0.11/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.13 % Command : run_portfolio.sh /export/starexec/sandbox2/benchmark/theBenchmark.p /export/starexec/sandbox2/tmp/tmp.jEcbI2t5po 0.13/0.34 % Computer : n024.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 180 0.13/0.34 % DateTime : Thu Aug 29 11:25:50 EDT 2019 0.13/0.34 % CPUTime : 18.93/19.25 % Running portfolio for 180 s 18.93/19.25 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 18.93/19.25 % TempDir : /export/starexec/sandbox2/tmp/tmp.jEcbI2t5po 18.93/19.25 % Recognized as monomorphic HO. 18.93/19.25 % Running /export/starexec/sandbox2/solver/bin/competitive.sh for 18 18.93/19.25 % Running /export/starexec/sandbox2/solver/bin/competitive.2.sh for 13 18.93/19.25 % Solved by: competitive.2.sh 18.93/19.25 % done 379 iterations in 0.755s 18.93/19.25 % hashcons stats for terms: size 4096, num 10141, sum length 22174, buckets: small 0, median 7, big 13 18.93/19.25 % proof state stats: {active 237, passive 1665, simpl 0} 18.93/19.25 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 18.93/19.25 % SZS output start Refutation 18.93/19.25 tff(binunionT_lem, axiom, binunionT_lem <=> 18.93/19.25 (![A,X]: 18.93/19.25 (in(X,powerset(A)) => 18.93/19.25 (![Y]: (in(Y,powerset(A)) => in(binunion(X,Y),powerset(A))))))). 18.93/19.25 tff('0', plain, 18.93/19.25 binunionT_lem = 18.93/19.25 (![X2,X3]: 18.93/19.25 (in(X3,powerset(X2)) => 18.93/19.25 (![X4]: (in(X4,powerset(X2)) => in(binunion(X3,X4),powerset(X2)))))), 18.93/19.25 define([status(thm)])). 18.93/19.25 tff(binintersectT_lem, axiom, binintersectT_lem <=> 18.93/19.25 (![A,X]: 18.93/19.25 (in(X,powerset(A)) => 18.93/19.25 (![Y]: (in(Y,powerset(A)) => in(binintersect(X,Y),powerset(A))))))). 18.93/19.25 tff('1', plain, 18.93/19.25 binintersectT_lem = 18.93/19.25 (![X2,X3]: 18.93/19.25 (in(X3,powerset(X2)) => 18.93/19.25 (![X4]: (in(X4,powerset(X2)) => in(binintersect(X3,X4),powerset(X2)))))), 18.93/19.25 define([status(thm)])). 18.93/19.25 tff(iftrueorfalse, axiom, iftrueorfalse <=> 18.93/19.25 (![A,Xphi:$o,Xx]: 18.93/19.25 (in(Xx,A) => 18.93/19.25 (![Xy]: 18.93/19.25 (in(Xy,A) => 18.93/19.25 in(if(A,Xphi,Xx,Xy),setadjoin(Xx,setadjoin(Xy,emptyset)))))))). 18.93/19.25 tff('2', plain, 18.93/19.25 iftrueorfalse = 18.93/19.25 (![X2,X3:$o,X4]: 18.93/19.25 (in(X4,X2) => 18.93/19.25 (![X5]: 18.93/19.25 (in(X5,X2) => 18.93/19.25 in(if(X2,X3,X4,X5),setadjoin(X4,setadjoin(X5,emptyset))))))), 18.93/19.25 define([status(thm)])). 18.93/19.25 tff(iffalse, axiom, iffalse <=> 18.93/19.25 (![A,Xphi:$o,Xx]: 18.93/19.25 (in(Xx,A) => (![Xy]: (in(Xy,A) => ((~Xphi) => (if(A,Xphi,Xx,Xy) = Xy))))))). 18.93/19.25 tff('3', plain, 18.93/19.25 iffalse = 18.93/19.25 (![X2,X3:$o,X4]: 18.93/19.25 (in(X4,X2) => 18.93/19.25 (![X5]: (in(X5,X2) => ((~X3) => (if(X2,X3,X4,X5) = X5)))))), 18.93/19.25 define([status(thm)])). 18.93/19.25 tff(iftrue, axiom, iftrue <=> 18.93/19.25 (![A,Xphi:$o,Xx]: 18.93/19.25 (in(Xx,A) => (![Xy]: (in(Xy,A) => (Xphi => (if(A,Xphi,Xx,Xy) = Xx))))))). 18.93/19.25 tff('4', plain, 18.93/19.25 iftrue = 18.93/19.25 (![X2,X3:$o,X4]: 18.93/19.25 (in(X4,X2) => (![X5]: (in(X5,X2) => (X3 => (if(X2,X3,X4,X5) = X4)))))), 18.93/19.25 define([status(thm)])). 18.93/19.25 tff(theeq, axiom, theeq <=> 18.93/19.25 (![X]: (singleton(X) => (![Xx]: (in(Xx,X) => (setunion(X) = Xx)))))). 18.93/19.25 tff('5', plain, 18.93/19.25 theeq = 18.93/19.25 (![X2]: (singleton(X2) => (![X3]: (in(X3,X2) => (setunion(X2) = X3))))), 18.93/19.25 define([status(thm)])). 18.93/19.25 tff(ifp, axiom, ifp <=> 18.93/19.25 (![A,Xphi:$o,Xx]: 18.93/19.25 (in(Xx,A) => (![Xy]: (in(Xy,A) => in(if(A,Xphi,Xx,Xy),A)))))). 18.93/19.25 tff('6', plain, 18.93/19.25 ifp = 18.93/19.25 (![X2,X3:$o,X4]: 18.93/19.25 (in(X4,X2) => (![X5]: (in(X5,X2) => in(if(X2,X3,X4,X5),X2))))), 18.93/19.25 define([status(thm)])). 18.93/19.25 tff(ifSingleton, axiom, ifSingleton <=> 18.93/19.25 (![A,Xphi:$o,Xx]: 18.93/19.25 (in(Xx,A) => 18.93/19.25 (![Xy]: 18.93/19.25 (in(Xy,A) => 18.93/19.25 singleton(dsetconstr(A, 18.93/19.25 ^[Xz]: 18.93/19.25 (((Xz = Xy) & (~Xphi)) | ((Xz = Xx) & Xphi))))))))). 18.93/19.25 tff('7', plain, 18.93/19.25 ifSingleton = 18.93/19.25 (![X2,X3:$o,X4]: 18.93/19.25 (in(X4,X2) => 18.93/19.25 (![X5]: 18.93/19.25 (in(X5,X2) => 18.93/19.25 singleton(dsetconstr(X2, 18.93/19.25 ^[V_1]: 18.93/19.25 (((V_1 = X5) & (~X3)) | ((V_1 = X4) & X3)))))))), 18.93/19.25 define([status(thm)])). 18.93/19.25 tff(iftrueProp2, axiom, iftrueProp2 <=> 18.93/19.25 (![A,Xphi:$o,Xx]: 18.93/19.25 (in(Xx,A) => 18.93/19.25 (![Xy]: 18.93/19.25 (in(Xy,A) => 18.93/19.25 (Xphi => 18.93/19.25 (dsetconstr(A,^[Xz]: (((Xz = Xy) & (~Xphi)) | ((Xz = Xx) & Xphi))) = 18.93/19.25 setadjoin(Xx,emptyset)))))))). 18.93/19.25 tff('8', plain, 18.93/19.25 iftrueProp2 = 18.93/19.25 (![X2,X3:$o,X4]: 18.93/19.25 (in(X4,X2) => 18.93/19.25 (![X5]: 18.93/19.25 (in(X5,X2) => 18.93/19.25 (X3 => 18.93/19.25 (dsetconstr(X2, 18.93/19.25 ^[V_1]: (((V_1 = X5) & (~X3)) | ((V_1 = X4) & X3))) = 18.93/19.25 setadjoin(X4,emptyset))))))), 18.93/19.25 define([status(thm)])). 18.93/19.25 tff(iftrueProp1, axiom, iftrueProp1 <=> 18.93/19.25 (![A,Xphi:$o,Xx]: 18.93/19.25 (in(Xx,A) => 18.93/19.25 (![Xy]: 18.93/19.25 (in(Xy,A) => 18.93/19.25 (Xphi => 18.93/19.25 in(Xx, 18.93/19.25 dsetconstr(A, 18.93/19.25 ^[Xz]: (((Xz = Xy) & (~Xphi)) | ((Xz = Xx) & Xphi)))))))))). 18.93/19.25 tff('9', plain, 18.93/19.25 iftrueProp1 = 18.93/19.25 (![X2,X3:$o,X4]: 18.93/19.25 (in(X4,X2) => 18.93/19.25 (![X5]: 18.93/19.25 (in(X5,X2) => 18.93/19.25 (X3 => 18.93/19.25 in(X4, 18.93/19.25 dsetconstr(X2, 18.93/19.25 ^[V_1]: (((V_1 = X5) & (~X3)) | ((V_1 = X4) & X3))))))))), 18.93/19.25 define([status(thm)])). 18.93/19.25 tff(iffalseProp2, axiom, iffalseProp2 <=> 18.93/19.25 (![A,Xphi:$o,Xx]: 18.93/19.25 (in(Xx,A) => 18.93/19.25 (![Xy]: 18.93/19.25 (in(Xy,A) => 18.93/19.25 ((~Xphi) => 18.93/19.25 (dsetconstr(A,^[Xz]: (((Xz = Xy) & (~Xphi)) | ((Xz = Xx) & Xphi))) = 18.93/19.25 setadjoin(Xy,emptyset)))))))). 18.93/19.25 tff('10', plain, 18.93/19.25 iffalseProp2 = 18.93/19.25 (![X2,X3:$o,X4]: 18.93/19.25 (in(X4,X2) => 18.93/19.25 (![X5]: 18.93/19.25 (in(X5,X2) => 18.93/19.25 ((~X3) => 18.93/19.25 (dsetconstr(X2, 18.93/19.25 ^[V_1]: (((V_1 = X5) & (~X3)) | ((V_1 = X4) & X3))) = 18.93/19.25 setadjoin(X5,emptyset))))))), 18.93/19.25 define([status(thm)])). 18.93/19.25 tff(iffalseProp1, axiom, iffalseProp1 <=> 18.93/19.25 (![A,Xphi:$o,Xx]: 18.93/19.25 (in(Xx,A) => 18.93/19.25 (![Xy]: 18.93/19.25 (in(Xy,A) => 18.93/19.25 ((~Xphi) => 18.93/19.25 in(Xy, 18.93/19.25 dsetconstr(A, 18.93/19.25 ^[Xz]: (((Xz = Xy) & (~Xphi)) | ((Xz = Xx) & Xphi)))))))))). 18.93/19.25 tff('11', plain, 18.93/19.25 iffalseProp1 = 18.93/19.25 (![X2,X3:$o,X4]: 18.93/19.25 (in(X4,X2) => 18.93/19.25 (![X5]: 18.93/19.25 (in(X5,X2) => 18.93/19.25 ((~X3) => 18.93/19.25 in(X5, 18.93/19.25 dsetconstr(X2, 18.93/19.25 ^[V_1]: (((V_1 = X5) & (~X3)) | ((V_1 = X4) & X3))))))))), 18.93/19.25 define([status(thm)])). 18.93/19.25 tff(eta2, axiom, eta2 <=> 18.93/19.25 (![A,B,Xf]: (in(Xf,funcSet(A,B)) => (lam(A,B,^[Xx]: ap(A,B,Xf,Xx)) = Xf)))). 18.93/19.25 tff('12', plain, 18.93/19.25 eta2 = 18.93/19.25 (![X2,X3,X4]: 18.93/19.25 (in(X4,funcSet(X2,X3)) => (lam(X2,X3,^[V_1]: ap(X2,X3,X4,V_1)) = X4))), 18.93/19.25 define([status(thm)])). 18.93/19.25 tff(beta2, axiom, beta2 <=> 18.93/19.25 (![A,B,Xf:($i > $i)]: 18.93/19.25 ((![Xx]: (in(Xx,A) => in(Xf(Xx),B))) => 18.93/19.25 (![Xx]: (in(Xx,A) => (ap(A,B,lam(A,B,^[Xy]: Xf(Xy)),Xx) = Xf(Xx))))))). 18.93/19.25 tff('13', plain, 18.93/19.25 beta2 = 18.93/19.25 (![X2,X3,X4:($i > $i)]: 18.93/19.25 ((![X5]: (in(X5,X2) => in(X4(X5),X3))) => 18.93/19.25 (![X6]: 18.93/19.25 (in(X6,X2) => (ap(X2,X3,lam(X2,X3,^[V_1]: X4(V_1)),X6) = X4(X6)))))), 18.93/19.25 define([status(thm)])). 18.93/19.25 tff(lam2lamEq, axiom, lam2lamEq <=> 18.93/19.25 (![A,B,Xf:($i > $i)]: 18.93/19.25 ((![Xx]: (in(Xx,A) => in(Xf(Xx),B))) => 18.93/19.25 (lam(A,B,^[Xx]: Xf(Xx)) = lam(A,B,^[Xx]: Xf(Xx)))))). 18.93/19.25 tff('14', plain, 18.93/19.25 lam2lamEq = 18.93/19.25 (![X2,X3,X4:($i > $i)]: 18.93/19.25 ((![X5]: (in(X5,X2) => in(X4(X5),X3))) => 18.93/19.25 (lam(X2,X3,^[V_1]: X4(V_1)) = lam(X2,X3,^[V_2]: X4(V_2))))), 18.93/19.25 define([status(thm)])). 18.93/19.25 tff(eta1, axiom, eta1 <=> 18.93/19.25 (![A,B,Xf]: (func(A,B,Xf) => (lam(A,B,^[Xx]: ap(A,B,Xf,Xx)) = Xf)))). 18.93/19.25 tff('15', plain, 18.93/19.25 eta1 = 18.93/19.25 (![X2,X3,X4]: 18.93/19.25 (func(X2,X3,X4) => (lam(X2,X3,^[V_1]: ap(X2,X3,X4,V_1)) = X4))), 18.93/19.25 define([status(thm)])). 18.93/19.25 tff(beta1, axiom, beta1 <=> 18.93/19.25 (![A,B,Xf:($i > $i)]: 18.93/19.25 ((![Xx]: (in(Xx,A) => in(Xf(Xx),B))) => 18.93/19.25 (![Xx]: (in(Xx,A) => (ap(A,B,lam(A,B,^[Xy]: Xf(Xy)),Xx) = Xf(Xx))))))). 18.93/19.26 tff('16', plain, 18.93/19.26 beta1 = 18.93/19.26 (![X2,X3,X4:($i > $i)]: 18.93/19.26 ((![X5]: (in(X5,X2) => in(X4(X5),X3))) => 18.93/19.26 (![X6]: 18.93/19.26 (in(X6,X2) => (ap(X2,X3,lam(X2,X3,^[V_1]: X4(V_1)),X6) = X4(X6)))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(ap2apEq2, axiom, ap2apEq2 <=> 18.93/19.26 (![A,B,Xf]: 18.93/19.26 (func(A,B,Xf) => (![Xx]: (in(Xx,A) => (ap(A,B,Xf,Xx) = ap(A,B,Xf,Xx))))))). 18.93/19.26 tff('17', plain, 18.93/19.26 ap2apEq2 = 18.93/19.26 (![X2,X3,X4]: 18.93/19.26 (func(X2,X3,X4) => 18.93/19.26 (![X5]: (in(X5,X2) => (ap(X2,X3,X4,X5) = ap(X2,X3,X4,X5)))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(ap2apEq1, axiom, ap2apEq1 <=> 18.93/19.26 (![A,B,Xf]: 18.93/19.26 (in(Xf,funcSet(A,B)) => 18.93/19.26 (![Xx]: (in(Xx,A) => (ap(A,B,Xf,Xx) = ap(A,B,Xf,Xx))))))). 18.93/19.26 tff('18', plain, 18.93/19.26 ap2apEq1 = 18.93/19.26 (![X2,X3,X4]: 18.93/19.26 (in(X4,funcSet(X2,X3)) => 18.93/19.26 (![X5]: (in(X5,X2) => (ap(X2,X3,X4,X5) = ap(X2,X3,X4,X5)))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(funcext2, axiom, funcext2 <=> 18.93/19.26 (![A,B,Xf]: 18.93/19.26 (in(Xf,funcSet(A,B)) => 18.93/19.26 (![Xg]: 18.93/19.26 (in(Xg,funcSet(A,B)) => 18.93/19.26 ((![Xx]: (in(Xx,A) => (ap(A,B,Xf,Xx) = ap(A,B,Xg,Xx)))) => 18.93/19.26 (Xf = Xg))))))). 18.93/19.26 tff('19', plain, 18.93/19.26 funcext2 = 18.93/19.26 (![X2,X3,X4]: 18.93/19.26 (in(X4,funcSet(X2,X3)) => 18.93/19.26 (![X5]: 18.93/19.26 (in(X5,funcSet(X2,X3)) => 18.93/19.26 ((![X6]: (in(X6,X2) => (ap(X2,X3,X4,X6) = ap(X2,X3,X5,X6)))) => 18.93/19.26 (X4 = X5)))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(funcext, axiom, funcext <=> 18.93/19.26 (![A,B,Xf]: 18.93/19.26 (func(A,B,Xf) => 18.93/19.26 (![Xg]: 18.93/19.26 (func(A,B,Xg) => 18.93/19.26 ((![Xx]: (in(Xx,A) => (ap(A,B,Xf,Xx) = ap(A,B,Xg,Xx)))) => 18.93/19.26 (Xf = Xg))))))). 18.93/19.26 tff('20', plain, 18.93/19.26 funcext = 18.93/19.26 (![X2,X3,X4]: 18.93/19.26 (func(X2,X3,X4) => 18.93/19.26 (![X5]: 18.93/19.26 (func(X2,X3,X5) => 18.93/19.26 ((![X6]: (in(X6,X2) => (ap(X2,X3,X4,X6) = ap(X2,X3,X5,X6)))) => 18.93/19.26 (X4 = X5)))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(eqbreln, axiom, eqbreln <=> 18.93/19.26 (![A,B,R]: 18.93/19.26 (breln(A,B,R) => 18.93/19.26 (![S]: 18.93/19.26 (breln(A,B,S) => 18.93/19.26 ((![Xx]: 18.93/19.26 (in(Xx,A) => 18.93/19.26 (![Xy]: 18.93/19.26 (in(Xy,B) => (in(kpair(Xx,Xy),R) => in(kpair(Xx,Xy),S)))))) => 18.93/19.26 ((![Xx]: 18.93/19.26 (in(Xx,A) => 18.93/19.26 (![Xy]: 18.93/19.26 (in(Xy,B) => (in(kpair(Xx,Xy),S) => in(kpair(Xx,Xy),R)))))) => 18.93/19.26 (R = S)))))))). 18.93/19.26 tff('21', plain, 18.93/19.26 eqbreln = 18.93/19.26 (![X2,X3,X4]: 18.93/19.26 (breln(X2,X3,X4) => 18.93/19.26 (![X5]: 18.93/19.26 (breln(X2,X3,X5) => 18.93/19.26 ((![X6]: 18.93/19.26 (in(X6,X2) => 18.93/19.26 (![X7]: 18.93/19.26 (in(X7,X3) => 18.93/19.26 (in(kpair(X6,X7),X4) => in(kpair(X6,X7),X5)))))) => 18.93/19.26 ((![X8]: 18.93/19.26 (in(X8,X2) => 18.93/19.26 (![X9]: 18.93/19.26 (in(X9,X3) => 18.93/19.26 (in(kpair(X8,X9),X5) => in(kpair(X8,X9),X4)))))) => 18.93/19.26 (X4 = X5))))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(subbreln, axiom, subbreln <=> 18.93/19.26 (![A,B,R]: 18.93/19.26 (breln(A,B,R) => 18.93/19.26 (![S]: 18.93/19.26 (breln(A,B,S) => 18.93/19.26 ((![Xx]: 18.93/19.26 (in(Xx,A) => 18.93/19.26 (![Xy]: 18.93/19.26 (in(Xy,B) => (in(kpair(Xx,Xy),R) => in(kpair(Xx,Xy),S)))))) => 18.93/19.26 subset(R,S))))))). 18.93/19.26 tff('22', plain, 18.93/19.26 subbreln = 18.93/19.26 (![X2,X3,X4]: 18.93/19.26 (breln(X2,X3,X4) => 18.93/19.26 (![X5]: 18.93/19.26 (breln(X2,X3,X5) => 18.93/19.26 ((![X6]: 18.93/19.26 (in(X6,X2) => 18.93/19.26 (![X7]: 18.93/19.26 (in(X7,X3) => 18.93/19.26 (in(kpair(X6,X7),X4) => in(kpair(X6,X7),X5)))))) => 18.93/19.26 subset(X4,X5)))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(funcGraphProp4, axiom, funcGraphProp4 <=> 18.93/19.26 (![A,B,Xf]: 18.93/19.26 (in(Xf,funcSet(A,B)) => 18.93/19.26 (![Xx]: 18.93/19.26 (in(Xx,A) => 18.93/19.26 (![Xy]: (in(Xy,B) => (in(kpair(Xx,Xy),Xf) => (ap(A,B,Xf,Xx) = Xy))))))))). 18.93/19.26 tff('23', plain, 18.93/19.26 funcGraphProp4 = 18.93/19.26 (![X2,X3,X4]: 18.93/19.26 (in(X4,funcSet(X2,X3)) => 18.93/19.26 (![X5]: 18.93/19.26 (in(X5,X2) => 18.93/19.26 (![X6]: 18.93/19.26 (in(X6,X3) => (in(kpair(X5,X6),X4) => (ap(X2,X3,X4,X5) = X6)))))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(funcextLem, axiom, funcextLem <=> 18.93/19.26 (![A,B,Xf]: 18.93/19.26 (func(A,B,Xf) => 18.93/19.26 (![Xg]: 18.93/19.26 (func(A,B,Xg) => 18.93/19.26 ((![Xx]: (in(Xx,A) => (ap(A,B,Xf,Xx) = ap(A,B,Xg,Xx)))) => 18.93/19.26 (![Xx]: 18.93/19.26 (in(Xx,A) => 18.93/19.26 (![Xy]: 18.93/19.26 (in(Xy,B) => (in(kpair(Xx,Xy),Xg) => in(kpair(Xx,Xy),Xf)))))))))))). 18.93/19.26 tff('24', plain, 18.93/19.26 funcextLem = 18.93/19.26 (![X2,X3,X4]: 18.93/19.26 (func(X2,X3,X4) => 18.93/19.26 (![X5]: 18.93/19.26 (func(X2,X3,X5) => 18.93/19.26 ((![X6]: (in(X6,X2) => (ap(X2,X3,X4,X6) = ap(X2,X3,X5,X6)))) => 18.93/19.26 (![X7]: 18.93/19.26 (in(X7,X2) => 18.93/19.26 (![X8]: 18.93/19.26 (in(X8,X3) => 18.93/19.26 (in(kpair(X7,X8),X5) => in(kpair(X7,X8),X4))))))))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(funcGraphProp2, axiom, funcGraphProp2 <=> 18.93/19.26 (![A,B,Xf]: 18.93/19.26 (func(A,B,Xf) => 18.93/19.26 (![Xx]: 18.93/19.26 (in(Xx,A) => 18.93/19.26 (![Xy]: (in(Xy,B) => (in(kpair(Xx,Xy),Xf) => (ap(A,B,Xf,Xx) = Xy))))))))). 18.93/19.26 tff('25', plain, 18.93/19.26 funcGraphProp2 = 18.93/19.26 (![X2,X3,X4]: 18.93/19.26 (func(X2,X3,X4) => 18.93/19.26 (![X5]: 18.93/19.26 (in(X5,X2) => 18.93/19.26 (![X6]: 18.93/19.26 (in(X6,X3) => (in(kpair(X5,X6),X4) => (ap(X2,X3,X4,X5) = X6)))))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(funcGraphProp3, axiom, funcGraphProp3 <=> 18.93/19.26 (![A,B,Xf]: 18.93/19.26 (in(Xf,funcSet(A,B)) => 18.93/19.26 (![Xx]: (in(Xx,A) => in(kpair(Xx,ap(A,B,Xf,Xx)),Xf)))))). 18.93/19.26 tff('26', plain, 18.93/19.26 funcGraphProp3 = 18.93/19.26 (![X2,X3,X4]: 18.93/19.26 (in(X4,funcSet(X2,X3)) => 18.93/19.26 (![X5]: (in(X5,X2) => in(kpair(X5,ap(X2,X3,X4,X5)),X4))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(funcGraphProp1, axiom, funcGraphProp1 <=> 18.93/19.26 (![A,B,Xf]: 18.93/19.26 (func(A,B,Xf) => (![Xx]: (in(Xx,A) => in(kpair(Xx,ap(A,B,Xf,Xx)),Xf)))))). 18.93/19.26 tff('27', plain, 18.93/19.26 funcGraphProp1 = 18.93/19.26 (![X2,X3,X4]: 18.93/19.26 (func(X2,X3,X4) => 18.93/19.26 (![X5]: (in(X5,X2) => in(kpair(X5,ap(X2,X3,X4,X5)),X4))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(ex1E2, axiom, ex1E2 <=> 18.93/19.26 (![A,Xphi:($i > $o)]: 18.93/19.26 (ex1(A,^[Xx]: Xphi(Xx)) => 18.93/19.26 (![Xx]: 18.93/19.26 (in(Xx,A) => 18.93/19.26 (![Xy]: (in(Xy,A) => (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy)))))))))). 18.93/19.26 tff('28', plain, 18.93/19.26 ex1E2 = 18.93/19.26 (![X2,X3:($i > $o)]: 18.93/19.26 (ex1(X2,^[V_1]: X3(V_1)) => 18.93/19.26 (![X4]: 18.93/19.26 (in(X4,X2) => 18.93/19.26 (![X5]: (in(X5,X2) => (X3(X4) => (X3(X5) => (X4 = X5))))))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(brelnall2, axiom, brelnall2 <=> 18.93/19.26 (![A,B,R]: 18.93/19.26 (breln(A,B,R) => 18.93/19.26 (![Xphi:($i > $o)]: 18.93/19.26 ((![Xx]: 18.93/19.26 (in(Xx,A) => 18.93/19.26 (![Xy]: 18.93/19.26 (in(Xy,B) => (in(kpair(Xx,Xy),R) => Xphi(kpair(Xx,Xy))))))) => 18.93/19.26 (![Xx]: (in(Xx,R) => Xphi(Xx)))))))). 18.93/19.26 tff('29', plain, 18.93/19.26 brelnall2 = 18.93/19.26 (![X2,X3,X4]: 18.93/19.26 (breln(X2,X3,X4) => 18.93/19.26 (![X5:($i > $o)]: 18.93/19.26 ((![X6]: 18.93/19.26 (in(X6,X2) => 18.93/19.26 (![X7]: 18.93/19.26 (in(X7,X3) => (in(kpair(X6,X7),X4) => X5(kpair(X6,X7))))))) => 18.93/19.26 (![X8]: (in(X8,X4) => X5(X8))))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(brelnall1, axiom, brelnall1 <=> 18.93/19.26 (![A,B,R]: 18.93/19.26 (breln(A,B,R) => 18.93/19.26 (![Xphi:($i > $o)]: 18.93/19.26 ((![Xx]: 18.93/19.26 (in(Xx,A) => 18.93/19.26 (![Xy]: 18.93/19.26 (in(Xy,B) => (in(kpair(Xx,Xy),R) => Xphi(kpair(Xx,Xy))))))) => 18.93/19.26 (![Xx]: (in(Xx,R) => Xphi(Xx)))))))). 18.93/19.26 tff('30', plain, 18.93/19.26 brelnall1 = 18.93/19.26 (![X2,X3,X4]: 18.93/19.26 (breln(X2,X3,X4) => 18.93/19.26 (![X5:($i > $o)]: 18.93/19.26 ((![X6]: 18.93/19.26 (in(X6,X2) => 18.93/19.26 (![X7]: 18.93/19.26 (in(X7,X3) => (in(kpair(X6,X7),X4) => X5(kpair(X6,X7))))))) => 18.93/19.26 (![X8]: (in(X8,X4) => X5(X8))))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(lam2p, axiom, lam2p <=> 18.93/19.26 (![A,B,Xf:($i > $i)]: 18.93/19.26 ((![Xx]: (in(Xx,A) => in(Xf(Xx),B))) => 18.93/19.26 in(lam(A,B,^[Xx]: Xf(Xx)),funcSet(A,B))))). 18.93/19.26 tff('31', plain, 18.93/19.26 lam2p = 18.93/19.26 (![X2,X3,X4:($i > $i)]: 18.93/19.26 ((![X5]: (in(X5,X2) => in(X4(X5),X3))) => 18.93/19.26 in(lam(X2,X3,^[V_1]: X4(V_1)),funcSet(X2,X3)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(lamp, axiom, lamp <=> 18.93/19.26 (![A,B,Xf:($i > $i)]: 18.93/19.26 ((![Xx]: (in(Xx,A) => in(Xf(Xx),B))) => func(A,B,lam(A,B,^[Xx]: Xf(Xx)))))). 18.93/19.26 tff('32', plain, 18.93/19.26 lamp = 18.93/19.26 (![X2,X3,X4:($i > $i)]: 18.93/19.26 ((![X5]: (in(X5,X2) => in(X4(X5),X3))) => 18.93/19.26 func(X2,X3,lam(X2,X3,^[V_1]: X4(V_1))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(lamProp, axiom, lamProp <=> 18.93/19.26 (![A,B,Xf:($i > $i)]: 18.93/19.26 ((![Xx]: (in(Xx,A) => in(Xf(Xx),B))) => 18.93/19.26 func(A,B,dpsetconstr(A,B,^[Xx,Xy]: (Xf(Xx) = Xy)))))). 18.93/19.26 tff('33', plain, 18.93/19.26 lamProp = 18.93/19.26 (![X2,X3,X4:($i > $i)]: 18.93/19.26 ((![X5]: (in(X5,X2) => in(X4(X5),X3))) => 18.93/19.26 func(X2,X3,dpsetconstr(X2,X3,^[V_1,V_2]: (X4(V_1) = V_2))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(funcinfuncset, axiom, funcinfuncset <=> 18.93/19.26 (![A,B,Xf]: (func(A,B,Xf) => in(Xf,funcSet(A,B))))). 18.93/19.26 tff('34', plain, 18.93/19.26 funcinfuncset = (![X2,X3,X4]: (func(X2,X3,X4) => in(X4,funcSet(X2,X3)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(ap2p, axiom, ap2p <=> 18.93/19.26 (![A,B,Xf]: 18.93/19.26 (in(Xf,funcSet(A,B)) => (![Xx]: (in(Xx,A) => in(ap(A,B,Xf,Xx),B)))))). 18.93/19.26 tff('35', plain, 18.93/19.26 ap2p = 18.93/19.26 (![X2,X3,X4]: 18.93/19.26 (in(X4,funcSet(X2,X3)) => 18.93/19.26 (![X5]: (in(X5,X2) => in(ap(X2,X3,X4,X5),X3))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(infuncsetfunc, axiom, infuncsetfunc <=> 18.93/19.26 (![A,B,Xf]: (in(Xf,funcSet(A,B)) => func(A,B,Xf)))). 18.93/19.26 tff('36', plain, 18.93/19.26 infuncsetfunc = (![X2,X3,X4]: (in(X4,funcSet(X2,X3)) => func(X2,X3,X4))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(app, axiom, app <=> 18.93/19.26 (![A,B,Xf]: (func(A,B,Xf) => (![Xx]: (in(Xx,A) => in(ap(A,B,Xf,Xx),B)))))). 18.93/19.26 tff('37', plain, 18.93/19.26 app = 18.93/19.26 (![X2,X3,X4]: 18.93/19.26 (func(X2,X3,X4) => (![X5]: (in(X5,X2) => in(ap(X2,X3,X4,X5),X3))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(apProp, axiom, apProp <=> 18.93/19.26 (![A,B,Xf]: 18.93/19.26 (func(A,B,Xf) => 18.93/19.26 (![Xx]: 18.93/19.26 (in(Xx,A) => 18.93/19.26 in(setunion(dsetconstr(B,^[Xy]: in(kpair(Xx,Xy),Xf))),B)))))). 18.93/19.26 tff('38', plain, 18.93/19.26 apProp = 18.93/19.26 (![X2,X3,X4]: 18.93/19.26 (func(X2,X3,X4) => 18.93/19.26 (![X5]: 18.93/19.26 (in(X5,X2) => 18.93/19.26 in(setunion(dsetconstr(X3,^[V_1]: in(kpair(X5,V_1),X4))),X3))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(funcImageSingleton, axiom, funcImageSingleton <=> 18.93/19.26 (![A,B,Xf]: 18.93/19.26 (func(A,B,Xf) => 18.93/19.26 (![Xx]: 18.93/19.26 (in(Xx,A) => singleton(dsetconstr(B,^[Xy]: in(kpair(Xx,Xy),Xf)))))))). 18.93/19.26 tff('39', plain, 18.93/19.26 funcImageSingleton = 18.93/19.26 (![X2,X3,X4]: 18.93/19.26 (func(X2,X3,X4) => 18.93/19.26 (![X5]: 18.93/19.26 (in(X5,X2) => 18.93/19.26 singleton(dsetconstr(X3,^[V_1]: in(kpair(X5,V_1),X4))))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(dpsetconstrER, axiom, dpsetconstrER <=> 18.93/19.26 (![A,B,Xphi:(($i * $i) > $o),Xx,Xy]: 18.93/19.26 (in(kpair(Xx,Xy),dpsetconstr(A,B,^[Xz,Xu]: Xphi(Xz,Xu))) => Xphi(Xx,Xy)))). 18.93/19.26 tff('40', plain, 18.93/19.26 dpsetconstrER = 18.93/19.26 (![X2,X3,X4:(($i * $i) > $o),X5,X6]: 18.93/19.26 (in(kpair(X5,X6),dpsetconstr(X2,X3,^[V_1,V_2]: X4(V_1,V_2))) => 18.93/19.26 X4(X5,X6))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(dpsetconstrEL2, axiom, dpsetconstrEL2 <=> 18.93/19.26 (![A,B,Xphi:(($i * $i) > $o),Xx,Xy]: 18.93/19.26 (in(kpair(Xx,Xy),dpsetconstr(A,B,^[Xz,Xu]: Xphi(Xz,Xu))) => in(Xy,B)))). 18.93/19.26 tff('41', plain, 18.93/19.26 dpsetconstrEL2 = 18.93/19.26 (![X2,X3,X4:(($i * $i) > $o),X5,X6]: 18.93/19.26 (in(kpair(X5,X6),dpsetconstr(X2,X3,^[V_1,V_2]: X4(V_1,V_2))) => 18.93/19.26 in(X6,X3))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(dpsetconstrEL1, axiom, dpsetconstrEL1 <=> 18.93/19.26 (![A,B,Xphi:(($i * $i) > $o),Xx,Xy]: 18.93/19.26 (in(kpair(Xx,Xy),dpsetconstr(A,B,^[Xz,Xu]: Xphi(Xz,Xu))) => in(Xx,A)))). 18.93/19.26 tff('42', plain, 18.93/19.26 dpsetconstrEL1 = 18.93/19.26 (![X2,X3,X4:(($i * $i) > $o),X5,X6]: 18.93/19.26 (in(kpair(X5,X6),dpsetconstr(X2,X3,^[V_1,V_2]: X4(V_1,V_2))) => 18.93/19.26 in(X5,X2))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(dpsetconstrERa, axiom, dpsetconstrERa <=> 18.93/19.26 (![A,B,Xphi:(($i * $i) > $o),Xx]: 18.93/19.26 (in(Xx,A) => 18.93/19.26 (![Xy]: 18.93/19.26 (in(Xy,B) => 18.93/19.26 (in(kpair(Xx,Xy),dpsetconstr(A,B,^[Xz,Xu]: Xphi(Xz,Xu))) => 18.93/19.26 Xphi(Xx,Xy))))))). 18.93/19.26 tff('43', plain, 18.93/19.26 dpsetconstrERa = 18.93/19.26 (![X2,X3,X4:(($i * $i) > $o),X5]: 18.93/19.26 (in(X5,X2) => 18.93/19.26 (![X6]: 18.93/19.26 (in(X6,X3) => 18.93/19.26 (in(kpair(X5,X6),dpsetconstr(X2,X3,^[V_1,V_2]: X4(V_1,V_2))) => 18.93/19.26 X4(X5,X6)))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(setOfPairsIsBReln, axiom, setOfPairsIsBReln <=> 18.93/19.26 (![A,B,Xphi:(($i * $i) > $o)]: 18.93/19.26 breln(A,B,dpsetconstr(A,B,^[Xx,Xy]: Xphi(Xx,Xy))))). 18.93/19.26 tff('44', plain, 18.93/19.26 setOfPairsIsBReln = 18.93/19.26 (![X2,X3,X4:(($i * $i) > $o)]: 18.93/19.26 breln(X2,X3,dpsetconstr(X2,X3,^[V_1,V_2]: X4(V_1,V_2)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(dpsetconstrSub, axiom, dpsetconstrSub <=> 18.93/19.26 (![A,B,Xphi:(($i * $i) > $o)]: 18.93/19.26 subset(dpsetconstr(A,B,^[Xx,Xy]: Xphi(Xx,Xy)),cartprod(A,B)))). 18.93/19.26 tff('45', plain, 18.93/19.26 dpsetconstrSub = 18.93/19.26 (![X2,X3,X4:(($i * $i) > $o)]: 18.93/19.26 subset(dpsetconstr(X2,X3,^[V_1,V_2]: X4(V_1,V_2)),cartprod(X2,X3))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(dpsetconstrI, axiom, dpsetconstrI <=> 18.93/19.26 (![A,B,Xphi:(($i * $i) > $o),Xx]: 18.93/19.26 (in(Xx,A) => 18.93/19.26 (![Xy]: 18.93/19.26 (in(Xy,B) => 18.93/19.26 (Xphi(Xx,Xy) => 18.93/19.26 in(kpair(Xx,Xy),dpsetconstr(A,B,^[Xz,Xu]: Xphi(Xz,Xu))))))))). 18.93/19.26 tff('46', plain, 18.93/19.26 dpsetconstrI = 18.93/19.26 (![X2,X3,X4:(($i * $i) > $o),X5]: 18.93/19.26 (in(X5,X2) => 18.93/19.26 (![X6]: 18.93/19.26 (in(X6,X3) => 18.93/19.26 (X4(X5,X6) => 18.93/19.26 in(kpair(X5,X6),dpsetconstr(X2,X3,^[V_1,V_2]: X4(V_1,V_2)))))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(breln, axiom, breln() = ^[A,B,C]: subset(C,cartprod(A,B))). 18.93/19.26 tff('47', plain, breln = (^[V_1,V_2,V_3]: subset(V_3,cartprod(V_1,V_2))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(cartprodpairsurjEq, axiom, cartprodpairsurjEq <=> 18.93/19.26 (![A,B,Xu]: (in(Xu,cartprod(A,B)) => (kpair(kfst(Xu),ksnd(Xu)) = Xu)))). 18.93/19.26 tff('48', plain, 18.93/19.26 cartprodpairsurjEq = 18.93/19.26 (![X2,X3,X4]: (in(X4,cartprod(X2,X3)) => (kpair(kfst(X4),ksnd(X4)) = X4))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(cartprodsndpairEq, axiom, cartprodsndpairEq <=> 18.93/19.26 (![A,B,Xx]: (in(Xx,A) => (![Xy]: (in(Xy,B) => (ksnd(kpair(Xx,Xy)) = Xy)))))). 18.93/19.26 tff('49', plain, 18.93/19.26 cartprodsndpairEq = 18.93/19.26 (![X2,X3,X4]: 18.93/19.26 (in(X4,X2) => (![X5]: (in(X5,X3) => (ksnd(kpair(X4,X5)) = X5))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(cartprodfstpairEq, axiom, cartprodfstpairEq <=> 18.93/19.26 (![A,B,Xx]: (in(Xx,A) => (![Xy]: (in(Xy,B) => (kfst(kpair(Xx,Xy)) = Xx)))))). 18.93/19.26 tff('50', plain, 18.93/19.26 cartprodfstpairEq = 18.93/19.26 (![X2,X3,X4]: 18.93/19.26 (in(X4,X2) => (![X5]: (in(X5,X3) => (kfst(kpair(X4,X5)) = X4))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(cartprodmempaircEq, axiom, cartprodmempaircEq <=> 18.93/19.26 (![A,B,Xx]: 18.93/19.26 (in(Xx,A) => (![Xy]: (in(Xy,B) => (kpair(Xx,Xy) = kpair(Xx,Xy))))))). 18.93/19.26 tff('51', plain, 18.93/19.26 cartprodmempaircEq = 18.93/19.26 (![X2,X3,X4]: 18.93/19.26 (in(X4,X2) => (![X5]: (in(X5,X3) => (kpair(X4,X5) = kpair(X4,X5)))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(cartprodpairmemER, axiom, cartprodpairmemER <=> 18.93/19.26 (![A,B,Xx,Xy]: (in(kpair(Xx,Xy),cartprod(A,B)) => in(Xy,B)))). 18.93/19.26 tff('52', plain, 18.93/19.26 cartprodpairmemER = 18.93/19.26 (![X2,X3,X4,X5]: (in(kpair(X4,X5),cartprod(X2,X3)) => in(X5,X3))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(cartprodpairmemEL, axiom, cartprodpairmemEL <=> 18.93/19.26 (![A,B,Xx,Xy]: (in(kpair(Xx,Xy),cartprod(A,B)) => in(Xx,A)))). 18.93/19.26 tff('53', plain, 18.93/19.26 cartprodpairmemEL = 18.93/19.26 (![X2,X3,X4,X5]: (in(kpair(X4,X5),cartprod(X2,X3)) => in(X4,X2))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(cartprodsndin, axiom, cartprodsndin <=> 18.93/19.26 (![A,B,Xu]: (in(Xu,cartprod(A,B)) => in(ksnd(Xu),B)))). 18.93/19.26 tff('54', plain, 18.93/19.26 cartprodsndin = 18.93/19.26 (![X2,X3,X4]: (in(X4,cartprod(X2,X3)) => in(ksnd(X4),X3))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(kpairsurjEq, axiom, kpairsurjEq <=> 18.93/19.26 (![Xu]: (iskpair(Xu) => (kpair(kfst(Xu),ksnd(Xu)) = Xu)))). 18.93/19.26 tff('55', plain, 18.93/19.26 kpairsurjEq = (![X2]: (iskpair(X2) => (kpair(kfst(X2),ksnd(X2)) = X2))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(ksndpairEq, axiom, ksndpairEq <=> (![Xx,Xy]: (ksnd(kpair(Xx,Xy)) = Xy))). 18.93/19.26 tff('56', plain, ksndpairEq = (![X2,X3]: (ksnd(kpair(X2,X3)) = X3)), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(ksndsingleton, axiom, ksndsingleton <=> 18.93/19.26 (![Xu]: 18.93/19.26 (iskpair(Xu) => 18.93/19.26 singleton(dsetconstr(setunion(Xu),^[Xx]: (Xu = kpair(kfst(Xu),Xx))))))). 18.93/19.26 tff('57', plain, 18.93/19.26 ksndsingleton = 18.93/19.26 (![X2]: 18.93/19.26 (iskpair(X2) => 18.93/19.26 singleton(dsetconstr(setunion(X2),^[V_1]: (X2 = kpair(kfst(X2),V_1)))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(setukpairinjR, axiom, setukpairinjR <=> 18.93/19.26 (![Xx,Xy,Xz,Xu]: ((kpair(Xx,Xy) = kpair(Xz,Xu)) => (Xy = Xu)))). 18.93/19.26 tff('58', plain, 18.93/19.26 setukpairinjR = 18.93/19.26 (![X2,X3,X4,X5]: ((kpair(X2,X3) = kpair(X4,X5)) => (X3 = X5))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(setukpairinjR2, axiom, setukpairinjR2 <=> 18.93/19.26 (![Xx,Xy,Xz,Xu]: 18.93/19.26 ((setadjoin(setadjoin(Xx,emptyset), 18.93/19.26 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)),emptyset)) = 18.93/19.26 setadjoin(setadjoin(Xz,emptyset), 18.93/19.26 setadjoin(setadjoin(Xz,setadjoin(Xu,emptyset)),emptyset))) => 18.93/19.26 (Xy = Xu)))). 18.93/19.26 tff('59', plain, 18.93/19.26 setukpairinjR2 = 18.93/19.26 (![X2,X3,X4,X5]: 18.93/19.26 ((setadjoin(setadjoin(X2,emptyset), 18.93/19.26 setadjoin(setadjoin(X2,setadjoin(X3,emptyset)),emptyset)) = 18.93/19.26 setadjoin(setadjoin(X4,emptyset), 18.93/19.26 setadjoin(setadjoin(X4,setadjoin(X5,emptyset)),emptyset))) => 18.93/19.26 (X3 = X5))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(upairequniteq, axiom, upairequniteq <=> 18.93/19.26 (![Xx,Xy,Xz]: 18.93/19.26 ((setadjoin(Xx,setadjoin(Xy,emptyset)) = setadjoin(Xz,emptyset)) => 18.93/19.26 (Xx = Xy)))). 18.93/19.26 tff('60', plain, 18.93/19.26 upairequniteq = 18.93/19.26 (![X2,X3,X4]: 18.93/19.26 ((setadjoin(X2,setadjoin(X3,emptyset)) = setadjoin(X4,emptyset)) => 18.93/19.26 (X2 = X3))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(setukpairinjR1, axiom, setukpairinjR1 <=> 18.93/19.26 (![Xx,Xy,Xz,Xu]: 18.93/19.26 ((setadjoin(setadjoin(Xx,emptyset), 18.93/19.26 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)),emptyset)) = 18.93/19.26 setadjoin(setadjoin(Xz,emptyset), 18.93/19.26 setadjoin(setadjoin(Xz,setadjoin(Xu,emptyset)),emptyset))) => 18.93/19.26 ((Xz = Xu) => (Xy = Xu))))). 18.93/19.26 tff('61', plain, 18.93/19.26 setukpairinjR1 = 18.93/19.26 (![X2,X3,X4,X5]: 18.93/19.26 ((setadjoin(setadjoin(X2,emptyset), 18.93/19.26 setadjoin(setadjoin(X2,setadjoin(X3,emptyset)),emptyset)) = 18.93/19.26 setadjoin(setadjoin(X4,emptyset), 18.93/19.26 setadjoin(setadjoin(X4,setadjoin(X5,emptyset)),emptyset))) => 18.93/19.26 ((X4 = X5) => (X3 = X5)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(setukpairinjR12, axiom, setukpairinjR12 <=> 18.93/19.26 (![Xx,Xy]: 18.93/19.26 ((Xx = Xy) => 18.93/19.26 (setadjoin(setadjoin(Xx,emptyset), 18.93/19.26 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)),emptyset)) = 18.93/19.26 setadjoin(setadjoin(Xx,emptyset),emptyset))))). 18.93/19.26 tff('62', plain, 18.93/19.26 setukpairinjR12 = 18.93/19.26 (![X2,X3]: 18.93/19.26 ((X2 = X3) => 18.93/19.26 (setadjoin(setadjoin(X2,emptyset), 18.93/19.26 setadjoin(setadjoin(X2,setadjoin(X3,emptyset)),emptyset)) = 18.93/19.26 setadjoin(setadjoin(X2,emptyset),emptyset)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(setukpairinjR11, axiom, setukpairinjR11 <=> 18.93/19.26 (![Xx,Xy]: 18.93/19.26 ((Xx = Xy) => 18.93/19.26 (setadjoin(Xx,setadjoin(Xy,emptyset)) = setadjoin(Xx,emptyset))))). 18.93/19.26 tff('63', plain, 18.93/19.26 setukpairinjR11 = 18.93/19.26 (![X2,X3]: 18.93/19.26 ((X2 = X3) => 18.93/19.26 (setadjoin(X2,setadjoin(X3,emptyset)) = setadjoin(X2,emptyset)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(setukpairinjL, axiom, setukpairinjL <=> 18.93/19.26 (![Xx,Xy,Xz,Xu]: ((kpair(Xx,Xy) = kpair(Xz,Xu)) => (Xx = Xz)))). 18.93/19.26 tff('64', plain, 18.93/19.26 setukpairinjL = 18.93/19.26 (![X2,X3,X4,X5]: ((kpair(X2,X3) = kpair(X4,X5)) => (X2 = X4))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(setukpairinjL2, axiom, setukpairinjL2 <=> 18.93/19.26 (![Xx,Xy,Xz,Xu]: 18.93/19.26 ((setadjoin(setadjoin(Xx,emptyset), 18.93/19.26 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)),emptyset)) = 18.93/19.26 setadjoin(setadjoin(Xz,emptyset), 18.93/19.26 setadjoin(setadjoin(Xz,setadjoin(Xu,emptyset)),emptyset))) => 18.93/19.26 (Xx = Xz)))). 18.93/19.26 tff('65', plain, 18.93/19.26 setukpairinjL2 = 18.93/19.26 (![X2,X3,X4,X5]: 18.93/19.26 ((setadjoin(setadjoin(X2,emptyset), 18.93/19.26 setadjoin(setadjoin(X2,setadjoin(X3,emptyset)),emptyset)) = 18.93/19.26 setadjoin(setadjoin(X4,emptyset), 18.93/19.26 setadjoin(setadjoin(X4,setadjoin(X5,emptyset)),emptyset))) => 18.93/19.26 (X2 = X4))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(cartprodfstin, axiom, cartprodfstin <=> 18.93/19.26 (![A,B,Xu]: (in(Xu,cartprod(A,B)) => in(kfst(Xu),A)))). 18.93/19.26 tff('66', plain, 18.93/19.26 cartprodfstin = 18.93/19.26 (![X2,X3,X4]: (in(X4,cartprod(X2,X3)) => in(kfst(X4),X2))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(kfstpairEq, axiom, kfstpairEq <=> (![Xx,Xy]: (kfst(kpair(Xx,Xy)) = Xx))). 18.93/19.26 tff('67', plain, kfstpairEq = (![X2,X3]: (kfst(kpair(X2,X3)) = X2)), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(theprop, axiom, theprop <=> (![X]: (singleton(X) => in(setunion(X),X)))). 18.93/19.26 tff('68', plain, theprop = (![X2]: (singleton(X2) => in(setunion(X2),X2))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(kfstsingleton, axiom, kfstsingleton <=> 18.93/19.26 (![Xu]: 18.93/19.26 (iskpair(Xu) => 18.93/19.26 singleton(dsetconstr(setunion(Xu),^[Xx]: in(setadjoin(Xx,emptyset),Xu)))))). 18.93/19.26 tff('69', plain, 18.93/19.26 kfstsingleton = 18.93/19.26 (![X2]: 18.93/19.26 (iskpair(X2) => 18.93/19.26 singleton(dsetconstr(setunion(X2), 18.93/19.26 ^[V_1]: in(setadjoin(V_1,emptyset),X2))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(setukpairinjL1, axiom, setukpairinjL1 <=> 18.93/19.26 (![Xx,Xy,Xz]: 18.93/19.26 (in(setadjoin(Xz,emptyset), 18.93/19.26 setadjoin(setadjoin(Xx,emptyset), 18.93/19.26 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)),emptyset))) => 18.93/19.26 (Xx = Xz)))). 18.93/19.26 tff('70', plain, 18.93/19.26 setukpairinjL1 = 18.93/19.26 (![X2,X3,X4]: 18.93/19.26 (in(setadjoin(X4,emptyset), 18.93/19.26 setadjoin(setadjoin(X2,emptyset), 18.93/19.26 setadjoin(setadjoin(X2,setadjoin(X3,emptyset)),emptyset))) => 18.93/19.26 (X2 = X4))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(singletonsuniq, axiom, singletonsuniq <=> 18.93/19.26 (![Xx,Xy]: ((setadjoin(Xx,emptyset) = setadjoin(Xy,emptyset)) => (Xx = Xy)))). 18.93/19.26 tff('71', plain, 18.93/19.26 singletonsuniq = 18.93/19.26 (![X2,X3]: 18.93/19.26 ((setadjoin(X2,emptyset) = setadjoin(X3,emptyset)) => (X2 = X3))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(ex1I2, axiom, ex1I2 <=> 18.93/19.26 (![A,Xphi:($i > $o)]: 18.93/19.26 ((![Xx]: 18.93/19.26 (in(Xx,A) => 18.93/19.26 (![Xy]: (in(Xy,A) => (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))) => 18.93/19.26 ((?[Xx]: (Xphi(Xx) & in(Xx,A))) => ex1(A,^[Xx]: Xphi(Xx)))))). 18.93/19.26 tff('72', plain, 18.93/19.26 ex1I2 = 18.93/19.26 (![X2,X3:($i > $o)]: 18.93/19.26 ((![X4]: 18.93/19.26 (in(X4,X2) => 18.93/19.26 (![X5]: (in(X5,X2) => (X3(X4) => (X3(X5) => (X4 = X5))))))) => 18.93/19.26 ((?[X6]: (X3(X6) & in(X6,X2))) => ex1(X2,^[V_1]: X3(V_1))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(ex1I, axiom, ex1I <=> 18.93/19.26 (![A,Xphi:($i > $o),Xx]: 18.93/19.26 (in(Xx,A) => 18.93/19.26 (Xphi(Xx) => 18.93/19.26 ((![Xy]: (in(Xy,A) => (Xphi(Xy) => (Xy = Xx)))) => 18.93/19.26 ex1(A,^[Xy]: Xphi(Xy))))))). 18.93/19.26 tff('73', plain, 18.93/19.26 ex1I = 18.93/19.26 (![X2,X3:($i > $o),X4]: 18.93/19.26 (in(X4,X2) => 18.93/19.26 (X3(X4) => 18.93/19.26 ((![X5]: (in(X5,X2) => (X3(X5) => (X5 = X4)))) => 18.93/19.26 ex1(X2,^[V_1]: X3(V_1)))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(ex1E1, axiom, ex1E1 <=> 18.93/19.26 (![A,Xphi:($i > $o)]: 18.93/19.26 (ex1(A,^[Xx]: Xphi(Xx)) => (?[Xx]: (Xphi(Xx) & in(Xx,A)))))). 18.93/19.26 tff('74', plain, 18.93/19.26 ex1E1 = 18.93/19.26 (![X2,X3:($i > $o)]: 18.93/19.26 (ex1(X2,^[V_1]: X3(V_1)) => (?[X4]: (X3(X4) & in(X4,X2))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(ex1, axiom, ex1() = 18.93/19.26 ^[A,Xphi:($i > $o)]: singleton(dsetconstr(A,^[Xx]: Xphi(Xx)))). 18.93/19.26 tff('75', plain, 18.93/19.26 ex1 = (^[V_1,V_2:($i > $o)]: singleton(dsetconstr(V_1,^[V_3]: V_2(V_3)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(singletonprop, axiom, singletonprop <=> 18.93/19.26 (![A,Xphi:($i > $o)]: 18.93/19.26 ((![Xx]: 18.93/19.26 (in(Xx,A) => 18.93/19.26 (![Xy]: (in(Xy,A) => (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))) => 18.93/19.26 ((?[Xx]: (Xphi(Xx) & in(Xx,A))) => 18.93/19.26 singleton(dsetconstr(A,^[Xx]: Xphi(Xx))))))). 18.93/19.26 tff('76', plain, 18.93/19.26 singletonprop = 18.93/19.26 (![X2,X3:($i > $o)]: 18.93/19.26 ((![X4]: 18.93/19.26 (in(X4,X2) => 18.93/19.26 (![X5]: (in(X5,X2) => (X3(X4) => (X3(X5) => (X4 = X5))))))) => 18.93/19.26 ((?[X6]: (X3(X6) & in(X6,X2))) => 18.93/19.26 singleton(dsetconstr(X2,^[V_1]: X3(V_1)))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(setunionsingleton, axiom, setunionsingleton <=> 18.93/19.26 (![Xx]: (setunion(setadjoin(Xx,emptyset)) = Xx))). 18.93/19.26 tff('77', plain, 18.93/19.26 setunionsingleton = (![X2]: (setunion(setadjoin(X2,emptyset)) = X2)), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(setunionsingleton2, axiom, setunionsingleton2 <=> 18.93/19.26 (![A]: subset(A,setunion(setadjoin(A,emptyset))))). 18.93/19.26 tff('78', plain, 18.93/19.26 setunionsingleton2 = (![X2]: subset(X2,setunion(setadjoin(X2,emptyset)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(setunionsingleton1, axiom, setunionsingleton1 <=> 18.93/19.26 (![A]: subset(setunion(setadjoin(A,emptyset)),A))). 