0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.13 % Command : run_portfolio.sh /export/starexec/sandbox/benchmark/theBenchmark.p /export/starexec/sandbox/tmp/tmp.1c17i9TPZW 0.12/0.33 % Computer : n026.cluster.edu 0.12/0.33 % Model : x86_64 x86_64 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.33 % Memory : 8042.1875MB 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.33 % CPULimit : 180 0.12/0.33 % DateTime : Thu Aug 29 16:13:50 EDT 2019 0.12/0.33 % CPUTime : 114.29/114.87 % Running portfolio for 180 s 114.29/114.87 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 114.29/114.87 % TempDir : /export/starexec/sandbox/tmp/tmp.1c17i9TPZW 114.29/114.87 % Recognized as monomorphic HO. 114.29/114.87 % Running /export/starexec/sandbox/solver/bin/competitive.sh for 18 114.29/114.87 % Running /export/starexec/sandbox/solver/bin/competitive.2.sh for 13 114.29/114.87 % Running /export/starexec/sandbox/solver/bin/competitive.3.sh for 3 114.29/114.87 % Running /export/starexec/sandbox/solver/bin/pragmatic.rudimentary.sh for 28 114.29/114.87 % Running /export/starexec/sandbox/solver/bin/pragmatic.rudimentary.1.sh for 12 114.29/114.87 % Running /export/starexec/sandbox/solver/bin/pragmatic.rudimentary.2.sh for 7 114.29/114.87 % Running /export/starexec/sandbox/solver/bin/pragmatic.shallow.sh for 3 114.29/114.87 % Running /export/starexec/sandbox/solver/bin/pragmatic.shallow.1.sh for 15 114.29/114.87 % Running /export/starexec/sandbox/solver/bin/pragmatic.shallow.2.sh for 12 114.29/114.87 % Running /export/starexec/sandbox/solver/bin/pragmatic.ll.e.sh for 19 114.29/114.87 % Solved by: pragmatic.ll.e.sh 114.29/114.87 % Running : timeout 16 /export/starexec/sandbox/solver/bin/eprover-ho /export/starexec/sandbox/tmp/tmp.1c17i9TPZW/e_input9cfefc --cpu-limit=14 --auto-schedule -s -p. 114.29/114.87 % done 468 iterations in 15.408s 114.29/114.87 % hashcons stats for terms: size 4096, num 22312, sum length 36102, buckets: small 3, median 7, big 22 114.29/114.87 % proof state stats: {active 191, passive 6076, simpl 0} 114.29/114.87 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 114.29/114.87 % SZS output start Refutation 114.29/114.87 tff(inPowerset, axiom, inPowerset <=> (![A]: in(A,powerset(A)))). 114.29/114.87 tff('0', plain, inPowerset = (![X2]: in(X2,powerset(X2))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(powersetE1, axiom, powersetE1 <=> 114.29/114.87 (![A,B]: (in(B,powerset(A)) => subset(B,A)))). 114.29/114.87 tff('1', plain, 114.29/114.87 powersetE1 = (![X2,X3]: (in(X3,powerset(X2)) => subset(X3,X2))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(powersetI1, axiom, powersetI1 <=> 114.29/114.87 (![A,B]: (subset(B,A) => in(B,powerset(A))))). 114.29/114.87 tff('2', plain, 114.29/114.87 powersetI1 = (![X2,X3]: (subset(X3,X2) => in(X3,powerset(X2)))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(subsetemptysetimpeq, axiom, subsetemptysetimpeq <=> 114.29/114.87 (![A]: (subset(A,emptyset) => (A = emptyset)))). 114.29/114.87 tff('3', plain, 114.29/114.87 subsetemptysetimpeq = (![X2]: (subset(X2,emptyset) => (X2 = emptyset))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(setextsub, axiom, setextsub <=> 114.29/114.87 (![A,B]: (subset(A,B) => (subset(B,A) => (A = B))))). 114.29/114.87 tff('4', plain, 114.29/114.87 setextsub = (![X2,X3]: (subset(X2,X3) => (subset(X3,X2) => (X2 = X3)))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(subset2powerset, axiom, subset2powerset <=> 114.29/114.87 (![A,B]: (subset(A,B) => in(A,powerset(B))))). 114.29/114.87 tff('5', plain, 114.29/114.87 subset2powerset = (![X2,X3]: (subset(X2,X3) => in(X2,powerset(X3)))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(setadjoinSub2, axiom, setadjoinSub2 <=> 114.29/114.87 (![A,Xx,B]: (subset(A,B) => subset(A,setadjoin(Xx,B))))). 114.29/114.87 tff('6', plain, 114.29/114.87 setadjoinSub2 = 114.29/114.87 (![X2,X3,X4]: (subset(X2,X4) => subset(X2,setadjoin(X3,X4)))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(setadjoinSub, axiom, setadjoinSub <=> 114.29/114.87 (![Xx,A]: subset(A,setadjoin(Xx,A)))). 114.29/114.87 tff('7', plain, setadjoinSub = (![X2,X3]: subset(X3,setadjoin(X2,X3))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(subsetTrans, axiom, subsetTrans <=> 114.29/114.87 (![A,B,C]: (subset(A,B) => (subset(B,C) => subset(A,C))))). 114.29/114.87 tff('8', plain, 114.29/114.87 subsetTrans = 114.29/114.87 (![X2,X3,X4]: (subset(X2,X3) => (subset(X3,X4) => subset(X2,X4)))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(subsetRefl, axiom, subsetRefl <=> (![A]: subset(A,A))). 114.29/114.87 tff('9', plain, subsetRefl = (![X2]: subset(X2,X2)), define([status(thm)])). 114.29/114.87 tff(notequalI2, axiom, notequalI2 <=> 114.29/114.87 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => (A != B))))). 114.29/114.87 tff('10', plain, 114.29/114.87 notequalI2 = (![X2,X3,X4]: (in(X4,X2) => ((~in(X4,X3)) => (X2 != X3)))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(notequalI1, axiom, notequalI1 <=> (![A,B]: ((~subset(A,B)) => (A != B)))). 114.29/114.87 tff('11', plain, notequalI1 = (![X2,X3]: ((~subset(X2,X3)) => (X2 != X3))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(notsubsetI, axiom, notsubsetI <=> 114.29/114.87 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => (~subset(A,B)))))). 114.29/114.87 tff('12', plain, 114.29/114.87 notsubsetI = 114.29/114.87 (![X2,X3,X4]: (in(X4,X2) => ((~in(X4,X3)) => (~subset(X2,X3))))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(subsetE2, axiom, subsetE2 <=> 114.29/114.87 (![A,B,Xx]: (subset(A,B) => ((~in(Xx,B)) => (~in(Xx,A)))))). 114.29/114.87 tff('13', plain, 114.29/114.87 subsetE2 = 114.29/114.87 (![X2,X3,X4]: (subset(X2,X3) => ((~in(X4,X3)) => (~in(X4,X2))))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(subsetE, axiom, subsetE <=> 114.29/114.87 (![A,B,Xx]: (subset(A,B) => (in(Xx,A) => in(Xx,B))))). 114.29/114.87 tff('14', plain, 114.29/114.87 subsetE = (![X2,X3,X4]: (subset(X2,X3) => (in(X4,X2) => in(X4,X3)))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(emptysetsubset, axiom, emptysetsubset <=> (![A]: subset(emptyset,A))). 114.29/114.87 tff('15', plain, emptysetsubset = (![X2]: subset(emptyset,X2)), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(subsetI2, axiom, subsetI2 <=> 114.29/114.87 (![A,B]: ((![Xx]: (in(Xx,A) => in(Xx,B))) => subset(A,B)))). 114.29/114.87 tff('16', plain, 114.29/114.87 subsetI2 = 114.29/114.87 (![X2,X3]: ((![X4]: (in(X4,X2) => in(X4,X3))) => subset(X2,X3))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(eqimpsubset1, axiom, eqimpsubset1 <=> (![A,B]: ((A = B) => subset(A,B)))). 114.29/114.87 tff('17', plain, eqimpsubset1 = (![X2,X3]: ((X2 = X3) => subset(X2,X3))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(eqimpsubset2, axiom, eqimpsubset2 <=> (![A,B]: ((A = B) => subset(B,A)))). 114.29/114.87 tff('18', plain, eqimpsubset2 = (![X2,X3]: ((X2 = X3) => subset(X3,X2))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(subsetI1, axiom, subsetI1 <=> 114.29/114.87 (![A,B]: ((![Xx]: (in(Xx,A) => in(Xx,B))) => subset(A,B)))). 114.29/114.87 tff('19', plain, 114.29/114.87 subsetI1 = 114.29/114.87 (![X2,X3]: ((![X4]: (in(X4,X2) => in(X4,X3))) => subset(X2,X3))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(dsetconstr__Cong, axiom, dsetconstr__Cong <=> 114.29/114.87 (![A,B]: 114.29/114.87 ((A = B) => 114.29/114.87 (![Xphi:($i > $o),Xpsi:($i > $o)]: 114.29/114.87 ((![Xx]: 114.29/114.87 (in(Xx,A) => 114.29/114.87 (![Xy]: (in(Xy,B) => ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy))))))) => 114.29/114.87 (dsetconstr(A,^[Xx]: Xphi(Xx)) = dsetconstr(B,^[Xx]: Xpsi(Xx)))))))). 114.29/114.87 tff('20', plain, 114.29/114.87 dsetconstr__Cong = 114.29/114.87 (![X2,X3]: 114.29/114.87 ((X2 = X3) => 114.29/114.87 (![X4:($i > $o),X5:($i > $o)]: 114.29/114.87 ((![X6]: 114.29/114.87 (in(X6,X2) => 114.29/114.87 (![X7]: (in(X7,X3) => ((X6 = X7) => (X4(X6) <=> X5(X7))))))) => 114.29/114.87 (dsetconstr(X2,^[V_1]: X4(V_1)) = dsetconstr(X3,^[V_2]: X5(V_2))))))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(descr__Cong, axiom, descr__Cong <=> 114.29/114.87 (![Xphi:($i > $o),Xpsi:($i > $o)]: 114.29/114.87 ((![Xx,Xy]: ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy)))) => 114.29/114.87 (exu(^[Xx]: Xphi(Xx)) => 114.29/114.87 (exu(^[Xx]: Xpsi(Xx)) => 114.29/114.87 (descr(^[Xx]: Xphi(Xx)) = descr(^[Xx]: Xpsi(Xx)))))))). 114.29/114.87 tff('21', plain, 114.29/114.87 descr__Cong = 114.29/114.87 (![X2:($i > $o),X3:($i > $o)]: 114.29/114.87 ((![X4,X5]: ((X4 = X5) => (X2(X4) <=> X3(X5)))) => 114.29/114.87 (exu(^[V_1]: X2(V_1)) => 114.29/114.87 (exu(^[V_2]: X3(V_2)) => 114.29/114.87 (descr(^[V_3]: X2(V_3)) = descr(^[V_4]: X3(V_4))))))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(exuEu, axiom, exuEu <=> 114.29/114.87 (![Xphi:($i > $o)]: 114.29/114.87 (exu(^[Xx]: Xphi(Xx)) => 114.29/114.87 (![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))). 114.29/114.87 tff('22', plain, 114.29/114.87 exuEu = 114.29/114.87 (![X2:($i > $o)]: 114.29/114.87 (exu(^[V_1]: X2(V_1)) => (![X3,X4]: (X2(X3) => (X2(X4) => (X3 = X4)))))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(omega__Cong, axiom, omega__Cong <=> (omega = omega)). 114.29/114.87 tff('23', plain, omega__Cong = (omega = omega), define([status(thm)])). 114.29/114.87 tff(setunion__Cong, axiom, setunion__Cong <=> 114.29/114.87 (![A,B]: ((A = B) => (setunion(A) = setunion(B))))). 114.29/114.87 tff('24', plain, 114.29/114.87 setunion__Cong = (![X2,X3]: ((X2 = X3) => (setunion(X2) = setunion(X3)))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(powerset__Cong, axiom, powerset__Cong <=> 114.29/114.87 (![A,B]: ((A = B) => (powerset(A) = powerset(B))))). 114.29/114.87 tff('25', plain, 114.29/114.87 powerset__Cong = (![X2,X3]: ((X2 = X3) => (powerset(X2) = powerset(X3)))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(setadjoin__Cong, axiom, setadjoin__Cong <=> 114.29/114.87 (![Xx,Xy]: 114.29/114.87 ((Xx = Xy) => 114.29/114.87 (![Xz,Xu]: ((Xz = Xu) => (setadjoin(Xx,Xz) = setadjoin(Xy,Xu))))))). 114.29/114.87 tff('26', plain, 114.29/114.87 setadjoin__Cong = 114.29/114.87 (![X2,X3]: 114.29/114.87 ((X2 = X3) => 114.29/114.87 (![X4,X5]: ((X4 = X5) => (setadjoin(X2,X4) = setadjoin(X3,X5)))))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(emptyset__Cong, axiom, emptyset__Cong <=> (emptyset = emptyset)). 114.29/114.87 tff('27', plain, emptyset__Cong = (emptyset = emptyset), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(exu__Cong, axiom, exu__Cong <=> 114.29/114.87 (![Xphi:($i > $o),Xpsi:($i > $o)]: 114.29/114.87 ((![Xx,Xy]: ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy)))) => 114.29/114.87 (exu(^[Xx]: Xphi(Xx)) <=> exu(^[Xx]: Xpsi(Xx)))))). 114.29/114.87 tff('28', plain, 114.29/114.87 exu__Cong = 114.29/114.87 (![X2:($i > $o),X3:($i > $o)]: 114.29/114.87 ((![X4,X5]: ((X4 = X5) => (X2(X4) <=> X3(X5)))) => 114.29/114.87 (exu(^[V_1]: X2(V_1)) <=> exu(^[V_2]: X3(V_2))))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(exuE3u, axiom, exuE3u <=> 114.29/114.87 (![Xphi:($i > $o)]: 114.29/114.87 (exu(^[Xx]: Xphi(Xx)) => 114.29/114.87 (![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))). 114.29/114.87 tff('29', plain, 114.29/114.87 exuE3u = 114.29/114.87 (![X2:($i > $o)]: 114.29/114.87 (exu(^[V_1]: X2(V_1)) => (![X3,X4]: (X2(X3) => (X2(X4) => (X3 = X4)))))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(in__Cong, axiom, in__Cong <=> 114.29/114.87 (![A,B]: ((A = B) => (![Xx,Xy]: ((Xx = Xy) => (in(Xx,A) <=> in(Xy,B))))))). 114.29/114.87 tff('30', plain, 114.29/114.87 in__Cong = 114.29/114.87 (![X2,X3]: 114.29/114.87 ((X2 = X3) => (![X4,X5]: ((X4 = X5) => (in(X4,X2) <=> in(X5,X3)))))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(inCongP, axiom, inCongP <=> 114.29/114.87 (![A,B]: ((A = B) => (![Xx,Xy]: ((Xx = Xy) => (in(Xx,A) => in(Xy,B))))))). 114.29/114.87 tff('31', plain, 114.29/114.87 inCongP = 114.29/114.87 (![X2,X3]: 114.29/114.87 ((X2 = X3) => (![X4,X5]: ((X4 = X5) => (in(X4,X2) => in(X5,X3)))))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(exuI2, axiom, exuI2 <=> 114.29/114.87 (![Xphi:($i > $o)]: 114.29/114.87 ((?[Xx]: (![Xy]: (Xphi(Xy) <=> (Xy = Xx)))) => exu(^[Xx]: Xphi(Xx))))). 114.29/114.87 tff('32', plain, 114.29/114.87 exuI2 = 114.29/114.87 (![X2:($i > $o)]: 114.29/114.87 ((?[X3]: (![X4]: (X2(X4) <=> (X4 = X3)))) => exu(^[V_1]: X2(V_1)))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(exuI3, axiom, exuI3 <=> 114.29/114.87 (![Xphi:($i > $o)]: 114.29/114.87 ((?[Xx]: Xphi(Xx)) => 114.29/114.87 ((![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy)))) => 114.29/114.87 exu(^[Xx]: Xphi(Xx)))))). 114.29/114.87 tff('33', plain, 114.29/114.87 exuI3 = 114.29/114.87 (![X2:($i > $o)]: 114.29/114.87 ((?