0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.13 % Command : run_portfolio.sh /export/starexec/sandbox/benchmark/theBenchmark.p /export/starexec/sandbox/tmp/tmp.DUETGTiCKa 0.13/0.34 % Computer : n027.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 180 0.13/0.34 % DateTime : Thu Aug 29 15:46:09 EDT 2019 0.13/0.35 % CPUTime : 102.30/102.92 % Running portfolio for 180 s 102.30/102.92 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 102.30/102.92 % TempDir : /export/starexec/sandbox/tmp/tmp.DUETGTiCKa 102.30/102.92 % Recognized as monomorphic HO. 102.30/102.92 % Running /export/starexec/sandbox/solver/bin/competitive.sh for 18 102.30/102.92 % Running /export/starexec/sandbox/solver/bin/competitive.2.sh for 13 102.30/102.92 % Running /export/starexec/sandbox/solver/bin/competitive.3.sh for 3 102.30/102.92 % Running /export/starexec/sandbox/solver/bin/pragmatic.rudimentary.sh for 28 102.30/102.92 % Running /export/starexec/sandbox/solver/bin/pragmatic.rudimentary.1.sh for 12 102.30/102.92 % Running /export/starexec/sandbox/solver/bin/pragmatic.rudimentary.2.sh for 7 102.30/102.92 % Running /export/starexec/sandbox/solver/bin/pragmatic.shallow.sh for 3 102.30/102.92 % Running /export/starexec/sandbox/solver/bin/pragmatic.shallow.1.sh for 14 102.30/102.92 % Running /export/starexec/sandbox/solver/bin/pragmatic.shallow.2.sh for 12 102.30/102.92 % Running /export/starexec/sandbox/solver/bin/pragmatic.ll.e.sh for 19 102.30/102.92 % Solved by: pragmatic.ll.e.sh 102.30/102.92 % Running : timeout 16 /export/starexec/sandbox/solver/bin/eprover-ho /export/starexec/sandbox/tmp/tmp.DUETGTiCKa/e_inputbf5d68 --cpu-limit=14 --auto-schedule -s -p. 102.30/102.92 % done 468 iterations in 4.248s 102.30/102.92 % hashcons stats for terms: size 4096, num 18021, sum length 36707, buckets: small 3, median 7, big 22 102.30/102.92 % proof state stats: {active 194, passive 6276, simpl 0} 102.30/102.92 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 102.30/102.92 % SZS output start Refutation 102.30/102.92 tff(setminusER, axiom, setminusER <=> 102.30/102.92 (![A,B,Xx]: (in(Xx,setminus(A,B)) => (~in(Xx,B))))). 102.30/102.92 tff('0', plain, 102.30/102.92 setminusER = (![X2,X3,X4]: (in(X4,setminus(X2,X3)) => (~in(X4,X3)))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(setminusEL, axiom, setminusEL <=> 102.30/102.92 (![A,B,Xx]: (in(Xx,setminus(A,B)) => in(Xx,A)))). 102.30/102.92 tff('1', plain, 102.30/102.92 setminusEL = (![X2,X3,X4]: (in(X4,setminus(X2,X3)) => in(X4,X2))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(setminusI, axiom, setminusI <=> 102.30/102.92 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => in(Xx,setminus(A,B)))))). 102.30/102.92 tff('2', plain, 102.30/102.92 setminusI = 102.30/102.92 (![X2,X3,X4]: (in(X4,X2) => ((~in(X4,X3)) => in(X4,setminus(X2,X3))))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(bs114d, axiom, bs114d <=> 102.30/102.92 (![A,B,C]: 102.30/102.92 (binintersect(A,binunion(B,C)) = 102.30/102.92 binunion(binintersect(A,B),binintersect(A,C))))). 102.30/102.92 tff('3', plain, 102.30/102.92 bs114d = 102.30/102.92 (![X2,X3,X4]: 102.30/102.92 (binintersect(X2,binunion(X3,X4)) = 102.30/102.92 binunion(binintersect(X2,X3),binintersect(X2,X4)))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(binintersectSubset1, axiom, binintersectSubset1 <=> 102.30/102.92 (![A,B]: ((binintersect(A,B) = A) => subset(A,B)))). 102.30/102.92 tff('4', plain, 102.30/102.92 binintersectSubset1 = 102.30/102.92 (![X2,X3]: ((binintersect(X2,X3) = X2) => subset(X2,X3))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(binintersectSubset4, axiom, binintersectSubset4 <=> 102.30/102.92 (![A,B]: (subset(B,A) => (binintersect(A,B) = B)))). 102.30/102.92 tff('5', plain, 102.30/102.92 binintersectSubset4 = 102.30/102.92 (![X2,X3]: (subset(X3,X2) => (binintersect(X2,X3) = X3))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(binintersectRsub, axiom, binintersectRsub <=> 102.30/102.92 (![A,B]: subset(binintersect(A,B),B))). 102.30/102.92 tff('6', plain, 102.30/102.92 binintersectRsub = (![X2,X3]: subset(binintersect(X2,X3),X3)), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(disjointsetsI1, axiom, disjointsetsI1 <=> 102.30/102.92 (![A,B]: 102.30/102.92 ((~(?[Xx]: (in(Xx,B) & in(Xx,A)))) => (binintersect(A,B) = emptyset)))). 102.30/102.92 tff('7', plain, 102.30/102.92 disjointsetsI1 = 102.30/102.92 (![X2,X3]: 102.30/102.92 ((~(?[X4]: (in(X4,X3) & in(X4,X2)))) => 102.30/102.92 (binintersect(X2,X3) = emptyset))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(binintersectER, axiom, binintersectER <=> 102.30/102.92 (![A,B,Xx]: (in(Xx,binintersect(A,B)) => in(Xx,B)))). 102.30/102.92 tff('8', plain, 102.30/102.92 binintersectER = (![X2,X3,X4]: (in(X4,binintersect(X2,X3)) => in(X4,X3))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(binintersectSubset3, axiom, binintersectSubset3 <=> 102.30/102.92 (![A,B]: ((binintersect(A,B) = B) => subset(B,A)))). 102.30/102.92 tff('9', plain, 102.30/102.92 binintersectSubset3 = 102.30/102.92 (![X2,X3]: ((binintersect(X2,X3) = X3) => subset(X3,X2))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(binintersectSubset2, axiom, binintersectSubset2 <=> 102.30/102.92 (![A,B]: (subset(A,B) => (binintersect(A,B) = A)))). 102.30/102.92 tff('10', plain, 102.30/102.92 binintersectSubset2 = 102.30/102.92 (![X2,X3]: (subset(X2,X3) => (binintersect(X2,X3) = X2))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(binintersectLsub, axiom, binintersectLsub <=> 102.30/102.92 (![A,B]: subset(binintersect(A,B),A))). 102.30/102.92 tff('11', plain, 102.30/102.92 binintersectLsub = (![X2,X3]: subset(binintersect(X2,X3),X2)), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(binintersectEL, axiom, binintersectEL <=> 102.30/102.92 (![A,B,Xx]: (in(Xx,binintersect(A,B)) => in(Xx,A)))). 102.30/102.92 tff('12', plain, 102.30/102.92 binintersectEL = (![X2,X3,X4]: (in(X4,binintersect(X2,X3)) => in(X4,X2))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(binintersectSubset5, axiom, binintersectSubset5 <=> 102.30/102.92 (![A,B,C]: (subset(C,A) => (subset(C,B) => subset(C,binintersect(A,B)))))). 102.30/102.92 tff('13', plain, 102.30/102.92 binintersectSubset5 = 102.30/102.92 (![X2,X3,X4]: 102.30/102.92 (subset(X4,X2) => (subset(X4,X3) => subset(X4,binintersect(X2,X3))))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(binintersectI, axiom, binintersectI <=> 102.30/102.92 (![A,B,Xx]: (in(Xx,A) => (in(Xx,B) => in(Xx,binintersect(A,B)))))). 102.30/102.92 tff('14', plain, 102.30/102.92 binintersectI = 102.30/102.92 (![X2,X3,X4]: (in(X4,X2) => (in(X4,X3) => in(X4,binintersect(X2,X3))))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(binunionRsub, axiom, binunionRsub <=> (![A,B]: subset(B,binunion(A,B)))). 102.30/102.92 tff('15', plain, binunionRsub = (![X2,X3]: subset(X3,binunion(X2,X3))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(binunionLsub, axiom, binunionLsub <=> (![A,B]: subset(A,binunion(A,B)))). 102.30/102.92 tff('16', plain, binunionLsub = (![X2,X3]: subset(X2,binunion(X2,X3))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(binunionE, axiom, binunionE <=> 102.30/102.92 (![A,B,Xx]: (in(Xx,binunion(A,B)) => (in(Xx,B) | in(Xx,A))))). 102.30/102.92 tff('17', plain, 102.30/102.92 binunionE = 102.30/102.92 (![X2,X3,X4]: (in(X4,binunion(X2,X3)) => (in(X4,X3) | in(X4,X2)))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(binunionEcases, axiom, binunionEcases <=> 102.30/102.92 (![A,B,Xx,Xphi:$o]: 102.30/102.92 (in(Xx,binunion(A,B)) => 102.30/102.92 ((in(Xx,A) => Xphi) => ((in(Xx,B) => Xphi) => Xphi))))). 102.30/102.92 tff('18', plain, 102.30/102.92 binunionEcases = 102.30/102.92 (![X2,X3,X4,X5:$o]: 102.30/102.92 (in(X4,binunion(X2,X3)) => 102.30/102.92 ((in(X4,X2) => X5) => ((in(X4,X3) => X5) => X5)))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(binunionIR, axiom, binunionIR <=> 102.30/102.92 (![A,B,Xx]: (in(Xx,B) => in(Xx,binunion(A,B))))). 102.30/102.92 tff('19', plain, 102.30/102.92 binunionIR = (![X2,X3,X4]: (in(X4,X3) => in(X4,binunion(X2,X3)))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(upairset2IR, axiom, upairset2IR <=> 102.30/102.92 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 102.30/102.92 tff('20', plain, 102.30/102.92 upairset2IR = (![X2,X3]: in(X3,setadjoin(X2,setadjoin(X3,emptyset)))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(binunionIL, axiom, binunionIL <=> 102.30/102.92 (![A,B,Xx]: (in(Xx,A) => in(Xx,binunion(A,B))))). 102.30/102.92 tff('21', plain, 102.30/102.92 binunionIL = (![X2,X3,X4]: (in(X4,X2) => in(X4,binunion(X2,X3)))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(sepSubset, axiom, sepSubset <=> 102.30/102.92 (![A,Xphi:($i > $o)]: subset(dsetconstr(A,^[Xx]: Xphi(Xx)),A))). 102.30/102.92 tff('22', plain, 102.30/102.92 sepSubset = 102.30/102.92 (![X2,X3:($i > $o)]: subset(dsetconstr(X2,^[V_1]: X3(V_1)),X2)), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(sepInPowerset, axiom, sepInPowerset <=> 102.30/102.92 (![A,Xphi:($i > $o)]: in(dsetconstr(A,^[Xx]: Xphi(Xx)),powerset(A)))). 102.30/102.92 tff('23', plain, 102.30/102.92 sepInPowerset = 102.30/102.92 (![X2,X3:($i > $o)]: in(dsetconstr(X2,^[V_1]: X3(V_1)),powerset(X2))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(powersetsubset, axiom, powersetsubset <=> 102.30/102.92 (![A,B]: (subset(A,B) => subset(powerset(A),powerset(B))))). 102.30/102.92 tff('24', plain, 102.30/102.92 powersetsubset = 102.30/102.92 (![X2,X3]: (subset(X2,X3) => subset(powerset(X2),powerset(X3)))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(inPowerset, axiom, inPowerset <=> (![A]: in(A,powerset(A)))). 102.30/102.92 tff('25', plain, inPowerset = (![X2]: in(X2,powerset(X2))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(powersetE1, axiom, powersetE1 <=> 102.30/102.92 (![A,B]: (in(B,powerset(A)) => subset(B,A)))). 