0.06/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.13 % Command : run_portfolio.sh /export/starexec/sandbox/benchmark/theBenchmark.p /export/starexec/sandbox/tmp/tmp.Gb1Mwfx9tN 0.14/0.34 % Computer : n021.cluster.edu 0.14/0.34 % Model : x86_64 x86_64 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.34 % Memory : 8042.1875MB 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.34 % CPULimit : 180 0.14/0.34 % DateTime : Thu Aug 29 14:27:19 EDT 2019 0.14/0.34 % CPUTime : 102.51/103.25 % Running portfolio for 180 s 102.51/103.25 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 102.51/103.25 % TempDir : /export/starexec/sandbox/tmp/tmp.Gb1Mwfx9tN 102.51/103.25 % Recognized as monomorphic HO. 102.51/103.25 % Running /export/starexec/sandbox/solver/bin/competitive.sh for 18 102.51/103.25 % Running /export/starexec/sandbox/solver/bin/competitive.2.sh for 13 102.51/103.25 % Running /export/starexec/sandbox/solver/bin/competitive.3.sh for 3 102.51/103.25 % Running /export/starexec/sandbox/solver/bin/pragmatic.rudimentary.sh for 28 102.51/103.25 % Running /export/starexec/sandbox/solver/bin/pragmatic.rudimentary.1.sh for 12 102.51/103.25 % Running /export/starexec/sandbox/solver/bin/pragmatic.rudimentary.2.sh for 7 102.51/103.25 % Running /export/starexec/sandbox/solver/bin/pragmatic.shallow.sh for 3 102.51/103.25 % Running /export/starexec/sandbox/solver/bin/pragmatic.shallow.1.sh for 14 102.51/103.25 % Running /export/starexec/sandbox/solver/bin/pragmatic.shallow.2.sh for 12 102.51/103.25 % Running /export/starexec/sandbox/solver/bin/pragmatic.ll.e.sh for 19 102.51/103.25 % Solved by: pragmatic.ll.e.sh 102.51/103.25 % Running : timeout 16 /export/starexec/sandbox/solver/bin/eprover-ho /export/starexec/sandbox/tmp/tmp.Gb1Mwfx9tN/e_input836e2d --cpu-limit=14 --auto-schedule -s -p. 102.51/103.25 % done 467 iterations in 4.709s 102.51/103.25 % hashcons stats for terms: size 4096, num 24025, sum length 37562, buckets: small 3, median 7, big 22 102.51/103.25 % proof state stats: {active 193, passive 6723, simpl 0} 102.51/103.25 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 102.51/103.25 % SZS output start Refutation 102.51/103.25 tff(binunionLsub, axiom, binunionLsub <=> (![A,B]: subset(A,binunion(A,B)))). 102.51/103.25 tff('0', plain, binunionLsub = (![X2,X3]: subset(X2,binunion(X2,X3))), 102.51/103.25 define([status(thm)])). 102.51/103.25 tff(binunionE, axiom, binunionE <=> 102.51/103.25 (![A,B,Xx]: (in(Xx,binunion(A,B)) => (in(Xx,B) | in(Xx,A))))). 102.51/103.25 tff('1', plain, 102.51/103.25 binunionE = 102.51/103.25 (![X2,X3,X4]: (in(X4,binunion(X2,X3)) => (in(X4,X3) | in(X4,X2)))), 102.51/103.25 define([status(thm)])). 102.51/103.25 tff(binunionEcases, axiom, binunionEcases <=> 102.51/103.25 (![A,B,Xx,Xphi:$o]: 102.51/103.25 (in(Xx,binunion(A,B)) => 102.51/103.25 ((in(Xx,A) => Xphi) => ((in(Xx,B) => Xphi) => Xphi))))). 102.51/103.25 tff('2', plain, 102.51/103.25 binunionEcases = 102.51/103.25 (![X2,X3,X4,X5:$o]: 102.51/103.26 (in(X4,binunion(X2,X3)) => 102.51/103.26 ((in(X4,X2) => X5) => ((in(X4,X3) => X5) => X5)))), 102.51/103.26 define([status(thm)])). 102.51/103.26 tff(binunionIR, axiom, binunionIR <=> 102.51/103.26 (![A,B,Xx]: (in(Xx,B) => in(Xx,binunion(A,B))))). 102.51/103.26 tff('3', plain, 102.51/103.26 binunionIR = (![X2,X3,X4]: (in(X4,X3) => in(X4,binunion(X2,X3)))), 102.51/103.26 define([status(thm)])). 102.51/103.26 tff(upairset2IR, axiom, upairset2IR <=> 102.51/103.26 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 102.51/103.26 tff('4', plain, 102.51/103.26 upairset2IR = (![X2,X3]: in(X3,setadjoin(X2,setadjoin(X3,emptyset)))), 102.51/103.26 define([status(thm)])). 102.51/103.26 tff(binunionIL, axiom, binunionIL <=> 102.51/103.26 (![A,B,Xx]: (in(Xx,A) => in(Xx,binunion(A,B))))). 102.51/103.26 tff('5', plain, 102.51/103.26 binunionIL = (![X2,X3,X4]: (in(X4,X2) => in(X4,binunion(X2,X3)))), 102.51/103.26 define([status(thm)])). 102.51/103.26 tff(sepSubset, axiom, sepSubset <=> 102.51/103.26 (![A,Xphi:($i > $o)]: subset(dsetconstr(A,^[Xx]: Xphi(Xx)),A))). 102.51/103.26 tff('6', plain, 102.51/103.26 sepSubset = 102.51/103.26 (![X2,X3:($i > $o)]: subset(dsetconstr(X2,^[V_1]: X3(V_1)),X2)), 102.51/103.26 define([status(thm)])). 102.51/103.26 tff(sepInPowerset, axiom, sepInPowerset <=> 102.51/103.26 (![A,Xphi:($i > $o)]: in(dsetconstr(A,^[Xx]: Xphi(Xx)),powerset(A)))). 102.51/103.26 tff('7', plain, 102.51/103.26 sepInPowerset = 102.51/103.26 (![X2,X3:($i > $o)]: in(dsetconstr(X2,^[V_1]: X3(V_1)),powerset(X2))), 102.51/103.26 define([status(thm)])). 102.51/103.26 tff(powersetsubset, axiom, powersetsubset <=> 102.51/103.26 (![A,B]: (subset(A,B) => subset(powerset(A),powerset(B))))). 102.51/103.26 tff('8', plain, 102.51/103.26 powersetsubset = 102.51/103.26 (![X2,X3]: (subset(X2,X3) => subset(powerset(X2),powerset(X3)))), 102.51/103.26 define([status(thm)])). 102.51/103.26 tff(inPowerset, axiom, inPowerset <=> (![A]: in(A,powerset(A)))). 102.51/103.26 tff('9', plain, inPowerset = (![X2]: in(X2,powerset(X2))), 102.51/103.26 define([status(thm)])). 102.51/103.26 tff(powersetE1, axiom, powersetE1 <=> 102.51/103.26 (![A,B]: (in(B,powerset(A)) => subset(B,A)))). 102.51/103.26 tff('10', plain, 102.51/103.26 powersetE1 = (![X2,X3]: (in(X3,powerset(X2)) => subset(X3,X2))), 102.51/103.26 define([status(thm)])). 102.51/103.26 tff(powersetI1, axiom, powersetI1 <=> 102.51/103.26 (![A,B]: (subset(B,A) => in(B,powerset(A))))). 102.51/103.26 tff('11', plain, 102.51/103.26 powersetI1 = (![X2,X3]: (subset(X3,X2) => in(X3,powerset(X2)))), 102.51/103.26 define([status(thm)])). 102.51/103.26 tff(subsetemptysetimpeq, axiom, subsetemptysetimpeq <=> 102.51/103.26 (![A]: (subset(A,emptyset) => (A = emptyset)))). 102.51/103.26 tff('12', plain, 102.51/103.26 subsetemptysetimpeq = (![X2]: (subset(X2,emptyset) => (X2 = emptyset))), 102.51/103.26 define([status(thm)])). 102.51/103.26 tff(setextsub, axiom, setextsub <=> 102.51/103.26 (![A,B]: (subset(A,B) => (subset(B,A) => (A = B))))). 102.51/103.26 tff('13', plain, 102.51/103.26 setextsub = (![X2,X3]: (subset(X2,X3) => (subset(X3,X2) => (X2 = X3)))), 102.51/103.26 define([status(thm)])). 102.51/103.26 tff(subset2powerset, axiom, subset2powerset <=> 102.51/103.26 (![A,B]: (subset(A,B) => in(A,powerset(B))))). 102.51/103.26 tff('14', plain, 102.51/103.26 subset2powerset = (![X2,X3]: (subset(X2,X3) => in(X2,powerset(X3)))), 102.51/103.26 define([status(thm)])). 102.51/103.26 tff(setadjoinSub2, axiom, setadjoinSub2 <=> 102.51/103.26 (![A,Xx,B]: (subset(A,B) => subset(A,setadjoin(Xx,B))))). 102.51/103.26 tff('15', plain, 102.51/103.26 setadjoinSub2 = 102.51/103.26 (![X2,X3,X4]: (subset(X2,X4) => subset(X2,setadjoin(X3,X4)))), 102.51/103.26 define([status(thm)])). 102.51/103.26 tff(setadjoinSub, axiom, setadjoinSub <=> 102.51/103.26 (![Xx,A]: subset(A,setadjoin(Xx,A)))). 102.51/103.26 tff('16', plain, setadjoinSub = (![X2,X3]: subset(X3,setadjoin(X2,X3))), 102.51/103.26 define([status(thm)])). 102.51/103.26 tff(subsetTrans, axiom, subsetTrans <=> 102.51/103.26 (![A,B,C]: (subset(A,B) => (subset(B,C) => subset(A,C))))). 102.51/103.26 tff('17', plain, 102.51/103.26 subsetTrans = 102.51/103.26 (![X2,X3,X4]: (subset(X2,X3) => (subset(X3,X4) => subset(X2,X4)))), 102.51/103.26 define([status(thm)])). 102.51/103.26 tff(subsetRefl, axiom, subsetRefl <=> (![A]: subset(A,A))). 102.51/103.26 tff('18', plain, subsetRefl = (![X2]: subset(X2,X2)), define([status(thm)])). 102.51/103.26 tff(notequalI2, axiom, notequalI2 <=> 102.51/103.26 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => (A != B))))). 102.51/103.26 tff('19', plain, 102.51/103.26 notequalI2 = (![X2,X3,X4]: (in(X4,X2) => ((~in(X4,X3)) => (X2 != X3)))), 102.51/103.26 define([status(thm)])). 102.51/103.26 tff(notequalI1, axiom, notequalI1 <=> (![A,B]: ((~subset(A,B)) => (A != B)))). 102.51/103.26 tff('20', plain, notequalI1 = (![X2,X3]: ((~subset(X2,X3)) => (X2 != X3))), 102.51/103.26 define([status(thm)])). 102.51/103.26 tff(notsubsetI, axiom, notsubsetI <=> 102.51/103.26 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => (~subset(A,B)))))). 102.51/103.26 tff('21', plain, 102.51/103.26 notsubsetI = 102.51/103.26 (![X2,X3,X4]: (in(X4,X2) => ((~in(X4,X3)) => (~subset(X2,X3))))), 102.51/103.26 define([status(thm)])). 102.51/103.26 tff(subsetE2, axiom, subsetE2 <=> 102.51/103.26 (![A,B,Xx]: (subset(A,B) => ((~in(Xx,B)) => (~in(Xx,A)))))). 102.51/103.26 tff('22', plain, 102.51/103.26 subsetE2 = 102.51/103.26 (![X2,X3,X4]: (subset(X2,X3) => ((~in(X4,X3)) => (~in(X4,X2))))), 102.51/103.26 define([status(thm)])). 102.51/103.26 tff(subsetE, axiom, subsetE <=> 102.51/103.26 (![A,B,Xx]: (subset(A,B) => (in(Xx,A) => in(Xx,B))))). 102.51/103.26 tff('23', plain, 102.51/103.26 subsetE = (![X2,X3,X4]: (subset(X2,X3) => (in(X4,X2) => in(X4,X3)))), 102.51/103.26 define([status(thm)])). 102.51/103.26 tff(emptysetsubset, axiom, emptysetsubset <=> (![A]: subset(emptyset,A))). 102.51/103.26 tff('24', plain, emptysetsubset = (![X2]: subset(emptyset,X2)), 102.51/103.26 define([status(thm)])). 102.51/103.26 tff(subsetI2, axiom, subsetI2 <=> 102.51/103.26 (![A,B]: ((![Xx]: (in(Xx,A) => in(Xx,B))) => subset(A,B)))). 102.51/103.26 tff('25', plain, 102.51/103.26 subsetI2 = 102.51/103.26 (![X2,X3]: ((![X4]: (in(X4,X2) => in(X4,X3))) => subset(X2,X3))), 102.51/103.26 define([status(thm)])). 102.51/103.26 tff(eqimpsubset1, axiom, eqimpsubset1 <=> (![A,B]: ((A = B) => subset(A,B)))). 102.51/103.26 tff('26', plain, eqimpsubset1 = (![X2,X3]: ((X2 = X3) => subset(X2,X3))), 102.51/103.26 define([status(thm)])). 102.51/103.26 tff(eqimpsubset2, axiom, eqimpsubset2 <=> (![A,B]: ((A = B) => subset(B,A)))). 102.51/103.26 tff('27', plain, eqimpsubset2 = (![X2,X3]: ((X2 = X3) => subset(X3,X2))), 102.51/103.26 define([status(thm)])). 102.51/103.26 tff(subsetI1, axiom, subsetI1 <=> 102.51/103.26 (![A,B]: ((![Xx]: (in(Xx,A) => in(Xx,B))) => subset(A,B)))). 102.51/103.26 tff('28', plain, 102.51/103.26 subsetI1 = 102.51/103.26 (![X2,X3]: ((![X4]: (in(X4,X2) => in(X4,X3))) => subset(X2,X3))), 102.51/103.26 define([status(thm)])). 102.51/103.26 tff(dsetconstr__Cong, axiom, dsetconstr__Cong <=> 102.51/103.26 (![A,B]: 102.51/103.26 ((A = B) => 102.51/103.26 (![Xphi:($i > $o),Xpsi:($i > $o)]: 102.51/103.26 ((![Xx]: 102.51/103.26 (in(Xx,A) => 102.51/103.26 (![Xy]: (in(Xy,B) => ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy))))))) => 102.51/103.26 (dsetconstr(A,^[Xx]: Xphi(Xx)) = dsetconstr(B,^[Xx]: Xpsi(Xx)))))))). 102.51/103.26 tff('29', plain, 102.51/103.26 dsetconstr__Cong = 102.51/103.26 (![X2,X3]: 102.51/103.26 ((X2 = X3) => 102.51/103.26 (![X4:($i > $o),X5:($i > $o)]: 102.51/103.26 ((![X6]: 102.51/103.26 (in(X6,X2) => 102.51/103.26 (![X7]: (in(X7,X3) => ((X6 = X7) => (X4(X6) <=> X5(X7))))))) => 102.51/103.26 (dsetconstr(X2,^[V_1]: X4(V_1)) = dsetconstr(X3,^[V_2]: X5(V_2))))))), 102.51/103.26 define([status(thm)])). 102.51/103.26 tff(descr__Cong, axiom, descr__Cong <=> 102.51/103.26 (![Xphi:($i > $o),Xpsi:($i > $o)]: 102.51/103.26 ((![Xx,Xy]: ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy)))) => 102.51/103.26 (exu(^[Xx]: Xphi(Xx)) => 102.51/103.26 (exu(^[Xx]: Xpsi(Xx)) => 102.51/103.26 (descr(^[Xx]: Xphi(Xx)) = descr(^[Xx]: Xpsi(Xx)))))))). 102.51/103.26 tff('30', plain, 102.51/103.26 descr__Cong = 102.51/103.26 (![X2:($i > $o),X3:($i > $o)]: 102.51/103.26 ((![X4,X5]: ((X4 = X5) => (X2(X4) <=> X3(X5)))) => 102.51/103.26 (exu(^[V_1]: X2(V_1)) => 102.51/103.26 (exu(^[V_2]: X3(V_2)) => 102.51/103.26 (descr(^[V_3]: X2(V_3)) = descr(^[V_4]: X3(V_4))))))), 102.51/103.26 define([status(thm)])). 102.51/103.26 tff(exuEu, axiom, exuEu <=> 102.51/103.26 (![Xphi:($i > $o)]: 102.51/103.26 (exu(^[Xx]: Xphi(Xx)) => 102.51/103.26 (![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))). 102.51/103.26 tff('31', plain, 102.51/103.26 exuEu = 102.51/103.26 (![X2:($i > $o)]: 102.51/103.26 (exu(^[V_1]: X2(V_1)) => (![X3,X4]: (X2(X3) => (X2(X4) => (X3 = X4)))))), 102.51/103.26 define([status(thm)])). 102.51/103.26 tff(omega__Cong, axiom, omega__Cong <=> (omega = omega)). 102.51/103.26 tff('32', plain, omega__Cong = (omega = omega), define([status(thm)])). 102.51/103.26 tff(setunion__Cong, axiom, setunion__Cong <=> 102.51/103.26 (![A,B]: ((A = B) => (setunion(A) = setunion(B))))). 102.51/103.26 tff('33', plain, 102.51/103.26 setunion__Cong = (![X2,X3]: ((X2 = X3) => (setunion(X2) = setunion(X3)))), 102.51/103.26 define([status(thm)])). 102.51/103.26 tff(powerset__Cong, axiom, powerset__Cong <=> 102.51/103.26 (![A,B]: ((A = B) => (powerset(A) = powerset(B))))). 102.51/103.26 tff('34', plain, 102.51/103.26 powerset__Cong = (![X2,X3]: ((X2 = X3) => (powerset(X2) = powerset(X3)))), 102.51/103.26 define([status(thm)])). 102.51/103.26 tff(setadjoin__Cong, axiom, setadjoin__Cong <=> 102.51/103.26 (![Xx,Xy]: 102.51/103.26 ((Xx = Xy) => 102.51/103.26 (![Xz,Xu]: ((Xz = Xu) => (setadjoin(Xx,Xz) = setadjoin(Xy,Xu))))))). 102.51/103.26 tff('35', plain, 102.51/103.26 setadjoin__Cong = 102.51/103.26 (![X2,X3]: 102.51/103.26 ((X2 = X3) => 102.51/103.26 (![X4,X5]: ((X4 = X5) => (setadjoin(X2,X4) = setadjoin(X3,X5)))))), 102.51/103.26 define([status(thm)])). 102.51/103.26 tff(emptyset__Cong, axiom, emptyset__Cong <=> (emptyset = emptyset)). 102.51/103.26 tff('36', plain, emptyset__Cong = (emptyset = emptyset), 102.51/103.26 define([status(thm)])). 102.51/103.26 tff(exu__Cong, axiom, exu__Cong <=> 102.51/103.26 (![Xphi:($i > $o),Xpsi:($i > $o)]: 102.51/103.26 ((![Xx,Xy]: ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy)))) => 102.51/103.26 (exu(^[Xx]: Xphi(Xx)) <=> exu(^[Xx]: Xpsi(Xx)))))). 102.51/103.26 tff('37', plain, 102.51/103.26 exu__Cong = 102.51/103.26 (![X2:($i > $o),X3:($i > $o)]: 102.51/103.26 ((![X4,X5]: ((X4 = X5) => (X2(X4) <=> X3(X5)))) => 102.51/103.26 (exu(^[V_1]: X2(V_1)) <=> exu(^[V_2]: X3(V_2))))), 102.51/103.26 define([status(thm)])). 