[X3]: X2(X3)) => 114.29/114.87 ((![X4,X5]: (X2(X4) => (X2(X5) => (X4 = X5)))) => 114.29/114.87 exu(^[V_1]: X2(V_1))))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(exuI1, axiom, exuI1 <=> 114.29/114.87 (![Xphi:($i > $o)]: 114.29/114.87 ((?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx))) => 114.29/114.87 exu(^[Xx]: Xphi(Xx))))). 114.29/114.87 tff('34', plain, 114.29/114.87 exuI1 = 114.29/114.87 (![X2:($i > $o)]: 114.29/114.87 ((?[X3]: ((![X4]: (X2(X4) => (X3 = X4))) & X2(X3))) => 114.29/114.87 exu(^[V_1]: X2(V_1)))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(notdallE, axiom, notdallE <=> 114.29/114.87 (![A,Xphi:($i > $o)]: 114.29/114.87 ((~(![Xx]: (in(Xx,A) => Xphi(Xx)))) => (?[Xx]: ((~Xphi(Xx)) & in(Xx,A)))))). 114.29/114.87 tff('35', plain, 114.29/114.87 notdallE = 114.29/114.87 (![X2,X3:($i > $o)]: 114.29/114.87 ((~(![X4]: (in(X4,X2) => X3(X4)))) => (?[X5]: ((~X3(X5)) & in(X5,X2))))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(notdexE, axiom, notdexE <=> 114.29/114.87 (![A,Xphi:($i > $o)]: 114.29/114.87 ((~(?[Xx]: (Xphi(Xx) & in(Xx,A)))) => (![Xx]: (in(Xx,A) => (~Xphi(Xx))))))). 114.29/114.87 tff('36', plain, 114.29/114.87 notdexE = 114.29/114.87 (![X2,X3:($i > $o)]: 114.29/114.87 ((~(?[X4]: (X3(X4) & in(X4,X2)))) => (![X5]: (in(X5,X2) => (~X3(X5)))))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(prop2set2propI, axiom, prop2set2propI <=> 114.29/114.87 (![Xphi:$o]: (Xphi => set2prop(prop2set(Xphi))))). 114.29/114.87 tff('37', plain, prop2set2propI = (![X2:$o]: (X2 => set2prop(prop2set(X2)))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(prop2setI, axiom, prop2setI <=> 114.29/114.87 (![Xphi:$o]: (Xphi => in(emptyset,prop2set(Xphi))))). 114.29/114.87 tff('38', plain, prop2setI = (![X2:$o]: (X2 => in(emptyset,prop2set(X2)))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(quantDeMorgan4, axiom, quantDeMorgan4 <=> 114.29/114.87 (![A,Xphi:($i > $o)]: 114.29/114.87 ((?[Xx]: ((~Xphi(Xx)) & in(Xx,A))) => (~(![Xx]: (in(Xx,A) => Xphi(Xx))))))). 114.29/114.87 tff('39', plain, 114.29/114.87 quantDeMorgan4 = 114.29/114.87 (![X2,X3:($i > $o)]: 114.29/114.87 ((?[X4]: ((~X3(X4)) & in(X4,X2))) => (~(![X5]: (in(X5,X2) => X3(X5)))))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(quantDeMorgan3, axiom, quantDeMorgan3 <=> 114.29/114.87 (![A,Xphi:($i > $o)]: 114.29/114.87 ((~(?[Xx]: (Xphi(Xx) & in(Xx,A)))) => (![Xx]: (in(Xx,A) => (~Xphi(Xx))))))). 114.29/114.87 tff('40', plain, 114.29/114.87 quantDeMorgan3 = 114.29/114.87 (![X2,X3:($i > $o)]: 114.29/114.87 ((~(?[X4]: (X3(X4) & in(X4,X2)))) => (![X5]: (in(X5,X2) => (~X3(X5)))))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(quantDeMorgan2, axiom, quantDeMorgan2 <=> 114.29/114.87 (![A,Xphi:($i > $o)]: 114.29/114.87 ((![Xx]: (in(Xx,A) => (~Xphi(Xx)))) => (~(?[Xx]: (Xphi(Xx) & in(Xx,A))))))). 114.29/114.87 tff('41', plain, 114.29/114.87 quantDeMorgan2 = 114.29/114.87 (![X2,X3:($i > $o)]: 114.29/114.87 ((![X4]: (in(X4,X2) => (~X3(X4)))) => (~(?[X5]: (X3(X5) & in(X5,X2)))))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(quantDeMorgan1, axiom, quantDeMorgan1 <=> 114.29/114.87 (![A,Xphi:($i > $o)]: 114.29/114.87 ((~(![Xx]: (in(Xx,A) => Xphi(Xx)))) => (?[Xx]: ((~Xphi(Xx)) & in(Xx,A)))))). 114.29/114.87 tff('42', plain, 114.29/114.87 quantDeMorgan1 = 114.29/114.87 (![X2,X3:($i > $o)]: 114.29/114.87 ((~(![X4]: (in(X4,X2) => X3(X4)))) => (?[X5]: ((~X3(X5)) & in(X5,X2))))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(vacuousDall, axiom, vacuousDall <=> 114.29/114.87 (![Xphi:($i > $o),Xx]: (in(Xx,emptyset) => Xphi(Xx)))). 114.29/114.87 tff('43', plain, 114.29/114.87 vacuousDall = (![X2:($i > $o),X3]: (in(X3,emptyset) => X2(X3))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(emptyE1, axiom, emptyE1 <=> 114.29/114.87 (![A,Xphi:($i > $o)]: 114.29/114.87 ((?[Xx]: (Xphi(Xx) & in(Xx,A))) => 114.29/114.87 ((dsetconstr(A,^[Xx]: Xphi(Xx)) = emptyset) => $false)))). 114.29/114.87 tff('44', plain, 114.29/114.87 emptyE1 = 114.29/114.87 (![X2,X3:($i > $o)]: 114.29/114.87 ((?[X4]: (X3(X4) & in(X4,X2))) => 114.29/114.87 ((dsetconstr(X2,^[V_1]: X3(V_1)) = emptyset) => $false))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(upairsetIR, axiom, upairsetIR <=> 114.29/114.87 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 114.29/114.87 tff('45', plain, 114.29/114.87 upairsetIR = (![X2,X3]: in(X3,setadjoin(X2,setadjoin(X3,emptyset)))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(upairsetIL, axiom, upairsetIL <=> 114.29/114.87 (![Xx,Xy]: in(Xx,setadjoin(Xx,setadjoin(Xy,emptyset))))). 114.29/114.87 tff('46', plain, 114.29/114.87 upairsetIL = (![X2,X3]: in(X2,setadjoin(X2,setadjoin(X3,emptyset)))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(upairsetE, axiom, upairsetE <=> 114.29/114.87 (![Xx,Xy,Xz]: 114.29/114.87 (in(Xz,setadjoin(Xx,setadjoin(Xy,emptyset))) => ((Xz = Xy) | (Xz = Xx))))). 114.29/114.87 tff('47', plain, 114.29/114.87 upairsetE = 114.29/114.87 (![X2,X3,X4]: 114.29/114.87 (in(X4,setadjoin(X2,setadjoin(X3,emptyset))) => 114.29/114.87 ((X4 = X3) | (X4 = X2)))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(singletonsswitch, axiom, singletonsswitch <=> 114.29/114.87 (![Xx,Xy]: (in(Xx,setadjoin(Xy,emptyset)) => in(Xy,setadjoin(Xx,emptyset))))). 114.29/114.87 tff('48', plain, 114.29/114.87 singletonsswitch = 114.29/114.87 (![X2,X3]: 114.29/114.87 (in(X2,setadjoin(X3,emptyset)) => in(X3,setadjoin(X2,emptyset)))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(eqinunit, axiom, eqinunit <=> 114.29/114.87 (![Xx,Xy]: ((Xx = Xy) => in(Xx,setadjoin(Xy,emptyset))))). 114.29/114.87 tff('49', plain, 114.29/114.87 eqinunit = (![X2,X3]: ((X2 = X3) => in(X2,setadjoin(X3,emptyset)))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(notinsingleton, axiom, notinsingleton <=> 114.29/114.87 (![Xx,Xy]: ((Xx != Xy) => (~in(Xy,setadjoin(Xx,emptyset)))))). 114.29/114.87 tff('50', plain, 114.29/114.87 notinsingleton = 114.29/114.87 (![X2,X3]: ((X2 != X3) => (~in(X3,setadjoin(X2,emptyset))))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(uniqinunit, axiom, uniqinunit <=> 114.29/114.87 (![Xx,Xy]: (in(Xx,setadjoin(Xy,emptyset)) => (Xx = Xy)))). 114.29/114.87 tff('51', plain, 114.29/114.87 uniqinunit = (![X2,X3]: (in(X2,setadjoin(X3,emptyset)) => (X2 = X3))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(nonemptyImpWitness, axiom, nonemptyImpWitness <=> 114.29/114.87 (![A]: (nonempty(A) => (?[Xx]: (in(Xx,A)))))). 114.29/114.87 tff('52', plain, 114.29/114.87 nonemptyImpWitness = (![X2]: (nonempty(X2) => (?[X3]: (in(X3,X2))))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(exuE2, axiom, exuE2 <=> 114.29/114.87 (![Xphi:($i > $o)]: 114.29/114.87 (exu(^[Xx]: Xphi(Xx)) => (?[Xx]: (![Xy]: (Xphi(Xy) <=> (Xy = Xx))))))). 114.29/114.87 tff('53', plain, 114.29/114.87 exuE2 = 114.29/114.87 (![X2:($i > $o)]: 114.29/114.87 (exu(^[V_1]: X2(V_1)) => (?[X3]: (![X4]: (X2(X4) <=> (X4 = X3)))))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(subPowSU, axiom, subPowSU <=> 114.29/114.87 (![A,Xx]: (in(Xx,A) => in(Xx,powerset(setunion(A)))))). 114.29/114.87 tff('54', plain, 114.29/114.87 subPowSU = (![X2,X3]: (in(X3,X2) => in(X3,powerset(setunion(X2))))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(setunionE, axiom, setunionE <=> 114.29/114.87 (![A,Xx]: 114.29/114.87 (in(Xx,setunion(A)) => 114.29/114.87 (![Xphi:$o]: ((![B]: (in(Xx,B) => (in(B,A) => Xphi))) => Xphi))))). 114.29/114.87 tff('55', plain, 114.29/114.87 setunionE = 114.29/114.87 (![X2,X3]: 114.29/114.87 (in(X3,setunion(X2)) => 114.29/114.87 (![X4:$o]: ((![X5]: (in(X3,X5) => (in(X5,X2) => X4))) => X4)))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(setunionI, axiom, setunionI <=> 114.29/114.87 (![A,Xx,B]: (in(Xx,B) => (in(B,A) => in(Xx,setunion(A)))))). 114.29/114.87 tff('56', plain, 114.29/114.87 setunionI = 114.29/114.87 (![X2,X3,X4]: (in(X3,X4) => (in(X4,X2) => in(X3,setunion(X2))))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(powersetE, axiom, powersetE <=> 114.29/114.87 (![A,B,Xx]: (in(B,powerset(A)) => (in(Xx,B) => in(Xx,A))))). 114.29/114.87 tff('57', plain, 114.29/114.87 powersetE = 114.29/114.87 (![X2,X3,X4]: (in(X3,powerset(X2)) => (in(X4,X3) => in(X4,X2)))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(emptyInPowerset, axiom, emptyInPowerset <=> 114.29/114.87 (![A]: in(emptyset,powerset(A)))). 114.29/114.87 tff('58', plain, emptyInPowerset = (![X2]: in(emptyset,powerset(X2))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(emptyinPowerset, axiom, emptyinPowerset <=> 114.29/114.87 (![A]: in(emptyset,powerset(A)))). 114.29/114.87 tff('59', plain, emptyinPowerset = (![X2]: in(emptyset,powerset(X2))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(powersetI, axiom, powersetI <=> 114.29/114.87 (![A,B]: ((![Xx]: (in(Xx,B) => in(Xx,A))) => in(B,powerset(A))))). 114.29/114.87 tff('60', plain, 114.29/114.87 powersetI = 114.29/114.87 (![X2,X3]: ((![X4]: (in(X4,X3) => in(X4,X2))) => in(X3,powerset(X2)))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(setoftrueEq, axiom, setoftrueEq <=> 114.29/114.87 (![A]: (dsetconstr(A,^[Xx]: $true) = A))). 114.29/114.87 tff('61', plain, setoftrueEq = (![X2]: (dsetconstr(X2,^[V_1]: $true) = X2)), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(setadjoinOr, axiom, setadjoinOr <=> 114.29/114.87 (![Xx,A,Xy]: (in(Xy,setadjoin(Xx,A)) => (in(Xy,A) | (Xy = Xx))))). 114.29/114.87 tff('62', plain, 114.29/114.87 setadjoinOr = 114.29/114.87 (![X2,X3,X4]: (in(X4,setadjoin(X2,X3)) => (in(X4,X3) | (X4 = X2)))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(setadjoinE, axiom, setadjoinE <=> 114.29/114.87 (![Xx,A,Xy]: 114.29/114.87 (in(Xy,setadjoin(Xx,A)) => 114.29/114.87 (![Xphi:$o]: (((Xy = Xx) => Xphi) => ((in(Xy,A) => Xphi) => Xphi)))))). 114.29/114.87 tff('63', plain, 114.29/114.87 setadjoinE = 114.29/114.87 (![X2,X3,X4]: 114.29/114.87 (in(X4,setadjoin(X2,X3)) => 114.29/114.87 (![X5:$o]: (((X4 = X2) => X5) => ((in(X4,X3) => X5) => X5))))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(setadjoinIR, axiom, setadjoinIR <=> 114.29/114.87 (![Xx,A,Xy]: (in(Xy,A) => in(Xy,setadjoin(Xx,A))))). 114.29/114.87 tff('64', plain, 114.29/114.87 setadjoinIR = (![X2,X3,X4]: (in(X4,X3) => in(X4,setadjoin(X2,X3)))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(emptyinunitempty, axiom, emptyinunitempty() = 114.29/114.87 in(emptyset,setadjoin(emptyset,emptyset))). 114.29/114.87 tff('65', plain, 114.29/114.87 emptyinunitempty = in(emptyset,setadjoin(emptyset,emptyset)), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(setadjoinIL, axiom, setadjoinIL <=> (![Xx,Xy]: in(Xx,setadjoin(Xx,Xy)))). 114.29/114.87 tff('66', plain, setadjoinIL = (![X2,X3]: in(X2,setadjoin(X2,X3))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(nonemptyI1, axiom, nonemptyI1 <=> 114.29/114.87 (![A]: ((?[Xx]: in(Xx,A)) => nonempty(A)))). 114.29/114.87 tff('67', plain, nonemptyI1 = (![X2]: ((?[X3]: in(X3,X2)) => nonempty(X2))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(nonemptyI, axiom, nonemptyI <=> 114.29/114.87 (![A,Xphi:($i > $o),Xx]: 114.29/114.87 (in(Xx,A) => (Xphi(Xx) => nonempty(dsetconstr(A,^[Xy]: Xphi(Xy))))))). 114.29/114.87 tff('68', plain, 114.29/114.87 nonemptyI = 114.29/114.87 (![X2,X3:($i > $o),X4]: 114.29/114.87 (in(X4,X2) => (X3(X4) => nonempty(dsetconstr(X2,^[V_1]: X3(V_1)))))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(nonemptyE1, axiom, nonemptyE1 <=> 114.29/114.87 (![A]: (nonempty(A) => (?[Xx]: in(Xx,A))))). 114.29/114.87 tff('69', plain, nonemptyE1 = (![X2]: (nonempty(X2) => (?[X3]: in(X3,X2)))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(nonempty, axiom, nonempty() = ^[Xx]: (Xx != emptyset)). 114.29/114.87 tff('70', plain, nonempty = (^[V_1]: (V_1 != emptyset)), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(setbeta, axiom, setbeta <=> 114.29/114.87 (![A,Xphi:($i > $o),Xx]: 114.29/114.87 (in(Xx,A) => (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) <=> Xphi(Xx))))). 114.29/114.87 tff('71', plain, 114.29/114.87 setbeta = 114.29/114.87 (![X2,X3:($i > $o),X4]: 114.29/114.87 (in(X4,X2) => (in(X4,dsetconstr(X2,^[V_1]: X3(V_1))) <=> X3(X4)))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(noeltsimpempty, axiom, noeltsimpempty <=> 114.29/114.87 (![A]: ((![Xx]: (~in(Xx,A))) => (A = emptyset)))). 114.29/114.87 tff('72', plain, 114.29/114.87 noeltsimpempty = (![X2]: ((![X3]: (~in(X3,X2))) => (X2 = emptyset))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(emptyI, axiom, emptyI <=> 114.29/114.87 (![A]: ((![Xx]: (~in(Xx,A))) => (A = emptyset)))). 114.29/114.87 tff('73', plain, 114.29/114.87 emptyI = (![X2]: ((![X3]: (~in(X3,X2))) => (X2 = emptyset))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(setext, axiom, setext <=> 114.29/114.87 (![A,B]: 114.29/114.87 ((![Xx]: (in(Xx,A) => in(Xx,B))) => 114.29/114.87 ((![Xx]: (in(Xx,B) => in(Xx,A))) => (A = B))))). 