0.10/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.10/0.14 % Command : run_portfolio.sh /export/starexec/sandbox2/benchmark/theBenchmark.p /export/starexec/sandbox2/tmp/tmp.4f0UdfPUFM 0.13/0.35 % Computer : n005.cluster.edu 0.13/0.35 % Model : x86_64 x86_64 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.35 % Memory : 8042.1875MB 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.35 % CPULimit : 180 0.13/0.35 % DateTime : Thu Aug 29 16:44:03 EDT 2019 0.13/0.35 % CPUTime : 112.62/113.34 % Running portfolio for 180 s 112.62/113.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 112.62/113.34 % TempDir : /export/starexec/sandbox2/tmp/tmp.4f0UdfPUFM 112.62/113.34 % Recognized as monomorphic HO. 112.62/113.34 % Running /export/starexec/sandbox2/solver/bin/competitive.sh for 18 112.62/113.34 % Running /export/starexec/sandbox2/solver/bin/competitive.2.sh for 13 112.62/113.34 % Running /export/starexec/sandbox2/solver/bin/competitive.3.sh for 3 112.62/113.34 % Running /export/starexec/sandbox2/solver/bin/pragmatic.rudimentary.sh for 28 112.62/113.34 % Running /export/starexec/sandbox2/solver/bin/pragmatic.rudimentary.1.sh for 12 112.62/113.34 % Running /export/starexec/sandbox2/solver/bin/pragmatic.rudimentary.2.sh for 7 112.62/113.34 % Running /export/starexec/sandbox2/solver/bin/pragmatic.shallow.sh for 3 112.62/113.34 % Running /export/starexec/sandbox2/solver/bin/pragmatic.shallow.1.sh for 14 112.62/113.34 % Running /export/starexec/sandbox2/solver/bin/pragmatic.shallow.2.sh for 12 112.62/113.34 % Running /export/starexec/sandbox2/solver/bin/pragmatic.ll.e.sh for 19 112.62/113.34 % Solved by: pragmatic.ll.e.sh 112.62/113.34 % Running : timeout 16 /export/starexec/sandbox2/solver/bin/eprover-ho /export/starexec/sandbox2/tmp/tmp.4f0UdfPUFM/e_inputf6766d --cpu-limit=14 --auto-schedule -s -p. 112.62/113.34 % done 479 iterations in 14.498s 112.62/113.34 % hashcons stats for terms: size 4096, num 25299, sum length 39867, buckets: small 0, median 7, big 22 112.62/113.34 % proof state stats: {active 196, passive 6645, simpl 0} 112.62/113.34 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 112.62/113.34 % SZS output start Refutation 112.62/113.34 tff(lam2p, axiom, lam2p <=> 112.62/113.34 (![A,B,Xf:($i > $i)]: 112.62/113.34 ((![Xx]: (in(Xx,A) => in(Xf(Xx),B))) => 112.62/113.34 in(lam(A,B,^[Xx]: Xf(Xx)),funcSet(A,B))))). 112.62/113.34 tff('0', plain, 112.62/113.34 lam2p = 112.62/113.34 (![X2,X3,X4:($i > $i)]: 112.62/113.34 ((![X5]: (in(X5,X2) => in(X4(X5),X3))) => 112.62/113.34 in(lam(X2,X3,^[V_1]: X4(V_1)),funcSet(X2,X3)))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(lamp, axiom, lamp <=> 112.62/113.34 (![A,B,Xf:($i > $i)]: 112.62/113.34 ((![Xx]: (in(Xx,A) => in(Xf(Xx),B))) => func(A,B,lam(A,B,^[Xx]: Xf(Xx)))))). 112.62/113.34 tff('1', plain, 112.62/113.34 lamp = 112.62/113.34 (![X2,X3,X4:($i > $i)]: 112.62/113.34 ((![X5]: (in(X5,X2) => in(X4(X5),X3))) => 112.62/113.34 func(X2,X3,lam(X2,X3,^[V_1]: X4(V_1))))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(lam, axiom, lam() = 112.62/113.34 ^[A,B,Xf:($i > $i)]: dpsetconstr(A,B,^[Xx,Xy]: (Xf(Xx) = Xy))). 112.62/113.34 tff('2', plain, 112.62/113.34 lam = 112.62/113.34 (^[V_1,V_2,V_3:($i > $i)]: 112.62/113.34 dpsetconstr(V_1,V_2,^[V_4,V_5]: (V_3(V_4) = V_5))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(lamProp, axiom, lamProp <=> 112.62/113.34 (![A,B,Xf:($i > $i)]: 112.62/113.34 ((![Xx]: (in(Xx,A) => in(Xf(Xx),B))) => 112.62/113.34 func(A,B,dpsetconstr(A,B,^[Xx,Xy]: (Xf(Xx) = Xy)))))). 112.62/113.34 tff('3', plain, 112.62/113.34 lamProp = 112.62/113.34 (![X2,X3,X4:($i > $i)]: 112.62/113.34 ((![X5]: (in(X5,X2) => in(X4(X5),X3))) => 112.62/113.34 func(X2,X3,dpsetconstr(X2,X3,^[V_1,V_2]: (X4(V_1) = V_2))))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(funcinfuncset, axiom, funcinfuncset <=> 112.62/113.34 (![A,B,Xf]: (func(A,B,Xf) => in(Xf,funcSet(A,B))))). 112.62/113.34 tff('4', plain, 112.62/113.34 funcinfuncset = (![X2,X3,X4]: (func(X2,X3,X4) => in(X4,funcSet(X2,X3)))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(ap2p, axiom, ap2p <=> 112.62/113.34 (![A,B,Xf]: 112.62/113.34 (in(Xf,funcSet(A,B)) => (![Xx]: (in(Xx,A) => in(ap(A,B,Xf,Xx),B)))))). 112.62/113.34 tff('5', plain, 112.62/113.34 ap2p = 112.62/113.34 (![X2,X3,X4]: 112.62/113.34 (in(X4,funcSet(X2,X3)) => 112.62/113.34 (![X5]: (in(X5,X2) => in(ap(X2,X3,X4,X5),X3))))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(infuncsetfunc, axiom, infuncsetfunc <=> 112.62/113.34 (![A,B,Xf]: (in(Xf,funcSet(A,B)) => func(A,B,Xf)))). 112.62/113.34 tff('6', plain, 112.62/113.34 infuncsetfunc = (![X2,X3,X4]: (in(X4,funcSet(X2,X3)) => func(X2,X3,X4))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(app, axiom, app <=> 112.62/113.34 (![A,B,Xf]: (func(A,B,Xf) => (![Xx]: (in(Xx,A) => in(ap(A,B,Xf,Xx),B)))))). 112.62/113.34 tff('7', plain, 112.62/113.34 app = 112.62/113.34 (![X2,X3,X4]: 112.62/113.34 (func(X2,X3,X4) => (![X5]: (in(X5,X2) => in(ap(X2,X3,X4,X5),X3))))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(ap, axiom, ap() = 112.62/113.34 ^[A,B,Xf,Xx]: setunion(dsetconstr(B,^[Xy]: in(kpair(Xx,Xy),Xf)))). 112.62/113.34 tff('8', plain, 112.62/113.34 ap = 112.62/113.34 (^[V_1,V_2,V_3,V_4]: 112.62/113.34 setunion(dsetconstr(V_2,^[V_5]: in(kpair(V_4,V_5),V_3)))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(apProp, axiom, apProp <=> 112.62/113.34 (![A,B,Xf]: 112.62/113.34 (func(A,B,Xf) => 112.62/113.34 (![Xx]: 112.62/113.34 (in(Xx,A) => 112.62/113.34 in(setunion(dsetconstr(B,^[Xy]: in(kpair(Xx,Xy),Xf))),B)))))). 112.62/113.34 tff('9', plain, 112.62/113.34 apProp = 112.62/113.34 (![X2,X3,X4]: 112.62/113.34 (func(X2,X3,X4) => 112.62/113.34 (![X5]: 112.62/113.34 (in(X5,X2) => 112.62/113.34 in(setunion(dsetconstr(X3,^[V_1]: in(kpair(X5,V_1),X4))),X3))))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(funcImageSingleton, axiom, funcImageSingleton <=> 112.62/113.34 (![A,B,Xf]: 112.62/113.34 (func(A,B,Xf) => 112.62/113.34 (![Xx]: 112.62/113.34 (in(Xx,A) => singleton(dsetconstr(B,^[Xy]: in(kpair(Xx,Xy),Xf)))))))). 112.62/113.34 tff('10', plain, 112.62/113.34 funcImageSingleton = 112.62/113.34 (![X2,X3,X4]: 112.62/113.34 (func(X2,X3,X4) => 112.62/113.34 (![X5]: 112.62/113.34 (in(X5,X2) => 112.62/113.34 singleton(dsetconstr(X3,^[V_1]: in(kpair(X5,V_1),X4))))))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(func, axiom, func() = 112.62/113.34 ^[A,B,R]: 112.62/113.34 ((![Xx]: (in(Xx,A) => ex1(B,^[Xy]: in(kpair(Xx,Xy),R)))) & breln(A,B,R))). 112.62/113.34 tff('11', plain, 112.62/113.34 func = 112.62/113.34 (^[V_1,V_2,V_3]: 112.62/113.34 ((![X2]: (in(X2,V_1) => ex1(V_2,^[V_4]: in(kpair(X2,V_4),V_3)))) & 112.62/113.34 breln(V_1,V_2,V_3))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(dpsetconstrER, axiom, dpsetconstrER <=> 112.62/113.34 (![A,B,Xphi:(($i * $i) > $o),Xx,Xy]: 112.62/113.34 (in(kpair(Xx,Xy),dpsetconstr(A,B,^[Xz,Xu]: Xphi(Xz,Xu))) => Xphi(Xx,Xy)))). 112.62/113.34 tff('12', plain, 112.62/113.34 dpsetconstrER = 112.62/113.34 (![X2,X3,X4:(($i * $i) > $o),X5,X6]: 112.62/113.34 (in(kpair(X5,X6),dpsetconstr(X2,X3,^[V_1,V_2]: X4(V_1,V_2))) => 112.62/113.34 X4(X5,X6))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(dpsetconstrEL2, axiom, dpsetconstrEL2 <=> 112.62/113.34 (![A,B,Xphi:(($i * $i) > $o),Xx,Xy]: 112.62/113.34 (in(kpair(Xx,Xy),dpsetconstr(A,B,^[Xz,Xu]: Xphi(Xz,Xu))) => in(Xy,B)))). 112.62/113.34 tff('13', plain, 112.62/113.34 dpsetconstrEL2 = 112.62/113.34 (![X2,X3,X4:(($i * $i) > $o),X5,X6]: 112.62/113.34 (in(kpair(X5,X6),dpsetconstr(X2,X3,^[V_1,V_2]: X4(V_1,V_2))) => 112.62/113.34 in(X6,X3))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(dpsetconstrEL1, axiom, dpsetconstrEL1 <=> 112.62/113.34 (![A,B,Xphi:(($i * $i) > $o),Xx,Xy]: 112.62/113.34 (in(kpair(Xx,Xy),dpsetconstr(A,B,^[Xz,Xu]: Xphi(Xz,Xu))) => in(Xx,A)))). 112.62/113.34 tff('14', plain, 112.62/113.34 dpsetconstrEL1 = 112.62/113.34 (![X2,X3,X4:(($i * $i) > $o),X5,X6]: 112.62/113.34 (in(kpair(X5,X6),dpsetconstr(X2,X3,^[V_1,V_2]: X4(V_1,V_2))) => 112.62/113.34 in(X5,X2))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(dpsetconstrERa, axiom, dpsetconstrERa <=> 112.62/113.34 (![A,B,Xphi:(($i * $i) > $o),Xx]: 112.62/113.34 (in(Xx,A) => 112.62/113.34 (![Xy]: 112.62/113.34 (in(Xy,B) => 112.62/113.34 (in(kpair(Xx,Xy),dpsetconstr(A,B,^[Xz,Xu]: Xphi(Xz,Xu))) => 112.62/113.34 Xphi(Xx,Xy))))))). 112.62/113.34 tff('15', plain, 112.62/113.34 dpsetconstrERa = 112.62/113.34 (![X2,X3,X4:(($i * $i) > $o),X5]: 112.62/113.34 (in(X5,X2) => 112.62/113.34 (![X6]: 112.62/113.34 (in(X6,X3) => 112.62/113.34 (in(kpair(X5,X6),dpsetconstr(X2,X3,^[V_1,V_2]: X4(V_1,V_2))) => 112.62/113.34 X4(X5,X6)))))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(setOfPairsIsBReln, axiom, setOfPairsIsBReln <=> 112.62/113.34 (![A,B,Xphi:(($i * $i) > $o)]: 112.62/113.34 breln(A,B,dpsetconstr(A,B,^[Xx,Xy]: Xphi(Xx,Xy))))). 112.62/113.34 tff('16', plain, 112.62/113.34 setOfPairsIsBReln = 112.62/113.34 (![X2,X3,X4:(($i * $i) > $o)]: 112.62/113.34 breln(X2,X3,dpsetconstr(X2,X3,^[V_1,V_2]: X4(V_1,V_2)))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(dpsetconstrSub, axiom, dpsetconstrSub <=> 112.62/113.34 (![A,B,Xphi:(($i * $i) > $o)]: 112.62/113.34 subset(dpsetconstr(A,B,^[Xx,Xy]: Xphi(Xx,Xy)),cartprod(A,B)))). 112.62/113.34 tff('17', plain, 112.62/113.34 dpsetconstrSub = 112.62/113.34 (![X2,X3,X4:(($i * $i) > $o)]: 112.62/113.34 subset(dpsetconstr(X2,X3,^[V_1,V_2]: X4(V_1,V_2)),cartprod(X2,X3))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(dpsetconstrI, axiom, dpsetconstrI <=> 112.62/113.34 (![A,B,Xphi:(($i * $i) > $o),Xx]: 112.62/113.34 (in(Xx,A) => 112.62/113.34 (![Xy]: 112.62/113.34 (in(Xy,B) => 112.62/113.34 (Xphi(Xx,Xy) => 112.62/113.34 in(kpair(Xx,Xy),dpsetconstr(A,B,^[Xz,Xu]: Xphi(Xz,Xu))))))))). 112.62/113.34 tff('18', plain, 112.62/113.34 dpsetconstrI = 112.62/113.34 (![X2,X3,X4:(($i * $i) > $o),X5]: 112.62/113.34 (in(X5,X2) => 112.62/113.34 (![X6]: 112.62/113.34 (in(X6,X3) => 112.62/113.34 (X4(X5,X6) => 112.62/113.34 in(kpair(X5,X6),dpsetconstr(X2,X3,^[V_1,V_2]: X4(V_1,V_2)))))))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(breln, axiom, breln() = ^[A,B,C]: subset(C,cartprod(A,B))). 112.62/113.34 tff('19', plain, breln = (^[V_1,V_2,V_3]: subset(V_3,cartprod(V_1,V_2))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(cartprodpairsurjEq, axiom, cartprodpairsurjEq <=> 112.62/113.34 (![A,B,Xu]: (in(Xu,cartprod(A,B)) => (kpair(kfst(Xu),ksnd(Xu)) = Xu)))). 112.62/113.34 tff('20', plain, 112.62/113.34 cartprodpairsurjEq = 112.62/113.34 (![X2,X3,X4]: (in(X4,cartprod(X2,X3)) => (kpair(kfst(X4),ksnd(X4)) = X4))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(cartprodsndpairEq, axiom, cartprodsndpairEq <=> 112.62/113.34 (![A,B,Xx]: (in(Xx,A) => (![Xy]: (in(Xy,B) => (ksnd(kpair(Xx,Xy)) = Xy)))))). 112.62/113.34 tff('21', plain, 112.62/113.34 cartprodsndpairEq = 112.62/113.34 (![X2,X3,X4]: 112.62/113.34 (in(X4,X2) => (![X5]: (in(X5,X3) => (ksnd(kpair(X4,X5)) = X5))))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(cartprodfstpairEq, axiom, cartprodfstpairEq <=> 112.62/113.34 (![A,B,Xx]: (in(Xx,A) => (![Xy]: (in(Xy,B) => (kfst(kpair(Xx,Xy)) = Xx)))))). 112.62/113.34 tff('22', plain, 112.62/113.34 cartprodfstpairEq = 112.62/113.34 (![X2,X3,X4]: 112.62/113.34 (in(X4,X2) => (![X5]: (in(X5,X3) => (kfst(kpair(X4,X5)) = X4))))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(cartprodmempaircEq, axiom, cartprodmempaircEq <=> 112.62/113.34 (![A,B,Xx]: 112.62/113.34 (in(Xx,A) => (![Xy]: (in(Xy,B) => (kpair(Xx,Xy) = kpair(Xx,Xy))))))). 112.62/113.34 tff('23', plain, 112.62/113.34 cartprodmempaircEq = 112.62/113.34 (![X2,X3,X4]: 112.62/113.34 (in(X4,X2) => (![X5]: (in(X5,X3) => (kpair(X4,X5) = kpair(X4,X5)))))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(cartprodpairmemER, axiom, cartprodpairmemER <=> 112.62/113.34 (![A,B,Xx,Xy]: (in(kpair(Xx,Xy),cartprod(A,B)) => in(Xy,B)))). 112.62/113.34 tff('24', plain, 112.62/113.34 cartprodpairmemER = 112.62/113.34 (![X2,X3,X4,X5]: (in(kpair(X4,X5),cartprod(X2,X3)) => in(X5,X3))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(cartprodpairmemEL, axiom, cartprodpairmemEL <=> 112.62/113.34 (![A,B,Xx,Xy]: (in(kpair(Xx,Xy),cartprod(A,B)) => in(Xx,A)))). 112.62/113.34 tff('25', plain, 112.62/113.34 cartprodpairmemEL = 112.62/113.34 (![X2,X3,X4,X5]: (in(kpair(X4,X5),cartprod(X2,X3)) => in(X4,X2))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(cartprodsndin, axiom, cartprodsndin <=> 112.62/113.34 (![A,B,Xu]: (in(Xu,cartprod(A,B)) => in(ksnd(Xu),B)))). 112.62/113.34 tff('26', plain, 112.62/113.34 cartprodsndin = 112.62/113.34 (![X2,X3,X4]: (in(X4,cartprod(X2,X3)) => in(ksnd(X4),X3))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(kpairsurjEq, axiom, kpairsurjEq <=> 112.62/113.34 (![Xu]: (iskpair(Xu) => (kpair(kfst(Xu),ksnd(Xu)) = Xu)))). 112.62/113.34 tff('27', plain, 112.62/113.34 kpairsurjEq = (![X2]: (iskpair(X2) => (kpair(kfst(X2),ksnd(X2)) = X2))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(ksndpairEq, axiom, ksndpairEq <=> (![Xx,Xy]: (ksnd(kpair(Xx,Xy)) = Xy))). 112.62/113.34 tff('28', plain, ksndpairEq = (![X2,X3]: (ksnd(kpair(X2,X3)) = X3)), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(ksndsingleton, axiom, ksndsingleton <=> 112.62/113.34 (![Xu]: 112.62/113.34 (iskpair(Xu) => 112.62/113.34 singleton(dsetconstr(setunion(Xu),^[Xx]: (Xu = kpair(kfst(Xu),Xx))))))). 112.62/113.34 tff('29', plain, 112.62/113.34 ksndsingleton = 112.62/113.34 (![X2]: 112.62/113.34 (iskpair(X2) => 112.62/113.34 singleton(dsetconstr(setunion(X2),^[V_1]: (X2 = kpair(kfst(X2),V_1)))))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(setukpairinjR, axiom, setukpairinjR <=> 112.62/113.34 (![Xx,Xy,Xz,Xu]: ((kpair(Xx,Xy) = kpair(Xz,Xu)) => (Xy = Xu)))). 112.62/113.34 tff('30', plain, 112.62/113.34 setukpairinjR = 112.62/113.34 (![X2,X3,X4,X5]: ((kpair(X2,X3) = kpair(X4,X5)) => (X3 = X5))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(setukpairinjR2, axiom, setukpairinjR2 <=> 112.62/113.34 (![Xx,Xy,Xz,Xu]: 112.62/113.34 ((setadjoin(setadjoin(Xx,emptyset), 112.62/113.34 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)),emptyset)) = 112.62/113.34 setadjoin(setadjoin(Xz,emptyset), 112.62/113.34 setadjoin(setadjoin(Xz,setadjoin(Xu,emptyset)),emptyset))) => 112.62/113.34 (Xy = Xu)))). 112.62/113.34 tff('31', plain, 112.62/113.34 setukpairinjR2 = 112.62/113.34 (![X2,X3,X4,X5]: 112.62/113.34 ((setadjoin(setadjoin(X2,emptyset), 112.62/113.34 setadjoin(setadjoin(X2,setadjoin(X3,emptyset)),emptyset)) = 112.62/113.34 setadjoin(setadjoin(X4,emptyset), 112.62/113.34 setadjoin(setadjoin(X4,setadjoin(X5,emptyset)),emptyset))) => 112.62/113.34 (X3 = X5))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(upairequniteq, axiom, upairequniteq <=> 112.62/113.34 (![Xx,Xy,Xz]: 112.62/113.34 ((setadjoin(Xx,setadjoin(Xy,emptyset)) = setadjoin(Xz,emptyset)) => 112.62/113.34 (Xx = Xy)))). 112.62/113.34 tff('32', plain, 112.62/113.34 upairequniteq = 112.62/113.34 (![X2,X3,X4]: 112.62/113.34 ((setadjoin(X2,setadjoin(X3,emptyset)) = setadjoin(X4,emptyset)) => 112.62/113.34 (X2 = X3))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(setukpairinjR1, axiom, setukpairinjR1 <=> 112.62/113.34 (![Xx,Xy,Xz,Xu]: 112.62/113.34 ((setadjoin(setadjoin(Xx,emptyset), 112.62/113.34 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)),emptyset)) = 112.62/113.34 setadjoin(setadjoin(Xz,emptyset), 112.62/113.34 setadjoin(setadjoin(Xz,setadjoin(Xu,emptyset)),emptyset))) => 112.62/113.34 ((Xz = Xu) => (Xy = Xu))))). 112.62/113.34 tff('33', plain, 112.62/113.34 setukpairinjR1 = 112.62/113.34 (![X2,X3,X4,X5]: 112.62/113.34 ((setadjoin(setadjoin(X2,emptyset), 112.62/113.34 setadjoin(setadjoin(X2,setadjoin(X3,emptyset)),emptyset)) = 112.62/113.34 setadjoin(setadjoin(X4,emptyset), 112.62/113.34 setadjoin(setadjoin(X4,setadjoin(X5,emptyset)),emptyset))) => 112.62/113.34 ((X4 = X5) => (X3 = X5)))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(setukpairinjR12, axiom, setukpairinjR12 <=> 112.62/113.34 (![Xx,Xy]: 112.62/113.34 ((Xx = Xy) => 112.62/113.34 (setadjoin(setadjoin(Xx,emptyset), 112.62/113.34 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)),emptyset)) = 112.62/113.34 setadjoin(setadjoin(Xx,emptyset),emptyset))))). 112.62/113.34 tff('34', plain, 112.62/113.34 setukpairinjR12 = 112.62/113.34 (![X2,X3]: 112.62/113.34 ((X2 = X3) => 112.62/113.34 (setadjoin(setadjoin(X2,emptyset), 112.62/113.34 setadjoin(setadjoin(X2,setadjoin(X3,emptyset)),emptyset)) = 112.62/113.34 setadjoin(setadjoin(X2,emptyset),emptyset)))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(setukpairinjR11, axiom, setukpairinjR11 <=> 112.62/113.34 (![Xx,Xy]: 112.62/113.34 ((Xx = Xy) => 112.62/113.34 (setadjoin(Xx,setadjoin(Xy,emptyset)) = setadjoin(Xx,emptyset))))). 112.62/113.34 tff('35', plain, 112.62/113.34 setukpairinjR11 = 112.62/113.34 (![X2,X3]: 112.62/113.34 ((X2 = X3) => 112.62/113.34 (setadjoin(X2,setadjoin(X3,emptyset)) = setadjoin(X2,emptyset)))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(setukpairinjL, axiom, setukpairinjL <=> 112.62/113.34 (![Xx,Xy,Xz,Xu]: ((kpair(Xx,Xy) = kpair(Xz,Xu)) => (Xx = Xz)))). 112.62/113.34 tff('36', plain, 112.62/113.34 setukpairinjL = 112.62/113.34 (![X2,X3,X4,X5]: ((kpair(X2,X3) = kpair(X4,X5)) => (X2 = X4))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(setukpairinjL2, axiom, setukpairinjL2 <=> 112.62/113.34 (![Xx,Xy,Xz,Xu]: 112.62/113.34 ((setadjoin(setadjoin(Xx,emptyset), 112.62/113.34 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)),emptyset)) = 112.62/113.34 setadjoin(setadjoin(Xz,emptyset), 112.62/113.34 setadjoin(setadjoin(Xz,setadjoin(Xu,emptyset)),emptyset))) => 112.62/113.34 (Xx = Xz)))). 112.62/113.34 tff('37', plain, 112.62/113.34 setukpairinjL2 = 112.62/113.34 (![X2,X3,X4,X5]: 112.62/113.34 ((setadjoin(setadjoin(X2,emptyset), 112.62/113.34 setadjoin(setadjoin(X2,setadjoin(X3,emptyset)),emptyset)) = 112.62/113.34 setadjoin(setadjoin(X4,emptyset), 112.62/113.34 setadjoin(setadjoin(X4,setadjoin(X5,emptyset)),emptyset))) => 112.62/113.34 (X2 = X4))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(cartprodfstin, axiom, cartprodfstin <=> 112.62/113.34 (![A,B,Xu]: (in(Xu,cartprod(A,B)) => in(kfst(Xu),A)))). 112.62/113.34 tff('38', plain, 112.62/113.34 cartprodfstin = 112.62/113.34 (![X2,X3,X4]: (in(X4,cartprod(X2,X3)) => in(kfst(X4),X2))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(kfstpairEq, axiom, kfstpairEq <=> (![Xx,Xy]: (kfst(kpair(Xx,Xy)) = Xx))). 112.62/113.34 tff('39', plain, kfstpairEq = (![X2,X3]: (kfst(kpair(X2,X3)) = X2)), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(theprop, axiom, theprop <=> (![X]: (singleton(X) => in(setunion(X),X)))). 112.62/113.34 tff('40', plain, theprop = (![X2]: (singleton(X2) => in(setunion(X2),X2))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(kfstsingleton, axiom, kfstsingleton <=> 112.62/113.34 (![Xu]: 112.62/113.34 (iskpair(Xu) => 112.62/113.34 singleton(dsetconstr(setunion(Xu),^[Xx]: in(setadjoin(Xx,emptyset),Xu)))))). 112.62/113.34 tff('41', plain, 112.62/113.34 kfstsingleton = 112.62/113.34 (![X2]: 112.62/113.34 (iskpair(X2) => 112.62/113.34 singleton(dsetconstr(setunion(X2), 112.62/113.34 ^[V_1]: in(setadjoin(V_1,emptyset),X2))))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(setukpairinjL1, axiom, setukpairinjL1 <=> 112.62/113.34 (![Xx,Xy,Xz]: 112.62/113.34 (in(setadjoin(Xz,emptyset), 112.62/113.34 setadjoin(setadjoin(Xx,emptyset), 112.62/113.34 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)),emptyset))) => 112.62/113.34 (Xx = Xz)))). 112.62/113.34 tff('42', plain, 112.62/113.34 setukpairinjL1 = 112.62/113.34 (![X2,X3,X4]: 112.62/113.34 (in(setadjoin(X4,emptyset), 112.62/113.34 setadjoin(setadjoin(X2,emptyset), 112.62/113.34 setadjoin(setadjoin(X2,setadjoin(X3,emptyset)),emptyset))) => 112.62/113.34 (X2 = X4))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(singletonsuniq, axiom, singletonsuniq <=> 112.62/113.34 (![Xx,Xy]: ((setadjoin(Xx,emptyset) = setadjoin(Xy,emptyset)) => (Xx = Xy)))). 112.62/113.34 tff('43', plain, 112.62/113.34 singletonsuniq = 112.62/113.34 (![X2,X3]: 112.62/113.34 ((setadjoin(X2,emptyset) = setadjoin(X3,emptyset)) => (X2 = X3))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(ex1I2, axiom, ex1I2 <=> 112.62/113.34 (![A,Xphi:($i > $o)]: 112.62/113.34 ((![Xx]: 112.62/113.34 (in(Xx,A) => 112.62/113.34 (![Xy]: (in(Xy,A) => (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))) => 112.62/113.34 ((?[Xx]: (Xphi(Xx) & in(Xx,A))) => ex1(A,^[Xx]: Xphi(Xx)))))). 112.62/113.34 tff('44', plain, 112.62/113.34 ex1I2 = 112.62/113.34 (![X2,X3:($i > $o)]: 112.62/113.34 ((![X4]: 112.62/113.34 (in(X4,X2) => 112.62/113.34 (![X5]: (in(X5,X2) => (X3(X4) => (X3(X5) => (X4 = X5))))))) => 112.62/113.34 ((?[X6]: (X3(X6) & in(X6,X2))) => ex1(X2,^[V_1]: X3(V_1))))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(ex1I, axiom, ex1I <=> 112.62/113.34 (![A,Xphi:($i > $o),Xx]: 112.62/113.34 (in(Xx,A) => 112.62/113.34 (Xphi(Xx) => 112.62/113.34 ((![Xy]: (in(Xy,A) => (Xphi(Xy) => (Xy = Xx)))) => 112.62/113.34 ex1(A,^[Xy]: Xphi(Xy))))))). 112.62/113.34 tff('45', plain, 112.62/113.34 ex1I = 112.62/113.34 (![X2,X3:($i > $o),X4]: 112.62/113.34 (in(X4,X2) => 112.62/113.34 (X3(X4) => 112.62/113.34 ((![X5]: (in(X5,X2) => (X3(X5) => (X5 = X4)))) => 112.62/113.34 ex1(X2,^[V_1]: X3(V_1)))))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(ex1E1, axiom, ex1E1 <=> 112.62/113.34 (![A,Xphi:($i > $o)]: 112.62/113.34 (ex1(A,^[Xx]: Xphi(Xx)) => (?[Xx]: (Xphi(Xx) & in(Xx,A)))))). 112.62/113.34 tff('46', plain, 112.62/113.34 ex1E1 = 112.62/113.34 (![X2,X3:($i > $o)]: 112.62/113.34 (ex1(X2,^[V_1]: X3(V_1)) => (?[X4]: (X3(X4) & in(X4,X2))))), 112.62/113.34 define([status(thm)])). 112.62/113.34 tff(ex1, axiom, ex1() = 112.62/113.34 ^[A,Xphi:($i > $o)]: singleton(dsetconstr(A,^[Xx]: Xphi(Xx)))). 112.62/113.34 tff('47', plain, 112.62/113.34 ex1 = (^[V_1,V_2:($i > $o)]: singleton(dsetconstr(V_1,^[V_3]: V_2(V_3)))), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(singletonprop, axiom, singletonprop <=> 112.62/113.35 (![A,Xphi:($i > $o)]: 112.62/113.35 ((![Xx]: 112.62/113.35 (in(Xx,A) => 112.62/113.35 (![Xy]: (in(Xy,A) => (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))) => 112.62/113.35 ((?[Xx]: (Xphi(Xx) & in(Xx,A))) => 112.62/113.35 singleton(dsetconstr(A,^[Xx]: Xphi(Xx))))))). 112.62/113.35 tff('48', plain, 112.62/113.35 singletonprop = 112.62/113.35 (![X2,X3:($i > $o)]: 112.62/113.35 ((![X4]: 112.62/113.35 (in(X4,X2) => 112.62/113.35 (![X5]: (in(X5,X2) => (X3(X4) => (X3(X5) => (X4 = X5))))))) => 112.62/113.35 ((?[X6]: (X3(X6) & in(X6,X2))) => 112.62/113.35 singleton(dsetconstr(X2,^[V_1]: X3(V_1)))))), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(singleton, axiom, singleton() = 112.62/113.35 ^[A]: (?[Xx]: ((A = setadjoin(Xx,emptyset)) & in(Xx,A)))). 112.62/113.35 tff('49', plain, 112.62/113.35 singleton = 112.62/113.35 (^[V_1]: (?[X2]: ((V_1 = setadjoin(X2,emptyset)) & in(X2,V_1)))), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(setunionsingleton, axiom, setunionsingleton <=> 112.62/113.35 (![Xx]: (setunion(setadjoin(Xx,emptyset)) = Xx))). 112.62/113.35 tff('50', plain, 112.62/113.35 setunionsingleton = (![X2]: (setunion(setadjoin(X2,emptyset)) = X2)), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(setunionsingleton2, axiom, setunionsingleton2 <=> 112.62/113.35 (![A]: subset(A,setunion(setadjoin(A,emptyset))))). 112.62/113.35 tff('51', plain, 112.62/113.35 setunionsingleton2 = (![X2]: subset(X2,setunion(setadjoin(X2,emptyset)))), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(setunionsingleton1, axiom, setunionsingleton1 <=> 112.62/113.35 (![A]: subset(setunion(setadjoin(A,emptyset)),A))). 112.62/113.35 tff('52', plain, 112.62/113.35 setunionsingleton1 = (![X2]: subset(setunion(setadjoin(X2,emptyset)),X2)), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(setunionE2, axiom, setunionE2 <=> 112.62/113.35 (![A,Xx]: (in(Xx,setunion(A)) => (?[X]: (in(Xx,X) & in(X,A)))))). 112.62/113.35 tff('53', plain, 112.62/113.35 setunionE2 = 112.62/113.35 (![X2,X3]: (in(X3,setunion(X2)) => (?[X4]: (in(X3,X4) & in(X4,X2))))), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(cartprodmempair, axiom, cartprodmempair <=> 112.62/113.35 (![A,B,Xu]: (in(Xu,cartprod(A,B)) => iskpair(Xu)))). 112.62/113.35 tff('54', plain, 112.62/113.35 cartprodmempair = (![X2,X3,X4]: (in(X4,cartprod(X2,X3)) => iskpair(X4))), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(cartprodmempair1, axiom, cartprodmempair1 <=> 112.62/113.35 (![A,B,Xu]: 112.62/113.35 (in(Xu,cartprod(A,B)) => 112.62/113.35 (?[Xx]: ((?[Xy]: ((Xu = kpair(Xx,Xy)) & in(Xy,B))) & in(Xx,A)))))). 112.62/113.35 tff('55', plain, 112.62/113.35 cartprodmempair1 = 112.62/113.35 (![X2,X3,X4]: 112.62/113.35 (in(X4,cartprod(X2,X3)) => 112.62/113.35 (?[X5]: ((?[X6]: ((X4 = kpair(X5,X6)) & in(X6,X3))) & in(X5,X2))))), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(cartprodpairin, axiom, cartprodpairin <=> 112.62/113.35 (![A,B,Xx]: 112.62/113.35 (in(Xx,A) => (![Xy]: (in(Xy,B) => in(kpair(Xx,Xy),cartprod(A,B))))))). 112.62/113.35 tff('56', plain, 112.62/113.35 cartprodpairin = 112.62/113.35 (![X2,X3,X4]: 112.62/113.35 (in(X4,X2) => (![X5]: (in(X5,X3) => in(kpair(X4,X5),cartprod(X2,X3)))))), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(ubforcartprodlem3, axiom, ubforcartprodlem3 <=> 112.62/113.35 (![A,B,Xx]: 112.62/113.35 (in(Xx,A) => 112.62/113.35 (![Xy]: 112.62/113.35 (in(Xy,B) => in(kpair(Xx,Xy),powerset(powerset(binunion(A,B))))))))). 112.62/113.35 tff('57', plain, 112.62/113.35 ubforcartprodlem3 = 112.62/113.35 (![X2,X3,X4]: 112.62/113.35 (in(X4,X2) => 112.62/113.35 (![X5]: 112.62/113.35 (in(X5,X3) => in(kpair(X4,X5),powerset(powerset(binunion(X2,X3)))))))), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(ubforcartprodlem2, axiom, ubforcartprodlem2 <=> 112.62/113.35 (![A,B,Xx]: 112.62/113.35 (in(Xx,A) => 112.62/113.35 (![Xy]: 112.62/113.35 (in(Xy,B) => 112.62/113.35 in(setadjoin(setadjoin(Xx,emptyset), 112.62/113.35 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 112.62/113.35 emptyset)), 112.62/113.35 powerset(powerset(binunion(A,B))))))))). 112.62/113.35 tff('58', plain, 112.62/113.35 ubforcartprodlem2 = 112.62/113.35 (![X2,X3,X4]: 112.62/113.35 (in(X4,X2) => 112.62/113.35 (![X5]: 112.62/113.35 (in(X5,X3) => 112.62/113.35 in(setadjoin(setadjoin(X4,emptyset), 112.62/113.35 setadjoin(setadjoin(X4,setadjoin(X5,emptyset)), 112.62/113.35 emptyset)), 112.62/113.35 powerset(powerset(binunion(X2,X3)))))))), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(ubforcartprodlem1, axiom, ubforcartprodlem1 <=> 112.62/113.35 (![A,B,Xx]: 112.62/113.35 (in(Xx,A) => 112.62/113.35 (![Xy]: 112.62/113.35 (in(Xy,B) => 112.62/113.35 subset(setadjoin(setadjoin(Xx,emptyset), 112.62/113.35 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 112.62/113.35 emptyset)), 112.62/113.35 powerset(binunion(A,B)))))))). 112.62/113.35 tff('59', plain, 112.62/113.35 ubforcartprodlem1 = 112.62/113.35 (![X2,X3,X4]: 112.62/113.35 (in(X4,X2) => 112.62/113.35 (![X5]: 112.62/113.35 (in(X5,X3) => 112.62/113.35 subset(setadjoin(setadjoin(X4,emptyset), 112.62/113.35 setadjoin(setadjoin(X4,setadjoin(X5,emptyset)), 112.62/113.35 emptyset)), 112.62/113.35 powerset(binunion(X2,X3))))))), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(upairinpowunion, axiom, upairinpowunion <=> 112.62/113.35 (![A,B,Xx]: 112.62/113.35 (in(Xx,A) => 112.62/113.35 (![Xy]: 112.62/113.35 (in(Xy,B) => 112.62/113.35 in(setadjoin(Xx,setadjoin(Xy,emptyset)),powerset(binunion(A,B)))))))). 112.62/113.35 tff('60', plain, 112.62/113.35 upairinpowunion = 112.62/113.35 (![X2,X3,X4]: 112.62/113.35 (in(X4,X2) => 112.62/113.35 (![X5]: 112.62/113.35 (in(X5,X3) => 112.62/113.35 in(setadjoin(X4,setadjoin(X5,emptyset)),powerset(binunion(X2,X3))))))), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(upairsubunion, axiom, upairsubunion <=> 112.62/113.35 (![A,B,Xx]: 112.62/113.35 (in(Xx,A) => 112.62/113.35 (![Xy]: 112.62/113.35 (in(Xy,B) => 112.62/113.35 subset(setadjoin(Xx,setadjoin(Xy,emptyset)),binunion(A,B))))))). 112.62/113.35 tff('61', plain, 112.62/113.35 upairsubunion = 112.62/113.35 (![X2,X3,X4]: 112.62/113.35 (in(X4,X2) => 112.62/113.35 (![X5]: 112.62/113.35 (in(X5,X3) => 112.62/113.35 subset(setadjoin(X4,setadjoin(X5,emptyset)),binunion(X2,X3)))))), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(upairset2E, axiom, upairset2E <=> 112.62/113.35 (![Xx,Xy,Xz]: 112.62/113.35 (in(Xz,setadjoin(Xx,setadjoin(Xy,emptyset))) => ((Xz = Xy) | (Xz = Xx))))). 112.62/113.35 tff('62', plain, 112.62/113.35 upairset2E = 112.62/113.35 (![X2,X3,X4]: 112.62/113.35 (in(X4,setadjoin(X2,setadjoin(X3,emptyset))) => 112.62/113.35 ((X4 = X3) | (X4 = X2)))), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(singletoninpowunion, axiom, singletoninpowunion <=> 112.62/113.35 (![A,B,Xx]: 112.62/113.35 (in(Xx,A) => in(setadjoin(Xx,emptyset),powerset(binunion(A,B)))))). 112.62/113.35 tff('63', plain, 112.62/113.35 singletoninpowunion = 112.62/113.35 (![X2,X3,X4]: 112.62/113.35 (in(X4,X2) => in(setadjoin(X4,emptyset),powerset(binunion(X2,X3))))), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(singletoninpowerset, axiom, singletoninpowerset <=> 112.62/113.35 (![A,Xx]: (in(Xx,A) => in(setadjoin(Xx,emptyset),powerset(A))))). 112.62/113.35 tff('64', plain, 112.62/113.35 singletoninpowerset = 112.62/113.35 (![X2,X3]: (in(X3,X2) => in(setadjoin(X3,emptyset),powerset(X2)))), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(singletonsubset, axiom, singletonsubset <=> 112.62/113.35 (![A,Xx]: (in(Xx,A) => subset(setadjoin(Xx,emptyset),A)))). 112.62/113.35 tff('65', plain, 112.62/113.35 singletonsubset = 112.62/113.35 (![X2,X3]: (in(X3,X2) => subset(setadjoin(X3,emptyset),X2))), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(kpairp, axiom, kpairp <=> (![Xx,Xy]: iskpair(kpair(Xx,Xy)))). 112.62/113.35 tff('66', plain, kpairp = (![X2,X3]: iskpair(kpair(X2,X3))), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(kpairiskpair, axiom, kpairiskpair <=> 112.62/113.35 (![Xx,Xy]: 112.62/113.35 iskpair(setadjoin(setadjoin(Xx,emptyset), 112.62/113.35 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 112.62/113.35 emptyset))))). 112.62/113.35 tff('67', plain, 112.62/113.35 kpairiskpair = 112.62/113.35 (![X2,X3]: 112.62/113.35 iskpair(setadjoin(setadjoin(X2,emptyset), 112.62/113.35 setadjoin(setadjoin(X2,setadjoin(X3,emptyset)), 112.62/113.35 emptyset)))), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(setukpairIR, axiom, setukpairIR <=> 112.62/113.35 (![Xx,Xy]: 112.62/113.35 in(Xy, 112.62/113.35 setunion(setadjoin(setadjoin(Xx,emptyset), 112.62/113.35 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 112.62/113.35 emptyset)))))). 112.62/113.35 tff('68', plain, 112.62/113.35 setukpairIR = 112.62/113.35 (![X2,X3]: 112.62/113.35 in(X3, 112.62/113.35 setunion(setadjoin(setadjoin(X2,emptyset), 112.62/113.35 setadjoin(setadjoin(X2,setadjoin(X3,emptyset)), 112.62/113.35 emptyset))))), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(setukpairIL, axiom, setukpairIL <=> 112.62/113.35 (![Xx,Xy]: 112.62/113.35 in(Xx, 112.62/113.35 setunion(setadjoin(setadjoin(Xx,emptyset), 112.62/113.35 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 112.62/113.35 emptyset)))))). 112.62/113.35 tff('69', plain, 112.62/113.35 setukpairIL = 112.62/113.35 (![X2,X3]: 112.62/113.35 in(X2, 112.62/113.35 setunion(setadjoin(setadjoin(X2,emptyset), 112.62/113.35 setadjoin(setadjoin(X2,setadjoin(X3,emptyset)), 112.62/113.35 emptyset))))), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(secondinupair, axiom, secondinupair <=> 112.62/113.35 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 112.62/113.35 tff('70', plain, 112.62/113.35 secondinupair = (![X2,X3]: in(X3,setadjoin(X2,setadjoin(X3,emptyset)))), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(symdiffIneg2, axiom, symdiffIneg2 <=> 112.62/113.35 (![A,B,Xx]: ((~in(Xx,A)) => ((~in(Xx,B)) => (~in(Xx,symdiff(A,B))))))). 112.62/113.35 tff('71', plain, 112.62/113.35 symdiffIneg2 = 112.62/113.35 (![X2,X3,X4]: 112.62/113.35 ((~in(X4,X2)) => ((~in(X4,X3)) => (~in(X4,symdiff(X2,X3)))))), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(symdiffIneg1, axiom, symdiffIneg1 <=> 112.62/113.35 (![A,B,Xx]: (in(Xx,A) => (in(Xx,B) => (~in(Xx,symdiff(A,B))))))). 112.62/113.35 tff('72', plain, 112.62/113.35 symdiffIneg1 = 112.62/113.35 (![X2,X3,X4]: (in(X4,X2) => (in(X4,X3) => (~in(X4,symdiff(X2,X3)))))), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(symdiffI2, axiom, symdiffI2 <=> 112.62/113.35 (![A,B,Xx]: ((~in(Xx,A)) => (in(Xx,B) => in(Xx,symdiff(A,B)))))). 112.62/113.35 tff('73', plain, 112.62/113.35 symdiffI2 = 112.62/113.35 (![X2,X3,X4]: ((~in(X4,X2)) => (in(X4,X3) => in(X4,symdiff(X2,X3))))), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(symdiffI1, axiom, symdiffI1 <=> 112.62/113.35 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => in(Xx,symdiff(A,B)))))). 