0.13/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.13/0.13 % Command : run_portfolio.sh /export/starexec/sandbox/benchmark/theBenchmark.p /export/starexec/sandbox/tmp/tmp.lbpRLAmrz2 0.14/0.34 % Computer : n004.cluster.edu 0.14/0.34 % Model : x86_64 x86_64 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.34 % Memory : 8042.1875MB 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.34 % CPULimit : 180 0.14/0.34 % DateTime : Thu Aug 29 13:13:08 EDT 2019 0.14/0.34 % CPUTime : 111.90/112.55 % Running portfolio for 180 s 111.90/112.55 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 111.90/112.55 % TempDir : /export/starexec/sandbox/tmp/tmp.lbpRLAmrz2 111.90/112.55 % Recognized as monomorphic HO. 111.90/112.55 % Running /export/starexec/sandbox/solver/bin/competitive.sh for 18 111.90/112.55 % Running /export/starexec/sandbox/solver/bin/competitive.2.sh for 13 111.90/112.55 % Running /export/starexec/sandbox/solver/bin/competitive.3.sh for 3 111.90/112.55 % Running /export/starexec/sandbox/solver/bin/pragmatic.rudimentary.sh for 28 111.90/112.55 % Running /export/starexec/sandbox/solver/bin/pragmatic.rudimentary.1.sh for 12 111.90/112.55 % Running /export/starexec/sandbox/solver/bin/pragmatic.rudimentary.2.sh for 7 111.90/112.55 % Running /export/starexec/sandbox/solver/bin/pragmatic.shallow.sh for 3 111.90/112.55 % Running /export/starexec/sandbox/solver/bin/pragmatic.shallow.1.sh for 15 111.90/112.55 % Running /export/starexec/sandbox/solver/bin/pragmatic.shallow.2.sh for 12 111.90/112.55 % Running /export/starexec/sandbox/solver/bin/pragmatic.ll.e.sh for 19 111.90/112.55 % Solved by: pragmatic.ll.e.sh 111.90/112.55 % Running : timeout 16 /export/starexec/sandbox/solver/bin/eprover-ho /export/starexec/sandbox/tmp/tmp.lbpRLAmrz2/e_input8c8bc6 --cpu-limit=14 --auto-schedule -s -p. 111.90/112.55 % done 468 iterations in 13.046s 111.90/112.55 % hashcons stats for terms: size 4096, num 21198, sum length 38007, buckets: small 3, median 7, big 22 111.90/112.55 % proof state stats: {active 190, passive 7378, simpl 0} 111.90/112.55 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 111.90/112.55 % SZS output start Refutation 111.90/112.55 tff(setukpairinjR2, axiom, setukpairinjR2 <=> 111.90/112.55 (![Xx,Xy,Xz,Xu]: 111.90/112.55 ((setadjoin(setadjoin(Xx,emptyset), 111.90/112.55 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)),emptyset)) = 111.90/112.55 setadjoin(setadjoin(Xz,emptyset), 111.90/112.55 setadjoin(setadjoin(Xz,setadjoin(Xu,emptyset)),emptyset))) => 111.90/112.55 (Xy = Xu)))). 111.90/112.55 tff('0', plain, 111.90/112.55 setukpairinjR2 = 111.90/112.55 (![X2,X3,X4,X5]: 111.90/112.55 ((setadjoin(setadjoin(X2,emptyset), 111.90/112.55 setadjoin(setadjoin(X2,setadjoin(X3,emptyset)),emptyset)) = 111.90/112.55 setadjoin(setadjoin(X4,emptyset), 111.90/112.55 setadjoin(setadjoin(X4,setadjoin(X5,emptyset)),emptyset))) => 111.90/112.55 (X3 = X5))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(upairequniteq, axiom, upairequniteq <=> 111.90/112.55 (![Xx,Xy,Xz]: 111.90/112.55 ((setadjoin(Xx,setadjoin(Xy,emptyset)) = setadjoin(Xz,emptyset)) => 111.90/112.55 (Xx = Xy)))). 111.90/112.55 tff('1', plain, 111.90/112.55 upairequniteq = 111.90/112.55 (![X2,X3,X4]: 111.90/112.55 ((setadjoin(X2,setadjoin(X3,emptyset)) = setadjoin(X4,emptyset)) => 111.90/112.55 (X2 = X3))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(setukpairinjR1, axiom, setukpairinjR1 <=> 111.90/112.55 (![Xx,Xy,Xz,Xu]: 111.90/112.55 ((setadjoin(setadjoin(Xx,emptyset), 111.90/112.55 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)),emptyset)) = 111.90/112.55 setadjoin(setadjoin(Xz,emptyset), 111.90/112.55 setadjoin(setadjoin(Xz,setadjoin(Xu,emptyset)),emptyset))) => 111.90/112.55 ((Xz = Xu) => (Xy = Xu))))). 111.90/112.55 tff('2', plain, 111.90/112.55 setukpairinjR1 = 111.90/112.55 (![X2,X3,X4,X5]: 111.90/112.55 ((setadjoin(setadjoin(X2,emptyset), 111.90/112.55 setadjoin(setadjoin(X2,setadjoin(X3,emptyset)),emptyset)) = 111.90/112.55 setadjoin(setadjoin(X4,emptyset), 111.90/112.55 setadjoin(setadjoin(X4,setadjoin(X5,emptyset)),emptyset))) => 111.90/112.55 ((X4 = X5) => (X3 = X5)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(setukpairinjR12, axiom, setukpairinjR12 <=> 111.90/112.55 (![Xx,Xy]: 111.90/112.55 ((Xx = Xy) => 111.90/112.55 (setadjoin(setadjoin(Xx,emptyset), 111.90/112.55 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)),emptyset)) = 111.90/112.55 setadjoin(setadjoin(Xx,emptyset),emptyset))))). 111.90/112.55 tff('3', plain, 111.90/112.55 setukpairinjR12 = 111.90/112.55 (![X2,X3]: 111.90/112.55 ((X2 = X3) => 111.90/112.55 (setadjoin(setadjoin(X2,emptyset), 111.90/112.55 setadjoin(setadjoin(X2,setadjoin(X3,emptyset)),emptyset)) = 111.90/112.55 setadjoin(setadjoin(X2,emptyset),emptyset)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(setukpairinjR11, axiom, setukpairinjR11 <=> 111.90/112.55 (![Xx,Xy]: 111.90/112.55 ((Xx = Xy) => 111.90/112.55 (setadjoin(Xx,setadjoin(Xy,emptyset)) = setadjoin(Xx,emptyset))))). 111.90/112.55 tff('4', plain, 111.90/112.55 setukpairinjR11 = 111.90/112.55 (![X2,X3]: 111.90/112.55 ((X2 = X3) => 111.90/112.55 (setadjoin(X2,setadjoin(X3,emptyset)) = setadjoin(X2,emptyset)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(setukpairinjL, axiom, setukpairinjL <=> 111.90/112.55 (![Xx,Xy,Xz,Xu]: ((kpair(Xx,Xy) = kpair(Xz,Xu)) => (Xx = Xz)))). 111.90/112.55 tff('5', plain, 111.90/112.55 setukpairinjL = 111.90/112.55 (![X2,X3,X4,X5]: ((kpair(X2,X3) = kpair(X4,X5)) => (X2 = X4))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(setukpairinjL2, axiom, setukpairinjL2 <=> 111.90/112.55 (![Xx,Xy,Xz,Xu]: 111.90/112.55 ((setadjoin(setadjoin(Xx,emptyset), 111.90/112.55 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)),emptyset)) = 111.90/112.55 setadjoin(setadjoin(Xz,emptyset), 111.90/112.55 setadjoin(setadjoin(Xz,setadjoin(Xu,emptyset)),emptyset))) => 111.90/112.55 (Xx = Xz)))). 111.90/112.55 tff('6', plain, 111.90/112.55 setukpairinjL2 = 111.90/112.55 (![X2,X3,X4,X5]: 111.90/112.55 ((setadjoin(setadjoin(X2,emptyset), 111.90/112.55 setadjoin(setadjoin(X2,setadjoin(X3,emptyset)),emptyset)) = 111.90/112.55 setadjoin(setadjoin(X4,emptyset), 111.90/112.55 setadjoin(setadjoin(X4,setadjoin(X5,emptyset)),emptyset))) => 111.90/112.55 (X2 = X4))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(cartprodfstin, axiom, cartprodfstin <=> 111.90/112.55 (![A,B,Xu]: (in(Xu,cartprod(A,B)) => in(kfst(Xu),A)))). 111.90/112.55 tff('7', plain, 111.90/112.55 cartprodfstin = 111.90/112.55 (![X2,X3,X4]: (in(X4,cartprod(X2,X3)) => in(kfst(X4),X2))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(kfstpairEq, axiom, kfstpairEq <=> (![Xx,Xy]: (kfst(kpair(Xx,Xy)) = Xx))). 111.90/112.55 tff('8', plain, kfstpairEq = (![X2,X3]: (kfst(kpair(X2,X3)) = X2)), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(theprop, axiom, theprop <=> (![X]: (singleton(X) => in(setunion(X),X)))). 111.90/112.55 tff('9', plain, theprop = (![X2]: (singleton(X2) => in(setunion(X2),X2))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(kfstsingleton, axiom, kfstsingleton <=> 111.90/112.55 (![Xu]: 111.90/112.55 (iskpair(Xu) => 111.90/112.55 singleton(dsetconstr(setunion(Xu),^[Xx]: in(setadjoin(Xx,emptyset),Xu)))))). 111.90/112.55 tff('10', plain, 111.90/112.55 kfstsingleton = 111.90/112.55 (![X2]: 111.90/112.55 (iskpair(X2) => 111.90/112.55 singleton(dsetconstr(setunion(X2), 111.90/112.55 ^[V_1]: in(setadjoin(V_1,emptyset),X2))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(setukpairinjL1, axiom, setukpairinjL1 <=> 111.90/112.55 (![Xx,Xy,Xz]: 111.90/112.55 (in(setadjoin(Xz,emptyset), 111.90/112.55 setadjoin(setadjoin(Xx,emptyset), 111.90/112.55 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)),emptyset))) => 111.90/112.55 (Xx = Xz)))). 111.90/112.55 tff('11', plain, 111.90/112.55 setukpairinjL1 = 111.90/112.55 (![X2,X3,X4]: 111.90/112.55 (in(setadjoin(X4,emptyset), 111.90/112.55 setadjoin(setadjoin(X2,emptyset), 111.90/112.55 setadjoin(setadjoin(X2,setadjoin(X3,emptyset)),emptyset))) => 111.90/112.55 (X2 = X4))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(singletonsuniq, axiom, singletonsuniq <=> 111.90/112.55 (![Xx,Xy]: ((setadjoin(Xx,emptyset) = setadjoin(Xy,emptyset)) => (Xx = Xy)))). 111.90/112.55 tff('12', plain, 111.90/112.55 singletonsuniq = 111.90/112.55 (![X2,X3]: 111.90/112.55 ((setadjoin(X2,emptyset) = setadjoin(X3,emptyset)) => (X2 = X3))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(ex1I2, axiom, ex1I2 <=> 111.90/112.55 (![A,Xphi:($i > $o)]: 111.90/112.55 ((![Xx]: 111.90/112.55 (in(Xx,A) => 111.90/112.55 (![Xy]: (in(Xy,A) => (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))) => 111.90/112.55 ((?[Xx]: (Xphi(Xx) & in(Xx,A))) => ex1(A,^[Xx]: Xphi(Xx)))))). 111.90/112.55 tff('13', plain, 111.90/112.55 ex1I2 = 111.90/112.55 (![X2,X3:($i > $o)]: 111.90/112.55 ((![X4]: 111.90/112.55 (in(X4,X2) => 111.90/112.55 (![X5]: (in(X5,X2) => (X3(X4) => (X3(X5) => (X4 = X5))))))) => 111.90/112.55 ((?[X6]: (X3(X6) & in(X6,X2))) => ex1(X2,^[V_1]: X3(V_1))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(ex1I, axiom, ex1I <=> 111.90/112.55 (![A,Xphi:($i > $o),Xx]: 111.90/112.55 (in(Xx,A) => 111.90/112.55 (Xphi(Xx) => 111.90/112.55 ((![Xy]: (in(Xy,A) => (Xphi(Xy) => (Xy = Xx)))) => 111.90/112.55 ex1(A,^[Xy]: Xphi(Xy))))))). 111.90/112.55 tff('14', plain, 111.90/112.55 ex1I = 111.90/112.55 (![X2,X3:($i > $o),X4]: 111.90/112.55 (in(X4,X2) => 111.90/112.55 (X3(X4) => 111.90/112.55 ((![X5]: (in(X5,X2) => (X3(X5) => (X5 = X4)))) => 111.90/112.55 ex1(X2,^[V_1]: X3(V_1)))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(ex1E1, axiom, ex1E1 <=> 111.90/112.55 (![A,Xphi:($i > $o)]: 111.90/112.55 (ex1(A,^[Xx]: Xphi(Xx)) => (?[Xx]: (Xphi(Xx) & in(Xx,A)))))). 111.90/112.55 tff('15', plain, 111.90/112.55 ex1E1 = 111.90/112.55 (![X2,X3:($i > $o)]: 111.90/112.55 (ex1(X2,^[V_1]: X3(V_1)) => (?[X4]: (X3(X4) & in(X4,X2))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(ex1, axiom, ex1() = 111.90/112.55 ^[A,Xphi:($i > $o)]: singleton(dsetconstr(A,^[Xx]: Xphi(Xx)))). 111.90/112.55 tff('16', plain, 111.90/112.55 ex1 = (^[V_1,V_2:($i > $o)]: singleton(dsetconstr(V_1,^[V_3]: V_2(V_3)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(singletonprop, axiom, singletonprop <=> 111.90/112.55 (![A,Xphi:($i > $o)]: 111.90/112.55 ((![Xx]: 111.90/112.55 (in(Xx,A) => 111.90/112.55 (![Xy]: (in(Xy,A) => (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))) => 111.90/112.55 ((?[Xx]: (Xphi(Xx) & in(Xx,A))) => 111.90/112.55 singleton(dsetconstr(A,^[Xx]: Xphi(Xx))))))). 111.90/112.55 tff('17', plain, 111.90/112.55 singletonprop = 111.90/112.55 (![X2,X3:($i > $o)]: 111.90/112.55 ((![X4]: 111.90/112.55 (in(X4,X2) => 111.90/112.55 (![X5]: (in(X5,X2) => (X3(X4) => (X3(X5) => (X4 = X5))))))) => 111.90/112.55 ((?[X6]: (X3(X6) & in(X6,X2))) => 111.90/112.55 singleton(dsetconstr(X2,^[V_1]: X3(V_1)))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(singleton, axiom, singleton() = 111.90/112.55 ^[A]: (?[Xx]: ((A = setadjoin(Xx,emptyset)) & in(Xx,A)))). 111.90/112.55 tff('18', plain, 111.90/112.55 singleton = 111.90/112.55 (^[V_1]: (?[X2]: ((V_1 = setadjoin(X2,emptyset)) & in(X2,V_1)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(setunionsingleton, axiom, setunionsingleton <=> 111.90/112.55 (![Xx]: (setunion(setadjoin(Xx,emptyset)) = Xx))). 111.90/112.55 tff('19', plain, 111.90/112.55 setunionsingleton = (![X2]: (setunion(setadjoin(X2,emptyset)) = X2)), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(setunionsingleton2, axiom, setunionsingleton2 <=> 111.90/112.55 (![A]: subset(A,setunion(setadjoin(A,emptyset))))). 111.90/112.55 tff('20', plain, 111.90/112.55 setunionsingleton2 = (![X2]: subset(X2,setunion(setadjoin(X2,emptyset)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(setunionsingleton1, axiom, setunionsingleton1 <=> 111.90/112.55 (![A]: subset(setunion(setadjoin(A,emptyset)),A))). 111.90/112.55 tff('21', plain, 111.90/112.55 setunionsingleton1 = (![X2]: subset(setunion(setadjoin(X2,emptyset)),X2)), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(setunionE2, axiom, setunionE2 <=> 111.90/112.55 (![A,Xx]: (in(Xx,setunion(A)) => (?[X]: (in(Xx,X) & in(X,A)))))). 111.90/112.55 tff('22', plain, 111.90/112.55 setunionE2 = 111.90/112.55 (![X2,X3]: (in(X3,setunion(X2)) => (?[X4]: (in(X3,X4) & in(X4,X2))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(cartprodmempair, axiom, cartprodmempair <=> 111.90/112.55 (![A,B,Xu]: (in(Xu,cartprod(A,B)) => iskpair(Xu)))). 111.90/112.55 tff('23', plain, 111.90/112.55 cartprodmempair = (![X2,X3,X4]: (in(X4,cartprod(X2,X3)) => iskpair(X4))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(cartprodmempair1, axiom, cartprodmempair1 <=> 111.90/112.55 (![A,B,Xu]: 111.90/112.55 (in(Xu,cartprod(A,B)) => 111.90/112.55 (?[Xx]: ((?[Xy]: ((Xu = kpair(Xx,Xy)) & in(Xy,B))) & in(Xx,A)))))). 111.90/112.55 tff('24', plain, 111.90/112.55 cartprodmempair1 = 111.90/112.55 (![X2,X3,X4]: 111.90/112.55 (in(X4,cartprod(X2,X3)) => 111.90/112.55 (?[X5]: ((?[X6]: ((X4 = kpair(X5,X6)) & in(X6,X3))) & in(X5,X2))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(cartprodpairin, axiom, cartprodpairin <=> 111.90/112.55 (![A,B,Xx]: 111.90/112.55 (in(Xx,A) => (![Xy]: (in(Xy,B) => in(kpair(Xx,Xy),cartprod(A,B))))))). 111.90/112.55 tff('25', plain, 111.90/112.55 cartprodpairin = 111.90/112.55 (![X2,X3,X4]: 111.90/112.55 (in(X4,X2) => (![X5]: (in(X5,X3) => in(kpair(X4,X5),cartprod(X2,X3)))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(ubforcartprodlem3, axiom, ubforcartprodlem3 <=> 111.90/112.55 (![A,B,Xx]: 111.90/112.55 (in(Xx,A) => 111.90/112.55 (![Xy]: 111.90/112.55 (in(Xy,B) => in(kpair(Xx,Xy),powerset(powerset(binunion(A,B))))))))). 111.90/112.55 tff('26', plain, 111.90/112.55 ubforcartprodlem3 = 111.90/112.55 (![X2,X3,X4]: 111.90/112.55 (in(X4,X2) => 111.90/112.55 (![X5]: 111.90/112.55 (in(X5,X3) => in(kpair(X4,X5),powerset(powerset(binunion(X2,X3)))))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(ubforcartprodlem2, axiom, ubforcartprodlem2 <=> 111.90/112.55 (![A,B,Xx]: 111.90/112.55 (in(Xx,A) => 111.90/112.55 (![Xy]: 111.90/112.55 (in(Xy,B) => 111.90/112.55 in(setadjoin(setadjoin(Xx,emptyset), 111.90/112.55 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 111.90/112.55 emptyset)), 111.90/112.55 powerset(powerset(binunion(A,B))))))))). 111.90/112.55 tff('27', plain, 111.90/112.55 ubforcartprodlem2 = 111.90/112.55 (![X2,X3,X4]: 111.90/112.55 (in(X4,X2) => 111.90/112.55 (![X5]: 111.90/112.55 (in(X5,X3) => 111.90/112.55 in(setadjoin(setadjoin(X4,emptyset), 111.90/112.55 setadjoin(setadjoin(X4,setadjoin(X5,emptyset)), 111.90/112.55 emptyset)), 111.90/112.55 powerset(powerset(binunion(X2,X3)))))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(ubforcartprodlem1, axiom, ubforcartprodlem1 <=> 111.90/112.55 (![A,B,Xx]: 111.90/112.55 (in(Xx,A) => 111.90/112.55 (![Xy]: 111.90/112.55 (in(Xy,B) => 111.90/112.55 subset(setadjoin(setadjoin(Xx,emptyset), 111.90/112.55 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 111.90/112.55 emptyset)), 111.90/112.55 powerset(binunion(A,B)))))))). 111.90/112.55 tff('28', plain, 111.90/112.55 ubforcartprodlem1 = 111.90/112.55 (![X2,X3,X4]: 111.90/112.55 (in(X4,X2) => 111.90/112.55 (![X5]: 111.90/112.55 (in(X5,X3) => 111.90/112.55 subset(setadjoin(setadjoin(X4,emptyset), 111.90/112.55 setadjoin(setadjoin(X4,setadjoin(X5,emptyset)), 111.90/112.55 emptyset)), 111.90/112.55 powerset(binunion(X2,X3))))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(upairinpowunion, axiom, upairinpowunion <=> 111.90/112.55 (![A,B,Xx]: 111.90/112.55 (in(Xx,A) => 111.90/112.55 (![Xy]: 111.90/112.55 (in(Xy,B) => 111.90/112.55 in(setadjoin(Xx,setadjoin(Xy,emptyset)),powerset(binunion(A,B)))))))). 111.90/112.55 tff('29', plain, 111.90/112.55 upairinpowunion = 111.90/112.55 (![X2,X3,X4]: 111.90/112.55 (in(X4,X2) => 111.90/112.55 (![X5]: 111.90/112.55 (in(X5,X3) => 111.90/112.55 in(setadjoin(X4,setadjoin(X5,emptyset)),powerset(binunion(X2,X3))))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(upairsubunion, axiom, upairsubunion <=> 111.90/112.55 (![A,B,Xx]: 111.90/112.55 (in(Xx,A) => 111.90/112.55 (![Xy]: 111.90/112.55 (in(Xy,B) => 111.90/112.55 subset(setadjoin(Xx,setadjoin(Xy,emptyset)),binunion(A,B))))))). 111.90/112.55 tff('30', plain, 111.90/112.55 upairsubunion = 111.90/112.55 (![X2,X3,X4]: 111.90/112.55 (in(X4,X2) => 111.90/112.55 (![X5]: 111.90/112.55 (in(X5,X3) => 111.90/112.55 subset(setadjoin(X4,setadjoin(X5,emptyset)),binunion(X2,X3)))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(upairset2E, axiom, upairset2E <=> 111.90/112.55 (![Xx,Xy,Xz]: 111.90/112.55 (in(Xz,setadjoin(Xx,setadjoin(Xy,emptyset))) => ((Xz = Xy) | (Xz = Xx))))). 111.90/112.55 tff('31', plain, 111.90/112.55 upairset2E = 111.90/112.55 (![X2,X3,X4]: 111.90/112.55 (in(X4,setadjoin(X2,setadjoin(X3,emptyset))) => 111.90/112.55 ((X4 = X3) | (X4 = X2)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(singletoninpowunion, axiom, singletoninpowunion <=> 111.90/112.55 (![A,B,Xx]: 111.90/112.55 (in(Xx,A) => in(setadjoin(Xx,emptyset),powerset(binunion(A,B)))))). 111.90/112.55 tff('32', plain, 111.90/112.55 singletoninpowunion = 111.90/112.55 (![X2,X3,X4]: 111.90/112.55 (in(X4,X2) => in(setadjoin(X4,emptyset),powerset(binunion(X2,X3))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(singletoninpowerset, axiom, singletoninpowerset <=> 111.90/112.55 (![A,Xx]: (in(Xx,A) => in(setadjoin(Xx,emptyset),powerset(A))))). 111.90/112.55 tff('33', plain, 111.90/112.55 singletoninpowerset = 111.90/112.55 (![X2,X3]: (in(X3,X2) => in(setadjoin(X3,emptyset),powerset(X2)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(singletonsubset, axiom, singletonsubset <=> 111.90/112.55 (![A,Xx]: (in(Xx,A) => subset(setadjoin(Xx,emptyset),A)))). 111.90/112.55 tff('34', plain, 111.90/112.55 singletonsubset = 111.90/112.55 (![X2,X3]: (in(X3,X2) => subset(setadjoin(X3,emptyset),X2))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(kpairp, axiom, kpairp <=> (![Xx,Xy]: iskpair(kpair(Xx,Xy)))). 111.90/112.55 tff('35', plain, kpairp = (![X2,X3]: iskpair(kpair(X2,X3))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(kpair, axiom, kpair() = 111.90/112.55 ^[Xx,Xy]: 111.90/112.55 setadjoin(setadjoin(Xx,emptyset), 111.90/112.55 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)),emptyset))). 111.90/112.55 tff('36', plain, 111.90/112.55 kpair = 111.90/112.55 (^[V_1,V_2]: 111.90/112.55 setadjoin(setadjoin(V_1,emptyset), 111.90/112.55 setadjoin(setadjoin(V_1,setadjoin(V_2,emptyset)),emptyset))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(kpairiskpair, axiom, kpairiskpair <=> 111.90/112.55 (![Xx,Xy]: 111.90/112.55 iskpair(setadjoin(setadjoin(Xx,emptyset), 111.90/112.55 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 111.90/112.55 emptyset))))). 111.90/112.55 tff('37', plain, 111.90/112.55 kpairiskpair = 111.90/112.55 (![X2,X3]: 111.90/112.55 iskpair(setadjoin(setadjoin(X2,emptyset), 111.90/112.55 setadjoin(setadjoin(X2,setadjoin(X3,emptyset)), 111.90/112.55 emptyset)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(setukpairIR, axiom, setukpairIR <=> 111.90/112.55 (![Xx,Xy]: 111.90/112.55 in(Xy, 111.90/112.55 setunion(setadjoin(setadjoin(Xx,emptyset), 111.90/112.55 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 111.90/112.55 emptyset)))))). 111.90/112.55 tff('38', plain, 111.90/112.55 setukpairIR = 111.90/112.55 (![X2,X3]: 111.90/112.55 in(X3, 111.90/112.55 setunion(setadjoin(setadjoin(X2,emptyset), 111.90/112.55 setadjoin(setadjoin(X2,setadjoin(X3,emptyset)), 111.90/112.55 emptyset))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(setukpairIL, axiom, setukpairIL <=> 111.90/112.55 (![Xx,Xy]: 111.90/112.55 in(Xx, 111.90/112.55 setunion(setadjoin(setadjoin(Xx,emptyset), 111.90/112.55 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 111.90/112.55 emptyset)))))). 111.90/112.55 tff('39', plain, 111.90/112.55 setukpairIL = 111.90/112.55 (![X2,X3]: 111.90/112.55 in(X2, 111.90/112.55 setunion(setadjoin(setadjoin(X2,emptyset), 111.90/112.55 setadjoin(setadjoin(X2,setadjoin(X3,emptyset)), 111.90/112.55 emptyset))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(secondinupair, axiom, secondinupair <=> 111.90/112.55 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 111.90/112.55 tff('40', plain, 111.90/112.55 secondinupair = (![X2,X3]: in(X3,setadjoin(X2,setadjoin(X3,emptyset)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(iskpair, axiom, iskpair() = 111.90/112.55 ^[A]: 111.90/112.55 (?[Xx]: 111.90/112.55 ((?[Xy]: 111.90/112.55 ((A = 111.90/112.55 setadjoin(setadjoin(Xx,emptyset), 111.90/112.55 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 111.90/112.55 emptyset))) & 111.90/112.55 in(Xy,setunion(A)))) & 111.90/112.55 in(Xx,setunion(A))))). 111.90/112.55 tff('41', plain, 111.90/112.55 iskpair = 111.90/112.55 (^[V_1]: 111.90/112.55 (?[X2]: 111.90/112.55 ((?[X3]: 111.90/112.55 ((V_1 = 111.90/112.55 setadjoin(setadjoin(X2,emptyset), 111.90/112.55 setadjoin(setadjoin(X2,setadjoin(X3,emptyset)), 111.90/112.55 emptyset))) & 111.90/112.55 in(X3,setunion(V_1)))) & 111.90/112.55 in(X2,setunion(V_1))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(symdiffIneg2, axiom, symdiffIneg2 <=> 111.90/112.55 (![A,B,Xx]: ((~in(Xx,A)) => ((~in(Xx,B)) => (~in(Xx,symdiff(A,B))))))). 111.90/112.55 tff('42', plain, 111.90/112.55 symdiffIneg2 = 111.90/112.55 (![X2,X3,X4]: 111.90/112.55 ((~in(X4,X2)) => ((~in(X4,X3)) => (~in(X4,symdiff(X2,X3)))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(symdiffIneg1, axiom, symdiffIneg1 <=> 111.90/112.55 (![A,B,Xx]: (in(Xx,A) => (in(Xx,B) => (~in(Xx,symdiff(A,B))))))). 111.90/112.55 tff('43', plain, 111.90/112.55 symdiffIneg1 = 111.90/112.55 (![X2,X3,X4]: (in(X4,X2) => (in(X4,X3) => (~in(X4,symdiff(X2,X3)))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(symdiffI2, axiom, symdiffI2 <=> 111.90/112.55 (![A,B,Xx]: ((~in(Xx,A)) => (in(Xx,B) => in(Xx,symdiff(A,B)))))). 111.90/112.55 tff('44', plain, 111.90/112.55 symdiffI2 = 111.90/112.55 (![X2,X3,X4]: ((~in(X4,X2)) => (in(X4,X3) => in(X4,symdiff(X2,X3))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(symdiffI1, axiom, symdiffI1 <=> 111.90/112.55 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => in(Xx,symdiff(A,B)))))). 111.90/112.55 tff('45', plain, 111.90/112.55 symdiffI1 = 111.90/112.55 (![X2,X3,X4]: (in(X4,X2) => ((~in(X4,X3)) => in(X4,symdiff(X2,X3))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(symdiffE, axiom, symdiffE <=> 111.90/112.55 (![A,B,Xx]: 111.90/112.55 (in(Xx,symdiff(A,B)) => 111.90/112.55 (![Xphi:$o]: 111.90/112.55 ((in(Xx,A) => ((~in(Xx,B)) => Xphi)) => 111.90/112.55 (((~in(Xx,A)) => (in(Xx,B) => Xphi)) => Xphi)))))). 111.90/112.55 tff('46', plain, 111.90/112.55 symdiffE = 111.90/112.55 (![X2,X3,X4]: 111.90/112.55 (in(X4,symdiff(X2,X3)) => 111.90/112.55 (![X5:$o]: 111.90/112.55 ((in(X4,X2) => ((~in(X4,X3)) => X5)) => 111.90/112.55 (((~in(X4,X2)) => (in(X4,X3) => X5)) => X5))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(setminusSubset1, axiom, setminusSubset1 <=> 111.90/112.55 (![A,B]: ((setminus(A,B) = emptyset) => subset(A,B)))). 111.90/112.55 tff('47', plain, 111.90/112.55 setminusSubset1 = 111.90/112.55 (![X2,X3]: ((setminus(X2,X3) = emptyset) => subset(X2,X3))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(setminusLsub, axiom, setminusLsub <=> (![A,B]: subset(setminus(A,B),A))). 111.90/112.55 tff('48', plain, setminusLsub = (![X2,X3]: subset(setminus(X2,X3),X2)), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(setminusIRneg, axiom, setminusIRneg <=> 111.90/112.55 (![A,B,Xx]: (in(Xx,B) => (~in(Xx,setminus(A,B)))))). 111.90/112.55 tff('49', plain, 111.90/112.55 setminusIRneg = (![X2,X3,X4]: (in(X4,X3) => (~in(X4,setminus(X2,X3))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(setminusILneg, axiom, setminusILneg <=> 111.90/112.55 (![A,B,Xx]: ((~in(Xx,A)) => (~in(Xx,setminus(A,B)))))). 111.90/112.55 tff('50', plain, 111.90/112.55 setminusILneg = 111.90/112.55 (![X2,X3,X4]: ((~in(X4,X2)) => (~in(X4,setminus(X2,X3))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(setminusELneg, axiom, setminusELneg <=> 111.90/112.55 (![A,B,Xx]: ((~in(Xx,setminus(A,B))) => ((~in(Xx,B)) => (~in(Xx,A)))))). 111.90/112.55 tff('51', plain, 111.90/112.55 setminusELneg = 111.90/112.55 (![X2,X3,X4]: 111.90/112.55 ((~in(X4,setminus(X2,X3))) => ((~in(X4,X3)) => (~in(X4,X2))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(setminusERneg, axiom, setminusERneg <=> 111.90/112.55 (![A,B,Xx]: ((~in(Xx,setminus(A,B))) => (in(Xx,A) => in(Xx,B))))). 111.90/112.55 tff('52', plain, 111.90/112.55 setminusERneg = 111.90/112.55 (![X2,X3,X4]: ((~in(X4,setminus(X2,X3))) => (in(X4,X2) => in(X4,X3)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(setminusSubset2, axiom, setminusSubset2 <=> 111.90/112.55 (![A,B]: (subset(A,B) => (setminus(A,B) = emptyset)))). 111.90/112.55 tff('53', plain, 111.90/112.55 setminusSubset2 = 111.90/112.55 (![X2,X3]: (subset(X2,X3) => (setminus(X2,X3) = emptyset))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(setminusER, axiom, setminusER <=> 111.90/112.55 (![A,B,Xx]: (in(Xx,setminus(A,B)) => (~in(Xx,B))))). 111.90/112.55 tff('54', plain, 111.90/112.55 setminusER = (![X2,X3,X4]: (in(X4,setminus(X2,X3)) => (~in(X4,X3)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(setminusEL, axiom, setminusEL <=> 111.90/112.55 (![A,B,Xx]: (in(Xx,setminus(A,B)) => in(Xx,A)))). 111.90/112.55 tff('55', plain, 111.90/112.55 setminusEL = (![X2,X3,X4]: (in(X4,setminus(X2,X3)) => in(X4,X2))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(setminusI, axiom, setminusI <=> 111.90/112.55 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => in(Xx,setminus(A,B)))))). 111.90/112.55 tff('56', plain, 111.90/112.55 setminusI = 111.90/112.55 (![X2,X3,X4]: (in(X4,X2) => ((~in(X4,X3)) => in(X4,setminus(X2,X3))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(bs114d, axiom, bs114d <=> 111.90/112.55 (![A,B,C]: 111.90/112.55 (binintersect(A,binunion(B,C)) = 111.90/112.55 binunion(binintersect(A,B),binintersect(A,C))))). 111.90/112.55 tff('57', plain, 111.90/112.55 bs114d = 111.90/112.55 (![X2,X3,X4]: 111.90/112.55 (binintersect(X2,binunion(X3,X4)) = 111.90/112.55 binunion(binintersect(X2,X3),binintersect(X2,X4)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(binintersectSubset1, axiom, binintersectSubset1 <=> 111.90/112.55 (![A,B]: ((binintersect(A,B) = A) => subset(A,B)))). 111.90/112.55 tff('58', plain, 111.90/112.55 binintersectSubset1 = 111.90/112.55 (![X2,X3]: ((binintersect(X2,X3) = X2) => subset(X2,X3))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(binintersectSubset4, axiom, binintersectSubset4 <=> 111.90/112.55 (![A,B]: (subset(B,A) => (binintersect(A,B) = B)))). 111.90/112.55 tff('59', plain, 111.90/112.55 binintersectSubset4 = 111.90/112.55 (![X2,X3]: (subset(X3,X2) => (binintersect(X2,X3) = X3))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(binintersectRsub, axiom, binintersectRsub <=> 111.90/112.55 (![A,B]: subset(binintersect(A,B),B))). 111.90/112.55 tff('60', plain, 111.90/112.55 binintersectRsub = (![X2,X3]: subset(binintersect(X2,X3),X3)), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(disjointsetsI1, axiom, disjointsetsI1 <=> 111.90/112.55 (![A,B]: 111.90/112.55 ((~(?[Xx]: (in(Xx,B) & in(Xx,A)))) => (binintersect(A,B) = emptyset)))). 111.90/112.55 tff('61', plain, 111.90/112.55 disjointsetsI1 = 111.90/112.55 (![X2,X3]: 111.90/112.55 ((~(?[X4]: (in(X4,X3) & in(X4,X2)))) => 111.90/112.55 (binintersect(X2,X3) = emptyset))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(binintersectER, axiom, binintersectER <=> 111.90/112.55 (![A,B,Xx]: (in(Xx,binintersect(A,B)) => in(Xx,B)))). 