102.30/102.92 tff('26', plain, 102.30/102.92 powersetE1 = (![X2,X3]: (in(X3,powerset(X2)) => subset(X3,X2))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(powersetI1, axiom, powersetI1 <=> 102.30/102.92 (![A,B]: (subset(B,A) => in(B,powerset(A))))). 102.30/102.92 tff('27', plain, 102.30/102.92 powersetI1 = (![X2,X3]: (subset(X3,X2) => in(X3,powerset(X2)))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(subsetemptysetimpeq, axiom, subsetemptysetimpeq <=> 102.30/102.92 (![A]: (subset(A,emptyset) => (A = emptyset)))). 102.30/102.92 tff('28', plain, 102.30/102.92 subsetemptysetimpeq = (![X2]: (subset(X2,emptyset) => (X2 = emptyset))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(setextsub, axiom, setextsub <=> 102.30/102.92 (![A,B]: (subset(A,B) => (subset(B,A) => (A = B))))). 102.30/102.92 tff('29', plain, 102.30/102.92 setextsub = (![X2,X3]: (subset(X2,X3) => (subset(X3,X2) => (X2 = X3)))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(subset2powerset, axiom, subset2powerset <=> 102.30/102.92 (![A,B]: (subset(A,B) => in(A,powerset(B))))). 102.30/102.92 tff('30', plain, 102.30/102.92 subset2powerset = (![X2,X3]: (subset(X2,X3) => in(X2,powerset(X3)))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(setadjoinSub2, axiom, setadjoinSub2 <=> 102.30/102.92 (![A,Xx,B]: (subset(A,B) => subset(A,setadjoin(Xx,B))))). 102.30/102.92 tff('31', plain, 102.30/102.92 setadjoinSub2 = 102.30/102.92 (![X2,X3,X4]: (subset(X2,X4) => subset(X2,setadjoin(X3,X4)))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(setadjoinSub, axiom, setadjoinSub <=> 102.30/102.92 (![Xx,A]: subset(A,setadjoin(Xx,A)))). 102.30/102.92 tff('32', plain, setadjoinSub = (![X2,X3]: subset(X3,setadjoin(X2,X3))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(subsetTrans, axiom, subsetTrans <=> 102.30/102.92 (![A,B,C]: (subset(A,B) => (subset(B,C) => subset(A,C))))). 102.30/102.92 tff('33', plain, 102.30/102.92 subsetTrans = 102.30/102.92 (![X2,X3,X4]: (subset(X2,X3) => (subset(X3,X4) => subset(X2,X4)))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(subsetRefl, axiom, subsetRefl <=> (![A]: subset(A,A))). 102.30/102.92 tff('34', plain, subsetRefl = (![X2]: subset(X2,X2)), define([status(thm)])). 102.30/102.92 tff(notequalI2, axiom, notequalI2 <=> 102.30/102.92 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => (A != B))))). 102.30/102.92 tff('35', plain, 102.30/102.92 notequalI2 = (![X2,X3,X4]: (in(X4,X2) => ((~in(X4,X3)) => (X2 != X3)))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(notequalI1, axiom, notequalI1 <=> (![A,B]: ((~subset(A,B)) => (A != B)))). 102.30/102.92 tff('36', plain, notequalI1 = (![X2,X3]: ((~subset(X2,X3)) => (X2 != X3))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(notsubsetI, axiom, notsubsetI <=> 102.30/102.92 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => (~subset(A,B)))))). 102.30/102.92 tff('37', plain, 102.30/102.92 notsubsetI = 102.30/102.92 (![X2,X3,X4]: (in(X4,X2) => ((~in(X4,X3)) => (~subset(X2,X3))))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(subsetE2, axiom, subsetE2 <=> 102.30/102.92 (![A,B,Xx]: (subset(A,B) => ((~in(Xx,B)) => (~in(Xx,A)))))). 102.30/102.92 tff('38', plain, 102.30/102.92 subsetE2 = 102.30/102.92 (![X2,X3,X4]: (subset(X2,X3) => ((~in(X4,X3)) => (~in(X4,X2))))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(subsetE, axiom, subsetE <=> 102.30/102.92 (![A,B,Xx]: (subset(A,B) => (in(Xx,A) => in(Xx,B))))). 102.30/102.92 tff('39', plain, 102.30/102.92 subsetE = (![X2,X3,X4]: (subset(X2,X3) => (in(X4,X2) => in(X4,X3)))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(emptysetsubset, axiom, emptysetsubset <=> (![A]: subset(emptyset,A))). 102.30/102.92 tff('40', plain, emptysetsubset = (![X2]: subset(emptyset,X2)), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(subsetI2, axiom, subsetI2 <=> 102.30/102.92 (![A,B]: ((![Xx]: (in(Xx,A) => in(Xx,B))) => subset(A,B)))). 102.30/102.92 tff('41', plain, 102.30/102.92 subsetI2 = 102.30/102.92 (![X2,X3]: ((![X4]: (in(X4,X2) => in(X4,X3))) => subset(X2,X3))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(eqimpsubset1, axiom, eqimpsubset1 <=> (![A,B]: ((A = B) => subset(A,B)))). 102.30/102.92 tff('42', plain, eqimpsubset1 = (![X2,X3]: ((X2 = X3) => subset(X2,X3))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(eqimpsubset2, axiom, eqimpsubset2 <=> (![A,B]: ((A = B) => subset(B,A)))). 102.30/102.92 tff('43', plain, eqimpsubset2 = (![X2,X3]: ((X2 = X3) => subset(X3,X2))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(subsetI1, axiom, subsetI1 <=> 102.30/102.92 (![A,B]: ((![Xx]: (in(Xx,A) => in(Xx,B))) => subset(A,B)))). 102.30/102.92 tff('44', plain, 102.30/102.92 subsetI1 = 102.30/102.92 (![X2,X3]: ((![X4]: (in(X4,X2) => in(X4,X3))) => subset(X2,X3))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(dsetconstr__Cong, axiom, dsetconstr__Cong <=> 102.30/102.92 (![A,B]: 102.30/102.92 ((A = B) => 102.30/102.92 (![Xphi:($i > $o),Xpsi:($i > $o)]: 102.30/102.92 ((![Xx]: 102.30/102.92 (in(Xx,A) => 102.30/102.92 (![Xy]: (in(Xy,B) => ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy))))))) => 102.30/102.92 (dsetconstr(A,^[Xx]: Xphi(Xx)) = dsetconstr(B,^[Xx]: Xpsi(Xx)))))))). 102.30/102.92 tff('45', plain, 102.30/102.92 dsetconstr__Cong = 102.30/102.92 (![X2,X3]: 102.30/102.92 ((X2 = X3) => 102.30/102.92 (![X4:($i > $o),X5:($i > $o)]: 102.30/102.92 ((![X6]: 102.30/102.92 (in(X6,X2) => 102.30/102.92 (![X7]: (in(X7,X3) => ((X6 = X7) => (X4(X6) <=> X5(X7))))))) => 102.30/102.92 (dsetconstr(X2,^[V_1]: X4(V_1)) = dsetconstr(X3,^[V_2]: X5(V_2))))))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(descr__Cong, axiom, descr__Cong <=> 102.30/102.92 (![Xphi:($i > $o),Xpsi:($i > $o)]: 102.30/102.92 ((![Xx,Xy]: ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy)))) => 102.30/102.92 (exu(^[Xx]: Xphi(Xx)) => 102.30/102.92 (exu(^[Xx]: Xpsi(Xx)) => 102.30/102.92 (descr(^[Xx]: Xphi(Xx)) = descr(^[Xx]: Xpsi(Xx)))))))). 102.30/102.92 tff('46', plain, 102.30/102.92 descr__Cong = 102.30/102.92 (![X2:($i > $o),X3:($i > $o)]: 102.30/102.92 ((![X4,X5]: ((X4 = X5) => (X2(X4) <=> X3(X5)))) => 102.30/102.92 (exu(^[V_1]: X2(V_1)) => 102.30/102.92 (exu(^[V_2]: X3(V_2)) => 102.30/102.92 (descr(^[V_3]: X2(V_3)) = descr(^[V_4]: X3(V_4))))))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(exuEu, axiom, exuEu <=> 102.30/102.92 (![Xphi:($i > $o)]: 102.30/102.92 (exu(^[Xx]: Xphi(Xx)) => 102.30/102.92 (![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))). 102.30/102.92 tff('47', plain, 102.30/102.92 exuEu = 102.30/102.92 (![X2:($i > $o)]: 102.30/102.92 (exu(^[V_1]: X2(V_1)) => (![X3,X4]: (X2(X3) => (X2(X4) => (X3 = X4)))))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(omega__Cong, axiom, omega__Cong <=> (omega = omega)). 102.30/102.92 tff('48', plain, omega__Cong = (omega = omega), define([status(thm)])). 102.30/102.92 tff(setunion__Cong, axiom, setunion__Cong <=> 102.30/102.92 (![A,B]: ((A = B) => (setunion(A) = setunion(B))))). 102.30/102.92 tff('49', plain, 102.30/102.92 setunion__Cong = (![X2,X3]: ((X2 = X3) => (setunion(X2) = setunion(X3)))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(powerset__Cong, axiom, powerset__Cong <=> 102.30/102.92 (![A,B]: ((A = B) => (powerset(A) = powerset(B))))). 102.30/102.92 tff('50', plain, 102.30/102.92 powerset__Cong = (![X2,X3]: ((X2 = X3) => (powerset(X2) = powerset(X3)))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(setadjoin__Cong, axiom, setadjoin__Cong <=> 102.30/102.92 (![Xx,Xy]: 102.30/102.92 ((Xx = Xy) => 102.30/102.92 (![Xz,Xu]: ((Xz = Xu) => (setadjoin(Xx,Xz) = setadjoin(Xy,Xu))))))). 102.30/102.92 tff('51', plain, 102.30/102.92 setadjoin__Cong = 102.30/102.92 (![X2,X3]: 102.30/102.92 ((X2 = X3) => 102.30/102.92 (![X4,X5]: ((X4 = X5) => (setadjoin(X2,X4) = setadjoin(X3,X5)))))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(emptyset__Cong, axiom, emptyset__Cong <=> (emptyset = emptyset)). 102.30/102.92 tff('52', plain, emptyset__Cong = (emptyset = emptyset), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(exu__Cong, axiom, exu__Cong <=> 102.30/102.92 (![Xphi:($i > $o),Xpsi:($i > $o)]: 102.30/102.92 ((![Xx,Xy]: ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy)))) => 102.30/102.92 (exu(^[Xx]: Xphi(Xx)) <=> exu(^[Xx]: Xpsi(Xx)))))). 102.30/102.92 tff('53', plain, 102.30/102.92 exu__Cong = 102.30/102.92 (![X2:($i > $o),X3:($i > $o)]: 102.30/102.92 ((![X4,X5]: ((X4 = X5) => (X2(X4) <=> X3(X5)))) => 102.30/102.92 (exu(^[V_1]: X2(V_1)) <=> exu(^[V_2]: X3(V_2))))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(exuE3u, axiom, exuE3u <=> 102.30/102.92 (![Xphi:($i > $o)]: 102.30/102.92 (exu(^[Xx]: Xphi(Xx)) => 102.30/102.92 (![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))). 102.30/102.92 tff('54', plain, 102.30/102.92 exuE3u = 102.30/102.92 (![X2:($i > $o)]: 102.30/102.92 (exu(^[V_1]: X2(V_1)) => (![X3,X4]: (X2(X3) => (X2(X4) => (X3 = X4)))))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(in__Cong, axiom, in__Cong <=> 102.30/102.92 (![A,B]: ((A = B) => (![Xx,Xy]: ((Xx = Xy) => (in(Xx,A) <=> in(Xy,B))))))). 102.30/102.92 tff('55', plain, 102.30/102.92 in__Cong = 102.30/102.92 (![X2,X3]: 102.30/102.92 ((X2 = X3) => (![X4,X5]: ((X4 = X5) => (in(X4,X2) <=> in(X5,X3)))))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(inCongP, axiom, inCongP <=> 102.30/102.92 (![A,B]: ((A = B) => (![Xx,Xy]: ((Xx = Xy) => (in(Xx,A) => in(Xy,B))))))). 102.30/102.92 tff('56', plain, 102.30/102.92 inCongP = 102.30/102.92 (![X2,X3]: 102.30/102.92 ((X2 = X3) => (![X4,X5]: ((X4 = X5) => (in(X4,X2) => in(X5,X3)))))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(exuI2, axiom, exuI2 <=> 102.30/102.92 (![Xphi:($i > $o)]: 102.30/102.92 ((?[Xx]: (![Xy]: (Xphi(Xy) <=> (Xy = Xx)))) => exu(^[Xx]: Xphi(Xx))))). 102.30/102.92 tff('57', plain, 102.30/102.92 exuI2 = 102.30/102.92 (![X2:($i > $o)]: 102.30/102.92 ((?[X3]: (![X4]: (X2(X4) <=> (X4 = X3)))) => exu(^[V_1]: X2(V_1)))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(exuI3, axiom, exuI3 <=> 102.30/102.92 (![Xphi:($i > $o)]: 102.30/102.92 ((?