18.93/19.26 tff('79', plain, 18.93/19.26 setunionsingleton1 = (![X2]: subset(setunion(setadjoin(X2,emptyset)),X2)), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(setunionE2, axiom, setunionE2 <=> 18.93/19.26 (![A,Xx]: (in(Xx,setunion(A)) => (?[X]: (in(Xx,X) & in(X,A)))))). 18.93/19.26 tff('80', plain, 18.93/19.26 setunionE2 = 18.93/19.26 (![X2,X3]: (in(X3,setunion(X2)) => (?[X4]: (in(X3,X4) & in(X4,X2))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(cartprodmempair, axiom, cartprodmempair <=> 18.93/19.26 (![A,B,Xu]: (in(Xu,cartprod(A,B)) => iskpair(Xu)))). 18.93/19.26 tff('81', plain, 18.93/19.26 cartprodmempair = (![X2,X3,X4]: (in(X4,cartprod(X2,X3)) => iskpair(X4))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(cartprodmempair1, axiom, cartprodmempair1 <=> 18.93/19.26 (![A,B,Xu]: 18.93/19.26 (in(Xu,cartprod(A,B)) => 18.93/19.26 (?[Xx]: ((?[Xy]: ((Xu = kpair(Xx,Xy)) & in(Xy,B))) & in(Xx,A)))))). 18.93/19.26 tff('82', plain, 18.93/19.26 cartprodmempair1 = 18.93/19.26 (![X2,X3,X4]: 18.93/19.26 (in(X4,cartprod(X2,X3)) => 18.93/19.26 (?[X5]: ((?[X6]: ((X4 = kpair(X5,X6)) & in(X6,X3))) & in(X5,X2))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(cartprodpairin, axiom, cartprodpairin <=> 18.93/19.26 (![A,B,Xx]: 18.93/19.26 (in(Xx,A) => (![Xy]: (in(Xy,B) => in(kpair(Xx,Xy),cartprod(A,B))))))). 18.93/19.26 tff('83', plain, 18.93/19.26 cartprodpairin = 18.93/19.26 (![X2,X3,X4]: 18.93/19.26 (in(X4,X2) => (![X5]: (in(X5,X3) => in(kpair(X4,X5),cartprod(X2,X3)))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(ubforcartprodlem3, axiom, ubforcartprodlem3 <=> 18.93/19.26 (![A,B,Xx]: 18.93/19.26 (in(Xx,A) => 18.93/19.26 (![Xy]: 18.93/19.26 (in(Xy,B) => in(kpair(Xx,Xy),powerset(powerset(binunion(A,B))))))))). 18.93/19.26 tff('84', plain, 18.93/19.26 ubforcartprodlem3 = 18.93/19.26 (![X2,X3,X4]: 18.93/19.26 (in(X4,X2) => 18.93/19.26 (![X5]: 18.93/19.26 (in(X5,X3) => in(kpair(X4,X5),powerset(powerset(binunion(X2,X3)))))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(ubforcartprodlem2, axiom, ubforcartprodlem2 <=> 18.93/19.26 (![A,B,Xx]: 18.93/19.26 (in(Xx,A) => 18.93/19.26 (![Xy]: 18.93/19.26 (in(Xy,B) => 18.93/19.26 in(setadjoin(setadjoin(Xx,emptyset), 18.93/19.26 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 18.93/19.26 emptyset)), 18.93/19.26 powerset(powerset(binunion(A,B))))))))). 18.93/19.26 tff('85', plain, 18.93/19.26 ubforcartprodlem2 = 18.93/19.26 (![X2,X3,X4]: 18.93/19.26 (in(X4,X2) => 18.93/19.26 (![X5]: 18.93/19.26 (in(X5,X3) => 18.93/19.26 in(setadjoin(setadjoin(X4,emptyset), 18.93/19.26 setadjoin(setadjoin(X4,setadjoin(X5,emptyset)), 18.93/19.26 emptyset)), 18.93/19.26 powerset(powerset(binunion(X2,X3)))))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(ubforcartprodlem1, axiom, ubforcartprodlem1 <=> 18.93/19.26 (![A,B,Xx]: 18.93/19.26 (in(Xx,A) => 18.93/19.26 (![Xy]: 18.93/19.26 (in(Xy,B) => 18.93/19.26 subset(setadjoin(setadjoin(Xx,emptyset), 18.93/19.26 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 18.93/19.26 emptyset)), 18.93/19.26 powerset(binunion(A,B)))))))). 18.93/19.26 tff('86', plain, 18.93/19.26 ubforcartprodlem1 = 18.93/19.26 (![X2,X3,X4]: 18.93/19.26 (in(X4,X2) => 18.93/19.26 (![X5]: 18.93/19.26 (in(X5,X3) => 18.93/19.26 subset(setadjoin(setadjoin(X4,emptyset), 18.93/19.26 setadjoin(setadjoin(X4,setadjoin(X5,emptyset)), 18.93/19.26 emptyset)), 18.93/19.26 powerset(binunion(X2,X3))))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(upairinpowunion, axiom, upairinpowunion <=> 18.93/19.26 (![A,B,Xx]: 18.93/19.26 (in(Xx,A) => 18.93/19.26 (![Xy]: 18.93/19.26 (in(Xy,B) => 18.93/19.26 in(setadjoin(Xx,setadjoin(Xy,emptyset)),powerset(binunion(A,B)))))))). 18.93/19.26 tff('87', plain, 18.93/19.26 upairinpowunion = 18.93/19.26 (![X2,X3,X4]: 18.93/19.26 (in(X4,X2) => 18.93/19.26 (![X5]: 18.93/19.26 (in(X5,X3) => 18.93/19.26 in(setadjoin(X4,setadjoin(X5,emptyset)),powerset(binunion(X2,X3))))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(upairsubunion, axiom, upairsubunion <=> 18.93/19.26 (![A,B,Xx]: 18.93/19.26 (in(Xx,A) => 18.93/19.26 (![Xy]: 18.93/19.26 (in(Xy,B) => 18.93/19.26 subset(setadjoin(Xx,setadjoin(Xy,emptyset)),binunion(A,B))))))). 18.93/19.26 tff('88', plain, 18.93/19.26 upairsubunion = 18.93/19.26 (![X2,X3,X4]: 18.93/19.26 (in(X4,X2) => 18.93/19.26 (![X5]: 18.93/19.26 (in(X5,X3) => 18.93/19.26 subset(setadjoin(X4,setadjoin(X5,emptyset)),binunion(X2,X3)))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(upairset2E, axiom, upairset2E <=> 18.93/19.26 (![Xx,Xy,Xz]: 18.93/19.26 (in(Xz,setadjoin(Xx,setadjoin(Xy,emptyset))) => ((Xz = Xy) | (Xz = Xx))))). 18.93/19.26 tff('89', plain, 18.93/19.26 upairset2E = 18.93/19.26 (![X2,X3,X4]: 18.93/19.26 (in(X4,setadjoin(X2,setadjoin(X3,emptyset))) => 18.93/19.26 ((X4 = X3) | (X4 = X2)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(singletoninpowunion, axiom, singletoninpowunion <=> 18.93/19.26 (![A,B,Xx]: 18.93/19.26 (in(Xx,A) => in(setadjoin(Xx,emptyset),powerset(binunion(A,B)))))). 18.93/19.26 tff('90', plain, 18.93/19.26 singletoninpowunion = 18.93/19.26 (![X2,X3,X4]: 18.93/19.26 (in(X4,X2) => in(setadjoin(X4,emptyset),powerset(binunion(X2,X3))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(singletoninpowerset, axiom, singletoninpowerset <=> 18.93/19.26 (![A,Xx]: (in(Xx,A) => in(setadjoin(Xx,emptyset),powerset(A))))). 18.93/19.26 tff('91', plain, 18.93/19.26 singletoninpowerset = 18.93/19.26 (![X2,X3]: (in(X3,X2) => in(setadjoin(X3,emptyset),powerset(X2)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(singletonsubset, axiom, singletonsubset <=> 18.93/19.26 (![A,Xx]: (in(Xx,A) => subset(setadjoin(Xx,emptyset),A)))). 18.93/19.26 tff('92', plain, 18.93/19.26 singletonsubset = 18.93/19.26 (![X2,X3]: (in(X3,X2) => subset(setadjoin(X3,emptyset),X2))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(kpairp, axiom, kpairp <=> (![Xx,Xy]: iskpair(kpair(Xx,Xy)))). 18.93/19.26 tff('93', plain, kpairp = (![X2,X3]: iskpair(kpair(X2,X3))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(kpairiskpair, axiom, kpairiskpair <=> 18.93/19.26 (![Xx,Xy]: 18.93/19.26 iskpair(setadjoin(setadjoin(Xx,emptyset), 18.93/19.26 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 18.93/19.26 emptyset))))). 18.93/19.26 tff('94', plain, 18.93/19.26 kpairiskpair = 18.93/19.26 (![X2,X3]: 18.93/19.26 iskpair(setadjoin(setadjoin(X2,emptyset), 18.93/19.26 setadjoin(setadjoin(X2,setadjoin(X3,emptyset)), 18.93/19.26 emptyset)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(setukpairIR, axiom, setukpairIR <=> 18.93/19.26 (![Xx,Xy]: 18.93/19.26 in(Xy, 18.93/19.26 setunion(setadjoin(setadjoin(Xx,emptyset), 18.93/19.26 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 18.93/19.26 emptyset)))))). 18.93/19.26 tff('95', plain, 18.93/19.26 setukpairIR = 18.93/19.26 (![X2,X3]: 18.93/19.26 in(X3, 18.93/19.26 setunion(setadjoin(setadjoin(X2,emptyset), 18.93/19.26 setadjoin(setadjoin(X2,setadjoin(X3,emptyset)), 18.93/19.26 emptyset))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(setukpairIL, axiom, setukpairIL <=> 18.93/19.26 (![Xx,Xy]: 18.93/19.26 in(Xx, 18.93/19.26 setunion(setadjoin(setadjoin(Xx,emptyset), 18.93/19.26 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 18.93/19.26 emptyset)))))). 18.93/19.26 tff('96', plain, 18.93/19.26 setukpairIL = 18.93/19.26 (![X2,X3]: 18.93/19.26 in(X2, 18.93/19.26 setunion(setadjoin(setadjoin(X2,emptyset), 18.93/19.26 setadjoin(setadjoin(X2,setadjoin(X3,emptyset)), 18.93/19.26 emptyset))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(secondinupair, axiom, secondinupair <=> 18.93/19.26 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 18.93/19.26 tff('97', plain, 18.93/19.26 secondinupair = (![X2,X3]: in(X3,setadjoin(X2,setadjoin(X3,emptyset)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(symdiffIneg2, axiom, symdiffIneg2 <=> 18.93/19.26 (![A,B,Xx]: ((~in(Xx,A)) => ((~in(Xx,B)) => (~in(Xx,symdiff(A,B))))))). 18.93/19.26 tff('98', plain, 18.93/19.26 symdiffIneg2 = 18.93/19.26 (![X2,X3,X4]: 18.93/19.26 ((~in(X4,X2)) => ((~in(X4,X3)) => (~in(X4,symdiff(X2,X3)))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(symdiffIneg1, axiom, symdiffIneg1 <=> 18.93/19.26 (![A,B,Xx]: (in(Xx,A) => (in(Xx,B) => (~in(Xx,symdiff(A,B))))))). 18.93/19.26 tff('99', plain, 18.93/19.26 symdiffIneg1 = 18.93/19.26 (![X2,X3,X4]: (in(X4,X2) => (in(X4,X3) => (~in(X4,symdiff(X2,X3)))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(symdiffI2, axiom, symdiffI2 <=> 18.93/19.26 (![A,B,Xx]: ((~in(Xx,A)) => (in(Xx,B) => in(Xx,symdiff(A,B)))))). 18.93/19.26 tff('100', plain, 18.93/19.26 symdiffI2 = 18.93/19.26 (![X2,X3,X4]: ((~in(X4,X2)) => (in(X4,X3) => in(X4,symdiff(X2,X3))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(symdiffI1, axiom, symdiffI1 <=> 18.93/19.26 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => in(Xx,symdiff(A,B)))))). 18.93/19.26 tff('101', plain, 18.93/19.26 symdiffI1 = 18.93/19.26 (![X2,X3,X4]: (in(X4,X2) => ((~in(X4,X3)) => in(X4,symdiff(X2,X3))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(symdiffE, axiom, symdiffE <=> 18.93/19.26 (![A,B,Xx]: 18.93/19.26 (in(Xx,symdiff(A,B)) => 18.93/19.26 (![Xphi:$o]: 18.93/19.26 ((in(Xx,A) => ((~in(Xx,B)) => Xphi)) => 18.93/19.26 (((~in(Xx,A)) => (in(Xx,B) => Xphi)) => Xphi)))))). 18.93/19.26 tff('102', plain, 18.93/19.26 symdiffE = 18.93/19.26 (![X2,X3,X4]: 18.93/19.26 (in(X4,symdiff(X2,X3)) => 18.93/19.26 (![X5:$o]: 18.93/19.26 ((in(X4,X2) => ((~in(X4,X3)) => X5)) => 18.93/19.26 (((~in(X4,X2)) => (in(X4,X3) => X5)) => X5))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(setminusSubset1, axiom, setminusSubset1 <=> 18.93/19.26 (![A,B]: ((setminus(A,B) = emptyset) => subset(A,B)))). 18.93/19.26 tff('103', plain, 18.93/19.26 setminusSubset1 = 18.93/19.26 (![X2,X3]: ((setminus(X2,X3) = emptyset) => subset(X2,X3))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(setminusLsub, axiom, setminusLsub <=> (![A,B]: subset(setminus(A,B),A))). 18.93/19.26 tff('104', plain, setminusLsub = (![X2,X3]: subset(setminus(X2,X3),X2)), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(setminusIRneg, axiom, setminusIRneg <=> 18.93/19.26 (![A,B,Xx]: (in(Xx,B) => (~in(Xx,setminus(A,B)))))). 18.93/19.26 tff('105', plain, 18.93/19.26 setminusIRneg = (![X2,X3,X4]: (in(X4,X3) => (~in(X4,setminus(X2,X3))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(setminusILneg, axiom, setminusILneg <=> 18.93/19.26 (![A,B,Xx]: ((~in(Xx,A)) => (~in(Xx,setminus(A,B)))))). 18.93/19.26 tff('106', plain, 18.93/19.26 setminusILneg = 18.93/19.26 (![X2,X3,X4]: ((~in(X4,X2)) => (~in(X4,setminus(X2,X3))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(setminusELneg, axiom, setminusELneg <=> 18.93/19.26 (![A,B,Xx]: ((~in(Xx,setminus(A,B))) => ((~in(Xx,B)) => (~in(Xx,A)))))). 18.93/19.26 tff('107', plain, 18.93/19.26 setminusELneg = 18.93/19.26 (![X2,X3,X4]: 18.93/19.26 ((~in(X4,setminus(X2,X3))) => ((~in(X4,X3)) => (~in(X4,X2))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(setminusERneg, axiom, setminusERneg <=> 18.93/19.26 (![A,B,Xx]: ((~in(Xx,setminus(A,B))) => (in(Xx,A) => in(Xx,B))))). 18.93/19.26 tff('108', plain, 18.93/19.26 setminusERneg = 18.93/19.26 (![X2,X3,X4]: ((~in(X4,setminus(X2,X3))) => (in(X4,X2) => in(X4,X3)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(setminusSubset2, axiom, setminusSubset2 <=> 18.93/19.26 (![A,B]: (subset(A,B) => (setminus(A,B) = emptyset)))). 18.93/19.26 tff('109', plain, 18.93/19.26 setminusSubset2 = 18.93/19.26 (![X2,X3]: (subset(X2,X3) => (setminus(X2,X3) = emptyset))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(setminusER, axiom, setminusER <=> 18.93/19.26 (![A,B,Xx]: (in(Xx,setminus(A,B)) => (~in(Xx,B))))). 18.93/19.26 tff('110', plain, 18.93/19.26 setminusER = (![X2,X3,X4]: (in(X4,setminus(X2,X3)) => (~in(X4,X3)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(setminusEL, axiom, setminusEL <=> 18.93/19.26 (![A,B,Xx]: (in(Xx,setminus(A,B)) => in(Xx,A)))). 18.93/19.26 tff('111', plain, 18.93/19.26 setminusEL = (![X2,X3,X4]: (in(X4,setminus(X2,X3)) => in(X4,X2))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(setminusI, axiom, setminusI <=> 18.93/19.26 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => in(Xx,setminus(A,B)))))). 18.93/19.26 tff('112', plain, 18.93/19.26 setminusI = 18.93/19.26 (![X2,X3,X4]: (in(X4,X2) => ((~in(X4,X3)) => in(X4,setminus(X2,X3))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(bs114d, axiom, bs114d <=> 18.93/19.26 (![A,B,C]: 18.93/19.26 (binintersect(A,binunion(B,C)) = 18.93/19.26 binunion(binintersect(A,B),binintersect(A,C))))). 18.93/19.26 tff('113', plain, 18.93/19.26 bs114d = 18.93/19.26 (![X2,X3,X4]: 18.93/19.26 (binintersect(X2,binunion(X3,X4)) = 18.93/19.26 binunion(binintersect(X2,X3),binintersect(X2,X4)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(binintersectSubset1, axiom, binintersectSubset1 <=> 18.93/19.26 (![A,B]: ((binintersect(A,B) = A) => subset(A,B)))). 18.93/19.26 tff('114', plain, 18.93/19.26 binintersectSubset1 = 18.93/19.26 (![X2,X3]: ((binintersect(X2,X3) = X2) => subset(X2,X3))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(binintersectSubset4, axiom, binintersectSubset4 <=> 18.93/19.26 (![A,B]: (subset(B,A) => (binintersect(A,B) = B)))). 18.93/19.26 tff('115', plain, 18.93/19.26 binintersectSubset4 = 18.93/19.26 (![X2,X3]: (subset(X3,X2) => (binintersect(X2,X3) = X3))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(binintersectRsub, axiom, binintersectRsub <=> 18.93/19.26 (![A,B]: subset(binintersect(A,B),B))). 18.93/19.26 tff('116', plain, 18.93/19.26 binintersectRsub = (![X2,X3]: subset(binintersect(X2,X3),X3)), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(disjointsetsI1, axiom, disjointsetsI1 <=> 18.93/19.26 (![A,B]: 18.93/19.26 ((~(?[Xx]: (in(Xx,B) & in(Xx,A)))) => (binintersect(A,B) = emptyset)))). 18.93/19.26 tff('117', plain, 18.93/19.26 disjointsetsI1 = 18.93/19.26 (![X2,X3]: 18.93/19.26 ((~(?[X4]: (in(X4,X3) & in(X4,X2)))) => 18.93/19.26 (binintersect(X2,X3) = emptyset))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(binintersectER, axiom, binintersectER <=> 18.93/19.26 (![A,B,Xx]: (in(Xx,binintersect(A,B)) => in(Xx,B)))). 18.93/19.26 tff('118', plain, 18.93/19.26 binintersectER = (![X2,X3,X4]: (in(X4,binintersect(X2,X3)) => in(X4,X3))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(binintersectSubset3, axiom, binintersectSubset3 <=> 18.93/19.26 (![A,B]: ((binintersect(A,B) = B) => subset(B,A)))). 18.93/19.26 tff('119', plain, 18.93/19.26 binintersectSubset3 = 18.93/19.26 (![X2,X3]: ((binintersect(X2,X3) = X3) => subset(X3,X2))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(binintersectSubset2, axiom, binintersectSubset2 <=> 18.93/19.26 (![A,B]: (subset(A,B) => (binintersect(A,B) = A)))). 18.93/19.26 tff('120', plain, 18.93/19.26 binintersectSubset2 = 18.93/19.26 (![X2,X3]: (subset(X2,X3) => (binintersect(X2,X3) = X2))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(binintersectLsub, axiom, binintersectLsub <=> 18.93/19.26 (![A,B]: subset(binintersect(A,B),A))). 18.93/19.26 tff('121', plain, 18.93/19.26 binintersectLsub = (![X2,X3]: subset(binintersect(X2,X3),X2)), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(binintersectEL, axiom, binintersectEL <=> 18.93/19.26 (![A,B,Xx]: (in(Xx,binintersect(A,B)) => in(Xx,A)))). 18.93/19.26 tff('122', plain, 18.93/19.26 binintersectEL = (![X2,X3,X4]: (in(X4,binintersect(X2,X3)) => in(X4,X2))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(binintersectSubset5, axiom, binintersectSubset5 <=> 18.93/19.26 (![A,B,C]: (subset(C,A) => (subset(C,B) => subset(C,binintersect(A,B)))))). 18.93/19.26 tff('123', plain, 18.93/19.26 binintersectSubset5 = 18.93/19.26 (![X2,X3,X4]: 18.93/19.26 (subset(X4,X2) => (subset(X4,X3) => subset(X4,binintersect(X2,X3))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(binintersectI, axiom, binintersectI <=> 18.93/19.26 (![A,B,Xx]: (in(Xx,A) => (in(Xx,B) => in(Xx,binintersect(A,B)))))). 18.93/19.26 tff('124', plain, 18.93/19.26 binintersectI = 18.93/19.26 (![X2,X3,X4]: (in(X4,X2) => (in(X4,X3) => in(X4,binintersect(X2,X3))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(binunionRsub, axiom, binunionRsub <=> (![A,B]: subset(B,binunion(A,B)))). 18.93/19.26 tff('125', plain, binunionRsub = (![X2,X3]: subset(X3,binunion(X2,X3))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(binunionLsub, axiom, binunionLsub <=> (![A,B]: subset(A,binunion(A,B)))). 18.93/19.26 tff('126', plain, binunionLsub = (![X2,X3]: subset(X2,binunion(X2,X3))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(binunionE, axiom, binunionE <=> 18.93/19.26 (![A,B,Xx]: (in(Xx,binunion(A,B)) => (in(Xx,B) | in(Xx,A))))). 18.93/19.26 tff('127', plain, 18.93/19.26 binunionE = 18.93/19.26 (![X2,X3,X4]: (in(X4,binunion(X2,X3)) => (in(X4,X3) | in(X4,X2)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(binunionEcases, axiom, binunionEcases <=> 18.93/19.26 (![A,B,Xx,Xphi:$o]: 18.93/19.26 (in(Xx,binunion(A,B)) => 18.93/19.26 ((in(Xx,A) => Xphi) => ((in(Xx,B) => Xphi) => Xphi))))). 18.93/19.26 tff('128', plain, 18.93/19.26 binunionEcases = 18.93/19.26 (![X2,X3,X4,X5:$o]: 18.93/19.26 (in(X4,binunion(X2,X3)) => 18.93/19.26 ((in(X4,X2) => X5) => ((in(X4,X3) => X5) => X5)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(binunionIR, axiom, binunionIR <=> 18.93/19.26 (![A,B,Xx]: (in(Xx,B) => in(Xx,binunion(A,B))))). 18.93/19.26 tff('129', plain, 18.93/19.26 binunionIR = (![X2,X3,X4]: (in(X4,X3) => in(X4,binunion(X2,X3)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(upairset2IR, axiom, upairset2IR <=> 18.93/19.26 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 18.93/19.26 tff('130', plain, 18.93/19.26 upairset2IR = (![X2,X3]: in(X3,setadjoin(X2,setadjoin(X3,emptyset)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(binunionIL, axiom, binunionIL <=> 18.93/19.26 (![A,B,Xx]: (in(Xx,A) => in(Xx,binunion(A,B))))). 18.93/19.26 tff('131', plain, 18.93/19.26 binunionIL = (![X2,X3,X4]: (in(X4,X2) => in(X4,binunion(X2,X3)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(sepSubset, axiom, sepSubset <=> 18.93/19.26 (![A,Xphi:($i > $o)]: subset(dsetconstr(A,^[Xx]: Xphi(Xx)),A))). 18.93/19.26 tff('132', plain, 18.93/19.26 sepSubset = 18.93/19.26 (![X2,X3:($i > $o)]: subset(dsetconstr(X2,^[V_1]: X3(V_1)),X2)), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(sepInPowerset, axiom, sepInPowerset <=> 18.93/19.26 (![A,Xphi:($i > $o)]: in(dsetconstr(A,^[Xx]: Xphi(Xx)),powerset(A)))). 18.93/19.26 tff('133', plain, 18.93/19.26 sepInPowerset = 18.93/19.26 (![X2,X3:($i > $o)]: in(dsetconstr(X2,^[V_1]: X3(V_1)),powerset(X2))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(powersetsubset, axiom, powersetsubset <=> 18.93/19.26 (![A,B]: (subset(A,B) => subset(powerset(A),powerset(B))))). 18.93/19.26 tff('134', plain, 18.93/19.26 powersetsubset = 18.93/19.26 (![X2,X3]: (subset(X2,X3) => subset(powerset(X2),powerset(X3)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(inPowerset, axiom, inPowerset <=> (![A]: in(A,powerset(A)))). 18.93/19.26 tff('135', plain, inPowerset = (![X2]: in(X2,powerset(X2))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(powersetE1, axiom, powersetE1 <=> 18.93/19.26 (![A,B]: (in(B,powerset(A)) => subset(B,A)))). 18.93/19.26 tff('136', plain, 18.93/19.26 powersetE1 = (![X2,X3]: (in(X3,powerset(X2)) => subset(X3,X2))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(powersetI1, axiom, powersetI1 <=> 18.93/19.26 (![A,B]: (subset(B,A) => in(B,powerset(A))))). 18.93/19.26 tff('137', plain, 18.93/19.26 powersetI1 = (![X2,X3]: (subset(X3,X2) => in(X3,powerset(X2)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(subsetemptysetimpeq, axiom, subsetemptysetimpeq <=> 18.93/19.26 (![A]: (subset(A,emptyset) => (A = emptyset)))). 18.93/19.26 tff('138', plain, 18.93/19.26 subsetemptysetimpeq = (![X2]: (subset(X2,emptyset) => (X2 = emptyset))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(setextsub, axiom, setextsub <=> 18.93/19.26 (![A,B]: (subset(A,B) => (subset(B,A) => (A = B))))). 18.93/19.26 tff('139', plain, 18.93/19.26 setextsub = (![X2,X3]: (subset(X2,X3) => (subset(X3,X2) => (X2 = X3)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(subset2powerset, axiom, subset2powerset <=> 18.93/19.26 (![A,B]: (subset(A,B) => in(A,powerset(B))))). 18.93/19.26 tff('140', plain, 18.93/19.26 subset2powerset = (![X2,X3]: (subset(X2,X3) => in(X2,powerset(X3)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(setadjoinSub2, axiom, setadjoinSub2 <=> 18.93/19.26 (![A,Xx,B]: (subset(A,B) => subset(A,setadjoin(Xx,B))))). 18.93/19.26 tff('141', plain, 18.93/19.26 setadjoinSub2 = 18.93/19.26 (![X2,X3,X4]: (subset(X2,X4) => subset(X2,setadjoin(X3,X4)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(setadjoinSub, axiom, setadjoinSub <=> 18.93/19.26 (![Xx,A]: subset(A,setadjoin(Xx,A)))). 18.93/19.26 tff('142', plain, setadjoinSub = (![X2,X3]: subset(X3,setadjoin(X2,X3))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(subsetTrans, axiom, subsetTrans <=> 18.93/19.26 (![A,B,C]: (subset(A,B) => (subset(B,C) => subset(A,C))))). 18.93/19.26 tff('143', plain, 18.93/19.26 subsetTrans = 18.93/19.26 (![X2,X3,X4]: (subset(X2,X3) => (subset(X3,X4) => subset(X2,X4)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(subsetRefl, axiom, subsetRefl <=> (![A]: subset(A,A))). 18.93/19.26 tff('144', plain, subsetRefl = (![X2]: subset(X2,X2)), define([status(thm)])). 18.93/19.26 tff(notequalI2, axiom, notequalI2 <=> 18.93/19.26 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => (A != B))))). 18.93/19.26 tff('145', plain, 18.93/19.26 notequalI2 = (![X2,X3,X4]: (in(X4,X2) => ((~in(X4,X3)) => (X2 != X3)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(notequalI1, axiom, notequalI1 <=> (![A,B]: ((~subset(A,B)) => (A != B)))). 18.93/19.26 tff('146', plain, notequalI1 = (![X2,X3]: ((~subset(X2,X3)) => (X2 != X3))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(notsubsetI, axiom, notsubsetI <=> 18.93/19.26 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => (~subset(A,B)))))). 18.93/19.26 tff('147', plain, 18.93/19.26 notsubsetI = 18.93/19.26 (![X2,X3,X4]: (in(X4,X2) => ((~in(X4,X3)) => (~subset(X2,X3))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(subsetE2, axiom, subsetE2 <=> 18.93/19.26 (![A,B,Xx]: (subset(A,B) => ((~in(Xx,B)) => (~in(Xx,A)))))). 18.93/19.26 tff('148', plain, 18.93/19.26 subsetE2 = 18.93/19.26 (![X2,X3,X4]: (subset(X2,X3) => ((~in(X4,X3)) => (~in(X4,X2))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(subsetE, axiom, subsetE <=> 18.93/19.26 (![A,B,Xx]: (subset(A,B) => (in(Xx,A) => in(Xx,B))))). 18.93/19.26 tff('149', plain, 18.93/19.26 subsetE = (![X2,X3,X4]: (subset(X2,X3) => (in(X4,X2) => in(X4,X3)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(emptysetsubset, axiom, emptysetsubset <=> (![A]: subset(emptyset,A))). 18.93/19.26 tff('150', plain, emptysetsubset = (![X2]: subset(emptyset,X2)), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(subsetI2, axiom, subsetI2 <=> 18.93/19.26 (![A,B]: ((![Xx]: (in(Xx,A) => in(Xx,B))) => subset(A,B)))). 18.93/19.26 tff('151', plain, 18.93/19.26 subsetI2 = 18.93/19.26 (![X2,X3]: ((![X4]: (in(X4,X2) => in(X4,X3))) => subset(X2,X3))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(eqimpsubset1, axiom, eqimpsubset1 <=> (![A,B]: ((A = B) => subset(A,B)))). 18.93/19.26 tff('152', plain, eqimpsubset1 = (![X2,X3]: ((X2 = X3) => subset(X2,X3))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(eqimpsubset2, axiom, eqimpsubset2 <=> (![A,B]: ((A = B) => subset(B,A)))). 18.93/19.26 tff('153', plain, eqimpsubset2 = (![X2,X3]: ((X2 = X3) => subset(X3,X2))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(subsetI1, axiom, subsetI1 <=> 18.93/19.26 (![A,B]: ((![Xx]: (in(Xx,A) => in(Xx,B))) => subset(A,B)))). 18.93/19.26 tff('154', plain, 18.93/19.26 subsetI1 = 18.93/19.26 (![X2,X3]: ((![X4]: (in(X4,X2) => in(X4,X3))) => subset(X2,X3))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(dsetconstr__Cong, axiom, dsetconstr__Cong <=> 18.93/19.26 (![A,B]: 18.93/19.26 ((A = B) => 18.93/19.26 (![Xphi:($i > $o),Xpsi:($i > $o)]: 18.93/19.26 ((![Xx]: 18.93/19.26 (in(Xx,A) => 18.93/19.26 (![Xy]: (in(Xy,B) => ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy))))))) => 18.93/19.26 (dsetconstr(A,^[Xx]: Xphi(Xx)) = dsetconstr(B,^[Xx]: Xpsi(Xx)))))))). 18.93/19.26 tff('155', plain, 18.93/19.26 dsetconstr__Cong = 18.93/19.26 (![X2,X3]: 18.93/19.26 ((X2 = X3) => 18.93/19.26 (![X4:($i > $o),X5:($i > $o)]: 18.93/19.26 ((![X6]: 18.93/19.26 (in(X6,X2) => 18.93/19.26 (![X7]: (in(X7,X3) => ((X6 = X7) => (X4(X6) <=> X5(X7))))))) => 18.93/19.26 (dsetconstr(X2,^[V_1]: X4(V_1)) = dsetconstr(X3,^[V_2]: X5(V_2))))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(descr__Cong, axiom, descr__Cong <=> 18.93/19.26 (![Xphi:($i > $o),Xpsi:($i > $o)]: 18.93/19.26 ((![Xx,Xy]: ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy)))) => 18.93/19.26 (exu(^[Xx]: Xphi(Xx)) => 18.93/19.26 (exu(^[Xx]: Xpsi(Xx)) => 18.93/19.26 (descr(^[Xx]: Xphi(Xx)) = descr(^[Xx]: Xpsi(Xx)))))))). 18.93/19.26 tff('156', plain, 18.93/19.26 descr__Cong = 18.93/19.26 (![X2:($i > $o),X3:($i > $o)]: 18.93/19.26 ((![X4,X5]: ((X4 = X5) => (X2(X4) <=> X3(X5)))) => 18.93/19.26 (exu(^[V_1]: X2(V_1)) => 18.93/19.26 (exu(^[V_2]: X3(V_2)) => 18.93/19.26 (descr(^[V_3]: X2(V_3)) = descr(^[V_4]: X3(V_4))))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(exuEu, axiom, exuEu <=> 18.93/19.26 (![Xphi:($i > $o)]: 18.93/19.26 (exu(^[Xx]: Xphi(Xx)) => 18.93/19.26 (![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))). 18.93/19.26 tff('157', plain, 18.93/19.26 exuEu = 18.93/19.26 (![X2:($i > $o)]: 18.93/19.26 (exu(^[V_1]: X2(V_1)) => (![X3,X4]: (X2(X3) => (X2(X4) => (X3 = X4)))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(omega__Cong, axiom, omega__Cong <=> (omega = omega)). 18.93/19.26 tff('158', plain, omega__Cong = (omega = omega), define([status(thm)])). 18.93/19.26 tff(setunion__Cong, axiom, setunion__Cong <=> 18.93/19.26 (![A,B]: ((A = B) => (setunion(A) = setunion(B))))). 18.93/19.26 tff('159', plain, 18.93/19.26 setunion__Cong = (![X2,X3]: ((X2 = X3) => (setunion(X2) = setunion(X3)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(powerset__Cong, axiom, powerset__Cong <=> 18.93/19.26 (![A,B]: ((A = B) => (powerset(A) = powerset(B))))). 18.93/19.26 tff('160', plain, 18.93/19.26 powerset__Cong = (![X2,X3]: ((X2 = X3) => (powerset(X2) = powerset(X3)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(setadjoin__Cong, axiom, setadjoin__Cong <=> 18.93/19.26 (![Xx,Xy]: 18.93/19.26 ((Xx = Xy) => 18.93/19.26 (![Xz,Xu]: ((Xz = Xu) => (setadjoin(Xx,Xz) = setadjoin(Xy,Xu))))))). 18.93/19.26 tff('161', plain, 18.93/19.26 setadjoin__Cong = 18.93/19.26 (![X2,X3]: 18.93/19.26 ((X2 = X3) => 18.93/19.26 (![X4,X5]: ((X4 = X5) => (setadjoin(X2,X4) = setadjoin(X3,X5)))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(emptyset__Cong, axiom, emptyset__Cong <=> (emptyset = emptyset)). 18.93/19.26 tff('162', plain, emptyset__Cong = (emptyset = emptyset), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(exu__Cong, axiom, exu__Cong <=> 18.93/19.26 (![Xphi:($i > $o),Xpsi:($i > $o)]: 18.93/19.26 ((![Xx,Xy]: ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy)))) => 18.93/19.26 (exu(^[Xx]: Xphi(Xx)) <=> exu(^[Xx]: Xpsi(Xx)))))). 18.93/19.26 tff('163', plain, 18.93/19.26 exu__Cong = 18.93/19.26 (![X2:($i > $o),X3:($i > $o)]: 18.93/19.26 ((![X4,X5]: ((X4 = X5) => (X2(X4) <=> X3(X5)))) => 18.93/19.26 (exu(^[V_1]: X2(V_1)) <=> exu(^[V_2]: X3(V_2))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(exuE3u, axiom, exuE3u <=> 18.93/19.26 (![Xphi:($i > $o)]: 18.93/19.26 (exu(^[Xx]: Xphi(Xx)) => 18.93/19.26 (![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))). 18.93/19.26 tff('164', plain, 18.93/19.26 exuE3u = 18.93/19.26 (![X2:($i > $o)]: 18.93/19.26 (exu(^[V_1]: X2(V_1)) => (![X3,X4]: (X2(X3) => (X2(X4) => (X3 = X4)))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(in__Cong, axiom, in__Cong <=> 18.93/19.26 (![A,B]: ((A = B) => (![Xx,Xy]: ((Xx = Xy) => (in(Xx,A) <=> in(Xy,B))))))). 18.93/19.26 tff('165', plain, 18.93/19.26 in__Cong = 18.93/19.26 (![X2,X3]: 18.93/19.26 ((X2 = X3) => (![X4,X5]: ((X4 = X5) => (in(X4,X2) <=> in(X5,X3)))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(inCongP, axiom, inCongP <=> 18.93/19.26 (![A,B]: ((A = B) => (![Xx,Xy]: ((Xx = Xy) => (in(Xx,A) => in(Xy,B))))))). 18.93/19.26 tff('166', plain, 18.93/19.26 inCongP = 18.93/19.26 (![X2,X3]: 18.93/19.26 ((X2 = X3) => (![X4,X5]: ((X4 = X5) => (in(X4,X2) => in(X5,X3)))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(exuI2, axiom, exuI2 <=> 18.93/19.26 (![Xphi:($i > $o)]: 18.93/19.26 ((?[Xx]: (![Xy]: (Xphi(Xy) <=> (Xy = Xx)))) => exu(^[Xx]: Xphi(Xx))))). 18.93/19.26 tff('167', plain, 18.93/19.26 exuI2 = 18.93/19.26 (![X2:($i > $o)]: 18.93/19.26 ((?[X3]: (![X4]: (X2(X4) <=> (X4 = X3)))) => exu(^[V_1]: X2(V_1)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(exuI3, axiom, exuI3 <=> 18.93/19.26 (![Xphi:($i > $o)]: 18.93/19.26 ((?[Xx]: Xphi(Xx)) => 18.93/19.26 ((![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy)))) => 18.93/19.26 exu(^[Xx]: Xphi(Xx)))))). 18.93/19.26 tff('168', plain, 18.93/19.26 exuI3 = 18.93/19.26 (![X2:($i > $o)]: 18.93/19.26 ((?[X3]: X2(X3)) => 18.93/19.26 ((![X4,X5]: (X2(X4) => (X2(X5) => (X4 = X5)))) => 18.93/19.26 exu(^[V_1]: X2(V_1))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(exuI1, axiom, exuI1 <=> 18.93/19.26 (![Xphi:($i > $o)]: 18.93/19.26 ((?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx))) => 18.93/19.26 exu(^[Xx]: Xphi(Xx))))). 18.93/19.26 tff('169', plain, 18.93/19.26 exuI1 = 18.93/19.26 (![X2:($i > $o)]: 18.93/19.26 ((?[X3]: ((![X4]: (X2(X4) => (X3 = X4))) & X2(X3))) => 18.93/19.26 exu(^[V_1]: X2(V_1)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(notdallE, axiom, notdallE <=> 18.93/19.26 (![A,Xphi:($i > $o)]: 18.93/19.26 ((~(![Xx]: (in(Xx,A) => Xphi(Xx)))) => (?[Xx]: ((~Xphi(Xx)) & in(Xx,A)))))). 18.93/19.26 tff('170', plain, 18.93/19.26 notdallE = 18.93/19.26 (![X2,X3:($i > $o)]: 18.93/19.26 ((~(![X4]: (in(X4,X2) => X3(X4)))) => (?[X5]: ((~X3(X5)) & in(X5,X2))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(notdexE, axiom, notdexE <=> 18.93/19.26 (![A,Xphi:($i > $o)]: 18.93/19.26 ((~(?[Xx]: (Xphi(Xx) & in(Xx,A)))) => (![Xx]: (in(Xx,A) => (~Xphi(Xx))))))). 18.93/19.26 tff('171', plain, 18.93/19.26 notdexE = 18.93/19.26 (![X2,X3:($i > $o)]: 18.93/19.26 ((~(?[X4]: (X3(X4) & in(X4,X2)))) => (![X5]: (in(X5,X2) => (~X3(X5)))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(prop2set2propI, axiom, prop2set2propI <=> 18.93/19.26 (![Xphi:$o]: (Xphi => set2prop(prop2set(Xphi))))). 18.93/19.26 tff('172', plain, 18.93/19.26 prop2set2propI = (![X2:$o]: (X2 => set2prop(prop2set(X2)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(prop2setI, axiom, prop2setI <=> 18.93/19.26 (![Xphi:$o]: (Xphi => in(emptyset,prop2set(Xphi))))). 18.93/19.26 tff('173', plain, prop2setI = (![X2:$o]: (X2 => in(emptyset,prop2set(X2)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(quantDeMorgan4, axiom, quantDeMorgan4 <=> 18.93/19.26 (![A,Xphi:($i > $o)]: 18.93/19.26 ((?[Xx]: ((~Xphi(Xx)) & in(Xx,A))) => (~(![Xx]: (in(Xx,A) => Xphi(Xx))))))). 18.93/19.26 tff('174', plain, 18.93/19.26 quantDeMorgan4 = 18.93/19.26 (![X2,X3:($i > $o)]: 18.93/19.26 ((?[X4]: ((~X3(X4)) & in(X4,X2))) => (~(![X5]: (in(X5,X2) => X3(X5)))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(quantDeMorgan3, axiom, quantDeMorgan3 <=> 18.93/19.26 (![A,Xphi:($i > $o)]: 18.93/19.26 ((~(?[Xx]: (Xphi(Xx) & in(Xx,A)))) => (![Xx]: (in(Xx,A) => (~Xphi(Xx))))))). 18.93/19.26 tff('175', plain, 18.93/19.26 quantDeMorgan3 = 18.93/19.26 (![X2,X3:($i > $o)]: 18.93/19.26 ((~(?[X4]: (X3(X4) & in(X4,X2)))) => (![X5]: (in(X5,X2) => (~X3(X5)))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(quantDeMorgan2, axiom, quantDeMorgan2 <=> 18.93/19.26 (![A,Xphi:($i > $o)]: 18.93/19.26 ((![Xx]: (in(Xx,A) => (~Xphi(Xx)))) => (~(?[Xx]: (Xphi(Xx) & in(Xx,A))))))). 18.93/19.26 tff('176', plain, 18.93/19.26 quantDeMorgan2 = 18.93/19.26 (![X2,X3:($i > $o)]: 18.93/19.26 ((![X4]: (in(X4,X2) => (~X3(X4)))) => (~(?[X5]: (X3(X5) & in(X5,X2)))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(quantDeMorgan1, axiom, quantDeMorgan1 <=> 18.93/19.26 (![A,Xphi:($i > $o)]: 18.93/19.26 ((~(![Xx]: (in(Xx,A) => Xphi(Xx)))) => (?[Xx]: ((~Xphi(Xx)) & in(Xx,A)))))). 18.93/19.26 tff('177', plain, 18.93/19.26 quantDeMorgan1 = 18.93/19.26 (![X2,X3:($i > $o)]: 18.93/19.26 ((~(![X4]: (in(X4,X2) => X3(X4)))) => (?[X5]: ((~X3(X5)) & in(X5,X2))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(vacuousDall, axiom, vacuousDall <=> 18.93/19.26 (![Xphi:($i > $o),Xx]: (in(Xx,emptyset) => Xphi(Xx)))). 18.93/19.26 tff('178', plain, 18.93/19.26 vacuousDall = (![X2:($i > $o),X3]: (in(X3,emptyset) => X2(X3))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(emptyE1, axiom, emptyE1 <=> 18.93/19.26 (![A,Xphi:($i > $o)]: 18.93/19.26 ((?[Xx]: (Xphi(Xx) & in(Xx,A))) => 18.93/19.26 ((dsetconstr(A,^[Xx]: Xphi(Xx)) = emptyset) => $false)))). 18.93/19.26 tff('179', plain, 18.93/19.26 emptyE1 = 18.93/19.26 (![X2,X3:($i > $o)]: 18.93/19.26 ((?[X4]: (X3(X4) & in(X4,X2))) => 18.93/19.26 ((dsetconstr(X2,^[V_1]: X3(V_1)) = emptyset) => $false))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(upairsetIR, axiom, upairsetIR <=> 18.93/19.26 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 18.93/19.26 tff('180', plain, 18.93/19.26 upairsetIR = (![X2,X3]: in(X3,setadjoin(X2,setadjoin(X3,emptyset)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(upairsetIL, axiom, upairsetIL <=> 18.93/19.26 (![Xx,Xy]: in(Xx,setadjoin(Xx,setadjoin(Xy,emptyset))))). 18.93/19.26 tff('181', plain, 18.93/19.26 upairsetIL = (![X2,X3]: in(X2,setadjoin(X2,setadjoin(X3,emptyset)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(upairsetE, axiom, upairsetE <=> 18.93/19.26 (![Xx,Xy,Xz]: 18.93/19.26 (in(Xz,setadjoin(Xx,setadjoin(Xy,emptyset))) => ((Xz = Xy) | (Xz = Xx))))). 18.93/19.26 tff('182', plain, 18.93/19.26 upairsetE = 18.93/19.26 (![X2,X3,X4]: 18.93/19.26 (in(X4,setadjoin(X2,setadjoin(X3,emptyset))) => 18.93/19.26 ((X4 = X3) | (X4 = X2)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(singletonsswitch, axiom, singletonsswitch <=> 18.93/19.26 (![Xx,Xy]: (in(Xx,setadjoin(Xy,emptyset)) => in(Xy,setadjoin(Xx,emptyset))))). 18.93/19.26 tff('183', plain, 18.93/19.26 singletonsswitch = 18.93/19.26 (![X2,X3]: 18.93/19.26 (in(X2,setadjoin(X3,emptyset)) => in(X3,setadjoin(X2,emptyset)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(eqinunit, axiom, eqinunit <=> 18.93/19.26 (![Xx,Xy]: ((Xx = Xy) => in(Xx,setadjoin(Xy,emptyset))))). 18.93/19.26 tff('184', plain, 18.93/19.26 eqinunit = (![X2,X3]: ((X2 = X3) => in(X2,setadjoin(X3,emptyset)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(notinsingleton, axiom, notinsingleton <=> 18.93/19.26 (![Xx,Xy]: ((Xx != Xy) => (~in(Xy,setadjoin(Xx,emptyset)))))). 18.93/19.26 tff('185', plain, 18.93/19.26 notinsingleton = 18.93/19.26 (![X2,X3]: ((X2 != X3) => (~in(X3,setadjoin(X2,emptyset))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(uniqinunit, axiom, uniqinunit <=> 18.93/19.26 (![Xx,Xy]: (in(Xx,setadjoin(Xy,emptyset)) => (Xx = Xy)))). 18.93/19.26 tff('186', plain, 18.93/19.26 uniqinunit = (![X2,X3]: (in(X2,setadjoin(X3,emptyset)) => (X2 = X3))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(nonemptyImpWitness, axiom, nonemptyImpWitness <=> 18.93/19.26 (![A]: (nonempty(A) => (?[Xx]: (in(Xx,A)))))). 18.93/19.26 tff('187', plain, 18.93/19.26 nonemptyImpWitness = (![X2]: (nonempty(X2) => (?[X3]: (in(X3,X2))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(exuE2, axiom, exuE2 <=> 18.93/19.26 (![Xphi:($i > $o)]: 18.93/19.26 (exu(^[Xx]: Xphi(Xx)) => (?[Xx]: (![Xy]: (Xphi(Xy) <=> (Xy = Xx))))))). 18.93/19.26 tff('188', plain, 18.93/19.26 exuE2 = 18.93/19.26 (![X2:($i > $o)]: 18.93/19.26 (exu(^[V_1]: X2(V_1)) => (?[X3]: (![X4]: (X2(X4) <=> (X4 = X3)))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(subPowSU, axiom, subPowSU <=> 18.93/19.26 (![A,Xx]: (in(Xx,A) => in(Xx,powerset(setunion(A)))))). 18.93/19.26 tff('189', plain, 18.93/19.26 subPowSU = (![X2,X3]: (in(X3,X2) => in(X3,powerset(setunion(X2))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(setunionE, axiom, setunionE <=> 18.93/19.26 (![A,Xx]: 18.93/19.26 (in(Xx,setunion(A)) => 18.93/19.26 (![Xphi:$o]: ((![B]: (in(Xx,B) => (in(B,A) => Xphi))) => Xphi))))). 18.93/19.26 tff('190', plain, 18.93/19.26 setunionE = 18.93/19.26 (![X2,X3]: 18.93/19.26 (in(X3,setunion(X2)) => 18.93/19.26 (![X4:$o]: ((![X5]: (in(X3,X5) => (in(X5,X2) => X4))) => X4)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(setunionI, axiom, setunionI <=> 18.93/19.26 (![A,Xx,B]: (in(Xx,B) => (in(B,A) => in(Xx,setunion(A)))))). 