0.10/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.10/0.15 % Command : run_portfolio.sh /export/starexec/sandbox/benchmark/theBenchmark.p /export/starexec/sandbox/tmp/tmp.bABN3IN70a 0.14/0.36 % Computer : n008.cluster.edu 0.14/0.36 % Model : x86_64 x86_64 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.36 % Memory : 8042.1875MB 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.36 % CPULimit : 1200 0.14/0.36 % DateTime : Tue Jul 13 14:03:14 EDT 2021 0.14/0.36 % CPUTime : 0.14/0.36 % Running portfolio for 120 s 0.14/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.14/0.36 % Number of cores: 8 0.14/0.36 % Python version: Python 3.6.8 0.14/0.37 % Running in HO mode 0.54/0.63 % Estimated wc time : 1286 0.54/0.63 % Estimated cpu time (7 cpus) : 183.71428571428572 0.54/0.70 % /export/starexec/sandbox/solver/bin/lams/s6.sh running for 21s 0.54/0.72 % /export/starexec/sandbox/solver/bin/lams/new_b3.2.norw.sh running for 15s 0.54/0.72 % /export/starexec/sandbox/solver/bin/lams/b.rpo.sh running for 21s 0.54/0.75 % /export/starexec/sandbox/solver/bin/lams/c.s.2.sh running for 68s 0.54/0.75 % /export/starexec/sandbox/solver/bin/lams/s6.ds.sh running for 10s 0.54/0.76 % /export/starexec/sandbox/solver/bin/lams/c.easy.sh running for 26s 0.54/0.76 % /export/starexec/sandbox/solver/bin/lams/old_b3.avatar.sh running for 15s 0.56/0.92 % Solved by lams/s6.ds.sh. 0.56/0.92 % done 0 iterations in 0.082s 0.56/0.92 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 0.56/0.92 % SZS output start Refutation 0.56/0.92 tff(ap, axiom, ap() = 0.56/0.92 ^[A,B,Xf,Xx]: setunion(dsetconstr(B,^[Xy]: in(kpair(Xx,Xy),Xf)))). 0.56/0.92 tff('0', plain, 0.56/0.92 ap = (^[A,B,Xf,Xx]: setunion(dsetconstr(B,^[Xy]: in(kpair(Xx,Xy),Xf)))), 0.56/0.92 inference('simplify_rw_rule', [status(thm)], [ap])). 0.56/0.92 tff('1', plain, 0.56/0.92 ap = 0.56/0.92 (^[V_1,V_2,V_3,V_4]: 0.56/0.92 setunion(dsetconstr(V_2,^[V_5]: in(kpair(V_4,V_5),V_3)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(apProp, axiom, apProp <=> 0.56/0.92 (![A,B,Xf]: 0.56/0.92 (func(A,B,Xf) => 0.56/0.92 (![Xx]: 0.56/0.92 (in(Xx,A) => 0.56/0.92 in(setunion(dsetconstr(B,^[Xy]: in(kpair(Xx,Xy),Xf))),B)))))). 0.56/0.92 tff('2', plain, 0.56/0.92 apProp = 0.56/0.92 (![X4,X6,X8]: 0.56/0.92 (func(X4,X6,X8) => 0.56/0.92 (![X10]: 0.56/0.92 (in(X10,X4) => 0.56/0.92 in(setunion(dsetconstr(X6,^[V_1]: in(kpair(X10,V_1),X8))),X6))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(funcImageSingleton, axiom, funcImageSingleton <=> 0.56/0.92 (![A,B,Xf]: 0.56/0.92 (func(A,B,Xf) => 0.56/0.92 (![Xx]: 0.56/0.92 (in(Xx,A) => singleton(dsetconstr(B,^[Xy]: in(kpair(Xx,Xy),Xf)))))))). 0.56/0.92 tff('3', plain, 0.56/0.92 funcImageSingleton = 0.56/0.92 (![X4,X6,X8]: 0.56/0.92 (func(X4,X6,X8) => 0.56/0.92 (![X10]: 0.56/0.92 (in(X10,X4) => 0.56/0.92 singleton(dsetconstr(X6,^[V_1]: in(kpair(X10,V_1),X8))))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(func, axiom, func() = 0.56/0.92 ^[A,B,R]: 0.56/0.92 (breln(A,B,R) & (![Xx]: (in(Xx,A) => ex1(B,^[Xy]: in(kpair(Xx,Xy),R)))))). 0.56/0.92 tff(breln, axiom, breln() = ^[A,B,C]: subset(C,cartprod(A,B))). 0.56/0.92 tff('4', plain, breln = (^[A,B,C]: subset(C,cartprod(A,B))), 0.56/0.92 inference('simplify_rw_rule', [status(thm)], [breln])). 0.56/0.92 tff('5', plain, breln = (^[V_1,V_2,V_3]: subset(V_3,cartprod(V_1,V_2))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(ex1, axiom, ex1() = 0.56/0.92 ^[A,Xphi:(($i > $o))]: singleton(dsetconstr(A,^[Xx]: Xphi(Xx)))). 0.56/0.92 tff(singleton, axiom, singleton() = 0.56/0.92 ^[A]: (?[Xx]: ((A = setadjoin(Xx,emptyset)) & in(Xx,A)))). 0.56/0.92 tff('6', plain, 0.56/0.92 singleton = (^[A]: (?[Xx]: ((A = setadjoin(Xx,emptyset)) & in(Xx,A)))), 0.56/0.92 inference('simplify_rw_rule', [status(thm)], [singleton])). 0.56/0.92 tff('7', plain, 0.56/0.92 singleton = 0.56/0.92 (^[V_1]: (?[X4]: ((V_1 = setadjoin(X4,emptyset)) & in(X4,V_1)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff('8', plain, 0.56/0.92 ex1 = (^[A,Xphi:(($i > $o))]: singleton(dsetconstr(A,^[Xx]: Xphi(Xx)))), 0.56/0.92 inference('simplify_rw_rule', [status(thm)], [ex1, '7'])). 0.56/0.92 tff('9', plain, 0.56/0.92 ex1 = 0.56/0.92 (^[V_1,V_2:(($i > $o))]: singleton(dsetconstr(V_1,^[V_3]: V_2(V_3)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff('10', plain, 0.56/0.92 func = 0.56/0.92 (^[A,B,R]: 0.56/0.92 (breln(A,B,R) & 0.56/0.92 (![Xx]: (in(Xx,A) => ex1(B,^[Xy]: in(kpair(Xx,Xy),R)))))), 0.56/0.92 inference('simplify_rw_rule', [status(thm)], [func, '5', '9', '7'])). 0.56/0.92 tff('11', plain, 0.56/0.92 func = 0.56/0.92 (^[V_1,V_2,V_3]: 0.56/0.92 (breln(V_1,V_2,V_3) & 0.56/0.92 (![X4]: (in(X4,V_1) => ex1(V_2,^[V_4]: in(kpair(X4,V_4),V_3)))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(dpsetconstrER, axiom, dpsetconstrER <=> 0.56/0.92 (![A,B,Xphi:(($i * $i) > $o),Xx,Xy]: 0.56/0.92 (in(kpair(Xx,Xy),dpsetconstr(A,B,^[Xz,Xu]: Xphi(Xz,Xu))) => Xphi(Xx,Xy)))). 0.56/0.92 tff('12', plain, 0.56/0.92 dpsetconstrER = 0.56/0.92 (![X4,X6,X8:(($i * $i) > $o),X10,X12]: 0.56/0.92 (in(kpair(X10,X12),dpsetconstr(X4,X6,^[V_1,V_2]: X8(V_1,V_2))) => 0.56/0.92 X8(X10,X12))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(dpsetconstrEL2, axiom, dpsetconstrEL2 <=> 0.56/0.92 (![A,B,Xphi:(($i * $i) > $o),Xx,Xy]: 0.56/0.92 (in(kpair(Xx,Xy),dpsetconstr(A,B,^[Xz,Xu]: Xphi(Xz,Xu))) => in(Xy,B)))). 0.56/0.92 tff('13', plain, 0.56/0.92 dpsetconstrEL2 = 0.56/0.92 (![X4,X6,X8:(($i * $i) > $o),X10,X12]: 0.56/0.92 (in(kpair(X10,X12),dpsetconstr(X4,X6,^[V_1,V_2]: X8(V_1,V_2))) => 0.56/0.92 in(X12,X6))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(dpsetconstrEL1, axiom, dpsetconstrEL1 <=> 0.56/0.92 (![A,B,Xphi:(($i * $i) > $o),Xx,Xy]: 0.56/0.92 (in(kpair(Xx,Xy),dpsetconstr(A,B,^[Xz,Xu]: Xphi(Xz,Xu))) => in(Xx,A)))). 0.56/0.92 tff('14', plain, 0.56/0.92 dpsetconstrEL1 = 0.56/0.92 (![X4,X6,X8:(($i * $i) > $o),X10,X12]: 0.56/0.92 (in(kpair(X10,X12),dpsetconstr(X4,X6,^[V_1,V_2]: X8(V_1,V_2))) => 0.56/0.92 in(X10,X4))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(dpsetconstrERa, axiom, dpsetconstrERa <=> 0.56/0.92 (![A,B,Xphi:(($i * $i) > $o),Xx]: 0.56/0.92 (in(Xx,A) => 0.56/0.92 (![Xy]: 0.56/0.92 (in(Xy,B) => 0.56/0.92 (in(kpair(Xx,Xy),dpsetconstr(A,B,^[Xz,Xu]: Xphi(Xz,Xu))) => 0.56/0.92 Xphi(Xx,Xy))))))). 0.56/0.92 tff('15', plain, 0.56/0.92 dpsetconstrERa = 0.56/0.92 (![X4,X6,X8:(($i * $i) > $o),X10]: 0.56/0.92 (in(X10,X4) => 0.56/0.92 (![X12]: 0.56/0.92 (in(X12,X6) => 0.56/0.92 (in(kpair(X10,X12),dpsetconstr(X4,X6,^[V_1,V_2]: X8(V_1,V_2))) => 0.56/0.92 X8(X10,X12)))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(setOfPairsIsBReln, axiom, setOfPairsIsBReln <=> 0.56/0.92 (![A,B,Xphi:(($i * $i) > $o)]: 0.56/0.92 breln(A,B,dpsetconstr(A,B,^[Xx,Xy]: Xphi(Xx,Xy))))). 0.56/0.92 tff('16', plain, 0.56/0.92 setOfPairsIsBReln = 0.56/0.92 (![X4,X6,X8:(($i * $i) > $o)]: 0.56/0.92 breln(X4,X6,dpsetconstr(X4,X6,^[V_1,V_2]: X8(V_1,V_2)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(dpsetconstrSub, axiom, dpsetconstrSub <=> 0.56/0.92 (![A,B,Xphi:(($i * $i) > $o)]: 0.56/0.92 subset(dpsetconstr(A,B,^[Xx,Xy]: Xphi(Xx,Xy)),cartprod(A,B)))). 0.56/0.92 tff('17', plain, 0.56/0.92 dpsetconstrSub = 0.56/0.92 (![X4,X6,X8:(($i * $i) > $o)]: 0.56/0.92 subset(dpsetconstr(X4,X6,^[V_1,V_2]: X8(V_1,V_2)),cartprod(X4,X6))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(dpsetconstrI, axiom, dpsetconstrI <=> 0.56/0.92 (![A,B,Xphi:(($i * $i) > $o),Xx]: 0.56/0.92 (in(Xx,A) => 0.56/0.92 (![Xy]: 0.56/0.92 (in(Xy,B) => 0.56/0.92 (Xphi(Xx,Xy) => 0.56/0.92 in(kpair(Xx,Xy),dpsetconstr(A,B,^[Xz,Xu]: Xphi(Xz,Xu))))))))). 0.56/0.92 tff('18', plain, 0.56/0.92 dpsetconstrI = 0.56/0.92 (![X4,X6,X8:(($i * $i) > $o),X10]: 0.56/0.92 (in(X10,X4) => 0.56/0.92 (![X12]: 0.56/0.92 (in(X12,X6) => 0.56/0.92 (X8(X10,X12) => 0.56/0.92 in(kpair(X10,X12),dpsetconstr(X4,X6,^[V_1,V_2]: X8(V_1,V_2)))))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(cartprodpairsurjEq, axiom, cartprodpairsurjEq <=> 0.56/0.92 (![A,B,Xu]: (in(Xu,cartprod(A,B)) => (kpair(kfst(Xu),ksnd(Xu)) = Xu)))). 0.56/0.92 tff('19', plain, 0.56/0.92 cartprodpairsurjEq = 0.56/0.92 (![X4,X6,X8]: (in(X8,cartprod(X4,X6)) => (kpair(kfst(X8),ksnd(X8)) = X8))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(cartprodsndpairEq, axiom, cartprodsndpairEq <=> 0.56/0.92 (![A,B,Xx]: (in(Xx,A) => (![Xy]: (in(Xy,B) => (ksnd(kpair(Xx,Xy)) = Xy)))))). 0.56/0.92 tff('20', plain, 0.56/0.92 cartprodsndpairEq = 0.56/0.92 (![X4,X6,X8]: 0.56/0.92 (in(X8,X4) => (![X10]: (in(X10,X6) => (ksnd(kpair(X8,X10)) = X10))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(cartprodfstpairEq, axiom, cartprodfstpairEq <=> 0.56/0.92 (![A,B,Xx]: (in(Xx,A) => (![Xy]: (in(Xy,B) => (kfst(kpair(Xx,Xy)) = Xx)))))). 0.56/0.92 tff('21', plain, 0.56/0.92 cartprodfstpairEq = 0.56/0.92 (![X4,X6,X8]: 0.56/0.92 (in(X8,X4) => (![X10]: (in(X10,X6) => (kfst(kpair(X8,X10)) = X8))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(cartprodmempaircEq, axiom, cartprodmempaircEq <=> 0.56/0.92 (![A,B,Xx]: 0.56/0.92 (in(Xx,A) => (![Xy]: (in(Xy,B) => (kpair(Xx,Xy) = kpair(Xx,Xy))))))). 0.56/0.92 tff('22', plain, 0.56/0.92 cartprodmempaircEq = 0.56/0.92 (![X4,X6,X8]: 0.56/0.92 (in(X8,X4) => 0.56/0.92 (![X10]: (in(X10,X6) => (kpair(X8,X10) = kpair(X8,X10)))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(cartprodpairmemER, axiom, cartprodpairmemER <=> 0.56/0.92 (![A,B,Xx,Xy]: (in(kpair(Xx,Xy),cartprod(A,B)) => in(Xy,B)))). 0.56/0.92 tff('23', plain, 0.56/0.92 cartprodpairmemER = 0.56/0.92 (![X4,X6,X8,X10]: (in(kpair(X8,X10),cartprod(X4,X6)) => in(X10,X6))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(cartprodpairmemEL, axiom, cartprodpairmemEL <=> 0.56/0.92 (![A,B,Xx,Xy]: (in(kpair(Xx,Xy),cartprod(A,B)) => in(Xx,A)))). 0.56/0.92 tff('24', plain, 0.56/0.92 cartprodpairmemEL = 0.56/0.92 (![X4,X6,X8,X10]: (in(kpair(X8,X10),cartprod(X4,X6)) => in(X8,X4))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(cartprodsndin, axiom, cartprodsndin <=> 0.56/0.92 (![A,B,Xu]: (in(Xu,cartprod(A,B)) => in(ksnd(Xu),B)))). 0.56/0.92 tff('25', plain, 0.56/0.92 cartprodsndin = 0.56/0.92 (![X4,X6,X8]: (in(X8,cartprod(X4,X6)) => in(ksnd(X8),X6))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(kpairsurjEq, axiom, kpairsurjEq <=> 0.56/0.92 (![Xu]: (iskpair(Xu) => (kpair(kfst(Xu),ksnd(Xu)) = Xu)))). 0.56/0.92 tff('26', plain, 0.56/0.92 kpairsurjEq = (![X4]: (iskpair(X4) => (kpair(kfst(X4),ksnd(X4)) = X4))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(ksndpairEq, axiom, ksndpairEq <=> (![Xx,Xy]: (ksnd(kpair(Xx,Xy)) = Xy))). 0.56/0.92 tff('27', plain, ksndpairEq = (![X4,X6]: (ksnd(kpair(X4,X6)) = X6)), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(ksndsingleton, axiom, ksndsingleton <=> 0.56/0.92 (![Xu]: 0.56/0.92 (iskpair(Xu) => 0.56/0.92 singleton(dsetconstr(setunion(Xu),^[Xx]: (Xu = kpair(kfst(Xu),Xx))))))). 0.56/0.92 tff('28', plain, 0.56/0.92 ksndsingleton = 0.56/0.92 (![X4]: 0.56/0.92 (iskpair(X4) => 0.56/0.92 singleton(dsetconstr(setunion(X4),^[V_1]: (X4 = kpair(kfst(X4),V_1)))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(setukpairinjR, axiom, setukpairinjR <=> 0.56/0.92 (![Xx,Xy,Xz,Xu]: ((kpair(Xx,Xy) = kpair(Xz,Xu)) => (Xy = Xu)))). 0.56/0.92 tff('29', plain, 0.56/0.92 setukpairinjR = 0.56/0.92 (![X4,X6,X8,X10]: ((kpair(X4,X6) = kpair(X8,X10)) => (X6 = X10))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(setukpairinjR2, axiom, setukpairinjR2 <=> 0.56/0.92 (![Xx,Xy,Xz,Xu]: 0.56/0.92 ((setadjoin(setadjoin(Xx,emptyset), 0.56/0.92 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)),emptyset)) = 0.56/0.92 setadjoin(setadjoin(Xz,emptyset), 0.56/0.92 setadjoin(setadjoin(Xz,setadjoin(Xu,emptyset)),emptyset))) => 0.56/0.92 (Xy = Xu)))). 0.56/0.92 tff('30', plain, 0.56/0.92 setukpairinjR2 = 0.56/0.92 (![X4,X6,X8,X10]: 0.56/0.92 ((setadjoin(setadjoin(X4,emptyset), 0.56/0.92 setadjoin(setadjoin(X4,setadjoin(X6,emptyset)),emptyset)) = 0.56/0.92 setadjoin(setadjoin(X8,emptyset), 0.56/0.92 setadjoin(setadjoin(X8,setadjoin(X10,emptyset)),emptyset))) => 0.56/0.92 (X6 = X10))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(upairequniteq, axiom, upairequniteq <=> 0.56/0.92 (![Xx,Xy,Xz]: 0.56/0.92 ((setadjoin(Xx,setadjoin(Xy,emptyset)) = setadjoin(Xz,emptyset)) => 0.56/0.92 (Xx = Xy)))). 0.56/0.92 tff('31', plain, 0.56/0.92 upairequniteq = 0.56/0.92 (![X4,X6,X8]: 0.56/0.92 ((setadjoin(X4,setadjoin(X6,emptyset)) = setadjoin(X8,emptyset)) => 0.56/0.92 (X4 = X6))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(setukpairinjR1, axiom, setukpairinjR1 <=> 0.56/0.92 (![Xx,Xy,Xz,Xu]: 0.56/0.92 ((setadjoin(setadjoin(Xx,emptyset), 0.56/0.92 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)),emptyset)) = 0.56/0.92 setadjoin(setadjoin(Xz,emptyset), 0.56/0.92 setadjoin(setadjoin(Xz,setadjoin(Xu,emptyset)),emptyset))) => 0.56/0.92 ((Xz = Xu) => (Xy = Xu))))). 0.56/0.92 tff('32', plain, 0.56/0.92 setukpairinjR1 = 0.56/0.92 (![X4,X6,X8,X10]: 0.56/0.92 ((setadjoin(setadjoin(X4,emptyset), 0.56/0.92 setadjoin(setadjoin(X4,setadjoin(X6,emptyset)),emptyset)) = 0.56/0.92 setadjoin(setadjoin(X8,emptyset), 0.56/0.92 setadjoin(setadjoin(X8,setadjoin(X10,emptyset)),emptyset))) => 0.56/0.92 ((X8 = X10) => (X6 = X10)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(setukpairinjR12, axiom, setukpairinjR12 <=> 0.56/0.92 (![Xx,Xy]: 0.56/0.92 ((Xx = Xy) => 0.56/0.92 (setadjoin(setadjoin(Xx,emptyset), 0.56/0.92 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)),emptyset)) = 0.56/0.92 setadjoin(setadjoin(Xx,emptyset),emptyset))))). 0.56/0.92 tff('33', plain, 0.56/0.92 setukpairinjR12 = 0.56/0.92 (![X4,X6]: 0.56/0.92 ((X4 = X6) => 0.56/0.92 (setadjoin(setadjoin(X4,emptyset), 0.56/0.92 setadjoin(setadjoin(X4,setadjoin(X6,emptyset)),emptyset)) = 0.56/0.92 setadjoin(setadjoin(X4,emptyset),emptyset)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(setukpairinjR11, axiom, setukpairinjR11 <=> 0.56/0.92 (![Xx,Xy]: 0.56/0.92 ((Xx = Xy) => 0.56/0.92 (setadjoin(Xx,setadjoin(Xy,emptyset)) = setadjoin(Xx,emptyset))))). 0.56/0.92 tff('34', plain, 0.56/0.92 setukpairinjR11 = 0.56/0.92 (![X4,X6]: 0.56/0.92 ((X4 = X6) => 0.56/0.92 (setadjoin(X4,setadjoin(X6,emptyset)) = setadjoin(X4,emptyset)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(setukpairinjL, axiom, setukpairinjL <=> 0.56/0.92 (![Xx,Xy,Xz,Xu]: ((kpair(Xx,Xy) = kpair(Xz,Xu)) => (Xx = Xz)))). 0.56/0.92 tff('35', plain, 0.56/0.92 setukpairinjL = 0.56/0.92 (![X4,X6,X8,X10]: ((kpair(X4,X6) = kpair(X8,X10)) => (X4 = X8))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(setukpairinjL2, axiom, setukpairinjL2 <=> 0.56/0.92 (![Xx,Xy,Xz,Xu]: 0.56/0.92 ((setadjoin(setadjoin(Xx,emptyset), 0.56/0.92 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)),emptyset)) = 0.56/0.92 setadjoin(setadjoin(Xz,emptyset), 0.56/0.92 setadjoin(setadjoin(Xz,setadjoin(Xu,emptyset)),emptyset))) => 0.56/0.92 (Xx = Xz)))). 0.56/0.92 tff('36', plain, 0.56/0.92 setukpairinjL2 = 0.56/0.92 (![X4,X6,X8,X10]: 0.56/0.92 ((setadjoin(setadjoin(X4,emptyset), 0.56/0.92 setadjoin(setadjoin(X4,setadjoin(X6,emptyset)),emptyset)) = 0.56/0.92 setadjoin(setadjoin(X8,emptyset), 0.56/0.92 setadjoin(setadjoin(X8,setadjoin(X10,emptyset)),emptyset))) => 0.56/0.92 (X4 = X8))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(cartprodfstin, axiom, cartprodfstin <=> 0.56/0.92 (![A,B,Xu]: (in(Xu,cartprod(A,B)) => in(kfst(Xu),A)))). 0.56/0.92 tff('37', plain, 0.56/0.92 cartprodfstin = 0.56/0.92 (![X4,X6,X8]: (in(X8,cartprod(X4,X6)) => in(kfst(X8),X4))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(kfstpairEq, axiom, kfstpairEq <=> (![Xx,Xy]: (kfst(kpair(Xx,Xy)) = Xx))). 0.56/0.92 tff('38', plain, kfstpairEq = (![X4,X6]: (kfst(kpair(X4,X6)) = X4)), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(theprop, axiom, theprop <=> (![X]: (singleton(X) => in(setunion(X),X)))). 0.56/0.92 tff('39', plain, theprop = (![X4]: (singleton(X4) => in(setunion(X4),X4))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(kfstsingleton, axiom, kfstsingleton <=> 0.56/0.92 (![Xu]: 0.56/0.92 (iskpair(Xu) => 0.56/0.92 singleton(dsetconstr(setunion(Xu),^[Xx]: in(setadjoin(Xx,emptyset),Xu)))))). 0.56/0.92 tff('40', plain, 0.56/0.92 kfstsingleton = 0.56/0.92 (![X4]: 0.56/0.92 (iskpair(X4) => 0.56/0.92 singleton(dsetconstr(setunion(X4), 0.56/0.92 ^[V_1]: in(setadjoin(V_1,emptyset),X4))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(setukpairinjL1, axiom, setukpairinjL1 <=> 0.56/0.92 (![Xx,Xy,Xz]: 0.56/0.92 (in(setadjoin(Xz,emptyset), 0.56/0.92 setadjoin(setadjoin(Xx,emptyset), 0.56/0.92 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)),emptyset))) => 0.56/0.92 (Xx = Xz)))). 0.56/0.92 tff('41', plain, 0.56/0.92 setukpairinjL1 = 0.56/0.92 (![X4,X6,X8]: 0.56/0.92 (in(setadjoin(X8,emptyset), 0.56/0.92 setadjoin(setadjoin(X4,emptyset), 0.56/0.92 setadjoin(setadjoin(X4,setadjoin(X6,emptyset)),emptyset))) => 0.56/0.92 (X4 = X8))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(singletonsuniq, axiom, singletonsuniq <=> 0.56/0.92 (![Xx,Xy]: ((setadjoin(Xx,emptyset) = setadjoin(Xy,emptyset)) => (Xx = Xy)))). 0.56/0.92 tff('42', plain, 0.56/0.92 singletonsuniq = 0.56/0.92 (![X4,X6]: 0.56/0.92 ((setadjoin(X4,emptyset) = setadjoin(X6,emptyset)) => (X4 = X6))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(ex1I2, axiom, ex1I2 <=> 0.56/0.92 (![A,Xphi:(($i > $o))]: 0.56/0.92 ((![Xx]: 0.56/0.92 (in(Xx,A) => 0.56/0.92 (![Xy]: (in(Xy,A) => (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))) => 0.56/0.92 ((?[Xx]: (Xphi(Xx) & in(Xx,A))) => ex1(A,^[Xx]: Xphi(Xx)))))). 0.56/0.92 tff('43', plain, 0.56/0.92 ex1I2 = 0.56/0.92 (![X4,X6:(($i > $o))]: 0.56/0.92 ((![X8]: 0.56/0.92 (in(X8,X4) => 0.56/0.92 (![X10]: (in(X10,X4) => (X6(X8) => (X6(X10) => (X8 = X10))))))) => 0.56/0.92 ((?[X12]: (X6(X12) & in(X12,X4))) => ex1(X4,^[V_1]: X6(V_1))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(ex1I, axiom, ex1I <=> 0.56/0.92 (![A,Xphi:(($i > $o)),Xx]: 0.56/0.92 (in(Xx,A) => 0.56/0.92 (Xphi(Xx) => 0.56/0.92 ((![Xy]: (in(Xy,A) => (Xphi(Xy) => (Xy = Xx)))) => 0.56/0.92 ex1(A,^[Xy]: Xphi(Xy))))))). 0.56/0.92 tff('44', plain, 0.56/0.92 ex1I = 0.56/0.92 (![X4,X6:(($i > $o)),X8]: 0.56/0.92 (in(X8,X4) => 0.56/0.92 (X6(X8) => 0.56/0.92 ((![X10]: (in(X10,X4) => (X6(X10) => (X10 = X8)))) => 0.56/0.92 ex1(X4,^[V_1]: X6(V_1)))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(ex1E1, axiom, ex1E1 <=> 0.56/0.92 (![A,Xphi:(($i > $o))]: 0.56/0.92 (ex1(A,^[Xx]: Xphi(Xx)) => (?[Xx]: (Xphi(Xx) & in(Xx,A)))))). 0.56/0.92 tff('45', plain, 0.56/0.92 ex1E1 = 0.56/0.92 (![X4,X6:(($i > $o))]: 0.56/0.92 (ex1(X4,^[V_1]: X6(V_1)) => (?[X8]: (X6(X8) & in(X8,X4))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(singletonprop, axiom, singletonprop <=> 0.56/0.92 (![A,Xphi:(($i > $o))]: 0.56/0.92 ((![Xx]: 0.56/0.92 (in(Xx,A) => 0.56/0.92 (![Xy]: (in(Xy,A) => (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))) => 0.56/0.92 ((?[Xx]: (Xphi(Xx) & in(Xx,A))) => 0.56/0.92 singleton(dsetconstr(A,^[Xx]: Xphi(Xx))))))). 0.56/0.92 tff('46', plain, 0.56/0.92 singletonprop = 0.56/0.92 (![X4,X6:(($i > $o))]: 0.56/0.92 ((![X8]: 0.56/0.92 (in(X8,X4) => 0.56/0.92 (![X10]: (in(X10,X4) => (X6(X8) => (X6(X10) => (X8 = X10))))))) => 0.56/0.92 ((?[X12]: (X6(X12) & in(X12,X4))) => 0.56/0.92 singleton(dsetconstr(X4,^[V_1]: X6(V_1)))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(setunionsingleton, axiom, setunionsingleton <=> 0.56/0.92 (![Xx]: (setunion(setadjoin(Xx,emptyset)) = Xx))). 0.56/0.92 tff('47', plain, 0.56/0.92 setunionsingleton = (![X4]: (setunion(setadjoin(X4,emptyset)) = X4)), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(setunionsingleton2, axiom, setunionsingleton2 <=> 0.56/0.92 (![A]: subset(A,setunion(setadjoin(A,emptyset))))). 0.56/0.92 tff('48', plain, 0.56/0.92 setunionsingleton2 = (![X4]: subset(X4,setunion(setadjoin(X4,emptyset)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(setunionsingleton1, axiom, setunionsingleton1 <=> 0.56/0.92 (![A]: subset(setunion(setadjoin(A,emptyset)),A))). 0.56/0.92 tff('49', plain, 0.56/0.92 setunionsingleton1 = (![X4]: subset(setunion(setadjoin(X4,emptyset)),X4)), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(setunionE2, axiom, setunionE2 <=> 0.56/0.92 (![A,Xx]: (in(Xx,setunion(A)) => (?[X]: (in(Xx,X) & in(X,A)))))). 0.56/0.92 tff('50', plain, 0.56/0.92 setunionE2 = 0.56/0.92 (![X4,X6]: (in(X6,setunion(X4)) => (?[X8]: (in(X6,X8) & in(X8,X4))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(cartprodmempair, axiom, cartprodmempair <=> 0.56/0.92 (![A,B,Xu]: (in(Xu,cartprod(A,B)) => iskpair(Xu)))). 0.56/0.92 tff('51', plain, 0.56/0.92 cartprodmempair = (![X4,X6,X8]: (in(X8,cartprod(X4,X6)) => iskpair(X8))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(cartprodmempair1, axiom, cartprodmempair1 <=> 0.56/0.92 (![A,B,Xu]: 0.56/0.92 (in(Xu,cartprod(A,B)) => 0.56/0.92 (?[Xx]: ((?[Xy]: ((Xu = kpair(Xx,Xy)) & in(Xy,B))) & in(Xx,A)))))). 0.56/0.92 tff('52', plain, 0.56/0.92 cartprodmempair1 = 0.56/0.92 (![X4,X6,X8]: 0.56/0.92 (in(X8,cartprod(X4,X6)) => 0.56/0.92 (?[X10]: 0.56/0.92 ((?[X12]: ((X8 = kpair(X10,X12)) & in(X12,X6))) & in(X10,X4))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(cartprodpairin, axiom, cartprodpairin <=> 0.56/0.92 (![A,B,Xx]: 0.56/0.92 (in(Xx,A) => (![Xy]: (in(Xy,B) => in(kpair(Xx,Xy),cartprod(A,B))))))). 0.56/0.92 tff('53', plain, 0.56/0.92 cartprodpairin = 0.56/0.92 (![X4,X6,X8]: 0.56/0.92 (in(X8,X4) => 0.56/0.92 (![X10]: (in(X10,X6) => in(kpair(X8,X10),cartprod(X4,X6)))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(ubforcartprodlem3, axiom, ubforcartprodlem3 <=> 0.56/0.92 (![A,B,Xx]: 0.56/0.92 (in(Xx,A) => 0.56/0.92 (![Xy]: 0.56/0.92 (in(Xy,B) => in(kpair(Xx,Xy),powerset(powerset(binunion(A,B))))))))). 0.56/0.92 tff('54', plain, 0.56/0.92 ubforcartprodlem3 = 0.56/0.92 (![X4,X6,X8]: 0.56/0.92 (in(X8,X4) => 0.56/0.92 (![X10]: 0.56/0.92 (in(X10,X6) => 0.56/0.92 in(kpair(X8,X10),powerset(powerset(binunion(X4,X6)))))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(ubforcartprodlem2, axiom, ubforcartprodlem2 <=> 0.56/0.92 (![A,B,Xx]: 0.56/0.92 (in(Xx,A) => 0.56/0.92 (![Xy]: 0.56/0.92 (in(Xy,B) => 0.56/0.92 in(setadjoin(setadjoin(Xx,emptyset), 0.56/0.92 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 0.56/0.92 emptyset)), 0.56/0.92 powerset(powerset(binunion(A,B))))))))). 0.56/0.92 tff('55', plain, 0.56/0.92 ubforcartprodlem2 = 0.56/0.92 (![X4,X6,X8]: 0.56/0.92 (in(X8,X4) => 0.56/0.92 (![X10]: 0.56/0.92 (in(X10,X6) => 0.56/0.92 in(setadjoin(setadjoin(X8,emptyset), 0.56/0.92 setadjoin(setadjoin(X8,setadjoin(X10,emptyset)), 0.56/0.92 emptyset)), 0.56/0.92 powerset(powerset(binunion(X4,X6)))))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(ubforcartprodlem1, axiom, ubforcartprodlem1 <=> 0.56/0.92 (![A,B,Xx]: 0.56/0.92 (in(Xx,A) => 0.56/0.92 (![Xy]: 0.56/0.92 (in(Xy,B) => 0.56/0.92 subset(setadjoin(setadjoin(Xx,emptyset), 0.56/0.92 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 0.56/0.92 emptyset)), 0.56/0.92 powerset(binunion(A,B)))))))). 0.56/0.92 tff('56', plain, 0.56/0.92 ubforcartprodlem1 = 0.56/0.92 (![X4,X6,X8]: 0.56/0.92 (in(X8,X4) => 0.56/0.92 (![X10]: 0.56/0.92 (in(X10,X6) => 0.56/0.92 subset(setadjoin(setadjoin(X8,emptyset), 0.56/0.92 setadjoin(setadjoin(X8,setadjoin(X10,emptyset)), 0.56/0.92 emptyset)), 0.56/0.92 powerset(binunion(X4,X6))))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(upairinpowunion, axiom, upairinpowunion <=> 0.56/0.92 (![A,B,Xx]: 0.56/0.92 (in(Xx,A) => 0.56/0.92 (![Xy]: 0.56/0.92 (in(Xy,B) => 0.56/0.92 in(setadjoin(Xx,setadjoin(Xy,emptyset)),powerset(binunion(A,B)))))))). 0.56/0.92 tff('57', plain, 0.56/0.92 upairinpowunion = 0.56/0.92 (![X4,X6,X8]: 0.56/0.92 (in(X8,X4) => 0.56/0.92 (![X10]: 0.56/0.92 (in(X10,X6) => 0.56/0.92 in(setadjoin(X8,setadjoin(X10,emptyset)), 0.56/0.92 powerset(binunion(X4,X6))))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(upairsubunion, axiom, upairsubunion <=> 0.56/0.92 (![A,B,Xx]: 0.56/0.92 (in(Xx,A) => 0.56/0.92 (![Xy]: 0.56/0.92 (in(Xy,B) => 0.56/0.92 subset(setadjoin(Xx,setadjoin(Xy,emptyset)),binunion(A,B))))))). 0.56/0.92 tff('58', plain, 0.56/0.92 upairsubunion = 0.56/0.92 (![X4,X6,X8]: 0.56/0.92 (in(X8,X4) => 0.56/0.92 (![X10]: 0.56/0.92 (in(X10,X6) => 0.56/0.92 subset(setadjoin(X8,setadjoin(X10,emptyset)),binunion(X4,X6)))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(upairset2E, axiom, upairset2E <=> 0.56/0.92 (![Xx,Xy,Xz]: 0.56/0.92 (in(Xz,setadjoin(Xx,setadjoin(Xy,emptyset))) => ((Xz = Xx) | (Xz = Xy))))). 0.56/0.92 tff('59', plain, 0.56/0.92 upairset2E = 0.56/0.92 (![X4,X6,X8]: 0.56/0.92 (in(X8,setadjoin(X4,setadjoin(X6,emptyset))) => 0.56/0.92 ((X8 = X4) | (X8 = X6)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(singletoninpowunion, axiom, singletoninpowunion <=> 0.56/0.92 (![A,B,Xx]: 0.56/0.92 (in(Xx,A) => in(setadjoin(Xx,emptyset),powerset(binunion(A,B)))))). 0.56/0.92 tff('60', plain, 0.56/0.92 singletoninpowunion = 0.56/0.92 (![X4,X6,X8]: 0.56/0.92 (in(X8,X4) => in(setadjoin(X8,emptyset),powerset(binunion(X4,X6))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(singletoninpowerset, axiom, singletoninpowerset <=> 0.56/0.92 (![A,Xx]: (in(Xx,A) => in(setadjoin(Xx,emptyset),powerset(A))))). 0.56/0.92 tff('61', plain, 0.56/0.92 singletoninpowerset = 0.56/0.92 (![X4,X6]: (in(X6,X4) => in(setadjoin(X6,emptyset),powerset(X4)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(singletonsubset, axiom, singletonsubset <=> 0.56/0.92 (![A,Xx]: (in(Xx,A) => subset(setadjoin(Xx,emptyset),A)))). 0.56/0.92 tff('62', plain, 0.56/0.92 singletonsubset = 0.56/0.92 (![X4,X6]: (in(X6,X4) => subset(setadjoin(X6,emptyset),X4))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(kpairp, axiom, kpairp <=> (![Xx,Xy]: iskpair(kpair(Xx,Xy)))). 0.56/0.92 tff('63', plain, kpairp = (![X4,X6]: iskpair(kpair(X4,X6))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(kpairiskpair, axiom, kpairiskpair <=> 0.56/0.92 (![Xx,Xy]: 0.56/0.92 iskpair(setadjoin(setadjoin(Xx,emptyset), 0.56/0.92 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 0.56/0.92 emptyset))))). 0.56/0.92 tff('64', plain, 0.56/0.92 kpairiskpair = 0.56/0.92 (![X4,X6]: 0.56/0.92 iskpair(setadjoin(setadjoin(X4,emptyset), 0.56/0.92 setadjoin(setadjoin(X4,setadjoin(X6,emptyset)), 0.56/0.92 emptyset)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(setukpairIR, axiom, setukpairIR <=> 0.56/0.92 (![Xx,Xy]: 0.56/0.92 in(Xy, 0.56/0.92 setunion(setadjoin(setadjoin(Xx,emptyset), 0.56/0.92 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 0.56/0.92 emptyset)))))). 