[Xx]: Xphi(Xx)) => 102.30/102.92 ((![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy)))) => 102.30/102.92 exu(^[Xx]: Xphi(Xx)))))). 102.30/102.92 tff('58', plain, 102.30/102.92 exuI3 = 102.30/102.92 (![X2:($i > $o)]: 102.30/102.92 ((?[X3]: X2(X3)) => 102.30/102.92 ((![X4,X5]: (X2(X4) => (X2(X5) => (X4 = X5)))) => 102.30/102.92 exu(^[V_1]: X2(V_1))))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(exuI1, axiom, exuI1 <=> 102.30/102.92 (![Xphi:($i > $o)]: 102.30/102.92 ((?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx))) => 102.30/102.92 exu(^[Xx]: Xphi(Xx))))). 102.30/102.92 tff('59', plain, 102.30/102.92 exuI1 = 102.30/102.92 (![X2:($i > $o)]: 102.30/102.92 ((?[X3]: ((![X4]: (X2(X4) => (X3 = X4))) & X2(X3))) => 102.30/102.92 exu(^[V_1]: X2(V_1)))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(notdallE, axiom, notdallE <=> 102.30/102.92 (![A,Xphi:($i > $o)]: 102.30/102.92 ((~(![Xx]: (in(Xx,A) => Xphi(Xx)))) => (?[Xx]: ((~Xphi(Xx)) & in(Xx,A)))))). 102.30/102.92 tff('60', plain, 102.30/102.92 notdallE = 102.30/102.92 (![X2,X3:($i > $o)]: 102.30/102.92 ((~(![X4]: (in(X4,X2) => X3(X4)))) => (?[X5]: ((~X3(X5)) & in(X5,X2))))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(notdexE, axiom, notdexE <=> 102.30/102.92 (![A,Xphi:($i > $o)]: 102.30/102.92 ((~(?[Xx]: (Xphi(Xx) & in(Xx,A)))) => (![Xx]: (in(Xx,A) => (~Xphi(Xx))))))). 102.30/102.92 tff('61', plain, 102.30/102.92 notdexE = 102.30/102.92 (![X2,X3:($i > $o)]: 102.30/102.92 ((~(?[X4]: (X3(X4) & in(X4,X2)))) => (![X5]: (in(X5,X2) => (~X3(X5)))))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(prop2set2propI, axiom, prop2set2propI <=> 102.30/102.92 (![Xphi:$o]: (Xphi => set2prop(prop2set(Xphi))))). 102.30/102.92 tff('62', plain, prop2set2propI = (![X2:$o]: (X2 => set2prop(prop2set(X2)))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(prop2setI, axiom, prop2setI <=> 102.30/102.92 (![Xphi:$o]: (Xphi => in(emptyset,prop2set(Xphi))))). 102.30/102.92 tff('63', plain, prop2setI = (![X2:$o]: (X2 => in(emptyset,prop2set(X2)))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(quantDeMorgan4, axiom, quantDeMorgan4 <=> 102.30/102.92 (![A,Xphi:($i > $o)]: 102.30/102.92 ((?[Xx]: ((~Xphi(Xx)) & in(Xx,A))) => (~(![Xx]: (in(Xx,A) => Xphi(Xx))))))). 102.30/102.92 tff('64', plain, 102.30/102.92 quantDeMorgan4 = 102.30/102.92 (![X2,X3:($i > $o)]: 102.30/102.92 ((?[X4]: ((~X3(X4)) & in(X4,X2))) => (~(![X5]: (in(X5,X2) => X3(X5)))))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(quantDeMorgan3, axiom, quantDeMorgan3 <=> 102.30/102.92 (![A,Xphi:($i > $o)]: 102.30/102.92 ((~(?[Xx]: (Xphi(Xx) & in(Xx,A)))) => (![Xx]: (in(Xx,A) => (~Xphi(Xx))))))). 102.30/102.92 tff('65', plain, 102.30/102.92 quantDeMorgan3 = 102.30/102.92 (![X2,X3:($i > $o)]: 102.30/102.92 ((~(?[X4]: (X3(X4) & in(X4,X2)))) => (![X5]: (in(X5,X2) => (~X3(X5)))))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(quantDeMorgan2, axiom, quantDeMorgan2 <=> 102.30/102.92 (![A,Xphi:($i > $o)]: 102.30/102.92 ((![Xx]: (in(Xx,A) => (~Xphi(Xx)))) => (~(?[Xx]: (Xphi(Xx) & in(Xx,A))))))). 102.30/102.92 tff('66', plain, 102.30/102.92 quantDeMorgan2 = 102.30/102.92 (![X2,X3:($i > $o)]: 102.30/102.92 ((![X4]: (in(X4,X2) => (~X3(X4)))) => (~(?[X5]: (X3(X5) & in(X5,X2)))))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(quantDeMorgan1, axiom, quantDeMorgan1 <=> 102.30/102.92 (![A,Xphi:($i > $o)]: 102.30/102.92 ((~(![Xx]: (in(Xx,A) => Xphi(Xx)))) => (?[Xx]: ((~Xphi(Xx)) & in(Xx,A)))))). 102.30/102.92 tff('67', plain, 102.30/102.92 quantDeMorgan1 = 102.30/102.92 (![X2,X3:($i > $o)]: 102.30/102.92 ((~(![X4]: (in(X4,X2) => X3(X4)))) => (?[X5]: ((~X3(X5)) & in(X5,X2))))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(vacuousDall, axiom, vacuousDall <=> 102.30/102.92 (![Xphi:($i > $o),Xx]: (in(Xx,emptyset) => Xphi(Xx)))). 102.30/102.92 tff('68', plain, 102.30/102.92 vacuousDall = (![X2:($i > $o),X3]: (in(X3,emptyset) => X2(X3))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(emptyE1, axiom, emptyE1 <=> 102.30/102.92 (![A,Xphi:($i > $o)]: 102.30/102.92 ((?[Xx]: (Xphi(Xx) & in(Xx,A))) => 102.30/102.92 ((dsetconstr(A,^[Xx]: Xphi(Xx)) = emptyset) => $false)))). 102.30/102.92 tff('69', plain, 102.30/102.92 emptyE1 = 102.30/102.92 (![X2,X3:($i > $o)]: 102.30/102.92 ((?[X4]: (X3(X4) & in(X4,X2))) => 102.30/102.92 ((dsetconstr(X2,^[V_1]: X3(V_1)) = emptyset) => $false))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(upairsetIR, axiom, upairsetIR <=> 102.30/102.92 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 102.30/102.92 tff('70', plain, 102.30/102.92 upairsetIR = (![X2,X3]: in(X3,setadjoin(X2,setadjoin(X3,emptyset)))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(upairsetIL, axiom, upairsetIL <=> 102.30/102.92 (![Xx,Xy]: in(Xx,setadjoin(Xx,setadjoin(Xy,emptyset))))). 102.30/102.92 tff('71', plain, 102.30/102.92 upairsetIL = (![X2,X3]: in(X2,setadjoin(X2,setadjoin(X3,emptyset)))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(upairsetE, axiom, upairsetE <=> 102.30/102.92 (![Xx,Xy,Xz]: 102.30/102.92 (in(Xz,setadjoin(Xx,setadjoin(Xy,emptyset))) => ((Xz = Xy) | (Xz = Xx))))). 102.30/102.92 tff('72', plain, 102.30/102.92 upairsetE = 102.30/102.92 (![X2,X3,X4]: 102.30/102.92 (in(X4,setadjoin(X2,setadjoin(X3,emptyset))) => 102.30/102.92 ((X4 = X3) | (X4 = X2)))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(singletonsswitch, axiom, singletonsswitch <=> 102.30/102.92 (![Xx,Xy]: (in(Xx,setadjoin(Xy,emptyset)) => in(Xy,setadjoin(Xx,emptyset))))). 102.30/102.92 tff('73', plain, 102.30/102.92 singletonsswitch = 102.30/102.92 (![X2,X3]: 102.30/102.92 (in(X2,setadjoin(X3,emptyset)) => in(X3,setadjoin(X2,emptyset)))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(eqinunit, axiom, eqinunit <=> 102.30/102.92 (![Xx,Xy]: ((Xx = Xy) => in(Xx,setadjoin(Xy,emptyset))))). 102.30/102.92 tff('74', plain, 102.30/102.92 eqinunit = (![X2,X3]: ((X2 = X3) => in(X2,setadjoin(X3,emptyset)))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(notinsingleton, axiom, notinsingleton <=> 102.30/102.92 (![Xx,Xy]: ((Xx != Xy) => (~in(Xy,setadjoin(Xx,emptyset)))))). 102.30/102.92 tff('75', plain, 102.30/102.92 notinsingleton = 102.30/102.92 (![X2,X3]: ((X2 != X3) => (~in(X3,setadjoin(X2,emptyset))))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(uniqinunit, axiom, uniqinunit <=> 102.30/102.92 (![Xx,Xy]: (in(Xx,setadjoin(Xy,emptyset)) => (Xx = Xy)))). 102.30/102.92 tff('76', plain, 102.30/102.92 uniqinunit = (![X2,X3]: (in(X2,setadjoin(X3,emptyset)) => (X2 = X3))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(nonemptyImpWitness, axiom, nonemptyImpWitness <=> 102.30/102.92 (![A]: (nonempty(A) => (?[Xx]: (in(Xx,A)))))). 102.30/102.92 tff('77', plain, 102.30/102.92 nonemptyImpWitness = (![X2]: (nonempty(X2) => (?[X3]: (in(X3,X2))))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(exuE2, axiom, exuE2 <=> 102.30/102.92 (![Xphi:($i > $o)]: 102.30/102.92 (exu(^[Xx]: Xphi(Xx)) => (?[Xx]: (![Xy]: (Xphi(Xy) <=> (Xy = Xx))))))). 102.30/102.92 tff('78', plain, 102.30/102.92 exuE2 = 102.30/102.92 (![X2:($i > $o)]: 102.30/102.92 (exu(^[V_1]: X2(V_1)) => (?[X3]: (![X4]: (X2(X4) <=> (X4 = X3)))))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(subPowSU, axiom, subPowSU <=> 102.30/102.92 (![A,Xx]: (in(Xx,A) => in(Xx,powerset(setunion(A)))))). 102.30/102.92 tff('79', plain, 102.30/102.92 subPowSU = (![X2,X3]: (in(X3,X2) => in(X3,powerset(setunion(X2))))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(setunionE, axiom, setunionE <=> 102.30/102.92 (![A,Xx]: 102.30/102.92 (in(Xx,setunion(A)) => 102.30/102.92 (![Xphi:$o]: ((![B]: (in(Xx,B) => (in(B,A) => Xphi))) => Xphi))))). 102.30/102.92 tff('80', plain, 102.30/102.92 setunionE = 102.30/102.92 (![X2,X3]: 102.30/102.92 (in(X3,setunion(X2)) => 102.30/102.92 (![X4:$o]: ((![X5]: (in(X3,X5) => (in(X5,X2) => X4))) => X4)))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(setunionI, axiom, setunionI <=> 102.30/102.92 (![A,Xx,B]: (in(Xx,B) => (in(B,A) => in(Xx,setunion(A)))))). 102.30/102.92 tff('81', plain, 102.30/102.92 setunionI = 102.30/102.92 (![X2,X3,X4]: (in(X3,X4) => (in(X4,X2) => in(X3,setunion(X2))))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(powersetE, axiom, powersetE <=> 102.30/102.92 (![A,B,Xx]: (in(B,powerset(A)) => (in(Xx,B) => in(Xx,A))))). 102.30/102.92 tff('82', plain, 102.30/102.92 powersetE = 102.30/102.92 (![X2,X3,X4]: (in(X3,powerset(X2)) => (in(X4,X3) => in(X4,X2)))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(emptyInPowerset, axiom, emptyInPowerset <=> 102.30/102.92 (![A]: in(emptyset,powerset(A)))). 102.30/102.92 tff('83', plain, emptyInPowerset = (![X2]: in(emptyset,powerset(X2))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(emptyinPowerset, axiom, emptyinPowerset <=> 102.30/102.92 (![A]: in(emptyset,powerset(A)))). 102.30/102.92 tff('84', plain, emptyinPowerset = (![X2]: in(emptyset,powerset(X2))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(powersetI, axiom, powersetI <=> 102.30/102.92 (![A,B]: ((![Xx]: (in(Xx,B) => in(Xx,A))) => in(B,powerset(A))))). 102.30/102.92 tff('85', plain, 102.30/102.92 powersetI = 102.30/102.92 (![X2,X3]: ((![X4]: (in(X4,X3) => in(X4,X2))) => in(X3,powerset(X2)))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(setoftrueEq, axiom, setoftrueEq <=> 102.30/102.92 (![A]: (dsetconstr(A,^[Xx]: $true) = A))). 102.30/102.92 tff('86', plain, setoftrueEq = (![X2]: (dsetconstr(X2,^[V_1]: $true) = X2)), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(setadjoinOr, axiom, setadjoinOr <=> 102.30/102.92 (![Xx,A,Xy]: (in(Xy,setadjoin(Xx,A)) => (in(Xy,A) | (Xy = Xx))))). 102.30/102.92 tff('87', plain, 102.30/102.92 setadjoinOr = 102.30/102.92 (![X2,X3,X4]: (in(X4,setadjoin(X2,X3)) => (in(X4,X3) | (X4 = X2)))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(setadjoinE, axiom, setadjoinE <=> 102.30/102.92 (![Xx,A,Xy]: 102.30/102.92 (in(Xy,setadjoin(Xx,A)) => 102.30/102.92 (![Xphi:$o]: (((Xy = Xx) => Xphi) => ((in(Xy,A) => Xphi) => Xphi)))))). 