18.93/19.26 tff('191', plain, 18.93/19.26 setunionI = 18.93/19.26 (![X2,X3,X4]: (in(X3,X4) => (in(X4,X2) => in(X3,setunion(X2))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(powersetE, axiom, powersetE <=> 18.93/19.26 (![A,B,Xx]: (in(B,powerset(A)) => (in(Xx,B) => in(Xx,A))))). 18.93/19.26 tff('192', plain, 18.93/19.26 powersetE = 18.93/19.26 (![X2,X3,X4]: (in(X3,powerset(X2)) => (in(X4,X3) => in(X4,X2)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(emptyInPowerset, axiom, emptyInPowerset <=> 18.93/19.26 (![A]: in(emptyset,powerset(A)))). 18.93/19.26 tff('193', plain, emptyInPowerset = (![X2]: in(emptyset,powerset(X2))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(emptyinPowerset, axiom, emptyinPowerset <=> 18.93/19.26 (![A]: in(emptyset,powerset(A)))). 18.93/19.26 tff('194', plain, emptyinPowerset = (![X2]: in(emptyset,powerset(X2))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(powersetI, axiom, powersetI <=> 18.93/19.26 (![A,B]: ((![Xx]: (in(Xx,B) => in(Xx,A))) => in(B,powerset(A))))). 18.93/19.26 tff('195', plain, 18.93/19.26 powersetI = 18.93/19.26 (![X2,X3]: ((![X4]: (in(X4,X3) => in(X4,X2))) => in(X3,powerset(X2)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(setoftrueEq, axiom, setoftrueEq <=> 18.93/19.26 (![A]: (dsetconstr(A,^[Xx]: $true) = A))). 18.93/19.26 tff('196', plain, setoftrueEq = (![X2]: (dsetconstr(X2,^[V_1]: $true) = X2)), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(setadjoinOr, axiom, setadjoinOr <=> 18.93/19.26 (![Xx,A,Xy]: (in(Xy,setadjoin(Xx,A)) => (in(Xy,A) | (Xy = Xx))))). 18.93/19.26 tff('197', plain, 18.93/19.26 setadjoinOr = 18.93/19.26 (![X2,X3,X4]: (in(X4,setadjoin(X2,X3)) => (in(X4,X3) | (X4 = X2)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(setadjoinE, axiom, setadjoinE <=> 18.93/19.26 (![Xx,A,Xy]: 18.93/19.26 (in(Xy,setadjoin(Xx,A)) => 18.93/19.26 (![Xphi:$o]: (((Xy = Xx) => Xphi) => ((in(Xy,A) => Xphi) => Xphi)))))). 18.93/19.26 tff('198', plain, 18.93/19.26 setadjoinE = 18.93/19.26 (![X2,X3,X4]: 18.93/19.26 (in(X4,setadjoin(X2,X3)) => 18.93/19.26 (![X5:$o]: (((X4 = X2) => X5) => ((in(X4,X3) => X5) => X5))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(setadjoinIR, axiom, setadjoinIR <=> 18.93/19.26 (![Xx,A,Xy]: (in(Xy,A) => in(Xy,setadjoin(Xx,A))))). 18.93/19.26 tff('199', plain, 18.93/19.26 setadjoinIR = (![X2,X3,X4]: (in(X4,X3) => in(X4,setadjoin(X2,X3)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(emptyinunitempty, axiom, emptyinunitempty() = 18.93/19.26 in(emptyset,setadjoin(emptyset,emptyset))). 18.93/19.26 tff('200', plain, 18.93/19.26 emptyinunitempty = in(emptyset,setadjoin(emptyset,emptyset)), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(setadjoinIL, axiom, setadjoinIL <=> (![Xx,Xy]: in(Xx,setadjoin(Xx,Xy)))). 18.93/19.26 tff('201', plain, setadjoinIL = (![X2,X3]: in(X2,setadjoin(X2,X3))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(nonemptyI1, axiom, nonemptyI1 <=> 18.93/19.26 (![A]: ((?[Xx]: in(Xx,A)) => nonempty(A)))). 18.93/19.26 tff('202', plain, nonemptyI1 = (![X2]: ((?[X3]: in(X3,X2)) => nonempty(X2))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(nonemptyI, axiom, nonemptyI <=> 18.93/19.26 (![A,Xphi:($i > $o),Xx]: 18.93/19.26 (in(Xx,A) => (Xphi(Xx) => nonempty(dsetconstr(A,^[Xy]: Xphi(Xy))))))). 18.93/19.26 tff('203', plain, 18.93/19.26 nonemptyI = 18.93/19.26 (![X2,X3:($i > $o),X4]: 18.93/19.26 (in(X4,X2) => (X3(X4) => nonempty(dsetconstr(X2,^[V_1]: X3(V_1)))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(nonemptyE1, axiom, nonemptyE1 <=> 18.93/19.26 (![A]: (nonempty(A) => (?[Xx]: in(Xx,A))))). 18.93/19.26 tff('204', plain, nonemptyE1 = (![X2]: (nonempty(X2) => (?[X3]: in(X3,X2)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(nonempty, axiom, nonempty() = ^[Xx]: (Xx != emptyset)). 18.93/19.26 tff('205', plain, nonempty = (^[V_1]: (V_1 != emptyset)), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(setbeta, axiom, setbeta <=> 18.93/19.26 (![A,Xphi:($i > $o),Xx]: 18.93/19.26 (in(Xx,A) => (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) <=> Xphi(Xx))))). 18.93/19.26 tff('206', plain, 18.93/19.26 setbeta = 18.93/19.26 (![X2,X3:($i > $o),X4]: 18.93/19.26 (in(X4,X2) => (in(X4,dsetconstr(X2,^[V_1]: X3(V_1))) <=> X3(X4)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(noeltsimpempty, axiom, noeltsimpempty <=> 18.93/19.26 (![A]: ((![Xx]: (~in(Xx,A))) => (A = emptyset)))). 18.93/19.26 tff('207', plain, 18.93/19.26 noeltsimpempty = (![X2]: ((![X3]: (~in(X3,X2))) => (X2 = emptyset))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(emptyI, axiom, emptyI <=> 18.93/19.26 (![A]: ((![Xx]: (~in(Xx,A))) => (A = emptyset)))). 18.93/19.26 tff('208', plain, 18.93/19.26 emptyI = (![X2]: ((![X3]: (~in(X3,X2))) => (X2 = emptyset))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(setext, axiom, setext <=> 18.93/19.26 (![A,B]: 18.93/19.26 ((![Xx]: (in(Xx,A) => in(Xx,B))) => 18.93/19.26 ((![Xx]: (in(Xx,B) => in(Xx,A))) => (A = B))))). 18.93/19.26 tff('209', plain, 18.93/19.26 setext = 18.93/19.26 (![X2,X3]: 18.93/19.26 ((![X4]: (in(X4,X2) => in(X4,X3))) => 18.93/19.26 ((![X5]: (in(X5,X3) => in(X5,X2))) => (X2 = X3)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(exuE3e, axiom, exuE3e <=> 18.93/19.26 (![Xphi:($i > $o)]: (exu(^[Xx]: Xphi(Xx)) => (?[Xx]: Xphi(Xx))))). 18.93/19.26 tff('210', plain, 18.93/19.26 exuE3e = (![X2:($i > $o)]: (exu(^[V_1]: X2(V_1)) => (?[X3]: X2(X3)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(notinemptyset, axiom, notinemptyset <=> (![Xx]: (~in(Xx,emptyset)))). 18.93/19.26 tff('211', plain, notinemptyset = (![X2]: (~in(X2,emptyset))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(emptysetimpfalse, axiom, emptysetimpfalse <=> 18.93/19.26 (![Xx]: (in(Xx,emptyset) => $false))). 18.93/19.26 tff('212', plain, emptysetimpfalse = (![X2]: (in(X2,emptyset) => $false)), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(emptysetE, axiom, emptysetE <=> 18.93/19.26 (![Xx]: (in(Xx,emptyset) => (![Xphi:$o]: Xphi)))). 18.93/19.26 tff('213', plain, emptysetE = (![X2]: (in(X2,emptyset) => (![X3:$o]: X3))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(prop2setE, axiom, prop2setE <=> 18.93/19.26 (![Xphi:$o,Xx]: (in(Xx,prop2set(Xphi)) => Xphi))). 18.93/19.26 tff('214', plain, prop2setE = (![X2:$o,X3]: (in(X3,prop2set(X2)) => X2)), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(exuE1, axiom, exuE1 <=> 18.93/19.26 (![Xphi:($i > $o)]: 18.93/19.26 (exu(^[Xx]: Xphi(Xx)) => 18.93/19.26 (?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx)))))). 18.93/19.26 tff('215', plain, 18.93/19.26 exuE1 = 18.93/19.26 (![X2:($i > $o)]: 18.93/19.26 (exu(^[V_1]: X2(V_1)) => 18.93/19.26 (?[X3]: ((![X4]: (X2(X4) => (X3 = X4))) & X2(X3))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(dsetconstrER, axiom, dsetconstrER <=> 18.93/19.26 (![A,Xphi:($i > $o),Xx]: (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) => Xphi(Xx)))). 18.93/19.26 tff('216', plain, 18.93/19.26 dsetconstrER = 18.93/19.26 (![X2,X3:($i > $o),X4]: (in(X4,dsetconstr(X2,^[V_1]: X3(V_1))) => X3(X4))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(dsetconstrEL, axiom, dsetconstrEL <=> 18.93/19.26 (![A,Xphi:($i > $o),Xx]: (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) => in(Xx,A)))). 18.93/19.26 tff('217', plain, 18.93/19.26 dsetconstrEL = 18.93/19.26 (![X2,X3:($i > $o),X4]: 18.93/19.26 (in(X4,dsetconstr(X2,^[V_1]: X3(V_1))) => in(X4,X2))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(dsetconstrI, axiom, dsetconstrI <=> 18.93/19.26 (![A,Xphi:($i > $o),Xx]: 18.93/19.26 (in(Xx,A) => (Xphi(Xx) => in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))))))). 18.93/19.26 tff('218', plain, 18.93/19.26 dsetconstrI = 18.93/19.26 (![X2,X3:($i > $o),X4]: 18.93/19.26 (in(X4,X2) => (X3(X4) => in(X4,dsetconstr(X2,^[V_1]: X3(V_1)))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(descrp, axiom, descrp <=> 18.93/19.26 (![Xphi:($i > $o)]: (exu(^[Xx]: Xphi(Xx)) => Xphi(descr(^[Xx]: Xphi(Xx)))))). 18.93/19.26 tff('219', plain, 18.93/19.26 descrp = 18.93/19.26 (![X2:($i > $o)]: (exu(^[V_1]: X2(V_1)) => X2(descr(^[V_2]: X2(V_2))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(wellorderingAx, axiom, wellorderingAx <=> 18.93/19.26 (![A]: 18.93/19.26 (?[B]: 18.93/19.26 ((![C]: 18.93/19.26 (((?[Xx]: in(Xx,C)) & (![Xx]: (in(Xx,C) => in(Xx,A)))) => 18.93/19.26 (?[D,Xx]: 18.93/19.26 ((![E]: 18.93/19.26 (in(E,B) => (in(Xx,E) | (![Xy]: (in(Xy,E) => in(Xy,D)))))) & 18.93/19.26 (~(?[Xy]: (in(Xy,C) & in(Xy,D)))) & in(Xx,C) & in(D,B))))) & 18.93/19.26 (![C,D]: 18.93/19.26 ((in(D,B) & in(C,B)) => 18.93/19.26 ((![Xx]: (in(Xx,D) => in(Xx,C))) | 18.93/19.26 (![Xx]: (in(Xx,C) => in(Xx,D)))))) & 18.93/19.26 (![Xx,Xy]: 18.93/19.26 ((in(Xy,A) & in(Xx,A)) => 18.93/19.26 ((![C]: (in(C,B) => (in(Xx,C) <=> in(Xy,C)))) => (Xx = Xy)))) & 18.93/19.26 (![C]: (in(C,B) => (![Xx]: (in(Xx,C) => in(Xx,A))))))))). 18.93/19.26 tff('220', plain, 18.93/19.26 wellorderingAx = 18.93/19.26 (![X2]: 18.93/19.26 (?[X3]: 18.93/19.26 ((![X4]: 18.93/19.26 (((?[X5]: in(X5,X4)) & (![X6]: (in(X6,X4) => in(X6,X2)))) => 18.93/19.26 (?[X7,X8]: 18.93/19.26 ((![X9]: 18.93/19.26 (in(X9,X3) => 18.93/19.26 (in(X8,X9) | (![X10]: (in(X10,X9) => in(X10,X7)))))) & 18.93/19.26 (~(?[X11]: (in(X11,X4) & in(X11,X7)))) & in(X8,X4) & 18.93/19.26 in(X7,X3))))) & 18.93/19.26 (![X12,X13]: 18.93/19.26 ((in(X13,X3) & in(X12,X3)) => 18.93/19.26 ((![X14]: (in(X14,X13) => in(X14,X12))) | 18.93/19.26 (![X15]: (in(X15,X12) => in(X15,X13)))))) & 18.93/19.26 (![X16,X17]: 18.93/19.26 ((in(X17,X2) & in(X16,X2)) => 18.93/19.26 ((![X18]: (in(X18,X3) => (in(X16,X18) <=> in(X17,X18)))) => 18.93/19.26 (X16 = X17)))) & 18.93/19.26 (![X19]: (in(X19,X3) => (![X20]: (in(X20,X19) => in(X20,X2)))))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(foundationAx, axiom, foundationAx <=> 18.93/19.26 (![A]: 18.93/19.26 ((?[Xx]: in(Xx,A)) => 18.93/19.26 (?[B]: ((~(?[Xx]: (in(Xx,A) & in(Xx,B)))) & in(B,A)))))). 18.93/19.26 tff('221', plain, 18.93/19.26 foundationAx = 18.93/19.26 (![X2]: 18.93/19.26 ((?[X3]: in(X3,X2)) => 18.93/19.26 (?[X4]: ((~(?[X5]: (in(X5,X2) & in(X5,X4)))) & in(X4,X2))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(replAx, axiom, replAx <=> 18.93/19.26 (![Xphi:(($i * $i) > $o),A]: 18.93/19.26 ((![Xx]: (in(Xx,A) => exu(^[Xy]: Xphi(Xx,Xy)))) => 18.93/19.26 (?[B]: (![Xx]: (in(Xx,B) <=> (?[Xy]: (Xphi(Xy,Xx) & in(Xy,A))))))))). 18.93/19.26 tff('222', plain, 18.93/19.26 replAx = 18.93/19.26 (![X2:(($i * $i) > $o),X3]: 18.93/19.26 ((![X4]: (in(X4,X3) => exu(^[V_1]: X2(X4,V_1)))) => 18.93/19.26 (?[X5]: (![X6]: (in(X6,X5) <=> (?[X7]: (X2(X7,X6) & in(X7,X3)))))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(omegaIndAx, axiom, omegaIndAx <=> 18.93/19.26 (![A]: 18.93/19.26 (((![Xx]: ((in(Xx,A) & in(Xx,omega)) => in(setadjoin(Xx,Xx),A))) & 18.93/19.26 in(emptyset,A)) => 18.93/19.26 (![Xx]: (in(Xx,omega) => in(Xx,A)))))). 18.93/19.26 tff('223', plain, 18.93/19.26 omegaIndAx = 18.93/19.26 (![X2]: 18.93/19.26 (((![X3]: ((in(X3,X2) & in(X3,omega)) => in(setadjoin(X3,X3),X2))) & 18.93/19.26 in(emptyset,X2)) => 18.93/19.26 (![X4]: (in(X4,omega) => in(X4,X2))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(omegaSAx, axiom, omegaSAx <=> 18.93/19.26 (![Xx]: (in(Xx,omega) => in(setadjoin(Xx,Xx),omega)))). 18.93/19.26 tff('224', plain, 18.93/19.26 omegaSAx = (![X2]: (in(X2,omega) => in(setadjoin(X2,X2),omega))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(omega0Ax, axiom, omega0Ax() = in(emptyset,omega)). 18.93/19.26 tff('225', plain, omega0Ax = in(emptyset,omega), define([status(thm)])). 18.93/19.26 tff(setunionAx, axiom, setunionAx <=> 18.93/19.26 (![A,Xx]: (in(Xx,setunion(A)) <=> (?[B]: (in(B,A) & in(Xx,B)))))). 18.93/19.26 tff('226', plain, 18.93/19.26 setunionAx = 18.93/19.26 (![X2,X3]: (in(X3,setunion(X2)) <=> (?[X4]: (in(X4,X2) & in(X3,X4))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(powersetAx, axiom, powersetAx <=> 18.93/19.26 (![A,B]: (in(B,powerset(A)) <=> (![Xx]: (in(Xx,B) => in(Xx,A)))))). 18.93/19.26 tff('227', plain, 18.93/19.26 powersetAx = 18.93/19.26 (![X2,X3]: (in(X3,powerset(X2)) <=> (![X4]: (in(X4,X3) => in(X4,X2))))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(setadjoinAx, axiom, setadjoinAx <=> 18.93/19.26 (![Xx,A,Xy]: (in(Xy,setadjoin(Xx,A)) <=> (in(Xy,A) | (Xy = Xx))))). 18.93/19.26 tff('228', plain, 18.93/19.26 setadjoinAx = 18.93/19.26 (![X2,X3,X4]: (in(X4,setadjoin(X2,X3)) <=> (in(X4,X3) | (X4 = X2)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(emptysetAx, axiom, emptysetAx <=> (![Xx]: (~in(Xx,emptyset)))). 18.93/19.26 tff('229', plain, emptysetAx = (![X2]: (~in(X2,emptyset))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(setextAx, axiom, setextAx <=> 18.93/19.26 (![A,B]: ((![Xx]: (in(Xx,A) <=> in(Xx,B))) => (A = B)))). 18.93/19.26 tff('230', plain, 18.93/19.26 setextAx = (![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(exu, axiom, exu() = 18.93/19.26 ^[Xphi:($i > $o)]: (?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx)))). 18.93/19.26 tff('231', plain, 18.93/19.26 exu = 18.93/19.26 (^[V_1:($i > $o)]: (?[X2]: ((![X3]: (V_1(X3) => (X2 = X3))) & V_1(X2)))), 18.93/19.26 define([status(thm)])). 18.93/19.26 tff(powersetT_lem, conjecture, 18.93/19.26 (setextAx => 18.93/19.26 (emptysetAx => 18.93/19.26 (setadjoinAx => 18.93/19.26 (powersetAx => 18.93/19.26 (setunionAx => 18.93/19.26 (omega0Ax => 18.93/19.26 (omegaSAx => 18.93/19.26 (omegaIndAx => 18.93/19.26 (replAx => 18.93/19.26 (foundationAx => 18.93/19.26 (wellorderingAx => 18.93/19.26 (descrp => 18.93/19.26 (dsetconstrI => 18.93/19.26 (dsetconstrEL => 18.93/19.26 (dsetconstrER => 18.93/19.26 (exuE1 => 18.93/19.26 (prop2setE => 18.93/19.26 (emptysetE => 18.93/19.26 (emptysetimpfalse => 18.93/19.26 (notinemptyset => 18.93/19.26 (exuE3e => 18.93/19.26 (setext => 18.93/19.26 (emptyI => 18.93/19.26 (noeltsimpempty => 18.93/19.26 (setbeta => 18.93/19.26 (nonemptyE1 => 18.93/19.26 (nonemptyI => 18.93/19.26 (nonemptyI1 => 18.93/19.26 (setadjoinIL => 18.93/19.26 (emptyinunitempty => 18.93/19.26 (setadjoinIR => 18.93/19.26 (setadjoinE => 18.93/19.26 (setadjoinOr => 18.93/19.26 (setoftrueEq => 18.93/19.26 (powersetI => 18.93/19.26 (emptyinPowerset => 18.93/19.26 (emptyInPowerset => 18.93/19.26 (powersetE => 18.93/19.26 (setunionI => 18.93/19.26 (setunionE => 18.93/19.26 (subPowSU => 18.93/19.26 (exuE2 => 18.93/19.26 (nonemptyImpWitness => 18.93/19.26 (uniqinunit => 18.93/19.26 (notinsingleton => 18.93/19.26 (eqinunit => 18.93/19.26 (singletonsswitch => 18.93/19.26 (upairsetE => 18.93/19.26 (upairsetIL => 18.93/19.26 (upairsetIR => 18.93/19.26 (emptyE1 => 18.93/19.26 (vacuousDall => 18.93/19.26 (quantDeMorgan1 => 18.93/19.26 (quantDeMorgan2 => 18.93/19.26 (quantDeMorgan3 => 18.93/19.26 (quantDeMorgan4 => 18.93/19.26 (prop2setI => 18.93/19.26 (prop2set2propI => 18.93/19.26 (notdexE => 18.93/19.26 (notdallE => 18.93/19.26 (exuI1 => 18.93/19.26 (exuI3 => 18.93/19.26 (exuI2 => 18.93/19.26 (inCongP => 18.93/19.26 (in__Cong => 18.93/19.26 (exuE3u => 18.93/19.26 ( 18.93/19.26 exu__Cong => 18.93/19.26 ( 18.93/19.26 emptyset__Cong => 18.93/19.26 ( 18.93/19.26 setadjoin__Cong => 18.93/19.26 ( 18.93/19.26 powerset__Cong => 18.93/19.26 ( 18.93/19.26 setunion__Cong => 18.93/19.26 ( 18.93/19.26 omega__Cong => 18.93/19.26 ( 18.93/19.26 exuEu => 18.93/19.26 ( 18.93/19.26 descr__Cong => 18.93/19.26 ( 18.93/19.26 dsetconstr__Cong => 18.93/19.26 ( 18.93/19.26 subsetI1 => 18.93/19.26 ( 18.93/19.26 eqimpsubset2 => 18.93/19.26 ( 18.93/19.26 eqimpsubset1 => 18.93/19.26 ( 18.93/19.26 subsetI2 => 18.93/19.26 ( 18.93/19.26 emptysetsubset => 18.93/19.26 ( 18.93/19.26 subsetE => 18.93/19.26 ( 18.93/19.26 subsetE2 => 18.93/19.26 ( 18.93/19.26 notsubsetI => 18.93/19.26 ( 18.93/19.26 notequalI1 => 18.93/19.26 ( 18.93/19.26 notequalI2 => 18.93/19.26 ( 18.93/19.26 subsetRefl => 18.93/19.26 ( 18.93/19.26 subsetTrans => 18.93/19.26 ( 18.93/19.26 setadjoinSub => 18.93/19.26 ( 18.93/19.26 setadjoinSub2 => 18.93/19.26 ( 18.93/19.26 subset2powerset => 18.93/19.26 ( 18.93/19.26 setextsub => 18.93/19.26 ( 18.93/19.26 subsetemptysetimpeq => 18.93/19.26 ( 18.93/19.26 powersetI1 => 18.93/19.26 ( 18.93/19.26 powersetE1 => 18.93/19.26 ( 18.93/19.26 inPowerset => 18.93/19.26 ( 18.93/19.26 powersetsubset => 18.93/19.26 ( 18.93/19.26 sepInPowerset => 18.93/19.26 ( 18.93/19.26 sepSubset => 18.93/19.26 ( 18.93/19.26 binunionIL => 18.93/19.26 ( 18.93/19.26 upairset2IR => 18.93/19.26 ( 18.93/19.26 binunionIR => 18.93/19.26 ( 18.93/19.26 binunionEcases => 18.93/19.26 ( 18.93/19.26 binunionE => 18.93/19.26 ( 18.93/19.26 binunionLsub => 18.93/19.26 ( 18.93/19.26 binunionRsub => 18.93/19.26 ( 18.93/19.26 binintersectI => 18.93/19.26 ( 18.93/19.26 binintersectSubset5 => 18.93/19.26 ( 18.93/19.26 binintersectEL => 18.93/19.26 ( 18.93/19.26 binintersectLsub => 18.93/19.26 ( 18.93/19.26 binintersectSubset2 => 18.93/19.26 ( 18.93/19.26 binintersectSubset3 => 18.93/19.26 ( 18.93/19.26 binintersectER => 18.93/19.26 ( 18.93/19.26 disjointsetsI1 => 18.93/19.26 ( 18.93/19.26 binintersectRsub => 18.93/19.26 ( 18.93/19.26 binintersectSubset4 => 18.93/19.26 ( 18.93/19.26 binintersectSubset1 => 18.93/19.26 ( 18.93/19.26 bs114d => 18.93/19.26 ( 18.93/19.26 setminusI => 18.93/19.26 ( 18.93/19.26 setminusEL => 18.93/19.26 ( 18.93/19.26 setminusER => 18.93/19.26 ( 18.93/19.26 setminusSubset2 => 18.93/19.26 ( 18.93/19.26 setminusERneg => 18.93/19.26 ( 18.93/19.26 setminusELneg => 18.93/19.26 ( 18.93/19.26 setminusILneg => 18.93/19.26 ( 18.93/19.26 setminusIRneg => 18.93/19.26 ( 18.93/19.26 setminusLsub => 18.93/19.26 ( 18.93/19.26 setminusSubset1 => 18.93/19.26 ( 18.93/19.26 symdiffE => 18.93/19.26 ( 18.93/19.26 symdiffI1 => 18.93/19.26 ( 18.93/19.26 symdiffI2 => 18.93/19.26 ( 18.93/19.26 symdiffIneg1 => 18.93/19.26 ( 18.93/19.26 symdiffIneg2 => 18.93/19.26 ( 18.93/19.26 secondinupair => 18.93/19.26 ( 18.93/19.26 setukpairIL => 18.93/19.26 ( 18.93/19.26 setukpairIR => 18.93/19.26 ( 18.93/19.26 kpairiskpair => 18.93/19.26 ( 18.93/19.26 kpairp => 18.93/19.26 ( 18.93/19.26 singletonsubset => 18.93/19.26 ( 18.93/19.26 singletoninpowerset => 18.93/19.26 ( 18.93/19.26 singletoninpowunion => 18.93/19.26 ( 18.93/19.26 upairset2E => 18.93/19.26 ( 18.93/19.26 upairsubunion => 18.93/19.26 ( 18.93/19.26 upairinpowunion => 18.93/19.26 ( 18.93/19.26 ubforcartprodlem1 => 18.93/19.26 ( 18.93/19.26 ubforcartprodlem2 => 18.93/19.26 ( 18.93/19.26 ubforcartprodlem3 => 18.93/19.26 ( 18.93/19.26 cartprodpairin => 18.93/19.26 ( 18.93/19.26 cartprodmempair1 => 18.93/19.26 ( 18.93/19.26 cartprodmempair => 18.93/19.26 ( 18.93/19.26 setunionE2 => 18.93/19.26 ( 18.93/19.26 setunionsingleton1 => 18.93/19.26 ( 18.93/19.26 setunionsingleton2 => 18.93/19.26 ( 18.93/19.26 setunionsingleton => 18.93/19.26 ( 18.93/19.26 singletonprop => 18.93/19.26 ( 18.93/19.26 ex1E1 => 18.93/19.26 ( 18.93/19.26 ex1I => 18.93/19.26 ( 18.93/19.26 ex1I2 => 18.93/19.26 ( 18.93/19.26 singletonsuniq => 18.93/19.26 ( 18.93/19.26 setukpairinjL1 => 18.93/19.26 ( 18.93/19.26 kfstsingleton => 18.93/19.26 ( 18.93/19.26 theprop => 18.93/19.26 ( 18.93/19.26 kfstpairEq => 18.93/19.26 ( 18.93/19.26 cartprodfstin => 18.93/19.26 ( 18.93/19.26 setukpairinjL2 => 18.93/19.26 ( 18.93/19.26 setukpairinjL => 18.93/19.26 ( 18.93/19.26 setukpairinjR11 => 18.93/19.26 ( 18.93/19.26 setukpairinjR12 => 18.93/19.26 ( 18.93/19.26 setukpairinjR1 => 18.93/19.26 ( 18.93/19.26 upairequniteq => 18.93/19.26 ( 18.93/19.26 setukpairinjR2 => 18.93/19.26 ( 18.93/19.26 setukpairinjR => 18.93/19.26 ( 18.93/19.26 ksndsingleton => 18.93/19.26 ( 18.93/19.26 ksndpairEq => 18.93/19.26 ( 18.93/19.26 kpairsurjEq => 18.93/19.26 ( 18.93/19.26 cartprodsndin => 18.93/19.26 ( 18.93/19.26 cartprodpairmemEL => 18.93/19.26 ( 18.93/19.26 cartprodpairmemER => 18.93/19.26 ( 18.93/19.26 cartprodmempaircEq => 18.93/19.26 ( 18.93/19.26 cartprodfstpairEq => 18.93/19.26 ( 18.93/19.26 cartprodsndpairEq => 18.93/19.26 ( 18.93/19.26 cartprodpairsurjEq => 18.93/19.26 ( 18.93/19.26 dpsetconstrI => 18.93/19.26 ( 18.93/19.26 dpsetconstrSub => 18.93/19.26 ( 18.93/19.26 setOfPairsIsBReln => 18.93/19.26 ( 18.93/19.26 dpsetconstrERa => 18.93/19.26 ( 18.93/19.26 dpsetconstrEL1 => 18.93/19.26 ( 18.93/19.26 dpsetconstrEL2 => 18.93/19.26 ( 18.93/19.26 dpsetconstrER => 18.93/19.26 ( 18.93/19.26 funcImageSingleton => 18.93/19.26 ( 18.93/19.26 apProp => 18.93/19.26 ( 18.93/19.26 app => 18.93/19.26 ( 18.93/19.26 infuncsetfunc => 18.93/19.26 ( 18.93/19.26 ap2p => 18.93/19.26 ( 18.93/19.26 funcinfuncset => 18.93/19.26 ( 18.93/19.26 lamProp => 18.93/19.26 ( 18.93/19.26 lamp => 18.93/19.26 ( 18.93/19.26 lam2p => 18.93/19.26 ( 18.93/19.26 brelnall1 => 18.93/19.26 ( 18.93/19.26 brelnall2 => 18.93/19.26 ( 18.93/19.26 ex1E2 => 18.93/19.26 ( 18.93/19.26 funcGraphProp1 => 18.93/19.26 ( 18.93/19.26 funcGraphProp3 => 18.93/19.26 ( 18.93/19.26 funcGraphProp2 => 18.93/19.26 ( 18.93/19.26 funcextLem => 18.93/19.26 ( 18.93/19.26 funcGraphProp4 => 18.93/19.26 ( 18.93/19.26 subbreln => 18.93/19.26 ( 18.93/19.26 eqbreln => 18.93/19.26 ( 18.93/19.26 funcext => 18.93/19.26 ( 18.93/19.26 funcext2 => 18.93/19.26 ( 18.93/19.26 ap2apEq1 => 18.93/19.26 ( 18.93/19.26 ap2apEq2 => 18.93/19.26 ( 18.93/19.26 beta1 => 18.93/19.26 ( 18.93/19.26 eta1 => 18.93/19.26 ( 18.93/19.26 lam2lamEq => 18.93/19.26 ( 18.93/19.26 beta2 => 18.93/19.26 ( 18.93/19.26 eta2 => 18.93/19.26 ( 18.93/19.26 iffalseProp1 => 18.93/19.26 ( 18.93/19.26 iffalseProp2 => 18.93/19.26 ( 18.93/19.26 iftrueProp1 => 18.93/19.26 ( 18.93/19.26 iftrueProp2 => 18.93/19.26 ( 18.93/19.26 ifSingleton => 18.93/19.26 ( 18.93/19.26 ifp => 18.93/19.26 ( 18.93/19.26 theeq => 18.93/19.26 ( 18.93/19.26 iftrue => 18.93/19.26 ( 18.93/19.26 iffalse => 18.93/19.26 ( 18.93/19.26 iftrueorfalse => 18.93/19.26 ( 18.93/19.26 binintersectT_lem => 18.93/19.26 ( 18.93/19.26 binunionT_lem => 18.93/19.26 ( 18.93/19.26 ![A,X]: 18.93/19.26 (in( 18.93/19.26 X, 18.93/19.26 powerset( 18.93/19.26 A)) => 18.93/19.26 in( 18.93/19.26 powerset( 18.93/19.26 X), 18.93/19.26 powerset( 18.93/19.26 powerset( 18.93/19.26 A)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 18.93/19.26 tff(zf_stmt_0, conjecture, 18.93/19.26 ((![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))) => 18.93/19.26 ((![X5]: (~in(X5,emptyset))) => 18.93/19.26 ((![X6,X7,X8]: (in(X8,setadjoin(X6,X7)) <=> ((X8 = X6) | in(X8,X7)))) => 18.93/19.26 ((![X9,X10]: 18.93/19.26 (in(X10,powerset(X9)) <=> (![X11]: (in(X11,X10) => in(X11,X9))))) => 18.93/19.26 ((![X12,X13]: 18.93/19.26 (in(X13,setunion(X12)) <=> (?[X14]: (in(X13,X14) & in(X14,X12))))) => 18.93/19.26 (in(emptyset,omega) => 18.93/19.26 ((![X15]: (in(X15,omega) => in(setadjoin(X15,X15),omega))) => 18.93/19.26 ((![X16]: 18.93/19.26 ((in(emptyset,X16) & 18.93/19.26 (![X17]: 18.93/19.26 ((in(X17,omega) & in(X17,X16)) => 18.93/19.26 in(setadjoin(X17,X17),X16)))) => 18.93/19.26 (![X18]: (in(X18,omega) => in(X18,X16))))) => 18.93/19.26 ((![X19:(($i * $i) > $o),X20]: 18.93/19.26 ((![X21]: 18.93/19.26 (in(X21,X20) => 18.93/19.26 (?[X22]: 18.93/19.26 (X19(X21,X22) & (![X23]: (X19(X21,X23) => (X22 = X23))))))) => 18.93/19.26 (?[X24]: 18.93/19.26 (![X25]: 18.93/19.26 (in(X25,X24) <=> (?[X26]: (in(X26,X20) & X19(X26,X25)))))))) => 18.93/19.26 ((![X27]: 18.93/19.26 ((?[X28]: in(X28,X27)) => 18.93/19.26 (?[X29]: 18.93/19.26 (in(X29,X27) & (~(?[X30]: (in(X30,X29) & in(X30,X27)))))))) => 18.93/19.26 ((![X31]: 18.93/19.26 (?[X32]: 18.93/19.26 ((![X48]: 18.93/19.26 (in(X48,X32) => (![X49]: (in(X49,X48) => in(X49,X31))))) & 18.93/19.26 (![X45,X46]: 18.93/19.26 ((in(X45,X31) & in(X46,X31)) => 18.93/19.26 ((![X47]: 18.93/19.26 (in(X47,X32) => (in(X45,X47) <=> in(X46,X47)))) => 18.93/19.26 (X45 = X46)))) & 18.93/19.26 (![X41,X42]: 18.93/19.26 ((in(X41,X32) & in(X42,X32)) => 18.93/19.26 ((![X44]: (in(X44,X41) => in(X44,X42))) | 18.93/19.26 (![X43]: (in(X43,X42) => in(X43,X41)))))) & 18.93/19.26 (![X33]: 18.93/19.26 (((![X35]: (in(X35,X33) => in(X35,X31))) & 18.93/19.26 (?[X34]: in(X34,X33))) => 18.93/19.26 (?[X36,X37]: 18.93/19.26 (in(X36,X32) & in(X37,X33) & 18.93/19.26 (~(?[X40]: (in(X40,X36) & in(X40,X33)))) & 18.93/19.26 (![X38]: 18.93/19.26 (in(X38,X32) => 18.93/19.26 ((![X39]: (in(X39,X38) => in(X39,X36))) | 18.93/19.26 in(X37,X38))))))))))) => 18.93/19.26 ((![X50:($i > $o)]: 18.93/19.26 ((?[X51]: (X50(X51) & (![X52]: (X50(X52) => (X51 = X52))))) => 18.93/19.26 X50(descr(^[V_1]: X50(V_1))))) => 18.93/19.26 ((![X53,X54:($i > $o),X55]: 18.93/19.26 (in(X55,X53) => 18.93/19.26 (X54(X55) => in(X55,dsetconstr(X53,^[V_2]: X54(V_2)))))) => 18.93/19.26 ((![X56,X57:($i > $o),X58]: 18.93/19.26 (in(X58,dsetconstr(X56,^[V_3]: X57(V_3))) => in(X58,X56))) => 18.93/19.26 ((![X59,X60:($i > $o),X61]: 18.93/19.26 (in(X61,dsetconstr(X59,^[V_4]: X60(V_4))) => X60(X61))) => 18.93/19.26 ((![X62:($i > $o)]: 18.93/19.26 ((?[X63]: 18.93/19.26 (X62(X63) & (![X64]: (X62(X64) => (X63 = X64))))) => 18.93/19.26 (?[X65]: 18.93/19.26 (X62(X65) & (![X66]: (X62(X66) => (X65 = X66))))))) => 18.93/19.26 ((![X67:$o,X68]: (in(X68,prop2set(X67)) => X67)) => 18.93/19.26 ((![X69]: (in(X69,emptyset) => (![X70:$o]: X70))) => 18.93/19.26 ((![X71]: (in(X71,emptyset) => $false)) => 18.93/19.26 ((![X72]: (~in(X72,emptyset))) => 18.93/19.26 ((![X73:($i > $o)]: 18.93/19.26 ((?[X74]: 18.93/19.26 (X73(X74) & (![X75]: (X73(X75) => (X74 = X75))))) => 18.93/19.26 (?[X76]: X73(X76)))) => 18.93/19.26 ((![X77,X78]: 18.93/19.26 ((![X79]: (in(X79,X77) => in(X79,X78))) => 18.93/19.26 ((![X80]: (in(X80,X78) => in(X80,X77))) => 18.93/19.26 (X77 = X78)))) => 18.93/19.26 ((![X81]: 18.93/19.26 ((![X82]: (~in(X82,X81))) => (X81 = emptyset))) => 18.93/19.26 ((![X83]: 18.93/19.26 ((![X84]: (~in(X84,X83))) => (X83 = emptyset))) => 18.93/19.26 ((![X85,X86:($i > $o),X87]: 18.93/19.26 (in(X87,X85) => 18.93/19.26 (in(X87,dsetconstr(X85,^[V_5]: X86(V_5))) <=> 18.93/19.26 X86(X87)))) => 18.93/19.26 ((![X88]: 18.93/19.26 ((X88 != emptyset) => (?[X89]: in(X89,X88)))) => 18.93/19.26 ((![X90,X91:($i > $o),X92]: 18.93/19.26 (in(X92,X90) => 18.93/19.26 (X91(X92) => 18.93/19.26 (dsetconstr(X90,^[V_6]: X91(V_6)) != 18.93/19.26 emptyset)))) => 18.93/19.26 ((![X93]: 18.93/19.26 ((?[X94]: in(X94,X93)) => (X93 != emptyset))) => 18.93/19.26 ((![X95,X96]: in(X95,setadjoin(X95,X96))) => 18.93/19.26 (in(emptyset,setadjoin(emptyset,emptyset)) => 18.93/19.26 ((![X97,X98,X99]: 18.93/19.26 (in(X99,X98) => 18.93/19.26 in(X99,setadjoin(X97,X98)))) => 18.93/19.26 ((![X100,X101,X102]: 18.93/19.26 (in(X102,setadjoin(X100,X101)) => 18.93/19.26 (![X103:$o]: 18.93/19.26 (((X102 = X100) => X103) => 18.93/19.26 ((in(X102,X101) => X103) => X103))))) => 18.93/19.26 ((![X104,X105,X106]: 18.93/19.26 (in(X106,setadjoin(X104,X105)) => 18.93/19.26 ((X106 = X104) | in(X106,X105)))) => 18.93/19.26 ((![X107]: 18.93/19.26 (dsetconstr(X107,^[V_7]: $true) = X107)) => 18.93/19.26 ((![X108,X109]: 18.93/19.26 ((![X110]: 18.93/19.26 (in(X110,X109) => in(X110,X108))) => 18.93/19.26 in(X109,powerset(X108)))) => 18.93/19.26 ((![X111]: in(emptyset,powerset(X111))) => 18.93/19.26 ((![X112]: in(emptyset,powerset(X112))) => 18.93/19.26 ((![X113,X114,X115]: 18.93/19.26 (in(X114,powerset(X113)) => 18.93/19.26 (in(X115,X114) => in(X115,X113)))) => 18.93/19.26 ((![X116,X117,X118]: 18.93/19.26 (in(X117,X118) => 18.93/19.26 (in(X118,X116) => 18.93/19.26 in(X117,setunion(X116))))) => 18.93/19.26 ((![X119,X120]: 18.93/19.26 (in(X120,setunion(X119)) => 18.93/19.26 (![X121:$o]: 18.93/19.26 ((![X122]: 18.93/19.26 (in(X120,X122) => 18.93/19.26 (in(X122,X119) => X121))) => 18.93/19.26 X121)))) => 18.93/19.26 ((![X123,X124]: 18.93/19.26 (in(X124,X123) => 18.93/19.26 in(X124, 18.93/19.26 powerset(setunion(X123))))) => 18.93/19.26 ((![X125:($i > $o)]: 18.93/19.26 ((?[X126]: 18.93/19.26 (X125(X126) & 18.93/19.26 (![X127]: 18.93/19.26 (X125(X127) => 18.93/19.26 (X126 = X127))))) => 18.93/19.26 (?[X128]: 18.93/19.26 (![X129]: 18.93/19.26 (X125(X129) <=> 18.93/19.26 (X129 = X128)))))) => 18.93/19.26 ((![X130]: 18.93/19.26 ((X130 != emptyset) => 18.93/19.26 (?[X131]: in(X131,X130)))) => 18.93/19.26 ((![X132,X133]: 18.93/19.26 (in(X132, 18.93/19.26 setadjoin(X133,emptyset)) => 18.93/19.26 (X132 = X133))) => 18.93/19.26 ((![X134,X135]: 18.93/19.26 ((X134 != X135) => 18.93/19.26 (~ 18.93/19.26 in(X135, 18.93/19.26 setadjoin(X134, 18.93/19.26 emptyset))))) => 18.93/19.26 ((![X136,X137]: 18.93/19.26 ((X136 = X137) => 18.93/19.26 in(X136, 18.93/19.26 setadjoin(X137, 18.93/19.26 emptyset)))) => 18.93/19.26 ((![X138,X139]: 18.93/19.26 (in(X138, 18.93/19.26 setadjoin(X139, 18.93/19.26 emptyset)) => 18.93/19.26 in(X139, 18.93/19.26 setadjoin(X138, 18.93/19.26 emptyset)))) => 18.93/19.26 ((![X140,X141,X142]: 18.93/19.26 (in(X142, 18.93/19.26 setadjoin(X140, 18.93/19.26 setadjoin( 18.93/19.26 X141, 18.93/19.26 emptyset))) => 18.93/19.26 ((X142 = X140) | 18.93/19.26 (X142 = X141)))) => 18.93/19.26 ((![X143,X144]: 18.93/19.26 in(X143, 18.93/19.26 setadjoin(X143, 18.93/19.26 setadjoin( 18.93/19.26 X144, 18.93/19.26 emptyset)))) => 18.93/19.26 ((![X145,X146]: 18.93/19.26 in(X146, 18.93/19.26 setadjoin(X145, 18.93/19.26 setadjoin( 18.93/19.26 X146, 18.93/19.26 emptyset)))) => 18.93/19.26 ((![X147,X148:($i > $o)]: 18.93/19.26 ((?[X149]: 18.93/19.26 (in(X149,X147) & 18.93/19.26 X148(X149))) => 18.93/19.26 ((dsetconstr( 18.93/19.26 X147, 18.93/19.26 ^[V_8]: X148(V_8)) = 18.93/19.26 emptyset) => 18.93/19.26 $false))) => 18.93/19.26 ((![X150:($i > $o),X151]: 18.93/19.26 (in(X151,emptyset) => 18.93/19.26 X150(X151))) => 18.93/19.26 ((![X152,X153:($i > $o)]: 18.93/19.26 ((~ 18.93/19.26 (![X154]: 18.93/19.26 (in(X154,X152) => 18.93/19.26 X153(X154)))) => 18.93/19.26 (?[X155]: 18.93/19.26 (in(X155,X152) & 18.93/19.26 (~X153(X155)))))) => 18.93/19.26 ((![X156, 18.93/19.26 X157:($i > $o)]: 18.93/19.26 ((![X158]: 18.93/19.26 (in(X158,X156) => 18.93/19.26 (~X157(X158)))) => 18.93/19.26 (~ 18.93/19.26 (?[X159]: 18.93/19.26 (in( 18.93/19.26 X159,X156) & 18.93/19.26 X157(X159)))))) => 18.93/19.26 ((![X160, 18.93/19.26 X161:($i > $o)]: 18.93/19.26 ((~ 18.93/19.26 (?[X162]: 18.93/19.26 (in( 18.93/19.26 X162,X160) & 18.93/19.26 X161(X162)))) => 18.93/19.26 (![X163]: 18.93/19.26 (in(X163,X160) => 18.93/19.26 (~X161(X163)))))) => 18.93/19.26 ((![X164, 18.93/19.26 X165:($i > $o)]: 18.93/19.26 ((?[X166]: 18.93/19.26 (in( 18.93/19.26 X166,X164) & 18.93/19.26 (~ 18.93/19.26 X165( 18.93/19.26 X166)))) => 18.93/19.26 (~ 18.93/19.26 (![X167]: 18.93/19.26 (in( 18.93/19.26 X167,X164) => 18.93/19.26 X165( 18.93/19.26 X167)))))) => 18.93/19.26 ((![X168:$o]: 18.93/19.26 (X168 => 18.93/19.26 in(emptyset, 18.93/19.26 prop2set( 18.93/19.26 X168)))) => 18.93/19.26 ((![X169:$o]: 18.93/19.26 (X169 => 18.93/19.26 set2prop( 18.93/19.26 prop2set( 18.93/19.26 X169)))) => 18.93/19.26 ((![X170, 18.93/19.26 X171:( 18.93/19.26 $i > $o)]: 18.93/19.26 ((~ 18.93/19.26 (?[X172]: 18.93/19.26 (in( 18.93/19.26 X172,X170) & 18.93/19.26 X171( 18.93/19.26 X172)))) => 18.93/19.26 (![X173]: 18.93/19.26 ( 18.93/19.26 in( 18.93/19.26 X173,X170) => 18.93/19.26 ( 18.93/19.26 ~ 18.93/19.26 X171( 18.93/19.26 X173)))))) => 18.93/19.26 ((![X174, 18.93/19.26 X175:( 18.93/19.26 $i > $o)]: 18.93/19.26 ((~ 18.93/19.26 ( 18.93/19.26 ![X176]: 18.93/19.26 (in( 18.93/19.26 X176,X174) => 18.93/19.26 X175( 18.93/19.26 X176)))) => 18.93/19.26 (?[X177]: 18.93/19.26 (in( 18.93/19.26 X177,X174) & 18.93/19.26 (~ 18.93/19.26 X175( 18.93/19.26 X177)))))) => 18.93/19.26 ((![X178:( 18.93/19.26 $i > $o)]: 18.93/19.26 ((?[X179]: 18.93/19.26 (X178( 18.93/19.26 X179) & 18.93/19.26 (![X180]: 18.93/19.26 (X178( 18.93/19.26 X180) => 18.93/19.26 (X179 = 18.93/19.26 X180))))) => 18.93/19.26 (?[X181]: 18.93/19.26 (X178( 18.93/19.26 X181) & 18.93/19.26 (![X182]: 18.93/19.26 (X178( 18.93/19.26 X182) => 18.93/19.26 (X181 = 18.93/19.26 X182))))))) => 18.93/19.26 ((![X183:( 18.93/19.26 $i > $o)]: 18.93/19.26 (( 18.93/19.26 ?[X184]: 18.93/19.26 X183( 18.93/19.26 X184)) => 18.93/19.26 ( 18.93/19.26 ( 18.93/19.26 ![X185, 18.93/19.26 X186]: 18.93/19.26 (X183( 18.93/19.26 X185) => 18.93/19.26 (X183( 18.93/19.26 X186) => 18.93/19.26 (X185 = 18.93/19.26 X186)))) => 18.93/19.26 ( 18.93/19.26 ?[X187]: 18.93/19.26 (X183( 18.93/19.26 X187) & 18.93/19.26 (![X188]: 18.93/19.26 (X183( 18.93/19.26 X188) => 18.93/19.26 (X187 = 18.93/19.26 X188)))))))) => 18.93/19.26 ((![X189:( 18.93/19.26 $i > $o)]: 18.93/19.26 ( 18.93/19.26 ( 18.93/19.26 ?[X190]: 18.93/19.26 (![X191]: 18.93/19.26 (X189( 18.93/19.26 X191) <=> 18.93/19.26 (X191 = 18.93/19.26 X190)))) => 18.93/19.26 ( 18.93/19.26 ?[X192]: 18.93/19.26 (X189( 18.93/19.26 X192) & 18.93/19.26 (![X193]: 18.93/19.26 (X189( 18.93/19.26 X193) => 18.93/19.26 (X192 = 18.93/19.26 X193))))))) => 18.93/19.26 ((![X194, 18.93/19.26 X195]: 18.93/19.26 (( 18.93/19.26 X194 = 18.93/19.26 X195) => 18.93/19.26 (![X196, 18.93/19.26 X197]: 18.93/19.26 (( 18.93/19.26 X196 = 18.93/19.26 X197) => 18.93/19.26 (in( 18.93/19.26 X196,X194) => 18.93/19.26 in( 18.93/19.26 X197,X195)))))) => 18.93/19.26 ((![X198, 18.93/19.26 X199]: 18.93/19.26 (( 18.93/19.26 X198 = 18.93/19.26 X199) => 18.93/19.26 (![X200, 18.93/19.26 X201]: 18.93/19.26 (( 18.93/19.26 X200 = 18.93/19.26 X201) => 18.93/19.26 (in( 18.93/19.26 X200,X198) <=> 18.93/19.26 in( 18.93/19.26 X201,X199)))))) => 18.93/19.26 (( 18.93/19.26 ![X202:( 18.93/19.26 $i > $o)]: 18.93/19.26 (( 18.93/19.26 ?[X203]: 18.93/19.26 (X202( 18.93/19.26 X203) & 18.93/19.26 (![X204]: 18.93/19.26 (X202( 18.93/19.26 X204) => 18.93/19.26 (X203 = 18.93/19.26 X204))))) => 18.93/19.26 (![X205, 18.93/19.26 X206]: 18.93/19.26 (X202( 18.93/19.26 X205) => 18.93/19.26 (X202( 18.93/19.26 X206) => 18.93/19.26 (X205 = 18.93/19.26 X206)))))) => 18.93/19.26 ( 18.93/19.26 ( 18.93/19.26 ![X207:( 18.93/19.26 $i > $o), 18.93/19.26 X208:( 18.93/19.26 $i > $o)]: 18.93/19.26 (( 18.93/19.26 ![X209, 18.93/19.26 X210]: 18.93/19.26 (( 18.93/19.26 X209 = 18.93/19.26 X210) => 18.93/19.26 (X207( 18.93/19.26 X209) <=> 18.93/19.26 X208( 18.93/19.26 X210)))) => 18.93/19.26 (( 18.93/19.26 ?[X211]: 18.93/19.26 (X207( 18.93/19.26 X211) & 18.93/19.26 (![X212]: 18.93/19.26 (X207( 18.93/19.26 X212) => 18.93/19.26 (X211 = 18.93/19.26 X212))))) <=> 18.93/19.26 (?[X213]: 18.93/19.26 (X208( 18.93/19.26 X213) & 18.93/19.26 (![X214]: 18.93/19.26 (X208( 18.93/19.26 X214) => 18.93/19.26 (X213 = 18.93/19.26 X214)))))))) => 18.93/19.26 ( 18.93/19.26 ( 18.93/19.26 emptyset = 18.93/19.26 emptyset) => 18.93/19.26 ( 18.93/19.26 ( 18.93/19.26 ![X215, 18.93/19.26 X216]: 18.93/19.26 (( 18.93/19.26 X215 = 18.93/19.26 X216) => 18.93/19.26 (![X217, 18.93/19.26 X218]: 18.93/19.26 (( 18.93/19.26 X217 = 18.93/19.26 X218) => 18.93/19.26 (setadjoin( 18.93/19.26 X215,X217) = 18.93/19.26 setadjoin( 18.93/19.26 X216,X218)))))) => 18.93/19.26 ( 18.93/19.26 ( 18.93/19.26 ![X219, 18.93/19.26 X220]: 18.93/19.26 (( 18.93/19.26 X219 = 18.93/19.26 X220) => 18.93/19.26 (powerset( 18.93/19.26 X219) = 18.93/19.26 powerset( 18.93/19.26 X220)))) => 18.93/19.26 ( 18.93/19.26 ( 18.93/19.26 ![X221, 18.93/19.26 X222]: 18.93/19.26 (( 18.93/19.26 X221 = 18.93/19.26 X222) => 18.93/19.26 (setunion( 18.93/19.26 X221) = 18.93/19.26 setunion( 18.93/19.26 X222)))) => 18.93/19.26 ( 18.93/19.26 ( 18.93/19.26 omega = 18.93/19.26 omega) => 18.93/19.26 ( 18.93/19.26 ( 18.93/19.26 ![X223:( 18.93/19.26 $i > $o)]: 18.93/19.26 (( 18.93/19.26 ?[X224]: 18.93/19.26 (X223( 18.93/19.26 X224) & 18.93/19.26 (![X225]: 18.93/19.26 (X223( 18.93/19.26 X225) => 18.93/19.26 (X224 = 18.93/19.26 X225))))) => 18.93/19.26 (![X226, 18.93/19.26 X227]: 18.93/19.26 (X223( 18.93/19.26 X226) => 18.93/19.26 (X223( 18.93/19.26 X227) => 18.93/19.26 (X226 = 18.93/19.26 X227)))))) => 18.93/19.26 ( 18.93/19.26 ( 18.93/19.26 ![X228:( 18.93/19.26 $i > $o), 18.93/19.26 X229:( 18.93/19.26 $i > $o)]: 18.93/19.26 (( 18.93/19.26 ![X230, 18.93/19.26 X231]: 18.93/19.26 (( 18.93/19.26 X230 = 18.93/19.26 X231) => 18.93/19.26 (X228( 18.93/19.26 X230) <=> 18.93/19.26 X229( 18.93/19.26 X231)))) => 18.93/19.26 (( 18.93/19.26 ?[X232]: 18.93/19.26 (X228( 18.93/19.26 X232) & 18.93/19.26 (![X233]: 18.93/19.26 (X228( 18.93/19.26 X233) => 18.93/19.26 (X232 = 18.93/19.26 X233))))) => 18.93/19.26 (( 18.93/19.26 ?