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.metnmIUY8f 0.13/0.35 % Computer : n027.cluster.edu 0.13/0.35 % Model : x86_64 x86_64 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.35 % Memory : 8042.1875MB 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.35 % CPULimit : 180 0.13/0.35 % DateTime : Thu Aug 29 13:30:39 EDT 2019 0.13/0.35 % CPUTime : 108.45/109.11 % Running portfolio for 180 s 108.45/109.11 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 108.45/109.11 % TempDir : /export/starexec/sandbox/tmp/tmp.metnmIUY8f 108.45/109.11 % Recognized as monomorphic HO. 108.45/109.11 % Running /export/starexec/sandbox/solver/bin/competitive.sh for 18 108.45/109.11 % Running /export/starexec/sandbox/solver/bin/competitive.2.sh for 13 108.45/109.11 % Running /export/starexec/sandbox/solver/bin/competitive.3.sh for 3 108.45/109.11 % Running /export/starexec/sandbox/solver/bin/pragmatic.rudimentary.sh for 28 108.45/109.11 % Running /export/starexec/sandbox/solver/bin/pragmatic.rudimentary.1.sh for 12 108.45/109.11 % Running /export/starexec/sandbox/solver/bin/pragmatic.rudimentary.2.sh for 7 108.45/109.11 % Running /export/starexec/sandbox/solver/bin/pragmatic.shallow.sh for 3 108.45/109.11 % Running /export/starexec/sandbox/solver/bin/pragmatic.shallow.1.sh for 14 108.45/109.11 % Running /export/starexec/sandbox/solver/bin/pragmatic.shallow.2.sh for 12 108.45/109.11 % Running /export/starexec/sandbox/solver/bin/pragmatic.ll.e.sh for 19 108.45/109.11 % Solved by: pragmatic.ll.e.sh 108.45/109.11 % Running : timeout 16 /export/starexec/sandbox/solver/bin/eprover-ho /export/starexec/sandbox/tmp/tmp.metnmIUY8f/e_inputd84f2d --cpu-limit=14 --auto-schedule -s -p. 108.45/109.11 % done 457 iterations in 10.451s 108.45/109.11 % hashcons stats for terms: size 4096, num 24031, sum length 37018, buckets: small 0, median 7, big 22 108.45/109.11 % proof state stats: {active 201, passive 6243, simpl 0} 108.45/109.11 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 108.45/109.11 % SZS output start Refutation 108.45/109.11 tff(subset2powerset, axiom, subset2powerset <=> 108.45/109.11 (![A,B]: (subset(A,B) => in(A,powerset(B))))). 108.45/109.11 tff('0', plain, 108.45/109.11 subset2powerset = (![X2,X3]: (subset(X2,X3) => in(X2,powerset(X3)))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(setadjoinSub2, axiom, setadjoinSub2 <=> 108.45/109.11 (![A,Xx,B]: (subset(A,B) => subset(A,setadjoin(Xx,B))))). 108.45/109.11 tff('1', plain, 108.45/109.11 setadjoinSub2 = 108.45/109.11 (![X2,X3,X4]: (subset(X2,X4) => subset(X2,setadjoin(X3,X4)))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(setadjoinSub, axiom, setadjoinSub <=> 108.45/109.11 (![Xx,A]: subset(A,setadjoin(Xx,A)))). 108.45/109.11 tff('2', plain, setadjoinSub = (![X2,X3]: subset(X3,setadjoin(X2,X3))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(subsetTrans, axiom, subsetTrans <=> 108.45/109.11 (![A,B,C]: (subset(A,B) => (subset(B,C) => subset(A,C))))). 108.45/109.11 tff('3', plain, 108.45/109.11 subsetTrans = 108.45/109.11 (![X2,X3,X4]: (subset(X2,X3) => (subset(X3,X4) => subset(X2,X4)))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(subsetRefl, axiom, subsetRefl <=> (![A]: subset(A,A))). 108.45/109.11 tff('4', plain, subsetRefl = (![X2]: subset(X2,X2)), define([status(thm)])). 108.45/109.11 tff(notequalI2, axiom, notequalI2 <=> 108.45/109.11 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => (A != B))))). 108.45/109.11 tff('5', plain, 108.45/109.11 notequalI2 = (![X2,X3,X4]: (in(X4,X2) => ((~in(X4,X3)) => (X2 != X3)))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(notequalI1, axiom, notequalI1 <=> (![A,B]: ((~subset(A,B)) => (A != B)))). 108.45/109.11 tff('6', plain, notequalI1 = (![X2,X3]: ((~subset(X2,X3)) => (X2 != X3))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(notsubsetI, axiom, notsubsetI <=> 108.45/109.11 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => (~subset(A,B)))))). 108.45/109.11 tff('7', plain, 108.45/109.11 notsubsetI = 108.45/109.11 (![X2,X3,X4]: (in(X4,X2) => ((~in(X4,X3)) => (~subset(X2,X3))))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(subsetE2, axiom, subsetE2 <=> 108.45/109.11 (![A,B,Xx]: (subset(A,B) => ((~in(Xx,B)) => (~in(Xx,A)))))). 108.45/109.11 tff('8', plain, 108.45/109.11 subsetE2 = 108.45/109.11 (![X2,X3,X4]: (subset(X2,X3) => ((~in(X4,X3)) => (~in(X4,X2))))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(subsetE, axiom, subsetE <=> 108.45/109.11 (![A,B,Xx]: (subset(A,B) => (in(Xx,A) => in(Xx,B))))). 108.45/109.11 tff('9', plain, 108.45/109.11 subsetE = (![X2,X3,X4]: (subset(X2,X3) => (in(X4,X2) => in(X4,X3)))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(emptysetsubset, axiom, emptysetsubset <=> (![A]: subset(emptyset,A))). 108.45/109.11 tff('10', plain, emptysetsubset = (![X2]: subset(emptyset,X2)), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(subsetI2, axiom, subsetI2 <=> 108.45/109.11 (![A,B]: ((![Xx]: (in(Xx,A) => in(Xx,B))) => subset(A,B)))). 108.45/109.11 tff('11', plain, 108.45/109.11 subsetI2 = 108.45/109.11 (![X2,X3]: ((![X4]: (in(X4,X2) => in(X4,X3))) => subset(X2,X3))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(eqimpsubset1, axiom, eqimpsubset1 <=> (![A,B]: ((A = B) => subset(A,B)))). 108.45/109.11 tff('12', plain, eqimpsubset1 = (![X2,X3]: ((X2 = X3) => subset(X2,X3))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(eqimpsubset2, axiom, eqimpsubset2 <=> (![A,B]: ((A = B) => subset(B,A)))). 108.45/109.11 tff('13', plain, eqimpsubset2 = (![X2,X3]: ((X2 = X3) => subset(X3,X2))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(subsetI1, axiom, subsetI1 <=> 108.45/109.11 (![A,B]: ((![Xx]: (in(Xx,A) => in(Xx,B))) => subset(A,B)))). 108.45/109.11 tff('14', plain, 108.45/109.11 subsetI1 = 108.45/109.11 (![X2,X3]: ((![X4]: (in(X4,X2) => in(X4,X3))) => subset(X2,X3))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(dsetconstr__Cong, axiom, dsetconstr__Cong <=> 108.45/109.11 (![A,B]: 108.45/109.11 ((A = B) => 108.45/109.11 (![Xphi:($i > $o),Xpsi:($i > $o)]: 108.45/109.11 ((![Xx]: 108.45/109.11 (in(Xx,A) => 108.45/109.11 (![Xy]: (in(Xy,B) => ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy))))))) => 108.45/109.11 (dsetconstr(A,^[Xx]: Xphi(Xx)) = dsetconstr(B,^[Xx]: Xpsi(Xx)))))))). 108.45/109.11 tff('15', plain, 108.45/109.11 dsetconstr__Cong = 108.45/109.11 (![X2,X3]: 108.45/109.11 ((X2 = X3) => 108.45/109.11 (![X4:($i > $o),X5:($i > $o)]: 108.45/109.11 ((![X6]: 108.45/109.11 (in(X6,X2) => 108.45/109.11 (![X7]: (in(X7,X3) => ((X6 = X7) => (X4(X6) <=> X5(X7))))))) => 108.45/109.11 (dsetconstr(X2,^[V_1]: X4(V_1)) = dsetconstr(X3,^[V_2]: X5(V_2))))))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(descr__Cong, axiom, descr__Cong <=> 108.45/109.11 (![Xphi:($i > $o),Xpsi:($i > $o)]: 108.45/109.11 ((![Xx,Xy]: ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy)))) => 108.45/109.11 (exu(^[Xx]: Xphi(Xx)) => 108.45/109.11 (exu(^[Xx]: Xpsi(Xx)) => 108.45/109.11 (descr(^[Xx]: Xphi(Xx)) = descr(^[Xx]: Xpsi(Xx)))))))). 108.45/109.11 tff('16', plain, 108.45/109.11 descr__Cong = 108.45/109.11 (![X2:($i > $o),X3:($i > $o)]: 108.45/109.11 ((![X4,X5]: ((X4 = X5) => (X2(X4) <=> X3(X5)))) => 108.45/109.11 (exu(^[V_1]: X2(V_1)) => 108.45/109.11 (exu(^[V_2]: X3(V_2)) => 108.45/109.11 (descr(^[V_3]: X2(V_3)) = descr(^[V_4]: X3(V_4))))))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(exuEu, axiom, exuEu <=> 108.45/109.11 (![Xphi:($i > $o)]: 108.45/109.11 (exu(^[Xx]: Xphi(Xx)) => 108.45/109.11 (![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))). 108.45/109.11 tff('17', plain, 108.45/109.11 exuEu = 108.45/109.11 (![X2:($i > $o)]: 108.45/109.11 (exu(^[V_1]: X2(V_1)) => (![X3,X4]: (X2(X3) => (X2(X4) => (X3 = X4)))))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(omega__Cong, axiom, omega__Cong <=> (omega = omega)). 108.45/109.11 tff('18', plain, omega__Cong = (omega = omega), define([status(thm)])). 108.45/109.11 tff(setunion__Cong, axiom, setunion__Cong <=> 108.45/109.11 (![A,B]: ((A = B) => (setunion(A) = setunion(B))))). 108.45/109.11 tff('19', plain, 108.45/109.11 setunion__Cong = (![X2,X3]: ((X2 = X3) => (setunion(X2) = setunion(X3)))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(powerset__Cong, axiom, powerset__Cong <=> 108.45/109.11 (![A,B]: ((A = B) => (powerset(A) = powerset(B))))). 108.45/109.11 tff('20', plain, 108.45/109.11 powerset__Cong = (![X2,X3]: ((X2 = X3) => (powerset(X2) = powerset(X3)))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(setadjoin__Cong, axiom, setadjoin__Cong <=> 108.45/109.11 (![Xx,Xy]: 108.45/109.11 ((Xx = Xy) => 108.45/109.11 (![Xz,Xu]: ((Xz = Xu) => (setadjoin(Xx,Xz) = setadjoin(Xy,Xu))))))). 108.45/109.11 tff('21', plain, 108.45/109.11 setadjoin__Cong = 108.45/109.11 (![X2,X3]: 108.45/109.11 ((X2 = X3) => 108.45/109.11 (![X4,X5]: ((X4 = X5) => (setadjoin(X2,X4) = setadjoin(X3,X5)))))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(emptyset__Cong, axiom, emptyset__Cong <=> (emptyset = emptyset)). 108.45/109.11 tff('22', plain, emptyset__Cong = (emptyset = emptyset), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(exu__Cong, axiom, exu__Cong <=> 108.45/109.11 (![Xphi:($i > $o),Xpsi:($i > $o)]: 108.45/109.11 ((![Xx,Xy]: ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy)))) => 108.45/109.11 (exu(^[Xx]: Xphi(Xx)) <=> exu(^[Xx]: Xpsi(Xx)))))). 108.45/109.11 tff('23', plain, 108.45/109.11 exu__Cong = 108.45/109.11 (![X2:($i > $o),X3:($i > $o)]: 108.45/109.11 ((![X4,X5]: ((X4 = X5) => (X2(X4) <=> X3(X5)))) => 108.45/109.11 (exu(^[V_1]: X2(V_1)) <=> exu(^[V_2]: X3(V_2))))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(exuE3u, axiom, exuE3u <=> 108.45/109.11 (![Xphi:($i > $o)]: 108.45/109.11 (exu(^[Xx]: Xphi(Xx)) => 108.45/109.11 (![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))). 108.45/109.11 tff('24', plain, 108.45/109.11 exuE3u = 108.45/109.11 (![X2:($i > $o)]: 108.45/109.11 (exu(^[V_1]: X2(V_1)) => (![X3,X4]: (X2(X3) => (X2(X4) => (X3 = X4)))))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(in__Cong, axiom, in__Cong <=> 108.45/109.11 (![A,B]: ((A = B) => (![Xx,Xy]: ((Xx = Xy) => (in(Xx,A) <=> in(Xy,B))))))). 108.45/109.11 tff('25', plain, 108.45/109.11 in__Cong = 108.45/109.11 (![X2,X3]: 108.45/109.11 ((X2 = X3) => (![X4,X5]: ((X4 = X5) => (in(X4,X2) <=> in(X5,X3)))))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(inCongP, axiom, inCongP <=> 108.45/109.11 (![A,B]: ((A = B) => (![Xx,Xy]: ((Xx = Xy) => (in(Xx,A) => in(Xy,B))))))). 108.45/109.11 tff('26', plain, 108.45/109.11 inCongP = 108.45/109.11 (![X2,X3]: 108.45/109.11 ((X2 = X3) => (![X4,X5]: ((X4 = X5) => (in(X4,X2) => in(X5,X3)))))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(exuI2, axiom, exuI2 <=> 108.45/109.11 (![Xphi:($i > $o)]: 108.45/109.11 ((?[Xx]: (![Xy]: (Xphi(Xy) <=> (Xy = Xx)))) => exu(^[Xx]: Xphi(Xx))))). 108.45/109.11 tff('27', plain, 108.45/109.11 exuI2 = 108.45/109.11 (![X2:($i > $o)]: 108.45/109.11 ((?[X3]: (![X4]: (X2(X4) <=> (X4 = X3)))) => exu(^[V_1]: X2(V_1)))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(exuI3, axiom, exuI3 <=> 108.45/109.11 (![Xphi:($i > $o)]: 108.45/109.11 ((?[Xx]: Xphi(Xx)) => 108.45/109.11 ((![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy)))) => 108.45/109.11 exu(^[Xx]: Xphi(Xx)))))). 108.45/109.11 tff('28', plain, 108.45/109.11 exuI3 = 108.45/109.11 (![X2:($i > $o)]: 108.45/109.11 ((?[X3]: X2(X3)) => 108.45/109.11 ((![X4,X5]: (X2(X4) => (X2(X5) => (X4 = X5)))) => 108.45/109.11 exu(^[V_1]: X2(V_1))))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(exuI1, axiom, exuI1 <=> 108.45/109.11 (![Xphi:($i > $o)]: 108.45/109.11 ((?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx))) => 108.45/109.11 exu(^[Xx]: Xphi(Xx))))). 108.45/109.11 tff('29', plain, 108.45/109.11 exuI1 = 108.45/109.11 (![X2:($i > $o)]: 108.45/109.11 ((?[X3]: ((![X4]: (X2(X4) => (X3 = X4))) & X2(X3))) => 108.45/109.11 exu(^[V_1]: X2(V_1)))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(notdallE, axiom, notdallE <=> 108.45/109.11 (![A,Xphi:($i > $o)]: 108.45/109.11 ((~(![Xx]: (in(Xx,A) => Xphi(Xx)))) => (?[Xx]: ((~Xphi(Xx)) & in(Xx,A)))))). 