0.06/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.13 % Command : run_portfolio.sh /export/starexec/sandbox/benchmark/theBenchmark.p /export/starexec/sandbox/tmp/tmp.3p2qcFWRe5 0.12/0.33 % Computer : n003.cluster.edu 0.12/0.33 % Model : x86_64 x86_64 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.33 % Memory : 8042.1875MB 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.33 % CPULimit : 1200 0.12/0.33 % DateTime : Tue Jul 13 14:10:24 EDT 2021 0.18/0.33 % CPUTime : 0.18/0.33 % Running portfolio for 120 s 0.18/0.33 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.18/0.33 % Number of cores: 8 0.18/0.34 % Python version: Python 3.6.8 0.18/0.34 % Running in HO mode 0.49/0.60 % Estimated wc time : 1286 0.49/0.60 % Estimated cpu time (7 cpus) : 183.71428571428572 0.49/0.69 % /export/starexec/sandbox/solver/bin/lams/s6.sh running for 21s 0.49/0.69 % /export/starexec/sandbox/solver/bin/lams/new_b3.2.norw.sh running for 15s 0.49/0.70 % /export/starexec/sandbox/solver/bin/lams/b.rpo.sh running for 21s 0.49/0.70 % /export/starexec/sandbox/solver/bin/lams/s6.ds.sh running for 10s 0.49/0.70 % /export/starexec/sandbox/solver/bin/lams/c.s.2.sh running for 68s 0.49/0.71 % /export/starexec/sandbox/solver/bin/lams/c.easy.sh running for 26s 0.51/0.72 % /export/starexec/sandbox/solver/bin/lams/old_b3.avatar.sh running for 15s 23.78/3.99 % Solved by lams/c.easy.sh. 23.78/3.99 % Running : timeout 10 /export/starexec/sandbox/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox/tmp/tmp.3p2qcFWRe5/e_input33f132 --cpu-limit=8 --auto -s -p. 23.78/3.99 % done 1056 iterations in 3.148s 23.78/3.99 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 23.78/3.99 % SZS output start Refutation 23.78/3.99 tff(setukpairinjR12, axiom, setukpairinjR12 <=> 23.78/3.99 (![Xx,Xy]: 23.78/3.99 ((Xx = Xy) => 23.78/3.99 (setadjoin(setadjoin(Xx,emptyset), 23.78/3.99 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)),emptyset)) = 23.78/3.99 setadjoin(setadjoin(Xx,emptyset),emptyset))))). 23.78/3.99 tff('0', plain, 23.78/3.99 setukpairinjR12 = 23.78/3.99 (![X4,X6]: 23.78/3.99 ((X4 = X6) => 23.78/3.99 (setadjoin(setadjoin(X4,emptyset), 23.78/3.99 setadjoin(setadjoin(X4,setadjoin(X6,emptyset)),emptyset)) = 23.78/3.99 setadjoin(setadjoin(X4,emptyset),emptyset)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(setukpairinjR11, axiom, setukpairinjR11 <=> 23.78/3.99 (![Xx,Xy]: 23.78/3.99 ((Xx = Xy) => 23.78/3.99 (setadjoin(Xx,setadjoin(Xy,emptyset)) = setadjoin(Xx,emptyset))))). 23.78/3.99 tff('1', plain, 23.78/3.99 setukpairinjR11 = 23.78/3.99 (![X4,X6]: 23.78/3.99 ((X4 = X6) => 23.78/3.99 (setadjoin(X4,setadjoin(X6,emptyset)) = setadjoin(X4,emptyset)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(setukpairinjL, axiom, setukpairinjL <=> 23.78/3.99 (![Xx,Xy,Xz,Xu]: ((kpair(Xx,Xy) = kpair(Xz,Xu)) => (Xx = Xz)))). 23.78/3.99 tff('2', plain, 23.78/3.99 setukpairinjL = 23.78/3.99 (![X4,X6,X8,X10]: ((kpair(X4,X6) = kpair(X8,X10)) => (X4 = X8))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(setukpairinjL2, axiom, setukpairinjL2 <=> 23.78/3.99 (![Xx,Xy,Xz,Xu]: 23.78/3.99 ((setadjoin(setadjoin(Xx,emptyset), 23.78/3.99 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)),emptyset)) = 23.78/3.99 setadjoin(setadjoin(Xz,emptyset), 23.78/3.99 setadjoin(setadjoin(Xz,setadjoin(Xu,emptyset)),emptyset))) => 23.78/3.99 (Xx = Xz)))). 23.78/3.99 tff('3', plain, 23.78/3.99 setukpairinjL2 = 23.78/3.99 (![X4,X6,X8,X10]: 23.78/3.99 ((setadjoin(setadjoin(X4,emptyset), 23.78/3.99 setadjoin(setadjoin(X4,setadjoin(X6,emptyset)),emptyset)) = 23.78/3.99 setadjoin(setadjoin(X8,emptyset), 23.78/3.99 setadjoin(setadjoin(X8,setadjoin(X10,emptyset)),emptyset))) => 23.78/3.99 (X4 = X8))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(cartprodfstin, axiom, cartprodfstin <=> 23.78/3.99 (![A,B,Xu]: (in(Xu,cartprod(A,B)) => in(kfst(Xu),A)))). 23.78/3.99 tff('4', plain, 23.78/3.99 cartprodfstin = 23.78/3.99 (![X4,X6,X8]: (in(X8,cartprod(X4,X6)) => in(kfst(X8),X4))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(kfstpairEq, axiom, kfstpairEq <=> (![Xx,Xy]: (kfst(kpair(Xx,Xy)) = Xx))). 23.78/3.99 tff('5', plain, kfstpairEq = (![X4,X6]: (kfst(kpair(X4,X6)) = X4)), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(theprop, axiom, theprop <=> (![X]: (singleton(X) => in(setunion(X),X)))). 23.78/3.99 tff('6', plain, theprop = (![X4]: (singleton(X4) => in(setunion(X4),X4))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(kfstsingleton, axiom, kfstsingleton <=> 23.78/3.99 (![Xu]: 23.78/3.99 (iskpair(Xu) => 23.78/3.99 singleton(dsetconstr(setunion(Xu),^[Xx]: in(setadjoin(Xx,emptyset),Xu)))))). 23.78/3.99 tff('7', plain, 23.78/3.99 kfstsingleton = 23.78/3.99 (![X4]: 23.78/3.99 (iskpair(X4) => 23.78/3.99 singleton(dsetconstr(setunion(X4), 23.78/3.99 ^[V_1]: in(setadjoin(V_1,emptyset),X4))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(setukpairinjL1, axiom, setukpairinjL1 <=> 23.78/3.99 (![Xx,Xy,Xz]: 23.78/3.99 (in(setadjoin(Xz,emptyset), 23.78/3.99 setadjoin(setadjoin(Xx,emptyset), 23.78/3.99 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)),emptyset))) => 23.78/3.99 (Xx = Xz)))). 23.78/3.99 tff('8', plain, 23.78/3.99 setukpairinjL1 = 23.78/3.99 (![X4,X6,X8]: 23.78/3.99 (in(setadjoin(X8,emptyset), 23.78/3.99 setadjoin(setadjoin(X4,emptyset), 23.78/3.99 setadjoin(setadjoin(X4,setadjoin(X6,emptyset)),emptyset))) => 23.78/3.99 (X4 = X8))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(singletonsuniq, axiom, singletonsuniq <=> 23.78/3.99 (![Xx,Xy]: ((setadjoin(Xx,emptyset) = setadjoin(Xy,emptyset)) => (Xx = Xy)))). 23.78/3.99 tff('9', plain, 23.78/3.99 singletonsuniq = 23.78/3.99 (![X4,X6]: 23.78/3.99 ((setadjoin(X4,emptyset) = setadjoin(X6,emptyset)) => (X4 = X6))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(ex1I2, axiom, ex1I2 <=> 23.78/3.99 (![A,Xphi:(($i > $o))]: 23.78/3.99 ((![Xx]: 23.78/3.99 (in(Xx,A) => 23.78/3.99 (![Xy]: (in(Xy,A) => (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))) => 23.78/3.99 ((?[Xx]: (Xphi(Xx) & in(Xx,A))) => ex1(A,^[Xx]: Xphi(Xx)))))). 23.78/3.99 tff('10', plain, 23.78/3.99 ex1I2 = 23.78/3.99 (![X4,X6:(($i > $o))]: 23.78/3.99 ((![X8]: 23.78/3.99 (in(X8,X4) => 23.78/3.99 (![X10]: (in(X10,X4) => (X6(X8) => (X6(X10) => (X8 = X10))))))) => 23.78/3.99 ((?[X12]: (X6(X12) & in(X12,X4))) => ex1(X4,^[V_1]: X6(V_1))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(ex1I, axiom, ex1I <=> 23.78/3.99 (![A,Xphi:(($i > $o)),Xx]: 23.78/3.99 (in(Xx,A) => 23.78/3.99 (Xphi(Xx) => 23.78/3.99 ((![Xy]: (in(Xy,A) => (Xphi(Xy) => (Xy = Xx)))) => 23.78/3.99 ex1(A,^[Xy]: Xphi(Xy))))))). 23.78/3.99 tff('11', plain, 23.78/3.99 ex1I = 23.78/3.99 (![X4,X6:(($i > $o)),X8]: 23.78/3.99 (in(X8,X4) => 23.78/3.99 (X6(X8) => 23.78/3.99 ((![X10]: (in(X10,X4) => (X6(X10) => (X10 = X8)))) => 23.78/3.99 ex1(X4,^[V_1]: X6(V_1)))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(ex1E1, axiom, ex1E1 <=> 23.78/3.99 (![A,Xphi:(($i > $o))]: 23.78/3.99 (ex1(A,^[Xx]: Xphi(Xx)) => (?[Xx]: (Xphi(Xx) & in(Xx,A)))))). 23.78/3.99 tff('12', plain, 23.78/3.99 ex1E1 = 23.78/3.99 (![X4,X6:(($i > $o))]: 23.78/3.99 (ex1(X4,^[V_1]: X6(V_1)) => (?[X8]: (X6(X8) & in(X8,X4))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(ex1, axiom, ex1() = 23.78/3.99 ^[A,Xphi:(($i > $o))]: singleton(dsetconstr(A,^[Xx]: Xphi(Xx)))). 23.78/3.99 tff(singleton, axiom, singleton() = 23.78/3.99 ^[A]: (?[Xx]: ((A = setadjoin(Xx,emptyset)) & in(Xx,A)))). 23.78/3.99 tff('13', plain, 23.78/3.99 singleton = (^[A]: (?[Xx]: ((A = setadjoin(Xx,emptyset)) & in(Xx,A)))), 23.78/3.99 inference('simplify_rw_rule', [status(thm)], [singleton])). 23.78/3.99 tff('14', plain, 23.78/3.99 singleton = 23.78/3.99 (^[V_1]: (?[X4]: ((V_1 = setadjoin(X4,emptyset)) & in(X4,V_1)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff('15', plain, 23.78/3.99 ex1 = (^[A,Xphi:(($i > $o))]: singleton(dsetconstr(A,^[Xx]: Xphi(Xx)))), 23.78/3.99 inference('simplify_rw_rule', [status(thm)], [ex1, '14'])). 23.78/3.99 tff('16', plain, 23.78/3.99 ex1 = 23.78/3.99 (^[V_1,V_2:(($i > $o))]: singleton(dsetconstr(V_1,^[V_3]: V_2(V_3)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(singletonprop, axiom, singletonprop <=> 23.78/3.99 (![A,Xphi:(($i > $o))]: 23.78/3.99 ((![Xx]: 23.78/3.99 (in(Xx,A) => 23.78/3.99 (![Xy]: (in(Xy,A) => (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))) => 23.78/3.99 ((?[Xx]: (Xphi(Xx) & in(Xx,A))) => 23.78/3.99 singleton(dsetconstr(A,^[Xx]: Xphi(Xx))))))). 23.78/3.99 tff('17', plain, 23.78/3.99 singletonprop = 23.78/3.99 (![X4,X6:(($i > $o))]: 23.78/3.99 ((![X8]: 23.78/3.99 (in(X8,X4) => 23.78/3.99 (![X10]: (in(X10,X4) => (X6(X8) => (X6(X10) => (X8 = X10))))))) => 23.78/3.99 ((?[X12]: (X6(X12) & in(X12,X4))) => 23.78/3.99 singleton(dsetconstr(X4,^[V_1]: X6(V_1)))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(setunionsingleton, axiom, setunionsingleton <=> 23.78/3.99 (![Xx]: (setunion(setadjoin(Xx,emptyset)) = Xx))). 23.78/3.99 tff('18', plain, 23.78/3.99 setunionsingleton = (![X4]: (setunion(setadjoin(X4,emptyset)) = X4)), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(setunionsingleton2, axiom, setunionsingleton2 <=> 23.78/3.99 (![A]: subset(A,setunion(setadjoin(A,emptyset))))). 23.78/3.99 tff('19', plain, 23.78/3.99 setunionsingleton2 = (![X4]: subset(X4,setunion(setadjoin(X4,emptyset)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(setunionsingleton1, axiom, setunionsingleton1 <=> 23.78/3.99 (![A]: subset(setunion(setadjoin(A,emptyset)),A))). 23.78/3.99 tff('20', plain, 23.78/3.99 setunionsingleton1 = (![X4]: subset(setunion(setadjoin(X4,emptyset)),X4)), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(setunionE2, axiom, setunionE2 <=> 23.78/3.99 (![A,Xx]: (in(Xx,setunion(A)) => (?[X]: (in(Xx,X) & in(X,A)))))). 23.78/3.99 tff('21', plain, 23.78/3.99 setunionE2 = 23.78/3.99 (![X4,X6]: (in(X6,setunion(X4)) => (?[X8]: (in(X6,X8) & in(X8,X4))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(cartprodmempair, axiom, cartprodmempair <=> 23.78/3.99 (![A,B,Xu]: (in(Xu,cartprod(A,B)) => iskpair(Xu)))). 23.78/3.99 tff('22', plain, 23.78/3.99 cartprodmempair = (![X4,X6,X8]: (in(X8,cartprod(X4,X6)) => iskpair(X8))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(cartprodmempair1, axiom, cartprodmempair1 <=> 23.78/3.99 (![A,B,Xu]: 23.78/3.99 (in(Xu,cartprod(A,B)) => 23.78/3.99 (?[Xx]: ((?[Xy]: ((Xu = kpair(Xx,Xy)) & in(Xy,B))) & in(Xx,A)))))). 23.78/3.99 tff('23', plain, 23.78/3.99 cartprodmempair1 = 23.78/3.99 (![X4,X6,X8]: 23.78/3.99 (in(X8,cartprod(X4,X6)) => 23.78/3.99 (?[X10]: 23.78/3.99 ((?[X12]: ((X8 = kpair(X10,X12)) & in(X12,X6))) & in(X10,X4))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(cartprodpairin, axiom, cartprodpairin <=> 23.78/3.99 (![A,B,Xx]: 23.78/3.99 (in(Xx,A) => (![Xy]: (in(Xy,B) => in(kpair(Xx,Xy),cartprod(A,B))))))). 23.78/3.99 tff('24', plain, 23.78/3.99 cartprodpairin = 23.78/3.99 (![X4,X6,X8]: 23.78/3.99 (in(X8,X4) => 23.78/3.99 (![X10]: (in(X10,X6) => in(kpair(X8,X10),cartprod(X4,X6)))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(ubforcartprodlem3, axiom, ubforcartprodlem3 <=> 23.78/3.99 (![A,B,Xx]: 23.78/3.99 (in(Xx,A) => 23.78/3.99 (![Xy]: 23.78/3.99 (in(Xy,B) => in(kpair(Xx,Xy),powerset(powerset(binunion(A,B))))))))). 23.78/3.99 tff('25', plain, 23.78/3.99 ubforcartprodlem3 = 23.78/3.99 (![X4,X6,X8]: 23.78/3.99 (in(X8,X4) => 23.78/3.99 (![X10]: 23.78/3.99 (in(X10,X6) => 23.78/3.99 in(kpair(X8,X10),powerset(powerset(binunion(X4,X6)))))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(ubforcartprodlem2, axiom, ubforcartprodlem2 <=> 23.78/3.99 (![A,B,Xx]: 23.78/3.99 (in(Xx,A) => 23.78/3.99 (![Xy]: 23.78/3.99 (in(Xy,B) => 23.78/3.99 in(setadjoin(setadjoin(Xx,emptyset), 23.78/3.99 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 23.78/3.99 emptyset)), 23.78/3.99 powerset(powerset(binunion(A,B))))))))). 23.78/3.99 tff('26', plain, 23.78/3.99 ubforcartprodlem2 = 23.78/3.99 (![X4,X6,X8]: 23.78/3.99 (in(X8,X4) => 23.78/3.99 (![X10]: 23.78/3.99 (in(X10,X6) => 23.78/3.99 in(setadjoin(setadjoin(X8,emptyset), 23.78/3.99 setadjoin(setadjoin(X8,setadjoin(X10,emptyset)), 23.78/3.99 emptyset)), 23.78/3.99 powerset(powerset(binunion(X4,X6)))))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(ubforcartprodlem1, axiom, ubforcartprodlem1 <=> 23.78/3.99 (![A,B,Xx]: 23.78/3.99 (in(Xx,A) => 23.78/3.99 (![Xy]: 23.78/3.99 (in(Xy,B) => 23.78/3.99 subset(setadjoin(setadjoin(Xx,emptyset), 23.78/3.99 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 23.78/3.99 emptyset)), 23.78/3.99 powerset(binunion(A,B)))))))). 23.78/3.99 tff('27', plain, 23.78/3.99 ubforcartprodlem1 = 23.78/3.99 (![X4,X6,X8]: 23.78/3.99 (in(X8,X4) => 23.78/3.99 (![X10]: 23.78/3.99 (in(X10,X6) => 23.78/3.99 subset(setadjoin(setadjoin(X8,emptyset), 23.78/3.99 setadjoin(setadjoin(X8,setadjoin(X10,emptyset)), 23.78/3.99 emptyset)), 23.78/3.99 powerset(binunion(X4,X6))))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(upairinpowunion, axiom, upairinpowunion <=> 23.78/3.99 (![A,B,Xx]: 23.78/3.99 (in(Xx,A) => 23.78/3.99 (![Xy]: 23.78/3.99 (in(Xy,B) => 23.78/3.99 in(setadjoin(Xx,setadjoin(Xy,emptyset)),powerset(binunion(A,B)))))))). 23.78/3.99 tff('28', plain, 23.78/3.99 upairinpowunion = 23.78/3.99 (![X4,X6,X8]: 23.78/3.99 (in(X8,X4) => 23.78/3.99 (![X10]: 23.78/3.99 (in(X10,X6) => 23.78/3.99 in(setadjoin(X8,setadjoin(X10,emptyset)), 23.78/3.99 powerset(binunion(X4,X6))))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(upairsubunion, axiom, upairsubunion <=> 23.78/3.99 (![A,B,Xx]: 23.78/3.99 (in(Xx,A) => 23.78/3.99 (![Xy]: 23.78/3.99 (in(Xy,B) => 23.78/3.99 subset(setadjoin(Xx,setadjoin(Xy,emptyset)),binunion(A,B))))))). 23.78/3.99 tff('29', plain, 23.78/3.99 upairsubunion = 23.78/3.99 (![X4,X6,X8]: 23.78/3.99 (in(X8,X4) => 23.78/3.99 (![X10]: 23.78/3.99 (in(X10,X6) => 23.78/3.99 subset(setadjoin(X8,setadjoin(X10,emptyset)),binunion(X4,X6)))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(upairset2E, axiom, upairset2E <=> 23.78/3.99 (![Xx,Xy,Xz]: 23.78/3.99 (in(Xz,setadjoin(Xx,setadjoin(Xy,emptyset))) => ((Xz = Xx) | (Xz = Xy))))). 23.78/3.99 tff('30', plain, 23.78/3.99 upairset2E = 23.78/3.99 (![X4,X6,X8]: 23.78/3.99 (in(X8,setadjoin(X4,setadjoin(X6,emptyset))) => 23.78/3.99 ((X8 = X4) | (X8 = X6)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(singletoninpowunion, axiom, singletoninpowunion <=> 23.78/3.99 (![A,B,Xx]: 23.78/3.99 (in(Xx,A) => in(setadjoin(Xx,emptyset),powerset(binunion(A,B)))))). 23.78/3.99 tff('31', plain, 23.78/3.99 singletoninpowunion = 23.78/3.99 (![X4,X6,X8]: 23.78/3.99 (in(X8,X4) => in(setadjoin(X8,emptyset),powerset(binunion(X4,X6))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(singletoninpowerset, axiom, singletoninpowerset <=> 23.78/3.99 (![A,Xx]: (in(Xx,A) => in(setadjoin(Xx,emptyset),powerset(A))))). 23.78/3.99 tff('32', plain, 23.78/3.99 singletoninpowerset = 23.78/3.99 (![X4,X6]: (in(X6,X4) => in(setadjoin(X6,emptyset),powerset(X4)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(singletonsubset, axiom, singletonsubset <=> 23.78/3.99 (![A,Xx]: (in(Xx,A) => subset(setadjoin(Xx,emptyset),A)))). 23.78/3.99 tff('33', plain, 23.78/3.99 singletonsubset = 23.78/3.99 (![X4,X6]: (in(X6,X4) => subset(setadjoin(X6,emptyset),X4))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(kpairp, axiom, kpairp <=> (![Xx,Xy]: iskpair(kpair(Xx,Xy)))). 23.78/3.99 tff('34', plain, kpairp = (![X4,X6]: iskpair(kpair(X4,X6))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(kpair, axiom, kpair() = 23.78/3.99 ^[Xx,Xy]: 23.78/3.99 setadjoin(setadjoin(Xx,emptyset), 23.78/3.99 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)),emptyset))). 23.78/3.99 tff('35', plain, 23.78/3.99 kpair = 23.78/3.99 (^[Xx,Xy]: 23.78/3.99 setadjoin(setadjoin(Xx,emptyset), 23.78/3.99 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)),emptyset))), 23.78/3.99 inference('simplify_rw_rule', [status(thm)], [kpair])). 23.78/3.99 tff('36', plain, 23.78/3.99 kpair = 23.78/3.99 (^[V_1,V_2]: 23.78/3.99 setadjoin(setadjoin(V_1,emptyset), 23.78/3.99 setadjoin(setadjoin(V_1,setadjoin(V_2,emptyset)),emptyset))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(kpairiskpair, axiom, kpairiskpair <=> 23.78/3.99 (![Xx,Xy]: 23.78/3.99 iskpair(setadjoin(setadjoin(Xx,emptyset), 23.78/3.99 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 23.78/3.99 emptyset))))). 23.78/3.99 tff('37', plain, 23.78/3.99 kpairiskpair = 23.78/3.99 (![X4,X6]: 23.78/3.99 iskpair(setadjoin(setadjoin(X4,emptyset), 23.78/3.99 setadjoin(setadjoin(X4,setadjoin(X6,emptyset)), 23.78/3.99 emptyset)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(setukpairIR, axiom, setukpairIR <=> 23.78/3.99 (![Xx,Xy]: 23.78/3.99 in(Xy, 23.78/3.99 setunion(setadjoin(setadjoin(Xx,emptyset), 23.78/3.99 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 23.78/3.99 emptyset)))))). 23.78/3.99 tff('38', plain, 23.78/3.99 setukpairIR = 23.78/3.99 (![X4,X6]: 23.78/3.99 in(X6, 23.78/3.99 setunion(setadjoin(setadjoin(X4,emptyset), 23.78/3.99 setadjoin(setadjoin(X4,setadjoin(X6,emptyset)), 23.78/3.99 emptyset))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(setukpairIL, axiom, setukpairIL <=> 23.78/3.99 (![Xx,Xy]: 23.78/3.99 in(Xx, 23.78/3.99 setunion(setadjoin(setadjoin(Xx,emptyset), 23.78/3.99 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 23.78/3.99 emptyset)))))). 23.78/3.99 tff('39', plain, 23.78/3.99 setukpairIL = 23.78/3.99 (![X4,X6]: 23.78/3.99 in(X4, 23.78/3.99 setunion(setadjoin(setadjoin(X4,emptyset), 23.78/3.99 setadjoin(setadjoin(X4,setadjoin(X6,emptyset)), 23.78/3.99 emptyset))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(secondinupair, axiom, secondinupair <=> 23.78/3.99 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 23.78/3.99 tff('40', plain, 23.78/3.99 secondinupair = (![X4,X6]: in(X6,setadjoin(X4,setadjoin(X6,emptyset)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(iskpair, axiom, iskpair() = 23.78/3.99 ^[A]: 23.78/3.99 (?[Xx]: 23.78/3.99 ((?[Xy]: 23.78/3.99 ((A = 23.78/3.99 setadjoin(setadjoin(Xx,emptyset), 23.78/3.99 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 23.78/3.99 emptyset))) & 23.78/3.99 in(Xy,setunion(A)))) & 23.78/3.99 in(Xx,setunion(A))))). 23.78/3.99 tff('41', plain, 23.78/3.99 iskpair = 23.78/3.99 (^[A]: 23.78/3.99 (?[Xx]: 23.78/3.99 ((?[Xy]: 23.78/3.99 ((A = 23.78/3.99 setadjoin(setadjoin(Xx,emptyset), 23.78/3.99 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 23.78/3.99 emptyset))) & 23.78/3.99 in(Xy,setunion(A)))) & 23.78/3.99 in(Xx,setunion(A))))), 23.78/3.99 inference('simplify_rw_rule', [status(thm)], [iskpair])). 23.78/3.99 tff('42', plain, 23.78/3.99 iskpair = 23.78/3.99 (^[V_1]: 23.78/3.99 (?[X4]: 23.78/3.99 ((?[X6]: 23.78/3.99 ((V_1 = 23.78/3.99 setadjoin(setadjoin(X4,emptyset), 23.78/3.99 setadjoin(setadjoin(X4,setadjoin(X6,emptyset)), 23.78/3.99 emptyset))) & 23.78/3.99 in(X6,setunion(V_1)))) & 23.78/3.99 in(X4,setunion(V_1))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(symdiffIneg2, axiom, symdiffIneg2 <=> 23.78/3.99 (![A,B,Xx]: ((~in(Xx,A)) => ((~in(Xx,B)) => (~in(Xx,symdiff(A,B))))))). 23.78/3.99 tff('43', plain, 23.78/3.99 symdiffIneg2 = 23.78/3.99 (![X4,X6,X8]: 23.78/3.99 ((~in(X8,X4)) => ((~in(X8,X6)) => (~in(X8,symdiff(X4,X6)))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(symdiffIneg1, axiom, symdiffIneg1 <=> 23.78/3.99 (![A,B,Xx]: (in(Xx,A) => (in(Xx,B) => (~in(Xx,symdiff(A,B))))))). 23.78/3.99 tff('44', plain, 23.78/3.99 symdiffIneg1 = 23.78/3.99 (![X4,X6,X8]: (in(X8,X4) => (in(X8,X6) => (~in(X8,symdiff(X4,X6)))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(symdiffI2, axiom, symdiffI2 <=> 23.78/3.99 (![A,B,Xx]: ((~in(Xx,A)) => (in(Xx,B) => in(Xx,symdiff(A,B)))))). 23.78/3.99 tff('45', plain, 23.78/3.99 symdiffI2 = 23.78/3.99 (![X4,X6,X8]: ((~in(X8,X4)) => (in(X8,X6) => in(X8,symdiff(X4,X6))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(symdiffI1, axiom, symdiffI1 <=> 23.78/3.99 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => in(Xx,symdiff(A,B)))))). 23.78/3.99 tff('46', plain, 23.78/3.99 symdiffI1 = 23.78/3.99 (![X4,X6,X8]: (in(X8,X4) => ((~in(X8,X6)) => in(X8,symdiff(X4,X6))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(symdiffE, axiom, symdiffE <=> 23.78/3.99 (![A,B,Xx]: 23.78/3.99 (in(Xx,symdiff(A,B)) => 23.78/3.99 (![Xphi:$o]: 23.78/3.99 ((in(Xx,A) => ((~in(Xx,B)) => Xphi)) => 23.78/3.99 (((~in(Xx,A)) => (in(Xx,B) => Xphi)) => Xphi)))))). 23.78/3.99 tff('47', plain, 23.78/3.99 symdiffE = 23.78/3.99 (![X4,X6,X8]: 23.78/3.99 (in(X8,symdiff(X4,X6)) => 23.78/3.99 (![X10:$o]: 23.78/3.99 ((in(X8,X4) => ((~in(X8,X6)) => X10)) => 23.78/3.99 (((~in(X8,X4)) => (in(X8,X6) => X10)) => X10))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(setminusSubset1, axiom, setminusSubset1 <=> 23.78/3.99 (![A,B]: ((setminus(A,B) = emptyset) => subset(A,B)))). 23.78/3.99 tff('48', plain, 23.78/3.99 setminusSubset1 = 23.78/3.99 (![X4,X6]: ((setminus(X4,X6) = emptyset) => subset(X4,X6))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(setminusLsub, axiom, setminusLsub <=> (![A,B]: subset(setminus(A,B),A))). 23.78/3.99 tff('49', plain, setminusLsub = (![X4,X6]: subset(setminus(X4,X6),X4)), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(setminusIRneg, axiom, setminusIRneg <=> 23.78/3.99 (![A,B,Xx]: (in(Xx,B) => (~in(Xx,setminus(A,B)))))). 23.78/3.99 tff('50', plain, 23.78/3.99 setminusIRneg = (![X4,X6,X8]: (in(X8,X6) => (~in(X8,setminus(X4,X6))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(setminusILneg, axiom, setminusILneg <=> 23.78/3.99 (![A,B,Xx]: ((~in(Xx,A)) => (~in(Xx,setminus(A,B)))))). 23.78/3.99 tff('51', plain, 23.78/3.99 setminusILneg = 23.78/3.99 (![X4,X6,X8]: ((~in(X8,X4)) => (~in(X8,setminus(X4,X6))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(setminusELneg, axiom, setminusELneg <=> 23.78/3.99 (![A,B,Xx]: ((~in(Xx,setminus(A,B))) => ((~in(Xx,B)) => (~in(Xx,A)))))). 23.78/3.99 tff('52', plain, 23.78/3.99 setminusELneg = 23.78/3.99 (![X4,X6,X8]: 23.78/3.99 ((~in(X8,setminus(X4,X6))) => ((~in(X8,X6)) => (~in(X8,X4))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(setminusERneg, axiom, setminusERneg <=> 23.78/3.99 (![A,B,Xx]: ((~in(Xx,setminus(A,B))) => (in(Xx,A) => in(Xx,B))))). 23.78/3.99 tff('53', plain, 23.78/3.99 setminusERneg = 23.78/3.99 (![X4,X6,X8]: ((~in(X8,setminus(X4,X6))) => (in(X8,X4) => in(X8,X6)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(setminusSubset2, axiom, setminusSubset2 <=> 23.78/3.99 (![A,B]: (subset(A,B) => (setminus(A,B) = emptyset)))). 23.78/3.99 tff('54', plain, 23.78/3.99 setminusSubset2 = 23.78/3.99 (![X4,X6]: (subset(X4,X6) => (setminus(X4,X6) = emptyset))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(setminusER, axiom, setminusER <=> 23.78/3.99 (![A,B,Xx]: (in(Xx,setminus(A,B)) => (~in(Xx,B))))). 23.78/3.99 tff('55', plain, 23.78/3.99 setminusER = (![X4,X6,X8]: (in(X8,setminus(X4,X6)) => (~in(X8,X6)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(setminusEL, axiom, setminusEL <=> 23.78/3.99 (![A,B,Xx]: (in(Xx,setminus(A,B)) => in(Xx,A)))). 23.78/3.99 tff('56', plain, 23.78/3.99 setminusEL = (![X4,X6,X8]: (in(X8,setminus(X4,X6)) => in(X8,X4))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(setminusI, axiom, setminusI <=> 23.78/3.99 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => in(Xx,setminus(A,B)))))). 23.78/3.99 tff('57', plain, 23.78/3.99 setminusI = 23.78/3.99 (![X4,X6,X8]: (in(X8,X4) => ((~in(X8,X6)) => in(X8,setminus(X4,X6))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(bs114d, axiom, bs114d <=> 23.78/3.99 (![A,B,C]: 23.78/3.99 (binintersect(A,binunion(B,C)) = 23.78/3.99 binunion(binintersect(A,B),binintersect(A,C))))). 23.78/3.99 tff('58', plain, 23.78/3.99 bs114d = 23.78/3.99 (![X4,X6,X8]: 23.78/3.99 (binintersect(X4,binunion(X6,X8)) = 23.78/3.99 binunion(binintersect(X4,X6),binintersect(X4,X8)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(binintersectSubset1, axiom, binintersectSubset1 <=> 23.78/3.99 (![A,B]: ((binintersect(A,B) = A) => subset(A,B)))). 23.78/3.99 tff('59', plain, 23.78/3.99 binintersectSubset1 = 23.78/3.99 (![X4,X6]: ((binintersect(X4,X6) = X4) => subset(X4,X6))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(binintersectSubset4, axiom, binintersectSubset4 <=> 23.78/3.99 (![A,B]: (subset(B,A) => (binintersect(A,B) = B)))). 23.78/3.99 tff('60', plain, 23.78/3.99 binintersectSubset4 = 23.78/3.99 (![X4,X6]: (subset(X6,X4) => (binintersect(X4,X6) = X6))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(binintersectRsub, axiom, binintersectRsub <=> 23.78/3.99 (![A,B]: subset(binintersect(A,B),B))). 23.78/3.99 tff('61', plain, 23.78/3.99 binintersectRsub = (![X4,X6]: subset(binintersect(X4,X6),X6)), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(disjointsetsI1, axiom, disjointsetsI1 <=> 23.78/3.99 (![A,B]: 23.78/3.99 ((~(?[Xx]: (in(Xx,B) & in(Xx,A)))) => (binintersect(A,B) = emptyset)))). 23.78/3.99 tff('62', plain, 23.78/3.99 disjointsetsI1 = 23.78/3.99 (![X4,X6]: 23.78/3.99 ((~(?[X8]: (in(X8,X6) & in(X8,X4)))) => 23.78/3.99 (binintersect(X4,X6) = emptyset))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(binintersectER, axiom, binintersectER <=> 23.78/3.99 (![A,B,Xx]: (in(Xx,binintersect(A,B)) => in(Xx,B)))). 23.78/3.99 tff('63', plain, 23.78/3.99 binintersectER = (![X4,X6,X8]: (in(X8,binintersect(X4,X6)) => in(X8,X6))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(binintersectSubset3, axiom, binintersectSubset3 <=> 23.78/3.99 (![A,B]: ((binintersect(A,B) = B) => subset(B,A)))). 