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.Iu8Avb6XvC 0.13/0.34 % Computer : n018.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 180 0.13/0.34 % DateTime : Thu Aug 29 14:34:51 EDT 2019 0.13/0.34 % CPUTime : 103.57/104.07 % Running portfolio for 180 s 103.57/104.07 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 103.57/104.07 % TempDir : /export/starexec/sandbox/tmp/tmp.Iu8Avb6XvC 103.57/104.07 % Recognized as monomorphic HO. 103.57/104.07 % Running /export/starexec/sandbox/solver/bin/competitive.sh for 18 103.57/104.07 % Running /export/starexec/sandbox/solver/bin/competitive.2.sh for 13 103.57/104.07 % Running /export/starexec/sandbox/solver/bin/competitive.3.sh for 3 103.57/104.07 % Running /export/starexec/sandbox/solver/bin/pragmatic.rudimentary.sh for 28 103.57/104.07 % Running /export/starexec/sandbox/solver/bin/pragmatic.rudimentary.1.sh for 12 103.57/104.07 % Running /export/starexec/sandbox/solver/bin/pragmatic.rudimentary.2.sh for 7 103.57/104.07 % Running /export/starexec/sandbox/solver/bin/pragmatic.shallow.sh for 3 103.57/104.07 % Running /export/starexec/sandbox/solver/bin/pragmatic.shallow.1.sh for 15 103.57/104.07 % Running /export/starexec/sandbox/solver/bin/pragmatic.shallow.2.sh for 12 103.57/104.07 % Running /export/starexec/sandbox/solver/bin/pragmatic.ll.e.sh for 19 103.57/104.07 % Solved by: pragmatic.ll.e.sh 103.57/104.07 % Running : timeout 16 /export/starexec/sandbox/solver/bin/eprover-ho /export/starexec/sandbox/tmp/tmp.Iu8Avb6XvC/e_input8be970 --cpu-limit=14 --auto-schedule -s -p. 103.57/104.07 % done 281 iterations in 4.759s 103.57/104.07 % hashcons stats for terms: size 4096, num 17451, sum length 34207, buckets: small 0, median 7, big 22 103.57/104.07 % proof state stats: {active 125, passive 3335, simpl 0} 103.57/104.07 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 103.57/104.07 % SZS output start Refutation 103.57/104.07 tff(binunionE, axiom, binunionE <=> 103.57/104.07 (![A,B,Xx]: (in(Xx,binunion(A,B)) => (in(Xx,B) | in(Xx,A))))). 103.57/104.07 tff('0', plain, 103.57/104.07 binunionE = 103.57/104.07 (![X2,X3,X4]: (in(X4,binunion(X2,X3)) => (in(X4,X3) | in(X4,X2)))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(binunionEcases, axiom, binunionEcases <=> 103.57/104.07 (![A,B,Xx,Xphi:$o]: 103.57/104.07 (in(Xx,binunion(A,B)) => 103.57/104.07 ((in(Xx,A) => Xphi) => ((in(Xx,B) => Xphi) => Xphi))))). 103.57/104.07 tff('1', plain, 103.57/104.07 binunionEcases = 103.57/104.07 (![X2,X3,X4,X5:$o]: 103.57/104.07 (in(X4,binunion(X2,X3)) => 103.57/104.07 ((in(X4,X2) => X5) => ((in(X4,X3) => X5) => X5)))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(binunionIR, axiom, binunionIR <=> 103.57/104.07 (![A,B,Xx]: (in(Xx,B) => in(Xx,binunion(A,B))))). 103.57/104.07 tff('2', plain, 103.57/104.07 binunionIR = (![X2,X3,X4]: (in(X4,X3) => in(X4,binunion(X2,X3)))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(upairset2IR, axiom, upairset2IR <=> 103.57/104.07 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 103.57/104.07 tff('3', plain, 103.57/104.07 upairset2IR = (![X2,X3]: in(X3,setadjoin(X2,setadjoin(X3,emptyset)))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(binunionIL, axiom, binunionIL <=> 103.57/104.07 (![A,B,Xx]: (in(Xx,A) => in(Xx,binunion(A,B))))). 103.57/104.07 tff('4', plain, 103.57/104.07 binunionIL = (![X2,X3,X4]: (in(X4,X2) => in(X4,binunion(X2,X3)))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(sepSubset, axiom, sepSubset <=> 103.57/104.07 (![A,Xphi:($i > $o)]: subset(dsetconstr(A,^[Xx]: Xphi(Xx)),A))). 103.57/104.07 tff('5', plain, 103.57/104.07 sepSubset = 103.57/104.07 (![X2,X3:($i > $o)]: subset(dsetconstr(X2,^[V_1]: X3(V_1)),X2)), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(sepInPowerset, axiom, sepInPowerset <=> 103.57/104.07 (![A,Xphi:($i > $o)]: in(dsetconstr(A,^[Xx]: Xphi(Xx)),powerset(A)))). 103.57/104.07 tff('6', plain, 103.57/104.07 sepInPowerset = 103.57/104.07 (![X2,X3:($i > $o)]: in(dsetconstr(X2,^[V_1]: X3(V_1)),powerset(X2))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(powersetsubset, axiom, powersetsubset <=> 103.57/104.07 (![A,B]: (subset(A,B) => subset(powerset(A),powerset(B))))). 103.57/104.07 tff('7', plain, 103.57/104.07 powersetsubset = 103.57/104.07 (![X2,X3]: (subset(X2,X3) => subset(powerset(X2),powerset(X3)))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(inPowerset, axiom, inPowerset <=> (![A]: in(A,powerset(A)))). 103.57/104.07 tff('8', plain, inPowerset = (![X2]: in(X2,powerset(X2))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(powersetE1, axiom, powersetE1 <=> 103.57/104.07 (![A,B]: (in(B,powerset(A)) => subset(B,A)))). 103.57/104.07 tff('9', plain, 103.57/104.07 powersetE1 = (![X2,X3]: (in(X3,powerset(X2)) => subset(X3,X2))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(powersetI1, axiom, powersetI1 <=> 103.57/104.07 (![A,B]: (subset(B,A) => in(B,powerset(A))))). 103.57/104.07 tff('10', plain, 103.57/104.07 powersetI1 = (![X2,X3]: (subset(X3,X2) => in(X3,powerset(X2)))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(subsetemptysetimpeq, axiom, subsetemptysetimpeq <=> 103.57/104.07 (![A]: (subset(A,emptyset) => (A = emptyset)))). 103.57/104.07 tff('11', plain, 103.57/104.07 subsetemptysetimpeq = (![X2]: (subset(X2,emptyset) => (X2 = emptyset))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(setextsub, axiom, setextsub <=> 103.57/104.07 (![A,B]: (subset(A,B) => (subset(B,A) => (A = B))))). 103.57/104.07 tff('12', plain, 103.57/104.07 setextsub = (![X2,X3]: (subset(X2,X3) => (subset(X3,X2) => (X2 = X3)))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(subset2powerset, axiom, subset2powerset <=> 103.57/104.07 (![A,B]: (subset(A,B) => in(A,powerset(B))))). 103.57/104.07 tff('13', plain, 103.57/104.07 subset2powerset = (![X2,X3]: (subset(X2,X3) => in(X2,powerset(X3)))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(setadjoinSub2, axiom, setadjoinSub2 <=> 103.57/104.07 (![A,Xx,B]: (subset(A,B) => subset(A,setadjoin(Xx,B))))). 103.57/104.07 tff('14', plain, 103.57/104.07 setadjoinSub2 = 103.57/104.07 (![X2,X3,X4]: (subset(X2,X4) => subset(X2,setadjoin(X3,X4)))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(setadjoinSub, axiom, setadjoinSub <=> 103.57/104.07 (![Xx,A]: subset(A,setadjoin(Xx,A)))). 103.57/104.07 tff('15', plain, setadjoinSub = (![X2,X3]: subset(X3,setadjoin(X2,X3))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(subsetTrans, axiom, subsetTrans <=> 103.57/104.07 (![A,B,C]: (subset(A,B) => (subset(B,C) => subset(A,C))))). 103.57/104.07 tff('16', plain, 103.57/104.07 subsetTrans = 103.57/104.07 (![X2,X3,X4]: (subset(X2,X3) => (subset(X3,X4) => subset(X2,X4)))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(subsetRefl, axiom, subsetRefl <=> (![A]: subset(A,A))). 103.57/104.07 tff('17', plain, subsetRefl = (![X2]: subset(X2,X2)), define([status(thm)])). 103.57/104.07 tff(notequalI2, axiom, notequalI2 <=> 103.57/104.07 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => (A != B))))). 103.57/104.07 tff('18', plain, 103.57/104.07 notequalI2 = (![X2,X3,X4]: (in(X4,X2) => ((~in(X4,X3)) => (X2 != X3)))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(notequalI1, axiom, notequalI1 <=> (![A,B]: ((~subset(A,B)) => (A != B)))). 103.57/104.07 tff('19', plain, notequalI1 = (![X2,X3]: ((~subset(X2,X3)) => (X2 != X3))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(notsubsetI, axiom, notsubsetI <=> 103.57/104.07 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => (~subset(A,B)))))). 103.57/104.07 tff('20', plain, 103.57/104.07 notsubsetI = 103.57/104.07 (![X2,X3,X4]: (in(X4,X2) => ((~in(X4,X3)) => (~subset(X2,X3))))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(subsetE2, axiom, subsetE2 <=> 103.57/104.07 (![A,B,Xx]: (subset(A,B) => ((~in(Xx,B)) => (~in(Xx,A)))))). 103.57/104.07 tff('21', plain, 103.57/104.07 subsetE2 = 103.57/104.07 (![X2,X3,X4]: (subset(X2,X3) => ((~in(X4,X3)) => (~in(X4,X2))))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(subsetE, axiom, subsetE <=> 103.57/104.07 (![A,B,Xx]: (subset(A,B) => (in(Xx,A) => in(Xx,B))))). 103.57/104.07 tff('22', plain, 103.57/104.07 subsetE = (![X2,X3,X4]: (subset(X2,X3) => (in(X4,X2) => in(X4,X3)))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(emptysetsubset, axiom, emptysetsubset <=> (![A]: subset(emptyset,A))). 103.57/104.07 tff('23', plain, emptysetsubset = (![X2]: subset(emptyset,X2)), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(subsetI2, axiom, subsetI2 <=> 103.57/104.07 (![A,B]: ((![Xx]: (in(Xx,A) => in(Xx,B))) => subset(A,B)))). 103.57/104.07 tff('24', plain, 103.57/104.07 subsetI2 = 103.57/104.07 (![X2,X3]: ((![X4]: (in(X4,X2) => in(X4,X3))) => subset(X2,X3))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(eqimpsubset1, axiom, eqimpsubset1 <=> (![A,B]: ((A = B) => subset(A,B)))). 103.57/104.07 tff('25', plain, eqimpsubset1 = (![X2,X3]: ((X2 = X3) => subset(X2,X3))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(eqimpsubset2, axiom, eqimpsubset2 <=> (![A,B]: ((A = B) => subset(B,A)))). 103.57/104.07 tff('26', plain, eqimpsubset2 = (![X2,X3]: ((X2 = X3) => subset(X3,X2))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(subsetI1, axiom, subsetI1 <=> 103.57/104.07 (![A,B]: ((![Xx]: (in(Xx,A) => in(Xx,B))) => subset(A,B)))). 103.57/104.07 tff('27', plain, 103.57/104.07 subsetI1 = 103.57/104.07 (![X2,X3]: ((![X4]: (in(X4,X2) => in(X4,X3))) => subset(X2,X3))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(dsetconstr__Cong, axiom, dsetconstr__Cong <=> 103.57/104.07 (![A,B]: 103.57/104.07 ((A = B) => 103.57/104.07 (![Xphi:($i > $o),Xpsi:($i > $o)]: 103.57/104.07 ((![Xx]: 103.57/104.07 (in(Xx,A) => 103.57/104.07 (![Xy]: (in(Xy,B) => ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy))))))) => 103.57/104.07 (dsetconstr(A,^[Xx]: Xphi(Xx)) = dsetconstr(B,^[Xx]: Xpsi(Xx)))))))). 103.57/104.07 tff('28', plain, 103.57/104.07 dsetconstr__Cong = 103.57/104.07 (![X2,X3]: 103.57/104.07 ((X2 = X3) => 103.57/104.07 (![X4:($i > $o),X5:($i > $o)]: 103.57/104.07 ((![X6]: 103.57/104.07 (in(X6,X2) => 103.57/104.07 (![X7]: (in(X7,X3) => ((X6 = X7) => (X4(X6) <=> X5(X7))))))) => 103.57/104.07 (dsetconstr(X2,^[V_1]: X4(V_1)) = dsetconstr(X3,^[V_2]: X5(V_2))))))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(descr__Cong, axiom, descr__Cong <=> 103.57/104.07 (![Xphi:($i > $o),Xpsi:($i > $o)]: 103.57/104.07 ((![Xx,Xy]: ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy)))) => 103.57/104.07 (exu(^[Xx]: Xphi(Xx)) => 103.57/104.07 (exu(^[Xx]: Xpsi(Xx)) => 103.57/104.07 (descr(^[Xx]: Xphi(Xx)) = descr(^[Xx]: Xpsi(Xx)))))))). 103.57/104.07 tff('29', plain, 103.57/104.07 descr__Cong = 103.57/104.07 (![X2:($i > $o),X3:($i > $o)]: 103.57/104.07 ((![X4,X5]: ((X4 = X5) => (X2(X4) <=> X3(X5)))) => 103.57/104.07 (exu(^[V_1]: X2(V_1)) => 103.57/104.07 (exu(^[V_2]: X3(V_2)) => 103.57/104.07 (descr(^[V_3]: X2(V_3)) = descr(^[V_4]: X3(V_4))))))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(exuEu, axiom, exuEu <=> 103.57/104.07 (![Xphi:($i > $o)]: 103.57/104.07 (exu(^[Xx]: Xphi(Xx)) => 103.57/104.07 (![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))). 103.57/104.07 tff('30', plain, 103.57/104.07 exuEu = 103.57/104.07 (![X2:($i > $o)]: 103.57/104.07 (exu(^[V_1]: X2(V_1)) => (![X3,X4]: (X2(X3) => (X2(X4) => (X3 = X4)))))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(omega__Cong, axiom, omega__Cong <=> (omega = omega)). 103.57/104.07 tff('31', plain, omega__Cong = (omega = omega), define([status(thm)])). 103.57/104.07 tff(setunion__Cong, axiom, setunion__Cong <=> 103.57/104.07 (![A,B]: ((A = B) => (setunion(A) = setunion(B))))). 103.57/104.07 tff('32', plain, 103.57/104.07 setunion__Cong = (![X2,X3]: ((X2 = X3) => (setunion(X2) = setunion(X3)))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(powerset__Cong, axiom, powerset__Cong <=> 103.57/104.07 (![A,B]: ((A = B) => (powerset(A) = powerset(B))))). 103.57/104.07 tff('33', plain, 103.57/104.07 powerset__Cong = (![X2,X3]: ((X2 = X3) => (powerset(X2) = powerset(X3)))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(setadjoin__Cong, axiom, setadjoin__Cong <=> 103.57/104.07 (![Xx,Xy]: 103.57/104.07 ((Xx = Xy) => 103.57/104.07 (![Xz,Xu]: ((Xz = Xu) => (setadjoin(Xx,Xz) = setadjoin(Xy,Xu))))))). 103.57/104.07 tff('34', plain, 103.57/104.07 setadjoin__Cong = 103.57/104.07 (![X2,X3]: 103.57/104.07 ((X2 = X3) => 103.57/104.07 (![X4,X5]: ((X4 = X5) => (setadjoin(X2,X4) = setadjoin(X3,X5)))))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(emptyset__Cong, axiom, emptyset__Cong <=> (emptyset = emptyset)). 103.57/104.07 tff('35', plain, emptyset__Cong = (emptyset = emptyset), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(exu__Cong, axiom, exu__Cong <=> 103.57/104.07 (![Xphi:($i > $o),Xpsi:($i > $o)]: 103.57/104.07 ((![Xx,Xy]: ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy)))) => 103.57/104.07 (exu(^[Xx]: Xphi(Xx)) <=> exu(^[Xx]: Xpsi(Xx)))))). 103.57/104.07 tff('36', plain, 103.57/104.07 exu__Cong = 103.57/104.07 (![X2:($i > $o),X3:($i > $o)]: 103.57/104.07 ((![X4,X5]: ((X4 = X5) => (X2(X4) <=> X3(X5)))) => 103.57/104.07 (exu(^[V_1]: X2(V_1)) <=> exu(^[V_2]: X3(V_2))))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(exuE3u, axiom, exuE3u <=> 103.57/104.07 (![Xphi:($i > $o)]: 103.57/104.07 (exu(^[Xx]: Xphi(Xx)) => 103.57/104.07 (![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))). 103.57/104.07 tff('37', plain, 103.57/104.07 exuE3u = 103.57/104.07 (![X2:($i > $o)]: 103.57/104.07 (exu(^[V_1]: X2(V_1)) => (![X3,X4]: (X2(X3) => (X2(X4) => (X3 = X4)))))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(in__Cong, axiom, in__Cong <=> 103.57/104.07 (![A,B]: ((A = B) => (![Xx,Xy]: ((Xx = Xy) => (in(Xx,A) <=> in(Xy,B))))))). 