0.07/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.14 % Command : run_portfolio.sh /export/starexec/sandbox/benchmark/theBenchmark.p /export/starexec/sandbox/tmp/tmp.a0iAyvKoE4 0.14/0.35 % Computer : n012.cluster.edu 0.14/0.35 % Model : x86_64 x86_64 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.35 % Memory : 8042.1875MB 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.35 % CPULimit : 180 0.14/0.35 % DateTime : Thu Aug 29 15:09:12 EDT 2019 0.14/0.35 % CPUTime : 108.83/109.40 % Running portfolio for 180 s 108.83/109.40 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 108.83/109.40 % TempDir : /export/starexec/sandbox/tmp/tmp.a0iAyvKoE4 108.83/109.40 % Recognized as monomorphic HO. 108.83/109.40 % Running /export/starexec/sandbox/solver/bin/competitive.sh for 18 108.83/109.40 % Running /export/starexec/sandbox/solver/bin/competitive.2.sh for 13 108.83/109.40 % Running /export/starexec/sandbox/solver/bin/competitive.3.sh for 3 108.83/109.40 % Running /export/starexec/sandbox/solver/bin/pragmatic.rudimentary.sh for 28 108.83/109.40 % Running /export/starexec/sandbox/solver/bin/pragmatic.rudimentary.1.sh for 12 108.83/109.40 % Running /export/starexec/sandbox/solver/bin/pragmatic.rudimentary.2.sh for 7 108.83/109.40 % Running /export/starexec/sandbox/solver/bin/pragmatic.shallow.sh for 3 108.83/109.40 % Running /export/starexec/sandbox/solver/bin/pragmatic.shallow.1.sh for 15 108.83/109.40 % Running /export/starexec/sandbox/solver/bin/pragmatic.shallow.2.sh for 12 108.83/109.40 % Running /export/starexec/sandbox/solver/bin/pragmatic.ll.e.sh for 19 108.83/109.40 % Solved by: pragmatic.ll.e.sh 108.83/109.40 % Running : timeout 16 /export/starexec/sandbox/solver/bin/eprover-ho /export/starexec/sandbox/tmp/tmp.a0iAyvKoE4/e_input962ed0 --cpu-limit=14 --auto-schedule -s -p. 108.83/109.40 % done 468 iterations in 9.868s 108.83/109.40 % hashcons stats for terms: size 4096, num 17590, sum length 35729, buckets: small 0, median 7, big 22 108.83/109.40 % proof state stats: {active 196, passive 6124, simpl 0} 108.83/109.40 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 108.83/109.40 % SZS output start Refutation 108.83/109.40 tff(binintersectLsub, axiom, binintersectLsub <=> 108.83/109.40 (![A,B]: subset(binintersect(A,B),A))). 108.83/109.40 tff('0', plain, 108.83/109.40 binintersectLsub = (![X2,X3]: subset(binintersect(X2,X3),X2)), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(binintersectEL, axiom, binintersectEL <=> 108.83/109.40 (![A,B,Xx]: (in(Xx,binintersect(A,B)) => in(Xx,A)))). 108.83/109.40 tff('1', plain, 108.83/109.40 binintersectEL = (![X2,X3,X4]: (in(X4,binintersect(X2,X3)) => in(X4,X2))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(binintersectSubset5, axiom, binintersectSubset5 <=> 108.83/109.40 (![A,B,C]: (subset(C,A) => (subset(C,B) => subset(C,binintersect(A,B)))))). 108.83/109.40 tff('2', plain, 108.83/109.40 binintersectSubset5 = 108.83/109.40 (![X2,X3,X4]: 108.83/109.40 (subset(X4,X2) => (subset(X4,X3) => subset(X4,binintersect(X2,X3))))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(binintersectI, axiom, binintersectI <=> 108.83/109.40 (![A,B,Xx]: (in(Xx,A) => (in(Xx,B) => in(Xx,binintersect(A,B)))))). 108.83/109.40 tff('3', plain, 108.83/109.40 binintersectI = 108.83/109.40 (![X2,X3,X4]: (in(X4,X2) => (in(X4,X3) => in(X4,binintersect(X2,X3))))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(binintersect, axiom, binintersect() = 108.83/109.40 ^[A,B]: dsetconstr(A,^[Xx]: in(Xx,B))). 108.83/109.40 tff('4', plain, 108.83/109.40 binintersect = (^[V_1,V_2]: dsetconstr(V_1,^[V_3]: in(V_3,V_2))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(binunionRsub, axiom, binunionRsub <=> (![A,B]: subset(B,binunion(A,B)))). 108.83/109.40 tff('5', plain, binunionRsub = (![X2,X3]: subset(X3,binunion(X2,X3))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(binunionLsub, axiom, binunionLsub <=> (![A,B]: subset(A,binunion(A,B)))). 108.83/109.40 tff('6', plain, binunionLsub = (![X2,X3]: subset(X2,binunion(X2,X3))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(binunionE, axiom, binunionE <=> 108.83/109.40 (![A,B,Xx]: (in(Xx,binunion(A,B)) => (in(Xx,B) | in(Xx,A))))). 108.83/109.40 tff('7', plain, 108.83/109.40 binunionE = 108.83/109.40 (![X2,X3,X4]: (in(X4,binunion(X2,X3)) => (in(X4,X3) | in(X4,X2)))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(binunionEcases, axiom, binunionEcases <=> 108.83/109.40 (![A,B,Xx,Xphi:$o]: 108.83/109.40 (in(Xx,binunion(A,B)) => 108.83/109.40 ((in(Xx,A) => Xphi) => ((in(Xx,B) => Xphi) => Xphi))))). 108.83/109.40 tff('8', plain, 108.83/109.40 binunionEcases = 108.83/109.40 (![X2,X3,X4,X5:$o]: 108.83/109.40 (in(X4,binunion(X2,X3)) => 108.83/109.40 ((in(X4,X2) => X5) => ((in(X4,X3) => X5) => X5)))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(binunionIR, axiom, binunionIR <=> 108.83/109.40 (![A,B,Xx]: (in(Xx,B) => in(Xx,binunion(A,B))))). 108.83/109.40 tff('9', plain, 108.83/109.40 binunionIR = (![X2,X3,X4]: (in(X4,X3) => in(X4,binunion(X2,X3)))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(upairset2IR, axiom, upairset2IR <=> 108.83/109.40 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 108.83/109.40 tff('10', plain, 108.83/109.40 upairset2IR = (![X2,X3]: in(X3,setadjoin(X2,setadjoin(X3,emptyset)))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(binunionIL, axiom, binunionIL <=> 108.83/109.40 (![A,B,Xx]: (in(Xx,A) => in(Xx,binunion(A,B))))). 108.83/109.40 tff('11', plain, 108.83/109.40 binunionIL = (![X2,X3,X4]: (in(X4,X2) => in(X4,binunion(X2,X3)))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(sepSubset, axiom, sepSubset <=> 108.83/109.40 (![A,Xphi:($i > $o)]: subset(dsetconstr(A,^[Xx]: Xphi(Xx)),A))). 108.83/109.40 tff('12', plain, 108.83/109.40 sepSubset = 108.83/109.40 (![X2,X3:($i > $o)]: subset(dsetconstr(X2,^[V_1]: X3(V_1)),X2)), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(sepInPowerset, axiom, sepInPowerset <=> 108.83/109.40 (![A,Xphi:($i > $o)]: in(dsetconstr(A,^[Xx]: Xphi(Xx)),powerset(A)))). 108.83/109.40 tff('13', plain, 108.83/109.40 sepInPowerset = 108.83/109.40 (![X2,X3:($i > $o)]: in(dsetconstr(X2,^[V_1]: X3(V_1)),powerset(X2))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(powersetsubset, axiom, powersetsubset <=> 108.83/109.40 (![A,B]: (subset(A,B) => subset(powerset(A),powerset(B))))). 108.83/109.40 tff('14', plain, 108.83/109.40 powersetsubset = 108.83/109.40 (![X2,X3]: (subset(X2,X3) => subset(powerset(X2),powerset(X3)))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(inPowerset, axiom, inPowerset <=> (![A]: in(A,powerset(A)))). 108.83/109.40 tff('15', plain, inPowerset = (![X2]: in(X2,powerset(X2))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(powersetE1, axiom, powersetE1 <=> 108.83/109.40 (![A,B]: (in(B,powerset(A)) => subset(B,A)))). 108.83/109.40 tff('16', plain, 108.83/109.40 powersetE1 = (![X2,X3]: (in(X3,powerset(X2)) => subset(X3,X2))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(powersetI1, axiom, powersetI1 <=> 108.83/109.40 (![A,B]: (subset(B,A) => in(B,powerset(A))))). 108.83/109.40 tff('17', plain, 108.83/109.40 powersetI1 = (![X2,X3]: (subset(X3,X2) => in(X3,powerset(X2)))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(subsetemptysetimpeq, axiom, subsetemptysetimpeq <=> 108.83/109.40 (![A]: (subset(A,emptyset) => (A = emptyset)))). 108.83/109.40 tff('18', plain, 108.83/109.40 subsetemptysetimpeq = (![X2]: (subset(X2,emptyset) => (X2 = emptyset))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(setextsub, axiom, setextsub <=> 108.83/109.40 (![A,B]: (subset(A,B) => (subset(B,A) => (A = B))))). 108.83/109.40 tff('19', plain, 108.83/109.40 setextsub = (![X2,X3]: (subset(X2,X3) => (subset(X3,X2) => (X2 = X3)))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(subset2powerset, axiom, subset2powerset <=> 108.83/109.40 (![A,B]: (subset(A,B) => in(A,powerset(B))))). 108.83/109.40 tff('20', plain, 108.83/109.40 subset2powerset = (![X2,X3]: (subset(X2,X3) => in(X2,powerset(X3)))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(setadjoinSub2, axiom, setadjoinSub2 <=> 108.83/109.40 (![A,Xx,B]: (subset(A,B) => subset(A,setadjoin(Xx,B))))). 108.83/109.40 tff('21', plain, 108.83/109.40 setadjoinSub2 = 108.83/109.40 (![X2,X3,X4]: (subset(X2,X4) => subset(X2,setadjoin(X3,X4)))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(setadjoinSub, axiom, setadjoinSub <=> 108.83/109.40 (![Xx,A]: subset(A,setadjoin(Xx,A)))). 108.83/109.40 tff('22', plain, setadjoinSub = (![X2,X3]: subset(X3,setadjoin(X2,X3))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(subsetTrans, axiom, subsetTrans <=> 108.83/109.40 (![A,B,C]: (subset(A,B) => (subset(B,C) => subset(A,C))))). 108.83/109.40 tff('23', plain, 108.83/109.40 subsetTrans = 108.83/109.40 (![X2,X3,X4]: (subset(X2,X3) => (subset(X3,X4) => subset(X2,X4)))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(subsetRefl, axiom, subsetRefl <=> (![A]: subset(A,A))). 108.83/109.40 tff('24', plain, subsetRefl = (![X2]: subset(X2,X2)), define([status(thm)])). 108.83/109.40 tff(notequalI2, axiom, notequalI2 <=> 108.83/109.40 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => (A != B))))). 108.83/109.40 tff('25', plain, 108.83/109.40 notequalI2 = (![X2,X3,X4]: (in(X4,X2) => ((~in(X4,X3)) => (X2 != X3)))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(notequalI1, axiom, notequalI1 <=> (![A,B]: ((~subset(A,B)) => (A != B)))). 108.83/109.40 tff('26', plain, notequalI1 = (![X2,X3]: ((~subset(X2,X3)) => (X2 != X3))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(notsubsetI, axiom, notsubsetI <=> 108.83/109.40 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => (~subset(A,B)))))). 108.83/109.40 tff('27', plain, 108.83/109.40 notsubsetI = 108.83/109.40 (![X2,X3,X4]: (in(X4,X2) => ((~in(X4,X3)) => (~subset(X2,X3))))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(subsetE2, axiom, subsetE2 <=> 108.83/109.40 (![A,B,Xx]: (subset(A,B) => ((~in(Xx,B)) => (~in(Xx,A)))))). 108.83/109.40 tff('28', plain, 108.83/109.40 subsetE2 = 108.83/109.40 (![X2,X3,X4]: (subset(X2,X3) => ((~in(X4,X3)) => (~in(X4,X2))))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(subsetE, axiom, subsetE <=> 108.83/109.40 (![A,B,Xx]: (subset(A,B) => (in(Xx,A) => in(Xx,B))))). 108.83/109.40 tff('29', plain, 108.83/109.40 subsetE = (![X2,X3,X4]: (subset(X2,X3) => (in(X4,X2) => in(X4,X3)))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(emptysetsubset, axiom, emptysetsubset <=> (![A]: subset(emptyset,A))). 108.83/109.40 tff('30', plain, emptysetsubset = (![X2]: subset(emptyset,X2)), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(subsetI2, axiom, subsetI2 <=> 108.83/109.40 (![A,B]: ((![Xx]: (in(Xx,A) => in(Xx,B))) => subset(A,B)))). 108.83/109.40 tff('31', plain, 108.83/109.40 subsetI2 = 108.83/109.40 (![X2,X3]: ((![X4]: (in(X4,X2) => in(X4,X3))) => subset(X2,X3))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(eqimpsubset1, axiom, eqimpsubset1 <=> (![A,B]: ((A = B) => subset(A,B)))). 108.83/109.40 tff('32', plain, eqimpsubset1 = (![X2,X3]: ((X2 = X3) => subset(X2,X3))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(eqimpsubset2, axiom, eqimpsubset2 <=> (![A,B]: ((A = B) => subset(B,A)))). 108.83/109.40 tff('33', plain, eqimpsubset2 = (![X2,X3]: ((X2 = X3) => subset(X3,X2))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(subsetI1, axiom, subsetI1 <=> 108.83/109.40 (![A,B]: ((![Xx]: (in(Xx,A) => in(Xx,B))) => subset(A,B)))). 108.83/109.40 tff('34', plain, 108.83/109.40 subsetI1 = 108.83/109.40 (![X2,X3]: ((![X4]: (in(X4,X2) => in(X4,X3))) => subset(X2,X3))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(dsetconstr__Cong, axiom, dsetconstr__Cong <=> 108.83/109.40 (![A,B]: 108.83/109.40 ((A = B) => 108.83/109.40 (![Xphi:($i > $o),Xpsi:($i > $o)]: 108.83/109.40 ((![Xx]: 108.83/109.40 (in(Xx,A) => 108.83/109.40 (![Xy]: (in(Xy,B) => ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy))))))) => 108.83/109.40 (dsetconstr(A,^[Xx]: Xphi(Xx)) = dsetconstr(B,^[Xx]: Xpsi(Xx)))))))). 108.83/109.40 tff('35', plain, 108.83/109.40 dsetconstr__Cong = 108.83/109.40 (![X2,X3]: 108.83/109.40 ((X2 = X3) => 108.83/109.40 (![X4:($i > $o),X5:($i > $o)]: 108.83/109.40 ((![X6]: 108.83/109.40 (in(X6,X2) => 108.83/109.40 (![X7]: (in(X7,X3) => ((X6 = X7) => (X4(X6) <=> X5(X7))))))) => 108.83/109.40 (dsetconstr(X2,^[V_1]: X4(V_1)) = dsetconstr(X3,^[V_2]: X5(V_2))))))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(descr__Cong, axiom, descr__Cong <=> 108.83/109.40 (![Xphi:($i > $o),Xpsi:($i > $o)]: 108.83/109.40 ((![Xx,Xy]: ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy)))) => 108.83/109.40 (exu(^[Xx]: Xphi(Xx)) => 108.83/109.40 (exu(^[Xx]: Xpsi(Xx)) => 108.83/109.40 (descr(^[Xx]: Xphi(Xx)) = descr(^[Xx]: Xpsi(Xx)))))))). 108.83/109.40 tff('36', plain, 108.83/109.40 descr__Cong = 108.83/109.40 (![X2:($i > $o),X3:($i > $o)]: 108.83/109.40 ((![X4,X5]: ((X4 = X5) => (X2(X4) <=> X3(X5)))) => 108.83/109.40 (exu(^[V_1]: X2(V_1)) => 108.83/109.40 (exu(^[V_2]: X3(V_2)) => 108.83/109.40 (descr(^[V_3]: X2(V_3)) = descr(^[V_4]: X3(V_4))))))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(exuEu, axiom, exuEu <=> 108.83/109.40 (![Xphi:($i > $o)]: 108.83/109.40 (exu(^[Xx]: Xphi(Xx)) => 108.83/109.40 (![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))). 108.83/109.40 tff('37', plain, 108.83/109.40 exuEu = 108.83/109.40 (![X2:($i > $o)]: 108.83/109.40 (exu(^[V_1]: X2(V_1)) => (![X3,X4]: (X2(X3) => (X2(X4) => (X3 = X4)))))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(omega__Cong, axiom, omega__Cong <=> (omega = omega)). 108.83/109.40 tff('38', plain, omega__Cong = (omega = omega), define([status(thm)])). 108.83/109.40 tff(setunion__Cong, axiom, setunion__Cong <=> 108.83/109.40 (![A,B]: ((A = B) => (setunion(A) = setunion(B))))). 108.83/109.40 tff('39', plain, 108.83/109.40 setunion__Cong = (![X2,X3]: ((X2 = X3) => (setunion(X2) = setunion(X3)))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(powerset__Cong, axiom, powerset__Cong <=> 108.83/109.40 (![A,B]: ((A = B) => (powerset(A) = powerset(B))))). 108.83/109.40 tff('40', plain, 108.83/109.40 powerset__Cong = (![X2,X3]: ((X2 = X3) => (powerset(X2) = powerset(X3)))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(setadjoin__Cong, axiom, setadjoin__Cong <=> 108.83/109.40 (![Xx,Xy]: 108.83/109.40 ((Xx = Xy) => 108.83/109.40 (![Xz,Xu]: ((Xz = Xu) => (setadjoin(Xx,Xz) = setadjoin(Xy,Xu))))))). 108.83/109.40 tff('41', plain, 108.83/109.40 setadjoin__Cong = 108.83/109.40 (![X2,X3]: 108.83/109.40 ((X2 = X3) => 108.83/109.40 (![X4,X5]: ((X4 = X5) => (setadjoin(X2,X4) = setadjoin(X3,X5)))))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(emptyset__Cong, axiom, emptyset__Cong <=> (emptyset = emptyset)). 