0.10/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.10/0.11 % Command : run_portfolio.sh /export/starexec/sandbox2/benchmark/theBenchmark.p /export/starexec/sandbox2/tmp/tmp.OTxaIPlOIe 0.10/0.30 % Computer : n021.cluster.edu 0.10/0.30 % Model : x86_64 x86_64 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.30 % Memory : 8042.1875MB 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.30 % CPULimit : 180 0.10/0.30 % DateTime : Thu Aug 29 14:31:04 EDT 2019 0.10/0.30 % CPUTime : 108.90/109.58 % Running portfolio for 180 s 108.90/109.58 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 108.90/109.58 % TempDir : /export/starexec/sandbox2/tmp/tmp.OTxaIPlOIe 108.90/109.58 % Recognized as monomorphic HO. 108.90/109.58 % Running /export/starexec/sandbox2/solver/bin/competitive.sh for 18 108.90/109.58 % Running /export/starexec/sandbox2/solver/bin/competitive.2.sh for 13 108.90/109.58 % Running /export/starexec/sandbox2/solver/bin/competitive.3.sh for 3 108.90/109.58 % Running /export/starexec/sandbox2/solver/bin/pragmatic.rudimentary.sh for 28 108.90/109.58 % Running /export/starexec/sandbox2/solver/bin/pragmatic.rudimentary.1.sh for 12 108.90/109.58 % Running /export/starexec/sandbox2/solver/bin/pragmatic.rudimentary.2.sh for 7 108.90/109.58 % Running /export/starexec/sandbox2/solver/bin/pragmatic.shallow.sh for 3 108.90/109.58 % Running /export/starexec/sandbox2/solver/bin/pragmatic.shallow.1.sh for 15 108.90/109.58 % Running /export/starexec/sandbox2/solver/bin/pragmatic.shallow.2.sh for 12 108.90/109.58 % Running /export/starexec/sandbox2/solver/bin/pragmatic.ll.e.sh for 19 108.90/109.58 % Solved by: pragmatic.ll.e.sh 108.90/109.58 % Running : timeout 16 /export/starexec/sandbox2/solver/bin/eprover-ho /export/starexec/sandbox2/tmp/tmp.OTxaIPlOIe/e_inputa5498b --cpu-limit=14 --auto-schedule -s -p. 108.90/109.58 % done 457 iterations in 10.148s 108.90/109.58 % hashcons stats for terms: size 4096, num 21740, sum length 35339, buckets: small 3, median 7, big 22 108.90/109.58 % proof state stats: {active 190, passive 6041, simpl 0} 108.90/109.58 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 108.90/109.58 % SZS output start Refutation 108.90/109.58 tff(powersetI1, axiom, powersetI1 <=> 108.90/109.58 (![A,B]: (subset(B,A) => in(B,powerset(A))))). 108.90/109.58 tff('0', plain, 108.90/109.58 powersetI1 = (![X2,X3]: (subset(X3,X2) => in(X3,powerset(X2)))), 108.90/109.58 define([status(thm)])). 108.90/109.58 tff(subsetemptysetimpeq, axiom, subsetemptysetimpeq <=> 108.90/109.58 (![A]: (subset(A,emptyset) => (A = emptyset)))). 108.90/109.58 tff('1', plain, 108.90/109.58 subsetemptysetimpeq = (![X2]: (subset(X2,emptyset) => (X2 = emptyset))), 108.90/109.58 define([status(thm)])). 108.90/109.58 tff(setextsub, axiom, setextsub <=> 108.90/109.58 (![A,B]: (subset(A,B) => (subset(B,A) => (A = B))))). 108.90/109.58 tff('2', plain, 108.90/109.58 setextsub = (![X2,X3]: (subset(X2,X3) => (subset(X3,X2) => (X2 = X3)))), 108.90/109.58 define([status(thm)])). 108.90/109.58 tff(subset2powerset, axiom, subset2powerset <=> 108.90/109.58 (![A,B]: (subset(A,B) => in(A,powerset(B))))). 108.90/109.58 tff('3', plain, 108.90/109.58 subset2powerset = (![X2,X3]: (subset(X2,X3) => in(X2,powerset(X3)))), 108.90/109.58 define([status(thm)])). 108.90/109.58 tff(setadjoinSub2, axiom, setadjoinSub2 <=> 108.90/109.58 (![A,Xx,B]: (subset(A,B) => subset(A,setadjoin(Xx,B))))). 108.90/109.58 tff('4', plain, 108.90/109.58 setadjoinSub2 = 108.90/109.58 (![X2,X3,X4]: (subset(X2,X4) => subset(X2,setadjoin(X3,X4)))), 108.90/109.58 define([status(thm)])). 108.90/109.58 tff(setadjoinSub, axiom, setadjoinSub <=> 108.90/109.58 (![Xx,A]: subset(A,setadjoin(Xx,A)))). 108.90/109.58 tff('5', plain, setadjoinSub = (![X2,X3]: subset(X3,setadjoin(X2,X3))), 108.90/109.58 define([status(thm)])). 108.90/109.58 tff(subsetTrans, axiom, subsetTrans <=> 108.90/109.58 (![A,B,C]: (subset(A,B) => (subset(B,C) => subset(A,C))))). 108.90/109.58 tff('6', plain, 108.90/109.58 subsetTrans = 108.90/109.58 (![X2,X3,X4]: (subset(X2,X3) => (subset(X3,X4) => subset(X2,X4)))), 108.90/109.58 define([status(thm)])). 108.90/109.58 tff(subsetRefl, axiom, subsetRefl <=> (![A]: subset(A,A))). 108.90/109.58 tff('7', plain, subsetRefl = (![X2]: subset(X2,X2)), define([status(thm)])). 108.90/109.58 tff(notequalI2, axiom, notequalI2 <=> 108.90/109.58 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => (A != B))))). 108.90/109.58 tff('8', plain, 108.90/109.58 notequalI2 = (![X2,X3,X4]: (in(X4,X2) => ((~in(X4,X3)) => (X2 != X3)))), 108.90/109.58 define([status(thm)])). 108.90/109.58 tff(notequalI1, axiom, notequalI1 <=> (![A,B]: ((~subset(A,B)) => (A != B)))). 108.90/109.58 tff('9', plain, notequalI1 = (![X2,X3]: ((~subset(X2,X3)) => (X2 != X3))), 108.90/109.58 define([status(thm)])). 108.90/109.58 tff(notsubsetI, axiom, notsubsetI <=> 108.90/109.58 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => (~subset(A,B)))))). 108.90/109.58 tff('10', plain, 108.90/109.58 notsubsetI = 108.90/109.58 (![X2,X3,X4]: (in(X4,X2) => ((~in(X4,X3)) => (~subset(X2,X3))))), 108.90/109.58 define([status(thm)])). 108.90/109.58 tff(subsetE2, axiom, subsetE2 <=> 108.90/109.58 (![A,B,Xx]: (subset(A,B) => ((~in(Xx,B)) => (~in(Xx,A)))))). 108.90/109.58 tff('11', plain, 108.90/109.58 subsetE2 = 108.90/109.58 (![X2,X3,X4]: (subset(X2,X3) => ((~in(X4,X3)) => (~in(X4,X2))))), 108.90/109.58 define([status(thm)])). 108.90/109.58 tff(subsetE, axiom, subsetE <=> 108.90/109.58 (![A,B,Xx]: (subset(A,B) => (in(Xx,A) => in(Xx,B))))). 108.90/109.58 tff('12', plain, 108.90/109.58 subsetE = (![X2,X3,X4]: (subset(X2,X3) => (in(X4,X2) => in(X4,X3)))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(emptysetsubset, axiom, emptysetsubset <=> (![A]: subset(emptyset,A))). 108.90/109.59 tff('13', plain, emptysetsubset = (![X2]: subset(emptyset,X2)), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(subsetI2, axiom, subsetI2 <=> 108.90/109.59 (![A,B]: ((![Xx]: (in(Xx,A) => in(Xx,B))) => subset(A,B)))). 108.90/109.59 tff('14', plain, 108.90/109.59 subsetI2 = 108.90/109.59 (![X2,X3]: ((![X4]: (in(X4,X2) => in(X4,X3))) => subset(X2,X3))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(eqimpsubset1, axiom, eqimpsubset1 <=> (![A,B]: ((A = B) => subset(A,B)))). 108.90/109.59 tff('15', plain, eqimpsubset1 = (![X2,X3]: ((X2 = X3) => subset(X2,X3))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(eqimpsubset2, axiom, eqimpsubset2 <=> (![A,B]: ((A = B) => subset(B,A)))). 108.90/109.59 tff('16', plain, eqimpsubset2 = (![X2,X3]: ((X2 = X3) => subset(X3,X2))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(subsetI1, axiom, subsetI1 <=> 108.90/109.59 (![A,B]: ((![Xx]: (in(Xx,A) => in(Xx,B))) => subset(A,B)))). 108.90/109.59 tff('17', plain, 108.90/109.59 subsetI1 = 108.90/109.59 (![X2,X3]: ((![X4]: (in(X4,X2) => in(X4,X3))) => subset(X2,X3))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(dsetconstr__Cong, axiom, dsetconstr__Cong <=> 108.90/109.59 (![A,B]: 108.90/109.59 ((A = B) => 108.90/109.59 (![Xphi:($i > $o),Xpsi:($i > $o)]: 108.90/109.59 ((![Xx]: 108.90/109.59 (in(Xx,A) => 108.90/109.59 (![Xy]: (in(Xy,B) => ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy))))))) => 108.90/109.59 (dsetconstr(A,^[Xx]: Xphi(Xx)) = dsetconstr(B,^[Xx]: Xpsi(Xx)))))))). 108.90/109.59 tff('18', plain, 108.90/109.59 dsetconstr__Cong = 108.90/109.59 (![X2,X3]: 108.90/109.59 ((X2 = X3) => 108.90/109.59 (![X4:($i > $o),X5:($i > $o)]: 108.90/109.59 ((![X6]: 108.90/109.59 (in(X6,X2) => 108.90/109.59 (![X7]: (in(X7,X3) => ((X6 = X7) => (X4(X6) <=> X5(X7))))))) => 108.90/109.59 (dsetconstr(X2,^[V_1]: X4(V_1)) = dsetconstr(X3,^[V_2]: X5(V_2))))))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(descr__Cong, axiom, descr__Cong <=> 108.90/109.59 (![Xphi:($i > $o),Xpsi:($i > $o)]: 108.90/109.59 ((![Xx,Xy]: ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy)))) => 108.90/109.59 (exu(^[Xx]: Xphi(Xx)) => 108.90/109.59 (exu(^[Xx]: Xpsi(Xx)) => 108.90/109.59 (descr(^[Xx]: Xphi(Xx)) = descr(^[Xx]: Xpsi(Xx)))))))). 108.90/109.59 tff('19', plain, 108.90/109.59 descr__Cong = 108.90/109.59 (![X2:($i > $o),X3:($i > $o)]: 108.90/109.59 ((![X4,X5]: ((X4 = X5) => (X2(X4) <=> X3(X5)))) => 108.90/109.59 (exu(^[V_1]: X2(V_1)) => 108.90/109.59 (exu(^[V_2]: X3(V_2)) => 108.90/109.59 (descr(^[V_3]: X2(V_3)) = descr(^[V_4]: X3(V_4))))))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(exuEu, axiom, exuEu <=> 108.90/109.59 (![Xphi:($i > $o)]: 108.90/109.59 (exu(^[Xx]: Xphi(Xx)) => 108.90/109.59 (![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))). 108.90/109.59 tff('20', plain, 108.90/109.59 exuEu = 108.90/109.59 (![X2:($i > $o)]: 108.90/109.59 (exu(^[V_1]: X2(V_1)) => (![X3,X4]: (X2(X3) => (X2(X4) => (X3 = X4)))))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(omega__Cong, axiom, omega__Cong <=> (omega = omega)). 108.90/109.59 tff('21', plain, omega__Cong = (omega = omega), define([status(thm)])). 108.90/109.59 tff(setunion__Cong, axiom, setunion__Cong <=> 108.90/109.59 (![A,B]: ((A = B) => (setunion(A) = setunion(B))))). 108.90/109.59 tff('22', plain, 108.90/109.59 setunion__Cong = (![X2,X3]: ((X2 = X3) => (setunion(X2) = setunion(X3)))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(powerset__Cong, axiom, powerset__Cong <=> 108.90/109.59 (![A,B]: ((A = B) => (powerset(A) = powerset(B))))). 108.90/109.59 tff('23', plain, 108.90/109.59 powerset__Cong = (![X2,X3]: ((X2 = X3) => (powerset(X2) = powerset(X3)))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(setadjoin__Cong, axiom, setadjoin__Cong <=> 108.90/109.59 (![Xx,Xy]: 108.90/109.59 ((Xx = Xy) => 108.90/109.59 (![Xz,Xu]: ((Xz = Xu) => (setadjoin(Xx,Xz) = setadjoin(Xy,Xu))))))). 108.90/109.59 tff('24', plain, 108.90/109.59 setadjoin__Cong = 108.90/109.59 (![X2,X3]: 108.90/109.59 ((X2 = X3) => 108.90/109.59 (![X4,X5]: ((X4 = X5) => (setadjoin(X2,X4) = setadjoin(X3,X5)))))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(emptyset__Cong, axiom, emptyset__Cong <=> (emptyset = emptyset)). 108.90/109.59 tff('25', plain, emptyset__Cong = (emptyset = emptyset), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(exu__Cong, axiom, exu__Cong <=> 108.90/109.59 (![Xphi:($i > $o),Xpsi:($i > $o)]: 108.90/109.59 ((![Xx,Xy]: ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy)))) => 108.90/109.59 (exu(^[Xx]: Xphi(Xx)) <=> exu(^[Xx]: Xpsi(Xx)))))). 108.90/109.59 tff('26', plain, 108.90/109.59 exu__Cong = 108.90/109.59 (![X2:($i > $o),X3:($i > $o)]: 108.90/109.59 ((![X4,X5]: ((X4 = X5) => (X2(X4) <=> X3(X5)))) => 108.90/109.59 (exu(^[V_1]: X2(V_1)) <=> exu(^[V_2]: X3(V_2))))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(exuE3u, axiom, exuE3u <=> 108.90/109.59 (![Xphi:($i > $o)]: 108.90/109.59 (exu(^[Xx]: Xphi(Xx)) => 108.90/109.59 (![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))). 108.90/109.59 tff('27', plain, 108.90/109.59 exuE3u = 108.90/109.59 (![X2:($i > $o)]: 108.90/109.59 (exu(^[V_1]: X2(V_1)) => (![X3,X4]: (X2(X3) => (X2(X4) => (X3 = X4)))))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(in__Cong, axiom, in__Cong <=> 108.90/109.59 (![A,B]: ((A = B) => (![Xx,Xy]: ((Xx = Xy) => (in(Xx,A) <=> in(Xy,B))))))). 108.90/109.59 tff('28', plain, 108.90/109.59 in__Cong = 108.90/109.59 (![X2,X3]: 108.90/109.59 ((X2 = X3) => (![X4,X5]: ((X4 = X5) => (in(X4,X2) <=> in(X5,X3)))))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(inCongP, axiom, inCongP <=> 108.90/109.59 (![A,B]: ((A = B) => (![Xx,Xy]: ((Xx = Xy) => (in(Xx,A) => in(Xy,B))))))). 108.90/109.59 tff('29', plain, 108.90/109.59 inCongP = 108.90/109.59 (![X2,X3]: 108.90/109.59 ((X2 = X3) => (![X4,X5]: ((X4 = X5) => (in(X4,X2) => in(X5,X3)))))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(exuI2, axiom, exuI2 <=> 108.90/109.59 (![Xphi:($i > $o)]: 108.90/109.59 ((?[Xx]: (![Xy]: (Xphi(Xy) <=> (Xy = Xx)))) => exu(^[Xx]: Xphi(Xx))))). 108.90/109.59 tff('30', plain, 108.90/109.59 exuI2 = 108.90/109.59 (![X2:($i > $o)]: 108.90/109.59 ((?[X3]: (![X4]: (X2(X4) <=> (X4 = X3)))) => exu(^[V_1]: X2(V_1)))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(exuI3, axiom, exuI3 <=> 108.90/109.59 (![Xphi:($i > $o)]: 108.90/109.59 ((?[Xx]: Xphi(Xx)) => 108.90/109.59 ((![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy)))) => 108.90/109.59 exu(^[Xx]: Xphi(Xx)))))). 108.90/109.59 tff('31', plain, 108.90/109.59 exuI3 = 108.90/109.59 (![X2:($i > $o)]: 108.90/109.59 ((?