103.57/104.07 tff('38', plain, 103.57/104.07 in__Cong = 103.57/104.07 (![X2,X3]: 103.57/104.07 ((X2 = X3) => (![X4,X5]: ((X4 = X5) => (in(X4,X2) <=> in(X5,X3)))))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(inCongP, axiom, inCongP <=> 103.57/104.07 (![A,B]: ((A = B) => (![Xx,Xy]: ((Xx = Xy) => (in(Xx,A) => in(Xy,B))))))). 103.57/104.07 tff('39', plain, 103.57/104.07 inCongP = 103.57/104.07 (![X2,X3]: 103.57/104.07 ((X2 = X3) => (![X4,X5]: ((X4 = X5) => (in(X4,X2) => in(X5,X3)))))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(exuI2, axiom, exuI2 <=> 103.57/104.07 (![Xphi:($i > $o)]: 103.57/104.07 ((?[Xx]: (![Xy]: (Xphi(Xy) <=> (Xy = Xx)))) => exu(^[Xx]: Xphi(Xx))))). 103.57/104.07 tff('40', plain, 103.57/104.07 exuI2 = 103.57/104.07 (![X2:($i > $o)]: 103.57/104.07 ((?[X3]: (![X4]: (X2(X4) <=> (X4 = X3)))) => exu(^[V_1]: X2(V_1)))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(exuI3, axiom, exuI3 <=> 103.57/104.07 (![Xphi:($i > $o)]: 103.57/104.07 ((?[Xx]: Xphi(Xx)) => 103.57/104.07 ((![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy)))) => 103.57/104.07 exu(^[Xx]: Xphi(Xx)))))). 103.57/104.07 tff('41', plain, 103.57/104.07 exuI3 = 103.57/104.07 (![X2:($i > $o)]: 103.57/104.07 ((?[X3]: X2(X3)) => 103.57/104.07 ((![X4,X5]: (X2(X4) => (X2(X5) => (X4 = X5)))) => 103.57/104.07 exu(^[V_1]: X2(V_1))))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(exuI1, axiom, exuI1 <=> 103.57/104.07 (![Xphi:($i > $o)]: 103.57/104.07 ((?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx))) => 103.57/104.07 exu(^[Xx]: Xphi(Xx))))). 103.57/104.07 tff('42', plain, 103.57/104.07 exuI1 = 103.57/104.07 (![X2:($i > $o)]: 103.57/104.07 ((?[X3]: ((![X4]: (X2(X4) => (X3 = X4))) & X2(X3))) => 103.57/104.07 exu(^[V_1]: X2(V_1)))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(notdallE, axiom, notdallE <=> 103.57/104.07 (![A,Xphi:($i > $o)]: 103.57/104.07 ((~(![Xx]: (in(Xx,A) => Xphi(Xx)))) => (?[Xx]: ((~Xphi(Xx)) & in(Xx,A)))))). 103.57/104.07 tff('43', plain, 103.57/104.07 notdallE = 103.57/104.07 (![X2,X3:($i > $o)]: 103.57/104.07 ((~(![X4]: (in(X4,X2) => X3(X4)))) => (?[X5]: ((~X3(X5)) & in(X5,X2))))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(notdexE, axiom, notdexE <=> 103.57/104.07 (![A,Xphi:($i > $o)]: 103.57/104.07 ((~(?[Xx]: (Xphi(Xx) & in(Xx,A)))) => (![Xx]: (in(Xx,A) => (~Xphi(Xx))))))). 103.57/104.07 tff('44', plain, 103.57/104.07 notdexE = 103.57/104.07 (![X2,X3:($i > $o)]: 103.57/104.07 ((~(?[X4]: (X3(X4) & in(X4,X2)))) => (![X5]: (in(X5,X2) => (~X3(X5)))))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(prop2set2propI, axiom, prop2set2propI <=> 103.57/104.07 (![Xphi:$o]: (Xphi => set2prop(prop2set(Xphi))))). 103.57/104.07 tff('45', plain, prop2set2propI = (![X2:$o]: (X2 => set2prop(prop2set(X2)))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(prop2setI, axiom, prop2setI <=> 103.57/104.07 (![Xphi:$o]: (Xphi => in(emptyset,prop2set(Xphi))))). 103.57/104.07 tff('46', plain, prop2setI = (![X2:$o]: (X2 => in(emptyset,prop2set(X2)))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(quantDeMorgan4, axiom, quantDeMorgan4 <=> 103.57/104.07 (![A,Xphi:($i > $o)]: 103.57/104.07 ((?[Xx]: ((~Xphi(Xx)) & in(Xx,A))) => (~(![Xx]: (in(Xx,A) => Xphi(Xx))))))). 103.57/104.07 tff('47', plain, 103.57/104.07 quantDeMorgan4 = 103.57/104.07 (![X2,X3:($i > $o)]: 103.57/104.07 ((?[X4]: ((~X3(X4)) & in(X4,X2))) => (~(![X5]: (in(X5,X2) => X3(X5)))))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(quantDeMorgan3, axiom, quantDeMorgan3 <=> 103.57/104.07 (![A,Xphi:($i > $o)]: 103.57/104.07 ((~(?[Xx]: (Xphi(Xx) & in(Xx,A)))) => (![Xx]: (in(Xx,A) => (~Xphi(Xx))))))). 103.57/104.07 tff('48', plain, 103.57/104.07 quantDeMorgan3 = 103.57/104.07 (![X2,X3:($i > $o)]: 103.57/104.07 ((~(?[X4]: (X3(X4) & in(X4,X2)))) => (![X5]: (in(X5,X2) => (~X3(X5)))))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(quantDeMorgan2, axiom, quantDeMorgan2 <=> 103.57/104.07 (![A,Xphi:($i > $o)]: 103.57/104.07 ((![Xx]: (in(Xx,A) => (~Xphi(Xx)))) => (~(?[Xx]: (Xphi(Xx) & in(Xx,A))))))). 103.57/104.07 tff('49', plain, 103.57/104.07 quantDeMorgan2 = 103.57/104.07 (![X2,X3:($i > $o)]: 103.57/104.07 ((![X4]: (in(X4,X2) => (~X3(X4)))) => (~(?[X5]: (X3(X5) & in(X5,X2)))))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(quantDeMorgan1, axiom, quantDeMorgan1 <=> 103.57/104.07 (![A,Xphi:($i > $o)]: 103.57/104.07 ((~(![Xx]: (in(Xx,A) => Xphi(Xx)))) => (?[Xx]: ((~Xphi(Xx)) & in(Xx,A)))))). 103.57/104.07 tff('50', plain, 103.57/104.07 quantDeMorgan1 = 103.57/104.07 (![X2,X3:($i > $o)]: 103.57/104.07 ((~(![X4]: (in(X4,X2) => X3(X4)))) => (?[X5]: ((~X3(X5)) & in(X5,X2))))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(vacuousDall, axiom, vacuousDall <=> 103.57/104.07 (![Xphi:($i > $o),Xx]: (in(Xx,emptyset) => Xphi(Xx)))). 103.57/104.07 tff('51', plain, 103.57/104.07 vacuousDall = (![X2:($i > $o),X3]: (in(X3,emptyset) => X2(X3))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(emptyE1, axiom, emptyE1 <=> 103.57/104.07 (![A,Xphi:($i > $o)]: 103.57/104.07 ((?[Xx]: (Xphi(Xx) & in(Xx,A))) => 103.57/104.07 ((dsetconstr(A,^[Xx]: Xphi(Xx)) = emptyset) => $false)))). 103.57/104.07 tff('52', plain, 103.57/104.07 emptyE1 = 103.57/104.07 (![X2,X3:($i > $o)]: 103.57/104.07 ((?[X4]: (X3(X4) & in(X4,X2))) => 103.57/104.07 ((dsetconstr(X2,^[V_1]: X3(V_1)) = emptyset) => $false))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(upairsetIR, axiom, upairsetIR <=> 103.57/104.07 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 103.57/104.07 tff('53', plain, 103.57/104.07 upairsetIR = (![X2,X3]: in(X3,setadjoin(X2,setadjoin(X3,emptyset)))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(upairsetIL, axiom, upairsetIL <=> 103.57/104.07 (![Xx,Xy]: in(Xx,setadjoin(Xx,setadjoin(Xy,emptyset))))). 103.57/104.07 tff('54', plain, 103.57/104.07 upairsetIL = (![X2,X3]: in(X2,setadjoin(X2,setadjoin(X3,emptyset)))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(upairsetE, axiom, upairsetE <=> 103.57/104.07 (![Xx,Xy,Xz]: 103.57/104.07 (in(Xz,setadjoin(Xx,setadjoin(Xy,emptyset))) => ((Xz = Xy) | (Xz = Xx))))). 103.57/104.07 tff('55', plain, 103.57/104.07 upairsetE = 103.57/104.07 (![X2,X3,X4]: 103.57/104.07 (in(X4,setadjoin(X2,setadjoin(X3,emptyset))) => 103.57/104.07 ((X4 = X3) | (X4 = X2)))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(singletonsswitch, axiom, singletonsswitch <=> 103.57/104.07 (![Xx,Xy]: (in(Xx,setadjoin(Xy,emptyset)) => in(Xy,setadjoin(Xx,emptyset))))). 103.57/104.07 tff('56', plain, 103.57/104.07 singletonsswitch = 103.57/104.07 (![X2,X3]: 103.57/104.07 (in(X2,setadjoin(X3,emptyset)) => in(X3,setadjoin(X2,emptyset)))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(eqinunit, axiom, eqinunit <=> 103.57/104.07 (![Xx,Xy]: ((Xx = Xy) => in(Xx,setadjoin(Xy,emptyset))))). 103.57/104.07 tff('57', plain, 103.57/104.07 eqinunit = (![X2,X3]: ((X2 = X3) => in(X2,setadjoin(X3,emptyset)))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(notinsingleton, axiom, notinsingleton <=> 103.57/104.07 (![Xx,Xy]: ((Xx != Xy) => (~in(Xy,setadjoin(Xx,emptyset)))))). 103.57/104.07 tff('58', plain, 103.57/104.07 notinsingleton = 103.57/104.07 (![X2,X3]: ((X2 != X3) => (~in(X3,setadjoin(X2,emptyset))))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(uniqinunit, axiom, uniqinunit <=> 103.57/104.07 (![Xx,Xy]: (in(Xx,setadjoin(Xy,emptyset)) => (Xx = Xy)))). 103.57/104.07 tff('59', plain, 103.57/104.07 uniqinunit = (![X2,X3]: (in(X2,setadjoin(X3,emptyset)) => (X2 = X3))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(nonemptyImpWitness, axiom, nonemptyImpWitness <=> 103.57/104.07 (![A]: (nonempty(A) => (?[Xx]: (in(Xx,A)))))). 103.57/104.07 tff('60', plain, 103.57/104.07 nonemptyImpWitness = (![X2]: (nonempty(X2) => (?[X3]: (in(X3,X2))))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(exuE2, axiom, exuE2 <=> 103.57/104.07 (![Xphi:($i > $o)]: 103.57/104.07 (exu(^[Xx]: Xphi(Xx)) => (?[Xx]: (![Xy]: (Xphi(Xy) <=> (Xy = Xx))))))). 103.57/104.07 tff('61', plain, 103.57/104.07 exuE2 = 103.57/104.07 (![X2:($i > $o)]: 103.57/104.07 (exu(^[V_1]: X2(V_1)) => (?[X3]: (![X4]: (X2(X4) <=> (X4 = X3)))))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(subPowSU, axiom, subPowSU <=> 103.57/104.07 (![A,Xx]: (in(Xx,A) => in(Xx,powerset(setunion(A)))))). 103.57/104.07 tff('62', plain, 103.57/104.07 subPowSU = (![X2,X3]: (in(X3,X2) => in(X3,powerset(setunion(X2))))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(setunionE, axiom, setunionE <=> 103.57/104.07 (![A,Xx]: 103.57/104.07 (in(Xx,setunion(A)) => 103.57/104.07 (![Xphi:$o]: ((![B]: (in(Xx,B) => (in(B,A) => Xphi))) => Xphi))))). 103.57/104.07 tff('63', plain, 103.57/104.07 setunionE = 103.57/104.07 (![X2,X3]: 103.57/104.07 (in(X3,setunion(X2)) => 103.57/104.07 (![X4:$o]: ((![X5]: (in(X3,X5) => (in(X5,X2) => X4))) => X4)))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(setunionI, axiom, setunionI <=> 103.57/104.07 (![A,Xx,B]: (in(Xx,B) => (in(B,A) => in(Xx,setunion(A)))))). 103.57/104.07 tff('64', plain, 103.57/104.07 setunionI = 103.57/104.07 (![X2,X3,X4]: (in(X3,X4) => (in(X4,X2) => in(X3,setunion(X2))))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(powersetE, axiom, powersetE <=> 103.57/104.07 (![A,B,Xx]: (in(B,powerset(A)) => (in(Xx,B) => in(Xx,A))))). 103.57/104.07 tff('65', plain, 103.57/104.07 powersetE = 103.57/104.07 (![X2,X3,X4]: (in(X3,powerset(X2)) => (in(X4,X3) => in(X4,X2)))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(emptyInPowerset, axiom, emptyInPowerset <=> 103.57/104.07 (![A]: in(emptyset,powerset(A)))). 103.57/104.07 tff('66', plain, emptyInPowerset = (![X2]: in(emptyset,powerset(X2))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(emptyinPowerset, axiom, emptyinPowerset <=> 103.57/104.07 (![A]: in(emptyset,powerset(A)))). 103.57/104.07 tff('67', plain, emptyinPowerset = (![X2]: in(emptyset,powerset(X2))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(powersetI, axiom, powersetI <=> 103.57/104.07 (![A,B]: ((![Xx]: (in(Xx,B) => in(Xx,A))) => in(B,powerset(A))))). 103.57/104.07 tff('68', plain, 103.57/104.07 powersetI = 103.57/104.07 (![X2,X3]: ((![X4]: (in(X4,X3) => in(X4,X2))) => in(X3,powerset(X2)))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(setoftrueEq, axiom, setoftrueEq <=> 103.57/104.07 (![A]: (dsetconstr(A,^[Xx]: $true) = A))). 103.57/104.07 tff('69', plain, setoftrueEq = (![X2]: (dsetconstr(X2,^[V_1]: $true) = X2)), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(setadjoinOr, axiom, setadjoinOr <=> 103.57/104.07 (![Xx,A,Xy]: (in(Xy,setadjoin(Xx,A)) => (in(Xy,A) | (Xy = Xx))))). 103.57/104.07 tff('70', plain, 103.57/104.07 setadjoinOr = 103.57/104.07 (![X2,X3,X4]: (in(X4,setadjoin(X2,X3)) => (in(X4,X3) | (X4 = X2)))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(setadjoinE, axiom, setadjoinE <=> 103.57/104.07 (![Xx,A,Xy]: 103.57/104.07 (in(Xy,setadjoin(Xx,A)) => 103.57/104.07 (![Xphi:$o]: (((Xy = Xx) => Xphi) => ((in(Xy,A) => Xphi) => Xphi)))))). 103.57/104.07 tff('71', plain, 103.57/104.07 setadjoinE = 103.57/104.07 (![X2,X3,X4]: 103.57/104.07 (in(X4,setadjoin(X2,X3)) => 103.57/104.07 (![X5:$o]: (((X4 = X2) => X5) => ((in(X4,X3) => X5) => X5))))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(setadjoinIR, axiom, setadjoinIR <=> 103.57/104.07 (![Xx,A,Xy]: (in(Xy,A) => in(Xy,setadjoin(Xx,A))))). 103.57/104.07 tff('72', plain, 103.57/104.07 setadjoinIR = (![X2,X3,X4]: (in(X4,X3) => in(X4,setadjoin(X2,X3)))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(emptyinunitempty, axiom, emptyinunitempty() = 103.57/104.07 in(emptyset,setadjoin(emptyset,emptyset))). 103.57/104.07 tff('73', plain, 103.57/104.07 emptyinunitempty = in(emptyset,setadjoin(emptyset,emptyset)), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(setadjoinIL, axiom, setadjoinIL <=> (![Xx,Xy]: in(Xx,setadjoin(Xx,Xy)))). 103.57/104.07 tff('74', plain, setadjoinIL = (![X2,X3]: in(X2,setadjoin(X2,X3))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(nonemptyI1, axiom, nonemptyI1 <=> 103.57/104.07 (![A]: ((?[Xx]: in(Xx,A)) => nonempty(A)))). 103.57/104.07 tff('75', plain, nonemptyI1 = (![X2]: ((?[X3]: in(X3,X2)) => nonempty(X2))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(nonemptyI, axiom, nonemptyI <=> 103.57/104.07 (![A,Xphi:($i > $o),Xx]: 103.57/104.07 (in(Xx,A) => (Xphi(Xx) => nonempty(dsetconstr(A,^[Xy]: Xphi(Xy))))))). 103.57/104.07 tff('76', plain, 103.57/104.07 nonemptyI = 103.57/104.07 (![X2,X3:($i > $o),X4]: 103.57/104.07 (in(X4,X2) => (X3(X4) => nonempty(dsetconstr(X2,^[V_1]: X3(V_1)))))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(nonemptyE1, axiom, nonemptyE1 <=> 103.57/104.07 (![A]: (nonempty(A) => (?[Xx]: in(Xx,A))))). 103.57/104.07 tff('77', plain, nonemptyE1 = (![X2]: (nonempty(X2) => (?[X3]: in(X3,X2)))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(nonempty, axiom, nonempty() = ^[Xx]: (Xx != emptyset)). 103.57/104.07 tff('78', plain, nonempty = (^[V_1]: (V_1 != emptyset)), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(setbeta, axiom, setbeta <=> 103.57/104.07 (![A,Xphi:($i > $o),Xx]: 103.57/104.07 (in(Xx,A) => (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) <=> Xphi(Xx))))). 103.57/104.07 tff('79', plain, 103.57/104.07 setbeta = 103.57/104.07 (![X2,X3:($i > $o),X4]: 103.57/104.07 (in(X4,X2) => (in(X4,dsetconstr(X2,^[V_1]: X3(V_1))) <=> X3(X4)))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(noeltsimpempty, axiom, noeltsimpempty <=> 103.57/104.07 (![A]: ((![Xx]: (~in(Xx,A))) => (A = emptyset)))). 103.57/104.07 tff('80', plain, 103.57/104.07 noeltsimpempty = (![X2]: ((![X3]: (~in(X3,X2))) => (X2 = emptyset))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(emptyI, axiom, emptyI <=> 103.57/104.07 (![A]: ((![Xx]: (~in(Xx,A))) => (A = emptyset)))). 