102.51/103.26 tff(exuE3u, axiom, exuE3u <=> 102.51/103.26 (![Xphi:($i > $o)]: 102.51/103.26 (exu(^[Xx]: Xphi(Xx)) => 102.51/103.26 (![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))). 102.51/103.26 tff('38', plain, 102.51/103.26 exuE3u = 102.51/103.26 (![X2:($i > $o)]: 102.51/103.26 (exu(^[V_1]: X2(V_1)) => (![X3,X4]: (X2(X3) => (X2(X4) => (X3 = X4)))))), 102.51/103.26 define([status(thm)])). 102.51/103.26 tff(in__Cong, axiom, in__Cong <=> 102.51/103.26 (![A,B]: ((A = B) => (![Xx,Xy]: ((Xx = Xy) => (in(Xx,A) <=> in(Xy,B))))))). 102.51/103.26 tff('39', plain, 102.51/103.26 in__Cong = 102.51/103.26 (![X2,X3]: 102.51/103.26 ((X2 = X3) => (![X4,X5]: ((X4 = X5) => (in(X4,X2) <=> in(X5,X3)))))), 102.51/103.26 define([status(thm)])). 102.51/103.26 tff(inCongP, axiom, inCongP <=> 102.51/103.26 (![A,B]: ((A = B) => (![Xx,Xy]: ((Xx = Xy) => (in(Xx,A) => in(Xy,B))))))). 102.51/103.26 tff('40', plain, 102.51/103.26 inCongP = 102.51/103.26 (![X2,X3]: 102.51/103.26 ((X2 = X3) => (![X4,X5]: ((X4 = X5) => (in(X4,X2) => in(X5,X3)))))), 102.51/103.26 define([status(thm)])). 102.51/103.26 tff(exuI2, axiom, exuI2 <=> 102.51/103.26 (![Xphi:($i > $o)]: 102.51/103.26 ((?[Xx]: (![Xy]: (Xphi(Xy) <=> (Xy = Xx)))) => exu(^[Xx]: Xphi(Xx))))). 102.51/103.26 tff('41', plain, 102.51/103.26 exuI2 = 102.51/103.26 (![X2:($i > $o)]: 102.51/103.26 ((?[X3]: (![X4]: (X2(X4) <=> (X4 = X3)))) => exu(^[V_1]: X2(V_1)))), 102.51/103.26 define([status(thm)])). 102.51/103.26 tff(exuI3, axiom, exuI3 <=> 102.51/103.26 (![Xphi:($i > $o)]: 102.51/103.26 ((?[Xx]: Xphi(Xx)) => 102.51/103.26 ((![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy)))) => 102.51/103.26 exu(^[Xx]: Xphi(Xx)))))). 102.51/103.26 tff('42', plain, 102.51/103.26 exuI3 = 102.51/103.26 (![X2:($i > $o)]: 102.51/103.26 ((?[X3]: X2(X3)) => 102.51/103.26 ((![X4,X5]: (X2(X4) => (X2(X5) => (X4 = X5)))) => 102.51/103.26 exu(^[V_1]: X2(V_1))))), 102.51/103.26 define([status(thm)])). 102.51/103.26 tff(exuI1, axiom, exuI1 <=> 102.51/103.26 (![Xphi:($i > $o)]: 102.51/103.26 ((?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx))) => 102.51/103.26 exu(^[Xx]: Xphi(Xx))))). 102.51/103.26 tff('43', plain, 102.51/103.26 exuI1 = 102.51/103.26 (![X2:($i > $o)]: 102.51/103.26 ((?[X3]: ((![X4]: (X2(X4) => (X3 = X4))) & X2(X3))) => 102.61/103.26 exu(^[V_1]: X2(V_1)))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(notdallE, axiom, notdallE <=> 102.61/103.26 (![A,Xphi:($i > $o)]: 102.61/103.26 ((~(![Xx]: (in(Xx,A) => Xphi(Xx)))) => (?[Xx]: ((~Xphi(Xx)) & in(Xx,A)))))). 102.61/103.26 tff('44', plain, 102.61/103.26 notdallE = 102.61/103.26 (![X2,X3:($i > $o)]: 102.61/103.26 ((~(![X4]: (in(X4,X2) => X3(X4)))) => (?[X5]: ((~X3(X5)) & in(X5,X2))))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(notdexE, axiom, notdexE <=> 102.61/103.26 (![A,Xphi:($i > $o)]: 102.61/103.26 ((~(?[Xx]: (Xphi(Xx) & in(Xx,A)))) => (![Xx]: (in(Xx,A) => (~Xphi(Xx))))))). 102.61/103.26 tff('45', plain, 102.61/103.26 notdexE = 102.61/103.26 (![X2,X3:($i > $o)]: 102.61/103.26 ((~(?[X4]: (X3(X4) & in(X4,X2)))) => (![X5]: (in(X5,X2) => (~X3(X5)))))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(prop2set2propI, axiom, prop2set2propI <=> 102.61/103.26 (![Xphi:$o]: (Xphi => set2prop(prop2set(Xphi))))). 102.61/103.26 tff('46', plain, prop2set2propI = (![X2:$o]: (X2 => set2prop(prop2set(X2)))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(prop2setI, axiom, prop2setI <=> 102.61/103.26 (![Xphi:$o]: (Xphi => in(emptyset,prop2set(Xphi))))). 102.61/103.26 tff('47', plain, prop2setI = (![X2:$o]: (X2 => in(emptyset,prop2set(X2)))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(quantDeMorgan4, axiom, quantDeMorgan4 <=> 102.61/103.26 (![A,Xphi:($i > $o)]: 102.61/103.26 ((?[Xx]: ((~Xphi(Xx)) & in(Xx,A))) => (~(![Xx]: (in(Xx,A) => Xphi(Xx))))))). 102.61/103.26 tff('48', plain, 102.61/103.26 quantDeMorgan4 = 102.61/103.26 (![X2,X3:($i > $o)]: 102.61/103.26 ((?[X4]: ((~X3(X4)) & in(X4,X2))) => (~(![X5]: (in(X5,X2) => X3(X5)))))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(quantDeMorgan3, axiom, quantDeMorgan3 <=> 102.61/103.26 (![A,Xphi:($i > $o)]: 102.61/103.26 ((~(?[Xx]: (Xphi(Xx) & in(Xx,A)))) => (![Xx]: (in(Xx,A) => (~Xphi(Xx))))))). 102.61/103.26 tff('49', plain, 102.61/103.26 quantDeMorgan3 = 102.61/103.26 (![X2,X3:($i > $o)]: 102.61/103.26 ((~(?[X4]: (X3(X4) & in(X4,X2)))) => (![X5]: (in(X5,X2) => (~X3(X5)))))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(quantDeMorgan2, axiom, quantDeMorgan2 <=> 102.61/103.26 (![A,Xphi:($i > $o)]: 102.61/103.26 ((![Xx]: (in(Xx,A) => (~Xphi(Xx)))) => (~(?[Xx]: (Xphi(Xx) & in(Xx,A))))))). 102.61/103.26 tff('50', plain, 102.61/103.26 quantDeMorgan2 = 102.61/103.26 (![X2,X3:($i > $o)]: 102.61/103.26 ((![X4]: (in(X4,X2) => (~X3(X4)))) => (~(?[X5]: (X3(X5) & in(X5,X2)))))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(quantDeMorgan1, axiom, quantDeMorgan1 <=> 102.61/103.26 (![A,Xphi:($i > $o)]: 102.61/103.26 ((~(![Xx]: (in(Xx,A) => Xphi(Xx)))) => (?[Xx]: ((~Xphi(Xx)) & in(Xx,A)))))). 102.61/103.26 tff('51', plain, 102.61/103.26 quantDeMorgan1 = 102.61/103.26 (![X2,X3:($i > $o)]: 102.61/103.26 ((~(![X4]: (in(X4,X2) => X3(X4)))) => (?[X5]: ((~X3(X5)) & in(X5,X2))))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(vacuousDall, axiom, vacuousDall <=> 102.61/103.26 (![Xphi:($i > $o),Xx]: (in(Xx,emptyset) => Xphi(Xx)))). 102.61/103.26 tff('52', plain, 102.61/103.26 vacuousDall = (![X2:($i > $o),X3]: (in(X3,emptyset) => X2(X3))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(emptyE1, axiom, emptyE1 <=> 102.61/103.26 (![A,Xphi:($i > $o)]: 102.61/103.26 ((?[Xx]: (Xphi(Xx) & in(Xx,A))) => 102.61/103.26 ((dsetconstr(A,^[Xx]: Xphi(Xx)) = emptyset) => $false)))). 102.61/103.26 tff('53', plain, 102.61/103.26 emptyE1 = 102.61/103.26 (![X2,X3:($i > $o)]: 102.61/103.26 ((?[X4]: (X3(X4) & in(X4,X2))) => 102.61/103.26 ((dsetconstr(X2,^[V_1]: X3(V_1)) = emptyset) => $false))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(upairsetIR, axiom, upairsetIR <=> 102.61/103.26 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 102.61/103.26 tff('54', plain, 102.61/103.26 upairsetIR = (![X2,X3]: in(X3,setadjoin(X2,setadjoin(X3,emptyset)))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(upairsetIL, axiom, upairsetIL <=> 102.61/103.26 (![Xx,Xy]: in(Xx,setadjoin(Xx,setadjoin(Xy,emptyset))))). 102.61/103.26 tff('55', plain, 102.61/103.26 upairsetIL = (![X2,X3]: in(X2,setadjoin(X2,setadjoin(X3,emptyset)))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(upairsetE, axiom, upairsetE <=> 102.61/103.26 (![Xx,Xy,Xz]: 102.61/103.26 (in(Xz,setadjoin(Xx,setadjoin(Xy,emptyset))) => ((Xz = Xy) | (Xz = Xx))))). 102.61/103.26 tff('56', plain, 102.61/103.26 upairsetE = 102.61/103.26 (![X2,X3,X4]: 102.61/103.26 (in(X4,setadjoin(X2,setadjoin(X3,emptyset))) => 102.61/103.26 ((X4 = X3) | (X4 = X2)))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(singletonsswitch, axiom, singletonsswitch <=> 102.61/103.26 (![Xx,Xy]: (in(Xx,setadjoin(Xy,emptyset)) => in(Xy,setadjoin(Xx,emptyset))))). 102.61/103.26 tff('57', plain, 102.61/103.26 singletonsswitch = 102.61/103.26 (![X2,X3]: 102.61/103.26 (in(X2,setadjoin(X3,emptyset)) => in(X3,setadjoin(X2,emptyset)))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(eqinunit, axiom, eqinunit <=> 102.61/103.26 (![Xx,Xy]: ((Xx = Xy) => in(Xx,setadjoin(Xy,emptyset))))). 102.61/103.26 tff('58', plain, 102.61/103.26 eqinunit = (![X2,X3]: ((X2 = X3) => in(X2,setadjoin(X3,emptyset)))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(notinsingleton, axiom, notinsingleton <=> 102.61/103.26 (![Xx,Xy]: ((Xx != Xy) => (~in(Xy,setadjoin(Xx,emptyset)))))). 102.61/103.26 tff('59', plain, 102.61/103.26 notinsingleton = 102.61/103.26 (![X2,X3]: ((X2 != X3) => (~in(X3,setadjoin(X2,emptyset))))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(uniqinunit, axiom, uniqinunit <=> 102.61/103.26 (![Xx,Xy]: (in(Xx,setadjoin(Xy,emptyset)) => (Xx = Xy)))). 102.61/103.26 tff('60', plain, 102.61/103.26 uniqinunit = (![X2,X3]: (in(X2,setadjoin(X3,emptyset)) => (X2 = X3))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(nonemptyImpWitness, axiom, nonemptyImpWitness <=> 102.61/103.26 (![A]: (nonempty(A) => (?[Xx]: (in(Xx,A)))))). 102.61/103.26 tff('61', plain, 102.61/103.26 nonemptyImpWitness = (![X2]: (nonempty(X2) => (?[X3]: (in(X3,X2))))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(exuE2, axiom, exuE2 <=> 102.61/103.26 (![Xphi:($i > $o)]: 102.61/103.26 (exu(^[Xx]: Xphi(Xx)) => (?[Xx]: (![Xy]: (Xphi(Xy) <=> (Xy = Xx))))))). 102.61/103.26 tff('62', plain, 102.61/103.26 exuE2 = 102.61/103.26 (![X2:($i > $o)]: 102.61/103.26 (exu(^[V_1]: X2(V_1)) => (?[X3]: (![X4]: (X2(X4) <=> (X4 = X3)))))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(subPowSU, axiom, subPowSU <=> 102.61/103.26 (![A,Xx]: (in(Xx,A) => in(Xx,powerset(setunion(A)))))). 102.61/103.26 tff('63', plain, 102.61/103.26 subPowSU = (![X2,X3]: (in(X3,X2) => in(X3,powerset(setunion(X2))))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(setunionE, axiom, setunionE <=> 102.61/103.26 (![A,Xx]: 102.61/103.26 (in(Xx,setunion(A)) => 102.61/103.26 (![Xphi:$o]: ((![B]: (in(Xx,B) => (in(B,A) => Xphi))) => Xphi))))). 102.61/103.26 tff('64', plain, 102.61/103.26 setunionE = 102.61/103.26 (![X2,X3]: 102.61/103.26 (in(X3,setunion(X2)) => 102.61/103.26 (![X4:$o]: ((![X5]: (in(X3,X5) => (in(X5,X2) => X4))) => X4)))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(setunionI, axiom, setunionI <=> 102.61/103.26 (![A,Xx,B]: (in(Xx,B) => (in(B,A) => in(Xx,setunion(A)))))). 102.61/103.26 tff('65', plain, 102.61/103.26 setunionI = 102.61/103.26 (![X2,X3,X4]: (in(X3,X4) => (in(X4,X2) => in(X3,setunion(X2))))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(powersetE, axiom, powersetE <=> 102.61/103.26 (![A,B,Xx]: (in(B,powerset(A)) => (in(Xx,B) => in(Xx,A))))). 102.61/103.26 tff('66', plain, 102.61/103.26 powersetE = 102.61/103.26 (![X2,X3,X4]: (in(X3,powerset(X2)) => (in(X4,X3) => in(X4,X2)))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(emptyInPowerset, axiom, emptyInPowerset <=> 102.61/103.26 (![A]: in(emptyset,powerset(A)))). 102.61/103.26 tff('67', plain, emptyInPowerset = (![X2]: in(emptyset,powerset(X2))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(emptyinPowerset, axiom, emptyinPowerset <=> 102.61/103.26 (![A]: in(emptyset,powerset(A)))). 102.61/103.26 tff('68', plain, emptyinPowerset = (![X2]: in(emptyset,powerset(X2))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(powersetI, axiom, powersetI <=> 102.61/103.26 (![A,B]: ((![Xx]: (in(Xx,B) => in(Xx,A))) => in(B,powerset(A))))). 102.61/103.26 tff('69', plain, 102.61/103.26 powersetI = 102.61/103.26 (![X2,X3]: ((![X4]: (in(X4,X3) => in(X4,X2))) => in(X3,powerset(X2)))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(setoftrueEq, axiom, setoftrueEq <=> 102.61/103.26 (![A]: (dsetconstr(A,^[Xx]: $true) = A))). 102.61/103.26 tff('70', plain, setoftrueEq = (![X2]: (dsetconstr(X2,^[V_1]: $true) = X2)), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(setadjoinOr, axiom, setadjoinOr <=> 102.61/103.26 (![Xx,A,Xy]: (in(Xy,setadjoin(Xx,A)) => (in(Xy,A) | (Xy = Xx))))). 102.61/103.26 tff('71', plain, 102.61/103.26 setadjoinOr = 102.61/103.26 (![X2,X3,X4]: (in(X4,setadjoin(X2,X3)) => (in(X4,X3) | (X4 = X2)))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(setadjoinE, axiom, setadjoinE <=> 102.61/103.26 (![Xx,A,Xy]: 102.61/103.26 (in(Xy,setadjoin(Xx,A)) => 102.61/103.26 (![Xphi:$o]: (((Xy = Xx) => Xphi) => ((in(Xy,A) => Xphi) => Xphi)))))). 102.61/103.26 tff('72', plain, 102.61/103.26 setadjoinE = 102.61/103.26 (![X2,X3,X4]: 102.61/103.26 (in(X4,setadjoin(X2,X3)) => 102.61/103.26 (![X5:$o]: (((X4 = X2) => X5) => ((in(X4,X3) => X5) => X5))))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(setadjoinIR, axiom, setadjoinIR <=> 102.61/103.26 (![Xx,A,Xy]: (in(Xy,A) => in(Xy,setadjoin(Xx,A))))). 102.61/103.26 tff('73', plain, 102.61/103.26 setadjoinIR = (![X2,X3,X4]: (in(X4,X3) => in(X4,setadjoin(X2,X3)))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(emptyinunitempty, axiom, emptyinunitempty() = 102.61/103.26 in(emptyset,setadjoin(emptyset,emptyset))). 102.61/103.26 tff('74', plain, 102.61/103.26 emptyinunitempty = in(emptyset,setadjoin(emptyset,emptyset)), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(setadjoinIL, axiom, setadjoinIL <=> (![Xx,Xy]: in(Xx,setadjoin(Xx,Xy)))). 102.61/103.26 tff('75', plain, setadjoinIL = (![X2,X3]: in(X2,setadjoin(X2,X3))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(nonemptyI1, axiom, nonemptyI1 <=> 102.61/103.26 (![A]: ((?[Xx]: in(Xx,A)) => nonempty(A)))). 102.61/103.26 tff('76', plain, nonemptyI1 = (![X2]: ((?[X3]: in(X3,X2)) => nonempty(X2))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(nonemptyI, axiom, nonemptyI <=> 102.61/103.26 (![A,Xphi:($i > $o),Xx]: 102.61/103.26 (in(Xx,A) => (Xphi(Xx) => nonempty(dsetconstr(A,^[Xy]: Xphi(Xy))))))). 102.61/103.26 tff('77', plain, 102.61/103.26 nonemptyI = 102.61/103.26 (![X2,X3:($i > $o),X4]: 102.61/103.26 (in(X4,X2) => (X3(X4) => nonempty(dsetconstr(X2,^[V_1]: X3(V_1)))))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(nonemptyE1, axiom, nonemptyE1 <=> 102.61/103.26 (![A]: (nonempty(A) => (?[Xx]: in(Xx,A))))). 102.61/103.26 tff('78', plain, nonemptyE1 = (![X2]: (nonempty(X2) => (?[X3]: in(X3,X2)))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(nonempty, axiom, nonempty() = ^[Xx]: (Xx != emptyset)). 102.61/103.26 tff('79', plain, nonempty = (^[V_1]: (V_1 != emptyset)), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(setbeta, axiom, setbeta <=> 102.61/103.26 (![A,Xphi:($i > $o),Xx]: 102.61/103.26 (in(Xx,A) => (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) <=> Xphi(Xx))))). 102.61/103.26 tff('80', plain, 102.61/103.26 setbeta = 102.61/103.26 (![X2,X3:($i > $o),X4]: 102.61/103.26 (in(X4,X2) => (in(X4,dsetconstr(X2,^[V_1]: X3(V_1))) <=> X3(X4)))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(noeltsimpempty, axiom, noeltsimpempty <=> 102.61/103.26 (![A]: ((![Xx]: (~in(Xx,A))) => (A = emptyset)))). 