0.10/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.10/0.13 % Command : run_portfolio.sh /export/starexec/sandbox2/benchmark/theBenchmark.p /export/starexec/sandbox2/tmp/tmp.oh4F5f5qyn 0.12/0.34 % Computer : n006.cluster.edu 0.12/0.34 % Model : x86_64 x86_64 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.34 % Memory : 8042.1875MB 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.34 % CPULimit : 180 0.12/0.34 % DateTime : Thu Aug 29 15:35:39 EDT 2019 0.12/0.34 % CPUTime : 138.76/139.84 % Running portfolio for 180 s 138.76/139.84 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 138.76/139.84 % TempDir : /export/starexec/sandbox2/tmp/tmp.oh4F5f5qyn 138.76/139.84 % Recognized as monomorphic HO. 138.76/139.84 % Running /export/starexec/sandbox2/solver/bin/competitive.sh for 18 138.76/139.84 % Running /export/starexec/sandbox2/solver/bin/competitive.2.sh for 13 138.76/139.84 % Running /export/starexec/sandbox2/solver/bin/competitive.3.sh for 3 138.76/139.84 % Running /export/starexec/sandbox2/solver/bin/pragmatic.rudimentary.sh for 28 138.76/139.84 % Running /export/starexec/sandbox2/solver/bin/pragmatic.rudimentary.1.sh for 12 138.76/139.84 % Running /export/starexec/sandbox2/solver/bin/pragmatic.rudimentary.2.sh for 7 138.76/139.84 % Running /export/starexec/sandbox2/solver/bin/pragmatic.shallow.sh for 3 138.76/139.84 % Running /export/starexec/sandbox2/solver/bin/pragmatic.shallow.1.sh for 14 138.76/139.84 % Running /export/starexec/sandbox2/solver/bin/pragmatic.shallow.2.sh for 12 138.76/139.84 % Running /export/starexec/sandbox2/solver/bin/pragmatic.ll.e.sh for 19 138.76/139.84 % Running /export/starexec/sandbox2/solver/bin/pragmatic.bools.sh for 13 138.76/139.84 % Running /export/starexec/sandbox2/solver/bin/pragmatic.bools.1.sh for 10 138.76/139.84 % Solved by: pragmatic.bools.1.sh 138.76/139.84 % done 857 iterations in 9.107s 138.76/139.84 % hashcons stats for terms: size 9223, num 45329, sum length 76241, buckets: small 0, median 7, big 22 138.76/139.84 % proof state stats: {active 293, passive 15135, simpl 0} 138.76/139.84 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 138.76/139.84 % SZS output start Refutation 138.76/139.84 tff(kpairsurjEq, axiom, kpairsurjEq <=> 138.76/139.84 (![Xu]: (iskpair(Xu) => (kpair(kfst(Xu),ksnd(Xu)) = Xu)))). 138.76/139.84 tff('0', plain, 138.76/139.84 kpairsurjEq = (![X2]: (iskpair(X2) => (kpair(kfst(X2),ksnd(X2)) = X2))), 138.76/139.84 define([status(thm)])). 138.76/139.84 tff(ksndpairEq, axiom, ksndpairEq <=> (![Xx,Xy]: (ksnd(kpair(Xx,Xy)) = Xy))). 138.76/139.84 tff('1', plain, ksndpairEq = (![X2,X3]: (ksnd(kpair(X2,X3)) = X3)), 138.76/139.84 define([status(thm)])). 138.76/139.84 tff(ksndsingleton, axiom, ksndsingleton <=> 138.76/139.84 (![Xu]: 138.76/139.84 (iskpair(Xu) => 138.76/139.84 singleton(dsetconstr(setunion(Xu),^[Xx]: (Xu = kpair(kfst(Xu),Xx))))))). 138.76/139.84 tff('2', plain, 138.76/139.84 ksndsingleton = 138.76/139.84 (![X2]: 138.76/139.84 (iskpair(X2) => 138.76/139.84 singleton(dsetconstr(setunion(X2),^[V_1]: (X2 = kpair(kfst(X2),V_1)))))), 138.86/139.84 define([status(thm)])). 138.86/139.84 tff(setukpairinjR, axiom, setukpairinjR <=> 138.86/139.84 (![Xx,Xy,Xz,Xu]: ((kpair(Xx,Xy) = kpair(Xz,Xu)) => (Xy = Xu)))). 138.86/139.84 tff('3', plain, 138.86/139.84 setukpairinjR = 138.86/139.84 (![X2,X3,X4,X5]: ((kpair(X2,X3) = kpair(X4,X5)) => (X3 = X5))), 138.86/139.84 define([status(thm)])). 138.86/139.84 tff(setukpairinjR2, axiom, setukpairinjR2 <=> 138.86/139.84 (![Xx,Xy,Xz,Xu]: 138.86/139.84 ((setadjoin(setadjoin(Xx,emptyset), 138.86/139.84 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)),emptyset)) = 138.86/139.84 setadjoin(setadjoin(Xz,emptyset), 138.86/139.84 setadjoin(setadjoin(Xz,setadjoin(Xu,emptyset)),emptyset))) => 138.86/139.84 (Xy = Xu)))). 138.86/139.84 tff('4', plain, 138.86/139.84 setukpairinjR2 = 138.86/139.84 (![X2,X3,X4,X5]: 138.86/139.84 ((setadjoin(setadjoin(X2,emptyset), 138.86/139.84 setadjoin(setadjoin(X2,setadjoin(X3,emptyset)),emptyset)) = 138.86/139.84 setadjoin(setadjoin(X4,emptyset), 138.86/139.84 setadjoin(setadjoin(X4,setadjoin(X5,emptyset)),emptyset))) => 138.86/139.84 (X3 = X5))), 138.86/139.84 define([status(thm)])). 138.86/139.84 tff(upairequniteq, axiom, upairequniteq <=> 138.86/139.84 (![Xx,Xy,Xz]: 138.86/139.84 ((setadjoin(Xx,setadjoin(Xy,emptyset)) = setadjoin(Xz,emptyset)) => 138.86/139.84 (Xx = Xy)))). 138.86/139.84 tff('5', plain, 138.86/139.84 upairequniteq = 138.86/139.84 (![X2,X3,X4]: 138.86/139.84 ((setadjoin(X2,setadjoin(X3,emptyset)) = setadjoin(X4,emptyset)) => 138.86/139.84 (X2 = X3))), 138.86/139.84 define([status(thm)])). 138.86/139.84 tff(setukpairinjR1, axiom, setukpairinjR1 <=> 138.86/139.84 (![Xx,Xy,Xz,Xu]: 138.86/139.84 ((setadjoin(setadjoin(Xx,emptyset), 138.86/139.84 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)),emptyset)) = 138.86/139.84 setadjoin(setadjoin(Xz,emptyset), 138.86/139.84 setadjoin(setadjoin(Xz,setadjoin(Xu,emptyset)),emptyset))) => 138.86/139.84 ((Xz = Xu) => (Xy = Xu))))). 138.86/139.84 tff('6', plain, 138.86/139.84 setukpairinjR1 = 138.86/139.84 (![X2,X3,X4,X5]: 138.86/139.84 ((setadjoin(setadjoin(X2,emptyset), 138.86/139.84 setadjoin(setadjoin(X2,setadjoin(X3,emptyset)),emptyset)) = 138.86/139.84 setadjoin(setadjoin(X4,emptyset), 138.86/139.84 setadjoin(setadjoin(X4,setadjoin(X5,emptyset)),emptyset))) => 138.86/139.84 ((X4 = X5) => (X3 = X5)))), 138.86/139.84 define([status(thm)])). 138.86/139.84 tff(setukpairinjR12, axiom, setukpairinjR12 <=> 138.86/139.84 (![Xx,Xy]: 138.86/139.84 ((Xx = Xy) => 138.86/139.84 (setadjoin(setadjoin(Xx,emptyset), 138.86/139.84 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)),emptyset)) = 138.86/139.84 setadjoin(setadjoin(Xx,emptyset),emptyset))))). 138.86/139.84 tff('7', plain, 138.86/139.84 setukpairinjR12 = 138.86/139.84 (![X2,X3]: 138.86/139.84 ((X2 = X3) => 138.86/139.84 (setadjoin(setadjoin(X2,emptyset), 138.86/139.84 setadjoin(setadjoin(X2,setadjoin(X3,emptyset)),emptyset)) = 138.86/139.84 setadjoin(setadjoin(X2,emptyset),emptyset)))), 138.86/139.84 define([status(thm)])). 138.86/139.84 tff(setukpairinjR11, axiom, setukpairinjR11 <=> 138.86/139.84 (![Xx,Xy]: 138.86/139.84 ((Xx = Xy) => 138.86/139.84 (setadjoin(Xx,setadjoin(Xy,emptyset)) = setadjoin(Xx,emptyset))))). 138.86/139.84 tff('8', plain, 138.86/139.84 setukpairinjR11 = 138.86/139.84 (![X2,X3]: 138.86/139.84 ((X2 = X3) => 138.86/139.84 (setadjoin(X2,setadjoin(X3,emptyset)) = setadjoin(X2,emptyset)))), 138.86/139.84 define([status(thm)])). 138.86/139.84 tff(setukpairinjL, axiom, setukpairinjL <=> 138.86/139.84 (![Xx,Xy,Xz,Xu]: ((kpair(Xx,Xy) = kpair(Xz,Xu)) => (Xx = Xz)))). 138.86/139.84 tff('9', plain, 138.86/139.84 setukpairinjL = 138.86/139.84 (![X2,X3,X4,X5]: ((kpair(X2,X3) = kpair(X4,X5)) => (X2 = X4))), 138.86/139.84 define([status(thm)])). 138.86/139.84 tff(setukpairinjL2, axiom, setukpairinjL2 <=> 138.86/139.84 (![Xx,Xy,Xz,Xu]: 138.86/139.84 ((setadjoin(setadjoin(Xx,emptyset), 138.86/139.84 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)),emptyset)) = 138.86/139.84 setadjoin(setadjoin(Xz,emptyset), 138.86/139.84 setadjoin(setadjoin(Xz,setadjoin(Xu,emptyset)),emptyset))) => 138.86/139.84 (Xx = Xz)))). 138.86/139.84 tff('10', plain, 138.86/139.84 setukpairinjL2 = 138.86/139.84 (![X2,X3,X4,X5]: 138.86/139.84 ((setadjoin(setadjoin(X2,emptyset), 138.86/139.84 setadjoin(setadjoin(X2,setadjoin(X3,emptyset)),emptyset)) = 138.86/139.84 setadjoin(setadjoin(X4,emptyset), 138.86/139.84 setadjoin(setadjoin(X4,setadjoin(X5,emptyset)),emptyset))) => 138.86/139.84 (X2 = X4))), 138.86/139.84 define([status(thm)])). 138.86/139.84 tff(cartprodfstin, axiom, cartprodfstin <=> 138.86/139.84 (![A,B,Xu]: (in(Xu,cartprod(A,B)) => in(kfst(Xu),A)))). 138.86/139.84 tff('11', plain, 138.86/139.84 cartprodfstin = 138.86/139.84 (![X2,X3,X4]: (in(X4,cartprod(X2,X3)) => in(kfst(X4),X2))), 138.86/139.84 define([status(thm)])). 138.86/139.84 tff(kfstpairEq, axiom, kfstpairEq <=> (![Xx,Xy]: (kfst(kpair(Xx,Xy)) = Xx))). 138.86/139.84 tff('12', plain, kfstpairEq = (![X2,X3]: (kfst(kpair(X2,X3)) = X2)), 138.86/139.84 define([status(thm)])). 138.86/139.84 tff(theprop, axiom, theprop <=> (![X]: (singleton(X) => in(setunion(X),X)))). 138.86/139.84 tff('13', plain, theprop = (![X2]: (singleton(X2) => in(setunion(X2),X2))), 138.86/139.84 define([status(thm)])). 138.86/139.84 tff(kfstsingleton, axiom, kfstsingleton <=> 138.86/139.84 (![Xu]: 138.86/139.84 (iskpair(Xu) => 138.86/139.84 singleton(dsetconstr(setunion(Xu),^[Xx]: in(setadjoin(Xx,emptyset),Xu)))))). 138.86/139.84 tff('14', plain, 138.86/139.84 kfstsingleton = 138.86/139.84 (![X2]: 138.86/139.84 (iskpair(X2) => 138.86/139.84 singleton(dsetconstr(setunion(X2), 138.86/139.84 ^[V_1]: in(setadjoin(V_1,emptyset),X2))))), 138.86/139.84 define([status(thm)])). 138.86/139.84 tff(setukpairinjL1, axiom, setukpairinjL1 <=> 138.86/139.84 (![Xx,Xy,Xz]: 138.86/139.84 (in(setadjoin(Xz,emptyset), 138.86/139.84 setadjoin(setadjoin(Xx,emptyset), 138.86/139.84 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)),emptyset))) => 138.86/139.84 (Xx = Xz)))). 138.86/139.84 tff('15', plain, 138.86/139.84 setukpairinjL1 = 138.86/139.84 (![X2,X3,X4]: 138.86/139.84 (in(setadjoin(X4,emptyset), 138.86/139.84 setadjoin(setadjoin(X2,emptyset), 138.86/139.84 setadjoin(setadjoin(X2,setadjoin(X3,emptyset)),emptyset))) => 138.86/139.84 (X2 = X4))), 138.86/139.84 define([status(thm)])). 138.86/139.84 tff(singletonsuniq, axiom, singletonsuniq <=> 138.86/139.84 (![Xx,Xy]: ((setadjoin(Xx,emptyset) = setadjoin(Xy,emptyset)) => (Xx = Xy)))). 138.86/139.84 tff('16', plain, 138.86/139.84 singletonsuniq = 138.86/139.84 (![X2,X3]: 138.86/139.84 ((setadjoin(X2,emptyset) = setadjoin(X3,emptyset)) => (X2 = X3))), 138.86/139.84 define([status(thm)])). 138.86/139.84 tff(ex1I2, axiom, ex1I2 <=> 138.86/139.84 (![A,Xphi:($i > $o)]: 138.86/139.84 ((![Xx]: 138.86/139.84 (in(Xx,A) => 138.86/139.84 (![Xy]: (in(Xy,A) => (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))) => 138.86/139.84 ((?[Xx]: (Xphi(Xx) & in(Xx,A))) => ex1(A,^[Xx]: Xphi(Xx)))))). 138.86/139.84 tff('17', plain, 138.86/139.84 ex1I2 = 138.86/139.84 (![X2,X3:($i > $o)]: 138.86/139.84 ((![X4]: 138.86/139.84 (in(X4,X2) => 138.86/139.84 (![X5]: (in(X5,X2) => (X3(X4) => (X3(X5) => (X4 = X5))))))) => 138.86/139.84 ((?[X6]: (X3(X6) & in(X6,X2))) => ex1(X2,^[V_1]: X3(V_1))))), 138.86/139.84 define([status(thm)])). 138.86/139.84 tff(ex1I, axiom, ex1I <=> 138.86/139.84 (![A,Xphi:($i > $o),Xx]: 138.86/139.85 (in(Xx,A) => 138.86/139.85 (Xphi(Xx) => 138.86/139.85 ((![Xy]: (in(Xy,A) => (Xphi(Xy) => (Xy = Xx)))) => 138.86/139.85 ex1(A,^[Xy]: Xphi(Xy))))))). 138.86/139.85 tff('18', plain, 138.86/139.85 ex1I = 138.86/139.85 (![X2,X3:($i > $o),X4]: 138.86/139.85 (in(X4,X2) => 138.86/139.85 (X3(X4) => 138.86/139.85 ((![X5]: (in(X5,X2) => (X3(X5) => (X5 = X4)))) => 138.86/139.85 ex1(X2,^[V_1]: X3(V_1)))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(ex1E1, axiom, ex1E1 <=> 138.86/139.85 (![A,Xphi:($i > $o)]: 138.86/139.85 (ex1(A,^[Xx]: Xphi(Xx)) => (?[Xx]: (Xphi(Xx) & in(Xx,A)))))). 138.86/139.85 tff('19', plain, 138.86/139.85 ex1E1 = 138.86/139.85 (![X2,X3:($i > $o)]: 138.86/139.85 (ex1(X2,^[V_1]: X3(V_1)) => (?[X4]: (X3(X4) & in(X4,X2))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(ex1, axiom, ex1() = 138.86/139.85 ^[A,Xphi:($i > $o)]: singleton(dsetconstr(A,^[Xx]: Xphi(Xx)))). 138.86/139.85 tff('20', plain, 138.86/139.85 ex1 = (^[V_1,V_2:($i > $o)]: singleton(dsetconstr(V_1,^[V_3]: V_2(V_3)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(singletonprop, axiom, singletonprop <=> 138.86/139.85 (![A,Xphi:($i > $o)]: 138.86/139.85 ((![Xx]: 138.86/139.85 (in(Xx,A) => 138.86/139.85 (![Xy]: (in(Xy,A) => (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))) => 138.86/139.85 ((?[Xx]: (Xphi(Xx) & in(Xx,A))) => 138.86/139.85 singleton(dsetconstr(A,^[Xx]: Xphi(Xx))))))). 138.86/139.85 tff('21', plain, 138.86/139.85 singletonprop = 138.86/139.85 (![X2,X3:($i > $o)]: 138.86/139.85 ((![X4]: 138.86/139.85 (in(X4,X2) => 138.86/139.85 (![X5]: (in(X5,X2) => (X3(X4) => (X3(X5) => (X4 = X5))))))) => 138.86/139.85 ((?[X6]: (X3(X6) & in(X6,X2))) => 138.86/139.85 singleton(dsetconstr(X2,^[V_1]: X3(V_1)))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(singleton, axiom, singleton() = 138.86/139.85 ^[A]: (?[Xx]: ((A = setadjoin(Xx,emptyset)) & in(Xx,A)))). 138.86/139.85 tff('22', plain, 138.86/139.85 singleton = 138.86/139.85 (^[V_1]: (?[X2]: ((V_1 = setadjoin(X2,emptyset)) & in(X2,V_1)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(setunionsingleton, axiom, setunionsingleton <=> 138.86/139.85 (![Xx]: (setunion(setadjoin(Xx,emptyset)) = Xx))). 138.86/139.85 tff('23', plain, 138.86/139.85 setunionsingleton = (![X2]: (setunion(setadjoin(X2,emptyset)) = X2)), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(setunionsingleton2, axiom, setunionsingleton2 <=> 138.86/139.85 (![A]: subset(A,setunion(setadjoin(A,emptyset))))). 138.86/139.85 tff('24', plain, 138.86/139.85 setunionsingleton2 = (![X2]: subset(X2,setunion(setadjoin(X2,emptyset)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(setunionsingleton1, axiom, setunionsingleton1 <=> 138.86/139.85 (![A]: subset(setunion(setadjoin(A,emptyset)),A))). 138.86/139.85 tff('25', plain, 138.86/139.85 setunionsingleton1 = (![X2]: subset(setunion(setadjoin(X2,emptyset)),X2)), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(setunionE2, axiom, setunionE2 <=> 138.86/139.85 (![A,Xx]: (in(Xx,setunion(A)) => (?[X]: (in(Xx,X) & in(X,A)))))). 138.86/139.85 tff('26', plain, 138.86/139.85 setunionE2 = 138.86/139.85 (![X2,X3]: (in(X3,setunion(X2)) => (?[X4]: (in(X3,X4) & in(X4,X2))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(cartprodmempair, axiom, cartprodmempair <=> 138.86/139.85 (![A,B,Xu]: (in(Xu,cartprod(A,B)) => iskpair(Xu)))). 138.86/139.85 tff('27', plain, 138.86/139.85 cartprodmempair = (![X2,X3,X4]: (in(X4,cartprod(X2,X3)) => iskpair(X4))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(cartprodmempair1, axiom, cartprodmempair1 <=> 138.86/139.85 (![A,B,Xu]: 138.86/139.85 (in(Xu,cartprod(A,B)) => 138.86/139.85 (?[Xx]: ((?[Xy]: ((Xu = kpair(Xx,Xy)) & in(Xy,B))) & in(Xx,A)))))). 138.86/139.85 tff('28', plain, 138.86/139.85 cartprodmempair1 = 138.86/139.85 (![X2,X3,X4]: 138.86/139.85 (in(X4,cartprod(X2,X3)) => 138.86/139.85 (?[X5]: ((?[X6]: ((X4 = kpair(X5,X6)) & in(X6,X3))) & in(X5,X2))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(cartprodpairin, axiom, cartprodpairin <=> 138.86/139.85 (![A,B,Xx]: 138.86/139.85 (in(Xx,A) => (![Xy]: (in(Xy,B) => in(kpair(Xx,Xy),cartprod(A,B))))))). 138.86/139.85 tff('29', plain, 138.86/139.85 cartprodpairin = 138.86/139.85 (![X2,X3,X4]: 138.86/139.85 (in(X4,X2) => (![X5]: (in(X5,X3) => in(kpair(X4,X5),cartprod(X2,X3)))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(ubforcartprodlem3, axiom, ubforcartprodlem3 <=> 138.86/139.85 (![A,B,Xx]: 138.86/139.85 (in(Xx,A) => 138.86/139.85 (![Xy]: 138.86/139.85 (in(Xy,B) => in(kpair(Xx,Xy),powerset(powerset(binunion(A,B))))))))). 138.86/139.85 tff('30', plain, 138.86/139.85 ubforcartprodlem3 = 138.86/139.85 (![X2,X3,X4]: 138.86/139.85 (in(X4,X2) => 138.86/139.85 (![X5]: 138.86/139.85 (in(X5,X3) => in(kpair(X4,X5),powerset(powerset(binunion(X2,X3)))))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(ubforcartprodlem2, axiom, ubforcartprodlem2 <=> 138.86/139.85 (![A,B,Xx]: 138.86/139.85 (in(Xx,A) => 138.86/139.85 (![Xy]: 138.86/139.85 (in(Xy,B) => 138.86/139.85 in(setadjoin(setadjoin(Xx,emptyset), 138.86/139.85 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 138.86/139.85 emptyset)), 138.86/139.85 powerset(powerset(binunion(A,B))))))))). 138.86/139.85 tff('31', plain, 138.86/139.85 ubforcartprodlem2 = 138.86/139.85 (![X2,X3,X4]: 138.86/139.85 (in(X4,X2) => 138.86/139.85 (![X5]: 138.86/139.85 (in(X5,X3) => 138.86/139.85 in(setadjoin(setadjoin(X4,emptyset), 138.86/139.85 setadjoin(setadjoin(X4,setadjoin(X5,emptyset)), 138.86/139.85 emptyset)), 138.86/139.85 powerset(powerset(binunion(X2,X3)))))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(ubforcartprodlem1, axiom, ubforcartprodlem1 <=> 138.86/139.85 (![A,B,Xx]: 138.86/139.85 (in(Xx,A) => 138.86/139.85 (![Xy]: 138.86/139.85 (in(Xy,B) => 138.86/139.85 subset(setadjoin(setadjoin(Xx,emptyset), 138.86/139.85 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 138.86/139.85 emptyset)), 138.86/139.85 powerset(binunion(A,B)))))))). 138.86/139.85 tff('32', plain, 138.86/139.85 ubforcartprodlem1 = 138.86/139.85 (![X2,X3,X4]: 138.86/139.85 (in(X4,X2) => 138.86/139.85 (![X5]: 138.86/139.85 (in(X5,X3) => 138.86/139.85 subset(setadjoin(setadjoin(X4,emptyset), 138.86/139.85 setadjoin(setadjoin(X4,setadjoin(X5,emptyset)), 138.86/139.85 emptyset)), 138.86/139.85 powerset(binunion(X2,X3))))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(upairinpowunion, axiom, upairinpowunion <=> 138.86/139.85 (![A,B,Xx]: 138.86/139.85 (in(Xx,A) => 138.86/139.85 (![Xy]: 138.86/139.85 (in(Xy,B) => 138.86/139.85 in(setadjoin(Xx,setadjoin(Xy,emptyset)),powerset(binunion(A,B)))))))). 138.86/139.85 tff('33', plain, 138.86/139.85 upairinpowunion = 138.86/139.85 (![X2,X3,X4]: 138.86/139.85 (in(X4,X2) => 138.86/139.85 (![X5]: 138.86/139.85 (in(X5,X3) => 138.86/139.85 in(setadjoin(X4,setadjoin(X5,emptyset)),powerset(binunion(X2,X3))))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(upairsubunion, axiom, upairsubunion <=> 138.86/139.85 (![A,B,Xx]: 138.86/139.85 (in(Xx,A) => 138.86/139.85 (![Xy]: 138.86/139.85 (in(Xy,B) => 138.86/139.85 subset(setadjoin(Xx,setadjoin(Xy,emptyset)),binunion(A,B))))))). 138.86/139.85 tff('34', plain, 138.86/139.85 upairsubunion = 138.86/139.85 (![X2,X3,X4]: 138.86/139.85 (in(X4,X2) => 138.86/139.85 (![X5]: 138.86/139.85 (in(X5,X3) => 138.86/139.85 subset(setadjoin(X4,setadjoin(X5,emptyset)),binunion(X2,X3)))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(upairset2E, axiom, upairset2E <=> 138.86/139.85 (![Xx,Xy,Xz]: 138.86/139.85 (in(Xz,setadjoin(Xx,setadjoin(Xy,emptyset))) => ((Xz = Xy) | (Xz = Xx))))). 138.86/139.85 tff('35', plain, 138.86/139.85 upairset2E = 138.86/139.85 (![X2,X3,X4]: 138.86/139.85 (in(X4,setadjoin(X2,setadjoin(X3,emptyset))) => 138.86/139.85 ((X4 = X3) | (X4 = X2)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(singletoninpowunion, axiom, singletoninpowunion <=> 138.86/139.85 (![A,B,Xx]: 138.86/139.85 (in(Xx,A) => in(setadjoin(Xx,emptyset),powerset(binunion(A,B)))))). 138.86/139.85 tff('36', plain, 138.86/139.85 singletoninpowunion = 138.86/139.85 (![X2,X3,X4]: 138.86/139.85 (in(X4,X2) => in(setadjoin(X4,emptyset),powerset(binunion(X2,X3))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(singletoninpowerset, axiom, singletoninpowerset <=> 138.86/139.85 (![A,Xx]: (in(Xx,A) => in(setadjoin(Xx,emptyset),powerset(A))))). 138.86/139.85 tff('37', plain, 138.86/139.85 singletoninpowerset = 138.86/139.85 (![X2,X3]: (in(X3,X2) => in(setadjoin(X3,emptyset),powerset(X2)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(singletonsubset, axiom, singletonsubset <=> 138.86/139.85 (![A,Xx]: (in(Xx,A) => subset(setadjoin(Xx,emptyset),A)))). 138.86/139.85 tff('38', plain, 138.86/139.85 singletonsubset = 138.86/139.85 (![X2,X3]: (in(X3,X2) => subset(setadjoin(X3,emptyset),X2))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(kpairp, axiom, kpairp <=> (![Xx,Xy]: iskpair(kpair(Xx,Xy)))). 138.86/139.85 tff('39', plain, kpairp = (![X2,X3]: iskpair(kpair(X2,X3))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(kpairiskpair, axiom, kpairiskpair <=> 138.86/139.85 (![Xx,Xy]: 138.86/139.85 iskpair(setadjoin(setadjoin(Xx,emptyset), 138.86/139.85 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 138.86/139.85 emptyset))))). 138.86/139.85 tff('40', plain, 138.86/139.85 kpairiskpair = 138.86/139.85 (![X2,X3]: 138.86/139.85 iskpair(setadjoin(setadjoin(X2,emptyset), 138.86/139.85 setadjoin(setadjoin(X2,setadjoin(X3,emptyset)), 138.86/139.85 emptyset)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(setukpairIR, axiom, setukpairIR <=> 138.86/139.85 (![Xx,Xy]: 138.86/139.85 in(Xy, 138.86/139.85 setunion(setadjoin(setadjoin(Xx,emptyset), 138.86/139.85 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 138.86/139.85 emptyset)))))). 138.86/139.85 tff('41', plain, 138.86/139.85 setukpairIR = 138.86/139.85 (![X2,X3]: 138.86/139.85 in(X3, 138.86/139.85 setunion(setadjoin(setadjoin(X2,emptyset), 138.86/139.85 setadjoin(setadjoin(X2,setadjoin(X3,emptyset)), 138.86/139.85 emptyset))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(setukpairIL, axiom, setukpairIL <=> 138.86/139.85 (![Xx,Xy]: 138.86/139.85 in(Xx, 138.86/139.85 setunion(setadjoin(setadjoin(Xx,emptyset), 138.86/139.85 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 138.86/139.85 emptyset)))))). 138.86/139.85 tff('42', plain, 138.86/139.85 setukpairIL = 138.86/139.85 (![X2,X3]: 138.86/139.85 in(X2, 138.86/139.85 setunion(setadjoin(setadjoin(X2,emptyset), 138.86/139.85 setadjoin(setadjoin(X2,setadjoin(X3,emptyset)), 138.86/139.85 emptyset))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(secondinupair, axiom, secondinupair <=> 138.86/139.85 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 138.86/139.85 tff('43', plain, 138.86/139.85 secondinupair = (![X2,X3]: in(X3,setadjoin(X2,setadjoin(X3,emptyset)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(symdiffIneg2, axiom, symdiffIneg2 <=> 138.86/139.85 (![A,B,Xx]: ((~in(Xx,A)) => ((~in(Xx,B)) => (~in(Xx,symdiff(A,B))))))). 138.86/139.85 tff('44', plain, 138.86/139.85 symdiffIneg2 = 138.86/139.85 (![X2,X3,X4]: 138.86/139.85 ((~in(X4,X2)) => ((~in(X4,X3)) => (~in(X4,symdiff(X2,X3)))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(symdiffIneg1, axiom, symdiffIneg1 <=> 138.86/139.85 (![A,B,Xx]: (in(Xx,A) => (in(Xx,B) => (~in(Xx,symdiff(A,B))))))). 138.86/139.85 tff('45', plain, 138.86/139.85 symdiffIneg1 = 138.86/139.85 (![X2,X3,X4]: (in(X4,X2) => (in(X4,X3) => (~in(X4,symdiff(X2,X3)))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(symdiffI2, axiom, symdiffI2 <=> 138.86/139.85 (![A,B,Xx]: ((~in(Xx,A)) => (in(Xx,B) => in(Xx,symdiff(A,B)))))). 138.86/139.85 tff('46', plain, 138.86/139.85 symdiffI2 = 138.86/139.85 (![X2,X3,X4]: ((~in(X4,X2)) => (in(X4,X3) => in(X4,symdiff(X2,X3))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(symdiffI1, axiom, symdiffI1 <=> 138.86/139.85 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => in(Xx,symdiff(A,B)))))). 138.86/139.85 tff('47', plain, 138.86/139.85 symdiffI1 = 138.86/139.85 (![X2,X3,X4]: (in(X4,X2) => ((~in(X4,X3)) => in(X4,symdiff(X2,X3))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(symdiffE, axiom, symdiffE <=> 138.86/139.85 (![A,B,Xx]: 138.86/139.85 (in(Xx,symdiff(A,B)) => 138.86/139.85 (![Xphi:$o]: 138.86/139.85 ((in(Xx,A) => ((~in(Xx,B)) => Xphi)) => 138.86/139.85 (((~in(Xx,A)) => (in(Xx,B) => Xphi)) => Xphi)))))). 138.86/139.85 tff('48', plain, 138.86/139.85 symdiffE = 138.86/139.85 (![X2,X3,X4]: 138.86/139.85 (in(X4,symdiff(X2,X3)) => 138.86/139.85 (![X5:$o]: 138.86/139.85 ((in(X4,X2) => ((~in(X4,X3)) => X5)) => 138.86/139.85 (((~in(X4,X2)) => (in(X4,X3) => X5)) => X5))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(setminusSubset1, axiom, setminusSubset1 <=> 138.86/139.85 (![A,B]: ((setminus(A,B) = emptyset) => subset(A,B)))). 138.86/139.85 tff('49', plain, 138.86/139.85 setminusSubset1 = 138.86/139.85 (![X2,X3]: ((setminus(X2,X3) = emptyset) => subset(X2,X3))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(setminusLsub, axiom, setminusLsub <=> (![A,B]: subset(setminus(A,B),A))). 138.86/139.85 tff('50', plain, setminusLsub = (![X2,X3]: subset(setminus(X2,X3),X2)), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(setminusIRneg, axiom, setminusIRneg <=> 138.86/139.85 (![A,B,Xx]: (in(Xx,B) => (~in(Xx,setminus(A,B)))))). 138.86/139.85 tff('51', plain, 138.86/139.85 setminusIRneg = (![X2,X3,X4]: (in(X4,X3) => (~in(X4,setminus(X2,X3))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(setminusILneg, axiom, setminusILneg <=> 138.86/139.85 (![A,B,Xx]: ((~in(Xx,A)) => (~in(Xx,setminus(A,B)))))). 138.86/139.85 tff('52', plain, 138.86/139.85 setminusILneg = 138.86/139.85 (![X2,X3,X4]: ((~in(X4,X2)) => (~in(X4,setminus(X2,X3))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(setminusELneg, axiom, setminusELneg <=> 138.86/139.85 (![A,B,Xx]: ((~in(Xx,setminus(A,B))) => ((~in(Xx,B)) => (~in(Xx,A)))))). 138.86/139.85 tff('53', plain, 138.86/139.85 setminusELneg = 138.86/139.85 (![X2,X3,X4]: 138.86/139.85 ((~in(X4,setminus(X2,X3))) => ((~in(X4,X3)) => (~in(X4,X2))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(setminusERneg, axiom, setminusERneg <=> 138.86/139.85 (![A,B,Xx]: ((~in(Xx,setminus(A,B))) => (in(Xx,A) => in(Xx,B))))). 138.86/139.85 tff('54', plain, 138.86/139.85 setminusERneg = 138.86/139.85 (![X2,X3,X4]: ((~in(X4,setminus(X2,X3))) => (in(X4,X2) => in(X4,X3)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(setminusSubset2, axiom, setminusSubset2 <=> 138.86/139.85 (![A,B]: (subset(A,B) => (setminus(A,B) = emptyset)))). 138.86/139.85 tff('55', plain, 138.86/139.85 setminusSubset2 = 138.86/139.85 (![X2,X3]: (subset(X2,X3) => (setminus(X2,X3) = emptyset))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(setminusER, axiom, setminusER <=> 138.86/139.85 (![A,B,Xx]: (in(Xx,setminus(A,B)) => (~in(Xx,B))))). 138.86/139.85 tff('56', plain, 138.86/139.85 setminusER = (![X2,X3,X4]: (in(X4,setminus(X2,X3)) => (~in(X4,X3)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(setminusEL, axiom, setminusEL <=> 138.86/139.85 (![A,B,Xx]: (in(Xx,setminus(A,B)) => in(Xx,A)))). 138.86/139.85 tff('57', plain, 138.86/139.85 setminusEL = (![X2,X3,X4]: (in(X4,setminus(X2,X3)) => in(X4,X2))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(setminusI, axiom, setminusI <=> 138.86/139.85 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => in(Xx,setminus(A,B)))))). 138.86/139.85 tff('58', plain, 138.86/139.85 setminusI = 138.86/139.85 (![X2,X3,X4]: (in(X4,X2) => ((~in(X4,X3)) => in(X4,setminus(X2,X3))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(bs114d, axiom, bs114d <=> 138.86/139.85 (![A,B,C]: 138.86/139.85 (binintersect(A,binunion(B,C)) = 138.86/139.85 binunion(binintersect(A,B),binintersect(A,C))))). 138.86/139.85 tff('59', plain, 138.86/139.85 bs114d = 138.86/139.85 (![X2,X3,X4]: 138.86/139.85 (binintersect(X2,binunion(X3,X4)) = 138.86/139.85 binunion(binintersect(X2,X3),binintersect(X2,X4)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(binintersectSubset1, axiom, binintersectSubset1 <=> 138.86/139.85 (![A,B]: ((binintersect(A,B) = A) => subset(A,B)))). 138.86/139.85 tff('60', plain, 138.86/139.85 binintersectSubset1 = 138.86/139.85 (![X2,X3]: ((binintersect(X2,X3) = X2) => subset(X2,X3))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(binintersectSubset4, axiom, binintersectSubset4 <=> 138.86/139.85 (![A,B]: (subset(B,A) => (binintersect(A,B) = B)))). 138.86/139.85 tff('61', plain, 138.86/139.85 binintersectSubset4 = 138.86/139.85 (![X2,X3]: (subset(X3,X2) => (binintersect(X2,X3) = X3))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(binintersectRsub, axiom, binintersectRsub <=> 138.86/139.85 (![A,B]: subset(binintersect(A,B),B))). 