23.78/3.99 tff('64', plain, 23.78/3.99 binintersectSubset3 = 23.78/3.99 (![X4,X6]: ((binintersect(X4,X6) = X6) => subset(X6,X4))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(binintersectSubset2, axiom, binintersectSubset2 <=> 23.78/3.99 (![A,B]: (subset(A,B) => (binintersect(A,B) = A)))). 23.78/3.99 tff('65', plain, 23.78/3.99 binintersectSubset2 = 23.78/3.99 (![X4,X6]: (subset(X4,X6) => (binintersect(X4,X6) = X4))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(binintersectLsub, axiom, binintersectLsub <=> 23.78/3.99 (![A,B]: subset(binintersect(A,B),A))). 23.78/3.99 tff('66', plain, 23.78/3.99 binintersectLsub = (![X4,X6]: subset(binintersect(X4,X6),X4)), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(binintersectEL, axiom, binintersectEL <=> 23.78/3.99 (![A,B,Xx]: (in(Xx,binintersect(A,B)) => in(Xx,A)))). 23.78/3.99 tff('67', plain, 23.78/3.99 binintersectEL = (![X4,X6,X8]: (in(X8,binintersect(X4,X6)) => in(X8,X4))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(binintersectSubset5, axiom, binintersectSubset5 <=> 23.78/3.99 (![A,B,C]: (subset(C,A) => (subset(C,B) => subset(C,binintersect(A,B)))))). 23.78/3.99 tff('68', plain, 23.78/3.99 binintersectSubset5 = 23.78/3.99 (![X4,X6,X8]: 23.78/3.99 (subset(X8,X4) => (subset(X8,X6) => subset(X8,binintersect(X4,X6))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(binintersectI, axiom, binintersectI <=> 23.78/3.99 (![A,B,Xx]: (in(Xx,A) => (in(Xx,B) => in(Xx,binintersect(A,B)))))). 23.78/3.99 tff('69', plain, 23.78/3.99 binintersectI = 23.78/3.99 (![X4,X6,X8]: (in(X8,X4) => (in(X8,X6) => in(X8,binintersect(X4,X6))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(binunionRsub, axiom, binunionRsub <=> (![A,B]: subset(B,binunion(A,B)))). 23.78/3.99 tff('70', plain, binunionRsub = (![X4,X6]: subset(X6,binunion(X4,X6))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(binunionLsub, axiom, binunionLsub <=> (![A,B]: subset(A,binunion(A,B)))). 23.78/3.99 tff('71', plain, binunionLsub = (![X4,X6]: subset(X4,binunion(X4,X6))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(binunionE, axiom, binunionE <=> 23.78/3.99 (![A,B,Xx]: (in(Xx,binunion(A,B)) => (in(Xx,A) | in(Xx,B))))). 23.78/3.99 tff('72', plain, 23.78/3.99 binunionE = 23.78/3.99 (![X4,X6,X8]: (in(X8,binunion(X4,X6)) => (in(X8,X4) | in(X8,X6)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(binunionEcases, axiom, binunionEcases <=> 23.78/3.99 (![A,B,Xx,Xphi:$o]: 23.78/3.99 (in(Xx,binunion(A,B)) => 23.78/3.99 ((in(Xx,A) => Xphi) => ((in(Xx,B) => Xphi) => Xphi))))). 23.78/3.99 tff('73', plain, 23.78/3.99 binunionEcases = 23.78/3.99 (![X4,X6,X8,X10:$o]: 23.78/3.99 (in(X8,binunion(X4,X6)) => 23.78/3.99 ((in(X8,X4) => X10) => ((in(X8,X6) => X10) => X10)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(binunionIR, axiom, binunionIR <=> 23.78/3.99 (![A,B,Xx]: (in(Xx,B) => in(Xx,binunion(A,B))))). 23.78/3.99 tff('74', plain, 23.78/3.99 binunionIR = (![X4,X6,X8]: (in(X8,X6) => in(X8,binunion(X4,X6)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(upairset2IR, axiom, upairset2IR <=> 23.78/3.99 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 23.78/3.99 tff('75', plain, 23.78/3.99 upairset2IR = (![X4,X6]: in(X6,setadjoin(X4,setadjoin(X6,emptyset)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(binunionIL, axiom, binunionIL <=> 23.78/3.99 (![A,B,Xx]: (in(Xx,A) => in(Xx,binunion(A,B))))). 23.78/3.99 tff('76', plain, 23.78/3.99 binunionIL = (![X4,X6,X8]: (in(X8,X4) => in(X8,binunion(X4,X6)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(sepSubset, axiom, sepSubset <=> 23.78/3.99 (![A,Xphi:(($i > $o))]: subset(dsetconstr(A,^[Xx]: Xphi(Xx)),A))). 23.78/3.99 tff('77', plain, 23.78/3.99 sepSubset = 23.78/3.99 (![X4,X6:(($i > $o))]: subset(dsetconstr(X4,^[V_1]: X6(V_1)),X4)), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(sepInPowerset, axiom, sepInPowerset <=> 23.78/3.99 (![A,Xphi:(($i > $o))]: in(dsetconstr(A,^[Xx]: Xphi(Xx)),powerset(A)))). 23.78/3.99 tff('78', plain, 23.78/3.99 sepInPowerset = 23.78/3.99 (![X4,X6:(($i > $o))]: in(dsetconstr(X4,^[V_1]: X6(V_1)),powerset(X4))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(powersetsubset, axiom, powersetsubset <=> 23.78/3.99 (![A,B]: (subset(A,B) => subset(powerset(A),powerset(B))))). 23.78/3.99 tff('79', plain, 23.78/3.99 powersetsubset = 23.78/3.99 (![X4,X6]: (subset(X4,X6) => subset(powerset(X4),powerset(X6)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(inPowerset, axiom, inPowerset <=> (![A]: in(A,powerset(A)))). 23.78/3.99 tff('80', plain, inPowerset = (![X4]: in(X4,powerset(X4))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(powersetE1, axiom, powersetE1 <=> 23.78/3.99 (![A,B]: (in(B,powerset(A)) => subset(B,A)))). 23.78/3.99 tff('81', plain, 23.78/3.99 powersetE1 = (![X4,X6]: (in(X6,powerset(X4)) => subset(X6,X4))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(powersetI1, axiom, powersetI1 <=> 23.78/3.99 (![A,B]: (subset(B,A) => in(B,powerset(A))))). 23.78/3.99 tff('82', plain, 23.78/3.99 powersetI1 = (![X4,X6]: (subset(X6,X4) => in(X6,powerset(X4)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(subsetemptysetimpeq, axiom, subsetemptysetimpeq <=> 23.78/3.99 (![A]: (subset(A,emptyset) => (A = emptyset)))). 23.78/3.99 tff('83', plain, 23.78/3.99 subsetemptysetimpeq = (![X4]: (subset(X4,emptyset) => (X4 = emptyset))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(setextsub, axiom, setextsub <=> 23.78/3.99 (![A,B]: (subset(A,B) => (subset(B,A) => (A = B))))). 23.78/3.99 tff('84', plain, 23.78/3.99 setextsub = (![X4,X6]: (subset(X4,X6) => (subset(X6,X4) => (X4 = X6)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(subset2powerset, axiom, subset2powerset <=> 23.78/3.99 (![A,B]: (subset(A,B) => in(A,powerset(B))))). 23.78/3.99 tff('85', plain, 23.78/3.99 subset2powerset = (![X4,X6]: (subset(X4,X6) => in(X4,powerset(X6)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(setadjoinSub2, axiom, setadjoinSub2 <=> 23.78/3.99 (![A,Xx,B]: (subset(A,B) => subset(A,setadjoin(Xx,B))))). 23.78/3.99 tff('86', plain, 23.78/3.99 setadjoinSub2 = 23.78/3.99 (![X4,X6,X8]: (subset(X4,X8) => subset(X4,setadjoin(X6,X8)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(setadjoinSub, axiom, setadjoinSub <=> 23.78/3.99 (![Xx,A]: subset(A,setadjoin(Xx,A)))). 23.78/3.99 tff('87', plain, setadjoinSub = (![X4,X6]: subset(X6,setadjoin(X4,X6))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(subsetTrans, axiom, subsetTrans <=> 23.78/3.99 (![A,B,C]: (subset(A,B) => (subset(B,C) => subset(A,C))))). 23.78/3.99 tff('88', plain, 23.78/3.99 subsetTrans = 23.78/3.99 (![X4,X6,X8]: (subset(X4,X6) => (subset(X6,X8) => subset(X4,X8)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(subsetRefl, axiom, subsetRefl <=> (![A]: subset(A,A))). 23.78/3.99 tff('89', plain, subsetRefl = (![X4]: subset(X4,X4)), define([status(thm)])). 23.78/3.99 tff(notequalI2, axiom, notequalI2 <=> 23.78/3.99 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => (A != B))))). 23.78/3.99 tff('90', plain, 23.78/3.99 notequalI2 = (![X4,X6,X8]: (in(X8,X4) => ((~in(X8,X6)) => (X4 != X6)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(notequalI1, axiom, notequalI1 <=> (![A,B]: ((~subset(A,B)) => (A != B)))). 23.78/3.99 tff('91', plain, notequalI1 = (![X4,X6]: ((~subset(X4,X6)) => (X4 != X6))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(notsubsetI, axiom, notsubsetI <=> 23.78/3.99 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => (~subset(A,B)))))). 23.78/3.99 tff('92', plain, 23.78/3.99 notsubsetI = 23.78/3.99 (![X4,X6,X8]: (in(X8,X4) => ((~in(X8,X6)) => (~subset(X4,X6))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(subsetE2, axiom, subsetE2 <=> 23.78/3.99 (![A,B,Xx]: (subset(A,B) => ((~in(Xx,B)) => (~in(Xx,A)))))). 23.78/3.99 tff('93', plain, 23.78/3.99 subsetE2 = 23.78/3.99 (![X4,X6,X8]: (subset(X4,X6) => ((~in(X8,X6)) => (~in(X8,X4))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(subsetE, axiom, subsetE <=> 23.78/3.99 (![A,B,Xx]: (subset(A,B) => (in(Xx,A) => in(Xx,B))))). 23.78/3.99 tff('94', plain, 23.78/3.99 subsetE = (![X4,X6,X8]: (subset(X4,X6) => (in(X8,X4) => in(X8,X6)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(emptysetsubset, axiom, emptysetsubset <=> (![A]: subset(emptyset,A))). 23.78/3.99 tff('95', plain, emptysetsubset = (![X4]: subset(emptyset,X4)), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(subsetI2, axiom, subsetI2 <=> 23.78/3.99 (![A,B]: ((![Xx]: (in(Xx,A) => in(Xx,B))) => subset(A,B)))). 23.78/3.99 tff('96', plain, 23.78/3.99 subsetI2 = 23.78/3.99 (![X4,X6]: ((![X8]: (in(X8,X4) => in(X8,X6))) => subset(X4,X6))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(eqimpsubset1, axiom, eqimpsubset1 <=> (![A,B]: ((A = B) => subset(A,B)))). 23.78/3.99 tff('97', plain, eqimpsubset1 = (![X4,X6]: ((X4 = X6) => subset(X4,X6))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(eqimpsubset2, axiom, eqimpsubset2 <=> (![A,B]: ((A = B) => subset(B,A)))). 23.78/3.99 tff('98', plain, eqimpsubset2 = (![X4,X6]: ((X4 = X6) => subset(X6,X4))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(subsetI1, axiom, subsetI1 <=> 23.78/3.99 (![A,B]: ((![Xx]: (in(Xx,A) => in(Xx,B))) => subset(A,B)))). 23.78/3.99 tff('99', plain, 23.78/3.99 subsetI1 = 23.78/3.99 (![X4,X6]: ((![X8]: (in(X8,X4) => in(X8,X6))) => subset(X4,X6))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(dsetconstr__Cong, axiom, dsetconstr__Cong <=> 23.78/3.99 (![A,B]: 23.78/3.99 ((A = B) => 23.78/3.99 (![Xphi:(($i > $o)),Xpsi:(($i > $o))]: 23.78/3.99 ((![Xx]: 23.78/3.99 (in(Xx,A) => 23.78/3.99 (![Xy]: (in(Xy,B) => ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy))))))) => 23.78/3.99 (dsetconstr(A,^[Xx]: Xphi(Xx)) = dsetconstr(B,^[Xx]: Xpsi(Xx)))))))). 23.78/3.99 tff('100', plain, 23.78/3.99 dsetconstr__Cong = 23.78/3.99 (![X4,X6]: 23.78/3.99 ((X4 = X6) => 23.78/3.99 (![X8:(($i > $o)),X10:(($i > $o))]: 23.78/3.99 ((![X12]: 23.78/3.99 (in(X12,X4) => 23.78/3.99 (![X14]: 23.78/3.99 (in(X14,X6) => ((X12 = X14) => (X8(X12) <=> X10(X14))))))) => 23.78/3.99 (dsetconstr(X4,^[V_1]: X8(V_1)) = dsetconstr(X6,^[V_2]: X10(V_2))))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(descr__Cong, axiom, descr__Cong <=> 23.78/3.99 (![Xphi:(($i > $o)),Xpsi:(($i > $o))]: 23.78/3.99 ((![Xx,Xy]: ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy)))) => 23.78/3.99 (exu(^[Xx]: Xphi(Xx)) => 23.78/3.99 (exu(^[Xx]: Xpsi(Xx)) => 23.78/3.99 (descr(^[Xx]: Xphi(Xx)) = descr(^[Xx]: Xpsi(Xx)))))))). 23.78/3.99 tff('101', plain, 23.78/3.99 descr__Cong = 23.78/3.99 (![X4:(($i > $o)),X6:(($i > $o))]: 23.78/3.99 ((![X8,X10]: ((X8 = X10) => (X4(X8) <=> X6(X10)))) => 23.78/3.99 (exu(^[V_1]: X4(V_1)) => 23.78/3.99 (exu(^[V_2]: X6(V_2)) => 23.78/3.99 (descr(^[V_3]: X4(V_3)) = descr(^[V_4]: X6(V_4))))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(exuEu, axiom, exuEu <=> 23.78/3.99 (![Xphi:(($i > $o))]: 23.78/3.99 (exu(^[Xx]: Xphi(Xx)) => 23.78/3.99 (![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))). 23.78/3.99 tff('102', plain, 23.78/3.99 exuEu = 23.78/3.99 (![X4:(($i > $o))]: 23.78/3.99 (exu(^[V_1]: X4(V_1)) => (![X6,X8]: (X4(X6) => (X4(X8) => (X6 = X8)))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(omega__Cong, axiom, omega__Cong <=> (omega = omega)). 23.78/3.99 tff('103', plain, omega__Cong = (omega = omega), define([status(thm)])). 23.78/3.99 tff(setunion__Cong, axiom, setunion__Cong <=> 23.78/3.99 (![A,B]: ((A = B) => (setunion(A) = setunion(B))))). 23.78/3.99 tff('104', plain, 23.78/3.99 setunion__Cong = (![X4,X6]: ((X4 = X6) => (setunion(X4) = setunion(X6)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(powerset__Cong, axiom, powerset__Cong <=> 23.78/3.99 (![A,B]: ((A = B) => (powerset(A) = powerset(B))))). 23.78/3.99 tff('105', plain, 23.78/3.99 powerset__Cong = (![X4,X6]: ((X4 = X6) => (powerset(X4) = powerset(X6)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(setadjoin__Cong, axiom, setadjoin__Cong <=> 23.78/3.99 (![Xx,Xy]: 23.78/3.99 ((Xx = Xy) => 23.78/3.99 (![Xz,Xu]: ((Xz = Xu) => (setadjoin(Xx,Xz) = setadjoin(Xy,Xu))))))). 23.78/3.99 tff('106', plain, 23.78/3.99 setadjoin__Cong = 23.78/3.99 (![X4,X6]: 23.78/3.99 ((X4 = X6) => 23.78/3.99 (![X8,X10]: ((X8 = X10) => (setadjoin(X4,X8) = setadjoin(X6,X10)))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(emptyset__Cong, axiom, emptyset__Cong <=> (emptyset = emptyset)). 23.78/3.99 tff('107', plain, emptyset__Cong = (emptyset = emptyset), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(exu__Cong, axiom, exu__Cong <=> 23.78/3.99 (![Xphi:(($i > $o)),Xpsi:(($i > $o))]: 23.78/3.99 ((![Xx,Xy]: ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy)))) => 23.78/3.99 (exu(^[Xx]: Xphi(Xx)) <=> exu(^[Xx]: Xpsi(Xx)))))). 23.78/3.99 tff('108', plain, 23.78/3.99 exu__Cong = 23.78/3.99 (![X4:(($i > $o)),X6:(($i > $o))]: 23.78/3.99 ((![X8,X10]: ((X8 = X10) => (X4(X8) <=> X6(X10)))) => 23.78/3.99 (exu(^[V_1]: X4(V_1)) <=> exu(^[V_2]: X6(V_2))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(exuE3u, axiom, exuE3u <=> 23.78/3.99 (![Xphi:(($i > $o))]: 23.78/3.99 (exu(^[Xx]: Xphi(Xx)) => 23.78/3.99 (![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))). 23.78/3.99 tff('109', plain, 23.78/3.99 exuE3u = 23.78/3.99 (![X4:(($i > $o))]: 23.78/3.99 (exu(^[V_1]: X4(V_1)) => (![X6,X8]: (X4(X6) => (X4(X8) => (X6 = X8)))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(in__Cong, axiom, in__Cong <=> 23.78/3.99 (![A,B]: ((A = B) => (![Xx,Xy]: ((Xx = Xy) => (in(Xx,A) <=> in(Xy,B))))))). 23.78/3.99 tff('110', plain, 23.78/3.99 in__Cong = 23.78/3.99 (![X4,X6]: 23.78/3.99 ((X4 = X6) => (![X8,X10]: ((X8 = X10) => (in(X8,X4) <=> in(X10,X6)))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(inCongP, axiom, inCongP <=> 23.78/3.99 (![A,B]: ((A = B) => (![Xx,Xy]: ((Xx = Xy) => (in(Xx,A) => in(Xy,B))))))). 23.78/3.99 tff('111', plain, 23.78/3.99 inCongP = 23.78/3.99 (![X4,X6]: 23.78/3.99 ((X4 = X6) => (![X8,X10]: ((X8 = X10) => (in(X8,X4) => in(X10,X6)))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(exuI2, axiom, exuI2 <=> 23.78/3.99 (![Xphi:(($i > $o))]: 23.78/3.99 ((?[Xx]: (![Xy]: (Xphi(Xy) <=> (Xy = Xx)))) => exu(^[Xx]: Xphi(Xx))))). 23.78/3.99 tff('112', plain, 23.78/3.99 exuI2 = 23.78/3.99 (![X4:(($i > $o))]: 23.78/3.99 ((?[X6]: (![X8]: (X4(X8) <=> (X8 = X6)))) => exu(^[V_1]: X4(V_1)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(exuI3, axiom, exuI3 <=> 23.78/3.99 (![Xphi:(($i > $o))]: 23.78/3.99 ((?[Xx]: Xphi(Xx)) => 23.78/3.99 ((![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy)))) => 23.78/3.99 exu(^[Xx]: Xphi(Xx)))))). 23.78/3.99 tff('113', plain, 23.78/3.99 exuI3 = 23.78/3.99 (![X4:(($i > $o))]: 23.78/3.99 ((?[X6]: X4(X6)) => 23.78/3.99 ((![X8,X10]: (X4(X8) => (X4(X10) => (X8 = X10)))) => 23.78/3.99 exu(^[V_1]: X4(V_1))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(exuI1, axiom, exuI1 <=> 23.78/3.99 (![Xphi:(($i > $o))]: 23.78/3.99 ((?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx))) => 23.78/3.99 exu(^[Xx]: Xphi(Xx))))). 23.78/3.99 tff('114', plain, 23.78/3.99 exuI1 = 23.78/3.99 (![X4:(($i > $o))]: 23.78/3.99 ((?[X6]: ((![X8]: (X4(X8) => (X6 = X8))) & X4(X6))) => 23.78/3.99 exu(^[V_1]: X4(V_1)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(notdallE, axiom, notdallE <=> 23.78/3.99 (![A,Xphi:(($i > $o))]: 23.78/3.99 ((~(![Xx]: (in(Xx,A) => Xphi(Xx)))) => (?[Xx]: ((~Xphi(Xx)) & in(Xx,A)))))). 23.78/3.99 tff('115', plain, 23.78/3.99 notdallE = 23.78/3.99 (![X4,X6:(($i > $o))]: 23.78/3.99 ((~(![X8]: (in(X8,X4) => X6(X8)))) => 23.78/3.99 (?[X10]: ((~X6(X10)) & in(X10,X4))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(notdexE, axiom, notdexE <=> 23.78/3.99 (![A,Xphi:(($i > $o))]: 23.78/3.99 ((~(?[Xx]: (Xphi(Xx) & in(Xx,A)))) => (![Xx]: (in(Xx,A) => (~Xphi(Xx))))))). 23.78/3.99 tff('116', plain, 23.78/3.99 notdexE = 23.78/3.99 (![X4,X6:(($i > $o))]: 23.78/3.99 ((~(?[X8]: (X6(X8) & in(X8,X4)))) => 23.78/3.99 (![X10]: (in(X10,X4) => (~X6(X10)))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(prop2set2propI, axiom, prop2set2propI <=> 23.78/3.99 (![Xphi:$o]: (Xphi => set2prop(prop2set(Xphi))))). 23.78/3.99 tff('117', plain, 23.78/3.99 prop2set2propI = (![X4:$o]: (X4 => set2prop(prop2set(X4)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(prop2setI, axiom, prop2setI <=> 23.78/3.99 (![Xphi:$o]: (Xphi => in(emptyset,prop2set(Xphi))))). 23.78/3.99 tff('118', plain, prop2setI = (![X4:$o]: (X4 => in(emptyset,prop2set(X4)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(quantDeMorgan4, axiom, quantDeMorgan4 <=> 23.78/3.99 (![A,Xphi:(($i > $o))]: 23.78/3.99 ((?[Xx]: ((~Xphi(Xx)) & in(Xx,A))) => (~(![Xx]: (in(Xx,A) => Xphi(Xx))))))). 23.78/3.99 tff('119', plain, 23.78/3.99 quantDeMorgan4 = 23.78/3.99 (![X4,X6:(($i > $o))]: 23.78/3.99 ((?[X8]: ((~X6(X8)) & in(X8,X4))) => 23.78/3.99 (~(![X10]: (in(X10,X4) => X6(X10)))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(quantDeMorgan3, axiom, quantDeMorgan3 <=> 23.78/3.99 (![A,Xphi:(($i > $o))]: 23.78/3.99 ((~(?[Xx]: (Xphi(Xx) & in(Xx,A)))) => (![Xx]: (in(Xx,A) => (~Xphi(Xx))))))). 23.78/3.99 tff('120', plain, 23.78/3.99 quantDeMorgan3 = 23.78/3.99 (![X4,X6:(($i > $o))]: 23.78/3.99 ((~(?[X8]: (X6(X8) & in(X8,X4)))) => 23.78/3.99 (![X10]: (in(X10,X4) => (~X6(X10)))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(quantDeMorgan2, axiom, quantDeMorgan2 <=> 23.78/3.99 (![A,Xphi:(($i > $o))]: 23.78/3.99 ((![Xx]: (in(Xx,A) => (~Xphi(Xx)))) => (~(?[Xx]: (Xphi(Xx) & in(Xx,A))))))). 23.78/3.99 tff('121', plain, 23.78/3.99 quantDeMorgan2 = 23.78/3.99 (![X4,X6:(($i > $o))]: 23.78/3.99 ((![X8]: (in(X8,X4) => (~X6(X8)))) => 23.78/3.99 (~(?[X10]: (X6(X10) & in(X10,X4)))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(quantDeMorgan1, axiom, quantDeMorgan1 <=> 23.78/3.99 (![A,Xphi:(($i > $o))]: 23.78/3.99 ((~(![Xx]: (in(Xx,A) => Xphi(Xx)))) => (?[Xx]: ((~Xphi(Xx)) & in(Xx,A)))))). 23.78/3.99 tff('122', plain, 23.78/3.99 quantDeMorgan1 = 23.78/3.99 (![X4,X6:(($i > $o))]: 23.78/3.99 ((~(![X8]: (in(X8,X4) => X6(X8)))) => 23.78/3.99 (?[X10]: ((~X6(X10)) & in(X10,X4))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(vacuousDall, axiom, vacuousDall <=> 23.78/3.99 (![Xphi:(($i > $o)),Xx]: (in(Xx,emptyset) => Xphi(Xx)))). 23.78/3.99 tff('123', plain, 23.78/3.99 vacuousDall = (![X4:(($i > $o)),X6]: (in(X6,emptyset) => X4(X6))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(emptyE1, axiom, emptyE1 <=> 23.78/3.99 (![A,Xphi:(($i > $o))]: 23.78/3.99 ((?[Xx]: (Xphi(Xx) & in(Xx,A))) => 23.78/3.99 ((dsetconstr(A,^[Xx]: Xphi(Xx)) = emptyset) => $false)))). 23.78/3.99 tff('124', plain, 23.78/3.99 emptyE1 = 23.78/3.99 (![X4,X6:(($i > $o))]: 23.78/3.99 ((?[X8]: (X6(X8) & in(X8,X4))) => 23.78/3.99 ((dsetconstr(X4,^[V_1]: X6(V_1)) = emptyset) => $false))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(upairsetIR, axiom, upairsetIR <=> 23.78/3.99 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 23.78/3.99 tff('125', plain, 23.78/3.99 upairsetIR = (![X4,X6]: in(X6,setadjoin(X4,setadjoin(X6,emptyset)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(upairsetIL, axiom, upairsetIL <=> 23.78/3.99 (![Xx,Xy]: in(Xx,setadjoin(Xx,setadjoin(Xy,emptyset))))). 23.78/3.99 tff('126', plain, 23.78/3.99 upairsetIL = (![X4,X6]: in(X4,setadjoin(X4,setadjoin(X6,emptyset)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(upairsetE, axiom, upairsetE <=> 23.78/3.99 (![Xx,Xy,Xz]: 23.78/3.99 (in(Xz,setadjoin(Xx,setadjoin(Xy,emptyset))) => ((Xz = Xx) | (Xz = Xy))))). 23.78/3.99 tff('127', plain, 23.78/3.99 upairsetE = 23.78/3.99 (![X4,X6,X8]: 23.78/3.99 (in(X8,setadjoin(X4,setadjoin(X6,emptyset))) => 23.78/3.99 ((X8 = X4) | (X8 = X6)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(singletonsswitch, axiom, singletonsswitch <=> 23.78/3.99 (![Xx,Xy]: (in(Xx,setadjoin(Xy,emptyset)) => in(Xy,setadjoin(Xx,emptyset))))). 23.78/3.99 tff('128', plain, 23.78/3.99 singletonsswitch = 23.78/3.99 (![X4,X6]: 23.78/3.99 (in(X4,setadjoin(X6,emptyset)) => in(X6,setadjoin(X4,emptyset)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(eqinunit, axiom, eqinunit <=> 23.78/3.99 (![Xx,Xy]: ((Xx = Xy) => in(Xx,setadjoin(Xy,emptyset))))). 23.78/3.99 tff('129', plain, 23.78/3.99 eqinunit = (![X4,X6]: ((X4 = X6) => in(X4,setadjoin(X6,emptyset)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(notinsingleton, axiom, notinsingleton <=> 23.78/3.99 (![Xx,Xy]: ((Xx != Xy) => (~in(Xy,setadjoin(Xx,emptyset)))))). 23.78/3.99 tff('130', plain, 23.78/3.99 notinsingleton = 23.78/3.99 (![X4,X6]: ((X4 != X6) => (~in(X6,setadjoin(X4,emptyset))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(uniqinunit, axiom, uniqinunit <=> 23.78/3.99 (![Xx,Xy]: (in(Xx,setadjoin(Xy,emptyset)) => (Xx = Xy)))). 23.78/3.99 tff('131', plain, 23.78/3.99 uniqinunit = (![X4,X6]: (in(X4,setadjoin(X6,emptyset)) => (X4 = X6))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(nonemptyImpWitness, axiom, nonemptyImpWitness <=> 23.78/3.99 (![A]: (nonempty(A) => (?[Xx]: in(Xx,A))))). 23.78/3.99 tff('132', plain, 23.78/3.99 nonemptyImpWitness = (![X4]: (nonempty(X4) => (?[X6]: in(X6,X4)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(exuE2, axiom, exuE2 <=> 23.78/3.99 (![Xphi:(($i > $o))]: 23.78/3.99 (exu(^[Xx]: Xphi(Xx)) => (?[Xx]: (![Xy]: (Xphi(Xy) <=> (Xy = Xx))))))). 23.78/3.99 tff('133', plain, 23.78/3.99 exuE2 = 23.78/3.99 (![X4:(($i > $o))]: 23.78/3.99 (exu(^[V_1]: X4(V_1)) => (?[X6]: (![X8]: (X4(X8) <=> (X8 = X6)))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(subPowSU, axiom, subPowSU <=> 23.78/3.99 (![A,Xx]: (in(Xx,A) => in(Xx,powerset(setunion(A)))))). 23.78/3.99 tff('134', plain, 23.78/3.99 subPowSU = (![X4,X6]: (in(X6,X4) => in(X6,powerset(setunion(X4))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(setunionE, axiom, setunionE <=> 23.78/3.99 (![A,Xx]: 23.78/3.99 (in(Xx,setunion(A)) => 23.78/3.99 (![Xphi:$o]: ((![B]: (in(Xx,B) => (in(B,A) => Xphi))) => Xphi))))). 23.78/3.99 tff('135', plain, 23.78/3.99 setunionE = 23.78/3.99 (![X4,X6]: 23.78/3.99 (in(X6,setunion(X4)) => 23.78/3.99 (![X8:$o]: ((![X10]: (in(X6,X10) => (in(X10,X4) => X8))) => X8)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(setunionI, axiom, setunionI <=> 23.78/3.99 (![A,Xx,B]: (in(Xx,B) => (in(B,A) => in(Xx,setunion(A)))))). 23.78/3.99 tff('136', plain, 23.78/3.99 setunionI = 23.78/3.99 (![X4,X6,X8]: (in(X6,X8) => (in(X8,X4) => in(X6,setunion(X4))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(powersetE, axiom, powersetE <=> 23.78/3.99 (![A,B,Xx]: (in(B,powerset(A)) => (in(Xx,B) => in(Xx,A))))). 23.78/3.99 tff('137', plain, 23.78/3.99 powersetE = 23.78/3.99 (![X4,X6,X8]: (in(X6,powerset(X4)) => (in(X8,X6) => in(X8,X4)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(emptyInPowerset, axiom, emptyInPowerset <=> 23.78/3.99 (![A]: in(emptyset,powerset(A)))). 23.78/3.99 tff('138', plain, emptyInPowerset = (![X4]: in(emptyset,powerset(X4))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(emptyinPowerset, axiom, emptyinPowerset <=> 23.78/3.99 (![A]: in(emptyset,powerset(A)))). 23.78/3.99 tff('139', plain, emptyinPowerset = (![X4]: in(emptyset,powerset(X4))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(powersetI, axiom, powersetI <=> 23.78/3.99 (![A,B]: ((![Xx]: (in(Xx,B) => in(Xx,A))) => in(B,powerset(A))))). 23.78/3.99 tff('140', plain, 23.78/3.99 powersetI = 23.78/3.99 (![X4,X6]: ((![X8]: (in(X8,X6) => in(X8,X4))) => in(X6,powerset(X4)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(setoftrueEq, axiom, setoftrueEq <=> 23.78/3.99 (![A]: (dsetconstr(A,^[Xx]: $true) = A))). 23.78/3.99 tff('141', plain, setoftrueEq = (![X4]: (dsetconstr(X4,^[V_1]: $true) = X4)), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(setadjoinOr, axiom, setadjoinOr <=> 23.78/3.99 (![Xx,A,Xy]: (in(Xy,setadjoin(Xx,A)) => ((Xy = Xx) | in(Xy,A))))). 23.78/3.99 tff('142', plain, 23.78/3.99 setadjoinOr = 23.78/3.99 (![X4,X6,X8]: (in(X8,setadjoin(X4,X6)) => ((X8 = X4) | in(X8,X6)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(setadjoinE, axiom, setadjoinE <=> 23.78/3.99 (![Xx,A,Xy]: 23.78/3.99 (in(Xy,setadjoin(Xx,A)) => 23.78/3.99 (![Xphi:$o]: (((Xy = Xx) => Xphi) => ((in(Xy,A) => Xphi) => Xphi)))))). 23.78/3.99 tff('143', plain, 23.78/3.99 setadjoinE = 23.78/3.99 (![X4,X6,X8]: 23.78/3.99 (in(X8,setadjoin(X4,X6)) => 23.78/3.99 (![X10:$o]: (((X8 = X4) => X10) => ((in(X8,X6) => X10) => X10))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(setadjoinIR, axiom, setadjoinIR <=> 23.78/3.99 (![Xx,A,Xy]: (in(Xy,A) => in(Xy,setadjoin(Xx,A))))). 23.78/3.99 tff('144', plain, 23.78/3.99 setadjoinIR = (![X4,X6,X8]: (in(X8,X6) => in(X8,setadjoin(X4,X6)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(emptyinunitempty, axiom, emptyinunitempty() = 23.78/3.99 in(emptyset,setadjoin(emptyset,emptyset))). 23.78/3.99 tff('145', plain, 23.78/3.99 emptyinunitempty = in(emptyset,setadjoin(emptyset,emptyset)), 23.78/3.99 inference('simplify_rw_rule', [status(thm)], [emptyinunitempty])). 23.78/3.99 tff('146', plain, 23.78/3.99 emptyinunitempty = in(emptyset,setadjoin(emptyset,emptyset)), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(setadjoinIL, axiom, setadjoinIL <=> (![Xx,Xy]: in(Xx,setadjoin(Xx,Xy)))). 23.78/3.99 tff('147', plain, setadjoinIL = (![X4,X6]: in(X4,setadjoin(X4,X6))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(nonemptyI1, axiom, nonemptyI1 <=> 23.78/3.99 (![A]: ((?[Xx]: in(Xx,A)) => nonempty(A)))). 23.78/3.99 tff('148', plain, nonemptyI1 = (![X4]: ((?