110.30 (X205 = 109.58/110.30 X206)))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X207:( 109.58/110.30 $i > $o), 109.58/110.30 X208:( 109.58/110.30 $i > $o)]: 109.58/110.30 (( 109.58/110.30 ![X209, 109.58/110.30 X210]: 109.58/110.30 (( 109.58/110.30 X209 = 109.58/110.30 X210) => 109.58/110.30 (X207( 109.58/110.30 X209) <=> 109.58/110.30 X208( 109.58/110.30 X210)))) => 109.58/110.30 (( 109.58/110.30 ?[X211]: 109.58/110.30 zip_tseitin5( 109.58/110.30 X211,X207)) <=> 109.58/110.30 (?[X213]: 109.58/110.30 zip_tseitin5( 109.58/110.30 X213,X208))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 emptyset = 109.58/110.30 emptyset) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X215, 109.58/110.30 X216]: 109.58/110.30 (( 109.58/110.30 X215 = 109.58/110.30 X216) => 109.58/110.30 (![X217, 109.58/110.30 X218]: 109.58/110.30 (( 109.58/110.30 X217 = 109.58/110.30 X218) => 109.58/110.30 (setadjoin( 109.58/110.30 X215,X217) = 109.58/110.30 setadjoin( 109.58/110.30 X216,X218)))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X219, 109.58/110.30 X220]: 109.58/110.30 (( 109.58/110.30 X219 = 109.58/110.30 X220) => 109.58/110.30 (powerset( 109.58/110.30 X219) = 109.58/110.30 powerset( 109.58/110.30 X220)))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X221, 109.58/110.30 X222]: 109.58/110.30 (( 109.58/110.30 X221 = 109.58/110.30 X222) => 109.58/110.30 (setunion( 109.58/110.30 X221) = 109.58/110.30 setunion( 109.58/110.30 X222)))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 omega = 109.58/110.30 omega) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X223:( 109.58/110.30 $i > $o)]: 109.58/110.30 (( 109.58/110.30 ?[X224]: 109.58/110.30 (( 109.58/110.30 ![X225]: 109.58/110.30 (X223( 109.58/110.30 X225) => 109.58/110.30 (X224 = 109.58/110.30 X225))) & 109.58/110.30 X223( 109.58/110.30 X224))) => 109.58/110.30 (![X226, 109.58/110.30 X227]: 109.58/110.30 (X223( 109.58/110.30 X226) => 109.58/110.30 (X223( 109.58/110.30 X227) => 109.58/110.30 (X226 = 109.58/110.30 X227)))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X228:( 109.58/110.30 $i > $o), 109.58/110.30 X229:( 109.58/110.30 $i > $o)]: 109.58/110.30 (( 109.58/110.30 ![X230, 109.58/110.30 X231]: 109.58/110.30 (( 109.58/110.30 X230 = 109.58/110.30 X231) => 109.58/110.30 (X228( 109.58/110.30 X230) <=> 109.58/110.30 X229( 109.58/110.30 X231)))) => 109.58/110.30 (( 109.58/110.30 ?[X232]: 109.58/110.30 (( 109.58/110.30 ![X233]: 109.58/110.30 (X228( 109.58/110.30 X233) => 109.58/110.30 (X232 = 109.58/110.30 X233))) & 109.58/110.30 X228( 109.58/110.30 X232))) => 109.58/110.30 (( 109.58/110.30 ?[X234]: 109.58/110.30 (( 109.58/110.30 ![X235]: 109.58/110.30 (X229( 109.58/110.30 X235) => 109.58/110.30 (X234 = 109.58/110.30 X235))) & 109.58/110.30 X229( 109.58/110.30 X234))) => 109.58/110.30 (descr( 109.58/110.30 '#ll_0'( 109.58/110.30 X228)) = 109.58/110.30 descr( 109.58/110.30 '#ll_0'( 109.58/110.30 X229))))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X236, 109.58/110.30 X237]: 109.58/110.30 (( 109.58/110.30 X236 = 109.58/110.30 X237) => 109.58/110.30 (![X238:( 109.58/110.30 $i > $o), 109.58/110.30 X239:( 109.58/110.30 $i > $o)]: 109.58/110.30 (( 109.58/110.30 ![X240]: 109.58/110.30 (in( 109.58/110.30 X240,X236) => 109.58/110.30 (![X241]: 109.58/110.30 (in( 109.58/110.30 X241,X237) => 109.58/110.30 (( 109.58/110.30 X240 = 109.58/110.30 X241) => 109.58/110.30 (X238( 109.58/110.30 X240) <=> 109.58/110.30 X239( 109.58/110.30 X241))))))) => 109.58/110.30 (dsetconstr( 109.58/110.30 X236, 109.58/110.30 '#ll_0'( 109.58/110.30 X238)) = 109.58/110.30 dsetconstr( 109.58/110.30 X237, 109.58/110.30 '#ll_0'( 109.58/110.30 X239))))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X242, 109.58/110.30 X243]: 109.58/110.30 (( 109.58/110.30 ![X244]: 109.58/110.30 (in( 109.58/110.30 X244,X242) => 109.58/110.30 in( 109.58/110.30 X244,X243))) => 109.58/110.30 subset( 109.58/110.30 X242,X243))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X245, 109.58/110.30 X246]: 109.58/110.30 (( 109.58/110.30 X245 = 109.58/110.30 X246) => 109.58/110.30 subset( 109.58/110.30 X246,X245))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X247, 109.58/110.30 X248]: 109.58/110.30 (( 109.58/110.30 X247 = 109.58/110.30 X248) => 109.58/110.30 subset( 109.58/110.30 X247,X248))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X249, 109.58/110.30 X250]: 109.58/110.30 (( 109.58/110.30 ![X251]: 109.58/110.30 (in( 109.58/110.30 X251,X249) => 109.58/110.30 in( 109.58/110.30 X251,X250))) => 109.58/110.30 subset( 109.58/110.30 X249,X250))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X252]: 109.58/110.30 subset( 109.58/110.30 emptyset, 109.58/110.30 X252)) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X253, 109.58/110.30 X254,X255]: 109.58/110.30 (subset( 109.58/110.30 X253,X254) => 109.58/110.30 (in( 109.58/110.30 X255,X253) => 109.58/110.30 in( 109.58/110.30 X255,X254)))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X256, 109.58/110.30 X257,X258]: 109.58/110.30 (subset( 109.58/110.30 X256,X257) => 109.58/110.30 (( 109.58/110.30 ~ 109.58/110.30 in( 109.58/110.30 X258,X257)) => 109.58/110.30 (~ 109.58/110.30 in( 109.58/110.30 X258,X256))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X259, 109.58/110.30 X260,X261]: 109.58/110.30 (in( 109.58/110.30 X261,X259) => 109.58/110.30 (( 109.58/110.30 ~ 109.58/110.30 in( 109.58/110.30 X261,X260)) => 109.58/110.30 (~ 109.58/110.30 subset( 109.58/110.30 X259,X260))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X262, 109.58/110.30 X263]: 109.58/110.30 (( 109.58/110.30 ~ 109.58/110.30 subset( 109.58/110.30 X262,X263)) => 109.58/110.30 (X262 != 109.58/110.30 X263))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X264, 109.58/110.30 X265,X266]: 109.58/110.30 (in( 109.58/110.30 X266,X264) => 109.58/110.30 (( 109.58/110.30 ~ 109.58/110.30 in( 109.58/110.30 X266,X265)) => 109.58/110.30 (X264 != 109.58/110.30 X265)))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X267]: 109.58/110.30 subset( 109.58/110.30 X267,X267)) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X268, 109.58/110.30 X269,X270]: 109.58/110.30 (subset( 109.58/110.30 X268,X269) => 109.58/110.30 (subset( 109.58/110.30 X269,X270) => 109.58/110.30 subset( 109.58/110.30 X268,X270)))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X271, 109.58/110.30 X272]: 109.58/110.30 subset( 109.58/110.30 X272, 109.58/110.30 setadjoin( 109.58/110.30 X271,X272))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X273, 109.58/110.30 X274,X275]: 109.58/110.30 (subset( 109.58/110.30 X273,X275) => 109.58/110.30 subset( 109.58/110.30 X273, 109.58/110.30 setadjoin( 109.58/110.30 X274,X275)))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X276, 109.58/110.30 X277]: 109.58/110.30 (subset( 109.58/110.30 X276,X277) => 109.58/110.30 in( 109.58/110.30 X276, 109.58/110.30 powerset( 109.58/110.30 X277)))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X278, 109.58/110.30 X279]: 109.58/110.30 (subset( 109.58/110.30 X278,X279) => 109.58/110.30 (subset( 109.58/110.30 X279,X278) => 109.58/110.30 (X278 = 109.58/110.30 X279)))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X280]: 109.58/110.30 (subset( 109.58/110.30 X280, 109.58/110.30 emptyset) => 109.58/110.30 (X280 = 109.58/110.30 emptyset))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X281, 109.58/110.30 X282]: 109.58/110.30 (subset( 109.58/110.30 X282,X281) => 109.58/110.30 in( 109.58/110.30 X282, 109.58/110.30 powerset( 109.58/110.30 X281)))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X283, 109.58/110.30 X284]: 109.58/110.30 (in( 109.58/110.30 X284, 109.58/110.30 powerset( 109.58/110.30 X283)) => 109.58/110.30 subset( 109.58/110.30 X284,X283))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X285]: 109.58/110.30 in( 109.58/110.30 X285, 109.58/110.30 powerset( 109.58/110.30 X285))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X286, 109.58/110.30 X287]: 109.58/110.30 (subset( 109.58/110.30 X286,X287) => 109.58/110.30 subset( 109.58/110.30 powerset( 109.58/110.30 X286), 109.58/110.30 powerset( 109.58/110.30 X287)))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X288, 109.58/110.30 X289:( 109.58/110.30 $i > $o)]: 109.58/110.30 in( 109.58/110.30 dsetconstr( 109.58/110.30 X288, 109.58/110.30 '#ll_0'( 109.58/110.30 X289)), 109.58/110.30 powerset( 109.58/110.30 X288))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X290, 109.58/110.30 X291:( 109.58/110.30 $i > $o)]: 109.58/110.30 subset( 109.58/110.30 dsetconstr( 109.58/110.30 X290, 109.58/110.30 '#ll_0'( 109.58/110.30 X291)), 109.58/110.30 X290)) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X292, 109.58/110.30 X293,X294]: 109.58/110.30 (in( 109.58/110.30 X294,X292) => 109.58/110.30 in( 109.58/110.30 X294, 109.58/110.30 binunion( 109.58/110.30 X292,X293)))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X295, 109.58/110.30 X296]: 109.58/110.30 in( 109.58/110.30 X296, 109.58/110.30 setadjoin( 109.58/110.30 X295, 109.58/110.30 setadjoin( 109.58/110.30 X296, 109.58/110.30 emptyset)))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X297, 109.58/110.30 X298,X299]: 109.58/110.30 (in( 109.58/110.30 X299,X298) => 109.58/110.30 in( 109.58/110.30 X299, 109.58/110.30 binunion( 109.58/110.30 X297,X298)))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X300, 109.58/110.30 X301, 109.58/110.30 X302, 109.58/110.30 X303:$o]: 109.58/110.30 (in( 109.58/110.30 X302, 109.58/110.30 binunion( 109.58/110.30 X300,X301)) => 109.58/110.30 (( 109.58/110.30 in( 109.58/110.30 X302,X300) => 109.58/110.30 X303) => 109.58/110.30 (( 109.58/110.30 in( 109.58/110.30 X302,X301) => 109.58/110.30 X303) => 109.58/110.30 X303)))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X304, 109.58/110.30 X305,X306]: 109.58/110.30 (in( 109.58/110.30 X306, 109.58/110.30 binunion( 109.58/110.30 X304,X305)) => 109.58/110.30 (in( 109.58/110.30 X306,X305) | 109.58/110.30 in( 109.58/110.30 X306,X304)))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X307, 109.58/110.30 X308]: 109.58/110.30 subset( 109.58/110.30 X307, 109.58/110.30 binunion( 109.58/110.30 X307,X308))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X309, 109.58/110.30 X310]: 109.58/110.30 subset( 109.58/110.30 X310, 109.58/110.30 binunion( 109.58/110.30 X309,X310))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X311, 109.58/110.30 X312,X313]: 109.58/110.30 (in( 109.58/110.30 X313,X311) => 109.58/110.30 (in( 109.58/110.30 X313,X312) => 109.58/110.30 in( 109.58/110.30 X313, 109.58/110.30 binintersect( 109.58/110.30 X311,X312))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X314, 109.58/110.30 X315,X316]: 109.58/110.30 (subset( 109.58/110.30 X316,X314) => 109.58/110.30 (subset( 109.58/110.30 X316,X315) => 109.58/110.30 subset( 109.58/110.30 X316, 109.58/110.30 binintersect( 109.58/110.30 X314,X315))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X317, 109.58/110.30 X318,X319]: 109.58/110.30 (in( 109.58/110.30 X319, 109.58/110.30 binintersect( 109.58/110.30 X317,X318)) => 109.58/110.30 in( 109.58/110.30 X319,X317))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X320, 109.58/110.30 X321]: 109.58/110.30 subset( 109.58/110.30 binintersect( 109.58/110.30 X320,X321), 109.58/110.30 X320)) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X322, 109.58/110.30 X323]: 109.58/110.30 (subset( 109.58/110.30 X322,X323) => 109.58/110.30 (binintersect( 109.58/110.30 X322,X323) = 109.58/110.30 X322))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X324, 109.58/110.30 X325]: 109.58/110.30 (( 109.58/110.30 binintersect( 109.58/110.30 X324,X325) = 109.58/110.30 X325) => 109.58/110.30 subset( 109.58/110.30 X325,X324))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X326, 109.58/110.30 X327,X328]: 109.58/110.30 (in( 109.58/110.30 X328, 109.58/110.30 binintersect( 109.58/110.30 X326,X327)) => 109.58/110.30 in( 109.58/110.30 X328,X327))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X329, 109.58/110.30 X330]: 109.58/110.30 (( 109.58/110.30 ~ 109.58/110.30 ( 109.58/110.30 ?