[X3]: X2(X3)) => 108.90/109.59 ((![X4,X5]: (X2(X4) => (X2(X5) => (X4 = X5)))) => 108.90/109.59 exu(^[V_1]: X2(V_1))))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(exuI1, axiom, exuI1 <=> 108.90/109.59 (![Xphi:($i > $o)]: 108.90/109.59 ((?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx))) => 108.90/109.59 exu(^[Xx]: Xphi(Xx))))). 108.90/109.59 tff('32', plain, 108.90/109.59 exuI1 = 108.90/109.59 (![X2:($i > $o)]: 108.90/109.59 ((?[X3]: ((![X4]: (X2(X4) => (X3 = X4))) & X2(X3))) => 108.90/109.59 exu(^[V_1]: X2(V_1)))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(notdallE, axiom, notdallE <=> 108.90/109.59 (![A,Xphi:($i > $o)]: 108.90/109.59 ((~(![Xx]: (in(Xx,A) => Xphi(Xx)))) => (?[Xx]: ((~Xphi(Xx)) & in(Xx,A)))))). 108.90/109.59 tff('33', plain, 108.90/109.59 notdallE = 108.90/109.59 (![X2,X3:($i > $o)]: 108.90/109.59 ((~(![X4]: (in(X4,X2) => X3(X4)))) => (?[X5]: ((~X3(X5)) & in(X5,X2))))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(notdexE, axiom, notdexE <=> 108.90/109.59 (![A,Xphi:($i > $o)]: 108.90/109.59 ((~(?[Xx]: (Xphi(Xx) & in(Xx,A)))) => (![Xx]: (in(Xx,A) => (~Xphi(Xx))))))). 108.90/109.59 tff('34', plain, 108.90/109.59 notdexE = 108.90/109.59 (![X2,X3:($i > $o)]: 108.90/109.59 ((~(?[X4]: (X3(X4) & in(X4,X2)))) => (![X5]: (in(X5,X2) => (~X3(X5)))))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(prop2set2propI, axiom, prop2set2propI <=> 108.90/109.59 (![Xphi:$o]: (Xphi => set2prop(prop2set(Xphi))))). 108.90/109.59 tff('35', plain, prop2set2propI = (![X2:$o]: (X2 => set2prop(prop2set(X2)))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(prop2setI, axiom, prop2setI <=> 108.90/109.59 (![Xphi:$o]: (Xphi => in(emptyset,prop2set(Xphi))))). 108.90/109.59 tff('36', plain, prop2setI = (![X2:$o]: (X2 => in(emptyset,prop2set(X2)))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(quantDeMorgan4, axiom, quantDeMorgan4 <=> 108.90/109.59 (![A,Xphi:($i > $o)]: 108.90/109.59 ((?[Xx]: ((~Xphi(Xx)) & in(Xx,A))) => (~(![Xx]: (in(Xx,A) => Xphi(Xx))))))). 108.90/109.59 tff('37', plain, 108.90/109.59 quantDeMorgan4 = 108.90/109.59 (![X2,X3:($i > $o)]: 108.90/109.59 ((?[X4]: ((~X3(X4)) & in(X4,X2))) => (~(![X5]: (in(X5,X2) => X3(X5)))))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(quantDeMorgan3, axiom, quantDeMorgan3 <=> 108.90/109.59 (![A,Xphi:($i > $o)]: 108.90/109.59 ((~(?[Xx]: (Xphi(Xx) & in(Xx,A)))) => (![Xx]: (in(Xx,A) => (~Xphi(Xx))))))). 108.90/109.59 tff('38', plain, 108.90/109.59 quantDeMorgan3 = 108.90/109.59 (![X2,X3:($i > $o)]: 108.90/109.59 ((~(?[X4]: (X3(X4) & in(X4,X2)))) => (![X5]: (in(X5,X2) => (~X3(X5)))))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(quantDeMorgan2, axiom, quantDeMorgan2 <=> 108.90/109.59 (![A,Xphi:($i > $o)]: 108.90/109.59 ((![Xx]: (in(Xx,A) => (~Xphi(Xx)))) => (~(?[Xx]: (Xphi(Xx) & in(Xx,A))))))). 108.90/109.59 tff('39', plain, 108.90/109.59 quantDeMorgan2 = 108.90/109.59 (![X2,X3:($i > $o)]: 108.90/109.59 ((![X4]: (in(X4,X2) => (~X3(X4)))) => (~(?[X5]: (X3(X5) & in(X5,X2)))))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(quantDeMorgan1, axiom, quantDeMorgan1 <=> 108.90/109.59 (![A,Xphi:($i > $o)]: 108.90/109.59 ((~(![Xx]: (in(Xx,A) => Xphi(Xx)))) => (?[Xx]: ((~Xphi(Xx)) & in(Xx,A)))))). 108.90/109.59 tff('40', plain, 108.90/109.59 quantDeMorgan1 = 108.90/109.59 (![X2,X3:($i > $o)]: 108.90/109.59 ((~(![X4]: (in(X4,X2) => X3(X4)))) => (?[X5]: ((~X3(X5)) & in(X5,X2))))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(vacuousDall, axiom, vacuousDall <=> 108.90/109.59 (![Xphi:($i > $o),Xx]: (in(Xx,emptyset) => Xphi(Xx)))). 108.90/109.59 tff('41', plain, 108.90/109.59 vacuousDall = (![X2:($i > $o),X3]: (in(X3,emptyset) => X2(X3))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(emptyE1, axiom, emptyE1 <=> 108.90/109.59 (![A,Xphi:($i > $o)]: 108.90/109.59 ((?[Xx]: (Xphi(Xx) & in(Xx,A))) => 108.90/109.59 ((dsetconstr(A,^[Xx]: Xphi(Xx)) = emptyset) => $false)))). 108.90/109.59 tff('42', plain, 108.90/109.59 emptyE1 = 108.90/109.59 (![X2,X3:($i > $o)]: 108.90/109.59 ((?[X4]: (X3(X4) & in(X4,X2))) => 108.90/109.59 ((dsetconstr(X2,^[V_1]: X3(V_1)) = emptyset) => $false))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(upairsetIR, axiom, upairsetIR <=> 108.90/109.59 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 108.90/109.59 tff('43', plain, 108.90/109.59 upairsetIR = (![X2,X3]: in(X3,setadjoin(X2,setadjoin(X3,emptyset)))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(upairsetIL, axiom, upairsetIL <=> 108.90/109.59 (![Xx,Xy]: in(Xx,setadjoin(Xx,setadjoin(Xy,emptyset))))). 108.90/109.59 tff('44', plain, 108.90/109.59 upairsetIL = (![X2,X3]: in(X2,setadjoin(X2,setadjoin(X3,emptyset)))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(upairsetE, axiom, upairsetE <=> 108.90/109.59 (![Xx,Xy,Xz]: 108.90/109.59 (in(Xz,setadjoin(Xx,setadjoin(Xy,emptyset))) => ((Xz = Xy) | (Xz = Xx))))). 108.90/109.59 tff('45', plain, 108.90/109.59 upairsetE = 108.90/109.59 (![X2,X3,X4]: 108.90/109.59 (in(X4,setadjoin(X2,setadjoin(X3,emptyset))) => 108.90/109.59 ((X4 = X3) | (X4 = X2)))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(singletonsswitch, axiom, singletonsswitch <=> 108.90/109.59 (![Xx,Xy]: (in(Xx,setadjoin(Xy,emptyset)) => in(Xy,setadjoin(Xx,emptyset))))). 108.90/109.59 tff('46', plain, 108.90/109.59 singletonsswitch = 108.90/109.59 (![X2,X3]: 108.90/109.59 (in(X2,setadjoin(X3,emptyset)) => in(X3,setadjoin(X2,emptyset)))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(eqinunit, axiom, eqinunit <=> 108.90/109.59 (![Xx,Xy]: ((Xx = Xy) => in(Xx,setadjoin(Xy,emptyset))))). 108.90/109.59 tff('47', plain, 108.90/109.59 eqinunit = (![X2,X3]: ((X2 = X3) => in(X2,setadjoin(X3,emptyset)))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(notinsingleton, axiom, notinsingleton <=> 108.90/109.59 (![Xx,Xy]: ((Xx != Xy) => (~in(Xy,setadjoin(Xx,emptyset)))))). 108.90/109.59 tff('48', plain, 108.90/109.59 notinsingleton = 108.90/109.59 (![X2,X3]: ((X2 != X3) => (~in(X3,setadjoin(X2,emptyset))))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(uniqinunit, axiom, uniqinunit <=> 108.90/109.59 (![Xx,Xy]: (in(Xx,setadjoin(Xy,emptyset)) => (Xx = Xy)))). 108.90/109.59 tff('49', plain, 108.90/109.59 uniqinunit = (![X2,X3]: (in(X2,setadjoin(X3,emptyset)) => (X2 = X3))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(nonemptyImpWitness, axiom, nonemptyImpWitness <=> 108.90/109.59 (![A]: (nonempty(A) => (?[Xx]: (in(Xx,A)))))). 108.90/109.59 tff('50', plain, 108.90/109.59 nonemptyImpWitness = (![X2]: (nonempty(X2) => (?[X3]: (in(X3,X2))))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(exuE2, axiom, exuE2 <=> 108.90/109.59 (![Xphi:($i > $o)]: 108.90/109.59 (exu(^[Xx]: Xphi(Xx)) => (?[Xx]: (![Xy]: (Xphi(Xy) <=> (Xy = Xx))))))). 108.90/109.59 tff('51', plain, 108.90/109.59 exuE2 = 108.90/109.59 (![X2:($i > $o)]: 108.90/109.59 (exu(^[V_1]: X2(V_1)) => (?[X3]: (![X4]: (X2(X4) <=> (X4 = X3)))))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(subPowSU, axiom, subPowSU <=> 108.90/109.59 (![A,Xx]: (in(Xx,A) => in(Xx,powerset(setunion(A)))))). 108.90/109.59 tff('52', plain, 108.90/109.59 subPowSU = (![X2,X3]: (in(X3,X2) => in(X3,powerset(setunion(X2))))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(setunionE, axiom, setunionE <=> 108.90/109.59 (![A,Xx]: 108.90/109.59 (in(Xx,setunion(A)) => 108.90/109.59 (![Xphi:$o]: ((![B]: (in(Xx,B) => (in(B,A) => Xphi))) => Xphi))))). 108.90/109.59 tff('53', plain, 108.90/109.59 setunionE = 108.90/109.59 (![X2,X3]: 108.90/109.59 (in(X3,setunion(X2)) => 108.90/109.59 (![X4:$o]: ((![X5]: (in(X3,X5) => (in(X5,X2) => X4))) => X4)))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(setunionI, axiom, setunionI <=> 108.90/109.59 (![A,Xx,B]: (in(Xx,B) => (in(B,A) => in(Xx,setunion(A)))))). 108.90/109.59 tff('54', plain, 108.90/109.59 setunionI = 108.90/109.59 (![X2,X3,X4]: (in(X3,X4) => (in(X4,X2) => in(X3,setunion(X2))))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(powersetE, axiom, powersetE <=> 108.90/109.59 (![A,B,Xx]: (in(B,powerset(A)) => (in(Xx,B) => in(Xx,A))))). 108.90/109.59 tff('55', plain, 108.90/109.59 powersetE = 108.90/109.59 (![X2,X3,X4]: (in(X3,powerset(X2)) => (in(X4,X3) => in(X4,X2)))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(emptyInPowerset, axiom, emptyInPowerset <=> 108.90/109.59 (![A]: in(emptyset,powerset(A)))). 108.90/109.59 tff('56', plain, emptyInPowerset = (![X2]: in(emptyset,powerset(X2))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(emptyinPowerset, axiom, emptyinPowerset <=> 108.90/109.59 (![A]: in(emptyset,powerset(A)))). 108.90/109.59 tff('57', plain, emptyinPowerset = (![X2]: in(emptyset,powerset(X2))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(powersetI, axiom, powersetI <=> 108.90/109.59 (![A,B]: ((![Xx]: (in(Xx,B) => in(Xx,A))) => in(B,powerset(A))))). 108.90/109.59 tff('58', plain, 108.90/109.59 powersetI = 108.90/109.59 (![X2,X3]: ((![X4]: (in(X4,X3) => in(X4,X2))) => in(X3,powerset(X2)))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(setoftrueEq, axiom, setoftrueEq <=> 108.90/109.59 (![A]: (dsetconstr(A,^[Xx]: $true) = A))). 108.90/109.59 tff('59', plain, setoftrueEq = (![X2]: (dsetconstr(X2,^[V_1]: $true) = X2)), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(setadjoinOr, axiom, setadjoinOr <=> 108.90/109.59 (![Xx,A,Xy]: (in(Xy,setadjoin(Xx,A)) => (in(Xy,A) | (Xy = Xx))))). 108.90/109.59 tff('60', plain, 108.90/109.59 setadjoinOr = 108.90/109.59 (![X2,X3,X4]: (in(X4,setadjoin(X2,X3)) => (in(X4,X3) | (X4 = X2)))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(setadjoinE, axiom, setadjoinE <=> 108.90/109.59 (![Xx,A,Xy]: 108.90/109.59 (in(Xy,setadjoin(Xx,A)) => 108.90/109.59 (![Xphi:$o]: (((Xy = Xx) => Xphi) => ((in(Xy,A) => Xphi) => Xphi)))))). 108.90/109.59 tff('61', plain, 108.90/109.59 setadjoinE = 108.90/109.59 (![X2,X3,X4]: 108.90/109.59 (in(X4,setadjoin(X2,X3)) => 108.90/109.59 (![X5:$o]: (((X4 = X2) => X5) => ((in(X4,X3) => X5) => X5))))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(setadjoinIR, axiom, setadjoinIR <=> 108.90/109.59 (![Xx,A,Xy]: (in(Xy,A) => in(Xy,setadjoin(Xx,A))))). 108.90/109.59 tff('62', plain, 108.90/109.59 setadjoinIR = (![X2,X3,X4]: (in(X4,X3) => in(X4,setadjoin(X2,X3)))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(emptyinunitempty, axiom, emptyinunitempty() = 108.90/109.59 in(emptyset,setadjoin(emptyset,emptyset))). 108.90/109.59 tff('63', plain, 108.90/109.59 emptyinunitempty = in(emptyset,setadjoin(emptyset,emptyset)), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(setadjoinIL, axiom, setadjoinIL <=> (![Xx,Xy]: in(Xx,setadjoin(Xx,Xy)))). 108.90/109.59 tff('64', plain, setadjoinIL = (![X2,X3]: in(X2,setadjoin(X2,X3))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(nonemptyI1, axiom, nonemptyI1 <=> 108.90/109.59 (![A]: ((?[Xx]: in(Xx,A)) => nonempty(A)))). 108.90/109.59 tff('65', plain, nonemptyI1 = (![X2]: ((?[X3]: in(X3,X2)) => nonempty(X2))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(nonemptyI, axiom, nonemptyI <=> 108.90/109.59 (![A,Xphi:($i > $o),Xx]: 108.90/109.59 (in(Xx,A) => (Xphi(Xx) => nonempty(dsetconstr(A,^[Xy]: Xphi(Xy))))))). 108.90/109.59 tff('66', plain, 108.90/109.59 nonemptyI = 108.90/109.59 (![X2,X3:($i > $o),X4]: 108.90/109.59 (in(X4,X2) => (X3(X4) => nonempty(dsetconstr(X2,^[V_1]: X3(V_1)))))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(nonemptyE1, axiom, nonemptyE1 <=> 108.90/109.59 (![A]: (nonempty(A) => (?[Xx]: in(Xx,A))))). 108.90/109.59 tff('67', plain, nonemptyE1 = (![X2]: (nonempty(X2) => (?[X3]: in(X3,X2)))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(nonempty, axiom, nonempty() = ^[Xx]: (Xx != emptyset)). 108.90/109.59 tff('68', plain, nonempty = (^[V_1]: (V_1 != emptyset)), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(setbeta, axiom, setbeta <=> 108.90/109.59 (![A,Xphi:($i > $o),Xx]: 108.90/109.59 (in(Xx,A) => (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) <=> Xphi(Xx))))). 108.90/109.59 tff('69', plain, 108.90/109.59 setbeta = 108.90/109.59 (![X2,X3:($i > $o),X4]: 108.90/109.59 (in(X4,X2) => (in(X4,dsetconstr(X2,^[V_1]: X3(V_1))) <=> X3(X4)))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(noeltsimpempty, axiom, noeltsimpempty <=> 108.90/109.59 (![A]: ((![Xx]: (~in(Xx,A))) => (A = emptyset)))). 108.90/109.59 tff('70', plain, 108.90/109.59 noeltsimpempty = (![X2]: ((![X3]: (~in(X3,X2))) => (X2 = emptyset))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(emptyI, axiom, emptyI <=> 108.90/109.59 (![A]: ((![Xx]: (~in(Xx,A))) => (A = emptyset)))). 