114.29/114.87 tff('74', plain, 114.29/114.87 setext = 114.29/114.87 (![X2,X3]: 114.29/114.87 ((![X4]: (in(X4,X2) => in(X4,X3))) => 114.29/114.87 ((![X5]: (in(X5,X3) => in(X5,X2))) => (X2 = X3)))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(exuE3e, axiom, exuE3e <=> 114.29/114.87 (![Xphi:($i > $o)]: (exu(^[Xx]: Xphi(Xx)) => (?[Xx]: Xphi(Xx))))). 114.29/114.87 tff('75', plain, 114.29/114.87 exuE3e = (![X2:($i > $o)]: (exu(^[V_1]: X2(V_1)) => (?[X3]: X2(X3)))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(notinemptyset, axiom, notinemptyset <=> (![Xx]: (~in(Xx,emptyset)))). 114.29/114.87 tff('76', plain, notinemptyset = (![X2]: (~in(X2,emptyset))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(emptysetimpfalse, axiom, emptysetimpfalse <=> 114.29/114.87 (![Xx]: (in(Xx,emptyset) => $false))). 114.29/114.87 tff('77', plain, emptysetimpfalse = (![X2]: (in(X2,emptyset) => $false)), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(emptysetE, axiom, emptysetE <=> 114.29/114.87 (![Xx]: (in(Xx,emptyset) => (![Xphi:$o]: Xphi)))). 114.29/114.87 tff('78', plain, emptysetE = (![X2]: (in(X2,emptyset) => (![X3:$o]: X3))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(prop2setE, axiom, prop2setE <=> 114.29/114.87 (![Xphi:$o,Xx]: (in(Xx,prop2set(Xphi)) => Xphi))). 114.29/114.87 tff('79', plain, prop2setE = (![X2:$o,X3]: (in(X3,prop2set(X2)) => X2)), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(exuE1, axiom, exuE1 <=> 114.29/114.87 (![Xphi:($i > $o)]: 114.29/114.87 (exu(^[Xx]: Xphi(Xx)) => 114.29/114.87 (?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx)))))). 114.29/114.87 tff('80', plain, 114.29/114.87 exuE1 = 114.29/114.87 (![X2:($i > $o)]: 114.29/114.87 (exu(^[V_1]: X2(V_1)) => 114.29/114.87 (?[X3]: ((![X4]: (X2(X4) => (X3 = X4))) & X2(X3))))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(dsetconstrER, axiom, dsetconstrER <=> 114.29/114.87 (![A,Xphi:($i > $o),Xx]: (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) => Xphi(Xx)))). 114.29/114.87 tff('81', plain, 114.29/114.87 dsetconstrER = 114.29/114.87 (![X2,X3:($i > $o),X4]: (in(X4,dsetconstr(X2,^[V_1]: X3(V_1))) => X3(X4))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(dsetconstrEL, axiom, dsetconstrEL <=> 114.29/114.87 (![A,Xphi:($i > $o),Xx]: (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) => in(Xx,A)))). 114.29/114.87 tff('82', plain, 114.29/114.87 dsetconstrEL = 114.29/114.87 (![X2,X3:($i > $o),X4]: 114.29/114.87 (in(X4,dsetconstr(X2,^[V_1]: X3(V_1))) => in(X4,X2))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(dsetconstrI, axiom, dsetconstrI <=> 114.29/114.87 (![A,Xphi:($i > $o),Xx]: 114.29/114.87 (in(Xx,A) => (Xphi(Xx) => in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))))))). 114.29/114.87 tff('83', plain, 114.29/114.87 dsetconstrI = 114.29/114.87 (![X2,X3:($i > $o),X4]: 114.29/114.87 (in(X4,X2) => (X3(X4) => in(X4,dsetconstr(X2,^[V_1]: X3(V_1)))))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(descrp, axiom, descrp <=> 114.29/114.87 (![Xphi:($i > $o)]: (exu(^[Xx]: Xphi(Xx)) => Xphi(descr(^[Xx]: Xphi(Xx)))))). 114.29/114.87 tff('84', plain, 114.29/114.87 descrp = 114.29/114.87 (![X2:($i > $o)]: (exu(^[V_1]: X2(V_1)) => X2(descr(^[V_2]: X2(V_2))))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(wellorderingAx, axiom, wellorderingAx <=> 114.29/114.87 (![A]: 114.29/114.87 (?[B]: 114.29/114.87 ((![C]: 114.29/114.87 (((?[Xx]: in(Xx,C)) & (![Xx]: (in(Xx,C) => in(Xx,A)))) => 114.29/114.87 (?[D,Xx]: 114.29/114.87 ((![E]: 114.29/114.87 (in(E,B) => (in(Xx,E) | (![Xy]: (in(Xy,E) => in(Xy,D)))))) & 114.29/114.87 (~(?[Xy]: (in(Xy,C) & in(Xy,D)))) & in(Xx,C) & in(D,B))))) & 114.29/114.87 (![C,D]: 114.29/114.87 ((in(D,B) & in(C,B)) => 114.29/114.87 ((![Xx]: (in(Xx,D) => in(Xx,C))) | 114.29/114.87 (![Xx]: (in(Xx,C) => in(Xx,D)))))) & 114.29/114.87 (![Xx,Xy]: 114.29/114.87 ((in(Xy,A) & in(Xx,A)) => 114.29/114.87 ((![C]: (in(C,B) => (in(Xx,C) <=> in(Xy,C)))) => (Xx = Xy)))) & 114.29/114.87 (![C]: (in(C,B) => (![Xx]: (in(Xx,C) => in(Xx,A))))))))). 114.29/114.87 tff('85', plain, 114.29/114.87 wellorderingAx = 114.29/114.87 (![X2]: 114.29/114.87 (?[X3]: 114.29/114.87 ((![X4]: 114.29/114.87 (((?[X5]: in(X5,X4)) & (![X6]: (in(X6,X4) => in(X6,X2)))) => 114.29/114.87 (?[X7,X8]: 114.29/114.87 ((![X9]: 114.29/114.87 (in(X9,X3) => 114.29/114.87 (in(X8,X9) | (![X10]: (in(X10,X9) => in(X10,X7)))))) & 114.29/114.87 (~(?[X11]: (in(X11,X4) & in(X11,X7)))) & in(X8,X4) & 114.29/114.87 in(X7,X3))))) & 114.29/114.87 (![X12,X13]: 114.29/114.87 ((in(X13,X3) & in(X12,X3)) => 114.29/114.87 ((![X14]: (in(X14,X13) => in(X14,X12))) | 114.29/114.87 (![X15]: (in(X15,X12) => in(X15,X13)))))) & 114.29/114.87 (![X16,X17]: 114.29/114.87 ((in(X17,X2) & in(X16,X2)) => 114.29/114.87 ((![X18]: (in(X18,X3) => (in(X16,X18) <=> in(X17,X18)))) => 114.29/114.87 (X16 = X17)))) & 114.29/114.87 (![X19]: (in(X19,X3) => (![X20]: (in(X20,X19) => in(X20,X2)))))))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(foundationAx, axiom, foundationAx <=> 114.29/114.87 (![A]: 114.29/114.87 ((?[Xx]: in(Xx,A)) => 114.29/114.87 (?[B]: ((~(?[Xx]: (in(Xx,A) & in(Xx,B)))) & in(B,A)))))). 114.29/114.87 tff('86', plain, 114.29/114.87 foundationAx = 114.29/114.87 (![X2]: 114.29/114.87 ((?[X3]: in(X3,X2)) => 114.29/114.87 (?[X4]: ((~(?[X5]: (in(X5,X2) & in(X5,X4)))) & in(X4,X2))))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(replAx, axiom, replAx <=> 114.29/114.87 (![Xphi:(($i * $i) > $o),A]: 114.29/114.87 ((![Xx]: (in(Xx,A) => exu(^[Xy]: Xphi(Xx,Xy)))) => 114.29/114.87 (?[B]: (![Xx]: (in(Xx,B) <=> (?[Xy]: (Xphi(Xy,Xx) & in(Xy,A))))))))). 114.29/114.87 tff('87', plain, 114.29/114.87 replAx = 114.29/114.87 (![X2:(($i * $i) > $o),X3]: 114.29/114.87 ((![X4]: (in(X4,X3) => exu(^[V_1]: X2(X4,V_1)))) => 114.29/114.87 (?[X5]: (![X6]: (in(X6,X5) <=> (?[X7]: (X2(X7,X6) & in(X7,X3)))))))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(omegaIndAx, axiom, omegaIndAx <=> 114.29/114.87 (![A]: 114.29/114.87 (((![Xx]: ((in(Xx,A) & in(Xx,omega)) => in(setadjoin(Xx,Xx),A))) & 114.29/114.87 in(emptyset,A)) => 114.29/114.87 (![Xx]: (in(Xx,omega) => in(Xx,A)))))). 114.29/114.87 tff('88', plain, 114.29/114.87 omegaIndAx = 114.29/114.87 (![X2]: 114.29/114.87 (((![X3]: ((in(X3,X2) & in(X3,omega)) => in(setadjoin(X3,X3),X2))) & 114.29/114.87 in(emptyset,X2)) => 114.29/114.87 (![X4]: (in(X4,omega) => in(X4,X2))))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(omegaSAx, axiom, omegaSAx <=> 114.29/114.87 (![Xx]: (in(Xx,omega) => in(setadjoin(Xx,Xx),omega)))). 114.29/114.87 tff('89', plain, 114.29/114.87 omegaSAx = (![X2]: (in(X2,omega) => in(setadjoin(X2,X2),omega))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(omega0Ax, axiom, omega0Ax() = in(emptyset,omega)). 114.29/114.87 tff('90', plain, omega0Ax = in(emptyset,omega), define([status(thm)])). 114.29/114.87 tff(setunionAx, axiom, setunionAx <=> 114.29/114.87 (![A,Xx]: (in(Xx,setunion(A)) <=> (?[B]: (in(B,A) & in(Xx,B)))))). 114.29/114.87 tff('91', plain, 114.29/114.87 setunionAx = 114.29/114.87 (![X2,X3]: (in(X3,setunion(X2)) <=> (?[X4]: (in(X4,X2) & in(X3,X4))))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(powersetAx, axiom, powersetAx <=> 114.29/114.87 (![A,B]: (in(B,powerset(A)) <=> (![Xx]: (in(Xx,B) => in(Xx,A)))))). 114.29/114.87 tff('92', plain, 114.29/114.87 powersetAx = 114.29/114.87 (![X2,X3]: (in(X3,powerset(X2)) <=> (![X4]: (in(X4,X3) => in(X4,X2))))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(setadjoinAx, axiom, setadjoinAx <=> 114.29/114.87 (![Xx,A,Xy]: (in(Xy,setadjoin(Xx,A)) <=> (in(Xy,A) | (Xy = Xx))))). 114.29/114.87 tff('93', plain, 114.29/114.87 setadjoinAx = 114.29/114.87 (![X2,X3,X4]: (in(X4,setadjoin(X2,X3)) <=> (in(X4,X3) | (X4 = X2)))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(emptysetAx, axiom, emptysetAx <=> (![Xx]: (~in(Xx,emptyset)))). 114.29/114.87 tff('94', plain, emptysetAx = (![X2]: (~in(X2,emptyset))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(setextAx, axiom, setextAx <=> 114.29/114.87 (![A,B]: ((![Xx]: (in(Xx,A) <=> in(Xx,B))) => (A = B)))). 114.29/114.87 tff('95', plain, 114.29/114.87 setextAx = (![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(exu, axiom, exu() = 114.29/114.87 ^[Xphi:($i > $o)]: (?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx)))). 114.29/114.87 tff('96', plain, 114.29/114.87 exu = 114.29/114.87 (^[V_1:($i > $o)]: (?[X2]: ((![X3]: (V_1(X3) => (X2 = X3))) & V_1(X2)))), 114.29/114.87 define([status(thm)])). 114.29/114.87 tff(powersetsubset, conjecture, 114.29/114.87 (setextAx => 114.29/114.87 (emptysetAx => 114.29/114.87 (setadjoinAx => 114.29/114.87 (powersetAx => 114.29/114.87 (setunionAx => 114.29/114.87 (omega0Ax => 114.29/114.87 (omegaSAx => 114.29/114.87 (omegaIndAx => 114.29/114.87 (replAx => 114.29/114.87 (foundationAx => 114.29/114.87 (wellorderingAx => 114.29/114.87 (descrp => 114.29/114.87 (dsetconstrI => 114.29/114.87 (dsetconstrEL => 114.29/114.87 (dsetconstrER => 114.29/114.87 (exuE1 => 114.29/114.87 (prop2setE => 114.29/114.87 (emptysetE => 114.29/114.87 (emptysetimpfalse => 114.29/114.87 (notinemptyset => 114.29/114.87 (exuE3e => 114.29/114.87 (setext => 114.29/114.87 (emptyI => 114.29/114.87 (noeltsimpempty => 114.29/114.87 (setbeta => 114.29/114.87 (nonemptyE1 => 114.29/114.87 (nonemptyI => 114.29/114.87 (nonemptyI1 => 114.29/114.87 (setadjoinIL => 114.29/114.87 (emptyinunitempty => 114.29/114.87 (setadjoinIR => 114.29/114.87 (setadjoinE => 114.29/114.87 (setadjoinOr => 114.29/114.87 (setoftrueEq => 114.29/114.87 (powersetI => 114.29/114.87 (emptyinPowerset => 114.29/114.87 (emptyInPowerset => 114.29/114.87 (powersetE => 114.29/114.87 (setunionI => 114.29/114.87 (setunionE => 114.29/114.87 (subPowSU => 114.29/114.87 (exuE2 => 114.29/114.87 (nonemptyImpWitness => 114.29/114.87 (uniqinunit => 114.29/114.87 (notinsingleton => 114.29/114.87 (eqinunit => 114.29/114.87 (singletonsswitch => 114.29/114.87 (upairsetE => 114.29/114.87 (upairsetIL => 114.29/114.87 (upairsetIR => 114.29/114.87 (emptyE1 => 114.29/114.87 (vacuousDall => 114.29/114.87 (quantDeMorgan1 => 114.29/114.87 (quantDeMorgan2 => 114.29/114.87 (quantDeMorgan3 => 114.29/114.87 (quantDeMorgan4 => 114.29/114.87 (prop2setI => 114.29/114.87 (prop2set2propI => 114.29/114.87 (notdexE => 114.29/114.87 (notdallE => 114.29/114.87 (exuI1 => 114.29/114.87 (exuI3 => 114.29/114.87 (exuI2 => 114.29/114.87 (inCongP => 114.29/114.87 (in__Cong => 114.29/114.87 (exuE3u => 114.29/114.87 ( 114.29/114.87 exu__Cong => 114.29/114.87 ( 114.29/114.87 emptyset__Cong => 114.29/114.87 ( 114.29/114.87 setadjoin__Cong => 114.29/114.87 ( 114.29/114.87 powerset__Cong => 114.29/114.87 ( 114.29/114.87 setunion__Cong => 114.29/114.87 ( 114.29/114.87 omega__Cong => 114.29/114.87 ( 114.29/114.87 exuEu => 114.29/114.87 ( 114.29/114.87 descr__Cong => 114.29/114.87 ( 114.29/114.87 dsetconstr__Cong => 114.29/114.87 ( 114.29/114.87 subsetI1 => 114.29/114.87 ( 114.29/114.87 eqimpsubset2 => 114.29/114.87 ( 114.29/114.87 eqimpsubset1 => 114.29/114.87 ( 114.29/114.87 subsetI2 => 114.29/114.87 ( 114.29/114.87 emptysetsubset => 114.29/114.87 ( 114.29/114.87 subsetE => 114.29/114.87 ( 114.29/114.87 subsetE2 => 114.29/114.87 ( 114.29/114.87 notsubsetI => 114.29/114.87 ( 114.29/114.87 notequalI1 => 114.29/114.87 ( 114.29/114.87 notequalI2 => 114.29/114.87 ( 114.29/114.87 subsetRefl => 114.29/114.87 ( 114.29/114.87 subsetTrans => 114.29/114.87 ( 114.29/114.87 setadjoinSub => 114.29/114.87 ( 114.29/114.87 setadjoinSub2 => 114.29/114.87 ( 114.29/114.87 subset2powerset => 114.29/114.87 ( 114.29/114.87 setextsub => 114.29/114.87 ( 114.29/114.87 subsetemptysetimpeq => 114.29/114.87 ( 114.29/114.87 powersetI1 => 114.29/114.87 ( 114.29/114.87 powersetE1 => 114.29/114.87 ( 114.29/114.87 inPowerset => 114.29/114.87 ( 114.29/114.87 ![A,B]: 114.29/114.87 (subset( 114.29/114.87 A,B) => 114.29/114.87 subset( 114.29/114.87 powerset( 114.29/114.87 A), 114.29/114.87 powerset( 114.29/114.87 B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 114.29/114.87 tff(zf_stmt_0, conjecture, 114.29/114.87 ((![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))) => 114.29/114.87 ((![X5]: (~in(X5,emptyset))) => 114.29/114.87 ((![X6,X7,X8]: (in(X8,setadjoin(X6,X7)) <=> ((X8 = X6) | in(X8,X7)))) => 114.29/114.87 ((![X9,X10]: 114.29/114.87 (in(X10,powerset(X9)) <=> (![X11]: (in(X11,X10) => in(X11,X9))))) => 114.29/114.87 ((![X12,X13]: 114.29/114.87 (in(X13,setunion(X12)) <=> (?