[X331]: 109.58/110.30 (in( 109.58/110.30 X331,X330) & 109.58/110.30 in( 109.58/110.30 X331,X329)))) => 109.58/110.30 (binintersect( 109.58/110.30 X329,X330) = 109.58/110.30 emptyset))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X332, 109.58/110.30 X333]: 109.58/110.30 subset( 109.58/110.30 binintersect( 109.58/110.30 X332,X333), 109.58/110.30 X333)) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X334, 109.58/110.30 X335]: 109.58/110.30 (subset( 109.58/110.30 X335,X334) => 109.58/110.30 (binintersect( 109.58/110.30 X334,X335) = 109.58/110.30 X335))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X336, 109.58/110.30 X337]: 109.58/110.30 (( 109.58/110.30 binintersect( 109.58/110.30 X336,X337) = 109.58/110.30 X336) => 109.58/110.30 subset( 109.58/110.30 X336,X337))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X338, 109.58/110.30 X339,X340]: 109.58/110.30 (binintersect( 109.58/110.30 X338, 109.58/110.30 binunion( 109.58/110.30 X339,X340)) = 109.58/110.30 binunion( 109.58/110.30 binintersect( 109.58/110.30 X338,X339), 109.58/110.30 binintersect( 109.58/110.30 X338,X340)))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X341, 109.58/110.30 X342,X343]: 109.58/110.30 (in( 109.58/110.30 X343,X341) => 109.58/110.30 (( 109.58/110.30 ~ 109.58/110.30 in( 109.58/110.30 X343,X342)) => 109.58/110.30 in( 109.58/110.30 X343, 109.58/110.30 setminus( 109.58/110.30 X341,X342))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X344, 109.58/110.30 X345,X346]: 109.58/110.30 (in( 109.58/110.30 X346, 109.58/110.30 setminus( 109.58/110.30 X344,X345)) => 109.58/110.30 in( 109.58/110.30 X346,X344))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X347, 109.58/110.30 X348,X349]: 109.58/110.30 (in( 109.58/110.30 X349, 109.58/110.30 setminus( 109.58/110.30 X347,X348)) => 109.58/110.30 (~ 109.58/110.30 in( 109.58/110.30 X349,X348)))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X350, 109.58/110.30 X351]: 109.58/110.30 (subset( 109.58/110.30 X350,X351) => 109.58/110.30 (setminus( 109.58/110.30 X350,X351) = 109.58/110.30 emptyset))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X352, 109.58/110.30 X353,X354]: 109.58/110.30 (( 109.58/110.30 ~ 109.58/110.30 in( 109.58/110.30 X354, 109.58/110.30 setminus( 109.58/110.30 X352,X353))) => 109.58/110.30 (in( 109.58/110.30 X354,X352) => 109.58/110.30 in( 109.58/110.30 X354,X353)))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X355, 109.58/110.30 X356,X357]: 109.58/110.30 (( 109.58/110.30 ~ 109.58/110.30 in( 109.58/110.30 X357, 109.58/110.30 setminus( 109.58/110.30 X355,X356))) => 109.58/110.30 (( 109.58/110.30 ~ 109.58/110.30 in( 109.58/110.30 X357,X356)) => 109.58/110.30 (~ 109.58/110.30 in( 109.58/110.30 X357,X355))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X358, 109.58/110.30 X359,X360]: 109.58/110.30 (( 109.58/110.30 ~ 109.58/110.30 in( 109.58/110.30 X360,X358)) => 109.58/110.30 (~ 109.58/110.30 in( 109.58/110.30 X360, 109.58/110.30 setminus( 109.58/110.30 X358,X359))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X361, 109.58/110.30 X362,X363]: 109.58/110.30 (in( 109.58/110.30 X363,X362) => 109.58/110.30 (~ 109.58/110.30 in( 109.58/110.30 X363, 109.58/110.30 setminus( 109.58/110.30 X361,X362))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X364, 109.58/110.30 X365]: 109.58/110.30 subset( 109.58/110.30 setminus( 109.58/110.30 X364,X365), 109.58/110.30 X364)) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X366, 109.58/110.30 X367]: 109.58/110.30 (( 109.58/110.30 setminus( 109.58/110.30 X366,X367) = 109.58/110.30 emptyset) => 109.58/110.30 subset( 109.58/110.30 X366,X367))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X368, 109.58/110.30 X369,X370]: 109.58/110.30 (in( 109.58/110.30 X370, 109.58/110.30 symdiff( 109.58/110.30 X368,X369)) => 109.58/110.30 (![X371:$o]: 109.58/110.30 (( 109.58/110.30 in( 109.58/110.30 X370,X368) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ~ 109.58/110.30 in( 109.58/110.30 X370,X369)) => 109.58/110.30 X371)) => 109.58/110.30 (( 109.58/110.30 ( 109.58/110.30 ~ 109.58/110.30 in( 109.58/110.30 X370,X368)) => 109.58/110.30 ( 109.58/110.30 in( 109.58/110.30 X370,X369) => 109.58/110.30 X371)) => 109.58/110.30 X371))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X372, 109.58/110.30 X373,X374]: 109.58/110.30 (in( 109.58/110.30 X374,X372) => 109.58/110.30 (( 109.58/110.30 ~ 109.58/110.30 in( 109.58/110.30 X374,X373)) => 109.58/110.30 in( 109.58/110.30 X374, 109.58/110.30 symdiff( 109.58/110.30 X372,X373))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X375, 109.58/110.30 X376,X377]: 109.58/110.30 (( 109.58/110.30 ~ 109.58/110.30 in( 109.58/110.30 X377,X375)) => 109.58/110.30 (in( 109.58/110.30 X377,X376) => 109.58/110.30 in( 109.58/110.30 X377, 109.58/110.30 symdiff( 109.58/110.30 X375,X376))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X378, 109.58/110.30 X379,X380]: 109.58/110.30 (in( 109.58/110.30 X380,X378) => 109.58/110.30 (in( 109.58/110.30 X380,X379) => 109.58/110.30 (~ 109.58/110.30 in( 109.58/110.30 X380, 109.58/110.30 symdiff( 109.58/110.30 X378,X379)))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X381, 109.58/110.30 X382,X383]: 109.58/110.30 (( 109.58/110.30 ~ 109.58/110.30 in( 109.58/110.30 X383,X381)) => 109.58/110.30 (( 109.58/110.30 ~ 109.58/110.30 in( 109.58/110.30 X383,X382)) => 109.58/110.30 (~ 109.58/110.30 in( 109.58/110.30 X383, 109.58/110.30 symdiff( 109.58/110.30 X381,X382)))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X384, 109.58/110.30 X385]: 109.58/110.30 in( 109.58/110.30 X385, 109.58/110.30 setadjoin( 109.58/110.30 X384, 109.58/110.30 setadjoin( 109.58/110.30 X385, 109.58/110.30 emptyset)))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X386, 109.58/110.30 X387]: 109.58/110.30 in( 109.58/110.30 X386, 109.58/110.30 setunion( 109.58/110.30 setadjoin( 109.58/110.30 setadjoin( 109.58/110.30 X386, 109.58/110.30 emptyset), 109.58/110.30 setadjoin( 109.58/110.30 setadjoin( 109.58/110.30 X386, 109.58/110.30 setadjoin( 109.58/110.30 X387, 109.58/110.30 emptyset)), 109.58/110.30 emptyset))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X388, 109.58/110.30 X389]: 109.58/110.30 in( 109.58/110.30 X389, 109.58/110.30 setunion( 109.58/110.30 setadjoin( 109.58/110.30 setadjoin( 109.58/110.30 X388, 109.58/110.30 emptyset), 109.58/110.30 setadjoin( 109.58/110.30 setadjoin( 109.58/110.30 X388, 109.58/110.30 setadjoin( 109.58/110.30 X389, 109.58/110.30 emptyset)), 109.58/110.30 emptyset))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X390, 109.58/110.30 X391]: 109.58/110.30 iskpair( 109.58/110.30 setadjoin( 109.58/110.30 setadjoin( 109.58/110.30 X390, 109.58/110.30 emptyset), 109.58/110.30 setadjoin( 109.58/110.30 setadjoin( 109.58/110.30 X390, 109.58/110.30 setadjoin( 109.58/110.30 X391, 109.58/110.30 emptyset)), 109.58/110.30 emptyset)))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X392, 109.58/110.30 X393]: 109.58/110.30 iskpair( 109.58/110.30 kpair( 109.58/110.30 X392,X393))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X394, 109.58/110.30 X395]: 109.58/110.30 (in( 109.58/110.30 X395,X394) => 109.58/110.30 subset( 109.58/110.30 setadjoin( 109.58/110.30 X395, 109.58/110.30 emptyset), 109.58/110.30 X394))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X396, 109.58/110.30 X397]: 109.58/110.30 (in( 109.58/110.30 X397,X396) => 109.58/110.30 in( 109.58/110.30 setadjoin( 109.58/110.30 X397, 109.58/110.30 emptyset), 109.58/110.30 powerset( 109.58/110.30 X396)))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X398, 109.58/110.30 X399,X400]: 109.58/110.30 (in( 109.58/110.30 X400,X398) => 109.58/110.30 in( 109.58/110.30 setadjoin( 109.58/110.30 X400, 109.58/110.30 emptyset), 109.58/110.30 powerset( 109.58/110.30 binunion( 109.58/110.30 X398,X399))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X401, 109.58/110.30 X402,X403]: 109.58/110.30 (in( 109.58/110.30 X403, 109.58/110.30 setadjoin( 109.58/110.30 X401, 109.58/110.30 setadjoin( 109.58/110.30 X402, 109.58/110.30 emptyset))) => 109.58/110.30 (( 109.58/110.30 X403 = 109.58/110.30 X402) | 109.58/110.30 (X403 = 109.58/110.30 X401)))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X404, 109.58/110.30 X405,X406]: 109.58/110.30 (in( 109.58/110.30 X406,X404) => 109.58/110.30 (![X407]: 109.58/110.30 (in( 109.58/110.30 X407,X405) => 109.58/110.30 subset( 109.58/110.30 setadjoin( 109.58/110.30 X406, 109.58/110.30 setadjoin( 109.58/110.30 X407, 109.58/110.30 emptyset)), 109.58/110.30 binunion( 109.58/110.30 X404,X405)))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X408, 109.58/110.30 X409,X410]: 109.58/110.30 (in( 109.58/110.30 X410,X408) => 109.58/110.30 (![X411]: 109.58/110.30 (in( 109.58/110.30 X411,X409) => 109.58/110.30 in( 109.58/110.30 setadjoin( 109.58/110.30 X410, 109.58/110.30 setadjoin( 109.58/110.30 X411, 109.58/110.30 emptyset)), 109.58/110.30 powerset( 109.58/110.30 binunion( 109.58/110.30 X408,X409))))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X412, 109.58/110.30 X413,X414]: 109.58/110.30 (in( 109.58/110.30 X414,X412) => 109.58/110.30 (![X415]: 109.58/110.30 (in( 109.58/110.30 X415,X413) => 109.58/110.30 subset( 109.58/110.30 setadjoin( 109.58/110.30 setadjoin( 109.58/110.30 X414, 109.58/110.30 emptyset), 109.58/110.30 setadjoin( 109.58/110.30 setadjoin( 109.58/110.30 X414, 109.58/110.30 setadjoin( 109.58/110.30 X415, 109.58/110.30 emptyset)), 109.58/110.30 emptyset)), 109.58/110.30 powerset( 109.58/110.30 binunion( 109.58/110.30 X412,X413))))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X416, 109.58/110.30 X417,X418]: 109.58/110.30 (in( 109.58/110.30 X418,X416) => 109.58/110.30 (![X419]: 109.58/110.30 (in( 109.58/110.30 X419,X417) => 109.58/110.30 in( 109.58/110.30 setadjoin( 109.58/110.30 setadjoin( 109.58/110.30 X418, 109.58/110.30 emptyset), 109.58/110.30 setadjoin( 109.58/110.30 setadjoin( 109.58/110.30 X418, 109.58/110.30 setadjoin( 109.58/110.30 X419, 109.58/110.30 emptyset)), 109.58/110.30 emptyset)), 109.58/110.30 powerset( 109.58/110.30 powerset( 109.58/110.30 binunion( 109.58/110.30 X416,X417)))))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X420, 109.58/110.30 X421,X422]: 109.58/110.30 (in( 109.58/110.30 X422,X420) => 109.58/110.30 (![X423]: 109.58/110.30 (in( 109.58/110.30 X423,X421) => 109.58/110.30 in( 109.58/110.30 kpair( 109.58/110.30 X422,X423), 109.58/110.30 powerset( 109.58/110.30 powerset( 109.58/110.30 binunion( 109.58/110.30 X420,X421)))))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X424, 109.58/110.30 X425,X426]: 109.58/110.30 (in( 109.58/110.30 X426,X424) => 109.58/110.30 (![X427]: 109.58/110.30 (in( 109.58/110.30 X427,X425) => 109.58/110.30 in( 109.58/110.30 kpair( 109.58/110.30 X426,X427), 109.58/110.30 cartprod( 109.58/110.30 X424,X425)))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X428, 109.58/110.30 X429,X430]: 109.58/110.30 (in( 109.58/110.30 X430, 109.58/110.30 cartprod( 109.58/110.30 X428,X429)) => 109.58/110.30 (?[X431]: 109.58/110.30 (( 109.58/110.30 ?[X432]: 109.58/110.30 (( 109.58/110.30 X430 = 109.58/110.30 kpair( 109.58/110.30 X431,X432)) & 109.58/110.30 in( 109.58/110.30 X432,X429))) & 109.58/110.30 in( 109.58/110.30 X431,X428))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X433, 109.58/110.30 X434,X435]: 109.58/110.30 (in( 109.58/110.30 X435, 109.58/110.30 cartprod( 109.58/110.30 X433,X434)) => 109.58/110.30 iskpair( 109.58/110.30 X435))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X436, 109.58/110.30 X437]: 109.58/110.30 (in( 109.58/110.30 X437, 109.58/110.30 setunion( 109.58/110.30 X436)) => 109.58/110.30 (?[X438]: 109.58/110.30 (in( 109.58/110.30 X437,X438) & 109.58/110.30 in( 109.58/110.30 X438,X436))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X439]: 109.58/110.30 subset( 109.58/110.30 setunion( 109.58/110.30 setadjoin( 109.58/110.30 X439, 109.58/110.30 emptyset)), 109.58/110.30 X439)) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X440]: 109.58/110.30 subset( 109.58/110.30 X440, 109.58/110.30 setunion( 109.58/110.30 setadjoin( 109.58/110.30 X440, 109.58/110.30 emptyset)))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X441]: 109.58/110.30 (setunion( 109.58/110.30 setadjoin( 109.58/110.30 X441, 109.58/110.30 emptyset)) = 109.58/110.30 X441)) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X442, 109.58/110.30 X443:( 109.58/110.30 $i > $o)]: 109.58/110.30 (( 109.58/110.30 ![X444]: 109.58/110.30 (in( 109.58/110.30 X444,X442) => 109.58/110.30 (![X445]: 109.58/110.30 (in( 109.58/110.30 X445,X442) => 109.58/110.30 (X443( 109.58/110.30 X444) => 109.58/110.30 (X443( 109.58/110.30 X445) => 109.58/110.30 (X444 = 109.58/110.30 X445))))))) => 109.58/110.30 (( 109.58/110.30 ?[X446]: 109.58/110.30 (X443( 109.58/110.30 X446) & 109.58/110.30 in( 109.58/110.30 X446,X442))) => 109.58/110.30 (?[X447]: 109.58/110.30 (( 109.58/110.30 dsetconstr( 109.58/110.30 X442, 109.58/110.30 '#ll_0'( 109.58/110.30 X443)) = 109.58/110.30 setadjoin( 109.58/110.30 X447, 109.58/110.30 emptyset)) & 109.58/110.30 in( 109.58/110.30 X447, 109.58/110.30 dsetconstr( 109.58/110.30 X442, 109.58/110.30 '#ll_0'( 109.58/110.30 X443)))))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X448, 109.58/110.30 X449:( 109.58/110.30 $i > $o)]: 109.58/110.30 (( 109.58/110.30 ?[X450]: 109.58/110.30 (( 109.58/110.30 dsetconstr( 109.58/110.30 X448, 109.58/110.30 '#ll_0'( 109.58/110.30 X449)) = 109.58/110.30 setadjoin( 109.58/110.30 X450, 109.58/110.30 emptyset)) & 109.58/110.30 in( 109.58/110.30 X450, 109.58/110.30 dsetconstr( 109.58/110.30 X448, 109.58/110.30 '#ll_0'( 109.58/110.30 X449))))) => 109.58/110.30 (?[X451]: 109.58/110.30 (X449( 109.58/110.30 X451) & 109.58/110.30 in( 109.58/110.30 X451,X448))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X452, 109.58/110.30 X453:( 109.58/110.30 $i > $o), 109.58/110.30 X454]: 109.58/110.30 (in( 109.58/110.30 X454,X452) => 109.58/110.30 (X453( 109.58/110.30 X454) => 109.58/110.30 (( 109.58/110.30 ![X455]: 109.58/110.30 (in( 109.58/110.30 X455,X452) => 109.58/110.30 (X453( 109.58/110.30 X455) => 109.58/110.30 (X455 = 109.58/110.30 X454)))) => 109.58/110.30 (?[X456]: 109.58/110.30 (( 109.58/110.30 dsetconstr( 109.58/110.30 X452, 109.58/110.30 '#ll_0'( 109.58/110.30 X453)) = 109.58/110.30 setadjoin( 109.58/110.30 X456, 109.58/110.30 emptyset)) & 109.58/110.30 in( 109.58/110.30 X456, 109.58/110.30 dsetconstr( 109.58/110.30 X452, 109.58/110.30 '#ll_0'( 109.58/110.30 X453))))))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X457, 109.58/110.30 X458:( 109.58/110.30 $i > $o)]: 109.58/110.30 (( 109.58/110.30 ![X459]: 109.58/110.30 (in( 109.58/110.30 X459,X457) => 109.58/110.30 (![X460]: 109.58/110.30 (in( 109.58/110.30 X460,X457) => 109.58/110.30 (X458( 109.58/110.30 X459) => 109.58/110.30 (X458( 109.58/110.30 X460) => 109.58/110.30 (X459 = 109.58/110.30 X460))))))) => 109.58/110.30 (( 109.58/110.30 ?[X461]: 109.58/110.30 (X458( 109.58/110.30 X461) & 109.58/110.30 in( 109.58/110.30 X461,X457))) => 109.58/110.30 (?[X462]: 109.58/110.30 (( 109.58/110.30 dsetconstr( 109.58/110.30 X457, 109.58/110.30 '#ll_0'( 109.58/110.30 X458)) = 109.58/110.30 setadjoin( 109.58/110.30 X462, 109.58/110.30 emptyset)) & 109.58/110.30 in( 109.58/110.30 X462, 109.58/110.30 dsetconstr( 109.58/110.30 X457, 109.58/110.30 '#ll_0'( 109.58/110.30 X458)))))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X463, 109.58/110.30 X464]: 109.58/110.30 (( 109.58/110.30 setadjoin( 109.58/110.30 X463, 109.58/110.30 emptyset) = 109.58/110.30 setadjoin( 109.58/110.30 X464, 109.58/110.30 emptyset)) => 109.58/110.30 (X463 = 109.58/110.30 X464))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X465, 109.58/110.30 X466,X467]: 109.58/110.30 (in( 109.58/110.30 setadjoin( 109.58/110.30 X467, 109.58/110.30 emptyset), 109.58/110.30 setadjoin( 109.58/110.30 setadjoin( 109.58/110.30 X465, 109.58/110.30 emptyset), 109.58/110.30 setadjoin( 109.58/110.30 setadjoin( 109.58/110.30 X465, 109.58/110.30 setadjoin( 109.58/110.30 X466, 109.58/110.30 emptyset)), 109.58/110.30 emptyset))) => 109.58/110.30 (X465 = 109.58/110.30 X467))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X468]: 109.58/110.30 (iskpair( 109.58/110.30 X468) => 109.58/110.30 (?