112.62/113.35 tff('74', plain, 112.62/113.35 symdiffI1 = 112.62/113.35 (![X2,X3,X4]: (in(X4,X2) => ((~in(X4,X3)) => in(X4,symdiff(X2,X3))))), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(symdiffE, axiom, symdiffE <=> 112.62/113.35 (![A,B,Xx]: 112.62/113.35 (in(Xx,symdiff(A,B)) => 112.62/113.35 (![Xphi:$o]: 112.62/113.35 ((in(Xx,A) => ((~in(Xx,B)) => Xphi)) => 112.62/113.35 (((~in(Xx,A)) => (in(Xx,B) => Xphi)) => Xphi)))))). 112.62/113.35 tff('75', plain, 112.62/113.35 symdiffE = 112.62/113.35 (![X2,X3,X4]: 112.62/113.35 (in(X4,symdiff(X2,X3)) => 112.62/113.35 (![X5:$o]: 112.62/113.35 ((in(X4,X2) => ((~in(X4,X3)) => X5)) => 112.62/113.35 (((~in(X4,X2)) => (in(X4,X3) => X5)) => X5))))), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(setminusSubset1, axiom, setminusSubset1 <=> 112.62/113.35 (![A,B]: ((setminus(A,B) = emptyset) => subset(A,B)))). 112.62/113.35 tff('76', plain, 112.62/113.35 setminusSubset1 = 112.62/113.35 (![X2,X3]: ((setminus(X2,X3) = emptyset) => subset(X2,X3))), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(setminusLsub, axiom, setminusLsub <=> (![A,B]: subset(setminus(A,B),A))). 112.62/113.35 tff('77', plain, setminusLsub = (![X2,X3]: subset(setminus(X2,X3),X2)), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(setminusIRneg, axiom, setminusIRneg <=> 112.62/113.35 (![A,B,Xx]: (in(Xx,B) => (~in(Xx,setminus(A,B)))))). 112.62/113.35 tff('78', plain, 112.62/113.35 setminusIRneg = (![X2,X3,X4]: (in(X4,X3) => (~in(X4,setminus(X2,X3))))), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(setminusILneg, axiom, setminusILneg <=> 112.62/113.35 (![A,B,Xx]: ((~in(Xx,A)) => (~in(Xx,setminus(A,B)))))). 112.62/113.35 tff('79', plain, 112.62/113.35 setminusILneg = 112.62/113.35 (![X2,X3,X4]: ((~in(X4,X2)) => (~in(X4,setminus(X2,X3))))), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(setminusELneg, axiom, setminusELneg <=> 112.62/113.35 (![A,B,Xx]: ((~in(Xx,setminus(A,B))) => ((~in(Xx,B)) => (~in(Xx,A)))))). 112.62/113.35 tff('80', plain, 112.62/113.35 setminusELneg = 112.62/113.35 (![X2,X3,X4]: 112.62/113.35 ((~in(X4,setminus(X2,X3))) => ((~in(X4,X3)) => (~in(X4,X2))))), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(setminusERneg, axiom, setminusERneg <=> 112.62/113.35 (![A,B,Xx]: ((~in(Xx,setminus(A,B))) => (in(Xx,A) => in(Xx,B))))). 112.62/113.35 tff('81', plain, 112.62/113.35 setminusERneg = 112.62/113.35 (![X2,X3,X4]: ((~in(X4,setminus(X2,X3))) => (in(X4,X2) => in(X4,X3)))), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(setminusSubset2, axiom, setminusSubset2 <=> 112.62/113.35 (![A,B]: (subset(A,B) => (setminus(A,B) = emptyset)))). 112.62/113.35 tff('82', plain, 112.62/113.35 setminusSubset2 = 112.62/113.35 (![X2,X3]: (subset(X2,X3) => (setminus(X2,X3) = emptyset))), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(setminusER, axiom, setminusER <=> 112.62/113.35 (![A,B,Xx]: (in(Xx,setminus(A,B)) => (~in(Xx,B))))). 112.62/113.35 tff('83', plain, 112.62/113.35 setminusER = (![X2,X3,X4]: (in(X4,setminus(X2,X3)) => (~in(X4,X3)))), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(setminusEL, axiom, setminusEL <=> 112.62/113.35 (![A,B,Xx]: (in(Xx,setminus(A,B)) => in(Xx,A)))). 112.62/113.35 tff('84', plain, 112.62/113.35 setminusEL = (![X2,X3,X4]: (in(X4,setminus(X2,X3)) => in(X4,X2))), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(setminusI, axiom, setminusI <=> 112.62/113.35 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => in(Xx,setminus(A,B)))))). 112.62/113.35 tff('85', plain, 112.62/113.35 setminusI = 112.62/113.35 (![X2,X3,X4]: (in(X4,X2) => ((~in(X4,X3)) => in(X4,setminus(X2,X3))))), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(bs114d, axiom, bs114d <=> 112.62/113.35 (![A,B,C]: 112.62/113.35 (binintersect(A,binunion(B,C)) = 112.62/113.35 binunion(binintersect(A,B),binintersect(A,C))))). 112.62/113.35 tff('86', plain, 112.62/113.35 bs114d = 112.62/113.35 (![X2,X3,X4]: 112.62/113.35 (binintersect(X2,binunion(X3,X4)) = 112.62/113.35 binunion(binintersect(X2,X3),binintersect(X2,X4)))), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(binintersectSubset1, axiom, binintersectSubset1 <=> 112.62/113.35 (![A,B]: ((binintersect(A,B) = A) => subset(A,B)))). 112.62/113.35 tff('87', plain, 112.62/113.35 binintersectSubset1 = 112.62/113.35 (![X2,X3]: ((binintersect(X2,X3) = X2) => subset(X2,X3))), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(binintersectSubset4, axiom, binintersectSubset4 <=> 112.62/113.35 (![A,B]: (subset(B,A) => (binintersect(A,B) = B)))). 112.62/113.35 tff('88', plain, 112.62/113.35 binintersectSubset4 = 112.62/113.35 (![X2,X3]: (subset(X3,X2) => (binintersect(X2,X3) = X3))), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(binintersectRsub, axiom, binintersectRsub <=> 112.62/113.35 (![A,B]: subset(binintersect(A,B),B))). 112.62/113.35 tff('89', plain, 112.62/113.35 binintersectRsub = (![X2,X3]: subset(binintersect(X2,X3),X3)), 112.62/113.35 define([status(thm)])). 112.62/113.35 tff(disjointsetsI1, axiom, disjointsetsI1 <=> 112.62/113.35 (![A,B]: 112.62/113.35 ((~(?[Xx]: (in(Xx,B) & in(Xx,A)))) => (binintersect(A,B) = emptyset)))). 112.62/113.35 tff('90', plain, 112.62/113.35 disjointsetsI1 = 112.62/113.35 (![X2,X3]: 112.62/113.35 ((~(?[X4]: (in(X4,X3) & in(X4,X2)))) => 112.63/113.35 (binintersect(X2,X3) = emptyset))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(binintersectER, axiom, binintersectER <=> 112.63/113.35 (![A,B,Xx]: (in(Xx,binintersect(A,B)) => in(Xx,B)))). 112.63/113.35 tff('91', plain, 112.63/113.35 binintersectER = (![X2,X3,X4]: (in(X4,binintersect(X2,X3)) => in(X4,X3))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(binintersectSubset3, axiom, binintersectSubset3 <=> 112.63/113.35 (![A,B]: ((binintersect(A,B) = B) => subset(B,A)))). 112.63/113.35 tff('92', plain, 112.63/113.35 binintersectSubset3 = 112.63/113.35 (![X2,X3]: ((binintersect(X2,X3) = X3) => subset(X3,X2))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(binintersectSubset2, axiom, binintersectSubset2 <=> 112.63/113.35 (![A,B]: (subset(A,B) => (binintersect(A,B) = A)))). 112.63/113.35 tff('93', plain, 112.63/113.35 binintersectSubset2 = 112.63/113.35 (![X2,X3]: (subset(X2,X3) => (binintersect(X2,X3) = X2))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(binintersectLsub, axiom, binintersectLsub <=> 112.63/113.35 (![A,B]: subset(binintersect(A,B),A))). 112.63/113.35 tff('94', plain, 112.63/113.35 binintersectLsub = (![X2,X3]: subset(binintersect(X2,X3),X2)), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(binintersectEL, axiom, binintersectEL <=> 112.63/113.35 (![A,B,Xx]: (in(Xx,binintersect(A,B)) => in(Xx,A)))). 112.63/113.35 tff('95', plain, 112.63/113.35 binintersectEL = (![X2,X3,X4]: (in(X4,binintersect(X2,X3)) => in(X4,X2))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(binintersectSubset5, axiom, binintersectSubset5 <=> 112.63/113.35 (![A,B,C]: (subset(C,A) => (subset(C,B) => subset(C,binintersect(A,B)))))). 112.63/113.35 tff('96', plain, 112.63/113.35 binintersectSubset5 = 112.63/113.35 (![X2,X3,X4]: 112.63/113.35 (subset(X4,X2) => (subset(X4,X3) => subset(X4,binintersect(X2,X3))))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(binintersectI, axiom, binintersectI <=> 112.63/113.35 (![A,B,Xx]: (in(Xx,A) => (in(Xx,B) => in(Xx,binintersect(A,B)))))). 112.63/113.35 tff('97', plain, 112.63/113.35 binintersectI = 112.63/113.35 (![X2,X3,X4]: (in(X4,X2) => (in(X4,X3) => in(X4,binintersect(X2,X3))))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(binunionRsub, axiom, binunionRsub <=> (![A,B]: subset(B,binunion(A,B)))). 112.63/113.35 tff('98', plain, binunionRsub = (![X2,X3]: subset(X3,binunion(X2,X3))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(binunionLsub, axiom, binunionLsub <=> (![A,B]: subset(A,binunion(A,B)))). 112.63/113.35 tff('99', plain, binunionLsub = (![X2,X3]: subset(X2,binunion(X2,X3))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(binunionE, axiom, binunionE <=> 112.63/113.35 (![A,B,Xx]: (in(Xx,binunion(A,B)) => (in(Xx,B) | in(Xx,A))))). 112.63/113.35 tff('100', plain, 112.63/113.35 binunionE = 112.63/113.35 (![X2,X3,X4]: (in(X4,binunion(X2,X3)) => (in(X4,X3) | in(X4,X2)))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(binunionEcases, axiom, binunionEcases <=> 112.63/113.35 (![A,B,Xx,Xphi:$o]: 112.63/113.35 (in(Xx,binunion(A,B)) => 112.63/113.35 ((in(Xx,A) => Xphi) => ((in(Xx,B) => Xphi) => Xphi))))). 112.63/113.35 tff('101', plain, 112.63/113.35 binunionEcases = 112.63/113.35 (![X2,X3,X4,X5:$o]: 112.63/113.35 (in(X4,binunion(X2,X3)) => 112.63/113.35 ((in(X4,X2) => X5) => ((in(X4,X3) => X5) => X5)))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(binunionIR, axiom, binunionIR <=> 112.63/113.35 (![A,B,Xx]: (in(Xx,B) => in(Xx,binunion(A,B))))). 112.63/113.35 tff('102', plain, 112.63/113.35 binunionIR = (![X2,X3,X4]: (in(X4,X3) => in(X4,binunion(X2,X3)))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(upairset2IR, axiom, upairset2IR <=> 112.63/113.35 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 112.63/113.35 tff('103', plain, 112.63/113.35 upairset2IR = (![X2,X3]: in(X3,setadjoin(X2,setadjoin(X3,emptyset)))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(binunionIL, axiom, binunionIL <=> 112.63/113.35 (![A,B,Xx]: (in(Xx,A) => in(Xx,binunion(A,B))))). 112.63/113.35 tff('104', plain, 112.63/113.35 binunionIL = (![X2,X3,X4]: (in(X4,X2) => in(X4,binunion(X2,X3)))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(sepSubset, axiom, sepSubset <=> 112.63/113.35 (![A,Xphi:($i > $o)]: subset(dsetconstr(A,^[Xx]: Xphi(Xx)),A))). 112.63/113.35 tff('105', plain, 112.63/113.35 sepSubset = 112.63/113.35 (![X2,X3:($i > $o)]: subset(dsetconstr(X2,^[V_1]: X3(V_1)),X2)), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(sepInPowerset, axiom, sepInPowerset <=> 112.63/113.35 (![A,Xphi:($i > $o)]: in(dsetconstr(A,^[Xx]: Xphi(Xx)),powerset(A)))). 112.63/113.35 tff('106', plain, 112.63/113.35 sepInPowerset = 112.63/113.35 (![X2,X3:($i > $o)]: in(dsetconstr(X2,^[V_1]: X3(V_1)),powerset(X2))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(powersetsubset, axiom, powersetsubset <=> 112.63/113.35 (![A,B]: (subset(A,B) => subset(powerset(A),powerset(B))))). 112.63/113.35 tff('107', plain, 112.63/113.35 powersetsubset = 112.63/113.35 (![X2,X3]: (subset(X2,X3) => subset(powerset(X2),powerset(X3)))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(inPowerset, axiom, inPowerset <=> (![A]: in(A,powerset(A)))). 112.63/113.35 tff('108', plain, inPowerset = (![X2]: in(X2,powerset(X2))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(powersetE1, axiom, powersetE1 <=> 112.63/113.35 (![A,B]: (in(B,powerset(A)) => subset(B,A)))). 112.63/113.35 tff('109', plain, 112.63/113.35 powersetE1 = (![X2,X3]: (in(X3,powerset(X2)) => subset(X3,X2))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(powersetI1, axiom, powersetI1 <=> 112.63/113.35 (![A,B]: (subset(B,A) => in(B,powerset(A))))). 112.63/113.35 tff('110', plain, 112.63/113.35 powersetI1 = (![X2,X3]: (subset(X3,X2) => in(X3,powerset(X2)))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(subsetemptysetimpeq, axiom, subsetemptysetimpeq <=> 112.63/113.35 (![A]: (subset(A,emptyset) => (A = emptyset)))). 112.63/113.35 tff('111', plain, 112.63/113.35 subsetemptysetimpeq = (![X2]: (subset(X2,emptyset) => (X2 = emptyset))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(setextsub, axiom, setextsub <=> 112.63/113.35 (![A,B]: (subset(A,B) => (subset(B,A) => (A = B))))). 112.63/113.35 tff('112', plain, 112.63/113.35 setextsub = (![X2,X3]: (subset(X2,X3) => (subset(X3,X2) => (X2 = X3)))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(subset2powerset, axiom, subset2powerset <=> 112.63/113.35 (![A,B]: (subset(A,B) => in(A,powerset(B))))). 112.63/113.35 tff('113', plain, 112.63/113.35 subset2powerset = (![X2,X3]: (subset(X2,X3) => in(X2,powerset(X3)))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(setadjoinSub2, axiom, setadjoinSub2 <=> 112.63/113.35 (![A,Xx,B]: (subset(A,B) => subset(A,setadjoin(Xx,B))))). 112.63/113.35 tff('114', plain, 112.63/113.35 setadjoinSub2 = 112.63/113.35 (![X2,X3,X4]: (subset(X2,X4) => subset(X2,setadjoin(X3,X4)))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(setadjoinSub, axiom, setadjoinSub <=> 112.63/113.35 (![Xx,A]: subset(A,setadjoin(Xx,A)))). 112.63/113.35 tff('115', plain, setadjoinSub = (![X2,X3]: subset(X3,setadjoin(X2,X3))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(subsetTrans, axiom, subsetTrans <=> 112.63/113.35 (![A,B,C]: (subset(A,B) => (subset(B,C) => subset(A,C))))). 112.63/113.35 tff('116', plain, 112.63/113.35 subsetTrans = 112.63/113.35 (![X2,X3,X4]: (subset(X2,X3) => (subset(X3,X4) => subset(X2,X4)))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(subsetRefl, axiom, subsetRefl <=> (![A]: subset(A,A))). 112.63/113.35 tff('117', plain, subsetRefl = (![X2]: subset(X2,X2)), define([status(thm)])). 112.63/113.35 tff(notequalI2, axiom, notequalI2 <=> 112.63/113.35 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => (A != B))))). 112.63/113.35 tff('118', plain, 112.63/113.35 notequalI2 = (![X2,X3,X4]: (in(X4,X2) => ((~in(X4,X3)) => (X2 != X3)))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(notequalI1, axiom, notequalI1 <=> (![A,B]: ((~subset(A,B)) => (A != B)))). 112.63/113.35 tff('119', plain, notequalI1 = (![X2,X3]: ((~subset(X2,X3)) => (X2 != X3))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(notsubsetI, axiom, notsubsetI <=> 112.63/113.35 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => (~subset(A,B)))))). 112.63/113.35 tff('120', plain, 112.63/113.35 notsubsetI = 112.63/113.35 (![X2,X3,X4]: (in(X4,X2) => ((~in(X4,X3)) => (~subset(X2,X3))))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(subsetE2, axiom, subsetE2 <=> 112.63/113.35 (![A,B,Xx]: (subset(A,B) => ((~in(Xx,B)) => (~in(Xx,A)))))). 112.63/113.35 tff('121', plain, 112.63/113.35 subsetE2 = 112.63/113.35 (![X2,X3,X4]: (subset(X2,X3) => ((~in(X4,X3)) => (~in(X4,X2))))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(subsetE, axiom, subsetE <=> 112.63/113.35 (![A,B,Xx]: (subset(A,B) => (in(Xx,A) => in(Xx,B))))). 112.63/113.35 tff('122', plain, 112.63/113.35 subsetE = (![X2,X3,X4]: (subset(X2,X3) => (in(X4,X2) => in(X4,X3)))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(emptysetsubset, axiom, emptysetsubset <=> (![A]: subset(emptyset,A))). 112.63/113.35 tff('123', plain, emptysetsubset = (![X2]: subset(emptyset,X2)), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(subsetI2, axiom, subsetI2 <=> 112.63/113.35 (![A,B]: ((![Xx]: (in(Xx,A) => in(Xx,B))) => subset(A,B)))). 112.63/113.35 tff('124', plain, 112.63/113.35 subsetI2 = 112.63/113.35 (![X2,X3]: ((![X4]: (in(X4,X2) => in(X4,X3))) => subset(X2,X3))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(eqimpsubset1, axiom, eqimpsubset1 <=> (![A,B]: ((A = B) => subset(A,B)))). 112.63/113.35 tff('125', plain, eqimpsubset1 = (![X2,X3]: ((X2 = X3) => subset(X2,X3))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(eqimpsubset2, axiom, eqimpsubset2 <=> (![A,B]: ((A = B) => subset(B,A)))). 112.63/113.35 tff('126', plain, eqimpsubset2 = (![X2,X3]: ((X2 = X3) => subset(X3,X2))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(subsetI1, axiom, subsetI1 <=> 112.63/113.35 (![A,B]: ((![Xx]: (in(Xx,A) => in(Xx,B))) => subset(A,B)))). 112.63/113.35 tff('127', plain, 112.63/113.35 subsetI1 = 112.63/113.35 (![X2,X3]: ((![X4]: (in(X4,X2) => in(X4,X3))) => subset(X2,X3))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(dsetconstr__Cong, axiom, dsetconstr__Cong <=> 112.63/113.35 (![A,B]: 112.63/113.35 ((A = B) => 112.63/113.35 (![Xphi:($i > $o),Xpsi:($i > $o)]: 112.63/113.35 ((![Xx]: 112.63/113.35 (in(Xx,A) => 112.63/113.35 (![Xy]: (in(Xy,B) => ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy))))))) => 112.63/113.35 (dsetconstr(A,^[Xx]: Xphi(Xx)) = dsetconstr(B,^[Xx]: Xpsi(Xx)))))))). 112.63/113.35 tff('128', plain, 112.63/113.35 dsetconstr__Cong = 112.63/113.35 (![X2,X3]: 112.63/113.35 ((X2 = X3) => 112.63/113.35 (![X4:($i > $o),X5:($i > $o)]: 112.63/113.35 ((![X6]: 112.63/113.35 (in(X6,X2) => 112.63/113.35 (![X7]: (in(X7,X3) => ((X6 = X7) => (X4(X6) <=> X5(X7))))))) => 112.63/113.35 (dsetconstr(X2,^[V_1]: X4(V_1)) = dsetconstr(X3,^[V_2]: X5(V_2))))))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(descr__Cong, axiom, descr__Cong <=> 112.63/113.35 (![Xphi:($i > $o),Xpsi:($i > $o)]: 112.63/113.35 ((![Xx,Xy]: ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy)))) => 112.63/113.35 (exu(^[Xx]: Xphi(Xx)) => 112.63/113.35 (exu(^[Xx]: Xpsi(Xx)) => 112.63/113.35 (descr(^[Xx]: Xphi(Xx)) = descr(^[Xx]: Xpsi(Xx)))))))). 112.63/113.35 tff('129', plain, 112.63/113.35 descr__Cong = 112.63/113.35 (![X2:($i > $o),X3:($i > $o)]: 112.63/113.35 ((![X4,X5]: ((X4 = X5) => (X2(X4) <=> X3(X5)))) => 112.63/113.35 (exu(^[V_1]: X2(V_1)) => 112.63/113.35 (exu(^[V_2]: X3(V_2)) => 112.63/113.35 (descr(^[V_3]: X2(V_3)) = descr(^[V_4]: X3(V_4))))))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(exuEu, axiom, exuEu <=> 112.63/113.35 (![Xphi:($i > $o)]: 112.63/113.35 (exu(^[Xx]: Xphi(Xx)) => 112.63/113.35 (![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))). 112.63/113.35 tff('130', plain, 112.63/113.35 exuEu = 112.63/113.35 (![X2:($i > $o)]: 112.63/113.35 (exu(^[V_1]: X2(V_1)) => (![X3,X4]: (X2(X3) => (X2(X4) => (X3 = X4)))))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(omega__Cong, axiom, omega__Cong <=> (omega = omega)). 112.63/113.35 tff('131', plain, omega__Cong = (omega = omega), define([status(thm)])). 112.63/113.35 tff(setunion__Cong, axiom, setunion__Cong <=> 112.63/113.35 (![A,B]: ((A = B) => (setunion(A) = setunion(B))))). 112.63/113.35 tff('132', plain, 112.63/113.35 setunion__Cong = (![X2,X3]: ((X2 = X3) => (setunion(X2) = setunion(X3)))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(powerset__Cong, axiom, powerset__Cong <=> 112.63/113.35 (![A,B]: ((A = B) => (powerset(A) = powerset(B))))). 112.63/113.35 tff('133', plain, 112.63/113.35 powerset__Cong = (![X2,X3]: ((X2 = X3) => (powerset(X2) = powerset(X3)))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(setadjoin__Cong, axiom, setadjoin__Cong <=> 112.63/113.35 (![Xx,Xy]: 112.63/113.35 ((Xx = Xy) => 112.63/113.35 (![Xz,Xu]: ((Xz = Xu) => (setadjoin(Xx,Xz) = setadjoin(Xy,Xu))))))). 112.63/113.35 tff('134', plain, 112.63/113.35 setadjoin__Cong = 112.63/113.35 (![X2,X3]: 112.63/113.35 ((X2 = X3) => 112.63/113.35 (![X4,X5]: ((X4 = X5) => (setadjoin(X2,X4) = setadjoin(X3,X5)))))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(emptyset__Cong, axiom, emptyset__Cong <=> (emptyset = emptyset)). 112.63/113.35 tff('135', plain, emptyset__Cong = (emptyset = emptyset), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(exu__Cong, axiom, exu__Cong <=> 112.63/113.35 (![Xphi:($i > $o),Xpsi:($i > $o)]: 112.63/113.35 ((![Xx,Xy]: ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy)))) => 112.63/113.35 (exu(^[Xx]: Xphi(Xx)) <=> exu(^[Xx]: Xpsi(Xx)))))). 112.63/113.35 tff('136', plain, 112.63/113.35 exu__Cong = 112.63/113.35 (![X2:($i > $o),X3:($i > $o)]: 112.63/113.35 ((![X4,X5]: ((X4 = X5) => (X2(X4) <=> X3(X5)))) => 112.63/113.35 (exu(^[V_1]: X2(V_1)) <=> exu(^[V_2]: X3(V_2))))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(exuE3u, axiom, exuE3u <=> 112.63/113.35 (![Xphi:($i > $o)]: 112.63/113.35 (exu(^[Xx]: Xphi(Xx)) => 112.63/113.35 (![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))). 112.63/113.35 tff('137', plain, 112.63/113.35 exuE3u = 112.63/113.35 (![X2:($i > $o)]: 112.63/113.35 (exu(^[V_1]: X2(V_1)) => (![X3,X4]: (X2(X3) => (X2(X4) => (X3 = X4)))))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(in__Cong, axiom, in__Cong <=> 112.63/113.35 (![A,B]: ((A = B) => (![Xx,Xy]: ((Xx = Xy) => (in(Xx,A) <=> in(Xy,B))))))). 112.63/113.35 tff('138', plain, 112.63/113.35 in__Cong = 112.63/113.35 (![X2,X3]: 112.63/113.35 ((X2 = X3) => (![X4,X5]: ((X4 = X5) => (in(X4,X2) <=> in(X5,X3)))))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(inCongP, axiom, inCongP <=> 112.63/113.35 (![A,B]: ((A = B) => (![Xx,Xy]: ((Xx = Xy) => (in(Xx,A) => in(Xy,B))))))). 112.63/113.35 tff('139', plain, 112.63/113.35 inCongP = 112.63/113.35 (![X2,X3]: 112.63/113.35 ((X2 = X3) => (![X4,X5]: ((X4 = X5) => (in(X4,X2) => in(X5,X3)))))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(exuI2, axiom, exuI2 <=> 112.63/113.35 (![Xphi:($i > $o)]: 112.63/113.35 ((?[Xx]: (![Xy]: (Xphi(Xy) <=> (Xy = Xx)))) => exu(^[Xx]: Xphi(Xx))))). 112.63/113.35 tff('140', plain, 112.63/113.35 exuI2 = 112.63/113.35 (![X2:($i > $o)]: 112.63/113.35 ((?[X3]: (![X4]: (X2(X4) <=> (X4 = X3)))) => exu(^[V_1]: X2(V_1)))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(exuI3, axiom, exuI3 <=> 112.63/113.35 (![Xphi:($i > $o)]: 112.63/113.35 ((?[Xx]: Xphi(Xx)) => 112.63/113.35 ((![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy)))) => 112.63/113.35 exu(^[Xx]: Xphi(Xx)))))). 112.63/113.35 tff('141', plain, 112.63/113.35 exuI3 = 112.63/113.35 (![X2:($i > $o)]: 112.63/113.35 ((?[X3]: X2(X3)) => 112.63/113.35 ((![X4,X5]: (X2(X4) => (X2(X5) => (X4 = X5)))) => 112.63/113.35 exu(^[V_1]: X2(V_1))))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(exuI1, axiom, exuI1 <=> 112.63/113.35 (![Xphi:($i > $o)]: 112.63/113.35 ((?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx))) => 112.63/113.35 exu(^[Xx]: Xphi(Xx))))). 112.63/113.35 tff('142', plain, 112.63/113.35 exuI1 = 112.63/113.35 (![X2:($i > $o)]: 112.63/113.35 ((?[X3]: ((![X4]: (X2(X4) => (X3 = X4))) & X2(X3))) => 112.63/113.35 exu(^[V_1]: X2(V_1)))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(notdallE, axiom, notdallE <=> 112.63/113.35 (![A,Xphi:($i > $o)]: 112.63/113.35 ((~(![Xx]: (in(Xx,A) => Xphi(Xx)))) => (?[Xx]: ((~Xphi(Xx)) & in(Xx,A)))))). 112.63/113.35 tff('143', plain, 112.63/113.35 notdallE = 112.63/113.35 (![X2,X3:($i > $o)]: 112.63/113.35 ((~(![X4]: (in(X4,X2) => X3(X4)))) => (?[X5]: ((~X3(X5)) & in(X5,X2))))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(notdexE, axiom, notdexE <=> 112.63/113.35 (![A,Xphi:($i > $o)]: 112.63/113.35 ((~(?[Xx]: (Xphi(Xx) & in(Xx,A)))) => (![Xx]: (in(Xx,A) => (~Xphi(Xx))))))). 112.63/113.35 tff('144', plain, 112.63/113.35 notdexE = 112.63/113.35 (![X2,X3:($i > $o)]: 112.63/113.35 ((~(?[X4]: (X3(X4) & in(X4,X2)))) => (![X5]: (in(X5,X2) => (~X3(X5)))))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(prop2set2propI, axiom, prop2set2propI <=> 112.63/113.35 (![Xphi:$o]: (Xphi => set2prop(prop2set(Xphi))))). 112.63/113.35 tff('145', plain, 112.63/113.35 prop2set2propI = (![X2:$o]: (X2 => set2prop(prop2set(X2)))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(prop2setI, axiom, prop2setI <=> 112.63/113.35 (![Xphi:$o]: (Xphi => in(emptyset,prop2set(Xphi))))). 112.63/113.35 tff('146', plain, prop2setI = (![X2:$o]: (X2 => in(emptyset,prop2set(X2)))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(quantDeMorgan4, axiom, quantDeMorgan4 <=> 112.63/113.35 (![A,Xphi:($i > $o)]: 112.63/113.35 ((?[Xx]: ((~Xphi(Xx)) & in(Xx,A))) => (~(![Xx]: (in(Xx,A) => Xphi(Xx))))))). 112.63/113.35 tff('147', plain, 112.63/113.35 quantDeMorgan4 = 112.63/113.35 (![X2,X3:($i > $o)]: 112.63/113.35 ((?[X4]: ((~X3(X4)) & in(X4,X2))) => (~(![X5]: (in(X5,X2) => X3(X5)))))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(quantDeMorgan3, axiom, quantDeMorgan3 <=> 112.63/113.35 (![A,Xphi:($i > $o)]: 112.63/113.35 ((~(?[Xx]: (Xphi(Xx) & in(Xx,A)))) => (![Xx]: (in(Xx,A) => (~Xphi(Xx))))))). 112.63/113.35 tff('148', plain, 112.63/113.35 quantDeMorgan3 = 112.63/113.35 (![X2,X3:($i > $o)]: 112.63/113.35 ((~(?[X4]: (X3(X4) & in(X4,X2)))) => (![X5]: (in(X5,X2) => (~X3(X5)))))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(quantDeMorgan2, axiom, quantDeMorgan2 <=> 112.63/113.35 (![A,Xphi:($i > $o)]: 112.63/113.35 ((![Xx]: (in(Xx,A) => (~Xphi(Xx)))) => (~(?[Xx]: (Xphi(Xx) & in(Xx,A))))))). 112.63/113.35 tff('149', plain, 112.63/113.35 quantDeMorgan2 = 112.63/113.35 (![X2,X3:($i > $o)]: 112.63/113.35 ((![X4]: (in(X4,X2) => (~X3(X4)))) => (~(?[X5]: (X3(X5) & in(X5,X2)))))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(quantDeMorgan1, axiom, quantDeMorgan1 <=> 112.63/113.35 (![A,Xphi:($i > $o)]: 112.63/113.35 ((~(![Xx]: (in(Xx,A) => Xphi(Xx)))) => (?[Xx]: ((~Xphi(Xx)) & in(Xx,A)))))). 112.63/113.35 tff('150', plain, 112.63/113.35 quantDeMorgan1 = 112.63/113.35 (![X2,X3:($i > $o)]: 112.63/113.35 ((~(![X4]: (in(X4,X2) => X3(X4)))) => (?[X5]: ((~X3(X5)) & in(X5,X2))))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(vacuousDall, axiom, vacuousDall <=> 112.63/113.35 (![Xphi:($i > $o),Xx]: (in(Xx,emptyset) => Xphi(Xx)))). 112.63/113.35 tff('151', plain, 112.63/113.35 vacuousDall = (![X2:($i > $o),X3]: (in(X3,emptyset) => X2(X3))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(emptyE1, axiom, emptyE1 <=> 112.63/113.35 (![A,Xphi:($i > $o)]: 112.63/113.35 ((?[Xx]: (Xphi(Xx) & in(Xx,A))) => 112.63/113.35 ((dsetconstr(A,^[Xx]: Xphi(Xx)) = emptyset) => $false)))). 112.63/113.35 tff('152', plain, 112.63/113.35 emptyE1 = 112.63/113.35 (![X2,X3:($i > $o)]: 112.63/113.35 ((?[X4]: (X3(X4) & in(X4,X2))) => 112.63/113.35 ((dsetconstr(X2,^[V_1]: X3(V_1)) = emptyset) => $false))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(upairsetIR, axiom, upairsetIR <=> 112.63/113.35 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 112.63/113.35 tff('153', plain, 112.63/113.35 upairsetIR = (![X2,X3]: in(X3,setadjoin(X2,setadjoin(X3,emptyset)))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(upairsetIL, axiom, upairsetIL <=> 112.63/113.35 (![Xx,Xy]: in(Xx,setadjoin(Xx,setadjoin(Xy,emptyset))))). 112.63/113.35 tff('154', plain, 112.63/113.35 upairsetIL = (![X2,X3]: in(X2,setadjoin(X2,setadjoin(X3,emptyset)))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(upairsetE, axiom, upairsetE <=> 112.63/113.35 (![Xx,Xy,Xz]: 112.63/113.35 (in(Xz,setadjoin(Xx,setadjoin(Xy,emptyset))) => ((Xz = Xy) | (Xz = Xx))))). 112.63/113.35 tff('155', plain, 112.63/113.35 upairsetE = 112.63/113.35 (![X2,X3,X4]: 112.63/113.35 (in(X4,setadjoin(X2,setadjoin(X3,emptyset))) => 112.63/113.35 ((X4 = X3) | (X4 = X2)))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(singletonsswitch, axiom, singletonsswitch <=> 112.63/113.35 (![Xx,Xy]: (in(Xx,setadjoin(Xy,emptyset)) => in(Xy,setadjoin(Xx,emptyset))))). 112.63/113.35 tff('156', plain, 112.63/113.35 singletonsswitch = 112.63/113.35 (![X2,X3]: 112.63/113.35 (in(X2,setadjoin(X3,emptyset)) => in(X3,setadjoin(X2,emptyset)))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(eqinunit, axiom, eqinunit <=> 112.63/113.35 (![Xx,Xy]: ((Xx = Xy) => in(Xx,setadjoin(Xy,emptyset))))). 112.63/113.35 tff('157', plain, 112.63/113.35 eqinunit = (![X2,X3]: ((X2 = X3) => in(X2,setadjoin(X3,emptyset)))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(notinsingleton, axiom, notinsingleton <=> 112.63/113.35 (![Xx,Xy]: ((Xx != Xy) => (~in(Xy,setadjoin(Xx,emptyset)))))). 112.63/113.35 tff('158', plain, 112.63/113.35 notinsingleton = 112.63/113.35 (![X2,X3]: ((X2 != X3) => (~in(X3,setadjoin(X2,emptyset))))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(uniqinunit, axiom, uniqinunit <=> 112.63/113.35 (![Xx,Xy]: (in(Xx,setadjoin(Xy,emptyset)) => (Xx = Xy)))). 112.63/113.35 tff('159', plain, 112.63/113.35 uniqinunit = (![X2,X3]: (in(X2,setadjoin(X3,emptyset)) => (X2 = X3))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(nonemptyImpWitness, axiom, nonemptyImpWitness <=> 112.63/113.35 (![A]: (nonempty(A) => (?[Xx]: (in(Xx,A)))))). 112.63/113.35 tff('160', plain, 112.63/113.35 nonemptyImpWitness = (![X2]: (nonempty(X2) => (?[X3]: (in(X3,X2))))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(exuE2, axiom, exuE2 <=> 112.63/113.35 (![Xphi:($i > $o)]: 112.63/113.35 (exu(^[Xx]: Xphi(Xx)) => (?[Xx]: (![Xy]: (Xphi(Xy) <=> (Xy = Xx))))))). 112.63/113.35 tff('161', plain, 112.63/113.35 exuE2 = 112.63/113.35 (![X2:($i > $o)]: 112.63/113.35 (exu(^[V_1]: X2(V_1)) => (?[X3]: (![X4]: (X2(X4) <=> (X4 = X3)))))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(subPowSU, axiom, subPowSU <=> 112.63/113.35 (![A,Xx]: (in(Xx,A) => in(Xx,powerset(setunion(A)))))). 112.63/113.35 tff('162', plain, 112.63/113.35 subPowSU = (![X2,X3]: (in(X3,X2) => in(X3,powerset(setunion(X2))))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(setunionE, axiom, setunionE <=> 112.63/113.35 (![A,Xx]: 112.63/113.35 (in(Xx,setunion(A)) => 112.63/113.35 (![Xphi:$o]: ((![B]: (in(Xx,B) => (in(B,A) => Xphi))) => Xphi))))). 112.63/113.35 tff('163', plain, 112.63/113.35 setunionE = 112.63/113.35 (![X2,X3]: 112.63/113.35 (in(X3,setunion(X2)) => 112.63/113.35 (![X4:$o]: ((![X5]: (in(X3,X5) => (in(X5,X2) => X4))) => X4)))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(setunionI, axiom, setunionI <=> 112.63/113.35 (![A,Xx,B]: (in(Xx,B) => (in(B,A) => in(Xx,setunion(A)))))). 112.63/113.35 tff('164', plain, 112.63/113.35 setunionI = 112.63/113.35 (![X2,X3,X4]: (in(X3,X4) => (in(X4,X2) => in(X3,setunion(X2))))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(powersetE, axiom, powersetE <=> 112.63/113.35 (![A,B,Xx]: (in(B,powerset(A)) => (in(Xx,B) => in(Xx,A))))). 112.63/113.35 tff('165', plain, 112.63/113.35 powersetE = 112.63/113.35 (![X2,X3,X4]: (in(X3,powerset(X2)) => (in(X4,X3) => in(X4,X2)))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(emptyInPowerset, axiom, emptyInPowerset <=> 112.63/113.35 (![A]: in(emptyset,powerset(A)))). 112.63/113.35 tff('166', plain, emptyInPowerset = (![X2]: in(emptyset,powerset(X2))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(emptyinPowerset, axiom, emptyinPowerset <=> 112.63/113.35 (![A]: in(emptyset,powerset(A)))). 112.63/113.35 tff('167', plain, emptyinPowerset = (![X2]: in(emptyset,powerset(X2))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(powersetI, axiom, powersetI <=> 112.63/113.35 (![A,B]: ((![Xx]: (in(Xx,B) => in(Xx,A))) => in(B,powerset(A))))). 112.63/113.35 tff('168', plain, 112.63/113.35 powersetI = 112.63/113.35 (![X2,X3]: ((![X4]: (in(X4,X3) => in(X4,X2))) => in(X3,powerset(X2)))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(setoftrueEq, axiom, setoftrueEq <=> 112.63/113.35 (![A]: (dsetconstr(A,^[Xx]: $true) = A))). 112.63/113.35 tff('169', plain, setoftrueEq = (![X2]: (dsetconstr(X2,^[V_1]: $true) = X2)), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(setadjoinOr, axiom, setadjoinOr <=> 112.63/113.35 (![Xx,A,Xy]: (in(Xy,setadjoin(Xx,A)) => (in(Xy,A) | (Xy = Xx))))). 112.63/113.35 tff('170', plain, 112.63/113.35 setadjoinOr = 112.63/113.35 (![X2,X3,X4]: (in(X4,setadjoin(X2,X3)) => (in(X4,X3) | (X4 = X2)))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(setadjoinE, axiom, setadjoinE <=> 112.63/113.35 (![Xx,A,Xy]: 112.63/113.35 (in(Xy,setadjoin(Xx,A)) => 112.63/113.35 (![Xphi:$o]: (((Xy = Xx) => Xphi) => ((in(Xy,A) => Xphi) => Xphi)))))). 112.63/113.35 tff('171', plain, 112.63/113.35 setadjoinE = 112.63/113.35 (![X2,X3,X4]: 112.63/113.35 (in(X4,setadjoin(X2,X3)) => 112.63/113.35 (![X5:$o]: (((X4 = X2) => X5) => ((in(X4,X3) => X5) => X5))))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(setadjoinIR, axiom, setadjoinIR <=> 112.63/113.35 (![Xx,A,Xy]: (in(Xy,A) => in(Xy,setadjoin(Xx,A))))). 112.63/113.35 tff('172', plain, 112.63/113.35 setadjoinIR = (![X2,X3,X4]: (in(X4,X3) => in(X4,setadjoin(X2,X3)))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(emptyinunitempty, axiom, emptyinunitempty() = 112.63/113.35 in(emptyset,setadjoin(emptyset,emptyset))). 112.63/113.35 tff('173', plain, 112.63/113.35 emptyinunitempty = in(emptyset,setadjoin(emptyset,emptyset)), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(setadjoinIL, axiom, setadjoinIL <=> (![Xx,Xy]: in(Xx,setadjoin(Xx,Xy)))). 112.63/113.35 tff('174', plain, setadjoinIL = (![X2,X3]: in(X2,setadjoin(X2,X3))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(nonemptyI1, axiom, nonemptyI1 <=> 112.63/113.35 (![A]: ((?[Xx]: in(Xx,A)) => nonempty(A)))). 112.63/113.35 tff('175', plain, nonemptyI1 = (![X2]: ((?[X3]: in(X3,X2)) => nonempty(X2))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(nonemptyI, axiom, nonemptyI <=> 112.63/113.35 (![A,Xphi:($i > $o),Xx]: 112.63/113.35 (in(Xx,A) => (Xphi(Xx) => nonempty(dsetconstr(A,^[Xy]: Xphi(Xy))))))). 112.63/113.35 tff('176', plain, 112.63/113.35 nonemptyI = 112.63/113.35 (![X2,X3:($i > $o),X4]: 112.63/113.35 (in(X4,X2) => (X3(X4) => nonempty(dsetconstr(X2,^[V_1]: X3(V_1)))))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(nonemptyE1, axiom, nonemptyE1 <=> 112.63/113.35 (![A]: (nonempty(A) => (?[Xx]: in(Xx,A))))). 112.63/113.35 tff('177', plain, nonemptyE1 = (![X2]: (nonempty(X2) => (?[X3]: in(X3,X2)))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(nonempty, axiom, nonempty() = ^[Xx]: (Xx != emptyset)). 112.63/113.35 tff('178', plain, nonempty = (^[V_1]: (V_1 != emptyset)), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(setbeta, axiom, setbeta <=> 112.63/113.35 (![A,Xphi:($i > $o),Xx]: 112.63/113.35 (in(Xx,A) => (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) <=> Xphi(Xx))))). 