138.86/139.85 tff('62', plain, 138.86/139.85 binintersectRsub = (![X2,X3]: subset(binintersect(X2,X3),X3)), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(disjointsetsI1, axiom, disjointsetsI1 <=> 138.86/139.85 (![A,B]: 138.86/139.85 ((~(?[Xx]: (in(Xx,B) & in(Xx,A)))) => (binintersect(A,B) = emptyset)))). 138.86/139.85 tff('63', plain, 138.86/139.85 disjointsetsI1 = 138.86/139.85 (![X2,X3]: 138.86/139.85 ((~(?[X4]: (in(X4,X3) & in(X4,X2)))) => 138.86/139.85 (binintersect(X2,X3) = emptyset))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(binintersectER, axiom, binintersectER <=> 138.86/139.85 (![A,B,Xx]: (in(Xx,binintersect(A,B)) => in(Xx,B)))). 138.86/139.85 tff('64', plain, 138.86/139.85 binintersectER = (![X2,X3,X4]: (in(X4,binintersect(X2,X3)) => in(X4,X3))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(binintersectSubset3, axiom, binintersectSubset3 <=> 138.86/139.85 (![A,B]: ((binintersect(A,B) = B) => subset(B,A)))). 138.86/139.85 tff('65', plain, 138.86/139.85 binintersectSubset3 = 138.86/139.85 (![X2,X3]: ((binintersect(X2,X3) = X3) => subset(X3,X2))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(binintersectSubset2, axiom, binintersectSubset2 <=> 138.86/139.85 (![A,B]: (subset(A,B) => (binintersect(A,B) = A)))). 138.86/139.85 tff('66', plain, 138.86/139.85 binintersectSubset2 = 138.86/139.85 (![X2,X3]: (subset(X2,X3) => (binintersect(X2,X3) = X2))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(binintersectLsub, axiom, binintersectLsub <=> 138.86/139.85 (![A,B]: subset(binintersect(A,B),A))). 138.86/139.85 tff('67', plain, 138.86/139.85 binintersectLsub = (![X2,X3]: subset(binintersect(X2,X3),X2)), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(binintersectEL, axiom, binintersectEL <=> 138.86/139.85 (![A,B,Xx]: (in(Xx,binintersect(A,B)) => in(Xx,A)))). 138.86/139.85 tff('68', plain, 138.86/139.85 binintersectEL = (![X2,X3,X4]: (in(X4,binintersect(X2,X3)) => in(X4,X2))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(binintersectSubset5, axiom, binintersectSubset5 <=> 138.86/139.85 (![A,B,C]: (subset(C,A) => (subset(C,B) => subset(C,binintersect(A,B)))))). 138.86/139.85 tff('69', plain, 138.86/139.85 binintersectSubset5 = 138.86/139.85 (![X2,X3,X4]: 138.86/139.85 (subset(X4,X2) => (subset(X4,X3) => subset(X4,binintersect(X2,X3))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(binintersectI, axiom, binintersectI <=> 138.86/139.85 (![A,B,Xx]: (in(Xx,A) => (in(Xx,B) => in(Xx,binintersect(A,B)))))). 138.86/139.85 tff('70', plain, 138.86/139.85 binintersectI = 138.86/139.85 (![X2,X3,X4]: (in(X4,X2) => (in(X4,X3) => in(X4,binintersect(X2,X3))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(binunionRsub, axiom, binunionRsub <=> (![A,B]: subset(B,binunion(A,B)))). 138.86/139.85 tff('71', plain, binunionRsub = (![X2,X3]: subset(X3,binunion(X2,X3))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(binunionLsub, axiom, binunionLsub <=> (![A,B]: subset(A,binunion(A,B)))). 138.86/139.85 tff('72', plain, binunionLsub = (![X2,X3]: subset(X2,binunion(X2,X3))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(binunionE, axiom, binunionE <=> 138.86/139.85 (![A,B,Xx]: (in(Xx,binunion(A,B)) => (in(Xx,B) | in(Xx,A))))). 138.86/139.85 tff('73', plain, 138.86/139.85 binunionE = 138.86/139.85 (![X2,X3,X4]: (in(X4,binunion(X2,X3)) => (in(X4,X3) | in(X4,X2)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(binunionEcases, axiom, binunionEcases <=> 138.86/139.85 (![A,B,Xx,Xphi:$o]: 138.86/139.85 (in(Xx,binunion(A,B)) => 138.86/139.85 ((in(Xx,A) => Xphi) => ((in(Xx,B) => Xphi) => Xphi))))). 138.86/139.85 tff('74', plain, 138.86/139.85 binunionEcases = 138.86/139.85 (![X2,X3,X4,X5:$o]: 138.86/139.85 (in(X4,binunion(X2,X3)) => 138.86/139.85 ((in(X4,X2) => X5) => ((in(X4,X3) => X5) => X5)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(binunionIR, axiom, binunionIR <=> 138.86/139.85 (![A,B,Xx]: (in(Xx,B) => in(Xx,binunion(A,B))))). 138.86/139.85 tff('75', plain, 138.86/139.85 binunionIR = (![X2,X3,X4]: (in(X4,X3) => in(X4,binunion(X2,X3)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(upairset2IR, axiom, upairset2IR <=> 138.86/139.85 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 138.86/139.85 tff('76', plain, 138.86/139.85 upairset2IR = (![X2,X3]: in(X3,setadjoin(X2,setadjoin(X3,emptyset)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(binunionIL, axiom, binunionIL <=> 138.86/139.85 (![A,B,Xx]: (in(Xx,A) => in(Xx,binunion(A,B))))). 138.86/139.85 tff('77', plain, 138.86/139.85 binunionIL = (![X2,X3,X4]: (in(X4,X2) => in(X4,binunion(X2,X3)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(sepSubset, axiom, sepSubset <=> 138.86/139.85 (![A,Xphi:($i > $o)]: subset(dsetconstr(A,^[Xx]: Xphi(Xx)),A))). 138.86/139.85 tff('78', plain, 138.86/139.85 sepSubset = 138.86/139.85 (![X2,X3:($i > $o)]: subset(dsetconstr(X2,^[V_1]: X3(V_1)),X2)), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(sepInPowerset, axiom, sepInPowerset <=> 138.86/139.85 (![A,Xphi:($i > $o)]: in(dsetconstr(A,^[Xx]: Xphi(Xx)),powerset(A)))). 138.86/139.85 tff('79', plain, 138.86/139.85 sepInPowerset = 138.86/139.85 (![X2,X3:($i > $o)]: in(dsetconstr(X2,^[V_1]: X3(V_1)),powerset(X2))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(powersetsubset, axiom, powersetsubset <=> 138.86/139.85 (![A,B]: (subset(A,B) => subset(powerset(A),powerset(B))))). 138.86/139.85 tff('80', plain, 138.86/139.85 powersetsubset = 138.86/139.85 (![X2,X3]: (subset(X2,X3) => subset(powerset(X2),powerset(X3)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(inPowerset, axiom, inPowerset <=> (![A]: in(A,powerset(A)))). 138.86/139.85 tff('81', plain, inPowerset = (![X2]: in(X2,powerset(X2))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(powersetE1, axiom, powersetE1 <=> 138.86/139.85 (![A,B]: (in(B,powerset(A)) => subset(B,A)))). 138.86/139.85 tff('82', plain, 138.86/139.85 powersetE1 = (![X2,X3]: (in(X3,powerset(X2)) => subset(X3,X2))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(powersetI1, axiom, powersetI1 <=> 138.86/139.85 (![A,B]: (subset(B,A) => in(B,powerset(A))))). 138.86/139.85 tff('83', plain, 138.86/139.85 powersetI1 = (![X2,X3]: (subset(X3,X2) => in(X3,powerset(X2)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(subsetemptysetimpeq, axiom, subsetemptysetimpeq <=> 138.86/139.85 (![A]: (subset(A,emptyset) => (A = emptyset)))). 138.86/139.85 tff('84', plain, 138.86/139.85 subsetemptysetimpeq = (![X2]: (subset(X2,emptyset) => (X2 = emptyset))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(setextsub, axiom, setextsub <=> 138.86/139.85 (![A,B]: (subset(A,B) => (subset(B,A) => (A = B))))). 138.86/139.85 tff('85', plain, 138.86/139.85 setextsub = (![X2,X3]: (subset(X2,X3) => (subset(X3,X2) => (X2 = X3)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(subset2powerset, axiom, subset2powerset <=> 138.86/139.85 (![A,B]: (subset(A,B) => in(A,powerset(B))))). 138.86/139.85 tff('86', plain, 138.86/139.85 subset2powerset = (![X2,X3]: (subset(X2,X3) => in(X2,powerset(X3)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(setadjoinSub2, axiom, setadjoinSub2 <=> 138.86/139.85 (![A,Xx,B]: (subset(A,B) => subset(A,setadjoin(Xx,B))))). 138.86/139.85 tff('87', plain, 138.86/139.85 setadjoinSub2 = 138.86/139.85 (![X2,X3,X4]: (subset(X2,X4) => subset(X2,setadjoin(X3,X4)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(setadjoinSub, axiom, setadjoinSub <=> 138.86/139.85 (![Xx,A]: subset(A,setadjoin(Xx,A)))). 138.86/139.85 tff('88', plain, setadjoinSub = (![X2,X3]: subset(X3,setadjoin(X2,X3))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(subsetTrans, axiom, subsetTrans <=> 138.86/139.85 (![A,B,C]: (subset(A,B) => (subset(B,C) => subset(A,C))))). 138.86/139.85 tff('89', plain, 138.86/139.85 subsetTrans = 138.86/139.85 (![X2,X3,X4]: (subset(X2,X3) => (subset(X3,X4) => subset(X2,X4)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(subsetRefl, axiom, subsetRefl <=> (![A]: subset(A,A))). 138.86/139.85 tff('90', plain, subsetRefl = (![X2]: subset(X2,X2)), define([status(thm)])). 138.86/139.85 tff(notequalI2, axiom, notequalI2 <=> 138.86/139.85 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => (A != B))))). 138.86/139.85 tff('91', plain, 138.86/139.85 notequalI2 = (![X2,X3,X4]: (in(X4,X2) => ((~in(X4,X3)) => (X2 != X3)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(notequalI1, axiom, notequalI1 <=> (![A,B]: ((~subset(A,B)) => (A != B)))). 138.86/139.85 tff('92', plain, notequalI1 = (![X2,X3]: ((~subset(X2,X3)) => (X2 != X3))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(notsubsetI, axiom, notsubsetI <=> 138.86/139.85 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => (~subset(A,B)))))). 138.86/139.85 tff('93', plain, 138.86/139.85 notsubsetI = 138.86/139.85 (![X2,X3,X4]: (in(X4,X2) => ((~in(X4,X3)) => (~subset(X2,X3))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(subsetE2, axiom, subsetE2 <=> 138.86/139.85 (![A,B,Xx]: (subset(A,B) => ((~in(Xx,B)) => (~in(Xx,A)))))). 138.86/139.85 tff('94', plain, 138.86/139.85 subsetE2 = 138.86/139.85 (![X2,X3,X4]: (subset(X2,X3) => ((~in(X4,X3)) => (~in(X4,X2))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(subsetE, axiom, subsetE <=> 138.86/139.85 (![A,B,Xx]: (subset(A,B) => (in(Xx,A) => in(Xx,B))))). 138.86/139.85 tff('95', plain, 138.86/139.85 subsetE = (![X2,X3,X4]: (subset(X2,X3) => (in(X4,X2) => in(X4,X3)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(emptysetsubset, axiom, emptysetsubset <=> (![A]: subset(emptyset,A))). 138.86/139.85 tff('96', plain, emptysetsubset = (![X2]: subset(emptyset,X2)), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(subsetI2, axiom, subsetI2 <=> 138.86/139.85 (![A,B]: ((![Xx]: (in(Xx,A) => in(Xx,B))) => subset(A,B)))). 138.86/139.85 tff('97', plain, 138.86/139.85 subsetI2 = 138.86/139.85 (![X2,X3]: ((![X4]: (in(X4,X2) => in(X4,X3))) => subset(X2,X3))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(eqimpsubset1, axiom, eqimpsubset1 <=> (![A,B]: ((A = B) => subset(A,B)))). 138.86/139.85 tff('98', plain, eqimpsubset1 = (![X2,X3]: ((X2 = X3) => subset(X2,X3))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(eqimpsubset2, axiom, eqimpsubset2 <=> (![A,B]: ((A = B) => subset(B,A)))). 138.86/139.85 tff('99', plain, eqimpsubset2 = (![X2,X3]: ((X2 = X3) => subset(X3,X2))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(subsetI1, axiom, subsetI1 <=> 138.86/139.85 (![A,B]: ((![Xx]: (in(Xx,A) => in(Xx,B))) => subset(A,B)))). 138.86/139.85 tff('100', plain, 138.86/139.85 subsetI1 = 138.86/139.85 (![X2,X3]: ((![X4]: (in(X4,X2) => in(X4,X3))) => subset(X2,X3))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(dsetconstr__Cong, axiom, dsetconstr__Cong <=> 138.86/139.85 (![A,B]: 138.86/139.85 ((A = B) => 138.86/139.85 (![Xphi:($i > $o),Xpsi:($i > $o)]: 138.86/139.85 ((![Xx]: 138.86/139.85 (in(Xx,A) => 138.86/139.85 (![Xy]: (in(Xy,B) => ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy))))))) => 138.86/139.85 (dsetconstr(A,^[Xx]: Xphi(Xx)) = dsetconstr(B,^[Xx]: Xpsi(Xx)))))))). 138.86/139.85 tff('101', plain, 138.86/139.85 dsetconstr__Cong = 138.86/139.85 (![X2,X3]: 138.86/139.85 ((X2 = X3) => 138.86/139.85 (![X4:($i > $o),X5:($i > $o)]: 138.86/139.85 ((![X6]: 138.86/139.85 (in(X6,X2) => 138.86/139.85 (![X7]: (in(X7,X3) => ((X6 = X7) => (X4(X6) <=> X5(X7))))))) => 138.86/139.85 (dsetconstr(X2,^[V_1]: X4(V_1)) = dsetconstr(X3,^[V_2]: X5(V_2))))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(descr__Cong, axiom, descr__Cong <=> 138.86/139.85 (![Xphi:($i > $o),Xpsi:($i > $o)]: 138.86/139.85 ((![Xx,Xy]: ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy)))) => 138.86/139.85 (exu(^[Xx]: Xphi(Xx)) => 138.86/139.85 (exu(^[Xx]: Xpsi(Xx)) => 138.86/139.85 (descr(^[Xx]: Xphi(Xx)) = descr(^[Xx]: Xpsi(Xx)))))))). 138.86/139.85 tff('102', plain, 138.86/139.85 descr__Cong = 138.86/139.85 (![X2:($i > $o),X3:($i > $o)]: 138.86/139.85 ((![X4,X5]: ((X4 = X5) => (X2(X4) <=> X3(X5)))) => 138.86/139.85 (exu(^[V_1]: X2(V_1)) => 138.86/139.85 (exu(^[V_2]: X3(V_2)) => 138.86/139.85 (descr(^[V_3]: X2(V_3)) = descr(^[V_4]: X3(V_4))))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(exuEu, axiom, exuEu <=> 138.86/139.85 (![Xphi:($i > $o)]: 138.86/139.85 (exu(^[Xx]: Xphi(Xx)) => 138.86/139.85 (![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))). 138.86/139.85 tff('103', plain, 138.86/139.85 exuEu = 138.86/139.85 (![X2:($i > $o)]: 138.86/139.85 (exu(^[V_1]: X2(V_1)) => (![X3,X4]: (X2(X3) => (X2(X4) => (X3 = X4)))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(omega__Cong, axiom, omega__Cong <=> (omega = omega)). 138.86/139.85 tff('104', plain, omega__Cong = (omega = omega), define([status(thm)])). 138.86/139.85 tff(setunion__Cong, axiom, setunion__Cong <=> 138.86/139.85 (![A,B]: ((A = B) => (setunion(A) = setunion(B))))). 138.86/139.85 tff('105', plain, 138.86/139.85 setunion__Cong = (![X2,X3]: ((X2 = X3) => (setunion(X2) = setunion(X3)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(powerset__Cong, axiom, powerset__Cong <=> 138.86/139.85 (![A,B]: ((A = B) => (powerset(A) = powerset(B))))). 138.86/139.85 tff('106', plain, 138.86/139.85 powerset__Cong = (![X2,X3]: ((X2 = X3) => (powerset(X2) = powerset(X3)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(setadjoin__Cong, axiom, setadjoin__Cong <=> 138.86/139.85 (![Xx,Xy]: 138.86/139.85 ((Xx = Xy) => 138.86/139.85 (![Xz,Xu]: ((Xz = Xu) => (setadjoin(Xx,Xz) = setadjoin(Xy,Xu))))))). 138.86/139.85 tff('107', plain, 138.86/139.85 setadjoin__Cong = 138.86/139.85 (![X2,X3]: 138.86/139.85 ((X2 = X3) => 138.86/139.85 (![X4,X5]: ((X4 = X5) => (setadjoin(X2,X4) = setadjoin(X3,X5)))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(emptyset__Cong, axiom, emptyset__Cong <=> (emptyset = emptyset)). 138.86/139.85 tff('108', plain, emptyset__Cong = (emptyset = emptyset), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(exu__Cong, axiom, exu__Cong <=> 138.86/139.85 (![Xphi:($i > $o),Xpsi:($i > $o)]: 138.86/139.85 ((![Xx,Xy]: ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy)))) => 138.86/139.85 (exu(^[Xx]: Xphi(Xx)) <=> exu(^[Xx]: Xpsi(Xx)))))). 138.86/139.85 tff('109', plain, 138.86/139.85 exu__Cong = 138.86/139.85 (![X2:($i > $o),X3:($i > $o)]: 138.86/139.85 ((![X4,X5]: ((X4 = X5) => (X2(X4) <=> X3(X5)))) => 138.86/139.85 (exu(^[V_1]: X2(V_1)) <=> exu(^[V_2]: X3(V_2))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(exuE3u, axiom, exuE3u <=> 138.86/139.85 (![Xphi:($i > $o)]: 138.86/139.85 (exu(^[Xx]: Xphi(Xx)) => 138.86/139.85 (![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))). 138.86/139.85 tff('110', plain, 138.86/139.85 exuE3u = 138.86/139.85 (![X2:($i > $o)]: 138.86/139.85 (exu(^[V_1]: X2(V_1)) => (![X3,X4]: (X2(X3) => (X2(X4) => (X3 = X4)))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(in__Cong, axiom, in__Cong <=> 138.86/139.85 (![A,B]: ((A = B) => (![Xx,Xy]: ((Xx = Xy) => (in(Xx,A) <=> in(Xy,B))))))). 138.86/139.85 tff('111', plain, 138.86/139.85 in__Cong = 138.86/139.85 (![X2,X3]: 138.86/139.85 ((X2 = X3) => (![X4,X5]: ((X4 = X5) => (in(X4,X2) <=> in(X5,X3)))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(inCongP, axiom, inCongP <=> 138.86/139.85 (![A,B]: ((A = B) => (![Xx,Xy]: ((Xx = Xy) => (in(Xx,A) => in(Xy,B))))))). 138.86/139.85 tff('112', plain, 138.86/139.85 inCongP = 138.86/139.85 (![X2,X3]: 138.86/139.85 ((X2 = X3) => (![X4,X5]: ((X4 = X5) => (in(X4,X2) => in(X5,X3)))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(exuI2, axiom, exuI2 <=> 138.86/139.85 (![Xphi:($i > $o)]: 138.86/139.85 ((?[Xx]: (![Xy]: (Xphi(Xy) <=> (Xy = Xx)))) => exu(^[Xx]: Xphi(Xx))))). 138.86/139.85 tff('113', plain, 138.86/139.85 exuI2 = 138.86/139.85 (![X2:($i > $o)]: 138.86/139.85 ((?[X3]: (![X4]: (X2(X4) <=> (X4 = X3)))) => exu(^[V_1]: X2(V_1)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(exuI3, axiom, exuI3 <=> 138.86/139.85 (![Xphi:($i > $o)]: 138.86/139.85 ((?[Xx]: Xphi(Xx)) => 138.86/139.85 ((![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy)))) => 138.86/139.85 exu(^[Xx]: Xphi(Xx)))))). 138.86/139.85 tff('114', plain, 138.86/139.85 exuI3 = 138.86/139.85 (![X2:($i > $o)]: 138.86/139.85 ((?[X3]: X2(X3)) => 138.86/139.85 ((![X4,X5]: (X2(X4) => (X2(X5) => (X4 = X5)))) => 138.86/139.85 exu(^[V_1]: X2(V_1))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(exuI1, axiom, exuI1 <=> 138.86/139.85 (![Xphi:($i > $o)]: 138.86/139.85 ((?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx))) => 138.86/139.85 exu(^[Xx]: Xphi(Xx))))). 138.86/139.85 tff('115', plain, 138.86/139.85 exuI1 = 138.86/139.85 (![X2:($i > $o)]: 138.86/139.85 ((?[X3]: ((![X4]: (X2(X4) => (X3 = X4))) & X2(X3))) => 138.86/139.85 exu(^[V_1]: X2(V_1)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(notdallE, axiom, notdallE <=> 138.86/139.85 (![A,Xphi:($i > $o)]: 138.86/139.85 ((~(![Xx]: (in(Xx,A) => Xphi(Xx)))) => (?[Xx]: ((~Xphi(Xx)) & in(Xx,A)))))). 138.86/139.85 tff('116', plain, 138.86/139.85 notdallE = 138.86/139.85 (![X2,X3:($i > $o)]: 138.86/139.85 ((~(![X4]: (in(X4,X2) => X3(X4)))) => (?[X5]: ((~X3(X5)) & in(X5,X2))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(notdexE, axiom, notdexE <=> 138.86/139.85 (![A,Xphi:($i > $o)]: 138.86/139.85 ((~(?[Xx]: (Xphi(Xx) & in(Xx,A)))) => (![Xx]: (in(Xx,A) => (~Xphi(Xx))))))). 138.86/139.85 tff('117', plain, 138.86/139.85 notdexE = 138.86/139.85 (![X2,X3:($i > $o)]: 138.86/139.85 ((~(?[X4]: (X3(X4) & in(X4,X2)))) => (![X5]: (in(X5,X2) => (~X3(X5)))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(prop2set2propI, axiom, prop2set2propI <=> 138.86/139.85 (![Xphi:$o]: (Xphi => set2prop(prop2set(Xphi))))). 138.86/139.85 tff('118', plain, 138.86/139.85 prop2set2propI = (![X2:$o]: (X2 => set2prop(prop2set(X2)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(prop2setI, axiom, prop2setI <=> 138.86/139.85 (![Xphi:$o]: (Xphi => in(emptyset,prop2set(Xphi))))). 138.86/139.85 tff('119', plain, prop2setI = (![X2:$o]: (X2 => in(emptyset,prop2set(X2)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(quantDeMorgan4, axiom, quantDeMorgan4 <=> 138.86/139.85 (![A,Xphi:($i > $o)]: 138.86/139.85 ((?[Xx]: ((~Xphi(Xx)) & in(Xx,A))) => (~(![Xx]: (in(Xx,A) => Xphi(Xx))))))). 138.86/139.85 tff('120', plain, 138.86/139.85 quantDeMorgan4 = 138.86/139.85 (![X2,X3:($i > $o)]: 138.86/139.85 ((?[X4]: ((~X3(X4)) & in(X4,X2))) => (~(![X5]: (in(X5,X2) => X3(X5)))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(quantDeMorgan3, axiom, quantDeMorgan3 <=> 138.86/139.85 (![A,Xphi:($i > $o)]: 138.86/139.85 ((~(?[Xx]: (Xphi(Xx) & in(Xx,A)))) => (![Xx]: (in(Xx,A) => (~Xphi(Xx))))))). 138.86/139.85 tff('121', plain, 138.86/139.85 quantDeMorgan3 = 138.86/139.85 (![X2,X3:($i > $o)]: 138.86/139.85 ((~(?[X4]: (X3(X4) & in(X4,X2)))) => (![X5]: (in(X5,X2) => (~X3(X5)))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(quantDeMorgan2, axiom, quantDeMorgan2 <=> 138.86/139.85 (![A,Xphi:($i > $o)]: 138.86/139.85 ((![Xx]: (in(Xx,A) => (~Xphi(Xx)))) => (~(?[Xx]: (Xphi(Xx) & in(Xx,A))))))). 138.86/139.85 tff('122', plain, 138.86/139.85 quantDeMorgan2 = 138.86/139.85 (![X2,X3:($i > $o)]: 138.86/139.85 ((![X4]: (in(X4,X2) => (~X3(X4)))) => (~(?[X5]: (X3(X5) & in(X5,X2)))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(quantDeMorgan1, axiom, quantDeMorgan1 <=> 138.86/139.85 (![A,Xphi:($i > $o)]: 138.86/139.85 ((~(![Xx]: (in(Xx,A) => Xphi(Xx)))) => (?[Xx]: ((~Xphi(Xx)) & in(Xx,A)))))). 138.86/139.85 tff('123', plain, 138.86/139.85 quantDeMorgan1 = 138.86/139.85 (![X2,X3:($i > $o)]: 138.86/139.85 ((~(![X4]: (in(X4,X2) => X3(X4)))) => (?[X5]: ((~X3(X5)) & in(X5,X2))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(vacuousDall, axiom, vacuousDall <=> 138.86/139.85 (![Xphi:($i > $o),Xx]: (in(Xx,emptyset) => Xphi(Xx)))). 138.86/139.85 tff('124', plain, 138.86/139.85 vacuousDall = (![X2:($i > $o),X3]: (in(X3,emptyset) => X2(X3))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(emptyE1, axiom, emptyE1 <=> 138.86/139.85 (![A,Xphi:($i > $o)]: 138.86/139.85 ((?[Xx]: (Xphi(Xx) & in(Xx,A))) => 138.86/139.85 ((dsetconstr(A,^[Xx]: Xphi(Xx)) = emptyset) => $false)))). 138.86/139.85 tff('125', plain, 138.86/139.85 emptyE1 = 138.86/139.85 (![X2,X3:($i > $o)]: 138.86/139.85 ((?[X4]: (X3(X4) & in(X4,X2))) => 138.86/139.85 ((dsetconstr(X2,^[V_1]: X3(V_1)) = emptyset) => $false))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(upairsetIR, axiom, upairsetIR <=> 138.86/139.85 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 138.86/139.85 tff('126', plain, 138.86/139.85 upairsetIR = (![X2,X3]: in(X3,setadjoin(X2,setadjoin(X3,emptyset)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(upairsetIL, axiom, upairsetIL <=> 138.86/139.85 (![Xx,Xy]: in(Xx,setadjoin(Xx,setadjoin(Xy,emptyset))))). 138.86/139.85 tff('127', plain, 138.86/139.85 upairsetIL = (![X2,X3]: in(X2,setadjoin(X2,setadjoin(X3,emptyset)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(upairsetE, axiom, upairsetE <=> 138.86/139.85 (![Xx,Xy,Xz]: 138.86/139.85 (in(Xz,setadjoin(Xx,setadjoin(Xy,emptyset))) => ((Xz = Xy) | (Xz = Xx))))). 138.86/139.85 tff('128', plain, 138.86/139.85 upairsetE = 138.86/139.85 (![X2,X3,X4]: 138.86/139.85 (in(X4,setadjoin(X2,setadjoin(X3,emptyset))) => 138.86/139.85 ((X4 = X3) | (X4 = X2)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(singletonsswitch, axiom, singletonsswitch <=> 138.86/139.85 (![Xx,Xy]: (in(Xx,setadjoin(Xy,emptyset)) => in(Xy,setadjoin(Xx,emptyset))))). 138.86/139.85 tff('129', plain, 138.86/139.85 singletonsswitch = 138.86/139.85 (![X2,X3]: 138.86/139.85 (in(X2,setadjoin(X3,emptyset)) => in(X3,setadjoin(X2,emptyset)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(eqinunit, axiom, eqinunit <=> 138.86/139.85 (![Xx,Xy]: ((Xx = Xy) => in(Xx,setadjoin(Xy,emptyset))))). 138.86/139.85 tff('130', plain, 138.86/139.85 eqinunit = (![X2,X3]: ((X2 = X3) => in(X2,setadjoin(X3,emptyset)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(notinsingleton, axiom, notinsingleton <=> 138.86/139.85 (![Xx,Xy]: ((Xx != Xy) => (~in(Xy,setadjoin(Xx,emptyset)))))). 138.86/139.85 tff('131', plain, 138.86/139.85 notinsingleton = 138.86/139.85 (![X2,X3]: ((X2 != X3) => (~in(X3,setadjoin(X2,emptyset))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(uniqinunit, axiom, uniqinunit <=> 138.86/139.85 (![Xx,Xy]: (in(Xx,setadjoin(Xy,emptyset)) => (Xx = Xy)))). 138.86/139.85 tff('132', plain, 138.86/139.85 uniqinunit = (![X2,X3]: (in(X2,setadjoin(X3,emptyset)) => (X2 = X3))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(nonemptyImpWitness, axiom, nonemptyImpWitness <=> 138.86/139.85 (![A]: (nonempty(A) => (?[Xx]: (in(Xx,A)))))). 138.86/139.85 tff('133', plain, 138.86/139.85 nonemptyImpWitness = (![X2]: (nonempty(X2) => (?[X3]: (in(X3,X2))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(exuE2, axiom, exuE2 <=> 138.86/139.85 (![Xphi:($i > $o)]: 138.86/139.85 (exu(^[Xx]: Xphi(Xx)) => (?[Xx]: (![Xy]: (Xphi(Xy) <=> (Xy = Xx))))))). 138.86/139.85 tff('134', plain, 138.86/139.85 exuE2 = 138.86/139.85 (![X2:($i > $o)]: 138.86/139.85 (exu(^[V_1]: X2(V_1)) => (?[X3]: (![X4]: (X2(X4) <=> (X4 = X3)))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(subPowSU, axiom, subPowSU <=> 138.86/139.85 (![A,Xx]: (in(Xx,A) => in(Xx,powerset(setunion(A)))))). 138.86/139.85 tff('135', plain, 138.86/139.85 subPowSU = (![X2,X3]: (in(X3,X2) => in(X3,powerset(setunion(X2))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(setunionE, axiom, setunionE <=> 138.86/139.85 (![A,Xx]: 138.86/139.85 (in(Xx,setunion(A)) => 138.86/139.85 (![Xphi:$o]: ((![B]: (in(Xx,B) => (in(B,A) => Xphi))) => Xphi))))). 138.86/139.85 tff('136', plain, 138.86/139.85 setunionE = 138.86/139.85 (![X2,X3]: 138.86/139.85 (in(X3,setunion(X2)) => 138.86/139.85 (![X4:$o]: ((![X5]: (in(X3,X5) => (in(X5,X2) => X4))) => X4)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(setunionI, axiom, setunionI <=> 138.86/139.85 (![A,Xx,B]: (in(Xx,B) => (in(B,A) => in(Xx,setunion(A)))))). 138.86/139.85 tff('137', plain, 138.86/139.85 setunionI = 138.86/139.85 (![X2,X3,X4]: (in(X3,X4) => (in(X4,X2) => in(X3,setunion(X2))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(powersetE, axiom, powersetE <=> 138.86/139.85 (![A,B,Xx]: (in(B,powerset(A)) => (in(Xx,B) => in(Xx,A))))). 138.86/139.85 tff('138', plain, 138.86/139.85 powersetE = 138.86/139.85 (![X2,X3,X4]: (in(X3,powerset(X2)) => (in(X4,X3) => in(X4,X2)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(emptyInPowerset, axiom, emptyInPowerset <=> 138.86/139.85 (![A]: in(emptyset,powerset(A)))). 138.86/139.85 tff('139', plain, emptyInPowerset = (![X2]: in(emptyset,powerset(X2))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(emptyinPowerset, axiom, emptyinPowerset <=> 138.86/139.85 (![A]: in(emptyset,powerset(A)))). 138.86/139.85 tff('140', plain, emptyinPowerset = (![X2]: in(emptyset,powerset(X2))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(powersetI, axiom, powersetI <=> 138.86/139.85 (![A,B]: ((![Xx]: (in(Xx,B) => in(Xx,A))) => in(B,powerset(A))))). 138.86/139.85 tff('141', plain, 138.86/139.85 powersetI = 138.86/139.85 (![X2,X3]: ((![X4]: (in(X4,X3) => in(X4,X2))) => in(X3,powerset(X2)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(setoftrueEq, axiom, setoftrueEq <=> 138.86/139.85 (![A]: (dsetconstr(A,^[Xx]: $true) = A))). 138.86/139.85 tff('142', plain, setoftrueEq = (![X2]: (dsetconstr(X2,^[V_1]: $true) = X2)), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(setadjoinOr, axiom, setadjoinOr <=> 138.86/139.85 (![Xx,A,Xy]: (in(Xy,setadjoin(Xx,A)) => (in(Xy,A) | (Xy = Xx))))). 138.86/139.85 tff('143', plain, 138.86/139.85 setadjoinOr = 138.86/139.85 (![X2,X3,X4]: (in(X4,setadjoin(X2,X3)) => (in(X4,X3) | (X4 = X2)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(setadjoinE, axiom, setadjoinE <=> 138.86/139.85 (![Xx,A,Xy]: 138.86/139.85 (in(Xy,setadjoin(Xx,A)) => 138.86/139.85 (![Xphi:$o]: (((Xy = Xx) => Xphi) => ((in(Xy,A) => Xphi) => Xphi)))))). 138.86/139.85 tff('144', plain, 138.86/139.85 setadjoinE = 138.86/139.85 (![X2,X3,X4]: 138.86/139.85 (in(X4,setadjoin(X2,X3)) => 138.86/139.85 (![X5:$o]: (((X4 = X2) => X5) => ((in(X4,X3) => X5) => X5))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(setadjoinIR, axiom, setadjoinIR <=> 138.86/139.85 (![Xx,A,Xy]: (in(Xy,A) => in(Xy,setadjoin(Xx,A))))). 138.86/139.85 tff('145', plain, 138.86/139.85 setadjoinIR = (![X2,X3,X4]: (in(X4,X3) => in(X4,setadjoin(X2,X3)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(emptyinunitempty, axiom, emptyinunitempty() = 138.86/139.85 in(emptyset,setadjoin(emptyset,emptyset))). 138.86/139.85 tff('146', plain, 138.86/139.85 emptyinunitempty = in(emptyset,setadjoin(emptyset,emptyset)), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(setadjoinIL, axiom, setadjoinIL <=> (![Xx,Xy]: in(Xx,setadjoin(Xx,Xy)))). 138.86/139.85 tff('147', plain, setadjoinIL = (![X2,X3]: in(X2,setadjoin(X2,X3))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(nonemptyI1, axiom, nonemptyI1 <=> 138.86/139.85 (![A]: ((?[Xx]: in(Xx,A)) => nonempty(A)))). 138.86/139.85 tff('148', plain, nonemptyI1 = (![X2]: ((?[X3]: in(X3,X2)) => nonempty(X2))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(nonemptyI, axiom, nonemptyI <=> 138.86/139.85 (![A,Xphi:($i > $o),Xx]: 138.86/139.85 (in(Xx,A) => (Xphi(Xx) => nonempty(dsetconstr(A,^[Xy]: Xphi(Xy))))))). 