[X14]: (in(X13,X14) & in(X14,X12))))) => 114.29/114.87 (in(emptyset,omega) => 114.29/114.87 ((![X15]: (in(X15,omega) => in(setadjoin(X15,X15),omega))) => 114.29/114.87 ((![X16]: 114.29/114.87 ((in(emptyset,X16) & 114.29/114.87 (![X17]: 114.29/114.87 ((in(X17,omega) & in(X17,X16)) => 114.29/114.87 in(setadjoin(X17,X17),X16)))) => 114.29/114.87 (![X18]: (in(X18,omega) => in(X18,X16))))) => 114.29/114.87 ((![X19:(($i * $i) > $o),X20]: 114.29/114.87 ((![X21]: 114.29/114.87 (in(X21,X20) => 114.29/114.87 (?[X22]: 114.29/114.87 (X19(X21,X22) & (![X23]: (X19(X21,X23) => (X22 = X23))))))) => 114.29/114.87 (?[X24]: 114.29/114.87 (![X25]: 114.29/114.87 (in(X25,X24) <=> (?[X26]: (in(X26,X20) & X19(X26,X25)))))))) => 114.29/114.87 ((![X27]: 114.29/114.87 ((?[X28]: in(X28,X27)) => 114.29/114.87 (?[X29]: 114.29/114.87 (in(X29,X27) & (~(?[X30]: (in(X30,X29) & in(X30,X27)))))))) => 114.29/114.87 ((![X31]: 114.29/114.87 (?[X32]: 114.29/114.87 ((![X48]: 114.29/114.87 (in(X48,X32) => (![X49]: (in(X49,X48) => in(X49,X31))))) & 114.29/114.87 (![X45,X46]: 114.29/114.87 ((in(X45,X31) & in(X46,X31)) => 114.29/114.87 ((![X47]: 114.29/114.87 (in(X47,X32) => (in(X45,X47) <=> in(X46,X47)))) => 114.29/114.87 (X45 = X46)))) & 114.29/114.87 (![X41,X42]: 114.29/114.87 ((in(X41,X32) & in(X42,X32)) => 114.29/114.87 ((![X44]: (in(X44,X41) => in(X44,X42))) | 114.29/114.87 (![X43]: (in(X43,X42) => in(X43,X41)))))) & 114.29/114.87 (![X33]: 114.29/114.87 (((![X35]: (in(X35,X33) => in(X35,X31))) & 114.29/114.87 (?[X34]: in(X34,X33))) => 114.29/114.87 (?[X36,X37]: 114.29/114.87 (in(X36,X32) & in(X37,X33) & 114.29/114.87 (~(?[X40]: (in(X40,X36) & in(X40,X33)))) & 114.29/114.87 (![X38]: 114.29/114.87 (in(X38,X32) => 114.29/114.87 ((![X39]: (in(X39,X38) => in(X39,X36))) | 114.29/114.87 in(X37,X38))))))))))) => 114.29/114.87 ((![X50:($i > $o)]: 114.29/114.87 ((?[X51]: (X50(X51) & (![X52]: (X50(X52) => (X51 = X52))))) => 114.29/114.87 X50(descr('#ll_0'(X50))))) => 114.29/114.87 ((![X53,X54:($i > $o),X55]: 114.29/114.87 (in(X55,X53) => 114.29/114.87 (X54(X55) => in(X55,dsetconstr(X53,'#ll_0'(X54)))))) => 114.29/114.87 ((![X56,X57:($i > $o),X58]: 114.29/114.87 (in(X58,dsetconstr(X56,'#ll_0'(X57))) => in(X58,X56))) => 114.29/114.87 ((![X59,X60:($i > $o),X61]: 114.29/114.87 (in(X61,dsetconstr(X59,'#ll_0'(X60))) => X60(X61))) => 114.29/114.87 ((![X62:($i > $o)]: 114.29/114.87 ((?[X63]: 114.29/114.87 (X62(X63) & (![X64]: (X62(X64) => (X63 = X64))))) => 114.29/114.87 (?[X65]: 114.29/114.87 (X62(X65) & (![X66]: (X62(X66) => (X65 = X66))))))) => 114.29/114.87 ((![X67:$o,X68]: (in(X68,prop2set(X67)) => X67)) => 114.29/114.87 ((![X69]: (in(X69,emptyset) => (![X70:$o]: X70))) => 114.29/114.87 ((![X71]: (in(X71,emptyset) => $false)) => 114.29/114.87 ((![X72]: (~in(X72,emptyset))) => 114.29/114.87 ((![X73:($i > $o)]: 114.29/114.87 ((?[X74]: 114.29/114.87 (X73(X74) & (![X75]: (X73(X75) => (X74 = X75))))) => 114.29/114.87 (?[X76]: X73(X76)))) => 114.29/114.87 ((![X77,X78]: 114.29/114.87 ((![X79]: (in(X79,X77) => in(X79,X78))) => 114.29/114.87 ((![X80]: (in(X80,X78) => in(X80,X77))) => 114.29/114.87 (X77 = X78)))) => 114.29/114.87 ((![X81]: 114.29/114.87 ((![X82]: (~in(X82,X81))) => (X81 = emptyset))) => 114.29/114.87 ((![X83]: 114.29/114.87 ((![X84]: (~in(X84,X83))) => (X83 = emptyset))) => 114.29/114.87 ((![X85,X86:($i > $o),X87]: 114.29/114.87 (in(X87,X85) => 114.29/114.87 (in(X87,dsetconstr(X85,'#ll_0'(X86))) <=> 114.29/114.87 X86(X87)))) => 114.29/114.87 ((![X88]: 114.29/114.87 ((X88 != emptyset) => (?[X89]: in(X89,X88)))) => 114.29/114.87 ((![X90,X91:($i > $o),X92]: 114.29/114.87 (in(X92,X90) => 114.29/114.87 (X91(X92) => 114.29/114.87 (dsetconstr(X90,'#ll_0'(X91)) != emptyset)))) => 114.29/114.87 ((![X93]: 114.29/114.87 ((?[X94]: in(X94,X93)) => (X93 != emptyset))) => 114.29/114.87 ((![X95,X96]: in(X95,setadjoin(X95,X96))) => 114.29/114.87 (in(emptyset,setadjoin(emptyset,emptyset)) => 114.29/114.87 ((![X97,X98,X99]: 114.29/114.87 (in(X99,X98) => 114.29/114.87 in(X99,setadjoin(X97,X98)))) => 114.29/114.87 ((![X100,X101,X102]: 114.29/114.87 (in(X102,setadjoin(X100,X101)) => 114.29/114.87 (![X103:$o]: 114.29/114.87 (((X102 = X100) => X103) => 114.29/114.87 ((in(X102,X101) => X103) => X103))))) => 114.29/114.87 ((![X104,X105,X106]: 114.29/114.87 (in(X106,setadjoin(X104,X105)) => 114.29/114.87 ((X106 = X104) | in(X106,X105)))) => 114.29/114.87 ((![X107]: 114.29/114.87 (dsetconstr(X107,'#ll_1') = X107)) => 114.29/114.87 ((![X108,X109]: 114.29/114.87 ((![X110]: 114.29/114.87 (in(X110,X109) => in(X110,X108))) => 114.29/114.87 in(X109,powerset(X108)))) => 114.29/114.87 ((![X111]: in(emptyset,powerset(X111))) => 114.29/114.87 ((![X112]: in(emptyset,powerset(X112))) => 114.29/114.87 ((![X113,X114,X115]: 114.29/114.87 (in(X114,powerset(X113)) => 114.29/114.87 (in(X115,X114) => in(X115,X113)))) => 114.29/114.87 ((![X116,X117,X118]: 114.29/114.87 (in(X117,X118) => 114.29/114.87 (in(X118,X116) => 114.29/114.87 in(X117,setunion(X116))))) => 114.29/114.87 ((![X119,X120]: 114.29/114.87 (in(X120,setunion(X119)) => 114.29/114.87 (![X121:$o]: 114.29/114.87 ((![X122]: 114.29/114.87 (in(X120,X122) => 114.29/114.87 (in(X122,X119) => X121))) => 114.29/114.87 X121)))) => 114.29/114.87 ((![X123,X124]: 114.29/114.87 (in(X124,X123) => 114.29/114.87 in(X124, 114.29/114.87 powerset(setunion(X123))))) => 114.29/114.87 ((![X125:($i > $o)]: 114.29/114.87 ((?[X126]: 114.29/114.87 (X125(X126) & 114.29/114.87 (![X127]: 114.29/114.87 (X125(X127) => 114.29/114.87 (X126 = X127))))) => 114.29/114.87 (?[X128]: 114.29/114.87 (![X129]: 114.29/114.87 (X125(X129) <=> 114.29/114.87 (X129 = X128)))))) => 114.29/114.87 ((![X130]: 114.29/114.87 ((X130 != emptyset) => 114.29/114.87 (?[X131]: in(X131,X130)))) => 114.29/114.87 ((![X132,X133]: 114.29/114.87 (in(X132, 114.29/114.87 setadjoin(X133,emptyset)) => 114.29/114.87 (X132 = X133))) => 114.29/114.87 ((![X134,X135]: 114.29/114.87 ((X134 != X135) => 114.29/114.87 (~ 114.29/114.87 in(X135, 114.29/114.87 setadjoin(X134, 114.29/114.87 emptyset))))) => 114.29/114.87 ((![X136,X137]: 114.29/114.87 ((X136 = X137) => 114.29/114.87 in(X136, 114.29/114.87 setadjoin(X137, 114.29/114.87 emptyset)))) => 114.29/114.87 ((![X138,X139]: 114.29/114.87 (in(X138, 114.29/114.87 setadjoin(X139, 114.29/114.87 emptyset)) => 114.29/114.87 in(X139, 114.29/114.87 setadjoin(X138, 114.29/114.87 emptyset)))) => 114.29/114.87 ((![X140,X141,X142]: 114.29/114.87 (in(X142, 114.29/114.87 setadjoin(X140, 114.29/114.87 setadjoin( 114.29/114.87 X141, 114.29/114.87 emptyset))) => 114.29/114.87 ((X142 = X140) | 114.29/114.87 (X142 = X141)))) => 114.29/114.87 ((![X143,X144]: 114.29/114.87 in(X143, 114.29/114.87 setadjoin(X143, 114.29/114.87 setadjoin( 114.29/114.87 X144, 114.29/114.87 emptyset)))) => 114.29/114.87 ((![X145,X146]: 114.29/114.87 in(X146, 114.29/114.87 setadjoin(X145, 114.29/114.87 setadjoin( 114.29/114.87 X146, 114.29/114.87 emptyset)))) => 114.29/114.87 ((![X147,X148:($i > $o)]: 114.29/114.87 ((?[X149]: 114.29/114.87 (in(X149,X147) & 114.29/114.87 X148(X149))) => 114.29/114.87 ((dsetconstr( 114.29/114.87 X147,'#ll_0'(X148)) = 114.29/114.87 emptyset) => 114.29/114.87 $false))) => 114.29/114.87 ((![X150:($i > $o),X151]: 114.29/114.87 (in(X151,emptyset) => 114.29/114.87 X150(X151))) => 114.29/114.87 ((![X152,X153:($i > $o)]: 114.29/114.87 ((~ 114.29/114.87 (![X154]: 114.29/114.87 (in(X154,X152) => 114.29/114.87 X153(X154)))) => 114.29/114.87 (?[X155]: 114.29/114.87 (in(X155,X152) & 114.29/114.87 (~X153(X155)))))) => 114.29/114.87 ((![X156, 114.29/114.87 X157:($i > $o)]: 114.29/114.87 ((![X158]: 114.29/114.87 (in(X158,X156) => 114.29/114.87 (~X157(X158)))) => 114.29/114.87 (~ 114.29/114.87 (?[X159]: 114.29/114.87 (in( 114.29/114.87 X159,X156) & 114.29/114.87 X157(X159)))))) => 114.29/114.87 ((![X160, 114.29/114.87 X161:($i > $o)]: 114.29/114.87 ((~ 114.29/114.87 (?[X162]: 114.29/114.87 (in( 114.29/114.87 X162,X160) & 114.29/114.87 X161(X162)))) => 114.29/114.87 (![X163]: 114.29/114.87 (in(X163,X160) => 114.29/114.87 (~X161(X163)))))) => 114.29/114.87 ((![X164, 114.29/114.87 X165:($i > $o)]: 114.29/114.87 ((?[X166]: 114.29/114.87 (in( 114.29/114.87 X166,X164) & 114.29/114.87 (~ 114.29/114.87 X165( 114.29/114.87 X166)))) => 114.29/114.87 (~ 114.29/114.87 (![X167]: 114.29/114.87 (in( 114.29/114.87 X167,X164) => 114.29/114.87 X165( 114.29/114.87 X167)))))) => 114.29/114.87 ((![X168:$o]: 114.29/114.87 (X168 => 114.29/114.87 in(emptyset, 114.29/114.87 prop2set( 114.29/114.87 X168)))) => 114.29/114.87 ((![X169:$o]: 114.29/114.87 (X169 => 114.29/114.87 set2prop( 114.29/114.87 prop2set( 114.29/114.87 X169)))) => 114.29/114.87 ((![X170, 114.29/114.87 X171:( 114.29/114.87 $i > $o)]: 114.29/114.87 ((~ 114.29/114.87 (?[X172]: 114.29/114.87 (in( 114.29/114.87 X172,X170) & 114.29/114.87 X171( 114.29/114.87 X172)))) => 114.29/114.87 (![X173]: 114.29/114.87 ( 114.29/114.87 in( 114.29/114.87 X173,X170) => 114.29/114.87 ( 114.29/114.87 ~ 114.29/114.87 X171( 114.29/114.87 X173)))))) => 114.29/114.87 ((![X174, 114.29/114.87 X175:( 114.29/114.87 $i > $o)]: 114.29/114.87 ((~ 114.29/114.87 ( 114.29/114.87 ![X176]: 114.29/114.87 (in( 114.29/114.87 X176,X174) => 114.29/114.87 X175( 114.29/114.87 X176)))) => 114.29/114.87 (?[X177]: 114.29/114.87 (in( 114.29/114.87 X177,X174) & 114.29/114.87 (~ 114.29/114.87 X175( 114.29/114.87 X177)))))) => 114.29/114.87 ((![X178:( 114.29/114.87 $i > $o)]: 114.29/114.87 ((?[X179]: 114.29/114.87 (X178( 114.29/114.87 X179) & 114.29/114.87 (![X180]: 114.29/114.87 (X178( 114.29/114.87 X180) => 114.29/114.87 (X179 = 114.29/114.87 X180))))) => 114.29/114.87 (?[X181]: 114.29/114.87 (X178( 114.29/114.87 X181) & 114.29/114.87 (![X182]: 114.29/114.87 (X178( 114.29/114.87 X182) => 114.29/114.87 (X181 = 114.29/114.87 X182))))))) => 114.29/114.87 ((![X183:( 114.29/114.87 $i > $o)]: 114.29/114.87 (( 114.29/114.87 ?[X184]: 114.29/114.87 X183( 114.29/114.87 X184)) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X185, 114.29/114.87 X186]: 114.29/114.87 (X183( 114.29/114.87 X185) => 114.29/114.87 (X183( 114.29/114.87 X186) => 114.29/114.87 (X185 = 114.29/114.87 X186)))) => 114.29/114.87 ( 114.29/114.87 ?[X187]: 114.29/114.87 (X183( 114.29/114.87 X187) & 114.29/114.87 (![X188]: 114.29/114.87 (X183( 114.29/114.87 X188) => 114.29/114.87 (X187 = 114.29/114.87 X188)))))))) => 114.29/114.87 ((![X189:( 114.29/114.87 $i > $o)]: 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ?[X190]: 114.29/114.87 (![X191]: 114.29/114.87 (X189( 114.29/114.87 X191) <=> 114.29/114.87 (X191 = 114.29/114.87 X190)))) => 114.29/114.87 ( 114.29/114.87 ?[X192]: 114.29/114.87 (X189( 114.29/114.87 X192) & 114.29/114.87 (![X193]: 114.29/114.87 (X189( 114.29/114.87 X193) => 114.29/114.87 (X192 = 114.29/114.87 X193))))))) => 114.29/114.87 ((![X194, 114.29/114.87 X195]: 114.29/114.87 (( 114.29/114.87 X194 = 114.29/114.87 X195) => 114.29/114.87 (![X196, 114.29/114.87 X197]: 114.29/114.87 (( 114.29/114.87 X196 = 114.29/114.87 X197) => 114.29/114.87 (in( 114.29/114.87 X196,X194) => 114.29/114.87 in( 114.29/114.87 X197,X195)))))) => 114.29/114.87 ((![X198, 114.29/114.87 X199]: 114.29/114.87 (( 114.29/114.87 X198 = 114.29/114.87 X199) => 114.29/114.87 (![X200, 114.29/114.87 X201]: 114.29/114.87 (( 114.29/114.87 X200 = 114.29/114.87 X201) => 114.29/114.87 (in( 114.29/114.87 X200,X198) <=> 114.29/114.87 in( 114.29/114.87 X201,X199)))))) => 114.29/114.87 (( 114.29/114.87 ![X202:( 114.29/114.87 $i > $o)]: 114.29/114.87 (( 114.29/114.87 ?[X203]: 114.29/114.87 (X202( 114.29/114.87 X203) & 114.29/114.87 (![X204]: 114.29/114.87 (X202( 114.29/114.87 X204) => 114.29/114.87 (X203 = 114.29/114.87 X204))))) => 114.29/114.87 (![X205, 114.29/114.87 X206]: 114.29/114.87 (X202( 114.29/114.87 X205) => 114.29/114.87 (X202( 114.29/114.87 X206) => 114.29/114.87 (X205 = 114.29/114.87 X206)))))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X207:( 114.29/114.87 $i > $o), 114.29/114.87 X208:( 114.29/114.87 $i > $o)]: 114.29/114.87 (( 114.29/114.87 ![X209, 114.29/114.87 X210]: 114.29/114.87 (( 114.29/114.87 X209 = 114.29/114.87 X210) => 114.29/114.87 (X207( 114.29/114.87 X209) <=> 114.29/114.87 X208( 114.29/114.87 X210)))) => 114.29/114.87 (( 114.29/114.87 ?[X211]: 114.29/114.87 (X207( 114.29/114.87 X211) & 114.29/114.87 (![X212]: 114.29/114.87 (X207( 114.29/114.87 X212) => 114.29/114.87 (X211 = 114.29/114.87 X212))))) <=> 114.29/114.87 (?