112.63/113.35 tff('179', plain, 112.63/113.35 setbeta = 112.63/113.35 (![X2,X3:($i > $o),X4]: 112.63/113.35 (in(X4,X2) => (in(X4,dsetconstr(X2,^[V_1]: X3(V_1))) <=> X3(X4)))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(noeltsimpempty, axiom, noeltsimpempty <=> 112.63/113.35 (![A]: ((![Xx]: (~in(Xx,A))) => (A = emptyset)))). 112.63/113.35 tff('180', plain, 112.63/113.35 noeltsimpempty = (![X2]: ((![X3]: (~in(X3,X2))) => (X2 = emptyset))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(emptyI, axiom, emptyI <=> 112.63/113.35 (![A]: ((![Xx]: (~in(Xx,A))) => (A = emptyset)))). 112.63/113.35 tff('181', plain, 112.63/113.35 emptyI = (![X2]: ((![X3]: (~in(X3,X2))) => (X2 = emptyset))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(setext, axiom, setext <=> 112.63/113.35 (![A,B]: 112.63/113.35 ((![Xx]: (in(Xx,A) => in(Xx,B))) => 112.63/113.35 ((![Xx]: (in(Xx,B) => in(Xx,A))) => (A = B))))). 112.63/113.35 tff('182', plain, 112.63/113.35 setext = 112.63/113.35 (![X2,X3]: 112.63/113.35 ((![X4]: (in(X4,X2) => in(X4,X3))) => 112.63/113.35 ((![X5]: (in(X5,X3) => in(X5,X2))) => (X2 = X3)))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(exuE3e, axiom, exuE3e <=> 112.63/113.35 (![Xphi:($i > $o)]: (exu(^[Xx]: Xphi(Xx)) => (?[Xx]: Xphi(Xx))))). 112.63/113.35 tff('183', plain, 112.63/113.35 exuE3e = (![X2:($i > $o)]: (exu(^[V_1]: X2(V_1)) => (?[X3]: X2(X3)))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(notinemptyset, axiom, notinemptyset <=> (![Xx]: (~in(Xx,emptyset)))). 112.63/113.35 tff('184', plain, notinemptyset = (![X2]: (~in(X2,emptyset))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(emptysetimpfalse, axiom, emptysetimpfalse <=> 112.63/113.35 (![Xx]: (in(Xx,emptyset) => $false))). 112.63/113.35 tff('185', plain, emptysetimpfalse = (![X2]: (in(X2,emptyset) => $false)), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(emptysetE, axiom, emptysetE <=> 112.63/113.35 (![Xx]: (in(Xx,emptyset) => (![Xphi:$o]: Xphi)))). 112.63/113.35 tff('186', plain, emptysetE = (![X2]: (in(X2,emptyset) => (![X3:$o]: X3))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(prop2setE, axiom, prop2setE <=> 112.63/113.35 (![Xphi:$o,Xx]: (in(Xx,prop2set(Xphi)) => Xphi))). 112.63/113.35 tff('187', plain, prop2setE = (![X2:$o,X3]: (in(X3,prop2set(X2)) => X2)), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(exuE1, axiom, exuE1 <=> 112.63/113.35 (![Xphi:($i > $o)]: 112.63/113.35 (exu(^[Xx]: Xphi(Xx)) => 112.63/113.35 (?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx)))))). 112.63/113.35 tff('188', plain, 112.63/113.35 exuE1 = 112.63/113.35 (![X2:($i > $o)]: 112.63/113.35 (exu(^[V_1]: X2(V_1)) => 112.63/113.35 (?[X3]: ((![X4]: (X2(X4) => (X3 = X4))) & X2(X3))))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(dsetconstrER, axiom, dsetconstrER <=> 112.63/113.35 (![A,Xphi:($i > $o),Xx]: (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) => Xphi(Xx)))). 112.63/113.35 tff('189', plain, 112.63/113.35 dsetconstrER = 112.63/113.35 (![X2,X3:($i > $o),X4]: (in(X4,dsetconstr(X2,^[V_1]: X3(V_1))) => X3(X4))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(dsetconstrEL, axiom, dsetconstrEL <=> 112.63/113.35 (![A,Xphi:($i > $o),Xx]: (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) => in(Xx,A)))). 112.63/113.35 tff('190', plain, 112.63/113.35 dsetconstrEL = 112.63/113.35 (![X2,X3:($i > $o),X4]: 112.63/113.35 (in(X4,dsetconstr(X2,^[V_1]: X3(V_1))) => in(X4,X2))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(dsetconstrI, axiom, dsetconstrI <=> 112.63/113.35 (![A,Xphi:($i > $o),Xx]: 112.63/113.35 (in(Xx,A) => (Xphi(Xx) => in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))))))). 112.63/113.35 tff('191', plain, 112.63/113.35 dsetconstrI = 112.63/113.35 (![X2,X3:($i > $o),X4]: 112.63/113.35 (in(X4,X2) => (X3(X4) => in(X4,dsetconstr(X2,^[V_1]: X3(V_1)))))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(descrp, axiom, descrp <=> 112.63/113.35 (![Xphi:($i > $o)]: (exu(^[Xx]: Xphi(Xx)) => Xphi(descr(^[Xx]: Xphi(Xx)))))). 112.63/113.35 tff('192', plain, 112.63/113.35 descrp = 112.63/113.35 (![X2:($i > $o)]: (exu(^[V_1]: X2(V_1)) => X2(descr(^[V_2]: X2(V_2))))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(wellorderingAx, axiom, wellorderingAx <=> 112.63/113.35 (![A]: 112.63/113.35 (?[B]: 112.63/113.35 ((![C]: 112.63/113.35 (((?[Xx]: in(Xx,C)) & (![Xx]: (in(Xx,C) => in(Xx,A)))) => 112.63/113.35 (?[D,Xx]: 112.63/113.35 ((![E]: 112.63/113.35 (in(E,B) => (in(Xx,E) | (![Xy]: (in(Xy,E) => in(Xy,D)))))) & 112.63/113.35 (~(?[Xy]: (in(Xy,C) & in(Xy,D)))) & in(Xx,C) & in(D,B))))) & 112.63/113.35 (![C,D]: 112.63/113.35 ((in(D,B) & in(C,B)) => 112.63/113.35 ((![Xx]: (in(Xx,D) => in(Xx,C))) | 112.63/113.35 (![Xx]: (in(Xx,C) => in(Xx,D)))))) & 112.63/113.35 (![Xx,Xy]: 112.63/113.35 ((in(Xy,A) & in(Xx,A)) => 112.63/113.35 ((![C]: (in(C,B) => (in(Xx,C) <=> in(Xy,C)))) => (Xx = Xy)))) & 112.63/113.35 (![C]: (in(C,B) => (![Xx]: (in(Xx,C) => in(Xx,A))))))))). 112.63/113.35 tff('193', plain, 112.63/113.35 wellorderingAx = 112.63/113.35 (![X2]: 112.63/113.35 (?[X3]: 112.63/113.35 ((![X4]: 112.63/113.35 (((?[X5]: in(X5,X4)) & (![X6]: (in(X6,X4) => in(X6,X2)))) => 112.63/113.35 (?[X7,X8]: 112.63/113.35 ((![X9]: 112.63/113.35 (in(X9,X3) => 112.63/113.35 (in(X8,X9) | (![X10]: (in(X10,X9) => in(X10,X7)))))) & 112.63/113.35 (~(?[X11]: (in(X11,X4) & in(X11,X7)))) & in(X8,X4) & 112.63/113.35 in(X7,X3))))) & 112.63/113.35 (![X12,X13]: 112.63/113.35 ((in(X13,X3) & in(X12,X3)) => 112.63/113.35 ((![X14]: (in(X14,X13) => in(X14,X12))) | 112.63/113.35 (![X15]: (in(X15,X12) => in(X15,X13)))))) & 112.63/113.35 (![X16,X17]: 112.63/113.35 ((in(X17,X2) & in(X16,X2)) => 112.63/113.35 ((![X18]: (in(X18,X3) => (in(X16,X18) <=> in(X17,X18)))) => 112.63/113.35 (X16 = X17)))) & 112.63/113.35 (![X19]: (in(X19,X3) => (![X20]: (in(X20,X19) => in(X20,X2)))))))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(foundationAx, axiom, foundationAx <=> 112.63/113.35 (![A]: 112.63/113.35 ((?[Xx]: in(Xx,A)) => 112.63/113.35 (?[B]: ((~(?[Xx]: (in(Xx,A) & in(Xx,B)))) & in(B,A)))))). 112.63/113.35 tff('194', plain, 112.63/113.35 foundationAx = 112.63/113.35 (![X2]: 112.63/113.35 ((?[X3]: in(X3,X2)) => 112.63/113.35 (?[X4]: ((~(?[X5]: (in(X5,X2) & in(X5,X4)))) & in(X4,X2))))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(replAx, axiom, replAx <=> 112.63/113.35 (![Xphi:(($i * $i) > $o),A]: 112.63/113.35 ((![Xx]: (in(Xx,A) => exu(^[Xy]: Xphi(Xx,Xy)))) => 112.63/113.35 (?[B]: (![Xx]: (in(Xx,B) <=> (?[Xy]: (Xphi(Xy,Xx) & in(Xy,A))))))))). 112.63/113.35 tff('195', plain, 112.63/113.35 replAx = 112.63/113.35 (![X2:(($i * $i) > $o),X3]: 112.63/113.35 ((![X4]: (in(X4,X3) => exu(^[V_1]: X2(X4,V_1)))) => 112.63/113.35 (?[X5]: (![X6]: (in(X6,X5) <=> (?[X7]: (X2(X7,X6) & in(X7,X3)))))))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(omegaIndAx, axiom, omegaIndAx <=> 112.63/113.35 (![A]: 112.63/113.35 (((![Xx]: ((in(Xx,A) & in(Xx,omega)) => in(setadjoin(Xx,Xx),A))) & 112.63/113.35 in(emptyset,A)) => 112.63/113.35 (![Xx]: (in(Xx,omega) => in(Xx,A)))))). 112.63/113.35 tff('196', plain, 112.63/113.35 omegaIndAx = 112.63/113.35 (![X2]: 112.63/113.35 (((![X3]: ((in(X3,X2) & in(X3,omega)) => in(setadjoin(X3,X3),X2))) & 112.63/113.35 in(emptyset,X2)) => 112.63/113.35 (![X4]: (in(X4,omega) => in(X4,X2))))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(omegaSAx, axiom, omegaSAx <=> 112.63/113.35 (![Xx]: (in(Xx,omega) => in(setadjoin(Xx,Xx),omega)))). 112.63/113.35 tff('197', plain, 112.63/113.35 omegaSAx = (![X2]: (in(X2,omega) => in(setadjoin(X2,X2),omega))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(omega0Ax, axiom, omega0Ax() = in(emptyset,omega)). 112.63/113.35 tff('198', plain, omega0Ax = in(emptyset,omega), define([status(thm)])). 112.63/113.35 tff(setunionAx, axiom, setunionAx <=> 112.63/113.35 (![A,Xx]: (in(Xx,setunion(A)) <=> (?[B]: (in(B,A) & in(Xx,B)))))). 112.63/113.35 tff('199', plain, 112.63/113.35 setunionAx = 112.63/113.35 (![X2,X3]: (in(X3,setunion(X2)) <=> (?[X4]: (in(X4,X2) & in(X3,X4))))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(powersetAx, axiom, powersetAx <=> 112.63/113.35 (![A,B]: (in(B,powerset(A)) <=> (![Xx]: (in(Xx,B) => in(Xx,A)))))). 112.63/113.35 tff('200', plain, 112.63/113.35 powersetAx = 112.63/113.35 (![X2,X3]: (in(X3,powerset(X2)) <=> (![X4]: (in(X4,X3) => in(X4,X2))))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(setadjoinAx, axiom, setadjoinAx <=> 112.63/113.35 (![Xx,A,Xy]: (in(Xy,setadjoin(Xx,A)) <=> (in(Xy,A) | (Xy = Xx))))). 112.63/113.35 tff('201', plain, 112.63/113.35 setadjoinAx = 112.63/113.35 (![X2,X3,X4]: (in(X4,setadjoin(X2,X3)) <=> (in(X4,X3) | (X4 = X2)))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(emptysetAx, axiom, emptysetAx <=> (![Xx]: (~in(Xx,emptyset)))). 112.63/113.35 tff('202', plain, emptysetAx = (![X2]: (~in(X2,emptyset))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(setextAx, axiom, setextAx <=> 112.63/113.35 (![A,B]: ((![Xx]: (in(Xx,A) <=> in(Xx,B))) => (A = B)))). 112.63/113.35 tff('203', plain, 112.63/113.35 setextAx = (![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(exu, axiom, exu() = 112.63/113.35 ^[Xphi:($i > $o)]: (?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx)))). 112.63/113.35 tff('204', plain, 112.63/113.35 exu = 112.63/113.35 (^[V_1:($i > $o)]: (?[X2]: ((![X3]: (V_1(X3) => (X2 = X3))) & V_1(X2)))), 112.63/113.35 define([status(thm)])). 112.63/113.35 tff(brelnall1, conjecture, 112.63/113.35 (setextAx => 112.63/113.35 (emptysetAx => 112.63/113.35 (setadjoinAx => 112.63/113.35 (powersetAx => 112.63/113.35 (setunionAx => 112.63/113.35 (omega0Ax => 112.63/113.35 (omegaSAx => 112.63/113.35 (omegaIndAx => 112.63/113.35 (replAx => 112.63/113.35 (foundationAx => 112.63/113.35 (wellorderingAx => 112.63/113.35 (descrp => 112.63/113.35 (dsetconstrI => 112.63/113.35 (dsetconstrEL => 112.63/113.35 (dsetconstrER => 112.63/113.35 (exuE1 => 112.63/113.35 (prop2setE => 112.63/113.35 (emptysetE => 112.63/113.35 (emptysetimpfalse => 112.63/113.35 (notinemptyset => 112.63/113.35 (exuE3e => 112.63/113.35 (setext => 112.63/113.35 (emptyI => 112.63/113.35 (noeltsimpempty => 112.63/113.35 (setbeta => 112.63/113.35 (nonemptyE1 => 112.63/113.35 (nonemptyI => 112.63/113.35 (nonemptyI1 => 112.63/113.35 (setadjoinIL => 112.63/113.35 (emptyinunitempty => 112.63/113.35 (setadjoinIR => 112.63/113.35 (setadjoinE => 112.63/113.35 (setadjoinOr => 112.63/113.35 (setoftrueEq => 112.63/113.35 (powersetI => 112.63/113.35 (emptyinPowerset => 112.63/113.35 (emptyInPowerset => 112.63/113.35 (powersetE => 112.63/113.35 (setunionI => 112.63/113.35 (setunionE => 112.63/113.35 (subPowSU => 112.63/113.35 (exuE2 => 112.63/113.35 (nonemptyImpWitness => 112.63/113.35 (uniqinunit => 112.63/113.35 (notinsingleton => 112.63/113.35 (eqinunit => 112.63/113.35 (singletonsswitch => 112.63/113.35 (upairsetE => 112.63/113.35 (upairsetIL => 112.63/113.35 (upairsetIR => 112.63/113.35 (emptyE1 => 112.63/113.35 (vacuousDall => 112.63/113.35 (quantDeMorgan1 => 112.63/113.35 (quantDeMorgan2 => 112.63/113.35 (quantDeMorgan3 => 112.63/113.35 (quantDeMorgan4 => 112.63/113.35 (prop2setI => 112.63/113.35 (prop2set2propI => 112.63/113.35 (notdexE => 112.63/113.35 (notdallE => 112.63/113.35 (exuI1 => 112.63/113.35 (exuI3 => 112.63/113.35 (exuI2 => 112.63/113.35 (inCongP => 112.63/113.35 (in__Cong => 112.63/113.35 (exuE3u => 112.63/113.35 ( 112.63/113.35 exu__Cong => 112.63/113.35 ( 112.63/113.35 emptyset__Cong => 112.63/113.35 ( 112.63/113.35 setadjoin__Cong => 112.63/113.35 ( 112.63/113.35 powerset__Cong => 112.63/113.35 ( 112.63/113.35 setunion__Cong => 112.63/113.35 ( 112.63/113.35 omega__Cong => 112.63/113.35 ( 112.63/113.35 exuEu => 112.63/113.35 ( 112.63/113.35 descr__Cong => 112.63/113.35 ( 112.63/113.35 dsetconstr__Cong => 112.63/113.35 ( 112.63/113.35 subsetI1 => 112.63/113.35 ( 112.63/113.35 eqimpsubset2 => 112.63/113.35 ( 112.63/113.35 eqimpsubset1 => 112.63/113.35 ( 112.63/113.35 subsetI2 => 112.63/113.35 ( 112.63/113.35 emptysetsubset => 112.63/113.35 ( 112.63/113.35 subsetE => 112.63/113.35 ( 112.63/113.35 subsetE2 => 112.63/113.35 ( 112.63/113.35 notsubsetI => 112.63/113.35 ( 112.63/113.35 notequalI1 => 112.63/113.35 ( 112.63/113.35 notequalI2 => 112.63/113.35 ( 112.63/113.35 subsetRefl => 112.63/113.35 ( 112.63/113.35 subsetTrans => 112.63/113.35 ( 112.63/113.35 setadjoinSub => 112.63/113.35 ( 112.63/113.35 setadjoinSub2 => 112.63/113.35 ( 112.63/113.35 subset2powerset => 112.63/113.35 ( 112.63/113.35 setextsub => 112.63/113.35 ( 112.63/113.35 subsetemptysetimpeq => 112.63/113.35 ( 112.63/113.35 powersetI1 => 112.63/113.35 ( 112.63/113.35 powersetE1 => 112.63/113.35 ( 112.63/113.35 inPowerset => 112.63/113.35 ( 112.63/113.35 powersetsubset => 112.63/113.35 ( 112.63/113.35 sepInPowerset => 112.63/113.35 ( 112.63/113.35 sepSubset => 112.63/113.35 ( 112.63/113.35 binunionIL => 112.63/113.35 ( 112.63/113.35 upairset2IR => 112.63/113.35 ( 112.63/113.35 binunionIR => 112.63/113.35 ( 112.63/113.35 binunionEcases => 112.63/113.35 ( 112.63/113.35 binunionE => 112.63/113.35 ( 112.63/113.35 binunionLsub => 112.63/113.35 ( 112.63/113.35 binunionRsub => 112.63/113.35 ( 112.63/113.35 binintersectI => 112.63/113.35 ( 112.63/113.35 binintersectSubset5 => 112.63/113.35 ( 112.63/113.35 binintersectEL => 112.63/113.35 ( 112.63/113.35 binintersectLsub => 112.63/113.35 ( 112.63/113.35 binintersectSubset2 => 112.63/113.35 ( 112.63/113.35 binintersectSubset3 => 112.63/113.35 ( 112.63/113.35 binintersectER => 112.63/113.35 ( 112.63/113.35 disjointsetsI1 => 112.63/113.35 ( 112.63/113.35 binintersectRsub => 112.63/113.35 ( 112.63/113.35 binintersectSubset4 => 112.63/113.35 ( 112.63/113.35 binintersectSubset1 => 112.63/113.35 ( 112.63/113.35 bs114d => 112.63/113.35 ( 112.63/113.35 setminusI => 112.63/113.35 ( 112.63/113.35 setminusEL => 112.63/113.35 ( 112.63/113.35 setminusER => 112.63/113.35 ( 112.63/113.35 setminusSubset2 => 112.63/113.35 ( 112.63/113.35 setminusERneg => 112.63/113.35 ( 112.63/113.35 setminusELneg => 112.63/113.35 ( 112.63/113.35 setminusILneg => 112.63/113.35 ( 112.63/113.35 setminusIRneg => 112.63/113.35 ( 112.63/113.35 setminusLsub => 112.63/113.35 ( 112.63/113.35 setminusSubset1 => 112.63/113.35 ( 112.63/113.35 symdiffE => 112.63/113.35 ( 112.63/113.35 symdiffI1 => 112.63/113.35 ( 112.63/113.35 symdiffI2 => 112.63/113.35 ( 112.63/113.35 symdiffIneg1 => 112.63/113.35 ( 112.63/113.35 symdiffIneg2 => 112.63/113.35 ( 112.63/113.35 secondinupair => 112.63/113.35 ( 112.63/113.35 setukpairIL => 112.63/113.35 ( 112.63/113.35 setukpairIR => 112.63/113.35 ( 112.63/113.35 kpairiskpair => 112.63/113.35 ( 112.63/113.35 kpairp => 112.63/113.35 ( 112.63/113.35 singletonsubset => 112.63/113.35 ( 112.63/113.35 singletoninpowerset => 112.63/113.35 ( 112.63/113.35 singletoninpowunion => 112.63/113.35 ( 112.63/113.35 upairset2E => 112.63/113.35 ( 112.63/113.35 upairsubunion => 112.63/113.35 ( 112.63/113.35 upairinpowunion => 112.63/113.35 ( 112.63/113.35 ubforcartprodlem1 => 112.63/113.35 ( 112.63/113.35 ubforcartprodlem2 => 112.63/113.35 ( 112.63/113.35 ubforcartprodlem3 => 112.63/113.35 ( 112.63/113.35 cartprodpairin => 112.63/113.35 ( 112.63/113.35 cartprodmempair1 => 112.63/113.35 ( 112.63/113.35 cartprodmempair => 112.63/113.35 ( 112.63/113.35 setunionE2 => 112.63/113.35 ( 112.63/113.35 setunionsingleton1 => 112.63/113.35 ( 112.63/113.35 setunionsingleton2 => 112.63/113.35 ( 112.63/113.35 setunionsingleton => 112.63/113.35 ( 112.63/113.35 singletonprop => 112.63/113.35 ( 112.63/113.35 ex1E1 => 112.63/113.35 ( 112.63/113.35 ex1I => 112.63/113.35 ( 112.63/113.35 ex1I2 => 112.63/113.35 ( 112.63/113.35 singletonsuniq => 112.63/113.35 ( 112.63/113.35 setukpairinjL1 => 112.63/113.35 ( 112.63/113.35 kfstsingleton => 112.63/113.35 ( 112.63/113.35 theprop => 112.63/113.35 ( 112.63/113.35 kfstpairEq => 112.63/113.35 ( 112.63/113.35 cartprodfstin => 112.63/113.35 ( 112.63/113.35 setukpairinjL2 => 112.63/113.35 ( 112.63/113.35 setukpairinjL => 112.63/113.35 ( 112.63/113.35 setukpairinjR11 => 112.63/113.35 ( 112.63/113.35 setukpairinjR12 => 112.63/113.35 ( 112.63/113.35 setukpairinjR1 => 112.63/113.35 ( 112.63/113.35 upairequniteq => 112.63/113.35 ( 112.63/113.35 setukpairinjR2 => 112.63/113.35 ( 112.63/113.35 setukpairinjR => 112.63/113.35 ( 112.63/113.35 ksndsingleton => 112.63/113.35 ( 112.63/113.35 ksndpairEq => 112.63/113.35 ( 112.63/113.35 kpairsurjEq => 112.63/113.35 ( 112.63/113.35 cartprodsndin => 112.63/113.35 ( 112.63/113.35 cartprodpairmemEL => 112.63/113.35 ( 112.63/113.35 cartprodpairmemER => 112.63/113.35 ( 112.63/113.35 cartprodmempaircEq => 112.63/113.35 ( 112.63/113.35 cartprodfstpairEq => 112.63/113.35 ( 112.63/113.35 cartprodsndpairEq => 112.63/113.35 ( 112.63/113.35 cartprodpairsurjEq => 112.63/113.35 ( 112.63/113.35 dpsetconstrI => 112.63/113.35 ( 112.63/113.35 dpsetconstrSub => 112.63/113.35 ( 112.63/113.35 setOfPairsIsBReln => 112.63/113.35 ( 112.63/113.35 dpsetconstrERa => 112.63/113.35 ( 112.63/113.35 dpsetconstrEL1 => 112.63/113.35 ( 112.63/113.35 dpsetconstrEL2 => 112.63/113.35 ( 112.63/113.35 dpsetconstrER => 112.63/113.35 ( 112.63/113.35 funcImageSingleton => 112.63/113.35 ( 112.63/113.35 apProp => 112.63/113.35 ( 112.63/113.35 app => 112.63/113.35 ( 112.63/113.35 infuncsetfunc => 112.63/113.35 ( 112.63/113.35 ap2p => 112.63/113.35 ( 112.63/113.35 funcinfuncset => 112.63/113.35 ( 112.63/113.35 lamProp => 112.63/113.35 ( 112.63/113.35 lamp => 112.63/113.35 ( 112.63/113.35 lam2p => 112.63/113.35 ( 112.63/113.35 ![A,B,R]: 112.63/113.35 (breln( 112.63/113.35 A,B,R) => 112.63/113.35 (![Xphi:( 112.63/113.35 $i > $o)]: 112.63/113.35 (( 112.63/113.35 ![Xx]: 112.63/113.35 (in(Xx,A) => 112.63/113.35 (![Xy]: 112.63/113.35 (in(Xy,B) => 112.63/113.35 (in( 112.63/113.35 kpair( 112.63/113.35 Xx,Xy),R) => 112.63/113.35 Xphi( 112.63/113.35 kpair( 112.63/113.35 Xx,Xy))))))) => 112.63/113.35 (![Xx]: 112.63/113.35 (in(Xx,R) => 112.63/113.35 Xphi(Xx))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 112.63/113.35 tff(zf_stmt_0, conjecture, 112.63/113.35 ((![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))) => 112.63/113.35 ((![X5]: (~in(X5,emptyset))) => 112.63/113.35 ((![X6,X7,X8]: (in(X8,setadjoin(X6,X7)) <=> ((X8 = X6) | in(X8,X7)))) => 112.63/113.35 ((![X9,X10]: 112.63/113.35 (in(X10,powerset(X9)) <=> (![X11]: (in(X11,X10) => in(X11,X9))))) => 112.63/113.35 ((![X12,X13]: 112.63/113.35 (in(X13,setunion(X12)) <=> (?[X14]: (in(X13,X14) & in(X14,X12))))) => 112.63/113.35 (in(emptyset,omega) => 112.63/113.35 ((![X15]: (in(X15,omega) => in(setadjoin(X15,X15),omega))) => 112.63/113.35 ((![X16]: 112.63/113.35 ((in(emptyset,X16) & 112.63/113.35 (![X17]: 112.63/113.35 ((in(X17,omega) & in(X17,X16)) => 112.63/113.35 in(setadjoin(X17,X17),X16)))) => 112.63/113.35 (![X18]: (in(X18,omega) => in(X18,X16))))) => 112.63/113.35 ((![X19:(($i * $i) > $o),X20]: 112.63/113.35 ((![X21]: 112.63/113.35 (in(X21,X20) => 112.63/113.35 (?[X22]: 112.63/113.35 (X19(X21,X22) & (![X23]: (X19(X21,X23) => (X22 = X23))))))) => 112.63/113.35 (?[X24]: 112.63/113.35 (![X25]: 112.63/113.35 (in(X25,X24) <=> (?[X26]: (in(X26,X20) & X19(X26,X25)))))))) => 112.63/113.35 ((![X27]: 112.63/113.35 ((?[X28]: in(X28,X27)) => 112.63/113.35 (?[X29]: 112.63/113.35 (in(X29,X27) & (~(?[X30]: (in(X30,X29) & in(X30,X27)))))))) => 112.63/113.35 ((![X31]: 112.63/113.35 (?[X32]: 112.63/113.35 ((![X48]: 112.63/113.35 (in(X48,X32) => (![X49]: (in(X49,X48) => in(X49,X31))))) & 112.63/113.35 (![X45,X46]: 112.63/113.35 ((in(X45,X31) & in(X46,X31)) => 112.63/113.35 ((![X47]: 112.63/113.35 (in(X47,X32) => (in(X45,X47) <=> in(X46,X47)))) => 112.63/113.35 (X45 = X46)))) & 112.63/113.35 (![X41,X42]: 112.63/113.35 ((in(X41,X32) & in(X42,X32)) => 112.63/113.35 ((![X44]: (in(X44,X41) => in(X44,X42))) | 112.63/113.35 (![X43]: (in(X43,X42) => in(X43,X41)))))) & 112.63/113.35 (![X33]: 112.63/113.35 (((![X35]: (in(X35,X33) => in(X35,X31))) & 112.63/113.35 (?[X34]: in(X34,X33))) => 112.63/113.35 (?[X36,X37]: 112.63/113.35 (in(X36,X32) & in(X37,X33) & 112.63/113.35 (~(?[X40]: (in(X40,X36) & in(X40,X33)))) & 112.63/113.35 (![X38]: 112.63/113.35 (in(X38,X32) => 112.63/113.35 ((![X39]: (in(X39,X38) => in(X39,X36))) | 112.63/113.35 in(X37,X38))))))))))) => 112.63/113.35 ((![X50:($i > $o)]: 112.63/113.35 ((?[X51]: (X50(X51) & (![X52]: (X50(X52) => (X51 = X52))))) => 112.63/113.35 X50(descr('#ll_6'(X50))))) => 112.63/113.35 ((![X53,X54:($i > $o),X55]: 112.63/113.35 (in(X55,X53) => 112.63/113.35 (X54(X55) => in(X55,dsetconstr(X53,'#ll_6'(X54)))))) => 112.63/113.35 ((![X56,X57:($i > $o),X58]: 112.63/113.35 (in(X58,dsetconstr(X56,'#ll_6'(X57))) => in(X58,X56))) => 112.63/113.35 ((![X59,X60:($i > $o),X61]: 112.63/113.35 (in(X61,dsetconstr(X59,'#ll_6'(X60))) => X60(X61))) => 112.63/113.35 ((![X62:($i > $o)]: 112.63/113.35 ((?[X63]: 112.63/113.35 (X62(X63) & (![X64]: (X62(X64) => (X63 = X64))))) => 112.63/113.35 (?[X65]: 112.63/113.35 (X62(X65) & (![X66]: (X62(X66) => (X65 = X66))))))) => 112.63/113.35 ((![X67:$o,X68]: (in(X68,prop2set(X67)) => X67)) => 112.63/113.35 ((![X69]: (in(X69,emptyset) => (![X70:$o]: X70))) => 112.63/113.35 ((![X71]: (in(X71,emptyset) => $false)) => 112.63/113.35 ((![X72]: (~in(X72,emptyset))) => 112.63/113.35 ((![X73:($i > $o)]: 112.63/113.35 ((?[X74]: 112.63/113.35 (X73(X74) & (![X75]: (X73(X75) => (X74 = X75))))) => 112.63/113.35 (?[X76]: X73(X76)))) => 112.63/113.35 ((![X77,X78]: 112.63/113.35 ((![X79]: (in(X79,X77) => in(X79,X78))) => 112.63/113.35 ((![X80]: (in(X80,X78) => in(X80,X77))) => 112.63/113.35 (X77 = X78)))) => 112.63/113.35 ((![X81]: 112.63/113.35 ((![X82]: (~in(X82,X81))) => (X81 = emptyset))) => 112.63/113.35 ((![X83]: 112.63/113.35 ((![X84]: (~in(X84,X83))) => (X83 = emptyset))) => 112.63/113.35 ((![X85,X86:($i > $o),X87]: 112.63/113.35 (in(X87,X85) => 112.63/113.35 (in(X87,dsetconstr(X85,'#ll_6'(X86))) <=> 112.63/113.35 X86(X87)))) => 112.63/113.35 ((![X88]: 112.63/113.35 ((X88 != emptyset) => (?[X89]: in(X89,X88)))) => 112.63/113.35 ((![X90,X91:($i > $o),X92]: 112.63/113.35 (in(X92,X90) => 112.63/113.35 (X91(X92) => 112.63/113.35 (dsetconstr(X90,'#ll_6'(X91)) != emptyset)))) => 112.63/113.35 ((![X93]: 112.63/113.35 ((?[X94]: in(X94,X93)) => (X93 != emptyset))) => 112.63/113.35 ((![X95,X96]: in(X95,setadjoin(X95,X96))) => 112.63/113.35 (in(emptyset,setadjoin(emptyset,emptyset)) => 112.63/113.35 ((![X97,X98,X99]: 112.63/113.35 (in(X99,X98) => 112.63/113.35 in(X99,setadjoin(X97,X98)))) => 112.63/113.35 ((![X100,X101,X102]: 112.63/113.35 (in(X102,setadjoin(X100,X101)) => 112.63/113.35 (![X103:$o]: 112.63/113.35 (((X102 = X100) => X103) => 112.63/113.35 ((in(X102,X101) => X103) => X103))))) => 112.63/113.35 ((![X104,X105,X106]: 112.63/113.35 (in(X106,setadjoin(X104,X105)) => 112.63/113.35 ((X106 = X104) | in(X106,X105)))) => 112.63/113.35 ((![X107]: 112.63/113.35 (dsetconstr(X107,'#ll_7') = X107)) => 112.63/113.35 ((![X108,X109]: 112.63/113.35 ((![X110]: 112.63/113.35 (in(X110,X109) => in(X110,X108))) => 112.63/113.35 in(X109,powerset(X108)))) => 112.63/113.35 ((![X111]: in(emptyset,powerset(X111))) => 112.63/113.35 ((![X112]: in(emptyset,powerset(X112))) => 112.63/113.35 ((![X113,X114,X115]: 112.63/113.35 (in(X114,powerset(X113)) => 112.63/113.35 (in(X115,X114) => in(X115,X113)))) => 112.63/113.35 ((![X116,X117,X118]: 112.63/113.35 (in(X117,X118) => 112.63/113.35 (in(X118,X116) => 112.63/113.35 in(X117,setunion(X116))))) => 112.63/113.35 ((![X119,X120]: 112.63/113.35 (in(X120,setunion(X119)) => 112.63/113.35 (![X121:$o]: 112.63/113.35 ((![X122]: 112.63/113.35 (in(X120,X122) => 112.63/113.35 (in(X122,X119) => X121))) => 112.63/113.35 X121)))) => 112.63/113.35 ((![X123,X124]: 112.63/113.35 (in(X124,X123) => 112.63/113.35 in(X124, 112.63/113.35 powerset(setunion(X123))))) => 112.63/113.35 ((![X125:($i > $o)]: 112.63/113.35 ((?[X126]: 112.63/113.35 (X125(X126) & 112.63/113.35 (![X127]: 112.63/113.35 (X125(X127) => 112.63/113.35 (X126 = X127))))) => 112.63/113.35 (?[X128]: 112.63/113.35 (![X129]: 112.63/113.35 (X125(X129) <=> 112.63/113.35 (X129 = X128)))))) => 112.63/113.35 ((![X130]: 112.63/113.35 ((X130 != emptyset) => 112.63/113.35 (?[X131]: in(X131,X130)))) => 112.63/113.35 ((![X132,X133]: 112.63/113.35 (in(X132, 112.63/113.35 setadjoin(X133,emptyset)) => 112.63/113.35 (X132 = X133))) => 112.63/113.35 ((![X134,X135]: 112.63/113.35 ((X134 != X135) => 112.63/113.35 (~ 112.63/113.35 in(X135, 112.63/113.35 setadjoin(X134, 112.63/113.35 emptyset))))) => 112.63/113.35 ((![X136,X137]: 112.63/113.35 ((X136 = X137) => 112.63/113.35 in(X136, 112.63/113.35 setadjoin(X137, 112.63/113.35 emptyset)))) => 112.63/113.35 ((![X138,X139]: 112.63/113.35 (in(X138, 112.63/113.35 setadjoin(X139, 112.63/113.35 emptyset)) => 112.63/113.35 in(X139, 112.63/113.35 setadjoin(X138, 112.63/113.35 emptyset)))) => 112.63/113.35 ((![X140,X141,X142]: 112.63/113.35 (in(X142, 112.63/113.35 setadjoin(X140, 112.63/113.35 setadjoin( 112.63/113.35 X141, 112.63/113.35 emptyset))) => 112.63/113.35 ((X142 = X140) | 112.63/113.35 (X142 = X141)))) => 112.63/113.35 ((![X143,X144]: 112.63/113.35 in(X143, 112.63/113.35 setadjoin(X143, 112.63/113.35 setadjoin( 112.63/113.35 X144, 112.63/113.35 emptyset)))) => 112.63/113.35 ((![X145,X146]: 112.63/113.35 in(X146, 112.63/113.35 setadjoin(X145, 112.63/113.35 setadjoin( 112.63/113.35 X146, 112.63/113.35 emptyset)))) => 112.63/113.35 ((![X147,X148:($i > $o)]: 112.63/113.35 ((?[X149]: 112.63/113.35 (in(X149,X147) & 112.63/113.35 X148(X149))) => 112.63/113.35 ((dsetconstr( 112.63/113.35 X147,'#ll_6'(X148)) = 112.63/113.35 emptyset) => 112.63/113.35 $false))) => 112.63/113.35 ((![X150:($i > $o),X151]: 112.63/113.35 (in(X151,emptyset) => 112.63/113.35 X150(X151))) => 112.63/113.35 ((![X152,X153:($i > $o)]: 112.63/113.35 ((~ 112.63/113.35 (![X154]: 112.63/113.35 (in(X154,X152) => 112.63/113.35 X153(X154)))) => 112.63/113.35 (?[X155]: 112.63/113.35 (in(X155,X152) & 112.63/113.35 (~X153(X155)))))) => 112.63/113.35 ((![X156, 112.63/113.35 X157:($i > $o)]: 112.63/113.35 ((![X158]: 112.63/113.35 (in(X158,X156) => 112.63/113.35 (~X157(X158)))) => 112.63/113.35 (~ 112.63/113.35 (?[X159]: 112.63/113.35 (in( 112.63/113.35 X159,X156) & 112.63/113.35 X157(X159)))))) => 112.63/113.35 ((![X160, 112.63/113.35 X161:($i > $o)]: 112.63/113.35 ((~ 112.63/113.35 (?[X162]: 112.63/113.35 (in( 112.63/113.35 X162,X160) & 112.63/113.35 X161(X162)))) => 112.63/113.35 (![X163]: 112.63/113.35 (in(X163,X160) => 112.63/113.35 (~X161(X163)))))) => 112.63/113.35 ((![X164, 112.63/113.35 X165:($i > $o)]: 112.63/113.35 ((?[X166]: 112.63/113.35 (in( 112.63/113.35 X166,X164) & 112.63/113.35 (~ 112.63/113.35 X165( 112.63/113.35 X166)))) => 112.63/113.35 (~ 112.63/113.35 (![X167]: 112.63/113.35 (in( 112.63/113.35 X167,X164) => 112.63/113.35 X165( 112.63/113.35 X167)))))) => 112.63/113.35 ((![X168:$o]: 112.63/113.35 (X168 => 112.63/113.35 in(emptyset, 112.63/113.35 prop2set( 112.63/113.35 X168)))) => 112.63/113.35 ((![X169:$o]: 112.63/113.35 (X169 => 112.63/113.35 set2prop( 112.63/113.35 prop2set( 112.63/113.35 X169)))) => 112.63/113.35 ((![X170, 112.63/113.35 X171:( 112.63/113.35 $i > $o)]: 112.63/113.35 ((~ 112.63/113.35 (?[X172]: 112.63/113.35 (in( 112.63/113.35 X172,X170) & 112.63/113.35 X171( 112.63/113.35 X172)))) => 112.63/113.35 (![X173]: 112.63/113.35 ( 112.63/113.35 in( 112.63/113.35 X173,X170) => 112.63/113.35 ( 112.63/113.35 ~ 112.63/113.35 X171( 112.63/113.35 X173)))))) => 112.63/113.35 ((![X174, 112.63/113.35 X175:( 112.63/113.35 $i > $o)]: 112.63/113.35 ((~ 112.63/113.35 ( 112.63/113.35 ![X176]: 112.63/113.35 (in( 112.63/113.35 X176,X174) => 112.63/113.35 X175( 112.63/113.35 X176)))) => 112.63/113.35 (?[X177]: 112.63/113.35 (in( 112.63/113.35 X177,X174) & 112.63/113.35 (~ 112.63/113.35 X175( 112.63/113.35 X177)))))) => 112.63/113.35 ((![X178:( 112.63/113.35 $i > $o)]: 112.63/113.35 ((?[X179]: 112.63/113.35 (X178( 112.63/113.35 X179) & 112.63/113.35 (![X180]: 112.63/113.35 (X178( 112.63/113.35 X180) => 112.63/113.35 (X179 = 112.63/113.35 X180))))) => 112.63/113.35 (?[X181]: 112.63/113.35 (X178( 112.63/113.35 X181) & 112.63/113.35 (![X182]: 112.63/113.35 (X178( 112.63/113.35 X182) => 112.63/113.35 (X181 = 112.63/113.35 X182))))))) => 112.63/113.35 ((![X183:( 112.63/113.35 $i > $o)]: 112.63/113.35 (( 112.63/113.35 ?[X184]: 112.63/113.35 X183( 112.63/113.35 X184)) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X185, 112.63/113.35 X186]: 112.63/113.35 (X183( 112.63/113.35 X185) => 112.63/113.35 (X183( 112.63/113.35 X186) => 112.63/113.35 (X185 = 112.63/113.35 X186)))) => 112.63/113.35 ( 112.63/113.35 ?[X187]: 112.63/113.35 (X183( 112.63/113.35 X187) & 112.63/113.35 (![X188]: 112.63/113.35 (X183( 112.63/113.35 X188) => 112.63/113.35 (X187 = 112.63/113.35 X188)))))))) => 112.63/113.35 ((![X189:( 112.63/113.35 $i > $o)]: 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ?[X190]: 112.63/113.35 (![X191]: 112.63/113.35 (X189( 112.63/113.35 X191) <=> 112.63/113.35 (X191 = 112.63/113.35 X190)))) => 112.63/113.35 ( 112.63/113.35 ?[X192]: 112.63/113.35 (X189( 112.63/113.35 X192) & 112.63/113.35 (![X193]: 112.63/113.35 (X189( 112.63/113.35 X193) => 112.63/113.35 (X192 = 112.63/113.35 X193))))))) => 112.63/113.35 ((![X194, 112.63/113.35 X195]: 112.63/113.35 (( 112.63/113.35 X194 = 112.63/113.35 X195) => 112.63/113.35 (![X196, 112.63/113.35 X197]: 112.63/113.35 (( 112.63/113.35 X196 = 112.63/113.35 X197) => 112.63/113.35 (in( 112.63/113.35 X196,X194) => 112.63/113.35 in( 112.63/113.35 X197,X195)))))) => 112.63/113.35 ((![X198, 112.63/113.35 X199]: 112.63/113.35 (( 112.63/113.35 X198 = 112.63/113.35 X199) => 112.63/113.35 (![X200, 112.63/113.35 X201]: 112.63/113.35 (( 112.63/113.35 X200 = 112.63/113.35 X201) => 112.63/113.35 (in( 112.63/113.35 X200,X198) <=> 112.63/113.35 in( 112.63/113.35 X201,X199)))))) => 112.63/113.35 (( 112.63/113.35 ![X202:( 112.63/113.35 $i > $o)]: 112.63/113.35 (( 112.63/113.35 ?[X203]: 112.63/113.35 (X202( 112.63/113.35 X203) & 112.63/113.35 (![X204]: 112.63/113.35 (X202( 112.63/113.35 X204) => 112.63/113.35 (X203 = 112.63/113.35 X204))))) => 112.63/113.35 (![X205, 112.63/113.35 X206]: 112.63/113.35 (X202( 112.63/113.35 X205) => 112.63/113.35 (X202( 112.63/113.35 X206) => 112.63/113.35 (X205 = 112.63/113.35 X206)))))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X207:( 112.63/113.35 $i > $o), 112.63/113.35 X208:( 112.63/113.35 $i > $o)]: 112.63/113.35 (( 112.63/113.35 ![X209, 112.63/113.35 X210]: 112.63/113.35 (( 112.63/113.35 X209 = 112.63/113.35 X210) => 112.63/113.35 (X207( 112.63/113.35 X209) <=> 112.63/113.35 X208( 112.63/113.35 X210)))) => 112.63/113.35 (( 112.63/113.35 ?[X211]: 112.63/113.35 (X207( 112.63/113.35 X211) & 112.63/113.35 (![X212]: 112.63/113.35 (X207( 112.63/113.35 X212) => 112.63/113.35 (X211 = 112.63/113.35 X212))))) <=> 112.63/113.35 (?[X213]: 112.63/113.35 (X208( 112.63/113.35 X213) & 112.63/113.35 (![X214]: 112.63/113.35 (X208( 112.63/113.35 X214) => 112.63/113.35 (X213 = 112.63/113.35 X214)))))))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 emptyset = 112.63/113.35 emptyset) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X215, 112.63/113.35 X216]: 112.63/113.35 (( 112.63/113.35 X215 = 112.63/113.35 X216) => 112.63/113.35 (![X217, 112.63/113.35 X218]: 112.63/113.35 (( 112.63/113.35 X217 = 112.63/113.35 X218) => 112.63/113.35 (setadjoin( 112.63/113.35 X215,X217) = 112.63/113.35 setadjoin( 112.63/113.35 X216,X218)))))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X219, 112.63/113.35 X220]: 112.63/113.35 (( 112.63/113.35 X219 = 112.63/113.35 X220) => 112.63/113.35 (powerset( 112.63/113.35 X219) = 112.63/113.35 powerset( 112.63/113.35 X220)))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X221, 112.63/113.35 X222]: 112.63/113.35 (( 112.63/113.35 X221 = 112.63/113.35 X222) => 112.63/113.35 (setunion( 112.63/113.35 X221) = 112.63/113.35 setunion( 112.63/113.35 X222)))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 omega = 112.63/113.35 omega) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X223:( 112.63/113.35 $i > $o)]: 112.63/113.35 (( 112.63/113.35 ?[X224]: 112.63/113.35 (X223( 112.63/113.35 X224) & 112.63/113.35 (![X225]: 112.63/113.35 (X223( 112.63/113.35 X225) => 112.63/113.35 (X224 = 112.63/113.35 X225))))) => 112.63/113.35 (![X226, 112.63/113.35 X227]: 112.63/113.35 (X223( 112.63/113.35 X226) => 112.63/113.35 (X223( 112.63/113.35 X227) => 112.63/113.35 (X226 = 112.63/113.35 X227)))))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X228:( 112.63/113.35 $i > $o), 112.63/113.35 X229:( 112.63/113.35 $i > $o)]: 112.63/113.35 (( 112.63/113.35 ![X230, 112.63/113.35 X231]: 112.63/113.35 (( 112.63/113.35 X230 = 112.63/113.35 X231) => 112.63/113.35 (X228( 112.63/113.35 X230) <=> 112.63/113.35 X229( 112.63/113.35 X231)))) => 112.63/113.35 (( 112.63/113.35 ?[X232]: 112.63/113.35 (X228( 112.63/113.35 X232) & 112.63/113.35 (![X233]: 112.63/113.35 (X228( 112.63/113.35 X233) => 112.63/113.35 (X232 = 112.63/113.35 X233))))) => 112.63/113.35 (( 112.63/113.35 ?