108.83/109.40 tff('42', plain, emptyset__Cong = (emptyset = emptyset), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(exu__Cong, axiom, exu__Cong <=> 108.83/109.40 (![Xphi:($i > $o),Xpsi:($i > $o)]: 108.83/109.40 ((![Xx,Xy]: ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy)))) => 108.83/109.40 (exu(^[Xx]: Xphi(Xx)) <=> exu(^[Xx]: Xpsi(Xx)))))). 108.83/109.40 tff('43', plain, 108.83/109.40 exu__Cong = 108.83/109.40 (![X2:($i > $o),X3:($i > $o)]: 108.83/109.40 ((![X4,X5]: ((X4 = X5) => (X2(X4) <=> X3(X5)))) => 108.83/109.40 (exu(^[V_1]: X2(V_1)) <=> exu(^[V_2]: X3(V_2))))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(exuE3u, axiom, exuE3u <=> 108.83/109.40 (![Xphi:($i > $o)]: 108.83/109.40 (exu(^[Xx]: Xphi(Xx)) => 108.83/109.40 (![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))). 108.83/109.40 tff('44', plain, 108.83/109.40 exuE3u = 108.83/109.40 (![X2:($i > $o)]: 108.83/109.40 (exu(^[V_1]: X2(V_1)) => (![X3,X4]: (X2(X3) => (X2(X4) => (X3 = X4)))))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(in__Cong, axiom, in__Cong <=> 108.83/109.40 (![A,B]: ((A = B) => (![Xx,Xy]: ((Xx = Xy) => (in(Xx,A) <=> in(Xy,B))))))). 108.83/109.40 tff('45', plain, 108.83/109.40 in__Cong = 108.83/109.40 (![X2,X3]: 108.83/109.40 ((X2 = X3) => (![X4,X5]: ((X4 = X5) => (in(X4,X2) <=> in(X5,X3)))))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(inCongP, axiom, inCongP <=> 108.83/109.40 (![A,B]: ((A = B) => (![Xx,Xy]: ((Xx = Xy) => (in(Xx,A) => in(Xy,B))))))). 108.83/109.40 tff('46', plain, 108.83/109.40 inCongP = 108.83/109.40 (![X2,X3]: 108.83/109.40 ((X2 = X3) => (![X4,X5]: ((X4 = X5) => (in(X4,X2) => in(X5,X3)))))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(exuI2, axiom, exuI2 <=> 108.83/109.40 (![Xphi:($i > $o)]: 108.83/109.40 ((?[Xx]: (![Xy]: (Xphi(Xy) <=> (Xy = Xx)))) => exu(^[Xx]: Xphi(Xx))))). 108.83/109.40 tff('47', plain, 108.83/109.40 exuI2 = 108.83/109.40 (![X2:($i > $o)]: 108.83/109.40 ((?[X3]: (![X4]: (X2(X4) <=> (X4 = X3)))) => exu(^[V_1]: X2(V_1)))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(exuI3, axiom, exuI3 <=> 108.83/109.40 (![Xphi:($i > $o)]: 108.83/109.40 ((?[Xx]: Xphi(Xx)) => 108.83/109.40 ((![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy)))) => 108.83/109.40 exu(^[Xx]: Xphi(Xx)))))). 108.83/109.40 tff('48', plain, 108.83/109.40 exuI3 = 108.83/109.40 (![X2:($i > $o)]: 108.83/109.40 ((?[X3]: X2(X3)) => 108.83/109.40 ((![X4,X5]: (X2(X4) => (X2(X5) => (X4 = X5)))) => 108.83/109.40 exu(^[V_1]: X2(V_1))))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(exuI1, axiom, exuI1 <=> 108.83/109.40 (![Xphi:($i > $o)]: 108.83/109.40 ((?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx))) => 108.83/109.40 exu(^[Xx]: Xphi(Xx))))). 108.83/109.40 tff('49', plain, 108.83/109.40 exuI1 = 108.83/109.40 (![X2:($i > $o)]: 108.83/109.40 ((?[X3]: ((![X4]: (X2(X4) => (X3 = X4))) & X2(X3))) => 108.83/109.40 exu(^[V_1]: X2(V_1)))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(notdallE, axiom, notdallE <=> 108.83/109.40 (![A,Xphi:($i > $o)]: 108.83/109.40 ((~(![Xx]: (in(Xx,A) => Xphi(Xx)))) => (?[Xx]: ((~Xphi(Xx)) & in(Xx,A)))))). 108.83/109.40 tff('50', plain, 108.83/109.40 notdallE = 108.83/109.40 (![X2,X3:($i > $o)]: 108.83/109.40 ((~(![X4]: (in(X4,X2) => X3(X4)))) => (?[X5]: ((~X3(X5)) & in(X5,X2))))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(notdexE, axiom, notdexE <=> 108.83/109.40 (![A,Xphi:($i > $o)]: 108.83/109.40 ((~(?[Xx]: (Xphi(Xx) & in(Xx,A)))) => (![Xx]: (in(Xx,A) => (~Xphi(Xx))))))). 108.83/109.40 tff('51', plain, 108.83/109.40 notdexE = 108.83/109.40 (![X2,X3:($i > $o)]: 108.83/109.40 ((~(?[X4]: (X3(X4) & in(X4,X2)))) => (![X5]: (in(X5,X2) => (~X3(X5)))))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(prop2set2propI, axiom, prop2set2propI <=> 108.83/109.40 (![Xphi:$o]: (Xphi => set2prop(prop2set(Xphi))))). 108.83/109.40 tff('52', plain, prop2set2propI = (![X2:$o]: (X2 => set2prop(prop2set(X2)))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(prop2setI, axiom, prop2setI <=> 108.83/109.40 (![Xphi:$o]: (Xphi => in(emptyset,prop2set(Xphi))))). 108.83/109.40 tff('53', plain, prop2setI = (![X2:$o]: (X2 => in(emptyset,prop2set(X2)))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(quantDeMorgan4, axiom, quantDeMorgan4 <=> 108.83/109.40 (![A,Xphi:($i > $o)]: 108.83/109.40 ((?[Xx]: ((~Xphi(Xx)) & in(Xx,A))) => (~(![Xx]: (in(Xx,A) => Xphi(Xx))))))). 108.83/109.40 tff('54', plain, 108.83/109.40 quantDeMorgan4 = 108.83/109.40 (![X2,X3:($i > $o)]: 108.83/109.40 ((?[X4]: ((~X3(X4)) & in(X4,X2))) => (~(![X5]: (in(X5,X2) => X3(X5)))))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(quantDeMorgan3, axiom, quantDeMorgan3 <=> 108.83/109.40 (![A,Xphi:($i > $o)]: 108.83/109.40 ((~(?[Xx]: (Xphi(Xx) & in(Xx,A)))) => (![Xx]: (in(Xx,A) => (~Xphi(Xx))))))). 108.83/109.40 tff('55', plain, 108.83/109.40 quantDeMorgan3 = 108.83/109.40 (![X2,X3:($i > $o)]: 108.83/109.40 ((~(?[X4]: (X3(X4) & in(X4,X2)))) => (![X5]: (in(X5,X2) => (~X3(X5)))))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(quantDeMorgan2, axiom, quantDeMorgan2 <=> 108.83/109.40 (![A,Xphi:($i > $o)]: 108.83/109.40 ((![Xx]: (in(Xx,A) => (~Xphi(Xx)))) => (~(?[Xx]: (Xphi(Xx) & in(Xx,A))))))). 108.83/109.40 tff('56', plain, 108.83/109.40 quantDeMorgan2 = 108.83/109.40 (![X2,X3:($i > $o)]: 108.83/109.40 ((![X4]: (in(X4,X2) => (~X3(X4)))) => (~(?[X5]: (X3(X5) & in(X5,X2)))))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(quantDeMorgan1, axiom, quantDeMorgan1 <=> 108.83/109.40 (![A,Xphi:($i > $o)]: 108.83/109.40 ((~(![Xx]: (in(Xx,A) => Xphi(Xx)))) => (?[Xx]: ((~Xphi(Xx)) & in(Xx,A)))))). 108.83/109.40 tff('57', plain, 108.83/109.40 quantDeMorgan1 = 108.83/109.40 (![X2,X3:($i > $o)]: 108.83/109.40 ((~(![X4]: (in(X4,X2) => X3(X4)))) => (?[X5]: ((~X3(X5)) & in(X5,X2))))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(vacuousDall, axiom, vacuousDall <=> 108.83/109.40 (![Xphi:($i > $o),Xx]: (in(Xx,emptyset) => Xphi(Xx)))). 108.83/109.40 tff('58', plain, 108.83/109.40 vacuousDall = (![X2:($i > $o),X3]: (in(X3,emptyset) => X2(X3))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(emptyE1, axiom, emptyE1 <=> 108.83/109.40 (![A,Xphi:($i > $o)]: 108.83/109.40 ((?[Xx]: (Xphi(Xx) & in(Xx,A))) => 108.83/109.40 ((dsetconstr(A,^[Xx]: Xphi(Xx)) = emptyset) => $false)))). 108.83/109.40 tff('59', plain, 108.83/109.40 emptyE1 = 108.83/109.40 (![X2,X3:($i > $o)]: 108.83/109.40 ((?[X4]: (X3(X4) & in(X4,X2))) => 108.83/109.40 ((dsetconstr(X2,^[V_1]: X3(V_1)) = emptyset) => $false))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(upairsetIR, axiom, upairsetIR <=> 108.83/109.40 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 108.83/109.40 tff('60', plain, 108.83/109.40 upairsetIR = (![X2,X3]: in(X3,setadjoin(X2,setadjoin(X3,emptyset)))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(upairsetIL, axiom, upairsetIL <=> 108.83/109.40 (![Xx,Xy]: in(Xx,setadjoin(Xx,setadjoin(Xy,emptyset))))). 108.83/109.40 tff('61', plain, 108.83/109.40 upairsetIL = (![X2,X3]: in(X2,setadjoin(X2,setadjoin(X3,emptyset)))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(upairsetE, axiom, upairsetE <=> 108.83/109.40 (![Xx,Xy,Xz]: 108.83/109.40 (in(Xz,setadjoin(Xx,setadjoin(Xy,emptyset))) => ((Xz = Xy) | (Xz = Xx))))). 108.83/109.40 tff('62', plain, 108.83/109.40 upairsetE = 108.83/109.40 (![X2,X3,X4]: 108.83/109.40 (in(X4,setadjoin(X2,setadjoin(X3,emptyset))) => 108.83/109.40 ((X4 = X3) | (X4 = X2)))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(singletonsswitch, axiom, singletonsswitch <=> 108.83/109.40 (![Xx,Xy]: (in(Xx,setadjoin(Xy,emptyset)) => in(Xy,setadjoin(Xx,emptyset))))). 108.83/109.40 tff('63', plain, 108.83/109.40 singletonsswitch = 108.83/109.40 (![X2,X3]: 108.83/109.40 (in(X2,setadjoin(X3,emptyset)) => in(X3,setadjoin(X2,emptyset)))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(eqinunit, axiom, eqinunit <=> 108.83/109.40 (![Xx,Xy]: ((Xx = Xy) => in(Xx,setadjoin(Xy,emptyset))))). 108.83/109.40 tff('64', plain, 108.83/109.40 eqinunit = (![X2,X3]: ((X2 = X3) => in(X2,setadjoin(X3,emptyset)))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(notinsingleton, axiom, notinsingleton <=> 108.83/109.40 (![Xx,Xy]: ((Xx != Xy) => (~in(Xy,setadjoin(Xx,emptyset)))))). 108.83/109.40 tff('65', plain, 108.83/109.40 notinsingleton = 108.83/109.40 (![X2,X3]: ((X2 != X3) => (~in(X3,setadjoin(X2,emptyset))))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(uniqinunit, axiom, uniqinunit <=> 108.83/109.40 (![Xx,Xy]: (in(Xx,setadjoin(Xy,emptyset)) => (Xx = Xy)))). 108.83/109.40 tff('66', plain, 108.83/109.40 uniqinunit = (![X2,X3]: (in(X2,setadjoin(X3,emptyset)) => (X2 = X3))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(nonemptyImpWitness, axiom, nonemptyImpWitness <=> 108.83/109.40 (![A]: (nonempty(A) => (?[Xx]: (in(Xx,A)))))). 108.83/109.40 tff('67', plain, 108.83/109.40 nonemptyImpWitness = (![X2]: (nonempty(X2) => (?[X3]: (in(X3,X2))))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(exuE2, axiom, exuE2 <=> 108.83/109.40 (![Xphi:($i > $o)]: 108.83/109.40 (exu(^[Xx]: Xphi(Xx)) => (?[Xx]: (![Xy]: (Xphi(Xy) <=> (Xy = Xx))))))). 108.83/109.40 tff('68', plain, 108.83/109.40 exuE2 = 108.83/109.40 (![X2:($i > $o)]: 108.83/109.40 (exu(^[V_1]: X2(V_1)) => (?[X3]: (![X4]: (X2(X4) <=> (X4 = X3)))))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(subPowSU, axiom, subPowSU <=> 108.83/109.40 (![A,Xx]: (in(Xx,A) => in(Xx,powerset(setunion(A)))))). 108.83/109.40 tff('69', plain, 108.83/109.40 subPowSU = (![X2,X3]: (in(X3,X2) => in(X3,powerset(setunion(X2))))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(setunionE, axiom, setunionE <=> 108.83/109.40 (![A,Xx]: 108.83/109.40 (in(Xx,setunion(A)) => 108.83/109.40 (![Xphi:$o]: ((![B]: (in(Xx,B) => (in(B,A) => Xphi))) => Xphi))))). 108.83/109.40 tff('70', plain, 108.83/109.40 setunionE = 108.83/109.40 (![X2,X3]: 108.83/109.40 (in(X3,setunion(X2)) => 108.83/109.40 (![X4:$o]: ((![X5]: (in(X3,X5) => (in(X5,X2) => X4))) => X4)))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(setunionI, axiom, setunionI <=> 108.83/109.40 (![A,Xx,B]: (in(Xx,B) => (in(B,A) => in(Xx,setunion(A)))))). 108.83/109.40 tff('71', plain, 108.83/109.40 setunionI = 108.83/109.40 (![X2,X3,X4]: (in(X3,X4) => (in(X4,X2) => in(X3,setunion(X2))))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(powersetE, axiom, powersetE <=> 108.83/109.40 (![A,B,Xx]: (in(B,powerset(A)) => (in(Xx,B) => in(Xx,A))))). 108.83/109.40 tff('72', plain, 108.83/109.40 powersetE = 108.83/109.40 (![X2,X3,X4]: (in(X3,powerset(X2)) => (in(X4,X3) => in(X4,X2)))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(emptyInPowerset, axiom, emptyInPowerset <=> 108.83/109.40 (![A]: in(emptyset,powerset(A)))). 108.83/109.40 tff('73', plain, emptyInPowerset = (![X2]: in(emptyset,powerset(X2))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(emptyinPowerset, axiom, emptyinPowerset <=> 108.83/109.40 (![A]: in(emptyset,powerset(A)))). 108.83/109.40 tff('74', plain, emptyinPowerset = (![X2]: in(emptyset,powerset(X2))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(powersetI, axiom, powersetI <=> 108.83/109.40 (![A,B]: ((![Xx]: (in(Xx,B) => in(Xx,A))) => in(B,powerset(A))))). 108.83/109.40 tff('75', plain, 108.83/109.40 powersetI = 108.83/109.40 (![X2,X3]: ((![X4]: (in(X4,X3) => in(X4,X2))) => in(X3,powerset(X2)))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(setoftrueEq, axiom, setoftrueEq <=> 108.83/109.40 (![A]: (dsetconstr(A,^[Xx]: $true) = A))). 108.83/109.40 tff('76', plain, setoftrueEq = (![X2]: (dsetconstr(X2,^[V_1]: $true) = X2)), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(setadjoinOr, axiom, setadjoinOr <=> 108.83/109.40 (![Xx,A,Xy]: (in(Xy,setadjoin(Xx,A)) => (in(Xy,A) | (Xy = Xx))))). 108.83/109.40 tff('77', plain, 108.83/109.40 setadjoinOr = 108.83/109.40 (![X2,X3,X4]: (in(X4,setadjoin(X2,X3)) => (in(X4,X3) | (X4 = X2)))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(setadjoinE, axiom, setadjoinE <=> 108.83/109.40 (![Xx,A,Xy]: 108.83/109.40 (in(Xy,setadjoin(Xx,A)) => 108.83/109.40 (![Xphi:$o]: (((Xy = Xx) => Xphi) => ((in(Xy,A) => Xphi) => Xphi)))))). 108.83/109.40 tff('78', plain, 108.83/109.40 setadjoinE = 108.83/109.40 (![X2,X3,X4]: 108.83/109.40 (in(X4,setadjoin(X2,X3)) => 108.83/109.40 (![X5:$o]: (((X4 = X2) => X5) => ((in(X4,X3) => X5) => X5))))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(setadjoinIR, axiom, setadjoinIR <=> 108.83/109.40 (![Xx,A,Xy]: (in(Xy,A) => in(Xy,setadjoin(Xx,A))))). 108.83/109.40 tff('79', plain, 108.83/109.40 setadjoinIR = (![X2,X3,X4]: (in(X4,X3) => in(X4,setadjoin(X2,X3)))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(emptyinunitempty, axiom, emptyinunitempty() = 108.83/109.40 in(emptyset,setadjoin(emptyset,emptyset))). 108.83/109.40 tff('80', plain, 108.83/109.40 emptyinunitempty = in(emptyset,setadjoin(emptyset,emptyset)), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(setadjoinIL, axiom, setadjoinIL <=> (![Xx,Xy]: in(Xx,setadjoin(Xx,Xy)))). 108.83/109.40 tff('81', plain, setadjoinIL = (![X2,X3]: in(X2,setadjoin(X2,X3))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(nonemptyI1, axiom, nonemptyI1 <=> 108.83/109.40 (![A]: ((?[Xx]: in(Xx,A)) => nonempty(A)))). 108.83/109.40 tff('82', plain, nonemptyI1 = (![X2]: ((?[X3]: in(X3,X2)) => nonempty(X2))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(nonemptyI, axiom, nonemptyI <=> 108.83/109.40 (![A,Xphi:($i > $o),Xx]: 108.83/109.40 (in(Xx,A) => (Xphi(Xx) => nonempty(dsetconstr(A,^[Xy]: Xphi(Xy))))))). 108.83/109.40 tff('83', plain, 108.83/109.40 nonemptyI = 108.83/109.40 (![X2,X3:($i > $o),X4]: 108.83/109.40 (in(X4,X2) => (X3(X4) => nonempty(dsetconstr(X2,^[V_1]: X3(V_1)))))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(nonemptyE1, axiom, nonemptyE1 <=> 108.83/109.40 (![A]: (nonempty(A) => (?[Xx]: in(Xx,A))))). 108.83/109.40 tff('84', plain, nonemptyE1 = (![X2]: (nonempty(X2) => (?[X3]: in(X3,X2)))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(nonempty, axiom, nonempty() = ^[Xx]: (Xx != emptyset)). 108.83/109.40 tff('85', plain, nonempty = (^[V_1]: (V_1 != emptyset)), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(setbeta, axiom, setbeta <=> 108.83/109.40 (![A,Xphi:($i > $o),Xx]: 108.83/109.40 (in(Xx,A) => (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) <=> Xphi(Xx))))). 108.83/109.40 tff('86', plain, 108.83/109.40 setbeta = 108.83/109.40 (![X2,X3:($i > $o),X4]: 108.83/109.40 (in(X4,X2) => (in(X4,dsetconstr(X2,^[V_1]: X3(V_1))) <=> X3(X4)))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(noeltsimpempty, axiom, noeltsimpempty <=> 108.83/109.40 (![A]: ((![Xx]: (~in(Xx,A))) => (A = emptyset)))). 