103.57/104.07 tff('81', plain, 103.57/104.07 emptyI = (![X2]: ((![X3]: (~in(X3,X2))) => (X2 = emptyset))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(setext, axiom, setext <=> 103.57/104.07 (![A,B]: 103.57/104.07 ((![Xx]: (in(Xx,A) => in(Xx,B))) => 103.57/104.07 ((![Xx]: (in(Xx,B) => in(Xx,A))) => (A = B))))). 103.57/104.07 tff('82', plain, 103.57/104.07 setext = 103.57/104.07 (![X2,X3]: 103.57/104.07 ((![X4]: (in(X4,X2) => in(X4,X3))) => 103.57/104.07 ((![X5]: (in(X5,X3) => in(X5,X2))) => (X2 = X3)))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(exuE3e, axiom, exuE3e <=> 103.57/104.07 (![Xphi:($i > $o)]: (exu(^[Xx]: Xphi(Xx)) => (?[Xx]: Xphi(Xx))))). 103.57/104.07 tff('83', plain, 103.57/104.07 exuE3e = (![X2:($i > $o)]: (exu(^[V_1]: X2(V_1)) => (?[X3]: X2(X3)))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(notinemptyset, axiom, notinemptyset <=> (![Xx]: (~in(Xx,emptyset)))). 103.57/104.07 tff('84', plain, notinemptyset = (![X2]: (~in(X2,emptyset))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(emptysetimpfalse, axiom, emptysetimpfalse <=> 103.57/104.07 (![Xx]: (in(Xx,emptyset) => $false))). 103.57/104.07 tff('85', plain, emptysetimpfalse = (![X2]: (in(X2,emptyset) => $false)), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(emptysetE, axiom, emptysetE <=> 103.57/104.07 (![Xx]: (in(Xx,emptyset) => (![Xphi:$o]: Xphi)))). 103.57/104.07 tff('86', plain, emptysetE = (![X2]: (in(X2,emptyset) => (![X3:$o]: X3))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(prop2setE, axiom, prop2setE <=> 103.57/104.07 (![Xphi:$o,Xx]: (in(Xx,prop2set(Xphi)) => Xphi))). 103.57/104.07 tff('87', plain, prop2setE = (![X2:$o,X3]: (in(X3,prop2set(X2)) => X2)), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(exuE1, axiom, exuE1 <=> 103.57/104.07 (![Xphi:($i > $o)]: 103.57/104.07 (exu(^[Xx]: Xphi(Xx)) => 103.57/104.07 (?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx)))))). 103.57/104.07 tff('88', plain, 103.57/104.07 exuE1 = 103.57/104.07 (![X2:($i > $o)]: 103.57/104.07 (exu(^[V_1]: X2(V_1)) => 103.57/104.07 (?[X3]: ((![X4]: (X2(X4) => (X3 = X4))) & X2(X3))))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(dsetconstrER, axiom, dsetconstrER <=> 103.57/104.07 (![A,Xphi:($i > $o),Xx]: (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) => Xphi(Xx)))). 103.57/104.07 tff('89', plain, 103.57/104.07 dsetconstrER = 103.57/104.07 (![X2,X3:($i > $o),X4]: (in(X4,dsetconstr(X2,^[V_1]: X3(V_1))) => X3(X4))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(dsetconstrEL, axiom, dsetconstrEL <=> 103.57/104.07 (![A,Xphi:($i > $o),Xx]: (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) => in(Xx,A)))). 103.57/104.07 tff('90', plain, 103.57/104.07 dsetconstrEL = 103.57/104.07 (![X2,X3:($i > $o),X4]: 103.57/104.07 (in(X4,dsetconstr(X2,^[V_1]: X3(V_1))) => in(X4,X2))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(dsetconstrI, axiom, dsetconstrI <=> 103.57/104.07 (![A,Xphi:($i > $o),Xx]: 103.57/104.07 (in(Xx,A) => (Xphi(Xx) => in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))))))). 103.57/104.07 tff('91', plain, 103.57/104.07 dsetconstrI = 103.57/104.07 (![X2,X3:($i > $o),X4]: 103.57/104.07 (in(X4,X2) => (X3(X4) => in(X4,dsetconstr(X2,^[V_1]: X3(V_1)))))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(descrp, axiom, descrp <=> 103.57/104.07 (![Xphi:($i > $o)]: (exu(^[Xx]: Xphi(Xx)) => Xphi(descr(^[Xx]: Xphi(Xx)))))). 103.57/104.07 tff('92', plain, 103.57/104.07 descrp = 103.57/104.07 (![X2:($i > $o)]: (exu(^[V_1]: X2(V_1)) => X2(descr(^[V_2]: X2(V_2))))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(wellorderingAx, axiom, wellorderingAx <=> 103.57/104.07 (![A]: 103.57/104.07 (?[B]: 103.57/104.07 ((![C]: 103.57/104.07 (((?[Xx]: in(Xx,C)) & (![Xx]: (in(Xx,C) => in(Xx,A)))) => 103.57/104.07 (?[D,Xx]: 103.57/104.07 ((![E]: 103.57/104.07 (in(E,B) => (in(Xx,E) | (![Xy]: (in(Xy,E) => in(Xy,D)))))) & 103.57/104.07 (~(?[Xy]: (in(Xy,C) & in(Xy,D)))) & in(Xx,C) & in(D,B))))) & 103.57/104.07 (![C,D]: 103.57/104.07 ((in(D,B) & in(C,B)) => 103.57/104.07 ((![Xx]: (in(Xx,D) => in(Xx,C))) | 103.57/104.07 (![Xx]: (in(Xx,C) => in(Xx,D)))))) & 103.57/104.07 (![Xx,Xy]: 103.57/104.07 ((in(Xy,A) & in(Xx,A)) => 103.57/104.07 ((![C]: (in(C,B) => (in(Xx,C) <=> in(Xy,C)))) => (Xx = Xy)))) & 103.57/104.07 (![C]: (in(C,B) => (![Xx]: (in(Xx,C) => in(Xx,A))))))))). 103.57/104.07 tff('93', plain, 103.57/104.07 wellorderingAx = 103.57/104.07 (![X2]: 103.57/104.07 (?[X3]: 103.57/104.07 ((![X4]: 103.57/104.07 (((?[X5]: in(X5,X4)) & (![X6]: (in(X6,X4) => in(X6,X2)))) => 103.57/104.07 (?[X7,X8]: 103.57/104.07 ((![X9]: 103.57/104.07 (in(X9,X3) => 103.57/104.07 (in(X8,X9) | (![X10]: (in(X10,X9) => in(X10,X7)))))) & 103.57/104.07 (~(?[X11]: (in(X11,X4) & in(X11,X7)))) & in(X8,X4) & 103.57/104.07 in(X7,X3))))) & 103.57/104.07 (![X12,X13]: 103.57/104.07 ((in(X13,X3) & in(X12,X3)) => 103.57/104.07 ((![X14]: (in(X14,X13) => in(X14,X12))) | 103.57/104.07 (![X15]: (in(X15,X12) => in(X15,X13)))))) & 103.57/104.07 (![X16,X17]: 103.57/104.07 ((in(X17,X2) & in(X16,X2)) => 103.57/104.07 ((![X18]: (in(X18,X3) => (in(X16,X18) <=> in(X17,X18)))) => 103.57/104.07 (X16 = X17)))) & 103.57/104.07 (![X19]: (in(X19,X3) => (![X20]: (in(X20,X19) => in(X20,X2)))))))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(foundationAx, axiom, foundationAx <=> 103.57/104.07 (![A]: 103.57/104.07 ((?[Xx]: in(Xx,A)) => 103.57/104.07 (?[B]: ((~(?[Xx]: (in(Xx,A) & in(Xx,B)))) & in(B,A)))))). 103.57/104.07 tff('94', plain, 103.57/104.07 foundationAx = 103.57/104.07 (![X2]: 103.57/104.07 ((?[X3]: in(X3,X2)) => 103.57/104.07 (?[X4]: ((~(?[X5]: (in(X5,X2) & in(X5,X4)))) & in(X4,X2))))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(replAx, axiom, replAx <=> 103.57/104.07 (![Xphi:(($i * $i) > $o),A]: 103.57/104.07 ((![Xx]: (in(Xx,A) => exu(^[Xy]: Xphi(Xx,Xy)))) => 103.57/104.07 (?[B]: (![Xx]: (in(Xx,B) <=> (?[Xy]: (Xphi(Xy,Xx) & in(Xy,A))))))))). 103.57/104.07 tff('95', plain, 103.57/104.07 replAx = 103.57/104.07 (![X2:(($i * $i) > $o),X3]: 103.57/104.07 ((![X4]: (in(X4,X3) => exu(^[V_1]: X2(X4,V_1)))) => 103.57/104.07 (?[X5]: (![X6]: (in(X6,X5) <=> (?[X7]: (X2(X7,X6) & in(X7,X3)))))))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(omegaIndAx, axiom, omegaIndAx <=> 103.57/104.07 (![A]: 103.57/104.07 (((![Xx]: ((in(Xx,A) & in(Xx,omega)) => in(setadjoin(Xx,Xx),A))) & 103.57/104.07 in(emptyset,A)) => 103.57/104.07 (![Xx]: (in(Xx,omega) => in(Xx,A)))))). 103.57/104.07 tff('96', plain, 103.57/104.07 omegaIndAx = 103.57/104.07 (![X2]: 103.57/104.07 (((![X3]: ((in(X3,X2) & in(X3,omega)) => in(setadjoin(X3,X3),X2))) & 103.57/104.07 in(emptyset,X2)) => 103.57/104.07 (![X4]: (in(X4,omega) => in(X4,X2))))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(omegaSAx, axiom, omegaSAx <=> 103.57/104.07 (![Xx]: (in(Xx,omega) => in(setadjoin(Xx,Xx),omega)))). 103.57/104.07 tff('97', plain, 103.57/104.07 omegaSAx = (![X2]: (in(X2,omega) => in(setadjoin(X2,X2),omega))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(omega0Ax, axiom, omega0Ax() = in(emptyset,omega)). 103.57/104.07 tff('98', plain, omega0Ax = in(emptyset,omega), define([status(thm)])). 103.57/104.07 tff(setunionAx, axiom, setunionAx <=> 103.57/104.07 (![A,Xx]: (in(Xx,setunion(A)) <=> (?[B]: (in(B,A) & in(Xx,B)))))). 103.57/104.07 tff('99', plain, 103.57/104.07 setunionAx = 103.57/104.07 (![X2,X3]: (in(X3,setunion(X2)) <=> (?[X4]: (in(X4,X2) & in(X3,X4))))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(powersetAx, axiom, powersetAx <=> 103.57/104.07 (![A,B]: (in(B,powerset(A)) <=> (![Xx]: (in(Xx,B) => in(Xx,A)))))). 103.57/104.07 tff('100', plain, 103.57/104.07 powersetAx = 103.57/104.07 (![X2,X3]: (in(X3,powerset(X2)) <=> (![X4]: (in(X4,X3) => in(X4,X2))))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(setadjoinAx, axiom, setadjoinAx <=> 103.57/104.07 (![Xx,A,Xy]: (in(Xy,setadjoin(Xx,A)) <=> (in(Xy,A) | (Xy = Xx))))). 103.57/104.07 tff('101', plain, 103.57/104.07 setadjoinAx = 103.57/104.07 (![X2,X3,X4]: (in(X4,setadjoin(X2,X3)) <=> (in(X4,X3) | (X4 = X2)))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(emptysetAx, axiom, emptysetAx <=> (![Xx]: (~in(Xx,emptyset)))). 103.57/104.07 tff('102', plain, emptysetAx = (![X2]: (~in(X2,emptyset))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(setextAx, axiom, setextAx <=> 103.57/104.07 (![A,B]: ((![Xx]: (in(Xx,A) <=> in(Xx,B))) => (A = B)))). 103.57/104.07 tff('103', plain, 103.57/104.07 setextAx = (![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(exu, axiom, exu() = 103.57/104.07 ^[Xphi:($i > $o)]: (?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx)))). 103.57/104.07 tff('104', plain, 103.57/104.07 exu = 103.57/104.07 (^[V_1:($i > $o)]: (?[X2]: ((![X3]: (V_1(X3) => (X2 = X3))) & V_1(X2)))), 103.57/104.07 define([status(thm)])). 103.57/104.07 tff(binunionLsub, conjecture, 103.57/104.07 (setextAx => 103.57/104.07 (emptysetAx => 103.57/104.07 (setadjoinAx => 103.57/104.07 (powersetAx => 103.57/104.07 (setunionAx => 103.57/104.07 (omega0Ax => 103.57/104.07 (omegaSAx => 103.57/104.07 (omegaIndAx => 103.57/104.07 (replAx => 103.57/104.07 (foundationAx => 103.57/104.07 (wellorderingAx => 103.57/104.07 (descrp => 103.57/104.07 (dsetconstrI => 103.57/104.07 (dsetconstrEL => 103.57/104.07 (dsetconstrER => 103.57/104.07 (exuE1 => 103.57/104.07 (prop2setE => 103.57/104.07 (emptysetE => 103.57/104.07 (emptysetimpfalse => 103.57/104.07 (notinemptyset => 103.57/104.07 (exuE3e => 103.57/104.07 (setext => 103.57/104.07 (emptyI => 103.57/104.07 (noeltsimpempty => 103.57/104.07 (setbeta => 103.57/104.07 (nonemptyE1 => 103.57/104.07 (nonemptyI => 103.57/104.07 (nonemptyI1 => 103.57/104.07 (setadjoinIL => 103.57/104.07 (emptyinunitempty => 103.57/104.07 (setadjoinIR => 103.57/104.07 (setadjoinE => 103.57/104.07 (setadjoinOr => 103.57/104.07 (setoftrueEq => 103.57/104.07 (powersetI => 103.57/104.07 (emptyinPowerset => 103.57/104.07 (emptyInPowerset => 103.57/104.07 (powersetE => 103.57/104.07 (setunionI => 103.57/104.07 (setunionE => 103.57/104.07 (subPowSU => 103.57/104.07 (exuE2 => 103.57/104.07 (nonemptyImpWitness => 103.57/104.07 (uniqinunit => 103.57/104.07 (notinsingleton => 103.57/104.07 (eqinunit => 103.57/104.07 (singletonsswitch => 103.57/104.07 (upairsetE => 103.57/104.07 (upairsetIL => 103.57/104.07 (upairsetIR => 103.57/104.07 (emptyE1 => 103.57/104.07 (vacuousDall => 103.57/104.07 (quantDeMorgan1 => 103.57/104.07 (quantDeMorgan2 => 103.57/104.07 (quantDeMorgan3 => 103.57/104.07 (quantDeMorgan4 => 103.57/104.07 (prop2setI => 103.57/104.07 (prop2set2propI => 103.57/104.07 (notdexE => 103.57/104.07 (notdallE => 103.57/104.07 (exuI1 => 103.57/104.07 (exuI3 => 103.57/104.07 (exuI2 => 103.57/104.07 (inCongP => 103.57/104.07 (in__Cong => 103.57/104.07 (exuE3u => 103.57/104.07 ( 103.57/104.07 exu__Cong => 103.57/104.07 ( 103.57/104.07 emptyset__Cong => 103.57/104.07 ( 103.57/104.07 setadjoin__Cong => 103.57/104.07 ( 103.57/104.07 powerset__Cong => 103.57/104.07 ( 103.57/104.07 setunion__Cong => 103.57/104.07 ( 103.57/104.07 omega__Cong => 103.57/104.07 ( 103.57/104.07 exuEu => 103.57/104.07 ( 103.57/104.07 descr__Cong => 103.57/104.07 ( 103.57/104.07 dsetconstr__Cong => 103.57/104.07 ( 103.57/104.07 subsetI1 => 103.57/104.07 ( 103.57/104.07 eqimpsubset2 => 103.57/104.07 ( 103.57/104.07 eqimpsubset1 => 103.57/104.07 ( 103.57/104.07 subsetI2 => 103.57/104.07 ( 103.57/104.07 emptysetsubset => 103.57/104.07 ( 103.57/104.07 subsetE => 103.57/104.07 ( 103.57/104.07 subsetE2 => 103.57/104.07 ( 103.57/104.07 notsubsetI => 103.57/104.07 ( 103.57/104.07 notequalI1 => 103.57/104.07 ( 103.57/104.07 notequalI2 => 103.57/104.07 ( 103.57/104.07 subsetRefl => 103.57/104.07 ( 103.57/104.07 subsetTrans => 103.57/104.07 ( 103.57/104.07 setadjoinSub => 103.57/104.07 ( 103.57/104.07 setadjoinSub2 => 103.57/104.07 ( 103.57/104.07 subset2powerset => 103.57/104.07 ( 103.57/104.07 setextsub => 103.57/104.07 ( 103.57/104.07 subsetemptysetimpeq => 103.57/104.07 ( 103.57/104.07 powersetI1 => 103.57/104.07 ( 103.57/104.07 powersetE1 => 103.57/104.07 ( 103.57/104.07 inPowerset => 103.57/104.07 ( 103.57/104.07 powersetsubset => 103.57/104.07 ( 103.57/104.07 sepInPowerset => 103.57/104.07 ( 103.57/104.07 sepSubset => 103.57/104.07 ( 103.57/104.07 binunionIL => 103.57/104.07 ( 103.57/104.07 upairset2IR => 103.57/104.07 ( 103.57/104.07 binunionIR => 103.57/104.07 ( 103.57/104.07 binunionEcases => 103.57/104.07 ( 103.57/104.07 binunionE => 103.57/104.07 ( 103.57/104.07 ![A,B]: 103.57/104.07 subset( 103.57/104.07 A, 103.57/104.07 binunion( 103.57/104.07 A,B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 103.57/104.07 tff(zf_stmt_0, conjecture, 103.57/104.07 ((![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))) => 103.57/104.07 ((![X5]: (~in(X5,emptyset))) => 103.57/104.07 ((![X6,X7,X8]: (in(X8,setadjoin(X6,X7)) <=> ((X8 = X6) | in(X8,X7)))) => 103.57/104.07 ((![X9,X10]: 103.57/104.07 (in(X10,powerset(X9)) <=> (![X11]: (in(X11,X10) => in(X11,X9))))) => 103.57/104.07 ((![X12,X13]: 103.57/104.07 (in(X13,setunion(X12)) <=> (?[X14]: (in(X13,X14) & in(X14,X12))))) => 103.57/104.07 (in(emptyset,omega) => 103.57/104.07 ((![X15]: (in(X15,omega) => in(setadjoin(X15,X15),omega))) => 103.57/104.07 ((![X16]: 103.57/104.07 ((in(emptyset,X16) & 103.57/104.07 (![X17]: 103.57/104.07 ((in(X17,omega) & in(X17,X16)) => 103.57/104.07 in(setadjoin(X17,X17),X16)))) => 103.57/104.07 (![X18]: (in(X18,omega) => in(X18,X16))))) => 103.57/104.07 ((![X19:(($i * $i) > $o),X20]: 103.57/104.07 ((![X21]: 103.57/104.07 (in(X21,X20) => 103.57/104.07 (?[X22]: 103.57/104.07 (X19(X21,X22) & (![X23]: (X19(X21,X23) => (X22 = X23))))))) => 103.57/104.07 (?[X24]: 103.57/104.07 (![X25]: 103.57/104.07 (in(X25,X24) <=> (?[X26]: (in(X26,X20) & X19(X26,X25)))))))) => 103.57/104.07 ((![X27]: 103.57/104.07 ((?