[X234]: 18.93/19.26 (X229( 18.93/19.26 X234) & 18.93/19.26 (![X235]: 18.93/19.26 (X229( 18.93/19.26 X235) => 18.93/19.26 (X234 = 18.93/19.26 X235))))) => 18.93/19.26 (descr( 18.93/19.26 ^[V_9]: 18.93/19.26 X228(V_9)) = 18.93/19.26 descr( 18.93/19.26 ^[V_10]: 18.93/19.26 X229( 18.93/19.26 V_10))))))) => 18.93/19.26 ( 18.93/19.26 ( 18.93/19.26 ![X236, 18.93/19.26 X237]: 18.93/19.26 (( 18.93/19.26 X236 = 18.93/19.26 X237) => 18.93/19.26 (![X238:( 18.93/19.26 $i > $o), 18.93/19.26 X239:( 18.93/19.26 $i > $o)]: 18.93/19.26 (( 18.93/19.26 ![X240]: 18.93/19.26 (in( 18.93/19.26 X240,X236) => 18.93/19.26 (![X241]: 18.93/19.26 (in( 18.93/19.26 X241,X237) => 18.93/19.26 (( 18.93/19.26 X240 = 18.93/19.26 X241) => 18.93/19.26 (X238( 18.93/19.26 X240) <=> 18.93/19.26 X239( 18.93/19.26 X241))))))) => 18.93/19.26 (dsetconstr( 18.93/19.26 X236, 18.93/19.26 ^[V_11]: 18.93/19.26 X238( 18.93/19.26 V_11)) = 18.93/19.26 dsetconstr( 18.93/19.26 X237, 18.93/19.26 ^[V_12]: 18.93/19.26 X239( 18.93/19.26 V_12))))))) => 18.93/19.26 ( 18.93/19.26 ( 18.93/19.26 ![X242, 18.93/19.26 X243]: 18.93/19.26 (( 18.93/19.26 ![X244]: 18.93/19.26 (in( 18.93/19.26 X244,X242) => 18.93/19.26 in( 18.93/19.26 X244,X243))) => 18.93/19.26 subset( 18.93/19.26 X242,X243))) => 18.93/19.26 ( 18.93/19.26 ( 18.93/19.26 ![X245, 18.93/19.26 X246]: 18.93/19.26 (( 18.93/19.26 X245 = 18.93/19.26 X246) => 18.93/19.26 subset( 18.93/19.26 X246,X245))) => 18.93/19.26 ( 18.93/19.26 ( 18.93/19.26 ![X247, 18.93/19.26 X248]: 18.93/19.26 (( 18.93/19.26 X247 = 18.93/19.26 X248) => 18.93/19.26 subset( 18.93/19.26 X247,X248))) => 18.93/19.26 ( 18.93/19.26 ( 18.93/19.26 ![X249, 18.93/19.26 X250]: 18.93/19.26 (( 18.93/19.26 ![X251]: 18.93/19.26 (in( 18.93/19.26 X251,X249) => 18.93/19.26 in( 18.93/19.26 X251,X250))) => 19.00/19.26 subset( 19.00/19.26 X249,X250))) => 19.00/19.26 ( 19.00/19.26 ( 19.00/19.26 ![X252]: 19.00/19.26 subset( 19.00/19.26 emptyset, 19.00/19.26 X252)) => 19.00/19.26 ( 19.00/19.26 ( 19.00/19.26 ![X253, 19.00/19.26 X254,X255]: 19.00/19.26 (subset( 19.00/19.26 X253,X254) => 19.00/19.26 (in( 19.00/19.26 X255,X253) => 19.00/19.26 in( 19.00/19.26 X255,X254)))) => 19.00/19.26 ( 19.00/19.26 ( 19.00/19.26 ![X256, 19.00/19.26 X257,X258]: 19.00/19.26 (subset( 19.00/19.26 X256,X257) => 19.00/19.26 (( 19.00/19.26 ~ 19.00/19.26 in( 19.00/19.26 X258,X257)) => 19.00/19.26 (~ 19.00/19.26 in( 19.00/19.26 X258,X256))))) => 19.00/19.26 ( 19.00/19.26 ( 19.00/19.26 ![X259, 19.00/19.26 X260,X261]: 19.00/19.26 (in( 19.00/19.26 X261,X259) => 19.00/19.26 (( 19.00/19.26 ~ 19.00/19.26 in( 19.00/19.26 X261,X260)) => 19.00/19.26 (~ 19.00/19.26 subset( 19.00/19.26 X259,X260))))) => 19.00/19.26 ( 19.00/19.26 ( 19.00/19.26 ![X262, 19.00/19.26 X263]: 19.00/19.26 (( 19.00/19.26 ~ 19.00/19.26 subset( 19.00/19.26 X262,X263)) => 19.00/19.26 (X262 != 19.00/19.26 X263))) => 19.00/19.26 ( 19.00/19.26 ( 19.00/19.26 ![X264, 19.00/19.26 X265,X266]: 19.00/19.26 (in( 19.00/19.26 X266,X264) => 19.00/19.26 (( 19.00/19.26 ~ 19.00/19.26 in( 19.00/19.26 X266,X265)) => 19.00/19.26 (X264 != 19.00/19.26 X265)))) => 19.00/19.26 ( 19.00/19.26 ( 19.00/19.26 ![X267]: 19.00/19.26 subset( 19.00/19.26 X267,X267)) => 19.00/19.26 ( 19.00/19.26 ( 19.00/19.26 ![X268, 19.00/19.26 X269,X270]: 19.00/19.26 (subset( 19.00/19.26 X268,X269) => 19.00/19.26 (subset( 19.00/19.26 X269,X270) => 19.00/19.26 subset( 19.00/19.26 X268,X270)))) => 19.00/19.26 ( 19.00/19.26 ( 19.00/19.26 ![X271, 19.00/19.26 X272]: 19.00/19.26 subset( 19.00/19.26 X272, 19.00/19.26 setadjoin( 19.00/19.26 X271,X272))) => 19.00/19.26 ( 19.00/19.26 ( 19.00/19.26 ![X273, 19.00/19.26 X274,X275]: 19.00/19.26 (subset( 19.00/19.27 X273,X275) => 19.00/19.27 subset( 19.00/19.27 X273, 19.00/19.27 setadjoin( 19.00/19.27 X274,X275)))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X276, 19.00/19.27 X277]: 19.00/19.27 (subset( 19.00/19.27 X276,X277) => 19.00/19.27 in( 19.00/19.27 X276, 19.00/19.27 powerset( 19.00/19.27 X277)))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X278, 19.00/19.27 X279]: 19.00/19.27 (subset( 19.00/19.27 X278,X279) => 19.00/19.27 (subset( 19.00/19.27 X279,X278) => 19.00/19.27 (X278 = 19.00/19.27 X279)))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X280]: 19.00/19.27 (subset( 19.00/19.27 X280, 19.00/19.27 emptyset) => 19.00/19.27 (X280 = 19.00/19.27 emptyset))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X281, 19.00/19.27 X282]: 19.00/19.27 (subset( 19.00/19.27 X282,X281) => 19.00/19.27 in( 19.00/19.27 X282, 19.00/19.27 powerset( 19.00/19.27 X281)))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X283, 19.00/19.27 X284]: 19.00/19.27 (in( 19.00/19.27 X284, 19.00/19.27 powerset( 19.00/19.27 X283)) => 19.00/19.27 subset( 19.00/19.27 X284,X283))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X285]: 19.00/19.27 in( 19.00/19.27 X285, 19.00/19.27 powerset( 19.00/19.27 X285))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X286, 19.00/19.27 X287]: 19.00/19.27 (subset( 19.00/19.27 X286,X287) => 19.00/19.27 subset( 19.00/19.27 powerset( 19.00/19.27 X286), 19.00/19.27 powerset( 19.00/19.27 X287)))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X288, 19.00/19.27 X289:( 19.00/19.27 $i > $o)]: 19.00/19.27 in( 19.00/19.27 dsetconstr( 19.00/19.27 X288, 19.00/19.27 ^[V_13]: 19.00/19.27 X289( 19.00/19.27 V_13)), 19.00/19.27 powerset( 19.00/19.27 X288))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X290, 19.00/19.27 X291:( 19.00/19.27 $i > $o)]: 19.00/19.27 subset( 19.00/19.27 dsetconstr( 19.00/19.27 X290, 19.00/19.27 ^[V_14]: 19.00/19.27 X291( 19.00/19.27 V_14)), 19.00/19.27 X290)) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X292, 19.00/19.27 X293,X294]: 19.00/19.27 (in( 19.00/19.27 X294,X292) => 19.00/19.27 in( 19.00/19.27 X294, 19.00/19.27 binunion( 19.00/19.27 X292,X293)))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X295, 19.00/19.27 X296]: 19.00/19.27 in( 19.00/19.27 X296, 19.00/19.27 setadjoin( 19.00/19.27 X295, 19.00/19.27 setadjoin( 19.00/19.27 X296, 19.00/19.27 emptyset)))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X297, 19.00/19.27 X298,X299]: 19.00/19.27 (in( 19.00/19.27 X299,X298) => 19.00/19.27 in( 19.00/19.27 X299, 19.00/19.27 binunion( 19.00/19.27 X297,X298)))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X300, 19.00/19.27 X301, 19.00/19.27 X302, 19.00/19.27 X303:$o]: 19.00/19.27 (in( 19.00/19.27 X302, 19.00/19.27 binunion( 19.00/19.27 X300,X301)) => 19.00/19.27 (( 19.00/19.27 in( 19.00/19.27 X302,X300) => 19.00/19.27 X303) => 19.00/19.27 (( 19.00/19.27 in( 19.00/19.27 X302,X301) => 19.00/19.27 X303) => 19.00/19.27 X303)))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X304, 19.00/19.27 X305,X306]: 19.00/19.27 (in( 19.00/19.27 X306, 19.00/19.27 binunion( 19.00/19.27 X304,X305)) => 19.00/19.27 (in( 19.00/19.27 X306,X304) | 19.00/19.27 in( 19.00/19.27 X306,X305)))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X307, 19.00/19.27 X308]: 19.00/19.27 subset( 19.00/19.27 X307, 19.00/19.27 binunion( 19.00/19.27 X307,X308))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X309, 19.00/19.27 X310]: 19.00/19.27 subset( 19.00/19.27 X310, 19.00/19.27 binunion( 19.00/19.27 X309,X310))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X311, 19.00/19.27 X312,X313]: 19.00/19.27 (in( 19.00/19.27 X313,X311) => 19.00/19.27 (in( 19.00/19.27 X313,X312) => 19.00/19.27 in( 19.00/19.27 X313, 19.00/19.27 binintersect( 19.00/19.27 X311,X312))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X314, 19.00/19.27 X315,X316]: 19.00/19.27 (subset( 19.00/19.27 X316,X314) => 19.00/19.27 (subset( 19.00/19.27 X316,X315) => 19.00/19.27 subset( 19.00/19.27 X316, 19.00/19.27 binintersect( 19.00/19.27 X314,X315))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X317, 19.00/19.27 X318,X319]: 19.00/19.27 (in( 19.00/19.27 X319, 19.00/19.27 binintersect( 19.00/19.27 X317,X318)) => 19.00/19.27 in( 19.00/19.27 X319,X317))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X320, 19.00/19.27 X321]: 19.00/19.27 subset( 19.00/19.27 binintersect( 19.00/19.27 X320,X321), 19.00/19.27 X320)) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X322, 19.00/19.27 X323]: 19.00/19.27 (subset( 19.00/19.27 X322,X323) => 19.00/19.27 (binintersect( 19.00/19.27 X322,X323) = 19.00/19.27 X322))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X324, 19.00/19.27 X325]: 19.00/19.27 (( 19.00/19.27 binintersect( 19.00/19.27 X324,X325) = 19.00/19.27 X325) => 19.00/19.27 subset( 19.00/19.27 X325,X324))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X326, 19.00/19.27 X327,X328]: 19.00/19.27 (in( 19.00/19.27 X328, 19.00/19.27 binintersect( 19.00/19.27 X326,X327)) => 19.00/19.27 in( 19.00/19.27 X328,X327))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X329, 19.00/19.27 X330]: 19.00/19.27 (( 19.00/19.27 ~ 19.00/19.27 ( 19.00/19.27 ?[X331]: 19.00/19.27 (in( 19.00/19.27 X331,X329) & 19.00/19.27 in( 19.00/19.27 X331,X330)))) => 19.00/19.27 (binintersect( 19.00/19.27 X329,X330) = 19.00/19.27 emptyset))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X332, 19.00/19.27 X333]: 19.00/19.27 subset( 19.00/19.27 binintersect( 19.00/19.27 X332,X333), 19.00/19.27 X333)) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X334, 19.00/19.27 X335]: 19.00/19.27 (subset( 19.00/19.27 X335,X334) => 19.00/19.27 (binintersect( 19.00/19.27 X334,X335) = 19.00/19.27 X335))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X336, 19.00/19.27 X337]: 19.00/19.27 (( 19.00/19.27 binintersect( 19.00/19.27 X336,X337) = 19.00/19.27 X336) => 19.00/19.27 subset( 19.00/19.27 X336,X337))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X338, 19.00/19.27 X339,X340]: 19.00/19.27 (binintersect( 19.00/19.27 X338, 19.00/19.27 binunion( 19.00/19.27 X339,X340)) = 19.00/19.27 binunion( 19.00/19.27 binintersect( 19.00/19.27 X338,X339), 19.00/19.27 binintersect( 19.00/19.27 X338,X340)))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X341, 19.00/19.27 X342,X343]: 19.00/19.27 (in( 19.00/19.27 X343,X341) => 19.00/19.27 (( 19.00/19.27 ~ 19.00/19.27 in( 19.00/19.27 X343,X342)) => 19.00/19.27 in( 19.00/19.27 X343, 19.00/19.27 setminus( 19.00/19.27 X341,X342))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X344, 19.00/19.27 X345,X346]: 19.00/19.27 (in( 19.00/19.27 X346, 19.00/19.27 setminus( 19.00/19.27 X344,X345)) => 19.00/19.27 in( 19.00/19.27 X346,X344))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X347, 19.00/19.27 X348,X349]: 19.00/19.27 (in( 19.00/19.27 X349, 19.00/19.27 setminus( 19.00/19.27 X347,X348)) => 19.00/19.27 (~ 19.00/19.27 in( 19.00/19.27 X349,X348)))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X350, 19.00/19.27 X351]: 19.00/19.27 (subset( 19.00/19.27 X350,X351) => 19.00/19.27 (setminus( 19.00/19.27 X350,X351) = 19.00/19.27 emptyset))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X352, 19.00/19.27 X353,X354]: 19.00/19.27 (( 19.00/19.27 ~ 19.00/19.27 in( 19.00/19.27 X354, 19.00/19.27 setminus( 19.00/19.27 X352,X353))) => 19.00/19.27 (in( 19.00/19.27 X354,X352) => 19.00/19.27 in( 19.00/19.27 X354,X353)))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X355, 19.00/19.27 X356,X357]: 19.00/19.27 (( 19.00/19.27 ~ 19.00/19.27 in( 19.00/19.27 X357, 19.00/19.27 setminus( 19.00/19.27 X355,X356))) => 19.00/19.27 (( 19.00/19.27 ~ 19.00/19.27 in( 19.00/19.27 X357,X356)) => 19.00/19.27 (~ 19.00/19.27 in( 19.00/19.27 X357,X355))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X358, 19.00/19.27 X359,X360]: 19.00/19.27 (( 19.00/19.27 ~ 19.00/19.27 in( 19.00/19.27 X360,X358)) => 19.00/19.27 (~ 19.00/19.27 in( 19.00/19.27 X360, 19.00/19.27 setminus( 19.00/19.27 X358,X359))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X361, 19.00/19.27 X362,X363]: 19.00/19.27 (in( 19.00/19.27 X363,X362) => 19.00/19.27 (~ 19.00/19.27 in( 19.00/19.27 X363, 19.00/19.27 setminus( 19.00/19.27 X361,X362))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X364, 19.00/19.27 X365]: 19.00/19.27 subset( 19.00/19.27 setminus( 19.00/19.27 X364,X365), 19.00/19.27 X364)) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X366, 19.00/19.27 X367]: 19.00/19.27 (( 19.00/19.27 setminus( 19.00/19.27 X366,X367) = 19.00/19.27 emptyset) => 19.00/19.27 subset( 19.00/19.27 X366,X367))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X368, 19.00/19.27 X369,X370]: 19.00/19.27 (in( 19.00/19.27 X370, 19.00/19.27 symdiff( 19.00/19.27 X368,X369)) => 19.00/19.27 (![X371:$o]: 19.00/19.27 (( 19.00/19.27 in( 19.00/19.27 X370,X368) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ~ 19.00/19.27 in( 19.00/19.27 X370,X369)) => 19.00/19.27 X371)) => 19.00/19.27 (( 19.00/19.27 ( 19.00/19.27 ~ 19.00/19.27 in( 19.00/19.27 X370,X368)) => 19.00/19.27 ( 19.00/19.27 in( 19.00/19.27 X370,X369) => 19.00/19.27 X371)) => 19.00/19.27 X371))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X372, 19.00/19.27 X373,X374]: 19.00/19.27 (in( 19.00/19.27 X374,X372) => 19.00/19.27 (( 19.00/19.27 ~ 19.00/19.27 in( 19.00/19.27 X374,X373)) => 19.00/19.27 in( 19.00/19.27 X374, 19.00/19.27 symdiff( 19.00/19.27 X372,X373))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X375, 19.00/19.27 X376,X377]: 19.00/19.27 (( 19.00/19.27 ~ 19.00/19.27 in( 19.00/19.27 X377,X375)) => 19.00/19.27 (in( 19.00/19.27 X377,X376) => 19.00/19.27 in( 19.00/19.27 X377, 19.00/19.27 symdiff( 19.00/19.27 X375,X376))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X378, 19.00/19.27 X379,X380]: 19.00/19.27 (in( 19.00/19.27 X380,X378) => 19.00/19.27 (in( 19.00/19.27 X380,X379) => 19.00/19.27 (~ 19.00/19.27 in( 19.00/19.27 X380, 19.00/19.27 symdiff( 19.00/19.27 X378,X379)))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X381, 19.00/19.27 X382,X383]: 19.00/19.27 (( 19.00/19.27 ~ 19.00/19.27 in( 19.00/19.27 X383,X381)) => 19.00/19.27 (( 19.00/19.27 ~ 19.00/19.27 in( 19.00/19.27 X383,X382)) => 19.00/19.27 (~ 19.00/19.27 in( 19.00/19.27 X383, 19.00/19.27 symdiff( 19.00/19.27 X381,X382)))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X384, 19.00/19.27 X385]: 19.00/19.27 in( 19.00/19.27 X385, 19.00/19.27 setadjoin( 19.00/19.27 X384, 19.00/19.27 setadjoin( 19.00/19.27 X385, 19.00/19.27 emptyset)))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X386, 19.00/19.27 X387]: 19.00/19.27 in( 19.00/19.27 X386, 19.00/19.27 setunion( 19.00/19.27 setadjoin( 19.00/19.27 setadjoin( 19.00/19.27 X386, 19.00/19.27 emptyset), 19.00/19.27 setadjoin( 19.00/19.27 setadjoin( 19.00/19.27 X386, 19.00/19.27 setadjoin( 19.00/19.27 X387, 19.00/19.27 emptyset)), 19.00/19.27 emptyset))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X388, 19.00/19.27 X389]: 19.00/19.27 in( 19.00/19.27 X389, 19.00/19.27 setunion( 19.00/19.27 setadjoin( 19.00/19.27 setadjoin( 19.00/19.27 X388, 19.00/19.27 emptyset), 19.00/19.27 setadjoin( 19.00/19.27 setadjoin( 19.00/19.27 X388, 19.00/19.27 setadjoin( 19.00/19.27 X389, 19.00/19.27 emptyset)), 19.00/19.27 emptyset))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X390, 19.00/19.27 X391]: 19.00/19.27 iskpair( 19.00/19.27 setadjoin( 19.00/19.27 setadjoin( 19.00/19.27 X390, 19.00/19.27 emptyset), 19.00/19.27 setadjoin( 19.00/19.27 setadjoin( 19.00/19.27 X390, 19.00/19.27 setadjoin( 19.00/19.27 X391, 19.00/19.27 emptyset)), 19.00/19.27 emptyset)))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X392, 19.00/19.27 X393]: 19.00/19.27 iskpair( 19.00/19.27 kpair( 19.00/19.27 X392,X393))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X394, 19.00/19.27 X395]: 19.00/19.27 (in( 19.00/19.27 X395,X394) => 19.00/19.27 subset( 19.00/19.27 setadjoin( 19.00/19.27 X395, 19.00/19.27 emptyset), 19.00/19.27 X394))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X396, 19.00/19.27 X397]: 19.00/19.27 (in( 19.00/19.27 X397,X396) => 19.00/19.27 in( 19.00/19.27 setadjoin( 19.00/19.27 X397, 19.00/19.27 emptyset), 19.00/19.27 powerset( 19.00/19.27 X396)))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X398, 19.00/19.27 X399,X400]: 19.00/19.27 (in( 19.00/19.27 X400,X398) => 19.00/19.27 in( 19.00/19.27 setadjoin( 19.00/19.27 X400, 19.00/19.27 emptyset), 19.00/19.27 powerset( 19.00/19.27 binunion( 19.00/19.27 X398,X399))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X401, 19.00/19.27 X402,X403]: 19.00/19.27 (in( 19.00/19.27 X403, 19.00/19.27 setadjoin( 19.00/19.27 X401, 19.00/19.27 setadjoin( 19.00/19.27 X402, 19.00/19.27 emptyset))) => 19.00/19.27 (( 19.00/19.27 X403 = 19.00/19.27 X401) | 19.00/19.27 (X403 = 19.00/19.27 X402)))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X404, 19.00/19.27 X405,X406]: 19.00/19.27 (in( 19.00/19.27 X406,X404) => 19.00/19.27 (![X407]: 19.00/19.27 (in( 19.00/19.27 X407,X405) => 19.00/19.27 subset( 19.00/19.27 setadjoin( 19.00/19.27 X406, 19.00/19.27 setadjoin( 19.00/19.27 X407, 19.00/19.27 emptyset)), 19.00/19.27 binunion( 19.00/19.27 X404,X405)))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X408, 19.00/19.27 X409,X410]: 19.00/19.27 (in( 19.00/19.27 X410,X408) => 19.00/19.27 (![X411]: 19.00/19.27 (in( 19.00/19.27 X411,X409) => 19.00/19.27 in( 19.00/19.27 setadjoin( 19.00/19.27 X410, 19.00/19.27 setadjoin( 19.00/19.27 X411, 19.00/19.27 emptyset)), 19.00/19.27 powerset( 19.00/19.27 binunion( 19.00/19.27 X408,X409))))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X412, 19.00/19.27 X413,X414]: 19.00/19.27 (in( 19.00/19.27 X414,X412) => 19.00/19.27 (![X415]: 19.00/19.27 (in( 19.00/19.27 X415,X413) => 19.00/19.27 subset( 19.00/19.27 setadjoin( 19.00/19.27 setadjoin( 19.00/19.27 X414, 19.00/19.27 emptyset), 19.00/19.27 setadjoin( 19.00/19.27 setadjoin( 19.00/19.27 X414, 19.00/19.27 setadjoin( 19.00/19.27 X415, 19.00/19.27 emptyset)), 19.00/19.27 emptyset)), 19.00/19.27 powerset( 19.00/19.27 binunion( 19.00/19.27 X412,X413))))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X416, 19.00/19.27 X417,X418]: 19.00/19.27 (in( 19.00/19.27 X418,X416) => 19.00/19.27 (![X419]: 19.00/19.27 (in( 19.00/19.27 X419,X417) => 19.00/19.27 in( 19.00/19.27 setadjoin( 19.00/19.27 setadjoin( 19.00/19.27 X418, 19.00/19.27 emptyset), 19.00/19.27 setadjoin( 19.00/19.27 setadjoin( 19.00/19.27 X418, 19.00/19.27 setadjoin( 19.00/19.27 X419, 19.00/19.27 emptyset)), 19.00/19.27 emptyset)), 19.00/19.27 powerset( 19.00/19.27 powerset( 19.00/19.27 binunion( 19.00/19.27 X416,X417)))))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X420, 19.00/19.27 X421,X422]: 19.00/19.27 (in( 19.00/19.27 X422,X420) => 19.00/19.27 (![X423]: 19.00/19.27 (in( 19.00/19.27 X423,X421) => 19.00/19.27 in( 19.00/19.27 kpair( 19.00/19.27 X422,X423), 19.00/19.27 powerset( 19.00/19.27 powerset( 19.00/19.27 binunion( 19.00/19.27 X420,X421)))))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X424, 19.00/19.27 X425,X426]: 19.00/19.27 (in( 19.00/19.27 X426,X424) => 19.00/19.27 (![X427]: 19.00/19.27 (in( 19.00/19.27 X427,X425) => 19.00/19.27 in( 19.00/19.27 kpair( 19.00/19.27 X426,X427), 19.00/19.27 cartprod( 19.00/19.27 X424,X425)))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X428, 19.00/19.27 X429,X430]: 19.00/19.27 (in( 19.00/19.27 X430, 19.00/19.27 cartprod( 19.00/19.27 X428,X429)) => 19.00/19.27 (?[X431]: 19.00/19.27 (in( 19.00/19.27 X431,X428) & 19.00/19.27 (?[X432]: 19.00/19.27 (in( 19.00/19.27 X432,X429) & 19.00/19.27 (X430 = 19.00/19.27 kpair( 19.00/19.27 X431,X432)))))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X433, 19.00/19.27 X434,X435]: 19.00/19.27 (in( 19.00/19.27 X435, 19.00/19.27 cartprod( 19.00/19.27 X433,X434)) => 19.00/19.27 iskpair( 19.00/19.27 X435))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X436, 19.00/19.27 X437]: 19.00/19.27 (in( 19.00/19.27 X437, 19.00/19.27 setunion( 19.00/19.27 X436)) => 19.00/19.27 (?[X438]: 19.00/19.27 (in( 19.00/19.27 X438,X436) & 19.00/19.27 in( 19.00/19.27 X437,X438))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X439]: 19.00/19.27 subset( 19.00/19.27 setunion( 19.00/19.27 setadjoin( 19.00/19.27 X439, 19.00/19.27 emptyset)), 19.00/19.27 X439)) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X440]: 19.00/19.27 subset( 19.00/19.27 X440, 19.00/19.27 setunion( 19.00/19.27 setadjoin( 19.00/19.27 X440, 19.00/19.27 emptyset)))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X441]: 19.00/19.27 (setunion( 19.00/19.27 setadjoin( 19.00/19.27 X441, 19.00/19.27 emptyset)) = 19.00/19.27 X441)) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X442, 19.00/19.27 X443:( 19.00/19.27 $i > $o)]: 19.00/19.27 (( 19.00/19.27 ![X444]: 19.00/19.27 (in( 19.00/19.27 X444,X442) => 19.00/19.27 (![X445]: 19.00/19.27 (in( 19.00/19.27 X445,X442) => 19.00/19.27 (X443( 19.00/19.27 X444) => 19.00/19.27 (X443( 19.00/19.27 X445) => 19.00/19.27 (X444 = 19.00/19.27 X445))))))) => 19.00/19.27 (( 19.00/19.27 ?[X446]: 19.00/19.27 (in( 19.00/19.27 X446,X442) & 19.00/19.27 X443( 19.00/19.27 X446))) => 19.00/19.27 singleton( 19.00/19.27 dsetconstr( 19.00/19.27 X442, 19.00/19.27 ^[V_15]: 19.00/19.27 X443( 19.00/19.27 V_15)))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X447, 19.00/19.27 X448:( 19.00/19.27 $i > $o)]: 19.00/19.27 (singleton( 19.00/19.27 dsetconstr( 19.00/19.27 X447, 19.00/19.27 ^[V_16]: 19.00/19.27 X448( 19.00/19.27 V_16))) => 19.00/19.27 (?[X449]: 19.00/19.27 (in( 19.00/19.27 X449,X447) & 19.00/19.27 X448( 19.00/19.27 X449))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X450, 19.00/19.27 X451:( 19.00/19.27 $i > $o), 19.00/19.27 X452]: 19.00/19.27 (in( 19.00/19.27 X452,X450) => 19.00/19.27 (X451( 19.00/19.27 X452) => 19.00/19.27 (( 19.00/19.27 ![X453]: 19.00/19.27 (in( 19.00/19.27 X453,X450) => 19.00/19.27 (X451( 19.00/19.27 X453) => 19.00/19.27 (X453 = 19.00/19.27 X452)))) => 19.00/19.27 singleton( 19.00/19.27 dsetconstr( 19.00/19.27 X450, 19.00/19.27 ^[V_17]: 19.00/19.27 X451( 19.00/19.27 V_17))))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X454, 19.00/19.27 X455:( 19.00/19.27 $i > $o)]: 19.00/19.27 (( 19.00/19.27 ![X456]: 19.00/19.27 (in( 19.00/19.27 X456,X454) => 19.00/19.27 (![X457]: 19.00/19.27 (in( 19.00/19.27 X457,X454) => 19.00/19.27 (X455( 19.00/19.27 X456) => 19.00/19.27 (X455( 19.00/19.27 X457) => 19.00/19.27 (X456 = 19.00/19.27 X457))))))) => 19.00/19.27 (( 19.00/19.27 ?[X458]: 19.00/19.27 (in( 19.00/19.27 X458,X454) & 19.00/19.27 X455( 19.00/19.27 X458))) => 19.00/19.27 singleton( 19.00/19.27 dsetconstr( 19.00/19.27 X454, 19.00/19.27 ^[V_18]: 19.00/19.27 X455( 19.00/19.27 V_18)))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X459, 19.00/19.27 X460]: 19.00/19.27 (( 19.00/19.27 setadjoin( 19.00/19.27 X459, 19.00/19.27 emptyset) = 19.00/19.27 setadjoin( 19.00/19.27 X460, 19.00/19.27 emptyset)) => 19.00/19.27 (X459 = 19.00/19.27 X460))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X461, 19.00/19.27 X462,X463]: 19.00/19.27 (in( 19.00/19.27 setadjoin( 19.00/19.27 X463, 19.00/19.27 emptyset), 19.00/19.27 setadjoin( 19.00/19.27 setadjoin( 19.00/19.27 X461, 19.00/19.27 emptyset), 19.00/19.27 setadjoin( 19.00/19.27 setadjoin( 19.00/19.27 X461, 19.00/19.27 setadjoin( 19.00/19.27 X462, 19.00/19.27 emptyset)), 19.00/19.27 emptyset))) => 19.00/19.27 (X461 = 19.00/19.27 X463))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X464]: 19.00/19.27 (iskpair( 19.00/19.27 X464) => 19.00/19.27 singleton( 19.00/19.27 dsetconstr( 19.00/19.27 setunion( 19.00/19.27 X464), 19.00/19.27 ^[V_19]: 19.00/19.27 in( 19.00/19.27 setadjoin( 19.00/19.27 V_19, 19.00/19.27 emptyset), 19.00/19.27 X464))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X465]: 19.00/19.27 (singleton( 19.00/19.27 X465) => 19.00/19.27 in( 19.00/19.27 setunion( 19.00/19.27 X465), 19.00/19.27 X465))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X466, 19.00/19.27 X467]: 19.00/19.27 (kfst( 19.00/19.27 kpair( 19.00/19.27 X466,X467)) = 19.00/19.27 X466)) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X468, 19.00/19.27 X469,X470]: 19.00/19.27 (in( 19.00/19.27 X470, 19.00/19.27 cartprod( 19.00/19.27 X468,X469)) => 19.00/19.27 in( 19.00/19.27 kfst( 19.00/19.27 X470), 19.00/19.27 X468))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X471, 19.00/19.27 X472, 19.00/19.27 X473,X474]: 19.00/19.27 (( 19.00/19.27 setadjoin( 19.00/19.27 setadjoin( 19.00/19.27 X471, 19.00/19.27 emptyset), 19.00/19.27 setadjoin( 19.00/19.27 setadjoin( 19.00/19.27 X471, 19.00/19.27 setadjoin( 19.00/19.27 X472, 19.00/19.27 emptyset)), 19.00/19.27 emptyset)) = 19.00/19.27 setadjoin( 19.00/19.27 setadjoin( 19.00/19.27 X473, 19.00/19.27 emptyset), 19.00/19.27 setadjoin( 19.00/19.27 setadjoin( 19.00/19.27 X473, 19.00/19.27 setadjoin( 19.00/19.27 X474, 19.00/19.27 emptyset)), 19.00/19.27 emptyset))) => 19.00/19.27 (X471 = 19.00/19.27 X473))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X475, 19.00/19.27 X476, 19.00/19.27 X477,X478]: 19.00/19.27 (( 19.00/19.27 kpair( 19.00/19.27 X475,X476) = 19.00/19.27 kpair( 19.00/19.27 X477,X478)) => 19.00/19.27 (X475 = 19.00/19.27 X477))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X479, 19.00/19.27 X480]: 19.00/19.27 (( 19.00/19.27 X479 = 19.00/19.27 X480) => 19.00/19.27 (setadjoin( 19.00/19.27 X479, 19.00/19.27 setadjoin( 19.00/19.27 X480, 19.00/19.27 emptyset)) = 19.00/19.27 setadjoin( 19.00/19.27 X479, 19.00/19.27 emptyset)))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X481, 19.00/19.27 X482]: 19.00/19.27 (( 19.00/19.27 X481 = 19.00/19.27 X482) => 19.00/19.27 (setadjoin( 19.00/19.27 setadjoin( 19.00/19.27 X481, 19.00/19.27 emptyset), 19.00/19.27 setadjoin( 19.00/19.27 setadjoin( 19.00/19.27 X481, 19.00/19.27 setadjoin( 19.00/19.27 X482, 19.00/19.27 emptyset)), 19.00/19.27 emptyset)) = 19.00/19.27 setadjoin( 19.00/19.27 setadjoin( 19.00/19.27 X481, 19.00/19.27 emptyset), 19.00/19.27 emptyset)))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X483, 19.00/19.27 X484, 19.00/19.27 X485,X486]: 19.00/19.27 (( 19.00/19.27 setadjoin( 19.00/19.27 setadjoin( 19.00/19.27 X483, 19.00/19.27 emptyset), 19.00/19.27 setadjoin( 19.00/19.27 setadjoin( 19.00/19.27 X483, 19.00/19.27 setadjoin( 19.00/19.27 X484, 19.00/19.27 emptyset)), 19.00/19.27 emptyset)) = 19.00/19.27 setadjoin( 19.00/19.27 setadjoin( 19.00/19.27 X485, 19.00/19.27 emptyset), 19.00/19.27 setadjoin( 19.00/19.27 setadjoin( 19.00/19.27 X485, 19.00/19.27 setadjoin( 19.00/19.27 X486, 19.00/19.27 emptyset)), 19.00/19.27 emptyset))) => 19.00/19.27 (( 19.00/19.27 X485 = 19.00/19.27 X486) => 19.00/19.27 (X484 = 19.00/19.27 X486)))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X487, 19.00/19.27 X488,X489]: 19.00/19.27 (( 19.00/19.27 setadjoin( 19.00/19.27 X487, 19.00/19.27 setadjoin( 19.00/19.27 X488, 19.00/19.27 emptyset)) = 19.00/19.27 setadjoin( 19.00/19.27 X489, 19.00/19.27 emptyset)) => 19.00/19.27 (X487 = 19.00/19.27 X488))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X490, 19.00/19.27 X491, 19.00/19.27 X492,X493]: 19.00/19.27 (( 19.00/19.27 setadjoin( 19.00/19.27 setadjoin( 19.00/19.27 X490, 19.00/19.27 emptyset), 19.00/19.27 setadjoin( 19.00/19.27 setadjoin( 19.00/19.27 X490, 19.00/19.27 setadjoin( 19.00/19.27 X491, 19.00/19.27 emptyset)), 19.00/19.27 emptyset)) = 19.00/19.27 setadjoin( 19.00/19.27 setadjoin( 19.00/19.27 X492, 19.00/19.27 emptyset), 19.00/19.27 setadjoin( 19.00/19.27 setadjoin( 19.00/19.27 X492, 19.00/19.27 setadjoin( 19.00/19.27 X493, 19.00/19.27 emptyset)), 19.00/19.27 emptyset))) => 19.00/19.27 (X491 = 19.00/19.27 X493))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X494, 19.00/19.27 X495, 19.00/19.27 X496,X497]: 19.00/19.27 (( 19.00/19.27 kpair( 19.00/19.27 X494,X495) = 19.00/19.27 kpair( 19.00/19.27 X496,X497)) => 19.00/19.27 (X495 = 19.00/19.27 X497))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X498]: 19.00/19.27 (iskpair( 19.00/19.27 X498) => 19.00/19.27 singleton( 19.00/19.27 dsetconstr( 19.00/19.27 setunion( 19.00/19.27 X498), 19.00/19.27 ^[V_20]: 19.00/19.27 (X498 = 19.00/19.27 kpair( 19.00/19.27 kfst( 19.00/19.27 X498), 19.00/19.27 V_20)))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X499, 19.00/19.27 X500]: 19.00/19.27 (ksnd( 19.00/19.27 kpair( 19.00/19.27 X499,X500)) = 19.00/19.27 X500)) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X501]: 19.00/19.27 (iskpair( 19.00/19.27 X501) => 19.00/19.27 (kpair( 19.00/19.27 kfst( 19.00/19.27 X501), 19.00/19.27 ksnd( 19.00/19.27 X501)) = 19.00/19.27 X501))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X502, 19.00/19.27 X503,X504]: 19.00/19.27 (in( 19.00/19.27 X504, 19.00/19.27 cartprod( 19.00/19.27 X502,X503)) => 19.00/19.27 in( 19.00/19.27 ksnd( 19.00/19.27 X504), 19.00/19.27 X503))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X505, 19.00/19.27 X506, 19.00/19.27 X507,X508]: 19.00/19.27 (in( 19.00/19.27 kpair( 19.00/19.27 X507,X508), 19.00/19.27 cartprod( 19.00/19.27 X505,X506)) => 19.00/19.27 in( 19.00/19.27 X507,X505))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X509, 19.00/19.27 X510, 19.00/19.27 X511,X512]: 19.00/19.27 (in( 19.00/19.27 kpair( 19.00/19.27 X511,X512), 19.00/19.27 cartprod( 19.00/19.27 X509,X510)) => 19.00/19.27 in( 19.00/19.27 X512,X510))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X513, 19.00/19.27 X514,X515]: 19.00/19.27 (in( 19.00/19.27 X515,X513) => 19.00/19.27 (![X516]: 19.00/19.27 (in( 19.00/19.27 X516,X514) => 19.00/19.27 (kpair( 19.00/19.27 X515,X516) = 19.00/19.27 kpair( 19.00/19.27 X515,X516)))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X517, 19.00/19.27 X518,X519]: 19.00/19.27 (in( 19.00/19.27 X519,X517) => 19.00/19.27 (![X520]: 19.00/19.27 (in( 19.00/19.27 X520,X518) => 19.00/19.27 (kfst( 19.00/19.27 kpair( 19.00/19.27 X519,X520)) = 19.00/19.27 X519))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X521, 19.00/19.27 X522,X523]: 19.00/19.27 (in( 19.00/19.27 X523,X521) => 19.00/19.27 (![X524]: 19.00/19.27 (in( 19.00/19.27 X524,X522) => 19.00/19.27 (ksnd( 19.00/19.27 kpair( 19.00/19.27 X523,X524)) = 19.00/19.27 X524))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X525, 19.00/19.27 X526,X527]: 19.00/19.27 (in( 19.00/19.27 X527, 19.00/19.27 cartprod( 19.00/19.27 X525,X526)) => 19.00/19.27 (kpair( 19.00/19.27 kfst( 19.00/19.27 X527), 19.00/19.27 ksnd( 19.00/19.27 X527)) = 19.00/19.27 X527))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X528, 19.00/19.27 X529, 19.00/19.27 X530:( 19.00/19.27 ($i * $i) > 19.00/19.27 $o),X531]: 19.00/19.27 (in( 19.00/19.27 X531,X528) => 19.00/19.27 (![X532]: 19.00/19.27 (in( 19.00/19.27 X532,X529) => 19.00/19.27 (X530( 19.00/19.27 X531,X532) => 19.00/19.27 in( 19.00/19.27 kpair( 19.00/19.27 X531,X532), 19.00/19.27 dpsetconstr( 19.00/19.27 X528, 19.00/19.27 X529, 19.00/19.27 ^[V_21, 19.00/19.27 V_22]: 19.00/19.27 X530( 19.00/19.27 V_21,V_22)))))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X533, 19.00/19.27 X534, 19.00/19.27 X535:( 19.00/19.27 ($i * $i) > 19.00/19.27 $o)]: 19.00/19.27 subset( 19.00/19.27 dpsetconstr( 19.00/19.27 X533, 19.00/19.27 X534, 19.00/19.27 ^[V_23, 19.00/19.27 V_24]: 19.00/19.27 X535( 19.00/19.27 V_23,V_24)), 19.00/19.27 cartprod( 19.00/19.27 X533,X534))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X536, 19.00/19.27 X537, 19.00/19.27 X538:( 19.00/19.27 ($i * $i) > 19.00/19.27 $o)]: 19.00/19.27 subset( 19.00/19.27 dpsetconstr( 19.00/19.27 X536, 19.00/19.27 X537, 19.00/19.27 ^[V_25, 19.00/19.27 V_26]: 19.00/19.27 X538( 19.00/19.27 V_25,V_26)), 19.00/19.27 cartprod( 19.00/19.27 X536,X537))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X539, 19.00/19.27 X540, 19.00/19.27 X541:( 19.00/19.27 ($i * $i) > 19.00/19.27 $o),X542]: 19.00/19.27 (in( 19.00/19.27 X542,X539) => 19.00/19.27 (![X543]: 19.00/19.27 (in( 19.00/19.27 X543,X540) => 19.00/19.27 (in( 19.00/19.27 kpair( 19.00/19.27 X542,X543), 19.00/19.27 dpsetconstr( 19.00/19.27 X539, 19.00/19.27 X540, 19.00/19.27 ^[V_27, 19.00/19.27 V_28]: 19.00/19.27 X541( 19.00/19.27 V_27,V_28))) => 19.00/19.27 X541( 19.00/19.27 X542,X543)))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X544, 19.00/19.27 X545, 19.00/19.27 X546:( 19.00/19.27 ($i * $i) > 19.00/19.27 $o),X547, 19.00/19.27 X548]: 19.00/19.27 (in( 19.00/19.27 kpair( 19.00/19.27 X547,X548), 19.00/19.27 dpsetconstr( 19.00/19.27 X544, 19.00/19.27 X545, 19.00/19.27 ^[V_29, 19.00/19.27 V_30]: 19.00/19.27 X546( 19.00/19.27 V_29,V_30))) => 19.00/19.27 in( 19.00/19.27 X547,X544))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X549, 19.00/19.27 X550, 19.00/19.27 X551:( 19.00/19.27 ($i * $i) > 19.00/19.27 $o),X552, 19.00/19.27 X553]: 19.00/19.27 (in( 19.00/19.27 kpair( 19.00/19.27 X552,X553), 19.00/19.27 dpsetconstr( 19.00/19.27 X549, 19.00/19.27 X550, 19.00/19.27 ^[V_31, 19.00/19.27 V_32]: 19.00/19.27 X551( 19.00/19.27 V_31,V_32))) => 19.00/19.27 in( 19.00/19.27 X553,X550))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X554, 19.00/19.27 X555, 19.00/19.27 X556:( 19.00/19.27 ($i * $i) > 19.00/19.27 $o),X557, 19.00/19.27 X558]: 19.00/19.27 (in( 19.00/19.27 kpair( 19.00/19.27 X557,X558), 19.00/19.27 dpsetconstr( 19.00/19.27 X554, 19.00/19.27 X555, 19.00/19.27 ^[V_33, 19.00/19.27 V_34]: 19.00/19.27 X556( 19.00/19.27 V_33,V_34))) => 19.00/19.27 X556( 19.00/19.27 X557,X558))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X559, 19.00/19.27 X560,X561]: 19.00/19.27 (func( 19.00/19.27 X559, 19.00/19.27 X560,X561) => 19.00/19.27 (![X562]: 19.00/19.27 (in( 19.00/19.27 X562,X559) => 19.00/19.27 singleton( 19.00/19.27 dsetconstr( 19.00/19.27 X560, 19.00/19.27 ^[V_35]: 19.00/19.27 in( 19.00/19.27 kpair( 19.00/19.27 X562,V_35), 19.00/19.27 X561))))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X563, 19.00/19.27 X564,X565]: 19.00/19.27 (func( 19.00/19.27 X563, 19.00/19.27 X564,X565) => 19.00/19.27 (![X566]: 19.00/19.27 (in( 19.00/19.27 X566,X563) => 19.00/19.27 in( 19.00/19.27 setunion( 19.00/19.27 dsetconstr( 19.00/19.27 X564, 19.00/19.27 ^[V_36]: 19.00/19.27 in( 19.00/19.27 kpair( 19.00/19.27 X566,V_36), 19.00/19.27 X565))), 19.00/19.27 X564))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X567, 19.00/19.27 X568,X569]: 19.00/19.27 (func( 19.00/19.27 X567, 19.00/19.27 X568,X569) => 19.00/19.27 (![X570]: 19.00/19.27 (in( 19.00/19.27 X570,X567) => 19.00/19.27 in( 19.00/19.27 ap( 19.00/19.27 X567, 19.00/19.27 X568, 19.00/19.27 X569,X570), 19.00/19.27 X568))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X571, 19.00/19.27 X572,X573]: 19.00/19.27 (in( 19.00/19.27 X573, 19.00/19.27 funcSet( 19.00/19.27 X571,X572)) => 19.00/19.27 func( 19.00/19.27 X571, 19.00/19.27 X572,X573))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X574, 19.00/19.27 X575,X576]: 19.00/19.27 (in( 19.00/19.27 X576, 19.00/19.27 funcSet( 19.00/19.27 X574,X575)) => 19.00/19.27 (![X577]: 19.00/19.27 (in( 19.00/19.27 X577,X574) => 19.00/19.27 in( 19.00/19.27 ap( 19.00/19.27 X574, 19.00/19.27 X575, 19.00/19.27 X576,X577), 19.00/19.27 X575))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X578, 19.00/19.27 X579,X580]: 19.00/19.27 (func( 19.00/19.27 X578, 19.00/19.27 X579,X580) => 19.00/19.27 in( 19.00/19.27 X580, 19.00/19.27 funcSet( 19.00/19.27 X578,X579)))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X581, 19.00/19.27 X582, 19.00/19.27 X583:( 19.00/19.27 $i > $i)]: 19.00/19.27 (( 19.00/19.27 ![X584]: 19.00/19.27 (in( 19.00/19.27 X584,X581) => 19.00/19.27 in( 19.00/19.27 X583( 19.00/19.27 X584), 19.00/19.27 X582))) => 19.00/19.27 func( 19.00/19.27 X581, 19.00/19.27 X582, 19.00/19.27 dpsetconstr( 19.00/19.27 X581, 19.00/19.27 X582, 19.00/19.27 ^[V_37, 19.00/19.27 V_38]: 19.00/19.27 (X583( 19.00/19.27 V_37) = 19.00/19.27 V_38))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X585, 19.00/19.27 X586, 19.00/19.27 X587:( 19.00/19.27 $i > $i)]: 19.00/19.27 (( 19.00/19.27 ![X588]: 19.00/19.27 (in( 19.00/19.27 X588,X585) => 19.00/19.27 in( 19.00/19.27 X587( 19.00/19.27 X588), 19.00/19.27 X586))) => 19.00/19.27 func( 19.00/19.27 X585, 19.00/19.27 X586, 19.00/19.27 lam( 19.00/19.27 X585, 19.00/19.27 X586, 19.00/19.27 ^[V_39]: 19.00/19.27 X587( 19.00/19.27 V_39))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X589, 19.00/19.27 X590, 19.00/19.27 X591:( 19.00/19.27 $i > $i)]: 19.00/19.27 (( 19.00/19.27 ![X592]: 19.00/19.27 (in( 19.00/19.27 X592,X589) => 19.00/19.27 in( 19.00/19.27 X591( 19.00/19.27 X592), 19.00/19.27 X590))) => 19.00/19.27 in( 19.00/19.27 lam( 19.00/19.27 X589, 19.00/19.27 X590, 19.00/19.27 ^[V_40]: 19.00/19.27 X591( 19.00/19.27 V_40)), 19.00/19.27 funcSet( 19.00/19.27 X589,X590)))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X593, 19.00/19.27 X594,X595]: 19.00/19.27 (subset( 19.00/19.27 X595, 19.00/19.27 cartprod( 19.00/19.27 X593,X594)) => 19.00/19.27 (![X596:( 19.00/19.27 $i > $o)]: 19.00/19.27 (( 19.00/19.27 ![X597]: 19.00/19.27 (in( 19.00/19.27 X597,X593) => 19.00/19.27 (![X598]: 19.00/19.27 (in( 19.00/19.27 X598,X594) => 19.00/19.27 (in( 19.00/19.27 kpair( 19.00/19.27 X597,X598), 19.00/19.27 X595) => 19.00/19.27 X596( 19.00/19.27 kpair( 19.00/19.27 X597,X598))))))) => 19.00/19.27 (![X599]: 19.00/19.27 (in( 19.00/19.27 X599,X595) => 19.00/19.27 X596( 19.00/19.27 X599))))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X600, 19.00/19.27 X601,X602]: 19.00/19.27 (subset( 19.00/19.27 X602, 19.00/19.27 cartprod( 19.00/19.27 X600,X601)) => 19.00/19.27 (![X603:( 19.00/19.27 $i > $o)]: 19.00/19.27 (( 19.00/19.27 ![X604]: 19.00/19.27 (in( 19.00/19.27 X604,X600) => 19.00/19.27 (![X605]: 19.00/19.27 (in( 19.00/19.27 X605,X601) => 19.00/19.27 (in( 19.00/19.27 kpair( 19.00/19.27 X604,X605), 19.00/19.27 X602) => 19.00/19.27 X603( 19.00/19.27 kpair( 19.00/19.27 X604,X605))))))) => 19.00/19.27 (![X606]: 19.00/19.27 (in( 19.00/19.27 X606,X602) => 19.00/19.27 X603( 19.00/19.27 