108.83/109.40 tff('87', plain, 108.83/109.40 noeltsimpempty = (![X2]: ((![X3]: (~in(X3,X2))) => (X2 = emptyset))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(emptyI, axiom, emptyI <=> 108.83/109.40 (![A]: ((![Xx]: (~in(Xx,A))) => (A = emptyset)))). 108.83/109.40 tff('88', plain, 108.83/109.40 emptyI = (![X2]: ((![X3]: (~in(X3,X2))) => (X2 = emptyset))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(setext, axiom, setext <=> 108.83/109.40 (![A,B]: 108.83/109.40 ((![Xx]: (in(Xx,A) => in(Xx,B))) => 108.83/109.40 ((![Xx]: (in(Xx,B) => in(Xx,A))) => (A = B))))). 108.83/109.40 tff('89', plain, 108.83/109.40 setext = 108.83/109.40 (![X2,X3]: 108.83/109.40 ((![X4]: (in(X4,X2) => in(X4,X3))) => 108.83/109.40 ((![X5]: (in(X5,X3) => in(X5,X2))) => (X2 = X3)))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(exuE3e, axiom, exuE3e <=> 108.83/109.40 (![Xphi:($i > $o)]: (exu(^[Xx]: Xphi(Xx)) => (?[Xx]: Xphi(Xx))))). 108.83/109.40 tff('90', plain, 108.83/109.40 exuE3e = (![X2:($i > $o)]: (exu(^[V_1]: X2(V_1)) => (?[X3]: X2(X3)))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(notinemptyset, axiom, notinemptyset <=> (![Xx]: (~in(Xx,emptyset)))). 108.83/109.40 tff('91', plain, notinemptyset = (![X2]: (~in(X2,emptyset))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(emptysetimpfalse, axiom, emptysetimpfalse <=> 108.83/109.40 (![Xx]: (in(Xx,emptyset) => $false))). 108.83/109.40 tff('92', plain, emptysetimpfalse = (![X2]: (in(X2,emptyset) => $false)), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(emptysetE, axiom, emptysetE <=> 108.83/109.40 (![Xx]: (in(Xx,emptyset) => (![Xphi:$o]: Xphi)))). 108.83/109.40 tff('93', plain, emptysetE = (![X2]: (in(X2,emptyset) => (![X3:$o]: X3))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(prop2setE, axiom, prop2setE <=> 108.83/109.40 (![Xphi:$o,Xx]: (in(Xx,prop2set(Xphi)) => Xphi))). 108.83/109.40 tff('94', plain, prop2setE = (![X2:$o,X3]: (in(X3,prop2set(X2)) => X2)), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(exuE1, axiom, exuE1 <=> 108.83/109.40 (![Xphi:($i > $o)]: 108.83/109.40 (exu(^[Xx]: Xphi(Xx)) => 108.83/109.40 (?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx)))))). 108.83/109.40 tff('95', plain, 108.83/109.40 exuE1 = 108.83/109.40 (![X2:($i > $o)]: 108.83/109.40 (exu(^[V_1]: X2(V_1)) => 108.83/109.40 (?[X3]: ((![X4]: (X2(X4) => (X3 = X4))) & X2(X3))))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(dsetconstrER, axiom, dsetconstrER <=> 108.83/109.40 (![A,Xphi:($i > $o),Xx]: (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) => Xphi(Xx)))). 108.83/109.40 tff('96', plain, 108.83/109.40 dsetconstrER = 108.83/109.40 (![X2,X3:($i > $o),X4]: (in(X4,dsetconstr(X2,^[V_1]: X3(V_1))) => X3(X4))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(dsetconstrEL, axiom, dsetconstrEL <=> 108.83/109.40 (![A,Xphi:($i > $o),Xx]: (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) => in(Xx,A)))). 108.83/109.40 tff('97', plain, 108.83/109.40 dsetconstrEL = 108.83/109.40 (![X2,X3:($i > $o),X4]: 108.83/109.40 (in(X4,dsetconstr(X2,^[V_1]: X3(V_1))) => in(X4,X2))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(dsetconstrI, axiom, dsetconstrI <=> 108.83/109.40 (![A,Xphi:($i > $o),Xx]: 108.83/109.40 (in(Xx,A) => (Xphi(Xx) => in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))))))). 108.83/109.40 tff('98', plain, 108.83/109.40 dsetconstrI = 108.83/109.40 (![X2,X3:($i > $o),X4]: 108.83/109.40 (in(X4,X2) => (X3(X4) => in(X4,dsetconstr(X2,^[V_1]: X3(V_1)))))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(descrp, axiom, descrp <=> 108.83/109.40 (![Xphi:($i > $o)]: (exu(^[Xx]: Xphi(Xx)) => Xphi(descr(^[Xx]: Xphi(Xx)))))). 108.83/109.40 tff('99', plain, 108.83/109.40 descrp = 108.83/109.40 (![X2:($i > $o)]: (exu(^[V_1]: X2(V_1)) => X2(descr(^[V_2]: X2(V_2))))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(wellorderingAx, axiom, wellorderingAx <=> 108.83/109.40 (![A]: 108.83/109.40 (?[B]: 108.83/109.40 ((![C]: 108.83/109.40 (((?[Xx]: in(Xx,C)) & (![Xx]: (in(Xx,C) => in(Xx,A)))) => 108.83/109.40 (?[D,Xx]: 108.83/109.40 ((![E]: 108.83/109.40 (in(E,B) => (in(Xx,E) | (![Xy]: (in(Xy,E) => in(Xy,D)))))) & 108.83/109.40 (~(?[Xy]: (in(Xy,C) & in(Xy,D)))) & in(Xx,C) & in(D,B))))) & 108.83/109.40 (![C,D]: 108.83/109.40 ((in(D,B) & in(C,B)) => 108.83/109.40 ((![Xx]: (in(Xx,D) => in(Xx,C))) | 108.83/109.40 (![Xx]: (in(Xx,C) => in(Xx,D)))))) & 108.83/109.40 (![Xx,Xy]: 108.83/109.40 ((in(Xy,A) & in(Xx,A)) => 108.83/109.40 ((![C]: (in(C,B) => (in(Xx,C) <=> in(Xy,C)))) => (Xx = Xy)))) & 108.83/109.40 (![C]: (in(C,B) => (![Xx]: (in(Xx,C) => in(Xx,A))))))))). 108.83/109.40 tff('100', plain, 108.83/109.40 wellorderingAx = 108.83/109.40 (![X2]: 108.83/109.40 (?[X3]: 108.83/109.40 ((![X4]: 108.83/109.40 (((?[X5]: in(X5,X4)) & (![X6]: (in(X6,X4) => in(X6,X2)))) => 108.83/109.40 (?[X7,X8]: 108.83/109.40 ((![X9]: 108.83/109.40 (in(X9,X3) => 108.83/109.40 (in(X8,X9) | (![X10]: (in(X10,X9) => in(X10,X7)))))) & 108.83/109.40 (~(?[X11]: (in(X11,X4) & in(X11,X7)))) & in(X8,X4) & 108.83/109.40 in(X7,X3))))) & 108.83/109.40 (![X12,X13]: 108.83/109.40 ((in(X13,X3) & in(X12,X3)) => 108.83/109.40 ((![X14]: (in(X14,X13) => in(X14,X12))) | 108.83/109.40 (![X15]: (in(X15,X12) => in(X15,X13)))))) & 108.83/109.40 (![X16,X17]: 108.83/109.40 ((in(X17,X2) & in(X16,X2)) => 108.83/109.40 ((![X18]: (in(X18,X3) => (in(X16,X18) <=> in(X17,X18)))) => 108.83/109.40 (X16 = X17)))) & 108.83/109.40 (![X19]: (in(X19,X3) => (![X20]: (in(X20,X19) => in(X20,X2)))))))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(foundationAx, axiom, foundationAx <=> 108.83/109.40 (![A]: 108.83/109.40 ((?[Xx]: in(Xx,A)) => 108.83/109.40 (?[B]: ((~(?[Xx]: (in(Xx,A) & in(Xx,B)))) & in(B,A)))))). 108.83/109.40 tff('101', plain, 108.83/109.40 foundationAx = 108.83/109.40 (![X2]: 108.83/109.40 ((?[X3]: in(X3,X2)) => 108.83/109.40 (?[X4]: ((~(?[X5]: (in(X5,X2) & in(X5,X4)))) & in(X4,X2))))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(replAx, axiom, replAx <=> 108.83/109.40 (![Xphi:(($i * $i) > $o),A]: 108.83/109.40 ((![Xx]: (in(Xx,A) => exu(^[Xy]: Xphi(Xx,Xy)))) => 108.83/109.40 (?[B]: (![Xx]: (in(Xx,B) <=> (?[Xy]: (Xphi(Xy,Xx) & in(Xy,A))))))))). 108.83/109.40 tff('102', plain, 108.83/109.40 replAx = 108.83/109.40 (![X2:(($i * $i) > $o),X3]: 108.83/109.40 ((![X4]: (in(X4,X3) => exu(^[V_1]: X2(X4,V_1)))) => 108.83/109.40 (?[X5]: (![X6]: (in(X6,X5) <=> (?[X7]: (X2(X7,X6) & in(X7,X3)))))))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(omegaIndAx, axiom, omegaIndAx <=> 108.83/109.40 (![A]: 108.83/109.40 (((![Xx]: ((in(Xx,A) & in(Xx,omega)) => in(setadjoin(Xx,Xx),A))) & 108.83/109.40 in(emptyset,A)) => 108.83/109.40 (![Xx]: (in(Xx,omega) => in(Xx,A)))))). 108.83/109.40 tff('103', plain, 108.83/109.40 omegaIndAx = 108.83/109.40 (![X2]: 108.83/109.40 (((![X3]: ((in(X3,X2) & in(X3,omega)) => in(setadjoin(X3,X3),X2))) & 108.83/109.40 in(emptyset,X2)) => 108.83/109.40 (![X4]: (in(X4,omega) => in(X4,X2))))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(omegaSAx, axiom, omegaSAx <=> 108.83/109.40 (![Xx]: (in(Xx,omega) => in(setadjoin(Xx,Xx),omega)))). 108.83/109.40 tff('104', plain, 108.83/109.40 omegaSAx = (![X2]: (in(X2,omega) => in(setadjoin(X2,X2),omega))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(omega0Ax, axiom, omega0Ax() = in(emptyset,omega)). 108.83/109.40 tff('105', plain, omega0Ax = in(emptyset,omega), define([status(thm)])). 108.83/109.40 tff(setunionAx, axiom, setunionAx <=> 108.83/109.40 (![A,Xx]: (in(Xx,setunion(A)) <=> (?[B]: (in(B,A) & in(Xx,B)))))). 108.83/109.40 tff('106', plain, 108.83/109.40 setunionAx = 108.83/109.40 (![X2,X3]: (in(X3,setunion(X2)) <=> (?[X4]: (in(X4,X2) & in(X3,X4))))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(powersetAx, axiom, powersetAx <=> 108.83/109.40 (![A,B]: (in(B,powerset(A)) <=> (![Xx]: (in(Xx,B) => in(Xx,A)))))). 108.83/109.40 tff('107', plain, 108.83/109.40 powersetAx = 108.83/109.40 (![X2,X3]: (in(X3,powerset(X2)) <=> (![X4]: (in(X4,X3) => in(X4,X2))))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(setadjoinAx, axiom, setadjoinAx <=> 108.83/109.40 (![Xx,A,Xy]: (in(Xy,setadjoin(Xx,A)) <=> (in(Xy,A) | (Xy = Xx))))). 108.83/109.40 tff('108', plain, 108.83/109.40 setadjoinAx = 108.83/109.40 (![X2,X3,X4]: (in(X4,setadjoin(X2,X3)) <=> (in(X4,X3) | (X4 = X2)))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(emptysetAx, axiom, emptysetAx <=> (![Xx]: (~in(Xx,emptyset)))). 108.83/109.40 tff('109', plain, emptysetAx = (![X2]: (~in(X2,emptyset))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(setextAx, axiom, setextAx <=> 108.83/109.40 (![A,B]: ((![Xx]: (in(Xx,A) <=> in(Xx,B))) => (A = B)))). 108.83/109.40 tff('110', plain, 108.83/109.40 setextAx = (![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(exu, axiom, exu() = 108.83/109.40 ^[Xphi:($i > $o)]: (?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx)))). 108.83/109.40 tff('111', plain, 108.83/109.40 exu = 108.83/109.40 (^[V_1:($i > $o)]: (?[X2]: ((![X3]: (V_1(X3) => (X2 = X3))) & V_1(X2)))), 108.83/109.40 define([status(thm)])). 108.83/109.40 tff(binintersectSubset2, conjecture, 108.83/109.40 (setextAx => 108.83/109.40 (emptysetAx => 108.83/109.40 (setadjoinAx => 108.83/109.40 (powersetAx => 108.83/109.40 (setunionAx => 108.83/109.40 (omega0Ax => 108.83/109.40 (omegaSAx => 108.83/109.40 (omegaIndAx => 108.83/109.40 (replAx => 108.83/109.40 (foundationAx => 108.83/109.40 (wellorderingAx => 108.83/109.40 (descrp => 108.83/109.40 (dsetconstrI => 108.83/109.40 (dsetconstrEL => 108.83/109.40 (dsetconstrER => 108.83/109.40 (exuE1 => 108.83/109.40 (prop2setE => 108.83/109.40 (emptysetE => 108.83/109.40 (emptysetimpfalse => 108.83/109.40 (notinemptyset => 108.83/109.40 (exuE3e => 108.83/109.40 (setext => 108.83/109.40 (emptyI => 108.83/109.40 (noeltsimpempty => 108.83/109.40 (setbeta => 108.83/109.40 (nonemptyE1 => 108.83/109.40 (nonemptyI => 108.83/109.40 (nonemptyI1 => 108.83/109.40 (setadjoinIL => 108.83/109.40 (emptyinunitempty => 108.83/109.40 (setadjoinIR => 108.83/109.40 (setadjoinE => 108.83/109.40 (setadjoinOr => 108.83/109.40 (setoftrueEq => 108.83/109.40 (powersetI => 108.83/109.40 (emptyinPowerset => 108.83/109.40 (emptyInPowerset => 108.83/109.40 (powersetE => 108.83/109.40 (setunionI => 108.83/109.40 (setunionE => 108.83/109.40 (subPowSU => 108.83/109.40 (exuE2 => 108.83/109.40 (nonemptyImpWitness => 108.83/109.40 (uniqinunit => 108.83/109.40 (notinsingleton => 108.83/109.40 (eqinunit => 108.83/109.40 (singletonsswitch => 108.83/109.40 (upairsetE => 108.83/109.40 (upairsetIL => 108.83/109.40 (upairsetIR => 108.83/109.40 (emptyE1 => 108.83/109.40 (vacuousDall => 108.83/109.40 (quantDeMorgan1 => 108.83/109.40 (quantDeMorgan2 => 108.83/109.40 (quantDeMorgan3 => 108.83/109.40 (quantDeMorgan4 => 108.83/109.40 (prop2setI => 108.83/109.40 (prop2set2propI => 108.83/109.40 (notdexE => 108.83/109.40 (notdallE => 108.83/109.40 (exuI1 => 108.83/109.40 (exuI3 => 108.83/109.40 (exuI2 => 108.83/109.40 (inCongP => 108.83/109.40 (in__Cong => 108.83/109.40 (exuE3u => 108.83/109.40 ( 108.83/109.40 exu__Cong => 108.83/109.40 ( 108.83/109.40 emptyset__Cong => 108.83/109.40 ( 108.83/109.40 setadjoin__Cong => 108.83/109.40 ( 108.83/109.40 powerset__Cong => 108.83/109.40 ( 108.83/109.40 setunion__Cong => 108.83/109.40 ( 108.83/109.40 omega__Cong => 108.83/109.40 ( 108.83/109.40 exuEu => 108.83/109.40 ( 108.83/109.40 descr__Cong => 108.83/109.40 ( 108.83/109.40 dsetconstr__Cong => 108.83/109.40 ( 108.83/109.40 subsetI1 => 108.83/109.40 ( 108.83/109.40 eqimpsubset2 => 108.83/109.40 ( 108.83/109.40 eqimpsubset1 => 108.83/109.40 ( 108.83/109.40 subsetI2 => 108.83/109.40 ( 108.83/109.40 emptysetsubset => 108.83/109.40 ( 108.83/109.40 subsetE => 108.83/109.40 ( 108.83/109.40 subsetE2 => 108.83/109.40 ( 108.83/109.40 notsubsetI => 108.83/109.40 ( 108.83/109.40 notequalI1 => 108.83/109.40 ( 108.83/109.40 notequalI2 => 108.83/109.40 ( 108.83/109.40 subsetRefl => 108.83/109.40 ( 108.83/109.40 subsetTrans => 108.83/109.40 ( 108.83/109.40 setadjoinSub => 108.83/109.40 ( 108.83/109.40 setadjoinSub2 => 108.83/109.40 ( 108.83/109.40 subset2powerset => 108.83/109.40 ( 108.83/109.40 setextsub => 108.83/109.40 ( 108.83/109.40 subsetemptysetimpeq => 108.83/109.40 ( 108.83/109.40 powersetI1 => 108.83/109.40 ( 108.83/109.40 powersetE1 => 108.83/109.40 ( 108.83/109.40 inPowerset => 108.83/109.40 ( 108.83/109.40 powersetsubset => 108.83/109.40 ( 108.83/109.40 sepInPowerset => 108.83/109.40 ( 108.83/109.40 sepSubset => 108.83/109.40 ( 108.83/109.40 binunionIL => 108.83/109.40 ( 108.83/109.40 upairset2IR => 108.83/109.40 ( 108.83/109.40 binunionIR => 108.83/109.40 ( 108.83/109.40 binunionEcases => 108.83/109.40 ( 108.83/109.40 binunionE => 108.83/109.40 ( 108.83/109.40 binunionLsub => 108.83/109.40 ( 108.83/109.40 binunionRsub => 108.83/109.40 ( 108.83/109.40 binintersectI => 108.83/109.40 ( 108.83/109.40 binintersectSubset5 => 108.83/109.40 ( 108.83/109.40 binintersectEL => 108.83/109.40 ( 108.83/109.40 binintersectLsub => 108.83/109.40 ( 108.83/109.40 ![A,B]: 108.83/109.40 (subset( 108.83/109.40 A,B) => 108.83/109.40 (binintersect( 108.83/109.40 A,B) = A))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 108.83/109.40 tff(zf_stmt_0, conjecture, 108.83/109.40 ((![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))) => 108.83/109.40 ((![X5]: (~in(X5,emptyset))) => 108.83/109.40 ((![X6,X7,X8]: (in(X8,setadjoin(X6,X7)) <=> ((X8 = X6) | in(X8,X7)))) => 108.83/109.40 ((![X9,X10]: 108.83/109.40 (in(X10,powerset(X9)) <=> (![X11]: (in(X11,X10) => in(X11,X9))))) => 108.83/109.40 ((![X12,X13]: 108.83/109.40 (in(X13,setunion(X12)) <=> (?[X14]: (in(X13,X14) & in(X14,X12))))) => 108.83/109.40 (in(emptyset,omega) => 108.83/109.40 ((![X15]: (in(X15,omega) => in(setadjoin(X15,X15),omega))) => 108.83/109.40 ((![X16]: 108.83/109.40 ((in(emptyset,X16) & 108.83/109.40 (![X17]: 108.83/109.40 ((in(X17,omega) & in(X17,X16)) => 108.83/109.40 in(setadjoin(X17,X17),X16)))) => 108.83/109.40 (![X18]: (in(X18,omega) => in(X18,X16))))) => 108.83/109.40 ((![X19:(($i * $i) > $o),X20]: 108.83/109.40 ((![X21]: 108.83/109.40 (in(X21,X20) => 108.83/109.40 (?[X22]: 108.83/109.40 (X19(X21,X22) & (![X23]: (X19(X21,X23) => (X22 = X23))))))) => 108.83/109.40 (?[X24]: 108.83/109.40 (![X25]: 108.83/109.40 (in(X25,X24) <=> (?[X26]: (in(X26,X20) & X19(X26,X25)))))))) => 108.83/109.40 ((![X27]: 108.83/109.40 ((?[X28]: in(X28,X27)) => 108.83/109.40 (?[X29]: 108.83/109.40 (in(X29,X27) & (~(?[X30]: (in(X30,X29) & in(X30,X27)))))))) => 108.83/109.40 ((![X31]: 108.83/109.40 (?