102.30/102.92 tff('88', plain, 102.30/102.92 setadjoinE = 102.30/102.92 (![X2,X3,X4]: 102.30/102.92 (in(X4,setadjoin(X2,X3)) => 102.30/102.92 (![X5:$o]: (((X4 = X2) => X5) => ((in(X4,X3) => X5) => X5))))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(setadjoinIR, axiom, setadjoinIR <=> 102.30/102.92 (![Xx,A,Xy]: (in(Xy,A) => in(Xy,setadjoin(Xx,A))))). 102.30/102.92 tff('89', plain, 102.30/102.92 setadjoinIR = (![X2,X3,X4]: (in(X4,X3) => in(X4,setadjoin(X2,X3)))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(emptyinunitempty, axiom, emptyinunitempty() = 102.30/102.92 in(emptyset,setadjoin(emptyset,emptyset))). 102.30/102.92 tff('90', plain, 102.30/102.92 emptyinunitempty = in(emptyset,setadjoin(emptyset,emptyset)), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(setadjoinIL, axiom, setadjoinIL <=> (![Xx,Xy]: in(Xx,setadjoin(Xx,Xy)))). 102.30/102.92 tff('91', plain, setadjoinIL = (![X2,X3]: in(X2,setadjoin(X2,X3))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(nonemptyI1, axiom, nonemptyI1 <=> 102.30/102.92 (![A]: ((?[Xx]: in(Xx,A)) => nonempty(A)))). 102.30/102.92 tff('92', plain, nonemptyI1 = (![X2]: ((?[X3]: in(X3,X2)) => nonempty(X2))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(nonemptyI, axiom, nonemptyI <=> 102.30/102.92 (![A,Xphi:($i > $o),Xx]: 102.30/102.92 (in(Xx,A) => (Xphi(Xx) => nonempty(dsetconstr(A,^[Xy]: Xphi(Xy))))))). 102.30/102.92 tff('93', plain, 102.30/102.92 nonemptyI = 102.30/102.92 (![X2,X3:($i > $o),X4]: 102.30/102.92 (in(X4,X2) => (X3(X4) => nonempty(dsetconstr(X2,^[V_1]: X3(V_1)))))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(nonemptyE1, axiom, nonemptyE1 <=> 102.30/102.92 (![A]: (nonempty(A) => (?[Xx]: in(Xx,A))))). 102.30/102.92 tff('94', plain, nonemptyE1 = (![X2]: (nonempty(X2) => (?[X3]: in(X3,X2)))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(nonempty, axiom, nonempty() = ^[Xx]: (Xx != emptyset)). 102.30/102.92 tff('95', plain, nonempty = (^[V_1]: (V_1 != emptyset)), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(setbeta, axiom, setbeta <=> 102.30/102.92 (![A,Xphi:($i > $o),Xx]: 102.30/102.92 (in(Xx,A) => (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) <=> Xphi(Xx))))). 102.30/102.92 tff('96', plain, 102.30/102.92 setbeta = 102.30/102.92 (![X2,X3:($i > $o),X4]: 102.30/102.92 (in(X4,X2) => (in(X4,dsetconstr(X2,^[V_1]: X3(V_1))) <=> X3(X4)))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(noeltsimpempty, axiom, noeltsimpempty <=> 102.30/102.92 (![A]: ((![Xx]: (~in(Xx,A))) => (A = emptyset)))). 102.30/102.92 tff('97', plain, 102.30/102.92 noeltsimpempty = (![X2]: ((![X3]: (~in(X3,X2))) => (X2 = emptyset))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(emptyI, axiom, emptyI <=> 102.30/102.92 (![A]: ((![Xx]: (~in(Xx,A))) => (A = emptyset)))). 102.30/102.92 tff('98', plain, 102.30/102.92 emptyI = (![X2]: ((![X3]: (~in(X3,X2))) => (X2 = emptyset))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(setext, axiom, setext <=> 102.30/102.92 (![A,B]: 102.30/102.92 ((![Xx]: (in(Xx,A) => in(Xx,B))) => 102.30/102.92 ((![Xx]: (in(Xx,B) => in(Xx,A))) => (A = B))))). 102.30/102.92 tff('99', plain, 102.30/102.92 setext = 102.30/102.92 (![X2,X3]: 102.30/102.92 ((![X4]: (in(X4,X2) => in(X4,X3))) => 102.30/102.92 ((![X5]: (in(X5,X3) => in(X5,X2))) => (X2 = X3)))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(exuE3e, axiom, exuE3e <=> 102.30/102.92 (![Xphi:($i > $o)]: (exu(^[Xx]: Xphi(Xx)) => (?[Xx]: Xphi(Xx))))). 102.30/102.92 tff('100', plain, 102.30/102.92 exuE3e = (![X2:($i > $o)]: (exu(^[V_1]: X2(V_1)) => (?[X3]: X2(X3)))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(notinemptyset, axiom, notinemptyset <=> (![Xx]: (~in(Xx,emptyset)))). 102.30/102.92 tff('101', plain, notinemptyset = (![X2]: (~in(X2,emptyset))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(emptysetimpfalse, axiom, emptysetimpfalse <=> 102.30/102.92 (![Xx]: (in(Xx,emptyset) => $false))). 102.30/102.92 tff('102', plain, emptysetimpfalse = (![X2]: (in(X2,emptyset) => $false)), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(emptysetE, axiom, emptysetE <=> 102.30/102.92 (![Xx]: (in(Xx,emptyset) => (![Xphi:$o]: Xphi)))). 102.30/102.92 tff('103', plain, emptysetE = (![X2]: (in(X2,emptyset) => (![X3:$o]: X3))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(prop2setE, axiom, prop2setE <=> 102.30/102.92 (![Xphi:$o,Xx]: (in(Xx,prop2set(Xphi)) => Xphi))). 102.30/102.92 tff('104', plain, prop2setE = (![X2:$o,X3]: (in(X3,prop2set(X2)) => X2)), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(exuE1, axiom, exuE1 <=> 102.30/102.92 (![Xphi:($i > $o)]: 102.30/102.92 (exu(^[Xx]: Xphi(Xx)) => 102.30/102.92 (?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx)))))). 102.30/102.92 tff('105', plain, 102.30/102.92 exuE1 = 102.30/102.92 (![X2:($i > $o)]: 102.30/102.92 (exu(^[V_1]: X2(V_1)) => 102.30/102.92 (?[X3]: ((![X4]: (X2(X4) => (X3 = X4))) & X2(X3))))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(dsetconstrER, axiom, dsetconstrER <=> 102.30/102.92 (![A,Xphi:($i > $o),Xx]: (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) => Xphi(Xx)))). 102.30/102.92 tff('106', plain, 102.30/102.92 dsetconstrER = 102.30/102.92 (![X2,X3:($i > $o),X4]: (in(X4,dsetconstr(X2,^[V_1]: X3(V_1))) => X3(X4))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(dsetconstrEL, axiom, dsetconstrEL <=> 102.30/102.92 (![A,Xphi:($i > $o),Xx]: (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) => in(Xx,A)))). 102.30/102.92 tff('107', plain, 102.30/102.92 dsetconstrEL = 102.30/102.92 (![X2,X3:($i > $o),X4]: 102.30/102.92 (in(X4,dsetconstr(X2,^[V_1]: X3(V_1))) => in(X4,X2))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(dsetconstrI, axiom, dsetconstrI <=> 102.30/102.92 (![A,Xphi:($i > $o),Xx]: 102.30/102.92 (in(Xx,A) => (Xphi(Xx) => in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))))))). 102.30/102.92 tff('108', plain, 102.30/102.92 dsetconstrI = 102.30/102.92 (![X2,X3:($i > $o),X4]: 102.30/102.92 (in(X4,X2) => (X3(X4) => in(X4,dsetconstr(X2,^[V_1]: X3(V_1)))))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(descrp, axiom, descrp <=> 102.30/102.92 (![Xphi:($i > $o)]: (exu(^[Xx]: Xphi(Xx)) => Xphi(descr(^[Xx]: Xphi(Xx)))))). 102.30/102.92 tff('109', plain, 102.30/102.92 descrp = 102.30/102.92 (![X2:($i > $o)]: (exu(^[V_1]: X2(V_1)) => X2(descr(^[V_2]: X2(V_2))))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(wellorderingAx, axiom, wellorderingAx <=> 102.30/102.92 (![A]: 102.30/102.92 (?[B]: 102.30/102.92 ((![C]: 102.30/102.92 (((?[Xx]: in(Xx,C)) & (![Xx]: (in(Xx,C) => in(Xx,A)))) => 102.30/102.92 (?[D,Xx]: 102.30/102.92 ((![E]: 102.30/102.92 (in(E,B) => (in(Xx,E) | (![Xy]: (in(Xy,E) => in(Xy,D)))))) & 102.30/102.92 (~(?[Xy]: (in(Xy,C) & in(Xy,D)))) & in(Xx,C) & in(D,B))))) & 102.30/102.92 (![C,D]: 102.30/102.92 ((in(D,B) & in(C,B)) => 102.30/102.92 ((![Xx]: (in(Xx,D) => in(Xx,C))) | 102.30/102.92 (![Xx]: (in(Xx,C) => in(Xx,D)))))) & 102.30/102.92 (![Xx,Xy]: 102.30/102.92 ((in(Xy,A) & in(Xx,A)) => 102.30/102.92 ((![C]: (in(C,B) => (in(Xx,C) <=> in(Xy,C)))) => (Xx = Xy)))) & 102.30/102.92 (![C]: (in(C,B) => (![Xx]: (in(Xx,C) => in(Xx,A))))))))). 102.30/102.92 tff('110', plain, 102.30/102.92 wellorderingAx = 102.30/102.92 (![X2]: 102.30/102.92 (?[X3]: 102.30/102.92 ((![X4]: 102.30/102.92 (((?[X5]: in(X5,X4)) & (![X6]: (in(X6,X4) => in(X6,X2)))) => 102.30/102.92 (?[X7,X8]: 102.30/102.92 ((![X9]: 102.30/102.92 (in(X9,X3) => 102.30/102.92 (in(X8,X9) | (![X10]: (in(X10,X9) => in(X10,X7)))))) & 102.30/102.92 (~(?[X11]: (in(X11,X4) & in(X11,X7)))) & in(X8,X4) & 102.30/102.92 in(X7,X3))))) & 102.30/102.92 (![X12,X13]: 102.30/102.92 ((in(X13,X3) & in(X12,X3)) => 102.30/102.92 ((![X14]: (in(X14,X13) => in(X14,X12))) | 102.30/102.92 (![X15]: (in(X15,X12) => in(X15,X13)))))) & 102.30/102.92 (![X16,X17]: 102.30/102.92 ((in(X17,X2) & in(X16,X2)) => 102.30/102.92 ((![X18]: (in(X18,X3) => (in(X16,X18) <=> in(X17,X18)))) => 102.30/102.92 (X16 = X17)))) & 102.30/102.92 (![X19]: (in(X19,X3) => (![X20]: (in(X20,X19) => in(X20,X2)))))))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(foundationAx, axiom, foundationAx <=> 102.30/102.92 (![A]: 102.30/102.92 ((?[Xx]: in(Xx,A)) => 102.30/102.92 (?[B]: ((~(?[Xx]: (in(Xx,A) & in(Xx,B)))) & in(B,A)))))). 102.30/102.92 tff('111', plain, 102.30/102.92 foundationAx = 102.30/102.92 (![X2]: 102.30/102.92 ((?[X3]: in(X3,X2)) => 102.30/102.92 (?[X4]: ((~(?[X5]: (in(X5,X2) & in(X5,X4)))) & in(X4,X2))))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(replAx, axiom, replAx <=> 102.30/102.92 (![Xphi:(($i * $i) > $o),A]: 102.30/102.92 ((![Xx]: (in(Xx,A) => exu(^[Xy]: Xphi(Xx,Xy)))) => 102.30/102.92 (?[B]: (![Xx]: (in(Xx,B) <=> (?[Xy]: (Xphi(Xy,Xx) & in(Xy,A))))))))). 102.30/102.92 tff('112', plain, 102.30/102.92 replAx = 102.30/102.92 (![X2:(($i * $i) > $o),X3]: 102.30/102.92 ((![X4]: (in(X4,X3) => exu(^[V_1]: X2(X4,V_1)))) => 102.30/102.92 (?[X5]: (![X6]: (in(X6,X5) <=> (?[X7]: (X2(X7,X6) & in(X7,X3)))))))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(omegaIndAx, axiom, omegaIndAx <=> 102.30/102.92 (![A]: 102.30/102.92 (((![Xx]: ((in(Xx,A) & in(Xx,omega)) => in(setadjoin(Xx,Xx),A))) & 102.30/102.92 in(emptyset,A)) => 102.30/102.92 (![Xx]: (in(Xx,omega) => in(Xx,A)))))). 102.30/102.92 tff('113', plain, 102.30/102.92 omegaIndAx = 102.30/102.92 (![X2]: 102.30/102.92 (((![X3]: ((in(X3,X2) & in(X3,omega)) => in(setadjoin(X3,X3),X2))) & 102.30/102.92 in(emptyset,X2)) => 102.30/102.92 (![X4]: (in(X4,omega) => in(X4,X2))))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(omegaSAx, axiom, omegaSAx <=> 102.30/102.92 (![Xx]: (in(Xx,omega) => in(setadjoin(Xx,Xx),omega)))). 102.30/102.92 tff('114', plain, 102.30/102.92 omegaSAx = (![X2]: (in(X2,omega) => in(setadjoin(X2,X2),omega))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(omega0Ax, axiom, omega0Ax() = in(emptyset,omega)). 