[X6]: in(X6,X4)) => nonempty(X4))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(nonemptyI, axiom, nonemptyI <=> 23.78/3.99 (![A,Xphi:(($i > $o)),Xx]: 23.78/3.99 (in(Xx,A) => (Xphi(Xx) => nonempty(dsetconstr(A,^[Xy]: Xphi(Xy))))))). 23.78/3.99 tff('149', plain, 23.78/3.99 nonemptyI = 23.78/3.99 (![X4,X6:(($i > $o)),X8]: 23.78/3.99 (in(X8,X4) => (X6(X8) => nonempty(dsetconstr(X4,^[V_1]: X6(V_1)))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(nonemptyE1, axiom, nonemptyE1 <=> 23.78/3.99 (![A]: (nonempty(A) => (?[Xx]: in(Xx,A))))). 23.78/3.99 tff('150', plain, nonemptyE1 = (![X4]: (nonempty(X4) => (?[X6]: in(X6,X4)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(nonempty, axiom, nonempty() = ^[Xx]: (Xx != emptyset)). 23.78/3.99 tff('151', plain, nonempty = (^[Xx]: (Xx != emptyset)), 23.78/3.99 inference('simplify_rw_rule', [status(thm)], [nonempty])). 23.78/3.99 tff('152', plain, nonempty = (^[V_1]: (V_1 != emptyset)), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(setbeta, axiom, setbeta <=> 23.78/3.99 (![A,Xphi:(($i > $o)),Xx]: 23.78/3.99 (in(Xx,A) => (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) <=> Xphi(Xx))))). 23.78/3.99 tff('153', plain, 23.78/3.99 setbeta = 23.78/3.99 (![X4,X6:(($i > $o)),X8]: 23.78/3.99 (in(X8,X4) => (in(X8,dsetconstr(X4,^[V_1]: X6(V_1))) <=> X6(X8)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(noeltsimpempty, axiom, noeltsimpempty <=> 23.78/3.99 (![A]: ((![Xx]: (~in(Xx,A))) => (A = emptyset)))). 23.78/3.99 tff('154', plain, 23.78/3.99 noeltsimpempty = (![X4]: ((![X6]: (~in(X6,X4))) => (X4 = emptyset))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(emptyI, axiom, emptyI <=> 23.78/3.99 (![A]: ((![Xx]: (~in(Xx,A))) => (A = emptyset)))). 23.78/3.99 tff('155', plain, 23.78/3.99 emptyI = (![X4]: ((![X6]: (~in(X6,X4))) => (X4 = emptyset))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(setext, axiom, setext <=> 23.78/3.99 (![A,B]: 23.78/3.99 ((![Xx]: (in(Xx,A) => in(Xx,B))) => 23.78/3.99 ((![Xx]: (in(Xx,B) => in(Xx,A))) => (A = B))))). 23.78/3.99 tff('156', plain, 23.78/3.99 setext = 23.78/3.99 (![X4,X6]: 23.78/3.99 ((![X8]: (in(X8,X4) => in(X8,X6))) => 23.78/3.99 ((![X10]: (in(X10,X6) => in(X10,X4))) => (X4 = X6)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(exuE3e, axiom, exuE3e <=> 23.78/3.99 (![Xphi:(($i > $o))]: (exu(^[Xx]: Xphi(Xx)) => (?[Xx]: Xphi(Xx))))). 23.78/3.99 tff('157', plain, 23.78/3.99 exuE3e = (![X4:(($i > $o))]: (exu(^[V_1]: X4(V_1)) => (?[X6]: X4(X6)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(notinemptyset, axiom, notinemptyset <=> (![Xx]: (~in(Xx,emptyset)))). 23.78/3.99 tff('158', plain, notinemptyset = (![X4]: (~in(X4,emptyset))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(emptysetimpfalse, axiom, emptysetimpfalse <=> 23.78/3.99 (![Xx]: (in(Xx,emptyset) => $false))). 23.78/3.99 tff('159', plain, emptysetimpfalse = (![X4]: (in(X4,emptyset) => $false)), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(emptysetE, axiom, emptysetE <=> 23.78/3.99 (![Xx]: (in(Xx,emptyset) => (![Xphi:$o]: Xphi)))). 23.78/3.99 tff('160', plain, emptysetE = (![X4]: (in(X4,emptyset) => (![X6:$o]: X6))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(prop2setE, axiom, prop2setE <=> 23.78/3.99 (![Xphi:$o,Xx]: (in(Xx,prop2set(Xphi)) => Xphi))). 23.78/3.99 tff('161', plain, prop2setE = (![X4:$o,X6]: (in(X6,prop2set(X4)) => X4)), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(exuE1, axiom, exuE1 <=> 23.78/3.99 (![Xphi:(($i > $o))]: 23.78/3.99 (exu(^[Xx]: Xphi(Xx)) => 23.78/3.99 (?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx)))))). 23.78/3.99 tff('162', plain, 23.78/3.99 exuE1 = 23.78/3.99 (![X4:(($i > $o))]: 23.78/3.99 (exu(^[V_1]: X4(V_1)) => 23.78/3.99 (?[X6]: ((![X8]: (X4(X8) => (X6 = X8))) & X4(X6))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(dsetconstrER, axiom, dsetconstrER <=> 23.78/3.99 (![A,Xphi:(($i > $o)),Xx]: 23.78/3.99 (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) => Xphi(Xx)))). 23.78/3.99 tff('163', plain, 23.78/3.99 dsetconstrER = 23.78/3.99 (![X4,X6:(($i > $o)),X8]: 23.78/3.99 (in(X8,dsetconstr(X4,^[V_1]: X6(V_1))) => X6(X8))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(dsetconstrEL, axiom, dsetconstrEL <=> 23.78/3.99 (![A,Xphi:(($i > $o)),Xx]: 23.78/3.99 (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) => in(Xx,A)))). 23.78/3.99 tff('164', plain, 23.78/3.99 dsetconstrEL = 23.78/3.99 (![X4,X6:(($i > $o)),X8]: 23.78/3.99 (in(X8,dsetconstr(X4,^[V_1]: X6(V_1))) => in(X8,X4))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(dsetconstrI, axiom, dsetconstrI <=> 23.78/3.99 (![A,Xphi:(($i > $o)),Xx]: 23.78/3.99 (in(Xx,A) => (Xphi(Xx) => in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))))))). 23.78/3.99 tff('165', plain, 23.78/3.99 dsetconstrI = 23.78/3.99 (![X4,X6:(($i > $o)),X8]: 23.78/3.99 (in(X8,X4) => (X6(X8) => in(X8,dsetconstr(X4,^[V_1]: X6(V_1)))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(descrp, axiom, descrp <=> 23.78/3.99 (![Xphi:(($i > $o))]: 23.78/3.99 (exu(^[Xx]: Xphi(Xx)) => Xphi(descr(^[Xx]: Xphi(Xx)))))). 23.78/3.99 tff('166', plain, 23.78/3.99 descrp = 23.78/3.99 (![X4:(($i > $o))]: (exu(^[V_1]: X4(V_1)) => X4(descr(^[V_2]: X4(V_2))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(wellorderingAx, axiom, wellorderingAx <=> 23.78/3.99 (![A]: 23.78/3.99 (?[B]: 23.78/3.99 ((![C]: 23.78/3.99 (((![Xx]: (in(Xx,C) => in(Xx,A))) & (?[Xx]: in(Xx,C))) => 23.78/3.99 (?[D,Xx]: 23.78/3.99 ((![E]: 23.78/3.99 (in(E,B) => ((![Xy]: (in(Xy,E) => in(Xy,D))) | in(Xx,E)))) & 23.78/3.99 (~(?[Xy]: (in(Xy,C) & in(Xy,D)))) & in(Xx,C) & in(D,B))))) & 23.78/3.99 (![C,D]: 23.78/3.99 ((in(C,B) & in(D,B)) => 23.78/3.99 ((![Xx]: (in(Xx,C) => in(Xx,D))) | 23.78/3.99 (![Xx]: (in(Xx,D) => in(Xx,C)))))) & 23.78/3.99 (![Xx,Xy]: 23.78/3.99 ((in(Xx,A) & in(Xy,A)) => 23.78/3.99 ((![C]: (in(C,B) => (in(Xx,C) <=> in(Xy,C)))) => (Xx = Xy)))) & 23.78/3.99 (![C]: (in(C,B) => (![Xx]: (in(Xx,C) => in(Xx,A))))))))). 23.78/3.99 tff('167', plain, 23.78/3.99 wellorderingAx = 23.78/3.99 (![X4]: 23.78/3.99 (?[X6]: 23.78/3.99 ((![X8]: 23.78/3.99 (((![X10]: (in(X10,X8) => in(X10,X4))) & (?[X12]: in(X12,X8))) => 23.78/3.99 (?[X14,X16]: 23.78/3.99 ((![X18]: 23.78/3.99 (in(X18,X6) => 23.78/3.99 ((![X20]: (in(X20,X18) => in(X20,X14))) | in(X16,X18)))) & 23.78/3.99 (~(?[X22]: (in(X22,X8) & in(X22,X14)))) & in(X16,X8) & 23.78/3.99 in(X14,X6))))) & 23.78/3.99 (![X24,X26]: 23.78/3.99 ((in(X24,X6) & in(X26,X6)) => 23.78/3.99 ((![X28]: (in(X28,X24) => in(X28,X26))) | 23.78/3.99 (![X30]: (in(X30,X26) => in(X30,X24)))))) & 23.78/3.99 (![X32,X34]: 23.78/3.99 ((in(X32,X4) & in(X34,X4)) => 23.78/3.99 ((![X36]: (in(X36,X6) => (in(X32,X36) <=> in(X34,X36)))) => 23.78/3.99 (X32 = X34)))) & 23.78/3.99 (![X38]: (in(X38,X6) => (![X40]: (in(X40,X38) => in(X40,X4)))))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(foundationAx, axiom, foundationAx <=> 23.78/3.99 (![A]: 23.78/3.99 ((?[Xx]: in(Xx,A)) => 23.78/3.99 (?[B]: ((~(?[Xx]: (in(Xx,A) & in(Xx,B)))) & in(B,A)))))). 23.78/3.99 tff('168', plain, 23.78/3.99 foundationAx = 23.78/3.99 (![X4]: 23.78/3.99 ((?[X6]: in(X6,X4)) => 23.78/3.99 (?[X8]: ((~(?[X10]: (in(X10,X4) & in(X10,X8)))) & in(X8,X4))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(replAx, axiom, replAx <=> 23.78/3.99 (![Xphi:(($i * $i) > $o),A]: 23.78/3.99 ((![Xx]: (in(Xx,A) => exu(^[Xy]: Xphi(Xx,Xy)))) => 23.78/3.99 (?[B]: (![Xx]: (in(Xx,B) <=> (?[Xy]: (Xphi(Xy,Xx) & in(Xy,A))))))))). 23.78/3.99 tff('169', plain, 23.78/3.99 replAx = 23.78/3.99 (![X4:(($i * $i) > $o),X6]: 23.78/3.99 ((![X8]: (in(X8,X6) => exu(^[V_1]: X4(X8,V_1)))) => 23.78/3.99 (?[X10]: 23.78/3.99 (![X12]: (in(X12,X10) <=> (?[X14]: (X4(X14,X12) & in(X14,X6)))))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(omegaIndAx, axiom, omegaIndAx <=> 23.78/3.99 (![A]: 23.78/3.99 ((in(emptyset,A) & 23.78/3.99 (![Xx]: ((in(Xx,omega) & in(Xx,A)) => in(setadjoin(Xx,Xx),A)))) => 23.78/3.99 (![Xx]: (in(Xx,omega) => in(Xx,A)))))). 23.78/3.99 tff('170', plain, 23.78/3.99 omegaIndAx = 23.78/3.99 (![X4]: 23.78/3.99 ((in(emptyset,X4) & 23.78/3.99 (![X6]: ((in(X6,omega) & in(X6,X4)) => in(setadjoin(X6,X6),X4)))) => 23.78/3.99 (![X8]: (in(X8,omega) => in(X8,X4))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(omegaSAx, axiom, omegaSAx <=> 23.78/3.99 (![Xx]: (in(Xx,omega) => in(setadjoin(Xx,Xx),omega)))). 23.78/3.99 tff('171', plain, 23.78/3.99 omegaSAx = (![X4]: (in(X4,omega) => in(setadjoin(X4,X4),omega))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(omega0Ax, axiom, omega0Ax() = in(emptyset,omega)). 23.78/3.99 tff('172', plain, omega0Ax = in(emptyset,omega), 23.78/3.99 inference('simplify_rw_rule', [status(thm)], [omega0Ax])). 23.78/3.99 tff('173', plain, omega0Ax = in(emptyset,omega), define([status(thm)])). 23.78/3.99 tff(setunionAx, axiom, setunionAx <=> 23.78/3.99 (![A,Xx]: (in(Xx,setunion(A)) <=> (?[B]: (in(B,A) & in(Xx,B)))))). 23.78/3.99 tff('174', plain, 23.78/3.99 setunionAx = 23.78/3.99 (![X4,X6]: (in(X6,setunion(X4)) <=> (?[X8]: (in(X8,X4) & in(X6,X8))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(powersetAx, axiom, powersetAx <=> 23.78/3.99 (![A,B]: (in(B,powerset(A)) <=> (![Xx]: (in(Xx,B) => in(Xx,A)))))). 23.78/3.99 tff('175', plain, 23.78/3.99 powersetAx = 23.78/3.99 (![X4,X6]: (in(X6,powerset(X4)) <=> (![X8]: (in(X8,X6) => in(X8,X4))))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(setadjoinAx, axiom, setadjoinAx <=> 23.78/3.99 (![Xx,A,Xy]: (in(Xy,setadjoin(Xx,A)) <=> ((Xy = Xx) | in(Xy,A))))). 23.78/3.99 tff('176', plain, 23.78/3.99 setadjoinAx = 23.78/3.99 (![X4,X6,X8]: (in(X8,setadjoin(X4,X6)) <=> ((X8 = X4) | in(X8,X6)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(emptysetAx, axiom, emptysetAx <=> (![Xx]: (~in(Xx,emptyset)))). 23.78/3.99 tff('177', plain, emptysetAx = (![X4]: (~in(X4,emptyset))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(setextAx, axiom, setextAx <=> 23.78/3.99 (![A,B]: ((![Xx]: (in(Xx,A) <=> in(Xx,B))) => (A = B)))). 23.78/3.99 tff('178', plain, 23.78/3.99 setextAx = (![X4,X6]: ((![X8]: (in(X8,X4) <=> in(X8,X6))) => (X4 = X6))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(exu, axiom, exu() = 23.78/3.99 ^[Xphi:(($i > $o))]: (?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx)))). 23.78/3.99 tff('179', plain, 23.78/3.99 exu = 23.78/3.99 (^[Xphi:(($i > $o))]: 23.78/3.99 (?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx)))), 23.78/3.99 inference('simplify_rw_rule', [status(thm)], [exu])). 23.78/3.99 tff('180', plain, 23.78/3.99 exu = 23.78/3.99 (^[V_1:(($i > $o))]: (?[X4]: ((![X6]: (V_1(X6) => (X4 = X6))) & V_1(X4)))), 23.78/3.99 define([status(thm)])). 23.78/3.99 tff(setukpairinjR1, conjecture, 23.78/3.99 (setextAx => 23.78/3.99 (emptysetAx => 23.78/3.99 (setadjoinAx => 23.78/3.99 (powersetAx => 23.78/3.99 (setunionAx => 23.78/3.99 (omega0Ax => 23.78/3.99 (omegaSAx => 23.78/3.99 (omegaIndAx => 23.78/3.99 (replAx => 23.78/3.99 (foundationAx => 23.78/3.99 (wellorderingAx => 23.78/3.99 (descrp => 23.78/3.99 (dsetconstrI => 23.78/3.99 (dsetconstrEL => 23.78/3.99 (dsetconstrER => 23.78/3.99 (exuE1 => 23.78/3.99 (prop2setE => 23.78/3.99 (emptysetE => 23.78/3.99 (emptysetimpfalse => 23.78/3.99 (notinemptyset => 23.78/3.99 (exuE3e => 23.78/3.99 (setext => 23.78/3.99 (emptyI => 23.78/3.99 (noeltsimpempty => 23.78/3.99 (setbeta => 23.78/3.99 (nonemptyE1 => 23.78/3.99 (nonemptyI => 23.78/3.99 (nonemptyI1 => 23.78/3.99 (setadjoinIL => 23.78/3.99 (emptyinunitempty => 23.78/3.99 (setadjoinIR => 23.78/3.99 (setadjoinE => 23.78/3.99 (setadjoinOr => 23.78/3.99 (setoftrueEq => 23.78/3.99 (powersetI => 23.78/3.99 (emptyinPowerset => 23.78/3.99 (emptyInPowerset => 23.78/3.99 (powersetE => 23.78/3.99 (setunionI => 23.78/3.99 (setunionE => 23.78/3.99 (subPowSU => 23.78/3.99 (exuE2 => 23.78/3.99 (nonemptyImpWitness => 23.78/3.99 (uniqinunit => 23.78/3.99 (notinsingleton => 23.78/3.99 (eqinunit => 23.78/3.99 (singletonsswitch => 23.78/3.99 (upairsetE => 23.78/3.99 (upairsetIL => 23.78/3.99 (upairsetIR => 23.78/3.99 (emptyE1 => 23.78/3.99 (vacuousDall => 23.78/3.99 (quantDeMorgan1 => 23.78/3.99 (quantDeMorgan2 => 23.78/3.99 (quantDeMorgan3 => 23.78/3.99 (quantDeMorgan4 => 23.78/3.99 (prop2setI => 23.78/3.99 (prop2set2propI => 23.78/3.99 (notdexE => 23.78/3.99 (notdallE => 23.78/3.99 (exuI1 => 23.78/3.99 (exuI3 => 23.78/3.99 (exuI2 => 23.78/3.99 (inCongP => 23.78/3.99 (in__Cong => 23.78/3.99 (exuE3u => 23.78/3.99 ( 23.78/3.99 exu__Cong => 23.78/3.99 ( 23.78/3.99 emptyset__Cong => 23.78/3.99 ( 23.78/3.99 setadjoin__Cong => 23.78/3.99 ( 23.78/3.99 powerset__Cong => 23.78/3.99 ( 23.78/3.99 setunion__Cong => 23.78/3.99 ( 23.78/3.99 omega__Cong => 23.78/3.99 ( 23.78/3.99 exuEu => 23.78/3.99 ( 23.78/3.99 descr__Cong => 23.78/3.99 ( 23.78/3.99 dsetconstr__Cong => 23.78/3.99 ( 23.78/3.99 subsetI1 => 23.78/3.99 ( 23.78/3.99 eqimpsubset2 => 23.78/3.99 ( 23.78/3.99 eqimpsubset1 => 23.78/3.99 ( 23.78/3.99 subsetI2 => 23.78/3.99 ( 23.78/3.99 emptysetsubset => 23.78/3.99 ( 23.78/3.99 subsetE => 23.78/3.99 ( 23.78/3.99 subsetE2 => 23.78/3.99 ( 23.78/3.99 notsubsetI => 23.78/3.99 ( 23.78/3.99 notequalI1 => 23.78/3.99 ( 23.78/3.99 notequalI2 => 23.78/3.99 ( 23.78/3.99 subsetRefl => 23.78/3.99 ( 23.78/3.99 subsetTrans => 23.78/3.99 ( 23.78/3.99 setadjoinSub => 23.78/3.99 ( 23.78/3.99 setadjoinSub2 => 23.78/3.99 ( 23.78/3.99 subset2powerset => 23.78/3.99 ( 23.78/3.99 setextsub => 23.78/3.99 ( 23.78/3.99 subsetemptysetimpeq => 23.78/3.99 ( 23.78/3.99 powersetI1 => 23.78/3.99 ( 23.78/3.99 powersetE1 => 23.78/3.99 ( 23.78/3.99 inPowerset => 23.78/3.99 ( 23.78/3.99 powersetsubset => 23.78/3.99 ( 23.78/3.99 sepInPowerset => 23.78/3.99 ( 23.78/3.99 sepSubset => 23.78/3.99 ( 23.78/3.99 binunionIL => 23.78/3.99 ( 23.78/3.99 upairset2IR => 23.78/3.99 ( 23.78/3.99 binunionIR => 23.78/3.99 ( 23.78/3.99 binunionEcases => 23.78/3.99 ( 23.78/3.99 binunionE => 23.78/3.99 ( 23.78/3.99 binunionLsub => 23.78/3.99 ( 23.78/3.99 binunionRsub => 23.78/3.99 ( 23.78/3.99 binintersectI => 23.78/3.99 ( 23.78/3.99 binintersectSubset5 => 23.78/3.99 ( 23.78/3.99 binintersectEL => 23.78/3.99 ( 23.78/3.99 binintersectLsub => 23.78/3.99 ( 23.78/3.99 binintersectSubset2 => 23.78/3.99 ( 23.78/3.99 binintersectSubset3 => 23.78/3.99 ( 23.78/3.99 binintersectER => 23.78/3.99 ( 23.78/3.99 disjointsetsI1 => 23.78/3.99 ( 23.78/3.99 binintersectRsub => 23.78/3.99 ( 23.78/3.99 binintersectSubset4 => 23.78/3.99 ( 23.78/3.99 binintersectSubset1 => 23.78/3.99 ( 23.78/3.99 bs114d => 23.78/3.99 ( 23.78/3.99 setminusI => 23.78/3.99 ( 23.78/3.99 setminusEL => 23.78/3.99 ( 23.78/3.99 setminusER => 23.78/3.99 ( 23.78/3.99 setminusSubset2 => 23.78/3.99 ( 23.78/3.99 setminusERneg => 23.78/3.99 ( 23.78/3.99 setminusELneg => 23.78/3.99 ( 23.78/3.99 setminusILneg => 23.78/3.99 ( 23.78/3.99 setminusIRneg => 23.78/3.99 ( 23.78/3.99 setminusLsub => 23.78/3.99 ( 23.78/3.99 setminusSubset1 => 23.78/3.99 ( 23.78/3.99 symdiffE => 23.78/3.99 ( 23.78/3.99 symdiffI1 => 23.78/3.99 ( 23.78/3.99 symdiffI2 => 23.78/3.99 ( 23.78/3.99 symdiffIneg1 => 23.78/3.99 ( 23.78/3.99 symdiffIneg2 => 23.78/3.99 ( 23.78/3.99 secondinupair => 23.78/3.99 ( 23.78/3.99 setukpairIL => 23.78/3.99 ( 23.78/3.99 setukpairIR => 23.78/3.99 ( 23.78/3.99 kpairiskpair => 23.78/3.99 ( 23.78/3.99 kpairp => 23.78/3.99 ( 23.78/3.99 singletonsubset => 23.78/3.99 ( 23.78/3.99 singletoninpowerset => 23.78/3.99 ( 23.78/3.99 singletoninpowunion => 23.78/3.99 ( 23.78/3.99 upairset2E => 23.78/3.99 ( 23.78/3.99 upairsubunion => 23.78/3.99 ( 23.78/3.99 upairinpowunion => 23.78/3.99 ( 23.78/3.99 ubforcartprodlem1 => 23.78/3.99 ( 23.78/3.99 ubforcartprodlem2 => 23.78/3.99 ( 23.78/3.99 ubforcartprodlem3 => 23.78/3.99 ( 23.78/3.99 cartprodpairin => 23.78/3.99 ( 23.78/3.99 cartprodmempair1 => 23.78/3.99 ( 23.78/3.99 cartprodmempair => 23.78/3.99 ( 23.78/3.99 setunionE2 => 23.78/3.99 ( 23.78/3.99 setunionsingleton1 => 23.78/3.99 ( 23.78/3.99 setunionsingleton2 => 23.78/3.99 ( 23.78/3.99 setunionsingleton => 23.78/3.99 ( 23.78/3.99 singletonprop => 23.78/3.99 ( 23.78/3.99 ex1E1 => 23.78/3.99 ( 23.78/3.99 ex1I => 23.78/3.99 ( 23.78/3.99 ex1I2 => 23.78/3.99 ( 23.78/3.99 singletonsuniq => 23.78/3.99 ( 23.78/3.99 setukpairinjL1 => 23.78/3.99 ( 23.78/3.99 kfstsingleton => 23.78/3.99 ( 23.78/3.99 theprop => 23.78/3.99 ( 23.78/3.99 kfstpairEq => 23.78/3.99 ( 23.78/3.99 cartprodfstin => 23.78/3.99 ( 23.78/3.99 setukpairinjL2 => 23.78/3.99 ( 23.78/3.99 setukpairinjL => 23.78/3.99 ( 23.78/3.99 setukpairinjR11 => 23.78/3.99 ( 23.78/3.99 setukpairinjR12 => 23.78/3.99 ( 23.78/3.99 ![Xx,Xy, 23.78/3.99 Xz,Xu]: 23.78/3.99 (( 23.78/3.99 setadjoin( 23.78/3.99 setadjoin( 23.78/3.99 Xx, 23.78/3.99 emptyset), 23.78/3.99 setadjoin( 23.78/3.99 setadjoin( 23.78/3.99 Xx, 23.78/3.99 setadjoin( 23.78/3.99 Xy, 23.78/3.99 emptyset)), 23.78/3.99 emptyset)) = 23.78/3.99 setadjoin( 23.78/3.99 setadjoin( 23.78/3.99 Xz, 23.78/3.99 emptyset), 23.78/3.99 setadjoin( 23.78/3.99 setadjoin( 23.78/3.99 Xz, 23.78/3.99 setadjoin( 23.78/3.99 Xu, 23.78/3.99 emptyset)), 23.78/3.99 emptyset))) => 23.78/3.99 (( 23.78/3.99 Xz = Xu) => 23.78/3.99 (Xy = Xu)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 23.78/3.99 tff(zf_stmt_0, conjecture, 23.78/3.99 ((![X4,X6]: ((![X8]: (in(X8,X4) <=> in(X8,X6))) => (X4 = X6))) => 23.78/3.99 ((![X10]: (~in(X10,emptyset))) => 23.78/3.99 ((![X12,X14,X16]: 23.78/3.99 (in(X16,setadjoin(X12,X14)) <=> (in(X16,X14) | (X16 = X12)))) => 23.78/3.99 ((![X18,X20]: 23.78/3.99 (in(X20,powerset(X18)) <=> (![X22]: (in(X22,X20) => in(X22,X18))))) => 23.78/3.99 ((![X24,X26]: 23.78/3.99 (in(X26,setunion(X24)) <=> (?[X28]: (in(X26,X28) & in(X28,X24))))) => 23.78/3.99 (in(emptyset,omega) => 23.78/3.99 ((![X30]: (in(X30,omega) => in(setadjoin(X30,X30),omega))) => 23.78/3.99 ((![X32]: 23.78/3.99 (((![X34]: 23.78/3.99 ((in(X34,X32) & in(X34,omega)) => 23.78/3.99 in(setadjoin(X34,X34),X32))) & 23.78/3.99 in(emptyset,X32)) => 23.78/3.99 (![X36]: (in(X36,omega) => in(X36,X32))))) => 23.78/3.99 ((![X38:(($i * $i) > $o),X40]: 23.78/3.99 ((![X42]: 23.78/3.99 (in(X42,X40) => 23.78/3.99 (?[X44]: 23.78/3.99 (X38(X42,X44) & (![X46]: (X38(X42,X46) => (X44 = X46))))))) => 23.78/3.99 (?[X48]: 23.78/3.99 (![X50]: 23.78/3.99 (in(X50,X48) <=> (?[X52]: (in(X52,X40) & X38(X52,X50)))))))) => 23.78/3.99 ((![X54]: 23.78/3.99 ((?[X56]: in(X56,X54)) => 23.78/3.99 (?[X58]: 23.78/3.99 (in(X58,X54) & (~(?[X60]: (in(X60,X58) & in(X60,X54)))))))) => 23.78/3.99 ((![X62]: 23.78/3.99 (?[X64]: 23.78/3.99 ((![X96]: 23.78/3.99 (in(X96,X64) => (![X98]: (in(X98,X96) => in(X98,X62))))) & 23.78/3.99 (![X90,X92]: 23.78/3.99 ((in(X92,X62) & in(X90,X62)) => 23.78/3.99 ((![X94]: 23.78/3.99 (in(X94,X64) => (in(X90,X94) <=> in(X92,X94)))) => 23.78/3.99 (X90 = X92)))) & 23.78/3.99 (![X82,X84]: 23.78/3.99 ((in(X84,X64) & in(X82,X64)) => 23.78/3.99 ((![X88]: (in(X88,X84) => in(X88,X82))) | 23.78/3.99 (![X86]: (in(X86,X82) => in(X86,X84)))))) & 23.78/3.99 (![X66]: 23.78/3.99 (((?[X70]: in(X70,X66)) & 23.78/3.99 (![X68]: (in(X68,X66) => in(X68,X62)))) => 23.78/3.99 (?[X72,X74]: 23.78/3.99 (in(X72,X64) & in(X74,X66) & 23.78/3.99 (~(?[X80]: (in(X80,X72) & in(X80,X66)))) & 23.78/3.99 (![X76]: 23.78/3.99 (in(X76,X64) => 23.78/3.99 (in(X74,X76) | 23.78/3.99 (![X78]: (in(X78,X76) => in(X78,X72))))))))))))) => 23.78/3.99 ((![X100:(($i > $o))]: 23.78/3.99 ((?[X102]: 23.78/3.99 (X100(X102) & (![X104]: (X100(X104) => (X102 = X104))))) => 23.78/3.99 X100(descr(^[V_1]: X100(V_1))))) => 23.78/3.99 ((![X106,X108:(($i > $o)),X110]: 23.78/3.99 (in(X110,X106) => 23.78/3.99 (X108(X110) => in(X110,dsetconstr(X106,^[V_2]: X108(V_2)))))) => 23.78/3.99 ((![X112,X114:(($i > $o)),X116]: 23.78/3.99 (in(X116,dsetconstr(X112,^[V_3]: X114(V_3))) => 23.78/3.99 in(X116,X112))) => 23.78/3.99 ((![X118,X120:(($i > $o)),X122]: 23.78/3.99 (in(X122,dsetconstr(X118,^[V_4]: X120(V_4))) => 23.78/3.99 X120(X122))) => 23.78/3.99 ((![X124:(($i > $o))]: 23.78/3.99 ((?[X126]: 23.78/3.99 (X124(X126) & 23.78/3.99 (![X128]: (X124(X128) => (X126 = X128))))) => 23.78/3.99 (?[X130]: 23.78/3.99 (X124(X130) & 23.78/3.99 (![X132]: (X124(X132) => (X130 = X132))))))) => 23.78/3.99 ((![X134:$o,X136]: (in(X136,prop2set(X134)) => X134)) => 23.78/3.99 ((![X138]: (in(X138,emptyset) => (![X140:$o]: X140))) => 23.78/3.99 ((![X142]: (in(X142,emptyset) => $false)) => 23.78/3.99 ((![X144]: (~in(X144,emptyset))) => 23.78/3.99 ((![X146:(($i > $o))]: 23.78/3.99 ((?[X148]: 23.78/3.99 (X146(X148) & 23.78/3.99 (![X150]: (X146(X150) => (X148 = X150))))) => 23.78/3.99 (?[X152]: X146(X152)))) => 23.78/3.99 ((![X154,X156]: 23.78/3.99 ((![X158]: (in(X158,X154) => in(X158,X156))) => 23.78/3.99 ((![X160]: (in(X160,X156) => in(X160,X154))) => 23.78/3.99 (X154 = X156)))) => 23.78/3.99 ((![X162]: 23.78/3.99 ((![X164]: (~in(X164,X162))) => (X162 = emptyset))) => 23.78/3.99 ((![X166]: 23.78/3.99 ((![X168]: (~in(X168,X166))) => 23.78/3.99 (X166 = emptyset))) => 23.78/3.99 ((![X170,X172:(($i > $o)),X174]: 23.78/3.99 (in(X174,X170) => 23.78/3.99 (in(X174,dsetconstr(X170,^[V_5]: X172(V_5))) <=> 23.78/3.99 X172(X174)))) => 23.78/3.99 ((![X176]: 23.78/3.99 ((X176 != emptyset) => 23.78/3.99 (?[X178]: in(X178,X176)))) => 23.78/3.99 ((![X180,X182:(($i > $o)),X184]: 23.78/3.99 (in(X184,X180) => 23.78/3.99 (X182(X184) => 23.78/3.99 (dsetconstr(X180,^[V_6]: X182(V_6)) != 23.78/3.99 emptyset)))) => 23.78/3.99 ((![X186]: 23.78/3.99 ((?[X188]: in(X188,X186)) => 23.78/3.99 (X186 != emptyset))) => 23.78/3.99 ((![X190,X192]: in(X190,setadjoin(X190,X192))) => 23.78/3.99 (in(emptyset,setadjoin(emptyset,emptyset)) => 23.78/3.99 ((![X194,X196,X198]: 23.78/3.99 (in(X198,X196) => 23.78/3.99 in(X198,setadjoin(X194,X196)))) => 23.78/3.99 ((![X200,X202,X204]: 23.78/3.99 (in(X204,setadjoin(X200,X202)) => 23.78/3.99 (![X206:$o]: 23.78/3.99 (((X204 = X200) => X206) => 23.78/3.99 ((in(X204,X202) => X206) => X206))))) => 23.78/3.99 ((![X208,X210,X212]: 23.78/3.99 (in(X212,setadjoin(X208,X210)) => 23.78/3.99 (in(X212,X210) | (X212 = X208)))) => 23.78/3.99 ((![X214]: 23.78/3.99 (dsetconstr(X214,^[V_7]: $true) = X214)) => 23.78/3.99 ((![X216,X218]: 23.78/3.99 ((![X220]: 23.78/3.99 (in(X220,X218) => in(X220,X216))) => 23.78/3.99 in(X218,powerset(X216)))) => 23.78/3.99 ((![X222]: in(emptyset,powerset(X222))) => 23.78/3.99 ((![X224]: in(emptyset,powerset(X224))) => 23.78/3.99 ((![X226,X228,X230]: 23.78/3.99 (in(X228,powerset(X226)) => 23.78/3.99 (in(X230,X228) => in(X230,X226)))) => 23.78/3.99 ((![X232,X234,X236]: 23.78/3.99 (in(X234,X236) => 23.78/3.99 (in(X236,X232) => 23.78/3.99 in(X234,setunion(X232))))) => 23.78/3.99 ((![X238,X240]: 23.78/3.99 (in(X240,setunion(X238)) => 23.78/3.99 (![X242:$o]: 23.78/3.99 ((![X244]: 23.78/3.99 (in(X240,X244) => 23.78/3.99 (in(X244,X238) => X242))) => 23.78/3.99 X242)))) => 23.78/3.99 ((![X246,X248]: 23.78/3.99 (in(X248,X246) => 23.78/3.99 in(X248, 23.78/3.99 powerset(setunion(X246))))) => 23.78/3.99 ((![X250:(($i > $o))]: 23.78/3.99 ((?[X252]: 23.78/3.99 (X250(X252) & 23.78/3.99 (![X254]: 23.78/3.99 (X250(X254) => 23.78/3.99 (X252 = X254))))) => 23.78/3.99 (?[X256]: 23.78/3.99 (![X258]: 23.78/3.99 (X250(X258) <=> 23.78/3.99 (X258 = X256)))))) => 23.78/3.99 ((![X260]: 23.78/3.99 ((X260 != emptyset) => 23.78/3.99 (?[X262]: in(X262,X260)))) => 23.78/3.99 ((![X264,X266]: 23.78/3.99 (in(X264, 23.78/3.99 setadjoin(X266,emptyset)) => 23.78/3.99 (X264 = X266))) => 23.78/3.99 ((![X268,X270]: 23.78/3.99 ((X268 != X270) => 23.78/3.99 (~ 23.78/3.99 in(X270, 23.78/3.99 setadjoin(X268, 23.78/3.99 emptyset))))) => 23.78/3.99 ((![X272,X274]: 23.78/3.99 ((X272 = X274) => 23.78/3.99 in(X272, 23.78/3.99 setadjoin(X274, 23.78/3.99 emptyset)))) => 23.78/3.99 ((![X276,X278]: 23.78/3.99 (in(X276, 23.78/3.99 setadjoin(X278, 23.78/3.99 emptyset)) => 23.78/3.99 in(X278, 23.78/3.99 setadjoin(X276, 23.78/3.99 emptyset)))) => 23.78/3.99 ((![X280,X282,X284]: 23.78/3.99 (in(X284, 23.78/3.99 setadjoin(X280, 23.78/3.99 setadjoin( 23.78/3.99 X282, 23.78/3.99 emptyset))) => 23.78/3.99 ((X284 = X282) | 23.78/3.99 (X284 = X280)))) => 23.78/3.99 ((![X286,X288]: 23.78/3.99 in(X286, 23.78/3.99 setadjoin(X286, 23.78/3.99 setadjoin( 23.78/3.99 X288, 23.78/3.99 emptyset)))) => 23.78/3.99 ((![X290,X292]: 23.78/3.99 in(X292, 23.78/3.99 setadjoin(X290, 23.78/3.99 setadjoin( 23.78/3.99 X292, 23.78/3.99 emptyset)))) => 23.78/3.99 ((![X294,X296:(($i > $o))]: 23.78/3.99 ((?[X298]: 23.78/3.99 (in(X298,X294) & 23.78/3.99 X296(X298))) => 23.78/3.99 ((dsetconstr( 23.78/3.99 X294, 23.78/3.99 ^[V_8]: X296(V_8)) = 23.78/3.99 emptyset) => 23.78/3.99 $false))) => 23.78/3.99 ((![X300:(($i > $o)), 23.78/3.99 X302]: 23.78/3.99 (in(X302,emptyset) => 23.78/3.99 X300(X302))) => 23.78/3.99 ((![X304, 23.78/3.99 X306:(($i > $o))]: 23.78/3.99 ((~ 23.78/3.99 (![X308]: 23.78/3.99 (in(X308,X304) => 23.78/3.99 X306(X308)))) => 23.78/3.99 (?[X310]: 23.78/3.99 (in(X310,X304) & 23.78/3.99 (~X306(X310)))))) => 23.78/3.99 ((![X312, 23.78/3.99 X314:(($i > $o))]: 23.78/3.99 ((![X316]: 23.78/3.99 (in(X316,X312) => 23.78/3.99 (~X314(X316)))) => 23.78/3.99 (~ 23.78/3.99 (?[X318]: 23.78/3.99 (in( 23.78/3.99 X318,X312) & 23.78/3.99 X314(X318)))))) => 23.78/3.99 ((![X320, 23.78/3.99 X322:(($i > $o))]: 23.78/3.99 ((~ 23.78/3.99 (?[X324]: 23.78/3.99 (in( 23.78/3.99 X324,X320) & 23.78/3.99 X322(X324)))) => 23.78/3.99 (![X326]: 23.78/3.99 (in(X326,X320) => 23.78/3.99 (~X322(X326)))))) => 23.78/3.99 ((![X328, 23.78/3.99 X330:(($i > $o))]: 23.78/3.99 ((?