[X32]: 108.83/109.40 ((![X48]: 108.83/109.40 (in(X48,X32) => (![X49]: (in(X49,X48) => in(X49,X31))))) & 108.83/109.40 (![X45,X46]: 108.83/109.40 ((in(X45,X31) & in(X46,X31)) => 108.83/109.40 ((![X47]: 108.83/109.40 (in(X47,X32) => (in(X45,X47) <=> in(X46,X47)))) => 108.83/109.40 (X45 = X46)))) & 108.83/109.40 (![X41,X42]: 108.83/109.40 ((in(X41,X32) & in(X42,X32)) => 108.83/109.40 ((![X44]: (in(X44,X41) => in(X44,X42))) | 108.83/109.40 (![X43]: (in(X43,X42) => in(X43,X41)))))) & 108.83/109.40 (![X33]: 108.83/109.40 (((![X35]: (in(X35,X33) => in(X35,X31))) & 108.83/109.40 (?[X34]: in(X34,X33))) => 108.83/109.40 (?[X36,X37]: 108.83/109.40 (in(X36,X32) & in(X37,X33) & 108.83/109.40 (~(?[X40]: (in(X40,X36) & in(X40,X33)))) & 108.83/109.40 (![X38]: 108.83/109.40 (in(X38,X32) => 108.83/109.40 ((![X39]: (in(X39,X38) => in(X39,X36))) | 108.83/109.40 in(X37,X38))))))))))) => 108.83/109.40 ((![X50:($i > $o)]: 108.83/109.40 ((?[X51]: (X50(X51) & (![X52]: (X50(X52) => (X51 = X52))))) => 108.83/109.40 X50(descr('#ll_1'(X50))))) => 108.83/109.40 ((![X53,X54:($i > $o),X55]: 108.83/109.40 (in(X55,X53) => 108.83/109.40 (X54(X55) => in(X55,dsetconstr(X53,'#ll_1'(X54)))))) => 108.83/109.40 ((![X56,X57:($i > $o),X58]: 108.83/109.40 (in(X58,dsetconstr(X56,'#ll_1'(X57))) => in(X58,X56))) => 108.83/109.40 ((![X59,X60:($i > $o),X61]: 108.83/109.40 (in(X61,dsetconstr(X59,'#ll_1'(X60))) => X60(X61))) => 108.83/109.40 ((![X62:($i > $o)]: 108.83/109.40 ((?[X63]: 108.83/109.40 (X62(X63) & (![X64]: (X62(X64) => (X63 = X64))))) => 108.83/109.40 (?[X65]: 108.83/109.40 (X62(X65) & (![X66]: (X62(X66) => (X65 = X66))))))) => 108.83/109.40 ((![X67:$o,X68]: (in(X68,prop2set(X67)) => X67)) => 108.83/109.40 ((![X69]: (in(X69,emptyset) => (![X70:$o]: X70))) => 108.83/109.40 ((![X71]: (in(X71,emptyset) => $false)) => 108.83/109.40 ((![X72]: (~in(X72,emptyset))) => 108.83/109.40 ((![X73:($i > $o)]: 108.83/109.40 ((?[X74]: 108.83/109.40 (X73(X74) & (![X75]: (X73(X75) => (X74 = X75))))) => 108.83/109.40 (?[X76]: X73(X76)))) => 108.83/109.40 ((![X77,X78]: 108.83/109.40 ((![X79]: (in(X79,X77) => in(X79,X78))) => 108.83/109.40 ((![X80]: (in(X80,X78) => in(X80,X77))) => 108.83/109.40 (X77 = X78)))) => 108.83/109.40 ((![X81]: 108.83/109.40 ((![X82]: (~in(X82,X81))) => (X81 = emptyset))) => 108.83/109.40 ((![X83]: 108.83/109.40 ((![X84]: (~in(X84,X83))) => (X83 = emptyset))) => 108.83/109.40 ((![X85,X86:($i > $o),X87]: 108.83/109.40 (in(X87,X85) => 108.83/109.40 (in(X87,dsetconstr(X85,'#ll_1'(X86))) <=> 108.83/109.40 X86(X87)))) => 108.83/109.40 ((![X88]: 108.83/109.40 ((X88 != emptyset) => (?[X89]: in(X89,X88)))) => 108.83/109.40 ((![X90,X91:($i > $o),X92]: 108.83/109.40 (in(X92,X90) => 108.83/109.40 (X91(X92) => 108.83/109.40 (dsetconstr(X90,'#ll_1'(X91)) != emptyset)))) => 108.83/109.40 ((![X93]: 108.83/109.40 ((?[X94]: in(X94,X93)) => (X93 != emptyset))) => 108.83/109.40 ((![X95,X96]: in(X95,setadjoin(X95,X96))) => 108.83/109.40 (in(emptyset,setadjoin(emptyset,emptyset)) => 108.83/109.40 ((![X97,X98,X99]: 108.83/109.40 (in(X99,X98) => 108.83/109.40 in(X99,setadjoin(X97,X98)))) => 108.83/109.40 ((![X100,X101,X102]: 108.83/109.40 (in(X102,setadjoin(X100,X101)) => 108.83/109.40 (![X103:$o]: 108.83/109.40 (((X102 = X100) => X103) => 108.83/109.40 ((in(X102,X101) => X103) => X103))))) => 108.83/109.40 ((![X104,X105,X106]: 108.83/109.40 (in(X106,setadjoin(X104,X105)) => 108.83/109.40 ((X106 = X104) | in(X106,X105)))) => 108.83/109.40 ((![X107]: 108.83/109.40 (dsetconstr(X107,'#ll_2') = X107)) => 108.83/109.40 ((![X108,X109]: 108.83/109.40 ((![X110]: 108.83/109.40 (in(X110,X109) => in(X110,X108))) => 108.83/109.40 in(X109,powerset(X108)))) => 108.83/109.40 ((![X111]: in(emptyset,powerset(X111))) => 108.83/109.41 ((![X112]: in(emptyset,powerset(X112))) => 108.83/109.41 ((![X113,X114,X115]: 108.83/109.41 (in(X114,powerset(X113)) => 108.83/109.41 (in(X115,X114) => in(X115,X113)))) => 108.83/109.41 ((![X116,X117,X118]: 108.83/109.41 (in(X117,X118) => 108.83/109.41 (in(X118,X116) => 108.83/109.41 in(X117,setunion(X116))))) => 108.83/109.41 ((![X119,X120]: 108.83/109.41 (in(X120,setunion(X119)) => 108.83/109.41 (![X121:$o]: 108.83/109.41 ((![X122]: 108.83/109.41 (in(X120,X122) => 108.83/109.41 (in(X122,X119) => X121))) => 108.83/109.41 X121)))) => 108.83/109.41 ((![X123,X124]: 108.83/109.41 (in(X124,X123) => 108.83/109.41 in(X124, 108.83/109.41 powerset(setunion(X123))))) => 108.83/109.41 ((![X125:($i > $o)]: 108.83/109.41 ((?[X126]: 108.83/109.41 (X125(X126) & 108.83/109.41 (![X127]: 108.83/109.41 (X125(X127) => 108.83/109.41 (X126 = X127))))) => 108.83/109.41 (?[X128]: 108.83/109.41 (![X129]: 108.83/109.41 (X125(X129) <=> 108.83/109.41 (X129 = X128)))))) => 108.83/109.41 ((![X130]: 108.83/109.41 ((X130 != emptyset) => 108.83/109.41 (?[X131]: in(X131,X130)))) => 108.83/109.41 ((![X132,X133]: 108.83/109.41 (in(X132, 108.83/109.41 setadjoin(X133,emptyset)) => 108.83/109.41 (X132 = X133))) => 108.83/109.41 ((![X134,X135]: 108.83/109.41 ((X134 != X135) => 108.83/109.41 (~ 108.83/109.41 in(X135, 108.83/109.41 setadjoin(X134, 108.83/109.41 emptyset))))) => 108.83/109.41 ((![X136,X137]: 108.83/109.41 ((X136 = X137) => 108.83/109.41 in(X136, 108.83/109.41 setadjoin(X137, 108.83/109.41 emptyset)))) => 108.83/109.41 ((![X138,X139]: 108.83/109.41 (in(X138, 108.83/109.41 setadjoin(X139, 108.83/109.41 emptyset)) => 108.83/109.41 in(X139, 108.83/109.41 setadjoin(X138, 108.83/109.41 emptyset)))) => 108.83/109.41 ((![X140,X141,X142]: 108.83/109.41 (in(X142, 108.83/109.41 setadjoin(X140, 108.83/109.41 setadjoin( 108.83/109.41 X141, 108.83/109.41 emptyset))) => 108.83/109.41 ((X142 = X140) | 108.83/109.41 (X142 = X141)))) => 108.83/109.41 ((![X143,X144]: 108.83/109.41 in(X143, 108.83/109.41 setadjoin(X143, 108.83/109.41 setadjoin( 108.83/109.41 X144, 108.83/109.41 emptyset)))) => 108.83/109.41 ((![X145,X146]: 108.83/109.41 in(X146, 108.83/109.41 setadjoin(X145, 108.83/109.41 setadjoin( 108.83/109.41 X146, 108.83/109.41 emptyset)))) => 108.83/109.41 ((![X147,X148:($i > $o)]: 108.83/109.41 ((?[X149]: 108.83/109.41 (in(X149,X147) & 108.83/109.41 X148(X149))) => 108.83/109.41 ((dsetconstr( 108.83/109.41 X147,'#ll_1'(X148)) = 108.83/109.41 emptyset) => 108.83/109.41 $false))) => 108.83/109.41 ((![X150:($i > $o),X151]: 108.83/109.41 (in(X151,emptyset) => 108.83/109.41 X150(X151))) => 108.83/109.41 ((![X152,X153:($i > $o)]: 108.83/109.41 ((~ 108.83/109.41 (![X154]: 108.83/109.41 (in(X154,X152) => 108.83/109.41 X153(X154)))) => 108.83/109.41 (?[X155]: 108.83/109.41 (in(X155,X152) & 108.83/109.41 (~X153(X155)))))) => 108.83/109.41 ((![X156, 108.83/109.41 X157:($i > $o)]: 108.83/109.41 ((![X158]: 108.83/109.41 (in(X158,X156) => 108.83/109.41 (~X157(X158)))) => 108.83/109.41 (~ 108.83/109.41 (?[X159]: 108.83/109.41 (in( 108.83/109.41 X159,X156) & 108.83/109.41 X157(X159)))))) => 108.83/109.41 ((![X160, 108.83/109.41 X161:($i > $o)]: 108.83/109.41 ((~ 108.83/109.41 (?[X162]: 108.83/109.41 (in( 108.83/109.41 X162,X160) & 108.83/109.41 X161(X162)))) => 108.83/109.41 (![X163]: 108.83/109.41 (in(X163,X160) => 108.83/109.41 (~X161(X163)))))) => 108.83/109.41 ((![X164, 108.83/109.41 X165:($i > $o)]: 108.83/109.41 ((?[X166]: 108.83/109.41 (in( 108.83/109.41 X166,X164) & 108.83/109.41 (~ 108.83/109.41 X165( 108.83/109.41 X166)))) => 108.83/109.41 (~ 108.83/109.41 (![X167]: 108.83/109.41 (in( 108.83/109.41 X167,X164) => 108.83/109.41 X165( 108.83/109.41 X167)))))) => 108.83/109.41 ((![X168:$o]: 108.83/109.41 (X168 => 108.83/109.41 in(emptyset, 108.83/109.41 prop2set( 108.83/109.41 X168)))) => 108.83/109.41 ((![X169:$o]: 108.83/109.41 (X169 => 108.83/109.41 set2prop( 108.83/109.41 prop2set( 108.83/109.41 X169)))) => 108.83/109.41 ((![X170, 108.83/109.41 X171:( 108.83/109.41 $i > $o)]: 108.83/109.41 ((~ 108.83/109.41 (?[X172]: 108.83/109.41 (in( 108.83/109.41 X172,X170) & 108.83/109.41 X171( 108.83/109.41 X172)))) => 108.83/109.41 (![X173]: 108.83/109.41 ( 108.83/109.41 in( 108.83/109.41 X173,X170) => 108.83/109.41 ( 108.83/109.41 ~ 108.83/109.41 X171( 108.83/109.41 X173)))))) => 108.83/109.41 ((![X174, 108.83/109.41 X175:( 108.83/109.41 $i > $o)]: 108.83/109.41 ((~ 108.83/109.41 ( 108.83/109.41 ![X176]: 108.83/109.41 (in( 108.83/109.41 X176,X174) => 108.83/109.41 X175( 108.83/109.41 X176)))) => 108.83/109.41 (?[X177]: 108.83/109.41 (in( 108.83/109.41 X177,X174) & 108.83/109.41 (~ 108.83/109.41 X175( 108.83/109.41 X177)))))) => 108.83/109.41 ((![X178:( 108.83/109.41 $i > $o)]: 108.83/109.41 ((?[X179]: 108.83/109.41 (X178( 108.83/109.41 X179) & 108.83/109.41 (![X180]: 108.83/109.41 (X178( 108.83/109.41 X180) => 108.83/109.41 (X179 = 108.83/109.41 X180))))) => 108.83/109.41 (?[X181]: 108.83/109.41 (X178( 108.83/109.41 X181) & 108.83/109.41 (![X182]: 108.83/109.41 (X178( 108.83/109.41 X182) => 108.83/109.41 (X181 = 108.83/109.41 X182))))))) => 108.83/109.41 ((![X183:( 108.83/109.41 $i > $o)]: 108.83/109.41 (( 108.83/109.41 ?[X184]: 108.83/109.41 X183( 108.83/109.41 X184)) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X185, 108.83/109.41 X186]: 108.83/109.41 (X183( 108.83/109.41 X185) => 108.83/109.41 (X183( 108.83/109.41 X186) => 108.83/109.41 (X185 = 108.83/109.41 X186)))) => 108.83/109.41 ( 108.83/109.41 ?[X187]: 108.83/109.41 (X183( 108.83/109.41 X187) & 108.83/109.41 (![X188]: 108.83/109.41 (X183( 108.83/109.41 X188) => 108.83/109.41 (X187 = 108.83/109.41 X188)))))))) => 108.83/109.41 ((![X189:( 108.83/109.41 $i > $o)]: 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ?[X190]: 108.83/109.41 (![X191]: 108.83/109.41 (X189( 108.83/109.41 X191) <=> 108.83/109.41 (X191 = 108.83/109.41 X190)))) => 108.83/109.41 ( 108.83/109.41 ?[X192]: 108.83/109.41 (X189( 108.83/109.41 X192) & 108.83/109.41 (![X193]: 108.83/109.41 (X189( 108.83/109.41 X193) => 108.83/109.41 (X192 = 108.83/109.41 X193))))))) => 108.83/109.41 ((![X194, 108.83/109.41 X195]: 108.83/109.41 (( 108.83/109.41 X194 = 108.83/109.41 X195) => 108.83/109.41 (![X196, 108.83/109.41 X197]: 108.83/109.41 (( 108.83/109.41 X196 = 108.83/109.41 X197) => 108.83/109.41 (in( 108.83/109.41 X196,X194) => 108.83/109.41 in( 108.83/109.41 X197,X195)))))) => 108.83/109.41 ((![X198, 108.83/109.41 X199]: 108.83/109.41 (( 108.83/109.41 X198 = 108.83/109.41 X199) => 108.83/109.41 (![X200, 108.83/109.41 X201]: 108.83/109.41 (( 108.83/109.41 X200 = 108.83/109.41 X201) => 108.83/109.41 (in( 108.83/109.41 X200,X198) <=> 108.83/109.41 in( 108.83/109.41 X201,X199)))))) => 108.83/109.41 (( 108.83/109.41 ![X202:( 108.83/109.41 $i > $o)]: 108.83/109.41 (( 108.83/109.41 ?[X203]: 108.83/109.41 (X202( 108.83/109.41 X203) & 108.83/109.41 (![X204]: 108.83/109.41 (X202( 108.83/109.41 X204) => 108.83/109.41 (X203 = 108.83/109.41 X204))))) => 108.83/109.41 (![X205, 108.83/109.41 X206]: 108.83/109.41 (X202( 108.83/109.41 X205) => 108.83/109.41 (X202( 108.83/109.41 X206) => 108.83/109.41 (X205 = 108.83/109.41 X206)))))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X207:( 108.83/109.41 $i > $o), 108.83/109.41 X208:( 108.83/109.41 $i > $o)]: 108.83/109.41 (( 108.83/109.41 ![X209, 108.83/109.41 X210]: 108.83/109.41 (( 108.83/109.41 X209 = 108.83/109.41 X210) => 108.83/109.41 (X207( 108.83/109.41 X209) <=> 108.83/109.41 X208( 108.83/109.41 X210)))) => 108.83/109.41 (( 108.83/109.41 ?[X211]: 108.83/109.41 (X207( 108.83/109.41 X211) & 108.83/109.41 (![X212]: 108.83/109.41 (X207( 108.83/109.41 X212) => 108.83/109.41 (X211 = 108.83/109.41 X212))))) <=> 108.83/109.41 (?[X213]: 108.83/109.41 (X208( 108.83/109.41 X213) & 108.83/109.41 (![X214]: 108.83/109.41 (X208( 108.83/109.41 X214) => 108.83/109.41 (X213 = 108.83/109.41 X214)))))))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 emptyset = 108.83/109.41 emptyset) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X215, 108.83/109.41 X216]: 108.83/109.41 (( 108.83/109.41 X215 = 108.83/109.41 X216) => 108.83/109.41 (![X217, 108.83/109.41 X218]: 108.83/109.41 (( 108.83/109.41 X217 = 108.83/109.41 X218) => 108.83/109.41 (setadjoin( 108.83/109.41 X215,X217) = 108.83/109.41 setadjoin( 108.83/109.41 X216,X218)))))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X219, 108.83/109.41 X220]: 108.83/109.41 (( 108.83/109.41 X219 = 108.83/109.41 X220) => 108.83/109.41 (powerset( 108.83/109.41 X219) = 108.83/109.41 powerset( 108.83/109.41 X220)))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X221, 108.83/109.41 X222]: 108.83/109.41 (( 108.83/109.41 X221 = 108.83/109.41 X222) => 108.83/109.41 (setunion( 108.83/109.41 X221) = 108.83/109.41 setunion( 108.83/109.41 X222)))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 omega = 108.83/109.41 omega) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X223:( 108.83/109.41 $i > $o)]: 108.83/109.41 (( 108.83/109.41 ?[X224]: 108.83/109.41 (X223( 108.83/109.41 X224) & 108.83/109.41 (![X225]: 108.83/109.41 (X223( 108.83/109.41 X225) => 108.83/109.41 (X224 = 108.83/109.41 X225))))) => 108.83/109.41 (![X226, 108.83/109.41 X227]: 108.83/109.41 (X223( 108.83/109.41 X226) => 108.83/109.41 (X223( 108.83/109.41 X227) => 108.83/109.41 (X226 = 108.83/109.41 X227)))))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X228:( 108.83/109.41 $i > $o), 108.83/109.41 X229:( 108.83/109.41 $i > $o)]: 108.83/109.41 (( 108.83/109.41 ![X230, 108.83/109.41 X231]: 108.83/109.41 (( 108.83/109.41 X230 = 108.83/109.41 X231) => 108.83/109.41 (X228( 108.83/109.41 X230) <=> 108.83/109.41 X229( 108.83/109.41 X231)))) => 108.83/109.41 (( 108.83/109.41 ?[X232]: 108.83/109.41 (X228( 108.83/109.41 X232) & 108.83/109.41 (![X233]: 108.83/109.41 (X228( 108.83/109.41 X233) => 108.83/109.41 (X232 = 108.83/109.41 X233))))) => 108.83/109.41 (( 108.83/109.41 ?