102.61/103.26 tff('81', plain, 102.61/103.26 noeltsimpempty = (![X2]: ((![X3]: (~in(X3,X2))) => (X2 = emptyset))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(emptyI, axiom, emptyI <=> 102.61/103.26 (![A]: ((![Xx]: (~in(Xx,A))) => (A = emptyset)))). 102.61/103.26 tff('82', plain, 102.61/103.26 emptyI = (![X2]: ((![X3]: (~in(X3,X2))) => (X2 = emptyset))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(setext, axiom, setext <=> 102.61/103.26 (![A,B]: 102.61/103.26 ((![Xx]: (in(Xx,A) => in(Xx,B))) => 102.61/103.26 ((![Xx]: (in(Xx,B) => in(Xx,A))) => (A = B))))). 102.61/103.26 tff('83', plain, 102.61/103.26 setext = 102.61/103.26 (![X2,X3]: 102.61/103.26 ((![X4]: (in(X4,X2) => in(X4,X3))) => 102.61/103.26 ((![X5]: (in(X5,X3) => in(X5,X2))) => (X2 = X3)))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(exuE3e, axiom, exuE3e <=> 102.61/103.26 (![Xphi:($i > $o)]: (exu(^[Xx]: Xphi(Xx)) => (?[Xx]: Xphi(Xx))))). 102.61/103.26 tff('84', plain, 102.61/103.26 exuE3e = (![X2:($i > $o)]: (exu(^[V_1]: X2(V_1)) => (?[X3]: X2(X3)))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(notinemptyset, axiom, notinemptyset <=> (![Xx]: (~in(Xx,emptyset)))). 102.61/103.26 tff('85', plain, notinemptyset = (![X2]: (~in(X2,emptyset))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(emptysetimpfalse, axiom, emptysetimpfalse <=> 102.61/103.26 (![Xx]: (in(Xx,emptyset) => $false))). 102.61/103.26 tff('86', plain, emptysetimpfalse = (![X2]: (in(X2,emptyset) => $false)), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(emptysetE, axiom, emptysetE <=> 102.61/103.26 (![Xx]: (in(Xx,emptyset) => (![Xphi:$o]: Xphi)))). 102.61/103.26 tff('87', plain, emptysetE = (![X2]: (in(X2,emptyset) => (![X3:$o]: X3))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(prop2setE, axiom, prop2setE <=> 102.61/103.26 (![Xphi:$o,Xx]: (in(Xx,prop2set(Xphi)) => Xphi))). 102.61/103.26 tff('88', plain, prop2setE = (![X2:$o,X3]: (in(X3,prop2set(X2)) => X2)), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(exuE1, axiom, exuE1 <=> 102.61/103.26 (![Xphi:($i > $o)]: 102.61/103.26 (exu(^[Xx]: Xphi(Xx)) => 102.61/103.26 (?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx)))))). 102.61/103.26 tff('89', plain, 102.61/103.26 exuE1 = 102.61/103.26 (![X2:($i > $o)]: 102.61/103.26 (exu(^[V_1]: X2(V_1)) => 102.61/103.26 (?[X3]: ((![X4]: (X2(X4) => (X3 = X4))) & X2(X3))))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(dsetconstrER, axiom, dsetconstrER <=> 102.61/103.26 (![A,Xphi:($i > $o),Xx]: (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) => Xphi(Xx)))). 102.61/103.26 tff('90', plain, 102.61/103.26 dsetconstrER = 102.61/103.26 (![X2,X3:($i > $o),X4]: (in(X4,dsetconstr(X2,^[V_1]: X3(V_1))) => X3(X4))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(dsetconstrEL, axiom, dsetconstrEL <=> 102.61/103.26 (![A,Xphi:($i > $o),Xx]: (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) => in(Xx,A)))). 102.61/103.26 tff('91', plain, 102.61/103.26 dsetconstrEL = 102.61/103.26 (![X2,X3:($i > $o),X4]: 102.61/103.26 (in(X4,dsetconstr(X2,^[V_1]: X3(V_1))) => in(X4,X2))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(dsetconstrI, axiom, dsetconstrI <=> 102.61/103.26 (![A,Xphi:($i > $o),Xx]: 102.61/103.26 (in(Xx,A) => (Xphi(Xx) => in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))))))). 102.61/103.26 tff('92', plain, 102.61/103.26 dsetconstrI = 102.61/103.26 (![X2,X3:($i > $o),X4]: 102.61/103.26 (in(X4,X2) => (X3(X4) => in(X4,dsetconstr(X2,^[V_1]: X3(V_1)))))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(descrp, axiom, descrp <=> 102.61/103.26 (![Xphi:($i > $o)]: (exu(^[Xx]: Xphi(Xx)) => Xphi(descr(^[Xx]: Xphi(Xx)))))). 102.61/103.26 tff('93', plain, 102.61/103.26 descrp = 102.61/103.26 (![X2:($i > $o)]: (exu(^[V_1]: X2(V_1)) => X2(descr(^[V_2]: X2(V_2))))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(wellorderingAx, axiom, wellorderingAx <=> 102.61/103.26 (![A]: 102.61/103.26 (?[B]: 102.61/103.26 ((![C]: 102.61/103.26 (((?[Xx]: in(Xx,C)) & (![Xx]: (in(Xx,C) => in(Xx,A)))) => 102.61/103.26 (?[D,Xx]: 102.61/103.26 ((![E]: 102.61/103.26 (in(E,B) => (in(Xx,E) | (![Xy]: (in(Xy,E) => in(Xy,D)))))) & 102.61/103.26 (~(?[Xy]: (in(Xy,C) & in(Xy,D)))) & in(Xx,C) & in(D,B))))) & 102.61/103.26 (![C,D]: 102.61/103.26 ((in(D,B) & in(C,B)) => 102.61/103.26 ((![Xx]: (in(Xx,D) => in(Xx,C))) | 102.61/103.26 (![Xx]: (in(Xx,C) => in(Xx,D)))))) & 102.61/103.26 (![Xx,Xy]: 102.61/103.26 ((in(Xy,A) & in(Xx,A)) => 102.61/103.26 ((![C]: (in(C,B) => (in(Xx,C) <=> in(Xy,C)))) => (Xx = Xy)))) & 102.61/103.26 (![C]: (in(C,B) => (![Xx]: (in(Xx,C) => in(Xx,A))))))))). 102.61/103.26 tff('94', plain, 102.61/103.26 wellorderingAx = 102.61/103.26 (![X2]: 102.61/103.26 (?[X3]: 102.61/103.26 ((![X4]: 102.61/103.26 (((?[X5]: in(X5,X4)) & (![X6]: (in(X6,X4) => in(X6,X2)))) => 102.61/103.26 (?[X7,X8]: 102.61/103.26 ((![X9]: 102.61/103.26 (in(X9,X3) => 102.61/103.26 (in(X8,X9) | (![X10]: (in(X10,X9) => in(X10,X7)))))) & 102.61/103.26 (~(?[X11]: (in(X11,X4) & in(X11,X7)))) & in(X8,X4) & 102.61/103.26 in(X7,X3))))) & 102.61/103.26 (![X12,X13]: 102.61/103.26 ((in(X13,X3) & in(X12,X3)) => 102.61/103.26 ((![X14]: (in(X14,X13) => in(X14,X12))) | 102.61/103.26 (![X15]: (in(X15,X12) => in(X15,X13)))))) & 102.61/103.26 (![X16,X17]: 102.61/103.26 ((in(X17,X2) & in(X16,X2)) => 102.61/103.26 ((![X18]: (in(X18,X3) => (in(X16,X18) <=> in(X17,X18)))) => 102.61/103.26 (X16 = X17)))) & 102.61/103.26 (![X19]: (in(X19,X3) => (![X20]: (in(X20,X19) => in(X20,X2)))))))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(foundationAx, axiom, foundationAx <=> 102.61/103.26 (![A]: 102.61/103.26 ((?[Xx]: in(Xx,A)) => 102.61/103.26 (?[B]: ((~(?[Xx]: (in(Xx,A) & in(Xx,B)))) & in(B,A)))))). 102.61/103.26 tff('95', plain, 102.61/103.26 foundationAx = 102.61/103.26 (![X2]: 102.61/103.26 ((?[X3]: in(X3,X2)) => 102.61/103.26 (?[X4]: ((~(?[X5]: (in(X5,X2) & in(X5,X4)))) & in(X4,X2))))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(replAx, axiom, replAx <=> 102.61/103.26 (![Xphi:(($i * $i) > $o),A]: 102.61/103.26 ((![Xx]: (in(Xx,A) => exu(^[Xy]: Xphi(Xx,Xy)))) => 102.61/103.26 (?[B]: (![Xx]: (in(Xx,B) <=> (?[Xy]: (Xphi(Xy,Xx) & in(Xy,A))))))))). 102.61/103.26 tff('96', plain, 102.61/103.26 replAx = 102.61/103.26 (![X2:(($i * $i) > $o),X3]: 102.61/103.26 ((![X4]: (in(X4,X3) => exu(^[V_1]: X2(X4,V_1)))) => 102.61/103.26 (?[X5]: (![X6]: (in(X6,X5) <=> (?[X7]: (X2(X7,X6) & in(X7,X3)))))))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(omegaIndAx, axiom, omegaIndAx <=> 102.61/103.26 (![A]: 102.61/103.26 (((![Xx]: ((in(Xx,A) & in(Xx,omega)) => in(setadjoin(Xx,Xx),A))) & 102.61/103.26 in(emptyset,A)) => 102.61/103.26 (![Xx]: (in(Xx,omega) => in(Xx,A)))))). 102.61/103.26 tff('97', plain, 102.61/103.26 omegaIndAx = 102.61/103.26 (![X2]: 102.61/103.26 (((![X3]: ((in(X3,X2) & in(X3,omega)) => in(setadjoin(X3,X3),X2))) & 102.61/103.26 in(emptyset,X2)) => 102.61/103.26 (![X4]: (in(X4,omega) => in(X4,X2))))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(omegaSAx, axiom, omegaSAx <=> 102.61/103.26 (![Xx]: (in(Xx,omega) => in(setadjoin(Xx,Xx),omega)))). 102.61/103.26 tff('98', plain, 102.61/103.26 omegaSAx = (![X2]: (in(X2,omega) => in(setadjoin(X2,X2),omega))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(omega0Ax, axiom, omega0Ax() = in(emptyset,omega)). 102.61/103.26 tff('99', plain, omega0Ax = in(emptyset,omega), define([status(thm)])). 102.61/103.26 tff(setunionAx, axiom, setunionAx <=> 102.61/103.26 (![A,Xx]: (in(Xx,setunion(A)) <=> (?[B]: (in(B,A) & in(Xx,B)))))). 102.61/103.26 tff('100', plain, 102.61/103.26 setunionAx = 102.61/103.26 (![X2,X3]: (in(X3,setunion(X2)) <=> (?[X4]: (in(X4,X2) & in(X3,X4))))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(powersetAx, axiom, powersetAx <=> 102.61/103.26 (![A,B]: (in(B,powerset(A)) <=> (![Xx]: (in(Xx,B) => in(Xx,A)))))). 102.61/103.26 tff('101', plain, 102.61/103.26 powersetAx = 102.61/103.26 (![X2,X3]: (in(X3,powerset(X2)) <=> (![X4]: (in(X4,X3) => in(X4,X2))))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(setadjoinAx, axiom, setadjoinAx <=> 102.61/103.26 (![Xx,A,Xy]: (in(Xy,setadjoin(Xx,A)) <=> (in(Xy,A) | (Xy = Xx))))). 102.61/103.26 tff('102', plain, 102.61/103.26 setadjoinAx = 102.61/103.26 (![X2,X3,X4]: (in(X4,setadjoin(X2,X3)) <=> (in(X4,X3) | (X4 = X2)))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(emptysetAx, axiom, emptysetAx <=> (![Xx]: (~in(Xx,emptyset)))). 102.61/103.26 tff('103', plain, emptysetAx = (![X2]: (~in(X2,emptyset))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(setextAx, axiom, setextAx <=> 102.61/103.26 (![A,B]: ((![Xx]: (in(Xx,A) <=> in(Xx,B))) => (A = B)))). 102.61/103.26 tff('104', plain, 102.61/103.26 setextAx = (![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(exu, axiom, exu() = 102.61/103.26 ^[Xphi:($i > $o)]: (?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx)))). 102.61/103.26 tff('105', plain, 102.61/103.26 exu = 102.61/103.26 (^[V_1:($i > $o)]: (?[X2]: ((![X3]: (V_1(X3) => (X2 = X3))) & V_1(X2)))), 102.61/103.26 define([status(thm)])). 102.61/103.26 tff(binunionRsub, conjecture, 102.61/103.26 (setextAx => 102.61/103.26 (emptysetAx => 102.61/103.26 (setadjoinAx => 102.61/103.26 (powersetAx => 102.61/103.26 (setunionAx => 102.61/103.26 (omega0Ax => 102.61/103.26 (omegaSAx => 102.61/103.26 (omegaIndAx => 102.61/103.26 (replAx => 102.61/103.26 (foundationAx => 102.61/103.26 (wellorderingAx => 102.61/103.26 (descrp => 102.61/103.26 (dsetconstrI => 102.61/103.26 (dsetconstrEL => 102.61/103.26 (dsetconstrER => 102.61/103.26 (exuE1 => 102.61/103.26 (prop2setE => 102.61/103.26 (emptysetE => 102.61/103.26 (emptysetimpfalse => 102.61/103.26 (notinemptyset => 102.61/103.26 (exuE3e => 102.61/103.26 (setext => 102.61/103.26 (emptyI => 102.61/103.26 (noeltsimpempty => 102.61/103.26 (setbeta => 102.61/103.26 (nonemptyE1 => 102.61/103.26 (nonemptyI => 102.61/103.26 (nonemptyI1 => 102.61/103.26 (setadjoinIL => 102.61/103.26 (emptyinunitempty => 102.61/103.26 (setadjoinIR => 102.61/103.26 (setadjoinE => 102.61/103.26 (setadjoinOr => 102.61/103.26 (setoftrueEq => 102.61/103.26 (powersetI => 102.61/103.26 (emptyinPowerset => 102.61/103.26 (emptyInPowerset => 102.61/103.26 (powersetE => 102.61/103.26 (setunionI => 102.61/103.26 (setunionE => 102.61/103.26 (subPowSU => 102.61/103.26 (exuE2 => 102.61/103.26 (nonemptyImpWitness => 102.61/103.26 (uniqinunit => 102.61/103.26 (notinsingleton => 102.61/103.26 (eqinunit => 102.61/103.26 (singletonsswitch => 102.61/103.26 (upairsetE => 102.61/103.26 (upairsetIL => 102.61/103.26 (upairsetIR => 102.61/103.26 (emptyE1 => 102.61/103.26 (vacuousDall => 102.61/103.26 (quantDeMorgan1 => 102.61/103.26 (quantDeMorgan2 => 102.61/103.26 (quantDeMorgan3 => 102.61/103.26 (quantDeMorgan4 => 102.61/103.26 (prop2setI => 102.61/103.26 (prop2set2propI => 102.61/103.26 (notdexE => 102.61/103.26 (notdallE => 102.61/103.26 (exuI1 => 102.61/103.26 (exuI3 => 102.61/103.26 (exuI2 => 102.61/103.26 (inCongP => 102.61/103.26 (in__Cong => 102.61/103.26 (exuE3u => 102.61/103.26 ( 102.61/103.26 exu__Cong => 102.61/103.26 ( 102.61/103.26 emptyset__Cong => 102.61/103.26 ( 102.61/103.26 setadjoin__Cong => 102.61/103.26 ( 102.61/103.26 powerset__Cong => 102.61/103.26 ( 102.61/103.26 setunion__Cong => 102.61/103.26 ( 102.61/103.26 omega__Cong => 102.61/103.26 ( 102.61/103.26 exuEu => 102.61/103.26 ( 102.61/103.26 descr__Cong => 102.61/103.26 ( 102.61/103.26 dsetconstr__Cong => 102.61/103.26 ( 102.61/103.26 subsetI1 => 102.61/103.26 ( 102.61/103.26 eqimpsubset2 => 102.61/103.26 ( 102.61/103.26 eqimpsubset1 => 102.61/103.26 ( 102.61/103.26 subsetI2 => 102.61/103.26 ( 102.61/103.26 emptysetsubset => 102.61/103.26 ( 102.61/103.26 subsetE => 102.61/103.26 ( 102.61/103.26 subsetE2 => 102.61/103.26 ( 102.61/103.26 notsubsetI => 102.61/103.26 ( 102.61/103.26 notequalI1 => 102.61/103.26 ( 102.61/103.26 notequalI2 => 102.61/103.26 ( 102.61/103.26 subsetRefl => 102.61/103.26 ( 102.61/103.26 subsetTrans => 102.61/103.26 ( 102.61/103.26 setadjoinSub => 102.61/103.26 ( 102.61/103.26 setadjoinSub2 => 102.61/103.26 ( 102.61/103.26 subset2powerset => 102.61/103.26 ( 102.61/103.26 setextsub => 102.61/103.26 ( 102.61/103.26 subsetemptysetimpeq => 102.61/103.26 ( 102.61/103.26 powersetI1 => 102.61/103.26 ( 102.61/103.26 powersetE1 => 102.61/103.26 ( 102.61/103.26 inPowerset => 102.61/103.26 ( 102.61/103.26 powersetsubset => 102.61/103.26 ( 102.61/103.26 sepInPowerset => 102.61/103.26 ( 102.61/103.26 sepSubset => 102.61/103.26 ( 102.61/103.26 binunionIL => 102.61/103.26 ( 102.61/103.26 upairset2IR => 102.61/103.26 ( 102.61/103.26 binunionIR => 102.61/103.26 ( 102.61/103.26 binunionEcases => 102.61/103.26 ( 102.61/103.26 binunionE => 102.61/103.26 ( 102.61/103.26 binunionLsub => 102.61/103.26 ( 102.61/103.26 ![A,B]: 102.61/103.26 subset( 102.61/103.26 B, 102.61/103.26 binunion( 102.61/103.26 A,B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 102.61/103.26 tff(zf_stmt_0, conjecture, 102.61/103.26 ((![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))) => 102.61/103.26 ((![X5]: (~in(X5,emptyset))) => 102.61/103.26 ((![X6,X7,X8]: (in(X8,setadjoin(X6,X7)) <=> ((X8 = X6) | in(X8,X7)))) => 102.61/103.26 ((![X9,X10]: 102.61/103.26 (in(X10,powerset(X9)) <=> (![X11]: (in(X11,X10) => in(X11,X9))))) => 102.61/103.26 ((![X12,X13]: 102.61/103.26 (in(X13,setunion(X12)) <=> (?[X14]: (in(X13,X14) & in(X14,X12))))) => 102.61/103.26 (in(emptyset,omega) => 102.61/103.26 ((![X15]: (in(X15,omega) => in(setadjoin(X15,X15),omega))) => 102.61/103.26 ((![X16]: 102.61/103.26 ((in(emptyset,X16) & 102.61/103.26 (![X17]: 102.61/103.26 ((in(X17,omega) & in(X17,X16)) => 102.61/103.26 in(setadjoin(X17,X17),X16)))) => 102.61/103.26 (![X18]: (in(X18,omega) => in(X18,X16))))) => 102.61/103.26 ((![X19:(($i * $i) > $o),X20]: 102.61/103.26 ((![X21]: 102.61/103.26 (in(X21,X20) => 102.61/103.26 (?