111.90/112.55 tff('62', plain, 111.90/112.55 binintersectER = (![X2,X3,X4]: (in(X4,binintersect(X2,X3)) => in(X4,X3))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(binintersectSubset3, axiom, binintersectSubset3 <=> 111.90/112.55 (![A,B]: ((binintersect(A,B) = B) => subset(B,A)))). 111.90/112.55 tff('63', plain, 111.90/112.55 binintersectSubset3 = 111.90/112.55 (![X2,X3]: ((binintersect(X2,X3) = X3) => subset(X3,X2))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(binintersectSubset2, axiom, binintersectSubset2 <=> 111.90/112.55 (![A,B]: (subset(A,B) => (binintersect(A,B) = A)))). 111.90/112.55 tff('64', plain, 111.90/112.55 binintersectSubset2 = 111.90/112.55 (![X2,X3]: (subset(X2,X3) => (binintersect(X2,X3) = X2))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(binintersectLsub, axiom, binintersectLsub <=> 111.90/112.55 (![A,B]: subset(binintersect(A,B),A))). 111.90/112.55 tff('65', plain, 111.90/112.55 binintersectLsub = (![X2,X3]: subset(binintersect(X2,X3),X2)), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(binintersectEL, axiom, binintersectEL <=> 111.90/112.55 (![A,B,Xx]: (in(Xx,binintersect(A,B)) => in(Xx,A)))). 111.90/112.55 tff('66', plain, 111.90/112.55 binintersectEL = (![X2,X3,X4]: (in(X4,binintersect(X2,X3)) => in(X4,X2))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(binintersectSubset5, axiom, binintersectSubset5 <=> 111.90/112.55 (![A,B,C]: (subset(C,A) => (subset(C,B) => subset(C,binintersect(A,B)))))). 111.90/112.55 tff('67', plain, 111.90/112.55 binintersectSubset5 = 111.90/112.55 (![X2,X3,X4]: 111.90/112.55 (subset(X4,X2) => (subset(X4,X3) => subset(X4,binintersect(X2,X3))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(binintersectI, axiom, binintersectI <=> 111.90/112.55 (![A,B,Xx]: (in(Xx,A) => (in(Xx,B) => in(Xx,binintersect(A,B)))))). 111.90/112.55 tff('68', plain, 111.90/112.55 binintersectI = 111.90/112.55 (![X2,X3,X4]: (in(X4,X2) => (in(X4,X3) => in(X4,binintersect(X2,X3))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(binunionRsub, axiom, binunionRsub <=> (![A,B]: subset(B,binunion(A,B)))). 111.90/112.55 tff('69', plain, binunionRsub = (![X2,X3]: subset(X3,binunion(X2,X3))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(binunionLsub, axiom, binunionLsub <=> (![A,B]: subset(A,binunion(A,B)))). 111.90/112.55 tff('70', plain, binunionLsub = (![X2,X3]: subset(X2,binunion(X2,X3))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(binunionE, axiom, binunionE <=> 111.90/112.55 (![A,B,Xx]: (in(Xx,binunion(A,B)) => (in(Xx,B) | in(Xx,A))))). 111.90/112.55 tff('71', plain, 111.90/112.55 binunionE = 111.90/112.55 (![X2,X3,X4]: (in(X4,binunion(X2,X3)) => (in(X4,X3) | in(X4,X2)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(binunionEcases, axiom, binunionEcases <=> 111.90/112.55 (![A,B,Xx,Xphi:$o]: 111.90/112.55 (in(Xx,binunion(A,B)) => 111.90/112.55 ((in(Xx,A) => Xphi) => ((in(Xx,B) => Xphi) => Xphi))))). 111.90/112.55 tff('72', plain, 111.90/112.55 binunionEcases = 111.90/112.55 (![X2,X3,X4,X5:$o]: 111.90/112.55 (in(X4,binunion(X2,X3)) => 111.90/112.55 ((in(X4,X2) => X5) => ((in(X4,X3) => X5) => X5)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(binunionIR, axiom, binunionIR <=> 111.90/112.55 (![A,B,Xx]: (in(Xx,B) => in(Xx,binunion(A,B))))). 111.90/112.55 tff('73', plain, 111.90/112.55 binunionIR = (![X2,X3,X4]: (in(X4,X3) => in(X4,binunion(X2,X3)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(upairset2IR, axiom, upairset2IR <=> 111.90/112.55 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 111.90/112.55 tff('74', plain, 111.90/112.55 upairset2IR = (![X2,X3]: in(X3,setadjoin(X2,setadjoin(X3,emptyset)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(binunionIL, axiom, binunionIL <=> 111.90/112.55 (![A,B,Xx]: (in(Xx,A) => in(Xx,binunion(A,B))))). 111.90/112.55 tff('75', plain, 111.90/112.55 binunionIL = (![X2,X3,X4]: (in(X4,X2) => in(X4,binunion(X2,X3)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(sepSubset, axiom, sepSubset <=> 111.90/112.55 (![A,Xphi:($i > $o)]: subset(dsetconstr(A,^[Xx]: Xphi(Xx)),A))). 111.90/112.55 tff('76', plain, 111.90/112.55 sepSubset = 111.90/112.55 (![X2,X3:($i > $o)]: subset(dsetconstr(X2,^[V_1]: X3(V_1)),X2)), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(sepInPowerset, axiom, sepInPowerset <=> 111.90/112.55 (![A,Xphi:($i > $o)]: in(dsetconstr(A,^[Xx]: Xphi(Xx)),powerset(A)))). 111.90/112.55 tff('77', plain, 111.90/112.55 sepInPowerset = 111.90/112.55 (![X2,X3:($i > $o)]: in(dsetconstr(X2,^[V_1]: X3(V_1)),powerset(X2))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(powersetsubset, axiom, powersetsubset <=> 111.90/112.55 (![A,B]: (subset(A,B) => subset(powerset(A),powerset(B))))). 111.90/112.55 tff('78', plain, 111.90/112.55 powersetsubset = 111.90/112.55 (![X2,X3]: (subset(X2,X3) => subset(powerset(X2),powerset(X3)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(inPowerset, axiom, inPowerset <=> (![A]: in(A,powerset(A)))). 111.90/112.55 tff('79', plain, inPowerset = (![X2]: in(X2,powerset(X2))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(powersetE1, axiom, powersetE1 <=> 111.90/112.55 (![A,B]: (in(B,powerset(A)) => subset(B,A)))). 111.90/112.55 tff('80', plain, 111.90/112.55 powersetE1 = (![X2,X3]: (in(X3,powerset(X2)) => subset(X3,X2))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(powersetI1, axiom, powersetI1 <=> 111.90/112.55 (![A,B]: (subset(B,A) => in(B,powerset(A))))). 111.90/112.55 tff('81', plain, 111.90/112.55 powersetI1 = (![X2,X3]: (subset(X3,X2) => in(X3,powerset(X2)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(subsetemptysetimpeq, axiom, subsetemptysetimpeq <=> 111.90/112.55 (![A]: (subset(A,emptyset) => (A = emptyset)))). 111.90/112.55 tff('82', plain, 111.90/112.55 subsetemptysetimpeq = (![X2]: (subset(X2,emptyset) => (X2 = emptyset))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(setextsub, axiom, setextsub <=> 111.90/112.55 (![A,B]: (subset(A,B) => (subset(B,A) => (A = B))))). 111.90/112.55 tff('83', plain, 111.90/112.55 setextsub = (![X2,X3]: (subset(X2,X3) => (subset(X3,X2) => (X2 = X3)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(subset2powerset, axiom, subset2powerset <=> 111.90/112.55 (![A,B]: (subset(A,B) => in(A,powerset(B))))). 111.90/112.55 tff('84', plain, 111.90/112.55 subset2powerset = (![X2,X3]: (subset(X2,X3) => in(X2,powerset(X3)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(setadjoinSub2, axiom, setadjoinSub2 <=> 111.90/112.55 (![A,Xx,B]: (subset(A,B) => subset(A,setadjoin(Xx,B))))). 111.90/112.55 tff('85', plain, 111.90/112.55 setadjoinSub2 = 111.90/112.55 (![X2,X3,X4]: (subset(X2,X4) => subset(X2,setadjoin(X3,X4)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(setadjoinSub, axiom, setadjoinSub <=> 111.90/112.55 (![Xx,A]: subset(A,setadjoin(Xx,A)))). 111.90/112.55 tff('86', plain, setadjoinSub = (![X2,X3]: subset(X3,setadjoin(X2,X3))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(subsetTrans, axiom, subsetTrans <=> 111.90/112.55 (![A,B,C]: (subset(A,B) => (subset(B,C) => subset(A,C))))). 111.90/112.55 tff('87', plain, 111.90/112.55 subsetTrans = 111.90/112.55 (![X2,X3,X4]: (subset(X2,X3) => (subset(X3,X4) => subset(X2,X4)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(subsetRefl, axiom, subsetRefl <=> (![A]: subset(A,A))). 111.90/112.55 tff('88', plain, subsetRefl = (![X2]: subset(X2,X2)), define([status(thm)])). 111.90/112.55 tff(notequalI2, axiom, notequalI2 <=> 111.90/112.55 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => (A != B))))). 111.90/112.55 tff('89', plain, 111.90/112.55 notequalI2 = (![X2,X3,X4]: (in(X4,X2) => ((~in(X4,X3)) => (X2 != X3)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(notequalI1, axiom, notequalI1 <=> (![A,B]: ((~subset(A,B)) => (A != B)))). 111.90/112.55 tff('90', plain, notequalI1 = (![X2,X3]: ((~subset(X2,X3)) => (X2 != X3))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(notsubsetI, axiom, notsubsetI <=> 111.90/112.55 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => (~subset(A,B)))))). 111.90/112.55 tff('91', plain, 111.90/112.55 notsubsetI = 111.90/112.55 (![X2,X3,X4]: (in(X4,X2) => ((~in(X4,X3)) => (~subset(X2,X3))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(subsetE2, axiom, subsetE2 <=> 111.90/112.55 (![A,B,Xx]: (subset(A,B) => ((~in(Xx,B)) => (~in(Xx,A)))))). 111.90/112.55 tff('92', plain, 111.90/112.55 subsetE2 = 111.90/112.55 (![X2,X3,X4]: (subset(X2,X3) => ((~in(X4,X3)) => (~in(X4,X2))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(subsetE, axiom, subsetE <=> 111.90/112.55 (![A,B,Xx]: (subset(A,B) => (in(Xx,A) => in(Xx,B))))). 111.90/112.55 tff('93', plain, 111.90/112.55 subsetE = (![X2,X3,X4]: (subset(X2,X3) => (in(X4,X2) => in(X4,X3)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(emptysetsubset, axiom, emptysetsubset <=> (![A]: subset(emptyset,A))). 111.90/112.55 tff('94', plain, emptysetsubset = (![X2]: subset(emptyset,X2)), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(subsetI2, axiom, subsetI2 <=> 111.90/112.55 (![A,B]: ((![Xx]: (in(Xx,A) => in(Xx,B))) => subset(A,B)))). 111.90/112.55 tff('95', plain, 111.90/112.55 subsetI2 = 111.90/112.55 (![X2,X3]: ((![X4]: (in(X4,X2) => in(X4,X3))) => subset(X2,X3))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(eqimpsubset1, axiom, eqimpsubset1 <=> (![A,B]: ((A = B) => subset(A,B)))). 111.90/112.55 tff('96', plain, eqimpsubset1 = (![X2,X3]: ((X2 = X3) => subset(X2,X3))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(eqimpsubset2, axiom, eqimpsubset2 <=> (![A,B]: ((A = B) => subset(B,A)))). 111.90/112.55 tff('97', plain, eqimpsubset2 = (![X2,X3]: ((X2 = X3) => subset(X3,X2))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(subsetI1, axiom, subsetI1 <=> 111.90/112.55 (![A,B]: ((![Xx]: (in(Xx,A) => in(Xx,B))) => subset(A,B)))). 111.90/112.55 tff('98', plain, 111.90/112.55 subsetI1 = 111.90/112.55 (![X2,X3]: ((![X4]: (in(X4,X2) => in(X4,X3))) => subset(X2,X3))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(dsetconstr__Cong, axiom, dsetconstr__Cong <=> 111.90/112.55 (![A,B]: 111.90/112.55 ((A = B) => 111.90/112.55 (![Xphi:($i > $o),Xpsi:($i > $o)]: 111.90/112.55 ((![Xx]: 111.90/112.55 (in(Xx,A) => 111.90/112.55 (![Xy]: (in(Xy,B) => ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy))))))) => 111.90/112.55 (dsetconstr(A,^[Xx]: Xphi(Xx)) = dsetconstr(B,^[Xx]: Xpsi(Xx)))))))). 111.90/112.55 tff('99', plain, 111.90/112.55 dsetconstr__Cong = 111.90/112.55 (![X2,X3]: 111.90/112.55 ((X2 = X3) => 111.90/112.55 (![X4:($i > $o),X5:($i > $o)]: 111.90/112.55 ((![X6]: 111.90/112.55 (in(X6,X2) => 111.90/112.55 (![X7]: (in(X7,X3) => ((X6 = X7) => (X4(X6) <=> X5(X7))))))) => 111.90/112.55 (dsetconstr(X2,^[V_1]: X4(V_1)) = dsetconstr(X3,^[V_2]: X5(V_2))))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(descr__Cong, axiom, descr__Cong <=> 111.90/112.55 (![Xphi:($i > $o),Xpsi:($i > $o)]: 111.90/112.55 ((![Xx,Xy]: ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy)))) => 111.90/112.55 (exu(^[Xx]: Xphi(Xx)) => 111.90/112.55 (exu(^[Xx]: Xpsi(Xx)) => 111.90/112.55 (descr(^[Xx]: Xphi(Xx)) = descr(^[Xx]: Xpsi(Xx)))))))). 111.90/112.55 tff('100', plain, 111.90/112.55 descr__Cong = 111.90/112.55 (![X2:($i > $o),X3:($i > $o)]: 111.90/112.55 ((![X4,X5]: ((X4 = X5) => (X2(X4) <=> X3(X5)))) => 111.90/112.55 (exu(^[V_1]: X2(V_1)) => 111.90/112.55 (exu(^[V_2]: X3(V_2)) => 111.90/112.55 (descr(^[V_3]: X2(V_3)) = descr(^[V_4]: X3(V_4))))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(exuEu, axiom, exuEu <=> 111.90/112.55 (![Xphi:($i > $o)]: 111.90/112.55 (exu(^[Xx]: Xphi(Xx)) => 111.90/112.55 (![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))). 111.90/112.55 tff('101', plain, 111.90/112.55 exuEu = 111.90/112.55 (![X2:($i > $o)]: 111.90/112.55 (exu(^[V_1]: X2(V_1)) => (![X3,X4]: (X2(X3) => (X2(X4) => (X3 = X4)))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(omega__Cong, axiom, omega__Cong <=> (omega = omega)). 111.90/112.55 tff('102', plain, omega__Cong = (omega = omega), define([status(thm)])). 111.90/112.55 tff(setunion__Cong, axiom, setunion__Cong <=> 111.90/112.55 (![A,B]: ((A = B) => (setunion(A) = setunion(B))))). 111.90/112.55 tff('103', plain, 111.90/112.55 setunion__Cong = (![X2,X3]: ((X2 = X3) => (setunion(X2) = setunion(X3)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(powerset__Cong, axiom, powerset__Cong <=> 111.90/112.55 (![A,B]: ((A = B) => (powerset(A) = powerset(B))))). 111.90/112.55 tff('104', plain, 111.90/112.55 powerset__Cong = (![X2,X3]: ((X2 = X3) => (powerset(X2) = powerset(X3)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(setadjoin__Cong, axiom, setadjoin__Cong <=> 111.90/112.55 (![Xx,Xy]: 111.90/112.55 ((Xx = Xy) => 111.90/112.55 (![Xz,Xu]: ((Xz = Xu) => (setadjoin(Xx,Xz) = setadjoin(Xy,Xu))))))). 111.90/112.55 tff('105', plain, 111.90/112.55 setadjoin__Cong = 111.90/112.55 (![X2,X3]: 111.90/112.55 ((X2 = X3) => 111.90/112.55 (![X4,X5]: ((X4 = X5) => (setadjoin(X2,X4) = setadjoin(X3,X5)))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(emptyset__Cong, axiom, emptyset__Cong <=> (emptyset = emptyset)). 111.90/112.55 tff('106', plain, emptyset__Cong = (emptyset = emptyset), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(exu__Cong, axiom, exu__Cong <=> 111.90/112.55 (![Xphi:($i > $o),Xpsi:($i > $o)]: 111.90/112.55 ((![Xx,Xy]: ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy)))) => 111.90/112.55 (exu(^[Xx]: Xphi(Xx)) <=> exu(^[Xx]: Xpsi(Xx)))))). 111.90/112.55 tff('107', plain, 111.90/112.55 exu__Cong = 111.90/112.55 (![X2:($i > $o),X3:($i > $o)]: 111.90/112.55 ((![X4,X5]: ((X4 = X5) => (X2(X4) <=> X3(X5)))) => 111.90/112.55 (exu(^[V_1]: X2(V_1)) <=> exu(^[V_2]: X3(V_2))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(exuE3u, axiom, exuE3u <=> 111.90/112.55 (![Xphi:($i > $o)]: 111.90/112.55 (exu(^[Xx]: Xphi(Xx)) => 111.90/112.55 (![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))). 111.90/112.55 tff('108', plain, 111.90/112.55 exuE3u = 111.90/112.55 (![X2:($i > $o)]: 111.90/112.55 (exu(^[V_1]: X2(V_1)) => (![X3,X4]: (X2(X3) => (X2(X4) => (X3 = X4)))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(in__Cong, axiom, in__Cong <=> 111.90/112.55 (![A,B]: ((A = B) => (![Xx,Xy]: ((Xx = Xy) => (in(Xx,A) <=> in(Xy,B))))))). 111.90/112.55 tff('109', plain, 111.90/112.55 in__Cong = 111.90/112.55 (![X2,X3]: 111.90/112.55 ((X2 = X3) => (![X4,X5]: ((X4 = X5) => (in(X4,X2) <=> in(X5,X3)))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(inCongP, axiom, inCongP <=> 111.90/112.55 (![A,B]: ((A = B) => (![Xx,Xy]: ((Xx = Xy) => (in(Xx,A) => in(Xy,B))))))). 111.90/112.55 tff('110', plain, 111.90/112.55 inCongP = 111.90/112.55 (![X2,X3]: 111.90/112.55 ((X2 = X3) => (![X4,X5]: ((X4 = X5) => (in(X4,X2) => in(X5,X3)))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(exuI2, axiom, exuI2 <=> 111.90/112.55 (![Xphi:($i > $o)]: 111.90/112.55 ((?[Xx]: (![Xy]: (Xphi(Xy) <=> (Xy = Xx)))) => exu(^[Xx]: Xphi(Xx))))). 111.90/112.55 tff('111', plain, 111.90/112.55 exuI2 = 111.90/112.55 (![X2:($i > $o)]: 111.90/112.55 ((?[X3]: (![X4]: (X2(X4) <=> (X4 = X3)))) => exu(^[V_1]: X2(V_1)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(exuI3, axiom, exuI3 <=> 111.90/112.55 (![Xphi:($i > $o)]: 111.90/112.55 ((?[Xx]: Xphi(Xx)) => 111.90/112.55 ((![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy)))) => 111.90/112.55 exu(^[Xx]: Xphi(Xx)))))). 111.90/112.55 tff('112', plain, 111.90/112.55 exuI3 = 111.90/112.55 (![X2:($i > $o)]: 111.90/112.55 ((?[X3]: X2(X3)) => 111.90/112.55 ((![X4,X5]: (X2(X4) => (X2(X5) => (X4 = X5)))) => 111.90/112.55 exu(^[V_1]: X2(V_1))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(exuI1, axiom, exuI1 <=> 111.90/112.55 (![Xphi:($i > $o)]: 111.90/112.55 ((?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx))) => 111.90/112.55 exu(^[Xx]: Xphi(Xx))))). 111.90/112.55 tff('113', plain, 111.90/112.55 exuI1 = 111.90/112.55 (![X2:($i > $o)]: 111.90/112.55 ((?[X3]: ((![X4]: (X2(X4) => (X3 = X4))) & X2(X3))) => 111.90/112.55 exu(^[V_1]: X2(V_1)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(notdallE, axiom, notdallE <=> 111.90/112.55 (![A,Xphi:($i > $o)]: 111.90/112.55 ((~(![Xx]: (in(Xx,A) => Xphi(Xx)))) => (?[Xx]: ((~Xphi(Xx)) & in(Xx,A)))))). 111.90/112.55 tff('114', plain, 111.90/112.55 notdallE = 111.90/112.55 (![X2,X3:($i > $o)]: 111.90/112.55 ((~(![X4]: (in(X4,X2) => X3(X4)))) => (?[X5]: ((~X3(X5)) & in(X5,X2))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(notdexE, axiom, notdexE <=> 111.90/112.55 (![A,Xphi:($i > $o)]: 111.90/112.55 ((~(?[Xx]: (Xphi(Xx) & in(Xx,A)))) => (![Xx]: (in(Xx,A) => (~Xphi(Xx))))))). 111.90/112.55 tff('115', plain, 111.90/112.55 notdexE = 111.90/112.55 (![X2,X3:($i > $o)]: 111.90/112.55 ((~(?[X4]: (X3(X4) & in(X4,X2)))) => (![X5]: (in(X5,X2) => (~X3(X5)))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(prop2set2propI, axiom, prop2set2propI <=> 111.90/112.55 (![Xphi:$o]: (Xphi => set2prop(prop2set(Xphi))))). 111.90/112.55 tff('116', plain, 111.90/112.55 prop2set2propI = (![X2:$o]: (X2 => set2prop(prop2set(X2)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(prop2setI, axiom, prop2setI <=> 111.90/112.55 (![Xphi:$o]: (Xphi => in(emptyset,prop2set(Xphi))))). 111.90/112.55 tff('117', plain, prop2setI = (![X2:$o]: (X2 => in(emptyset,prop2set(X2)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(quantDeMorgan4, axiom, quantDeMorgan4 <=> 111.90/112.55 (![A,Xphi:($i > $o)]: 111.90/112.55 ((?[Xx]: ((~Xphi(Xx)) & in(Xx,A))) => (~(![Xx]: (in(Xx,A) => Xphi(Xx))))))). 111.90/112.55 tff('118', plain, 111.90/112.55 quantDeMorgan4 = 111.90/112.55 (![X2,X3:($i > $o)]: 111.90/112.55 ((?[X4]: ((~X3(X4)) & in(X4,X2))) => (~(![X5]: (in(X5,X2) => X3(X5)))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(quantDeMorgan3, axiom, quantDeMorgan3 <=> 111.90/112.55 (![A,Xphi:($i > $o)]: 111.90/112.55 ((~(?[Xx]: (Xphi(Xx) & in(Xx,A)))) => (![Xx]: (in(Xx,A) => (~Xphi(Xx))))))). 111.90/112.55 tff('119', plain, 111.90/112.55 quantDeMorgan3 = 111.90/112.55 (![X2,X3:($i > $o)]: 111.90/112.55 ((~(?[X4]: (X3(X4) & in(X4,X2)))) => (![X5]: (in(X5,X2) => (~X3(X5)))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(quantDeMorgan2, axiom, quantDeMorgan2 <=> 111.90/112.55 (![A,Xphi:($i > $o)]: 111.90/112.55 ((![Xx]: (in(Xx,A) => (~Xphi(Xx)))) => (~(?[Xx]: (Xphi(Xx) & in(Xx,A))))))). 111.90/112.55 tff('120', plain, 111.90/112.55 quantDeMorgan2 = 111.90/112.55 (![X2,X3:($i > $o)]: 111.90/112.55 ((![X4]: (in(X4,X2) => (~X3(X4)))) => (~(?[X5]: (X3(X5) & in(X5,X2)))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(quantDeMorgan1, axiom, quantDeMorgan1 <=> 111.90/112.55 (![A,Xphi:($i > $o)]: 111.90/112.55 ((~(![Xx]: (in(Xx,A) => Xphi(Xx)))) => (?[Xx]: ((~Xphi(Xx)) & in(Xx,A)))))). 111.90/112.55 tff('121', plain, 111.90/112.55 quantDeMorgan1 = 111.90/112.55 (![X2,X3:($i > $o)]: 111.90/112.55 ((~(![X4]: (in(X4,X2) => X3(X4)))) => (?[X5]: ((~X3(X5)) & in(X5,X2))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(vacuousDall, axiom, vacuousDall <=> 111.90/112.55 (![Xphi:($i > $o),Xx]: (in(Xx,emptyset) => Xphi(Xx)))). 111.90/112.55 tff('122', plain, 111.90/112.55 vacuousDall = (![X2:($i > $o),X3]: (in(X3,emptyset) => X2(X3))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(emptyE1, axiom, emptyE1 <=> 111.90/112.55 (![A,Xphi:($i > $o)]: 111.90/112.55 ((?[Xx]: (Xphi(Xx) & in(Xx,A))) => 111.90/112.55 ((dsetconstr(A,^[Xx]: Xphi(Xx)) = emptyset) => $false)))). 111.90/112.55 tff('123', plain, 111.90/112.55 emptyE1 = 111.90/112.55 (![X2,X3:($i > $o)]: 111.90/112.55 ((?[X4]: (X3(X4) & in(X4,X2))) => 111.90/112.55 ((dsetconstr(X2,^[V_1]: X3(V_1)) = emptyset) => $false))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(upairsetIR, axiom, upairsetIR <=> 111.90/112.55 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 111.90/112.55 tff('124', plain, 111.90/112.55 upairsetIR = (![X2,X3]: in(X3,setadjoin(X2,setadjoin(X3,emptyset)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(upairsetIL, axiom, upairsetIL <=> 111.90/112.55 (![Xx,Xy]: in(Xx,setadjoin(Xx,setadjoin(Xy,emptyset))))). 111.90/112.55 tff('125', plain, 111.90/112.55 upairsetIL = (![X2,X3]: in(X2,setadjoin(X2,setadjoin(X3,emptyset)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(upairsetE, axiom, upairsetE <=> 111.90/112.55 (![Xx,Xy,Xz]: 111.90/112.55 (in(Xz,setadjoin(Xx,setadjoin(Xy,emptyset))) => ((Xz = Xy) | (Xz = Xx))))). 111.90/112.55 tff('126', plain, 111.90/112.55 upairsetE = 111.90/112.55 (![X2,X3,X4]: 111.90/112.55 (in(X4,setadjoin(X2,setadjoin(X3,emptyset))) => 111.90/112.55 ((X4 = X3) | (X4 = X2)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(singletonsswitch, axiom, singletonsswitch <=> 111.90/112.55 (![Xx,Xy]: (in(Xx,setadjoin(Xy,emptyset)) => in(Xy,setadjoin(Xx,emptyset))))). 111.90/112.55 tff('127', plain, 111.90/112.55 singletonsswitch = 111.90/112.55 (![X2,X3]: 111.90/112.55 (in(X2,setadjoin(X3,emptyset)) => in(X3,setadjoin(X2,emptyset)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(eqinunit, axiom, eqinunit <=> 111.90/112.55 (![Xx,Xy]: ((Xx = Xy) => in(Xx,setadjoin(Xy,emptyset))))). 111.90/112.55 tff('128', plain, 111.90/112.55 eqinunit = (![X2,X3]: ((X2 = X3) => in(X2,setadjoin(X3,emptyset)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(notinsingleton, axiom, notinsingleton <=> 111.90/112.55 (![Xx,Xy]: ((Xx != Xy) => (~in(Xy,setadjoin(Xx,emptyset)))))). 111.90/112.55 tff('129', plain, 111.90/112.55 notinsingleton = 111.90/112.55 (![X2,X3]: ((X2 != X3) => (~in(X3,setadjoin(X2,emptyset))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(uniqinunit, axiom, uniqinunit <=> 111.90/112.55 (![Xx,Xy]: (in(Xx,setadjoin(Xy,emptyset)) => (Xx = Xy)))). 111.90/112.55 tff('130', plain, 111.90/112.55 uniqinunit = (![X2,X3]: (in(X2,setadjoin(X3,emptyset)) => (X2 = X3))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(nonemptyImpWitness, axiom, nonemptyImpWitness <=> 111.90/112.55 (![A]: (nonempty(A) => (?[Xx]: (in(Xx,A)))))). 111.90/112.55 tff('131', plain, 111.90/112.55 nonemptyImpWitness = (![X2]: (nonempty(X2) => (?[X3]: (in(X3,X2))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(exuE2, axiom, exuE2 <=> 111.90/112.55 (![Xphi:($i > $o)]: 111.90/112.55 (exu(^[Xx]: Xphi(Xx)) => (?[Xx]: (![Xy]: (Xphi(Xy) <=> (Xy = Xx))))))). 111.90/112.55 tff('132', plain, 111.90/112.55 exuE2 = 111.90/112.55 (![X2:($i > $o)]: 111.90/112.55 (exu(^[V_1]: X2(V_1)) => (?[X3]: (![X4]: (X2(X4) <=> (X4 = X3)))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(subPowSU, axiom, subPowSU <=> 111.90/112.55 (![A,Xx]: (in(Xx,A) => in(Xx,powerset(setunion(A)))))). 111.90/112.55 tff('133', plain, 111.90/112.55 subPowSU = (![X2,X3]: (in(X3,X2) => in(X3,powerset(setunion(X2))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(setunionE, axiom, setunionE <=> 111.90/112.55 (![A,Xx]: 111.90/112.55 (in(Xx,setunion(A)) => 111.90/112.55 (![Xphi:$o]: ((![B]: (in(Xx,B) => (in(B,A) => Xphi))) => Xphi))))). 111.90/112.55 tff('134', plain, 111.90/112.55 setunionE = 111.90/112.55 (![X2,X3]: 111.90/112.55 (in(X3,setunion(X2)) => 111.90/112.55 (![X4:$o]: ((![X5]: (in(X3,X5) => (in(X5,X2) => X4))) => X4)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(setunionI, axiom, setunionI <=> 111.90/112.55 (![A,Xx,B]: (in(Xx,B) => (in(B,A) => in(Xx,setunion(A)))))). 111.90/112.55 tff('135', plain, 111.90/112.55 setunionI = 111.90/112.55 (![X2,X3,X4]: (in(X3,X4) => (in(X4,X2) => in(X3,setunion(X2))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(powersetE, axiom, powersetE <=> 111.90/112.55 (![A,B,Xx]: (in(B,powerset(A)) => (in(Xx,B) => in(Xx,A))))). 111.90/112.55 tff('136', plain, 111.90/112.55 powersetE = 111.90/112.55 (![X2,X3,X4]: (in(X3,powerset(X2)) => (in(X4,X3) => in(X4,X2)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(emptyInPowerset, axiom, emptyInPowerset <=> 111.90/112.55 (![A]: in(emptyset,powerset(A)))). 111.90/112.55 tff('137', plain, emptyInPowerset = (![X2]: in(emptyset,powerset(X2))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(emptyinPowerset, axiom, emptyinPowerset <=> 111.90/112.55 (![A]: in(emptyset,powerset(A)))). 111.90/112.55 tff('138', plain, emptyinPowerset = (![X2]: in(emptyset,powerset(X2))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(powersetI, axiom, powersetI <=> 111.90/112.55 (![A,B]: ((![Xx]: (in(Xx,B) => in(Xx,A))) => in(B,powerset(A))))). 111.90/112.55 tff('139', plain, 111.90/112.55 powersetI = 111.90/112.55 (![X2,X3]: ((![X4]: (in(X4,X3) => in(X4,X2))) => in(X3,powerset(X2)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(setoftrueEq, axiom, setoftrueEq <=> 111.90/112.55 (![A]: (dsetconstr(A,^[Xx]: $true) = A))). 111.90/112.55 tff('140', plain, setoftrueEq = (![X2]: (dsetconstr(X2,^[V_1]: $true) = X2)), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(setadjoinOr, axiom, setadjoinOr <=> 111.90/112.55 (![Xx,A,Xy]: (in(Xy,setadjoin(Xx,A)) => (in(Xy,A) | (Xy = Xx))))). 111.90/112.55 tff('141', plain, 111.90/112.55 setadjoinOr = 111.90/112.55 (![X2,X3,X4]: (in(X4,setadjoin(X2,X3)) => (in(X4,X3) | (X4 = X2)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(setadjoinE, axiom, setadjoinE <=> 111.90/112.55 (![Xx,A,Xy]: 111.90/112.55 (in(Xy,setadjoin(Xx,A)) => 111.90/112.55 (![Xphi:$o]: (((Xy = Xx) => Xphi) => ((in(Xy,A) => Xphi) => Xphi)))))). 111.90/112.55 tff('142', plain, 111.90/112.55 setadjoinE = 111.90/112.55 (![X2,X3,X4]: 111.90/112.55 (in(X4,setadjoin(X2,X3)) => 111.90/112.55 (![X5:$o]: (((X4 = X2) => X5) => ((in(X4,X3) => X5) => X5))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(setadjoinIR, axiom, setadjoinIR <=> 111.90/112.55 (![Xx,A,Xy]: (in(Xy,A) => in(Xy,setadjoin(Xx,A))))). 111.90/112.55 tff('143', plain, 111.90/112.55 setadjoinIR = (![X2,X3,X4]: (in(X4,X3) => in(X4,setadjoin(X2,X3)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(emptyinunitempty, axiom, emptyinunitempty() = 111.90/112.55 in(emptyset,setadjoin(emptyset,emptyset))). 111.90/112.55 tff('144', plain, 111.90/112.55 emptyinunitempty = in(emptyset,setadjoin(emptyset,emptyset)), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(setadjoinIL, axiom, setadjoinIL <=> (![Xx,Xy]: in(Xx,setadjoin(Xx,Xy)))). 111.90/112.55 tff('145', plain, setadjoinIL = (![X2,X3]: in(X2,setadjoin(X2,X3))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(nonemptyI1, axiom, nonemptyI1 <=> 111.90/112.55 (![A]: ((?[Xx]: in(Xx,A)) => nonempty(A)))). 111.90/112.55 tff('146', plain, nonemptyI1 = (![X2]: ((?[X3]: in(X3,X2)) => nonempty(X2))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(nonemptyI, axiom, nonemptyI <=> 111.90/112.55 (![A,Xphi:($i > $o),Xx]: 111.90/112.55 (in(Xx,A) => (Xphi(Xx) => nonempty(dsetconstr(A,^[Xy]: Xphi(Xy))))))). 111.90/112.55 tff('147', plain, 111.90/112.55 nonemptyI = 111.90/112.55 (![X2,X3:($i > $o),X4]: 111.90/112.55 (in(X4,X2) => (X3(X4) => nonempty(dsetconstr(X2,^[V_1]: X3(V_1)))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(nonemptyE1, axiom, nonemptyE1 <=> 111.90/112.55 (![A]: (nonempty(A) => (?[Xx]: in(Xx,A))))). 111.90/112.55 tff('148', plain, nonemptyE1 = (![X2]: (nonempty(X2) => (?[X3]: in(X3,X2)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(nonempty, axiom, nonempty() = ^[Xx]: (Xx != emptyset)). 111.90/112.55 tff('149', plain, nonempty = (^[V_1]: (V_1 != emptyset)), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(setbeta, axiom, setbeta <=> 111.90/112.55 (![A,Xphi:($i > $o),Xx]: 111.90/112.55 (in(Xx,A) => (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) <=> Xphi(Xx))))). 111.90/112.55 tff('150', plain, 111.90/112.55 setbeta = 111.90/112.55 (![X2,X3:($i > $o),X4]: 111.90/112.55 (in(X4,X2) => (in(X4,dsetconstr(X2,^[V_1]: X3(V_1))) <=> X3(X4)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(noeltsimpempty, axiom, noeltsimpempty <=> 111.90/112.55 (![A]: ((![Xx]: (~in(Xx,A))) => (A = emptyset)))). 