108.45/109.11 tff('30', plain, 108.45/109.11 notdallE = 108.45/109.11 (![X2,X3:($i > $o)]: 108.45/109.11 ((~(![X4]: (in(X4,X2) => X3(X4)))) => (?[X5]: ((~X3(X5)) & in(X5,X2))))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(notdexE, axiom, notdexE <=> 108.45/109.11 (![A,Xphi:($i > $o)]: 108.45/109.11 ((~(?[Xx]: (Xphi(Xx) & in(Xx,A)))) => (![Xx]: (in(Xx,A) => (~Xphi(Xx))))))). 108.45/109.11 tff('31', plain, 108.45/109.11 notdexE = 108.45/109.11 (![X2,X3:($i > $o)]: 108.45/109.11 ((~(?[X4]: (X3(X4) & in(X4,X2)))) => (![X5]: (in(X5,X2) => (~X3(X5)))))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(prop2set2propI, axiom, prop2set2propI <=> 108.45/109.11 (![Xphi:$o]: (Xphi => set2prop(prop2set(Xphi))))). 108.45/109.11 tff('32', plain, prop2set2propI = (![X2:$o]: (X2 => set2prop(prop2set(X2)))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(prop2setI, axiom, prop2setI <=> 108.45/109.11 (![Xphi:$o]: (Xphi => in(emptyset,prop2set(Xphi))))). 108.45/109.11 tff('33', plain, prop2setI = (![X2:$o]: (X2 => in(emptyset,prop2set(X2)))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(quantDeMorgan4, axiom, quantDeMorgan4 <=> 108.45/109.11 (![A,Xphi:($i > $o)]: 108.45/109.11 ((?[Xx]: ((~Xphi(Xx)) & in(Xx,A))) => (~(![Xx]: (in(Xx,A) => Xphi(Xx))))))). 108.45/109.11 tff('34', plain, 108.45/109.11 quantDeMorgan4 = 108.45/109.11 (![X2,X3:($i > $o)]: 108.45/109.11 ((?[X4]: ((~X3(X4)) & in(X4,X2))) => (~(![X5]: (in(X5,X2) => X3(X5)))))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(quantDeMorgan3, axiom, quantDeMorgan3 <=> 108.45/109.11 (![A,Xphi:($i > $o)]: 108.45/109.11 ((~(?[Xx]: (Xphi(Xx) & in(Xx,A)))) => (![Xx]: (in(Xx,A) => (~Xphi(Xx))))))). 108.45/109.11 tff('35', plain, 108.45/109.11 quantDeMorgan3 = 108.45/109.11 (![X2,X3:($i > $o)]: 108.45/109.11 ((~(?[X4]: (X3(X4) & in(X4,X2)))) => (![X5]: (in(X5,X2) => (~X3(X5)))))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(quantDeMorgan2, axiom, quantDeMorgan2 <=> 108.45/109.11 (![A,Xphi:($i > $o)]: 108.45/109.11 ((![Xx]: (in(Xx,A) => (~Xphi(Xx)))) => (~(?[Xx]: (Xphi(Xx) & in(Xx,A))))))). 108.45/109.11 tff('36', plain, 108.45/109.11 quantDeMorgan2 = 108.45/109.11 (![X2,X3:($i > $o)]: 108.45/109.11 ((![X4]: (in(X4,X2) => (~X3(X4)))) => (~(?[X5]: (X3(X5) & in(X5,X2)))))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(quantDeMorgan1, axiom, quantDeMorgan1 <=> 108.45/109.11 (![A,Xphi:($i > $o)]: 108.45/109.11 ((~(![Xx]: (in(Xx,A) => Xphi(Xx)))) => (?[Xx]: ((~Xphi(Xx)) & in(Xx,A)))))). 108.45/109.11 tff('37', plain, 108.45/109.11 quantDeMorgan1 = 108.45/109.11 (![X2,X3:($i > $o)]: 108.45/109.11 ((~(![X4]: (in(X4,X2) => X3(X4)))) => (?[X5]: ((~X3(X5)) & in(X5,X2))))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(vacuousDall, axiom, vacuousDall <=> 108.45/109.11 (![Xphi:($i > $o),Xx]: (in(Xx,emptyset) => Xphi(Xx)))). 108.45/109.11 tff('38', plain, 108.45/109.11 vacuousDall = (![X2:($i > $o),X3]: (in(X3,emptyset) => X2(X3))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(emptyE1, axiom, emptyE1 <=> 108.45/109.11 (![A,Xphi:($i > $o)]: 108.45/109.11 ((?[Xx]: (Xphi(Xx) & in(Xx,A))) => 108.45/109.11 ((dsetconstr(A,^[Xx]: Xphi(Xx)) = emptyset) => $false)))). 108.45/109.11 tff('39', plain, 108.45/109.11 emptyE1 = 108.45/109.11 (![X2,X3:($i > $o)]: 108.45/109.11 ((?[X4]: (X3(X4) & in(X4,X2))) => 108.45/109.11 ((dsetconstr(X2,^[V_1]: X3(V_1)) = emptyset) => $false))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(upairsetIR, axiom, upairsetIR <=> 108.45/109.11 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 108.45/109.11 tff('40', plain, 108.45/109.11 upairsetIR = (![X2,X3]: in(X3,setadjoin(X2,setadjoin(X3,emptyset)))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(upairsetIL, axiom, upairsetIL <=> 108.45/109.11 (![Xx,Xy]: in(Xx,setadjoin(Xx,setadjoin(Xy,emptyset))))). 108.45/109.11 tff('41', plain, 108.45/109.11 upairsetIL = (![X2,X3]: in(X2,setadjoin(X2,setadjoin(X3,emptyset)))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(upairsetE, axiom, upairsetE <=> 108.45/109.11 (![Xx,Xy,Xz]: 108.45/109.11 (in(Xz,setadjoin(Xx,setadjoin(Xy,emptyset))) => ((Xz = Xy) | (Xz = Xx))))). 108.45/109.11 tff('42', plain, 108.45/109.11 upairsetE = 108.45/109.11 (![X2,X3,X4]: 108.45/109.11 (in(X4,setadjoin(X2,setadjoin(X3,emptyset))) => 108.45/109.11 ((X4 = X3) | (X4 = X2)))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(singletonsswitch, axiom, singletonsswitch <=> 108.45/109.11 (![Xx,Xy]: (in(Xx,setadjoin(Xy,emptyset)) => in(Xy,setadjoin(Xx,emptyset))))). 108.45/109.11 tff('43', plain, 108.45/109.11 singletonsswitch = 108.45/109.11 (![X2,X3]: 108.45/109.11 (in(X2,setadjoin(X3,emptyset)) => in(X3,setadjoin(X2,emptyset)))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(eqinunit, axiom, eqinunit <=> 108.45/109.11 (![Xx,Xy]: ((Xx = Xy) => in(Xx,setadjoin(Xy,emptyset))))). 108.45/109.11 tff('44', plain, 108.45/109.11 eqinunit = (![X2,X3]: ((X2 = X3) => in(X2,setadjoin(X3,emptyset)))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(notinsingleton, axiom, notinsingleton <=> 108.45/109.11 (![Xx,Xy]: ((Xx != Xy) => (~in(Xy,setadjoin(Xx,emptyset)))))). 108.45/109.11 tff('45', plain, 108.45/109.11 notinsingleton = 108.45/109.11 (![X2,X3]: ((X2 != X3) => (~in(X3,setadjoin(X2,emptyset))))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(uniqinunit, axiom, uniqinunit <=> 108.45/109.11 (![Xx,Xy]: (in(Xx,setadjoin(Xy,emptyset)) => (Xx = Xy)))). 108.45/109.11 tff('46', plain, 108.45/109.11 uniqinunit = (![X2,X3]: (in(X2,setadjoin(X3,emptyset)) => (X2 = X3))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(nonemptyImpWitness, axiom, nonemptyImpWitness <=> 108.45/109.11 (![A]: (nonempty(A) => (?[Xx]: (in(Xx,A)))))). 108.45/109.11 tff('47', plain, 108.45/109.11 nonemptyImpWitness = (![X2]: (nonempty(X2) => (?[X3]: (in(X3,X2))))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(exuE2, axiom, exuE2 <=> 108.45/109.11 (![Xphi:($i > $o)]: 108.45/109.11 (exu(^[Xx]: Xphi(Xx)) => (?[Xx]: (![Xy]: (Xphi(Xy) <=> (Xy = Xx))))))). 108.45/109.11 tff('48', plain, 108.45/109.11 exuE2 = 108.45/109.11 (![X2:($i > $o)]: 108.45/109.11 (exu(^[V_1]: X2(V_1)) => (?[X3]: (![X4]: (X2(X4) <=> (X4 = X3)))))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(subPowSU, axiom, subPowSU <=> 108.45/109.11 (![A,Xx]: (in(Xx,A) => in(Xx,powerset(setunion(A)))))). 108.45/109.11 tff('49', plain, 108.45/109.11 subPowSU = (![X2,X3]: (in(X3,X2) => in(X3,powerset(setunion(X2))))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(setunionE, axiom, setunionE <=> 108.45/109.11 (![A,Xx]: 108.45/109.11 (in(Xx,setunion(A)) => 108.45/109.11 (![Xphi:$o]: ((![B]: (in(Xx,B) => (in(B,A) => Xphi))) => Xphi))))). 108.45/109.11 tff('50', plain, 108.45/109.11 setunionE = 108.45/109.11 (![X2,X3]: 108.45/109.11 (in(X3,setunion(X2)) => 108.45/109.11 (![X4:$o]: ((![X5]: (in(X3,X5) => (in(X5,X2) => X4))) => X4)))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(setunionI, axiom, setunionI <=> 108.45/109.11 (![A,Xx,B]: (in(Xx,B) => (in(B,A) => in(Xx,setunion(A)))))). 108.45/109.11 tff('51', plain, 108.45/109.11 setunionI = 108.45/109.11 (![X2,X3,X4]: (in(X3,X4) => (in(X4,X2) => in(X3,setunion(X2))))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(powersetE, axiom, powersetE <=> 108.45/109.11 (![A,B,Xx]: (in(B,powerset(A)) => (in(Xx,B) => in(Xx,A))))). 108.45/109.11 tff('52', plain, 108.45/109.11 powersetE = 108.45/109.11 (![X2,X3,X4]: (in(X3,powerset(X2)) => (in(X4,X3) => in(X4,X2)))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(emptyInPowerset, axiom, emptyInPowerset <=> 108.45/109.11 (![A]: in(emptyset,powerset(A)))). 108.45/109.11 tff('53', plain, emptyInPowerset = (![X2]: in(emptyset,powerset(X2))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(emptyinPowerset, axiom, emptyinPowerset <=> 108.45/109.11 (![A]: in(emptyset,powerset(A)))). 108.45/109.11 tff('54', plain, emptyinPowerset = (![X2]: in(emptyset,powerset(X2))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(powersetI, axiom, powersetI <=> 108.45/109.11 (![A,B]: ((![Xx]: (in(Xx,B) => in(Xx,A))) => in(B,powerset(A))))). 108.45/109.11 tff('55', plain, 108.45/109.11 powersetI = 108.45/109.11 (![X2,X3]: ((![X4]: (in(X4,X3) => in(X4,X2))) => in(X3,powerset(X2)))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(setoftrueEq, axiom, setoftrueEq <=> 108.45/109.11 (![A]: (dsetconstr(A,^[Xx]: $true) = A))). 108.45/109.11 tff('56', plain, setoftrueEq = (![X2]: (dsetconstr(X2,^[V_1]: $true) = X2)), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(setadjoinOr, axiom, setadjoinOr <=> 108.45/109.11 (![Xx,A,Xy]: (in(Xy,setadjoin(Xx,A)) => (in(Xy,A) | (Xy = Xx))))). 108.45/109.11 tff('57', plain, 108.45/109.11 setadjoinOr = 108.45/109.11 (![X2,X3,X4]: (in(X4,setadjoin(X2,X3)) => (in(X4,X3) | (X4 = X2)))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(setadjoinE, axiom, setadjoinE <=> 108.45/109.11 (![Xx,A,Xy]: 108.45/109.11 (in(Xy,setadjoin(Xx,A)) => 108.45/109.11 (![Xphi:$o]: (((Xy = Xx) => Xphi) => ((in(Xy,A) => Xphi) => Xphi)))))). 108.45/109.11 tff('58', plain, 108.45/109.11 setadjoinE = 108.45/109.11 (![X2,X3,X4]: 108.45/109.11 (in(X4,setadjoin(X2,X3)) => 108.45/109.11 (![X5:$o]: (((X4 = X2) => X5) => ((in(X4,X3) => X5) => X5))))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(setadjoinIR, axiom, setadjoinIR <=> 108.45/109.11 (![Xx,A,Xy]: (in(Xy,A) => in(Xy,setadjoin(Xx,A))))). 108.45/109.11 tff('59', plain, 108.45/109.11 setadjoinIR = (![X2,X3,X4]: (in(X4,X3) => in(X4,setadjoin(X2,X3)))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(emptyinunitempty, axiom, emptyinunitempty() = 108.45/109.11 in(emptyset,setadjoin(emptyset,emptyset))). 108.45/109.11 tff('60', plain, 108.45/109.11 emptyinunitempty = in(emptyset,setadjoin(emptyset,emptyset)), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(setadjoinIL, axiom, setadjoinIL <=> (![Xx,Xy]: in(Xx,setadjoin(Xx,Xy)))). 108.45/109.11 tff('61', plain, setadjoinIL = (![X2,X3]: in(X2,setadjoin(X2,X3))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(nonemptyI1, axiom, nonemptyI1 <=> 108.45/109.11 (![A]: ((?[Xx]: in(Xx,A)) => nonempty(A)))). 108.45/109.11 tff('62', plain, nonemptyI1 = (![X2]: ((?[X3]: in(X3,X2)) => nonempty(X2))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(nonemptyI, axiom, nonemptyI <=> 108.45/109.11 (![A,Xphi:($i > $o),Xx]: 108.45/109.11 (in(Xx,A) => (Xphi(Xx) => nonempty(dsetconstr(A,^[Xy]: Xphi(Xy))))))). 108.45/109.11 tff('63', plain, 108.45/109.11 nonemptyI = 108.45/109.11 (![X2,X3:($i > $o),X4]: 108.45/109.11 (in(X4,X2) => (X3(X4) => nonempty(dsetconstr(X2,^[V_1]: X3(V_1)))))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(nonemptyE1, axiom, nonemptyE1 <=> 108.45/109.11 (![A]: (nonempty(A) => (?[Xx]: in(Xx,A))))). 108.45/109.11 tff('64', plain, nonemptyE1 = (![X2]: (nonempty(X2) => (?[X3]: in(X3,X2)))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(nonempty, axiom, nonempty() = ^[Xx]: (Xx != emptyset)). 108.45/109.11 tff('65', plain, nonempty = (^[V_1]: (V_1 != emptyset)), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(setbeta, axiom, setbeta <=> 108.45/109.11 (![A,Xphi:($i > $o),Xx]: 108.45/109.11 (in(Xx,A) => (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) <=> Xphi(Xx))))). 108.45/109.11 tff('66', plain, 108.45/109.11 setbeta = 108.45/109.11 (![X2,X3:($i > $o),X4]: 108.45/109.11 (in(X4,X2) => (in(X4,dsetconstr(X2,^[V_1]: X3(V_1))) <=> X3(X4)))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(noeltsimpempty, axiom, noeltsimpempty <=> 108.45/109.11 (![A]: ((![Xx]: (~in(Xx,A))) => (A = emptyset)))). 108.45/109.11 tff('67', plain, 108.45/109.11 noeltsimpempty = (![X2]: ((![X3]: (~in(X3,X2))) => (X2 = emptyset))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(emptyI, axiom, emptyI <=> 108.45/109.11 (![A]: ((![Xx]: (~in(Xx,A))) => (A = emptyset)))). 108.45/109.11 tff('68', plain, 108.45/109.11 emptyI = (![X2]: ((![X3]: (~in(X3,X2))) => (X2 = emptyset))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(setext, axiom, setext <=> 108.45/109.11 (![A,B]: 108.45/109.11 ((![Xx]: (in(Xx,A) => in(Xx,B))) => 108.45/109.11 ((![Xx]: (in(Xx,B) => in(Xx,A))) => (A = B))))). 