0.56/0.92 tff('65', plain, 0.56/0.92 setukpairIR = 0.56/0.92 (![X4,X6]: 0.56/0.92 in(X6, 0.56/0.92 setunion(setadjoin(setadjoin(X4,emptyset), 0.56/0.92 setadjoin(setadjoin(X4,setadjoin(X6,emptyset)), 0.56/0.92 emptyset))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(setukpairIL, axiom, setukpairIL <=> 0.56/0.92 (![Xx,Xy]: 0.56/0.92 in(Xx, 0.56/0.92 setunion(setadjoin(setadjoin(Xx,emptyset), 0.56/0.92 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 0.56/0.92 emptyset)))))). 0.56/0.92 tff('66', plain, 0.56/0.92 setukpairIL = 0.56/0.92 (![X4,X6]: 0.56/0.92 in(X4, 0.56/0.92 setunion(setadjoin(setadjoin(X4,emptyset), 0.56/0.92 setadjoin(setadjoin(X4,setadjoin(X6,emptyset)), 0.56/0.92 emptyset))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(secondinupair, axiom, secondinupair <=> 0.56/0.92 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 0.56/0.92 tff('67', plain, 0.56/0.92 secondinupair = (![X4,X6]: in(X6,setadjoin(X4,setadjoin(X6,emptyset)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(symdiffIneg2, axiom, symdiffIneg2 <=> 0.56/0.92 (![A,B,Xx]: ((~in(Xx,A)) => ((~in(Xx,B)) => (~in(Xx,symdiff(A,B))))))). 0.56/0.92 tff('68', plain, 0.56/0.92 symdiffIneg2 = 0.56/0.92 (![X4,X6,X8]: 0.56/0.92 ((~in(X8,X4)) => ((~in(X8,X6)) => (~in(X8,symdiff(X4,X6)))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(symdiffIneg1, axiom, symdiffIneg1 <=> 0.56/0.92 (![A,B,Xx]: (in(Xx,A) => (in(Xx,B) => (~in(Xx,symdiff(A,B))))))). 0.56/0.92 tff('69', plain, 0.56/0.92 symdiffIneg1 = 0.56/0.92 (![X4,X6,X8]: (in(X8,X4) => (in(X8,X6) => (~in(X8,symdiff(X4,X6)))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(symdiffI2, axiom, symdiffI2 <=> 0.56/0.92 (![A,B,Xx]: ((~in(Xx,A)) => (in(Xx,B) => in(Xx,symdiff(A,B)))))). 0.56/0.92 tff('70', plain, 0.56/0.92 symdiffI2 = 0.56/0.92 (![X4,X6,X8]: ((~in(X8,X4)) => (in(X8,X6) => in(X8,symdiff(X4,X6))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(symdiffI1, axiom, symdiffI1 <=> 0.56/0.92 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => in(Xx,symdiff(A,B)))))). 0.56/0.92 tff('71', plain, 0.56/0.92 symdiffI1 = 0.56/0.92 (![X4,X6,X8]: (in(X8,X4) => ((~in(X8,X6)) => in(X8,symdiff(X4,X6))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(symdiffE, axiom, symdiffE <=> 0.56/0.92 (![A,B,Xx]: 0.56/0.92 (in(Xx,symdiff(A,B)) => 0.56/0.92 (![Xphi:$o]: 0.56/0.92 ((in(Xx,A) => ((~in(Xx,B)) => Xphi)) => 0.56/0.92 (((~in(Xx,A)) => (in(Xx,B) => Xphi)) => Xphi)))))). 0.56/0.92 tff('72', plain, 0.56/0.92 symdiffE = 0.56/0.92 (![X4,X6,X8]: 0.56/0.92 (in(X8,symdiff(X4,X6)) => 0.56/0.92 (![X10:$o]: 0.56/0.92 ((in(X8,X4) => ((~in(X8,X6)) => X10)) => 0.56/0.92 (((~in(X8,X4)) => (in(X8,X6) => X10)) => X10))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(setminusSubset1, axiom, setminusSubset1 <=> 0.56/0.92 (![A,B]: ((setminus(A,B) = emptyset) => subset(A,B)))). 0.56/0.92 tff('73', plain, 0.56/0.92 setminusSubset1 = 0.56/0.92 (![X4,X6]: ((setminus(X4,X6) = emptyset) => subset(X4,X6))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(setminusLsub, axiom, setminusLsub <=> (![A,B]: subset(setminus(A,B),A))). 0.56/0.92 tff('74', plain, setminusLsub = (![X4,X6]: subset(setminus(X4,X6),X4)), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(setminusIRneg, axiom, setminusIRneg <=> 0.56/0.92 (![A,B,Xx]: (in(Xx,B) => (~in(Xx,setminus(A,B)))))). 0.56/0.92 tff('75', plain, 0.56/0.92 setminusIRneg = (![X4,X6,X8]: (in(X8,X6) => (~in(X8,setminus(X4,X6))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(setminusILneg, axiom, setminusILneg <=> 0.56/0.92 (![A,B,Xx]: ((~in(Xx,A)) => (~in(Xx,setminus(A,B)))))). 0.56/0.92 tff('76', plain, 0.56/0.92 setminusILneg = 0.56/0.92 (![X4,X6,X8]: ((~in(X8,X4)) => (~in(X8,setminus(X4,X6))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(setminusELneg, axiom, setminusELneg <=> 0.56/0.92 (![A,B,Xx]: ((~in(Xx,setminus(A,B))) => ((~in(Xx,B)) => (~in(Xx,A)))))). 0.56/0.92 tff('77', plain, 0.56/0.92 setminusELneg = 0.56/0.92 (![X4,X6,X8]: 0.56/0.92 ((~in(X8,setminus(X4,X6))) => ((~in(X8,X6)) => (~in(X8,X4))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(setminusERneg, axiom, setminusERneg <=> 0.56/0.92 (![A,B,Xx]: ((~in(Xx,setminus(A,B))) => (in(Xx,A) => in(Xx,B))))). 0.56/0.92 tff('78', plain, 0.56/0.92 setminusERneg = 0.56/0.92 (![X4,X6,X8]: ((~in(X8,setminus(X4,X6))) => (in(X8,X4) => in(X8,X6)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(setminusSubset2, axiom, setminusSubset2 <=> 0.56/0.92 (![A,B]: (subset(A,B) => (setminus(A,B) = emptyset)))). 0.56/0.92 tff('79', plain, 0.56/0.92 setminusSubset2 = 0.56/0.92 (![X4,X6]: (subset(X4,X6) => (setminus(X4,X6) = emptyset))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(setminusER, axiom, setminusER <=> 0.56/0.92 (![A,B,Xx]: (in(Xx,setminus(A,B)) => (~in(Xx,B))))). 0.56/0.92 tff('80', plain, 0.56/0.92 setminusER = (![X4,X6,X8]: (in(X8,setminus(X4,X6)) => (~in(X8,X6)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(setminusEL, axiom, setminusEL <=> 0.56/0.92 (![A,B,Xx]: (in(Xx,setminus(A,B)) => in(Xx,A)))). 0.56/0.92 tff('81', plain, 0.56/0.92 setminusEL = (![X4,X6,X8]: (in(X8,setminus(X4,X6)) => in(X8,X4))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(setminusI, axiom, setminusI <=> 0.56/0.92 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => in(Xx,setminus(A,B)))))). 0.56/0.92 tff('82', plain, 0.56/0.92 setminusI = 0.56/0.92 (![X4,X6,X8]: (in(X8,X4) => ((~in(X8,X6)) => in(X8,setminus(X4,X6))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(bs114d, axiom, bs114d <=> 0.56/0.92 (![A,B,C]: 0.56/0.92 (binintersect(A,binunion(B,C)) = 0.56/0.92 binunion(binintersect(A,B),binintersect(A,C))))). 0.56/0.92 tff('83', plain, 0.56/0.92 bs114d = 0.56/0.92 (![X4,X6,X8]: 0.56/0.92 (binintersect(X4,binunion(X6,X8)) = 0.56/0.92 binunion(binintersect(X4,X6),binintersect(X4,X8)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(binintersectSubset1, axiom, binintersectSubset1 <=> 0.56/0.92 (![A,B]: ((binintersect(A,B) = A) => subset(A,B)))). 0.56/0.92 tff('84', plain, 0.56/0.92 binintersectSubset1 = 0.56/0.92 (![X4,X6]: ((binintersect(X4,X6) = X4) => subset(X4,X6))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(binintersectSubset4, axiom, binintersectSubset4 <=> 0.56/0.92 (![A,B]: (subset(B,A) => (binintersect(A,B) = B)))). 0.56/0.92 tff('85', plain, 0.56/0.92 binintersectSubset4 = 0.56/0.92 (![X4,X6]: (subset(X6,X4) => (binintersect(X4,X6) = X6))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(binintersectRsub, axiom, binintersectRsub <=> 0.56/0.92 (![A,B]: subset(binintersect(A,B),B))). 0.56/0.92 tff('86', plain, 0.56/0.92 binintersectRsub = (![X4,X6]: subset(binintersect(X4,X6),X6)), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(disjointsetsI1, axiom, disjointsetsI1 <=> 0.56/0.92 (![A,B]: 0.56/0.92 ((~(?[Xx]: (in(Xx,B) & in(Xx,A)))) => (binintersect(A,B) = emptyset)))). 0.56/0.92 tff('87', plain, 0.56/0.92 disjointsetsI1 = 0.56/0.92 (![X4,X6]: 0.56/0.92 ((~(?[X8]: (in(X8,X6) & in(X8,X4)))) => 0.56/0.92 (binintersect(X4,X6) = emptyset))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(binintersectER, axiom, binintersectER <=> 0.56/0.92 (![A,B,Xx]: (in(Xx,binintersect(A,B)) => in(Xx,B)))). 0.56/0.92 tff('88', plain, 0.56/0.92 binintersectER = (![X4,X6,X8]: (in(X8,binintersect(X4,X6)) => in(X8,X6))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(binintersectSubset3, axiom, binintersectSubset3 <=> 0.56/0.92 (![A,B]: ((binintersect(A,B) = B) => subset(B,A)))). 0.56/0.92 tff('89', plain, 0.56/0.92 binintersectSubset3 = 0.56/0.92 (![X4,X6]: ((binintersect(X4,X6) = X6) => subset(X6,X4))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(binintersectSubset2, axiom, binintersectSubset2 <=> 0.56/0.92 (![A,B]: (subset(A,B) => (binintersect(A,B) = A)))). 0.56/0.92 tff('90', plain, 0.56/0.92 binintersectSubset2 = 0.56/0.92 (![X4,X6]: (subset(X4,X6) => (binintersect(X4,X6) = X4))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(binintersectLsub, axiom, binintersectLsub <=> 0.56/0.92 (![A,B]: subset(binintersect(A,B),A))). 0.56/0.92 tff('91', plain, 0.56/0.92 binintersectLsub = (![X4,X6]: subset(binintersect(X4,X6),X4)), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(binintersectEL, axiom, binintersectEL <=> 0.56/0.92 (![A,B,Xx]: (in(Xx,binintersect(A,B)) => in(Xx,A)))). 0.56/0.92 tff('92', plain, 0.56/0.92 binintersectEL = (![X4,X6,X8]: (in(X8,binintersect(X4,X6)) => in(X8,X4))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(binintersectSubset5, axiom, binintersectSubset5 <=> 0.56/0.92 (![A,B,C]: (subset(C,A) => (subset(C,B) => subset(C,binintersect(A,B)))))). 0.56/0.92 tff('93', plain, 0.56/0.92 binintersectSubset5 = 0.56/0.92 (![X4,X6,X8]: 0.56/0.92 (subset(X8,X4) => (subset(X8,X6) => subset(X8,binintersect(X4,X6))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(binintersectI, axiom, binintersectI <=> 0.56/0.92 (![A,B,Xx]: (in(Xx,A) => (in(Xx,B) => in(Xx,binintersect(A,B)))))). 0.56/0.92 tff('94', plain, 0.56/0.92 binintersectI = 0.56/0.92 (![X4,X6,X8]: (in(X8,X4) => (in(X8,X6) => in(X8,binintersect(X4,X6))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(binunionRsub, axiom, binunionRsub <=> (![A,B]: subset(B,binunion(A,B)))). 0.56/0.92 tff('95', plain, binunionRsub = (![X4,X6]: subset(X6,binunion(X4,X6))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(binunionLsub, axiom, binunionLsub <=> (![A,B]: subset(A,binunion(A,B)))). 0.56/0.92 tff('96', plain, binunionLsub = (![X4,X6]: subset(X4,binunion(X4,X6))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(binunionE, axiom, binunionE <=> 0.56/0.92 (![A,B,Xx]: (in(Xx,binunion(A,B)) => (in(Xx,A) | in(Xx,B))))). 0.56/0.92 tff('97', plain, 0.56/0.92 binunionE = 0.56/0.92 (![X4,X6,X8]: (in(X8,binunion(X4,X6)) => (in(X8,X4) | in(X8,X6)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(binunionEcases, axiom, binunionEcases <=> 0.56/0.92 (![A,B,Xx,Xphi:$o]: 0.56/0.92 (in(Xx,binunion(A,B)) => 0.56/0.92 ((in(Xx,A) => Xphi) => ((in(Xx,B) => Xphi) => Xphi))))). 0.56/0.92 tff('98', plain, 0.56/0.92 binunionEcases = 0.56/0.92 (![X4,X6,X8,X10:$o]: 0.56/0.92 (in(X8,binunion(X4,X6)) => 0.56/0.92 ((in(X8,X4) => X10) => ((in(X8,X6) => X10) => X10)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(binunionIR, axiom, binunionIR <=> 0.56/0.92 (![A,B,Xx]: (in(Xx,B) => in(Xx,binunion(A,B))))). 0.56/0.92 tff('99', plain, 0.56/0.92 binunionIR = (![X4,X6,X8]: (in(X8,X6) => in(X8,binunion(X4,X6)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(upairset2IR, axiom, upairset2IR <=> 0.56/0.92 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 0.56/0.92 tff('100', plain, 0.56/0.92 upairset2IR = (![X4,X6]: in(X6,setadjoin(X4,setadjoin(X6,emptyset)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(binunionIL, axiom, binunionIL <=> 0.56/0.92 (![A,B,Xx]: (in(Xx,A) => in(Xx,binunion(A,B))))). 0.56/0.92 tff('101', plain, 0.56/0.92 binunionIL = (![X4,X6,X8]: (in(X8,X4) => in(X8,binunion(X4,X6)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(sepSubset, axiom, sepSubset <=> 0.56/0.92 (![A,Xphi:(($i > $o))]: subset(dsetconstr(A,^[Xx]: Xphi(Xx)),A))). 0.56/0.92 tff('102', plain, 0.56/0.92 sepSubset = 0.56/0.92 (![X4,X6:(($i > $o))]: subset(dsetconstr(X4,^[V_1]: X6(V_1)),X4)), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(sepInPowerset, axiom, sepInPowerset <=> 0.56/0.92 (![A,Xphi:(($i > $o))]: in(dsetconstr(A,^[Xx]: Xphi(Xx)),powerset(A)))). 0.56/0.92 tff('103', plain, 0.56/0.92 sepInPowerset = 0.56/0.92 (![X4,X6:(($i > $o))]: in(dsetconstr(X4,^[V_1]: X6(V_1)),powerset(X4))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(powersetsubset, axiom, powersetsubset <=> 0.56/0.92 (![A,B]: (subset(A,B) => subset(powerset(A),powerset(B))))). 0.56/0.92 tff('104', plain, 0.56/0.92 powersetsubset = 0.56/0.92 (![X4,X6]: (subset(X4,X6) => subset(powerset(X4),powerset(X6)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(inPowerset, axiom, inPowerset <=> (![A]: in(A,powerset(A)))). 0.56/0.92 tff('105', plain, inPowerset = (![X4]: in(X4,powerset(X4))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(powersetE1, axiom, powersetE1 <=> 0.56/0.92 (![A,B]: (in(B,powerset(A)) => subset(B,A)))). 0.56/0.92 tff('106', plain, 0.56/0.92 powersetE1 = (![X4,X6]: (in(X6,powerset(X4)) => subset(X6,X4))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(powersetI1, axiom, powersetI1 <=> 0.56/0.92 (![A,B]: (subset(B,A) => in(B,powerset(A))))). 0.56/0.92 tff('107', plain, 0.56/0.92 powersetI1 = (![X4,X6]: (subset(X6,X4) => in(X6,powerset(X4)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(subsetemptysetimpeq, axiom, subsetemptysetimpeq <=> 0.56/0.92 (![A]: (subset(A,emptyset) => (A = emptyset)))). 0.56/0.92 tff('108', plain, 0.56/0.92 subsetemptysetimpeq = (![X4]: (subset(X4,emptyset) => (X4 = emptyset))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(setextsub, axiom, setextsub <=> 0.56/0.92 (![A,B]: (subset(A,B) => (subset(B,A) => (A = B))))). 0.56/0.92 tff('109', plain, 0.56/0.92 setextsub = (![X4,X6]: (subset(X4,X6) => (subset(X6,X4) => (X4 = X6)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(subset2powerset, axiom, subset2powerset <=> 0.56/0.92 (![A,B]: (subset(A,B) => in(A,powerset(B))))). 0.56/0.92 tff('110', plain, 0.56/0.92 subset2powerset = (![X4,X6]: (subset(X4,X6) => in(X4,powerset(X6)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(setadjoinSub2, axiom, setadjoinSub2 <=> 0.56/0.92 (![A,Xx,B]: (subset(A,B) => subset(A,setadjoin(Xx,B))))). 0.56/0.92 tff('111', plain, 0.56/0.92 setadjoinSub2 = 0.56/0.92 (![X4,X6,X8]: (subset(X4,X8) => subset(X4,setadjoin(X6,X8)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(setadjoinSub, axiom, setadjoinSub <=> 0.56/0.92 (![Xx,A]: subset(A,setadjoin(Xx,A)))). 0.56/0.92 tff('112', plain, setadjoinSub = (![X4,X6]: subset(X6,setadjoin(X4,X6))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(subsetTrans, axiom, subsetTrans <=> 0.56/0.92 (![A,B,C]: (subset(A,B) => (subset(B,C) => subset(A,C))))). 0.56/0.92 tff('113', plain, 0.56/0.92 subsetTrans = 0.56/0.92 (![X4,X6,X8]: (subset(X4,X6) => (subset(X6,X8) => subset(X4,X8)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(subsetRefl, axiom, subsetRefl <=> (![A]: subset(A,A))). 0.56/0.92 tff('114', plain, subsetRefl = (![X4]: subset(X4,X4)), define([status(thm)])). 0.56/0.92 tff(notequalI2, axiom, notequalI2 <=> 0.56/0.92 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => (A != B))))). 0.56/0.92 tff('115', plain, 0.56/0.92 notequalI2 = (![X4,X6,X8]: (in(X8,X4) => ((~in(X8,X6)) => (X4 != X6)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(notequalI1, axiom, notequalI1 <=> (![A,B]: ((~subset(A,B)) => (A != B)))). 0.56/0.92 tff('116', plain, notequalI1 = (![X4,X6]: ((~subset(X4,X6)) => (X4 != X6))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(notsubsetI, axiom, notsubsetI <=> 0.56/0.92 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => (~subset(A,B)))))). 0.56/0.92 tff('117', plain, 0.56/0.92 notsubsetI = 0.56/0.92 (![X4,X6,X8]: (in(X8,X4) => ((~in(X8,X6)) => (~subset(X4,X6))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(subsetE2, axiom, subsetE2 <=> 0.56/0.92 (![A,B,Xx]: (subset(A,B) => ((~in(Xx,B)) => (~in(Xx,A)))))). 0.56/0.92 tff('118', plain, 0.56/0.92 subsetE2 = 0.56/0.92 (![X4,X6,X8]: (subset(X4,X6) => ((~in(X8,X6)) => (~in(X8,X4))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(subsetE, axiom, subsetE <=> 0.56/0.92 (![A,B,Xx]: (subset(A,B) => (in(Xx,A) => in(Xx,B))))). 0.56/0.92 tff('119', plain, 0.56/0.92 subsetE = (![X4,X6,X8]: (subset(X4,X6) => (in(X8,X4) => in(X8,X6)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(emptysetsubset, axiom, emptysetsubset <=> (![A]: subset(emptyset,A))). 0.56/0.92 tff('120', plain, emptysetsubset = (![X4]: subset(emptyset,X4)), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(subsetI2, axiom, subsetI2 <=> 0.56/0.92 (![A,B]: ((![Xx]: (in(Xx,A) => in(Xx,B))) => subset(A,B)))). 0.56/0.92 tff('121', plain, 0.56/0.92 subsetI2 = 0.56/0.92 (![X4,X6]: ((![X8]: (in(X8,X4) => in(X8,X6))) => subset(X4,X6))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(eqimpsubset1, axiom, eqimpsubset1 <=> (![A,B]: ((A = B) => subset(A,B)))). 0.56/0.92 tff('122', plain, eqimpsubset1 = (![X4,X6]: ((X4 = X6) => subset(X4,X6))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(eqimpsubset2, axiom, eqimpsubset2 <=> (![A,B]: ((A = B) => subset(B,A)))). 0.56/0.92 tff('123', plain, eqimpsubset2 = (![X4,X6]: ((X4 = X6) => subset(X6,X4))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(subsetI1, axiom, subsetI1 <=> 0.56/0.92 (![A,B]: ((![Xx]: (in(Xx,A) => in(Xx,B))) => subset(A,B)))). 0.56/0.92 tff('124', plain, 0.56/0.92 subsetI1 = 0.56/0.92 (![X4,X6]: ((![X8]: (in(X8,X4) => in(X8,X6))) => subset(X4,X6))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(dsetconstr__Cong, axiom, dsetconstr__Cong <=> 0.56/0.92 (![A,B]: 0.56/0.92 ((A = B) => 0.56/0.92 (![Xphi:(($i > $o)),Xpsi:(($i > $o))]: 0.56/0.92 ((![Xx]: 0.56/0.92 (in(Xx,A) => 0.56/0.92 (![Xy]: (in(Xy,B) => ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy))))))) => 0.56/0.92 (dsetconstr(A,^[Xx]: Xphi(Xx)) = dsetconstr(B,^[Xx]: Xpsi(Xx)))))))). 0.56/0.92 tff('125', plain, 0.56/0.92 dsetconstr__Cong = 0.56/0.92 (![X4,X6]: 0.56/0.92 ((X4 = X6) => 0.56/0.92 (![X8:(($i > $o)),X10:(($i > $o))]: 0.56/0.92 ((![X12]: 0.56/0.92 (in(X12,X4) => 0.56/0.92 (![X14]: 0.56/0.92 (in(X14,X6) => ((X12 = X14) => (X8(X12) <=> X10(X14))))))) => 0.56/0.92 (dsetconstr(X4,^[V_1]: X8(V_1)) = dsetconstr(X6,^[V_2]: X10(V_2))))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(descr__Cong, axiom, descr__Cong <=> 0.56/0.92 (![Xphi:(($i > $o)),Xpsi:(($i > $o))]: 0.56/0.92 ((![Xx,Xy]: ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy)))) => 0.56/0.92 (exu(^[Xx]: Xphi(Xx)) => 0.56/0.92 (exu(^[Xx]: Xpsi(Xx)) => 0.56/0.92 (descr(^[Xx]: Xphi(Xx)) = descr(^[Xx]: Xpsi(Xx)))))))). 0.56/0.92 tff('126', plain, 0.56/0.92 descr__Cong = 0.56/0.92 (![X4:(($i > $o)),X6:(($i > $o))]: 0.56/0.92 ((![X8,X10]: ((X8 = X10) => (X4(X8) <=> X6(X10)))) => 0.56/0.92 (exu(^[V_1]: X4(V_1)) => 0.56/0.92 (exu(^[V_2]: X6(V_2)) => 0.56/0.92 (descr(^[V_3]: X4(V_3)) = descr(^[V_4]: X6(V_4))))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(exuEu, axiom, exuEu <=> 0.56/0.92 (![Xphi:(($i > $o))]: 0.56/0.92 (exu(^[Xx]: Xphi(Xx)) => 0.56/0.92 (![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))). 0.56/0.92 tff('127', plain, 0.56/0.92 exuEu = 0.56/0.92 (![X4:(($i > $o))]: 0.56/0.92 (exu(^[V_1]: X4(V_1)) => (![X6,X8]: (X4(X6) => (X4(X8) => (X6 = X8)))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(omega__Cong, axiom, omega__Cong <=> (omega = omega)). 0.56/0.92 tff('128', plain, omega__Cong = (omega = omega), define([status(thm)])). 0.56/0.92 tff(setunion__Cong, axiom, setunion__Cong <=> 0.56/0.92 (![A,B]: ((A = B) => (setunion(A) = setunion(B))))). 0.56/0.92 tff('129', plain, 0.56/0.92 setunion__Cong = (![X4,X6]: ((X4 = X6) => (setunion(X4) = setunion(X6)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(powerset__Cong, axiom, powerset__Cong <=> 0.56/0.92 (![A,B]: ((A = B) => (powerset(A) = powerset(B))))). 0.56/0.92 tff('130', plain, 0.56/0.92 powerset__Cong = (![X4,X6]: ((X4 = X6) => (powerset(X4) = powerset(X6)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(setadjoin__Cong, axiom, setadjoin__Cong <=> 0.56/0.92 (![Xx,Xy]: 0.56/0.92 ((Xx = Xy) => 0.56/0.92 (![Xz,Xu]: ((Xz = Xu) => (setadjoin(Xx,Xz) = setadjoin(Xy,Xu))))))). 0.56/0.92 tff('131', plain, 0.56/0.92 setadjoin__Cong = 0.56/0.92 (![X4,X6]: 0.56/0.92 ((X4 = X6) => 0.56/0.92 (![X8,X10]: ((X8 = X10) => (setadjoin(X4,X8) = setadjoin(X6,X10)))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(emptyset__Cong, axiom, emptyset__Cong <=> (emptyset = emptyset)). 0.56/0.92 tff('132', plain, emptyset__Cong = (emptyset = emptyset), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(exu__Cong, axiom, exu__Cong <=> 0.56/0.92 (![Xphi:(($i > $o)),Xpsi:(($i > $o))]: 0.56/0.92 ((![Xx,Xy]: ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy)))) => 0.56/0.92 (exu(^[Xx]: Xphi(Xx)) <=> exu(^[Xx]: Xpsi(Xx)))))). 0.56/0.92 tff('133', plain, 0.56/0.92 exu__Cong = 0.56/0.92 (![X4:(($i > $o)),X6:(($i > $o))]: 0.56/0.92 ((![X8,X10]: ((X8 = X10) => (X4(X8) <=> X6(X10)))) => 0.56/0.92 (exu(^[V_1]: X4(V_1)) <=> exu(^[V_2]: X6(V_2))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(exuE3u, axiom, exuE3u <=> 0.56/0.92 (![Xphi:(($i > $o))]: 0.56/0.92 (exu(^[Xx]: Xphi(Xx)) => 0.56/0.92 (![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))). 0.56/0.92 tff('134', plain, 0.56/0.92 exuE3u = 0.56/0.92 (![X4:(($i > $o))]: 0.56/0.92 (exu(^[V_1]: X4(V_1)) => (![X6,X8]: (X4(X6) => (X4(X8) => (X6 = X8)))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(in__Cong, axiom, in__Cong <=> 0.56/0.92 (![A,B]: ((A = B) => (![Xx,Xy]: ((Xx = Xy) => (in(Xx,A) <=> in(Xy,B))))))). 0.56/0.92 tff('135', plain, 0.56/0.92 in__Cong = 0.56/0.92 (![X4,X6]: 0.56/0.92 ((X4 = X6) => (![X8,X10]: ((X8 = X10) => (in(X8,X4) <=> in(X10,X6)))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(inCongP, axiom, inCongP <=> 0.56/0.92 (![A,B]: ((A = B) => (![Xx,Xy]: ((Xx = Xy) => (in(Xx,A) => in(Xy,B))))))). 0.56/0.92 tff('136', plain, 0.56/0.92 inCongP = 0.56/0.92 (![X4,X6]: 0.56/0.92 ((X4 = X6) => (![X8,X10]: ((X8 = X10) => (in(X8,X4) => in(X10,X6)))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(exuI2, axiom, exuI2 <=> 0.56/0.92 (![Xphi:(($i > $o))]: 0.56/0.92 ((?[Xx]: (![Xy]: (Xphi(Xy) <=> (Xy = Xx)))) => exu(^[Xx]: Xphi(Xx))))). 0.56/0.92 tff('137', plain, 0.56/0.92 exuI2 = 0.56/0.92 (![X4:(($i > $o))]: 0.56/0.92 ((?[X6]: (![X8]: (X4(X8) <=> (X8 = X6)))) => exu(^[V_1]: X4(V_1)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(exuI3, axiom, exuI3 <=> 0.56/0.92 (![Xphi:(($i > $o))]: 0.56/0.92 ((?[Xx]: Xphi(Xx)) => 0.56/0.92 ((![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy)))) => 0.56/0.92 exu(^[Xx]: Xphi(Xx)))))). 0.56/0.92 tff('138', plain, 0.56/0.92 exuI3 = 0.56/0.92 (![X4:(($i > $o))]: 0.56/0.92 ((?[X6]: X4(X6)) => 0.56/0.92 ((![X8,X10]: (X4(X8) => (X4(X10) => (X8 = X10)))) => 0.56/0.92 exu(^[V_1]: X4(V_1))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(exuI1, axiom, exuI1 <=> 0.56/0.92 (![Xphi:(($i > $o))]: 0.56/0.92 ((?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx))) => 0.56/0.92 exu(^[Xx]: Xphi(Xx))))). 0.56/0.92 tff('139', plain, 0.56/0.92 exuI1 = 0.56/0.92 (![X4:(($i > $o))]: 0.56/0.92 ((?[X6]: ((![X8]: (X4(X8) => (X6 = X8))) & X4(X6))) => 0.56/0.92 exu(^[V_1]: X4(V_1)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(notdallE, axiom, notdallE <=> 0.56/0.92 (![A,Xphi:(($i > $o))]: 0.56/0.92 ((~(![Xx]: (in(Xx,A) => Xphi(Xx)))) => (?[Xx]: ((~Xphi(Xx)) & in(Xx,A)))))). 0.56/0.92 tff('140', plain, 0.56/0.92 notdallE = 0.56/0.92 (![X4,X6:(($i > $o))]: 0.56/0.92 ((~(![X8]: (in(X8,X4) => X6(X8)))) => 0.56/0.92 (?[X10]: ((~X6(X10)) & in(X10,X4))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(notdexE, axiom, notdexE <=> 0.56/0.92 (![A,Xphi:(($i > $o))]: 0.56/0.92 ((~(?[Xx]: (Xphi(Xx) & in(Xx,A)))) => (![Xx]: (in(Xx,A) => (~Xphi(Xx))))))). 0.56/0.92 tff('141', plain, 0.56/0.92 notdexE = 0.56/0.92 (![X4,X6:(($i > $o))]: 0.56/0.92 ((~(?[X8]: (X6(X8) & in(X8,X4)))) => 0.56/0.92 (![X10]: (in(X10,X4) => (~X6(X10)))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(prop2set2propI, axiom, prop2set2propI <=> 0.56/0.92 (![Xphi:$o]: (Xphi => set2prop(prop2set(Xphi))))). 0.56/0.92 tff('142', plain, 0.56/0.92 prop2set2propI = (![X4:$o]: (X4 => set2prop(prop2set(X4)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(prop2setI, axiom, prop2setI <=> 0.56/0.92 (![Xphi:$o]: (Xphi => in(emptyset,prop2set(Xphi))))). 0.56/0.92 tff('143', plain, prop2setI = (![X4:$o]: (X4 => in(emptyset,prop2set(X4)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(quantDeMorgan4, axiom, quantDeMorgan4 <=> 0.56/0.92 (![A,Xphi:(($i > $o))]: 0.56/0.92 ((?[Xx]: ((~Xphi(Xx)) & in(Xx,A))) => (~(![Xx]: (in(Xx,A) => Xphi(Xx))))))). 0.56/0.92 tff('144', plain, 0.56/0.92 quantDeMorgan4 = 0.56/0.92 (![X4,X6:(($i > $o))]: 0.56/0.92 ((?[X8]: ((~X6(X8)) & in(X8,X4))) => 0.56/0.92 (~(![X10]: (in(X10,X4) => X6(X10)))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(quantDeMorgan3, axiom, quantDeMorgan3 <=> 0.56/0.92 (![A,Xphi:(($i > $o))]: 0.56/0.92 ((~(?[Xx]: (Xphi(Xx) & in(Xx,A)))) => (![Xx]: (in(Xx,A) => (~Xphi(Xx))))))). 0.56/0.92 tff('145', plain, 0.56/0.92 quantDeMorgan3 = 0.56/0.92 (![X4,X6:(($i > $o))]: 0.56/0.92 ((~(?[X8]: (X6(X8) & in(X8,X4)))) => 0.56/0.92 (![X10]: (in(X10,X4) => (~X6(X10)))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(quantDeMorgan2, axiom, quantDeMorgan2 <=> 0.56/0.92 (![A,Xphi:(($i > $o))]: 0.56/0.92 ((![Xx]: (in(Xx,A) => (~Xphi(Xx)))) => (~(?[Xx]: (Xphi(Xx) & in(Xx,A))))))). 0.56/0.92 tff('146', plain, 0.56/0.92 quantDeMorgan2 = 0.56/0.92 (![X4,X6:(($i > $o))]: 0.56/0.92 ((![X8]: (in(X8,X4) => (~X6(X8)))) => 0.56/0.92 (~(?[X10]: (X6(X10) & in(X10,X4)))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(quantDeMorgan1, axiom, quantDeMorgan1 <=> 0.56/0.92 (![A,Xphi:(($i > $o))]: 0.56/0.92 ((~(![Xx]: (in(Xx,A) => Xphi(Xx)))) => (?[Xx]: ((~Xphi(Xx)) & in(Xx,A)))))). 0.56/0.92 tff('147', plain, 0.56/0.92 quantDeMorgan1 = 0.56/0.92 (![X4,X6:(($i > $o))]: 0.56/0.92 ((~(![X8]: (in(X8,X4) => X6(X8)))) => 0.56/0.92 (?[X10]: ((~X6(X10)) & in(X10,X4))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(vacuousDall, axiom, vacuousDall <=> 0.56/0.92 (![Xphi:(($i > $o)),Xx]: (in(Xx,emptyset) => Xphi(Xx)))). 0.56/0.92 tff('148', plain, 0.56/0.92 vacuousDall = (![X4:(($i > $o)),X6]: (in(X6,emptyset) => X4(X6))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(emptyE1, axiom, emptyE1 <=> 0.56/0.92 (![A,Xphi:(($i > $o))]: 0.56/0.92 ((?[Xx]: (Xphi(Xx) & in(Xx,A))) => 0.56/0.92 ((dsetconstr(A,^[Xx]: Xphi(Xx)) = emptyset) => $false)))). 0.56/0.92 tff('149', plain, 0.56/0.92 emptyE1 = 0.56/0.92 (![X4,X6:(($i > $o))]: 0.56/0.92 ((?[X8]: (X6(X8) & in(X8,X4))) => 0.56/0.92 ((dsetconstr(X4,^[V_1]: X6(V_1)) = emptyset) => $false))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(upairsetIR, axiom, upairsetIR <=> 0.56/0.92 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 0.56/0.92 tff('150', plain, 0.56/0.92 upairsetIR = (![X4,X6]: in(X6,setadjoin(X4,setadjoin(X6,emptyset)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(upairsetIL, axiom, upairsetIL <=> 0.56/0.92 (![Xx,Xy]: in(Xx,setadjoin(Xx,setadjoin(Xy,emptyset))))). 0.56/0.92 tff('151', plain, 0.56/0.92 upairsetIL = (![X4,X6]: in(X4,setadjoin(X4,setadjoin(X6,emptyset)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(upairsetE, axiom, upairsetE <=> 0.56/0.92 (![Xx,Xy,Xz]: 0.56/0.92 (in(Xz,setadjoin(Xx,setadjoin(Xy,emptyset))) => ((Xz = Xx) | (Xz = Xy))))). 0.56/0.92 tff('152', plain, 0.56/0.92 upairsetE = 0.56/0.92 (![X4,X6,X8]: 0.56/0.92 (in(X8,setadjoin(X4,setadjoin(X6,emptyset))) => 0.56/0.92 ((X8 = X4) | (X8 = X6)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(singletonsswitch, axiom, singletonsswitch <=> 0.56/0.92 (![Xx,Xy]: (in(Xx,setadjoin(Xy,emptyset)) => in(Xy,setadjoin(Xx,emptyset))))). 