108.90/109.59 tff('71', plain, 108.90/109.59 emptyI = (![X2]: ((![X3]: (~in(X3,X2))) => (X2 = emptyset))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(setext, axiom, setext <=> 108.90/109.59 (![A,B]: 108.90/109.59 ((![Xx]: (in(Xx,A) => in(Xx,B))) => 108.90/109.59 ((![Xx]: (in(Xx,B) => in(Xx,A))) => (A = B))))). 108.90/109.59 tff('72', plain, 108.90/109.59 setext = 108.90/109.59 (![X2,X3]: 108.90/109.59 ((![X4]: (in(X4,X2) => in(X4,X3))) => 108.90/109.59 ((![X5]: (in(X5,X3) => in(X5,X2))) => (X2 = X3)))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(exuE3e, axiom, exuE3e <=> 108.90/109.59 (![Xphi:($i > $o)]: (exu(^[Xx]: Xphi(Xx)) => (?[Xx]: Xphi(Xx))))). 108.90/109.59 tff('73', plain, 108.90/109.59 exuE3e = (![X2:($i > $o)]: (exu(^[V_1]: X2(V_1)) => (?[X3]: X2(X3)))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(notinemptyset, axiom, notinemptyset <=> (![Xx]: (~in(Xx,emptyset)))). 108.90/109.59 tff('74', plain, notinemptyset = (![X2]: (~in(X2,emptyset))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(emptysetimpfalse, axiom, emptysetimpfalse <=> 108.90/109.59 (![Xx]: (in(Xx,emptyset) => $false))). 108.90/109.59 tff('75', plain, emptysetimpfalse = (![X2]: (in(X2,emptyset) => $false)), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(emptysetE, axiom, emptysetE <=> 108.90/109.59 (![Xx]: (in(Xx,emptyset) => (![Xphi:$o]: Xphi)))). 108.90/109.59 tff('76', plain, emptysetE = (![X2]: (in(X2,emptyset) => (![X3:$o]: X3))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(prop2setE, axiom, prop2setE <=> 108.90/109.59 (![Xphi:$o,Xx]: (in(Xx,prop2set(Xphi)) => Xphi))). 108.90/109.59 tff('77', plain, prop2setE = (![X2:$o,X3]: (in(X3,prop2set(X2)) => X2)), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(exuE1, axiom, exuE1 <=> 108.90/109.59 (![Xphi:($i > $o)]: 108.90/109.59 (exu(^[Xx]: Xphi(Xx)) => 108.90/109.59 (?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx)))))). 108.90/109.59 tff('78', plain, 108.90/109.59 exuE1 = 108.90/109.59 (![X2:($i > $o)]: 108.90/109.59 (exu(^[V_1]: X2(V_1)) => 108.90/109.59 (?[X3]: ((![X4]: (X2(X4) => (X3 = X4))) & X2(X3))))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(dsetconstrER, axiom, dsetconstrER <=> 108.90/109.59 (![A,Xphi:($i > $o),Xx]: (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) => Xphi(Xx)))). 108.90/109.59 tff('79', plain, 108.90/109.59 dsetconstrER = 108.90/109.59 (![X2,X3:($i > $o),X4]: (in(X4,dsetconstr(X2,^[V_1]: X3(V_1))) => X3(X4))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(dsetconstrEL, axiom, dsetconstrEL <=> 108.90/109.59 (![A,Xphi:($i > $o),Xx]: (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) => in(Xx,A)))). 108.90/109.59 tff('80', plain, 108.90/109.59 dsetconstrEL = 108.90/109.59 (![X2,X3:($i > $o),X4]: 108.90/109.59 (in(X4,dsetconstr(X2,^[V_1]: X3(V_1))) => in(X4,X2))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(dsetconstrI, axiom, dsetconstrI <=> 108.90/109.59 (![A,Xphi:($i > $o),Xx]: 108.90/109.59 (in(Xx,A) => (Xphi(Xx) => in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))))))). 108.90/109.59 tff('81', plain, 108.90/109.59 dsetconstrI = 108.90/109.59 (![X2,X3:($i > $o),X4]: 108.90/109.59 (in(X4,X2) => (X3(X4) => in(X4,dsetconstr(X2,^[V_1]: X3(V_1)))))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(descrp, axiom, descrp <=> 108.90/109.59 (![Xphi:($i > $o)]: (exu(^[Xx]: Xphi(Xx)) => Xphi(descr(^[Xx]: Xphi(Xx)))))). 108.90/109.59 tff('82', plain, 108.90/109.59 descrp = 108.90/109.59 (![X2:($i > $o)]: (exu(^[V_1]: X2(V_1)) => X2(descr(^[V_2]: X2(V_2))))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(wellorderingAx, axiom, wellorderingAx <=> 108.90/109.59 (![A]: 108.90/109.59 (?[B]: 108.90/109.59 ((![C]: 108.90/109.59 (((?[Xx]: in(Xx,C)) & (![Xx]: (in(Xx,C) => in(Xx,A)))) => 108.90/109.59 (?[D,Xx]: 108.90/109.59 ((![E]: 108.90/109.59 (in(E,B) => (in(Xx,E) | (![Xy]: (in(Xy,E) => in(Xy,D)))))) & 108.90/109.59 (~(?[Xy]: (in(Xy,C) & in(Xy,D)))) & in(Xx,C) & in(D,B))))) & 108.90/109.59 (![C,D]: 108.90/109.59 ((in(D,B) & in(C,B)) => 108.90/109.59 ((![Xx]: (in(Xx,D) => in(Xx,C))) | 108.90/109.59 (![Xx]: (in(Xx,C) => in(Xx,D)))))) & 108.90/109.59 (![Xx,Xy]: 108.90/109.59 ((in(Xy,A) & in(Xx,A)) => 108.90/109.59 ((![C]: (in(C,B) => (in(Xx,C) <=> in(Xy,C)))) => (Xx = Xy)))) & 108.90/109.59 (![C]: (in(C,B) => (![Xx]: (in(Xx,C) => in(Xx,A))))))))). 108.90/109.59 tff('83', plain, 108.90/109.59 wellorderingAx = 108.90/109.59 (![X2]: 108.90/109.59 (?[X3]: 108.90/109.59 ((![X4]: 108.90/109.59 (((?[X5]: in(X5,X4)) & (![X6]: (in(X6,X4) => in(X6,X2)))) => 108.90/109.59 (?[X7,X8]: 108.90/109.59 ((![X9]: 108.90/109.59 (in(X9,X3) => 108.90/109.59 (in(X8,X9) | (![X10]: (in(X10,X9) => in(X10,X7)))))) & 108.90/109.59 (~(?[X11]: (in(X11,X4) & in(X11,X7)))) & in(X8,X4) & 108.90/109.59 in(X7,X3))))) & 108.90/109.59 (![X12,X13]: 108.90/109.59 ((in(X13,X3) & in(X12,X3)) => 108.90/109.59 ((![X14]: (in(X14,X13) => in(X14,X12))) | 108.90/109.59 (![X15]: (in(X15,X12) => in(X15,X13)))))) & 108.90/109.59 (![X16,X17]: 108.90/109.59 ((in(X17,X2) & in(X16,X2)) => 108.90/109.59 ((![X18]: (in(X18,X3) => (in(X16,X18) <=> in(X17,X18)))) => 108.90/109.59 (X16 = X17)))) & 108.90/109.59 (![X19]: (in(X19,X3) => (![X20]: (in(X20,X19) => in(X20,X2)))))))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(foundationAx, axiom, foundationAx <=> 108.90/109.59 (![A]: 108.90/109.59 ((?[Xx]: in(Xx,A)) => 108.90/109.59 (?[B]: ((~(?[Xx]: (in(Xx,A) & in(Xx,B)))) & in(B,A)))))). 108.90/109.59 tff('84', plain, 108.90/109.59 foundationAx = 108.90/109.59 (![X2]: 108.90/109.59 ((?[X3]: in(X3,X2)) => 108.90/109.59 (?[X4]: ((~(?[X5]: (in(X5,X2) & in(X5,X4)))) & in(X4,X2))))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(replAx, axiom, replAx <=> 108.90/109.59 (![Xphi:(($i * $i) > $o),A]: 108.90/109.59 ((![Xx]: (in(Xx,A) => exu(^[Xy]: Xphi(Xx,Xy)))) => 108.90/109.59 (?[B]: (![Xx]: (in(Xx,B) <=> (?[Xy]: (Xphi(Xy,Xx) & in(Xy,A))))))))). 108.90/109.59 tff('85', plain, 108.90/109.59 replAx = 108.90/109.59 (![X2:(($i * $i) > $o),X3]: 108.90/109.59 ((![X4]: (in(X4,X3) => exu(^[V_1]: X2(X4,V_1)))) => 108.90/109.59 (?[X5]: (![X6]: (in(X6,X5) <=> (?[X7]: (X2(X7,X6) & in(X7,X3)))))))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(omegaIndAx, axiom, omegaIndAx <=> 108.90/109.59 (![A]: 108.90/109.59 (((![Xx]: ((in(Xx,A) & in(Xx,omega)) => in(setadjoin(Xx,Xx),A))) & 108.90/109.59 in(emptyset,A)) => 108.90/109.59 (![Xx]: (in(Xx,omega) => in(Xx,A)))))). 108.90/109.59 tff('86', plain, 108.90/109.59 omegaIndAx = 108.90/109.59 (![X2]: 108.90/109.59 (((![X3]: ((in(X3,X2) & in(X3,omega)) => in(setadjoin(X3,X3),X2))) & 108.90/109.59 in(emptyset,X2)) => 108.90/109.59 (![X4]: (in(X4,omega) => in(X4,X2))))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(omegaSAx, axiom, omegaSAx <=> 108.90/109.59 (![Xx]: (in(Xx,omega) => in(setadjoin(Xx,Xx),omega)))). 108.90/109.59 tff('87', plain, 108.90/109.59 omegaSAx = (![X2]: (in(X2,omega) => in(setadjoin(X2,X2),omega))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(omega0Ax, axiom, omega0Ax() = in(emptyset,omega)). 108.90/109.59 tff('88', plain, omega0Ax = in(emptyset,omega), define([status(thm)])). 108.90/109.59 tff(setunionAx, axiom, setunionAx <=> 108.90/109.59 (![A,Xx]: (in(Xx,setunion(A)) <=> (?[B]: (in(B,A) & in(Xx,B)))))). 108.90/109.59 tff('89', plain, 108.90/109.59 setunionAx = 108.90/109.59 (![X2,X3]: (in(X3,setunion(X2)) <=> (?[X4]: (in(X4,X2) & in(X3,X4))))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(powersetAx, axiom, powersetAx <=> 108.90/109.59 (![A,B]: (in(B,powerset(A)) <=> (![Xx]: (in(Xx,B) => in(Xx,A)))))). 108.90/109.59 tff('90', plain, 108.90/109.59 powersetAx = 108.90/109.59 (![X2,X3]: (in(X3,powerset(X2)) <=> (![X4]: (in(X4,X3) => in(X4,X2))))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(setadjoinAx, axiom, setadjoinAx <=> 108.90/109.59 (![Xx,A,Xy]: (in(Xy,setadjoin(Xx,A)) <=> (in(Xy,A) | (Xy = Xx))))). 108.90/109.59 tff('91', plain, 108.90/109.59 setadjoinAx = 108.90/109.59 (![X2,X3,X4]: (in(X4,setadjoin(X2,X3)) <=> (in(X4,X3) | (X4 = X2)))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(emptysetAx, axiom, emptysetAx <=> (![Xx]: (~in(Xx,emptyset)))). 108.90/109.59 tff('92', plain, emptysetAx = (![X2]: (~in(X2,emptyset))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(setextAx, axiom, setextAx <=> 108.90/109.59 (![A,B]: ((![Xx]: (in(Xx,A) <=> in(Xx,B))) => (A = B)))). 108.90/109.59 tff('93', plain, 108.90/109.59 setextAx = (![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(exu, axiom, exu() = 108.90/109.59 ^[Xphi:($i > $o)]: (?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx)))). 108.90/109.59 tff('94', plain, 108.90/109.59 exu = 108.90/109.59 (^[V_1:($i > $o)]: (?[X2]: ((![X3]: (V_1(X3) => (X2 = X3))) & V_1(X2)))), 108.90/109.59 define([status(thm)])). 108.90/109.59 tff(powersetE1, conjecture, 108.90/109.59 (setextAx => 108.90/109.59 (emptysetAx => 108.90/109.59 (setadjoinAx => 108.90/109.59 (powersetAx => 108.90/109.59 (setunionAx => 108.90/109.59 (omega0Ax => 108.90/109.59 (omegaSAx => 108.90/109.59 (omegaIndAx => 108.90/109.59 (replAx => 108.90/109.59 (foundationAx => 108.90/109.59 (wellorderingAx => 108.90/109.59 (descrp => 108.90/109.59 (dsetconstrI => 108.90/109.59 (dsetconstrEL => 108.90/109.59 (dsetconstrER => 108.90/109.59 (exuE1 => 108.90/109.59 (prop2setE => 108.90/109.59 (emptysetE => 108.90/109.59 (emptysetimpfalse => 108.90/109.59 (notinemptyset => 108.90/109.59 (exuE3e => 108.90/109.59 (setext => 108.90/109.59 (emptyI => 108.90/109.59 (noeltsimpempty => 108.90/109.59 (setbeta => 108.90/109.59 (nonemptyE1 => 108.90/109.59 (nonemptyI => 108.90/109.59 (nonemptyI1 => 108.90/109.59 (setadjoinIL => 108.90/109.59 (emptyinunitempty => 108.90/109.59 (setadjoinIR => 108.90/109.59 (setadjoinE => 108.90/109.59 (setadjoinOr => 108.90/109.59 (setoftrueEq => 108.90/109.59 (powersetI => 108.90/109.59 (emptyinPowerset => 108.90/109.59 (emptyInPowerset => 108.90/109.59 (powersetE => 108.90/109.59 (setunionI => 108.90/109.59 (setunionE => 108.90/109.59 (subPowSU => 108.90/109.59 (exuE2 => 108.90/109.59 (nonemptyImpWitness => 108.90/109.59 (uniqinunit => 108.90/109.59 (notinsingleton => 108.90/109.59 (eqinunit => 108.90/109.59 (singletonsswitch => 108.90/109.59 (upairsetE => 108.90/109.59 (upairsetIL => 108.90/109.59 (upairsetIR => 108.90/109.59 (emptyE1 => 108.90/109.59 (vacuousDall => 108.90/109.59 (quantDeMorgan1 => 108.90/109.59 (quantDeMorgan2 => 108.90/109.59 (quantDeMorgan3 => 108.90/109.59 (quantDeMorgan4 => 108.90/109.59 (prop2setI => 108.90/109.59 (prop2set2propI => 108.90/109.59 (notdexE => 108.90/109.59 (notdallE => 108.90/109.59 (exuI1 => 108.90/109.59 (exuI3 => 108.90/109.59 (exuI2 => 108.90/109.59 (inCongP => 108.90/109.59 (in__Cong => 108.90/109.59 (exuE3u => 108.90/109.59 ( 108.90/109.59 exu__Cong => 108.90/109.59 ( 108.90/109.59 emptyset__Cong => 108.90/109.59 ( 108.90/109.59 setadjoin__Cong => 108.90/109.59 ( 108.90/109.59 powerset__Cong => 108.90/109.59 ( 108.90/109.59 setunion__Cong => 108.90/109.59 ( 108.90/109.59 omega__Cong => 108.90/109.59 ( 108.90/109.59 exuEu => 108.90/109.59 ( 108.90/109.59 descr__Cong => 108.90/109.59 ( 108.90/109.59 dsetconstr__Cong => 108.90/109.59 ( 108.90/109.59 subsetI1 => 108.90/109.59 ( 108.90/109.59 eqimpsubset2 => 108.90/109.59 ( 108.90/109.59 eqimpsubset1 => 108.90/109.59 ( 108.90/109.59 subsetI2 => 108.90/109.59 ( 108.90/109.59 emptysetsubset => 108.90/109.59 ( 108.90/109.59 subsetE => 108.90/109.59 ( 108.90/109.59 subsetE2 => 108.90/109.59 ( 108.90/109.59 notsubsetI => 108.90/109.59 ( 108.90/109.59 notequalI1 => 108.90/109.59 ( 108.90/109.59 notequalI2 => 108.90/109.59 ( 108.90/109.59 subsetRefl => 108.90/109.59 ( 108.90/109.59 subsetTrans => 108.90/109.59 ( 108.90/109.59 setadjoinSub => 108.90/109.59 ( 108.90/109.59 setadjoinSub2 => 108.90/109.59 ( 108.90/109.59 subset2powerset => 108.90/109.59 ( 108.90/109.59 setextsub => 108.90/109.59 ( 108.90/109.59 subsetemptysetimpeq => 108.90/109.59 ( 108.90/109.59 powersetI1 => 108.90/109.59 ( 108.90/109.59 ![A,B]: 108.90/109.59 (in( 108.90/109.59 B, 108.90/109.59 powerset( 108.90/109.59 A)) => 108.90/109.59 subset( 108.90/109.59 B,A))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 108.90/109.59 tff(zf_stmt_0, conjecture, 108.90/109.59 ((![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))) => 108.90/109.59 ((![X5]: (~in(X5,emptyset))) => 108.90/109.59 ((![X6,X7,X8]: (in(X8,setadjoin(X6,X7)) <=> ((X8 = X6) | in(X8,X7)))) => 108.90/109.59 ((![X9,X10]: 108.90/109.59 (in(X10,powerset(X9)) <=> (![X11]: (in(X11,X10) => in(X11,X9))))) => 108.90/109.59 ((![X12,X13]: 108.90/109.59 (in(X13,setunion(X12)) <=> (?