[X234]: 112.63/113.35 (X229( 112.63/113.35 X234) & 112.63/113.35 (![X235]: 112.63/113.35 (X229( 112.63/113.35 X235) => 112.63/113.35 (X234 = 112.63/113.35 X235))))) => 112.63/113.35 (descr( 112.63/113.35 '#ll_6'( 112.63/113.35 X228)) = 112.63/113.35 descr( 112.63/113.35 '#ll_6'( 112.63/113.35 X229))))))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X236, 112.63/113.35 X237]: 112.63/113.35 (( 112.63/113.35 X236 = 112.63/113.35 X237) => 112.63/113.35 (![X238:( 112.63/113.35 $i > $o), 112.63/113.35 X239:( 112.63/113.35 $i > $o)]: 112.63/113.35 (( 112.63/113.35 ![X240]: 112.63/113.35 (in( 112.63/113.35 X240,X236) => 112.63/113.35 (![X241]: 112.63/113.35 (in( 112.63/113.35 X241,X237) => 112.63/113.35 (( 112.63/113.35 X240 = 112.63/113.35 X241) => 112.63/113.35 (X238( 112.63/113.35 X240) <=> 112.63/113.35 X239( 112.63/113.35 X241))))))) => 112.63/113.35 (dsetconstr( 112.63/113.35 X236, 112.63/113.35 '#ll_6'( 112.63/113.35 X238)) = 112.63/113.35 dsetconstr( 112.63/113.35 X237, 112.63/113.35 '#ll_6'( 112.63/113.35 X239))))))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X242, 112.63/113.35 X243]: 112.63/113.35 (( 112.63/113.35 ![X244]: 112.63/113.35 (in( 112.63/113.35 X244,X242) => 112.63/113.35 in( 112.63/113.35 X244,X243))) => 112.63/113.35 subset( 112.63/113.35 X242,X243))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X245, 112.63/113.35 X246]: 112.63/113.35 (( 112.63/113.35 X245 = 112.63/113.35 X246) => 112.63/113.35 subset( 112.63/113.35 X246,X245))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X247, 112.63/113.35 X248]: 112.63/113.35 (( 112.63/113.35 X247 = 112.63/113.35 X248) => 112.63/113.35 subset( 112.63/113.35 X247,X248))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X249, 112.63/113.35 X250]: 112.63/113.35 (( 112.63/113.35 ![X251]: 112.63/113.35 (in( 112.63/113.35 X251,X249) => 112.63/113.35 in( 112.63/113.35 X251,X250))) => 112.63/113.35 subset( 112.63/113.35 X249,X250))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X252]: 112.63/113.35 subset( 112.63/113.35 emptyset, 112.63/113.35 X252)) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X253, 112.63/113.35 X254,X255]: 112.63/113.35 (subset( 112.63/113.35 X253,X254) => 112.63/113.35 (in( 112.63/113.35 X255,X253) => 112.63/113.35 in( 112.63/113.35 X255,X254)))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X256, 112.63/113.35 X257,X258]: 112.63/113.35 (subset( 112.63/113.35 X256,X257) => 112.63/113.35 (( 112.63/113.35 ~ 112.63/113.35 in( 112.63/113.35 X258,X257)) => 112.63/113.35 (~ 112.63/113.35 in( 112.63/113.35 X258,X256))))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X259, 112.63/113.35 X260,X261]: 112.63/113.35 (in( 112.63/113.35 X261,X259) => 112.63/113.35 (( 112.63/113.35 ~ 112.63/113.35 in( 112.63/113.35 X261,X260)) => 112.63/113.35 (~ 112.63/113.35 subset( 112.63/113.35 X259,X260))))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X262, 112.63/113.35 X263]: 112.63/113.35 (( 112.63/113.35 ~ 112.63/113.35 subset( 112.63/113.35 X262,X263)) => 112.63/113.35 (X262 != 112.63/113.35 X263))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X264, 112.63/113.35 X265,X266]: 112.63/113.35 (in( 112.63/113.35 X266,X264) => 112.63/113.35 (( 112.63/113.35 ~ 112.63/113.35 in( 112.63/113.35 X266,X265)) => 112.63/113.35 (X264 != 112.63/113.35 X265)))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X267]: 112.63/113.35 subset( 112.63/113.35 X267,X267)) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X268, 112.63/113.35 X269,X270]: 112.63/113.35 (subset( 112.63/113.35 X268,X269) => 112.63/113.35 (subset( 112.63/113.35 X269,X270) => 112.63/113.35 subset( 112.63/113.35 X268,X270)))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X271, 112.63/113.35 X272]: 112.63/113.35 subset( 112.63/113.35 X272, 112.63/113.35 setadjoin( 112.63/113.35 X271,X272))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X273, 112.63/113.35 X274,X275]: 112.63/113.35 (subset( 112.63/113.35 X273,X275) => 112.63/113.35 subset( 112.63/113.35 X273, 112.63/113.35 setadjoin( 112.63/113.35 X274,X275)))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X276, 112.63/113.35 X277]: 112.63/113.35 (subset( 112.63/113.35 X276,X277) => 112.63/113.35 in( 112.63/113.35 X276, 112.63/113.35 powerset( 112.63/113.35 X277)))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X278, 112.63/113.35 X279]: 112.63/113.35 (subset( 112.63/113.35 X278,X279) => 112.63/113.35 (subset( 112.63/113.35 X279,X278) => 112.63/113.35 (X278 = 112.63/113.35 X279)))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X280]: 112.63/113.35 (subset( 112.63/113.35 X280, 112.63/113.35 emptyset) => 112.63/113.35 (X280 = 112.63/113.35 emptyset))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X281, 112.63/113.35 X282]: 112.63/113.35 (subset( 112.63/113.35 X282,X281) => 112.63/113.35 in( 112.63/113.35 X282, 112.63/113.35 powerset( 112.63/113.35 X281)))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X283, 112.63/113.35 X284]: 112.63/113.35 (in( 112.63/113.35 X284, 112.63/113.35 powerset( 112.63/113.35 X283)) => 112.63/113.35 subset( 112.63/113.35 X284,X283))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X285]: 112.63/113.35 in( 112.63/113.35 X285, 112.63/113.35 powerset( 112.63/113.35 X285))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X286, 112.63/113.35 X287]: 112.63/113.35 (subset( 112.63/113.35 X286,X287) => 112.63/113.35 subset( 112.63/113.35 powerset( 112.63/113.35 X286), 112.63/113.35 powerset( 112.63/113.35 X287)))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X288, 112.63/113.35 X289:( 112.63/113.35 $i > $o)]: 112.63/113.35 in( 112.63/113.35 dsetconstr( 112.63/113.35 X288, 112.63/113.35 '#ll_6'( 112.63/113.35 X289)), 112.63/113.35 powerset( 112.63/113.35 X288))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X290, 112.63/113.35 X291:( 112.63/113.35 $i > $o)]: 112.63/113.35 subset( 112.63/113.35 dsetconstr( 112.63/113.35 X290, 112.63/113.35 '#ll_6'( 112.63/113.35 X291)), 112.63/113.35 X290)) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X292, 112.63/113.35 X293,X294]: 112.63/113.35 (in( 112.63/113.35 X294,X292) => 112.63/113.35 in( 112.63/113.35 X294, 112.63/113.35 binunion( 112.63/113.35 X292,X293)))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X295, 112.63/113.35 X296]: 112.63/113.35 in( 112.63/113.35 X296, 112.63/113.35 setadjoin( 112.63/113.35 X295, 112.63/113.35 setadjoin( 112.63/113.35 X296, 112.63/113.35 emptyset)))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X297, 112.63/113.35 X298,X299]: 112.63/113.35 (in( 112.63/113.35 X299,X298) => 112.63/113.35 in( 112.63/113.35 X299, 112.63/113.35 binunion( 112.63/113.35 X297,X298)))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X300, 112.63/113.35 X301, 112.63/113.35 X302, 112.63/113.35 X303:$o]: 112.63/113.35 (in( 112.63/113.35 X302, 112.63/113.35 binunion( 112.63/113.35 X300,X301)) => 112.63/113.35 (( 112.63/113.35 in( 112.63/113.35 X302,X300) => 112.63/113.35 X303) => 112.63/113.35 (( 112.63/113.35 in( 112.63/113.35 X302,X301) => 112.63/113.35 X303) => 112.63/113.35 X303)))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X304, 112.63/113.35 X305,X306]: 112.63/113.35 (in( 112.63/113.35 X306, 112.63/113.35 binunion( 112.63/113.35 X304,X305)) => 112.63/113.35 (in( 112.63/113.35 X306,X304) | 112.63/113.35 in( 112.63/113.35 X306,X305)))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X307, 112.63/113.35 X308]: 112.63/113.35 subset( 112.63/113.35 X307, 112.63/113.35 binunion( 112.63/113.35 X307,X308))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X309, 112.63/113.35 X310]: 112.63/113.35 subset( 112.63/113.35 X310, 112.63/113.35 binunion( 112.63/113.35 X309,X310))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X311, 112.63/113.35 X312,X313]: 112.63/113.35 (in( 112.63/113.35 X313,X311) => 112.63/113.35 (in( 112.63/113.35 X313,X312) => 112.63/113.35 in( 112.63/113.35 X313, 112.63/113.35 binintersect( 112.63/113.35 X311,X312))))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X314, 112.63/113.35 X315,X316]: 112.63/113.35 (subset( 112.63/113.35 X316,X314) => 112.63/113.35 (subset( 112.63/113.35 X316,X315) => 112.63/113.35 subset( 112.63/113.35 X316, 112.63/113.35 binintersect( 112.63/113.35 X314,X315))))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X317, 112.63/113.35 X318,X319]: 112.63/113.35 (in( 112.63/113.35 X319, 112.63/113.35 binintersect( 112.63/113.35 X317,X318)) => 112.63/113.35 in( 112.63/113.35 X319,X317))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X320, 112.63/113.35 X321]: 112.63/113.35 subset( 112.63/113.35 binintersect( 112.63/113.35 X320,X321), 112.63/113.35 X320)) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X322, 112.63/113.35 X323]: 112.63/113.35 (subset( 112.63/113.35 X322,X323) => 112.63/113.35 (binintersect( 112.63/113.35 X322,X323) = 112.63/113.35 X322))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X324, 112.63/113.35 X325]: 112.63/113.35 (( 112.63/113.35 binintersect( 112.63/113.35 X324,X325) = 112.63/113.35 X325) => 112.63/113.35 subset( 112.63/113.35 X325,X324))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X326, 112.63/113.35 X327,X328]: 112.63/113.35 (in( 112.63/113.35 X328, 112.63/113.35 binintersect( 112.63/113.35 X326,X327)) => 112.63/113.35 in( 112.63/113.35 X328,X327))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X329, 112.63/113.35 X330]: 112.63/113.35 (( 112.63/113.35 ~ 112.63/113.35 ( 112.63/113.35 ?[X331]: 112.63/113.35 (in( 112.63/113.35 X331,X329) & 112.63/113.35 in( 112.63/113.35 X331,X330)))) => 112.63/113.35 (binintersect( 112.63/113.35 X329,X330) = 112.63/113.35 emptyset))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X332, 112.63/113.35 X333]: 112.63/113.35 subset( 112.63/113.35 binintersect( 112.63/113.35 X332,X333), 112.63/113.35 X333)) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X334, 112.63/113.35 X335]: 112.63/113.35 (subset( 112.63/113.35 X335,X334) => 112.63/113.35 (binintersect( 112.63/113.35 X334,X335) = 112.63/113.35 X335))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X336, 112.63/113.35 X337]: 112.63/113.35 (( 112.63/113.35 binintersect( 112.63/113.35 X336,X337) = 112.63/113.35 X336) => 112.63/113.35 subset( 112.63/113.35 X336,X337))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X338, 112.63/113.35 X339,X340]: 112.63/113.35 (binintersect( 112.63/113.35 X338, 112.63/113.35 binunion( 112.63/113.35 X339,X340)) = 112.63/113.35 binunion( 112.63/113.35 binintersect( 112.63/113.35 X338,X339), 112.63/113.35 binintersect( 112.63/113.35 X338,X340)))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X341, 112.63/113.35 X342,X343]: 112.63/113.35 (in( 112.63/113.35 X343,X341) => 112.63/113.35 (( 112.63/113.35 ~ 112.63/113.35 in( 112.63/113.35 X343,X342)) => 112.63/113.35 in( 112.63/113.35 X343, 112.63/113.35 setminus( 112.63/113.35 X341,X342))))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X344, 112.63/113.35 X345,X346]: 112.63/113.35 (in( 112.63/113.35 X346, 112.63/113.35 setminus( 112.63/113.35 X344,X345)) => 112.63/113.35 in( 112.63/113.35 X346,X344))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X347, 112.63/113.35 X348,X349]: 112.63/113.35 (in( 112.63/113.35 X349, 112.63/113.35 setminus( 112.63/113.35 X347,X348)) => 112.63/113.35 (~ 112.63/113.35 in( 112.63/113.35 X349,X348)))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X350, 112.63/113.35 X351]: 112.63/113.35 (subset( 112.63/113.35 X350,X351) => 112.63/113.35 (setminus( 112.63/113.35 X350,X351) = 112.63/113.35 emptyset))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X352, 112.63/113.35 X353,X354]: 112.63/113.35 (( 112.63/113.35 ~ 112.63/113.35 in( 112.63/113.35 X354, 112.63/113.35 setminus( 112.63/113.35 X352,X353))) => 112.63/113.35 (in( 112.63/113.35 X354,X352) => 112.63/113.35 in( 112.63/113.35 X354,X353)))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X355, 112.63/113.35 X356,X357]: 112.63/113.35 (( 112.63/113.35 ~ 112.63/113.35 in( 112.63/113.35 X357, 112.63/113.35 setminus( 112.63/113.35 X355,X356))) => 112.63/113.35 (( 112.63/113.35 ~ 112.63/113.35 in( 112.63/113.35 X357,X356)) => 112.63/113.35 (~ 112.63/113.35 in( 112.63/113.35 X357,X355))))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X358, 112.63/113.35 X359,X360]: 112.63/113.35 (( 112.63/113.35 ~ 112.63/113.35 in( 112.63/113.35 X360,X358)) => 112.63/113.35 (~ 112.63/113.35 in( 112.63/113.35 X360, 112.63/113.35 setminus( 112.63/113.35 X358,X359))))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X361, 112.63/113.35 X362,X363]: 112.63/113.35 (in( 112.63/113.35 X363,X362) => 112.63/113.35 (~ 112.63/113.35 in( 112.63/113.35 X363, 112.63/113.35 setminus( 112.63/113.35 X361,X362))))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X364, 112.63/113.35 X365]: 112.63/113.35 subset( 112.63/113.35 setminus( 112.63/113.35 X364,X365), 112.63/113.35 X364)) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X366, 112.63/113.35 X367]: 112.63/113.35 (( 112.63/113.35 setminus( 112.63/113.35 X366,X367) = 112.63/113.35 emptyset) => 112.63/113.35 subset( 112.63/113.35 X366,X367))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X368, 112.63/113.35 X369,X370]: 112.63/113.35 (in( 112.63/113.35 X370, 112.63/113.35 symdiff( 112.63/113.35 X368,X369)) => 112.63/113.35 (![X371:$o]: 112.63/113.35 (( 112.63/113.35 in( 112.63/113.35 X370,X368) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ~ 112.63/113.35 in( 112.63/113.35 X370,X369)) => 112.63/113.35 X371)) => 112.63/113.35 (( 112.63/113.35 ( 112.63/113.35 ~ 112.63/113.35 in( 112.63/113.35 X370,X368)) => 112.63/113.35 ( 112.63/113.35 in( 112.63/113.35 X370,X369) => 112.63/113.35 X371)) => 112.63/113.35 X371))))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X372, 112.63/113.35 X373,X374]: 112.63/113.35 (in( 112.63/113.35 X374,X372) => 112.63/113.35 (( 112.63/113.35 ~ 112.63/113.35 in( 112.63/113.35 X374,X373)) => 112.63/113.35 in( 112.63/113.35 X374, 112.63/113.35 symdiff( 112.63/113.35 X372,X373))))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X375, 112.63/113.35 X376,X377]: 112.63/113.35 (( 112.63/113.35 ~ 112.63/113.35 in( 112.63/113.35 X377,X375)) => 112.63/113.35 (in( 112.63/113.35 X377,X376) => 112.63/113.35 in( 112.63/113.35 X377, 112.63/113.35 symdiff( 112.63/113.35 X375,X376))))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X378, 112.63/113.35 X379,X380]: 112.63/113.35 (in( 112.63/113.35 X380,X378) => 112.63/113.35 (in( 112.63/113.35 X380,X379) => 112.63/113.35 (~ 112.63/113.35 in( 112.63/113.35 X380, 112.63/113.35 symdiff( 112.63/113.35 X378,X379)))))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X381, 112.63/113.35 X382,X383]: 112.63/113.35 (( 112.63/113.35 ~ 112.63/113.35 in( 112.63/113.35 X383,X381)) => 112.63/113.35 (( 112.63/113.35 ~ 112.63/113.35 in( 112.63/113.35 X383,X382)) => 112.63/113.35 (~ 112.63/113.35 in( 112.63/113.35 X383, 112.63/113.35 symdiff( 112.63/113.35 X381,X382)))))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X384, 112.63/113.35 X385]: 112.63/113.35 in( 112.63/113.35 X385, 112.63/113.35 setadjoin( 112.63/113.35 X384, 112.63/113.35 setadjoin( 112.63/113.35 X385, 112.63/113.35 emptyset)))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X386, 112.63/113.35 X387]: 112.63/113.35 in( 112.63/113.35 X386, 112.63/113.35 setunion( 112.63/113.35 setadjoin( 112.63/113.35 setadjoin( 112.63/113.35 X386, 112.63/113.35 emptyset), 112.63/113.35 setadjoin( 112.63/113.35 setadjoin( 112.63/113.35 X386, 112.63/113.35 setadjoin( 112.63/113.35 X387, 112.63/113.35 emptyset)), 112.63/113.35 emptyset))))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X388, 112.63/113.35 X389]: 112.63/113.35 in( 112.63/113.35 X389, 112.63/113.35 setunion( 112.63/113.35 setadjoin( 112.63/113.35 setadjoin( 112.63/113.35 X388, 112.63/113.35 emptyset), 112.63/113.35 setadjoin( 112.63/113.35 setadjoin( 112.63/113.35 X388, 112.63/113.35 setadjoin( 112.63/113.35 X389, 112.63/113.35 emptyset)), 112.63/113.35 emptyset))))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X390, 112.63/113.35 X391]: 112.63/113.35 iskpair( 112.63/113.35 setadjoin( 112.63/113.35 setadjoin( 112.63/113.35 X390, 112.63/113.35 emptyset), 112.63/113.35 setadjoin( 112.63/113.35 setadjoin( 112.63/113.35 X390, 112.63/113.35 setadjoin( 112.63/113.35 X391, 112.63/113.35 emptyset)), 112.63/113.35 emptyset)))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X392, 112.63/113.35 X393]: 112.63/113.35 iskpair( 112.63/113.35 kpair( 112.63/113.35 X392,X393))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X394, 112.63/113.35 X395]: 112.63/113.35 (in( 112.63/113.35 X395,X394) => 112.63/113.35 subset( 112.63/113.35 setadjoin( 112.63/113.35 X395, 112.63/113.35 emptyset), 112.63/113.35 X394))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X396, 112.63/113.35 X397]: 112.63/113.35 (in( 112.63/113.35 X397,X396) => 112.63/113.35 in( 112.63/113.35 setadjoin( 112.63/113.35 X397, 112.63/113.35 emptyset), 112.63/113.35 powerset( 112.63/113.35 X396)))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X398, 112.63/113.35 X399,X400]: 112.63/113.35 (in( 112.63/113.35 X400,X398) => 112.63/113.35 in( 112.63/113.35 setadjoin( 112.63/113.35 X400, 112.63/113.35 emptyset), 112.63/113.35 powerset( 112.63/113.35 binunion( 112.63/113.35 X398,X399))))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X401, 112.63/113.35 X402,X403]: 112.63/113.35 (in( 112.63/113.35 X403, 112.63/113.35 setadjoin( 112.63/113.35 X401, 112.63/113.35 setadjoin( 112.63/113.35 X402, 112.63/113.35 emptyset))) => 112.63/113.35 (( 112.63/113.35 X403 = 112.63/113.35 X401) | 112.63/113.35 (X403 = 112.63/113.35 X402)))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X404, 112.63/113.35 X405,X406]: 112.63/113.35 (in( 112.63/113.35 X406,X404) => 112.63/113.35 (![X407]: 112.63/113.35 (in( 112.63/113.35 X407,X405) => 112.63/113.35 subset( 112.63/113.35 setadjoin( 112.63/113.35 X406, 112.63/113.35 setadjoin( 112.63/113.35 X407, 112.63/113.35 emptyset)), 112.63/113.35 binunion( 112.63/113.35 X404,X405)))))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X408, 112.63/113.35 X409,X410]: 112.63/113.35 (in( 112.63/113.35 X410,X408) => 112.63/113.35 (![X411]: 112.63/113.35 (in( 112.63/113.35 X411,X409) => 112.63/113.35 in( 112.63/113.35 setadjoin( 112.63/113.35 X410, 112.63/113.35 setadjoin( 112.63/113.35 X411, 112.63/113.35 emptyset)), 112.63/113.35 powerset( 112.63/113.35 binunion( 112.63/113.35 X408,X409))))))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X412, 112.63/113.35 X413,X414]: 112.63/113.35 (in( 112.63/113.35 X414,X412) => 112.63/113.35 (![X415]: 112.63/113.35 (in( 112.63/113.35 X415,X413) => 112.63/113.35 subset( 112.63/113.35 setadjoin( 112.63/113.35 setadjoin( 112.63/113.35 X414, 112.63/113.35 emptyset), 112.63/113.35 setadjoin( 112.63/113.35 setadjoin( 112.63/113.35 X414, 112.63/113.35 setadjoin( 112.63/113.35 X415, 112.63/113.35 emptyset)), 112.63/113.35 emptyset)), 112.63/113.35 powerset( 112.63/113.35 binunion( 112.63/113.35 X412,X413))))))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X416, 112.63/113.35 X417,X418]: 112.63/113.35 (in( 112.63/113.35 X418,X416) => 112.63/113.35 (![X419]: 112.63/113.35 (in( 112.63/113.35 X419,X417) => 112.63/113.35 in( 112.63/113.35 setadjoin( 112.63/113.35 setadjoin( 112.63/113.35 X418, 112.63/113.35 emptyset), 112.63/113.35 setadjoin( 112.63/113.35 setadjoin( 112.63/113.35 X418, 112.63/113.35 setadjoin( 112.63/113.35 X419, 112.63/113.35 emptyset)), 112.63/113.35 emptyset)), 112.63/113.35 powerset( 112.63/113.35 powerset( 112.63/113.35 binunion( 112.63/113.35 X416,X417)))))))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X420, 112.63/113.35 X421,X422]: 112.63/113.35 (in( 112.63/113.35 X422,X420) => 112.63/113.35 (![X423]: 112.63/113.35 (in( 112.63/113.35 X423,X421) => 112.63/113.35 in( 112.63/113.35 kpair( 112.63/113.35 X422,X423), 112.63/113.35 powerset( 112.63/113.35 powerset( 112.63/113.35 binunion( 112.63/113.35 X420,X421)))))))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X424, 112.63/113.35 X425,X426]: 112.63/113.35 (in( 112.63/113.35 X426,X424) => 112.63/113.35 (![X427]: 112.63/113.35 (in( 112.63/113.35 X427,X425) => 112.63/113.35 in( 112.63/113.35 kpair( 112.63/113.35 X426,X427), 112.63/113.35 cartprod( 112.63/113.35 X424,X425)))))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X428, 112.63/113.35 X429,X430]: 112.63/113.35 (in( 112.63/113.35 X430, 112.63/113.35 cartprod( 112.63/113.35 X428,X429)) => 112.63/113.35 (?[X431]: 112.63/113.35 (in( 112.63/113.35 X431,X428) & 112.63/113.35 (?[X432]: 112.63/113.35 (in( 112.63/113.35 X432,X429) & 112.63/113.35 (X430 = 112.63/113.35 kpair( 112.63/113.35 X431,X432)))))))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X433, 112.63/113.35 X434,X435]: 112.63/113.35 (in( 112.63/113.35 X435, 112.63/113.35 cartprod( 112.63/113.35 X433,X434)) => 112.63/113.35 iskpair( 112.63/113.35 X435))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X436, 112.63/113.35 X437]: 112.63/113.35 (in( 112.63/113.35 X437, 112.63/113.35 setunion( 112.63/113.35 X436)) => 112.63/113.35 (?[X438]: 112.63/113.35 (in( 112.63/113.35 X438,X436) & 112.63/113.35 in( 112.63/113.35 X437,X438))))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X439]: 112.63/113.35 subset( 112.63/113.35 setunion( 112.63/113.35 setadjoin( 112.63/113.35 X439, 112.63/113.35 emptyset)), 112.63/113.35 X439)) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X440]: 112.63/113.35 subset( 112.63/113.35 X440, 112.63/113.35 setunion( 112.63/113.35 setadjoin( 112.63/113.35 X440, 112.63/113.35 emptyset)))) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X441]: 112.63/113.35 (setunion( 112.63/113.35 setadjoin( 112.63/113.35 X441, 112.63/113.35 emptyset)) = 112.63/113.35 X441)) => 112.63/113.35 ( 112.63/113.35 ( 112.63/113.35 ![X442, 112.63/113.35 X443:( 112.63/113.35 $i > $o)]: 112.63/113.35 (( 112.63/113.35 ![X444]: 112.63/113.35 (in( 112.63/113.35 X444,X442) => 112.63/113.35 (![X445]: 112.63/113.35 (in( 112.63/113.35 X445,X442) => 112.63/113.35 (X443( 112.63/113.35 X444) => 112.63/113.35 (X443( 112.63/113.35 X445) => 112.63/113.35 (X444 = 112.63/113.35 X445))))))) => 112.63/113.35 (( 112.63/113.35 ?[X446]: 112.63/113.35 (in( 112.63/113.35 X446,X442) & 112.63/113.35 X443( 112.63/113.35 X446))) => 112.63/113.35 (?[X447]: 112.63/113.35 (in( 112.63/113.35 X447, 112.63/113.35 dsetconstr( 112.63/113.35 X442, 112.63/113.35 '#ll_6'( 112.63/113.35 X443))) & 112.63/113.35 (dsetconstr( 112.63/113.35 X442, 112.63/113.35 '#ll_6'( 112.63/113.35 X443)) = 112.63/113.35 setadjoin( 112.63/113.36 X447, 112.63/113.36 emptyset))))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X448, 112.63/113.36 X449:( 112.63/113.36 $i > $o)]: 112.63/113.36 (( 112.63/113.36 ?[X450]: 112.63/113.36 (in( 112.63/113.36 X450, 112.63/113.36 dsetconstr( 112.63/113.36 X448, 112.63/113.36 '#ll_6'( 112.63/113.36 X449))) & 112.63/113.36 (dsetconstr( 112.63/113.36 X448, 112.63/113.36 '#ll_6'( 112.63/113.36 X449)) = 112.63/113.36 setadjoin( 112.63/113.36 X450, 112.63/113.36 emptyset)))) => 112.63/113.36 (?[X451]: 112.63/113.36 (in( 112.63/113.36 X451,X448) & 112.63/113.36 X449( 112.63/113.36 X451))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X452, 112.63/113.36 X453:( 112.63/113.36 $i > $o), 112.63/113.36 X454]: 112.63/113.36 (in( 112.63/113.36 X454,X452) => 112.63/113.36 (X453( 112.63/113.36 X454) => 112.63/113.36 (( 112.63/113.36 ![X455]: 112.63/113.36 (in( 112.63/113.36 X455,X452) => 112.63/113.36 (X453( 112.63/113.36 X455) => 112.63/113.36 (X455 = 112.63/113.36 X454)))) => 112.63/113.36 (?[X456]: 112.63/113.36 (in( 112.63/113.36 X456, 112.63/113.36 dsetconstr( 112.63/113.36 X452, 112.63/113.36 '#ll_6'( 112.63/113.36 X453))) & 112.63/113.36 (dsetconstr( 112.63/113.36 X452, 112.63/113.36 '#ll_6'( 112.63/113.36 X453)) = 112.63/113.36 setadjoin( 112.63/113.36 X456, 112.63/113.36 emptyset)))))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X457, 112.63/113.36 X458:( 112.63/113.36 $i > $o)]: 112.63/113.36 (( 112.63/113.36 ![X459]: 112.63/113.36 (in( 112.63/113.36 X459,X457) => 112.63/113.36 (![X460]: 112.63/113.36 (in( 112.63/113.36 X460,X457) => 112.63/113.36 (X458( 112.63/113.36 X459) => 112.63/113.36 (X458( 112.63/113.36 X460) => 112.63/113.36 (X459 = 112.63/113.36 X460))))))) => 112.63/113.36 (( 112.63/113.36 ?[X461]: 112.63/113.36 (in( 112.63/113.36 X461,X457) & 112.63/113.36 X458( 112.63/113.36 X461))) => 112.63/113.36 (?[X462]: 112.63/113.36 (in( 112.63/113.36 X462, 112.63/113.36 dsetconstr( 112.63/113.36 X457, 112.63/113.36 '#ll_6'( 112.63/113.36 X458))) & 112.63/113.36 (dsetconstr( 112.63/113.36 X457, 112.63/113.36 '#ll_6'( 112.63/113.36 X458)) = 112.63/113.36 setadjoin( 112.63/113.36 X462, 112.63/113.36 emptyset))))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X463, 112.63/113.36 X464]: 112.63/113.36 (( 112.63/113.36 setadjoin( 112.63/113.36 X463, 112.63/113.36 emptyset) = 112.63/113.36 setadjoin( 112.63/113.36 X464, 112.63/113.36 emptyset)) => 112.63/113.36 (X463 = 112.63/113.36 X464))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X465, 112.63/113.36 X466,X467]: 112.63/113.36 (in( 112.63/113.36 setadjoin( 112.63/113.36 X467, 112.63/113.36 emptyset), 112.63/113.36 setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X465, 112.63/113.36 emptyset), 112.63/113.36 setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X465, 112.63/113.36 setadjoin( 112.63/113.36 X466, 112.63/113.36 emptyset)), 112.63/113.36 emptyset))) => 112.63/113.36 (X465 = 112.63/113.36 X467))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X468]: 112.63/113.36 (iskpair( 112.63/113.36 X468) => 112.63/113.36 (?[X469]: 112.63/113.36 (in( 112.63/113.36 X469, 112.63/113.36 dsetconstr( 112.63/113.36 setunion( 112.63/113.36 X468), 112.63/113.36 '#ll_5'( 112.63/113.36 X468))) & 112.63/113.36 (dsetconstr( 112.63/113.36 setunion( 112.63/113.36 X468), 112.63/113.36 '#ll_5'( 112.63/113.36 X468)) = 112.63/113.36 setadjoin( 112.63/113.36 X469, 112.63/113.36 emptyset)))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X470]: 112.63/113.36 (( 112.63/113.36 ?[X471]: 112.63/113.36 (in( 112.63/113.36 X471,X470) & 112.63/113.36 (X470 = 112.63/113.36 setadjoin( 112.63/113.36 X471, 112.63/113.36 emptyset)))) => 112.63/113.36 in( 112.63/113.36 setunion( 112.63/113.36 X470), 112.63/113.36 X470))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X472, 112.63/113.36 X473]: 112.63/113.36 (kfst( 112.63/113.36 kpair( 112.63/113.36 X472,X473)) = 112.63/113.36 X472)) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X474, 112.63/113.36 X475,X476]: 112.63/113.36 (in( 112.63/113.36 X476, 112.63/113.36 cartprod( 112.63/113.36 X474,X475)) => 112.63/113.36 in( 112.63/113.36 kfst( 112.63/113.36 X476), 112.63/113.36 X474))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X477, 112.63/113.36 X478, 112.63/113.36 X479,X480]: 112.63/113.36 (( 112.63/113.36 setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X477, 112.63/113.36 emptyset), 112.63/113.36 setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X477, 112.63/113.36 setadjoin( 112.63/113.36 X478, 112.63/113.36 emptyset)), 112.63/113.36 emptyset)) = 112.63/113.36 setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X479, 112.63/113.36 emptyset), 112.63/113.36 setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X479, 112.63/113.36 setadjoin( 112.63/113.36 X480, 112.63/113.36 emptyset)), 112.63/113.36 emptyset))) => 112.63/113.36 (X477 = 112.63/113.36 X479))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X481, 112.63/113.36 X482, 112.63/113.36 X483,X484]: 112.63/113.36 (( 112.63/113.36 kpair( 112.63/113.36 X481,X482) = 112.63/113.36 kpair( 112.63/113.36 X483,X484)) => 112.63/113.36 (X481 = 112.63/113.36 X483))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X485, 112.63/113.36 X486]: 112.63/113.36 (( 112.63/113.36 X485 = 112.63/113.36 X486) => 112.63/113.36 (setadjoin( 112.63/113.36 X485, 112.63/113.36 setadjoin( 112.63/113.36 X486, 112.63/113.36 emptyset)) = 112.63/113.36 setadjoin( 112.63/113.36 X485, 112.63/113.36 emptyset)))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X487, 112.63/113.36 X488]: 112.63/113.36 (( 112.63/113.36 X487 = 112.63/113.36 X488) => 112.63/113.36 (setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X487, 112.63/113.36 emptyset), 112.63/113.36 setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X487, 112.63/113.36 setadjoin( 112.63/113.36 X488, 112.63/113.36 emptyset)), 112.63/113.36 emptyset)) = 112.63/113.36 setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X487, 112.63/113.36 emptyset), 112.63/113.36 emptyset)))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X489, 112.63/113.36 X490, 112.63/113.36 X491,X492]: 112.63/113.36 (( 112.63/113.36 setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X489, 112.63/113.36 emptyset), 112.63/113.36 setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X489, 112.63/113.36 setadjoin( 112.63/113.36 X490, 112.63/113.36 emptyset)), 112.63/113.36 emptyset)) = 112.63/113.36 setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X491, 112.63/113.36 emptyset), 112.63/113.36 setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X491, 112.63/113.36 setadjoin( 112.63/113.36 X492, 112.63/113.36 emptyset)), 112.63/113.36 emptyset))) => 112.63/113.36 (( 112.63/113.36 X491 = 112.63/113.36 X492) => 112.63/113.36 (X490 = 112.63/113.36 X492)))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X493, 112.63/113.36 X494,X495]: 112.63/113.36 (( 112.63/113.36 setadjoin( 112.63/113.36 X493, 112.63/113.36 setadjoin( 112.63/113.36 X494, 112.63/113.36 emptyset)) = 112.63/113.36 setadjoin( 112.63/113.36 X495, 112.63/113.36 emptyset)) => 112.63/113.36 (X493 = 112.63/113.36 X494))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X496, 112.63/113.36 X497, 112.63/113.36 X498,X499]: 112.63/113.36 (( 112.63/113.36 setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X496, 112.63/113.36 emptyset), 112.63/113.36 setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X496, 112.63/113.36 setadjoin( 112.63/113.36 X497, 112.63/113.36 emptyset)), 112.63/113.36 emptyset)) = 112.63/113.36 setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X498, 112.63/113.36 emptyset), 112.63/113.36 setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X498, 112.63/113.36 setadjoin( 112.63/113.36 X499, 112.63/113.36 emptyset)), 112.63/113.36 emptyset))) => 112.63/113.36 (X497 = 112.63/113.36 X499))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X500, 112.63/113.36 X501, 112.63/113.36 X502,X503]: 112.63/113.36 (( 112.63/113.36 kpair( 112.63/113.36 X500,X501) = 112.63/113.36 kpair( 112.63/113.36 X502,X503)) => 112.63/113.36 (X501 = 112.63/113.36 X503))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X504]: 112.63/113.36 (iskpair( 112.63/113.36 X504) => 112.63/113.36 (?