[X469]: 109.58/110.30 (( 109.58/110.30 dsetconstr( 109.58/110.30 setunion( 109.58/110.30 X468), 109.58/110.30 '#ll_6'( 109.58/110.30 X468)) = 109.58/110.30 setadjoin( 109.58/110.30 X469, 109.58/110.30 emptyset)) & 109.58/110.30 in( 109.58/110.30 X469, 109.58/110.30 dsetconstr( 109.58/110.30 setunion( 109.58/110.30 X468), 109.58/110.30 '#ll_6'( 109.58/110.30 X468))))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X470]: 109.58/110.30 (( 109.58/110.30 ?[X471]: 109.58/110.30 (( 109.58/110.30 X470 = 109.58/110.30 setadjoin( 109.58/110.30 X471, 109.58/110.30 emptyset)) & 109.58/110.30 in( 109.58/110.30 X471,X470))) => 109.58/110.30 in( 109.58/110.30 setunion( 109.58/110.30 X470), 109.58/110.30 X470))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X472, 109.58/110.30 X473]: 109.58/110.30 (kfst( 109.58/110.30 kpair( 109.58/110.30 X472,X473)) = 109.58/110.30 X472)) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X474, 109.58/110.30 X475,X476]: 109.58/110.30 (in( 109.58/110.30 X476, 109.58/110.30 cartprod( 109.58/110.30 X474,X475)) => 109.58/110.30 in( 109.58/110.30 kfst( 109.58/110.30 X476), 109.58/110.30 X474))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X477, 109.58/110.30 X478, 109.58/110.30 X479,X480]: 109.58/110.30 (( 109.58/110.30 setadjoin( 109.58/110.30 setadjoin( 109.58/110.30 X477, 109.58/110.30 emptyset), 109.58/110.30 setadjoin( 109.58/110.30 setadjoin( 109.58/110.30 X477, 109.58/110.30 setadjoin( 109.58/110.30 X478, 109.58/110.30 emptyset)), 109.58/110.30 emptyset)) = 109.58/110.30 setadjoin( 109.58/110.30 setadjoin( 109.58/110.30 X479, 109.58/110.30 emptyset), 109.58/110.30 setadjoin( 109.58/110.30 setadjoin( 109.58/110.30 X479, 109.58/110.30 setadjoin( 109.58/110.30 X480, 109.58/110.30 emptyset)), 109.58/110.30 emptyset))) => 109.58/110.30 (X477 = 109.58/110.30 X479))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X481, 109.58/110.30 X482, 109.58/110.30 X483,X484]: 109.58/110.30 (( 109.58/110.30 kpair( 109.58/110.30 X481,X482) = 109.58/110.30 kpair( 109.58/110.30 X483,X484)) => 109.58/110.30 (X481 = 109.58/110.30 X483))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X485, 109.58/110.30 X486]: 109.58/110.30 (( 109.58/110.30 X485 = 109.58/110.30 X486) => 109.58/110.30 (setadjoin( 109.58/110.30 X485, 109.58/110.30 setadjoin( 109.58/110.30 X486, 109.58/110.30 emptyset)) = 109.58/110.30 setadjoin( 109.58/110.30 X485, 109.58/110.30 emptyset)))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X487, 109.58/110.30 X488]: 109.58/110.30 (( 109.58/110.30 X487 = 109.58/110.30 X488) => 109.58/110.30 (setadjoin( 109.58/110.30 setadjoin( 109.58/110.30 X487, 109.58/110.30 emptyset), 109.58/110.30 setadjoin( 109.58/110.30 setadjoin( 109.58/110.30 X487, 109.58/110.30 setadjoin( 109.58/110.30 X488, 109.58/110.30 emptyset)), 109.58/110.30 emptyset)) = 109.58/110.30 setadjoin( 109.58/110.30 setadjoin( 109.58/110.30 X487, 109.58/110.30 emptyset), 109.58/110.30 emptyset)))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X489, 109.58/110.30 X490, 109.58/110.30 X491,X492]: 109.58/110.30 (( 109.58/110.30 setadjoin( 109.58/110.30 setadjoin( 109.58/110.30 X489, 109.58/110.30 emptyset), 109.58/110.30 setadjoin( 109.58/110.30 setadjoin( 109.58/110.30 X489, 109.58/110.30 setadjoin( 109.58/110.30 X490, 109.58/110.30 emptyset)), 109.58/110.30 emptyset)) = 109.58/110.30 setadjoin( 109.58/110.30 setadjoin( 109.58/110.30 X491, 109.58/110.30 emptyset), 109.58/110.30 setadjoin( 109.58/110.30 setadjoin( 109.58/110.30 X491, 109.58/110.30 setadjoin( 109.58/110.30 X492, 109.58/110.30 emptyset)), 109.58/110.30 emptyset))) => 109.58/110.30 (( 109.58/110.30 X491 = 109.58/110.30 X492) => 109.58/110.30 (X490 = 109.58/110.30 X492)))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X493, 109.58/110.30 X494,X495]: 109.58/110.30 (( 109.58/110.30 setadjoin( 109.58/110.30 X493, 109.58/110.30 setadjoin( 109.58/110.30 X494, 109.58/110.30 emptyset)) = 109.58/110.30 setadjoin( 109.58/110.30 X495, 109.58/110.30 emptyset)) => 109.58/110.30 (X493 = 109.58/110.30 X494))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X496, 109.58/110.30 X497, 109.58/110.30 X498,X499]: 109.58/110.30 (( 109.58/110.30 setadjoin( 109.58/110.30 setadjoin( 109.58/110.30 X496, 109.58/110.30 emptyset), 109.58/110.30 setadjoin( 109.58/110.30 setadjoin( 109.58/110.30 X496, 109.58/110.30 setadjoin( 109.58/110.30 X497, 109.58/110.30 emptyset)), 109.58/110.30 emptyset)) = 109.58/110.30 setadjoin( 109.58/110.30 setadjoin( 109.58/110.30 X498, 109.58/110.30 emptyset), 109.58/110.30 setadjoin( 109.58/110.30 setadjoin( 109.58/110.30 X498, 109.58/110.30 setadjoin( 109.58/110.30 X499, 109.58/110.30 emptyset)), 109.58/110.30 emptyset))) => 109.58/110.30 (X497 = 109.58/110.30 X499))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X500, 109.58/110.30 X501, 109.58/110.30 X502,X503]: 109.58/110.30 (( 109.58/110.30 kpair( 109.58/110.30 X500,X501) = 109.58/110.30 kpair( 109.58/110.30 X502,X503)) => 109.58/110.30 (X501 = 109.58/110.30 X503))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X504]: 109.58/110.30 (iskpair( 109.58/110.30 X504) => 109.58/110.30 (?[X505]: 109.58/110.30 (( 109.58/110.30 dsetconstr( 109.58/110.30 setunion( 109.58/110.30 X504), 109.58/110.30 '#ll_5'( 109.58/110.30 X504)) = 109.58/110.30 setadjoin( 109.58/110.30 X505, 109.58/110.30 emptyset)) & 109.58/110.30 in( 109.58/110.30 X505, 109.58/110.30 dsetconstr( 109.58/110.30 setunion( 109.58/110.30 X504), 109.58/110.30 '#ll_5'( 109.58/110.30 X504))))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X506, 109.58/110.30 X507]: 109.58/110.30 (ksnd( 109.58/110.30 kpair( 109.58/110.30 X506,X507)) = 109.58/110.30 X507)) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X508]: 109.58/110.30 (iskpair( 109.58/110.30 X508) => 109.58/110.30 (kpair( 109.58/110.30 kfst( 109.58/110.30 X508), 109.58/110.30 ksnd( 109.58/110.30 X508)) = 109.58/110.30 X508))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X509, 109.58/110.30 X510,X511]: 109.58/110.30 (in( 109.58/110.30 X511, 109.58/110.30 cartprod( 109.58/110.30 X509,X510)) => 109.58/110.30 in( 109.58/110.30 ksnd( 109.58/110.30 X511), 109.58/110.30 X510))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X512, 109.58/110.30 X513, 109.58/110.30 X514,X515]: 109.58/110.30 (in( 109.58/110.30 kpair( 109.58/110.30 X514,X515), 109.58/110.30 cartprod( 109.58/110.30 X512,X513)) => 109.58/110.30 in( 109.58/110.30 X514,X512))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X516, 109.58/110.30 X517, 109.58/110.30 X518,X519]: 109.58/110.30 (in( 109.58/110.30 kpair( 109.58/110.30 X518,X519), 109.58/110.30 cartprod( 109.58/110.30 X516,X517)) => 109.58/110.30 in( 109.58/110.30 X519,X517))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X520, 109.58/110.30 X521,X522]: 109.58/110.30 (in( 109.58/110.30 X522,X520) => 109.58/110.30 (![X523]: 109.58/110.30 (in( 109.58/110.30 X523,X521) => 109.58/110.30 (kpair( 109.58/110.30 X522,X523) = 109.58/110.30 kpair( 109.58/110.30 X522,X523)))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X524, 109.58/110.30 X525,X526]: 109.58/110.30 (in( 109.58/110.30 X526,X524) => 109.58/110.30 (![X527]: 109.58/110.30 (in( 109.58/110.30 X527,X525) => 109.58/110.30 (kfst( 109.58/110.30 kpair( 109.58/110.30 X526,X527)) = 109.58/110.30 X526))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X528, 109.58/110.30 X529,X530]: 109.58/110.30 (in( 109.58/110.30 X530,X528) => 109.58/110.30 (![X531]: 109.58/110.30 (in( 109.58/110.30 X531,X529) => 109.58/110.30 (ksnd( 109.58/110.30 kpair( 109.58/110.30 X530,X531)) = 109.58/110.30 X531))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X532, 109.58/110.30 X533,X534]: 109.58/110.30 (in( 109.58/110.30 X534, 109.58/110.30 cartprod( 109.58/110.30 X532,X533)) => 109.58/110.30 (kpair( 109.58/110.30 kfst( 109.58/110.30 X534), 109.58/110.30 ksnd( 109.58/110.30 X534)) = 109.58/110.30 X534))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X535, 109.58/110.30 X536, 109.58/110.30 X537:( 109.58/110.30 ($i * $i) > 109.58/110.30 $o),X538]: 109.58/110.30 (in( 109.58/110.30 X538,X535) => 109.58/110.30 (![X539]: 109.58/110.30 (in( 109.58/110.30 X539,X536) => 109.58/110.30 (X537( 109.58/110.30 X538,X539) => 109.58/110.30 in( 109.58/110.30 kpair( 109.58/110.30 X538,X539), 109.58/110.30 dpsetconstr( 109.58/110.30 X535, 109.58/110.30 X536, 109.58/110.30 '#ll_4'( 109.58/110.30 X537)))))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X540, 109.58/110.30 X541, 109.58/110.30 X542:( 109.58/110.30 ($i * $i) > 109.58/110.30 $o)]: 109.58/110.30 subset( 109.58/110.30 dpsetconstr( 109.58/110.30 X540, 109.58/110.30 X541, 109.58/110.30 '#ll_4'( 109.58/110.30 X542)), 109.58/110.30 cartprod( 109.58/110.30 X540,X541))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X543, 109.58/110.30 X544, 109.58/110.30 X545:( 109.58/110.30 ($i * $i) > 109.58/110.30 $o)]: 109.58/110.30 subset( 109.58/110.30 dpsetconstr( 109.58/110.30 X543, 109.58/110.30 X544, 109.58/110.30 '#ll_4'( 109.58/110.30 X545)), 109.58/110.30 cartprod( 109.58/110.30 X543,X544))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X546, 109.58/110.30 X547, 109.58/110.30 X548:( 109.58/110.30 ($i * $i) > 109.58/110.30 $o),X549]: 109.58/110.30 (in( 109.58/110.30 X549,X546) => 109.58/110.30 (![X550]: 109.58/110.30 (in( 109.58/110.30 X550,X547) => 109.58/110.30 (in( 109.58/110.30 kpair( 109.58/110.30 X549,X550), 109.58/110.30 dpsetconstr( 109.58/110.30 X546, 109.58/110.30 X547, 109.58/110.30 '#ll_4'( 109.58/110.30 X548))) => 109.58/110.30 X548( 109.58/110.30 X549,X550)))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X551, 109.58/110.30 X552, 109.58/110.30 X553:( 109.58/110.30 ($i * $i) > 109.58/110.30 $o),X554, 109.58/110.30 X555]: 109.58/110.30 (in( 109.58/110.30 kpair( 109.58/110.30 X554,X555), 109.58/110.30 dpsetconstr( 109.58/110.30 X551, 109.58/110.30 X552, 109.58/110.30 '#ll_4'( 109.58/110.30 X553))) => 109.58/110.30 in( 109.58/110.30 X554,X551))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X556, 109.58/110.30 X557, 109.58/110.30 X558:( 109.58/110.30 ($i * $i) > 109.58/110.30 $o),X559, 109.58/110.30 X560]: 109.58/110.30 (in( 109.58/110.30 kpair( 109.58/110.30 X559,X560), 109.58/110.30 dpsetconstr( 109.58/110.30 X556, 109.58/110.30 X557, 109.58/110.30 '#ll_4'( 109.58/110.30 X558))) => 109.58/110.30 in( 109.58/110.30 X560,X557))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X561, 109.58/110.30 X562, 109.58/110.30 X563:( 109.58/110.30 ($i * $i) > 109.58/110.30 $o),X564, 109.58/110.30 X565]: 109.58/110.30 (in( 109.58/110.30 kpair( 109.58/110.30 X564,X565), 109.58/110.30 dpsetconstr( 109.58/110.30 X561, 109.58/110.30 X562, 109.58/110.30 '#ll_4'( 109.58/110.30 X563))) => 109.58/110.30 X563( 109.58/110.30 X564,X565))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X566, 109.58/110.30 X567,X568]: 109.58/110.30 (( 109.58/110.30 ( 109.58/110.30 ![X569]: 109.58/110.30 (in( 109.58/110.30 X569,X566) => 109.58/110.30 (?[X570]: 109.58/110.30 (( 109.58/110.30 dsetconstr( 109.58/110.30 X567, 109.58/110.30 '#ll_3'( 109.58/110.30 X569,X568)) = 109.58/110.30 setadjoin( 109.58/110.30 X570, 109.58/110.30 emptyset)) & 109.58/110.30 in( 109.58/110.30 X570, 109.58/110.30 dsetconstr( 109.58/110.30 X567, 109.58/110.30 '#ll_3'( 109.58/110.30 X569,X568))))))) & 109.58/110.30 subset( 109.58/110.30 X568, 109.58/110.30 cartprod( 109.58/110.30 X566,X567))) => 109.58/110.30 (![X571]: 109.58/110.30 (in( 109.58/110.30 X571,X566) => 109.58/110.30 (?[X572]: 109.58/110.30 (( 109.58/110.30 dsetconstr( 109.58/110.30 X567, 109.58/110.30 '#ll_3'( 109.58/110.30 X571,X568)) = 109.58/110.30 setadjoin( 109.58/110.30 X572, 109.58/110.30 emptyset)) & 109.58/110.30 in( 109.58/110.30 X572, 109.58/110.30 dsetconstr( 109.58/110.30 X567, 109.58/110.30 '#ll_3'( 109.58/110.30 X571,X568))))))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X573, 109.58/110.30 X574,X575]: 109.58/110.30 (( 109.58/110.30 ( 109.58/110.30 ![X576]: 109.58/110.30 (in( 109.58/110.30 X576,X573) => 109.58/110.30 (?[X577]: 109.58/110.30 (( 109.58/110.30 dsetconstr( 109.58/110.30 X574, 109.58/110.30 '#ll_3'( 109.58/110.30 X576,X575)) = 109.58/110.30 setadjoin( 109.58/110.30 X577, 109.58/110.30 emptyset)) & 109.58/110.30 in( 109.58/110.30 X577, 109.58/110.30 dsetconstr( 109.58/110.30 X574, 109.58/110.30 '#ll_3'( 109.58/110.30 X576,X575))))))) & 109.58/110.30 subset( 109.58/110.30 X575, 109.58/110.30 cartprod( 109.58/110.30 X573,X574))) => 109.58/110.30 (![X578]: 109.58/110.30 (in( 109.58/110.30 X578,X573) => 109.58/110.30 in( 109.58/110.30 setunion( 109.58/110.30 dsetconstr( 109.58/110.30 X574, 109.58/110.30 '#ll_3'( 109.58/110.30 X578,X575))), 109.58/110.30 X574))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X579, 109.58/110.30 X580,X581]: 109.58/110.30 (( 109.58/110.30 ( 109.58/110.30 ![X582]: 109.58/110.30 (in( 109.58/110.30 X582,X579) => 109.58/110.30 (?