[X213]: 114.29/114.87 (X208( 114.29/114.87 X213) & 114.29/114.87 (![X214]: 114.29/114.87 (X208( 114.29/114.87 X214) => 114.29/114.87 (X213 = 114.29/114.87 X214)))))))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 emptyset = 114.29/114.87 emptyset) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X215, 114.29/114.87 X216]: 114.29/114.87 (( 114.29/114.87 X215 = 114.29/114.87 X216) => 114.29/114.87 (![X217, 114.29/114.87 X218]: 114.29/114.87 (( 114.29/114.87 X217 = 114.29/114.87 X218) => 114.29/114.87 (setadjoin( 114.29/114.87 X215,X217) = 114.29/114.87 setadjoin( 114.29/114.87 X216,X218)))))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X219, 114.29/114.87 X220]: 114.29/114.87 (( 114.29/114.87 X219 = 114.29/114.87 X220) => 114.29/114.87 (powerset( 114.29/114.87 X219) = 114.29/114.87 powerset( 114.29/114.87 X220)))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X221, 114.29/114.87 X222]: 114.29/114.87 (( 114.29/114.87 X221 = 114.29/114.87 X222) => 114.29/114.87 (setunion( 114.29/114.87 X221) = 114.29/114.87 setunion( 114.29/114.87 X222)))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 omega = 114.29/114.87 omega) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X223:( 114.29/114.87 $i > $o)]: 114.29/114.87 (( 114.29/114.87 ?[X224]: 114.29/114.87 (X223( 114.29/114.87 X224) & 114.29/114.87 (![X225]: 114.29/114.87 (X223( 114.29/114.87 X225) => 114.29/114.87 (X224 = 114.29/114.87 X225))))) => 114.29/114.87 (![X226, 114.29/114.87 X227]: 114.29/114.87 (X223( 114.29/114.87 X226) => 114.29/114.87 (X223( 114.29/114.87 X227) => 114.29/114.87 (X226 = 114.29/114.87 X227)))))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X228:( 114.29/114.87 $i > $o), 114.29/114.87 X229:( 114.29/114.87 $i > $o)]: 114.29/114.87 (( 114.29/114.87 ![X230, 114.29/114.87 X231]: 114.29/114.87 (( 114.29/114.87 X230 = 114.29/114.87 X231) => 114.29/114.87 (X228( 114.29/114.87 X230) <=> 114.29/114.87 X229( 114.29/114.87 X231)))) => 114.29/114.87 (( 114.29/114.87 ?[X232]: 114.29/114.87 (X228( 114.29/114.87 X232) & 114.29/114.87 (![X233]: 114.29/114.87 (X228( 114.29/114.87 X233) => 114.29/114.87 (X232 = 114.29/114.87 X233))))) => 114.29/114.87 (( 114.29/114.87 ?[X234]: 114.29/114.87 (X229( 114.29/114.87 X234) & 114.29/114.87 (![X235]: 114.29/114.87 (X229( 114.29/114.87 X235) => 114.29/114.87 (X234 = 114.29/114.87 X235))))) => 114.29/114.87 (descr( 114.29/114.87 '#ll_0'( 114.29/114.87 X228)) = 114.29/114.87 descr( 114.29/114.87 '#ll_0'( 114.29/114.87 X229))))))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X236, 114.29/114.87 X237]: 114.29/114.87 (( 114.29/114.87 X236 = 114.29/114.87 X237) => 114.29/114.87 (![X238:( 114.29/114.87 $i > $o), 114.29/114.87 X239:( 114.29/114.87 $i > $o)]: 114.29/114.87 (( 114.29/114.87 ![X240]: 114.29/114.87 (in( 114.29/114.87 X240,X236) => 114.29/114.87 (![X241]: 114.29/114.87 (in( 114.29/114.87 X241,X237) => 114.29/114.87 (( 114.29/114.87 X240 = 114.29/114.87 X241) => 114.29/114.87 (X238( 114.29/114.87 X240) <=> 114.29/114.87 X239( 114.29/114.87 X241))))))) => 114.29/114.87 (dsetconstr( 114.29/114.87 X236, 114.29/114.87 '#ll_0'( 114.29/114.87 X238)) = 114.29/114.87 dsetconstr( 114.29/114.87 X237, 114.29/114.87 '#ll_0'( 114.29/114.87 X239))))))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X242, 114.29/114.87 X243]: 114.29/114.87 (( 114.29/114.87 ![X244]: 114.29/114.87 (in( 114.29/114.87 X244,X242) => 114.29/114.87 in( 114.29/114.87 X244,X243))) => 114.29/114.87 subset( 114.29/114.87 X242,X243))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X245, 114.29/114.87 X246]: 114.29/114.87 (( 114.29/114.87 X245 = 114.29/114.87 X246) => 114.29/114.87 subset( 114.29/114.87 X246,X245))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X247, 114.29/114.87 X248]: 114.29/114.87 (( 114.29/114.87 X247 = 114.29/114.87 X248) => 114.29/114.87 subset( 114.29/114.87 X247,X248))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X249, 114.29/114.87 X250]: 114.29/114.87 (( 114.29/114.87 ![X251]: 114.29/114.87 (in( 114.29/114.87 X251,X249) => 114.29/114.87 in( 114.29/114.87 X251,X250))) => 114.29/114.87 subset( 114.29/114.87 X249,X250))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X252]: 114.29/114.87 subset( 114.29/114.87 emptyset, 114.29/114.87 X252)) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X253, 114.29/114.87 X254,X255]: 114.29/114.87 (subset( 114.29/114.87 X253,X254) => 114.29/114.87 (in( 114.29/114.87 X255,X253) => 114.29/114.87 in( 114.29/114.87 X255,X254)))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X256, 114.29/114.87 X257,X258]: 114.29/114.87 (subset( 114.29/114.87 X256,X257) => 114.29/114.87 (( 114.29/114.87 ~ 114.29/114.87 in( 114.29/114.87 X258,X257)) => 114.29/114.87 (~ 114.29/114.87 in( 114.29/114.87 X258,X256))))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X259, 114.29/114.87 X260,X261]: 114.29/114.87 (in( 114.29/114.87 X261,X259) => 114.29/114.87 (( 114.29/114.87 ~ 114.29/114.87 in( 114.29/114.87 X261,X260)) => 114.29/114.87 (~ 114.29/114.87 subset( 114.29/114.87 X259,X260))))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X262, 114.29/114.87 X263]: 114.29/114.87 (( 114.29/114.87 ~ 114.29/114.87 subset( 114.29/114.87 X262,X263)) => 114.29/114.87 (X262 != 114.29/114.87 X263))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X264, 114.29/114.87 X265,X266]: 114.29/114.87 (in( 114.29/114.87 X266,X264) => 114.29/114.87 (( 114.29/114.87 ~ 114.29/114.87 in( 114.29/114.87 X266,X265)) => 114.29/114.87 (X264 != 114.29/114.87 X265)))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X267]: 114.29/114.87 subset( 114.29/114.87 X267,X267)) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X268, 114.29/114.87 X269,X270]: 114.29/114.87 (subset( 114.29/114.87 X268,X269) => 114.29/114.87 (subset( 114.29/114.87 X269,X270) => 114.29/114.87 subset( 114.29/114.87 X268,X270)))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X271, 114.29/114.87 X272]: 114.29/114.87 subset( 114.29/114.87 X272, 114.29/114.87 setadjoin( 114.29/114.87 X271,X272))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X273, 114.29/114.87 X274,X275]: 114.29/114.87 (subset( 114.29/114.87 X273,X275) => 114.29/114.87 subset( 114.29/114.87 X273, 114.29/114.87 setadjoin( 114.29/114.87 X274,X275)))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X276, 114.29/114.87 X277]: 114.29/114.87 (subset( 114.29/114.87 X276,X277) => 114.29/114.87 in( 114.29/114.87 X276, 114.29/114.87 powerset( 114.29/114.87 X277)))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X278, 114.29/114.87 X279]: 114.29/114.87 (subset( 114.29/114.87 X278,X279) => 114.29/114.87 (subset( 114.29/114.87 X279,X278) => 114.29/114.87 (X278 = 114.29/114.87 X279)))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X280]: 114.29/114.87 (subset( 114.29/114.87 X280, 114.29/114.87 emptyset) => 114.29/114.87 (X280 = 114.29/114.87 emptyset))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X281, 114.29/114.87 X282]: 114.29/114.87 (subset( 114.29/114.87 X282,X281) => 114.29/114.87 in( 114.29/114.87 X282, 114.29/114.87 powerset( 114.29/114.87 X281)))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X283, 114.29/114.87 X284]: 114.29/114.87 (in( 114.29/114.87 X284, 114.29/114.87 powerset( 114.29/114.87 X283)) => 114.29/114.87 subset( 114.29/114.87 X284,X283))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X285]: 114.29/114.87 in( 114.29/114.87 X285, 114.29/114.87 powerset( 114.29/114.87 X285))) => 114.29/114.87 ( 114.29/114.87 ![X286, 114.29/114.87 X287]: 114.29/114.87 (subset( 114.29/114.87 X286,X287) => 114.29/114.87 subset( 114.29/114.87 powerset( 114.29/114.87 X286), 114.29/114.87 powerset( 114.29/114.87 X287)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 114.29/114.87 tff(zf_stmt_1, type, zip_tseitin5 : ($i * $i > $o) > $o). 114.29/114.87 tff(zf_stmt_2, axiom, 114.29/114.87 (zip_tseitin5(X211,X207) <=> 114.29/114.87 ((![X212]: zip_tseitin4(X212,X211,X207)) & X207(X211)))). 114.29/114.87 tff(zf_stmt_3, type, zip_tseitin4 : ($i * $i * $i > $o) > $o). 114.29/114.87 tff(zf_stmt_4, axiom, 114.29/114.87 (zip_tseitin4(X212,X211,X207) <=> (X207(X212) => (X211 = X212)))). 114.29/114.87 tff(zf_stmt_5, type, zip_tseitin3 : ($i * $i * $i * ($i * $i) > $o) > $o). 114.29/114.87 tff(zf_stmt_6, axiom, 114.29/114.87 (zip_tseitin3(X26,X25,X20,X19) <=> (X19(X26,X25) & in(X26,X20)))). 114.29/114.87 tff(zf_stmt_7, type, zip_tseitin2 : ($i * $i * $i) > $o). 114.29/114.87 tff(zf_stmt_8, axiom, 114.29/114.87 (zip_tseitin2(X14,X13,X12) <=> (in(X14,X12) & in(X13,X14)))). 114.29/114.87 tff(zf_stmt_9, type, zip_tseitin1 : ($i * $i * $i) > $o). 114.29/114.87 tff(zf_stmt_10, axiom, 114.29/114.87 (zip_tseitin1(X11,X10,X9) <=> (in(X11,X10) => in(X11,X9)))). 114.29/114.87 tff(zf_stmt_11, type, zip_tseitin0 : ($i * $i * $i) > $o). 114.29/114.87 tff(zf_stmt_12, axiom, (zip_tseitin0(X8,X7,X6) <=> (in(X8,X7) | (X8 = X6)))). 114.29/114.87 tff(zf_stmt_13, conjecture, 114.29/114.87 ((![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))) => 114.29/114.87 ((![X5]: (~in(X5,emptyset))) => 114.29/114.87 ((![X6,X7,X8]: (in(X8,setadjoin(X6,X7)) <=> zip_tseitin0(X8,X7,X6))) => 114.29/114.87 ((![X9,X10]: 114.29/114.87 (in(X10,powerset(X9)) <=> (![X11]: zip_tseitin1(X11,X10,X9)))) => 114.29/114.87 ((![X12,X13]: 114.29/114.87 (in(X13,setunion(X12)) <=> (?[X14]: zip_tseitin2(X14,X13,X12)))) => 114.29/114.87 (in(emptyset,omega) => 114.29/114.87 ((![X15]: (in(X15,omega) => in(setadjoin(X15,X15),omega))) => 114.29/114.87 ((![X16]: 114.29/114.87 (((![X17]: 114.29/114.87 ((in(X17,X16) & in(X17,omega)) => 114.29/114.87 in(setadjoin(X17,X17),X16))) & 114.29/114.87 in(emptyset,X16)) => 114.29/114.87 (![X18]: (in(X18,omega) => in(X18,X16))))) => 114.29/114.87 ((![X19:(($i * $i) > $o),X20]: 114.29/114.87 ((![X21]: 114.29/114.87 (in(X21,X20) => 114.29/114.87 (?[X22]: 114.29/114.87 ((![X23]: (X19(X21,X23) => (X22 = X23))) & X19(X21,X22))))) => 114.29/114.87 (?[X24]: 114.29/114.87 (![X25]: 114.29/114.87 (in(X25,X24) <=> (?[X26]: zip_tseitin3(X26,X25,X20,X19))))))) => 114.29/114.87 ((![X27]: 114.29/114.87 ((?[X28]: in(X28,X27)) => 114.29/114.87 (?[X29]: 114.29/114.87 ((~(?[X30]: (in(X30,X27) & in(X30,X29)))) & in(X29,X27))))) => 114.29/114.87 ((![X31]: 114.29/114.87 (?[X32]: 114.29/114.87 ((![X33]: 114.29/114.87 (((?[X34]: in(X34,X33)) & 114.29/114.87 (![X35]: (in(X35,X33) => in(X35,X31)))) => 114.29/114.87 (?[X36,X37]: 114.29/114.87 ((![X38]: 114.29/114.87 (in(X38,X32) => 114.29/114.87 (in(X37,X38) | 114.29/114.87 (![X39]: (in(X39,X38) => in(X39,X36)))))) & 114.29/114.87 (~(?[X40]: (in(X40,X33) & in(X40,X36)))) & 114.29/114.87 in(X37,X33) & in(X36,X32))))) & 114.29/114.87 (![X41,X42]: 114.29/114.87 ((in(X42,X32) & in(X41,X32)) => 114.29/114.87 ((![X43]: (in(X43,X42) => in(X43,X41))) | 114.29/114.87 (![X44]: (in(X44,X41) => in(X44,X42)))))) & 114.29/114.87 (![X45,X46]: 114.29/114.87 ((in(X46,X31) & in(X45,X31)) => 114.29/114.87 ((![X47]: 114.29/114.87 (in(X47,X32) => (in(X45,X47) <=> in(X46,X47)))) => 114.29/114.87 (X45 = X46)))) & 114.29/114.87 (![X48]: 114.29/114.87 (in(X48,X32) => (![X49]: (in(X49,X48) => in(X49,X31)))))))) => 114.29/114.87 ((![X50:($i > $o)]: 114.29/114.87 ((?[X51]: ((![X52]: (X50(X52) => (X51 = X52))) & X50(X51))) => 114.29/114.87 X50(descr('#ll_0'(X50))))) => 114.29/114.87 ((![X53,X54:($i > $o),X55]: 114.29/114.87 (in(X55,X53) => 114.29/114.87 (X54(X55) => in(X55,dsetconstr(X53,'#ll_0'(X54)))))) => 114.29/114.87 ((![X56,X57:($i > $o),X58]: 114.29/114.87 (in(X58,dsetconstr(X56,'#ll_0'(X57))) => in(X58,X56))) => 114.29/114.87 ((![X59,X60:($i > $o),X61]: 114.29/114.87 (in(X61,dsetconstr(X59,'#ll_0'(X60))) => X60(X61))) => 114.29/114.87 ((![X62:($i > $o)]: 114.29/114.87 ((?[X63]: 114.29/114.87 ((![X64]: (X62(X64) => (X63 = X64))) & X62(X63))) => 114.29/114.87 (?[X65]: 114.29/114.87 ((![X66]: (X62(X66) => (X65 = X66))) & X62(X65))))) => 114.29/114.87 ((![X67:$o,X68]: (in(X68,prop2set(X67)) => X67)) => 114.29/114.87 ((![X69]: (in(X69,emptyset) => (![X70:$o]: X70))) => 114.29/114.87 ((![X71]: (in(X71,emptyset) => $false)) => 114.29/114.87 ((![X72]: (~in(X72,emptyset))) => 114.29/114.87 ((![X73:($i > $o)]: 114.29/114.87 ((?[X74]: 114.29/114.87 ((![X75]: (X73(X75) => (X74 = X75))) & X73(X74))) => 114.29/114.87 (?[X76]: X73(X76)))) => 114.29/114.87 ((![X77,X78]: 114.29/114.87 ((![X79]: (in(X79,X77) => in(X79,X78))) => 114.29/114.87 ((![X80]: (in(X80,X78) => in(X80,X77))) => 114.29/114.87 (X77 = X78)))) => 114.29/114.87 ((![X81]: 114.29/114.87 ((![X82]: (~in(X82,X81))) => (X81 = emptyset))) => 114.29/114.87 ((![X83]: 114.29/114.87 ((![X84]: (~in(X84,X83))) => (X83 = emptyset))) => 114.29/114.87 ((![X85,X86:($i > $o),X87]: 114.29/114.87 (in(X87,X85) => 114.29/114.87 (in(X87,dsetconstr(X85,'#ll_0'(X86))) <=> 114.29/114.87 X86(X87)))) => 114.29/114.87 ((![X88]: 114.29/114.87 ((X88 != emptyset) => (?[X89]: in(X89,X88)))) => 114.29/114.87 ((![X90,X91:($i > $o),X92]: 114.29/114.87 (in(X92,X90) => 114.29/114.87 (X91(X92) => 114.29/114.87 (dsetconstr(X90,'#ll_0'(X91)) != emptyset)))) => 114.29/114.87 ((![X93]: 114.29/114.87 ((?