138.86/139.85 tff('149', plain, 138.86/139.85 nonemptyI = 138.86/139.85 (![X2,X3:($i > $o),X4]: 138.86/139.85 (in(X4,X2) => (X3(X4) => nonempty(dsetconstr(X2,^[V_1]: X3(V_1)))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(nonemptyE1, axiom, nonemptyE1 <=> 138.86/139.85 (![A]: (nonempty(A) => (?[Xx]: in(Xx,A))))). 138.86/139.85 tff('150', plain, nonemptyE1 = (![X2]: (nonempty(X2) => (?[X3]: in(X3,X2)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(nonempty, axiom, nonempty() = ^[Xx]: (Xx != emptyset)). 138.86/139.85 tff('151', plain, nonempty = (^[V_1]: (V_1 != emptyset)), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(setbeta, axiom, setbeta <=> 138.86/139.85 (![A,Xphi:($i > $o),Xx]: 138.86/139.85 (in(Xx,A) => (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) <=> Xphi(Xx))))). 138.86/139.85 tff('152', plain, 138.86/139.85 setbeta = 138.86/139.85 (![X2,X3:($i > $o),X4]: 138.86/139.85 (in(X4,X2) => (in(X4,dsetconstr(X2,^[V_1]: X3(V_1))) <=> X3(X4)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(noeltsimpempty, axiom, noeltsimpempty <=> 138.86/139.85 (![A]: ((![Xx]: (~in(Xx,A))) => (A = emptyset)))). 138.86/139.85 tff('153', plain, 138.86/139.85 noeltsimpempty = (![X2]: ((![X3]: (~in(X3,X2))) => (X2 = emptyset))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(emptyI, axiom, emptyI <=> 138.86/139.85 (![A]: ((![Xx]: (~in(Xx,A))) => (A = emptyset)))). 138.86/139.85 tff('154', plain, 138.86/139.85 emptyI = (![X2]: ((![X3]: (~in(X3,X2))) => (X2 = emptyset))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(setext, axiom, setext <=> 138.86/139.85 (![A,B]: 138.86/139.85 ((![Xx]: (in(Xx,A) => in(Xx,B))) => 138.86/139.85 ((![Xx]: (in(Xx,B) => in(Xx,A))) => (A = B))))). 138.86/139.85 tff('155', plain, 138.86/139.85 setext = 138.86/139.85 (![X2,X3]: 138.86/139.85 ((![X4]: (in(X4,X2) => in(X4,X3))) => 138.86/139.85 ((![X5]: (in(X5,X3) => in(X5,X2))) => (X2 = X3)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(exuE3e, axiom, exuE3e <=> 138.86/139.85 (![Xphi:($i > $o)]: (exu(^[Xx]: Xphi(Xx)) => (?[Xx]: Xphi(Xx))))). 138.86/139.85 tff('156', plain, 138.86/139.85 exuE3e = (![X2:($i > $o)]: (exu(^[V_1]: X2(V_1)) => (?[X3]: X2(X3)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(notinemptyset, axiom, notinemptyset <=> (![Xx]: (~in(Xx,emptyset)))). 138.86/139.85 tff('157', plain, notinemptyset = (![X2]: (~in(X2,emptyset))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(emptysetimpfalse, axiom, emptysetimpfalse <=> 138.86/139.85 (![Xx]: (in(Xx,emptyset) => $false))). 138.86/139.85 tff('158', plain, emptysetimpfalse = (![X2]: (in(X2,emptyset) => $false)), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(emptysetE, axiom, emptysetE <=> 138.86/139.85 (![Xx]: (in(Xx,emptyset) => (![Xphi:$o]: Xphi)))). 138.86/139.85 tff('159', plain, emptysetE = (![X2]: (in(X2,emptyset) => (![X3:$o]: X3))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(prop2setE, axiom, prop2setE <=> 138.86/139.85 (![Xphi:$o,Xx]: (in(Xx,prop2set(Xphi)) => Xphi))). 138.86/139.85 tff('160', plain, prop2setE = (![X2:$o,X3]: (in(X3,prop2set(X2)) => X2)), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(exuE1, axiom, exuE1 <=> 138.86/139.85 (![Xphi:($i > $o)]: 138.86/139.85 (exu(^[Xx]: Xphi(Xx)) => 138.86/139.85 (?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx)))))). 138.86/139.85 tff('161', plain, 138.86/139.85 exuE1 = 138.86/139.85 (![X2:($i > $o)]: 138.86/139.85 (exu(^[V_1]: X2(V_1)) => 138.86/139.85 (?[X3]: ((![X4]: (X2(X4) => (X3 = X4))) & X2(X3))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(dsetconstrER, axiom, dsetconstrER <=> 138.86/139.85 (![A,Xphi:($i > $o),Xx]: (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) => Xphi(Xx)))). 138.86/139.85 tff('162', plain, 138.86/139.85 dsetconstrER = 138.86/139.85 (![X2,X3:($i > $o),X4]: (in(X4,dsetconstr(X2,^[V_1]: X3(V_1))) => X3(X4))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(dsetconstrEL, axiom, dsetconstrEL <=> 138.86/139.85 (![A,Xphi:($i > $o),Xx]: (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) => in(Xx,A)))). 138.86/139.85 tff('163', plain, 138.86/139.85 dsetconstrEL = 138.86/139.85 (![X2,X3:($i > $o),X4]: 138.86/139.85 (in(X4,dsetconstr(X2,^[V_1]: X3(V_1))) => in(X4,X2))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(dsetconstrI, axiom, dsetconstrI <=> 138.86/139.85 (![A,Xphi:($i > $o),Xx]: 138.86/139.85 (in(Xx,A) => (Xphi(Xx) => in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))))))). 138.86/139.85 tff('164', plain, 138.86/139.85 dsetconstrI = 138.86/139.85 (![X2,X3:($i > $o),X4]: 138.86/139.85 (in(X4,X2) => (X3(X4) => in(X4,dsetconstr(X2,^[V_1]: X3(V_1)))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(descrp, axiom, descrp <=> 138.86/139.85 (![Xphi:($i > $o)]: (exu(^[Xx]: Xphi(Xx)) => Xphi(descr(^[Xx]: Xphi(Xx)))))). 138.86/139.85 tff('165', plain, 138.86/139.85 descrp = 138.86/139.85 (![X2:($i > $o)]: (exu(^[V_1]: X2(V_1)) => X2(descr(^[V_2]: X2(V_2))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(wellorderingAx, axiom, wellorderingAx <=> 138.86/139.85 (![A]: 138.86/139.85 (?[B]: 138.86/139.85 ((![C]: 138.86/139.85 (((?[Xx]: in(Xx,C)) & (![Xx]: (in(Xx,C) => in(Xx,A)))) => 138.86/139.85 (?[D,Xx]: 138.86/139.85 ((![E]: 138.86/139.85 (in(E,B) => (in(Xx,E) | (![Xy]: (in(Xy,E) => in(Xy,D)))))) & 138.86/139.85 (~(?[Xy]: (in(Xy,C) & in(Xy,D)))) & in(Xx,C) & in(D,B))))) & 138.86/139.85 (![C,D]: 138.86/139.85 ((in(D,B) & in(C,B)) => 138.86/139.85 ((![Xx]: (in(Xx,D) => in(Xx,C))) | 138.86/139.85 (![Xx]: (in(Xx,C) => in(Xx,D)))))) & 138.86/139.85 (![Xx,Xy]: 138.86/139.85 ((in(Xy,A) & in(Xx,A)) => 138.86/139.85 ((![C]: (in(C,B) => (in(Xx,C) <=> in(Xy,C)))) => (Xx = Xy)))) & 138.86/139.85 (![C]: (in(C,B) => (![Xx]: (in(Xx,C) => in(Xx,A))))))))). 138.86/139.85 tff('166', plain, 138.86/139.85 wellorderingAx = 138.86/139.85 (![X2]: 138.86/139.85 (?[X3]: 138.86/139.85 ((![X4]: 138.86/139.85 (((?[X5]: in(X5,X4)) & (![X6]: (in(X6,X4) => in(X6,X2)))) => 138.86/139.85 (?[X7,X8]: 138.86/139.85 ((![X9]: 138.86/139.85 (in(X9,X3) => 138.86/139.85 (in(X8,X9) | (![X10]: (in(X10,X9) => in(X10,X7)))))) & 138.86/139.85 (~(?[X11]: (in(X11,X4) & in(X11,X7)))) & in(X8,X4) & 138.86/139.85 in(X7,X3))))) & 138.86/139.85 (![X12,X13]: 138.86/139.85 ((in(X13,X3) & in(X12,X3)) => 138.86/139.85 ((![X14]: (in(X14,X13) => in(X14,X12))) | 138.86/139.85 (![X15]: (in(X15,X12) => in(X15,X13)))))) & 138.86/139.85 (![X16,X17]: 138.86/139.85 ((in(X17,X2) & in(X16,X2)) => 138.86/139.85 ((![X18]: (in(X18,X3) => (in(X16,X18) <=> in(X17,X18)))) => 138.86/139.85 (X16 = X17)))) & 138.86/139.85 (![X19]: (in(X19,X3) => (![X20]: (in(X20,X19) => in(X20,X2)))))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(foundationAx, axiom, foundationAx <=> 138.86/139.85 (![A]: 138.86/139.85 ((?[Xx]: in(Xx,A)) => 138.86/139.85 (?[B]: ((~(?[Xx]: (in(Xx,A) & in(Xx,B)))) & in(B,A)))))). 138.86/139.85 tff('167', plain, 138.86/139.85 foundationAx = 138.86/139.85 (![X2]: 138.86/139.85 ((?[X3]: in(X3,X2)) => 138.86/139.85 (?[X4]: ((~(?[X5]: (in(X5,X2) & in(X5,X4)))) & in(X4,X2))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(replAx, axiom, replAx <=> 138.86/139.85 (![Xphi:(($i * $i) > $o),A]: 138.86/139.85 ((![Xx]: (in(Xx,A) => exu(^[Xy]: Xphi(Xx,Xy)))) => 138.86/139.85 (?[B]: (![Xx]: (in(Xx,B) <=> (?[Xy]: (Xphi(Xy,Xx) & in(Xy,A))))))))). 138.86/139.85 tff('168', plain, 138.86/139.85 replAx = 138.86/139.85 (![X2:(($i * $i) > $o),X3]: 138.86/139.85 ((![X4]: (in(X4,X3) => exu(^[V_1]: X2(X4,V_1)))) => 138.86/139.85 (?[X5]: (![X6]: (in(X6,X5) <=> (?[X7]: (X2(X7,X6) & in(X7,X3)))))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(omegaIndAx, axiom, omegaIndAx <=> 138.86/139.85 (![A]: 138.86/139.85 (((![Xx]: ((in(Xx,A) & in(Xx,omega)) => in(setadjoin(Xx,Xx),A))) & 138.86/139.85 in(emptyset,A)) => 138.86/139.85 (![Xx]: (in(Xx,omega) => in(Xx,A)))))). 138.86/139.85 tff('169', plain, 138.86/139.85 omegaIndAx = 138.86/139.85 (![X2]: 138.86/139.85 (((![X3]: ((in(X3,X2) & in(X3,omega)) => in(setadjoin(X3,X3),X2))) & 138.86/139.85 in(emptyset,X2)) => 138.86/139.85 (![X4]: (in(X4,omega) => in(X4,X2))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(omegaSAx, axiom, omegaSAx <=> 138.86/139.85 (![Xx]: (in(Xx,omega) => in(setadjoin(Xx,Xx),omega)))). 138.86/139.85 tff('170', plain, 138.86/139.85 omegaSAx = (![X2]: (in(X2,omega) => in(setadjoin(X2,X2),omega))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(omega0Ax, axiom, omega0Ax() = in(emptyset,omega)). 138.86/139.85 tff('171', plain, omega0Ax = in(emptyset,omega), define([status(thm)])). 138.86/139.85 tff(setunionAx, axiom, setunionAx <=> 138.86/139.85 (![A,Xx]: (in(Xx,setunion(A)) <=> (?[B]: (in(B,A) & in(Xx,B)))))). 138.86/139.85 tff('172', plain, 138.86/139.85 setunionAx = 138.86/139.85 (![X2,X3]: (in(X3,setunion(X2)) <=> (?[X4]: (in(X4,X2) & in(X3,X4))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(powersetAx, axiom, powersetAx <=> 138.86/139.85 (![A,B]: (in(B,powerset(A)) <=> (![Xx]: (in(Xx,B) => in(Xx,A)))))). 138.86/139.85 tff('173', plain, 138.86/139.85 powersetAx = 138.86/139.85 (![X2,X3]: (in(X3,powerset(X2)) <=> (![X4]: (in(X4,X3) => in(X4,X2))))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(setadjoinAx, axiom, setadjoinAx <=> 138.86/139.85 (![Xx,A,Xy]: (in(Xy,setadjoin(Xx,A)) <=> (in(Xy,A) | (Xy = Xx))))). 138.86/139.85 tff('174', plain, 138.86/139.85 setadjoinAx = 138.86/139.85 (![X2,X3,X4]: (in(X4,setadjoin(X2,X3)) <=> (in(X4,X3) | (X4 = X2)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(emptysetAx, axiom, emptysetAx <=> (![Xx]: (~in(Xx,emptyset)))). 138.86/139.85 tff('175', plain, emptysetAx = (![X2]: (~in(X2,emptyset))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(setextAx, axiom, setextAx <=> 138.86/139.85 (![A,B]: ((![Xx]: (in(Xx,A) <=> in(Xx,B))) => (A = B)))). 138.86/139.85 tff('176', plain, 138.86/139.85 setextAx = (![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(exu, axiom, exu() = 138.86/139.85 ^[Xphi:($i > $o)]: (?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx)))). 138.86/139.85 tff('177', plain, 138.86/139.85 exu = 138.86/139.85 (^[V_1:($i > $o)]: (?[X2]: ((![X3]: (V_1(X3) => (X2 = X3))) & V_1(X2)))), 138.86/139.85 define([status(thm)])). 138.86/139.85 tff(cartprodsndin, conjecture, 138.86/139.85 (setextAx => 138.86/139.85 (emptysetAx => 138.86/139.85 (setadjoinAx => 138.86/139.85 (powersetAx => 138.86/139.85 (setunionAx => 138.86/139.85 (omega0Ax => 138.86/139.85 (omegaSAx => 138.86/139.85 (omegaIndAx => 138.86/139.85 (replAx => 138.86/139.85 (foundationAx => 138.86/139.85 (wellorderingAx => 138.86/139.85 (descrp => 138.86/139.85 (dsetconstrI => 138.86/139.85 (dsetconstrEL => 138.86/139.85 (dsetconstrER => 138.86/139.85 (exuE1 => 138.86/139.85 (prop2setE => 138.86/139.85 (emptysetE => 138.86/139.85 (emptysetimpfalse => 138.86/139.85 (notinemptyset => 138.86/139.85 (exuE3e => 138.86/139.85 (setext => 138.86/139.85 (emptyI => 138.86/139.85 (noeltsimpempty => 138.86/139.85 (setbeta => 138.86/139.85 (nonemptyE1 => 138.86/139.85 (nonemptyI => 138.86/139.85 (nonemptyI1 => 138.86/139.85 (setadjoinIL => 138.86/139.85 (emptyinunitempty => 138.86/139.85 (setadjoinIR => 138.86/139.85 (setadjoinE => 138.86/139.85 (setadjoinOr => 138.86/139.85 (setoftrueEq => 138.86/139.85 (powersetI => 138.86/139.85 (emptyinPowerset => 138.86/139.85 (emptyInPowerset => 138.86/139.85 (powersetE => 138.86/139.85 (setunionI => 138.86/139.85 (setunionE => 138.86/139.85 (subPowSU => 138.86/139.85 (exuE2 => 138.86/139.85 (nonemptyImpWitness => 138.86/139.85 (uniqinunit => 138.86/139.85 (notinsingleton => 138.86/139.85 (eqinunit => 138.86/139.85 (singletonsswitch => 138.86/139.85 (upairsetE => 138.86/139.85 (upairsetIL => 138.86/139.85 (upairsetIR => 138.86/139.85 (emptyE1 => 138.86/139.85 (vacuousDall => 138.86/139.85 (quantDeMorgan1 => 138.86/139.85 (quantDeMorgan2 => 138.86/139.85 (quantDeMorgan3 => 138.86/139.85 (quantDeMorgan4 => 138.86/139.85 (prop2setI => 138.86/139.85 (prop2set2propI => 138.86/139.85 (notdexE => 138.86/139.85 (notdallE => 138.86/139.85 (exuI1 => 138.86/139.85 (exuI3 => 138.86/139.85 (exuI2 => 138.86/139.85 (inCongP => 138.86/139.85 (in__Cong => 138.86/139.85 (exuE3u => 138.86/139.85 ( 138.86/139.85 exu__Cong => 138.86/139.85 ( 138.86/139.85 emptyset__Cong => 138.86/139.85 ( 138.86/139.85 setadjoin__Cong => 138.86/139.85 ( 138.86/139.85 powerset__Cong => 138.86/139.85 ( 138.86/139.85 setunion__Cong => 138.86/139.85 ( 138.86/139.85 omega__Cong => 138.86/139.85 ( 138.86/139.85 exuEu => 138.86/139.85 ( 138.86/139.85 descr__Cong => 138.86/139.85 ( 138.86/139.85 dsetconstr__Cong => 138.86/139.85 ( 138.86/139.85 subsetI1 => 138.86/139.85 ( 138.86/139.85 eqimpsubset2 => 138.86/139.85 ( 138.86/139.85 eqimpsubset1 => 138.86/139.85 ( 138.86/139.85 subsetI2 => 138.86/139.85 ( 138.86/139.85 emptysetsubset => 138.86/139.85 ( 138.86/139.85 subsetE => 138.86/139.85 ( 138.86/139.85 subsetE2 => 138.86/139.85 ( 138.86/139.85 notsubsetI => 138.86/139.85 ( 138.86/139.85 notequalI1 => 138.86/139.85 ( 138.86/139.85 notequalI2 => 138.86/139.85 ( 138.86/139.85 subsetRefl => 138.86/139.85 ( 138.86/139.85 subsetTrans => 138.86/139.85 ( 138.86/139.85 setadjoinSub => 138.86/139.85 ( 138.86/139.85 setadjoinSub2 => 138.86/139.85 ( 138.86/139.85 subset2powerset => 138.86/139.85 ( 138.86/139.85 setextsub => 138.86/139.85 ( 138.86/139.85 subsetemptysetimpeq => 138.86/139.85 ( 138.86/139.85 powersetI1 => 138.86/139.85 ( 138.86/139.85 powersetE1 => 138.86/139.85 ( 138.86/139.85 inPowerset => 138.86/139.85 ( 138.86/139.85 powersetsubset => 138.86/139.85 ( 138.86/139.85 sepInPowerset => 138.86/139.85 ( 138.86/139.85 sepSubset => 138.86/139.85 ( 138.86/139.85 binunionIL => 138.86/139.85 ( 138.86/139.85 upairset2IR => 138.86/139.85 ( 138.86/139.85 binunionIR => 138.86/139.85 ( 138.86/139.85 binunionEcases => 138.86/139.85 ( 138.86/139.85 binunionE => 138.86/139.85 ( 138.86/139.85 binunionLsub => 138.86/139.85 ( 138.86/139.85 binunionRsub => 138.86/139.85 ( 138.86/139.85 binintersectI => 138.86/139.85 ( 138.86/139.85 binintersectSubset5 => 138.86/139.85 ( 138.86/139.85 binintersectEL => 138.86/139.85 ( 138.86/139.85 binintersectLsub => 138.86/139.85 ( 138.86/139.85 binintersectSubset2 => 138.86/139.85 ( 138.86/139.85 binintersectSubset3 => 138.86/139.85 ( 138.86/139.85 binintersectER => 138.86/139.85 ( 138.86/139.85 disjointsetsI1 => 138.86/139.85 ( 138.86/139.85 binintersectRsub => 138.86/139.85 ( 138.86/139.85 binintersectSubset4 => 138.86/139.85 ( 138.86/139.85 binintersectSubset1 => 138.86/139.85 ( 138.86/139.85 bs114d => 138.86/139.85 ( 138.86/139.85 setminusI => 138.86/139.85 ( 138.86/139.85 setminusEL => 138.86/139.85 ( 138.86/139.85 setminusER => 138.86/139.85 ( 138.86/139.85 setminusSubset2 => 138.86/139.85 ( 138.86/139.85 setminusERneg => 138.86/139.85 ( 138.86/139.85 setminusELneg => 138.86/139.85 ( 138.86/139.85 setminusILneg => 138.86/139.85 ( 138.86/139.85 setminusIRneg => 138.86/139.85 ( 138.86/139.85 setminusLsub => 138.86/139.85 ( 138.86/139.85 setminusSubset1 => 138.86/139.85 ( 138.86/139.85 symdiffE => 138.86/139.85 ( 138.86/139.85 symdiffI1 => 138.86/139.85 ( 138.86/139.85 symdiffI2 => 138.86/139.85 ( 138.86/139.85 symdiffIneg1 => 138.86/139.85 ( 138.86/139.85 symdiffIneg2 => 138.86/139.85 ( 138.86/139.85 secondinupair => 138.86/139.85 ( 138.86/139.85 setukpairIL => 138.86/139.85 ( 138.86/139.85 setukpairIR => 138.86/139.85 ( 138.86/139.85 kpairiskpair => 138.86/139.85 ( 138.86/139.85 kpairp => 138.86/139.85 ( 138.86/139.85 singletonsubset => 138.86/139.85 ( 138.86/139.85 singletoninpowerset => 138.86/139.85 ( 138.86/139.85 singletoninpowunion => 138.86/139.85 ( 138.86/139.85 upairset2E => 138.86/139.85 ( 138.86/139.85 upairsubunion => 138.86/139.85 ( 138.86/139.85 upairinpowunion => 138.86/139.85 ( 138.86/139.85 ubforcartprodlem1 => 138.86/139.85 ( 138.86/139.85 ubforcartprodlem2 => 138.86/139.85 ( 138.86/139.85 ubforcartprodlem3 => 138.86/139.85 ( 138.86/139.85 cartprodpairin => 138.86/139.85 ( 138.86/139.85 cartprodmempair1 => 138.86/139.85 ( 138.86/139.85 cartprodmempair => 138.86/139.85 ( 138.86/139.85 setunionE2 => 138.86/139.85 ( 138.86/139.85 setunionsingleton1 => 138.86/139.85 ( 138.86/139.85 setunionsingleton2 => 138.86/139.85 ( 138.86/139.85 setunionsingleton => 138.86/139.85 ( 138.86/139.85 singletonprop => 138.86/139.85 ( 138.86/139.85 ex1E1 => 138.86/139.85 ( 138.86/139.85 ex1I => 138.86/139.85 ( 138.86/139.85 ex1I2 => 138.86/139.85 ( 138.86/139.85 singletonsuniq => 138.86/139.85 ( 138.86/139.85 setukpairinjL1 => 138.86/139.85 ( 138.86/139.85 kfstsingleton => 138.86/139.85 ( 138.86/139.85 theprop => 138.86/139.85 ( 138.86/139.85 kfstpairEq => 138.86/139.85 ( 138.86/139.85 cartprodfstin => 138.86/139.85 ( 138.86/139.85 setukpairinjL2 => 138.86/139.85 ( 138.86/139.85 setukpairinjL => 138.86/139.85 ( 138.86/139.85 setukpairinjR11 => 138.86/139.85 ( 138.86/139.85 setukpairinjR12 => 138.86/139.85 ( 138.86/139.85 setukpairinjR1 => 138.86/139.85 ( 138.86/139.85 upairequniteq => 138.86/139.85 ( 138.86/139.85 setukpairinjR2 => 138.86/139.85 ( 138.86/139.85 setukpairinjR => 138.86/139.85 ( 138.86/139.85 ksndsingleton => 138.86/139.85 ( 138.86/139.85 ksndpairEq => 138.86/139.85 ( 138.86/139.85 kpairsurjEq => 138.86/139.85 ( 138.86/139.85 ![A,B,Xu]: 138.86/139.85 (in( 138.86/139.85 Xu, 138.86/139.85 cartprod( 138.86/139.85 A,B)) => 138.86/139.85 in( 138.86/139.85 ksnd(Xu), 138.86/139.85 B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 138.86/139.85 tff(zf_stmt_0, conjecture, 138.86/139.85 ((![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))) => 138.86/139.85 ((![X5]: (~in(X5,emptyset))) => 138.86/139.85 ((![X6,X7,X8]: (in(X8,setadjoin(X6,X7)) <=> ((X8 = X6) | in(X8,X7)))) => 138.86/139.85 ((![X9,X10]: 138.86/139.85 (in(X10,powerset(X9)) <=> (![X11]: (in(X11,X10) => in(X11,X9))))) => 138.86/139.85 ((![X12,X13]: 138.86/139.85 (in(X13,setunion(X12)) <=> (?[X14]: (in(X13,X14) & in(X14,X12))))) => 138.86/139.85 (in(emptyset,omega) => 138.86/139.85 ((![X15]: (in(X15,omega) => in(setadjoin(X15,X15),omega))) => 138.86/139.85 ((![X16]: 138.86/139.85 ((in(emptyset,X16) & 138.86/139.85 (![X17]: 138.86/139.85 ((in(X17,omega) & in(X17,X16)) => 138.86/139.85 in(setadjoin(X17,X17),X16)))) => 138.86/139.85 (![X18]: (in(X18,omega) => in(X18,X16))))) => 138.86/139.85 ((![X19:(($i * $i) > $o),X20]: 138.86/139.85 ((![X21]: 138.86/139.85 (in(X21,X20) => 138.86/139.85 (?[X22]: 138.86/139.85 (X19(X21,X22) & (![X23]: (X19(X21,X23) => (X22 = X23))))))) => 138.86/139.85 (?[X24]: 138.86/139.85 (![X25]: 138.86/139.85 (in(X25,X24) <=> (?[X26]: (in(X26,X20) & X19(X26,X25)))))))) => 138.86/139.85 ((![X27]: 138.86/139.85 ((?[X28]: in(X28,X27)) => 138.86/139.85 (?[X29]: 138.86/139.85 (in(X29,X27) & (~(?[X30]: (in(X30,X29) & in(X30,X27)))))))) => 138.86/139.85 ((![X31]: 138.86/139.85 (?[X32]: 138.86/139.85 ((![X48]: 138.86/139.85 (in(X48,X32) => (![X49]: (in(X49,X48) => in(X49,X31))))) & 138.86/139.85 (![X45,X46]: 138.86/139.85 ((in(X45,X31) & in(X46,X31)) => 138.86/139.85 ((![X47]: 138.86/139.85 (in(X47,X32) => (in(X45,X47) <=> in(X46,X47)))) => 138.86/139.85 (X45 = X46)))) & 138.86/139.85 (![X41,X42]: 138.86/139.85 ((in(X41,X32) & in(X42,X32)) => 138.86/139.85 ((![X44]: (in(X44,X41) => in(X44,X42))) | 138.86/139.85 (![X43]: (in(X43,X42) => in(X43,X41)))))) & 138.86/139.85 (![X33]: 138.86/139.85 (((![X35]: (in(X35,X33) => in(X35,X31))) & 138.86/139.85 (?[X34]: in(X34,X33))) => 138.86/139.85 (?[X36,X37]: 138.86/139.85 (in(X36,X32) & in(X37,X33) & 138.86/139.85 (~(?[X40]: (in(X40,X36) & in(X40,X33)))) & 138.86/139.85 (![X38]: 138.86/139.85 (in(X38,X32) => 138.86/139.85 ((![X39]: (in(X39,X38) => in(X39,X36))) | 138.86/139.85 in(X37,X38))))))))))) => 138.86/139.85 ((![X50:($i > $o)]: 138.86/139.85 ((?[X51]: (X50(X51) & (![X52]: (X50(X52) => (X51 = X52))))) => 138.86/139.85 X50(descr(^[V_1]: X50(V_1))))) => 138.86/139.85 ((![X53,X54:($i > $o),X55]: 138.86/139.85 (in(X55,X53) => 138.86/139.85 (X54(X55) => in(X55,dsetconstr(X53,^[V_2]: X54(V_2)))))) => 138.86/139.85 ((![X56,X57:($i > $o),X58]: 138.86/139.85 (in(X58,dsetconstr(X56,^[V_3]: X57(V_3))) => in(X58,X56))) => 138.86/139.85 ((![X59,X60:($i > $o),X61]: 138.86/139.85 (in(X61,dsetconstr(X59,^[V_4]: X60(V_4))) => X60(X61))) => 138.86/139.85 ((![X62:($i > $o)]: 138.86/139.85 ((?[X63]: 138.86/139.85 (X62(X63) & (![X64]: (X62(X64) => (X63 = X64))))) => 138.86/139.85 (?[X65]: 138.86/139.85 (X62(X65) & (![X66]: (X62(X66) => (X65 = X66))))))) => 138.86/139.85 ((![X67:$o,X68]: (in(X68,prop2set(X67)) => X67)) => 138.86/139.85 ((![X69]: (in(X69,emptyset) => (![X70:$o]: X70))) => 138.86/139.85 ((![X71]: (in(X71,emptyset) => $false)) => 138.86/139.85 ((![X72]: (~in(X72,emptyset))) => 138.86/139.85 ((![X73:($i > $o)]: 138.86/139.85 ((?[X74]: 138.86/139.85 (X73(X74) & (![X75]: (X73(X75) => (X74 = X75))))) => 138.86/139.85 (?[X76]: X73(X76)))) => 138.86/139.85 ((![X77,X78]: 138.86/139.85 ((![X79]: (in(X79,X77) => in(X79,X78))) => 138.86/139.85 ((![X80]: (in(X80,X78) => in(X80,X77))) => 138.86/139.85 (X77 = X78)))) => 138.86/139.85 ((![X81]: 138.86/139.85 ((![X82]: (~in(X82,X81))) => (X81 = emptyset))) => 138.86/139.85 ((![X83]: 138.86/139.85 ((![X84]: (~in(X84,X83))) => (X83 = emptyset))) => 138.86/139.85 ((![X85,X86:($i > $o),X87]: 138.86/139.85 (in(X87,X85) => 138.86/139.85 (in(X87,dsetconstr(X85,^[V_5]: X86(V_5))) <=> 138.86/139.85 X86(X87)))) => 138.86/139.85 ((![X88]: 138.86/139.85 ((X88 != emptyset) => (?[X89]: in(X89,X88)))) => 138.86/139.85 ((![X90,X91:($i > $o),X92]: 138.86/139.85 (in(X92,X90) => 138.86/139.85 (X91(X92) => 138.86/139.85 (dsetconstr(X90,^[V_6]: X91(V_6)) != 138.86/139.85 emptyset)))) => 138.86/139.85 ((![X93]: 138.86/139.85 ((?[X94]: in(X94,X93)) => (X93 != emptyset))) => 138.86/139.85 ((![X95,X96]: in(X95,setadjoin(X95,X96))) => 138.86/139.85 (in(emptyset,setadjoin(emptyset,emptyset)) => 138.86/139.85 ((![X97,X98,X99]: 138.86/139.85 (in(X99,X98) => 138.86/139.85 in(X99,setadjoin(X97,X98)))) => 138.86/139.85 ((![X100,X101,X102]: 138.86/139.85 (in(X102,setadjoin(X100,X101)) => 138.86/139.85 (![X103:$o]: 138.86/139.85 (((X102 = X100) => X103) => 138.86/139.85 ((in(X102,X101) => X103) => X103))))) => 138.86/139.85 ((![X104,X105,X106]: 138.86/139.85 (in(X106,setadjoin(X104,X105)) => 138.86/139.85 ((X106 = X104) | in(X106,X105)))) => 138.86/139.85 ((![X107]: 138.86/139.85 (dsetconstr(X107,^[V_7]: $true) = X107)) => 138.86/139.85 ((![X108,X109]: 138.86/139.85 ((![X110]: 138.86/139.85 (in(X110,X109) => in(X110,X108))) => 138.86/139.85 in(X109,powerset(X108)))) => 138.86/139.85 ((![X111]: in(emptyset,powerset(X111))) => 138.86/139.85 ((![X112]: in(emptyset,powerset(X112))) => 138.86/139.85 ((![X113,X114,X115]: 138.86/139.85 (in(X114,powerset(X113)) => 138.86/139.85 (in(X115,X114) => in(X115,X113)))) => 138.86/139.85 ((![X116,X117,X118]: 138.86/139.85 (in(X117,X118) => 138.86/139.85 (in(X118,X116) => 138.86/139.85 in(X117,setunion(X116))))) => 138.86/139.85 ((![X119,X120]: 138.86/139.85 (in(X120,setunion(X119)) => 138.86/139.85 (![X121:$o]: 138.86/139.85 ((![X122]: 138.86/139.85 (in(X120,X122) => 138.86/139.85 (in(X122,X119) => X121))) => 138.86/139.85 X121)))) => 138.86/139.85 ((![X123,X124]: 138.86/139.85 (in(X124,X123) => 138.86/139.85 in(X124, 138.86/139.85 powerset(setunion(X123))))) => 138.86/139.85 ((![X125:($i > $o)]: 138.86/139.85 ((?[X126]: 138.86/139.85 (X125(X126) & 138.86/139.85 (![X127]: 138.86/139.85 (X125(X127) => 138.86/139.85 (X126 = X127))))) => 138.86/139.85 (?[X128]: 138.86/139.85 (![X129]: 138.86/139.85 (X125(X129) <=> 138.86/139.85 (X129 = X128)))))) => 138.86/139.85 ((![X130]: 138.86/139.85 ((X130 != emptyset) => 138.86/139.85 (?[X131]: in(X131,X130)))) => 138.86/139.85 ((![X132,X133]: 138.86/139.85 (in(X132, 138.86/139.85 setadjoin(X133,emptyset)) => 138.86/139.85 (X132 = X133))) => 138.86/139.85 ((![X134,X135]: 138.86/139.85 ((X134 != X135) => 138.86/139.85 (~ 138.86/139.85 in(X135, 138.86/139.85 setadjoin(X134, 138.86/139.85 emptyset))))) => 138.86/139.85 ((![X136,X137]: 138.86/139.85 ((X136 = X137) => 138.86/139.85 in(X136, 138.86/139.85 setadjoin(X137, 138.86/139.85 emptyset)))) => 138.86/139.85 ((![X138,X139]: 138.86/139.85 (in(X138, 138.86/139.85 setadjoin(X139, 138.86/139.85 emptyset)) => 138.86/139.85 in(X139, 138.86/139.85 setadjoin(X138, 138.86/139.85 emptyset)))) => 138.86/139.85 ((![X140,X141,X142]: 138.86/139.85 (in(X142, 138.86/139.85 setadjoin(X140, 138.86/139.85 setadjoin( 138.86/139.85 X141, 138.86/139.85 emptyset))) => 138.86/139.85 ((X142 = X140) | 138.86/139.85 (X142 = X141)))) => 138.86/139.85 ((![X143,X144]: 138.86/139.85 in(X143, 138.86/139.85 setadjoin(X143, 138.86/139.85 setadjoin( 138.86/139.85 X144, 138.86/139.85 emptyset)))) => 138.86/139.85 ((![X145,X146]: 138.86/139.85 in(X146, 138.86/139.85 setadjoin(X145, 138.86/139.85 setadjoin( 138.86/139.85 X146, 138.86/139.85 emptyset)))) => 138.86/139.85 ((![X147,X148:($i > $o)]: 138.86/139.85 ((?[X149]: 138.86/139.85 (in(X149,X147) & 138.86/139.85 X148(X149))) => 138.86/139.85 ((dsetconstr( 138.86/139.85 X147, 138.86/139.85 ^[V_8]: X148(V_8)) = 138.86/139.85 emptyset) => 138.86/139.85 $false))) => 138.86/139.85 ((![X150:($i > $o),X151]: 138.86/139.85 (in(X151,emptyset) => 138.86/139.85 X150(X151))) => 138.86/139.85 ((![X152,X153:($i > $o)]: 138.86/139.85 ((~ 138.86/139.85 (![X154]: 138.86/139.85 (in(X154,X152) => 138.86/139.85 X153(X154)))) => 138.86/139.85 (?[X155]: 138.86/139.85 (in(X155,X152) & 138.86/139.85 (~X153(X155)))))) => 138.86/139.85 ((![X156, 138.86/139.85 X157:($i > $o)]: 138.86/139.85 ((![X158]: 138.86/139.85 (in(X158,X156) => 138.86/139.85 (~X157(X158)))) => 138.86/139.85 (~ 138.86/139.85 (?[X159]: 138.86/139.85 (in( 138.86/139.85 X159,X156) & 138.86/139.85 X157(X159)))))) => 138.86/139.85 ((![X160, 138.86/139.85 X161:($i > $o)]: 138.86/139.85 ((~ 138.86/139.85 (?[X162]: 138.86/139.85 (in( 138.86/139.85 X162,X160) & 138.86/139.85 X161(X162)))) => 138.86/139.85 (![X163]: 138.86/139.85 (in(X163,X160) => 138.86/139.85 (~X161(X163)))))) => 138.86/139.85 ((![X164, 138.86/139.85 X165:($i > $o)]: 138.86/139.85 ((?[X166]: 138.86/139.85 (in( 138.86/139.85 X166,X164) & 138.86/139.85 (~ 138.86/139.85 X165( 138.86/139.85 X166)))) => 138.86/139.85 (~ 138.86/139.85 (![X167]: 138.86/139.85 (in( 138.86/139.85 X167,X164) => 138.86/139.85 X165( 138.86/139.85 X167)))))) => 138.86/139.85 ((![X168:$o]: 138.86/139.85 (X168 => 138.86/139.85 in(emptyset, 138.86/139.85 prop2set( 138.86/139.85 X168)))) => 138.86/139.85 ((![X169:$o]: 138.86/139.85 (X169 => 138.86/139.85 set2prop( 138.86/139.85 prop2set( 138.86/139.85 X169)))) => 138.86/139.85 ((![X170, 138.86/139.85 X171:( 138.86/139.85 $i > $o)]: 138.86/139.85 ((~ 138.86/139.85 (?[X172]: 138.86/139.85 (in( 138.86/139.85 X172,X170) & 138.86/139.85 X171( 138.86/139.85 X172)))) => 138.86/139.85 (![X173]: 138.86/139.85 ( 138.86/139.85 in( 138.86/139.85 X173,X170) => 138.86/139.85 ( 138.86/139.85 ~ 138.86/139.85 X171( 138.86/139.85 X173)))))) => 138.86/139.85 ((![X174, 138.86/139.85 X175:( 138.86/139.85 $i > $o)]: 138.86/139.85 ((~ 138.86/139.85 ( 138.86/139.85 ![X176]: 138.86/139.85 (in( 138.86/139.85 X176,X174) => 138.86/139.85 X175( 138.86/139.85 X176)))) => 138.86/139.85 (?