111.90/112.55 tff('151', plain, 111.90/112.55 noeltsimpempty = (![X2]: ((![X3]: (~in(X3,X2))) => (X2 = emptyset))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(emptyI, axiom, emptyI <=> 111.90/112.55 (![A]: ((![Xx]: (~in(Xx,A))) => (A = emptyset)))). 111.90/112.55 tff('152', plain, 111.90/112.55 emptyI = (![X2]: ((![X3]: (~in(X3,X2))) => (X2 = emptyset))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(setext, axiom, setext <=> 111.90/112.55 (![A,B]: 111.90/112.55 ((![Xx]: (in(Xx,A) => in(Xx,B))) => 111.90/112.55 ((![Xx]: (in(Xx,B) => in(Xx,A))) => (A = B))))). 111.90/112.55 tff('153', plain, 111.90/112.55 setext = 111.90/112.55 (![X2,X3]: 111.90/112.55 ((![X4]: (in(X4,X2) => in(X4,X3))) => 111.90/112.55 ((![X5]: (in(X5,X3) => in(X5,X2))) => (X2 = X3)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(exuE3e, axiom, exuE3e <=> 111.90/112.55 (![Xphi:($i > $o)]: (exu(^[Xx]: Xphi(Xx)) => (?[Xx]: Xphi(Xx))))). 111.90/112.55 tff('154', plain, 111.90/112.55 exuE3e = (![X2:($i > $o)]: (exu(^[V_1]: X2(V_1)) => (?[X3]: X2(X3)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(notinemptyset, axiom, notinemptyset <=> (![Xx]: (~in(Xx,emptyset)))). 111.90/112.55 tff('155', plain, notinemptyset = (![X2]: (~in(X2,emptyset))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(emptysetimpfalse, axiom, emptysetimpfalse <=> 111.90/112.55 (![Xx]: (in(Xx,emptyset) => $false))). 111.90/112.55 tff('156', plain, emptysetimpfalse = (![X2]: (in(X2,emptyset) => $false)), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(emptysetE, axiom, emptysetE <=> 111.90/112.55 (![Xx]: (in(Xx,emptyset) => (![Xphi:$o]: Xphi)))). 111.90/112.55 tff('157', plain, emptysetE = (![X2]: (in(X2,emptyset) => (![X3:$o]: X3))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(prop2setE, axiom, prop2setE <=> 111.90/112.55 (![Xphi:$o,Xx]: (in(Xx,prop2set(Xphi)) => Xphi))). 111.90/112.55 tff('158', plain, prop2setE = (![X2:$o,X3]: (in(X3,prop2set(X2)) => X2)), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(exuE1, axiom, exuE1 <=> 111.90/112.55 (![Xphi:($i > $o)]: 111.90/112.55 (exu(^[Xx]: Xphi(Xx)) => 111.90/112.55 (?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx)))))). 111.90/112.55 tff('159', plain, 111.90/112.55 exuE1 = 111.90/112.55 (![X2:($i > $o)]: 111.90/112.55 (exu(^[V_1]: X2(V_1)) => 111.90/112.55 (?[X3]: ((![X4]: (X2(X4) => (X3 = X4))) & X2(X3))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(dsetconstrER, axiom, dsetconstrER <=> 111.90/112.55 (![A,Xphi:($i > $o),Xx]: (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) => Xphi(Xx)))). 111.90/112.55 tff('160', plain, 111.90/112.55 dsetconstrER = 111.90/112.55 (![X2,X3:($i > $o),X4]: (in(X4,dsetconstr(X2,^[V_1]: X3(V_1))) => X3(X4))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(dsetconstrEL, axiom, dsetconstrEL <=> 111.90/112.55 (![A,Xphi:($i > $o),Xx]: (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) => in(Xx,A)))). 111.90/112.55 tff('161', plain, 111.90/112.55 dsetconstrEL = 111.90/112.55 (![X2,X3:($i > $o),X4]: 111.90/112.55 (in(X4,dsetconstr(X2,^[V_1]: X3(V_1))) => in(X4,X2))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(dsetconstrI, axiom, dsetconstrI <=> 111.90/112.55 (![A,Xphi:($i > $o),Xx]: 111.90/112.55 (in(Xx,A) => (Xphi(Xx) => in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))))))). 111.90/112.55 tff('162', plain, 111.90/112.55 dsetconstrI = 111.90/112.55 (![X2,X3:($i > $o),X4]: 111.90/112.55 (in(X4,X2) => (X3(X4) => in(X4,dsetconstr(X2,^[V_1]: X3(V_1)))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(descrp, axiom, descrp <=> 111.90/112.55 (![Xphi:($i > $o)]: (exu(^[Xx]: Xphi(Xx)) => Xphi(descr(^[Xx]: Xphi(Xx)))))). 111.90/112.55 tff('163', plain, 111.90/112.55 descrp = 111.90/112.55 (![X2:($i > $o)]: (exu(^[V_1]: X2(V_1)) => X2(descr(^[V_2]: X2(V_2))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(wellorderingAx, axiom, wellorderingAx <=> 111.90/112.55 (![A]: 111.90/112.55 (?[B]: 111.90/112.55 ((![C]: 111.90/112.55 (((?[Xx]: in(Xx,C)) & (![Xx]: (in(Xx,C) => in(Xx,A)))) => 111.90/112.55 (?[D,Xx]: 111.90/112.55 ((![E]: 111.90/112.55 (in(E,B) => (in(Xx,E) | (![Xy]: (in(Xy,E) => in(Xy,D)))))) & 111.90/112.55 (~(?[Xy]: (in(Xy,C) & in(Xy,D)))) & in(Xx,C) & in(D,B))))) & 111.90/112.55 (![C,D]: 111.90/112.55 ((in(D,B) & in(C,B)) => 111.90/112.55 ((![Xx]: (in(Xx,D) => in(Xx,C))) | 111.90/112.55 (![Xx]: (in(Xx,C) => in(Xx,D)))))) & 111.90/112.55 (![Xx,Xy]: 111.90/112.55 ((in(Xy,A) & in(Xx,A)) => 111.90/112.55 ((![C]: (in(C,B) => (in(Xx,C) <=> in(Xy,C)))) => (Xx = Xy)))) & 111.90/112.55 (![C]: (in(C,B) => (![Xx]: (in(Xx,C) => in(Xx,A))))))))). 111.90/112.55 tff('164', plain, 111.90/112.55 wellorderingAx = 111.90/112.55 (![X2]: 111.90/112.55 (?[X3]: 111.90/112.55 ((![X4]: 111.90/112.55 (((?[X5]: in(X5,X4)) & (![X6]: (in(X6,X4) => in(X6,X2)))) => 111.90/112.55 (?[X7,X8]: 111.90/112.55 ((![X9]: 111.90/112.55 (in(X9,X3) => 111.90/112.55 (in(X8,X9) | (![X10]: (in(X10,X9) => in(X10,X7)))))) & 111.90/112.55 (~(?[X11]: (in(X11,X4) & in(X11,X7)))) & in(X8,X4) & 111.90/112.55 in(X7,X3))))) & 111.90/112.55 (![X12,X13]: 111.90/112.55 ((in(X13,X3) & in(X12,X3)) => 111.90/112.55 ((![X14]: (in(X14,X13) => in(X14,X12))) | 111.90/112.55 (![X15]: (in(X15,X12) => in(X15,X13)))))) & 111.90/112.55 (![X16,X17]: 111.90/112.55 ((in(X17,X2) & in(X16,X2)) => 111.90/112.55 ((![X18]: (in(X18,X3) => (in(X16,X18) <=> in(X17,X18)))) => 111.90/112.55 (X16 = X17)))) & 111.90/112.55 (![X19]: (in(X19,X3) => (![X20]: (in(X20,X19) => in(X20,X2)))))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(foundationAx, axiom, foundationAx <=> 111.90/112.55 (![A]: 111.90/112.55 ((?[Xx]: in(Xx,A)) => 111.90/112.55 (?[B]: ((~(?[Xx]: (in(Xx,A) & in(Xx,B)))) & in(B,A)))))). 111.90/112.55 tff('165', plain, 111.90/112.55 foundationAx = 111.90/112.55 (![X2]: 111.90/112.55 ((?[X3]: in(X3,X2)) => 111.90/112.55 (?[X4]: ((~(?[X5]: (in(X5,X2) & in(X5,X4)))) & in(X4,X2))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(replAx, axiom, replAx <=> 111.90/112.55 (![Xphi:(($i * $i) > $o),A]: 111.90/112.55 ((![Xx]: (in(Xx,A) => exu(^[Xy]: Xphi(Xx,Xy)))) => 111.90/112.55 (?[B]: (![Xx]: (in(Xx,B) <=> (?[Xy]: (Xphi(Xy,Xx) & in(Xy,A))))))))). 111.90/112.55 tff('166', plain, 111.90/112.55 replAx = 111.90/112.55 (![X2:(($i * $i) > $o),X3]: 111.90/112.55 ((![X4]: (in(X4,X3) => exu(^[V_1]: X2(X4,V_1)))) => 111.90/112.55 (?[X5]: (![X6]: (in(X6,X5) <=> (?[X7]: (X2(X7,X6) & in(X7,X3)))))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(omegaIndAx, axiom, omegaIndAx <=> 111.90/112.55 (![A]: 111.90/112.55 (((![Xx]: ((in(Xx,A) & in(Xx,omega)) => in(setadjoin(Xx,Xx),A))) & 111.90/112.55 in(emptyset,A)) => 111.90/112.55 (![Xx]: (in(Xx,omega) => in(Xx,A)))))). 111.90/112.55 tff('167', plain, 111.90/112.55 omegaIndAx = 111.90/112.55 (![X2]: 111.90/112.55 (((![X3]: ((in(X3,X2) & in(X3,omega)) => in(setadjoin(X3,X3),X2))) & 111.90/112.55 in(emptyset,X2)) => 111.90/112.55 (![X4]: (in(X4,omega) => in(X4,X2))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(omegaSAx, axiom, omegaSAx <=> 111.90/112.55 (![Xx]: (in(Xx,omega) => in(setadjoin(Xx,Xx),omega)))). 111.90/112.55 tff('168', plain, 111.90/112.55 omegaSAx = (![X2]: (in(X2,omega) => in(setadjoin(X2,X2),omega))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(omega0Ax, axiom, omega0Ax() = in(emptyset,omega)). 111.90/112.55 tff('169', plain, omega0Ax = in(emptyset,omega), define([status(thm)])). 111.90/112.55 tff(setunionAx, axiom, setunionAx <=> 111.90/112.55 (![A,Xx]: (in(Xx,setunion(A)) <=> (?[B]: (in(B,A) & in(Xx,B)))))). 111.90/112.55 tff('170', plain, 111.90/112.55 setunionAx = 111.90/112.55 (![X2,X3]: (in(X3,setunion(X2)) <=> (?[X4]: (in(X4,X2) & in(X3,X4))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(powersetAx, axiom, powersetAx <=> 111.90/112.55 (![A,B]: (in(B,powerset(A)) <=> (![Xx]: (in(Xx,B) => in(Xx,A)))))). 111.90/112.55 tff('171', plain, 111.90/112.55 powersetAx = 111.90/112.55 (![X2,X3]: (in(X3,powerset(X2)) <=> (![X4]: (in(X4,X3) => in(X4,X2))))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(setadjoinAx, axiom, setadjoinAx <=> 111.90/112.55 (![Xx,A,Xy]: (in(Xy,setadjoin(Xx,A)) <=> (in(Xy,A) | (Xy = Xx))))). 111.90/112.55 tff('172', plain, 111.90/112.55 setadjoinAx = 111.90/112.55 (![X2,X3,X4]: (in(X4,setadjoin(X2,X3)) <=> (in(X4,X3) | (X4 = X2)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(emptysetAx, axiom, emptysetAx <=> (![Xx]: (~in(Xx,emptyset)))). 111.90/112.55 tff('173', plain, emptysetAx = (![X2]: (~in(X2,emptyset))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(setextAx, axiom, setextAx <=> 111.90/112.55 (![A,B]: ((![Xx]: (in(Xx,A) <=> in(Xx,B))) => (A = B)))). 111.90/112.55 tff('174', plain, 111.90/112.55 setextAx = (![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(exu, axiom, exu() = 111.90/112.55 ^[Xphi:($i > $o)]: (?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx)))). 111.90/112.55 tff('175', plain, 111.90/112.55 exu = 111.90/112.55 (^[V_1:($i > $o)]: (?[X2]: ((![X3]: (V_1(X3) => (X2 = X3))) & V_1(X2)))), 111.90/112.55 define([status(thm)])). 111.90/112.55 tff(setukpairinjR, conjecture, 111.90/112.55 (setextAx => 111.90/112.55 (emptysetAx => 111.90/112.55 (setadjoinAx => 111.90/112.55 (powersetAx => 111.90/112.55 (setunionAx => 111.90/112.55 (omega0Ax => 111.90/112.55 (omegaSAx => 111.90/112.55 (omegaIndAx => 111.90/112.55 (replAx => 111.90/112.55 (foundationAx => 111.90/112.55 (wellorderingAx => 111.90/112.55 (descrp => 111.90/112.55 (dsetconstrI => 111.90/112.55 (dsetconstrEL => 111.90/112.55 (dsetconstrER => 111.90/112.55 (exuE1 => 111.90/112.55 (prop2setE => 111.90/112.55 (emptysetE => 111.90/112.55 (emptysetimpfalse => 111.90/112.55 (notinemptyset => 111.90/112.55 (exuE3e => 111.90/112.55 (setext => 111.90/112.55 (emptyI => 111.90/112.55 (noeltsimpempty => 111.90/112.55 (setbeta => 111.90/112.55 (nonemptyE1 => 111.90/112.55 (nonemptyI => 111.90/112.55 (nonemptyI1 => 111.90/112.55 (setadjoinIL => 111.90/112.55 (emptyinunitempty => 111.90/112.55 (setadjoinIR => 111.90/112.55 (setadjoinE => 111.90/112.55 (setadjoinOr => 111.90/112.55 (setoftrueEq => 111.90/112.55 (powersetI => 111.90/112.55 (emptyinPowerset => 111.90/112.55 (emptyInPowerset => 111.90/112.55 (powersetE => 111.90/112.55 (setunionI => 111.90/112.55 (setunionE => 111.90/112.55 (subPowSU => 111.90/112.55 (exuE2 => 111.90/112.55 (nonemptyImpWitness => 111.90/112.55 (uniqinunit => 111.90/112.55 (notinsingleton => 111.90/112.55 (eqinunit => 111.90/112.55 (singletonsswitch => 111.90/112.55 (upairsetE => 111.90/112.55 (upairsetIL => 111.90/112.55 (upairsetIR => 111.90/112.55 (emptyE1 => 111.90/112.55 (vacuousDall => 111.90/112.55 (quantDeMorgan1 => 111.90/112.55 (quantDeMorgan2 => 111.90/112.55 (quantDeMorgan3 => 111.90/112.55 (quantDeMorgan4 => 111.90/112.55 (prop2setI => 111.90/112.55 (prop2set2propI => 111.90/112.55 (notdexE => 111.90/112.55 (notdallE => 111.90/112.55 (exuI1 => 111.90/112.55 (exuI3 => 111.90/112.55 (exuI2 => 111.90/112.55 (inCongP => 111.90/112.55 (in__Cong => 111.90/112.55 (exuE3u => 111.90/112.55 ( 111.90/112.55 exu__Cong => 111.90/112.55 ( 111.90/112.55 emptyset__Cong => 111.90/112.55 ( 111.90/112.55 setadjoin__Cong => 111.90/112.55 ( 111.90/112.55 powerset__Cong => 111.90/112.55 ( 111.90/112.55 setunion__Cong => 111.90/112.55 ( 111.90/112.55 omega__Cong => 111.90/112.55 ( 111.90/112.55 exuEu => 111.90/112.55 ( 111.90/112.55 descr__Cong => 111.90/112.55 ( 111.90/112.55 dsetconstr__Cong => 111.90/112.55 ( 111.90/112.55 subsetI1 => 111.90/112.55 ( 111.90/112.55 eqimpsubset2 => 111.90/112.55 ( 111.90/112.55 eqimpsubset1 => 111.90/112.55 ( 111.90/112.55 subsetI2 => 111.90/112.55 ( 111.90/112.55 emptysetsubset => 111.90/112.55 ( 111.90/112.55 subsetE => 111.90/112.55 ( 111.90/112.55 subsetE2 => 111.90/112.55 ( 111.90/112.55 notsubsetI => 111.90/112.55 ( 111.90/112.55 notequalI1 => 111.90/112.55 ( 111.90/112.55 notequalI2 => 111.90/112.55 ( 111.90/112.55 subsetRefl => 111.90/112.55 ( 111.90/112.55 subsetTrans => 111.90/112.55 ( 111.90/112.55 setadjoinSub => 111.90/112.55 ( 111.90/112.55 setadjoinSub2 => 111.90/112.55 ( 111.90/112.55 subset2powerset => 111.90/112.55 ( 111.90/112.55 setextsub => 111.90/112.55 ( 111.90/112.55 subsetemptysetimpeq => 111.90/112.55 ( 111.90/112.55 powersetI1 => 111.90/112.55 ( 111.90/112.55 powersetE1 => 111.90/112.55 ( 111.90/112.55 inPowerset => 111.90/112.55 ( 111.90/112.55 powersetsubset => 111.90/112.55 ( 111.90/112.55 sepInPowerset => 111.90/112.55 ( 111.90/112.55 sepSubset => 111.90/112.55 ( 111.90/112.55 binunionIL => 111.90/112.55 ( 111.90/112.55 upairset2IR => 111.90/112.55 ( 111.90/112.55 binunionIR => 111.90/112.55 ( 111.90/112.55 binunionEcases => 111.90/112.55 ( 111.90/112.55 binunionE => 111.90/112.55 ( 111.90/112.55 binunionLsub => 111.90/112.55 ( 111.90/112.55 binunionRsub => 111.90/112.55 ( 111.90/112.55 binintersectI => 111.90/112.55 ( 111.90/112.55 binintersectSubset5 => 111.90/112.55 ( 111.90/112.55 binintersectEL => 111.90/112.55 ( 111.90/112.55 binintersectLsub => 111.90/112.55 ( 111.90/112.55 binintersectSubset2 => 111.90/112.55 ( 111.90/112.55 binintersectSubset3 => 111.90/112.55 ( 111.90/112.55 binintersectER => 111.90/112.55 ( 111.90/112.55 disjointsetsI1 => 111.90/112.55 ( 111.90/112.55 binintersectRsub => 111.90/112.55 ( 111.90/112.55 binintersectSubset4 => 111.90/112.55 ( 111.90/112.55 binintersectSubset1 => 111.90/112.55 ( 111.90/112.55 bs114d => 111.90/112.55 ( 111.90/112.55 setminusI => 111.90/112.55 ( 111.90/112.55 setminusEL => 111.90/112.55 ( 111.90/112.55 setminusER => 111.90/112.55 ( 111.90/112.55 setminusSubset2 => 111.90/112.55 ( 111.90/112.55 setminusERneg => 111.90/112.55 ( 111.90/112.55 setminusELneg => 111.90/112.55 ( 111.90/112.55 setminusILneg => 111.90/112.55 ( 111.90/112.55 setminusIRneg => 111.90/112.55 ( 111.90/112.55 setminusLsub => 111.90/112.55 ( 111.90/112.55 setminusSubset1 => 111.90/112.55 ( 111.90/112.55 symdiffE => 111.90/112.55 ( 111.90/112.55 symdiffI1 => 111.90/112.55 ( 111.90/112.55 symdiffI2 => 111.90/112.55 ( 111.90/112.55 symdiffIneg1 => 111.90/112.55 ( 111.90/112.55 symdiffIneg2 => 111.90/112.55 ( 111.90/112.55 secondinupair => 111.90/112.55 ( 111.90/112.55 setukpairIL => 111.90/112.55 ( 111.90/112.55 setukpairIR => 111.90/112.55 ( 111.90/112.55 kpairiskpair => 111.90/112.55 ( 111.90/112.55 kpairp => 111.90/112.55 ( 111.90/112.55 singletonsubset => 111.90/112.55 ( 111.90/112.55 singletoninpowerset => 111.90/112.55 ( 111.90/112.55 singletoninpowunion => 111.90/112.55 ( 111.90/112.55 upairset2E => 111.90/112.55 ( 111.90/112.55 upairsubunion => 111.90/112.55 ( 111.90/112.55 upairinpowunion => 111.90/112.55 ( 111.90/112.55 ubforcartprodlem1 => 111.90/112.55 ( 111.90/112.55 ubforcartprodlem2 => 111.90/112.55 ( 111.90/112.55 ubforcartprodlem3 => 111.90/112.55 ( 111.90/112.55 cartprodpairin => 111.90/112.55 ( 111.90/112.55 cartprodmempair1 => 111.90/112.55 ( 111.90/112.55 cartprodmempair => 111.90/112.55 ( 111.90/112.55 setunionE2 => 111.90/112.55 ( 111.90/112.55 setunionsingleton1 => 111.90/112.55 ( 111.90/112.55 setunionsingleton2 => 111.90/112.55 ( 111.90/112.55 setunionsingleton => 111.90/112.55 ( 111.90/112.55 singletonprop => 111.90/112.55 ( 111.90/112.55 ex1E1 => 111.90/112.55 ( 111.90/112.55 ex1I => 111.90/112.55 ( 111.90/112.55 ex1I2 => 111.90/112.55 ( 111.90/112.55 singletonsuniq => 111.90/112.55 ( 111.90/112.55 setukpairinjL1 => 111.90/112.55 ( 111.90/112.55 kfstsingleton => 111.90/112.55 ( 111.90/112.55 theprop => 111.90/112.55 ( 111.90/112.55 kfstpairEq => 111.90/112.55 ( 111.90/112.55 cartprodfstin => 111.90/112.55 ( 111.90/112.55 setukpairinjL2 => 111.90/112.55 ( 111.90/112.55 setukpairinjL => 111.90/112.55 ( 111.90/112.55 setukpairinjR11 => 111.90/112.55 ( 111.90/112.55 setukpairinjR12 => 111.90/112.55 ( 111.90/112.55 setukpairinjR1 => 111.90/112.55 ( 111.90/112.55 upairequniteq => 111.90/112.55 ( 111.90/112.55 setukpairinjR2 => 111.90/112.55 ( 111.90/112.55 ![Xx,Xy, 111.90/112.55 Xz,Xu]: 111.90/112.55 (( 111.90/112.55 kpair( 111.90/112.55 Xx,Xy) = 111.90/112.55 kpair( 111.90/112.55 Xz,Xu)) => 111.90/112.55 (Xy = Xu)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 111.90/112.55 tff(zf_stmt_0, conjecture, 111.90/112.55 ((![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))) => 111.90/112.55 ((![X5]: (~in(X5,emptyset))) => 111.90/112.55 ((![X6,X7,X8]: (in(X8,setadjoin(X6,X7)) <=> ((X8 = X6) | in(X8,X7)))) => 111.90/112.55 ((![X9,X10]: 111.90/112.55 (in(X10,powerset(X9)) <=> (![X11]: (in(X11,X10) => in(X11,X9))))) => 111.90/112.55 ((![X12,X13]: 111.90/112.55 (in(X13,setunion(X12)) <=> (?[X14]: (in(X13,X14) & in(X14,X12))))) => 111.90/112.55 (in(emptyset,omega) => 111.90/112.55 ((![X15]: (in(X15,omega) => in(setadjoin(X15,X15),omega))) => 111.90/112.55 ((![X16]: 111.90/112.55 ((in(emptyset,X16) & 111.90/112.55 (![X17]: 111.90/112.55 ((in(X17,omega) & in(X17,X16)) => 111.90/112.55 in(setadjoin(X17,X17),X16)))) => 111.90/112.55 (![X18]: (in(X18,omega) => in(X18,X16))))) => 111.90/112.55 ((![X19:(($i * $i) > $o),X20]: 111.90/112.55 ((![X21]: 111.90/112.55 (in(X21,X20) => 111.90/112.55 (?[X22]: 111.90/112.55 (X19(X21,X22) & (![X23]: (X19(X21,X23) => (X22 = X23))))))) => 111.90/112.55 (?[X24]: 111.90/112.55 (![X25]: 111.90/112.55 (in(X25,X24) <=> (?[X26]: (in(X26,X20) & X19(X26,X25)))))))) => 111.90/112.55 ((![X27]: 111.90/112.55 ((?[X28]: in(X28,X27)) => 111.90/112.55 (?[X29]: 111.90/112.55 (in(X29,X27) & (~(?[X30]: (in(X30,X29) & in(X30,X27)))))))) => 111.90/112.55 ((![X31]: 111.90/112.55 (?[X32]: 111.90/112.55 ((![X48]: 111.90/112.55 (in(X48,X32) => (![X49]: (in(X49,X48) => in(X49,X31))))) & 111.90/112.55 (![X45,X46]: 111.90/112.55 ((in(X45,X31) & in(X46,X31)) => 111.90/112.55 ((![X47]: 111.90/112.55 (in(X47,X32) => (in(X45,X47) <=> in(X46,X47)))) => 111.90/112.55 (X45 = X46)))) & 111.90/112.55 (![X41,X42]: 111.90/112.55 ((in(X41,X32) & in(X42,X32)) => 111.90/112.55 ((![X44]: (in(X44,X41) => in(X44,X42))) | 111.90/112.55 (![X43]: (in(X43,X42) => in(X43,X41)))))) & 111.90/112.55 (![X33]: 111.90/112.55 (((![X35]: (in(X35,X33) => in(X35,X31))) & 111.90/112.55 (?[X34]: in(X34,X33))) => 111.90/112.55 (?[X36,X37]: 111.90/112.55 (in(X36,X32) & in(X37,X33) & 111.90/112.55 (~(?[X40]: (in(X40,X36) & in(X40,X33)))) & 111.90/112.55 (![X38]: 111.90/112.55 (in(X38,X32) => 111.90/112.55 ((![X39]: (in(X39,X38) => in(X39,X36))) | 111.90/112.55 in(X37,X38))))))))))) => 111.90/112.55 ((![X50:($i > $o)]: 111.90/112.55 ((?[X51]: (X50(X51) & (![X52]: (X50(X52) => (X51 = X52))))) => 111.90/112.55 X50(descr('#ll_1'(X50))))) => 111.90/112.55 ((![X53,X54:($i > $o),X55]: 111.90/112.55 (in(X55,X53) => 111.90/112.55 (X54(X55) => in(X55,dsetconstr(X53,'#ll_1'(X54)))))) => 111.90/112.55 ((![X56,X57:($i > $o),X58]: 111.90/112.55 (in(X58,dsetconstr(X56,'#ll_1'(X57))) => in(X58,X56))) => 111.90/112.55 ((![X59,X60:($i > $o),X61]: 111.90/112.55 (in(X61,dsetconstr(X59,'#ll_1'(X60))) => X60(X61))) => 111.90/112.55 ((![X62:($i > $o)]: 111.90/112.55 ((?[X63]: 111.90/112.55 (X62(X63) & (![X64]: (X62(X64) => (X63 = X64))))) => 111.90/112.55 (?[X65]: 111.90/112.55 (X62(X65) & (![X66]: (X62(X66) => (X65 = X66))))))) => 111.90/112.55 ((![X67:$o,X68]: (in(X68,prop2set(X67)) => X67)) => 111.90/112.55 ((![X69]: (in(X69,emptyset) => (![X70:$o]: X70))) => 111.90/112.55 ((![X71]: (in(X71,emptyset) => $false)) => 111.90/112.55 ((![X72]: (~in(X72,emptyset))) => 111.90/112.55 ((![X73:($i > $o)]: 111.90/112.55 ((?[X74]: 111.90/112.55 (X73(X74) & (![X75]: (X73(X75) => (X74 = X75))))) => 111.90/112.55 (?[X76]: X73(X76)))) => 111.90/112.55 ((![X77,X78]: 111.90/112.55 ((![X79]: (in(X79,X77) => in(X79,X78))) => 111.90/112.55 ((![X80]: (in(X80,X78) => in(X80,X77))) => 111.90/112.55 (X77 = X78)))) => 111.90/112.55 ((![X81]: 111.90/112.55 ((![X82]: (~in(X82,X81))) => (X81 = emptyset))) => 111.90/112.55 ((![X83]: 111.90/112.55 ((![X84]: (~in(X84,X83))) => (X83 = emptyset))) => 111.90/112.55 ((![X85,X86:($i > $o),X87]: 111.90/112.55 (in(X87,X85) => 111.90/112.55 (in(X87,dsetconstr(X85,'#ll_1'(X86))) <=> 111.90/112.55 X86(X87)))) => 111.90/112.55 ((![X88]: 111.90/112.55 ((X88 != emptyset) => (?[X89]: in(X89,X88)))) => 111.90/112.55 ((![X90,X91:($i > $o),X92]: 111.90/112.55 (in(X92,X90) => 111.90/112.55 (X91(X92) => 111.90/112.55 (dsetconstr(X90,'#ll_1'(X91)) != emptyset)))) => 111.90/112.55 ((![X93]: 111.90/112.55 ((?[X94]: in(X94,X93)) => (X93 != emptyset))) => 111.90/112.55 ((![X95,X96]: in(X95,setadjoin(X95,X96))) => 111.90/112.55 (in(emptyset,setadjoin(emptyset,emptyset)) => 111.90/112.55 ((![X97,X98,X99]: 111.90/112.55 (in(X99,X98) => 111.90/112.55 in(X99,setadjoin(X97,X98)))) => 111.90/112.55 ((![X100,X101,X102]: 111.90/112.55 (in(X102,setadjoin(X100,X101)) => 111.90/112.55 (![X103:$o]: 111.90/112.55 (((X102 = X100) => X103) => 111.90/112.55 ((in(X102,X101) => X103) => X103))))) => 111.90/112.55 ((![X104,X105,X106]: 111.90/112.55 (in(X106,setadjoin(X104,X105)) => 111.90/112.55 ((X106 = X104) | in(X106,X105)))) => 111.90/112.55 ((![X107]: 111.90/112.55 (dsetconstr(X107,'#ll_2') = X107)) => 111.90/112.55 ((![X108,X109]: 111.90/112.55 ((![X110]: 111.90/112.55 (in(X110,X109) => in(X110,X108))) => 111.90/112.55 in(X109,powerset(X108)))) => 111.90/112.55 ((![X111]: in(emptyset,powerset(X111))) => 111.90/112.55 ((![X112]: in(emptyset,powerset(X112))) => 111.90/112.55 ((![X113,X114,X115]: 111.90/112.55 (in(X114,powerset(X113)) => 111.90/112.55 (in(X115,X114) => in(X115,X113)))) => 111.90/112.55 ((![X116,X117,X118]: 111.90/112.55 (in(X117,X118) => 111.90/112.55 (in(X118,X116) => 111.90/112.55 in(X117,setunion(X116))))) => 111.90/112.55 ((![X119,X120]: 111.90/112.55 (in(X120,setunion(X119)) => 111.90/112.55 (![X121:$o]: 111.90/112.55 ((![X122]: 111.90/112.55 (in(X120,X122) => 111.90/112.55 (in(X122,X119) => X121))) => 111.90/112.55 X121)))) => 111.90/112.55 ((![X123,X124]: 111.90/112.55 (in(X124,X123) => 111.90/112.55 in(X124, 111.90/112.55 powerset(setunion(X123))))) => 111.90/112.55 ((![X125:($i > $o)]: 111.90/112.55 ((?[X126]: 111.90/112.55 (X125(X126) & 111.90/112.55 (![X127]: 111.90/112.55 (X125(X127) => 111.90/112.55 (X126 = X127))))) => 111.90/112.55 (?[X128]: 111.90/112.55 (![X129]: 111.90/112.55 (X125(X129) <=> 111.90/112.55 (X129 = X128)))))) => 111.90/112.55 ((![X130]: 111.90/112.55 ((X130 != emptyset) => 111.90/112.55 (?[X131]: in(X131,X130)))) => 111.90/112.55 ((![X132,X133]: 111.90/112.55 (in(X132, 111.90/112.55 setadjoin(X133,emptyset)) => 111.90/112.55 (X132 = X133))) => 111.90/112.55 ((![X134,X135]: 111.90/112.55 ((X134 != X135) => 111.90/112.55 (~ 111.90/112.55 in(X135, 111.90/112.55 setadjoin(X134, 111.90/112.55 emptyset))))) => 111.90/112.55 ((![X136,X137]: 111.90/112.55 ((X136 = X137) => 111.90/112.55 in(X136, 111.90/112.55 setadjoin(X137, 111.90/112.55 emptyset)))) => 111.90/112.55 ((![X138,X139]: 111.90/112.55 (in(X138, 111.90/112.55 setadjoin(X139, 111.90/112.55 emptyset)) => 111.90/112.55 in(X139, 111.90/112.55 setadjoin(X138, 111.90/112.55 emptyset)))) => 111.90/112.55 ((![X140,X141,X142]: 111.90/112.55 (in(X142, 111.90/112.55 setadjoin(X140, 111.90/112.55 setadjoin( 111.90/112.55 X141, 111.90/112.55 emptyset))) => 111.90/112.55 ((X142 = X140) | 111.90/112.55 (X142 = X141)))) => 111.90/112.55 ((![X143,X144]: 111.90/112.55 in(X143, 111.90/112.55 setadjoin(X143, 111.90/112.55 setadjoin( 111.90/112.55 X144, 111.90/112.55 emptyset)))) => 111.90/112.55 ((![X145,X146]: 111.90/112.55 in(X146, 111.90/112.55 setadjoin(X145, 111.90/112.55 setadjoin( 111.90/112.55 X146, 111.90/112.55 emptyset)))) => 111.90/112.55 ((![X147,X148:($i > $o)]: 111.90/112.55 ((?[X149]: 111.90/112.55 (in(X149,X147) & 111.90/112.55 X148(X149))) => 111.90/112.55 ((dsetconstr( 111.90/112.55 X147,'#ll_1'(X148)) = 111.90/112.55 emptyset) => 111.90/112.55 $false))) => 111.90/112.55 ((![X150:($i > $o),X151]: 111.90/112.55 (in(X151,emptyset) => 111.90/112.55 X150(X151))) => 111.90/112.55 ((![X152,X153:($i > $o)]: 111.90/112.55 ((~ 111.90/112.55 (![X154]: 111.90/112.55 (in(X154,X152) => 111.90/112.55 X153(X154)))) => 111.90/112.55 (?[X155]: 111.90/112.55 (in(X155,X152) & 111.90/112.55 (~X153(X155)))))) => 111.90/112.55 ((![X156, 111.90/112.55 X157:($i > $o)]: 111.90/112.55 ((![X158]: 111.90/112.55 (in(X158,X156) => 111.90/112.55 (~X157(X158)))) => 111.90/112.55 (~ 111.90/112.55 (?[X159]: 111.90/112.55 (in( 111.90/112.55 X159,X156) & 111.90/112.55 X157(X159)))))) => 111.90/112.55 ((![X160, 111.90/112.55 X161:($i > $o)]: 111.90/112.55 ((~ 111.90/112.55 (?[X162]: 111.90/112.55 (in( 111.90/112.55 X162,X160) & 111.90/112.55 X161(X162)))) => 111.90/112.55 (![X163]: 111.90/112.55 (in(X163,X160) => 111.90/112.55 (~X161(X163)))))) => 111.90/112.55 ((![X164, 111.90/112.55 X165:($i > $o)]: 111.90/112.55 ((?[X166]: 111.90/112.55 (in( 111.90/112.55 X166,X164) & 111.90/112.55 (~ 111.90/112.55 X165( 111.90/112.55 X166)))) => 111.90/112.55 (~ 111.90/112.55 (![X167]: 111.90/112.55 (in( 111.90/112.55 X167,X164) => 111.90/112.55 X165( 111.90/112.55 X167)))))) => 111.90/112.55 ((![X168:$o]: 111.90/112.55 (X168 => 111.90/112.55 in(emptyset, 111.90/112.55 prop2set( 111.90/112.55 X168)))) => 111.90/112.55 ((![X169:$o]: 111.90/112.55 (X169 => 111.90/112.55 set2prop( 111.90/112.55 prop2set( 111.90/112.55 X169)))) => 111.90/112.55 ((![X170, 111.90/112.55 X171:( 111.90/112.55 $i > $o)]: 111.90/112.55 ((~ 111.90/112.55 (?[X172]: 111.90/112.55 (in( 111.90/112.55 X172,X170) & 111.90/112.55 X171( 111.90/112.55 X172)))) => 111.90/112.55 (![X173]: 111.90/112.55 ( 111.90/112.55 in( 111.90/112.55 X173,X170) => 111.90/112.55 ( 111.90/112.55 ~ 111.90/112.55 X171( 111.90/112.55 X173)))))) => 111.90/112.55 ((![X174, 111.90/112.55 X175:( 111.90/112.55 $i > $o)]: 111.90/112.55 ((~ 111.90/112.55 ( 111.90/112.55 ![X176]: 111.90/112.55 (in( 111.90/112.55 X176,X174) => 111.90/112.55 X175( 111.90/112.55 X176)))) => 111.90/112.55 (?[X177]: 111.90/112.55 (in( 111.90/112.55 X177,X174) & 111.90/112.55 (~ 111.90/112.55 X175( 111.90/112.55 X177)))))) => 111.90/112.55 ((![X178:( 111.90/112.55 $i > $o)]: 111.90/112.55 ((?[X179]: 111.90/112.55 (X178( 111.90/112.55 X179) & 111.90/112.55 (![X180]: 111.90/112.55 (X178( 111.90/112.55 X180) => 111.90/112.55 (X179 = 111.90/112.55 X180))))) => 111.90/112.55 (?[X181]: 111.90/112.55 (X178( 111.90/112.55 X181) & 111.90/112.55 (![X182]: 111.90/112.55 (X178( 111.90/112.55 X182) => 111.90/112.55 (X181 = 111.90/112.55 X182))))))) => 111.90/112.55 ((![X183:( 111.90/112.55 $i > $o)]: 111.90/112.55 (( 111.90/112.55 ?[X184]: 111.90/112.55 X183( 111.90/112.55 X184)) => 111.90/112.55 ( 111.90/112.55 ( 111.90/112.55 ![X185, 111.90/112.55 X186]: 111.90/112.55 (X183( 111.90/112.55 X185) => 111.90/112.55 (X183( 111.90/112.55 X186) => 111.90/112.55 (X185 = 111.90/112.55 X186)))) => 111.90/112.55 ( 111.90/112.55 ?[X187]: 111.90/112.55 (X183( 111.90/112.55 X187) & 111.90/112.55 (![X188]: 111.90/112.55 (X183( 111.90/112.55 X188) => 111.90/112.55 (X187 = 111.90/112.55 X188)))))))) => 111.90/112.55 ((![X189:( 111.90/112.55 $i > $o)]: 111.90/112.55 ( 111.90/112.55 ( 111.90/112.55 ?[X190]: 111.90/112.55 (![X191]: 111.90/112.55 (X189( 111.90/112.55 X191) <=> 111.90/112.55 (X191 = 111.90/112.55 X190)))) => 111.90/112.55 ( 111.90/112.55 ?[X192]: 111.90/112.55 (X189( 111.90/112.55 X192) & 111.90/112.55 (![X193]: 111.90/112.55 (X189( 111.90/112.55 X193) => 111.90/112.55 (X192 = 111.90/112.55 X193))))))) => 111.90/112.55 ((![X194, 111.90/112.55 X195]: 111.90/112.55 (( 111.90/112.55 X194 = 111.90/112.55 X195) => 111.90/112.55 (![X196, 111.90/112.55 X197]: 111.90/112.55 (( 111.90/112.55 X196 = 111.90/112.55 X197) => 111.90/112.55 (in( 111.90/112.55 X196,X194) => 111.90/112.55 in( 111.90/112.55 X197,X195)))))) => 111.90/112.55 ((![X198, 111.90/112.55 X199]: 111.90/112.55 (( 111.90/112.55 X198 = 111.90/112.55 X199) => 111.90/112.55 (![X200, 111.90/112.55 X201]: 111.90/112.55 (( 111.90/112.55 X200 = 111.90/112.55 X201) => 111.90/112.55 (in( 111.90/112.55 X200,X198) <=> 111.90/112.55 in( 111.90/112.55 X201,X199)))))) => 111.90/112.55 (( 111.90/112.55 ![X202:( 111.90/112.55 $i > $o)]: 111.90/112.55 (( 111.90/112.55 ?