[X234]: 108.83/109.41 (X229( 108.83/109.41 X234) & 108.83/109.41 (![X235]: 108.83/109.41 (X229( 108.83/109.41 X235) => 108.83/109.41 (X234 = 108.83/109.41 X235))))) => 108.83/109.41 (descr( 108.83/109.41 '#ll_1'( 108.83/109.41 X228)) = 108.83/109.41 descr( 108.83/109.41 '#ll_1'( 108.83/109.41 X229))))))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X236, 108.83/109.41 X237]: 108.83/109.41 (( 108.83/109.41 X236 = 108.83/109.41 X237) => 108.83/109.41 (![X238:( 108.83/109.41 $i > $o), 108.83/109.41 X239:( 108.83/109.41 $i > $o)]: 108.83/109.41 (( 108.83/109.41 ![X240]: 108.83/109.41 (in( 108.83/109.41 X240,X236) => 108.83/109.41 (![X241]: 108.83/109.41 (in( 108.83/109.41 X241,X237) => 108.83/109.41 (( 108.83/109.41 X240 = 108.83/109.41 X241) => 108.83/109.41 (X238( 108.83/109.41 X240) <=> 108.83/109.41 X239( 108.83/109.41 X241))))))) => 108.83/109.41 (dsetconstr( 108.83/109.41 X236, 108.83/109.41 '#ll_1'( 108.83/109.41 X238)) = 108.83/109.41 dsetconstr( 108.83/109.41 X237, 108.83/109.41 '#ll_1'( 108.83/109.41 X239))))))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X242, 108.83/109.41 X243]: 108.83/109.41 (( 108.83/109.41 ![X244]: 108.83/109.41 (in( 108.83/109.41 X244,X242) => 108.83/109.41 in( 108.83/109.41 X244,X243))) => 108.83/109.41 subset( 108.83/109.41 X242,X243))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X245, 108.83/109.41 X246]: 108.83/109.41 (( 108.83/109.41 X245 = 108.83/109.41 X246) => 108.83/109.41 subset( 108.83/109.41 X246,X245))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X247, 108.83/109.41 X248]: 108.83/109.41 (( 108.83/109.41 X247 = 108.83/109.41 X248) => 108.83/109.41 subset( 108.83/109.41 X247,X248))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X249, 108.83/109.41 X250]: 108.83/109.41 (( 108.83/109.41 ![X251]: 108.83/109.41 (in( 108.83/109.41 X251,X249) => 108.83/109.41 in( 108.83/109.41 X251,X250))) => 108.83/109.41 subset( 108.83/109.41 X249,X250))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X252]: 108.83/109.41 subset( 108.83/109.41 emptyset, 108.83/109.41 X252)) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X253, 108.83/109.41 X254,X255]: 108.83/109.41 (subset( 108.83/109.41 X253,X254) => 108.83/109.41 (in( 108.83/109.41 X255,X253) => 108.83/109.41 in( 108.83/109.41 X255,X254)))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X256, 108.83/109.41 X257,X258]: 108.83/109.41 (subset( 108.83/109.41 X256,X257) => 108.83/109.41 (( 108.83/109.41 ~ 108.83/109.41 in( 108.83/109.41 X258,X257)) => 108.83/109.41 (~ 108.83/109.41 in( 108.83/109.41 X258,X256))))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X259, 108.83/109.41 X260,X261]: 108.83/109.41 (in( 108.83/109.41 X261,X259) => 108.83/109.41 (( 108.83/109.41 ~ 108.83/109.41 in( 108.83/109.41 X261,X260)) => 108.83/109.41 (~ 108.83/109.41 subset( 108.83/109.41 X259,X260))))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X262, 108.83/109.41 X263]: 108.83/109.41 (( 108.83/109.41 ~ 108.83/109.41 subset( 108.83/109.41 X262,X263)) => 108.83/109.41 (X262 != 108.83/109.41 X263))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X264, 108.83/109.41 X265,X266]: 108.83/109.41 (in( 108.83/109.41 X266,X264) => 108.83/109.41 (( 108.83/109.41 ~ 108.83/109.41 in( 108.83/109.41 X266,X265)) => 108.83/109.41 (X264 != 108.83/109.41 X265)))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X267]: 108.83/109.41 subset( 108.83/109.41 X267,X267)) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X268, 108.83/109.41 X269,X270]: 108.83/109.41 (subset( 108.83/109.41 X268,X269) => 108.83/109.41 (subset( 108.83/109.41 X269,X270) => 108.83/109.41 subset( 108.83/109.41 X268,X270)))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X271, 108.83/109.41 X272]: 108.83/109.41 subset( 108.83/109.41 X272, 108.83/109.41 setadjoin( 108.83/109.41 X271,X272))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X273, 108.83/109.41 X274,X275]: 108.83/109.41 (subset( 108.83/109.41 X273,X275) => 108.83/109.41 subset( 108.83/109.41 X273, 108.83/109.41 setadjoin( 108.83/109.41 X274,X275)))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X276, 108.83/109.41 X277]: 108.83/109.41 (subset( 108.83/109.41 X276,X277) => 108.83/109.41 in( 108.83/109.41 X276, 108.83/109.41 powerset( 108.83/109.41 X277)))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X278, 108.83/109.41 X279]: 108.83/109.41 (subset( 108.83/109.41 X278,X279) => 108.83/109.41 (subset( 108.83/109.41 X279,X278) => 108.83/109.41 (X278 = 108.83/109.41 X279)))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X280]: 108.83/109.41 (subset( 108.83/109.41 X280, 108.83/109.41 emptyset) => 108.83/109.41 (X280 = 108.83/109.41 emptyset))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X281, 108.83/109.41 X282]: 108.83/109.41 (subset( 108.83/109.41 X282,X281) => 108.83/109.41 in( 108.83/109.41 X282, 108.83/109.41 powerset( 108.83/109.41 X281)))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X283, 108.83/109.41 X284]: 108.83/109.41 (in( 108.83/109.41 X284, 108.83/109.41 powerset( 108.83/109.41 X283)) => 108.83/109.41 subset( 108.83/109.41 X284,X283))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X285]: 108.83/109.41 in( 108.83/109.41 X285, 108.83/109.41 powerset( 108.83/109.41 X285))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X286, 108.83/109.41 X287]: 108.83/109.41 (subset( 108.83/109.41 X286,X287) => 108.83/109.41 subset( 108.83/109.41 powerset( 108.83/109.41 X286), 108.83/109.41 powerset( 108.83/109.41 X287)))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X288, 108.83/109.41 X289:( 108.83/109.41 $i > $o)]: 108.83/109.41 in( 108.83/109.41 dsetconstr( 108.83/109.41 X288, 108.83/109.41 '#ll_1'( 108.83/109.41 X289)), 108.83/109.41 powerset( 108.83/109.41 X288))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X290, 108.83/109.41 X291:( 108.83/109.41 $i > $o)]: 108.83/109.41 subset( 108.83/109.41 dsetconstr( 108.83/109.41 X290, 108.83/109.41 '#ll_1'( 108.83/109.41 X291)), 108.83/109.41 X290)) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X292, 108.83/109.41 X293,X294]: 108.83/109.41 (in( 108.83/109.41 X294,X292) => 108.83/109.41 in( 108.83/109.41 X294, 108.83/109.41 binunion( 108.83/109.41 X292,X293)))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X295, 108.83/109.41 X296]: 108.83/109.41 in( 108.83/109.41 X296, 108.83/109.41 setadjoin( 108.83/109.41 X295, 108.83/109.41 setadjoin( 108.83/109.41 X296, 108.83/109.41 emptyset)))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X297, 108.83/109.41 X298,X299]: 108.83/109.41 (in( 108.83/109.41 X299,X298) => 108.83/109.41 in( 108.83/109.41 X299, 108.83/109.41 binunion( 108.83/109.41 X297,X298)))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X300, 108.83/109.41 X301, 108.83/109.41 X302, 108.83/109.41 X303:$o]: 108.83/109.41 (in( 108.83/109.41 X302, 108.83/109.41 binunion( 108.83/109.41 X300,X301)) => 108.83/109.41 (( 108.83/109.41 in( 108.83/109.41 X302,X300) => 108.83/109.41 X303) => 108.83/109.41 (( 108.83/109.41 in( 108.83/109.41 X302,X301) => 108.83/109.41 X303) => 108.83/109.41 X303)))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X304, 108.83/109.41 X305,X306]: 108.83/109.41 (in( 108.83/109.41 X306, 108.83/109.41 binunion( 108.83/109.41 X304,X305)) => 108.83/109.41 (in( 108.83/109.41 X306,X304) | 108.83/109.41 in( 108.83/109.41 X306,X305)))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X307, 108.83/109.41 X308]: 108.83/109.41 subset( 108.83/109.41 X307, 108.83/109.41 binunion( 108.83/109.41 X307,X308))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X309, 108.83/109.41 X310]: 108.83/109.41 subset( 108.83/109.41 X310, 108.83/109.41 binunion( 108.83/109.41 X309,X310))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X311, 108.83/109.41 X312,X313]: 108.83/109.41 (in( 108.83/109.41 X313,X311) => 108.83/109.41 (in( 108.83/109.41 X313,X312) => 108.83/109.41 in( 108.83/109.41 X313, 108.83/109.41 dsetconstr( 108.83/109.41 X311, 108.83/109.41 '#ll_0'( 108.83/109.41 X312)))))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X314, 108.83/109.41 X315,X316]: 108.83/109.41 (subset( 108.83/109.41 X316,X314) => 108.83/109.41 (subset( 108.83/109.41 X316,X315) => 108.83/109.41 subset( 108.83/109.41 X316, 108.83/109.41 dsetconstr( 108.83/109.41 X314, 108.83/109.41 '#ll_0'( 108.83/109.41 X315)))))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X317, 108.83/109.41 X318,X319]: 108.83/109.41 (in( 108.83/109.41 X319, 108.83/109.41 dsetconstr( 108.83/109.41 X317, 108.83/109.41 '#ll_0'( 108.83/109.41 X318))) => 108.83/109.41 in( 108.83/109.41 X319,X317))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X320, 108.83/109.41 X321]: 108.83/109.41 subset( 108.83/109.41 dsetconstr( 108.83/109.41 X320, 108.83/109.41 '#ll_0'( 108.83/109.41 X321)), 108.83/109.41 X320)) => 108.83/109.41 ( 108.83/109.41 ![X322, 108.83/109.41 X323]: 108.83/109.41 (subset( 108.83/109.41 X322,X323) => 108.83/109.41 (dsetconstr( 108.83/109.41 X322, 108.83/109.41 '#ll_0'( 108.83/109.41 X323)) = 108.83/109.41 X322))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 108.83/109.41 tff(zf_stmt_1, type, zip_tseitin5 : ($i * $i > $o) > $o). 108.83/109.41 tff(zf_stmt_2, axiom, 108.83/109.41 (zip_tseitin5(X211,X207) <=> 108.83/109.41 ((![X212]: zip_tseitin4(X212,X211,X207)) & X207(X211)))). 108.83/109.41 tff(zf_stmt_3, type, zip_tseitin4 : ($i * $i * $i > $o) > $o). 108.83/109.41 tff(zf_stmt_4, axiom, 108.83/109.41 (zip_tseitin4(X212,X211,X207) <=> (X207(X212) => (X211 = X212)))). 108.83/109.41 tff(zf_stmt_5, type, zip_tseitin3 : ($i * $i * $i * ($i * $i) > $o) > $o). 108.83/109.41 tff(zf_stmt_6, axiom, 108.83/109.41 (zip_tseitin3(X26,X25,X20,X19) <=> (X19(X26,X25) & in(X26,X20)))). 108.83/109.41 tff(zf_stmt_7, type, zip_tseitin2 : ($i * $i * $i) > $o). 108.83/109.41 tff(zf_stmt_8, axiom, 108.83/109.41 (zip_tseitin2(X14,X13,X12) <=> (in(X14,X12) & in(X13,X14)))). 108.83/109.41 tff(zf_stmt_9, type, zip_tseitin1 : ($i * $i * $i) > $o). 108.83/109.41 tff(zf_stmt_10, axiom, 108.83/109.41 (zip_tseitin1(X11,X10,X9) <=> (in(X11,X10) => in(X11,X9)))). 108.83/109.41 tff(zf_stmt_11, type, zip_tseitin0 : ($i * $i * $i) > $o). 108.83/109.41 tff(zf_stmt_12, axiom, (zip_tseitin0(X8,X7,X6) <=> (in(X8,X7) | (X8 = X6)))). 108.83/109.41 tff(zf_stmt_13, conjecture, 108.83/109.41 ((![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))) => 108.83/109.41 ((![X5]: (~in(X5,emptyset))) => 108.83/109.41 ((![X6,X7,X8]: (in(X8,setadjoin(X6,X7)) <=> zip_tseitin0(X8,X7,X6))) => 108.83/109.41 ((![X9,X10]: 108.83/109.41 (in(X10,powerset(X9)) <=> (![X11]: zip_tseitin1(X11,X10,X9)))) => 108.83/109.41 ((![X12,X13]: 108.83/109.41 (in(X13,setunion(X12)) <=> (?[X14]: zip_tseitin2(X14,X13,X12)))) => 108.83/109.41 (in(emptyset,omega) => 108.83/109.41 ((![X15]: (in(X15,omega) => in(setadjoin(X15,X15),omega))) => 108.83/109.41 ((![X16]: 108.83/109.41 (((![X17]: 108.83/109.41 ((in(X17,X16) & in(X17,omega)) => 108.83/109.41 in(setadjoin(X17,X17),X16))) & 108.83/109.41 in(emptyset,X16)) => 108.83/109.41 (![X18]: (in(X18,omega) => in(X18,X16))))) => 108.83/109.41 ((![X19:(($i * $i) > $o),X20]: 108.83/109.41 ((![X21]: 108.83/109.41 (in(X21,X20) => 108.83/109.41 (?[X22]: 108.83/109.41 ((![X23]: (X19(X21,X23) => (X22 = X23))) & X19(X21,X22))))) => 108.83/109.41 (?[X24]: 108.83/109.41 (![X25]: 108.83/109.41 (in(X25,X24) <=> (?[X26]: zip_tseitin3(X26,X25,X20,X19))))))) => 108.83/109.41 ((![X27]: 108.83/109.41 ((?[X28]: in(X28,X27)) => 108.83/109.41 (?[X29]: 108.83/109.41 ((~(?[X30]: (in(X30,X27) & in(X30,X29)))) & in(X29,X27))))) => 108.83/109.41 ((![X31]: 108.83/109.41 (?[X32]: 108.83/109.41 ((![X33]: 108.83/109.41 (((?[X34]: in(X34,X33)) & 108.83/109.41 (![X35]: (in(X35,X33) => in(X35,X31)))) => 108.83/109.41 (?[X36,X37]: 108.83/109.41 ((![X38]: 108.83/109.41 (in(X38,X32) => 108.83/109.41 (in(X37,X38) | 108.83/109.41 (![X39]: (in(X39,X38) => in(X39,X36)))))) & 108.83/109.41 (~(?[X40]: (in(X40,X33) & in(X40,X36)))) & 108.83/109.41 in(X37,X33) & in(X36,X32))))) & 108.83/109.41 (![X41,X42]: 108.83/109.41 ((in(X42,X32) & in(X41,X32)) => 108.83/109.41 ((![X43]: (in(X43,X42) => in(X43,X41))) | 108.83/109.41 (![X44]: (in(X44,X41) => in(X44,X42)))))) & 108.83/109.41 (![X45,X46]: 108.83/109.41 ((in(X46,X31) & in(X45,X31)) => 108.83/109.41 ((![X47]: 108.83/109.41 (in(X47,X32) => (in(X45,X47) <=> in(X46,X47)))) => 108.83/109.41 (X45 = X46)))) & 108.83/109.41 (![X48]: 108.83/109.41 (in(X48,X32) => (![X49]: (in(X49,X48) => in(X49,X31)))))))) => 108.83/109.41 ((![X50:($i > $o)]: 108.83/109.41 ((?[X51]: ((![X52]: (X50(X52) => (X51 = X52))) & X50(X51))) => 108.83/109.41 X50(descr('#ll_1'(X50))))) => 108.83/109.41 ((![X53,X54:($i > $o),X55]: 108.83/109.41 (in(X55,X53) => 108.83/109.41 (X54(X55) => in(X55,dsetconstr(X53,'#ll_1'(X54)))))) => 108.83/109.41 ((![X56,X57:($i > $o),X58]: 108.83/109.41 (in(X58,dsetconstr(X56,'#ll_1'(X57))) => in(X58,X56))) => 108.83/109.41 ((![X59,X60:($i > $o),X61]: 108.83/109.41 (in(X61,dsetconstr(X59,'#ll_1'(X60))) => X60(X61))) => 108.83/109.41 ((![X62:($i > $o)]: 108.83/109.41 ((?[X63]: 108.83/109.41 ((![X64]: (X62(X64) => (X63 = X64))) & X62(X63))) => 108.83/109.41 (?[X65]: 108.83/109.41 ((![X66]: (X62(X66) => (X65 = X66))) & X62(X65))))) => 108.83/109.41 ((![X67:$o,X68]: (in(X68,prop2set(X67)) => X67)) => 108.83/109.41 ((![X69]: (in(X69,emptyset) => (![X70:$o]: X70))) => 108.83/109.41 ((![X71]: (in(X71,emptyset) => $false)) => 108.83/109.41 ((![X72]: (~in(X72,emptyset))) => 108.83/109.41 ((![X73:($i > $o)]: 108.83/109.41 ((?[X74]: 108.83/109.41 ((![X75]: (X73(X75) => (X74 = X75))) & X73(X74))) => 108.83/109.41 (?[X76]: X73(X76)))) => 108.83/109.41 ((![X77,X78]: 108.83/109.41 ((![X79]: (in(X79,X77) => in(X79,X78))) => 108.83/109.41 ((![X80]: (in(X80,X78) => in(X80,X77))) => 108.83/109.41 (X77 = X78)))) => 108.83/109.41 ((![X81]: 108.83/109.41 ((![X82]: (~in(X82,X81))) => (X81 = emptyset))) => 108.83/109.41 ((![X83]: 108.83/109.41 ((![X84]: (~in(X84,X83))) => (X83 = emptyset))) => 108.83/109.41 ((![X85,X86:($i > $o),X87]: 108.83/109.41 (in(X87,X85) => 108.83/109.41 (in(X87,dsetconstr(X85,'#ll_1'(X86))) <=> 108.83/109.41 X86(X87)))) => 108.83/109.41 ((![X88]: 108.83/109.41 ((X88 != emptyset) => (?[X89]: in(X89,X88)))) => 108.83/109.41 ((![X90,X91:($i > $o),X92]: 108.83/109.41 (in(X92,X90) => 108.83/109.41 (X91(X92) => 108.83/109.41 (dsetconstr(X90,'#ll_1'(X91)) != emptyset)))) => 108.83/109.41 ((![X93]: 108.83/109.41 ((?[X94]: in(X94,X93)) => (X93 != emptyset))) => 108.83/109.41 ((![X95,X96]: in(X95,setadjoin(X95,X96))) => 108.83/109.41 (in(emptyset,setadjoin(emptyset,emptyset)) => 108.83/109.41 ((![X97,X98,X99]: 108.83/109.41 (in(X99,X98) => 108.83/109.41 in(X99,setadjoin(X97,X98)))) => 108.83/109.41 ((![X100,X101,X102]: 108.83/109.41 (in(X102,setadjoin(X100,X101)) => 108.83/109.41 (![X103:$o]: 108.83/109.41 (((X102 = X100) => X103) => 108.83/109.41 ((in(X102,X101) => X103) => X103))))) => 108.83/109.41 ((![X104,X105,X106]: 108.83/109.41 (in(X106,setadjoin(X104,X105)) => 108.83/109.41 (in(X106,X105) | (X106 = X104)))) => 108.83/109.41 ((![X107]: 108.83/109.41 (dsetconstr(X107,'#ll_2') = X107)) => 108.83/109.41 ((![X108,X109]: 108.83/109.41 ((![X110]: 108.83/109.41 (in(X110,X109) => in(X110,X108))) => 108.83/109.41 in(X109,powerset(X108)))) => 108.83/109.41 ((![X111]: in(emptyset,powerset(X111))) => 108.83/109.41 ((![X112]: in(emptyset,powerset(X112))) => 108.83/109.41 ((![X113,X114,X115]: 108.83/109.41 (in(X114,powerset(X113)) => 108.83/109.41 (in(X115,X114) => in(X115,X113)))) => 108.83/109.41 ((![X116,X117,X118]: 108.83/109.41 (in(X117,X118) => 108.83/109.41 (in(X118,X116) => 108.83/109.41 in(X117,setunion(X116))))) => 108.83/109.41 ((![X119,X120]: 108.83/109.41 (in(X120,setunion(X119)) => 108.83/109.41 (![X121:$o]: 108.83/109.41 ((![X122]: 108.83/109.41 (in(X120,X122) => 108.83/109.41 (in(X122,X119) => X121))) => 108.83/109.41 X121)))) => 108.83/109.41 ((![X123,X124]: 108.83/109.41 (in(X124,X123) => 108.83/109.41 in(X124, 108.83/109.41 powerset(setunion(X123))))) => 108.83/109.41 ((![X125:($i > $o)]: 108.83/109.41 ((?