[X94]: in(X94,X93)) => (X93 != emptyset))) => 114.29/114.87 ((![X95,X96]: in(X95,setadjoin(X95,X96))) => 114.29/114.87 (in(emptyset,setadjoin(emptyset,emptyset)) => 114.29/114.87 ((![X97,X98,X99]: 114.29/114.87 (in(X99,X98) => 114.29/114.87 in(X99,setadjoin(X97,X98)))) => 114.29/114.87 ((![X100,X101,X102]: 114.29/114.87 (in(X102,setadjoin(X100,X101)) => 114.29/114.87 (![X103:$o]: 114.29/114.87 (((X102 = X100) => X103) => 114.29/114.87 ((in(X102,X101) => X103) => X103))))) => 114.29/114.87 ((![X104,X105,X106]: 114.29/114.87 (in(X106,setadjoin(X104,X105)) => 114.29/114.87 (in(X106,X105) | (X106 = X104)))) => 114.29/114.87 ((![X107]: 114.29/114.87 (dsetconstr(X107,'#ll_1') = X107)) => 114.29/114.87 ((![X108,X109]: 114.29/114.87 ((![X110]: 114.29/114.87 (in(X110,X109) => in(X110,X108))) => 114.29/114.87 in(X109,powerset(X108)))) => 114.29/114.87 ((![X111]: in(emptyset,powerset(X111))) => 114.29/114.87 ((![X112]: in(emptyset,powerset(X112))) => 114.29/114.87 ((![X113,X114,X115]: 114.29/114.87 (in(X114,powerset(X113)) => 114.29/114.87 (in(X115,X114) => in(X115,X113)))) => 114.29/114.87 ((![X116,X117,X118]: 114.29/114.87 (in(X117,X118) => 114.29/114.87 (in(X118,X116) => 114.29/114.87 in(X117,setunion(X116))))) => 114.29/114.87 ((![X119,X120]: 114.29/114.87 (in(X120,setunion(X119)) => 114.29/114.87 (![X121:$o]: 114.29/114.87 ((![X122]: 114.29/114.87 (in(X120,X122) => 114.29/114.87 (in(X122,X119) => X121))) => 114.29/114.87 X121)))) => 114.29/114.87 ((![X123,X124]: 114.29/114.87 (in(X124,X123) => 114.29/114.87 in(X124, 114.29/114.87 powerset(setunion(X123))))) => 114.29/114.87 ((![X125:($i > $o)]: 114.29/114.87 ((?[X126]: 114.29/114.87 ((![X127]: 114.29/114.87 (X125(X127) => 114.29/114.87 (X126 = X127))) & 114.29/114.87 X125(X126))) => 114.29/114.87 (?[X128]: 114.29/114.87 (![X129]: 114.29/114.87 (X125(X129) <=> 114.29/114.87 (X129 = X128)))))) => 114.29/114.87 ((![X130]: 114.29/114.87 ((X130 != emptyset) => 114.29/114.87 (?[X131]: in(X131,X130)))) => 114.29/114.87 ((![X132,X133]: 114.29/114.87 (in(X132, 114.29/114.87 setadjoin(X133,emptyset)) => 114.29/114.87 (X132 = X133))) => 114.29/114.87 ((![X134,X135]: 114.29/114.87 ((X134 != X135) => 114.29/114.87 (~ 114.29/114.87 in(X135, 114.29/114.87 setadjoin(X134, 114.29/114.87 emptyset))))) => 114.29/114.87 ((![X136,X137]: 114.29/114.87 ((X136 = X137) => 114.29/114.87 in(X136, 114.29/114.87 setadjoin(X137, 114.29/114.87 emptyset)))) => 114.29/114.87 ((![X138,X139]: 114.29/114.87 (in(X138, 114.29/114.87 setadjoin(X139, 114.29/114.87 emptyset)) => 114.29/114.87 in(X139, 114.29/114.87 setadjoin(X138, 114.29/114.87 emptyset)))) => 114.29/114.87 ((![X140,X141,X142]: 114.29/114.87 (in(X142, 114.29/114.87 setadjoin(X140, 114.29/114.87 setadjoin( 114.29/114.87 X141, 114.29/114.87 emptyset))) => 114.29/114.87 ((X142 = X141) | 114.29/114.87 (X142 = X140)))) => 114.29/114.87 ((![X143,X144]: 114.29/114.87 in(X143, 114.29/114.87 setadjoin(X143, 114.29/114.87 setadjoin( 114.29/114.87 X144, 114.29/114.87 emptyset)))) => 114.29/114.87 ((![X145,X146]: 114.29/114.87 in(X146, 114.29/114.87 setadjoin(X145, 114.29/114.87 setadjoin( 114.29/114.87 X146, 114.29/114.87 emptyset)))) => 114.29/114.87 ((![X147,X148:($i > $o)]: 114.29/114.87 ((?[X149]: 114.29/114.87 (X148(X149) & 114.29/114.87 in(X149,X147))) => 114.29/114.87 ((dsetconstr( 114.29/114.87 X147,'#ll_0'(X148)) = 114.29/114.87 emptyset) => 114.29/114.87 $false))) => 114.29/114.87 ((![X150:($i > $o),X151]: 114.29/114.87 (in(X151,emptyset) => 114.29/114.87 X150(X151))) => 114.29/114.87 ((![X152,X153:($i > $o)]: 114.29/114.87 ((~ 114.29/114.87 (![X154]: 114.29/114.87 (in(X154,X152) => 114.29/114.87 X153(X154)))) => 114.29/114.87 (?[X155]: 114.29/114.87 ((~X153(X155)) & 114.29/114.87 in(X155,X152))))) => 114.29/114.87 ((![X156, 114.29/114.87 X157:($i > $o)]: 114.29/114.87 ((![X158]: 114.29/114.87 (in(X158,X156) => 114.29/114.87 (~X157(X158)))) => 114.29/114.87 (~ 114.29/114.87 (?[X159]: 114.29/114.87 (X157(X159) & 114.29/114.87 in( 114.29/114.87 X159,X156)))))) => 114.29/114.87 ((![X160, 114.29/114.87 X161:($i > $o)]: 114.29/114.87 ((~ 114.29/114.87 (?[X162]: 114.29/114.87 (X161(X162) & 114.29/114.87 in( 114.29/114.87 X162,X160)))) => 114.29/114.87 (![X163]: 114.29/114.87 (in(X163,X160) => 114.29/114.87 (~X161(X163)))))) => 114.29/114.87 ((![X164, 114.29/114.87 X165:($i > $o)]: 114.29/114.87 ((?[X166]: 114.29/114.87 ((~ 114.29/114.87 X165( 114.29/114.87 X166)) & 114.29/114.87 in( 114.29/114.87 X166,X164))) => 114.29/114.87 (~ 114.29/114.87 (![X167]: 114.29/114.87 (in( 114.29/114.87 X167,X164) => 114.29/114.87 X165( 114.29/114.87 X167)))))) => 114.29/114.87 ((![X168:$o]: 114.29/114.87 (X168 => 114.29/114.87 in(emptyset, 114.29/114.87 prop2set( 114.29/114.87 X168)))) => 114.29/114.87 ((![X169:$o]: 114.29/114.87 (X169 => 114.29/114.87 set2prop( 114.29/114.87 prop2set( 114.29/114.87 X169)))) => 114.29/114.87 ((![X170, 114.29/114.87 X171:( 114.29/114.87 $i > $o)]: 114.29/114.87 ((~ 114.29/114.87 (?[X172]: 114.29/114.87 (X171( 114.29/114.87 X172) & 114.29/114.87 in( 114.29/114.87 X172,X170)))) => 114.29/114.87 (![X173]: 114.29/114.87 ( 114.29/114.87 in( 114.29/114.87 X173,X170) => 114.29/114.87 ( 114.29/114.87 ~ 114.29/114.87 X171( 114.29/114.87 X173)))))) => 114.29/114.87 ((![X174, 114.29/114.87 X175:( 114.29/114.87 $i > $o)]: 114.29/114.87 ((~ 114.29/114.87 ( 114.29/114.87 ![X176]: 114.29/114.87 (in( 114.29/114.87 X176,X174) => 114.29/114.87 X175( 114.29/114.87 X176)))) => 114.29/114.87 (?[X177]: 114.29/114.87 (( 114.29/114.87 ~ 114.29/114.87 X175( 114.29/114.87 X177)) & 114.29/114.87 in( 114.29/114.87 X177,X174))))) => 114.29/114.87 ((![X178:( 114.29/114.87 $i > $o)]: 114.29/114.87 ((?[X179]: 114.29/114.87 (( 114.29/114.87 ![X180]: 114.29/114.87 (X178( 114.29/114.87 X180) => 114.29/114.87 (X179 = 114.29/114.87 X180))) & 114.29/114.87 X178( 114.29/114.87 X179))) => 114.29/114.87 (?[X181]: 114.29/114.87 (( 114.29/114.87 ![X182]: 114.29/114.87 (X178( 114.29/114.87 X182) => 114.29/114.87 (X181 = 114.29/114.87 X182))) & 114.29/114.87 X178( 114.29/114.87 X181))))) => 114.29/114.87 ((![X183:( 114.29/114.87 $i > $o)]: 114.29/114.87 (( 114.29/114.87 ?[X184]: 114.29/114.87 X183( 114.29/114.87 X184)) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X185, 114.29/114.87 X186]: 114.29/114.87 (X183( 114.29/114.87 X185) => 114.29/114.87 (X183( 114.29/114.87 X186) => 114.29/114.87 (X185 = 114.29/114.87 X186)))) => 114.29/114.87 ( 114.29/114.87 ?[X187]: 114.29/114.87 (( 114.29/114.87 ![X188]: 114.29/114.87 (X183( 114.29/114.87 X188) => 114.29/114.87 (X187 = 114.29/114.87 X188))) & 114.29/114.87 X183( 114.29/114.87 X187)))))) => 114.29/114.87 ((![X189:( 114.29/114.87 $i > $o)]: 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ?[X190]: 114.29/114.87 (![X191]: 114.29/114.87 (X189( 114.29/114.87 X191) <=> 114.29/114.87 (X191 = 114.29/114.87 X190)))) => 114.29/114.87 ( 114.29/114.87 ?[X192]: 114.29/114.87 (( 114.29/114.87 ![X193]: 114.29/114.87 (X189( 114.29/114.87 X193) => 114.29/114.87 (X192 = 114.29/114.87 X193))) & 114.29/114.87 X189( 114.29/114.87 X192))))) => 114.29/114.87 ((![X194, 114.29/114.87 X195]: 114.29/114.87 (( 114.29/114.87 X194 = 114.29/114.87 X195) => 114.29/114.87 (![X196, 114.29/114.87 X197]: 114.29/114.87 (( 114.29/114.87 X196 = 114.29/114.87 X197) => 114.29/114.87 (in( 114.29/114.87 X196,X194) => 114.29/114.87 in( 114.29/114.87 X197,X195)))))) => 114.29/114.87 ((![X198, 114.29/114.87 X199]: 114.29/114.87 (( 114.29/114.87 X198 = 114.29/114.87 X199) => 114.29/114.87 (![X200, 114.29/114.87 X201]: 114.29/114.87 (( 114.29/114.87 X200 = 114.29/114.87 X201) => 114.29/114.87 (in( 114.29/114.87 X200,X198) <=> 114.29/114.87 in( 114.29/114.87 X201,X199)))))) => 114.29/114.87 (( 114.29/114.87 ![X202:( 114.29/114.87 $i > $o)]: 114.29/114.87 (( 114.29/114.87 ?[X203]: 114.29/114.87 (( 114.29/114.87 ![X204]: 114.29/114.87 (X202( 114.29/114.87 X204) => 114.29/114.87 (X203 = 114.29/114.87 X204))) & 114.29/114.87 X202( 114.29/114.87 X203))) => 114.29/114.87 (![X205, 114.29/114.87 X206]: 114.29/114.87 (X202( 114.29/114.87 X205) => 114.29/114.87 (X202( 114.29/114.87 X206) => 114.29/114.87 (X205 = 114.29/114.87 X206)))))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X207:( 114.29/114.87 $i > $o), 114.29/114.87 X208:( 114.29/114.87 $i > $o)]: 114.29/114.87 (( 114.29/114.87 ![X209, 114.29/114.87 X210]: 114.29/114.87 (( 114.29/114.87 X209 = 114.29/114.87 X210) => 114.29/114.87 (X207( 114.29/114.87 X209) <=> 114.29/114.87 X208( 114.29/114.87 X210)))) => 114.29/114.87 (( 114.29/114.87 ?[X211]: 114.29/114.87 zip_tseitin5( 114.29/114.87 X211,X207)) <=> 114.29/114.87 (?[X213]: 114.29/114.87 zip_tseitin5( 114.29/114.87 X213,X208))))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 emptyset = 114.29/114.87 emptyset) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X215, 114.29/114.87 X216]: 114.29/114.87 (( 114.29/114.87 X215 = 114.29/114.87 X216) => 114.29/114.87 (![X217, 114.29/114.87 X218]: 114.29/114.87 (( 114.29/114.87 X217 = 114.29/114.87 X218) => 114.29/114.87 (setadjoin( 114.29/114.87 X215,X217) = 114.29/114.87 setadjoin( 114.29/114.87 X216,X218)))))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X219, 114.29/114.87 X220]: 114.29/114.87 (( 114.29/114.87 X219 = 114.29/114.87 X220) => 114.29/114.87 (powerset( 114.29/114.87 X219) = 114.29/114.87 powerset( 114.29/114.87 X220)))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X221, 114.29/114.87 X222]: 114.29/114.87 (( 114.29/114.87 X221 = 114.29/114.87 X222) => 114.29/114.87 (setunion( 114.29/114.87 X221) = 114.29/114.87 setunion( 114.29/114.87 X222)))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 omega = 114.29/114.87 omega) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X223:( 114.29/114.87 $i > $o)]: 114.29/114.87 (( 114.29/114.87 ?[X224]: 114.29/114.87 (( 114.29/114.87 ![X225]: 114.29/114.87 (X223( 114.29/114.87 X225) => 114.29/114.87 (X224 = 114.29/114.87 X225))) & 114.29/114.87 X223( 114.29/114.87 X224))) => 114.29/114.87 (![X226, 114.29/114.87 X227]: 114.29/114.87 (X223( 114.29/114.87 X226) => 114.29/114.87 (X223( 114.29/114.87 X227) => 114.29/114.87 (X226 = 114.29/114.87 X227)))))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X228:( 114.29/114.87 $i > $o), 114.29/114.87 X229:( 114.29/114.87 $i > $o)]: 114.29/114.87 (( 114.29/114.87 ![X230, 114.29/114.87 X231]: 114.29/114.87 (( 114.29/114.87 X230 = 114.29/114.87 X231) => 114.29/114.87 (X228( 114.29/114.87 X230) <=> 114.29/114.87 X229( 114.29/114.87 X231)))) => 114.29/114.87 (( 114.29/114.87 ?[X232]: 114.29/114.87 (( 114.29/114.87 ![X233]: 114.29/114.87 (X228( 114.29/114.87 X233) => 114.29/114.87 (X232 = 114.29/114.87 X233))) & 114.29/114.87 X228( 114.29/114.87 X232))) => 114.29/114.87 (( 114.29/114.87 ?[X234]: 114.29/114.87 (( 114.29/114.87 ![X235]: 114.29/114.87 (X229( 114.29/114.87 X235) => 114.29/114.87 (X234 = 114.29/114.87 X235))) & 114.29/114.87 X229( 114.29/114.87 X234))) => 114.29/114.87 (descr( 114.29/114.87 '#ll_0'( 114.29/114.87 X228)) = 114.29/114.87 descr( 114.29/114.87 '#ll_0'( 114.29/114.87 X229))))))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X236, 114.29/114.87 X237]: 114.29/114.87 (( 114.29/114.87 X236 = 114.29/114.87 X237) => 114.29/114.87 (![X238:( 114.29/114.87 $i > $o), 114.29/114.87 X239:( 114.29/114.87 $i > $o)]: 114.29/114.87 (( 114.29/114.87 ![X240]: 114.29/114.87 (in( 114.29/114.87 X240,X236) => 114.29/114.87 (![X241]: 114.29/114.87 (in( 114.29/114.87 X241,X237) => 114.29/114.87 (( 114.29/114.87 X240 = 114.29/114.87 X241) => 114.29/114.87 (X238( 114.29/114.87 X240) <=> 114.29/114.87 X239( 114.29/114.87 X241))))))) => 114.29/114.87 (dsetconstr( 114.29/114.87 X236, 114.29/114.87 '#ll_0'( 114.29/114.87 X238)) = 114.29/114.87 dsetconstr( 114.29/114.87 X237, 114.29/114.87 '#ll_0'( 114.29/114.87 X239))))))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X242, 114.29/114.87 X243]: 114.29/114.87 (( 114.29/114.87 ![X244]: 114.29/114.87 (in( 114.29/114.87 X244,X242) => 114.29/114.87 in( 114.29/114.87 X244,X243))) => 114.29/114.87 subset( 114.29/114.87 X242,X243))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X245, 114.29/114.87 X246]: 114.29/114.87 (( 114.29/114.87 X245 = 114.29/114.87 X246) => 114.29/114.87 subset( 114.29/114.87 X246,X245))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X247, 114.29/114.87 X248]: 114.29/114.87 (( 114.29/114.87 X247 = 114.29/114.87 X248) => 114.29/114.87 subset( 114.29/114.87 X247,X248))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X249, 114.29/114.87 X250]: 114.29/114.87 (( 114.29/114.87 ![X251]: 114.29/114.87 (in( 114.29/114.87 X251,X249) => 114.29/114.87 in( 114.29/114.87 X251,X250))) => 114.29/114.87 subset( 114.29/114.87 X249,X250))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X252]: 114.29/114.87 subset( 114.29/114.87 emptyset, 114.29/114.87 X252)) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X253, 114.29/114.87 X254,X255]: 114.29/114.87 (subset( 114.29/114.87 X253,X254) => 114.29/114.87 (in( 114.29/114.87 X255,X253) => 114.29/114.87 in( 114.29/114.87 