[X583]: 109.58/110.30 (( 109.58/110.30 dsetconstr( 109.58/110.30 X580, 109.58/110.30 '#ll_3'( 109.58/110.30 X582,X581)) = 109.58/110.30 setadjoin( 109.58/110.30 X583, 109.58/110.30 emptyset)) & 109.58/110.30 in( 109.58/110.30 X583, 109.58/110.30 dsetconstr( 109.58/110.30 X580, 109.58/110.30 '#ll_3'( 109.58/110.30 X582,X581))))))) & 109.58/110.30 subset( 109.58/110.30 X581, 109.58/110.30 cartprod( 109.58/110.30 X579,X580))) => 109.58/110.30 (![X584]: 109.58/110.30 (in( 109.58/110.30 X584,X579) => 109.58/110.30 in( 109.58/110.30 setunion( 109.58/110.30 dsetconstr( 109.58/110.30 X580, 109.58/110.30 '#ll_3'( 109.58/110.30 X584,X581))), 109.58/110.30 X580))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X585, 109.58/110.30 X586,X587]: 109.58/110.30 (in( 109.58/110.30 X587, 109.58/110.30 funcSet( 109.58/110.30 X585,X586)) => 109.58/110.30 (( 109.58/110.30 ![X588]: 109.58/110.30 (in( 109.58/110.30 X588,X585) => 109.58/110.30 (?[X589]: 109.58/110.30 (( 109.58/110.30 dsetconstr( 109.58/110.30 X586, 109.58/110.30 '#ll_3'( 109.58/110.30 X588,X587)) = 109.58/110.30 setadjoin( 109.58/110.30 X589, 109.58/110.30 emptyset)) & 109.58/110.30 in( 109.58/110.30 X589, 109.58/110.30 dsetconstr( 109.58/110.30 X586, 109.58/110.30 '#ll_3'( 109.58/110.30 X588,X587))))))) & 109.58/110.30 subset( 109.58/110.30 X587, 109.58/110.30 cartprod( 109.58/110.30 X585,X586))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X590, 109.58/110.30 X591,X592]: 109.58/110.30 (in( 109.58/110.30 X592, 109.58/110.30 funcSet( 109.58/110.30 X590,X591)) => 109.58/110.30 (![X593]: 109.58/110.30 (in( 109.58/110.30 X593,X590) => 109.58/110.30 in( 109.58/110.30 setunion( 109.58/110.30 dsetconstr( 109.58/110.30 X591, 109.58/110.30 '#ll_3'( 109.58/110.30 X593,X592))), 109.58/110.30 X591))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X594, 109.58/110.30 X595,X596]: 109.58/110.30 (( 109.58/110.30 ( 109.58/110.30 ![X597]: 109.58/110.30 (in( 109.58/110.30 X597,X594) => 109.58/110.30 (?[X598]: 109.58/110.30 (( 109.58/110.30 dsetconstr( 109.58/110.30 X595, 109.58/110.30 '#ll_3'( 109.58/110.30 X597,X596)) = 109.58/110.30 setadjoin( 109.58/110.30 X598, 109.58/110.30 emptyset)) & 109.58/110.30 in( 109.58/110.30 X598, 109.58/110.30 dsetconstr( 109.58/110.30 X595, 109.58/110.30 '#ll_3'( 109.58/110.30 X597,X596))))))) & 109.58/110.30 subset( 109.58/110.30 X596, 109.58/110.30 cartprod( 109.58/110.30 X594,X595))) => 109.58/110.30 in( 109.58/110.30 X596, 109.58/110.30 funcSet( 109.58/110.30 X594,X595)))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X599, 109.58/110.30 X600, 109.58/110.30 X601:( 109.58/110.30 $i > $i)]: 109.58/110.30 (( 109.58/110.30 ![X602]: 109.58/110.30 (in( 109.58/110.30 X602,X599) => 109.58/110.30 in( 109.58/110.30 X601( 109.58/110.30 X602), 109.58/110.30 X600))) => 109.58/110.30 (( 109.58/110.30 ![X603]: 109.58/110.30 (in( 109.58/110.30 X603,X599) => 109.58/110.30 (?[X604]: 109.58/110.30 (( 109.58/110.30 dsetconstr( 109.58/110.30 X600, 109.58/110.30 '#ll_2'( 109.58/110.30 X603, 109.58/110.30 X601, 109.58/110.30 X600,X599)) = 109.58/110.30 setadjoin( 109.58/110.30 X604, 109.58/110.30 emptyset)) & 109.58/110.30 in( 109.58/110.30 X604, 109.58/110.30 dsetconstr( 109.58/110.30 X600, 109.58/110.30 '#ll_2'( 109.58/110.30 X603, 109.58/110.30 X601, 109.58/110.30 X600,X599))))))) & 109.58/110.30 subset( 109.58/110.30 dpsetconstr( 109.58/110.30 X599, 109.58/110.30 X600, 109.58/110.30 '#ll_1'( 109.58/110.30 X601)), 109.58/110.30 cartprod( 109.58/110.30 X599,X600))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X605, 109.58/110.30 X606, 109.58/110.30 X607:( 109.58/110.30 $i > $i)]: 109.58/110.30 (( 109.58/110.30 ![X608]: 109.58/110.30 (in( 109.58/110.30 X608,X605) => 109.58/110.30 in( 109.58/110.30 X607( 109.58/110.30 X608), 109.58/110.30 X606))) => 109.58/110.30 (( 109.58/110.30 ![X609]: 109.58/110.30 (in( 109.58/110.30 X609,X605) => 109.58/110.30 (?[X610]: 109.58/110.30 (( 109.58/110.30 dsetconstr( 109.58/110.30 X606, 109.58/110.30 '#ll_2'( 109.58/110.30 X609, 109.58/110.30 X607, 109.58/110.30 X606,X605)) = 109.58/110.30 setadjoin( 109.58/110.30 X610, 109.58/110.30 emptyset)) & 109.58/110.30 in( 109.58/110.30 X610, 109.58/110.30 dsetconstr( 109.58/110.30 X606, 109.58/110.30 '#ll_2'( 109.58/110.30 X609, 109.58/110.30 X607, 109.58/110.30 X606,X605))))))) & 109.58/110.30 subset( 109.58/110.30 dpsetconstr( 109.58/110.30 X605, 109.58/110.30 X606, 109.58/110.30 '#ll_1'( 109.58/110.30 X607)), 109.58/110.30 cartprod( 109.58/110.30 X605,X606))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X611, 109.58/110.30 X612, 109.58/110.30 X613:( 109.58/110.30 $i > $i)]: 109.58/110.30 (( 109.58/110.30 ![X614]: 109.58/110.30 (in( 109.58/110.30 X614,X611) => 109.58/110.30 in( 109.58/110.30 X613( 109.58/110.30 X614), 109.58/110.30 X612))) => 109.58/110.30 in( 109.58/110.30 dpsetconstr( 109.58/110.30 X611, 109.58/110.30 X612, 109.58/110.30 '#ll_1'( 109.58/110.30 X613)), 109.58/110.30 funcSet( 109.58/110.30 X611,X612)))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X615, 109.58/110.30 X616,X617]: 109.58/110.30 (subset( 109.58/110.30 X617, 109.58/110.30 cartprod( 109.58/110.30 X615,X616)) => 109.58/110.30 (![X618:( 109.58/110.30 $i > $o)]: 109.58/110.30 (( 109.58/110.30 ![X619]: 109.58/110.30 (in( 109.58/110.30 X619,X615) => 109.58/110.30 (![X620]: 109.58/110.30 (in( 109.58/110.30 X620,X616) => 109.58/110.30 (in( 109.58/110.30 kpair( 109.58/110.30 X619,X620), 109.58/110.30 X617) => 109.58/110.30 X618( 109.58/110.30 kpair( 109.58/110.30 X619,X620))))))) => 109.58/110.30 (![X621]: 109.58/110.30 (in( 109.58/110.30 X621,X617) => 109.58/110.30 X618( 109.58/110.30 X621))))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X622, 109.58/110.30 X623,X624]: 109.58/110.30 (subset( 109.58/110.30 X624, 109.58/110.30 cartprod( 109.58/110.30 X622,X623)) => 109.58/110.30 (![X625:( 109.58/110.30 $i > $o)]: 109.58/110.30 (( 109.58/110.30 ![X626]: 109.58/110.30 (in( 109.58/110.30 X626,X622) => 109.58/110.30 (![X627]: 109.58/110.30 (in( 109.58/110.30 X627,X623) => 109.58/110.30 (in( 109.58/110.30 kpair( 109.58/110.30 X626,X627), 109.58/110.30 X624) => 109.58/110.30 X625( 109.58/110.30 kpair( 109.58/110.30 X626,X627))))))) => 109.58/110.30 (![X628]: 109.58/110.30 (in( 109.58/110.30 X628,X624) => 109.58/110.30 X625( 109.58/110.30 X628))))))) => 109.58/110.30 ( 109.58/110.30 ![X629, 109.58/110.30 X630:( 109.58/110.30 $i > $o)]: 109.58/110.30 (( 109.58/110.30 ?[X631]: 109.58/110.30 (( 109.58/110.30 dsetconstr( 109.58/110.30 X629, 109.58/110.30 '#ll_0'( 109.58/110.30 X630)) = 109.58/110.30 setadjoin( 109.58/110.30 X631, 109.58/110.30 emptyset)) & 109.58/110.30 in( 109.58/110.30 X631, 109.58/110.30 dsetconstr( 109.58/110.30 X629, 109.58/110.30 '#ll_0'( 109.58/110.30 X630))))) => 109.58/110.30 (![X632]: 109.58/110.30 (in( 109.58/110.30 X632,X629) => 109.58/110.30 (![X633]: 109.58/110.30 (in( 109.58/110.30 X633,X629) => 109.58/110.30 (X630( 109.58/110.30 X632) => 109.58/110.30 (X630( 109.58/110.30 X633) => 109.58/110.30 (X632 = 109.58/110.30 X633))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 109.58/110.30 tff(zf_stmt_14, negated_conjecture, 109.58/110.30 (~ 109.58/110.30 ((![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))) => 109.58/110.30 ((![X5]: (~in(X5,emptyset))) => 109.58/110.30 ((![X6,X7,X8]: (in(X8,setadjoin(X6,X7)) <=> zip_tseitin0(X8,X7,X6))) => 109.58/110.30 ((![X9,X10]: 109.58/110.30 (in(X10,powerset(X9)) <=> (![X11]: zip_tseitin1(X11,X10,X9)))) => 109.58/110.30 ((![X12,X13]: 109.58/110.30 (in(X13,setunion(X12)) <=> (?[X14]: zip_tseitin2(X14,X13,X12)))) => 109.58/110.30 (in(emptyset,omega) => 109.58/110.30 ((![X15]: (in(X15,omega) => in(setadjoin(X15,X15),omega))) => 109.58/110.30 ((![X16]: 109.58/110.30 (((![X17]: 109.58/110.30 ((in(X17,X16) & in(X17,omega)) => 109.58/110.30 in(setadjoin(X17,X17),X16))) & 109.58/110.30 in(emptyset,X16)) => 109.58/110.30 (![X18]: (in(X18,omega) => in(X18,X16))))) => 109.58/110.30 ((![X19:(($i * $i) > $o),X20]: 109.58/110.30 ((![X21]: 109.58/110.30 (in(X21,X20) => 109.58/110.30 (?[X22]: 109.58/110.30 ((![X23]: (X19(X21,X23) => (X22 = X23))) & 109.58/110.30 X19(X21,X22))))) => 109.58/110.30 (?[X24]: 109.58/110.30 (![X25]: 109.58/110.30 (in(X25,X24) <=> 109.58/110.30 (?[X26]: zip_tseitin3(X26,X25,X20,X19))))))) => 109.58/110.30 ((![X27]: 109.58/110.30 ((?[X28]: in(X28,X27)) => 109.58/110.30 (?[X29]: 109.58/110.30 ((~(?[X30]: (in(X30,X27) & in(X30,X29)))) & in(X29,X27))))) => 109.58/110.30 ((![X31]: 109.58/110.30 (?[X32]: 109.58/110.30 ((![X33]: 109.58/110.30 (((?[X34]: in(X34,X33)) & 109.58/110.30 (![X35]: (in(X35,X33) => in(X35,X31)))) => 109.58/110.30 (?[X36,X37]: 109.58/110.30 ((![X38]: 109.58/110.30 (in(X38,X32) => 109.58/110.30 (in(X37,X38) | 109.58/110.30 (![X39]: (in(X39,X38) => in(X39,X36)))))) & 109.58/110.30 (~(?[X40]: (in(X40,X33) & in(X40,X36)))) & 109.58/110.30 in(X37,X33) & in(X36,X32))))) & 109.58/110.30 (![X41,X42]: 109.58/110.30 ((in(X42,X32) & in(X41,X32)) => 109.58/110.30 ((![X43]: (in(X43,X42) => in(X43,X41))) | 109.58/110.30 (![X44]: (in(X44,X41) => in(X44,X42)))))) & 109.58/110.30 (![X45,X46]: 109.58/110.30 ((in(X46,X31) & in(X45,X31)) => 109.58/110.30 ((![X47]: 109.58/110.30 (in(X47,X32) => (in(X45,X47) <=> in(X46,X47)))) => 109.58/110.30 (X45 = X46)))) & 109.58/110.30 (![X48]: 109.58/110.30 (in(X48,X32) => 109.58/110.30 (![X49]: (in(X49,X48) => in(X49,X31)))))))) => 109.58/110.30 ((![X50:($i > $o)]: 109.58/110.30 ((?[X51]: ((![X52]: (X50(X52) => (X51 = X52))) & X50(X51))) => 109.58/110.30 X50(descr('#ll_0'(X50))))) => 109.58/110.30 ((![X53,X54:($i > $o),X55]: 109.58/110.30 (in(X55,X53) => 109.58/110.30 (X54(X55) => in(X55,dsetconstr(X53,'#ll_0'(X54)))))) => 109.58/110.30 ((![X56,X57:($i > $o),X58]: 109.58/110.30 (in(X58,dsetconstr(X56,'#ll_0'(X57))) => in(X58,X56))) => 109.58/110.30 ((![X59,X60:($i > $o),X61]: 109.58/110.30 (in(X61,dsetconstr(X59,'#ll_0'(X60))) => X60(X61))) => 109.58/110.30 ((![X62:($i > $o)]: 109.58/110.30 ((?[X63]: 109.58/110.30 ((![X64]: (X62(X64) => (X63 = X64))) & X62(X63))) => 109.58/110.30 (?[X65]: 109.58/110.30 ((![X66]: (X62(X66) => (X65 = X66))) & X62(X65))))) => 109.58/110.30 ((![X67:$o,X68]: (in(X68,prop2set(X67)) => X67)) => 109.58/110.30 ((![X69]: (in(X69,emptyset) => (![X70:$o]: X70))) => 109.58/110.30 ((![X71]: (in(X71,emptyset) => $false)) => 109.58/110.30 ((![X72]: (~in(X72,emptyset))) => 109.58/110.30 ((![X73:($i > $o)]: 109.58/110.30 ((?[X74]: 109.58/110.30 ((![X75]: (X73(X75) => (X74 = X75))) & 109.58/110.30 X73(X74))) => 109.58/110.30 (?[X76]: X73(X76)))) => 109.58/110.30 ((![X77,X78]: 109.58/110.30 ((![X79]: (in(X79,X77) => in(X79,X78))) => 109.58/110.30 ((![X80]: (in(X80,X78) => in(X80,X77))) => 109.58/110.30 (X77 = X78)))) => 109.58/110.30 ((![X81]: 109.58/110.30 ((![X82]: (~in(X82,X81))) => (X81 = emptyset))) => 109.58/110.30 ((![X83]: 109.58/110.30 ((![X84]: (~in(X84,X83))) => (X83 = emptyset))) => 109.58/110.30 ((![X85,X86:($i > $o),X87]: 109.58/110.30 (in(X87,X85) => 109.58/110.30 (in(X87,dsetconstr(X85,'#ll_0'(X86))) <=> 109.58/110.30 X86(X87)))) => 109.58/110.30 ((![X88]: 109.58/110.30 ((X88 != emptyset) => (?[X89]: in(X89,X88)))) => 109.58/110.30 ((![X90,X91:($i > $o),X92]: 109.58/110.30 (in(X92,X90) => 109.58/110.30 (X91(X92) => 109.58/110.30 (dsetconstr(X90,'#ll_0'(X91)) != emptyset)))) => 109.58/110.30 ((![X93]: 109.58/110.30 ((?[X94]: in(X94,X93)) => 109.58/110.30 (X93 != emptyset))) => 109.58/110.30 ((![X95,X96]: in(X95,setadjoin(X95,X96))) => 109.58/110.30 (in(emptyset,setadjoin(emptyset,emptyset)) => 109.58/110.30 ((![X97,X98,X99]: 109.58/110.30 (in(X99,X98) => 109.58/110.30 in(X99,setadjoin(X97,X98)))) => 109.58/110.30 ((![X100,X101,X102]: 109.58/110.30 (in(X102,setadjoin(X100,X101)) => 109.58/110.30 (![X103:$o]: 109.58/110.30 (((X102 = X100) => X103) => 109.58/110.30 ((in(X102,X101) => X103) => X103))))) => 109.58/110.30 ((![X104,X105,X106]: 109.58/110.30 (in(X106,setadjoin(X104,X105)) => 109.58/110.30 (in(X106,X105) | (X106 = X104)))) => 109.58/110.30 ((![X107]: 109.58/110.30 (dsetconstr(X107,'#ll_7') = X107)) => 109.58/110.30 ((![X108,X109]: 109.58/110.30 ((![X110]: 109.58/110.30 (in(X110,X109) => in(X110,X108))) => 109.58/110.30 in(X109,powerset(X108)))) => 109.58/110.30 ((![X111]: in(emptyset,powerset(X111))) => 109.58/110.30 ((![X112]: 109.58/110.30 in(emptyset,powerset(X112))) => 109.58/110.30 ((![X113,X114,X115]: 109.58/110.30 (in(X114,powerset(X113)) => 109.58/110.30 (in(X115,X114) => in(X115,X113)))) => 109.58/110.30 ((![X116,X117,X118]: 109.58/110.30 (in(X117,X118) => 109.58/110.30 (in(X118,X116) => 109.58/110.30 in(X117,setunion(X116))))) => 109.58/110.30 ((![X119,X120]: 109.58/110.30 (in(X120,setunion(X119)) => 109.58/110.30 (![X121:$o]: 109.58/110.30 ((![X122]: 109.58/110.30 (in(X120,X122) => 109.58/110.30 (in(X122,X119) => 109.58/110.30 X121))) => 109.58/110.30 X121)))) => 109.58/110.30 ((![X123,X124]: 109.58/110.30 (in(X124,X123) => 109.58/110.30 in(X124, 109.58/110.30 powerset(setunion(X123))))) => 109.58/110.30 ((![X125:($i > $o)]: 109.58/110.30 ((?[X126]: 109.58/110.30 ((![X127]: 109.58/110.30 (X125(X127) => 109.58/110.30 (X126 = X127))) & 109.58/110.30 X125(X126))) => 109.58/110.30 (?[X128]: 109.58/110.30 (![X129]: 109.58/110.30 (X125(X129) <=> 109.58/110.30 (X129 = X128)))))) => 109.58/110.30 ((![X130]: 109.58/110.30 ((X130 != emptyset) => 109.58/110.30 (?[X131]: in(X131,X130)))) => 109.58/110.30 ((![X132,X133]: 109.58/110.30 (in(X132, 109.58/110.30 setadjoin(X133, 109.58/110.30 emptyset)) => 109.58/110.30 (X132 = X133))) => 109.58/110.30 ((![X134,X135]: 109.58/110.30 ((X134 != X135) => 109.58/110.30 (~ 109.58/110.30 in(X135, 109.58/110.30 setadjoin(X134, 109.58/110.30 emptyset))))) => 109.58/110.30 ((![X136,X137]: 109.58/110.30 ((X136 = X137) => 109.58/110.30 in(X136, 109.58/110.30 setadjoin(X137, 109.58/110.30 emptyset)))) => 109.58/110.30 ((![X138,X139]: 109.58/110.30 (in(X138, 109.58/110.30 setadjoin(X139, 109.58/110.30 emptyset)) => 109.58/110.30 in(X139, 109.58/110.30 setadjoin(X138, 109.58/110.30 emptyset)))) => 109.58/110.30 ((![X140,X141,X142]: 109.58/110.30 (in(X142, 109.58/110.30 setadjoin( 109.58/110.30 X140, 109.58/110.30 setadjoin( 109.58/110.30 X141,emptyset))) => 109.58/110.30 ((X142 = X141) | 109.58/110.30 (X142 = X140)))) => 109.58/110.30 ((![X143,X144]: 109.58/110.30 in(X143, 109.58/110.30 setadjoin( 109.58/110.30 X143, 109.58/110.30 setadjoin( 109.58/110.30 X144,emptyset)))) => 109.58/110.30 ((![X145,X146]: 109.58/110.30 in(X146, 109.58/110.30 setadjoin( 109.58/110.30 X145, 109.58/110.30 setadjoin( 109.58/110.30 X146,emptyset)))) => 109.58/110.30 ((![X147,X148:($i > $o)]: 109.58/110.30 ((?