[X332]: 23.78/3.99 (in( 23.78/3.99 X332,X328) & 23.78/3.99 (~ 23.78/3.99 X330( 23.78/3.99 X332)))) => 23.78/3.99 (~ 23.78/3.99 (![X334]: 23.78/3.99 (in( 23.78/3.99 X334,X328) => 23.78/3.99 X330( 23.78/3.99 X334)))))) => 23.78/3.99 ((![X336:$o]: 23.78/3.99 (X336 => 23.78/3.99 in(emptyset, 23.78/3.99 prop2set( 23.78/3.99 X336)))) => 23.78/3.99 ((![X338:$o]: 23.78/3.99 (X338 => 23.78/3.99 set2prop( 23.78/3.99 prop2set( 23.78/3.99 X338)))) => 23.78/3.99 ((![X340, 23.78/3.99 X342:( 23.78/3.99 ($i > $o))]: 23.78/3.99 ((~ 23.78/3.99 (?[X344]: 23.78/3.99 (in( 23.78/3.99 X344,X340) & 23.78/3.99 X342( 23.78/3.99 X344)))) => 23.78/3.99 (![X346]: 23.78/3.99 ( 23.78/3.99 in( 23.78/3.99 X346,X340) => 23.78/3.99 ( 23.78/3.99 ~ 23.78/3.99 X342( 23.78/3.99 X346)))))) => 23.78/3.99 ((![X348, 23.78/3.99 X350:( 23.78/3.99 ($i > $o))]: 23.78/3.99 ((~ 23.78/3.99 ( 23.78/3.99 ![X352]: 23.78/3.99 (in( 23.78/3.99 X352,X348) => 23.78/3.99 X350( 23.78/3.99 X352)))) => 23.78/3.99 (?[X354]: 23.78/3.99 (in( 23.78/3.99 X354,X348) & 23.78/3.99 (~ 23.78/3.99 X350( 23.78/3.99 X354)))))) => 23.78/3.99 ((![X356:( 23.78/3.99 ($i > $o))]: 23.78/3.99 ((?[X358]: 23.78/3.99 (X356( 23.78/3.99 X358) & 23.78/3.99 (![X360]: 23.78/3.99 (X356( 23.78/3.99 X360) => 23.78/3.99 (X358 = 23.78/3.99 X360))))) => 23.78/3.99 (?[X362]: 23.78/3.99 (X356( 23.78/3.99 X362) & 23.78/3.99 (![X364]: 23.78/3.99 (X356( 23.78/3.99 X364) => 23.78/3.99 (X362 = 23.78/3.99 X364))))))) => 23.78/3.99 ((![X366:( 23.78/3.99 ($i > $o))]: 23.78/3.99 (( 23.78/3.99 ?[X368]: 23.78/3.99 X366( 23.78/3.99 X368)) => 23.78/3.99 ( 23.78/3.99 ( 23.78/3.99 ![X370, 23.78/3.99 X372]: 23.78/3.99 (X366( 23.78/3.99 X370) => 23.78/3.99 (X366( 23.78/3.99 X372) => 23.78/3.99 (X370 = 23.78/3.99 X372)))) => 23.78/3.99 ( 23.78/3.99 ?[X374]: 23.78/3.99 (X366( 23.78/3.99 X374) & 23.78/3.99 (![X376]: 23.78/3.99 (X366( 23.78/3.99 X376) => 23.78/3.99 (X374 = 23.78/3.99 X376)))))))) => 23.78/3.99 ((![X378:( 23.78/3.99 ( 23.78/3.99 $i > $o))]: 23.78/3.99 ( 23.78/3.99 ( 23.78/3.99 ?[X380]: 23.78/3.99 (![X382]: 23.78/3.99 (X378( 23.78/3.99 X382) <=> 23.78/3.99 (X382 = 23.78/3.99 X380)))) => 23.78/3.99 ( 23.78/3.99 ?[X384]: 23.78/3.99 (X378( 23.78/3.99 X384) & 23.78/3.99 (![X386]: 23.78/3.99 (X378( 23.78/3.99 X386) => 23.78/3.99 (X384 = 23.78/3.99 X386))))))) => 23.78/3.99 ((![X388, 23.78/3.99 X390]: 23.78/3.99 (( 23.78/3.99 X388 = 23.78/3.99 X390) => 23.78/3.99 (![X392, 23.78/3.99 X394]: 23.78/3.99 (( 23.78/3.99 X392 = 23.78/3.99 X394) => 23.78/3.99 (in( 23.78/3.99 X392,X388) => 23.78/3.99 in( 23.78/3.99 X394,X390)))))) => 23.78/3.99 ((![X396, 23.78/3.99 X398]: 23.78/3.99 (( 23.78/3.99 X396 = 23.78/3.99 X398) => 23.78/3.99 (![X400, 23.78/3.99 X402]: 23.78/3.99 (( 23.78/3.99 X400 = 23.78/3.99 X402) => 23.78/3.99 (in( 23.78/3.99 X400,X396) <=> 23.78/3.99 in( 23.78/3.99 X402,X398)))))) => 23.78/3.99 (( 23.78/3.99 ![X404:( 23.78/3.99 ( 23.78/3.99 $i > $o))]: 23.78/3.99 (( 23.78/3.99 ?[X406]: 23.78/3.99 (X404( 23.78/3.99 X406) & 23.78/3.99 (![X408]: 23.78/4.00 (X404( 23.78/4.00 X408) => 23.78/4.00 (X406 = 23.78/4.00 X408))))) => 23.78/4.00 (![X410, 23.78/4.00 X412]: 23.78/4.00 (X404( 23.78/4.00 X410) => 23.78/4.00 (X404( 23.78/4.00 X412) => 23.78/4.00 (X410 = 23.78/4.00 X412)))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X414:( 23.78/4.00 ( 23.78/4.00 $i > $o)), 23.78/4.00 X416:( 23.78/4.00 ( 23.78/4.00 $i > $o))]: 23.78/4.00 (( 23.78/4.00 ![X418, 23.78/4.00 X420]: 23.78/4.00 (( 23.78/4.00 X418 = 23.78/4.00 X420) => 23.78/4.00 (X414( 23.78/4.00 X418) <=> 23.78/4.00 X416( 23.78/4.00 X420)))) => 23.78/4.00 (( 23.78/4.00 ?[X422]: 23.78/4.00 (X414( 23.78/4.00 X422) & 23.78/4.00 (![X424]: 23.78/4.00 (X414( 23.78/4.00 X424) => 23.78/4.00 (X422 = 23.78/4.00 X424))))) <=> 23.78/4.00 (?[X426]: 23.78/4.00 (X416( 23.78/4.00 X426) & 23.78/4.00 (![X428]: 23.78/4.00 (X416( 23.78/4.00 X428) => 23.78/4.00 (X426 = 23.78/4.00 X428)))))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 emptyset = 23.78/4.00 emptyset) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X430, 23.78/4.00 X432]: 23.78/4.00 (( 23.78/4.00 X430 = 23.78/4.00 X432) => 23.78/4.00 (![X434, 23.78/4.00 X436]: 23.78/4.00 (( 23.78/4.00 X434 = 23.78/4.00 X436) => 23.78/4.00 (setadjoin( 23.78/4.00 X430,X434) = 23.78/4.00 setadjoin( 23.78/4.00 X432,X436)))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X438, 23.78/4.00 X440]: 23.78/4.00 (( 23.78/4.00 X438 = 23.78/4.00 X440) => 23.78/4.00 (powerset( 23.78/4.00 X438) = 23.78/4.00 powerset( 23.78/4.00 X440)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X442, 23.78/4.00 X444]: 23.78/4.00 (( 23.78/4.00 X442 = 23.78/4.00 X444) => 23.78/4.00 (setunion( 23.78/4.00 X442) = 23.78/4.00 setunion( 23.78/4.00 X444)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 omega = 23.78/4.00 omega) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X446:( 23.78/4.00 ( 23.78/4.00 $i > $o))]: 23.78/4.00 (( 23.78/4.00 ?[X448]: 23.78/4.00 (X446( 23.78/4.00 X448) & 23.78/4.00 (![X450]: 23.78/4.00 (X446( 23.78/4.00 X450) => 23.78/4.00 (X448 = 23.78/4.00 X450))))) => 23.78/4.00 (![X452, 23.78/4.00 X454]: 23.78/4.00 (X446( 23.78/4.00 X452) => 23.78/4.00 (X446( 23.78/4.00 X454) => 23.78/4.00 (X452 = 23.78/4.00 X454)))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X456:( 23.78/4.00 ( 23.78/4.00 $i > $o)), 23.78/4.00 X458:( 23.78/4.00 ( 23.78/4.00 $i > $o))]: 23.78/4.00 (( 23.78/4.00 ![X460, 23.78/4.00 X462]: 23.78/4.00 (( 23.78/4.00 X460 = 23.78/4.00 X462) => 23.78/4.00 (X456( 23.78/4.00 X460) <=> 23.78/4.00 X458( 23.78/4.00 X462)))) => 23.78/4.00 (( 23.78/4.00 ?[X464]: 23.78/4.00 (X456( 23.78/4.00 X464) & 23.78/4.00 (![X466]: 23.78/4.00 (X456( 23.78/4.00 X466) => 23.78/4.00 (X464 = 23.78/4.00 X466))))) => 23.78/4.00 (( 23.78/4.00 ?[X468]: 23.78/4.00 (X458( 23.78/4.00 X468) & 23.78/4.00 (![X470]: 23.78/4.00 (X458( 23.78/4.00 X470) => 23.78/4.00 (X468 = 23.78/4.00 X470))))) => 23.78/4.00 (descr( 23.78/4.00 ^[V_9]: 23.78/4.00 X456(V_9)) = 23.78/4.00 descr( 23.78/4.00 ^[V_10]: 23.78/4.00 X458( 23.78/4.00 V_10))))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X472, 23.78/4.00 X474]: 23.78/4.00 (( 23.78/4.00 X472 = 23.78/4.00 X474) => 23.78/4.00 (![X476:( 23.78/4.00 ( 23.78/4.00 $i > $o)), 23.78/4.00 X478:( 23.78/4.00 ( 23.78/4.00 $i > $o))]: 23.78/4.00 (( 23.78/4.00 ![X480]: 23.78/4.00 (in( 23.78/4.00 X480,X472) => 23.78/4.00 (![X482]: 23.78/4.00 (in( 23.78/4.00 X482,X474) => 23.78/4.00 (( 23.78/4.00 X480 = 23.78/4.00 X482) => 23.78/4.00 (X476( 23.78/4.00 X480) <=> 23.78/4.00 X478( 23.78/4.00 X482))))))) => 23.78/4.00 (dsetconstr( 23.78/4.00 X472, 23.78/4.00 ^[V_11]: 23.78/4.00 X476( 23.78/4.00 V_11)) = 23.78/4.00 dsetconstr( 23.78/4.00 X474, 23.78/4.00 ^[V_12]: 23.78/4.00 X478( 23.78/4.00 V_12))))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X484, 23.78/4.00 X486]: 23.78/4.00 (( 23.78/4.00 ![X488]: 23.78/4.00 (in( 23.78/4.00 X488,X484) => 23.78/4.00 in( 23.78/4.00 X488,X486))) => 23.78/4.00 subset( 23.78/4.00 X484,X486))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X490, 23.78/4.00 X492]: 23.78/4.00 (( 23.78/4.00 X490 = 23.78/4.00 X492) => 23.78/4.00 subset( 23.78/4.00 X492,X490))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X494, 23.78/4.00 X496]: 23.78/4.00 (( 23.78/4.00 X494 = 23.78/4.00 X496) => 23.78/4.00 subset( 23.78/4.00 X494,X496))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X498, 23.78/4.00 X500]: 23.78/4.00 (( 23.78/4.00 ![X502]: 23.78/4.00 (in( 23.78/4.00 X502,X498) => 23.78/4.00 in( 23.78/4.00 X502,X500))) => 23.78/4.00 subset( 23.78/4.00 X498,X500))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X504]: 23.78/4.00 subset( 23.78/4.00 emptyset, 23.78/4.00 X504)) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X506, 23.78/4.00 X508,X510]: 23.78/4.00 (subset( 23.78/4.00 X506,X508) => 23.78/4.00 (in( 23.78/4.00 X510,X506) => 23.78/4.00 in( 23.78/4.00 X510,X508)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X512, 23.78/4.00 X514,X516]: 23.78/4.00 (subset( 23.78/4.00 X512,X514) => 23.78/4.00 (( 23.78/4.00 ~ 23.78/4.00 in( 23.78/4.00 X516,X514)) => 23.78/4.00 (~ 23.78/4.00 in( 23.78/4.00 X516,X512))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X518, 23.78/4.00 X520,X522]: 23.78/4.00 (in( 23.78/4.00 X522,X518) => 23.78/4.00 (( 23.78/4.00 ~ 23.78/4.00 in( 23.78/4.00 X522,X520)) => 23.78/4.00 (~ 23.78/4.00 subset( 23.78/4.00 X518,X520))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X524, 23.78/4.00 X526]: 23.78/4.00 (( 23.78/4.00 ~ 23.78/4.00 subset( 23.78/4.00 X524,X526)) => 23.78/4.00 (X524 != 23.78/4.00 X526))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X528, 23.78/4.00 X530,X532]: 23.78/4.00 (in( 23.78/4.00 X532,X528) => 23.78/4.00 (( 23.78/4.00 ~ 23.78/4.00 in( 23.78/4.00 X532,X530)) => 23.78/4.00 (X528 != 23.78/4.00 X530)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X534]: 23.78/4.00 subset( 23.78/4.00 X534,X534)) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X536, 23.78/4.00 X538,X540]: 23.78/4.00 (subset( 23.78/4.00 X536,X538) => 23.78/4.00 (subset( 23.78/4.00 X538,X540) => 23.78/4.00 subset( 23.78/4.00 X536,X540)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X542, 23.78/4.00 X544]: 23.78/4.00 subset( 23.78/4.00 X544, 23.78/4.00 setadjoin( 23.78/4.00 X542,X544))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X546, 23.78/4.00 X548,X550]: 23.78/4.00 (subset( 23.78/4.00 X546,X550) => 23.78/4.00 subset( 23.78/4.00 X546, 23.78/4.00 setadjoin( 23.78/4.00 X548,X550)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X552, 23.78/4.00 X554]: 23.78/4.00 (subset( 23.78/4.00 X552,X554) => 23.78/4.00 in( 23.78/4.00 X552, 23.78/4.00 powerset( 23.78/4.00 X554)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X556, 23.78/4.00 X558]: 23.78/4.00 (subset( 23.78/4.00 X556,X558) => 23.78/4.00 (subset( 23.78/4.00 X558,X556) => 23.78/4.00 (X556 = 23.78/4.00 X558)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X560]: 23.78/4.00 (subset( 23.78/4.00 X560, 23.78/4.00 emptyset) => 23.78/4.00 (X560 = 23.78/4.00 emptyset))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X562, 23.78/4.00 X564]: 23.78/4.00 (subset( 23.78/4.00 X564,X562) => 23.78/4.00 in( 23.78/4.00 X564, 23.78/4.00 powerset( 23.78/4.00 X562)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X566, 23.78/4.00 X568]: 23.78/4.00 (in( 23.78/4.00 X568, 23.78/4.00 powerset( 23.78/4.00 X566)) => 23.78/4.00 subset( 23.78/4.00 X568,X566))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X570]: 23.78/4.00 in( 23.78/4.00 X570, 23.78/4.00 powerset( 23.78/4.00 X570))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X572, 23.78/4.00 X574]: 23.78/4.00 (subset( 23.78/4.00 X572,X574) => 23.78/4.00 subset( 23.78/4.00 powerset( 23.78/4.00 X572), 23.78/4.00 powerset( 23.78/4.00 X574)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X576, 23.78/4.00 X578:( 23.78/4.00 ( 23.78/4.00 $i > $o))]: 23.78/4.00 in( 23.78/4.00 dsetconstr( 23.78/4.00 X576, 23.78/4.00 ^[V_13]: 23.78/4.00 X578( 23.78/4.00 V_13)), 23.78/4.00 powerset( 23.78/4.00 X576))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X580, 23.78/4.00 X582:( 23.78/4.00 ( 23.78/4.00 $i > $o))]: 23.78/4.00 subset( 23.78/4.00 dsetconstr( 23.78/4.00 X580, 23.78/4.00 ^[V_14]: 23.78/4.00 X582( 23.78/4.00 V_14)), 23.78/4.00 X580)) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X584, 23.78/4.00 X586,X588]: 23.78/4.00 (in( 23.78/4.00 X588,X584) => 23.78/4.00 in( 23.78/4.00 X588, 23.78/4.00 binunion( 23.78/4.00 X584,X586)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X590, 23.78/4.00 X592]: 23.78/4.00 in( 23.78/4.00 X592, 23.78/4.00 setadjoin( 23.78/4.00 X590, 23.78/4.00 setadjoin( 23.78/4.00 X592, 23.78/4.00 emptyset)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X594, 23.78/4.00 X596,X598]: 23.78/4.00 (in( 23.78/4.00 X598,X596) => 23.78/4.00 in( 23.78/4.00 X598, 23.78/4.00 binunion( 23.78/4.00 X594,X596)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X600, 23.78/4.00 X602, 23.78/4.00 X604, 23.78/4.00 X606:$o]: 23.78/4.00 (in( 23.78/4.00 X604, 23.78/4.00 binunion( 23.78/4.00 X600,X602)) => 23.78/4.00 (( 23.78/4.00 in( 23.78/4.00 X604,X600) => 23.78/4.00 X606) => 23.78/4.00 (( 23.78/4.00 in( 23.78/4.00 X604,X602) => 23.78/4.00 X606) => 23.78/4.00 X606)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X608, 23.78/4.00 X610,X612]: 23.78/4.00 (in( 23.78/4.00 X612, 23.78/4.00 binunion( 23.78/4.00 X608,X610)) => 23.78/4.00 (in( 23.78/4.00 X612,X610) | 23.78/4.00 in( 23.78/4.00 X612,X608)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X614, 23.78/4.00 X616]: 23.78/4.00 subset( 23.78/4.00 X614, 23.78/4.00 binunion( 23.78/4.00 X614,X616))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X618, 23.78/4.00 X620]: 23.78/4.00 subset( 23.78/4.00 X620, 23.78/4.00 binunion( 23.78/4.00 X618,X620))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X622, 23.78/4.00 X624,X626]: 23.78/4.00 (in( 23.78/4.00 X626,X622) => 23.78/4.00 (in( 23.78/4.00 X626,X624) => 23.78/4.00 in( 23.78/4.00 X626, 23.78/4.00 binintersect( 23.78/4.00 X622,X624))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X628, 23.78/4.00 X630,X632]: 23.78/4.00 (subset( 23.78/4.00 X632,X628) => 23.78/4.00 (subset( 23.78/4.00 X632,X630) => 23.78/4.00 subset( 23.78/4.00 X632, 23.78/4.00 binintersect( 23.78/4.00 X628,X630))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X634, 23.78/4.00 X636,X638]: 23.78/4.00 (in( 23.78/4.00 X638, 23.78/4.00 binintersect( 23.78/4.00 X634,X636)) => 23.78/4.00 in( 23.78/4.00 X638,X634))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X640, 23.78/4.00 X642]: 23.78/4.00 subset( 23.78/4.00 binintersect( 23.78/4.00 X640,X642), 23.78/4.00 X640)) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X644, 23.78/4.00 X646]: 23.78/4.00 (subset( 23.78/4.00 X644,X646) => 23.78/4.00 (binintersect( 23.78/4.00 X644,X646) = 23.78/4.00 X644))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X648, 23.78/4.00 X650]: 23.78/4.00 (( 23.78/4.00 binintersect( 23.78/4.00 X648,X650) = 23.78/4.00 X650) => 23.78/4.00 subset( 23.78/4.00 X650,X648))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X652, 23.78/4.00 X654,X656]: 23.78/4.00 (in( 23.78/4.00 X656, 23.78/4.00 binintersect( 23.78/4.00 X652,X654)) => 23.78/4.00 in( 23.78/4.00 X656,X654))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X658, 23.78/4.00 X660]: 23.78/4.00 (( 23.78/4.00 ~ 23.78/4.00 ( 23.78/4.00 ?[X662]: 23.78/4.00 (in( 23.78/4.00 X662,X658) & 23.78/4.00 in( 23.78/4.00 X662,X660)))) => 23.78/4.00 (binintersect( 23.78/4.00 X658,X660) = 23.78/4.00 emptyset))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X664, 23.78/4.00 X666]: 23.78/4.00 subset( 23.78/4.00 binintersect( 23.78/4.00 X664,X666), 23.78/4.00 X666)) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X668, 23.78/4.00 X670]: 23.78/4.00 (subset( 23.78/4.00 X670,X668) => 23.78/4.00 (binintersect( 23.78/4.00 X668,X670) = 23.78/4.00 X670))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X672, 23.78/4.00 X674]: 23.78/4.00 (( 23.78/4.00 binintersect( 23.78/4.00 X672,X674) = 23.78/4.00 X672) => 23.78/4.00 subset( 23.78/4.00 X672,X674))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X676, 23.78/4.00 X678,X680]: 23.78/4.00 (binintersect( 23.78/4.00 X676, 23.78/4.00 binunion( 23.78/4.00 X678,X680)) = 23.78/4.00 binunion( 23.78/4.00 binintersect( 23.78/4.00 X676,X678), 23.78/4.00 binintersect( 23.78/4.00 X676,X680)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X682, 23.78/4.00 X684,X686]: 23.78/4.00 (in( 23.78/4.00 X686,X682) => 23.78/4.00 (( 23.78/4.00 ~ 23.78/4.00 in( 23.78/4.00 X686,X684)) => 23.78/4.00 in( 23.78/4.00 X686, 23.78/4.00 setminus( 23.78/4.00 X682,X684))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X688, 23.78/4.00 X690,X692]: 23.78/4.00 (in( 23.78/4.00 X692, 23.78/4.00 setminus( 23.78/4.00 X688,X690)) => 23.78/4.00 in( 23.78/4.00 X692,X688))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X694, 23.78/4.00 X696,X698]: 23.78/4.00 (in( 23.78/4.00 X698, 23.78/4.00 setminus( 23.78/4.00 X694,X696)) => 23.78/4.00 (~ 23.78/4.00 in( 23.78/4.00 X698,X696)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X700, 23.78/4.00 X702]: 23.78/4.00 (subset( 23.78/4.00 X700,X702) => 23.78/4.00 (setminus( 23.78/4.00 X700,X702) = 23.78/4.00 emptyset))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X704, 23.78/4.00 X706,X708]: 23.78/4.00 (( 23.78/4.00 ~ 23.78/4.00 in( 23.78/4.00 X708, 23.78/4.00 setminus( 23.78/4.00 X704,X706))) => 23.78/4.00 (in( 23.78/4.00 X708,X704) => 23.78/4.00 in( 23.78/4.00 X708,X706)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X710, 23.78/4.00 X712,X714]: 23.78/4.00 (( 23.78/4.00 ~ 23.78/4.00 in( 23.78/4.00 X714, 23.78/4.00 setminus( 23.78/4.00 X710,X712))) => 23.78/4.00 (( 23.78/4.00 ~ 23.78/4.00 in( 23.78/4.00 X714,X712)) => 23.78/4.00 (~ 23.78/4.00 in( 23.78/4.00 X714,X710))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X716, 23.78/4.00 X718,X720]: 23.78/4.00 (( 23.78/4.00 ~ 23.78/4.00 in( 23.78/4.00 X720,X716)) => 23.78/4.00 (~ 23.78/4.00 in( 23.78/4.00 X720, 23.78/4.00 setminus( 23.78/4.00 X716,X718))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X722, 23.78/4.00 X724,X726]: 23.78/4.00 (in( 23.78/4.00 X726,X724) => 23.78/4.00 (~ 23.78/4.00 in( 23.78/4.00 X726, 23.78/4.00 setminus( 23.78/4.00 X722,X724))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X728, 23.78/4.00 X730]: 23.78/4.00 subset( 23.78/4.00 setminus( 23.78/4.00 X728,X730), 23.78/4.00 X728)) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X732, 23.78/4.00 X734]: 23.78/4.00 (( 23.78/4.00 setminus( 23.78/4.00 X732,X734) = 23.78/4.00 emptyset) => 23.78/4.00 subset( 23.78/4.00 X732,X734))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X736, 23.78/4.00 X738,X740]: 23.78/4.00 (in( 23.78/4.00 X740, 23.78/4.00 symdiff( 23.78/4.00 X736,X738)) => 23.78/4.00 (![X742:$o]: 23.78/4.00 (( 23.78/4.00 in( 23.78/4.00 X740,X736) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ~ 23.78/4.00 in( 23.78/4.00 X740,X738)) => 23.78/4.00 X742)) => 23.78/4.00 (( 23.78/4.00 ( 23.78/4.00 ~ 23.78/4.00 in( 23.78/4.00 X740,X736)) => 23.78/4.00 ( 23.78/4.00 in( 23.78/4.00 X740,X738) => 23.78/4.00 X742)) => 23.78/4.00 X742))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X744, 23.78/4.00 X746,X748]: 23.78/4.00 (in( 23.78/4.00 X748,X744) => 23.78/4.00 (( 23.78/4.00 ~ 23.78/4.00 in( 23.78/4.00 X748,X746)) => 23.78/4.00 in( 23.78/4.00 X748, 23.78/4.00 symdiff( 23.78/4.00 X744,X746))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X750, 23.78/4.00 X752,X754]: 23.78/4.00 (( 23.78/4.00 ~ 23.78/4.00 in( 23.78/4.00 X754,X750)) => 23.78/4.00 (in( 23.78/4.00 X754,X752) => 23.78/4.00 in( 23.78/4.00 X754, 23.78/4.00 symdiff( 23.78/4.00 X750,X752))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X756, 23.78/4.00 X758,X760]: 23.78/4.00 (in( 23.78/4.00 X760,X756) => 23.78/4.00 (in( 23.78/4.00 X760,X758) => 23.78/4.00 (~ 23.78/4.00 in( 23.78/4.00 X760, 23.78/4.00 symdiff( 23.78/4.00 X756,X758)))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X762, 23.78/4.00 X764,X766]: 23.78/4.00 (( 23.78/4.00 ~ 23.78/4.00 in( 23.78/4.00 X766,X762)) => 23.78/4.00 (( 23.78/4.00 ~ 23.78/4.00 in( 23.78/4.00 X766,X764)) => 23.78/4.00 (~ 23.78/4.00 in( 23.78/4.00 X766, 23.78/4.00 symdiff( 23.78/4.00 X762,X764)))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X768, 23.78/4.00 X770]: 23.78/4.00 in( 23.78/4.00 X770, 23.78/4.00 setadjoin( 23.78/4.00 X768, 23.78/4.00 setadjoin( 23.78/4.00 X770, 23.78/4.00 emptyset)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X772, 23.78/4.00 X774]: 23.78/4.00 in( 23.78/4.00 X772, 23.78/4.00 setunion( 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X772, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X772, 23.78/4.00 setadjoin( 23.78/4.00 X774, 23.78/4.00 emptyset)), 23.78/4.00 emptyset))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X776, 23.78/4.00 X778]: 23.78/4.00 in( 23.78/4.00 X778, 23.78/4.00 setunion( 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X776, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X776, 23.78/4.00 setadjoin( 23.78/4.00 X778, 23.78/4.00 emptyset)), 23.78/4.00 emptyset))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X780, 23.78/4.00 X782]: 23.78/4.00 (?[X784]: 23.78/4.00 (in( 23.78/4.00 X784, 23.78/4.00 setunion( 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X780, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X780, 23.78/4.00 setadjoin( 23.78/4.00 X782, 23.78/4.00 emptyset)), 23.78/4.00 emptyset)))) & 23.78/4.00 (?[X786]: 23.78/4.00 (in( 23.78/4.00 X786, 23.78/4.00 setunion( 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X780, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X780, 23.78/4.00 setadjoin( 23.78/4.00 X782, 23.78/4.00 emptyset)), 23.78/4.00 emptyset)))) & 23.78/4.00 (setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X780, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X780, 23.78/4.00 setadjoin( 23.78/4.00 X782, 23.78/4.00 emptyset)), 23.78/4.00 emptyset)) = 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X784, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X784, 23.78/4.00 setadjoin( 23.78/4.00 X786, 23.78/4.00 emptyset)), 23.78/4.00 emptyset)))))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X788, 23.78/4.00 X790]: 23.78/4.00 (?[X792]: 23.78/4.00 (in( 23.78/4.00 X792, 23.78/4.00 setunion( 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X788, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X788, 23.78/4.00 setadjoin( 23.78/4.00 X790, 23.78/4.00 emptyset)), 23.78/4.00 emptyset)))) & 23.78/4.00 (?[X794]: 23.78/4.00 (in( 23.78/4.00 X794, 23.78/4.00 setunion( 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X788, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X788, 23.78/4.00 setadjoin( 23.78/4.00 X790, 23.78/4.00 emptyset)), 23.78/4.00 emptyset)))) & 23.78/4.00 (setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X788, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X788, 23.78/4.00 setadjoin( 23.78/4.00 X790, 23.78/4.00 emptyset)), 23.78/4.00 emptyset)) = 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X792, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X792, 23.78/4.00 setadjoin( 23.78/4.00 X794, 23.78/4.00 emptyset)), 23.78/4.00 emptyset)))))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X796, 23.78/4.00 X798]: 23.78/4.00 (in( 23.78/4.00 X798,X796) => 23.78/4.00 subset( 23.78/4.00 setadjoin( 23.78/4.00 X798, 23.78/4.00 emptyset), 23.78/4.00 X796))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X800, 23.78/4.00 X802]: 23.78/4.00 (in( 23.78/4.00 X802,X800) => 23.78/4.00 in( 23.78/4.00 setadjoin( 23.78/4.00 X802, 23.78/4.00 emptyset), 23.78/4.00 powerset( 23.78/4.00 X800)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X804, 23.78/4.00 X806,X808]: 23.78/4.00 (in( 23.78/4.00 X808,X804) => 23.78/4.00 in( 23.78/4.00 setadjoin( 23.78/4.00 X808, 23.78/4.00 emptyset), 23.78/4.00 powerset( 23.78/4.00 binunion( 23.78/4.00 X804,X806))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X810, 23.78/4.00 X812,X814]: 23.78/4.00 (in( 23.78/4.00 X814, 23.78/4.00 setadjoin( 23.78/4.00 X810, 23.78/4.00 setadjoin( 23.78/4.00 X812, 23.78/4.00 emptyset))) => 23.78/4.00 (( 23.78/4.00 X814 = 23.78/4.00 X812) | 23.78/4.00 (X814 = 23.78/4.00 X810)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X816, 23.78/4.00 X818,X820]: 23.78/4.00 (in( 23.78/4.00 X820,X816) => 23.78/4.00 (![X822]: 23.78/4.00 (in( 23.78/4.00 X822,X818) => 23.78/4.00 subset( 23.78/4.00 setadjoin( 23.78/4.00 X820, 23.78/4.00 setadjoin( 23.78/4.00 X822, 23.78/4.00 emptyset)), 23.78/4.00 binunion( 23.78/4.00 X816,X818)))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X824, 23.78/4.00 X826,X828]: 23.78/4.00 (in( 23.78/4.00 X828,X824) => 23.78/4.00 (![X830]: 23.78/4.00 (in( 23.78/4.00 X830,X826) => 23.78/4.00 in( 23.78/4.00 setadjoin( 23.78/4.00 X828, 23.78/4.00 setadjoin( 23.78/4.00 X830, 23.78/4.00 emptyset)), 23.78/4.00 powerset( 23.78/4.00 binunion( 23.78/4.00 X824,X826))))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X832, 23.78/4.00 X834,X836]: 23.78/4.00 (in( 23.78/4.00 X836,X832) => 23.78/4.00 (![X838]: 23.78/4.00 (in( 23.78/4.00 X838,X834) => 23.78/4.00 subset( 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X836, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X836, 23.78/4.00 setadjoin( 23.78/4.00 X838, 23.78/4.00 emptyset)), 23.78/4.00 emptyset)), 23.78/4.00 powerset( 23.78/4.00 binunion( 23.78/4.00 X832,X834))))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X840, 23.78/4.00 X842,X844]: 23.78/4.00 (in( 23.78/4.00 X844,X840) => 23.78/4.00 (![X846]: 23.78/4.00 (in( 23.78/4.00 X846,X842) => 23.78/4.00 in( 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X844, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X844, 23.78/4.00 setadjoin( 23.78/4.00 X846, 23.78/4.00 emptyset)), 23.78/4.00 emptyset)), 23.78/4.00 powerset( 23.78/4.00 powerset( 23.78/4.00 binunion( 23.78/4.00 X840,X842)))))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X848, 23.78/4.00 X850,X852]: 23.78/4.00 (in( 23.78/4.00 X852,X848) => 23.78/4.00 (![X854]: 23.78/4.00 (in( 23.78/4.00 X854,X850) => 23.78/4.00 in( 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X852, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X852, 23.78/4.00 setadjoin( 23.78/4.00 X854, 23.78/4.00 emptyset)), 23.78/4.00 emptyset)), 23.78/4.00 powerset( 23.78/4.00 powerset( 23.78/4.00 binunion( 23.78/4.00 X848,X850)))))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X856, 23.78/4.00 X858,X860]: 23.78/4.00 (in( 23.78/4.00 X860,X856) => 23.78/4.00 (![X862]: 23.78/4.00 (in( 23.78/4.00 X862,X858) => 23.78/4.00 in( 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X860, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X860, 23.78/4.00 setadjoin( 23.78/4.00 X862, 23.78/4.00 emptyset)), 23.78/4.00 emptyset)), 23.78/4.00 cartprod( 23.78/4.00 X856,X858)))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X864, 23.78/4.00 X866,X868]: 23.78/4.00 (in( 23.78/4.00 X868, 23.78/4.00 cartprod( 23.78/4.00 X864,X866)) => 23.78/4.00 (?