[X203]: 111.90/112.55 (X202( 111.90/112.55 X203) & 111.90/112.55 (![X204]: 111.90/112.55 (X202( 111.90/112.55 X204) => 111.90/112.55 (X203 = 111.90/112.55 X204))))) => 111.90/112.55 (![X205, 111.90/112.55 X206]: 111.90/112.55 (X202( 111.90/112.55 X205) => 111.90/112.55 (X202( 111.90/112.55 X206) => 111.90/112.55 (X205 = 111.90/112.55 X206)))))) => 111.90/112.55 ( 111.90/112.55 ( 111.90/112.55 ![X207:( 111.90/112.55 $i > $o), 111.90/112.55 X208:( 111.90/112.55 $i > $o)]: 111.90/112.55 (( 111.90/112.55 ![X209, 111.90/112.55 X210]: 111.90/112.55 (( 111.90/112.55 X209 = 111.90/112.55 X210) => 111.90/112.55 (X207( 111.90/112.55 X209) <=> 111.90/112.55 X208( 111.90/112.55 X210)))) => 111.90/112.55 (( 111.90/112.55 ?[X211]: 111.90/112.55 (X207( 111.90/112.55 X211) & 111.90/112.55 (![X212]: 111.90/112.55 (X207( 111.90/112.55 X212) => 111.90/112.55 (X211 = 111.90/112.55 X212))))) <=> 111.90/112.55 (?[X213]: 111.90/112.55 (X208( 111.90/112.55 X213) & 111.90/112.55 (![X214]: 111.90/112.55 (X208( 111.90/112.55 X214) => 111.90/112.55 (X213 = 111.90/112.55 X214)))))))) => 111.90/112.55 ( 111.90/112.55 ( 111.90/112.55 emptyset = 111.90/112.55 emptyset) => 111.90/112.55 ( 111.90/112.55 ( 111.90/112.55 ![X215, 111.90/112.55 X216]: 111.90/112.55 (( 111.90/112.55 X215 = 111.90/112.55 X216) => 111.90/112.55 (![X217, 111.90/112.55 X218]: 111.90/112.55 (( 111.90/112.55 X217 = 111.90/112.55 X218) => 111.90/112.55 (setadjoin( 111.90/112.55 X215,X217) = 111.90/112.55 setadjoin( 111.90/112.55 X216,X218)))))) => 111.90/112.55 ( 111.90/112.55 ( 111.90/112.55 ![X219, 111.90/112.55 X220]: 111.90/112.55 (( 111.90/112.55 X219 = 111.90/112.55 X220) => 111.90/112.55 (powerset( 111.90/112.55 X219) = 111.90/112.55 powerset( 111.90/112.55 X220)))) => 111.90/112.55 ( 111.90/112.55 ( 111.90/112.55 ![X221, 111.90/112.55 X222]: 111.90/112.55 (( 111.90/112.55 X221 = 111.90/112.55 X222) => 111.90/112.55 (setunion( 111.90/112.55 X221) = 111.90/112.55 setunion( 111.90/112.55 X222)))) => 111.90/112.55 ( 111.90/112.55 ( 111.90/112.55 omega = 111.90/112.55 omega) => 111.90/112.55 ( 111.90/112.55 ( 111.90/112.55 ![X223:( 111.90/112.55 $i > $o)]: 111.90/112.55 (( 111.90/112.55 ?[X224]: 111.90/112.55 (X223( 111.90/112.55 X224) & 111.90/112.55 (![X225]: 111.90/112.55 (X223( 111.90/112.55 X225) => 111.90/112.55 (X224 = 111.90/112.55 X225))))) => 111.90/112.55 (![X226, 111.90/112.55 X227]: 111.90/112.55 (X223( 111.90/112.55 X226) => 111.90/112.55 (X223( 111.90/112.55 X227) => 111.90/112.55 (X226 = 111.90/112.55 X227)))))) => 111.90/112.55 ( 111.90/112.55 ( 111.90/112.55 ![X228:( 111.90/112.55 $i > $o), 111.90/112.55 X229:( 111.90/112.55 $i > $o)]: 111.90/112.55 (( 111.90/112.55 ![X230, 111.90/112.55 X231]: 111.90/112.55 (( 111.90/112.55 X230 = 111.90/112.55 X231) => 111.90/112.55 (X228( 111.90/112.55 X230) <=> 111.90/112.55 X229( 111.90/112.55 X231)))) => 111.90/112.55 (( 111.90/112.55 ?[X232]: 111.90/112.55 (X228( 111.90/112.55 X232) & 111.90/112.55 (![X233]: 111.90/112.55 (X228( 111.90/112.55 X233) => 111.90/112.55 (X232 = 111.90/112.55 X233))))) => 111.90/112.55 (( 111.90/112.55 ?[X234]: 111.90/112.55 (X229( 111.90/112.55 X234) & 111.90/112.55 (![X235]: 111.90/112.55 (X229( 111.90/112.55 X235) => 111.90/112.55 (X234 = 111.90/112.55 X235))))) => 111.90/112.55 (descr( 111.90/112.55 '#ll_1'( 111.90/112.55 X228)) = 111.90/112.55 descr( 111.90/112.55 '#ll_1'( 111.90/112.55 X229))))))) => 111.90/112.55 ( 111.90/112.55 ( 111.90/112.55 ![X236, 111.90/112.55 X237]: 111.90/112.55 (( 111.90/112.55 X236 = 111.90/112.55 X237) => 111.90/112.55 (![X238:( 111.90/112.55 $i > $o), 111.90/112.55 X239:( 111.90/112.55 $i > $o)]: 111.90/112.55 (( 111.90/112.55 ![X240]: 111.90/112.55 (in( 111.90/112.55 X240,X236) => 111.90/112.55 (![X241]: 111.90/112.55 (in( 111.90/112.55 X241,X237) => 111.90/112.55 (( 111.90/112.55 X240 = 111.90/112.55 X241) => 111.90/112.55 (X238( 111.90/112.55 X240) <=> 111.90/112.55 X239( 111.90/112.55 X241))))))) => 111.90/112.55 (dsetconstr( 111.90/112.55 X236, 111.90/112.55 '#ll_1'( 111.90/112.55 X238)) = 111.90/112.55 dsetconstr( 111.90/112.55 X237, 111.90/112.55 '#ll_1'( 111.90/112.55 X239))))))) => 111.90/112.55 ( 111.90/112.55 ( 111.90/112.55 ![X242, 111.90/112.55 X243]: 111.90/112.55 (( 111.90/112.55 ![X244]: 111.90/112.55 (in( 111.90/112.55 X244,X242) => 111.90/112.55 in( 111.90/112.55 X244,X243))) => 111.90/112.55 subset( 111.90/112.55 X242,X243))) => 111.90/112.55 ( 111.90/112.55 ( 111.90/112.55 ![X245, 111.90/112.55 X246]: 111.90/112.55 (( 111.90/112.55 X245 = 111.90/112.55 X246) => 111.90/112.55 subset( 111.90/112.55 X246,X245))) => 111.90/112.55 ( 111.90/112.55 ( 111.90/112.55 ![X247, 111.90/112.55 X248]: 111.90/112.55 (( 111.90/112.55 X247 = 111.90/112.55 X248) => 111.90/112.55 subset( 111.90/112.55 X247,X248))) => 111.90/112.55 ( 111.90/112.55 ( 111.90/112.55 ![X249, 111.90/112.55 X250]: 111.90/112.55 (( 111.90/112.55 ![X251]: 111.90/112.55 (in( 111.90/112.55 X251,X249) => 111.90/112.55 in( 111.90/112.55 X251,X250))) => 111.90/112.55 subset( 111.90/112.55 X249,X250))) => 111.90/112.55 ( 111.90/112.55 ( 111.90/112.55 ![X252]: 111.90/112.55 subset( 111.90/112.55 emptyset, 111.90/112.55 X252)) => 111.90/112.55 ( 111.90/112.55 ( 111.90/112.55 ![X253, 111.90/112.55 X254,X255]: 111.90/112.55 (subset( 111.90/112.55 X253,X254) => 111.90/112.55 (in( 111.90/112.55 X255,X253) => 111.90/112.55 in( 111.90/112.55 X255,X254)))) => 111.90/112.55 ( 111.90/112.55 ( 111.90/112.55 ![X256, 111.90/112.55 X257,X258]: 111.90/112.55 (subset( 111.90/112.55 X256,X257) => 111.90/112.55 (( 111.90/112.55 ~ 111.90/112.55 in( 111.90/112.55 X258,X257)) => 111.90/112.55 (~ 111.90/112.55 in( 111.90/112.55 X258,X256))))) => 111.90/112.55 ( 111.90/112.55 ( 111.90/112.55 ![X259, 111.90/112.55 X260,X261]: 111.90/112.55 (in( 111.90/112.55 X261,X259) => 111.90/112.55 (( 111.90/112.55 ~ 111.90/112.55 in( 111.90/112.55 X261,X260)) => 111.90/112.55 (~ 111.90/112.55 subset( 111.90/112.55 X259,X260))))) => 111.90/112.55 ( 111.90/112.55 ( 111.90/112.55 ![X262, 111.90/112.55 X263]: 111.90/112.55 (( 111.90/112.55 ~ 111.90/112.55 subset( 111.90/112.55 X262,X263)) => 111.90/112.55 (X262 != 111.90/112.55 X263))) => 111.90/112.55 ( 111.90/112.55 ( 111.90/112.55 ![X264, 111.90/112.55 X265,X266]: 111.90/112.55 (in( 111.90/112.55 X266,X264) => 111.90/112.55 (( 111.90/112.55 ~ 111.90/112.55 in( 111.90/112.55 X266,X265)) => 111.90/112.55 (X264 != 111.90/112.55 X265)))) => 111.90/112.55 ( 111.90/112.55 ( 111.90/112.55 ![X267]: 111.90/112.55 subset( 111.90/112.55 X267,X267)) => 111.90/112.55 ( 111.90/112.55 ( 111.90/112.55 ![X268, 111.90/112.55 X269,X270]: 111.90/112.55 (subset( 111.90/112.55 X268,X269) => 111.90/112.55 (subset( 111.90/112.55 X269,X270) => 111.90/112.55 subset( 111.90/112.55 X268,X270)))) => 111.90/112.55 ( 111.90/112.55 ( 111.90/112.55 ![X271, 111.90/112.55 X272]: 111.90/112.55 subset( 111.90/112.55 X272, 111.90/112.56 setadjoin( 111.90/112.56 X271,X272))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X273, 111.90/112.56 X274,X275]: 111.90/112.56 (subset( 111.90/112.56 X273,X275) => 111.90/112.56 subset( 111.90/112.56 X273, 111.90/112.56 setadjoin( 111.90/112.56 X274,X275)))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X276, 111.90/112.56 X277]: 111.90/112.56 (subset( 111.90/112.56 X276,X277) => 111.90/112.56 in( 111.90/112.56 X276, 111.90/112.56 powerset( 111.90/112.56 X277)))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X278, 111.90/112.56 X279]: 111.90/112.56 (subset( 111.90/112.56 X278,X279) => 111.90/112.56 (subset( 111.90/112.56 X279,X278) => 111.90/112.56 (X278 = 111.90/112.56 X279)))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X280]: 111.90/112.56 (subset( 111.90/112.56 X280, 111.90/112.56 emptyset) => 111.90/112.56 (X280 = 111.90/112.56 emptyset))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X281, 111.90/112.56 X282]: 111.90/112.56 (subset( 111.90/112.56 X282,X281) => 111.90/112.56 in( 111.90/112.56 X282, 111.90/112.56 powerset( 111.90/112.56 X281)))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X283, 111.90/112.56 X284]: 111.90/112.56 (in( 111.90/112.56 X284, 111.90/112.56 powerset( 111.90/112.56 X283)) => 111.90/112.56 subset( 111.90/112.56 X284,X283))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X285]: 111.90/112.56 in( 111.90/112.56 X285, 111.90/112.56 powerset( 111.90/112.56 X285))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X286, 111.90/112.56 X287]: 111.90/112.56 (subset( 111.90/112.56 X286,X287) => 111.90/112.56 subset( 111.90/112.56 powerset( 111.90/112.56 X286), 111.90/112.56 powerset( 111.90/112.56 X287)))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X288, 111.90/112.56 X289:( 111.90/112.56 $i > $o)]: 111.90/112.56 in( 111.90/112.56 dsetconstr( 111.90/112.56 X288, 111.90/112.56 '#ll_1'( 111.90/112.56 X289)), 111.90/112.56 powerset( 111.90/112.56 X288))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X290, 111.90/112.56 X291:( 111.90/112.56 $i > $o)]: 111.90/112.56 subset( 111.90/112.56 dsetconstr( 111.90/112.56 X290, 111.90/112.56 '#ll_1'( 111.90/112.56 X291)), 111.90/112.56 X290)) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X292, 111.90/112.56 X293,X294]: 111.90/112.56 (in( 111.90/112.56 X294,X292) => 111.90/112.56 in( 111.90/112.56 X294, 111.90/112.56 binunion( 111.90/112.56 X292,X293)))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X295, 111.90/112.56 X296]: 111.90/112.56 in( 111.90/112.56 X296, 111.90/112.56 setadjoin( 111.90/112.56 X295, 111.90/112.56 setadjoin( 111.90/112.56 X296, 111.90/112.56 emptyset)))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X297, 111.90/112.56 X298,X299]: 111.90/112.56 (in( 111.90/112.56 X299,X298) => 111.90/112.56 in( 111.90/112.56 X299, 111.90/112.56 binunion( 111.90/112.56 X297,X298)))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X300, 111.90/112.56 X301, 111.90/112.56 X302, 111.90/112.56 X303:$o]: 111.90/112.56 (in( 111.90/112.56 X302, 111.90/112.56 binunion( 111.90/112.56 X300,X301)) => 111.90/112.56 (( 111.90/112.56 in( 111.90/112.56 X302,X300) => 111.90/112.56 X303) => 111.90/112.56 (( 111.90/112.56 in( 111.90/112.56 X302,X301) => 111.90/112.56 X303) => 111.90/112.56 X303)))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X304, 111.90/112.56 X305,X306]: 111.90/112.56 (in( 111.90/112.56 X306, 111.90/112.56 binunion( 111.90/112.56 X304,X305)) => 111.90/112.56 (in( 111.90/112.56 X306,X304) | 111.90/112.56 in( 111.90/112.56 X306,X305)))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X307, 111.90/112.56 X308]: 111.90/112.56 subset( 111.90/112.56 X307, 111.90/112.56 binunion( 111.90/112.56 X307,X308))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X309, 111.90/112.56 X310]: 111.90/112.56 subset( 111.90/112.56 X310, 111.90/112.56 binunion( 111.90/112.56 X309,X310))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X311, 111.90/112.56 X312,X313]: 111.90/112.56 (in( 111.90/112.56 X313,X311) => 111.90/112.56 (in( 111.90/112.56 X313,X312) => 111.90/112.56 in( 111.90/112.56 X313, 111.90/112.56 binintersect( 111.90/112.56 X311,X312))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X314, 111.90/112.56 X315,X316]: 111.90/112.56 (subset( 111.90/112.56 X316,X314) => 111.90/112.56 (subset( 111.90/112.56 X316,X315) => 111.90/112.56 subset( 111.90/112.56 X316, 111.90/112.56 binintersect( 111.90/112.56 X314,X315))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X317, 111.90/112.56 X318,X319]: 111.90/112.56 (in( 111.90/112.56 X319, 111.90/112.56 binintersect( 111.90/112.56 X317,X318)) => 111.90/112.56 in( 111.90/112.56 X319,X317))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X320, 111.90/112.56 X321]: 111.90/112.56 subset( 111.90/112.56 binintersect( 111.90/112.56 X320,X321), 111.90/112.56 X320)) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X322, 111.90/112.56 X323]: 111.90/112.56 (subset( 111.90/112.56 X322,X323) => 111.90/112.56 (binintersect( 111.90/112.56 X322,X323) = 111.90/112.56 X322))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X324, 111.90/112.56 X325]: 111.90/112.56 (( 111.90/112.56 binintersect( 111.90/112.56 X324,X325) = 111.90/112.56 X325) => 111.90/112.56 subset( 111.90/112.56 X325,X324))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X326, 111.90/112.56 X327,X328]: 111.90/112.56 (in( 111.90/112.56 X328, 111.90/112.56 binintersect( 111.90/112.56 X326,X327)) => 111.90/112.56 in( 111.90/112.56 X328,X327))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X329, 111.90/112.56 X330]: 111.90/112.56 (( 111.90/112.56 ~ 111.90/112.56 ( 111.90/112.56 ?[X331]: 111.90/112.56 (in( 111.90/112.56 X331,X329) & 111.90/112.56 in( 111.90/112.56 X331,X330)))) => 111.90/112.56 (binintersect( 111.90/112.56 X329,X330) = 111.90/112.56 emptyset))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X332, 111.90/112.56 X333]: 111.90/112.56 subset( 111.90/112.56 binintersect( 111.90/112.56 X332,X333), 111.90/112.56 X333)) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X334, 111.90/112.56 X335]: 111.90/112.56 (subset( 111.90/112.56 X335,X334) => 111.90/112.56 (binintersect( 111.90/112.56 X334,X335) = 111.90/112.56 X335))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X336, 111.90/112.56 X337]: 111.90/112.56 (( 111.90/112.56 binintersect( 111.90/112.56 X336,X337) = 111.90/112.56 X336) => 111.90/112.56 subset( 111.90/112.56 X336,X337))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X338, 111.90/112.56 X339,X340]: 111.90/112.56 (binintersect( 111.90/112.56 X338, 111.90/112.56 binunion( 111.90/112.56 X339,X340)) = 111.90/112.56 binunion( 111.90/112.56 binintersect( 111.90/112.56 X338,X339), 111.90/112.56 binintersect( 111.90/112.56 X338,X340)))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X341, 111.90/112.56 X342,X343]: 111.90/112.56 (in( 111.90/112.56 X343,X341) => 111.90/112.56 (( 111.90/112.56 ~ 111.90/112.56 in( 111.90/112.56 X343,X342)) => 111.90/112.56 in( 111.90/112.56 X343, 111.90/112.56 setminus( 111.90/112.56 X341,X342))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X344, 111.90/112.56 X345,X346]: 111.90/112.56 (in( 111.90/112.56 X346, 111.90/112.56 setminus( 111.90/112.56 X344,X345)) => 111.90/112.56 in( 111.90/112.56 X346,X344))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X347, 111.90/112.56 X348,X349]: 111.90/112.56 (in( 111.90/112.56 X349, 111.90/112.56 setminus( 111.90/112.56 X347,X348)) => 111.90/112.56 (~ 111.90/112.56 in( 111.90/112.56 X349,X348)))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X350, 111.90/112.56 X351]: 111.90/112.56 (subset( 111.90/112.56 X350,X351) => 111.90/112.56 (setminus( 111.90/112.56 X350,X351) = 111.90/112.56 emptyset))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X352, 111.90/112.56 X353,X354]: 111.90/112.56 (( 111.90/112.56 ~ 111.90/112.56 in( 111.90/112.56 X354, 111.90/112.56 setminus( 111.90/112.56 X352,X353))) => 111.90/112.56 (in( 111.90/112.56 X354,X352) => 111.90/112.56 in( 111.90/112.56 X354,X353)))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X355, 111.90/112.56 X356,X357]: 111.90/112.56 (( 111.90/112.56 ~ 111.90/112.56 in( 111.90/112.56 X357, 111.90/112.56 setminus( 111.90/112.56 X355,X356))) => 111.90/112.56 (( 111.90/112.56 ~ 111.90/112.56 in( 111.90/112.56 X357,X356)) => 111.90/112.56 (~ 111.90/112.56 in( 111.90/112.56 X357,X355))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X358, 111.90/112.56 X359,X360]: 111.90/112.56 (( 111.90/112.56 ~ 111.90/112.56 in( 111.90/112.56 X360,X358)) => 111.90/112.56 (~ 111.90/112.56 in( 111.90/112.56 X360, 111.90/112.56 setminus( 111.90/112.56 X358,X359))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X361, 111.90/112.56 X362,X363]: 111.90/112.56 (in( 111.90/112.56 X363,X362) => 111.90/112.56 (~ 111.90/112.56 in( 111.90/112.56 X363, 111.90/112.56 setminus( 111.90/112.56 X361,X362))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X364, 111.90/112.56 X365]: 111.90/112.56 subset( 111.90/112.56 setminus( 111.90/112.56 X364,X365), 111.90/112.56 X364)) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X366, 111.90/112.56 X367]: 111.90/112.56 (( 111.90/112.56 setminus( 111.90/112.56 X366,X367) = 111.90/112.56 emptyset) => 111.90/112.56 subset( 111.90/112.56 X366,X367))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X368, 111.90/112.56 X369,X370]: 111.90/112.56 (in( 111.90/112.56 X370, 111.90/112.56 symdiff( 111.90/112.56 X368,X369)) => 111.90/112.56 (![X371:$o]: 111.90/112.56 (( 111.90/112.56 in( 111.90/112.56 X370,X368) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ~ 111.90/112.56 in( 111.90/112.56 X370,X369)) => 111.90/112.56 X371)) => 111.90/112.56 (( 111.90/112.56 ( 111.90/112.56 ~ 111.90/112.56 in( 111.90/112.56 X370,X368)) => 111.90/112.56 ( 111.90/112.56 in( 111.90/112.56 X370,X369) => 111.90/112.56 X371)) => 111.90/112.56 X371))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X372, 111.90/112.56 X373,X374]: 111.90/112.56 (in( 111.90/112.56 X374,X372) => 111.90/112.56 (( 111.90/112.56 ~ 111.90/112.56 in( 111.90/112.56 X374,X373)) => 111.90/112.56 in( 111.90/112.56 X374, 111.90/112.56 symdiff( 111.90/112.56 X372,X373))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X375, 111.90/112.56 X376,X377]: 111.90/112.56 (( 111.90/112.56 ~ 111.90/112.56 in( 111.90/112.56 X377,X375)) => 111.90/112.56 (in( 111.90/112.56 X377,X376) => 111.90/112.56 in( 111.90/112.56 X377, 111.90/112.56 symdiff( 111.90/112.56 X375,X376))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X378, 111.90/112.56 X379,X380]: 111.90/112.56 (in( 111.90/112.56 X380,X378) => 111.90/112.56 (in( 111.90/112.56 X380,X379) => 111.90/112.56 (~ 111.90/112.56 in( 111.90/112.56 X380, 111.90/112.56 symdiff( 111.90/112.56 X378,X379)))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X381, 111.90/112.56 X382,X383]: 111.90/112.56 (( 111.90/112.56 ~ 111.90/112.56 in( 111.90/112.56 X383,X381)) => 111.90/112.56 (( 111.90/112.56 ~ 111.90/112.56 in( 111.90/112.56 X383,X382)) => 111.90/112.56 (~ 111.90/112.56 in( 111.90/112.56 X383, 111.90/112.56 symdiff( 111.90/112.56 X381,X382)))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X384, 111.90/112.56 X385]: 111.90/112.56 in( 111.90/112.56 X385, 111.90/112.56 setadjoin( 111.90/112.56 X384, 111.90/112.56 setadjoin( 111.90/112.56 X385, 111.90/112.56 emptyset)))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X386, 111.90/112.56 X387]: 111.90/112.56 in( 111.90/112.56 X386, 111.90/112.56 setunion( 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X386, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X386, 111.90/112.56 setadjoin( 111.90/112.56 X387, 111.90/112.56 emptyset)), 111.90/112.56 emptyset))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X388, 111.90/112.56 X389]: 111.90/112.56 in( 111.90/112.56 X389, 111.90/112.56 setunion( 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X388, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X388, 111.90/112.56 setadjoin( 111.90/112.56 X389, 111.90/112.56 emptyset)), 111.90/112.56 emptyset))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X390, 111.90/112.56 X391]: 111.90/112.56 (?[X392]: 111.90/112.56 (in( 111.90/112.56 X392, 111.90/112.56 setunion( 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X390, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X390, 111.90/112.56 setadjoin( 111.90/112.56 X391, 111.90/112.56 emptyset)), 111.90/112.56 emptyset)))) & 111.90/112.56 (?[X393]: 111.90/112.56 (in( 111.90/112.56 X393, 111.90/112.56 setunion( 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X390, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X390, 111.90/112.56 setadjoin( 111.90/112.56 X391, 111.90/112.56 emptyset)), 111.90/112.56 emptyset)))) & 111.90/112.56 (setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X390, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X390, 111.90/112.56 setadjoin( 111.90/112.56 X391, 111.90/112.56 emptyset)), 111.90/112.56 emptyset)) = 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X392, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X392, 111.90/112.56 setadjoin( 111.90/112.56 X393, 111.90/112.56 emptyset)), 111.90/112.56 emptyset)))))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X394, 111.90/112.56 X395]: 111.90/112.56 (?[X396]: 111.90/112.56 (in( 111.90/112.56 X396, 111.90/112.56 setunion( 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X394, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X394, 111.90/112.56 setadjoin( 111.90/112.56 X395, 111.90/112.56 emptyset)), 111.90/112.56 emptyset)))) & 111.90/112.56 (?[X397]: 111.90/112.56 (in( 111.90/112.56 X397, 111.90/112.56 setunion( 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X394, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X394, 111.90/112.56 setadjoin( 111.90/112.56 X395, 111.90/112.56 emptyset)), 111.90/112.56 emptyset)))) & 111.90/112.56 (setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X394, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X394, 111.90/112.56 setadjoin( 111.90/112.56 X395, 111.90/112.56 emptyset)), 111.90/112.56 emptyset)) = 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X396, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X396, 111.90/112.56 setadjoin( 111.90/112.56 X397, 111.90/112.56 emptyset)), 111.90/112.56 emptyset)))))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X398, 111.90/112.56 X399]: 111.90/112.56 (in( 111.90/112.56 X399,X398) => 111.90/112.56 subset( 111.90/112.56 setadjoin( 111.90/112.56 X399, 111.90/112.56 emptyset), 111.90/112.56 X398))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X400, 111.90/112.56 X401]: 111.90/112.56 (in( 111.90/112.56 X401,X400) => 111.90/112.56 in( 111.90/112.56 setadjoin( 111.90/112.56 X401, 111.90/112.56 emptyset), 111.90/112.56 powerset( 111.90/112.56 X400)))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X402, 111.90/112.56 X403,X404]: 111.90/112.56 (in( 111.90/112.56 X404,X402) => 111.90/112.56 in( 111.90/112.56 setadjoin( 111.90/112.56 X404, 111.90/112.56 emptyset), 111.90/112.56 powerset( 111.90/112.56 binunion( 111.90/112.56 X402,X403))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X405, 111.90/112.56 X406,X407]: 111.90/112.56 (in( 111.90/112.56 X407, 111.90/112.56 setadjoin( 111.90/112.56 X405, 111.90/112.56 setadjoin( 111.90/112.56 X406, 111.90/112.56 emptyset))) => 111.90/112.56 (( 111.90/112.56 X407 = 111.90/112.56 X405) | 111.90/112.56 (X407 = 111.90/112.56 X406)))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X408, 111.90/112.56 X409,X410]: 111.90/112.56 (in( 111.90/112.56 X410,X408) => 111.90/112.56 (![X411]: 111.90/112.56 (in( 111.90/112.56 X411,X409) => 111.90/112.56 subset( 111.90/112.56 setadjoin( 111.90/112.56 X410, 111.90/112.56 setadjoin( 111.90/112.56 X411, 111.90/112.56 emptyset)), 111.90/112.56 binunion( 111.90/112.56 X408,X409)))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X412, 111.90/112.56 X413,X414]: 111.90/112.56 (in( 111.90/112.56 X414,X412) => 111.90/112.56 (![X415]: 111.90/112.56 (in( 111.90/112.56 X415,X413) => 111.90/112.56 in( 111.90/112.56 setadjoin( 111.90/112.56 X414, 111.90/112.56 setadjoin( 111.90/112.56 X415, 111.90/112.56 emptyset)), 111.90/112.56 powerset( 111.90/112.56 binunion( 111.90/112.56 X412,X413))))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X416, 111.90/112.56 X417,X418]: 111.90/112.56 (in( 111.90/112.56 X418,X416) => 111.90/112.56 (![X419]: 111.90/112.56 (in( 111.90/112.56 X419,X417) => 111.90/112.56 subset( 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X418, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X418, 111.90/112.56 setadjoin( 111.90/112.56 X419, 111.90/112.56 emptyset)), 111.90/112.56 emptyset)), 111.90/112.56 powerset( 111.90/112.56 binunion( 111.90/112.56 X416,X417))))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X420, 111.90/112.56 X421,X422]: 111.90/112.56 (in( 111.90/112.56 X422,X420) => 111.90/112.56 (![X423]: 111.90/112.56 (in( 111.90/112.56 X423,X421) => 111.90/112.56 in( 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X422, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X422, 111.90/112.56 setadjoin( 111.90/112.56 X423, 111.90/112.56 emptyset)), 111.90/112.56 emptyset)), 111.90/112.56 powerset( 111.90/112.56 powerset( 111.90/112.56 binunion( 111.90/112.56 X420,X421)))))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X424, 111.90/112.56 X425,X426]: 111.90/112.56 (in( 111.90/112.56 X426,X424) => 111.90/112.56 (![X427]: 111.90/112.56 (in( 111.90/112.56 X427,X425) => 111.90/112.56 in( 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X426, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X426, 111.90/112.56 setadjoin( 111.90/112.56 X427, 111.90/112.56 emptyset)), 111.90/112.56 emptyset)), 111.90/112.56 powerset( 111.90/112.56 powerset( 111.90/112.56 binunion( 111.90/112.56 X424,X425)))))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X428, 111.90/112.56 X429,X430]: 111.90/112.56 (in( 111.90/112.56 X430,X428) => 111.90/112.56 (![X431]: 111.90/112.56 (in( 111.90/112.56 X431,X429) => 111.90/112.56 in( 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X430, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X430, 111.90/112.56 setadjoin( 111.90/112.56 X431, 111.90/112.56 emptyset)), 111.90/112.56 emptyset)), 111.90/112.56 cartprod( 111.90/112.56 X428,X429)))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X432, 111.90/112.56 X433,X434]: 111.90/112.56 (in( 111.90/112.56 X434, 111.90/112.56 cartprod( 111.90/112.56 X432,X433)) => 111.90/112.56 (?[X435]: 111.90/112.56 (in( 111.90/112.56 X435,X432) & 111.90/112.56 (?[X436]: 111.90/112.56 (in( 111.90/112.56 X436,X433) & 111.90/112.56 (X434 = 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X435, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X435, 111.90/112.56 setadjoin( 111.90/112.56 X436, 111.90/112.56 emptyset)), 111.90/112.56 emptyset))))))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X437, 111.90/112.56 X438,X439]: 111.90/112.56 (in( 111.90/112.56 X439, 111.90/112.56 cartprod( 111.90/112.56 X437,X438)) => 111.90/112.56 (?[X440]: 111.90/112.56 (in( 111.90/112.56 X440, 111.90/112.56 setunion( 111.90/112.56 X439)) & 111.90/112.56 (?[X441]: 111.90/112.56 (in( 111.90/112.56 X441, 111.90/112.56 setunion( 111.90/112.56 X439)) & 111.90/112.56 (X439 = 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X440, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X440, 111.90/112.56 setadjoin( 111.90/112.56 X441, 111.90/112.56 emptyset)), 111.90/112.56 emptyset))))))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X442, 111.90/112.56 X443]: 111.90/112.56 (in( 111.90/112.56 X443, 111.90/112.56 setunion( 111.90/112.56 X442)) => 111.90/112.56 (?[X444]: 111.90/112.56 (in( 111.90/112.56 X444,X442) & 111.90/112.56 in( 111.90/112.56 X443,X444))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X445]: 111.90/112.56 subset( 111.90/112.56 setunion( 111.90/112.56 setadjoin( 111.90/112.56 X445, 111.90/112.56 emptyset)), 111.90/112.56 X445)) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X446]: 111.90/112.56 subset( 111.90/112.56 X446, 111.90/112.56 setunion( 111.90/112.56 setadjoin( 111.90/112.56 X446, 111.90/112.56 emptyset)))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X447]: 111.90/112.56 (setunion( 111.90/112.56 setadjoin( 111.90/112.56 X447, 111.90/112.56 emptyset)) = 111.90/112.56 X447)) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X448, 111.90/112.56 X449:( 111.90/112.56 $i > $o)]: 111.90/112.56 (( 111.90/112.56 ![X450]: 111.90/112.56 (in( 111.90/112.56 X450,X448) => 111.90/112.56 (![X451]: 111.90/112.56 (in( 111.90/112.56 X451,X448) => 111.90/112.56 (X449( 111.90/112.56 X450) => 111.90/112.56 (X449( 111.90/112.56 X451) => 111.90/112.56 (X450 = 111.90/112.56 X451))))))) => 111.90/112.56 (( 111.90/112.56 ?