0.56/0.92 tff('153', plain, 0.56/0.92 singletonsswitch = 0.56/0.92 (![X4,X6]: 0.56/0.92 (in(X4,setadjoin(X6,emptyset)) => in(X6,setadjoin(X4,emptyset)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(eqinunit, axiom, eqinunit <=> 0.56/0.92 (![Xx,Xy]: ((Xx = Xy) => in(Xx,setadjoin(Xy,emptyset))))). 0.56/0.92 tff('154', plain, 0.56/0.92 eqinunit = (![X4,X6]: ((X4 = X6) => in(X4,setadjoin(X6,emptyset)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(notinsingleton, axiom, notinsingleton <=> 0.56/0.92 (![Xx,Xy]: ((Xx != Xy) => (~in(Xy,setadjoin(Xx,emptyset)))))). 0.56/0.92 tff('155', plain, 0.56/0.92 notinsingleton = 0.56/0.92 (![X4,X6]: ((X4 != X6) => (~in(X6,setadjoin(X4,emptyset))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(uniqinunit, axiom, uniqinunit <=> 0.56/0.92 (![Xx,Xy]: (in(Xx,setadjoin(Xy,emptyset)) => (Xx = Xy)))). 0.56/0.92 tff('156', plain, 0.56/0.92 uniqinunit = (![X4,X6]: (in(X4,setadjoin(X6,emptyset)) => (X4 = X6))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(nonemptyImpWitness, axiom, nonemptyImpWitness <=> 0.56/0.92 (![A]: (nonempty(A) => (?[Xx]: in(Xx,A))))). 0.56/0.92 tff('157', plain, 0.56/0.92 nonemptyImpWitness = (![X4]: (nonempty(X4) => (?[X6]: in(X6,X4)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(exuE2, axiom, exuE2 <=> 0.56/0.92 (![Xphi:(($i > $o))]: 0.56/0.92 (exu(^[Xx]: Xphi(Xx)) => (?[Xx]: (![Xy]: (Xphi(Xy) <=> (Xy = Xx))))))). 0.56/0.92 tff('158', plain, 0.56/0.92 exuE2 = 0.56/0.92 (![X4:(($i > $o))]: 0.56/0.92 (exu(^[V_1]: X4(V_1)) => (?[X6]: (![X8]: (X4(X8) <=> (X8 = X6)))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(subPowSU, axiom, subPowSU <=> 0.56/0.92 (![A,Xx]: (in(Xx,A) => in(Xx,powerset(setunion(A)))))). 0.56/0.92 tff('159', plain, 0.56/0.92 subPowSU = (![X4,X6]: (in(X6,X4) => in(X6,powerset(setunion(X4))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(setunionE, axiom, setunionE <=> 0.56/0.92 (![A,Xx]: 0.56/0.92 (in(Xx,setunion(A)) => 0.56/0.92 (![Xphi:$o]: ((![B]: (in(Xx,B) => (in(B,A) => Xphi))) => Xphi))))). 0.56/0.92 tff('160', plain, 0.56/0.92 setunionE = 0.56/0.92 (![X4,X6]: 0.56/0.92 (in(X6,setunion(X4)) => 0.56/0.92 (![X8:$o]: ((![X10]: (in(X6,X10) => (in(X10,X4) => X8))) => X8)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(setunionI, axiom, setunionI <=> 0.56/0.92 (![A,Xx,B]: (in(Xx,B) => (in(B,A) => in(Xx,setunion(A)))))). 0.56/0.92 tff('161', plain, 0.56/0.92 setunionI = 0.56/0.92 (![X4,X6,X8]: (in(X6,X8) => (in(X8,X4) => in(X6,setunion(X4))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(powersetE, axiom, powersetE <=> 0.56/0.92 (![A,B,Xx]: (in(B,powerset(A)) => (in(Xx,B) => in(Xx,A))))). 0.56/0.92 tff('162', plain, 0.56/0.92 powersetE = 0.56/0.92 (![X4,X6,X8]: (in(X6,powerset(X4)) => (in(X8,X6) => in(X8,X4)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(emptyInPowerset, axiom, emptyInPowerset <=> 0.56/0.92 (![A]: in(emptyset,powerset(A)))). 0.56/0.92 tff('163', plain, emptyInPowerset = (![X4]: in(emptyset,powerset(X4))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(emptyinPowerset, axiom, emptyinPowerset <=> 0.56/0.92 (![A]: in(emptyset,powerset(A)))). 0.56/0.92 tff('164', plain, emptyinPowerset = (![X4]: in(emptyset,powerset(X4))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(powersetI, axiom, powersetI <=> 0.56/0.92 (![A,B]: ((![Xx]: (in(Xx,B) => in(Xx,A))) => in(B,powerset(A))))). 0.56/0.92 tff('165', plain, 0.56/0.92 powersetI = 0.56/0.92 (![X4,X6]: ((![X8]: (in(X8,X6) => in(X8,X4))) => in(X6,powerset(X4)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(setoftrueEq, axiom, setoftrueEq <=> 0.56/0.92 (![A]: (dsetconstr(A,^[Xx]: $true) = A))). 0.56/0.92 tff('166', plain, setoftrueEq = (![X4]: (dsetconstr(X4,^[V_1]: $true) = X4)), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(setadjoinOr, axiom, setadjoinOr <=> 0.56/0.92 (![Xx,A,Xy]: (in(Xy,setadjoin(Xx,A)) => ((Xy = Xx) | in(Xy,A))))). 0.56/0.92 tff('167', plain, 0.56/0.92 setadjoinOr = 0.56/0.92 (![X4,X6,X8]: (in(X8,setadjoin(X4,X6)) => ((X8 = X4) | in(X8,X6)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(setadjoinE, axiom, setadjoinE <=> 0.56/0.92 (![Xx,A,Xy]: 0.56/0.92 (in(Xy,setadjoin(Xx,A)) => 0.56/0.92 (![Xphi:$o]: (((Xy = Xx) => Xphi) => ((in(Xy,A) => Xphi) => Xphi)))))). 0.56/0.92 tff('168', plain, 0.56/0.92 setadjoinE = 0.56/0.92 (![X4,X6,X8]: 0.56/0.92 (in(X8,setadjoin(X4,X6)) => 0.56/0.92 (![X10:$o]: (((X8 = X4) => X10) => ((in(X8,X6) => X10) => X10))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(setadjoinIR, axiom, setadjoinIR <=> 0.56/0.92 (![Xx,A,Xy]: (in(Xy,A) => in(Xy,setadjoin(Xx,A))))). 0.56/0.92 tff('169', plain, 0.56/0.92 setadjoinIR = (![X4,X6,X8]: (in(X8,X6) => in(X8,setadjoin(X4,X6)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(emptyinunitempty, axiom, emptyinunitempty() = 0.56/0.92 in(emptyset,setadjoin(emptyset,emptyset))). 0.56/0.92 tff('170', plain, 0.56/0.92 emptyinunitempty = in(emptyset,setadjoin(emptyset,emptyset)), 0.56/0.92 inference('simplify_rw_rule', [status(thm)], [emptyinunitempty])). 0.56/0.92 tff('171', plain, 0.56/0.92 emptyinunitempty = in(emptyset,setadjoin(emptyset,emptyset)), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(setadjoinIL, axiom, setadjoinIL <=> (![Xx,Xy]: in(Xx,setadjoin(Xx,Xy)))). 0.56/0.92 tff('172', plain, setadjoinIL = (![X4,X6]: in(X4,setadjoin(X4,X6))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(nonemptyI1, axiom, nonemptyI1 <=> 0.56/0.92 (![A]: ((?[Xx]: in(Xx,A)) => nonempty(A)))). 0.56/0.92 tff('173', plain, nonemptyI1 = (![X4]: ((?[X6]: in(X6,X4)) => nonempty(X4))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(nonemptyI, axiom, nonemptyI <=> 0.56/0.92 (![A,Xphi:(($i > $o)),Xx]: 0.56/0.92 (in(Xx,A) => (Xphi(Xx) => nonempty(dsetconstr(A,^[Xy]: Xphi(Xy))))))). 0.56/0.92 tff('174', plain, 0.56/0.92 nonemptyI = 0.56/0.92 (![X4,X6:(($i > $o)),X8]: 0.56/0.92 (in(X8,X4) => (X6(X8) => nonempty(dsetconstr(X4,^[V_1]: X6(V_1)))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(nonemptyE1, axiom, nonemptyE1 <=> 0.56/0.92 (![A]: (nonempty(A) => (?[Xx]: in(Xx,A))))). 0.56/0.92 tff('175', plain, nonemptyE1 = (![X4]: (nonempty(X4) => (?[X6]: in(X6,X4)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(nonempty, axiom, nonempty() = ^[Xx]: (Xx != emptyset)). 0.56/0.92 tff('176', plain, nonempty = (^[Xx]: (Xx != emptyset)), 0.56/0.92 inference('simplify_rw_rule', [status(thm)], [nonempty])). 0.56/0.92 tff('177', plain, nonempty = (^[V_1]: (V_1 != emptyset)), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(setbeta, axiom, setbeta <=> 0.56/0.92 (![A,Xphi:(($i > $o)),Xx]: 0.56/0.92 (in(Xx,A) => (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) <=> Xphi(Xx))))). 0.56/0.92 tff('178', plain, 0.56/0.92 setbeta = 0.56/0.92 (![X4,X6:(($i > $o)),X8]: 0.56/0.92 (in(X8,X4) => (in(X8,dsetconstr(X4,^[V_1]: X6(V_1))) <=> X6(X8)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(noeltsimpempty, axiom, noeltsimpempty <=> 0.56/0.92 (![A]: ((![Xx]: (~in(Xx,A))) => (A = emptyset)))). 0.56/0.92 tff('179', plain, 0.56/0.92 noeltsimpempty = (![X4]: ((![X6]: (~in(X6,X4))) => (X4 = emptyset))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(emptyI, axiom, emptyI <=> 0.56/0.92 (![A]: ((![Xx]: (~in(Xx,A))) => (A = emptyset)))). 0.56/0.92 tff('180', plain, 0.56/0.92 emptyI = (![X4]: ((![X6]: (~in(X6,X4))) => (X4 = emptyset))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(setext, axiom, setext <=> 0.56/0.92 (![A,B]: 0.56/0.92 ((![Xx]: (in(Xx,A) => in(Xx,B))) => 0.56/0.92 ((![Xx]: (in(Xx,B) => in(Xx,A))) => (A = B))))). 0.56/0.92 tff('181', plain, 0.56/0.92 setext = 0.56/0.92 (![X4,X6]: 0.56/0.92 ((![X8]: (in(X8,X4) => in(X8,X6))) => 0.56/0.92 ((![X10]: (in(X10,X6) => in(X10,X4))) => (X4 = X6)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(exuE3e, axiom, exuE3e <=> 0.56/0.92 (![Xphi:(($i > $o))]: (exu(^[Xx]: Xphi(Xx)) => (?[Xx]: Xphi(Xx))))). 0.56/0.92 tff('182', plain, 0.56/0.92 exuE3e = (![X4:(($i > $o))]: (exu(^[V_1]: X4(V_1)) => (?[X6]: X4(X6)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(notinemptyset, axiom, notinemptyset <=> (![Xx]: (~in(Xx,emptyset)))). 0.56/0.92 tff('183', plain, notinemptyset = (![X4]: (~in(X4,emptyset))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(emptysetimpfalse, axiom, emptysetimpfalse <=> 0.56/0.92 (![Xx]: (in(Xx,emptyset) => $false))). 0.56/0.92 tff('184', plain, emptysetimpfalse = (![X4]: (in(X4,emptyset) => $false)), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(emptysetE, axiom, emptysetE <=> 0.56/0.92 (![Xx]: (in(Xx,emptyset) => (![Xphi:$o]: Xphi)))). 0.56/0.92 tff('185', plain, emptysetE = (![X4]: (in(X4,emptyset) => (![X6:$o]: X6))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(prop2setE, axiom, prop2setE <=> 0.56/0.92 (![Xphi:$o,Xx]: (in(Xx,prop2set(Xphi)) => Xphi))). 0.56/0.92 tff('186', plain, prop2setE = (![X4:$o,X6]: (in(X6,prop2set(X4)) => X4)), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(exuE1, axiom, exuE1 <=> 0.56/0.92 (![Xphi:(($i > $o))]: 0.56/0.92 (exu(^[Xx]: Xphi(Xx)) => 0.56/0.92 (?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx)))))). 0.56/0.92 tff('187', plain, 0.56/0.92 exuE1 = 0.56/0.92 (![X4:(($i > $o))]: 0.56/0.92 (exu(^[V_1]: X4(V_1)) => 0.56/0.92 (?[X6]: ((![X8]: (X4(X8) => (X6 = X8))) & X4(X6))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(dsetconstrER, axiom, dsetconstrER <=> 0.56/0.92 (![A,Xphi:(($i > $o)),Xx]: 0.56/0.92 (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) => Xphi(Xx)))). 0.56/0.92 tff('188', plain, 0.56/0.92 dsetconstrER = 0.56/0.92 (![X4,X6:(($i > $o)),X8]: 0.56/0.92 (in(X8,dsetconstr(X4,^[V_1]: X6(V_1))) => X6(X8))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(dsetconstrEL, axiom, dsetconstrEL <=> 0.56/0.92 (![A,Xphi:(($i > $o)),Xx]: 0.56/0.92 (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) => in(Xx,A)))). 0.56/0.92 tff('189', plain, 0.56/0.92 dsetconstrEL = 0.56/0.92 (![X4,X6:(($i > $o)),X8]: 0.56/0.92 (in(X8,dsetconstr(X4,^[V_1]: X6(V_1))) => in(X8,X4))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(dsetconstrI, axiom, dsetconstrI <=> 0.56/0.92 (![A,Xphi:(($i > $o)),Xx]: 0.56/0.92 (in(Xx,A) => (Xphi(Xx) => in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))))))). 0.56/0.92 tff('190', plain, 0.56/0.92 dsetconstrI = 0.56/0.92 (![X4,X6:(($i > $o)),X8]: 0.56/0.92 (in(X8,X4) => (X6(X8) => in(X8,dsetconstr(X4,^[V_1]: X6(V_1)))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(descrp, axiom, descrp <=> 0.56/0.92 (![Xphi:(($i > $o))]: 0.56/0.92 (exu(^[Xx]: Xphi(Xx)) => Xphi(descr(^[Xx]: Xphi(Xx)))))). 0.56/0.92 tff('191', plain, 0.56/0.92 descrp = 0.56/0.92 (![X4:(($i > $o))]: (exu(^[V_1]: X4(V_1)) => X4(descr(^[V_2]: X4(V_2))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(wellorderingAx, axiom, wellorderingAx <=> 0.56/0.92 (![A]: 0.56/0.92 (?[B]: 0.56/0.92 ((![C]: 0.56/0.92 (((![Xx]: (in(Xx,C) => in(Xx,A))) & (?[Xx]: in(Xx,C))) => 0.56/0.92 (?[D,Xx]: 0.56/0.92 ((![E]: 0.56/0.92 (in(E,B) => ((![Xy]: (in(Xy,E) => in(Xy,D))) | in(Xx,E)))) & 0.56/0.92 (~(?[Xy]: (in(Xy,C) & in(Xy,D)))) & in(Xx,C) & in(D,B))))) & 0.56/0.92 (![C,D]: 0.56/0.92 ((in(C,B) & in(D,B)) => 0.56/0.92 ((![Xx]: (in(Xx,C) => in(Xx,D))) | 0.56/0.92 (![Xx]: (in(Xx,D) => in(Xx,C)))))) & 0.56/0.92 (![Xx,Xy]: 0.56/0.92 ((in(Xx,A) & in(Xy,A)) => 0.56/0.92 ((![C]: (in(C,B) => (in(Xx,C) <=> in(Xy,C)))) => (Xx = Xy)))) & 0.56/0.92 (![C]: (in(C,B) => (![Xx]: (in(Xx,C) => in(Xx,A))))))))). 0.56/0.92 tff('192', plain, 0.56/0.92 wellorderingAx = 0.56/0.92 (![X4]: 0.56/0.92 (?[X6]: 0.56/0.92 ((![X8]: 0.56/0.92 (((![X10]: (in(X10,X8) => in(X10,X4))) & (?[X12]: in(X12,X8))) => 0.56/0.92 (?[X14,X16]: 0.56/0.92 ((![X18]: 0.56/0.92 (in(X18,X6) => 0.56/0.92 ((![X20]: (in(X20,X18) => in(X20,X14))) | in(X16,X18)))) & 0.56/0.92 (~(?[X22]: (in(X22,X8) & in(X22,X14)))) & in(X16,X8) & 0.56/0.92 in(X14,X6))))) & 0.56/0.92 (![X24,X26]: 0.56/0.92 ((in(X24,X6) & in(X26,X6)) => 0.56/0.92 ((![X28]: (in(X28,X24) => in(X28,X26))) | 0.56/0.92 (![X30]: (in(X30,X26) => in(X30,X24)))))) & 0.56/0.92 (![X32,X34]: 0.56/0.92 ((in(X32,X4) & in(X34,X4)) => 0.56/0.92 ((![X36]: (in(X36,X6) => (in(X32,X36) <=> in(X34,X36)))) => 0.56/0.92 (X32 = X34)))) & 0.56/0.92 (![X38]: (in(X38,X6) => (![X40]: (in(X40,X38) => in(X40,X4)))))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(foundationAx, axiom, foundationAx <=> 0.56/0.92 (![A]: 0.56/0.92 ((?[Xx]: in(Xx,A)) => 0.56/0.92 (?[B]: ((~(?[Xx]: (in(Xx,A) & in(Xx,B)))) & in(B,A)))))). 0.56/0.92 tff('193', plain, 0.56/0.92 foundationAx = 0.56/0.92 (![X4]: 0.56/0.92 ((?[X6]: in(X6,X4)) => 0.56/0.92 (?[X8]: ((~(?[X10]: (in(X10,X4) & in(X10,X8)))) & in(X8,X4))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(replAx, axiom, replAx <=> 0.56/0.92 (![Xphi:(($i * $i) > $o),A]: 0.56/0.92 ((![Xx]: (in(Xx,A) => exu(^[Xy]: Xphi(Xx,Xy)))) => 0.56/0.92 (?[B]: (![Xx]: (in(Xx,B) <=> (?[Xy]: (Xphi(Xy,Xx) & in(Xy,A))))))))). 0.56/0.92 tff('194', plain, 0.56/0.92 replAx = 0.56/0.92 (![X4:(($i * $i) > $o),X6]: 0.56/0.92 ((![X8]: (in(X8,X6) => exu(^[V_1]: X4(X8,V_1)))) => 0.56/0.92 (?[X10]: 0.56/0.92 (![X12]: (in(X12,X10) <=> (?[X14]: (X4(X14,X12) & in(X14,X6)))))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(omegaIndAx, axiom, omegaIndAx <=> 0.56/0.92 (![A]: 0.56/0.92 ((in(emptyset,A) & 0.56/0.92 (![Xx]: ((in(Xx,omega) & in(Xx,A)) => in(setadjoin(Xx,Xx),A)))) => 0.56/0.92 (![Xx]: (in(Xx,omega) => in(Xx,A)))))). 0.56/0.92 tff('195', plain, 0.56/0.92 omegaIndAx = 0.56/0.92 (![X4]: 0.56/0.92 ((in(emptyset,X4) & 0.56/0.92 (![X6]: ((in(X6,omega) & in(X6,X4)) => in(setadjoin(X6,X6),X4)))) => 0.56/0.92 (![X8]: (in(X8,omega) => in(X8,X4))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(omegaSAx, axiom, omegaSAx <=> 0.56/0.92 (![Xx]: (in(Xx,omega) => in(setadjoin(Xx,Xx),omega)))). 0.56/0.92 tff('196', plain, 0.56/0.92 omegaSAx = (![X4]: (in(X4,omega) => in(setadjoin(X4,X4),omega))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(omega0Ax, axiom, omega0Ax() = in(emptyset,omega)). 0.56/0.92 tff('197', plain, omega0Ax = in(emptyset,omega), 0.56/0.92 inference('simplify_rw_rule', [status(thm)], [omega0Ax])). 0.56/0.92 tff('198', plain, omega0Ax = in(emptyset,omega), define([status(thm)])). 0.56/0.92 tff(setunionAx, axiom, setunionAx <=> 0.56/0.92 (![A,Xx]: (in(Xx,setunion(A)) <=> (?[B]: (in(B,A) & in(Xx,B)))))). 0.56/0.92 tff('199', plain, 0.56/0.92 setunionAx = 0.56/0.92 (![X4,X6]: (in(X6,setunion(X4)) <=> (?[X8]: (in(X8,X4) & in(X6,X8))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(powersetAx, axiom, powersetAx <=> 0.56/0.92 (![A,B]: (in(B,powerset(A)) <=> (![Xx]: (in(Xx,B) => in(Xx,A)))))). 0.56/0.92 tff('200', plain, 0.56/0.92 powersetAx = 0.56/0.92 (![X4,X6]: (in(X6,powerset(X4)) <=> (![X8]: (in(X8,X6) => in(X8,X4))))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(setadjoinAx, axiom, setadjoinAx <=> 0.56/0.92 (![Xx,A,Xy]: (in(Xy,setadjoin(Xx,A)) <=> ((Xy = Xx) | in(Xy,A))))). 0.56/0.92 tff('201', plain, 0.56/0.92 setadjoinAx = 0.56/0.92 (![X4,X6,X8]: (in(X8,setadjoin(X4,X6)) <=> ((X8 = X4) | in(X8,X6)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(emptysetAx, axiom, emptysetAx <=> (![Xx]: (~in(Xx,emptyset)))). 0.56/0.92 tff('202', plain, emptysetAx = (![X4]: (~in(X4,emptyset))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(setextAx, axiom, setextAx <=> 0.56/0.92 (![A,B]: ((![Xx]: (in(Xx,A) <=> in(Xx,B))) => (A = B)))). 0.56/0.92 tff('203', plain, 0.56/0.92 setextAx = (![X4,X6]: ((![X8]: (in(X8,X4) <=> in(X8,X6))) => (X4 = X6))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(exu, axiom, exu() = 0.56/0.92 ^[Xphi:(($i > $o))]: (?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx)))). 0.56/0.92 tff('204', plain, 0.56/0.92 exu = 0.56/0.92 (^[Xphi:(($i > $o))]: 0.56/0.92 (?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx)))), 0.56/0.92 inference('simplify_rw_rule', [status(thm)], [exu])). 0.56/0.92 tff('205', plain, 0.56/0.92 exu = 0.56/0.92 (^[V_1:(($i > $o))]: (?[X4]: ((![X6]: (V_1(X6) => (X4 = X6))) & V_1(X4)))), 0.56/0.92 define([status(thm)])). 0.56/0.92 tff(app, conjecture, 0.56/0.92 (setextAx => 0.56/0.92 (emptysetAx => 0.56/0.92 (setadjoinAx => 0.56/0.92 (powersetAx => 0.56/0.92 (setunionAx => 0.56/0.92 (omega0Ax => 0.56/0.92 (omegaSAx => 0.56/0.92 (omegaIndAx => 0.56/0.92 (replAx => 0.56/0.92 (foundationAx => 0.56/0.92 (wellorderingAx => 0.56/0.92 (descrp => 0.56/0.92 (dsetconstrI => 0.56/0.92 (dsetconstrEL => 0.56/0.92 (dsetconstrER => 0.56/0.92 (exuE1 => 0.56/0.92 (prop2setE => 0.56/0.92 (emptysetE => 0.56/0.92 (emptysetimpfalse => 0.56/0.92 (notinemptyset => 0.56/0.92 (exuE3e => 0.56/0.92 (setext => 0.56/0.92 (emptyI => 0.56/0.92 (noeltsimpempty => 0.56/0.92 (setbeta => 0.56/0.92 (nonemptyE1 => 0.56/0.92 (nonemptyI => 0.56/0.92 (nonemptyI1 => 0.56/0.92 (setadjoinIL => 0.56/0.92 (emptyinunitempty => 0.56/0.92 (setadjoinIR => 0.56/0.92 (setadjoinE => 0.56/0.92 (setadjoinOr => 0.56/0.92 (setoftrueEq => 0.56/0.92 (powersetI => 0.56/0.92 (emptyinPowerset => 0.56/0.92 (emptyInPowerset => 0.56/0.92 (powersetE => 0.56/0.92 (setunionI => 0.56/0.92 (setunionE => 0.56/0.92 (subPowSU => 0.56/0.92 (exuE2 => 0.56/0.92 (nonemptyImpWitness => 0.56/0.92 (uniqinunit => 0.56/0.92 (notinsingleton => 0.56/0.92 (eqinunit => 0.56/0.92 (singletonsswitch => 0.56/0.92 (upairsetE => 0.56/0.92 (upairsetIL => 0.56/0.92 (upairsetIR => 0.56/0.92 (emptyE1 => 0.56/0.92 (vacuousDall => 0.56/0.92 (quantDeMorgan1 => 0.56/0.92 (quantDeMorgan2 => 0.56/0.92 (quantDeMorgan3 => 0.56/0.92 (quantDeMorgan4 => 0.56/0.92 (prop2setI => 0.56/0.92 (prop2set2propI => 0.56/0.92 (notdexE => 0.56/0.92 (notdallE => 0.56/0.92 (exuI1 => 0.56/0.92 (exuI3 => 0.56/0.92 (exuI2 => 0.56/0.92 (inCongP => 0.56/0.92 (in__Cong => 0.56/0.92 (exuE3u => 0.56/0.92 ( 0.56/0.92 exu__Cong => 0.56/0.92 ( 0.56/0.92 emptyset__Cong => 0.56/0.92 ( 0.56/0.92 setadjoin__Cong => 0.56/0.92 ( 0.56/0.92 powerset__Cong => 0.56/0.92 ( 0.56/0.92 setunion__Cong => 0.56/0.92 ( 0.56/0.92 omega__Cong => 0.56/0.92 ( 0.56/0.92 exuEu => 0.56/0.92 ( 0.56/0.92 descr__Cong => 0.56/0.92 ( 0.56/0.92 dsetconstr__Cong => 0.56/0.92 ( 0.56/0.92 subsetI1 => 0.56/0.92 ( 0.56/0.92 eqimpsubset2 => 0.56/0.92 ( 0.56/0.92 eqimpsubset1 => 0.56/0.92 ( 0.56/0.92 subsetI2 => 0.56/0.92 ( 0.56/0.92 emptysetsubset => 0.56/0.92 ( 0.56/0.92 subsetE => 0.56/0.92 ( 0.56/0.92 subsetE2 => 0.56/0.92 ( 0.56/0.92 notsubsetI => 0.56/0.92 ( 0.56/0.92 notequalI1 => 0.56/0.92 ( 0.56/0.92 notequalI2 => 0.56/0.92 ( 0.56/0.92 subsetRefl => 0.56/0.92 ( 0.56/0.92 subsetTrans => 0.56/0.92 ( 0.56/0.92 setadjoinSub => 0.56/0.92 ( 0.56/0.92 setadjoinSub2 => 0.56/0.92 ( 0.56/0.92 subset2powerset => 0.56/0.92 ( 0.56/0.92 setextsub => 0.56/0.92 ( 0.56/0.92 subsetemptysetimpeq => 0.56/0.92 ( 0.56/0.92 powersetI1 => 0.56/0.92 ( 0.56/0.92 powersetE1 => 0.56/0.92 ( 0.56/0.92 inPowerset => 0.56/0.92 ( 0.56/0.92 powersetsubset => 0.56/0.92 ( 0.56/0.92 sepInPowerset => 0.56/0.92 ( 0.56/0.92 sepSubset => 0.56/0.92 ( 0.56/0.92 binunionIL => 0.56/0.92 ( 0.56/0.92 upairset2IR => 0.56/0.92 ( 0.56/0.92 binunionIR => 0.56/0.92 ( 0.56/0.92 binunionEcases => 0.56/0.92 ( 0.56/0.92 binunionE => 0.56/0.92 ( 0.56/0.92 binunionLsub => 0.56/0.92 ( 0.56/0.92 binunionRsub => 0.56/0.92 ( 0.56/0.92 binintersectI => 0.56/0.92 ( 0.56/0.92 binintersectSubset5 => 0.56/0.92 ( 0.56/0.92 binintersectEL => 0.56/0.92 ( 0.56/0.92 binintersectLsub => 0.56/0.92 ( 0.56/0.92 binintersectSubset2 => 0.56/0.92 ( 0.56/0.92 binintersectSubset3 => 0.56/0.92 ( 0.56/0.92 binintersectER => 0.56/0.92 ( 0.56/0.92 disjointsetsI1 => 0.56/0.92 ( 0.56/0.92 binintersectRsub => 0.56/0.92 ( 0.56/0.92 binintersectSubset4 => 0.56/0.92 ( 0.56/0.92 binintersectSubset1 => 0.56/0.92 ( 0.56/0.92 bs114d => 0.56/0.92 ( 0.56/0.92 setminusI => 0.56/0.92 ( 0.56/0.92 setminusEL => 0.56/0.92 ( 0.56/0.92 setminusER => 0.56/0.92 ( 0.56/0.92 setminusSubset2 => 0.56/0.92 ( 0.56/0.92 setminusERneg => 0.56/0.92 ( 0.56/0.92 setminusELneg => 0.56/0.92 ( 0.56/0.92 setminusILneg => 0.56/0.92 ( 0.56/0.92 setminusIRneg => 0.56/0.92 ( 0.56/0.92 setminusLsub => 0.56/0.92 ( 0.56/0.92 setminusSubset1 => 0.56/0.92 ( 0.56/0.92 symdiffE => 0.56/0.92 ( 0.56/0.92 symdiffI1 => 0.56/0.92 ( 0.56/0.92 symdiffI2 => 0.56/0.92 ( 0.56/0.92 symdiffIneg1 => 0.56/0.92 ( 0.56/0.92 symdiffIneg2 => 0.56/0.92 ( 0.56/0.92 secondinupair => 0.56/0.92 ( 0.56/0.92 setukpairIL => 0.56/0.92 ( 0.56/0.92 setukpairIR => 0.56/0.92 ( 0.56/0.92 kpairiskpair => 0.56/0.92 ( 0.56/0.92 kpairp => 0.56/0.92 ( 0.56/0.92 singletonsubset => 0.56/0.92 ( 0.56/0.92 singletoninpowerset => 0.56/0.92 ( 0.56/0.92 singletoninpowunion => 0.56/0.92 ( 0.56/0.92 upairset2E => 0.56/0.92 ( 0.56/0.92 upairsubunion => 0.56/0.92 ( 0.56/0.92 upairinpowunion => 0.56/0.92 ( 0.56/0.92 ubforcartprodlem1 => 0.56/0.92 ( 0.56/0.92 ubforcartprodlem2 => 0.56/0.92 ( 0.56/0.92 ubforcartprodlem3 => 0.56/0.92 ( 0.56/0.92 cartprodpairin => 0.56/0.92 ( 0.56/0.92 cartprodmempair1 => 0.56/0.92 ( 0.56/0.92 cartprodmempair => 0.56/0.92 ( 0.56/0.92 setunionE2 => 0.56/0.92 ( 0.56/0.92 setunionsingleton1 => 0.56/0.92 ( 0.56/0.92 setunionsingleton2 => 0.56/0.92 ( 0.56/0.92 setunionsingleton => 0.56/0.92 ( 0.56/0.92 singletonprop => 0.56/0.92 ( 0.56/0.92 ex1E1 => 0.56/0.92 ( 0.56/0.92 ex1I => 0.56/0.92 ( 0.56/0.92 ex1I2 => 0.56/0.92 ( 0.56/0.92 singletonsuniq => 0.56/0.92 ( 0.56/0.92 setukpairinjL1 => 0.56/0.92 ( 0.56/0.92 kfstsingleton => 0.56/0.92 ( 0.56/0.92 theprop => 0.56/0.92 ( 0.56/0.92 kfstpairEq => 0.56/0.92 ( 0.56/0.92 cartprodfstin => 0.56/0.92 ( 0.56/0.92 setukpairinjL2 => 0.56/0.92 ( 0.56/0.92 setukpairinjL => 0.56/0.92 ( 0.56/0.92 setukpairinjR11 => 0.56/0.92 ( 0.56/0.92 setukpairinjR12 => 0.56/0.92 ( 0.56/0.92 setukpairinjR1 => 0.56/0.92 ( 0.56/0.92 upairequniteq => 0.56/0.92 ( 0.56/0.92 setukpairinjR2 => 0.56/0.92 ( 0.56/0.92 setukpairinjR => 0.56/0.92 ( 0.56/0.92 ksndsingleton => 0.56/0.92 ( 0.56/0.92 ksndpairEq => 0.56/0.92 ( 0.56/0.92 kpairsurjEq => 0.56/0.92 ( 0.56/0.92 cartprodsndin => 0.56/0.92 ( 0.56/0.92 cartprodpairmemEL => 0.56/0.92 ( 0.56/0.92 cartprodpairmemER => 0.56/0.92 ( 0.56/0.92 cartprodmempaircEq => 0.56/0.92 ( 0.56/0.92 cartprodfstpairEq => 0.56/0.92 ( 0.56/0.92 cartprodsndpairEq => 0.56/0.92 ( 0.56/0.92 cartprodpairsurjEq => 0.56/0.92 ( 0.56/0.92 dpsetconstrI => 0.56/0.92 ( 0.56/0.92 dpsetconstrSub => 0.56/0.92 ( 0.56/0.92 setOfPairsIsBReln => 0.56/0.92 ( 0.56/0.92 dpsetconstrERa => 0.56/0.92 ( 0.56/0.92 dpsetconstrEL1 => 0.56/0.92 ( 0.56/0.92 dpsetconstrEL2 => 0.56/0.92 ( 0.56/0.92 dpsetconstrER => 0.56/0.92 ( 0.56/0.92 funcImageSingleton => 0.56/0.92 ( 0.56/0.92 apProp => 0.56/0.92 ( 0.56/0.92 ![A,B,Xf]: 0.56/0.92 (func( 0.56/0.92 A,B,Xf) => 0.56/0.92 (![Xx]: 0.56/0.92 (in(Xx,A) => 0.56/0.92 in( 0.56/0.92 ap( 0.56/0.92 A,B,Xf,Xx), 0.56/0.92 B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 0.56/0.92 tff(zf_stmt_0, conjecture, 0.56/0.92 ((![X4,X6]: ((![X8]: (in(X8,X4) <=> in(X8,X6))) => (X4 = X6))) => 0.56/0.92 ((![X10]: (~in(X10,emptyset))) => 0.56/0.92 ((![X12,X14,X16]: 0.56/0.92 (in(X16,setadjoin(X12,X14)) <=> (in(X16,X14) | (X16 = X12)))) => 0.56/0.92 ((![X18,X20]: 0.56/0.92 (in(X20,powerset(X18)) <=> (![X22]: (in(X22,X20) => in(X22,X18))))) => 0.56/0.92 ((![X24,X26]: 0.56/0.92 (in(X26,setunion(X24)) <=> (?[X28]: (in(X26,X28) & in(X28,X24))))) => 0.56/0.92 (in(emptyset,omega) => 0.56/0.92 ((![X30]: (in(X30,omega) => in(setadjoin(X30,X30),omega))) => 0.56/0.92 ((![X32]: 0.56/0.92 (((![X34]: 0.56/0.92 ((in(X34,X32) & in(X34,omega)) => 0.56/0.92 in(setadjoin(X34,X34),X32))) & 0.56/0.92 in(emptyset,X32)) => 0.56/0.92 (![X36]: (in(X36,omega) => in(X36,X32))))) => 0.56/0.92 ((![X38:(($i * $i) > $o),X40]: 0.56/0.92 ((![X42]: 0.56/0.92 (in(X42,X40) => 0.56/0.92 (?[X44]: 0.56/0.92 (X38(X42,X44) & (![X46]: (X38(X42,X46) => (X44 = X46))))))) => 0.56/0.92 (?[X48]: 0.56/0.92 (![X50]: 0.56/0.92 (in(X50,X48) <=> (?[X52]: (in(X52,X40) & X38(X52,X50)))))))) => 0.56/0.92 ((![X54]: 0.56/0.92 ((?[X56]: in(X56,X54)) => 0.56/0.92 (?[X58]: 0.56/0.92 (in(X58,X54) & (~(?[X60]: (in(X60,X58) & in(X60,X54)))))))) => 0.56/0.92 ((![X62]: 0.56/0.92 (?[X64]: 0.56/0.92 ((![X96]: 0.56/0.92 (in(X96,X64) => (![X98]: (in(X98,X96) => in(X98,X62))))) & 0.56/0.92 (![X90,X92]: 0.56/0.92 ((in(X92,X62) & in(X90,X62)) => 0.56/0.92 ((![X94]: 0.56/0.92 (in(X94,X64) => (in(X90,X94) <=> in(X92,X94)))) => 0.56/0.92 (X90 = X92)))) & 0.56/0.92 (![X82,X84]: 0.56/0.92 ((in(X84,X64) & in(X82,X64)) => 0.56/0.92 ((![X88]: (in(X88,X84) => in(X88,X82))) | 0.56/0.92 (![X86]: (in(X86,X82) => in(X86,X84)))))) & 0.56/0.92 (![X66]: 0.56/0.92 (((?[X70]: in(X70,X66)) & 0.56/0.92 (![X68]: (in(X68,X66) => in(X68,X62)))) => 0.56/0.92 (?[X72,X74]: 0.56/0.92 (in(X72,X64) & in(X74,X66) & 0.56/0.92 (~(?[X80]: (in(X80,X72) & in(X80,X66)))) & 0.56/0.92 (![X76]: 0.56/0.92 (in(X76,X64) => 0.56/0.92 (in(X74,X76) | 0.56/0.92 (![X78]: (in(X78,X76) => in(X78,X72))))))))))))) => 0.56/0.92 ((![X100:(($i > $o))]: 0.56/0.92 ((?[X102]: 0.56/0.92 (X100(X102) & (![X104]: (X100(X104) => (X102 = X104))))) => 0.56/0.92 X100(descr(^[V_1]: X100(V_1))))) => 0.56/0.92 ((![X106,X108:(($i > $o)),X110]: 0.56/0.92 (in(X110,X106) => 0.56/0.92 (X108(X110) => in(X110,dsetconstr(X106,^[V_2]: X108(V_2)))))) => 0.56/0.92 ((![X112,X114:(($i > $o)),X116]: 0.56/0.92 (in(X116,dsetconstr(X112,^[V_3]: X114(V_3))) => 0.56/0.92 in(X116,X112))) => 0.56/0.92 ((![X118,X120:(($i > $o)),X122]: 0.56/0.92 (in(X122,dsetconstr(X118,^[V_4]: X120(V_4))) => 0.56/0.92 X120(X122))) => 0.56/0.92 ((![X124:(($i > $o))]: 0.56/0.92 ((?[X126]: 0.56/0.92 (X124(X126) & 0.56/0.92 (![X128]: (X124(X128) => (X126 = X128))))) => 0.56/0.92 (?[X130]: 0.56/0.92 (X124(X130) & 0.56/0.92 (![X132]: (X124(X132) => (X130 = X132))))))) => 0.56/0.92 ((![X134:$o,X136]: (in(X136,prop2set(X134)) => X134)) => 0.56/0.92 ((![X138]: (in(X138,emptyset) => (![X140:$o]: X140))) => 0.56/0.92 ((![X142]: (~in(X142,emptyset))) => 0.56/0.92 ((![X144]: (~in(X144,emptyset))) => 0.56/0.92 ((![X146:(($i > $o))]: 0.56/0.92 ((?[X148]: 0.56/0.92 (X146(X148) & 0.56/0.92 (![X150]: (X146(X150) => (X148 = X150))))) => 0.56/0.92 (?[X152]: X146(X152)))) => 0.56/0.92 ((![X154,X156]: 0.56/0.92 ((![X158]: (in(X158,X154) => in(X158,X156))) => 0.56/0.92 ((![X160]: (in(X160,X156) => in(X160,X154))) => 0.56/0.92 (X154 = X156)))) => 0.56/0.92 ((![X162]: 0.56/0.92 ((![X164]: (~in(X164,X162))) => (X162 = emptyset))) => 0.56/0.92 ((![X166]: 0.56/0.92 ((![X168]: (~in(X168,X166))) => 0.56/0.92 (X166 = emptyset))) => 0.56/0.92 ((![X170,X172:(($i > $o)),X174]: 0.56/0.92 (in(X174,X170) => 0.56/0.92 (in(X174,dsetconstr(X170,^[V_5]: X172(V_5))) <=> 0.56/0.92 X172(X174)))) => 0.56/0.92 ((![X176]: 0.56/0.92 ((X176 != emptyset) => 0.56/0.92 (?[X178]: in(X178,X176)))) => 0.56/0.92 ((![X180,X182:(($i > $o)),X184]: 0.56/0.92 (in(X184,X180) => 0.56/0.92 (X182(X184) => 0.56/0.92 (dsetconstr(X180,^[V_6]: X182(V_6)) != 0.56/0.92 emptyset)))) => 0.56/0.92 ((![X186]: 0.56/0.92 ((?