[X14]: (in(X13,X14) & in(X14,X12))))) => 108.90/109.59 (in(emptyset,omega) => 108.90/109.59 ((![X15]: (in(X15,omega) => in(setadjoin(X15,X15),omega))) => 108.90/109.59 ((![X16]: 108.90/109.59 ((in(emptyset,X16) & 108.90/109.59 (![X17]: 108.90/109.59 ((in(X17,omega) & in(X17,X16)) => 108.90/109.59 in(setadjoin(X17,X17),X16)))) => 108.90/109.59 (![X18]: (in(X18,omega) => in(X18,X16))))) => 108.90/109.59 ((![X19:(($i * $i) > $o),X20]: 108.90/109.59 ((![X21]: 108.90/109.59 (in(X21,X20) => 108.90/109.59 (?[X22]: 108.90/109.59 (X19(X21,X22) & (![X23]: (X19(X21,X23) => (X22 = X23))))))) => 108.90/109.59 (?[X24]: 108.90/109.59 (![X25]: 108.90/109.59 (in(X25,X24) <=> (?[X26]: (in(X26,X20) & X19(X26,X25)))))))) => 108.90/109.59 ((![X27]: 108.90/109.59 ((?[X28]: in(X28,X27)) => 108.90/109.59 (?[X29]: 108.90/109.59 (in(X29,X27) & (~(?[X30]: (in(X30,X29) & in(X30,X27)))))))) => 108.90/109.59 ((![X31]: 108.90/109.59 (?[X32]: 108.90/109.59 ((![X48]: 108.90/109.59 (in(X48,X32) => (![X49]: (in(X49,X48) => in(X49,X31))))) & 108.90/109.59 (![X45,X46]: 108.90/109.59 ((in(X45,X31) & in(X46,X31)) => 108.90/109.59 ((![X47]: 108.90/109.59 (in(X47,X32) => (in(X45,X47) <=> in(X46,X47)))) => 108.90/109.59 (X45 = X46)))) & 108.90/109.59 (![X41,X42]: 108.90/109.59 ((in(X41,X32) & in(X42,X32)) => 108.90/109.59 ((![X44]: (in(X44,X41) => in(X44,X42))) | 108.90/109.59 (![X43]: (in(X43,X42) => in(X43,X41)))))) & 108.90/109.59 (![X33]: 108.90/109.59 (((![X35]: (in(X35,X33) => in(X35,X31))) & 108.90/109.59 (?[X34]: in(X34,X33))) => 108.90/109.59 (?[X36,X37]: 108.90/109.59 (in(X36,X32) & in(X37,X33) & 108.90/109.59 (~(?[X40]: (in(X40,X36) & in(X40,X33)))) & 108.90/109.59 (![X38]: 108.90/109.59 (in(X38,X32) => 108.90/109.59 ((![X39]: (in(X39,X38) => in(X39,X36))) | 108.90/109.59 in(X37,X38))))))))))) => 108.90/109.59 ((![X50:($i > $o)]: 108.90/109.59 ((?[X51]: (X50(X51) & (![X52]: (X50(X52) => (X51 = X52))))) => 108.90/109.59 X50(descr('#ll_0'(X50))))) => 108.90/109.59 ((![X53,X54:($i > $o),X55]: 108.90/109.59 (in(X55,X53) => 108.90/109.59 (X54(X55) => in(X55,dsetconstr(X53,'#ll_0'(X54)))))) => 108.90/109.59 ((![X56,X57:($i > $o),X58]: 108.90/109.59 (in(X58,dsetconstr(X56,'#ll_0'(X57))) => in(X58,X56))) => 108.90/109.59 ((![X59,X60:($i > $o),X61]: 108.90/109.59 (in(X61,dsetconstr(X59,'#ll_0'(X60))) => X60(X61))) => 108.90/109.59 ((![X62:($i > $o)]: 108.90/109.59 ((?[X63]: 108.90/109.59 (X62(X63) & (![X64]: (X62(X64) => (X63 = X64))))) => 108.90/109.59 (?[X65]: 108.90/109.59 (X62(X65) & (![X66]: (X62(X66) => (X65 = X66))))))) => 108.90/109.59 ((![X67:$o,X68]: (in(X68,prop2set(X67)) => X67)) => 108.90/109.59 ((![X69]: (in(X69,emptyset) => (![X70:$o]: X70))) => 108.90/109.59 ((![X71]: (in(X71,emptyset) => $false)) => 108.90/109.59 ((![X72]: (~in(X72,emptyset))) => 108.90/109.59 ((![X73:($i > $o)]: 108.90/109.59 ((?[X74]: 108.90/109.59 (X73(X74) & (![X75]: (X73(X75) => (X74 = X75))))) => 108.90/109.59 (?[X76]: X73(X76)))) => 108.90/109.59 ((![X77,X78]: 108.90/109.59 ((![X79]: (in(X79,X77) => in(X79,X78))) => 108.90/109.59 ((![X80]: (in(X80,X78) => in(X80,X77))) => 108.90/109.59 (X77 = X78)))) => 108.90/109.59 ((![X81]: 108.90/109.59 ((![X82]: (~in(X82,X81))) => (X81 = emptyset))) => 108.90/109.59 ((![X83]: 108.90/109.59 ((![X84]: (~in(X84,X83))) => (X83 = emptyset))) => 108.90/109.59 ((![X85,X86:($i > $o),X87]: 108.90/109.59 (in(X87,X85) => 108.90/109.59 (in(X87,dsetconstr(X85,'#ll_0'(X86))) <=> 108.90/109.59 X86(X87)))) => 108.90/109.59 ((![X88]: 108.90/109.59 ((X88 != emptyset) => (?[X89]: in(X89,X88)))) => 108.90/109.59 ((![X90,X91:($i > $o),X92]: 108.90/109.59 (in(X92,X90) => 108.90/109.59 (X91(X92) => 108.90/109.59 (dsetconstr(X90,'#ll_0'(X91)) != emptyset)))) => 108.90/109.59 ((![X93]: 108.90/109.59 ((?[X94]: in(X94,X93)) => (X93 != emptyset))) => 108.90/109.59 ((![X95,X96]: in(X95,setadjoin(X95,X96))) => 108.90/109.59 (in(emptyset,setadjoin(emptyset,emptyset)) => 108.90/109.59 ((![X97,X98,X99]: 108.90/109.59 (in(X99,X98) => 108.90/109.59 in(X99,setadjoin(X97,X98)))) => 108.90/109.59 ((![X100,X101,X102]: 108.90/109.59 (in(X102,setadjoin(X100,X101)) => 108.90/109.59 (![X103:$o]: 108.90/109.59 (((X102 = X100) => X103) => 108.90/109.59 ((in(X102,X101) => X103) => X103))))) => 108.90/109.59 ((![X104,X105,X106]: 108.90/109.59 (in(X106,setadjoin(X104,X105)) => 108.90/109.59 ((X106 = X104) | in(X106,X105)))) => 108.90/109.59 ((![X107]: 108.90/109.59 (dsetconstr(X107,'#ll_1') = X107)) => 108.90/109.59 ((![X108,X109]: 108.90/109.59 ((![X110]: 108.90/109.59 (in(X110,X109) => in(X110,X108))) => 108.90/109.59 in(X109,powerset(X108)))) => 108.90/109.59 ((![X111]: in(emptyset,powerset(X111))) => 108.90/109.59 ((![X112]: in(emptyset,powerset(X112))) => 108.90/109.59 ((![X113,X114,X115]: 108.90/109.59 (in(X114,powerset(X113)) => 108.90/109.59 (in(X115,X114) => in(X115,X113)))) => 108.90/109.59 ((![X116,X117,X118]: 108.90/109.59 (in(X117,X118) => 108.90/109.59 (in(X118,X116) => 108.90/109.59 in(X117,setunion(X116))))) => 108.90/109.59 ((![X119,X120]: 108.90/109.59 (in(X120,setunion(X119)) => 108.90/109.59 (![X121:$o]: 108.90/109.59 ((![X122]: 108.90/109.59 (in(X120,X122) => 108.90/109.59 (in(X122,X119) => X121))) => 108.90/109.59 X121)))) => 108.90/109.59 ((![X123,X124]: 108.90/109.59 (in(X124,X123) => 108.90/109.59 in(X124, 108.90/109.59 powerset(setunion(X123))))) => 108.90/109.59 ((![X125:($i > $o)]: 108.90/109.59 ((?[X126]: 108.90/109.59 (X125(X126) & 108.90/109.59 (![X127]: 108.90/109.59 (X125(X127) => 108.90/109.59 (X126 = X127))))) => 108.90/109.59 (?[X128]: 108.90/109.59 (![X129]: 108.90/109.59 (X125(X129) <=> 108.90/109.59 (X129 = X128)))))) => 108.90/109.59 ((![X130]: 108.90/109.59 ((X130 != emptyset) => 108.90/109.59 (?[X131]: in(X131,X130)))) => 108.90/109.59 ((![X132,X133]: 108.90/109.59 (in(X132, 108.90/109.59 setadjoin(X133,emptyset)) => 108.90/109.59 (X132 = X133))) => 108.90/109.59 ((![X134,X135]: 108.90/109.59 ((X134 != X135) => 108.90/109.59 (~ 108.90/109.59 in(X135, 108.90/109.59 setadjoin(X134, 108.90/109.59 emptyset))))) => 108.90/109.59 ((![X136,X137]: 108.90/109.59 ((X136 = X137) => 108.90/109.59 in(X136, 108.90/109.59 setadjoin(X137, 108.90/109.59 emptyset)))) => 108.90/109.59 ((![X138,X139]: 108.90/109.59 (in(X138, 108.90/109.59 setadjoin(X139, 108.90/109.59 emptyset)) => 108.90/109.59 in(X139, 108.90/109.59 setadjoin(X138, 108.90/109.59 emptyset)))) => 108.90/109.59 ((![X140,X141,X142]: 108.90/109.59 (in(X142, 108.90/109.59 setadjoin(X140, 108.90/109.59 setadjoin( 108.90/109.59 X141, 108.90/109.59 emptyset))) => 108.90/109.59 ((X142 = X140) | 108.90/109.59 (X142 = X141)))) => 108.90/109.59 ((![X143,X144]: 108.90/109.59 in(X143, 108.90/109.59 setadjoin(X143, 108.90/109.59 setadjoin( 108.90/109.59 X144, 108.90/109.59 emptyset)))) => 108.90/109.59 ((![X145,X146]: 108.90/109.59 in(X146, 108.90/109.59 setadjoin(X145, 108.90/109.59 setadjoin( 108.90/109.59 X146, 108.90/109.59 emptyset)))) => 108.90/109.59 ((![X147,X148:($i > $o)]: 108.90/109.59 ((?[X149]: 108.90/109.59 (in(X149,X147) & 108.90/109.59 X148(X149))) => 108.90/109.59 ((dsetconstr( 108.90/109.59 X147,'#ll_0'(X148)) = 108.90/109.59 emptyset) => 108.90/109.59 $false))) => 108.90/109.59 ((![X150:($i > $o),X151]: 108.90/109.59 (in(X151,emptyset) => 108.90/109.59 X150(X151))) => 108.90/109.59 ((![X152,X153:($i > $o)]: 108.90/109.59 ((~ 108.90/109.59 (![X154]: 108.90/109.59 (in(X154,X152) => 108.90/109.59 X153(X154)))) => 108.90/109.59 (?[X155]: 108.90/109.59 (in(X155,X152) & 108.90/109.59 (~X153(X155)))))) => 108.90/109.59 ((![X156, 108.90/109.59 X157:($i > $o)]: 108.90/109.59 ((![X158]: 108.90/109.59 (in(X158,X156) => 108.90/109.59 (~X157(X158)))) => 108.90/109.59 (~ 108.90/109.59 (?[X159]: 108.90/109.59 (in( 108.90/109.59 X159,X156) & 108.90/109.59 X157(X159)))))) => 108.90/109.59 ((![X160, 108.90/109.59 X161:($i > $o)]: 108.90/109.59 ((~ 108.90/109.59 (?[X162]: 108.90/109.59 (in( 108.90/109.59 X162,X160) & 108.90/109.59 X161(X162)))) => 108.90/109.59 (![X163]: 108.90/109.59 (in(X163,X160) => 108.90/109.59 (~X161(X163)))))) => 108.90/109.59 ((![X164, 108.90/109.59 X165:($i > $o)]: 108.90/109.59 ((?[X166]: 108.90/109.59 (in( 108.90/109.59 X166,X164) & 108.90/109.59 (~ 108.90/109.59 X165( 108.90/109.59 X166)))) => 108.90/109.59 (~ 108.90/109.59 (![X167]: 108.90/109.59 (in( 108.90/109.59 X167,X164) => 108.90/109.59 X165( 108.90/109.59 X167)))))) => 108.90/109.59 ((![X168:$o]: 108.90/109.59 (X168 => 108.90/109.59 in(emptyset, 108.90/109.59 prop2set( 108.90/109.59 X168)))) => 108.90/109.59 ((![X169:$o]: 108.90/109.59 (X169 => 108.90/109.59 set2prop( 108.90/109.59 prop2set( 108.90/109.59 X169)))) => 108.90/109.59 ((![X170, 108.90/109.59 X171:( 108.90/109.59 $i > $o)]: 108.90/109.59 ((~ 108.90/109.59 (?[X172]: 108.90/109.59 (in( 108.90/109.59 X172,X170) & 108.90/109.59 X171( 108.90/109.59 X172)))) => 108.90/109.59 (![X173]: 108.90/109.59 ( 108.90/109.59 in( 108.90/109.59 X173,X170) => 108.90/109.59 ( 108.90/109.59 ~ 108.90/109.59 X171( 108.90/109.59 X173)))))) => 108.90/109.59 ((![X174, 108.90/109.59 X175:( 108.90/109.59 $i > $o)]: 108.90/109.59 ((~ 108.90/109.59 ( 108.90/109.59 ![X176]: 108.90/109.59 (in( 108.90/109.59 X176,X174) => 108.90/109.59 X175( 108.90/109.59 X176)))) => 108.90/109.59 (?[X177]: 108.90/109.59 (in( 108.90/109.59 X177,X174) & 108.90/109.59 (~ 108.90/109.59 X175( 108.90/109.59 X177)))))) => 108.90/109.59 ((![X178:( 108.90/109.59 $i > $o)]: 108.90/109.59 ((?[X179]: 108.90/109.59 (X178( 108.90/109.59 X179) & 108.90/109.59 (![X180]: 108.90/109.59 (X178( 108.90/109.59 X180) => 108.90/109.59 (X179 = 108.90/109.59 X180))))) => 108.90/109.59 (?[X181]: 108.90/109.59 (X178( 108.90/109.59 X181) & 108.90/109.59 (![X182]: 108.90/109.59 (X178( 108.90/109.59 X182) => 108.90/109.59 (X181 = 108.90/109.59 X182))))))) => 108.90/109.59 ((![X183:( 108.90/109.59 $i > $o)]: 108.90/109.59 (( 108.90/109.59 ?[X184]: 108.90/109.59 X183( 108.90/109.59 X184)) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X185, 108.90/109.59 X186]: 108.90/109.59 (X183( 108.90/109.59 X185) => 108.90/109.59 (X183( 108.90/109.59 X186) => 108.90/109.59 (X185 = 108.90/109.59 X186)))) => 108.90/109.59 ( 108.90/109.59 ?[X187]: 108.90/109.59 (X183( 108.90/109.59 X187) & 108.90/109.59 (![X188]: 108.90/109.59 (X183( 108.90/109.59 X188) => 108.90/109.59 (X187 = 108.90/109.59 X188)))))))) => 108.90/109.59 ((![X189:( 108.90/109.59 $i > $o)]: 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ?[X190]: 108.90/109.59 (![X191]: 108.90/109.59 (X189( 108.90/109.59 X191) <=> 108.90/109.59 (X191 = 108.90/109.59 X190)))) => 108.90/109.59 ( 108.90/109.59 ?[X192]: 108.90/109.59 (X189( 108.90/109.59 X192) & 108.90/109.59 (![X193]: 108.90/109.59 (X189( 108.90/109.59 X193) => 108.90/109.59 (X192 = 108.90/109.59 X193))))))) => 108.90/109.59 ((![X194, 108.90/109.59 X195]: 108.90/109.59 (( 108.90/109.59 X194 = 108.90/109.59 X195) => 108.90/109.59 (![X196, 108.90/109.59 X197]: 108.90/109.59 (( 108.90/109.59 X196 = 108.90/109.59 X197) => 108.90/109.59 (in( 108.90/109.59 X196,X194) => 108.90/109.59 in( 108.90/109.59 X197,X195)))))) => 108.90/109.59 ((![X198, 108.90/109.59 X199]: 108.90/109.59 (( 108.90/109.59 X198 = 108.90/109.59 X199) => 108.90/109.59 (![X200, 108.90/109.59 X201]: 108.90/109.59 (( 108.90/109.59 X200 = 108.90/109.59 X201) => 108.90/109.59 (in( 108.90/109.59 X200,X198) <=> 108.90/109.59 in( 108.90/109.59 X201,X199)))))) => 108.90/109.59 (( 108.90/109.59 ![X202:( 108.90/109.59 $i > $o)]: 108.90/109.59 (( 108.90/109.59 ?[X203]: 108.90/109.59 (X202( 108.90/109.59 X203) & 108.90/109.59 (![X204]: 108.90/109.59 (X202( 108.90/109.59 X204) => 108.90/109.59 (X203 = 108.90/109.59 X204))))) => 108.90/109.59 (![X205, 108.90/109.59 X206]: 108.90/109.59 (X202( 108.90/109.59 X205) => 108.90/109.59 (X202( 108.90/109.59 X206) => 108.90/109.59 (X205 = 108.90/109.59 X206)))))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X207:( 108.90/109.59 $i > $o), 108.90/109.59 X208:( 108.90/109.59 $i > $o)]: 108.90/109.59 (( 108.90/109.59 ![X209, 108.90/109.59 X210]: 108.90/109.59 (( 108.90/109.59 X209 = 108.90/109.59 X210) => 108.90/109.59 (X207( 108.90/109.59 X209) <=> 108.90/109.59 X208( 108.90/109.59 X210)))) => 108.90/109.59 (( 108.90/109.59 ?[X211]: 108.90/109.59 (X207( 108.90/109.59 X211) & 108.90/109.59 (![X212]: 108.90/109.59 (X207( 108.90/109.59 X212) => 108.90/109.59 (X211 = 108.90/109.59 X212))))) <=> 108.90/109.59 (?