[X22]: 102.61/103.26 (X19(X21,X22) & (![X23]: (X19(X21,X23) => (X22 = X23))))))) => 102.61/103.26 (?[X24]: 102.61/103.26 (![X25]: 102.61/103.26 (in(X25,X24) <=> (?[X26]: (in(X26,X20) & X19(X26,X25)))))))) => 102.61/103.26 ((![X27]: 102.61/103.26 ((?[X28]: in(X28,X27)) => 102.61/103.26 (?[X29]: 102.61/103.26 (in(X29,X27) & (~(?[X30]: (in(X30,X29) & in(X30,X27)))))))) => 102.61/103.26 ((![X31]: 102.61/103.26 (?[X32]: 102.61/103.26 ((![X48]: 102.61/103.26 (in(X48,X32) => (![X49]: (in(X49,X48) => in(X49,X31))))) & 102.61/103.26 (![X45,X46]: 102.61/103.26 ((in(X45,X31) & in(X46,X31)) => 102.61/103.26 ((![X47]: 102.61/103.26 (in(X47,X32) => (in(X45,X47) <=> in(X46,X47)))) => 102.61/103.26 (X45 = X46)))) & 102.61/103.26 (![X41,X42]: 102.61/103.26 ((in(X41,X32) & in(X42,X32)) => 102.61/103.26 ((![X44]: (in(X44,X41) => in(X44,X42))) | 102.61/103.26 (![X43]: (in(X43,X42) => in(X43,X41)))))) & 102.61/103.26 (![X33]: 102.61/103.26 (((![X35]: (in(X35,X33) => in(X35,X31))) & 102.61/103.26 (?[X34]: in(X34,X33))) => 102.61/103.26 (?[X36,X37]: 102.61/103.26 (in(X36,X32) & in(X37,X33) & 102.61/103.26 (~(?[X40]: (in(X40,X36) & in(X40,X33)))) & 102.61/103.26 (![X38]: 102.61/103.26 (in(X38,X32) => 102.61/103.26 ((![X39]: (in(X39,X38) => in(X39,X36))) | 102.61/103.26 in(X37,X38))))))))))) => 102.61/103.26 ((![X50:($i > $o)]: 102.61/103.26 ((?[X51]: (X50(X51) & (![X52]: (X50(X52) => (X51 = X52))))) => 102.61/103.26 X50(descr('#ll_0'(X50))))) => 102.61/103.26 ((![X53,X54:($i > $o),X55]: 102.61/103.26 (in(X55,X53) => 102.61/103.26 (X54(X55) => in(X55,dsetconstr(X53,'#ll_0'(X54)))))) => 102.61/103.26 ((![X56,X57:($i > $o),X58]: 102.61/103.26 (in(X58,dsetconstr(X56,'#ll_0'(X57))) => in(X58,X56))) => 102.61/103.26 ((![X59,X60:($i > $o),X61]: 102.61/103.26 (in(X61,dsetconstr(X59,'#ll_0'(X60))) => X60(X61))) => 102.61/103.26 ((![X62:($i > $o)]: 102.61/103.26 ((?[X63]: 102.61/103.26 (X62(X63) & (![X64]: (X62(X64) => (X63 = X64))))) => 102.61/103.26 (?[X65]: 102.61/103.26 (X62(X65) & (![X66]: (X62(X66) => (X65 = X66))))))) => 102.61/103.26 ((![X67:$o,X68]: (in(X68,prop2set(X67)) => X67)) => 102.61/103.26 ((![X69]: (in(X69,emptyset) => (![X70:$o]: X70))) => 102.61/103.26 ((![X71]: (in(X71,emptyset) => $false)) => 102.61/103.26 ((![X72]: (~in(X72,emptyset))) => 102.61/103.26 ((![X73:($i > $o)]: 102.61/103.26 ((?[X74]: 102.61/103.26 (X73(X74) & (![X75]: (X73(X75) => (X74 = X75))))) => 102.61/103.26 (?[X76]: X73(X76)))) => 102.61/103.26 ((![X77,X78]: 102.61/103.26 ((![X79]: (in(X79,X77) => in(X79,X78))) => 102.61/103.26 ((![X80]: (in(X80,X78) => in(X80,X77))) => 102.61/103.26 (X77 = X78)))) => 102.61/103.26 ((![X81]: 102.61/103.26 ((![X82]: (~in(X82,X81))) => (X81 = emptyset))) => 102.61/103.26 ((![X83]: 102.61/103.26 ((![X84]: (~in(X84,X83))) => (X83 = emptyset))) => 102.61/103.26 ((![X85,X86:($i > $o),X87]: 102.61/103.26 (in(X87,X85) => 102.61/103.26 (in(X87,dsetconstr(X85,'#ll_0'(X86))) <=> 102.61/103.26 X86(X87)))) => 102.61/103.26 ((![X88]: 102.61/103.26 ((X88 != emptyset) => (?[X89]: in(X89,X88)))) => 102.61/103.26 ((![X90,X91:($i > $o),X92]: 102.61/103.26 (in(X92,X90) => 102.61/103.26 (X91(X92) => 102.61/103.26 (dsetconstr(X90,'#ll_0'(X91)) != emptyset)))) => 102.61/103.26 ((![X93]: 102.61/103.26 ((?[X94]: in(X94,X93)) => (X93 != emptyset))) => 102.61/103.26 ((![X95,X96]: in(X95,setadjoin(X95,X96))) => 102.61/103.26 (in(emptyset,setadjoin(emptyset,emptyset)) => 102.61/103.26 ((![X97,X98,X99]: 102.61/103.26 (in(X99,X98) => 102.61/103.26 in(X99,setadjoin(X97,X98)))) => 102.61/103.26 ((![X100,X101,X102]: 102.61/103.26 (in(X102,setadjoin(X100,X101)) => 102.61/103.26 (![X103:$o]: 102.61/103.26 (((X102 = X100) => X103) => 102.61/103.26 ((in(X102,X101) => X103) => X103))))) => 102.61/103.26 ((![X104,X105,X106]: 102.61/103.26 (in(X106,setadjoin(X104,X105)) => 102.61/103.26 ((X106 = X104) | in(X106,X105)))) => 102.61/103.26 ((![X107]: 102.61/103.26 (dsetconstr(X107,'#ll_1') = X107)) => 102.61/103.26 ((![X108,X109]: 102.61/103.26 ((![X110]: 102.61/103.26 (in(X110,X109) => in(X110,X108))) => 102.61/103.26 in(X109,powerset(X108)))) => 102.61/103.26 ((![X111]: in(emptyset,powerset(X111))) => 102.61/103.26 ((![X112]: in(emptyset,powerset(X112))) => 102.61/103.26 ((![X113,X114,X115]: 102.61/103.26 (in(X114,powerset(X113)) => 102.61/103.26 (in(X115,X114) => in(X115,X113)))) => 102.61/103.26 ((![X116,X117,X118]: 102.61/103.26 (in(X117,X118) => 102.61/103.26 (in(X118,X116) => 102.61/103.26 in(X117,setunion(X116))))) => 102.61/103.26 ((![X119,X120]: 102.61/103.26 (in(X120,setunion(X119)) => 102.61/103.26 (![X121:$o]: 102.61/103.26 ((![X122]: 102.61/103.26 (in(X120,X122) => 102.61/103.26 (in(X122,X119) => X121))) => 102.61/103.26 X121)))) => 102.61/103.26 ((![X123,X124]: 102.61/103.26 (in(X124,X123) => 102.61/103.26 in(X124, 102.61/103.26 powerset(setunion(X123))))) => 102.61/103.26 ((![X125:($i > $o)]: 102.61/103.26 ((?[X126]: 102.61/103.26 (X125(X126) & 102.61/103.26 (![X127]: 102.61/103.26 (X125(X127) => 102.61/103.26 (X126 = X127))))) => 102.61/103.26 (?[X128]: 102.61/103.26 (![X129]: 102.61/103.26 (X125(X129) <=> 102.61/103.26 (X129 = X128)))))) => 102.61/103.26 ((![X130]: 102.61/103.26 ((X130 != emptyset) => 102.61/103.26 (?[X131]: in(X131,X130)))) => 102.61/103.26 ((![X132,X133]: 102.61/103.26 (in(X132, 102.61/103.26 setadjoin(X133,emptyset)) => 102.61/103.26 (X132 = X133))) => 102.61/103.26 ((![X134,X135]: 102.61/103.26 ((X134 != X135) => 102.61/103.26 (~ 102.61/103.26 in(X135, 102.61/103.26 setadjoin(X134, 102.61/103.26 emptyset))))) => 102.61/103.26 ((![X136,X137]: 102.61/103.26 ((X136 = X137) => 102.61/103.26 in(X136, 102.61/103.26 setadjoin(X137, 102.61/103.26 emptyset)))) => 102.61/103.26 ((![X138,X139]: 102.61/103.26 (in(X138, 102.61/103.26 setadjoin(X139, 102.61/103.26 emptyset)) => 102.61/103.26 in(X139, 102.61/103.26 setadjoin(X138, 102.61/103.26 emptyset)))) => 102.61/103.26 ((![X140,X141,X142]: 102.61/103.26 (in(X142, 102.61/103.26 setadjoin(X140, 102.61/103.26 setadjoin( 102.61/103.26 X141, 102.61/103.26 emptyset))) => 102.61/103.26 ((X142 = X140) | 102.61/103.26 (X142 = X141)))) => 102.61/103.26 ((![X143,X144]: 102.61/103.26 in(X143, 102.61/103.26 setadjoin(X143, 102.61/103.26 setadjoin( 102.61/103.26 X144, 102.61/103.26 emptyset)))) => 102.61/103.26 ((![X145,X146]: 102.61/103.26 in(X146, 102.61/103.26 setadjoin(X145, 102.61/103.26 setadjoin( 102.61/103.26 X146, 102.61/103.26 emptyset)))) => 102.61/103.26 ((![X147,X148:($i > $o)]: 102.61/103.26 ((?[X149]: 102.61/103.26 (in(X149,X147) & 102.61/103.26 X148(X149))) => 102.61/103.26 ((dsetconstr( 102.61/103.26 X147,'#ll_0'(X148)) = 102.61/103.26 emptyset) => 102.61/103.26 $false))) => 102.61/103.26 ((![X150:($i > $o),X151]: 102.61/103.26 (in(X151,emptyset) => 102.61/103.26 X150(X151))) => 102.61/103.26 ((![X152,X153:($i > $o)]: 102.61/103.26 ((~ 102.61/103.26 (![X154]: 102.61/103.26 (in(X154,X152) => 102.61/103.26 X153(X154)))) => 102.61/103.26 (?[X155]: 102.61/103.26 (in(X155,X152) & 102.61/103.26 (~X153(X155)))))) => 102.61/103.26 ((![X156, 102.61/103.26 X157:($i > $o)]: 102.61/103.26 ((![X158]: 102.61/103.26 (in(X158,X156) => 102.61/103.26 (~X157(X158)))) => 102.61/103.26 (~ 102.61/103.26 (?[X159]: 102.61/103.26 (in( 102.61/103.26 X159,X156) & 102.61/103.26 X157(X159)))))) => 102.61/103.26 ((![X160, 102.61/103.26 X161:($i > $o)]: 102.61/103.26 ((~ 102.61/103.26 (?[X162]: 102.61/103.26 (in( 102.61/103.26 X162,X160) & 102.61/103.26 X161(X162)))) => 102.61/103.26 (![X163]: 102.61/103.26 (in(X163,X160) => 102.61/103.26 (~X161(X163)))))) => 102.61/103.26 ((![X164, 102.61/103.26 X165:($i > $o)]: 102.61/103.26 ((?[X166]: 102.61/103.26 (in( 102.61/103.26 X166,X164) & 102.61/103.26 (~ 102.61/103.26 X165( 102.61/103.26 X166)))) => 102.61/103.26 (~ 102.61/103.26 (![X167]: 102.61/103.26 (in( 102.61/103.26 X167,X164) => 102.61/103.26 X165( 102.61/103.26 X167)))))) => 102.61/103.26 ((![X168:$o]: 102.61/103.26 (X168 => 102.61/103.26 in(emptyset, 102.61/103.26 prop2set( 102.61/103.26 X168)))) => 102.61/103.26 ((![X169:$o]: 102.61/103.26 (X169 => 102.61/103.26 set2prop( 102.61/103.26 prop2set( 102.61/103.26 X169)))) => 102.61/103.26 ((![X170, 102.61/103.26 X171:( 102.61/103.26 $i > $o)]: 102.61/103.26 ((~ 102.61/103.26 (?[X172]: 102.61/103.26 (in( 102.61/103.26 X172,X170) & 102.61/103.26 X171( 102.61/103.26 X172)))) => 102.61/103.26 (![X173]: 102.61/103.26 ( 102.61/103.26 in( 102.61/103.26 X173,X170) => 102.61/103.26 ( 102.61/103.26 ~ 102.61/103.26 X171( 102.61/103.26 X173)))))) => 102.61/103.26 ((![X174, 102.61/103.26 X175:( 102.61/103.26 $i > $o)]: 102.61/103.26 ((~ 102.61/103.26 ( 102.61/103.26 ![X176]: 102.61/103.26 (in( 102.61/103.26 X176,X174) => 102.61/103.26 X175( 102.61/103.26 X176)))) => 102.61/103.26 (?[X177]: 102.61/103.26 (in( 102.61/103.26 X177,X174) & 102.61/103.26 (~ 102.61/103.26 X175( 102.61/103.26 X177)))))) => 102.61/103.26 ((![X178:( 102.61/103.26 $i > $o)]: 102.61/103.26 ((?[X179]: 102.61/103.26 (X178( 102.61/103.26 X179) & 102.61/103.26 (![X180]: 102.61/103.26 (X178( 102.61/103.26 X180) => 102.61/103.26 (X179 = 102.61/103.26 X180))))) => 102.61/103.26 (?[X181]: 102.61/103.26 (X178( 102.61/103.26 X181) & 102.61/103.26 (![X182]: 102.61/103.26 (X178( 102.61/103.26 X182) => 102.61/103.26 (X181 = 102.61/103.26 X182))))))) => 102.61/103.26 ((![X183:( 102.61/103.26 $i > $o)]: 102.61/103.26 (( 102.61/103.26 ?[X184]: 102.61/103.26 X183( 102.61/103.26 X184)) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X185, 102.61/103.26 X186]: 102.61/103.26 (X183( 102.61/103.26 X185) => 102.61/103.26 (X183( 102.61/103.26 X186) => 102.61/103.26 (X185 = 102.61/103.26 X186)))) => 102.61/103.26 ( 102.61/103.26 ?[X187]: 102.61/103.26 (X183( 102.61/103.26 X187) & 102.61/103.26 (![X188]: 102.61/103.26 (X183( 102.61/103.26 X188) => 102.61/103.26 (X187 = 102.61/103.26 X188)))))))) => 102.61/103.26 ((![X189:( 102.61/103.26 $i > $o)]: 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ?[X190]: 102.61/103.26 (![X191]: 102.61/103.26 (X189( 102.61/103.26 X191) <=> 102.61/103.26 (X191 = 102.61/103.26 X190)))) => 102.61/103.26 ( 102.61/103.26 ?[X192]: 102.61/103.26 (X189( 102.61/103.26 X192) & 102.61/103.26 (![X193]: 102.61/103.26 (X189( 102.61/103.26 X193) => 102.61/103.26 (X192 = 102.61/103.26 X193))))))) => 102.61/103.26 ((![X194, 102.61/103.26 X195]: 102.61/103.26 (( 102.61/103.26 X194 = 102.61/103.26 X195) => 102.61/103.26 (![X196, 102.61/103.26 X197]: 102.61/103.26 (( 102.61/103.26 X196 = 102.61/103.26 X197) => 102.61/103.26 (in( 102.61/103.26 X196,X194) => 102.61/103.26 in( 102.61/103.26 X197,X195)))))) => 102.61/103.26 ((![X198, 102.61/103.26 X199]: 102.61/103.26 (( 102.61/103.26 X198 = 102.61/103.26 X199) => 102.61/103.26 (![X200, 102.61/103.26 X201]: 102.61/103.26 (( 102.61/103.26 X200 = 102.61/103.26 X201) => 102.61/103.26 (in( 102.61/103.26 X200,X198) <=> 102.61/103.26 in( 102.61/103.26 X201,X199)))))) => 102.61/103.26 (( 102.61/103.26 ![X202:( 102.61/103.26 $i > $o)]: 102.61/103.26 (( 102.61/103.26 ?[X203]: 102.61/103.26 (X202( 102.61/103.26 X203) & 102.61/103.26 (![X204]: 102.61/103.26 (X202( 102.61/103.26 X204) => 102.61/103.26 (X203 = 102.61/103.26 X204))))) => 102.61/103.26 (![X205, 102.61/103.26 X206]: 102.61/103.26 (X202( 102.61/103.26 X205) => 102.61/103.26 (X202( 102.61/103.26 X206) => 102.61/103.26 (X205 = 102.61/103.26 X206)))))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X207:( 102.61/103.26 $i > $o), 102.61/103.26 X208:( 102.61/103.26 $i > $o)]: 102.61/103.26 (( 102.61/103.26 ![X209, 102.61/103.26 X210]: 102.61/103.26 (( 102.61/103.26 X209 = 102.61/103.26 X210) => 102.61/103.26 (X207( 102.61/103.26 X209) <=> 102.61/103.26 X208( 102.61/103.26 X210)))) => 102.61/103.26 (( 102.61/103.26 ?[X211]: 102.61/103.26 (X207( 102.61/103.26 X211) & 102.61/103.26 (![X212]: 102.61/103.26 (X207( 102.61/103.26 X212) => 102.61/103.26 (X211 = 102.61/103.26 X212))))) <=> 102.61/103.26 (?[X213]: 102.61/103.26 (X208( 102.61/103.26 X213) & 102.61/103.26 (![X214]: 102.61/103.26 (X208( 102.61/103.26 X214) => 102.61/103.26 (X213 = 102.61/103.26 X214)))))))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 emptyset = 102.61/103.26 emptyset) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X215, 102.61/103.26 X216]: 102.61/103.26 (( 102.61/103.26 X215 = 102.61/103.26 X216) => 102.61/103.26 (![X217, 102.61/103.26 X218]: 102.61/103.26 (( 102.61/103.26 X217 = 102.61/103.26 X218) => 102.61/103.26 (setadjoin( 102.61/103.26 X215,X217) = 102.61/103.26 setadjoin( 102.61/103.26 X216,X218)))))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X219, 102.61/103.26 X220]: 102.61/103.26 (( 102.61/103.26 X219 = 102.61/103.26 X220) => 102.61/103.26 (powerset( 102.61/103.26 X219) = 102.61/103.26 powerset( 102.61/103.26 X220)))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X221, 102.61/103.26 X222]: 102.61/103.26 (( 102.61/103.26 X221 = 102.61/103.26 X222) => 102.61/103.26 (setunion( 102.61/103.26 X221) = 102.61/103.26 setunion( 102.61/103.26 X222)))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 omega = 102.61/103.26 omega) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X223:( 102.61/103.26 $i > $o)]: 102.61/103.26 (( 102.61/103.26 ?[X224]: 102.61/103.26 (X223( 102.61/103.26 X224) & 102.61/103.26 (![X225]: 102.61/103.26 (X223( 102.61/103.26 X225) => 102.61/103.26 (X224 = 102.61/103.26 X225))))) => 102.61/103.26 (![X226, 102.61/103.26 X227]: 102.61/103.26 (X223( 102.61/103.26 X226) => 102.61/103.26 (X223( 102.61/103.26 X227) => 102.61/103.26 (X226 = 102.61/103.26 X227)))))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X228:( 102.61/103.26 $i > $o), 102.61/103.26 X229:( 102.61/103.26 $i > $o)]: 102.61/103.26 (( 102.61/103.26 ![X230, 102.61/103.26 X231]: 102.61/103.26 (( 102.61/103.26 X230 = 102.61/103.26 X231) => 102.61/103.26 (X228( 102.61/103.26 X230) <=> 102.61/103.26 X229( 102.61/103.26 X231)))) => 102.61/103.26 (( 102.61/103.26 ?