[X188]: in(X188,X186)) => 0.56/0.92 (X186 != emptyset))) => 0.56/0.92 ((![X190,X192]: in(X190,setadjoin(X190,X192))) => 0.56/0.92 (in(emptyset,setadjoin(emptyset,emptyset)) => 0.56/0.92 ((![X194,X196,X198]: 0.56/0.92 (in(X198,X196) => 0.56/0.92 in(X198,setadjoin(X194,X196)))) => 0.56/0.92 ((![X200,X202,X204]: 0.56/0.92 (in(X204,setadjoin(X200,X202)) => 0.56/0.92 (![X206:$o]: 0.56/0.92 (((X204 = X200) => X206) => 0.56/0.92 ((in(X204,X202) => X206) => X206))))) => 0.56/0.92 ((![X208,X210,X212]: 0.56/0.92 (in(X212,setadjoin(X208,X210)) => 0.56/0.92 (in(X212,X210) | (X212 = X208)))) => 0.56/0.92 ((![X214]: 0.56/0.92 (dsetconstr(X214,^[V_7]: $true) = X214)) => 0.56/0.92 ((![X216,X218]: 0.56/0.92 ((![X220]: 0.56/0.92 (in(X220,X218) => in(X220,X216))) => 0.56/0.92 in(X218,powerset(X216)))) => 0.56/0.92 ((![X222]: in(emptyset,powerset(X222))) => 0.56/0.92 ((![X224]: in(emptyset,powerset(X224))) => 0.56/0.92 ((![X226,X228,X230]: 0.56/0.92 (in(X228,powerset(X226)) => 0.56/0.92 (in(X230,X228) => in(X230,X226)))) => 0.56/0.92 ((![X232,X234,X236]: 0.56/0.92 (in(X234,X236) => 0.56/0.92 (in(X236,X232) => 0.56/0.92 in(X234,setunion(X232))))) => 0.56/0.92 ((![X238,X240]: 0.56/0.92 (in(X240,setunion(X238)) => 0.56/0.92 (![X242:$o]: 0.56/0.92 ((![X244]: 0.56/0.92 (in(X240,X244) => 0.56/0.92 (in(X244,X238) => X242))) => 0.56/0.92 X242)))) => 0.56/0.92 ((![X246,X248]: 0.56/0.92 (in(X248,X246) => 0.56/0.92 in(X248, 0.56/0.92 powerset(setunion(X246))))) => 0.56/0.92 ((![X250:(($i > $o))]: 0.56/0.92 ((?[X252]: 0.56/0.92 (X250(X252) & 0.56/0.92 (![X254]: 0.56/0.92 (X250(X254) => 0.56/0.92 (X252 = X254))))) => 0.56/0.92 (?[X256]: 0.56/0.92 (![X258]: 0.56/0.92 (X250(X258) <=> 0.56/0.92 (X258 = X256)))))) => 0.56/0.92 ((![X260]: 0.56/0.92 ((X260 != emptyset) => 0.56/0.92 (?[X262]: in(X262,X260)))) => 0.56/0.92 ((![X264,X266]: 0.56/0.92 (in(X264, 0.56/0.92 setadjoin(X266,emptyset)) => 0.56/0.92 (X264 = X266))) => 0.56/0.92 ((![X268,X270]: 0.56/0.92 ((X268 != X270) => 0.56/0.92 (~ 0.56/0.92 in(X270, 0.56/0.92 setadjoin(X268, 0.56/0.92 emptyset))))) => 0.56/0.92 ((![X272,X274]: 0.56/0.92 ((X272 = X274) => 0.56/0.92 in(X272, 0.56/0.92 setadjoin(X274, 0.56/0.92 emptyset)))) => 0.56/0.92 ((![X276,X278]: 0.56/0.92 (in(X276, 0.56/0.92 setadjoin(X278, 0.56/0.92 emptyset)) => 0.56/0.92 in(X278, 0.56/0.92 setadjoin(X276, 0.56/0.92 emptyset)))) => 0.56/0.92 ((![X280,X282,X284]: 0.56/0.92 (in(X284, 0.56/0.92 setadjoin(X280, 0.56/0.92 setadjoin( 0.56/0.92 X282, 0.56/0.92 emptyset))) => 0.56/0.92 ((X284 = X282) | 0.56/0.92 (X284 = X280)))) => 0.56/0.92 ((![X286,X288]: 0.56/0.92 in(X286, 0.56/0.92 setadjoin(X286, 0.56/0.92 setadjoin( 0.56/0.92 X288, 0.56/0.92 emptyset)))) => 0.56/0.92 ((![X290,X292]: 0.56/0.92 in(X292, 0.56/0.92 setadjoin(X290, 0.56/0.92 setadjoin( 0.56/0.92 X292, 0.56/0.92 emptyset)))) => 0.56/0.92 ((![X294,X296:(($i > $o))]: 0.56/0.92 ((?[X298]: 0.56/0.92 (in(X298,X294) & 0.56/0.92 X296(X298))) => 0.56/0.92 (dsetconstr( 0.56/0.92 X294, 0.56/0.92 ^[V_8]: X296(V_8)) != 0.56/0.92 emptyset))) => 0.56/0.92 ((![X300:(($i > $o)), 0.56/0.92 X302]: 0.56/0.92 (in(X302,emptyset) => 0.56/0.92 X300(X302))) => 0.56/0.92 ((![X304, 0.56/0.92 X306:(($i > $o))]: 0.56/0.92 ((~ 0.56/0.92 (![X308]: 0.56/0.92 (in(X308,X304) => 0.56/0.92 X306(X308)))) => 0.56/0.92 (?[X310]: 0.56/0.92 (in(X310,X304) & 0.56/0.92 (~X306(X310)))))) => 0.56/0.92 ((![X312, 0.56/0.92 X314:(($i > $o))]: 0.56/0.92 ((![X316]: 0.56/0.92 (in(X316,X312) => 0.56/0.92 (~X314(X316)))) => 0.56/0.92 (~ 0.56/0.92 (?[X318]: 0.56/0.92 (in( 0.56/0.92 X318,X312) & 0.56/0.92 X314(X318)))))) => 0.56/0.92 ((![X320, 0.56/0.92 X322:(($i > $o))]: 0.56/0.92 ((~ 0.56/0.92 (?[X324]: 0.56/0.92 (in( 0.56/0.92 X324,X320) & 0.56/0.92 X322(X324)))) => 0.56/0.92 (![X326]: 0.56/0.92 (in(X326,X320) => 0.56/0.92 (~X322(X326)))))) => 0.56/0.92 ((![X328, 0.56/0.92 X330:(($i > $o))]: 0.56/0.92 ((?[X332]: 0.56/0.92 (in( 0.56/0.92 X332,X328) & 0.56/0.92 (~ 0.56/0.92 X330( 0.56/0.92 X332)))) => 0.56/0.92 (~ 0.56/0.92 (![X334]: 0.56/0.92 (in( 0.56/0.92 X334,X328) => 0.56/0.92 X330( 0.56/0.92 X334)))))) => 0.56/0.92 ((![X336:$o]: 0.56/0.92 (X336 => 0.56/0.92 in(emptyset, 0.56/0.92 prop2set( 0.56/0.92 X336)))) => 0.56/0.92 ((![X338:$o]: 0.56/0.92 (X338 => 0.56/0.92 set2prop( 0.56/0.92 prop2set( 0.56/0.92 X338)))) => 0.56/0.92 ((![X340, 0.56/0.92 X342:( 0.56/0.92 ($i > $o))]: 0.56/0.92 ((~ 0.56/0.92 (?[X344]: 0.56/0.92 (in( 0.56/0.92 X344,X340) & 0.56/0.92 X342( 0.56/0.92 X344)))) => 0.56/0.92 (![X346]: 0.56/0.92 ( 0.56/0.92 in( 0.56/0.92 X346,X340) => 0.56/0.92 ( 0.56/0.92 ~ 0.56/0.92 X342( 0.56/0.92 X346)))))) => 0.56/0.92 ((![X348, 0.56/0.92 X350:( 0.56/0.92 ($i > $o))]: 0.56/0.92 ((~ 0.56/0.92 ( 0.56/0.92 ![X352]: 0.56/0.92 (in( 0.56/0.92 X352,X348) => 0.56/0.92 X350( 0.56/0.92 X352)))) => 0.56/0.92 (?[X354]: 0.56/0.92 (in( 0.56/0.92 X354,X348) & 0.56/0.92 (~ 0.56/0.92 X350( 0.56/0.92 X354)))))) => 0.56/0.92 ((![X356:( 0.56/0.92 ($i > $o))]: 0.56/0.92 ((?[X358]: 0.56/0.92 (X356( 0.56/0.92 X358) & 0.56/0.92 (![X360]: 0.56/0.92 (X356( 0.56/0.92 X360) => 0.56/0.92 (X358 = 0.56/0.92 X360))))) => 0.56/0.92 (?[X362]: 0.56/0.92 (X356( 0.56/0.92 X362) & 0.56/0.92 (![X364]: 0.56/0.92 (X356( 0.56/0.92 X364) => 0.56/0.92 (X362 = 0.56/0.92 X364))))))) => 0.56/0.92 ((![X366:( 0.56/0.92 ($i > $o))]: 0.56/0.92 (( 0.56/0.92 ?[X368]: 0.56/0.92 X366( 0.56/0.92 X368)) => 0.56/0.92 ( 0.56/0.92 ( 0.56/0.92 ![X370, 0.56/0.92 X372]: 0.56/0.92 (X366( 0.56/0.92 X370) => 0.56/0.92 (X366( 0.56/0.92 X372) => 0.56/0.92 (X370 = 0.56/0.92 X372)))) => 0.56/0.92 ( 0.56/0.92 ?[X374]: 0.56/0.92 (X366( 0.56/0.92 X374) & 0.56/0.92 (![X376]: 0.56/0.92 (X366( 0.56/0.92 X376) => 0.56/0.92 (X374 = 0.56/0.92 X376)))))))) => 0.56/0.92 ((![X378:( 0.56/0.92 ( 0.56/0.92 $i > $o))]: 0.56/0.92 ( 0.56/0.92 ( 0.56/0.92 ?[X380]: 0.56/0.92 (![X382]: 0.56/0.92 (X378( 0.56/0.92 X382) <=> 0.56/0.92 (X382 = 0.56/0.92 X380)))) => 0.56/0.92 ( 0.56/0.92 ?[X384]: 0.56/0.92 (X378( 0.56/0.92 X384) & 0.56/0.92 (![X386]: 0.56/0.92 (X378( 0.56/0.92 X386) => 0.56/0.92 (X384 = 0.56/0.92 X386))))))) => 0.56/0.92 ((![X388, 0.56/0.92 X390]: 0.56/0.92 (( 0.56/0.92 X388 = 0.56/0.92 X390) => 0.56/0.92 (![X392, 0.56/0.92 X394]: 0.56/0.92 (( 0.56/0.92 X392 = 0.56/0.92 X394) => 0.56/0.92 (in( 0.56/0.92 X392,X388) => 0.56/0.92 in( 0.56/0.92 X394,X390)))))) => 0.56/0.92 ((![X396, 0.56/0.92 X398]: 0.56/0.92 (( 0.56/0.92 X396 = 0.56/0.92 X398) => 0.56/0.92 (![X400, 0.56/0.92 X402]: 0.56/0.92 (( 0.56/0.92 X400 = 0.56/0.92 X402) => 0.56/0.92 (in( 0.56/0.92 X400,X396) <=> 0.56/0.92 in( 0.56/0.92 X402,X398)))))) => 0.56/0.92 (( 0.56/0.92 ![X404:( 0.56/0.92 ( 0.56/0.92 $i > $o))]: 0.56/0.92 (( 0.56/0.92 ?[X406]: 0.56/0.92 (X404( 0.56/0.92 X406) & 0.56/0.92 (![X408]: 0.56/0.92 (X404( 0.56/0.92 X408) => 0.56/0.92 (X406 = 0.56/0.92 X408))))) => 0.56/0.92 (![X410, 0.56/0.92 X412]: 0.56/0.92 (X404( 0.56/0.92 X410) => 0.56/0.92 (X404( 0.56/0.92 X412) => 0.56/0.92 (X410 = 0.56/0.92 X412)))))) => 0.56/0.92 ( 0.56/0.92 ( 0.56/0.92 ![X414:( 0.56/0.92 ( 0.56/0.92 $i > $o)), 0.56/0.92 X416:( 0.56/0.92 ( 0.56/0.92 $i > $o))]: 0.56/0.92 (( 0.56/0.92 ![X418, 0.56/0.92 X420]: 0.56/0.92 (( 0.56/0.92 X418 = 0.56/0.92 X420) => 0.56/0.92 (X414( 0.56/0.92 X418) <=> 0.56/0.92 X416( 0.56/0.92 X420)))) => 0.56/0.92 (( 0.56/0.92 ?[X422]: 0.56/0.92 (X414( 0.56/0.92 X422) & 0.56/0.92 (![X424]: 0.56/0.92 (X414( 0.56/0.92 X424) => 0.56/0.92 (X422 = 0.56/0.92 X424))))) <=> 0.56/0.92 (?[X426]: 0.56/0.92 (X416( 0.56/0.92 X426) & 0.56/0.92 (![X428]: 0.56/0.92 (X416( 0.56/0.92 X428) => 0.56/0.92 (X426 = 0.56/0.92 X428)))))))) => 0.56/0.92 ( 0.56/0.92 ( 0.56/0.92 emptyset = 0.56/0.92 emptyset) => 0.56/0.92 ( 0.56/0.92 ( 0.56/0.92 ![X430, 0.56/0.92 X432]: 0.56/0.92 (( 0.56/0.92 X430 = 0.56/0.92 X432) => 0.56/0.92 (![X434, 0.56/0.92 X436]: 0.56/0.92 (( 0.56/0.92 X434 = 0.56/0.92 X436) => 0.56/0.92 (setadjoin( 0.56/0.92 X430,X434) = 0.56/0.92 setadjoin( 0.56/0.92 X432,X436)))))) => 0.56/0.92 ( 0.56/0.92 ( 0.56/0.92 ![X438, 0.56/0.92 X440]: 0.56/0.92 (( 0.56/0.92 X438 = 0.56/0.92 X440) => 0.56/0.92 (powerset( 0.56/0.92 X438) = 0.56/0.92 powerset( 0.56/0.92 X440)))) => 0.56/0.92 ( 0.56/0.92 ( 0.56/0.92 ![X442, 0.56/0.92 X444]: 0.56/0.92 (( 0.56/0.92 X442 = 0.56/0.92 X444) => 0.56/0.92 (setunion( 0.56/0.92 X442) = 0.56/0.92 setunion( 0.56/0.92 X444)))) => 0.56/0.92 ( 0.56/0.92 ( 0.56/0.92 omega = 0.56/0.92 omega) => 0.56/0.92 ( 0.56/0.92 ( 0.56/0.92 ![X446:( 0.56/0.92 ( 0.56/0.92 $i > $o))]: 0.56/0.92 (( 0.56/0.92 ?[X448]: 0.56/0.92 (X446( 0.56/0.92 X448) & 0.56/0.92 (![X450]: 0.56/0.92 (X446( 0.56/0.92 X450) => 0.56/0.92 (X448 = 0.56/0.92 X450))))) => 0.56/0.92 (![X452, 0.56/0.92 X454]: 0.56/0.92 (X446( 0.56/0.92 X452) => 0.56/0.92 (X446( 0.56/0.92 X454) => 0.56/0.92 (X452 = 0.56/0.92 X454)))))) => 0.56/0.92 ( 0.56/0.92 ( 0.56/0.92 ![X456:( 0.56/0.92 ( 0.56/0.92 $i > $o)), 0.56/0.92 X458:( 0.56/0.92 ( 0.56/0.92 $i > $o))]: 0.56/0.92 (( 0.56/0.92 ![X460, 0.56/0.92 X462]: 0.56/0.92 (( 0.56/0.92 X460 = 0.56/0.92 X462) => 0.56/0.92 (X456( 0.56/0.92 X460) <=> 0.56/0.92 X458( 0.56/0.92 X462)))) => 0.56/0.92 (( 0.56/0.92 ?[X464]: 0.56/0.92 (X456( 0.56/0.92 X464) & 0.56/0.92 (![X466]: 0.56/0.92 (X456( 0.56/0.92 X466) => 0.56/0.92 (X464 = 0.56/0.92 X466))))) => 0.56/0.92 (( 0.56/0.92 ?[X468]: 0.56/0.92 (X458( 0.56/0.92 X468) & 0.56/0.92 (![X470]: 0.56/0.92 (X458( 0.56/0.92 X470) => 0.56/0.92 (X468 = 0.56/0.92 X470))))) => 0.56/0.92 (descr( 0.56/0.92 ^[V_9]: 0.56/0.92 X456(V_9)) = 0.56/0.92 descr( 0.56/0.92 ^[V_10]: 0.56/0.92 X458( 0.56/0.92 V_10))))))) => 0.56/0.92 ( 0.56/0.92 ( 0.56/0.92 ![X472, 0.56/0.92 X474]: 0.56/0.92 (( 0.56/0.92 X472 = 0.56/0.92 X474) => 0.56/0.92 (![X476:( 0.56/0.92 ( 0.56/0.92 $i > $o)), 0.56/0.92 X478:( 0.56/0.92 ( 0.56/0.92 $i > $o))]: 0.56/0.92 (( 0.56/0.92 ![X480]: 0.56/0.92 (in( 0.56/0.92 X480,X472) => 0.56/0.92 (![X482]: 0.56/0.92 (in( 0.56/0.92 X482,X474) => 0.56/0.92 (( 0.56/0.92 X480 = 0.56/0.92 X482) => 0.56/0.92 (X476( 0.56/0.92 X480) <=> 0.56/0.92 X478( 0.57/0.92 X482))))))) => 0.57/0.92 (dsetconstr( 0.57/0.92 X472, 0.57/0.92 ^[V_11]: 0.57/0.92 X476( 0.57/0.92 V_11)) = 0.57/0.92 dsetconstr( 0.57/0.92 X474, 0.57/0.92 ^[V_12]: 0.57/0.92 X478( 0.57/0.92 V_12))))))) => 0.57/0.92 ( 0.57/0.92 ( 0.57/0.92 ![X484, 0.57/0.92 X486]: 0.57/0.92 (( 0.57/0.92 ![X488]: 0.57/0.92 (in( 0.57/0.92 X488,X484) => 0.57/0.92 in( 0.57/0.92 X488,X486))) => 0.57/0.92 subset( 0.57/0.92 X484,X486))) => 0.57/0.92 ( 0.57/0.92 ( 0.57/0.92 ![X490, 0.57/0.92 X492]: 0.57/0.92 (( 0.57/0.92 X490 = 0.57/0.92 X492) => 0.57/0.92 subset( 0.57/0.92 X492,X490))) => 0.57/0.92 ( 0.57/0.92 ( 0.57/0.92 ![X494, 0.57/0.92 X496]: 0.57/0.92 (( 0.57/0.92 X494 = 0.57/0.92 X496) => 0.57/0.92 subset( 0.57/0.92 X494,X496))) => 0.57/0.92 ( 0.57/0.92 ( 0.57/0.92 ![X498, 0.57/0.92 X500]: 0.57/0.92 (( 0.57/0.92 ![X502]: 0.57/0.92 (in( 0.57/0.92 X502,X498) => 0.57/0.92 in( 0.57/0.92 X502,X500))) => 0.57/0.92 subset( 0.57/0.92 X498,X500))) => 0.57/0.92 ( 0.57/0.92 ( 0.57/0.92 ![X504]: 0.57/0.92 subset( 0.57/0.92 emptyset, 0.57/0.92 X504)) => 0.57/0.92 ( 0.57/0.92 ( 0.57/0.92 ![X506, 0.57/0.92 X508,X510]: 0.57/0.92 (subset( 0.57/0.92 X506,X508) => 0.57/0.92 (in( 0.57/0.92 X510,X506) => 0.57/0.92 in( 0.57/0.92 X510,X508)))) => 0.57/0.92 ( 0.57/0.92 ( 0.57/0.92 ![X512, 0.57/0.92 X514,X516]: 0.57/0.92 (subset( 0.57/0.92 X512,X514) => 0.57/0.92 (( 0.57/0.92 ~ 0.57/0.92 in( 0.57/0.92 X516,X514)) => 0.57/0.92 (~ 0.57/0.92 in( 0.57/0.92 X516,X512))))) => 0.57/0.92 ( 0.57/0.92 ( 0.57/0.92 ![X518, 0.57/0.92 X520,X522]: 0.57/0.92 (in( 0.57/0.92 X522,X518) => 0.57/0.92 (( 0.57/0.92 ~ 0.57/0.92 in( 0.57/0.92 X522,X520)) => 0.57/0.92 (~ 0.57/0.92 subset( 0.57/0.92 X518,X520))))) => 0.57/0.92 ( 0.57/0.92 ( 0.57/0.92 ![X524, 0.57/0.92 X526]: 0.57/0.92 (( 0.57/0.92 ~ 0.57/0.92 subset( 0.57/0.92 X524,X526)) => 0.57/0.92 (X524 != 0.57/0.92 X526))) => 0.57/0.92 ( 0.57/0.92 ( 0.57/0.92 ![X528, 0.57/0.92 X530,X532]: 0.57/0.92 (in( 0.57/0.92 X532,X528) => 0.57/0.92 (( 0.57/0.92 ~ 0.57/0.92 in( 0.57/0.92 X532,X530)) => 0.57/0.92 (X528 != 0.57/0.92 X530)))) => 0.57/0.92 ( 0.57/0.92 ( 0.57/0.92 ![X534]: 0.57/0.92 subset( 0.57/0.92 X534,X534)) => 0.57/0.92 ( 0.57/0.92 ( 0.57/0.92 ![X536, 0.57/0.92 X538,X540]: 0.57/0.92 (subset( 0.57/0.92 X536,X538) => 0.57/0.92 (subset( 0.57/0.92 X538,X540) => 0.57/0.92 subset( 0.57/0.92 X536,X540)))) => 0.57/0.92 ( 0.57/0.92 ( 0.57/0.92 ![X542, 0.57/0.92 X544]: 0.57/0.92 subset( 0.57/0.92 X544, 0.57/0.92 setadjoin( 0.57/0.92 X542,X544))) => 0.57/0.92 ( 0.57/0.92 ( 0.57/0.92 ![X546, 0.57/0.92 X548,X550]: 0.57/0.92 (subset( 0.57/0.92 X546,X550) => 0.57/0.92 subset( 0.57/0.92 X546, 0.57/0.92 setadjoin( 0.57/0.92 X548,X550)))) => 0.57/0.92 ( 0.57/0.92 ( 0.57/0.92 ![X552, 0.57/0.92 X554]: 0.57/0.92 (subset( 0.57/0.92 X552,X554) => 0.57/0.92 in( 0.57/0.92 X552, 0.57/0.92 powerset( 0.57/0.92 X554)))) => 0.57/0.92 ( 0.57/0.92 ( 0.57/0.92 ![X556, 0.57/0.93 X558]: 0.57/0.93 (subset( 0.57/0.93 X556,X558) => 0.57/0.93 (subset( 0.57/0.93 X558,X556) => 0.57/0.93 (X556 = 0.57/0.93 X558)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X560]: 0.57/0.93 (subset( 0.57/0.93 X560, 0.57/0.93 emptyset) => 0.57/0.93 (X560 = 0.57/0.93 emptyset))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X562, 0.57/0.93 X564]: 0.57/0.93 (subset( 0.57/0.93 X564,X562) => 0.57/0.93 in( 0.57/0.93 X564, 0.57/0.93 powerset( 0.57/0.93 X562)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X566, 0.57/0.93 X568]: 0.57/0.93 (in( 0.57/0.93 X568, 0.57/0.93 powerset( 0.57/0.93 X566)) => 0.57/0.93 subset( 0.57/0.93 X568,X566))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X570]: 0.57/0.93 in( 0.57/0.93 X570, 0.57/0.93 powerset( 0.57/0.93 X570))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X572, 0.57/0.93 X574]: 0.57/0.93 (subset( 0.57/0.93 X572,X574) => 0.57/0.93 subset( 0.57/0.93 powerset( 0.57/0.93 X572), 0.57/0.93 powerset( 0.57/0.93 X574)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X576, 0.57/0.93 X578:( 0.57/0.93 ( 0.57/0.93 $i > $o))]: 0.57/0.93 in( 0.57/0.93 dsetconstr( 0.57/0.93 X576, 0.57/0.93 ^[V_13]: 0.57/0.93 X578( 0.57/0.93 V_13)), 0.57/0.93 powerset( 0.57/0.93 X576))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X580, 0.57/0.93 X582:( 0.57/0.93 ( 0.57/0.93 $i > $o))]: 0.57/0.93 subset( 0.57/0.93 dsetconstr( 0.57/0.93 X580, 0.57/0.93 ^[V_14]: 0.57/0.93 X582( 0.57/0.93 V_14)), 0.57/0.93 X580)) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X584, 0.57/0.93 X586,X588]: 0.57/0.93 (in( 0.57/0.93 X588,X584) => 0.57/0.93 in( 0.57/0.93 X588, 0.57/0.93 binunion( 0.57/0.93 X584,X586)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X590, 0.57/0.93 X592]: 0.57/0.93 in( 0.57/0.93 X592, 0.57/0.93 setadjoin( 0.57/0.93 X590, 0.57/0.93 setadjoin( 0.57/0.93 X592, 0.57/0.93 emptyset)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X594, 0.57/0.93 X596,X598]: 0.57/0.93 (in( 0.57/0.93 X598,X596) => 0.57/0.93 in( 0.57/0.93 X598, 0.57/0.93 binunion( 0.57/0.93 X594,X596)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X600, 0.57/0.93 X602, 0.57/0.93 X604, 0.57/0.93 X606:$o]: 0.57/0.93 (in( 0.57/0.93 X604, 0.57/0.93 binunion( 0.57/0.93 X600,X602)) => 0.57/0.93 (( 0.57/0.93 in( 0.57/0.93 X604,X600) => 0.57/0.93 X606) => 0.57/0.93 (( 0.57/0.93 in( 0.57/0.93 X604,X602) => 0.57/0.93 X606) => 0.57/0.93 X606)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X608, 0.57/0.93 X610,X612]: 0.57/0.93 (in( 0.57/0.93 X612, 0.57/0.93 binunion( 0.57/0.93 X608,X610)) => 0.57/0.93 (in( 0.57/0.93 X612,X610) | 0.57/0.93 in( 0.57/0.93 X612,X608)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X614, 0.57/0.93 X616]: 0.57/0.93 subset( 0.57/0.93 X614, 0.57/0.93 binunion( 0.57/0.93 X614,X616))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X618, 0.57/0.93 X620]: 0.57/0.93 subset( 0.57/0.93 X620, 0.57/0.93 binunion( 0.57/0.93 X618,X620))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X622, 0.57/0.93 X624,X626]: 0.57/0.93 (in( 0.57/0.93 X626,X622) => 0.57/0.93 (in( 0.57/0.93 X626,X624) => 0.57/0.93 in( 0.57/0.93 X626, 0.57/0.93 binintersect( 0.57/0.93 X622,X624))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X628, 0.57/0.93 X630,X632]: 0.57/0.93 (subset( 0.57/0.93 X632,X628) => 0.57/0.93 (subset( 0.57/0.93 X632,X630) => 0.57/0.93 subset( 0.57/0.93 X632, 0.57/0.93 binintersect( 0.57/0.93 X628,X630))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X634, 0.57/0.93 X636,X638]: 0.57/0.93 (in( 0.57/0.93 X638, 0.57/0.93 binintersect( 0.57/0.93 X634,X636)) => 0.57/0.93 in( 0.57/0.93 X638,X634))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X640, 0.57/0.93 X642]: 0.57/0.93 subset( 0.57/0.93 binintersect( 0.57/0.93 X640,X642), 0.57/0.93 X640)) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X644, 0.57/0.93 X646]: 0.57/0.93 (subset( 0.57/0.93 X644,X646) => 0.57/0.93 (binintersect( 0.57/0.93 X644,X646) = 0.57/0.93 X644))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X648, 0.57/0.93 X650]: 0.57/0.93 (( 0.57/0.93 binintersect( 0.57/0.93 X648,X650) = 0.57/0.93 X650) => 0.57/0.93 subset( 0.57/0.93 X650,X648))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X652, 0.57/0.93 X654,X656]: 0.57/0.93 (in( 0.57/0.93 X656, 0.57/0.93 binintersect( 0.57/0.93 X652,X654)) => 0.57/0.93 in( 0.57/0.93 X656,X654))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X658, 0.57/0.93 X660]: 0.57/0.93 (( 0.57/0.93 ~ 0.57/0.93 ( 0.57/0.93 ?[X662]: 0.57/0.93 (in( 0.57/0.93 X662,X658) & 0.57/0.93 in( 0.57/0.93 X662,X660)))) => 0.57/0.93 (binintersect( 0.57/0.93 X658,X660) = 0.57/0.93 emptyset))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X664, 0.57/0.93 X666]: 0.57/0.93 subset( 0.57/0.93 binintersect( 0.57/0.93 X664,X666), 0.57/0.93 X666)) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X668, 0.57/0.93 X670]: 0.57/0.93 (subset( 0.57/0.93 X670,X668) => 0.57/0.93 (binintersect( 0.57/0.93 X668,X670) = 0.57/0.93 X670))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X672, 0.57/0.93 X674]: 0.57/0.93 (( 0.57/0.93 binintersect( 0.57/0.93 X672,X674) = 0.57/0.93 X672) => 0.57/0.93 subset( 0.57/0.93 X672,X674))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X676, 0.57/0.93 X678,X680]: 0.57/0.93 (binintersect( 0.57/0.93 X676, 0.57/0.93 binunion( 0.57/0.93 X678,X680)) = 0.57/0.93 binunion( 0.57/0.93 binintersect( 0.57/0.93 X676,X678), 0.57/0.93 binintersect( 0.57/0.93 X676,X680)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X682, 0.57/0.93 X684,X686]: 0.57/0.93 (in( 0.57/0.93 X686,X682) => 0.57/0.93 (( 0.57/0.93 ~ 0.57/0.93 in( 0.57/0.93 X686,X684)) => 0.57/0.93 in( 0.57/0.93 X686, 0.57/0.93 setminus( 0.57/0.93 X682,X684))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X688, 0.57/0.93 X690,X692]: 0.57/0.93 (in( 0.57/0.93 X692, 0.57/0.93 setminus( 0.57/0.93 X688,X690)) => 0.57/0.93 in( 0.57/0.93 X692,X688))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X694, 0.57/0.93 X696,X698]: 0.57/0.93 (in( 0.57/0.93 X698, 0.57/0.93 setminus( 0.57/0.93 X694,X696)) => 0.57/0.93 (~ 0.57/0.93 in( 0.57/0.93 X698,X696)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X700, 0.57/0.93 X702]: 0.57/0.93 (subset( 0.57/0.93 X700,X702) => 0.57/0.93 (setminus( 0.57/0.93 X700,X702) = 0.57/0.93 emptyset))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X704, 0.57/0.93 X706,X708]: 0.57/0.93 (( 0.57/0.93 ~ 0.57/0.93 in( 0.57/0.93 X708, 0.57/0.93 setminus( 0.57/0.93 X704,X706))) => 0.57/0.93 (in( 0.57/0.93 X708,X704) => 0.57/0.93 in( 0.57/0.93 X708,X706)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X710, 0.57/0.93 X712,X714]: 0.57/0.93 (( 0.57/0.93 ~ 0.57/0.93 in( 0.57/0.93 X714, 0.57/0.93 setminus( 0.57/0.93 X710,X712))) => 0.57/0.93 (( 0.57/0.93 ~ 0.57/0.93 in( 0.57/0.93 X714,X712)) => 0.57/0.93 (~ 0.57/0.93 in( 0.57/0.93 X714,X710))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X716, 0.57/0.93 X718,X720]: 0.57/0.93 (( 0.57/0.93 ~ 0.57/0.93 in( 0.57/0.93 X720,X716)) => 0.57/0.93 (~ 0.57/0.93 in( 0.57/0.93 X720, 0.57/0.93 setminus( 0.57/0.93 X716,X718))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X722, 0.57/0.93 X724,X726]: 0.57/0.93 (in( 0.57/0.93 X726,X724) => 0.57/0.93 (~ 0.57/0.93 in( 0.57/0.93 X726, 0.57/0.93 setminus( 0.57/0.93 X722,X724))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X728, 0.57/0.93 X730]: 0.57/0.93 subset( 0.57/0.93 setminus( 0.57/0.93 X728,X730), 0.57/0.93 X728)) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X732, 0.57/0.93 X734]: 0.57/0.93 (( 0.57/0.93 setminus( 0.57/0.93 X732,X734) = 0.57/0.93 emptyset) => 0.57/0.93 subset( 0.57/0.93 X732,X734))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X736, 0.57/0.93 X738,X740]: 0.57/0.93 (in( 0.57/0.93 X740, 0.57/0.93 symdiff( 0.57/0.93 X736,X738)) => 0.57/0.93 (![X742:$o]: 0.57/0.93 (( 0.57/0.93 in( 0.57/0.93 X740,X736) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ~ 0.57/0.93 in( 0.57/0.93 X740,X738)) => 0.57/0.93 X742)) => 0.57/0.93 (( 0.57/0.93 ( 0.57/0.93 ~ 0.57/0.93 in( 0.57/0.93 X740,X736)) => 0.57/0.93 ( 0.57/0.93 in( 0.57/0.93 X740,X738) => 0.57/0.93 X742)) => 0.57/0.93 X742))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X744, 0.57/0.93 X746,X748]: 0.57/0.93 (in( 0.57/0.93 X748,X744) => 0.57/0.93 (( 0.57/0.93 ~ 0.57/0.93 in( 0.57/0.93 X748,X746)) => 0.57/0.93 in( 0.57/0.93 X748, 0.57/0.93 symdiff( 0.57/0.93 X744,X746))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X750, 0.57/0.93 X752,X754]: 0.57/0.93 (( 0.57/0.93 ~ 0.57/0.93 in( 0.57/0.93 X754,X750)) => 0.57/0.93 (in( 0.57/0.93 X754,X752) => 0.57/0.93 in( 0.57/0.93 X754, 0.57/0.93 symdiff( 0.57/0.93 X750,X752))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X756, 0.57/0.93 X758,X760]: 0.57/0.93 (in( 0.57/0.93 X760,X756) => 0.57/0.93 (in( 0.57/0.93 X760,X758) => 0.57/0.93 (~ 0.57/0.93 in( 0.57/0.93 X760, 0.57/0.93 symdiff( 0.57/0.93 X756,X758)))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X762, 0.57/0.93 X764,X766]: 0.57/0.93 (( 0.57/0.93 ~ 0.57/0.93 in( 0.57/0.93 X766,X762)) => 0.57/0.93 (( 0.57/0.93 ~ 0.57/0.93 in( 0.57/0.93 X766,X764)) => 0.57/0.93 (~ 0.57/0.93 in( 0.57/0.93 X766, 0.57/0.93 symdiff( 0.57/0.93 X762,X764)))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X768, 0.57/0.93 X770]: 0.57/0.93 in( 0.57/0.93 X770, 0.57/0.93 setadjoin( 0.57/0.93 X768, 0.57/0.93 setadjoin( 0.57/0.93 X770, 0.57/0.93 emptyset)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X772, 0.57/0.93 X774]: 0.57/0.93 in( 0.57/0.93 X772, 0.57/0.93 setunion( 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X772, 0.57/0.93 emptyset), 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X772, 0.57/0.93 setadjoin( 0.57/0.93 X774, 0.57/0.93 emptyset)), 0.57/0.93 emptyset))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X776, 0.57/0.93 X778]: 0.57/0.93 in( 0.57/0.93 X778, 0.57/0.93 setunion( 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X776, 0.57/0.93 emptyset), 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X776, 0.57/0.93 setadjoin( 0.57/0.93 X778, 0.57/0.93 emptyset)), 0.57/0.93 emptyset))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X780, 0.57/0.93 X782]: 0.57/0.93 iskpair( 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X780, 0.57/0.93 emptyset), 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X780, 0.57/0.93 setadjoin( 0.57/0.93 X782, 0.57/0.93 emptyset)), 0.57/0.93 emptyset)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X784, 0.57/0.93 X786]: 0.57/0.93 iskpair( 0.57/0.93 kpair( 0.57/0.93 X784,X786))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X788, 0.57/0.93 X790]: 0.57/0.93 (in( 0.57/0.93 X790,X788) => 0.57/0.93 subset( 0.57/0.93 setadjoin( 0.57/0.93 X790, 0.57/0.93 emptyset), 0.57/0.93 X788))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X792, 0.57/0.93 X794]: 0.57/0.93 (in( 0.57/0.93 X794,X792) => 0.57/0.93 in( 0.57/0.93 setadjoin( 0.57/0.93 X794, 0.57/0.93 emptyset), 0.57/0.93 powerset( 0.57/0.93 X792)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X796, 0.57/0.93 X798,X800]: 0.57/0.93 (in( 0.57/0.93 X800,X796) => 0.57/0.93 in( 0.57/0.93 setadjoin( 0.57/0.93 X800, 0.57/0.93 emptyset), 0.57/0.93 powerset( 0.57/0.93 binunion( 0.57/0.93 X796,X798))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X802, 0.57/0.93 X804,X806]: 0.57/0.93 (in( 0.57/0.93 X806, 0.57/0.93 setadjoin( 0.57/0.93 X802, 0.57/0.93 setadjoin( 0.57/0.93 X804, 0.57/0.93 emptyset))) => 0.57/0.93 (( 0.57/0.93 X806 = 0.57/0.93 X804) | 0.57/0.93 (X806 = 0.57/0.93 X802)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X808, 0.57/0.93 X810,X812]: 0.57/0.93 (in( 0.57/0.93 X812,X808) => 0.57/0.93 (![X814]: 0.57/0.93 (in( 0.57/0.93 X814,X810) => 0.57/0.93 subset( 0.57/0.93 setadjoin( 0.57/0.93 X812, 0.57/0.93 setadjoin( 0.57/0.93 X814, 0.57/0.93 emptyset)), 0.57/0.93 binunion( 0.57/0.93 X808,X810)))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X816, 0.57/0.93 X818,X820]: 0.57/0.93 (in( 0.57/0.93 X820,X816) => 0.57/0.93 (![X822]: 0.57/0.93 (in( 0.57/0.93 X822,X818) => 0.57/0.93 in( 0.57/0.93 setadjoin( 0.57/0.93 X820, 0.57/0.93 setadjoin( 0.57/0.93 X822, 0.57/0.93 emptyset)), 0.57/0.93 powerset( 0.57/0.93 binunion( 0.57/0.93 X816,X818))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X824, 0.57/0.93 X826,X828]: 0.57/0.93 (in( 0.57/0.93 X828,X824) => 0.57/0.93 (![X830]: 0.57/0.93 (in( 0.57/0.93 X830,X826) => 0.57/0.93 subset( 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X828, 0.57/0.93 emptyset), 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X828, 0.57/0.93 setadjoin( 0.57/0.93 X830, 0.57/0.93 emptyset)), 0.57/0.93 emptyset)), 0.57/0.93 powerset( 0.57/0.93 binunion( 0.57/0.93 X824,X826))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X832, 0.57/0.93 X834,X836]: 0.57/0.93 (in( 0.57/0.93 X836,X832) => 0.57/0.93 (![X838]: 0.57/0.93 (in( 0.57/0.93 X838,X834) => 0.57/0.93 in( 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X836, 0.57/0.93 emptyset), 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X836, 0.57/0.93 setadjoin( 0.57/0.93 X838, 0.57/0.93 emptyset)), 0.57/0.93 emptyset)), 0.57/0.93 powerset( 0.57/0.93 powerset( 0.57/0.93 binunion( 0.57/0.93 X832,X834)))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X840, 0.57/0.93 X842,X844]: 0.57/0.93 (in( 0.57/0.93 X844,X840) => 0.57/0.93 (![X846]: 0.57/0.93 (in( 0.57/0.93 X846,X842) => 0.57/0.93 in( 0.57/0.93 kpair( 0.57/0.93 X844,X846), 0.57/0.93 powerset( 0.57/0.93 powerset( 0.57/0.93 binunion( 0.57/0.93 X840,X842)))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X848, 0.57/0.93 X850,X852]: 0.57/0.93 (in( 0.57/0.93 X852,X848) => 0.57/0.93 (![X854]: 0.57/0.93 (in( 0.57/0.93 X854,X850) => 0.57/0.93 in( 0.57/0.93 kpair( 0.57/0.93 X852,X854), 0.57/0.93 cartprod( 0.57/0.93 X848,X850)))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X856, 0.57/0.93 X858,X860]: 0.57/0.93 (in( 0.57/0.93 X860, 0.57/0.93 cartprod( 0.57/0.93 X856,X858)) => 0.57/0.93 (?[X862]: 0.57/0.93 (in( 0.57/0.93 X862,X856) & 0.57/0.93 (?