[X213]: 108.90/109.59 (X208( 108.90/109.59 X213) & 108.90/109.59 (![X214]: 108.90/109.59 (X208( 108.90/109.59 X214) => 108.90/109.59 (X213 = 108.90/109.59 X214)))))))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 emptyset = 108.90/109.59 emptyset) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X215, 108.90/109.59 X216]: 108.90/109.59 (( 108.90/109.59 X215 = 108.90/109.59 X216) => 108.90/109.59 (![X217, 108.90/109.59 X218]: 108.90/109.59 (( 108.90/109.59 X217 = 108.90/109.59 X218) => 108.90/109.59 (setadjoin( 108.90/109.59 X215,X217) = 108.90/109.59 setadjoin( 108.90/109.59 X216,X218)))))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X219, 108.90/109.59 X220]: 108.90/109.59 (( 108.90/109.59 X219 = 108.90/109.59 X220) => 108.90/109.59 (powerset( 108.90/109.59 X219) = 108.90/109.59 powerset( 108.90/109.59 X220)))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X221, 108.90/109.59 X222]: 108.90/109.59 (( 108.90/109.59 X221 = 108.90/109.59 X222) => 108.90/109.59 (setunion( 108.90/109.59 X221) = 108.90/109.59 setunion( 108.90/109.59 X222)))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 omega = 108.90/109.59 omega) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X223:( 108.90/109.59 $i > $o)]: 108.90/109.59 (( 108.90/109.59 ?[X224]: 108.90/109.59 (X223( 108.90/109.59 X224) & 108.90/109.59 (![X225]: 108.90/109.59 (X223( 108.90/109.59 X225) => 108.90/109.59 (X224 = 108.90/109.59 X225))))) => 108.90/109.59 (![X226, 108.90/109.59 X227]: 108.90/109.59 (X223( 108.90/109.59 X226) => 108.90/109.59 (X223( 108.90/109.59 X227) => 108.90/109.59 (X226 = 108.90/109.59 X227)))))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X228:( 108.90/109.59 $i > $o), 108.90/109.59 X229:( 108.90/109.59 $i > $o)]: 108.90/109.59 (( 108.90/109.59 ![X230, 108.90/109.59 X231]: 108.90/109.59 (( 108.90/109.59 X230 = 108.90/109.59 X231) => 108.90/109.59 (X228( 108.90/109.59 X230) <=> 108.90/109.59 X229( 108.90/109.59 X231)))) => 108.90/109.59 (( 108.90/109.59 ?[X232]: 108.90/109.59 (X228( 108.90/109.59 X232) & 108.90/109.59 (![X233]: 108.90/109.59 (X228( 108.90/109.59 X233) => 108.90/109.59 (X232 = 108.90/109.59 X233))))) => 108.90/109.59 (( 108.90/109.59 ?[X234]: 108.90/109.59 (X229( 108.90/109.59 X234) & 108.90/109.59 (![X235]: 108.90/109.59 (X229( 108.90/109.59 X235) => 108.90/109.59 (X234 = 108.90/109.59 X235))))) => 108.90/109.59 (descr( 108.90/109.59 '#ll_0'( 108.90/109.59 X228)) = 108.90/109.59 descr( 108.90/109.59 '#ll_0'( 108.90/109.59 X229))))))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X236, 108.90/109.59 X237]: 108.90/109.59 (( 108.90/109.59 X236 = 108.90/109.59 X237) => 108.90/109.59 (![X238:( 108.90/109.59 $i > $o), 108.90/109.59 X239:( 108.90/109.59 $i > $o)]: 108.90/109.59 (( 108.90/109.59 ![X240]: 108.90/109.59 (in( 108.90/109.59 X240,X236) => 108.90/109.59 (![X241]: 108.90/109.59 (in( 108.90/109.59 X241,X237) => 108.90/109.59 (( 108.90/109.59 X240 = 108.90/109.59 X241) => 108.90/109.59 (X238( 108.90/109.59 X240) <=> 108.90/109.59 X239( 108.90/109.59 X241))))))) => 108.90/109.59 (dsetconstr( 108.90/109.59 X236, 108.90/109.59 '#ll_0'( 108.90/109.59 X238)) = 108.90/109.59 dsetconstr( 108.90/109.59 X237, 108.90/109.59 '#ll_0'( 108.90/109.59 X239))))))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X242, 108.90/109.59 X243]: 108.90/109.59 (( 108.90/109.59 ![X244]: 108.90/109.59 (in( 108.90/109.59 X244,X242) => 108.90/109.59 in( 108.90/109.59 X244,X243))) => 108.90/109.59 subset( 108.90/109.59 X242,X243))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X245, 108.90/109.59 X246]: 108.90/109.59 (( 108.90/109.59 X245 = 108.90/109.59 X246) => 108.90/109.59 subset( 108.90/109.59 X246,X245))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X247, 108.90/109.59 X248]: 108.90/109.59 (( 108.90/109.59 X247 = 108.90/109.59 X248) => 108.90/109.59 subset( 108.90/109.59 X247,X248))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X249, 108.90/109.59 X250]: 108.90/109.59 (( 108.90/109.59 ![X251]: 108.90/109.59 (in( 108.90/109.59 X251,X249) => 108.90/109.59 in( 108.90/109.59 X251,X250))) => 108.90/109.59 subset( 108.90/109.59 X249,X250))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X252]: 108.90/109.59 subset( 108.90/109.59 emptyset, 108.90/109.59 X252)) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X253, 108.90/109.59 X254,X255]: 108.90/109.59 (subset( 108.90/109.59 X253,X254) => 108.90/109.59 (in( 108.90/109.59 X255,X253) => 108.90/109.59 in( 108.90/109.59 X255,X254)))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X256, 108.90/109.59 X257,X258]: 108.90/109.59 (subset( 108.90/109.59 X256,X257) => 108.90/109.59 (( 108.90/109.59 ~ 108.90/109.59 in( 108.90/109.59 X258,X257)) => 108.90/109.59 (~ 108.90/109.59 in( 108.90/109.59 X258,X256))))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X259, 108.90/109.59 X260,X261]: 108.90/109.59 (in( 108.90/109.59 X261,X259) => 108.90/109.59 (( 108.90/109.59 ~ 108.90/109.59 in( 108.90/109.59 X261,X260)) => 108.90/109.59 (~ 108.90/109.59 subset( 108.90/109.59 X259,X260))))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X262, 108.90/109.59 X263]: 108.90/109.59 (( 108.90/109.59 ~ 108.90/109.59 subset( 108.90/109.59 X262,X263)) => 108.90/109.59 (X262 != 108.90/109.59 X263))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X264, 108.90/109.59 X265,X266]: 108.90/109.59 (in( 108.90/109.59 X266,X264) => 108.90/109.59 (( 108.90/109.59 ~ 108.90/109.59 in( 108.90/109.59 X266,X265)) => 108.90/109.59 (X264 != 108.90/109.59 X265)))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X267]: 108.90/109.59 subset( 108.90/109.59 X267,X267)) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X268, 108.90/109.59 X269,X270]: 108.90/109.59 (subset( 108.90/109.59 X268,X269) => 108.90/109.59 (subset( 108.90/109.59 X269,X270) => 108.90/109.59 subset( 108.90/109.59 X268,X270)))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X271, 108.90/109.59 X272]: 108.90/109.59 subset( 108.90/109.59 X272, 108.90/109.59 setadjoin( 108.90/109.59 X271,X272))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X273, 108.90/109.59 X274,X275]: 108.90/109.59 (subset( 108.90/109.59 X273,X275) => 108.90/109.59 subset( 108.90/109.59 X273, 108.90/109.59 setadjoin( 108.90/109.59 X274,X275)))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X276, 108.90/109.59 X277]: 108.90/109.59 (subset( 108.90/109.59 X276,X277) => 108.90/109.59 in( 108.90/109.59 X276, 108.90/109.59 powerset( 108.90/109.59 X277)))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X278, 108.90/109.59 X279]: 108.90/109.59 (subset( 108.90/109.59 X278,X279) => 108.90/109.59 (subset( 108.90/109.59 X279,X278) => 108.90/109.59 (X278 = 108.90/109.59 X279)))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X280]: 108.90/109.59 (subset( 108.90/109.59 X280, 108.90/109.59 emptyset) => 108.90/109.59 (X280 = 108.90/109.59 emptyset))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X281, 108.90/109.59 X282]: 108.90/109.59 (subset( 108.90/109.59 X282,X281) => 108.90/109.59 in( 108.90/109.59 X282, 108.90/109.59 powerset( 108.90/109.59 X281)))) => 108.90/109.59 ( 108.90/109.59 ![X283, 108.90/109.59 X284]: 108.90/109.59 (in( 108.90/109.59 X284, 108.90/109.59 powerset( 108.90/109.59 X283)) => 108.90/109.59 subset( 108.90/109.59 X284,X283))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 108.90/109.59 tff(zf_stmt_1, type, zip_tseitin5 : ($i * $i > $o) > $o). 108.90/109.59 tff(zf_stmt_2, axiom, 108.90/109.59 (zip_tseitin5(X211,X207) <=> 108.90/109.59 ((![X212]: zip_tseitin4(X212,X211,X207)) & X207(X211)))). 108.90/109.59 tff(zf_stmt_3, type, zip_tseitin4 : ($i * $i * $i > $o) > $o). 108.90/109.59 tff(zf_stmt_4, axiom, 108.90/109.59 (zip_tseitin4(X212,X211,X207) <=> (X207(X212) => (X211 = X212)))). 108.90/109.59 tff(zf_stmt_5, type, zip_tseitin3 : ($i * $i * $i * ($i * $i) > $o) > $o). 108.90/109.59 tff(zf_stmt_6, axiom, 108.90/109.59 (zip_tseitin3(X26,X25,X20,X19) <=> (X19(X26,X25) & in(X26,X20)))). 108.90/109.59 tff(zf_stmt_7, type, zip_tseitin2 : ($i * $i * $i) > $o). 108.90/109.59 tff(zf_stmt_8, axiom, 108.90/109.59 (zip_tseitin2(X14,X13,X12) <=> (in(X14,X12) & in(X13,X14)))). 108.90/109.59 tff(zf_stmt_9, type, zip_tseitin1 : ($i * $i * $i) > $o). 108.90/109.59 tff(zf_stmt_10, axiom, 108.90/109.59 (zip_tseitin1(X11,X10,X9) <=> (in(X11,X10) => in(X11,X9)))). 108.90/109.59 tff(zf_stmt_11, type, zip_tseitin0 : ($i * $i * $i) > $o). 108.90/109.59 tff(zf_stmt_12, axiom, (zip_tseitin0(X8,X7,X6) <=> (in(X8,X7) | (X8 = X6)))). 108.90/109.59 tff(zf_stmt_13, conjecture, 108.90/109.59 ((![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))) => 108.90/109.59 ((![X5]: (~in(X5,emptyset))) => 108.90/109.59 ((![X6,X7,X8]: (in(X8,setadjoin(X6,X7)) <=> zip_tseitin0(X8,X7,X6))) => 108.90/109.59 ((![X9,X10]: 108.90/109.59 (in(X10,powerset(X9)) <=> (![X11]: zip_tseitin1(X11,X10,X9)))) => 108.90/109.59 ((![X12,X13]: 108.90/109.59 (in(X13,setunion(X12)) <=> (?[X14]: zip_tseitin2(X14,X13,X12)))) => 108.90/109.59 (in(emptyset,omega) => 108.90/109.59 ((![X15]: (in(X15,omega) => in(setadjoin(X15,X15),omega))) => 108.90/109.59 ((![X16]: 108.90/109.59 (((![X17]: 108.90/109.59 ((in(X17,X16) & in(X17,omega)) => 108.90/109.59 in(setadjoin(X17,X17),X16))) & 108.90/109.59 in(emptyset,X16)) => 108.90/109.59 (![X18]: (in(X18,omega) => in(X18,X16))))) => 108.90/109.59 ((![X19:(($i * $i) > $o),X20]: 108.90/109.59 ((![X21]: 108.90/109.59 (in(X21,X20) => 108.90/109.59 (?[X22]: 108.90/109.59 ((![X23]: (X19(X21,X23) => (X22 = X23))) & X19(X21,X22))))) => 108.90/109.59 (?[X24]: 108.90/109.59 (![X25]: 108.90/109.59 (in(X25,X24) <=> (?[X26]: zip_tseitin3(X26,X25,X20,X19))))))) => 108.90/109.59 ((![X27]: 108.90/109.59 ((?[X28]: in(X28,X27)) => 108.90/109.59 (?[X29]: 108.90/109.59 ((~(?[X30]: (in(X30,X27) & in(X30,X29)))) & in(X29,X27))))) => 108.90/109.59 ((![X31]: 108.90/109.59 (?[X32]: 108.90/109.59 ((![X33]: 108.90/109.59 (((?[X34]: in(X34,X33)) & 108.90/109.59 (![X35]: (in(X35,X33) => in(X35,X31)))) => 108.90/109.59 (?[X36,X37]: 108.90/109.59 ((![X38]: 108.90/109.59 (in(X38,X32) => 108.90/109.59 (in(X37,X38) | 108.90/109.59 (![X39]: (in(X39,X38) => in(X39,X36)))))) & 108.90/109.59 (~(?[X40]: (in(X40,X33) & in(X40,X36)))) & 108.90/109.59 in(X37,X33) & in(X36,X32))))) & 108.90/109.59 (![X41,X42]: 108.90/109.59 ((in(X42,X32) & in(X41,X32)) => 108.90/109.59 ((![X43]: (in(X43,X42) => in(X43,X41))) | 108.90/109.59 (![X44]: (in(X44,X41) => in(X44,X42)))))) & 108.90/109.59 (![X45,X46]: 108.90/109.59 ((in(X46,X31) & in(X45,X31)) => 108.90/109.59 ((![X47]: 108.90/109.59 (in(X47,X32) => (in(X45,X47) <=> in(X46,X47)))) => 108.90/109.59 (X45 = X46)))) & 108.90/109.59 (![X48]: 108.90/109.59 (in(X48,X32) => (![X49]: (in(X49,X48) => in(X49,X31)))))))) => 108.90/109.59 ((![X50:($i > $o)]: 108.90/109.59 ((?[X51]: ((![X52]: (X50(X52) => (X51 = X52))) & X50(X51))) => 108.90/109.59 X50(descr('#ll_0'(X50))))) => 108.90/109.59 ((![X53,X54:($i > $o),X55]: 108.90/109.59 (in(X55,X53) => 108.90/109.59 (X54(X55) => in(X55,dsetconstr(X53,'#ll_0'(X54)))))) => 108.90/109.59 ((![X56,X57:($i > $o),X58]: 108.90/109.59 (in(X58,dsetconstr(X56,'#ll_0'(X57))) => in(X58,X56))) => 108.90/109.59 ((![X59,X60:($i > $o),X61]: 108.90/109.59 (in(X61,dsetconstr(X59,'#ll_0'(X60))) => X60(X61))) => 108.90/109.59 ((![X62:($i > $o)]: 108.90/109.59 ((?[X63]: 108.90/109.59 ((![X64]: (X62(X64) => (X63 = X64))) & X62(X63))) => 108.90/109.59 (?[X65]: 108.90/109.59 ((![X66]: (X62(X66) => (X65 = X66))) & X62(X65))))) => 108.90/109.59 ((![X67:$o,X68]: (in(X68,prop2set(X67)) => X67)) => 108.90/109.59 ((![X69]: (in(X69,emptyset) => (![X70:$o]: X70))) => 108.90/109.59 ((![X71]: (in(X71,emptyset) => $false)) => 108.90/109.59 ((![X72]: (~in(X72,emptyset))) => 108.90/109.59 ((![X73:($i > $o)]: 108.90/109.59 ((?[X74]: 108.90/109.59 ((![X75]: (X73(X75) => (X74 = X75))) & X73(X74))) => 108.90/109.59 (?[X76]: X73(X76)))) => 108.90/109.59 ((![X77,X78]: 108.90/109.59 ((![X79]: (in(X79,X77) => in(X79,X78))) => 108.90/109.59 ((![X80]: (in(X80,X78) => in(X80,X77))) => 108.90/109.59 (X77 = X78)))) => 108.90/109.59 ((![X81]: 108.90/109.59 ((![X82]: (~in(X82,X81))) => (X81 = emptyset))) => 108.90/109.59 ((![X83]: 108.90/109.59 ((![X84]: (~in(X84,X83))) => (X83 = emptyset))) => 108.90/109.59 ((![X85,X86:($i > $o),X87]: 108.90/109.59 (in(X87,X85) => 108.90/109.59 (in(X87,dsetconstr(X85,'#ll_0'(X86))) <=> 108.90/109.59 X86(X87)))) => 108.90/109.59 ((![X88]: 108.90/109.59 ((X88 != emptyset) => (?