[X177]: 138.86/139.85 (in( 138.86/139.85 X177,X174) & 138.86/139.85 (~ 138.86/139.85 X175( 138.86/139.85 X177)))))) => 138.86/139.85 ((![X178:( 138.86/139.85 $i > $o)]: 138.86/139.85 ((?[X179]: 138.86/139.85 (X178( 138.86/139.85 X179) & 138.86/139.85 (![X180]: 138.86/139.85 (X178( 138.86/139.85 X180) => 138.86/139.85 (X179 = 138.86/139.85 X180))))) => 138.86/139.85 (?[X181]: 138.86/139.85 (X178( 138.86/139.85 X181) & 138.86/139.85 (![X182]: 138.86/139.85 (X178( 138.86/139.85 X182) => 138.86/139.85 (X181 = 138.86/139.85 X182))))))) => 138.86/139.85 ((![X183:( 138.86/139.85 $i > $o)]: 138.86/139.85 (( 138.86/139.85 ?[X184]: 138.86/139.85 X183( 138.86/139.85 X184)) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X185, 138.86/139.85 X186]: 138.86/139.85 (X183( 138.86/139.85 X185) => 138.86/139.85 (X183( 138.86/139.85 X186) => 138.86/139.85 (X185 = 138.86/139.85 X186)))) => 138.86/139.85 ( 138.86/139.85 ?[X187]: 138.86/139.85 (X183( 138.86/139.85 X187) & 138.86/139.85 (![X188]: 138.86/139.85 (X183( 138.86/139.85 X188) => 138.86/139.85 (X187 = 138.86/139.85 X188)))))))) => 138.86/139.85 ((![X189:( 138.86/139.85 $i > $o)]: 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ?[X190]: 138.86/139.85 (![X191]: 138.86/139.85 (X189( 138.86/139.85 X191) <=> 138.86/139.85 (X191 = 138.86/139.85 X190)))) => 138.86/139.85 ( 138.86/139.85 ?[X192]: 138.86/139.85 (X189( 138.86/139.85 X192) & 138.86/139.85 (![X193]: 138.86/139.85 (X189( 138.86/139.85 X193) => 138.86/139.85 (X192 = 138.86/139.85 X193))))))) => 138.86/139.85 ((![X194, 138.86/139.85 X195]: 138.86/139.85 (( 138.86/139.85 X194 = 138.86/139.85 X195) => 138.86/139.85 (![X196, 138.86/139.85 X197]: 138.86/139.85 (( 138.86/139.85 X196 = 138.86/139.85 X197) => 138.86/139.85 (in( 138.86/139.85 X196,X194) => 138.86/139.85 in( 138.86/139.85 X197,X195)))))) => 138.86/139.85 ((![X198, 138.86/139.85 X199]: 138.86/139.85 (( 138.86/139.85 X198 = 138.86/139.85 X199) => 138.86/139.85 (![X200, 138.86/139.85 X201]: 138.86/139.85 (( 138.86/139.85 X200 = 138.86/139.85 X201) => 138.86/139.85 (in( 138.86/139.85 X200,X198) <=> 138.86/139.85 in( 138.86/139.85 X201,X199)))))) => 138.86/139.85 (( 138.86/139.85 ![X202:( 138.86/139.85 $i > $o)]: 138.86/139.85 (( 138.86/139.85 ?[X203]: 138.86/139.85 (X202( 138.86/139.85 X203) & 138.86/139.85 (![X204]: 138.86/139.85 (X202( 138.86/139.85 X204) => 138.86/139.85 (X203 = 138.86/139.85 X204))))) => 138.86/139.85 (![X205, 138.86/139.85 X206]: 138.86/139.85 (X202( 138.86/139.85 X205) => 138.86/139.85 (X202( 138.86/139.85 X206) => 138.86/139.85 (X205 = 138.86/139.85 X206)))))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X207:( 138.86/139.85 $i > $o), 138.86/139.85 X208:( 138.86/139.85 $i > $o)]: 138.86/139.85 (( 138.86/139.85 ![X209, 138.86/139.85 X210]: 138.86/139.85 (( 138.86/139.85 X209 = 138.86/139.85 X210) => 138.86/139.85 (X207( 138.86/139.85 X209) <=> 138.86/139.85 X208( 138.86/139.85 X210)))) => 138.86/139.85 (( 138.86/139.85 ?[X211]: 138.86/139.85 (X207( 138.86/139.85 X211) & 138.86/139.85 (![X212]: 138.86/139.85 (X207( 138.86/139.85 X212) => 138.86/139.85 (X211 = 138.86/139.85 X212))))) <=> 138.86/139.85 (?[X213]: 138.86/139.85 (X208( 138.86/139.85 X213) & 138.86/139.85 (![X214]: 138.86/139.85 (X208( 138.86/139.85 X214) => 138.86/139.85 (X213 = 138.86/139.85 X214)))))))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 emptyset = 138.86/139.85 emptyset) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X215, 138.86/139.85 X216]: 138.86/139.85 (( 138.86/139.85 X215 = 138.86/139.85 X216) => 138.86/139.85 (![X217, 138.86/139.85 X218]: 138.86/139.85 (( 138.86/139.85 X217 = 138.86/139.85 X218) => 138.86/139.85 (setadjoin( 138.86/139.85 X215,X217) = 138.86/139.85 setadjoin( 138.86/139.85 X216,X218)))))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X219, 138.86/139.85 X220]: 138.86/139.85 (( 138.86/139.85 X219 = 138.86/139.85 X220) => 138.86/139.85 (powerset( 138.86/139.85 X219) = 138.86/139.85 powerset( 138.86/139.85 X220)))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X221, 138.86/139.85 X222]: 138.86/139.85 (( 138.86/139.85 X221 = 138.86/139.85 X222) => 138.86/139.85 (setunion( 138.86/139.85 X221) = 138.86/139.85 setunion( 138.86/139.85 X222)))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 omega = 138.86/139.85 omega) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X223:( 138.86/139.85 $i > $o)]: 138.86/139.85 (( 138.86/139.85 ?[X224]: 138.86/139.85 (X223( 138.86/139.85 X224) & 138.86/139.85 (![X225]: 138.86/139.85 (X223( 138.86/139.85 X225) => 138.86/139.85 (X224 = 138.86/139.85 X225))))) => 138.86/139.85 (![X226, 138.86/139.85 X227]: 138.86/139.85 (X223( 138.86/139.85 X226) => 138.86/139.85 (X223( 138.86/139.85 X227) => 138.86/139.85 (X226 = 138.86/139.85 X227)))))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X228:( 138.86/139.85 $i > $o), 138.86/139.85 X229:( 138.86/139.85 $i > $o)]: 138.86/139.85 (( 138.86/139.85 ![X230, 138.86/139.85 X231]: 138.86/139.85 (( 138.86/139.85 X230 = 138.86/139.85 X231) => 138.86/139.85 (X228( 138.86/139.85 X230) <=> 138.86/139.85 X229( 138.86/139.85 X231)))) => 138.86/139.85 (( 138.86/139.85 ?[X232]: 138.86/139.85 (X228( 138.86/139.85 X232) & 138.86/139.85 (![X233]: 138.86/139.85 (X228( 138.86/139.85 X233) => 138.86/139.85 (X232 = 138.86/139.85 X233))))) => 138.86/139.85 (( 138.86/139.85 ?[X234]: 138.86/139.85 (X229( 138.86/139.85 X234) & 138.86/139.85 (![X235]: 138.86/139.85 (X229( 138.86/139.85 X235) => 138.86/139.85 (X234 = 138.86/139.85 X235))))) => 138.86/139.85 (descr( 138.86/139.85 ^[V_9]: 138.86/139.85 X228(V_9)) = 138.86/139.85 descr( 138.86/139.85 ^[V_10]: 138.86/139.85 X229( 138.86/139.85 V_10))))))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X236, 138.86/139.85 X237]: 138.86/139.85 (( 138.86/139.85 X236 = 138.86/139.85 X237) => 138.86/139.85 (![X238:( 138.86/139.85 $i > $o), 138.86/139.85 X239:( 138.86/139.85 $i > $o)]: 138.86/139.85 (( 138.86/139.85 ![X240]: 138.86/139.85 (in( 138.86/139.85 X240,X236) => 138.86/139.85 (![X241]: 138.86/139.85 (in( 138.86/139.85 X241,X237) => 138.86/139.85 (( 138.86/139.85 X240 = 138.86/139.85 X241) => 138.86/139.85 (X238( 138.86/139.85 X240) <=> 138.86/139.85 X239( 138.86/139.85 X241))))))) => 138.86/139.85 (dsetconstr( 138.86/139.85 X236, 138.86/139.85 ^[V_11]: 138.86/139.85 X238( 138.86/139.85 V_11)) = 138.86/139.85 dsetconstr( 138.86/139.85 X237, 138.86/139.85 ^[V_12]: 138.86/139.85 X239( 138.86/139.85 V_12))))))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X242, 138.86/139.85 X243]: 138.86/139.85 (( 138.86/139.85 ![X244]: 138.86/139.85 (in( 138.86/139.85 X244,X242) => 138.86/139.85 in( 138.86/139.85 X244,X243))) => 138.86/139.85 subset( 138.86/139.85 X242,X243))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X245, 138.86/139.85 X246]: 138.86/139.85 (( 138.86/139.85 X245 = 138.86/139.85 X246) => 138.86/139.85 subset( 138.86/139.85 X246,X245))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X247, 138.86/139.85 X248]: 138.86/139.85 (( 138.86/139.85 X247 = 138.86/139.85 X248) => 138.86/139.85 subset( 138.86/139.85 X247,X248))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X249, 138.86/139.85 X250]: 138.86/139.85 (( 138.86/139.85 ![X251]: 138.86/139.85 (in( 138.86/139.85 X251,X249) => 138.86/139.85 in( 138.86/139.85 X251,X250))) => 138.86/139.85 subset( 138.86/139.85 X249,X250))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X252]: 138.86/139.85 subset( 138.86/139.85 emptyset, 138.86/139.85 X252)) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X253, 138.86/139.85 X254,X255]: 138.86/139.85 (subset( 138.86/139.85 X253,X254) => 138.86/139.85 (in( 138.86/139.85 X255,X253) => 138.86/139.85 in( 138.86/139.85 X255,X254)))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X256, 138.86/139.85 X257,X258]: 138.86/139.85 (subset( 138.86/139.85 X256,X257) => 138.86/139.85 (( 138.86/139.85 ~ 138.86/139.85 in( 138.86/139.85 X258,X257)) => 138.86/139.85 (~ 138.86/139.85 in( 138.86/139.85 X258,X256))))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X259, 138.86/139.85 X260,X261]: 138.86/139.85 (in( 138.86/139.85 X261,X259) => 138.86/139.85 (( 138.86/139.85 ~ 138.86/139.85 in( 138.86/139.85 X261,X260)) => 138.86/139.85 (~ 138.86/139.85 subset( 138.86/139.85 X259,X260))))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X262, 138.86/139.85 X263]: 138.86/139.85 (( 138.86/139.85 ~ 138.86/139.85 subset( 138.86/139.85 X262,X263)) => 138.86/139.85 (X262 != 138.86/139.85 X263))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X264, 138.86/139.85 X265,X266]: 138.86/139.85 (in( 138.86/139.85 X266,X264) => 138.86/139.85 (( 138.86/139.85 ~ 138.86/139.85 in( 138.86/139.85 X266,X265)) => 138.86/139.85 (X264 != 138.86/139.85 X265)))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X267]: 138.86/139.85 subset( 138.86/139.85 X267,X267)) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X268, 138.86/139.85 X269,X270]: 138.86/139.85 (subset( 138.86/139.85 X268,X269) => 138.86/139.85 (subset( 138.86/139.85 X269,X270) => 138.86/139.85 subset( 138.86/139.85 X268,X270)))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X271, 138.86/139.85 X272]: 138.86/139.85 subset( 138.86/139.85 X272, 138.86/139.85 setadjoin( 138.86/139.85 X271,X272))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X273, 138.86/139.85 X274,X275]: 138.86/139.85 (subset( 138.86/139.85 X273,X275) => 138.86/139.85 subset( 138.86/139.85 X273, 138.86/139.85 setadjoin( 138.86/139.85 X274,X275)))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X276, 138.86/139.85 X277]: 138.86/139.85 (subset( 138.86/139.85 X276,X277) => 138.86/139.85 in( 138.86/139.85 X276, 138.86/139.85 powerset( 138.86/139.85 X277)))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X278, 138.86/139.85 X279]: 138.86/139.85 (subset( 138.86/139.85 X278,X279) => 138.86/139.85 (subset( 138.86/139.85 X279,X278) => 138.86/139.85 (X278 = 138.86/139.85 X279)))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X280]: 138.86/139.85 (subset( 138.86/139.85 X280, 138.86/139.85 emptyset) => 138.86/139.85 (X280 = 138.86/139.85 emptyset))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X281, 138.86/139.85 X282]: 138.86/139.85 (subset( 138.86/139.85 X282,X281) => 138.86/139.85 in( 138.86/139.85 X282, 138.86/139.85 powerset( 138.86/139.85 X281)))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X283, 138.86/139.85 X284]: 138.86/139.85 (in( 138.86/139.85 X284, 138.86/139.85 powerset( 138.86/139.85 X283)) => 138.86/139.85 subset( 138.86/139.85 X284,X283))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X285]: 138.86/139.85 in( 138.86/139.85 X285, 138.86/139.85 powerset( 138.86/139.85 X285))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X286, 138.86/139.85 X287]: 138.86/139.85 (subset( 138.86/139.85 X286,X287) => 138.86/139.85 subset( 138.86/139.85 powerset( 138.86/139.85 X286), 138.86/139.85 powerset( 138.86/139.85 X287)))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X288, 138.86/139.85 X289:( 138.86/139.85 $i > $o)]: 138.86/139.85 in( 138.86/139.85 dsetconstr( 138.86/139.85 X288, 138.86/139.85 ^[V_13]: 138.86/139.85 X289( 138.86/139.85 V_13)), 138.86/139.85 powerset( 138.86/139.85 X288))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X290, 138.86/139.85 X291:( 138.86/139.85 $i > $o)]: 138.86/139.85 subset( 138.86/139.85 dsetconstr( 138.86/139.85 X290, 138.86/139.85 ^[V_14]: 138.86/139.85 X291( 138.86/139.85 V_14)), 138.86/139.85 X290)) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X292, 138.86/139.85 X293,X294]: 138.86/139.85 (in( 138.86/139.85 X294,X292) => 138.86/139.85 in( 138.86/139.85 X294, 138.86/139.85 binunion( 138.86/139.85 X292,X293)))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X295, 138.86/139.85 X296]: 138.86/139.85 in( 138.86/139.85 X296, 138.86/139.85 setadjoin( 138.86/139.85 X295, 138.86/139.85 setadjoin( 138.86/139.85 X296, 138.86/139.85 emptyset)))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X297, 138.86/139.85 X298,X299]: 138.86/139.85 (in( 138.86/139.85 X299,X298) => 138.86/139.85 in( 138.86/139.85 X299, 138.86/139.85 binunion( 138.86/139.85 X297,X298)))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X300, 138.86/139.85 X301, 138.86/139.85 X302, 138.86/139.85 X303:$o]: 138.86/139.85 (in( 138.86/139.85 X302, 138.86/139.85 binunion( 138.86/139.85 X300,X301)) => 138.86/139.85 (( 138.86/139.85 in( 138.86/139.85 X302,X300) => 138.86/139.85 X303) => 138.86/139.85 (( 138.86/139.85 in( 138.86/139.85 X302,X301) => 138.86/139.85 X303) => 138.86/139.85 X303)))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X304, 138.86/139.85 X305,X306]: 138.86/139.85 (in( 138.86/139.85 X306, 138.86/139.85 binunion( 138.86/139.85 X304,X305)) => 138.86/139.85 (in( 138.86/139.85 X306,X304) | 138.86/139.85 in( 138.86/139.85 X306,X305)))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X307, 138.86/139.85 X308]: 138.86/139.85 subset( 138.86/139.85 X307, 138.86/139.85 binunion( 138.86/139.85 X307,X308))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X309, 138.86/139.85 X310]: 138.86/139.85 subset( 138.86/139.85 X310, 138.86/139.85 binunion( 138.86/139.85 X309,X310))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X311, 138.86/139.85 X312,X313]: 138.86/139.85 (in( 138.86/139.85 X313,X311) => 138.86/139.85 (in( 138.86/139.85 X313,X312) => 138.86/139.85 in( 138.86/139.85 X313, 138.86/139.85 binintersect( 138.86/139.85 X311,X312))))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X314, 138.86/139.85 X315,X316]: 138.86/139.85 (subset( 138.86/139.85 X316,X314) => 138.86/139.85 (subset( 138.86/139.85 X316,X315) => 138.86/139.85 subset( 138.86/139.85 X316, 138.86/139.85 binintersect( 138.86/139.85 X314,X315))))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X317, 138.86/139.85 X318,X319]: 138.86/139.85 (in( 138.86/139.85 X319, 138.86/139.85 binintersect( 138.86/139.85 X317,X318)) => 138.86/139.85 in( 138.86/139.85 X319,X317))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X320, 138.86/139.85 X321]: 138.86/139.85 subset( 138.86/139.85 binintersect( 138.86/139.85 X320,X321), 138.86/139.85 X320)) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X322, 138.86/139.85 X323]: 138.86/139.85 (subset( 138.86/139.85 X322,X323) => 138.86/139.85 (binintersect( 138.86/139.85 X322,X323) = 138.86/139.85 X322))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X324, 138.86/139.85 X325]: 138.86/139.85 (( 138.86/139.85 binintersect( 138.86/139.85 X324,X325) = 138.86/139.85 X325) => 138.86/139.85 subset( 138.86/139.85 X325,X324))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X326, 138.86/139.85 X327,X328]: 138.86/139.85 (in( 138.86/139.85 X328, 138.86/139.85 binintersect( 138.86/139.85 X326,X327)) => 138.86/139.85 in( 138.86/139.85 X328,X327))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X329, 138.86/139.85 X330]: 138.86/139.85 (( 138.86/139.85 ~ 138.86/139.85 ( 138.86/139.85 ?[X331]: 138.86/139.85 (in( 138.86/139.85 X331,X329) & 138.86/139.85 in( 138.86/139.85 X331,X330)))) => 138.86/139.85 (binintersect( 138.86/139.85 X329,X330) = 138.86/139.85 emptyset))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X332, 138.86/139.85 X333]: 138.86/139.85 subset( 138.86/139.85 binintersect( 138.86/139.85 X332,X333), 138.86/139.85 X333)) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X334, 138.86/139.85 X335]: 138.86/139.85 (subset( 138.86/139.85 X335,X334) => 138.86/139.85 (binintersect( 138.86/139.85 X334,X335) = 138.86/139.85 X335))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X336, 138.86/139.85 X337]: 138.86/139.85 (( 138.86/139.85 binintersect( 138.86/139.85 X336,X337) = 138.86/139.85 X336) => 138.86/139.85 subset( 138.86/139.85 X336,X337))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X338, 138.86/139.85 X339,X340]: 138.86/139.85 (binintersect( 138.86/139.85 X338, 138.86/139.85 binunion( 138.86/139.85 X339,X340)) = 138.86/139.85 binunion( 138.86/139.85 binintersect( 138.86/139.85 X338,X339), 138.86/139.85 binintersect( 138.86/139.85 X338,X340)))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X341, 138.86/139.85 X342,X343]: 138.86/139.85 (in( 138.86/139.85 X343,X341) => 138.86/139.85 (( 138.86/139.85 ~ 138.86/139.85 in( 138.86/139.85 X343,X342)) => 138.86/139.85 in( 138.86/139.85 X343, 138.86/139.85 setminus( 138.86/139.85 X341,X342))))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X344, 138.86/139.85 X345,X346]: 138.86/139.85 (in( 138.86/139.85 X346, 138.86/139.85 setminus( 138.86/139.85 X344,X345)) => 138.86/139.85 in( 138.86/139.85 X346,X344))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X347, 138.86/139.85 X348,X349]: 138.86/139.85 (in( 138.86/139.85 X349, 138.86/139.85 setminus( 138.86/139.85 X347,X348)) => 138.86/139.85 (~ 138.86/139.85 in( 138.86/139.85 X349,X348)))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X350, 138.86/139.85 X351]: 138.86/139.85 (subset( 138.86/139.85 X350,X351) => 138.86/139.85 (setminus( 138.86/139.85 X350,X351) = 138.86/139.85 emptyset))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X352, 138.86/139.85 X353,X354]: 138.86/139.85 (( 138.86/139.85 ~ 138.86/139.85 in( 138.86/139.85 X354, 138.86/139.85 setminus( 138.86/139.85 X352,X353))) => 138.86/139.85 (in( 138.86/139.85 X354,X352) => 138.86/139.85 in( 138.86/139.85 X354,X353)))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X355, 138.86/139.85 X356,X357]: 138.86/139.85 (( 138.86/139.85 ~ 138.86/139.85 in( 138.86/139.85 X357, 138.86/139.85 setminus( 138.86/139.85 X355,X356))) => 138.86/139.85 (( 138.86/139.85 ~ 138.86/139.85 in( 138.86/139.85 X357,X356)) => 138.86/139.85 (~ 138.86/139.85 in( 138.86/139.85 X357,X355))))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X358, 138.86/139.85 X359,X360]: 138.86/139.85 (( 138.86/139.85 ~ 138.86/139.85 in( 138.86/139.85 X360,X358)) => 138.86/139.85 (~ 138.86/139.85 in( 138.86/139.85 X360, 138.86/139.85 setminus( 138.86/139.85 X358,X359))))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X361, 138.86/139.85 X362,X363]: 138.86/139.85 (in( 138.86/139.85 X363,X362) => 138.86/139.85 (~ 138.86/139.85 in( 138.86/139.85 X363, 138.86/139.85 setminus( 138.86/139.85 X361,X362))))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X364, 138.86/139.85 X365]: 138.86/139.85 subset( 138.86/139.85 setminus( 138.86/139.85 X364,X365), 138.86/139.85 X364)) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X366, 138.86/139.85 X367]: 138.86/139.85 (( 138.86/139.85 setminus( 138.86/139.85 X366,X367) = 138.86/139.85 emptyset) => 138.86/139.85 subset( 138.86/139.85 X366,X367))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X368, 138.86/139.85 X369,X370]: 138.86/139.85 (in( 138.86/139.85 X370, 138.86/139.85 symdiff( 138.86/139.85 X368,X369)) => 138.86/139.85 (![X371:$o]: 138.86/139.85 (( 138.86/139.85 in( 138.86/139.85 X370,X368) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ~ 138.86/139.85 in( 138.86/139.85 X370,X369)) => 138.86/139.85 X371)) => 138.86/139.85 (( 138.86/139.85 ( 138.86/139.85 ~ 138.86/139.85 in( 138.86/139.85 X370,X368)) => 138.86/139.85 ( 138.86/139.85 in( 138.86/139.85 X370,X369) => 138.86/139.85 X371)) => 138.86/139.85 X371))))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X372, 138.86/139.85 X373,X374]: 138.86/139.85 (in( 138.86/139.85 X374,X372) => 138.86/139.85 (( 138.86/139.85 ~ 138.86/139.85 in( 138.86/139.85 X374,X373)) => 138.86/139.85 in( 138.86/139.85 X374, 138.86/139.85 symdiff( 138.86/139.85 X372,X373))))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X375, 138.86/139.85 X376,X377]: 138.86/139.85 (( 138.86/139.85 ~ 138.86/139.85 in( 138.86/139.85 X377,X375)) => 138.86/139.85 (in( 138.86/139.85 X377,X376) => 138.86/139.85 in( 138.86/139.85 X377, 138.86/139.85 symdiff( 138.86/139.85 X375,X376))))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X378, 138.86/139.85 X379,X380]: 138.86/139.85 (in( 138.86/139.85 X380,X378) => 138.86/139.85 (in( 138.86/139.85 X380,X379) => 138.86/139.85 (~ 138.86/139.85 in( 138.86/139.85 X380, 138.86/139.85 symdiff( 138.86/139.85 X378,X379)))))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X381, 138.86/139.85 X382,X383]: 138.86/139.85 (( 138.86/139.85 ~ 138.86/139.85 in( 138.86/139.85 X383,X381)) => 138.86/139.85 (( 138.86/139.85 ~ 138.86/139.85 in( 138.86/139.85 X383,X382)) => 138.86/139.85 (~ 138.86/139.85 in( 138.86/139.85 X383, 138.86/139.85 symdiff( 138.86/139.85 X381,X382)))))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X384, 138.86/139.85 X385]: 138.86/139.85 in( 138.86/139.85 X385, 138.86/139.85 setadjoin( 138.86/139.85 X384, 138.86/139.85 setadjoin( 138.86/139.85 X385, 138.86/139.85 emptyset)))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X386, 138.86/139.85 X387]: 138.86/139.85 in( 138.86/139.85 X386, 138.86/139.85 setunion( 138.86/139.85 setadjoin( 138.86/139.85 setadjoin( 138.86/139.85 X386, 138.86/139.85 emptyset), 138.86/139.85 setadjoin( 138.86/139.85 setadjoin( 138.86/139.85 X386, 138.86/139.85 setadjoin( 138.86/139.85 X387, 138.86/139.85 emptyset)), 138.86/139.85 emptyset))))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X388, 138.86/139.85 X389]: 138.86/139.85 in( 138.86/139.85 X389, 138.86/139.85 setunion( 138.86/139.85 setadjoin( 138.86/139.85 setadjoin( 138.86/139.85 X388, 138.86/139.85 emptyset), 138.86/139.85 setadjoin( 138.86/139.85 setadjoin( 138.86/139.85 X388, 138.86/139.85 setadjoin( 138.86/139.85 X389, 138.86/139.85 emptyset)), 138.86/139.85 emptyset))))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X390, 138.86/139.85 X391]: 138.86/139.85 iskpair( 138.86/139.85 setadjoin( 138.86/139.85 setadjoin( 138.86/139.85 X390, 138.86/139.85 emptyset), 138.86/139.85 setadjoin( 138.86/139.85 setadjoin( 138.86/139.85 X390, 138.86/139.85 setadjoin( 138.86/139.85 X391, 138.86/139.85 emptyset)), 138.86/139.85 emptyset)))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X392, 138.86/139.85 X393]: 138.86/139.85 iskpair( 138.86/139.85 kpair( 138.86/139.85 X392,X393))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X394, 138.86/139.85 X395]: 138.86/139.85 (in( 138.86/139.85 X395,X394) => 138.86/139.85 subset( 138.86/139.85 setadjoin( 138.86/139.85 X395, 138.86/139.85 emptyset), 138.86/139.85 X394))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X396, 138.86/139.85 X397]: 138.86/139.85 (in( 138.86/139.85 X397,X396) => 138.86/139.85 in( 138.86/139.85 setadjoin( 138.86/139.85 X397, 138.86/139.85 emptyset), 138.86/139.85 powerset( 138.86/139.85 X396)))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X398, 138.86/139.85 X399,X400]: 138.86/139.85 (in( 138.86/139.85 X400,X398) => 138.86/139.85 in( 138.86/139.85 setadjoin( 138.86/139.85 X400, 138.86/139.85 emptyset), 138.86/139.85 powerset( 138.86/139.85 binunion( 138.86/139.85 X398,X399))))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X401, 138.86/139.85 X402,X403]: 138.86/139.85 (in( 138.86/139.85 X403, 138.86/139.85 setadjoin( 138.86/139.85 X401, 138.86/139.85 setadjoin( 138.86/139.85 X402, 138.86/139.85 emptyset))) => 138.86/139.85 (( 138.86/139.85 X403 = 138.86/139.85 X401) | 138.86/139.85 (X403 = 138.86/139.85 X402)))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X404, 138.86/139.85 X405,X406]: 138.86/139.85 (in( 138.86/139.85 X406,X404) => 138.86/139.85 (![X407]: 138.86/139.85 (in( 138.86/139.85 X407,X405) => 138.86/139.85 subset( 138.86/139.85 setadjoin( 138.86/139.85 X406, 138.86/139.85 setadjoin( 138.86/139.85 X407, 138.86/139.85 emptyset)), 138.86/139.85 binunion( 138.86/139.85 X404,X405)))))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X408, 138.86/139.85 X409,X410]: 138.86/139.85 (in( 138.86/139.85 X410,X408) => 138.86/139.85 (![X411]: 138.86/139.85 (in( 138.86/139.85 X411,X409) => 138.86/139.85 in( 138.86/139.85 setadjoin( 138.86/139.85 X410, 138.86/139.85 setadjoin( 138.86/139.85 X411, 138.86/139.85 emptyset)), 138.86/139.85 powerset( 138.86/139.85 binunion( 138.86/139.85 X408,X409))))))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X412, 138.86/139.85 X413,X414]: 138.86/139.85 (in( 138.86/139.85 X414,X412) => 138.86/139.85 (![X415]: 138.86/139.85 (in( 138.86/139.85 X415,X413) => 138.86/139.85 subset( 138.86/139.85 setadjoin( 138.86/139.85 setadjoin( 138.86/139.85 X414, 138.86/139.85 emptyset), 138.86/139.85 setadjoin( 138.86/139.85 setadjoin( 138.86/139.85 X414, 138.86/139.85 setadjoin( 138.86/139.85 X415, 138.86/139.85 emptyset)), 138.86/139.85 emptyset)), 138.86/139.85 powerset( 138.86/139.85 binunion( 138.86/139.85 X412,X413))))))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X416, 138.86/139.85 X417,X418]: 138.86/139.85 (in( 138.86/139.85 X418,X416) => 138.86/139.85 (![X419]: 138.86/139.85 (in( 138.86/139.85 X419,X417) => 138.86/139.85 in( 138.86/139.85 setadjoin( 138.86/139.85 setadjoin( 138.86/139.85 X418, 138.86/139.85 emptyset), 138.86/139.85 setadjoin( 138.86/139.85 setadjoin( 138.86/139.85 X418, 138.86/139.85 setadjoin( 138.86/139.85 X419, 138.86/139.85 emptyset)), 138.86/139.85 emptyset)), 138.86/139.85 powerset( 138.86/139.85 powerset( 138.86/139.85 binunion( 138.86/139.85 X416,X417)))))))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X420, 138.86/139.85 X421,X422]: 138.86/139.85 (in( 138.86/139.85 X422,X420) => 138.86/139.85 (![X423]: 138.86/139.85 (in( 138.86/139.85 X423,X421) => 138.86/139.85 in( 138.86/139.85 kpair( 138.86/139.85 X422,X423), 138.86/139.85 powerset( 138.86/139.85 powerset( 138.86/139.85 binunion( 138.86/139.85 X420,X421)))))))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X424, 138.86/139.85 X425,X426]: 138.86/139.85 (in( 138.86/139.85 X426,X424) => 138.86/139.85 (![X427]: 138.86/139.85 (in( 138.86/139.85 X427,X425) => 138.86/139.85 in( 138.86/139.85 kpair( 138.86/139.85 X426,X427), 138.86/139.85 cartprod( 138.86/139.85 X424,X425)))))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X428, 138.86/139.85 X429,X430]: 138.86/139.85 (in( 138.86/139.85 X430, 138.86/139.85 cartprod( 138.86/139.85 X428,X429)) => 138.86/139.85 (?[X431]: 138.86/139.85 (in( 138.86/139.85 X431,X428) & 138.86/139.85 (?[X432]: 138.86/139.85 (in( 138.86/139.85 X432,X429) & 138.86/139.85 (X430 = 138.86/139.85 kpair( 138.86/139.85 X431,X432)))))))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X433, 138.86/139.85 X434,X435]: 138.86/139.85 (in( 138.86/139.85 X435, 138.86/139.85 cartprod( 138.86/139.85 X433,X434)) => 138.86/139.85 iskpair( 138.86/139.85 X435))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X436, 138.86/139.85 X437]: 138.86/139.85 (in( 138.86/139.85 X437, 138.86/139.85 setunion( 138.86/139.85 X436)) => 138.86/139.85 (?[X438]: 138.86/139.85 (in( 138.86/139.85 X438,X436) & 138.86/139.85 in( 138.86/139.85 X437,X438))))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X439]: 138.86/139.85 subset( 138.86/139.85 setunion( 138.86/139.85 setadjoin( 138.86/139.85 X439, 138.86/139.85 emptyset)), 138.86/139.85 X439)) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X440]: 138.86/139.85 subset( 138.86/139.85 X440, 138.86/139.85 setunion( 138.86/139.85 setadjoin( 138.86/139.85 X440, 138.86/139.85 emptyset)))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X441]: 138.86/139.85 (setunion( 138.86/139.85 setadjoin( 138.86/139.85 X441, 138.86/139.85 emptyset)) = 138.86/139.85 X441)) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X442, 138.86/139.85 X443:( 138.86/139.85 $i > $o)]: 138.86/139.85 (( 138.86/139.85 ![X444]: 138.86/139.85 (in( 138.86/139.85 X444,X442) => 138.86/139.85 (![X445]: 138.86/139.85 (in( 138.86/139.85 X445,X442) => 138.86/139.85 (X443( 138.86/139.85 X444) => 138.86/139.85 (X443( 138.86/139.85 X445) => 138.86/139.85 (X444 = 138.86/139.85 X445))))))) => 138.86/139.85 (( 138.86/139.85 ?