[X149]: 109.58/110.30 (X148(X149) & 109.58/110.30 in(X149,X147))) => 109.58/110.30 ((dsetconstr( 109.58/110.30 X147, 109.58/110.30 '#ll_0'(X148)) = 109.58/110.30 emptyset) => 109.58/110.30 $false))) => 109.58/110.30 ((![X150:($i > $o), 109.58/110.30 X151]: 109.58/110.30 (in(X151,emptyset) => 109.58/110.30 X150(X151))) => 109.58/110.30 ((![X152, 109.58/110.30 X153:($i > $o)]: 109.58/110.30 ((~ 109.58/110.30 (![X154]: 109.58/110.30 (in( 109.58/110.30 X154,X152) => 109.58/110.30 X153(X154)))) => 109.58/110.30 (?[X155]: 109.58/110.30 ((~X153(X155)) & 109.58/110.30 in(X155,X152))))) => 109.58/110.30 ((![X156, 109.58/110.30 X157:($i > $o)]: 109.58/110.30 ((![X158]: 109.58/110.30 (in( 109.58/110.30 X158,X156) => 109.58/110.30 (~ 109.58/110.30 X157( 109.58/110.30 X158)))) => 109.58/110.30 (~ 109.58/110.30 (?[X159]: 109.58/110.30 (X157( 109.58/110.30 X159) & 109.58/110.30 in( 109.58/110.30 X159,X156)))))) => 109.58/110.30 ((![X160, 109.58/110.30 X161:($i > $o)]: 109.58/110.30 ((~ 109.58/110.30 (?[X162]: 109.58/110.30 ( 109.58/110.30 X161( 109.58/110.30 X162) & 109.58/110.30 in( 109.58/110.30 X162,X160)))) => 109.58/110.30 (![X163]: 109.58/110.30 (in( 109.58/110.30 X163,X160) => 109.58/110.30 (~ 109.58/110.30 X161( 109.58/110.30 X163)))))) => 109.58/110.30 ((![X164, 109.58/110.30 X165:( 109.58/110.30 $i > $o)]: 109.58/110.30 ((?[X166]: 109.58/110.30 (( 109.58/110.30 ~ 109.58/110.30 X165( 109.58/110.30 X166)) & 109.58/110.30 in( 109.58/110.30 X166,X164))) => 109.58/110.30 (~ 109.58/110.30 (![X167]: 109.58/110.30 (in( 109.58/110.30 X167,X164) => 109.58/110.30 X165( 109.58/110.30 X167)))))) => 109.58/110.30 ((![X168:$o]: 109.58/110.30 (X168 => 109.58/110.30 in(emptyset, 109.58/110.30 prop2set( 109.58/110.30 X168)))) => 109.58/110.30 ((![X169:$o]: 109.58/110.30 (X169 => 109.58/110.30 set2prop( 109.58/110.30 prop2set( 109.58/110.30 X169)))) => 109.58/110.30 ((![X170, 109.58/110.30 X171:( 109.58/110.30 $i > $o)]: 109.58/110.30 ((~ 109.58/110.30 ( 109.58/110.30 ?[X172]: 109.58/110.30 (X171( 109.58/110.30 X172) & 109.58/110.30 in( 109.58/110.30 X172,X170)))) => 109.58/110.30 (![X173]: 109.58/110.30 (in( 109.58/110.30 X173,X170) => 109.58/110.30 (~ 109.58/110.30 X171( 109.58/110.30 X173)))))) => 109.58/110.30 ((![X174, 109.58/110.30 X175:( 109.58/110.30 $i > $o)]: 109.58/110.30 (( 109.58/110.30 ~ 109.58/110.30 ( 109.58/110.30 ![X176]: 109.58/110.30 (in( 109.58/110.30 X176,X174) => 109.58/110.30 X175( 109.58/110.30 X176)))) => 109.58/110.30 ( 109.58/110.30 ?[X177]: 109.58/110.30 (( 109.58/110.30 ~ 109.58/110.30 X175( 109.58/110.30 X177)) & 109.58/110.30 in( 109.58/110.30 X177,X174))))) => 109.58/110.30 ((![X178:( 109.58/110.30 $i > $o)]: 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ?[X179]: 109.58/110.30 (( 109.58/110.30 ![X180]: 109.58/110.30 (X178( 109.58/110.30 X180) => 109.58/110.30 (X179 = 109.58/110.30 X180))) & 109.58/110.30 X178( 109.58/110.30 X179))) => 109.58/110.30 ( 109.58/110.30 ?[X181]: 109.58/110.30 (( 109.58/110.30 ![X182]: 109.58/110.30 (X178( 109.58/110.30 X182) => 109.58/110.30 (X181 = 109.58/110.30 X182))) & 109.58/110.30 X178( 109.58/110.30 X181))))) => 109.58/110.30 ((![X183:( 109.58/110.30 $i > $o)]: 109.58/110.30 (( 109.58/110.30 ?[X184]: 109.58/110.30 X183( 109.58/110.30 X184)) => 109.58/110.30 (( 109.58/110.30 ![X185, 109.58/110.30 X186]: 109.58/110.30 (X183( 109.58/110.30 X185) => 109.58/110.30 (X183( 109.58/110.30 X186) => 109.58/110.30 (X185 = 109.58/110.30 X186)))) => 109.58/110.30 (?[X187]: 109.58/110.30 (( 109.58/110.30 ![X188]: 109.58/110.30 (X183( 109.58/110.30 X188) => 109.58/110.30 (X187 = 109.58/110.30 X188))) & 109.58/110.30 X183( 109.58/110.30 X187)))))) => 109.58/110.30 ((![X189:( 109.58/110.30 $i > $o)]: 109.58/110.30 (( 109.58/110.30 ?[X190]: 109.58/110.30 (![X191]: 109.58/110.30 (X189( 109.58/110.30 X191) <=> 109.58/110.30 (X191 = 109.58/110.30 X190)))) => 109.58/110.30 (?[X192]: 109.58/110.30 (( 109.58/110.30 ![X193]: 109.58/110.30 (X189( 109.58/110.30 X193) => 109.58/110.30 (X192 = 109.58/110.30 X193))) & 109.58/110.30 X189( 109.58/110.30 X192))))) => 109.58/110.30 (( 109.58/110.30 ![X194, 109.58/110.30 X195]: 109.58/110.30 (( 109.58/110.30 X194 = 109.58/110.30 X195) => 109.58/110.30 (![X196, 109.58/110.30 X197]: 109.58/110.30 (( 109.58/110.30 X196 = 109.58/110.30 X197) => 109.58/110.30 (in( 109.58/110.30 X196,X194) => 109.58/110.30 in( 109.58/110.30 X197,X195)))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X198, 109.58/110.30 X199]: 109.58/110.30 (( 109.58/110.30 X198 = 109.58/110.30 X199) => 109.58/110.30 (![X200, 109.58/110.30 X201]: 109.58/110.30 (( 109.58/110.30 X200 = 109.58/110.30 X201) => 109.58/110.30 (in( 109.58/110.30 X200,X198) <=> 109.58/110.30 in( 109.58/110.30 X201,X199)))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X202:( 109.58/110.30 $i > $o)]: 109.58/110.30 (( 109.58/110.30 ?[X203]: 109.58/110.30 (( 109.58/110.30 ![X204]: 109.58/110.30 (X202( 109.58/110.30 X204) => 109.58/110.30 (X203 = 109.58/110.30 X204))) & 109.58/110.30 X202( 109.58/110.30 X203))) => 109.58/110.30 (![X205, 109.58/110.30 X206]: 109.58/110.30 (X202( 109.58/110.30 X205) => 109.58/110.30 (X202( 109.58/110.30 X206) => 109.58/110.30 (X205 = 109.58/110.30 X206)))))) => 109.58/110.30 ( 109.58/110.30 ( 109.58/110.30 ![X207:( 109.58/110.30 $i > $o), 109.58/110.30 X208:( 109.58/110.30 $i > $o)]: 109.58/110.30 (( 109.58/110.30 ![X209, 109.58/110.30 X210]: 109.58/110.30 (( 109.58/110.30 X209 = 109.58/110.30 X210) => 109.58/110.30 (X207( 109.58/110.30 X209) <=> 109.58/110.30 X208( 109.58/110.30 X210)))) => 109.58/110.30 (( 109.58/110.30 ?[X211]: 109.58/110.30 zip_tseitin5( 109.58/110.30 X211,X207)) <=> 109.58/110.30 (?[X213]: 109.58/110.30 zip_tseitin5( 109.58/110.30 X213,X208))))) => 109.58/110.30 ( 109.58/110.31 ( 109.58/110.31 emptyset = 109.58/110.31 emptyset) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X215, 109.58/110.31 X216]: 109.58/110.31 (( 109.58/110.31 X215 = 109.58/110.31 X216) => 109.58/110.31 (![X217, 109.58/110.31 X218]: 109.58/110.31 (( 109.58/110.31 X217 = 109.58/110.31 X218) => 109.58/110.31 (setadjoin( 109.58/110.31 X215,X217) = 109.58/110.31 setadjoin( 109.58/110.31 X216,X218)))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X219, 109.58/110.31 X220]: 109.58/110.31 (( 109.58/110.31 X219 = 109.58/110.31 X220) => 109.58/110.31 (powerset( 109.58/110.31 X219) = 109.58/110.31 powerset( 109.58/110.31 X220)))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X221, 109.58/110.31 X222]: 109.58/110.31 (( 109.58/110.31 X221 = 109.58/110.31 X222) => 109.58/110.31 (setunion( 109.58/110.31 X221) = 109.58/110.31 setunion( 109.58/110.31 X222)))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 omega = 109.58/110.31 omega) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X223:( 109.58/110.31 $i > $o)]: 109.58/110.31 (( 109.58/110.31 ?[X224]: 109.58/110.31 (( 109.58/110.31 ![X225]: 109.58/110.31 (X223( 109.58/110.31 X225) => 109.58/110.31 (X224 = 109.58/110.31 X225))) & 109.58/110.31 X223( 109.58/110.31 X224))) => 109.58/110.31 (![X226, 109.58/110.31 X227]: 109.58/110.31 (X223( 109.58/110.31 X226) => 109.58/110.31 (X223( 109.58/110.31 X227) => 109.58/110.31 (X226 = 109.58/110.31 X227)))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X228:( 109.58/110.31 $i > $o), 109.58/110.31 X229:( 109.58/110.31 $i > $o)]: 109.58/110.31 (( 109.58/110.31 ![X230, 109.58/110.31 X231]: 109.58/110.31 (( 109.58/110.31 X230 = 109.58/110.31 X231) => 109.58/110.31 (X228( 109.58/110.31 X230) <=> 109.58/110.31 X229( 109.58/110.31 X231)))) => 109.58/110.31 (( 109.58/110.31 ?[X232]: 109.58/110.31 (( 109.58/110.31 ![X233]: 109.58/110.31 (X228( 109.58/110.31 X233) => 109.58/110.31 (X232 = 109.58/110.31 X233))) & 109.58/110.31 X228( 109.58/110.31 X232))) => 109.58/110.31 (( 109.58/110.31 ?[X234]: 109.58/110.31 (( 109.58/110.31 ![X235]: 109.58/110.31 (X229( 109.58/110.31 X235) => 109.58/110.31 (X234 = 109.58/110.31 X235))) & 109.58/110.31 X229( 109.58/110.31 X234))) => 109.58/110.31 (descr( 109.58/110.31 '#ll_0'( 109.58/110.31 X228)) = 109.58/110.31 descr( 109.58/110.31 '#ll_0'( 109.58/110.31 X229))))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X236, 109.58/110.31 X237]: 109.58/110.31 (( 109.58/110.31 X236 = 109.58/110.31 X237) => 109.58/110.31 (![X238:( 109.58/110.31 $i > $o), 109.58/110.31 X239:( 109.58/110.31 $i > $o)]: 109.58/110.31 (( 109.58/110.31 ![X240]: 109.58/110.31 (in( 109.58/110.31 X240,X236) => 109.58/110.31 (![X241]: 109.58/110.31 (in( 109.58/110.31 X241,X237) => 109.58/110.31 (( 109.58/110.31 X240 = 109.58/110.31 X241) => 109.58/110.31 (X238( 109.58/110.31 X240) <=> 109.58/110.31 X239( 109.58/110.31 X241))))))) => 109.58/110.31 (dsetconstr( 109.58/110.31 X236, 109.58/110.31 '#ll_0'( 109.58/110.31 X238)) = 109.58/110.31 dsetconstr( 109.58/110.31 X237, 109.58/110.31 '#ll_0'( 109.58/110.31 X239))))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X242, 109.58/110.31 X243]: 109.58/110.31 (( 109.58/110.31 ![X244]: 109.58/110.31 (in( 109.58/110.31 X244,X242) => 109.58/110.31 in( 109.58/110.31 X244,X243))) => 109.58/110.31 subset( 109.58/110.31 X242,X243))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X245, 109.58/110.31 X246]: 109.58/110.31 (( 109.58/110.31 X245 = 109.58/110.31 X246) => 109.58/110.31 subset( 109.58/110.31 X246,X245))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X247, 109.58/110.31 X248]: 109.58/110.31 (( 109.58/110.31 X247 = 109.58/110.31 X248) => 109.58/110.31 subset( 109.58/110.31 X247,X248))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X249, 109.58/110.31 X250]: 109.58/110.31 (( 109.58/110.31 ![X251]: 109.58/110.31 (in( 109.58/110.31 X251,X249) => 109.58/110.31 in( 109.58/110.31 X251,X250))) => 109.58/110.31 subset( 109.58/110.31 X249,X250))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X252]: 109.58/110.31 subset( 109.58/110.31 emptyset, 109.58/110.31 X252)) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X253, 109.58/110.31 X254,X255]: 109.58/110.31 (subset( 109.58/110.31 X253,X254) => 109.58/110.31 (in( 109.58/110.31 X255,X253) => 109.58/110.31 in( 109.58/110.31 X255,X254)))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X256, 109.58/110.31 X257,X258]: 109.58/110.31 (subset( 109.58/110.31 X256,X257) => 109.58/110.31 (( 109.58/110.31 ~ 109.58/110.31 in( 109.58/110.31 X258,X257)) => 109.58/110.31 (~ 109.58/110.31 in( 109.58/110.31 X258,X256))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X259, 109.58/110.31 X260,X261]: 109.58/110.31 (in( 109.58/110.31 X261,X259) => 109.58/110.31 (( 109.58/110.31 ~ 109.58/110.31 in( 109.58/110.31 X261,X260)) => 109.58/110.31 (~ 109.58/110.31 subset( 109.58/110.31 X259,X260))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X262, 109.58/110.31 X263]: 109.58/110.31 (( 109.58/110.31 ~ 109.58/110.31 subset( 109.58/110.31 X262,X263)) => 109.58/110.31 (X262 != 109.58/110.31 X263))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X264, 109.58/110.31 X265,X266]: 109.58/110.31 (in( 109.58/110.31 X266,X264) => 109.58/110.31 (( 109.58/110.31 ~ 109.58/110.31 in( 109.58/110.31 X266,X265)) => 109.58/110.31 (X264 != 109.58/110.31 X265)))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X267]: 109.58/110.31 subset( 109.58/110.31 X267,X267)) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X268, 109.58/110.31 X269,X270]: 109.58/110.31 (subset( 109.58/110.31 X268,X269) => 109.58/110.31 (subset( 109.58/110.31 X269,X270) => 109.58/110.31 subset( 109.58/110.31 X268,X270)))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X271, 109.58/110.31 X272]: 109.58/110.31 subset( 109.58/110.31 X272, 109.58/110.31 setadjoin( 109.58/110.31 X271,X272))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X273, 109.58/110.31 X274,X275]: 109.58/110.31 (subset( 109.58/110.31 X273,X275) => 109.58/110.31 subset( 109.58/110.31 X273, 109.58/110.31 setadjoin( 109.58/110.31 X274,X275)))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X276, 109.58/110.31 X277]: 109.58/110.31 (subset( 109.58/110.31 X276,X277) => 109.58/110.31 in( 109.58/110.31 X276, 109.58/110.31 powerset( 109.58/110.31 X277)))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X278, 109.58/110.31 X279]: 109.58/110.31 (subset( 109.58/110.31 X278,X279) => 109.58/110.31 (subset( 109.58/110.31 X279,X278) => 109.58/110.31 (X278 = 109.58/110.31 X279)))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X280]: 109.58/110.31 (subset( 109.58/110.31 X280, 109.58/110.31 emptyset) => 109.58/110.31 (X280 = 109.58/110.31 emptyset))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X281, 109.58/110.31 X282]: 109.58/110.31 (subset( 109.58/110.31 X282,X281) => 109.58/110.31 in( 109.58/110.31 X282, 109.58/110.31 powerset( 109.58/110.31 X281)))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X283, 109.58/110.31 X284]: 109.58/110.31 (in( 109.58/110.31 X284, 109.58/110.31 powerset( 109.58/110.31 X283)) => 109.58/110.31 subset( 109.58/110.31 X284,X283))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X285]: 109.58/110.31 in( 109.58/110.31 X285, 109.58/110.31 powerset( 109.58/110.31 X285))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X286, 109.58/110.31 X287]: 109.58/110.31 (subset( 109.58/110.31 X286,X287) => 109.58/110.31 subset( 109.58/110.31 powerset( 109.58/110.31 X286), 109.58/110.31 powerset( 109.58/110.31 X287)))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X288, 109.58/110.31 X289:( 109.58/110.31 $i > $o)]: 109.58/110.31 in( 109.58/110.31 dsetconstr( 109.58/110.31 X288, 109.58/110.31 '#ll_0'( 109.58/110.31 