[X505]: 112.63/113.36 (in( 112.63/113.36 X505, 112.63/113.36 dsetconstr( 112.63/113.36 setunion( 112.63/113.36 X504), 112.63/113.36 '#ll_4'( 112.63/113.36 X504))) & 112.63/113.36 (dsetconstr( 112.63/113.36 setunion( 112.63/113.36 X504), 112.63/113.36 '#ll_4'( 112.63/113.36 X504)) = 112.63/113.36 setadjoin( 112.63/113.36 X505, 112.63/113.36 emptyset)))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X506, 112.63/113.36 X507]: 112.63/113.36 (ksnd( 112.63/113.36 kpair( 112.63/113.36 X506,X507)) = 112.63/113.36 X507)) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X508]: 112.63/113.36 (iskpair( 112.63/113.36 X508) => 112.63/113.36 (kpair( 112.63/113.36 kfst( 112.63/113.36 X508), 112.63/113.36 ksnd( 112.63/113.36 X508)) = 112.63/113.36 X508))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X509, 112.63/113.36 X510,X511]: 112.63/113.36 (in( 112.63/113.36 X511, 112.63/113.36 cartprod( 112.63/113.36 X509,X510)) => 112.63/113.36 in( 112.63/113.36 ksnd( 112.63/113.36 X511), 112.63/113.36 X510))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X512, 112.63/113.36 X513, 112.63/113.36 X514,X515]: 112.63/113.36 (in( 112.63/113.36 kpair( 112.63/113.36 X514,X515), 112.63/113.36 cartprod( 112.63/113.36 X512,X513)) => 112.63/113.36 in( 112.63/113.36 X514,X512))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X516, 112.63/113.36 X517, 112.63/113.36 X518,X519]: 112.63/113.36 (in( 112.63/113.36 kpair( 112.63/113.36 X518,X519), 112.63/113.36 cartprod( 112.63/113.36 X516,X517)) => 112.63/113.36 in( 112.63/113.36 X519,X517))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X520, 112.63/113.36 X521,X522]: 112.63/113.36 (in( 112.63/113.36 X522,X520) => 112.63/113.36 (![X523]: 112.63/113.36 (in( 112.63/113.36 X523,X521) => 112.63/113.36 (kpair( 112.63/113.36 X522,X523) = 112.63/113.36 kpair( 112.63/113.36 X522,X523)))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X524, 112.63/113.36 X525,X526]: 112.63/113.36 (in( 112.63/113.36 X526,X524) => 112.63/113.36 (![X527]: 112.63/113.36 (in( 112.63/113.36 X527,X525) => 112.63/113.36 (kfst( 112.63/113.36 kpair( 112.63/113.36 X526,X527)) = 112.63/113.36 X526))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X528, 112.63/113.36 X529,X530]: 112.63/113.36 (in( 112.63/113.36 X530,X528) => 112.63/113.36 (![X531]: 112.63/113.36 (in( 112.63/113.36 X531,X529) => 112.63/113.36 (ksnd( 112.63/113.36 kpair( 112.63/113.36 X530,X531)) = 112.63/113.36 X531))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X532, 112.63/113.36 X533,X534]: 112.63/113.36 (in( 112.63/113.36 X534, 112.63/113.36 cartprod( 112.63/113.36 X532,X533)) => 112.63/113.36 (kpair( 112.63/113.36 kfst( 112.63/113.36 X534), 112.63/113.36 ksnd( 112.63/113.36 X534)) = 112.63/113.36 X534))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X535, 112.63/113.36 X536, 112.63/113.36 X537:( 112.63/113.36 ($i * $i) > 112.63/113.36 $o),X538]: 112.63/113.36 (in( 112.63/113.36 X538,X535) => 112.63/113.36 (![X539]: 112.63/113.36 (in( 112.63/113.36 X539,X536) => 112.63/113.36 (X537( 112.63/113.36 X538,X539) => 112.63/113.36 in( 112.63/113.36 kpair( 112.63/113.36 X538,X539), 112.63/113.36 dpsetconstr( 112.63/113.36 X535, 112.63/113.36 X536, 112.63/113.36 '#ll_3'( 112.63/113.36 X537)))))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X540, 112.63/113.36 X541, 112.63/113.36 X542:( 112.63/113.36 ($i * $i) > 112.63/113.36 $o)]: 112.63/113.36 subset( 112.63/113.36 dpsetconstr( 112.63/113.36 X540, 112.63/113.36 X541, 112.63/113.36 '#ll_3'( 112.63/113.36 X542)), 112.63/113.36 cartprod( 112.63/113.36 X540,X541))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X543, 112.63/113.36 X544, 112.63/113.36 X545:( 112.63/113.36 ($i * $i) > 112.63/113.36 $o)]: 112.63/113.36 subset( 112.63/113.36 dpsetconstr( 112.63/113.36 X543, 112.63/113.36 X544, 112.63/113.36 '#ll_3'( 112.63/113.36 X545)), 112.63/113.36 cartprod( 112.63/113.36 X543,X544))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X546, 112.63/113.36 X547, 112.63/113.36 X548:( 112.63/113.36 ($i * $i) > 112.63/113.36 $o),X549]: 112.63/113.36 (in( 112.63/113.36 X549,X546) => 112.63/113.36 (![X550]: 112.63/113.36 (in( 112.63/113.36 X550,X547) => 112.63/113.36 (in( 112.63/113.36 kpair( 112.63/113.36 X549,X550), 112.63/113.36 dpsetconstr( 112.63/113.36 X546, 112.63/113.36 X547, 112.63/113.36 '#ll_3'( 112.63/113.36 X548))) => 112.63/113.36 X548( 112.63/113.36 X549,X550)))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X551, 112.63/113.36 X552, 112.63/113.36 X553:( 112.63/113.36 ($i * $i) > 112.63/113.36 $o),X554, 112.63/113.36 X555]: 112.63/113.36 (in( 112.63/113.36 kpair( 112.63/113.36 X554,X555), 112.63/113.36 dpsetconstr( 112.63/113.36 X551, 112.63/113.36 X552, 112.63/113.36 '#ll_3'( 112.63/113.36 X553))) => 112.63/113.36 in( 112.63/113.36 X554,X551))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X556, 112.63/113.36 X557, 112.63/113.36 X558:( 112.63/113.36 ($i * $i) > 112.63/113.36 $o),X559, 112.63/113.36 X560]: 112.63/113.36 (in( 112.63/113.36 kpair( 112.63/113.36 X559,X560), 112.63/113.36 dpsetconstr( 112.63/113.36 X556, 112.63/113.36 X557, 112.63/113.36 '#ll_3'( 112.63/113.36 X558))) => 112.63/113.36 in( 112.63/113.36 X560,X557))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X561, 112.63/113.36 X562, 112.63/113.36 X563:( 112.63/113.36 ($i * $i) > 112.63/113.36 $o),X564, 112.63/113.36 X565]: 112.63/113.36 (in( 112.63/113.36 kpair( 112.63/113.36 X564,X565), 112.63/113.36 dpsetconstr( 112.63/113.36 X561, 112.63/113.36 X562, 112.63/113.36 '#ll_3'( 112.63/113.36 X563))) => 112.63/113.36 X563( 112.63/113.36 X564,X565))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X566, 112.63/113.36 X567,X568]: 112.63/113.36 (( 112.63/113.36 subset( 112.63/113.36 X568, 112.63/113.36 cartprod( 112.63/113.36 X566,X567)) & 112.63/113.36 ( 112.63/113.36 ![X569]: 112.63/113.36 (in( 112.63/113.36 X569,X566) => 112.63/113.36 (?[X570]: 112.63/113.36 (in( 112.63/113.36 X570, 112.63/113.36 dsetconstr( 112.63/113.36 X567, 112.63/113.36 '#ll_2'( 112.63/113.36 X569,X568))) & 112.63/113.36 (dsetconstr( 112.63/113.36 X567, 112.63/113.36 '#ll_2'( 112.63/113.36 X569,X568)) = 112.63/113.36 setadjoin( 112.63/113.36 X570, 112.63/113.36 emptyset))))))) => 112.63/113.36 (![X571]: 112.63/113.36 (in( 112.63/113.36 X571,X566) => 112.63/113.36 (?[X572]: 112.63/113.36 (in( 112.63/113.36 X572, 112.63/113.36 dsetconstr( 112.63/113.36 X567, 112.63/113.36 '#ll_2'( 112.63/113.36 X571,X568))) & 112.63/113.36 (dsetconstr( 112.63/113.36 X567, 112.63/113.36 '#ll_2'( 112.63/113.36 X571,X568)) = 112.63/113.36 setadjoin( 112.63/113.36 X572, 112.63/113.36 emptyset)))))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X573, 112.63/113.36 X574,X575]: 112.63/113.36 (( 112.63/113.36 subset( 112.63/113.36 X575, 112.63/113.36 cartprod( 112.63/113.36 X573,X574)) & 112.63/113.36 ( 112.63/113.36 ![X576]: 112.63/113.36 (in( 112.63/113.36 X576,X573) => 112.63/113.36 (?[X577]: 112.63/113.36 (in( 112.63/113.36 X577, 112.63/113.36 dsetconstr( 112.63/113.36 X574, 112.63/113.36 '#ll_2'( 112.63/113.36 X576,X575))) & 112.63/113.36 (dsetconstr( 112.63/113.36 X574, 112.63/113.36 '#ll_2'( 112.63/113.36 X576,X575)) = 112.63/113.36 setadjoin( 112.63/113.36 X577, 112.63/113.36 emptyset))))))) => 112.63/113.36 (![X578]: 112.63/113.36 (in( 112.63/113.36 X578,X573) => 112.63/113.36 in( 112.63/113.36 setunion( 112.63/113.36 dsetconstr( 112.63/113.36 X574, 112.63/113.36 '#ll_2'( 112.63/113.36 X578,X575))), 112.63/113.36 X574))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X579, 112.63/113.36 X580,X581]: 112.63/113.36 (( 112.63/113.36 subset( 112.63/113.36 X581, 112.63/113.36 cartprod( 112.63/113.36 X579,X580)) & 112.63/113.36 ( 112.63/113.36 ![X582]: 112.63/113.36 (in( 112.63/113.36 X582,X579) => 112.63/113.36 (?[X583]: 112.63/113.36 (in( 112.63/113.36 X583, 112.63/113.36 dsetconstr( 112.63/113.36 X580, 112.63/113.36 '#ll_2'( 112.63/113.36 X582,X581))) & 112.63/113.36 (dsetconstr( 112.63/113.36 X580, 112.63/113.36 '#ll_2'( 112.63/113.36 X582,X581)) = 112.63/113.36 setadjoin( 112.63/113.36 X583, 112.63/113.36 emptyset))))))) => 112.63/113.36 (![X584]: 112.63/113.36 (in( 112.63/113.36 X584,X579) => 112.63/113.36 in( 112.63/113.36 setunion( 112.63/113.36 dsetconstr( 112.63/113.36 X580, 112.63/113.36 '#ll_2'( 112.63/113.36 X584,X581))), 112.63/113.36 X580))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X585, 112.63/113.36 X586,X587]: 112.63/113.36 (in( 112.63/113.36 X587, 112.63/113.36 funcSet( 112.63/113.36 X585,X586)) => 112.63/113.36 (subset( 112.63/113.36 X587, 112.63/113.36 cartprod( 112.63/113.36 X585,X586)) & 112.63/113.36 (![X588]: 112.63/113.36 (in( 112.63/113.36 X588,X585) => 112.63/113.36 (?[X589]: 112.63/113.36 (in( 112.63/113.36 X589, 112.63/113.36 dsetconstr( 112.63/113.36 X586, 112.63/113.36 '#ll_2'( 112.63/113.36 X588,X587))) & 112.63/113.36 (dsetconstr( 112.63/113.36 X586, 112.63/113.36 '#ll_2'( 112.63/113.36 X588,X587)) = 112.63/113.36 setadjoin( 112.63/113.36 X589, 112.63/113.36 emptyset))))))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X590, 112.63/113.36 X591,X592]: 112.63/113.36 (in( 112.63/113.36 X592, 112.63/113.36 funcSet( 112.63/113.36 X590,X591)) => 112.63/113.36 (![X593]: 112.63/113.36 (in( 112.63/113.36 X593,X590) => 112.63/113.36 in( 112.63/113.36 setunion( 112.63/113.36 dsetconstr( 112.63/113.36 X591, 112.63/113.36 '#ll_2'( 112.63/113.36 X593,X592))), 112.63/113.36 X591))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X594, 112.63/113.36 X595,X596]: 112.63/113.36 (( 112.63/113.36 subset( 112.63/113.36 X596, 112.63/113.36 cartprod( 112.63/113.36 X594,X595)) & 112.63/113.36 ( 112.63/113.36 ![X597]: 112.63/113.36 (in( 112.63/113.36 X597,X594) => 112.63/113.36 (?[X598]: 112.63/113.36 (in( 112.63/113.36 X598, 112.63/113.36 dsetconstr( 112.63/113.36 X595, 112.63/113.36 '#ll_2'( 112.63/113.36 X597,X596))) & 112.63/113.36 (dsetconstr( 112.63/113.36 X595, 112.63/113.36 '#ll_2'( 112.63/113.36 X597,X596)) = 112.63/113.36 setadjoin( 112.63/113.36 X598, 112.63/113.36 emptyset))))))) => 112.63/113.36 in( 112.63/113.36 X596, 112.63/113.36 funcSet( 112.63/113.36 X594,X595)))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X599, 112.63/113.36 X600, 112.63/113.36 X601:( 112.63/113.36 $i > $i)]: 112.63/113.36 (( 112.63/113.36 ![X602]: 112.63/113.36 (in( 112.63/113.36 X602,X599) => 112.63/113.36 in( 112.63/113.36 X601( 112.63/113.36 X602), 112.63/113.36 X600))) => 112.63/113.36 (subset( 112.63/113.36 dpsetconstr( 112.63/113.36 X599, 112.63/113.36 X600, 112.63/113.36 '#ll_0'( 112.63/113.36 X601)), 112.63/113.36 cartprod( 112.63/113.36 X599,X600)) & 112.63/113.36 (![X603]: 112.63/113.36 (in( 112.63/113.36 X603,X599) => 112.63/113.36 (?[X604]: 112.63/113.36 (in( 112.63/113.36 X604, 112.63/113.36 dsetconstr( 112.63/113.36 X600, 112.63/113.36 '#ll_1'( 112.63/113.36 X603, 112.63/113.36 X601, 112.63/113.36 X600,X599))) & 112.63/113.36 (dsetconstr( 112.63/113.36 X600, 112.63/113.36 '#ll_1'( 112.63/113.36 X603, 112.63/113.36 X601, 112.63/113.36 X600,X599)) = 112.63/113.36 setadjoin( 112.63/113.36 X604, 112.63/113.36 emptyset))))))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X605, 112.63/113.36 X606, 112.63/113.36 X607:( 112.63/113.36 $i > $i)]: 112.63/113.36 (( 112.63/113.36 ![X608]: 112.63/113.36 (in( 112.63/113.36 X608,X605) => 112.63/113.36 in( 112.63/113.36 X607( 112.63/113.36 X608), 112.63/113.36 X606))) => 112.63/113.36 (subset( 112.63/113.36 dpsetconstr( 112.63/113.36 X605, 112.63/113.36 X606, 112.63/113.36 '#ll_0'( 112.63/113.36 X607)), 112.63/113.36 cartprod( 112.63/113.36 X605,X606)) & 112.63/113.36 (![X609]: 112.63/113.36 (in( 112.63/113.36 X609,X605) => 112.63/113.36 (?[X610]: 112.63/113.36 (in( 112.63/113.36 X610, 112.63/113.36 dsetconstr( 112.63/113.36 X606, 112.63/113.36 '#ll_1'( 112.63/113.36 X609, 112.63/113.36 X607, 112.63/113.36 X606,X605))) & 112.63/113.36 (dsetconstr( 112.63/113.36 X606, 112.63/113.36 '#ll_1'( 112.63/113.36 X609, 112.63/113.36 X607, 112.63/113.36 X606,X605)) = 112.63/113.36 setadjoin( 112.63/113.36 X610, 112.63/113.36 emptyset))))))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X611, 112.63/113.36 X612, 112.63/113.36 X613:( 112.63/113.36 $i > $i)]: 112.63/113.36 (( 112.63/113.36 ![X614]: 112.63/113.36 (in( 112.63/113.36 X614,X611) => 112.63/113.36 in( 112.63/113.36 X613( 112.63/113.36 X614), 112.63/113.36 X612))) => 112.63/113.36 in( 112.63/113.36 dpsetconstr( 112.63/113.36 X611, 112.63/113.36 X612, 112.63/113.36 '#ll_0'( 112.63/113.36 X613)), 112.63/113.36 funcSet( 112.63/113.36 X611,X612)))) => 112.63/113.36 ( 112.63/113.36 ![X615, 112.63/113.36 X616,X617]: 112.63/113.36 (subset( 112.63/113.36 X617, 112.63/113.36 cartprod( 112.63/113.36 X615,X616)) => 112.63/113.36 (![X618:( 112.63/113.36 $i > $o)]: 112.63/113.36 (( 112.63/113.36 ![X619]: 112.63/113.36 (in( 112.63/113.36 X619,X615) => 112.63/113.36 (![X620]: 112.63/113.36 (in( 112.63/113.36 X620,X616) => 112.63/113.36 (in( 112.63/113.36 kpair( 112.63/113.36 X619,X620), 112.63/113.36 X617) => 112.63/113.36 X618( 112.63/113.36 kpair( 112.63/113.36 X619,X620))))))) => 112.63/113.36 (![X621]: 112.63/113.36 (in( 112.63/113.36 X621,X617) => 112.63/113.36 X618( 112.63/113.36 X621))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 112.63/113.36 tff(zf_stmt_1, type, zip_tseitin5 : ($i * $i > $o) > $o). 112.63/113.36 tff(zf_stmt_2, axiom, 112.63/113.36 (zip_tseitin5(X211,X207) <=> 112.63/113.36 ((![X212]: zip_tseitin4(X212,X211,X207)) & X207(X211)))). 112.63/113.36 tff(zf_stmt_3, type, zip_tseitin4 : ($i * $i * $i > $o) > $o). 112.63/113.36 tff(zf_stmt_4, axiom, 112.63/113.36 (zip_tseitin4(X212,X211,X207) <=> (X207(X212) => (X211 = X212)))). 112.63/113.36 tff(zf_stmt_5, type, zip_tseitin3 : ($i * $i * $i * ($i * $i) > $o) > $o). 112.63/113.36 tff(zf_stmt_6, axiom, 112.63/113.36 (zip_tseitin3(X26,X25,X20,X19) <=> (X19(X26,X25) & in(X26,X20)))). 112.63/113.36 tff(zf_stmt_7, type, zip_tseitin2 : ($i * $i * $i) > $o). 112.63/113.36 tff(zf_stmt_8, axiom, 112.63/113.36 (zip_tseitin2(X14,X13,X12) <=> (in(X14,X12) & in(X13,X14)))). 112.63/113.36 tff(zf_stmt_9, type, zip_tseitin1 : ($i * $i * $i) > $o). 112.63/113.36 tff(zf_stmt_10, axiom, 112.63/113.36 (zip_tseitin1(X11,X10,X9) <=> (in(X11,X10) => in(X11,X9)))). 112.63/113.36 tff(zf_stmt_11, type, zip_tseitin0 : ($i * $i * $i) > $o). 112.63/113.36 tff(zf_stmt_12, axiom, (zip_tseitin0(X8,X7,X6) <=> (in(X8,X7) | (X8 = X6)))). 112.63/113.36 tff(zf_stmt_13, conjecture, 112.63/113.36 ((![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))) => 112.63/113.36 ((![X5]: (~in(X5,emptyset))) => 112.63/113.36 ((![X6,X7,X8]: (in(X8,setadjoin(X6,X7)) <=> zip_tseitin0(X8,X7,X6))) => 112.63/113.36 ((![X9,X10]: 112.63/113.36 (in(X10,powerset(X9)) <=> (![X11]: zip_tseitin1(X11,X10,X9)))) => 112.63/113.36 ((![X12,X13]: 112.63/113.36 (in(X13,setunion(X12)) <=> (?[X14]: zip_tseitin2(X14,X13,X12)))) => 112.63/113.36 (in(emptyset,omega) => 112.63/113.36 ((![X15]: (in(X15,omega) => in(setadjoin(X15,X15),omega))) => 112.63/113.36 ((![X16]: 112.63/113.36 (((![X17]: 112.63/113.36 ((in(X17,X16) & in(X17,omega)) => 112.63/113.36 in(setadjoin(X17,X17),X16))) & 112.63/113.36 in(emptyset,X16)) => 112.63/113.36 (![X18]: (in(X18,omega) => in(X18,X16))))) => 112.63/113.36 ((![X19:(($i * $i) > $o),X20]: 112.63/113.36 ((![X21]: 112.63/113.36 (in(X21,X20) => 112.63/113.36 (?[X22]: 112.63/113.36 ((![X23]: (X19(X21,X23) => (X22 = X23))) & X19(X21,X22))))) => 112.63/113.36 (?[X24]: 112.63/113.36 (![X25]: 112.63/113.36 (in(X25,X24) <=> (?[X26]: zip_tseitin3(X26,X25,X20,X19))))))) => 112.63/113.36 ((![X27]: 112.63/113.36 ((?[X28]: in(X28,X27)) => 112.63/113.36 (?[X29]: 112.63/113.36 ((~(?[X30]: (in(X30,X27) & in(X30,X29)))) & in(X29,X27))))) => 112.63/113.36 ((![X31]: 112.63/113.36 (?[X32]: 112.63/113.36 ((![X33]: 112.63/113.36 (((?[X34]: in(X34,X33)) & 112.63/113.36 (![X35]: (in(X35,X33) => in(X35,X31)))) => 112.63/113.36 (?[X36,X37]: 112.63/113.36 ((![X38]: 112.63/113.36 (in(X38,X32) => 112.63/113.36 (in(X37,X38) | 112.63/113.36 (![X39]: (in(X39,X38) => in(X39,X36)))))) & 112.63/113.36 (~(?[X40]: (in(X40,X33) & in(X40,X36)))) & 112.63/113.36 in(X37,X33) & in(X36,X32))))) & 112.63/113.36 (![X41,X42]: 112.63/113.36 ((in(X42,X32) & in(X41,X32)) => 112.63/113.36 ((![X43]: (in(X43,X42) => in(X43,X41))) | 112.63/113.36 (![X44]: (in(X44,X41) => in(X44,X42)))))) & 112.63/113.36 (![X45,X46]: 112.63/113.36 ((in(X46,X31) & in(X45,X31)) => 112.63/113.36 ((![X47]: 112.63/113.36 (in(X47,X32) => (in(X45,X47) <=> in(X46,X47)))) => 112.63/113.36 (X45 = X46)))) & 112.63/113.36 (![X48]: 112.63/113.36 (in(X48,X32) => (![X49]: (in(X49,X48) => in(X49,X31)))))))) => 112.63/113.36 ((![X50:($i > $o)]: 112.63/113.36 ((?[X51]: ((![X52]: (X50(X52) => (X51 = X52))) & X50(X51))) => 112.63/113.36 X50(descr('#ll_6'(X50))))) => 112.63/113.36 ((![X53,X54:($i > $o),X55]: 112.63/113.36 (in(X55,X53) => 112.63/113.36 (X54(X55) => in(X55,dsetconstr(X53,'#ll_6'(X54)))))) => 112.63/113.36 ((![X56,X57:($i > $o),X58]: 112.63/113.36 (in(X58,dsetconstr(X56,'#ll_6'(X57))) => in(X58,X56))) => 112.63/113.36 ((![X59,X60:($i > $o),X61]: 112.63/113.36 (in(X61,dsetconstr(X59,'#ll_6'(X60))) => X60(X61))) => 112.63/113.36 ((![X62:($i > $o)]: 112.63/113.36 ((?[X63]: 112.63/113.36 ((![X64]: (X62(X64) => (X63 = X64))) & X62(X63))) => 112.63/113.36 (?[X65]: 112.63/113.36 ((![X66]: (X62(X66) => (X65 = X66))) & X62(X65))))) => 112.63/113.36 ((![X67:$o,X68]: (in(X68,prop2set(X67)) => X67)) => 112.63/113.36 ((![X69]: (in(X69,emptyset) => (![X70:$o]: X70))) => 112.63/113.36 ((![X71]: (in(X71,emptyset) => $false)) => 112.63/113.36 ((![X72]: (~in(X72,emptyset))) => 112.63/113.36 ((![X73:($i > $o)]: 112.63/113.36 ((?[X74]: 112.63/113.36 ((![X75]: (X73(X75) => (X74 = X75))) & X73(X74))) => 112.63/113.36 (?[X76]: X73(X76)))) => 112.63/113.36 ((![X77,X78]: 112.63/113.36 ((![X79]: (in(X79,X77) => in(X79,X78))) => 112.63/113.36 ((![X80]: (in(X80,X78) => in(X80,X77))) => 112.63/113.36 (X77 = X78)))) => 112.63/113.36 ((![X81]: 112.63/113.36 ((![X82]: (~in(X82,X81))) => (X81 = emptyset))) => 112.63/113.36 ((![X83]: 112.63/113.36 ((![X84]: (~in(X84,X83))) => (X83 = emptyset))) => 112.63/113.36 ((![X85,X86:($i > $o),X87]: 112.63/113.36 (in(X87,X85) => 112.63/113.36 (in(X87,dsetconstr(X85,'#ll_6'(X86))) <=> 112.63/113.36 X86(X87)))) => 112.63/113.36 ((![X88]: 112.63/113.36 ((X88 != emptyset) => (?[X89]: in(X89,X88)))) => 112.63/113.36 ((![X90,X91:($i > $o),X92]: 112.63/113.36 (in(X92,X90) => 112.63/113.36 (X91(X92) => 112.63/113.36 (dsetconstr(X90,'#ll_6'(X91)) != emptyset)))) => 112.63/113.36 ((![X93]: 112.63/113.36 ((?[X94]: in(X94,X93)) => (X93 != emptyset))) => 112.63/113.36 ((![X95,X96]: in(X95,setadjoin(X95,X96))) => 112.63/113.36 (in(emptyset,setadjoin(emptyset,emptyset)) => 112.63/113.36 ((![X97,X98,X99]: 112.63/113.36 (in(X99,X98) => 112.63/113.36 in(X99,setadjoin(X97,X98)))) => 112.63/113.36 ((![X100,X101,X102]: 112.63/113.36 (in(X102,setadjoin(X100,X101)) => 112.63/113.36 (![X103:$o]: 112.63/113.36 (((X102 = X100) => X103) => 112.63/113.36 ((in(X102,X101) => X103) => X103))))) => 112.63/113.36 ((![X104,X105,X106]: 112.63/113.36 (in(X106,setadjoin(X104,X105)) => 112.63/113.36 (in(X106,X105) | (X106 = X104)))) => 112.63/113.36 ((![X107]: 112.63/113.36 (dsetconstr(X107,'#ll_7') = X107)) => 112.63/113.36 ((![X108,X109]: 112.63/113.36 ((![X110]: 112.63/113.36 (in(X110,X109) => in(X110,X108))) => 112.63/113.36 in(X109,powerset(X108)))) => 112.63/113.36 ((![X111]: in(emptyset,powerset(X111))) => 112.63/113.36 ((![X112]: in(emptyset,powerset(X112))) => 112.63/113.36 ((![X113,X114,X115]: 112.63/113.36 (in(X114,powerset(X113)) => 112.63/113.36 (in(X115,X114) => in(X115,X113)))) => 112.63/113.36 ((![X116,X117,X118]: 112.63/113.36 (in(X117,X118) => 112.63/113.36 (in(X118,X116) => 112.63/113.36 in(X117,setunion(X116))))) => 112.63/113.36 ((![X119,X120]: 112.63/113.36 (in(X120,setunion(X119)) => 112.63/113.36 (![X121:$o]: 112.63/113.36 ((![X122]: 112.63/113.36 (in(X120,X122) => 112.63/113.36 (in(X122,X119) => X121))) => 112.63/113.36 X121)))) => 112.63/113.36 ((![X123,X124]: 112.63/113.36 (in(X124,X123) => 112.63/113.36 in(X124, 112.63/113.36 powerset(setunion(X123))))) => 112.63/113.36 ((![X125:($i > $o)]: 112.63/113.36 ((?[X126]: 112.63/113.36 ((![X127]: 112.63/113.36 (X125(X127) => 112.63/113.36 (X126 = X127))) & 112.63/113.36 X125(X126))) => 112.63/113.36 (?[X128]: 112.63/113.36 (![X129]: 112.63/113.36 (X125(X129) <=> 112.63/113.36 (X129 = X128)))))) => 112.63/113.36 ((![X130]: 112.63/113.36 ((X130 != emptyset) => 112.63/113.36 (?[X131]: in(X131,X130)))) => 112.63/113.36 ((![X132,X133]: 112.63/113.36 (in(X132, 112.63/113.36 setadjoin(X133,emptyset)) => 112.63/113.36 (X132 = X133))) => 112.63/113.36 ((![X134,X135]: 112.63/113.36 ((X134 != X135) => 112.63/113.36 (~ 112.63/113.36 in(X135, 112.63/113.36 setadjoin(X134, 112.63/113.36 emptyset))))) => 112.63/113.36 ((![X136,X137]: 112.63/113.36 ((X136 = X137) => 112.63/113.36 in(X136, 112.63/113.36 setadjoin(X137, 112.63/113.36 emptyset)))) => 112.63/113.36 ((![X138,X139]: 112.63/113.36 (in(X138, 112.63/113.36 setadjoin(X139, 112.63/113.36 emptyset)) => 112.63/113.36 in(X139, 112.63/113.36 setadjoin(X138, 112.63/113.36 emptyset)))) => 112.63/113.36 ((![X140,X141,X142]: 112.63/113.36 (in(X142, 112.63/113.36 setadjoin(X140, 112.63/113.36 setadjoin( 112.63/113.36 X141, 112.63/113.36 emptyset))) => 112.63/113.36 ((X142 = X141) | 112.63/113.36 (X142 = X140)))) => 112.63/113.36 ((![X143,X144]: 112.63/113.36 in(X143, 112.63/113.36 setadjoin(X143, 112.63/113.36 setadjoin( 112.63/113.36 X144, 112.63/113.36 emptyset)))) => 112.63/113.36 ((![X145,X146]: 112.63/113.36 in(X146, 112.63/113.36 setadjoin(X145, 112.63/113.36 setadjoin( 112.63/113.36 X146, 112.63/113.36 emptyset)))) => 112.63/113.36 ((![X147,X148:($i > $o)]: 112.63/113.36 ((?[X149]: 112.63/113.36 (X148(X149) & 112.63/113.36 in(X149,X147))) => 112.63/113.36 ((dsetconstr( 112.63/113.36 X147,'#ll_6'(X148)) = 112.63/113.36 emptyset) => 112.63/113.36 $false))) => 112.63/113.36 ((![X150:($i > $o),X151]: 112.63/113.36 (in(X151,emptyset) => 112.63/113.36 X150(X151))) => 112.63/113.36 ((![X152,X153:($i > $o)]: 112.63/113.36 ((~ 112.63/113.36 (![X154]: 112.63/113.36 (in(X154,X152) => 112.63/113.36 X153(X154)))) => 112.63/113.36 (?[X155]: 112.63/113.36 ((~X153(X155)) & 112.63/113.36 in(X155,X152))))) => 112.63/113.36 ((![X156, 112.63/113.36 X157:($i > $o)]: 112.63/113.36 ((![X158]: 112.63/113.36 (in(X158,X156) => 112.63/113.36 (~X157(X158)))) => 112.63/113.36 (~ 112.63/113.36 (?[X159]: 112.63/113.36 (X157(X159) & 112.63/113.36 in( 112.63/113.36 X159,X156)))))) => 112.63/113.36 ((![X160, 112.63/113.36 X161:($i > $o)]: 112.63/113.36 ((~ 112.63/113.36 (?[X162]: 112.63/113.36 (X161(X162) & 112.63/113.36 in( 112.63/113.36 X162,X160)))) => 112.63/113.36 (![X163]: 112.63/113.36 (in(X163,X160) => 112.63/113.36 (~X161(X163)))))) => 112.63/113.36 ((![X164, 112.63/113.36 X165:($i > $o)]: 112.63/113.36 ((?[X166]: 112.63/113.36 ((~ 112.63/113.36 X165( 112.63/113.36 X166)) & 112.63/113.36 in( 112.63/113.36 X166,X164))) => 112.63/113.36 (~ 112.63/113.36 (![X167]: 112.63/113.36 (in( 112.63/113.36 X167,X164) => 112.63/113.36 X165( 112.63/113.36 X167)))))) => 112.63/113.36 ((![X168:$o]: 112.63/113.36 (X168 => 112.63/113.36 in(emptyset, 112.63/113.36 prop2set( 112.63/113.36 X168)))) => 112.63/113.36 ((![X169:$o]: 112.63/113.36 (X169 => 112.63/113.36 set2prop( 112.63/113.36 prop2set( 112.63/113.36 X169)))) => 112.63/113.36 ((![X170, 112.63/113.36 X171:( 112.63/113.36 $i > $o)]: 112.63/113.36 ((~ 112.63/113.36 (?[X172]: 112.63/113.36 (X171( 112.63/113.36 X172) & 112.63/113.36 in( 112.63/113.36 X172,X170)))) => 112.63/113.36 (![X173]: 112.63/113.36 ( 112.63/113.36 in( 112.63/113.36 X173,X170) => 112.63/113.36 ( 112.63/113.36 ~ 112.63/113.36 X171( 112.63/113.36 X173)))))) => 112.63/113.36 ((![X174, 112.63/113.36 X175:( 112.63/113.36 $i > $o)]: 112.63/113.36 ((~ 112.63/113.36 ( 112.63/113.36 ![X176]: 112.63/113.36 (in( 112.63/113.36 X176,X174) => 112.63/113.36 X175( 112.63/113.36 X176)))) => 112.63/113.36 (?[X177]: 112.63/113.36 (( 112.63/113.36 ~ 112.63/113.36 X175( 112.63/113.36 X177)) & 112.63/113.36 in( 112.63/113.36 X177,X174))))) => 112.63/113.36 ((![X178:( 112.63/113.36 $i > $o)]: 112.63/113.36 ((?[X179]: 112.63/113.36 (( 112.63/113.36 ![X180]: 112.63/113.36 (X178( 112.63/113.36 X180) => 112.63/113.36 (X179 = 112.63/113.36 X180))) & 112.63/113.36 X178( 112.63/113.36 X179))) => 112.63/113.36 (?[X181]: 112.63/113.36 (( 112.63/113.36 ![X182]: 112.63/113.36 (X178( 112.63/113.36 X182) => 112.63/113.36 (X181 = 112.63/113.36 X182))) & 112.63/113.36 X178( 112.63/113.36 X181))))) => 112.63/113.36 ((![X183:( 112.63/113.36 $i > $o)]: 112.63/113.36 (( 112.63/113.36 ?[X184]: 112.63/113.36 X183( 112.63/113.36 X184)) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X185, 112.63/113.36 X186]: 112.63/113.36 (X183( 112.63/113.36 X185) => 112.63/113.36 (X183( 112.63/113.36 X186) => 112.63/113.36 (X185 = 112.63/113.36 X186)))) => 112.63/113.36 ( 112.63/113.36 ?[X187]: 112.63/113.36 (( 112.63/113.36 ![X188]: 112.63/113.36 (X183( 112.63/113.36 X188) => 112.63/113.36 (X187 = 112.63/113.36 X188))) & 112.63/113.36 X183( 112.63/113.36 X187)))))) => 112.63/113.36 ((![X189:( 112.63/113.36 $i > $o)]: 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ?[X190]: 112.63/113.36 (![X191]: 112.63/113.36 (X189( 112.63/113.36 X191) <=> 112.63/113.36 (X191 = 112.63/113.36 X190)))) => 112.63/113.36 ( 112.63/113.36 ?[X192]: 112.63/113.36 (( 112.63/113.36 ![X193]: 112.63/113.36 (X189( 112.63/113.36 X193) => 112.63/113.36 (X192 = 112.63/113.36 X193))) & 112.63/113.36 X189( 112.63/113.36 X192))))) => 112.63/113.36 ((![X194, 112.63/113.36 X195]: 112.63/113.36 (( 112.63/113.36 X194 = 112.63/113.36 X195) => 112.63/113.36 (![X196, 112.63/113.36 X197]: 112.63/113.36 (( 112.63/113.36 X196 = 112.63/113.36 X197) => 112.63/113.36 (in( 112.63/113.36 X196,X194) => 112.63/113.36 in( 112.63/113.36 X197,X195)))))) => 112.63/113.36 ((![X198, 112.63/113.36 X199]: 112.63/113.36 (( 112.63/113.36 X198 = 112.63/113.36 X199) => 112.63/113.36 (![X200, 112.63/113.36 X201]: 112.63/113.36 (( 112.63/113.36 X200 = 112.63/113.36 X201) => 112.63/113.36 (in( 112.63/113.36 X200,X198) <=> 112.63/113.36 in( 112.63/113.36 X201,X199)))))) => 112.63/113.36 (( 112.63/113.36 ![X202:( 112.63/113.36 $i > $o)]: 112.63/113.36 (( 112.63/113.36 ?[X203]: 112.63/113.36 (( 112.63/113.36 ![X204]: 112.63/113.36 (X202( 112.63/113.36 X204) => 112.63/113.36 (X203 = 112.63/113.36 X204))) & 112.63/113.36 X202( 112.63/113.36 X203))) => 112.63/113.36 (![X205, 112.63/113.36 X206]: 112.63/113.36 (X202( 112.63/113.36 X205) => 112.63/113.36 (X202( 112.63/113.36 X206) => 112.63/113.36 (X205 = 112.63/113.36 X206)))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X207:( 112.63/113.36 $i > $o), 112.63/113.36 X208:( 112.63/113.36 $i > $o)]: 112.63/113.36 (( 112.63/113.36 ![X209, 112.63/113.36 X210]: 112.63/113.36 (( 112.63/113.36 X209 = 112.63/113.36 X210) => 112.63/113.36 (X207( 112.63/113.36 X209) <=> 112.63/113.36 X208( 112.63/113.36 X210)))) => 112.63/113.36 (( 112.63/113.36 ?[X211]: 112.63/113.36 zip_tseitin5( 112.63/113.36 X211,X207)) <=> 112.63/113.36 (?[X213]: 112.63/113.36 zip_tseitin5( 112.63/113.36 X213,X208))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 emptyset = 112.63/113.36 emptyset) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X215, 112.63/113.36 X216]: 112.63/113.36 (( 112.63/113.36 X215 = 112.63/113.36 X216) => 112.63/113.36 (![X217, 112.63/113.36 X218]: 112.63/113.36 (( 112.63/113.36 X217 = 112.63/113.36 X218) => 112.63/113.36 (setadjoin( 112.63/113.36 X215,X217) = 112.63/113.36 setadjoin( 112.63/113.36 X216,X218)))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X219, 112.63/113.36 X220]: 112.63/113.36 (( 112.63/113.36 X219 = 112.63/113.36 X220) => 112.63/113.36 (powerset( 112.63/113.36 X219) = 112.63/113.36 powerset( 112.63/113.36 X220)))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X221, 112.63/113.36 X222]: 112.63/113.36 (( 112.63/113.36 X221 = 112.63/113.36 X222) => 112.63/113.36 (setunion( 112.63/113.36 X221) = 112.63/113.36 setunion( 112.63/113.36 X222)))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 omega = 112.63/113.36 omega) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X223:( 112.63/113.36 $i > $o)]: 112.63/113.36 (( 112.63/113.36 ?[X224]: 112.63/113.36 (( 112.63/113.36 ![X225]: 112.63/113.36 (X223( 112.63/113.36 X225) => 112.63/113.36 (X224 = 112.63/113.36 X225))) & 112.63/113.36 X223( 112.63/113.36 X224))) => 112.63/113.36 (![X226, 112.63/113.36 X227]: 112.63/113.36 (X223( 112.63/113.36 X226) => 112.63/113.36 (X223( 112.63/113.36 X227) => 112.63/113.36 (X226 = 112.63/113.36 X227)))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X228:( 112.63/113.36 $i > $o), 112.63/113.36 X229:( 112.63/113.36 $i > $o)]: 112.63/113.36 (( 112.63/113.36 ![X230, 112.63/113.36 X231]: 112.63/113.36 (( 112.63/113.36 X230 = 112.63/113.36 X231) => 112.63/113.36 (X228( 112.63/113.36 X230) <=> 112.63/113.36 X229( 112.63/113.36 X231)))) => 112.63/113.36 (( 112.63/113.36 ?[X232]: 112.63/113.36 (( 112.63/113.36 ![X233]: 112.63/113.36 (X228( 112.63/113.36 X233) => 112.63/113.36 (X232 = 112.63/113.36 X233))) & 112.63/113.36 X228( 112.63/113.36 X232))) => 112.63/113.36 (( 112.63/113.36 ?[X234]: 112.63/113.36 (( 112.63/113.36 ![X235]: 112.63/113.36 (X229( 112.63/113.36 X235) => 112.63/113.36 (X234 = 112.63/113.36 X235))) & 112.63/113.36 X229( 112.63/113.36 X234))) => 112.63/113.36 (descr( 112.63/113.36 '#ll_6'( 112.63/113.36 X228)) = 112.63/113.36 descr( 112.63/113.36 '#ll_6'( 112.63/113.36 X229))))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X236, 112.63/113.36 X237]: 112.63/113.36 (( 112.63/113.36 X236 = 112.63/113.36 X237) => 112.63/113.36 (![X238:( 112.63/113.36 $i > $o), 112.63/113.36 X239:( 112.63/113.36 $i > $o)]: 112.63/113.36 (( 112.63/113.36 ![X240]: 112.63/113.36 (in( 112.63/113.36 X240,X236) => 112.63/113.36 (![X241]: 112.63/113.36 (in( 112.63/113.36 X241,X237) => 112.63/113.36 (( 112.63/113.36 X240 = 112.63/113.36 X241) => 112.63/113.36 (X238( 112.63/113.36 X240) <=> 112.63/113.36 X239( 112.63/113.36 X241))))))) => 112.63/113.36 (dsetconstr( 112.63/113.36 X236, 112.63/113.36 '#ll_6'( 112.63/113.36 X238)) = 112.63/113.36 dsetconstr( 112.63/113.36 X237, 112.63/113.36 '#ll_6'( 112.63/113.36 X239))))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X242, 112.63/113.36 X243]: 112.63/113.36 (( 112.63/113.36 ![X244]: 112.63/113.36 (in( 112.63/113.36 X244,X242) => 112.63/113.36 in( 112.63/113.36 X244,X243))) => 112.63/113.36 subset( 112.63/113.36 X242,X243))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X245, 112.63/113.36 X246]: 112.63/113.36 (( 112.63/113.36 X245 = 112.63/113.36 X246) => 112.63/113.36 subset( 112.63/113.36 X246,X245))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X247, 112.63/113.36 X248]: 112.63/113.36 (( 112.63/113.36 X247 = 112.63/113.36 X248) => 112.63/113.36 subset( 112.63/113.36 X247,X248))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X249, 112.63/113.36 X250]: 112.63/113.36 (( 112.63/113.36 ![X251]: 112.63/113.36 (in( 112.63/113.36 X251,X249) => 112.63/113.36 in( 112.63/113.36 X251,X250))) => 112.63/113.36 subset( 112.63/113.36 X249,X250))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X252]: 112.63/113.36 subset( 112.63/113.36 emptyset, 112.63/113.36 X252)) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X253, 112.63/113.36 X254,X255]: 112.63/113.36 (subset( 112.63/113.36 X253,X254) => 112.63/113.36 (in( 112.63/113.36 X255,X253) => 112.63/113.36 in( 112.63/113.36 X255,X254)))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X256, 112.63/113.36 X257,X258]: 112.63/113.36 (subset( 112.63/113.36 X256,X257) => 112.63/113.36 (( 112.63/113.36 ~ 112.63/113.36 in( 112.63/113.36 X258,X257)) => 112.63/113.36 (~ 112.63/113.36 in( 112.63/113.36 X258,X256))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X259, 112.63/113.36 X260,X261]: 112.63/113.36 (in( 112.63/113.36 X261,X259) => 112.63/113.36 (( 112.63/113.36 ~ 112.63/113.36 in( 112.63/113.36 X261,X260)) => 112.63/113.36 (~ 112.63/113.36 subset( 112.63/113.36 X259,X260))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X262, 112.63/113.36 X263]: 112.63/113.36 (( 112.63/113.36 ~ 112.63/113.36 subset( 112.63/113.36 X262,X263)) => 112.63/113.36 (X262 != 112.63/113.36 X263))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X264, 112.63/113.36 X265,X266]: 112.63/113.36 (in( 112.63/113.36 X266,X264) => 112.63/113.36 (( 112.63/113.36 ~ 112.63/113.36 in( 112.63/113.36 X266,X265)) => 112.63/113.36 (X264 != 112.63/113.36 X265)))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X267]: 112.63/113.36 subset( 112.63/113.36 X267,X267)) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X268, 112.63/113.36 X269,X270]: 112.63/113.36 (subset( 112.63/113.36 X268,X269) => 112.63/113.36 (subset( 112.63/113.36 X269,X270) => 112.63/113.36 subset( 112.63/113.36 X268,X270)))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X271, 112.63/113.36 X272]: 112.63/113.36 subset( 112.63/113.36 X272, 112.63/113.36 setadjoin( 112.63/113.36 X271,X272))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X273, 112.63/113.36 X274,X275]: 112.63/113.36 (subset( 112.63/113.36 X273,X275) => 112.63/113.36 subset( 112.63/113.36 X273, 112.63/113.36 setadjoin( 112.63/113.36 X274,X275)))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X276, 112.63/113.36 X277]: 112.63/113.36 (subset( 112.63/113.36 X276,X277) => 112.63/113.36 in( 112.63/113.36 X276, 112.63/113.36 powerset( 112.63/113.36 X277)))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X278, 112.63/113.36 X279]: 112.63/113.36 (subset( 112.63/113.36 X278,X279) => 112.63/113.36 (subset( 112.63/113.36 X279,X278) => 112.63/113.36 (X278 = 112.63/113.36 X279)))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X280]: 112.63/113.36 (subset( 112.63/113.36 X280, 112.63/113.36 emptyset) => 112.63/113.36 (X280 = 112.63/113.36 emptyset))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X281, 112.63/113.36 X282]: 112.63/113.36 (subset( 112.63/113.36 X282,X281) => 112.63/113.36 in( 112.63/113.36 X282, 112.63/113.36 powerset( 112.63/113.36 X281)))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X283, 112.63/113.36 X284]: 112.63/113.36 (in( 112.63/113.36 X284, 112.63/113.36 powerset( 112.63/113.36 X283)) => 112.63/113.36 subset( 112.63/113.36 X284,X283))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X285]: 112.63/113.36 in( 112.63/113.36 X285, 112.63/113.36 powerset( 112.63/113.36 X285))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X286, 112.63/113.36 X287]: 112.63/113.36 (subset( 112.63/113.36 X286,X287) => 112.63/113.36 subset( 112.63/113.36 powerset( 112.63/113.36 X286), 112.63/113.36 powerset( 112.63/113.36 X287)))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X288, 112.63/113.36 X289:( 112.63/113.36 $i > $o)]: 112.63/113.36 in( 112.63/113.36 dsetconstr( 112.63/113.36 X288, 112.63/113.36 '#ll_6'( 112.63/113.36 X289)), 112.63/113.36 powerset( 112.63/113.36 X288))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X290, 112.63/113.36 X291:( 112.63/113.36 $i > $o)]: 112.63/113.36 subset( 112.63/113.36 dsetconstr( 112.63/113.36 X290, 112.63/113.36 '#ll_6'( 112.63/113.36 X291)), 112.63/113.36 X290)) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X292, 112.63/113.36 X293,X294]: 112.63/113.36 (in( 112.63/113.36 X294,X292) => 112.63/113.36 in( 112.63/113.36 X294, 112.63/113.36 binunion( 112.63/113.36 X292,X293)))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X295, 112.63/113.36 X296]: 112.63/113.36 in( 112.63/113.36 X296, 112.63/113.36 setadjoin( 112.63/113.36 X295, 112.63/113.36 setadjoin( 112.63/113.36 X296, 112.63/113.36 emptyset)))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X297, 112.63/113.36 X298,X299]: 112.63/113.36 (in( 112.63/113.36 X299,X298) => 112.63/113.36 in( 112.63/113.36 X299, 112.63/113.36 binunion( 112.63/113.36 X297,X298)))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X300, 112.63/113.36 X301, 112.63/113.36 X302, 112.63/113.36 X303:$o]: 112.63/113.36 (in( 112.63/113.36 X302, 112.63/113.36 binunion( 112.63/113.36 X300,X301)) => 112.63/113.36 (( 112.63/113.36 in( 112.63/113.36 X302,X300) => 112.63/113.36 X303) => 112.63/113.36 (( 112.63/113.36 in( 112.63/113.36 X302,X301) => 112.63/113.36 X303) => 112.63/113.36 X303)))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X304, 112.63/113.36 X305,X306]: 112.63/113.36 (in( 112.63/113.36 X306, 112.63/113.36 binunion( 112.63/113.36 X304,X305)) => 112.63/113.36 (in( 112.63/113.36 X306,X305) | 112.63/113.36 in( 112.63/113.36 X306,X304)))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X307, 112.63/113.36 X308]: 112.63/113.36 subset( 112.63/113.36 X307, 112.63/113.36 binunion( 112.63/113.36 X307,X308))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X309, 112.63/113.36 X310]: 112.63/113.36 subset( 112.63/113.36 X310, 112.63/113.36 binunion( 112.63/113.36 X309,X310))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X311, 112.63/113.36 X312,X313]: 112.63/113.36 (in( 112.63/113.36 X313,X311) => 112.63/113.36 (in( 112.63/113.36 X313,X312) => 112.63/113.36 in( 112.63/113.36 X313, 112.63/113.36 binintersect( 112.63/113.36 X311,X312))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X314, 112.63/113.36 X315,X316]: 112.63/113.36 (subset( 112.63/113.36 X316,X314) => 112.63/113.36 (subset( 112.63/113.36 X316,X315) => 112.63/113.36 subset( 112.63/113.36 X316, 112.63/113.36 binintersect( 112.63/113.36 X314,X315))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X317, 112.63/113.36 X318,X319]: 112.63/113.36 (in( 112.63/113.36 X319, 112.63/113.36 binintersect( 112.63/113.36 X317,X318)) => 112.63/113.36 in( 112.63/113.36 X319,X317))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X320, 112.63/113.36 X321]: 112.63/113.36 subset( 112.63/113.36 binintersect( 112.63/113.36 X320,X321), 112.63/113.36 X320)) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X322, 112.63/113.36 X323]: 112.63/113.36 (subset( 112.63/113.36 X322,X323) => 112.63/113.36 (binintersect( 112.63/113.36 X322,X323) = 112.63/113.36 X322))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X324, 112.63/113.36 X325]: 112.63/113.36 (( 112.63/113.36 binintersect( 112.63/113.36 X324,X325) = 112.63/113.36 X325) => 112.63/113.36 subset( 112.63/113.36 X325,X324))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X326, 112.63/113.36 X327,X328]: 112.63/113.36 (in( 112.63/113.36 X328, 112.63/113.36 binintersect( 112.63/113.36 X326,X327)) => 112.63/113.36 in( 112.63/113.36 X328,X327))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X329, 112.63/113.36 X330]: 112.63/113.36 (( 112.63/113.36 ~ 112.63/113.36 ( 112.63/113.36 ?