X606))))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X607, 19.00/19.27 X608:( 19.00/19.27 $i > $o)]: 19.00/19.27 (singleton( 19.00/19.27 dsetconstr( 19.00/19.27 X607, 19.00/19.27 ^[V_41]: 19.00/19.27 X608( 19.00/19.27 V_41))) => 19.00/19.27 (![X609]: 19.00/19.27 (in( 19.00/19.27 X609,X607) => 19.00/19.27 (![X610]: 19.00/19.27 (in( 19.00/19.27 X610,X607) => 19.00/19.27 (X608( 19.00/19.27 X609) => 19.00/19.27 (X608( 19.00/19.27 X610) => 19.00/19.27 (X609 = 19.00/19.27 X610))))))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X611, 19.00/19.27 X612,X613]: 19.00/19.27 (func( 19.00/19.27 X611, 19.00/19.27 X612,X613) => 19.00/19.27 (![X614]: 19.00/19.27 (in( 19.00/19.27 X614,X611) => 19.00/19.27 in( 19.00/19.27 kpair( 19.00/19.27 X614, 19.00/19.27 ap( 19.00/19.27 X611, 19.00/19.27 X612, 19.00/19.27 X613,X614)), 19.00/19.27 X613))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X615, 19.00/19.27 X616,X617]: 19.00/19.27 (in( 19.00/19.27 X617, 19.00/19.27 funcSet( 19.00/19.27 X615,X616)) => 19.00/19.27 (![X618]: 19.00/19.27 (in( 19.00/19.27 X618,X615) => 19.00/19.27 in( 19.00/19.27 kpair( 19.00/19.27 X618, 19.00/19.27 ap( 19.00/19.27 X615, 19.00/19.27 X616, 19.00/19.27 X617,X618)), 19.00/19.27 X617))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X619, 19.00/19.27 X620,X621]: 19.00/19.27 (func( 19.00/19.27 X619, 19.00/19.27 X620,X621) => 19.00/19.27 (![X622]: 19.00/19.27 (in( 19.00/19.27 X622,X619) => 19.00/19.27 (![X623]: 19.00/19.27 (in( 19.00/19.27 X623,X620) => 19.00/19.27 (in( 19.00/19.27 kpair( 19.00/19.27 X622,X623), 19.00/19.27 X621) => 19.00/19.27 (ap( 19.00/19.27 X619, 19.00/19.27 X620, 19.00/19.27 X621,X622) = 19.00/19.27 X623)))))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X624, 19.00/19.27 X625,X626]: 19.00/19.27 (func( 19.00/19.27 X624, 19.00/19.27 X625,X626) => 19.00/19.27 (![X627]: 19.00/19.27 (func( 19.00/19.27 X624, 19.00/19.27 X625,X627) => 19.00/19.27 (( 19.00/19.27 ![X628]: 19.00/19.27 (in( 19.00/19.27 X628,X624) => 19.00/19.27 (ap( 19.00/19.27 X624, 19.00/19.27 X625, 19.00/19.27 X626,X628) = 19.00/19.27 ap( 19.00/19.27 X624, 19.00/19.27 X625, 19.00/19.27 X627,X628)))) => 19.00/19.27 (![X629]: 19.00/19.27 (in( 19.00/19.27 X629,X624) => 19.00/19.27 (![X630]: 19.00/19.27 (in( 19.00/19.27 X630,X625) => 19.00/19.27 (in( 19.00/19.27 kpair( 19.00/19.27 X629,X630), 19.00/19.27 X627) => 19.00/19.27 in( 19.00/19.27 kpair( 19.00/19.27 X629,X630), 19.00/19.27 X626))))))))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X631, 19.00/19.27 X632,X633]: 19.00/19.27 (in( 19.00/19.27 X633, 19.00/19.27 funcSet( 19.00/19.27 X631,X632)) => 19.00/19.27 (![X634]: 19.00/19.27 (in( 19.00/19.27 X634,X631) => 19.00/19.27 (![X635]: 19.00/19.27 (in( 19.00/19.27 X635,X632) => 19.00/19.27 (in( 19.00/19.27 kpair( 19.00/19.27 X634,X635), 19.00/19.27 X633) => 19.00/19.27 (ap( 19.00/19.27 X631, 19.00/19.27 X632, 19.00/19.27 X633,X634) = 19.00/19.27 X635)))))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X636, 19.00/19.27 X637,X638]: 19.00/19.27 (subset( 19.00/19.27 X638, 19.00/19.27 cartprod( 19.00/19.27 X636,X637)) => 19.00/19.27 (![X639]: 19.00/19.27 (subset( 19.00/19.27 X639, 19.00/19.27 cartprod( 19.00/19.27 X636,X637)) => 19.00/19.27 (( 19.00/19.27 ![X640]: 19.00/19.27 (in( 19.00/19.27 X640,X636) => 19.00/19.27 (![X641]: 19.00/19.27 (in( 19.00/19.27 X641,X637) => 19.00/19.27 (in( 19.00/19.27 kpair( 19.00/19.27 X640,X641), 19.00/19.27 X638) => 19.00/19.27 in( 19.00/19.27 kpair( 19.00/19.27 X640,X641), 19.00/19.27 X639)))))) => 19.00/19.27 subset( 19.00/19.27 X638,X639)))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X642, 19.00/19.27 X643,X644]: 19.00/19.27 (subset( 19.00/19.27 X644, 19.00/19.27 cartprod( 19.00/19.27 X642,X643)) => 19.00/19.27 (![X645]: 19.00/19.27 (subset( 19.00/19.27 X645, 19.00/19.27 cartprod( 19.00/19.27 X642,X643)) => 19.00/19.27 (( 19.00/19.27 ![X646]: 19.00/19.27 (in( 19.00/19.27 X646,X642) => 19.00/19.27 (![X647]: 19.00/19.27 (in( 19.00/19.27 X647,X643) => 19.00/19.27 (in( 19.00/19.27 kpair( 19.00/19.27 X646,X647), 19.00/19.27 X644) => 19.00/19.27 in( 19.00/19.27 kpair( 19.00/19.27 X646,X647), 19.00/19.27 X645)))))) => 19.00/19.27 (( 19.00/19.27 ![X648]: 19.00/19.27 (in( 19.00/19.27 X648,X642) => 19.00/19.27 (![X649]: 19.00/19.27 (in( 19.00/19.27 X649,X643) => 19.00/19.27 (in( 19.00/19.27 kpair( 19.00/19.27 X648,X649), 19.00/19.27 X645) => 19.00/19.27 in( 19.00/19.27 kpair( 19.00/19.27 X648,X649), 19.00/19.27 X644)))))) => 19.00/19.27 (X644 = 19.00/19.27 X645))))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X650, 19.00/19.27 X651,X652]: 19.00/19.27 (func( 19.00/19.27 X650, 19.00/19.27 X651,X652) => 19.00/19.27 (![X653]: 19.00/19.27 (func( 19.00/19.27 X650, 19.00/19.27 X651,X653) => 19.00/19.27 (( 19.00/19.27 ![X654]: 19.00/19.27 (in( 19.00/19.27 X654,X650) => 19.00/19.27 (ap( 19.00/19.27 X650, 19.00/19.27 X651, 19.00/19.27 X652,X654) = 19.00/19.27 ap( 19.00/19.27 X650, 19.00/19.27 X651, 19.00/19.27 X653,X654)))) => 19.00/19.27 (X652 = 19.00/19.27 X653)))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X655, 19.00/19.27 X656,X657]: 19.00/19.27 (in( 19.00/19.27 X657, 19.00/19.27 funcSet( 19.00/19.27 X655,X656)) => 19.00/19.27 (![X658]: 19.00/19.27 (in( 19.00/19.27 X658, 19.00/19.27 funcSet( 19.00/19.27 X655,X656)) => 19.00/19.27 (( 19.00/19.27 ![X659]: 19.00/19.27 (in( 19.00/19.27 X659,X655) => 19.00/19.27 (ap( 19.00/19.27 X655, 19.00/19.27 X656, 19.00/19.27 X657,X659) = 19.00/19.27 ap( 19.00/19.27 X655, 19.00/19.27 X656, 19.00/19.27 X658,X659)))) => 19.00/19.27 (X657 = 19.00/19.27 X658)))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X660, 19.00/19.27 X661,X662]: 19.00/19.27 (in( 19.00/19.27 X662, 19.00/19.27 funcSet( 19.00/19.27 X660,X661)) => 19.00/19.27 (![X663]: 19.00/19.27 (in( 19.00/19.27 X663,X660) => 19.00/19.27 (ap( 19.00/19.27 X660, 19.00/19.27 X661, 19.00/19.27 X662,X663) = 19.00/19.27 ap( 19.00/19.27 X660, 19.00/19.27 X661, 19.00/19.27 X662,X663)))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X664, 19.00/19.27 X665,X666]: 19.00/19.27 (func( 19.00/19.27 X664, 19.00/19.27 X665,X666) => 19.00/19.27 (![X667]: 19.00/19.27 (in( 19.00/19.27 X667,X664) => 19.00/19.27 (ap( 19.00/19.27 X664, 19.00/19.27 X665, 19.00/19.27 X666,X667) = 19.00/19.27 ap( 19.00/19.27 X664, 19.00/19.27 X665, 19.00/19.27 X666,X667)))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X668, 19.00/19.27 X669, 19.00/19.27 X670:( 19.00/19.27 $i > $i)]: 19.00/19.27 (( 19.00/19.27 ![X671]: 19.00/19.27 (in( 19.00/19.27 X671,X668) => 19.00/19.27 in( 19.00/19.27 X670( 19.00/19.27 X671), 19.00/19.27 X669))) => 19.00/19.27 (![X672]: 19.00/19.27 (in( 19.00/19.27 X672,X668) => 19.00/19.27 (ap( 19.00/19.27 X668, 19.00/19.27 X669, 19.00/19.27 lam( 19.00/19.27 X668, 19.00/19.27 X669, 19.00/19.27 ^[V_42]: 19.00/19.27 X670( 19.00/19.27 V_42)), 19.00/19.27 X672) = 19.00/19.27 X670( 19.00/19.27 X672)))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X673, 19.00/19.27 X674,X675]: 19.00/19.27 (func( 19.00/19.27 X673, 19.00/19.27 X674,X675) => 19.00/19.27 (lam( 19.00/19.27 X673, 19.00/19.27 X674, 19.00/19.27 ^[V_43]: 19.00/19.27 ap( 19.00/19.27 X673, 19.00/19.27 X674, 19.00/19.27 X675,V_43)) = 19.00/19.27 X675))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X676, 19.00/19.27 X677, 19.00/19.27 X678:( 19.00/19.27 $i > $i)]: 19.00/19.27 (( 19.00/19.27 ![X679]: 19.00/19.27 (in( 19.00/19.27 X679,X676) => 19.00/19.27 in( 19.00/19.27 X678( 19.00/19.27 X679), 19.00/19.27 X677))) => 19.00/19.27 (lam( 19.00/19.27 X676, 19.00/19.27 X677, 19.00/19.27 ^[V_44]: 19.00/19.27 X678( 19.00/19.27 V_44)) = 19.00/19.27 lam( 19.00/19.27 X676, 19.00/19.27 X677, 19.00/19.27 ^[V_45]: 19.00/19.27 X678( 19.00/19.27 V_45))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X680, 19.00/19.27 X681, 19.00/19.27 X682:( 19.00/19.27 $i > $i)]: 19.00/19.27 (( 19.00/19.27 ![X683]: 19.00/19.27 (in( 19.00/19.27 X683,X680) => 19.00/19.27 in( 19.00/19.27 X682( 19.00/19.27 X683), 19.00/19.27 X681))) => 19.00/19.27 (![X684]: 19.00/19.27 (in( 19.00/19.27 X684,X680) => 19.00/19.27 (ap( 19.00/19.27 X680, 19.00/19.27 X681, 19.00/19.27 lam( 19.00/19.27 X680, 19.00/19.27 X681, 19.00/19.27 ^[V_46]: 19.00/19.27 X682( 19.00/19.27 V_46)), 19.00/19.27 X684) = 19.00/19.27 X682( 19.00/19.27 X684)))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X685, 19.00/19.27 X686,X687]: 19.00/19.27 (in( 19.00/19.27 X687, 19.00/19.27 funcSet( 19.00/19.27 X685,X686)) => 19.00/19.27 (lam( 19.00/19.27 X685, 19.00/19.27 X686, 19.00/19.27 ^[V_47]: 19.00/19.27 ap( 19.00/19.27 X685, 19.00/19.27 X686, 19.00/19.27 X687,V_47)) = 19.00/19.27 X687))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X688, 19.00/19.27 X689:$o, 19.00/19.27 X690]: 19.00/19.27 (in( 19.00/19.27 X690,X688) => 19.00/19.27 (![X691]: 19.00/19.27 (in( 19.00/19.27 X691,X688) => 19.00/19.27 (( 19.00/19.27 ~X689) => 19.00/19.27 in( 19.00/19.27 X691, 19.00/19.27 dsetconstr( 19.00/19.27 X688, 19.00/19.27 ^[V_48]: 19.00/19.27 (( 19.00/19.27 X689 & 19.00/19.27 ( 19.00/19.27 V_48 = 19.00/19.27 X690)) | 19.00/19.27 (( 19.00/19.27 ~X689) & 19.00/19.27 (V_48 = 19.00/19.27 X691)))))))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X692, 19.00/19.27 X693:$o, 19.00/19.27 X694]: 19.00/19.27 (in( 19.00/19.27 X694,X692) => 19.00/19.27 (![X695]: 19.00/19.27 (in( 19.00/19.27 X695,X692) => 19.00/19.27 (( 19.00/19.27 ~X693) => 19.00/19.27 (dsetconstr( 19.00/19.27 X692, 19.00/19.27 ^[V_49]: 19.00/19.27 (( 19.00/19.27 X693 & 19.00/19.27 ( 19.00/19.27 V_49 = 19.00/19.27 X694)) | 19.00/19.27 (( 19.00/19.27 ~X693) & 19.00/19.27 (V_49 = 19.00/19.27 X695)))) = 19.00/19.27 setadjoin( 19.00/19.27 X695, 19.00/19.27 emptyset))))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X696, 19.00/19.27 X697:$o, 19.00/19.27 X698]: 19.00/19.27 (in( 19.00/19.27 X698,X696) => 19.00/19.27 (![X699]: 19.00/19.27 (in( 19.00/19.27 X699,X696) => 19.00/19.27 (X697 => 19.00/19.27 in( 19.00/19.27 X698, 19.00/19.27 dsetconstr( 19.00/19.27 X696, 19.00/19.27 ^[V_50]: 19.00/19.27 (( 19.00/19.27 X697 & 19.00/19.27 ( 19.00/19.27 V_50 = 19.00/19.27 X698)) | 19.00/19.27 (( 19.00/19.27 ~X697) & 19.00/19.27 (V_50 = 19.00/19.27 X699)))))))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X700, 19.00/19.27 X701:$o, 19.00/19.27 X702]: 19.00/19.27 (in( 19.00/19.27 X702,X700) => 19.00/19.27 (![X703]: 19.00/19.27 (in( 19.00/19.27 X703,X700) => 19.00/19.27 (X701 => 19.00/19.27 (dsetconstr( 19.00/19.27 X700, 19.00/19.27 ^[V_51]: 19.00/19.27 (( 19.00/19.27 X701 & 19.00/19.27 ( 19.00/19.27 V_51 = 19.00/19.27 X702)) | 19.00/19.27 (( 19.00/19.27 ~X701) & 19.00/19.27 (V_51 = 19.00/19.27 X703)))) = 19.00/19.27 setadjoin( 19.00/19.27 X702, 19.00/19.27 emptyset))))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X704, 19.00/19.27 X705:$o, 19.00/19.27 X706]: 19.00/19.27 (in( 19.00/19.27 X706,X704) => 19.00/19.27 (![X707]: 19.00/19.27 (in( 19.00/19.27 X707,X704) => 19.00/19.27 singleton( 19.00/19.27 dsetconstr( 19.00/19.27 X704, 19.00/19.27 ^[V_52]: 19.00/19.27 (( 19.00/19.27 X705 & 19.00/19.27 ( 19.00/19.27 V_52 = 19.00/19.27 X706)) | 19.00/19.27 (( 19.00/19.27 ~X705) & 19.00/19.27 (V_52 = 19.00/19.27 X707))))))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X708, 19.00/19.27 X709:$o, 19.00/19.27 X710]: 19.00/19.27 (in( 19.00/19.27 X710,X708) => 19.00/19.27 (![X711]: 19.00/19.27 (in( 19.00/19.27 X711,X708) => 19.00/19.27 in( 19.00/19.27 if( 19.00/19.27 X708, 19.00/19.27 X709, 19.00/19.27 X710,X711), 19.00/19.27 X708))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X712]: 19.00/19.27 (singleton( 19.00/19.27 X712) => 19.00/19.27 (![X713]: 19.00/19.27 (in( 19.00/19.27 X713,X712) => 19.00/19.27 (setunion( 19.00/19.27 X712) = 19.00/19.27 X713))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X714, 19.00/19.27 X715:$o, 19.00/19.27 X716]: 19.00/19.27 (in( 19.00/19.27 X716,X714) => 19.00/19.27 (![X717]: 19.00/19.27 (in( 19.00/19.27 X717,X714) => 19.00/19.27 (X715 => 19.00/19.27 (if( 19.00/19.27 X714, 19.00/19.27 X715, 19.00/19.27 X716,X717) = 19.00/19.27 X716)))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X718, 19.00/19.27 X719:$o, 19.00/19.27 X720]: 19.00/19.27 (in( 19.00/19.27 X720,X718) => 19.00/19.27 (![X721]: 19.00/19.27 (in( 19.00/19.27 X721,X718) => 19.00/19.27 (( 19.00/19.27 ~X719) => 19.00/19.27 (if( 19.00/19.27 X718, 19.00/19.27 X719, 19.00/19.27 X720,X721) = 19.00/19.27 X721)))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X722, 19.00/19.27 X723:$o, 19.00/19.27 X724]: 19.00/19.27 (in( 19.00/19.27 X724,X722) => 19.00/19.27 (![X725]: 19.00/19.27 (in( 19.00/19.27 X725,X722) => 19.00/19.27 in( 19.00/19.27 if( 19.00/19.27 X722, 19.00/19.27 X723, 19.00/19.27 X724,X725), 19.00/19.27 setadjoin( 19.00/19.27 X724, 19.00/19.27 setadjoin( 19.00/19.27 X725, 19.00/19.27 emptyset))))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X726, 19.00/19.27 X727]: 19.00/19.27 (in( 19.00/19.27 X727, 19.00/19.27 powerset( 19.00/19.27 X726)) => 19.00/19.27 (![X728]: 19.00/19.27 (in( 19.00/19.27 X728, 19.00/19.27 powerset( 19.00/19.27 X726)) => 19.00/19.27 in( 19.00/19.27 binintersect( 19.00/19.27 X727,X728), 19.00/19.27 powerset( 19.00/19.27 X726)))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X729, 19.00/19.27 X730]: 19.00/19.27 (in( 19.00/19.27 X730, 19.00/19.27 powerset( 19.00/19.27 X729)) => 19.00/19.27 (![X731]: 19.00/19.27 (in( 19.00/19.27 X731, 19.00/19.27 powerset( 19.00/19.27 X729)) => 19.00/19.27 in( 19.00/19.27 binunion( 19.00/19.27 X730,X731), 19.00/19.27 powerset( 19.00/19.27 X729)))))) => 19.00/19.27 ( 19.00/19.27 ![X732, 19.00/19.27 X733]: 19.00/19.27 (in( 19.00/19.27 X733, 19.00/19.27 powerset( 19.00/19.27 X732)) => 19.00/19.27 in( 19.00/19.27 powerset( 19.00/19.27 X733), 19.00/19.27 powerset( 19.00/19.27 powerset( 19.00/19.27 X732)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 19.00/19.27 tff(zf_stmt_1, type, zip_tseitin5 : ($i * $i > $o) > $o). 19.00/19.27 tff(zf_stmt_2, axiom, 19.00/19.27 (zip_tseitin5(X211,X207) <=> 19.00/19.27 ((![X212]: zip_tseitin4(X212,X211,X207)) & X207(X211)))). 19.00/19.27 tff(zf_stmt_3, type, zip_tseitin4 : ($i * $i * $i > $o) > $o). 19.00/19.27 tff(zf_stmt_4, axiom, 19.00/19.27 (zip_tseitin4(X212,X211,X207) <=> (X207(X212) => (X211 = X212)))). 19.00/19.27 tff(zf_stmt_5, type, zip_tseitin3 : ($i * $i * $i * ($i * $i) > $o) > $o). 19.00/19.27 tff(zf_stmt_6, axiom, 19.00/19.27 (zip_tseitin3(X26,X25,X20,X19) <=> (X19(X26,X25) & in(X26,X20)))). 19.00/19.27 tff(zf_stmt_7, type, zip_tseitin2 : ($i * $i * $i) > $o). 19.00/19.27 tff(zf_stmt_8, axiom, 19.00/19.27 (zip_tseitin2(X14,X13,X12) <=> (in(X14,X12) & in(X13,X14)))). 19.00/19.27 tff(zf_stmt_9, type, zip_tseitin1 : ($i * $i * $i) > $o). 19.00/19.27 tff(zf_stmt_10, axiom, 19.00/19.27 (zip_tseitin1(X11,X10,X9) <=> (in(X11,X10) => in(X11,X9)))). 19.00/19.27 tff(zf_stmt_11, type, zip_tseitin0 : ($i * $i * $i) > $o). 19.00/19.27 tff(zf_stmt_12, axiom, (zip_tseitin0(X8,X7,X6) <=> (in(X8,X7) | (X8 = X6)))). 19.00/19.27 tff(zf_stmt_13, conjecture, 19.00/19.27 ((![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))) => 19.00/19.27 ((![X5]: (~in(X5,emptyset))) => 19.00/19.27 ((![X6,X7,X8]: (in(X8,setadjoin(X6,X7)) <=> zip_tseitin0(X8,X7,X6))) => 19.00/19.27 ((![X9,X10]: 19.00/19.27 (in(X10,powerset(X9)) <=> (![X11]: zip_tseitin1(X11,X10,X9)))) => 19.00/19.27 ((![X12,X13]: 19.00/19.27 (in(X13,setunion(X12)) <=> (?[X14]: zip_tseitin2(X14,X13,X12)))) => 19.00/19.27 (in(emptyset,omega) => 19.00/19.27 ((![X15]: (in(X15,omega) => in(setadjoin(X15,X15),omega))) => 19.00/19.27 ((![X16]: 19.00/19.27 (((![X17]: 19.00/19.27 ((in(X17,X16) & in(X17,omega)) => 19.00/19.27 in(setadjoin(X17,X17),X16))) & 19.00/19.27 in(emptyset,X16)) => 19.00/19.27 (![X18]: (in(X18,omega) => in(X18,X16))))) => 19.00/19.27 ((![X19:(($i * $i) > $o),X20]: 19.00/19.27 ((![X21]: 19.00/19.27 (in(X21,X20) => 19.00/19.27 (?[X22]: 19.00/19.27 ((![X23]: (X19(X21,X23) => (X22 = X23))) & X19(X21,X22))))) => 19.00/19.27 (?[X24]: 19.00/19.27 (![X25]: 19.00/19.27 (in(X25,X24) <=> (?[X26]: zip_tseitin3(X26,X25,X20,X19))))))) => 19.00/19.27 ((![X27]: 19.00/19.27 ((?[X28]: in(X28,X27)) => 19.00/19.27 (?[X29]: 19.00/19.27 ((~(?[X30]: (in(X30,X27) & in(X30,X29)))) & in(X29,X27))))) => 19.00/19.27 ((![X31]: 19.00/19.27 (?[X32]: 19.00/19.27 ((![X33]: 19.00/19.27 (((?[X34]: in(X34,X33)) & 19.00/19.27 (![X35]: (in(X35,X33) => in(X35,X31)))) => 19.00/19.27 (?[X36,X37]: 19.00/19.27 ((![X38]: 19.00/19.27 (in(X38,X32) => 19.00/19.27 (in(X37,X38) | 19.00/19.27 (![X39]: (in(X39,X38) => in(X39,X36)))))) & 19.00/19.27 (~(?[X40]: (in(X40,X33) & in(X40,X36)))) & 19.00/19.27 in(X37,X33) & in(X36,X32))))) & 19.00/19.27 (![X41,X42]: 19.00/19.27 ((in(X42,X32) & in(X41,X32)) => 19.00/19.27 ((![X43]: (in(X43,X42) => in(X43,X41))) | 19.00/19.27 (![X44]: (in(X44,X41) => in(X44,X42)))))) & 19.00/19.27 (![X45,X46]: 19.00/19.27 ((in(X46,X31) & in(X45,X31)) => 19.00/19.27 ((![X47]: 19.00/19.27 (in(X47,X32) => (in(X45,X47) <=> in(X46,X47)))) => 19.00/19.27 (X45 = X46)))) & 19.00/19.27 (![X48]: 19.00/19.27 (in(X48,X32) => (![X49]: (in(X49,X48) => in(X49,X31)))))))) => 19.00/19.27 ((![X50:($i > $o)]: 19.00/19.27 ((?[X51]: ((![X52]: (X50(X52) => (X51 = X52))) & X50(X51))) => 19.00/19.27 X50(descr(^[V_1]: X50(V_1))))) => 19.00/19.27 ((![X53,X54:($i > $o),X55]: 19.00/19.27 (in(X55,X53) => 19.00/19.27 (X54(X55) => in(X55,dsetconstr(X53,^[V_2]: X54(V_2)))))) => 19.00/19.27 ((![X56,X57:($i > $o),X58]: 19.00/19.27 (in(X58,dsetconstr(X56,^[V_3]: X57(V_3))) => in(X58,X56))) => 19.00/19.27 ((![X59,X60:($i > $o),X61]: 19.00/19.27 (in(X61,dsetconstr(X59,^[V_4]: X60(V_4))) => X60(X61))) => 19.00/19.27 ((![X62:($i > $o)]: 19.00/19.27 ((?[X63]: 19.00/19.27 ((![X64]: (X62(X64) => (X63 = X64))) & X62(X63))) => 19.00/19.27 (?[X65]: 19.00/19.27 ((![X66]: (X62(X66) => (X65 = X66))) & X62(X65))))) => 19.00/19.27 ((![X67:$o,X68]: (in(X68,prop2set(X67)) => X67)) => 19.00/19.27 ((![X69]: (in(X69,emptyset) => (![X70:$o]: X70))) => 19.00/19.27 ((![X71]: (in(X71,emptyset) => $false)) => 19.00/19.27 ((![X72]: (~in(X72,emptyset))) => 19.00/19.27 ((![X73:($i > $o)]: 19.00/19.27 ((?[X74]: 19.00/19.27 ((![X75]: (X73(X75) => (X74 = X75))) & X73(X74))) => 19.00/19.27 (?[X76]: X73(X76)))) => 19.00/19.27 ((![X77,X78]: 19.00/19.27 ((![X79]: (in(X79,X77) => in(X79,X78))) => 19.00/19.27 ((![X80]: (in(X80,X78) => in(X80,X77))) => 19.00/19.27 (X77 = X78)))) => 19.00/19.27 ((![X81]: 19.00/19.27 ((![X82]: (~in(X82,X81))) => (X81 = emptyset))) => 19.00/19.27 ((![X83]: 19.00/19.27 ((![X84]: (~in(X84,X83))) => (X83 = emptyset))) => 19.00/19.27 ((![X85,X86:($i > $o),X87]: 19.00/19.27 (in(X87,X85) => 19.00/19.27 (in(X87,dsetconstr(X85,^[V_5]: X86(V_5))) <=> 19.00/19.27 X86(X87)))) => 19.00/19.27 ((![X88]: 19.00/19.27 ((X88 != emptyset) => (?[X89]: in(X89,X88)))) => 19.00/19.27 ((![X90,X91:($i > $o),X92]: 19.00/19.27 (in(X92,X90) => 19.00/19.27 (X91(X92) => 19.00/19.27 (dsetconstr(X90,^[V_6]: X91(V_6)) != 19.00/19.27 emptyset)))) => 19.00/19.27 ((![X93]: 19.00/19.27 ((?[X94]: in(X94,X93)) => (X93 != emptyset))) => 19.00/19.27 ((![X95,X96]: in(X95,setadjoin(X95,X96))) => 19.00/19.27 (in(emptyset,setadjoin(emptyset,emptyset)) => 19.00/19.27 ((![X97,X98,X99]: 19.00/19.27 (in(X99,X98) => 19.00/19.27 in(X99,setadjoin(X97,X98)))) => 19.00/19.27 ((![X100,X101,X102]: 19.00/19.27 (in(X102,setadjoin(X100,X101)) => 19.00/19.27 (![X103:$o]: 19.00/19.27 (((X102 = X100) => X103) => 19.00/19.27 ((in(X102,X101) => X103) => X103))))) => 19.00/19.27 ((![X104,X105,X106]: 19.00/19.27 (in(X106,setadjoin(X104,X105)) => 19.00/19.27 (in(X106,X105) | (X106 = X104)))) => 19.00/19.27 ((![X107]: 19.00/19.27 (dsetconstr(X107,^[V_7]: $true) = X107)) => 19.00/19.27 ((![X108,X109]: 19.00/19.27 ((![X110]: 19.00/19.27 (in(X110,X109) => in(X110,X108))) => 19.00/19.27 in(X109,powerset(X108)))) => 19.00/19.27 ((![X111]: in(emptyset,powerset(X111))) => 19.00/19.27 ((![X112]: in(emptyset,powerset(X112))) => 19.00/19.27 ((![X113,X114,X115]: 19.00/19.27 (in(X114,powerset(X113)) => 19.00/19.27 (in(X115,X114) => in(X115,X113)))) => 19.00/19.27 ((![X116,X117,X118]: 19.00/19.27 (in(X117,X118) => 19.00/19.27 (in(X118,X116) => 19.00/19.27 in(X117,setunion(X116))))) => 19.00/19.27 ((![X119,X120]: 19.00/19.27 (in(X120,setunion(X119)) => 19.00/19.27 (![X121:$o]: 19.00/19.27 ((![X122]: 19.00/19.27 (in(X120,X122) => 19.00/19.27 (in(X122,X119) => X121))) => 19.00/19.27 X121)))) => 19.00/19.27 ((![X123,X124]: 19.00/19.27 (in(X124,X123) => 19.00/19.27 in(X124, 19.00/19.27 powerset(setunion(X123))))) => 19.00/19.27 ((![X125:($i > $o)]: 19.00/19.27 ((?[X126]: 19.00/19.27 ((![X127]: 19.00/19.27 (X125(X127) => 19.00/19.27 (X126 = X127))) & 19.00/19.27 X125(X126))) => 19.00/19.27 (?[X128]: 19.00/19.27 (![X129]: 19.00/19.27 (X125(X129) <=> 19.00/19.27 (X129 = X128)))))) => 19.00/19.27 ((![X130]: 19.00/19.27 ((X130 != emptyset) => 19.00/19.27 (?[X131]: in(X131,X130)))) => 19.00/19.27 ((![X132,X133]: 19.00/19.27 (in(X132, 19.00/19.27 setadjoin(X133,emptyset)) => 19.00/19.27 (X132 = X133))) => 19.00/19.27 ((![X134,X135]: 19.00/19.27 ((X134 != X135) => 19.00/19.27 (~ 19.00/19.27 in(X135, 19.00/19.27 setadjoin(X134, 19.00/19.27 emptyset))))) => 19.00/19.27 ((![X136,X137]: 19.00/19.27 ((X136 = X137) => 19.00/19.27 in(X136, 19.00/19.27 setadjoin(X137, 19.00/19.27 emptyset)))) => 19.00/19.27 ((![X138,X139]: 19.00/19.27 (in(X138, 19.00/19.27 setadjoin(X139, 19.00/19.27 emptyset)) => 19.00/19.27 in(X139, 19.00/19.27 setadjoin(X138, 19.00/19.27 emptyset)))) => 19.00/19.27 ((![X140,X141,X142]: 19.00/19.27 (in(X142, 19.00/19.27 setadjoin(X140, 19.00/19.27 setadjoin( 19.00/19.27 X141, 19.00/19.27 emptyset))) => 19.00/19.27 ((X142 = X141) | 19.00/19.27 (X142 = X140)))) => 19.00/19.27 ((![X143,X144]: 19.00/19.27 in(X143, 19.00/19.27 setadjoin(X143, 19.00/19.27 setadjoin( 19.00/19.27 X144, 19.00/19.27 emptyset)))) => 19.00/19.27 ((![X145,X146]: 19.00/19.27 in(X146, 19.00/19.27 setadjoin(X145, 19.00/19.27 setadjoin( 19.00/19.27 X146, 19.00/19.27 emptyset)))) => 19.00/19.27 ((![X147,X148:($i > $o)]: 19.00/19.27 ((?[X149]: 19.00/19.27 (X148(X149) & 19.00/19.27 in(X149,X147))) => 19.00/19.27 ((dsetconstr( 19.00/19.27 X147, 19.00/19.27 ^[V_8]: X148(V_8)) = 19.00/19.27 emptyset) => 19.00/19.27 $false))) => 19.00/19.27 ((![X150:($i > $o),X151]: 19.00/19.27 (in(X151,emptyset) => 19.00/19.27 X150(X151))) => 19.00/19.27 ((![X152,X153:($i > $o)]: 19.00/19.27 ((~ 19.00/19.27 (![X154]: 19.00/19.27 (in(X154,X152) => 19.00/19.27 X153(X154)))) => 19.00/19.27 (?[X155]: 19.00/19.27 ((~X153(X155)) & 19.00/19.27 in(X155,X152))))) => 19.00/19.27 ((![X156, 19.00/19.27 X157:($i > $o)]: 19.00/19.27 ((![X158]: 19.00/19.27 (in(X158,X156) => 19.00/19.27 (~X157(X158)))) => 19.00/19.27 (~ 19.00/19.27 (?[X159]: 19.00/19.27 (X157(X159) & 19.00/19.27 in( 19.00/19.27 X159,X156)))))) => 19.00/19.27 ((![X160, 19.00/19.27 X161:($i > $o)]: 19.00/19.27 ((~ 19.00/19.27 (?[X162]: 19.00/19.27 (X161(X162) & 19.00/19.27 in( 19.00/19.27 X162,X160)))) => 19.00/19.27 (![X163]: 19.00/19.27 (in(X163,X160) => 19.00/19.27 (~X161(X163)))))) => 19.00/19.27 ((![X164, 19.00/19.27 X165:($i > $o)]: 19.00/19.27 ((?[X166]: 19.00/19.27 ((~ 19.00/19.27 X165( 19.00/19.27 X166)) & 19.00/19.27 in( 19.00/19.27 X166,X164))) => 19.00/19.27 (~ 19.00/19.27 (![X167]: 19.00/19.27 (in( 19.00/19.27 X167,X164) => 19.00/19.27 X165( 19.00/19.27 X167)))))) => 19.00/19.27 ((![X168:$o]: 19.00/19.27 (X168 => 19.00/19.27 in(emptyset, 19.00/19.27 prop2set( 19.00/19.27 X168)))) => 19.00/19.27 ((![X169:$o]: 19.00/19.27 (X169 => 19.00/19.27 set2prop( 19.00/19.27 prop2set( 19.00/19.27 X169)))) => 19.00/19.27 ((![X170, 19.00/19.27 X171:( 19.00/19.27 $i > $o)]: 19.00/19.27 ((~ 19.00/19.27 (?[X172]: 19.00/19.27 (X171( 19.00/19.27 X172) & 19.00/19.27 in( 19.00/19.27 X172,X170)))) => 19.00/19.27 (![X173]: 19.00/19.27 ( 19.00/19.27 in( 19.00/19.27 X173,X170) => 19.00/19.27 ( 19.00/19.27 ~ 19.00/19.27 X171( 19.00/19.27 X173)))))) => 19.00/19.27 ((![X174, 19.00/19.27 X175:( 19.00/19.27 $i > $o)]: 19.00/19.27 ((~ 19.00/19.27 ( 19.00/19.27 ![X176]: 19.00/19.27 (in( 19.00/19.27 X176,X174) => 19.00/19.27 X175( 19.00/19.27 X176)))) => 19.00/19.27 (?[X177]: 19.00/19.27 (( 19.00/19.27 ~ 19.00/19.27 X175( 19.00/19.27 X177)) & 19.00/19.27 in( 19.00/19.27 X177,X174))))) => 19.00/19.27 ((![X178:( 19.00/19.27 $i > $o)]: 19.00/19.27 ((?[X179]: 19.00/19.27 (( 19.00/19.27 ![X180]: 19.00/19.27 (X178( 19.00/19.27 X180) => 19.00/19.27 (X179 = 19.00/19.27 X180))) & 19.00/19.27 X178( 19.00/19.27 X179))) => 19.00/19.27 (?[X181]: 19.00/19.27 (( 19.00/19.27 ![X182]: 19.00/19.27 (X178( 19.00/19.27 X182) => 19.00/19.27 (X181 = 19.00/19.27 X182))) & 19.00/19.27 X178( 19.00/19.27 X181))))) => 19.00/19.27 ((![X183:( 19.00/19.27 $i > $o)]: 19.00/19.27 (( 19.00/19.27 ?[X184]: 19.00/19.27 X183( 19.00/19.27 X184)) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X185, 19.00/19.27 X186]: 19.00/19.27 (X183( 19.00/19.27 X185) => 19.00/19.27 (X183( 19.00/19.27 X186) => 19.00/19.27 (X185 = 19.00/19.27 X186)))) => 19.00/19.27 ( 19.00/19.27 ?[X187]: 19.00/19.27 (( 19.00/19.27 ![X188]: 19.00/19.27 (X183( 19.00/19.27 X188) => 19.00/19.27 (X187 = 19.00/19.27 X188))) & 19.00/19.27 X183( 19.00/19.27 X187)))))) => 19.00/19.27 ((![X189:( 19.00/19.27 $i > $o)]: 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ?[X190]: 19.00/19.27 (![X191]: 19.00/19.27 (X189( 19.00/19.27 X191) <=> 19.00/19.27 (X191 = 19.00/19.27 X190)))) => 19.00/19.27 ( 19.00/19.27 ?[X192]: 19.00/19.27 (( 19.00/19.27 ![X193]: 19.00/19.27 (X189( 19.00/19.27 X193) => 19.00/19.27 (X192 = 19.00/19.27 X193))) & 19.00/19.27 X189( 19.00/19.27 X192))))) => 19.00/19.27 ((![X194, 19.00/19.27 X195]: 19.00/19.27 (( 19.00/19.27 X194 = 19.00/19.27 X195) => 19.00/19.27 (![X196, 19.00/19.27 X197]: 19.00/19.27 (( 19.00/19.27 X196 = 19.00/19.27 X197) => 19.00/19.27 (in( 19.00/19.27 X196,X194) => 19.00/19.27 in( 19.00/19.27 X197,X195)))))) => 19.00/19.27 ((![X198, 19.00/19.27 X199]: 19.00/19.27 (( 19.00/19.27 X198 = 19.00/19.27 X199) => 19.00/19.27 (![X200, 19.00/19.27 X201]: 19.00/19.27 (( 19.00/19.27 X200 = 19.00/19.27 X201) => 19.00/19.27 (in( 19.00/19.27 X200,X198) <=> 19.00/19.27 in( 19.00/19.27 X201,X199)))))) => 19.00/19.27 (( 19.00/19.27 ![X202:( 19.00/19.27 $i > $o)]: 19.00/19.27 (( 19.00/19.27 ?[X203]: 19.00/19.27 (( 19.00/19.27 ![X204]: 19.00/19.27 (X202( 19.00/19.27 X204) => 19.00/19.27 (X203 = 19.00/19.27 X204))) & 19.00/19.27 X202( 19.00/19.27 X203))) => 19.00/19.27 (![X205, 19.00/19.27 X206]: 19.00/19.27 (X202( 19.00/19.27 X205) => 19.00/19.27 (X202( 19.00/19.27 X206) => 19.00/19.27 (X205 = 19.00/19.27 X206)))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X207:( 19.00/19.27 $i > $o), 19.00/19.27 X208:( 19.00/19.27 $i > $o)]: 19.00/19.27 (( 19.00/19.27 ![X209, 19.00/19.27 X210]: 19.00/19.27 (( 19.00/19.27 X209 = 19.00/19.27 X210) => 19.00/19.27 (X207( 19.00/19.27 X209) <=> 19.00/19.27 X208( 19.00/19.27 X210)))) => 19.00/19.27 (( 19.00/19.27 ?[X211]: 19.00/19.27 zip_tseitin5( 19.00/19.27 X211,X207)) <=> 19.00/19.27 (?[X213]: 19.00/19.27 zip_tseitin5( 19.00/19.27 X213,X208))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 emptyset = 19.00/19.27 emptyset) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X215, 19.00/19.27 X216]: 19.00/19.27 (( 19.00/19.27 X215 = 19.00/19.27 X216) => 19.00/19.27 (![X217, 19.00/19.27 X218]: 19.00/19.27 (( 19.00/19.27 X217 = 19.00/19.27 X218) => 19.00/19.27 (setadjoin( 19.00/19.27 X215,X217) = 19.00/19.27 setadjoin( 19.00/19.27 X216,X218)))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X219, 19.00/19.27 X220]: 19.00/19.27 (( 19.00/19.27 X219 = 19.00/19.27 X220) => 19.00/19.27 (powerset( 19.00/19.27 X219) = 19.00/19.27 powerset( 19.00/19.27 X220)))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X221, 19.00/19.27 X222]: 19.00/19.27 (( 19.00/19.27 X221 = 19.00/19.27 X222) => 19.00/19.27 (setunion( 19.00/19.27 X221) = 19.00/19.27 setunion( 19.00/19.27 X222)))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 omega = 19.00/19.27 omega) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X223:( 19.00/19.27 $i > $o)]: 19.00/19.27 (( 19.00/19.27 ?[X224]: 19.00/19.27 (( 19.00/19.27 ![X225]: 19.00/19.27 (X223( 19.00/19.27 X225) => 19.00/19.27 (X224 = 19.00/19.27 X225))) & 19.00/19.27 X223( 19.00/19.27 X224))) => 19.00/19.27 (![X226, 19.00/19.27 X227]: 19.00/19.27 (X223( 19.00/19.27 X226) => 19.00/19.27 (X223( 19.00/19.27 X227) => 19.00/19.27 (X226 = 19.00/19.27 X227)))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X228:( 19.00/19.27 $i > $o), 19.00/19.27 X229:( 19.00/19.27 $i > $o)]: 19.00/19.27 (( 19.00/19.27 ![X230, 19.00/19.27 X231]: 19.00/19.27 (( 19.00/19.27 X230 = 19.00/19.27 X231) => 19.00/19.27 (X228( 19.00/19.27 X230) <=> 19.00/19.27 X229( 19.00/19.27 X231)))) => 19.00/19.27 (( 19.00/19.27 ?[X232]: 19.00/19.27 (( 19.00/19.27 ![X233]: 19.00/19.27 (X228( 19.00/19.27 X233) => 19.00/19.27 (X232 = 19.00/19.27 X233))) & 19.00/19.27 X228( 19.00/19.27 X232))) => 19.00/19.27 (( 19.00/19.27 ?[X234]: 19.00/19.27 (( 19.00/19.27 ![X235]: 19.00/19.27 (X229( 19.00/19.27 X235) => 19.00/19.27 (X234 = 19.00/19.27 X235))) & 19.00/19.27 X229( 19.00/19.27 X234))) => 19.00/19.27 (descr( 19.00/19.27 ^[V_9]: 19.00/19.27 X228(V_9)) = 19.00/19.27 descr( 19.00/19.27 ^[V_10]: 19.00/19.27 X229( 19.00/19.27 V_10))))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X236, 19.00/19.27 X237]: 19.00/19.27 (( 19.00/19.27 X236 = 19.00/19.27 X237) => 19.00/19.27 (![X238:( 19.00/19.27 $i > $o), 19.00/19.27 X239:( 19.00/19.27 $i > $o)]: 19.00/19.27 (( 19.00/19.27 ![X240]: 19.00/19.27 (in( 19.00/19.27 X240,X236) => 19.00/19.27 (![X241]: 19.00/19.27 (in( 19.00/19.27 X241,X237) => 19.00/19.27 (( 19.00/19.27 X240 = 19.00/19.27 X241) => 19.00/19.27 (X238( 19.00/19.27 X240) <=> 19.00/19.27 X239( 19.00/19.27 X241))))))) => 19.00/19.27 (dsetconstr( 19.00/19.27 X236, 19.00/19.27 ^[V_11]: 19.00/19.27 X238( 19.00/19.27 V_11)) = 19.00/19.27 dsetconstr( 19.00/19.27 X237, 19.00/19.27 ^[V_12]: 19.00/19.27 X239( 19.00/19.27 V_12))))))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X242, 19.00/19.27 X243]: 19.00/19.27 (( 19.00/19.27 ![X244]: 19.00/19.27 (in( 19.00/19.27 X244,X242) => 19.00/19.27 in( 19.00/19.27 X244,X243))) => 19.00/19.27 subset( 19.00/19.27 X242,X243))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X245, 19.00/19.27 X246]: 19.00/19.27 (( 19.00/19.27 X245 = 19.00/19.27 X246) => 19.00/19.27 subset( 19.00/19.27 X246,X245))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X247, 19.00/19.27 X248]: 19.00/19.27 (( 19.00/19.27 X247 = 19.00/19.27 X248) => 19.00/19.27 subset( 19.00/19.27 X247,X248))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X249, 19.00/19.27 X250]: 19.00/19.27 (( 19.00/19.27 ![X251]: 19.00/19.27 (in( 19.00/19.27 X251,X249) => 19.00/19.27 in( 19.00/19.27 X251,X250))) => 19.00/19.27 subset( 19.00/19.27 X249,X250))) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X252]: 19.00/19.27 subset( 19.00/19.27 emptyset, 19.00/19.27 X252)) => 19.00/19.27 ( 19.00/19.27 ( 19.00/19.27 ![X253, 19.00/19.27 X254,X255]: 19.00/19.27 (subset( 19.00/19.27 X253,X254) => 19.00/19.27 (in( 19.00/19.27 X255,X253) => 19.00/19.27 in( 19.00/19.27 X255,X254)))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X256, 19.00/19.28 X257,X258]: 19.00/19.28 (subset( 19.00/19.28 X256,X257) => 19.00/19.28 (( 19.00/19.28 ~ 19.00/19.28 in( 19.00/19.28 X258,X257)) => 19.00/19.28 (~ 19.00/19.28 in( 19.00/19.28 X258,X256))))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X259, 19.00/19.28 X260,X261]: 19.00/19.28 (in( 19.00/19.28 X261,X259) => 19.00/19.28 (( 19.00/19.28 ~ 19.00/19.28 in( 19.00/19.28 X261,X260)) => 19.00/19.28 (~ 19.00/19.28 subset( 19.00/19.28 X259,X260))))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X262, 19.00/19.28 X263]: 19.00/19.28 (( 19.00/19.28 ~ 19.00/19.28 subset( 19.00/19.28 X262,X263)) => 19.00/19.28 (X262 != 19.00/19.28 X263))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X264, 19.00/19.28 X265,X266]: 19.00/19.28 (in( 19.00/19.28 X266,X264) => 19.00/19.28 (( 19.00/19.28 ~ 19.00/19.28 in( 19.00/19.28 X266,X265)) => 19.00/19.28 (X264 != 19.00/19.28 X265)))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X267]: 19.00/19.28 subset( 19.00/19.28 X267,X267)) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X268, 19.00/19.28 X269,X270]: 19.00/19.28 (subset( 19.00/19.28 X268,X269) => 19.00/19.28 (subset( 19.00/19.28 X269,X270) => 19.00/19.28 subset( 19.00/19.28 X268,X270)))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X271, 19.00/19.28 X272]: 19.00/19.28 subset( 19.00/19.28 X272, 19.00/19.28 setadjoin( 19.00/19.28 X271,X272))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X273, 19.00/19.28 X274,X275]: 19.00/19.28 (subset( 19.00/19.28 X273,X275) => 19.00/19.28 subset( 19.00/19.28 X273, 19.00/19.28 setadjoin( 19.00/19.28 X274,X275)))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X276, 19.00/19.28 X277]: 19.00/19.28 (subset( 19.00/19.28 X276,X277) => 19.00/19.28 in( 19.00/19.28 X276, 19.00/19.28 powerset( 19.00/19.28 X277)))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X278, 19.00/19.28 X279]: 19.00/19.28 (subset( 19.00/19.28 X278,X279) => 19.00/19.28 (subset( 19.00/19.28 X279,X278) => 19.00/19.28 (X278 = 19.00/19.28 X279)))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X280]: 19.00/19.28 (subset( 19.00/19.28 X280, 19.00/19.28 emptyset) => 19.00/19.28 (X280 = 19.00/19.28 emptyset))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X281, 19.00/19.28 X282]: 19.00/19.28 (subset( 19.00/19.28 X282,X281) => 19.00/19.28 in( 19.00/19.28 X282, 19.00/19.28 powerset( 19.00/19.28 X281)))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X283, 19.00/19.28 X284]: 19.00/19.28 (in( 19.00/19.28 X284, 19.00/19.28 powerset( 19.00/19.28 X283)) => 19.00/19.28 subset( 19.00/19.28 X284,X283))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X285]: 19.00/19.28 in( 19.00/19.28 X285, 19.00/19.28 powerset( 19.00/19.28 X285))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X286, 19.00/19.28 X287]: 19.00/19.28 (subset( 19.00/19.28 X286,X287) => 19.00/19.28 subset( 19.00/19.28 powerset( 19.00/19.28 X286), 19.00/19.28 powerset( 19.00/19.28 X287)))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X288, 19.00/19.28 X289:( 19.00/19.28 $i > $o)]: 19.00/19.28 in( 19.00/19.28 dsetconstr( 19.00/19.28 X288, 19.00/19.28 ^[V_13]: 19.00/19.28 X289( 19.00/19.28 V_13)), 19.00/19.28 powerset( 19.00/19.28 X288))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X290, 19.00/19.28 X291:( 19.00/19.28 $i > $o)]: 19.00/19.28 subset( 19.00/19.28 dsetconstr( 19.00/19.28 X290, 19.00/19.28 ^[V_14]: 19.00/19.28 X291( 19.00/19.28 V_14)), 19.00/19.28 X290)) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X292, 19.00/19.28 X293,X294]: 19.00/19.28 (in( 19.00/19.28 X294,X292) => 19.00/19.28 in( 19.00/19.28 X294, 19.00/19.28 binunion( 19.00/19.28 X292,X293)))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X295, 19.00/19.28 X296]: 19.00/19.28 in( 19.00/19.28 X296, 19.00/19.28 setadjoin( 19.00/19.28 X295, 19.00/19.28 setadjoin( 19.00/19.28 X296, 19.00/19.28 emptyset)))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X297, 19.00/19.28 X298,X299]: 19.00/19.28 (in( 19.00/19.28 X299,X298) => 19.00/19.28 in( 19.00/19.28 X299, 19.00/19.28 binunion( 19.00/19.28 X297,X298)))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X300, 19.00/19.28 X301, 19.00/19.28 X302, 19.00/19.28 X303:$o]: 19.00/19.28 (in( 19.00/19.28 X302, 19.00/19.28 binunion( 19.00/19.28 X300,X301)) => 19.00/19.28 (( 19.00/19.28 in( 19.00/19.28 X302,X300) => 19.00/19.28 X303) => 19.00/19.28 (( 19.00/19.28 in( 19.00/19.28 X302,X301) => 19.00/19.28 X303) => 19.00/19.28 X303)))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X304, 19.00/19.28 X305,X306]: 19.00/19.28 (in( 19.00/19.28 X306, 19.00/19.28 binunion( 19.00/19.28 X304,X305)) => 19.00/19.28 (in( 19.00/19.28 X306,X305) | 19.00/19.28 in( 19.00/19.28 X306,X304)))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X307, 19.00/19.28 X308]: 19.00/19.28 subset( 19.00/19.28 X307, 19.00/19.28 binunion( 19.00/19.28 X307,X308))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X309, 19.00/19.28 X310]: 19.00/19.28 subset( 19.00/19.28 X310, 19.00/19.28 binunion( 19.00/19.28 X309,X310))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X311, 19.00/19.28 X312,X313]: 19.00/19.28 (in( 19.00/19.28 X313,X311) => 19.00/19.28 (in( 19.00/19.28 X313,X312) => 19.00/19.28 in( 19.00/19.28 X313, 19.00/19.28 binintersect( 19.00/19.28 X311,X312))))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X314, 19.00/19.28 X315,X316]: 19.00/19.28 (subset( 19.00/19.28 X316,X314) => 19.00/19.28 (subset( 19.00/19.28 X316,X315) => 19.00/19.28 subset( 19.00/19.28 X316, 19.00/19.28 binintersect( 19.00/19.28 X314,X315))))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X317, 19.00/19.28 X318,X319]: 19.00/19.28 (in( 19.00/19.28 X319, 19.00/19.28 binintersect( 19.00/19.28 X317,X318)) => 19.00/19.28 in( 19.00/19.28 X319,X317))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X320, 19.00/19.28 X321]: 19.00/19.28 subset( 19.00/19.28 binintersect( 19.00/19.28 X320,X321), 19.00/19.28 X320)) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X322, 19.00/19.28 X323]: 19.00/19.28 (subset( 19.00/19.28 X322,X323) => 19.00/19.28 (binintersect( 19.00/19.28 X322,X323) = 19.00/19.28 X322))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X324, 19.00/19.28 X325]: 19.00/19.28 (( 19.00/19.28 binintersect( 19.00/19.28 X324,X325) = 19.00/19.28 X325) => 19.00/19.28 subset( 19.00/19.28 X325,X324))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X326, 19.00/19.28 X327,X328]: 19.00/19.28 (in( 19.00/19.28 X328, 19.00/19.28 binintersect( 19.00/19.28 X326,X327)) => 19.00/19.28 in( 19.00/19.28 X328,X327))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X329, 19.00/19.28 X330]: 19.00/19.28 (( 19.00/19.28 ~ 19.00/19.28 ( 19.00/19.28 ?