[X28]: in(X28,X27)) => 103.57/104.07 (?[X29]: 103.57/104.07 (in(X29,X27) & (~(?[X30]: (in(X30,X29) & in(X30,X27)))))))) => 103.57/104.07 ((![X31]: 103.57/104.07 (?[X32]: 103.57/104.07 ((![X48]: 103.57/104.07 (in(X48,X32) => (![X49]: (in(X49,X48) => in(X49,X31))))) & 103.57/104.07 (![X45,X46]: 103.57/104.07 ((in(X45,X31) & in(X46,X31)) => 103.57/104.07 ((![X47]: 103.57/104.07 (in(X47,X32) => (in(X45,X47) <=> in(X46,X47)))) => 103.57/104.07 (X45 = X46)))) & 103.57/104.07 (![X41,X42]: 103.57/104.07 ((in(X41,X32) & in(X42,X32)) => 103.57/104.07 ((![X44]: (in(X44,X41) => in(X44,X42))) | 103.57/104.07 (![X43]: (in(X43,X42) => in(X43,X41)))))) & 103.57/104.07 (![X33]: 103.57/104.07 (((![X35]: (in(X35,X33) => in(X35,X31))) & 103.57/104.07 (?[X34]: in(X34,X33))) => 103.57/104.07 (?[X36,X37]: 103.57/104.07 (in(X36,X32) & in(X37,X33) & 103.57/104.07 (~(?[X40]: (in(X40,X36) & in(X40,X33)))) & 103.57/104.07 (![X38]: 103.57/104.07 (in(X38,X32) => 103.57/104.07 ((![X39]: (in(X39,X38) => in(X39,X36))) | 103.57/104.07 in(X37,X38))))))))))) => 103.57/104.07 ((![X50:($i > $o)]: 103.57/104.07 ((?[X51]: (X50(X51) & (![X52]: (X50(X52) => (X51 = X52))))) => 103.57/104.07 X50(descr('#ll_0'(X50))))) => 103.57/104.07 ((![X53,X54:($i > $o),X55]: 103.57/104.07 (in(X55,X53) => 103.57/104.07 (X54(X55) => in(X55,dsetconstr(X53,'#ll_0'(X54)))))) => 103.57/104.07 ((![X56,X57:($i > $o),X58]: 103.57/104.07 (in(X58,dsetconstr(X56,'#ll_0'(X57))) => in(X58,X56))) => 103.57/104.07 ((![X59,X60:($i > $o),X61]: 103.57/104.07 (in(X61,dsetconstr(X59,'#ll_0'(X60))) => X60(X61))) => 103.57/104.07 ((![X62:($i > $o)]: 103.57/104.07 ((?[X63]: 103.57/104.07 (X62(X63) & (![X64]: (X62(X64) => (X63 = X64))))) => 103.57/104.07 (?[X65]: 103.57/104.07 (X62(X65) & (![X66]: (X62(X66) => (X65 = X66))))))) => 103.57/104.07 ((![X67:$o,X68]: (in(X68,prop2set(X67)) => X67)) => 103.57/104.07 ((![X69]: (in(X69,emptyset) => (![X70:$o]: X70))) => 103.57/104.07 ((![X71]: (in(X71,emptyset) => $false)) => 103.57/104.07 ((![X72]: (~in(X72,emptyset))) => 103.57/104.07 ((![X73:($i > $o)]: 103.57/104.07 ((?[X74]: 103.57/104.07 (X73(X74) & (![X75]: (X73(X75) => (X74 = X75))))) => 103.57/104.07 (?[X76]: X73(X76)))) => 103.57/104.07 ((![X77,X78]: 103.57/104.07 ((![X79]: (in(X79,X77) => in(X79,X78))) => 103.57/104.07 ((![X80]: (in(X80,X78) => in(X80,X77))) => 103.57/104.07 (X77 = X78)))) => 103.57/104.07 ((![X81]: 103.57/104.07 ((![X82]: (~in(X82,X81))) => (X81 = emptyset))) => 103.57/104.07 ((![X83]: 103.57/104.07 ((![X84]: (~in(X84,X83))) => (X83 = emptyset))) => 103.57/104.07 ((![X85,X86:($i > $o),X87]: 103.57/104.07 (in(X87,X85) => 103.57/104.07 (in(X87,dsetconstr(X85,'#ll_0'(X86))) <=> 103.57/104.07 X86(X87)))) => 103.57/104.07 ((![X88]: 103.57/104.07 ((X88 != emptyset) => (?[X89]: in(X89,X88)))) => 103.57/104.07 ((![X90,X91:($i > $o),X92]: 103.57/104.07 (in(X92,X90) => 103.57/104.07 (X91(X92) => 103.57/104.07 (dsetconstr(X90,'#ll_0'(X91)) != emptyset)))) => 103.57/104.07 ((![X93]: 103.57/104.07 ((?[X94]: in(X94,X93)) => (X93 != emptyset))) => 103.57/104.07 ((![X95,X96]: in(X95,setadjoin(X95,X96))) => 103.57/104.07 (in(emptyset,setadjoin(emptyset,emptyset)) => 103.57/104.07 ((![X97,X98,X99]: 103.57/104.07 (in(X99,X98) => 103.57/104.07 in(X99,setadjoin(X97,X98)))) => 103.57/104.07 ((![X100,X101,X102]: 103.57/104.07 (in(X102,setadjoin(X100,X101)) => 103.57/104.07 (![X103:$o]: 103.57/104.07 (((X102 = X100) => X103) => 103.57/104.07 ((in(X102,X101) => X103) => X103))))) => 103.57/104.07 ((![X104,X105,X106]: 103.57/104.07 (in(X106,setadjoin(X104,X105)) => 103.57/104.07 ((X106 = X104) | in(X106,X105)))) => 103.57/104.07 ((![X107]: 103.57/104.07 (dsetconstr(X107,'#ll_1') = X107)) => 103.57/104.07 ((![X108,X109]: 103.57/104.07 ((![X110]: 103.57/104.07 (in(X110,X109) => in(X110,X108))) => 103.57/104.07 in(X109,powerset(X108)))) => 103.57/104.07 ((![X111]: in(emptyset,powerset(X111))) => 103.57/104.07 ((![X112]: in(emptyset,powerset(X112))) => 103.57/104.07 ((![X113,X114,X115]: 103.57/104.07 (in(X114,powerset(X113)) => 103.57/104.07 (in(X115,X114) => in(X115,X113)))) => 103.57/104.07 ((![X116,X117,X118]: 103.57/104.07 (in(X117,X118) => 103.57/104.07 (in(X118,X116) => 103.57/104.07 in(X117,setunion(X116))))) => 103.57/104.07 ((![X119,X120]: 103.57/104.07 (in(X120,setunion(X119)) => 103.57/104.07 (![X121:$o]: 103.57/104.07 ((![X122]: 103.57/104.07 (in(X120,X122) => 103.57/104.07 (in(X122,X119) => X121))) => 103.57/104.07 X121)))) => 103.57/104.07 ((![X123,X124]: 103.57/104.07 (in(X124,X123) => 103.57/104.07 in(X124, 103.57/104.07 powerset(setunion(X123))))) => 103.57/104.07 ((![X125:($i > $o)]: 103.57/104.07 ((?[X126]: 103.57/104.07 (X125(X126) & 103.57/104.08 (![X127]: 103.57/104.08 (X125(X127) => 103.57/104.08 (X126 = X127))))) => 103.57/104.08 (?[X128]: 103.57/104.08 (![X129]: 103.57/104.08 (X125(X129) <=> 103.57/104.08 (X129 = X128)))))) => 103.57/104.08 ((![X130]: 103.57/104.08 ((X130 != emptyset) => 103.57/104.08 (?[X131]: in(X131,X130)))) => 103.57/104.08 ((![X132,X133]: 103.57/104.08 (in(X132, 103.57/104.08 setadjoin(X133,emptyset)) => 103.57/104.08 (X132 = X133))) => 103.57/104.08 ((![X134,X135]: 103.57/104.08 ((X134 != X135) => 103.57/104.08 (~ 103.57/104.08 in(X135, 103.57/104.08 setadjoin(X134, 103.57/104.08 emptyset))))) => 103.57/104.08 ((![X136,X137]: 103.57/104.08 ((X136 = X137) => 103.57/104.08 in(X136, 103.57/104.08 setadjoin(X137, 103.57/104.08 emptyset)))) => 103.57/104.08 ((![X138,X139]: 103.57/104.08 (in(X138, 103.57/104.08 setadjoin(X139, 103.57/104.08 emptyset)) => 103.57/104.08 in(X139, 103.57/104.08 setadjoin(X138, 103.57/104.08 emptyset)))) => 103.57/104.08 ((![X140,X141,X142]: 103.57/104.08 (in(X142, 103.57/104.08 setadjoin(X140, 103.57/104.08 setadjoin( 103.57/104.08 X141, 103.57/104.08 emptyset))) => 103.57/104.08 ((X142 = X140) | 103.57/104.08 (X142 = X141)))) => 103.57/104.08 ((![X143,X144]: 103.57/104.08 in(X143, 103.57/104.08 setadjoin(X143, 103.57/104.08 setadjoin( 103.57/104.08 X144, 103.57/104.08 emptyset)))) => 103.57/104.08 ((![X145,X146]: 103.57/104.08 in(X146, 103.57/104.08 setadjoin(X145, 103.57/104.08 setadjoin( 103.57/104.08 X146, 103.57/104.08 emptyset)))) => 103.57/104.08 ((![X147,X148:($i > $o)]: 103.57/104.08 ((?[X149]: 103.57/104.08 (in(X149,X147) & 103.57/104.08 X148(X149))) => 103.57/104.08 ((dsetconstr( 103.57/104.08 X147,'#ll_0'(X148)) = 103.57/104.08 emptyset) => 103.57/104.08 $false))) => 103.57/104.08 ((![X150:($i > $o),X151]: 103.57/104.08 (in(X151,emptyset) => 103.57/104.08 X150(X151))) => 103.57/104.08 ((![X152,X153:($i > $o)]: 103.57/104.08 ((~ 103.57/104.08 (![X154]: 103.57/104.08 (in(X154,X152) => 103.57/104.08 X153(X154)))) => 103.57/104.08 (?[X155]: 103.57/104.08 (in(X155,X152) & 103.57/104.08 (~X153(X155)))))) => 103.57/104.08 ((![X156, 103.57/104.08 X157:($i > $o)]: 103.57/104.08 ((![X158]: 103.57/104.08 (in(X158,X156) => 103.57/104.08 (~X157(X158)))) => 103.57/104.08 (~ 103.57/104.08 (?[X159]: 103.57/104.08 (in( 103.57/104.08 X159,X156) & 103.57/104.08 X157(X159)))))) => 103.57/104.08 ((![X160, 103.57/104.08 X161:($i > $o)]: 103.57/104.08 ((~ 103.57/104.08 (?[X162]: 103.57/104.08 (in( 103.57/104.08 X162,X160) & 103.57/104.08 X161(X162)))) => 103.57/104.08 (![X163]: 103.57/104.08 (in(X163,X160) => 103.57/104.08 (~X161(X163)))))) => 103.57/104.08 ((![X164, 103.57/104.08 X165:($i > $o)]: 103.57/104.08 ((?[X166]: 103.57/104.08 (in( 103.57/104.08 X166,X164) & 103.57/104.08 (~ 103.57/104.08 X165( 103.57/104.08 X166)))) => 103.57/104.08 (~ 103.57/104.08 (![X167]: 103.57/104.08 (in( 103.57/104.08 X167,X164) => 103.57/104.08 X165( 103.57/104.08 X167)))))) => 103.57/104.08 ((![X168:$o]: 103.57/104.08 (X168 => 103.57/104.08 in(emptyset, 103.57/104.08 prop2set( 103.57/104.08 X168)))) => 103.57/104.08 ((![X169:$o]: 103.57/104.08 (X169 => 103.57/104.08 set2prop( 103.57/104.08 prop2set( 103.57/104.08 X169)))) => 103.57/104.08 ((![X170, 103.57/104.08 X171:( 103.57/104.08 $i > $o)]: 103.57/104.08 ((~ 103.57/104.08 (?[X172]: 103.57/104.08 (in( 103.57/104.08 X172,X170) & 103.57/104.08 X171( 103.57/104.08 X172)))) => 103.57/104.08 (![X173]: 103.57/104.08 ( 103.57/104.08 in( 103.57/104.08 X173,X170) => 103.57/104.08 ( 103.57/104.08 ~ 103.57/104.08 X171( 103.57/104.08 X173)))))) => 103.57/104.08 ((![X174, 103.57/104.08 X175:( 103.57/104.08 $i > $o)]: 103.57/104.08 ((~ 103.57/104.08 ( 103.57/104.08 ![X176]: 103.57/104.08 (in( 103.57/104.08 X176,X174) => 103.57/104.08 X175( 103.57/104.08 X176)))) => 103.57/104.08 (?[X177]: 103.57/104.08 (in( 103.57/104.08 X177,X174) & 103.57/104.08 (~ 103.57/104.08 X175( 103.57/104.08 X177)))))) => 103.57/104.08 ((![X178:( 103.57/104.08 $i > $o)]: 103.57/104.08 ((?[X179]: 103.57/104.08 (X178( 103.57/104.08 X179) & 103.57/104.08 (![X180]: 103.57/104.08 (X178( 103.57/104.08 X180) => 103.57/104.08 (X179 = 103.57/104.08 X180))))) => 103.57/104.08 (?[X181]: 103.57/104.08 (X178( 103.57/104.08 X181) & 103.57/104.08 (![X182]: 103.57/104.08 (X178( 103.57/104.08 X182) => 103.57/104.08 (X181 = 103.57/104.08 X182))))))) => 103.57/104.08 ((![X183:( 103.57/104.08 $i > $o)]: 103.57/104.08 (( 103.57/104.08 ?[X184]: 103.57/104.08 X183( 103.57/104.08 X184)) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X185, 103.57/104.08 X186]: 103.57/104.08 (X183( 103.57/104.08 X185) => 103.57/104.08 (X183( 103.57/104.08 X186) => 103.57/104.08 (X185 = 103.57/104.08 X186)))) => 103.57/104.08 ( 103.57/104.08 ?[X187]: 103.57/104.08 (X183( 103.57/104.08 X187) & 103.57/104.08 (![X188]: 103.57/104.08 (X183( 103.57/104.08 X188) => 103.57/104.08 (X187 = 103.57/104.08 X188)))))))) => 103.57/104.08 ((![X189:( 103.57/104.08 $i > $o)]: 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ?[X190]: 103.57/104.08 (![X191]: 103.57/104.08 (X189( 103.57/104.08 X191) <=> 103.57/104.08 (X191 = 103.57/104.08 X190)))) => 103.57/104.08 ( 103.57/104.08 ?[X192]: 103.57/104.08 (X189( 103.57/104.08 X192) & 103.57/104.08 (![X193]: 103.57/104.08 (X189( 103.57/104.08 X193) => 103.57/104.08 (X192 = 103.57/104.08 X193))))))) => 103.57/104.08 ((![X194, 103.57/104.08 X195]: 103.57/104.08 (( 103.57/104.08 X194 = 103.57/104.08 X195) => 103.57/104.08 (![X196, 103.57/104.08 X197]: 103.57/104.08 (( 103.57/104.08 X196 = 103.57/104.08 X197) => 103.57/104.08 (in( 103.57/104.08 X196,X194) => 103.57/104.08 in( 103.57/104.08 X197,X195)))))) => 103.57/104.08 ((![X198, 103.57/104.08 X199]: 103.57/104.08 (( 103.57/104.08 X198 = 103.57/104.08 X199) => 103.57/104.08 (![X200, 103.57/104.08 X201]: 103.57/104.08 (( 103.57/104.08 X200 = 103.57/104.08 X201) => 103.57/104.08 (in( 103.57/104.08 X200,X198) <=> 103.57/104.08 in( 103.57/104.08 X201,X199)))))) => 103.57/104.08 (( 103.57/104.08 ![X202:( 103.57/104.08 $i > $o)]: 103.57/104.08 (( 103.57/104.08 ?[X203]: 103.57/104.08 (X202( 103.57/104.08 X203) & 103.57/104.08 (![X204]: 103.57/104.08 (X202( 103.57/104.08 X204) => 103.57/104.08 (X203 = 103.57/104.08 X204))))) => 103.57/104.08 (![X205, 103.57/104.08 X206]: 103.57/104.08 (X202( 103.57/104.08 X205) => 103.57/104.08 (X202( 103.57/104.08 X206) => 103.57/104.08 (X205 = 103.57/104.08 X206)))))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X207:( 103.57/104.08 $i > $o), 103.57/104.08 X208:( 103.57/104.08 $i > $o)]: 103.57/104.08 (( 103.57/104.08 ![X209, 103.57/104.08 X210]: 103.57/104.08 (( 103.57/104.08 X209 = 103.57/104.08 X210) => 103.57/104.08 (X207( 103.57/104.08 X209) <=> 103.57/104.08 X208( 103.57/104.08 X210)))) => 103.57/104.08 (( 103.57/104.08 ?[X211]: 103.57/104.08 (X207( 103.57/104.08 X211) & 103.57/104.08 (![X212]: 103.57/104.08 (X207( 103.57/104.08 X212) => 103.57/104.08 (X211 = 103.57/104.08 X212))))) <=> 103.57/104.08 (?[X213]: 103.57/104.08 (X208( 103.57/104.08 X213) & 103.57/104.08 (![X214]: 103.57/104.08 (X208( 103.57/104.08 X214) => 103.57/104.08 (X213 = 103.57/104.08 X214)))))))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 emptyset = 103.57/104.08 emptyset) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X215, 103.57/104.08 X216]: 103.57/104.08 (( 103.57/104.08 X215 = 103.57/104.08 X216) => 103.57/104.08 (![X217, 103.57/104.08 X218]: 103.57/104.08 (( 103.57/104.08 X217 = 103.57/104.08 X218) => 103.57/104.08 (setadjoin( 103.57/104.08 X215,X217) = 103.57/104.08 setadjoin( 103.57/104.08 X216,X218)))))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X219, 103.57/104.08 X220]: 103.57/104.08 (( 103.57/104.08 X219 = 103.57/104.08 X220) => 103.57/104.08 (powerset( 103.57/104.08 X219) = 103.57/104.08 powerset( 103.57/104.08 X220)))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X221, 103.57/104.08 X222]: 103.57/104.08 (( 103.57/104.08 X221 = 103.57/104.08 X222) => 103.57/104.08 (setunion( 103.57/104.08 X221) = 103.57/104.08 setunion( 103.57/104.08 X222)))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 omega = 103.57/104.08 omega) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X223:( 103.57/104.08 $i > $o)]: 103.57/104.08 (( 103.57/104.08 ?[X224]: 103.57/104.08 (X223( 103.57/104.08 X224) & 103.57/104.08 (![X225]: 103.57/104.08 (X223( 103.57/104.08 X225) => 103.57/104.08 (X224 = 103.57/104.08 X225))))) => 103.57/104.08 (![X226, 103.57/104.08 X227]: 103.57/104.08 (X223( 103.57/104.08 X226) => 103.57/104.08 (X223( 103.57/104.08 X227) => 103.57/104.08 (X226 = 103.57/104.08 X227)))))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X228:( 103.57/104.08 $i > $o), 103.57/104.08 X229:( 103.57/104.08 $i > $o)]: 103.57/104.08 (( 103.57/104.08 ![X230, 103.57/104.08 X231]: 103.57/104.08 (( 103.57/104.08 X230 = 103.57/104.08 X231) => 103.57/104.08 (X228( 103.57/104.08 X230) <=> 103.57/104.08 X229( 103.57/104.08 X231)))) => 103.57/104.08 (( 103.57/104.08 ?[X232]: 103.57/104.08 (X228( 103.57/104.08 X232) & 103.57/104.08 (![X233]: 103.57/104.08 (X228( 103.57/104.08 X233) => 103.57/104.08 (X232 = 103.57/104.08 X233))))) => 103.57/104.08 (( 103.57/104.08 ?