[X232]: 102.61/103.26 (X228( 102.61/103.26 X232) & 102.61/103.26 (![X233]: 102.61/103.26 (X228( 102.61/103.26 X233) => 102.61/103.26 (X232 = 102.61/103.26 X233))))) => 102.61/103.26 (( 102.61/103.26 ?[X234]: 102.61/103.26 (X229( 102.61/103.26 X234) & 102.61/103.26 (![X235]: 102.61/103.26 (X229( 102.61/103.26 X235) => 102.61/103.26 (X234 = 102.61/103.26 X235))))) => 102.61/103.26 (descr( 102.61/103.26 '#ll_0'( 102.61/103.26 X228)) = 102.61/103.26 descr( 102.61/103.26 '#ll_0'( 102.61/103.26 X229))))))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X236, 102.61/103.26 X237]: 102.61/103.26 (( 102.61/103.26 X236 = 102.61/103.26 X237) => 102.61/103.26 (![X238:( 102.61/103.26 $i > $o), 102.61/103.26 X239:( 102.61/103.26 $i > $o)]: 102.61/103.26 (( 102.61/103.26 ![X240]: 102.61/103.26 (in( 102.61/103.26 X240,X236) => 102.61/103.26 (![X241]: 102.61/103.26 (in( 102.61/103.26 X241,X237) => 102.61/103.26 (( 102.61/103.26 X240 = 102.61/103.26 X241) => 102.61/103.26 (X238( 102.61/103.26 X240) <=> 102.61/103.26 X239( 102.61/103.26 X241))))))) => 102.61/103.26 (dsetconstr( 102.61/103.26 X236, 102.61/103.26 '#ll_0'( 102.61/103.26 X238)) = 102.61/103.26 dsetconstr( 102.61/103.26 X237, 102.61/103.26 '#ll_0'( 102.61/103.26 X239))))))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X242, 102.61/103.26 X243]: 102.61/103.26 (( 102.61/103.26 ![X244]: 102.61/103.26 (in( 102.61/103.26 X244,X242) => 102.61/103.26 in( 102.61/103.26 X244,X243))) => 102.61/103.26 subset( 102.61/103.26 X242,X243))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X245, 102.61/103.26 X246]: 102.61/103.26 (( 102.61/103.26 X245 = 102.61/103.26 X246) => 102.61/103.26 subset( 102.61/103.26 X246,X245))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X247, 102.61/103.26 X248]: 102.61/103.26 (( 102.61/103.26 X247 = 102.61/103.26 X248) => 102.61/103.26 subset( 102.61/103.26 X247,X248))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X249, 102.61/103.26 X250]: 102.61/103.26 (( 102.61/103.26 ![X251]: 102.61/103.26 (in( 102.61/103.26 X251,X249) => 102.61/103.26 in( 102.61/103.26 X251,X250))) => 102.61/103.26 subset( 102.61/103.26 X249,X250))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X252]: 102.61/103.26 subset( 102.61/103.26 emptyset, 102.61/103.26 X252)) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X253, 102.61/103.26 X254,X255]: 102.61/103.26 (subset( 102.61/103.26 X253,X254) => 102.61/103.26 (in( 102.61/103.26 X255,X253) => 102.61/103.26 in( 102.61/103.26 X255,X254)))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X256, 102.61/103.26 X257,X258]: 102.61/103.26 (subset( 102.61/103.26 X256,X257) => 102.61/103.26 (( 102.61/103.26 ~ 102.61/103.26 in( 102.61/103.26 X258,X257)) => 102.61/103.26 (~ 102.61/103.26 in( 102.61/103.26 X258,X256))))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X259, 102.61/103.26 X260,X261]: 102.61/103.26 (in( 102.61/103.26 X261,X259) => 102.61/103.26 (( 102.61/103.26 ~ 102.61/103.26 in( 102.61/103.26 X261,X260)) => 102.61/103.26 (~ 102.61/103.26 subset( 102.61/103.26 X259,X260))))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X262, 102.61/103.26 X263]: 102.61/103.26 (( 102.61/103.26 ~ 102.61/103.26 subset( 102.61/103.26 X262,X263)) => 102.61/103.26 (X262 != 102.61/103.26 X263))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X264, 102.61/103.26 X265,X266]: 102.61/103.26 (in( 102.61/103.26 X266,X264) => 102.61/103.26 (( 102.61/103.26 ~ 102.61/103.26 in( 102.61/103.26 X266,X265)) => 102.61/103.26 (X264 != 102.61/103.26 X265)))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X267]: 102.61/103.26 subset( 102.61/103.26 X267,X267)) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X268, 102.61/103.26 X269,X270]: 102.61/103.26 (subset( 102.61/103.26 X268,X269) => 102.61/103.26 (subset( 102.61/103.26 X269,X270) => 102.61/103.26 subset( 102.61/103.26 X268,X270)))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X271, 102.61/103.26 X272]: 102.61/103.26 subset( 102.61/103.26 X272, 102.61/103.26 setadjoin( 102.61/103.26 X271,X272))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X273, 102.61/103.26 X274,X275]: 102.61/103.26 (subset( 102.61/103.26 X273,X275) => 102.61/103.26 subset( 102.61/103.26 X273, 102.61/103.26 setadjoin( 102.61/103.26 X274,X275)))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X276, 102.61/103.26 X277]: 102.61/103.26 (subset( 102.61/103.26 X276,X277) => 102.61/103.26 in( 102.61/103.26 X276, 102.61/103.26 powerset( 102.61/103.26 X277)))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X278, 102.61/103.26 X279]: 102.61/103.26 (subset( 102.61/103.26 X278,X279) => 102.61/103.26 (subset( 102.61/103.26 X279,X278) => 102.61/103.26 (X278 = 102.61/103.26 X279)))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X280]: 102.61/103.26 (subset( 102.61/103.26 X280, 102.61/103.26 emptyset) => 102.61/103.26 (X280 = 102.61/103.26 emptyset))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X281, 102.61/103.26 X282]: 102.61/103.26 (subset( 102.61/103.26 X282,X281) => 102.61/103.26 in( 102.61/103.26 X282, 102.61/103.26 powerset( 102.61/103.26 X281)))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X283, 102.61/103.26 X284]: 102.61/103.26 (in( 102.61/103.26 X284, 102.61/103.26 powerset( 102.61/103.26 X283)) => 102.61/103.26 subset( 102.61/103.26 X284,X283))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X285]: 102.61/103.26 in( 102.61/103.26 X285, 102.61/103.26 powerset( 102.61/103.26 X285))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X286, 102.61/103.26 X287]: 102.61/103.26 (subset( 102.61/103.26 X286,X287) => 102.61/103.26 subset( 102.61/103.26 powerset( 102.61/103.26 X286), 102.61/103.26 powerset( 102.61/103.26 X287)))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X288, 102.61/103.26 X289:( 102.61/103.26 $i > $o)]: 102.61/103.26 in( 102.61/103.26 dsetconstr( 102.61/103.26 X288, 102.61/103.26 '#ll_0'( 102.61/103.26 X289)), 102.61/103.26 powerset( 102.61/103.26 X288))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X290, 102.61/103.26 X291:( 102.61/103.26 $i > $o)]: 102.61/103.26 subset( 102.61/103.26 dsetconstr( 102.61/103.26 X290, 102.61/103.26 '#ll_0'( 102.61/103.26 X291)), 102.61/103.26 X290)) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X292, 102.61/103.26 X293,X294]: 102.61/103.26 (in( 102.61/103.26 X294,X292) => 102.61/103.26 in( 102.61/103.26 X294, 102.61/103.26 binunion( 102.61/103.26 X292,X293)))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X295, 102.61/103.26 X296]: 102.61/103.26 in( 102.61/103.26 X296, 102.61/103.26 setadjoin( 102.61/103.26 X295, 102.61/103.26 setadjoin( 102.61/103.26 X296, 102.61/103.26 emptyset)))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X297, 102.61/103.26 X298,X299]: 102.61/103.26 (in( 102.61/103.26 X299,X298) => 102.61/103.26 in( 102.61/103.26 X299, 102.61/103.26 binunion( 102.61/103.26 X297,X298)))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X300, 102.61/103.26 X301, 102.61/103.26 X302, 102.61/103.26 X303:$o]: 102.61/103.26 (in( 102.61/103.26 X302, 102.61/103.26 binunion( 102.61/103.26 X300,X301)) => 102.61/103.26 (( 102.61/103.26 in( 102.61/103.26 X302,X300) => 102.61/103.26 X303) => 102.61/103.26 (( 102.61/103.26 in( 102.61/103.26 X302,X301) => 102.61/103.26 X303) => 102.61/103.26 X303)))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X304, 102.61/103.26 X305,X306]: 102.61/103.26 (in( 102.61/103.26 X306, 102.61/103.26 binunion( 102.61/103.26 X304,X305)) => 102.61/103.26 (in( 102.61/103.26 X306,X304) | 102.61/103.26 in( 102.61/103.26 X306,X305)))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X307, 102.61/103.26 X308]: 102.61/103.26 subset( 102.61/103.26 X307, 102.61/103.26 binunion( 102.61/103.26 X307,X308))) => 102.61/103.26 ( 102.61/103.26 ![X309, 102.61/103.26 X310]: 102.61/103.26 subset( 102.61/103.26 X310, 102.61/103.26 binunion( 102.61/103.26 X309,X310)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 102.61/103.26 tff(zf_stmt_1, type, zip_tseitin5 : ($i * $i > $o) > $o). 102.61/103.26 tff(zf_stmt_2, axiom, 102.61/103.26 (zip_tseitin5(X211,X207) <=> 102.61/103.26 ((![X212]: zip_tseitin4(X212,X211,X207)) & X207(X211)))). 102.61/103.26 tff(zf_stmt_3, type, zip_tseitin4 : ($i * $i * $i > $o) > $o). 102.61/103.26 tff(zf_stmt_4, axiom, 102.61/103.26 (zip_tseitin4(X212,X211,X207) <=> (X207(X212) => (X211 = X212)))). 102.61/103.26 tff(zf_stmt_5, type, zip_tseitin3 : ($i * $i * $i * ($i * $i) > $o) > $o). 102.61/103.26 tff(zf_stmt_6, axiom, 102.61/103.26 (zip_tseitin3(X26,X25,X20,X19) <=> (X19(X26,X25) & in(X26,X20)))). 102.61/103.26 tff(zf_stmt_7, type, zip_tseitin2 : ($i * $i * $i) > $o). 102.61/103.26 tff(zf_stmt_8, axiom, 102.61/103.26 (zip_tseitin2(X14,X13,X12) <=> (in(X14,X12) & in(X13,X14)))). 102.61/103.26 tff(zf_stmt_9, type, zip_tseitin1 : ($i * $i * $i) > $o). 102.61/103.26 tff(zf_stmt_10, axiom, 102.61/103.26 (zip_tseitin1(X11,X10,X9) <=> (in(X11,X10) => in(X11,X9)))). 102.61/103.26 tff(zf_stmt_11, type, zip_tseitin0 : ($i * $i * $i) > $o). 102.61/103.26 tff(zf_stmt_12, axiom, (zip_tseitin0(X8,X7,X6) <=> (in(X8,X7) | (X8 = X6)))). 102.61/103.26 tff(zf_stmt_13, conjecture, 102.61/103.26 ((![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))) => 102.61/103.26 ((![X5]: (~in(X5,emptyset))) => 102.61/103.26 ((![X6,X7,X8]: (in(X8,setadjoin(X6,X7)) <=> zip_tseitin0(X8,X7,X6))) => 102.61/103.26 ((![X9,X10]: 102.61/103.26 (in(X10,powerset(X9)) <=> (![X11]: zip_tseitin1(X11,X10,X9)))) => 102.61/103.26 ((![X12,X13]: 102.61/103.26 (in(X13,setunion(X12)) <=> (?[X14]: zip_tseitin2(X14,X13,X12)))) => 102.61/103.26 (in(emptyset,omega) => 102.61/103.26 ((![X15]: (in(X15,omega) => in(setadjoin(X15,X15),omega))) => 102.61/103.26 ((![X16]: 102.61/103.26 (((![X17]: 102.61/103.26 ((in(X17,X16) & in(X17,omega)) => 102.61/103.26 in(setadjoin(X17,X17),X16))) & 102.61/103.26 in(emptyset,X16)) => 102.61/103.26 (![X18]: (in(X18,omega) => in(X18,X16))))) => 102.61/103.26 ((![X19:(($i * $i) > $o),X20]: 102.61/103.26 ((![X21]: 102.61/103.26 (in(X21,X20) => 102.61/103.26 (?[X22]: 102.61/103.26 ((![X23]: (X19(X21,X23) => (X22 = X23))) & X19(X21,X22))))) => 102.61/103.26 (?[X24]: 102.61/103.26 (![X25]: 102.61/103.26 (in(X25,X24) <=> (?[X26]: zip_tseitin3(X26,X25,X20,X19))))))) => 102.61/103.26 ((![X27]: 102.61/103.26 ((?[X28]: in(X28,X27)) => 102.61/103.26 (?[X29]: 102.61/103.26 ((~(?[X30]: (in(X30,X27) & in(X30,X29)))) & in(X29,X27))))) => 102.61/103.26 ((![X31]: 102.61/103.26 (?[X32]: 102.61/103.26 ((![X33]: 102.61/103.26 (((?[X34]: in(X34,X33)) & 102.61/103.26 (![X35]: (in(X35,X33) => in(X35,X31)))) => 102.61/103.26 (?[X36,X37]: 102.61/103.26 ((![X38]: 102.61/103.26 (in(X38,X32) => 102.61/103.26 (in(X37,X38) | 102.61/103.26 (![X39]: (in(X39,X38) => in(X39,X36)))))) & 102.61/103.26 (~(?[X40]: (in(X40,X33) & in(X40,X36)))) & 102.61/103.26 in(X37,X33) & in(X36,X32))))) & 102.61/103.26 (![X41,X42]: 102.61/103.26 ((in(X42,X32) & in(X41,X32)) => 102.61/103.26 ((![X43]: (in(X43,X42) => in(X43,X41))) | 102.61/103.26 (![X44]: (in(X44,X41) => in(X44,X42)))))) & 102.61/103.26 (![X45,X46]: 102.61/103.26 ((in(X46,X31) & in(X45,X31)) => 102.61/103.26 ((![X47]: 102.61/103.26 (in(X47,X32) => (in(X45,X47) <=> in(X46,X47)))) => 102.61/103.26 (X45 = X46)))) & 102.61/103.26 (![X48]: 102.61/103.26 (in(X48,X32) => (![X49]: (in(X49,X48) => in(X49,X31)))))))) => 102.61/103.26 ((![X50:($i > $o)]: 102.61/103.26 ((?[X51]: ((![X52]: (X50(X52) => (X51 = X52))) & X50(X51))) => 102.61/103.26 X50(descr('#ll_0'(X50))))) => 102.61/103.26 ((![X53,X54:($i > $o),X55]: 102.61/103.26 (in(X55,X53) => 102.61/103.26 (X54(X55) => in(X55,dsetconstr(X53,'#ll_0'(X54)))))) => 102.61/103.26 ((![X56,X57:($i > $o),X58]: 102.61/103.26 (in(X58,dsetconstr(X56,'#ll_0'(X57))) => in(X58,X56))) => 102.61/103.26 ((![X59,X60:($i > $o),X61]: 102.61/103.26 (in(X61,dsetconstr(X59,'#ll_0'(X60))) => X60(X61))) => 102.61/103.26 ((![X62:($i > $o)]: 102.61/103.26 ((?[X63]: 102.61/103.26 ((![X64]: (X62(X64) => (X63 = X64))) & X62(X63))) => 102.61/103.26 (?[X65]: 102.61/103.26 ((![X66]: (X62(X66) => (X65 = X66))) & X62(X65))))) => 102.61/103.26 ((![X67:$o,X68]: (in(X68,prop2set(X67)) => X67)) => 102.61/103.26 ((![X69]: (in(X69,emptyset) => (![X70:$o]: X70))) => 102.61/103.26 ((![X71]: (in(X71,emptyset) => $false)) => 102.61/103.26 ((![X72]: (~in(X72,emptyset))) => 102.61/103.26 ((![X73:($i > $o)]: 102.61/103.26 ((?[X74]: 102.61/103.26 ((![X75]: (X73(X75) => (X74 = X75))) & X73(X74))) => 102.61/103.26 (?[X76]: X73(X76)))) => 102.61/103.26 ((![X77,X78]: 102.61/103.26 ((![X79]: (in(X79,X77) => in(X79,X78))) => 102.61/103.26 ((![X80]: (in(X80,X78) => in(X80,X77))) => 102.61/103.26 (X77 = X78)))) => 102.61/103.26 ((![X81]: 102.61/103.26 ((![X82]: (~in(X82,X81))) => (X81 = emptyset))) => 102.61/103.26 ((![X83]: 102.61/103.26 ((![X84]: (~in(X84,X83))) => (X83 = emptyset))) => 102.61/103.26 ((![X85,X86:($i > $o),X87]: 102.61/103.26 (in(X87,X85) => 102.61/103.26 (in(X87,dsetconstr(X85,'#ll_0'(X86))) <=> 102.61/103.26 X86(X87)))) => 102.61/103.26 ((![X88]: 102.61/103.26 ((X88 != emptyset) => (?[X89]: in(X89,X88)))) => 102.61/103.26 ((![X90,X91:($i > $o),X92]: 102.61/103.26 (in(X92,X90) => 102.61/103.26 (X91(X92) => 102.61/103.26 (dsetconstr(X90,'#ll_0'(X91)) != emptyset)))) => 102.61/103.26 ((![X93]: 102.61/103.26 ((?