[X446]: 138.86/139.85 (in( 138.86/139.85 X446,X442) & 138.86/139.85 X443( 138.86/139.85 X446))) => 138.86/139.85 (?[X447]: 138.86/139.85 (in( 138.86/139.85 X447, 138.86/139.85 dsetconstr( 138.86/139.85 X442, 138.86/139.85 ^[V_16]: 138.86/139.85 X443( 138.86/139.85 V_16))) & 138.86/139.85 (dsetconstr( 138.86/139.85 X442, 138.86/139.85 ^[V_15]: 138.86/139.85 X443( 138.86/139.85 V_15)) = 138.86/139.85 setadjoin( 138.86/139.85 X447, 138.86/139.85 emptyset))))))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X448, 138.86/139.85 X449:( 138.86/139.85 $i > $o)]: 138.86/139.85 (( 138.86/139.85 ?[X450]: 138.86/139.85 (in( 138.86/139.85 X450, 138.86/139.85 dsetconstr( 138.86/139.85 X448, 138.86/139.85 ^[V_18]: 138.86/139.85 X449( 138.86/139.85 V_18))) & 138.86/139.85 (dsetconstr( 138.86/139.85 X448, 138.86/139.85 ^[V_17]: 138.86/139.85 X449( 138.86/139.85 V_17)) = 138.86/139.85 setadjoin( 138.86/139.85 X450, 138.86/139.85 emptyset)))) => 138.86/139.85 (?[X451]: 138.86/139.85 (in( 138.86/139.85 X451,X448) & 138.86/139.85 X449( 138.86/139.85 X451))))) => 138.86/139.85 ( 138.86/139.85 ( 138.86/139.85 ![X452, 138.86/139.85 X453:( 138.86/139.85 $i > $o), 138.86/139.85 X454]: 138.86/139.85 (in( 138.86/139.85 X454,X452) => 138.86/139.85 (X453( 138.86/139.85 X454) => 138.86/139.86 (( 138.86/139.86 ![X455]: 138.86/139.86 (in( 138.86/139.86 X455,X452) => 138.86/139.86 (X453( 138.86/139.86 X455) => 138.86/139.86 (X455 = 138.86/139.86 X454)))) => 138.86/139.86 (?[X456]: 138.86/139.86 (in( 138.86/139.86 X456, 138.86/139.86 dsetconstr( 138.86/139.86 X452, 138.86/139.86 ^[V_20]: 138.86/139.86 X453( 138.86/139.86 V_20))) & 138.86/139.86 (dsetconstr( 138.86/139.86 X452, 138.86/139.86 ^[V_19]: 138.86/139.86 X453( 138.86/139.86 V_19)) = 138.86/139.86 setadjoin( 138.86/139.86 X456, 138.86/139.86 emptyset)))))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X457, 138.86/139.86 X458:( 138.86/139.86 $i > $o)]: 138.86/139.86 (( 138.86/139.86 ![X459]: 138.86/139.86 (in( 138.86/139.86 X459,X457) => 138.86/139.86 (![X460]: 138.86/139.86 (in( 138.86/139.86 X460,X457) => 138.86/139.86 (X458( 138.86/139.86 X459) => 138.86/139.86 (X458( 138.86/139.86 X460) => 138.86/139.86 (X459 = 138.86/139.86 X460))))))) => 138.86/139.86 (( 138.86/139.86 ?[X461]: 138.86/139.86 (in( 138.86/139.86 X461,X457) & 138.86/139.86 X458( 138.86/139.86 X461))) => 138.86/139.86 (?[X462]: 138.86/139.86 (in( 138.86/139.86 X462, 138.86/139.86 dsetconstr( 138.86/139.86 X457, 138.86/139.86 ^[V_22]: 138.86/139.86 X458( 138.86/139.86 V_22))) & 138.86/139.86 (dsetconstr( 138.86/139.86 X457, 138.86/139.86 ^[V_21]: 138.86/139.86 X458( 138.86/139.86 V_21)) = 138.86/139.86 setadjoin( 138.86/139.86 X462, 138.86/139.86 emptyset))))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X463, 138.86/139.86 X464]: 138.86/139.86 (( 138.86/139.86 setadjoin( 138.86/139.86 X463, 138.86/139.86 emptyset) = 138.86/139.86 setadjoin( 138.86/139.86 X464, 138.86/139.86 emptyset)) => 138.86/139.86 (X463 = 138.86/139.86 X464))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X465, 138.86/139.86 X466,X467]: 138.86/139.86 (in( 138.86/139.86 setadjoin( 138.86/139.86 X467, 138.86/139.86 emptyset), 138.86/139.86 setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X465, 138.86/139.86 emptyset), 138.86/139.86 setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X465, 138.86/139.86 setadjoin( 138.86/139.86 X466, 138.86/139.86 emptyset)), 138.86/139.86 emptyset))) => 138.86/139.86 (X465 = 138.86/139.86 X467))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X468]: 138.86/139.86 (iskpair( 138.86/139.86 X468) => 138.86/139.86 (?[X469]: 138.86/139.86 (in( 138.86/139.86 X469, 138.86/139.86 dsetconstr( 138.86/139.86 setunion( 138.86/139.86 X468), 138.86/139.86 ^[V_24]: 138.86/139.86 in( 138.86/139.86 setadjoin( 138.86/139.86 V_24, 138.86/139.86 emptyset), 138.86/139.86 X468))) & 138.86/139.86 (dsetconstr( 138.86/139.86 setunion( 138.86/139.86 X468), 138.86/139.86 ^[V_23]: 138.86/139.86 in( 138.86/139.86 setadjoin( 138.86/139.86 V_23, 138.86/139.86 emptyset), 138.86/139.86 X468)) = 138.86/139.86 setadjoin( 138.86/139.86 X469, 138.86/139.86 emptyset)))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X470]: 138.86/139.86 (( 138.86/139.86 ?[X471]: 138.86/139.86 (in( 138.86/139.86 X471,X470) & 138.86/139.86 (X470 = 138.86/139.86 setadjoin( 138.86/139.86 X471, 138.86/139.86 emptyset)))) => 138.86/139.86 in( 138.86/139.86 setunion( 138.86/139.86 X470), 138.86/139.86 X470))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X472, 138.86/139.86 X473]: 138.86/139.86 (kfst( 138.86/139.86 kpair( 138.86/139.86 X472,X473)) = 138.86/139.86 X472)) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X474, 138.86/139.86 X475,X476]: 138.86/139.86 (in( 138.86/139.86 X476, 138.86/139.86 cartprod( 138.86/139.86 X474,X475)) => 138.86/139.86 in( 138.86/139.86 kfst( 138.86/139.86 X476), 138.86/139.86 X474))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X477, 138.86/139.86 X478, 138.86/139.86 X479,X480]: 138.86/139.86 (( 138.86/139.86 setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X477, 138.86/139.86 emptyset), 138.86/139.86 setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X477, 138.86/139.86 setadjoin( 138.86/139.86 X478, 138.86/139.86 emptyset)), 138.86/139.86 emptyset)) = 138.86/139.86 setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X479, 138.86/139.86 emptyset), 138.86/139.86 setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X479, 138.86/139.86 setadjoin( 138.86/139.86 X480, 138.86/139.86 emptyset)), 138.86/139.86 emptyset))) => 138.86/139.86 (X477 = 138.86/139.86 X479))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X481, 138.86/139.86 X482, 138.86/139.86 X483,X484]: 138.86/139.86 (( 138.86/139.86 kpair( 138.86/139.86 X481,X482) = 138.86/139.86 kpair( 138.86/139.86 X483,X484)) => 138.86/139.86 (X481 = 138.86/139.86 X483))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X485, 138.86/139.86 X486]: 138.86/139.86 (( 138.86/139.86 X485 = 138.86/139.86 X486) => 138.86/139.86 (setadjoin( 138.86/139.86 X485, 138.86/139.86 setadjoin( 138.86/139.86 X486, 138.86/139.86 emptyset)) = 138.86/139.86 setadjoin( 138.86/139.86 X485, 138.86/139.86 emptyset)))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X487, 138.86/139.86 X488]: 138.86/139.86 (( 138.86/139.86 X487 = 138.86/139.86 X488) => 138.86/139.86 (setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X487, 138.86/139.86 emptyset), 138.86/139.86 setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X487, 138.86/139.86 setadjoin( 138.86/139.86 X488, 138.86/139.86 emptyset)), 138.86/139.86 emptyset)) = 138.86/139.86 setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X487, 138.86/139.86 emptyset), 138.86/139.86 emptyset)))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X489, 138.86/139.86 X490, 138.86/139.86 X491,X492]: 138.86/139.86 (( 138.86/139.86 setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X489, 138.86/139.86 emptyset), 138.86/139.86 setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X489, 138.86/139.86 setadjoin( 138.86/139.86 X490, 138.86/139.86 emptyset)), 138.86/139.86 emptyset)) = 138.86/139.86 setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X491, 138.86/139.86 emptyset), 138.86/139.86 setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X491, 138.86/139.86 setadjoin( 138.86/139.86 X492, 138.86/139.86 emptyset)), 138.86/139.86 emptyset))) => 138.86/139.86 (( 138.86/139.86 X491 = 138.86/139.86 X492) => 138.86/139.86 (X490 = 138.86/139.86 X492)))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X493, 138.86/139.86 X494,X495]: 138.86/139.86 (( 138.86/139.86 setadjoin( 138.86/139.86 X493, 138.86/139.86 setadjoin( 138.86/139.86 X494, 138.86/139.86 emptyset)) = 138.86/139.86 setadjoin( 138.86/139.86 X495, 138.86/139.86 emptyset)) => 138.86/139.86 (X493 = 138.86/139.86 X494))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X496, 138.86/139.86 X497, 138.86/139.86 X498,X499]: 138.86/139.86 (( 138.86/139.86 setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X496, 138.86/139.86 emptyset), 138.86/139.86 setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X496, 138.86/139.86 setadjoin( 138.86/139.86 X497, 138.86/139.86 emptyset)), 138.86/139.86 emptyset)) = 138.86/139.86 setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X498, 138.86/139.86 emptyset), 138.86/139.86 setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X498, 138.86/139.86 setadjoin( 138.86/139.86 X499, 138.86/139.86 emptyset)), 138.86/139.86 emptyset))) => 138.86/139.86 (X497 = 138.86/139.86 X499))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X500, 138.86/139.86 X501, 138.86/139.86 X502,X503]: 138.86/139.86 (( 138.86/139.86 kpair( 138.86/139.86 X500,X501) = 138.86/139.86 kpair( 138.86/139.86 X502,X503)) => 138.86/139.86 (X501 = 138.86/139.86 X503))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X504]: 138.86/139.86 (iskpair( 138.86/139.86 X504) => 138.86/139.86 (?[X505]: 138.86/139.86 (in( 138.86/139.86 X505, 138.86/139.86 dsetconstr( 138.86/139.86 setunion( 138.86/139.86 X504), 138.86/139.86 ^[V_26]: 138.86/139.86 (X504 = 138.86/139.86 kpair( 138.86/139.86 kfst( 138.86/139.86 X504), 138.86/139.86 V_26)))) & 138.86/139.86 (dsetconstr( 138.86/139.86 setunion( 138.86/139.86 X504), 138.86/139.86 ^[V_25]: 138.86/139.86 (X504 = 138.86/139.86 kpair( 138.86/139.86 kfst( 138.86/139.86 X504), 138.86/139.86 V_25))) = 138.86/139.86 setadjoin( 138.86/139.86 X505, 138.86/139.86 emptyset)))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X506, 138.86/139.86 X507]: 138.86/139.86 (ksnd( 138.86/139.86 kpair( 138.86/139.86 X506,X507)) = 138.86/139.86 X507)) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X508]: 138.86/139.86 (iskpair( 138.86/139.86 X508) => 138.86/139.86 (kpair( 138.86/139.86 kfst( 138.86/139.86 X508), 138.86/139.86 ksnd( 138.86/139.86 X508)) = 138.86/139.86 X508))) => 138.86/139.86 ( 138.86/139.86 ![X509, 138.86/139.86 X510,X511]: 138.86/139.86 (in( 138.86/139.86 X511, 138.86/139.86 cartprod( 138.86/139.86 X509,X510)) => 138.86/139.86 in( 138.86/139.86 ksnd( 138.86/139.86 X511), 138.86/139.86 X510)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 138.86/139.86 tff(zf_stmt_1, type, zip_tseitin5 : ($i * $i > $o) > $o). 138.86/139.86 tff(zf_stmt_2, axiom, 138.86/139.86 (zip_tseitin5(X211,X207) <=> 138.86/139.86 ((![X212]: zip_tseitin4(X212,X211,X207)) & X207(X211)))). 138.86/139.86 tff(zf_stmt_3, type, zip_tseitin4 : ($i * $i * $i > $o) > $o). 138.86/139.86 tff(zf_stmt_4, axiom, 138.86/139.86 (zip_tseitin4(X212,X211,X207) <=> (X207(X212) => (X211 = X212)))). 138.86/139.86 tff(zf_stmt_5, type, zip_tseitin3 : ($i * $i * $i * ($i * $i) > $o) > $o). 138.86/139.86 tff(zf_stmt_6, axiom, 138.86/139.86 (zip_tseitin3(X26,X25,X20,X19) <=> (X19(X26,X25) & in(X26,X20)))). 138.86/139.86 tff(zf_stmt_7, type, zip_tseitin2 : ($i * $i * $i) > $o). 138.86/139.86 tff(zf_stmt_8, axiom, 138.86/139.86 (zip_tseitin2(X14,X13,X12) <=> (in(X14,X12) & in(X13,X14)))). 138.86/139.86 tff(zf_stmt_9, type, zip_tseitin1 : ($i * $i * $i) > $o). 138.86/139.86 tff(zf_stmt_10, axiom, 138.86/139.86 (zip_tseitin1(X11,X10,X9) <=> (in(X11,X10) => in(X11,X9)))). 138.86/139.86 tff(zf_stmt_11, type, zip_tseitin0 : ($i * $i * $i) > $o). 138.86/139.86 tff(zf_stmt_12, axiom, (zip_tseitin0(X8,X7,X6) <=> (in(X8,X7) | (X8 = X6)))). 138.86/139.86 tff(zf_stmt_13, conjecture, 138.86/139.86 ((![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))) => 138.86/139.86 ((![X5]: (~in(X5,emptyset))) => 138.86/139.86 ((![X6,X7,X8]: (in(X8,setadjoin(X6,X7)) <=> zip_tseitin0(X8,X7,X6))) => 138.86/139.86 ((![X9,X10]: 138.86/139.86 (in(X10,powerset(X9)) <=> (![X11]: zip_tseitin1(X11,X10,X9)))) => 138.86/139.86 ((![X12,X13]: 138.86/139.86 (in(X13,setunion(X12)) <=> (?[X14]: zip_tseitin2(X14,X13,X12)))) => 138.86/139.86 (in(emptyset,omega) => 138.86/139.86 ((![X15]: (in(X15,omega) => in(setadjoin(X15,X15),omega))) => 138.86/139.86 ((![X16]: 138.86/139.86 (((![X17]: 138.86/139.86 ((in(X17,X16) & in(X17,omega)) => 138.86/139.86 in(setadjoin(X17,X17),X16))) & 138.86/139.86 in(emptyset,X16)) => 138.86/139.86 (![X18]: (in(X18,omega) => in(X18,X16))))) => 138.86/139.86 ((![X19:(($i * $i) > $o),X20]: 138.86/139.86 ((![X21]: 138.86/139.86 (in(X21,X20) => 138.86/139.86 (?[X22]: 138.86/139.86 ((![X23]: (X19(X21,X23) => (X22 = X23))) & X19(X21,X22))))) => 138.86/139.86 (?[X24]: 138.86/139.86 (![X25]: 138.86/139.86 (in(X25,X24) <=> (?[X26]: zip_tseitin3(X26,X25,X20,X19))))))) => 138.86/139.86 ((![X27]: 138.86/139.86 ((?[X28]: in(X28,X27)) => 138.86/139.86 (?[X29]: 138.86/139.86 ((~(?[X30]: (in(X30,X27) & in(X30,X29)))) & in(X29,X27))))) => 138.86/139.86 ((![X31]: 138.86/139.86 (?[X32]: 138.86/139.86 ((![X33]: 138.86/139.86 (((?[X34]: in(X34,X33)) & 138.86/139.86 (![X35]: (in(X35,X33) => in(X35,X31)))) => 138.86/139.86 (?[X36,X37]: 138.86/139.86 ((![X38]: 138.86/139.86 (in(X38,X32) => 138.86/139.86 (in(X37,X38) | 138.86/139.86 (![X39]: (in(X39,X38) => in(X39,X36)))))) & 138.86/139.86 (~(?[X40]: (in(X40,X33) & in(X40,X36)))) & 138.86/139.86 in(X37,X33) & in(X36,X32))))) & 138.86/139.86 (![X41,X42]: 138.86/139.86 ((in(X42,X32) & in(X41,X32)) => 138.86/139.86 ((![X43]: (in(X43,X42) => in(X43,X41))) | 138.86/139.86 (![X44]: (in(X44,X41) => in(X44,X42)))))) & 138.86/139.86 (![X45,X46]: 138.86/139.86 ((in(X46,X31) & in(X45,X31)) => 138.86/139.86 ((![X47]: 138.86/139.86 (in(X47,X32) => (in(X45,X47) <=> in(X46,X47)))) => 138.86/139.86 (X45 = X46)))) & 138.86/139.86 (![X48]: 138.86/139.86 (in(X48,X32) => (![X49]: (in(X49,X48) => in(X49,X31)))))))) => 138.86/139.86 ((![X50:($i > $o)]: 138.86/139.86 ((?[X51]: ((![X52]: (X50(X52) => (X51 = X52))) & X50(X51))) => 138.86/139.86 X50(descr(^[V_1]: X50(V_1))))) => 138.86/139.86 ((![X53,X54:($i > $o),X55]: 138.86/139.86 (in(X55,X53) => 138.86/139.86 (X54(X55) => in(X55,dsetconstr(X53,^[V_2]: X54(V_2)))))) => 138.86/139.86 ((![X56,X57:($i > $o),X58]: 138.86/139.86 (in(X58,dsetconstr(X56,^[V_3]: X57(V_3))) => in(X58,X56))) => 138.86/139.86 ((![X59,X60:($i > $o),X61]: 138.86/139.86 (in(X61,dsetconstr(X59,^[V_4]: X60(V_4))) => X60(X61))) => 138.86/139.86 ((![X62:($i > $o)]: 138.86/139.86 ((?[X63]: 138.86/139.86 ((![X64]: (X62(X64) => (X63 = X64))) & X62(X63))) => 138.86/139.86 (?[X65]: 138.86/139.86 ((![X66]: (X62(X66) => (X65 = X66))) & X62(X65))))) => 138.86/139.86 ((![X67:$o,X68]: (in(X68,prop2set(X67)) => X67)) => 138.86/139.86 ((![X69]: (in(X69,emptyset) => (![X70:$o]: X70))) => 138.86/139.86 ((![X71]: (in(X71,emptyset) => $false)) => 138.86/139.86 ((![X72]: (~in(X72,emptyset))) => 138.86/139.86 ((![X73:($i > $o)]: 138.86/139.86 ((?[X74]: 138.86/139.86 ((![X75]: (X73(X75) => (X74 = X75))) & X73(X74))) => 138.86/139.86 (?[X76]: X73(X76)))) => 138.86/139.86 ((![X77,X78]: 138.86/139.86 ((![X79]: (in(X79,X77) => in(X79,X78))) => 138.86/139.86 ((![X80]: (in(X80,X78) => in(X80,X77))) => 138.86/139.86 (X77 = X78)))) => 138.86/139.86 ((![X81]: 138.86/139.86 ((![X82]: (~in(X82,X81))) => (X81 = emptyset))) => 138.86/139.86 ((![X83]: 138.86/139.86 ((![X84]: (~in(X84,X83))) => (X83 = emptyset))) => 138.86/139.86 ((![X85,X86:($i > $o),X87]: 138.86/139.86 (in(X87,X85) => 138.86/139.86 (in(X87,dsetconstr(X85,^[V_5]: X86(V_5))) <=> 138.86/139.86 X86(X87)))) => 138.86/139.86 ((![X88]: 138.86/139.86 ((X88 != emptyset) => (?[X89]: in(X89,X88)))) => 138.86/139.86 ((![X90,X91:($i > $o),X92]: 138.86/139.86 (in(X92,X90) => 138.86/139.86 (X91(X92) => 138.86/139.86 (dsetconstr(X90,^[V_6]: X91(V_6)) != 138.86/139.86 emptyset)))) => 138.86/139.86 ((![X93]: 138.86/139.86 ((?[X94]: in(X94,X93)) => (X93 != emptyset))) => 138.86/139.86 ((![X95,X96]: in(X95,setadjoin(X95,X96))) => 138.86/139.86 (in(emptyset,setadjoin(emptyset,emptyset)) => 138.86/139.86 ((![X97,X98,X99]: 138.86/139.86 (in(X99,X98) => 138.86/139.86 in(X99,setadjoin(X97,X98)))) => 138.86/139.86 ((![X100,X101,X102]: 138.86/139.86 (in(X102,setadjoin(X100,X101)) => 138.86/139.86 (![X103:$o]: 138.86/139.86 (((X102 = X100) => X103) => 138.86/139.86 ((in(X102,X101) => X103) => X103))))) => 138.86/139.86 ((![X104,X105,X106]: 138.86/139.86 (in(X106,setadjoin(X104,X105)) => 138.86/139.86 (in(X106,X105) | (X106 = X104)))) => 138.86/139.86 ((![X107]: 138.86/139.86 (dsetconstr(X107,^[V_7]: $true) = X107)) => 138.86/139.86 ((![X108,X109]: 138.86/139.86 ((![X110]: 138.86/139.86 (in(X110,X109) => in(X110,X108))) => 138.86/139.86 in(X109,powerset(X108)))) => 138.86/139.86 ((![X111]: in(emptyset,powerset(X111))) => 138.86/139.86 ((![X112]: in(emptyset,powerset(X112))) => 138.86/139.86 ((![X113,X114,X115]: 138.86/139.86 (in(X114,powerset(X113)) => 138.86/139.86 (in(X115,X114) => in(X115,X113)))) => 138.86/139.86 ((![X116,X117,X118]: 138.86/139.86 (in(X117,X118) => 138.86/139.86 (in(X118,X116) => 138.86/139.86 in(X117,setunion(X116))))) => 138.86/139.86 ((![X119,X120]: 138.86/139.86 (in(X120,setunion(X119)) => 138.86/139.86 (![X121:$o]: 138.86/139.86 ((![X122]: 138.86/139.86 (in(X120,X122) => 138.86/139.86 (in(X122,X119) => X121))) => 138.86/139.86 X121)))) => 138.86/139.86 ((![X123,X124]: 138.86/139.86 (in(X124,X123) => 138.86/139.86 in(X124, 138.86/139.86 powerset(setunion(X123))))) => 138.86/139.86 ((![X125:($i > $o)]: 138.86/139.86 ((?[X126]: 138.86/139.86 ((![X127]: 138.86/139.86 (X125(X127) => 138.86/139.86 (X126 = X127))) & 138.86/139.86 X125(X126))) => 138.86/139.86 (?[X128]: 138.86/139.86 (![X129]: 138.86/139.86 (X125(X129) <=> 138.86/139.86 (X129 = X128)))))) => 138.86/139.86 ((![X130]: 138.86/139.86 ((X130 != emptyset) => 138.86/139.86 (?[X131]: in(X131,X130)))) => 138.86/139.86 ((![X132,X133]: 138.86/139.86 (in(X132, 138.86/139.86 setadjoin(X133,emptyset)) => 138.86/139.86 (X132 = X133))) => 138.86/139.86 ((![X134,X135]: 138.86/139.86 ((X134 != X135) => 138.86/139.86 (~ 138.86/139.86 in(X135, 138.86/139.86 setadjoin(X134, 138.86/139.86 emptyset))))) => 138.86/139.86 ((![X136,X137]: 138.86/139.86 ((X136 = X137) => 138.86/139.86 in(X136, 138.86/139.86 setadjoin(X137, 138.86/139.86 emptyset)))) => 138.86/139.86 ((![X138,X139]: 138.86/139.86 (in(X138, 138.86/139.86 setadjoin(X139, 138.86/139.86 emptyset)) => 138.86/139.86 in(X139, 138.86/139.86 setadjoin(X138, 138.86/139.86 emptyset)))) => 138.86/139.86 ((![X140,X141,X142]: 138.86/139.86 (in(X142, 138.86/139.86 setadjoin(X140, 138.86/139.86 setadjoin( 138.86/139.86 X141, 138.86/139.86 emptyset))) => 138.86/139.86 ((X142 = X141) | 138.86/139.86 (X142 = X140)))) => 138.86/139.86 ((![X143,X144]: 138.86/139.86 in(X143, 138.86/139.86 setadjoin(X143, 138.86/139.86 setadjoin( 138.86/139.86 X144, 138.86/139.86 emptyset)))) => 138.86/139.86 ((![X145,X146]: 138.86/139.86 in(X146, 138.86/139.86 setadjoin(X145, 138.86/139.86 setadjoin( 138.86/139.86 X146, 138.86/139.86 emptyset)))) => 138.86/139.86 ((![X147,X148:($i > $o)]: 138.86/139.86 ((?[X149]: 138.86/139.86 (X148(X149) & 138.86/139.86 in(X149,X147))) => 138.86/139.86 ((dsetconstr( 138.86/139.86 X147, 138.86/139.86 ^[V_8]: X148(V_8)) = 138.86/139.86 emptyset) => 138.86/139.86 $false))) => 138.86/139.86 ((![X150:($i > $o),X151]: 138.86/139.86 (in(X151,emptyset) => 138.86/139.86 X150(X151))) => 138.86/139.86 ((![X152,X153:($i > $o)]: 138.86/139.86 ((~ 138.86/139.86 (![X154]: 138.86/139.86 (in(X154,X152) => 138.86/139.86 X153(X154)))) => 138.86/139.86 (?[X155]: 138.86/139.86 ((~X153(X155)) & 138.86/139.86 in(X155,X152))))) => 138.86/139.86 ((![X156, 138.86/139.86 X157:($i > $o)]: 138.86/139.86 ((![X158]: 138.86/139.86 (in(X158,X156) => 138.86/139.86 (~X157(X158)))) => 138.86/139.86 (~ 138.86/139.86 (?[X159]: 138.86/139.86 (X157(X159) & 138.86/139.86 in( 138.86/139.86 X159,X156)))))) => 138.86/139.86 ((![X160, 138.86/139.86 X161:($i > $o)]: 138.86/139.86 ((~ 138.86/139.86 (?[X162]: 138.86/139.86 (X161(X162) & 138.86/139.86 in( 138.86/139.86 X162,X160)))) => 138.86/139.86 (![X163]: 138.86/139.86 (in(X163,X160) => 138.86/139.86 (~X161(X163)))))) => 138.86/139.86 ((![X164, 138.86/139.86 X165:($i > $o)]: 138.86/139.86 ((?[X166]: 138.86/139.86 ((~ 138.86/139.86 X165( 138.86/139.86 X166)) & 138.86/139.86 in( 138.86/139.86 X166,X164))) => 138.86/139.86 (~ 138.86/139.86 (![X167]: 138.86/139.86 (in( 138.86/139.86 X167,X164) => 138.86/139.86 X165( 138.86/139.86 X167)))))) => 138.86/139.86 ((![X168:$o]: 138.86/139.86 (X168 => 138.86/139.86 in(emptyset, 138.86/139.86 prop2set( 138.86/139.86 X168)))) => 138.86/139.86 ((![X169:$o]: 138.86/139.86 (X169 => 138.86/139.86 set2prop( 138.86/139.86 prop2set( 138.86/139.86 X169)))) => 138.86/139.86 ((![X170, 138.86/139.86 X171:( 138.86/139.86 $i > $o)]: 138.86/139.86 ((~ 138.86/139.86 (?[X172]: 138.86/139.86 (X171( 138.86/139.86 X172) & 138.86/139.86 in( 138.86/139.86 X172,X170)))) => 138.86/139.86 (![X173]: 138.86/139.86 ( 138.86/139.86 in( 138.86/139.86 X173,X170) => 138.86/139.86 ( 138.86/139.86 ~ 138.86/139.86 X171( 138.86/139.86 X173)))))) => 138.86/139.86 ((![X174, 138.86/139.86 X175:( 138.86/139.86 $i > $o)]: 138.86/139.86 ((~ 138.86/139.86 ( 138.86/139.86 ![X176]: 138.86/139.86 (in( 138.86/139.86 X176,X174) => 138.86/139.86 X175( 138.86/139.86 X176)))) => 138.86/139.86 (?[X177]: 138.86/139.86 (( 138.86/139.86 ~ 138.86/139.86 X175( 138.86/139.86 X177)) & 138.86/139.86 in( 138.86/139.86 X177,X174))))) => 138.86/139.86 ((![X178:( 138.86/139.86 $i > $o)]: 138.86/139.86 ((?[X179]: 138.86/139.86 (( 138.86/139.86 ![X180]: 138.86/139.86 (X178( 138.86/139.86 X180) => 138.86/139.86 (X179 = 138.86/139.86 X180))) & 138.86/139.86 X178( 138.86/139.86 X179))) => 138.86/139.86 (?[X181]: 138.86/139.86 (( 138.86/139.86 ![X182]: 138.86/139.86 (X178( 138.86/139.86 X182) => 138.86/139.86 (X181 = 138.86/139.86 X182))) & 138.86/139.86 X178( 138.86/139.86 X181))))) => 138.86/139.86 ((![X183:( 138.86/139.86 $i > $o)]: 138.86/139.86 (( 138.86/139.86 ?[X184]: 138.86/139.86 X183( 138.86/139.86 X184)) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X185, 138.86/139.86 X186]: 138.86/139.86 (X183( 138.86/139.86 X185) => 138.86/139.86 (X183( 138.86/139.86 X186) => 138.86/139.86 (X185 = 138.86/139.86 X186)))) => 138.86/139.86 ( 138.86/139.86 ?[X187]: 138.86/139.86 (( 138.86/139.86 ![X188]: 138.86/139.86 (X183( 138.86/139.86 X188) => 138.86/139.86 (X187 = 138.86/139.86 X188))) & 138.86/139.86 X183( 138.86/139.86 X187)))))) => 138.86/139.86 ((![X189:( 138.86/139.86 $i > $o)]: 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ?[X190]: 138.86/139.86 (![X191]: 138.86/139.86 (X189( 138.86/139.86 X191) <=> 138.86/139.86 (X191 = 138.86/139.86 X190)))) => 138.86/139.86 ( 138.86/139.86 ?[X192]: 138.86/139.86 (( 138.86/139.86 ![X193]: 138.86/139.86 (X189( 138.86/139.86 X193) => 138.86/139.86 (X192 = 138.86/139.86 X193))) & 138.86/139.86 X189( 138.86/139.86 X192))))) => 138.86/139.86 ((![X194, 138.86/139.86 X195]: 138.86/139.86 (( 138.86/139.86 X194 = 138.86/139.86 X195) => 138.86/139.86 (![X196, 138.86/139.86 X197]: 138.86/139.86 (( 138.86/139.86 X196 = 138.86/139.86 X197) => 138.86/139.86 (in( 138.86/139.86 X196,X194) => 138.86/139.86 in( 138.86/139.86 X197,X195)))))) => 138.86/139.86 ((![X198, 138.86/139.86 X199]: 138.86/139.86 (( 138.86/139.86 X198 = 138.86/139.86 X199) => 138.86/139.86 (![X200, 138.86/139.86 X201]: 138.86/139.86 (( 138.86/139.86 X200 = 138.86/139.86 X201) => 138.86/139.86 (in( 138.86/139.86 X200,X198) <=> 138.86/139.86 in( 138.86/139.86 X201,X199)))))) => 138.86/139.86 (( 138.86/139.86 ![X202:( 138.86/139.86 $i > $o)]: 138.86/139.86 (( 138.86/139.86 ?[X203]: 138.86/139.86 (( 138.86/139.86 ![X204]: 138.86/139.86 (X202( 138.86/139.86 X204) => 138.86/139.86 (X203 = 138.86/139.86 X204))) & 138.86/139.86 X202( 138.86/139.86 X203))) => 138.86/139.86 (![X205, 138.86/139.86 X206]: 138.86/139.86 (X202( 138.86/139.86 X205) => 138.86/139.86 (X202( 138.86/139.86 X206) => 138.86/139.86 (X205 = 138.86/139.86 X206)))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X207:( 138.86/139.86 $i > $o), 138.86/139.86 X208:( 138.86/139.86 $i > $o)]: 138.86/139.86 (( 138.86/139.86 ![X209, 138.86/139.86 X210]: 138.86/139.86 (( 138.86/139.86 X209 = 138.86/139.86 X210) => 138.86/139.86 (X207( 138.86/139.86 X209) <=> 138.86/139.86 X208( 138.86/139.86 X210)))) => 138.86/139.86 (( 138.86/139.86 ?[X211]: 138.86/139.86 zip_tseitin5( 138.86/139.86 X211,X207)) <=> 138.86/139.86 (?[X213]: 138.86/139.86 zip_tseitin5( 138.86/139.86 X213,X208))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 emptyset = 138.86/139.86 emptyset) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X215, 138.86/139.86 X216]: 138.86/139.86 (( 138.86/139.86 X215 = 138.86/139.86 X216) => 138.86/139.86 (![X217, 138.86/139.86 X218]: 138.86/139.86 (( 138.86/139.86 X217 = 138.86/139.86 X218) => 138.86/139.86 (setadjoin( 138.86/139.86 X215,X217) = 138.86/139.86 setadjoin( 138.86/139.86 X216,X218)))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X219, 138.86/139.86 X220]: 138.86/139.86 (( 138.86/139.86 X219 = 138.86/139.86 X220) => 138.86/139.86 (powerset( 138.86/139.86 X219) = 138.86/139.86 powerset( 138.86/139.86 X220)))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X221, 138.86/139.86 X222]: 138.86/139.86 (( 138.86/139.86 X221 = 138.86/139.86 X222) => 138.86/139.86 (setunion( 138.86/139.86 X221) = 138.86/139.86 setunion( 138.86/139.86 X222)))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 omega = 138.86/139.86 omega) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X223:( 138.86/139.86 $i > $o)]: 138.86/139.86 (( 138.86/139.86 ?[X224]: 138.86/139.86 (( 138.86/139.86 ![X225]: 138.86/139.86 (X223( 138.86/139.86 X225) => 138.86/139.86 (X224 = 138.86/139.86 X225))) & 138.86/139.86 X223( 138.86/139.86 X224))) => 138.86/139.86 (![X226, 138.86/139.86 X227]: 138.86/139.86 (X223( 138.86/139.86 X226) => 138.86/139.86 (X223( 138.86/139.86 X227) => 138.86/139.86 (X226 = 138.86/139.86 X227)))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X228:( 138.86/139.86 $i > $o), 138.86/139.86 X229:( 138.86/139.86 $i > $o)]: 138.86/139.86 (( 138.86/139.86 ![X230, 138.86/139.86 X231]: 138.86/139.86 (( 138.86/139.86 X230 = 138.86/139.86 X231) => 138.86/139.86 (X228( 138.86/139.86 X230) <=> 138.86/139.86 X229( 138.86/139.86 X231)))) => 138.86/139.86 (( 138.86/139.86 ?[X232]: 138.86/139.86 (( 138.86/139.86 ![X233]: 138.86/139.86 (X228( 138.86/139.86 X233) => 138.86/139.86 (X232 = 138.86/139.86 X233))) & 138.86/139.86 X228( 138.86/139.86 X232))) => 138.86/139.86 (( 138.86/139.86 ?