[X870]: 23.78/4.00 (in( 23.78/4.00 X870,X864) & 23.78/4.00 (?[X872]: 23.78/4.00 (in( 23.78/4.00 X872,X866) & 23.78/4.00 (X868 = 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X870, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X870, 23.78/4.00 setadjoin( 23.78/4.00 X872, 23.78/4.00 emptyset)), 23.78/4.00 emptyset))))))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X874, 23.78/4.00 X876,X878]: 23.78/4.00 (in( 23.78/4.00 X878, 23.78/4.00 cartprod( 23.78/4.00 X874,X876)) => 23.78/4.00 (?[X880]: 23.78/4.00 (in( 23.78/4.00 X880, 23.78/4.00 setunion( 23.78/4.00 X878)) & 23.78/4.00 (?[X882]: 23.78/4.00 (in( 23.78/4.00 X882, 23.78/4.00 setunion( 23.78/4.00 X878)) & 23.78/4.00 (X878 = 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X880, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X880, 23.78/4.00 setadjoin( 23.78/4.00 X882, 23.78/4.00 emptyset)), 23.78/4.00 emptyset))))))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X884, 23.78/4.00 X886]: 23.78/4.00 (in( 23.78/4.00 X886, 23.78/4.00 setunion( 23.78/4.00 X884)) => 23.78/4.00 (?[X888]: 23.78/4.00 (in( 23.78/4.00 X888,X884) & 23.78/4.00 in( 23.78/4.00 X886,X888))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X890]: 23.78/4.00 subset( 23.78/4.00 setunion( 23.78/4.00 setadjoin( 23.78/4.00 X890, 23.78/4.00 emptyset)), 23.78/4.00 X890)) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X892]: 23.78/4.00 subset( 23.78/4.00 X892, 23.78/4.00 setunion( 23.78/4.00 setadjoin( 23.78/4.00 X892, 23.78/4.00 emptyset)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X894]: 23.78/4.00 (setunion( 23.78/4.00 setadjoin( 23.78/4.00 X894, 23.78/4.00 emptyset)) = 23.78/4.00 X894)) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X896, 23.78/4.00 X898:( 23.78/4.00 ( 23.78/4.00 $i > $o))]: 23.78/4.00 (( 23.78/4.00 ![X900]: 23.78/4.00 (in( 23.78/4.00 X900,X896) => 23.78/4.00 (![X902]: 23.78/4.00 (in( 23.78/4.00 X902,X896) => 23.78/4.00 (X898( 23.78/4.00 X900) => 23.78/4.00 (X898( 23.78/4.00 X902) => 23.78/4.00 (X900 = 23.78/4.00 X902))))))) => 23.78/4.00 (( 23.78/4.00 ?[X904]: 23.78/4.00 (in( 23.78/4.00 X904,X896) & 23.78/4.00 X898( 23.78/4.00 X904))) => 23.78/4.00 (?[X906]: 23.78/4.00 (in( 23.78/4.00 X906, 23.78/4.00 dsetconstr( 23.78/4.00 X896, 23.78/4.00 ^[V_16]: 23.78/4.00 X898( 23.78/4.00 V_16))) & 23.78/4.00 (dsetconstr( 23.78/4.00 X896, 23.78/4.00 ^[V_15]: 23.78/4.00 X898( 23.78/4.00 V_15)) = 23.78/4.00 setadjoin( 23.78/4.00 X906, 23.78/4.00 emptyset))))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X908, 23.78/4.00 X910:( 23.78/4.00 ( 23.78/4.00 $i > $o))]: 23.78/4.00 (( 23.78/4.00 ?[X912]: 23.78/4.00 (in( 23.78/4.00 X912, 23.78/4.00 dsetconstr( 23.78/4.00 X908, 23.78/4.00 ^[V_18]: 23.78/4.00 X910( 23.78/4.00 V_18))) & 23.78/4.00 (dsetconstr( 23.78/4.00 X908, 23.78/4.00 ^[V_17]: 23.78/4.00 X910( 23.78/4.00 V_17)) = 23.78/4.00 setadjoin( 23.78/4.00 X912, 23.78/4.00 emptyset)))) => 23.78/4.00 (?[X914]: 23.78/4.00 (in( 23.78/4.00 X914,X908) & 23.78/4.00 X910( 23.78/4.00 X914))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X916, 23.78/4.00 X918:( 23.78/4.00 ( 23.78/4.00 $i > $o)), 23.78/4.00 X920]: 23.78/4.00 (in( 23.78/4.00 X920,X916) => 23.78/4.00 (X918( 23.78/4.00 X920) => 23.78/4.00 (( 23.78/4.00 ![X922]: 23.78/4.00 (in( 23.78/4.00 X922,X916) => 23.78/4.00 (X918( 23.78/4.00 X922) => 23.78/4.00 (X922 = 23.78/4.00 X920)))) => 23.78/4.00 (?[X924]: 23.78/4.00 (in( 23.78/4.00 X924, 23.78/4.00 dsetconstr( 23.78/4.00 X916, 23.78/4.00 ^[V_20]: 23.78/4.00 X918( 23.78/4.00 V_20))) & 23.78/4.00 (dsetconstr( 23.78/4.00 X916, 23.78/4.00 ^[V_19]: 23.78/4.00 X918( 23.78/4.00 V_19)) = 23.78/4.00 setadjoin( 23.78/4.00 X924, 23.78/4.00 emptyset)))))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X926, 23.78/4.00 X928:( 23.78/4.00 ( 23.78/4.00 $i > $o))]: 23.78/4.00 (( 23.78/4.00 ![X930]: 23.78/4.00 (in( 23.78/4.00 X930,X926) => 23.78/4.00 (![X932]: 23.78/4.00 (in( 23.78/4.00 X932,X926) => 23.78/4.00 (X928( 23.78/4.00 X930) => 23.78/4.00 (X928( 23.78/4.00 X932) => 23.78/4.00 (X930 = 23.78/4.00 X932))))))) => 23.78/4.00 (( 23.78/4.00 ?[X934]: 23.78/4.00 (in( 23.78/4.00 X934,X926) & 23.78/4.00 X928( 23.78/4.00 X934))) => 23.78/4.00 (?[X936]: 23.78/4.00 (in( 23.78/4.00 X936, 23.78/4.00 dsetconstr( 23.78/4.00 X926, 23.78/4.00 ^[V_22]: 23.78/4.00 X928( 23.78/4.00 V_22))) & 23.78/4.00 (dsetconstr( 23.78/4.00 X926, 23.78/4.00 ^[V_21]: 23.78/4.00 X928( 23.78/4.00 V_21)) = 23.78/4.00 setadjoin( 23.78/4.00 X936, 23.78/4.00 emptyset))))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X938, 23.78/4.00 X940]: 23.78/4.00 (( 23.78/4.00 setadjoin( 23.78/4.00 X938, 23.78/4.00 emptyset) = 23.78/4.00 setadjoin( 23.78/4.00 X940, 23.78/4.00 emptyset)) => 23.78/4.00 (X938 = 23.78/4.00 X940))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X942, 23.78/4.00 X944,X946]: 23.78/4.00 (in( 23.78/4.00 setadjoin( 23.78/4.00 X946, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X942, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X942, 23.78/4.00 setadjoin( 23.78/4.00 X944, 23.78/4.00 emptyset)), 23.78/4.00 emptyset))) => 23.78/4.00 (X942 = 23.78/4.00 X946))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X948]: 23.78/4.00 (( 23.78/4.00 ?[X950]: 23.78/4.00 (in( 23.78/4.00 X950, 23.78/4.00 setunion( 23.78/4.00 X948)) & 23.78/4.00 (?[X952]: 23.78/4.00 (in( 23.78/4.00 X952, 23.78/4.00 setunion( 23.78/4.00 X948)) & 23.78/4.00 (X948 = 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X950, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X950, 23.78/4.00 setadjoin( 23.78/4.00 X952, 23.78/4.00 emptyset)), 23.78/4.00 emptyset))))))) => 23.78/4.00 (?[X954]: 23.78/4.00 (in( 23.78/4.00 X954, 23.78/4.00 dsetconstr( 23.78/4.00 setunion( 23.78/4.00 X948), 23.78/4.00 ^[V_24]: 23.78/4.00 in( 23.78/4.00 setadjoin( 23.78/4.00 V_24, 23.78/4.00 emptyset), 23.78/4.00 X948))) & 23.78/4.00 (dsetconstr( 23.78/4.00 setunion( 23.78/4.00 X948), 23.78/4.00 ^[V_23]: 23.78/4.00 in( 23.78/4.00 setadjoin( 23.78/4.00 V_23, 23.78/4.00 emptyset), 23.78/4.00 X948)) = 23.78/4.00 setadjoin( 23.78/4.00 X954, 23.78/4.00 emptyset)))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X956]: 23.78/4.00 (( 23.78/4.00 ?[X958]: 23.78/4.00 (in( 23.78/4.00 X958,X956) & 23.78/4.00 (X956 = 23.78/4.00 setadjoin( 23.78/4.00 X958, 23.78/4.00 emptyset)))) => 23.78/4.00 in( 23.78/4.00 setunion( 23.78/4.00 X956), 23.78/4.00 X956))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X960, 23.78/4.00 X962]: 23.78/4.00 (kfst( 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X960, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X960, 23.78/4.00 setadjoin( 23.78/4.00 X962, 23.78/4.00 emptyset)), 23.78/4.00 emptyset))) = 23.78/4.00 X960)) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X964, 23.78/4.00 X966,X968]: 23.78/4.00 (in( 23.78/4.00 X968, 23.78/4.00 cartprod( 23.78/4.00 X964,X966)) => 23.78/4.00 in( 23.78/4.00 kfst( 23.78/4.00 X968), 23.78/4.00 X964))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X970, 23.78/4.00 X972, 23.78/4.00 X974,X976]: 23.78/4.00 (( 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X970, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X970, 23.78/4.00 setadjoin( 23.78/4.00 X972, 23.78/4.00 emptyset)), 23.78/4.00 emptyset)) = 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X974, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X974, 23.78/4.00 setadjoin( 23.78/4.00 X976, 23.78/4.00 emptyset)), 23.78/4.00 emptyset))) => 23.78/4.00 (X970 = 23.78/4.00 X974))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X978, 23.78/4.00 X980, 23.78/4.00 X982,X984]: 23.78/4.00 (( 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X978, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X978, 23.78/4.00 setadjoin( 23.78/4.00 X980, 23.78/4.00 emptyset)), 23.78/4.00 emptyset)) = 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X982, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X982, 23.78/4.00 setadjoin( 23.78/4.00 X984, 23.78/4.00 emptyset)), 23.78/4.00 emptyset))) => 23.78/4.00 (X978 = 23.78/4.00 X982))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X986, 23.78/4.00 X988]: 23.78/4.00 (( 23.78/4.00 X986 = 23.78/4.00 X988) => 23.78/4.00 (setadjoin( 23.78/4.00 X986, 23.78/4.00 setadjoin( 23.78/4.00 X988, 23.78/4.00 emptyset)) = 23.78/4.00 setadjoin( 23.78/4.00 X986, 23.78/4.00 emptyset)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X990, 23.78/4.00 X992]: 23.78/4.00 (( 23.78/4.00 X990 = 23.78/4.00 X992) => 23.78/4.00 (setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X990, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X990, 23.78/4.00 setadjoin( 23.78/4.00 X992, 23.78/4.00 emptyset)), 23.78/4.00 emptyset)) = 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X990, 23.78/4.00 emptyset), 23.78/4.00 emptyset)))) => 23.78/4.00 ( 23.78/4.00 ![X994, 23.78/4.00 X996, 23.78/4.00 X998, 23.78/4.00 X1000]: 23.78/4.00 (( 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X994, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X994, 23.78/4.00 setadjoin( 23.78/4.00 X996, 23.78/4.00 emptyset)), 23.78/4.00 emptyset)) = 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X998, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X998, 23.78/4.00 setadjoin( 23.78/4.00 X1000, 23.78/4.00 emptyset)), 23.78/4.00 emptyset))) => 23.78/4.00 (( 23.78/4.00 X998 = 23.78/4.00 X1000) => 23.78/4.00 (X996 = 23.78/4.00 X1000)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 23.78/4.00 tff(zf_stmt_1, type, zip_tseitin_5 : ($i * ($i > $o)) > $o). 23.78/4.00 tff(zf_stmt_2, axiom, 23.78/4.00 (zip_tseitin_5(X422,X414) <=> 23.78/4.00 ((![X424]: zip_tseitin_4(X424,X422,X414)) & X414(X422)))). 23.78/4.00 tff(zf_stmt_3, type, zip_tseitin_4 : ($i * $i * ($i > $o)) > $o). 23.78/4.00 tff(zf_stmt_4, axiom, 23.78/4.00 (zip_tseitin_4(X424,X422,X414) <=> (X414(X424) => (X422 = X424)))). 23.78/4.00 tff(zf_stmt_5, type, zip_tseitin_3 : ($i * $i * $i * ($i * $i) > $o) > $o). 23.78/4.00 tff(zf_stmt_6, axiom, 23.78/4.00 (zip_tseitin_3(X52,X50,X40,X38) <=> (X38(X52,X50) & in(X52,X40)))). 23.78/4.00 tff(zf_stmt_7, type, zip_tseitin_2 : ($i * $i * $i) > $o). 23.78/4.00 tff(zf_stmt_8, axiom, 23.78/4.00 (zip_tseitin_2(X28,X26,X24) <=> (in(X28,X24) & in(X26,X28)))). 23.78/4.00 tff(zf_stmt_9, type, zip_tseitin_1 : ($i * $i * $i) > $o). 23.78/4.00 tff(zf_stmt_10, axiom, 23.78/4.00 (zip_tseitin_1(X22,X20,X18) <=> (in(X22,X20) => in(X22,X18)))). 23.78/4.00 tff(zf_stmt_11, type, zip_tseitin_0 : ($i * $i * $i) > $o). 23.78/4.00 tff(zf_stmt_12, axiom, 23.78/4.00 (zip_tseitin_0(X16,X14,X12) <=> ((X16 = X12) | in(X16,X14)))). 23.78/4.00 tff(zf_stmt_13, conjecture, 23.78/4.00 ((![X4,X6]: ((![X8]: (in(X8,X4) <=> in(X8,X6))) => (X4 = X6))) => 23.78/4.00 ((![X10]: (~in(X10,emptyset))) => 23.78/4.00 ((![X12,X14,X16]: 23.78/4.00 (in(X16,setadjoin(X12,X14)) <=> zip_tseitin_0(X16,X14,X12))) => 23.78/4.00 ((![X18,X20]: 23.78/4.00 (in(X20,powerset(X18)) <=> (![X22]: zip_tseitin_1(X22,X20,X18)))) => 23.78/4.00 ((![X24,X26]: 23.78/4.00 (in(X26,setunion(X24)) <=> (?[X28]: zip_tseitin_2(X28,X26,X24)))) => 23.78/4.00 (in(emptyset,omega) => 23.78/4.00 ((![X30]: (in(X30,omega) => in(setadjoin(X30,X30),omega))) => 23.78/4.00 ((![X32]: 23.78/4.00 ((in(emptyset,X32) & 23.78/4.00 (![X34]: 23.78/4.00 ((in(X34,omega) & in(X34,X32)) => 23.78/4.00 in(setadjoin(X34,X34),X32)))) => 23.78/4.00 (![X36]: (in(X36,omega) => in(X36,X32))))) => 23.78/4.00 ((![X38:(($i * $i) > $o),X40]: 23.78/4.00 ((![X42]: 23.78/4.00 (in(X42,X40) => 23.78/4.00 (?[X44]: 23.78/4.00 ((![X46]: (X38(X42,X46) => (X44 = X46))) & X38(X42,X44))))) => 23.78/4.00 (?[X48]: 23.78/4.00 (![X50]: 23.78/4.00 (in(X50,X48) <=> 23.78/4.00 (?[X52]: zip_tseitin_3(X52,X50,X40,X38))))))) => 23.78/4.00 ((![X54]: 23.78/4.00 ((?[X56]: in(X56,X54)) => 23.78/4.00 (?[X58]: 23.78/4.00 ((~(?[X60]: (in(X60,X54) & in(X60,X58)))) & in(X58,X54))))) => 23.78/4.00 ((![X62]: 23.78/4.00 (?[X64]: 23.78/4.00 ((![X66]: 23.78/4.00 (((![X68]: (in(X68,X66) => in(X68,X62))) & 23.78/4.00 (?[X70]: in(X70,X66))) => 23.78/4.00 (?[X72,X74]: 23.78/4.00 ((![X76]: 23.78/4.00 (in(X76,X64) => 23.78/4.00 ((![X78]: (in(X78,X76) => in(X78,X72))) | 23.78/4.00 in(X74,X76)))) & 23.78/4.00 (~(?[X80]: (in(X80,X66) & in(X80,X72)))) & 23.78/4.00 in(X74,X66) & in(X72,X64))))) & 23.78/4.00 (![X82,X84]: 23.78/4.00 ((in(X82,X64) & in(X84,X64)) => 23.78/4.00 ((![X86]: (in(X86,X82) => in(X86,X84))) | 23.78/4.00 (![X88]: (in(X88,X84) => in(X88,X82)))))) & 23.78/4.00 (![X90,X92]: 23.78/4.00 ((in(X90,X62) & in(X92,X62)) => 23.78/4.00 ((![X94]: 23.78/4.00 (in(X94,X64) => (in(X90,X94) <=> in(X92,X94)))) => 23.78/4.00 (X90 = X92)))) & 23.78/4.00 (![X96]: 23.78/4.00 (in(X96,X64) => (![X98]: (in(X98,X96) => in(X98,X62)))))))) => 23.78/4.00 ((![X100:(($i > $o))]: 23.78/4.00 ((?[X102]: 23.78/4.00 ((![X104]: (X100(X104) => (X102 = X104))) & X100(X102))) => 23.78/4.00 X100(descr(^[V_1]: X100(V_1))))) => 23.78/4.00 ((![X106,X108:(($i > $o)),X110]: 23.78/4.00 (in(X110,X106) => 23.78/4.00 (X108(X110) => in(X110,dsetconstr(X106,^[V_2]: X108(V_2)))))) => 23.78/4.00 ((![X112,X114:(($i > $o)),X116]: 23.78/4.00 (in(X116,dsetconstr(X112,^[V_3]: X114(V_3))) => 23.78/4.00 in(X116,X112))) => 23.78/4.00 ((![X118,X120:(($i > $o)),X122]: 23.78/4.00 (in(X122,dsetconstr(X118,^[V_4]: X120(V_4))) => 23.78/4.00 X120(X122))) => 23.78/4.00 ((![X124:(($i > $o))]: 23.78/4.00 ((?[X126]: 23.78/4.00 ((![X128]: (X124(X128) => (X126 = X128))) & 23.78/4.00 X124(X126))) => 23.78/4.00 (?[X130]: 23.78/4.00 ((![X132]: (X124(X132) => (X130 = X132))) & 23.78/4.00 X124(X130))))) => 23.78/4.00 ((![X134:$o,X136]: (in(X136,prop2set(X134)) => X134)) => 23.78/4.00 ((![X138]: (in(X138,emptyset) => (![X140:$o]: X140))) => 23.78/4.00 ((![X142]: (~in(X142,emptyset))) => 23.78/4.00 ((![X144]: (~in(X144,emptyset))) => 23.78/4.00 ((![X146:(($i > $o))]: 23.78/4.00 ((?[X148]: 23.78/4.00 ((![X150]: (X146(X150) => (X148 = X150))) & 23.78/4.00 X146(X148))) => 23.78/4.00 (?[X152]: X146(X152)))) => 23.78/4.00 ((![X154,X156]: 23.78/4.00 ((![X158]: (in(X158,X154) => in(X158,X156))) => 23.78/4.00 ((![X160]: (in(X160,X156) => in(X160,X154))) => 23.78/4.00 (X154 = X156)))) => 23.78/4.00 ((![X162]: 23.78/4.00 ((![X164]: (~in(X164,X162))) => (X162 = emptyset))) => 23.78/4.00 ((![X166]: 23.78/4.00 ((![X168]: (~in(X168,X166))) => 23.78/4.00 (X166 = emptyset))) => 23.78/4.00 ((![X170,X172:(($i > $o)),X174]: 23.78/4.00 (in(X174,X170) => 23.78/4.00 (in(X174,dsetconstr(X170,^[V_5]: X172(V_5))) <=> 23.78/4.00 X172(X174)))) => 23.78/4.00 ((![X176]: 23.78/4.00 ((X176 != emptyset) => 23.78/4.00 (?[X178]: in(X178,X176)))) => 23.78/4.00 ((![X180,X182:(($i > $o)),X184]: 23.78/4.00 (in(X184,X180) => 23.78/4.00 (X182(X184) => 23.78/4.00 (dsetconstr(X180,^[V_6]: X182(V_6)) != 23.78/4.00 emptyset)))) => 23.78/4.00 ((![X186]: 23.78/4.00 ((?[X188]: in(X188,X186)) => 23.78/4.00 (X186 != emptyset))) => 23.78/4.00 ((![X190,X192]: in(X190,setadjoin(X190,X192))) => 23.78/4.00 (in(emptyset,setadjoin(emptyset,emptyset)) => 23.78/4.00 ((![X194,X196,X198]: 23.78/4.00 (in(X198,X196) => 23.78/4.00 in(X198,setadjoin(X194,X196)))) => 23.78/4.00 ((![X200,X202,X204]: 23.78/4.00 (in(X204,setadjoin(X200,X202)) => 23.78/4.00 (![X206:$o]: 23.78/4.00 (((X204 = X200) => X206) => 23.78/4.00 ((in(X204,X202) => X206) => X206))))) => 23.78/4.00 ((![X208,X210,X212]: 23.78/4.00 (in(X212,setadjoin(X208,X210)) => 23.78/4.00 ((X212 = X208) | in(X212,X210)))) => 23.78/4.00 ((![X214]: 23.78/4.00 (dsetconstr(X214,^[V_7]: $true) = X214)) => 23.78/4.00 ((![X216,X218]: 23.78/4.00 ((![X220]: 23.78/4.00 (in(X220,X218) => in(X220,X216))) => 23.78/4.00 in(X218,powerset(X216)))) => 23.78/4.00 ((![X222]: in(emptyset,powerset(X222))) => 23.78/4.00 ((![X224]: in(emptyset,powerset(X224))) => 23.78/4.00 ((![X226,X228,X230]: 23.78/4.00 (in(X228,powerset(X226)) => 23.78/4.00 (in(X230,X228) => in(X230,X226)))) => 23.78/4.00 ((![X232,X234,X236]: 23.78/4.00 (in(X234,X236) => 23.78/4.00 (in(X236,X232) => 23.78/4.00 in(X234,setunion(X232))))) => 23.78/4.00 ((![X238,X240]: 23.78/4.00 (in(X240,setunion(X238)) => 23.78/4.00 (![X242:$o]: 23.78/4.00 ((![X244]: 23.78/4.00 (in(X240,X244) => 23.78/4.00 (in(X244,X238) => X242))) => 23.78/4.00 X242)))) => 23.78/4.00 ((![X246,X248]: 23.78/4.00 (in(X248,X246) => 23.78/4.00 in(X248, 23.78/4.00 powerset(setunion(X246))))) => 23.78/4.00 ((![X250:(($i > $o))]: 23.78/4.00 ((?[X252]: 23.78/4.00 ((![X254]: 23.78/4.00 (X250(X254) => 23.78/4.00 (X252 = X254))) & 23.78/4.00 X250(X252))) => 23.78/4.00 (?[X256]: 23.78/4.00 (![X258]: 23.78/4.00 (X250(X258) <=> 23.78/4.00 (X258 = X256)))))) => 23.78/4.00 ((![X260]: 23.78/4.00 ((X260 != emptyset) => 23.78/4.00 (?[X262]: in(X262,X260)))) => 23.78/4.00 ((![X264,X266]: 23.78/4.00 (in(X264, 23.78/4.00 setadjoin(X266,emptyset)) => 23.78/4.00 (X264 = X266))) => 23.78/4.00 ((![X268,X270]: 23.78/4.00 ((X268 != X270) => 23.78/4.00 (~ 23.78/4.00 in(X270, 23.78/4.00 setadjoin(X268, 23.78/4.00 emptyset))))) => 23.78/4.00 ((![X272,X274]: 23.78/4.00 ((X272 = X274) => 23.78/4.00 in(X272, 23.78/4.00 setadjoin(X274, 23.78/4.00 emptyset)))) => 23.78/4.00 ((![X276,X278]: 23.78/4.00 (in(X276, 23.78/4.00 setadjoin(X278, 23.78/4.00 emptyset)) => 23.78/4.00 in(X278, 23.78/4.00 setadjoin(X276, 23.78/4.00 emptyset)))) => 23.78/4.00 ((![X280,X282,X284]: 23.78/4.00 (in(X284, 23.78/4.00 setadjoin(X280, 23.78/4.00 setadjoin( 23.78/4.00 X282, 23.78/4.00 emptyset))) => 23.78/4.00 ((X284 = X280) | 23.78/4.00 (X284 = X282)))) => 23.78/4.00 ((![X286,X288]: 23.78/4.00 in(X286, 23.78/4.00 setadjoin(X286, 23.78/4.00 setadjoin( 23.78/4.00 X288, 23.78/4.00 emptyset)))) => 23.78/4.00 ((![X290,X292]: 23.78/4.00 in(X292, 23.78/4.00 setadjoin(X290, 23.78/4.00 setadjoin( 23.78/4.00 X292, 23.78/4.00 emptyset)))) => 23.78/4.00 ((![X294,X296:(($i > $o))]: 23.78/4.00 ((?[X298]: 23.78/4.00 (X296(X298) & 23.78/4.00 in(X298,X294))) => 23.78/4.00 (dsetconstr( 23.78/4.00 X294, 23.78/4.00 ^[V_8]: X296(V_8)) != 23.78/4.00 emptyset))) => 23.78/4.00 ((![X300:(($i > $o)), 23.78/4.00 X302]: 23.78/4.00 (in(X302,emptyset) => 23.78/4.00 X300(X302))) => 23.78/4.00 ((![X304, 23.78/4.00 X306:(($i > $o))]: 23.78/4.00 ((~ 23.78/4.00 (![X308]: 23.78/4.00 (in(X308,X304) => 23.78/4.00 X306(X308)))) => 23.78/4.00 (?[X310]: 23.78/4.00 ((~X306(X310)) & 23.78/4.00 in(X310,X304))))) => 23.78/4.00 ((![X312, 23.78/4.00 X314:(($i > $o))]: 23.78/4.00 ((![X316]: 23.78/4.00 (in(X316,X312) => 23.78/4.00 (~X314(X316)))) => 23.78/4.00 (~ 23.78/4.00 (?[X318]: 23.78/4.00 (X314(X318) & 23.78/4.00 in( 23.78/4.00 X318,X312)))))) => 23.78/4.00 ((![X320, 23.78/4.00 X322:(($i > $o))]: 23.78/4.00 ((~ 23.78/4.00 (?[X324]: 23.78/4.00 (X322(X324) & 23.78/4.00 in( 23.78/4.00 X324,X320)))) => 23.78/4.00 (![X326]: 23.78/4.00 (in(X326,X320) => 23.78/4.00 (~X322(X326)))))) => 23.78/4.00 ((![X328, 23.78/4.00 X330:(($i > $o))]: 23.78/4.00 ((?[X332]: 23.78/4.00 ((~ 23.78/4.00 X330( 23.78/4.00 X332)) & 23.78/4.00 in( 23.78/4.00 X332,X328))) => 23.78/4.00 (~ 23.78/4.00 (![X334]: 23.78/4.00 (in( 23.78/4.00 X334,X328) => 23.78/4.00 X330( 23.78/4.00 X334)))))) => 23.78/4.00 ((![X336:$o]: 23.78/4.00 (X336 => 23.78/4.00 in(emptyset, 23.78/4.00 prop2set( 23.78/4.00 X336)))) => 23.78/4.00 ((![X338:$o]: 23.78/4.00 (X338 => 23.78/4.00 set2prop( 23.78/4.00 prop2set( 23.78/4.00 X338)))) => 23.78/4.00 ((![X340, 23.78/4.00 X342:( 23.78/4.00 ($i > $o))]: 23.78/4.00 ((~ 23.78/4.00 (?[X344]: 23.78/4.00 (X342( 23.78/4.00 X344) & 23.78/4.00 in( 23.78/4.00 X344,X340)))) => 23.78/4.00 (![X346]: 23.78/4.00 ( 23.78/4.00 in( 23.78/4.00 X346,X340) => 23.78/4.00 ( 23.78/4.00 ~ 23.78/4.00 X342( 23.78/4.00 X346)))))) => 23.78/4.00 ((![X348, 23.78/4.00 X350:( 23.78/4.00 ($i > $o))]: 23.78/4.00 ((~ 23.78/4.00 ( 23.78/4.00 ![X352]: 23.78/4.00 (in( 23.78/4.00 X352,X348) => 23.78/4.00 X350( 23.78/4.00 X352)))) => 23.78/4.00 (?[X354]: 23.78/4.00 (( 23.78/4.00 ~ 23.78/4.00 X350( 23.78/4.00 X354)) & 23.78/4.00 in( 23.78/4.00 X354,X348))))) => 23.78/4.00 ((![X356:( 23.78/4.00 ($i > $o))]: 23.78/4.00 ((?[X358]: 23.78/4.00 (( 23.78/4.00 ![X360]: 23.78/4.00 (X356( 23.78/4.00 X360) => 23.78/4.00 (X358 = 23.78/4.00 X360))) & 23.78/4.00 X356( 23.78/4.00 X358))) => 23.78/4.00 (?[X362]: 23.78/4.00 (( 23.78/4.00 ![X364]: 23.78/4.00 (X356( 23.78/4.00 X364) => 23.78/4.00 (X362 = 23.78/4.00 X364))) & 23.78/4.00 X356( 23.78/4.00 X362))))) => 23.78/4.00 ((![X366:( 23.78/4.00 ($i > $o))]: 23.78/4.00 (( 23.78/4.00 ?[X368]: 23.78/4.00 X366( 23.78/4.00 X368)) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X370, 23.78/4.00 X372]: 23.78/4.00 (X366( 23.78/4.00 X370) => 23.78/4.00 (X366( 23.78/4.00 X372) => 23.78/4.00 (X370 = 23.78/4.00 X372)))) => 23.78/4.00 ( 23.78/4.00 ?[X374]: 23.78/4.00 (( 23.78/4.00 ![X376]: 23.78/4.00 (X366( 23.78/4.00 X376) => 23.78/4.00 (X374 = 23.78/4.00 X376))) & 23.78/4.00 X366( 23.78/4.00 X374)))))) => 23.78/4.00 ((![X378:( 23.78/4.00 ( 23.78/4.00 $i > $o))]: 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ?[X380]: 23.78/4.00 (![X382]: 23.78/4.00 (X378( 23.78/4.00 X382) <=> 23.78/4.00 (X382 = 23.78/4.00 X380)))) => 23.78/4.00 ( 23.78/4.00 ?[X384]: 23.78/4.00 (( 23.78/4.00 ![X386]: 23.78/4.00 (X378( 23.78/4.00 X386) => 23.78/4.00 (X384 = 23.78/4.00 X386))) & 23.78/4.00 X378( 23.78/4.00 X384))))) => 23.78/4.00 ((![X388, 23.78/4.00 X390]: 23.78/4.00 (( 23.78/4.00 X388 = 23.78/4.00 X390) => 23.78/4.00 (![X392, 23.78/4.00 X394]: 23.78/4.00 (( 23.78/4.00 X392 = 23.78/4.00 X394) => 23.78/4.00 (in( 23.78/4.00 X392,X388) => 23.78/4.00 in( 23.78/4.00 X394,X390)))))) => 23.78/4.00 ((![X396, 23.78/4.00 X398]: 23.78/4.00 (( 23.78/4.00 X396 = 23.78/4.00 X398) => 23.78/4.00 (![X400, 23.78/4.00 X402]: 23.78/4.00 (( 23.78/4.00 X400 = 23.78/4.00 X402) => 23.78/4.00 (in( 23.78/4.00 X400,X396) <=> 23.78/4.00 in( 23.78/4.00 X402,X398)))))) => 23.78/4.00 (( 23.78/4.00 ![X404:( 23.78/4.00 ( 23.78/4.00 $i > $o))]: 23.78/4.00 (( 23.78/4.00 ?[X406]: 23.78/4.00 (( 23.78/4.00 ![X408]: 23.78/4.00 (X404( 23.78/4.00 X408) => 23.78/4.00 (X406 = 23.78/4.00 X408))) & 23.78/4.00 X404( 23.78/4.00 X406))) => 23.78/4.00 (![X410, 23.78/4.00 X412]: 23.78/4.00 (X404( 23.78/4.00 X410) => 23.78/4.00 (X404( 23.78/4.00 X412) => 23.78/4.00 (X410 = 23.78/4.00 X412)))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X414:( 23.78/4.00 ( 23.78/4.00 $i > $o)), 23.78/4.00 X416:( 23.78/4.00 ( 23.78/4.00 $i > $o))]: 23.78/4.00 (( 23.78/4.00 ![X418, 23.78/4.00 X420]: 23.78/4.00 (( 23.78/4.00 X418 = 23.78/4.00 X420) => 23.78/4.00 (X414( 23.78/4.00 X418) <=> 23.78/4.00 X416( 23.78/4.00 X420)))) => 23.78/4.00 (( 23.78/4.00 ?[X422]: 23.78/4.00 zip_tseitin_5( 23.78/4.00 X422,X414)) <=> 23.78/4.00 (?[X426]: 23.78/4.00 zip_tseitin_5( 23.78/4.00 X426,X416))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 emptyset = 23.78/4.00 emptyset) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X430, 23.78/4.00 X432]: 23.78/4.00 (( 23.78/4.00 X430 = 23.78/4.00 X432) => 23.78/4.00 (![X434, 23.78/4.00 X436]: 23.78/4.00 (( 23.78/4.00 X434 = 23.78/4.00 X436) => 23.78/4.00 (setadjoin( 23.78/4.00 X430,X434) = 23.78/4.00 setadjoin( 23.78/4.00 X432,X436)))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X438, 23.78/4.00 X440]: 23.78/4.00 (( 23.78/4.00 X438 = 23.78/4.00 X440) => 23.78/4.00 (powerset( 23.78/4.00 X438) = 23.78/4.00 powerset( 23.78/4.00 X440)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X442, 23.78/4.00 X444]: 23.78/4.00 (( 23.78/4.00 X442 = 23.78/4.00 X444) => 23.78/4.00 (setunion( 23.78/4.00 X442) = 23.78/4.00 setunion( 23.78/4.00 X444)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 omega = 23.78/4.00 omega) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X446:( 23.78/4.00 ( 23.78/4.00 $i > $o))]: 23.78/4.00 (( 23.78/4.00 ?[X448]: 23.78/4.00 (( 23.78/4.00 ![X450]: 23.78/4.00 (X446( 23.78/4.00 X450) => 23.78/4.00 (X448 = 23.78/4.00 X450))) & 23.78/4.00 X446( 23.78/4.00 X448))) => 23.78/4.00 (![X452, 23.78/4.00 X454]: 23.78/4.00 (X446( 23.78/4.00 X452) => 23.78/4.00 (X446( 23.78/4.00 X454) => 23.78/4.00 (X452 = 23.78/4.00 X454)))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X456:( 23.78/4.00 ( 23.78/4.00 $i > $o)), 23.78/4.00 X458:( 23.78/4.00 ( 23.78/4.00 $i > $o))]: 23.78/4.00 (( 23.78/4.00 ![X460, 23.78/4.00 X462]: 23.78/4.00 (( 23.78/4.00 X460 = 23.78/4.00 X462) => 23.78/4.00 (X456( 23.78/4.00 X460) <=> 23.78/4.00 X458( 23.78/4.00 X462)))) => 23.78/4.00 (( 23.78/4.00 ?[X464]: 23.78/4.00 (( 23.78/4.00 ![X466]: 23.78/4.00 (X456( 23.78/4.00 X466) => 23.78/4.00 (X464 = 23.78/4.00 X466))) & 23.78/4.00 X456( 23.78/4.00 X464))) => 23.78/4.00 (( 23.78/4.00 ?