X255,X254)))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X256, 114.29/114.87 X257,X258]: 114.29/114.87 (subset( 114.29/114.87 X256,X257) => 114.29/114.87 (( 114.29/114.87 ~ 114.29/114.87 in( 114.29/114.87 X258,X257)) => 114.29/114.87 (~ 114.29/114.87 in( 114.29/114.87 X258,X256))))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X259, 114.29/114.87 X260,X261]: 114.29/114.87 (in( 114.29/114.87 X261,X259) => 114.29/114.87 (( 114.29/114.87 ~ 114.29/114.87 in( 114.29/114.87 X261,X260)) => 114.29/114.87 (~ 114.29/114.87 subset( 114.29/114.87 X259,X260))))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X262, 114.29/114.87 X263]: 114.29/114.87 (( 114.29/114.87 ~ 114.29/114.87 subset( 114.29/114.87 X262,X263)) => 114.29/114.87 (X262 != 114.29/114.87 X263))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X264, 114.29/114.87 X265,X266]: 114.29/114.87 (in( 114.29/114.87 X266,X264) => 114.29/114.87 (( 114.29/114.87 ~ 114.29/114.87 in( 114.29/114.87 X266,X265)) => 114.29/114.87 (X264 != 114.29/114.87 X265)))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X267]: 114.29/114.87 subset( 114.29/114.87 X267,X267)) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X268, 114.29/114.87 X269,X270]: 114.29/114.87 (subset( 114.29/114.87 X268,X269) => 114.29/114.87 (subset( 114.29/114.87 X269,X270) => 114.29/114.87 subset( 114.29/114.87 X268,X270)))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X271, 114.29/114.87 X272]: 114.29/114.87 subset( 114.29/114.87 X272, 114.29/114.87 setadjoin( 114.29/114.87 X271,X272))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X273, 114.29/114.87 X274,X275]: 114.29/114.87 (subset( 114.29/114.87 X273,X275) => 114.29/114.87 subset( 114.29/114.87 X273, 114.29/114.87 setadjoin( 114.29/114.87 X274,X275)))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X276, 114.29/114.87 X277]: 114.29/114.87 (subset( 114.29/114.87 X276,X277) => 114.29/114.87 in( 114.29/114.87 X276, 114.29/114.87 powerset( 114.29/114.87 X277)))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X278, 114.29/114.87 X279]: 114.29/114.87 (subset( 114.29/114.87 X278,X279) => 114.29/114.87 (subset( 114.29/114.87 X279,X278) => 114.29/114.87 (X278 = 114.29/114.87 X279)))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X280]: 114.29/114.87 (subset( 114.29/114.87 X280, 114.29/114.87 emptyset) => 114.29/114.87 (X280 = 114.29/114.87 emptyset))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X281, 114.29/114.87 X282]: 114.29/114.87 (subset( 114.29/114.87 X282,X281) => 114.29/114.87 in( 114.29/114.87 X282, 114.29/114.87 powerset( 114.29/114.87 X281)))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X283, 114.29/114.87 X284]: 114.29/114.87 (in( 114.29/114.87 X284, 114.29/114.87 powerset( 114.29/114.87 X283)) => 114.29/114.87 subset( 114.29/114.87 X284,X283))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X285]: 114.29/114.87 in( 114.29/114.87 X285, 114.29/114.87 powerset( 114.29/114.87 X285))) => 114.29/114.87 ( 114.29/114.87 ![X286, 114.29/114.87 X287]: 114.29/114.87 (subset( 114.29/114.87 X286,X287) => 114.29/114.87 subset( 114.29/114.87 powerset( 114.29/114.87 X286), 114.29/114.87 powerset( 114.29/114.87 X287)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 114.29/114.87 tff(zf_stmt_14, negated_conjecture, 114.29/114.87 (~ 114.29/114.87 ((![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))) => 114.29/114.87 ((![X5]: (~in(X5,emptyset))) => 114.29/114.87 ((![X6,X7,X8]: (in(X8,setadjoin(X6,X7)) <=> zip_tseitin0(X8,X7,X6))) => 114.29/114.87 ((![X9,X10]: 114.29/114.87 (in(X10,powerset(X9)) <=> (![X11]: zip_tseitin1(X11,X10,X9)))) => 114.29/114.87 ((![X12,X13]: 114.29/114.87 (in(X13,setunion(X12)) <=> (?[X14]: zip_tseitin2(X14,X13,X12)))) => 114.29/114.87 (in(emptyset,omega) => 114.29/114.87 ((![X15]: (in(X15,omega) => in(setadjoin(X15,X15),omega))) => 114.29/114.87 ((![X16]: 114.29/114.87 (((![X17]: 114.29/114.87 ((in(X17,X16) & in(X17,omega)) => 114.29/114.87 in(setadjoin(X17,X17),X16))) & 114.29/114.87 in(emptyset,X16)) => 114.29/114.87 (![X18]: (in(X18,omega) => in(X18,X16))))) => 114.29/114.87 ((![X19:(($i * $i) > $o),X20]: 114.29/114.87 ((![X21]: 114.29/114.87 (in(X21,X20) => 114.29/114.87 (?[X22]: 114.29/114.87 ((![X23]: (X19(X21,X23) => (X22 = X23))) & 114.29/114.87 X19(X21,X22))))) => 114.29/114.87 (?[X24]: 114.29/114.87 (![X25]: 114.29/114.87 (in(X25,X24) <=> 114.29/114.87 (?[X26]: zip_tseitin3(X26,X25,X20,X19))))))) => 114.29/114.87 ((![X27]: 114.29/114.87 ((?[X28]: in(X28,X27)) => 114.29/114.87 (?[X29]: 114.29/114.87 ((~(?[X30]: (in(X30,X27) & in(X30,X29)))) & in(X29,X27))))) => 114.29/114.87 ((![X31]: 114.29/114.87 (?[X32]: 114.29/114.87 ((![X33]: 114.29/114.87 (((?[X34]: in(X34,X33)) & 114.29/114.87 (![X35]: (in(X35,X33) => in(X35,X31)))) => 114.29/114.87 (?[X36,X37]: 114.29/114.87 ((![X38]: 114.29/114.87 (in(X38,X32) => 114.29/114.87 (in(X37,X38) | 114.29/114.87 (![X39]: (in(X39,X38) => in(X39,X36)))))) & 114.29/114.87 (~(?[X40]: (in(X40,X33) & in(X40,X36)))) & 114.29/114.87 in(X37,X33) & in(X36,X32))))) & 114.29/114.87 (![X41,X42]: 114.29/114.87 ((in(X42,X32) & in(X41,X32)) => 114.29/114.87 ((![X43]: (in(X43,X42) => in(X43,X41))) | 114.29/114.87 (![X44]: (in(X44,X41) => in(X44,X42)))))) & 114.29/114.87 (![X45,X46]: 114.29/114.87 ((in(X46,X31) & in(X45,X31)) => 114.29/114.87 ((![X47]: 114.29/114.87 (in(X47,X32) => (in(X45,X47) <=> in(X46,X47)))) => 114.29/114.87 (X45 = X46)))) & 114.29/114.87 (![X48]: 114.29/114.87 (in(X48,X32) => 114.29/114.87 (![X49]: (in(X49,X48) => in(X49,X31)))))))) => 114.29/114.87 ((![X50:($i > $o)]: 114.29/114.87 ((?[X51]: ((![X52]: (X50(X52) => (X51 = X52))) & X50(X51))) => 114.29/114.87 X50(descr('#ll_0'(X50))))) => 114.29/114.87 ((![X53,X54:($i > $o),X55]: 114.29/114.87 (in(X55,X53) => 114.29/114.87 (X54(X55) => in(X55,dsetconstr(X53,'#ll_0'(X54)))))) => 114.29/114.87 ((![X56,X57:($i > $o),X58]: 114.29/114.87 (in(X58,dsetconstr(X56,'#ll_0'(X57))) => in(X58,X56))) => 114.29/114.87 ((![X59,X60:($i > $o),X61]: 114.29/114.87 (in(X61,dsetconstr(X59,'#ll_0'(X60))) => X60(X61))) => 114.29/114.87 ((![X62:($i > $o)]: 114.29/114.87 ((?[X63]: 114.29/114.87 ((![X64]: (X62(X64) => (X63 = X64))) & X62(X63))) => 114.29/114.87 (?[X65]: 114.29/114.87 ((![X66]: (X62(X66) => (X65 = X66))) & X62(X65))))) => 114.29/114.87 ((![X67:$o,X68]: (in(X68,prop2set(X67)) => X67)) => 114.29/114.87 ((![X69]: (in(X69,emptyset) => (![X70:$o]: X70))) => 114.29/114.87 ((![X71]: (in(X71,emptyset) => $false)) => 114.29/114.87 ((![X72]: (~in(X72,emptyset))) => 114.29/114.87 ((![X73:($i > $o)]: 114.29/114.87 ((?[X74]: 114.29/114.87 ((![X75]: (X73(X75) => (X74 = X75))) & 114.29/114.87 X73(X74))) => 114.29/114.87 (?[X76]: X73(X76)))) => 114.29/114.87 ((![X77,X78]: 114.29/114.87 ((![X79]: (in(X79,X77) => in(X79,X78))) => 114.29/114.87 ((![X80]: (in(X80,X78) => in(X80,X77))) => 114.29/114.87 (X77 = X78)))) => 114.29/114.87 ((![X81]: 114.29/114.87 ((![X82]: (~in(X82,X81))) => (X81 = emptyset))) => 114.29/114.87 ((![X83]: 114.29/114.87 ((![X84]: (~in(X84,X83))) => (X83 = emptyset))) => 114.29/114.87 ((![X85,X86:($i > $o),X87]: 114.29/114.87 (in(X87,X85) => 114.29/114.87 (in(X87,dsetconstr(X85,'#ll_0'(X86))) <=> 114.29/114.87 X86(X87)))) => 114.29/114.87 ((![X88]: 114.29/114.87 ((X88 != emptyset) => (?[X89]: in(X89,X88)))) => 114.29/114.87 ((![X90,X91:($i > $o),X92]: 114.29/114.87 (in(X92,X90) => 114.29/114.87 (X91(X92) => 114.29/114.87 (dsetconstr(X90,'#ll_0'(X91)) != emptyset)))) => 114.29/114.87 ((![X93]: 114.29/114.87 ((?[X94]: in(X94,X93)) => 114.29/114.87 (X93 != emptyset))) => 114.29/114.87 ((![X95,X96]: in(X95,setadjoin(X95,X96))) => 114.29/114.87 (in(emptyset,setadjoin(emptyset,emptyset)) => 114.29/114.87 ((![X97,X98,X99]: 114.29/114.87 (in(X99,X98) => 114.29/114.87 in(X99,setadjoin(X97,X98)))) => 114.29/114.87 ((![X100,X101,X102]: 114.29/114.87 (in(X102,setadjoin(X100,X101)) => 114.29/114.87 (![X103:$o]: 114.29/114.87 (((X102 = X100) => X103) => 114.29/114.87 ((in(X102,X101) => X103) => X103))))) => 114.29/114.87 ((![X104,X105,X106]: 114.29/114.87 (in(X106,setadjoin(X104,X105)) => 114.29/114.87 (in(X106,X105) | (X106 = X104)))) => 114.29/114.87 ((![X107]: 114.29/114.87 (dsetconstr(X107,'#ll_1') = X107)) => 114.29/114.87 ((![X108,X109]: 114.29/114.87 ((![X110]: 114.29/114.87 (in(X110,X109) => in(X110,X108))) => 114.29/114.87 in(X109,powerset(X108)))) => 114.29/114.87 ((![X111]: in(emptyset,powerset(X111))) => 114.29/114.87 ((![X112]: 114.29/114.87 in(emptyset,powerset(X112))) => 114.29/114.87 ((![X113,X114,X115]: 114.29/114.87 (in(X114,powerset(X113)) => 114.29/114.87 (in(X115,X114) => in(X115,X113)))) => 114.29/114.87 ((![X116,X117,X118]: 114.29/114.87 (in(X117,X118) => 114.29/114.87 (in(X118,X116) => 114.29/114.87 in(X117,setunion(X116))))) => 114.29/114.87 ((![X119,X120]: 114.29/114.87 (in(X120,setunion(X119)) => 114.29/114.87 (![X121:$o]: 114.29/114.87 ((![X122]: 114.29/114.87 (in(X120,X122) => 114.29/114.87 (in(X122,X119) => 114.29/114.87 X121))) => 114.29/114.87 X121)))) => 114.29/114.87 ((![X123,X124]: 114.29/114.87 (in(X124,X123) => 114.29/114.87 in(X124, 114.29/114.87 powerset(setunion(X123))))) => 114.29/114.87 ((![X125:($i > $o)]: 114.29/114.87 ((?[X126]: 114.29/114.87 ((![X127]: 114.29/114.87 (X125(X127) => 114.29/114.87 (X126 = X127))) & 114.29/114.87 X125(X126))) => 114.29/114.87 (?[X128]: 114.29/114.87 (![X129]: 114.29/114.87 (X125(X129) <=> 114.29/114.87 (X129 = X128)))))) => 114.29/114.87 ((![X130]: 114.29/114.87 ((X130 != emptyset) => 114.29/114.87 (?[X131]: in(X131,X130)))) => 114.29/114.87 ((![X132,X133]: 114.29/114.87 (in(X132, 114.29/114.87 setadjoin(X133, 114.29/114.87 emptyset)) => 114.29/114.87 (X132 = X133))) => 114.29/114.87 ((![X134,X135]: 114.29/114.87 ((X134 != X135) => 114.29/114.87 (~ 114.29/114.87 in(X135, 114.29/114.87 setadjoin(X134, 114.29/114.87 emptyset))))) => 114.29/114.87 ((![X136,X137]: 114.29/114.87 ((X136 = X137) => 114.29/114.87 in(X136, 114.29/114.87 setadjoin(X137, 114.29/114.87 emptyset)))) => 114.29/114.87 ((![X138,X139]: 114.29/114.87 (in(X138, 114.29/114.87 setadjoin(X139, 114.29/114.87 emptyset)) => 114.29/114.87 in(X139, 114.29/114.87 setadjoin(X138, 114.29/114.87 emptyset)))) => 114.29/114.87 ((![X140,X141,X142]: 114.29/114.87 (in(X142, 114.29/114.87 setadjoin( 114.29/114.87 X140, 114.29/114.87 setadjoin( 114.29/114.87 X141,emptyset))) => 114.29/114.87 ((X142 = X141) | 114.29/114.87 (X142 = X140)))) => 114.29/114.87 ((![X143,X144]: 114.29/114.87 in(X143, 114.29/114.87 setadjoin( 114.29/114.87 X143, 114.29/114.87 setadjoin( 114.29/114.87 X144,emptyset)))) => 114.29/114.87 ((![X145,X146]: 114.29/114.87 in(X146, 114.29/114.87 setadjoin( 114.29/114.87 X145, 114.29/114.87 setadjoin( 114.29/114.87 X146,emptyset)))) => 114.29/114.87 ((![X147,X148:($i > $o)]: 114.29/114.87 ((?[X149]: 114.29/114.87 (X148(X149) & 114.29/114.87 in(X149,X147))) => 114.29/114.87 ((dsetconstr( 114.29/114.87 X147, 114.29/114.87 '#ll_0'(X148)) = 114.29/114.87 emptyset) => 114.29/114.87 $false))) => 114.29/114.87 ((![X150:($i > $o), 114.29/114.87 X151]: 114.29/114.87 (in(X151,emptyset) => 114.29/114.87 X150(X151))) => 114.29/114.87 ((![X152, 114.29/114.87 X153:($i > $o)]: 114.29/114.87 ((~ 114.29/114.87 (![X154]: 114.29/114.87 (in( 114.29/114.87 X154,X152) => 114.29/114.87 X153(X154)))) => 114.29/114.87 (?[X155]: 114.29/114.87 ((~X153(X155)) & 114.29/114.87 in(X155,X152))))) => 114.29/114.87 ((![X156, 114.29/114.87 X157:($i > $o)]: 114.29/114.87 ((![X158]: 114.29/114.87 (in( 114.29/114.87 X158,X156) => 114.29/114.87 (~ 114.29/114.87 X157( 114.29/114.87 X158)))) => 114.29/114.87 (~ 114.29/114.87 (?[X159]: 114.29/114.87 (X157( 114.29/114.87 X159) & 114.29/114.87 in( 114.29/114.87 X159,X156)))))) => 114.29/114.87 ((![X160, 114.29/114.87 X161:($i > $o)]: 114.29/114.87 ((~ 114.29/114.87 (?[X162]: 114.29/114.87 ( 114.29/114.87 X161( 114.29/114.87 X162) & 114.29/114.87 in( 114.29/114.87 X162,X160)))) => 114.29/114.87 (![X163]: 114.29/114.87 (in( 114.29/114.87 X163,X160) => 114.29/114.87 (~ 114.29/114.87 X161( 114.29/114.87 X163)))))) => 114.29/114.87 ((![X164, 114.29/114.87 X165:( 114.29/114.87 $i > $o)]: 114.29/114.87 ((?[X166]: 114.29/114.87 (( 114.29/114.87 ~ 114.29/114.87 X165( 114.29/114.87 X166)) & 114.29/114.87 in( 114.29/114.87 X166,X164))) => 114.29/114.87 (~ 114.29/114.87 (![X167]: 114.29/114.87 (in( 114.29/114.87 X167,X164) => 114.29/114.87 X165( 114.29/114.87 X167)))))) => 114.29/114.87 ((![X168:$o]: 114.29/114.87 (X168 => 114.29/114.87 in(emptyset, 114.29/114.87 prop2set( 114.29/114.87 X168)))) => 114.29/114.87 ((![X169:$o]: 114.29/114.87 (X169 => 114.29/114.87 set2prop( 114.29/114.87 prop2set( 114.29/114.87 X169)))) => 114.29/114.87 ((![X170, 114.29/114.87 X171:( 114.29/114.87 $i > $o)]: 114.29/114.87 ((~ 114.29/114.87 ( 114.29/114.87 ?