[X234]: 138.86/139.86 (( 138.86/139.86 ![X235]: 138.86/139.86 (X229( 138.86/139.86 X235) => 138.86/139.86 (X234 = 138.86/139.86 X235))) & 138.86/139.86 X229( 138.86/139.86 X234))) => 138.86/139.86 (descr( 138.86/139.86 ^[V_9]: 138.86/139.86 X228(V_9)) = 138.86/139.86 descr( 138.86/139.86 ^[V_10]: 138.86/139.86 X229( 138.86/139.86 V_10))))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X236, 138.86/139.86 X237]: 138.86/139.86 (( 138.86/139.86 X236 = 138.86/139.86 X237) => 138.86/139.86 (![X238:( 138.86/139.86 $i > $o), 138.86/139.86 X239:( 138.86/139.86 $i > $o)]: 138.86/139.86 (( 138.86/139.86 ![X240]: 138.86/139.86 (in( 138.86/139.86 X240,X236) => 138.86/139.86 (![X241]: 138.86/139.86 (in( 138.86/139.86 X241,X237) => 138.86/139.86 (( 138.86/139.86 X240 = 138.86/139.86 X241) => 138.86/139.86 (X238( 138.86/139.86 X240) <=> 138.86/139.86 X239( 138.86/139.86 X241))))))) => 138.86/139.86 (dsetconstr( 138.86/139.86 X236, 138.86/139.86 ^[V_11]: 138.86/139.86 X238( 138.86/139.86 V_11)) = 138.86/139.86 dsetconstr( 138.86/139.86 X237, 138.86/139.86 ^[V_12]: 138.86/139.86 X239( 138.86/139.86 V_12))))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X242, 138.86/139.86 X243]: 138.86/139.86 (( 138.86/139.86 ![X244]: 138.86/139.86 (in( 138.86/139.86 X244,X242) => 138.86/139.86 in( 138.86/139.86 X244,X243))) => 138.86/139.86 subset( 138.86/139.86 X242,X243))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X245, 138.86/139.86 X246]: 138.86/139.86 (( 138.86/139.86 X245 = 138.86/139.86 X246) => 138.86/139.86 subset( 138.86/139.86 X246,X245))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X247, 138.86/139.86 X248]: 138.86/139.86 (( 138.86/139.86 X247 = 138.86/139.86 X248) => 138.86/139.86 subset( 138.86/139.86 X247,X248))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X249, 138.86/139.86 X250]: 138.86/139.86 (( 138.86/139.86 ![X251]: 138.86/139.86 (in( 138.86/139.86 X251,X249) => 138.86/139.86 in( 138.86/139.86 X251,X250))) => 138.86/139.86 subset( 138.86/139.86 X249,X250))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X252]: 138.86/139.86 subset( 138.86/139.86 emptyset, 138.86/139.86 X252)) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X253, 138.86/139.86 X254,X255]: 138.86/139.86 (subset( 138.86/139.86 X253,X254) => 138.86/139.86 (in( 138.86/139.86 X255,X253) => 138.86/139.86 in( 138.86/139.86 X255,X254)))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X256, 138.86/139.86 X257,X258]: 138.86/139.86 (subset( 138.86/139.86 X256,X257) => 138.86/139.86 (( 138.86/139.86 ~ 138.86/139.86 in( 138.86/139.86 X258,X257)) => 138.86/139.86 (~ 138.86/139.86 in( 138.86/139.86 X258,X256))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X259, 138.86/139.86 X260,X261]: 138.86/139.86 (in( 138.86/139.86 X261,X259) => 138.86/139.86 (( 138.86/139.86 ~ 138.86/139.86 in( 138.86/139.86 X261,X260)) => 138.86/139.86 (~ 138.86/139.86 subset( 138.86/139.86 X259,X260))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X262, 138.86/139.86 X263]: 138.86/139.86 (( 138.86/139.86 ~ 138.86/139.86 subset( 138.86/139.86 X262,X263)) => 138.86/139.86 (X262 != 138.86/139.86 X263))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X264, 138.86/139.86 X265,X266]: 138.86/139.86 (in( 138.86/139.86 X266,X264) => 138.86/139.86 (( 138.86/139.86 ~ 138.86/139.86 in( 138.86/139.86 X266,X265)) => 138.86/139.86 (X264 != 138.86/139.86 X265)))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X267]: 138.86/139.86 subset( 138.86/139.86 X267,X267)) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X268, 138.86/139.86 X269,X270]: 138.86/139.86 (subset( 138.86/139.86 X268,X269) => 138.86/139.86 (subset( 138.86/139.86 X269,X270) => 138.86/139.86 subset( 138.86/139.86 X268,X270)))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X271, 138.86/139.86 X272]: 138.86/139.86 subset( 138.86/139.86 X272, 138.86/139.86 setadjoin( 138.86/139.86 X271,X272))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X273, 138.86/139.86 X274,X275]: 138.86/139.86 (subset( 138.86/139.86 X273,X275) => 138.86/139.86 subset( 138.86/139.86 X273, 138.86/139.86 setadjoin( 138.86/139.86 X274,X275)))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X276, 138.86/139.86 X277]: 138.86/139.86 (subset( 138.86/139.86 X276,X277) => 138.86/139.86 in( 138.86/139.86 X276, 138.86/139.86 powerset( 138.86/139.86 X277)))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X278, 138.86/139.86 X279]: 138.86/139.86 (subset( 138.86/139.86 X278,X279) => 138.86/139.86 (subset( 138.86/139.86 X279,X278) => 138.86/139.86 (X278 = 138.86/139.86 X279)))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X280]: 138.86/139.86 (subset( 138.86/139.86 X280, 138.86/139.86 emptyset) => 138.86/139.86 (X280 = 138.86/139.86 emptyset))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X281, 138.86/139.86 X282]: 138.86/139.86 (subset( 138.86/139.86 X282,X281) => 138.86/139.86 in( 138.86/139.86 X282, 138.86/139.86 powerset( 138.86/139.86 X281)))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X283, 138.86/139.86 X284]: 138.86/139.86 (in( 138.86/139.86 X284, 138.86/139.86 powerset( 138.86/139.86 X283)) => 138.86/139.86 subset( 138.86/139.86 X284,X283))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X285]: 138.86/139.86 in( 138.86/139.86 X285, 138.86/139.86 powerset( 138.86/139.86 X285))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X286, 138.86/139.86 X287]: 138.86/139.86 (subset( 138.86/139.86 X286,X287) => 138.86/139.86 subset( 138.86/139.86 powerset( 138.86/139.86 X286), 138.86/139.86 powerset( 138.86/139.86 X287)))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X288, 138.86/139.86 X289:( 138.86/139.86 $i > $o)]: 138.86/139.86 in( 138.86/139.86 dsetconstr( 138.86/139.86 X288, 138.86/139.86 ^[V_13]: 138.86/139.86 X289( 138.86/139.86 V_13)), 138.86/139.86 powerset( 138.86/139.86 X288))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X290, 138.86/139.86 X291:( 138.86/139.86 $i > $o)]: 138.86/139.86 subset( 138.86/139.86 dsetconstr( 138.86/139.86 X290, 138.86/139.86 ^[V_14]: 138.86/139.86 X291( 138.86/139.86 V_14)), 138.86/139.86 X290)) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X292, 138.86/139.86 X293,X294]: 138.86/139.86 (in( 138.86/139.86 X294,X292) => 138.86/139.86 in( 138.86/139.86 X294, 138.86/139.86 binunion( 138.86/139.86 X292,X293)))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X295, 138.86/139.86 X296]: 138.86/139.86 in( 138.86/139.86 X296, 138.86/139.86 setadjoin( 138.86/139.86 X295, 138.86/139.86 setadjoin( 138.86/139.86 X296, 138.86/139.86 emptyset)))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X297, 138.86/139.86 X298,X299]: 138.86/139.86 (in( 138.86/139.86 X299,X298) => 138.86/139.86 in( 138.86/139.86 X299, 138.86/139.86 binunion( 138.86/139.86 X297,X298)))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X300, 138.86/139.86 X301, 138.86/139.86 X302, 138.86/139.86 X303:$o]: 138.86/139.86 (in( 138.86/139.86 X302, 138.86/139.86 binunion( 138.86/139.86 X300,X301)) => 138.86/139.86 (( 138.86/139.86 in( 138.86/139.86 X302,X300) => 138.86/139.86 X303) => 138.86/139.86 (( 138.86/139.86 in( 138.86/139.86 X302,X301) => 138.86/139.86 X303) => 138.86/139.86 X303)))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X304, 138.86/139.86 X305,X306]: 138.86/139.86 (in( 138.86/139.86 X306, 138.86/139.86 binunion( 138.86/139.86 X304,X305)) => 138.86/139.86 (in( 138.86/139.86 X306,X305) | 138.86/139.86 in( 138.86/139.86 X306,X304)))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X307, 138.86/139.86 X308]: 138.86/139.86 subset( 138.86/139.86 X307, 138.86/139.86 binunion( 138.86/139.86 X307,X308))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X309, 138.86/139.86 X310]: 138.86/139.86 subset( 138.86/139.86 X310, 138.86/139.86 binunion( 138.86/139.86 X309,X310))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X311, 138.86/139.86 X312,X313]: 138.86/139.86 (in( 138.86/139.86 X313,X311) => 138.86/139.86 (in( 138.86/139.86 X313,X312) => 138.86/139.86 in( 138.86/139.86 X313, 138.86/139.86 binintersect( 138.86/139.86 X311,X312))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X314, 138.86/139.86 X315,X316]: 138.86/139.86 (subset( 138.86/139.86 X316,X314) => 138.86/139.86 (subset( 138.86/139.86 X316,X315) => 138.86/139.86 subset( 138.86/139.86 X316, 138.86/139.86 binintersect( 138.86/139.86 X314,X315))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X317, 138.86/139.86 X318,X319]: 138.86/139.86 (in( 138.86/139.86 X319, 138.86/139.86 binintersect( 138.86/139.86 X317,X318)) => 138.86/139.86 in( 138.86/139.86 X319,X317))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X320, 138.86/139.86 X321]: 138.86/139.86 subset( 138.86/139.86 binintersect( 138.86/139.86 X320,X321), 138.86/139.86 X320)) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X322, 138.86/139.86 X323]: 138.86/139.86 (subset( 138.86/139.86 X322,X323) => 138.86/139.86 (binintersect( 138.86/139.86 X322,X323) = 138.86/139.86 X322))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X324, 138.86/139.86 X325]: 138.86/139.86 (( 138.86/139.86 binintersect( 138.86/139.86 X324,X325) = 138.86/139.86 X325) => 138.86/139.86 subset( 138.86/139.86 X325,X324))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X326, 138.86/139.86 X327,X328]: 138.86/139.86 (in( 138.86/139.86 X328, 138.86/139.86 binintersect( 138.86/139.86 X326,X327)) => 138.86/139.86 in( 138.86/139.86 X328,X327))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X329, 138.86/139.86 X330]: 138.86/139.86 (( 138.86/139.86 ~ 138.86/139.86 ( 138.86/139.86 ?[X331]: 138.86/139.86 (in( 138.86/139.86 X331,X330) & 138.86/139.86 in( 138.86/139.86 X331,X329)))) => 138.86/139.86 (binintersect( 138.86/139.86 X329,X330) = 138.86/139.86 emptyset))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X332, 138.86/139.86 X333]: 138.86/139.86 subset( 138.86/139.86 binintersect( 138.86/139.86 X332,X333), 138.86/139.86 X333)) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X334, 138.86/139.86 X335]: 138.86/139.86 (subset( 138.86/139.86 X335,X334) => 138.86/139.86 (binintersect( 138.86/139.86 X334,X335) = 138.86/139.86 X335))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X336, 138.86/139.86 X337]: 138.86/139.86 (( 138.86/139.86 binintersect( 138.86/139.86 X336,X337) = 138.86/139.86 X336) => 138.86/139.86 subset( 138.86/139.86 X336,X337))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X338, 138.86/139.86 X339,X340]: 138.86/139.86 (binintersect( 138.86/139.86 X338, 138.86/139.86 binunion( 138.86/139.86 X339,X340)) = 138.86/139.86 binunion( 138.86/139.86 binintersect( 138.86/139.86 X338,X339), 138.86/139.86 binintersect( 138.86/139.86 X338,X340)))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X341, 138.86/139.86 X342,X343]: 138.86/139.86 (in( 138.86/139.86 X343,X341) => 138.86/139.86 (( 138.86/139.86 ~ 138.86/139.86 in( 138.86/139.86 X343,X342)) => 138.86/139.86 in( 138.86/139.86 X343, 138.86/139.86 setminus( 138.86/139.86 X341,X342))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X344, 138.86/139.86 X345,X346]: 138.86/139.86 (in( 138.86/139.86 X346, 138.86/139.86 setminus( 138.86/139.86 X344,X345)) => 138.86/139.86 in( 138.86/139.86 X346,X344))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X347, 138.86/139.86 X348,X349]: 138.86/139.86 (in( 138.86/139.86 X349, 138.86/139.86 setminus( 138.86/139.86 X347,X348)) => 138.86/139.86 (~ 138.86/139.86 in( 138.86/139.86 X349,X348)))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X350, 138.86/139.86 X351]: 138.86/139.86 (subset( 138.86/139.86 X350,X351) => 138.86/139.86 (setminus( 138.86/139.86 X350,X351) = 138.86/139.86 emptyset))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X352, 138.86/139.86 X353,X354]: 138.86/139.86 (( 138.86/139.86 ~ 138.86/139.86 in( 138.86/139.86 X354, 138.86/139.86 setminus( 138.86/139.86 X352,X353))) => 138.86/139.86 (in( 138.86/139.86 X354,X352) => 138.86/139.86 in( 138.86/139.86 X354,X353)))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X355, 138.86/139.86 X356,X357]: 138.86/139.86 (( 138.86/139.86 ~ 138.86/139.86 in( 138.86/139.86 X357, 138.86/139.86 setminus( 138.86/139.86 X355,X356))) => 138.86/139.86 (( 138.86/139.86 ~ 138.86/139.86 in( 138.86/139.86 X357,X356)) => 138.86/139.86 (~ 138.86/139.86 in( 138.86/139.86 X357,X355))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X358, 138.86/139.86 X359,X360]: 138.86/139.86 (( 138.86/139.86 ~ 138.86/139.86 in( 138.86/139.86 X360,X358)) => 138.86/139.86 (~ 138.86/139.86 in( 138.86/139.86 X360, 138.86/139.86 setminus( 138.86/139.86 X358,X359))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X361, 138.86/139.86 X362,X363]: 138.86/139.86 (in( 138.86/139.86 X363,X362) => 138.86/139.86 (~ 138.86/139.86 in( 138.86/139.86 X363, 138.86/139.86 setminus( 138.86/139.86 X361,X362))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X364, 138.86/139.86 X365]: 138.86/139.86 subset( 138.86/139.86 setminus( 138.86/139.86 X364,X365), 138.86/139.86 X364)) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X366, 138.86/139.86 X367]: 138.86/139.86 (( 138.86/139.86 setminus( 138.86/139.86 X366,X367) = 138.86/139.86 emptyset) => 138.86/139.86 subset( 138.86/139.86 X366,X367))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X368, 138.86/139.86 X369,X370]: 138.86/139.86 (in( 138.86/139.86 X370, 138.86/139.86 symdiff( 138.86/139.86 X368,X369)) => 138.86/139.86 (![X371:$o]: 138.86/139.86 (( 138.86/139.86 in( 138.86/139.86 X370,X368) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ~ 138.86/139.86 in( 138.86/139.86 X370,X369)) => 138.86/139.86 X371)) => 138.86/139.86 (( 138.86/139.86 ( 138.86/139.86 ~ 138.86/139.86 in( 138.86/139.86 X370,X368)) => 138.86/139.86 ( 138.86/139.86 in( 138.86/139.86 X370,X369) => 138.86/139.86 X371)) => 138.86/139.86 X371))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X372, 138.86/139.86 X373,X374]: 138.86/139.86 (in( 138.86/139.86 X374,X372) => 138.86/139.86 (( 138.86/139.86 ~ 138.86/139.86 in( 138.86/139.86 X374,X373)) => 138.86/139.86 in( 138.86/139.86 X374, 138.86/139.86 symdiff( 138.86/139.86 X372,X373))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X375, 138.86/139.86 X376,X377]: 138.86/139.86 (( 138.86/139.86 ~ 138.86/139.86 in( 138.86/139.86 X377,X375)) => 138.86/139.86 (in( 138.86/139.86 X377,X376) => 138.86/139.86 in( 138.86/139.86 X377, 138.86/139.86 symdiff( 138.86/139.86 X375,X376))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X378, 138.86/139.86 X379,X380]: 138.86/139.86 (in( 138.86/139.86 X380,X378) => 138.86/139.86 (in( 138.86/139.86 X380,X379) => 138.86/139.86 (~ 138.86/139.86 in( 138.86/139.86 X380, 138.86/139.86 symdiff( 138.86/139.86 X378,X379)))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X381, 138.86/139.86 X382,X383]: 138.86/139.86 (( 138.86/139.86 ~ 138.86/139.86 in( 138.86/139.86 X383,X381)) => 138.86/139.86 (( 138.86/139.86 ~ 138.86/139.86 in( 138.86/139.86 X383,X382)) => 138.86/139.86 (~ 138.86/139.86 in( 138.86/139.86 X383, 138.86/139.86 symdiff( 138.86/139.86 X381,X382)))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X384, 138.86/139.86 X385]: 138.86/139.86 in( 138.86/139.86 X385, 138.86/139.86 setadjoin( 138.86/139.86 X384, 138.86/139.86 setadjoin( 138.86/139.86 X385, 138.86/139.86 emptyset)))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X386, 138.86/139.86 X387]: 138.86/139.86 in( 138.86/139.86 X386, 138.86/139.86 setunion( 138.86/139.86 setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X386, 138.86/139.86 emptyset), 138.86/139.86 setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X386, 138.86/139.86 setadjoin( 138.86/139.86 X387, 138.86/139.86 emptyset)), 138.86/139.86 emptyset))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X388, 138.86/139.86 X389]: 138.86/139.86 in( 138.86/139.86 X389, 138.86/139.86 setunion( 138.86/139.86 setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X388, 138.86/139.86 emptyset), 138.86/139.86 setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X388, 138.86/139.86 setadjoin( 138.86/139.86 X389, 138.86/139.86 emptyset)), 138.86/139.86 emptyset))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X390, 138.86/139.86 X391]: 138.86/139.86 iskpair( 138.86/139.86 setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X390, 138.86/139.86 emptyset), 138.86/139.86 setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X390, 138.86/139.86 setadjoin( 138.86/139.86 X391, 138.86/139.86 emptyset)), 138.86/139.86 emptyset)))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X392, 138.86/139.86 X393]: 138.86/139.86 iskpair( 138.86/139.86 kpair( 138.86/139.86 X392,X393))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X394, 138.86/139.86 X395]: 138.86/139.86 (in( 138.86/139.86 X395,X394) => 138.86/139.86 subset( 138.86/139.86 setadjoin( 138.86/139.86 X395, 138.86/139.86 emptyset), 138.86/139.86 X394))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X396, 138.86/139.86 X397]: 138.86/139.86 (in( 138.86/139.86 X397,X396) => 138.86/139.86 in( 138.86/139.86 setadjoin( 138.86/139.86 X397, 138.86/139.86 emptyset), 138.86/139.86 powerset( 138.86/139.86 X396)))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X398, 138.86/139.86 X399,X400]: 138.86/139.86 (in( 138.86/139.86 X400,X398) => 138.86/139.86 in( 138.86/139.86 setadjoin( 138.86/139.86 X400, 138.86/139.86 emptyset), 138.86/139.86 powerset( 138.86/139.86 binunion( 138.86/139.86 X398,X399))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X401, 138.86/139.86 X402,X403]: 138.86/139.86 (in( 138.86/139.86 X403, 138.86/139.86 setadjoin( 138.86/139.86 X401, 138.86/139.86 setadjoin( 138.86/139.86 X402, 138.86/139.86 emptyset))) => 138.86/139.86 (( 138.86/139.86 X403 = 138.86/139.86 X402) | 138.86/139.86 (X403 = 138.86/139.86 X401)))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X404, 138.86/139.86 X405,X406]: 138.86/139.86 (in( 138.86/139.86 X406,X404) => 138.86/139.86 (![X407]: 138.86/139.86 (in( 138.86/139.86 X407,X405) => 138.86/139.86 subset( 138.86/139.86 setadjoin( 138.86/139.86 X406, 138.86/139.86 setadjoin( 138.86/139.86 X407, 138.86/139.86 emptyset)), 138.86/139.86 binunion( 138.86/139.86 X404,X405)))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X408, 138.86/139.86 X409,X410]: 138.86/139.86 (in( 138.86/139.86 X410,X408) => 138.86/139.86 (![X411]: 138.86/139.86 (in( 138.86/139.86 X411,X409) => 138.86/139.86 in( 138.86/139.86 setadjoin( 138.86/139.86 X410, 138.86/139.86 setadjoin( 138.86/139.86 X411, 138.86/139.86 emptyset)), 138.86/139.86 powerset( 138.86/139.86 binunion( 138.86/139.86 X408,X409))))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X412, 138.86/139.86 X413,X414]: 138.86/139.86 (in( 138.86/139.86 X414,X412) => 138.86/139.86 (![X415]: 138.86/139.86 (in( 138.86/139.86 X415,X413) => 138.86/139.86 subset( 138.86/139.86 setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X414, 138.86/139.86 emptyset), 138.86/139.86 setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X414, 138.86/139.86 setadjoin( 138.86/139.86 X415, 138.86/139.86 emptyset)), 138.86/139.86 emptyset)), 138.86/139.86 powerset( 138.86/139.86 binunion( 138.86/139.86 X412,X413))))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X416, 138.86/139.86 X417,X418]: 138.86/139.86 (in( 138.86/139.86 X418,X416) => 138.86/139.86 (![X419]: 138.86/139.86 (in( 138.86/139.86 X419,X417) => 138.86/139.86 in( 138.86/139.86 setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X418, 138.86/139.86 emptyset), 138.86/139.86 setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X418, 138.86/139.86 setadjoin( 138.86/139.86 X419, 138.86/139.86 emptyset)), 138.86/139.86 emptyset)), 138.86/139.86 powerset( 138.86/139.86 powerset( 138.86/139.86 binunion( 138.86/139.86 X416,X417)))))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X420, 138.86/139.86 X421,X422]: 138.86/139.86 (in( 138.86/139.86 X422,X420) => 138.86/139.86 (![X423]: 138.86/139.86 (in( 138.86/139.86 X423,X421) => 138.86/139.86 in( 138.86/139.86 kpair( 138.86/139.86 X422,X423), 138.86/139.86 powerset( 138.86/139.86 powerset( 138.86/139.86 binunion( 138.86/139.86 X420,X421)))))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X424, 138.86/139.86 X425,X426]: 138.86/139.86 (in( 138.86/139.86 X426,X424) => 138.86/139.86 (![X427]: 138.86/139.86 (in( 138.86/139.86 X427,X425) => 138.86/139.86 in( 138.86/139.86 kpair( 138.86/139.86 X426,X427), 138.86/139.86 cartprod( 138.86/139.86 X424,X425)))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X428, 138.86/139.86 X429,X430]: 138.86/139.86 (in( 138.86/139.86 X430, 138.86/139.86 cartprod( 138.86/139.86 X428,X429)) => 138.86/139.86 (?[X431]: 138.86/139.86 (( 138.86/139.86 ?[X432]: 138.86/139.86 (( 138.86/139.86 X430 = 138.86/139.86 kpair( 138.86/139.86 X431,X432)) & 138.86/139.86 in( 138.86/139.86 X432,X429))) & 138.86/139.86 in( 138.86/139.86 X431,X428))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X433, 138.86/139.86 X434,X435]: 138.86/139.86 (in( 138.86/139.86 X435, 138.86/139.86 cartprod( 138.86/139.86 X433,X434)) => 138.86/139.86 iskpair( 138.86/139.86 X435))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X436, 138.86/139.86 X437]: 138.86/139.86 (in( 138.86/139.86 X437, 138.86/139.86 setunion( 138.86/139.86 X436)) => 138.86/139.86 (?[X438]: 138.86/139.86 (in( 138.86/139.86 X437,X438) & 138.86/139.86 in( 138.86/139.86 X438,X436))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X439]: 138.86/139.86 subset( 138.86/139.86 setunion( 138.86/139.86 setadjoin( 138.86/139.86 X439, 138.86/139.86 emptyset)), 138.86/139.86 X439)) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X440]: 138.86/139.86 subset( 138.86/139.86 X440, 138.86/139.86 setunion( 138.86/139.86 setadjoin( 138.86/139.86 X440, 138.86/139.86 emptyset)))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X441]: 138.86/139.86 (setunion( 138.86/139.86 setadjoin( 138.86/139.86 X441, 138.86/139.86 emptyset)) = 138.86/139.86 X441)) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X442, 138.86/139.86 X443:( 138.86/139.86 $i > $o)]: 138.86/139.86 (( 138.86/139.86 ![X444]: 138.86/139.86 (in( 138.86/139.86 X444,X442) => 138.86/139.86 (![X445]: 138.86/139.86 (in( 138.86/139.86 X445,X442) => 138.86/139.86 (X443( 138.86/139.86 X444) => 138.86/139.86 (X443( 138.86/139.86 X445) => 138.86/139.86 (X444 = 138.86/139.86 X445))))))) => 138.86/139.86 (( 138.86/139.86 ?[X446]: 138.86/139.86 (X443( 138.86/139.86 X446) & 138.86/139.86 in( 138.86/139.86 X446,X442))) => 138.86/139.86 (?[X447]: 138.86/139.86 (( 138.86/139.86 dsetconstr( 138.86/139.86 X442, 138.86/139.86 ^[V_15]: 138.86/139.86 X443( 138.86/139.86 V_15)) = 138.86/139.86 setadjoin( 138.86/139.86 X447, 138.86/139.86 emptyset)) & 138.86/139.86 in( 138.86/139.86 X447, 138.86/139.86 dsetconstr( 138.86/139.86 X442, 138.86/139.86 ^[V_16]: 138.86/139.86 X443( 138.86/139.86 V_16)))))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X448, 138.86/139.86 X449:( 138.86/139.86 $i > $o)]: 138.86/139.86 (( 138.86/139.86 ?[X450]: 138.86/139.86 (( 138.86/139.86 dsetconstr( 138.86/139.86 X448, 138.86/139.86 ^[V_17]: 138.86/139.86 X449( 138.86/139.86 V_17)) = 138.86/139.86 setadjoin( 138.86/139.86 X450, 138.86/139.86 emptyset)) & 138.86/139.86 in( 138.86/139.86 X450, 138.86/139.86 dsetconstr( 138.86/139.86 X448, 138.86/139.86 ^[V_18]: 138.86/139.86 X449( 138.86/139.86 V_18))))) => 138.86/139.86 (?[X451]: 138.86/139.86 (X449( 138.86/139.86 X451) & 138.86/139.86 in( 138.86/139.86 X451,X448))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X452, 138.86/139.86 X453:( 138.86/139.86 $i > $o), 138.86/139.86 X454]: 138.86/139.86 (in( 138.86/139.86 X454,X452) => 138.86/139.86 (X453( 138.86/139.86 X454) => 138.86/139.86 (( 138.86/139.86 ![X455]: 138.86/139.86 (in( 138.86/139.86 X455,X452) => 138.86/139.86 (X453( 138.86/139.86 X455) => 138.86/139.86 (X455 = 138.86/139.86 X454)))) => 138.86/139.86 (?[X456]: 138.86/139.86 (( 138.86/139.86 dsetconstr( 138.86/139.86 X452, 138.86/139.86 ^[V_19]: 138.86/139.86 X453( 138.86/139.86 V_19)) = 138.86/139.86 setadjoin( 138.86/139.86 X456, 138.86/139.86 emptyset)) & 138.86/139.86 in( 138.86/139.86 X456, 138.86/139.86 dsetconstr( 138.86/139.86 X452, 138.86/139.86 ^[V_20]: 138.86/139.86 X453( 138.86/139.86 V_20))))))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X457, 138.86/139.86 X458:( 138.86/139.86 $i > $o)]: 138.86/139.86 (( 138.86/139.86 ![X459]: 138.86/139.86 (in( 138.86/139.86 X459,X457) => 138.86/139.86 (![X460]: 138.86/139.86 (in( 138.86/139.86 X460,X457) => 138.86/139.86 (X458( 138.86/139.86 X459) => 138.86/139.86 (X458( 138.86/139.86 X460) => 138.86/139.86 (X459 = 138.86/139.86 X460))))))) => 138.86/139.86 (( 138.86/139.86 ?[X461]: 138.86/139.86 (X458( 138.86/139.86 X461) & 138.86/139.86 in( 138.86/139.86 X461,X457))) => 138.86/139.86 (?[X462]: 138.86/139.86 (( 138.86/139.86 dsetconstr( 138.86/139.86 X457, 138.86/139.86 ^[V_21]: 138.86/139.86 X458( 138.86/139.86 V_21)) = 138.86/139.86 setadjoin( 138.86/139.86 X462, 138.86/139.86 emptyset)) & 138.86/139.86 in( 138.86/139.86 X462, 138.86/139.86 dsetconstr( 138.86/139.86 X457, 138.86/139.86 ^[V_22]: 138.86/139.86 X458( 138.86/139.86 V_22)))))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X463, 138.86/139.86 X464]: 138.86/139.86 (( 138.86/139.86 setadjoin( 138.86/139.86 X463, 138.86/139.86 emptyset) = 138.86/139.86 setadjoin( 138.86/139.86 X464, 138.86/139.86 emptyset)) => 138.86/139.86 (X463 = 138.86/139.86 X464))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X465, 138.86/139.86 X466,X467]: 138.86/139.86 (in( 138.86/139.86 setadjoin( 138.86/139.86 X467, 138.86/139.86 emptyset), 138.86/139.86 setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X465, 138.86/139.86 emptyset), 138.86/139.86 setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X465, 138.86/139.86 setadjoin( 138.86/139.86 X466, 138.86/139.86 emptyset)), 138.86/139.86 emptyset))) => 138.86/139.86 (X465 = 138.86/139.86 X467))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X468]: 138.86/139.86 (iskpair( 138.86/139.86 X468) => 138.86/139.86 (?[X469]: 138.86/139.86 (( 138.86/139.86 dsetconstr( 138.86/139.86 setunion( 138.86/139.86 X468), 138.86/139.86 ^[V_23]: 138.86/139.86 in( 138.86/139.86 setadjoin( 138.86/139.86 V_23, 138.86/139.86 emptyset), 138.86/139.86 X468)) = 138.86/139.86 setadjoin( 138.86/139.86 X469, 138.86/139.86 emptyset)) & 138.86/139.86 in( 138.86/139.86 X469, 138.86/139.86 dsetconstr( 138.86/139.86 setunion( 138.86/139.86 X468), 138.86/139.86 ^[V_24]: 138.86/139.86 in( 138.86/139.86 setadjoin( 138.86/139.86 V_24, 138.86/139.86 emptyset), 138.86/139.86 X468))))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X470]: 138.86/139.86 (( 138.86/139.86 ?