[X864]: 0.57/0.93 (in( 0.57/0.93 X864,X858) & 0.57/0.93 (X860 = 0.57/0.93 kpair( 0.57/0.93 X862,X864)))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X866, 0.57/0.93 X868,X870]: 0.57/0.93 (in( 0.57/0.93 X870, 0.57/0.93 cartprod( 0.57/0.93 X866,X868)) => 0.57/0.93 iskpair( 0.57/0.93 X870))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X872, 0.57/0.93 X874]: 0.57/0.93 (in( 0.57/0.93 X874, 0.57/0.93 setunion( 0.57/0.93 X872)) => 0.57/0.93 (?[X876]: 0.57/0.93 (in( 0.57/0.93 X876,X872) & 0.57/0.93 in( 0.57/0.93 X874,X876))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X878]: 0.57/0.93 subset( 0.57/0.93 setunion( 0.57/0.93 setadjoin( 0.57/0.93 X878, 0.57/0.93 emptyset)), 0.57/0.93 X878)) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X880]: 0.57/0.93 subset( 0.57/0.93 X880, 0.57/0.93 setunion( 0.57/0.93 setadjoin( 0.57/0.93 X880, 0.57/0.93 emptyset)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X882]: 0.57/0.93 (setunion( 0.57/0.93 setadjoin( 0.57/0.93 X882, 0.57/0.93 emptyset)) = 0.57/0.93 X882)) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X884, 0.57/0.93 X886:( 0.57/0.93 ( 0.57/0.93 $i > $o))]: 0.57/0.93 (( 0.57/0.93 ![X888]: 0.57/0.93 (in( 0.57/0.93 X888,X884) => 0.57/0.93 (![X890]: 0.57/0.93 (in( 0.57/0.93 X890,X884) => 0.57/0.93 (X886( 0.57/0.93 X888) => 0.57/0.93 (X886( 0.57/0.93 X890) => 0.57/0.93 (X888 = 0.57/0.93 X890))))))) => 0.57/0.93 (( 0.57/0.93 ?[X892]: 0.57/0.93 (in( 0.57/0.93 X892,X884) & 0.57/0.93 X886( 0.57/0.93 X892))) => 0.57/0.93 (?[X894]: 0.57/0.93 (in( 0.57/0.93 X894, 0.57/0.93 dsetconstr( 0.57/0.93 X884, 0.57/0.93 ^[V_16]: 0.57/0.93 X886( 0.57/0.93 V_16))) & 0.57/0.93 (dsetconstr( 0.57/0.93 X884, 0.57/0.93 ^[V_15]: 0.57/0.93 X886( 0.57/0.93 V_15)) = 0.57/0.93 setadjoin( 0.57/0.93 X894, 0.57/0.93 emptyset))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X896, 0.57/0.93 X898:( 0.57/0.93 ( 0.57/0.93 $i > $o))]: 0.57/0.93 (( 0.57/0.93 ?[X900]: 0.57/0.93 (in( 0.57/0.93 X900, 0.57/0.93 dsetconstr( 0.57/0.93 X896, 0.57/0.93 ^[V_18]: 0.57/0.93 X898( 0.57/0.93 V_18))) & 0.57/0.93 (dsetconstr( 0.57/0.93 X896, 0.57/0.93 ^[V_17]: 0.57/0.93 X898( 0.57/0.93 V_17)) = 0.57/0.93 setadjoin( 0.57/0.93 X900, 0.57/0.93 emptyset)))) => 0.57/0.93 (?[X902]: 0.57/0.93 (in( 0.57/0.93 X902,X896) & 0.57/0.93 X898( 0.57/0.93 X902))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X904, 0.57/0.93 X906:( 0.57/0.93 ( 0.57/0.93 $i > $o)), 0.57/0.93 X908]: 0.57/0.93 (in( 0.57/0.93 X908,X904) => 0.57/0.93 (X906( 0.57/0.93 X908) => 0.57/0.93 (( 0.57/0.93 ![X910]: 0.57/0.93 (in( 0.57/0.93 X910,X904) => 0.57/0.93 (X906( 0.57/0.93 X910) => 0.57/0.93 (X910 = 0.57/0.93 X908)))) => 0.57/0.93 (?[X912]: 0.57/0.93 (in( 0.57/0.93 X912, 0.57/0.93 dsetconstr( 0.57/0.93 X904, 0.57/0.93 ^[V_20]: 0.57/0.93 X906( 0.57/0.93 V_20))) & 0.57/0.93 (dsetconstr( 0.57/0.93 X904, 0.57/0.93 ^[V_19]: 0.57/0.93 X906( 0.57/0.93 V_19)) = 0.57/0.93 setadjoin( 0.57/0.93 X912, 0.57/0.93 emptyset)))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X914, 0.57/0.93 X916:( 0.57/0.93 ( 0.57/0.93 $i > $o))]: 0.57/0.93 (( 0.57/0.93 ![X918]: 0.57/0.93 (in( 0.57/0.93 X918,X914) => 0.57/0.93 (![X920]: 0.57/0.93 (in( 0.57/0.93 X920,X914) => 0.57/0.93 (X916( 0.57/0.93 X918) => 0.57/0.93 (X916( 0.57/0.93 X920) => 0.57/0.93 (X918 = 0.57/0.93 X920))))))) => 0.57/0.93 (( 0.57/0.93 ?[X922]: 0.57/0.93 (in( 0.57/0.93 X922,X914) & 0.57/0.93 X916( 0.57/0.93 X922))) => 0.57/0.93 (?[X924]: 0.57/0.93 (in( 0.57/0.93 X924, 0.57/0.93 dsetconstr( 0.57/0.93 X914, 0.57/0.93 ^[V_22]: 0.57/0.93 X916( 0.57/0.93 V_22))) & 0.57/0.93 (dsetconstr( 0.57/0.93 X914, 0.57/0.93 ^[V_21]: 0.57/0.93 X916( 0.57/0.93 V_21)) = 0.57/0.93 setadjoin( 0.57/0.93 X924, 0.57/0.93 emptyset))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X926, 0.57/0.93 X928]: 0.57/0.93 (( 0.57/0.93 setadjoin( 0.57/0.93 X926, 0.57/0.93 emptyset) = 0.57/0.93 setadjoin( 0.57/0.93 X928, 0.57/0.93 emptyset)) => 0.57/0.93 (X926 = 0.57/0.93 X928))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X930, 0.57/0.93 X932,X934]: 0.57/0.93 (in( 0.57/0.93 setadjoin( 0.57/0.93 X934, 0.57/0.93 emptyset), 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X930, 0.57/0.93 emptyset), 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X930, 0.57/0.93 setadjoin( 0.57/0.93 X932, 0.57/0.93 emptyset)), 0.57/0.93 emptyset))) => 0.57/0.93 (X930 = 0.57/0.93 X934))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X936]: 0.57/0.93 (iskpair( 0.57/0.93 X936) => 0.57/0.93 (?[X938]: 0.57/0.93 (in( 0.57/0.93 X938, 0.57/0.93 dsetconstr( 0.57/0.93 setunion( 0.57/0.93 X936), 0.57/0.93 ^[V_24]: 0.57/0.93 in( 0.57/0.93 setadjoin( 0.57/0.93 V_24, 0.57/0.93 emptyset), 0.57/0.93 X936))) & 0.57/0.93 (dsetconstr( 0.57/0.93 setunion( 0.57/0.93 X936), 0.57/0.93 ^[V_23]: 0.57/0.93 in( 0.57/0.93 setadjoin( 0.57/0.93 V_23, 0.57/0.93 emptyset), 0.57/0.93 X936)) = 0.57/0.93 setadjoin( 0.57/0.93 X938, 0.57/0.93 emptyset)))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X940]: 0.57/0.93 (( 0.57/0.93 ?[X942]: 0.57/0.93 (in( 0.57/0.93 X942,X940) & 0.57/0.93 (X940 = 0.57/0.93 setadjoin( 0.57/0.93 X942, 0.57/0.93 emptyset)))) => 0.57/0.93 in( 0.57/0.93 setunion( 0.57/0.93 X940), 0.57/0.93 X940))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X944, 0.57/0.93 X946]: 0.57/0.93 (kfst( 0.57/0.93 kpair( 0.57/0.93 X944,X946)) = 0.57/0.93 X944)) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X948, 0.57/0.93 X950,X952]: 0.57/0.93 (in( 0.57/0.93 X952, 0.57/0.93 cartprod( 0.57/0.93 X948,X950)) => 0.57/0.93 in( 0.57/0.93 kfst( 0.57/0.93 X952), 0.57/0.93 X948))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X954, 0.57/0.93 X956, 0.57/0.93 X958,X960]: 0.57/0.93 (( 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X954, 0.57/0.93 emptyset), 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X954, 0.57/0.93 setadjoin( 0.57/0.93 X956, 0.57/0.93 emptyset)), 0.57/0.93 emptyset)) = 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X958, 0.57/0.93 emptyset), 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X958, 0.57/0.93 setadjoin( 0.57/0.93 X960, 0.57/0.93 emptyset)), 0.57/0.93 emptyset))) => 0.57/0.93 (X954 = 0.57/0.93 X958))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X962, 0.57/0.93 X964, 0.57/0.93 X966,X968]: 0.57/0.93 (( 0.57/0.93 kpair( 0.57/0.93 X962,X964) = 0.57/0.93 kpair( 0.57/0.93 X966,X968)) => 0.57/0.93 (X962 = 0.57/0.93 X966))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X970, 0.57/0.93 X972]: 0.57/0.93 (( 0.57/0.93 X970 = 0.57/0.93 X972) => 0.57/0.93 (setadjoin( 0.57/0.93 X970, 0.57/0.93 setadjoin( 0.57/0.93 X972, 0.57/0.93 emptyset)) = 0.57/0.93 setadjoin( 0.57/0.93 X970, 0.57/0.93 emptyset)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X974, 0.57/0.93 X976]: 0.57/0.93 (( 0.57/0.93 X974 = 0.57/0.93 X976) => 0.57/0.93 (setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X974, 0.57/0.93 emptyset), 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X974, 0.57/0.93 setadjoin( 0.57/0.93 X976, 0.57/0.93 emptyset)), 0.57/0.93 emptyset)) = 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X974, 0.57/0.93 emptyset), 0.57/0.93 emptyset)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X978, 0.57/0.93 X980, 0.57/0.93 X982,X984]: 0.57/0.93 (( 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X978, 0.57/0.93 emptyset), 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X978, 0.57/0.93 setadjoin( 0.57/0.93 X980, 0.57/0.93 emptyset)), 0.57/0.93 emptyset)) = 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X982, 0.57/0.93 emptyset), 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X982, 0.57/0.93 setadjoin( 0.57/0.93 X984, 0.57/0.93 emptyset)), 0.57/0.93 emptyset))) => 0.57/0.93 (( 0.57/0.93 X982 = 0.57/0.93 X984) => 0.57/0.93 (X980 = 0.57/0.93 X984)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X986, 0.57/0.93 X988,X990]: 0.57/0.93 (( 0.57/0.93 setadjoin( 0.57/0.93 X986, 0.57/0.93 setadjoin( 0.57/0.93 X988, 0.57/0.93 emptyset)) = 0.57/0.93 setadjoin( 0.57/0.93 X990, 0.57/0.93 emptyset)) => 0.57/0.93 (X986 = 0.57/0.93 X988))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X992, 0.57/0.93 X994, 0.57/0.93 X996,X998]: 0.57/0.93 (( 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X992, 0.57/0.93 emptyset), 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X992, 0.57/0.93 setadjoin( 0.57/0.93 X994, 0.57/0.93 emptyset)), 0.57/0.93 emptyset)) = 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X996, 0.57/0.93 emptyset), 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X996, 0.57/0.93 setadjoin( 0.57/0.93 X998, 0.57/0.93 emptyset)), 0.57/0.93 emptyset))) => 0.57/0.93 (X994 = 0.57/0.93 X998))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X1000, 0.57/0.93 X1002, 0.57/0.93 X1004, 0.57/0.93 X1006]: 0.57/0.93 (( 0.57/0.93 kpair( 0.57/0.93 X1000, 0.57/0.93 X1002) = 0.57/0.93 kpair( 0.57/0.93 X1004, 0.57/0.93 X1006)) => 0.57/0.93 (X1002 = 0.57/0.93 X1006))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X1008]: 0.57/0.93 (iskpair( 0.57/0.93 X1008) => 0.57/0.93 (?[X1010]: 0.57/0.93 (in( 0.57/0.93 X1010, 0.57/0.93 dsetconstr( 0.57/0.93 setunion( 0.57/0.93 X1008), 0.57/0.93 ^[V_26]: 0.57/0.93 (X1008 = 0.57/0.93 kpair( 0.57/0.93 kfst( 0.57/0.93 X1008), 0.57/0.93 V_26)))) & 0.57/0.93 (dsetconstr( 0.57/0.93 setunion( 0.57/0.93 X1008), 0.57/0.93 ^[V_25]: 0.57/0.93 (X1008 = 0.57/0.93 kpair( 0.57/0.93 kfst( 0.57/0.93 X1008), 0.57/0.93 V_25))) = 0.57/0.93 setadjoin( 0.57/0.93 X1010, 0.57/0.93 emptyset)))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X1012, 0.57/0.93 X1014]: 0.57/0.93 (ksnd( 0.57/0.93 kpair( 0.57/0.93 X1012, 0.57/0.93 X1014)) = 0.57/0.93 X1014)) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X1016]: 0.57/0.93 (iskpair( 0.57/0.93 X1016) => 0.57/0.93 (kpair( 0.57/0.93 kfst( 0.57/0.93 X1016), 0.57/0.93 ksnd( 0.57/0.93 X1016)) = 0.57/0.93 X1016))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X1018, 0.57/0.93 X1020, 0.57/0.93 X1022]: 0.57/0.93 (in( 0.57/0.93 X1022, 0.57/0.93 cartprod( 0.57/0.93 X1018, 0.57/0.93 X1020)) => 0.57/0.93 in( 0.57/0.93 ksnd( 0.57/0.93 X1022), 0.57/0.93 X1020))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X1024, 0.57/0.93 X1026, 0.57/0.93 X1028, 0.57/0.93 X1030]: 0.57/0.93 (in( 0.57/0.93 kpair( 0.57/0.93 X1028, 0.57/0.93 X1030), 0.57/0.93 cartprod( 0.57/0.93 X1024, 0.57/0.93 X1026)) => 0.57/0.93 in( 0.57/0.93 X1028, 0.57/0.93 X1024))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X1032, 0.57/0.93 X1034, 0.57/0.93 X1036, 0.57/0.93 X1038]: 0.57/0.93 (in( 0.57/0.93 kpair( 0.57/0.93 X1036, 0.57/0.93 X1038), 0.57/0.93 cartprod( 0.57/0.93 X1032, 0.57/0.93 X1034)) => 0.57/0.93 in( 0.57/0.93 X1038, 0.57/0.93 X1034))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X1040, 0.57/0.93 X1042, 0.57/0.93 X1044]: 0.57/0.93 (in( 0.57/0.93 X1044, 0.57/0.93 X1040) => 0.57/0.93 (![X1046]: 0.57/0.93 (in( 0.57/0.93 X1046, 0.57/0.93 X1042) => 0.57/0.93 (kpair( 0.57/0.93 X1044, 0.57/0.93 X1046) = 0.57/0.93 kpair( 0.57/0.93 X1044, 0.57/0.93 X1046)))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X1048, 0.57/0.93 X1050, 0.57/0.93 X1052]: 0.57/0.93 (in( 0.57/0.93 X1052, 0.57/0.93 X1048) => 0.57/0.93 (![X1054]: 0.57/0.93 (in( 0.57/0.93 X1054, 0.57/0.93 X1050) => 0.57/0.93 (kfst( 0.57/0.93 kpair( 0.57/0.93 X1052, 0.57/0.93 X1054)) = 0.57/0.93 X1052))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X1056, 0.57/0.93 X1058, 0.57/0.93 X1060]: 0.57/0.93 (in( 0.57/0.93 X1060, 0.57/0.93 X1056) => 0.57/0.93 (![X1062]: 0.57/0.93 (in( 0.57/0.93 X1062, 0.57/0.93 X1058) => 0.57/0.93 (ksnd( 0.57/0.93 kpair( 0.57/0.93 X1060, 0.57/0.93 X1062)) = 0.57/0.93 X1062))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X1064, 0.57/0.93 X1066, 0.57/0.93 X1068]: 0.57/0.93 (in( 0.57/0.93 X1068, 0.57/0.93 cartprod( 0.57/0.93 X1064, 0.57/0.93 X1066)) => 0.57/0.93 (kpair( 0.57/0.93 kfst( 0.57/0.93 X1068), 0.57/0.93 ksnd( 0.57/0.93 X1068)) = 0.57/0.93 X1068))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X1070, 0.57/0.93 X1072, 0.57/0.93 X1074:( 0.57/0.93 ($i * $i) > 0.57/0.93 $o),X1076]: 0.57/0.93 (in( 0.57/0.93 X1076, 0.57/0.93 X1070) => 0.57/0.93 (![X1078]: 0.57/0.93 (in( 0.57/0.93 X1078, 0.57/0.93 X1072) => 0.57/0.93 (X1074( 0.57/0.93 X1076, 0.57/0.93 X1078) => 0.57/0.93 in( 0.57/0.93 kpair( 0.57/0.93 X1076, 0.57/0.93 X1078), 0.57/0.93 dpsetconstr( 0.57/0.93 X1070, 0.57/0.93 X1072, 0.57/0.93 ^[V_27, 0.57/0.93 V_28]: 0.57/0.93 X1074( 0.57/0.93 V_27,V_28)))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X1080, 0.57/0.93 X1082, 0.57/0.93 X1084:( 0.57/0.93 ($i * $i) > 0.57/0.93 $o)]: 0.57/0.93 subset( 0.57/0.93 dpsetconstr( 0.57/0.93 X1080, 0.57/0.93 X1082, 0.57/0.93 ^[V_29, 0.57/0.93 V_30]: 0.57/0.93 X1084( 0.57/0.93 V_29,V_30)), 0.57/0.93 cartprod( 0.57/0.93 X1080, 0.57/0.93 X1082))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X1086, 0.57/0.93 X1088, 0.57/0.93 X1090:( 0.57/0.93 ($i * $i) > 0.57/0.93 $o)]: 0.57/0.93 subset( 0.57/0.93 dpsetconstr( 0.57/0.93 X1086, 0.57/0.93 X1088, 0.57/0.93 ^[V_31, 0.57/0.93 V_32]: 0.57/0.93 X1090( 0.57/0.93 V_31,V_32)), 0.57/0.93 cartprod( 0.57/0.93 X1086, 0.57/0.93 X1088))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X1092, 0.57/0.93 X1094, 0.57/0.93 X1096:( 0.57/0.93 ($i * $i) > 0.57/0.93 $o),X1098]: 0.57/0.93 (in( 0.57/0.93 X1098, 0.57/0.93 X1092) => 0.57/0.93 (![X1100]: 0.57/0.93 (in( 0.57/0.93 X1100, 0.57/0.93 X1094) => 0.57/0.93 (in( 0.57/0.93 kpair( 0.57/0.93 X1098, 0.57/0.93 X1100), 0.57/0.93 dpsetconstr( 0.57/0.93 X1092, 0.57/0.93 X1094, 0.57/0.93 ^[V_33, 0.57/0.93 V_34]: 0.57/0.93 X1096( 0.57/0.93 V_33,V_34))) => 0.57/0.93 X1096( 0.57/0.93 X1098, 0.57/0.93 X1100)))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X1102, 0.57/0.93 X1104, 0.57/0.93 X1106:( 0.57/0.93 ($i * $i) > 0.57/0.93 $o), 0.57/0.93 X1108, 0.57/0.93 X1110]: 0.57/0.93 (in( 0.57/0.93 kpair( 0.57/0.93 X1108, 0.57/0.93 X1110), 0.57/0.93 dpsetconstr( 0.57/0.93 X1102, 0.57/0.93 X1104, 0.57/0.93 ^[V_35, 0.57/0.93 V_36]: 0.57/0.93 X1106( 0.57/0.93 V_35,V_36))) => 0.57/0.93 in( 0.57/0.93 X1108, 0.57/0.93 X1102))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X1112, 0.57/0.93 X1114, 0.57/0.93 X1116:( 0.57/0.93 ($i * $i) > 0.57/0.93 $o), 0.57/0.93 X1118, 0.57/0.93 X1120]: 0.57/0.93 (in( 0.57/0.93 kpair( 0.57/0.93 X1118, 0.57/0.93 X1120), 0.57/0.93 dpsetconstr( 0.57/0.93 X1112, 0.57/0.93 X1114, 0.57/0.93 ^[V_37, 0.57/0.93 V_38]: 0.57/0.93 X1116( 0.57/0.93 V_37,V_38))) => 0.57/0.93 in( 0.57/0.93 X1120, 0.57/0.93 X1114))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X1122, 0.57/0.93 X1124, 0.57/0.93 X1126:( 0.57/0.93 ($i * $i) > 0.57/0.93 $o), 0.57/0.93 X1128, 0.57/0.93 X1130]: 0.57/0.93 (in( 0.57/0.93 kpair( 0.57/0.93 X1128, 0.57/0.93 X1130), 0.57/0.93 dpsetconstr( 0.57/0.93 X1122, 0.57/0.93 X1124, 0.57/0.93 ^[V_39, 0.57/0.93 V_40]: 0.57/0.93 X1126( 0.57/0.93 V_39,V_40))) => 0.57/0.93 X1126( 0.57/0.93 X1128, 0.57/0.93 X1130))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X1132, 0.57/0.93 X1134, 0.57/0.93 X1136]: 0.57/0.93 (( 0.57/0.93 ( 0.57/0.93 ![X1138]: 0.57/0.93 (in( 0.57/0.93 X1138, 0.57/0.93 X1132) => 0.57/0.93 (?[X1140]: 0.57/0.93 (in( 0.57/0.93 X1140, 0.57/0.93 dsetconstr( 0.57/0.93 X1134, 0.57/0.93 ^[V_42]: 0.57/0.93 in( 0.57/0.93 kpair( 0.57/0.93 X1138, 0.57/0.93 V_42), 0.57/0.93 X1136))) & 0.57/0.93 (dsetconstr( 0.57/0.93 X1134, 0.57/0.93 ^[V_41]: 0.57/0.93 in( 0.57/0.93 kpair( 0.57/0.93 X1138, 0.57/0.93 V_41), 0.57/0.93 X1136)) = 0.57/0.93 setadjoin( 0.57/0.93 X1140, 0.57/0.93 emptyset)))))) & 0.57/0.93 subset( 0.57/0.93 X1136, 0.57/0.93 cartprod( 0.57/0.93 X1132, 0.57/0.93 X1134))) => 0.57/0.93 (![X1142]: 0.57/0.93 (in( 0.57/0.93 X1142, 0.57/0.93 X1132) => 0.57/0.93 (?[X1144]: 0.57/0.93 (in( 0.57/0.93 X1144, 0.57/0.93 dsetconstr( 0.57/0.93 X1134, 0.57/0.93 ^[V_44]: 0.57/0.93 in( 0.57/0.93 kpair( 0.57/0.93 X1142, 0.57/0.93 V_44), 0.57/0.93 X1136))) & 0.57/0.93 (dsetconstr( 0.57/0.93 X1134, 0.57/0.93 ^[V_43]: 0.57/0.93 in( 0.57/0.93 kpair( 0.57/0.93 X1142, 0.57/0.93 V_43), 0.57/0.93 X1136)) = 0.57/0.93 setadjoin( 0.57/0.93 X1144, 0.57/0.93 emptyset)))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X1146, 0.57/0.93 X1148, 0.57/0.93 X1150]: 0.57/0.93 (( 0.57/0.93 ( 0.57/0.93 ![X1152]: 0.57/0.93 (in( 0.57/0.93 X1152, 0.57/0.93 X1146) => 0.57/0.93 (?[X1154]: 0.57/0.93 (in( 0.57/0.93 X1154, 0.57/0.93 dsetconstr( 0.57/0.93 X1148, 0.57/0.93 ^[V_46]: 0.57/0.93 in( 0.57/0.93 kpair( 0.57/0.93 X1152, 0.57/0.93 V_46), 0.57/0.93 X1150))) & 0.57/0.93 (dsetconstr( 0.57/0.93 X1148, 0.57/0.93 ^[V_45]: 0.57/0.93 in( 0.57/0.93 kpair( 0.57/0.93 X1152, 0.57/0.93 V_45), 0.57/0.93 X1150)) = 0.57/0.93 setadjoin( 0.57/0.93 X1154, 0.57/0.93 emptyset)))))) & 0.57/0.93 subset( 0.57/0.93 X1150, 0.57/0.93 cartprod( 0.57/0.93 X1146, 0.57/0.93 X1148))) => 0.57/0.93 (![X1156]: 0.57/0.93 (in( 0.57/0.93 X1156, 0.57/0.93 X1146) => 0.57/0.93 in( 0.57/0.93 setunion( 0.57/0.93 dsetconstr( 0.57/0.93 X1148, 0.57/0.93 ^[V_47]: 0.57/0.93 in( 0.57/0.93 kpair( 0.57/0.93 X1156, 0.57/0.93 V_47), 0.57/0.93 X1150))), 0.57/0.93 X1148))))) => 0.57/0.93 ( 0.57/0.93 ![X1158, 0.57/0.93 X1160, 0.57/0.93 X1162]: 0.57/0.93 (( 0.57/0.93 ( 0.57/0.93 ![X1164]: 0.57/0.93 (in( 0.57/0.93 X1164, 0.57/0.93 X1158) => 0.57/0.93 (?[X1166]: 0.57/0.93 (in( 0.57/0.93 X1166, 0.57/0.93 dsetconstr( 0.57/0.93 X1160, 0.57/0.93 ^[V_49]: 0.57/0.93 in( 0.57/0.93 kpair( 0.57/0.93 X1164, 0.57/0.93 V_49), 0.57/0.93 X1162))) & 0.57/0.93 (dsetconstr( 0.57/0.93 X1160, 0.57/0.93 ^[V_48]: 0.57/0.93 in( 0.57/0.93 kpair( 0.57/0.93 X1164, 0.57/0.93 V_48), 0.57/0.93 X1162)) = 0.57/0.93 setadjoin( 0.57/0.93 X1166, 0.57/0.93 emptyset)))))) & 0.57/0.93 subset( 0.57/0.93 X1162, 0.57/0.93 cartprod( 0.57/0.93 X1158, 0.57/0.93 X1160))) => 0.57/0.93 (![X1168]: 0.57/0.93 (in( 0.57/0.93 X1168, 0.57/0.93 X1158) => 0.57/0.93 in( 0.57/0.93 setunion( 0.57/0.93 dsetconstr( 0.57/0.93 X1160, 0.57/0.93 ^[V_50]: 0.57/0.93 in( 0.57/0.93 kpair( 0.57/0.93 X1168, 0.57/0.93 V_50), 0.57/0.93 X1162))), 0.57/0.93 X1160)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 0.57/0.93 tff(zf_stmt_1, negated_conjecture, 0.57/0.93 (~ 0.57/0.93 ((![X4,X6]: ((![X8]: (in(X8,X4) <=> in(X8,X6))) => (X4 = X6))) => 0.57/0.93 ((![X10]: (~in(X10,emptyset))) => 0.57/0.93 ((![X12,X14,X16]: 0.57/0.93 (in(X16,setadjoin(X12,X14)) <=> (in(X16,X14) | (X16 = X12)))) => 0.57/0.93 ((![X18,X20]: 0.57/0.93 (in(X20,powerset(X18)) <=> (![X22]: (in(X22,X20) => in(X22,X18))))) => 0.57/0.93 ((![X24,X26]: 0.57/0.93 (in(X26,setunion(X24)) <=> (?[X28]: (in(X26,X28) & in(X28,X24))))) => 0.57/0.93 (in(emptyset,omega) => 0.57/0.93 ((![X30]: (in(X30,omega) => in(setadjoin(X30,X30),omega))) => 0.57/0.93 ((![X32]: 0.57/0.93 (((![X34]: 0.57/0.93 ((in(X34,X32) & in(X34,omega)) => 0.57/0.93 in(setadjoin(X34,X34),X32))) & 0.57/0.93 in(emptyset,X32)) => 0.57/0.93 (![X36]: (in(X36,omega) => in(X36,X32))))) => 0.57/0.93 ((![X38:(($i * $i) > $o),X40]: 0.57/0.93 ((![X42]: 0.57/0.93 (in(X42,X40) => 0.57/0.93 (?[X44]: 0.57/0.93 (X38(X42,X44) & 0.57/0.93 (![X46]: (X38(X42,X46) => (X44 = X46))))))) => 0.57/0.93 (?[X48]: 0.57/0.93 (![X50]: 0.57/0.93 (in(X50,X48) <=> 0.57/0.93 (?[X52]: (in(X52,X40) & X38(X52,X50)))))))) => 0.57/0.93 ((![X54]: 0.57/0.93 ((?[X56]: in(X56,X54)) => 0.57/0.93 (?[X58]: 0.57/0.93 (in(X58,X54) & (~(?[X60]: (in(X60,X58) & in(X60,X54)))))))) => 0.57/0.93 ((![X62]: 0.57/0.93 (?[X64]: 0.57/0.93 ((![X96]: 0.57/0.93 (in(X96,X64) => 0.57/0.93 (![X98]: (in(X98,X96) => in(X98,X62))))) & 0.57/0.93 (![X90,X92]: 0.57/0.93 ((in(X92,X62) & in(X90,X62)) => 0.57/0.93 ((![X94]: 0.57/0.93 (in(X94,X64) => (in(X90,X94) <=> in(X92,X94)))) => 0.57/0.93 (X90 = X92)))) & 0.57/0.93 (![X82,X84]: 0.57/0.93 ((in(X84,X64) & in(X82,X64)) => 0.57/0.93 ((![X88]: (in(X88,X84) => in(X88,X82))) | 0.57/0.93 (![X86]: (in(X86,X82) => in(X86,X84)))))) & 0.57/0.93 (![X66]: 0.57/0.93 (((?[X70]: in(X70,X66)) & 0.57/0.93 (![X68]: (in(X68,X66) => in(X68,X62)))) => 0.57/0.93 (?[X72,X74]: 0.57/0.93 (in(X72,X64) & in(X74,X66) & 0.57/0.93 (~(?[X80]: (in(X80,X72) & in(X80,X66)))) & 0.57/0.93 (![X76]: 0.57/0.93 (in(X76,X64) => 0.57/0.93 (in(X74,X76) | 0.57/0.93 (![X78]: (in(X78,X76) => in(X78,X72))))))))))))) => 0.57/0.93 ((![X100:(($i > $o))]: 0.57/0.93 ((?[X102]: 0.57/0.93 (X100(X102) & (![X104]: (X100(X104) => (X102 = X104))))) => 0.57/0.93 X100(descr(^[V_1]: X100(V_1))))) => 0.57/0.93 ((![X106,X108:(($i > $o)),X110]: 0.57/0.93 (in(X110,X106) => 0.57/0.93 (X108(X110) => 0.57/0.93 in(X110,dsetconstr(X106,^[V_2]: X108(V_2)))))) => 0.57/0.93 ((![X112,X114:(($i > $o)),X116]: 0.57/0.93 (in(X116,dsetconstr(X112,^[V_3]: X114(V_3))) => 0.57/0.93 in(X116,X112))) => 0.57/0.93 ((![X118,X120:(($i > $o)),X122]: 0.57/0.93 (in(X122,dsetconstr(X118,^[V_4]: X120(V_4))) => 0.57/0.93 X120(X122))) => 0.57/0.93 ((![X124:(($i > $o))]: 0.57/0.93 ((?[X126]: 0.57/0.93 (X124(X126) & 0.57/0.93 (![X128]: (X124(X128) => (X126 = X128))))) => 0.57/0.93 (?[X130]: 0.57/0.93 (X124(X130) & 0.57/0.93 (![X132]: (X124(X132) => (X130 = X132))))))) => 0.57/0.93 ((![X134:$o,X136]: (in(X136,prop2set(X134)) => X134)) => 0.57/0.93 ((![X138]: (in(X138,emptyset) => (![X140:$o]: X140))) => 0.57/0.93 ((![X142]: (~in(X142,emptyset))) => 0.57/0.93 ((![X144]: (~in(X144,emptyset))) => 0.57/0.93 ((![X146:(($i > $o))]: 0.57/0.93 ((?[X148]: 0.57/0.93 (X146(X148) & 0.57/0.93 (![X150]: (X146(X150) => (X148 = X150))))) => 0.57/0.93 (?[X152]: X146(X152)))) => 0.57/0.93 ((![X154,X156]: 0.57/0.93 ((![X158]: (in(X158,X154) => in(X158,X156))) => 0.57/0.93 ((![X160]: (in(X160,X156) => in(X160,X154))) => 0.57/0.93 (X154 = X156)))) => 0.57/0.93 ((![X162]: 0.57/0.93 ((![X164]: (~in(X164,X162))) => 0.57/0.93 (X162 = emptyset))) => 0.57/0.93 ((![X166]: 0.57/0.93 ((![X168]: (~in(X168,X166))) => 0.57/0.93 (X166 = emptyset))) => 0.57/0.93 ((![X170,X172:(($i > $o)),X174]: 0.57/0.93 (in(X174,X170) => 0.57/0.93 (in(X174,dsetconstr(X170,^[V_5]: X172(V_5))) <=> 0.57/0.93 X172(X174)))) => 0.57/0.93 ((![X176]: 0.57/0.93 ((X176 != emptyset) => 0.57/0.93 (?[X178]: in(X178,X176)))) => 0.57/0.93 ((![X180,X182:(($i > $o)),X184]: 0.57/0.93 (in(X184,X180) => 0.57/0.93 (X182(X184) => 0.57/0.93 (dsetconstr(X180,^[V_6]: X182(V_6)) != 0.57/0.93 emptyset)))) => 0.57/0.93 ((![X186]: 0.57/0.93 ((?[X188]: in(X188,X186)) => 0.57/0.93 (X186 != emptyset))) => 0.57/0.93 ((![X190,X192]: in(X190,setadjoin(X190,X192))) => 0.57/0.93 (in(emptyset,setadjoin(emptyset,emptyset)) => 0.57/0.93 ((![X194,X196,X198]: 0.57/0.93 (in(X198,X196) => 0.57/0.93 in(X198,setadjoin(X194,X196)))) => 0.57/0.93 ((![X200,X202,X204]: 0.57/0.93 (in(X204,setadjoin(X200,X202)) => 0.57/0.93 (![X206:$o]: 0.57/0.93 (((X204 = X200) => X206) => 0.57/0.93 ((in(X204,X202) => X206) => X206))))) => 0.57/0.93 ((![X208,X210,X212]: 0.57/0.93 (in(X212,setadjoin(X208,X210)) => 0.57/0.93 (in(X212,X210) | (X212 = X208)))) => 0.57/0.93 ((![X214]: 0.57/0.93 (dsetconstr(X214,^[V_7]: $true) = 0.57/0.93 X214)) => 0.57/0.93 ((![X216,X218]: 0.57/0.93 ((![X220]: 0.57/0.93 (in(X220,X218) => in(X220,X216))) => 0.57/0.93 in(X218,powerset(X216)))) => 0.57/0.93 ((![X222]: in(emptyset,powerset(X222))) => 0.57/0.93 ((![X224]: 0.57/0.93 in(emptyset,powerset(X224))) => 0.57/0.93 ((![X226,X228,X230]: 0.57/0.93 (in(X228,powerset(X226)) => 0.57/0.93 (in(X230,X228) => in(X230,X226)))) => 0.57/0.93 ((![X232,X234,X236]: 0.57/0.93 (in(X234,X236) => 0.57/0.93 (in(X236,X232) => 0.57/0.93 in(X234,setunion(X232))))) => 0.57/0.93 ((![X238,X240]: 0.57/0.93 (in(X240,setunion(X238)) => 0.57/0.93 (![X242:$o]: 0.57/0.93 ((![X244]: 0.57/0.93 (in(X240,X244) => 0.57/0.93 (in(X244,X238) => 0.57/0.93 X242))) => 0.57/0.93 X242)))) => 0.57/0.93 ((![X246,X248]: 0.57/0.93 (in(X248,X246) => 0.57/0.93 in(X248, 0.57/0.93 powerset(setunion(X246))))) => 0.57/0.93 ((![X250:(($i > $o))]: 0.57/0.93 ((?[X252]: 0.57/0.93 (X250(X252) & 0.57/0.93 (![X254]: 0.57/0.93 (X250(X254) => 0.57/0.93 (X252 = X254))))) => 0.57/0.93 (?[X256]: 0.57/0.93 (![X258]: 0.57/0.93 (X250(X258) <=> 0.57/0.93 (X258 = X256)))))) => 0.57/0.93 ((![X260]: 0.57/0.93 ((X260 != emptyset) => 0.57/0.93 (?[X262]: in(X262,X260)))) => 0.57/0.93 ((![X264,X266]: 0.57/0.93 (in(X264, 0.57/0.93 setadjoin(X266, 0.57/0.93 emptyset)) => 0.57/0.93 (X264 = X266))) => 0.57/0.93 ((![X268,X270]: 0.57/0.93 ((X268 != X270) => 0.57/0.93 (~ 0.57/0.93 in(X270, 0.57/0.93 setadjoin(X268, 0.57/0.93 emptyset))))) => 0.57/0.93 ((![X272,X274]: 0.57/0.93 ((X272 = X274) => 0.57/0.93 in(X272, 0.57/0.93 setadjoin(X274, 0.57/0.93 emptyset)))) => 0.57/0.93 ((![X276,X278]: 0.57/0.93 (in(X276, 0.57/0.93 setadjoin(X278, 0.57/0.93 emptyset)) => 0.57/0.93 in(X278, 0.57/0.93 setadjoin(X276, 0.57/0.93 emptyset)))) => 0.57/0.93 ((![X280,X282,X284]: 0.57/0.93 (in(X284, 0.57/0.93 setadjoin( 0.57/0.93 X280, 0.57/0.93 setadjoin( 0.57/0.93 X282,emptyset))) => 0.57/0.93 ((X284 = X282) | 0.57/0.93 (X284 = X280)))) => 0.57/0.93 ((![X286,X288]: 0.57/0.93 in(X286, 0.57/0.93 setadjoin( 0.57/0.93 X286, 0.57/0.93 setadjoin( 0.57/0.93 X288,emptyset)))) => 0.57/0.93 ((![X290,X292]: 0.57/0.93 in(X292, 0.57/0.93 setadjoin( 0.57/0.93 X290, 0.57/0.93 setadjoin( 0.57/0.93 X292,emptyset)))) => 0.57/0.93 ((![X294, 0.57/0.93 X296:(($i > $o))]: 0.57/0.93 ((?[X298]: 0.57/0.93 (in(X298,X294) & 0.57/0.93 X296(X298))) => 0.57/0.93 (dsetconstr( 0.57/0.93 X294, 0.57/0.93 ^[V_8]: X296(V_8)) != 0.57/0.93 emptyset))) => 0.57/0.93 ((![X300:(($i > $o)), 0.57/0.93 X302]: 0.57/0.93 (in(X302,emptyset) => 0.57/0.93 X300(X302))) => 0.57/0.93 ((![X304, 0.57/0.93 X306:(($i > $o))]: 0.57/0.93 ((~ 0.57/0.93 (![X308]: 0.57/0.93 (in( 0.57/0.93 X308,X304) => 0.57/0.93 X306(X308)))) => 0.57/0.93 (?[X310]: 0.57/0.93 (in(X310,X304) & 0.57/0.93 (~X306(X310)))))) => 0.57/0.93 ((![X312, 0.57/0.93 X314:(($i > $o))]: 0.57/0.93 ((![X316]: 0.57/0.93 (in( 0.57/0.93 X316,X312) => 0.57/0.93 (~ 0.57/0.93 X314( 0.57/0.93 X316)))) => 0.57/0.93 (~ 0.57/0.93 (?[X318]: 0.57/0.93 (in( 0.57/0.93 X318,X312) & 0.57/0.93 X314( 0.57/0.93 X318)))))) => 0.57/0.93 ((![X320, 0.57/0.93 X322:(($i > $o))]: 0.57/0.93 ((~ 0.57/0.93 (?[X324]: 0.57/0.93 ( 0.57/0.93 in( 0.57/0.93 X324,X320) & 0.57/0.93 X322( 0.57/0.93 X324)))) => 0.57/0.93 (![X326]: 0.57/0.93 (in( 0.57/0.93 X326,X320) => 0.57/0.93 (~ 0.57/0.93 X322( 0.57/0.93 X326)))))) => 0.57/0.93 ((![X328, 0.57/0.93 X330:( 0.57/0.93 ($i > $o))]: 0.57/0.93 ((?[X332]: 0.57/0.93 (in( 0.57/0.93 X332,X328) & 0.57/0.93 ( 0.57/0.93 ~ 0.57/0.93 X330( 0.57/0.93 X332)))) => 0.57/0.93 (~ 0.57/0.93 (![X334]: 0.57/0.93 (in( 0.57/0.93 X334,X328) => 0.57/0.93 X330( 0.57/0.93 X334)))))) => 0.57/0.93 ((![X336:$o]: 0.57/0.93 (X336 => 0.57/0.93 in(emptyset, 0.57/0.93 prop2set( 0.57/0.93 X336)))) => 0.57/0.93 ((![X338:$o]: 0.57/0.93 (X338 => 0.57/0.93 set2prop( 0.57/0.93 prop2set( 0.57/0.93 X338)))) => 0.57/0.93 ((![X340, 0.57/0.93 X342:( 0.57/0.93 ($i > $o))]: 0.57/0.93 ((~ 0.57/0.93 ( 0.57/0.93 ?