[X452]: 111.90/112.56 (in( 111.90/112.56 X452,X448) & 111.90/112.56 X449( 111.90/112.56 X452))) => 111.90/112.56 (?[X453]: 111.90/112.56 (in( 111.90/112.56 X453, 111.90/112.56 dsetconstr( 111.90/112.56 X448, 111.90/112.56 '#ll_1'( 111.90/112.56 X449))) & 111.90/112.56 (dsetconstr( 111.90/112.56 X448, 111.90/112.56 '#ll_1'( 111.90/112.56 X449)) = 111.90/112.56 setadjoin( 111.90/112.56 X453, 111.90/112.56 emptyset))))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X454, 111.90/112.56 X455:( 111.90/112.56 $i > $o)]: 111.90/112.56 (( 111.90/112.56 ?[X456]: 111.90/112.56 (in( 111.90/112.56 X456, 111.90/112.56 dsetconstr( 111.90/112.56 X454, 111.90/112.56 '#ll_1'( 111.90/112.56 X455))) & 111.90/112.56 (dsetconstr( 111.90/112.56 X454, 111.90/112.56 '#ll_1'( 111.90/112.56 X455)) = 111.90/112.56 setadjoin( 111.90/112.56 X456, 111.90/112.56 emptyset)))) => 111.90/112.56 (?[X457]: 111.90/112.56 (in( 111.90/112.56 X457,X454) & 111.90/112.56 X455( 111.90/112.56 X457))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X458, 111.90/112.56 X459:( 111.90/112.56 $i > $o), 111.90/112.56 X460]: 111.90/112.56 (in( 111.90/112.56 X460,X458) => 111.90/112.56 (X459( 111.90/112.56 X460) => 111.90/112.56 (( 111.90/112.56 ![X461]: 111.90/112.56 (in( 111.90/112.56 X461,X458) => 111.90/112.56 (X459( 111.90/112.56 X461) => 111.90/112.56 (X461 = 111.90/112.56 X460)))) => 111.90/112.56 (?[X462]: 111.90/112.56 (in( 111.90/112.56 X462, 111.90/112.56 dsetconstr( 111.90/112.56 X458, 111.90/112.56 '#ll_1'( 111.90/112.56 X459))) & 111.90/112.56 (dsetconstr( 111.90/112.56 X458, 111.90/112.56 '#ll_1'( 111.90/112.56 X459)) = 111.90/112.56 setadjoin( 111.90/112.56 X462, 111.90/112.56 emptyset)))))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X463, 111.90/112.56 X464:( 111.90/112.56 $i > $o)]: 111.90/112.56 (( 111.90/112.56 ![X465]: 111.90/112.56 (in( 111.90/112.56 X465,X463) => 111.90/112.56 (![X466]: 111.90/112.56 (in( 111.90/112.56 X466,X463) => 111.90/112.56 (X464( 111.90/112.56 X465) => 111.90/112.56 (X464( 111.90/112.56 X466) => 111.90/112.56 (X465 = 111.90/112.56 X466))))))) => 111.90/112.56 (( 111.90/112.56 ?[X467]: 111.90/112.56 (in( 111.90/112.56 X467,X463) & 111.90/112.56 X464( 111.90/112.56 X467))) => 111.90/112.56 (?[X468]: 111.90/112.56 (in( 111.90/112.56 X468, 111.90/112.56 dsetconstr( 111.90/112.56 X463, 111.90/112.56 '#ll_1'( 111.90/112.56 X464))) & 111.90/112.56 (dsetconstr( 111.90/112.56 X463, 111.90/112.56 '#ll_1'( 111.90/112.56 X464)) = 111.90/112.56 setadjoin( 111.90/112.56 X468, 111.90/112.56 emptyset))))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X469, 111.90/112.56 X470]: 111.90/112.56 (( 111.90/112.56 setadjoin( 111.90/112.56 X469, 111.90/112.56 emptyset) = 111.90/112.56 setadjoin( 111.90/112.56 X470, 111.90/112.56 emptyset)) => 111.90/112.56 (X469 = 111.90/112.56 X470))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X471, 111.90/112.56 X472,X473]: 111.90/112.56 (in( 111.90/112.56 setadjoin( 111.90/112.56 X473, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X471, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X471, 111.90/112.56 setadjoin( 111.90/112.56 X472, 111.90/112.56 emptyset)), 111.90/112.56 emptyset))) => 111.90/112.56 (X471 = 111.90/112.56 X473))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X474]: 111.90/112.56 (( 111.90/112.56 ?[X475]: 111.90/112.56 (in( 111.90/112.56 X475, 111.90/112.56 setunion( 111.90/112.56 X474)) & 111.90/112.56 (?[X476]: 111.90/112.56 (in( 111.90/112.56 X476, 111.90/112.56 setunion( 111.90/112.56 X474)) & 111.90/112.56 (X474 = 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X475, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X475, 111.90/112.56 setadjoin( 111.90/112.56 X476, 111.90/112.56 emptyset)), 111.90/112.56 emptyset))))))) => 111.90/112.56 (?[X477]: 111.90/112.56 (in( 111.90/112.56 X477, 111.90/112.56 dsetconstr( 111.90/112.56 setunion( 111.90/112.56 X474), 111.90/112.56 '#ll_0'( 111.90/112.56 X474))) & 111.90/112.56 (dsetconstr( 111.90/112.56 setunion( 111.90/112.56 X474), 111.90/112.56 '#ll_0'( 111.90/112.56 X474)) = 111.90/112.56 setadjoin( 111.90/112.56 X477, 111.90/112.56 emptyset)))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X478]: 111.90/112.56 (( 111.90/112.56 ?[X479]: 111.90/112.56 (in( 111.90/112.56 X479,X478) & 111.90/112.56 (X478 = 111.90/112.56 setadjoin( 111.90/112.56 X479, 111.90/112.56 emptyset)))) => 111.90/112.56 in( 111.90/112.56 setunion( 111.90/112.56 X478), 111.90/112.56 X478))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X480, 111.90/112.56 X481]: 111.90/112.56 (kfst( 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X480, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X480, 111.90/112.56 setadjoin( 111.90/112.56 X481, 111.90/112.56 emptyset)), 111.90/112.56 emptyset))) = 111.90/112.56 X480)) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X482, 111.90/112.56 X483,X484]: 111.90/112.56 (in( 111.90/112.56 X484, 111.90/112.56 cartprod( 111.90/112.56 X482,X483)) => 111.90/112.56 in( 111.90/112.56 kfst( 111.90/112.56 X484), 111.90/112.56 X482))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X485, 111.90/112.56 X486, 111.90/112.56 X487,X488]: 111.90/112.56 (( 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X485, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X485, 111.90/112.56 setadjoin( 111.90/112.56 X486, 111.90/112.56 emptyset)), 111.90/112.56 emptyset)) = 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X487, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X487, 111.90/112.56 setadjoin( 111.90/112.56 X488, 111.90/112.56 emptyset)), 111.90/112.56 emptyset))) => 111.90/112.56 (X485 = 111.90/112.56 X487))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X489, 111.90/112.56 X490, 111.90/112.56 X491,X492]: 111.90/112.56 (( 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X489, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X489, 111.90/112.56 setadjoin( 111.90/112.56 X490, 111.90/112.56 emptyset)), 111.90/112.56 emptyset)) = 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X491, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X491, 111.90/112.56 setadjoin( 111.90/112.56 X492, 111.90/112.56 emptyset)), 111.90/112.56 emptyset))) => 111.90/112.56 (X489 = 111.90/112.56 X491))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X493, 111.90/112.56 X494]: 111.90/112.56 (( 111.90/112.56 X493 = 111.90/112.56 X494) => 111.90/112.56 (setadjoin( 111.90/112.56 X493, 111.90/112.56 setadjoin( 111.90/112.56 X494, 111.90/112.56 emptyset)) = 111.90/112.56 setadjoin( 111.90/112.56 X493, 111.90/112.56 emptyset)))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X495, 111.90/112.56 X496]: 111.90/112.56 (( 111.90/112.56 X495 = 111.90/112.56 X496) => 111.90/112.56 (setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X495, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X495, 111.90/112.56 setadjoin( 111.90/112.56 X496, 111.90/112.56 emptyset)), 111.90/112.56 emptyset)) = 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X495, 111.90/112.56 emptyset), 111.90/112.56 emptyset)))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X497, 111.90/112.56 X498, 111.90/112.56 X499,X500]: 111.90/112.56 (( 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X497, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X497, 111.90/112.56 setadjoin( 111.90/112.56 X498, 111.90/112.56 emptyset)), 111.90/112.56 emptyset)) = 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X499, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X499, 111.90/112.56 setadjoin( 111.90/112.56 X500, 111.90/112.56 emptyset)), 111.90/112.56 emptyset))) => 111.90/112.56 (( 111.90/112.56 X499 = 111.90/112.56 X500) => 111.90/112.56 (X498 = 111.90/112.56 X500)))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X501, 111.90/112.56 X502,X503]: 111.90/112.56 (( 111.90/112.56 setadjoin( 111.90/112.56 X501, 111.90/112.56 setadjoin( 111.90/112.56 X502, 111.90/112.56 emptyset)) = 111.90/112.56 setadjoin( 111.90/112.56 X503, 111.90/112.56 emptyset)) => 111.90/112.56 (X501 = 111.90/112.56 X502))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X504, 111.90/112.56 X505, 111.90/112.56 X506,X507]: 111.90/112.56 (( 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X504, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X504, 111.90/112.56 setadjoin( 111.90/112.56 X505, 111.90/112.56 emptyset)), 111.90/112.56 emptyset)) = 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X506, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X506, 111.90/112.56 setadjoin( 111.90/112.56 X507, 111.90/112.56 emptyset)), 111.90/112.56 emptyset))) => 111.90/112.56 (X505 = 111.90/112.56 X507))) => 111.90/112.56 ( 111.90/112.56 ![X508, 111.90/112.56 X509, 111.90/112.56 X510,X511]: 111.90/112.56 (( 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X508, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X508, 111.90/112.56 setadjoin( 111.90/112.56 X509, 111.90/112.56 emptyset)), 111.90/112.56 emptyset)) = 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X510, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X510, 111.90/112.56 setadjoin( 111.90/112.56 X511, 111.90/112.56 emptyset)), 111.90/112.56 emptyset))) => 111.90/112.56 (X509 = 111.90/112.56 X511)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 111.90/112.56 tff(zf_stmt_1, type, zip_tseitin5 : ($i * $i > $o) > $o). 111.90/112.56 tff(zf_stmt_2, axiom, 111.90/112.56 (zip_tseitin5(X211,X207) <=> 111.90/112.56 ((![X212]: zip_tseitin4(X212,X211,X207)) & X207(X211)))). 111.90/112.56 tff(zf_stmt_3, type, zip_tseitin4 : ($i * $i * $i > $o) > $o). 111.90/112.56 tff(zf_stmt_4, axiom, 111.90/112.56 (zip_tseitin4(X212,X211,X207) <=> (X207(X212) => (X211 = X212)))). 111.90/112.56 tff(zf_stmt_5, type, zip_tseitin3 : ($i * $i * $i * ($i * $i) > $o) > $o). 111.90/112.56 tff(zf_stmt_6, axiom, 111.90/112.56 (zip_tseitin3(X26,X25,X20,X19) <=> (X19(X26,X25) & in(X26,X20)))). 111.90/112.56 tff(zf_stmt_7, type, zip_tseitin2 : ($i * $i * $i) > $o). 111.90/112.56 tff(zf_stmt_8, axiom, 111.90/112.56 (zip_tseitin2(X14,X13,X12) <=> (in(X14,X12) & in(X13,X14)))). 111.90/112.56 tff(zf_stmt_9, type, zip_tseitin1 : ($i * $i * $i) > $o). 111.90/112.56 tff(zf_stmt_10, axiom, 111.90/112.56 (zip_tseitin1(X11,X10,X9) <=> (in(X11,X10) => in(X11,X9)))). 111.90/112.56 tff(zf_stmt_11, type, zip_tseitin0 : ($i * $i * $i) > $o). 111.90/112.56 tff(zf_stmt_12, axiom, (zip_tseitin0(X8,X7,X6) <=> (in(X8,X7) | (X8 = X6)))). 111.90/112.56 tff(zf_stmt_13, conjecture, 111.90/112.56 ((![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))) => 111.90/112.56 ((![X5]: (~in(X5,emptyset))) => 111.90/112.56 ((![X6,X7,X8]: (in(X8,setadjoin(X6,X7)) <=> zip_tseitin0(X8,X7,X6))) => 111.90/112.56 ((![X9,X10]: 111.90/112.56 (in(X10,powerset(X9)) <=> (![X11]: zip_tseitin1(X11,X10,X9)))) => 111.90/112.56 ((![X12,X13]: 111.90/112.56 (in(X13,setunion(X12)) <=> (?[X14]: zip_tseitin2(X14,X13,X12)))) => 111.90/112.56 (in(emptyset,omega) => 111.90/112.56 ((![X15]: (in(X15,omega) => in(setadjoin(X15,X15),omega))) => 111.90/112.56 ((![X16]: 111.90/112.56 (((![X17]: 111.90/112.56 ((in(X17,X16) & in(X17,omega)) => 111.90/112.56 in(setadjoin(X17,X17),X16))) & 111.90/112.56 in(emptyset,X16)) => 111.90/112.56 (![X18]: (in(X18,omega) => in(X18,X16))))) => 111.90/112.56 ((![X19:(($i * $i) > $o),X20]: 111.90/112.56 ((![X21]: 111.90/112.56 (in(X21,X20) => 111.90/112.56 (?[X22]: 111.90/112.56 ((![X23]: (X19(X21,X23) => (X22 = X23))) & X19(X21,X22))))) => 111.90/112.56 (?[X24]: 111.90/112.56 (![X25]: 111.90/112.56 (in(X25,X24) <=> (?[X26]: zip_tseitin3(X26,X25,X20,X19))))))) => 111.90/112.56 ((![X27]: 111.90/112.56 ((?[X28]: in(X28,X27)) => 111.90/112.56 (?[X29]: 111.90/112.56 ((~(?[X30]: (in(X30,X27) & in(X30,X29)))) & in(X29,X27))))) => 111.90/112.56 ((![X31]: 111.90/112.56 (?[X32]: 111.90/112.56 ((![X33]: 111.90/112.56 (((?[X34]: in(X34,X33)) & 111.90/112.56 (![X35]: (in(X35,X33) => in(X35,X31)))) => 111.90/112.56 (?[X36,X37]: 111.90/112.56 ((![X38]: 111.90/112.56 (in(X38,X32) => 111.90/112.56 (in(X37,X38) | 111.90/112.56 (![X39]: (in(X39,X38) => in(X39,X36)))))) & 111.90/112.56 (~(?[X40]: (in(X40,X33) & in(X40,X36)))) & 111.90/112.56 in(X37,X33) & in(X36,X32))))) & 111.90/112.56 (![X41,X42]: 111.90/112.56 ((in(X42,X32) & in(X41,X32)) => 111.90/112.56 ((![X43]: (in(X43,X42) => in(X43,X41))) | 111.90/112.56 (![X44]: (in(X44,X41) => in(X44,X42)))))) & 111.90/112.56 (![X45,X46]: 111.90/112.56 ((in(X46,X31) & in(X45,X31)) => 111.90/112.56 ((![X47]: 111.90/112.56 (in(X47,X32) => (in(X45,X47) <=> in(X46,X47)))) => 111.90/112.56 (X45 = X46)))) & 111.90/112.56 (![X48]: 111.90/112.56 (in(X48,X32) => (![X49]: (in(X49,X48) => in(X49,X31)))))))) => 111.90/112.56 ((![X50:($i > $o)]: 111.90/112.56 ((?[X51]: ((![X52]: (X50(X52) => (X51 = X52))) & X50(X51))) => 111.90/112.56 X50(descr('#ll_1'(X50))))) => 111.90/112.56 ((![X53,X54:($i > $o),X55]: 111.90/112.56 (in(X55,X53) => 111.90/112.56 (X54(X55) => in(X55,dsetconstr(X53,'#ll_1'(X54)))))) => 111.90/112.56 ((![X56,X57:($i > $o),X58]: 111.90/112.56 (in(X58,dsetconstr(X56,'#ll_1'(X57))) => in(X58,X56))) => 111.90/112.56 ((![X59,X60:($i > $o),X61]: 111.90/112.56 (in(X61,dsetconstr(X59,'#ll_1'(X60))) => X60(X61))) => 111.90/112.56 ((![X62:($i > $o)]: 111.90/112.56 ((?[X63]: 111.90/112.56 ((![X64]: (X62(X64) => (X63 = X64))) & X62(X63))) => 111.90/112.56 (?[X65]: 111.90/112.56 ((![X66]: (X62(X66) => (X65 = X66))) & X62(X65))))) => 111.90/112.56 ((![X67:$o,X68]: (in(X68,prop2set(X67)) => X67)) => 111.90/112.56 ((![X69]: (in(X69,emptyset) => (![X70:$o]: X70))) => 111.90/112.56 ((![X71]: (in(X71,emptyset) => $false)) => 111.90/112.56 ((![X72]: (~in(X72,emptyset))) => 111.90/112.56 ((![X73:($i > $o)]: 111.90/112.56 ((?[X74]: 111.90/112.56 ((![X75]: (X73(X75) => (X74 = X75))) & X73(X74))) => 111.90/112.56 (?[X76]: X73(X76)))) => 111.90/112.56 ((![X77,X78]: 111.90/112.56 ((![X79]: (in(X79,X77) => in(X79,X78))) => 111.90/112.56 ((![X80]: (in(X80,X78) => in(X80,X77))) => 111.90/112.56 (X77 = X78)))) => 111.90/112.56 ((![X81]: 111.90/112.56 ((![X82]: (~in(X82,X81))) => (X81 = emptyset))) => 111.90/112.56 ((![X83]: 111.90/112.56 ((![X84]: (~in(X84,X83))) => (X83 = emptyset))) => 111.90/112.56 ((![X85,X86:($i > $o),X87]: 111.90/112.56 (in(X87,X85) => 111.90/112.56 (in(X87,dsetconstr(X85,'#ll_1'(X86))) <=> 111.90/112.56 X86(X87)))) => 111.90/112.56 ((![X88]: 111.90/112.56 ((X88 != emptyset) => (?[X89]: in(X89,X88)))) => 111.90/112.56 ((![X90,X91:($i > $o),X92]: 111.90/112.56 (in(X92,X90) => 111.90/112.56 (X91(X92) => 111.90/112.56 (dsetconstr(X90,'#ll_1'(X91)) != emptyset)))) => 111.90/112.56 ((![X93]: 111.90/112.56 ((?[X94]: in(X94,X93)) => (X93 != emptyset))) => 111.90/112.56 ((![X95,X96]: in(X95,setadjoin(X95,X96))) => 111.90/112.56 (in(emptyset,setadjoin(emptyset,emptyset)) => 111.90/112.56 ((![X97,X98,X99]: 111.90/112.56 (in(X99,X98) => 111.90/112.56 in(X99,setadjoin(X97,X98)))) => 111.90/112.56 ((![X100,X101,X102]: 111.90/112.56 (in(X102,setadjoin(X100,X101)) => 111.90/112.56 (![X103:$o]: 111.90/112.56 (((X102 = X100) => X103) => 111.90/112.56 ((in(X102,X101) => X103) => X103))))) => 111.90/112.56 ((![X104,X105,X106]: 111.90/112.56 (in(X106,setadjoin(X104,X105)) => 111.90/112.56 (in(X106,X105) | (X106 = X104)))) => 111.90/112.56 ((![X107]: 111.90/112.56 (dsetconstr(X107,'#ll_2') = X107)) => 111.90/112.56 ((![X108,X109]: 111.90/112.56 ((![X110]: 111.90/112.56 (in(X110,X109) => in(X110,X108))) => 111.90/112.56 in(X109,powerset(X108)))) => 111.90/112.56 ((![X111]: in(emptyset,powerset(X111))) => 111.90/112.56 ((![X112]: in(emptyset,powerset(X112))) => 111.90/112.56 ((![X113,X114,X115]: 111.90/112.56 (in(X114,powerset(X113)) => 111.90/112.56 (in(X115,X114) => in(X115,X113)))) => 111.90/112.56 ((![X116,X117,X118]: 111.90/112.56 (in(X117,X118) => 111.90/112.56 (in(X118,X116) => 111.90/112.56 in(X117,setunion(X116))))) => 111.90/112.56 ((![X119,X120]: 111.90/112.56 (in(X120,setunion(X119)) => 111.90/112.56 (![X121:$o]: 111.90/112.56 ((![X122]: 111.90/112.56 (in(X120,X122) => 111.90/112.56 (in(X122,X119) => X121))) => 111.90/112.56 X121)))) => 111.90/112.56 ((![X123,X124]: 111.90/112.56 (in(X124,X123) => 111.90/112.56 in(X124, 111.90/112.56 powerset(setunion(X123))))) => 111.90/112.56 ((![X125:($i > $o)]: 111.90/112.56 ((?[X126]: 111.90/112.56 ((![X127]: 111.90/112.56 (X125(X127) => 111.90/112.56 (X126 = X127))) & 111.90/112.56 X125(X126))) => 111.90/112.56 (?[X128]: 111.90/112.56 (![X129]: 111.90/112.56 (X125(X129) <=> 111.90/112.56 (X129 = X128)))))) => 111.90/112.56 ((![X130]: 111.90/112.56 ((X130 != emptyset) => 111.90/112.56 (?[X131]: in(X131,X130)))) => 111.90/112.56 ((![X132,X133]: 111.90/112.56 (in(X132, 111.90/112.56 setadjoin(X133,emptyset)) => 111.90/112.56 (X132 = X133))) => 111.90/112.56 ((![X134,X135]: 111.90/112.56 ((X134 != X135) => 111.90/112.56 (~ 111.90/112.56 in(X135, 111.90/112.56 setadjoin(X134, 111.90/112.56 emptyset))))) => 111.90/112.56 ((![X136,X137]: 111.90/112.56 ((X136 = X137) => 111.90/112.56 in(X136, 111.90/112.56 setadjoin(X137, 111.90/112.56 emptyset)))) => 111.90/112.56 ((![X138,X139]: 111.90/112.56 (in(X138, 111.90/112.56 setadjoin(X139, 111.90/112.56 emptyset)) => 111.90/112.56 in(X139, 111.90/112.56 setadjoin(X138, 111.90/112.56 emptyset)))) => 111.90/112.56 ((![X140,X141,X142]: 111.90/112.56 (in(X142, 111.90/112.56 setadjoin(X140, 111.90/112.56 setadjoin( 111.90/112.56 X141, 111.90/112.56 emptyset))) => 111.90/112.56 ((X142 = X141) | 111.90/112.56 (X142 = X140)))) => 111.90/112.56 ((![X143,X144]: 111.90/112.56 in(X143, 111.90/112.56 setadjoin(X143, 111.90/112.56 setadjoin( 111.90/112.56 X144, 111.90/112.56 emptyset)))) => 111.90/112.56 ((![X145,X146]: 111.90/112.56 in(X146, 111.90/112.56 setadjoin(X145, 111.90/112.56 setadjoin( 111.90/112.56 X146, 111.90/112.56 emptyset)))) => 111.90/112.56 ((![X147,X148:($i > $o)]: 111.90/112.56 ((?[X149]: 111.90/112.56 (X148(X149) & 111.90/112.56 in(X149,X147))) => 111.90/112.56 ((dsetconstr( 111.90/112.56 X147,'#ll_1'(X148)) = 111.90/112.56 emptyset) => 111.90/112.56 $false))) => 111.90/112.56 ((![X150:($i > $o),X151]: 111.90/112.56 (in(X151,emptyset) => 111.90/112.56 X150(X151))) => 111.90/112.56 ((![X152,X153:($i > $o)]: 111.90/112.56 ((~ 111.90/112.56 (![X154]: 111.90/112.56 (in(X154,X152) => 111.90/112.56 X153(X154)))) => 111.90/112.56 (?[X155]: 111.90/112.56 ((~X153(X155)) & 111.90/112.56 in(X155,X152))))) => 111.90/112.56 ((![X156, 111.90/112.56 X157:($i > $o)]: 111.90/112.56 ((![X158]: 111.90/112.56 (in(X158,X156) => 111.90/112.56 (~X157(X158)))) => 111.90/112.56 (~ 111.90/112.56 (?[X159]: 111.90/112.56 (X157(X159) & 111.90/112.56 in( 111.90/112.56 X159,X156)))))) => 111.90/112.56 ((![X160, 111.90/112.56 X161:($i > $o)]: 111.90/112.56 ((~ 111.90/112.56 (?[X162]: 111.90/112.56 (X161(X162) & 111.90/112.56 in( 111.90/112.56 X162,X160)))) => 111.90/112.56 (![X163]: 111.90/112.56 (in(X163,X160) => 111.90/112.56 (~X161(X163)))))) => 111.90/112.56 ((![X164, 111.90/112.56 X165:($i > $o)]: 111.90/112.56 ((?[X166]: 111.90/112.56 ((~ 111.90/112.56 X165( 111.90/112.56 X166)) & 111.90/112.56 in( 111.90/112.56 X166,X164))) => 111.90/112.56 (~ 111.90/112.56 (![X167]: 111.90/112.56 (in( 111.90/112.56 X167,X164) => 111.90/112.56 X165( 111.90/112.56 X167)))))) => 111.90/112.56 ((![X168:$o]: 111.90/112.56 (X168 => 111.90/112.56 in(emptyset, 111.90/112.56 prop2set( 111.90/112.56 X168)))) => 111.90/112.56 ((![X169:$o]: 111.90/112.56 (X169 => 111.90/112.56 set2prop( 111.90/112.56 prop2set( 111.90/112.56 X169)))) => 111.90/112.56 ((![X170, 111.90/112.56 X171:( 111.90/112.56 $i > $o)]: 111.90/112.56 ((~ 111.90/112.56 (?[X172]: 111.90/112.56 (X171( 111.90/112.56 X172) & 111.90/112.56 in( 111.90/112.56 X172,X170)))) => 111.90/112.56 (![X173]: 111.90/112.56 ( 111.90/112.56 in( 111.90/112.56 X173,X170) => 111.90/112.56 ( 111.90/112.56 ~ 111.90/112.56 X171( 111.90/112.56 X173)))))) => 111.90/112.56 ((![X174, 111.90/112.56 X175:( 111.90/112.56 $i > $o)]: 111.90/112.56 ((~ 111.90/112.56 ( 111.90/112.56 ![X176]: 111.90/112.56 (in( 111.90/112.56 X176,X174) => 111.90/112.56 X175( 111.90/112.56 X176)))) => 111.90/112.56 (?[X177]: 111.90/112.56 (( 111.90/112.56 ~ 111.90/112.56 X175( 111.90/112.56 X177)) & 111.90/112.56 in( 111.90/112.56 X177,X174))))) => 111.90/112.56 ((![X178:( 111.90/112.56 $i > $o)]: 111.90/112.56 ((?[X179]: 111.90/112.56 (( 111.90/112.56 ![X180]: 111.90/112.56 (X178( 111.90/112.56 X180) => 111.90/112.56 (X179 = 111.90/112.56 X180))) & 111.90/112.56 X178( 111.90/112.56 X179))) => 111.90/112.56 (?[X181]: 111.90/112.56 (( 111.90/112.56 ![X182]: 111.90/112.56 (X178( 111.90/112.56 X182) => 111.90/112.56 (X181 = 111.90/112.56 X182))) & 111.90/112.56 X178( 111.90/112.56 X181))))) => 111.90/112.56 ((![X183:( 111.90/112.56 $i > $o)]: 111.90/112.56 (( 111.90/112.56 ?[X184]: 111.90/112.56 X183( 111.90/112.56 X184)) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X185, 111.90/112.56 X186]: 111.90/112.56 (X183( 111.90/112.56 X185) => 111.90/112.56 (X183( 111.90/112.56 X186) => 111.90/112.56 (X185 = 111.90/112.56 X186)))) => 111.90/112.56 ( 111.90/112.56 ?[X187]: 111.90/112.56 (( 111.90/112.56 ![X188]: 111.90/112.56 (X183( 111.90/112.56 X188) => 111.90/112.56 (X187 = 111.90/112.56 X188))) & 111.90/112.56 X183( 111.90/112.56 X187)))))) => 111.90/112.56 ((![X189:( 111.90/112.56 $i > $o)]: 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ?[X190]: 111.90/112.56 (![X191]: 111.90/112.56 (X189( 111.90/112.56 X191) <=> 111.90/112.56 (X191 = 111.90/112.56 X190)))) => 111.90/112.56 ( 111.90/112.56 ?[X192]: 111.90/112.56 (( 111.90/112.56 ![X193]: 111.90/112.56 (X189( 111.90/112.56 X193) => 111.90/112.56 (X192 = 111.90/112.56 X193))) & 111.90/112.56 X189( 111.90/112.56 X192))))) => 111.90/112.56 ((![X194, 111.90/112.56 X195]: 111.90/112.56 (( 111.90/112.56 X194 = 111.90/112.56 X195) => 111.90/112.56 (![X196, 111.90/112.56 X197]: 111.90/112.56 (( 111.90/112.56 X196 = 111.90/112.56 X197) => 111.90/112.56 (in( 111.90/112.56 X196,X194) => 111.90/112.56 in( 111.90/112.56 X197,X195)))))) => 111.90/112.56 ((![X198, 111.90/112.56 X199]: 111.90/112.56 (( 111.90/112.56 X198 = 111.90/112.56 X199) => 111.90/112.56 (![X200, 111.90/112.56 X201]: 111.90/112.56 (( 111.90/112.56 X200 = 111.90/112.56 X201) => 111.90/112.56 (in( 111.90/112.56 X200,X198) <=> 111.90/112.56 in( 111.90/112.56 X201,X199)))))) => 111.90/112.56 (( 111.90/112.56 ![X202:( 111.90/112.56 $i > $o)]: 111.90/112.56 (( 111.90/112.56 ?[X203]: 111.90/112.56 (( 111.90/112.56 ![X204]: 111.90/112.56 (X202( 111.90/112.56 X204) => 111.90/112.56 (X203 = 111.90/112.56 X204))) & 111.90/112.56 X202( 111.90/112.56 X203))) => 111.90/112.56 (![X205, 111.90/112.56 X206]: 111.90/112.56 (X202( 111.90/112.56 X205) => 111.90/112.56 (X202( 111.90/112.56 X206) => 111.90/112.56 (X205 = 111.90/112.56 X206)))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X207:( 111.90/112.56 $i > $o), 111.90/112.56 X208:( 111.90/112.56 $i > $o)]: 111.90/112.56 (( 111.90/112.56 ![X209, 111.90/112.56 X210]: 111.90/112.56 (( 111.90/112.56 X209 = 111.90/112.56 X210) => 111.90/112.56 (X207( 111.90/112.56 X209) <=> 111.90/112.56 X208( 111.90/112.56 X210)))) => 111.90/112.56 (( 111.90/112.56 ?[X211]: 111.90/112.56 zip_tseitin5( 111.90/112.56 X211,X207)) <=> 111.90/112.56 (?[X213]: 111.90/112.56 zip_tseitin5( 111.90/112.56 X213,X208))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 emptyset = 111.90/112.56 emptyset) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X215, 111.90/112.56 X216]: 111.90/112.56 (( 111.90/112.56 X215 = 111.90/112.56 X216) => 111.90/112.56 (![X217, 111.90/112.56 X218]: 111.90/112.56 (( 111.90/112.56 X217 = 111.90/112.56 X218) => 111.90/112.56 (setadjoin( 111.90/112.56 X215,X217) = 111.90/112.56 setadjoin( 111.90/112.56 X216,X218)))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X219, 111.90/112.56 X220]: 111.90/112.56 (( 111.90/112.56 X219 = 111.90/112.56 X220) => 111.90/112.56 (powerset( 111.90/112.56 X219) = 111.90/112.56 powerset( 111.90/112.56 X220)))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X221, 111.90/112.56 X222]: 111.90/112.56 (( 111.90/112.56 X221 = 111.90/112.56 X222) => 111.90/112.56 (setunion( 111.90/112.56 X221) = 111.90/112.56 setunion( 111.90/112.56 X222)))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 omega = 111.90/112.56 omega) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X223:( 111.90/112.56 $i > $o)]: 111.90/112.56 (( 111.90/112.56 ?[X224]: 111.90/112.56 (( 111.90/112.56 ![X225]: 111.90/112.56 (X223( 111.90/112.56 X225) => 111.90/112.56 (X224 = 111.90/112.56 X225))) & 111.90/112.56 X223( 111.90/112.56 X224))) => 111.90/112.56 (![X226, 111.90/112.56 X227]: 111.90/112.56 (X223( 111.90/112.56 X226) => 111.90/112.56 (X223( 111.90/112.56 X227) => 111.90/112.56 (X226 = 111.90/112.56 X227)))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X228:( 111.90/112.56 $i > $o), 111.90/112.56 X229:( 111.90/112.56 $i > $o)]: 111.90/112.56 (( 111.90/112.56 ![X230, 111.90/112.56 X231]: 111.90/112.56 (( 111.90/112.56 X230 = 111.90/112.56 X231) => 111.90/112.56 (X228( 111.90/112.56 X230) <=> 111.90/112.56 X229( 111.90/112.56 X231)))) => 111.90/112.56 (( 111.90/112.56 ?[X232]: 111.90/112.56 (( 111.90/112.56 ![X233]: 111.90/112.56 (X228( 111.90/112.56 X233) => 111.90/112.56 (X232 = 111.90/112.56 X233))) & 111.90/112.56 X228( 111.90/112.56 X232))) => 111.90/112.56 (( 111.90/112.56 ?