[X471]: 138.86/139.86 (( 138.86/139.86 X470 = 138.86/139.86 setadjoin( 138.86/139.86 X471, 138.86/139.86 emptyset)) & 138.86/139.86 in( 138.86/139.86 X471,X470))) => 138.86/139.86 in( 138.86/139.86 setunion( 138.86/139.86 X470), 138.86/139.86 X470))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X472, 138.86/139.86 X473]: 138.86/139.86 (kfst( 138.86/139.86 kpair( 138.86/139.86 X472,X473)) = 138.86/139.86 X472)) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X474, 138.86/139.86 X475,X476]: 138.86/139.86 (in( 138.86/139.86 X476, 138.86/139.86 cartprod( 138.86/139.86 X474,X475)) => 138.86/139.86 in( 138.86/139.86 kfst( 138.86/139.86 X476), 138.86/139.86 X474))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X477, 138.86/139.86 X478, 138.86/139.86 X479,X480]: 138.86/139.86 (( 138.86/139.86 setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X477, 138.86/139.86 emptyset), 138.86/139.86 setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X477, 138.86/139.86 setadjoin( 138.86/139.86 X478, 138.86/139.86 emptyset)), 138.86/139.86 emptyset)) = 138.86/139.86 setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X479, 138.86/139.86 emptyset), 138.86/139.86 setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X479, 138.86/139.86 setadjoin( 138.86/139.86 X480, 138.86/139.86 emptyset)), 138.86/139.86 emptyset))) => 138.86/139.86 (X477 = 138.86/139.86 X479))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X481, 138.86/139.86 X482, 138.86/139.86 X483,X484]: 138.86/139.86 (( 138.86/139.86 kpair( 138.86/139.86 X481,X482) = 138.86/139.86 kpair( 138.86/139.86 X483,X484)) => 138.86/139.86 (X481 = 138.86/139.86 X483))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X485, 138.86/139.86 X486]: 138.86/139.86 (( 138.86/139.86 X485 = 138.86/139.86 X486) => 138.86/139.86 (setadjoin( 138.86/139.86 X485, 138.86/139.86 setadjoin( 138.86/139.86 X486, 138.86/139.86 emptyset)) = 138.86/139.86 setadjoin( 138.86/139.86 X485, 138.86/139.86 emptyset)))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X487, 138.86/139.86 X488]: 138.86/139.86 (( 138.86/139.86 X487 = 138.86/139.86 X488) => 138.86/139.86 (setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X487, 138.86/139.86 emptyset), 138.86/139.86 setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X487, 138.86/139.86 setadjoin( 138.86/139.86 X488, 138.86/139.86 emptyset)), 138.86/139.86 emptyset)) = 138.86/139.86 setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X487, 138.86/139.86 emptyset), 138.86/139.86 emptyset)))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X489, 138.86/139.86 X490, 138.86/139.86 X491,X492]: 138.86/139.86 (( 138.86/139.86 setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X489, 138.86/139.86 emptyset), 138.86/139.86 setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X489, 138.86/139.86 setadjoin( 138.86/139.86 X490, 138.86/139.86 emptyset)), 138.86/139.86 emptyset)) = 138.86/139.86 setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X491, 138.86/139.86 emptyset), 138.86/139.86 setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X491, 138.86/139.86 setadjoin( 138.86/139.86 X492, 138.86/139.86 emptyset)), 138.86/139.86 emptyset))) => 138.86/139.86 (( 138.86/139.86 X491 = 138.86/139.86 X492) => 138.86/139.86 (X490 = 138.86/139.86 X492)))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X493, 138.86/139.86 X494,X495]: 138.86/139.86 (( 138.86/139.86 setadjoin( 138.86/139.86 X493, 138.86/139.86 setadjoin( 138.86/139.86 X494, 138.86/139.86 emptyset)) = 138.86/139.86 setadjoin( 138.86/139.86 X495, 138.86/139.86 emptyset)) => 138.86/139.86 (X493 = 138.86/139.86 X494))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X496, 138.86/139.86 X497, 138.86/139.86 X498,X499]: 138.86/139.86 (( 138.86/139.86 setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X496, 138.86/139.86 emptyset), 138.86/139.86 setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X496, 138.86/139.86 setadjoin( 138.86/139.86 X497, 138.86/139.86 emptyset)), 138.86/139.86 emptyset)) = 138.86/139.86 setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X498, 138.86/139.86 emptyset), 138.86/139.86 setadjoin( 138.86/139.86 setadjoin( 138.86/139.86 X498, 138.86/139.86 setadjoin( 138.86/139.86 X499, 138.86/139.86 emptyset)), 138.86/139.86 emptyset))) => 138.86/139.86 (X497 = 138.86/139.86 X499))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X500, 138.86/139.86 X501, 138.86/139.86 X502,X503]: 138.86/139.86 (( 138.86/139.86 kpair( 138.86/139.86 X500,X501) = 138.86/139.86 kpair( 138.86/139.86 X502,X503)) => 138.86/139.86 (X501 = 138.86/139.86 X503))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X504]: 138.86/139.86 (iskpair( 138.86/139.86 X504) => 138.86/139.86 (?[X505]: 138.86/139.86 (( 138.86/139.86 dsetconstr( 138.86/139.86 setunion( 138.86/139.86 X504), 138.86/139.86 ^[V_25]: 138.86/139.86 (X504 = 138.86/139.86 kpair( 138.86/139.86 kfst( 138.86/139.86 X504), 138.86/139.86 V_25))) = 138.86/139.86 setadjoin( 138.86/139.86 X505, 138.86/139.86 emptyset)) & 138.86/139.86 in( 138.86/139.86 X505, 138.86/139.86 dsetconstr( 138.86/139.86 setunion( 138.86/139.86 X504), 138.86/139.86 ^[V_26]: 138.86/139.86 (X504 = 138.86/139.86 kpair( 138.86/139.86 kfst( 138.86/139.86 X504), 138.86/139.86 V_26)))))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X506, 138.86/139.86 X507]: 138.86/139.86 (ksnd( 138.86/139.86 kpair( 138.86/139.86 X506,X507)) = 138.86/139.86 X507)) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X508]: 138.86/139.86 (iskpair( 138.86/139.86 X508) => 138.86/139.86 (kpair( 138.86/139.86 kfst( 138.86/139.86 X508), 138.86/139.86 ksnd( 138.86/139.86 X508)) = 138.86/139.86 X508))) => 138.86/139.86 ( 138.86/139.86 ![X509, 138.86/139.86 X510,X511]: 138.86/139.86 (in( 138.86/139.86 X511, 138.86/139.86 cartprod( 138.86/139.86 X509,X510)) => 138.86/139.86 in( 138.86/139.86 ksnd( 138.86/139.86 X511), 138.86/139.86 X510)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 138.86/139.86 tff(zf_stmt_14, negated_conjecture, 138.86/139.86 (~ 138.86/139.86 ((![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))) => 138.86/139.86 ((![X5]: (~in(X5,emptyset))) => 138.86/139.86 ((![X6,X7,X8]: (in(X8,setadjoin(X6,X7)) <=> zip_tseitin0(X8,X7,X6))) => 138.86/139.86 ((![X9,X10]: 138.86/139.86 (in(X10,powerset(X9)) <=> (![X11]: zip_tseitin1(X11,X10,X9)))) => 138.86/139.86 ((![X12,X13]: 138.86/139.86 (in(X13,setunion(X12)) <=> (?[X14]: zip_tseitin2(X14,X13,X12)))) => 138.86/139.86 (in(emptyset,omega) => 138.86/139.86 ((![X15]: (in(X15,omega) => in(setadjoin(X15,X15),omega))) => 138.86/139.86 ((![X16]: 138.86/139.86 (((![X17]: 138.86/139.86 ((in(X17,X16) & in(X17,omega)) => 138.86/139.86 in(setadjoin(X17,X17),X16))) & 138.86/139.86 in(emptyset,X16)) => 138.86/139.86 (![X18]: (in(X18,omega) => in(X18,X16))))) => 138.86/139.86 ((![X19:(($i * $i) > $o),X20]: 138.86/139.86 ((![X21]: 138.86/139.86 (in(X21,X20) => 138.86/139.86 (?[X22]: 138.86/139.86 ((![X23]: (X19(X21,X23) => (X22 = X23))) & 138.86/139.86 X19(X21,X22))))) => 138.86/139.86 (?[X24]: 138.86/139.86 (![X25]: 138.86/139.86 (in(X25,X24) <=> 138.86/139.86 (?[X26]: zip_tseitin3(X26,X25,X20,X19))))))) => 138.86/139.86 ((![X27]: 138.86/139.86 ((?[X28]: in(X28,X27)) => 138.86/139.86 (?[X29]: 138.86/139.86 ((~(?[X30]: (in(X30,X27) & in(X30,X29)))) & in(X29,X27))))) => 138.86/139.86 ((![X31]: 138.86/139.86 (?[X32]: 138.86/139.86 ((![X33]: 138.86/139.86 (((?[X34]: in(X34,X33)) & 138.86/139.86 (![X35]: (in(X35,X33) => in(X35,X31)))) => 138.86/139.86 (?[X36,X37]: 138.86/139.86 ((![X38]: 138.86/139.86 (in(X38,X32) => 138.86/139.86 (in(X37,X38) | 138.86/139.86 (![X39]: (in(X39,X38) => in(X39,X36)))))) & 138.86/139.86 (~(?[X40]: (in(X40,X33) & in(X40,X36)))) & 138.86/139.86 in(X37,X33) & in(X36,X32))))) & 138.86/139.86 (![X41,X42]: 138.86/139.86 ((in(X42,X32) & in(X41,X32)) => 138.86/139.86 ((![X43]: (in(X43,X42) => in(X43,X41))) | 138.86/139.86 (![X44]: (in(X44,X41) => in(X44,X42)))))) & 138.86/139.86 (![X45,X46]: 138.86/139.86 ((in(X46,X31) & in(X45,X31)) => 138.86/139.86 ((![X47]: 138.86/139.86 (in(X47,X32) => (in(X45,X47) <=> in(X46,X47)))) => 138.86/139.86 (X45 = X46)))) & 138.86/139.86 (![X48]: 138.86/139.86 (in(X48,X32) => 138.86/139.86 (![X49]: (in(X49,X48) => in(X49,X31)))))))) => 138.86/139.86 ((![X50:($i > $o)]: 138.86/139.86 ((?[X51]: ((![X52]: (X50(X52) => (X51 = X52))) & X50(X51))) => 138.86/139.86 X50(descr(^[V_1]: X50(V_1))))) => 138.86/139.86 ((![X53,X54:($i > $o),X55]: 138.86/139.86 (in(X55,X53) => 138.86/139.86 (X54(X55) => in(X55,dsetconstr(X53,^[V_2]: X54(V_2)))))) => 138.86/139.86 ((![X56,X57:($i > $o),X58]: 138.86/139.86 (in(X58,dsetconstr(X56,^[V_3]: X57(V_3))) => in(X58,X56))) => 138.86/139.86 ((![X59,X60:($i > $o),X61]: 138.86/139.86 (in(X61,dsetconstr(X59,^[V_4]: X60(V_4))) => X60(X61))) => 138.86/139.86 ((![X62:($i > $o)]: 138.86/139.86 ((?[X63]: 138.86/139.86 ((![X64]: (X62(X64) => (X63 = X64))) & X62(X63))) => 138.86/139.86 (?[X65]: 138.86/139.86 ((![X66]: (X62(X66) => (X65 = X66))) & X62(X65))))) => 138.86/139.86 ((![X67:$o,X68]: (in(X68,prop2set(X67)) => X67)) => 138.86/139.86 ((![X69]: (in(X69,emptyset) => (![X70:$o]: X70))) => 138.86/139.86 ((![X71]: (in(X71,emptyset) => $false)) => 138.86/139.86 ((![X72]: (~in(X72,emptyset))) => 138.86/139.86 ((![X73:($i > $o)]: 138.86/139.86 ((?[X74]: 138.86/139.86 ((![X75]: (X73(X75) => (X74 = X75))) & 138.86/139.86 X73(X74))) => 138.86/139.86 (?[X76]: X73(X76)))) => 138.86/139.86 ((![X77,X78]: 138.86/139.86 ((![X79]: (in(X79,X77) => in(X79,X78))) => 138.86/139.86 ((![X80]: (in(X80,X78) => in(X80,X77))) => 138.86/139.86 (X77 = X78)))) => 138.86/139.86 ((![X81]: 138.86/139.86 ((![X82]: (~in(X82,X81))) => (X81 = emptyset))) => 138.86/139.86 ((![X83]: 138.86/139.86 ((![X84]: (~in(X84,X83))) => (X83 = emptyset))) => 138.86/139.86 ((![X85,X86:($i > $o),X87]: 138.86/139.86 (in(X87,X85) => 138.86/139.86 (in(X87,dsetconstr(X85,^[V_5]: X86(V_5))) <=> 138.86/139.86 X86(X87)))) => 138.86/139.86 ((![X88]: 138.86/139.86 ((X88 != emptyset) => (?[X89]: in(X89,X88)))) => 138.86/139.86 ((![X90,X91:($i > $o),X92]: 138.86/139.86 (in(X92,X90) => 138.86/139.86 (X91(X92) => 138.86/139.86 (dsetconstr(X90,^[V_6]: X91(V_6)) != 138.86/139.86 emptyset)))) => 138.86/139.86 ((![X93]: 138.86/139.86 ((?[X94]: in(X94,X93)) => 138.86/139.86 (X93 != emptyset))) => 138.86/139.86 ((![X95,X96]: in(X95,setadjoin(X95,X96))) => 138.86/139.86 (in(emptyset,setadjoin(emptyset,emptyset)) => 138.86/139.86 ((![X97,X98,X99]: 138.86/139.86 (in(X99,X98) => 138.86/139.86 in(X99,setadjoin(X97,X98)))) => 138.86/139.86 ((![X100,X101,X102]: 138.86/139.86 (in(X102,setadjoin(X100,X101)) => 138.86/139.86 (![X103:$o]: 138.86/139.86 (((X102 = X100) => X103) => 138.86/139.86 ((in(X102,X101) => X103) => X103))))) => 138.86/139.86 ((![X104,X105,X106]: 138.86/139.86 (in(X106,setadjoin(X104,X105)) => 138.86/139.86 (in(X106,X105) | (X106 = X104)))) => 138.86/139.86 ((![X107]: 138.86/139.86 (dsetconstr(X107,^[V_7]: $true) = 138.86/139.86 X107)) => 138.86/139.86 ((![X108,X109]: 138.86/139.86 ((![X110]: 138.86/139.86 (in(X110,X109) => in(X110,X108))) => 138.86/139.86 in(X109,powerset(X108)))) => 138.86/139.86 ((![X111]: in(emptyset,powerset(X111))) => 138.86/139.86 ((![X112]: 138.86/139.86 in(emptyset,powerset(X112))) => 138.86/139.86 ((![X113,X114,X115]: 138.86/139.86 (in(X114,powerset(X113)) => 138.86/139.86 (in(X115,X114) => in(X115,X113)))) => 138.86/139.86 ((![X116,X117,X118]: 138.86/139.86 (in(X117,X118) => 138.86/139.86 (in(X118,X116) => 138.86/139.86 in(X117,setunion(X116))))) => 138.86/139.86 ((![X119,X120]: 138.86/139.86 (in(X120,setunion(X119)) => 138.86/139.86 (![X121:$o]: 138.86/139.86 ((![X122]: 138.86/139.86 (in(X120,X122) => 138.86/139.86 (in(X122,X119) => 138.86/139.86 X121))) => 138.86/139.86 X121)))) => 138.86/139.86 ((![X123,X124]: 138.86/139.86 (in(X124,X123) => 138.86/139.86 in(X124, 138.86/139.86 powerset(setunion(X123))))) => 138.86/139.86 ((![X125:($i > $o)]: 138.86/139.86 ((?[X126]: 138.86/139.86 ((![X127]: 138.86/139.86 (X125(X127) => 138.86/139.86 (X126 = X127))) & 138.86/139.86 X125(X126))) => 138.86/139.86 (?[X128]: 138.86/139.86 (![X129]: 138.86/139.86 (X125(X129) <=> 138.86/139.86 (X129 = X128)))))) => 138.86/139.86 ((![X130]: 138.86/139.86 ((X130 != emptyset) => 138.86/139.86 (?[X131]: in(X131,X130)))) => 138.86/139.86 ((![X132,X133]: 138.86/139.86 (in(X132, 138.86/139.86 setadjoin(X133, 138.86/139.86 emptyset)) => 138.86/139.86 (X132 = X133))) => 138.86/139.86 ((![X134,X135]: 138.86/139.86 ((X134 != X135) => 138.86/139.86 (~ 138.86/139.86 in(X135, 138.86/139.86 setadjoin(X134, 138.86/139.86 emptyset))))) => 138.86/139.86 ((![X136,X137]: 138.86/139.86 ((X136 = X137) => 138.86/139.86 in(X136, 138.86/139.86 setadjoin(X137, 138.86/139.86 emptyset)))) => 138.86/139.86 ((![X138,X139]: 138.86/139.86 (in(X138, 138.86/139.86 setadjoin(X139, 138.86/139.86 emptyset)) => 138.86/139.86 in(X139, 138.86/139.86 setadjoin(X138, 138.86/139.86 emptyset)))) => 138.86/139.86 ((![X140,X141,X142]: 138.86/139.86 (in(X142, 138.86/139.86 setadjoin( 138.86/139.86 X140, 138.86/139.86 setadjoin( 138.86/139.86 X141,emptyset))) => 138.86/139.86 ((X142 = X141) | 138.86/139.86 (X142 = X140)))) => 138.86/139.86 ((![X143,X144]: 138.86/139.86 in(X143, 138.86/139.86 setadjoin( 138.86/139.86 X143, 138.86/139.86 setadjoin( 138.86/139.86 X144,emptyset)))) => 138.86/139.86 ((![X145,X146]: 138.86/139.86 in(X146, 138.86/139.86 setadjoin( 138.86/139.86 X145, 138.86/139.86 setadjoin( 138.86/139.86 X146,emptyset)))) => 138.86/139.86 ((![X147,X148:($i > $o)]: 138.86/139.86 ((?[X149]: 138.86/139.86 (X148(X149) & 138.86/139.86 in(X149,X147))) => 138.86/139.86 ((dsetconstr( 138.86/139.86 X147, 138.86/139.86 ^[V_8]: 138.86/139.86 X148(V_8)) = 138.86/139.86 emptyset) => 138.86/139.86 $false))) => 138.86/139.86 ((![X150:($i > $o), 138.86/139.86 X151]: 138.86/139.86 (in(X151,emptyset) => 138.86/139.86 X150(X151))) => 138.86/139.86 ((![X152, 138.86/139.86 X153:($i > $o)]: 138.86/139.86 ((~ 138.86/139.86 (![X154]: 138.86/139.86 (in( 138.86/139.86 X154,X152) => 138.86/139.86 X153(X154)))) => 138.86/139.86 (?[X155]: 138.86/139.86 ((~X153(X155)) & 138.86/139.86 in(X155,X152))))) => 138.86/139.86 ((![X156, 138.86/139.86 X157:($i > $o)]: 138.86/139.86 ((![X158]: 138.86/139.86 (in( 138.86/139.86 X158,X156) => 138.86/139.86 (~ 138.86/139.86 X157( 138.86/139.86 X158)))) => 138.86/139.86 (~ 138.86/139.86 (?[X159]: 138.86/139.86 (X157( 138.86/139.86 X159) & 138.86/139.86 in( 138.86/139.86 X159,X156)))))) => 138.86/139.86 ((![X160, 138.86/139.86 X161:($i > $o)]: 138.86/139.86 ((~ 138.86/139.86 (?[X162]: 138.86/139.86 ( 138.86/139.86 X161( 138.86/139.86 X162) & 138.86/139.86 in( 138.86/139.86 X162,X160)))) => 138.86/139.86 (![X163]: 138.86/139.86 (in( 138.86/139.86 X163,X160) => 138.86/139.86 (~ 138.86/139.86 X161( 138.86/139.86 X163)))))) => 138.86/139.86 ((![X164, 138.86/139.86 X165:( 138.86/139.86 $i > $o)]: 138.86/139.86 ((?[X166]: 138.86/139.86 (( 138.86/139.86 ~ 138.86/139.86 X165( 138.86/139.86 X166)) & 138.86/139.86 in( 138.86/139.86 X166,X164))) => 138.86/139.86 (~ 138.86/139.86 (![X167]: 138.86/139.86 (in( 138.86/139.86 X167,X164) => 138.86/139.86 X165( 138.86/139.86 X167)))))) => 138.86/139.86 ((![X168:$o]: 138.86/139.86 (X168 => 138.86/139.86 in(emptyset, 138.86/139.86 prop2set( 138.86/139.86 X168)))) => 138.86/139.86 ((![X169:$o]: 138.86/139.86 (X169 => 138.86/139.86 set2prop( 138.86/139.86 prop2set( 138.86/139.86 X169)))) => 138.86/139.86 ((![X170, 138.86/139.86 X171:( 138.86/139.86 $i > $o)]: 138.86/139.86 ((~ 138.86/139.86 ( 138.86/139.86 ?[X172]: 138.86/139.86 (X171( 138.86/139.86 X172) & 138.86/139.86 in( 138.86/139.86 X172,X170)))) => 138.86/139.86 (![X173]: 138.86/139.86 (in( 138.86/139.86 X173,X170) => 138.86/139.86 (~ 138.86/139.86 X171( 138.86/139.86 X173)))))) => 138.86/139.86 ((![X174, 138.86/139.86 X175:( 138.86/139.86 $i > $o)]: 138.86/139.86 (( 138.86/139.86 ~ 138.86/139.86 ( 138.86/139.86 ![X176]: 138.86/139.86 (in( 138.86/139.86 X176,X174) => 138.86/139.86 X175( 138.86/139.86 X176)))) => 138.86/139.86 ( 138.86/139.86 ?[X177]: 138.86/139.86 (( 138.86/139.86 ~ 138.86/139.86 X175( 138.86/139.86 X177)) & 138.86/139.86 in( 138.86/139.86 X177,X174))))) => 138.86/139.86 ((![X178:( 138.86/139.86 $i > $o)]: 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ?[X179]: 138.86/139.86 (( 138.86/139.86 ![X180]: 138.86/139.86 (X178( 138.86/139.86 X180) => 138.86/139.86 (X179 = 138.86/139.86 X180))) & 138.86/139.86 X178( 138.86/139.86 X179))) => 138.86/139.86 ( 138.86/139.86 ?[X181]: 138.86/139.86 (( 138.86/139.86 ![X182]: 138.86/139.86 (X178( 138.86/139.86 X182) => 138.86/139.86 (X181 = 138.86/139.86 X182))) & 138.86/139.86 X178( 138.86/139.86 X181))))) => 138.86/139.86 ((![X183:( 138.86/139.86 $i > $o)]: 138.86/139.86 (( 138.86/139.86 ?[X184]: 138.86/139.86 X183( 138.86/139.86 X184)) => 138.86/139.86 (( 138.86/139.86 ![X185, 138.86/139.86 X186]: 138.86/139.86 (X183( 138.86/139.86 X185) => 138.86/139.86 (X183( 138.86/139.86 X186) => 138.86/139.86 (X185 = 138.86/139.86 X186)))) => 138.86/139.86 (?[X187]: 138.86/139.86 (( 138.86/139.86 ![X188]: 138.86/139.86 (X183( 138.86/139.86 X188) => 138.86/139.86 (X187 = 138.86/139.86 X188))) & 138.86/139.86 X183( 138.86/139.86 X187)))))) => 138.86/139.86 ((![X189:( 138.86/139.86 $i > $o)]: 138.86/139.86 (( 138.86/139.86 ?[X190]: 138.86/139.86 (![X191]: 138.86/139.86 (X189( 138.86/139.86 X191) <=> 138.86/139.86 (X191 = 138.86/139.86 X190)))) => 138.86/139.86 (?[X192]: 138.86/139.86 (( 138.86/139.86 ![X193]: 138.86/139.86 (X189( 138.86/139.86 X193) => 138.86/139.86 (X192 = 138.86/139.86 X193))) & 138.86/139.86 X189( 138.86/139.86 X192))))) => 138.86/139.86 (( 138.86/139.86 ![X194, 138.86/139.86 X195]: 138.86/139.86 (( 138.86/139.86 X194 = 138.86/139.86 X195) => 138.86/139.86 (![X196, 138.86/139.86 X197]: 138.86/139.86 (( 138.86/139.86 X196 = 138.86/139.86 X197) => 138.86/139.86 (in( 138.86/139.86 X196,X194) => 138.86/139.86 in( 138.86/139.86 X197,X195)))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X198, 138.86/139.86 X199]: 138.86/139.86 (( 138.86/139.86 X198 = 138.86/139.86 X199) => 138.86/139.86 (![X200, 138.86/139.86 X201]: 138.86/139.86 (( 138.86/139.86 X200 = 138.86/139.86 X201) => 138.86/139.86 (in( 138.86/139.86 X200,X198) <=> 138.86/139.86 in( 138.86/139.86 X201,X199)))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X202:( 138.86/139.86 $i > $o)]: 138.86/139.86 (( 138.86/139.86 ?[X203]: 138.86/139.86 (( 138.86/139.86 ![X204]: 138.86/139.86 (X202( 138.86/139.86 X204) => 138.86/139.86 (X203 = 138.86/139.86 X204))) & 138.86/139.86 X202( 138.86/139.86 X203))) => 138.86/139.86 (![X205, 138.86/139.86 X206]: 138.86/139.86 (X202( 138.86/139.86 X205) => 138.86/139.86 (X202( 138.86/139.86 X206) => 138.86/139.86 (X205 = 138.86/139.86 X206)))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X207:( 138.86/139.86 $i > $o), 138.86/139.86 X208:( 138.86/139.86 $i > $o)]: 138.86/139.86 (( 138.86/139.86 ![X209, 138.86/139.86 X210]: 138.86/139.86 (( 138.86/139.86 X209 = 138.86/139.86 X210) => 138.86/139.86 (X207( 138.86/139.86 X209) <=> 138.86/139.86 X208( 138.86/139.86 X210)))) => 138.86/139.86 (( 138.86/139.86 ?[X211]: 138.86/139.86 zip_tseitin5( 138.86/139.86 X211,X207)) <=> 138.86/139.86 (?[X213]: 138.86/139.86 zip_tseitin5( 138.86/139.86 X213,X208))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 emptyset = 138.86/139.86 emptyset) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X215, 138.86/139.86 X216]: 138.86/139.86 (( 138.86/139.86 X215 = 138.86/139.86 X216) => 138.86/139.86 (![X217, 138.86/139.86 X218]: 138.86/139.86 (( 138.86/139.86 X217 = 138.86/139.86 X218) => 138.86/139.86 (setadjoin( 138.86/139.86 X215,X217) = 138.86/139.86 setadjoin( 138.86/139.86 X216,X218)))))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X219, 138.86/139.86 X220]: 138.86/139.86 (( 138.86/139.86 X219 = 138.86/139.86 X220) => 138.86/139.86 (powerset( 138.86/139.86 X219) = 138.86/139.86 powerset( 138.86/139.86 X220)))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X221, 138.86/139.86 X222]: 138.86/139.86 (( 138.86/139.86 X221 = 138.86/139.86 X222) => 138.86/139.86 (setunion( 138.86/139.86 X221) = 138.86/139.86 setunion( 138.86/139.86 X222)))) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 omega = 138.86/139.86 omega) => 138.86/139.86 ( 138.86/139.86 ( 138.86/139.86 ![X223:( 138.86/139.86 $i > $o)]: 138.86/139.86 (( 138.86/139.86 ?[X224]: 138.86/139.86 (( 138.86/139.86 ![X225]: 138.86/139.86 (X223( 138.86/139.86 X225) => 138.86/139.86 (X224 = 138.86/139.86 X225))) & 138.86/139.86 X223( 138.86/139.86 X224))) => 138.86/139.86 (![X226, 138.86/139.86 X227]: 138.86/139.86 (X223( 138.86/139.87 X226) => 138.86/139.87 (X223( 138.86/139.87 X227) => 138.86/139.87 (X226 = 138.86/139.87 X227)))))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X228:( 138.86/139.87 $i > $o), 138.86/139.87 X229:( 138.86/139.87 $i > $o)]: 138.86/139.87 (( 138.86/139.87 ![X230, 138.86/139.87 X231]: 138.86/139.87 (( 138.86/139.87 X230 = 138.86/139.87 X231) => 138.86/139.87 (X228( 138.86/139.87 X230) <=> 138.86/139.87 X229( 138.86/139.87 X231)))) => 138.86/139.87 (( 138.86/139.87 ?[X232]: 138.86/139.87 (( 138.86/139.87 ![X233]: 138.86/139.87 (X228( 138.86/139.87 X233) => 138.86/139.87 (X232 = 138.86/139.87 X233))) & 138.86/139.87 X228( 138.86/139.87 X232))) => 138.86/139.87 (( 138.86/139.87 ?[X234]: 138.86/139.87 (( 138.86/139.87 ![X235]: 138.86/139.87 (X229( 138.86/139.87 X235) => 138.86/139.87 (X234 = 138.86/139.87 X235))) & 138.86/139.87 X229( 138.86/139.87 X234))) => 138.86/139.87 (descr( 138.86/139.87 ^[V_9]: 138.86/139.87 X228(V_9)) = 138.86/139.87 descr( 138.86/139.87 ^[V_10]: 138.86/139.87 X229( 138.86/139.87 V_10))))))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X236, 138.86/139.87 X237]: 138.86/139.87 (( 138.86/139.87 X236 = 138.86/139.87 X237) => 138.86/139.87 (![X238:( 138.86/139.87 $i > $o), 138.86/139.87 X239:( 138.86/139.87 $i > $o)]: 138.86/139.87 (( 138.86/139.87 ![X240]: 138.86/139.87 (in( 138.86/139.87 X240,X236) => 138.86/139.87 (![X241]: 138.86/139.87 (in( 138.86/139.87 X241,X237) => 138.86/139.87 (( 138.86/139.87 X240 = 138.86/139.87 X241) => 138.86/139.87 (X238( 138.86/139.87 X240) <=> 138.86/139.87 X239( 138.86/139.87 X241))))))) => 138.86/139.87 (dsetconstr( 138.86/139.87 X236, 138.86/139.87 ^[V_11]: 138.86/139.87 X238( 138.86/139.87 V_11)) = 138.86/139.87 dsetconstr( 138.86/139.87 X237, 138.86/139.87 ^[V_12]: 138.86/139.87 X239( 138.86/139.87 V_12))))))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X242, 138.86/139.87 X243]: 138.86/139.87 (( 138.86/139.87 ![X244]: 138.86/139.87 (in( 138.86/139.87 X244,X242) => 138.86/139.87 in( 138.86/139.87 X244,X243))) => 138.86/139.87 subset( 138.86/139.87 X242,X243))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X245, 138.86/139.87 X246]: 138.86/139.87 (( 138.86/139.87 X245 = 138.86/139.87 X246) => 138.86/139.87 subset( 138.86/139.87 X246,X245))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X247, 138.86/139.87 X248]: 138.86/139.87 (( 138.86/139.87 X247 = 138.86/139.87 X248) => 138.86/139.87 subset( 138.86/139.87 X247,X248))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X249, 138.86/139.87 X250]: 138.86/139.87 (( 138.86/139.87 ![X251]: 138.86/139.87 (in( 138.86/139.87 X251,X249) => 138.86/139.87 in( 138.86/139.87 X251,X250))) => 138.86/139.87 subset( 138.86/139.87 X249,X250))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X252]: 138.86/139.87 subset( 138.86/139.87 emptyset, 138.86/139.87 X252)) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X253, 138.86/139.87 X254,X255]: 138.86/139.87 (subset( 138.86/139.87 X253,X254) => 138.86/139.87 (in( 138.86/139.87 X255,X253) => 138.86/139.87 in( 138.86/139.87 X255,X254)))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X256, 138.86/139.87 X257,X258]: 138.86/139.87 (subset( 138.86/139.87 X256,X257) => 138.86/139.87 (( 138.86/139.87 ~ 138.86/139.87 in( 138.86/139.87 X258,X257)) => 138.86/139.87 (~ 138.86/139.87 in( 138.86/139.87 X258,X256))))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X259, 138.86/139.87 X260,X261]: 138.86/139.87 (in( 138.86/139.87 X261,X259) => 138.86/139.87 (( 138.86/139.87 ~ 138.86/139.87 in( 138.86/139.87 X261,X260)) => 138.86/139.87 (~ 138.86/139.87 subset( 138.86/139.87 X259,X260))))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X262, 138.86/139.87 X263]: 138.86/139.87 (( 138.86/139.87 ~ 138.86/139.87 subset( 138.86/139.87 X262,X263)) => 138.86/139.87 (X262 != 138.86/139.87 X263))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X264, 138.86/139.87 X265,X266]: 138.86/139.87 (in( 138.86/139.87 X266,X264) => 138.86/139.87 (( 138.86/139.87 ~ 138.86/139.87 in( 138.86/139.87 X266,X265)) => 138.86/139.87 (X264 != 138.86/139.87 X265)))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X267]: 138.86/139.87 subset( 138.86/139.87 X267,X267)) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X268, 138.86/139.87 X269,X270]: 138.86/139.87 (subset( 138.86/139.87 X268,X269) => 138.86/139.87 (subset( 138.86/139.87 X269,X270) => 138.86/139.87 subset( 138.86/139.87 X268,X270)))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X271, 138.86/139.87 X272]: 138.86/139.87 subset( 138.86/139.87 X272, 138.86/139.87 setadjoin( 138.86/139.87 X271,X272))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X273, 138.86/139.87 X274,X275]: 138.86/139.87 (subset( 138.86/139.87 X273,X275) => 138.86/139.87 subset( 138.86/139.87 X273, 138.86/139.87 setadjoin( 138.86/139.87 X274,X275)))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X276, 138.86/139.87 X277]: 138.86/139.87 (subset( 138.86/139.87 X276,X277) => 138.86/139.87 in( 138.86/139.87 X276, 138.86/139.87 powerset( 138.86/139.87 X277)))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X278, 138.86/139.87 X279]: 138.86/139.87 (subset( 138.86/139.87 X278,X279) => 138.86/139.87 (subset( 138.86/139.87 X279,X278) => 138.86/139.87 (X278 = 138.86/139.87 X279)))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X280]: 138.86/139.87 (subset( 138.86/139.87 X280, 138.86/139.87 emptyset) => 138.86/139.87 (X280 = 138.86/139.87 emptyset))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X281, 138.86/139.87 X282]: 138.86/139.87 (subset( 138.86/139.87 X282,X281) => 138.86/139.87 in( 138.86/139.87 X282, 138.86/139.87 powerset( 138.86/139.87 X281)))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X283, 138.86/139.87 X284]: 138.86/139.87 (in( 138.86/139.87 X284, 138.86/139.87 powerset( 138.86/139.87 X283)) => 138.86/139.87 subset( 138.86/139.87 X284,X283))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X285]: 138.86/139.87 in( 138.86/139.87 X285, 138.86/139.87 powerset( 138.86/139.87 X285))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X286, 138.86/139.87 X287]: 138.86/139.87 (subset( 138.86/139.87 X286,X287) => 138.86/139.87 subset( 138.86/139.87 powerset( 138.86/139.87 X286), 138.86/139.87 powerset( 138.86/139.87 X287)))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X288, 138.86/139.87 X289:( 138.86/139.87 $i > $o)]: 138.86/139.87 in( 138.86/139.87 dsetconstr( 138.86/139.87 X288, 138.86/139.87 ^[V_13]: 138.86/139.87 X289( 138.86/139.87 V_13)), 138.86/139.87 powerset( 138.86/139.87 X288))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X290, 138.86/139.87 X291:( 138.86/139.87 $i > $o)]: 138.86/139.87 subset( 138.86/139.87 dsetconstr( 138.86/139.87 X290, 138.86/139.87 ^[V_14]: 138.86/139.87 X291( 138.86/139.87 V_14)), 138.86/139.87 X290)) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X292, 138.86/139.87 X293,X294]: 138.86/139.87 (in( 138.86/139.87 X294,X292) => 138.86/139.87 in( 138.86/139.87 X294, 138.86/139.87 binunion( 138.86/139.87 X292,X293)))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X295, 138.86/139.87 X296]: 138.86/139.87 in( 138.86/139.87 X296, 138.86/139.87 setadjoin( 138.86/139.87 X295, 138.86/139.87 setadjoin( 138.86/139.87 X296, 138.86/139.87 emptyset)))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X297, 138.86/139.87 X298,X299]: 138.86/139.87 (in( 138.86/139.87 X299,X298) => 138.86/139.87 in( 138.86/139.87 X299, 138.86/139.87 binunion( 138.86/139.87 X297,X298)))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X300, 138.86/139.87 X301, 138.86/139.87 X302, 138.86/139.87 X303:$o]: 138.86/139.87 (in( 138.86/139.87 X302, 138.86/139.87 binunion( 138.86/139.87 X300,X301)) => 138.86/139.87 (( 138.86/139.87 in( 138.86/139.87 X302,X300) => 138.86/139.87 X303) => 138.86/139.87 (( 138.86/139.87 in( 138.86/139.87 X302,X301) => 138.86/139.87 X303) => 138.86/139.87 X303)))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X304, 138.86/139.87 X305,X306]: 138.86/139.87 (in( 138.86/139.87 X306, 138.86/139.87 binunion( 138.86/139.87 X304,X305)) => 138.86/139.87 (in( 138.86/139.87 X306,X305) | 138.86/139.87 in( 138.86/139.87 X306,X304)))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X307, 138.86/139.87 X308]: 138.86/139.87 subset( 138.86/139.87 X307, 138.86/139.87 binunion( 138.86/139.87 X307,X308))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X309, 138.86/139.87 X310]: 138.86/139.87 subset( 138.86/139.87 X310, 138.86/139.87 binunion( 138.86/139.87 X309,X310))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X311, 138.86/139.87 X312,X313]: 138.86/139.87 (in( 138.86/139.87 X313,X311) => 138.86/139.87 (in( 138.86/139.87 X313,X312) => 138.86/139.87 in( 138.86/139.87 X313, 138.86/139.87 binintersect( 138.86/139.87 X311,X312))))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X314, 138.86/139.87 X315,X316]: 138.86/139.87 (subset( 138.86/139.87 X316,X314) => 138.86/139.87 (subset( 138.86/139.87 X316,X315) => 138.86/139.87 subset( 138.86/139.87 X316, 138.86/139.87 binintersect( 138.86/139.87 X314,X315))))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X317, 138.86/139.87 X318,X319]: 138.86/139.87 (in( 138.86/139.87 X319, 138.86/139.87 binintersect( 138.86/139.87 X317,X318)) => 138.86/139.87 in( 138.86/139.87 X319,X317))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X320, 138.86/139.87 X321]: 138.86/139.87 subset( 138.86/139.87 binintersect( 138.86/139.87 X320,X321), 138.86/139.87 X320)) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X322, 138.86/139.87 X323]: 138.86/139.87 (subset( 138.86/139.87 X322,X323) => 138.86/139.87 (binintersect( 138.86/139.87 X322,X323) = 138.86/139.87 X322))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X324, 138.86/139.87 X325]: 138.86/139.87 (( 138.86/139.87 binintersect( 138.86/139.87 X324,X325) = 138.86/139.87 X325) => 138.86/139.87 subset( 138.86/139.87 X325,X324))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X326, 138.86/139.87 X327,X328]: 138.86/139.87 (in( 138.86/139.87 X328, 138.86/139.87 binintersect( 138.86/139.87 X326,X327)) => 138.86/139.87 in( 138.86/139.87 X328,X327))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X329, 138.86/139.87 X330]: 138.86/139.87 (( 138.86/139.87 ~ 138.86/139.87 ( 138.86/139.87 ?