[X468]: 23.78/4.00 (( 23.78/4.00 ![X470]: 23.78/4.00 (X458( 23.78/4.00 X470) => 23.78/4.00 (X468 = 23.78/4.00 X470))) & 23.78/4.00 X458( 23.78/4.00 X468))) => 23.78/4.00 (descr( 23.78/4.00 ^[V_9]: 23.78/4.00 X456(V_9)) = 23.78/4.00 descr( 23.78/4.00 ^[V_10]: 23.78/4.00 X458( 23.78/4.00 V_10))))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X472, 23.78/4.00 X474]: 23.78/4.00 (( 23.78/4.00 X472 = 23.78/4.00 X474) => 23.78/4.00 (![X476:( 23.78/4.00 ( 23.78/4.00 $i > $o)), 23.78/4.00 X478:( 23.78/4.00 ( 23.78/4.00 $i > $o))]: 23.78/4.00 (( 23.78/4.00 ![X480]: 23.78/4.00 (in( 23.78/4.00 X480,X472) => 23.78/4.00 (![X482]: 23.78/4.00 (in( 23.78/4.00 X482,X474) => 23.78/4.00 (( 23.78/4.00 X480 = 23.78/4.00 X482) => 23.78/4.00 (X476( 23.78/4.00 X480) <=> 23.78/4.00 X478( 23.78/4.00 X482))))))) => 23.78/4.00 (dsetconstr( 23.78/4.00 X472, 23.78/4.00 ^[V_11]: 23.78/4.00 X476( 23.78/4.00 V_11)) = 23.78/4.00 dsetconstr( 23.78/4.00 X474, 23.78/4.00 ^[V_12]: 23.78/4.00 X478( 23.78/4.00 V_12))))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X484, 23.78/4.00 X486]: 23.78/4.00 (( 23.78/4.00 ![X488]: 23.78/4.00 (in( 23.78/4.00 X488,X484) => 23.78/4.00 in( 23.78/4.00 X488,X486))) => 23.78/4.00 subset( 23.78/4.00 X484,X486))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X490, 23.78/4.00 X492]: 23.78/4.00 (( 23.78/4.00 X490 = 23.78/4.00 X492) => 23.78/4.00 subset( 23.78/4.00 X492,X490))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X494, 23.78/4.00 X496]: 23.78/4.00 (( 23.78/4.00 X494 = 23.78/4.00 X496) => 23.78/4.00 subset( 23.78/4.00 X494,X496))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X498, 23.78/4.00 X500]: 23.78/4.00 (( 23.78/4.00 ![X502]: 23.78/4.00 (in( 23.78/4.00 X502,X498) => 23.78/4.00 in( 23.78/4.00 X502,X500))) => 23.78/4.00 subset( 23.78/4.00 X498,X500))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X504]: 23.78/4.00 subset( 23.78/4.00 emptyset, 23.78/4.00 X504)) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X506, 23.78/4.00 X508,X510]: 23.78/4.00 (subset( 23.78/4.00 X506,X508) => 23.78/4.00 (in( 23.78/4.00 X510,X506) => 23.78/4.00 in( 23.78/4.00 X510,X508)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X512, 23.78/4.00 X514,X516]: 23.78/4.00 (subset( 23.78/4.00 X512,X514) => 23.78/4.00 (( 23.78/4.00 ~ 23.78/4.00 in( 23.78/4.00 X516,X514)) => 23.78/4.00 (~ 23.78/4.00 in( 23.78/4.00 X516,X512))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X518, 23.78/4.00 X520,X522]: 23.78/4.00 (in( 23.78/4.00 X522,X518) => 23.78/4.00 (( 23.78/4.00 ~ 23.78/4.00 in( 23.78/4.00 X522,X520)) => 23.78/4.00 (~ 23.78/4.00 subset( 23.78/4.00 X518,X520))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X524, 23.78/4.00 X526]: 23.78/4.00 (( 23.78/4.00 ~ 23.78/4.00 subset( 23.78/4.00 X524,X526)) => 23.78/4.00 (X524 != 23.78/4.00 X526))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X528, 23.78/4.00 X530,X532]: 23.78/4.00 (in( 23.78/4.00 X532,X528) => 23.78/4.00 (( 23.78/4.00 ~ 23.78/4.00 in( 23.78/4.00 X532,X530)) => 23.78/4.00 (X528 != 23.78/4.00 X530)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X534]: 23.78/4.00 subset( 23.78/4.00 X534,X534)) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X536, 23.78/4.00 X538,X540]: 23.78/4.00 (subset( 23.78/4.00 X536,X538) => 23.78/4.00 (subset( 23.78/4.00 X538,X540) => 23.78/4.00 subset( 23.78/4.00 X536,X540)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X542, 23.78/4.00 X544]: 23.78/4.00 subset( 23.78/4.00 X544, 23.78/4.00 setadjoin( 23.78/4.00 X542,X544))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X546, 23.78/4.00 X548,X550]: 23.78/4.00 (subset( 23.78/4.00 X546,X550) => 23.78/4.00 subset( 23.78/4.00 X546, 23.78/4.00 setadjoin( 23.78/4.00 X548,X550)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X552, 23.78/4.00 X554]: 23.78/4.00 (subset( 23.78/4.00 X552,X554) => 23.78/4.00 in( 23.78/4.00 X552, 23.78/4.00 powerset( 23.78/4.00 X554)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X556, 23.78/4.00 X558]: 23.78/4.00 (subset( 23.78/4.00 X556,X558) => 23.78/4.00 (subset( 23.78/4.00 X558,X556) => 23.78/4.00 (X556 = 23.78/4.00 X558)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X560]: 23.78/4.00 (subset( 23.78/4.00 X560, 23.78/4.00 emptyset) => 23.78/4.00 (X560 = 23.78/4.00 emptyset))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X562, 23.78/4.00 X564]: 23.78/4.00 (subset( 23.78/4.00 X564,X562) => 23.78/4.00 in( 23.78/4.00 X564, 23.78/4.00 powerset( 23.78/4.00 X562)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X566, 23.78/4.00 X568]: 23.78/4.00 (in( 23.78/4.00 X568, 23.78/4.00 powerset( 23.78/4.00 X566)) => 23.78/4.00 subset( 23.78/4.00 X568,X566))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X570]: 23.78/4.00 in( 23.78/4.00 X570, 23.78/4.00 powerset( 23.78/4.00 X570))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X572, 23.78/4.00 X574]: 23.78/4.00 (subset( 23.78/4.00 X572,X574) => 23.78/4.00 subset( 23.78/4.00 powerset( 23.78/4.00 X572), 23.78/4.00 powerset( 23.78/4.00 X574)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X576, 23.78/4.00 X578:( 23.78/4.00 ( 23.78/4.00 $i > $o))]: 23.78/4.00 in( 23.78/4.00 dsetconstr( 23.78/4.00 X576, 23.78/4.00 ^[V_13]: 23.78/4.00 X578( 23.78/4.00 V_13)), 23.78/4.00 powerset( 23.78/4.00 X576))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X580, 23.78/4.00 X582:( 23.78/4.00 ( 23.78/4.00 $i > $o))]: 23.78/4.00 subset( 23.78/4.00 dsetconstr( 23.78/4.00 X580, 23.78/4.00 ^[V_14]: 23.78/4.00 X582( 23.78/4.00 V_14)), 23.78/4.00 X580)) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X584, 23.78/4.00 X586,X588]: 23.78/4.00 (in( 23.78/4.00 X588,X584) => 23.78/4.00 in( 23.78/4.00 X588, 23.78/4.00 binunion( 23.78/4.00 X584,X586)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X590, 23.78/4.00 X592]: 23.78/4.00 in( 23.78/4.00 X592, 23.78/4.00 setadjoin( 23.78/4.00 X590, 23.78/4.00 setadjoin( 23.78/4.00 X592, 23.78/4.00 emptyset)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X594, 23.78/4.00 X596,X598]: 23.78/4.00 (in( 23.78/4.00 X598,X596) => 23.78/4.00 in( 23.78/4.00 X598, 23.78/4.00 binunion( 23.78/4.00 X594,X596)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X600, 23.78/4.00 X602, 23.78/4.00 X604, 23.78/4.00 X606:$o]: 23.78/4.00 (in( 23.78/4.00 X604, 23.78/4.00 binunion( 23.78/4.00 X600,X602)) => 23.78/4.00 (( 23.78/4.00 in( 23.78/4.00 X604,X600) => 23.78/4.00 X606) => 23.78/4.00 (( 23.78/4.00 in( 23.78/4.00 X604,X602) => 23.78/4.00 X606) => 23.78/4.00 X606)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X608, 23.78/4.00 X610,X612]: 23.78/4.00 (in( 23.78/4.00 X612, 23.78/4.00 binunion( 23.78/4.00 X608,X610)) => 23.78/4.00 (in( 23.78/4.00 X612,X608) | 23.78/4.00 in( 23.78/4.00 X612,X610)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X614, 23.78/4.00 X616]: 23.78/4.00 subset( 23.78/4.00 X614, 23.78/4.00 binunion( 23.78/4.00 X614,X616))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X618, 23.78/4.00 X620]: 23.78/4.00 subset( 23.78/4.00 X620, 23.78/4.00 binunion( 23.78/4.00 X618,X620))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X622, 23.78/4.00 X624,X626]: 23.78/4.00 (in( 23.78/4.00 X626,X622) => 23.78/4.00 (in( 23.78/4.00 X626,X624) => 23.78/4.00 in( 23.78/4.00 X626, 23.78/4.00 binintersect( 23.78/4.00 X622,X624))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X628, 23.78/4.00 X630,X632]: 23.78/4.00 (subset( 23.78/4.00 X632,X628) => 23.78/4.00 (subset( 23.78/4.00 X632,X630) => 23.78/4.00 subset( 23.78/4.00 X632, 23.78/4.00 binintersect( 23.78/4.00 X628,X630))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X634, 23.78/4.00 X636,X638]: 23.78/4.00 (in( 23.78/4.00 X638, 23.78/4.00 binintersect( 23.78/4.00 X634,X636)) => 23.78/4.00 in( 23.78/4.00 X638,X634))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X640, 23.78/4.00 X642]: 23.78/4.00 subset( 23.78/4.00 binintersect( 23.78/4.00 X640,X642), 23.78/4.00 X640)) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X644, 23.78/4.00 X646]: 23.78/4.00 (subset( 23.78/4.00 X644,X646) => 23.78/4.00 (binintersect( 23.78/4.00 X644,X646) = 23.78/4.00 X644))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X648, 23.78/4.00 X650]: 23.78/4.00 (( 23.78/4.00 binintersect( 23.78/4.00 X648,X650) = 23.78/4.00 X650) => 23.78/4.00 subset( 23.78/4.00 X650,X648))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X652, 23.78/4.00 X654,X656]: 23.78/4.00 (in( 23.78/4.00 X656, 23.78/4.00 binintersect( 23.78/4.00 X652,X654)) => 23.78/4.00 in( 23.78/4.00 X656,X654))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X658, 23.78/4.00 X660]: 23.78/4.00 (( 23.78/4.00 ~ 23.78/4.00 ( 23.78/4.00 ?[X662]: 23.78/4.00 (in( 23.78/4.00 X662,X660) & 23.78/4.00 in( 23.78/4.00 X662,X658)))) => 23.78/4.00 (binintersect( 23.78/4.00 X658,X660) = 23.78/4.00 emptyset))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X664, 23.78/4.00 X666]: 23.78/4.00 subset( 23.78/4.00 binintersect( 23.78/4.00 X664,X666), 23.78/4.00 X666)) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X668, 23.78/4.00 X670]: 23.78/4.00 (subset( 23.78/4.00 X670,X668) => 23.78/4.00 (binintersect( 23.78/4.00 X668,X670) = 23.78/4.00 X670))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X672, 23.78/4.00 X674]: 23.78/4.00 (( 23.78/4.00 binintersect( 23.78/4.00 X672,X674) = 23.78/4.00 X672) => 23.78/4.00 subset( 23.78/4.00 X672,X674))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X676, 23.78/4.00 X678,X680]: 23.78/4.00 (binintersect( 23.78/4.00 X676, 23.78/4.00 binunion( 23.78/4.00 X678,X680)) = 23.78/4.00 binunion( 23.78/4.00 binintersect( 23.78/4.00 X676,X678), 23.78/4.00 binintersect( 23.78/4.00 X676,X680)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X682, 23.78/4.00 X684,X686]: 23.78/4.00 (in( 23.78/4.00 X686,X682) => 23.78/4.00 (( 23.78/4.00 ~ 23.78/4.00 in( 23.78/4.00 X686,X684)) => 23.78/4.00 in( 23.78/4.00 X686, 23.78/4.00 setminus( 23.78/4.00 X682,X684))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X688, 23.78/4.00 X690,X692]: 23.78/4.00 (in( 23.78/4.00 X692, 23.78/4.00 setminus( 23.78/4.00 X688,X690)) => 23.78/4.00 in( 23.78/4.00 X692,X688))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X694, 23.78/4.00 X696,X698]: 23.78/4.00 (in( 23.78/4.00 X698, 23.78/4.00 setminus( 23.78/4.00 X694,X696)) => 23.78/4.00 (~ 23.78/4.00 in( 23.78/4.00 X698,X696)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X700, 23.78/4.00 X702]: 23.78/4.00 (subset( 23.78/4.00 X700,X702) => 23.78/4.00 (setminus( 23.78/4.00 X700,X702) = 23.78/4.00 emptyset))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X704, 23.78/4.00 X706,X708]: 23.78/4.00 (( 23.78/4.00 ~ 23.78/4.00 in( 23.78/4.00 X708, 23.78/4.00 setminus( 23.78/4.00 X704,X706))) => 23.78/4.00 (in( 23.78/4.00 X708,X704) => 23.78/4.00 in( 23.78/4.00 X708,X706)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X710, 23.78/4.00 X712,X714]: 23.78/4.00 (( 23.78/4.00 ~ 23.78/4.00 in( 23.78/4.00 X714, 23.78/4.00 setminus( 23.78/4.00 X710,X712))) => 23.78/4.00 (( 23.78/4.00 ~ 23.78/4.00 in( 23.78/4.00 X714,X712)) => 23.78/4.00 (~ 23.78/4.00 in( 23.78/4.00 X714,X710))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X716, 23.78/4.00 X718,X720]: 23.78/4.00 (( 23.78/4.00 ~ 23.78/4.00 in( 23.78/4.00 X720,X716)) => 23.78/4.00 (~ 23.78/4.00 in( 23.78/4.00 X720, 23.78/4.00 setminus( 23.78/4.00 X716,X718))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X722, 23.78/4.00 X724,X726]: 23.78/4.00 (in( 23.78/4.00 X726,X724) => 23.78/4.00 (~ 23.78/4.00 in( 23.78/4.00 X726, 23.78/4.00 setminus( 23.78/4.00 X722,X724))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X728, 23.78/4.00 X730]: 23.78/4.00 subset( 23.78/4.00 setminus( 23.78/4.00 X728,X730), 23.78/4.00 X728)) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X732, 23.78/4.00 X734]: 23.78/4.00 (( 23.78/4.00 setminus( 23.78/4.00 X732,X734) = 23.78/4.00 emptyset) => 23.78/4.00 subset( 23.78/4.00 X732,X734))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X736, 23.78/4.00 X738,X740]: 23.78/4.00 (in( 23.78/4.00 X740, 23.78/4.00 symdiff( 23.78/4.00 X736,X738)) => 23.78/4.00 (![X742:$o]: 23.78/4.00 (( 23.78/4.00 in( 23.78/4.00 X740,X736) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ~ 23.78/4.00 in( 23.78/4.00 X740,X738)) => 23.78/4.00 X742)) => 23.78/4.00 (( 23.78/4.00 ( 23.78/4.00 ~ 23.78/4.00 in( 23.78/4.00 X740,X736)) => 23.78/4.00 ( 23.78/4.00 in( 23.78/4.00 X740,X738) => 23.78/4.00 X742)) => 23.78/4.00 X742))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X744, 23.78/4.00 X746,X748]: 23.78/4.00 (in( 23.78/4.00 X748,X744) => 23.78/4.00 (( 23.78/4.00 ~ 23.78/4.00 in( 23.78/4.00 X748,X746)) => 23.78/4.00 in( 23.78/4.00 X748, 23.78/4.00 symdiff( 23.78/4.00 X744,X746))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X750, 23.78/4.00 X752,X754]: 23.78/4.00 (( 23.78/4.00 ~ 23.78/4.00 in( 23.78/4.00 X754,X750)) => 23.78/4.00 (in( 23.78/4.00 X754,X752) => 23.78/4.00 in( 23.78/4.00 X754, 23.78/4.00 symdiff( 23.78/4.00 X750,X752))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X756, 23.78/4.00 X758,X760]: 23.78/4.00 (in( 23.78/4.00 X760,X756) => 23.78/4.00 (in( 23.78/4.00 X760,X758) => 23.78/4.00 (~ 23.78/4.00 in( 23.78/4.00 X760, 23.78/4.00 symdiff( 23.78/4.00 X756,X758)))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X762, 23.78/4.00 X764,X766]: 23.78/4.00 (( 23.78/4.00 ~ 23.78/4.00 in( 23.78/4.00 X766,X762)) => 23.78/4.00 (( 23.78/4.00 ~ 23.78/4.00 in( 23.78/4.00 X766,X764)) => 23.78/4.00 (~ 23.78/4.00 in( 23.78/4.00 X766, 23.78/4.00 symdiff( 23.78/4.00 X762,X764)))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X768, 23.78/4.00 X770]: 23.78/4.00 in( 23.78/4.00 X770, 23.78/4.00 setadjoin( 23.78/4.00 X768, 23.78/4.00 setadjoin( 23.78/4.00 X770, 23.78/4.00 emptyset)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X772, 23.78/4.00 X774]: 23.78/4.00 in( 23.78/4.00 X772, 23.78/4.00 setunion( 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X772, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X772, 23.78/4.00 setadjoin( 23.78/4.00 X774, 23.78/4.00 emptyset)), 23.78/4.00 emptyset))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X776, 23.78/4.00 X778]: 23.78/4.00 in( 23.78/4.00 X778, 23.78/4.00 setunion( 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X776, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X776, 23.78/4.00 setadjoin( 23.78/4.00 X778, 23.78/4.00 emptyset)), 23.78/4.00 emptyset))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X780, 23.78/4.00 X782]: 23.78/4.00 (?[X784]: 23.78/4.00 (( 23.78/4.00 ?[X786]: 23.78/4.00 (( 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X780, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X780, 23.78/4.00 setadjoin( 23.78/4.00 X782, 23.78/4.00 emptyset)), 23.78/4.00 emptyset)) = 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X784, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X784, 23.78/4.00 setadjoin( 23.78/4.00 X786, 23.78/4.00 emptyset)), 23.78/4.00 emptyset))) & 23.78/4.00 in( 23.78/4.00 X786, 23.78/4.00 setunion( 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X780, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X780, 23.78/4.00 setadjoin( 23.78/4.00 X782, 23.78/4.00 emptyset)), 23.78/4.00 emptyset)))))) & 23.78/4.00 in( 23.78/4.00 X784, 23.78/4.00 setunion( 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X780, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X780, 23.78/4.00 setadjoin( 23.78/4.00 X782, 23.78/4.00 emptyset)), 23.78/4.00 emptyset))))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X788, 23.78/4.00 X790]: 23.78/4.00 (?[X792]: 23.78/4.00 (( 23.78/4.00 ?[X794]: 23.78/4.00 (( 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X788, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X788, 23.78/4.00 setadjoin( 23.78/4.00 X790, 23.78/4.00 emptyset)), 23.78/4.00 emptyset)) = 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X792, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X792, 23.78/4.00 setadjoin( 23.78/4.00 X794, 23.78/4.00 emptyset)), 23.78/4.00 emptyset))) & 23.78/4.00 in( 23.78/4.00 X794, 23.78/4.00 setunion( 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X788, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X788, 23.78/4.00 setadjoin( 23.78/4.00 X790, 23.78/4.00 emptyset)), 23.78/4.00 emptyset)))))) & 23.78/4.00 in( 23.78/4.00 X792, 23.78/4.00 setunion( 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X788, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X788, 23.78/4.00 setadjoin( 23.78/4.00 X790, 23.78/4.00 emptyset)), 23.78/4.00 emptyset))))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X796, 23.78/4.00 X798]: 23.78/4.00 (in( 23.78/4.00 X798,X796) => 23.78/4.00 subset( 23.78/4.00 setadjoin( 23.78/4.00 X798, 23.78/4.00 emptyset), 23.78/4.00 X796))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X800, 23.78/4.00 X802]: 23.78/4.00 (in( 23.78/4.00 X802,X800) => 23.78/4.00 in( 23.78/4.00 setadjoin( 23.78/4.00 X802, 23.78/4.00 emptyset), 23.78/4.00 powerset( 23.78/4.00 X800)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X804, 23.78/4.00 X806,X808]: 23.78/4.00 (in( 23.78/4.00 X808,X804) => 23.78/4.00 in( 23.78/4.00 setadjoin( 23.78/4.00 X808, 23.78/4.00 emptyset), 23.78/4.00 powerset( 23.78/4.00 binunion( 23.78/4.00 X804,X806))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X810, 23.78/4.00 X812,X814]: 23.78/4.00 (in( 23.78/4.00 X814, 23.78/4.00 setadjoin( 23.78/4.00 X810, 23.78/4.00 setadjoin( 23.78/4.00 X812, 23.78/4.00 emptyset))) => 23.78/4.00 (( 23.78/4.00 X814 = 23.78/4.00 X810) | 23.78/4.00 (X814 = 23.78/4.00 X812)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X816, 23.78/4.00 X818,X820]: 23.78/4.00 (in( 23.78/4.00 X820,X816) => 23.78/4.00 (![X822]: 23.78/4.00 (in( 23.78/4.00 X822,X818) => 23.78/4.00 subset( 23.78/4.00 setadjoin( 23.78/4.00 X820, 23.78/4.00 setadjoin( 23.78/4.00 X822, 23.78/4.00 emptyset)), 23.78/4.00 binunion( 23.78/4.00 X816,X818)))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X824, 23.78/4.00 X826,X828]: 23.78/4.00 (in( 23.78/4.00 X828,X824) => 23.78/4.00 (![X830]: 23.78/4.00 (in( 23.78/4.00 X830,X826) => 23.78/4.00 in( 23.78/4.00 setadjoin( 23.78/4.00 X828, 23.78/4.00 setadjoin( 23.78/4.00 X830, 23.78/4.00 emptyset)), 23.78/4.00 powerset( 23.78/4.00 binunion( 23.78/4.00 X824,X826))))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X832, 23.78/4.00 X834,X836]: 23.78/4.00 (in( 23.78/4.00 X836,X832) => 23.78/4.00 (![X838]: 23.78/4.00 (in( 23.78/4.00 X838,X834) => 23.78/4.00 subset( 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X836, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X836, 23.78/4.00 setadjoin( 23.78/4.00 X838, 23.78/4.00 emptyset)), 23.78/4.00 emptyset)), 23.78/4.00 powerset( 23.78/4.00 binunion( 23.78/4.00 X832,X834))))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X840, 23.78/4.00 X842,X844]: 23.78/4.00 (in( 23.78/4.00 X844,X840) => 23.78/4.00 (![X846]: 23.78/4.00 (in( 23.78/4.00 X846,X842) => 23.78/4.00 in( 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X844, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X844, 23.78/4.00 setadjoin( 23.78/4.00 X846, 23.78/4.00 emptyset)), 23.78/4.00 emptyset)), 23.78/4.00 powerset( 23.78/4.00 powerset( 23.78/4.00 binunion( 23.78/4.00 X840,X842)))))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X848, 23.78/4.00 X850,X852]: 23.78/4.00 (in( 23.78/4.00 X852,X848) => 23.78/4.00 (![X854]: 23.78/4.00 (in( 23.78/4.00 X854,X850) => 23.78/4.00 in( 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X852, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X852, 23.78/4.00 setadjoin( 23.78/4.00 X854, 23.78/4.00 emptyset)), 23.78/4.00 emptyset)), 23.78/4.00 powerset( 23.78/4.00 powerset( 23.78/4.00 binunion( 23.78/4.00 X848,X850)))))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X856, 23.78/4.00 X858,X860]: 23.78/4.00 (in( 23.78/4.00 X860,X856) => 23.78/4.00 (![X862]: 23.78/4.00 (in( 23.78/4.00 X862,X858) => 23.78/4.00 in( 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X860, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X860, 23.78/4.00 setadjoin( 23.78/4.00 X862, 23.78/4.00 emptyset)), 23.78/4.00 emptyset)), 23.78/4.00 cartprod( 23.78/4.00 X856,X858)))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X864, 23.78/4.00 X866,X868]: 23.78/4.00 (in( 23.78/4.00 X868, 23.78/4.00 cartprod( 23.78/4.00 X864,X866)) => 23.78/4.00 (?[X870]: 23.78/4.00 (( 23.78/4.00 ?[X872]: 23.78/4.00 (( 23.78/4.00 X868 = 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X870, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X870, 23.78/4.00 setadjoin( 23.78/4.00 X872, 23.78/4.00 emptyset)), 23.78/4.00 emptyset))) & 23.78/4.00 in( 23.78/4.00 X872,X866))) & 23.78/4.00 in( 23.78/4.00 X870,X864))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X874, 23.78/4.00 X876,X878]: 23.78/4.00 (in( 23.78/4.00 X878, 23.78/4.00 cartprod( 23.78/4.00 X874,X876)) => 23.78/4.00 (?[X880]: 23.78/4.00 (( 23.78/4.00 ?[X882]: 23.78/4.00 (( 23.78/4.00 X878 = 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X880, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X880, 23.78/4.00 setadjoin( 23.78/4.00 X882, 23.78/4.00 emptyset)), 23.78/4.00 emptyset))) & 23.78/4.00 in( 23.78/4.00 X882, 23.78/4.00 setunion( 23.78/4.00 X878)))) & 23.78/4.00 in( 23.78/4.00 X880, 23.78/4.00 setunion( 23.78/4.00 X878)))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X884, 23.78/4.00 X886]: 23.78/4.00 (in( 23.78/4.00 X886, 23.78/4.00 setunion( 23.78/4.00 X884)) => 23.78/4.00 (?[X888]: 23.78/4.00 (in( 23.78/4.00 X886,X888) & 23.78/4.00 in( 23.78/4.00 X888,X884))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X890]: 23.78/4.00 subset( 23.78/4.00 setunion( 23.78/4.00 setadjoin( 23.78/4.00 X890, 23.78/4.00 emptyset)), 23.78/4.00 X890)) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X892]: 23.78/4.00 subset( 23.78/4.00 X892, 23.78/4.00 setunion( 23.78/4.00 setadjoin( 23.78/4.00 X892, 23.78/4.00 emptyset)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X894]: 23.78/4.00 (setunion( 23.78/4.00 setadjoin( 23.78/4.00 X894, 23.78/4.00 emptyset)) = 23.78/4.00 X894)) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X896, 23.78/4.00 X898:( 23.78/4.00 ( 23.78/4.00 $i > $o))]: 23.78/4.00 (( 23.78/4.00 ![X900]: 23.78/4.00 (in( 23.78/4.00 X900,X896) => 23.78/4.00 (![X902]: 23.78/4.00 (in( 23.78/4.00 X902,X896) => 23.78/4.00 (X898( 23.78/4.00 X900) => 23.78/4.00 (X898( 23.78/4.00 X902) => 23.78/4.00 (X900 = 23.78/4.00 X902))))))) => 23.78/4.00 (( 23.78/4.00 ?[X904]: 23.78/4.00 (X898( 23.78/4.00 X904) & 23.78/4.00 in( 23.78/4.00 X904,X896))) => 23.78/4.00 (?[X906]: 23.78/4.00 (( 23.78/4.00 dsetconstr( 23.78/4.00 X896, 23.78/4.00 ^[V_15]: 23.78/4.00 X898( 23.78/4.00 V_15)) = 23.78/4.00 setadjoin( 23.78/4.00 X906, 23.78/4.00 emptyset)) & 23.78/4.00 in( 23.78/4.00 X906, 23.78/4.00 dsetconstr( 23.78/4.00 X896, 23.78/4.00 ^[V_16]: 23.78/4.00 X898( 23.78/4.00 V_16)))))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X908, 23.78/4.00 X910:( 23.78/4.00 ( 23.78/4.00 $i > $o))]: 23.78/4.00 (( 23.78/4.00 ?[X912]: 23.78/4.00 (( 23.78/4.00 dsetconstr( 23.78/4.00 X908, 23.78/4.00 ^[V_17]: 23.78/4.00 X910( 23.78/4.00 V_17)) = 23.78/4.00 setadjoin( 23.78/4.00 X912, 23.78/4.00 emptyset)) & 23.78/4.00 in( 23.78/4.00 X912, 23.78/4.00 dsetconstr( 23.78/4.00 X908, 23.78/4.00 ^[V_18]: 23.78/4.00 X910( 23.78/4.00 V_18))))) => 23.78/4.00 (?[X914]: 23.78/4.00 (X910( 23.78/4.00 X914) & 23.78/4.00 in( 23.78/4.00 X914,X908))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X916, 23.78/4.00 X918:( 23.78/4.00 ( 23.78/4.00 $i > $o)), 23.78/4.00 X920]: 23.78/4.00 (in( 23.78/4.00 X920,X916) => 23.78/4.00 (X918( 23.78/4.00 X920) => 23.78/4.00 (( 23.78/4.00 ![X922]: 23.78/4.00 (in( 23.78/4.00 X922,X916) => 23.78/4.00 (X918( 23.78/4.00 X922) => 23.78/4.00 (X922 = 23.78/4.00 X920)))) => 23.78/4.00 (?[X924]: 23.78/4.00 (( 23.78/4.00 dsetconstr( 23.78/4.00 X916, 23.78/4.00 ^[V_19]: 23.78/4.00 X918( 23.78/4.00 V_19)) = 23.78/4.00 setadjoin( 23.78/4.00 X924, 23.78/4.00 emptyset)) & 23.78/4.00 in( 23.78/4.00 X924, 23.78/4.00 dsetconstr( 23.78/4.00 X916, 23.78/4.00 ^[V_20]: 23.78/4.00 X918( 23.78/4.00 V_20))))))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X926, 23.78/4.00 X928:( 23.78/4.00 ( 23.78/4.00 $i > $o))]: 23.78/4.00 (( 23.78/4.00 ![X930]: 23.78/4.00 (in( 23.78/4.00 X930,X926) => 23.78/4.00 (![X932]: 23.78/4.00 (in( 23.78/4.00 X932,X926) => 23.78/4.00 (X928( 23.78/4.00 X930) => 23.78/4.00 (X928( 23.78/4.00 X932) => 23.78/4.00 (X930 = 23.78/4.00 X932))))))) => 23.78/4.00 (( 23.78/4.00 ?[X934]: 23.78/4.00 (X928( 23.78/4.00 X934) & 23.78/4.00 in( 23.78/4.00 X934,X926))) => 23.78/4.00 (?[X936]: 23.78/4.00 (( 23.78/4.00 dsetconstr( 23.78/4.00 X926, 23.78/4.00 ^[V_21]: 23.78/4.00 X928( 23.78/4.00 V_21)) = 23.78/4.00 setadjoin( 23.78/4.00 X936, 23.78/4.00 emptyset)) & 23.78/4.00 in( 23.78/4.00 X936, 23.78/4.00 dsetconstr( 23.78/4.00 X926, 23.78/4.00 ^[V_22]: 23.78/4.00 X928( 23.78/4.00 V_22)))))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X938, 23.78/4.00 X940]: 23.78/4.00 (( 23.78/4.00 setadjoin( 23.78/4.00 X938, 23.78/4.00 emptyset) = 23.78/4.00 setadjoin( 23.78/4.00 X940, 23.78/4.00 emptyset)) => 23.78/4.00 (X938 = 23.78/4.00 X940))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X942, 23.78/4.00 X944,X946]: 23.78/4.00 (in( 23.78/4.00 setadjoin( 23.78/4.00 X946, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X942, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X942, 23.78/4.00 setadjoin( 23.78/4.00 X944, 23.78/4.00 emptyset)), 23.78/4.00 emptyset))) => 23.78/4.00 (X942 = 23.78/4.00 X946))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X948]: 23.78/4.00 (( 23.78/4.00 ?[X950]: 23.78/4.00 (( 23.78/4.00 ?[X952]: 23.78/4.00 (( 23.78/4.00 X948 = 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X950, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X950, 23.78/4.00 setadjoin( 23.78/4.00 X952, 23.78/4.00 emptyset)), 23.78/4.00 emptyset))) & 23.78/4.00 in( 23.78/4.00 X952, 23.78/4.00 setunion( 23.78/4.00 X948)))) & 23.78/4.00 in( 23.78/4.00 X950, 23.78/4.00 setunion( 23.78/4.00 X948)))) => 23.78/4.00 (?