[X94]: in(X94,X93)) => (X93 != emptyset))) => 102.61/103.26 ((![X95,X96]: in(X95,setadjoin(X95,X96))) => 102.61/103.26 (in(emptyset,setadjoin(emptyset,emptyset)) => 102.61/103.26 ((![X97,X98,X99]: 102.61/103.26 (in(X99,X98) => 102.61/103.26 in(X99,setadjoin(X97,X98)))) => 102.61/103.26 ((![X100,X101,X102]: 102.61/103.26 (in(X102,setadjoin(X100,X101)) => 102.61/103.26 (![X103:$o]: 102.61/103.26 (((X102 = X100) => X103) => 102.61/103.26 ((in(X102,X101) => X103) => X103))))) => 102.61/103.26 ((![X104,X105,X106]: 102.61/103.26 (in(X106,setadjoin(X104,X105)) => 102.61/103.26 (in(X106,X105) | (X106 = X104)))) => 102.61/103.26 ((![X107]: 102.61/103.26 (dsetconstr(X107,'#ll_1') = X107)) => 102.61/103.26 ((![X108,X109]: 102.61/103.26 ((![X110]: 102.61/103.26 (in(X110,X109) => in(X110,X108))) => 102.61/103.26 in(X109,powerset(X108)))) => 102.61/103.26 ((![X111]: in(emptyset,powerset(X111))) => 102.61/103.26 ((![X112]: in(emptyset,powerset(X112))) => 102.61/103.26 ((![X113,X114,X115]: 102.61/103.26 (in(X114,powerset(X113)) => 102.61/103.26 (in(X115,X114) => in(X115,X113)))) => 102.61/103.26 ((![X116,X117,X118]: 102.61/103.26 (in(X117,X118) => 102.61/103.26 (in(X118,X116) => 102.61/103.26 in(X117,setunion(X116))))) => 102.61/103.26 ((![X119,X120]: 102.61/103.26 (in(X120,setunion(X119)) => 102.61/103.26 (![X121:$o]: 102.61/103.26 ((![X122]: 102.61/103.26 (in(X120,X122) => 102.61/103.26 (in(X122,X119) => X121))) => 102.61/103.26 X121)))) => 102.61/103.26 ((![X123,X124]: 102.61/103.26 (in(X124,X123) => 102.61/103.26 in(X124, 102.61/103.26 powerset(setunion(X123))))) => 102.61/103.26 ((![X125:($i > $o)]: 102.61/103.26 ((?[X126]: 102.61/103.26 ((![X127]: 102.61/103.26 (X125(X127) => 102.61/103.26 (X126 = X127))) & 102.61/103.26 X125(X126))) => 102.61/103.26 (?[X128]: 102.61/103.26 (![X129]: 102.61/103.26 (X125(X129) <=> 102.61/103.26 (X129 = X128)))))) => 102.61/103.26 ((![X130]: 102.61/103.26 ((X130 != emptyset) => 102.61/103.26 (?[X131]: in(X131,X130)))) => 102.61/103.26 ((![X132,X133]: 102.61/103.26 (in(X132, 102.61/103.26 setadjoin(X133,emptyset)) => 102.61/103.26 (X132 = X133))) => 102.61/103.26 ((![X134,X135]: 102.61/103.26 ((X134 != X135) => 102.61/103.26 (~ 102.61/103.26 in(X135, 102.61/103.26 setadjoin(X134, 102.61/103.26 emptyset))))) => 102.61/103.26 ((![X136,X137]: 102.61/103.26 ((X136 = X137) => 102.61/103.26 in(X136, 102.61/103.26 setadjoin(X137, 102.61/103.26 emptyset)))) => 102.61/103.26 ((![X138,X139]: 102.61/103.26 (in(X138, 102.61/103.26 setadjoin(X139, 102.61/103.26 emptyset)) => 102.61/103.26 in(X139, 102.61/103.26 setadjoin(X138, 102.61/103.26 emptyset)))) => 102.61/103.26 ((![X140,X141,X142]: 102.61/103.26 (in(X142, 102.61/103.26 setadjoin(X140, 102.61/103.26 setadjoin( 102.61/103.26 X141, 102.61/103.26 emptyset))) => 102.61/103.26 ((X142 = X141) | 102.61/103.26 (X142 = X140)))) => 102.61/103.26 ((![X143,X144]: 102.61/103.26 in(X143, 102.61/103.26 setadjoin(X143, 102.61/103.26 setadjoin( 102.61/103.26 X144, 102.61/103.26 emptyset)))) => 102.61/103.26 ((![X145,X146]: 102.61/103.26 in(X146, 102.61/103.26 setadjoin(X145, 102.61/103.26 setadjoin( 102.61/103.26 X146, 102.61/103.26 emptyset)))) => 102.61/103.26 ((![X147,X148:($i > $o)]: 102.61/103.26 ((?[X149]: 102.61/103.26 (X148(X149) & 102.61/103.26 in(X149,X147))) => 102.61/103.26 ((dsetconstr( 102.61/103.26 X147,'#ll_0'(X148)) = 102.61/103.26 emptyset) => 102.61/103.26 $false))) => 102.61/103.26 ((![X150:($i > $o),X151]: 102.61/103.26 (in(X151,emptyset) => 102.61/103.26 X150(X151))) => 102.61/103.26 ((![X152,X153:($i > $o)]: 102.61/103.26 ((~ 102.61/103.26 (![X154]: 102.61/103.26 (in(X154,X152) => 102.61/103.26 X153(X154)))) => 102.61/103.26 (?[X155]: 102.61/103.26 ((~X153(X155)) & 102.61/103.26 in(X155,X152))))) => 102.61/103.26 ((![X156, 102.61/103.26 X157:($i > $o)]: 102.61/103.26 ((![X158]: 102.61/103.26 (in(X158,X156) => 102.61/103.26 (~X157(X158)))) => 102.61/103.26 (~ 102.61/103.26 (?[X159]: 102.61/103.26 (X157(X159) & 102.61/103.26 in( 102.61/103.26 X159,X156)))))) => 102.61/103.26 ((![X160, 102.61/103.26 X161:($i > $o)]: 102.61/103.26 ((~ 102.61/103.26 (?[X162]: 102.61/103.26 (X161(X162) & 102.61/103.26 in( 102.61/103.26 X162,X160)))) => 102.61/103.26 (![X163]: 102.61/103.26 (in(X163,X160) => 102.61/103.26 (~X161(X163)))))) => 102.61/103.26 ((![X164, 102.61/103.26 X165:($i > $o)]: 102.61/103.26 ((?[X166]: 102.61/103.26 ((~ 102.61/103.26 X165( 102.61/103.26 X166)) & 102.61/103.26 in( 102.61/103.26 X166,X164))) => 102.61/103.26 (~ 102.61/103.26 (![X167]: 102.61/103.26 (in( 102.61/103.26 X167,X164) => 102.61/103.26 X165( 102.61/103.26 X167)))))) => 102.61/103.26 ((![X168:$o]: 102.61/103.26 (X168 => 102.61/103.26 in(emptyset, 102.61/103.26 prop2set( 102.61/103.26 X168)))) => 102.61/103.26 ((![X169:$o]: 102.61/103.26 (X169 => 102.61/103.26 set2prop( 102.61/103.26 prop2set( 102.61/103.26 X169)))) => 102.61/103.26 ((![X170, 102.61/103.26 X171:( 102.61/103.26 $i > $o)]: 102.61/103.26 ((~ 102.61/103.26 (?[X172]: 102.61/103.26 (X171( 102.61/103.26 X172) & 102.61/103.26 in( 102.61/103.26 X172,X170)))) => 102.61/103.26 (![X173]: 102.61/103.26 ( 102.61/103.26 in( 102.61/103.26 X173,X170) => 102.61/103.26 ( 102.61/103.26 ~ 102.61/103.26 X171( 102.61/103.26 X173)))))) => 102.61/103.26 ((![X174, 102.61/103.26 X175:( 102.61/103.26 $i > $o)]: 102.61/103.26 ((~ 102.61/103.26 ( 102.61/103.26 ![X176]: 102.61/103.26 (in( 102.61/103.26 X176,X174) => 102.61/103.26 X175( 102.61/103.26 X176)))) => 102.61/103.26 (?[X177]: 102.61/103.26 (( 102.61/103.26 ~ 102.61/103.26 X175( 102.61/103.26 X177)) & 102.61/103.26 in( 102.61/103.26 X177,X174))))) => 102.61/103.26 ((![X178:( 102.61/103.26 $i > $o)]: 102.61/103.26 ((?[X179]: 102.61/103.26 (( 102.61/103.26 ![X180]: 102.61/103.26 (X178( 102.61/103.26 X180) => 102.61/103.26 (X179 = 102.61/103.26 X180))) & 102.61/103.26 X178( 102.61/103.26 X179))) => 102.61/103.26 (?[X181]: 102.61/103.26 (( 102.61/103.26 ![X182]: 102.61/103.26 (X178( 102.61/103.26 X182) => 102.61/103.26 (X181 = 102.61/103.26 X182))) & 102.61/103.26 X178( 102.61/103.26 X181))))) => 102.61/103.26 ((![X183:( 102.61/103.26 $i > $o)]: 102.61/103.26 (( 102.61/103.26 ?[X184]: 102.61/103.26 X183( 102.61/103.26 X184)) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X185, 102.61/103.26 X186]: 102.61/103.26 (X183( 102.61/103.26 X185) => 102.61/103.26 (X183( 102.61/103.26 X186) => 102.61/103.26 (X185 = 102.61/103.26 X186)))) => 102.61/103.26 ( 102.61/103.26 ?[X187]: 102.61/103.26 (( 102.61/103.26 ![X188]: 102.61/103.26 (X183( 102.61/103.26 X188) => 102.61/103.26 (X187 = 102.61/103.26 X188))) & 102.61/103.26 X183( 102.61/103.26 X187)))))) => 102.61/103.26 ((![X189:( 102.61/103.26 $i > $o)]: 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ?[X190]: 102.61/103.26 (![X191]: 102.61/103.26 (X189( 102.61/103.26 X191) <=> 102.61/103.26 (X191 = 102.61/103.26 X190)))) => 102.61/103.26 ( 102.61/103.26 ?[X192]: 102.61/103.26 (( 102.61/103.26 ![X193]: 102.61/103.26 (X189( 102.61/103.26 X193) => 102.61/103.26 (X192 = 102.61/103.26 X193))) & 102.61/103.26 X189( 102.61/103.26 X192))))) => 102.61/103.26 ((![X194, 102.61/103.26 X195]: 102.61/103.26 (( 102.61/103.26 X194 = 102.61/103.26 X195) => 102.61/103.26 (![X196, 102.61/103.26 X197]: 102.61/103.26 (( 102.61/103.26 X196 = 102.61/103.26 X197) => 102.61/103.26 (in( 102.61/103.26 X196,X194) => 102.61/103.26 in( 102.61/103.26 X197,X195)))))) => 102.61/103.26 ((![X198, 102.61/103.26 X199]: 102.61/103.26 (( 102.61/103.26 X198 = 102.61/103.26 X199) => 102.61/103.26 (![X200, 102.61/103.26 X201]: 102.61/103.26 (( 102.61/103.26 X200 = 102.61/103.26 X201) => 102.61/103.26 (in( 102.61/103.26 X200,X198) <=> 102.61/103.26 in( 102.61/103.26 X201,X199)))))) => 102.61/103.26 (( 102.61/103.26 ![X202:( 102.61/103.26 $i > $o)]: 102.61/103.26 (( 102.61/103.26 ?[X203]: 102.61/103.26 (( 102.61/103.26 ![X204]: 102.61/103.26 (X202( 102.61/103.26 X204) => 102.61/103.26 (X203 = 102.61/103.26 X204))) & 102.61/103.26 X202( 102.61/103.26 X203))) => 102.61/103.26 (![X205, 102.61/103.26 X206]: 102.61/103.26 (X202( 102.61/103.26 X205) => 102.61/103.26 (X202( 102.61/103.26 X206) => 102.61/103.26 (X205 = 102.61/103.26 X206)))))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X207:( 102.61/103.26 $i > $o), 102.61/103.26 X208:( 102.61/103.26 $i > $o)]: 102.61/103.26 (( 102.61/103.26 ![X209, 102.61/103.26 X210]: 102.61/103.26 (( 102.61/103.26 X209 = 102.61/103.26 X210) => 102.61/103.26 (X207( 102.61/103.26 X209) <=> 102.61/103.26 X208( 102.61/103.26 X210)))) => 102.61/103.26 (( 102.61/103.26 ?[X211]: 102.61/103.26 zip_tseitin5( 102.61/103.26 X211,X207)) <=> 102.61/103.26 (?[X213]: 102.61/103.26 zip_tseitin5( 102.61/103.26 X213,X208))))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 emptyset = 102.61/103.26 emptyset) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X215, 102.61/103.26 X216]: 102.61/103.26 (( 102.61/103.26 X215 = 102.61/103.26 X216) => 102.61/103.26 (![X217, 102.61/103.26 X218]: 102.61/103.26 (( 102.61/103.26 X217 = 102.61/103.26 X218) => 102.61/103.26 (setadjoin( 102.61/103.26 X215,X217) = 102.61/103.26 setadjoin( 102.61/103.26 X216,X218)))))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X219, 102.61/103.26 X220]: 102.61/103.26 (( 102.61/103.26 X219 = 102.61/103.26 X220) => 102.61/103.26 (powerset( 102.61/103.26 X219) = 102.61/103.26 powerset( 102.61/103.26 X220)))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X221, 102.61/103.26 X222]: 102.61/103.26 (( 102.61/103.26 X221 = 102.61/103.26 X222) => 102.61/103.26 (setunion( 102.61/103.26 X221) = 102.61/103.26 setunion( 102.61/103.26 X222)))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 omega = 102.61/103.26 omega) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X223:( 102.61/103.26 $i > $o)]: 102.61/103.26 (( 102.61/103.26 ?[X224]: 102.61/103.26 (( 102.61/103.26 ![X225]: 102.61/103.26 (X223( 102.61/103.26 X225) => 102.61/103.26 (X224 = 102.61/103.26 X225))) & 102.61/103.26 X223( 102.61/103.26 X224))) => 102.61/103.26 (![X226, 102.61/103.26 X227]: 102.61/103.26 (X223( 102.61/103.26 X226) => 102.61/103.26 (X223( 102.61/103.26 X227) => 102.61/103.26 (X226 = 102.61/103.26 X227)))))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X228:( 102.61/103.26 $i > $o), 102.61/103.26 X229:( 102.61/103.26 $i > $o)]: 102.61/103.26 (( 102.61/103.26 ![X230, 102.61/103.26 X231]: 102.61/103.26 (( 102.61/103.26 X230 = 102.61/103.26 X231) => 102.61/103.26 (X228( 102.61/103.26 X230) <=> 102.61/103.26 X229( 102.61/103.26 X231)))) => 102.61/103.26 (( 102.61/103.26 ?[X232]: 102.61/103.26 (( 102.61/103.26 ![X233]: 102.61/103.26 (X228( 102.61/103.26 X233) => 102.61/103.26 (X232 = 102.61/103.26 X233))) & 102.61/103.26 X228( 102.61/103.26 X232))) => 102.61/103.26 (( 102.61/103.26 ?[X234]: 102.61/103.26 (( 102.61/103.26 ![X235]: 102.61/103.26 (X229( 102.61/103.26 X235) => 102.61/103.26 (X234 = 102.61/103.26 X235))) & 102.61/103.26 X229( 102.61/103.26 X234))) => 102.61/103.26 (descr( 102.61/103.26 '#ll_0'( 102.61/103.26 X228)) = 102.61/103.26 descr( 102.61/103.26 '#ll_0'( 102.61/103.26 X229))))))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X236, 102.61/103.26 X237]: 102.61/103.26 (( 102.61/103.26 X236 = 102.61/103.26 X237) => 102.61/103.26 (![X238:( 102.61/103.26 $i > $o), 102.61/103.26 X239:( 102.61/103.26 $i > $o)]: 102.61/103.26 (( 102.61/103.26 ![X240]: 102.61/103.26 (in( 102.61/103.26 X240,X236) => 102.61/103.26 (![X241]: 102.61/103.26 (in( 102.61/103.26 X241,X237) => 102.61/103.26 (( 102.61/103.26 X240 = 102.61/103.26 X241) => 102.61/103.26 (X238( 102.61/103.26 X240) <=> 102.61/103.26 X239( 102.61/103.26 X241))))))) => 102.61/103.26 (dsetconstr( 102.61/103.26 X236, 102.61/103.26 '#ll_0'( 102.61/103.26 X238)) = 102.61/103.26 dsetconstr( 102.61/103.26 X237, 102.61/103.26 '#ll_0'( 102.61/103.26 X239))))))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X242, 102.61/103.26 X243]: 102.61/103.26 (( 102.61/103.26 ![X244]: 102.61/103.26 (in( 102.61/103.26 X244,X242) => 102.61/103.26 in( 102.61/103.26 X244,X243))) => 102.61/103.26 subset( 102.61/103.26 X242,X243))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X245, 102.61/103.26 X246]: 102.61/103.26 (( 102.61/103.26 X245 = 102.61/103.26 X246) => 102.61/103.26 subset( 102.61/103.26 X246,X245))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X247, 102.61/103.26 X248]: 102.61/103.26 (( 102.61/103.26 X247 = 102.61/103.26 X248) => 102.61/103.26 subset( 102.61/103.26 X247,X248))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X249, 102.61/103.26 X250]: 102.61/103.26 (( 102.61/103.26 ![X251]: 102.61/103.26 (in( 102.61/103.26 X251,X249) => 102.61/103.26 in( 102.61/103.26 X251,X250))) => 102.61/103.26 subset( 102.61/103.26 X249,X250))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X252]: 102.61/103.26 subset( 102.61/103.26 emptyset, 102.61/103.26 X252)) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X253, 102.61/103.26 X254,X255]: 102.61/103.26 (subset( 102.61/103.26 X253,X254) => 102.61/103.26 (in( 102.61/103.26 X255,X253) => 102.61/103.26 in( 102.61/103.26 X255,X254)))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X256, 102.61/103.26 X257,X258]: 102.61/103.26 (subset( 102.61/103.26 X256,X257) => 102.61/103.26 (( 102.61/103.26 ~ 102.61/103.26 in( 102.61/103.26 X258,X257)) => 102.61/103.26 (~ 102.61/103.26 in( 102.61/103.26 X258,X256))))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X259, 102.61/103.26 X260,X261]: 102.61/103.26 (in( 102.61/103.26 X261,X259) => 102.61/103.26 (( 102.61/103.26 ~ 102.61/103.26 in( 102.61/103.26 X261,X260)) => 102.61/103.26 (~ 102.61/103.26 subset( 102.61/103.26 X259,X260))))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X262, 102.61/103.26 X263]: 102.61/103.26 (( 102.61/103.26 ~ 102.61/103.26 subset( 102.61/103.26 X262,X263)) => 102.61/103.26 (X262 != 102.61/103.26 X263))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X264, 102.61/103.26 X265,X266]: 102.61/103.26 (in( 102.61/103.26 X266,X264) => 102.61/103.26 (( 102.61/103.26 ~ 102.61/103.26 in( 102.61/103.26 X266,X265)) => 102.61/103.26 (X264 != 102.61/103.26 X265)))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X267]: 102.61/103.26 subset( 102.61/103.26 X267,X267)) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X268, 102.61/103.26 X269,X270]: 102.61/103.26 (subset( 102.61/103.26 X268,X269) => 102.61/103.26 (subset( 102.61/103.26 X269,X270) => 102.61/103.26 subset( 102.61/103.26 X268,X270)))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X271, 102.61/103.26 X272]: 102.61/103.26 subset( 102.61/103.26 X272, 102.61/103.26 setadjoin( 102.61/103.26 