[X234]: 103.57/104.08 (X229( 103.57/104.08 X234) & 103.57/104.08 (![X235]: 103.57/104.08 (X229( 103.57/104.08 X235) => 103.57/104.08 (X234 = 103.57/104.08 X235))))) => 103.57/104.08 (descr( 103.57/104.08 '#ll_0'( 103.57/104.08 X228)) = 103.57/104.08 descr( 103.57/104.08 '#ll_0'( 103.57/104.08 X229))))))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X236, 103.57/104.08 X237]: 103.57/104.08 (( 103.57/104.08 X236 = 103.57/104.08 X237) => 103.57/104.08 (![X238:( 103.57/104.08 $i > $o), 103.57/104.08 X239:( 103.57/104.08 $i > $o)]: 103.57/104.08 (( 103.57/104.08 ![X240]: 103.57/104.08 (in( 103.57/104.08 X240,X236) => 103.57/104.08 (![X241]: 103.57/104.08 (in( 103.57/104.08 X241,X237) => 103.57/104.08 (( 103.57/104.08 X240 = 103.57/104.08 X241) => 103.57/104.08 (X238( 103.57/104.08 X240) <=> 103.57/104.08 X239( 103.57/104.08 X241))))))) => 103.57/104.08 (dsetconstr( 103.57/104.08 X236, 103.57/104.08 '#ll_0'( 103.57/104.08 X238)) = 103.57/104.08 dsetconstr( 103.57/104.08 X237, 103.57/104.08 '#ll_0'( 103.57/104.08 X239))))))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X242, 103.57/104.08 X243]: 103.57/104.08 (( 103.57/104.08 ![X244]: 103.57/104.08 (in( 103.57/104.08 X244,X242) => 103.57/104.08 in( 103.57/104.08 X244,X243))) => 103.57/104.08 subset( 103.57/104.08 X242,X243))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X245, 103.57/104.08 X246]: 103.57/104.08 (( 103.57/104.08 X245 = 103.57/104.08 X246) => 103.57/104.08 subset( 103.57/104.08 X246,X245))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X247, 103.57/104.08 X248]: 103.57/104.08 (( 103.57/104.08 X247 = 103.57/104.08 X248) => 103.57/104.08 subset( 103.57/104.08 X247,X248))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X249, 103.57/104.08 X250]: 103.57/104.08 (( 103.57/104.08 ![X251]: 103.57/104.08 (in( 103.57/104.08 X251,X249) => 103.57/104.08 in( 103.57/104.08 X251,X250))) => 103.57/104.08 subset( 103.57/104.08 X249,X250))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X252]: 103.57/104.08 subset( 103.57/104.08 emptyset, 103.57/104.08 X252)) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X253, 103.57/104.08 X254,X255]: 103.57/104.08 (subset( 103.57/104.08 X253,X254) => 103.57/104.08 (in( 103.57/104.08 X255,X253) => 103.57/104.08 in( 103.57/104.08 X255,X254)))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X256, 103.57/104.08 X257,X258]: 103.57/104.08 (subset( 103.57/104.08 X256,X257) => 103.57/104.08 (( 103.57/104.08 ~ 103.57/104.08 in( 103.57/104.08 X258,X257)) => 103.57/104.08 (~ 103.57/104.08 in( 103.57/104.08 X258,X256))))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X259, 103.57/104.08 X260,X261]: 103.57/104.08 (in( 103.57/104.08 X261,X259) => 103.57/104.08 (( 103.57/104.08 ~ 103.57/104.08 in( 103.57/104.08 X261,X260)) => 103.57/104.08 (~ 103.57/104.08 subset( 103.57/104.08 X259,X260))))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X262, 103.57/104.08 X263]: 103.57/104.08 (( 103.57/104.08 ~ 103.57/104.08 subset( 103.57/104.08 X262,X263)) => 103.57/104.08 (X262 != 103.57/104.08 X263))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X264, 103.57/104.08 X265,X266]: 103.57/104.08 (in( 103.57/104.08 X266,X264) => 103.57/104.08 (( 103.57/104.08 ~ 103.57/104.08 in( 103.57/104.08 X266,X265)) => 103.57/104.08 (X264 != 103.57/104.08 X265)))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X267]: 103.57/104.08 subset( 103.57/104.08 X267,X267)) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X268, 103.57/104.08 X269,X270]: 103.57/104.08 (subset( 103.57/104.08 X268,X269) => 103.57/104.08 (subset( 103.57/104.08 X269,X270) => 103.57/104.08 subset( 103.57/104.08 X268,X270)))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X271, 103.57/104.08 X272]: 103.57/104.08 subset( 103.57/104.08 X272, 103.57/104.08 setadjoin( 103.57/104.08 X271,X272))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X273, 103.57/104.08 X274,X275]: 103.57/104.08 (subset( 103.57/104.08 X273,X275) => 103.57/104.08 subset( 103.57/104.08 X273, 103.57/104.08 setadjoin( 103.57/104.08 X274,X275)))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X276, 103.57/104.08 X277]: 103.57/104.08 (subset( 103.57/104.08 X276,X277) => 103.57/104.08 in( 103.57/104.08 X276, 103.57/104.08 powerset( 103.57/104.08 X277)))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X278, 103.57/104.08 X279]: 103.57/104.08 (subset( 103.57/104.08 X278,X279) => 103.57/104.08 (subset( 103.57/104.08 X279,X278) => 103.57/104.08 (X278 = 103.57/104.08 X279)))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X280]: 103.57/104.08 (subset( 103.57/104.08 X280, 103.57/104.08 emptyset) => 103.57/104.08 (X280 = 103.57/104.08 emptyset))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X281, 103.57/104.08 X282]: 103.57/104.08 (subset( 103.57/104.08 X282,X281) => 103.57/104.08 in( 103.57/104.08 X282, 103.57/104.08 powerset( 103.57/104.08 X281)))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X283, 103.57/104.08 X284]: 103.57/104.08 (in( 103.57/104.08 X284, 103.57/104.08 powerset( 103.57/104.08 X283)) => 103.57/104.08 subset( 103.57/104.08 X284,X283))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X285]: 103.57/104.08 in( 103.57/104.08 X285, 103.57/104.08 powerset( 103.57/104.08 X285))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X286, 103.57/104.08 X287]: 103.57/104.08 (subset( 103.57/104.08 X286,X287) => 103.57/104.08 subset( 103.57/104.08 powerset( 103.57/104.08 X286), 103.57/104.08 powerset( 103.57/104.08 X287)))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X288, 103.57/104.08 X289:( 103.57/104.08 $i > $o)]: 103.57/104.08 in( 103.57/104.08 dsetconstr( 103.57/104.08 X288, 103.57/104.08 '#ll_0'( 103.57/104.08 X289)), 103.57/104.08 powerset( 103.57/104.08 X288))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X290, 103.57/104.08 X291:( 103.57/104.08 $i > $o)]: 103.57/104.08 subset( 103.57/104.08 dsetconstr( 103.57/104.08 X290, 103.57/104.08 '#ll_0'( 103.57/104.08 X291)), 103.57/104.08 X290)) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X292, 103.57/104.08 X293,X294]: 103.57/104.08 (in( 103.57/104.08 X294,X292) => 103.57/104.08 in( 103.57/104.08 X294, 103.57/104.08 binunion( 103.57/104.08 X292,X293)))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X295, 103.57/104.08 X296]: 103.57/104.08 in( 103.57/104.08 X296, 103.57/104.08 setadjoin( 103.57/104.08 X295, 103.57/104.08 setadjoin( 103.57/104.08 X296, 103.57/104.08 emptyset)))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X297, 103.57/104.08 X298,X299]: 103.57/104.08 (in( 103.57/104.08 X299,X298) => 103.57/104.08 in( 103.57/104.08 X299, 103.57/104.08 binunion( 103.57/104.08 X297,X298)))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X300, 103.57/104.08 X301, 103.57/104.08 X302, 103.57/104.08 X303:$o]: 103.57/104.08 (in( 103.57/104.08 X302, 103.57/104.08 binunion( 103.57/104.08 X300,X301)) => 103.57/104.08 (( 103.57/104.08 in( 103.57/104.08 X302,X300) => 103.57/104.08 X303) => 103.57/104.08 (( 103.57/104.08 in( 103.57/104.08 X302,X301) => 103.57/104.08 X303) => 103.57/104.08 X303)))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X304, 103.57/104.08 X305,X306]: 103.57/104.08 (in( 103.57/104.08 X306, 103.57/104.08 binunion( 103.57/104.08 X304,X305)) => 103.57/104.08 (in( 103.57/104.08 X306,X304) | 103.57/104.08 in( 103.57/104.08 X306,X305)))) => 103.57/104.08 ( 103.57/104.08 ![X307, 103.57/104.08 X308]: 103.57/104.08 subset( 103.57/104.08 X307, 103.57/104.08 binunion( 103.57/104.08 X307,X308))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 103.57/104.08 tff(zf_stmt_1, type, zip_tseitin5 : ($i * $i > $o) > $o). 103.57/104.08 tff(zf_stmt_2, axiom, 103.57/104.08 (zip_tseitin5(X211,X207) <=> 103.57/104.08 ((![X212]: zip_tseitin4(X212,X211,X207)) & X207(X211)))). 103.57/104.08 tff(zf_stmt_3, type, zip_tseitin4 : ($i * $i * $i > $o) > $o). 103.57/104.08 tff(zf_stmt_4, axiom, 103.57/104.08 (zip_tseitin4(X212,X211,X207) <=> (X207(X212) => (X211 = X212)))). 103.57/104.08 tff(zf_stmt_5, type, zip_tseitin3 : ($i * $i * $i * ($i * $i) > $o) > $o). 103.57/104.08 tff(zf_stmt_6, axiom, 103.57/104.08 (zip_tseitin3(X26,X25,X20,X19) <=> (X19(X26,X25) & in(X26,X20)))). 103.57/104.08 tff(zf_stmt_7, type, zip_tseitin2 : ($i * $i * $i) > $o). 103.57/104.08 tff(zf_stmt_8, axiom, 103.57/104.08 (zip_tseitin2(X14,X13,X12) <=> (in(X14,X12) & in(X13,X14)))). 103.57/104.08 tff(zf_stmt_9, type, zip_tseitin1 : ($i * $i * $i) > $o). 103.57/104.08 tff(zf_stmt_10, axiom, 103.57/104.08 (zip_tseitin1(X11,X10,X9) <=> (in(X11,X10) => in(X11,X9)))). 103.57/104.08 tff(zf_stmt_11, type, zip_tseitin0 : ($i * $i * $i) > $o). 103.57/104.08 tff(zf_stmt_12, axiom, (zip_tseitin0(X8,X7,X6) <=> (in(X8,X7) | (X8 = X6)))). 103.57/104.08 tff(zf_stmt_13, conjecture, 103.57/104.08 ((![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))) => 103.57/104.08 ((![X5]: (~in(X5,emptyset))) => 103.57/104.08 ((![X6,X7,X8]: (in(X8,setadjoin(X6,X7)) <=> zip_tseitin0(X8,X7,X6))) => 103.57/104.08 ((![X9,X10]: 103.57/104.08 (in(X10,powerset(X9)) <=> (![X11]: zip_tseitin1(X11,X10,X9)))) => 103.57/104.08 ((![X12,X13]: 103.57/104.08 (in(X13,setunion(X12)) <=> (?[X14]: zip_tseitin2(X14,X13,X12)))) => 103.57/104.08 (in(emptyset,omega) => 103.57/104.08 ((![X15]: (in(X15,omega) => in(setadjoin(X15,X15),omega))) => 103.57/104.08 ((![X16]: 103.57/104.08 (((![X17]: 103.57/104.08 ((in(X17,X16) & in(X17,omega)) => 103.57/104.08 in(setadjoin(X17,X17),X16))) & 103.57/104.08 in(emptyset,X16)) => 103.57/104.08 (![X18]: (in(X18,omega) => in(X18,X16))))) => 103.57/104.08 ((![X19:(($i * $i) > $o),X20]: 103.57/104.08 ((![X21]: 103.57/104.08 (in(X21,X20) => 103.57/104.08 (?[X22]: 103.57/104.08 ((![X23]: (X19(X21,X23) => (X22 = X23))) & X19(X21,X22))))) => 103.57/104.08 (?[X24]: 103.57/104.08 (![X25]: 103.57/104.08 (in(X25,X24) <=> (?[X26]: zip_tseitin3(X26,X25,X20,X19))))))) => 103.57/104.08 ((![X27]: 103.57/104.08 ((?[X28]: in(X28,X27)) => 103.57/104.08 (?[X29]: 103.57/104.08 ((~(?[X30]: (in(X30,X27) & in(X30,X29)))) & in(X29,X27))))) => 103.57/104.08 ((![X31]: 103.57/104.08 (?[X32]: 103.57/104.08 ((![X33]: 103.57/104.08 (((?[X34]: in(X34,X33)) & 103.57/104.08 (![X35]: (in(X35,X33) => in(X35,X31)))) => 103.57/104.08 (?[X36,X37]: 103.57/104.08 ((![X38]: 103.57/104.08 (in(X38,X32) => 103.57/104.08 (in(X37,X38) | 103.57/104.08 (![X39]: (in(X39,X38) => in(X39,X36)))))) & 103.57/104.08 (~(?[X40]: (in(X40,X33) & in(X40,X36)))) & 103.57/104.08 in(X37,X33) & in(X36,X32))))) & 103.57/104.08 (![X41,X42]: 103.57/104.08 ((in(X42,X32) & in(X41,X32)) => 103.57/104.08 ((![X43]: (in(X43,X42) => in(X43,X41))) | 103.57/104.08 (![X44]: (in(X44,X41) => in(X44,X42)))))) & 103.57/104.08 (![X45,X46]: 103.57/104.08 ((in(X46,X31) & in(X45,X31)) => 103.57/104.08 ((![X47]: 103.57/104.08 (in(X47,X32) => (in(X45,X47) <=> in(X46,X47)))) => 103.57/104.08 (X45 = X46)))) & 103.57/104.08 (![X48]: 103.57/104.08 (in(X48,X32) => (![X49]: (in(X49,X48) => in(X49,X31)))))))) => 103.57/104.08 ((![X50:($i > $o)]: 103.57/104.08 ((?[X51]: ((![X52]: (X50(X52) => (X51 = X52))) & X50(X51))) => 103.57/104.08 X50(descr('#ll_0'(X50))))) => 103.57/104.08 ((![X53,X54:($i > $o),X55]: 103.57/104.08 (in(X55,X53) => 103.57/104.08 (X54(X55) => in(X55,dsetconstr(X53,'#ll_0'(X54)))))) => 103.57/104.08 ((![X56,X57:($i > $o),X58]: 103.57/104.08 (in(X58,dsetconstr(X56,'#ll_0'(X57))) => in(X58,X56))) => 103.57/104.08 ((![X59,X60:($i > $o),X61]: 103.57/104.08 (in(X61,dsetconstr(X59,'#ll_0'(X60))) => X60(X61))) => 103.57/104.08 ((![X62:($i > $o)]: 103.57/104.08 ((?[X63]: 103.57/104.08 ((![X64]: (X62(X64) => (X63 = X64))) & X62(X63))) => 103.57/104.08 (?[X65]: 103.57/104.08 ((![X66]: (X62(X66) => (X65 = X66))) & X62(X65))))) => 103.57/104.08 ((![X67:$o,X68]: (in(X68,prop2set(X67)) => X67)) => 103.57/104.08 ((![X69]: (in(X69,emptyset) => (![X70:$o]: X70))) => 103.57/104.08 ((![X71]: (in(X71,emptyset) => $false)) => 103.57/104.08 ((![X72]: (~in(X72,emptyset))) => 103.57/104.08 ((![X73:($i > $o)]: 103.57/104.08 ((?[X74]: 103.57/104.08 ((![X75]: (X73(X75) => (X74 = X75))) & X73(X74))) => 103.57/104.08 (?[X76]: X73(X76)))) => 103.57/104.08 ((![X77,X78]: 103.57/104.08 ((![X79]: (in(X79,X77) => in(X79,X78))) => 103.57/104.08 ((![X80]: (in(X80,X78) => in(X80,X77))) => 103.57/104.08 (X77 = X78)))) => 103.57/104.08 ((![X81]: 103.57/104.08 ((![X82]: (~in(X82,X81))) => (X81 = emptyset))) => 103.57/104.08 ((![X83]: 103.57/104.08 ((![X84]: (~in(X84,X83))) => (X83 = emptyset))) => 103.57/104.08 ((![X85,X86:($i > $o),X87]: 103.57/104.08 (in(X87,X85) => 103.57/104.08 (in(X87,dsetconstr(X85,'#ll_0'(X86))) <=> 103.57/104.08 X86(X87)))) => 103.57/104.08 ((![X88]: 103.57/104.08 ((X88 != emptyset) => (?[X89]: in(X89,X88)))) => 103.57/104.08 ((![X90,X91:($i > $o),X92]: 103.57/104.08 (in(X92,X90) => 103.57/104.08 (X91(X92) => 103.57/104.08 (dsetconstr(X90,'#ll_0'(X91)) != emptyset)))) => 103.57/104.08 ((![X93]: 103.57/104.08 ((?[X94]: in(X94,X93)) => (X93 != emptyset))) => 103.57/104.08 ((![X95,X96]: in(X95,setadjoin(X95,X96))) => 103.57/104.08 (in(emptyset,setadjoin(emptyset,emptyset)) => 103.57/104.08 ((![X97,X98,X99]: 103.57/104.08 (in(X99,X98) => 103.57/104.08 in(X99,setadjoin(X97,X98)))) => 103.57/104.08 ((![X100,X101,X102]: 103.57/104.08 (in(X102,setadjoin(X100,X101)) => 103.57/104.08 (![X103:$o]: 103.57/104.08 (((X102 = X100) => X103) => 103.57/104.08 ((in(X102,X101) => X103) => X103))))) => 103.57/104.08 ((![X104,X105,X106]: 103.57/104.08 (in(X106,setadjoin(X104,X105)) => 103.57/104.08 (in(X106,X105) | (X106 = X104)))) => 103.57/104.08 ((![X107]: 103.57/104.08 (dsetconstr(X107,'#ll_1') = X107)) => 103.57/104.08 ((![X108,X109]: 103.57/104.08 ((![X110]: 103.57/104.08 (in(X110,X109) => in(X110,X108))) => 103.57/104.08 in(X109,powerset(X108)))) => 103.57/104.08 ((![X111]: in(emptyset,powerset(X111))) => 103.57/104.08 ((![X112]: in(emptyset,powerset(X112))) => 103.57/104.08 ((![X113,X114,X115]: 103.57/104.08 (in(X114,powerset(X113)) => 103.57/104.08 (in(X115,X114) => in(X115,X113)))) => 103.57/104.08 ((![X116,X117,X118]: 103.57/104.08 (in(X117,X118) => 103.57/104.08 (in(X118,X116) => 103.57/104.08 in(X117,setunion(X116))))) => 103.57/104.08 ((![X119,X120]: 103.57/104.08 (in(X120,setunion(X119)) => 103.57/104.08 (![X121:$o]: 103.57/104.08 ((![X122]: 103.57/104.08 (in(X120,X122) => 103.57/104.08 (in(X122,X119) => X121))) => 103.57/104.08 X121)))) => 103.57/104.08 ((![X123,X124]: 103.57/104.08 (in(X124,X123) => 103.57/104.08 in(X124, 103.57/104.08 powerset(setunion(X123))))) => 103.57/104.08 ((![X125:($i > $o)]: 103.57/104.08 ((?