108.45/109.11 tff('69', plain, 108.45/109.11 setext = 108.45/109.11 (![X2,X3]: 108.45/109.11 ((![X4]: (in(X4,X2) => in(X4,X3))) => 108.45/109.11 ((![X5]: (in(X5,X3) => in(X5,X2))) => (X2 = X3)))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(exuE3e, axiom, exuE3e <=> 108.45/109.11 (![Xphi:($i > $o)]: (exu(^[Xx]: Xphi(Xx)) => (?[Xx]: Xphi(Xx))))). 108.45/109.11 tff('70', plain, 108.45/109.11 exuE3e = (![X2:($i > $o)]: (exu(^[V_1]: X2(V_1)) => (?[X3]: X2(X3)))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(notinemptyset, axiom, notinemptyset <=> (![Xx]: (~in(Xx,emptyset)))). 108.45/109.11 tff('71', plain, notinemptyset = (![X2]: (~in(X2,emptyset))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(emptysetimpfalse, axiom, emptysetimpfalse <=> 108.45/109.11 (![Xx]: (in(Xx,emptyset) => $false))). 108.45/109.11 tff('72', plain, emptysetimpfalse = (![X2]: (in(X2,emptyset) => $false)), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(emptysetE, axiom, emptysetE <=> 108.45/109.11 (![Xx]: (in(Xx,emptyset) => (![Xphi:$o]: Xphi)))). 108.45/109.11 tff('73', plain, emptysetE = (![X2]: (in(X2,emptyset) => (![X3:$o]: X3))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(prop2setE, axiom, prop2setE <=> 108.45/109.11 (![Xphi:$o,Xx]: (in(Xx,prop2set(Xphi)) => Xphi))). 108.45/109.11 tff('74', plain, prop2setE = (![X2:$o,X3]: (in(X3,prop2set(X2)) => X2)), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(exuE1, axiom, exuE1 <=> 108.45/109.11 (![Xphi:($i > $o)]: 108.45/109.11 (exu(^[Xx]: Xphi(Xx)) => 108.45/109.11 (?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx)))))). 108.45/109.11 tff('75', plain, 108.45/109.11 exuE1 = 108.45/109.11 (![X2:($i > $o)]: 108.45/109.11 (exu(^[V_1]: X2(V_1)) => 108.45/109.11 (?[X3]: ((![X4]: (X2(X4) => (X3 = X4))) & X2(X3))))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(dsetconstrER, axiom, dsetconstrER <=> 108.45/109.11 (![A,Xphi:($i > $o),Xx]: (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) => Xphi(Xx)))). 108.45/109.11 tff('76', plain, 108.45/109.11 dsetconstrER = 108.45/109.11 (![X2,X3:($i > $o),X4]: (in(X4,dsetconstr(X2,^[V_1]: X3(V_1))) => X3(X4))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(dsetconstrEL, axiom, dsetconstrEL <=> 108.45/109.11 (![A,Xphi:($i > $o),Xx]: (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) => in(Xx,A)))). 108.45/109.11 tff('77', plain, 108.45/109.11 dsetconstrEL = 108.45/109.11 (![X2,X3:($i > $o),X4]: 108.45/109.11 (in(X4,dsetconstr(X2,^[V_1]: X3(V_1))) => in(X4,X2))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(dsetconstrI, axiom, dsetconstrI <=> 108.45/109.11 (![A,Xphi:($i > $o),Xx]: 108.45/109.11 (in(Xx,A) => (Xphi(Xx) => in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))))))). 108.45/109.11 tff('78', plain, 108.45/109.11 dsetconstrI = 108.45/109.11 (![X2,X3:($i > $o),X4]: 108.45/109.11 (in(X4,X2) => (X3(X4) => in(X4,dsetconstr(X2,^[V_1]: X3(V_1)))))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(descrp, axiom, descrp <=> 108.45/109.11 (![Xphi:($i > $o)]: (exu(^[Xx]: Xphi(Xx)) => Xphi(descr(^[Xx]: Xphi(Xx)))))). 108.45/109.11 tff('79', plain, 108.45/109.11 descrp = 108.45/109.11 (![X2:($i > $o)]: (exu(^[V_1]: X2(V_1)) => X2(descr(^[V_2]: X2(V_2))))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(wellorderingAx, axiom, wellorderingAx <=> 108.45/109.11 (![A]: 108.45/109.11 (?[B]: 108.45/109.11 ((![C]: 108.45/109.11 (((?[Xx]: in(Xx,C)) & (![Xx]: (in(Xx,C) => in(Xx,A)))) => 108.45/109.11 (?[D,Xx]: 108.45/109.11 ((![E]: 108.45/109.11 (in(E,B) => (in(Xx,E) | (![Xy]: (in(Xy,E) => in(Xy,D)))))) & 108.45/109.11 (~(?[Xy]: (in(Xy,C) & in(Xy,D)))) & in(Xx,C) & in(D,B))))) & 108.45/109.11 (![C,D]: 108.45/109.11 ((in(D,B) & in(C,B)) => 108.45/109.11 ((![Xx]: (in(Xx,D) => in(Xx,C))) | 108.45/109.11 (![Xx]: (in(Xx,C) => in(Xx,D)))))) & 108.45/109.11 (![Xx,Xy]: 108.45/109.11 ((in(Xy,A) & in(Xx,A)) => 108.45/109.11 ((![C]: (in(C,B) => (in(Xx,C) <=> in(Xy,C)))) => (Xx = Xy)))) & 108.45/109.11 (![C]: (in(C,B) => (![Xx]: (in(Xx,C) => in(Xx,A))))))))). 108.45/109.11 tff('80', plain, 108.45/109.11 wellorderingAx = 108.45/109.11 (![X2]: 108.45/109.11 (?[X3]: 108.45/109.11 ((![X4]: 108.45/109.11 (((?[X5]: in(X5,X4)) & (![X6]: (in(X6,X4) => in(X6,X2)))) => 108.45/109.11 (?[X7,X8]: 108.45/109.11 ((![X9]: 108.45/109.11 (in(X9,X3) => 108.45/109.11 (in(X8,X9) | (![X10]: (in(X10,X9) => in(X10,X7)))))) & 108.45/109.11 (~(?[X11]: (in(X11,X4) & in(X11,X7)))) & in(X8,X4) & 108.45/109.11 in(X7,X3))))) & 108.45/109.11 (![X12,X13]: 108.45/109.11 ((in(X13,X3) & in(X12,X3)) => 108.45/109.11 ((![X14]: (in(X14,X13) => in(X14,X12))) | 108.45/109.11 (![X15]: (in(X15,X12) => in(X15,X13)))))) & 108.45/109.11 (![X16,X17]: 108.45/109.11 ((in(X17,X2) & in(X16,X2)) => 108.45/109.11 ((![X18]: (in(X18,X3) => (in(X16,X18) <=> in(X17,X18)))) => 108.45/109.11 (X16 = X17)))) & 108.45/109.11 (![X19]: (in(X19,X3) => (![X20]: (in(X20,X19) => in(X20,X2)))))))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(foundationAx, axiom, foundationAx <=> 108.45/109.11 (![A]: 108.45/109.11 ((?[Xx]: in(Xx,A)) => 108.45/109.11 (?[B]: ((~(?[Xx]: (in(Xx,A) & in(Xx,B)))) & in(B,A)))))). 108.45/109.11 tff('81', plain, 108.45/109.11 foundationAx = 108.45/109.11 (![X2]: 108.45/109.11 ((?[X3]: in(X3,X2)) => 108.45/109.11 (?[X4]: ((~(?[X5]: (in(X5,X2) & in(X5,X4)))) & in(X4,X2))))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(replAx, axiom, replAx <=> 108.45/109.11 (![Xphi:(($i * $i) > $o),A]: 108.45/109.11 ((![Xx]: (in(Xx,A) => exu(^[Xy]: Xphi(Xx,Xy)))) => 108.45/109.11 (?[B]: (![Xx]: (in(Xx,B) <=> (?[Xy]: (Xphi(Xy,Xx) & in(Xy,A))))))))). 108.45/109.11 tff('82', plain, 108.45/109.11 replAx = 108.45/109.11 (![X2:(($i * $i) > $o),X3]: 108.45/109.11 ((![X4]: (in(X4,X3) => exu(^[V_1]: X2(X4,V_1)))) => 108.45/109.11 (?[X5]: (![X6]: (in(X6,X5) <=> (?[X7]: (X2(X7,X6) & in(X7,X3)))))))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(omegaIndAx, axiom, omegaIndAx <=> 108.45/109.11 (![A]: 108.45/109.11 (((![Xx]: ((in(Xx,A) & in(Xx,omega)) => in(setadjoin(Xx,Xx),A))) & 108.45/109.11 in(emptyset,A)) => 108.45/109.11 (![Xx]: (in(Xx,omega) => in(Xx,A)))))). 108.45/109.11 tff('83', plain, 108.45/109.11 omegaIndAx = 108.45/109.11 (![X2]: 108.45/109.11 (((![X3]: ((in(X3,X2) & in(X3,omega)) => in(setadjoin(X3,X3),X2))) & 108.45/109.11 in(emptyset,X2)) => 108.45/109.11 (![X4]: (in(X4,omega) => in(X4,X2))))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(omegaSAx, axiom, omegaSAx <=> 108.45/109.11 (![Xx]: (in(Xx,omega) => in(setadjoin(Xx,Xx),omega)))). 108.45/109.11 tff('84', plain, 108.45/109.11 omegaSAx = (![X2]: (in(X2,omega) => in(setadjoin(X2,X2),omega))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(omega0Ax, axiom, omega0Ax() = in(emptyset,omega)). 108.45/109.11 tff('85', plain, omega0Ax = in(emptyset,omega), define([status(thm)])). 108.45/109.11 tff(setunionAx, axiom, setunionAx <=> 108.45/109.11 (![A,Xx]: (in(Xx,setunion(A)) <=> (?[B]: (in(B,A) & in(Xx,B)))))). 108.45/109.11 tff('86', plain, 108.45/109.11 setunionAx = 108.45/109.11 (![X2,X3]: (in(X3,setunion(X2)) <=> (?[X4]: (in(X4,X2) & in(X3,X4))))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(powersetAx, axiom, powersetAx <=> 108.45/109.11 (![A,B]: (in(B,powerset(A)) <=> (![Xx]: (in(Xx,B) => in(Xx,A)))))). 108.45/109.11 tff('87', plain, 108.45/109.11 powersetAx = 108.45/109.11 (![X2,X3]: (in(X3,powerset(X2)) <=> (![X4]: (in(X4,X3) => in(X4,X2))))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(setadjoinAx, axiom, setadjoinAx <=> 108.45/109.11 (![Xx,A,Xy]: (in(Xy,setadjoin(Xx,A)) <=> (in(Xy,A) | (Xy = Xx))))). 108.45/109.11 tff('88', plain, 108.45/109.11 setadjoinAx = 108.45/109.11 (![X2,X3,X4]: (in(X4,setadjoin(X2,X3)) <=> (in(X4,X3) | (X4 = X2)))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(emptysetAx, axiom, emptysetAx <=> (![Xx]: (~in(Xx,emptyset)))). 108.45/109.11 tff('89', plain, emptysetAx = (![X2]: (~in(X2,emptyset))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(setextAx, axiom, setextAx <=> 108.45/109.11 (![A,B]: ((![Xx]: (in(Xx,A) <=> in(Xx,B))) => (A = B)))). 108.45/109.11 tff('90', plain, 108.45/109.11 setextAx = (![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(exu, axiom, exu() = 108.45/109.11 ^[Xphi:($i > $o)]: (?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx)))). 108.45/109.11 tff('91', plain, 108.45/109.11 exu = 108.45/109.11 (^[V_1:($i > $o)]: (?[X2]: ((![X3]: (V_1(X3) => (X2 = X3))) & V_1(X2)))), 108.45/109.11 define([status(thm)])). 108.45/109.11 tff(setextsub, conjecture, 108.45/109.11 (setextAx => 108.45/109.11 (emptysetAx => 108.45/109.11 (setadjoinAx => 108.45/109.11 (powersetAx => 108.45/109.11 (setunionAx => 108.45/109.11 (omega0Ax => 108.45/109.11 (omegaSAx => 108.45/109.11 (omegaIndAx => 108.45/109.11 (replAx => 108.45/109.11 (foundationAx => 108.45/109.11 (wellorderingAx => 108.45/109.11 (descrp => 108.45/109.11 (dsetconstrI => 108.45/109.11 (dsetconstrEL => 108.45/109.11 (dsetconstrER => 108.45/109.11 (exuE1 => 108.45/109.11 (prop2setE => 108.45/109.11 (emptysetE => 108.45/109.11 (emptysetimpfalse => 108.45/109.11 (notinemptyset => 108.45/109.11 (exuE3e => 108.45/109.11 (setext => 108.45/109.11 (emptyI => 108.45/109.11 (noeltsimpempty => 108.45/109.11 (setbeta => 108.45/109.11 (nonemptyE1 => 108.45/109.11 (nonemptyI => 108.45/109.11 (nonemptyI1 => 108.45/109.11 (setadjoinIL => 108.45/109.11 (emptyinunitempty => 108.45/109.11 (setadjoinIR => 108.45/109.11 (setadjoinE => 108.45/109.11 (setadjoinOr => 108.45/109.11 (setoftrueEq => 108.45/109.11 (powersetI => 108.45/109.11 (emptyinPowerset => 108.45/109.11 (emptyInPowerset => 108.45/109.11 (powersetE => 108.45/109.11 (setunionI => 108.45/109.11 (setunionE => 108.45/109.11 (subPowSU => 108.45/109.11 (exuE2 => 108.45/109.11 (nonemptyImpWitness => 108.45/109.11 (uniqinunit => 108.45/109.11 (notinsingleton => 108.45/109.11 (eqinunit => 108.45/109.11 (singletonsswitch => 108.45/109.11 (upairsetE => 108.45/109.11 (upairsetIL => 108.45/109.11 (upairsetIR => 108.45/109.11 (emptyE1 => 108.45/109.11 (vacuousDall => 108.45/109.11 (quantDeMorgan1 => 108.45/109.11 (quantDeMorgan2 => 108.45/109.11 (quantDeMorgan3 => 108.45/109.11 (quantDeMorgan4 => 108.45/109.11 (prop2setI => 108.45/109.11 (prop2set2propI => 108.45/109.11 (notdexE => 108.45/109.11 (notdallE => 108.45/109.11 (exuI1 => 108.45/109.11 (exuI3 => 108.45/109.11 (exuI2 => 108.45/109.11 (inCongP => 108.45/109.11 (in__Cong => 108.45/109.11 (exuE3u => 108.45/109.11 ( 108.45/109.11 exu__Cong => 108.45/109.11 ( 108.45/109.11 emptyset__Cong => 108.45/109.11 ( 108.45/109.11 setadjoin__Cong => 108.45/109.11 ( 108.45/109.11 powerset__Cong => 108.45/109.11 ( 108.45/109.11 setunion__Cong => 108.45/109.11 ( 108.45/109.11 omega__Cong => 108.45/109.11 ( 108.45/109.11 exuEu => 108.45/109.11 ( 108.45/109.11 descr__Cong => 108.45/109.11 ( 108.45/109.11 dsetconstr__Cong => 108.45/109.11 ( 108.45/109.11 subsetI1 => 108.45/109.11 ( 108.45/109.11 eqimpsubset2 => 108.45/109.11 ( 108.45/109.11 eqimpsubset1 => 108.45/109.11 ( 108.45/109.11 subsetI2 => 108.45/109.11 ( 108.45/109.11 emptysetsubset => 108.45/109.11 ( 108.45/109.11 subsetE => 108.45/109.11 ( 108.45/109.11 subsetE2 => 108.45/109.11 ( 108.45/109.11 notsubsetI => 108.45/109.11 ( 108.45/109.11 notequalI1 => 108.45/109.11 ( 108.45/109.11 notequalI2 => 108.45/109.11 ( 108.45/109.11 subsetRefl => 108.45/109.11 ( 108.45/109.11 subsetTrans => 108.45/109.11 ( 108.45/109.11 setadjoinSub => 108.45/109.11 ( 108.45/109.11 setadjoinSub2 => 108.45/109.11 ( 108.45/109.11 subset2powerset => 108.45/109.11 ( 108.45/109.11 ![A,B]: 108.45/109.11 (subset( 108.45/109.11 A,B) => 108.45/109.11 (subset( 108.45/109.11 B,A) => 108.45/109.11 (A = B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 108.45/109.11 tff(zf_stmt_0, conjecture, 108.45/109.11 ((![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))) => 108.45/109.11 ((![X5]: (~in(X5,emptyset))) => 108.45/109.11 ((![X6,X7,X8]: (in(X8,setadjoin(X6,X7)) <=> ((X8 = X6) | in(X8,X7)))) => 108.45/109.11 ((![X9,X10]: 108.45/109.11 (in(X10,powerset(X9)) <=> (![X11]: (in(X11,X10) => in(X11,X9))))) => 108.45/109.11 ((![X12,X13]: 108.45/109.11 (in(X13,setunion(X12)) <=> (?