102.30/102.92 tff('115', plain, omega0Ax = in(emptyset,omega), define([status(thm)])). 102.30/102.92 tff(setunionAx, axiom, setunionAx <=> 102.30/102.92 (![A,Xx]: (in(Xx,setunion(A)) <=> (?[B]: (in(B,A) & in(Xx,B)))))). 102.30/102.92 tff('116', plain, 102.30/102.92 setunionAx = 102.30/102.92 (![X2,X3]: (in(X3,setunion(X2)) <=> (?[X4]: (in(X4,X2) & in(X3,X4))))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(powersetAx, axiom, powersetAx <=> 102.30/102.92 (![A,B]: (in(B,powerset(A)) <=> (![Xx]: (in(Xx,B) => in(Xx,A)))))). 102.30/102.92 tff('117', plain, 102.30/102.92 powersetAx = 102.30/102.92 (![X2,X3]: (in(X3,powerset(X2)) <=> (![X4]: (in(X4,X3) => in(X4,X2))))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(setadjoinAx, axiom, setadjoinAx <=> 102.30/102.92 (![Xx,A,Xy]: (in(Xy,setadjoin(Xx,A)) <=> (in(Xy,A) | (Xy = Xx))))). 102.30/102.92 tff('118', plain, 102.30/102.92 setadjoinAx = 102.30/102.92 (![X2,X3,X4]: (in(X4,setadjoin(X2,X3)) <=> (in(X4,X3) | (X4 = X2)))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(emptysetAx, axiom, emptysetAx <=> (![Xx]: (~in(Xx,emptyset)))). 102.30/102.92 tff('119', plain, emptysetAx = (![X2]: (~in(X2,emptyset))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(setextAx, axiom, setextAx <=> 102.30/102.92 (![A,B]: ((![Xx]: (in(Xx,A) <=> in(Xx,B))) => (A = B)))). 102.30/102.92 tff('120', plain, 102.30/102.92 setextAx = (![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(exu, axiom, exu() = 102.30/102.92 ^[Xphi:($i > $o)]: (?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx)))). 102.30/102.92 tff('121', plain, 102.30/102.92 exu = 102.30/102.92 (^[V_1:($i > $o)]: (?[X2]: ((![X3]: (V_1(X3) => (X2 = X3))) & V_1(X2)))), 102.30/102.92 define([status(thm)])). 102.30/102.92 tff(setminusSubset2, conjecture, 102.30/102.92 (setextAx => 102.30/102.92 (emptysetAx => 102.30/102.92 (setadjoinAx => 102.30/102.92 (powersetAx => 102.30/102.92 (setunionAx => 102.30/102.92 (omega0Ax => 102.30/102.92 (omegaSAx => 102.30/102.92 (omegaIndAx => 102.30/102.92 (replAx => 102.30/102.92 (foundationAx => 102.30/102.92 (wellorderingAx => 102.30/102.92 (descrp => 102.30/102.92 (dsetconstrI => 102.30/102.92 (dsetconstrEL => 102.30/102.92 (dsetconstrER => 102.30/102.92 (exuE1 => 102.30/102.92 (prop2setE => 102.30/102.92 (emptysetE => 102.30/102.92 (emptysetimpfalse => 102.30/102.92 (notinemptyset => 102.30/102.92 (exuE3e => 102.30/102.92 (setext => 102.30/102.92 (emptyI => 102.30/102.92 (noeltsimpempty => 102.30/102.92 (setbeta => 102.30/102.92 (nonemptyE1 => 102.30/102.92 (nonemptyI => 102.30/102.92 (nonemptyI1 => 102.30/102.92 (setadjoinIL => 102.30/102.92 (emptyinunitempty => 102.30/102.92 (setadjoinIR => 102.30/102.92 (setadjoinE => 102.30/102.92 (setadjoinOr => 102.30/102.92 (setoftrueEq => 102.30/102.92 (powersetI => 102.30/102.92 (emptyinPowerset => 102.30/102.92 (emptyInPowerset => 102.30/102.92 (powersetE => 102.30/102.92 (setunionI => 102.30/102.92 (setunionE => 102.30/102.92 (subPowSU => 102.30/102.92 (exuE2 => 102.30/102.92 (nonemptyImpWitness => 102.30/102.92 (uniqinunit => 102.30/102.92 (notinsingleton => 102.30/102.92 (eqinunit => 102.30/102.92 (singletonsswitch => 102.30/102.92 (upairsetE => 102.30/102.92 (upairsetIL => 102.30/102.92 (upairsetIR => 102.30/102.92 (emptyE1 => 102.30/102.92 (vacuousDall => 102.30/102.92 (quantDeMorgan1 => 102.30/102.92 (quantDeMorgan2 => 102.30/102.92 (quantDeMorgan3 => 102.30/102.92 (quantDeMorgan4 => 102.30/102.92 (prop2setI => 102.30/102.92 (prop2set2propI => 102.30/102.92 (notdexE => 102.30/102.92 (notdallE => 102.30/102.92 (exuI1 => 102.30/102.92 (exuI3 => 102.30/102.92 (exuI2 => 102.30/102.92 (inCongP => 102.30/102.92 (in__Cong => 102.30/102.92 (exuE3u => 102.30/102.92 ( 102.30/102.92 exu__Cong => 102.30/102.92 ( 102.30/102.92 emptyset__Cong => 102.30/102.92 ( 102.30/102.92 setadjoin__Cong => 102.30/102.92 ( 102.30/102.92 powerset__Cong => 102.30/102.92 ( 102.30/102.92 setunion__Cong => 102.30/102.92 ( 102.30/102.92 omega__Cong => 102.30/102.92 ( 102.30/102.92 exuEu => 102.30/102.92 ( 102.30/102.92 descr__Cong => 102.30/102.92 ( 102.30/102.92 dsetconstr__Cong => 102.30/102.92 ( 102.30/102.92 subsetI1 => 102.30/102.92 ( 102.30/102.92 eqimpsubset2 => 102.30/102.92 ( 102.30/102.92 eqimpsubset1 => 102.30/102.92 ( 102.30/102.92 subsetI2 => 102.30/102.92 ( 102.30/102.92 emptysetsubset => 102.30/102.92 ( 102.30/102.92 subsetE => 102.30/102.92 ( 102.30/102.92 subsetE2 => 102.30/102.92 ( 102.30/102.92 notsubsetI => 102.30/102.92 ( 102.30/102.92 notequalI1 => 102.30/102.92 ( 102.30/102.92 notequalI2 => 102.30/102.92 ( 102.30/102.92 subsetRefl => 102.30/102.92 ( 102.30/102.92 subsetTrans => 102.30/102.92 ( 102.30/102.92 setadjoinSub => 102.30/102.92 ( 102.30/102.92 setadjoinSub2 => 102.30/102.92 ( 102.30/102.92 subset2powerset => 102.30/102.92 ( 102.30/102.92 setextsub => 102.30/102.92 ( 102.30/102.92 subsetemptysetimpeq => 102.30/102.92 ( 102.30/102.92 powersetI1 => 102.30/102.92 ( 102.30/102.92 powersetE1 => 102.30/102.92 ( 102.30/102.92 inPowerset => 102.30/102.92 ( 102.30/102.92 powersetsubset => 102.30/102.92 ( 102.30/102.92 sepInPowerset => 102.30/102.92 ( 102.30/102.92 sepSubset => 102.30/102.92 ( 102.30/102.92 binunionIL => 102.30/102.92 ( 102.30/102.92 upairset2IR => 102.30/102.92 ( 102.30/102.92 binunionIR => 102.30/102.92 ( 102.30/102.92 binunionEcases => 102.30/102.92 ( 102.30/102.92 binunionE => 102.30/102.92 ( 102.30/102.92 binunionLsub => 102.30/102.92 ( 102.30/102.92 binunionRsub => 102.30/102.92 ( 102.30/102.92 binintersectI => 102.30/102.92 ( 102.30/102.92 binintersectSubset5 => 102.30/102.92 ( 102.30/102.92 binintersectEL => 102.30/102.92 ( 102.30/102.92 binintersectLsub => 102.30/102.92 ( 102.30/102.92 binintersectSubset2 => 102.30/102.92 ( 102.30/102.92 binintersectSubset3 => 102.30/102.92 ( 102.30/102.92 binintersectER => 102.30/102.92 ( 102.30/102.92 disjointsetsI1 => 102.30/102.92 ( 102.30/102.92 binintersectRsub => 102.30/102.92 ( 102.30/102.92 binintersectSubset4 => 102.30/102.92 ( 102.30/102.92 binintersectSubset1 => 102.30/102.92 ( 102.30/102.92 bs114d => 102.30/102.92 ( 102.30/102.92 setminusI => 102.30/102.92 ( 102.30/102.92 setminusEL => 102.30/102.92 ( 102.30/102.92 setminusER => 102.30/102.92 ( 102.30/102.92 ![A,B]: 102.30/102.92 (subset( 102.30/102.92 A,B) => 102.30/102.92 (setminus( 102.30/102.92 A,B) = 102.30/102.92 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 102.30/102.92 tff(zf_stmt_0, conjecture, 102.30/102.92 ((![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))) => 102.30/102.92 ((![X5]: (~in(X5,emptyset))) => 102.30/102.92 ((![X6,X7,X8]: (in(X8,setadjoin(X6,X7)) <=> ((X8 = X6) | in(X8,X7)))) => 102.30/102.92 ((![X9,X10]: 102.30/102.92 (in(X10,powerset(X9)) <=> (![X11]: (in(X11,X10) => in(X11,X9))))) => 102.30/102.92 ((![X12,X13]: 102.30/102.92 (in(X13,setunion(X12)) <=> (?[X14]: (in(X13,X14) & in(X14,X12))))) => 102.30/102.92 (in(emptyset,omega) => 102.30/102.92 ((![X15]: (in(X15,omega) => in(setadjoin(X15,X15),omega))) => 102.30/102.92 ((![X16]: 102.30/102.92 ((in(emptyset,X16) & 102.30/102.92 (![X17]: 102.30/102.92 ((in(X17,omega) & in(X17,X16)) => 102.30/102.92 in(setadjoin(X17,X17),X16)))) => 102.30/102.92 (![X18]: (in(X18,omega) => in(X18,X16))))) => 102.30/102.92 ((![X19:(($i * $i) > $o),X20]: 102.30/102.92 ((![X21]: 102.30/102.92 (in(X21,X20) => 102.30/102.92 (?[X22]: 102.30/102.92 (X19(X21,X22) & (![X23]: (X19(X21,X23) => (X22 = X23))))))) => 102.30/102.92 (?[X24]: 102.30/102.92 (![X25]: 102.30/102.92 (in(X25,X24) <=> (?[X26]: (in(X26,X20) & X19(X26,X25)))))))) => 102.30/102.92 ((![X27]: 102.30/102.92 ((?[X28]: in(X28,X27)) => 102.30/102.92 (?[X29]: 102.30/102.92 (in(X29,X27) & (~(?[X30]: (in(X30,X29) & in(X30,X27)))))))) => 102.30/102.92 ((![X31]: 102.30/102.92 (?[X32]: 102.30/102.92 ((![X48]: 102.30/102.92 (in(X48,X32) => (![X49]: (in(X49,X48) => in(X49,X31))))) & 102.30/102.92 (![X45,X46]: 102.30/102.92 ((in(X45,X31) & in(X46,X31)) => 102.30/102.92 ((![X47]: 102.30/102.92 (in(X47,X32) => (in(X45,X47) <=> in(X46,X47)))) => 102.30/102.92 (X45 = X46)))) & 102.30/102.92 (![X41,X42]: 102.30/102.92 ((in(X41,X32) & in(X42,X32)) => 102.30/102.92 ((![X44]: (in(X44,X41) => in(X44,X42))) | 102.30/102.92 (![X43]: (in(X43,X42) => in(X43,X41)))))) & 102.30/102.92 (![X33]: 102.30/102.92 (((![X35]: (in(X35,X33) => in(X35,X31))) & 102.30/102.92 (?[X34]: in(X34,X33))) => 102.30/102.92 (?[X36,X37]: 102.30/102.92 (in(X36,X32) & in(X37,X33) & 102.30/102.92 (~(?[X40]: (in(X40,X36) & in(X40,X33)))) & 102.30/102.92 (![X38]: 102.30/102.92 (in(X38,X32) => 102.30/102.92 ((![X39]: (in(X39,X38) => in(X39,X36))) | 102.30/102.92 in(X37,X38))))))))))) => 102.30/102.92 ((![X50:($i > $o)]: 102.30/102.92 ((?[X51]: (X50(X51) & (![X52]: (X50(X52) => (X51 = X52))))) => 102.30/102.92 X50(descr('#ll_0'(X50))))) => 102.30/102.92 ((![X53,X54:($i > $o),X55]: 102.30/102.92 (in(X55,X53) => 102.30/102.92 (X54(X55) => in(X55,dsetconstr(X53,'#ll_0'(X54)))))) => 102.30/102.92 ((![X56,X57:($i > $o),X58]: 102.30/102.92 (in(X58,dsetconstr(X56,'#ll_0'(X57))) => in(X58,X56))) => 102.30/102.92 ((![X59,X60:($i > $o),X61]: 102.30/102.92 (in(X61,dsetconstr(X59,'#ll_0'(X60))) => X60(X61))) => 102.30/102.92 ((![X62:($i > $o)]: 102.30/102.92 ((?[X63]: 102.30/102.92 (X62(X63) & (![X64]: (X62(X64) => (X63 = X64))))) => 102.30/102.92 (?[X65]: 102.30/102.92 (X62(X65) & (![X66]: (X62(X66) => (X65 = X66))))))) => 102.30/102.92 ((![X67:$o,X68]: (in(X68,prop2set(X67)) => X67)) => 102.30/102.92 ((![X69]: (in(X69,emptyset) => (![X70:$o]: X70))) => 102.30/102.92 ((![X71]: (in(X71,emptyset) => $false)) => 102.30/102.92 ((![X72]: (~in(X72,emptyset))) => 102.30/102.92 ((![X73:($i > $o)]: 102.30/102.92 ((?[X74]: 102.30/102.92 (X73(X74) & (![X75]: (X73(X75) => (X74 = X75))))) => 102.30/102.92 (?