X289)), 109.58/110.31 powerset( 109.58/110.31 X288))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X290, 109.58/110.31 X291:( 109.58/110.31 $i > $o)]: 109.58/110.31 subset( 109.58/110.31 dsetconstr( 109.58/110.31 X290, 109.58/110.31 '#ll_0'( 109.58/110.31 X291)), 109.58/110.31 X290)) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X292, 109.58/110.31 X293,X294]: 109.58/110.31 (in( 109.58/110.31 X294,X292) => 109.58/110.31 in( 109.58/110.31 X294, 109.58/110.31 binunion( 109.58/110.31 X292,X293)))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X295, 109.58/110.31 X296]: 109.58/110.31 in( 109.58/110.31 X296, 109.58/110.31 setadjoin( 109.58/110.31 X295, 109.58/110.31 setadjoin( 109.58/110.31 X296, 109.58/110.31 emptyset)))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X297, 109.58/110.31 X298,X299]: 109.58/110.31 (in( 109.58/110.31 X299,X298) => 109.58/110.31 in( 109.58/110.31 X299, 109.58/110.31 binunion( 109.58/110.31 X297,X298)))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X300, 109.58/110.31 X301, 109.58/110.31 X302, 109.58/110.31 X303:$o]: 109.58/110.31 (in( 109.58/110.31 X302, 109.58/110.31 binunion( 109.58/110.31 X300,X301)) => 109.58/110.31 (( 109.58/110.31 in( 109.58/110.31 X302,X300) => 109.58/110.31 X303) => 109.58/110.31 (( 109.58/110.31 in( 109.58/110.31 X302,X301) => 109.58/110.31 X303) => 109.58/110.31 X303)))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X304, 109.58/110.31 X305,X306]: 109.58/110.31 (in( 109.58/110.31 X306, 109.58/110.31 binunion( 109.58/110.31 X304,X305)) => 109.58/110.31 (in( 109.58/110.31 X306,X305) | 109.58/110.31 in( 109.58/110.31 X306,X304)))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X307, 109.58/110.31 X308]: 109.58/110.31 subset( 109.58/110.31 X307, 109.58/110.31 binunion( 109.58/110.31 X307,X308))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X309, 109.58/110.31 X310]: 109.58/110.31 subset( 109.58/110.31 X310, 109.58/110.31 binunion( 109.58/110.31 X309,X310))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X311, 109.58/110.31 X312,X313]: 109.58/110.31 (in( 109.58/110.31 X313,X311) => 109.58/110.31 (in( 109.58/110.31 X313,X312) => 109.58/110.31 in( 109.58/110.31 X313, 109.58/110.31 binintersect( 109.58/110.31 X311,X312))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X314, 109.58/110.31 X315,X316]: 109.58/110.31 (subset( 109.58/110.31 X316,X314) => 109.58/110.31 (subset( 109.58/110.31 X316,X315) => 109.58/110.31 subset( 109.58/110.31 X316, 109.58/110.31 binintersect( 109.58/110.31 X314,X315))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X317, 109.58/110.31 X318,X319]: 109.58/110.31 (in( 109.58/110.31 X319, 109.58/110.31 binintersect( 109.58/110.31 X317,X318)) => 109.58/110.31 in( 109.58/110.31 X319,X317))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X320, 109.58/110.31 X321]: 109.58/110.31 subset( 109.58/110.31 binintersect( 109.58/110.31 X320,X321), 109.58/110.31 X320)) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X322, 109.58/110.31 X323]: 109.58/110.31 (subset( 109.58/110.31 X322,X323) => 109.58/110.31 (binintersect( 109.58/110.31 X322,X323) = 109.58/110.31 X322))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X324, 109.58/110.31 X325]: 109.58/110.31 (( 109.58/110.31 binintersect( 109.58/110.31 X324,X325) = 109.58/110.31 X325) => 109.58/110.31 subset( 109.58/110.31 X325,X324))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X326, 109.58/110.31 X327,X328]: 109.58/110.31 (in( 109.58/110.31 X328, 109.58/110.31 binintersect( 109.58/110.31 X326,X327)) => 109.58/110.31 in( 109.58/110.31 X328,X327))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X329, 109.58/110.31 X330]: 109.58/110.31 (( 109.58/110.31 ~ 109.58/110.31 ( 109.58/110.31 ?[X331]: 109.58/110.31 (in( 109.58/110.31 X331,X330) & 109.58/110.31 in( 109.58/110.31 X331,X329)))) => 109.58/110.31 (binintersect( 109.58/110.31 X329,X330) = 109.58/110.31 emptyset))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X332, 109.58/110.31 X333]: 109.58/110.31 subset( 109.58/110.31 binintersect( 109.58/110.31 X332,X333), 109.58/110.31 X333)) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X334, 109.58/110.31 X335]: 109.58/110.31 (subset( 109.58/110.31 X335,X334) => 109.58/110.31 (binintersect( 109.58/110.31 X334,X335) = 109.58/110.31 X335))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X336, 109.58/110.31 X337]: 109.58/110.31 (( 109.58/110.31 binintersect( 109.58/110.31 X336,X337) = 109.58/110.31 X336) => 109.58/110.31 subset( 109.58/110.31 X336,X337))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X338, 109.58/110.31 X339,X340]: 109.58/110.31 (binintersect( 109.58/110.31 X338, 109.58/110.31 binunion( 109.58/110.31 X339,X340)) = 109.58/110.31 binunion( 109.58/110.31 binintersect( 109.58/110.31 X338,X339), 109.58/110.31 binintersect( 109.58/110.31 X338,X340)))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X341, 109.58/110.31 X342,X343]: 109.58/110.31 (in( 109.58/110.31 X343,X341) => 109.58/110.31 (( 109.58/110.31 ~ 109.58/110.31 in( 109.58/110.31 X343,X342)) => 109.58/110.31 in( 109.58/110.31 X343, 109.58/110.31 setminus( 109.58/110.31 X341,X342))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X344, 109.58/110.31 X345,X346]: 109.58/110.31 (in( 109.58/110.31 X346, 109.58/110.31 setminus( 109.58/110.31 X344,X345)) => 109.58/110.31 in( 109.58/110.31 X346,X344))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X347, 109.58/110.31 X348,X349]: 109.58/110.31 (in( 109.58/110.31 X349, 109.58/110.31 setminus( 109.58/110.31 X347,X348)) => 109.58/110.31 (~ 109.58/110.31 in( 109.58/110.31 X349,X348)))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X350, 109.58/110.31 X351]: 109.58/110.31 (subset( 109.58/110.31 X350,X351) => 109.58/110.31 (setminus( 109.58/110.31 X350,X351) = 109.58/110.31 emptyset))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X352, 109.58/110.31 X353,X354]: 109.58/110.31 (( 109.58/110.31 ~ 109.58/110.31 in( 109.58/110.31 X354, 109.58/110.31 setminus( 109.58/110.31 X352,X353))) => 109.58/110.31 (in( 109.58/110.31 X354,X352) => 109.58/110.31 in( 109.58/110.31 X354,X353)))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X355, 109.58/110.31 X356,X357]: 109.58/110.31 (( 109.58/110.31 ~ 109.58/110.31 in( 109.58/110.31 X357, 109.58/110.31 setminus( 109.58/110.31 X355,X356))) => 109.58/110.31 (( 109.58/110.31 ~ 109.58/110.31 in( 109.58/110.31 X357,X356)) => 109.58/110.31 (~ 109.58/110.31 in( 109.58/110.31 X357,X355))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X358, 109.58/110.31 X359,X360]: 109.58/110.31 (( 109.58/110.31 ~ 109.58/110.31 in( 109.58/110.31 X360,X358)) => 109.58/110.31 (~ 109.58/110.31 in( 109.58/110.31 X360, 109.58/110.31 setminus( 109.58/110.31 X358,X359))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X361, 109.58/110.31 X362,X363]: 109.58/110.31 (in( 109.58/110.31 X363,X362) => 109.58/110.31 (~ 109.58/110.31 in( 109.58/110.31 X363, 109.58/110.31 setminus( 109.58/110.31 X361,X362))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X364, 109.58/110.31 X365]: 109.58/110.31 subset( 109.58/110.31 setminus( 109.58/110.31 X364,X365), 109.58/110.31 X364)) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X366, 109.58/110.31 X367]: 109.58/110.31 (( 109.58/110.31 setminus( 109.58/110.31 X366,X367) = 109.58/110.31 emptyset) => 109.58/110.31 subset( 109.58/110.31 X366,X367))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X368, 109.58/110.31 X369,X370]: 109.58/110.31 (in( 109.58/110.31 X370, 109.58/110.31 symdiff( 109.58/110.31 X368,X369)) => 109.58/110.31 (![X371:$o]: 109.58/110.31 (( 109.58/110.31 in( 109.58/110.31 X370,X368) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ~ 109.58/110.31 in( 109.58/110.31 X370,X369)) => 109.58/110.31 X371)) => 109.58/110.31 (( 109.58/110.31 ( 109.58/110.31 ~ 109.58/110.31 in( 109.58/110.31 X370,X368)) => 109.58/110.31 ( 109.58/110.31 in( 109.58/110.31 X370,X369) => 109.58/110.31 X371)) => 109.58/110.31 X371))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X372, 109.58/110.31 X373,X374]: 109.58/110.31 (in( 109.58/110.31 X374,X372) => 109.58/110.31 (( 109.58/110.31 ~ 109.58/110.31 in( 109.58/110.31 X374,X373)) => 109.58/110.31 in( 109.58/110.31 X374, 109.58/110.31 symdiff( 109.58/110.31 X372,X373))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X375, 109.58/110.31 X376,X377]: 109.58/110.31 (( 109.58/110.31 ~ 109.58/110.31 in( 109.58/110.31 X377,X375)) => 109.58/110.31 (in( 109.58/110.31 X377,X376) => 109.58/110.31 in( 109.58/110.31 X377, 109.58/110.31 symdiff( 109.58/110.31 X375,X376))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X378, 109.58/110.31 X379,X380]: 109.58/110.31 (in( 109.58/110.31 X380,X378) => 109.58/110.31 (in( 109.58/110.31 X380,X379) => 109.58/110.31 (~ 109.58/110.31 in( 109.58/110.31 X380, 109.58/110.31 symdiff( 109.58/110.31 X378,X379)))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X381, 109.58/110.31 X382,X383]: 109.58/110.31 (( 109.58/110.31 ~ 109.58/110.31 in( 109.58/110.31 X383,X381)) => 109.58/110.31 (( 109.58/110.31 ~ 109.58/110.31 in( 109.58/110.31 X383,X382)) => 109.58/110.31 (~ 109.58/110.31 in( 109.58/110.31 X383, 109.58/110.31 symdiff( 109.58/110.31 X381,X382)))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X384, 109.58/110.31 X385]: 109.58/110.31 in( 109.58/110.31 X385, 109.58/110.31 setadjoin( 109.58/110.31 X384, 109.58/110.31 setadjoin( 109.58/110.31 X385, 109.58/110.31 emptyset)))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X386, 109.58/110.31 X387]: 109.58/110.31 in( 109.58/110.31 X386, 109.58/110.31 setunion( 109.58/110.31 setadjoin( 109.58/110.31 setadjoin( 109.58/110.31 X386, 109.58/110.31 emptyset), 109.58/110.31 setadjoin( 109.58/110.31 setadjoin( 109.58/110.31 X386, 109.58/110.31 setadjoin( 109.58/110.31 X387, 109.58/110.31 emptyset)), 109.58/110.31 emptyset))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X388, 109.58/110.31 X389]: 109.58/110.31 in( 109.58/110.31 X389, 109.58/110.31 setunion( 109.58/110.31 setadjoin( 109.58/110.31 setadjoin( 109.58/110.31 X388, 109.58/110.31 emptyset), 109.58/110.31 setadjoin( 109.58/110.31 setadjoin( 109.58/110.31 X388, 109.58/110.31 setadjoin( 109.58/110.31 X389, 109.58/110.31 emptyset)), 109.58/110.31 emptyset))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X390, 109.58/110.31 X391]: 109.58/110.31 iskpair( 109.58/110.31 setadjoin( 109.58/110.31 setadjoin( 109.58/110.31 X390, 109.58/110.31 emptyset), 109.58/110.31 setadjoin( 109.58/110.31 setadjoin( 109.58/110.31 X390, 109.58/110.31 setadjoin( 109.58/110.31 X391, 109.58/110.31 emptyset)), 109.58/110.31 emptyset)))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X392, 109.58/110.31 X393]: 109.58/110.31 iskpair( 109.58/110.31 kpair( 109.58/110.31 X392,X393))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X394, 109.58/110.31 X395]: 109.58/110.31 (in( 109.58/110.31 X395,X394) => 109.58/110.31 subset( 109.58/110.31 setadjoin( 109.58/110.31 X395, 109.58/110.31 emptyset), 109.58/110.31 X394))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X396, 109.58/110.31 X397]: 109.58/110.31 (in( 109.58/110.31 X397,X396) => 109.58/110.31 in( 109.58/110.31 setadjoin( 109.58/110.31 X397, 109.58/110.31 emptyset), 109.58/110.31 powerset( 109.58/110.31 X396)))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X398, 109.58/110.31 X399,X400]: 109.58/110.31 (in( 109.58/110.31 X400,X398) => 109.58/110.31 in( 109.58/110.31 setadjoin( 109.58/110.31 X400, 109.58/110.31 emptyset), 109.58/110.31 powerset( 109.58/110.31 binunion( 109.58/110.31 X398,X399))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X401, 109.58/110.31 X402,X403]: 109.58/110.31 (in( 109.58/110.31 X403, 109.58/110.31 setadjoin( 109.58/110.31 X401, 109.58/110.31 setadjoin( 109.58/110.31 X402, 109.58/110.31 emptyset))) => 109.58/110.31 (( 109.58/110.31 X403 = 109.58/110.31 X402) | 109.58/110.31 (X403 = 109.58/110.31 X401)))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X404, 109.58/110.31 X405,X406]: 109.58/110.31 (in( 109.58/110.31 X406,X404) => 109.58/110.31 (![X407]: 109.58/110.31 (in( 109.58/110.31 X407,X405) => 109.58/110.31 subset( 109.58/110.31 setadjoin( 109.58/110.31 X406, 109.58/110.31 setadjoin( 109.58/110.31 X407, 109.58/110.31 emptyset)), 109.58/110.31 binunion( 109.58/110.31 X404,X405)))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X408, 109.58/110.31 X409,X410]: 109.58/110.31 (in( 109.58/110.31 X410,X408) => 109.58/110.31 (![X411]: 109.58/110.31 (in( 109.58/110.31 X411,X409) => 109.58/110.31 in( 109.58/110.31 setadjoin( 109.58/110.31 X410, 109.58/110.31 setadjoin( 109.58/110.31 X411, 109.58/110.31 emptyset)), 109.58/110.31 powerset( 109.58/110.31 binunion( 109.58/110.31 X408,X409))))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X412, 109.58/110.31 X413,X414]: 109.58/110.31 (in( 109.58/110.31 X414,X412) => 109.58/110.31 (![X415]: 109.58/110.31 (in( 109.58/110.31 X415,X413) => 109.58/110.31 subset( 109.58/110.31 setadjoin( 109.58/110.31 setadjoin( 109.58/110.31 X414, 109.58/110.31 emptyset), 109.58/110.31 setadjoin( 109.58/110.31 setadjoin( 109.58/110.31 X414, 109.58/110.31 setadjoin( 109.58/110.31 X415, 109.58/110.31 emptyset)), 109.58/110.31 emptyset)), 109.58/110.31 powerset( 109.58/110.31 binunion( 109.58/110.31 X412,X413))))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X416, 109.58/110.31 X417,X418]: 109.58/110.31 (in( 109.58/110.31 X418,X416) => 109.58/110.31 (![X419]: 109.58/110.31 (in( 109.58/110.31 X419,X417) => 109.58/110.31 in( 109.58/110.31 setadjoin( 109.58/110.31 setadjoin( 109.58/110.31 X418, 109.58/110.31 emptyset), 109.58/110.31 setadjoin( 109.58/110.31 setadjoin( 109.58/110.31 X418, 109.58/110.31 setadjoin( 109.58/110.31 X419, 109.58/110.31 emptyset)), 109.58/110.31 emptyset)), 109.58/110.31 powerset( 109.58/110.31 powerset( 109.58/110.31 binunion( 109.58/110.31 X416,X417)))))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X420, 109.58/110.31 X421,X422]: 109.58/110.31 (in( 109.58/110.31 X422,X420) => 109.58/110.31 (![X423]: 109.58/110.31 (in( 109.58/110.31 X423,X421) => 109.58/110.31 in( 109.58/110.31 kpair( 109.58/110.31 X422,X423), 109.58/110.31 powerset( 109.58/110.31 powerset( 109.58/110.31 binunion( 109.58/110.31 X420,X421)))))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X424, 109.58/110.31 X425,X426]: 109.58/110.31 (in( 109.58/110.31 X426,X424) => 109.58/110.31 (![X427]: 109.58/110.31 (in( 109.58/110.31 X427,X425) => 109.58/110.31 in( 109.58/110.31 kpair( 109.58/110.31 X426,X427), 109.58/110.31 cartprod( 109.58/110.31 X424,X425)))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X428, 109.58/110.31 X429,X430]: 109.58/110.31 (in( 109.58/110.31 X430, 109.58/110.31 cartprod( 109.58/110.31 X428,X429)) => 109.58/110.31 (?