[X126]: 108.83/109.41 ((![X127]: 108.83/109.41 (X125(X127) => 108.83/109.41 (X126 = X127))) & 108.83/109.41 X125(X126))) => 108.83/109.41 (?[X128]: 108.83/109.41 (![X129]: 108.83/109.41 (X125(X129) <=> 108.83/109.41 (X129 = X128)))))) => 108.83/109.41 ((![X130]: 108.83/109.41 ((X130 != emptyset) => 108.83/109.41 (?[X131]: in(X131,X130)))) => 108.83/109.41 ((![X132,X133]: 108.83/109.41 (in(X132, 108.83/109.41 setadjoin(X133,emptyset)) => 108.83/109.41 (X132 = X133))) => 108.83/109.41 ((![X134,X135]: 108.83/109.41 ((X134 != X135) => 108.83/109.41 (~ 108.83/109.41 in(X135, 108.83/109.41 setadjoin(X134, 108.83/109.41 emptyset))))) => 108.83/109.41 ((![X136,X137]: 108.83/109.41 ((X136 = X137) => 108.83/109.41 in(X136, 108.83/109.41 setadjoin(X137, 108.83/109.41 emptyset)))) => 108.83/109.41 ((![X138,X139]: 108.83/109.41 (in(X138, 108.83/109.41 setadjoin(X139, 108.83/109.41 emptyset)) => 108.83/109.41 in(X139, 108.83/109.41 setadjoin(X138, 108.83/109.41 emptyset)))) => 108.83/109.41 ((![X140,X141,X142]: 108.83/109.41 (in(X142, 108.83/109.41 setadjoin(X140, 108.83/109.41 setadjoin( 108.83/109.41 X141, 108.83/109.41 emptyset))) => 108.83/109.41 ((X142 = X141) | 108.83/109.41 (X142 = X140)))) => 108.83/109.41 ((![X143,X144]: 108.83/109.41 in(X143, 108.83/109.41 setadjoin(X143, 108.83/109.41 setadjoin( 108.83/109.41 X144, 108.83/109.41 emptyset)))) => 108.83/109.41 ((![X145,X146]: 108.83/109.41 in(X146, 108.83/109.41 setadjoin(X145, 108.83/109.41 setadjoin( 108.83/109.41 X146, 108.83/109.41 emptyset)))) => 108.83/109.41 ((![X147,X148:($i > $o)]: 108.83/109.41 ((?[X149]: 108.83/109.41 (X148(X149) & 108.83/109.41 in(X149,X147))) => 108.83/109.41 ((dsetconstr( 108.83/109.41 X147,'#ll_1'(X148)) = 108.83/109.41 emptyset) => 108.83/109.41 $false))) => 108.83/109.41 ((![X150:($i > $o),X151]: 108.83/109.41 (in(X151,emptyset) => 108.83/109.41 X150(X151))) => 108.83/109.41 ((![X152,X153:($i > $o)]: 108.83/109.41 ((~ 108.83/109.41 (![X154]: 108.83/109.41 (in(X154,X152) => 108.83/109.41 X153(X154)))) => 108.83/109.41 (?[X155]: 108.83/109.41 ((~X153(X155)) & 108.83/109.41 in(X155,X152))))) => 108.83/109.41 ((![X156, 108.83/109.41 X157:($i > $o)]: 108.83/109.41 ((![X158]: 108.83/109.41 (in(X158,X156) => 108.83/109.41 (~X157(X158)))) => 108.83/109.41 (~ 108.83/109.41 (?[X159]: 108.83/109.41 (X157(X159) & 108.83/109.41 in( 108.83/109.41 X159,X156)))))) => 108.83/109.41 ((![X160, 108.83/109.41 X161:($i > $o)]: 108.83/109.41 ((~ 108.83/109.41 (?[X162]: 108.83/109.41 (X161(X162) & 108.83/109.41 in( 108.83/109.41 X162,X160)))) => 108.83/109.41 (![X163]: 108.83/109.41 (in(X163,X160) => 108.83/109.41 (~X161(X163)))))) => 108.83/109.41 ((![X164, 108.83/109.41 X165:($i > $o)]: 108.83/109.41 ((?[X166]: 108.83/109.41 ((~ 108.83/109.41 X165( 108.83/109.41 X166)) & 108.83/109.41 in( 108.83/109.41 X166,X164))) => 108.83/109.41 (~ 108.83/109.41 (![X167]: 108.83/109.41 (in( 108.83/109.41 X167,X164) => 108.83/109.41 X165( 108.83/109.41 X167)))))) => 108.83/109.41 ((![X168:$o]: 108.83/109.41 (X168 => 108.83/109.41 in(emptyset, 108.83/109.41 prop2set( 108.83/109.41 X168)))) => 108.83/109.41 ((![X169:$o]: 108.83/109.41 (X169 => 108.83/109.41 set2prop( 108.83/109.41 prop2set( 108.83/109.41 X169)))) => 108.83/109.41 ((![X170, 108.83/109.41 X171:( 108.83/109.41 $i > $o)]: 108.83/109.41 ((~ 108.83/109.41 (?[X172]: 108.83/109.41 (X171( 108.83/109.41 X172) & 108.83/109.41 in( 108.83/109.41 X172,X170)))) => 108.83/109.41 (![X173]: 108.83/109.41 ( 108.83/109.41 in( 108.83/109.41 X173,X170) => 108.83/109.41 ( 108.83/109.41 ~ 108.83/109.41 X171( 108.83/109.41 X173)))))) => 108.83/109.41 ((![X174, 108.83/109.41 X175:( 108.83/109.41 $i > $o)]: 108.83/109.41 ((~ 108.83/109.41 ( 108.83/109.41 ![X176]: 108.83/109.41 (in( 108.83/109.41 X176,X174) => 108.83/109.41 X175( 108.83/109.41 X176)))) => 108.83/109.41 (?[X177]: 108.83/109.41 (( 108.83/109.41 ~ 108.83/109.41 X175( 108.83/109.41 X177)) & 108.83/109.41 in( 108.83/109.41 X177,X174))))) => 108.83/109.41 ((![X178:( 108.83/109.41 $i > $o)]: 108.83/109.41 ((?[X179]: 108.83/109.41 (( 108.83/109.41 ![X180]: 108.83/109.41 (X178( 108.83/109.41 X180) => 108.83/109.41 (X179 = 108.83/109.41 X180))) & 108.83/109.41 X178( 108.83/109.41 X179))) => 108.83/109.41 (?[X181]: 108.83/109.41 (( 108.83/109.41 ![X182]: 108.83/109.41 (X178( 108.83/109.41 X182) => 108.83/109.41 (X181 = 108.83/109.41 X182))) & 108.83/109.41 X178( 108.83/109.41 X181))))) => 108.83/109.41 ((![X183:( 108.83/109.41 $i > $o)]: 108.83/109.41 (( 108.83/109.41 ?[X184]: 108.83/109.41 X183( 108.83/109.41 X184)) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X185, 108.83/109.41 X186]: 108.83/109.41 (X183( 108.83/109.41 X185) => 108.83/109.41 (X183( 108.83/109.41 X186) => 108.83/109.41 (X185 = 108.83/109.41 X186)))) => 108.83/109.41 ( 108.83/109.41 ?[X187]: 108.83/109.41 (( 108.83/109.41 ![X188]: 108.83/109.41 (X183( 108.83/109.41 X188) => 108.83/109.41 (X187 = 108.83/109.41 X188))) & 108.83/109.41 X183( 108.83/109.41 X187)))))) => 108.83/109.41 ((![X189:( 108.83/109.41 $i > $o)]: 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ?[X190]: 108.83/109.41 (![X191]: 108.83/109.41 (X189( 108.83/109.41 X191) <=> 108.83/109.41 (X191 = 108.83/109.41 X190)))) => 108.83/109.41 ( 108.83/109.41 ?[X192]: 108.83/109.41 (( 108.83/109.41 ![X193]: 108.83/109.41 (X189( 108.83/109.41 X193) => 108.83/109.41 (X192 = 108.83/109.41 X193))) & 108.83/109.41 X189( 108.83/109.41 X192))))) => 108.83/109.41 ((![X194, 108.83/109.41 X195]: 108.83/109.41 (( 108.83/109.41 X194 = 108.83/109.41 X195) => 108.83/109.41 (![X196, 108.83/109.41 X197]: 108.83/109.41 (( 108.83/109.41 X196 = 108.83/109.41 X197) => 108.83/109.41 (in( 108.83/109.41 X196,X194) => 108.83/109.41 in( 108.83/109.41 X197,X195)))))) => 108.83/109.41 ((![X198, 108.83/109.41 X199]: 108.83/109.41 (( 108.83/109.41 X198 = 108.83/109.41 X199) => 108.83/109.41 (![X200, 108.83/109.41 X201]: 108.83/109.41 (( 108.83/109.41 X200 = 108.83/109.41 X201) => 108.83/109.41 (in( 108.83/109.41 X200,X198) <=> 108.83/109.41 in( 108.83/109.41 X201,X199)))))) => 108.83/109.41 (( 108.83/109.41 ![X202:( 108.83/109.41 $i > $o)]: 108.83/109.41 (( 108.83/109.41 ?[X203]: 108.83/109.41 (( 108.83/109.41 ![X204]: 108.83/109.41 (X202( 108.83/109.41 X204) => 108.83/109.41 (X203 = 108.83/109.41 X204))) & 108.83/109.41 X202( 108.83/109.41 X203))) => 108.83/109.41 (![X205, 108.83/109.41 X206]: 108.83/109.41 (X202( 108.83/109.41 X205) => 108.83/109.41 (X202( 108.83/109.41 X206) => 108.83/109.41 (X205 = 108.83/109.41 X206)))))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X207:( 108.83/109.41 $i > $o), 108.83/109.41 X208:( 108.83/109.41 $i > $o)]: 108.83/109.41 (( 108.83/109.41 ![X209, 108.83/109.41 X210]: 108.83/109.41 (( 108.83/109.41 X209 = 108.83/109.41 X210) => 108.83/109.41 (X207( 108.83/109.41 X209) <=> 108.83/109.41 X208( 108.83/109.41 X210)))) => 108.83/109.41 (( 108.83/109.41 ?[X211]: 108.83/109.41 zip_tseitin5( 108.83/109.41 X211,X207)) <=> 108.83/109.41 (?[X213]: 108.83/109.41 zip_tseitin5( 108.83/109.41 X213,X208))))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 emptyset = 108.83/109.41 emptyset) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X215, 108.83/109.41 X216]: 108.83/109.41 (( 108.83/109.41 X215 = 108.83/109.41 X216) => 108.83/109.41 (![X217, 108.83/109.41 X218]: 108.83/109.41 (( 108.83/109.41 X217 = 108.83/109.41 X218) => 108.83/109.41 (setadjoin( 108.83/109.41 X215,X217) = 108.83/109.41 setadjoin( 108.83/109.41 X216,X218)))))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X219, 108.83/109.41 X220]: 108.83/109.41 (( 108.83/109.41 X219 = 108.83/109.41 X220) => 108.83/109.41 (powerset( 108.83/109.41 X219) = 108.83/109.41 powerset( 108.83/109.41 X220)))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X221, 108.83/109.41 X222]: 108.83/109.41 (( 108.83/109.41 X221 = 108.83/109.41 X222) => 108.83/109.41 (setunion( 108.83/109.41 X221) = 108.83/109.41 setunion( 108.83/109.41 X222)))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 omega = 108.83/109.41 omega) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X223:( 108.83/109.41 $i > $o)]: 108.83/109.41 (( 108.83/109.41 ?[X224]: 108.83/109.41 (( 108.83/109.41 ![X225]: 108.83/109.41 (X223( 108.83/109.41 X225) => 108.83/109.41 (X224 = 108.83/109.41 X225))) & 108.83/109.41 X223( 108.83/109.41 X224))) => 108.83/109.41 (![X226, 108.83/109.41 X227]: 108.83/109.41 (X223( 108.83/109.41 X226) => 108.83/109.41 (X223( 108.83/109.41 X227) => 108.83/109.41 (X226 = 108.83/109.41 X227)))))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X228:( 108.83/109.41 $i > $o), 108.83/109.41 X229:( 108.83/109.41 $i > $o)]: 108.83/109.41 (( 108.83/109.41 ![X230, 108.83/109.41 X231]: 108.83/109.41 (( 108.83/109.41 X230 = 108.83/109.41 X231) => 108.83/109.41 (X228( 108.83/109.41 X230) <=> 108.83/109.41 X229( 108.83/109.41 X231)))) => 108.83/109.41 (( 108.83/109.41 ?[X232]: 108.83/109.41 (( 108.83/109.41 ![X233]: 108.83/109.41 (X228( 108.83/109.41 X233) => 108.83/109.41 (X232 = 108.83/109.41 X233))) & 108.83/109.41 X228( 108.83/109.41 X232))) => 108.83/109.41 (( 108.83/109.41 ?[X234]: 108.83/109.41 (( 108.83/109.41 ![X235]: 108.83/109.41 (X229( 108.83/109.41 X235) => 108.83/109.41 (X234 = 108.83/109.41 X235))) & 108.83/109.41 X229( 108.83/109.41 X234))) => 108.83/109.41 (descr( 108.83/109.41 '#ll_1'( 108.83/109.41 X228)) = 108.83/109.41 descr( 108.83/109.41 '#ll_1'( 108.83/109.41 X229))))))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X236, 108.83/109.41 X237]: 108.83/109.41 (( 108.83/109.41 X236 = 108.83/109.41 X237) => 108.83/109.41 (![X238:( 108.83/109.41 $i > $o), 108.83/109.41 X239:( 108.83/109.41 $i > $o)]: 108.83/109.41 (( 108.83/109.41 ![X240]: 108.83/109.41 (in( 108.83/109.41 X240,X236) => 108.83/109.41 (![X241]: 108.83/109.41 (in( 108.83/109.41 X241,X237) => 108.83/109.41 (( 108.83/109.41 X240 = 108.83/109.41 X241) => 108.83/109.41 (X238( 108.83/109.41 X240) <=> 108.83/109.41 X239( 108.83/109.41 X241))))))) => 108.83/109.41 (dsetconstr( 108.83/109.41 X236, 108.83/109.41 '#ll_1'( 108.83/109.41 X238)) = 108.83/109.41 dsetconstr( 108.83/109.41 X237, 108.83/109.41 '#ll_1'( 108.83/109.41 X239))))))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X242, 108.83/109.41 X243]: 108.83/109.41 (( 108.83/109.41 ![X244]: 108.83/109.41 (in( 108.83/109.41 X244,X242) => 108.83/109.41 in( 108.83/109.41 X244,X243))) => 108.83/109.41 subset( 108.83/109.41 X242,X243))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X245, 108.83/109.41 X246]: 108.83/109.41 (( 108.83/109.41 X245 = 108.83/109.41 X246) => 108.83/109.41 subset( 108.83/109.41 X246,X245))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X247, 108.83/109.41 X248]: 108.83/109.41 (( 108.83/109.41 X247 = 108.83/109.41 X248) => 108.83/109.41 subset( 108.83/109.41 X247,X248))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X249, 108.83/109.41 X250]: 108.83/109.41 (( 108.83/109.41 ![X251]: 108.83/109.41 (in( 108.83/109.41 X251,X249) => 108.83/109.41 in( 108.83/109.41 X251,X250))) => 108.83/109.41 subset( 108.83/109.41 X249,X250))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X252]: 108.83/109.41 subset( 108.83/109.41 emptyset, 108.83/109.41 X252)) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X253, 108.83/109.41 X254,X255]: 108.83/109.41 (subset( 108.83/109.41 X253,X254) => 108.83/109.41 (in( 108.83/109.41 X255,X253) => 108.83/109.41 in( 108.83/109.41 X255,X254)))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X256, 108.83/109.41 X257,X258]: 108.83/109.41 (subset( 108.83/109.41 X256,X257) => 108.83/109.41 (( 108.83/109.41 ~ 108.83/109.41 in( 108.83/109.41 X258,X257)) => 108.83/109.41 (~ 108.83/109.41 in( 108.83/109.41 X258,X256))))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X259, 108.83/109.41 X260,X261]: 108.83/109.41 (in( 108.83/109.41 X261,X259) => 108.83/109.41 (( 108.83/109.41 ~ 108.83/109.41 in( 108.83/109.41 X261,X260)) => 108.83/109.41 (~ 108.83/109.41 subset( 108.83/109.41 X259,X260))))) => 108.83/109.41 ( 108.83/109.41 ( 108.83/109.41 ![X262, 108.83/109.41 X263]: 108.83/109.41 (( 108.83/109.41 ~ 108.83/109.41 subset( 108.83/109.41 X262,X263)) => 108.83/109.41 (X262 != 108.83/109.41 X263))) => 108.83/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X264, 108.91/109.41 X265,X266]: 108.91/109.41 (in( 108.91/109.41 X266,X264) => 108.91/109.41 (( 108.91/109.41 ~ 108.91/109.41 in( 108.91/109.41 X266,X265)) => 108.91/109.41 (X264 != 108.91/109.41 X265)))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X267]: 108.91/109.41 subset( 108.91/109.41 X267,X267)) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X268, 108.91/109.41 X269,X270]: 108.91/109.41 (subset( 108.91/109.41 X268,X269) => 108.91/109.41 (subset( 108.91/109.41 X269,X270) => 108.91/109.41 subset( 108.91/109.41 X268,X270)))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X271, 108.91/109.41 X272]: 108.91/109.41 subset( 108.91/109.41 X272, 108.91/109.41 setadjoin( 108.91/109.41 X271,X272))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X273, 108.91/109.41 X274,X275]: 108.91/109.41 (subset( 108.91/109.41 X273,X275) => 108.91/109.41 subset( 108.91/109.41 X273, 108.91/109.41 setadjoin( 108.91/109.41 X274,X275)))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X276, 108.91/109.41 X277]: 108.91/109.41 (subset( 108.91/109.41 X276,X277) => 108.91/109.41 in( 108.91/109.41 X276, 108.91/109.41 powerset( 108.91/109.41 X277)))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X278, 108.91/109.41 X279]: 108.91/109.41 (subset( 108.91/109.41 X278,X279) => 108.91/109.41 (subset( 108.91/109.41 X279,X278) => 108.91/109.41 (X278 = 108.91/109.41 X279)))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X280]: 108.91/109.41 (subset( 108.91/109.41 X280, 108.91/109.41 emptyset) => 108.91/109.41 (X280 = 108.91/109.41 emptyset))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X281, 108.91/109.41 X282]: 108.91/109.41 (subset( 108.91/109.41 X282,X281) => 108.91/109.41 in( 108.91/109.41 X282, 108.91/109.41 powerset( 108.91/109.41 X281)))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X283, 108.91/109.41 X284]: 108.91/109.41 (in( 108.91/109.41 X284, 108.91/109.41 powerset( 108.91/109.41 X283)) => 108.91/109.41 subset( 108.91/109.41 X284,X283))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X285]: 108.91/109.41 in( 108.91/109.41 X285, 108.91/109.41 powerset( 108.91/109.41 X285))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X286, 108.91/109.41 X287]: 108.91/109.41 (subset( 108.91/109.41 