[X954]: 23.78/4.00 (( 23.78/4.00 dsetconstr( 23.78/4.00 setunion( 23.78/4.00 X948), 23.78/4.00 ^[V_23]: 23.78/4.00 in( 23.78/4.00 setadjoin( 23.78/4.00 V_23, 23.78/4.00 emptyset), 23.78/4.00 X948)) = 23.78/4.00 setadjoin( 23.78/4.00 X954, 23.78/4.00 emptyset)) & 23.78/4.00 in( 23.78/4.00 X954, 23.78/4.00 dsetconstr( 23.78/4.00 setunion( 23.78/4.00 X948), 23.78/4.00 ^[V_24]: 23.78/4.00 in( 23.78/4.00 setadjoin( 23.78/4.00 V_24, 23.78/4.00 emptyset), 23.78/4.00 X948))))))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X956]: 23.78/4.00 (( 23.78/4.00 ?[X958]: 23.78/4.00 (( 23.78/4.00 X956 = 23.78/4.00 setadjoin( 23.78/4.00 X958, 23.78/4.00 emptyset)) & 23.78/4.00 in( 23.78/4.00 X958,X956))) => 23.78/4.00 in( 23.78/4.00 setunion( 23.78/4.00 X956), 23.78/4.00 X956))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X960, 23.78/4.00 X962]: 23.78/4.00 (kfst( 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X960, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X960, 23.78/4.00 setadjoin( 23.78/4.00 X962, 23.78/4.00 emptyset)), 23.78/4.00 emptyset))) = 23.78/4.00 X960)) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X964, 23.78/4.00 X966,X968]: 23.78/4.00 (in( 23.78/4.00 X968, 23.78/4.00 cartprod( 23.78/4.00 X964,X966)) => 23.78/4.00 in( 23.78/4.00 kfst( 23.78/4.00 X968), 23.78/4.00 X964))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X970, 23.78/4.00 X972, 23.78/4.00 X974,X976]: 23.78/4.00 (( 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X970, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X970, 23.78/4.00 setadjoin( 23.78/4.00 X972, 23.78/4.00 emptyset)), 23.78/4.00 emptyset)) = 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X974, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X974, 23.78/4.00 setadjoin( 23.78/4.00 X976, 23.78/4.00 emptyset)), 23.78/4.00 emptyset))) => 23.78/4.00 (X970 = 23.78/4.00 X974))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X978, 23.78/4.00 X980, 23.78/4.00 X982,X984]: 23.78/4.00 (( 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X978, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X978, 23.78/4.00 setadjoin( 23.78/4.00 X980, 23.78/4.00 emptyset)), 23.78/4.00 emptyset)) = 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X982, 23.78/4.00 emptyset), 23.78/4.00 setadjoin( 23.78/4.00 setadjoin( 23.78/4.00 X982, 23.78/4.00 setadjoin( 23.78/4.00 X984, 23.78/4.00 emptyset)), 23.78/4.00 emptyset))) => 23.78/4.00 (X978 = 23.78/4.00 X982))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X986, 23.78/4.00 X988]: 23.78/4.00 (( 23.78/4.00 X986 = 23.78/4.00 X988) => 23.78/4.00 (setadjoin( 23.78/4.00 X986, 23.78/4.00 setadjoin( 23.78/4.00 X988, 23.78/4.00 emptyset)) = 23.78/4.00 setadjoin( 23.78/4.00 X986, 23.78/4.00 emptyset)))) => 23.78/4.00 ( 23.78/4.00 ( 23.78/4.00 ![X990, 23.78/4.00 X992]: 23.78/4.00 (( 23.78/4.00 X990 = 23.78/4.00 X992) => 23.78/4.00 (setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X990, 23.78/4.01 emptyset), 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X990, 23.78/4.01 setadjoin( 23.78/4.01 X992, 23.78/4.01 emptyset)), 23.78/4.01 emptyset)) = 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X990, 23.78/4.01 emptyset), 23.78/4.01 emptyset)))) => 23.78/4.01 ( 23.78/4.01 ![X994, 23.78/4.01 X996, 23.78/4.01 X998, 23.78/4.01 X1000]: 23.78/4.01 (( 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X994, 23.78/4.01 emptyset), 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X994, 23.78/4.01 setadjoin( 23.78/4.01 X996, 23.78/4.01 emptyset)), 23.78/4.01 emptyset)) = 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X998, 23.78/4.01 emptyset), 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X998, 23.78/4.01 setadjoin( 23.78/4.01 X1000, 23.78/4.01 emptyset)), 23.78/4.01 emptyset))) => 23.78/4.01 (( 23.78/4.01 X998 = 23.78/4.01 X1000) => 23.78/4.01 (X996 = 23.78/4.01 X1000)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 23.78/4.01 tff(zf_stmt_14, negated_conjecture, 23.78/4.01 (~ 23.78/4.01 ((![X4,X6]: ((![X8]: (in(X8,X4) <=> in(X8,X6))) => (X4 = X6))) => 23.78/4.01 ((![X10]: (~in(X10,emptyset))) => 23.78/4.01 ((![X12,X14,X16]: 23.78/4.01 (in(X16,setadjoin(X12,X14)) <=> zip_tseitin_0(X16,X14,X12))) => 23.78/4.01 ((![X18,X20]: 23.78/4.01 (in(X20,powerset(X18)) <=> (![X22]: zip_tseitin_1(X22,X20,X18)))) => 23.78/4.01 ((![X24,X26]: 23.78/4.01 (in(X26,setunion(X24)) <=> (?[X28]: zip_tseitin_2(X28,X26,X24)))) => 23.78/4.01 (in(emptyset,omega) => 23.78/4.01 ((![X30]: (in(X30,omega) => in(setadjoin(X30,X30),omega))) => 23.78/4.01 ((![X32]: 23.78/4.01 ((in(emptyset,X32) & 23.78/4.01 (![X34]: 23.78/4.01 ((in(X34,omega) & in(X34,X32)) => 23.78/4.01 in(setadjoin(X34,X34),X32)))) => 23.78/4.01 (![X36]: (in(X36,omega) => in(X36,X32))))) => 23.78/4.01 ((![X38:(($i * $i) > $o),X40]: 23.78/4.01 ((![X42]: 23.78/4.01 (in(X42,X40) => 23.78/4.01 (?[X44]: 23.78/4.01 ((![X46]: (X38(X42,X46) => (X44 = X46))) & 23.78/4.01 X38(X42,X44))))) => 23.78/4.01 (?[X48]: 23.78/4.01 (![X50]: 23.78/4.01 (in(X50,X48) <=> 23.78/4.01 (?[X52]: zip_tseitin_3(X52,X50,X40,X38))))))) => 23.78/4.01 ((![X54]: 23.78/4.01 ((?[X56]: in(X56,X54)) => 23.78/4.01 (?[X58]: 23.78/4.01 ((~(?[X60]: (in(X60,X54) & in(X60,X58)))) & in(X58,X54))))) => 23.78/4.01 ((![X62]: 23.78/4.01 (?[X64]: 23.78/4.01 ((![X66]: 23.78/4.01 (((![X68]: (in(X68,X66) => in(X68,X62))) & 23.78/4.01 (?[X70]: in(X70,X66))) => 23.78/4.01 (?[X72,X74]: 23.78/4.01 ((![X76]: 23.78/4.01 (in(X76,X64) => 23.78/4.01 ((![X78]: (in(X78,X76) => in(X78,X72))) | 23.78/4.01 in(X74,X76)))) & 23.78/4.01 (~(?[X80]: (in(X80,X66) & in(X80,X72)))) & 23.78/4.01 in(X74,X66) & in(X72,X64))))) & 23.78/4.01 (![X82,X84]: 23.78/4.01 ((in(X82,X64) & in(X84,X64)) => 23.78/4.01 ((![X86]: (in(X86,X82) => in(X86,X84))) | 23.78/4.01 (![X88]: (in(X88,X84) => in(X88,X82)))))) & 23.78/4.01 (![X90,X92]: 23.78/4.01 ((in(X90,X62) & in(X92,X62)) => 23.78/4.01 ((![X94]: 23.78/4.01 (in(X94,X64) => (in(X90,X94) <=> in(X92,X94)))) => 23.78/4.01 (X90 = X92)))) & 23.78/4.01 (![X96]: 23.78/4.01 (in(X96,X64) => 23.78/4.01 (![X98]: (in(X98,X96) => in(X98,X62)))))))) => 23.78/4.01 ((![X100:(($i > $o))]: 23.78/4.01 ((?[X102]: 23.78/4.01 ((![X104]: (X100(X104) => (X102 = X104))) & X100(X102))) => 23.78/4.01 X100(descr(^[V_1]: X100(V_1))))) => 23.78/4.01 ((![X106,X108:(($i > $o)),X110]: 23.78/4.01 (in(X110,X106) => 23.78/4.01 (X108(X110) => 23.78/4.01 in(X110,dsetconstr(X106,^[V_2]: X108(V_2)))))) => 23.78/4.01 ((![X112,X114:(($i > $o)),X116]: 23.78/4.01 (in(X116,dsetconstr(X112,^[V_3]: X114(V_3))) => 23.78/4.01 in(X116,X112))) => 23.78/4.01 ((![X118,X120:(($i > $o)),X122]: 23.78/4.01 (in(X122,dsetconstr(X118,^[V_4]: X120(V_4))) => 23.78/4.01 X120(X122))) => 23.78/4.01 ((![X124:(($i > $o))]: 23.78/4.01 ((?[X126]: 23.78/4.01 ((![X128]: (X124(X128) => (X126 = X128))) & 23.78/4.01 X124(X126))) => 23.78/4.01 (?[X130]: 23.78/4.01 ((![X132]: (X124(X132) => (X130 = X132))) & 23.78/4.01 X124(X130))))) => 23.78/4.01 ((![X134:$o,X136]: (in(X136,prop2set(X134)) => X134)) => 23.78/4.01 ((![X138]: (in(X138,emptyset) => (![X140:$o]: X140))) => 23.78/4.01 ((![X142]: (~in(X142,emptyset))) => 23.78/4.01 ((![X144]: (~in(X144,emptyset))) => 23.78/4.01 ((![X146:(($i > $o))]: 23.78/4.01 ((?[X148]: 23.78/4.01 ((![X150]: (X146(X150) => (X148 = X150))) & 23.78/4.01 X146(X148))) => 23.78/4.01 (?[X152]: X146(X152)))) => 23.78/4.01 ((![X154,X156]: 23.78/4.01 ((![X158]: (in(X158,X154) => in(X158,X156))) => 23.78/4.01 ((![X160]: (in(X160,X156) => in(X160,X154))) => 23.78/4.01 (X154 = X156)))) => 23.78/4.01 ((![X162]: 23.78/4.01 ((![X164]: (~in(X164,X162))) => 23.78/4.01 (X162 = emptyset))) => 23.78/4.01 ((![X166]: 23.78/4.01 ((![X168]: (~in(X168,X166))) => 23.78/4.01 (X166 = emptyset))) => 23.78/4.01 ((![X170,X172:(($i > $o)),X174]: 23.78/4.01 (in(X174,X170) => 23.78/4.01 (in(X174,dsetconstr(X170,^[V_5]: X172(V_5))) <=> 23.78/4.01 X172(X174)))) => 23.78/4.01 ((![X176]: 23.78/4.01 ((X176 != emptyset) => 23.78/4.01 (?[X178]: in(X178,X176)))) => 23.78/4.01 ((![X180,X182:(($i > $o)),X184]: 23.78/4.01 (in(X184,X180) => 23.78/4.01 (X182(X184) => 23.78/4.01 (dsetconstr(X180,^[V_6]: X182(V_6)) != 23.78/4.01 emptyset)))) => 23.78/4.01 ((![X186]: 23.78/4.01 ((?[X188]: in(X188,X186)) => 23.78/4.01 (X186 != emptyset))) => 23.78/4.01 ((![X190,X192]: in(X190,setadjoin(X190,X192))) => 23.78/4.01 (in(emptyset,setadjoin(emptyset,emptyset)) => 23.78/4.01 ((![X194,X196,X198]: 23.78/4.01 (in(X198,X196) => 23.78/4.01 in(X198,setadjoin(X194,X196)))) => 23.78/4.01 ((![X200,X202,X204]: 23.78/4.01 (in(X204,setadjoin(X200,X202)) => 23.78/4.01 (![X206:$o]: 23.78/4.01 (((X204 = X200) => X206) => 23.78/4.01 ((in(X204,X202) => X206) => X206))))) => 23.78/4.01 ((![X208,X210,X212]: 23.78/4.01 (in(X212,setadjoin(X208,X210)) => 23.78/4.01 ((X212 = X208) | in(X212,X210)))) => 23.78/4.01 ((![X214]: 23.78/4.01 (dsetconstr(X214,^[V_7]: $true) = 23.78/4.01 X214)) => 23.78/4.01 ((![X216,X218]: 23.78/4.01 ((![X220]: 23.78/4.01 (in(X220,X218) => in(X220,X216))) => 23.78/4.01 in(X218,powerset(X216)))) => 23.78/4.01 ((![X222]: in(emptyset,powerset(X222))) => 23.78/4.01 ((![X224]: 23.78/4.01 in(emptyset,powerset(X224))) => 23.78/4.01 ((![X226,X228,X230]: 23.78/4.01 (in(X228,powerset(X226)) => 23.78/4.01 (in(X230,X228) => in(X230,X226)))) => 23.78/4.01 ((![X232,X234,X236]: 23.78/4.01 (in(X234,X236) => 23.78/4.01 (in(X236,X232) => 23.78/4.01 in(X234,setunion(X232))))) => 23.78/4.01 ((![X238,X240]: 23.78/4.01 (in(X240,setunion(X238)) => 23.78/4.01 (![X242:$o]: 23.78/4.01 ((![X244]: 23.78/4.01 (in(X240,X244) => 23.78/4.01 (in(X244,X238) => 23.78/4.01 X242))) => 23.78/4.01 X242)))) => 23.78/4.01 ((![X246,X248]: 23.78/4.01 (in(X248,X246) => 23.78/4.01 in(X248, 23.78/4.01 powerset(setunion(X246))))) => 23.78/4.01 ((![X250:(($i > $o))]: 23.78/4.01 ((?[X252]: 23.78/4.01 ((![X254]: 23.78/4.01 (X250(X254) => 23.78/4.01 (X252 = X254))) & 23.78/4.01 X250(X252))) => 23.78/4.01 (?[X256]: 23.78/4.01 (![X258]: 23.78/4.01 (X250(X258) <=> 23.78/4.01 (X258 = X256)))))) => 23.78/4.01 ((![X260]: 23.78/4.01 ((X260 != emptyset) => 23.78/4.01 (?[X262]: in(X262,X260)))) => 23.78/4.01 ((![X264,X266]: 23.78/4.01 (in(X264, 23.78/4.01 setadjoin(X266, 23.78/4.01 emptyset)) => 23.78/4.01 (X264 = X266))) => 23.78/4.01 ((![X268,X270]: 23.78/4.01 ((X268 != X270) => 23.78/4.01 (~ 23.78/4.01 in(X270, 23.78/4.01 setadjoin(X268, 23.78/4.01 emptyset))))) => 23.78/4.01 ((![X272,X274]: 23.78/4.01 ((X272 = X274) => 23.78/4.01 in(X272, 23.78/4.01 setadjoin(X274, 23.78/4.01 emptyset)))) => 23.78/4.01 ((![X276,X278]: 23.78/4.01 (in(X276, 23.78/4.01 setadjoin(X278, 23.78/4.01 emptyset)) => 23.78/4.01 in(X278, 23.78/4.01 setadjoin(X276, 23.78/4.01 emptyset)))) => 23.78/4.01 ((![X280,X282,X284]: 23.78/4.01 (in(X284, 23.78/4.01 setadjoin( 23.78/4.01 X280, 23.78/4.01 setadjoin( 23.78/4.01 X282,emptyset))) => 23.78/4.01 ((X284 = X280) | 23.78/4.01 (X284 = X282)))) => 23.78/4.01 ((![X286,X288]: 23.78/4.01 in(X286, 23.78/4.01 setadjoin( 23.78/4.01 X286, 23.78/4.01 setadjoin( 23.78/4.01 X288,emptyset)))) => 23.78/4.01 ((![X290,X292]: 23.78/4.01 in(X292, 23.78/4.01 setadjoin( 23.78/4.01 X290, 23.78/4.01 setadjoin( 23.78/4.01 X292,emptyset)))) => 23.78/4.01 ((![X294, 23.78/4.01 X296:(($i > $o))]: 23.78/4.01 ((?[X298]: 23.78/4.01 (X296(X298) & 23.78/4.01 in(X298,X294))) => 23.78/4.01 (dsetconstr( 23.78/4.01 X294, 23.78/4.01 ^[V_8]: X296(V_8)) != 23.78/4.01 emptyset))) => 23.78/4.01 ((![X300:(($i > $o)), 23.78/4.01 X302]: 23.78/4.01 (in(X302,emptyset) => 23.78/4.01 X300(X302))) => 23.78/4.01 ((![X304, 23.78/4.01 X306:(($i > $o))]: 23.78/4.01 ((~ 23.78/4.01 (![X308]: 23.78/4.01 (in( 23.78/4.01 X308,X304) => 23.78/4.01 X306(X308)))) => 23.78/4.01 (?[X310]: 23.78/4.01 ((~X306(X310)) & 23.78/4.01 in(X310,X304))))) => 23.78/4.01 ((![X312, 23.78/4.01 X314:(($i > $o))]: 23.78/4.01 ((![X316]: 23.78/4.01 (in( 23.78/4.01 X316,X312) => 23.78/4.01 (~ 23.78/4.01 X314( 23.78/4.01 X316)))) => 23.78/4.01 (~ 23.78/4.01 (?[X318]: 23.78/4.01 (X314( 23.78/4.01 X318) & 23.78/4.01 in( 23.78/4.01 X318,X312)))))) => 23.78/4.01 ((![X320, 23.78/4.01 X322:(($i > $o))]: 23.78/4.01 ((~ 23.78/4.01 (?[X324]: 23.78/4.01 ( 23.78/4.01 X322( 23.78/4.01 X324) & 23.78/4.01 in( 23.78/4.01 X324,X320)))) => 23.78/4.01 (![X326]: 23.78/4.01 (in( 23.78/4.01 X326,X320) => 23.78/4.01 (~ 23.78/4.01 X322( 23.78/4.01 X326)))))) => 23.78/4.01 ((![X328, 23.78/4.01 X330:( 23.78/4.01 ($i > $o))]: 23.78/4.01 ((?[X332]: 23.78/4.01 (( 23.78/4.01 ~ 23.78/4.01 X330( 23.78/4.01 X332)) & 23.78/4.01 in( 23.78/4.01 X332,X328))) => 23.78/4.01 (~ 23.78/4.01 (![X334]: 23.78/4.01 (in( 23.78/4.01 X334,X328) => 23.78/4.01 X330( 23.78/4.01 X334)))))) => 23.78/4.01 ((![X336:$o]: 23.78/4.01 (X336 => 23.78/4.01 in(emptyset, 23.78/4.01 prop2set( 23.78/4.01 X336)))) => 23.78/4.01 ((![X338:$o]: 23.78/4.01 (X338 => 23.78/4.01 set2prop( 23.78/4.01 prop2set( 23.78/4.01 X338)))) => 23.78/4.01 ((![X340, 23.78/4.01 X342:( 23.78/4.01 ($i > $o))]: 23.78/4.01 ((~ 23.78/4.01 ( 23.78/4.01 ?[X344]: 23.78/4.01 (X342( 23.78/4.01 X344) & 23.78/4.01 in( 23.78/4.01 X344,X340)))) => 23.78/4.01 (![X346]: 23.78/4.01 (in( 23.78/4.01 X346,X340) => 23.78/4.01 (~ 23.78/4.01 X342( 23.78/4.01 X346)))))) => 23.78/4.01 ((![X348, 23.78/4.01 X350:( 23.78/4.01 ($i > $o))]: 23.78/4.01 (( 23.78/4.01 ~ 23.78/4.01 ( 23.78/4.01 ![X352]: 23.78/4.01 (in( 23.78/4.01 X352,X348) => 23.78/4.01 X350( 23.78/4.01 X352)))) => 23.78/4.01 ( 23.78/4.01 ?[X354]: 23.78/4.01 (( 23.78/4.01 ~ 23.78/4.01 X350( 23.78/4.01 X354)) & 23.78/4.01 in( 23.78/4.01 X354,X348))))) => 23.78/4.01 ((![X356:( 23.78/4.01 ( 23.78/4.01 $i > $o))]: 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ?[X358]: 23.78/4.01 (( 23.78/4.01 ![X360]: 23.78/4.01 (X356( 23.78/4.01 X360) => 23.78/4.01 (X358 = 23.78/4.01 X360))) & 23.78/4.01 X356( 23.78/4.01 X358))) => 23.78/4.01 ( 23.78/4.01 ?[X362]: 23.78/4.01 (( 23.78/4.01 ![X364]: 23.78/4.01 (X356( 23.78/4.01 X364) => 23.78/4.01 (X362 = 23.78/4.01 X364))) & 23.78/4.01 X356( 23.78/4.01 X362))))) => 23.78/4.01 ((![X366:( 23.78/4.01 ( 23.78/4.01 $i > $o))]: 23.78/4.01 (( 23.78/4.01 ?[X368]: 23.78/4.01 X366( 23.78/4.01 X368)) => 23.78/4.01 (( 23.78/4.01 ![X370, 23.78/4.01 X372]: 23.78/4.01 (X366( 23.78/4.01 X370) => 23.78/4.01 (X366( 23.78/4.01 X372) => 23.78/4.01 (X370 = 23.78/4.01 X372)))) => 23.78/4.01 (?[X374]: 23.78/4.01 (( 23.78/4.01 ![X376]: 23.78/4.01 (X366( 23.78/4.01 X376) => 23.78/4.01 (X374 = 23.78/4.01 X376))) & 23.78/4.01 X366( 23.78/4.01 X374)))))) => 23.78/4.01 ((![X378:( 23.78/4.01 ( 23.78/4.01 $i > $o))]: 23.78/4.01 (( 23.78/4.01 ?[X380]: 23.78/4.01 (![X382]: 23.78/4.01 (X378( 23.78/4.01 X382) <=> 23.78/4.01 (X382 = 23.78/4.01 X380)))) => 23.78/4.01 (?[X384]: 23.78/4.01 (( 23.78/4.01 ![X386]: 23.78/4.01 (X378( 23.78/4.01 X386) => 23.78/4.01 (X384 = 23.78/4.01 X386))) & 23.78/4.01 X378( 23.78/4.01 X384))))) => 23.78/4.01 (( 23.78/4.01 ![X388, 23.78/4.01 X390]: 23.78/4.01 (( 23.78/4.01 X388 = 23.78/4.01 X390) => 23.78/4.01 (![X392, 23.78/4.01 X394]: 23.78/4.01 (( 23.78/4.01 X392 = 23.78/4.01 X394) => 23.78/4.01 (in( 23.78/4.01 X392,X388) => 23.78/4.01 in( 23.78/4.01 X394,X390)))))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X396, 23.78/4.01 X398]: 23.78/4.01 (( 23.78/4.01 X396 = 23.78/4.01 X398) => 23.78/4.01 (![X400, 23.78/4.01 X402]: 23.78/4.01 (( 23.78/4.01 X400 = 23.78/4.01 X402) => 23.78/4.01 (in( 23.78/4.01 X400,X396) <=> 23.78/4.01 in( 23.78/4.01 X402,X398)))))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X404:( 23.78/4.01 ( 23.78/4.01 $i > $o))]: 23.78/4.01 (( 23.78/4.01 ?[X406]: 23.78/4.01 (( 23.78/4.01 ![X408]: 23.78/4.01 (X404( 23.78/4.01 X408) => 23.78/4.01 (X406 = 23.78/4.01 X408))) & 23.78/4.01 X404( 23.78/4.01 X406))) => 23.78/4.01 (![X410, 23.78/4.01 X412]: 23.78/4.01 (X404( 23.78/4.01 X410) => 23.78/4.01 (X404( 23.78/4.01 X412) => 23.78/4.01 (X410 = 23.78/4.01 X412)))))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X414:( 23.78/4.01 ( 23.78/4.01 $i > $o)), 23.78/4.01 X416:( 23.78/4.01 ( 23.78/4.01 $i > $o))]: 23.78/4.01 (( 23.78/4.01 ![X418, 23.78/4.01 X420]: 23.78/4.01 (( 23.78/4.01 X418 = 23.78/4.01 X420) => 23.78/4.01 (X414( 23.78/4.01 X418) <=> 23.78/4.01 X416( 23.78/4.01 X420)))) => 23.78/4.01 (( 23.78/4.01 ?[X422]: 23.78/4.01 zip_tseitin_5( 23.78/4.01 X422,X414)) <=> 23.78/4.01 (?[X426]: 23.78/4.01 zip_tseitin_5( 23.78/4.01 X426,X416))))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 emptyset = 23.78/4.01 emptyset) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X430, 23.78/4.01 X432]: 23.78/4.01 (( 23.78/4.01 X430 = 23.78/4.01 X432) => 23.78/4.01 (![X434, 23.78/4.01 X436]: 23.78/4.01 (( 23.78/4.01 X434 = 23.78/4.01 X436) => 23.78/4.01 (setadjoin( 23.78/4.01 X430,X434) = 23.78/4.01 setadjoin( 23.78/4.01 X432,X436)))))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X438, 23.78/4.01 X440]: 23.78/4.01 (( 23.78/4.01 X438 = 23.78/4.01 X440) => 23.78/4.01 (powerset( 23.78/4.01 X438) = 23.78/4.01 powerset( 23.78/4.01 X440)))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X442, 23.78/4.01 X444]: 23.78/4.01 (( 23.78/4.01 X442 = 23.78/4.01 X444) => 23.78/4.01 (setunion( 23.78/4.01 X442) = 23.78/4.01 setunion( 23.78/4.01 X444)))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 omega = 23.78/4.01 omega) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X446:( 23.78/4.01 ( 23.78/4.01 $i > $o))]: 23.78/4.01 (( 23.78/4.01 ?[X448]: 23.78/4.01 (( 23.78/4.01 ![X450]: 23.78/4.01 (X446( 23.78/4.01 X450) => 23.78/4.01 (X448 = 23.78/4.01 X450))) & 23.78/4.01 X446( 23.78/4.01 X448))) => 23.78/4.01 (![X452, 23.78/4.01 X454]: 23.78/4.01 (X446( 23.78/4.01 X452) => 23.78/4.01 (X446( 23.78/4.01 X454) => 23.78/4.01 (X452 = 23.78/4.01 X454)))))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X456:( 23.78/4.01 ( 23.78/4.01 $i > $o)), 23.78/4.01 X458:( 23.78/4.01 ( 23.78/4.01 $i > $o))]: 23.78/4.01 (( 23.78/4.01 ![X460, 23.78/4.01 X462]: 23.78/4.01 (( 23.78/4.01 X460 = 23.78/4.01 X462) => 23.78/4.01 (X456( 23.78/4.01 X460) <=> 23.78/4.01 X458( 23.78/4.01 X462)))) => 23.78/4.01 (( 23.78/4.01 ?[X464]: 23.78/4.01 (( 23.78/4.01 ![X466]: 23.78/4.01 (X456( 23.78/4.01 X466) => 23.78/4.01 (X464 = 23.78/4.01 X466))) & 23.78/4.01 X456( 23.78/4.01 X464))) => 23.78/4.01 (( 23.78/4.01 ?[X468]: 23.78/4.01 (( 23.78/4.01 ![X470]: 23.78/4.01 (X458( 23.78/4.01 X470) => 23.78/4.01 (X468 = 23.78/4.01 X470))) & 23.78/4.01 X458( 23.78/4.01 X468))) => 23.78/4.01 (descr( 23.78/4.01 ^[V_9]: 23.78/4.01 X456(V_9)) = 23.78/4.01 descr( 23.78/4.01 ^[V_10]: 23.78/4.01 X458( 23.78/4.01 V_10))))))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X472, 23.78/4.01 X474]: 23.78/4.01 (( 23.78/4.01 X472 = 23.78/4.01 X474) => 23.78/4.01 (![X476:( 23.78/4.01 ( 23.78/4.01 $i > $o)), 23.78/4.01 X478:( 23.78/4.01 ( 23.78/4.01 $i > $o))]: 23.78/4.01 (( 23.78/4.01 ![X480]: 23.78/4.01 (in( 23.78/4.01 X480,X472) => 23.78/4.01 (![X482]: 23.78/4.01 (in( 23.78/4.01 X482,X474) => 23.78/4.01 (( 23.78/4.01 X480 = 23.78/4.01 X482) => 23.78/4.01 (X476( 23.78/4.01 X480) <=> 23.78/4.01 X478( 23.78/4.01 X482))))))) => 23.78/4.01 (dsetconstr( 23.78/4.01 X472, 23.78/4.01 ^[V_11]: 23.78/4.01 X476( 23.78/4.01 V_11)) = 23.78/4.01 dsetconstr( 23.78/4.01 X474, 23.78/4.01 ^[V_12]: 23.78/4.01 X478( 23.78/4.01 V_12))))))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X484, 23.78/4.01 X486]: 23.78/4.01 (( 23.78/4.01 ![X488]: 23.78/4.01 (in( 23.78/4.01 X488,X484) => 23.78/4.01 in( 23.78/4.01 X488,X486))) => 23.78/4.01 subset( 23.78/4.01 X484,X486))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X490, 23.78/4.01 X492]: 23.78/4.01 (( 23.78/4.01 X490 = 23.78/4.01 X492) => 23.78/4.01 subset( 23.78/4.01 X492,X490))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X494, 23.78/4.01 X496]: 23.78/4.01 (( 23.78/4.01 X494 = 23.78/4.01 X496) => 23.78/4.01 subset( 23.78/4.01 X494,X496))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X498, 23.78/4.01 X500]: 23.78/4.01 (( 23.78/4.01 ![X502]: 23.78/4.01 (in( 23.78/4.01 X502,X498) => 23.78/4.01 in( 23.78/4.01 X502,X500))) => 23.78/4.01 subset( 23.78/4.01 X498,X500))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X504]: 23.78/4.01 subset( 23.78/4.01 emptyset, 23.78/4.01 X504)) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X506, 23.78/4.01 X508,X510]: 23.78/4.01 (subset( 23.78/4.01 X506,X508) => 23.78/4.01 (in( 23.78/4.01 X510,X506) => 23.78/4.01 in( 23.78/4.01 X510,X508)))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X512, 23.78/4.01 X514,X516]: 23.78/4.01 (subset( 23.78/4.01 X512,X514) => 23.78/4.01 (( 23.78/4.01 ~ 23.78/4.01 in( 23.78/4.01 X516,X514)) => 23.78/4.01 (~ 23.78/4.01 in( 23.78/4.01 X516,X512))))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X518, 23.78/4.01 X520,X522]: 23.78/4.01 (in( 23.78/4.01 X522,X518) => 23.78/4.01 (( 23.78/4.01 ~ 23.78/4.01 in( 23.78/4.01 X522,X520)) => 23.78/4.01 (~ 23.78/4.01 subset( 23.78/4.01 X518,X520))))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X524, 23.78/4.01 X526]: 23.78/4.01 (( 23.78/4.01 ~ 23.78/4.01 subset( 23.78/4.01 X524,X526)) => 23.78/4.01 (X524 != 23.78/4.01 X526))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X528, 23.78/4.01 X530,X532]: 23.78/4.01 (in( 23.78/4.01 X532,X528) => 23.78/4.01 (( 23.78/4.01 ~ 23.78/4.01 in( 23.78/4.01 X532,X530)) => 23.78/4.01 (X528 != 23.78/4.01 X530)))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X534]: 23.78/4.01 subset( 23.78/4.01 X534,X534)) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X536, 23.78/4.01 X538,X540]: 23.78/4.01 (subset( 23.78/4.01 X536,X538) => 23.78/4.01 (subset( 23.78/4.01 X538,X540) => 23.78/4.01 subset( 23.78/4.01 X536,X540)))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X542, 23.78/4.01 X544]: 23.78/4.01 subset( 23.78/4.01 X544, 23.78/4.01 setadjoin( 23.78/4.01 X542,X544))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X546, 23.78/4.01 X548,X550]: 23.78/4.01 (subset( 23.78/4.01 X546,X550) => 23.78/4.01 subset( 23.78/4.01 X546, 23.78/4.01 setadjoin( 23.78/4.01 X548,X550)))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X552, 23.78/4.01 X554]: 23.78/4.01 (subset( 23.78/4.01 X552,X554) => 23.78/4.01 in( 23.78/4.01 X552, 23.78/4.01 powerset( 23.78/4.01 X554)))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X556, 23.78/4.01 X558]: 23.78/4.01 (subset( 23.78/4.01 X556,X558) => 23.78/4.01 (subset( 23.78/4.01 X558,X556) => 23.78/4.01 (X556 = 23.78/4.01 X558)))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X560]: 23.78/4.01 (subset( 23.78/4.01 X560, 23.78/4.01 emptyset) => 23.78/4.01 (X560 = 23.78/4.01 emptyset))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X562, 23.78/4.01 X564]: 23.78/4.01 (subset( 23.78/4.01 X564,X562) => 23.78/4.01 in( 23.78/4.01 X564, 23.78/4.01 powerset( 23.78/4.01 X562)))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X566, 23.78/4.01 X568]: 23.78/4.01 (in( 23.78/4.01 X568, 23.78/4.01 powerset( 23.78/4.01 X566)) => 23.78/4.01 subset( 23.78/4.01 X568,X566))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X570]: 23.78/4.01 in( 23.78/4.01 X570, 23.78/4.01 powerset( 23.78/4.01 X570))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X572, 23.78/4.01 X574]: 23.78/4.01 (subset( 23.78/4.01 X572,X574) => 23.78/4.01 subset( 23.78/4.01 powerset( 23.78/4.01 X572), 23.78/4.01 powerset( 23.78/4.01 X574)))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X576, 23.78/4.01 X578:( 23.78/4.01 ( 23.78/4.01 $i > $o))]: 23.78/4.01 in( 23.78/4.01 dsetconstr( 23.78/4.01 X576, 23.78/4.01 ^[V_13]: 23.78/4.01 X578( 23.78/4.01 V_13)), 23.78/4.01 powerset( 23.78/4.01 X576))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X580, 23.78/4.01 X582:( 23.78/4.01 ( 23.78/4.01 $i > $o))]: 23.78/4.01 subset( 23.78/4.01 dsetconstr( 23.78/4.01 X580, 23.78/4.01 ^[V_14]: 23.78/4.01 X582( 23.78/4.01 V_14)), 23.78/4.01 X580)) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X584, 23.78/4.01 X586,X588]: 23.78/4.01 (in( 23.78/4.01 X588,X584) => 23.78/4.01 in( 23.78/4.01 X588, 23.78/4.01 binunion( 23.78/4.01 X584,X586)))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X590, 23.78/4.01 X592]: 23.78/4.01 in( 23.78/4.01 X592, 23.78/4.01 setadjoin( 23.78/4.01 X590, 23.78/4.01 setadjoin( 23.78/4.01 X592, 23.78/4.01 emptyset)))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X594, 23.78/4.01 X596,X598]: 23.78/4.01 (in( 23.78/4.01 X598,X596) => 23.78/4.01 in( 23.78/4.01 X598, 23.78/4.01 binunion( 23.78/4.01 X594,X596)))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X600, 23.78/4.01 X602, 23.78/4.01 X604, 23.78/4.01 X606:$o]: 23.78/4.01 (in( 23.78/4.01 X604, 23.78/4.01 binunion( 23.78/4.01 X600,X602)) => 23.78/4.01 (( 23.78/4.01 in( 23.78/4.01 X604,X600) => 23.78/4.01 X606) => 23.78/4.01 (( 23.78/4.01 in( 23.78/4.01 X604,X602) => 23.78/4.01 X606) => 23.78/4.01 X606)))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X608, 23.78/4.01 X610,X612]: 23.78/4.01 (in( 23.78/4.01 X612, 23.78/4.01 binunion( 23.78/4.01 X608,X610)) => 23.78/4.01 (in( 23.78/4.01 X612,X608) | 23.78/4.01 in( 23.78/4.01 X612,X610)))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X614, 23.78/4.01 X616]: 23.78/4.01 subset( 23.78/4.01 X614, 23.78/4.01 binunion( 23.78/4.01 X614,X616))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X618, 23.78/4.01 X620]: 23.78/4.01 subset( 23.78/4.01 X620, 23.78/4.01 binunion( 23.78/4.01 X618,X620))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X622, 23.78/4.01 X624,X626]: 23.78/4.01 (in( 23.78/4.01 X626,X622) => 23.78/4.01 (in( 23.78/4.01 X626,X624) => 23.78/4.01 in( 23.78/4.01 X626, 23.78/4.01 binintersect( 23.78/4.01 X622,X624))))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X628, 23.78/4.01 X630,X632]: 23.78/4.01 (subset( 23.78/4.01 X632,X628) => 23.78/4.01 (subset( 23.78/4.01 X632,X630) => 23.78/4.01 subset( 23.78/4.01 X632, 23.78/4.01 binintersect( 23.78/4.01 X628,X630))))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X634, 23.78/4.01 X636,X638]: 23.78/4.01 (in( 23.78/4.01 X638, 23.78/4.01 binintersect( 23.78/4.01 X634,X636)) => 23.78/4.01 in( 23.78/4.01 X638,X634))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X640, 23.78/4.01 X642]: 23.78/4.01 subset( 23.78/4.01 binintersect( 23.78/4.01 X640,X642), 23.78/4.01 X640)) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X644, 23.78/4.01 X646]: 23.78/4.01 (subset( 23.78/4.01 X644,X646) => 23.78/4.01 (binintersect( 23.78/4.01 X644,X646) = 23.78/4.01 X644))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X648, 23.78/4.01 X650]: 23.78/4.01 (( 23.78/4.01 binintersect( 23.78/4.01 X648,X650) = 23.78/4.01 X650) => 23.78/4.01 subset( 23.78/4.01 X650,X648))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X652, 23.78/4.01 X654,X656]: 23.78/4.01 (in( 23.78/4.01 X656, 23.78/4.01 binintersect( 23.78/4.01 X652,X654)) => 23.78/4.01 in( 23.78/4.01 X656,X654))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X658, 23.78/4.01 X660]: 23.78/4.01 (( 23.78/4.01 ~ 23.78/4.01 ( 23.78/4.01 ?