[X234]: 111.90/112.56 (( 111.90/112.56 ![X235]: 111.90/112.56 (X229( 111.90/112.56 X235) => 111.90/112.56 (X234 = 111.90/112.56 X235))) & 111.90/112.56 X229( 111.90/112.56 X234))) => 111.90/112.56 (descr( 111.90/112.56 '#ll_1'( 111.90/112.56 X228)) = 111.90/112.56 descr( 111.90/112.56 '#ll_1'( 111.90/112.56 X229))))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X236, 111.90/112.56 X237]: 111.90/112.56 (( 111.90/112.56 X236 = 111.90/112.56 X237) => 111.90/112.56 (![X238:( 111.90/112.56 $i > $o), 111.90/112.56 X239:( 111.90/112.56 $i > $o)]: 111.90/112.56 (( 111.90/112.56 ![X240]: 111.90/112.56 (in( 111.90/112.56 X240,X236) => 111.90/112.56 (![X241]: 111.90/112.56 (in( 111.90/112.56 X241,X237) => 111.90/112.56 (( 111.90/112.56 X240 = 111.90/112.56 X241) => 111.90/112.56 (X238( 111.90/112.56 X240) <=> 111.90/112.56 X239( 111.90/112.56 X241))))))) => 111.90/112.56 (dsetconstr( 111.90/112.56 X236, 111.90/112.56 '#ll_1'( 111.90/112.56 X238)) = 111.90/112.56 dsetconstr( 111.90/112.56 X237, 111.90/112.56 '#ll_1'( 111.90/112.56 X239))))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X242, 111.90/112.56 X243]: 111.90/112.56 (( 111.90/112.56 ![X244]: 111.90/112.56 (in( 111.90/112.56 X244,X242) => 111.90/112.56 in( 111.90/112.56 X244,X243))) => 111.90/112.56 subset( 111.90/112.56 X242,X243))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X245, 111.90/112.56 X246]: 111.90/112.56 (( 111.90/112.56 X245 = 111.90/112.56 X246) => 111.90/112.56 subset( 111.90/112.56 X246,X245))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X247, 111.90/112.56 X248]: 111.90/112.56 (( 111.90/112.56 X247 = 111.90/112.56 X248) => 111.90/112.56 subset( 111.90/112.56 X247,X248))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X249, 111.90/112.56 X250]: 111.90/112.56 (( 111.90/112.56 ![X251]: 111.90/112.56 (in( 111.90/112.56 X251,X249) => 111.90/112.56 in( 111.90/112.56 X251,X250))) => 111.90/112.56 subset( 111.90/112.56 X249,X250))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X252]: 111.90/112.56 subset( 111.90/112.56 emptyset, 111.90/112.56 X252)) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X253, 111.90/112.56 X254,X255]: 111.90/112.56 (subset( 111.90/112.56 X253,X254) => 111.90/112.56 (in( 111.90/112.56 X255,X253) => 111.90/112.56 in( 111.90/112.56 X255,X254)))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X256, 111.90/112.56 X257,X258]: 111.90/112.56 (subset( 111.90/112.56 X256,X257) => 111.90/112.56 (( 111.90/112.56 ~ 111.90/112.56 in( 111.90/112.56 X258,X257)) => 111.90/112.56 (~ 111.90/112.56 in( 111.90/112.56 X258,X256))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X259, 111.90/112.56 X260,X261]: 111.90/112.56 (in( 111.90/112.56 X261,X259) => 111.90/112.56 (( 111.90/112.56 ~ 111.90/112.56 in( 111.90/112.56 X261,X260)) => 111.90/112.56 (~ 111.90/112.56 subset( 111.90/112.56 X259,X260))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X262, 111.90/112.56 X263]: 111.90/112.56 (( 111.90/112.56 ~ 111.90/112.56 subset( 111.90/112.56 X262,X263)) => 111.90/112.56 (X262 != 111.90/112.56 X263))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X264, 111.90/112.56 X265,X266]: 111.90/112.56 (in( 111.90/112.56 X266,X264) => 111.90/112.56 (( 111.90/112.56 ~ 111.90/112.56 in( 111.90/112.56 X266,X265)) => 111.90/112.56 (X264 != 111.90/112.56 X265)))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X267]: 111.90/112.56 subset( 111.90/112.56 X267,X267)) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X268, 111.90/112.56 X269,X270]: 111.90/112.56 (subset( 111.90/112.56 X268,X269) => 111.90/112.56 (subset( 111.90/112.56 X269,X270) => 111.90/112.56 subset( 111.90/112.56 X268,X270)))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X271, 111.90/112.56 X272]: 111.90/112.56 subset( 111.90/112.56 X272, 111.90/112.56 setadjoin( 111.90/112.56 X271,X272))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X273, 111.90/112.56 X274,X275]: 111.90/112.56 (subset( 111.90/112.56 X273,X275) => 111.90/112.56 subset( 111.90/112.56 X273, 111.90/112.56 setadjoin( 111.90/112.56 X274,X275)))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X276, 111.90/112.56 X277]: 111.90/112.56 (subset( 111.90/112.56 X276,X277) => 111.90/112.56 in( 111.90/112.56 X276, 111.90/112.56 powerset( 111.90/112.56 X277)))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X278, 111.90/112.56 X279]: 111.90/112.56 (subset( 111.90/112.56 X278,X279) => 111.90/112.56 (subset( 111.90/112.56 X279,X278) => 111.90/112.56 (X278 = 111.90/112.56 X279)))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X280]: 111.90/112.56 (subset( 111.90/112.56 X280, 111.90/112.56 emptyset) => 111.90/112.56 (X280 = 111.90/112.56 emptyset))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X281, 111.90/112.56 X282]: 111.90/112.56 (subset( 111.90/112.56 X282,X281) => 111.90/112.56 in( 111.90/112.56 X282, 111.90/112.56 powerset( 111.90/112.56 X281)))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X283, 111.90/112.56 X284]: 111.90/112.56 (in( 111.90/112.56 X284, 111.90/112.56 powerset( 111.90/112.56 X283)) => 111.90/112.56 subset( 111.90/112.56 X284,X283))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X285]: 111.90/112.56 in( 111.90/112.56 X285, 111.90/112.56 powerset( 111.90/112.56 X285))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X286, 111.90/112.56 X287]: 111.90/112.56 (subset( 111.90/112.56 X286,X287) => 111.90/112.56 subset( 111.90/112.56 powerset( 111.90/112.56 X286), 111.90/112.56 powerset( 111.90/112.56 X287)))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X288, 111.90/112.56 X289:( 111.90/112.56 $i > $o)]: 111.90/112.56 in( 111.90/112.56 dsetconstr( 111.90/112.56 X288, 111.90/112.56 '#ll_1'( 111.90/112.56 X289)), 111.90/112.56 powerset( 111.90/112.56 X288))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X290, 111.90/112.56 X291:( 111.90/112.56 $i > $o)]: 111.90/112.56 subset( 111.90/112.56 dsetconstr( 111.90/112.56 X290, 111.90/112.56 '#ll_1'( 111.90/112.56 X291)), 111.90/112.56 X290)) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X292, 111.90/112.56 X293,X294]: 111.90/112.56 (in( 111.90/112.56 X294,X292) => 111.90/112.56 in( 111.90/112.56 X294, 111.90/112.56 binunion( 111.90/112.56 X292,X293)))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X295, 111.90/112.56 X296]: 111.90/112.56 in( 111.90/112.56 X296, 111.90/112.56 setadjoin( 111.90/112.56 X295, 111.90/112.56 setadjoin( 111.90/112.56 X296, 111.90/112.56 emptyset)))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X297, 111.90/112.56 X298,X299]: 111.90/112.56 (in( 111.90/112.56 X299,X298) => 111.90/112.56 in( 111.90/112.56 X299, 111.90/112.56 binunion( 111.90/112.56 X297,X298)))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X300, 111.90/112.56 X301, 111.90/112.56 X302, 111.90/112.56 X303:$o]: 111.90/112.56 (in( 111.90/112.56 X302, 111.90/112.56 binunion( 111.90/112.56 X300,X301)) => 111.90/112.56 (( 111.90/112.56 in( 111.90/112.56 X302,X300) => 111.90/112.56 X303) => 111.90/112.56 (( 111.90/112.56 in( 111.90/112.56 X302,X301) => 111.90/112.56 X303) => 111.90/112.56 X303)))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X304, 111.90/112.56 X305,X306]: 111.90/112.56 (in( 111.90/112.56 X306, 111.90/112.56 binunion( 111.90/112.56 X304,X305)) => 111.90/112.56 (in( 111.90/112.56 X306,X305) | 111.90/112.56 in( 111.90/112.56 X306,X304)))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X307, 111.90/112.56 X308]: 111.90/112.56 subset( 111.90/112.56 X307, 111.90/112.56 binunion( 111.90/112.56 X307,X308))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X309, 111.90/112.56 X310]: 111.90/112.56 subset( 111.90/112.56 X310, 111.90/112.56 binunion( 111.90/112.56 X309,X310))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X311, 111.90/112.56 X312,X313]: 111.90/112.56 (in( 111.90/112.56 X313,X311) => 111.90/112.56 (in( 111.90/112.56 X313,X312) => 111.90/112.56 in( 111.90/112.56 X313, 111.90/112.56 binintersect( 111.90/112.56 X311,X312))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X314, 111.90/112.56 X315,X316]: 111.90/112.56 (subset( 111.90/112.56 X316,X314) => 111.90/112.56 (subset( 111.90/112.56 X316,X315) => 111.90/112.56 subset( 111.90/112.56 X316, 111.90/112.56 binintersect( 111.90/112.56 X314,X315))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X317, 111.90/112.56 X318,X319]: 111.90/112.56 (in( 111.90/112.56 X319, 111.90/112.56 binintersect( 111.90/112.56 X317,X318)) => 111.90/112.56 in( 111.90/112.56 X319,X317))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X320, 111.90/112.56 X321]: 111.90/112.56 subset( 111.90/112.56 binintersect( 111.90/112.56 X320,X321), 111.90/112.56 X320)) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X322, 111.90/112.56 X323]: 111.90/112.56 (subset( 111.90/112.56 X322,X323) => 111.90/112.56 (binintersect( 111.90/112.56 X322,X323) = 111.90/112.56 X322))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X324, 111.90/112.56 X325]: 111.90/112.56 (( 111.90/112.56 binintersect( 111.90/112.56 X324,X325) = 111.90/112.56 X325) => 111.90/112.56 subset( 111.90/112.56 X325,X324))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X326, 111.90/112.56 X327,X328]: 111.90/112.56 (in( 111.90/112.56 X328, 111.90/112.56 binintersect( 111.90/112.56 X326,X327)) => 111.90/112.56 in( 111.90/112.56 X328,X327))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X329, 111.90/112.56 X330]: 111.90/112.56 (( 111.90/112.56 ~ 111.90/112.56 ( 111.90/112.56 ?[X331]: 111.90/112.56 (in( 111.90/112.56 X331,X330) & 111.90/112.56 in( 111.90/112.56 X331,X329)))) => 111.90/112.56 (binintersect( 111.90/112.56 X329,X330) = 111.90/112.56 emptyset))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X332, 111.90/112.56 X333]: 111.90/112.56 subset( 111.90/112.56 binintersect( 111.90/112.56 X332,X333), 111.90/112.56 X333)) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X334, 111.90/112.56 X335]: 111.90/112.56 (subset( 111.90/112.56 X335,X334) => 111.90/112.56 (binintersect( 111.90/112.56 X334,X335) = 111.90/112.56 X335))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X336, 111.90/112.56 X337]: 111.90/112.56 (( 111.90/112.56 binintersect( 111.90/112.56 X336,X337) = 111.90/112.56 X336) => 111.90/112.56 subset( 111.90/112.56 X336,X337))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X338, 111.90/112.56 X339,X340]: 111.90/112.56 (binintersect( 111.90/112.56 X338, 111.90/112.56 binunion( 111.90/112.56 X339,X340)) = 111.90/112.56 binunion( 111.90/112.56 binintersect( 111.90/112.56 X338,X339), 111.90/112.56 binintersect( 111.90/112.56 X338,X340)))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X341, 111.90/112.56 X342,X343]: 111.90/112.56 (in( 111.90/112.56 X343,X341) => 111.90/112.56 (( 111.90/112.56 ~ 111.90/112.56 in( 111.90/112.56 X343,X342)) => 111.90/112.56 in( 111.90/112.56 X343, 111.90/112.56 setminus( 111.90/112.56 X341,X342))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X344, 111.90/112.56 X345,X346]: 111.90/112.56 (in( 111.90/112.56 X346, 111.90/112.56 setminus( 111.90/112.56 X344,X345)) => 111.90/112.56 in( 111.90/112.56 X346,X344))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X347, 111.90/112.56 X348,X349]: 111.90/112.56 (in( 111.90/112.56 X349, 111.90/112.56 setminus( 111.90/112.56 X347,X348)) => 111.90/112.56 (~ 111.90/112.56 in( 111.90/112.56 X349,X348)))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X350, 111.90/112.56 X351]: 111.90/112.56 (subset( 111.90/112.56 X350,X351) => 111.90/112.56 (setminus( 111.90/112.56 X350,X351) = 111.90/112.56 emptyset))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X352, 111.90/112.56 X353,X354]: 111.90/112.56 (( 111.90/112.56 ~ 111.90/112.56 in( 111.90/112.56 X354, 111.90/112.56 setminus( 111.90/112.56 X352,X353))) => 111.90/112.56 (in( 111.90/112.56 X354,X352) => 111.90/112.56 in( 111.90/112.56 X354,X353)))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X355, 111.90/112.56 X356,X357]: 111.90/112.56 (( 111.90/112.56 ~ 111.90/112.56 in( 111.90/112.56 X357, 111.90/112.56 setminus( 111.90/112.56 X355,X356))) => 111.90/112.56 (( 111.90/112.56 ~ 111.90/112.56 in( 111.90/112.56 X357,X356)) => 111.90/112.56 (~ 111.90/112.56 in( 111.90/112.56 X357,X355))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X358, 111.90/112.56 X359,X360]: 111.90/112.56 (( 111.90/112.56 ~ 111.90/112.56 in( 111.90/112.56 X360,X358)) => 111.90/112.56 (~ 111.90/112.56 in( 111.90/112.56 X360, 111.90/112.56 setminus( 111.90/112.56 X358,X359))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X361, 111.90/112.56 X362,X363]: 111.90/112.56 (in( 111.90/112.56 X363,X362) => 111.90/112.56 (~ 111.90/112.56 in( 111.90/112.56 X363, 111.90/112.56 setminus( 111.90/112.56 X361,X362))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X364, 111.90/112.56 X365]: 111.90/112.56 subset( 111.90/112.56 setminus( 111.90/112.56 X364,X365), 111.90/112.56 X364)) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X366, 111.90/112.56 X367]: 111.90/112.56 (( 111.90/112.56 setminus( 111.90/112.56 X366,X367) = 111.90/112.56 emptyset) => 111.90/112.56 subset( 111.90/112.56 X366,X367))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X368, 111.90/112.56 X369,X370]: 111.90/112.56 (in( 111.90/112.56 X370, 111.90/112.56 symdiff( 111.90/112.56 X368,X369)) => 111.90/112.56 (![X371:$o]: 111.90/112.56 (( 111.90/112.56 in( 111.90/112.56 X370,X368) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ~ 111.90/112.56 in( 111.90/112.56 X370,X369)) => 111.90/112.56 X371)) => 111.90/112.56 (( 111.90/112.56 ( 111.90/112.56 ~ 111.90/112.56 in( 111.90/112.56 X370,X368)) => 111.90/112.56 ( 111.90/112.56 in( 111.90/112.56 X370,X369) => 111.90/112.56 X371)) => 111.90/112.56 X371))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X372, 111.90/112.56 X373,X374]: 111.90/112.56 (in( 111.90/112.56 X374,X372) => 111.90/112.56 (( 111.90/112.56 ~ 111.90/112.56 in( 111.90/112.56 X374,X373)) => 111.90/112.56 in( 111.90/112.56 X374, 111.90/112.56 symdiff( 111.90/112.56 X372,X373))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X375, 111.90/112.56 X376,X377]: 111.90/112.56 (( 111.90/112.56 ~ 111.90/112.56 in( 111.90/112.56 X377,X375)) => 111.90/112.56 (in( 111.90/112.56 X377,X376) => 111.90/112.56 in( 111.90/112.56 X377, 111.90/112.56 symdiff( 111.90/112.56 X375,X376))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X378, 111.90/112.56 X379,X380]: 111.90/112.56 (in( 111.90/112.56 X380,X378) => 111.90/112.56 (in( 111.90/112.56 X380,X379) => 111.90/112.56 (~ 111.90/112.56 in( 111.90/112.56 X380, 111.90/112.56 symdiff( 111.90/112.56 X378,X379)))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X381, 111.90/112.56 X382,X383]: 111.90/112.56 (( 111.90/112.56 ~ 111.90/112.56 in( 111.90/112.56 X383,X381)) => 111.90/112.56 (( 111.90/112.56 ~ 111.90/112.56 in( 111.90/112.56 X383,X382)) => 111.90/112.56 (~ 111.90/112.56 in( 111.90/112.56 X383, 111.90/112.56 symdiff( 111.90/112.56 X381,X382)))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X384, 111.90/112.56 X385]: 111.90/112.56 in( 111.90/112.56 X385, 111.90/112.56 setadjoin( 111.90/112.56 X384, 111.90/112.56 setadjoin( 111.90/112.56 X385, 111.90/112.56 emptyset)))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X386, 111.90/112.56 X387]: 111.90/112.56 in( 111.90/112.56 X386, 111.90/112.56 setunion( 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X386, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X386, 111.90/112.56 setadjoin( 111.90/112.56 X387, 111.90/112.56 emptyset)), 111.90/112.56 emptyset))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X388, 111.90/112.56 X389]: 111.90/112.56 in( 111.90/112.56 X389, 111.90/112.56 setunion( 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X388, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X388, 111.90/112.56 setadjoin( 111.90/112.56 X389, 111.90/112.56 emptyset)), 111.90/112.56 emptyset))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X390, 111.90/112.56 X391]: 111.90/112.56 (?[X392]: 111.90/112.56 (( 111.90/112.56 ?[X393]: 111.90/112.56 (( 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X390, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X390, 111.90/112.56 setadjoin( 111.90/112.56 X391, 111.90/112.56 emptyset)), 111.90/112.56 emptyset)) = 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X392, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X392, 111.90/112.56 setadjoin( 111.90/112.56 X393, 111.90/112.56 emptyset)), 111.90/112.56 emptyset))) & 111.90/112.56 in( 111.90/112.56 X393, 111.90/112.56 setunion( 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X390, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X390, 111.90/112.56 setadjoin( 111.90/112.56 X391, 111.90/112.56 emptyset)), 111.90/112.56 emptyset)))))) & 111.90/112.56 in( 111.90/112.56 X392, 111.90/112.56 setunion( 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X390, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X390, 111.90/112.56 setadjoin( 111.90/112.56 X391, 111.90/112.56 emptyset)), 111.90/112.56 emptyset))))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X394, 111.90/112.56 X395]: 111.90/112.56 (?[X396]: 111.90/112.56 (( 111.90/112.56 ?[X397]: 111.90/112.56 (( 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X394, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X394, 111.90/112.56 setadjoin( 111.90/112.56 X395, 111.90/112.56 emptyset)), 111.90/112.56 emptyset)) = 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X396, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X396, 111.90/112.56 setadjoin( 111.90/112.56 X397, 111.90/112.56 emptyset)), 111.90/112.56 emptyset))) & 111.90/112.56 in( 111.90/112.56 X397, 111.90/112.56 setunion( 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X394, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X394, 111.90/112.56 setadjoin( 111.90/112.56 X395, 111.90/112.56 emptyset)), 111.90/112.56 emptyset)))))) & 111.90/112.56 in( 111.90/112.56 X396, 111.90/112.56 setunion( 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X394, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X394, 111.90/112.56 setadjoin( 111.90/112.56 X395, 111.90/112.56 emptyset)), 111.90/112.56 emptyset))))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X398, 111.90/112.56 X399]: 111.90/112.56 (in( 111.90/112.56 X399,X398) => 111.90/112.56 subset( 111.90/112.56 setadjoin( 111.90/112.56 X399, 111.90/112.56 emptyset), 111.90/112.56 X398))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X400, 111.90/112.56 X401]: 111.90/112.56 (in( 111.90/112.56 X401,X400) => 111.90/112.56 in( 111.90/112.56 setadjoin( 111.90/112.56 X401, 111.90/112.56 emptyset), 111.90/112.56 powerset( 111.90/112.56 X400)))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X402, 111.90/112.56 X403,X404]: 111.90/112.56 (in( 111.90/112.56 X404,X402) => 111.90/112.56 in( 111.90/112.56 setadjoin( 111.90/112.56 X404, 111.90/112.56 emptyset), 111.90/112.56 powerset( 111.90/112.56 binunion( 111.90/112.56 X402,X403))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X405, 111.90/112.56 X406,X407]: 111.90/112.56 (in( 111.90/112.56 X407, 111.90/112.56 setadjoin( 111.90/112.56 X405, 111.90/112.56 setadjoin( 111.90/112.56 X406, 111.90/112.56 emptyset))) => 111.90/112.56 (( 111.90/112.56 X407 = 111.90/112.56 X406) | 111.90/112.56 (X407 = 111.90/112.56 X405)))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X408, 111.90/112.56 X409,X410]: 111.90/112.56 (in( 111.90/112.56 X410,X408) => 111.90/112.56 (![X411]: 111.90/112.56 (in( 111.90/112.56 X411,X409) => 111.90/112.56 subset( 111.90/112.56 setadjoin( 111.90/112.56 X410, 111.90/112.56 setadjoin( 111.90/112.56 X411, 111.90/112.56 emptyset)), 111.90/112.56 binunion( 111.90/112.56 X408,X409)))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X412, 111.90/112.56 X413,X414]: 111.90/112.56 (in( 111.90/112.56 X414,X412) => 111.90/112.56 (![X415]: 111.90/112.56 (in( 111.90/112.56 X415,X413) => 111.90/112.56 in( 111.90/112.56 setadjoin( 111.90/112.56 X414, 111.90/112.56 setadjoin( 111.90/112.56 X415, 111.90/112.56 emptyset)), 111.90/112.56 powerset( 111.90/112.56 binunion( 111.90/112.56 X412,X413))))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X416, 111.90/112.56 X417,X418]: 111.90/112.56 (in( 111.90/112.56 X418,X416) => 111.90/112.56 (![X419]: 111.90/112.56 (in( 111.90/112.56 X419,X417) => 111.90/112.56 subset( 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X418, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X418, 111.90/112.56 setadjoin( 111.90/112.56 X419, 111.90/112.56 emptyset)), 111.90/112.56 emptyset)), 111.90/112.56 powerset( 111.90/112.56 binunion( 111.90/112.56 X416,X417))))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X420, 111.90/112.56 X421,X422]: 111.90/112.56 (in( 111.90/112.56 X422,X420) => 111.90/112.56 (![X423]: 111.90/112.56 (in( 111.90/112.56 X423,X421) => 111.90/112.56 in( 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X422, 111.90/112.56 emptyset), 111.90/112.56 setadjoin( 111.90/112.56 setadjoin( 111.90/112.56 X422, 111.90/112.56 setadjoin( 111.90/112.56 X423, 111.90/112.56 emptyset)), 111.90/112.56 emptyset)), 111.90/112.56 powerset( 111.90/112.56 powerset( 111.90/112.56 binunion( 111.90/112.56 X420,X421)))))))) => 111.90/112.56 ( 111.90/112.56 ( 111.90/112.56 ![X424, 111.90/112.56 X425,X426]: 111.90/112.56 (in( 111.90/112.56 X426,X424) => 111.90/112.56 (![X427]: 111.90/112.56 (in( 111.90/112.56 X427,X425) => 111.90/112.56 in( 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X426, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X426, 111.90/112.57 setadjoin( 111.90/112.57 X427, 111.90/112.57 emptyset)), 111.90/112.57 emptyset)), 111.90/112.57 powerset( 111.90/112.57 powerset( 111.90/112.57 binunion( 111.90/112.57 X424,X425)))))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X428, 111.90/112.57 X429,X430]: 111.90/112.57 (in( 111.90/112.57 X430,X428) => 111.90/112.57 (![X431]: 111.90/112.57 (in( 111.90/112.57 X431,X429) => 111.90/112.57 in( 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X430, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X430, 111.90/112.57 setadjoin( 111.90/112.57 X431, 111.90/112.57 emptyset)), 111.90/112.57 emptyset)), 111.90/112.57 cartprod( 111.90/112.57 X428,X429)))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X432, 111.90/112.57 X433,X434]: 111.90/112.57 (in( 111.90/112.57 X434, 111.90/112.57 cartprod( 111.90/112.57 X432,X433)) => 111.90/112.57 (?[X435]: 111.90/112.57 (( 111.90/112.57 ?[X436]: 111.90/112.57 (( 111.90/112.57 X434 = 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X435, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X435, 111.90/112.57 setadjoin( 111.90/112.57 X436, 111.90/112.57 emptyset)), 111.90/112.57 emptyset))) & 111.90/112.57 in( 111.90/112.57 X436,X433))) & 111.90/112.57 in( 111.90/112.57 X435,X432))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X437, 111.90/112.57 X438,X439]: 111.90/112.57 (in( 111.90/112.57 X439, 111.90/112.57 cartprod( 111.90/112.57 X437,X438)) => 111.90/112.57 (?[X440]: 111.90/112.57 (( 111.90/112.57 ?[X441]: 111.90/112.57 (( 111.90/112.57 X439 = 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X440, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X440, 111.90/112.57 setadjoin( 111.90/112.57 X441, 111.90/112.57 emptyset)), 111.90/112.57 emptyset))) & 111.90/112.57 in( 111.90/112.57 X441, 111.90/112.57 setunion( 111.90/112.57 X439)))) & 111.90/112.57 in( 111.90/112.57 X440, 111.90/112.57 setunion( 111.90/112.57 X439)))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X442, 111.90/112.57 X443]: 111.90/112.57 (in( 111.90/112.57 X443, 111.90/112.57 setunion( 111.90/112.57 X442)) => 111.90/112.57 (?[X444]: 111.90/112.57 (in( 111.90/112.57 X443,X444) & 111.90/112.57 in( 111.90/112.57 X444,X442))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X445]: 111.90/112.57 subset( 111.90/112.57 setunion( 111.90/112.57 setadjoin( 111.90/112.57 X445, 111.90/112.57 emptyset)), 111.90/112.57 X445)) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X446]: 111.90/112.57 subset( 111.90/112.57 X446, 111.90/112.57 setunion( 111.90/112.57 setadjoin( 111.90/112.57 X446, 111.90/112.57 emptyset)))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X447]: 111.90/112.57 (setunion( 111.90/112.57 setadjoin( 111.90/112.57 X447, 111.90/112.57 emptyset)) = 111.90/112.57 X447)) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X448, 111.90/112.57 X449:( 111.90/112.57 $i > $o)]: 111.90/112.57 (( 111.90/112.57 ![X450]: 111.90/112.57 (in( 111.90/112.57 X450,X448) => 111.90/112.57 (![X451]: 111.90/112.57 (in( 111.90/112.57 X451,X448) => 111.90/112.57 (X449( 111.90/112.57 X450) => 111.90/112.57 (X449( 111.90/112.57 X451) => 111.90/112.57 (X450 = 111.90/112.57 X451))))))) => 111.90/112.57 (( 111.90/112.57 ?[X452]: 111.90/112.57 (X449( 111.90/112.57 X452) & 111.90/112.57 in( 111.90/112.57 X452,X448))) => 111.90/112.57 (?[X453]: 111.90/112.57 (( 111.90/112.57 dsetconstr( 111.90/112.57 X448, 111.90/112.57 '#ll_1'( 111.90/112.57 X449)) = 111.90/112.57 setadjoin( 111.90/112.57 X453, 111.90/112.57 emptyset)) & 111.90/112.57 in( 111.90/112.57 X453, 111.90/112.57 dsetconstr( 111.90/112.57 X448, 111.90/112.57 '#ll_1'( 111.90/112.57 X449)))))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X454, 111.90/112.57 X455:( 111.90/112.57 $i > $o)]: 111.90/112.57 (( 111.90/112.57 ?[X456]: 111.90/112.57 (( 111.90/112.57 dsetconstr( 111.90/112.57 X454, 111.90/112.57 '#ll_1'( 111.90/112.57 X455)) = 111.90/112.57 setadjoin( 111.90/112.57 X456, 111.90/112.57 emptyset)) & 111.90/112.57 in( 111.90/112.57 X456, 111.90/112.57 dsetconstr( 111.90/112.57 X454, 111.90/112.57 '#ll_1'( 111.90/112.57 X455))))) => 111.90/112.57 (?[X457]: 111.90/112.57 (X455( 111.90/112.57 X457) & 111.90/112.57 in( 111.90/112.57 X457,X454))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X458, 111.90/112.57 X459:( 111.90/112.57 $i > $o), 111.90/112.57 X460]: 111.90/112.57 (in( 111.90/112.57 X460,X458) => 111.90/112.57 (X459( 111.90/112.57 X460) => 111.90/112.57 (( 111.90/112.57 ![X461]: 111.90/112.57 (in( 111.90/112.57 X461,X458) => 111.90/112.57 (X459( 111.90/112.57 X461) => 111.90/112.57 (X461 = 111.90/112.57 X460)))) => 111.90/112.57 (?[X462]: 111.90/112.57 (( 111.90/112.57 dsetconstr( 111.90/112.57 X458, 111.90/112.57 '#ll_1'( 111.90/112.57 X459)) = 111.90/112.57 setadjoin( 111.90/112.57 X462, 111.90/112.57 emptyset)) & 111.90/112.57 in( 111.90/112.57 X462, 111.90/112.57 dsetconstr( 111.90/112.57 X458, 111.90/112.57 '#ll_1'( 111.90/112.57 X459))))))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X463, 111.90/112.57 X464:( 111.90/112.57 $i > $o)]: 111.90/112.57 (( 111.90/112.57 ![X465]: 111.90/112.57 (in( 111.90/112.57 X465,X463) => 111.90/112.57 (![X466]: 111.90/112.57 (in( 111.90/112.57 X466,X463) => 111.90/112.57 (X464( 111.90/112.57 X465) => 111.90/112.57 (X464( 111.90/112.57 X466) => 111.90/112.57 (X465 = 111.90/112.57 X466))))))) => 111.90/112.57 (( 111.90/112.57 ?[X467]: 111.90/112.57 (X464( 111.90/112.57 X467) & 111.90/112.57 in( 111.90/112.57 X467,X463))) => 111.90/112.57 (?[X468]: 111.90/112.57 (( 111.90/112.57 dsetconstr( 111.90/112.57 X463, 111.90/112.57 '#ll_1'( 111.90/112.57 X464)) = 111.90/112.57 setadjoin( 111.90/112.57 X468, 111.90/112.57 emptyset)) & 111.90/112.57 in( 111.90/112.57 X468, 111.90/112.57 dsetconstr( 111.90/112.57 X463, 111.90/112.57 '#ll_1'( 111.90/112.57 X464)))))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X469, 111.90/112.57 X470]: 111.90/112.57 (( 111.90/112.57 setadjoin( 111.90/112.57 X469, 111.90/112.57 emptyset) = 111.90/112.57 setadjoin( 111.90/112.57 X470, 111.90/112.57 emptyset)) => 111.90/112.57 (X469 = 111.90/112.57 X470))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X471, 111.90/112.57 X472,X473]: 111.90/112.57 (in( 111.90/112.57 setadjoin( 111.90/112.57 X473, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X471, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X471, 111.90/112.57 setadjoin( 111.90/112.57 X472, 111.90/112.57 emptyset)), 111.90/112.57 emptyset))) => 111.90/112.57 (X471 = 111.90/112.57 X473))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X474]: 111.90/112.57 (( 111.90/112.57 ?[X475]: 111.90/112.57 (( 111.90/112.57 ?[X476]: 111.90/112.57 (( 111.90/112.57 X474 = 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X475, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X475, 111.90/112.57 setadjoin( 111.90/112.57 X476, 111.90/112.57 emptyset)), 111.90/112.57 emptyset))) & 111.90/112.57 in( 111.90/112.57 X476, 111.90/112.57 setunion( 111.90/112.57 X474)))) & 111.90/112.57 in( 111.90/112.57 X475, 111.90/112.57 setunion( 111.90/112.57 X474)))) => 111.90/112.57 (?[X477]: 111.90/112.57 (( 111.90/112.57 dsetconstr( 111.90/112.57 setunion( 111.90/112.57 X474), 111.90/112.57 '#ll_0'( 111.90/112.57 X474)) = 111.90/112.57 setadjoin( 111.90/112.57 X477, 111.90/112.57 emptyset)) & 111.90/112.57 in( 111.90/112.57 X477, 111.90/112.57 dsetconstr( 111.90/112.57 setunion( 111.90/112.57 X474), 111.90/112.57 '#ll_0'( 111.90/112.57 X474))))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X478]: 111.90/112.57 (( 111.90/112.57 ?