X286,X287) => 108.91/109.41 subset( 108.91/109.41 powerset( 108.91/109.41 X286), 108.91/109.41 powerset( 108.91/109.41 X287)))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X288, 108.91/109.41 X289:( 108.91/109.41 $i > $o)]: 108.91/109.41 in( 108.91/109.41 dsetconstr( 108.91/109.41 X288, 108.91/109.41 '#ll_1'( 108.91/109.41 X289)), 108.91/109.41 powerset( 108.91/109.41 X288))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X290, 108.91/109.41 X291:( 108.91/109.41 $i > $o)]: 108.91/109.41 subset( 108.91/109.41 dsetconstr( 108.91/109.41 X290, 108.91/109.41 '#ll_1'( 108.91/109.41 X291)), 108.91/109.41 X290)) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X292, 108.91/109.41 X293,X294]: 108.91/109.41 (in( 108.91/109.41 X294,X292) => 108.91/109.41 in( 108.91/109.41 X294, 108.91/109.41 binunion( 108.91/109.41 X292,X293)))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X295, 108.91/109.41 X296]: 108.91/109.41 in( 108.91/109.41 X296, 108.91/109.41 setadjoin( 108.91/109.41 X295, 108.91/109.41 setadjoin( 108.91/109.41 X296, 108.91/109.41 emptyset)))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X297, 108.91/109.41 X298,X299]: 108.91/109.41 (in( 108.91/109.41 X299,X298) => 108.91/109.41 in( 108.91/109.41 X299, 108.91/109.41 binunion( 108.91/109.41 X297,X298)))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X300, 108.91/109.41 X301, 108.91/109.41 X302, 108.91/109.41 X303:$o]: 108.91/109.41 (in( 108.91/109.41 X302, 108.91/109.41 binunion( 108.91/109.41 X300,X301)) => 108.91/109.41 (( 108.91/109.41 in( 108.91/109.41 X302,X300) => 108.91/109.41 X303) => 108.91/109.41 (( 108.91/109.41 in( 108.91/109.41 X302,X301) => 108.91/109.41 X303) => 108.91/109.41 X303)))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X304, 108.91/109.41 X305,X306]: 108.91/109.41 (in( 108.91/109.41 X306, 108.91/109.41 binunion( 108.91/109.41 X304,X305)) => 108.91/109.41 (in( 108.91/109.41 X306,X305) | 108.91/109.41 in( 108.91/109.41 X306,X304)))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X307, 108.91/109.41 X308]: 108.91/109.41 subset( 108.91/109.41 X307, 108.91/109.41 binunion( 108.91/109.41 X307,X308))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X309, 108.91/109.41 X310]: 108.91/109.41 subset( 108.91/109.41 X310, 108.91/109.41 binunion( 108.91/109.41 X309,X310))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X311, 108.91/109.41 X312,X313]: 108.91/109.41 (in( 108.91/109.41 X313,X311) => 108.91/109.41 (in( 108.91/109.41 X313,X312) => 108.91/109.41 in( 108.91/109.41 X313, 108.91/109.41 dsetconstr( 108.91/109.41 X311, 108.91/109.41 '#ll_0'( 108.91/109.41 X312)))))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X314, 108.91/109.41 X315,X316]: 108.91/109.41 (subset( 108.91/109.41 X316,X314) => 108.91/109.41 (subset( 108.91/109.41 X316,X315) => 108.91/109.41 subset( 108.91/109.41 X316, 108.91/109.41 dsetconstr( 108.91/109.41 X314, 108.91/109.41 '#ll_0'( 108.91/109.41 X315)))))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X317, 108.91/109.41 X318,X319]: 108.91/109.41 (in( 108.91/109.41 X319, 108.91/109.41 dsetconstr( 108.91/109.41 X317, 108.91/109.41 '#ll_0'( 108.91/109.41 X318))) => 108.91/109.41 in( 108.91/109.41 X319,X317))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X320, 108.91/109.41 X321]: 108.91/109.41 subset( 108.91/109.41 dsetconstr( 108.91/109.41 X320, 108.91/109.41 '#ll_0'( 108.91/109.41 X321)), 108.91/109.41 X320)) => 108.91/109.41 ( 108.91/109.41 ![X322, 108.91/109.41 X323]: 108.91/109.41 (subset( 108.91/109.41 X322,X323) => 108.91/109.41 (dsetconstr( 108.91/109.41 X322, 108.91/109.41 '#ll_0'( 108.91/109.41 X323)) = 108.91/109.41 X322))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 108.91/109.41 tff(zf_stmt_14, negated_conjecture, 108.91/109.41 (~ 108.91/109.41 ((![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))) => 108.91/109.41 ((![X5]: (~in(X5,emptyset))) => 108.91/109.41 ((![X6,X7,X8]: (in(X8,setadjoin(X6,X7)) <=> zip_tseitin0(X8,X7,X6))) => 108.91/109.41 ((![X9,X10]: 108.91/109.41 (in(X10,powerset(X9)) <=> (![X11]: zip_tseitin1(X11,X10,X9)))) => 108.91/109.41 ((![X12,X13]: 108.91/109.41 (in(X13,setunion(X12)) <=> (?[X14]: zip_tseitin2(X14,X13,X12)))) => 108.91/109.41 (in(emptyset,omega) => 108.91/109.41 ((![X15]: (in(X15,omega) => in(setadjoin(X15,X15),omega))) => 108.91/109.41 ((![X16]: 108.91/109.41 (((![X17]: 108.91/109.41 ((in(X17,X16) & in(X17,omega)) => 108.91/109.41 in(setadjoin(X17,X17),X16))) & 108.91/109.41 in(emptyset,X16)) => 108.91/109.41 (![X18]: (in(X18,omega) => in(X18,X16))))) => 108.91/109.41 ((![X19:(($i * $i) > $o),X20]: 108.91/109.41 ((![X21]: 108.91/109.41 (in(X21,X20) => 108.91/109.41 (?[X22]: 108.91/109.41 ((![X23]: (X19(X21,X23) => (X22 = X23))) & 108.91/109.41 X19(X21,X22))))) => 108.91/109.41 (?[X24]: 108.91/109.41 (![X25]: 108.91/109.41 (in(X25,X24) <=> 108.91/109.41 (?[X26]: zip_tseitin3(X26,X25,X20,X19))))))) => 108.91/109.41 ((![X27]: 108.91/109.41 ((?[X28]: in(X28,X27)) => 108.91/109.41 (?[X29]: 108.91/109.41 ((~(?[X30]: (in(X30,X27) & in(X30,X29)))) & in(X29,X27))))) => 108.91/109.41 ((![X31]: 108.91/109.41 (?[X32]: 108.91/109.41 ((![X33]: 108.91/109.41 (((?[X34]: in(X34,X33)) & 108.91/109.41 (![X35]: (in(X35,X33) => in(X35,X31)))) => 108.91/109.41 (?[X36,X37]: 108.91/109.41 ((![X38]: 108.91/109.41 (in(X38,X32) => 108.91/109.41 (in(X37,X38) | 108.91/109.41 (![X39]: (in(X39,X38) => in(X39,X36)))))) & 108.91/109.41 (~(?[X40]: (in(X40,X33) & in(X40,X36)))) & 108.91/109.41 in(X37,X33) & in(X36,X32))))) & 108.91/109.41 (![X41,X42]: 108.91/109.41 ((in(X42,X32) & in(X41,X32)) => 108.91/109.41 ((![X43]: (in(X43,X42) => in(X43,X41))) | 108.91/109.41 (![X44]: (in(X44,X41) => in(X44,X42)))))) & 108.91/109.41 (![X45,X46]: 108.91/109.41 ((in(X46,X31) & in(X45,X31)) => 108.91/109.41 ((![X47]: 108.91/109.41 (in(X47,X32) => (in(X45,X47) <=> in(X46,X47)))) => 108.91/109.41 (X45 = X46)))) & 108.91/109.41 (![X48]: 108.91/109.41 (in(X48,X32) => 108.91/109.41 (![X49]: (in(X49,X48) => in(X49,X31)))))))) => 108.91/109.41 ((![X50:($i > $o)]: 108.91/109.41 ((?[X51]: ((![X52]: (X50(X52) => (X51 = X52))) & X50(X51))) => 108.91/109.41 X50(descr('#ll_1'(X50))))) => 108.91/109.41 ((![X53,X54:($i > $o),X55]: 108.91/109.41 (in(X55,X53) => 108.91/109.41 (X54(X55) => in(X55,dsetconstr(X53,'#ll_1'(X54)))))) => 108.91/109.41 ((![X56,X57:($i > $o),X58]: 108.91/109.41 (in(X58,dsetconstr(X56,'#ll_1'(X57))) => in(X58,X56))) => 108.91/109.41 ((![X59,X60:($i > $o),X61]: 108.91/109.41 (in(X61,dsetconstr(X59,'#ll_1'(X60))) => X60(X61))) => 108.91/109.41 ((![X62:($i > $o)]: 108.91/109.41 ((?[X63]: 108.91/109.41 ((![X64]: (X62(X64) => (X63 = X64))) & X62(X63))) => 108.91/109.41 (?[X65]: 108.91/109.41 ((![X66]: (X62(X66) => (X65 = X66))) & X62(X65))))) => 108.91/109.41 ((![X67:$o,X68]: (in(X68,prop2set(X67)) => X67)) => 108.91/109.41 ((![X69]: (in(X69,emptyset) => (![X70:$o]: X70))) => 108.91/109.41 ((![X71]: (in(X71,emptyset) => $false)) => 108.91/109.41 ((![X72]: (~in(X72,emptyset))) => 108.91/109.41 ((![X73:($i > $o)]: 108.91/109.41 ((?[X74]: 108.91/109.41 ((![X75]: (X73(X75) => (X74 = X75))) & 108.91/109.41 X73(X74))) => 108.91/109.41 (?[X76]: X73(X76)))) => 108.91/109.41 ((![X77,X78]: 108.91/109.41 ((![X79]: (in(X79,X77) => in(X79,X78))) => 108.91/109.41 ((![X80]: (in(X80,X78) => in(X80,X77))) => 108.91/109.41 (X77 = X78)))) => 108.91/109.41 ((![X81]: 108.91/109.41 ((![X82]: (~in(X82,X81))) => (X81 = emptyset))) => 108.91/109.41 ((![X83]: 108.91/109.41 ((![X84]: (~in(X84,X83))) => (X83 = emptyset))) => 108.91/109.41 ((![X85,X86:($i > $o),X87]: 108.91/109.41 (in(X87,X85) => 108.91/109.41 (in(X87,dsetconstr(X85,'#ll_1'(X86))) <=> 108.91/109.41 X86(X87)))) => 108.91/109.41 ((![X88]: 108.91/109.41 ((X88 != emptyset) => (?[X89]: in(X89,X88)))) => 108.91/109.41 ((![X90,X91:($i > $o),X92]: 108.91/109.41 (in(X92,X90) => 108.91/109.41 (X91(X92) => 108.91/109.41 (dsetconstr(X90,'#ll_1'(X91)) != emptyset)))) => 108.91/109.41 ((![X93]: 108.91/109.41 ((?[X94]: in(X94,X93)) => 108.91/109.41 (X93 != emptyset))) => 108.91/109.41 ((![X95,X96]: in(X95,setadjoin(X95,X96))) => 108.91/109.41 (in(emptyset,setadjoin(emptyset,emptyset)) => 108.91/109.41 ((![X97,X98,X99]: 108.91/109.41 (in(X99,X98) => 108.91/109.41 in(X99,setadjoin(X97,X98)))) => 108.91/109.41 ((![X100,X101,X102]: 108.91/109.41 (in(X102,setadjoin(X100,X101)) => 108.91/109.41 (![X103:$o]: 108.91/109.41 (((X102 = X100) => X103) => 108.91/109.41 ((in(X102,X101) => X103) => X103))))) => 108.91/109.41 ((![X104,X105,X106]: 108.91/109.41 (in(X106,setadjoin(X104,X105)) => 108.91/109.41 (in(X106,X105) | (X106 = X104)))) => 108.91/109.41 ((![X107]: 108.91/109.41 (dsetconstr(X107,'#ll_2') = X107)) => 108.91/109.41 ((![X108,X109]: 108.91/109.41 ((![X110]: 108.91/109.41 (in(X110,X109) => in(X110,X108))) => 108.91/109.41 in(X109,powerset(X108)))) => 108.91/109.41 ((![X111]: in(emptyset,powerset(X111))) => 108.91/109.41 ((![X112]: 108.91/109.41 in(emptyset,powerset(X112))) => 108.91/109.41 ((![X113,X114,X115]: 108.91/109.41 (in(X114,powerset(X113)) => 108.91/109.41 (in(X115,X114) => in(X115,X113)))) => 108.91/109.41 ((![X116,X117,X118]: 108.91/109.41 (in(X117,X118) => 108.91/109.41 (in(X118,X116) => 108.91/109.41 in(X117,setunion(X116))))) => 108.91/109.41 ((![X119,X120]: 108.91/109.41 (in(X120,setunion(X119)) => 108.91/109.41 (![X121:$o]: 108.91/109.41 ((![X122]: 108.91/109.41 (in(X120,X122) => 108.91/109.41 (in(X122,X119) => 108.91/109.41 X121))) => 108.91/109.41 X121)))) => 108.91/109.41 ((![X123,X124]: 108.91/109.41 (in(X124,X123) => 108.91/109.41 in(X124, 108.91/109.41 powerset(setunion(X123))))) => 108.91/109.41 ((![X125:($i > $o)]: 108.91/109.41 ((?[X126]: 108.91/109.41 ((![X127]: 108.91/109.41 (X125(X127) => 108.91/109.41 (X126 = X127))) & 108.91/109.41 X125(X126))) => 108.91/109.41 (?[X128]: 108.91/109.41 (![X129]: 108.91/109.41 (X125(X129) <=> 108.91/109.41 (X129 = X128)))))) => 108.91/109.41 ((![X130]: 108.91/109.41 ((X130 != emptyset) => 108.91/109.41 (?[X131]: in(X131,X130)))) => 108.91/109.41 ((![X132,X133]: 108.91/109.41 (in(X132, 108.91/109.41 setadjoin(X133, 108.91/109.41 emptyset)) => 108.91/109.41 (X132 = X133))) => 108.91/109.41 ((![X134,X135]: 108.91/109.41 ((X134 != X135) => 108.91/109.41 (~ 108.91/109.41 in(X135, 108.91/109.41 setadjoin(X134, 108.91/109.41 emptyset))))) => 108.91/109.41 ((![X136,X137]: 108.91/109.41 ((X136 = X137) => 108.91/109.41 in(X136, 108.91/109.41 setadjoin(X137, 108.91/109.41 emptyset)))) => 108.91/109.41 ((![X138,X139]: 108.91/109.41 (in(X138, 108.91/109.41 setadjoin(X139, 108.91/109.41 emptyset)) => 108.91/109.41 in(X139, 108.91/109.41 setadjoin(X138, 108.91/109.41 emptyset)))) => 108.91/109.41 ((![X140,X141,X142]: 108.91/109.41 (in(X142, 108.91/109.41 setadjoin( 108.91/109.41 X140, 108.91/109.41 setadjoin( 108.91/109.41 X141,emptyset))) => 108.91/109.41 ((X142 = X141) | 108.91/109.41 (X142 = X140)))) => 108.91/109.41 ((![X143,X144]: 108.91/109.41 in(X143, 108.91/109.41 setadjoin( 108.91/109.41 X143, 108.91/109.41 setadjoin( 108.91/109.41 X144,emptyset)))) => 108.91/109.41 ((![X145,X146]: 108.91/109.41 in(X146, 108.91/109.41 setadjoin( 108.91/109.41 X145, 108.91/109.41 setadjoin( 108.91/109.41 X146,emptyset)))) => 108.91/109.41 ((![X147,X148:($i > $o)]: 108.91/109.41 ((?[X149]: 108.91/109.41 (X148(X149) & 108.91/109.41 in(X149,X147))) => 108.91/109.41 ((dsetconstr( 108.91/109.41 X147, 108.91/109.41 '#ll_1'(X148)) = 108.91/109.41 emptyset) => 108.91/109.41 $false))) => 108.91/109.41 ((![X150:($i > $o), 108.91/109.41 X151]: 108.91/109.41 (in(X151,emptyset) => 108.91/109.41 X150(X151))) => 108.91/109.41 ((![X152, 108.91/109.41 X153:($i > $o)]: 108.91/109.41 ((~ 108.91/109.41 (![X154]: 108.91/109.41 (in( 108.91/109.41 X154,X152) => 108.91/109.41 X153(X154)))) => 108.91/109.41 (?[X155]: 108.91/109.41 ((~X153(X155)) & 108.91/109.41 in(X155,X152))))) => 108.91/109.41 ((![X156, 108.91/109.41 X157:($i > $o)]: 108.91/109.41 ((![X158]: 108.91/109.41 (in( 108.91/109.41 X158,X156) => 108.91/109.41 (~ 108.91/109.41 X157( 108.91/109.41 X158)))) => 108.91/109.41 (~ 108.91/109.41 (?[X159]: 108.91/109.41 (X157( 108.91/109.41 X159) & 108.91/109.41 in( 108.91/109.41 X159,X156)))))) => 108.91/109.41 ((![X160, 108.91/109.41 X161:($i > $o)]: 108.91/109.41 ((~ 108.91/109.41 (?[X162]: 108.91/109.41 ( 108.91/109.41 X161( 108.91/109.41 X162) & 108.91/109.41 in( 108.91/109.41 X162,X160)))) => 108.91/109.41 (![X163]: 108.91/109.41 (in( 108.91/109.41 X163,X160) => 108.91/109.41 (~ 108.91/109.41 X161( 108.91/109.41 X163)))))) => 108.91/109.41 ((![X164, 108.91/109.41 X165:( 108.91/109.41 $i > $o)]: 108.91/109.41 ((?[X166]: 108.91/109.41 (( 108.91/109.41 ~ 108.91/109.41 X165( 108.91/109.41 X166)) & 108.91/109.41 in( 108.91/109.41 X166,X164))) => 108.91/109.41 (~ 108.91/109.41 (![X167]: 108.91/109.41 (in( 108.91/109.41 X167,X164) => 108.91/109.41 X165( 108.91/109.41 X167)))))) => 108.91/109.41 ((![X168:$o]: 108.91/109.41 (X168 => 108.91/109.41 in(emptyset, 108.91/109.41 prop2set( 108.91/109.41 X168)))) => 108.91/109.41 ((![X169:$o]: 108.91/109.41 (X169 => 108.91/109.41 set2prop( 108.91/109.41 prop2set( 108.91/109.41 X169)))) => 108.91/109.41 ((![X170, 108.91/109.41 X171:( 108.91/109.41 $i > $o)]: 108.91/109.41 ((~ 108.91/109.41 ( 108.91/109.41 ?[X172]: 108.91/109.41 (X171( 108.91/109.41 X172) & 108.91/109.41 in( 108.91/109.41 X172,X170)))) => 108.91/109.41 (![X173]: 108.91/109.41 (in( 108.91/109.41 X173,X170) => 108.91/109.41 (~ 108.91/109.41 X171( 108.91/109.41 X173)))))) => 108.91/109.41 ((![X174, 108.91/109.41 X175:( 108.91/109.41 $i > $o)]: 108.91/109.41 (( 108.91/109.41 ~ 108.91/109.41 ( 108.91/109.41 ![X176]: 108.91/109.41 (in( 108.91/109.41 X176,X174) => 108.91/109.41 X175( 108.91/109.41 X176)))) => 108.91/109.41 ( 108.91/109.41 ?[X177]: 108.91/109.41 (( 108.91/109.41 ~ 108.91/109.41 X175( 108.91/109.41 X177)) & 108.91/109.41 in( 108.91/109.41 X177,X174))))) => 108.91/109.41 ((![X178:( 108.91/109.41 $i > $o)]: 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ?[X179]: 108.91/109.41 (( 108.91/109.41 ![X180]: 108.91/109.41 (X178( 108.91/109.41 X180) => 108.91/109.41 (X179 = 108.91/109.41 X180))) & 108.91/109.41 X178( 108.91/109.41 X179))) => 108.91/109.41 ( 108.91/109.41 ?[X181]: 108.91/109.41 (( 108.91/109.41 ![X182]: 108.91/109.41 (X178( 108.91/109.41 X182) => 108.91/109.41 (X181 = 108.91/109.41 X182))) & 108.91/109.41 X178( 108.91/109.41 X181))))) => 108.91/109.41 ((![X183:( 108.91/109.41 $i > $o)]: 108.91/109.41 (( 108.91/109.41 ?[X184]: 108.91/109.41 X183( 108.91/109.41 X184)) => 108.91/109.41 (( 108.91/109.41 ![X185, 108.91/109.41 X186]: 108.91/109.41 (X183( 108.91/109.41 X185) => 108.91/109.41 (X183( 108.91/109.41 X186) => 108.91/109.41 (X185 = 108.91/109.41 X186)))) => 108.91/109.41 (?