[X344]: 0.57/0.93 (in( 0.57/0.93 X344,X340) & 0.57/0.93 X342( 0.57/0.93 X344)))) => 0.57/0.93 (![X346]: 0.57/0.93 (in( 0.57/0.93 X346,X340) => 0.57/0.93 (~ 0.57/0.93 X342( 0.57/0.93 X346)))))) => 0.57/0.93 ((![X348, 0.57/0.93 X350:( 0.57/0.93 ($i > $o))]: 0.57/0.93 (( 0.57/0.93 ~ 0.57/0.93 ( 0.57/0.93 ![X352]: 0.57/0.93 (in( 0.57/0.93 X352,X348) => 0.57/0.93 X350( 0.57/0.93 X352)))) => 0.57/0.93 ( 0.57/0.93 ?[X354]: 0.57/0.93 (in( 0.57/0.93 X354,X348) & 0.57/0.93 (~ 0.57/0.93 X350( 0.57/0.93 X354)))))) => 0.57/0.93 ((![X356:( 0.57/0.93 ( 0.57/0.93 $i > $o))]: 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ?[X358]: 0.57/0.93 (X356( 0.57/0.93 X358) & 0.57/0.93 (![X360]: 0.57/0.93 (X356( 0.57/0.93 X360) => 0.57/0.93 (X358 = 0.57/0.93 X360))))) => 0.57/0.93 ( 0.57/0.93 ?[X362]: 0.57/0.93 (X356( 0.57/0.93 X362) & 0.57/0.93 (![X364]: 0.57/0.93 (X356( 0.57/0.93 X364) => 0.57/0.93 (X362 = 0.57/0.93 X364))))))) => 0.57/0.93 ((![X366:( 0.57/0.93 ( 0.57/0.93 $i > $o))]: 0.57/0.93 (( 0.57/0.93 ?[X368]: 0.57/0.93 X366( 0.57/0.93 X368)) => 0.57/0.93 (( 0.57/0.93 ![X370, 0.57/0.93 X372]: 0.57/0.93 (X366( 0.57/0.93 X370) => 0.57/0.93 (X366( 0.57/0.93 X372) => 0.57/0.93 (X370 = 0.57/0.93 X372)))) => 0.57/0.93 (?[X374]: 0.57/0.93 (X366( 0.57/0.93 X374) & 0.57/0.93 (![X376]: 0.57/0.93 (X366( 0.57/0.93 X376) => 0.57/0.93 (X374 = 0.57/0.93 X376)))))))) => 0.57/0.93 ((![X378:( 0.57/0.93 ( 0.57/0.93 $i > $o))]: 0.57/0.93 (( 0.57/0.93 ?[X380]: 0.57/0.93 (![X382]: 0.57/0.93 (X378( 0.57/0.93 X382) <=> 0.57/0.93 (X382 = 0.57/0.93 X380)))) => 0.57/0.93 (?[X384]: 0.57/0.93 (X378( 0.57/0.93 X384) & 0.57/0.93 (![X386]: 0.57/0.93 (X378( 0.57/0.93 X386) => 0.57/0.93 (X384 = 0.57/0.93 X386))))))) => 0.57/0.93 (( 0.57/0.93 ![X388, 0.57/0.93 X390]: 0.57/0.93 (( 0.57/0.93 X388 = 0.57/0.93 X390) => 0.57/0.93 (![X392, 0.57/0.93 X394]: 0.57/0.93 (( 0.57/0.93 X392 = 0.57/0.93 X394) => 0.57/0.93 (in( 0.57/0.93 X392,X388) => 0.57/0.93 in( 0.57/0.93 X394,X390)))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X396, 0.57/0.93 X398]: 0.57/0.93 (( 0.57/0.93 X396 = 0.57/0.93 X398) => 0.57/0.93 (![X400, 0.57/0.93 X402]: 0.57/0.93 (( 0.57/0.93 X400 = 0.57/0.93 X402) => 0.57/0.93 (in( 0.57/0.93 X400,X396) <=> 0.57/0.93 in( 0.57/0.93 X402,X398)))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X404:( 0.57/0.93 ( 0.57/0.93 $i > $o))]: 0.57/0.93 (( 0.57/0.93 ?[X406]: 0.57/0.93 (X404( 0.57/0.93 X406) & 0.57/0.93 (![X408]: 0.57/0.93 (X404( 0.57/0.93 X408) => 0.57/0.93 (X406 = 0.57/0.93 X408))))) => 0.57/0.93 (![X410, 0.57/0.93 X412]: 0.57/0.93 (X404( 0.57/0.93 X410) => 0.57/0.93 (X404( 0.57/0.93 X412) => 0.57/0.93 (X410 = 0.57/0.93 X412)))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X414:( 0.57/0.93 ( 0.57/0.93 $i > $o)), 0.57/0.93 X416:( 0.57/0.93 ( 0.57/0.93 $i > $o))]: 0.57/0.93 (( 0.57/0.93 ![X418, 0.57/0.93 X420]: 0.57/0.93 (( 0.57/0.93 X418 = 0.57/0.93 X420) => 0.57/0.93 (X414( 0.57/0.93 X418) <=> 0.57/0.93 X416( 0.57/0.93 X420)))) => 0.57/0.93 (( 0.57/0.93 ?[X422]: 0.57/0.93 (X414( 0.57/0.93 X422) & 0.57/0.93 (![X424]: 0.57/0.93 (X414( 0.57/0.93 X424) => 0.57/0.93 (X422 = 0.57/0.93 X424))))) <=> 0.57/0.93 (?[X426]: 0.57/0.93 (X416( 0.57/0.93 X426) & 0.57/0.93 (![X428]: 0.57/0.93 (X416( 0.57/0.93 X428) => 0.57/0.93 (X426 = 0.57/0.93 X428)))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 emptyset = 0.57/0.93 emptyset) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X430, 0.57/0.93 X432]: 0.57/0.93 (( 0.57/0.93 X430 = 0.57/0.93 X432) => 0.57/0.93 (![X434, 0.57/0.93 X436]: 0.57/0.93 (( 0.57/0.93 X434 = 0.57/0.93 X436) => 0.57/0.93 (setadjoin( 0.57/0.93 X430,X434) = 0.57/0.93 setadjoin( 0.57/0.93 X432,X436)))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X438, 0.57/0.93 X440]: 0.57/0.93 (( 0.57/0.93 X438 = 0.57/0.93 X440) => 0.57/0.93 (powerset( 0.57/0.93 X438) = 0.57/0.93 powerset( 0.57/0.93 X440)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X442, 0.57/0.93 X444]: 0.57/0.93 (( 0.57/0.93 X442 = 0.57/0.93 X444) => 0.57/0.93 (setunion( 0.57/0.93 X442) = 0.57/0.93 setunion( 0.57/0.93 X444)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 omega = 0.57/0.93 omega) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X446:( 0.57/0.93 ( 0.57/0.93 $i > $o))]: 0.57/0.93 (( 0.57/0.93 ?[X448]: 0.57/0.93 (X446( 0.57/0.93 X448) & 0.57/0.93 (![X450]: 0.57/0.93 (X446( 0.57/0.93 X450) => 0.57/0.93 (X448 = 0.57/0.93 X450))))) => 0.57/0.93 (![X452, 0.57/0.93 X454]: 0.57/0.93 (X446( 0.57/0.93 X452) => 0.57/0.93 (X446( 0.57/0.93 X454) => 0.57/0.93 (X452 = 0.57/0.93 X454)))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X456:( 0.57/0.93 ( 0.57/0.93 $i > $o)), 0.57/0.93 X458:( 0.57/0.93 ( 0.57/0.93 $i > $o))]: 0.57/0.93 (( 0.57/0.93 ![X460, 0.57/0.93 X462]: 0.57/0.93 (( 0.57/0.93 X460 = 0.57/0.93 X462) => 0.57/0.93 (X456( 0.57/0.93 X460) <=> 0.57/0.93 X458( 0.57/0.93 X462)))) => 0.57/0.93 (( 0.57/0.93 ?[X464]: 0.57/0.93 (X456( 0.57/0.93 X464) & 0.57/0.93 (![X466]: 0.57/0.93 (X456( 0.57/0.93 X466) => 0.57/0.93 (X464 = 0.57/0.93 X466))))) => 0.57/0.93 (( 0.57/0.93 ?[X468]: 0.57/0.93 (X458( 0.57/0.93 X468) & 0.57/0.93 (![X470]: 0.57/0.93 (X458( 0.57/0.93 X470) => 0.57/0.93 (X468 = 0.57/0.93 X470))))) => 0.57/0.93 (descr( 0.57/0.93 ^[V_9]: 0.57/0.93 X456(V_9)) = 0.57/0.93 descr( 0.57/0.93 ^[V_10]: 0.57/0.93 X458( 0.57/0.93 V_10))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X472, 0.57/0.93 X474]: 0.57/0.93 (( 0.57/0.93 X472 = 0.57/0.93 X474) => 0.57/0.93 (![X476:( 0.57/0.93 ( 0.57/0.93 $i > $o)), 0.57/0.93 X478:( 0.57/0.93 ( 0.57/0.93 $i > $o))]: 0.57/0.93 (( 0.57/0.93 ![X480]: 0.57/0.93 (in( 0.57/0.93 X480,X472) => 0.57/0.93 (![X482]: 0.57/0.93 (in( 0.57/0.93 X482,X474) => 0.57/0.93 (( 0.57/0.93 X480 = 0.57/0.93 X482) => 0.57/0.93 (X476( 0.57/0.93 X480) <=> 0.57/0.93 X478( 0.57/0.93 X482))))))) => 0.57/0.93 (dsetconstr( 0.57/0.93 X472, 0.57/0.93 ^[V_11]: 0.57/0.93 X476( 0.57/0.93 V_11)) = 0.57/0.93 dsetconstr( 0.57/0.93 X474, 0.57/0.93 ^[V_12]: 0.57/0.93 X478( 0.57/0.93 V_12))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X484, 0.57/0.93 X486]: 0.57/0.93 (( 0.57/0.93 ![X488]: 0.57/0.93 (in( 0.57/0.93 X488,X484) => 0.57/0.93 in( 0.57/0.93 X488,X486))) => 0.57/0.93 subset( 0.57/0.93 X484,X486))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X490, 0.57/0.93 X492]: 0.57/0.93 (( 0.57/0.93 X490 = 0.57/0.93 X492) => 0.57/0.93 subset( 0.57/0.93 X492,X490))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X494, 0.57/0.93 X496]: 0.57/0.93 (( 0.57/0.93 X494 = 0.57/0.93 X496) => 0.57/0.93 subset( 0.57/0.93 X494,X496))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X498, 0.57/0.93 X500]: 0.57/0.93 (( 0.57/0.93 ![X502]: 0.57/0.93 (in( 0.57/0.93 X502,X498) => 0.57/0.93 in( 0.57/0.93 X502,X500))) => 0.57/0.93 subset( 0.57/0.93 X498,X500))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X504]: 0.57/0.93 subset( 0.57/0.93 emptyset, 0.57/0.93 X504)) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X506, 0.57/0.93 X508,X510]: 0.57/0.93 (subset( 0.57/0.93 X506,X508) => 0.57/0.93 (in( 0.57/0.93 X510,X506) => 0.57/0.93 in( 0.57/0.93 X510,X508)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X512, 0.57/0.93 X514,X516]: 0.57/0.93 (subset( 0.57/0.93 X512,X514) => 0.57/0.93 (( 0.57/0.93 ~ 0.57/0.93 in( 0.57/0.93 X516,X514)) => 0.57/0.93 (~ 0.57/0.93 in( 0.57/0.93 X516,X512))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X518, 0.57/0.93 X520,X522]: 0.57/0.93 (in( 0.57/0.93 X522,X518) => 0.57/0.93 (( 0.57/0.93 ~ 0.57/0.93 in( 0.57/0.93 X522,X520)) => 0.57/0.93 (~ 0.57/0.93 subset( 0.57/0.93 X518,X520))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X524, 0.57/0.93 X526]: 0.57/0.93 (( 0.57/0.93 ~ 0.57/0.93 subset( 0.57/0.93 X524,X526)) => 0.57/0.93 (X524 != 0.57/0.93 X526))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X528, 0.57/0.93 X530,X532]: 0.57/0.93 (in( 0.57/0.93 X532,X528) => 0.57/0.93 (( 0.57/0.93 ~ 0.57/0.93 in( 0.57/0.93 X532,X530)) => 0.57/0.93 (X528 != 0.57/0.93 X530)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X534]: 0.57/0.93 subset( 0.57/0.93 X534,X534)) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X536, 0.57/0.93 X538,X540]: 0.57/0.93 (subset( 0.57/0.93 X536,X538) => 0.57/0.93 (subset( 0.57/0.93 X538,X540) => 0.57/0.93 subset( 0.57/0.93 X536,X540)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X542, 0.57/0.93 X544]: 0.57/0.93 subset( 0.57/0.93 X544, 0.57/0.93 setadjoin( 0.57/0.93 X542,X544))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X546, 0.57/0.93 X548,X550]: 0.57/0.93 (subset( 0.57/0.93 X546,X550) => 0.57/0.93 subset( 0.57/0.93 X546, 0.57/0.93 setadjoin( 0.57/0.93 X548,X550)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X552, 0.57/0.93 X554]: 0.57/0.93 (subset( 0.57/0.93 X552,X554) => 0.57/0.93 in( 0.57/0.93 X552, 0.57/0.93 powerset( 0.57/0.93 X554)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X556, 0.57/0.93 X558]: 0.57/0.93 (subset( 0.57/0.93 X556,X558) => 0.57/0.93 (subset( 0.57/0.93 X558,X556) => 0.57/0.93 (X556 = 0.57/0.93 X558)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X560]: 0.57/0.93 (subset( 0.57/0.93 X560, 0.57/0.93 emptyset) => 0.57/0.93 (X560 = 0.57/0.93 emptyset))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X562, 0.57/0.93 X564]: 0.57/0.93 (subset( 0.57/0.93 X564,X562) => 0.57/0.93 in( 0.57/0.93 X564, 0.57/0.93 powerset( 0.57/0.93 X562)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X566, 0.57/0.93 X568]: 0.57/0.93 (in( 0.57/0.93 X568, 0.57/0.93 powerset( 0.57/0.93 X566)) => 0.57/0.93 subset( 0.57/0.93 X568,X566))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X570]: 0.57/0.93 in( 0.57/0.93 X570, 0.57/0.93 powerset( 0.57/0.93 X570))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X572, 0.57/0.93 X574]: 0.57/0.93 (subset( 0.57/0.93 X572,X574) => 0.57/0.93 subset( 0.57/0.93 powerset( 0.57/0.93 X572), 0.57/0.93 powerset( 0.57/0.93 X574)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X576, 0.57/0.93 X578:( 0.57/0.93 ( 0.57/0.93 $i > $o))]: 0.57/0.93 in( 0.57/0.93 dsetconstr( 0.57/0.93 X576, 0.57/0.93 ^[V_13]: 0.57/0.93 X578( 0.57/0.93 V_13)), 0.57/0.93 powerset( 0.57/0.93 X576))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X580, 0.57/0.93 X582:( 0.57/0.93 ( 0.57/0.93 $i > $o))]: 0.57/0.93 subset( 0.57/0.93 dsetconstr( 0.57/0.93 X580, 0.57/0.93 ^[V_14]: 0.57/0.93 X582( 0.57/0.93 V_14)), 0.57/0.93 X580)) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X584, 0.57/0.93 X586,X588]: 0.57/0.93 (in( 0.57/0.93 X588,X584) => 0.57/0.93 in( 0.57/0.93 X588, 0.57/0.93 binunion( 0.57/0.93 X584,X586)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X590, 0.57/0.93 X592]: 0.57/0.93 in( 0.57/0.93 X592, 0.57/0.93 setadjoin( 0.57/0.93 X590, 0.57/0.93 setadjoin( 0.57/0.93 X592, 0.57/0.93 emptyset)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X594, 0.57/0.93 X596,X598]: 0.57/0.93 (in( 0.57/0.93 X598,X596) => 0.57/0.93 in( 0.57/0.93 X598, 0.57/0.93 binunion( 0.57/0.93 X594,X596)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X600, 0.57/0.93 X602, 0.57/0.93 X604, 0.57/0.93 X606:$o]: 0.57/0.93 (in( 0.57/0.93 X604, 0.57/0.93 binunion( 0.57/0.93 X600,X602)) => 0.57/0.93 (( 0.57/0.93 in( 0.57/0.93 X604,X600) => 0.57/0.93 X606) => 0.57/0.93 (( 0.57/0.93 in( 0.57/0.93 X604,X602) => 0.57/0.93 X606) => 0.57/0.93 X606)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X608, 0.57/0.93 X610,X612]: 0.57/0.93 (in( 0.57/0.93 X612, 0.57/0.93 binunion( 0.57/0.93 X608,X610)) => 0.57/0.93 (in( 0.57/0.93 X612,X610) | 0.57/0.93 in( 0.57/0.93 X612,X608)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X614, 0.57/0.93 X616]: 0.57/0.93 subset( 0.57/0.93 X614, 0.57/0.93 binunion( 0.57/0.93 X614,X616))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X618, 0.57/0.93 X620]: 0.57/0.93 subset( 0.57/0.93 X620, 0.57/0.93 binunion( 0.57/0.93 X618,X620))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X622, 0.57/0.93 X624,X626]: 0.57/0.93 (in( 0.57/0.93 X626,X622) => 0.57/0.93 (in( 0.57/0.93 X626,X624) => 0.57/0.93 in( 0.57/0.93 X626, 0.57/0.93 binintersect( 0.57/0.93 X622,X624))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X628, 0.57/0.93 X630,X632]: 0.57/0.93 (subset( 0.57/0.93 X632,X628) => 0.57/0.93 (subset( 0.57/0.93 X632,X630) => 0.57/0.93 subset( 0.57/0.93 X632, 0.57/0.93 binintersect( 0.57/0.93 X628,X630))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X634, 0.57/0.93 X636,X638]: 0.57/0.93 (in( 0.57/0.93 X638, 0.57/0.93 binintersect( 0.57/0.93 X634,X636)) => 0.57/0.93 in( 0.57/0.93 X638,X634))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X640, 0.57/0.93 X642]: 0.57/0.93 subset( 0.57/0.93 binintersect( 0.57/0.93 X640,X642), 0.57/0.93 X640)) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X644, 0.57/0.93 X646]: 0.57/0.93 (subset( 0.57/0.93 X644,X646) => 0.57/0.93 (binintersect( 0.57/0.93 X644,X646) = 0.57/0.93 X644))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X648, 0.57/0.93 X650]: 0.57/0.93 (( 0.57/0.93 binintersect( 0.57/0.93 X648,X650) = 0.57/0.93 X650) => 0.57/0.93 subset( 0.57/0.93 X650,X648))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X652, 0.57/0.93 X654,X656]: 0.57/0.93 (in( 0.57/0.93 X656, 0.57/0.93 binintersect( 0.57/0.93 X652,X654)) => 0.57/0.93 in( 0.57/0.93 X656,X654))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X658, 0.57/0.93 X660]: 0.57/0.93 (( 0.57/0.93 ~ 0.57/0.93 ( 0.57/0.93 ?[X662]: 0.57/0.93 (in( 0.57/0.93 X662,X658) & 0.57/0.93 in( 0.57/0.93 X662,X660)))) => 0.57/0.93 (binintersect( 0.57/0.93 X658,X660) = 0.57/0.93 emptyset))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X664, 0.57/0.93 X666]: 0.57/0.93 subset( 0.57/0.93 binintersect( 0.57/0.93 X664,X666), 0.57/0.93 X666)) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X668, 0.57/0.93 X670]: 0.57/0.93 (subset( 0.57/0.93 X670,X668) => 0.57/0.93 (binintersect( 0.57/0.93 X668,X670) = 0.57/0.93 X670))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X672, 0.57/0.93 X674]: 0.57/0.93 (( 0.57/0.93 binintersect( 0.57/0.93 X672,X674) = 0.57/0.93 X672) => 0.57/0.93 subset( 0.57/0.93 X672,X674))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X676, 0.57/0.93 X678,X680]: 0.57/0.93 (binintersect( 0.57/0.93 X676, 0.57/0.93 binunion( 0.57/0.93 X678,X680)) = 0.57/0.93 binunion( 0.57/0.93 binintersect( 0.57/0.93 X676,X678), 0.57/0.93 binintersect( 0.57/0.93 X676,X680)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X682, 0.57/0.93 X684,X686]: 0.57/0.93 (in( 0.57/0.93 X686,X682) => 0.57/0.93 (( 0.57/0.93 ~ 0.57/0.93 in( 0.57/0.93 X686,X684)) => 0.57/0.93 in( 0.57/0.93 X686, 0.57/0.93 setminus( 0.57/0.93 X682,X684))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X688, 0.57/0.93 X690,X692]: 0.57/0.93 (in( 0.57/0.93 X692, 0.57/0.93 setminus( 0.57/0.93 X688,X690)) => 0.57/0.93 in( 0.57/0.93 X692,X688))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X694, 0.57/0.93 X696,X698]: 0.57/0.93 (in( 0.57/0.93 X698, 0.57/0.93 setminus( 0.57/0.93 X694,X696)) => 0.57/0.93 (~ 0.57/0.93 in( 0.57/0.93 X698,X696)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X700, 0.57/0.93 X702]: 0.57/0.93 (subset( 0.57/0.93 X700,X702) => 0.57/0.93 (setminus( 0.57/0.93 X700,X702) = 0.57/0.93 emptyset))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X704, 0.57/0.93 X706,X708]: 0.57/0.93 (( 0.57/0.93 ~ 0.57/0.93 in( 0.57/0.93 X708, 0.57/0.93 setminus( 0.57/0.93 X704,X706))) => 0.57/0.93 (in( 0.57/0.93 X708,X704) => 0.57/0.93 in( 0.57/0.93 X708,X706)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X710, 0.57/0.93 X712,X714]: 0.57/0.93 (( 0.57/0.93 ~ 0.57/0.93 in( 0.57/0.93 X714, 0.57/0.93 setminus( 0.57/0.93 X710,X712))) => 0.57/0.93 (( 0.57/0.93 ~ 0.57/0.93 in( 0.57/0.93 X714,X712)) => 0.57/0.93 (~ 0.57/0.93 in( 0.57/0.93 X714,X710))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X716, 0.57/0.93 X718,X720]: 0.57/0.93 (( 0.57/0.93 ~ 0.57/0.93 in( 0.57/0.93 X720,X716)) => 0.57/0.93 (~ 0.57/0.93 in( 0.57/0.93 X720, 0.57/0.93 setminus( 0.57/0.93 X716,X718))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X722, 0.57/0.93 X724,X726]: 0.57/0.93 (in( 0.57/0.93 X726,X724) => 0.57/0.93 (~ 0.57/0.93 in( 0.57/0.93 X726, 0.57/0.93 setminus( 0.57/0.93 X722,X724))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X728, 0.57/0.93 X730]: 0.57/0.93 subset( 0.57/0.93 setminus( 0.57/0.93 X728,X730), 0.57/0.93 X728)) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X732, 0.57/0.93 X734]: 0.57/0.93 (( 0.57/0.93 setminus( 0.57/0.93 X732,X734) = 0.57/0.93 emptyset) => 0.57/0.93 subset( 0.57/0.93 X732,X734))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X736, 0.57/0.93 X738,X740]: 0.57/0.93 (in( 0.57/0.93 X740, 0.57/0.93 symdiff( 0.57/0.93 X736,X738)) => 0.57/0.93 (![X742:$o]: 0.57/0.93 (( 0.57/0.93 in( 0.57/0.93 X740,X736) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ~ 0.57/0.93 in( 0.57/0.93 X740,X738)) => 0.57/0.93 X742)) => 0.57/0.93 (( 0.57/0.93 ( 0.57/0.93 ~ 0.57/0.93 in( 0.57/0.93 X740,X736)) => 0.57/0.93 ( 0.57/0.93 in( 0.57/0.93 X740,X738) => 0.57/0.93 X742)) => 0.57/0.93 X742))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X744, 0.57/0.93 X746,X748]: 0.57/0.93 (in( 0.57/0.93 X748,X744) => 0.57/0.93 (( 0.57/0.93 ~ 0.57/0.93 in( 0.57/0.93 X748,X746)) => 0.57/0.93 in( 0.57/0.93 X748, 0.57/0.93 symdiff( 0.57/0.93 X744,X746))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X750, 0.57/0.93 X752,X754]: 0.57/0.93 (( 0.57/0.93 ~ 0.57/0.93 in( 0.57/0.93 X754,X750)) => 0.57/0.93 (in( 0.57/0.93 X754,X752) => 0.57/0.93 in( 0.57/0.93 X754, 0.57/0.93 symdiff( 0.57/0.93 X750,X752))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X756, 0.57/0.93 X758,X760]: 0.57/0.93 (in( 0.57/0.93 X760,X756) => 0.57/0.93 (in( 0.57/0.93 X760,X758) => 0.57/0.93 (~ 0.57/0.93 in( 0.57/0.93 X760, 0.57/0.93 symdiff( 0.57/0.93 X756,X758)))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X762, 0.57/0.93 X764,X766]: 0.57/0.93 (( 0.57/0.93 ~ 0.57/0.93 in( 0.57/0.93 X766,X762)) => 0.57/0.93 (( 0.57/0.93 ~ 0.57/0.93 in( 0.57/0.93 X766,X764)) => 0.57/0.93 (~ 0.57/0.93 in( 0.57/0.93 X766, 0.57/0.93 symdiff( 0.57/0.93 X762,X764)))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X768, 0.57/0.93 X770]: 0.57/0.93 in( 0.57/0.93 X770, 0.57/0.93 setadjoin( 0.57/0.93 X768, 0.57/0.93 setadjoin( 0.57/0.93 X770, 0.57/0.93 emptyset)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X772, 0.57/0.93 X774]: 0.57/0.93 in( 0.57/0.93 X772, 0.57/0.93 setunion( 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X772, 0.57/0.93 emptyset), 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X772, 0.57/0.93 setadjoin( 0.57/0.93 X774, 0.57/0.93 emptyset)), 0.57/0.93 emptyset))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X776, 0.57/0.93 X778]: 0.57/0.93 in( 0.57/0.93 X778, 0.57/0.93 setunion( 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X776, 0.57/0.93 emptyset), 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X776, 0.57/0.93 setadjoin( 0.57/0.93 X778, 0.57/0.93 emptyset)), 0.57/0.93 emptyset))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X780, 0.57/0.93 X782]: 0.57/0.93 iskpair( 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X780, 0.57/0.93 emptyset), 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X780, 0.57/0.93 setadjoin( 0.57/0.93 X782, 0.57/0.93 emptyset)), 0.57/0.93 emptyset)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X784, 0.57/0.93 X786]: 0.57/0.93 iskpair( 0.57/0.93 kpair( 0.57/0.93 X784,X786))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X788, 0.57/0.93 X790]: 0.57/0.93 (in( 0.57/0.93 X790,X788) => 0.57/0.93 subset( 0.57/0.93 setadjoin( 0.57/0.93 X790, 0.57/0.93 emptyset), 0.57/0.93 X788))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X792, 0.57/0.93 X794]: 0.57/0.93 (in( 0.57/0.93 X794,X792) => 0.57/0.93 in( 0.57/0.93 setadjoin( 0.57/0.93 X794, 0.57/0.93 emptyset), 0.57/0.93 powerset( 0.57/0.93 X792)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X796, 0.57/0.93 X798,X800]: 0.57/0.93 (in( 0.57/0.93 X800,X796) => 0.57/0.93 in( 0.57/0.93 setadjoin( 0.57/0.93 X800, 0.57/0.93 emptyset), 0.57/0.93 powerset( 0.57/0.93 binunion( 0.57/0.93 X796,X798))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X802, 0.57/0.93 X804,X806]: 0.57/0.93 (in( 0.57/0.93 X806, 0.57/0.93 setadjoin( 0.57/0.93 X802, 0.57/0.93 setadjoin( 0.57/0.93 X804, 0.57/0.93 emptyset))) => 0.57/0.93 (( 0.57/0.93 X806 = 0.57/0.93 X804) | 0.57/0.93 (X806 = 0.57/0.93 X802)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X808, 0.57/0.93 X810,X812]: 0.57/0.93 (in( 0.57/0.93 X812,X808) => 0.57/0.93 (![X814]: 0.57/0.93 (in( 0.57/0.93 X814,X810) => 0.57/0.93 subset( 0.57/0.93 setadjoin( 0.57/0.93 X812, 0.57/0.93 setadjoin( 0.57/0.93 X814, 0.57/0.93 emptyset)), 0.57/0.93 binunion( 0.57/0.93 X808,X810)))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X816, 0.57/0.93 X818,X820]: 0.57/0.93 (in( 0.57/0.93 X820,X816) => 0.57/0.93 (![X822]: 0.57/0.93 (in( 0.57/0.93 X822,X818) => 0.57/0.93 in( 0.57/0.93 setadjoin( 0.57/0.93 X820, 0.57/0.93 setadjoin( 0.57/0.93 X822, 0.57/0.93 emptyset)), 0.57/0.93 powerset( 0.57/0.93 binunion( 0.57/0.93 X816,X818))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X824, 0.57/0.93 X826,X828]: 0.57/0.93 (in( 0.57/0.93 X828,X824) => 0.57/0.93 (![X830]: 0.57/0.93 (in( 0.57/0.93 X830,X826) => 0.57/0.93 subset( 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X828, 0.57/0.93 emptyset), 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X828, 0.57/0.93 setadjoin( 0.57/0.93 X830, 0.57/0.93 emptyset)), 0.57/0.93 emptyset)), 0.57/0.93 powerset( 0.57/0.93 binunion( 0.57/0.93 X824,X826))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X832, 0.57/0.93 X834,X836]: 0.57/0.93 (in( 0.57/0.93 X836,X832) => 0.57/0.93 (![X838]: 0.57/0.93 (in( 0.57/0.93 X838,X834) => 0.57/0.93 in( 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X836, 0.57/0.93 emptyset), 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X836, 0.57/0.93 setadjoin( 0.57/0.93 X838, 0.57/0.93 emptyset)), 0.57/0.93 emptyset)), 0.57/0.93 powerset( 0.57/0.93 powerset( 0.57/0.93 binunion( 0.57/0.93 X832,X834)))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X840, 0.57/0.93 X842,X844]: 0.57/0.93 (in( 0.57/0.93 X844,X840) => 0.57/0.93 (![X846]: 0.57/0.93 (in( 0.57/0.93 X846,X842) => 0.57/0.93 in( 0.57/0.93 kpair( 0.57/0.93 X844,X846), 0.57/0.93 powerset( 0.57/0.93 powerset( 0.57/0.93 binunion( 0.57/0.93 X840,X842)))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X848, 0.57/0.93 X850,X852]: 0.57/0.93 (in( 0.57/0.93 X852,X848) => 0.57/0.93 (![X854]: 0.57/0.93 (in( 0.57/0.93 X854,X850) => 0.57/0.93 in( 0.57/0.93 kpair( 0.57/0.93 X852,X854), 0.57/0.93 cartprod( 0.57/0.93 X848,X850)))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X856, 0.57/0.93 X858,X860]: 0.57/0.93 (in( 0.57/0.93 X860, 0.57/0.93 cartprod( 0.57/0.93 X856,X858)) => 0.57/0.93 (?[X862]: 0.57/0.93 (in( 0.57/0.93 X862,X856) & 0.57/0.93 (?[X864]: 0.57/0.93 (in( 0.57/0.93 X864,X858) & 0.57/0.93 (X860 = 0.57/0.93 kpair( 0.57/0.93 X862,X864)))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X866, 0.57/0.93 X868,X870]: 0.57/0.93 (in( 0.57/0.93 X870, 0.57/0.93 cartprod( 0.57/0.93 X866,X868)) => 0.57/0.93 iskpair( 0.57/0.93 X870))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X872, 0.57/0.93 X874]: 0.57/0.93 (in( 0.57/0.93 X874, 0.57/0.93 setunion( 0.57/0.93 X872)) => 0.57/0.93 (?[X876]: 0.57/0.93 (in( 0.57/0.93 X876,X872) & 0.57/0.93 in( 0.57/0.93 X874,X876))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X878]: 0.57/0.93 subset( 0.57/0.93 setunion( 0.57/0.93 setadjoin( 0.57/0.93 X878, 0.57/0.93 emptyset)), 0.57/0.93 X878)) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X880]: 0.57/0.93 subset( 0.57/0.93 X880, 0.57/0.93 setunion( 0.57/0.93 setadjoin( 0.57/0.93 X880, 0.57/0.93 emptyset)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X882]: 0.57/0.93 (setunion( 0.57/0.93 setadjoin( 0.57/0.93 X882, 0.57/0.93 emptyset)) = 0.57/0.93 X882)) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X884, 0.57/0.93 X886:( 0.57/0.93 ( 0.57/0.93 $i > $o))]: 0.57/0.93 (( 0.57/0.93 ![X888]: 0.57/0.93 (in( 0.57/0.93 X888,X884) => 0.57/0.93 (![X890]: 0.57/0.93 (in( 0.57/0.93 X890,X884) => 0.57/0.93 (X886( 0.57/0.93 X888) => 0.57/0.93 (X886( 0.57/0.93 X890) => 0.57/0.93 (X888 = 0.57/0.93 X890))))))) => 0.57/0.93 (( 0.57/0.93 ?[X892]: 0.57/0.93 (in( 0.57/0.93 X892,X884) & 0.57/0.93 X886( 0.57/0.93 X892))) => 0.57/0.93 (?[X894]: 0.57/0.93 (in( 0.57/0.93 X894, 0.57/0.93 dsetconstr( 0.57/0.93 X884, 0.57/0.93 ^[V_16]: 0.57/0.93 X886( 0.57/0.93 V_16))) & 0.57/0.93 (dsetconstr( 0.57/0.93 X884, 0.57/0.93 ^[V_15]: 0.57/0.93 X886( 0.57/0.93 V_15)) = 0.57/0.93 setadjoin( 0.57/0.93 X894, 0.57/0.93 emptyset))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X896, 0.57/0.93 X898:( 0.57/0.93 ( 0.57/0.93 $i > $o))]: 0.57/0.93 (( 0.57/0.93 ?[X900]: 0.57/0.93 (in( 0.57/0.93 X900, 0.57/0.93 dsetconstr( 0.57/0.93 X896, 0.57/0.93 ^[V_18]: 0.57/0.93 X898( 0.57/0.93 V_18))) & 0.57/0.93 (dsetconstr( 0.57/0.93 X896, 0.57/0.93 ^[V_17]: 0.57/0.93 X898( 0.57/0.93 V_17)) = 0.57/0.93 setadjoin( 0.57/0.93 X900, 0.57/0.93 emptyset)))) => 0.57/0.93 (?[X902]: 0.57/0.93 (in( 0.57/0.93 X902,X896) & 0.57/0.93 X898( 0.57/0.93 X902))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X904, 0.57/0.93 X906:( 0.57/0.93 ( 0.57/0.93 $i > $o)), 0.57/0.93 X908]: 0.57/0.93 (in( 0.57/0.93 X908,X904) => 0.57/0.93 (X906( 0.57/0.93 X908) => 0.57/0.93 (( 0.57/0.93 ![X910]: 0.57/0.93 (in( 0.57/0.93 X910,X904) => 0.57/0.93 (X906( 0.57/0.93 X910) => 0.57/0.93 (X910 = 0.57/0.93 X908)))) => 0.57/0.93 (?[X912]: 0.57/0.93 (in( 0.57/0.93 X912, 0.57/0.93 dsetconstr( 0.57/0.93 X904, 0.57/0.93 ^[V_20]: 0.57/0.93 X906( 0.57/0.93 V_20))) & 0.57/0.93 (dsetconstr( 0.57/0.93 X904, 0.57/0.93 ^[V_19]: 0.57/0.93 X906( 0.57/0.93 V_19)) = 0.57/0.93 setadjoin( 0.57/0.93 X912, 0.57/0.93 emptyset)))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X914, 0.57/0.93 X916:( 0.57/0.93 ( 0.57/0.93 $i > $o))]: 0.57/0.93 (( 0.57/0.93 ![X918]: 0.57/0.93 (in( 0.57/0.93 X918,X914) => 0.57/0.93 (![X920]: 0.57/0.93 (in( 0.57/0.93 X920,X914) => 0.57/0.93 (X916( 0.57/0.93 X918) => 0.57/0.93 (X916( 0.57/0.93 X920) => 0.57/0.93 (X918 = 0.57/0.93 X920))))))) => 0.57/0.93 (( 0.57/0.93 ?[X922]: 0.57/0.93 (in( 0.57/0.93 X922,X914) & 0.57/0.93 X916( 0.57/0.93 X922))) => 0.57/0.93 (?[X924]: 0.57/0.93 (in( 0.57/0.93 X924, 0.57/0.93 dsetconstr( 0.57/0.93 X914, 0.57/0.93 ^[V_22]: 0.57/0.93 X916( 0.57/0.93 V_22))) & 0.57/0.93 (dsetconstr( 0.57/0.93 X914, 0.57/0.93 ^[V_21]: 0.57/0.93 X916( 0.57/0.93 V_21)) = 0.57/0.93 setadjoin( 0.57/0.93 X924, 0.57/0.93 emptyset))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X926, 0.57/0.93 X928]: 0.57/0.93 (( 0.57/0.93 setadjoin( 0.57/0.93 X926, 0.57/0.93 emptyset) = 0.57/0.93 setadjoin( 0.57/0.93 X928, 0.57/0.93 emptyset)) => 0.57/0.93 (X926 = 0.57/0.93 X928))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X930, 0.57/0.93 X932,X934]: 0.57/0.93 (in( 0.57/0.93 setadjoin( 0.57/0.93 X934, 0.57/0.93 emptyset), 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X930, 0.57/0.93 emptyset), 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X930, 0.57/0.93 setadjoin( 0.57/0.93 X932, 0.57/0.93 emptyset)), 0.57/0.93 emptyset))) => 0.57/0.93 (X930 = 0.57/0.93 X934))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X936]: 0.57/0.93 (iskpair( 0.57/0.93 X936) => 0.57/0.93 (?