[X331]: 112.63/113.36 (in( 112.63/113.36 X331,X330) & 112.63/113.36 in( 112.63/113.36 X331,X329)))) => 112.63/113.36 (binintersect( 112.63/113.36 X329,X330) = 112.63/113.36 emptyset))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X332, 112.63/113.36 X333]: 112.63/113.36 subset( 112.63/113.36 binintersect( 112.63/113.36 X332,X333), 112.63/113.36 X333)) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X334, 112.63/113.36 X335]: 112.63/113.36 (subset( 112.63/113.36 X335,X334) => 112.63/113.36 (binintersect( 112.63/113.36 X334,X335) = 112.63/113.36 X335))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X336, 112.63/113.36 X337]: 112.63/113.36 (( 112.63/113.36 binintersect( 112.63/113.36 X336,X337) = 112.63/113.36 X336) => 112.63/113.36 subset( 112.63/113.36 X336,X337))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X338, 112.63/113.36 X339,X340]: 112.63/113.36 (binintersect( 112.63/113.36 X338, 112.63/113.36 binunion( 112.63/113.36 X339,X340)) = 112.63/113.36 binunion( 112.63/113.36 binintersect( 112.63/113.36 X338,X339), 112.63/113.36 binintersect( 112.63/113.36 X338,X340)))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X341, 112.63/113.36 X342,X343]: 112.63/113.36 (in( 112.63/113.36 X343,X341) => 112.63/113.36 (( 112.63/113.36 ~ 112.63/113.36 in( 112.63/113.36 X343,X342)) => 112.63/113.36 in( 112.63/113.36 X343, 112.63/113.36 setminus( 112.63/113.36 X341,X342))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X344, 112.63/113.36 X345,X346]: 112.63/113.36 (in( 112.63/113.36 X346, 112.63/113.36 setminus( 112.63/113.36 X344,X345)) => 112.63/113.36 in( 112.63/113.36 X346,X344))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X347, 112.63/113.36 X348,X349]: 112.63/113.36 (in( 112.63/113.36 X349, 112.63/113.36 setminus( 112.63/113.36 X347,X348)) => 112.63/113.36 (~ 112.63/113.36 in( 112.63/113.36 X349,X348)))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X350, 112.63/113.36 X351]: 112.63/113.36 (subset( 112.63/113.36 X350,X351) => 112.63/113.36 (setminus( 112.63/113.36 X350,X351) = 112.63/113.36 emptyset))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X352, 112.63/113.36 X353,X354]: 112.63/113.36 (( 112.63/113.36 ~ 112.63/113.36 in( 112.63/113.36 X354, 112.63/113.36 setminus( 112.63/113.36 X352,X353))) => 112.63/113.36 (in( 112.63/113.36 X354,X352) => 112.63/113.36 in( 112.63/113.36 X354,X353)))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X355, 112.63/113.36 X356,X357]: 112.63/113.36 (( 112.63/113.36 ~ 112.63/113.36 in( 112.63/113.36 X357, 112.63/113.36 setminus( 112.63/113.36 X355,X356))) => 112.63/113.36 (( 112.63/113.36 ~ 112.63/113.36 in( 112.63/113.36 X357,X356)) => 112.63/113.36 (~ 112.63/113.36 in( 112.63/113.36 X357,X355))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X358, 112.63/113.36 X359,X360]: 112.63/113.36 (( 112.63/113.36 ~ 112.63/113.36 in( 112.63/113.36 X360,X358)) => 112.63/113.36 (~ 112.63/113.36 in( 112.63/113.36 X360, 112.63/113.36 setminus( 112.63/113.36 X358,X359))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X361, 112.63/113.36 X362,X363]: 112.63/113.36 (in( 112.63/113.36 X363,X362) => 112.63/113.36 (~ 112.63/113.36 in( 112.63/113.36 X363, 112.63/113.36 setminus( 112.63/113.36 X361,X362))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X364, 112.63/113.36 X365]: 112.63/113.36 subset( 112.63/113.36 setminus( 112.63/113.36 X364,X365), 112.63/113.36 X364)) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X366, 112.63/113.36 X367]: 112.63/113.36 (( 112.63/113.36 setminus( 112.63/113.36 X366,X367) = 112.63/113.36 emptyset) => 112.63/113.36 subset( 112.63/113.36 X366,X367))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X368, 112.63/113.36 X369,X370]: 112.63/113.36 (in( 112.63/113.36 X370, 112.63/113.36 symdiff( 112.63/113.36 X368,X369)) => 112.63/113.36 (![X371:$o]: 112.63/113.36 (( 112.63/113.36 in( 112.63/113.36 X370,X368) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ~ 112.63/113.36 in( 112.63/113.36 X370,X369)) => 112.63/113.36 X371)) => 112.63/113.36 (( 112.63/113.36 ( 112.63/113.36 ~ 112.63/113.36 in( 112.63/113.36 X370,X368)) => 112.63/113.36 ( 112.63/113.36 in( 112.63/113.36 X370,X369) => 112.63/113.36 X371)) => 112.63/113.36 X371))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X372, 112.63/113.36 X373,X374]: 112.63/113.36 (in( 112.63/113.36 X374,X372) => 112.63/113.36 (( 112.63/113.36 ~ 112.63/113.36 in( 112.63/113.36 X374,X373)) => 112.63/113.36 in( 112.63/113.36 X374, 112.63/113.36 symdiff( 112.63/113.36 X372,X373))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X375, 112.63/113.36 X376,X377]: 112.63/113.36 (( 112.63/113.36 ~ 112.63/113.36 in( 112.63/113.36 X377,X375)) => 112.63/113.36 (in( 112.63/113.36 X377,X376) => 112.63/113.36 in( 112.63/113.36 X377, 112.63/113.36 symdiff( 112.63/113.36 X375,X376))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X378, 112.63/113.36 X379,X380]: 112.63/113.36 (in( 112.63/113.36 X380,X378) => 112.63/113.36 (in( 112.63/113.36 X380,X379) => 112.63/113.36 (~ 112.63/113.36 in( 112.63/113.36 X380, 112.63/113.36 symdiff( 112.63/113.36 X378,X379)))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X381, 112.63/113.36 X382,X383]: 112.63/113.36 (( 112.63/113.36 ~ 112.63/113.36 in( 112.63/113.36 X383,X381)) => 112.63/113.36 (( 112.63/113.36 ~ 112.63/113.36 in( 112.63/113.36 X383,X382)) => 112.63/113.36 (~ 112.63/113.36 in( 112.63/113.36 X383, 112.63/113.36 symdiff( 112.63/113.36 X381,X382)))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X384, 112.63/113.36 X385]: 112.63/113.36 in( 112.63/113.36 X385, 112.63/113.36 setadjoin( 112.63/113.36 X384, 112.63/113.36 setadjoin( 112.63/113.36 X385, 112.63/113.36 emptyset)))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X386, 112.63/113.36 X387]: 112.63/113.36 in( 112.63/113.36 X386, 112.63/113.36 setunion( 112.63/113.36 setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X386, 112.63/113.36 emptyset), 112.63/113.36 setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X386, 112.63/113.36 setadjoin( 112.63/113.36 X387, 112.63/113.36 emptyset)), 112.63/113.36 emptyset))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X388, 112.63/113.36 X389]: 112.63/113.36 in( 112.63/113.36 X389, 112.63/113.36 setunion( 112.63/113.36 setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X388, 112.63/113.36 emptyset), 112.63/113.36 setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X388, 112.63/113.36 setadjoin( 112.63/113.36 X389, 112.63/113.36 emptyset)), 112.63/113.36 emptyset))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X390, 112.63/113.36 X391]: 112.63/113.36 iskpair( 112.63/113.36 setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X390, 112.63/113.36 emptyset), 112.63/113.36 setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X390, 112.63/113.36 setadjoin( 112.63/113.36 X391, 112.63/113.36 emptyset)), 112.63/113.36 emptyset)))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X392, 112.63/113.36 X393]: 112.63/113.36 iskpair( 112.63/113.36 kpair( 112.63/113.36 X392,X393))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X394, 112.63/113.36 X395]: 112.63/113.36 (in( 112.63/113.36 X395,X394) => 112.63/113.36 subset( 112.63/113.36 setadjoin( 112.63/113.36 X395, 112.63/113.36 emptyset), 112.63/113.36 X394))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X396, 112.63/113.36 X397]: 112.63/113.36 (in( 112.63/113.36 X397,X396) => 112.63/113.36 in( 112.63/113.36 setadjoin( 112.63/113.36 X397, 112.63/113.36 emptyset), 112.63/113.36 powerset( 112.63/113.36 X396)))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X398, 112.63/113.36 X399,X400]: 112.63/113.36 (in( 112.63/113.36 X400,X398) => 112.63/113.36 in( 112.63/113.36 setadjoin( 112.63/113.36 X400, 112.63/113.36 emptyset), 112.63/113.36 powerset( 112.63/113.36 binunion( 112.63/113.36 X398,X399))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X401, 112.63/113.36 X402,X403]: 112.63/113.36 (in( 112.63/113.36 X403, 112.63/113.36 setadjoin( 112.63/113.36 X401, 112.63/113.36 setadjoin( 112.63/113.36 X402, 112.63/113.36 emptyset))) => 112.63/113.36 (( 112.63/113.36 X403 = 112.63/113.36 X402) | 112.63/113.36 (X403 = 112.63/113.36 X401)))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X404, 112.63/113.36 X405,X406]: 112.63/113.36 (in( 112.63/113.36 X406,X404) => 112.63/113.36 (![X407]: 112.63/113.36 (in( 112.63/113.36 X407,X405) => 112.63/113.36 subset( 112.63/113.36 setadjoin( 112.63/113.36 X406, 112.63/113.36 setadjoin( 112.63/113.36 X407, 112.63/113.36 emptyset)), 112.63/113.36 binunion( 112.63/113.36 X404,X405)))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X408, 112.63/113.36 X409,X410]: 112.63/113.36 (in( 112.63/113.36 X410,X408) => 112.63/113.36 (![X411]: 112.63/113.36 (in( 112.63/113.36 X411,X409) => 112.63/113.36 in( 112.63/113.36 setadjoin( 112.63/113.36 X410, 112.63/113.36 setadjoin( 112.63/113.36 X411, 112.63/113.36 emptyset)), 112.63/113.36 powerset( 112.63/113.36 binunion( 112.63/113.36 X408,X409))))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X412, 112.63/113.36 X413,X414]: 112.63/113.36 (in( 112.63/113.36 X414,X412) => 112.63/113.36 (![X415]: 112.63/113.36 (in( 112.63/113.36 X415,X413) => 112.63/113.36 subset( 112.63/113.36 setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X414, 112.63/113.36 emptyset), 112.63/113.36 setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X414, 112.63/113.36 setadjoin( 112.63/113.36 X415, 112.63/113.36 emptyset)), 112.63/113.36 emptyset)), 112.63/113.36 powerset( 112.63/113.36 binunion( 112.63/113.36 X412,X413))))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X416, 112.63/113.36 X417,X418]: 112.63/113.36 (in( 112.63/113.36 X418,X416) => 112.63/113.36 (![X419]: 112.63/113.36 (in( 112.63/113.36 X419,X417) => 112.63/113.36 in( 112.63/113.36 setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X418, 112.63/113.36 emptyset), 112.63/113.36 setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X418, 112.63/113.36 setadjoin( 112.63/113.36 X419, 112.63/113.36 emptyset)), 112.63/113.36 emptyset)), 112.63/113.36 powerset( 112.63/113.36 powerset( 112.63/113.36 binunion( 112.63/113.36 X416,X417)))))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X420, 112.63/113.36 X421,X422]: 112.63/113.36 (in( 112.63/113.36 X422,X420) => 112.63/113.36 (![X423]: 112.63/113.36 (in( 112.63/113.36 X423,X421) => 112.63/113.36 in( 112.63/113.36 kpair( 112.63/113.36 X422,X423), 112.63/113.36 powerset( 112.63/113.36 powerset( 112.63/113.36 binunion( 112.63/113.36 X420,X421)))))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X424, 112.63/113.36 X425,X426]: 112.63/113.36 (in( 112.63/113.36 X426,X424) => 112.63/113.36 (![X427]: 112.63/113.36 (in( 112.63/113.36 X427,X425) => 112.63/113.36 in( 112.63/113.36 kpair( 112.63/113.36 X426,X427), 112.63/113.36 cartprod( 112.63/113.36 X424,X425)))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X428, 112.63/113.36 X429,X430]: 112.63/113.36 (in( 112.63/113.36 X430, 112.63/113.36 cartprod( 112.63/113.36 X428,X429)) => 112.63/113.36 (?[X431]: 112.63/113.36 (( 112.63/113.36 ?[X432]: 112.63/113.36 (( 112.63/113.36 X430 = 112.63/113.36 kpair( 112.63/113.36 X431,X432)) & 112.63/113.36 in( 112.63/113.36 X432,X429))) & 112.63/113.36 in( 112.63/113.36 X431,X428))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X433, 112.63/113.36 X434,X435]: 112.63/113.36 (in( 112.63/113.36 X435, 112.63/113.36 cartprod( 112.63/113.36 X433,X434)) => 112.63/113.36 iskpair( 112.63/113.36 X435))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X436, 112.63/113.36 X437]: 112.63/113.36 (in( 112.63/113.36 X437, 112.63/113.36 setunion( 112.63/113.36 X436)) => 112.63/113.36 (?[X438]: 112.63/113.36 (in( 112.63/113.36 X437,X438) & 112.63/113.36 in( 112.63/113.36 X438,X436))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X439]: 112.63/113.36 subset( 112.63/113.36 setunion( 112.63/113.36 setadjoin( 112.63/113.36 X439, 112.63/113.36 emptyset)), 112.63/113.36 X439)) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X440]: 112.63/113.36 subset( 112.63/113.36 X440, 112.63/113.36 setunion( 112.63/113.36 setadjoin( 112.63/113.36 X440, 112.63/113.36 emptyset)))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X441]: 112.63/113.36 (setunion( 112.63/113.36 setadjoin( 112.63/113.36 X441, 112.63/113.36 emptyset)) = 112.63/113.36 X441)) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X442, 112.63/113.36 X443:( 112.63/113.36 $i > $o)]: 112.63/113.36 (( 112.63/113.36 ![X444]: 112.63/113.36 (in( 112.63/113.36 X444,X442) => 112.63/113.36 (![X445]: 112.63/113.36 (in( 112.63/113.36 X445,X442) => 112.63/113.36 (X443( 112.63/113.36 X444) => 112.63/113.36 (X443( 112.63/113.36 X445) => 112.63/113.36 (X444 = 112.63/113.36 X445))))))) => 112.63/113.36 (( 112.63/113.36 ?[X446]: 112.63/113.36 (X443( 112.63/113.36 X446) & 112.63/113.36 in( 112.63/113.36 X446,X442))) => 112.63/113.36 (?[X447]: 112.63/113.36 (( 112.63/113.36 dsetconstr( 112.63/113.36 X442, 112.63/113.36 '#ll_6'( 112.63/113.36 X443)) = 112.63/113.36 setadjoin( 112.63/113.36 X447, 112.63/113.36 emptyset)) & 112.63/113.36 in( 112.63/113.36 X447, 112.63/113.36 dsetconstr( 112.63/113.36 X442, 112.63/113.36 '#ll_6'( 112.63/113.36 X443)))))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X448, 112.63/113.36 X449:( 112.63/113.36 $i > $o)]: 112.63/113.36 (( 112.63/113.36 ?[X450]: 112.63/113.36 (( 112.63/113.36 dsetconstr( 112.63/113.36 X448, 112.63/113.36 '#ll_6'( 112.63/113.36 X449)) = 112.63/113.36 setadjoin( 112.63/113.36 X450, 112.63/113.36 emptyset)) & 112.63/113.36 in( 112.63/113.36 X450, 112.63/113.36 dsetconstr( 112.63/113.36 X448, 112.63/113.36 '#ll_6'( 112.63/113.36 X449))))) => 112.63/113.36 (?[X451]: 112.63/113.36 (X449( 112.63/113.36 X451) & 112.63/113.36 in( 112.63/113.36 X451,X448))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X452, 112.63/113.36 X453:( 112.63/113.36 $i > $o), 112.63/113.36 X454]: 112.63/113.36 (in( 112.63/113.36 X454,X452) => 112.63/113.36 (X453( 112.63/113.36 X454) => 112.63/113.36 (( 112.63/113.36 ![X455]: 112.63/113.36 (in( 112.63/113.36 X455,X452) => 112.63/113.36 (X453( 112.63/113.36 X455) => 112.63/113.36 (X455 = 112.63/113.36 X454)))) => 112.63/113.36 (?[X456]: 112.63/113.36 (( 112.63/113.36 dsetconstr( 112.63/113.36 X452, 112.63/113.36 '#ll_6'( 112.63/113.36 X453)) = 112.63/113.36 setadjoin( 112.63/113.36 X456, 112.63/113.36 emptyset)) & 112.63/113.36 in( 112.63/113.36 X456, 112.63/113.36 dsetconstr( 112.63/113.36 X452, 112.63/113.36 '#ll_6'( 112.63/113.36 X453))))))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X457, 112.63/113.36 X458:( 112.63/113.36 $i > $o)]: 112.63/113.36 (( 112.63/113.36 ![X459]: 112.63/113.36 (in( 112.63/113.36 X459,X457) => 112.63/113.36 (![X460]: 112.63/113.36 (in( 112.63/113.36 X460,X457) => 112.63/113.36 (X458( 112.63/113.36 X459) => 112.63/113.36 (X458( 112.63/113.36 X460) => 112.63/113.36 (X459 = 112.63/113.36 X460))))))) => 112.63/113.36 (( 112.63/113.36 ?[X461]: 112.63/113.36 (X458( 112.63/113.36 X461) & 112.63/113.36 in( 112.63/113.36 X461,X457))) => 112.63/113.36 (?[X462]: 112.63/113.36 (( 112.63/113.36 dsetconstr( 112.63/113.36 X457, 112.63/113.36 '#ll_6'( 112.63/113.36 X458)) = 112.63/113.36 setadjoin( 112.63/113.36 X462, 112.63/113.36 emptyset)) & 112.63/113.36 in( 112.63/113.36 X462, 112.63/113.36 dsetconstr( 112.63/113.36 X457, 112.63/113.36 '#ll_6'( 112.63/113.36 X458)))))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X463, 112.63/113.36 X464]: 112.63/113.36 (( 112.63/113.36 setadjoin( 112.63/113.36 X463, 112.63/113.36 emptyset) = 112.63/113.36 setadjoin( 112.63/113.36 X464, 112.63/113.36 emptyset)) => 112.63/113.36 (X463 = 112.63/113.36 X464))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X465, 112.63/113.36 X466,X467]: 112.63/113.36 (in( 112.63/113.36 setadjoin( 112.63/113.36 X467, 112.63/113.36 emptyset), 112.63/113.36 setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X465, 112.63/113.36 emptyset), 112.63/113.36 setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X465, 112.63/113.36 setadjoin( 112.63/113.36 X466, 112.63/113.36 emptyset)), 112.63/113.36 emptyset))) => 112.63/113.36 (X465 = 112.63/113.36 X467))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X468]: 112.63/113.36 (iskpair( 112.63/113.36 X468) => 112.63/113.36 (?[X469]: 112.63/113.36 (( 112.63/113.36 dsetconstr( 112.63/113.36 setunion( 112.63/113.36 X468), 112.63/113.36 '#ll_5'( 112.63/113.36 X468)) = 112.63/113.36 setadjoin( 112.63/113.36 X469, 112.63/113.36 emptyset)) & 112.63/113.36 in( 112.63/113.36 X469, 112.63/113.36 dsetconstr( 112.63/113.36 setunion( 112.63/113.36 X468), 112.63/113.36 '#ll_5'( 112.63/113.36 X468))))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X470]: 112.63/113.36 (( 112.63/113.36 ?[X471]: 112.63/113.36 (( 112.63/113.36 X470 = 112.63/113.36 setadjoin( 112.63/113.36 X471, 112.63/113.36 emptyset)) & 112.63/113.36 in( 112.63/113.36 X471,X470))) => 112.63/113.36 in( 112.63/113.36 setunion( 112.63/113.36 X470), 112.63/113.36 X470))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X472, 112.63/113.36 X473]: 112.63/113.36 (kfst( 112.63/113.36 kpair( 112.63/113.36 X472,X473)) = 112.63/113.36 X472)) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X474, 112.63/113.36 X475,X476]: 112.63/113.36 (in( 112.63/113.36 X476, 112.63/113.36 cartprod( 112.63/113.36 X474,X475)) => 112.63/113.36 in( 112.63/113.36 kfst( 112.63/113.36 X476), 112.63/113.36 X474))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X477, 112.63/113.36 X478, 112.63/113.36 X479,X480]: 112.63/113.36 (( 112.63/113.36 setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X477, 112.63/113.36 emptyset), 112.63/113.36 setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X477, 112.63/113.36 setadjoin( 112.63/113.36 X478, 112.63/113.36 emptyset)), 112.63/113.36 emptyset)) = 112.63/113.36 setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X479, 112.63/113.36 emptyset), 112.63/113.36 setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X479, 112.63/113.36 setadjoin( 112.63/113.36 X480, 112.63/113.36 emptyset)), 112.63/113.36 emptyset))) => 112.63/113.36 (X477 = 112.63/113.36 X479))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X481, 112.63/113.36 X482, 112.63/113.36 X483,X484]: 112.63/113.36 (( 112.63/113.36 kpair( 112.63/113.36 X481,X482) = 112.63/113.36 kpair( 112.63/113.36 X483,X484)) => 112.63/113.36 (X481 = 112.63/113.36 X483))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X485, 112.63/113.36 X486]: 112.63/113.36 (( 112.63/113.36 X485 = 112.63/113.36 X486) => 112.63/113.36 (setadjoin( 112.63/113.36 X485, 112.63/113.36 setadjoin( 112.63/113.36 X486, 112.63/113.36 emptyset)) = 112.63/113.36 setadjoin( 112.63/113.36 X485, 112.63/113.36 emptyset)))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X487, 112.63/113.36 X488]: 112.63/113.36 (( 112.63/113.36 X487 = 112.63/113.36 X488) => 112.63/113.36 (setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X487, 112.63/113.36 emptyset), 112.63/113.36 setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X487, 112.63/113.36 setadjoin( 112.63/113.36 X488, 112.63/113.36 emptyset)), 112.63/113.36 emptyset)) = 112.63/113.36 setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X487, 112.63/113.36 emptyset), 112.63/113.36 emptyset)))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X489, 112.63/113.36 X490, 112.63/113.36 X491,X492]: 112.63/113.36 (( 112.63/113.36 setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X489, 112.63/113.36 emptyset), 112.63/113.36 setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X489, 112.63/113.36 setadjoin( 112.63/113.36 X490, 112.63/113.36 emptyset)), 112.63/113.36 emptyset)) = 112.63/113.36 setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X491, 112.63/113.36 emptyset), 112.63/113.36 setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X491, 112.63/113.36 setadjoin( 112.63/113.36 X492, 112.63/113.36 emptyset)), 112.63/113.36 emptyset))) => 112.63/113.36 (( 112.63/113.36 X491 = 112.63/113.36 X492) => 112.63/113.36 (X490 = 112.63/113.36 X492)))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X493, 112.63/113.36 X494,X495]: 112.63/113.36 (( 112.63/113.36 setadjoin( 112.63/113.36 X493, 112.63/113.36 setadjoin( 112.63/113.36 X494, 112.63/113.36 emptyset)) = 112.63/113.36 setadjoin( 112.63/113.36 X495, 112.63/113.36 emptyset)) => 112.63/113.36 (X493 = 112.63/113.36 X494))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X496, 112.63/113.36 X497, 112.63/113.36 X498,X499]: 112.63/113.36 (( 112.63/113.36 setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X496, 112.63/113.36 emptyset), 112.63/113.36 setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X496, 112.63/113.36 setadjoin( 112.63/113.36 X497, 112.63/113.36 emptyset)), 112.63/113.36 emptyset)) = 112.63/113.36 setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X498, 112.63/113.36 emptyset), 112.63/113.36 setadjoin( 112.63/113.36 setadjoin( 112.63/113.36 X498, 112.63/113.36 setadjoin( 112.63/113.36 X499, 112.63/113.36 emptyset)), 112.63/113.36 emptyset))) => 112.63/113.36 (X497 = 112.63/113.36 X499))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X500, 112.63/113.36 X501, 112.63/113.36 X502,X503]: 112.63/113.36 (( 112.63/113.36 kpair( 112.63/113.36 X500,X501) = 112.63/113.36 kpair( 112.63/113.36 X502,X503)) => 112.63/113.36 (X501 = 112.63/113.36 X503))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X504]: 112.63/113.36 (iskpair( 112.63/113.36 X504) => 112.63/113.36 (?[X505]: 112.63/113.36 (( 112.63/113.36 dsetconstr( 112.63/113.36 setunion( 112.63/113.36 X504), 112.63/113.36 '#ll_4'( 112.63/113.36 X504)) = 112.63/113.36 setadjoin( 112.63/113.36 X505, 112.63/113.36 emptyset)) & 112.63/113.36 in( 112.63/113.36 X505, 112.63/113.36 dsetconstr( 112.63/113.36 setunion( 112.63/113.36 X504), 112.63/113.36 '#ll_4'( 112.63/113.36 X504))))))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X506, 112.63/113.36 X507]: 112.63/113.36 (ksnd( 112.63/113.36 kpair( 112.63/113.36 X506,X507)) = 112.63/113.36 X507)) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X508]: 112.63/113.36 (iskpair( 112.63/113.36 X508) => 112.63/113.36 (kpair( 112.63/113.36 kfst( 112.63/113.36 X508), 112.63/113.36 ksnd( 112.63/113.36 X508)) = 112.63/113.36 X508))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X509, 112.63/113.36 X510,X511]: 112.63/113.36 (in( 112.63/113.36 X511, 112.63/113.36 cartprod( 112.63/113.36 X509,X510)) => 112.63/113.36 in( 112.63/113.36 ksnd( 112.63/113.36 X511), 112.63/113.36 X510))) => 112.63/113.36 ( 112.63/113.36 ( 112.63/113.36 ![X512, 112.63/113.36 X513, 112.63/113.36 X514,X515]: 112.63/113.36 (in( 112.63/113.36 kpair( 112.63/113.36 X514,X515), 112.63/113.36 cartprod( 112.63/113.36 X512,X513)) => 112.63/113.36 in( 112.63/113.36 X514,X512))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X516, 112.63/113.37 X517, 112.63/113.37 X518,X519]: 112.63/113.37 (in( 112.63/113.37 kpair( 112.63/113.37 X518,X519), 112.63/113.37 cartprod( 112.63/113.37 X516,X517)) => 112.63/113.37 in( 112.63/113.37 X519,X517))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X520, 112.63/113.37 X521,X522]: 112.63/113.37 (in( 112.63/113.37 X522,X520) => 112.63/113.37 (![X523]: 112.63/113.37 (in( 112.63/113.37 X523,X521) => 112.63/113.37 (kpair( 112.63/113.37 X522,X523) = 112.63/113.37 kpair( 112.63/113.37 X522,X523)))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X524, 112.63/113.37 X525,X526]: 112.63/113.37 (in( 112.63/113.37 X526,X524) => 112.63/113.37 (![X527]: 112.63/113.37 (in( 112.63/113.37 X527,X525) => 112.63/113.37 (kfst( 112.63/113.37 kpair( 112.63/113.37 X526,X527)) = 112.63/113.37 X526))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X528, 112.63/113.37 X529,X530]: 112.63/113.37 (in( 112.63/113.37 X530,X528) => 112.63/113.37 (![X531]: 112.63/113.37 (in( 112.63/113.37 X531,X529) => 112.63/113.37 (ksnd( 112.63/113.37 kpair( 112.63/113.37 X530,X531)) = 112.63/113.37 X531))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X532, 112.63/113.37 X533,X534]: 112.63/113.37 (in( 112.63/113.37 X534, 112.63/113.37 cartprod( 112.63/113.37 X532,X533)) => 112.63/113.37 (kpair( 112.63/113.37 kfst( 112.63/113.37 X534), 112.63/113.37 ksnd( 112.63/113.37 X534)) = 112.63/113.37 X534))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X535, 112.63/113.37 X536, 112.63/113.37 X537:( 112.63/113.37 ($i * $i) > 112.63/113.37 $o),X538]: 112.63/113.37 (in( 112.63/113.37 X538,X535) => 112.63/113.37 (![X539]: 112.63/113.37 (in( 112.63/113.37 X539,X536) => 112.63/113.37 (X537( 112.63/113.37 X538,X539) => 112.63/113.37 in( 112.63/113.37 kpair( 112.63/113.37 X538,X539), 112.63/113.37 dpsetconstr( 112.63/113.37 X535, 112.63/113.37 X536, 112.63/113.37 '#ll_3'( 112.63/113.37 X537)))))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X540, 112.63/113.37 X541, 112.63/113.37 X542:( 112.63/113.37 ($i * $i) > 112.63/113.37 $o)]: 112.63/113.37 subset( 112.63/113.37 dpsetconstr( 112.63/113.37 X540, 112.63/113.37 X541, 112.63/113.37 '#ll_3'( 112.63/113.37 X542)), 112.63/113.37 cartprod( 112.63/113.37 X540,X541))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X543, 112.63/113.37 X544, 112.63/113.37 X545:( 112.63/113.37 ($i * $i) > 112.63/113.37 $o)]: 112.63/113.37 subset( 112.63/113.37 dpsetconstr( 112.63/113.37 X543, 112.63/113.37 X544, 112.63/113.37 '#ll_3'( 112.63/113.37 X545)), 112.63/113.37 cartprod( 112.63/113.37 X543,X544))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X546, 112.63/113.37 X547, 112.63/113.37 X548:( 112.63/113.37 ($i * $i) > 112.63/113.37 $o),X549]: 112.63/113.37 (in( 112.63/113.37 X549,X546) => 112.63/113.37 (![X550]: 112.63/113.37 (in( 112.63/113.37 X550,X547) => 112.63/113.37 (in( 112.63/113.37 kpair( 112.63/113.37 X549,X550), 112.63/113.37 dpsetconstr( 112.63/113.37 X546, 112.63/113.37 X547, 112.63/113.37 '#ll_3'( 112.63/113.37 X548))) => 112.63/113.37 X548( 112.63/113.37 X549,X550)))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X551, 112.63/113.37 X552, 112.63/113.37 X553:( 112.63/113.37 ($i * $i) > 112.63/113.37 $o),X554, 112.63/113.37 X555]: 112.63/113.37 (in( 112.63/113.37 kpair( 112.63/113.37 X554,X555), 112.63/113.37 dpsetconstr( 112.63/113.37 X551, 112.63/113.37 X552, 112.63/113.37 '#ll_3'( 112.63/113.37 X553))) => 112.63/113.37 in( 112.63/113.37 X554,X551))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X556, 112.63/113.37 X557, 112.63/113.37 X558:( 112.63/113.37 ($i * $i) > 112.63/113.37 $o),X559, 112.63/113.37 X560]: 112.63/113.37 (in( 112.63/113.37 kpair( 112.63/113.37 X559,X560), 112.63/113.37 dpsetconstr( 112.63/113.37 X556, 112.63/113.37 X557, 112.63/113.37 '#ll_3'( 112.63/113.37 X558))) => 112.63/113.37 in( 112.63/113.37 X560,X557))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X561, 112.63/113.37 X562, 112.63/113.37 X563:( 112.63/113.37 ($i * $i) > 112.63/113.37 $o),X564, 112.63/113.37 X565]: 112.63/113.37 (in( 112.63/113.37 kpair( 112.63/113.37 X564,X565), 112.63/113.37 dpsetconstr( 112.63/113.37 X561, 112.63/113.37 X562, 112.63/113.37 '#ll_3'( 112.63/113.37 X563))) => 112.63/113.37 X563( 112.63/113.37 X564,X565))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X566, 112.63/113.37 X567,X568]: 112.63/113.37 (( 112.63/113.37 ( 112.63/113.37 ![X569]: 112.63/113.37 (in( 112.63/113.37 X569,X566) => 112.63/113.37 (?[X570]: 112.63/113.37 (( 112.63/113.37 dsetconstr( 112.63/113.37 X567, 112.63/113.37 '#ll_2'( 112.63/113.37 X569,X568)) = 112.63/113.37 setadjoin( 112.63/113.37 X570, 112.63/113.37 emptyset)) & 112.63/113.37 in( 112.63/113.37 X570, 112.63/113.37 dsetconstr( 112.63/113.37 X567, 112.63/113.37 '#ll_2'( 112.63/113.37 X569,X568))))))) & 112.63/113.37 subset( 112.63/113.37 X568, 112.63/113.37 cartprod( 112.63/113.37 X566,X567))) => 112.63/113.37 (![X571]: 112.63/113.37 (in( 112.63/113.37 X571,X566) => 112.63/113.37 (?[X572]: 112.63/113.37 (( 112.63/113.37 dsetconstr( 112.63/113.37 X567, 112.63/113.37 '#ll_2'( 112.63/113.37 X571,X568)) = 112.63/113.37 setadjoin( 112.63/113.37 X572, 112.63/113.37 emptyset)) & 112.63/113.37 in( 112.63/113.37 X572, 112.63/113.37 dsetconstr( 112.63/113.37 X567, 112.63/113.37 '#ll_2'( 112.63/113.37 X571,X568))))))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X573, 112.63/113.37 X574,X575]: 112.63/113.37 (( 112.63/113.37 ( 112.63/113.37 ![X576]: 112.63/113.37 (in( 112.63/113.37 X576,X573) => 112.63/113.37 (?[X577]: 112.63/113.37 (( 112.63/113.37 dsetconstr( 112.63/113.37 X574, 112.63/113.37 '#ll_2'( 112.63/113.37 X576,X575)) = 112.63/113.37 setadjoin( 112.63/113.37 X577, 112.63/113.37 emptyset)) & 112.63/113.37 in( 112.63/113.37 X577, 112.63/113.37 dsetconstr( 112.63/113.37 X574, 112.63/113.37 '#ll_2'( 112.63/113.37 X576,X575))))))) & 112.63/113.37 subset( 112.63/113.37 X575, 112.63/113.37 cartprod( 112.63/113.37 X573,X574))) => 112.63/113.37 (![X578]: 112.63/113.37 (in( 112.63/113.37 X578,X573) => 112.63/113.37 in( 112.63/113.37 setunion( 112.63/113.37 dsetconstr( 112.63/113.37 X574, 112.63/113.37 '#ll_2'( 112.63/113.37 X578,X575))), 112.63/113.37 X574))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X579, 112.63/113.37 X580,X581]: 112.63/113.37 (( 112.63/113.37 ( 112.63/113.37 ![X582]: 112.63/113.37 (in( 112.63/113.37 X582,X579) => 112.63/113.37 (?[X583]: 112.63/113.37 (( 112.63/113.37 dsetconstr( 112.63/113.37 X580, 112.63/113.37 '#ll_2'( 112.63/113.37 X582,X581)) = 112.63/113.37 setadjoin( 112.63/113.37 X583, 112.63/113.37 emptyset)) & 112.63/113.37 in( 112.63/113.37 X583, 112.63/113.37 dsetconstr( 112.63/113.37 X580, 112.63/113.37 '#ll_2'( 112.63/113.37 X582,X581))))))) & 112.63/113.37 subset( 112.63/113.37 X581, 112.63/113.37 cartprod( 112.63/113.37 X579,X580))) => 112.63/113.37 (![X584]: 112.63/113.37 (in( 112.63/113.37 X584,X579) => 112.63/113.37 in( 112.63/113.37 setunion( 112.63/113.37 dsetconstr( 112.63/113.37 X580, 112.63/113.37 '#ll_2'( 112.63/113.37 X584,X581))), 112.63/113.37 X580))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X585, 112.63/113.37 X586,X587]: 112.63/113.37 (in( 112.63/113.37 X587, 112.63/113.37 funcSet( 112.63/113.37 X585,X586)) => 112.63/113.37 (( 112.63/113.37 ![X588]: 112.63/113.37 (in( 112.63/113.37 X588,X585) => 112.63/113.37 (?