[X126]: 103.57/104.08 ((![X127]: 103.57/104.08 (X125(X127) => 103.57/104.08 (X126 = X127))) & 103.57/104.08 X125(X126))) => 103.57/104.08 (?[X128]: 103.57/104.08 (![X129]: 103.57/104.08 (X125(X129) <=> 103.57/104.08 (X129 = X128)))))) => 103.57/104.08 ((![X130]: 103.57/104.08 ((X130 != emptyset) => 103.57/104.08 (?[X131]: in(X131,X130)))) => 103.57/104.08 ((![X132,X133]: 103.57/104.08 (in(X132, 103.57/104.08 setadjoin(X133,emptyset)) => 103.57/104.08 (X132 = X133))) => 103.57/104.08 ((![X134,X135]: 103.57/104.08 ((X134 != X135) => 103.57/104.08 (~ 103.57/104.08 in(X135, 103.57/104.08 setadjoin(X134, 103.57/104.08 emptyset))))) => 103.57/104.08 ((![X136,X137]: 103.57/104.08 ((X136 = X137) => 103.57/104.08 in(X136, 103.57/104.08 setadjoin(X137, 103.57/104.08 emptyset)))) => 103.57/104.08 ((![X138,X139]: 103.57/104.08 (in(X138, 103.57/104.08 setadjoin(X139, 103.57/104.08 emptyset)) => 103.57/104.08 in(X139, 103.57/104.08 setadjoin(X138, 103.57/104.08 emptyset)))) => 103.57/104.08 ((![X140,X141,X142]: 103.57/104.08 (in(X142, 103.57/104.08 setadjoin(X140, 103.57/104.08 setadjoin( 103.57/104.08 X141, 103.57/104.08 emptyset))) => 103.57/104.08 ((X142 = X141) | 103.57/104.08 (X142 = X140)))) => 103.57/104.08 ((![X143,X144]: 103.57/104.08 in(X143, 103.57/104.08 setadjoin(X143, 103.57/104.08 setadjoin( 103.57/104.08 X144, 103.57/104.08 emptyset)))) => 103.57/104.08 ((![X145,X146]: 103.57/104.08 in(X146, 103.57/104.08 setadjoin(X145, 103.57/104.08 setadjoin( 103.57/104.08 X146, 103.57/104.08 emptyset)))) => 103.57/104.08 ((![X147,X148:($i > $o)]: 103.57/104.08 ((?[X149]: 103.57/104.08 (X148(X149) & 103.57/104.08 in(X149,X147))) => 103.57/104.08 ((dsetconstr( 103.57/104.08 X147,'#ll_0'(X148)) = 103.57/104.08 emptyset) => 103.57/104.08 $false))) => 103.57/104.08 ((![X150:($i > $o),X151]: 103.57/104.08 (in(X151,emptyset) => 103.57/104.08 X150(X151))) => 103.57/104.08 ((![X152,X153:($i > $o)]: 103.57/104.08 ((~ 103.57/104.08 (![X154]: 103.57/104.08 (in(X154,X152) => 103.57/104.08 X153(X154)))) => 103.57/104.08 (?[X155]: 103.57/104.08 ((~X153(X155)) & 103.57/104.08 in(X155,X152))))) => 103.57/104.08 ((![X156, 103.57/104.08 X157:($i > $o)]: 103.57/104.08 ((![X158]: 103.57/104.08 (in(X158,X156) => 103.57/104.08 (~X157(X158)))) => 103.57/104.08 (~ 103.57/104.08 (?[X159]: 103.57/104.08 (X157(X159) & 103.57/104.08 in( 103.57/104.08 X159,X156)))))) => 103.57/104.08 ((![X160, 103.57/104.08 X161:($i > $o)]: 103.57/104.08 ((~ 103.57/104.08 (?[X162]: 103.57/104.08 (X161(X162) & 103.57/104.08 in( 103.57/104.08 X162,X160)))) => 103.57/104.08 (![X163]: 103.57/104.08 (in(X163,X160) => 103.57/104.08 (~X161(X163)))))) => 103.57/104.08 ((![X164, 103.57/104.08 X165:($i > $o)]: 103.57/104.08 ((?[X166]: 103.57/104.08 ((~ 103.57/104.08 X165( 103.57/104.08 X166)) & 103.57/104.08 in( 103.57/104.08 X166,X164))) => 103.57/104.08 (~ 103.57/104.08 (![X167]: 103.57/104.08 (in( 103.57/104.08 X167,X164) => 103.57/104.08 X165( 103.57/104.08 X167)))))) => 103.57/104.08 ((![X168:$o]: 103.57/104.08 (X168 => 103.57/104.08 in(emptyset, 103.57/104.08 prop2set( 103.57/104.08 X168)))) => 103.57/104.08 ((![X169:$o]: 103.57/104.08 (X169 => 103.57/104.08 set2prop( 103.57/104.08 prop2set( 103.57/104.08 X169)))) => 103.57/104.08 ((![X170, 103.57/104.08 X171:( 103.57/104.08 $i > $o)]: 103.57/104.08 ((~ 103.57/104.08 (?[X172]: 103.57/104.08 (X171( 103.57/104.08 X172) & 103.57/104.08 in( 103.57/104.08 X172,X170)))) => 103.57/104.08 (![X173]: 103.57/104.08 ( 103.57/104.08 in( 103.57/104.08 X173,X170) => 103.57/104.08 ( 103.57/104.08 ~ 103.57/104.08 X171( 103.57/104.08 X173)))))) => 103.57/104.08 ((![X174, 103.57/104.08 X175:( 103.57/104.08 $i > $o)]: 103.57/104.08 ((~ 103.57/104.08 ( 103.57/104.08 ![X176]: 103.57/104.08 (in( 103.57/104.08 X176,X174) => 103.57/104.08 X175( 103.57/104.08 X176)))) => 103.57/104.08 (?[X177]: 103.57/104.08 (( 103.57/104.08 ~ 103.57/104.08 X175( 103.57/104.08 X177)) & 103.57/104.08 in( 103.57/104.08 X177,X174))))) => 103.57/104.08 ((![X178:( 103.57/104.08 $i > $o)]: 103.57/104.08 ((?[X179]: 103.57/104.08 (( 103.57/104.08 ![X180]: 103.57/104.08 (X178( 103.57/104.08 X180) => 103.57/104.08 (X179 = 103.57/104.08 X180))) & 103.57/104.08 X178( 103.57/104.08 X179))) => 103.57/104.08 (?[X181]: 103.57/104.08 (( 103.57/104.08 ![X182]: 103.57/104.08 (X178( 103.57/104.08 X182) => 103.57/104.08 (X181 = 103.57/104.08 X182))) & 103.57/104.08 X178( 103.57/104.08 X181))))) => 103.57/104.08 ((![X183:( 103.57/104.08 $i > $o)]: 103.57/104.08 (( 103.57/104.08 ?[X184]: 103.57/104.08 X183( 103.57/104.08 X184)) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X185, 103.57/104.08 X186]: 103.57/104.08 (X183( 103.57/104.08 X185) => 103.57/104.08 (X183( 103.57/104.08 X186) => 103.57/104.08 (X185 = 103.57/104.08 X186)))) => 103.57/104.08 ( 103.57/104.08 ?[X187]: 103.57/104.08 (( 103.57/104.08 ![X188]: 103.57/104.08 (X183( 103.57/104.08 X188) => 103.57/104.08 (X187 = 103.57/104.08 X188))) & 103.57/104.08 X183( 103.57/104.08 X187)))))) => 103.57/104.08 ((![X189:( 103.57/104.08 $i > $o)]: 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ?[X190]: 103.57/104.08 (![X191]: 103.57/104.08 (X189( 103.57/104.08 X191) <=> 103.57/104.08 (X191 = 103.57/104.08 X190)))) => 103.57/104.08 ( 103.57/104.08 ?[X192]: 103.57/104.08 (( 103.57/104.08 ![X193]: 103.57/104.08 (X189( 103.57/104.08 X193) => 103.57/104.08 (X192 = 103.57/104.08 X193))) & 103.57/104.08 X189( 103.57/104.08 X192))))) => 103.57/104.08 ((![X194, 103.57/104.08 X195]: 103.57/104.08 (( 103.57/104.08 X194 = 103.57/104.08 X195) => 103.57/104.08 (![X196, 103.57/104.08 X197]: 103.57/104.08 (( 103.57/104.08 X196 = 103.57/104.08 X197) => 103.57/104.08 (in( 103.57/104.08 X196,X194) => 103.57/104.08 in( 103.57/104.08 X197,X195)))))) => 103.57/104.08 ((![X198, 103.57/104.08 X199]: 103.57/104.08 (( 103.57/104.08 X198 = 103.57/104.08 X199) => 103.57/104.08 (![X200, 103.57/104.08 X201]: 103.57/104.08 (( 103.57/104.08 X200 = 103.57/104.08 X201) => 103.57/104.08 (in( 103.57/104.08 X200,X198) <=> 103.57/104.08 in( 103.57/104.08 X201,X199)))))) => 103.57/104.08 (( 103.57/104.08 ![X202:( 103.57/104.08 $i > $o)]: 103.57/104.08 (( 103.57/104.08 ?[X203]: 103.57/104.08 (( 103.57/104.08 ![X204]: 103.57/104.08 (X202( 103.57/104.08 X204) => 103.57/104.08 (X203 = 103.57/104.08 X204))) & 103.57/104.08 X202( 103.57/104.08 X203))) => 103.57/104.08 (![X205, 103.57/104.08 X206]: 103.57/104.08 (X202( 103.57/104.08 X205) => 103.57/104.08 (X202( 103.57/104.08 X206) => 103.57/104.08 (X205 = 103.57/104.08 X206)))))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X207:( 103.57/104.08 $i > $o), 103.57/104.08 X208:( 103.57/104.08 $i > $o)]: 103.57/104.08 (( 103.57/104.08 ![X209, 103.57/104.08 X210]: 103.57/104.08 (( 103.57/104.08 X209 = 103.57/104.08 X210) => 103.57/104.08 (X207( 103.57/104.08 X209) <=> 103.57/104.08 X208( 103.57/104.08 X210)))) => 103.57/104.08 (( 103.57/104.08 ?[X211]: 103.57/104.08 zip_tseitin5( 103.57/104.08 X211,X207)) <=> 103.57/104.08 (?[X213]: 103.57/104.08 zip_tseitin5( 103.57/104.08 X213,X208))))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 emptyset = 103.57/104.08 emptyset) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X215, 103.57/104.08 X216]: 103.57/104.08 (( 103.57/104.08 X215 = 103.57/104.08 X216) => 103.57/104.08 (![X217, 103.57/104.08 X218]: 103.57/104.08 (( 103.57/104.08 X217 = 103.57/104.08 X218) => 103.57/104.08 (setadjoin( 103.57/104.08 X215,X217) = 103.57/104.08 setadjoin( 103.57/104.08 X216,X218)))))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X219, 103.57/104.08 X220]: 103.57/104.08 (( 103.57/104.08 X219 = 103.57/104.08 X220) => 103.57/104.08 (powerset( 103.57/104.08 X219) = 103.57/104.08 powerset( 103.57/104.08 X220)))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X221, 103.57/104.08 X222]: 103.57/104.08 (( 103.57/104.08 X221 = 103.57/104.08 X222) => 103.57/104.08 (setunion( 103.57/104.08 X221) = 103.57/104.08 setunion( 103.57/104.08 X222)))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 omega = 103.57/104.08 omega) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X223:( 103.57/104.08 $i > $o)]: 103.57/104.08 (( 103.57/104.08 ?[X224]: 103.57/104.08 (( 103.57/104.08 ![X225]: 103.57/104.08 (X223( 103.57/104.08 X225) => 103.57/104.08 (X224 = 103.57/104.08 X225))) & 103.57/104.08 X223( 103.57/104.08 X224))) => 103.57/104.08 (![X226, 103.57/104.08 X227]: 103.57/104.08 (X223( 103.57/104.08 X226) => 103.57/104.08 (X223( 103.57/104.08 X227) => 103.57/104.08 (X226 = 103.57/104.08 X227)))))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X228:( 103.57/104.08 $i > $o), 103.57/104.08 X229:( 103.57/104.08 $i > $o)]: 103.57/104.08 (( 103.57/104.08 ![X230, 103.57/104.08 X231]: 103.57/104.08 (( 103.57/104.08 X230 = 103.57/104.08 X231) => 103.57/104.08 (X228( 103.57/104.08 X230) <=> 103.57/104.08 X229( 103.57/104.08 X231)))) => 103.57/104.08 (( 103.57/104.08 ?[X232]: 103.57/104.08 (( 103.57/104.08 ![X233]: 103.57/104.08 (X228( 103.57/104.08 X233) => 103.57/104.08 (X232 = 103.57/104.08 X233))) & 103.57/104.08 X228( 103.57/104.08 X232))) => 103.57/104.08 (( 103.57/104.08 ?[X234]: 103.57/104.08 (( 103.57/104.08 ![X235]: 103.57/104.08 (X229( 103.57/104.08 X235) => 103.57/104.08 (X234 = 103.57/104.08 X235))) & 103.57/104.08 X229( 103.57/104.08 X234))) => 103.57/104.08 (descr( 103.57/104.08 '#ll_0'( 103.57/104.08 X228)) = 103.57/104.08 descr( 103.57/104.08 '#ll_0'( 103.57/104.08 X229))))))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X236, 103.57/104.08 X237]: 103.57/104.08 (( 103.57/104.08 X236 = 103.57/104.08 X237) => 103.57/104.08 (![X238:( 103.57/104.08 $i > $o), 103.57/104.08 X239:( 103.57/104.08 $i > $o)]: 103.57/104.08 (( 103.57/104.08 ![X240]: 103.57/104.08 (in( 103.57/104.08 X240,X236) => 103.57/104.08 (![X241]: 103.57/104.08 (in( 103.57/104.08 X241,X237) => 103.57/104.08 (( 103.57/104.08 X240 = 103.57/104.08 X241) => 103.57/104.08 (X238( 103.57/104.08 X240) <=> 103.57/104.08 X239( 103.57/104.08 X241))))))) => 103.57/104.08 (dsetconstr( 103.57/104.08 X236, 103.57/104.08 '#ll_0'( 103.57/104.08 X238)) = 103.57/104.08 dsetconstr( 103.57/104.08 X237, 103.57/104.08 '#ll_0'( 103.57/104.08 X239))))))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X242, 103.57/104.08 X243]: 103.57/104.08 (( 103.57/104.08 ![X244]: 103.57/104.08 (in( 103.57/104.08 X244,X242) => 103.57/104.08 in( 103.57/104.08 X244,X243))) => 103.57/104.08 subset( 103.57/104.08 X242,X243))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X245, 103.57/104.08 X246]: 103.57/104.08 (( 103.57/104.08 X245 = 103.57/104.08 X246) => 103.57/104.08 subset( 103.57/104.08 X246,X245))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X247, 103.57/104.08 X248]: 103.57/104.08 (( 103.57/104.08 X247 = 103.57/104.08 X248) => 103.57/104.08 subset( 103.57/104.08 X247,X248))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X249, 103.57/104.08 X250]: 103.57/104.08 (( 103.57/104.08 ![X251]: 103.57/104.08 (in( 103.57/104.08 X251,X249) => 103.57/104.08 in( 103.57/104.08 X251,X250))) => 103.57/104.08 subset( 103.57/104.08 X249,X250))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X252]: 103.57/104.08 subset( 103.57/104.08 emptyset, 103.57/104.08 X252)) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X253, 103.57/104.08 X254,X255]: 103.57/104.08 (subset( 103.57/104.08 X253,X254) => 103.57/104.08 (in( 103.57/104.08 X255,X253) => 103.57/104.08 in( 103.57/104.08 X255,X254)))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X256, 103.57/104.08 X257,X258]: 103.57/104.08 (subset( 103.57/104.08 X256,X257) => 103.57/104.08 (( 103.57/104.08 ~ 103.57/104.08 in( 103.57/104.08 X258,X257)) => 103.57/104.08 (~ 103.57/104.08 in( 103.57/104.08 X258,X256))))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X259, 103.57/104.08 X260,X261]: 103.57/104.08 (in( 103.57/104.08 X261,X259) => 103.57/104.08 (( 103.57/104.08 ~ 103.57/104.08 in( 103.57/104.08 X261,X260)) => 103.57/104.08 (~ 103.57/104.08 subset( 103.57/104.08 X259,X260))))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X262, 103.57/104.08 X263]: 103.57/104.08 (( 103.57/104.08 ~ 103.57/104.08 subset( 103.57/104.08 X262,X263)) => 103.57/104.08 (X262 != 103.57/104.08 X263))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X264, 103.57/104.08 X265,X266]: 103.57/104.08 (in( 103.57/104.08 X266,X264) => 103.57/104.08 (( 103.57/104.08 ~ 103.57/104.08 in( 103.57/104.08 X266,X265)) => 103.57/104.08 (X264 != 103.57/104.08 X265)))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X267]: 103.57/104.08 subset( 103.57/104.08 X267,X267)) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X268, 103.57/104.08 X269,X270]: 103.57/104.08 (subset( 103.57/104.08 X268,X269) => 103.57/104.08 (subset( 103.57/104.08 X269,X270) => 103.57/104.08 subset( 103.57/104.08 X268,X270)))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X271, 103.57/104.08 X272]: 103.57/104.08 subset( 103.57/104.08 X272, 103.57/104.08 setadjoin( 103.57/104.08 X271,X272))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X273, 103.57/104.08 X274,X275]: 103.57/104.08 (subset( 103.57/104.08 X273,X275) => 103.57/104.08 