[X662]: 23.78/4.01 (in( 23.78/4.01 X662,X660) & 23.78/4.01 in( 23.78/4.01 X662,X658)))) => 23.78/4.01 (binintersect( 23.78/4.01 X658,X660) = 23.78/4.01 emptyset))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X664, 23.78/4.01 X666]: 23.78/4.01 subset( 23.78/4.01 binintersect( 23.78/4.01 X664,X666), 23.78/4.01 X666)) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X668, 23.78/4.01 X670]: 23.78/4.01 (subset( 23.78/4.01 X670,X668) => 23.78/4.01 (binintersect( 23.78/4.01 X668,X670) = 23.78/4.01 X670))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X672, 23.78/4.01 X674]: 23.78/4.01 (( 23.78/4.01 binintersect( 23.78/4.01 X672,X674) = 23.78/4.01 X672) => 23.78/4.01 subset( 23.78/4.01 X672,X674))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X676, 23.78/4.01 X678,X680]: 23.78/4.01 (binintersect( 23.78/4.01 X676, 23.78/4.01 binunion( 23.78/4.01 X678,X680)) = 23.78/4.01 binunion( 23.78/4.01 binintersect( 23.78/4.01 X676,X678), 23.78/4.01 binintersect( 23.78/4.01 X676,X680)))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X682, 23.78/4.01 X684,X686]: 23.78/4.01 (in( 23.78/4.01 X686,X682) => 23.78/4.01 (( 23.78/4.01 ~ 23.78/4.01 in( 23.78/4.01 X686,X684)) => 23.78/4.01 in( 23.78/4.01 X686, 23.78/4.01 setminus( 23.78/4.01 X682,X684))))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X688, 23.78/4.01 X690,X692]: 23.78/4.01 (in( 23.78/4.01 X692, 23.78/4.01 setminus( 23.78/4.01 X688,X690)) => 23.78/4.01 in( 23.78/4.01 X692,X688))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X694, 23.78/4.01 X696,X698]: 23.78/4.01 (in( 23.78/4.01 X698, 23.78/4.01 setminus( 23.78/4.01 X694,X696)) => 23.78/4.01 (~ 23.78/4.01 in( 23.78/4.01 X698,X696)))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X700, 23.78/4.01 X702]: 23.78/4.01 (subset( 23.78/4.01 X700,X702) => 23.78/4.01 (setminus( 23.78/4.01 X700,X702) = 23.78/4.01 emptyset))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X704, 23.78/4.01 X706,X708]: 23.78/4.01 (( 23.78/4.01 ~ 23.78/4.01 in( 23.78/4.01 X708, 23.78/4.01 setminus( 23.78/4.01 X704,X706))) => 23.78/4.01 (in( 23.78/4.01 X708,X704) => 23.78/4.01 in( 23.78/4.01 X708,X706)))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X710, 23.78/4.01 X712,X714]: 23.78/4.01 (( 23.78/4.01 ~ 23.78/4.01 in( 23.78/4.01 X714, 23.78/4.01 setminus( 23.78/4.01 X710,X712))) => 23.78/4.01 (( 23.78/4.01 ~ 23.78/4.01 in( 23.78/4.01 X714,X712)) => 23.78/4.01 (~ 23.78/4.01 in( 23.78/4.01 X714,X710))))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X716, 23.78/4.01 X718,X720]: 23.78/4.01 (( 23.78/4.01 ~ 23.78/4.01 in( 23.78/4.01 X720,X716)) => 23.78/4.01 (~ 23.78/4.01 in( 23.78/4.01 X720, 23.78/4.01 setminus( 23.78/4.01 X716,X718))))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X722, 23.78/4.01 X724,X726]: 23.78/4.01 (in( 23.78/4.01 X726,X724) => 23.78/4.01 (~ 23.78/4.01 in( 23.78/4.01 X726, 23.78/4.01 setminus( 23.78/4.01 X722,X724))))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X728, 23.78/4.01 X730]: 23.78/4.01 subset( 23.78/4.01 setminus( 23.78/4.01 X728,X730), 23.78/4.01 X728)) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X732, 23.78/4.01 X734]: 23.78/4.01 (( 23.78/4.01 setminus( 23.78/4.01 X732,X734) = 23.78/4.01 emptyset) => 23.78/4.01 subset( 23.78/4.01 X732,X734))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X736, 23.78/4.01 X738,X740]: 23.78/4.01 (in( 23.78/4.01 X740, 23.78/4.01 symdiff( 23.78/4.01 X736,X738)) => 23.78/4.01 (![X742:$o]: 23.78/4.01 (( 23.78/4.01 in( 23.78/4.01 X740,X736) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ~ 23.78/4.01 in( 23.78/4.01 X740,X738)) => 23.78/4.01 X742)) => 23.78/4.01 (( 23.78/4.01 ( 23.78/4.01 ~ 23.78/4.01 in( 23.78/4.01 X740,X736)) => 23.78/4.01 ( 23.78/4.01 in( 23.78/4.01 X740,X738) => 23.78/4.01 X742)) => 23.78/4.01 X742))))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X744, 23.78/4.01 X746,X748]: 23.78/4.01 (in( 23.78/4.01 X748,X744) => 23.78/4.01 (( 23.78/4.01 ~ 23.78/4.01 in( 23.78/4.01 X748,X746)) => 23.78/4.01 in( 23.78/4.01 X748, 23.78/4.01 symdiff( 23.78/4.01 X744,X746))))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X750, 23.78/4.01 X752,X754]: 23.78/4.01 (( 23.78/4.01 ~ 23.78/4.01 in( 23.78/4.01 X754,X750)) => 23.78/4.01 (in( 23.78/4.01 X754,X752) => 23.78/4.01 in( 23.78/4.01 X754, 23.78/4.01 symdiff( 23.78/4.01 X750,X752))))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X756, 23.78/4.01 X758,X760]: 23.78/4.01 (in( 23.78/4.01 X760,X756) => 23.78/4.01 (in( 23.78/4.01 X760,X758) => 23.78/4.01 (~ 23.78/4.01 in( 23.78/4.01 X760, 23.78/4.01 symdiff( 23.78/4.01 X756,X758)))))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X762, 23.78/4.01 X764,X766]: 23.78/4.01 (( 23.78/4.01 ~ 23.78/4.01 in( 23.78/4.01 X766,X762)) => 23.78/4.01 (( 23.78/4.01 ~ 23.78/4.01 in( 23.78/4.01 X766,X764)) => 23.78/4.01 (~ 23.78/4.01 in( 23.78/4.01 X766, 23.78/4.01 symdiff( 23.78/4.01 X762,X764)))))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X768, 23.78/4.01 X770]: 23.78/4.01 in( 23.78/4.01 X770, 23.78/4.01 setadjoin( 23.78/4.01 X768, 23.78/4.01 setadjoin( 23.78/4.01 X770, 23.78/4.01 emptyset)))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X772, 23.78/4.01 X774]: 23.78/4.01 in( 23.78/4.01 X772, 23.78/4.01 setunion( 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X772, 23.78/4.01 emptyset), 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X772, 23.78/4.01 setadjoin( 23.78/4.01 X774, 23.78/4.01 emptyset)), 23.78/4.01 emptyset))))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X776, 23.78/4.01 X778]: 23.78/4.01 in( 23.78/4.01 X778, 23.78/4.01 setunion( 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X776, 23.78/4.01 emptyset), 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X776, 23.78/4.01 setadjoin( 23.78/4.01 X778, 23.78/4.01 emptyset)), 23.78/4.01 emptyset))))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X780, 23.78/4.01 X782]: 23.78/4.01 (?[X784]: 23.78/4.01 (( 23.78/4.01 ?[X786]: 23.78/4.01 (( 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X780, 23.78/4.01 emptyset), 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X780, 23.78/4.01 setadjoin( 23.78/4.01 X782, 23.78/4.01 emptyset)), 23.78/4.01 emptyset)) = 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X784, 23.78/4.01 emptyset), 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X784, 23.78/4.01 setadjoin( 23.78/4.01 X786, 23.78/4.01 emptyset)), 23.78/4.01 emptyset))) & 23.78/4.01 in( 23.78/4.01 X786, 23.78/4.01 setunion( 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X780, 23.78/4.01 emptyset), 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X780, 23.78/4.01 setadjoin( 23.78/4.01 X782, 23.78/4.01 emptyset)), 23.78/4.01 emptyset)))))) & 23.78/4.01 in( 23.78/4.01 X784, 23.78/4.01 setunion( 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X780, 23.78/4.01 emptyset), 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X780, 23.78/4.01 setadjoin( 23.78/4.01 X782, 23.78/4.01 emptyset)), 23.78/4.01 emptyset))))))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X788, 23.78/4.01 X790]: 23.78/4.01 (?[X792]: 23.78/4.01 (( 23.78/4.01 ?[X794]: 23.78/4.01 (( 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X788, 23.78/4.01 emptyset), 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X788, 23.78/4.01 setadjoin( 23.78/4.01 X790, 23.78/4.01 emptyset)), 23.78/4.01 emptyset)) = 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X792, 23.78/4.01 emptyset), 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X792, 23.78/4.01 setadjoin( 23.78/4.01 X794, 23.78/4.01 emptyset)), 23.78/4.01 emptyset))) & 23.78/4.01 in( 23.78/4.01 X794, 23.78/4.01 setunion( 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X788, 23.78/4.01 emptyset), 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X788, 23.78/4.01 setadjoin( 23.78/4.01 X790, 23.78/4.01 emptyset)), 23.78/4.01 emptyset)))))) & 23.78/4.01 in( 23.78/4.01 X792, 23.78/4.01 setunion( 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X788, 23.78/4.01 emptyset), 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X788, 23.78/4.01 setadjoin( 23.78/4.01 X790, 23.78/4.01 emptyset)), 23.78/4.01 emptyset))))))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X796, 23.78/4.01 X798]: 23.78/4.01 (in( 23.78/4.01 X798,X796) => 23.78/4.01 subset( 23.78/4.01 setadjoin( 23.78/4.01 X798, 23.78/4.01 emptyset), 23.78/4.01 X796))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X800, 23.78/4.01 X802]: 23.78/4.01 (in( 23.78/4.01 X802,X800) => 23.78/4.01 in( 23.78/4.01 setadjoin( 23.78/4.01 X802, 23.78/4.01 emptyset), 23.78/4.01 powerset( 23.78/4.01 X800)))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X804, 23.78/4.01 X806,X808]: 23.78/4.01 (in( 23.78/4.01 X808,X804) => 23.78/4.01 in( 23.78/4.01 setadjoin( 23.78/4.01 X808, 23.78/4.01 emptyset), 23.78/4.01 powerset( 23.78/4.01 binunion( 23.78/4.01 X804,X806))))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X810, 23.78/4.01 X812,X814]: 23.78/4.01 (in( 23.78/4.01 X814, 23.78/4.01 setadjoin( 23.78/4.01 X810, 23.78/4.01 setadjoin( 23.78/4.01 X812, 23.78/4.01 emptyset))) => 23.78/4.01 (( 23.78/4.01 X814 = 23.78/4.01 X810) | 23.78/4.01 (X814 = 23.78/4.01 X812)))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X816, 23.78/4.01 X818,X820]: 23.78/4.01 (in( 23.78/4.01 X820,X816) => 23.78/4.01 (![X822]: 23.78/4.01 (in( 23.78/4.01 X822,X818) => 23.78/4.01 subset( 23.78/4.01 setadjoin( 23.78/4.01 X820, 23.78/4.01 setadjoin( 23.78/4.01 X822, 23.78/4.01 emptyset)), 23.78/4.01 binunion( 23.78/4.01 X816,X818)))))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X824, 23.78/4.01 X826,X828]: 23.78/4.01 (in( 23.78/4.01 X828,X824) => 23.78/4.01 (![X830]: 23.78/4.01 (in( 23.78/4.01 X830,X826) => 23.78/4.01 in( 23.78/4.01 setadjoin( 23.78/4.01 X828, 23.78/4.01 setadjoin( 23.78/4.01 X830, 23.78/4.01 emptyset)), 23.78/4.01 powerset( 23.78/4.01 binunion( 23.78/4.01 X824,X826))))))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X832, 23.78/4.01 X834,X836]: 23.78/4.01 (in( 23.78/4.01 X836,X832) => 23.78/4.01 (![X838]: 23.78/4.01 (in( 23.78/4.01 X838,X834) => 23.78/4.01 subset( 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X836, 23.78/4.01 emptyset), 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X836, 23.78/4.01 setadjoin( 23.78/4.01 X838, 23.78/4.01 emptyset)), 23.78/4.01 emptyset)), 23.78/4.01 powerset( 23.78/4.01 binunion( 23.78/4.01 X832,X834))))))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X840, 23.78/4.01 X842,X844]: 23.78/4.01 (in( 23.78/4.01 X844,X840) => 23.78/4.01 (![X846]: 23.78/4.01 (in( 23.78/4.01 X846,X842) => 23.78/4.01 in( 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X844, 23.78/4.01 emptyset), 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X844, 23.78/4.01 setadjoin( 23.78/4.01 X846, 23.78/4.01 emptyset)), 23.78/4.01 emptyset)), 23.78/4.01 powerset( 23.78/4.01 powerset( 23.78/4.01 binunion( 23.78/4.01 X840,X842)))))))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X848, 23.78/4.01 X850,X852]: 23.78/4.01 (in( 23.78/4.01 X852,X848) => 23.78/4.01 (![X854]: 23.78/4.01 (in( 23.78/4.01 X854,X850) => 23.78/4.01 in( 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X852, 23.78/4.01 emptyset), 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X852, 23.78/4.01 setadjoin( 23.78/4.01 X854, 23.78/4.01 emptyset)), 23.78/4.01 emptyset)), 23.78/4.01 powerset( 23.78/4.01 powerset( 23.78/4.01 binunion( 23.78/4.01 X848,X850)))))))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X856, 23.78/4.01 X858,X860]: 23.78/4.01 (in( 23.78/4.01 X860,X856) => 23.78/4.01 (![X862]: 23.78/4.01 (in( 23.78/4.01 X862,X858) => 23.78/4.01 in( 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X860, 23.78/4.01 emptyset), 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X860, 23.78/4.01 setadjoin( 23.78/4.01 X862, 23.78/4.01 emptyset)), 23.78/4.01 emptyset)), 23.78/4.01 cartprod( 23.78/4.01 X856,X858)))))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X864, 23.78/4.01 X866,X868]: 23.78/4.01 (in( 23.78/4.01 X868, 23.78/4.01 cartprod( 23.78/4.01 X864,X866)) => 23.78/4.01 (?[X870]: 23.78/4.01 (( 23.78/4.01 ?[X872]: 23.78/4.01 (( 23.78/4.01 X868 = 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X870, 23.78/4.01 emptyset), 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X870, 23.78/4.01 setadjoin( 23.78/4.01 X872, 23.78/4.01 emptyset)), 23.78/4.01 emptyset))) & 23.78/4.01 in( 23.78/4.01 X872,X866))) & 23.78/4.01 in( 23.78/4.01 X870,X864))))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X874, 23.78/4.01 X876,X878]: 23.78/4.01 (in( 23.78/4.01 X878, 23.78/4.01 cartprod( 23.78/4.01 X874,X876)) => 23.78/4.01 (?[X880]: 23.78/4.01 (( 23.78/4.01 ?[X882]: 23.78/4.01 (( 23.78/4.01 X878 = 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X880, 23.78/4.01 emptyset), 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X880, 23.78/4.01 setadjoin( 23.78/4.01 X882, 23.78/4.01 emptyset)), 23.78/4.01 emptyset))) & 23.78/4.01 in( 23.78/4.01 X882, 23.78/4.01 setunion( 23.78/4.01 X878)))) & 23.78/4.01 in( 23.78/4.01 X880, 23.78/4.01 setunion( 23.78/4.01 X878)))))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X884, 23.78/4.01 X886]: 23.78/4.01 (in( 23.78/4.01 X886, 23.78/4.01 setunion( 23.78/4.01 X884)) => 23.78/4.01 (?[X888]: 23.78/4.01 (in( 23.78/4.01 X886,X888) & 23.78/4.01 in( 23.78/4.01 X888,X884))))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X890]: 23.78/4.01 subset( 23.78/4.01 setunion( 23.78/4.01 setadjoin( 23.78/4.01 X890, 23.78/4.01 emptyset)), 23.78/4.01 X890)) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X892]: 23.78/4.01 subset( 23.78/4.01 X892, 23.78/4.01 setunion( 23.78/4.01 setadjoin( 23.78/4.01 X892, 23.78/4.01 emptyset)))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X894]: 23.78/4.01 (setunion( 23.78/4.01 setadjoin( 23.78/4.01 X894, 23.78/4.01 emptyset)) = 23.78/4.01 X894)) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X896, 23.78/4.01 X898:( 23.78/4.01 ( 23.78/4.01 $i > $o))]: 23.78/4.01 (( 23.78/4.01 ![X900]: 23.78/4.01 (in( 23.78/4.01 X900,X896) => 23.78/4.01 (![X902]: 23.78/4.01 (in( 23.78/4.01 X902,X896) => 23.78/4.01 (X898( 23.78/4.01 X900) => 23.78/4.01 (X898( 23.78/4.01 X902) => 23.78/4.01 (X900 = 23.78/4.01 X902))))))) => 23.78/4.01 (( 23.78/4.01 ?[X904]: 23.78/4.01 (X898( 23.78/4.01 X904) & 23.78/4.01 in( 23.78/4.01 X904,X896))) => 23.78/4.01 (?[X906]: 23.78/4.01 (( 23.78/4.01 dsetconstr( 23.78/4.01 X896, 23.78/4.01 ^[V_15]: 23.78/4.01 X898( 23.78/4.01 V_15)) = 23.78/4.01 setadjoin( 23.78/4.01 X906, 23.78/4.01 emptyset)) & 23.78/4.01 in( 23.78/4.01 X906, 23.78/4.01 dsetconstr( 23.78/4.01 X896, 23.78/4.01 ^[V_16]: 23.78/4.01 X898( 23.78/4.01 V_16)))))))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X908, 23.78/4.01 X910:( 23.78/4.01 ( 23.78/4.01 $i > $o))]: 23.78/4.01 (( 23.78/4.01 ?[X912]: 23.78/4.01 (( 23.78/4.01 dsetconstr( 23.78/4.01 X908, 23.78/4.01 ^[V_17]: 23.78/4.01 X910( 23.78/4.01 V_17)) = 23.78/4.01 setadjoin( 23.78/4.01 X912, 23.78/4.01 emptyset)) & 23.78/4.01 in( 23.78/4.01 X912, 23.78/4.01 dsetconstr( 23.78/4.01 X908, 23.78/4.01 ^[V_18]: 23.78/4.01 X910( 23.78/4.01 V_18))))) => 23.78/4.01 (?[X914]: 23.78/4.01 (X910( 23.78/4.01 X914) & 23.78/4.01 in( 23.78/4.01 X914,X908))))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X916, 23.78/4.01 X918:( 23.78/4.01 ( 23.78/4.01 $i > $o)), 23.78/4.01 X920]: 23.78/4.01 (in( 23.78/4.01 X920,X916) => 23.78/4.01 (X918( 23.78/4.01 X920) => 23.78/4.01 (( 23.78/4.01 ![X922]: 23.78/4.01 (in( 23.78/4.01 X922,X916) => 23.78/4.01 (X918( 23.78/4.01 X922) => 23.78/4.01 (X922 = 23.78/4.01 X920)))) => 23.78/4.01 (?[X924]: 23.78/4.01 (( 23.78/4.01 dsetconstr( 23.78/4.01 X916, 23.78/4.01 ^[V_19]: 23.78/4.01 X918( 23.78/4.01 V_19)) = 23.78/4.01 setadjoin( 23.78/4.01 X924, 23.78/4.01 emptyset)) & 23.78/4.01 in( 23.78/4.01 X924, 23.78/4.01 dsetconstr( 23.78/4.01 X916, 23.78/4.01 ^[V_20]: 23.78/4.01 X918( 23.78/4.01 V_20))))))))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X926, 23.78/4.01 X928:( 23.78/4.01 ( 23.78/4.01 $i > $o))]: 23.78/4.01 (( 23.78/4.01 ![X930]: 23.78/4.01 (in( 23.78/4.01 X930,X926) => 23.78/4.01 (![X932]: 23.78/4.01 (in( 23.78/4.01 X932,X926) => 23.78/4.01 (X928( 23.78/4.01 X930) => 23.78/4.01 (X928( 23.78/4.01 X932) => 23.78/4.01 (X930 = 23.78/4.01 X932))))))) => 23.78/4.01 (( 23.78/4.01 ?[X934]: 23.78/4.01 (X928( 23.78/4.01 X934) & 23.78/4.01 in( 23.78/4.01 X934,X926))) => 23.78/4.01 (?[X936]: 23.78/4.01 (( 23.78/4.01 dsetconstr( 23.78/4.01 X926, 23.78/4.01 ^[V_21]: 23.78/4.01 X928( 23.78/4.01 V_21)) = 23.78/4.01 setadjoin( 23.78/4.01 X936, 23.78/4.01 emptyset)) & 23.78/4.01 in( 23.78/4.01 X936, 23.78/4.01 dsetconstr( 23.78/4.01 X926, 23.78/4.01 ^[V_22]: 23.78/4.01 X928( 23.78/4.01 V_22)))))))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X938, 23.78/4.01 X940]: 23.78/4.01 (( 23.78/4.01 setadjoin( 23.78/4.01 X938, 23.78/4.01 emptyset) = 23.78/4.01 setadjoin( 23.78/4.01 X940, 23.78/4.01 emptyset)) => 23.78/4.01 (X938 = 23.78/4.01 X940))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X942, 23.78/4.01 X944,X946]: 23.78/4.01 (in( 23.78/4.01 setadjoin( 23.78/4.01 X946, 23.78/4.01 emptyset), 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X942, 23.78/4.01 emptyset), 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X942, 23.78/4.01 setadjoin( 23.78/4.01 X944, 23.78/4.01 emptyset)), 23.78/4.01 emptyset))) => 23.78/4.01 (X942 = 23.78/4.01 X946))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X948]: 23.78/4.01 (( 23.78/4.01 ?[X950]: 23.78/4.01 (( 23.78/4.01 ?[X952]: 23.78/4.01 (( 23.78/4.01 X948 = 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X950, 23.78/4.01 emptyset), 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X950, 23.78/4.01 setadjoin( 23.78/4.01 X952, 23.78/4.01 emptyset)), 23.78/4.01 emptyset))) & 23.78/4.01 in( 23.78/4.01 X952, 23.78/4.01 setunion( 23.78/4.01 X948)))) & 23.78/4.01 in( 23.78/4.01 X950, 23.78/4.01 setunion( 23.78/4.01 X948)))) => 23.78/4.01 (?[X954]: 23.78/4.01 (( 23.78/4.01 dsetconstr( 23.78/4.01 setunion( 23.78/4.01 X948), 23.78/4.01 ^[V_23]: 23.78/4.01 in( 23.78/4.01 setadjoin( 23.78/4.01 V_23, 23.78/4.01 emptyset), 23.78/4.01 X948)) = 23.78/4.01 setadjoin( 23.78/4.01 X954, 23.78/4.01 emptyset)) & 23.78/4.01 in( 23.78/4.01 X954, 23.78/4.01 dsetconstr( 23.78/4.01 setunion( 23.78/4.01 X948), 23.78/4.01 ^[V_24]: 23.78/4.01 in( 23.78/4.01 setadjoin( 23.78/4.01 V_24, 23.78/4.01 emptyset), 23.78/4.01 X948))))))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X956]: 23.78/4.01 (( 23.78/4.01 ?[X958]: 23.78/4.01 (( 23.78/4.01 X956 = 23.78/4.01 setadjoin( 23.78/4.01 X958, 23.78/4.01 emptyset)) & 23.78/4.01 in( 23.78/4.01 X958,X956))) => 23.78/4.01 in( 23.78/4.01 setunion( 23.78/4.01 X956), 23.78/4.01 X956))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X960, 23.78/4.01 X962]: 23.78/4.01 (kfst( 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X960, 23.78/4.01 emptyset), 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X960, 23.78/4.01 setadjoin( 23.78/4.01 X962, 23.78/4.01 emptyset)), 23.78/4.01 emptyset))) = 23.78/4.01 X960)) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X964, 23.78/4.01 X966,X968]: 23.78/4.01 (in( 23.78/4.01 X968, 23.78/4.01 cartprod( 23.78/4.01 X964,X966)) => 23.78/4.01 in( 23.78/4.01 kfst( 23.78/4.01 X968), 23.78/4.01 X964))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X970, 23.78/4.01 X972, 23.78/4.01 X974,X976]: 23.78/4.01 (( 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X970, 23.78/4.01 emptyset), 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X970, 23.78/4.01 setadjoin( 23.78/4.01 X972, 23.78/4.01 emptyset)), 23.78/4.01 emptyset)) = 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X974, 23.78/4.01 emptyset), 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X974, 23.78/4.01 setadjoin( 23.78/4.01 X976, 23.78/4.01 emptyset)), 23.78/4.01 emptyset))) => 23.78/4.01 (X970 = 23.78/4.01 X974))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X978, 23.78/4.01 X980, 23.78/4.01 X982,X984]: 23.78/4.01 (( 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X978, 23.78/4.01 emptyset), 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X978, 23.78/4.01 setadjoin( 23.78/4.01 X980, 23.78/4.01 emptyset)), 23.78/4.01 emptyset)) = 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X982, 23.78/4.01 emptyset), 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X982, 23.78/4.01 setadjoin( 23.78/4.01 X984, 23.78/4.01 emptyset)), 23.78/4.01 emptyset))) => 23.78/4.01 (X978 = 23.78/4.01 X982))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X986, 23.78/4.01 X988]: 23.78/4.01 (( 23.78/4.01 X986 = 23.78/4.01 X988) => 23.78/4.01 (setadjoin( 23.78/4.01 X986, 23.78/4.01 setadjoin( 23.78/4.01 X988, 23.78/4.01 emptyset)) = 23.78/4.01 setadjoin( 23.78/4.01 X986, 23.78/4.01 emptyset)))) => 23.78/4.01 ( 23.78/4.01 ( 23.78/4.01 ![X990, 23.78/4.01 X992]: 23.78/4.01 (( 23.78/4.01 X990 = 23.78/4.01 X992) => 23.78/4.01 (setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X990, 23.78/4.01 emptyset), 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X990, 23.78/4.01 setadjoin( 23.78/4.01 X992, 23.78/4.01 emptyset)), 23.78/4.01 emptyset)) = 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X990, 23.78/4.01 emptyset), 23.78/4.01 emptyset)))) => 23.78/4.01 ( 23.78/4.01 ![X994, 23.78/4.01 X996, 23.78/4.01 X998, 23.78/4.01 X1000]: 23.78/4.01 (( 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X994, 23.78/4.01 emptyset), 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X994, 23.78/4.01 setadjoin( 23.78/4.01 X996, 23.78/4.01 emptyset)), 23.78/4.01 emptyset)) = 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X998, 23.78/4.01 emptyset), 23.78/4.01 setadjoin( 23.78/4.01 setadjoin( 23.78/4.01 X998, 23.78/4.01 setadjoin( 23.78/4.01 X1000, 23.78/4.01 emptyset)), 23.78/4.01 emptyset))) => 23.78/4.01 (( 23.78/4.01 X998 = 23.78/4.01 X1000) => 23.78/4.01 (X996 = 23.78/4.01 X1000))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 23.78/4.01 tff('181', plain, sk_X996 != sk_X1000, 23.78/4.01 inference('cnf', [status(esa)], [zf_stmt_14])). 23.78/4.01 tff('182', plain, sk_X998 = sk_X1000, 23.78/4.01 inference('cnf', [status(esa)], [zf_stmt_14])). 23.78/4.01 tff('183', plain, sk_X996 != sk_X998, 23.78/4.01 inference('demod', [status(thm)], ['181', '182'])). 23.78/4.01 tff('184', plain, 23.78/4.01 ![X678, X679]: 23.78/4.01 in(X678, 23.78/4.01 setunion( 23.78/4.01 setadjoin(setadjoin(X679, emptyset), 23.78/4.01 setadjoin(setadjoin(X679, setadjoin(X678, emptyset)), emptyset)))), 23.78/4.01 inference('cnf', [status(esa)], [zf_stmt_14])). 23.78/4.01 tff('185', plain, ![X703]: setunion(setadjoin(X703, emptyset)) = X703, 23.78/4.01 inference('cnf', [status(esa)], [zf_stmt_14])). 23.78/4.01 tff('186', plain, 23.78/4.01 ![X559, X560]: (~ in(X559, setadjoin(X560, emptyset)) | X560 = X559), 23.78/4.01 inference('cnf', [status(esa)], [zf_stmt_14])). 23.78/4.01 tff('187', plain, 23.78/4.01 setadjoin(setadjoin(sk_X994, emptyset), 23.78/4.01 setadjoin(setadjoin(sk_X994, setadjoin(sk_X996, emptyset)), emptyset)) 23.78/4.01 = setadjoin(setadjoin(sk_X998, emptyset), 23.78/4.01 setadjoin(setadjoin(sk_X998, setadjoin(sk_X1000, emptyset)), 23.78/4.01 emptyset)), 23.78/4.01 inference('cnf', [status(esa)], [zf_stmt_14])). 23.78/4.01 tff('188', plain, sk_X998 = sk_X1000, 23.78/4.01 inference('cnf', [status(esa)], [zf_stmt_14])). 23.78/4.01 tff('189', plain, 23.78/4.01 setadjoin(setadjoin(sk_X994, emptyset), 23.78/4.01 setadjoin(setadjoin(sk_X994, setadjoin(sk_X996, emptyset)), emptyset)) 23.78/4.01 = setadjoin(setadjoin(sk_X998, emptyset), 23.78/4.01 setadjoin(setadjoin(sk_X998, setadjoin(sk_X998, emptyset)), 23.78/4.01 emptyset)), 23.78/4.01 inference('demod', [status(thm)], ['187', '188'])). 23.78/4.01 tff('190', plain, ![X542, X543]: in(X542, setadjoin(X542, X543)), 23.78/4.01 inference('cnf', [status(esa)], [zf_stmt_14])). 23.78/4.01 tff('191', plain, 23.78/4.01 ![X724, X725]: 23.78/4.01 (setadjoin(X724, setadjoin(X725, emptyset)) = setadjoin(X724, emptyset) 23.78/4.01 | X724 != X725), 23.78/4.01 inference('cnf', [status(esa)], [zf_stmt_14])). 23.78/4.01 tff('192', plain, $false, 23.78/4.01 inference('eprover', [status(thm)], 23.78/4.01 ['183', '184', '185', '186', '189', '190', '191'])). 23.78/4.01 23.78/4.01 % SZS output end Refutation 23.78/4.01 23.78/4.01 23.78/4.01 % /export/starexec/sandbox/solver/bin/lams/old_sp2.sh running for 17s 23.78/4.01 % Terminating... 24.22/4.14 % Runner terminated. 24.22/4.16 % Zipperpin 1.5 exiting 24.22/4.16 EOF