[X479]: 111.90/112.57 (( 111.90/112.57 X478 = 111.90/112.57 setadjoin( 111.90/112.57 X479, 111.90/112.57 emptyset)) & 111.90/112.57 in( 111.90/112.57 X479,X478))) => 111.90/112.57 in( 111.90/112.57 setunion( 111.90/112.57 X478), 111.90/112.57 X478))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X480, 111.90/112.57 X481]: 111.90/112.57 (kfst( 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X480, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X480, 111.90/112.57 setadjoin( 111.90/112.57 X481, 111.90/112.57 emptyset)), 111.90/112.57 emptyset))) = 111.90/112.57 X480)) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X482, 111.90/112.57 X483,X484]: 111.90/112.57 (in( 111.90/112.57 X484, 111.90/112.57 cartprod( 111.90/112.57 X482,X483)) => 111.90/112.57 in( 111.90/112.57 kfst( 111.90/112.57 X484), 111.90/112.57 X482))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X485, 111.90/112.57 X486, 111.90/112.57 X487,X488]: 111.90/112.57 (( 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X485, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X485, 111.90/112.57 setadjoin( 111.90/112.57 X486, 111.90/112.57 emptyset)), 111.90/112.57 emptyset)) = 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X487, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X487, 111.90/112.57 setadjoin( 111.90/112.57 X488, 111.90/112.57 emptyset)), 111.90/112.57 emptyset))) => 111.90/112.57 (X485 = 111.90/112.57 X487))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X489, 111.90/112.57 X490, 111.90/112.57 X491,X492]: 111.90/112.57 (( 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X489, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X489, 111.90/112.57 setadjoin( 111.90/112.57 X490, 111.90/112.57 emptyset)), 111.90/112.57 emptyset)) = 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X491, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X491, 111.90/112.57 setadjoin( 111.90/112.57 X492, 111.90/112.57 emptyset)), 111.90/112.57 emptyset))) => 111.90/112.57 (X489 = 111.90/112.57 X491))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X493, 111.90/112.57 X494]: 111.90/112.57 (( 111.90/112.57 X493 = 111.90/112.57 X494) => 111.90/112.57 (setadjoin( 111.90/112.57 X493, 111.90/112.57 setadjoin( 111.90/112.57 X494, 111.90/112.57 emptyset)) = 111.90/112.57 setadjoin( 111.90/112.57 X493, 111.90/112.57 emptyset)))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X495, 111.90/112.57 X496]: 111.90/112.57 (( 111.90/112.57 X495 = 111.90/112.57 X496) => 111.90/112.57 (setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X495, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X495, 111.90/112.57 setadjoin( 111.90/112.57 X496, 111.90/112.57 emptyset)), 111.90/112.57 emptyset)) = 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X495, 111.90/112.57 emptyset), 111.90/112.57 emptyset)))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X497, 111.90/112.57 X498, 111.90/112.57 X499,X500]: 111.90/112.57 (( 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X497, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X497, 111.90/112.57 setadjoin( 111.90/112.57 X498, 111.90/112.57 emptyset)), 111.90/112.57 emptyset)) = 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X499, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X499, 111.90/112.57 setadjoin( 111.90/112.57 X500, 111.90/112.57 emptyset)), 111.90/112.57 emptyset))) => 111.90/112.57 (( 111.90/112.57 X499 = 111.90/112.57 X500) => 111.90/112.57 (X498 = 111.90/112.57 X500)))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X501, 111.90/112.57 X502,X503]: 111.90/112.57 (( 111.90/112.57 setadjoin( 111.90/112.57 X501, 111.90/112.57 setadjoin( 111.90/112.57 X502, 111.90/112.57 emptyset)) = 111.90/112.57 setadjoin( 111.90/112.57 X503, 111.90/112.57 emptyset)) => 111.90/112.57 (X501 = 111.90/112.57 X502))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X504, 111.90/112.57 X505, 111.90/112.57 X506,X507]: 111.90/112.57 (( 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X504, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X504, 111.90/112.57 setadjoin( 111.90/112.57 X505, 111.90/112.57 emptyset)), 111.90/112.57 emptyset)) = 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X506, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X506, 111.90/112.57 setadjoin( 111.90/112.57 X507, 111.90/112.57 emptyset)), 111.90/112.57 emptyset))) => 111.90/112.57 (X505 = 111.90/112.57 X507))) => 111.90/112.57 ( 111.90/112.57 ![X508, 111.90/112.57 X509, 111.90/112.57 X510,X511]: 111.90/112.57 (( 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X508, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X508, 111.90/112.57 setadjoin( 111.90/112.57 X509, 111.90/112.57 emptyset)), 111.90/112.57 emptyset)) = 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X510, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X510, 111.90/112.57 setadjoin( 111.90/112.57 X511, 111.90/112.57 emptyset)), 111.90/112.57 emptyset))) => 111.90/112.57 (X509 = 111.90/112.57 X511)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 111.90/112.57 tff(zf_stmt_14, negated_conjecture, 111.90/112.57 (~ 111.90/112.57 ((![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))) => 111.90/112.57 ((![X5]: (~in(X5,emptyset))) => 111.90/112.57 ((![X6,X7,X8]: (in(X8,setadjoin(X6,X7)) <=> zip_tseitin0(X8,X7,X6))) => 111.90/112.57 ((![X9,X10]: 111.90/112.57 (in(X10,powerset(X9)) <=> (![X11]: zip_tseitin1(X11,X10,X9)))) => 111.90/112.57 ((![X12,X13]: 111.90/112.57 (in(X13,setunion(X12)) <=> (?[X14]: zip_tseitin2(X14,X13,X12)))) => 111.90/112.57 (in(emptyset,omega) => 111.90/112.57 ((![X15]: (in(X15,omega) => in(setadjoin(X15,X15),omega))) => 111.90/112.57 ((![X16]: 111.90/112.57 (((![X17]: 111.90/112.57 ((in(X17,X16) & in(X17,omega)) => 111.90/112.57 in(setadjoin(X17,X17),X16))) & 111.90/112.57 in(emptyset,X16)) => 111.90/112.57 (![X18]: (in(X18,omega) => in(X18,X16))))) => 111.90/112.57 ((![X19:(($i * $i) > $o),X20]: 111.90/112.57 ((![X21]: 111.90/112.57 (in(X21,X20) => 111.90/112.57 (?[X22]: 111.90/112.57 ((![X23]: (X19(X21,X23) => (X22 = X23))) & 111.90/112.57 X19(X21,X22))))) => 111.90/112.57 (?[X24]: 111.90/112.57 (![X25]: 111.90/112.57 (in(X25,X24) <=> 111.90/112.57 (?[X26]: zip_tseitin3(X26,X25,X20,X19))))))) => 111.90/112.57 ((![X27]: 111.90/112.57 ((?[X28]: in(X28,X27)) => 111.90/112.57 (?[X29]: 111.90/112.57 ((~(?[X30]: (in(X30,X27) & in(X30,X29)))) & in(X29,X27))))) => 111.90/112.57 ((![X31]: 111.90/112.57 (?[X32]: 111.90/112.57 ((![X33]: 111.90/112.57 (((?[X34]: in(X34,X33)) & 111.90/112.57 (![X35]: (in(X35,X33) => in(X35,X31)))) => 111.90/112.57 (?[X36,X37]: 111.90/112.57 ((![X38]: 111.90/112.57 (in(X38,X32) => 111.90/112.57 (in(X37,X38) | 111.90/112.57 (![X39]: (in(X39,X38) => in(X39,X36)))))) & 111.90/112.57 (~(?[X40]: (in(X40,X33) & in(X40,X36)))) & 111.90/112.57 in(X37,X33) & in(X36,X32))))) & 111.90/112.57 (![X41,X42]: 111.90/112.57 ((in(X42,X32) & in(X41,X32)) => 111.90/112.57 ((![X43]: (in(X43,X42) => in(X43,X41))) | 111.90/112.57 (![X44]: (in(X44,X41) => in(X44,X42)))))) & 111.90/112.57 (![X45,X46]: 111.90/112.57 ((in(X46,X31) & in(X45,X31)) => 111.90/112.57 ((![X47]: 111.90/112.57 (in(X47,X32) => (in(X45,X47) <=> in(X46,X47)))) => 111.90/112.57 (X45 = X46)))) & 111.90/112.57 (![X48]: 111.90/112.57 (in(X48,X32) => 111.90/112.57 (![X49]: (in(X49,X48) => in(X49,X31)))))))) => 111.90/112.57 ((![X50:($i > $o)]: 111.90/112.57 ((?[X51]: ((![X52]: (X50(X52) => (X51 = X52))) & X50(X51))) => 111.90/112.57 X50(descr('#ll_1'(X50))))) => 111.90/112.57 ((![X53,X54:($i > $o),X55]: 111.90/112.57 (in(X55,X53) => 111.90/112.57 (X54(X55) => in(X55,dsetconstr(X53,'#ll_1'(X54)))))) => 111.90/112.57 ((![X56,X57:($i > $o),X58]: 111.90/112.57 (in(X58,dsetconstr(X56,'#ll_1'(X57))) => in(X58,X56))) => 111.90/112.57 ((![X59,X60:($i > $o),X61]: 111.90/112.57 (in(X61,dsetconstr(X59,'#ll_1'(X60))) => X60(X61))) => 111.90/112.57 ((![X62:($i > $o)]: 111.90/112.57 ((?[X63]: 111.90/112.57 ((![X64]: (X62(X64) => (X63 = X64))) & X62(X63))) => 111.90/112.57 (?[X65]: 111.90/112.57 ((![X66]: (X62(X66) => (X65 = X66))) & X62(X65))))) => 111.90/112.57 ((![X67:$o,X68]: (in(X68,prop2set(X67)) => X67)) => 111.90/112.57 ((![X69]: (in(X69,emptyset) => (![X70:$o]: X70))) => 111.90/112.57 ((![X71]: (in(X71,emptyset) => $false)) => 111.90/112.57 ((![X72]: (~in(X72,emptyset))) => 111.90/112.57 ((![X73:($i > $o)]: 111.90/112.57 ((?[X74]: 111.90/112.57 ((![X75]: (X73(X75) => (X74 = X75))) & 111.90/112.57 X73(X74))) => 111.90/112.57 (?[X76]: X73(X76)))) => 111.90/112.57 ((![X77,X78]: 111.90/112.57 ((![X79]: (in(X79,X77) => in(X79,X78))) => 111.90/112.57 ((![X80]: (in(X80,X78) => in(X80,X77))) => 111.90/112.57 (X77 = X78)))) => 111.90/112.57 ((![X81]: 111.90/112.57 ((![X82]: (~in(X82,X81))) => (X81 = emptyset))) => 111.90/112.57 ((![X83]: 111.90/112.57 ((![X84]: (~in(X84,X83))) => (X83 = emptyset))) => 111.90/112.57 ((![X85,X86:($i > $o),X87]: 111.90/112.57 (in(X87,X85) => 111.90/112.57 (in(X87,dsetconstr(X85,'#ll_1'(X86))) <=> 111.90/112.57 X86(X87)))) => 111.90/112.57 ((![X88]: 111.90/112.57 ((X88 != emptyset) => (?[X89]: in(X89,X88)))) => 111.90/112.57 ((![X90,X91:($i > $o),X92]: 111.90/112.57 (in(X92,X90) => 111.90/112.57 (X91(X92) => 111.90/112.57 (dsetconstr(X90,'#ll_1'(X91)) != emptyset)))) => 111.90/112.57 ((![X93]: 111.90/112.57 ((?[X94]: in(X94,X93)) => 111.90/112.57 (X93 != emptyset))) => 111.90/112.57 ((![X95,X96]: in(X95,setadjoin(X95,X96))) => 111.90/112.57 (in(emptyset,setadjoin(emptyset,emptyset)) => 111.90/112.57 ((![X97,X98,X99]: 111.90/112.57 (in(X99,X98) => 111.90/112.57 in(X99,setadjoin(X97,X98)))) => 111.90/112.57 ((![X100,X101,X102]: 111.90/112.57 (in(X102,setadjoin(X100,X101)) => 111.90/112.57 (![X103:$o]: 111.90/112.57 (((X102 = X100) => X103) => 111.90/112.57 ((in(X102,X101) => X103) => X103))))) => 111.90/112.57 ((![X104,X105,X106]: 111.90/112.57 (in(X106,setadjoin(X104,X105)) => 111.90/112.57 (in(X106,X105) | (X106 = X104)))) => 111.90/112.57 ((![X107]: 111.90/112.57 (dsetconstr(X107,'#ll_2') = X107)) => 111.90/112.57 ((![X108,X109]: 111.90/112.57 ((![X110]: 111.90/112.57 (in(X110,X109) => in(X110,X108))) => 111.90/112.57 in(X109,powerset(X108)))) => 111.90/112.57 ((![X111]: in(emptyset,powerset(X111))) => 111.90/112.57 ((![X112]: 111.90/112.57 in(emptyset,powerset(X112))) => 111.90/112.57 ((![X113,X114,X115]: 111.90/112.57 (in(X114,powerset(X113)) => 111.90/112.57 (in(X115,X114) => in(X115,X113)))) => 111.90/112.57 ((![X116,X117,X118]: 111.90/112.57 (in(X117,X118) => 111.90/112.57 (in(X118,X116) => 111.90/112.57 in(X117,setunion(X116))))) => 111.90/112.57 ((![X119,X120]: 111.90/112.57 (in(X120,setunion(X119)) => 111.90/112.57 (![X121:$o]: 111.90/112.57 ((![X122]: 111.90/112.57 (in(X120,X122) => 111.90/112.57 (in(X122,X119) => 111.90/112.57 X121))) => 111.90/112.57 X121)))) => 111.90/112.57 ((![X123,X124]: 111.90/112.57 (in(X124,X123) => 111.90/112.57 in(X124, 111.90/112.57 powerset(setunion(X123))))) => 111.90/112.57 ((![X125:($i > $o)]: 111.90/112.57 ((?[X126]: 111.90/112.57 ((![X127]: 111.90/112.57 (X125(X127) => 111.90/112.57 (X126 = X127))) & 111.90/112.57 X125(X126))) => 111.90/112.57 (?[X128]: 111.90/112.57 (![X129]: 111.90/112.57 (X125(X129) <=> 111.90/112.57 (X129 = X128)))))) => 111.90/112.57 ((![X130]: 111.90/112.57 ((X130 != emptyset) => 111.90/112.57 (?[X131]: in(X131,X130)))) => 111.90/112.57 ((![X132,X133]: 111.90/112.57 (in(X132, 111.90/112.57 setadjoin(X133, 111.90/112.57 emptyset)) => 111.90/112.57 (X132 = X133))) => 111.90/112.57 ((![X134,X135]: 111.90/112.57 ((X134 != X135) => 111.90/112.57 (~ 111.90/112.57 in(X135, 111.90/112.57 setadjoin(X134, 111.90/112.57 emptyset))))) => 111.90/112.57 ((![X136,X137]: 111.90/112.57 ((X136 = X137) => 111.90/112.57 in(X136, 111.90/112.57 setadjoin(X137, 111.90/112.57 emptyset)))) => 111.90/112.57 ((![X138,X139]: 111.90/112.57 (in(X138, 111.90/112.57 setadjoin(X139, 111.90/112.57 emptyset)) => 111.90/112.57 in(X139, 111.90/112.57 setadjoin(X138, 111.90/112.57 emptyset)))) => 111.90/112.57 ((![X140,X141,X142]: 111.90/112.57 (in(X142, 111.90/112.57 setadjoin( 111.90/112.57 X140, 111.90/112.57 setadjoin( 111.90/112.57 X141,emptyset))) => 111.90/112.57 ((X142 = X141) | 111.90/112.57 (X142 = X140)))) => 111.90/112.57 ((![X143,X144]: 111.90/112.57 in(X143, 111.90/112.57 setadjoin( 111.90/112.57 X143, 111.90/112.57 setadjoin( 111.90/112.57 X144,emptyset)))) => 111.90/112.57 ((![X145,X146]: 111.90/112.57 in(X146, 111.90/112.57 setadjoin( 111.90/112.57 X145, 111.90/112.57 setadjoin( 111.90/112.57 X146,emptyset)))) => 111.90/112.57 ((![X147,X148:($i > $o)]: 111.90/112.57 ((?[X149]: 111.90/112.57 (X148(X149) & 111.90/112.57 in(X149,X147))) => 111.90/112.57 ((dsetconstr( 111.90/112.57 X147, 111.90/112.57 '#ll_1'(X148)) = 111.90/112.57 emptyset) => 111.90/112.57 $false))) => 111.90/112.57 ((![X150:($i > $o), 111.90/112.57 X151]: 111.90/112.57 (in(X151,emptyset) => 111.90/112.57 X150(X151))) => 111.90/112.57 ((![X152, 111.90/112.57 X153:($i > $o)]: 111.90/112.57 ((~ 111.90/112.57 (![X154]: 111.90/112.57 (in( 111.90/112.57 X154,X152) => 111.90/112.57 X153(X154)))) => 111.90/112.57 (?[X155]: 111.90/112.57 ((~X153(X155)) & 111.90/112.57 in(X155,X152))))) => 111.90/112.57 ((![X156, 111.90/112.57 X157:($i > $o)]: 111.90/112.57 ((![X158]: 111.90/112.57 (in( 111.90/112.57 X158,X156) => 111.90/112.57 (~ 111.90/112.57 X157( 111.90/112.57 X158)))) => 111.90/112.57 (~ 111.90/112.57 (?[X159]: 111.90/112.57 (X157( 111.90/112.57 X159) & 111.90/112.57 in( 111.90/112.57 X159,X156)))))) => 111.90/112.57 ((![X160, 111.90/112.57 X161:($i > $o)]: 111.90/112.57 ((~ 111.90/112.57 (?[X162]: 111.90/112.57 ( 111.90/112.57 X161( 111.90/112.57 X162) & 111.90/112.57 in( 111.90/112.57 X162,X160)))) => 111.90/112.57 (![X163]: 111.90/112.57 (in( 111.90/112.57 X163,X160) => 111.90/112.57 (~ 111.90/112.57 X161( 111.90/112.57 X163)))))) => 111.90/112.57 ((![X164, 111.90/112.57 X165:( 111.90/112.57 $i > $o)]: 111.90/112.57 ((?[X166]: 111.90/112.57 (( 111.90/112.57 ~ 111.90/112.57 X165( 111.90/112.57 X166)) & 111.90/112.57 in( 111.90/112.57 X166,X164))) => 111.90/112.57 (~ 111.90/112.57 (![X167]: 111.90/112.57 (in( 111.90/112.57 X167,X164) => 111.90/112.57 X165( 111.90/112.57 X167)))))) => 111.90/112.57 ((![X168:$o]: 111.90/112.57 (X168 => 111.90/112.57 in(emptyset, 111.90/112.57 prop2set( 111.90/112.57 X168)))) => 111.90/112.57 ((![X169:$o]: 111.90/112.57 (X169 => 111.90/112.57 set2prop( 111.90/112.57 prop2set( 111.90/112.57 X169)))) => 111.90/112.57 ((![X170, 111.90/112.57 X171:( 111.90/112.57 $i > $o)]: 111.90/112.57 ((~ 111.90/112.57 ( 111.90/112.57 ?[X172]: 111.90/112.57 (X171( 111.90/112.57 X172) & 111.90/112.57 in( 111.90/112.57 X172,X170)))) => 111.90/112.57 (![X173]: 111.90/112.57 (in( 111.90/112.57 X173,X170) => 111.90/112.57 (~ 111.90/112.57 X171( 111.90/112.57 X173)))))) => 111.90/112.57 ((![X174, 111.90/112.57 X175:( 111.90/112.57 $i > $o)]: 111.90/112.57 (( 111.90/112.57 ~ 111.90/112.57 ( 111.90/112.57 ![X176]: 111.90/112.57 (in( 111.90/112.57 X176,X174) => 111.90/112.57 X175( 111.90/112.57 X176)))) => 111.90/112.57 ( 111.90/112.57 ?[X177]: 111.90/112.57 (( 111.90/112.57 ~ 111.90/112.57 X175( 111.90/112.57 X177)) & 111.90/112.57 in( 111.90/112.57 X177,X174))))) => 111.90/112.57 ((![X178:( 111.90/112.57 $i > $o)]: 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ?[X179]: 111.90/112.57 (( 111.90/112.57 ![X180]: 111.90/112.57 (X178( 111.90/112.57 X180) => 111.90/112.57 (X179 = 111.90/112.57 X180))) & 111.90/112.57 X178( 111.90/112.57 X179))) => 111.90/112.57 ( 111.90/112.57 ?[X181]: 111.90/112.57 (( 111.90/112.57 ![X182]: 111.90/112.57 (X178( 111.90/112.57 X182) => 111.90/112.57 (X181 = 111.90/112.57 X182))) & 111.90/112.57 X178( 111.90/112.57 X181))))) => 111.90/112.57 ((![X183:( 111.90/112.57 $i > $o)]: 111.90/112.57 (( 111.90/112.57 ?[X184]: 111.90/112.57 X183( 111.90/112.57 X184)) => 111.90/112.57 (( 111.90/112.57 ![X185, 111.90/112.57 X186]: 111.90/112.57 (X183( 111.90/112.57 X185) => 111.90/112.57 (X183( 111.90/112.57 X186) => 111.90/112.57 (X185 = 111.90/112.57 X186)))) => 111.90/112.57 (?[X187]: 111.90/112.57 (( 111.90/112.57 ![X188]: 111.90/112.57 (X183( 111.90/112.57 X188) => 111.90/112.57 (X187 = 111.90/112.57 X188))) & 111.90/112.57 X183( 111.90/112.57 X187)))))) => 111.90/112.57 ((![X189:( 111.90/112.57 $i > $o)]: 111.90/112.57 (( 111.90/112.57 ?[X190]: 111.90/112.57 (![X191]: 111.90/112.57 (X189( 111.90/112.57 X191) <=> 111.90/112.57 (X191 = 111.90/112.57 X190)))) => 111.90/112.57 (?[X192]: 111.90/112.57 (( 111.90/112.57 ![X193]: 111.90/112.57 (X189( 111.90/112.57 X193) => 111.90/112.57 (X192 = 111.90/112.57 X193))) & 111.90/112.57 X189( 111.90/112.57 X192))))) => 111.90/112.57 (( 111.90/112.57 ![X194, 111.90/112.57 X195]: 111.90/112.57 (( 111.90/112.57 X194 = 111.90/112.57 X195) => 111.90/112.57 (![X196, 111.90/112.57 X197]: 111.90/112.57 (( 111.90/112.57 X196 = 111.90/112.57 X197) => 111.90/112.57 (in( 111.90/112.57 X196,X194) => 111.90/112.57 in( 111.90/112.57 X197,X195)))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X198, 111.90/112.57 X199]: 111.90/112.57 (( 111.90/112.57 X198 = 111.90/112.57 X199) => 111.90/112.57 (![X200, 111.90/112.57 X201]: 111.90/112.57 (( 111.90/112.57 X200 = 111.90/112.57 X201) => 111.90/112.57 (in( 111.90/112.57 X200,X198) <=> 111.90/112.57 in( 111.90/112.57 X201,X199)))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X202:( 111.90/112.57 $i > $o)]: 111.90/112.57 (( 111.90/112.57 ?[X203]: 111.90/112.57 (( 111.90/112.57 ![X204]: 111.90/112.57 (X202( 111.90/112.57 X204) => 111.90/112.57 (X203 = 111.90/112.57 X204))) & 111.90/112.57 X202( 111.90/112.57 X203))) => 111.90/112.57 (![X205, 111.90/112.57 X206]: 111.90/112.57 (X202( 111.90/112.57 X205) => 111.90/112.57 (X202( 111.90/112.57 X206) => 111.90/112.57 (X205 = 111.90/112.57 X206)))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X207:( 111.90/112.57 $i > $o), 111.90/112.57 X208:( 111.90/112.57 $i > $o)]: 111.90/112.57 (( 111.90/112.57 ![X209, 111.90/112.57 X210]: 111.90/112.57 (( 111.90/112.57 X209 = 111.90/112.57 X210) => 111.90/112.57 (X207( 111.90/112.57 X209) <=> 111.90/112.57 X208( 111.90/112.57 X210)))) => 111.90/112.57 (( 111.90/112.57 ?[X211]: 111.90/112.57 zip_tseitin5( 111.90/112.57 X211,X207)) <=> 111.90/112.57 (?[X213]: 111.90/112.57 zip_tseitin5( 111.90/112.57 X213,X208))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 emptyset = 111.90/112.57 emptyset) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X215, 111.90/112.57 X216]: 111.90/112.57 (( 111.90/112.57 X215 = 111.90/112.57 X216) => 111.90/112.57 (![X217, 111.90/112.57 X218]: 111.90/112.57 (( 111.90/112.57 X217 = 111.90/112.57 X218) => 111.90/112.57 (setadjoin( 111.90/112.57 X215,X217) = 111.90/112.57 setadjoin( 111.90/112.57 X216,X218)))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X219, 111.90/112.57 X220]: 111.90/112.57 (( 111.90/112.57 X219 = 111.90/112.57 X220) => 111.90/112.57 (powerset( 111.90/112.57 X219) = 111.90/112.57 powerset( 111.90/112.57 X220)))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X221, 111.90/112.57 X222]: 111.90/112.57 (( 111.90/112.57 X221 = 111.90/112.57 X222) => 111.90/112.57 (setunion( 111.90/112.57 X221) = 111.90/112.57 setunion( 111.90/112.57 X222)))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 omega = 111.90/112.57 omega) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X223:( 111.90/112.57 $i > $o)]: 111.90/112.57 (( 111.90/112.57 ?[X224]: 111.90/112.57 (( 111.90/112.57 ![X225]: 111.90/112.57 (X223( 111.90/112.57 X225) => 111.90/112.57 (X224 = 111.90/112.57 X225))) & 111.90/112.57 X223( 111.90/112.57 X224))) => 111.90/112.57 (![X226, 111.90/112.57 X227]: 111.90/112.57 (X223( 111.90/112.57 X226) => 111.90/112.57 (X223( 111.90/112.57 X227) => 111.90/112.57 (X226 = 111.90/112.57 X227)))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X228:( 111.90/112.57 $i > $o), 111.90/112.57 X229:( 111.90/112.57 $i > $o)]: 111.90/112.57 (( 111.90/112.57 ![X230, 111.90/112.57 X231]: 111.90/112.57 (( 111.90/112.57 X230 = 111.90/112.57 X231) => 111.90/112.57 (X228( 111.90/112.57 X230) <=> 111.90/112.57 X229( 111.90/112.57 X231)))) => 111.90/112.57 (( 111.90/112.57 ?[X232]: 111.90/112.57 (( 111.90/112.57 ![X233]: 111.90/112.57 (X228( 111.90/112.57 X233) => 111.90/112.57 (X232 = 111.90/112.57 X233))) & 111.90/112.57 X228( 111.90/112.57 X232))) => 111.90/112.57 (( 111.90/112.57 ?[X234]: 111.90/112.57 (( 111.90/112.57 ![X235]: 111.90/112.57 (X229( 111.90/112.57 X235) => 111.90/112.57 (X234 = 111.90/112.57 X235))) & 111.90/112.57 X229( 111.90/112.57 X234))) => 111.90/112.57 (descr( 111.90/112.57 '#ll_1'( 111.90/112.57 X228)) = 111.90/112.57 descr( 111.90/112.57 '#ll_1'( 111.90/112.57 X229))))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X236, 111.90/112.57 X237]: 111.90/112.57 (( 111.90/112.57 X236 = 111.90/112.57 X237) => 111.90/112.57 (![X238:( 111.90/112.57 $i > $o), 111.90/112.57 X239:( 111.90/112.57 $i > $o)]: 111.90/112.57 (( 111.90/112.57 ![X240]: 111.90/112.57 (in( 111.90/112.57 X240,X236) => 111.90/112.57 (![X241]: 111.90/112.57 (in( 111.90/112.57 X241,X237) => 111.90/112.57 (( 111.90/112.57 X240 = 111.90/112.57 X241) => 111.90/112.57 (X238( 111.90/112.57 X240) <=> 111.90/112.57 X239( 111.90/112.57 X241))))))) => 111.90/112.57 (dsetconstr( 111.90/112.57 X236, 111.90/112.57 '#ll_1'( 111.90/112.57 X238)) = 111.90/112.57 dsetconstr( 111.90/112.57 X237, 111.90/112.57 '#ll_1'( 111.90/112.57 X239))))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X242, 111.90/112.57 X243]: 111.90/112.57 (( 111.90/112.57 ![X244]: 111.90/112.57 (in( 111.90/112.57 X244,X242) => 111.90/112.57 in( 111.90/112.57 X244,X243))) => 111.90/112.57 subset( 111.90/112.57 X242,X243))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X245, 111.90/112.57 X246]: 111.90/112.57 (( 111.90/112.57 X245 = 111.90/112.57 X246) => 111.90/112.57 subset( 111.90/112.57 X246,X245))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X247, 111.90/112.57 X248]: 111.90/112.57 (( 111.90/112.57 X247 = 111.90/112.57 X248) => 111.90/112.57 subset( 111.90/112.57 X247,X248))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X249, 111.90/112.57 X250]: 111.90/112.57 (( 111.90/112.57 ![X251]: 111.90/112.57 (in( 111.90/112.57 X251,X249) => 111.90/112.57 in( 111.90/112.57 X251,X250))) => 111.90/112.57 subset( 111.90/112.57 X249,X250))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X252]: 111.90/112.57 subset( 111.90/112.57 emptyset, 111.90/112.57 X252)) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X253, 111.90/112.57 X254,X255]: 111.90/112.57 (subset( 111.90/112.57 X253,X254) => 111.90/112.57 (in( 111.90/112.57 X255,X253) => 111.90/112.57 in( 111.90/112.57 X255,X254)))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X256, 111.90/112.57 X257,X258]: 111.90/112.57 (subset( 111.90/112.57 X256,X257) => 111.90/112.57 (( 111.90/112.57 ~ 111.90/112.57 in( 111.90/112.57 X258,X257)) => 111.90/112.57 (~ 111.90/112.57 in( 111.90/112.57 X258,X256))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X259, 111.90/112.57 X260,X261]: 111.90/112.57 (in( 111.90/112.57 X261,X259) => 111.90/112.57 (( 111.90/112.57 ~ 111.90/112.57 in( 111.90/112.57 X261,X260)) => 111.90/112.57 (~ 111.90/112.57 subset( 111.90/112.57 X259,X260))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X262, 111.90/112.57 X263]: 111.90/112.57 (( 111.90/112.57 ~ 111.90/112.57 subset( 111.90/112.57 X262,X263)) => 111.90/112.57 (X262 != 111.90/112.57 X263))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X264, 111.90/112.57 X265,X266]: 111.90/112.57 (in( 111.90/112.57 X266,X264) => 111.90/112.57 (( 111.90/112.57 ~ 111.90/112.57 in( 111.90/112.57 X266,X265)) => 111.90/112.57 (X264 != 111.90/112.57 X265)))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X267]: 111.90/112.57 subset( 111.90/112.57 X267,X267)) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X268, 111.90/112.57 X269,X270]: 111.90/112.57 (subset( 111.90/112.57 X268,X269) => 111.90/112.57 (subset( 111.90/112.57 X269,X270) => 111.90/112.57 subset( 111.90/112.57 X268,X270)))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X271, 111.90/112.57 X272]: 111.90/112.57 subset( 111.90/112.57 X272, 111.90/112.57 setadjoin( 111.90/112.57 X271,X272))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X273, 111.90/112.57 X274,X275]: 111.90/112.57 (subset( 111.90/112.57 X273,X275) => 111.90/112.57 subset( 111.90/112.57 X273, 111.90/112.57 setadjoin( 111.90/112.57 X274,X275)))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X276, 111.90/112.57 X277]: 111.90/112.57 (subset( 111.90/112.57 X276,X277) => 111.90/112.57 in( 111.90/112.57 X276, 111.90/112.57 powerset( 111.90/112.57 X277)))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X278, 111.90/112.57 X279]: 111.90/112.57 (subset( 111.90/112.57 X278,X279) => 111.90/112.57 (subset( 111.90/112.57 X279,X278) => 111.90/112.57 (X278 = 111.90/112.57 X279)))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X280]: 111.90/112.57 (subset( 111.90/112.57 X280, 111.90/112.57 emptyset) => 111.90/112.57 (X280 = 111.90/112.57 emptyset))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X281, 111.90/112.57 X282]: 111.90/112.57 (subset( 111.90/112.57 X282,X281) => 111.90/112.57 in( 111.90/112.57 X282, 111.90/112.57 powerset( 111.90/112.57 X281)))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X283, 111.90/112.57 X284]: 111.90/112.57 (in( 111.90/112.57 X284, 111.90/112.57 powerset( 111.90/112.57 X283)) => 111.90/112.57 subset( 111.90/112.57 X284,X283))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X285]: 111.90/112.57 in( 111.90/112.57 X285, 111.90/112.57 powerset( 111.90/112.57 X285))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X286, 111.90/112.57 X287]: 111.90/112.57 (subset( 111.90/112.57 X286,X287) => 111.90/112.57 subset( 111.90/112.57 powerset( 111.90/112.57 X286), 111.90/112.57 powerset( 111.90/112.57 X287)))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X288, 111.90/112.57 X289:( 111.90/112.57 $i > $o)]: 111.90/112.57 in( 111.90/112.57 dsetconstr( 111.90/112.57 X288, 111.90/112.57 '#ll_1'( 111.90/112.57 X289)), 111.90/112.57 powerset( 111.90/112.57 X288))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X290, 111.90/112.57 X291:( 111.90/112.57 $i > $o)]: 111.90/112.57 subset( 111.90/112.57 dsetconstr( 111.90/112.57 X290, 111.90/112.57 '#ll_1'( 111.90/112.57 X291)), 111.90/112.57 X290)) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X292, 111.90/112.57 X293,X294]: 111.90/112.57 (in( 111.90/112.57 X294,X292) => 111.90/112.57 in( 111.90/112.57 X294, 111.90/112.57 binunion( 111.90/112.57 X292,X293)))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X295, 111.90/112.57 X296]: 111.90/112.57 in( 111.90/112.57 X296, 111.90/112.57 setadjoin( 111.90/112.57 X295, 111.90/112.57 setadjoin( 111.90/112.57 X296, 111.90/112.57 emptyset)))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X297, 111.90/112.57 X298,X299]: 111.90/112.57 (in( 111.90/112.57 X299,X298) => 111.90/112.57 in( 111.90/112.57 X299, 111.90/112.57 binunion( 111.90/112.57 X297,X298)))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X300, 111.90/112.57 X301, 111.90/112.57 X302, 111.90/112.57 X303:$o]: 111.90/112.57 (in( 111.90/112.57 X302, 111.90/112.57 binunion( 111.90/112.57 X300,X301)) => 111.90/112.57 (( 111.90/112.57 in( 111.90/112.57 X302,X300) => 111.90/112.57 X303) => 111.90/112.57 (( 111.90/112.57 in( 111.90/112.57 X302,X301) => 111.90/112.57 X303) => 111.90/112.57 X303)))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X304, 111.90/112.57 X305,X306]: 111.90/112.57 (in( 111.90/112.57 X306, 111.90/112.57 binunion( 111.90/112.57 X304,X305)) => 111.90/112.57 (in( 111.90/112.57 X306,X305) | 111.90/112.57 in( 111.90/112.57 X306,X304)))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X307, 111.90/112.57 X308]: 111.90/112.57 subset( 111.90/112.57 X307, 111.90/112.57 binunion( 111.90/112.57 X307,X308))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X309, 111.90/112.57 X310]: 111.90/112.57 subset( 111.90/112.57 X310, 111.90/112.57 binunion( 111.90/112.57 X309,X310))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X311, 111.90/112.57 X312,X313]: 111.90/112.57 (in( 111.90/112.57 X313,X311) => 111.90/112.57 (in( 111.90/112.57 X313,X312) => 111.90/112.57 in( 111.90/112.57 X313, 111.90/112.57 binintersect( 111.90/112.57 X311,X312))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X314, 111.90/112.57 X315,X316]: 111.90/112.57 (subset( 111.90/112.57 X316,X314) => 111.90/112.57 (subset( 111.90/112.57 X316,X315) => 111.90/112.57 subset( 111.90/112.57 X316, 111.90/112.57 binintersect( 111.90/112.57 X314,X315))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X317, 111.90/112.57 X318,X319]: 111.90/112.57 (in( 111.90/112.57 X319, 111.90/112.57 binintersect( 111.90/112.57 X317,X318)) => 111.90/112.57 in( 111.90/112.57 X319,X317))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X320, 111.90/112.57 X321]: 111.90/112.57 subset( 111.90/112.57 binintersect( 111.90/112.57 X320,X321), 111.90/112.57 X320)) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X322, 111.90/112.57 X323]: 111.90/112.57 (subset( 111.90/112.57 X322,X323) => 111.90/112.57 (binintersect( 111.90/112.57 X322,X323) = 111.90/112.57 X322))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X324, 111.90/112.57 X325]: 111.90/112.57 (( 111.90/112.57 binintersect( 111.90/112.57 X324,X325) = 111.90/112.57 X325) => 111.90/112.57 subset( 111.90/112.57 X325,X324))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X326, 111.90/112.57 X327,X328]: 111.90/112.57 (in( 111.90/112.57 X328, 111.90/112.57 binintersect( 111.90/112.57 X326,X327)) => 111.90/112.57 in( 111.90/112.57 X328,X327))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X329, 111.90/112.57 X330]: 111.90/112.57 (( 111.90/112.57 ~ 111.90/112.57 ( 111.90/112.57 ?