[X589]: 112.63/113.37 (( 112.63/113.37 dsetconstr( 112.63/113.37 X586, 112.63/113.37 '#ll_2'( 112.63/113.37 X588,X587)) = 112.63/113.37 setadjoin( 112.63/113.37 X589, 112.63/113.37 emptyset)) & 112.63/113.37 in( 112.63/113.37 X589, 112.63/113.37 dsetconstr( 112.63/113.37 X586, 112.63/113.37 '#ll_2'( 112.63/113.37 X588,X587))))))) & 112.63/113.37 subset( 112.63/113.37 X587, 112.63/113.37 cartprod( 112.63/113.37 X585,X586))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X590, 112.63/113.37 X591,X592]: 112.63/113.37 (in( 112.63/113.37 X592, 112.63/113.37 funcSet( 112.63/113.37 X590,X591)) => 112.63/113.37 (![X593]: 112.63/113.37 (in( 112.63/113.37 X593,X590) => 112.63/113.37 in( 112.63/113.37 setunion( 112.63/113.37 dsetconstr( 112.63/113.37 X591, 112.63/113.37 '#ll_2'( 112.63/113.37 X593,X592))), 112.63/113.37 X591))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X594, 112.63/113.37 X595,X596]: 112.63/113.37 (( 112.63/113.37 ( 112.63/113.37 ![X597]: 112.63/113.37 (in( 112.63/113.37 X597,X594) => 112.63/113.37 (?[X598]: 112.63/113.37 (( 112.63/113.37 dsetconstr( 112.63/113.37 X595, 112.63/113.37 '#ll_2'( 112.63/113.37 X597,X596)) = 112.63/113.37 setadjoin( 112.63/113.37 X598, 112.63/113.37 emptyset)) & 112.63/113.37 in( 112.63/113.37 X598, 112.63/113.37 dsetconstr( 112.63/113.37 X595, 112.63/113.37 '#ll_2'( 112.63/113.37 X597,X596))))))) & 112.63/113.37 subset( 112.63/113.37 X596, 112.63/113.37 cartprod( 112.63/113.37 X594,X595))) => 112.63/113.37 in( 112.63/113.37 X596, 112.63/113.37 funcSet( 112.63/113.37 X594,X595)))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X599, 112.63/113.37 X600, 112.63/113.37 X601:( 112.63/113.37 $i > $i)]: 112.63/113.37 (( 112.63/113.37 ![X602]: 112.63/113.37 (in( 112.63/113.37 X602,X599) => 112.63/113.37 in( 112.63/113.37 X601( 112.63/113.37 X602), 112.63/113.37 X600))) => 112.63/113.37 (( 112.63/113.37 ![X603]: 112.63/113.37 (in( 112.63/113.37 X603,X599) => 112.63/113.37 (?[X604]: 112.63/113.37 (( 112.63/113.37 dsetconstr( 112.63/113.37 X600, 112.63/113.37 '#ll_1'( 112.63/113.37 X603, 112.63/113.37 X601, 112.63/113.37 X600,X599)) = 112.63/113.37 setadjoin( 112.63/113.37 X604, 112.63/113.37 emptyset)) & 112.63/113.37 in( 112.63/113.37 X604, 112.63/113.37 dsetconstr( 112.63/113.37 X600, 112.63/113.37 '#ll_1'( 112.63/113.37 X603, 112.63/113.37 X601, 112.63/113.37 X600,X599))))))) & 112.63/113.37 subset( 112.63/113.37 dpsetconstr( 112.63/113.37 X599, 112.63/113.37 X600, 112.63/113.37 '#ll_0'( 112.63/113.37 X601)), 112.63/113.37 cartprod( 112.63/113.37 X599,X600))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X605, 112.63/113.37 X606, 112.63/113.37 X607:( 112.63/113.37 $i > $i)]: 112.63/113.37 (( 112.63/113.37 ![X608]: 112.63/113.37 (in( 112.63/113.37 X608,X605) => 112.63/113.37 in( 112.63/113.37 X607( 112.63/113.37 X608), 112.63/113.37 X606))) => 112.63/113.37 (( 112.63/113.37 ![X609]: 112.63/113.37 (in( 112.63/113.37 X609,X605) => 112.63/113.37 (?[X610]: 112.63/113.37 (( 112.63/113.37 dsetconstr( 112.63/113.37 X606, 112.63/113.37 '#ll_1'( 112.63/113.37 X609, 112.63/113.37 X607, 112.63/113.37 X606,X605)) = 112.63/113.37 setadjoin( 112.63/113.37 X610, 112.63/113.37 emptyset)) & 112.63/113.37 in( 112.63/113.37 X610, 112.63/113.37 dsetconstr( 112.63/113.37 X606, 112.63/113.37 '#ll_1'( 112.63/113.37 X609, 112.63/113.37 X607, 112.63/113.37 X606,X605))))))) & 112.63/113.37 subset( 112.63/113.37 dpsetconstr( 112.63/113.37 X605, 112.63/113.37 X606, 112.63/113.37 '#ll_0'( 112.63/113.37 X607)), 112.63/113.37 cartprod( 112.63/113.37 X605,X606))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X611, 112.63/113.37 X612, 112.63/113.37 X613:( 112.63/113.37 $i > $i)]: 112.63/113.37 (( 112.63/113.37 ![X614]: 112.63/113.37 (in( 112.63/113.37 X614,X611) => 112.63/113.37 in( 112.63/113.37 X613( 112.63/113.37 X614), 112.63/113.37 X612))) => 112.63/113.37 in( 112.63/113.37 dpsetconstr( 112.63/113.37 X611, 112.63/113.37 X612, 112.63/113.37 '#ll_0'( 112.63/113.37 X613)), 112.63/113.37 funcSet( 112.63/113.37 X611,X612)))) => 112.63/113.37 ( 112.63/113.37 ![X615, 112.63/113.37 X616,X617]: 112.63/113.37 (subset( 112.63/113.37 X617, 112.63/113.37 cartprod( 112.63/113.37 X615,X616)) => 112.63/113.37 (![X618:( 112.63/113.37 $i > $o)]: 112.63/113.37 (( 112.63/113.37 ![X619]: 112.63/113.37 (in( 112.63/113.37 X619,X615) => 112.63/113.37 (![X620]: 112.63/113.37 (in( 112.63/113.37 X620,X616) => 112.63/113.37 (in( 112.63/113.37 kpair( 112.63/113.37 X619,X620), 112.63/113.37 X617) => 112.63/113.37 X618( 112.63/113.37 kpair( 112.63/113.37 X619,X620))))))) => 112.63/113.37 (![X621]: 112.63/113.37 (in( 112.63/113.37 X621,X617) => 112.63/113.37 X618( 112.63/113.37 X621))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 112.63/113.37 tff(zf_stmt_14, negated_conjecture, 112.63/113.37 (~ 112.63/113.37 ((![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))) => 112.63/113.37 ((![X5]: (~in(X5,emptyset))) => 112.63/113.37 ((![X6,X7,X8]: (in(X8,setadjoin(X6,X7)) <=> zip_tseitin0(X8,X7,X6))) => 112.63/113.37 ((![X9,X10]: 112.63/113.37 (in(X10,powerset(X9)) <=> (![X11]: zip_tseitin1(X11,X10,X9)))) => 112.63/113.37 ((![X12,X13]: 112.63/113.37 (in(X13,setunion(X12)) <=> (?[X14]: zip_tseitin2(X14,X13,X12)))) => 112.63/113.37 (in(emptyset,omega) => 112.63/113.37 ((![X15]: (in(X15,omega) => in(setadjoin(X15,X15),omega))) => 112.63/113.37 ((![X16]: 112.63/113.37 (((![X17]: 112.63/113.37 ((in(X17,X16) & in(X17,omega)) => 112.63/113.37 in(setadjoin(X17,X17),X16))) & 112.63/113.37 in(emptyset,X16)) => 112.63/113.37 (![X18]: (in(X18,omega) => in(X18,X16))))) => 112.63/113.37 ((![X19:(($i * $i) > $o),X20]: 112.63/113.37 ((![X21]: 112.63/113.37 (in(X21,X20) => 112.63/113.37 (?[X22]: 112.63/113.37 ((![X23]: (X19(X21,X23) => (X22 = X23))) & 112.63/113.37 X19(X21,X22))))) => 112.63/113.37 (?[X24]: 112.63/113.37 (![X25]: 112.63/113.37 (in(X25,X24) <=> 112.63/113.37 (?[X26]: zip_tseitin3(X26,X25,X20,X19))))))) => 112.63/113.37 ((![X27]: 112.63/113.37 ((?[X28]: in(X28,X27)) => 112.63/113.37 (?[X29]: 112.63/113.37 ((~(?[X30]: (in(X30,X27) & in(X30,X29)))) & in(X29,X27))))) => 112.63/113.37 ((![X31]: 112.63/113.37 (?[X32]: 112.63/113.37 ((![X33]: 112.63/113.37 (((?[X34]: in(X34,X33)) & 112.63/113.37 (![X35]: (in(X35,X33) => in(X35,X31)))) => 112.63/113.37 (?[X36,X37]: 112.63/113.37 ((![X38]: 112.63/113.37 (in(X38,X32) => 112.63/113.37 (in(X37,X38) | 112.63/113.37 (![X39]: (in(X39,X38) => in(X39,X36)))))) & 112.63/113.37 (~(?[X40]: (in(X40,X33) & in(X40,X36)))) & 112.63/113.37 in(X37,X33) & in(X36,X32))))) & 112.63/113.37 (![X41,X42]: 112.63/113.37 ((in(X42,X32) & in(X41,X32)) => 112.63/113.37 ((![X43]: (in(X43,X42) => in(X43,X41))) | 112.63/113.37 (![X44]: (in(X44,X41) => in(X44,X42)))))) & 112.63/113.37 (![X45,X46]: 112.63/113.37 ((in(X46,X31) & in(X45,X31)) => 112.63/113.37 ((![X47]: 112.63/113.37 (in(X47,X32) => (in(X45,X47) <=> in(X46,X47)))) => 112.63/113.37 (X45 = X46)))) & 112.63/113.37 (![X48]: 112.63/113.37 (in(X48,X32) => 112.63/113.37 (![X49]: (in(X49,X48) => in(X49,X31)))))))) => 112.63/113.37 ((![X50:($i > $o)]: 112.63/113.37 ((?[X51]: ((![X52]: (X50(X52) => (X51 = X52))) & X50(X51))) => 112.63/113.37 X50(descr('#ll_6'(X50))))) => 112.63/113.37 ((![X53,X54:($i > $o),X55]: 112.63/113.37 (in(X55,X53) => 112.63/113.37 (X54(X55) => in(X55,dsetconstr(X53,'#ll_6'(X54)))))) => 112.63/113.37 ((![X56,X57:($i > $o),X58]: 112.63/113.37 (in(X58,dsetconstr(X56,'#ll_6'(X57))) => in(X58,X56))) => 112.63/113.37 ((![X59,X60:($i > $o),X61]: 112.63/113.37 (in(X61,dsetconstr(X59,'#ll_6'(X60))) => X60(X61))) => 112.63/113.37 ((![X62:($i > $o)]: 112.63/113.37 ((?[X63]: 112.63/113.37 ((![X64]: (X62(X64) => (X63 = X64))) & X62(X63))) => 112.63/113.37 (?[X65]: 112.63/113.37 ((![X66]: (X62(X66) => (X65 = X66))) & X62(X65))))) => 112.63/113.37 ((![X67:$o,X68]: (in(X68,prop2set(X67)) => X67)) => 112.63/113.37 ((![X69]: (in(X69,emptyset) => (![X70:$o]: X70))) => 112.63/113.37 ((![X71]: (in(X71,emptyset) => $false)) => 112.63/113.37 ((![X72]: (~in(X72,emptyset))) => 112.63/113.37 ((![X73:($i > $o)]: 112.63/113.37 ((?[X74]: 112.63/113.37 ((![X75]: (X73(X75) => (X74 = X75))) & 112.63/113.37 X73(X74))) => 112.63/113.37 (?[X76]: X73(X76)))) => 112.63/113.37 ((![X77,X78]: 112.63/113.37 ((![X79]: (in(X79,X77) => in(X79,X78))) => 112.63/113.37 ((![X80]: (in(X80,X78) => in(X80,X77))) => 112.63/113.37 (X77 = X78)))) => 112.63/113.37 ((![X81]: 112.63/113.37 ((![X82]: (~in(X82,X81))) => (X81 = emptyset))) => 112.63/113.37 ((![X83]: 112.63/113.37 ((![X84]: (~in(X84,X83))) => (X83 = emptyset))) => 112.63/113.37 ((![X85,X86:($i > $o),X87]: 112.63/113.37 (in(X87,X85) => 112.63/113.37 (in(X87,dsetconstr(X85,'#ll_6'(X86))) <=> 112.63/113.37 X86(X87)))) => 112.63/113.37 ((![X88]: 112.63/113.37 ((X88 != emptyset) => (?[X89]: in(X89,X88)))) => 112.63/113.37 ((![X90,X91:($i > $o),X92]: 112.63/113.37 (in(X92,X90) => 112.63/113.37 (X91(X92) => 112.63/113.37 (dsetconstr(X90,'#ll_6'(X91)) != emptyset)))) => 112.63/113.37 ((![X93]: 112.63/113.37 ((?[X94]: in(X94,X93)) => 112.63/113.37 (X93 != emptyset))) => 112.63/113.37 ((![X95,X96]: in(X95,setadjoin(X95,X96))) => 112.63/113.37 (in(emptyset,setadjoin(emptyset,emptyset)) => 112.63/113.37 ((![X97,X98,X99]: 112.63/113.37 (in(X99,X98) => 112.63/113.37 in(X99,setadjoin(X97,X98)))) => 112.63/113.37 ((![X100,X101,X102]: 112.63/113.37 (in(X102,setadjoin(X100,X101)) => 112.63/113.37 (![X103:$o]: 112.63/113.37 (((X102 = X100) => X103) => 112.63/113.37 ((in(X102,X101) => X103) => X103))))) => 112.63/113.37 ((![X104,X105,X106]: 112.63/113.37 (in(X106,setadjoin(X104,X105)) => 112.63/113.37 (in(X106,X105) | (X106 = X104)))) => 112.63/113.37 ((![X107]: 112.63/113.37 (dsetconstr(X107,'#ll_7') = X107)) => 112.63/113.37 ((![X108,X109]: 112.63/113.37 ((![X110]: 112.63/113.37 (in(X110,X109) => in(X110,X108))) => 112.63/113.37 in(X109,powerset(X108)))) => 112.63/113.37 ((![X111]: in(emptyset,powerset(X111))) => 112.63/113.37 ((![X112]: 112.63/113.37 in(emptyset,powerset(X112))) => 112.63/113.37 ((![X113,X114,X115]: 112.63/113.37 (in(X114,powerset(X113)) => 112.63/113.37 (in(X115,X114) => in(X115,X113)))) => 112.63/113.37 ((![X116,X117,X118]: 112.63/113.37 (in(X117,X118) => 112.63/113.37 (in(X118,X116) => 112.63/113.37 in(X117,setunion(X116))))) => 112.63/113.37 ((![X119,X120]: 112.63/113.37 (in(X120,setunion(X119)) => 112.63/113.37 (![X121:$o]: 112.63/113.37 ((![X122]: 112.63/113.37 (in(X120,X122) => 112.63/113.37 (in(X122,X119) => 112.63/113.37 X121))) => 112.63/113.37 X121)))) => 112.63/113.37 ((![X123,X124]: 112.63/113.37 (in(X124,X123) => 112.63/113.37 in(X124, 112.63/113.37 powerset(setunion(X123))))) => 112.63/113.37 ((![X125:($i > $o)]: 112.63/113.37 ((?[X126]: 112.63/113.37 ((![X127]: 112.63/113.37 (X125(X127) => 112.63/113.37 (X126 = X127))) & 112.63/113.37 X125(X126))) => 112.63/113.37 (?[X128]: 112.63/113.37 (![X129]: 112.63/113.37 (X125(X129) <=> 112.63/113.37 (X129 = X128)))))) => 112.63/113.37 ((![X130]: 112.63/113.37 ((X130 != emptyset) => 112.63/113.37 (?[X131]: in(X131,X130)))) => 112.63/113.37 ((![X132,X133]: 112.63/113.37 (in(X132, 112.63/113.37 setadjoin(X133, 112.63/113.37 emptyset)) => 112.63/113.37 (X132 = X133))) => 112.63/113.37 ((![X134,X135]: 112.63/113.37 ((X134 != X135) => 112.63/113.37 (~ 112.63/113.37 in(X135, 112.63/113.37 setadjoin(X134, 112.63/113.37 emptyset))))) => 112.63/113.37 ((![X136,X137]: 112.63/113.37 ((X136 = X137) => 112.63/113.37 in(X136, 112.63/113.37 setadjoin(X137, 112.63/113.37 emptyset)))) => 112.63/113.37 ((![X138,X139]: 112.63/113.37 (in(X138, 112.63/113.37 setadjoin(X139, 112.63/113.37 emptyset)) => 112.63/113.37 in(X139, 112.63/113.37 setadjoin(X138, 112.63/113.37 emptyset)))) => 112.63/113.37 ((![X140,X141,X142]: 112.63/113.37 (in(X142, 112.63/113.37 setadjoin( 112.63/113.37 X140, 112.63/113.37 setadjoin( 112.63/113.37 X141,emptyset))) => 112.63/113.37 ((X142 = X141) | 112.63/113.37 (X142 = X140)))) => 112.63/113.37 ((![X143,X144]: 112.63/113.37 in(X143, 112.63/113.37 setadjoin( 112.63/113.37 X143, 112.63/113.37 setadjoin( 112.63/113.37 X144,emptyset)))) => 112.63/113.37 ((![X145,X146]: 112.63/113.37 in(X146, 112.63/113.37 setadjoin( 112.63/113.37 X145, 112.63/113.37 setadjoin( 112.63/113.37 X146,emptyset)))) => 112.63/113.37 ((![X147,X148:($i > $o)]: 112.63/113.37 ((?[X149]: 112.63/113.37 (X148(X149) & 112.63/113.37 in(X149,X147))) => 112.63/113.37 ((dsetconstr( 112.63/113.37 X147, 112.63/113.37 '#ll_6'(X148)) = 112.63/113.37 emptyset) => 112.63/113.37 $false))) => 112.63/113.37 ((![X150:($i > $o), 112.63/113.37 X151]: 112.63/113.37 (in(X151,emptyset) => 112.63/113.37 X150(X151))) => 112.63/113.37 ((![X152, 112.63/113.37 X153:($i > $o)]: 112.63/113.37 ((~ 112.63/113.37 (![X154]: 112.63/113.37 (in( 112.63/113.37 X154,X152) => 112.63/113.37 X153(X154)))) => 112.63/113.37 (?[X155]: 112.63/113.37 ((~X153(X155)) & 112.63/113.37 in(X155,X152))))) => 112.63/113.37 ((![X156, 112.63/113.37 X157:($i > $o)]: 112.63/113.37 ((![X158]: 112.63/113.37 (in( 112.63/113.37 X158,X156) => 112.63/113.37 (~ 112.63/113.37 X157( 112.63/113.37 X158)))) => 112.63/113.37 (~ 112.63/113.37 (?[X159]: 112.63/113.37 (X157( 112.63/113.37 X159) & 112.63/113.37 in( 112.63/113.37 X159,X156)))))) => 112.63/113.37 ((![X160, 112.63/113.37 X161:($i > $o)]: 112.63/113.37 ((~ 112.63/113.37 (?[X162]: 112.63/113.37 ( 112.63/113.37 X161( 112.63/113.37 X162) & 112.63/113.37 in( 112.63/113.37 X162,X160)))) => 112.63/113.37 (![X163]: 112.63/113.37 (in( 112.63/113.37 X163,X160) => 112.63/113.37 (~ 112.63/113.37 X161( 112.63/113.37 X163)))))) => 112.63/113.37 ((![X164, 112.63/113.37 X165:( 112.63/113.37 $i > $o)]: 112.63/113.37 ((?[X166]: 112.63/113.37 (( 112.63/113.37 ~ 112.63/113.37 X165( 112.63/113.37 X166)) & 112.63/113.37 in( 112.63/113.37 X166,X164))) => 112.63/113.37 (~ 112.63/113.37 (![X167]: 112.63/113.37 (in( 112.63/113.37 X167,X164) => 112.63/113.37 X165( 112.63/113.37 X167)))))) => 112.63/113.37 ((![X168:$o]: 112.63/113.37 (X168 => 112.63/113.37 in(emptyset, 112.63/113.37 prop2set( 112.63/113.37 X168)))) => 112.63/113.37 ((![X169:$o]: 112.63/113.37 (X169 => 112.63/113.37 set2prop( 112.63/113.37 prop2set( 112.63/113.37 X169)))) => 112.63/113.37 ((![X170, 112.63/113.37 X171:( 112.63/113.37 $i > $o)]: 112.63/113.37 ((~ 112.63/113.37 ( 112.63/113.37 ?[X172]: 112.63/113.37 (X171( 112.63/113.37 X172) & 112.63/113.37 in( 112.63/113.37 X172,X170)))) => 112.63/113.37 (![X173]: 112.63/113.37 (in( 112.63/113.37 X173,X170) => 112.63/113.37 (~ 112.63/113.37 X171( 112.63/113.37 X173)))))) => 112.63/113.37 ((![X174, 112.63/113.37 X175:( 112.63/113.37 $i > $o)]: 112.63/113.37 (( 112.63/113.37 ~ 112.63/113.37 ( 112.63/113.37 ![X176]: 112.63/113.37 (in( 112.63/113.37 X176,X174) => 112.63/113.37 X175( 112.63/113.37 X176)))) => 112.63/113.37 ( 112.63/113.37 ?[X177]: 112.63/113.37 (( 112.63/113.37 ~ 112.63/113.37 X175( 112.63/113.37 X177)) & 112.63/113.37 in( 112.63/113.37 X177,X174))))) => 112.63/113.37 ((![X178:( 112.63/113.37 $i > $o)]: 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ?[X179]: 112.63/113.37 (( 112.63/113.37 ![X180]: 112.63/113.37 (X178( 112.63/113.37 X180) => 112.63/113.37 (X179 = 112.63/113.37 X180))) & 112.63/113.37 X178( 112.63/113.37 X179))) => 112.63/113.37 ( 112.63/113.37 ?[X181]: 112.63/113.37 (( 112.63/113.37 ![X182]: 112.63/113.37 (X178( 112.63/113.37 X182) => 112.63/113.37 (X181 = 112.63/113.37 X182))) & 112.63/113.37 X178( 112.63/113.37 X181))))) => 112.63/113.37 ((![X183:( 112.63/113.37 $i > $o)]: 112.63/113.37 (( 112.63/113.37 ?[X184]: 112.63/113.37 X183( 112.63/113.37 X184)) => 112.63/113.37 (( 112.63/113.37 ![X185, 112.63/113.37 X186]: 112.63/113.37 (X183( 112.63/113.37 X185) => 112.63/113.37 (X183( 112.63/113.37 X186) => 112.63/113.37 (X185 = 112.63/113.37 X186)))) => 112.63/113.37 (?[X187]: 112.63/113.37 (( 112.63/113.37 ![X188]: 112.63/113.37 (X183( 112.63/113.37 X188) => 112.63/113.37 (X187 = 112.63/113.37 X188))) & 112.63/113.37 X183( 112.63/113.37 X187)))))) => 112.63/113.37 ((![X189:( 112.63/113.37 $i > $o)]: 112.63/113.37 (( 112.63/113.37 ?[X190]: 112.63/113.37 (![X191]: 112.63/113.37 (X189( 112.63/113.37 X191) <=> 112.63/113.37 (X191 = 112.63/113.37 X190)))) => 112.63/113.37 (?[X192]: 112.63/113.37 (( 112.63/113.37 ![X193]: 112.63/113.37 (X189( 112.63/113.37 X193) => 112.63/113.37 (X192 = 112.63/113.37 X193))) & 112.63/113.37 X189( 112.63/113.37 X192))))) => 112.63/113.37 (( 112.63/113.37 ![X194, 112.63/113.37 X195]: 112.63/113.37 (( 112.63/113.37 X194 = 112.63/113.37 X195) => 112.63/113.37 (![X196, 112.63/113.37 X197]: 112.63/113.37 (( 112.63/113.37 X196 = 112.63/113.37 X197) => 112.63/113.37 (in( 112.63/113.37 X196,X194) => 112.63/113.37 in( 112.63/113.37 X197,X195)))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X198, 112.63/113.37 X199]: 112.63/113.37 (( 112.63/113.37 X198 = 112.63/113.37 X199) => 112.63/113.37 (![X200, 112.63/113.37 X201]: 112.63/113.37 (( 112.63/113.37 X200 = 112.63/113.37 X201) => 112.63/113.37 (in( 112.63/113.37 X200,X198) <=> 112.63/113.37 in( 112.63/113.37 X201,X199)))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X202:( 112.63/113.37 $i > $o)]: 112.63/113.37 (( 112.63/113.37 ?[X203]: 112.63/113.37 (( 112.63/113.37 ![X204]: 112.63/113.37 (X202( 112.63/113.37 X204) => 112.63/113.37 (X203 = 112.63/113.37 X204))) & 112.63/113.37 X202( 112.63/113.37 X203))) => 112.63/113.37 (![X205, 112.63/113.37 X206]: 112.63/113.37 (X202( 112.63/113.37 X205) => 112.63/113.37 (X202( 112.63/113.37 X206) => 112.63/113.37 (X205 = 112.63/113.37 X206)))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X207:( 112.63/113.37 $i > $o), 112.63/113.37 X208:( 112.63/113.37 $i > $o)]: 112.63/113.37 (( 112.63/113.37 ![X209, 112.63/113.37 X210]: 112.63/113.37 (( 112.63/113.37 X209 = 112.63/113.37 X210) => 112.63/113.37 (X207( 112.63/113.37 X209) <=> 112.63/113.37 X208( 112.63/113.37 X210)))) => 112.63/113.37 (( 112.63/113.37 ?[X211]: 112.63/113.37 zip_tseitin5( 112.63/113.37 X211,X207)) <=> 112.63/113.37 (?[X213]: 112.63/113.37 zip_tseitin5( 112.63/113.37 X213,X208))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 emptyset = 112.63/113.37 emptyset) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X215, 112.63/113.37 X216]: 112.63/113.37 (( 112.63/113.37 X215 = 112.63/113.37 X216) => 112.63/113.37 (![X217, 112.63/113.37 X218]: 112.63/113.37 (( 112.63/113.37 X217 = 112.63/113.37 X218) => 112.63/113.37 (setadjoin( 112.63/113.37 X215,X217) = 112.63/113.37 setadjoin( 112.63/113.37 X216,X218)))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X219, 112.63/113.37 X220]: 112.63/113.37 (( 112.63/113.37 X219 = 112.63/113.37 X220) => 112.63/113.37 (powerset( 112.63/113.37 X219) = 112.63/113.37 powerset( 112.63/113.37 X220)))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X221, 112.63/113.37 X222]: 112.63/113.37 (( 112.63/113.37 X221 = 112.63/113.37 X222) => 112.63/113.37 (setunion( 112.63/113.37 X221) = 112.63/113.37 setunion( 112.63/113.37 X222)))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 omega = 112.63/113.37 omega) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X223:( 112.63/113.37 $i > $o)]: 112.63/113.37 (( 112.63/113.37 ?[X224]: 112.63/113.37 (( 112.63/113.37 ![X225]: 112.63/113.37 (X223( 112.63/113.37 X225) => 112.63/113.37 (X224 = 112.63/113.37 X225))) & 112.63/113.37 X223( 112.63/113.37 X224))) => 112.63/113.37 (![X226, 112.63/113.37 X227]: 112.63/113.37 (X223( 112.63/113.37 X226) => 112.63/113.37 (X223( 112.63/113.37 X227) => 112.63/113.37 (X226 = 112.63/113.37 X227)))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X228:( 112.63/113.37 $i > $o), 112.63/113.37 X229:( 112.63/113.37 $i > $o)]: 112.63/113.37 (( 112.63/113.37 ![X230, 112.63/113.37 X231]: 112.63/113.37 (( 112.63/113.37 X230 = 112.63/113.37 X231) => 112.63/113.37 (X228( 112.63/113.37 X230) <=> 112.63/113.37 X229( 112.63/113.37 X231)))) => 112.63/113.37 (( 112.63/113.37 ?[X232]: 112.63/113.37 (( 112.63/113.37 ![X233]: 112.63/113.37 (X228( 112.63/113.37 X233) => 112.63/113.37 (X232 = 112.63/113.37 X233))) & 112.63/113.37 X228( 112.63/113.37 X232))) => 112.63/113.37 (( 112.63/113.37 ?[X234]: 112.63/113.37 (( 112.63/113.37 ![X235]: 112.63/113.37 (X229( 112.63/113.37 X235) => 112.63/113.37 (X234 = 112.63/113.37 X235))) & 112.63/113.37 X229( 112.63/113.37 X234))) => 112.63/113.37 (descr( 112.63/113.37 '#ll_6'( 112.63/113.37 X228)) = 112.63/113.37 descr( 112.63/113.37 '#ll_6'( 112.63/113.37 X229))))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X236, 112.63/113.37 X237]: 112.63/113.37 (( 112.63/113.37 X236 = 112.63/113.37 X237) => 112.63/113.37 (![X238:( 112.63/113.37 $i > $o), 112.63/113.37 X239:( 112.63/113.37 $i > $o)]: 112.63/113.37 (( 112.63/113.37 ![X240]: 112.63/113.37 (in( 112.63/113.37 X240,X236) => 112.63/113.37 (![X241]: 112.63/113.37 (in( 112.63/113.37 X241,X237) => 112.63/113.37 (( 112.63/113.37 X240 = 112.63/113.37 X241) => 112.63/113.37 (X238( 112.63/113.37 X240) <=> 112.63/113.37 X239( 112.63/113.37 X241))))))) => 112.63/113.37 (dsetconstr( 112.63/113.37 X236, 112.63/113.37 '#ll_6'( 112.63/113.37 X238)) = 112.63/113.37 dsetconstr( 112.63/113.37 X237, 112.63/113.37 '#ll_6'( 112.63/113.37 X239))))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X242, 112.63/113.37 X243]: 112.63/113.37 (( 112.63/113.37 ![X244]: 112.63/113.37 (in( 112.63/113.37 X244,X242) => 112.63/113.37 in( 112.63/113.37 X244,X243))) => 112.63/113.37 subset( 112.63/113.37 X242,X243))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X245, 112.63/113.37 X246]: 112.63/113.37 (( 112.63/113.37 X245 = 112.63/113.37 X246) => 112.63/113.37 subset( 112.63/113.37 X246,X245))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X247, 112.63/113.37 X248]: 112.63/113.37 (( 112.63/113.37 X247 = 112.63/113.37 X248) => 112.63/113.37 subset( 112.63/113.37 X247,X248))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X249, 112.63/113.37 X250]: 112.63/113.37 (( 112.63/113.37 ![X251]: 112.63/113.37 (in( 112.63/113.37 X251,X249) => 112.63/113.37 in( 112.63/113.37 X251,X250))) => 112.63/113.37 subset( 112.63/113.37 X249,X250))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X252]: 112.63/113.37 subset( 112.63/113.37 emptyset, 112.63/113.37 X252)) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X253, 112.63/113.37 X254,X255]: 112.63/113.37 (subset( 112.63/113.37 X253,X254) => 112.63/113.37 (in( 112.63/113.37 X255,X253) => 112.63/113.37 in( 112.63/113.37 X255,X254)))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X256, 112.63/113.37 X257,X258]: 112.63/113.37 (subset( 112.63/113.37 X256,X257) => 112.63/113.37 (( 112.63/113.37 ~ 112.63/113.37 in( 112.63/113.37 X258,X257)) => 112.63/113.37 (~ 112.63/113.37 in( 112.63/113.37 X258,X256))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X259, 112.63/113.37 X260,X261]: 112.63/113.37 (in( 112.63/113.37 X261,X259) => 112.63/113.37 (( 112.63/113.37 ~ 112.63/113.37 in( 112.63/113.37 X261,X260)) => 112.63/113.37 (~ 112.63/113.37 subset( 112.63/113.37 X259,X260))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X262, 112.63/113.37 X263]: 112.63/113.37 (( 112.63/113.37 ~ 112.63/113.37 subset( 112.63/113.37 X262,X263)) => 112.63/113.37 (X262 != 112.63/113.37 X263))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X264, 112.63/113.37 X265,X266]: 112.63/113.37 (in( 112.63/113.37 X266,X264) => 112.63/113.37 (( 112.63/113.37 ~ 112.63/113.37 in( 112.63/113.37 X266,X265)) => 112.63/113.37 (X264 != 112.63/113.37 X265)))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X267]: 112.63/113.37 subset( 112.63/113.37 X267,X267)) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X268, 112.63/113.37 X269,X270]: 112.63/113.37 (subset( 112.63/113.37 X268,X269) => 112.63/113.37 (subset( 112.63/113.37 X269,X270) => 112.63/113.37 subset( 112.63/113.37 X268,X270)))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X271, 112.63/113.37 X272]: 112.63/113.37 subset( 112.63/113.37 X272, 112.63/113.37 setadjoin( 112.63/113.37 X271,X272))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X273, 112.63/113.37 X274,X275]: 112.63/113.37 (subset( 112.63/113.37 X273,X275) => 112.63/113.37 subset( 112.63/113.37 X273, 112.63/113.37 setadjoin( 112.63/113.37 X274,X275)))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X276, 112.63/113.37 X277]: 112.63/113.37 (subset( 112.63/113.37 X276,X277) => 112.63/113.37 in( 112.63/113.37 X276, 112.63/113.37 powerset( 112.63/113.37 X277)))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X278, 112.63/113.37 X279]: 112.63/113.37 (subset( 112.63/113.37 X278,X279) => 112.63/113.37 (subset( 112.63/113.37 X279,X278) => 112.63/113.37 (X278 = 112.63/113.37 X279)))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X280]: 112.63/113.37 (subset( 112.63/113.37 X280, 112.63/113.37 emptyset) => 112.63/113.37 (X280 = 112.63/113.37 emptyset))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X281, 112.63/113.37 X282]: 112.63/113.37 (subset( 112.63/113.37 X282,X281) => 112.63/113.37 in( 112.63/113.37 X282, 112.63/113.37 powerset( 112.63/113.37 X281)))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X283, 112.63/113.37 X284]: 112.63/113.37 (in( 112.63/113.37 X284, 112.63/113.37 powerset( 112.63/113.37 X283)) => 112.63/113.37 subset( 112.63/113.37 X284,X283))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X285]: 112.63/113.37 in( 112.63/113.37 X285, 112.63/113.37 powerset( 112.63/113.37 X285))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X286, 112.63/113.37 X287]: 112.63/113.37 (subset( 112.63/113.37 X286,X287) => 112.63/113.37 subset( 112.63/113.37 powerset( 112.63/113.37 X286), 112.63/113.37 powerset( 112.63/113.37 X287)))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X288, 112.63/113.37 X289:( 112.63/113.37 $i > $o)]: 112.63/113.37 in( 112.63/113.37 dsetconstr( 112.63/113.37 X288, 112.63/113.37 '#ll_6'( 112.63/113.37 X289)), 112.63/113.37 powerset( 112.63/113.37 X288))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X290, 112.63/113.37 X291:( 112.63/113.37 $i > $o)]: 112.63/113.37 subset( 112.63/113.37 dsetconstr( 112.63/113.37 X290, 112.63/113.37 '#ll_6'( 112.63/113.37 X291)), 112.63/113.37 X290)) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X292, 112.63/113.37 X293,X294]: 112.63/113.37 (in( 112.63/113.37 X294,X292) => 112.63/113.37 in( 112.63/113.37 X294, 112.63/113.37 binunion( 112.63/113.37 X292,X293)))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X295, 112.63/113.37 X296]: 112.63/113.37 in( 112.63/113.37 X296, 112.63/113.37 setadjoin( 112.63/113.37 X295, 112.63/113.37 setadjoin( 112.63/113.37 X296, 112.63/113.37 emptyset)))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X297, 112.63/113.37 X298,X299]: 112.63/113.37 (in( 112.63/113.37 X299,X298) => 112.63/113.37 in( 112.63/113.37 X299, 112.63/113.37 binunion( 112.63/113.37 X297,X298)))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X300, 112.63/113.37 X301, 112.63/113.37 X302, 112.63/113.37 X303:$o]: 112.63/113.37 (in( 112.63/113.37 X302, 112.63/113.37 binunion( 112.63/113.37 X300,X301)) => 112.63/113.37 (( 112.63/113.37 in( 112.63/113.37 X302,X300) => 112.63/113.37 X303) => 112.63/113.37 (( 112.63/113.37 in( 112.63/113.37 X302,X301) => 112.63/113.37 X303) => 112.63/113.37 X303)))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X304, 112.63/113.37 X305,X306]: 112.63/113.37 (in( 112.63/113.37 X306, 112.63/113.37 binunion( 112.63/113.37 X304,X305)) => 112.63/113.37 (in( 112.63/113.37 X306,X305) | 112.63/113.37 in( 112.63/113.37 X306,X304)))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X307, 112.63/113.37 X308]: 112.63/113.37 subset( 112.63/113.37 X307, 112.63/113.37 binunion( 112.63/113.37 X307,X308))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X309, 112.63/113.37 X310]: 112.63/113.37 subset( 112.63/113.37 X310, 112.63/113.37 binunion( 112.63/113.37 X309,X310))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X311, 112.63/113.37 X312,X313]: 112.63/113.37 (in( 112.63/113.37 X313,X311) => 112.63/113.37 (in( 112.63/113.37 X313,X312) => 112.63/113.37 in( 112.63/113.37 X313, 112.63/113.37 binintersect( 112.63/113.37 X311,X312))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X314, 112.63/113.37 X315,X316]: 112.63/113.37 (subset( 112.63/113.37 X316,X314) => 112.63/113.37 (subset( 112.63/113.37 X316,X315) => 112.63/113.37 subset( 112.63/113.37 X316, 112.63/113.37 binintersect( 112.63/113.37 X314,X315))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X317, 112.63/113.37 X318,X319]: 112.63/113.37 (in( 112.63/113.37 X319, 112.63/113.37 binintersect( 112.63/113.37 X317,X318)) => 112.63/113.37 in( 112.63/113.37 X319,X317))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X320, 112.63/113.37 X321]: 112.63/113.37 subset( 112.63/113.37 binintersect( 112.63/113.37 X320,X321), 112.63/113.37 X320)) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X322, 112.63/113.37 X323]: 112.63/113.37 (subset( 112.63/113.37 X322,X323) => 112.63/113.37 (binintersect( 112.63/113.37 X322,X323) = 112.63/113.37 X322))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X324, 112.63/113.37 X325]: 112.63/113.37 (( 112.63/113.37 binintersect( 112.63/113.37 X324,X325) = 112.63/113.37 X325) => 112.63/113.37 subset( 112.63/113.37 X325,X324))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X326, 112.63/113.37 X327,X328]: 112.63/113.37 (in( 112.63/113.37 X328, 112.63/113.37 binintersect( 112.63/113.37 X326,X327)) => 112.63/113.37 in( 112.63/113.37 X328,X327))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X329, 112.63/113.37 X330]: 112.63/113.37 (( 112.63/113.37 ~ 112.63/113.37 ( 112.63/113.37 ?