[X431]: 109.58/110.31 (( 109.58/110.31 ?[X432]: 109.58/110.31 (( 109.58/110.31 X430 = 109.58/110.31 kpair( 109.58/110.31 X431,X432)) & 109.58/110.31 in( 109.58/110.31 X432,X429))) & 109.58/110.31 in( 109.58/110.31 X431,X428))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X433, 109.58/110.31 X434,X435]: 109.58/110.31 (in( 109.58/110.31 X435, 109.58/110.31 cartprod( 109.58/110.31 X433,X434)) => 109.58/110.31 iskpair( 109.58/110.31 X435))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X436, 109.58/110.31 X437]: 109.58/110.31 (in( 109.58/110.31 X437, 109.58/110.31 setunion( 109.58/110.31 X436)) => 109.58/110.31 (?[X438]: 109.58/110.31 (in( 109.58/110.31 X437,X438) & 109.58/110.31 in( 109.58/110.31 X438,X436))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X439]: 109.58/110.31 subset( 109.58/110.31 setunion( 109.58/110.31 setadjoin( 109.58/110.31 X439, 109.58/110.31 emptyset)), 109.58/110.31 X439)) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X440]: 109.58/110.31 subset( 109.58/110.31 X440, 109.58/110.31 setunion( 109.58/110.31 setadjoin( 109.58/110.31 X440, 109.58/110.31 emptyset)))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X441]: 109.58/110.31 (setunion( 109.58/110.31 setadjoin( 109.58/110.31 X441, 109.58/110.31 emptyset)) = 109.58/110.31 X441)) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X442, 109.58/110.31 X443:( 109.58/110.31 $i > $o)]: 109.58/110.31 (( 109.58/110.31 ![X444]: 109.58/110.31 (in( 109.58/110.31 X444,X442) => 109.58/110.31 (![X445]: 109.58/110.31 (in( 109.58/110.31 X445,X442) => 109.58/110.31 (X443( 109.58/110.31 X444) => 109.58/110.31 (X443( 109.58/110.31 X445) => 109.58/110.31 (X444 = 109.58/110.31 X445))))))) => 109.58/110.31 (( 109.58/110.31 ?[X446]: 109.58/110.31 (X443( 109.58/110.31 X446) & 109.58/110.31 in( 109.58/110.31 X446,X442))) => 109.58/110.31 (?[X447]: 109.58/110.31 (( 109.58/110.31 dsetconstr( 109.58/110.31 X442, 109.58/110.31 '#ll_0'( 109.58/110.31 X443)) = 109.58/110.31 setadjoin( 109.58/110.31 X447, 109.58/110.31 emptyset)) & 109.58/110.31 in( 109.58/110.31 X447, 109.58/110.31 dsetconstr( 109.58/110.31 X442, 109.58/110.31 '#ll_0'( 109.58/110.31 X443)))))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X448, 109.58/110.31 X449:( 109.58/110.31 $i > $o)]: 109.58/110.31 (( 109.58/110.31 ?[X450]: 109.58/110.31 (( 109.58/110.31 dsetconstr( 109.58/110.31 X448, 109.58/110.31 '#ll_0'( 109.58/110.31 X449)) = 109.58/110.31 setadjoin( 109.58/110.31 X450, 109.58/110.31 emptyset)) & 109.58/110.31 in( 109.58/110.31 X450, 109.58/110.31 dsetconstr( 109.58/110.31 X448, 109.58/110.31 '#ll_0'( 109.58/110.31 X449))))) => 109.58/110.31 (?[X451]: 109.58/110.31 (X449( 109.58/110.31 X451) & 109.58/110.31 in( 109.58/110.31 X451,X448))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X452, 109.58/110.31 X453:( 109.58/110.31 $i > $o), 109.58/110.31 X454]: 109.58/110.31 (in( 109.58/110.31 X454,X452) => 109.58/110.31 (X453( 109.58/110.31 X454) => 109.58/110.31 (( 109.58/110.31 ![X455]: 109.58/110.31 (in( 109.58/110.31 X455,X452) => 109.58/110.31 (X453( 109.58/110.31 X455) => 109.58/110.31 (X455 = 109.58/110.31 X454)))) => 109.58/110.31 (?[X456]: 109.58/110.31 (( 109.58/110.31 dsetconstr( 109.58/110.31 X452, 109.58/110.31 '#ll_0'( 109.58/110.31 X453)) = 109.58/110.31 setadjoin( 109.58/110.31 X456, 109.58/110.31 emptyset)) & 109.58/110.31 in( 109.58/110.31 X456, 109.58/110.31 dsetconstr( 109.58/110.31 X452, 109.58/110.31 '#ll_0'( 109.58/110.31 X453))))))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X457, 109.58/110.31 X458:( 109.58/110.31 $i > $o)]: 109.58/110.31 (( 109.58/110.31 ![X459]: 109.58/110.31 (in( 109.58/110.31 X459,X457) => 109.58/110.31 (![X460]: 109.58/110.31 (in( 109.58/110.31 X460,X457) => 109.58/110.31 (X458( 109.58/110.31 X459) => 109.58/110.31 (X458( 109.58/110.31 X460) => 109.58/110.31 (X459 = 109.58/110.31 X460))))))) => 109.58/110.31 (( 109.58/110.31 ?[X461]: 109.58/110.31 (X458( 109.58/110.31 X461) & 109.58/110.31 in( 109.58/110.31 X461,X457))) => 109.58/110.31 (?[X462]: 109.58/110.31 (( 109.58/110.31 dsetconstr( 109.58/110.31 X457, 109.58/110.31 '#ll_0'( 109.58/110.31 X458)) = 109.58/110.31 setadjoin( 109.58/110.31 X462, 109.58/110.31 emptyset)) & 109.58/110.31 in( 109.58/110.31 X462, 109.58/110.31 dsetconstr( 109.58/110.31 X457, 109.58/110.31 '#ll_0'( 109.58/110.31 X458)))))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X463, 109.58/110.31 X464]: 109.58/110.31 (( 109.58/110.31 setadjoin( 109.58/110.31 X463, 109.58/110.31 emptyset) = 109.58/110.31 setadjoin( 109.58/110.31 X464, 109.58/110.31 emptyset)) => 109.58/110.31 (X463 = 109.58/110.31 X464))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X465, 109.58/110.31 X466,X467]: 109.58/110.31 (in( 109.58/110.31 setadjoin( 109.58/110.31 X467, 109.58/110.31 emptyset), 109.58/110.31 setadjoin( 109.58/110.31 setadjoin( 109.58/110.31 X465, 109.58/110.31 emptyset), 109.58/110.31 setadjoin( 109.58/110.31 setadjoin( 109.58/110.31 X465, 109.58/110.31 setadjoin( 109.58/110.31 X466, 109.58/110.31 emptyset)), 109.58/110.31 emptyset))) => 109.58/110.31 (X465 = 109.58/110.31 X467))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X468]: 109.58/110.31 (iskpair( 109.58/110.31 X468) => 109.58/110.31 (?[X469]: 109.58/110.31 (( 109.58/110.31 dsetconstr( 109.58/110.31 setunion( 109.58/110.31 X468), 109.58/110.31 '#ll_6'( 109.58/110.31 X468)) = 109.58/110.31 setadjoin( 109.58/110.31 X469, 109.58/110.31 emptyset)) & 109.58/110.31 in( 109.58/110.31 X469, 109.58/110.31 dsetconstr( 109.58/110.31 setunion( 109.58/110.31 X468), 109.58/110.31 '#ll_6'( 109.58/110.31 X468))))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X470]: 109.58/110.31 (( 109.58/110.31 ?[X471]: 109.58/110.31 (( 109.58/110.31 X470 = 109.58/110.31 setadjoin( 109.58/110.31 X471, 109.58/110.31 emptyset)) & 109.58/110.31 in( 109.58/110.31 X471,X470))) => 109.58/110.31 in( 109.58/110.31 setunion( 109.58/110.31 X470), 109.58/110.31 X470))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X472, 109.58/110.31 X473]: 109.58/110.31 (kfst( 109.58/110.31 kpair( 109.58/110.31 X472,X473)) = 109.58/110.31 X472)) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X474, 109.58/110.31 X475,X476]: 109.58/110.31 (in( 109.58/110.31 X476, 109.58/110.31 cartprod( 109.58/110.31 X474,X475)) => 109.58/110.31 in( 109.58/110.31 kfst( 109.58/110.31 X476), 109.58/110.31 X474))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X477, 109.58/110.31 X478, 109.58/110.31 X479,X480]: 109.58/110.31 (( 109.58/110.31 setadjoin( 109.58/110.31 setadjoin( 109.58/110.31 X477, 109.58/110.31 emptyset), 109.58/110.31 setadjoin( 109.58/110.31 setadjoin( 109.58/110.31 X477, 109.58/110.31 setadjoin( 109.58/110.31 X478, 109.58/110.31 emptyset)), 109.58/110.31 emptyset)) = 109.58/110.31 setadjoin( 109.58/110.31 setadjoin( 109.58/110.31 X479, 109.58/110.31 emptyset), 109.58/110.31 setadjoin( 109.58/110.31 setadjoin( 109.58/110.31 X479, 109.58/110.31 setadjoin( 109.58/110.31 X480, 109.58/110.31 emptyset)), 109.58/110.31 emptyset))) => 109.58/110.31 (X477 = 109.58/110.31 X479))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X481, 109.58/110.31 X482, 109.58/110.31 X483,X484]: 109.58/110.31 (( 109.58/110.31 kpair( 109.58/110.31 X481,X482) = 109.58/110.31 kpair( 109.58/110.31 X483,X484)) => 109.58/110.31 (X481 = 109.58/110.31 X483))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X485, 109.58/110.31 X486]: 109.58/110.31 (( 109.58/110.31 X485 = 109.58/110.31 X486) => 109.58/110.31 (setadjoin( 109.58/110.31 X485, 109.58/110.31 setadjoin( 109.58/110.31 X486, 109.58/110.31 emptyset)) = 109.58/110.31 setadjoin( 109.58/110.31 X485, 109.58/110.31 emptyset)))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X487, 109.58/110.31 X488]: 109.58/110.31 (( 109.58/110.31 X487 = 109.58/110.31 X488) => 109.58/110.31 (setadjoin( 109.58/110.31 setadjoin( 109.58/110.31 X487, 109.58/110.31 emptyset), 109.58/110.31 setadjoin( 109.58/110.31 setadjoin( 109.58/110.31 X487, 109.58/110.31 setadjoin( 109.58/110.31 X488, 109.58/110.31 emptyset)), 109.58/110.31 emptyset)) = 109.58/110.31 setadjoin( 109.58/110.31 setadjoin( 109.58/110.31 X487, 109.58/110.31 emptyset), 109.58/110.31 emptyset)))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X489, 109.58/110.31 X490, 109.58/110.31 X491,X492]: 109.58/110.31 (( 109.58/110.31 setadjoin( 109.58/110.31 setadjoin( 109.58/110.31 X489, 109.58/110.31 emptyset), 109.58/110.31 setadjoin( 109.58/110.31 setadjoin( 109.58/110.31 X489, 109.58/110.31 setadjoin( 109.58/110.31 X490, 109.58/110.31 emptyset)), 109.58/110.31 emptyset)) = 109.58/110.31 setadjoin( 109.58/110.31 setadjoin( 109.58/110.31 X491, 109.58/110.31 emptyset), 109.58/110.31 setadjoin( 109.58/110.31 setadjoin( 109.58/110.31 X491, 109.58/110.31 setadjoin( 109.58/110.31 X492, 109.58/110.31 emptyset)), 109.58/110.31 emptyset))) => 109.58/110.31 (( 109.58/110.31 X491 = 109.58/110.31 X492) => 109.58/110.31 (X490 = 109.58/110.31 X492)))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X493, 109.58/110.31 X494,X495]: 109.58/110.31 (( 109.58/110.31 setadjoin( 109.58/110.31 X493, 109.58/110.31 setadjoin( 109.58/110.31 X494, 109.58/110.31 emptyset)) = 109.58/110.31 setadjoin( 109.58/110.31 X495, 109.58/110.31 emptyset)) => 109.58/110.31 (X493 = 109.58/110.31 X494))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X496, 109.58/110.31 X497, 109.58/110.31 X498,X499]: 109.58/110.31 (( 109.58/110.31 setadjoin( 109.58/110.31 setadjoin( 109.58/110.31 X496, 109.58/110.31 emptyset), 109.58/110.31 setadjoin( 109.58/110.31 setadjoin( 109.58/110.31 X496, 109.58/110.31 setadjoin( 109.58/110.31 X497, 109.58/110.31 emptyset)), 109.58/110.31 emptyset)) = 109.58/110.31 setadjoin( 109.58/110.31 setadjoin( 109.58/110.31 X498, 109.58/110.31 emptyset), 109.58/110.31 setadjoin( 109.58/110.31 setadjoin( 109.58/110.31 X498, 109.58/110.31 setadjoin( 109.58/110.31 X499, 109.58/110.31 emptyset)), 109.58/110.31 emptyset))) => 109.58/110.31 (X497 = 109.58/110.31 X499))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X500, 109.58/110.31 X501, 109.58/110.31 X502,X503]: 109.58/110.31 (( 109.58/110.31 kpair( 109.58/110.31 X500,X501) = 109.58/110.31 kpair( 109.58/110.31 X502,X503)) => 109.58/110.31 (X501 = 109.58/110.31 X503))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X504]: 109.58/110.31 (iskpair( 109.58/110.31 X504) => 109.58/110.31 (?[X505]: 109.58/110.31 (( 109.58/110.31 dsetconstr( 109.58/110.31 setunion( 109.58/110.31 X504), 109.58/110.31 '#ll_5'( 109.58/110.31 X504)) = 109.58/110.31 setadjoin( 109.58/110.31 X505, 109.58/110.31 emptyset)) & 109.58/110.31 in( 109.58/110.31 X505, 109.58/110.31 dsetconstr( 109.58/110.31 setunion( 109.58/110.31 X504), 109.58/110.31 '#ll_5'( 109.58/110.31 X504))))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X506, 109.58/110.31 X507]: 109.58/110.31 (ksnd( 109.58/110.31 kpair( 109.58/110.31 X506,X507)) = 109.58/110.31 X507)) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X508]: 109.58/110.31 (iskpair( 109.58/110.31 X508) => 109.58/110.31 (kpair( 109.58/110.31 kfst( 109.58/110.31 X508), 109.58/110.31 ksnd( 109.58/110.31 X508)) = 109.58/110.31 X508))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X509, 109.58/110.31 X510,X511]: 109.58/110.31 (in( 109.58/110.31 X511, 109.58/110.31 cartprod( 109.58/110.31 X509,X510)) => 109.58/110.31 in( 109.58/110.31 ksnd( 109.58/110.31 X511), 109.58/110.31 X510))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X512, 109.58/110.31 X513, 109.58/110.31 X514,X515]: 109.58/110.31 (in( 109.58/110.31 kpair( 109.58/110.31 X514,X515), 109.58/110.31 cartprod( 109.58/110.31 X512,X513)) => 109.58/110.31 in( 109.58/110.31 X514,X512))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X516, 109.58/110.31 X517, 109.58/110.31 X518,X519]: 109.58/110.31 (in( 109.58/110.31 kpair( 109.58/110.31 X518,X519), 109.58/110.31 cartprod( 109.58/110.31 X516,X517)) => 109.58/110.31 in( 109.58/110.31 X519,X517))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X520, 109.58/110.31 X521,X522]: 109.58/110.31 (in( 109.58/110.31 X522,X520) => 109.58/110.31 (![X523]: 109.58/110.31 (in( 109.58/110.31 X523,X521) => 109.58/110.31 (kpair( 109.58/110.31 X522,X523) = 109.58/110.31 kpair( 109.58/110.31 X522,X523)))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X524, 109.58/110.31 X525,X526]: 109.58/110.31 (in( 109.58/110.31 X526,X524) => 109.58/110.31 (![X527]: 109.58/110.31 (in( 109.58/110.31 X527,X525) => 109.58/110.31 (kfst( 109.58/110.31 kpair( 109.58/110.31 X526,X527)) = 109.58/110.31 X526))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X528, 109.58/110.31 X529,X530]: 109.58/110.31 (in( 109.58/110.31 X530,X528) => 109.58/110.31 (![X531]: 109.58/110.31 (in( 109.58/110.31 X531,X529) => 109.58/110.31 (ksnd( 109.58/110.31 kpair( 109.58/110.31 X530,X531)) = 109.58/110.31 X531))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X532, 109.58/110.31 X533,X534]: 109.58/110.31 (in( 109.58/110.31 X534, 109.58/110.31 cartprod( 