[X14]: (in(X13,X14) & in(X14,X12))))) => 108.45/109.11 (in(emptyset,omega) => 108.45/109.11 ((![X15]: (in(X15,omega) => in(setadjoin(X15,X15),omega))) => 108.45/109.11 ((![X16]: 108.45/109.11 ((in(emptyset,X16) & 108.45/109.11 (![X17]: 108.45/109.11 ((in(X17,omega) & in(X17,X16)) => 108.45/109.11 in(setadjoin(X17,X17),X16)))) => 108.45/109.11 (![X18]: (in(X18,omega) => in(X18,X16))))) => 108.45/109.11 ((![X19:(($i * $i) > $o),X20]: 108.45/109.11 ((![X21]: 108.45/109.11 (in(X21,X20) => 108.45/109.11 (?[X22]: 108.45/109.11 (X19(X21,X22) & (![X23]: (X19(X21,X23) => (X22 = X23))))))) => 108.45/109.11 (?[X24]: 108.45/109.11 (![X25]: 108.45/109.11 (in(X25,X24) <=> (?[X26]: (in(X26,X20) & X19(X26,X25)))))))) => 108.45/109.11 ((![X27]: 108.45/109.11 ((?[X28]: in(X28,X27)) => 108.45/109.11 (?[X29]: 108.45/109.11 (in(X29,X27) & (~(?[X30]: (in(X30,X29) & in(X30,X27)))))))) => 108.45/109.11 ((![X31]: 108.45/109.11 (?[X32]: 108.45/109.11 ((![X48]: 108.45/109.11 (in(X48,X32) => (![X49]: (in(X49,X48) => in(X49,X31))))) & 108.45/109.11 (![X45,X46]: 108.45/109.11 ((in(X45,X31) & in(X46,X31)) => 108.45/109.11 ((![X47]: 108.45/109.11 (in(X47,X32) => (in(X45,X47) <=> in(X46,X47)))) => 108.45/109.11 (X45 = X46)))) & 108.45/109.11 (![X41,X42]: 108.45/109.11 ((in(X41,X32) & in(X42,X32)) => 108.45/109.11 ((![X44]: (in(X44,X41) => in(X44,X42))) | 108.45/109.11 (![X43]: (in(X43,X42) => in(X43,X41)))))) & 108.45/109.11 (![X33]: 108.45/109.11 (((![X35]: (in(X35,X33) => in(X35,X31))) & 108.45/109.11 (?[X34]: in(X34,X33))) => 108.45/109.11 (?[X36,X37]: 108.45/109.11 (in(X36,X32) & in(X37,X33) & 108.45/109.11 (~(?[X40]: (in(X40,X36) & in(X40,X33)))) & 108.45/109.11 (![X38]: 108.45/109.11 (in(X38,X32) => 108.45/109.11 ((![X39]: (in(X39,X38) => in(X39,X36))) | 108.45/109.11 in(X37,X38))))))))))) => 108.45/109.11 ((![X50:($i > $o)]: 108.45/109.11 ((?[X51]: (X50(X51) & (![X52]: (X50(X52) => (X51 = X52))))) => 108.45/109.11 X50(descr('#ll_0'(X50))))) => 108.45/109.11 ((![X53,X54:($i > $o),X55]: 108.45/109.11 (in(X55,X53) => 108.45/109.11 (X54(X55) => in(X55,dsetconstr(X53,'#ll_0'(X54)))))) => 108.45/109.11 ((![X56,X57:($i > $o),X58]: 108.45/109.11 (in(X58,dsetconstr(X56,'#ll_0'(X57))) => in(X58,X56))) => 108.45/109.11 ((![X59,X60:($i > $o),X61]: 108.45/109.11 (in(X61,dsetconstr(X59,'#ll_0'(X60))) => X60(X61))) => 108.45/109.11 ((![X62:($i > $o)]: 108.45/109.11 ((?[X63]: 108.45/109.11 (X62(X63) & (![X64]: (X62(X64) => (X63 = X64))))) => 108.45/109.11 (?[X65]: 108.45/109.11 (X62(X65) & (![X66]: (X62(X66) => (X65 = X66))))))) => 108.45/109.11 ((![X67:$o,X68]: (in(X68,prop2set(X67)) => X67)) => 108.45/109.11 ((![X69]: (in(X69,emptyset) => (![X70:$o]: X70))) => 108.45/109.11 ((![X71]: (in(X71,emptyset) => $false)) => 108.45/109.11 ((![X72]: (~in(X72,emptyset))) => 108.45/109.11 ((![X73:($i > $o)]: 108.45/109.11 ((?[X74]: 108.45/109.11 (X73(X74) & (![X75]: (X73(X75) => (X74 = X75))))) => 108.45/109.11 (?[X76]: X73(X76)))) => 108.45/109.11 ((![X77,X78]: 108.45/109.11 ((![X79]: (in(X79,X77) => in(X79,X78))) => 108.45/109.11 ((![X80]: (in(X80,X78) => in(X80,X77))) => 108.45/109.11 (X77 = X78)))) => 108.45/109.11 ((![X81]: 108.45/109.11 ((![X82]: (~in(X82,X81))) => (X81 = emptyset))) => 108.45/109.11 ((![X83]: 108.45/109.11 ((![X84]: (~in(X84,X83))) => (X83 = emptyset))) => 108.45/109.11 ((![X85,X86:($i > $o),X87]: 108.45/109.11 (in(X87,X85) => 108.45/109.11 (in(X87,dsetconstr(X85,'#ll_0'(X86))) <=> 108.45/109.11 X86(X87)))) => 108.45/109.11 ((![X88]: 108.45/109.11 ((X88 != emptyset) => (?[X89]: in(X89,X88)))) => 108.45/109.11 ((![X90,X91:($i > $o),X92]: 108.45/109.11 (in(X92,X90) => 108.45/109.11 (X91(X92) => 108.45/109.11 (dsetconstr(X90,'#ll_0'(X91)) != emptyset)))) => 108.45/109.11 ((![X93]: 108.45/109.11 ((?[X94]: in(X94,X93)) => (X93 != emptyset))) => 108.45/109.11 ((![X95,X96]: in(X95,setadjoin(X95,X96))) => 108.45/109.11 (in(emptyset,setadjoin(emptyset,emptyset)) => 108.45/109.11 ((![X97,X98,X99]: 108.45/109.11 (in(X99,X98) => 108.45/109.11 in(X99,setadjoin(X97,X98)))) => 108.45/109.11 ((![X100,X101,X102]: 108.45/109.11 (in(X102,setadjoin(X100,X101)) => 108.45/109.11 (![X103:$o]: 108.45/109.11 (((X102 = X100) => X103) => 108.45/109.11 ((in(X102,X101) => X103) => X103))))) => 108.45/109.11 ((![X104,X105,X106]: 108.45/109.11 (in(X106,setadjoin(X104,X105)) => 108.45/109.11 ((X106 = X104) | in(X106,X105)))) => 108.45/109.11 ((![X107]: 108.45/109.11 (dsetconstr(X107,'#ll_1') = X107)) => 108.45/109.11 ((![X108,X109]: 108.45/109.11 ((![X110]: 108.45/109.11 (in(X110,X109) => in(X110,X108))) => 108.45/109.11 in(X109,powerset(X108)))) => 108.45/109.11 ((![X111]: in(emptyset,powerset(X111))) => 108.45/109.11 ((![X112]: in(emptyset,powerset(X112))) => 108.45/109.11 ((![X113,X114,X115]: 108.45/109.11 (in(X114,powerset(X113)) => 108.45/109.11 (in(X115,X114) => in(X115,X113)))) => 108.45/109.11 ((![X116,X117,X118]: 108.45/109.11 (in(X117,X118) => 108.45/109.11 (in(X118,X116) => 108.45/109.11 in(X117,setunion(X116))))) => 108.45/109.11 ((![X119,X120]: 108.45/109.11 (in(X120,setunion(X119)) => 108.45/109.11 (![X121:$o]: 108.45/109.11 ((![X122]: 108.45/109.11 (in(X120,X122) => 108.45/109.11 (in(X122,X119) => X121))) => 108.45/109.11 X121)))) => 108.45/109.11 ((![X123,X124]: 108.45/109.11 (in(X124,X123) => 108.45/109.11 in(X124, 108.45/109.11 powerset(setunion(X123))))) => 108.45/109.11 ((![X125:($i > $o)]: 108.45/109.11 ((?[X126]: 108.45/109.11 (X125(X126) & 108.45/109.11 (![X127]: 108.45/109.11 (X125(X127) => 108.45/109.11 (X126 = X127))))) => 108.45/109.11 (?[X128]: 108.45/109.11 (![X129]: 108.45/109.11 (X125(X129) <=> 108.45/109.11 (X129 = X128)))))) => 108.45/109.11 ((![X130]: 108.45/109.11 ((X130 != emptyset) => 108.45/109.11 (?[X131]: in(X131,X130)))) => 108.45/109.11 ((![X132,X133]: 108.45/109.11 (in(X132, 108.45/109.11 setadjoin(X133,emptyset)) => 108.45/109.11 (X132 = X133))) => 108.45/109.11 ((![X134,X135]: 108.45/109.11 ((X134 != X135) => 108.45/109.11 (~ 108.45/109.11 in(X135, 108.45/109.11 setadjoin(X134, 108.45/109.11 emptyset))))) => 108.45/109.11 ((![X136,X137]: 108.45/109.11 ((X136 = X137) => 108.45/109.11 in(X136, 108.45/109.11 setadjoin(X137, 108.45/109.11 emptyset)))) => 108.45/109.11 ((![X138,X139]: 108.45/109.11 (in(X138, 108.45/109.11 setadjoin(X139, 108.45/109.11 emptyset)) => 108.45/109.11 in(X139, 108.45/109.11 setadjoin(X138, 108.45/109.11 emptyset)))) => 108.45/109.11 ((![X140,X141,X142]: 108.45/109.11 (in(X142, 108.45/109.11 setadjoin(X140, 108.45/109.11 setadjoin( 108.45/109.11 X141, 108.45/109.11 emptyset))) => 108.45/109.11 ((X142 = X140) | 108.45/109.11 (X142 = X141)))) => 108.45/109.11 ((![X143,X144]: 108.45/109.11 in(X143, 108.45/109.11 setadjoin(X143, 108.45/109.11 setadjoin( 108.45/109.11 X144, 108.45/109.11 emptyset)))) => 108.45/109.11 ((![X145,X146]: 108.45/109.11 in(X146, 108.45/109.11 setadjoin(X145, 108.45/109.11 setadjoin( 108.45/109.11 X146, 108.45/109.11 emptyset)))) => 108.45/109.11 ((![X147,X148:($i > $o)]: 108.45/109.11 ((?[X149]: 108.45/109.11 (in(X149,X147) & 108.45/109.11 X148(X149))) => 108.45/109.11 ((dsetconstr( 108.45/109.11 X147,'#ll_0'(X148)) = 108.45/109.11 emptyset) => 108.45/109.11 $false))) => 108.45/109.11 ((![X150:($i > $o),X151]: 108.45/109.11 (in(X151,emptyset) => 108.45/109.11 X150(X151))) => 108.45/109.11 ((![X152,X153:($i > $o)]: 108.45/109.11 ((~ 108.45/109.11 (![X154]: 108.45/109.11 (in(X154,X152) => 108.45/109.11 X153(X154)))) => 108.45/109.11 (?[X155]: 108.45/109.11 (in(X155,X152) & 108.45/109.11 (~X153(X155)))))) => 108.45/109.11 ((![X156, 108.45/109.11 X157:($i > $o)]: 108.45/109.11 ((![X158]: 108.45/109.11 (in(X158,X156) => 108.45/109.11 (~X157(X158)))) => 108.45/109.11 (~ 108.45/109.11 (?[X159]: 108.45/109.11 (in( 108.45/109.11 X159,X156) & 108.45/109.11 X157(X159)))))) => 108.45/109.11 ((![X160, 108.45/109.11 X161:($i > $o)]: 108.45/109.11 ((~ 108.45/109.11 (?[X162]: 108.45/109.11 (in( 108.45/109.11 X162,X160) & 108.45/109.11 X161(X162)))) => 108.45/109.11 (![X163]: 108.45/109.11 (in(X163,X160) => 108.45/109.11 (~X161(X163)))))) => 108.45/109.11 ((![X164, 108.45/109.11 X165:($i > $o)]: 108.45/109.11 ((?[X166]: 108.45/109.11 (in( 108.45/109.11 X166,X164) & 108.45/109.11 (~ 108.45/109.11 X165( 108.45/109.11 X166)))) => 108.45/109.11 (~ 108.45/109.11 (![X167]: 108.45/109.11 (in( 108.45/109.11 X167,X164) => 108.45/109.11 X165( 108.45/109.11 X167)))))) => 108.45/109.11 ((![X168:$o]: 108.45/109.11 (X168 => 108.45/109.11 in(emptyset, 108.45/109.11 prop2set( 108.45/109.11 X168)))) => 108.45/109.11 ((![X169:$o]: 108.45/109.11 (X169 => 108.45/109.11 set2prop( 108.45/109.11 prop2set( 108.45/109.11 X169)))) => 108.45/109.11 ((![X170, 108.45/109.11 X171:( 108.45/109.11 $i > $o)]: 108.45/109.11 ((~ 108.45/109.11 (?[X172]: 108.45/109.11 (in( 108.45/109.11 X172,X170) & 108.45/109.11 X171( 108.45/109.11 X172)))) => 108.45/109.11 (![X173]: 108.45/109.11 ( 108.45/109.11 in( 108.45/109.11 X173,X170) => 108.45/109.11 ( 108.45/109.11 ~ 108.45/109.11 X171( 108.45/109.11 X173)))))) => 108.45/109.11 ((![X174, 108.45/109.11 X175:( 108.45/109.11 $i > $o)]: 108.45/109.11 ((~ 108.45/109.11 ( 108.45/109.11 ![X176]: 108.45/109.11 (in( 108.45/109.11 X176,X174) => 108.45/109.11 X175( 108.45/109.11 X176)))) => 108.45/109.11 (?[X177]: 108.45/109.11 (in( 108.45/109.11 X177,X174) & 108.45/109.11 (~ 108.45/109.11 X175( 108.45/109.11 X177)))))) => 108.45/109.11 ((![X178:( 108.45/109.11 $i > $o)]: 108.45/109.11 ((?[X179]: 108.45/109.11 (X178( 108.45/109.11 X179) & 108.45/109.11 (![X180]: 108.45/109.11 (X178( 108.45/109.11 X180) => 108.45/109.11 (X179 = 108.45/109.11 X180))))) => 108.45/109.11 (?[X181]: 108.45/109.11 (X178( 108.45/109.11 X181) & 108.45/109.11 (![X182]: 108.45/109.11 (X178( 108.45/109.11 X182) => 108.45/109.11 (X181 = 108.45/109.11 X182))))))) => 108.45/109.11 ((![X183:( 108.45/109.11 $i > $o)]: 108.45/109.11 (( 108.45/109.11 ?[X184]: 108.45/109.11 X183( 108.45/109.11 X184)) => 108.45/109.11 ( 108.45/109.11 ( 108.45/109.11 ![X185, 108.45/109.11 X186]: 108.45/109.11 (X183( 108.45/109.11 X185) => 108.45/109.11 (X183( 108.45/109.11 X186) => 108.45/109.11 (X185 = 108.45/109.11 X186)))) => 108.45/109.11 ( 108.45/109.11 ?[X187]: 108.45/109.11 (X183( 108.45/109.11 X187) & 108.45/109.11 (![X188]: 108.45/109.11 (X183( 108.45/109.11 X188) => 108.45/109.11 (X187 = 108.45/109.11 X188)))))))) => 108.45/109.11 ((![X189:( 108.45/109.11 $i > $o)]: 108.45/109.11 ( 108.45/109.11 ( 108.45/109.11 ?[X190]: 108.45/109.11 (![X191]: 108.45/109.11 (X189( 108.45/109.11 X191) <=> 108.45/109.11 (X191 = 108.45/109.11 X190)))) => 108.45/109.11 ( 108.45/109.11 ?[X192]: 108.45/109.11 (X189( 108.45/109.11 X192) & 108.45/109.11 (![X193]: 108.45/109.11 (X189( 108.45/109.11 X193) => 108.45/109.11 (X192 = 108.45/109.11 X193))))))) => 108.45/109.11 ((![X194, 108.45/109.11 X195]: 108.45/109.11 (( 108.45/109.11 X194 = 108.45/109.11 X195) => 108.45/109.11 (![X196, 108.45/109.11 X197]: 108.45/109.11 (( 108.45/109.11 X196 = 108.45/109.11 X197) => 108.45/109.11 (in( 108.45/109.11 X196,X194) => 108.45/109.11 in( 108.45/109.11 X197,X195)))))) => 108.45/109.11 ((![X198, 108.45/109.11 X199]: 108.45/109.11 (( 108.45/109.11 X198 = 108.45/109.11 X199) => 108.45/109.11 (![X200, 108.45/109.11 X201]: 108.45/109.11 (( 108.45/109.11 X200 = 108.45/109.11 X201) => 108.45/109.11 (in( 108.45/109.11 X200,X198) <=> 108.45/109.11 in( 108.45/109.11 X201,X199)))))) => 108.45/109.11 (( 108.45/109.11 ![X202:( 108.45/109.11 $i > $o)]: 108.45/109.11 (( 108.45/109.11 ?[X203]: 108.45/109.11 (X202( 108.45/109.11 X203) & 108.45/109.11 (![X204]: 108.45/109.11 (X202( 108.45/109.11 X204) => 108.45/109.11 (X203 = 108.45/109.11 X204))))) => 108.45/109.11 (![X205, 108.45/109.11 X206]: 108.45/109.11 (X202( 108.45/109.11 X205) => 108.45/109.11 (X202( 108.45/109.11 X206) => 108.45/109.11 (X205 = 108.45/109.11 X206)))))) => 108.45/109.11 ( 108.45/109.11 ( 108.45/109.11 ![X207:( 108.45/109.11 $i > $o), 108.45/109.11 X208:( 108.45/109.11 $i > $o)]: 108.45/109.11 (( 108.45/109.11 ![X209, 108.45/109.11 X210]: 108.45/109.11 (( 108.45/109.11 X209 = 108.45/109.11 X210) => 108.45/109.11 (X207( 108.45/109.11 X209) <=> 108.45/109.11 X208( 108.45/109.11 X210)))) => 108.45/109.11 (( 108.45/109.11 ?[X211]: 108.45/109.11 (X207( 108.45/109.11 X211) & 108.45/109.11 (![X212]: 108.45/109.11 (X207( 108.45/109.11 X212) => 108.45/109.11 (X211 = 108.45/109.11 X212))))) <=> 108.45/109.11 (?