[X331]: 19.00/19.28 (in( 19.00/19.28 X331,X330) & 19.00/19.28 in( 19.00/19.28 X331,X329)))) => 19.00/19.28 (binintersect( 19.00/19.28 X329,X330) = 19.00/19.28 emptyset))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X332, 19.00/19.28 X333]: 19.00/19.28 subset( 19.00/19.28 binintersect( 19.00/19.28 X332,X333), 19.00/19.28 X333)) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X334, 19.00/19.28 X335]: 19.00/19.28 (subset( 19.00/19.28 X335,X334) => 19.00/19.28 (binintersect( 19.00/19.28 X334,X335) = 19.00/19.28 X335))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X336, 19.00/19.28 X337]: 19.00/19.28 (( 19.00/19.28 binintersect( 19.00/19.28 X336,X337) = 19.00/19.28 X336) => 19.00/19.28 subset( 19.00/19.28 X336,X337))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X338, 19.00/19.28 X339,X340]: 19.00/19.28 (binintersect( 19.00/19.28 X338, 19.00/19.28 binunion( 19.00/19.28 X339,X340)) = 19.00/19.28 binunion( 19.00/19.28 binintersect( 19.00/19.28 X338,X339), 19.00/19.28 binintersect( 19.00/19.28 X338,X340)))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X341, 19.00/19.28 X342,X343]: 19.00/19.28 (in( 19.00/19.28 X343,X341) => 19.00/19.28 (( 19.00/19.28 ~ 19.00/19.28 in( 19.00/19.28 X343,X342)) => 19.00/19.28 in( 19.00/19.28 X343, 19.00/19.28 setminus( 19.00/19.28 X341,X342))))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X344, 19.00/19.28 X345,X346]: 19.00/19.28 (in( 19.00/19.28 X346, 19.00/19.28 setminus( 19.00/19.28 X344,X345)) => 19.00/19.28 in( 19.00/19.28 X346,X344))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X347, 19.00/19.28 X348,X349]: 19.00/19.28 (in( 19.00/19.28 X349, 19.00/19.28 setminus( 19.00/19.28 X347,X348)) => 19.00/19.28 (~ 19.00/19.28 in( 19.00/19.28 X349,X348)))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X350, 19.00/19.28 X351]: 19.00/19.28 (subset( 19.00/19.28 X350,X351) => 19.00/19.28 (setminus( 19.00/19.28 X350,X351) = 19.00/19.28 emptyset))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X352, 19.00/19.28 X353,X354]: 19.00/19.28 (( 19.00/19.28 ~ 19.00/19.28 in( 19.00/19.28 X354, 19.00/19.28 setminus( 19.00/19.28 X352,X353))) => 19.00/19.28 (in( 19.00/19.28 X354,X352) => 19.00/19.28 in( 19.00/19.28 X354,X353)))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X355, 19.00/19.28 X356,X357]: 19.00/19.28 (( 19.00/19.28 ~ 19.00/19.28 in( 19.00/19.28 X357, 19.00/19.28 setminus( 19.00/19.28 X355,X356))) => 19.00/19.28 (( 19.00/19.28 ~ 19.00/19.28 in( 19.00/19.28 X357,X356)) => 19.00/19.28 (~ 19.00/19.28 in( 19.00/19.28 X357,X355))))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X358, 19.00/19.28 X359,X360]: 19.00/19.28 (( 19.00/19.28 ~ 19.00/19.28 in( 19.00/19.28 X360,X358)) => 19.00/19.28 (~ 19.00/19.28 in( 19.00/19.28 X360, 19.00/19.28 setminus( 19.00/19.28 X358,X359))))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X361, 19.00/19.28 X362,X363]: 19.00/19.28 (in( 19.00/19.28 X363,X362) => 19.00/19.28 (~ 19.00/19.28 in( 19.00/19.28 X363, 19.00/19.28 setminus( 19.00/19.28 X361,X362))))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X364, 19.00/19.28 X365]: 19.00/19.28 subset( 19.00/19.28 setminus( 19.00/19.28 X364,X365), 19.00/19.28 X364)) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X366, 19.00/19.28 X367]: 19.00/19.28 (( 19.00/19.28 setminus( 19.00/19.28 X366,X367) = 19.00/19.28 emptyset) => 19.00/19.28 subset( 19.00/19.28 X366,X367))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X368, 19.00/19.28 X369,X370]: 19.00/19.28 (in( 19.00/19.28 X370, 19.00/19.28 symdiff( 19.00/19.28 X368,X369)) => 19.00/19.28 (![X371:$o]: 19.00/19.28 (( 19.00/19.28 in( 19.00/19.28 X370,X368) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ~ 19.00/19.28 in( 19.00/19.28 X370,X369)) => 19.00/19.28 X371)) => 19.00/19.28 (( 19.00/19.28 ( 19.00/19.28 ~ 19.00/19.28 in( 19.00/19.28 X370,X368)) => 19.00/19.28 ( 19.00/19.28 in( 19.00/19.28 X370,X369) => 19.00/19.28 X371)) => 19.00/19.28 X371))))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X372, 19.00/19.28 X373,X374]: 19.00/19.28 (in( 19.00/19.28 X374,X372) => 19.00/19.28 (( 19.00/19.28 ~ 19.00/19.28 in( 19.00/19.28 X374,X373)) => 19.00/19.28 in( 19.00/19.28 X374, 19.00/19.28 symdiff( 19.00/19.28 X372,X373))))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X375, 19.00/19.28 X376,X377]: 19.00/19.28 (( 19.00/19.28 ~ 19.00/19.28 in( 19.00/19.28 X377,X375)) => 19.00/19.28 (in( 19.00/19.28 X377,X376) => 19.00/19.28 in( 19.00/19.28 X377, 19.00/19.28 symdiff( 19.00/19.28 X375,X376))))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X378, 19.00/19.28 X379,X380]: 19.00/19.28 (in( 19.00/19.28 X380,X378) => 19.00/19.28 (in( 19.00/19.28 X380,X379) => 19.00/19.28 (~ 19.00/19.28 in( 19.00/19.28 X380, 19.00/19.28 symdiff( 19.00/19.28 X378,X379)))))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X381, 19.00/19.28 X382,X383]: 19.00/19.28 (( 19.00/19.28 ~ 19.00/19.28 in( 19.00/19.28 X383,X381)) => 19.00/19.28 (( 19.00/19.28 ~ 19.00/19.28 in( 19.00/19.28 X383,X382)) => 19.00/19.28 (~ 19.00/19.28 in( 19.00/19.28 X383, 19.00/19.28 symdiff( 19.00/19.28 X381,X382)))))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X384, 19.00/19.28 X385]: 19.00/19.28 in( 19.00/19.28 X385, 19.00/19.28 setadjoin( 19.00/19.28 X384, 19.00/19.28 setadjoin( 19.00/19.28 X385, 19.00/19.28 emptyset)))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X386, 19.00/19.28 X387]: 19.00/19.28 in( 19.00/19.28 X386, 19.00/19.28 setunion( 19.00/19.28 setadjoin( 19.00/19.28 setadjoin( 19.00/19.28 X386, 19.00/19.28 emptyset), 19.00/19.28 setadjoin( 19.00/19.28 setadjoin( 19.00/19.28 X386, 19.00/19.28 setadjoin( 19.00/19.28 X387, 19.00/19.28 emptyset)), 19.00/19.28 emptyset))))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X388, 19.00/19.28 X389]: 19.00/19.28 in( 19.00/19.28 X389, 19.00/19.28 setunion( 19.00/19.28 setadjoin( 19.00/19.28 setadjoin( 19.00/19.28 X388, 19.00/19.28 emptyset), 19.00/19.28 setadjoin( 19.00/19.28 setadjoin( 19.00/19.28 X388, 19.00/19.28 setadjoin( 19.00/19.28 X389, 19.00/19.28 emptyset)), 19.00/19.28 emptyset))))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X390, 19.00/19.28 X391]: 19.00/19.28 iskpair( 19.00/19.28 setadjoin( 19.00/19.28 setadjoin( 19.00/19.28 X390, 19.00/19.28 emptyset), 19.00/19.28 setadjoin( 19.00/19.28 setadjoin( 19.00/19.28 X390, 19.00/19.28 setadjoin( 19.00/19.28 X391, 19.00/19.28 emptyset)), 19.00/19.28 emptyset)))) => 19.00/19.28 ( 19.00/19.28 ( 19.00/19.28 ![X392, 19.00/19.28 X393]: 19.00/19.28 iskpair( 19.00/19.28 kpair( 19.02/19.28 X392,X393))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X394, 19.02/19.28 X395]: 19.02/19.28 (in( 19.02/19.28 X395,X394) => 19.02/19.28 subset( 19.02/19.28 setadjoin( 19.02/19.28 X395, 19.02/19.28 emptyset), 19.02/19.28 X394))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X396, 19.02/19.28 X397]: 19.02/19.28 (in( 19.02/19.28 X397,X396) => 19.02/19.28 in( 19.02/19.28 setadjoin( 19.02/19.28 X397, 19.02/19.28 emptyset), 19.02/19.28 powerset( 19.02/19.28 X396)))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X398, 19.02/19.28 X399,X400]: 19.02/19.28 (in( 19.02/19.28 X400,X398) => 19.02/19.28 in( 19.02/19.28 setadjoin( 19.02/19.28 X400, 19.02/19.28 emptyset), 19.02/19.28 powerset( 19.02/19.28 binunion( 19.02/19.28 X398,X399))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X401, 19.02/19.28 X402,X403]: 19.02/19.28 (in( 19.02/19.28 X403, 19.02/19.28 setadjoin( 19.02/19.28 X401, 19.02/19.28 setadjoin( 19.02/19.28 X402, 19.02/19.28 emptyset))) => 19.02/19.28 (( 19.02/19.28 X403 = 19.02/19.28 X402) | 19.02/19.28 (X403 = 19.02/19.28 X401)))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X404, 19.02/19.28 X405,X406]: 19.02/19.28 (in( 19.02/19.28 X406,X404) => 19.02/19.28 (![X407]: 19.02/19.28 (in( 19.02/19.28 X407,X405) => 19.02/19.28 subset( 19.02/19.28 setadjoin( 19.02/19.28 X406, 19.02/19.28 setadjoin( 19.02/19.28 X407, 19.02/19.28 emptyset)), 19.02/19.28 binunion( 19.02/19.28 X404,X405)))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X408, 19.02/19.28 X409,X410]: 19.02/19.28 (in( 19.02/19.28 X410,X408) => 19.02/19.28 (![X411]: 19.02/19.28 (in( 19.02/19.28 X411,X409) => 19.02/19.28 in( 19.02/19.28 setadjoin( 19.02/19.28 X410, 19.02/19.28 setadjoin( 19.02/19.28 X411, 19.02/19.28 emptyset)), 19.02/19.28 powerset( 19.02/19.28 binunion( 19.02/19.28 X408,X409))))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X412, 19.02/19.28 X413,X414]: 19.02/19.28 (in( 19.02/19.28 X414,X412) => 19.02/19.28 (![X415]: 19.02/19.28 (in( 19.02/19.28 X415,X413) => 19.02/19.28 subset( 19.02/19.28 setadjoin( 19.02/19.28 setadjoin( 19.02/19.28 X414, 19.02/19.28 emptyset), 19.02/19.28 setadjoin( 19.02/19.28 setadjoin( 19.02/19.28 X414, 19.02/19.28 setadjoin( 19.02/19.28 X415, 19.02/19.28 emptyset)), 19.02/19.28 emptyset)), 19.02/19.28 powerset( 19.02/19.28 binunion( 19.02/19.28 X412,X413))))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X416, 19.02/19.28 X417,X418]: 19.02/19.28 (in( 19.02/19.28 X418,X416) => 19.02/19.28 (![X419]: 19.02/19.28 (in( 19.02/19.28 X419,X417) => 19.02/19.28 in( 19.02/19.28 setadjoin( 19.02/19.28 setadjoin( 19.02/19.28 X418, 19.02/19.28 emptyset), 19.02/19.28 setadjoin( 19.02/19.28 setadjoin( 19.02/19.28 X418, 19.02/19.28 setadjoin( 19.02/19.28 X419, 19.02/19.28 emptyset)), 19.02/19.28 emptyset)), 19.02/19.28 powerset( 19.02/19.28 powerset( 19.02/19.28 binunion( 19.02/19.28 X416,X417)))))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X420, 19.02/19.28 X421,X422]: 19.02/19.28 (in( 19.02/19.28 X422,X420) => 19.02/19.28 (![X423]: 19.02/19.28 (in( 19.02/19.28 X423,X421) => 19.02/19.28 in( 19.02/19.28 kpair( 19.02/19.28 X422,X423), 19.02/19.28 powerset( 19.02/19.28 powerset( 19.02/19.28 binunion( 19.02/19.28 X420,X421)))))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X424, 19.02/19.28 X425,X426]: 19.02/19.28 (in( 19.02/19.28 X426,X424) => 19.02/19.28 (![X427]: 19.02/19.28 (in( 19.02/19.28 X427,X425) => 19.02/19.28 in( 19.02/19.28 kpair( 19.02/19.28 X426,X427), 19.02/19.28 cartprod( 19.02/19.28 X424,X425)))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X428, 19.02/19.28 X429,X430]: 19.02/19.28 (in( 19.02/19.28 X430, 19.02/19.28 cartprod( 19.02/19.28 X428,X429)) => 19.02/19.28 (?[X431]: 19.02/19.28 (( 19.02/19.28 ?[X432]: 19.02/19.28 (( 19.02/19.28 X430 = 19.02/19.28 kpair( 19.02/19.28 X431,X432)) & 19.02/19.28 in( 19.02/19.28 X432,X429))) & 19.02/19.28 in( 19.02/19.28 X431,X428))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X433, 19.02/19.28 X434,X435]: 19.02/19.28 (in( 19.02/19.28 X435, 19.02/19.28 cartprod( 19.02/19.28 X433,X434)) => 19.02/19.28 iskpair( 19.02/19.28 X435))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X436, 19.02/19.28 X437]: 19.02/19.28 (in( 19.02/19.28 X437, 19.02/19.28 setunion( 19.02/19.28 X436)) => 19.02/19.28 (?[X438]: 19.02/19.28 (in( 19.02/19.28 X437,X438) & 19.02/19.28 in( 19.02/19.28 X438,X436))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X439]: 19.02/19.28 subset( 19.02/19.28 setunion( 19.02/19.28 setadjoin( 19.02/19.28 X439, 19.02/19.28 emptyset)), 19.02/19.28 X439)) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X440]: 19.02/19.28 subset( 19.02/19.28 X440, 19.02/19.28 setunion( 19.02/19.28 setadjoin( 19.02/19.28 X440, 19.02/19.28 emptyset)))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X441]: 19.02/19.28 (setunion( 19.02/19.28 setadjoin( 19.02/19.28 X441, 19.02/19.28 emptyset)) = 19.02/19.28 X441)) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X442, 19.02/19.28 X443:( 19.02/19.28 $i > $o)]: 19.02/19.28 (( 19.02/19.28 ![X444]: 19.02/19.28 (in( 19.02/19.28 X444,X442) => 19.02/19.28 (![X445]: 19.02/19.28 (in( 19.02/19.28 X445,X442) => 19.02/19.28 (X443( 19.02/19.28 X444) => 19.02/19.28 (X443( 19.02/19.28 X445) => 19.02/19.28 (X444 = 19.02/19.28 X445))))))) => 19.02/19.28 (( 19.02/19.28 ?[X446]: 19.02/19.28 (X443( 19.02/19.28 X446) & 19.02/19.28 in( 19.02/19.28 X446,X442))) => 19.02/19.28 singleton( 19.02/19.28 dsetconstr( 19.02/19.28 X442, 19.02/19.28 ^[V_15]: 19.02/19.28 X443( 19.02/19.28 V_15)))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X447, 19.02/19.28 X448:( 19.02/19.28 $i > $o)]: 19.02/19.28 (singleton( 19.02/19.28 dsetconstr( 19.02/19.28 X447, 19.02/19.28 ^[V_16]: 19.02/19.28 X448( 19.02/19.28 V_16))) => 19.02/19.28 (?[X449]: 19.02/19.28 (X448( 19.02/19.28 X449) & 19.02/19.28 in( 19.02/19.28 X449,X447))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X450, 19.02/19.28 X451:( 19.02/19.28 $i > $o), 19.02/19.28 X452]: 19.02/19.28 (in( 19.02/19.28 X452,X450) => 19.02/19.28 (X451( 19.02/19.28 X452) => 19.02/19.28 (( 19.02/19.28 ![X453]: 19.02/19.28 (in( 19.02/19.28 X453,X450) => 19.02/19.28 (X451( 19.02/19.28 X453) => 19.02/19.28 (X453 = 19.02/19.28 X452)))) => 19.02/19.28 singleton( 19.02/19.28 dsetconstr( 19.02/19.28 X450, 19.02/19.28 ^[V_17]: 19.02/19.28 X451( 19.02/19.28 V_17))))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X454, 19.02/19.28 X455:( 19.02/19.28 $i > $o)]: 19.02/19.28 (( 19.02/19.28 ![X456]: 19.02/19.28 (in( 19.02/19.28 X456,X454) => 19.02/19.28 (![X457]: 19.02/19.28 (in( 19.02/19.28 X457,X454) => 19.02/19.28 (X455( 19.02/19.28 X456) => 19.02/19.28 (X455( 19.02/19.28 X457) => 19.02/19.28 (X456 = 19.02/19.28 X457))))))) => 19.02/19.28 (( 19.02/19.28 ?[X458]: 19.02/19.28 (X455( 19.02/19.28 X458) & 19.02/19.28 in( 19.02/19.28 X458,X454))) => 19.02/19.28 singleton( 19.02/19.28 dsetconstr( 19.02/19.28 X454, 19.02/19.28 ^[V_18]: 19.02/19.28 X455( 19.02/19.28 V_18)))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X459, 19.02/19.28 X460]: 19.02/19.28 (( 19.02/19.28 setadjoin( 19.02/19.28 X459, 19.02/19.28 emptyset) = 19.02/19.28 setadjoin( 19.02/19.28 X460, 19.02/19.28 emptyset)) => 19.02/19.28 (X459 = 19.02/19.28 X460))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X461, 19.02/19.28 X462,X463]: 19.02/19.28 (in( 19.02/19.28 setadjoin( 19.02/19.28 X463, 19.02/19.28 emptyset), 19.02/19.28 setadjoin( 19.02/19.28 setadjoin( 19.02/19.28 X461, 19.02/19.28 emptyset), 19.02/19.28 setadjoin( 19.02/19.28 setadjoin( 19.02/19.28 X461, 19.02/19.28 setadjoin( 19.02/19.28 X462, 19.02/19.28 emptyset)), 19.02/19.28 emptyset))) => 19.02/19.28 (X461 = 19.02/19.28 X463))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X464]: 19.02/19.28 (iskpair( 19.02/19.28 X464) => 19.02/19.28 singleton( 19.02/19.28 dsetconstr( 19.02/19.28 setunion( 19.02/19.28 X464), 19.02/19.28 ^[V_19]: 19.02/19.28 in( 19.02/19.28 setadjoin( 19.02/19.28 V_19, 19.02/19.28 emptyset), 19.02/19.28 X464))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X465]: 19.02/19.28 (singleton( 19.02/19.28 X465) => 19.02/19.28 in( 19.02/19.28 setunion( 19.02/19.28 X465), 19.02/19.28 X465))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X466, 19.02/19.28 X467]: 19.02/19.28 (kfst( 19.02/19.28 kpair( 19.02/19.28 X466,X467)) = 19.02/19.28 X466)) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X468, 19.02/19.28 X469,X470]: 19.02/19.28 (in( 19.02/19.28 X470, 19.02/19.28 cartprod( 19.02/19.28 X468,X469)) => 19.02/19.28 in( 19.02/19.28 kfst( 19.02/19.28 X470), 19.02/19.28 X468))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X471, 19.02/19.28 X472, 19.02/19.28 X473,X474]: 19.02/19.28 (( 19.02/19.28 setadjoin( 19.02/19.28 setadjoin( 19.02/19.28 X471, 19.02/19.28 emptyset), 19.02/19.28 setadjoin( 19.02/19.28 setadjoin( 19.02/19.28 X471, 19.02/19.28 setadjoin( 19.02/19.28 X472, 19.02/19.28 emptyset)), 19.02/19.28 emptyset)) = 19.02/19.28 setadjoin( 19.02/19.28 setadjoin( 19.02/19.28 X473, 19.02/19.28 emptyset), 19.02/19.28 setadjoin( 19.02/19.28 setadjoin( 19.02/19.28 X473, 19.02/19.28 setadjoin( 19.02/19.28 X474, 19.02/19.28 emptyset)), 19.02/19.28 emptyset))) => 19.02/19.28 (X471 = 19.02/19.28 X473))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X475, 19.02/19.28 X476, 19.02/19.28 X477,X478]: 19.02/19.28 (( 19.02/19.28 kpair( 19.02/19.28 X475,X476) = 19.02/19.28 kpair( 19.02/19.28 X477,X478)) => 19.02/19.28 (X475 = 19.02/19.28 X477))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X479, 19.02/19.28 X480]: 19.02/19.28 (( 19.02/19.28 X479 = 19.02/19.28 X480) => 19.02/19.28 (setadjoin( 19.02/19.28 X479, 19.02/19.28 setadjoin( 19.02/19.28 X480, 19.02/19.28 emptyset)) = 19.02/19.28 setadjoin( 19.02/19.28 X479, 19.02/19.28 emptyset)))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X481, 19.02/19.28 X482]: 19.02/19.28 (( 19.02/19.28 X481 = 19.02/19.28 X482) => 19.02/19.28 (setadjoin( 19.02/19.28 setadjoin( 19.02/19.28 X481, 19.02/19.28 emptyset), 19.02/19.28 setadjoin( 19.02/19.28 setadjoin( 19.02/19.28 X481, 19.02/19.28 setadjoin( 19.02/19.28 X482, 19.02/19.28 emptyset)), 19.02/19.28 emptyset)) = 19.02/19.28 setadjoin( 19.02/19.28 setadjoin( 19.02/19.28 X481, 19.02/19.28 emptyset), 19.02/19.28 emptyset)))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X483, 19.02/19.28 X484, 19.02/19.28 X485,X486]: 19.02/19.28 (( 19.02/19.28 setadjoin( 19.02/19.28 setadjoin( 19.02/19.28 X483, 19.02/19.28 emptyset), 19.02/19.28 setadjoin( 19.02/19.28 setadjoin( 19.02/19.28 X483, 19.02/19.28 setadjoin( 19.02/19.28 X484, 19.02/19.28 emptyset)), 19.02/19.28 emptyset)) = 19.02/19.28 setadjoin( 19.02/19.28 setadjoin( 19.02/19.28 X485, 19.02/19.28 emptyset), 19.02/19.28 setadjoin( 19.02/19.28 setadjoin( 19.02/19.28 X485, 19.02/19.28 setadjoin( 19.02/19.28 X486, 19.02/19.28 emptyset)), 19.02/19.28 emptyset))) => 19.02/19.28 (( 19.02/19.28 X485 = 19.02/19.28 X486) => 19.02/19.28 (X484 = 19.02/19.28 X486)))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X487, 19.02/19.28 X488,X489]: 19.02/19.28 (( 19.02/19.28 setadjoin( 19.02/19.28 X487, 19.02/19.28 setadjoin( 19.02/19.28 X488, 19.02/19.28 emptyset)) = 19.02/19.28 setadjoin( 19.02/19.28 X489, 19.02/19.28 emptyset)) => 19.02/19.28 (X487 = 19.02/19.28 X488))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X490, 19.02/19.28 X491, 19.02/19.28 X492,X493]: 19.02/19.28 (( 19.02/19.28 setadjoin( 19.02/19.28 setadjoin( 19.02/19.28 X490, 19.02/19.28 emptyset), 19.02/19.28 setadjoin( 19.02/19.28 setadjoin( 19.02/19.28 X490, 19.02/19.28 setadjoin( 19.02/19.28 X491, 19.02/19.28 emptyset)), 19.02/19.28 emptyset)) = 19.02/19.28 setadjoin( 19.02/19.28 setadjoin( 19.02/19.28 X492, 19.02/19.28 emptyset), 19.02/19.28 setadjoin( 19.02/19.28 setadjoin( 19.02/19.28 X492, 19.02/19.28 setadjoin( 19.02/19.28 X493, 19.02/19.28 emptyset)), 19.02/19.28 emptyset))) => 19.02/19.28 (X491 = 19.02/19.28 X493))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X494, 19.02/19.28 X495, 19.02/19.28 X496,X497]: 19.02/19.28 (( 19.02/19.28 kpair( 19.02/19.28 X494,X495) = 19.02/19.28 kpair( 19.02/19.28 X496,X497)) => 19.02/19.28 (X495 = 19.02/19.28 X497))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X498]: 19.02/19.28 (iskpair( 19.02/19.28 X498) => 19.02/19.28 singleton( 19.02/19.28 dsetconstr( 19.02/19.28 setunion( 19.02/19.28 X498), 19.02/19.28 ^[V_20]: 19.02/19.28 (X498 = 19.02/19.28 kpair( 19.02/19.28 kfst( 19.02/19.28 X498), 19.02/19.28 V_20)))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X499, 19.02/19.28 X500]: 19.02/19.28 (ksnd( 19.02/19.28 kpair( 19.02/19.28 X499,X500)) = 19.02/19.28 X500)) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X501]: 19.02/19.28 (iskpair( 19.02/19.28 X501) => 19.02/19.28 (kpair( 19.02/19.28 kfst( 19.02/19.28 X501), 19.02/19.28 ksnd( 19.02/19.28 X501)) = 19.02/19.28 X501))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X502, 19.02/19.28 X503,X504]: 19.02/19.28 (in( 19.02/19.28 X504, 19.02/19.28 cartprod( 19.02/19.28 X502,X503)) => 19.02/19.28 in( 19.02/19.28 ksnd( 19.02/19.28 X504), 19.02/19.28 X503))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X505, 19.02/19.28 X506, 19.02/19.28 X507,X508]: 19.02/19.28 (in( 19.02/19.28 kpair( 19.02/19.28 X507,X508), 19.02/19.28 cartprod( 19.02/19.28 X505,X506)) => 19.02/19.28 in( 19.02/19.28 X507,X505))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X509, 19.02/19.28 X510, 19.02/19.28 X511,X512]: 19.02/19.28 (in( 19.02/19.28 kpair( 19.02/19.28 X511,X512), 19.02/19.28 cartprod( 19.02/19.28 X509,X510)) => 19.02/19.28 in( 19.02/19.28 X512,X510))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X513, 19.02/19.28 X514,X515]: 19.02/19.28 (in( 19.02/19.28 X515,X513) => 19.02/19.28 (![X516]: 19.02/19.28 (in( 19.02/19.28 X516,X514) => 19.02/19.28 (kpair( 19.02/19.28 X515,X516) = 19.02/19.28 kpair( 19.02/19.28 X515,X516)))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X517, 19.02/19.28 X518,X519]: 19.02/19.28 (in( 19.02/19.28 X519,X517) => 19.02/19.28 (![X520]: 19.02/19.28 (in( 19.02/19.28 X520,X518) => 19.02/19.28 (kfst( 19.02/19.28 kpair( 19.02/19.28 X519,X520)) = 19.02/19.28 X519))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X521, 19.02/19.28 X522,X523]: 19.02/19.28 (in( 19.02/19.28 X523,X521) => 19.02/19.28 (![X524]: 19.02/19.28 (in( 19.02/19.28 X524,X522) => 19.02/19.28 (ksnd( 19.02/19.28 kpair( 19.02/19.28 X523,X524)) = 19.02/19.28 X524))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X525, 19.02/19.28 X526,X527]: 19.02/19.28 (in( 19.02/19.28 X527, 19.02/19.28 cartprod( 19.02/19.28 X525,X526)) => 19.02/19.28 (kpair( 19.02/19.28 kfst( 19.02/19.28 X527), 19.02/19.28 ksnd( 19.02/19.28 X527)) = 19.02/19.28 X527))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X528, 19.02/19.28 X529, 19.02/19.28 X530:( 19.02/19.28 ($i * $i) > 19.02/19.28 $o),X531]: 19.02/19.28 (in( 19.02/19.28 X531,X528) => 19.02/19.28 (![X532]: 19.02/19.28 (in( 19.02/19.28 X532,X529) => 19.02/19.28 (X530( 19.02/19.28 X531,X532) => 19.02/19.28 in( 19.02/19.28 kpair( 19.02/19.28 X531,X532), 19.02/19.28 dpsetconstr( 19.02/19.28 X528, 19.02/19.28 X529, 19.02/19.28 ^[V_21, 19.02/19.28 V_22]: 19.02/19.28 X530( 19.02/19.28 V_21,V_22)))))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X533, 19.02/19.28 X534, 19.02/19.28 X535:( 19.02/19.28 ($i * $i) > 19.02/19.28 $o)]: 19.02/19.28 subset( 19.02/19.28 dpsetconstr( 19.02/19.28 X533, 19.02/19.28 X534, 19.02/19.28 ^[V_23, 19.02/19.28 V_24]: 19.02/19.28 X535( 19.02/19.28 V_23,V_24)), 19.02/19.28 cartprod( 19.02/19.28 X533,X534))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X536, 19.02/19.28 X537, 19.02/19.28 X538:( 19.02/19.28 ($i * $i) > 19.02/19.28 $o)]: 19.02/19.28 subset( 19.02/19.28 dpsetconstr( 19.02/19.28 X536, 19.02/19.28 X537, 19.02/19.28 ^[V_25, 19.02/19.28 V_26]: 19.02/19.28 X538( 19.02/19.28 V_25,V_26)), 19.02/19.28 cartprod( 19.02/19.28 X536,X537))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X539, 19.02/19.28 X540, 19.02/19.28 X541:( 19.02/19.28 ($i * $i) > 19.02/19.28 $o),X542]: 19.02/19.28 (in( 19.02/19.28 X542,X539) => 19.02/19.28 (![X543]: 19.02/19.28 (in( 19.02/19.28 X543,X540) => 19.02/19.28 (in( 19.02/19.28 kpair( 19.02/19.28 X542,X543), 19.02/19.28 dpsetconstr( 19.02/19.28 X539, 19.02/19.28 X540, 19.02/19.28 ^[V_27, 19.02/19.28 V_28]: 19.02/19.28 X541( 19.02/19.28 V_27,V_28))) => 19.02/19.28 X541( 19.02/19.28 X542,X543)))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X544, 19.02/19.28 X545, 19.02/19.28 X546:( 19.02/19.28 ($i * $i) > 19.02/19.28 $o),X547, 19.02/19.28 X548]: 19.02/19.28 (in( 19.02/19.28 kpair( 19.02/19.28 X547,X548), 19.02/19.28 dpsetconstr( 19.02/19.28 X544, 19.02/19.28 X545, 19.02/19.28 ^[V_29, 19.02/19.28 V_30]: 19.02/19.28 X546( 19.02/19.28 V_29,V_30))) => 19.02/19.28 in( 19.02/19.28 X547,X544))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X549, 19.02/19.28 X550, 19.02/19.28 X551:( 19.02/19.28 ($i * $i) > 19.02/19.28 $o),X552, 19.02/19.28 X553]: 19.02/19.28 (in( 19.02/19.28 kpair( 19.02/19.28 X552,X553), 19.02/19.28 dpsetconstr( 19.02/19.28 X549, 19.02/19.28 X550, 19.02/19.28 ^[V_31, 19.02/19.28 V_32]: 19.02/19.28 X551( 19.02/19.28 V_31,V_32))) => 19.02/19.28 in( 19.02/19.28 X553,X550))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X554, 19.02/19.28 X555, 19.02/19.28 X556:( 19.02/19.28 ($i * $i) > 19.02/19.28 $o),X557, 19.02/19.28 X558]: 19.02/19.28 (in( 19.02/19.28 kpair( 19.02/19.28 X557,X558), 19.02/19.28 dpsetconstr( 19.02/19.28 X554, 19.02/19.28 X555, 19.02/19.28 ^[V_33, 19.02/19.28 V_34]: 19.02/19.28 X556( 19.02/19.28 V_33,V_34))) => 19.02/19.28 X556( 19.02/19.28 X557,X558))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X559, 19.02/19.28 X560,X561]: 19.02/19.28 (func( 19.02/19.28 X559, 19.02/19.28 X560,X561) => 19.02/19.28 (![X562]: 19.02/19.28 (in( 19.02/19.28 X562,X559) => 19.02/19.28 singleton( 19.02/19.28 dsetconstr( 19.02/19.28 X560, 19.02/19.28 ^[V_35]: 19.02/19.28 in( 19.02/19.28 kpair( 19.02/19.28 X562,V_35), 19.02/19.28 X561))))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X563, 19.02/19.28 X564,X565]: 19.02/19.28 (func( 19.02/19.28 X563, 19.02/19.28 X564,X565) => 19.02/19.28 (![X566]: 19.02/19.28 (in( 19.02/19.28 X566,X563) => 19.02/19.28 in( 19.02/19.28 setunion( 19.02/19.28 dsetconstr( 19.02/19.28 X564, 19.02/19.28 ^[V_36]: 19.02/19.28 in( 19.02/19.28 kpair( 19.02/19.28 X566,V_36), 19.02/19.28 X565))), 19.02/19.28 X564))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X567, 19.02/19.28 X568,X569]: 19.02/19.28 (func( 19.02/19.28 X567, 19.02/19.28 X568,X569) => 19.02/19.28 (![X570]: 19.02/19.28 (in( 19.02/19.28 X570,X567) => 19.02/19.28 in( 19.02/19.28 ap( 19.02/19.28 X567, 19.02/19.28 X568, 19.02/19.28 X569,X570), 19.02/19.28 X568))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X571, 19.02/19.28 X572,X573]: 19.02/19.28 (in( 19.02/19.28 X573, 19.02/19.28 funcSet( 19.02/19.28 X571,X572)) => 19.02/19.28 func( 19.02/19.28 X571, 19.02/19.28 X572,X573))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X574, 19.02/19.28 X575,X576]: 19.02/19.28 (in( 19.02/19.28 X576, 19.02/19.28 funcSet( 19.02/19.28 X574,X575)) => 19.02/19.28 (![X577]: 19.02/19.28 (in( 19.02/19.28 X577,X574) => 19.02/19.28 in( 19.02/19.28 ap( 19.02/19.28 X574, 19.02/19.28 X575, 19.02/19.28 X576,X577), 19.02/19.28 X575))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X578, 19.02/19.28 X579,X580]: 19.02/19.28 (func( 19.02/19.28 X578, 19.02/19.28 X579,X580) => 19.02/19.28 in( 19.02/19.28 X580, 19.02/19.28 funcSet( 19.02/19.28 X578,X579)))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X581, 19.02/19.28 X582, 19.02/19.28 X583:( 19.02/19.28 $i > $i)]: 19.02/19.28 (( 19.02/19.28 ![X584]: 19.02/19.28 (in( 19.02/19.28 X584,X581) => 19.02/19.28 in( 19.02/19.28 X583( 19.02/19.28 X584), 19.02/19.28 X582))) => 19.02/19.28 func( 19.02/19.28 X581, 19.02/19.28 X582, 19.02/19.28 dpsetconstr( 19.02/19.28 X581, 19.02/19.28 X582, 19.02/19.28 ^[V_37, 19.02/19.28 V_38]: 19.02/19.28 (X583( 19.02/19.28 V_37) = 19.02/19.28 V_38))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X585, 19.02/19.28 X586, 19.02/19.28 X587:( 19.02/19.28 $i > $i)]: 19.02/19.28 (( 19.02/19.28 ![X588]: 19.02/19.28 (in( 19.02/19.28 X588,X585) => 19.02/19.28 in( 19.02/19.28 X587( 19.02/19.28 X588), 19.02/19.28 X586))) => 19.02/19.28 func( 19.02/19.28 X585, 19.02/19.28 X586, 19.02/19.28 lam( 19.02/19.28 X585, 19.02/19.28 X586, 19.02/19.28 ^[V_39]: 19.02/19.28 X587( 19.02/19.28 V_39))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X589, 19.02/19.28 X590, 19.02/19.28 X591:( 19.02/19.28 $i > $i)]: 19.02/19.28 (( 19.02/19.28 ![X592]: 19.02/19.28 (in( 19.02/19.28 X592,X589) => 19.02/19.28 in( 19.02/19.28 X591( 19.02/19.28 X592), 19.02/19.28 X590))) => 19.02/19.28 in( 19.02/19.28 lam( 19.02/19.28 X589, 19.02/19.28 X590, 19.02/19.28 ^[V_40]: 19.02/19.28 X591( 19.02/19.28 V_40)), 19.02/19.28 funcSet( 19.02/19.28 X589,X590)))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X593, 19.02/19.28 X594,X595]: 19.02/19.28 (subset( 19.02/19.28 X595, 19.02/19.28 cartprod( 19.02/19.28 X593,X594)) => 19.02/19.28 (![X596:( 19.02/19.28 $i > $o)]: 19.02/19.28 (( 19.02/19.28 ![X597]: 19.02/19.28 (in( 19.02/19.28 X597,X593) => 19.02/19.28 (![X598]: 19.02/19.28 (in( 19.02/19.28 X598,X594) => 19.02/19.28 (in( 19.02/19.28 kpair( 19.02/19.28 X597,X598), 19.02/19.28 X595) => 19.02/19.28 X596( 19.02/19.28 kpair( 19.02/19.28 X597,X598))))))) => 19.02/19.28 (![X599]: 19.02/19.28 (in( 19.02/19.28 X599,X595) => 19.02/19.28 X596( 19.02/19.28 X599))))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X600, 19.02/19.28 X601,X602]: 19.02/19.28 (subset( 19.02/19.28 X602, 19.02/19.28 cartprod( 19.02/19.28 X600,X601)) => 19.02/19.28 (![X603:( 19.02/19.28 $i > $o)]: 19.02/19.28 (( 19.02/19.28 ![X604]: 19.02/19.28 (in( 19.02/19.28 X604,X600) => 19.02/19.28 (![X605]: 19.02/19.28 (in( 19.02/19.28 X605,X601) => 19.02/19.28 (in( 19.02/19.28 kpair( 19.02/19.28 X604,X605), 19.02/19.28 X602) => 19.02/19.28 X603( 19.02/19.28 kpair( 19.02/19.28 X604,X605))))))) => 19.02/19.28 (![X606]: 19.02/19.28 (in( 19.02/19.28 X606,X602) => 19.02/19.28 X603( 19.02/19.28 X606))))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X607, 19.02/19.28 X608:( 19.02/19.28 $i > $o)]: 19.02/19.28 (singleton( 19.02/19.28 dsetconstr( 19.02/19.28 X607, 19.02/19.28 ^[V_41]: 19.02/19.28 X608( 19.02/19.28 V_41))) => 19.02/19.28 (![X609]: 19.02/19.28 (in( 19.02/19.28 X609,X607) => 19.02/19.28 (![X610]: 19.02/19.28 (in( 19.02/19.28 X610,X607) => 19.02/19.28 (X608( 19.02/19.28 X609) => 19.02/19.28 (X608( 19.02/19.28 X610) => 19.02/19.28 (X609 = 19.02/19.28 X610))))))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X611, 19.02/19.28 X612,X613]: 19.02/19.28 (func( 19.02/19.28 X611, 19.02/19.28 X612,X613) => 19.02/19.28 (![X614]: 19.02/19.28 (in( 19.02/19.28 X614,X611) => 19.02/19.28 in( 19.02/19.28 kpair( 19.02/19.28 X614, 19.02/19.28 ap( 19.02/19.28 X611, 19.02/19.28 X612, 19.02/19.28 X613,X614)), 19.02/19.28 X613))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X615, 19.02/19.28 X616,X617]: 19.02/19.28 (in( 19.02/19.28 X617, 19.02/19.28 funcSet( 19.02/19.28 X615,X616)) => 19.02/19.28 (![X618]: 19.02/19.28 (in( 19.02/19.28 X618,X615) => 19.02/19.28 in( 19.02/19.28 kpair( 19.02/19.28 X618, 19.02/19.28 ap( 19.02/19.28 X615, 19.02/19.28 X616, 19.02/19.28 X617,X618)), 19.02/19.28 X617))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X619, 19.02/19.28 X620,X621]: 19.02/19.28 (func( 19.02/19.28 X619, 19.02/19.28 X620,X621) => 19.02/19.28 (![X622]: 19.02/19.28 (in( 19.02/19.28 X622,X619) => 19.02/19.28 (![X623]: 19.02/19.28 (in( 19.02/19.28 X623,X620) => 19.02/19.28 (in( 19.02/19.28 kpair( 19.02/19.28 X622,X623), 19.02/19.28 X621) => 19.02/19.28 (ap( 19.02/19.28 X619, 19.02/19.28 X620, 19.02/19.28 X621,X622) = 19.02/19.28 X623)))))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X624, 19.02/19.28 X625,X626]: 19.02/19.28 (func( 19.02/19.28 X624, 19.02/19.28 X625,X626) => 19.02/19.28 (![X627]: 19.02/19.28 (func( 19.02/19.28 X624, 19.02/19.28 X625,X627) => 19.02/19.28 (( 19.02/19.28 ![X628]: 19.02/19.28 (in( 19.02/19.28 X628,X624) => 19.02/19.28 (ap( 19.02/19.28 X624, 19.02/19.28 X625, 19.02/19.28 X626,X628) = 19.02/19.28 ap( 19.02/19.28 X624, 19.02/19.28 X625, 19.02/19.28 X627,X628)))) => 19.02/19.28 (![X629]: 19.02/19.28 (in( 19.02/19.28 X629,X624) => 19.02/19.28 (![X630]: 19.02/19.28 (in( 19.02/19.28 X630,X625) => 19.02/19.28 (in( 19.02/19.28 kpair( 19.02/19.28 X629,X630), 19.02/19.28 X627) => 19.02/19.28 in( 19.02/19.28 kpair( 19.02/19.28 X629,X630), 19.02/19.28 X626))))))))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X631, 19.02/19.28 X632,X633]: 19.02/19.28 (in( 19.02/19.28 X633, 19.02/19.28 funcSet( 19.02/19.28 X631,X632)) => 19.02/19.28 (![X634]: 19.02/19.28 (in( 19.02/19.28 X634,X631) => 19.02/19.28 (![X635]: 19.02/19.28 (in( 19.02/19.28 X635,X632) => 19.02/19.28 (in( 19.02/19.28 kpair( 19.02/19.28 X634,X635), 19.02/19.28 X633) => 19.02/19.28 (ap( 19.02/19.28 X631, 19.02/19.28 X632, 19.02/19.28 X633,X634) = 19.02/19.28 X635)))))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X636, 19.02/19.28 X637,X638]: 19.02/19.28 (subset( 19.02/19.28 X638, 19.02/19.28 cartprod( 19.02/19.28 X636,X637)) => 19.02/19.28 (![X639]: 19.02/19.28 (subset( 19.02/19.28 X639, 19.02/19.28 cartprod( 19.02/19.28 X636,X637)) => 19.02/19.28 (( 19.02/19.28 ![X640]: 19.02/19.28 (in( 19.02/19.28 X640,X636) => 19.02/19.28 (![X641]: 19.02/19.28 (in( 19.02/19.28 X641,X637) => 19.02/19.28 (in( 19.02/19.28 kpair( 19.02/19.28 X640,X641), 19.02/19.28 X638) => 19.02/19.28 in( 19.02/19.28 kpair( 19.02/19.28 X640,X641), 19.02/19.28 X639)))))) => 19.02/19.28 subset( 19.02/19.28 X638,X639)))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X642, 19.02/19.28 X643,X644]: 19.02/19.28 (subset( 19.02/19.28 X644, 19.02/19.28 cartprod( 19.02/19.28 X642,X643)) => 19.02/19.28 (![X645]: 19.02/19.28 (subset( 19.02/19.28 X645, 19.02/19.28 cartprod( 19.02/19.28 X642,X643)) => 19.02/19.28 (( 19.02/19.28 ![X646]: 19.02/19.28 (in( 19.02/19.28 X646,X642) => 19.02/19.28 (![X647]: 19.02/19.28 (in( 19.02/19.28 X647,X643) => 19.02/19.28 (in( 19.02/19.28 kpair( 19.02/19.28 X646,X647), 19.02/19.28 X644) => 19.02/19.28 in( 19.02/19.28 kpair( 19.02/19.28 X646,X647), 19.02/19.28 X645)))))) => 19.02/19.28 (( 19.02/19.28 ![X648]: 19.02/19.28 (in( 19.02/19.28 X648,X642) => 19.02/19.28 (![X649]: 19.02/19.28 (in( 19.02/19.28 X649,X643) => 19.02/19.28 (in( 19.02/19.28 kpair( 19.02/19.28 X648,X649), 19.02/19.28 X645) => 19.02/19.28 in( 19.02/19.28 kpair( 19.02/19.28 X648,X649), 19.02/19.28 X644)))))) => 19.02/19.28 (X644 = 19.02/19.28 X645))))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X650, 19.02/19.28 X651,X652]: 19.02/19.28 (func( 19.02/19.28 X650, 19.02/19.28 X651,X652) => 19.02/19.28 (![X653]: 19.02/19.28 (func( 19.02/19.28 X650, 19.02/19.28 X651,X653) => 19.02/19.28 (( 19.02/19.28 ![X654]: 19.02/19.28 (in( 19.02/19.28 X654,X650) => 19.02/19.28 (ap( 19.02/19.28 X650, 19.02/19.28 X651, 19.02/19.28 X652,X654) = 19.02/19.28 ap( 19.02/19.28 X650, 19.02/19.28 X651, 19.02/19.28 X653,X654)))) => 19.02/19.28 (X652 = 19.02/19.28 X653)))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X655, 19.02/19.28 X656,X657]: 19.02/19.28 (in( 19.02/19.28 X657, 19.02/19.28 funcSet( 19.02/19.28 X655,X656)) => 19.02/19.28 (![X658]: 19.02/19.28 (in( 19.02/19.28 X658, 19.02/19.28 funcSet( 19.02/19.28 X655,X656)) => 19.02/19.28 (( 19.02/19.28 ![X659]: 19.02/19.28 (in( 19.02/19.28 X659,X655) => 19.02/19.28 (ap( 19.02/19.28 X655, 19.02/19.28 X656, 19.02/19.28 X657,X659) = 19.02/19.28 ap( 19.02/19.28 X655, 19.02/19.28 X656, 19.02/19.28 X658,X659)))) => 19.02/19.28 (X657 = 19.02/19.28 X658)))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X660, 19.02/19.28 X661,X662]: 19.02/19.28 (in( 19.02/19.28 X662, 19.02/19.28 funcSet( 19.02/19.28 X660,X661)) => 19.02/19.28 (![X663]: 19.02/19.28 (in( 19.02/19.28 X663,X660) => 19.02/19.28 (ap( 19.02/19.28 X660, 19.02/19.28 X661, 19.02/19.28 X662,X663) = 19.02/19.28 ap( 19.02/19.28 X660, 19.02/19.28 X661, 19.02/19.28 X662,X663)))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X664, 19.02/19.28 X665,X666]: 19.02/19.28 (func( 19.02/19.28 X664, 19.02/19.28 X665,X666) => 19.02/19.28 (![X667]: 19.02/19.28 (in( 19.02/19.28 X667,X664) => 19.02/19.28 (ap( 19.02/19.28 X664, 19.02/19.28 X665, 19.02/19.28 X666,X667) = 19.02/19.28 ap( 19.02/19.28 X664, 19.02/19.28 X665, 19.02/19.28 X666,X667)))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X668, 19.02/19.28 X669, 19.02/19.28 X670:( 19.02/19.28 $i > $i)]: 19.02/19.28 (( 19.02/19.28 ![X671]: 19.02/19.28 (in( 19.02/19.28 X671,X668) => 19.02/19.28 in( 19.02/19.28 X670( 19.02/19.28 X671), 19.02/19.28 X669))) => 19.02/19.28 (![X672]: 19.02/19.28 (in( 19.02/19.28 X672,X668) => 19.02/19.28 (ap( 19.02/19.28 X668, 19.02/19.28 X669, 19.02/19.28 lam( 19.02/19.28 X668, 19.02/19.28 X669, 19.02/19.28 ^[V_42]: 19.02/19.28 X670( 19.02/19.28 V_42)), 19.02/19.28 X672) = 19.02/19.28 X670( 19.02/19.28 X672)))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X673, 19.02/19.28 X674,X675]: 19.02/19.28 (func( 19.02/19.28 X673, 19.02/19.28 X674,X675) => 19.02/19.28 (lam( 19.02/19.28 X673, 19.02/19.28 X674, 19.02/19.28 ^[V_43]: 19.02/19.28 ap( 19.02/19.28 X673, 19.02/19.28 X674, 19.02/19.28 X675,V_43)) = 19.02/19.28 