109.58/110.31 X532,X533)) => 109.58/110.31 (kpair( 109.58/110.31 kfst( 109.58/110.31 X534), 109.58/110.31 ksnd( 109.58/110.31 X534)) = 109.58/110.31 X534))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X535, 109.58/110.31 X536, 109.58/110.31 X537:( 109.58/110.31 ($i * $i) > 109.58/110.31 $o),X538]: 109.58/110.31 (in( 109.58/110.31 X538,X535) => 109.58/110.31 (![X539]: 109.58/110.31 (in( 109.58/110.31 X539,X536) => 109.58/110.31 (X537( 109.58/110.31 X538,X539) => 109.58/110.31 in( 109.58/110.31 kpair( 109.58/110.31 X538,X539), 109.58/110.31 dpsetconstr( 109.58/110.31 X535, 109.58/110.31 X536, 109.58/110.31 '#ll_4'( 109.58/110.31 X537)))))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X540, 109.58/110.31 X541, 109.58/110.31 X542:( 109.58/110.31 ($i * $i) > 109.58/110.31 $o)]: 109.58/110.31 subset( 109.58/110.31 dpsetconstr( 109.58/110.31 X540, 109.58/110.31 X541, 109.58/110.31 '#ll_4'( 109.58/110.31 X542)), 109.58/110.31 cartprod( 109.58/110.31 X540,X541))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X543, 109.58/110.31 X544, 109.58/110.31 X545:( 109.58/110.31 ($i * $i) > 109.58/110.31 $o)]: 109.58/110.31 subset( 109.58/110.31 dpsetconstr( 109.58/110.31 X543, 109.58/110.31 X544, 109.58/110.31 '#ll_4'( 109.58/110.31 X545)), 109.58/110.31 cartprod( 109.58/110.31 X543,X544))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X546, 109.58/110.31 X547, 109.58/110.31 X548:( 109.58/110.31 ($i * $i) > 109.58/110.31 $o),X549]: 109.58/110.31 (in( 109.58/110.31 X549,X546) => 109.58/110.31 (![X550]: 109.58/110.31 (in( 109.58/110.31 X550,X547) => 109.58/110.31 (in( 109.58/110.31 kpair( 109.58/110.31 X549,X550), 109.58/110.31 dpsetconstr( 109.58/110.31 X546, 109.58/110.31 X547, 109.58/110.31 '#ll_4'( 109.58/110.31 X548))) => 109.58/110.31 X548( 109.58/110.31 X549,X550)))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X551, 109.58/110.31 X552, 109.58/110.31 X553:( 109.58/110.31 ($i * $i) > 109.58/110.31 $o),X554, 109.58/110.31 X555]: 109.58/110.31 (in( 109.58/110.31 kpair( 109.58/110.31 X554,X555), 109.58/110.31 dpsetconstr( 109.58/110.31 X551, 109.58/110.31 X552, 109.58/110.31 '#ll_4'( 109.58/110.31 X553))) => 109.58/110.31 in( 109.58/110.31 X554,X551))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X556, 109.58/110.31 X557, 109.58/110.31 X558:( 109.58/110.31 ($i * $i) > 109.58/110.31 $o),X559, 109.58/110.31 X560]: 109.58/110.31 (in( 109.58/110.31 kpair( 109.58/110.31 X559,X560), 109.58/110.31 dpsetconstr( 109.58/110.31 X556, 109.58/110.31 X557, 109.58/110.31 '#ll_4'( 109.58/110.31 X558))) => 109.58/110.31 in( 109.58/110.31 X560,X557))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X561, 109.58/110.31 X562, 109.58/110.31 X563:( 109.58/110.31 ($i * $i) > 109.58/110.31 $o),X564, 109.58/110.31 X565]: 109.58/110.31 (in( 109.58/110.31 kpair( 109.58/110.31 X564,X565), 109.58/110.31 dpsetconstr( 109.58/110.31 X561, 109.58/110.31 X562, 109.58/110.31 '#ll_4'( 109.58/110.31 X563))) => 109.58/110.31 X563( 109.58/110.31 X564,X565))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X566, 109.58/110.31 X567,X568]: 109.58/110.31 (( 109.58/110.31 ( 109.58/110.31 ![X569]: 109.58/110.31 (in( 109.58/110.31 X569,X566) => 109.58/110.31 (?[X570]: 109.58/110.31 (( 109.58/110.31 dsetconstr( 109.58/110.31 X567, 109.58/110.31 '#ll_3'( 109.58/110.31 X569,X568)) = 109.58/110.31 setadjoin( 109.58/110.31 X570, 109.58/110.31 emptyset)) & 109.58/110.31 in( 109.58/110.31 X570, 109.58/110.31 dsetconstr( 109.58/110.31 X567, 109.58/110.31 '#ll_3'( 109.58/110.31 X569,X568))))))) & 109.58/110.31 subset( 109.58/110.31 X568, 109.58/110.31 cartprod( 109.58/110.31 X566,X567))) => 109.58/110.31 (![X571]: 109.58/110.31 (in( 109.58/110.31 X571,X566) => 109.58/110.31 (?[X572]: 109.58/110.31 (( 109.58/110.31 dsetconstr( 109.58/110.31 X567, 109.58/110.31 '#ll_3'( 109.58/110.31 X571,X568)) = 109.58/110.31 setadjoin( 109.58/110.31 X572, 109.58/110.31 emptyset)) & 109.58/110.31 in( 109.58/110.31 X572, 109.58/110.31 dsetconstr( 109.58/110.31 X567, 109.58/110.31 '#ll_3'( 109.58/110.31 X571,X568))))))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X573, 109.58/110.31 X574,X575]: 109.58/110.31 (( 109.58/110.31 ( 109.58/110.31 ![X576]: 109.58/110.31 (in( 109.58/110.31 X576,X573) => 109.58/110.31 (?[X577]: 109.58/110.31 (( 109.58/110.31 dsetconstr( 109.58/110.31 X574, 109.58/110.31 '#ll_3'( 109.58/110.31 X576,X575)) = 109.58/110.31 setadjoin( 109.58/110.31 X577, 109.58/110.31 emptyset)) & 109.58/110.31 in( 109.58/110.31 X577, 109.58/110.31 dsetconstr( 109.58/110.31 X574, 109.58/110.31 '#ll_3'( 109.58/110.31 X576,X575))))))) & 109.58/110.31 subset( 109.58/110.31 X575, 109.58/110.31 cartprod( 109.58/110.31 X573,X574))) => 109.58/110.31 (![X578]: 109.58/110.31 (in( 109.58/110.31 X578,X573) => 109.58/110.31 in( 109.58/110.31 setunion( 109.58/110.31 dsetconstr( 109.58/110.31 X574, 109.58/110.31 '#ll_3'( 109.58/110.31 X578,X575))), 109.58/110.31 X574))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X579, 109.58/110.31 X580,X581]: 109.58/110.31 (( 109.58/110.31 ( 109.58/110.31 ![X582]: 109.58/110.31 (in( 109.58/110.31 X582,X579) => 109.58/110.31 (?[X583]: 109.58/110.31 (( 109.58/110.31 dsetconstr( 109.58/110.31 X580, 109.58/110.31 '#ll_3'( 109.58/110.31 X582,X581)) = 109.58/110.31 setadjoin( 109.58/110.31 X583, 109.58/110.31 emptyset)) & 109.58/110.31 in( 109.58/110.31 X583, 109.58/110.31 dsetconstr( 109.58/110.31 X580, 109.58/110.31 '#ll_3'( 109.58/110.31 X582,X581))))))) & 109.58/110.31 subset( 109.58/110.31 X581, 109.58/110.31 cartprod( 109.58/110.31 X579,X580))) => 109.58/110.31 (![X584]: 109.58/110.31 (in( 109.58/110.31 X584,X579) => 109.58/110.31 in( 109.58/110.31 setunion( 109.58/110.31 dsetconstr( 109.58/110.31 X580, 109.58/110.31 '#ll_3'( 109.58/110.31 X584,X581))), 109.58/110.31 X580))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X585, 109.58/110.31 X586,X587]: 109.58/110.31 (in( 109.58/110.31 X587, 109.58/110.31 funcSet( 109.58/110.31 X585,X586)) => 109.58/110.31 (( 109.58/110.31 ![X588]: 109.58/110.31 (in( 109.58/110.31 X588,X585) => 109.58/110.31 (?[X589]: 109.58/110.31 (( 109.58/110.31 dsetconstr( 109.58/110.31 X586, 109.58/110.31 '#ll_3'( 109.58/110.31 X588,X587)) = 109.58/110.31 setadjoin( 109.58/110.31 X589, 109.58/110.31 emptyset)) & 109.58/110.31 in( 109.58/110.31 X589, 109.58/110.31 dsetconstr( 109.58/110.31 X586, 109.58/110.31 '#ll_3'( 109.58/110.31 X588,X587))))))) & 109.58/110.31 subset( 109.58/110.31 X587, 109.58/110.31 cartprod( 109.58/110.31 X585,X586))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X590, 109.58/110.31 X591,X592]: 109.58/110.31 (in( 109.58/110.31 X592, 109.58/110.31 funcSet( 109.58/110.31 X590,X591)) => 109.58/110.31 (![X593]: 109.58/110.31 (in( 109.58/110.31 X593,X590) => 109.58/110.31 in( 109.58/110.31 setunion( 109.58/110.31 dsetconstr( 109.58/110.31 X591, 109.58/110.31 '#ll_3'( 109.58/110.31 X593,X592))), 109.58/110.31 X591))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X594, 109.58/110.31 X595,X596]: 109.58/110.31 (( 109.58/110.31 ( 109.58/110.31 ![X597]: 109.58/110.31 (in( 109.58/110.31 X597,X594) => 109.58/110.31 (?[X598]: 109.58/110.31 (( 109.58/110.31 dsetconstr( 109.58/110.31 X595, 109.58/110.31 '#ll_3'( 109.58/110.31 X597,X596)) = 109.58/110.31 setadjoin( 109.58/110.31 X598, 109.58/110.31 emptyset)) & 109.58/110.31 in( 109.58/110.31 X598, 109.58/110.31 dsetconstr( 109.58/110.31 X595, 109.58/110.31 '#ll_3'( 109.58/110.31 X597,X596))))))) & 109.58/110.31 subset( 109.58/110.31 X596, 109.58/110.31 cartprod( 109.58/110.31 X594,X595))) => 109.58/110.31 in( 109.58/110.31 X596, 109.58/110.31 funcSet( 109.58/110.31 X594,X595)))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X599, 109.58/110.31 X600, 109.58/110.31 X601:( 109.58/110.31 $i > $i)]: 109.58/110.31 (( 109.58/110.31 ![X602]: 109.58/110.31 (in( 109.58/110.31 X602,X599) => 109.58/110.31 in( 109.58/110.31 X601( 109.58/110.31 X602), 109.58/110.31 X600))) => 109.58/110.31 (( 109.58/110.31 ![X603]: 109.58/110.31 (in( 109.58/110.31 X603,X599) => 109.58/110.31 (?[X604]: 109.58/110.31 (( 109.58/110.31 dsetconstr( 109.58/110.31 X600, 109.58/110.31 '#ll_2'( 109.58/110.31 X603, 109.58/110.31 X601, 109.58/110.31 X600,X599)) = 109.58/110.31 setadjoin( 109.58/110.31 X604, 109.58/110.31 emptyset)) & 109.58/110.31 in( 109.58/110.31 X604, 109.58/110.31 dsetconstr( 109.58/110.31 X600, 109.58/110.31 '#ll_2'( 109.58/110.31 X603, 109.58/110.31 X601, 109.58/110.31 X600,X599))))))) & 109.58/110.31 subset( 109.58/110.31 dpsetconstr( 109.58/110.31 X599, 109.58/110.31 X600, 109.58/110.31 '#ll_1'( 109.58/110.31 X601)), 109.58/110.31 cartprod( 109.58/110.31 X599,X600))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X605, 109.58/110.31 X606, 109.58/110.31 X607:( 109.58/110.31 $i > $i)]: 109.58/110.31 (( 109.58/110.31 ![X608]: 109.58/110.31 (in( 109.58/110.31 X608,X605) => 109.58/110.31 in( 109.58/110.31 X607( 109.58/110.31 X608), 109.58/110.31 X606))) => 109.58/110.31 (( 109.58/110.31 ![X609]: 109.58/110.31 (in( 109.58/110.31 X609,X605) => 109.58/110.31 (?[X610]: 109.58/110.31 (( 109.58/110.31 dsetconstr( 109.58/110.31 X606, 109.58/110.31 '#ll_2'( 109.58/110.31 X609, 109.58/110.31 X607, 109.58/110.31 X606,X605)) = 109.58/110.31 setadjoin( 109.58/110.31 X610, 109.58/110.31 emptyset)) & 109.58/110.31 in( 109.58/110.31 X610, 109.58/110.31 dsetconstr( 109.58/110.31 X606, 109.58/110.31 '#ll_2'( 109.58/110.31 X609, 109.58/110.31 X607, 109.58/110.31 X606,X605))))))) & 109.58/110.31 subset( 109.58/110.31 dpsetconstr( 109.58/110.31 X605, 109.58/110.31 X606, 109.58/110.31 '#ll_1'( 109.58/110.31 X607)), 109.58/110.31 cartprod( 109.58/110.31 X605,X606))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X611, 109.58/110.31 X612, 109.58/110.31 X613:( 109.58/110.31 $i > $i)]: 109.58/110.31 (( 109.58/110.31 ![X614]: 109.58/110.31 (in( 109.58/110.31 X614,X611) => 109.58/110.31 in( 109.58/110.31 X613( 109.58/110.31 X614), 109.58/110.31 X612))) => 109.58/110.31 in( 109.58/110.31 dpsetconstr( 109.58/110.31 X611, 109.58/110.31 X612, 109.58/110.31 '#ll_1'( 109.58/110.31 X613)), 109.58/110.31 funcSet( 109.58/110.31 X611,X612)))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X615, 109.58/110.31 X616,X617]: 109.58/110.31 (subset( 109.58/110.31 X617, 109.58/110.31 cartprod( 109.58/110.31 X615,X616)) => 109.58/110.31 (![X618:( 109.58/110.31 $i > $o)]: 109.58/110.31 (( 109.58/110.31 ![X619]: 109.58/110.31 (in( 109.58/110.31 X619,X615) => 109.58/110.31 (![X620]: 109.58/110.31 (in( 109.58/110.31 X620,X616) => 109.58/110.31 (in( 109.58/110.31 kpair( 109.58/110.31 X619,X620), 109.58/110.31 X617) => 109.58/110.31 X618( 109.58/110.31 kpair( 109.58/110.31 X619,X620))))))) => 109.58/110.31 (![X621]: 109.58/110.31 (in( 109.58/110.31 X621,X617) => 109.58/110.31 X618( 109.58/110.31 X621))))))) => 109.58/110.31 ( 109.58/110.31 ( 109.58/110.31 ![X622, 109.58/110.31 X623,X624]: 109.58/110.31 (subset( 109.58/110.31 X624, 109.58/110.31 cartprod( 109.58/110.31 X622,X623)) => 109.58/110.31 (![X625:( 109.58/110.31 $i > $o)]: 109.58/110.31 (( 109.58/110.31 ![X626]: 109.58/110.31 (in( 109.58/110.31 X626,X622) => 109.58/110.31 (![X627]: 109.58/110.31 (in( 109.58/110.31 X627,X623) => 109.58/110.31 (in( 109.58/110.31 kpair( 109.58/110.31 X626,X627), 109.58/110.31 X624) => 109.58/110.31 X625( 109.58/110.31 kpair( 109.58/110.31 X626,X627))))))) => 109.58/110.31 (![X628]: 109.58/110.31 (in( 109.58/110.31 X628,X624) => 109.58/110.31 X625( 109.58/110.31 X628))))))) => 109.58/110.31 ( 109.58/110.31 ![X629, 109.58/110.31 X630:( 109.58/110.31 $i > $o)]: 109.58/110.31 (( 109.58/110.31 ?[X631]: 109.58/110.31 (( 109.58/110.31 dsetconstr( 109.58/110.31 X629, 109.58/110.31 '#ll_0'( 109.58/110.31 X630)) = 109.58/110.31 setadjoin( 109.58/110.31 X631, 109.58/110.31 emptyset)) & 109.58/110.31 in( 109.58/110.31 X631, 109.58/110.31 dsetconstr( 109.58/110.31 X629, 109.58/110.31 '#ll_0'( 109.58/110.31 X630))))) => 109.58/110.31 (![X632]: 109.58/110.31 (in( 109.58/110.31 X632,X629) => 109.58/110.31 (![X633]: 109.58/110.31 (in( 109.58/110.31 X633,X629) => 109.58/110.31 (X630( 109.58/110.31 X632) => 109.58/110.31 (X630( 109.58/110.31 X633) => 109.58/110.31 (X632 = 109.58/110.31 X633)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 109.58/110.31 tff('207', plain, sk_X632_ != sk_X633_, 109.58/110.31 inference('cnf', [status(esa)], [zf_stmt_14])). 109.58/110.31 tff('208', plain, in(sk_X632_, sk_X629_), 109.58/110.31 inference('cnf', [status(esa)], [zf_stmt_14])). 109.58/110.31 tff('209', plain, sk_X630_(sk_X632_), 109.58/110.31 inference('cnf', [status(esa)], [zf_stmt_14])). 109.58/110.31 tff('210', plain, ![X665]: ~ in(X665, emptyset), 109.58/110.31 inference('cnf', [status(esa)], [zf_stmt_14])). 109.58/110.31 tff('211', plain, 109.58/110.31 dsetconstr(sk_X629_, '#ll_0'(sk_X630_)) = setadjoin(sk_X631_, emptyset), 109.58/110.31 inference('cnf', [status(esa)], [zf_stmt_14])). 109.58/110.31 tff('212', plain, in(sk_X633_, sk_X629_), 109.58/110.31 inference('cnf', [status(esa)], [zf_stmt_14])). 109.58/110.31 tff('213', plain, 109.58/110.31 ![X680, X681, X682]: 109.58/110.31 (X681 = X680 | in(X681, X682) | ~ in(X681, setadjoin(X680, X682))), 109.58/110.31 inference('cnf', [status(esa)], [zf_stmt_14])). 109.58/110.31 tff('214', plain, sk_X630_(sk_X633_), 109.58/110.31 inference('cnf', [status(esa)], [zf_stmt_14])). 109.58/110.31 tff('215', plain, 109.58/110.31 ![X657 : $i > $o, X658, X659]: 109.58/110.31 (~ X657(X658) 109.58/110.31 | in(X658, dsetconstr(X659, '#ll_0'(X657))) 109.58/110.31 | ~ in(X658, X659)), 109.58/110.31 inference('cnf', [status(esa)], [zf_stmt_14])). 109.58/110.31 tff('216', plain, $false, 109.58/110.31 inference('eprover', [status(thm)], 109.58/110.31 ['207', '208', '209', '210', '211', '212', '213', '214', '215'])). 109.58/110.31 109.58/110.31 % SZS output end Refutation 109.58/110.31 % Zipperpin 1.5 exiting 109.73/110.31 EOF