[X213]: 108.45/109.11 (X208( 108.45/109.11 X213) & 108.45/109.11 (![X214]: 108.45/109.11 (X208( 108.45/109.11 X214) => 108.45/109.11 (X213 = 108.45/109.11 X214)))))))) => 108.45/109.11 ( 108.45/109.11 ( 108.45/109.11 emptyset = 108.45/109.11 emptyset) => 108.45/109.11 ( 108.45/109.11 ( 108.45/109.11 ![X215, 108.45/109.11 X216]: 108.45/109.11 (( 108.45/109.11 X215 = 108.45/109.11 X216) => 108.45/109.11 (![X217, 108.45/109.11 X218]: 108.45/109.11 (( 108.45/109.11 X217 = 108.45/109.11 X218) => 108.45/109.11 (setadjoin( 108.45/109.11 X215,X217) = 108.45/109.11 setadjoin( 108.45/109.11 X216,X218)))))) => 108.45/109.11 ( 108.45/109.11 ( 108.45/109.11 ![X219, 108.45/109.11 X220]: 108.45/109.11 (( 108.45/109.11 X219 = 108.45/109.11 X220) => 108.45/109.11 (powerset( 108.45/109.11 X219) = 108.45/109.11 powerset( 108.45/109.11 X220)))) => 108.45/109.11 ( 108.45/109.11 ( 108.45/109.11 ![X221, 108.45/109.11 X222]: 108.45/109.11 (( 108.45/109.11 X221 = 108.45/109.11 X222) => 108.45/109.11 (setunion( 108.45/109.11 X221) = 108.45/109.11 setunion( 108.45/109.11 X222)))) => 108.45/109.11 ( 108.45/109.11 ( 108.45/109.11 omega = 108.45/109.11 omega) => 108.45/109.11 ( 108.45/109.11 ( 108.45/109.11 ![X223:( 108.45/109.11 $i > $o)]: 108.45/109.11 (( 108.45/109.11 ?[X224]: 108.45/109.11 (X223( 108.45/109.11 X224) & 108.45/109.11 (![X225]: 108.45/109.11 (X223( 108.45/109.11 X225) => 108.45/109.11 (X224 = 108.45/109.11 X225))))) => 108.45/109.11 (![X226, 108.45/109.11 X227]: 108.45/109.11 (X223( 108.45/109.11 X226) => 108.45/109.11 (X223( 108.45/109.11 X227) => 108.45/109.11 (X226 = 108.45/109.11 X227)))))) => 108.45/109.11 ( 108.45/109.11 ( 108.45/109.11 ![X228:( 108.45/109.11 $i > $o), 108.45/109.11 X229:( 108.45/109.11 $i > $o)]: 108.45/109.11 (( 108.45/109.11 ![X230, 108.45/109.12 X231]: 108.45/109.12 (( 108.45/109.12 X230 = 108.45/109.12 X231) => 108.45/109.12 (X228( 108.45/109.12 X230) <=> 108.45/109.12 X229( 108.45/109.12 X231)))) => 108.45/109.12 (( 108.45/109.12 ?[X232]: 108.45/109.12 (X228( 108.45/109.12 X232) & 108.45/109.12 (![X233]: 108.45/109.12 (X228( 108.45/109.12 X233) => 108.45/109.12 (X232 = 108.45/109.12 X233))))) => 108.45/109.12 (( 108.45/109.12 ?[X234]: 108.45/109.12 (X229( 108.45/109.12 X234) & 108.45/109.12 (![X235]: 108.45/109.12 (X229( 108.45/109.12 X235) => 108.45/109.12 (X234 = 108.45/109.12 X235))))) => 108.45/109.12 (descr( 108.45/109.12 '#ll_0'( 108.45/109.12 X228)) = 108.45/109.12 descr( 108.45/109.12 '#ll_0'( 108.45/109.12 X229))))))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X236, 108.45/109.12 X237]: 108.45/109.12 (( 108.45/109.12 X236 = 108.45/109.12 X237) => 108.45/109.12 (![X238:( 108.45/109.12 $i > $o), 108.45/109.12 X239:( 108.45/109.12 $i > $o)]: 108.45/109.12 (( 108.45/109.12 ![X240]: 108.45/109.12 (in( 108.45/109.12 X240,X236) => 108.45/109.12 (![X241]: 108.45/109.12 (in( 108.45/109.12 X241,X237) => 108.45/109.12 (( 108.45/109.12 X240 = 108.45/109.12 X241) => 108.45/109.12 (X238( 108.45/109.12 X240) <=> 108.45/109.12 X239( 108.45/109.12 X241))))))) => 108.45/109.12 (dsetconstr( 108.45/109.12 X236, 108.45/109.12 '#ll_0'( 108.45/109.12 X238)) = 108.45/109.12 dsetconstr( 108.45/109.12 X237, 108.45/109.12 '#ll_0'( 108.45/109.12 X239))))))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X242, 108.45/109.12 X243]: 108.45/109.12 (( 108.45/109.12 ![X244]: 108.45/109.12 (in( 108.45/109.12 X244,X242) => 108.45/109.12 in( 108.45/109.12 X244,X243))) => 108.45/109.12 subset( 108.45/109.12 X242,X243))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X245, 108.45/109.12 X246]: 108.45/109.12 (( 108.45/109.12 X245 = 108.45/109.12 X246) => 108.45/109.12 subset( 108.45/109.12 X246,X245))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X247, 108.45/109.12 X248]: 108.45/109.12 (( 108.45/109.12 X247 = 108.45/109.12 X248) => 108.45/109.12 subset( 108.45/109.12 X247,X248))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X249, 108.45/109.12 X250]: 108.45/109.12 (( 108.45/109.12 ![X251]: 108.45/109.12 (in( 108.45/109.12 X251,X249) => 108.45/109.12 in( 108.45/109.12 X251,X250))) => 108.45/109.12 subset( 108.45/109.12 X249,X250))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X252]: 108.45/109.12 subset( 108.45/109.12 emptyset, 108.45/109.12 X252)) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X253, 108.45/109.12 X254,X255]: 108.45/109.12 (subset( 108.45/109.12 X253,X254) => 108.45/109.12 (in( 108.45/109.12 X255,X253) => 108.45/109.12 in( 108.45/109.12 X255,X254)))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X256, 108.45/109.12 X257,X258]: 108.45/109.12 (subset( 108.45/109.12 X256,X257) => 108.45/109.12 (( 108.45/109.12 ~ 108.45/109.12 in( 108.45/109.12 X258,X257)) => 108.45/109.12 (~ 108.45/109.12 in( 108.45/109.12 X258,X256))))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X259, 108.45/109.12 X260,X261]: 108.45/109.12 (in( 108.45/109.12 X261,X259) => 108.45/109.12 (( 108.45/109.12 ~ 108.45/109.12 in( 108.45/109.12 X261,X260)) => 108.45/109.12 (~ 108.45/109.12 subset( 108.45/109.12 X259,X260))))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X262, 108.45/109.12 X263]: 108.45/109.12 (( 108.45/109.12 ~ 108.45/109.12 subset( 108.45/109.12 X262,X263)) => 108.45/109.12 (X262 != 108.45/109.12 X263))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X264, 108.45/109.12 X265,X266]: 108.45/109.12 (in( 108.45/109.12 X266,X264) => 108.45/109.12 (( 108.45/109.12 ~ 108.45/109.12 in( 108.45/109.12 X266,X265)) => 108.45/109.12 (X264 != 108.45/109.12 X265)))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X267]: 108.45/109.12 subset( 108.45/109.12 X267,X267)) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X268, 108.45/109.12 X269,X270]: 108.45/109.12 (subset( 108.45/109.12 X268,X269) => 108.45/109.12 (subset( 108.45/109.12 X269,X270) => 108.45/109.12 subset( 108.45/109.12 X268,X270)))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X271, 108.45/109.12 X272]: 108.45/109.12 subset( 108.45/109.12 X272, 108.45/109.12 setadjoin( 108.45/109.12 X271,X272))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X273, 108.45/109.12 X274,X275]: 108.45/109.12 (subset( 108.45/109.12 X273,X275) => 108.45/109.12 subset( 108.45/109.12 X273, 108.45/109.12 setadjoin( 108.45/109.12 X274,X275)))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X276, 108.45/109.12 X277]: 108.45/109.12 (subset( 108.45/109.12 X276,X277) => 108.45/109.12 in( 108.45/109.12 X276, 108.45/109.12 powerset( 108.45/109.12 X277)))) => 108.45/109.12 ( 108.45/109.12 ![X278, 108.45/109.12 X279]: 108.45/109.12 (subset( 108.45/109.12 X278,X279) => 108.45/109.12 (subset( 108.45/109.12 X279,X278) => 108.45/109.12 (X278 = 108.45/109.12 X279))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 108.45/109.12 tff(zf_stmt_1, type, zip_tseitin5 : ($i * $i > $o) > $o). 108.45/109.12 tff(zf_stmt_2, axiom, 108.45/109.12 (zip_tseitin5(X211,X207) <=> 108.45/109.12 ((![X212]: zip_tseitin4(X212,X211,X207)) & X207(X211)))). 108.45/109.12 tff(zf_stmt_3, type, zip_tseitin4 : ($i * $i * $i > $o) > $o). 108.45/109.12 tff(zf_stmt_4, axiom, 108.45/109.12 (zip_tseitin4(X212,X211,X207) <=> (X207(X212) => (X211 = X212)))). 108.45/109.12 tff(zf_stmt_5, type, zip_tseitin3 : ($i * $i * $i * ($i * $i) > $o) > $o). 108.45/109.12 tff(zf_stmt_6, axiom, 108.45/109.12 (zip_tseitin3(X26,X25,X20,X19) <=> (X19(X26,X25) & in(X26,X20)))). 108.45/109.12 tff(zf_stmt_7, type, zip_tseitin2 : ($i * $i * $i) > $o). 108.45/109.12 tff(zf_stmt_8, axiom, 108.45/109.12 (zip_tseitin2(X14,X13,X12) <=> (in(X14,X12) & in(X13,X14)))). 108.45/109.12 tff(zf_stmt_9, type, zip_tseitin1 : ($i * $i * $i) > $o). 108.45/109.12 tff(zf_stmt_10, axiom, 108.45/109.12 (zip_tseitin1(X11,X10,X9) <=> (in(X11,X10) => in(X11,X9)))). 108.45/109.12 tff(zf_stmt_11, type, zip_tseitin0 : ($i * $i * $i) > $o). 108.45/109.12 tff(zf_stmt_12, axiom, (zip_tseitin0(X8,X7,X6) <=> (in(X8,X7) | (X8 = X6)))). 108.45/109.12 tff(zf_stmt_13, conjecture, 108.45/109.12 ((![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))) => 108.45/109.12 ((![X5]: (~in(X5,emptyset))) => 108.45/109.12 ((![X6,X7,X8]: (in(X8,setadjoin(X6,X7)) <=> zip_tseitin0(X8,X7,X6))) => 108.45/109.12 ((![X9,X10]: 108.45/109.12 (in(X10,powerset(X9)) <=> (![X11]: zip_tseitin1(X11,X10,X9)))) => 108.45/109.12 ((![X12,X13]: 108.45/109.12 (in(X13,setunion(X12)) <=> (?[X14]: zip_tseitin2(X14,X13,X12)))) => 108.45/109.12 (in(emptyset,omega) => 108.45/109.12 ((![X15]: (in(X15,omega) => in(setadjoin(X15,X15),omega))) => 108.45/109.12 ((![X16]: 108.45/109.12 (((![X17]: 108.45/109.12 ((in(X17,X16) & in(X17,omega)) => 108.45/109.12 in(setadjoin(X17,X17),X16))) & 108.45/109.12 in(emptyset,X16)) => 108.45/109.12 (![X18]: (in(X18,omega) => in(X18,X16))))) => 108.45/109.12 ((![X19:(($i * $i) > $o),X20]: 108.45/109.12 ((![X21]: 108.45/109.12 (in(X21,X20) => 108.45/109.12 (?[X22]: 108.45/109.12 ((![X23]: (X19(X21,X23) => (X22 = X23))) & X19(X21,X22))))) => 108.45/109.12 (?[X24]: 108.45/109.12 (![X25]: 108.45/109.12 (in(X25,X24) <=> (?[X26]: zip_tseitin3(X26,X25,X20,X19))))))) => 108.45/109.12 ((![X27]: 108.45/109.12 ((?[X28]: in(X28,X27)) => 108.45/109.12 (?[X29]: 108.45/109.12 ((~(?[X30]: (in(X30,X27) & in(X30,X29)))) & in(X29,X27))))) => 108.45/109.12 ((![X31]: 108.45/109.12 (?[X32]: 108.45/109.12 ((![X33]: 108.45/109.12 (((?[X34]: in(X34,X33)) & 108.45/109.12 (![X35]: (in(X35,X33) => in(X35,X31)))) => 108.45/109.12 (?[X36,X37]: 108.45/109.12 ((![X38]: 108.45/109.12 (in(X38,X32) => 108.45/109.12 (in(X37,X38) | 108.45/109.12 (![X39]: (in(X39,X38) => in(X39,X36)))))) & 108.45/109.12 (~(?[X40]: (in(X40,X33) & in(X40,X36)))) & 108.45/109.12 in(X37,X33) & in(X36,X32))))) & 108.45/109.12 (![X41,X42]: 108.45/109.12 ((in(X42,X32) & in(X41,X32)) => 108.45/109.12 ((![X43]: (in(X43,X42) => in(X43,X41))) | 108.45/109.12 (![X44]: (in(X44,X41) => in(X44,X42)))))) & 108.45/109.12 (![X45,X46]: 108.45/109.12 ((in(X46,X31) & in(X45,X31)) => 108.45/109.12 ((![X47]: 108.45/109.12 (in(X47,X32) => (in(X45,X47) <=> in(X46,X47)))) => 108.45/109.12 (X45 = X46)))) & 108.45/109.12 (![X48]: 108.45/109.12 (in(X48,X32) => (![X49]: (in(X49,X48) => in(X49,X31)))))))) => 108.45/109.12 ((![X50:($i > $o)]: 108.45/109.12 ((?[X51]: ((![X52]: (X50(X52) => (X51 = X52))) & X50(X51))) => 108.45/109.12 X50(descr('#ll_0'(X50))))) => 108.45/109.12 ((![X53,X54:($i > $o),X55]: 108.45/109.12 (in(X55,X53) => 108.45/109.12 (X54(X55) => in(X55,dsetconstr(X53,'#ll_0'(X54)))))) => 108.45/109.12 ((![X56,X57:($i > $o),X58]: 108.45/109.12 (in(X58,dsetconstr(X56,'#ll_0'(X57))) => in(X58,X56))) => 108.45/109.12 ((![X59,X60:($i > $o),X61]: 108.45/109.12 (in(X61,dsetconstr(X59,'#ll_0'(X60))) => X60(X61))) => 108.45/109.12 ((![X62:($i > $o)]: 108.45/109.12 ((?[X63]: 108.45/109.12 ((![X64]: (X62(X64) => (X63 = X64))) & X62(X63))) => 108.45/109.12 (?[X65]: 108.45/109.12 ((![X66]: (X62(X66) => (X65 = X66))) & X62(X65))))) => 108.45/109.12 ((![X67:$o,X68]: (in(X68,prop2set(X67)) => X67)) => 108.45/109.12 ((![X69]: (in(X69,emptyset) => (![X70:$o]: X70))) => 108.45/109.12 ((![X71]: (in(X71,emptyset) => $false)) => 108.45/109.12 ((![X72]: (~in(X72,emptyset))) => 108.45/109.12 ((![X73:($i > $o)]: 108.45/109.12 ((?[X74]: 108.45/109.12 ((![X75]: (X73(X75) => (X74 = X75))) & X73(X74))) => 108.45/109.12 (?[X76]: X73(X76)))) => 108.45/109.12 ((![X77,X78]: 108.45/109.12 ((![X79]: (in(X79,X77) => in(X79,X78))) => 108.45/109.12 ((![X80]: (in(X80,X78) => in(X80,X77))) => 108.45/109.12 (X77 = X78)))) => 108.45/109.12 ((![X81]: 108.45/109.12 ((![X82]: (~in(X82,X81))) => (X81 = emptyset))) => 108.45/109.12 ((![X83]: 108.45/109.12 ((![X84]: (~in(X84,X83))) => (X83 = emptyset))) => 108.45/109.12 ((![X85,X86:($i > $o),X87]: 108.45/109.12 (in(X87,X85) => 108.45/109.12 (in(X87,dsetconstr(X85,'#ll_0'(X86))) <=> 108.45/109.12 X86(X87)))) => 108.45/109.12 ((![X88]: 108.45/109.12 ((X88 != emptyset) => (?[X89]: in(X89,X88)))) => 108.45/109.12 ((![X90,X91:($i > $o),X92]: 108.45/109.12 (in(X92,X90) => 108.45/109.12 (X91(X92) => 108.45/109.12 (dsetconstr(X90,'#ll_0'(X91)) != emptyset)))) => 108.45/109.12 ((![X93]: 108.45/109.12 ((?