X675))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X676, 19.02/19.28 X677, 19.02/19.28 X678:( 19.02/19.28 $i > $i)]: 19.02/19.28 (( 19.02/19.28 ![X679]: 19.02/19.28 (in( 19.02/19.28 X679,X676) => 19.02/19.28 in( 19.02/19.28 X678( 19.02/19.28 X679), 19.02/19.28 X677))) => 19.02/19.28 (lam( 19.02/19.28 X676, 19.02/19.28 X677, 19.02/19.28 ^[V_44]: 19.02/19.28 X678( 19.02/19.28 V_44)) = 19.02/19.28 lam( 19.02/19.28 X676, 19.02/19.28 X677, 19.02/19.28 ^[V_45]: 19.02/19.28 X678( 19.02/19.28 V_45))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X680, 19.02/19.28 X681, 19.02/19.28 X682:( 19.02/19.28 $i > $i)]: 19.02/19.28 (( 19.02/19.28 ![X683]: 19.02/19.28 (in( 19.02/19.28 X683,X680) => 19.02/19.28 in( 19.02/19.28 X682( 19.02/19.28 X683), 19.02/19.28 X681))) => 19.02/19.28 (![X684]: 19.02/19.28 (in( 19.02/19.28 X684,X680) => 19.02/19.28 (ap( 19.02/19.28 X680, 19.02/19.28 X681, 19.02/19.28 lam( 19.02/19.28 X680, 19.02/19.28 X681, 19.02/19.28 ^[V_46]: 19.02/19.28 X682( 19.02/19.28 V_46)), 19.02/19.28 X684) = 19.02/19.28 X682( 19.02/19.28 X684)))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X685, 19.02/19.28 X686,X687]: 19.02/19.28 (in( 19.02/19.28 X687, 19.02/19.28 funcSet( 19.02/19.28 X685,X686)) => 19.02/19.28 (lam( 19.02/19.28 X685, 19.02/19.28 X686, 19.02/19.28 ^[V_47]: 19.02/19.28 ap( 19.02/19.28 X685, 19.02/19.28 X686, 19.02/19.28 X687,V_47)) = 19.02/19.28 X687))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X688, 19.02/19.28 X689:$o, 19.02/19.28 X690]: 19.02/19.28 (in( 19.02/19.28 X690,X688) => 19.02/19.28 (![X691]: 19.02/19.28 (in( 19.02/19.28 X691,X688) => 19.02/19.28 (( 19.02/19.28 ~X689) => 19.02/19.28 in( 19.02/19.28 X691, 19.02/19.28 dsetconstr( 19.02/19.28 X688, 19.02/19.28 ^[V_48]: 19.02/19.28 (( 19.02/19.28 X689 & 19.02/19.28 ( 19.02/19.28 V_48 = 19.02/19.28 X690)) | 19.02/19.28 (( 19.02/19.28 ~X689) & 19.02/19.28 (V_48 = 19.02/19.28 X691)))))))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X692, 19.02/19.28 X693:$o, 19.02/19.28 X694]: 19.02/19.28 (in( 19.02/19.28 X694,X692) => 19.02/19.28 (![X695]: 19.02/19.28 (in( 19.02/19.28 X695,X692) => 19.02/19.28 (( 19.02/19.28 ~X693) => 19.02/19.28 (dsetconstr( 19.02/19.28 X692, 19.02/19.28 ^[V_49]: 19.02/19.28 (( 19.02/19.28 X693 & 19.02/19.28 ( 19.02/19.28 V_49 = 19.02/19.28 X694)) | 19.02/19.28 (( 19.02/19.28 ~X693) & 19.02/19.28 (V_49 = 19.02/19.28 X695)))) = 19.02/19.28 setadjoin( 19.02/19.28 X695, 19.02/19.28 emptyset))))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X696, 19.02/19.28 X697:$o, 19.02/19.28 X698]: 19.02/19.28 (in( 19.02/19.28 X698,X696) => 19.02/19.28 (![X699]: 19.02/19.28 (in( 19.02/19.28 X699,X696) => 19.02/19.28 (X697 => 19.02/19.28 in( 19.02/19.28 X698, 19.02/19.28 dsetconstr( 19.02/19.28 X696, 19.02/19.28 ^[V_50]: 19.02/19.28 (( 19.02/19.28 X697 & 19.02/19.28 ( 19.02/19.28 V_50 = 19.02/19.28 X698)) | 19.02/19.28 (( 19.02/19.28 ~X697) & 19.02/19.28 (V_50 = 19.02/19.28 X699)))))))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X700, 19.02/19.28 X701:$o, 19.02/19.28 X702]: 19.02/19.28 (in( 19.02/19.28 X702,X700) => 19.02/19.28 (![X703]: 19.02/19.28 (in( 19.02/19.28 X703,X700) => 19.02/19.28 (X701 => 19.02/19.28 (dsetconstr( 19.02/19.28 X700, 19.02/19.28 ^[V_51]: 19.02/19.28 (( 19.02/19.28 X701 & 19.02/19.28 ( 19.02/19.28 V_51 = 19.02/19.28 X702)) | 19.02/19.28 (( 19.02/19.28 ~X701) & 19.02/19.28 (V_51 = 19.02/19.28 X703)))) = 19.02/19.28 setadjoin( 19.02/19.28 X702, 19.02/19.28 emptyset))))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X704, 19.02/19.28 X705:$o, 19.02/19.28 X706]: 19.02/19.28 (in( 19.02/19.28 X706,X704) => 19.02/19.28 (![X707]: 19.02/19.28 (in( 19.02/19.28 X707,X704) => 19.02/19.28 singleton( 19.02/19.28 dsetconstr( 19.02/19.28 X704, 19.02/19.28 ^[V_52]: 19.02/19.28 (( 19.02/19.28 X705 & 19.02/19.28 ( 19.02/19.28 V_52 = 19.02/19.28 X706)) | 19.02/19.28 (( 19.02/19.28 ~X705) & 19.02/19.28 (V_52 = 19.02/19.28 X707))))))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X708, 19.02/19.28 X709:$o, 19.02/19.28 X710]: 19.02/19.28 (in( 19.02/19.28 X710,X708) => 19.02/19.28 (![X711]: 19.02/19.28 (in( 19.02/19.28 X711,X708) => 19.02/19.28 in( 19.02/19.28 if( 19.02/19.28 X708, 19.02/19.28 X709, 19.02/19.28 X710,X711), 19.02/19.28 X708))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X712]: 19.02/19.28 (singleton( 19.02/19.28 X712) => 19.02/19.28 (![X713]: 19.02/19.28 (in( 19.02/19.28 X713,X712) => 19.02/19.28 (setunion( 19.02/19.28 X712) = 19.02/19.28 X713))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X714, 19.02/19.28 X715:$o, 19.02/19.28 X716]: 19.02/19.28 (in( 19.02/19.28 X716,X714) => 19.02/19.28 (![X717]: 19.02/19.28 (in( 19.02/19.28 X717,X714) => 19.02/19.28 (X715 => 19.02/19.28 (if( 19.02/19.28 X714, 19.02/19.28 X715, 19.02/19.28 X716,X717) = 19.02/19.28 X716)))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X718, 19.02/19.28 X719:$o, 19.02/19.28 X720]: 19.02/19.28 (in( 19.02/19.28 X720,X718) => 19.02/19.28 (![X721]: 19.02/19.28 (in( 19.02/19.28 X721,X718) => 19.02/19.28 (( 19.02/19.28 ~X719) => 19.02/19.28 (if( 19.02/19.28 X718, 19.02/19.28 X719, 19.02/19.28 X720,X721) = 19.02/19.28 X721)))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X722, 19.02/19.28 X723:$o, 19.02/19.28 X724]: 19.02/19.28 (in( 19.02/19.28 X724,X722) => 19.02/19.28 (![X725]: 19.02/19.28 (in( 19.02/19.28 X725,X722) => 19.02/19.28 in( 19.02/19.28 if( 19.02/19.28 X722, 19.02/19.28 X723, 19.02/19.28 X724,X725), 19.02/19.28 setadjoin( 19.02/19.28 X724, 19.02/19.28 setadjoin( 19.02/19.28 X725, 19.02/19.28 emptyset))))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X726, 19.02/19.28 X727]: 19.02/19.28 (in( 19.02/19.28 X727, 19.02/19.28 powerset( 19.02/19.28 X726)) => 19.02/19.28 (![X728]: 19.02/19.28 (in( 19.02/19.28 X728, 19.02/19.28 powerset( 19.02/19.28 X726)) => 19.02/19.28 in( 19.02/19.28 binintersect( 19.02/19.28 X727,X728), 19.02/19.28 powerset( 19.02/19.28 X726)))))) => 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ![X729, 19.02/19.28 X730]: 19.02/19.28 (in( 19.02/19.28 X730, 19.02/19.28 powerset( 19.02/19.28 X729)) => 19.02/19.28 (![X731]: 19.02/19.28 (in( 19.02/19.28 X731, 19.02/19.28 powerset( 19.02/19.28 X729)) => 19.02/19.28 in( 19.02/19.28 binunion( 19.02/19.28 X730,X731), 19.02/19.28 powerset( 19.02/19.28 X729)))))) => 19.02/19.28 ( 19.02/19.28 ![X732, 19.02/19.28 X733]: 19.02/19.28 (in( 19.02/19.28 X733, 19.02/19.28 powerset( 19.02/19.28 X732)) => 19.02/19.28 in( 19.02/19.28 powerset( 19.02/19.28 X733), 19.02/19.28 powerset( 19.02/19.28 powerset( 19.02/19.28 X732)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 19.02/19.28 tff(zf_stmt_14, negated_conjecture, 19.02/19.28 (~ 19.02/19.28 ((![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))) => 19.02/19.28 ((![X5]: (~in(X5,emptyset))) => 19.02/19.28 ((![X6,X7,X8]: (in(X8,setadjoin(X6,X7)) <=> zip_tseitin0(X8,X7,X6))) => 19.02/19.28 ((![X9,X10]: 19.02/19.28 (in(X10,powerset(X9)) <=> (![X11]: zip_tseitin1(X11,X10,X9)))) => 19.02/19.28 ((![X12,X13]: 19.02/19.28 (in(X13,setunion(X12)) <=> (?[X14]: zip_tseitin2(X14,X13,X12)))) => 19.02/19.28 (in(emptyset,omega) => 19.02/19.28 ((![X15]: (in(X15,omega) => in(setadjoin(X15,X15),omega))) => 19.02/19.28 ((![X16]: 19.02/19.28 (((![X17]: 19.02/19.28 ((in(X17,X16) & in(X17,omega)) => 19.02/19.28 in(setadjoin(X17,X17),X16))) & 19.02/19.28 in(emptyset,X16)) => 19.02/19.28 (![X18]: (in(X18,omega) => in(X18,X16))))) => 19.02/19.28 ((![X19:(($i * $i) > $o),X20]: 19.02/19.28 ((![X21]: 19.02/19.28 (in(X21,X20) => 19.02/19.28 (?[X22]: 19.02/19.28 ((![X23]: (X19(X21,X23) => (X22 = X23))) & 19.02/19.28 X19(X21,X22))))) => 19.02/19.28 (?[X24]: 19.02/19.28 (![X25]: 19.02/19.28 (in(X25,X24) <=> 19.02/19.28 (?[X26]: zip_tseitin3(X26,X25,X20,X19))))))) => 19.02/19.28 ((![X27]: 19.02/19.28 ((?[X28]: in(X28,X27)) => 19.02/19.28 (?[X29]: 19.02/19.28 ((~(?[X30]: (in(X30,X27) & in(X30,X29)))) & in(X29,X27))))) => 19.02/19.28 ((![X31]: 19.02/19.28 (?[X32]: 19.02/19.28 ((![X33]: 19.02/19.28 (((?[X34]: in(X34,X33)) & 19.02/19.28 (![X35]: (in(X35,X33) => in(X35,X31)))) => 19.02/19.28 (?[X36,X37]: 19.02/19.28 ((![X38]: 19.02/19.28 (in(X38,X32) => 19.02/19.28 (in(X37,X38) | 19.02/19.28 (![X39]: (in(X39,X38) => in(X39,X36)))))) & 19.02/19.28 (~(?[X40]: (in(X40,X33) & in(X40,X36)))) & 19.02/19.28 in(X37,X33) & in(X36,X32))))) & 19.02/19.28 (![X41,X42]: 19.02/19.28 ((in(X42,X32) & in(X41,X32)) => 19.02/19.28 ((![X43]: (in(X43,X42) => in(X43,X41))) | 19.02/19.28 (![X44]: (in(X44,X41) => in(X44,X42)))))) & 19.02/19.28 (![X45,X46]: 19.02/19.28 ((in(X46,X31) & in(X45,X31)) => 19.02/19.28 ((![X47]: 19.02/19.28 (in(X47,X32) => (in(X45,X47) <=> in(X46,X47)))) => 19.02/19.28 (X45 = X46)))) & 19.02/19.28 (![X48]: 19.02/19.28 (in(X48,X32) => 19.02/19.28 (![X49]: (in(X49,X48) => in(X49,X31)))))))) => 19.02/19.28 ((![X50:($i > $o)]: 19.02/19.28 ((?[X51]: ((![X52]: (X50(X52) => (X51 = X52))) & X50(X51))) => 19.02/19.28 X50(descr(^[V_1]: X50(V_1))))) => 19.02/19.28 ((![X53,X54:($i > $o),X55]: 19.02/19.28 (in(X55,X53) => 19.02/19.28 (X54(X55) => in(X55,dsetconstr(X53,^[V_2]: X54(V_2)))))) => 19.02/19.28 ((![X56,X57:($i > $o),X58]: 19.02/19.28 (in(X58,dsetconstr(X56,^[V_3]: X57(V_3))) => in(X58,X56))) => 19.02/19.28 ((![X59,X60:($i > $o),X61]: 19.02/19.28 (in(X61,dsetconstr(X59,^[V_4]: X60(V_4))) => X60(X61))) => 19.02/19.28 ((![X62:($i > $o)]: 19.02/19.28 ((?[X63]: 19.02/19.28 ((![X64]: (X62(X64) => (X63 = X64))) & X62(X63))) => 19.02/19.28 (?[X65]: 19.02/19.28 ((![X66]: (X62(X66) => (X65 = X66))) & X62(X65))))) => 19.02/19.28 ((![X67:$o,X68]: (in(X68,prop2set(X67)) => X67)) => 19.02/19.28 ((![X69]: (in(X69,emptyset) => (![X70:$o]: X70))) => 19.02/19.28 ((![X71]: (in(X71,emptyset) => $false)) => 19.02/19.28 ((![X72]: (~in(X72,emptyset))) => 19.02/19.28 ((![X73:($i > $o)]: 19.02/19.28 ((?[X74]: 19.02/19.28 ((![X75]: (X73(X75) => (X74 = X75))) & 19.02/19.28 X73(X74))) => 19.02/19.28 (?[X76]: X73(X76)))) => 19.02/19.28 ((![X77,X78]: 19.02/19.28 ((![X79]: (in(X79,X77) => in(X79,X78))) => 19.02/19.28 ((![X80]: (in(X80,X78) => in(X80,X77))) => 19.02/19.28 (X77 = X78)))) => 19.02/19.28 ((![X81]: 19.02/19.28 ((![X82]: (~in(X82,X81))) => (X81 = emptyset))) => 19.02/19.28 ((![X83]: 19.02/19.28 ((![X84]: (~in(X84,X83))) => (X83 = emptyset))) => 19.02/19.28 ((![X85,X86:($i > $o),X87]: 19.02/19.28 (in(X87,X85) => 19.02/19.28 (in(X87,dsetconstr(X85,^[V_5]: X86(V_5))) <=> 19.02/19.28 X86(X87)))) => 19.02/19.28 ((![X88]: 19.02/19.28 ((X88 != emptyset) => (?[X89]: in(X89,X88)))) => 19.02/19.28 ((![X90,X91:($i > $o),X92]: 19.02/19.28 (in(X92,X90) => 19.02/19.28 (X91(X92) => 19.02/19.28 (dsetconstr(X90,^[V_6]: X91(V_6)) != 19.02/19.28 emptyset)))) => 19.02/19.28 ((![X93]: 19.02/19.28 ((?[X94]: in(X94,X93)) => 19.02/19.28 (X93 != emptyset))) => 19.02/19.28 ((![X95,X96]: in(X95,setadjoin(X95,X96))) => 19.02/19.28 (in(emptyset,setadjoin(emptyset,emptyset)) => 19.02/19.28 ((![X97,X98,X99]: 19.02/19.28 (in(X99,X98) => 19.02/19.28 in(X99,setadjoin(X97,X98)))) => 19.02/19.28 ((![X100,X101,X102]: 19.02/19.28 (in(X102,setadjoin(X100,X101)) => 19.02/19.28 (![X103:$o]: 19.02/19.28 (((X102 = X100) => X103) => 19.02/19.28 ((in(X102,X101) => X103) => X103))))) => 19.02/19.28 ((![X104,X105,X106]: 19.02/19.28 (in(X106,setadjoin(X104,X105)) => 19.02/19.28 (in(X106,X105) | (X106 = X104)))) => 19.02/19.28 ((![X107]: 19.02/19.28 (dsetconstr(X107,^[V_7]: $true) = 19.02/19.28 X107)) => 19.02/19.28 ((![X108,X109]: 19.02/19.28 ((![X110]: 19.02/19.28 (in(X110,X109) => in(X110,X108))) => 19.02/19.28 in(X109,powerset(X108)))) => 19.02/19.28 ((![X111]: in(emptyset,powerset(X111))) => 19.02/19.28 ((![X112]: 19.02/19.28 in(emptyset,powerset(X112))) => 19.02/19.28 ((![X113,X114,X115]: 19.02/19.28 (in(X114,powerset(X113)) => 19.02/19.28 (in(X115,X114) => in(X115,X113)))) => 19.02/19.28 ((![X116,X117,X118]: 19.02/19.28 (in(X117,X118) => 19.02/19.28 (in(X118,X116) => 19.02/19.28 in(X117,setunion(X116))))) => 19.02/19.28 ((![X119,X120]: 19.02/19.28 (in(X120,setunion(X119)) => 19.02/19.28 (![X121:$o]: 19.02/19.28 ((![X122]: 19.02/19.28 (in(X120,X122) => 19.02/19.28 (in(X122,X119) => 19.02/19.28 X121))) => 19.02/19.28 X121)))) => 19.02/19.28 ((![X123,X124]: 19.02/19.28 (in(X124,X123) => 19.02/19.28 in(X124, 19.02/19.28 powerset(setunion(X123))))) => 19.02/19.28 ((![X125:($i > $o)]: 19.02/19.28 ((?[X126]: 19.02/19.28 ((![X127]: 19.02/19.28 (X125(X127) => 19.02/19.28 (X126 = X127))) & 19.02/19.28 X125(X126))) => 19.02/19.28 (?[X128]: 19.02/19.28 (![X129]: 19.02/19.28 (X125(X129) <=> 19.02/19.28 (X129 = X128)))))) => 19.02/19.28 ((![X130]: 19.02/19.28 ((X130 != emptyset) => 19.02/19.28 (?[X131]: in(X131,X130)))) => 19.02/19.28 ((![X132,X133]: 19.02/19.28 (in(X132, 19.02/19.28 setadjoin(X133, 19.02/19.28 emptyset)) => 19.02/19.28 (X132 = X133))) => 19.02/19.28 ((![X134,X135]: 19.02/19.28 ((X134 != X135) => 19.02/19.28 (~ 19.02/19.28 in(X135, 19.02/19.28 setadjoin(X134, 19.02/19.28 emptyset))))) => 19.02/19.28 ((![X136,X137]: 19.02/19.28 ((X136 = X137) => 19.02/19.28 in(X136, 19.02/19.28 setadjoin(X137, 19.02/19.28 emptyset)))) => 19.02/19.28 ((![X138,X139]: 19.02/19.28 (in(X138, 19.02/19.28 setadjoin(X139, 19.02/19.28 emptyset)) => 19.02/19.28 in(X139, 19.02/19.28 setadjoin(X138, 19.02/19.28 emptyset)))) => 19.02/19.28 ((![X140,X141,X142]: 19.02/19.28 (in(X142, 19.02/19.28 setadjoin( 19.02/19.28 X140, 19.02/19.28 setadjoin( 19.02/19.28 X141,emptyset))) => 19.02/19.28 ((X142 = X141) | 19.02/19.28 (X142 = X140)))) => 19.02/19.28 ((![X143,X144]: 19.02/19.28 in(X143, 19.02/19.28 setadjoin( 19.02/19.28 X143, 19.02/19.28 setadjoin( 19.02/19.28 X144,emptyset)))) => 19.02/19.28 ((![X145,X146]: 19.02/19.28 in(X146, 19.02/19.28 setadjoin( 19.02/19.28 X145, 19.02/19.28 setadjoin( 19.02/19.28 X146,emptyset)))) => 19.02/19.28 ((![X147,X148:($i > $o)]: 19.02/19.28 ((?[X149]: 19.02/19.28 (X148(X149) & 19.02/19.28 in(X149,X147))) => 19.02/19.28 ((dsetconstr( 19.02/19.28 X147, 19.02/19.28 ^[V_8]: 19.02/19.28 X148(V_8)) = 19.02/19.28 emptyset) => 19.02/19.28 $false))) => 19.02/19.28 ((![X150:($i > $o), 19.02/19.28 X151]: 19.02/19.28 (in(X151,emptyset) => 19.02/19.28 X150(X151))) => 19.02/19.28 ((![X152, 19.02/19.28 X153:($i > $o)]: 19.02/19.28 ((~ 19.02/19.28 (![X154]: 19.02/19.28 (in( 19.02/19.28 X154,X152) => 19.02/19.28 X153(X154)))) => 19.02/19.28 (?[X155]: 19.02/19.28 ((~X153(X155)) & 19.02/19.28 in(X155,X152))))) => 19.02/19.28 ((![X156, 19.02/19.28 X157:($i > $o)]: 19.02/19.28 ((![X158]: 19.02/19.28 (in( 19.02/19.28 X158,X156) => 19.02/19.28 (~ 19.02/19.28 X157( 19.02/19.28 X158)))) => 19.02/19.28 (~ 19.02/19.28 (?[X159]: 19.02/19.28 (X157( 19.02/19.28 X159) & 19.02/19.28 in( 19.02/19.28 X159,X156)))))) => 19.02/19.28 ((![X160, 19.02/19.28 X161:($i > $o)]: 19.02/19.28 ((~ 19.02/19.28 (?[X162]: 19.02/19.28 ( 19.02/19.28 X161( 19.02/19.28 X162) & 19.02/19.28 in( 19.02/19.28 X162,X160)))) => 19.02/19.28 (![X163]: 19.02/19.28 (in( 19.02/19.28 X163,X160) => 19.02/19.28 (~ 19.02/19.28 X161( 19.02/19.28 X163)))))) => 19.02/19.28 ((![X164, 19.02/19.28 X165:( 19.02/19.28 $i > $o)]: 19.02/19.28 ((?[X166]: 19.02/19.28 (( 19.02/19.28 ~ 19.02/19.28 X165( 19.02/19.28 X166)) & 19.02/19.28 in( 19.02/19.28 X166,X164))) => 19.02/19.28 (~ 19.02/19.28 (![X167]: 19.02/19.28 (in( 19.02/19.28 X167,X164) => 19.02/19.28 X165( 19.02/19.28 X167)))))) => 19.02/19.28 ((![X168:$o]: 19.02/19.28 (X168 => 19.02/19.28 in(emptyset, 19.02/19.28 prop2set( 19.02/19.28 X168)))) => 19.02/19.28 ((![X169:$o]: 19.02/19.28 (X169 => 19.02/19.28 set2prop( 19.02/19.28 prop2set( 19.02/19.28 X169)))) => 19.02/19.28 ((![X170, 19.02/19.28 X171:( 19.02/19.28 $i > $o)]: 19.02/19.28 ((~ 19.02/19.28 ( 19.02/19.28 ?[X172]: 19.02/19.28 (X171( 19.02/19.28 X172) & 19.02/19.28 in( 19.02/19.28 X172,X170)))) => 19.02/19.28 (![X173]: 19.02/19.28 (in( 19.02/19.28 X173,X170) => 19.02/19.28 (~ 19.02/19.28 X171( 19.02/19.28 X173)))))) => 19.02/19.28 ((![X174, 19.02/19.28 X175:( 19.02/19.28 $i > $o)]: 19.02/19.28 (( 19.02/19.28 ~ 19.02/19.28 ( 19.02/19.28 ![X176]: 19.02/19.28 (in( 19.02/19.28 X176,X174) => 19.02/19.28 X175( 19.02/19.28 X176)))) => 19.02/19.28 ( 19.02/19.28 ?[X177]: 19.02/19.28 (( 19.02/19.28 ~ 19.02/19.28 X175( 19.02/19.28 X177)) & 19.02/19.28 in( 19.02/19.28 X177,X174))))) => 19.02/19.28 ((![X178:( 19.02/19.28 $i > $o)]: 19.02/19.28 ( 19.02/19.28 ( 19.02/19.28 ?[X179]: 19.02/19.28 (( 19.02/19.28 ![X180]: 19.02/19.28 (X178( 19.02/19.29 X180) => 19.02/19.29 (X179 = 19.02/19.29 X180))) & 19.02/19.29 X178( 19.02/19.29 X179))) => 19.02/19.29 ( 19.02/19.29 ?[X181]: 19.02/19.29 (( 19.02/19.29 ![X182]: 19.02/19.29 (X178( 19.02/19.29 X182) => 19.02/19.29 (X181 = 19.02/19.29 X182))) & 19.02/19.29 X178( 19.02/19.29 X181))))) => 19.02/19.29 ((![X183:( 19.02/19.29 $i > $o)]: 19.02/19.29 (( 19.02/19.29 ?[X184]: 19.02/19.29 X183( 19.02/19.29 X184)) => 19.02/19.29 (( 19.02/19.29 ![X185, 19.02/19.29 X186]: 19.02/19.29 (X183( 19.02/19.29 X185) => 19.02/19.29 (X183( 19.02/19.29 X186) => 19.02/19.29 (X185 = 19.02/19.29 X186)))) => 19.02/19.29 (?[X187]: 19.02/19.29 (( 19.02/19.29 ![X188]: 19.02/19.29 (X183( 19.02/19.29 X188) => 19.02/19.29 (X187 = 19.02/19.29 X188))) & 19.02/19.29 X183( 19.02/19.29 X187)))))) => 19.02/19.29 ((![X189:( 19.02/19.29 $i > $o)]: 19.02/19.29 (( 19.02/19.29 ?[X190]: 19.02/19.29 (![X191]: 19.02/19.29 (X189( 19.02/19.29 X191) <=> 19.02/19.29 (X191 = 19.02/19.29 X190)))) => 19.02/19.29 (?[X192]: 19.02/19.29 (( 19.02/19.29 ![X193]: 19.02/19.29 (X189( 19.02/19.29 X193) => 19.02/19.29 (X192 = 19.02/19.29 X193))) & 19.02/19.29 X189( 19.02/19.29 X192))))) => 19.02/19.29 (( 19.02/19.29 ![X194, 19.02/19.29 X195]: 19.02/19.29 (( 19.02/19.29 X194 = 19.02/19.29 X195) => 19.02/19.29 (![X196, 19.02/19.29 X197]: 19.02/19.29 (( 19.02/19.29 X196 = 19.02/19.29 X197) => 19.02/19.29 (in( 19.02/19.29 X196,X194) => 19.02/19.29 in( 19.02/19.29 X197,X195)))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X198, 19.02/19.29 X199]: 19.02/19.29 (( 19.02/19.29 X198 = 19.02/19.29 X199) => 19.02/19.29 (![X200, 19.02/19.29 X201]: 19.02/19.29 (( 19.02/19.29 X200 = 19.02/19.29 X201) => 19.02/19.29 (in( 19.02/19.29 X200,X198) <=> 19.02/19.29 in( 19.02/19.29 X201,X199)))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X202:( 19.02/19.29 $i > $o)]: 19.02/19.29 (( 19.02/19.29 ?[X203]: 19.02/19.29 (( 19.02/19.29 ![X204]: 19.02/19.29 (X202( 19.02/19.29 X204) => 19.02/19.29 (X203 = 19.02/19.29 X204))) & 19.02/19.29 X202( 19.02/19.29 X203))) => 19.02/19.29 (![X205, 19.02/19.29 X206]: 19.02/19.29 (X202( 19.02/19.29 X205) => 19.02/19.29 (X202( 19.02/19.29 X206) => 19.02/19.29 (X205 = 19.02/19.29 X206)))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X207:( 19.02/19.29 $i > $o), 19.02/19.29 X208:( 19.02/19.29 $i > $o)]: 19.02/19.29 (( 19.02/19.29 ![X209, 19.02/19.29 X210]: 19.02/19.29 (( 19.02/19.29 X209 = 19.02/19.29 X210) => 19.02/19.29 (X207( 19.02/19.29 X209) <=> 19.02/19.29 X208( 19.02/19.29 X210)))) => 19.02/19.29 (( 19.02/19.29 ?[X211]: 19.02/19.29 zip_tseitin5( 19.02/19.29 X211,X207)) <=> 19.02/19.29 (?[X213]: 19.02/19.29 zip_tseitin5( 19.02/19.29 X213,X208))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 emptyset = 19.02/19.29 emptyset) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X215, 19.02/19.29 X216]: 19.02/19.29 (( 19.02/19.29 X215 = 19.02/19.29 X216) => 19.02/19.29 (![X217, 19.02/19.29 X218]: 19.02/19.29 (( 19.02/19.29 X217 = 19.02/19.29 X218) => 19.02/19.29 (setadjoin( 19.02/19.29 X215,X217) = 19.02/19.29 setadjoin( 19.02/19.29 X216,X218)))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X219, 19.02/19.29 X220]: 19.02/19.29 (( 19.02/19.29 X219 = 19.02/19.29 X220) => 19.02/19.29 (powerset( 19.02/19.29 X219) = 19.02/19.29 powerset( 19.02/19.29 X220)))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X221, 19.02/19.29 X222]: 19.02/19.29 (( 19.02/19.29 X221 = 19.02/19.29 X222) => 19.02/19.29 (setunion( 19.02/19.29 X221) = 19.02/19.29 setunion( 19.02/19.29 X222)))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 omega = 19.02/19.29 omega) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X223:( 19.02/19.29 $i > $o)]: 19.02/19.29 (( 19.02/19.29 ?[X224]: 19.02/19.29 (( 19.02/19.29 ![X225]: 19.02/19.29 (X223( 19.02/19.29 X225) => 19.02/19.29 (X224 = 19.02/19.29 X225))) & 19.02/19.29 X223( 19.02/19.29 X224))) => 19.02/19.29 (![X226, 19.02/19.29 X227]: 19.02/19.29 (X223( 19.02/19.29 X226) => 19.02/19.29 (X223( 19.02/19.29 X227) => 19.02/19.29 (X226 = 19.02/19.29 X227)))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X228:( 19.02/19.29 $i > $o), 19.02/19.29 X229:( 19.02/19.29 $i > $o)]: 19.02/19.29 (( 19.02/19.29 ![X230, 19.02/19.29 X231]: 19.02/19.29 (( 19.02/19.29 X230 = 19.02/19.29 X231) => 19.02/19.29 (X228( 19.02/19.29 X230) <=> 19.02/19.29 X229( 19.02/19.29 X231)))) => 19.02/19.29 (( 19.02/19.29 ?[X232]: 19.02/19.29 (( 19.02/19.29 ![X233]: 19.02/19.29 (X228( 19.02/19.29 X233) => 19.02/19.29 (X232 = 19.02/19.29 X233))) & 19.02/19.29 X228( 19.02/19.29 X232))) => 19.02/19.29 (( 19.02/19.29 ?[X234]: 19.02/19.29 (( 19.02/19.29 ![X235]: 19.02/19.29 (X229( 19.02/19.29 X235) => 19.02/19.29 (X234 = 19.02/19.29 X235))) & 19.02/19.29 X229( 19.02/19.29 X234))) => 19.02/19.29 (descr( 19.02/19.29 ^[V_9]: 19.02/19.29 X228(V_9)) = 19.02/19.29 descr( 19.02/19.29 ^[V_10]: 19.02/19.29 X229( 19.02/19.29 V_10))))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X236, 19.02/19.29 X237]: 19.02/19.29 (( 19.02/19.29 X236 = 19.02/19.29 X237) => 19.02/19.29 (![X238:( 19.02/19.29 $i > $o), 19.02/19.29 X239:( 19.02/19.29 $i > $o)]: 19.02/19.29 (( 19.02/19.29 ![X240]: 19.02/19.29 (in( 19.02/19.29 X240,X236) => 19.02/19.29 (![X241]: 19.02/19.29 (in( 19.02/19.29 X241,X237) => 19.02/19.29 (( 19.02/19.29 X240 = 19.02/19.29 X241) => 19.02/19.29 (X238( 19.02/19.29 X240) <=> 19.02/19.29 X239( 19.02/19.29 X241))))))) => 19.02/19.29 (dsetconstr( 19.02/19.29 X236, 19.02/19.29 ^[V_11]: 19.02/19.29 X238( 19.02/19.29 V_11)) = 19.02/19.29 dsetconstr( 19.02/19.29 X237, 19.02/19.29 ^[V_12]: 19.02/19.29 X239( 19.02/19.29 V_12))))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X242, 19.02/19.29 X243]: 19.02/19.29 (( 19.02/19.29 ![X244]: 19.02/19.29 (in( 19.02/19.29 X244,X242) => 19.02/19.29 in( 19.02/19.29 X244,X243))) => 19.02/19.29 subset( 19.02/19.29 X242,X243))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X245, 19.02/19.29 X246]: 19.02/19.29 (( 19.02/19.29 X245 = 19.02/19.29 X246) => 19.02/19.29 subset( 19.02/19.29 X246,X245))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X247, 19.02/19.29 X248]: 19.02/19.29 (( 19.02/19.29 X247 = 19.02/19.29 X248) => 19.02/19.29 subset( 19.02/19.29 X247,X248))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X249, 19.02/19.29 X250]: 19.02/19.29 (( 19.02/19.29 ![X251]: 19.02/19.29 (in( 19.02/19.29 X251,X249) => 19.02/19.29 in( 19.02/19.29 X251,X250))) => 19.02/19.29 subset( 19.02/19.29 X249,X250))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X252]: 19.02/19.29 subset( 19.02/19.29 emptyset, 19.02/19.29 X252)) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X253, 19.02/19.29 X254,X255]: 19.02/19.29 (subset( 19.02/19.29 X253,X254) => 19.02/19.29 (in( 19.02/19.29 X255,X253) => 19.02/19.29 in( 19.02/19.29 X255,X254)))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X256, 19.02/19.29 X257,X258]: 19.02/19.29 (subset( 19.02/19.29 X256,X257) => 19.02/19.29 (( 19.02/19.29 ~ 19.02/19.29 in( 19.02/19.29 X258,X257)) => 19.02/19.29 (~ 19.02/19.29 in( 19.02/19.29 X258,X256))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X259, 19.02/19.29 X260,X261]: 19.02/19.29 (in( 19.02/19.29 X261,X259) => 19.02/19.29 (( 19.02/19.29 ~ 19.02/19.29 in( 19.02/19.29 X261,X260)) => 19.02/19.29 (~ 19.02/19.29 subset( 19.02/19.29 X259,X260))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X262, 19.02/19.29 X263]: 19.02/19.29 (( 19.02/19.29 ~ 19.02/19.29 subset( 19.02/19.29 X262,X263)) => 19.02/19.29 (X262 != 19.02/19.29 X263))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X264, 19.02/19.29 X265,X266]: 19.02/19.29 (in( 19.02/19.29 X266,X264) => 19.02/19.29 (( 19.02/19.29 ~ 19.02/19.29 in( 19.02/19.29 X266,X265)) => 19.02/19.29 (X264 != 19.02/19.29 X265)))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X267]: 19.02/19.29 subset( 19.02/19.29 X267,X267)) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X268, 19.02/19.29 X269,X270]: 19.02/19.29 (subset( 19.02/19.29 X268,X269) => 19.02/19.29 (subset( 19.02/19.29 X269,X270) => 19.02/19.29 subset( 19.02/19.29 X268,X270)))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X271, 19.02/19.29 X272]: 19.02/19.29 subset( 19.02/19.29 X272, 19.02/19.29 setadjoin( 19.02/19.29 X271,X272))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X273, 19.02/19.29 X274,X275]: 19.02/19.29 (subset( 19.02/19.29 X273,X275) => 19.02/19.29 subset( 19.02/19.29 X273, 19.02/19.29 setadjoin( 19.02/19.29 X274,X275)))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X276, 19.02/19.29 X277]: 19.02/19.29 (subset( 19.02/19.29 X276,X277) => 19.02/19.29 in( 19.02/19.29 X276, 19.02/19.29 powerset( 19.02/19.29 X277)))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X278, 19.02/19.29 X279]: 19.02/19.29 (subset( 19.02/19.29 X278,X279) => 19.02/19.29 (subset( 19.02/19.29 X279,X278) => 19.02/19.29 (X278 = 19.02/19.29 X279)))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X280]: 19.02/19.29 (subset( 19.02/19.29 X280, 19.02/19.29 emptyset) => 19.02/19.29 (X280 = 19.02/19.29 emptyset))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X281, 19.02/19.29 X282]: 19.02/19.29 (subset( 19.02/19.29 X282,X281) => 19.02/19.29 in( 19.02/19.29 X282, 19.02/19.29 powerset( 19.02/19.29 X281)))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X283, 19.02/19.29 X284]: 19.02/19.29 (in( 19.02/19.29 X284, 19.02/19.29 powerset( 19.02/19.29 X283)) => 19.02/19.29 subset( 19.02/19.29 X284,X283))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X285]: 19.02/19.29 in( 19.02/19.29 X285, 19.02/19.29 powerset( 19.02/19.29 X285))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X286, 19.02/19.29 X287]: 19.02/19.29 (subset( 19.02/19.29 X286,X287) => 19.02/19.29 subset( 19.02/19.29 powerset( 19.02/19.29 X286), 19.02/19.29 powerset( 19.02/19.29 X287)))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X288, 19.02/19.29 X289:( 19.02/19.29 $i > $o)]: 19.02/19.29 in( 19.02/19.29 dsetconstr( 19.02/19.29 X288, 19.02/19.29 ^[V_13]: 19.02/19.29 X289( 19.02/19.29 V_13)), 19.02/19.29 powerset( 19.02/19.29 X288))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X290, 19.02/19.29 X291:( 19.02/19.29 $i > $o)]: 19.02/19.29 subset( 19.02/19.29 dsetconstr( 19.02/19.29 X290, 19.02/19.29 ^[V_14]: 19.02/19.29 X291( 19.02/19.29 V_14)), 19.02/19.29 X290)) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X292, 19.02/19.29 X293,X294]: 19.02/19.29 (in( 19.02/19.29 X294,X292) => 19.02/19.29 in( 19.02/19.29 X294, 19.02/19.29 binunion( 19.02/19.29 X292,X293)))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X295, 19.02/19.29 X296]: 19.02/19.29 in( 19.02/19.29 X296, 19.02/19.29 setadjoin( 19.02/19.29 X295, 19.02/19.29 setadjoin( 19.02/19.29 X296, 19.02/19.29 emptyset)))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X297, 19.02/19.29 X298,X299]: 19.02/19.29 (in( 19.02/19.29 X299,X298) => 19.02/19.29 in( 19.02/19.29 X299, 19.02/19.29 binunion( 19.02/19.29 X297,X298)))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X300, 19.02/19.29 X301, 19.02/19.29 X302, 19.02/19.29 X303:$o]: 19.02/19.29 (in( 19.02/19.29 X302, 19.02/19.29 binunion( 19.02/19.29 X300,X301)) => 19.02/19.29 (( 19.02/19.29 in( 19.02/19.29 X302,X300) => 19.02/19.29 X303) => 19.02/19.29 (( 19.02/19.29 in( 19.02/19.29 X302,X301) => 19.02/19.29 X303) => 19.02/19.29 X303)))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X304, 19.02/19.29 X305,X306]: 19.02/19.29 (in( 19.02/19.29 X306, 19.02/19.29 binunion( 19.02/19.29 X304,X305)) => 19.02/19.29 (in( 19.02/19.29 X306,X305) | 19.02/19.29 in( 19.02/19.29 X306,X304)))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X307, 19.02/19.29 X308]: 19.02/19.29 subset( 19.02/19.29 X307, 19.02/19.29 binunion( 19.02/19.29 X307,X308))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X309, 19.02/19.29 X310]: 19.02/19.29 subset( 19.02/19.29 X310, 19.02/19.29 binunion( 19.02/19.29 X309,X310))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X311, 19.02/19.29 X312,X313]: 19.02/19.29 (in( 19.02/19.29 X313,X311) => 19.02/19.29 (in( 19.02/19.29 X313,X312) => 19.02/19.29 in( 19.02/19.29 X313, 19.02/19.29 binintersect( 19.02/19.29 X311,X312))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X314, 19.02/19.29 X315,X316]: 19.02/19.29 (subset( 19.02/19.29 X316,X314) => 19.02/19.29 (subset( 19.02/19.29 X316,X315) => 19.02/19.29 subset( 19.02/19.29 X316, 19.02/19.29 binintersect( 19.02/19.29 X314,X315))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X317, 19.02/19.29 X318,X319]: 19.02/19.29 (in( 19.02/19.29 X319, 19.02/19.29 binintersect( 19.02/19.29 X317,X318)) => 19.02/19.29 in( 19.02/19.29 X319,X317))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X320, 19.02/19.29 X321]: 19.02/19.29 subset( 19.02/19.29 binintersect( 19.02/19.29 X320,X321), 19.02/19.29 X320)) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X322, 19.02/19.29 X323]: 19.02/19.29 (subset( 19.02/19.29 X322,X323) => 19.02/19.29 (binintersect( 19.02/19.29 X322,X323) = 19.02/19.29 X322))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X324, 19.02/19.29 X325]: 19.02/19.29 (( 19.02/19.29 binintersect( 19.02/19.29 X324,X325) = 19.02/19.29 X325) => 19.02/19.29 subset( 19.02/19.29 X325,X324))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X326, 19.02/19.29 X327,X328]: 19.02/19.29 (in( 19.02/19.29 X328, 19.02/19.29 binintersect( 19.02/19.29 X326,X327)) => 19.02/19.29 in( 19.02/19.29 X328,X327))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X329, 19.02/19.29 X330]: 19.02/19.29 (( 19.02/19.29 ~ 19.02/19.29 ( 19.02/19.29 ?[X331]: 19.02/19.29 (in( 19.02/19.29 X331,X330) & 19.02/19.29 in( 19.02/19.29 X331,X329)))) => 19.02/19.29 (binintersect( 19.02/19.29 X329,X330) = 19.02/19.29 emptyset))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X332, 19.02/19.29 X333]: 19.02/19.29 subset( 19.02/19.29 binintersect( 19.02/19.29 X332,X333), 19.02/19.29 X333)) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X334, 19.02/19.29 X335]: 19.02/19.29 (subset( 19.02/19.29 X335,X334) => 19.02/19.29 (binintersect( 19.02/19.29 X334,X335) = 19.02/19.29 X335))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X336, 19.02/19.29 X337]: 19.02/19.29 (( 19.02/19.29 binintersect( 19.02/19.29 X336,X337) = 19.02/19.29 X336) => 19.02/19.29 subset( 19.02/19.29 X336,X337))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X338, 19.02/19.29 X339,X340]: 19.02/19.29 (binintersect( 19.02/19.29 X338, 19.02/19.29 binunion( 19.02/19.29 X339,X340)) = 19.02/19.29 binunion( 19.02/19.29 binintersect( 19.02/19.29 X338,X339), 19.02/19.29 binintersect( 19.02/19.29 X338,X340)))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X341, 19.02/19.29 X342,X343]: 19.02/19.29 (in( 19.02/19.29 X343,X341) => 19.02/19.29 (( 19.02/19.29 ~ 19.02/19.29 in( 19.02/19.29 X343,X342)) => 19.02/19.29 in( 19.02/19.29 X343, 19.02/19.29 setminus( 19.02/19.29 X341,X342))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X344, 19.02/19.29 X345,X346]: 19.02/19.29 (in( 19.02/19.29 X346, 19.02/19.29 setminus( 19.02/19.29 X344,X345)) => 19.02/19.29 in( 19.02/19.29 X346,X344))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X347, 19.02/19.29 X348,X349]: 19.02/19.29 (in( 19.02/19.29 X349, 19.02/19.29 setminus( 19.02/19.29 X347,X348)) => 19.02/19.29 (~ 19.02/19.29 in( 19.02/19.29 X349,X348)))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X350, 19.02/19.29 X351]: 19.02/19.29 (subset( 19.02/19.29 X350,X351) => 19.02/19.29 (setminus( 19.02/19.29 X350,X351) = 19.02/19.29 emptyset))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X352, 19.02/19.29 X353,X354]: 19.02/19.29 (( 19.02/19.29 ~ 19.02/19.29 in( 19.02/19.29 X354, 19.02/19.29 setminus( 19.02/19.29 X352,X353))) => 19.02/19.29 (in( 19.02/19.29 X354,X352) => 19.02/19.29 in( 19.02/19.29 X354,X353)))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X355, 19.02/19.29 X356,X357]: 19.02/19.29 (( 19.02/19.29 ~ 19.02/19.29 in( 19.02/19.29 X357, 19.02/19.29 setminus( 19.02/19.29 X355,X356))) => 19.02/19.29 (( 19.02/19.29 ~ 19.02/19.29 in( 19.02/19.29 X357,X356)) => 19.02/19.29 (~ 19.02/19.29 in( 19.02/19.29 X357,X355))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X358, 19.02/19.29 X359,X360]: 19.02/19.29 (( 19.02/19.29 ~ 19.02/19.29 in( 19.02/19.29 X360,X358)) => 19.02/19.29 (~ 19.02/19.29 in( 19.02/19.29 X360, 19.02/19.29 setminus( 19.02/19.29 X358,X359))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X361, 19.02/19.29 X362,X363]: 19.02/19.29 (in( 19.02/19.29 X363,X362) => 19.02/19.29 (~ 19.02/19.29 in( 19.02/19.29 X363, 19.02/19.29 setminus( 19.02/19.29 X361,X362))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X364, 19.02/19.29 X365]: 19.02/19.29 subset( 19.02/19.29 setminus( 19.02/19.29 X364,X365), 19.02/19.29 X364)) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X366, 19.02/19.29 X367]: 19.02/19.29 (( 19.02/19.29 setminus( 19.02/19.29 X366,X367) = 19.02/19.29 emptyset) => 19.02/19.29 subset( 19.02/19.29 X366,X367))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X368, 19.02/19.29 X369,X370]: 19.02/19.29 (in( 19.02/19.29 X370, 19.02/19.29 symdiff( 19.02/19.29 X368,X369)) => 19.02/19.29 (![X371:$o]: 19.02/19.29 (( 19.02/19.29 in( 19.02/19.29 X370,X368) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ~ 19.02/19.29 in( 19.02/19.29 X370,X369)) => 19.02/19.29 X371)) => 19.02/19.29 (( 19.02/19.29 ( 19.02/19.29 ~ 19.02/19.29 in( 19.02/19.29 X370,X368)) => 19.02/19.29 ( 19.02/19.29 in( 19.02/19.29 X370,X369) => 19.02/19.29 X371)) => 19.02/19.29 X371))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X372, 19.02/19.29 X373,X374]: 19.02/19.29 (in( 19.02/19.29 X374,X372) => 19.02/19.29 (( 19.02/19.29 ~ 19.02/19.29 in( 19.02/19.29 X374,X373)) => 19.02/19.29 in( 19.02/19.29 X374, 19.02/19.29 symdiff( 19.02/19.29 X372,X373))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X375, 19.02/19.29 X376,X377]: 19.02/19.29 (( 19.02/19.29 ~ 19.02/19.29 in( 19.02/19.29 X377,X375)) => 19.02/19.29 (in( 19.02/19.29 X377,X376) => 19.02/19.29 in( 19.02/19.29 X377, 19.02/19.29 symdiff( 19.02/19.29 X375,X376))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X378, 19.02/19.29 X379,X380]: 19.02/19.29 (in( 19.02/19.29 X380,X378) => 19.02/19.29 (in( 19.02/19.29 X380,X379) => 19.02/19.29 (~ 19.02/19.29 in( 19.02/19.29 X380, 19.02/19.29 symdiff( 19.02/19.29 X378,X379)))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X381, 19.02/19.29 X382,X383]: 19.02/19.29 (( 19.02/19.29 ~ 19.02/19.29 in( 19.02/19.29 X383,X381)) => 19.02/19.29 (( 19.02/19.29 ~ 19.02/19.29 in( 19.02/19.29 X383,X382)) => 19.02/19.29 (~ 19.02/19.29 in( 19.02/19.29 X383, 19.02/19.29 symdiff( 19.02/19.29 X381,X382)))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X384, 19.02/19.29 X385]: 19.02/19.29 in( 19.02/19.29 X385, 19.02/19.29 setadjoin( 19.02/19.29 X384, 19.02/19.29 setadjoin( 19.02/19.29 X385, 19.02/19.29 emptyset)))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X386, 19.02/19.29 X387]: 19.02/19.29 in( 19.02/19.29 X386, 19.02/19.29 setunion( 19.02/19.29 setadjoin( 19.02/19.29 setadjoin( 19.02/19.29 X386, 19.02/19.29 emptyset), 19.02/19.29 setadjoin( 19.02/19.29 setadjoin( 19.02/19.29 X386, 19.02/19.29 setadjoin( 19.02/19.29 X387, 19.02/19.29 emptyset)), 19.02/19.29 emptyset))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X388, 19.02/19.29 X389]: 19.02/19.29 in( 19.02/19.29 X389, 19.02/19.29 setunion( 19.02/19.29 setadjoin( 19.02/19.29 setadjoin( 19.02/19.29 X388, 19.02/19.29 emptyset), 19.02/19.29 setadjoin( 19.02/19.29 setadjoin( 19.02/19.29 X388, 19.02/19.29 setadjoin( 19.02/19.29 X389, 19.02/19.29 emptyset)), 19.02/19.29 emptyset))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X390, 19.02/19.29 X391]: 19.02/19.29 iskpair( 19.02/19.29 setadjoin( 19.02/19.29 setadjoin( 19.02/19.29 X390, 19.02/19.29 emptyset), 19.02/19.29 setadjoin( 19.02/19.29 setadjoin( 19.02/19.29 X390, 19.02/19.29 setadjoin( 19.02/19.29 X391, 19.02/19.29 emptyset)), 19.02/19.29 emptyset)))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X392, 19.02/19.29 X393]: 19.02/19.29 iskpair( 19.02/19.29 kpair( 19.02/19.29 X392,X393))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X394, 19.02/19.29 X395]: 19.02/19.29 (in( 19.02/19.29 X395,X394) => 19.02/19.29 subset( 19.02/19.29 setadjoin( 19.02/19.29 X395, 19.02/19.29 emptyset), 19.02/19.29 X394))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X396, 19.02/19.29 X397]: 19.02/19.29 (in( 19.02/19.29 X397,X396) => 19.02/19.29 in( 19.02/19.29 setadjoin( 19.02/19.29 X397, 19.02/19.29 emptyset), 19.02/19.29 powerset( 19.02/19.29 X396)))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X398, 19.02/19.29 X399,X400]: 19.02/19.29 (in( 19.02/19.29 X400,X398) => 19.02/19.29 in( 19.02/19.29 setadjoin( 19.02/19.29 X400, 19.02/19.29 emptyset), 19.02/19.29 powerset( 19.02/19.29 binunion( 19.02/19.29 X398,X399))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X401, 19.02/19.29 X402,X403]: 19.02/19.29 (in( 19.02/19.29 X403, 19.02/19.29 setadjoin( 19.02/19.29 X401, 19.02/19.29 setadjoin( 19.02/19.29 X402, 19.02/19.29 emptyset))) => 19.02/19.29 (( 19.02/19.29 X403 = 19.02/19.29 X402) | 19.02/19.29 (X403 = 19.02/19.29 X401)))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X404, 19.02/19.29 X405,X406]: 19.02/19.29 (in( 19.02/19.29 X406,X404) => 19.02/19.29 (![X407]: 19.02/19.29 (in( 19.02/19.29 X407,X405) => 19.02/19.29 subset( 19.02/19.29 setadjoin( 19.02/19.29 X406, 19.02/19.29 setadjoin( 19.02/19.29 X407, 19.02/19.29 emptyset)), 19.02/19.29 binunion( 19.02/19.29 X404,X405)))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X408, 19.02/19.29 X409,X410]: 19.02/19.29 (in( 19.02/19.29 X410,X408) => 19.02/19.29 (![X411]: 19.02/19.29 (in( 19.02/19.29 X411,X409) => 19.02/19.29 in( 19.02/19.29 setadjoin( 19.02/19.29 X410, 19.02/19.29 setadjoin( 19.02/19.29 X411, 19.02/19.29 emptyset)), 19.02/19.29 powerset( 19.02/19.29 binunion( 19.02/19.29 X408,X409))))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X412, 19.02/19.29 X413,X414]: 19.02/19.29 (in( 19.02/19.29 X414,X412) => 19.02/19.29 (![X415]: 19.02/19.29 (in( 19.02/19.29 X415,X413) => 19.02/19.29 subset( 19.02/19.29 setadjoin( 19.02/19.29 setadjoin( 19.02/19.29 X414, 19.02/19.29 emptyset), 19.02/19.29 setadjoin( 19.02/19.29 setadjoin( 19.02/19.29 X414, 19.02/19.29 setadjoin( 19.02/19.29 X415, 19.02/19.29 emptyset)), 19.02/19.29 emptyset)), 19.02/19.29 powerset( 19.02/19.29 binunion( 19.02/19.29 X412,X413))))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X416, 19.02/19.29 X417,X418]: 19.02/19.29 (in( 19.02/19.29 X418,X416) => 19.02/19.29 (![X419]: 19.02/19.29 (in( 19.02/19.29 X419,X417) => 19.02/19.29 in( 19.02/19.29 setadjoin( 19.02/19.29 setadjoin( 19.02/19.29 X418, 19.02/19.29 emptyset), 19.02/19.29 setadjoin( 19.02/19.29 setadjoin( 19.02/19.29 X418, 19.02/19.29 setadjoin( 19.02/19.29 X419, 19.02/19.29 emptyset)), 19.02/19.29 emptyset)), 19.02/19.29 powerset( 19.02/19.29 powerset( 19.02/19.29 binunion( 19.02/19.29 X416,X417)))))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X420, 19.02/19.29 X421,X422]: 19.02/19.29 (in( 19.02/19.29 X422,X420) => 19.02/19.29 (![X423]: 19.02/19.29 (in( 19.02/19.29 X423,X421) => 19.02/19.29 in( 19.02/19.29 kpair( 19.02/19.29 X422,X423), 19.02/19.29 powerset( 19.02/19.29 powerset( 19.02/19.29 binunion( 19.02/19.29 X420,X421)))))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X424, 19.02/19.29 X425,X426]: 19.02/19.29 (in( 19.02/19.29 X426,X424) => 19.02/19.29 (![X427]: 19.02/19.29 (in( 19.02/19.29 X427,X425) => 19.02/19.29 in( 19.02/19.29 kpair( 19.02/19.29 X426,X427), 19.02/19.29 cartprod( 19.02/19.29 X424,X425)))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X428, 19.02/19.29 X429,X430]: 19.02/19.29 (in( 19.02/19.29 X430, 19.02/19.29 cartprod( 19.02/19.29 X428,X429)) => 19.02/19.29 (?