[X172]: 114.29/114.87 (X171( 114.29/114.87 X172) & 114.29/114.87 in( 114.29/114.87 X172,X170)))) => 114.29/114.87 (![X173]: 114.29/114.87 (in( 114.29/114.87 X173,X170) => 114.29/114.87 (~ 114.29/114.87 X171( 114.29/114.87 X173)))))) => 114.29/114.87 ((![X174, 114.29/114.87 X175:( 114.29/114.87 $i > $o)]: 114.29/114.87 (( 114.29/114.87 ~ 114.29/114.87 ( 114.29/114.87 ![X176]: 114.29/114.87 (in( 114.29/114.87 X176,X174) => 114.29/114.87 X175( 114.29/114.87 X176)))) => 114.29/114.87 ( 114.29/114.87 ?[X177]: 114.29/114.87 (( 114.29/114.87 ~ 114.29/114.87 X175( 114.29/114.87 X177)) & 114.29/114.87 in( 114.29/114.87 X177,X174))))) => 114.29/114.87 ((![X178:( 114.29/114.87 $i > $o)]: 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ?[X179]: 114.29/114.87 (( 114.29/114.87 ![X180]: 114.29/114.87 (X178( 114.29/114.87 X180) => 114.29/114.87 (X179 = 114.29/114.87 X180))) & 114.29/114.87 X178( 114.29/114.87 X179))) => 114.29/114.87 ( 114.29/114.87 ?[X181]: 114.29/114.87 (( 114.29/114.87 ![X182]: 114.29/114.87 (X178( 114.29/114.87 X182) => 114.29/114.87 (X181 = 114.29/114.87 X182))) & 114.29/114.87 X178( 114.29/114.87 X181))))) => 114.29/114.87 ((![X183:( 114.29/114.87 $i > $o)]: 114.29/114.87 (( 114.29/114.87 ?[X184]: 114.29/114.87 X183( 114.29/114.87 X184)) => 114.29/114.87 (( 114.29/114.87 ![X185, 114.29/114.87 X186]: 114.29/114.87 (X183( 114.29/114.87 X185) => 114.29/114.87 (X183( 114.29/114.87 X186) => 114.29/114.87 (X185 = 114.29/114.87 X186)))) => 114.29/114.87 (?[X187]: 114.29/114.87 (( 114.29/114.87 ![X188]: 114.29/114.87 (X183( 114.29/114.87 X188) => 114.29/114.87 (X187 = 114.29/114.87 X188))) & 114.29/114.87 X183( 114.29/114.87 X187)))))) => 114.29/114.87 ((![X189:( 114.29/114.87 $i > $o)]: 114.29/114.87 (( 114.29/114.87 ?[X190]: 114.29/114.87 (![X191]: 114.29/114.87 (X189( 114.29/114.87 X191) <=> 114.29/114.87 (X191 = 114.29/114.87 X190)))) => 114.29/114.87 (?[X192]: 114.29/114.87 (( 114.29/114.87 ![X193]: 114.29/114.87 (X189( 114.29/114.87 X193) => 114.29/114.87 (X192 = 114.29/114.87 X193))) & 114.29/114.87 X189( 114.29/114.87 X192))))) => 114.29/114.87 (( 114.29/114.87 ![X194, 114.29/114.87 X195]: 114.29/114.87 (( 114.29/114.87 X194 = 114.29/114.87 X195) => 114.29/114.87 (![X196, 114.29/114.87 X197]: 114.29/114.87 (( 114.29/114.87 X196 = 114.29/114.87 X197) => 114.29/114.87 (in( 114.29/114.87 X196,X194) => 114.29/114.87 in( 114.29/114.87 X197,X195)))))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X198, 114.29/114.87 X199]: 114.29/114.87 (( 114.29/114.87 X198 = 114.29/114.87 X199) => 114.29/114.87 (![X200, 114.29/114.87 X201]: 114.29/114.87 (( 114.29/114.87 X200 = 114.29/114.87 X201) => 114.29/114.87 (in( 114.29/114.87 X200,X198) <=> 114.29/114.87 in( 114.29/114.87 X201,X199)))))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X202:( 114.29/114.87 $i > $o)]: 114.29/114.87 (( 114.29/114.87 ?[X203]: 114.29/114.87 (( 114.29/114.87 ![X204]: 114.29/114.87 (X202( 114.29/114.87 X204) => 114.29/114.87 (X203 = 114.29/114.87 X204))) & 114.29/114.87 X202( 114.29/114.87 X203))) => 114.29/114.87 (![X205, 114.29/114.87 X206]: 114.29/114.87 (X202( 114.29/114.87 X205) => 114.29/114.87 (X202( 114.29/114.87 X206) => 114.29/114.87 (X205 = 114.29/114.87 X206)))))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X207:( 114.29/114.87 $i > $o), 114.29/114.87 X208:( 114.29/114.87 $i > $o)]: 114.29/114.87 (( 114.29/114.87 ![X209, 114.29/114.87 X210]: 114.29/114.87 (( 114.29/114.87 X209 = 114.29/114.87 X210) => 114.29/114.87 (X207( 114.29/114.87 X209) <=> 114.29/114.87 X208( 114.29/114.87 X210)))) => 114.29/114.87 (( 114.29/114.87 ?[X211]: 114.29/114.87 zip_tseitin5( 114.29/114.87 X211,X207)) <=> 114.29/114.87 (?[X213]: 114.29/114.87 zip_tseitin5( 114.29/114.87 X213,X208))))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 emptyset = 114.29/114.87 emptyset) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X215, 114.29/114.87 X216]: 114.29/114.87 (( 114.29/114.87 X215 = 114.29/114.87 X216) => 114.29/114.87 (![X217, 114.29/114.87 X218]: 114.29/114.87 (( 114.29/114.87 X217 = 114.29/114.87 X218) => 114.29/114.87 (setadjoin( 114.29/114.87 X215,X217) = 114.29/114.87 setadjoin( 114.29/114.87 X216,X218)))))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X219, 114.29/114.87 X220]: 114.29/114.87 (( 114.29/114.87 X219 = 114.29/114.87 X220) => 114.29/114.87 (powerset( 114.29/114.87 X219) = 114.29/114.87 powerset( 114.29/114.87 X220)))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X221, 114.29/114.87 X222]: 114.29/114.87 (( 114.29/114.87 X221 = 114.29/114.87 X222) => 114.29/114.87 (setunion( 114.29/114.87 X221) = 114.29/114.87 setunion( 114.29/114.87 X222)))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 omega = 114.29/114.87 omega) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X223:( 114.29/114.87 $i > $o)]: 114.29/114.87 (( 114.29/114.87 ?[X224]: 114.29/114.87 (( 114.29/114.87 ![X225]: 114.29/114.87 (X223( 114.29/114.87 X225) => 114.29/114.87 (X224 = 114.29/114.87 X225))) & 114.29/114.87 X223( 114.29/114.87 X224))) => 114.29/114.87 (![X226, 114.29/114.87 X227]: 114.29/114.87 (X223( 114.29/114.87 X226) => 114.29/114.87 (X223( 114.29/114.87 X227) => 114.29/114.87 (X226 = 114.29/114.87 X227)))))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X228:( 114.29/114.87 $i > $o), 114.29/114.87 X229:( 114.29/114.87 $i > $o)]: 114.29/114.87 (( 114.29/114.87 ![X230, 114.29/114.87 X231]: 114.29/114.87 (( 114.29/114.87 X230 = 114.29/114.87 X231) => 114.29/114.87 (X228( 114.29/114.87 X230) <=> 114.29/114.87 X229( 114.29/114.87 X231)))) => 114.29/114.87 (( 114.29/114.87 ?[X232]: 114.29/114.87 (( 114.29/114.87 ![X233]: 114.29/114.87 (X228( 114.29/114.87 X233) => 114.29/114.87 (X232 = 114.29/114.87 X233))) & 114.29/114.87 X228( 114.29/114.87 X232))) => 114.29/114.87 (( 114.29/114.87 ?[X234]: 114.29/114.87 (( 114.29/114.87 ![X235]: 114.29/114.87 (X229( 114.29/114.87 X235) => 114.29/114.87 (X234 = 114.29/114.87 X235))) & 114.29/114.87 X229( 114.29/114.87 X234))) => 114.29/114.87 (descr( 114.29/114.87 '#ll_0'( 114.29/114.87 X228)) = 114.29/114.87 descr( 114.29/114.87 '#ll_0'( 114.29/114.87 X229))))))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X236, 114.29/114.87 X237]: 114.29/114.87 (( 114.29/114.87 X236 = 114.29/114.87 X237) => 114.29/114.87 (![X238:( 114.29/114.87 $i > $o), 114.29/114.87 X239:( 114.29/114.87 $i > $o)]: 114.29/114.87 (( 114.29/114.87 ![X240]: 114.29/114.87 (in( 114.29/114.87 X240,X236) => 114.29/114.87 (![X241]: 114.29/114.87 (in( 114.29/114.87 X241,X237) => 114.29/114.87 (( 114.29/114.87 X240 = 114.29/114.87 X241) => 114.29/114.87 (X238( 114.29/114.87 X240) <=> 114.29/114.87 X239( 114.29/114.87 X241))))))) => 114.29/114.87 (dsetconstr( 114.29/114.87 X236, 114.29/114.87 '#ll_0'( 114.29/114.87 X238)) = 114.29/114.87 dsetconstr( 114.29/114.87 X237, 114.29/114.87 '#ll_0'( 114.29/114.87 X239))))))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X242, 114.29/114.87 X243]: 114.29/114.87 (( 114.29/114.87 ![X244]: 114.29/114.87 (in( 114.29/114.87 X244,X242) => 114.29/114.87 in( 114.29/114.87 X244,X243))) => 114.29/114.87 subset( 114.29/114.87 X242,X243))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X245, 114.29/114.87 X246]: 114.29/114.87 (( 114.29/114.87 X245 = 114.29/114.87 X246) => 114.29/114.87 subset( 114.29/114.87 X246,X245))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X247, 114.29/114.87 X248]: 114.29/114.87 (( 114.29/114.87 X247 = 114.29/114.87 X248) => 114.29/114.87 subset( 114.29/114.87 X247,X248))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X249, 114.29/114.87 X250]: 114.29/114.87 (( 114.29/114.87 ![X251]: 114.29/114.87 (in( 114.29/114.87 X251,X249) => 114.29/114.87 in( 114.29/114.87 X251,X250))) => 114.29/114.87 subset( 114.29/114.87 X249,X250))) => 114.29/114.87 ( 114.29/114.87 ( 114.29/114.87 ![X252]: 114.29/114.88 subset( 114.29/114.88 emptyset, 114.29/114.88 X252)) => 114.29/114.88 ( 114.29/114.88 ( 114.29/114.88 ![X253, 114.29/114.88 X254,X255]: 114.29/114.88 (subset( 114.29/114.88 X253,X254) => 114.29/114.88 (in( 114.29/114.88 X255,X253) => 114.29/114.88 in( 114.29/114.88 X255,X254)))) => 114.29/114.88 ( 114.29/114.88 ( 114.29/114.88 ![X256, 114.29/114.88 X257,X258]: 114.29/114.88 (subset( 114.29/114.88 X256,X257) => 114.29/114.88 (( 114.29/114.88 ~ 114.29/114.88 in( 114.29/114.88 X258,X257)) => 114.29/114.88 (~ 114.29/114.88 in( 114.29/114.88 X258,X256))))) => 114.29/114.88 ( 114.29/114.88 ( 114.29/114.88 ![X259, 114.29/114.88 X260,X261]: 114.29/114.88 (in( 114.29/114.88 X261,X259) => 114.29/114.88 (( 114.29/114.88 ~ 114.29/114.88 in( 114.29/114.88 X261,X260)) => 114.29/114.88 (~ 114.29/114.88 subset( 114.29/114.88 X259,X260))))) => 114.29/114.88 ( 114.29/114.88 ( 114.29/114.88 ![X262, 114.29/114.88 X263]: 114.29/114.88 (( 114.29/114.88 ~ 114.29/114.88 subset( 114.29/114.88 X262,X263)) => 114.29/114.88 (X262 != 114.29/114.88 X263))) => 114.29/114.88 ( 114.29/114.88 ( 114.29/114.88 ![X264, 114.29/114.88 X265,X266]: 114.29/114.88 (in( 114.29/114.88 X266,X264) => 114.29/114.88 (( 114.29/114.88 ~ 114.29/114.88 in( 114.29/114.88 X266,X265)) => 114.29/114.88 (X264 != 114.29/114.88 X265)))) => 114.29/114.88 ( 114.29/114.88 ( 114.29/114.88 ![X267]: 114.29/114.88 subset( 114.29/114.88 X267,X267)) => 114.29/114.88 ( 114.29/114.88 ( 114.29/114.88 ![X268, 114.29/114.88 X269,X270]: 114.29/114.88 (subset( 114.29/114.88 X268,X269) => 114.29/114.88 (subset( 114.29/114.88 X269,X270) => 114.29/114.88 subset( 114.29/114.88 X268,X270)))) => 114.29/114.88 ( 114.29/114.88 ( 114.29/114.88 ![X271, 114.29/114.88 X272]: 114.29/114.88 subset( 114.29/114.88 X272, 114.29/114.88 setadjoin( 114.29/114.88 X271,X272))) => 114.29/114.88 ( 114.29/114.88 ( 114.29/114.88 ![X273, 114.29/114.88 X274,X275]: 114.29/114.88 (subset( 114.29/114.88 X273,X275) => 114.29/114.88 subset( 114.29/114.88 X273, 114.29/114.88 setadjoin( 114.29/114.88 X274,X275)))) => 114.29/114.88 ( 114.29/114.88 ( 114.29/114.88 ![X276, 114.29/114.88 X277]: 114.29/114.88 (subset( 114.29/114.88 X276,X277) => 114.29/114.88 in( 114.29/114.88 X276, 114.29/114.88 powerset( 114.29/114.88 X277)))) => 114.29/114.88 ( 114.29/114.88 ( 114.29/114.88 ![X278, 114.29/114.88 X279]: 114.29/114.88 (subset( 114.29/114.88 X278,X279) => 114.29/114.88 (subset( 114.29/114.88 X279,X278) => 114.29/114.88 (X278 = 114.29/114.88 X279)))) => 114.29/114.88 ( 114.29/114.88 ( 114.29/114.88 ![X280]: 114.29/114.88 (subset( 114.29/114.88 X280, 114.29/114.88 emptyset) => 114.29/114.88 (X280 = 114.29/114.88 emptyset))) => 114.29/114.88 ( 114.29/114.88 ( 114.29/114.88 ![X281, 114.29/114.88 X282]: 114.29/114.88 (subset( 114.29/114.88 X282,X281) => 114.29/114.88 in( 114.29/114.88 X282, 114.29/114.88 powerset( 114.29/114.88 X281)))) => 114.29/114.88 ( 114.29/114.88 ( 114.29/114.88 ![X283, 114.29/114.88 X284]: 114.29/114.88 (in( 114.29/114.88 X284, 114.29/114.88 powerset( 114.29/114.88 X283)) => 114.29/114.88 subset( 114.29/114.88 X284,X283))) => 114.29/114.88 ( 114.29/114.88 ( 114.29/114.88 ![X285]: 114.29/114.88 in( 114.29/114.88 X285, 114.29/114.88 powerset( 114.29/114.88 X285))) => 114.29/114.88 ( 114.29/114.88 ![X286, 114.29/114.88 X287]: 114.29/114.88 (subset( 114.29/114.88 X286,X287) => 114.29/114.88 subset( 114.29/114.88 powerset( 114.29/114.88 X286), 114.29/114.88 powerset( 114.29/114.88 X287))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 114.29/114.88 tff('97', plain, 114.29/114.88 ![X402, X403]: (subset(X402, X403) | in(sk_X251_(X403, X402), X402)), 114.29/114.88 inference('cnf', [status(esa)], [zf_stmt_14])). 114.29/114.88 tff('98', plain, 114.29/114.88 ![X424, X425]: (subset(X424, X425) | ~ in(X424, powerset(X425))), 114.29/114.88 inference('cnf', [status(esa)], [zf_stmt_14])). 114.29/114.88 tff('99', plain, 114.29/114.88 ![X402, X403]: (subset(X402, X403) | ~ in(sk_X251_(X403, X402), X403)), 114.29/114.88 inference('cnf', [status(esa)], [zf_stmt_14])). 114.29/114.88 tff('100', plain, ~ subset(powerset(sk_X286_), powerset(sk_X287_)), 114.29/114.88 inference('cnf', [status(esa)], [zf_stmt_14])). 114.29/114.88 tff('101', plain, subset(sk_X286_, sk_X287_), 114.29/114.88 inference('cnf', [status(esa)], [zf_stmt_14])). 114.29/114.88 tff('102', plain, 114.29/114.88 ![X421, X422]: (in(X421, powerset(X422)) | ~ subset(X421, X422)), 114.29/114.88 inference('cnf', [status(esa)], [zf_stmt_14])). 114.29/114.88 tff('103', plain, 114.29/114.88 ![X413, X414, X415]: 114.29/114.88 (~ subset(X413, X414) | subset(X413, X415) | ~ subset(X414, X415)), 114.29/114.88 inference('cnf', [status(esa)], [zf_stmt_14])). 114.29/114.88 tff('104', plain, $false, 114.29/114.88 inference('eprover', [status(thm)], 114.29/114.88 ['97', '98', '99', '100', '101', '102', '103'])). 114.29/114.88 114.29/114.88 % SZS output end Refutation 114.29/114.88 % Zipperpin 1.5 exiting 114.29/114.88 EOF