[X938]: 0.57/0.93 (in( 0.57/0.93 X938, 0.57/0.93 dsetconstr( 0.57/0.93 setunion( 0.57/0.93 X936), 0.57/0.93 ^[V_24]: 0.57/0.93 in( 0.57/0.93 setadjoin( 0.57/0.93 V_24, 0.57/0.93 emptyset), 0.57/0.93 X936))) & 0.57/0.93 (dsetconstr( 0.57/0.93 setunion( 0.57/0.93 X936), 0.57/0.93 ^[V_23]: 0.57/0.93 in( 0.57/0.93 setadjoin( 0.57/0.93 V_23, 0.57/0.93 emptyset), 0.57/0.93 X936)) = 0.57/0.93 setadjoin( 0.57/0.93 X938, 0.57/0.93 emptyset)))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X940]: 0.57/0.93 (( 0.57/0.93 ?[X942]: 0.57/0.93 (in( 0.57/0.93 X942,X940) & 0.57/0.93 (X940 = 0.57/0.93 setadjoin( 0.57/0.93 X942, 0.57/0.93 emptyset)))) => 0.57/0.93 in( 0.57/0.93 setunion( 0.57/0.93 X940), 0.57/0.93 X940))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X944, 0.57/0.93 X946]: 0.57/0.93 (kfst( 0.57/0.93 kpair( 0.57/0.93 X944,X946)) = 0.57/0.93 X944)) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X948, 0.57/0.93 X950,X952]: 0.57/0.93 (in( 0.57/0.93 X952, 0.57/0.93 cartprod( 0.57/0.93 X948,X950)) => 0.57/0.93 in( 0.57/0.93 kfst( 0.57/0.93 X952), 0.57/0.93 X948))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X954, 0.57/0.93 X956, 0.57/0.93 X958,X960]: 0.57/0.93 (( 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X954, 0.57/0.93 emptyset), 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X954, 0.57/0.93 setadjoin( 0.57/0.93 X956, 0.57/0.93 emptyset)), 0.57/0.93 emptyset)) = 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X958, 0.57/0.93 emptyset), 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X958, 0.57/0.93 setadjoin( 0.57/0.93 X960, 0.57/0.93 emptyset)), 0.57/0.93 emptyset))) => 0.57/0.93 (X954 = 0.57/0.93 X958))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X962, 0.57/0.93 X964, 0.57/0.93 X966,X968]: 0.57/0.93 (( 0.57/0.93 kpair( 0.57/0.93 X962,X964) = 0.57/0.93 kpair( 0.57/0.93 X966,X968)) => 0.57/0.93 (X962 = 0.57/0.93 X966))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X970, 0.57/0.93 X972]: 0.57/0.93 (( 0.57/0.93 X970 = 0.57/0.93 X972) => 0.57/0.93 (setadjoin( 0.57/0.93 X970, 0.57/0.93 setadjoin( 0.57/0.93 X972, 0.57/0.93 emptyset)) = 0.57/0.93 setadjoin( 0.57/0.93 X970, 0.57/0.93 emptyset)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X974, 0.57/0.93 X976]: 0.57/0.93 (( 0.57/0.93 X974 = 0.57/0.93 X976) => 0.57/0.93 (setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X974, 0.57/0.93 emptyset), 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X974, 0.57/0.93 setadjoin( 0.57/0.93 X976, 0.57/0.93 emptyset)), 0.57/0.93 emptyset)) = 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X974, 0.57/0.93 emptyset), 0.57/0.93 emptyset)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X978, 0.57/0.93 X980, 0.57/0.93 X982,X984]: 0.57/0.93 (( 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X978, 0.57/0.93 emptyset), 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X978, 0.57/0.93 setadjoin( 0.57/0.93 X980, 0.57/0.93 emptyset)), 0.57/0.93 emptyset)) = 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X982, 0.57/0.93 emptyset), 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X982, 0.57/0.93 setadjoin( 0.57/0.93 X984, 0.57/0.93 emptyset)), 0.57/0.93 emptyset))) => 0.57/0.93 (( 0.57/0.93 X982 = 0.57/0.93 X984) => 0.57/0.93 (X980 = 0.57/0.93 X984)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X986, 0.57/0.93 X988,X990]: 0.57/0.93 (( 0.57/0.93 setadjoin( 0.57/0.93 X986, 0.57/0.93 setadjoin( 0.57/0.93 X988, 0.57/0.93 emptyset)) = 0.57/0.93 setadjoin( 0.57/0.93 X990, 0.57/0.93 emptyset)) => 0.57/0.93 (X986 = 0.57/0.93 X988))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X992, 0.57/0.93 X994, 0.57/0.93 X996,X998]: 0.57/0.93 (( 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X992, 0.57/0.93 emptyset), 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X992, 0.57/0.93 setadjoin( 0.57/0.93 X994, 0.57/0.93 emptyset)), 0.57/0.93 emptyset)) = 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X996, 0.57/0.93 emptyset), 0.57/0.93 setadjoin( 0.57/0.93 setadjoin( 0.57/0.93 X996, 0.57/0.93 setadjoin( 0.57/0.93 X998, 0.57/0.93 emptyset)), 0.57/0.93 emptyset))) => 0.57/0.93 (X994 = 0.57/0.93 X998))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X1000, 0.57/0.93 X1002, 0.57/0.93 X1004, 0.57/0.93 X1006]: 0.57/0.93 (( 0.57/0.93 kpair( 0.57/0.93 X1000, 0.57/0.93 X1002) = 0.57/0.93 kpair( 0.57/0.93 X1004, 0.57/0.93 X1006)) => 0.57/0.93 (X1002 = 0.57/0.93 X1006))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X1008]: 0.57/0.93 (iskpair( 0.57/0.93 X1008) => 0.57/0.93 (?[X1010]: 0.57/0.93 (in( 0.57/0.93 X1010, 0.57/0.93 dsetconstr( 0.57/0.93 setunion( 0.57/0.93 X1008), 0.57/0.93 ^[V_26]: 0.57/0.93 (X1008 = 0.57/0.93 kpair( 0.57/0.93 kfst( 0.57/0.93 X1008), 0.57/0.93 V_26)))) & 0.57/0.93 (dsetconstr( 0.57/0.93 setunion( 0.57/0.93 X1008), 0.57/0.93 ^[V_25]: 0.57/0.93 (X1008 = 0.57/0.93 kpair( 0.57/0.93 kfst( 0.57/0.93 X1008), 0.57/0.93 V_25))) = 0.57/0.93 setadjoin( 0.57/0.93 X1010, 0.57/0.93 emptyset)))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X1012, 0.57/0.93 X1014]: 0.57/0.93 (ksnd( 0.57/0.93 kpair( 0.57/0.93 X1012, 0.57/0.93 X1014)) = 0.57/0.93 X1014)) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X1016]: 0.57/0.93 (iskpair( 0.57/0.93 X1016) => 0.57/0.93 (kpair( 0.57/0.93 kfst( 0.57/0.93 X1016), 0.57/0.93 ksnd( 0.57/0.93 X1016)) = 0.57/0.93 X1016))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X1018, 0.57/0.93 X1020, 0.57/0.93 X1022]: 0.57/0.93 (in( 0.57/0.93 X1022, 0.57/0.93 cartprod( 0.57/0.93 X1018, 0.57/0.93 X1020)) => 0.57/0.93 in( 0.57/0.93 ksnd( 0.57/0.93 X1022), 0.57/0.93 X1020))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X1024, 0.57/0.93 X1026, 0.57/0.93 X1028, 0.57/0.93 X1030]: 0.57/0.93 (in( 0.57/0.93 kpair( 0.57/0.93 X1028, 0.57/0.93 X1030), 0.57/0.93 cartprod( 0.57/0.93 X1024, 0.57/0.93 X1026)) => 0.57/0.93 in( 0.57/0.93 X1028, 0.57/0.93 X1024))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X1032, 0.57/0.93 X1034, 0.57/0.93 X1036, 0.57/0.93 X1038]: 0.57/0.93 (in( 0.57/0.93 kpair( 0.57/0.93 X1036, 0.57/0.93 X1038), 0.57/0.93 cartprod( 0.57/0.93 X1032, 0.57/0.93 X1034)) => 0.57/0.93 in( 0.57/0.93 X1038, 0.57/0.93 X1034))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X1040, 0.57/0.93 X1042, 0.57/0.93 X1044]: 0.57/0.93 (in( 0.57/0.93 X1044, 0.57/0.93 X1040) => 0.57/0.93 (![X1046]: 0.57/0.93 (in( 0.57/0.93 X1046, 0.57/0.93 X1042) => 0.57/0.93 (kpair( 0.57/0.93 X1044, 0.57/0.93 X1046) = 0.57/0.93 kpair( 0.57/0.93 X1044, 0.57/0.93 X1046)))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X1048, 0.57/0.93 X1050, 0.57/0.93 X1052]: 0.57/0.93 (in( 0.57/0.93 X1052, 0.57/0.93 X1048) => 0.57/0.93 (![X1054]: 0.57/0.93 (in( 0.57/0.93 X1054, 0.57/0.93 X1050) => 0.57/0.93 (kfst( 0.57/0.93 kpair( 0.57/0.93 X1052, 0.57/0.93 X1054)) = 0.57/0.93 X1052))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X1056, 0.57/0.93 X1058, 0.57/0.93 X1060]: 0.57/0.93 (in( 0.57/0.93 X1060, 0.57/0.93 X1056) => 0.57/0.93 (![X1062]: 0.57/0.93 (in( 0.57/0.93 X1062, 0.57/0.93 X1058) => 0.57/0.93 (ksnd( 0.57/0.93 kpair( 0.57/0.93 X1060, 0.57/0.93 X1062)) = 0.57/0.93 X1062))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X1064, 0.57/0.93 X1066, 0.57/0.93 X1068]: 0.57/0.93 (in( 0.57/0.93 X1068, 0.57/0.93 cartprod( 0.57/0.93 X1064, 0.57/0.93 X1066)) => 0.57/0.93 (kpair( 0.57/0.93 kfst( 0.57/0.93 X1068), 0.57/0.93 ksnd( 0.57/0.93 X1068)) = 0.57/0.93 X1068))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X1070, 0.57/0.93 X1072, 0.57/0.93 X1074:( 0.57/0.93 ($i * $i) > 0.57/0.93 $o),X1076]: 0.57/0.93 (in( 0.57/0.93 X1076, 0.57/0.93 X1070) => 0.57/0.93 (![X1078]: 0.57/0.93 (in( 0.57/0.93 X1078, 0.57/0.93 X1072) => 0.57/0.93 (X1074( 0.57/0.93 X1076, 0.57/0.93 X1078) => 0.57/0.93 in( 0.57/0.93 kpair( 0.57/0.93 X1076, 0.57/0.93 X1078), 0.57/0.93 dpsetconstr( 0.57/0.93 X1070, 0.57/0.93 X1072, 0.57/0.93 ^[V_27, 0.57/0.93 V_28]: 0.57/0.93 X1074( 0.57/0.93 V_27,V_28)))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X1080, 0.57/0.93 X1082, 0.57/0.93 X1084:( 0.57/0.93 ($i * $i) > 0.57/0.93 $o)]: 0.57/0.93 subset( 0.57/0.93 dpsetconstr( 0.57/0.93 X1080, 0.57/0.93 X1082, 0.57/0.93 ^[V_29, 0.57/0.93 V_30]: 0.57/0.93 X1084( 0.57/0.93 V_29,V_30)), 0.57/0.93 cartprod( 0.57/0.93 X1080, 0.57/0.93 X1082))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X1086, 0.57/0.93 X1088, 0.57/0.93 X1090:( 0.57/0.93 ($i * $i) > 0.57/0.93 $o)]: 0.57/0.93 subset( 0.57/0.93 dpsetconstr( 0.57/0.93 X1086, 0.57/0.93 X1088, 0.57/0.93 ^[V_31, 0.57/0.93 V_32]: 0.57/0.93 X1090( 0.57/0.93 V_31,V_32)), 0.57/0.93 cartprod( 0.57/0.93 X1086, 0.57/0.93 X1088))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X1092, 0.57/0.93 X1094, 0.57/0.93 X1096:( 0.57/0.93 ($i * $i) > 0.57/0.93 $o),X1098]: 0.57/0.93 (in( 0.57/0.93 X1098, 0.57/0.93 X1092) => 0.57/0.93 (![X1100]: 0.57/0.93 (in( 0.57/0.93 X1100, 0.57/0.93 X1094) => 0.57/0.93 (in( 0.57/0.93 kpair( 0.57/0.93 X1098, 0.57/0.93 X1100), 0.57/0.93 dpsetconstr( 0.57/0.93 X1092, 0.57/0.93 X1094, 0.57/0.93 ^[V_33, 0.57/0.93 V_34]: 0.57/0.93 X1096( 0.57/0.93 V_33,V_34))) => 0.57/0.93 X1096( 0.57/0.93 X1098, 0.57/0.93 X1100)))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X1102, 0.57/0.93 X1104, 0.57/0.93 X1106:( 0.57/0.93 ($i * $i) > 0.57/0.93 $o), 0.57/0.93 X1108, 0.57/0.93 X1110]: 0.57/0.93 (in( 0.57/0.93 kpair( 0.57/0.93 X1108, 0.57/0.93 X1110), 0.57/0.93 dpsetconstr( 0.57/0.93 X1102, 0.57/0.93 X1104, 0.57/0.93 ^[V_35, 0.57/0.93 V_36]: 0.57/0.93 X1106( 0.57/0.93 V_35,V_36))) => 0.57/0.93 in( 0.57/0.93 X1108, 0.57/0.93 X1102))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X1112, 0.57/0.93 X1114, 0.57/0.93 X1116:( 0.57/0.93 ($i * $i) > 0.57/0.93 $o), 0.57/0.93 X1118, 0.57/0.93 X1120]: 0.57/0.93 (in( 0.57/0.93 kpair( 0.57/0.93 X1118, 0.57/0.93 X1120), 0.57/0.93 dpsetconstr( 0.57/0.93 X1112, 0.57/0.93 X1114, 0.57/0.93 ^[V_37, 0.57/0.93 V_38]: 0.57/0.93 X1116( 0.57/0.93 V_37,V_38))) => 0.57/0.93 in( 0.57/0.93 X1120, 0.57/0.93 X1114))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X1122, 0.57/0.93 X1124, 0.57/0.93 X1126:( 0.57/0.93 ($i * $i) > 0.57/0.93 $o), 0.57/0.93 X1128, 0.57/0.93 X1130]: 0.57/0.93 (in( 0.57/0.93 kpair( 0.57/0.93 X1128, 0.57/0.93 X1130), 0.57/0.93 dpsetconstr( 0.57/0.93 X1122, 0.57/0.93 X1124, 0.57/0.93 ^[V_39, 0.57/0.93 V_40]: 0.57/0.93 X1126( 0.57/0.93 V_39,V_40))) => 0.57/0.93 X1126( 0.57/0.93 X1128, 0.57/0.93 X1130))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 ![X1132, 0.57/0.93 X1134, 0.57/0.93 X1136]: 0.57/0.93 (( 0.57/0.93 ( 0.57/0.93 ![X1138]: 0.57/0.93 (in( 0.57/0.93 X1138, 0.57/0.93 X1132) => 0.57/0.93 (?[X1140]: 0.57/0.93 (in( 0.57/0.93 X1140, 0.57/0.93 dsetconstr( 0.57/0.93 X1134, 0.57/0.93 ^[V_42]: 0.57/0.93 in( 0.57/0.93 kpair( 0.57/0.93 X1138, 0.57/0.93 V_42), 0.57/0.93 X1136))) & 0.57/0.93 (dsetconstr( 0.57/0.93 X1134, 0.57/0.93 ^[V_41]: 0.57/0.93 in( 0.57/0.93 kpair( 0.57/0.93 X1138, 0.57/0.93 V_41), 0.57/0.93 X1136)) = 0.57/0.93 setadjoin( 0.57/0.93 X1140, 0.57/0.93 emptyset)))))) & 0.57/0.93 subset( 0.57/0.93 X1136, 0.57/0.93 cartprod( 0.57/0.93 X1132, 0.57/0.93 X1134))) => 0.57/0.93 (![X1142]: 0.57/0.93 (in( 0.57/0.93 X1142, 0.57/0.93 X1132) => 0.57/0.93 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$true)) = 0.57/0.93 Y0)))) => 0.57/0.93 ((!!((^[Y0 : $i]: 0.57/0.93 (!!((^[Y1 : $i]: 0.57/0.93 ((!!((^[Y2 : $i]: 0.57/0.93 (in(Y2, Y1) => 0.57/0.93 in(Y2, Y0))))) => 0.57/0.93 in(Y1, powerset(Y0))))))))) => 0.57/0.93 ((!!((^[Y0 : $i]: 0.57/0.93 in(emptyset, powerset(Y0))))) => 0.57/0.93 ((!!((^[Y0 : $i]: 0.57/0.93 in(emptyset, powerset(Y0))))) => 0.57/0.93 ((!!((^[Y0 : $i]: 0.57/0.93 (!!((^[Y1 : $i]: 0.57/0.93 (!!((^[Y2 : $i]: 0.57/0.93 (in(Y1, 0.57/0.93 powerset( 0.57/0.93 Y0)) => 0.57/0.93 (in(Y2, Y1) => 0.57/0.93 in(Y2, Y0)))))))))))) => 0.57/0.93 ((!!((^[Y0 : $i]: 0.57/0.93 (!!((^[Y1 : $i]: 0.57/0.93 (!!((^[Y2 : $i]: 0.57/0.93 (in(Y1, Y2) => 0.57/0.93 (in(Y2, 0.57/0.93 Y0) => 0.57/0.93 in(Y1, 0.57/0.93 setunion( 0.57/0.93 Y0))))))))))))) => 0.57/0.93 ((!!((^[Y0 : $i]: 0.57/0.93 (!!((^[Y1 : $i]: 0.57/0.93 (in(Y1, 0.57/0.93 setunion(Y0)) => 0.57/0.93 (!!((^[Y2 : $o]: 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 !!(( 0.57/0.93 ^[Y3 : $i]: 0.57/0.93 (in(Y1, 0.57/0.93 Y3) => 0.57/0.93 (in(Y3, 0.57/0.93 Y0) => Y2))))) => 0.57/0.93 Y2))))))))))) => 0.57/0.93 ((!!((^[Y0 : $i]: 0.57/0.93 (!!((^[Y1 : $i]: 0.57/0.93 (in(Y1, Y0) => 0.57/0.93 in(Y1, 0.57/0.93 powerset( 0.57/0.93 setunion( 0.57/0.93 Y0)))))))))) => 0.57/0.93 ((!!((^[Y0 : $i > $o]: 0.57/0.93 ((??((^[Y1 : $i]: 0.57/0.93 (Y0(Y1) & 0.57/0.93 (!!(( 0.57/0.93 ^[Y2 : $i]: 0.57/0.93 (Y0(Y2) => 0.57/0.93 ( 0.57/0.93 Y1 = Y2))))))))) => 0.57/0.93 (??((^[Y1 : $i]: 0.57/0.93 (!!((^[Y2 : $i]: 0.57/0.93 (Y0(Y2) <=> 0.57/0.93 (Y2 = Y1)))))))))))) => 0.57/0.93 ((!!((^[Y0 : $i]: 0.57/0.93 ((Y0 != emptyset) => 0.57/0.93 (??((^[Y1 : $i]: 0.57/0.93 in(Y1, Y0)))))))) => 0.57/0.93 ((!!((^[Y0 : $i]: 0.57/0.93 (!!((^[Y1 : $i]: 0.57/0.93 (in(Y0, 0.57/0.93 setadjoin( 0.57/0.93 Y1, 0.57/0.93 emptyset)) => 0.57/0.93 (Y0 = Y1)))))))) => 0.57/0.93 ((!!((^[Y0 : $i]: 0.57/0.93 (!!((^[Y1 : $i]: 0.57/0.93 ((Y0 != Y1) => 0.57/0.93 (~( 0.57/0.93 in(Y1, 0.57/0.93 setadjoin( 0.57/0.93 Y0, 0.57/0.93 emptyset))))))))))) => 0.57/0.93 ((!!((^[Y0 : $i]: 0.57/0.93 (!!((^[Y1 : $i]: 0.57/0.93 ((Y0 = Y1) => 0.57/0.93 in(Y0, 0.57/0.93 setadjoin( 0.57/0.93 Y1, 0.57/0.93 emptyset))))))))) => 0.57/0.93 ((!!((^[Y0 : $i]: 0.57/0.93 (!!((^[Y1 : $i]: 0.57/0.93 (in(Y0, 0.57/0.93 setadjoin( 0.57/0.93 Y1, 0.57/0.93 emptyset)) => 0.57/0.93 in(Y1, 0.57/0.93 setadjoin( 0.57/0.93 Y0, 0.57/0.93 emptyset))))))))) => 0.57/0.93 ((!!((^[Y0 : $i]: 0.57/0.93 (!!((^[Y1 : $i]: 0.57/0.93 ( 0.57/0.93 !!(( 0.57/0.93 ^[Y2 : $i]: 0.57/0.93 (in(Y2, 0.57/0.93 setadjoin( 0.57/0.93 Y0, 0.57/0.93 setadjoin( 0.57/0.93 Y1, 0.57/0.93 emptyset))) => 0.57/0.93 (( 0.57/0.93 Y2 = Y1) | 0.57/0.93 (Y2 = Y0)))))))))))) => 0.57/0.93 ((!!((^[Y0 : $i]: 0.57/0.93 (!!((^[Y1 : $i]: 0.57/0.93 in(Y0, 0.57/0.93 setadjoin( 0.57/0.93 Y0, 0.57/0.93 setadjoin( 0.57/0.93 Y1, 0.57/0.93 emptyset))))))))) => 0.57/0.93 ((!!((^[Y0 : $i]: 0.57/0.93 (!!((^[Y1 : $i]: 0.57/0.93 in(Y1, 0.57/0.93 setadjoin( 0.57/0.93 Y0, 0.57/0.93 setadjoin( 0.57/0.93 Y1, 0.57/0.93 emptyset))))))))) => 0.57/0.93 ((!!((^[Y0 : $i]: 0.57/0.93 (!!(( 0.57/0.93 ^[Y1 : $i > $o]: 0.57/0.93 (( 0.57/0.93 ??(( 0.57/0.93 ^[Y2 : $i]: 0.57/0.93 (in(Y2, 0.57/0.93 Y0) & 0.57/0.93 Y1(Y2))))) => 0.57/0.93 ( 0.57/0.93 dsetconstr( 0.57/0.93 Y0, 0.57/0.93 (^[Y2 : $i]: 0.57/0.93 Y1(Y2))) != 0.57/0.93 emptyset)))))))) => 0.57/0.93 ((!!((^[Y0 : $i > $o]: 0.57/0.93 (!!(( 0.57/0.93 ^[Y1 : $i]: 0.57/0.93 ( 0.57/0.93 in(Y1, 0.57/0.93 emptyset) => 0.57/0.93 Y0(Y1)))))))) => 0.57/0.93 ((!!((^[Y0 : $i]: 0.57/0.93 (!!(( 0.57/0.93 ^[Y1 : $i > $o]: 0.57/0.93 (( 0.57/0.93 ~(( 0.57/0.93 !!(( 0.57/0.93 ^[Y2 : $i]: 0.57/0.93 (in(Y2, 0.57/0.93 Y0) => 0.57/0.93 Y1(Y2))))))) => 0.57/0.93 (??(( 0.57/0.93 ^[Y2 : $i]: 0.57/0.93 (in(Y2, 0.57/0.93 Y0) & 0.57/0.93 (~( 0.57/0.93 Y1(Y2)))))))))))))) => 0.57/0.93 ((!!((^[Y0 : $i]: 0.57/0.93 (!!(( 0.57/0.93 ^[Y1 : $i > $o]: 0.57/0.93 (( 0.57/0.93 !!(( 0.57/0.93 ^[Y2 : $i]: 0.57/0.93 (in(Y2, 0.57/0.93 Y0) => 0.57/0.93 (~( 0.57/0.93 Y1(Y2))))))) => 0.57/0.93 (~(( 0.57/0.93 ??(( 0.57/0.93 ^[Y2 : $i]: 0.57/0.93 (in(Y2, 0.57/0.93 Y0) & 0.57/0.93 Y1(Y2)))))))))))))) => 0.57/0.93 ((!!((^[Y0 : $i]: 0.57/0.93 ( 0.57/0.93 !!(( 0.57/0.93 ^[Y1 : $i > $o]: 0.57/0.93 (( 0.57/0.93 ~(( 0.57/0.93 ??(( 0.57/0.93 ^[Y2 : $i]: 0.57/0.93 (in(Y2, 0.57/0.93 Y0) & 0.57/0.93 Y1(Y2))))))) => 0.57/0.93 (!!(( 0.57/0.93 ^[Y2 : $i]: 0.57/0.93 (in(Y2, 0.57/0.93 Y0) => 0.57/0.93 (~( 0.57/0.93 Y1(Y2)))))))))))))) => 0.57/0.93 ((!!((^[Y0 : $i]: 0.57/0.93 (!!(( 0.57/0.93 ^[Y1 : $i > $o]: 0.57/0.93 (( 0.57/0.93 ??(( 0.57/0.93 ^[Y2 : $i]: 0.57/0.93 (in(Y2, 0.57/0.93 Y0) & 0.57/0.93 (~( 0.57/0.93 Y1(Y2))))))) => 0.57/0.93 (~(( 0.57/0.93 !!(( 0.57/0.93 ^[Y2 : $i]: 0.57/0.93 (in(Y2, 0.57/0.93 Y0) => 0.57/0.93 Y1(Y2)))))))))))))) => 0.57/0.93 ((!!((^[Y0 : $o]: 0.57/0.93 (Y0 => 0.57/0.93 in( 0.57/0.93 emptyset, 0.57/0.93 prop2set( 0.57/0.93 Y0)))))) => 0.57/0.93 ((!!(( 0.57/0.93 ^[Y0 : $o]: 0.57/0.93 (Y0 => 0.57/0.93 set2prop( 0.57/0.93 prop2set( 0.57/0.93 Y0)))))) => 0.57/0.93 ((!!(( 0.57/0.93 ^[Y0 : $i]: 0.57/0.93 ( 0.57/0.93 !!(( 0.57/0.93 ^[Y1 : $i > $o]: 0.57/0.93 (( 0.57/0.93 ~(( 0.57/0.93 ??(( 0.57/0.93 ^[Y2 : $i]: 0.57/0.93 (in(Y2, 0.57/0.93 Y0) & 0.57/0.93 Y1(Y2))))))) => 0.57/0.93 (!!(( 0.57/0.93 ^[Y2 : $i]: 0.57/0.93 (in(Y2, 0.57/0.93 Y0) => 0.57/0.93 (~( 0.57/0.93 Y1(Y2)))))))))))))) => 0.57/0.93 ((!!(( 0.57/0.93 ^[Y0 : $i]: 0.57/0.93 (!!(( 0.57/0.93 ^[Y1 : $i > $o]: 0.57/0.93 (( 0.57/0.93 ~(( 0.57/0.93 !!(( 0.57/0.93 ^[Y2 : $i]: 0.57/0.93 (in(Y2, 0.57/0.93 Y0) => 0.57/0.93 Y1(Y2))))))) => 0.57/0.93 (??(( 0.57/0.93 ^[Y2 : $i]: 0.57/0.93 (in(Y2, 0.57/0.93 Y0) & 0.57/0.93 (~( 0.57/0.93 Y1(Y2)))))))))))))) => 0.57/0.93 ((!!(( 0.57/0.93 ^[Y0 : $i > $o]: 0.57/0.93 (( 0.57/0.93 ??(( 0.57/0.93 ^[Y1 : $i]: 0.57/0.93 (Y0(Y1) & 0.57/0.93 (!!(( 0.57/0.93 ^[Y2 : $i]: 0.57/0.93 (Y0(Y2) => 0.57/0.93 (Y1 = Y2))))))))) => 0.57/0.93 (??(( 0.57/0.93 ^[Y1 : $i]: 0.57/0.93 (Y0(Y1) & 0.57/0.93 (!!(( 0.57/0.93 ^[Y2 : $i]: 0.57/0.93 (Y0(Y2) => 0.57/0.93 (Y1 = Y2))))))))))))) => 0.57/0.93 (( 0.57/0.93 !!(( 0.57/0.93 ^[Y0 : $i > $o]: 0.57/0.93 (( 0.57/0.93 ??(( 0.57/0.93 ^[Y1 : $i]: 0.57/0.93 Y0(Y1)))) => 0.57/0.93 (( 0.57/0.93 !!(( 0.57/0.93 ^[Y1 : $i]: 0.57/0.93 (!!(( 0.57/0.93 ^[Y2 : $i]: 0.57/0.93 (Y0(Y1) => 0.57/0.93 (Y0(Y2) => 0.57/0.93 (Y1 = Y2))))))))) => 0.57/0.93 (??(( 0.57/0.93 ^[Y1 : $i]: 0.57/0.93 (Y0(Y1) & 0.57/0.93 (!!(( 0.57/0.93 ^[Y2 : $i]: 0.57/0.93 (Y0(Y2) => 0.57/0.93 (Y1 = Y2)))))))))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 !!(( 0.57/0.93 ^[Y0 : $i > $o]: 0.57/0.93 (( 0.57/0.93 ??(( 0.57/0.93 ^[Y1 : $i]: 0.57/0.93 (!!(( 0.57/0.93 ^[Y2 : $i]: 0.57/0.93 (Y0(Y2) <=> 0.57/0.93 (Y2 = Y1)))))))) => 0.57/0.93 (??(( 0.57/0.93 ^[Y1 : $i]: 0.57/0.93 (Y0(Y1) & 0.57/0.93 (!!(( 0.57/0.93 ^[Y2 : $i]: 0.57/0.93 (Y0(Y2) => 0.57/0.93 (Y1 = Y2))))))))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 !!(( 0.57/0.93 ^[Y0 : $i]: 0.57/0.93 (!!(( 0.57/0.93 ^[Y1 : $i]: 0.57/0.93 (( 0.57/0.93 Y0 = Y1) => 0.57/0.93 (!!(( 0.57/0.93 ^[Y2 : $i]: 0.57/0.93 (!!(( 0.57/0.93 ^[Y3 : $i]: 0.57/0.93 (( 0.57/0.93 Y2 = Y3) => 0.57/0.93 (in(Y2, 0.57/0.93 Y0) => 0.57/0.93 in(Y3, 0.57/0.93 Y1)))))))))))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 !!(( 0.57/0.93 ^[Y0 : $i]: 0.57/0.93 (!!(( 0.57/0.93 ^[Y1 : $i]: 0.57/0.93 (( 0.57/0.93 Y0 = Y1) => 0.57/0.93 (!!(( 0.57/0.93 ^[Y2 : $i]: 0.57/0.93 (!!(( 0.57/0.93 ^[Y3 : $i]: 0.57/0.93 (( 0.57/0.93 Y2 = Y3) => 0.57/0.93 (in(Y2, 0.57/0.93 Y0) <=> 0.57/0.93 in(Y3, 0.57/0.93 Y1)))))))))))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 !!(( 0.57/0.93 ^[Y0 : $i > $o]: 0.57/0.93 (( 0.57/0.93 ??(( 0.57/0.93 ^[Y1 : $i]: 0.57/0.93 (Y0(Y1) & 0.57/0.93 (!!(( 0.57/0.93 ^[Y2 : $i]: 0.57/0.93 (Y0(Y2) => 0.57/0.93 (Y1 = Y2))))))))) => 0.57/0.93 (!!(( 0.57/0.93 ^[Y1 : $i]: 0.57/0.93 (!!(( 0.57/0.93 ^[Y2 : $i]: 0.57/0.93 (Y0(Y1) => 0.57/0.93 (Y0(Y2) => 0.57/0.93 (Y1 = Y2))))))))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 !!(( 0.57/0.93 ^[Y0 : $i > $o]: 0.57/0.93 (!!(( 0.57/0.93 ^[Y1 : $i > $o]: 0.57/0.93 (( 0.57/0.93 !!(( 0.57/0.93 ^[Y2 : $i]: 0.57/0.93 (!!(( 0.57/0.93 ^[Y3 : $i]: 0.57/0.93 (( 0.57/0.93 Y2 = Y3) => 0.57/0.93 (Y0(Y2) <=> 0.57/0.93 Y1(Y3))))))))) => 0.57/0.93 (( 0.57/0.93 ??(( 0.57/0.93 ^[Y2 : $i]: 0.57/0.93 (Y0(Y2) & 0.57/0.93 (!!(( 0.57/0.93 ^[Y3 : $i]: 0.57/0.93 (Y0(Y3) => 0.57/0.93 (Y2 = Y3))))))))) <=> 0.57/0.93 (??(( 0.57/0.93 ^[Y2 : $i]: 0.57/0.93 (Y1(Y2) & 0.57/0.93 (!!(( 0.57/0.93 ^[Y3 : $i]: 0.57/0.93 (Y1(Y3) => 0.57/0.93 (Y2 = Y3))))))))))))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 emptyset = 0.57/0.93 emptyset) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 !!(( 0.57/0.93 ^[Y0 : $i]: 0.57/0.93 (!!(( 0.57/0.93 ^[Y1 : $i]: 0.57/0.93 (( 0.57/0.93 Y0 = Y1) => 0.57/0.93 (!!(( 0.57/0.93 ^[Y2 : $i]: 0.57/0.93 (!!(( 0.57/0.93 ^[Y3 : $i]: 0.57/0.93 (( 0.57/0.93 Y2 = Y3) => 0.57/0.93 (setadjoin( 0.57/0.93 Y0, Y2) = 0.57/0.93 setadjoin( 0.57/0.93 Y1, Y3)))))))))))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 !!(( 0.57/0.93 ^[Y0 : $i]: 0.57/0.93 (!!(( 0.57/0.93 ^[Y1 : $i]: 0.57/0.93 (( 0.57/0.93 Y0 = Y1) => 0.57/0.93 (powerset( 0.57/0.93 Y0) = 0.57/0.93 powerset( 0.57/0.93 Y1))))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 !!(( 0.57/0.93 ^[Y0 : $i]: 0.57/0.93 (!!(( 0.57/0.93 ^[Y1 : $i]: 0.57/0.93 (( 0.57/0.93 Y0 = Y1) => 0.57/0.93 (setunion( 0.57/0.93 Y0) = 0.57/0.93 setunion( 0.57/0.93 Y1))))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 omega = 0.57/0.93 omega) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 !!(( 0.57/0.93 ^[Y0 : $i > $o]: 0.57/0.93 (( 0.57/0.93 ??(( 0.57/0.93 ^[Y1 : $i]: 0.57/0.93 (Y0(Y1) & 0.57/0.93 (!!(( 0.57/0.93 ^[Y2 : $i]: 0.57/0.93 (Y0(Y2) => 0.57/0.93 (Y1 = Y2))))))))) => 0.57/0.93 (!!(( 0.57/0.93 ^[Y1 : $i]: 0.57/0.93 (!!(( 0.57/0.93 ^[Y2 : $i]: 0.57/0.93 (Y0(Y1) => 0.57/0.93 (Y0(Y2) => 0.57/0.93 (Y1 = Y2))))))))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 !!(( 0.57/0.93 ^[Y0 : $i > $o]: 0.57/0.93 (!!(( 0.57/0.93 ^[Y1 : $i > $o]: 0.57/0.93 (( 0.57/0.93 !!(( 0.57/0.93 ^[Y2 : $i]: 0.57/0.93 (!!(( 0.57/0.93 ^[Y3 : $i]: 0.57/0.93 (( 0.57/0.93 Y2 = Y3) => 0.57/0.93 (Y0(Y2) <=> 0.57/0.93 Y1(Y3))))))))) => 0.57/0.93 (( 0.57/0.93 ??(( 0.57/0.93 ^[Y2 : $i]: 0.57/0.93 (Y0(Y2) & 0.57/0.93 (!!(( 0.57/0.93 ^[Y3 : $i]: 0.57/0.93 (Y0(Y3) => 0.57/0.93 (Y2 = Y3))))))))) => 0.57/0.93 (( 0.57/0.93 ??(( 0.57/0.93 ^[Y2 : $i]: 0.57/0.93 (Y1(Y2) & 0.57/0.93 (!!(( 0.57/0.93 ^[Y3 : $i]: 0.57/0.93 (Y1(Y3) => 0.57/0.93 (Y2 = Y3))))))))) => 0.57/0.93 (descr( 0.57/0.93 (^[Y2 : $i]: 0.57/0.93 Y0(Y2))) = 0.57/0.93 descr( 0.57/0.93 (^[Y2 : $i]: 0.57/0.93 Y1(Y2))))))))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 !!(( 0.57/0.93 ^[Y0 : $i]: 0.57/0.93 (!!(( 0.57/0.93 ^[Y1 : $i]: 0.57/0.93 (( 0.57/0.93 Y0 = Y1) => 0.57/0.93 (!!(( 0.57/0.93 ^[Y2 : $i > $o]: 0.57/0.93 (!!(( 0.57/0.93 ^[Y3 : $i > $o]: 0.57/0.93 (( 0.57/0.93 !!(( 0.57/0.93 ^[Y4 : $i]: 0.57/0.93 (in(Y4, 0.57/0.93 Y0) => 0.57/0.93 (!!(( 0.57/0.93 ^[Y5 : $i]: 0.57/0.93 (in(Y5, 0.57/0.93 Y1) => 0.57/0.93 (( 0.57/0.93 Y4 = Y5) => 0.57/0.93 (Y2(Y4) <=> 0.57/0.93 Y3(Y5))))))))))) => 0.57/0.93 (dsetconstr( 0.57/0.93 Y0, 0.57/0.93 (^[Y4 : $i]: 0.57/0.93 Y2(Y4))) = 0.57/0.93 dsetconstr( 0.57/0.93 Y1, 0.57/0.93 (^[Y4 : $i]: 0.57/0.93 Y3(Y4)))))))))))))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 !!(( 0.57/0.93 ^[Y0 : $i]: 0.57/0.93 (!!(( 0.57/0.93 ^[Y1 : $i]: 0.57/0.93 (( 0.57/0.93 !!(( 0.57/0.93 ^[Y2 : $i]: 0.57/0.93 (in(Y2, 0.57/0.93 Y0) => 0.57/0.93 in(Y2, 0.57/0.93 Y1))))) => 0.57/0.93 subset( 0.57/0.93 Y0, Y1)))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 !!(( 0.57/0.93 ^[Y0 : $i]: 0.57/0.93 (!!(( 0.57/0.93 ^[Y1 : $i]: 0.57/0.93 (( 0.57/0.93 Y0 = Y1) => 0.57/0.93 subset( 0.57/0.93 Y1, Y0)))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 !!(( 0.57/0.93 ^[Y0 : $i]: 0.57/0.93 (!!(( 0.57/0.93 ^[Y1 : $i]: 0.57/0.93 (( 0.57/0.93 Y0 = Y1) => 0.57/0.93 subset( 0.57/0.93 Y0, Y1)))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 !!(( 0.57/0.93 ^[Y0 : $i]: 0.57/0.93 (!!(( 0.57/0.93 ^[Y1 : $i]: 0.57/0.93 (( 0.57/0.93 !!(( 0.57/0.93 ^[Y2 : $i]: 0.57/0.93 (in(Y2, 0.57/0.93 Y0) => 0.57/0.93 in(Y2, 0.57/0.93 Y1))))) => 0.57/0.93 subset( 0.57/0.93 Y0, Y1)))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 !!(( 0.57/0.93 ^[Y0 : $i]: 0.57/0.93 subset( 0.57/0.93 emptyset, 0.57/0.93 Y0)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 !!(( 0.57/0.93 ^[Y0 : $i]: 0.57/0.93 (!!(( 0.57/0.93 ^[Y1 : $i]: 0.57/0.93 (!!(( 0.57/0.93 ^[Y2 : $i]: 0.57/0.93 (subset( 0.57/0.93 Y0, Y1) => 0.57/0.93 (in(Y2, 0.57/0.93 Y0) => 0.57/0.93 in(Y2, 0.57/0.93 Y1)))))))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 !!(( 0.57/0.93 ^[Y0 : $i]: 0.57/0.93 (!!(( 0.57/0.93 ^[Y1 : $i]: 0.57/0.93 (!!(( 0.57/0.93 ^[Y2 : $i]: 0.57/0.93 (subset( 0.57/0.93 Y0, Y1) => 0.57/0.93 (( 0.57/0.93 ~( 0.57/0.93 in(Y2, 0.57/0.93 Y1))) => 0.57/0.93 (~( 0.57/0.93 in(Y2, 0.57/0.93 Y0)))))))))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 !!(( 0.57/0.93 ^[Y0 : $i]: 0.57/0.93 (!!(( 0.57/0.93 ^[Y1 : $i]: 0.57/0.93 (!!(( 0.57/0.93 ^[Y2 : $i]: 0.57/0.93 (in(Y2, 0.57/0.93 Y0) => 0.57/0.93 (( 0.57/0.93 ~( 0.57/0.93 in(Y2, 0.57/0.93 Y1))) => 0.57/0.93 (~( 0.57/0.93 subset( 0.57/0.93 Y0, Y1)))))))))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 !!(( 0.57/0.93 ^[Y0 : $i]: 0.57/0.93 (!!(( 0.57/0.93 ^[Y1 : $i]: 0.57/0.93 (( 0.57/0.93 ~( 0.57/0.93 subset( 0.57/0.93 Y0, Y1))) => 0.57/0.93 (Y0 != Y1)))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 !!(( 0.57/0.93 ^[Y0 : $i]: 0.57/0.93 (!!(( 0.57/0.93 ^[Y1 : $i]: 0.57/0.93 (!!(( 0.57/0.93 ^[Y2 : $i]: 0.57/0.93 (in(Y2, 0.57/0.93 Y0) => 0.57/0.93 (( 0.57/0.93 ~( 0.57/0.93 in(Y2, 0.57/0.93 Y1))) => 0.57/0.93 (Y0 != Y1)))))))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 !!(( 0.57/0.93 ^[Y0 : $i]: 0.57/0.93 subset( 0.57/0.93 Y0, Y0)))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 !!(( 0.57/0.93 ^[Y0 : $i]: 0.57/0.93 (!!(( 0.57/0.93 ^[Y1 : $i]: 0.57/0.93 (!!(( 0.57/0.93 ^[Y2 : $i]: 0.57/0.93 (subset( 0.57/0.93 Y0, Y1) => 0.57/0.93 (subset( 0.57/0.93 Y1, Y2) => 0.57/0.93 subset( 0.57/0.93 Y0, Y2)))))))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 !!(( 0.57/0.93 ^[Y0 : $i]: 0.57/0.93 (!!(( 0.57/0.93 ^[Y1 : $i]: 0.57/0.93 subset( 0.57/0.93 Y1, 0.57/0.93 setadjoin( 0.57/0.93 Y0, Y1)))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 !!(( 0.57/0.93 ^[Y0 : $i]: 0.57/0.93 (!!(( 0.57/0.93 ^[Y1 : $i]: 0.57/0.93 (!!