[X94]: in(X94,X93)) => (X93 != emptyset))) => 108.45/109.12 ((![X95,X96]: in(X95,setadjoin(X95,X96))) => 108.45/109.12 (in(emptyset,setadjoin(emptyset,emptyset)) => 108.45/109.12 ((![X97,X98,X99]: 108.45/109.12 (in(X99,X98) => 108.45/109.12 in(X99,setadjoin(X97,X98)))) => 108.45/109.12 ((![X100,X101,X102]: 108.45/109.12 (in(X102,setadjoin(X100,X101)) => 108.45/109.12 (![X103:$o]: 108.45/109.12 (((X102 = X100) => X103) => 108.45/109.12 ((in(X102,X101) => X103) => X103))))) => 108.45/109.12 ((![X104,X105,X106]: 108.45/109.12 (in(X106,setadjoin(X104,X105)) => 108.45/109.12 (in(X106,X105) | (X106 = X104)))) => 108.45/109.12 ((![X107]: 108.45/109.12 (dsetconstr(X107,'#ll_1') = X107)) => 108.45/109.12 ((![X108,X109]: 108.45/109.12 ((![X110]: 108.45/109.12 (in(X110,X109) => in(X110,X108))) => 108.45/109.12 in(X109,powerset(X108)))) => 108.45/109.12 ((![X111]: in(emptyset,powerset(X111))) => 108.45/109.12 ((![X112]: in(emptyset,powerset(X112))) => 108.45/109.12 ((![X113,X114,X115]: 108.45/109.12 (in(X114,powerset(X113)) => 108.45/109.12 (in(X115,X114) => in(X115,X113)))) => 108.45/109.12 ((![X116,X117,X118]: 108.45/109.12 (in(X117,X118) => 108.45/109.12 (in(X118,X116) => 108.45/109.12 in(X117,setunion(X116))))) => 108.45/109.12 ((![X119,X120]: 108.45/109.12 (in(X120,setunion(X119)) => 108.45/109.12 (![X121:$o]: 108.45/109.12 ((![X122]: 108.45/109.12 (in(X120,X122) => 108.45/109.12 (in(X122,X119) => X121))) => 108.45/109.12 X121)))) => 108.45/109.12 ((![X123,X124]: 108.45/109.12 (in(X124,X123) => 108.45/109.12 in(X124, 108.45/109.12 powerset(setunion(X123))))) => 108.45/109.12 ((![X125:($i > $o)]: 108.45/109.12 ((?[X126]: 108.45/109.12 ((![X127]: 108.45/109.12 (X125(X127) => 108.45/109.12 (X126 = X127))) & 108.45/109.12 X125(X126))) => 108.45/109.12 (?[X128]: 108.45/109.12 (![X129]: 108.45/109.12 (X125(X129) <=> 108.45/109.12 (X129 = X128)))))) => 108.45/109.12 ((![X130]: 108.45/109.12 ((X130 != emptyset) => 108.45/109.12 (?[X131]: in(X131,X130)))) => 108.45/109.12 ((![X132,X133]: 108.45/109.12 (in(X132, 108.45/109.12 setadjoin(X133,emptyset)) => 108.45/109.12 (X132 = X133))) => 108.45/109.12 ((![X134,X135]: 108.45/109.12 ((X134 != X135) => 108.45/109.12 (~ 108.45/109.12 in(X135, 108.45/109.12 setadjoin(X134, 108.45/109.12 emptyset))))) => 108.45/109.12 ((![X136,X137]: 108.45/109.12 ((X136 = X137) => 108.45/109.12 in(X136, 108.45/109.12 setadjoin(X137, 108.45/109.12 emptyset)))) => 108.45/109.12 ((![X138,X139]: 108.45/109.12 (in(X138, 108.45/109.12 setadjoin(X139, 108.45/109.12 emptyset)) => 108.45/109.12 in(X139, 108.45/109.12 setadjoin(X138, 108.45/109.12 emptyset)))) => 108.45/109.12 ((![X140,X141,X142]: 108.45/109.12 (in(X142, 108.45/109.12 setadjoin(X140, 108.45/109.12 setadjoin( 108.45/109.12 X141, 108.45/109.12 emptyset))) => 108.45/109.12 ((X142 = X141) | 108.45/109.12 (X142 = X140)))) => 108.45/109.12 ((![X143,X144]: 108.45/109.12 in(X143, 108.45/109.12 setadjoin(X143, 108.45/109.12 setadjoin( 108.45/109.12 X144, 108.45/109.12 emptyset)))) => 108.45/109.12 ((![X145,X146]: 108.45/109.12 in(X146, 108.45/109.12 setadjoin(X145, 108.45/109.12 setadjoin( 108.45/109.12 X146, 108.45/109.12 emptyset)))) => 108.45/109.12 ((![X147,X148:($i > $o)]: 108.45/109.12 ((?[X149]: 108.45/109.12 (X148(X149) & 108.45/109.12 in(X149,X147))) => 108.45/109.12 ((dsetconstr( 108.45/109.12 X147,'#ll_0'(X148)) = 108.45/109.12 emptyset) => 108.45/109.12 $false))) => 108.45/109.12 ((![X150:($i > $o),X151]: 108.45/109.12 (in(X151,emptyset) => 108.45/109.12 X150(X151))) => 108.45/109.12 ((![X152,X153:($i > $o)]: 108.45/109.12 ((~ 108.45/109.12 (![X154]: 108.45/109.12 (in(X154,X152) => 108.45/109.12 X153(X154)))) => 108.45/109.12 (?[X155]: 108.45/109.12 ((~X153(X155)) & 108.45/109.12 in(X155,X152))))) => 108.45/109.12 ((![X156, 108.45/109.12 X157:($i > $o)]: 108.45/109.12 ((![X158]: 108.45/109.12 (in(X158,X156) => 108.45/109.12 (~X157(X158)))) => 108.45/109.12 (~ 108.45/109.12 (?[X159]: 108.45/109.12 (X157(X159) & 108.45/109.12 in( 108.45/109.12 X159,X156)))))) => 108.45/109.12 ((![X160, 108.45/109.12 X161:($i > $o)]: 108.45/109.12 ((~ 108.45/109.12 (?[X162]: 108.45/109.12 (X161(X162) & 108.45/109.12 in( 108.45/109.12 X162,X160)))) => 108.45/109.12 (![X163]: 108.45/109.12 (in(X163,X160) => 108.45/109.12 (~X161(X163)))))) => 108.45/109.12 ((![X164, 108.45/109.12 X165:($i > $o)]: 108.45/109.12 ((?[X166]: 108.45/109.12 ((~ 108.45/109.12 X165( 108.45/109.12 X166)) & 108.45/109.12 in( 108.45/109.12 X166,X164))) => 108.45/109.12 (~ 108.45/109.12 (![X167]: 108.45/109.12 (in( 108.45/109.12 X167,X164) => 108.45/109.12 X165( 108.45/109.12 X167)))))) => 108.45/109.12 ((![X168:$o]: 108.45/109.12 (X168 => 108.45/109.12 in(emptyset, 108.45/109.12 prop2set( 108.45/109.12 X168)))) => 108.45/109.12 ((![X169:$o]: 108.45/109.12 (X169 => 108.45/109.12 set2prop( 108.45/109.12 prop2set( 108.45/109.12 X169)))) => 108.45/109.12 ((![X170, 108.45/109.12 X171:( 108.45/109.12 $i > $o)]: 108.45/109.12 ((~ 108.45/109.12 (?[X172]: 108.45/109.12 (X171( 108.45/109.12 X172) & 108.45/109.12 in( 108.45/109.12 X172,X170)))) => 108.45/109.12 (![X173]: 108.45/109.12 ( 108.45/109.12 in( 108.45/109.12 X173,X170) => 108.45/109.12 ( 108.45/109.12 ~ 108.45/109.12 X171( 108.45/109.12 X173)))))) => 108.45/109.12 ((![X174, 108.45/109.12 X175:( 108.45/109.12 $i > $o)]: 108.45/109.12 ((~ 108.45/109.12 ( 108.45/109.12 ![X176]: 108.45/109.12 (in( 108.45/109.12 X176,X174) => 108.45/109.12 X175( 108.45/109.12 X176)))) => 108.45/109.12 (?[X177]: 108.45/109.12 (( 108.45/109.12 ~ 108.45/109.12 X175( 108.45/109.12 X177)) & 108.45/109.12 in( 108.45/109.12 X177,X174))))) => 108.45/109.12 ((![X178:( 108.45/109.12 $i > $o)]: 108.45/109.12 ((?[X179]: 108.45/109.12 (( 108.45/109.12 ![X180]: 108.45/109.12 (X178( 108.45/109.12 X180) => 108.45/109.12 (X179 = 108.45/109.12 X180))) & 108.45/109.12 X178( 108.45/109.12 X179))) => 108.45/109.12 (?[X181]: 108.45/109.12 (( 108.45/109.12 ![X182]: 108.45/109.12 (X178( 108.45/109.12 X182) => 108.45/109.12 (X181 = 108.45/109.12 X182))) & 108.45/109.12 X178( 108.45/109.12 X181))))) => 108.45/109.12 ((![X183:( 108.45/109.12 $i > $o)]: 108.45/109.12 (( 108.45/109.12 ?[X184]: 108.45/109.12 X183( 108.45/109.12 X184)) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X185, 108.45/109.12 X186]: 108.45/109.12 (X183( 108.45/109.12 X185) => 108.45/109.12 (X183( 108.45/109.12 X186) => 108.45/109.12 (X185 = 108.45/109.12 X186)))) => 108.45/109.12 ( 108.45/109.12 ?[X187]: 108.45/109.12 (( 108.45/109.12 ![X188]: 108.45/109.12 (X183( 108.45/109.12 X188) => 108.45/109.12 (X187 = 108.45/109.12 X188))) & 108.45/109.12 X183( 108.45/109.12 X187)))))) => 108.45/109.12 ((![X189:( 108.45/109.12 $i > $o)]: 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ?[X190]: 108.45/109.12 (![X191]: 108.45/109.12 (X189( 108.45/109.12 X191) <=> 108.45/109.12 (X191 = 108.45/109.12 X190)))) => 108.45/109.12 ( 108.45/109.12 ?[X192]: 108.45/109.12 (( 108.45/109.12 ![X193]: 108.45/109.12 (X189( 108.45/109.12 X193) => 108.45/109.12 (X192 = 108.45/109.12 X193))) & 108.45/109.12 X189( 108.45/109.12 X192))))) => 108.45/109.12 ((![X194, 108.45/109.12 X195]: 108.45/109.12 (( 108.45/109.12 X194 = 108.45/109.12 X195) => 108.45/109.12 (![X196, 108.45/109.12 X197]: 108.45/109.12 (( 108.45/109.12 X196 = 108.45/109.12 X197) => 108.45/109.12 (in( 108.45/109.12 X196,X194) => 108.45/109.12 in( 108.45/109.12 X197,X195)))))) => 108.45/109.12 ((![X198, 108.45/109.12 X199]: 108.45/109.12 (( 108.45/109.12 X198 = 108.45/109.12 X199) => 108.45/109.12 (![X200, 108.45/109.12 X201]: 108.45/109.12 (( 108.45/109.12 X200 = 108.45/109.12 X201) => 108.45/109.12 (in( 108.45/109.12 X200,X198) <=> 108.45/109.12 in( 108.45/109.12 X201,X199)))))) => 108.45/109.12 (( 108.45/109.12 ![X202:( 108.45/109.12 $i > $o)]: 108.45/109.12 (( 108.45/109.12 ?[X203]: 108.45/109.12 (( 108.45/109.12 ![X204]: 108.45/109.12 (X202( 108.45/109.12 X204) => 108.45/109.12 (X203 = 108.45/109.12 X204))) & 108.45/109.12 X202( 108.45/109.12 X203))) => 108.45/109.12 (![X205, 108.45/109.12 X206]: 108.45/109.12 (X202( 108.45/109.12 X205) => 108.45/109.12 (X202( 108.45/109.12 X206) => 108.45/109.12 (X205 = 108.45/109.12 X206)))))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X207:( 108.45/109.12 $i > $o), 108.45/109.12 X208:( 108.45/109.12 $i > $o)]: 108.45/109.12 (( 108.45/109.12 ![X209, 108.45/109.12 X210]: 108.45/109.12 (( 108.45/109.12 X209 = 108.45/109.12 X210) => 108.45/109.12 (X207( 108.45/109.12 X209) <=> 108.45/109.12 X208( 108.45/109.12 X210)))) => 108.45/109.12 (( 108.45/109.12 ?[X211]: 108.45/109.12 zip_tseitin5( 108.45/109.12 X211,X207)) <=> 108.45/109.12 (?[X213]: 108.45/109.12 zip_tseitin5( 108.45/109.12 X213,X208))))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 emptyset = 108.45/109.12 emptyset) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X215, 108.45/109.12 X216]: 108.45/109.12 (( 108.45/109.12 X215 = 108.45/109.12 X216) => 108.45/109.12 (![X217, 108.45/109.12 X218]: 108.45/109.12 (( 108.45/109.12 X217 = 108.45/109.12 X218) => 108.45/109.12 (setadjoin( 108.45/109.12 X215,X217) = 108.45/109.12 setadjoin( 108.45/109.12 X216,X218)))))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X219, 108.45/109.12 X220]: 108.45/109.12 (( 108.45/109.12 X219 = 108.45/109.12 X220) => 108.45/109.12 (powerset( 108.45/109.12 X219) = 108.45/109.12 powerset( 108.45/109.12 X220)))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X221, 108.45/109.12 X222]: 108.45/109.12 (( 108.45/109.12 X221 = 108.45/109.12 X222) => 108.45/109.12 (setunion( 108.45/109.12 X221) = 108.45/109.12 setunion( 108.45/109.12 X222)))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 omega = 108.45/109.12 omega) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X223:( 108.45/109.12 $i > $o)]: 108.45/109.12 (( 108.45/109.12 ?[X224]: 108.45/109.12 (( 108.45/109.12 ![X225]: 108.45/109.12 (X223( 108.45/109.12 X225) => 108.45/109.12 (X224 = 108.45/109.12 X225))) & 108.45/109.12 X223( 108.45/109.12 X224))) => 108.45/109.12 (![X226, 108.45/109.12 X227]: 108.45/109.12 (X223( 108.45/109.12 X226) => 108.45/109.12 (X223( 108.45/109.12 X227) => 108.45/109.12 (X226 = 108.45/109.12 X227)))))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X228:( 108.45/109.12 $i > $o), 108.45/109.12 X229:( 108.45/109.12 $i > $o)]: 108.45/109.12 (( 108.45/109.12 ![X230, 108.45/109.12 X231]: 108.45/109.12 (( 108.45/109.12 X230 = 108.45/109.12 X231) => 108.45/109.12 (X228( 108.45/109.12 X230) <=> 108.45/109.12 X229( 108.45/109.12 X231)))) => 108.45/109.12 (( 108.45/109.12 ?[X232]: 108.45/109.12 (( 108.45/109.12 ![X233]: 108.45/109.12 (X228( 108.45/109.12 X233) => 108.45/109.12 (X232 = 108.45/109.12 X233))) & 108.45/109.12 X228( 108.45/109.12 X232))) => 108.45/109.12 (( 108.45/109.12 ?