[X89]: in(X89,X88)))) => 108.90/109.59 ((![X90,X91:($i > $o),X92]: 108.90/109.59 (in(X92,X90) => 108.90/109.59 (X91(X92) => 108.90/109.59 (dsetconstr(X90,'#ll_0'(X91)) != emptyset)))) => 108.90/109.59 ((![X93]: 108.90/109.59 ((?[X94]: in(X94,X93)) => (X93 != emptyset))) => 108.90/109.59 ((![X95,X96]: in(X95,setadjoin(X95,X96))) => 108.90/109.59 (in(emptyset,setadjoin(emptyset,emptyset)) => 108.90/109.59 ((![X97,X98,X99]: 108.90/109.59 (in(X99,X98) => 108.90/109.59 in(X99,setadjoin(X97,X98)))) => 108.90/109.59 ((![X100,X101,X102]: 108.90/109.59 (in(X102,setadjoin(X100,X101)) => 108.90/109.59 (![X103:$o]: 108.90/109.59 (((X102 = X100) => X103) => 108.90/109.59 ((in(X102,X101) => X103) => X103))))) => 108.90/109.59 ((![X104,X105,X106]: 108.90/109.59 (in(X106,setadjoin(X104,X105)) => 108.90/109.59 (in(X106,X105) | (X106 = X104)))) => 108.90/109.59 ((![X107]: 108.90/109.59 (dsetconstr(X107,'#ll_1') = X107)) => 108.90/109.59 ((![X108,X109]: 108.90/109.59 ((![X110]: 108.90/109.59 (in(X110,X109) => in(X110,X108))) => 108.90/109.59 in(X109,powerset(X108)))) => 108.90/109.59 ((![X111]: in(emptyset,powerset(X111))) => 108.90/109.59 ((![X112]: in(emptyset,powerset(X112))) => 108.90/109.59 ((![X113,X114,X115]: 108.90/109.59 (in(X114,powerset(X113)) => 108.90/109.59 (in(X115,X114) => in(X115,X113)))) => 108.90/109.59 ((![X116,X117,X118]: 108.90/109.59 (in(X117,X118) => 108.90/109.59 (in(X118,X116) => 108.90/109.59 in(X117,setunion(X116))))) => 108.90/109.59 ((![X119,X120]: 108.90/109.59 (in(X120,setunion(X119)) => 108.90/109.59 (![X121:$o]: 108.90/109.59 ((![X122]: 108.90/109.59 (in(X120,X122) => 108.90/109.59 (in(X122,X119) => X121))) => 108.90/109.59 X121)))) => 108.90/109.59 ((![X123,X124]: 108.90/109.59 (in(X124,X123) => 108.90/109.59 in(X124, 108.90/109.59 powerset(setunion(X123))))) => 108.90/109.59 ((![X125:($i > $o)]: 108.90/109.59 ((?[X126]: 108.90/109.59 ((![X127]: 108.90/109.59 (X125(X127) => 108.90/109.59 (X126 = X127))) & 108.90/109.59 X125(X126))) => 108.90/109.59 (?[X128]: 108.90/109.59 (![X129]: 108.90/109.59 (X125(X129) <=> 108.90/109.59 (X129 = X128)))))) => 108.90/109.59 ((![X130]: 108.90/109.59 ((X130 != emptyset) => 108.90/109.59 (?[X131]: in(X131,X130)))) => 108.90/109.59 ((![X132,X133]: 108.90/109.59 (in(X132, 108.90/109.59 setadjoin(X133,emptyset)) => 108.90/109.59 (X132 = X133))) => 108.90/109.59 ((![X134,X135]: 108.90/109.59 ((X134 != X135) => 108.90/109.59 (~ 108.90/109.59 in(X135, 108.90/109.59 setadjoin(X134, 108.90/109.59 emptyset))))) => 108.90/109.59 ((![X136,X137]: 108.90/109.59 ((X136 = X137) => 108.90/109.59 in(X136, 108.90/109.59 setadjoin(X137, 108.90/109.59 emptyset)))) => 108.90/109.59 ((![X138,X139]: 108.90/109.59 (in(X138, 108.90/109.59 setadjoin(X139, 108.90/109.59 emptyset)) => 108.90/109.59 in(X139, 108.90/109.59 setadjoin(X138, 108.90/109.59 emptyset)))) => 108.90/109.59 ((![X140,X141,X142]: 108.90/109.59 (in(X142, 108.90/109.59 setadjoin(X140, 108.90/109.59 setadjoin( 108.90/109.59 X141, 108.90/109.59 emptyset))) => 108.90/109.59 ((X142 = X141) | 108.90/109.59 (X142 = X140)))) => 108.90/109.59 ((![X143,X144]: 108.90/109.59 in(X143, 108.90/109.59 setadjoin(X143, 108.90/109.59 setadjoin( 108.90/109.59 X144, 108.90/109.59 emptyset)))) => 108.90/109.59 ((![X145,X146]: 108.90/109.59 in(X146, 108.90/109.59 setadjoin(X145, 108.90/109.59 setadjoin( 108.90/109.59 X146, 108.90/109.59 emptyset)))) => 108.90/109.59 ((![X147,X148:($i > $o)]: 108.90/109.59 ((?[X149]: 108.90/109.59 (X148(X149) & 108.90/109.59 in(X149,X147))) => 108.90/109.59 ((dsetconstr( 108.90/109.59 X147,'#ll_0'(X148)) = 108.90/109.59 emptyset) => 108.90/109.59 $false))) => 108.90/109.59 ((![X150:($i > $o),X151]: 108.90/109.59 (in(X151,emptyset) => 108.90/109.59 X150(X151))) => 108.90/109.59 ((![X152,X153:($i > $o)]: 108.90/109.59 ((~ 108.90/109.59 (![X154]: 108.90/109.59 (in(X154,X152) => 108.90/109.59 X153(X154)))) => 108.90/109.59 (?[X155]: 108.90/109.59 ((~X153(X155)) & 108.90/109.59 in(X155,X152))))) => 108.90/109.59 ((![X156, 108.90/109.59 X157:($i > $o)]: 108.90/109.59 ((![X158]: 108.90/109.59 (in(X158,X156) => 108.90/109.59 (~X157(X158)))) => 108.90/109.59 (~ 108.90/109.59 (?[X159]: 108.90/109.59 (X157(X159) & 108.90/109.59 in( 108.90/109.59 X159,X156)))))) => 108.90/109.59 ((![X160, 108.90/109.59 X161:($i > $o)]: 108.90/109.59 ((~ 108.90/109.59 (?[X162]: 108.90/109.59 (X161(X162) & 108.90/109.59 in( 108.90/109.59 X162,X160)))) => 108.90/109.59 (![X163]: 108.90/109.59 (in(X163,X160) => 108.90/109.59 (~X161(X163)))))) => 108.90/109.59 ((![X164, 108.90/109.59 X165:($i > $o)]: 108.90/109.59 ((?[X166]: 108.90/109.59 ((~ 108.90/109.59 X165( 108.90/109.59 X166)) & 108.90/109.59 in( 108.90/109.59 X166,X164))) => 108.90/109.59 (~ 108.90/109.59 (![X167]: 108.90/109.59 (in( 108.90/109.59 X167,X164) => 108.90/109.59 X165( 108.90/109.59 X167)))))) => 108.90/109.59 ((![X168:$o]: 108.90/109.59 (X168 => 108.90/109.59 in(emptyset, 108.90/109.59 prop2set( 108.90/109.59 X168)))) => 108.90/109.59 ((![X169:$o]: 108.90/109.59 (X169 => 108.90/109.59 set2prop( 108.90/109.59 prop2set( 108.90/109.59 X169)))) => 108.90/109.59 ((![X170, 108.90/109.59 X171:( 108.90/109.59 $i > $o)]: 108.90/109.59 ((~ 108.90/109.59 (?[X172]: 108.90/109.59 (X171( 108.90/109.59 X172) & 108.90/109.59 in( 108.90/109.59 X172,X170)))) => 108.90/109.59 (![X173]: 108.90/109.59 ( 108.90/109.59 in( 108.90/109.59 X173,X170) => 108.90/109.59 ( 108.90/109.59 ~ 108.90/109.59 X171( 108.90/109.59 X173)))))) => 108.90/109.59 ((![X174, 108.90/109.59 X175:( 108.90/109.59 $i > $o)]: 108.90/109.59 ((~ 108.90/109.59 ( 108.90/109.59 ![X176]: 108.90/109.59 (in( 108.90/109.59 X176,X174) => 108.90/109.59 X175( 108.90/109.59 X176)))) => 108.90/109.59 (?[X177]: 108.90/109.59 (( 108.90/109.59 ~ 108.90/109.59 X175( 108.90/109.59 X177)) & 108.90/109.59 in( 108.90/109.59 X177,X174))))) => 108.90/109.59 ((![X178:( 108.90/109.59 $i > $o)]: 108.90/109.59 ((?[X179]: 108.90/109.59 (( 108.90/109.59 ![X180]: 108.90/109.59 (X178( 108.90/109.59 X180) => 108.90/109.59 (X179 = 108.90/109.59 X180))) & 108.90/109.59 X178( 108.90/109.59 X179))) => 108.90/109.59 (?[X181]: 108.90/109.59 (( 108.90/109.59 ![X182]: 108.90/109.59 (X178( 108.90/109.59 X182) => 108.90/109.59 (X181 = 108.90/109.59 X182))) & 108.90/109.59 X178( 108.90/109.59 X181))))) => 108.90/109.59 ((![X183:( 108.90/109.59 $i > $o)]: 108.90/109.59 (( 108.90/109.59 ?[X184]: 108.90/109.59 X183( 108.90/109.59 X184)) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X185, 108.90/109.59 X186]: 108.90/109.59 (X183( 108.90/109.59 X185) => 108.90/109.59 (X183( 108.90/109.59 X186) => 108.90/109.59 (X185 = 108.90/109.59 X186)))) => 108.90/109.59 ( 108.90/109.59 ?[X187]: 108.90/109.59 (( 108.90/109.59 ![X188]: 108.90/109.59 (X183( 108.90/109.59 X188) => 108.90/109.59 (X187 = 108.90/109.59 X188))) & 108.90/109.59 X183( 108.90/109.59 X187)))))) => 108.90/109.59 ((![X189:( 108.90/109.59 $i > $o)]: 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ?[X190]: 108.90/109.59 (![X191]: 108.90/109.59 (X189( 108.90/109.59 X191) <=> 108.90/109.59 (X191 = 108.90/109.59 X190)))) => 108.90/109.59 ( 108.90/109.59 ?[X192]: 108.90/109.59 (( 108.90/109.59 ![X193]: 108.90/109.59 (X189( 108.90/109.59 X193) => 108.90/109.59 (X192 = 108.90/109.59 X193))) & 108.90/109.59 X189( 108.90/109.59 X192))))) => 108.90/109.59 ((![X194, 108.90/109.59 X195]: 108.90/109.59 (( 108.90/109.59 X194 = 108.90/109.59 X195) => 108.90/109.59 (![X196, 108.90/109.59 X197]: 108.90/109.59 (( 108.90/109.59 X196 = 108.90/109.59 X197) => 108.90/109.59 (in( 108.90/109.59 X196,X194) => 108.90/109.59 in( 108.90/109.59 X197,X195)))))) => 108.90/109.59 ((![X198, 108.90/109.59 X199]: 108.90/109.59 (( 108.90/109.59 X198 = 108.90/109.59 X199) => 108.90/109.59 (![X200, 108.90/109.59 X201]: 108.90/109.59 (( 108.90/109.59 X200 = 108.90/109.59 X201) => 108.90/109.59 (in( 108.90/109.59 X200,X198) <=> 108.90/109.59 in( 108.90/109.59 X201,X199)))))) => 108.90/109.59 (( 108.90/109.59 ![X202:( 108.90/109.59 $i > $o)]: 108.90/109.59 (( 108.90/109.59 ?[X203]: 108.90/109.59 (( 108.90/109.59 ![X204]: 108.90/109.59 (X202( 108.90/109.59 X204) => 108.90/109.59 (X203 = 108.90/109.59 X204))) & 108.90/109.59 X202( 108.90/109.59 X203))) => 108.90/109.59 (![X205, 108.90/109.59 X206]: 108.90/109.59 (X202( 108.90/109.59 X205) => 108.90/109.59 (X202( 108.90/109.59 X206) => 108.90/109.59 (X205 = 108.90/109.59 X206)))))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X207:( 108.90/109.59 $i > $o), 108.90/109.59 X208:( 108.90/109.59 $i > $o)]: 108.90/109.59 (( 108.90/109.59 ![X209, 108.90/109.59 X210]: 108.90/109.59 (( 108.90/109.59 X209 = 108.90/109.59 X210) => 108.90/109.59 (X207( 108.90/109.59 X209) <=> 108.90/109.59 X208( 108.90/109.59 X210)))) => 108.90/109.59 (( 108.90/109.59 ?[X211]: 108.90/109.59 zip_tseitin5( 108.90/109.59 X211,X207)) <=> 108.90/109.59 (?[X213]: 108.90/109.59 zip_tseitin5( 108.90/109.59 X213,X208))))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 emptyset = 108.90/109.59 emptyset) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X215, 108.90/109.59 X216]: 108.90/109.59 (( 108.90/109.59 X215 = 108.90/109.59 X216) => 108.90/109.59 (![X217, 108.90/109.59 X218]: 108.90/109.59 (( 108.90/109.59 X217 = 108.90/109.59 X218) => 108.90/109.59 (setadjoin( 108.90/109.59 X215,X217) = 108.90/109.59 setadjoin( 108.90/109.59 X216,X218)))))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X219, 108.90/109.59 X220]: 108.90/109.59 (( 108.90/109.59 X219 = 108.90/109.59 X220) => 108.90/109.59 (powerset( 108.90/109.59 X219) = 108.90/109.59 powerset( 108.90/109.59 X220)))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X221, 108.90/109.59 X222]: 108.90/109.59 (( 108.90/109.59 X221 = 108.90/109.59 X222) => 108.90/109.59 (setunion( 108.90/109.59 X221) = 108.90/109.59 setunion( 108.90/109.59 X222)))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 omega = 108.90/109.59 omega) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X223:( 108.90/109.59 $i > $o)]: 108.90/109.59 (( 108.90/109.59 ?[X224]: 108.90/109.59 (( 108.90/109.59 ![X225]: 108.90/109.59 (X223( 108.90/109.59 X225) => 108.90/109.59 (X224 = 108.90/109.59 X225))) & 108.90/109.59 X223( 108.90/109.59 X224))) => 108.90/109.59 (![X226, 108.90/109.59 X227]: 108.90/109.59 (X223( 108.90/109.59 X226) => 108.90/109.59 (X223( 108.90/109.59 X227) => 108.90/109.59 (X226 = 108.90/109.59 X227)))))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X228:( 108.90/109.59 $i > $o), 108.90/109.59 X229:( 108.90/109.59 $i > $o)]: 108.90/109.59 (( 108.90/109.59 ![X230, 108.90/109.59 X231]: 108.90/109.59 (( 108.90/109.59 X230 = 108.90/109.59 X231) => 108.90/109.59 (X228( 108.90/109.59 X230) <=> 108.90/109.59 X229( 108.90/109.59 X231)))) => 108.90/109.59 (( 108.90/109.59 ?[X232]: 108.90/109.59 (( 108.90/109.59 ![X233]: 108.90/109.59 (X228( 108.90/109.59 X233) => 108.90/109.59 (X232 = 108.90/109.59 X233))) & 108.90/109.59 X228( 108.90/109.59 X232))) => 108.90/109.59 (( 108.90/109.59 ?