[X76]: X73(X76)))) => 102.30/102.92 ((![X77,X78]: 102.30/102.92 ((![X79]: (in(X79,X77) => in(X79,X78))) => 102.30/102.92 ((![X80]: (in(X80,X78) => in(X80,X77))) => 102.30/102.92 (X77 = X78)))) => 102.30/102.92 ((![X81]: 102.30/102.92 ((![X82]: (~in(X82,X81))) => (X81 = emptyset))) => 102.30/102.92 ((![X83]: 102.30/102.92 ((![X84]: (~in(X84,X83))) => (X83 = emptyset))) => 102.30/102.92 ((![X85,X86:($i > $o),X87]: 102.30/102.92 (in(X87,X85) => 102.30/102.92 (in(X87,dsetconstr(X85,'#ll_0'(X86))) <=> 102.30/102.92 X86(X87)))) => 102.30/102.92 ((![X88]: 102.30/102.92 ((X88 != emptyset) => (?[X89]: in(X89,X88)))) => 102.30/102.92 ((![X90,X91:($i > $o),X92]: 102.30/102.92 (in(X92,X90) => 102.30/102.92 (X91(X92) => 102.30/102.92 (dsetconstr(X90,'#ll_0'(X91)) != emptyset)))) => 102.30/102.92 ((![X93]: 102.30/102.92 ((?[X94]: in(X94,X93)) => (X93 != emptyset))) => 102.30/102.92 ((![X95,X96]: in(X95,setadjoin(X95,X96))) => 102.30/102.92 (in(emptyset,setadjoin(emptyset,emptyset)) => 102.30/102.92 ((![X97,X98,X99]: 102.30/102.92 (in(X99,X98) => 102.30/102.92 in(X99,setadjoin(X97,X98)))) => 102.30/102.92 ((![X100,X101,X102]: 102.30/102.92 (in(X102,setadjoin(X100,X101)) => 102.30/102.92 (![X103:$o]: 102.30/102.92 (((X102 = X100) => X103) => 102.30/102.92 ((in(X102,X101) => X103) => X103))))) => 102.30/102.92 ((![X104,X105,X106]: 102.30/102.92 (in(X106,setadjoin(X104,X105)) => 102.30/102.92 ((X106 = X104) | in(X106,X105)))) => 102.30/102.92 ((![X107]: 102.30/102.92 (dsetconstr(X107,'#ll_1') = X107)) => 102.30/102.92 ((![X108,X109]: 102.30/102.92 ((![X110]: 102.30/102.92 (in(X110,X109) => in(X110,X108))) => 102.30/102.92 in(X109,powerset(X108)))) => 102.30/102.92 ((![X111]: in(emptyset,powerset(X111))) => 102.30/102.92 ((![X112]: in(emptyset,powerset(X112))) => 102.30/102.92 ((![X113,X114,X115]: 102.30/102.92 (in(X114,powerset(X113)) => 102.30/102.92 (in(X115,X114) => in(X115,X113)))) => 102.30/102.92 ((![X116,X117,X118]: 102.30/102.92 (in(X117,X118) => 102.30/102.92 (in(X118,X116) => 102.30/102.92 in(X117,setunion(X116))))) => 102.30/102.92 ((![X119,X120]: 102.30/102.92 (in(X120,setunion(X119)) => 102.30/102.92 (![X121:$o]: 102.30/102.92 ((![X122]: 102.30/102.92 (in(X120,X122) => 102.30/102.92 (in(X122,X119) => X121))) => 102.30/102.92 X121)))) => 102.30/102.92 ((![X123,X124]: 102.30/102.92 (in(X124,X123) => 102.30/102.92 in(X124, 102.30/102.92 powerset(setunion(X123))))) => 102.30/102.92 ((![X125:($i > $o)]: 102.30/102.92 ((?[X126]: 102.30/102.92 (X125(X126) & 102.30/102.92 (![X127]: 102.30/102.92 (X125(X127) => 102.30/102.92 (X126 = X127))))) => 102.30/102.92 (?[X128]: 102.30/102.92 (![X129]: 102.30/102.92 (X125(X129) <=> 102.30/102.92 (X129 = X128)))))) => 102.30/102.92 ((![X130]: 102.30/102.92 ((X130 != emptyset) => 102.30/102.92 (?[X131]: in(X131,X130)))) => 102.30/102.92 ((![X132,X133]: 102.30/102.92 (in(X132, 102.30/102.92 setadjoin(X133,emptyset)) => 102.30/102.92 (X132 = X133))) => 102.30/102.92 ((![X134,X135]: 102.30/102.92 ((X134 != X135) => 102.30/102.92 (~ 102.30/102.92 in(X135, 102.30/102.92 setadjoin(X134, 102.30/102.92 emptyset))))) => 102.30/102.92 ((![X136,X137]: 102.30/102.92 ((X136 = X137) => 102.30/102.92 in(X136, 102.30/102.92 setadjoin(X137, 102.30/102.92 emptyset)))) => 102.30/102.92 ((![X138,X139]: 102.30/102.92 (in(X138, 102.30/102.92 setadjoin(X139, 102.30/102.92 emptyset)) => 102.30/102.92 in(X139, 102.30/102.92 setadjoin(X138, 102.30/102.92 emptyset)))) => 102.30/102.92 ((![X140,X141,X142]: 102.30/102.92 (in(X142, 102.30/102.92 setadjoin(X140, 102.30/102.92 setadjoin( 102.30/102.92 X141, 102.30/102.92 emptyset))) => 102.30/102.92 ((X142 = X140) | 102.30/102.92 (X142 = X141)))) => 102.30/102.92 ((![X143,X144]: 102.30/102.92 in(X143, 102.30/102.92 setadjoin(X143, 102.30/102.92 setadjoin( 102.30/102.92 X144, 102.30/102.92 emptyset)))) => 102.30/102.92 ((![X145,X146]: 102.30/102.92 in(X146, 102.30/102.92 setadjoin(X145, 102.30/102.92 setadjoin( 102.30/102.92 X146, 102.30/102.92 emptyset)))) => 102.30/102.92 ((![X147,X148:($i > $o)]: 102.30/102.92 ((?[X149]: 102.30/102.92 (in(X149,X147) & 102.30/102.92 X148(X149))) => 102.30/102.92 ((dsetconstr( 102.30/102.92 X147,'#ll_0'(X148)) = 102.30/102.92 emptyset) => 102.30/102.92 $false))) => 102.30/102.92 ((![X150:($i > $o),X151]: 102.30/102.92 (in(X151,emptyset) => 102.30/102.92 X150(X151))) => 102.30/102.92 ((![X152,X153:($i > $o)]: 102.30/102.92 ((~ 102.30/102.92 (![X154]: 102.30/102.92 (in(X154,X152) => 102.30/102.92 X153(X154)))) => 102.30/102.92 (?[X155]: 102.30/102.92 (in(X155,X152) & 102.30/102.92 (~X153(X155)))))) => 102.30/102.92 ((![X156, 102.30/102.92 X157:($i > $o)]: 102.30/102.92 ((![X158]: 102.30/102.92 (in(X158,X156) => 102.30/102.92 (~X157(X158)))) => 102.30/102.92 (~ 102.30/102.92 (?[X159]: 102.30/102.92 (in( 102.30/102.92 X159,X156) & 102.30/102.92 X157(X159)))))) => 102.30/102.92 ((![X160, 102.30/102.92 X161:($i > $o)]: 102.30/102.92 ((~ 102.30/102.92 (?[X162]: 102.30/102.92 (in( 102.30/102.92 X162,X160) & 102.30/102.92 X161(X162)))) => 102.30/102.92 (![X163]: 102.30/102.92 (in(X163,X160) => 102.30/102.92 (~X161(X163)))))) => 102.30/102.92 ((![X164, 102.30/102.92 X165:($i > $o)]: 102.30/102.92 ((?[X166]: 102.30/102.92 (in( 102.30/102.92 X166,X164) & 102.30/102.92 (~ 102.30/102.92 X165( 102.30/102.92 X166)))) => 102.30/102.92 (~ 102.30/102.92 (![X167]: 102.30/102.92 (in( 102.30/102.92 X167,X164) => 102.30/102.92 X165( 102.30/102.92 X167)))))) => 102.30/102.92 ((![X168:$o]: 102.30/102.92 (X168 => 102.30/102.92 in(emptyset, 102.30/102.92 prop2set( 102.30/102.92 X168)))) => 102.30/102.92 ((![X169:$o]: 102.30/102.92 (X169 => 102.30/102.92 set2prop( 102.30/102.92 prop2set( 102.30/102.92 X169)))) => 102.30/102.92 ((![X170, 102.30/102.92 X171:( 102.30/102.92 $i > $o)]: 102.30/102.92 ((~ 102.30/102.92 (?[X172]: 102.30/102.92 (in( 102.30/102.92 X172,X170) & 102.30/102.92 X171( 102.30/102.92 X172)))) => 102.30/102.92 (![X173]: 102.30/102.92 ( 102.30/102.92 in( 102.30/102.92 X173,X170) => 102.30/102.92 ( 102.30/102.92 ~ 102.30/102.92 X171( 102.30/102.92 X173)))))) => 102.30/102.92 ((![X174, 102.30/102.92 X175:( 102.30/102.92 $i > $o)]: 102.30/102.92 ((~ 102.30/102.92 ( 102.30/102.92 ![X176]: 102.30/102.92 (in( 102.30/102.92 X176,X174) => 102.30/102.92 X175( 102.30/102.92 X176)))) => 102.30/102.92 (?[X177]: 102.30/102.92 (in( 102.30/102.92 X177,X174) & 102.30/102.92 (~ 102.30/102.92 X175( 102.30/102.92 X177)))))) => 102.30/102.92 ((![X178:( 102.30/102.92 $i > $o)]: 102.30/102.92 ((?[X179]: 102.30/102.92 (X178( 102.30/102.92 X179) & 102.30/102.92 (![X180]: 102.30/102.92 (X178( 102.30/102.92 X180) => 102.30/102.92 (X179 = 102.30/102.92 X180))))) => 102.30/102.92 (?[X181]: 102.30/102.92 (X178( 102.30/102.92 X181) & 102.30/102.92 (![X182]: 102.30/102.92 (X178( 102.30/102.92 X182) => 102.30/102.92 (X181 = 102.30/102.92 X182))))))) => 102.30/102.92 ((![X183:( 102.30/102.92 $i > $o)]: 102.30/102.92 (( 102.30/102.92 ?[X184]: 102.30/102.92 X183( 102.30/102.92 X184)) => 102.30/102.92 ( 102.30/102.92 ( 102.30/102.92 ![X185, 102.30/102.92 X186]: 102.30/102.92 (X183( 102.30/102.92 X185) => 102.30/102.92 (X183( 102.30/102.92 X186) => 102.30/102.92 (X185 = 102.30/102.92 X186)))) => 102.30/102.92 ( 102.30/102.92 ?[X187]: 102.30/102.92 (X183( 102.30/102.92 X187) & 102.30/102.92 (![X188]: 102.30/102.92 (X183( 102.30/102.92 X188) => 102.30/102.92 (X187 = 102.30/102.92 X188)))))))) => 102.30/102.92 ((![X189:( 102.30/102.92 $i > $o)]: 102.30/102.92 ( 102.30/102.92 ( 102.30/102.92 ?[X190]: 102.30/102.92 (![X191]: 102.30/102.92 (X189( 102.30/102.92 X191) <=> 102.30/102.92 (X191 = 102.30/102.92 X190)))) => 102.30/102.92 ( 102.30/102.92 ?[X192]: 102.30/102.92 (X189( 102.30/102.92 X192) & 102.30/102.92 (![X193]: 102.30/102.92 (X189( 102.30/102.92 X193) => 102.30/102.92 (X192 = 102.30/102.92 X193))))))) => 102.30/102.92 ((![X194, 102.30/102.92 X195]: 102.30/102.92 (( 102.30/102.92 X194 = 102.30/102.92 X195) => 102.30/102.92 (![X196, 102.30/102.92 X197]: 102.30/102.92 (( 102.30/102.92 X196 = 102.30/102.92 X197) => 102.30/102.92 (in( 102.30/102.92 X196,X194) => 102.30/102.92 in( 102.30/102.92 X197,X195)))))) => 102.30/102.92 ((![X198, 102.30/102.92 X199]: 102.30/102.92 (( 102.30/102.92 X198 = 102.30/102.92 X199) => 102.30/102.92 (![X200, 102.30/102.92 X201]: 102.30/102.92 (( 102.30/102.92 X200 = 102.30/102.92 X201) => 102.30/102.92 (in( 102.30/102.92 X200,X198) <=> 102.30/102.92 in( 102.30/102.92 X201,X199)))))) => 102.30/102.92 (( 102.30/102.92 ![X202:( 102.30/102.92 $i > $o)]: 102.30/102.92 (( 102.30/102.92 ?[X203]: 102.30/102.92 (X202( 102.30/102.92 X203) & 102.30/102.92 (![X204]: 102.30/102.92 (X202( 102.30/102.92 X204) => 102.30/102.92 (X203 = 102.30/102.92 X204))))) => 102.30/102.92 (![X205, 102.30/102.92 X206]: 102.30/102.92 (X202( 102.30/102.92 X205) => 102.30/102.92 (X202( 102.30/102.92 X206) => 102.30/102.92 (X205 = 102.30/102.92 X206)))))) => 102.30/102.92 ( 102.30/102.92 ( 102.30/102.92 ![X207:( 102.30/102.92 $i > $o), 102.30/102.92 X208:( 102.30/102.92 $i > $o)]: 102.30/102.92 (( 102.30/102.92 ![X209, 102.30/102.92 X210]: 102.30/102.92 (( 102.30/102.92 X209 = 102.30/102.92 X210) => 102.30/102.92 (X207( 102.30/102.92 X209) <=> 102.30/102.92 X208( 102.30/102.92 X210)))) => 102.30/102.92 (( 102.30/102.92 ?[X211]: 102.30/102.92 (X207( 102.30/102.92 X211) & 102.30/102.92 (![X212]: 102.30/102.92 (X207( 102.30/102.93 X212) => 102.30/102.93 (X211 = 102.30/102.93 X212))))) <=> 102.30/102.93 (?