[X234]: 108.45/109.12 (( 108.45/109.12 ![X235]: 108.45/109.12 (X229( 108.45/109.12 X235) => 108.45/109.12 (X234 = 108.45/109.12 X235))) & 108.45/109.12 X229( 108.45/109.12 X234))) => 108.45/109.12 (descr( 108.45/109.12 '#ll_0'( 108.45/109.12 X228)) = 108.45/109.12 descr( 108.45/109.12 '#ll_0'( 108.45/109.12 X229))))))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X236, 108.45/109.12 X237]: 108.45/109.12 (( 108.45/109.12 X236 = 108.45/109.12 X237) => 108.45/109.12 (![X238:( 108.45/109.12 $i > $o), 108.45/109.12 X239:( 108.45/109.12 $i > $o)]: 108.45/109.12 (( 108.45/109.12 ![X240]: 108.45/109.12 (in( 108.45/109.12 X240,X236) => 108.45/109.12 (![X241]: 108.45/109.12 (in( 108.45/109.12 X241,X237) => 108.45/109.12 (( 108.45/109.12 X240 = 108.45/109.12 X241) => 108.45/109.12 (X238( 108.45/109.12 X240) <=> 108.45/109.12 X239( 108.45/109.12 X241))))))) => 108.45/109.12 (dsetconstr( 108.45/109.12 X236, 108.45/109.12 '#ll_0'( 108.45/109.12 X238)) = 108.45/109.12 dsetconstr( 108.45/109.12 X237, 108.45/109.12 '#ll_0'( 108.45/109.12 X239))))))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X242, 108.45/109.12 X243]: 108.45/109.12 (( 108.45/109.12 ![X244]: 108.45/109.12 (in( 108.45/109.12 X244,X242) => 108.45/109.12 in( 108.45/109.12 X244,X243))) => 108.45/109.12 subset( 108.45/109.12 X242,X243))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X245, 108.45/109.12 X246]: 108.45/109.12 (( 108.45/109.12 X245 = 108.45/109.12 X246) => 108.45/109.12 subset( 108.45/109.12 X246,X245))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X247, 108.45/109.12 X248]: 108.45/109.12 (( 108.45/109.12 X247 = 108.45/109.12 X248) => 108.45/109.12 subset( 108.45/109.12 X247,X248))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X249, 108.45/109.12 X250]: 108.45/109.12 (( 108.45/109.12 ![X251]: 108.45/109.12 (in( 108.45/109.12 X251,X249) => 108.45/109.12 in( 108.45/109.12 X251,X250))) => 108.45/109.12 subset( 108.45/109.12 X249,X250))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X252]: 108.45/109.12 subset( 108.45/109.12 emptyset, 108.45/109.12 X252)) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X253, 108.45/109.12 X254,X255]: 108.45/109.12 (subset( 108.45/109.12 X253,X254) => 108.45/109.12 (in( 108.45/109.12 X255,X253) => 108.45/109.12 in( 108.45/109.12 X255,X254)))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X256, 108.45/109.12 X257,X258]: 108.45/109.12 (subset( 108.45/109.12 X256,X257) => 108.45/109.12 (( 108.45/109.12 ~ 108.45/109.12 in( 108.45/109.12 X258,X257)) => 108.45/109.12 (~ 108.45/109.12 in( 108.45/109.12 X258,X256))))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X259, 108.45/109.12 X260,X261]: 108.45/109.12 (in( 108.45/109.12 X261,X259) => 108.45/109.12 (( 108.45/109.12 ~ 108.45/109.12 in( 108.45/109.12 X261,X260)) => 108.45/109.12 (~ 108.45/109.12 subset( 108.45/109.12 X259,X260))))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X262, 108.45/109.12 X263]: 108.45/109.12 (( 108.45/109.12 ~ 108.45/109.12 subset( 108.45/109.12 X262,X263)) => 108.45/109.12 (X262 != 108.45/109.12 X263))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X264, 108.45/109.12 X265,X266]: 108.45/109.12 (in( 108.45/109.12 X266,X264) => 108.45/109.12 (( 108.45/109.12 ~ 108.45/109.12 in( 108.45/109.12 X266,X265)) => 108.45/109.12 (X264 != 108.45/109.12 X265)))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X267]: 108.45/109.12 subset( 108.45/109.12 X267,X267)) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X268, 108.45/109.12 X269,X270]: 108.45/109.12 (subset( 108.45/109.12 X268,X269) => 108.45/109.12 (subset( 108.45/109.12 X269,X270) => 108.45/109.12 subset( 108.45/109.12 X268,X270)))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X271, 108.45/109.12 X272]: 108.45/109.12 subset( 108.45/109.12 X272, 108.45/109.12 setadjoin( 108.45/109.12 X271,X272))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X273, 108.45/109.12 X274,X275]: 108.45/109.12 (subset( 108.45/109.12 X273,X275) => 108.45/109.12 subset( 108.45/109.12 X273, 108.45/109.12 setadjoin( 108.45/109.12 X274,X275)))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X276, 108.45/109.12 X277]: 108.45/109.12 (subset( 108.45/109.12 X276,X277) => 108.45/109.12 in( 108.45/109.12 X276, 108.45/109.12 powerset( 108.45/109.12 X277)))) => 108.45/109.12 ( 108.45/109.12 ![X278, 108.45/109.12 X279]: 108.45/109.12 (subset( 108.45/109.12 X278,X279) => 108.45/109.12 (subset( 108.45/109.12 X279,X278) => 108.45/109.12 (X278 = 108.45/109.12 X279))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 108.45/109.12 tff(zf_stmt_14, negated_conjecture, 108.45/109.12 (~ 108.45/109.12 ((![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))) => 108.45/109.12 ((![X5]: (~in(X5,emptyset))) => 108.45/109.12 ((![X6,X7,X8]: (in(X8,setadjoin(X6,X7)) <=> zip_tseitin0(X8,X7,X6))) => 108.45/109.12 ((![X9,X10]: 108.45/109.12 (in(X10,powerset(X9)) <=> (![X11]: zip_tseitin1(X11,X10,X9)))) => 108.45/109.12 ((![X12,X13]: 108.45/109.12 (in(X13,setunion(X12)) <=> (?[X14]: zip_tseitin2(X14,X13,X12)))) => 108.45/109.12 (in(emptyset,omega) => 108.45/109.12 ((![X15]: (in(X15,omega) => in(setadjoin(X15,X15),omega))) => 108.45/109.12 ((![X16]: 108.45/109.12 (((![X17]: 108.45/109.12 ((in(X17,X16) & in(X17,omega)) => 108.45/109.12 in(setadjoin(X17,X17),X16))) & 108.45/109.12 in(emptyset,X16)) => 108.45/109.12 (![X18]: (in(X18,omega) => in(X18,X16))))) => 108.45/109.12 ((![X19:(($i * $i) > $o),X20]: 108.45/109.12 ((![X21]: 108.45/109.12 (in(X21,X20) => 108.45/109.12 (?[X22]: 108.45/109.12 ((![X23]: (X19(X21,X23) => (X22 = X23))) & 108.45/109.12 X19(X21,X22))))) => 108.45/109.12 (?[X24]: 108.45/109.12 (![X25]: 108.45/109.12 (in(X25,X24) <=> 108.45/109.12 (?[X26]: zip_tseitin3(X26,X25,X20,X19))))))) => 108.45/109.12 ((![X27]: 108.45/109.12 ((?[X28]: in(X28,X27)) => 108.45/109.12 (?[X29]: 108.45/109.12 ((~(?[X30]: (in(X30,X27) & in(X30,X29)))) & in(X29,X27))))) => 108.45/109.12 ((![X31]: 108.45/109.12 (?[X32]: 108.45/109.12 ((![X33]: 108.45/109.12 (((?[X34]: in(X34,X33)) & 108.45/109.12 (![X35]: (in(X35,X33) => in(X35,X31)))) => 108.45/109.12 (?[X36,X37]: 108.45/109.12 ((![X38]: 108.45/109.12 (in(X38,X32) => 108.45/109.12 (in(X37,X38) | 108.45/109.12 (![X39]: (in(X39,X38) => in(X39,X36)))))) & 108.45/109.12 (~(?[X40]: (in(X40,X33) & in(X40,X36)))) & 108.45/109.12 in(X37,X33) & in(X36,X32))))) & 108.45/109.12 (![X41,X42]: 108.45/109.12 ((in(X42,X32) & in(X41,X32)) => 108.45/109.12 ((![X43]: (in(X43,X42) => in(X43,X41))) | 108.45/109.12 (![X44]: (in(X44,X41) => in(X44,X42)))))) & 108.45/109.12 (![X45,X46]: 108.45/109.12 ((in(X46,X31) & in(X45,X31)) => 108.45/109.12 ((![X47]: 108.45/109.12 (in(X47,X32) => (in(X45,X47) <=> in(X46,X47)))) => 108.45/109.12 (X45 = X46)))) & 108.45/109.12 (![X48]: 108.45/109.12 (in(X48,X32) => 108.45/109.12 (![X49]: (in(X49,X48) => in(X49,X31)))))))) => 108.45/109.12 ((![X50:($i > $o)]: 108.45/109.12 ((?[X51]: ((![X52]: (X50(X52) => (X51 = X52))) & X50(X51))) => 108.45/109.12 X50(descr('#ll_0'(X50))))) => 108.45/109.12 ((![X53,X54:($i > $o),X55]: 108.45/109.12 (in(X55,X53) => 108.45/109.12 (X54(X55) => in(X55,dsetconstr(X53,'#ll_0'(X54)))))) => 108.45/109.12 ((![X56,X57:($i > $o),X58]: 108.45/109.12 (in(X58,dsetconstr(X56,'#ll_0'(X57))) => in(X58,X56))) => 108.45/109.12 ((![X59,X60:($i > $o),X61]: 108.45/109.12 (in(X61,dsetconstr(X59,'#ll_0'(X60))) => X60(X61))) => 108.45/109.12 ((![X62:($i > $o)]: 108.45/109.12 ((?[X63]: 108.45/109.12 ((![X64]: (X62(X64) => (X63 = X64))) & X62(X63))) => 108.45/109.12 (?[X65]: 108.45/109.12 ((![X66]: (X62(X66) => (X65 = X66))) & X62(X65))))) => 108.45/109.12 ((![X67:$o,X68]: (in(X68,prop2set(X67)) => X67)) => 108.45/109.12 ((![X69]: (in(X69,emptyset) => (![X70:$o]: X70))) => 108.45/109.12 ((![X71]: (in(X71,emptyset) => $false)) => 108.45/109.12 ((![X72]: (~in(X72,emptyset))) => 108.45/109.12 ((![X73:($i > $o)]: 108.45/109.12 ((?[X74]: 108.45/109.12 ((![X75]: (X73(X75) => (X74 = X75))) & 108.45/109.12 X73(X74))) => 108.45/109.12 (?[X76]: X73(X76)))) => 108.45/109.12 ((![X77,X78]: 108.45/109.12 ((![X79]: (in(X79,X77) => in(X79,X78))) => 108.45/109.12 ((![X80]: (in(X80,X78) => in(X80,X77))) => 108.45/109.12 (X77 = X78)))) => 108.45/109.12 ((![X81]: 108.45/109.12 ((![X82]: (~in(X82,X81))) => (X81 = emptyset))) => 108.45/109.12 ((![X83]: 108.45/109.12 ((![X84]: (~in(X84,X83))) => (X83 = emptyset))) => 108.45/109.12 ((![X85,X86:($i > $o),X87]: 108.45/109.12 (in(X87,X85) => 108.45/109.12 (in(X87,dsetconstr(X85,'#ll_0'(X86))) <=> 108.45/109.12 X86(X87)))) => 108.45/109.12 ((![X88]: 108.45/109.12 ((X88 != emptyset) => (?[X89]: in(X89,X88)))) => 108.45/109.12 ((![X90,X91:($i > $o),X92]: 108.45/109.12 (in(X92,X90) => 108.45/109.12 (X91(X92) => 108.45/109.12 (dsetconstr(X90,'#ll_0'(X91)) != emptyset)))) => 108.45/109.12 ((![X93]: 108.45/109.12 ((?[X94]: in(X94,X93)) => 108.45/109.12 (X93 != emptyset))) => 108.45/109.12 ((![X95,X96]: in(X95,setadjoin(X95,X96))) => 108.45/109.12 (in(emptyset,setadjoin(emptyset,emptyset)) => 108.45/109.12 ((![X97,X98,X99]: 108.45/109.12 (in(X99,X98) => 108.45/109.12 in(X99,setadjoin(X97,X98)))) => 108.45/109.12 ((![X100,X101,X102]: 108.45/109.12 (in(X102,setadjoin(X100,X101)) => 108.45/109.12 (![X103:$o]: 108.45/109.12 (((X102 = X100) => X103) => 108.45/109.12 ((in(X102,X101) => X103) => X103))))) => 108.45/109.12 ((![X104,X105,X106]: 108.45/109.12 (in(X106,setadjoin(X104,X105)) => 108.45/109.12 (in(X106,X105) | (X106 = X104)))) => 108.45/109.12 ((![X107]: 108.45/109.12 (dsetconstr(X107,'#ll_1') = X107)) => 108.45/109.12 ((![X108,X109]: 108.45/109.12 ((![X110]: 108.45/109.12 (in(X110,X109) => in(X110,X108))) => 108.45/109.12 in(X109,powerset(X108)))) => 108.45/109.12 ((![X111]: in(emptyset,powerset(X111))) => 108.45/109.12 ((![X112]: 108.45/109.12 in(emptyset,powerset(X112))) => 108.45/109.12 ((![X113,X114,X115]: 108.45/109.12 (in(X114,powerset(X113)) => 108.45/109.12 (in(X115,X114) => in(X115,X113)))) => 108.45/109.12 ((![X116,X117,X118]: 108.45/109.12 (in(X117,X118) => 108.45/109.12 (in(X118,X116) => 108.45/109.12 in(X117,setunion(X116))))) => 108.45/109.12 ((![X119,X120]: 108.45/109.12 (in(X120,setunion(X119)) => 108.45/109.12 (![X121:$o]: 108.45/109.12 ((![X122]: 108.45/109.12 (in(X120,X122) => 108.45/109.12 (in(X122,X119) => 108.45/109.12 X121))) => 108.45/109.12 X121)))) => 108.45/109.12 ((![X123,X124]: 108.45/109.12 (in(X124,X123) => 108.45/109.12 in(X124, 108.45/109.12 powerset(setunion(X123))))) => 108.45/109.12 ((![X125:($i > $o)]: 108.45/109.12 ((?[X126]: 108.45/109.12 ((![X127]: 108.45/109.12 (X125(X127) => 108.45/109.12 (X126 = X127))) & 108.45/109.12 X125(X126))) => 108.45/109.12 (?[X128]: 108.45/109.12 (![X129]: 108.45/109.12 (X125(X129) <=> 108.45/109.12 (X129 = X128)))))) => 108.45/109.12 ((![X130]: 108.45/109.12 ((X130 != emptyset) => 108.45/109.12 (?[X131]: in(X131,X130)))) => 108.45/109.12 ((![X132,X133]: 108.45/109.12 (in(X132, 108.45/109.12 setadjoin(X133, 108.45/109.12 emptyset)) => 108.45/109.12 (X132 = X133))) => 108.45/109.12 ((![X134,X135]: 108.45/109.12 ((X134 != X135) => 108.45/109.12 (~ 108.45/109.12 in(X135, 108.45/109.12 setadjoin(X134, 108.45/109.12 emptyset))))) => 108.45/109.12 ((![X136,X137]: 108.45/109.12 ((X136 = X137) => 108.45/109.12 in(X136, 108.45/109.12 setadjoin(X137, 108.45/109.12 emptyset)))) => 108.45/109.12 ((![X138,X139]: 108.45/109.12 (in(X138, 108.45/109.12 setadjoin(X139, 108.45/109.12 emptyset)) => 108.45/109.12 in(X139, 108.45/109.12 setadjoin(X138, 108.45/109.12 emptyset)))) => 108.45/109.12 ((![X140,X141,X142]: 108.45/109.12 (in(X142, 108.45/109.12 setadjoin( 108.45/109.12 X140, 108.45/109.12 setadjoin( 108.45/109.12 X141,emptyset))) => 108.45/109.12 ((X142 = X141) | 108.45/109.12 (X142 = X140)))) => 108.45/109.12 ((![X143,X144]: 108.45/109.12 in(X143, 108.45/109.12 setadjoin( 108.45/109.12 X143, 108.45/109.12 setadjoin( 108.45/109.12 X144,emptyset)))) => 108.45/109.12 ((![X145,X146]: 108.45/109.12 in(X146, 108.45/109.12 setadjoin( 108.45/109.12 X145, 108.45/109.12 setadjoin( 108.45/109.12 X146,emptyset)))) => 108.45/109.12 ((![X147,X148:($i > $o)]: 108.45/109.12 ((?[X149]: 108.45/109.12 (X148(X149) & 108.45/109.12 in(X149,X147))) => 108.45/109.12 ((dsetconstr( 108.45/109.12 X147, 108.45/109.12 '#ll_0'(X148)) = 108.45/109.12 emptyset) => 108.45/109.12 $false))) => 108.45/109.12 ((![X150:($i > $o), 108.45/109.12 X151]: 108.45/109.12 (in(X151,emptyset) => 108.45/109.12 X150(X151))) => 108.45/109.12 ((![X152, 108.45/109.12 X153:($i > $o)]: 108.45/109.12 ((~ 108.45/109.12 (![X154]: 108.45/109.12 (in( 108.45/109.12 X154,X152) => 108.45/109.12 X153(X154)))) => 108.45/109.12 (?[X155]: 108.45/109.12 ((~X153(X155)) & 108.45/109.12 in(X155,X152))))) => 108.45/109.12 ((![X156, 108.45/109.12 X157:($i > $o)]: 108.45/109.12 ((![X158]: 108.45/109.12 (in( 108.45/109.12 X158,X156) => 108.45/109.12 (~ 108.45/109.12 X157( 108.45/109.12 X158)))) => 108.45/109.12 (~ 108.45/109.12 (?[X159]: 108.45/109.12 (X157( 108.45/109.12 X159) & 108.45/109.12 in( 108.45/109.12 X159,X156)))))) => 108.45/109.12 ((![X160, 108.45/109.12 X161:($i > $o)]: 108.45/109.12 ((~ 108.45/109.12 (?[X162]: 108.45/109.12 ( 108.45/109.12 X161( 108.45/109.12 X162) & 108.45/109.12 in( 108.45/109.12 X162,X160)))) => 108.45/109.12 (![X163]: 108.45/109.12 (in( 108.45/109.12 X163,X160) => 108.45/109.12 (~ 108.45/109.12 X161( 108.45/109.12 X163)))))) => 108.45/109.12 ((![X164, 108.45/109.12 X165:( 108.45/109.12 $i > $o)]: 108.45/109.12 ((?[X166]: 108.45/109.12 (( 108.45/109.12 ~ 108.45/109.12 X165( 108.45/109.12 X166)) & 108.45/109.12 in( 108.45/109.12 X166,X164))) => 108.45/109.12 (~ 108.45/109.12 (![X167]: 108.45/109.12 (in( 108.45/109.12 X167,X164) => 108.45/109.12 X165( 108.45/109.12 X167)))))) => 108.45/109.12 ((![X168:$o]: 108.45/109.12 (X168 => 108.45/109.12 in(emptyset, 108.45/109.12 prop2set( 108.45/109.12 X168)))) => 108.45/109.12 ((![X169:$o]: 108.45/109.12 (X169 => 108.45/109.12 set2prop( 108.45/109.12 prop2set( 108.45/109.12 X169)))) => 108.45/109.12 ((![X170, 108.45/109.12 X171:( 108.45/109.12 $i > $o)]: 108.45/109.12 ((~ 108.45/109.12 ( 108.45/109.12 ?