[X331]: 111.90/112.57 (in( 111.90/112.57 X331,X330) & 111.90/112.57 in( 111.90/112.57 X331,X329)))) => 111.90/112.57 (binintersect( 111.90/112.57 X329,X330) = 111.90/112.57 emptyset))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X332, 111.90/112.57 X333]: 111.90/112.57 subset( 111.90/112.57 binintersect( 111.90/112.57 X332,X333), 111.90/112.57 X333)) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X334, 111.90/112.57 X335]: 111.90/112.57 (subset( 111.90/112.57 X335,X334) => 111.90/112.57 (binintersect( 111.90/112.57 X334,X335) = 111.90/112.57 X335))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X336, 111.90/112.57 X337]: 111.90/112.57 (( 111.90/112.57 binintersect( 111.90/112.57 X336,X337) = 111.90/112.57 X336) => 111.90/112.57 subset( 111.90/112.57 X336,X337))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X338, 111.90/112.57 X339,X340]: 111.90/112.57 (binintersect( 111.90/112.57 X338, 111.90/112.57 binunion( 111.90/112.57 X339,X340)) = 111.90/112.57 binunion( 111.90/112.57 binintersect( 111.90/112.57 X338,X339), 111.90/112.57 binintersect( 111.90/112.57 X338,X340)))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X341, 111.90/112.57 X342,X343]: 111.90/112.57 (in( 111.90/112.57 X343,X341) => 111.90/112.57 (( 111.90/112.57 ~ 111.90/112.57 in( 111.90/112.57 X343,X342)) => 111.90/112.57 in( 111.90/112.57 X343, 111.90/112.57 setminus( 111.90/112.57 X341,X342))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X344, 111.90/112.57 X345,X346]: 111.90/112.57 (in( 111.90/112.57 X346, 111.90/112.57 setminus( 111.90/112.57 X344,X345)) => 111.90/112.57 in( 111.90/112.57 X346,X344))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X347, 111.90/112.57 X348,X349]: 111.90/112.57 (in( 111.90/112.57 X349, 111.90/112.57 setminus( 111.90/112.57 X347,X348)) => 111.90/112.57 (~ 111.90/112.57 in( 111.90/112.57 X349,X348)))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X350, 111.90/112.57 X351]: 111.90/112.57 (subset( 111.90/112.57 X350,X351) => 111.90/112.57 (setminus( 111.90/112.57 X350,X351) = 111.90/112.57 emptyset))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X352, 111.90/112.57 X353,X354]: 111.90/112.57 (( 111.90/112.57 ~ 111.90/112.57 in( 111.90/112.57 X354, 111.90/112.57 setminus( 111.90/112.57 X352,X353))) => 111.90/112.57 (in( 111.90/112.57 X354,X352) => 111.90/112.57 in( 111.90/112.57 X354,X353)))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X355, 111.90/112.57 X356,X357]: 111.90/112.57 (( 111.90/112.57 ~ 111.90/112.57 in( 111.90/112.57 X357, 111.90/112.57 setminus( 111.90/112.57 X355,X356))) => 111.90/112.57 (( 111.90/112.57 ~ 111.90/112.57 in( 111.90/112.57 X357,X356)) => 111.90/112.57 (~ 111.90/112.57 in( 111.90/112.57 X357,X355))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X358, 111.90/112.57 X359,X360]: 111.90/112.57 (( 111.90/112.57 ~ 111.90/112.57 in( 111.90/112.57 X360,X358)) => 111.90/112.57 (~ 111.90/112.57 in( 111.90/112.57 X360, 111.90/112.57 setminus( 111.90/112.57 X358,X359))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X361, 111.90/112.57 X362,X363]: 111.90/112.57 (in( 111.90/112.57 X363,X362) => 111.90/112.57 (~ 111.90/112.57 in( 111.90/112.57 X363, 111.90/112.57 setminus( 111.90/112.57 X361,X362))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X364, 111.90/112.57 X365]: 111.90/112.57 subset( 111.90/112.57 setminus( 111.90/112.57 X364,X365), 111.90/112.57 X364)) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X366, 111.90/112.57 X367]: 111.90/112.57 (( 111.90/112.57 setminus( 111.90/112.57 X366,X367) = 111.90/112.57 emptyset) => 111.90/112.57 subset( 111.90/112.57 X366,X367))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X368, 111.90/112.57 X369,X370]: 111.90/112.57 (in( 111.90/112.57 X370, 111.90/112.57 symdiff( 111.90/112.57 X368,X369)) => 111.90/112.57 (![X371:$o]: 111.90/112.57 (( 111.90/112.57 in( 111.90/112.57 X370,X368) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ~ 111.90/112.57 in( 111.90/112.57 X370,X369)) => 111.90/112.57 X371)) => 111.90/112.57 (( 111.90/112.57 ( 111.90/112.57 ~ 111.90/112.57 in( 111.90/112.57 X370,X368)) => 111.90/112.57 ( 111.90/112.57 in( 111.90/112.57 X370,X369) => 111.90/112.57 X371)) => 111.90/112.57 X371))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X372, 111.90/112.57 X373,X374]: 111.90/112.57 (in( 111.90/112.57 X374,X372) => 111.90/112.57 (( 111.90/112.57 ~ 111.90/112.57 in( 111.90/112.57 X374,X373)) => 111.90/112.57 in( 111.90/112.57 X374, 111.90/112.57 symdiff( 111.90/112.57 X372,X373))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X375, 111.90/112.57 X376,X377]: 111.90/112.57 (( 111.90/112.57 ~ 111.90/112.57 in( 111.90/112.57 X377,X375)) => 111.90/112.57 (in( 111.90/112.57 X377,X376) => 111.90/112.57 in( 111.90/112.57 X377, 111.90/112.57 symdiff( 111.90/112.57 X375,X376))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X378, 111.90/112.57 X379,X380]: 111.90/112.57 (in( 111.90/112.57 X380,X378) => 111.90/112.57 (in( 111.90/112.57 X380,X379) => 111.90/112.57 (~ 111.90/112.57 in( 111.90/112.57 X380, 111.90/112.57 symdiff( 111.90/112.57 X378,X379)))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X381, 111.90/112.57 X382,X383]: 111.90/112.57 (( 111.90/112.57 ~ 111.90/112.57 in( 111.90/112.57 X383,X381)) => 111.90/112.57 (( 111.90/112.57 ~ 111.90/112.57 in( 111.90/112.57 X383,X382)) => 111.90/112.57 (~ 111.90/112.57 in( 111.90/112.57 X383, 111.90/112.57 symdiff( 111.90/112.57 X381,X382)))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X384, 111.90/112.57 X385]: 111.90/112.57 in( 111.90/112.57 X385, 111.90/112.57 setadjoin( 111.90/112.57 X384, 111.90/112.57 setadjoin( 111.90/112.57 X385, 111.90/112.57 emptyset)))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X386, 111.90/112.57 X387]: 111.90/112.57 in( 111.90/112.57 X386, 111.90/112.57 setunion( 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X386, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X386, 111.90/112.57 setadjoin( 111.90/112.57 X387, 111.90/112.57 emptyset)), 111.90/112.57 emptyset))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X388, 111.90/112.57 X389]: 111.90/112.57 in( 111.90/112.57 X389, 111.90/112.57 setunion( 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X388, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X388, 111.90/112.57 setadjoin( 111.90/112.57 X389, 111.90/112.57 emptyset)), 111.90/112.57 emptyset))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X390, 111.90/112.57 X391]: 111.90/112.57 (?[X392]: 111.90/112.57 (( 111.90/112.57 ?[X393]: 111.90/112.57 (( 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X390, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X390, 111.90/112.57 setadjoin( 111.90/112.57 X391, 111.90/112.57 emptyset)), 111.90/112.57 emptyset)) = 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X392, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X392, 111.90/112.57 setadjoin( 111.90/112.57 X393, 111.90/112.57 emptyset)), 111.90/112.57 emptyset))) & 111.90/112.57 in( 111.90/112.57 X393, 111.90/112.57 setunion( 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X390, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X390, 111.90/112.57 setadjoin( 111.90/112.57 X391, 111.90/112.57 emptyset)), 111.90/112.57 emptyset)))))) & 111.90/112.57 in( 111.90/112.57 X392, 111.90/112.57 setunion( 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X390, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X390, 111.90/112.57 setadjoin( 111.90/112.57 X391, 111.90/112.57 emptyset)), 111.90/112.57 emptyset))))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X394, 111.90/112.57 X395]: 111.90/112.57 (?[X396]: 111.90/112.57 (( 111.90/112.57 ?[X397]: 111.90/112.57 (( 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X394, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X394, 111.90/112.57 setadjoin( 111.90/112.57 X395, 111.90/112.57 emptyset)), 111.90/112.57 emptyset)) = 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X396, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X396, 111.90/112.57 setadjoin( 111.90/112.57 X397, 111.90/112.57 emptyset)), 111.90/112.57 emptyset))) & 111.90/112.57 in( 111.90/112.57 X397, 111.90/112.57 setunion( 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X394, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X394, 111.90/112.57 setadjoin( 111.90/112.57 X395, 111.90/112.57 emptyset)), 111.90/112.57 emptyset)))))) & 111.90/112.57 in( 111.90/112.57 X396, 111.90/112.57 setunion( 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X394, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X394, 111.90/112.57 setadjoin( 111.90/112.57 X395, 111.90/112.57 emptyset)), 111.90/112.57 emptyset))))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X398, 111.90/112.57 X399]: 111.90/112.57 (in( 111.90/112.57 X399,X398) => 111.90/112.57 subset( 111.90/112.57 setadjoin( 111.90/112.57 X399, 111.90/112.57 emptyset), 111.90/112.57 X398))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X400, 111.90/112.57 X401]: 111.90/112.57 (in( 111.90/112.57 X401,X400) => 111.90/112.57 in( 111.90/112.57 setadjoin( 111.90/112.57 X401, 111.90/112.57 emptyset), 111.90/112.57 powerset( 111.90/112.57 X400)))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X402, 111.90/112.57 X403,X404]: 111.90/112.57 (in( 111.90/112.57 X404,X402) => 111.90/112.57 in( 111.90/112.57 setadjoin( 111.90/112.57 X404, 111.90/112.57 emptyset), 111.90/112.57 powerset( 111.90/112.57 binunion( 111.90/112.57 X402,X403))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X405, 111.90/112.57 X406,X407]: 111.90/112.57 (in( 111.90/112.57 X407, 111.90/112.57 setadjoin( 111.90/112.57 X405, 111.90/112.57 setadjoin( 111.90/112.57 X406, 111.90/112.57 emptyset))) => 111.90/112.57 (( 111.90/112.57 X407 = 111.90/112.57 X406) | 111.90/112.57 (X407 = 111.90/112.57 X405)))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X408, 111.90/112.57 X409,X410]: 111.90/112.57 (in( 111.90/112.57 X410,X408) => 111.90/112.57 (![X411]: 111.90/112.57 (in( 111.90/112.57 X411,X409) => 111.90/112.57 subset( 111.90/112.57 setadjoin( 111.90/112.57 X410, 111.90/112.57 setadjoin( 111.90/112.57 X411, 111.90/112.57 emptyset)), 111.90/112.57 binunion( 111.90/112.57 X408,X409)))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X412, 111.90/112.57 X413,X414]: 111.90/112.57 (in( 111.90/112.57 X414,X412) => 111.90/112.57 (![X415]: 111.90/112.57 (in( 111.90/112.57 X415,X413) => 111.90/112.57 in( 111.90/112.57 setadjoin( 111.90/112.57 X414, 111.90/112.57 setadjoin( 111.90/112.57 X415, 111.90/112.57 emptyset)), 111.90/112.57 powerset( 111.90/112.57 binunion( 111.90/112.57 X412,X413))))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X416, 111.90/112.57 X417,X418]: 111.90/112.57 (in( 111.90/112.57 X418,X416) => 111.90/112.57 (![X419]: 111.90/112.57 (in( 111.90/112.57 X419,X417) => 111.90/112.57 subset( 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X418, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X418, 111.90/112.57 setadjoin( 111.90/112.57 X419, 111.90/112.57 emptyset)), 111.90/112.57 emptyset)), 111.90/112.57 powerset( 111.90/112.57 binunion( 111.90/112.57 X416,X417))))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X420, 111.90/112.57 X421,X422]: 111.90/112.57 (in( 111.90/112.57 X422,X420) => 111.90/112.57 (![X423]: 111.90/112.57 (in( 111.90/112.57 X423,X421) => 111.90/112.57 in( 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X422, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X422, 111.90/112.57 setadjoin( 111.90/112.57 X423, 111.90/112.57 emptyset)), 111.90/112.57 emptyset)), 111.90/112.57 powerset( 111.90/112.57 powerset( 111.90/112.57 binunion( 111.90/112.57 X420,X421)))))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X424, 111.90/112.57 X425,X426]: 111.90/112.57 (in( 111.90/112.57 X426,X424) => 111.90/112.57 (![X427]: 111.90/112.57 (in( 111.90/112.57 X427,X425) => 111.90/112.57 in( 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X426, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X426, 111.90/112.57 setadjoin( 111.90/112.57 X427, 111.90/112.57 emptyset)), 111.90/112.57 emptyset)), 111.90/112.57 powerset( 111.90/112.57 powerset( 111.90/112.57 binunion( 111.90/112.57 X424,X425)))))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X428, 111.90/112.57 X429,X430]: 111.90/112.57 (in( 111.90/112.57 X430,X428) => 111.90/112.57 (![X431]: 111.90/112.57 (in( 111.90/112.57 X431,X429) => 111.90/112.57 in( 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X430, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X430, 111.90/112.57 setadjoin( 111.90/112.57 X431, 111.90/112.57 emptyset)), 111.90/112.57 emptyset)), 111.90/112.57 cartprod( 111.90/112.57 X428,X429)))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X432, 111.90/112.57 X433,X434]: 111.90/112.57 (in( 111.90/112.57 X434, 111.90/112.57 cartprod( 111.90/112.57 X432,X433)) => 111.90/112.57 (?[X435]: 111.90/112.57 (( 111.90/112.57 ?[X436]: 111.90/112.57 (( 111.90/112.57 X434 = 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X435, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X435, 111.90/112.57 setadjoin( 111.90/112.57 X436, 111.90/112.57 emptyset)), 111.90/112.57 emptyset))) & 111.90/112.57 in( 111.90/112.57 X436,X433))) & 111.90/112.57 in( 111.90/112.57 X435,X432))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X437, 111.90/112.57 X438,X439]: 111.90/112.57 (in( 111.90/112.57 X439, 111.90/112.57 cartprod( 111.90/112.57 X437,X438)) => 111.90/112.57 (?[X440]: 111.90/112.57 (( 111.90/112.57 ?[X441]: 111.90/112.57 (( 111.90/112.57 X439 = 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X440, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X440, 111.90/112.57 setadjoin( 111.90/112.57 X441, 111.90/112.57 emptyset)), 111.90/112.57 emptyset))) & 111.90/112.57 in( 111.90/112.57 X441, 111.90/112.57 setunion( 111.90/112.57 X439)))) & 111.90/112.57 in( 111.90/112.57 X440, 111.90/112.57 setunion( 111.90/112.57 X439)))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X442, 111.90/112.57 X443]: 111.90/112.57 (in( 111.90/112.57 X443, 111.90/112.57 setunion( 111.90/112.57 X442)) => 111.90/112.57 (?[X444]: 111.90/112.57 (in( 111.90/112.57 X443,X444) & 111.90/112.57 in( 111.90/112.57 X444,X442))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X445]: 111.90/112.57 subset( 111.90/112.57 setunion( 111.90/112.57 setadjoin( 111.90/112.57 X445, 111.90/112.57 emptyset)), 111.90/112.57 X445)) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X446]: 111.90/112.57 subset( 111.90/112.57 X446, 111.90/112.57 setunion( 111.90/112.57 setadjoin( 111.90/112.57 X446, 111.90/112.57 emptyset)))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X447]: 111.90/112.57 (setunion( 111.90/112.57 setadjoin( 111.90/112.57 X447, 111.90/112.57 emptyset)) = 111.90/112.57 X447)) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X448, 111.90/112.57 X449:( 111.90/112.57 $i > $o)]: 111.90/112.57 (( 111.90/112.57 ![X450]: 111.90/112.57 (in( 111.90/112.57 X450,X448) => 111.90/112.57 (![X451]: 111.90/112.57 (in( 111.90/112.57 X451,X448) => 111.90/112.57 (X449( 111.90/112.57 X450) => 111.90/112.57 (X449( 111.90/112.57 X451) => 111.90/112.57 (X450 = 111.90/112.57 X451))))))) => 111.90/112.57 (( 111.90/112.57 ?[X452]: 111.90/112.57 (X449( 111.90/112.57 X452) & 111.90/112.57 in( 111.90/112.57 X452,X448))) => 111.90/112.57 (?[X453]: 111.90/112.57 (( 111.90/112.57 dsetconstr( 111.90/112.57 X448, 111.90/112.57 '#ll_1'( 111.90/112.57 X449)) = 111.90/112.57 setadjoin( 111.90/112.57 X453, 111.90/112.57 emptyset)) & 111.90/112.57 in( 111.90/112.57 X453, 111.90/112.57 dsetconstr( 111.90/112.57 X448, 111.90/112.57 '#ll_1'( 111.90/112.57 X449)))))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X454, 111.90/112.57 X455:( 111.90/112.57 $i > $o)]: 111.90/112.57 (( 111.90/112.57 ?[X456]: 111.90/112.57 (( 111.90/112.57 dsetconstr( 111.90/112.57 X454, 111.90/112.57 '#ll_1'( 111.90/112.57 X455)) = 111.90/112.57 setadjoin( 111.90/112.57 X456, 111.90/112.57 emptyset)) & 111.90/112.57 in( 111.90/112.57 X456, 111.90/112.57 dsetconstr( 111.90/112.57 X454, 111.90/112.57 '#ll_1'( 111.90/112.57 X455))))) => 111.90/112.57 (?[X457]: 111.90/112.57 (X455( 111.90/112.57 X457) & 111.90/112.57 in( 111.90/112.57 X457,X454))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X458, 111.90/112.57 X459:( 111.90/112.57 $i > $o), 111.90/112.57 X460]: 111.90/112.57 (in( 111.90/112.57 X460,X458) => 111.90/112.57 (X459( 111.90/112.57 X460) => 111.90/112.57 (( 111.90/112.57 ![X461]: 111.90/112.57 (in( 111.90/112.57 X461,X458) => 111.90/112.57 (X459( 111.90/112.57 X461) => 111.90/112.57 (X461 = 111.90/112.57 X460)))) => 111.90/112.57 (?[X462]: 111.90/112.57 (( 111.90/112.57 dsetconstr( 111.90/112.57 X458, 111.90/112.57 '#ll_1'( 111.90/112.57 X459)) = 111.90/112.57 setadjoin( 111.90/112.57 X462, 111.90/112.57 emptyset)) & 111.90/112.57 in( 111.90/112.57 X462, 111.90/112.57 dsetconstr( 111.90/112.57 X458, 111.90/112.57 '#ll_1'( 111.90/112.57 X459))))))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X463, 111.90/112.57 X464:( 111.90/112.57 $i > $o)]: 111.90/112.57 (( 111.90/112.57 ![X465]: 111.90/112.57 (in( 111.90/112.57 X465,X463) => 111.90/112.57 (![X466]: 111.90/112.57 (in( 111.90/112.57 X466,X463) => 111.90/112.57 (X464( 111.90/112.57 X465) => 111.90/112.57 (X464( 111.90/112.57 X466) => 111.90/112.57 (X465 = 111.90/112.57 X466))))))) => 111.90/112.57 (( 111.90/112.57 ?[X467]: 111.90/112.57 (X464( 111.90/112.57 X467) & 111.90/112.57 in( 111.90/112.57 X467,X463))) => 111.90/112.57 (?[X468]: 111.90/112.57 (( 111.90/112.57 dsetconstr( 111.90/112.57 X463, 111.90/112.57 '#ll_1'( 111.90/112.57 X464)) = 111.90/112.57 setadjoin( 111.90/112.57 X468, 111.90/112.57 emptyset)) & 111.90/112.57 in( 111.90/112.57 X468, 111.90/112.57 dsetconstr( 111.90/112.57 X463, 111.90/112.57 '#ll_1'( 111.90/112.57 X464)))))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X469, 111.90/112.57 X470]: 111.90/112.57 (( 111.90/112.57 setadjoin( 111.90/112.57 X469, 111.90/112.57 emptyset) = 111.90/112.57 setadjoin( 111.90/112.57 X470, 111.90/112.57 emptyset)) => 111.90/112.57 (X469 = 111.90/112.57 X470))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X471, 111.90/112.57 X472,X473]: 111.90/112.57 (in( 111.90/112.57 setadjoin( 111.90/112.57 X473, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X471, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X471, 111.90/112.57 setadjoin( 111.90/112.57 X472, 111.90/112.57 emptyset)), 111.90/112.57 emptyset))) => 111.90/112.57 (X471 = 111.90/112.57 X473))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X474]: 111.90/112.57 (( 111.90/112.57 ?[X475]: 111.90/112.57 (( 111.90/112.57 ?[X476]: 111.90/112.57 (( 111.90/112.57 X474 = 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X475, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X475, 111.90/112.57 setadjoin( 111.90/112.57 X476, 111.90/112.57 emptyset)), 111.90/112.57 emptyset))) & 111.90/112.57 in( 111.90/112.57 X476, 111.90/112.57 setunion( 111.90/112.57 X474)))) & 111.90/112.57 in( 111.90/112.57 X475, 111.90/112.57 setunion( 111.90/112.57 X474)))) => 111.90/112.57 (?[X477]: 111.90/112.57 (( 111.90/112.57 dsetconstr( 111.90/112.57 setunion( 111.90/112.57 X474), 111.90/112.57 '#ll_0'( 111.90/112.57 X474)) = 111.90/112.57 setadjoin( 111.90/112.57 X477, 111.90/112.57 emptyset)) & 111.90/112.57 in( 111.90/112.57 X477, 111.90/112.57 dsetconstr( 111.90/112.57 setunion( 111.90/112.57 X474), 111.90/112.57 '#ll_0'( 111.90/112.57 X474))))))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X478]: 111.90/112.57 (( 111.90/112.57 ?[X479]: 111.90/112.57 (( 111.90/112.57 X478 = 111.90/112.57 setadjoin( 111.90/112.57 X479, 111.90/112.57 emptyset)) & 111.90/112.57 in( 111.90/112.57 X479,X478))) => 111.90/112.57 in( 111.90/112.57 setunion( 111.90/112.57 X478), 111.90/112.57 X478))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X480, 111.90/112.57 X481]: 111.90/112.57 (kfst( 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X480, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X480, 111.90/112.57 setadjoin( 111.90/112.57 X481, 111.90/112.57 emptyset)), 111.90/112.57 emptyset))) = 111.90/112.57 X480)) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X482, 111.90/112.57 X483,X484]: 111.90/112.57 (in( 111.90/112.57 X484, 111.90/112.57 cartprod( 111.90/112.57 X482,X483)) => 111.90/112.57 in( 111.90/112.57 kfst( 111.90/112.57 X484), 111.90/112.57 X482))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X485, 111.90/112.57 X486, 111.90/112.57 X487,X488]: 111.90/112.57 (( 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X485, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X485, 111.90/112.57 setadjoin( 111.90/112.57 X486, 111.90/112.57 emptyset)), 111.90/112.57 emptyset)) = 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X487, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X487, 111.90/112.57 setadjoin( 111.90/112.57 X488, 111.90/112.57 emptyset)), 111.90/112.57 emptyset))) => 111.90/112.57 (X485 = 111.90/112.57 X487))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X489, 111.90/112.57 X490, 111.90/112.57 X491,X492]: 111.90/112.57 (( 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X489, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X489, 111.90/112.57 setadjoin( 111.90/112.57 X490, 111.90/112.57 emptyset)), 111.90/112.57 emptyset)) = 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X491, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X491, 111.90/112.57 setadjoin( 111.90/112.57 X492, 111.90/112.57 emptyset)), 111.90/112.57 emptyset))) => 111.90/112.57 (X489 = 111.90/112.57 X491))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X493, 111.90/112.57 X494]: 111.90/112.57 (( 111.90/112.57 X493 = 111.90/112.57 X494) => 111.90/112.57 (setadjoin( 111.90/112.57 X493, 111.90/112.57 setadjoin( 111.90/112.57 X494, 111.90/112.57 emptyset)) = 111.90/112.57 setadjoin( 111.90/112.57 X493, 111.90/112.57 emptyset)))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X495, 111.90/112.57 X496]: 111.90/112.57 (( 111.90/112.57 X495 = 111.90/112.57 X496) => 111.90/112.57 (setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X495, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X495, 111.90/112.57 setadjoin( 111.90/112.57 X496, 111.90/112.57 emptyset)), 111.90/112.57 emptyset)) = 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X495, 111.90/112.57 emptyset), 111.90/112.57 emptyset)))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X497, 111.90/112.57 X498, 111.90/112.57 X499,X500]: 111.90/112.57 (( 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X497, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X497, 111.90/112.57 setadjoin( 111.90/112.57 X498, 111.90/112.57 emptyset)), 111.90/112.57 emptyset)) = 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X499, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X499, 111.90/112.57 setadjoin( 111.90/112.57 X500, 111.90/112.57 emptyset)), 111.90/112.57 emptyset))) => 111.90/112.57 (( 111.90/112.57 X499 = 111.90/112.57 X500) => 111.90/112.57 (X498 = 111.90/112.57 X500)))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X501, 111.90/112.57 X502,X503]: 111.90/112.57 (( 111.90/112.57 setadjoin( 111.90/112.57 X501, 111.90/112.57 setadjoin( 111.90/112.57 X502, 111.90/112.57 emptyset)) = 111.90/112.57 setadjoin( 111.90/112.57 X503, 111.90/112.57 emptyset)) => 111.90/112.57 (X501 = 111.90/112.57 X502))) => 111.90/112.57 ( 111.90/112.57 ( 111.90/112.57 ![X504, 111.90/112.57 X505, 111.90/112.57 X506,X507]: 111.90/112.57 (( 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X504, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X504, 111.90/112.57 setadjoin( 111.90/112.57 X505, 111.90/112.57 emptyset)), 111.90/112.57 emptyset)) = 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X506, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X506, 111.90/112.57 setadjoin( 111.90/112.57 X507, 111.90/112.57 emptyset)), 111.90/112.57 emptyset))) => 111.90/112.57 (X505 = 111.90/112.57 X507))) => 111.90/112.57 ( 111.90/112.57 ![X508, 111.90/112.57 X509, 111.90/112.57 X510,X511]: 111.90/112.57 (( 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X508, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X508, 111.90/112.57 setadjoin( 111.90/112.57 X509, 111.90/112.57 emptyset)), 111.90/112.57 emptyset)) = 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X510, 111.90/112.57 emptyset), 111.90/112.57 setadjoin( 111.90/112.57 setadjoin( 111.90/112.57 X510, 111.90/112.57 setadjoin( 111.90/112.57 X511, 111.90/112.57 emptyset)), 111.90/112.57 emptyset))) => 111.90/112.57 (X509 = 111.90/112.57 X511))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 111.90/112.57 tff('176', plain, sk_X509_ != sk_X511_, 111.90/112.57 inference('cnf', [status(esa)], [zf_stmt_14])). 111.90/112.57 tff('177', plain, 111.90/112.57 ![X738, X739, X740, X741]: 111.90/112.57 (X739 = X738 111.90/112.57 | setadjoin(setadjoin(X741, emptyset), 111.90/112.57 setadjoin(setadjoin(X741, setadjoin(X739, emptyset)), emptyset)) 111.90/112.57 != setadjoin(setadjoin(X740, emptyset), 111.90/112.57 setadjoin(setadjoin(X740, setadjoin(X738, emptyset)), 111.90/112.57 emptyset))), 111.90/112.57 inference('cnf', [status(esa)], [zf_stmt_14])). 111.90/112.57 tff('178', plain, 111.90/112.57 setadjoin(setadjoin(sk_X508_, emptyset), 111.90/112.57 setadjoin(setadjoin(sk_X508_, setadjoin(sk_X509_, emptyset)), emptyset)) 111.90/112.57 = setadjoin(setadjoin(sk_X510_, emptyset), 111.90/112.57 setadjoin(setadjoin(sk_X510_, setadjoin(sk_X511_, emptyset)), 111.90/112.57 emptyset)), 111.90/112.57 inference('cnf', [status(esa)], [zf_stmt_14])). 111.90/112.57 tff('179', plain, 111.90/112.57 ![X752, X753]: 111.90/112.57 kfst( 111.90/112.57 setadjoin(setadjoin(X752, emptyset), 111.90/112.57 setadjoin(setadjoin(X752, setadjoin(X753, emptyset)), emptyset))) 111.90/112.57 = X752, 111.90/112.57 inference('cnf', [status(esa)], [zf_stmt_14])). 111.90/112.57 tff('180', plain, $false, 111.90/112.57 inference('eprover', [status(thm)], ['176', '177', '178', '179'])). 111.90/112.57 111.90/112.57 % SZS output end Refutation 111.90/112.57 % Zipperpin 1.5 exiting 111.90/112.57 EOF