[X331]: 112.63/113.37 (in( 112.63/113.37 X331,X330) & 112.63/113.37 in( 112.63/113.37 X331,X329)))) => 112.63/113.37 (binintersect( 112.63/113.37 X329,X330) = 112.63/113.37 emptyset))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X332, 112.63/113.37 X333]: 112.63/113.37 subset( 112.63/113.37 binintersect( 112.63/113.37 X332,X333), 112.63/113.37 X333)) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X334, 112.63/113.37 X335]: 112.63/113.37 (subset( 112.63/113.37 X335,X334) => 112.63/113.37 (binintersect( 112.63/113.37 X334,X335) = 112.63/113.37 X335))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X336, 112.63/113.37 X337]: 112.63/113.37 (( 112.63/113.37 binintersect( 112.63/113.37 X336,X337) = 112.63/113.37 X336) => 112.63/113.37 subset( 112.63/113.37 X336,X337))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X338, 112.63/113.37 X339,X340]: 112.63/113.37 (binintersect( 112.63/113.37 X338, 112.63/113.37 binunion( 112.63/113.37 X339,X340)) = 112.63/113.37 binunion( 112.63/113.37 binintersect( 112.63/113.37 X338,X339), 112.63/113.37 binintersect( 112.63/113.37 X338,X340)))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X341, 112.63/113.37 X342,X343]: 112.63/113.37 (in( 112.63/113.37 X343,X341) => 112.63/113.37 (( 112.63/113.37 ~ 112.63/113.37 in( 112.63/113.37 X343,X342)) => 112.63/113.37 in( 112.63/113.37 X343, 112.63/113.37 setminus( 112.63/113.37 X341,X342))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X344, 112.63/113.37 X345,X346]: 112.63/113.37 (in( 112.63/113.37 X346, 112.63/113.37 setminus( 112.63/113.37 X344,X345)) => 112.63/113.37 in( 112.63/113.37 X346,X344))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X347, 112.63/113.37 X348,X349]: 112.63/113.37 (in( 112.63/113.37 X349, 112.63/113.37 setminus( 112.63/113.37 X347,X348)) => 112.63/113.37 (~ 112.63/113.37 in( 112.63/113.37 X349,X348)))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X350, 112.63/113.37 X351]: 112.63/113.37 (subset( 112.63/113.37 X350,X351) => 112.63/113.37 (setminus( 112.63/113.37 X350,X351) = 112.63/113.37 emptyset))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X352, 112.63/113.37 X353,X354]: 112.63/113.37 (( 112.63/113.37 ~ 112.63/113.37 in( 112.63/113.37 X354, 112.63/113.37 setminus( 112.63/113.37 X352,X353))) => 112.63/113.37 (in( 112.63/113.37 X354,X352) => 112.63/113.37 in( 112.63/113.37 X354,X353)))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X355, 112.63/113.37 X356,X357]: 112.63/113.37 (( 112.63/113.37 ~ 112.63/113.37 in( 112.63/113.37 X357, 112.63/113.37 setminus( 112.63/113.37 X355,X356))) => 112.63/113.37 (( 112.63/113.37 ~ 112.63/113.37 in( 112.63/113.37 X357,X356)) => 112.63/113.37 (~ 112.63/113.37 in( 112.63/113.37 X357,X355))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X358, 112.63/113.37 X359,X360]: 112.63/113.37 (( 112.63/113.37 ~ 112.63/113.37 in( 112.63/113.37 X360,X358)) => 112.63/113.37 (~ 112.63/113.37 in( 112.63/113.37 X360, 112.63/113.37 setminus( 112.63/113.37 X358,X359))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X361, 112.63/113.37 X362,X363]: 112.63/113.37 (in( 112.63/113.37 X363,X362) => 112.63/113.37 (~ 112.63/113.37 in( 112.63/113.37 X363, 112.63/113.37 setminus( 112.63/113.37 X361,X362))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X364, 112.63/113.37 X365]: 112.63/113.37 subset( 112.63/113.37 setminus( 112.63/113.37 X364,X365), 112.63/113.37 X364)) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X366, 112.63/113.37 X367]: 112.63/113.37 (( 112.63/113.37 setminus( 112.63/113.37 X366,X367) = 112.63/113.37 emptyset) => 112.63/113.37 subset( 112.63/113.37 X366,X367))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X368, 112.63/113.37 X369,X370]: 112.63/113.37 (in( 112.63/113.37 X370, 112.63/113.37 symdiff( 112.63/113.37 X368,X369)) => 112.63/113.37 (![X371:$o]: 112.63/113.37 (( 112.63/113.37 in( 112.63/113.37 X370,X368) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ~ 112.63/113.37 in( 112.63/113.37 X370,X369)) => 112.63/113.37 X371)) => 112.63/113.37 (( 112.63/113.37 ( 112.63/113.37 ~ 112.63/113.37 in( 112.63/113.37 X370,X368)) => 112.63/113.37 ( 112.63/113.37 in( 112.63/113.37 X370,X369) => 112.63/113.37 X371)) => 112.63/113.37 X371))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X372, 112.63/113.37 X373,X374]: 112.63/113.37 (in( 112.63/113.37 X374,X372) => 112.63/113.37 (( 112.63/113.37 ~ 112.63/113.37 in( 112.63/113.37 X374,X373)) => 112.63/113.37 in( 112.63/113.37 X374, 112.63/113.37 symdiff( 112.63/113.37 X372,X373))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X375, 112.63/113.37 X376,X377]: 112.63/113.37 (( 112.63/113.37 ~ 112.63/113.37 in( 112.63/113.37 X377,X375)) => 112.63/113.37 (in( 112.63/113.37 X377,X376) => 112.63/113.37 in( 112.63/113.37 X377, 112.63/113.37 symdiff( 112.63/113.37 X375,X376))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X378, 112.63/113.37 X379,X380]: 112.63/113.37 (in( 112.63/113.37 X380,X378) => 112.63/113.37 (in( 112.63/113.37 X380,X379) => 112.63/113.37 (~ 112.63/113.37 in( 112.63/113.37 X380, 112.63/113.37 symdiff( 112.63/113.37 X378,X379)))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X381, 112.63/113.37 X382,X383]: 112.63/113.37 (( 112.63/113.37 ~ 112.63/113.37 in( 112.63/113.37 X383,X381)) => 112.63/113.37 (( 112.63/113.37 ~ 112.63/113.37 in( 112.63/113.37 X383,X382)) => 112.63/113.37 (~ 112.63/113.37 in( 112.63/113.37 X383, 112.63/113.37 symdiff( 112.63/113.37 X381,X382)))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X384, 112.63/113.37 X385]: 112.63/113.37 in( 112.63/113.37 X385, 112.63/113.37 setadjoin( 112.63/113.37 X384, 112.63/113.37 setadjoin( 112.63/113.37 X385, 112.63/113.37 emptyset)))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X386, 112.63/113.37 X387]: 112.63/113.37 in( 112.63/113.37 X386, 112.63/113.37 setunion( 112.63/113.37 setadjoin( 112.63/113.37 setadjoin( 112.63/113.37 X386, 112.63/113.37 emptyset), 112.63/113.37 setadjoin( 112.63/113.37 setadjoin( 112.63/113.37 X386, 112.63/113.37 setadjoin( 112.63/113.37 X387, 112.63/113.37 emptyset)), 112.63/113.37 emptyset))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X388, 112.63/113.37 X389]: 112.63/113.37 in( 112.63/113.37 X389, 112.63/113.37 setunion( 112.63/113.37 setadjoin( 112.63/113.37 setadjoin( 112.63/113.37 X388, 112.63/113.37 emptyset), 112.63/113.37 setadjoin( 112.63/113.37 setadjoin( 112.63/113.37 X388, 112.63/113.37 setadjoin( 112.63/113.37 X389, 112.63/113.37 emptyset)), 112.63/113.37 emptyset))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X390, 112.63/113.37 X391]: 112.63/113.37 iskpair( 112.63/113.37 setadjoin( 112.63/113.37 setadjoin( 112.63/113.37 X390, 112.63/113.37 emptyset), 112.63/113.37 setadjoin( 112.63/113.37 setadjoin( 112.63/113.37 X390, 112.63/113.37 setadjoin( 112.63/113.37 X391, 112.63/113.37 emptyset)), 112.63/113.37 emptyset)))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X392, 112.63/113.37 X393]: 112.63/113.37 iskpair( 112.63/113.37 kpair( 112.63/113.37 X392,X393))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X394, 112.63/113.37 X395]: 112.63/113.37 (in( 112.63/113.37 X395,X394) => 112.63/113.37 subset( 112.63/113.37 setadjoin( 112.63/113.37 X395, 112.63/113.37 emptyset), 112.63/113.37 X394))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X396, 112.63/113.37 X397]: 112.63/113.37 (in( 112.63/113.37 X397,X396) => 112.63/113.37 in( 112.63/113.37 setadjoin( 112.63/113.37 X397, 112.63/113.37 emptyset), 112.63/113.37 powerset( 112.63/113.37 X396)))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X398, 112.63/113.37 X399,X400]: 112.63/113.37 (in( 112.63/113.37 X400,X398) => 112.63/113.37 in( 112.63/113.37 setadjoin( 112.63/113.37 X400, 112.63/113.37 emptyset), 112.63/113.37 powerset( 112.63/113.37 binunion( 112.63/113.37 X398,X399))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X401, 112.63/113.37 X402,X403]: 112.63/113.37 (in( 112.63/113.37 X403, 112.63/113.37 setadjoin( 112.63/113.37 X401, 112.63/113.37 setadjoin( 112.63/113.37 X402, 112.63/113.37 emptyset))) => 112.63/113.37 (( 112.63/113.37 X403 = 112.63/113.37 X402) | 112.63/113.37 (X403 = 112.63/113.37 X401)))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X404, 112.63/113.37 X405,X406]: 112.63/113.37 (in( 112.63/113.37 X406,X404) => 112.63/113.37 (![X407]: 112.63/113.37 (in( 112.63/113.37 X407,X405) => 112.63/113.37 subset( 112.63/113.37 setadjoin( 112.63/113.37 X406, 112.63/113.37 setadjoin( 112.63/113.37 X407, 112.63/113.37 emptyset)), 112.63/113.37 binunion( 112.63/113.37 X404,X405)))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X408, 112.63/113.37 X409,X410]: 112.63/113.37 (in( 112.63/113.37 X410,X408) => 112.63/113.37 (![X411]: 112.63/113.37 (in( 112.63/113.37 X411,X409) => 112.63/113.37 in( 112.63/113.37 setadjoin( 112.63/113.37 X410, 112.63/113.37 setadjoin( 112.63/113.37 X411, 112.63/113.37 emptyset)), 112.63/113.37 powerset( 112.63/113.37 binunion( 112.63/113.37 X408,X409))))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X412, 112.63/113.37 X413,X414]: 112.63/113.37 (in( 112.63/113.37 X414,X412) => 112.63/113.37 (![X415]: 112.63/113.37 (in( 112.63/113.37 X415,X413) => 112.63/113.37 subset( 112.63/113.37 setadjoin( 112.63/113.37 setadjoin( 112.63/113.37 X414, 112.63/113.37 emptyset), 112.63/113.37 setadjoin( 112.63/113.37 setadjoin( 112.63/113.37 X414, 112.63/113.37 setadjoin( 112.63/113.37 X415, 112.63/113.37 emptyset)), 112.63/113.37 emptyset)), 112.63/113.37 powerset( 112.63/113.37 binunion( 112.63/113.37 X412,X413))))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X416, 112.63/113.37 X417,X418]: 112.63/113.37 (in( 112.63/113.37 X418,X416) => 112.63/113.37 (![X419]: 112.63/113.37 (in( 112.63/113.37 X419,X417) => 112.63/113.37 in( 112.63/113.37 setadjoin( 112.63/113.37 setadjoin( 112.63/113.37 X418, 112.63/113.37 emptyset), 112.63/113.37 setadjoin( 112.63/113.37 setadjoin( 112.63/113.37 X418, 112.63/113.37 setadjoin( 112.63/113.37 X419, 112.63/113.37 emptyset)), 112.63/113.37 emptyset)), 112.63/113.37 powerset( 112.63/113.37 powerset( 112.63/113.37 binunion( 112.63/113.37 X416,X417)))))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X420, 112.63/113.37 X421,X422]: 112.63/113.37 (in( 112.63/113.37 X422,X420) => 112.63/113.37 (![X423]: 112.63/113.37 (in( 112.63/113.37 X423,X421) => 112.63/113.37 in( 112.63/113.37 kpair( 112.63/113.37 X422,X423), 112.63/113.37 powerset( 112.63/113.37 powerset( 112.63/113.37 binunion( 112.63/113.37 X420,X421)))))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X424, 112.63/113.37 X425,X426]: 112.63/113.37 (in( 112.63/113.37 X426,X424) => 112.63/113.37 (![X427]: 112.63/113.37 (in( 112.63/113.37 X427,X425) => 112.63/113.37 in( 112.63/113.37 kpair( 112.63/113.37 X426,X427), 112.63/113.37 cartprod( 112.63/113.37 X424,X425)))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X428, 112.63/113.37 X429,X430]: 112.63/113.37 (in( 112.63/113.37 X430, 112.63/113.37 cartprod( 112.63/113.37 X428,X429)) => 112.63/113.37 (?[X431]: 112.63/113.37 (( 112.63/113.37 ?[X432]: 112.63/113.37 (( 112.63/113.37 X430 = 112.63/113.37 kpair( 112.63/113.37 X431,X432)) & 112.63/113.37 in( 112.63/113.37 X432,X429))) & 112.63/113.37 in( 112.63/113.37 X431,X428))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X433, 112.63/113.37 X434,X435]: 112.63/113.37 (in( 112.63/113.37 X435, 112.63/113.37 cartprod( 112.63/113.37 X433,X434)) => 112.63/113.37 iskpair( 112.63/113.37 X435))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X436, 112.63/113.37 X437]: 112.63/113.37 (in( 112.63/113.37 X437, 112.63/113.37 setunion( 112.63/113.37 X436)) => 112.63/113.37 (?[X438]: 112.63/113.37 (in( 112.63/113.37 X437,X438) & 112.63/113.37 in( 112.63/113.37 X438,X436))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X439]: 112.63/113.37 subset( 112.63/113.37 setunion( 112.63/113.37 setadjoin( 112.63/113.37 X439, 112.63/113.37 emptyset)), 112.63/113.37 X439)) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X440]: 112.63/113.37 subset( 112.63/113.37 X440, 112.63/113.37 setunion( 112.63/113.37 setadjoin( 112.63/113.37 X440, 112.63/113.37 emptyset)))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X441]: 112.63/113.37 (setunion( 112.63/113.37 setadjoin( 112.63/113.37 X441, 112.63/113.37 emptyset)) = 112.63/113.37 X441)) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X442, 112.63/113.37 X443:( 112.63/113.37 $i > $o)]: 112.63/113.37 (( 112.63/113.37 ![X444]: 112.63/113.37 (in( 112.63/113.37 X444,X442) => 112.63/113.37 (![X445]: 112.63/113.37 (in( 112.63/113.37 X445,X442) => 112.63/113.37 (X443( 112.63/113.37 X444) => 112.63/113.37 (X443( 112.63/113.37 X445) => 112.63/113.37 (X444 = 112.63/113.37 X445))))))) => 112.63/113.37 (( 112.63/113.37 ?[X446]: 112.63/113.37 (X443( 112.63/113.37 X446) & 112.63/113.37 in( 112.63/113.37 X446,X442))) => 112.63/113.37 (?[X447]: 112.63/113.37 (( 112.63/113.37 dsetconstr( 112.63/113.37 X442, 112.63/113.37 '#ll_6'( 112.63/113.37 X443)) = 112.63/113.37 setadjoin( 112.63/113.37 X447, 112.63/113.37 emptyset)) & 112.63/113.37 in( 112.63/113.37 X447, 112.63/113.37 dsetconstr( 112.63/113.37 X442, 112.63/113.37 '#ll_6'( 112.63/113.37 X443)))))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X448, 112.63/113.37 X449:( 112.63/113.37 $i > $o)]: 112.63/113.37 (( 112.63/113.37 ?[X450]: 112.63/113.37 (( 112.63/113.37 dsetconstr( 112.63/113.37 X448, 112.63/113.37 '#ll_6'( 112.63/113.37 X449)) = 112.63/113.37 setadjoin( 112.63/113.37 X450, 112.63/113.37 emptyset)) & 112.63/113.37 in( 112.63/113.37 X450, 112.63/113.37 dsetconstr( 112.63/113.37 X448, 112.63/113.37 '#ll_6'( 112.63/113.37 X449))))) => 112.63/113.37 (?[X451]: 112.63/113.37 (X449( 112.63/113.37 X451) & 112.63/113.37 in( 112.63/113.37 X451,X448))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X452, 112.63/113.37 X453:( 112.63/113.37 $i > $o), 112.63/113.37 X454]: 112.63/113.37 (in( 112.63/113.37 X454,X452) => 112.63/113.37 (X453( 112.63/113.37 X454) => 112.63/113.37 (( 112.63/113.37 ![X455]: 112.63/113.37 (in( 112.63/113.37 X455,X452) => 112.63/113.37 (X453( 112.63/113.37 X455) => 112.63/113.37 (X455 = 112.63/113.37 X454)))) => 112.63/113.37 (?[X456]: 112.63/113.37 (( 112.63/113.37 dsetconstr( 112.63/113.37 X452, 112.63/113.37 '#ll_6'( 112.63/113.37 X453)) = 112.63/113.37 setadjoin( 112.63/113.37 X456, 112.63/113.37 emptyset)) & 112.63/113.37 in( 112.63/113.37 X456, 112.63/113.37 dsetconstr( 112.63/113.37 X452, 112.63/113.37 '#ll_6'( 112.63/113.37 X453))))))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X457, 112.63/113.37 X458:( 112.63/113.37 $i > $o)]: 112.63/113.37 (( 112.63/113.37 ![X459]: 112.63/113.37 (in( 112.63/113.37 X459,X457) => 112.63/113.37 (![X460]: 112.63/113.37 (in( 112.63/113.37 X460,X457) => 112.63/113.37 (X458( 112.63/113.37 X459) => 112.63/113.37 (X458( 112.63/113.37 X460) => 112.63/113.37 (X459 = 112.63/113.37 X460))))))) => 112.63/113.37 (( 112.63/113.37 ?[X461]: 112.63/113.37 (X458( 112.63/113.37 X461) & 112.63/113.37 in( 112.63/113.37 X461,X457))) => 112.63/113.37 (?[X462]: 112.63/113.37 (( 112.63/113.37 dsetconstr( 112.63/113.37 X457, 112.63/113.37 '#ll_6'( 112.63/113.37 X458)) = 112.63/113.37 setadjoin( 112.63/113.37 X462, 112.63/113.37 emptyset)) & 112.63/113.37 in( 112.63/113.37 X462, 112.63/113.37 dsetconstr( 112.63/113.37 X457, 112.63/113.37 '#ll_6'( 112.63/113.37 X458)))))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X463, 112.63/113.37 X464]: 112.63/113.37 (( 112.63/113.37 setadjoin( 112.63/113.37 X463, 112.63/113.37 emptyset) = 112.63/113.37 setadjoin( 112.63/113.37 X464, 112.63/113.37 emptyset)) => 112.63/113.37 (X463 = 112.63/113.37 X464))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X465, 112.63/113.37 X466,X467]: 112.63/113.37 (in( 112.63/113.37 setadjoin( 112.63/113.37 X467, 112.63/113.37 emptyset), 112.63/113.37 setadjoin( 112.63/113.37 setadjoin( 112.63/113.37 X465, 112.63/113.37 emptyset), 112.63/113.37 setadjoin( 112.63/113.37 setadjoin( 112.63/113.37 X465, 112.63/113.37 setadjoin( 112.63/113.37 X466, 112.63/113.37 emptyset)), 112.63/113.37 emptyset))) => 112.63/113.37 (X465 = 112.63/113.37 X467))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X468]: 112.63/113.37 (iskpair( 112.63/113.37 X468) => 112.63/113.37 (?[X469]: 112.63/113.37 (( 112.63/113.37 dsetconstr( 112.63/113.37 setunion( 112.63/113.37 X468), 112.63/113.37 '#ll_5'( 112.63/113.37 X468)) = 112.63/113.37 setadjoin( 112.63/113.37 X469, 112.63/113.37 emptyset)) & 112.63/113.37 in( 112.63/113.37 X469, 112.63/113.37 dsetconstr( 112.63/113.37 setunion( 112.63/113.37 X468), 112.63/113.37 '#ll_5'( 112.63/113.37 X468))))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X470]: 112.63/113.37 (( 112.63/113.37 ?[X471]: 112.63/113.37 (( 112.63/113.37 X470 = 112.63/113.37 setadjoin( 112.63/113.37 X471, 112.63/113.37 emptyset)) & 112.63/113.37 in( 112.63/113.37 X471,X470))) => 112.63/113.37 in( 112.63/113.37 setunion( 112.63/113.37 X470), 112.63/113.37 X470))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X472, 112.63/113.37 X473]: 112.63/113.37 (kfst( 112.63/113.37 kpair( 112.63/113.37 X472,X473)) = 112.63/113.37 X472)) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X474, 112.63/113.37 X475,X476]: 112.63/113.37 (in( 112.63/113.37 X476, 112.63/113.37 cartprod( 112.63/113.37 X474,X475)) => 112.63/113.37 in( 112.63/113.37 kfst( 112.63/113.37 X476), 112.63/113.37 X474))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X477, 112.63/113.37 X478, 112.63/113.37 X479,X480]: 112.63/113.37 (( 112.63/113.37 setadjoin( 112.63/113.37 setadjoin( 112.63/113.37 X477, 112.63/113.37 emptyset), 112.63/113.37 setadjoin( 112.63/113.37 setadjoin( 112.63/113.37 X477, 112.63/113.37 setadjoin( 112.63/113.37 X478, 112.63/113.37 emptyset)), 112.63/113.37 emptyset)) = 112.63/113.37 setadjoin( 112.63/113.37 setadjoin( 112.63/113.37 X479, 112.63/113.37 emptyset), 112.63/113.37 setadjoin( 112.63/113.37 setadjoin( 112.63/113.37 X479, 112.63/113.37 setadjoin( 112.63/113.37 X480, 112.63/113.37 emptyset)), 112.63/113.37 emptyset))) => 112.63/113.37 (X477 = 112.63/113.37 X479))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X481, 112.63/113.37 X482, 112.63/113.37 X483,X484]: 112.63/113.37 (( 112.63/113.37 kpair( 112.63/113.37 X481,X482) = 112.63/113.37 kpair( 112.63/113.37 X483,X484)) => 112.63/113.37 (X481 = 112.63/113.37 X483))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X485, 112.63/113.37 X486]: 112.63/113.37 (( 112.63/113.37 X485 = 112.63/113.37 X486) => 112.63/113.37 (setadjoin( 112.63/113.37 X485, 112.63/113.37 setadjoin( 112.63/113.37 X486, 112.63/113.37 emptyset)) = 112.63/113.37 setadjoin( 112.63/113.37 X485, 112.63/113.37 emptyset)))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X487, 112.63/113.37 X488]: 112.63/113.37 (( 112.63/113.37 X487 = 112.63/113.37 X488) => 112.63/113.37 (setadjoin( 112.63/113.37 setadjoin( 112.63/113.37 X487, 112.63/113.37 emptyset), 112.63/113.37 setadjoin( 112.63/113.37 setadjoin( 112.63/113.37 X487, 112.63/113.37 setadjoin( 112.63/113.37 X488, 112.63/113.37 emptyset)), 112.63/113.37 emptyset)) = 112.63/113.37 setadjoin( 112.63/113.37 setadjoin( 112.63/113.37 X487, 112.63/113.37 emptyset), 112.63/113.37 emptyset)))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X489, 112.63/113.37 X490, 112.63/113.37 X491,X492]: 112.63/113.37 (( 112.63/113.37 setadjoin( 112.63/113.37 setadjoin( 112.63/113.37 X489, 112.63/113.37 emptyset), 112.63/113.37 setadjoin( 112.63/113.37 setadjoin( 112.63/113.37 X489, 112.63/113.37 setadjoin( 112.63/113.37 X490, 112.63/113.37 emptyset)), 112.63/113.37 emptyset)) = 112.63/113.37 setadjoin( 112.63/113.37 setadjoin( 112.63/113.37 X491, 112.63/113.37 emptyset), 112.63/113.37 setadjoin( 112.63/113.37 setadjoin( 112.63/113.37 X491, 112.63/113.37 setadjoin( 112.63/113.37 X492, 112.63/113.37 emptyset)), 112.63/113.37 emptyset))) => 112.63/113.37 (( 112.63/113.37 X491 = 112.63/113.37 X492) => 112.63/113.37 (X490 = 112.63/113.37 X492)))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X493, 112.63/113.37 X494,X495]: 112.63/113.37 (( 112.63/113.37 setadjoin( 112.63/113.37 X493, 112.63/113.37 setadjoin( 112.63/113.37 X494, 112.63/113.37 emptyset)) = 112.63/113.37 setadjoin( 112.63/113.37 X495, 112.63/113.37 emptyset)) => 112.63/113.37 (X493 = 112.63/113.37 X494))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X496, 112.63/113.37 X497, 112.63/113.37 X498,X499]: 112.63/113.37 (( 112.63/113.37 setadjoin( 112.63/113.37 setadjoin( 112.63/113.37 X496, 112.63/113.37 emptyset), 112.63/113.37 setadjoin( 112.63/113.37 setadjoin( 112.63/113.37 X496, 112.63/113.37 setadjoin( 112.63/113.37 X497, 112.63/113.37 emptyset)), 112.63/113.37 emptyset)) = 112.63/113.37 setadjoin( 112.63/113.37 setadjoin( 112.63/113.37 X498, 112.63/113.37 emptyset), 112.63/113.37 setadjoin( 112.63/113.37 setadjoin( 112.63/113.37 X498, 112.63/113.37 setadjoin( 112.63/113.37 X499, 112.63/113.37 emptyset)), 112.63/113.37 emptyset))) => 112.63/113.37 (X497 = 112.63/113.37 X499))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X500, 112.63/113.37 X501, 112.63/113.37 X502,X503]: 112.63/113.37 (( 112.63/113.37 kpair( 112.63/113.37 X500,X501) = 112.63/113.37 kpair( 112.63/113.37 X502,X503)) => 112.63/113.37 (X501 = 112.63/113.37 X503))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X504]: 112.63/113.37 (iskpair( 112.63/113.37 X504) => 112.63/113.37 (?[X505]: 112.63/113.37 (( 112.63/113.37 dsetconstr( 112.63/113.37 setunion( 112.63/113.37 X504), 112.63/113.37 '#ll_4'( 112.63/113.37 X504)) = 112.63/113.37 setadjoin( 112.63/113.37 X505, 112.63/113.37 emptyset)) & 112.63/113.37 in( 112.63/113.37 X505, 112.63/113.37 dsetconstr( 112.63/113.37 setunion( 112.63/113.37 X504), 112.63/113.37 '#ll_4'( 112.63/113.37 X504))))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X506, 112.63/113.37 X507]: 112.63/113.37 (ksnd( 112.63/113.37 kpair( 112.63/113.37 X506,X507)) = 112.63/113.37 X507)) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X508]: 112.63/113.37 (iskpair( 112.63/113.37 X508) => 112.63/113.37 (kpair( 112.63/113.37 kfst( 112.63/113.37 X508), 112.63/113.37 ksnd( 112.63/113.37 X508)) = 112.63/113.37 X508))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X509, 112.63/113.37 X510,X511]: 112.63/113.37 (in( 112.63/113.37 X511, 112.63/113.37 cartprod( 112.63/113.37 X509,X510)) => 112.63/113.37 in( 112.63/113.37 ksnd( 112.63/113.37 X511), 112.63/113.37 X510))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X512, 112.63/113.37 X513, 112.63/113.37 X514,X515]: 112.63/113.37 (in( 112.63/113.37 kpair( 112.63/113.37 X514,X515), 112.63/113.37 cartprod( 112.63/113.37 X512,X513)) => 112.63/113.37 in( 112.63/113.37 X514,X512))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X516, 112.63/113.37 X517, 112.63/113.37 X518,X519]: 112.63/113.37 (in( 112.63/113.37 kpair( 112.63/113.37 X518,X519), 112.63/113.37 cartprod( 112.63/113.37 X516,X517)) => 112.63/113.37 in( 112.63/113.37 X519,X517))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X520, 112.63/113.37 X521,X522]: 112.63/113.37 (in( 112.63/113.37 X522,X520) => 112.63/113.37 (![X523]: 112.63/113.37 (in( 112.63/113.37 X523,X521) => 112.63/113.37 (kpair( 112.63/113.37 X522,X523) = 112.63/113.37 kpair( 112.63/113.37 X522,X523)))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X524, 112.63/113.37 X525,X526]: 112.63/113.37 (in( 112.63/113.37 X526,X524) => 112.63/113.37 (![X527]: 112.63/113.37 (in( 112.63/113.37 X527,X525) => 112.63/113.37 (kfst( 112.63/113.37 kpair( 112.63/113.37 X526,X527)) = 112.63/113.37 X526))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X528, 112.63/113.37 X529,X530]: 112.63/113.37 (in( 112.63/113.37 X530,X528) => 112.63/113.37 (![X531]: 112.63/113.37 (in( 112.63/113.37 X531,X529) => 112.63/113.37 (ksnd( 112.63/113.37 kpair( 112.63/113.37 X530,X531)) = 112.63/113.37 X531))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X532, 112.63/113.37 X533,X534]: 112.63/113.37 (in( 112.63/113.37 X534, 112.63/113.37 cartprod( 112.63/113.37 X532,X533)) => 112.63/113.37 (kpair( 112.63/113.37 kfst( 112.63/113.37 X534), 112.63/113.37 ksnd( 112.63/113.37 X534)) = 112.63/113.37 X534))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X535, 112.63/113.37 X536, 112.63/113.37 X537:( 112.63/113.37 ($i * $i) > 112.63/113.37 $o),X538]: 112.63/113.37 (in( 112.63/113.37 X538,X535) => 112.63/113.37 (![X539]: 112.63/113.37 (in( 112.63/113.37 X539,X536) => 112.63/113.37 (X537( 112.63/113.37 X538,X539) => 112.63/113.37 in( 112.63/113.37 kpair( 112.63/113.37 X538,X539), 112.63/113.37 dpsetconstr( 112.63/113.37 X535, 112.63/113.37 X536, 112.63/113.37 '#ll_3'( 112.63/113.37 X537)))))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X540, 112.63/113.37 X541, 112.63/113.37 X542:( 112.63/113.37 ($i * $i) > 112.63/113.37 $o)]: 112.63/113.37 subset( 112.63/113.37 dpsetconstr( 112.63/113.37 X540, 112.63/113.37 X541, 112.63/113.37 '#ll_3'( 112.63/113.37 X542)), 112.63/113.37 cartprod( 112.63/113.37 X540,X541))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X543, 112.63/113.37 X544, 112.63/113.37 X545:( 112.63/113.37 ($i * $i) > 112.63/113.37 $o)]: 112.63/113.37 subset( 112.63/113.37 dpsetconstr( 112.63/113.37 X543, 112.63/113.37 X544, 112.63/113.37 '#ll_3'( 112.63/113.37 X545)), 112.63/113.37 cartprod( 112.63/113.37 X543,X544))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X546, 112.63/113.37 X547, 112.63/113.37 X548:( 112.63/113.37 ($i * $i) > 112.63/113.37 $o),X549]: 112.63/113.37 (in( 112.63/113.37 X549,X546) => 112.63/113.37 (![X550]: 112.63/113.37 (in( 112.63/113.37 X550,X547) => 112.63/113.37 (in( 112.63/113.37 kpair( 112.63/113.37 X549,X550), 112.63/113.37 dpsetconstr( 112.63/113.37 X546, 112.63/113.37 X547, 112.63/113.37 '#ll_3'( 112.63/113.37 X548))) => 112.63/113.37 X548( 112.63/113.37 X549,X550)))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X551, 112.63/113.37 X552, 112.63/113.37 X553:( 112.63/113.37 ($i * $i) > 112.63/113.37 $o),X554, 112.63/113.37 X555]: 112.63/113.37 (in( 112.63/113.37 kpair( 112.63/113.37 X554,X555), 112.63/113.37 dpsetconstr( 112.63/113.37 X551, 112.63/113.37 X552, 112.63/113.37 '#ll_3'( 112.63/113.37 X553))) => 112.63/113.37 in( 112.63/113.37 X554,X551))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X556, 112.63/113.37 X557, 112.63/113.37 X558:( 112.63/113.37 ($i * $i) > 112.63/113.37 $o),X559, 112.63/113.37 X560]: 112.63/113.37 (in( 112.63/113.37 kpair( 112.63/113.37 X559,X560), 112.63/113.37 dpsetconstr( 112.63/113.37 X556, 112.63/113.37 X557, 112.63/113.37 '#ll_3'( 112.63/113.37 X558))) => 112.63/113.37 in( 112.63/113.37 X560,X557))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X561, 112.63/113.37 X562, 112.63/113.37 X563:( 112.63/113.37 ($i * $i) > 112.63/113.37 $o),X564, 112.63/113.37 X565]: 112.63/113.37 (in( 112.63/113.37 kpair( 112.63/113.37 X564,X565), 112.63/113.37 dpsetconstr( 112.63/113.37 X561, 112.63/113.37 X562, 112.63/113.37 '#ll_3'( 112.63/113.37 X563))) => 112.63/113.37 X563( 112.63/113.37 X564,X565))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X566, 112.63/113.37 X567,X568]: 112.63/113.37 (( 112.63/113.37 ( 112.63/113.37 ![X569]: 112.63/113.37 (in( 112.63/113.37 X569,X566) => 112.63/113.37 (?[X570]: 112.63/113.37 (( 112.63/113.37 dsetconstr( 112.63/113.37 X567, 112.63/113.37 '#ll_2'( 112.63/113.37 X569,X568)) = 112.63/113.37 setadjoin( 112.63/113.37 X570, 112.63/113.37 emptyset)) & 112.63/113.37 in( 112.63/113.37 X570, 112.63/113.37 dsetconstr( 112.63/113.37 X567, 112.63/113.37 '#ll_2'( 112.63/113.37 X569,X568))))))) & 112.63/113.37 subset( 112.63/113.37 X568, 112.63/113.37 cartprod( 112.63/113.37 X566,X567))) => 112.63/113.37 (![X571]: 112.63/113.37 (in( 112.63/113.37 X571,X566) => 112.63/113.37 (?[X572]: 112.63/113.37 (( 112.63/113.37 dsetconstr( 112.63/113.37 X567, 112.63/113.37 '#ll_2'( 112.63/113.37 X571,X568)) = 112.63/113.37 setadjoin( 112.63/113.37 X572, 112.63/113.37 emptyset)) & 112.63/113.37 in( 112.63/113.37 X572, 112.63/113.37 dsetconstr( 112.63/113.37 X567, 112.63/113.37 '#ll_2'( 112.63/113.37 X571,X568))))))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X573, 112.63/113.37 X574,X575]: 112.63/113.37 (( 112.63/113.37 ( 112.63/113.37 ![X576]: 112.63/113.37 (in( 112.63/113.37 X576,X573) => 112.63/113.37 (?[X577]: 112.63/113.37 (( 112.63/113.37 dsetconstr( 112.63/113.37 X574, 112.63/113.37 '#ll_2'( 112.63/113.37 X576,X575)) = 112.63/113.37 setadjoin( 112.63/113.37 X577, 112.63/113.37 emptyset)) & 112.63/113.37 in( 112.63/113.37 X577, 112.63/113.37 dsetconstr( 112.63/113.37 X574, 112.63/113.37 '#ll_2'( 112.63/113.37 X576,X575))))))) & 112.63/113.37 subset( 112.63/113.37 X575, 112.63/113.37 cartprod( 112.63/113.37 X573,X574))) => 112.63/113.37 (![X578]: 112.63/113.37 (in( 112.63/113.37 X578,X573) => 112.63/113.37 in( 112.63/113.37 setunion( 112.63/113.37 dsetconstr( 112.63/113.37 X574, 112.63/113.37 '#ll_2'( 112.63/113.37 X578,X575))), 112.63/113.37 X574))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X579, 112.63/113.37 X580,X581]: 112.63/113.37 (( 112.63/113.37 ( 112.63/113.37 ![X582]: 112.63/113.37 (in( 112.63/113.37 X582,X579) => 112.63/113.37 (?[X583]: 112.63/113.37 (( 112.63/113.37 dsetconstr( 112.63/113.37 X580, 112.63/113.37 '#ll_2'( 112.63/113.37 X582,X581)) = 112.63/113.37 setadjoin( 112.63/113.37 X583, 112.63/113.37 emptyset)) & 112.63/113.37 in( 112.63/113.37 X583, 112.63/113.37 dsetconstr( 112.63/113.37 X580, 112.63/113.37 '#ll_2'( 112.63/113.37 X582,X581))))))) & 112.63/113.37 subset( 112.63/113.37 X581, 112.63/113.37 cartprod( 112.63/113.37 X579,X580))) => 112.63/113.37 (![X584]: 112.63/113.37 (in( 112.63/113.37 X584,X579) => 112.63/113.37 in( 112.63/113.37 setunion( 112.63/113.37 dsetconstr( 112.63/113.37 X580, 112.63/113.37 '#ll_2'( 112.63/113.37 X584,X581))), 112.63/113.37 X580))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X585, 112.63/113.37 X586,X587]: 112.63/113.37 (in( 112.63/113.37 X587, 112.63/113.37 funcSet( 112.63/113.37 X585,X586)) => 112.63/113.37 (( 112.63/113.37 ![X588]: 112.63/113.37 (in( 112.63/113.37 X588,X585) => 112.63/113.37 (?[X589]: 112.63/113.37 (( 112.63/113.37 dsetconstr( 112.63/113.37 X586, 112.63/113.37 '#ll_2'( 112.63/113.37 X588,X587)) = 112.63/113.37 setadjoin( 112.63/113.37 X589, 112.63/113.37 emptyset)) & 112.63/113.37 in( 112.63/113.37 X589, 112.63/113.37 dsetconstr( 112.63/113.37 X586, 112.63/113.37 '#ll_2'( 112.63/113.37 X588,X587))))))) & 112.63/113.37 subset( 112.63/113.37 X587, 112.63/113.37 cartprod( 112.63/113.37 X585,X586))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X590, 112.63/113.37 X591,X592]: 112.63/113.37 (in( 112.63/113.37 X592, 112.63/113.37 funcSet( 112.63/113.37 X590,X591)) => 112.63/113.37 (![X593]: 112.63/113.37 (in( 112.63/113.37 X593,X590) => 112.63/113.37 in( 112.63/113.37 setunion( 112.63/113.37 dsetconstr( 112.63/113.37 X591, 112.63/113.37 '#ll_2'( 112.63/113.37 X593,X592))), 112.63/113.37 X591))))) => 112.63/113.37 ( 112.63/113.37 ( 112.63/113.37 ![X594, 112.63/113.37 X595,X596]: 112.63/113.37 (( 112.63/113.37 ( 112.63/113.37 ![X597]: 112.63/113.37 (in( 112.63/113.37 X597,X594) => 112.63/113.37 (?[X598]: 112.63/113.37 (( 112.63/113.37 dsetconstr( 112.63/113.37 X595, 112.63/113.37 '#ll_2'( 112.63/113.37 X597,X596)) = 112.63/113.37 setadjoin( 112.63/113.37 X598, 112.63/113.37 emptyset)) & 112.63/113.37 in( 112.63/113.37 X598, 112.63/113.37 dsetconstr( 112.63/113.37 X595, 112.63/113.37 '#ll_2'( 112.63/113.37 X597,X596))))))) & 112.63/113.37 subset( 112.63/113.37 X596, 112.63/113.37 cartprod( 112.63/113.37 X594,X595))) => 112.63/113.37 in( 112.63/113.37 X596, 112.63/113.37 funcSet( 112.63/113.37 X594,X595)))) => 112.63/113.38 ( 112.63/113.38 ( 112.63/113.38 ![X599, 112.63/113.38 X600, 112.63/113.38 X601:( 112.63/113.38 $i > $i)]: 112.63/113.38 (( 112.63/113.38 ![X602]: 112.63/113.38 (in( 112.63/113.38 X602,X599) => 112.63/113.38 in( 112.63/113.38 X601( 112.63/113.38 X602), 112.63/113.38 X600))) => 112.63/113.38 (( 112.63/113.38 ![X603]: 112.63/113.38 (in( 112.63/113.38 X603,X599) => 112.63/113.38 (?[X604]: 112.63/113.38 (( 112.63/113.38 dsetconstr( 112.63/113.38 X600, 112.63/113.38 '#ll_1'( 112.63/113.38 X603, 112.63/113.38 X601, 112.63/113.38 X600,X599)) = 112.63/113.38 setadjoin( 112.63/113.38 X604, 112.63/113.38 emptyset)) & 112.63/113.38 in( 112.63/113.38 X604, 112.63/113.38 dsetconstr( 112.63/113.38 X600, 112.63/113.38 '#ll_1'( 112.63/113.38 X603, 112.63/113.38 X601, 112.63/113.38 X600,X599))))))) & 112.63/113.38 subset( 112.63/113.38 dpsetconstr( 112.63/113.38 X599, 112.63/113.38 X600, 112.63/113.38 '#ll_0'( 112.63/113.38 X601)), 112.63/113.38 cartprod( 112.63/113.38 X599,X600))))) => 112.63/113.38 ( 112.63/113.38 ( 112.63/113.38 ![X605, 112.63/113.38 X606, 112.63/113.38 X607:( 112.63/113.38 $i > $i)]: 112.63/113.38 (( 112.63/113.38 ![X608]: 112.63/113.38 (in( 112.63/113.38 X608,X605) => 112.63/113.38 in( 112.63/113.38 X607( 112.63/113.38 X608), 112.63/113.38 X606))) => 112.63/113.38 (( 112.63/113.38 ![X609]: 112.63/113.38 (in( 112.63/113.38 X609,X605) => 112.63/113.38 (?[X610]: 112.63/113.38 (( 112.63/113.38 dsetconstr( 112.63/113.38 X606, 112.63/113.38 '#ll_1'( 112.63/113.38 X609, 112.63/113.38 X607, 112.63/113.38 X606,X605)) = 112.63/113.38 setadjoin( 112.63/113.38 X610, 112.63/113.38 emptyset)) & 112.63/113.38 in( 112.63/113.38 X610, 112.63/113.38 dsetconstr( 112.63/113.38 X606, 112.63/113.38 '#ll_1'( 112.63/113.38 X609, 112.63/113.38 X607, 112.63/113.38 X606,X605))))))) & 112.63/113.38 subset( 112.63/113.38 dpsetconstr( 112.63/113.38 X605, 112.63/113.38 X606, 112.63/113.38 '#ll_0'( 112.63/113.38 X607)), 112.63/113.38 cartprod( 112.63/113.38 X605,X606))))) => 112.63/113.38 ( 112.63/113.38 ( 112.63/113.38 ![X611, 112.63/113.38 X612, 112.63/113.38 X613:( 112.63/113.38 $i > $i)]: 112.63/113.38 (( 112.63/113.38 ![X614]: 112.63/113.38 (in( 112.63/113.38 X614,X611) => 112.63/113.38 in( 112.63/113.38 X613( 112.63/113.38 X614), 112.63/113.38 X612))) => 112.63/113.38 in( 112.63/113.38 dpsetconstr( 112.63/113.38 X611, 112.63/113.38 X612, 112.63/113.38 '#ll_0'( 112.63/113.38 X613)), 112.63/113.38 funcSet( 112.63/113.38 X611,X612)))) => 112.63/113.38 ( 112.63/113.38 ![X615, 112.63/113.38 X616,X617]: 112.63/113.38 (subset( 112.63/113.38 X617, 112.63/113.38 cartprod( 112.63/113.38 X615,X616)) => 112.63/113.38 (![X618:( 112.63/113.38 $i > $o)]: 112.63/113.38 (( 112.63/113.38 ![X619]: 112.63/113.38 (in( 112.63/113.38 X619,X615) => 112.63/113.38 (![X620]: 112.63/113.38 (in( 112.63/113.38 X620,X616) => 112.63/113.38 (in( 112.63/113.38 kpair( 112.63/113.38 X619,X620), 112.63/113.38 X617) => 112.63/113.38 X618( 112.63/113.38 kpair( 112.63/113.38 X619,X620))))))) => 112.63/113.38 (![X621]: 112.63/113.38 (in( 112.63/113.38 X621,X617) => 112.63/113.38 X618( 112.63/113.38 X621)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 112.63/113.38 tff('205', plain, ~ sk_X618_(sk_X621_), 112.63/113.38 inference('cnf', [status(esa)], [zf_stmt_14])). 112.63/113.38 tff('206', plain, 112.63/113.38 ![X900, X901]: 112.63/113.38 (~ in(X900, sk_X616_) 112.63/113.38 | sk_X618_(kpair(X901, X900)) 112.63/113.38 | ~ in(kpair(X901, X900), sk_X617_) 112.63/113.38 | ~ in(X901, sk_X615_)), 112.63/113.38 inference('cnf', [status(esa)], [zf_stmt_14])). 112.63/113.38 tff('207', plain, 112.63/113.38 ![X852, X853, X854]: 112.63/113.38 (in(ksnd(X852), X853) | ~ in(X852, cartprod(X854, X853))), 112.63/113.38 inference('cnf', [status(esa)], [zf_stmt_14])). 112.63/113.38 tff('208', plain, 112.63/113.38 ![X834, X835, X836]: 112.63/113.38 (in(kfst(X834), X835) | ~ in(X834, cartprod(X835, X836))), 112.63/113.38 inference('cnf', [status(esa)], [zf_stmt_14])). 112.63/113.38 tff('209', plain, subset(sk_X617_, cartprod(sk_X615_, sk_X616_)), 112.63/113.38 inference('cnf', [status(esa)], [zf_stmt_14])). 112.63/113.38 tff('210', plain, 112.63/113.38 ![X863, X864, X865]: 112.63/113.38 (kpair(kfst(X863), ksnd(X863)) = X863 112.63/113.38 | ~ in(X863, cartprod(X864, X865))), 112.63/113.38 inference('cnf', [status(esa)], [zf_stmt_14])). 112.63/113.38 tff('211', plain, in(sk_X621_, sk_X617_), 112.63/113.38 inference('cnf', [status(esa)], [zf_stmt_14])). 112.63/113.38 tff('212', plain, 112.63/113.38 ![X729, X730, X731]: 112.63/113.38 (~ subset(X729, X730) | in(X731, X730) | ~ in(X731, X729)), 112.63/113.38 inference('cnf', [status(esa)], [zf_stmt_14])). 112.63/113.38 tff('213', plain, $false, 112.63/113.38 inference('eprover', [status(thm)], 112.63/113.38 ['205', '206', '207', '208', '209', '210', '211', '212'])). 112.63/113.38 112.63/113.38 % SZS output end Refutation 112.63/113.38 % Zipperpin 1.5 exiting 112.63/113.38 EOF