[X234]: 108.90/109.59 (( 108.90/109.59 ![X235]: 108.90/109.59 (X229( 108.90/109.59 X235) => 108.90/109.59 (X234 = 108.90/109.59 X235))) & 108.90/109.59 X229( 108.90/109.59 X234))) => 108.90/109.59 (descr( 108.90/109.59 '#ll_0'( 108.90/109.59 X228)) = 108.90/109.59 descr( 108.90/109.59 '#ll_0'( 108.90/109.59 X229))))))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X236, 108.90/109.59 X237]: 108.90/109.59 (( 108.90/109.59 X236 = 108.90/109.59 X237) => 108.90/109.59 (![X238:( 108.90/109.59 $i > $o), 108.90/109.59 X239:( 108.90/109.59 $i > $o)]: 108.90/109.59 (( 108.90/109.59 ![X240]: 108.90/109.59 (in( 108.90/109.59 X240,X236) => 108.90/109.59 (![X241]: 108.90/109.59 (in( 108.90/109.59 X241,X237) => 108.90/109.59 (( 108.90/109.59 X240 = 108.90/109.59 X241) => 108.90/109.59 (X238( 108.90/109.59 X240) <=> 108.90/109.59 X239( 108.90/109.59 X241))))))) => 108.90/109.59 (dsetconstr( 108.90/109.59 X236, 108.90/109.59 '#ll_0'( 108.90/109.59 X238)) = 108.90/109.59 dsetconstr( 108.90/109.59 X237, 108.90/109.59 '#ll_0'( 108.90/109.59 X239))))))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X242, 108.90/109.59 X243]: 108.90/109.59 (( 108.90/109.59 ![X244]: 108.90/109.59 (in( 108.90/109.59 X244,X242) => 108.90/109.59 in( 108.90/109.59 X244,X243))) => 108.90/109.59 subset( 108.90/109.59 X242,X243))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X245, 108.90/109.59 X246]: 108.90/109.59 (( 108.90/109.59 X245 = 108.90/109.59 X246) => 108.90/109.59 subset( 108.90/109.59 X246,X245))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X247, 108.90/109.59 X248]: 108.90/109.59 (( 108.90/109.59 X247 = 108.90/109.59 X248) => 108.90/109.59 subset( 108.90/109.59 X247,X248))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X249, 108.90/109.59 X250]: 108.90/109.59 (( 108.90/109.59 ![X251]: 108.90/109.59 (in( 108.90/109.59 X251,X249) => 108.90/109.59 in( 108.90/109.59 X251,X250))) => 108.90/109.59 subset( 108.90/109.59 X249,X250))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X252]: 108.90/109.59 subset( 108.90/109.59 emptyset, 108.90/109.59 X252)) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X253, 108.90/109.59 X254,X255]: 108.90/109.59 (subset( 108.90/109.59 X253,X254) => 108.90/109.59 (in( 108.90/109.59 X255,X253) => 108.90/109.59 in( 108.90/109.59 X255,X254)))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X256, 108.90/109.59 X257,X258]: 108.90/109.59 (subset( 108.90/109.59 X256,X257) => 108.90/109.59 (( 108.90/109.59 ~ 108.90/109.59 in( 108.90/109.59 X258,X257)) => 108.90/109.59 (~ 108.90/109.59 in( 108.90/109.59 X258,X256))))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X259, 108.90/109.59 X260,X261]: 108.90/109.59 (in( 108.90/109.59 X261,X259) => 108.90/109.59 (( 108.90/109.59 ~ 108.90/109.59 in( 108.90/109.59 X261,X260)) => 108.90/109.59 (~ 108.90/109.59 subset( 108.90/109.59 X259,X260))))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X262, 108.90/109.59 X263]: 108.90/109.59 (( 108.90/109.59 ~ 108.90/109.59 subset( 108.90/109.59 X262,X263)) => 108.90/109.59 (X262 != 108.90/109.59 X263))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X264, 108.90/109.59 X265,X266]: 108.90/109.59 (in( 108.90/109.59 X266,X264) => 108.90/109.59 (( 108.90/109.59 ~ 108.90/109.59 in( 108.90/109.59 X266,X265)) => 108.90/109.59 (X264 != 108.90/109.59 X265)))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X267]: 108.90/109.59 subset( 108.90/109.59 X267,X267)) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X268, 108.90/109.59 X269,X270]: 108.90/109.59 (subset( 108.90/109.59 X268,X269) => 108.90/109.59 (subset( 108.90/109.59 X269,X270) => 108.90/109.59 subset( 108.90/109.59 X268,X270)))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X271, 108.90/109.59 X272]: 108.90/109.59 subset( 108.90/109.59 X272, 108.90/109.59 setadjoin( 108.90/109.59 X271,X272))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X273, 108.90/109.59 X274,X275]: 108.90/109.59 (subset( 108.90/109.59 X273,X275) => 108.90/109.59 subset( 108.90/109.59 X273, 108.90/109.59 setadjoin( 108.90/109.59 X274,X275)))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X276, 108.90/109.59 X277]: 108.90/109.59 (subset( 108.90/109.59 X276,X277) => 108.90/109.59 in( 108.90/109.59 X276, 108.90/109.59 powerset( 108.90/109.59 X277)))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X278, 108.90/109.59 X279]: 108.90/109.59 (subset( 108.90/109.59 X278,X279) => 108.90/109.59 (subset( 108.90/109.59 X279,X278) => 108.90/109.59 (X278 = 108.90/109.59 X279)))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X280]: 108.90/109.59 (subset( 108.90/109.59 X280, 108.90/109.59 emptyset) => 108.90/109.59 (X280 = 108.90/109.59 emptyset))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X281, 108.90/109.59 X282]: 108.90/109.59 (subset( 108.90/109.59 X282,X281) => 108.90/109.59 in( 108.90/109.59 X282, 108.90/109.59 powerset( 108.90/109.59 X281)))) => 108.90/109.59 ( 108.90/109.59 ![X283, 108.90/109.59 X284]: 108.90/109.59 (in( 108.90/109.59 X284, 108.90/109.59 powerset( 108.90/109.59 X283)) => 108.90/109.59 subset( 108.90/109.59 X284,X283))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 108.90/109.59 tff(zf_stmt_14, negated_conjecture, 108.90/109.59 (~ 108.90/109.59 ((![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))) => 108.90/109.59 ((![X5]: (~in(X5,emptyset))) => 108.90/109.59 ((![X6,X7,X8]: (in(X8,setadjoin(X6,X7)) <=> zip_tseitin0(X8,X7,X6))) => 108.90/109.59 ((![X9,X10]: 108.90/109.59 (in(X10,powerset(X9)) <=> (![X11]: zip_tseitin1(X11,X10,X9)))) => 108.90/109.59 ((![X12,X13]: 108.90/109.59 (in(X13,setunion(X12)) <=> (?[X14]: zip_tseitin2(X14,X13,X12)))) => 108.90/109.59 (in(emptyset,omega) => 108.90/109.59 ((![X15]: (in(X15,omega) => in(setadjoin(X15,X15),omega))) => 108.90/109.59 ((![X16]: 108.90/109.59 (((![X17]: 108.90/109.59 ((in(X17,X16) & in(X17,omega)) => 108.90/109.59 in(setadjoin(X17,X17),X16))) & 108.90/109.59 in(emptyset,X16)) => 108.90/109.59 (![X18]: (in(X18,omega) => in(X18,X16))))) => 108.90/109.59 ((![X19:(($i * $i) > $o),X20]: 108.90/109.59 ((![X21]: 108.90/109.59 (in(X21,X20) => 108.90/109.59 (?[X22]: 108.90/109.59 ((![X23]: (X19(X21,X23) => (X22 = X23))) & 108.90/109.59 X19(X21,X22))))) => 108.90/109.59 (?[X24]: 108.90/109.59 (![X25]: 108.90/109.59 (in(X25,X24) <=> 108.90/109.59 (?[X26]: zip_tseitin3(X26,X25,X20,X19))))))) => 108.90/109.59 ((![X27]: 108.90/109.59 ((?[X28]: in(X28,X27)) => 108.90/109.59 (?[X29]: 108.90/109.59 ((~(?[X30]: (in(X30,X27) & in(X30,X29)))) & in(X29,X27))))) => 108.90/109.59 ((![X31]: 108.90/109.59 (?[X32]: 108.90/109.59 ((![X33]: 108.90/109.59 (((?[X34]: in(X34,X33)) & 108.90/109.59 (![X35]: (in(X35,X33) => in(X35,X31)))) => 108.90/109.59 (?[X36,X37]: 108.90/109.59 ((![X38]: 108.90/109.59 (in(X38,X32) => 108.90/109.59 (in(X37,X38) | 108.90/109.59 (![X39]: (in(X39,X38) => in(X39,X36)))))) & 108.90/109.59 (~(?[X40]: (in(X40,X33) & in(X40,X36)))) & 108.90/109.59 in(X37,X33) & in(X36,X32))))) & 108.90/109.59 (![X41,X42]: 108.90/109.59 ((in(X42,X32) & in(X41,X32)) => 108.90/109.59 ((![X43]: (in(X43,X42) => in(X43,X41))) | 108.90/109.59 (![X44]: (in(X44,X41) => in(X44,X42)))))) & 108.90/109.59 (![X45,X46]: 108.90/109.59 ((in(X46,X31) & in(X45,X31)) => 108.90/109.59 ((![X47]: 108.90/109.59 (in(X47,X32) => (in(X45,X47) <=> in(X46,X47)))) => 108.90/109.59 (X45 = X46)))) & 108.90/109.59 (![X48]: 108.90/109.59 (in(X48,X32) => 108.90/109.59 (![X49]: (in(X49,X48) => in(X49,X31)))))))) => 108.90/109.59 ((![X50:($i > $o)]: 108.90/109.59 ((?[X51]: ((![X52]: (X50(X52) => (X51 = X52))) & X50(X51))) => 108.90/109.59 X50(descr('#ll_0'(X50))))) => 108.90/109.59 ((![X53,X54:($i > $o),X55]: 108.90/109.59 (in(X55,X53) => 108.90/109.59 (X54(X55) => in(X55,dsetconstr(X53,'#ll_0'(X54)))))) => 108.90/109.59 ((![X56,X57:($i > $o),X58]: 108.90/109.59 (in(X58,dsetconstr(X56,'#ll_0'(X57))) => in(X58,X56))) => 108.90/109.59 ((![X59,X60:($i > $o),X61]: 108.90/109.59 (in(X61,dsetconstr(X59,'#ll_0'(X60))) => X60(X61))) => 108.90/109.59 ((![X62:($i > $o)]: 108.90/109.59 ((?[X63]: 108.90/109.59 ((![X64]: (X62(X64) => (X63 = X64))) & X62(X63))) => 108.90/109.59 (?[X65]: 108.90/109.59 ((![X66]: (X62(X66) => (X65 = X66))) & X62(X65))))) => 108.90/109.59 ((![X67:$o,X68]: (in(X68,prop2set(X67)) => X67)) => 108.90/109.59 ((![X69]: (in(X69,emptyset) => (![X70:$o]: X70))) => 108.90/109.59 ((![X71]: (in(X71,emptyset) => $false)) => 108.90/109.59 ((![X72]: (~in(X72,emptyset))) => 108.90/109.59 ((![X73:($i > $o)]: 108.90/109.59 ((?[X74]: 108.90/109.59 ((![X75]: (X73(X75) => (X74 = X75))) & 108.90/109.59 X73(X74))) => 108.90/109.59 (?[X76]: X73(X76)))) => 108.90/109.59 ((![X77,X78]: 108.90/109.59 ((![X79]: (in(X79,X77) => in(X79,X78))) => 108.90/109.59 ((![X80]: (in(X80,X78) => in(X80,X77))) => 108.90/109.59 (X77 = X78)))) => 108.90/109.59 ((![X81]: 108.90/109.59 ((![X82]: (~in(X82,X81))) => (X81 = emptyset))) => 108.90/109.59 ((![X83]: 108.90/109.59 ((![X84]: (~in(X84,X83))) => (X83 = emptyset))) => 108.90/109.59 ((![X85,X86:($i > $o),X87]: 108.90/109.59 (in(X87,X85) => 108.90/109.59 (in(X87,dsetconstr(X85,'#ll_0'(X86))) <=> 108.90/109.59 X86(X87)))) => 108.90/109.59 ((![X88]: 108.90/109.59 ((X88 != emptyset) => (?[X89]: in(X89,X88)))) => 108.90/109.59 ((![X90,X91:($i > $o),X92]: 108.90/109.59 (in(X92,X90) => 108.90/109.59 (X91(X92) => 108.90/109.59 (dsetconstr(X90,'#ll_0'(X91)) != emptyset)))) => 108.90/109.59 ((![X93]: 108.90/109.59 ((?[X94]: in(X94,X93)) => 108.90/109.59 (X93 != emptyset))) => 108.90/109.59 ((![X95,X96]: in(X95,setadjoin(X95,X96))) => 108.90/109.59 (in(emptyset,setadjoin(emptyset,emptyset)) => 108.90/109.59 ((![X97,X98,X99]: 108.90/109.59 (in(X99,X98) => 108.90/109.59 in(X99,setadjoin(X97,X98)))) => 108.90/109.59 ((![X100,X101,X102]: 108.90/109.59 (in(X102,setadjoin(X100,X101)) => 108.90/109.59 (![X103:$o]: 108.90/109.59 (((X102 = X100) => X103) => 108.90/109.59 ((in(X102,X101) => X103) => X103))))) => 108.90/109.59 ((![X104,X105,X106]: 108.90/109.59 (in(X106,setadjoin(X104,X105)) => 108.90/109.59 (in(X106,X105) | (X106 = X104)))) => 108.90/109.59 ((![X107]: 108.90/109.59 (dsetconstr(X107,'#ll_1') = X107)) => 108.90/109.59 ((![X108,X109]: 108.90/109.59 ((![X110]: 108.90/109.59 (in(X110,X109) => in(X110,X108))) => 108.90/109.59 in(X109,powerset(X108)))) => 108.90/109.59 ((![X111]: in(emptyset,powerset(X111))) => 108.90/109.59 ((![X112]: 108.90/109.59 in(emptyset,powerset(X112))) => 108.90/109.59 ((![X113,X114,X115]: 108.90/109.59 (in(X114,powerset(X113)) => 108.90/109.59 (in(X115,X114) => in(X115,X113)))) => 108.90/109.59 ((![X116,X117,X118]: 108.90/109.59 (in(X117,X118) => 108.90/109.59 (in(X118,X116) => 108.90/109.59 in(X117,setunion(X116))))) => 108.90/109.59 ((![X119,X120]: 108.90/109.59 (in(X120,setunion(X119)) => 108.90/109.59 (![X121:$o]: 108.90/109.59 ((![X122]: 108.90/109.59 (in(X120,X122) => 108.90/109.59 (in(X122,X119) => 108.90/109.59 X121))) => 108.90/109.59 X121)))) => 108.90/109.59 ((![X123,X124]: 108.90/109.59 (in(X124,X123) => 108.90/109.59 in(X124, 108.90/109.59 powerset(setunion(X123))))) => 108.90/109.59 ((![X125:($i > $o)]: 108.90/109.59 ((?[X126]: 108.90/109.59 ((![X127]: 108.90/109.59 (X125(X127) => 108.90/109.59 (X126 = X127))) & 108.90/109.59 X125(X126))) => 108.90/109.59 (?[X128]: 108.90/109.59 (![X129]: 108.90/109.59 (X125(X129) <=> 108.90/109.59 (X129 = X128)))))) => 108.90/109.59 ((![X130]: 108.90/109.59 ((X130 != emptyset) => 108.90/109.59 (?[X131]: in(X131,X130)))) => 108.90/109.59 ((![X132,X133]: 108.90/109.59 (in(X132, 108.90/109.59 setadjoin(X133, 108.90/109.59 emptyset)) => 108.90/109.59 (X132 = X133))) => 108.90/109.59 ((![X134,X135]: 108.90/109.59 ((X134 != X135) => 108.90/109.59 (~ 108.90/109.59 in(X135, 108.90/109.59 setadjoin(X134, 108.90/109.59 emptyset))))) => 108.90/109.59 ((![X136,X137]: 108.90/109.59 ((X136 = X137) => 108.90/109.59 in(X136, 108.90/109.59 setadjoin(X137, 108.90/109.59 emptyset)))) => 108.90/109.59 ((![X138,X139]: 108.90/109.59 (in(X138, 108.90/109.59 setadjoin(X139, 108.90/109.59 emptyset)) => 108.90/109.59 in(X139, 108.90/109.59 setadjoin(X138, 108.90/109.59 emptyset)))) => 108.90/109.59 ((![X140,X141,X142]: 108.90/109.59 (in(X142, 108.90/109.59 setadjoin( 108.90/109.59 X140, 108.90/109.59 setadjoin( 108.90/109.59 X141,emptyset))) => 108.90/109.59 ((X142 = X141) | 108.90/109.59 (X142 = X140)))) => 108.90/109.59 ((![X143,X144]: 108.90/109.59 in(X143, 108.90/109.59 setadjoin( 108.90/109.59 X143, 108.90/109.59 setadjoin( 108.90/109.59 X144,emptyset)))) => 108.90/109.59 ((![X145,X146]: 108.90/109.59 in(X146, 108.90/109.59 setadjoin( 108.90/109.59 X145, 108.90/109.59 setadjoin( 108.90/109.59 X146,emptyset)))) => 108.90/109.59 ((![X147,X148:($i > $o)]: 108.90/109.59 ((?[X149]: 108.90/109.59 (X148(X149) & 108.90/109.59 in(X149,X147))) => 108.90/109.59 ((dsetconstr( 108.90/109.59 X147, 108.90/109.59 '#ll_0'(X148)) = 108.90/109.59 emptyset) => 108.90/109.59 $false))) => 108.90/109.59 ((![X150:($i > $o), 108.90/109.59 X151]: 108.90/109.59 (in(X151,emptyset) => 108.90/109.59 X150(X151))) => 108.90/109.59 ((![X152, 108.90/109.59 X153:($i > $o)]: 108.90/109.59 ((~ 108.90/109.59 (![X154]: 108.90/109.59 (in( 108.90/109.59 X154,X152) => 108.90/109.59 X153(X154)))) => 108.90/109.59 (?[X155]: 108.90/109.59 ((~X153(X155)) & 108.90/109.59 in(X155,X152))))) => 108.90/109.59 ((![X156, 108.90/109.59 X157:($i > $o)]: 108.90/109.59 ((![X158]: 108.90/109.59 (in( 108.90/109.59 X158,X156) => 108.90/109.59 (~ 108.90/109.59 X157( 108.90/109.59 X158)))) => 108.90/109.59 (~ 108.90/109.59 (?[X159]: 108.90/109.59 (X157( 108.90/109.59 X159) & 108.90/109.59 in( 108.90/109.59 X159,X156)))))) => 108.90/109.59 ((![X160, 108.90/109.59 X161:($i > $o)]: 108.90/109.59 ((~ 108.90/109.59 (?[X162]: 108.90/109.59 ( 108.90/109.59 X161( 108.90/109.59 X162) & 108.90/109.59 in( 108.90/109.59 X162,X160)))) => 108.90/109.59 (![X163]: 108.90/109.59 (in( 108.90/109.59 X163,X160) => 108.90/109.59 (~ 108.90/109.59 X161( 108.90/109.59 X163)))))) => 108.90/109.59 ((![X164, 108.90/109.59 X165:( 108.90/109.59 $i > $o)]: 108.90/109.59 ((?