subset( 103.57/104.08 X273, 103.57/104.08 setadjoin( 103.57/104.08 X274,X275)))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X276, 103.57/104.08 X277]: 103.57/104.08 (subset( 103.57/104.08 X276,X277) => 103.57/104.08 in( 103.57/104.08 X276, 103.57/104.08 powerset( 103.57/104.08 X277)))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X278, 103.57/104.08 X279]: 103.57/104.08 (subset( 103.57/104.08 X278,X279) => 103.57/104.08 (subset( 103.57/104.08 X279,X278) => 103.57/104.08 (X278 = 103.57/104.08 X279)))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X280]: 103.57/104.08 (subset( 103.57/104.08 X280, 103.57/104.08 emptyset) => 103.57/104.08 (X280 = 103.57/104.08 emptyset))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X281, 103.57/104.08 X282]: 103.57/104.08 (subset( 103.57/104.08 X282,X281) => 103.57/104.08 in( 103.57/104.08 X282, 103.57/104.08 powerset( 103.57/104.08 X281)))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X283, 103.57/104.08 X284]: 103.57/104.08 (in( 103.57/104.08 X284, 103.57/104.08 powerset( 103.57/104.08 X283)) => 103.57/104.08 subset( 103.57/104.08 X284,X283))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X285]: 103.57/104.08 in( 103.57/104.08 X285, 103.57/104.08 powerset( 103.57/104.08 X285))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X286, 103.57/104.08 X287]: 103.57/104.08 (subset( 103.57/104.08 X286,X287) => 103.57/104.08 subset( 103.57/104.08 powerset( 103.57/104.08 X286), 103.57/104.08 powerset( 103.57/104.08 X287)))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X288, 103.57/104.08 X289:( 103.57/104.08 $i > $o)]: 103.57/104.08 in( 103.57/104.08 dsetconstr( 103.57/104.08 X288, 103.57/104.08 '#ll_0'( 103.57/104.08 X289)), 103.57/104.08 powerset( 103.57/104.08 X288))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X290, 103.57/104.08 X291:( 103.57/104.08 $i > $o)]: 103.57/104.08 subset( 103.57/104.08 dsetconstr( 103.57/104.08 X290, 103.57/104.08 '#ll_0'( 103.57/104.08 X291)), 103.57/104.08 X290)) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X292, 103.57/104.08 X293,X294]: 103.57/104.08 (in( 103.57/104.08 X294,X292) => 103.57/104.08 in( 103.57/104.08 X294, 103.57/104.08 binunion( 103.57/104.08 X292,X293)))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X295, 103.57/104.08 X296]: 103.57/104.08 in( 103.57/104.08 X296, 103.57/104.08 setadjoin( 103.57/104.08 X295, 103.57/104.08 setadjoin( 103.57/104.08 X296, 103.57/104.08 emptyset)))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X297, 103.57/104.08 X298,X299]: 103.57/104.08 (in( 103.57/104.08 X299,X298) => 103.57/104.08 in( 103.57/104.08 X299, 103.57/104.08 binunion( 103.57/104.08 X297,X298)))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X300, 103.57/104.08 X301, 103.57/104.08 X302, 103.57/104.08 X303:$o]: 103.57/104.08 (in( 103.57/104.08 X302, 103.57/104.08 binunion( 103.57/104.08 X300,X301)) => 103.57/104.08 (( 103.57/104.08 in( 103.57/104.08 X302,X300) => 103.57/104.08 X303) => 103.57/104.08 (( 103.57/104.08 in( 103.57/104.08 X302,X301) => 103.57/104.08 X303) => 103.57/104.08 X303)))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X304, 103.57/104.08 X305,X306]: 103.57/104.08 (in( 103.57/104.08 X306, 103.57/104.08 binunion( 103.57/104.08 X304,X305)) => 103.57/104.08 (in( 103.57/104.08 X306,X305) | 103.57/104.08 in( 103.57/104.08 X306,X304)))) => 103.57/104.08 ( 103.57/104.08 ![X307, 103.57/104.08 X308]: 103.57/104.08 subset( 103.57/104.08 X307, 103.57/104.08 binunion( 103.57/104.08 X307,X308))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 103.57/104.08 tff(zf_stmt_14, negated_conjecture, 103.57/104.08 (~ 103.57/104.08 ((![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))) => 103.57/104.08 ((![X5]: (~in(X5,emptyset))) => 103.57/104.08 ((![X6,X7,X8]: (in(X8,setadjoin(X6,X7)) <=> zip_tseitin0(X8,X7,X6))) => 103.57/104.08 ((![X9,X10]: 103.57/104.08 (in(X10,powerset(X9)) <=> (![X11]: zip_tseitin1(X11,X10,X9)))) => 103.57/104.08 ((![X12,X13]: 103.57/104.08 (in(X13,setunion(X12)) <=> (?[X14]: zip_tseitin2(X14,X13,X12)))) => 103.57/104.08 (in(emptyset,omega) => 103.57/104.08 ((![X15]: (in(X15,omega) => in(setadjoin(X15,X15),omega))) => 103.57/104.08 ((![X16]: 103.57/104.08 (((![X17]: 103.57/104.08 ((in(X17,X16) & in(X17,omega)) => 103.57/104.08 in(setadjoin(X17,X17),X16))) & 103.57/104.08 in(emptyset,X16)) => 103.57/104.08 (![X18]: (in(X18,omega) => in(X18,X16))))) => 103.57/104.08 ((![X19:(($i * $i) > $o),X20]: 103.57/104.08 ((![X21]: 103.57/104.08 (in(X21,X20) => 103.57/104.08 (?[X22]: 103.57/104.08 ((![X23]: (X19(X21,X23) => (X22 = X23))) & 103.57/104.08 X19(X21,X22))))) => 103.57/104.08 (?[X24]: 103.57/104.08 (![X25]: 103.57/104.08 (in(X25,X24) <=> 103.57/104.08 (?[X26]: zip_tseitin3(X26,X25,X20,X19))))))) => 103.57/104.08 ((![X27]: 103.57/104.08 ((?[X28]: in(X28,X27)) => 103.57/104.08 (?[X29]: 103.57/104.08 ((~(?[X30]: (in(X30,X27) & in(X30,X29)))) & in(X29,X27))))) => 103.57/104.08 ((![X31]: 103.57/104.08 (?[X32]: 103.57/104.08 ((![X33]: 103.57/104.08 (((?[X34]: in(X34,X33)) & 103.57/104.08 (![X35]: (in(X35,X33) => in(X35,X31)))) => 103.57/104.08 (?[X36,X37]: 103.57/104.08 ((![X38]: 103.57/104.08 (in(X38,X32) => 103.57/104.08 (in(X37,X38) | 103.57/104.08 (![X39]: (in(X39,X38) => in(X39,X36)))))) & 103.57/104.08 (~(?[X40]: (in(X40,X33) & in(X40,X36)))) & 103.57/104.08 in(X37,X33) & in(X36,X32))))) & 103.57/104.08 (![X41,X42]: 103.57/104.08 ((in(X42,X32) & in(X41,X32)) => 103.57/104.08 ((![X43]: (in(X43,X42) => in(X43,X41))) | 103.57/104.08 (![X44]: (in(X44,X41) => in(X44,X42)))))) & 103.57/104.08 (![X45,X46]: 103.57/104.08 ((in(X46,X31) & in(X45,X31)) => 103.57/104.08 ((![X47]: 103.57/104.08 (in(X47,X32) => (in(X45,X47) <=> in(X46,X47)))) => 103.57/104.08 (X45 = X46)))) & 103.57/104.08 (![X48]: 103.57/104.08 (in(X48,X32) => 103.57/104.08 (![X49]: (in(X49,X48) => in(X49,X31)))))))) => 103.57/104.08 ((![X50:($i > $o)]: 103.57/104.08 ((?[X51]: ((![X52]: (X50(X52) => (X51 = X52))) & X50(X51))) => 103.57/104.08 X50(descr('#ll_0'(X50))))) => 103.57/104.08 ((![X53,X54:($i > $o),X55]: 103.57/104.08 (in(X55,X53) => 103.57/104.08 (X54(X55) => in(X55,dsetconstr(X53,'#ll_0'(X54)))))) => 103.57/104.08 ((![X56,X57:($i > $o),X58]: 103.57/104.08 (in(X58,dsetconstr(X56,'#ll_0'(X57))) => in(X58,X56))) => 103.57/104.08 ((![X59,X60:($i > $o),X61]: 103.57/104.08 (in(X61,dsetconstr(X59,'#ll_0'(X60))) => X60(X61))) => 103.57/104.08 ((![X62:($i > $o)]: 103.57/104.08 ((?[X63]: 103.57/104.08 ((![X64]: (X62(X64) => (X63 = X64))) & X62(X63))) => 103.57/104.08 (?[X65]: 103.57/104.08 ((![X66]: (X62(X66) => (X65 = X66))) & X62(X65))))) => 103.57/104.08 ((![X67:$o,X68]: (in(X68,prop2set(X67)) => X67)) => 103.57/104.08 ((![X69]: (in(X69,emptyset) => (![X70:$o]: X70))) => 103.57/104.08 ((![X71]: (in(X71,emptyset) => $false)) => 103.57/104.08 ((![X72]: (~in(X72,emptyset))) => 103.57/104.08 ((![X73:($i > $o)]: 103.57/104.08 ((?[X74]: 103.57/104.08 ((![X75]: (X73(X75) => (X74 = X75))) & 103.57/104.08 X73(X74))) => 103.57/104.08 (?[X76]: X73(X76)))) => 103.57/104.08 ((![X77,X78]: 103.57/104.08 ((![X79]: (in(X79,X77) => in(X79,X78))) => 103.57/104.08 ((![X80]: (in(X80,X78) => in(X80,X77))) => 103.57/104.08 (X77 = X78)))) => 103.57/104.08 ((![X81]: 103.57/104.08 ((![X82]: (~in(X82,X81))) => (X81 = emptyset))) => 103.57/104.08 ((![X83]: 103.57/104.08 ((![X84]: (~in(X84,X83))) => (X83 = emptyset))) => 103.57/104.08 ((![X85,X86:($i > $o),X87]: 103.57/104.08 (in(X87,X85) => 103.57/104.08 (in(X87,dsetconstr(X85,'#ll_0'(X86))) <=> 103.57/104.08 X86(X87)))) => 103.57/104.08 ((![X88]: 103.57/104.08 ((X88 != emptyset) => (?[X89]: in(X89,X88)))) => 103.57/104.08 ((![X90,X91:($i > $o),X92]: 103.57/104.08 (in(X92,X90) => 103.57/104.08 (X91(X92) => 103.57/104.08 (dsetconstr(X90,'#ll_0'(X91)) != emptyset)))) => 103.57/104.08 ((![X93]: 103.57/104.08 ((?[X94]: in(X94,X93)) => 103.57/104.08 (X93 != emptyset))) => 103.57/104.08 ((![X95,X96]: in(X95,setadjoin(X95,X96))) => 103.57/104.08 (in(emptyset,setadjoin(emptyset,emptyset)) => 103.57/104.08 ((![X97,X98,X99]: 103.57/104.08 (in(X99,X98) => 103.57/104.08 in(X99,setadjoin(X97,X98)))) => 103.57/104.08 ((![X100,X101,X102]: 103.57/104.08 (in(X102,setadjoin(X100,X101)) => 103.57/104.08 (![X103:$o]: 103.57/104.08 (((X102 = X100) => X103) => 103.57/104.08 ((in(X102,X101) => X103) => X103))))) => 103.57/104.08 ((![X104,X105,X106]: 103.57/104.08 (in(X106,setadjoin(X104,X105)) => 103.57/104.08 (in(X106,X105) | (X106 = X104)))) => 103.57/104.08 ((![X107]: 103.57/104.08 (dsetconstr(X107,'#ll_1') = X107)) => 103.57/104.08 ((![X108,X109]: 103.57/104.08 ((![X110]: 103.57/104.08 (in(X110,X109) => in(X110,X108))) => 103.57/104.08 in(X109,powerset(X108)))) => 103.57/104.08 ((![X111]: in(emptyset,powerset(X111))) => 103.57/104.08 ((![X112]: 103.57/104.08 in(emptyset,powerset(X112))) => 103.57/104.08 ((![X113,X114,X115]: 103.57/104.08 (in(X114,powerset(X113)) => 103.57/104.08 (in(X115,X114) => in(X115,X113)))) => 103.57/104.08 ((![X116,X117,X118]: 103.57/104.08 (in(X117,X118) => 103.57/104.08 (in(X118,X116) => 103.57/104.08 in(X117,setunion(X116))))) => 103.57/104.08 ((![X119,X120]: 103.57/104.08 (in(X120,setunion(X119)) => 103.57/104.08 (![X121:$o]: 103.57/104.08 ((![X122]: 103.57/104.08 (in(X120,X122) => 103.57/104.08 (in(X122,X119) => 103.57/104.08 X121))) => 103.57/104.08 X121)))) => 103.57/104.08 ((![X123,X124]: 103.57/104.08 (in(X124,X123) => 103.57/104.08 in(X124, 103.57/104.08 powerset(setunion(X123))))) => 103.57/104.08 ((![X125:($i > $o)]: 103.57/104.08 ((?[X126]: 103.57/104.08 ((![X127]: 103.57/104.08 (X125(X127) => 103.57/104.08 (X126 = X127))) & 103.57/104.08 X125(X126))) => 103.57/104.08 (?[X128]: 103.57/104.08 (![X129]: 103.57/104.08 (X125(X129) <=> 103.57/104.08 (X129 = X128)))))) => 103.57/104.08 ((![X130]: 103.57/104.08 ((X130 != emptyset) => 103.57/104.08 (?[X131]: in(X131,X130)))) => 103.57/104.08 ((![X132,X133]: 103.57/104.08 (in(X132, 103.57/104.08 setadjoin(X133, 103.57/104.08 emptyset)) => 103.57/104.08 (X132 = X133))) => 103.57/104.08 ((![X134,X135]: 103.57/104.08 ((X134 != X135) => 103.57/104.08 (~ 103.57/104.08 in(X135, 103.57/104.08 setadjoin(X134, 103.57/104.08 emptyset))))) => 103.57/104.08 ((![X136,X137]: 103.57/104.08 ((X136 = X137) => 103.57/104.08 in(X136, 103.57/104.08 setadjoin(X137, 103.57/104.08 emptyset)))) => 103.57/104.08 ((![X138,X139]: 103.57/104.08 (in(X138, 103.57/104.08 setadjoin(X139, 103.57/104.08 emptyset)) => 103.57/104.08 in(X139, 103.57/104.08 setadjoin(X138, 103.57/104.08 emptyset)))) => 103.57/104.08 ((![X140,X141,X142]: 103.57/104.08 (in(X142, 103.57/104.08 setadjoin( 103.57/104.08 X140, 103.57/104.08 setadjoin( 103.57/104.08 X141,emptyset))) => 103.57/104.08 ((X142 = X141) | 103.57/104.08 (X142 = X140)))) => 103.57/104.08 ((![X143,X144]: 103.57/104.08 in(X143, 103.57/104.08 setadjoin( 103.57/104.08 X143, 103.57/104.08 setadjoin( 103.57/104.08 X144,emptyset)))) => 103.57/104.08 ((![X145,X146]: 103.57/104.08 in(X146, 103.57/104.08 setadjoin( 103.57/104.08 X145, 103.57/104.08 setadjoin( 103.57/104.08 X146,emptyset)))) => 103.57/104.08 ((![X147,X148:($i > $o)]: 103.57/104.08 ((?[X149]: 103.57/104.08 (X148(X149) & 103.57/104.08 in(X149,X147))) => 103.57/104.08 ((dsetconstr( 103.57/104.08 X147, 103.57/104.08 '#ll_0'(X148)) = 103.57/104.08 emptyset) => 103.57/104.08 $false))) => 103.57/104.08 ((![X150:($i > $o), 103.57/104.08 X151]: 103.57/104.08 (in(X151,emptyset) => 103.57/104.08 X150(X151))) => 103.57/104.08 ((![X152, 103.57/104.08 X153:($i > $o)]: 103.57/104.08 ((~ 103.57/104.08 (![X154]: 103.57/104.08 (in( 103.57/104.08 X154,X152) => 103.57/104.08 X153(X154)))) => 103.57/104.08 (?[X155]: 103.57/104.08 ((~X153(X155)) & 103.57/104.08 in(X155,X152))))) => 103.57/104.08 ((![X156, 103.57/104.08 X157:($i > $o)]: 103.57/104.08 ((![X158]: 103.57/104.08 (in( 103.57/104.08 X158,X156) => 103.57/104.08 (~ 103.57/104.08 X157( 103.57/104.08 X158)))) => 103.57/104.08 (~ 103.57/104.08 (?[X159]: 103.57/104.08 (X157( 103.57/104.08 X159) & 103.57/104.08 in( 103.57/104.08 X159,X156)))))) => 103.57/104.08 ((![X160, 103.57/104.08 X161:($i > $o)]: 103.57/104.08 ((~ 103.57/104.08 (?[X162]: 103.57/104.08 ( 103.57/104.08 X161( 103.57/104.08 X162) & 103.57/104.08 in( 103.57/104.08 X162,X160)))) => 103.57/104.08 (![X163]: 103.57/104.08 (in( 103.57/104.08 X163,X160) => 103.57/104.08 (~ 103.57/104.08 X161( 103.57/104.08 X163)))))) => 103.57/104.08 ((![X164, 103.57/104.08 X165:( 103.57/104.08 $i > $o)]: 103.57/104.08 ((?[X166]: 103.57/104.08 (( 103.57/104.08 ~ 103.57/104.08 X165( 103.57/104.08 X166)) & 103.57/104.08 in( 103.57/104.08 X166,X164))) => 103.57/104.08 (~ 103.57/104.08 (![X167]: 103.57/104.08 (in( 103.57/104.08 X167,X164) => 103.57/104.08 X165( 103.57/104.08 X167)))))) => 103.57/104.08 ((![X168:$o]: 103.57/104.08 (X168 => 103.57/104.08 in(emptyset, 103.57/104.08 prop2set( 103.57/104.08 X168)))) => 103.57/104.08 ((![X169:$o]: 103.57/104.08 (X169 => 103.57/104.08 set2prop( 103.57/104.08 prop2set( 103.57/104.08 X169)))) => 103.57/104.08 ((![X170, 103.57/104.08 X171:( 103.57/104.08 $i > $o)]: 103.57/104.08 ((~ 103.57/104.08 ( 103.57/104.08 ?[X172]: 103.57/104.08 (X171( 103.57/104.08 X172) & 103.57/104.08 in( 103.57/104.08 X172,X170)))) => 103.57/104.08 (![X173]: 103.57/104.08 (in( 103.57/104.08 X173,X170) => 103.57/104.08 (~ 103.57/104.08 X171( 103.57/104.08 X173)))))) => 103.57/104.08 ((![X174, 103.57/104.08 X175:( 103.57/104.08 $i > $o)]: 103.57/104.08 (( 103.57/104.08 ~ 103.57/104.08 ( 103.57/104.08 ![X176]: 103.57/104.08 (in( 103.57/104.08 X176,X174) => 103.57/104.08 X175( 103.57/104.08 X176)))) => 103.57/104.08 ( 103.57/104.08 ?[X177]: 103.57/104.08 (( 103.57/104.08 ~ 103.57/104.08 X175( 103.57/104.08 X177)) & 103.57/104.08 in( 103.57/104.08 X177,X174))))) => 103.57/104.08 ((![X178:( 103.57/104.08 $i > $o)]: 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ?[X179]: 103.57/104.08 (( 103.57/104.08 ![X180]: 103.57/104.08 (X178( 103.57/104.08 X180) => 103.57/104.08 (X179 = 103.57/104.08 X180))) & 103.57/104.08 X178( 103.57/104.08 X179))) => 103.57/104.08 ( 103.57/104.08 ?[X181]: 103.57/104.08 (( 103.57/104.08 ![X182]: 103.57/104.08 (X178( 103.57/104.08 X182) => 103.57/104.08 (X181 = 103.57/104.08 X182))) & 103.57/104.08 X178( 103.57/104.08 X181))))) => 103.57/104.08 ((![X183:( 103.57/104.08 $i > $o)]: 103.57/104.08 (( 103.57/104.08 ?[X184]: 103.57/104.08 X183( 103.57/104.08 X184)) => 103.57/104.08 (( 103.57/104.08 ![X185, 103.57/104.08 X186]: 103.57/104.08 (X183( 103.57/104.08 X185) => 103.57/104.08 (X183( 103.57/104.08 X186) => 103.57/104.08 (X185 = 103.57/104.08 X186)))) => 103.57/104.08 (?[X187]: 103.57/104.08 (( 103.57/104.08 ![X188]: 103.57/104.08 (X183( 103.57/104.08 X188) => 103.57/104.08 (X187 = 103.57/104.08 X188))) & 103.57/104.08 X183( 103.57/104.08 X187)))))) => 103.57/104.08 ((![X189:( 103.57/104.08 $i > $o)]: 103.57/104.08 (( 103.57/104.08 ?[X190]: 103.57/104.08 (![X191]: 103.57/104.08 (X189( 103.57/104.08 X191) <=> 103.57/104.08 (X191 = 103.57/104.08 X190)))) => 103.57/104.08 (?[X192]: 103.57/104.08 (( 103.57/104.08 ![X193]: 103.57/104.08 (X189( 103.57/104.08 X193) => 103.57/104.08 (X192 = 103.57/104.08 X193))) & 103.57/104.08 X189( 103.57/104.08 X192))))) => 103.57/104.08 (( 103.57/104.08 ![X194, 103.57/104.08 X195]: 103.57/104.08 (( 103.57/104.08 X194 = 103.57/104.08 X195) => 103.57/104.08 (![X196, 103.57/104.08 X197]: 103.57/104.08 (( 103.57/104.08 X196 = 103.57/104.08 X197) => 103.57/104.08 (in( 103.57/104.08 X196,X194) => 103.57/104.08 in( 103.57/104.08 X197,X195)))))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X198, 103.57/104.08 X199]: 103.57/104.08 (( 103.57/104.08 X198 = 103.57/104.08 X199) => 103.57/104.08 (![X200, 103.57/104.08 X201]: 103.57/104.08 (( 103.57/104.08 X200 = 103.57/104.08 X201) => 103.57/104.08 (in( 103.57/104.08 X200,X198) <=> 103.57/104.08 in( 103.57/104.08 X201,X199)))))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X202:( 103.57/104.08 $i > $o)]: 103.57/104.08 (( 103.57/104.08 ?[X203]: 103.57/104.08 (( 103.57/104.08 ![X204]: 103.57/104.08 (X202( 103.57/104.08 X204) => 103.57/104.08 (X203 = 103.57/104.08 X204))) & 103.57/104.08 X202( 103.57/104.08 X203))) => 103.57/104.08 (![X205, 103.57/104.08 X206]: 103.57/104.08 (X202( 103.57/104.08 X205) => 103.57/104.08 (X202( 103.57/104.08 X206) => 103.57/104.08 (X205 = 103.57/104.08 X206)))))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X207:( 103.57/104.08 $i > $o), 103.57/104.08 X208:( 103.57/104.08 $i > $o)]: 103.57/104.08 (( 103.57/104.08 ![X209, 103.57/104.08 X210]: 103.57/104.08 (( 103.57/104.08 X209 = 103.57/104.08 X210) => 103.57/104.08 (X207( 103.57/104.08 X209) <=> 103.57/104.08 X208( 103.57/104.08 X210)))) => 103.57/104.08 (( 103.57/104.08 ?[X211]: 103.57/104.08 zip_tseitin5( 103.57/104.08 X211,X207)) <=> 103.57/104.08 (?[X213]: 103.57/104.08 zip_tseitin5( 103.57/104.08 X213,X208))))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 emptyset = 103.57/104.08 emptyset) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X215, 103.57/104.08 X216]: 103.57/104.08 (( 103.57/104.08 X215 = 103.57/104.08 X216) => 103.57/104.08 (![X217, 103.57/104.08 X218]: 103.57/104.08 (( 103.57/104.08 X217 = 103.57/104.08 X218) => 103.57/104.08 (setadjoin( 103.57/104.08 X215,X217) = 103.57/104.08 setadjoin( 103.57/104.08 X216,X218)))))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X219, 103.57/104.08 X220]: 103.57/104.08 (( 103.57/104.08 X219 = 103.57/104.08 X220) => 103.57/104.08 (powerset( 103.57/104.08 X219) = 103.57/104.08 powerset( 103.57/104.08 X220)))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X221, 103.57/104.08 X222]: 103.57/104.08 (( 103.57/104.08 X221 = 103.57/104.08 X222) => 103.57/104.08 (setunion( 103.57/104.08 X221) = 103.57/104.08 setunion( 103.57/104.08 X222)))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 omega = 103.57/104.08 omega) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X223:( 103.57/104.08 $i > $o)]: 103.57/104.08 (( 103.57/104.08 ?[X224]: 103.57/104.08 (( 103.57/104.08 ![X225]: 103.57/104.08 (X223( 103.57/104.08 X225) => 103.57/104.08 (X224 = 103.57/104.08 X225))) & 103.57/104.08 X223( 103.57/104.08 X224))) => 103.57/104.08 (![X226, 103.57/104.08 X227]: 103.57/104.08 (X223( 103.57/104.08 X226) => 103.57/104.08 (X223( 103.57/104.08 X227) => 103.57/104.08 (X226 = 103.57/104.08 X227)))))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X228:( 103.57/104.08 $i > $o), 103.57/104.08 X229:( 103.57/104.08 $i > $o)]: 103.57/104.08 (( 103.57/104.08 ![X230, 103.57/104.08 X231]: 103.57/104.08 (( 103.57/104.08 X230 = 103.57/104.08 X231) => 103.57/104.08 (X228( 103.57/104.08 X230) <=> 103.57/104.08 X229( 103.57/104.08 X231)))) => 103.57/104.08 (( 103.57/104.08 ?[X232]: 103.57/104.08 (( 103.57/104.08 ![X233]: 103.57/104.08 (X228( 103.57/104.08 X233) => 103.57/104.08 (X232 = 103.57/104.08 X233))) & 103.57/104.08 X228( 103.57/104.08 X232))) => 103.57/104.08 (( 103.57/104.08 ?[X234]: 103.57/104.08 (( 103.57/104.08 ![X235]: 103.57/104.08 (X229( 103.57/104.08 X235) => 103.57/104.08 (X234 = 103.57/104.08 X235))) & 103.57/104.08 X229( 103.57/104.08 X234))) => 103.57/104.08 (descr( 103.57/104.08 '#ll_0'( 103.57/104.08 X228)) = 103.57/104.08 descr( 103.57/104.08 '#ll_0'( 103.57/104.08 X229))))))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X236, 103.57/104.08 X237]: 103.57/104.08 (( 103.57/104.08 X236 = 103.57/104.08 X237) => 103.57/104.08 (![X238:( 103.57/104.08 $i > $o), 103.57/104.08 X239:( 103.57/104.08 $i > $o)]: 103.57/104.08 (( 103.57/104.08 ![X240]: 103.57/104.08 (in( 103.57/104.08 X240,X236) => 103.57/104.08 (![X241]: 103.57/104.08 (in( 103.57/104.08 X241,X237) => 103.57/104.08 (( 103.57/104.08 X240 = 103.57/104.08 X241) => 103.57/104.08 (X238( 103.57/104.08 X240) <=> 103.57/104.08 X239( 103.57/104.08 X241))))))) => 103.57/104.08 (dsetconstr( 103.57/104.08 X236, 103.57/104.08 '#ll_0'( 103.57/104.08 X238)) = 103.57/104.08 dsetconstr( 103.57/104.08 X237, 103.57/104.08 '#ll_0'( 103.57/104.08 X239))))))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X242, 103.57/104.08 X243]: 103.57/104.08 (( 103.57/104.08 ![X244]: 103.57/104.08 (in( 103.57/104.08 X244,X242) => 103.57/104.08 in( 103.57/104.08 X244,X243))) => 103.57/104.08 subset( 103.57/104.08 X242,X243))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X245, 103.57/104.08 X246]: 103.57/104.08 (( 103.57/104.08 X245 = 103.57/104.08 X246) => 103.57/104.08 subset( 103.57/104.08 X246,X245))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X247, 103.57/104.08 X248]: 103.57/104.08 (( 103.57/104.08 X247 = 103.57/104.08 X248) => 103.57/104.08 subset( 103.57/104.08 X247,X248))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X249, 103.57/104.08 X250]: 103.57/104.08 (( 103.57/104.08 ![X251]: 103.57/104.08 (in( 103.57/104.08 X251,X249) => 103.57/104.08 in( 103.57/104.08 X251,X250))) => 103.57/104.08 subset( 103.57/104.08 X249,X250))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X252]: 103.57/104.08 subset( 103.57/104.08 emptyset, 103.57/104.08 X252)) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X253, 103.57/104.08 X254,X255]: 103.57/104.08 (subset( 103.57/104.08 X253,X254) => 103.57/104.08 (in( 103.57/104.08 X255,X253) => 103.57/104.08 in( 103.57/104.08 X255,X254)))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X256, 103.57/104.08 X257,X258]: 103.57/104.08 (subset( 103.57/104.08 X256,X257) => 103.57/104.08 (( 103.57/104.08 ~ 103.57/104.08 in( 103.57/104.08 X258,X257)) => 103.57/104.08 (~ 103.57/104.08 in( 103.57/104.08 X258,X256))))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X259, 103.57/104.08 X260,X261]: 103.57/104.08 (in( 103.57/104.08 X261,X259) => 103.57/104.08 (( 103.57/104.08 ~ 103.57/104.08 in( 103.57/104.08 X261,X260)) => 103.57/104.08 (~ 103.57/104.08 subset( 103.57/104.08 X259,X260))))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X262, 103.57/104.08 X263]: 103.57/104.08 (( 103.57/104.08 ~ 103.57/104.08 subset( 103.57/104.08 X262,X263)) => 103.57/104.08 (X262 != 103.57/104.08 X263))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X264, 103.57/104.08 X265,X266]: 103.57/104.08 (in( 103.57/104.08 X266,X264) => 103.57/104.08 (( 103.57/104.08 ~ 103.57/104.08 in( 103.57/104.08 X266,X265)) => 103.57/104.08 (X264 != 103.57/104.08 X265)))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X267]: 103.57/104.08 subset( 103.57/104.08 X267,X267)) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X268, 103.57/104.08 X269,X270]: 103.57/104.08 (subset( 103.57/104.08 X268,X269) => 103.57/104.08 (subset( 103.57/104.08 X269,X270) => 103.57/104.08 subset( 103.57/104.08 X268,X270)))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X271, 103.57/104.08 X272]: 103.57/104.08 subset( 103.57/104.08 X272, 103.57/104.08 setadjoin( 103.57/104.08 X271,X272))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X273, 103.57/104.08 X274,X275]: 103.57/104.08 (subset( 103.57/104.08 X273,X275) => 103.57/104.08 subset( 103.57/104.08 X273, 103.57/104.08 setadjoin( 103.57/104.08 X274,X275)))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X276, 103.57/104.08 X277]: 103.57/104.08 (subset( 103.57/104.08 X276,X277) => 103.57/104.08 in( 103.57/104.08 X276, 103.57/104.08 powerset( 103.57/104.08 X277)))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X278, 103.57/104.08 X279]: 103.57/104.08 (subset( 103.57/104.08 X278,X279) => 103.57/104.08 (subset( 103.57/104.08 X279,X278) => 103.57/104.08 (X278 = 103.57/104.08 X279)))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X280]: 103.57/104.08 (subset( 103.57/104.08 X280, 103.57/104.08 emptyset) => 103.57/104.08 (X280 = 103.57/104.08 emptyset))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X281, 103.57/104.08 X282]: 103.57/104.08 (subset( 103.57/104.08 X282,X281) => 103.57/104.08 in( 103.57/104.08 X282, 103.57/104.08 powerset( 103.57/104.08 X281)))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X283, 103.57/104.08 X284]: 103.57/104.08 (in( 103.57/104.08 X284, 103.57/104.08 powerset( 103.57/104.08 X283)) => 103.57/104.08 subset( 103.57/104.08 X284,X283))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X285]: 103.57/104.08 in( 103.57/104.08 X285, 103.57/104.08 powerset( 103.57/104.08 X285))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X286, 103.57/104.08 X287]: 103.57/104.08 (subset( 103.57/104.08 X286,X287) => 103.57/104.08 subset( 103.57/104.08 powerset( 103.57/104.08 X286), 103.57/104.08 powerset( 103.57/104.08 X287)))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X288, 103.57/104.08 X289:( 103.57/104.08 $i > $o)]: 103.57/104.08 in( 103.57/104.08 dsetconstr( 103.57/104.08 X288, 103.57/104.08 '#ll_0'( 103.57/104.08 X289)), 103.57/104.08 powerset( 103.57/104.08 X288))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X290, 103.57/104.08 X291:( 103.57/104.08 $i > $o)]: 103.57/104.08 subset( 103.57/104.08 dsetconstr( 103.57/104.08 X290, 103.57/104.08 '#ll_0'( 103.57/104.08 X291)), 103.57/104.08 X290)) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X292, 103.57/104.08 X293,X294]: 103.57/104.08 (in( 103.57/104.08 X294,X292) => 103.57/104.08 in( 103.57/104.08 X294, 103.57/104.08 binunion( 103.57/104.08 X292,X293)))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X295, 103.57/104.08 X296]: 103.57/104.08 in( 103.57/104.08 X296, 103.57/104.08 setadjoin( 103.57/104.08 X295, 103.57/104.08 setadjoin( 103.57/104.08 X296, 103.57/104.08 emptyset)))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X297, 103.57/104.08 X298,X299]: 103.57/104.08 (in( 103.57/104.08 X299,X298) => 103.57/104.08 in( 103.57/104.08 X299, 103.57/104.08 binunion( 103.57/104.08 X297,X298)))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X300, 103.57/104.08 X301, 103.57/104.08 X302, 103.57/104.08 X303:$o]: 103.57/104.08 (in( 103.57/104.08 X302, 103.57/104.08 binunion( 103.57/104.08 X300,X301)) => 103.57/104.08 (( 103.57/104.08 in( 103.57/104.08 X302,X300) => 103.57/104.08 X303) => 103.57/104.08 (( 103.57/104.08 in( 103.57/104.08 X302,X301) => 103.57/104.08 X303) => 103.57/104.08 X303)))) => 103.57/104.08 ( 103.57/104.08 ( 103.57/104.08 ![X304, 103.57/104.08 X305,X306]: 103.57/104.08 (in( 103.57/104.08 X306, 103.57/104.08 binunion( 103.57/104.08 X304,X305)) => 103.57/104.08 (in( 103.57/104.08 X306,X305) | 103.57/104.08 in( 103.57/104.08 X306,X304)))) => 103.57/104.08 ( 103.57/104.08 ![X307, 103.57/104.08 X308]: 103.57/104.08 subset( 103.57/104.08 X307, 103.57/104.08 binunion( 103.57/104.08 X307,X308)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 103.57/104.08 tff('105', plain, ~ subset(sk_X307_, binunion(sk_X307_, sk_X308_)), 103.57/104.08 inference('cnf', [status(esa)], [zf_stmt_14])). 103.57/104.08 tff('106', plain, 103.57/104.08 ![X466, X467]: (subset(X466, X467) | ~ in(X466, powerset(X467))), 103.57/104.08 inference('cnf', [status(esa)], [zf_stmt_14])). 103.57/104.08 tff('107', plain, 103.57/104.08 ![X365, X366]: 103.57/104.08 (in(X365, powerset(X366)) | in(sk_X110_(X365, X366), X365)), 103.57/104.08 inference('cnf', [status(esa)], [zf_stmt_14])). 103.57/104.08 tff('108', plain, 103.57/104.08 ![X447, X448, X449]: (in(X447, binunion(X448, X449)) | ~ in(X447, X448)), 103.57/104.08 inference('cnf', [status(esa)], [zf_stmt_14])). 103.57/104.08 tff('109', plain, 103.57/104.08 ![X365, X366]: 103.57/104.08 (in(X365, powerset(X366)) | ~ in(sk_X110_(X365, X366), X366)), 103.57/104.08 inference('cnf', [status(esa)], [zf_stmt_14])). 103.57/104.08 tff('110', plain, $false, 103.57/104.08 inference('eprover', [status(thm)], ['105', '106', '107', '108', '109'])). 103.57/104.08 103.57/104.08 % SZS output end Refutation 103.57/104.08 % Zipperpin 1.5 exiting 103.57/104.09 EOF