[X431]: 19.02/19.29 (( 19.02/19.29 ?[X432]: 19.02/19.29 (( 19.02/19.29 X430 = 19.02/19.29 kpair( 19.02/19.29 X431,X432)) & 19.02/19.29 in( 19.02/19.29 X432,X429))) & 19.02/19.29 in( 19.02/19.29 X431,X428))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X433, 19.02/19.29 X434,X435]: 19.02/19.29 (in( 19.02/19.29 X435, 19.02/19.29 cartprod( 19.02/19.29 X433,X434)) => 19.02/19.29 iskpair( 19.02/19.29 X435))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X436, 19.02/19.29 X437]: 19.02/19.29 (in( 19.02/19.29 X437, 19.02/19.29 setunion( 19.02/19.29 X436)) => 19.02/19.29 (?[X438]: 19.02/19.29 (in( 19.02/19.29 X437,X438) & 19.02/19.29 in( 19.02/19.29 X438,X436))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X439]: 19.02/19.29 subset( 19.02/19.29 setunion( 19.02/19.29 setadjoin( 19.02/19.29 X439, 19.02/19.29 emptyset)), 19.02/19.29 X439)) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X440]: 19.02/19.29 subset( 19.02/19.29 X440, 19.02/19.29 setunion( 19.02/19.29 setadjoin( 19.02/19.29 X440, 19.02/19.29 emptyset)))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X441]: 19.02/19.29 (setunion( 19.02/19.29 setadjoin( 19.02/19.29 X441, 19.02/19.29 emptyset)) = 19.02/19.29 X441)) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X442, 19.02/19.29 X443:( 19.02/19.29 $i > $o)]: 19.02/19.29 (( 19.02/19.29 ![X444]: 19.02/19.29 (in( 19.02/19.29 X444,X442) => 19.02/19.29 (![X445]: 19.02/19.29 (in( 19.02/19.29 X445,X442) => 19.02/19.29 (X443( 19.02/19.29 X444) => 19.02/19.29 (X443( 19.02/19.29 X445) => 19.02/19.29 (X444 = 19.02/19.29 X445))))))) => 19.02/19.29 (( 19.02/19.29 ?[X446]: 19.02/19.29 (X443( 19.02/19.29 X446) & 19.02/19.29 in( 19.02/19.29 X446,X442))) => 19.02/19.29 singleton( 19.02/19.29 dsetconstr( 19.02/19.29 X442, 19.02/19.29 ^[V_15]: 19.02/19.29 X443( 19.02/19.29 V_15)))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X447, 19.02/19.29 X448:( 19.02/19.29 $i > $o)]: 19.02/19.29 (singleton( 19.02/19.29 dsetconstr( 19.02/19.29 X447, 19.02/19.29 ^[V_16]: 19.02/19.29 X448( 19.02/19.29 V_16))) => 19.02/19.29 (?[X449]: 19.02/19.29 (X448( 19.02/19.29 X449) & 19.02/19.29 in( 19.02/19.29 X449,X447))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X450, 19.02/19.29 X451:( 19.02/19.29 $i > $o), 19.02/19.29 X452]: 19.02/19.29 (in( 19.02/19.29 X452,X450) => 19.02/19.29 (X451( 19.02/19.29 X452) => 19.02/19.29 (( 19.02/19.29 ![X453]: 19.02/19.29 (in( 19.02/19.29 X453,X450) => 19.02/19.29 (X451( 19.02/19.29 X453) => 19.02/19.29 (X453 = 19.02/19.29 X452)))) => 19.02/19.29 singleton( 19.02/19.29 dsetconstr( 19.02/19.29 X450, 19.02/19.29 ^[V_17]: 19.02/19.29 X451( 19.02/19.29 V_17))))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X454, 19.02/19.29 X455:( 19.02/19.29 $i > $o)]: 19.02/19.29 (( 19.02/19.29 ![X456]: 19.02/19.29 (in( 19.02/19.29 X456,X454) => 19.02/19.29 (![X457]: 19.02/19.29 (in( 19.02/19.29 X457,X454) => 19.02/19.29 (X455( 19.02/19.29 X456) => 19.02/19.29 (X455( 19.02/19.29 X457) => 19.02/19.29 (X456 = 19.02/19.29 X457))))))) => 19.02/19.29 (( 19.02/19.29 ?[X458]: 19.02/19.29 (X455( 19.02/19.29 X458) & 19.02/19.29 in( 19.02/19.29 X458,X454))) => 19.02/19.29 singleton( 19.02/19.29 dsetconstr( 19.02/19.29 X454, 19.02/19.29 ^[V_18]: 19.02/19.29 X455( 19.02/19.29 V_18)))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X459, 19.02/19.29 X460]: 19.02/19.29 (( 19.02/19.29 setadjoin( 19.02/19.29 X459, 19.02/19.29 emptyset) = 19.02/19.29 setadjoin( 19.02/19.29 X460, 19.02/19.29 emptyset)) => 19.02/19.29 (X459 = 19.02/19.29 X460))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X461, 19.02/19.29 X462,X463]: 19.02/19.29 (in( 19.02/19.29 setadjoin( 19.02/19.29 X463, 19.02/19.29 emptyset), 19.02/19.29 setadjoin( 19.02/19.29 setadjoin( 19.02/19.29 X461, 19.02/19.29 emptyset), 19.02/19.29 setadjoin( 19.02/19.29 setadjoin( 19.02/19.29 X461, 19.02/19.29 setadjoin( 19.02/19.29 X462, 19.02/19.29 emptyset)), 19.02/19.29 emptyset))) => 19.02/19.29 (X461 = 19.02/19.29 X463))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X464]: 19.02/19.29 (iskpair( 19.02/19.29 X464) => 19.02/19.29 singleton( 19.02/19.29 dsetconstr( 19.02/19.29 setunion( 19.02/19.29 X464), 19.02/19.29 ^[V_19]: 19.02/19.29 in( 19.02/19.29 setadjoin( 19.02/19.29 V_19, 19.02/19.29 emptyset), 19.02/19.29 X464))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X465]: 19.02/19.29 (singleton( 19.02/19.29 X465) => 19.02/19.29 in( 19.02/19.29 setunion( 19.02/19.29 X465), 19.02/19.29 X465))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X466, 19.02/19.29 X467]: 19.02/19.29 (kfst( 19.02/19.29 kpair( 19.02/19.29 X466,X467)) = 19.02/19.29 X466)) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X468, 19.02/19.29 X469,X470]: 19.02/19.29 (in( 19.02/19.29 X470, 19.02/19.29 cartprod( 19.02/19.29 X468,X469)) => 19.02/19.29 in( 19.02/19.29 kfst( 19.02/19.29 X470), 19.02/19.29 X468))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X471, 19.02/19.29 X472, 19.02/19.29 X473,X474]: 19.02/19.29 (( 19.02/19.29 setadjoin( 19.02/19.29 setadjoin( 19.02/19.29 X471, 19.02/19.29 emptyset), 19.02/19.29 setadjoin( 19.02/19.29 setadjoin( 19.02/19.29 X471, 19.02/19.29 setadjoin( 19.02/19.29 X472, 19.02/19.29 emptyset)), 19.02/19.29 emptyset)) = 19.02/19.29 setadjoin( 19.02/19.29 setadjoin( 19.02/19.29 X473, 19.02/19.29 emptyset), 19.02/19.29 setadjoin( 19.02/19.29 setadjoin( 19.02/19.29 X473, 19.02/19.29 setadjoin( 19.02/19.29 X474, 19.02/19.29 emptyset)), 19.02/19.29 emptyset))) => 19.02/19.29 (X471 = 19.02/19.29 X473))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X475, 19.02/19.29 X476, 19.02/19.29 X477,X478]: 19.02/19.29 (( 19.02/19.29 kpair( 19.02/19.29 X475,X476) = 19.02/19.29 kpair( 19.02/19.29 X477,X478)) => 19.02/19.29 (X475 = 19.02/19.29 X477))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X479, 19.02/19.29 X480]: 19.02/19.29 (( 19.02/19.29 X479 = 19.02/19.29 X480) => 19.02/19.29 (setadjoin( 19.02/19.29 X479, 19.02/19.29 setadjoin( 19.02/19.29 X480, 19.02/19.29 emptyset)) = 19.02/19.29 setadjoin( 19.02/19.29 X479, 19.02/19.29 emptyset)))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X481, 19.02/19.29 X482]: 19.02/19.29 (( 19.02/19.29 X481 = 19.02/19.29 X482) => 19.02/19.29 (setadjoin( 19.02/19.29 setadjoin( 19.02/19.29 X481, 19.02/19.29 emptyset), 19.02/19.29 setadjoin( 19.02/19.29 setadjoin( 19.02/19.29 X481, 19.02/19.29 setadjoin( 19.02/19.29 X482, 19.02/19.29 emptyset)), 19.02/19.29 emptyset)) = 19.02/19.29 setadjoin( 19.02/19.29 setadjoin( 19.02/19.29 X481, 19.02/19.29 emptyset), 19.02/19.29 emptyset)))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X483, 19.02/19.29 X484, 19.02/19.29 X485,X486]: 19.02/19.29 (( 19.02/19.29 setadjoin( 19.02/19.29 setadjoin( 19.02/19.29 X483, 19.02/19.29 emptyset), 19.02/19.29 setadjoin( 19.02/19.29 setadjoin( 19.02/19.29 X483, 19.02/19.29 setadjoin( 19.02/19.29 X484, 19.02/19.29 emptyset)), 19.02/19.29 emptyset)) = 19.02/19.29 setadjoin( 19.02/19.29 setadjoin( 19.02/19.29 X485, 19.02/19.29 emptyset), 19.02/19.29 setadjoin( 19.02/19.29 setadjoin( 19.02/19.29 X485, 19.02/19.29 setadjoin( 19.02/19.29 X486, 19.02/19.29 emptyset)), 19.02/19.29 emptyset))) => 19.02/19.29 (( 19.02/19.29 X485 = 19.02/19.29 X486) => 19.02/19.29 (X484 = 19.02/19.29 X486)))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X487, 19.02/19.29 X488,X489]: 19.02/19.29 (( 19.02/19.29 setadjoin( 19.02/19.29 X487, 19.02/19.29 setadjoin( 19.02/19.29 X488, 19.02/19.29 emptyset)) = 19.02/19.29 setadjoin( 19.02/19.29 X489, 19.02/19.29 emptyset)) => 19.02/19.29 (X487 = 19.02/19.29 X488))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X490, 19.02/19.29 X491, 19.02/19.29 X492,X493]: 19.02/19.29 (( 19.02/19.29 setadjoin( 19.02/19.29 setadjoin( 19.02/19.29 X490, 19.02/19.29 emptyset), 19.02/19.29 setadjoin( 19.02/19.29 setadjoin( 19.02/19.29 X490, 19.02/19.29 setadjoin( 19.02/19.29 X491, 19.02/19.29 emptyset)), 19.02/19.29 emptyset)) = 19.02/19.29 setadjoin( 19.02/19.29 setadjoin( 19.02/19.29 X492, 19.02/19.29 emptyset), 19.02/19.29 setadjoin( 19.02/19.29 setadjoin( 19.02/19.29 X492, 19.02/19.29 setadjoin( 19.02/19.29 X493, 19.02/19.29 emptyset)), 19.02/19.29 emptyset))) => 19.02/19.29 (X491 = 19.02/19.29 X493))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X494, 19.02/19.29 X495, 19.02/19.29 X496,X497]: 19.02/19.29 (( 19.02/19.29 kpair( 19.02/19.29 X494,X495) = 19.02/19.29 kpair( 19.02/19.29 X496,X497)) => 19.02/19.29 (X495 = 19.02/19.29 X497))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X498]: 19.02/19.29 (iskpair( 19.02/19.29 X498) => 19.02/19.29 singleton( 19.02/19.29 dsetconstr( 19.02/19.29 setunion( 19.02/19.29 X498), 19.02/19.29 ^[V_20]: 19.02/19.29 (X498 = 19.02/19.29 kpair( 19.02/19.29 kfst( 19.02/19.29 X498), 19.02/19.29 V_20)))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X499, 19.02/19.29 X500]: 19.02/19.29 (ksnd( 19.02/19.29 kpair( 19.02/19.29 X499,X500)) = 19.02/19.29 X500)) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X501]: 19.02/19.29 (iskpair( 19.02/19.29 X501) => 19.02/19.29 (kpair( 19.02/19.29 kfst( 19.02/19.29 X501), 19.02/19.29 ksnd( 19.02/19.29 X501)) = 19.02/19.29 X501))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X502, 19.02/19.29 X503,X504]: 19.02/19.29 (in( 19.02/19.29 X504, 19.02/19.29 cartprod( 19.02/19.29 X502,X503)) => 19.02/19.29 in( 19.02/19.29 ksnd( 19.02/19.29 X504), 19.02/19.29 X503))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X505, 19.02/19.29 X506, 19.02/19.29 X507,X508]: 19.02/19.29 (in( 19.02/19.29 kpair( 19.02/19.29 X507,X508), 19.02/19.29 cartprod( 19.02/19.29 X505,X506)) => 19.02/19.29 in( 19.02/19.29 X507,X505))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X509, 19.02/19.29 X510, 19.02/19.29 X511,X512]: 19.02/19.29 (in( 19.02/19.29 kpair( 19.02/19.29 X511,X512), 19.02/19.29 cartprod( 19.02/19.29 X509,X510)) => 19.02/19.29 in( 19.02/19.29 X512,X510))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X513, 19.02/19.29 X514,X515]: 19.02/19.29 (in( 19.02/19.29 X515,X513) => 19.02/19.29 (![X516]: 19.02/19.29 (in( 19.02/19.29 X516,X514) => 19.02/19.29 (kpair( 19.02/19.29 X515,X516) = 19.02/19.29 kpair( 19.02/19.29 X515,X516)))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X517, 19.02/19.29 X518,X519]: 19.02/19.29 (in( 19.02/19.29 X519,X517) => 19.02/19.29 (![X520]: 19.02/19.29 (in( 19.02/19.29 X520,X518) => 19.02/19.29 (kfst( 19.02/19.29 kpair( 19.02/19.29 X519,X520)) = 19.02/19.29 X519))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X521, 19.02/19.29 X522,X523]: 19.02/19.29 (in( 19.02/19.29 X523,X521) => 19.02/19.29 (![X524]: 19.02/19.29 (in( 19.02/19.29 X524,X522) => 19.02/19.29 (ksnd( 19.02/19.29 kpair( 19.02/19.29 X523,X524)) = 19.02/19.29 X524))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X525, 19.02/19.29 X526,X527]: 19.02/19.29 (in( 19.02/19.29 X527, 19.02/19.29 cartprod( 19.02/19.29 X525,X526)) => 19.02/19.29 (kpair( 19.02/19.29 kfst( 19.02/19.29 X527), 19.02/19.29 ksnd( 19.02/19.29 X527)) = 19.02/19.29 X527))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X528, 19.02/19.29 X529, 19.02/19.29 X530:( 19.02/19.29 ($i * $i) > 19.02/19.29 $o),X531]: 19.02/19.29 (in( 19.02/19.29 X531,X528) => 19.02/19.29 (![X532]: 19.02/19.29 (in( 19.02/19.29 X532,X529) => 19.02/19.29 (X530( 19.02/19.29 X531,X532) => 19.02/19.29 in( 19.02/19.29 kpair( 19.02/19.29 X531,X532), 19.02/19.29 dpsetconstr( 19.02/19.29 X528, 19.02/19.29 X529, 19.02/19.29 ^[V_21, 19.02/19.29 V_22]: 19.02/19.29 X530( 19.02/19.29 V_21,V_22)))))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X533, 19.02/19.29 X534, 19.02/19.29 X535:( 19.02/19.29 ($i * $i) > 19.02/19.29 $o)]: 19.02/19.29 subset( 19.02/19.29 dpsetconstr( 19.02/19.29 X533, 19.02/19.29 X534, 19.02/19.29 ^[V_23, 19.02/19.29 V_24]: 19.02/19.29 X535( 19.02/19.29 V_23,V_24)), 19.02/19.29 cartprod( 19.02/19.29 X533,X534))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X536, 19.02/19.29 X537, 19.02/19.29 X538:( 19.02/19.29 ($i * $i) > 19.02/19.29 $o)]: 19.02/19.29 subset( 19.02/19.29 dpsetconstr( 19.02/19.29 X536, 19.02/19.29 X537, 19.02/19.29 ^[V_25, 19.02/19.29 V_26]: 19.02/19.29 X538( 19.02/19.29 V_25,V_26)), 19.02/19.29 cartprod( 19.02/19.29 X536,X537))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X539, 19.02/19.29 X540, 19.02/19.29 X541:( 19.02/19.29 ($i * $i) > 19.02/19.29 $o),X542]: 19.02/19.29 (in( 19.02/19.29 X542,X539) => 19.02/19.29 (![X543]: 19.02/19.29 (in( 19.02/19.29 X543,X540) => 19.02/19.29 (in( 19.02/19.29 kpair( 19.02/19.29 X542,X543), 19.02/19.29 dpsetconstr( 19.02/19.29 X539, 19.02/19.29 X540, 19.02/19.29 ^[V_27, 19.02/19.29 V_28]: 19.02/19.29 X541( 19.02/19.29 V_27,V_28))) => 19.02/19.29 X541( 19.02/19.29 X542,X543)))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X544, 19.02/19.29 X545, 19.02/19.29 X546:( 19.02/19.29 ($i * $i) > 19.02/19.29 $o),X547, 19.02/19.29 X548]: 19.02/19.29 (in( 19.02/19.29 kpair( 19.02/19.29 X547,X548), 19.02/19.29 dpsetconstr( 19.02/19.29 X544, 19.02/19.29 X545, 19.02/19.29 ^[V_29, 19.02/19.29 V_30]: 19.02/19.29 X546( 19.02/19.29 V_29,V_30))) => 19.02/19.29 in( 19.02/19.29 X547,X544))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X549, 19.02/19.29 X550, 19.02/19.29 X551:( 19.02/19.29 ($i * $i) > 19.02/19.29 $o),X552, 19.02/19.29 X553]: 19.02/19.29 (in( 19.02/19.29 kpair( 19.02/19.29 X552,X553), 19.02/19.29 dpsetconstr( 19.02/19.29 X549, 19.02/19.29 X550, 19.02/19.29 ^[V_31, 19.02/19.29 V_32]: 19.02/19.29 X551( 19.02/19.29 V_31,V_32))) => 19.02/19.29 in( 19.02/19.29 X553,X550))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X554, 19.02/19.29 X555, 19.02/19.29 X556:( 19.02/19.29 ($i * $i) > 19.02/19.29 $o),X557, 19.02/19.29 X558]: 19.02/19.29 (in( 19.02/19.29 kpair( 19.02/19.29 X557,X558), 19.02/19.29 dpsetconstr( 19.02/19.29 X554, 19.02/19.29 X555, 19.02/19.29 ^[V_33, 19.02/19.29 V_34]: 19.02/19.29 X556( 19.02/19.29 V_33,V_34))) => 19.02/19.29 X556( 19.02/19.29 X557,X558))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X559, 19.02/19.29 X560,X561]: 19.02/19.29 (func( 19.02/19.29 X559, 19.02/19.29 X560,X561) => 19.02/19.29 (![X562]: 19.02/19.29 (in( 19.02/19.29 X562,X559) => 19.02/19.29 singleton( 19.02/19.29 dsetconstr( 19.02/19.29 X560, 19.02/19.29 ^[V_35]: 19.02/19.29 in( 19.02/19.29 kpair( 19.02/19.29 X562,V_35), 19.02/19.29 X561))))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X563, 19.02/19.29 X564,X565]: 19.02/19.29 (func( 19.02/19.29 X563, 19.02/19.29 X564,X565) => 19.02/19.29 (![X566]: 19.02/19.29 (in( 19.02/19.29 X566,X563) => 19.02/19.29 in( 19.02/19.29 setunion( 19.02/19.29 dsetconstr( 19.02/19.29 X564, 19.02/19.29 ^[V_36]: 19.02/19.29 in( 19.02/19.29 kpair( 19.02/19.29 X566,V_36), 19.02/19.29 X565))), 19.02/19.29 X564))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X567, 19.02/19.29 X568,X569]: 19.02/19.29 (func( 19.02/19.29 X567, 19.02/19.29 X568,X569) => 19.02/19.29 (![X570]: 19.02/19.29 (in( 19.02/19.29 X570,X567) => 19.02/19.29 in( 19.02/19.29 ap( 19.02/19.29 X567, 19.02/19.29 X568, 19.02/19.29 X569,X570), 19.02/19.29 X568))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X571, 19.02/19.29 X572,X573]: 19.02/19.29 (in( 19.02/19.29 X573, 19.02/19.29 funcSet( 19.02/19.29 X571,X572)) => 19.02/19.29 func( 19.02/19.29 X571, 19.02/19.29 X572,X573))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X574, 19.02/19.29 X575,X576]: 19.02/19.29 (in( 19.02/19.29 X576, 19.02/19.29 funcSet( 19.02/19.29 X574,X575)) => 19.02/19.29 (![X577]: 19.02/19.29 (in( 19.02/19.29 X577,X574) => 19.02/19.29 in( 19.02/19.29 ap( 19.02/19.29 X574, 19.02/19.29 X575, 19.02/19.29 X576,X577), 19.02/19.29 X575))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X578, 19.02/19.29 X579,X580]: 19.02/19.29 (func( 19.02/19.29 X578, 19.02/19.29 X579,X580) => 19.02/19.29 in( 19.02/19.29 X580, 19.02/19.29 funcSet( 19.02/19.29 X578,X579)))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X581, 19.02/19.29 X582, 19.02/19.29 X583:( 19.02/19.29 $i > $i)]: 19.02/19.29 (( 19.02/19.29 ![X584]: 19.02/19.29 (in( 19.02/19.29 X584,X581) => 19.02/19.29 in( 19.02/19.29 X583( 19.02/19.29 X584), 19.02/19.29 X582))) => 19.02/19.29 func( 19.02/19.29 X581, 19.02/19.29 X582, 19.02/19.29 dpsetconstr( 19.02/19.29 X581, 19.02/19.29 X582, 19.02/19.29 ^[V_37, 19.02/19.29 V_38]: 19.02/19.29 (X583( 19.02/19.29 V_37) = 19.02/19.29 V_38))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X585, 19.02/19.29 X586, 19.02/19.29 X587:( 19.02/19.29 $i > $i)]: 19.02/19.29 (( 19.02/19.29 ![X588]: 19.02/19.29 (in( 19.02/19.29 X588,X585) => 19.02/19.29 in( 19.02/19.29 X587( 19.02/19.29 X588), 19.02/19.29 X586))) => 19.02/19.29 func( 19.02/19.29 X585, 19.02/19.29 X586, 19.02/19.29 lam( 19.02/19.29 X585, 19.02/19.29 X586, 19.02/19.29 ^[V_39]: 19.02/19.29 X587( 19.02/19.29 V_39))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X589, 19.02/19.29 X590, 19.02/19.29 X591:( 19.02/19.29 $i > $i)]: 19.02/19.29 (( 19.02/19.29 ![X592]: 19.02/19.29 (in( 19.02/19.29 X592,X589) => 19.02/19.29 in( 19.02/19.29 X591( 19.02/19.29 X592), 19.02/19.29 X590))) => 19.02/19.29 in( 19.02/19.29 lam( 19.02/19.29 X589, 19.02/19.29 X590, 19.02/19.29 ^[V_40]: 19.02/19.29 X591( 19.02/19.29 V_40)), 19.02/19.29 funcSet( 19.02/19.29 X589,X590)))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X593, 19.02/19.29 X594,X595]: 19.02/19.29 (subset( 19.02/19.29 X595, 19.02/19.29 cartprod( 19.02/19.29 X593,X594)) => 19.02/19.29 (![X596:( 19.02/19.29 $i > $o)]: 19.02/19.29 (( 19.02/19.29 ![X597]: 19.02/19.29 (in( 19.02/19.29 X597,X593) => 19.02/19.29 (![X598]: 19.02/19.29 (in( 19.02/19.29 X598,X594) => 19.02/19.29 (in( 19.02/19.29 kpair( 19.02/19.29 X597,X598), 19.02/19.29 X595) => 19.02/19.29 X596( 19.02/19.29 kpair( 19.02/19.29 X597,X598))))))) => 19.02/19.29 (![X599]: 19.02/19.29 (in( 19.02/19.29 X599,X595) => 19.02/19.29 X596( 19.02/19.29 X599))))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X600, 19.02/19.29 X601,X602]: 19.02/19.29 (subset( 19.02/19.29 X602, 19.02/19.29 cartprod( 19.02/19.29 X600,X601)) => 19.02/19.29 (![X603:( 19.02/19.29 $i > $o)]: 19.02/19.29 (( 19.02/19.29 ![X604]: 19.02/19.29 (in( 19.02/19.29 X604,X600) => 19.02/19.29 (![X605]: 19.02/19.29 (in( 19.02/19.29 X605,X601) => 19.02/19.29 (in( 19.02/19.29 kpair( 19.02/19.29 X604,X605), 19.02/19.29 X602) => 19.02/19.29 X603( 19.02/19.29 kpair( 19.02/19.29 X604,X605))))))) => 19.02/19.29 (![X606]: 19.02/19.29 (in( 19.02/19.29 X606,X602) => 19.02/19.29 X603( 19.02/19.29 X606))))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X607, 19.02/19.29 X608:( 19.02/19.29 $i > $o)]: 19.02/19.29 (singleton( 19.02/19.29 dsetconstr( 19.02/19.29 X607, 19.02/19.29 ^[V_41]: 19.02/19.29 X608( 19.02/19.29 V_41))) => 19.02/19.29 (![X609]: 19.02/19.29 (in( 19.02/19.29 X609,X607) => 19.02/19.29 (![X610]: 19.02/19.29 (in( 19.02/19.29 X610,X607) => 19.02/19.29 (X608( 19.02/19.29 X609) => 19.02/19.29 (X608( 19.02/19.29 X610) => 19.02/19.29 (X609 = 19.02/19.29 X610))))))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X611, 19.02/19.29 X612,X613]: 19.02/19.29 (func( 19.02/19.29 X611, 19.02/19.29 X612,X613) => 19.02/19.29 (![X614]: 19.02/19.29 (in( 19.02/19.29 X614,X611) => 19.02/19.29 in( 19.02/19.29 kpair( 19.02/19.29 X614, 19.02/19.29 ap( 19.02/19.29 X611, 19.02/19.29 X612, 19.02/19.29 X613,X614)), 19.02/19.29 X613))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X615, 19.02/19.29 X616,X617]: 19.02/19.29 (in( 19.02/19.29 X617, 19.02/19.29 funcSet( 19.02/19.29 X615,X616)) => 19.02/19.29 (![X618]: 19.02/19.29 (in( 19.02/19.29 X618,X615) => 19.02/19.29 in( 19.02/19.29 kpair( 19.02/19.29 X618, 19.02/19.29 ap( 19.02/19.29 X615, 19.02/19.29 X616, 19.02/19.29 X617,X618)), 19.02/19.29 X617))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X619, 19.02/19.29 X620,X621]: 19.02/19.29 (func( 19.02/19.29 X619, 19.02/19.29 X620,X621) => 19.02/19.29 (![X622]: 19.02/19.29 (in( 19.02/19.29 X622,X619) => 19.02/19.29 (![X623]: 19.02/19.29 (in( 19.02/19.29 X623,X620) => 19.02/19.29 (in( 19.02/19.29 kpair( 19.02/19.29 X622,X623), 19.02/19.29 X621) => 19.02/19.29 (ap( 19.02/19.29 X619, 19.02/19.29 X620, 19.02/19.29 X621,X622) = 19.02/19.29 X623)))))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X624, 19.02/19.29 X625,X626]: 19.02/19.29 (func( 19.02/19.29 X624, 19.02/19.29 X625,X626) => 19.02/19.29 (![X627]: 19.02/19.29 (func( 19.02/19.29 X624, 19.02/19.29 X625,X627) => 19.02/19.29 (( 19.02/19.29 ![X628]: 19.02/19.29 (in( 19.02/19.29 X628,X624) => 19.02/19.29 (ap( 19.02/19.29 X624, 19.02/19.29 X625, 19.02/19.29 X626,X628) = 19.02/19.29 ap( 19.02/19.29 X624, 19.02/19.29 X625, 19.02/19.29 X627,X628)))) => 19.02/19.29 (![X629]: 19.02/19.29 (in( 19.02/19.29 X629,X624) => 19.02/19.29 (![X630]: 19.02/19.29 (in( 19.02/19.29 X630,X625) => 19.02/19.29 (in( 19.02/19.29 kpair( 19.02/19.29 X629,X630), 19.02/19.29 X627) => 19.02/19.29 in( 19.02/19.29 kpair( 19.02/19.29 X629,X630), 19.02/19.29 X626))))))))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X631, 19.02/19.29 X632,X633]: 19.02/19.29 (in( 19.02/19.29 X633, 19.02/19.29 funcSet( 19.02/19.29 X631,X632)) => 19.02/19.29 (![X634]: 19.02/19.29 (in( 19.02/19.29 X634,X631) => 19.02/19.29 (![X635]: 19.02/19.29 (in( 19.02/19.29 X635,X632) => 19.02/19.29 (in( 19.02/19.29 kpair( 19.02/19.29 X634,X635), 19.02/19.29 X633) => 19.02/19.29 (ap( 19.02/19.29 X631, 19.02/19.29 X632, 19.02/19.29 X633,X634) = 19.02/19.29 X635)))))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X636, 19.02/19.29 X637,X638]: 19.02/19.29 (subset( 19.02/19.29 X638, 19.02/19.29 cartprod( 19.02/19.29 X636,X637)) => 19.02/19.29 (![X639]: 19.02/19.29 (subset( 19.02/19.29 X639, 19.02/19.29 cartprod( 19.02/19.29 X636,X637)) => 19.02/19.29 (( 19.02/19.29 ![X640]: 19.02/19.29 (in( 19.02/19.29 X640,X636) => 19.02/19.29 (![X641]: 19.02/19.29 (in( 19.02/19.29 X641,X637) => 19.02/19.29 (in( 19.02/19.29 kpair( 19.02/19.29 X640,X641), 19.02/19.29 X638) => 19.02/19.29 in( 19.02/19.29 kpair( 19.02/19.29 X640,X641), 19.02/19.29 X639)))))) => 19.02/19.29 subset( 19.02/19.29 X638,X639)))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X642, 19.02/19.29 X643,X644]: 19.02/19.29 (subset( 19.02/19.29 X644, 19.02/19.29 cartprod( 19.02/19.29 X642,X643)) => 19.02/19.29 (![X645]: 19.02/19.29 (subset( 19.02/19.29 X645, 19.02/19.29 cartprod( 19.02/19.29 X642,X643)) => 19.02/19.29 (( 19.02/19.29 ![X646]: 19.02/19.29 (in( 19.02/19.29 X646,X642) => 19.02/19.29 (![X647]: 19.02/19.29 (in( 19.02/19.29 X647,X643) => 19.02/19.29 (in( 19.02/19.29 kpair( 19.02/19.29 X646,X647), 19.02/19.29 X644) => 19.02/19.29 in( 19.02/19.29 kpair( 19.02/19.29 X646,X647), 19.02/19.29 X645)))))) => 19.02/19.29 (( 19.02/19.29 ![X648]: 19.02/19.29 (in( 19.02/19.29 X648,X642) => 19.02/19.29 (![X649]: 19.02/19.29 (in( 19.02/19.29 X649,X643) => 19.02/19.29 (in( 19.02/19.29 kpair( 19.02/19.29 X648,X649), 19.02/19.29 X645) => 19.02/19.29 in( 19.02/19.29 kpair( 19.02/19.29 X648,X649), 19.02/19.29 X644)))))) => 19.02/19.29 (X644 = 19.02/19.29 X645))))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X650, 19.02/19.29 X651,X652]: 19.02/19.29 (func( 19.02/19.29 X650, 19.02/19.29 X651,X652) => 19.02/19.29 (![X653]: 19.02/19.29 (func( 19.02/19.29 X650, 19.02/19.29 X651,X653) => 19.02/19.29 (( 19.02/19.29 ![X654]: 19.02/19.29 (in( 19.02/19.29 X654,X650) => 19.02/19.29 (ap( 19.02/19.29 X650, 19.02/19.29 X651, 19.02/19.29 X652,X654) = 19.02/19.29 ap( 19.02/19.29 X650, 19.02/19.29 X651, 19.02/19.29 X653,X654)))) => 19.02/19.29 (X652 = 19.02/19.29 X653)))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X655, 19.02/19.29 X656,X657]: 19.02/19.29 (in( 19.02/19.29 X657, 19.02/19.29 funcSet( 19.02/19.29 X655,X656)) => 19.02/19.29 (![X658]: 19.02/19.29 (in( 19.02/19.29 X658, 19.02/19.29 funcSet( 19.02/19.29 X655,X656)) => 19.02/19.29 (( 19.02/19.29 ![X659]: 19.02/19.29 (in( 19.02/19.29 X659,X655) => 19.02/19.29 (ap( 19.02/19.29 X655, 19.02/19.29 X656, 19.02/19.29 X657,X659) = 19.02/19.29 ap( 19.02/19.29 X655, 19.02/19.29 X656, 19.02/19.29 X658,X659)))) => 19.02/19.29 (X657 = 19.02/19.29 X658)))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X660, 19.02/19.29 X661,X662]: 19.02/19.29 (in( 19.02/19.29 X662, 19.02/19.29 funcSet( 19.02/19.29 X660,X661)) => 19.02/19.29 (![X663]: 19.02/19.29 (in( 19.02/19.29 X663,X660) => 19.02/19.29 (ap( 19.02/19.29 X660, 19.02/19.29 X661, 19.02/19.29 X662,X663) = 19.02/19.29 ap( 19.02/19.29 X660, 19.02/19.29 X661, 19.02/19.29 X662,X663)))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X664, 19.02/19.29 X665,X666]: 19.02/19.29 (func( 19.02/19.29 X664, 19.02/19.29 X665,X666) => 19.02/19.29 (![X667]: 19.02/19.29 (in( 19.02/19.29 X667,X664) => 19.02/19.29 (ap( 19.02/19.29 X664, 19.02/19.29 X665, 19.02/19.29 X666,X667) = 19.02/19.29 ap( 19.02/19.29 X664, 19.02/19.29 X665, 19.02/19.29 X666,X667)))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X668, 19.02/19.29 X669, 19.02/19.29 X670:( 19.02/19.29 $i > $i)]: 19.02/19.29 (( 19.02/19.29 ![X671]: 19.02/19.29 (in( 19.02/19.29 X671,X668) => 19.02/19.29 in( 19.02/19.29 X670( 19.02/19.29 X671), 19.02/19.29 X669))) => 19.02/19.29 (![X672]: 19.02/19.29 (in( 19.02/19.29 X672,X668) => 19.02/19.29 (ap( 19.02/19.29 X668, 19.02/19.29 X669, 19.02/19.29 lam( 19.02/19.29 X668, 19.02/19.29 X669, 19.02/19.29 ^[V_42]: 19.02/19.29 X670( 19.02/19.29 V_42)), 19.02/19.29 X672) = 19.02/19.29 X670( 19.02/19.29 X672)))))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X673, 19.02/19.29 X674,X675]: 19.02/19.29 (func( 19.02/19.29 X673, 19.02/19.29 X674,X675) => 19.02/19.29 (lam( 19.02/19.29 X673, 19.02/19.29 X674, 19.02/19.29 ^[V_43]: 19.02/19.29 ap( 19.02/19.29 X673, 19.02/19.29 X674, 19.02/19.29 X675,V_43)) = 19.02/19.29 X675))) => 19.02/19.29 ( 19.02/19.29 ( 19.02/19.29 ![X676, 19.02/19.30 X677, 19.02/19.30 X678:( 19.02/19.30 $i > $i)]: 19.02/19.30 (( 19.02/19.30 ![X679]: 19.02/19.30 (in( 19.02/19.30 X679,X676) => 19.02/19.30 in( 19.02/19.30 X678( 19.02/19.30 X679), 19.02/19.30 X677))) => 19.02/19.30 (lam( 19.02/19.30 X676, 19.02/19.30 X677, 19.02/19.30 ^[V_44]: 19.02/19.30 X678( 19.02/19.30 V_44)) = 19.02/19.30 lam( 19.02/19.30 X676, 19.02/19.30 X677, 19.02/19.30 ^[V_45]: 19.02/19.30 X678( 19.02/19.30 V_45))))) => 19.02/19.30 ( 19.02/19.30 ( 19.02/19.30 ![X680, 19.02/19.30 X681, 19.02/19.30 X682:( 19.02/19.30 $i > $i)]: 19.02/19.30 (( 19.02/19.30 ![X683]: 19.02/19.30 (in( 19.02/19.30 X683,X680) => 19.02/19.30 in( 19.02/19.30 X682( 19.02/19.30 X683), 19.02/19.30 X681))) => 19.02/19.30 (![X684]: 19.02/19.30 (in( 19.02/19.30 X684,X680) => 19.02/19.30 (ap( 19.02/19.30 X680, 19.02/19.30 X681, 19.02/19.30 lam( 19.02/19.30 X680, 19.02/19.30 X681, 19.02/19.30 ^[V_46]: 19.02/19.30 X682( 19.02/19.30 V_46)), 19.02/19.30 X684) = 19.02/19.30 X682( 19.02/19.30 X684)))))) => 19.02/19.30 ( 19.02/19.30 ( 19.02/19.30 ![X685, 19.02/19.30 X686,X687]: 19.02/19.30 (in( 19.02/19.30 X687, 19.02/19.30 funcSet( 19.02/19.30 X685,X686)) => 19.02/19.30 (lam( 19.02/19.30 X685, 19.02/19.30 X686, 19.02/19.30 ^[V_47]: 19.02/19.30 ap( 19.02/19.30 X685, 19.02/19.30 X686, 19.02/19.30 X687,V_47)) = 19.02/19.30 X687))) => 19.02/19.30 ( 19.02/19.30 ( 19.02/19.30 ![X688, 19.02/19.30 X689:$o, 19.02/19.30 X690]: 19.02/19.30 (in( 19.02/19.30 X690,X688) => 19.02/19.30 (![X691]: 19.02/19.30 (in( 19.02/19.30 X691,X688) => 19.02/19.30 (( 19.02/19.30 ~X689) => 19.02/19.30 in( 19.02/19.30 X691, 19.02/19.30 dsetconstr( 19.02/19.30 X688, 19.02/19.30 ^[V_48]: 19.02/19.30 (( 19.02/19.30 X689 & 19.02/19.30 ( 19.02/19.30 V_48 = 19.02/19.30 X690)) | 19.02/19.30 (( 19.02/19.30 ~X689) & 19.02/19.30 (V_48 = 19.02/19.30 X691)))))))))) => 19.02/19.30 ( 19.02/19.30 ( 19.02/19.30 ![X692, 19.02/19.30 X693:$o, 19.02/19.30 X694]: 19.02/19.30 (in( 19.02/19.30 X694,X692) => 19.02/19.30 (![X695]: 19.02/19.30 (in( 19.02/19.30 X695,X692) => 19.02/19.30 (( 19.02/19.30 ~X693) => 19.02/19.30 (dsetconstr( 19.02/19.30 X692, 19.02/19.30 ^[V_49]: 19.02/19.30 (( 19.02/19.30 X693 & 19.02/19.30 ( 19.02/19.30 V_49 = 19.02/19.30 X694)) | 19.02/19.30 (( 19.02/19.30 ~X693) & 19.02/19.30 (V_49 = 19.02/19.30 X695)))) = 19.02/19.30 setadjoin( 19.02/19.30 X695, 19.02/19.30 emptyset))))))) => 19.02/19.30 ( 19.02/19.30 ( 19.02/19.30 ![X696, 19.02/19.30 X697:$o, 19.02/19.30 X698]: 19.02/19.30 (in( 19.02/19.30 X698,X696) => 19.02/19.30 (![X699]: 19.02/19.30 (in( 19.02/19.30 X699,X696) => 19.02/19.30 (X697 => 19.02/19.30 in( 19.02/19.30 X698, 19.02/19.30 dsetconstr( 19.02/19.30 X696, 19.02/19.30 ^[V_50]: 19.02/19.30 (( 19.02/19.30 X697 & 19.02/19.30 ( 19.02/19.30 V_50 = 19.02/19.30 X698)) | 19.02/19.30 (( 19.02/19.30 ~X697) & 19.02/19.30 (V_50 = 19.02/19.30 X699)))))))))) => 19.02/19.30 ( 19.02/19.30 ( 19.02/19.30 ![X700, 19.02/19.30 X701:$o, 19.02/19.30 X702]: 19.02/19.30 (in( 19.02/19.30 X702,X700) => 19.02/19.30 (![X703]: 19.02/19.30 (in( 19.02/19.30 X703,X700) => 19.02/19.30 (X701 => 19.02/19.30 (dsetconstr( 19.02/19.30 X700, 19.02/19.30 ^[V_51]: 19.02/19.30 (( 19.02/19.30 X701 & 19.02/19.30 ( 19.02/19.30 V_51 = 19.02/19.30 X702)) | 19.02/19.30 (( 19.02/19.30 ~X701) & 19.02/19.30 (V_51 = 19.02/19.30 X703)))) = 19.02/19.30 setadjoin( 19.02/19.30 X702, 19.02/19.30 emptyset))))))) => 19.02/19.30 ( 19.02/19.30 ( 19.02/19.30 ![X704, 19.02/19.30 X705:$o, 19.02/19.30 X706]: 19.02/19.30 (in( 19.02/19.30 X706,X704) => 19.02/19.30 (![X707]: 19.02/19.30 (in( 19.02/19.30 X707,X704) => 19.02/19.30 singleton( 19.02/19.30 dsetconstr( 19.02/19.30 X704, 19.02/19.30 ^[V_52]: 19.02/19.30 (( 19.02/19.30 X705 & 19.02/19.30 ( 19.02/19.30 V_52 = 19.02/19.30 X706)) | 19.02/19.30 (( 19.02/19.30 ~X705) & 19.02/19.30 (V_52 = 19.02/19.30 X707))))))))) => 19.02/19.30 ( 19.02/19.30 ( 19.02/19.30 ![X708, 19.02/19.30 X709:$o, 19.02/19.30 X710]: 19.02/19.30 (in( 19.02/19.30 X710,X708) => 19.02/19.30 (![X711]: 19.02/19.30 (in( 19.02/19.30 X711,X708) => 19.02/19.30 in( 19.02/19.30 if( 19.02/19.30 X708, 19.02/19.30 X709, 19.02/19.30 X710,X711), 19.02/19.30 X708))))) => 19.02/19.30 ( 19.02/19.30 ( 19.02/19.30 ![X712]: 19.02/19.30 (singleton( 19.02/19.30 X712) => 19.02/19.30 (![X713]: 19.02/19.30 (in( 19.02/19.30 X713,X712) => 19.02/19.30 (setunion( 19.02/19.30 X712) = 19.02/19.30 X713))))) => 19.02/19.30 ( 19.02/19.30 ( 19.02/19.30 ![X714, 19.02/19.30 X715:$o, 19.02/19.30 X716]: 19.02/19.30 (in( 19.02/19.30 X716,X714) => 19.02/19.30 (![X717]: 19.02/19.30 (in( 19.02/19.30 X717,X714) => 19.02/19.30 (X715 => 19.02/19.30 (if( 19.02/19.30 X714, 19.02/19.30 X715, 19.02/19.30 X716,X717) = 19.02/19.30 X716)))))) => 19.02/19.30 ( 19.02/19.30 ( 19.02/19.30 ![X718, 19.02/19.30 X719:$o, 19.02/19.30 X720]: 19.02/19.30 (in( 19.02/19.30 X720,X718) => 19.02/19.30 (![X721]: 19.02/19.30 (in( 19.02/19.30 X721,X718) => 19.02/19.30 (( 19.02/19.30 ~X719) => 19.02/19.30 (if( 19.02/19.30 X718, 19.02/19.30 X719, 19.02/19.30 X720,X721) = 19.02/19.30 X721)))))) => 19.02/19.30 ( 19.02/19.30 ( 19.02/19.30 ![X722, 19.02/19.30 X723:$o, 19.02/19.30 X724]: 19.02/19.30 (in( 19.02/19.30 X724,X722) => 19.02/19.30 (![X725]: 19.02/19.30 (in( 19.02/19.30 X725,X722) => 19.02/19.30 in( 19.02/19.30 if( 19.02/19.30 X722, 19.02/19.30 X723, 19.02/19.30 X724,X725), 19.02/19.30 setadjoin( 19.02/19.30 X724, 19.02/19.30 setadjoin( 19.02/19.30 X725, 19.02/19.30 emptyset))))))) => 19.02/19.30 ( 19.02/19.30 ( 19.02/19.30 ![X726, 19.02/19.30 X727]: 19.02/19.30 (in( 19.02/19.30 X727, 19.02/19.30 powerset( 19.02/19.30 X726)) => 19.02/19.30 (![X728]: 19.02/19.30 (in( 19.02/19.30 X728, 19.02/19.30 powerset( 19.02/19.30 X726)) => 19.02/19.30 in( 19.02/19.30 binintersect( 19.02/19.30 X727,X728), 19.02/19.30 powerset( 19.02/19.30 X726)))))) => 19.02/19.30 ( 19.02/19.30 ( 19.02/19.30 ![X729, 19.02/19.30 X730]: 19.02/19.30 (in( 19.02/19.30 X730, 19.02/19.30 powerset( 19.02/19.30 X729)) => 19.02/19.30 (![X731]: 19.02/19.30 (in( 19.02/19.30 X731, 19.02/19.30 powerset( 19.02/19.30 X729)) => 19.02/19.30 in( 19.02/19.30 binunion( 19.02/19.30 X730,X731), 19.02/19.30 powerset( 19.02/19.30 X729)))))) => 19.02/19.30 ( 19.02/19.30 ![X732, 19.02/19.30 X733]: 19.02/19.30 (in( 19.02/19.30 X733, 19.02/19.30 powerset( 19.02/19.30 X732)) => 19.02/19.30 in( 19.02/19.30 powerset( 19.02/19.30 X733), 19.02/19.30 powerset( 19.02/19.30 powerset( 19.02/19.30 X732))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 19.02/19.30 tff('232', plain, in(sk_X733_, powerset(sk_X732_)), 19.02/19.30 inference('cnf', [status(esa)], [zf_stmt_14])). 19.02/19.30 tff('233', plain, 19.02/19.30 ![X1292, X1293]: (subset(X1292, X1293) | ~ in(X1292, powerset(X1293))), 19.02/19.30 inference('cnf', [status(esa)], [zf_stmt_14])). 19.02/19.30 tff('234', plain, subset(sk_X733_, sk_X732_), 19.02/19.30 inference('sup-', [status(thm)], ['232', '233'])). 19.02/19.30 tff('235', plain, 19.02/19.30 ![X1290, X1291]: 19.02/19.30 (subset(powerset(X1290), powerset(X1291)) | ~ subset(X1290, X1291)), 19.02/19.30 inference('cnf', [status(esa)], [zf_stmt_14])). 19.02/19.30 tff('236', plain, subset(powerset(sk_X733_), powerset(sk_X732_)), 19.02/19.30 inference('sup-', [status(thm)], ['234', '235'])). 19.02/19.30 tff('237', plain, 19.02/19.30 ![X872, X873]: (in(X872, powerset(X873)) | ~ subset(X872, X873)), 19.02/19.30 inference('cnf', [status(esa)], [zf_stmt_14])). 19.02/19.30 tff('238', plain, in(powerset(sk_X733_), powerset(powerset(sk_X732_))), 19.02/19.30 inference('sup-', [status(thm)], ['236', '237'])). 19.02/19.30 tff('239', plain, ~ in(powerset(sk_X733_), powerset(powerset(sk_X732_))), 19.02/19.30 inference('cnf', [status(esa)], [zf_stmt_14])). 19.02/19.30 tff('240', plain, $false, inference('sup-', [status(thm)], ['238', '239'])). 19.02/19.30 19.02/19.30 % SZS output end Refutation 19.02/19.30 % Zipperpin 1.5 exiting 19.02/19.30 EOF