X271,X272))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X273, 102.61/103.26 X274,X275]: 102.61/103.26 (subset( 102.61/103.26 X273,X275) => 102.61/103.26 subset( 102.61/103.26 X273, 102.61/103.26 setadjoin( 102.61/103.26 X274,X275)))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X276, 102.61/103.26 X277]: 102.61/103.26 (subset( 102.61/103.26 X276,X277) => 102.61/103.26 in( 102.61/103.26 X276, 102.61/103.26 powerset( 102.61/103.26 X277)))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X278, 102.61/103.26 X279]: 102.61/103.26 (subset( 102.61/103.26 X278,X279) => 102.61/103.26 (subset( 102.61/103.26 X279,X278) => 102.61/103.26 (X278 = 102.61/103.26 X279)))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X280]: 102.61/103.26 (subset( 102.61/103.26 X280, 102.61/103.26 emptyset) => 102.61/103.26 (X280 = 102.61/103.26 emptyset))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X281, 102.61/103.26 X282]: 102.61/103.26 (subset( 102.61/103.26 X282,X281) => 102.61/103.26 in( 102.61/103.26 X282, 102.61/103.26 powerset( 102.61/103.26 X281)))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X283, 102.61/103.26 X284]: 102.61/103.26 (in( 102.61/103.26 X284, 102.61/103.26 powerset( 102.61/103.26 X283)) => 102.61/103.26 subset( 102.61/103.26 X284,X283))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X285]: 102.61/103.26 in( 102.61/103.26 X285, 102.61/103.26 powerset( 102.61/103.26 X285))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X286, 102.61/103.26 X287]: 102.61/103.26 (subset( 102.61/103.26 X286,X287) => 102.61/103.26 subset( 102.61/103.26 powerset( 102.61/103.26 X286), 102.61/103.26 powerset( 102.61/103.26 X287)))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X288, 102.61/103.26 X289:( 102.61/103.26 $i > $o)]: 102.61/103.26 in( 102.61/103.26 dsetconstr( 102.61/103.26 X288, 102.61/103.26 '#ll_0'( 102.61/103.26 X289)), 102.61/103.26 powerset( 102.61/103.26 X288))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X290, 102.61/103.26 X291:( 102.61/103.26 $i > $o)]: 102.61/103.26 subset( 102.61/103.26 dsetconstr( 102.61/103.26 X290, 102.61/103.26 '#ll_0'( 102.61/103.26 X291)), 102.61/103.26 X290)) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X292, 102.61/103.26 X293,X294]: 102.61/103.26 (in( 102.61/103.26 X294,X292) => 102.61/103.26 in( 102.61/103.26 X294, 102.61/103.26 binunion( 102.61/103.26 X292,X293)))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X295, 102.61/103.26 X296]: 102.61/103.26 in( 102.61/103.26 X296, 102.61/103.26 setadjoin( 102.61/103.26 X295, 102.61/103.26 setadjoin( 102.61/103.26 X296, 102.61/103.26 emptyset)))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X297, 102.61/103.26 X298,X299]: 102.61/103.26 (in( 102.61/103.26 X299,X298) => 102.61/103.26 in( 102.61/103.26 X299, 102.61/103.26 binunion( 102.61/103.26 X297,X298)))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X300, 102.61/103.26 X301, 102.61/103.26 X302, 102.61/103.26 X303:$o]: 102.61/103.26 (in( 102.61/103.26 X302, 102.61/103.26 binunion( 102.61/103.26 X300,X301)) => 102.61/103.26 (( 102.61/103.26 in( 102.61/103.26 X302,X300) => 102.61/103.26 X303) => 102.61/103.26 (( 102.61/103.26 in( 102.61/103.26 X302,X301) => 102.61/103.26 X303) => 102.61/103.26 X303)))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X304, 102.61/103.26 X305,X306]: 102.61/103.26 (in( 102.61/103.26 X306, 102.61/103.26 binunion( 102.61/103.26 X304,X305)) => 102.61/103.26 (in( 102.61/103.26 X306,X305) | 102.61/103.26 in( 102.61/103.26 X306,X304)))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X307, 102.61/103.26 X308]: 102.61/103.26 subset( 102.61/103.26 X307, 102.61/103.26 binunion( 102.61/103.26 X307,X308))) => 102.61/103.26 ( 102.61/103.26 ![X309, 102.61/103.26 X310]: 102.61/103.26 subset( 102.61/103.26 X310, 102.61/103.26 binunion( 102.61/103.26 X309,X310)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 102.61/103.26 tff(zf_stmt_14, negated_conjecture, 102.61/103.26 (~ 102.61/103.26 ((![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))) => 102.61/103.26 ((![X5]: (~in(X5,emptyset))) => 102.61/103.26 ((![X6,X7,X8]: (in(X8,setadjoin(X6,X7)) <=> zip_tseitin0(X8,X7,X6))) => 102.61/103.26 ((![X9,X10]: 102.61/103.26 (in(X10,powerset(X9)) <=> (![X11]: zip_tseitin1(X11,X10,X9)))) => 102.61/103.26 ((![X12,X13]: 102.61/103.26 (in(X13,setunion(X12)) <=> (?[X14]: zip_tseitin2(X14,X13,X12)))) => 102.61/103.26 (in(emptyset,omega) => 102.61/103.26 ((![X15]: (in(X15,omega) => in(setadjoin(X15,X15),omega))) => 102.61/103.26 ((![X16]: 102.61/103.26 (((![X17]: 102.61/103.26 ((in(X17,X16) & in(X17,omega)) => 102.61/103.26 in(setadjoin(X17,X17),X16))) & 102.61/103.26 in(emptyset,X16)) => 102.61/103.26 (![X18]: (in(X18,omega) => in(X18,X16))))) => 102.61/103.26 ((![X19:(($i * $i) > $o),X20]: 102.61/103.26 ((![X21]: 102.61/103.26 (in(X21,X20) => 102.61/103.26 (?[X22]: 102.61/103.26 ((![X23]: (X19(X21,X23) => (X22 = X23))) & 102.61/103.26 X19(X21,X22))))) => 102.61/103.26 (?[X24]: 102.61/103.26 (![X25]: 102.61/103.26 (in(X25,X24) <=> 102.61/103.26 (?[X26]: zip_tseitin3(X26,X25,X20,X19))))))) => 102.61/103.26 ((![X27]: 102.61/103.26 ((?[X28]: in(X28,X27)) => 102.61/103.26 (?[X29]: 102.61/103.26 ((~(?[X30]: (in(X30,X27) & in(X30,X29)))) & in(X29,X27))))) => 102.61/103.26 ((![X31]: 102.61/103.26 (?[X32]: 102.61/103.26 ((![X33]: 102.61/103.26 (((?[X34]: in(X34,X33)) & 102.61/103.26 (![X35]: (in(X35,X33) => in(X35,X31)))) => 102.61/103.26 (?[X36,X37]: 102.61/103.26 ((![X38]: 102.61/103.26 (in(X38,X32) => 102.61/103.26 (in(X37,X38) | 102.61/103.26 (![X39]: (in(X39,X38) => in(X39,X36)))))) & 102.61/103.26 (~(?[X40]: (in(X40,X33) & in(X40,X36)))) & 102.61/103.26 in(X37,X33) & in(X36,X32))))) & 102.61/103.26 (![X41,X42]: 102.61/103.26 ((in(X42,X32) & in(X41,X32)) => 102.61/103.26 ((![X43]: (in(X43,X42) => in(X43,X41))) | 102.61/103.26 (![X44]: (in(X44,X41) => in(X44,X42)))))) & 102.61/103.26 (![X45,X46]: 102.61/103.26 ((in(X46,X31) & in(X45,X31)) => 102.61/103.26 ((![X47]: 102.61/103.26 (in(X47,X32) => (in(X45,X47) <=> in(X46,X47)))) => 102.61/103.26 (X45 = X46)))) & 102.61/103.26 (![X48]: 102.61/103.26 (in(X48,X32) => 102.61/103.26 (![X49]: (in(X49,X48) => in(X49,X31)))))))) => 102.61/103.26 ((![X50:($i > $o)]: 102.61/103.26 ((?[X51]: ((![X52]: (X50(X52) => (X51 = X52))) & X50(X51))) => 102.61/103.26 X50(descr('#ll_0'(X50))))) => 102.61/103.26 ((![X53,X54:($i > $o),X55]: 102.61/103.26 (in(X55,X53) => 102.61/103.26 (X54(X55) => in(X55,dsetconstr(X53,'#ll_0'(X54)))))) => 102.61/103.26 ((![X56,X57:($i > $o),X58]: 102.61/103.26 (in(X58,dsetconstr(X56,'#ll_0'(X57))) => in(X58,X56))) => 102.61/103.26 ((![X59,X60:($i > $o),X61]: 102.61/103.26 (in(X61,dsetconstr(X59,'#ll_0'(X60))) => X60(X61))) => 102.61/103.26 ((![X62:($i > $o)]: 102.61/103.26 ((?[X63]: 102.61/103.26 ((![X64]: (X62(X64) => (X63 = X64))) & X62(X63))) => 102.61/103.26 (?[X65]: 102.61/103.26 ((![X66]: (X62(X66) => (X65 = X66))) & X62(X65))))) => 102.61/103.26 ((![X67:$o,X68]: (in(X68,prop2set(X67)) => X67)) => 102.61/103.26 ((![X69]: (in(X69,emptyset) => (![X70:$o]: X70))) => 102.61/103.26 ((![X71]: (in(X71,emptyset) => $false)) => 102.61/103.26 ((![X72]: (~in(X72,emptyset))) => 102.61/103.26 ((![X73:($i > $o)]: 102.61/103.26 ((?[X74]: 102.61/103.26 ((![X75]: (X73(X75) => (X74 = X75))) & 102.61/103.26 X73(X74))) => 102.61/103.26 (?[X76]: X73(X76)))) => 102.61/103.26 ((![X77,X78]: 102.61/103.26 ((![X79]: (in(X79,X77) => in(X79,X78))) => 102.61/103.26 ((![X80]: (in(X80,X78) => in(X80,X77))) => 102.61/103.26 (X77 = X78)))) => 102.61/103.26 ((![X81]: 102.61/103.26 ((![X82]: (~in(X82,X81))) => (X81 = emptyset))) => 102.61/103.26 ((![X83]: 102.61/103.26 ((![X84]: (~in(X84,X83))) => (X83 = emptyset))) => 102.61/103.26 ((![X85,X86:($i > $o),X87]: 102.61/103.26 (in(X87,X85) => 102.61/103.26 (in(X87,dsetconstr(X85,'#ll_0'(X86))) <=> 102.61/103.26 X86(X87)))) => 102.61/103.26 ((![X88]: 102.61/103.26 ((X88 != emptyset) => (?[X89]: in(X89,X88)))) => 102.61/103.26 ((![X90,X91:($i > $o),X92]: 102.61/103.26 (in(X92,X90) => 102.61/103.26 (X91(X92) => 102.61/103.26 (dsetconstr(X90,'#ll_0'(X91)) != emptyset)))) => 102.61/103.26 ((![X93]: 102.61/103.26 ((?[X94]: in(X94,X93)) => 102.61/103.26 (X93 != emptyset))) => 102.61/103.26 ((![X95,X96]: in(X95,setadjoin(X95,X96))) => 102.61/103.26 (in(emptyset,setadjoin(emptyset,emptyset)) => 102.61/103.26 ((![X97,X98,X99]: 102.61/103.26 (in(X99,X98) => 102.61/103.26 in(X99,setadjoin(X97,X98)))) => 102.61/103.26 ((![X100,X101,X102]: 102.61/103.26 (in(X102,setadjoin(X100,X101)) => 102.61/103.26 (![X103:$o]: 102.61/103.26 (((X102 = X100) => X103) => 102.61/103.26 ((in(X102,X101) => X103) => X103))))) => 102.61/103.26 ((![X104,X105,X106]: 102.61/103.26 (in(X106,setadjoin(X104,X105)) => 102.61/103.26 (in(X106,X105) | (X106 = X104)))) => 102.61/103.26 ((![X107]: 102.61/103.26 (dsetconstr(X107,'#ll_1') = X107)) => 102.61/103.26 ((![X108,X109]: 102.61/103.26 ((![X110]: 102.61/103.26 (in(X110,X109) => in(X110,X108))) => 102.61/103.26 in(X109,powerset(X108)))) => 102.61/103.26 ((![X111]: in(emptyset,powerset(X111))) => 102.61/103.26 ((![X112]: 102.61/103.26 in(emptyset,powerset(X112))) => 102.61/103.26 ((![X113,X114,X115]: 102.61/103.26 (in(X114,powerset(X113)) => 102.61/103.26 (in(X115,X114) => in(X115,X113)))) => 102.61/103.26 ((![X116,X117,X118]: 102.61/103.26 (in(X117,X118) => 102.61/103.26 (in(X118,X116) => 102.61/103.26 in(X117,setunion(X116))))) => 102.61/103.26 ((![X119,X120]: 102.61/103.26 (in(X120,setunion(X119)) => 102.61/103.26 (![X121:$o]: 102.61/103.26 ((![X122]: 102.61/103.26 (in(X120,X122) => 102.61/103.26 (in(X122,X119) => 102.61/103.26 X121))) => 102.61/103.26 X121)))) => 102.61/103.26 ((![X123,X124]: 102.61/103.26 (in(X124,X123) => 102.61/103.26 in(X124, 102.61/103.26 powerset(setunion(X123))))) => 102.61/103.26 ((![X125:($i > $o)]: 102.61/103.26 ((?[X126]: 102.61/103.26 ((![X127]: 102.61/103.26 (X125(X127) => 102.61/103.26 (X126 = X127))) & 102.61/103.26 X125(X126))) => 102.61/103.26 (?[X128]: 102.61/103.26 (![X129]: 102.61/103.26 (X125(X129) <=> 102.61/103.26 (X129 = X128)))))) => 102.61/103.26 ((![X130]: 102.61/103.26 ((X130 != emptyset) => 102.61/103.26 (?[X131]: in(X131,X130)))) => 102.61/103.26 ((![X132,X133]: 102.61/103.26 (in(X132, 102.61/103.26 setadjoin(X133, 102.61/103.26 emptyset)) => 102.61/103.26 (X132 = X133))) => 102.61/103.26 ((![X134,X135]: 102.61/103.26 ((X134 != X135) => 102.61/103.26 (~ 102.61/103.26 in(X135, 102.61/103.26 setadjoin(X134, 102.61/103.26 emptyset))))) => 102.61/103.26 ((![X136,X137]: 102.61/103.26 ((X136 = X137) => 102.61/103.26 in(X136, 102.61/103.26 setadjoin(X137, 102.61/103.26 emptyset)))) => 102.61/103.26 ((![X138,X139]: 102.61/103.26 (in(X138, 102.61/103.26 setadjoin(X139, 102.61/103.26 emptyset)) => 102.61/103.26 in(X139, 102.61/103.26 setadjoin(X138, 102.61/103.26 emptyset)))) => 102.61/103.26 ((![X140,X141,X142]: 102.61/103.26 (in(X142, 102.61/103.26 setadjoin( 102.61/103.26 X140, 102.61/103.26 setadjoin( 102.61/103.26 X141,emptyset))) => 102.61/103.26 ((X142 = X141) | 102.61/103.26 (X142 = X140)))) => 102.61/103.26 ((![X143,X144]: 102.61/103.26 in(X143, 102.61/103.26 setadjoin( 102.61/103.26 X143, 102.61/103.26 setadjoin( 102.61/103.26 X144,emptyset)))) => 102.61/103.26 ((![X145,X146]: 102.61/103.26 in(X146, 102.61/103.26 setadjoin( 102.61/103.26 X145, 102.61/103.26 setadjoin( 102.61/103.26 X146,emptyset)))) => 102.61/103.26 ((![X147,X148:($i > $o)]: 102.61/103.26 ((?[X149]: 102.61/103.26 (X148(X149) & 102.61/103.26 in(X149,X147))) => 102.61/103.26 ((dsetconstr( 102.61/103.26 X147, 102.61/103.26 '#ll_0'(X148)) = 102.61/103.26 emptyset) => 102.61/103.26 $false))) => 102.61/103.26 ((![X150:($i > $o), 102.61/103.26 X151]: 102.61/103.26 (in(X151,emptyset) => 102.61/103.26 X150(X151))) => 102.61/103.26 ((![X152, 102.61/103.26 X153:($i > $o)]: 102.61/103.26 ((~ 102.61/103.26 (![X154]: 102.61/103.26 (in( 102.61/103.26 X154,X152) => 102.61/103.26 X153(X154)))) => 102.61/103.26 (?[X155]: 102.61/103.26 ((~X153(X155)) & 102.61/103.26 in(X155,X152))))) => 102.61/103.26 ((![X156, 102.61/103.26 X157:($i > $o)]: 102.61/103.26 ((![X158]: 102.61/103.26 (in( 102.61/103.26 X158,X156) => 102.61/103.26 (~ 102.61/103.26 X157( 102.61/103.26 X158)))) => 102.61/103.26 (~ 102.61/103.26 (?[X159]: 102.61/103.26 (X157( 102.61/103.26 X159) & 102.61/103.26 in( 102.61/103.26 X159,X156)))))) => 102.61/103.26 ((![X160, 102.61/103.26 X161:($i > $o)]: 102.61/103.26 ((~ 102.61/103.26 (?[X162]: 102.61/103.26 ( 102.61/103.26 X161( 102.61/103.26 X162) & 102.61/103.26 in( 102.61/103.26 X162,X160)))) => 102.61/103.26 (![X163]: 102.61/103.26 (in( 102.61/103.26 X163,X160) => 102.61/103.26 (~ 102.61/103.26 X161( 102.61/103.26 X163)))))) => 102.61/103.26 ((![X164, 102.61/103.26 X165:( 102.61/103.26 $i > $o)]: 102.61/103.26 ((?[X166]: 102.61/103.26 (( 102.61/103.26 ~ 102.61/103.26 X165( 102.61/103.26 X166)) & 102.61/103.26 in( 102.61/103.26 X166,X164))) => 102.61/103.26 (~ 102.61/103.26 (![X167]: 102.61/103.26 (in( 102.61/103.26 X167,X164) => 102.61/103.26 X165( 102.61/103.26 X167)))))) => 102.61/103.26 ((![X168:$o]: 102.61/103.26 (X168 => 102.61/103.26 in(emptyset, 102.61/103.26 prop2set( 102.61/103.26 X168)))) => 102.61/103.26 ((![X169:$o]: 102.61/103.26 (X169 => 102.61/103.26 set2prop( 102.61/103.26 prop2set( 102.61/103.26 X169)))) => 102.61/103.26 ((![X170, 102.61/103.26 X171:( 102.61/103.26 $i > $o)]: 102.61/103.26 ((~ 102.61/103.26 ( 102.61/103.26 ?[X172]: 102.61/103.26 (X171( 102.61/103.26 X172) & 102.61/103.26 in( 102.61/103.26 X172,X170)))) => 102.61/103.26 (![X173]: 102.61/103.26 (in( 102.61/103.26 X173,X170) => 102.61/103.26 (~ 102.61/103.26 X171( 102.61/103.26 X173)))))) => 102.61/103.26 ((![X174, 102.61/103.26 X175:( 102.61/103.26 $i > $o)]: 102.61/103.26 (( 102.61/103.26 ~ 102.61/103.26 ( 102.61/103.26 ![X176]: 102.61/103.26 (in( 102.61/103.26 X176,X174) => 102.61/103.26 X175( 102.61/103.26 X176)))) => 102.61/103.26 ( 102.61/103.26 ?