[X166]: 108.90/109.59 (( 108.90/109.59 ~ 108.90/109.59 X165( 108.90/109.59 X166)) & 108.90/109.59 in( 108.90/109.59 X166,X164))) => 108.90/109.59 (~ 108.90/109.59 (![X167]: 108.90/109.59 (in( 108.90/109.59 X167,X164) => 108.90/109.59 X165( 108.90/109.59 X167)))))) => 108.90/109.59 ((![X168:$o]: 108.90/109.59 (X168 => 108.90/109.59 in(emptyset, 108.90/109.59 prop2set( 108.90/109.59 X168)))) => 108.90/109.59 ((![X169:$o]: 108.90/109.59 (X169 => 108.90/109.59 set2prop( 108.90/109.59 prop2set( 108.90/109.59 X169)))) => 108.90/109.59 ((![X170, 108.90/109.59 X171:( 108.90/109.59 $i > $o)]: 108.90/109.59 ((~ 108.90/109.59 ( 108.90/109.59 ?[X172]: 108.90/109.59 (X171( 108.90/109.59 X172) & 108.90/109.59 in( 108.90/109.59 X172,X170)))) => 108.90/109.59 (![X173]: 108.90/109.59 (in( 108.90/109.59 X173,X170) => 108.90/109.59 (~ 108.90/109.59 X171( 108.90/109.59 X173)))))) => 108.90/109.59 ((![X174, 108.90/109.59 X175:( 108.90/109.59 $i > $o)]: 108.90/109.59 (( 108.90/109.59 ~ 108.90/109.59 ( 108.90/109.59 ![X176]: 108.90/109.59 (in( 108.90/109.59 X176,X174) => 108.90/109.59 X175( 108.90/109.59 X176)))) => 108.90/109.59 ( 108.90/109.59 ?[X177]: 108.90/109.59 (( 108.90/109.59 ~ 108.90/109.59 X175( 108.90/109.59 X177)) & 108.90/109.59 in( 108.90/109.59 X177,X174))))) => 108.90/109.59 ((![X178:( 108.90/109.59 $i > $o)]: 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ?[X179]: 108.90/109.59 (( 108.90/109.59 ![X180]: 108.90/109.59 (X178( 108.90/109.59 X180) => 108.90/109.59 (X179 = 108.90/109.59 X180))) & 108.90/109.59 X178( 108.90/109.59 X179))) => 108.90/109.59 ( 108.90/109.59 ?[X181]: 108.90/109.59 (( 108.90/109.59 ![X182]: 108.90/109.59 (X178( 108.90/109.59 X182) => 108.90/109.59 (X181 = 108.90/109.59 X182))) & 108.90/109.59 X178( 108.90/109.59 X181))))) => 108.90/109.59 ((![X183:( 108.90/109.59 $i > $o)]: 108.90/109.59 (( 108.90/109.59 ?[X184]: 108.90/109.59 X183( 108.90/109.59 X184)) => 108.90/109.59 (( 108.90/109.59 ![X185, 108.90/109.59 X186]: 108.90/109.59 (X183( 108.90/109.59 X185) => 108.90/109.59 (X183( 108.90/109.59 X186) => 108.90/109.59 (X185 = 108.90/109.59 X186)))) => 108.90/109.59 (?[X187]: 108.90/109.59 (( 108.90/109.59 ![X188]: 108.90/109.59 (X183( 108.90/109.59 X188) => 108.90/109.59 (X187 = 108.90/109.59 X188))) & 108.90/109.59 X183( 108.90/109.59 X187)))))) => 108.90/109.59 ((![X189:( 108.90/109.59 $i > $o)]: 108.90/109.59 (( 108.90/109.59 ?[X190]: 108.90/109.59 (![X191]: 108.90/109.59 (X189( 108.90/109.59 X191) <=> 108.90/109.59 (X191 = 108.90/109.59 X190)))) => 108.90/109.59 (?[X192]: 108.90/109.59 (( 108.90/109.59 ![X193]: 108.90/109.59 (X189( 108.90/109.59 X193) => 108.90/109.59 (X192 = 108.90/109.59 X193))) & 108.90/109.59 X189( 108.90/109.59 X192))))) => 108.90/109.59 (( 108.90/109.59 ![X194, 108.90/109.59 X195]: 108.90/109.59 (( 108.90/109.59 X194 = 108.90/109.59 X195) => 108.90/109.59 (![X196, 108.90/109.59 X197]: 108.90/109.59 (( 108.90/109.59 X196 = 108.90/109.59 X197) => 108.90/109.59 (in( 108.90/109.59 X196,X194) => 108.90/109.59 in( 108.90/109.59 X197,X195)))))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X198, 108.90/109.59 X199]: 108.90/109.59 (( 108.90/109.59 X198 = 108.90/109.59 X199) => 108.90/109.59 (![X200, 108.90/109.59 X201]: 108.90/109.59 (( 108.90/109.59 X200 = 108.90/109.59 X201) => 108.90/109.59 (in( 108.90/109.59 X200,X198) <=> 108.90/109.59 in( 108.90/109.59 X201,X199)))))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X202:( 108.90/109.59 $i > $o)]: 108.90/109.59 (( 108.90/109.59 ?[X203]: 108.90/109.59 (( 108.90/109.59 ![X204]: 108.90/109.59 (X202( 108.90/109.59 X204) => 108.90/109.59 (X203 = 108.90/109.59 X204))) & 108.90/109.59 X202( 108.90/109.59 X203))) => 108.90/109.59 (![X205, 108.90/109.59 X206]: 108.90/109.59 (X202( 108.90/109.59 X205) => 108.90/109.59 (X202( 108.90/109.59 X206) => 108.90/109.59 (X205 = 108.90/109.59 X206)))))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X207:( 108.90/109.59 $i > $o), 108.90/109.59 X208:( 108.90/109.59 $i > $o)]: 108.90/109.59 (( 108.90/109.59 ![X209, 108.90/109.59 X210]: 108.90/109.59 (( 108.90/109.59 X209 = 108.90/109.59 X210) => 108.90/109.59 (X207( 108.90/109.59 X209) <=> 108.90/109.59 X208( 108.90/109.59 X210)))) => 108.90/109.59 (( 108.90/109.59 ?[X211]: 108.90/109.59 zip_tseitin5( 108.90/109.59 X211,X207)) <=> 108.90/109.59 (?[X213]: 108.90/109.59 zip_tseitin5( 108.90/109.59 X213,X208))))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 emptyset = 108.90/109.59 emptyset) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X215, 108.90/109.59 X216]: 108.90/109.59 (( 108.90/109.59 X215 = 108.90/109.59 X216) => 108.90/109.59 (![X217, 108.90/109.59 X218]: 108.90/109.59 (( 108.90/109.59 X217 = 108.90/109.59 X218) => 108.90/109.59 (setadjoin( 108.90/109.59 X215,X217) = 108.90/109.59 setadjoin( 108.90/109.59 X216,X218)))))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X219, 108.90/109.59 X220]: 108.90/109.59 (( 108.90/109.59 X219 = 108.90/109.59 X220) => 108.90/109.59 (powerset( 108.90/109.59 X219) = 108.90/109.59 powerset( 108.90/109.59 X220)))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X221, 108.90/109.59 X222]: 108.90/109.59 (( 108.90/109.59 X221 = 108.90/109.59 X222) => 108.90/109.59 (setunion( 108.90/109.59 X221) = 108.90/109.59 setunion( 108.90/109.59 X222)))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 omega = 108.90/109.59 omega) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X223:( 108.90/109.59 $i > $o)]: 108.90/109.59 (( 108.90/109.59 ?[X224]: 108.90/109.59 (( 108.90/109.59 ![X225]: 108.90/109.59 (X223( 108.90/109.59 X225) => 108.90/109.59 (X224 = 108.90/109.59 X225))) & 108.90/109.59 X223( 108.90/109.59 X224))) => 108.90/109.59 (![X226, 108.90/109.59 X227]: 108.90/109.59 (X223( 108.90/109.59 X226) => 108.90/109.59 (X223( 108.90/109.59 X227) => 108.90/109.59 (X226 = 108.90/109.59 X227)))))) => 108.90/109.59 ( 108.90/109.59 ( 108.90/109.59 ![X228:( 108.90/109.60 $i > $o), 108.90/109.60 X229:( 108.90/109.60 $i > $o)]: 108.90/109.60 (( 108.90/109.60 ![X230, 108.90/109.60 X231]: 108.90/109.60 (( 108.90/109.60 X230 = 108.90/109.60 X231) => 108.90/109.60 (X228( 108.90/109.60 X230) <=> 108.90/109.60 X229( 108.90/109.60 X231)))) => 108.90/109.60 (( 108.90/109.60 ?[X232]: 108.90/109.60 (( 108.90/109.60 ![X233]: 108.90/109.60 (X228( 108.90/109.60 X233) => 108.90/109.60 (X232 = 108.90/109.60 X233))) & 108.90/109.60 X228( 108.90/109.60 X232))) => 108.90/109.60 (( 108.90/109.60 ?[X234]: 108.90/109.60 (( 108.90/109.60 ![X235]: 108.90/109.60 (X229( 108.90/109.60 X235) => 108.90/109.60 (X234 = 108.90/109.60 X235))) & 108.90/109.60 X229( 108.90/109.60 X234))) => 108.90/109.60 (descr( 108.90/109.60 '#ll_0'( 108.90/109.60 X228)) = 108.90/109.60 descr( 108.90/109.60 '#ll_0'( 108.90/109.60 X229))))))) => 108.90/109.60 ( 108.90/109.60 ( 108.90/109.60 ![X236, 108.90/109.60 X237]: 108.90/109.60 (( 108.90/109.60 X236 = 108.90/109.60 X237) => 108.90/109.60 (![X238:( 108.90/109.60 $i > $o), 108.90/109.60 X239:( 108.90/109.60 $i > $o)]: 108.90/109.60 (( 108.90/109.60 ![X240]: 108.90/109.60 (in( 108.90/109.60 X240,X236) => 108.90/109.60 (![X241]: 108.90/109.60 (in( 108.90/109.60 X241,X237) => 108.90/109.60 (( 108.90/109.60 X240 = 108.90/109.60 X241) => 108.90/109.60 (X238( 108.90/109.60 X240) <=> 108.90/109.60 X239( 108.90/109.60 X241))))))) => 108.90/109.60 (dsetconstr( 108.90/109.60 X236, 108.90/109.60 '#ll_0'( 108.90/109.60 X238)) = 108.90/109.60 dsetconstr( 108.90/109.60 X237, 108.90/109.60 '#ll_0'( 108.90/109.60 X239))))))) => 108.90/109.60 ( 108.90/109.60 ( 108.90/109.60 ![X242, 108.90/109.60 X243]: 108.90/109.60 (( 108.90/109.60 ![X244]: 108.90/109.60 (in( 108.90/109.60 X244,X242) => 108.90/109.60 in( 108.90/109.60 X244,X243))) => 108.90/109.60 subset( 108.90/109.60 X242,X243))) => 108.90/109.60 ( 108.90/109.60 ( 108.90/109.60 ![X245, 108.90/109.60 X246]: 108.90/109.60 (( 108.90/109.60 X245 = 108.90/109.60 X246) => 108.90/109.60 subset( 108.90/109.60 X246,X245))) => 108.90/109.60 ( 108.90/109.60 ( 108.90/109.60 ![X247, 108.90/109.60 X248]: 108.90/109.60 (( 108.90/109.60 X247 = 108.90/109.60 X248) => 108.90/109.60 subset( 108.90/109.60 X247,X248))) => 108.90/109.60 ( 108.90/109.60 ( 108.90/109.60 ![X249, 108.90/109.60 X250]: 108.90/109.60 (( 108.90/109.60 ![X251]: 108.90/109.60 (in( 108.90/109.60 X251,X249) => 108.90/109.60 in( 108.90/109.60 X251,X250))) => 108.90/109.60 subset( 108.90/109.60 X249,X250))) => 108.90/109.60 ( 108.90/109.60 ( 108.90/109.60 ![X252]: 108.90/109.60 subset( 108.90/109.60 emptyset, 108.90/109.60 X252)) => 108.90/109.60 ( 108.90/109.60 ( 108.90/109.60 ![X253, 108.90/109.60 X254,X255]: 108.90/109.60 (subset( 108.90/109.60 X253,X254) => 108.90/109.60 (in( 108.90/109.60 X255,X253) => 108.90/109.60 in( 108.90/109.60 X255,X254)))) => 108.90/109.60 ( 108.90/109.60 ( 108.90/109.60 ![X256, 108.90/109.60 X257,X258]: 108.90/109.60 (subset( 108.90/109.60 X256,X257) => 108.90/109.60 (( 108.90/109.60 ~ 108.90/109.60 in( 108.90/109.60 X258,X257)) => 108.90/109.60 (~ 108.90/109.60 in( 108.90/109.60 X258,X256))))) => 108.90/109.60 ( 108.90/109.60 ( 108.90/109.60 ![X259, 108.90/109.60 X260,X261]: 108.90/109.60 (in( 108.90/109.60 X261,X259) => 108.90/109.60 (( 108.90/109.60 ~ 108.90/109.60 in( 108.90/109.60 X261,X260)) => 108.90/109.60 (~ 108.90/109.60 subset( 108.90/109.60 X259,X260))))) => 108.90/109.60 ( 108.90/109.60 ( 108.90/109.60 ![X262, 108.90/109.60 X263]: 108.90/109.60 (( 108.90/109.60 ~ 108.90/109.60 subset( 108.90/109.60 X262,X263)) => 108.90/109.60 (X262 != 108.90/109.60 X263))) => 108.90/109.60 ( 108.90/109.60 ( 108.90/109.60 ![X264, 108.90/109.60 X265,X266]: 108.90/109.60 (in( 108.90/109.60 X266,X264) => 108.90/109.60 (( 108.90/109.60 ~ 108.90/109.60 in( 108.90/109.60 X266,X265)) => 108.90/109.60 (X264 != 108.90/109.60 X265)))) => 108.90/109.60 ( 108.90/109.60 ( 108.90/109.60 ![X267]: 108.90/109.60 subset( 108.90/109.60 X267,X267)) => 108.90/109.60 ( 108.90/109.60 ( 108.90/109.60 ![X268, 108.90/109.60 X269,X270]: 108.90/109.60 (subset( 108.90/109.60 X268,X269) => 108.90/109.60 (subset( 108.90/109.60 X269,X270) => 108.90/109.60 subset( 108.90/109.60 X268,X270)))) => 108.90/109.60 ( 108.90/109.60 ( 108.90/109.60 ![X271, 108.90/109.60 X272]: 108.90/109.60 subset( 108.90/109.60 X272, 108.90/109.60 setadjoin( 108.90/109.60 X271,X272))) => 108.90/109.60 ( 108.90/109.60 ( 108.90/109.60 ![X273, 108.90/109.60 X274,X275]: 108.90/109.60 (subset( 108.90/109.60 X273,X275) => 108.90/109.60 subset( 108.90/109.60 X273, 108.90/109.60 setadjoin( 108.90/109.60 X274,X275)))) => 108.90/109.60 ( 108.90/109.60 ( 108.90/109.60 ![X276, 108.90/109.60 X277]: 108.90/109.60 (subset( 108.90/109.60 X276,X277) => 108.90/109.60 in( 108.90/109.60 X276, 108.90/109.60 powerset( 108.90/109.60 X277)))) => 108.90/109.60 ( 108.90/109.60 ( 108.90/109.60 ![X278, 108.90/109.60 X279]: 108.90/109.60 (subset( 108.90/109.60 X278,X279) => 108.90/109.60 (subset( 108.90/109.60 X279,X278) => 108.90/109.60 (X278 = 108.90/109.60 X279)))) => 108.90/109.60 ( 108.90/109.60 ( 108.90/109.60 ![X280]: 108.90/109.60 (subset( 108.90/109.60 X280, 108.90/109.60 emptyset) => 108.90/109.60 (X280 = 108.90/109.60 emptyset))) => 108.90/109.60 ( 108.90/109.60 ( 108.90/109.60 ![X281, 108.90/109.60 X282]: 108.90/109.60 (subset( 108.90/109.60 X282,X281) => 108.90/109.60 in( 108.90/109.60 X282, 108.90/109.60 powerset( 108.90/109.60 X281)))) => 108.90/109.60 ( 108.90/109.60 ![X283, 108.90/109.60 X284]: 108.90/109.60 (in( 108.90/109.60 X284, 108.90/109.60 powerset( 108.90/109.60 X283)) => 108.90/109.60 subset( 108.90/109.60 X284,X283)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 108.90/109.60 tff('95', plain, ~ subset(sk_X284_, sk_X283_), 108.90/109.60 inference('cnf', [status(esa)], [zf_stmt_14])). 108.90/109.60 tff('96', plain, 108.90/109.60 ![X399, X400]: (subset(X399, X400) | in(sk_X251_(X400, X399), X399)), 108.90/109.60 inference('cnf', [status(esa)], [zf_stmt_14])). 108.90/109.60 tff('97', plain, in(sk_X284_, powerset(sk_X283_)), 108.90/109.60 inference('cnf', [status(esa)], [zf_stmt_14])). 108.90/109.60 tff('98', plain, 108.90/109.60 ![X399, X400]: (subset(X399, X400) | ~ in(sk_X251_(X400, X399), X400)), 108.90/109.60 inference('cnf', [status(esa)], [zf_stmt_14])). 108.90/109.60 tff('99', plain, 108.90/109.60 ![X481, X482, X483]: 108.90/109.60 (~ in(X481, powerset(X482)) | in(X483, X482) | ~ in(X483, X481)), 108.90/109.60 inference('cnf', [status(esa)], [zf_stmt_14])). 108.90/109.60 tff('100', plain, $false, 108.90/109.60 inference('eprover', [status(thm)], ['95', '96', '97', '98', '99'])). 108.90/109.60 108.90/109.60 % SZS output end Refutation 108.90/109.60 % Zipperpin 1.5 exiting 108.90/109.60 EOF