[X187]: 108.91/109.41 (( 108.91/109.41 ![X188]: 108.91/109.41 (X183( 108.91/109.41 X188) => 108.91/109.41 (X187 = 108.91/109.41 X188))) & 108.91/109.41 X183( 108.91/109.41 X187)))))) => 108.91/109.41 ((![X189:( 108.91/109.41 $i > $o)]: 108.91/109.41 (( 108.91/109.41 ?[X190]: 108.91/109.41 (![X191]: 108.91/109.41 (X189( 108.91/109.41 X191) <=> 108.91/109.41 (X191 = 108.91/109.41 X190)))) => 108.91/109.41 (?[X192]: 108.91/109.41 (( 108.91/109.41 ![X193]: 108.91/109.41 (X189( 108.91/109.41 X193) => 108.91/109.41 (X192 = 108.91/109.41 X193))) & 108.91/109.41 X189( 108.91/109.41 X192))))) => 108.91/109.41 (( 108.91/109.41 ![X194, 108.91/109.41 X195]: 108.91/109.41 (( 108.91/109.41 X194 = 108.91/109.41 X195) => 108.91/109.41 (![X196, 108.91/109.41 X197]: 108.91/109.41 (( 108.91/109.41 X196 = 108.91/109.41 X197) => 108.91/109.41 (in( 108.91/109.41 X196,X194) => 108.91/109.41 in( 108.91/109.41 X197,X195)))))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X198, 108.91/109.41 X199]: 108.91/109.41 (( 108.91/109.41 X198 = 108.91/109.41 X199) => 108.91/109.41 (![X200, 108.91/109.41 X201]: 108.91/109.41 (( 108.91/109.41 X200 = 108.91/109.41 X201) => 108.91/109.41 (in( 108.91/109.41 X200,X198) <=> 108.91/109.41 in( 108.91/109.41 X201,X199)))))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X202:( 108.91/109.41 $i > $o)]: 108.91/109.41 (( 108.91/109.41 ?[X203]: 108.91/109.41 (( 108.91/109.41 ![X204]: 108.91/109.41 (X202( 108.91/109.41 X204) => 108.91/109.41 (X203 = 108.91/109.41 X204))) & 108.91/109.41 X202( 108.91/109.41 X203))) => 108.91/109.41 (![X205, 108.91/109.41 X206]: 108.91/109.41 (X202( 108.91/109.41 X205) => 108.91/109.41 (X202( 108.91/109.41 X206) => 108.91/109.41 (X205 = 108.91/109.41 X206)))))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X207:( 108.91/109.41 $i > $o), 108.91/109.41 X208:( 108.91/109.41 $i > $o)]: 108.91/109.41 (( 108.91/109.41 ![X209, 108.91/109.41 X210]: 108.91/109.41 (( 108.91/109.41 X209 = 108.91/109.41 X210) => 108.91/109.41 (X207( 108.91/109.41 X209) <=> 108.91/109.41 X208( 108.91/109.41 X210)))) => 108.91/109.41 (( 108.91/109.41 ?[X211]: 108.91/109.41 zip_tseitin5( 108.91/109.41 X211,X207)) <=> 108.91/109.41 (?[X213]: 108.91/109.41 zip_tseitin5( 108.91/109.41 X213,X208))))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 emptyset = 108.91/109.41 emptyset) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X215, 108.91/109.41 X216]: 108.91/109.41 (( 108.91/109.41 X215 = 108.91/109.41 X216) => 108.91/109.41 (![X217, 108.91/109.41 X218]: 108.91/109.41 (( 108.91/109.41 X217 = 108.91/109.41 X218) => 108.91/109.41 (setadjoin( 108.91/109.41 X215,X217) = 108.91/109.41 setadjoin( 108.91/109.41 X216,X218)))))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X219, 108.91/109.41 X220]: 108.91/109.41 (( 108.91/109.41 X219 = 108.91/109.41 X220) => 108.91/109.41 (powerset( 108.91/109.41 X219) = 108.91/109.41 powerset( 108.91/109.41 X220)))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X221, 108.91/109.41 X222]: 108.91/109.41 (( 108.91/109.41 X221 = 108.91/109.41 X222) => 108.91/109.41 (setunion( 108.91/109.41 X221) = 108.91/109.41 setunion( 108.91/109.41 X222)))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 omega = 108.91/109.41 omega) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X223:( 108.91/109.41 $i > $o)]: 108.91/109.41 (( 108.91/109.41 ?[X224]: 108.91/109.41 (( 108.91/109.41 ![X225]: 108.91/109.41 (X223( 108.91/109.41 X225) => 108.91/109.41 (X224 = 108.91/109.41 X225))) & 108.91/109.41 X223( 108.91/109.41 X224))) => 108.91/109.41 (![X226, 108.91/109.41 X227]: 108.91/109.41 (X223( 108.91/109.41 X226) => 108.91/109.41 (X223( 108.91/109.41 X227) => 108.91/109.41 (X226 = 108.91/109.41 X227)))))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X228:( 108.91/109.41 $i > $o), 108.91/109.41 X229:( 108.91/109.41 $i > $o)]: 108.91/109.41 (( 108.91/109.41 ![X230, 108.91/109.41 X231]: 108.91/109.41 (( 108.91/109.41 X230 = 108.91/109.41 X231) => 108.91/109.41 (X228( 108.91/109.41 X230) <=> 108.91/109.41 X229( 108.91/109.41 X231)))) => 108.91/109.41 (( 108.91/109.41 ?[X232]: 108.91/109.41 (( 108.91/109.41 ![X233]: 108.91/109.41 (X228( 108.91/109.41 X233) => 108.91/109.41 (X232 = 108.91/109.41 X233))) & 108.91/109.41 X228( 108.91/109.41 X232))) => 108.91/109.41 (( 108.91/109.41 ?[X234]: 108.91/109.41 (( 108.91/109.41 ![X235]: 108.91/109.41 (X229( 108.91/109.41 X235) => 108.91/109.41 (X234 = 108.91/109.41 X235))) & 108.91/109.41 X229( 108.91/109.41 X234))) => 108.91/109.41 (descr( 108.91/109.41 '#ll_1'( 108.91/109.41 X228)) = 108.91/109.41 descr( 108.91/109.41 '#ll_1'( 108.91/109.41 X229))))))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X236, 108.91/109.41 X237]: 108.91/109.41 (( 108.91/109.41 X236 = 108.91/109.41 X237) => 108.91/109.41 (![X238:( 108.91/109.41 $i > $o), 108.91/109.41 X239:( 108.91/109.41 $i > $o)]: 108.91/109.41 (( 108.91/109.41 ![X240]: 108.91/109.41 (in( 108.91/109.41 X240,X236) => 108.91/109.41 (![X241]: 108.91/109.41 (in( 108.91/109.41 X241,X237) => 108.91/109.41 (( 108.91/109.41 X240 = 108.91/109.41 X241) => 108.91/109.41 (X238( 108.91/109.41 X240) <=> 108.91/109.41 X239( 108.91/109.41 X241))))))) => 108.91/109.41 (dsetconstr( 108.91/109.41 X236, 108.91/109.41 '#ll_1'( 108.91/109.41 X238)) = 108.91/109.41 dsetconstr( 108.91/109.41 X237, 108.91/109.41 '#ll_1'( 108.91/109.41 X239))))))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X242, 108.91/109.41 X243]: 108.91/109.41 (( 108.91/109.41 ![X244]: 108.91/109.41 (in( 108.91/109.41 X244,X242) => 108.91/109.41 in( 108.91/109.41 X244,X243))) => 108.91/109.41 subset( 108.91/109.41 X242,X243))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X245, 108.91/109.41 X246]: 108.91/109.41 (( 108.91/109.41 X245 = 108.91/109.41 X246) => 108.91/109.41 subset( 108.91/109.41 X246,X245))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X247, 108.91/109.41 X248]: 108.91/109.41 (( 108.91/109.41 X247 = 108.91/109.41 X248) => 108.91/109.41 subset( 108.91/109.41 X247,X248))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X249, 108.91/109.41 X250]: 108.91/109.41 (( 108.91/109.41 ![X251]: 108.91/109.41 (in( 108.91/109.41 X251,X249) => 108.91/109.41 in( 108.91/109.41 X251,X250))) => 108.91/109.41 subset( 108.91/109.41 X249,X250))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X252]: 108.91/109.41 subset( 108.91/109.41 emptyset, 108.91/109.41 X252)) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X253, 108.91/109.41 X254,X255]: 108.91/109.41 (subset( 108.91/109.41 X253,X254) => 108.91/109.41 (in( 108.91/109.41 X255,X253) => 108.91/109.41 in( 108.91/109.41 X255,X254)))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X256, 108.91/109.41 X257,X258]: 108.91/109.41 (subset( 108.91/109.41 X256,X257) => 108.91/109.41 (( 108.91/109.41 ~ 108.91/109.41 in( 108.91/109.41 X258,X257)) => 108.91/109.41 (~ 108.91/109.41 in( 108.91/109.41 X258,X256))))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X259, 108.91/109.41 X260,X261]: 108.91/109.41 (in( 108.91/109.41 X261,X259) => 108.91/109.41 (( 108.91/109.41 ~ 108.91/109.41 in( 108.91/109.41 X261,X260)) => 108.91/109.41 (~ 108.91/109.41 subset( 108.91/109.41 X259,X260))))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X262, 108.91/109.41 X263]: 108.91/109.41 (( 108.91/109.41 ~ 108.91/109.41 subset( 108.91/109.41 X262,X263)) => 108.91/109.41 (X262 != 108.91/109.41 X263))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X264, 108.91/109.41 X265,X266]: 108.91/109.41 (in( 108.91/109.41 X266,X264) => 108.91/109.41 (( 108.91/109.41 ~ 108.91/109.41 in( 108.91/109.41 X266,X265)) => 108.91/109.41 (X264 != 108.91/109.41 X265)))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X267]: 108.91/109.41 subset( 108.91/109.41 X267,X267)) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X268, 108.91/109.41 X269,X270]: 108.91/109.41 (subset( 108.91/109.41 X268,X269) => 108.91/109.41 (subset( 108.91/109.41 X269,X270) => 108.91/109.41 subset( 108.91/109.41 X268,X270)))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X271, 108.91/109.41 X272]: 108.91/109.41 subset( 108.91/109.41 X272, 108.91/109.41 setadjoin( 108.91/109.41 X271,X272))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X273, 108.91/109.41 X274,X275]: 108.91/109.41 (subset( 108.91/109.41 X273,X275) => 108.91/109.41 subset( 108.91/109.41 X273, 108.91/109.41 setadjoin( 108.91/109.41 X274,X275)))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X276, 108.91/109.41 X277]: 108.91/109.41 (subset( 108.91/109.41 X276,X277) => 108.91/109.41 in( 108.91/109.41 X276, 108.91/109.41 powerset( 108.91/109.41 X277)))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X278, 108.91/109.41 X279]: 108.91/109.41 (subset( 108.91/109.41 X278,X279) => 108.91/109.41 (subset( 108.91/109.41 X279,X278) => 108.91/109.41 (X278 = 108.91/109.41 X279)))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X280]: 108.91/109.41 (subset( 108.91/109.41 X280, 108.91/109.41 emptyset) => 108.91/109.41 (X280 = 108.91/109.41 emptyset))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X281, 108.91/109.41 X282]: 108.91/109.41 (subset( 108.91/109.41 X282,X281) => 108.91/109.41 in( 108.91/109.41 X282, 108.91/109.41 powerset( 108.91/109.41 X281)))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X283, 108.91/109.41 X284]: 108.91/109.41 (in( 108.91/109.41 X284, 108.91/109.41 powerset( 108.91/109.41 X283)) => 108.91/109.41 subset( 108.91/109.41 X284,X283))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X285]: 108.91/109.41 in( 108.91/109.41 X285, 108.91/109.41 powerset( 108.91/109.41 X285))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X286, 108.91/109.41 X287]: 108.91/109.41 (subset( 108.91/109.41 X286,X287) => 108.91/109.41 subset( 108.91/109.41 powerset( 108.91/109.41 X286), 108.91/109.41 powerset( 108.91/109.41 X287)))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X288, 108.91/109.41 X289:( 108.91/109.41 $i > $o)]: 108.91/109.41 in( 108.91/109.41 dsetconstr( 108.91/109.41 X288, 108.91/109.41 '#ll_1'( 108.91/109.41 X289)), 108.91/109.41 powerset( 108.91/109.41 X288))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X290, 108.91/109.41 X291:( 108.91/109.41 $i > $o)]: 108.91/109.41 subset( 108.91/109.41 dsetconstr( 108.91/109.41 X290, 108.91/109.41 '#ll_1'( 108.91/109.41 X291)), 108.91/109.41 X290)) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X292, 108.91/109.41 X293,X294]: 108.91/109.41 (in( 108.91/109.41 X294,X292) => 108.91/109.41 in( 108.91/109.41 X294, 108.91/109.41 binunion( 108.91/109.41 X292,X293)))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X295, 108.91/109.41 X296]: 108.91/109.41 in( 108.91/109.41 X296, 108.91/109.41 setadjoin( 108.91/109.41 X295, 108.91/109.41 setadjoin( 108.91/109.41 X296, 108.91/109.41 emptyset)))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X297, 108.91/109.41 X298,X299]: 108.91/109.41 (in( 108.91/109.41 X299,X298) => 108.91/109.41 in( 108.91/109.41 X299, 108.91/109.41 binunion( 108.91/109.41 X297,X298)))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X300, 108.91/109.41 X301, 108.91/109.41 X302, 108.91/109.41 X303:$o]: 108.91/109.41 (in( 108.91/109.41 X302, 108.91/109.41 binunion( 108.91/109.41 X300,X301)) => 108.91/109.41 (( 108.91/109.41 in( 108.91/109.41 X302,X300) => 108.91/109.41 X303) => 108.91/109.41 (( 108.91/109.41 in( 108.91/109.41 X302,X301) => 108.91/109.41 X303) => 108.91/109.41 X303)))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X304, 108.91/109.41 X305,X306]: 108.91/109.41 (in( 108.91/109.41 X306, 108.91/109.41 binunion( 108.91/109.41 X304,X305)) => 108.91/109.41 (in( 108.91/109.41 X306,X305) | 108.91/109.41 in( 108.91/109.41 X306,X304)))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X307, 108.91/109.41 X308]: 108.91/109.41 subset( 108.91/109.41 X307, 108.91/109.41 binunion( 108.91/109.41 X307,X308))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X309, 108.91/109.41 X310]: 108.91/109.41 subset( 108.91/109.41 X310, 108.91/109.41 binunion( 108.91/109.41 X309,X310))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X311, 108.91/109.41 X312,X313]: 108.91/109.41 (in( 108.91/109.41 X313,X311) => 108.91/109.41 (in( 108.91/109.41 X313,X312) => 108.91/109.41 in( 108.91/109.41 X313, 108.91/109.41 dsetconstr( 108.91/109.41 X311, 108.91/109.41 '#ll_0'( 108.91/109.41 X312)))))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X314, 108.91/109.41 X315,X316]: 108.91/109.41 (subset( 108.91/109.41 X316,X314) => 108.91/109.41 (subset( 108.91/109.41 X316,X315) => 108.91/109.41 subset( 108.91/109.41 X316, 108.91/109.41 dsetconstr( 108.91/109.41 X314, 108.91/109.41 '#ll_0'( 108.91/109.41 X315)))))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X317, 108.91/109.41 X318,X319]: 108.91/109.41 (in( 108.91/109.41 X319, 108.91/109.41 dsetconstr( 108.91/109.41 X317, 108.91/109.41 '#ll_0'( 108.91/109.41 X318))) => 108.91/109.41 in( 108.91/109.41 X319,X317))) => 108.91/109.41 ( 108.91/109.41 ( 108.91/109.41 ![X320, 108.91/109.41 X321]: 108.91/109.41 subset( 108.91/109.41 dsetconstr( 108.91/109.41 X320, 108.91/109.41 '#ll_0'( 108.91/109.41 X321)), 108.91/109.41 X320)) => 108.91/109.41 ( 108.91/109.41 ![X322, 108.91/109.41 X323]: 108.91/109.41 (subset( 108.91/109.41 X322,X323) => 108.91/109.41 (dsetconstr( 108.91/109.41 X322, 108.91/109.41 '#ll_0'( 108.91/109.41 X323)) = 108.91/109.41 X322)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 108.91/109.41 tff('112', plain, subset(sk_X322_, sk_X323_), 108.91/109.41 inference('cnf', [status(esa)], [zf_stmt_14])). 108.91/109.41 tff('113', plain, dsetconstr(sk_X322_, '#ll_0'(sk_X323_)) != sk_X322_, 108.91/109.41 inference('cnf', [status(esa)], [zf_stmt_14])). 108.91/109.41 tff('114', plain, ![X505]: subset(X505, X505), 108.91/109.41 inference('cnf', [status(esa)], [zf_stmt_14])). 108.91/109.41 tff('115', plain, 108.91/109.41 ![X475, X476, X477]: 108.91/109.41 (~ subset(X475, X476) 108.91/109.41 | subset(X475, dsetconstr(X477, '#ll_0'(X476))) 108.91/109.41 | ~ subset(X475, X477)), 108.91/109.41 inference('cnf', [status(esa)], [zf_stmt_14])). 108.91/109.41 tff('116', plain, 108.91/109.41 ![X478, X479]: subset(dsetconstr(X478, '#ll_0'(X479)), X478), 108.91/109.41 inference('cnf', [status(esa)], [zf_stmt_14])). 108.91/109.41 tff('117', plain, 108.91/109.41 ![X457, X458]: 108.91/109.41 (~ subset(X457, X458) | X458 = X457 | ~ subset(X458, X457)), 108.91/109.42 inference('cnf', [status(esa)], [zf_stmt_14])). 108.91/109.42 tff('118', plain, $false, 108.91/109.42 inference('eprover', [status(thm)], 108.91/109.42 ['112', '113', '114', '115', '116', '117'])). 108.91/109.42 108.91/109.42 % SZS output end Refutation 108.91/109.42 % Zipperpin 1.5 exiting 108.91/109.42 EOF