[X177]: 102.61/103.26 (( 102.61/103.26 ~ 102.61/103.26 X175( 102.61/103.26 X177)) & 102.61/103.26 in( 102.61/103.26 X177,X174))))) => 102.61/103.26 ((![X178:( 102.61/103.26 $i > $o)]: 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ?[X179]: 102.61/103.26 (( 102.61/103.26 ![X180]: 102.61/103.26 (X178( 102.61/103.26 X180) => 102.61/103.26 (X179 = 102.61/103.26 X180))) & 102.61/103.26 X178( 102.61/103.26 X179))) => 102.61/103.26 ( 102.61/103.26 ?[X181]: 102.61/103.26 (( 102.61/103.26 ![X182]: 102.61/103.26 (X178( 102.61/103.26 X182) => 102.61/103.26 (X181 = 102.61/103.26 X182))) & 102.61/103.26 X178( 102.61/103.26 X181))))) => 102.61/103.26 ((![X183:( 102.61/103.26 $i > $o)]: 102.61/103.26 (( 102.61/103.26 ?[X184]: 102.61/103.26 X183( 102.61/103.26 X184)) => 102.61/103.26 (( 102.61/103.26 ![X185, 102.61/103.26 X186]: 102.61/103.26 (X183( 102.61/103.26 X185) => 102.61/103.26 (X183( 102.61/103.26 X186) => 102.61/103.26 (X185 = 102.61/103.26 X186)))) => 102.61/103.26 (?[X187]: 102.61/103.26 (( 102.61/103.26 ![X188]: 102.61/103.26 (X183( 102.61/103.26 X188) => 102.61/103.26 (X187 = 102.61/103.26 X188))) & 102.61/103.26 X183( 102.61/103.26 X187)))))) => 102.61/103.26 ((![X189:( 102.61/103.26 $i > $o)]: 102.61/103.26 (( 102.61/103.26 ?[X190]: 102.61/103.26 (![X191]: 102.61/103.26 (X189( 102.61/103.26 X191) <=> 102.61/103.26 (X191 = 102.61/103.26 X190)))) => 102.61/103.26 (?[X192]: 102.61/103.26 (( 102.61/103.26 ![X193]: 102.61/103.26 (X189( 102.61/103.26 X193) => 102.61/103.26 (X192 = 102.61/103.26 X193))) & 102.61/103.26 X189( 102.61/103.26 X192))))) => 102.61/103.26 (( 102.61/103.26 ![X194, 102.61/103.26 X195]: 102.61/103.26 (( 102.61/103.26 X194 = 102.61/103.26 X195) => 102.61/103.26 (![X196, 102.61/103.26 X197]: 102.61/103.26 (( 102.61/103.26 X196 = 102.61/103.26 X197) => 102.61/103.26 (in( 102.61/103.26 X196,X194) => 102.61/103.26 in( 102.61/103.26 X197,X195)))))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X198, 102.61/103.26 X199]: 102.61/103.26 (( 102.61/103.26 X198 = 102.61/103.26 X199) => 102.61/103.26 (![X200, 102.61/103.26 X201]: 102.61/103.26 (( 102.61/103.26 X200 = 102.61/103.26 X201) => 102.61/103.26 (in( 102.61/103.26 X200,X198) <=> 102.61/103.26 in( 102.61/103.26 X201,X199)))))) => 102.61/103.26 ( 102.61/103.26 ( 102.61/103.26 ![X202:( 102.61/103.26 $i > $o)]: 102.61/103.26 (( 102.61/103.26 ?[X203]: 102.61/103.26 (( 102.61/103.26 ![X204]: 102.61/103.26 (X202( 102.61/103.26 X204) => 102.61/103.26 (X203 = 102.61/103.26 X204))) & 102.61/103.26 X202( 102.61/103.26 X203))) => 102.61/103.27 (![X205, 102.61/103.27 X206]: 102.61/103.27 (X202( 102.61/103.27 X205) => 102.61/103.27 (X202( 102.61/103.27 X206) => 102.61/103.27 (X205 = 102.61/103.27 X206)))))) => 102.61/103.27 ( 102.61/103.27 ( 102.61/103.27 ![X207:( 102.61/103.27 $i > $o), 102.61/103.27 X208:( 102.61/103.27 $i > $o)]: 102.61/103.27 (( 102.61/103.27 ![X209, 102.61/103.27 X210]: 102.61/103.27 (( 102.61/103.27 X209 = 102.61/103.27 X210) => 102.61/103.27 (X207( 102.61/103.27 X209) <=> 102.61/103.27 X208( 102.61/103.27 X210)))) => 102.61/103.27 (( 102.61/103.27 ?[X211]: 102.61/103.27 zip_tseitin5( 102.61/103.27 X211,X207)) <=> 102.61/103.27 (?[X213]: 102.61/103.27 zip_tseitin5( 102.61/103.27 X213,X208))))) => 102.61/103.27 ( 102.61/103.27 ( 102.61/103.27 emptyset = 102.61/103.27 emptyset) => 102.61/103.27 ( 102.61/103.27 ( 102.61/103.27 ![X215, 102.61/103.27 X216]: 102.61/103.27 (( 102.61/103.27 X215 = 102.61/103.27 X216) => 102.61/103.27 (![X217, 102.61/103.27 X218]: 102.61/103.27 (( 102.61/103.27 X217 = 102.61/103.27 X218) => 102.61/103.27 (setadjoin( 102.61/103.27 X215,X217) = 102.61/103.27 setadjoin( 102.61/103.27 X216,X218)))))) => 102.61/103.27 ( 102.61/103.27 ( 102.61/103.27 ![X219, 102.61/103.27 X220]: 102.61/103.27 (( 102.61/103.27 X219 = 102.61/103.27 X220) => 102.61/103.27 (powerset( 102.61/103.27 X219) = 102.61/103.27 powerset( 102.61/103.27 X220)))) => 102.61/103.27 ( 102.61/103.27 ( 102.61/103.27 ![X221, 102.61/103.27 X222]: 102.61/103.27 (( 102.61/103.27 X221 = 102.61/103.27 X222) => 102.61/103.27 (setunion( 102.61/103.27 X221) = 102.61/103.27 setunion( 102.61/103.27 X222)))) => 102.61/103.27 ( 102.61/103.27 ( 102.61/103.27 omega = 102.61/103.27 omega) => 102.61/103.27 ( 102.61/103.27 ( 102.61/103.27 ![X223:( 102.61/103.27 $i > $o)]: 102.61/103.27 (( 102.61/103.27 ?[X224]: 102.61/103.27 (( 102.61/103.27 ![X225]: 102.61/103.27 (X223( 102.61/103.27 X225) => 102.61/103.27 (X224 = 102.61/103.27 X225))) & 102.61/103.27 X223( 102.61/103.27 X224))) => 102.61/103.27 (![X226, 102.61/103.27 X227]: 102.61/103.27 (X223( 102.61/103.27 X226) => 102.61/103.27 (X223( 102.61/103.27 X227) => 102.61/103.27 (X226 = 102.61/103.27 X227)))))) => 102.61/103.27 ( 102.61/103.27 ( 102.61/103.27 ![X228:( 102.61/103.27 $i > $o), 102.61/103.27 X229:( 102.61/103.27 $i > $o)]: 102.61/103.27 (( 102.61/103.27 ![X230, 102.61/103.27 X231]: 102.61/103.27 (( 102.61/103.27 X230 = 102.61/103.27 X231) => 102.61/103.27 (X228( 102.61/103.27 X230) <=> 102.61/103.27 X229( 102.61/103.27 X231)))) => 102.61/103.27 (( 102.61/103.27 ?[X232]: 102.61/103.27 (( 102.61/103.27 ![X233]: 102.61/103.27 (X228( 102.61/103.27 X233) => 102.61/103.27 (X232 = 102.61/103.27 X233))) & 102.61/103.27 X228( 102.61/103.27 X232))) => 102.61/103.27 (( 102.61/103.27 ?[X234]: 102.61/103.27 (( 102.61/103.27 ![X235]: 102.61/103.27 (X229( 102.61/103.27 X235) => 102.61/103.27 (X234 = 102.61/103.27 X235))) & 102.61/103.27 X229( 102.61/103.27 X234))) => 102.61/103.27 (descr( 102.61/103.27 '#ll_0'( 102.61/103.27 X228)) = 102.61/103.27 descr( 102.61/103.27 '#ll_0'( 102.61/103.27 X229))))))) => 102.61/103.27 ( 102.61/103.27 ( 102.61/103.27 ![X236, 102.61/103.27 X237]: 102.61/103.27 (( 102.61/103.27 X236 = 102.61/103.27 X237) => 102.61/103.27 (![X238:( 102.61/103.27 $i > $o), 102.61/103.27 X239:( 102.61/103.27 $i > $o)]: 102.61/103.27 (( 102.61/103.27 ![X240]: 102.61/103.27 (in( 102.61/103.27 X240,X236) => 102.61/103.27 (![X241]: 102.61/103.27 (in( 102.61/103.27 X241,X237) => 102.61/103.27 (( 102.61/103.27 X240 = 102.61/103.27 X241) => 102.61/103.27 (X238( 102.61/103.27 X240) <=> 102.61/103.27 X239( 102.61/103.27 X241))))))) => 102.61/103.27 (dsetconstr( 102.61/103.27 X236, 102.61/103.27 '#ll_0'( 102.61/103.27 X238)) = 102.61/103.27 dsetconstr( 102.61/103.27 X237, 102.61/103.27 '#ll_0'( 102.61/103.27 X239))))))) => 102.61/103.27 ( 102.61/103.27 ( 102.61/103.27 ![X242, 102.61/103.27 X243]: 102.61/103.27 (( 102.61/103.27 ![X244]: 102.61/103.27 (in( 102.61/103.27 X244,X242) => 102.61/103.27 in( 102.61/103.27 X244,X243))) => 102.61/103.27 subset( 102.61/103.27 X242,X243))) => 102.61/103.27 ( 102.61/103.27 ( 102.61/103.27 ![X245, 102.61/103.27 X246]: 102.61/103.27 (( 102.61/103.27 X245 = 102.61/103.27 X246) => 102.61/103.27 subset( 102.61/103.27 X246,X245))) => 102.61/103.27 ( 102.61/103.27 ( 102.61/103.27 ![X247, 102.61/103.27 X248]: 102.61/103.27 (( 102.61/103.27 X247 = 102.61/103.27 X248) => 102.61/103.27 subset( 102.61/103.27 X247,X248))) => 102.61/103.27 ( 102.61/103.27 ( 102.61/103.27 ![X249, 102.61/103.27 X250]: 102.61/103.27 (( 102.61/103.27 ![X251]: 102.61/103.27 (in( 102.61/103.27 X251,X249) => 102.61/103.27 in( 102.61/103.27 X251,X250))) => 102.61/103.27 subset( 102.61/103.27 X249,X250))) => 102.61/103.27 ( 102.61/103.27 ( 102.61/103.27 ![X252]: 102.61/103.27 subset( 102.61/103.27 emptyset, 102.61/103.27 X252)) => 102.61/103.27 ( 102.61/103.27 ( 102.61/103.27 ![X253, 102.61/103.27 X254,X255]: 102.61/103.27 (subset( 102.61/103.27 X253,X254) => 102.61/103.27 (in( 102.61/103.27 X255,X253) => 102.61/103.27 in( 102.61/103.27 X255,X254)))) => 102.61/103.27 ( 102.61/103.27 ( 102.61/103.27 ![X256, 102.61/103.27 X257,X258]: 102.61/103.27 (subset( 102.61/103.27 X256,X257) => 102.61/103.27 (( 102.61/103.27 ~ 102.61/103.27 in( 102.61/103.27 X258,X257)) => 102.61/103.27 (~ 102.61/103.27 in( 102.61/103.27 X258,X256))))) => 102.61/103.27 ( 102.61/103.27 ( 102.61/103.27 ![X259, 102.61/103.27 X260,X261]: 102.61/103.27 (in( 102.61/103.27 X261,X259) => 102.61/103.27 (( 102.61/103.27 ~ 102.61/103.27 in( 102.61/103.27 X261,X260)) => 102.61/103.27 (~ 102.61/103.27 subset( 102.61/103.27 X259,X260))))) => 102.61/103.27 ( 102.61/103.27 ( 102.61/103.27 ![X262, 102.61/103.27 X263]: 102.61/103.27 (( 102.61/103.27 ~ 102.61/103.27 subset( 102.61/103.27 X262,X263)) => 102.61/103.27 (X262 != 102.61/103.27 X263))) => 102.61/103.27 ( 102.61/103.27 ( 102.61/103.27 ![X264, 102.61/103.27 X265,X266]: 102.61/103.27 (in( 102.61/103.27 X266,X264) => 102.61/103.27 (( 102.61/103.27 ~ 102.61/103.27 in( 102.61/103.27 X266,X265)) => 102.61/103.27 (X264 != 102.61/103.27 X265)))) => 102.61/103.27 ( 102.61/103.27 ( 102.61/103.27 ![X267]: 102.61/103.27 subset( 102.61/103.27 X267,X267)) => 102.61/103.27 ( 102.61/103.27 ( 102.61/103.27 ![X268, 102.61/103.27 X269,X270]: 102.61/103.27 (subset( 102.61/103.27 X268,X269) => 102.61/103.27 (subset( 102.61/103.27 X269,X270) => 102.61/103.27 subset( 102.61/103.27 X268,X270)))) => 102.61/103.27 ( 102.61/103.27 ( 102.61/103.27 ![X271, 102.61/103.27 X272]: 102.61/103.27 subset( 102.61/103.27 X272, 102.61/103.27 setadjoin( 102.61/103.27 X271,X272))) => 102.61/103.27 ( 102.61/103.27 ( 102.61/103.27 ![X273, 102.61/103.27 X274,X275]: 102.61/103.27 (subset( 102.61/103.27 X273,X275) => 102.61/103.27 subset( 102.61/103.27 X273, 102.61/103.27 setadjoin( 102.61/103.27 X274,X275)))) => 102.61/103.27 ( 102.61/103.27 ( 102.61/103.27 ![X276, 102.61/103.27 X277]: 102.61/103.27 (subset( 102.61/103.27 X276,X277) => 102.61/103.27 in( 102.61/103.27 X276, 102.61/103.27 powerset( 102.61/103.27 X277)))) => 102.61/103.27 ( 102.61/103.27 ( 102.61/103.27 ![X278, 102.61/103.27 X279]: 102.61/103.27 (subset( 102.61/103.27 X278,X279) => 102.61/103.27 (subset( 102.61/103.27 X279,X278) => 102.61/103.27 (X278 = 102.61/103.27 X279)))) => 102.61/103.27 ( 102.61/103.27 ( 102.61/103.27 ![X280]: 102.61/103.27 (subset( 102.61/103.27 X280, 102.61/103.27 emptyset) => 102.61/103.27 (X280 = 102.61/103.27 emptyset))) => 102.61/103.27 ( 102.61/103.27 ( 102.61/103.27 ![X281, 102.61/103.27 X282]: 102.61/103.27 (subset( 102.61/103.27 X282,X281) => 102.61/103.27 in( 102.61/103.27 X282, 102.61/103.27 powerset( 102.61/103.27 X281)))) => 102.61/103.27 ( 102.61/103.27 ( 102.61/103.27 ![X283, 102.61/103.27 X284]: 102.61/103.27 (in( 102.61/103.27 X284, 102.61/103.27 powerset( 102.61/103.27 X283)) => 102.61/103.27 subset( 102.61/103.27 X284,X283))) => 102.61/103.27 ( 102.61/103.27 ( 102.61/103.27 ![X285]: 102.61/103.27 in( 102.61/103.27 X285, 102.61/103.27 powerset( 102.61/103.27 X285))) => 102.61/103.27 ( 102.61/103.27 ( 102.61/103.27 ![X286, 102.61/103.27 X287]: 102.61/103.27 (subset( 102.61/103.27 X286,X287) => 102.61/103.27 subset( 102.61/103.27 powerset( 102.61/103.27 X286), 102.61/103.27 powerset( 102.61/103.27 X287)))) => 102.61/103.27 ( 102.61/103.27 ( 102.61/103.27 ![X288, 102.61/103.27 X289:( 102.61/103.27 $i > $o)]: 102.61/103.27 in( 102.61/103.27 dsetconstr( 102.61/103.27 X288, 102.61/103.27 '#ll_0'( 102.61/103.27 X289)), 102.61/103.27 powerset( 102.61/103.27 X288))) => 102.61/103.27 ( 102.61/103.27 ( 102.61/103.27 ![X290, 102.61/103.27 X291:( 102.61/103.27 $i > $o)]: 102.61/103.27 subset( 102.61/103.27 dsetconstr( 102.61/103.27 X290, 102.61/103.27 '#ll_0'( 102.61/103.27 X291)), 102.61/103.27 X290)) => 102.61/103.27 ( 102.61/103.27 ( 102.61/103.27 ![X292, 102.61/103.27 X293,X294]: 102.61/103.27 (in( 102.61/103.27 X294,X292) => 102.61/103.27 in( 102.61/103.27 X294, 102.61/103.27 binunion( 102.61/103.27 X292,X293)))) => 102.61/103.27 ( 102.61/103.27 ( 102.61/103.27 ![X295, 102.61/103.27 X296]: 102.61/103.27 in( 102.61/103.27 X296, 102.61/103.27 setadjoin( 102.61/103.27 X295, 102.61/103.27 setadjoin( 102.61/103.27 X296, 102.61/103.27 emptyset)))) => 102.61/103.27 ( 102.61/103.27 ( 102.61/103.27 ![X297, 102.61/103.27 X298,X299]: 102.61/103.27 (in( 102.61/103.27 X299,X298) => 102.61/103.27 in( 102.61/103.27 X299, 102.61/103.27 binunion( 102.61/103.27 X297,X298)))) => 102.61/103.27 ( 102.61/103.27 ( 102.61/103.27 ![X300, 102.61/103.27 X301, 102.61/103.27 X302, 102.61/103.27 X303:$o]: 102.61/103.27 (in( 102.61/103.27 X302, 102.61/103.27 binunion( 102.61/103.27 X300,X301)) => 102.61/103.27 (( 102.61/103.27 in( 102.61/103.27 X302,X300) => 102.61/103.27 X303) => 102.61/103.27 (( 102.61/103.27 in( 102.61/103.27 X302,X301) => 102.61/103.27 X303) => 102.61/103.27 X303)))) => 102.61/103.27 ( 102.61/103.27 ( 102.61/103.27 ![X304, 102.61/103.27 X305,X306]: 102.61/103.27 (in( 102.61/103.27 X306, 102.61/103.27 binunion( 102.61/103.27 X304,X305)) => 102.61/103.27 (in( 102.61/103.27 X306,X305) | 102.61/103.27 in( 102.61/103.27 X306,X304)))) => 102.61/103.27 ( 102.61/103.27 ( 102.61/103.27 ![X307, 102.61/103.27 X308]: 102.61/103.27 subset( 102.61/103.27 X307, 102.61/103.27 binunion( 102.61/103.27 X307,X308))) => 102.61/103.27 ( 102.61/103.27 ![X309, 102.61/103.27 X310]: 102.61/103.27 subset( 102.61/103.27 X310, 102.61/103.27 binunion( 102.61/103.27 X309,X310))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 102.61/103.27 tff('106', plain, ~ subset(sk_X310_, binunion(sk_X309_, sk_X310_)), 102.61/103.27 inference('cnf', [status(esa)], [zf_stmt_14])). 102.61/103.27 tff('107', plain, 102.61/103.27 ![X425, X426]: (subset(X425, X426) | in(sk_X251_(X426, X425), X425)), 102.61/103.27 inference('cnf', [status(esa)], [zf_stmt_14])). 102.61/103.27 tff('108', plain, 102.61/103.27 ![X452, X453, X454]: (in(X452, binunion(X453, X454)) | ~ in(X452, X454)), 102.61/103.27 inference('cnf', [status(esa)], [zf_stmt_14])). 102.61/103.27 tff('109', plain, 102.61/103.27 ![X425, X426]: (subset(X425, X426) | ~ in(sk_X251_(X426, X425), X426)), 102.61/103.27 inference('cnf', [status(esa)], [zf_stmt_14])). 102.61/103.27 tff('110', plain, $false, 102.61/103.27 inference('eprover', [status(thm)], ['106', '107', '108', '109'])). 102.61/103.27 102.61/103.27 % SZS output end Refutation 102.61/103.27 % Zipperpin 1.5 exiting 102.61/103.27 EOF