[X213]: 102.30/102.93 (X208( 102.30/102.93 X213) & 102.30/102.93 (![X214]: 102.30/102.93 (X208( 102.30/102.93 X214) => 102.30/102.93 (X213 = 102.30/102.93 X214)))))))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 emptyset = 102.30/102.93 emptyset) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X215, 102.30/102.93 X216]: 102.30/102.93 (( 102.30/102.93 X215 = 102.30/102.93 X216) => 102.30/102.93 (![X217, 102.30/102.93 X218]: 102.30/102.93 (( 102.30/102.93 X217 = 102.30/102.93 X218) => 102.30/102.93 (setadjoin( 102.30/102.93 X215,X217) = 102.30/102.93 setadjoin( 102.30/102.93 X216,X218)))))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X219, 102.30/102.93 X220]: 102.30/102.93 (( 102.30/102.93 X219 = 102.30/102.93 X220) => 102.30/102.93 (powerset( 102.30/102.93 X219) = 102.30/102.93 powerset( 102.30/102.93 X220)))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X221, 102.30/102.93 X222]: 102.30/102.93 (( 102.30/102.93 X221 = 102.30/102.93 X222) => 102.30/102.93 (setunion( 102.30/102.93 X221) = 102.30/102.93 setunion( 102.30/102.93 X222)))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 omega = 102.30/102.93 omega) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X223:( 102.30/102.93 $i > $o)]: 102.30/102.93 (( 102.30/102.93 ?[X224]: 102.30/102.93 (X223( 102.30/102.93 X224) & 102.30/102.93 (![X225]: 102.30/102.93 (X223( 102.30/102.93 X225) => 102.30/102.93 (X224 = 102.30/102.93 X225))))) => 102.30/102.93 (![X226, 102.30/102.93 X227]: 102.30/102.93 (X223( 102.30/102.93 X226) => 102.30/102.93 (X223( 102.30/102.93 X227) => 102.30/102.93 (X226 = 102.30/102.93 X227)))))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X228:( 102.30/102.93 $i > $o), 102.30/102.93 X229:( 102.30/102.93 $i > $o)]: 102.30/102.93 (( 102.30/102.93 ![X230, 102.30/102.93 X231]: 102.30/102.93 (( 102.30/102.93 X230 = 102.30/102.93 X231) => 102.30/102.93 (X228( 102.30/102.93 X230) <=> 102.30/102.93 X229( 102.30/102.93 X231)))) => 102.30/102.93 (( 102.30/102.93 ?[X232]: 102.30/102.93 (X228( 102.30/102.93 X232) & 102.30/102.93 (![X233]: 102.30/102.93 (X228( 102.30/102.93 X233) => 102.30/102.93 (X232 = 102.30/102.93 X233))))) => 102.30/102.93 (( 102.30/102.93 ?[X234]: 102.30/102.93 (X229( 102.30/102.93 X234) & 102.30/102.93 (![X235]: 102.30/102.93 (X229( 102.30/102.93 X235) => 102.30/102.93 (X234 = 102.30/102.93 X235))))) => 102.30/102.93 (descr( 102.30/102.93 '#ll_0'( 102.30/102.93 X228)) = 102.30/102.93 descr( 102.30/102.93 '#ll_0'( 102.30/102.93 X229))))))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X236, 102.30/102.93 X237]: 102.30/102.93 (( 102.30/102.93 X236 = 102.30/102.93 X237) => 102.30/102.93 (![X238:( 102.30/102.93 $i > $o), 102.30/102.93 X239:( 102.30/102.93 $i > $o)]: 102.30/102.93 (( 102.30/102.93 ![X240]: 102.30/102.93 (in( 102.30/102.93 X240,X236) => 102.30/102.93 (![X241]: 102.30/102.93 (in( 102.30/102.93 X241,X237) => 102.30/102.93 (( 102.30/102.93 X240 = 102.30/102.93 X241) => 102.30/102.93 (X238( 102.30/102.93 X240) <=> 102.30/102.93 X239( 102.30/102.93 X241))))))) => 102.30/102.93 (dsetconstr( 102.30/102.93 X236, 102.30/102.93 '#ll_0'( 102.30/102.93 X238)) = 102.30/102.93 dsetconstr( 102.30/102.93 X237, 102.30/102.93 '#ll_0'( 102.30/102.93 X239))))))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X242, 102.30/102.93 X243]: 102.30/102.93 (( 102.30/102.93 ![X244]: 102.30/102.93 (in( 102.30/102.93 X244,X242) => 102.30/102.93 in( 102.30/102.93 X244,X243))) => 102.30/102.93 subset( 102.30/102.93 X242,X243))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X245, 102.30/102.93 X246]: 102.30/102.93 (( 102.30/102.93 X245 = 102.30/102.93 X246) => 102.30/102.93 subset( 102.30/102.93 X246,X245))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X247, 102.30/102.93 X248]: 102.30/102.93 (( 102.30/102.93 X247 = 102.30/102.93 X248) => 102.30/102.93 subset( 102.30/102.93 X247,X248))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X249, 102.30/102.93 X250]: 102.30/102.93 (( 102.30/102.93 ![X251]: 102.30/102.93 (in( 102.30/102.93 X251,X249) => 102.30/102.93 in( 102.30/102.93 X251,X250))) => 102.30/102.93 subset( 102.30/102.93 X249,X250))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X252]: 102.30/102.93 subset( 102.30/102.93 emptyset, 102.30/102.93 X252)) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X253, 102.30/102.93 X254,X255]: 102.30/102.93 (subset( 102.30/102.93 X253,X254) => 102.30/102.93 (in( 102.30/102.93 X255,X253) => 102.30/102.93 in( 102.30/102.93 X255,X254)))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X256, 102.30/102.93 X257,X258]: 102.30/102.93 (subset( 102.30/102.93 X256,X257) => 102.30/102.93 (( 102.30/102.93 ~ 102.30/102.93 in( 102.30/102.93 X258,X257)) => 102.30/102.93 (~ 102.30/102.93 in( 102.30/102.93 X258,X256))))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X259, 102.30/102.93 X260,X261]: 102.30/102.93 (in( 102.30/102.93 X261,X259) => 102.30/102.93 (( 102.30/102.93 ~ 102.30/102.93 in( 102.30/102.93 X261,X260)) => 102.30/102.93 (~ 102.30/102.93 subset( 102.30/102.93 X259,X260))))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X262, 102.30/102.93 X263]: 102.30/102.93 (( 102.30/102.93 ~ 102.30/102.93 subset( 102.30/102.93 X262,X263)) => 102.30/102.93 (X262 != 102.30/102.93 X263))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X264, 102.30/102.93 X265,X266]: 102.30/102.93 (in( 102.30/102.93 X266,X264) => 102.30/102.93 (( 102.30/102.93 ~ 102.30/102.93 in( 102.30/102.93 X266,X265)) => 102.30/102.93 (X264 != 102.30/102.93 X265)))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X267]: 102.30/102.93 subset( 102.30/102.93 X267,X267)) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X268, 102.30/102.93 X269,X270]: 102.30/102.93 (subset( 102.30/102.93 X268,X269) => 102.30/102.93 (subset( 102.30/102.93 X269,X270) => 102.30/102.93 subset( 102.30/102.93 X268,X270)))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X271, 102.30/102.93 X272]: 102.30/102.93 subset( 102.30/102.93 X272, 102.30/102.93 setadjoin( 102.30/102.93 X271,X272))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X273, 102.30/102.93 X274,X275]: 102.30/102.93 (subset( 102.30/102.93 X273,X275) => 102.30/102.93 subset( 102.30/102.93 X273, 102.30/102.93 setadjoin( 102.30/102.93 X274,X275)))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X276, 102.30/102.93 X277]: 102.30/102.93 (subset( 102.30/102.93 X276,X277) => 102.30/102.93 in( 102.30/102.93 X276, 102.30/102.93 powerset( 102.30/102.93 X277)))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X278, 102.30/102.93 X279]: 102.30/102.93 (subset( 102.30/102.93 X278,X279) => 102.30/102.93 (subset( 102.30/102.93 X279,X278) => 102.30/102.93 (X278 = 102.30/102.93 X279)))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X280]: 102.30/102.93 (subset( 102.30/102.93 X280, 102.30/102.93 emptyset) => 102.30/102.93 (X280 = 102.30/102.93 emptyset))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X281, 102.30/102.93 X282]: 102.30/102.93 (subset( 102.30/102.93 X282,X281) => 102.30/102.93 in( 102.30/102.93 X282, 102.30/102.93 powerset( 102.30/102.93 X281)))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X283, 102.30/102.93 X284]: 102.30/102.93 (in( 102.30/102.93 X284, 102.30/102.93 powerset( 102.30/102.93 X283)) => 102.30/102.93 subset( 102.30/102.93 X284,X283))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X285]: 102.30/102.93 in( 102.30/102.93 X285, 102.30/102.93 powerset( 102.30/102.93 X285))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X286, 102.30/102.93 X287]: 102.30/102.93 (subset( 102.30/102.93 X286,X287) => 102.30/102.93 subset( 102.30/102.93 powerset( 102.30/102.93 X286), 102.30/102.93 powerset( 102.30/102.93 X287)))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X288, 102.30/102.93 X289:( 102.30/102.93 $i > $o)]: 102.30/102.93 in( 102.30/102.93 dsetconstr( 102.30/102.93 X288, 102.30/102.93 '#ll_0'( 102.30/102.93 X289)), 102.30/102.93 powerset( 102.30/102.93 X288))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X290, 102.30/102.93 X291:( 102.30/102.93 $i > $o)]: 102.30/102.93 subset( 102.30/102.93 dsetconstr( 102.30/102.93 X290, 102.30/102.93 '#ll_0'( 102.30/102.93 X291)), 102.30/102.93 X290)) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X292, 102.30/102.93 X293,X294]: 102.30/102.93 (in( 102.30/102.93 X294,X292) => 102.30/102.93 in( 102.30/102.93 X294, 102.30/102.93 binunion( 102.30/102.93 X292,X293)))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X295, 102.30/102.93 X296]: 102.30/102.93 in( 102.30/102.93 X296, 102.30/102.93 setadjoin( 102.30/102.93 X295, 102.30/102.93 setadjoin( 102.30/102.93 X296, 102.30/102.93 emptyset)))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X297, 102.30/102.93 X298,X299]: 102.30/102.93 (in( 102.30/102.93 X299,X298) => 102.30/102.93 in( 102.30/102.93 X299, 102.30/102.93 binunion( 102.30/102.93 X297,X298)))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X300, 102.30/102.93 X301, 102.30/102.93 X302, 102.30/102.93 X303:$o]: 102.30/102.93 (in( 102.30/102.93 X302, 102.30/102.93 binunion( 102.30/102.93 X300,X301)) => 102.30/102.93 (( 102.30/102.93 in( 102.30/102.93 X302,X300) => 102.30/102.93 X303) => 102.30/102.93 (( 102.30/102.93 in( 102.30/102.93 X302,X301) => 102.30/102.93 X303) => 102.30/102.93 X303)))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X304, 102.30/102.93 X305,X306]: 102.30/102.93 (in( 102.30/102.93 X306, 102.30/102.93 binunion( 102.30/102.93 X304,X305)) => 102.30/102.93 (in( 102.30/102.93 X306,X304) | 102.30/102.93 in( 102.30/102.93 X306,X305)))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X307, 102.30/102.93 X308]: 102.30/102.93 subset( 102.30/102.93 X307, 102.30/102.93 binunion( 102.30/102.93 X307,X308))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X309, 102.30/102.93 X310]: 102.30/102.93 subset( 102.30/102.93 X310, 102.30/102.93 binunion( 102.30/102.93 X309,X310))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X311, 102.30/102.93 X312,X313]: 102.30/102.93 (in( 102.30/102.93 X313,X311) => 102.30/102.93 (in( 102.30/102.93 X313,X312) => 102.30/102.93 in( 102.30/102.93 X313, 102.30/102.93 binintersect( 102.30/102.93 X311,X312))))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X314, 102.30/102.93 X315,X316]: 102.30/102.93 (subset( 102.30/102.93 X316,X314) => 102.30/102.93 (subset( 102.30/102.93 X316,X315) => 102.30/102.93 subset( 102.30/102.93 X316, 102.30/102.93 binintersect( 102.30/102.93 X314,X315))))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X317, 102.30/102.93 X318,X319]: 102.30/102.93 (in( 102.30/102.93 X319, 102.30/102.93 binintersect( 102.30/102.93 X317,X318)) => 102.30/102.93 in( 102.30/102.93 X319,X317))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X320, 102.30/102.93 X321]: 102.30/102.93 subset( 102.30/102.93 binintersect( 102.30/102.93 X320,X321), 102.30/102.93 X320)) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X322, 102.30/102.93 X323]: 102.30/102.93 (subset( 102.30/102.93 X322,X323) => 102.30/102.93 (binintersect( 102.30/102.93 X322,X323) = 102.30/102.93 X322))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X324, 102.30/102.93 X325]: 102.30/102.93 (( 102.30/102.93 binintersect( 102.30/102.93 X324,X325) = 102.30/102.93 X325) => 102.30/102.93 subset( 102.30/102.93 X325,X324))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X326, 102.30/102.93 X327,X328]: 102.30/102.93 (in( 102.30/102.93 X328, 102.30/102.93 binintersect( 102.30/102.93 X326,X327)) => 102.30/102.93 in( 102.30/102.93 X328,X327))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X329, 102.30/102.93 X330]: 102.30/102.93 (( 102.30/102.93 ~ 102.30/102.93 ( 102.30/102.93 ?