[X172]: 108.45/109.12 (X171( 108.45/109.12 X172) & 108.45/109.12 in( 108.45/109.12 X172,X170)))) => 108.45/109.12 (![X173]: 108.45/109.12 (in( 108.45/109.12 X173,X170) => 108.45/109.12 (~ 108.45/109.12 X171( 108.45/109.12 X173)))))) => 108.45/109.12 ((![X174, 108.45/109.12 X175:( 108.45/109.12 $i > $o)]: 108.45/109.12 (( 108.45/109.12 ~ 108.45/109.12 ( 108.45/109.12 ![X176]: 108.45/109.12 (in( 108.45/109.12 X176,X174) => 108.45/109.12 X175( 108.45/109.12 X176)))) => 108.45/109.12 ( 108.45/109.12 ?[X177]: 108.45/109.12 (( 108.45/109.12 ~ 108.45/109.12 X175( 108.45/109.12 X177)) & 108.45/109.12 in( 108.45/109.12 X177,X174))))) => 108.45/109.12 ((![X178:( 108.45/109.12 $i > $o)]: 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ?[X179]: 108.45/109.12 (( 108.45/109.12 ![X180]: 108.45/109.12 (X178( 108.45/109.12 X180) => 108.45/109.12 (X179 = 108.45/109.12 X180))) & 108.45/109.12 X178( 108.45/109.12 X179))) => 108.45/109.12 ( 108.45/109.12 ?[X181]: 108.45/109.12 (( 108.45/109.12 ![X182]: 108.45/109.12 (X178( 108.45/109.12 X182) => 108.45/109.12 (X181 = 108.45/109.12 X182))) & 108.45/109.12 X178( 108.45/109.12 X181))))) => 108.45/109.12 ((![X183:( 108.45/109.12 $i > $o)]: 108.45/109.12 (( 108.45/109.12 ?[X184]: 108.45/109.12 X183( 108.45/109.12 X184)) => 108.45/109.12 (( 108.45/109.12 ![X185, 108.45/109.12 X186]: 108.45/109.12 (X183( 108.45/109.12 X185) => 108.45/109.12 (X183( 108.45/109.12 X186) => 108.45/109.12 (X185 = 108.45/109.12 X186)))) => 108.45/109.12 (?[X187]: 108.45/109.12 (( 108.45/109.12 ![X188]: 108.45/109.12 (X183( 108.45/109.12 X188) => 108.45/109.12 (X187 = 108.45/109.12 X188))) & 108.45/109.12 X183( 108.45/109.12 X187)))))) => 108.45/109.12 ((![X189:( 108.45/109.12 $i > $o)]: 108.45/109.12 (( 108.45/109.12 ?[X190]: 108.45/109.12 (![X191]: 108.45/109.12 (X189( 108.45/109.12 X191) <=> 108.45/109.12 (X191 = 108.45/109.12 X190)))) => 108.45/109.12 (?[X192]: 108.45/109.12 (( 108.45/109.12 ![X193]: 108.45/109.12 (X189( 108.45/109.12 X193) => 108.45/109.12 (X192 = 108.45/109.12 X193))) & 108.45/109.12 X189( 108.45/109.12 X192))))) => 108.45/109.12 (( 108.45/109.12 ![X194, 108.45/109.12 X195]: 108.45/109.12 (( 108.45/109.12 X194 = 108.45/109.12 X195) => 108.45/109.12 (![X196, 108.45/109.12 X197]: 108.45/109.12 (( 108.45/109.12 X196 = 108.45/109.12 X197) => 108.45/109.12 (in( 108.45/109.12 X196,X194) => 108.45/109.12 in( 108.45/109.12 X197,X195)))))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X198, 108.45/109.12 X199]: 108.45/109.12 (( 108.45/109.12 X198 = 108.45/109.12 X199) => 108.45/109.12 (![X200, 108.45/109.12 X201]: 108.45/109.12 (( 108.45/109.12 X200 = 108.45/109.12 X201) => 108.45/109.12 (in( 108.45/109.12 X200,X198) <=> 108.45/109.12 in( 108.45/109.12 X201,X199)))))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X202:( 108.45/109.12 $i > $o)]: 108.45/109.12 (( 108.45/109.12 ?[X203]: 108.45/109.12 (( 108.45/109.12 ![X204]: 108.45/109.12 (X202( 108.45/109.12 X204) => 108.45/109.12 (X203 = 108.45/109.12 X204))) & 108.45/109.12 X202( 108.45/109.12 X203))) => 108.45/109.12 (![X205, 108.45/109.12 X206]: 108.45/109.12 (X202( 108.45/109.12 X205) => 108.45/109.12 (X202( 108.45/109.12 X206) => 108.45/109.12 (X205 = 108.45/109.12 X206)))))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X207:( 108.45/109.12 $i > $o), 108.45/109.12 X208:( 108.45/109.12 $i > $o)]: 108.45/109.12 (( 108.45/109.12 ![X209, 108.45/109.12 X210]: 108.45/109.12 (( 108.45/109.12 X209 = 108.45/109.12 X210) => 108.45/109.12 (X207( 108.45/109.12 X209) <=> 108.45/109.12 X208( 108.45/109.12 X210)))) => 108.45/109.12 (( 108.45/109.12 ?[X211]: 108.45/109.12 zip_tseitin5( 108.45/109.12 X211,X207)) <=> 108.45/109.12 (?[X213]: 108.45/109.12 zip_tseitin5( 108.45/109.12 X213,X208))))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 emptyset = 108.45/109.12 emptyset) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X215, 108.45/109.12 X216]: 108.45/109.12 (( 108.45/109.12 X215 = 108.45/109.12 X216) => 108.45/109.12 (![X217, 108.45/109.12 X218]: 108.45/109.12 (( 108.45/109.12 X217 = 108.45/109.12 X218) => 108.45/109.12 (setadjoin( 108.45/109.12 X215,X217) = 108.45/109.12 setadjoin( 108.45/109.12 X216,X218)))))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X219, 108.45/109.12 X220]: 108.45/109.12 (( 108.45/109.12 X219 = 108.45/109.12 X220) => 108.45/109.12 (powerset( 108.45/109.12 X219) = 108.45/109.12 powerset( 108.45/109.12 X220)))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X221, 108.45/109.12 X222]: 108.45/109.12 (( 108.45/109.12 X221 = 108.45/109.12 X222) => 108.45/109.12 (setunion( 108.45/109.12 X221) = 108.45/109.12 setunion( 108.45/109.12 X222)))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 omega = 108.45/109.12 omega) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X223:( 108.45/109.12 $i > $o)]: 108.45/109.12 (( 108.45/109.12 ?[X224]: 108.45/109.12 (( 108.45/109.12 ![X225]: 108.45/109.12 (X223( 108.45/109.12 X225) => 108.45/109.12 (X224 = 108.45/109.12 X225))) & 108.45/109.12 X223( 108.45/109.12 X224))) => 108.45/109.12 (![X226, 108.45/109.12 X227]: 108.45/109.12 (X223( 108.45/109.12 X226) => 108.45/109.12 (X223( 108.45/109.12 X227) => 108.45/109.12 (X226 = 108.45/109.12 X227)))))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X228:( 108.45/109.12 $i > $o), 108.45/109.12 X229:( 108.45/109.12 $i > $o)]: 108.45/109.12 (( 108.45/109.12 ![X230, 108.45/109.12 X231]: 108.45/109.12 (( 108.45/109.12 X230 = 108.45/109.12 X231) => 108.45/109.12 (X228( 108.45/109.12 X230) <=> 108.45/109.12 X229( 108.45/109.12 X231)))) => 108.45/109.12 (( 108.45/109.12 ?[X232]: 108.45/109.12 (( 108.45/109.12 ![X233]: 108.45/109.12 (X228( 108.45/109.12 X233) => 108.45/109.12 (X232 = 108.45/109.12 X233))) & 108.45/109.12 X228( 108.45/109.12 X232))) => 108.45/109.12 (( 108.45/109.12 ?[X234]: 108.45/109.12 (( 108.45/109.12 ![X235]: 108.45/109.12 (X229( 108.45/109.12 X235) => 108.45/109.12 (X234 = 108.45/109.12 X235))) & 108.45/109.12 X229( 108.45/109.12 X234))) => 108.45/109.12 (descr( 108.45/109.12 '#ll_0'( 108.45/109.12 X228)) = 108.45/109.12 descr( 108.45/109.12 '#ll_0'( 108.45/109.12 X229))))))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X236, 108.45/109.12 X237]: 108.45/109.12 (( 108.45/109.12 X236 = 108.45/109.12 X237) => 108.45/109.12 (![X238:( 108.45/109.12 $i > $o), 108.45/109.12 X239:( 108.45/109.12 $i > $o)]: 108.45/109.12 (( 108.45/109.12 ![X240]: 108.45/109.12 (in( 108.45/109.12 X240,X236) => 108.45/109.12 (![X241]: 108.45/109.12 (in( 108.45/109.12 X241,X237) => 108.45/109.12 (( 108.45/109.12 X240 = 108.45/109.12 X241) => 108.45/109.12 (X238( 108.45/109.12 X240) <=> 108.45/109.12 X239( 108.45/109.12 X241))))))) => 108.45/109.12 (dsetconstr( 108.45/109.12 X236, 108.45/109.12 '#ll_0'( 108.45/109.12 X238)) = 108.45/109.12 dsetconstr( 108.45/109.12 X237, 108.45/109.12 '#ll_0'( 108.45/109.12 X239))))))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X242, 108.45/109.12 X243]: 108.45/109.12 (( 108.45/109.12 ![X244]: 108.45/109.12 (in( 108.45/109.12 X244,X242) => 108.45/109.12 in( 108.45/109.12 X244,X243))) => 108.45/109.12 subset( 108.45/109.12 X242,X243))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X245, 108.45/109.12 X246]: 108.45/109.12 (( 108.45/109.12 X245 = 108.45/109.12 X246) => 108.45/109.12 subset( 108.45/109.12 X246,X245))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X247, 108.45/109.12 X248]: 108.45/109.12 (( 108.45/109.12 X247 = 108.45/109.12 X248) => 108.45/109.12 subset( 108.45/109.12 X247,X248))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X249, 108.45/109.12 X250]: 108.45/109.12 (( 108.45/109.12 ![X251]: 108.45/109.12 (in( 108.45/109.12 X251,X249) => 108.45/109.12 in( 108.45/109.12 X251,X250))) => 108.45/109.12 subset( 108.45/109.12 X249,X250))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X252]: 108.45/109.12 subset( 108.45/109.12 emptyset, 108.45/109.12 X252)) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X253, 108.45/109.12 X254,X255]: 108.45/109.12 (subset( 108.45/109.12 X253,X254) => 108.45/109.12 (in( 108.45/109.12 X255,X253) => 108.45/109.12 in( 108.45/109.12 X255,X254)))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X256, 108.45/109.12 X257,X258]: 108.45/109.12 (subset( 108.45/109.12 X256,X257) => 108.45/109.12 (( 108.45/109.12 ~ 108.45/109.12 in( 108.45/109.12 X258,X257)) => 108.45/109.12 (~ 108.45/109.12 in( 108.45/109.12 X258,X256))))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X259, 108.45/109.12 X260,X261]: 108.45/109.12 (in( 108.45/109.12 X261,X259) => 108.45/109.12 (( 108.45/109.12 ~ 108.45/109.12 in( 108.45/109.12 X261,X260)) => 108.45/109.12 (~ 108.45/109.12 subset( 108.45/109.12 X259,X260))))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X262, 108.45/109.12 X263]: 108.45/109.12 (( 108.45/109.12 ~ 108.45/109.12 subset( 108.45/109.12 X262,X263)) => 108.45/109.12 (X262 != 108.45/109.12 X263))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X264, 108.45/109.12 X265,X266]: 108.45/109.12 (in( 108.45/109.12 X266,X264) => 108.45/109.12 (( 108.45/109.12 ~ 108.45/109.12 in( 108.45/109.12 X266,X265)) => 108.45/109.12 (X264 != 108.45/109.12 X265)))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X267]: 108.45/109.12 subset( 108.45/109.12 X267,X267)) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X268, 108.45/109.12 X269,X270]: 108.45/109.12 (subset( 108.45/109.12 X268,X269) => 108.45/109.12 (subset( 108.45/109.12 X269,X270) => 108.45/109.12 subset( 108.45/109.12 X268,X270)))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X271, 108.45/109.12 X272]: 108.45/109.12 subset( 108.45/109.12 X272, 108.45/109.12 setadjoin( 108.45/109.12 X271,X272))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X273, 108.45/109.12 X274,X275]: 108.45/109.12 (subset( 108.45/109.12 X273,X275) => 108.45/109.12 subset( 108.45/109.12 X273, 108.45/109.12 setadjoin( 108.45/109.12 X274,X275)))) => 108.45/109.12 ( 108.45/109.12 ( 108.45/109.12 ![X276, 108.45/109.12 X277]: 108.45/109.12 (subset( 108.45/109.12 X276,X277) => 108.45/109.12 in( 108.45/109.12 X276, 108.45/109.12 powerset( 108.45/109.12 X277)))) => 108.45/109.12 ( 108.45/109.12 ![X278, 108.45/109.12 X279]: 108.45/109.12 (subset( 108.45/109.12 X278,X279) => 108.45/109.12 (subset( 108.45/109.12 X279,X278) => 108.45/109.12 (X278 = 108.45/109.12 X279)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 108.45/109.12 tff('92', plain, 108.45/109.12 ![X484, X485]: 108.45/109.12 (~ in(sk_X80_(X484, X485), X485) 108.45/109.12 | X485 = X484 108.45/109.12 | in(sk_X79_(X484, X485), X485)), 108.45/109.12 inference('cnf', [status(esa)], [zf_stmt_14])). 108.45/109.12 tff('93', plain, 108.45/109.12 ![X484, X485]: 108.45/109.12 (~ in(sk_X80_(X484, X485), X485) 108.45/109.12 | X485 = X484 108.45/109.12 | ~ in(sk_X79_(X484, X485), X484)), 108.45/109.12 inference('cnf', [status(esa)], [zf_stmt_14])). 108.45/109.12 tff('94', plain, sk_X278_ != sk_X279_, 108.45/109.12 inference('cnf', [status(esa)], [zf_stmt_14])). 108.45/109.12 tff('95', plain, subset(sk_X279_, sk_X278_), 108.45/109.12 inference('cnf', [status(esa)], [zf_stmt_14])). 108.45/109.12 tff('96', plain, 108.45/109.12 ![X484, X485]: 108.45/109.12 (in(sk_X80_(X484, X485), X484) 108.45/109.12 | X485 = X484 108.45/109.12 | in(sk_X79_(X484, X485), X485)), 108.45/109.12 inference('cnf', [status(esa)], [zf_stmt_14])). 108.45/109.12 tff('97', plain, subset(sk_X278_, sk_X279_), 108.45/109.12 inference('cnf', [status(esa)], [zf_stmt_14])). 108.45/109.12 tff('98', plain, 108.45/109.12 ![X484, X485]: 108.45/109.12 (in(sk_X80_(X484, X485), X484) 108.45/109.12 | X485 = X484 108.45/109.12 | ~ in(sk_X79_(X484, X485), X484)), 108.45/109.12 inference('cnf', [status(esa)], [zf_stmt_14])). 108.45/109.12 tff('99', plain, 108.45/109.12 ![X396, X397, X398]: 108.45/109.12 (~ subset(X396, X397) | in(X398, X397) | ~ in(X398, X396)), 108.45/109.12 inference('cnf', [status(esa)], [zf_stmt_14])). 108.45/109.12 tff('100', plain, $false, 108.45/109.12 inference('eprover', [status(thm)], 108.45/109.12 ['92', '93', '94', '95', '96', '97', '98', '99'])). 108.45/109.12 108.45/109.12 % SZS output end Refutation 108.45/109.12 % Zipperpin 1.5 exiting 108.45/109.12 EOF