(( 0.57/0.93 ^[Y2 : $i]: 0.57/0.93 (subset( 0.57/0.93 Y0, Y2) => 0.57/0.93 subset( 0.57/0.93 Y0, 0.57/0.93 setadjoin( 0.57/0.93 Y1, Y2)))))))))))) => 0.57/0.93 ( 0.57/0.93 ( 0.57/0.93 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (subset( 0.57/0.94 Y0, Y1) => 0.57/0.94 in(Y0, 0.57/0.94 powerset( 0.57/0.94 Y1))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (subset( 0.57/0.94 Y0, Y1) => 0.57/0.94 (subset( 0.57/0.94 Y1, Y0) => 0.57/0.94 (Y0 = Y1))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (subset( 0.57/0.94 Y0, 0.57/0.94 emptyset) => 0.57/0.94 (Y0 = 0.57/0.94 emptyset))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (subset( 0.57/0.94 Y1, Y0) => 0.57/0.94 in(Y1, 0.57/0.94 powerset( 0.57/0.94 Y0))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (in(Y1, 0.57/0.94 powerset( 0.57/0.94 Y0)) => 0.57/0.94 subset( 0.57/0.94 Y1, Y0)))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 in(Y0, 0.57/0.94 powerset( 0.57/0.94 Y0))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (subset( 0.57/0.94 Y0, Y1) => 0.57/0.94 subset( 0.57/0.94 powerset( 0.57/0.94 Y0), 0.57/0.94 powerset( 0.57/0.94 Y1))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i > $o]: 0.57/0.94 in( 0.57/0.94 dsetconstr( 0.57/0.94 Y0, 0.57/0.94 (^[Y2 : $i]: 0.57/0.94 Y1(Y2))), 0.57/0.94 powerset( 0.57/0.94 Y0)))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i > $o]: 0.57/0.94 subset( 0.57/0.94 dsetconstr( 0.57/0.94 Y0, 0.57/0.94 (^[Y2 : $i]: 0.57/0.94 Y1(Y2))), 0.57/0.94 Y0))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (in(Y2, 0.57/0.94 Y0) => 0.57/0.94 in(Y2, 0.57/0.94 binunion( 0.57/0.94 Y0, Y1)))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 in(Y1, 0.57/0.94 setadjoin( 0.57/0.94 Y0, 0.57/0.94 setadjoin( 0.57/0.94 Y1, 0.57/0.94 emptyset))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (in(Y2, 0.57/0.94 Y1) => 0.57/0.94 in(Y2, 0.57/0.94 binunion( 0.57/0.94 Y0, Y1)))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y3 : $o]: 0.57/0.94 (in(Y2, 0.57/0.94 binunion( 0.57/0.94 Y0, Y1)) => 0.57/0.94 (( 0.57/0.94 in(Y2, 0.57/0.94 Y0) => Y3) => 0.57/0.94 (( 0.57/0.94 in(Y2, 0.57/0.94 Y1) => Y3) => 0.57/0.94 Y3))))))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (in(Y2, 0.57/0.94 binunion( 0.57/0.94 Y0, Y1)) => 0.57/0.94 (in(Y2, 0.57/0.94 Y1) | 0.57/0.94 in(Y2, 0.57/0.94 Y0)))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 subset( 0.57/0.94 Y0, 0.57/0.94 binunion( 0.57/0.94 Y0, Y1)))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 subset( 0.57/0.94 Y1, 0.57/0.94 binunion( 0.57/0.94 Y0, Y1)))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (in(Y2, 0.57/0.94 Y0) => 0.57/0.94 (in(Y2, 0.57/0.94 Y1) => 0.57/0.94 in(Y2, 0.57/0.94 binintersect( 0.57/0.94 Y0, Y1))))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (subset( 0.57/0.94 Y2, Y0) => 0.57/0.94 (subset( 0.57/0.94 Y2, Y1) => 0.57/0.94 subset( 0.57/0.94 Y2, 0.57/0.94 binintersect( 0.57/0.94 Y0, Y1))))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (in(Y2, 0.57/0.94 binintersect( 0.57/0.94 Y0, Y1)) => 0.57/0.94 in(Y2, 0.57/0.94 Y0))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 subset( 0.57/0.94 binintersect( 0.57/0.94 Y0, Y1), 0.57/0.94 Y0))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (subset( 0.57/0.94 Y0, Y1) => 0.57/0.94 (binintersect( 0.57/0.94 Y0, Y1) = 0.57/0.94 Y0)))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (( 0.57/0.94 binintersect( 0.57/0.94 Y0, Y1) = 0.57/0.94 Y1) => 0.57/0.94 subset( 0.57/0.94 Y1, Y0)))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (in(Y2, 0.57/0.94 binintersect( 0.57/0.94 Y0, Y1)) => 0.57/0.94 in(Y2, 0.57/0.94 Y1))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (( 0.57/0.94 ~(( 0.57/0.94 ??(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (in(Y2, 0.57/0.94 Y0) & 0.57/0.94 in(Y2, 0.57/0.94 Y1))))))) => 0.57/0.94 (binintersect( 0.57/0.94 Y0, Y1) = 0.57/0.94 emptyset)))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 subset( 0.57/0.94 binintersect( 0.57/0.94 Y0, Y1), 0.57/0.94 Y1))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (subset( 0.57/0.94 Y1, Y0) => 0.57/0.94 (binintersect( 0.57/0.94 Y0, Y1) = 0.57/0.94 Y1)))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (( 0.57/0.94 binintersect( 0.57/0.94 Y0, Y1) = 0.57/0.94 Y0) => 0.57/0.94 subset( 0.57/0.94 Y0, Y1)))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (binintersect( 0.57/0.94 Y0, 0.57/0.94 binunion( 0.57/0.94 Y1, Y2)) = 0.57/0.94 binunion( 0.57/0.94 binintersect( 0.57/0.94 Y0, Y1), 0.57/0.94 binintersect( 0.57/0.94 Y0, Y2)))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (in(Y2, 0.57/0.94 Y0) => 0.57/0.94 (( 0.57/0.94 ~( 0.57/0.94 in(Y2, 0.57/0.94 Y1))) => 0.57/0.94 in(Y2, 0.57/0.94 setminus( 0.57/0.94 Y0, Y1))))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (in(Y2, 0.57/0.94 setminus( 0.57/0.94 Y0, Y1)) => 0.57/0.94 in(Y2, 0.57/0.94 Y0))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (in(Y2, 0.57/0.94 setminus( 0.57/0.94 Y0, Y1)) => 0.57/0.94 (~( 0.57/0.94 in(Y2, 0.57/0.94 Y1))))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (subset( 0.57/0.94 Y0, Y1) => 0.57/0.94 (setminus( 0.57/0.94 Y0, Y1) = 0.57/0.94 emptyset)))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (( 0.57/0.94 ~( 0.57/0.94 in(Y2, 0.57/0.94 setminus( 0.57/0.94 Y0, Y1)))) => 0.57/0.94 (in(Y2, 0.57/0.94 Y0) => 0.57/0.94 in(Y2, 0.57/0.94 Y1)))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (( 0.57/0.94 ~( 0.57/0.94 in(Y2, 0.57/0.94 setminus( 0.57/0.94 Y0, Y1)))) => 0.57/0.94 (( 0.57/0.94 ~( 0.57/0.94 in(Y2, 0.57/0.94 Y1))) => 0.57/0.94 (~( 0.57/0.94 in(Y2, 0.57/0.94 Y0)))))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (( 0.57/0.94 ~( 0.57/0.94 in(Y2, 0.57/0.94 Y0))) => 0.57/0.94 (~( 0.57/0.94 in(Y2, 0.57/0.94 setminus( 0.57/0.94 Y0, Y1)))))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (in(Y2, 0.57/0.94 Y1) => 0.57/0.94 (~( 0.57/0.94 in(Y2, 0.57/0.94 setminus( 0.57/0.94 Y0, Y1)))))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 subset( 0.57/0.94 setminus( 0.57/0.94 Y0, Y1), 0.57/0.94 Y0))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (( 0.57/0.94 setminus( 0.57/0.94 Y0, Y1) = 0.57/0.94 emptyset) => 0.57/0.94 subset( 0.57/0.94 Y0, Y1)))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (in(Y2, 0.57/0.94 symdiff( 0.57/0.94 Y0, Y1)) => 0.57/0.94 (!!(( 0.57/0.94 ^[Y3 : $o]: 0.57/0.94 (( 0.57/0.94 in(Y2, 0.57/0.94 Y0) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 ~( 0.57/0.94 in(Y2, 0.57/0.94 Y1))) => 0.57/0.94 Y3)) => 0.57/0.94 (( 0.57/0.94 ( 0.57/0.94 ~( 0.57/0.94 in(Y2, 0.57/0.94 Y0))) => 0.57/0.94 ( 0.57/0.94 in(Y2, 0.57/0.94 Y1) => Y3)) => 0.57/0.94 Y3))))))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (in(Y2, 0.57/0.94 Y0) => 0.57/0.94 (( 0.57/0.94 ~( 0.57/0.94 in(Y2, 0.57/0.94 Y1))) => 0.57/0.94 in(Y2, 0.57/0.94 symdiff( 0.57/0.94 Y0, Y1))))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (( 0.57/0.94 ~( 0.57/0.94 in(Y2, 0.57/0.94 Y0))) => 0.57/0.94 (in(Y2, 0.57/0.94 Y1) => 0.57/0.94 in(Y2, 0.57/0.94 symdiff( 0.57/0.94 Y0, Y1))))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (in(Y2, 0.57/0.94 Y0) => 0.57/0.94 (in(Y2, 0.57/0.94 Y1) => 0.57/0.94 (~( 0.57/0.94 in(Y2, 0.57/0.94 symdiff( 0.57/0.94 Y0, Y1))))))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (( 0.57/0.94 ~( 0.57/0.94 in(Y2, 0.57/0.94 Y0))) => 0.57/0.94 (( 0.57/0.94 ~( 0.57/0.94 in(Y2, 0.57/0.94 Y1))) => 0.57/0.94 (~( 0.57/0.94 in(Y2, 0.57/0.94 symdiff( 0.57/0.94 Y0, Y1))))))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 in(Y1, 0.57/0.94 setadjoin( 0.57/0.94 Y0, 0.57/0.94 setadjoin( 0.57/0.94 Y1, 0.57/0.94 emptyset))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 in(Y0, 0.57/0.94 setunion( 0.57/0.94 setadjoin( 0.57/0.94 setadjoin( 0.57/0.94 Y0, 0.57/0.94 emptyset), 0.57/0.94 setadjoin( 0.57/0.94 setadjoin( 0.57/0.94 Y0, 0.57/0.94 setadjoin( 0.57/0.94 Y1, 0.57/0.94 emptyset)), 0.57/0.94 emptyset)))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 in(Y1, 0.57/0.94 setunion( 0.57/0.94 setadjoin( 0.57/0.94 setadjoin( 0.57/0.94 Y0, 0.57/0.94 emptyset), 0.57/0.94 setadjoin( 0.57/0.94 setadjoin( 0.57/0.94 Y0, 0.57/0.94 setadjoin( 0.57/0.94 Y1, 0.57/0.94 emptyset)), 0.57/0.94 emptyset)))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 iskpair( 0.57/0.94 setadjoin( 0.57/0.94 setadjoin( 0.57/0.94 Y0, 0.57/0.94 emptyset), 0.57/0.94 setadjoin( 0.57/0.94 setadjoin( 0.57/0.94 Y0, 0.57/0.94 setadjoin( 0.57/0.94 Y1, 0.57/0.94 emptyset)), 0.57/0.94 emptyset))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 iskpair( 0.57/0.94 kpair( 0.57/0.94 Y0, Y1)))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (in(Y1, 0.57/0.94 Y0) => 0.57/0.94 subset( 0.57/0.94 setadjoin( 0.57/0.94 Y1, 0.57/0.94 emptyset), 0.57/0.94 Y0)))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (in(Y1, 0.57/0.94 Y0) => 0.57/0.94 in( 0.57/0.94 setadjoin( 0.57/0.94 Y1, 0.57/0.94 emptyset), 0.57/0.94 powerset( 0.57/0.94 Y0))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (in(Y2, 0.57/0.94 Y0) => 0.57/0.94 in( 0.57/0.94 setadjoin( 0.57/0.94 Y2, 0.57/0.94 emptyset), 0.57/0.94 powerset( 0.57/0.94 binunion( 0.57/0.94 Y0, Y1))))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (in(Y2, 0.57/0.94 setadjoin( 0.57/0.94 Y0, 0.57/0.94 setadjoin( 0.57/0.94 Y1, 0.57/0.94 emptyset))) => 0.57/0.94 (( 0.57/0.94 Y2 = Y1) | 0.57/0.94 (Y2 = Y0)))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (in(Y2, 0.57/0.94 Y0) => 0.57/0.94 (!!(( 0.57/0.94 ^[Y3 : $i]: 0.57/0.94 (in(Y3, 0.57/0.94 Y1) => 0.57/0.94 subset( 0.57/0.94 setadjoin( 0.57/0.94 Y2, 0.57/0.94 setadjoin( 0.57/0.94 Y3, 0.57/0.94 emptyset)), 0.57/0.94 binunion( 0.57/0.94 Y0, Y1)))))))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (in(Y2, 0.57/0.94 Y0) => 0.57/0.94 (!!(( 0.57/0.94 ^[Y3 : $i]: 0.57/0.94 (in(Y3, 0.57/0.94 Y1) => 0.57/0.94 in( 0.57/0.94 setadjoin( 0.57/0.94 Y2, 0.57/0.94 setadjoin( 0.57/0.94 Y3, 0.57/0.94 emptyset)), 0.57/0.94 powerset( 0.57/0.94 binunion( 0.57/0.94 Y0, Y1))))))))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (in(Y2, 0.57/0.94 Y0) => 0.57/0.94 (!!(( 0.57/0.94 ^[Y3 : $i]: 0.57/0.94 (in(Y3, 0.57/0.94 Y1) => 0.57/0.94 subset( 0.57/0.94 setadjoin( 0.57/0.94 setadjoin( 0.57/0.94 Y2, 0.57/0.94 emptyset), 0.57/0.94 setadjoin( 0.57/0.94 setadjoin( 0.57/0.94 Y2, 0.57/0.94 setadjoin( 0.57/0.94 Y3, 0.57/0.94 emptyset)), 0.57/0.94 emptyset)), 0.57/0.94 powerset( 0.57/0.94 binunion( 0.57/0.94 Y0, Y1))))))))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (in(Y2, 0.57/0.94 Y0) => 0.57/0.94 (!!(( 0.57/0.94 ^[Y3 : $i]: 0.57/0.94 (in(Y3, 0.57/0.94 Y1) => 0.57/0.94 in( 0.57/0.94 setadjoin( 0.57/0.94 setadjoin( 0.57/0.94 Y2, 0.57/0.94 emptyset), 0.57/0.94 setadjoin( 0.57/0.94 setadjoin( 0.57/0.94 Y2, 0.57/0.94 setadjoin( 0.57/0.94 Y3, 0.57/0.94 emptyset)), 0.57/0.94 emptyset)), 0.57/0.94 powerset( 0.57/0.94 powerset( 0.57/0.94 binunion( 0.57/0.94 Y0, Y1)))))))))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (in(Y2, 0.57/0.94 Y0) => 0.57/0.94 (!!(( 0.57/0.94 ^[Y3 : $i]: 0.57/0.94 (in(Y3, 0.57/0.94 Y1) => 0.57/0.94 in( 0.57/0.94 kpair( 0.57/0.94 Y2, Y3), 0.57/0.94 powerset( 0.57/0.94 powerset( 0.57/0.94 binunion( 0.57/0.94 Y0, Y1)))))))))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (in(Y2, 0.57/0.94 Y0) => 0.57/0.94 (!!(( 0.57/0.94 ^[Y3 : $i]: 0.57/0.94 (in(Y3, 0.57/0.94 Y1) => 0.57/0.94 in( 0.57/0.94 kpair( 0.57/0.94 Y2, Y3), 0.57/0.94 cartprod( 0.57/0.94 Y0, Y1)))))))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (in(Y2, 0.57/0.94 cartprod( 0.57/0.94 Y0, Y1)) => 0.57/0.94 (??(( 0.57/0.94 ^[Y3 : $i]: 0.57/0.94 (in(Y3, 0.57/0.94 Y0) & 0.57/0.94 (??(( 0.57/0.94 ^[Y4 : $i]: 0.57/0.94 (in(Y4, 0.57/0.94 Y1) & 0.57/0.94 (Y2 = 0.57/0.94 kpair( 0.57/0.94 Y3, Y4)))))))))))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (in(Y2, 0.57/0.94 cartprod( 0.57/0.94 Y0, Y1)) => 0.57/0.94 iskpair( 0.57/0.94 Y2))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (in(Y1, 0.57/0.94 setunion( 0.57/0.94 Y0)) => 0.57/0.94 (??(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (in(Y2, 0.57/0.94 Y0) & 0.57/0.94 in(Y1, 0.57/0.94 Y2)))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 subset( 0.57/0.94 setunion( 0.57/0.94 setadjoin( 0.57/0.94 Y0, 0.57/0.94 emptyset)), 0.57/0.94 Y0)))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 subset( 0.57/0.94 Y0, 0.57/0.94 setunion( 0.57/0.94 setadjoin( 0.57/0.94 Y0, 0.57/0.94 emptyset)))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (setunion( 0.57/0.94 setadjoin( 0.57/0.94 Y0, 0.57/0.94 emptyset)) = 0.57/0.94 Y0)))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i > $o]: 0.57/0.94 (( 0.57/0.94 !!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (in(Y2, 0.57/0.94 Y0) => 0.57/0.94 (!!(( 0.57/0.94 ^[Y3 : $i]: 0.57/0.94 (in(Y3, 0.57/0.94 Y0) => 0.57/0.94 (Y1(Y2) => 0.57/0.94 (Y1(Y3) => 0.57/0.94 (Y2 = Y3))))))))))) => 0.57/0.94 (( 0.57/0.94 ??(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (in(Y2, 0.57/0.94 Y0) & 0.57/0.94 Y1(Y2))))) => 0.57/0.94 (??(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (in(Y2, 0.57/0.94 dsetconstr( 0.57/0.94 Y0, 0.57/0.94 (^[Y3 : $i]: 0.57/0.94 Y1(Y3)))) & 0.57/0.94 (dsetconstr( 0.57/0.94 Y0, 0.57/0.94 (^[Y3 : $i]: 0.57/0.94 Y1(Y3))) = 0.57/0.94 setadjoin( 0.57/0.94 Y2, 0.57/0.94 emptyset)))))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i > $o]: 0.57/0.94 (( 0.57/0.94 ??(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (in(Y2, 0.57/0.94 dsetconstr( 0.57/0.94 Y0, 0.57/0.94 (^[Y3 : $i]: 0.57/0.94 Y1(Y3)))) & 0.57/0.94 (dsetconstr( 0.57/0.94 Y0, 0.57/0.94 (^[Y3 : $i]: 0.57/0.94 Y1(Y3))) = 0.57/0.94 setadjoin( 0.57/0.94 Y2, 0.57/0.94 emptyset)))))) => 0.57/0.94 (??(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (in(Y2, 0.57/0.94 Y0) & 0.57/0.94 Y1(Y2)))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i > $o]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (in(Y2, 0.57/0.94 Y0) => 0.57/0.94 (Y1(Y2) => 0.57/0.94 (( 0.57/0.94 !!(( 0.57/0.94 ^[Y3 : $i]: 0.57/0.94 (in(Y3, 0.57/0.94 Y0) => 0.57/0.94 (Y1(Y3) => 0.57/0.94 (Y3 = Y2)))))) => 0.57/0.94 (??(( 0.57/0.94 ^[Y3 : $i]: 0.57/0.94 (in(Y3, 0.57/0.94 dsetconstr( 0.57/0.94 Y0, 0.57/0.94 (^[Y4 : $i]: 0.57/0.94 Y1(Y4)))) & 0.57/0.94 (dsetconstr( 0.57/0.94 Y0, 0.57/0.94 (^[Y4 : $i]: 0.57/0.94 Y1(Y4))) = 0.57/0.94 setadjoin( 0.57/0.94 Y3, 0.57/0.94 emptyset)))))))))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i > $o]: 0.57/0.94 (( 0.57/0.94 !!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (in(Y2, 0.57/0.94 Y0) => 0.57/0.94 (!!(( 0.57/0.94 ^[Y3 : $i]: 0.57/0.94 (in(Y3, 0.57/0.94 Y0) => 0.57/0.94 (Y1(Y2) => 0.57/0.94 (Y1(Y3) => 0.57/0.94 (Y2 = Y3))))))))))) => 0.57/0.94 (( 0.57/0.94 ??(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (in(Y2, 0.57/0.94 Y0) & 0.57/0.94 Y1(Y2))))) => 0.57/0.94 (??(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (in(Y2, 0.57/0.94 dsetconstr( 0.57/0.94 Y0, 0.57/0.94 (^[Y3 : $i]: 0.57/0.94 Y1(Y3)))) & 0.57/0.94 (dsetconstr( 0.57/0.94 Y0, 0.57/0.94 (^[Y3 : $i]: 0.57/0.94 Y1(Y3))) = 0.57/0.94 setadjoin( 0.57/0.94 Y2, 0.57/0.94 emptyset)))))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (( 0.57/0.94 setadjoin( 0.57/0.94 Y0, 0.57/0.94 emptyset) = 0.57/0.94 setadjoin( 0.57/0.94 Y1, 0.57/0.94 emptyset)) => 0.57/0.94 (Y0 = Y1)))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (in( 0.57/0.94 setadjoin( 0.57/0.94 Y2, 0.57/0.94 emptyset), 0.57/0.94 setadjoin( 0.57/0.94 setadjoin( 0.57/0.94 Y0, 0.57/0.94 emptyset), 0.57/0.94 setadjoin( 0.57/0.94 setadjoin( 0.57/0.94 Y0, 0.57/0.94 setadjoin( 0.57/0.94 Y1, 0.57/0.94 emptyset)), 0.57/0.94 emptyset))) => 0.57/0.94 (Y0 = Y2))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (iskpair( 0.57/0.94 Y0) => 0.57/0.94 (??(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (in(Y1, 0.57/0.94 dsetconstr( 0.57/0.94 setunion( 0.57/0.94 Y0), 0.57/0.94 (^[Y2 : $i]: 0.57/0.94 in( 0.57/0.94 setadjoin( 0.57/0.94 Y2, 0.57/0.94 emptyset), 0.57/0.94 Y0)))) & 0.57/0.94 (dsetconstr( 0.57/0.94 setunion( 0.57/0.94 Y0), 0.57/0.94 (^[Y2 : $i]: 0.57/0.94 in( 0.57/0.94 setadjoin( 0.57/0.94 Y2, 0.57/0.94 emptyset), 0.57/0.94 Y0))) = 0.57/0.94 setadjoin( 0.57/0.94 Y1, 0.57/0.94 emptyset)))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (( 0.57/0.94 ??(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (in(Y1, 0.57/0.94 Y0) & 0.57/0.94 (Y0 = 0.57/0.94 setadjoin( 0.57/0.94 Y1, 0.57/0.94 emptyset)))))) => 0.57/0.94 in( 0.57/0.94 setunion( 0.57/0.94 Y0), Y0))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (kfst( 0.57/0.94 kpair( 0.57/0.94 Y0, Y1)) = 0.57/0.94 Y0))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (in(Y2, 0.57/0.94 cartprod( 0.57/0.94 Y0, Y1)) => 0.57/0.94 in( 0.57/0.94 kfst(Y2), 0.57/0.94 Y0))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y3 : $i]: 0.57/0.94 (( 0.57/0.94 setadjoin( 0.57/0.94 setadjoin( 0.57/0.94 Y0, 0.57/0.94 emptyset), 0.57/0.94 setadjoin( 0.57/0.94 setadjoin( 0.57/0.94 Y0, 0.57/0.94 setadjoin( 0.57/0.94 Y1, 0.57/0.94 emptyset)), 0.57/0.94 emptyset)) = 0.57/0.94 setadjoin( 0.57/0.94 setadjoin( 0.57/0.94 Y2, 0.57/0.94 emptyset), 0.57/0.94 setadjoin( 0.57/0.94 setadjoin( 0.57/0.94 Y2, 0.57/0.94 setadjoin( 0.57/0.94 Y3, 0.57/0.94 emptyset)), 0.57/0.94 emptyset))) => 0.57/0.94 (Y0 = Y2)))))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y3 : $i]: 0.57/0.94 (( 0.57/0.94 kpair( 0.57/0.94 Y0, Y1) = 0.57/0.94 kpair( 0.57/0.94 Y2, Y3)) => 0.57/0.94 (Y0 = Y2)))))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (( 0.57/0.94 Y0 = Y1) => 0.57/0.94 (setadjoin( 0.57/0.94 Y0, 0.57/0.94 setadjoin( 0.57/0.94 Y1, 0.57/0.94 emptyset)) = 0.57/0.94 setadjoin( 0.57/0.94 Y0, 0.57/0.94 emptyset))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (( 0.57/0.94 Y0 = Y1) => 0.57/0.94 (setadjoin( 0.57/0.94 setadjoin( 0.57/0.94 Y0, 0.57/0.94 emptyset), 0.57/0.94 setadjoin( 0.57/0.94 setadjoin( 0.57/0.94 Y0, 0.57/0.94 setadjoin( 0.57/0.94 Y1, 0.57/0.94 emptyset)), 0.57/0.94 emptyset)) = 0.57/0.94 setadjoin( 0.57/0.94 setadjoin( 0.57/0.94 Y0, 0.57/0.94 emptyset), 0.57/0.94 emptyset))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y3 : $i]: 0.57/0.94 (( 0.57/0.94 setadjoin( 0.57/0.94 setadjoin( 0.57/0.94 Y0, 0.57/0.94 emptyset), 0.57/0.94 setadjoin( 0.57/0.94 setadjoin( 0.57/0.94 Y0, 0.57/0.94 setadjoin( 0.57/0.94 Y1, 0.57/0.94 emptyset)), 0.57/0.94 emptyset)) = 0.57/0.94 setadjoin( 0.57/0.94 setadjoin( 0.57/0.94 Y2, 0.57/0.94 emptyset), 0.57/0.94 setadjoin( 0.57/0.94 setadjoin( 0.57/0.94 Y2, 0.57/0.94 setadjoin( 0.57/0.94 Y3, 0.57/0.94 emptyset)), 0.57/0.94 emptyset))) => 0.57/0.94 (( 0.57/0.94 Y2 = Y3) => 0.57/0.94 (Y1 = Y3))))))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (( 0.57/0.94 setadjoin( 0.57/0.94 Y0, 0.57/0.94 setadjoin( 0.57/0.94 Y1, 0.57/0.94 emptyset)) = 0.57/0.94 setadjoin( 0.57/0.94 Y2, 0.57/0.94 emptyset)) => 0.57/0.94 (Y0 = Y1))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y3 : $i]: 0.57/0.94 (( 0.57/0.94 setadjoin( 0.57/0.94 setadjoin( 0.57/0.94 Y0, 0.57/0.94 emptyset), 0.57/0.94 setadjoin( 0.57/0.94 setadjoin( 0.57/0.94 Y0, 0.57/0.94 setadjoin( 0.57/0.94 Y1, 0.57/0.94 emptyset)), 0.57/0.94 emptyset)) = 0.57/0.94 setadjoin( 0.57/0.94 setadjoin( 0.57/0.94 Y2, 0.57/0.94 emptyset), 0.57/0.94 setadjoin( 0.57/0.94 setadjoin( 0.57/0.94 Y2, 0.57/0.94 setadjoin( 0.57/0.94 Y3, 0.57/0.94 emptyset)), 0.57/0.94 emptyset))) => 0.57/0.94 (Y1 = Y3)))))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y3 : $i]: 0.57/0.94 (( 0.57/0.94 kpair( 0.57/0.94 Y0, Y1) = 0.57/0.94 kpair( 0.57/0.94 Y2, Y3)) => 0.57/0.94 (Y1 = Y3)))))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (iskpair( 0.57/0.94 Y0) => 0.57/0.94 (??(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (in(Y1, 0.57/0.94 dsetconstr( 0.57/0.94 setunion( 0.57/0.94 Y0), 0.57/0.94 (^[Y2 : $i]: 0.57/0.94 (Y0 = 0.57/0.94 kpair( 0.57/0.94 kfst(Y0), 0.57/0.94 Y2))))) & 0.57/0.94 (dsetconstr( 0.57/0.94 setunion( 0.57/0.94 Y0), 0.57/0.94 (^[Y2 : $i]: 0.57/0.94 (Y0 = 0.57/0.94 kpair( 0.57/0.94 kfst(Y0), 0.57/0.94 Y2)))) = 0.57/0.94 setadjoin( 0.57/0.94 Y1, 0.57/0.94 emptyset)))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (ksnd( 0.57/0.94 kpair( 0.57/0.94 Y0, Y1)) = 0.57/0.94 Y1))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (iskpair( 0.57/0.94 Y0) => 0.57/0.94 (kpair( 0.57/0.94 kfst(Y0), 0.57/0.94 ksnd(Y0)) = 0.57/0.94 Y0))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (in(Y2, 0.57/0.94 cartprod( 0.57/0.94 Y0, Y1)) => 0.57/0.94 in( 0.57/0.94 ksnd(Y2), 0.57/0.94 Y1))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y3 : $i]: 0.57/0.94 (in( 0.57/0.94 kpair( 0.57/0.94 Y2, Y3), 0.57/0.94 cartprod( 0.57/0.94 Y0, Y1)) => 0.57/0.94 in(Y2, 0.57/0.94 Y0)))))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y3 : $i]: 0.57/0.94 (in( 0.57/0.94 kpair( 0.57/0.94 Y2, Y3), 0.57/0.94 cartprod( 0.57/0.94 Y0, Y1)) => 0.57/0.94 in(Y3, 0.57/0.94 Y1)))))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (in(Y2, 0.57/0.94 Y0) => 0.57/0.94 (!!(( 0.57/0.94 ^[Y3 : $i]: 0.57/0.94 (in(Y3, 0.57/0.94 Y1) => 0.57/0.94 (kpair( 0.57/0.94 Y2, Y3) = 0.57/0.94 kpair( 0.57/0.94 Y2, Y3)))))))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (in(Y2, 0.57/0.94 Y0) => 0.57/0.94 (!!(( 0.57/0.94 ^[Y3 : $i]: 0.57/0.94 (in(Y3, 0.57/0.94 Y1) => 0.57/0.94 (kfst( 0.57/0.94 kpair( 0.57/0.94 Y2, Y3)) = 0.57/0.94 Y2))))))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (in(Y2, 0.57/0.94 Y0) => 0.57/0.94 (!!(( 0.57/0.94 ^[Y3 : $i]: 0.57/0.94 (in(Y3, 0.57/0.94 Y1) => 0.57/0.94 (ksnd( 0.57/0.94 kpair( 0.57/0.94 Y2, Y3)) = 0.57/0.94 Y3))))))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (in(Y2, 0.57/0.94 cartprod( 0.57/0.94 Y0, Y1)) => 0.57/0.94 (kpair( 0.57/0.94 kfst(Y2), 0.57/0.94 ksnd(Y2)) = 0.57/0.94 Y2))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : ( 0.57/0.94 $i * $i) > $o]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y3 : $i]: 0.57/0.94 (in(Y3, 0.57/0.94 Y0) => 0.57/0.94 (!!(( 0.57/0.94 ^[Y4 : $i]: 0.57/0.94 (in(Y4, 0.57/0.94 Y1) => 0.57/0.94 (Y2(Y3, 0.57/0.94 Y4) => 0.57/0.94 in( 0.57/0.94 kpair( 0.57/0.94 Y3, Y4), 0.57/0.94 dpsetconstr( 0.57/0.94 Y0, Y1, 0.57/0.94 (^[Y5 : $i, 0.57/0.94 Y6 : $i]: 0.57/0.94 Y2(Y5, 0.57/0.94 Y6)))))))))))))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : ( 0.57/0.94 $i * $i) > $o]: 0.57/0.94 subset( 0.57/0.94 dpsetconstr( 0.57/0.94 Y0, Y1, 0.57/0.94 (^[Y3 : $i, 0.57/0.94 Y4 : $i]: 0.57/0.94 Y2(Y3, 0.57/0.94 Y4))), 0.57/0.94 cartprod( 0.57/0.94 Y0, Y1))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : ( 0.57/0.94 $i * $i) > $o]: 0.57/0.94 subset( 0.57/0.94 dpsetconstr( 0.57/0.94 Y0, Y1, 0.57/0.94 (^[Y3 : $i, 0.57/0.94 Y4 : $i]: 0.57/0.94 Y2(Y3, 0.57/0.94 Y4))), 0.57/0.94 cartprod( 0.57/0.94 Y0, Y1))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : ( 0.57/0.94 $i * $i) > $o]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y3 : $i]: 0.57/0.94 (in(Y3, 0.57/0.94 Y0) => 0.57/0.94 (!!(( 0.57/0.94 ^[Y4 : $i]: 0.57/0.94 (in(Y4, 0.57/0.94 Y1) => 0.57/0.94 (in( 0.57/0.94 kpair( 0.57/0.94 Y3, Y4), 0.57/0.94 dpsetconstr( 0.57/0.94 Y0, Y1, 0.57/0.94 (^[Y5 : $i, 0.57/0.94 Y6 : $i]: 0.57/0.94 Y2(Y5, 0.57/0.94 Y6)))) => 0.57/0.94 Y2(Y3, 0.57/0.94 Y4))))))))))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : ( 0.57/0.94 $i * $i) > $o]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y3 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y4 : $i]: 0.57/0.94 (in( 0.57/0.94 kpair( 0.57/0.94 Y3, Y4), 0.57/0.94 dpsetconstr( 0.57/0.94 Y0, Y1, 0.57/0.94 (^[Y5 : $i, 0.57/0.94 Y6 : $i]: 0.57/0.94 Y2(Y5, 0.57/0.94 Y6)))) => 0.57/0.94 in(Y3, 0.57/0.94 Y0))))))))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : ( 0.57/0.94 $i * $i) > $o]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y3 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y4 : $i]: 0.57/0.94 (in( 0.57/0.94 kpair( 0.57/0.94 Y3, Y4), 0.57/0.94 dpsetconstr( 0.57/0.94 Y0, Y1, 0.57/0.94 (^[Y5 : $i, 0.57/0.94 Y6 : $i]: 0.57/0.94 Y2(Y5, 0.57/0.94 Y6)))) => 0.57/0.94 in(Y4, 0.57/0.94 Y1))))))))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : ( 0.57/0.94 $i * $i) > $o]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y3 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y4 : $i]: 0.57/0.94 (in( 0.57/0.94 kpair( 0.57/0.94 Y3, Y4), 0.57/0.94 dpsetconstr( 0.57/0.94 Y0, Y1, 0.57/0.94 (^[Y5 : $i, 0.57/0.94 Y6 : $i]: 0.57/0.94 Y2(Y5, 0.57/0.94 Y6)))) => 0.57/0.94 Y2(Y3, 0.57/0.94 Y4))))))))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y3 : $i]: 0.57/0.94 (in(Y3, 0.57/0.94 Y0) => 0.57/0.94 (??(( 0.57/0.94 ^[Y4 : $i]: 0.57/0.94 (in(Y4, 0.57/0.94 dsetconstr( 0.57/0.94 Y1, 0.57/0.94 (^[Y5 : $i]: 0.57/0.94 in( 0.57/0.94 kpair( 0.57/0.94 Y3, Y5), 0.57/0.94 Y2)))) & 0.57/0.94 (dsetconstr( 0.57/0.94 Y1, 0.57/0.94 (^[Y5 : $i]: 0.57/0.94 in( 0.57/0.94 kpair( 0.57/0.94 Y3, Y5), 0.57/0.94 Y2))) = 0.57/0.94 setadjoin( 0.57/0.94 Y4, 0.57/0.94 emptyset)))))))))) & 0.57/0.94 subset( 0.57/0.94 Y2, 0.57/0.94 cartprod( 0.57/0.94 Y0, Y1))) => 0.57/0.94 (!!(( 0.57/0.94 ^[Y3 : $i]: 0.57/0.94 (in(Y3, 0.57/0.94 Y0) => 0.57/0.94 (??(( 0.57/0.94 ^[Y4 : $i]: 0.57/0.94 (in(Y4, 0.57/0.94 dsetconstr( 0.57/0.94 Y1, 0.57/0.94 (^[Y5 : $i]: 0.57/0.94 in( 0.57/0.94 kpair( 0.57/0.94 Y3, Y5), 0.57/0.94 Y2)))) & 0.57/0.94 (dsetconstr( 0.57/0.94 Y1, 0.57/0.94 (^[Y5 : $i]: 0.57/0.94 in( 0.57/0.94 kpair( 0.57/0.94 Y3, Y5), 0.57/0.94 Y2))) = 0.57/0.94 setadjoin( 0.57/0.94 Y4, 0.57/0.94 emptyset)))))))))))))))))))) => 0.57/0.94 ( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y3 : $i]: 0.57/0.94 (in(Y3, 0.57/0.94 Y0) => 0.57/0.94 (??(( 0.57/0.94 ^[Y4 : $i]: 0.57/0.94 (in(Y4, 0.57/0.94 dsetconstr( 0.57/0.94 Y1, 0.57/0.94 (^[Y5 : $i]: 0.57/0.94 in( 0.57/0.94 kpair( 0.57/0.94 Y3, Y5), 0.57/0.94 Y2)))) & 0.57/0.94 (dsetconstr( 0.57/0.94 Y1, 0.57/0.94 (^[Y5 : $i]: 0.57/0.94 in( 0.57/0.94 kpair( 0.57/0.94 Y3, Y5), 0.57/0.94 Y2))) = 0.57/0.94 setadjoin( 0.57/0.94 Y4, 0.57/0.94 emptyset)))))))))) & 0.57/0.94 subset( 0.57/0.94 Y2, 0.57/0.94 cartprod( 0.57/0.94 Y0, Y1))) => 0.57/0.94 (!!(( 0.57/0.94 ^[Y3 : $i]: 0.57/0.94 (in(Y3, 0.57/0.94 Y0) => 0.57/0.94 in( 0.57/0.94 setunion( 0.57/0.94 dsetconstr( 0.57/0.94 Y1, 0.57/0.94 (^[Y4 : $i]: 0.57/0.94 in( 0.57/0.94 kpair( 0.57/0.94 Y3, Y4), 0.57/0.94 Y2)))), 0.57/0.94 Y1))))))))))))))) => 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y0 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y1 : $i]: 0.57/0.94 (!!(( 0.57/0.94 ^[Y2 : $i]: 0.57/0.94 (( 0.57/0.94 ( 0.57/0.94 !!(( 0.57/0.94 ^[Y3 : $i]: 0.57/0.94 (in(Y3, 0.57/0.94 Y0) => 0.57/0.94 (??(( 0.57/0.94 ^[Y4 : $i]: 0.57/0.94 (in(Y4, 0.57/0.94 dsetconstr( 0.57/0.94 Y1, 0.57/0.94 (^[Y5 : $i]: 0.57/0.94 in( 0.57/0.94 kpair( 0.57/0.94 Y3, Y5), 0.57/0.94 Y2)))) & 0.57/0.94 (dsetconstr( 0.57/0.94 Y1, 0.57/0.94 (^[Y5 : $i]: 0.57/0.94 in( 0.57/0.94 kpair( 0.57/0.94 Y3, Y5), 0.57/0.94 Y2))) = 0.57/0.94 setadjoin( 0.57/0.94 Y4, 0.57/0.94 emptyset)))))))))) & 0.57/0.94 subset( 0.57/0.94 Y2, 0.57/0.94 cartprod( 0.57/0.94 Y0, Y1))) => 0.57/0.94 (!!(( 0.57/0.94 ^[Y3 : $i]: 0.57/0.94 (in(Y3, 0.57/0.94 Y0) => 0.57/0.94 in( 0.57/0.94 setunion( 0.57/0.94 dsetconstr( 0.57/0.94 Y1, 0.57/0.94 (^[Y4 : $i]: 0.57/0.94 in( 0.57/0.94 kpair( 0.57/0.94 Y3, Y4), 0.57/0.94 Y2)))), 0.57/0.94 Y1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0.57/0.94 inference('cnf', [status(esa)], [zf_stmt_1])). 0.57/0.94 tff('207', plain, $false, 0.57/0.94 inference('simplify boolean subterms', [status(thm)], ['206'])). 0.57/0.94 0.57/0.94 % SZS output end Refutation 0.57/0.94 0.57/0.94 0.57/0.94 % /export/starexec/sandbox/solver/bin/lams/old_sp2.sh running for 17s 0.57/0.94 % /export/starexec/sandbox/solver/bin/lams/b.sh running for 31s 0.57/0.94 % Terminating... 1.75/1.05 % Runner terminated. 1.75/1.06 % Zipperpin 1.5 exiting 1.75/1.06 EOF