[X331]: 138.86/139.87 (in( 138.86/139.87 X331,X330) & 138.86/139.87 in( 138.86/139.87 X331,X329)))) => 138.86/139.87 (binintersect( 138.86/139.87 X329,X330) = 138.86/139.87 emptyset))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X332, 138.86/139.87 X333]: 138.86/139.87 subset( 138.86/139.87 binintersect( 138.86/139.87 X332,X333), 138.86/139.87 X333)) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X334, 138.86/139.87 X335]: 138.86/139.87 (subset( 138.86/139.87 X335,X334) => 138.86/139.87 (binintersect( 138.86/139.87 X334,X335) = 138.86/139.87 X335))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X336, 138.86/139.87 X337]: 138.86/139.87 (( 138.86/139.87 binintersect( 138.86/139.87 X336,X337) = 138.86/139.87 X336) => 138.86/139.87 subset( 138.86/139.87 X336,X337))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X338, 138.86/139.87 X339,X340]: 138.86/139.87 (binintersect( 138.86/139.87 X338, 138.86/139.87 binunion( 138.86/139.87 X339,X340)) = 138.86/139.87 binunion( 138.86/139.87 binintersect( 138.86/139.87 X338,X339), 138.86/139.87 binintersect( 138.86/139.87 X338,X340)))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X341, 138.86/139.87 X342,X343]: 138.86/139.87 (in( 138.86/139.87 X343,X341) => 138.86/139.87 (( 138.86/139.87 ~ 138.86/139.87 in( 138.86/139.87 X343,X342)) => 138.86/139.87 in( 138.86/139.87 X343, 138.86/139.87 setminus( 138.86/139.87 X341,X342))))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X344, 138.86/139.87 X345,X346]: 138.86/139.87 (in( 138.86/139.87 X346, 138.86/139.87 setminus( 138.86/139.87 X344,X345)) => 138.86/139.87 in( 138.86/139.87 X346,X344))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X347, 138.86/139.87 X348,X349]: 138.86/139.87 (in( 138.86/139.87 X349, 138.86/139.87 setminus( 138.86/139.87 X347,X348)) => 138.86/139.87 (~ 138.86/139.87 in( 138.86/139.87 X349,X348)))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X350, 138.86/139.87 X351]: 138.86/139.87 (subset( 138.86/139.87 X350,X351) => 138.86/139.87 (setminus( 138.86/139.87 X350,X351) = 138.86/139.87 emptyset))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X352, 138.86/139.87 X353,X354]: 138.86/139.87 (( 138.86/139.87 ~ 138.86/139.87 in( 138.86/139.87 X354, 138.86/139.87 setminus( 138.86/139.87 X352,X353))) => 138.86/139.87 (in( 138.86/139.87 X354,X352) => 138.86/139.87 in( 138.86/139.87 X354,X353)))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X355, 138.86/139.87 X356,X357]: 138.86/139.87 (( 138.86/139.87 ~ 138.86/139.87 in( 138.86/139.87 X357, 138.86/139.87 setminus( 138.86/139.87 X355,X356))) => 138.86/139.87 (( 138.86/139.87 ~ 138.86/139.87 in( 138.86/139.87 X357,X356)) => 138.86/139.87 (~ 138.86/139.87 in( 138.86/139.87 X357,X355))))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X358, 138.86/139.87 X359,X360]: 138.86/139.87 (( 138.86/139.87 ~ 138.86/139.87 in( 138.86/139.87 X360,X358)) => 138.86/139.87 (~ 138.86/139.87 in( 138.86/139.87 X360, 138.86/139.87 setminus( 138.86/139.87 X358,X359))))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X361, 138.86/139.87 X362,X363]: 138.86/139.87 (in( 138.86/139.87 X363,X362) => 138.86/139.87 (~ 138.86/139.87 in( 138.86/139.87 X363, 138.86/139.87 setminus( 138.86/139.87 X361,X362))))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X364, 138.86/139.87 X365]: 138.86/139.87 subset( 138.86/139.87 setminus( 138.86/139.87 X364,X365), 138.86/139.87 X364)) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X366, 138.86/139.87 X367]: 138.86/139.87 (( 138.86/139.87 setminus( 138.86/139.87 X366,X367) = 138.86/139.87 emptyset) => 138.86/139.87 subset( 138.86/139.87 X366,X367))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X368, 138.86/139.87 X369,X370]: 138.86/139.87 (in( 138.86/139.87 X370, 138.86/139.87 symdiff( 138.86/139.87 X368,X369)) => 138.86/139.87 (![X371:$o]: 138.86/139.87 (( 138.86/139.87 in( 138.86/139.87 X370,X368) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ~ 138.86/139.87 in( 138.86/139.87 X370,X369)) => 138.86/139.87 X371)) => 138.86/139.87 (( 138.86/139.87 ( 138.86/139.87 ~ 138.86/139.87 in( 138.86/139.87 X370,X368)) => 138.86/139.87 ( 138.86/139.87 in( 138.86/139.87 X370,X369) => 138.86/139.87 X371)) => 138.86/139.87 X371))))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X372, 138.86/139.87 X373,X374]: 138.86/139.87 (in( 138.86/139.87 X374,X372) => 138.86/139.87 (( 138.86/139.87 ~ 138.86/139.87 in( 138.86/139.87 X374,X373)) => 138.86/139.87 in( 138.86/139.87 X374, 138.86/139.87 symdiff( 138.86/139.87 X372,X373))))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X375, 138.86/139.87 X376,X377]: 138.86/139.87 (( 138.86/139.87 ~ 138.86/139.87 in( 138.86/139.87 X377,X375)) => 138.86/139.87 (in( 138.86/139.87 X377,X376) => 138.86/139.87 in( 138.86/139.87 X377, 138.86/139.87 symdiff( 138.86/139.87 X375,X376))))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X378, 138.86/139.87 X379,X380]: 138.86/139.87 (in( 138.86/139.87 X380,X378) => 138.86/139.87 (in( 138.86/139.87 X380,X379) => 138.86/139.87 (~ 138.86/139.87 in( 138.86/139.87 X380, 138.86/139.87 symdiff( 138.86/139.87 X378,X379)))))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X381, 138.86/139.87 X382,X383]: 138.86/139.87 (( 138.86/139.87 ~ 138.86/139.87 in( 138.86/139.87 X383,X381)) => 138.86/139.87 (( 138.86/139.87 ~ 138.86/139.87 in( 138.86/139.87 X383,X382)) => 138.86/139.87 (~ 138.86/139.87 in( 138.86/139.87 X383, 138.86/139.87 symdiff( 138.86/139.87 X381,X382)))))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X384, 138.86/139.87 X385]: 138.86/139.87 in( 138.86/139.87 X385, 138.86/139.87 setadjoin( 138.86/139.87 X384, 138.86/139.87 setadjoin( 138.86/139.87 X385, 138.86/139.87 emptyset)))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X386, 138.86/139.87 X387]: 138.86/139.87 in( 138.86/139.87 X386, 138.86/139.87 setunion( 138.86/139.87 setadjoin( 138.86/139.87 setadjoin( 138.86/139.87 X386, 138.86/139.87 emptyset), 138.86/139.87 setadjoin( 138.86/139.87 setadjoin( 138.86/139.87 X386, 138.86/139.87 setadjoin( 138.86/139.87 X387, 138.86/139.87 emptyset)), 138.86/139.87 emptyset))))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X388, 138.86/139.87 X389]: 138.86/139.87 in( 138.86/139.87 X389, 138.86/139.87 setunion( 138.86/139.87 setadjoin( 138.86/139.87 setadjoin( 138.86/139.87 X388, 138.86/139.87 emptyset), 138.86/139.87 setadjoin( 138.86/139.87 setadjoin( 138.86/139.87 X388, 138.86/139.87 setadjoin( 138.86/139.87 X389, 138.86/139.87 emptyset)), 138.86/139.87 emptyset))))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X390, 138.86/139.87 X391]: 138.86/139.87 iskpair( 138.86/139.87 setadjoin( 138.86/139.87 setadjoin( 138.86/139.87 X390, 138.86/139.87 emptyset), 138.86/139.87 setadjoin( 138.86/139.87 setadjoin( 138.86/139.87 X390, 138.86/139.87 setadjoin( 138.86/139.87 X391, 138.86/139.87 emptyset)), 138.86/139.87 emptyset)))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X392, 138.86/139.87 X393]: 138.86/139.87 iskpair( 138.86/139.87 kpair( 138.86/139.87 X392,X393))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X394, 138.86/139.87 X395]: 138.86/139.87 (in( 138.86/139.87 X395,X394) => 138.86/139.87 subset( 138.86/139.87 setadjoin( 138.86/139.87 X395, 138.86/139.87 emptyset), 138.86/139.87 X394))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X396, 138.86/139.87 X397]: 138.86/139.87 (in( 138.86/139.87 X397,X396) => 138.86/139.87 in( 138.86/139.87 setadjoin( 138.86/139.87 X397, 138.86/139.87 emptyset), 138.86/139.87 powerset( 138.86/139.87 X396)))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X398, 138.86/139.87 X399,X400]: 138.86/139.87 (in( 138.86/139.87 X400,X398) => 138.86/139.87 in( 138.86/139.87 setadjoin( 138.86/139.87 X400, 138.86/139.87 emptyset), 138.86/139.87 powerset( 138.86/139.87 binunion( 138.86/139.87 X398,X399))))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X401, 138.86/139.87 X402,X403]: 138.86/139.87 (in( 138.86/139.87 X403, 138.86/139.87 setadjoin( 138.86/139.87 X401, 138.86/139.87 setadjoin( 138.86/139.87 X402, 138.86/139.87 emptyset))) => 138.86/139.87 (( 138.86/139.87 X403 = 138.86/139.87 X402) | 138.86/139.87 (X403 = 138.86/139.87 X401)))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X404, 138.86/139.87 X405,X406]: 138.86/139.87 (in( 138.86/139.87 X406,X404) => 138.86/139.87 (![X407]: 138.86/139.87 (in( 138.86/139.87 X407,X405) => 138.86/139.87 subset( 138.86/139.87 setadjoin( 138.86/139.87 X406, 138.86/139.87 setadjoin( 138.86/139.87 X407, 138.86/139.87 emptyset)), 138.86/139.87 binunion( 138.86/139.87 X404,X405)))))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X408, 138.86/139.87 X409,X410]: 138.86/139.87 (in( 138.86/139.87 X410,X408) => 138.86/139.87 (![X411]: 138.86/139.87 (in( 138.86/139.87 X411,X409) => 138.86/139.87 in( 138.86/139.87 setadjoin( 138.86/139.87 X410, 138.86/139.87 setadjoin( 138.86/139.87 X411, 138.86/139.87 emptyset)), 138.86/139.87 powerset( 138.86/139.87 binunion( 138.86/139.87 X408,X409))))))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X412, 138.86/139.87 X413,X414]: 138.86/139.87 (in( 138.86/139.87 X414,X412) => 138.86/139.87 (![X415]: 138.86/139.87 (in( 138.86/139.87 X415,X413) => 138.86/139.87 subset( 138.86/139.87 setadjoin( 138.86/139.87 setadjoin( 138.86/139.87 X414, 138.86/139.87 emptyset), 138.86/139.87 setadjoin( 138.86/139.87 setadjoin( 138.86/139.87 X414, 138.86/139.87 setadjoin( 138.86/139.87 X415, 138.86/139.87 emptyset)), 138.86/139.87 emptyset)), 138.86/139.87 powerset( 138.86/139.87 binunion( 138.86/139.87 X412,X413))))))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X416, 138.86/139.87 X417,X418]: 138.86/139.87 (in( 138.86/139.87 X418,X416) => 138.86/139.87 (![X419]: 138.86/139.87 (in( 138.86/139.87 X419,X417) => 138.86/139.87 in( 138.86/139.87 setadjoin( 138.86/139.87 setadjoin( 138.86/139.87 X418, 138.86/139.87 emptyset), 138.86/139.87 setadjoin( 138.86/139.87 setadjoin( 138.86/139.87 X418, 138.86/139.87 setadjoin( 138.86/139.87 X419, 138.86/139.87 emptyset)), 138.86/139.87 emptyset)), 138.86/139.87 powerset( 138.86/139.87 powerset( 138.86/139.87 binunion( 138.86/139.87 X416,X417)))))))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X420, 138.86/139.87 X421,X422]: 138.86/139.87 (in( 138.86/139.87 X422,X420) => 138.86/139.87 (![X423]: 138.86/139.87 (in( 138.86/139.87 X423,X421) => 138.86/139.87 in( 138.86/139.87 kpair( 138.86/139.87 X422,X423), 138.86/139.87 powerset( 138.86/139.87 powerset( 138.86/139.87 binunion( 138.86/139.87 X420,X421)))))))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X424, 138.86/139.87 X425,X426]: 138.86/139.87 (in( 138.86/139.87 X426,X424) => 138.86/139.87 (![X427]: 138.86/139.87 (in( 138.86/139.87 X427,X425) => 138.86/139.87 in( 138.86/139.87 kpair( 138.86/139.87 X426,X427), 138.86/139.87 cartprod( 138.86/139.87 X424,X425)))))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X428, 138.86/139.87 X429,X430]: 138.86/139.87 (in( 138.86/139.87 X430, 138.86/139.87 cartprod( 138.86/139.87 X428,X429)) => 138.86/139.87 (?[X431]: 138.86/139.87 (( 138.86/139.87 ?[X432]: 138.86/139.87 (( 138.86/139.87 X430 = 138.86/139.87 kpair( 138.86/139.87 X431,X432)) & 138.86/139.87 in( 138.86/139.87 X432,X429))) & 138.86/139.87 in( 138.86/139.87 X431,X428))))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X433, 138.86/139.87 X434,X435]: 138.86/139.87 (in( 138.86/139.87 X435, 138.86/139.87 cartprod( 138.86/139.87 X433,X434)) => 138.86/139.87 iskpair( 138.86/139.87 X435))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X436, 138.86/139.87 X437]: 138.86/139.87 (in( 138.86/139.87 X437, 138.86/139.87 setunion( 138.86/139.87 X436)) => 138.86/139.87 (?[X438]: 138.86/139.87 (in( 138.86/139.87 X437,X438) & 138.86/139.87 in( 138.86/139.87 X438,X436))))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X439]: 138.86/139.87 subset( 138.86/139.87 setunion( 138.86/139.87 setadjoin( 138.86/139.87 X439, 138.86/139.87 emptyset)), 138.86/139.87 X439)) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X440]: 138.86/139.87 subset( 138.86/139.87 X440, 138.86/139.87 setunion( 138.86/139.87 setadjoin( 138.86/139.87 X440, 138.86/139.87 emptyset)))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X441]: 138.86/139.87 (setunion( 138.86/139.87 setadjoin( 138.86/139.87 X441, 138.86/139.87 emptyset)) = 138.86/139.87 X441)) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X442, 138.86/139.87 X443:( 138.86/139.87 $i > $o)]: 138.86/139.87 (( 138.86/139.87 ![X444]: 138.86/139.87 (in( 138.86/139.87 X444,X442) => 138.86/139.87 (![X445]: 138.86/139.87 (in( 138.86/139.87 X445,X442) => 138.86/139.87 (X443( 138.86/139.87 X444) => 138.86/139.87 (X443( 138.86/139.87 X445) => 138.86/139.87 (X444 = 138.86/139.87 X445))))))) => 138.86/139.87 (( 138.86/139.87 ?[X446]: 138.86/139.87 (X443( 138.86/139.87 X446) & 138.86/139.87 in( 138.86/139.87 X446,X442))) => 138.86/139.87 (?[X447]: 138.86/139.87 (( 138.86/139.87 dsetconstr( 138.86/139.87 X442, 138.86/139.87 ^[V_15]: 138.86/139.87 X443( 138.86/139.87 V_15)) = 138.86/139.87 setadjoin( 138.86/139.87 X447, 138.86/139.87 emptyset)) & 138.86/139.87 in( 138.86/139.87 X447, 138.86/139.87 dsetconstr( 138.86/139.87 X442, 138.86/139.87 ^[V_16]: 138.86/139.87 X443( 138.86/139.87 V_16)))))))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X448, 138.86/139.87 X449:( 138.86/139.87 $i > $o)]: 138.86/139.87 (( 138.86/139.87 ?[X450]: 138.86/139.87 (( 138.86/139.87 dsetconstr( 138.86/139.87 X448, 138.86/139.87 ^[V_17]: 138.86/139.87 X449( 138.86/139.87 V_17)) = 138.86/139.87 setadjoin( 138.86/139.87 X450, 138.86/139.87 emptyset)) & 138.86/139.87 in( 138.86/139.87 X450, 138.86/139.87 dsetconstr( 138.86/139.87 X448, 138.86/139.87 ^[V_18]: 138.86/139.87 X449( 138.86/139.87 V_18))))) => 138.86/139.87 (?[X451]: 138.86/139.87 (X449( 138.86/139.87 X451) & 138.86/139.87 in( 138.86/139.87 X451,X448))))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X452, 138.86/139.87 X453:( 138.86/139.87 $i > $o), 138.86/139.87 X454]: 138.86/139.87 (in( 138.86/139.87 X454,X452) => 138.86/139.87 (X453( 138.86/139.87 X454) => 138.86/139.87 (( 138.86/139.87 ![X455]: 138.86/139.87 (in( 138.86/139.87 X455,X452) => 138.86/139.87 (X453( 138.86/139.87 X455) => 138.86/139.87 (X455 = 138.86/139.87 X454)))) => 138.86/139.87 (?[X456]: 138.86/139.87 (( 138.86/139.87 dsetconstr( 138.86/139.87 X452, 138.86/139.87 ^[V_19]: 138.86/139.87 X453( 138.86/139.87 V_19)) = 138.86/139.87 setadjoin( 138.86/139.87 X456, 138.86/139.87 emptyset)) & 138.86/139.87 in( 138.86/139.87 X456, 138.86/139.87 dsetconstr( 138.86/139.87 X452, 138.86/139.87 ^[V_20]: 138.86/139.87 X453( 138.86/139.87 V_20))))))))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X457, 138.86/139.87 X458:( 138.86/139.87 $i > $o)]: 138.86/139.87 (( 138.86/139.87 ![X459]: 138.86/139.87 (in( 138.86/139.87 X459,X457) => 138.86/139.87 (![X460]: 138.86/139.87 (in( 138.86/139.87 X460,X457) => 138.86/139.87 (X458( 138.86/139.87 X459) => 138.86/139.87 (X458( 138.86/139.87 X460) => 138.86/139.87 (X459 = 138.86/139.87 X460))))))) => 138.86/139.87 (( 138.86/139.87 ?[X461]: 138.86/139.87 (X458( 138.86/139.87 X461) & 138.86/139.87 in( 138.86/139.87 X461,X457))) => 138.86/139.87 (?[X462]: 138.86/139.87 (( 138.86/139.87 dsetconstr( 138.86/139.87 X457, 138.86/139.87 ^[V_21]: 138.86/139.87 X458( 138.86/139.87 V_21)) = 138.86/139.87 setadjoin( 138.86/139.87 X462, 138.86/139.87 emptyset)) & 138.86/139.87 in( 138.86/139.87 X462, 138.86/139.87 dsetconstr( 138.86/139.87 X457, 138.86/139.87 ^[V_22]: 138.86/139.87 X458( 138.86/139.87 V_22)))))))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X463, 138.86/139.87 X464]: 138.86/139.87 (( 138.86/139.87 setadjoin( 138.86/139.87 X463, 138.86/139.87 emptyset) = 138.86/139.87 setadjoin( 138.86/139.87 X464, 138.86/139.87 emptyset)) => 138.86/139.87 (X463 = 138.86/139.87 X464))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X465, 138.86/139.87 X466,X467]: 138.86/139.87 (in( 138.86/139.87 setadjoin( 138.86/139.87 X467, 138.86/139.87 emptyset), 138.86/139.87 setadjoin( 138.86/139.87 setadjoin( 138.86/139.87 X465, 138.86/139.87 emptyset), 138.86/139.87 setadjoin( 138.86/139.87 setadjoin( 138.86/139.87 X465, 138.86/139.87 setadjoin( 138.86/139.87 X466, 138.86/139.87 emptyset)), 138.86/139.87 emptyset))) => 138.86/139.87 (X465 = 138.86/139.87 X467))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X468]: 138.86/139.87 (iskpair( 138.86/139.87 X468) => 138.86/139.87 (?[X469]: 138.86/139.87 (( 138.86/139.87 dsetconstr( 138.86/139.87 setunion( 138.86/139.87 X468), 138.86/139.87 ^[V_23]: 138.86/139.87 in( 138.86/139.87 setadjoin( 138.86/139.87 V_23, 138.86/139.87 emptyset), 138.86/139.87 X468)) = 138.86/139.87 setadjoin( 138.86/139.87 X469, 138.86/139.87 emptyset)) & 138.86/139.87 in( 138.86/139.87 X469, 138.86/139.87 dsetconstr( 138.86/139.87 setunion( 138.86/139.87 X468), 138.86/139.87 ^[V_24]: 138.86/139.87 in( 138.86/139.87 setadjoin( 138.86/139.87 V_24, 138.86/139.87 emptyset), 138.86/139.87 X468))))))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X470]: 138.86/139.87 (( 138.86/139.87 ?[X471]: 138.86/139.87 (( 138.86/139.87 X470 = 138.86/139.87 setadjoin( 138.86/139.87 X471, 138.86/139.87 emptyset)) & 138.86/139.87 in( 138.86/139.87 X471,X470))) => 138.86/139.87 in( 138.86/139.87 setunion( 138.86/139.87 X470), 138.86/139.87 X470))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X472, 138.86/139.87 X473]: 138.86/139.87 (kfst( 138.86/139.87 kpair( 138.86/139.87 X472,X473)) = 138.86/139.87 X472)) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X474, 138.86/139.87 X475,X476]: 138.86/139.87 (in( 138.86/139.87 X476, 138.86/139.87 cartprod( 138.86/139.87 X474,X475)) => 138.86/139.87 in( 138.86/139.87 kfst( 138.86/139.87 X476), 138.86/139.87 X474))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X477, 138.86/139.87 X478, 138.86/139.87 X479,X480]: 138.86/139.87 (( 138.86/139.87 setadjoin( 138.86/139.87 setadjoin( 138.86/139.87 X477, 138.86/139.87 emptyset), 138.86/139.87 setadjoin( 138.86/139.87 setadjoin( 138.86/139.87 X477, 138.86/139.87 setadjoin( 138.86/139.87 X478, 138.86/139.87 emptyset)), 138.86/139.87 emptyset)) = 138.86/139.87 setadjoin( 138.86/139.87 setadjoin( 138.86/139.87 X479, 138.86/139.87 emptyset), 138.86/139.87 setadjoin( 138.86/139.87 setadjoin( 138.86/139.87 X479, 138.86/139.87 setadjoin( 138.86/139.87 X480, 138.86/139.87 emptyset)), 138.86/139.87 emptyset))) => 138.86/139.87 (X477 = 138.86/139.87 X479))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X481, 138.86/139.87 X482, 138.86/139.87 X483,X484]: 138.86/139.87 (( 138.86/139.87 kpair( 138.86/139.87 X481,X482) = 138.86/139.87 kpair( 138.86/139.87 X483,X484)) => 138.86/139.87 (X481 = 138.86/139.87 X483))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X485, 138.86/139.87 X486]: 138.86/139.87 (( 138.86/139.87 X485 = 138.86/139.87 X486) => 138.86/139.87 (setadjoin( 138.86/139.87 X485, 138.86/139.87 setadjoin( 138.86/139.87 X486, 138.86/139.87 emptyset)) = 138.86/139.87 setadjoin( 138.86/139.87 X485, 138.86/139.87 emptyset)))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X487, 138.86/139.87 X488]: 138.86/139.87 (( 138.86/139.87 X487 = 138.86/139.87 X488) => 138.86/139.87 (setadjoin( 138.86/139.87 setadjoin( 138.86/139.87 X487, 138.86/139.87 emptyset), 138.86/139.87 setadjoin( 138.86/139.87 setadjoin( 138.86/139.87 X487, 138.86/139.87 setadjoin( 138.86/139.87 X488, 138.86/139.87 emptyset)), 138.86/139.87 emptyset)) = 138.86/139.87 setadjoin( 138.86/139.87 setadjoin( 138.86/139.87 X487, 138.86/139.87 emptyset), 138.86/139.87 emptyset)))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X489, 138.86/139.87 X490, 138.86/139.87 X491,X492]: 138.86/139.87 (( 138.86/139.87 setadjoin( 138.86/139.87 setadjoin( 138.86/139.87 X489, 138.86/139.87 emptyset), 138.86/139.87 setadjoin( 138.86/139.87 setadjoin( 138.86/139.87 X489, 138.86/139.87 setadjoin( 138.86/139.87 X490, 138.86/139.87 emptyset)), 138.86/139.87 emptyset)) = 138.86/139.87 setadjoin( 138.86/139.87 setadjoin( 138.86/139.87 X491, 138.86/139.87 emptyset), 138.86/139.87 setadjoin( 138.86/139.87 setadjoin( 138.86/139.87 X491, 138.86/139.87 setadjoin( 138.86/139.87 X492, 138.86/139.87 emptyset)), 138.86/139.87 emptyset))) => 138.86/139.87 (( 138.86/139.87 X491 = 138.86/139.87 X492) => 138.86/139.87 (X490 = 138.86/139.87 X492)))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X493, 138.86/139.87 X494,X495]: 138.86/139.87 (( 138.86/139.87 setadjoin( 138.86/139.87 X493, 138.86/139.87 setadjoin( 138.86/139.87 X494, 138.86/139.87 emptyset)) = 138.86/139.87 setadjoin( 138.86/139.87 X495, 138.86/139.87 emptyset)) => 138.86/139.87 (X493 = 138.86/139.87 X494))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X496, 138.86/139.87 X497, 138.86/139.87 X498,X499]: 138.86/139.87 (( 138.86/139.87 setadjoin( 138.86/139.87 setadjoin( 138.86/139.87 X496, 138.86/139.87 emptyset), 138.86/139.87 setadjoin( 138.86/139.87 setadjoin( 138.86/139.87 X496, 138.86/139.87 setadjoin( 138.86/139.87 X497, 138.86/139.87 emptyset)), 138.86/139.87 emptyset)) = 138.86/139.87 setadjoin( 138.86/139.87 setadjoin( 138.86/139.87 X498, 138.86/139.87 emptyset), 138.86/139.87 setadjoin( 138.86/139.87 setadjoin( 138.86/139.87 X498, 138.86/139.87 setadjoin( 138.86/139.87 X499, 138.86/139.87 emptyset)), 138.86/139.87 emptyset))) => 138.86/139.87 (X497 = 138.86/139.87 X499))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X500, 138.86/139.87 X501, 138.86/139.87 X502,X503]: 138.86/139.87 (( 138.86/139.87 kpair( 138.86/139.87 X500,X501) = 138.86/139.87 kpair( 138.86/139.87 X502,X503)) => 138.86/139.87 (X501 = 138.86/139.87 X503))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X504]: 138.86/139.87 (iskpair( 138.86/139.87 X504) => 138.86/139.87 (?[X505]: 138.86/139.87 (( 138.86/139.87 dsetconstr( 138.86/139.87 setunion( 138.86/139.87 X504), 138.86/139.87 ^[V_25]: 138.86/139.87 (X504 = 138.86/139.87 kpair( 138.86/139.87 kfst( 138.86/139.87 X504), 138.86/139.87 V_25))) = 138.86/139.87 setadjoin( 138.86/139.87 X505, 138.86/139.87 emptyset)) & 138.86/139.87 in( 138.86/139.87 X505, 138.86/139.87 dsetconstr( 138.86/139.87 setunion( 138.86/139.87 X504), 138.86/139.87 ^[V_26]: 138.86/139.87 (X504 = 138.86/139.87 kpair( 138.86/139.87 kfst( 138.86/139.87 X504), 138.86/139.87 V_26)))))))) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X506, 138.86/139.87 X507]: 138.86/139.87 (ksnd( 138.86/139.87 kpair( 138.86/139.87 X506,X507)) = 138.86/139.87 X507)) => 138.86/139.87 ( 138.86/139.87 ( 138.86/139.87 ![X508]: 138.86/139.87 (iskpair( 138.86/139.87 X508) => 138.86/139.87 (kpair( 138.86/139.87 kfst( 138.86/139.87 X508), 138.86/139.87 ksnd( 138.86/139.87 X508)) = 138.86/139.87 X508))) => 138.86/139.87 ( 138.86/139.87 ![X509, 138.86/139.87 X510,X511]: 138.86/139.87 (in( 138.86/139.87 X511, 138.86/139.87 cartprod( 138.86/139.87 X509,X510)) => 138.86/139.87 in( 138.86/139.87 ksnd( 138.86/139.87 X511), 138.86/139.87 X510))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 138.86/139.87 tff('178', plain, in(sk_X511_, cartprod(sk_X509_, sk_X510_)), 138.86/139.87 inference('cnf', [status(esa)], [zf_stmt_14])). 138.86/139.87 tff('179', plain, 138.86/139.87 ![X777, X778, X779]: 138.86/139.87 (in(sk_X432_(X777, X778, X779), X778) 138.86/139.87 | ~ in(X777, cartprod(X779, X778))), 138.86/139.87 inference('cnf', [status(esa)], [zf_stmt_14])). 138.86/139.87 tff('180', plain, in(sk_X432_(sk_X511_, sk_X510_, sk_X509_), sk_X510_), 138.86/139.87 inference('sup-', [status(thm)], ['178', '179'])). 138.86/139.87 tff('181', plain, 138.86/139.87 ![X777, X778, X779]: 138.86/139.87 (X777 = kpair(sk_X431_(X777, X778, X779), sk_X432_(X777, X778, X779)) 138.86/139.87 | ~ in(X777, cartprod(X779, X778))), 138.86/139.87 inference('cnf', [status(esa)], [zf_stmt_14])). 138.86/139.87 tff('182', plain, 138.86/139.87 sk_X511_ 138.86/139.87 = kpair(sk_X431_(sk_X511_, sk_X510_, sk_X509_), 138.86/139.87 sk_X432_(sk_X511_, sk_X510_, sk_X509_)), 138.86/139.87 inference('sup-', [status(thm)], ['178', '181'])). 138.86/139.87 tff('183', plain, ![X745, X746]: ksnd(kpair(X746, X745)) = X745, 138.86/139.87 inference('cnf', [status(esa)], [zf_stmt_14])). 138.86/139.87 tff('184', plain, ksnd(sk_X511_) = sk_X432_(sk_X511_, sk_X510_, sk_X509_), 138.86/139.87 inference('sup+', [status(thm)], ['182', '183'])). 138.86/139.87 tff('185', plain, ~ in(ksnd(sk_X511_), sk_X510_), 138.86/139.87 inference('cnf', [status(esa)], [zf_stmt_14])). 138.86/139.87 tff('186', plain, ~ in(sk_X432_(sk_X511_, sk_X510_, sk_X509_), sk_X510_), 138.86/139.87 inference('sup-', [status(thm)], ['184', '185'])). 138.86/139.87 tff('187', plain, $false, inference('sup-', [status(thm)], ['180', '186'])). 138.86/139.87 138.86/139.87 % SZS output end Refutation 138.86/139.87 % Zipperpin 1.5 exiting 138.86/139.87 EOF