[X331]: 102.30/102.93 (in( 102.30/102.93 X331,X329) & 102.30/102.93 in( 102.30/102.93 X331,X330)))) => 102.30/102.93 (binintersect( 102.30/102.93 X329,X330) = 102.30/102.93 emptyset))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X332, 102.30/102.93 X333]: 102.30/102.93 subset( 102.30/102.93 binintersect( 102.30/102.93 X332,X333), 102.30/102.93 X333)) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X334, 102.30/102.93 X335]: 102.30/102.93 (subset( 102.30/102.93 X335,X334) => 102.30/102.93 (binintersect( 102.30/102.93 X334,X335) = 102.30/102.93 X335))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X336, 102.30/102.93 X337]: 102.30/102.93 (( 102.30/102.93 binintersect( 102.30/102.93 X336,X337) = 102.30/102.93 X336) => 102.30/102.93 subset( 102.30/102.93 X336,X337))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X338, 102.30/102.93 X339,X340]: 102.30/102.93 (binintersect( 102.30/102.93 X338, 102.30/102.93 binunion( 102.30/102.93 X339,X340)) = 102.30/102.93 binunion( 102.30/102.93 binintersect( 102.30/102.93 X338,X339), 102.30/102.93 binintersect( 102.30/102.93 X338,X340)))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X341, 102.30/102.93 X342,X343]: 102.30/102.93 (in( 102.30/102.93 X343,X341) => 102.30/102.93 (( 102.30/102.93 ~ 102.30/102.93 in( 102.30/102.93 X343,X342)) => 102.30/102.93 in( 102.30/102.93 X343, 102.30/102.93 setminus( 102.30/102.93 X341,X342))))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X344, 102.30/102.93 X345,X346]: 102.30/102.93 (in( 102.30/102.93 X346, 102.30/102.93 setminus( 102.30/102.93 X344,X345)) => 102.30/102.93 in( 102.30/102.93 X346,X344))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X347, 102.30/102.93 X348,X349]: 102.30/102.93 (in( 102.30/102.93 X349, 102.30/102.93 setminus( 102.30/102.93 X347,X348)) => 102.30/102.93 (~ 102.30/102.93 in( 102.30/102.93 X349,X348)))) => 102.30/102.93 ( 102.30/102.93 ![X350, 102.30/102.93 X351]: 102.30/102.93 (subset( 102.30/102.93 X350,X351) => 102.30/102.93 (setminus( 102.30/102.93 X350,X351) = 102.30/102.93 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 102.30/102.93 tff(zf_stmt_1, type, zip_tseitin5 : ($i * $i > $o) > $o). 102.30/102.93 tff(zf_stmt_2, axiom, 102.30/102.93 (zip_tseitin5(X211,X207) <=> 102.30/102.93 ((![X212]: zip_tseitin4(X212,X211,X207)) & X207(X211)))). 102.30/102.93 tff(zf_stmt_3, type, zip_tseitin4 : ($i * $i * $i > $o) > $o). 102.30/102.93 tff(zf_stmt_4, axiom, 102.30/102.93 (zip_tseitin4(X212,X211,X207) <=> (X207(X212) => (X211 = X212)))). 102.30/102.93 tff(zf_stmt_5, type, zip_tseitin3 : ($i * $i * $i * ($i * $i) > $o) > $o). 102.30/102.93 tff(zf_stmt_6, axiom, 102.30/102.93 (zip_tseitin3(X26,X25,X20,X19) <=> (X19(X26,X25) & in(X26,X20)))). 102.30/102.93 tff(zf_stmt_7, type, zip_tseitin2 : ($i * $i * $i) > $o). 102.30/102.93 tff(zf_stmt_8, axiom, 102.30/102.93 (zip_tseitin2(X14,X13,X12) <=> (in(X14,X12) & in(X13,X14)))). 102.30/102.93 tff(zf_stmt_9, type, zip_tseitin1 : ($i * $i * $i) > $o). 102.30/102.93 tff(zf_stmt_10, axiom, 102.30/102.93 (zip_tseitin1(X11,X10,X9) <=> (in(X11,X10) => in(X11,X9)))). 102.30/102.93 tff(zf_stmt_11, type, zip_tseitin0 : ($i * $i * $i) > $o). 102.30/102.93 tff(zf_stmt_12, axiom, (zip_tseitin0(X8,X7,X6) <=> (in(X8,X7) | (X8 = X6)))). 102.30/102.93 tff(zf_stmt_13, conjecture, 102.30/102.93 ((![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))) => 102.30/102.93 ((![X5]: (~in(X5,emptyset))) => 102.30/102.93 ((![X6,X7,X8]: (in(X8,setadjoin(X6,X7)) <=> zip_tseitin0(X8,X7,X6))) => 102.30/102.93 ((![X9,X10]: 102.30/102.93 (in(X10,powerset(X9)) <=> (![X11]: zip_tseitin1(X11,X10,X9)))) => 102.30/102.93 ((![X12,X13]: 102.30/102.93 (in(X13,setunion(X12)) <=> (?[X14]: zip_tseitin2(X14,X13,X12)))) => 102.30/102.93 (in(emptyset,omega) => 102.30/102.93 ((![X15]: (in(X15,omega) => in(setadjoin(X15,X15),omega))) => 102.30/102.93 ((![X16]: 102.30/102.93 (((![X17]: 102.30/102.93 ((in(X17,X16) & in(X17,omega)) => 102.30/102.93 in(setadjoin(X17,X17),X16))) & 102.30/102.93 in(emptyset,X16)) => 102.30/102.93 (![X18]: (in(X18,omega) => in(X18,X16))))) => 102.30/102.93 ((![X19:(($i * $i) > $o),X20]: 102.30/102.93 ((![X21]: 102.30/102.93 (in(X21,X20) => 102.30/102.93 (?[X22]: 102.30/102.93 ((![X23]: (X19(X21,X23) => (X22 = X23))) & X19(X21,X22))))) => 102.30/102.93 (?[X24]: 102.30/102.93 (![X25]: 102.30/102.93 (in(X25,X24) <=> (?[X26]: zip_tseitin3(X26,X25,X20,X19))))))) => 102.30/102.93 ((![X27]: 102.30/102.93 ((?[X28]: in(X28,X27)) => 102.30/102.93 (?[X29]: 102.30/102.93 ((~(?[X30]: (in(X30,X27) & in(X30,X29)))) & in(X29,X27))))) => 102.30/102.93 ((![X31]: 102.30/102.93 (?[X32]: 102.30/102.93 ((![X33]: 102.30/102.93 (((?[X34]: in(X34,X33)) & 102.30/102.93 (![X35]: (in(X35,X33) => in(X35,X31)))) => 102.30/102.93 (?[X36,X37]: 102.30/102.93 ((![X38]: 102.30/102.93 (in(X38,X32) => 102.30/102.93 (in(X37,X38) | 102.30/102.93 (![X39]: (in(X39,X38) => in(X39,X36)))))) & 102.30/102.93 (~(?[X40]: (in(X40,X33) & in(X40,X36)))) & 102.30/102.93 in(X37,X33) & in(X36,X32))))) & 102.30/102.93 (![X41,X42]: 102.30/102.93 ((in(X42,X32) & in(X41,X32)) => 102.30/102.93 ((![X43]: (in(X43,X42) => in(X43,X41))) | 102.30/102.93 (![X44]: (in(X44,X41) => in(X44,X42)))))) & 102.30/102.93 (![X45,X46]: 102.30/102.93 ((in(X46,X31) & in(X45,X31)) => 102.30/102.93 ((![X47]: 102.30/102.93 (in(X47,X32) => (in(X45,X47) <=> in(X46,X47)))) => 102.30/102.93 (X45 = X46)))) & 102.30/102.93 (![X48]: 102.30/102.93 (in(X48,X32) => (![X49]: (in(X49,X48) => in(X49,X31)))))))) => 102.30/102.93 ((![X50:($i > $o)]: 102.30/102.93 ((?[X51]: ((![X52]: (X50(X52) => (X51 = X52))) & X50(X51))) => 102.30/102.93 X50(descr('#ll_0'(X50))))) => 102.30/102.93 ((![X53,X54:($i > $o),X55]: 102.30/102.93 (in(X55,X53) => 102.30/102.93 (X54(X55) => in(X55,dsetconstr(X53,'#ll_0'(X54)))))) => 102.30/102.93 ((![X56,X57:($i > $o),X58]: 102.30/102.93 (in(X58,dsetconstr(X56,'#ll_0'(X57))) => in(X58,X56))) => 102.30/102.93 ((![X59,X60:($i > $o),X61]: 102.30/102.93 (in(X61,dsetconstr(X59,'#ll_0'(X60))) => X60(X61))) => 102.30/102.93 ((![X62:($i > $o)]: 102.30/102.93 ((?[X63]: 102.30/102.93 ((![X64]: (X62(X64) => (X63 = X64))) & X62(X63))) => 102.30/102.93 (?[X65]: 102.30/102.93 ((![X66]: (X62(X66) => (X65 = X66))) & X62(X65))))) => 102.30/102.93 ((![X67:$o,X68]: (in(X68,prop2set(X67)) => X67)) => 102.30/102.93 ((![X69]: (in(X69,emptyset) => (![X70:$o]: X70))) => 102.30/102.93 ((![X71]: (in(X71,emptyset) => $false)) => 102.30/102.93 ((![X72]: (~in(X72,emptyset))) => 102.30/102.93 ((![X73:($i > $o)]: 102.30/102.93 ((?[X74]: 102.30/102.93 ((![X75]: (X73(X75) => (X74 = X75))) & X73(X74))) => 102.30/102.93 (?[X76]: X73(X76)))) => 102.30/102.93 ((![X77,X78]: 102.30/102.93 ((![X79]: (in(X79,X77) => in(X79,X78))) => 102.30/102.93 ((![X80]: (in(X80,X78) => in(X80,X77))) => 102.30/102.93 (X77 = X78)))) => 102.30/102.93 ((![X81]: 102.30/102.93 ((![X82]: (~in(X82,X81))) => (X81 = emptyset))) => 102.30/102.93 ((![X83]: 102.30/102.93 ((![X84]: (~in(X84,X83))) => (X83 = emptyset))) => 102.30/102.93 ((![X85,X86:($i > $o),X87]: 102.30/102.93 (in(X87,X85) => 102.30/102.93 (in(X87,dsetconstr(X85,'#ll_0'(X86))) <=> 102.30/102.93 X86(X87)))) => 102.30/102.93 ((![X88]: 102.30/102.93 ((X88 != emptyset) => (?[X89]: in(X89,X88)))) => 102.30/102.93 ((![X90,X91:($i > $o),X92]: 102.30/102.93 (in(X92,X90) => 102.30/102.93 (X91(X92) => 102.30/102.93 (dsetconstr(X90,'#ll_0'(X91)) != emptyset)))) => 102.30/102.93 ((![X93]: 102.30/102.93 ((?[X94]: in(X94,X93)) => (X93 != emptyset))) => 102.30/102.93 ((![X95,X96]: in(X95,setadjoin(X95,X96))) => 102.30/102.93 (in(emptyset,setadjoin(emptyset,emptyset)) => 102.30/102.93 ((![X97,X98,X99]: 102.30/102.93 (in(X99,X98) => 102.30/102.93 in(X99,setadjoin(X97,X98)))) => 102.30/102.93 ((![X100,X101,X102]: 102.30/102.93 (in(X102,setadjoin(X100,X101)) => 102.30/102.93 (![X103:$o]: 102.30/102.93 (((X102 = X100) => X103) => 102.30/102.93 ((in(X102,X101) => X103) => X103))))) => 102.30/102.93 ((![X104,X105,X106]: 102.30/102.93 (in(X106,setadjoin(X104,X105)) => 102.30/102.93 (in(X106,X105) | (X106 = X104)))) => 102.30/102.93 ((![X107]: 102.30/102.93 (dsetconstr(X107,'#ll_1') = X107)) => 102.30/102.93 ((![X108,X109]: 102.30/102.93 ((![X110]: 102.30/102.93 (in(X110,X109) => in(X110,X108))) => 102.30/102.93 in(X109,powerset(X108)))) => 102.30/102.93 ((![X111]: in(emptyset,powerset(X111))) => 102.30/102.93 ((![X112]: in(emptyset,powerset(X112))) => 102.30/102.93 ((![X113,X114,X115]: 102.30/102.93 (in(X114,powerset(X113)) => 102.30/102.93 (in(X115,X114) => in(X115,X113)))) => 102.30/102.93 ((![X116,X117,X118]: 102.30/102.93 (in(X117,X118) => 102.30/102.93 (in(X118,X116) => 102.30/102.93 in(X117,setunion(X116))))) => 102.30/102.93 ((![X119,X120]: 102.30/102.93 (in(X120,setunion(X119)) => 102.30/102.93 (![X121:$o]: 102.30/102.93 ((![X122]: 102.30/102.93 (in(X120,X122) => 102.30/102.93 (in(X122,X119) => X121))) => 102.30/102.93 X121)))) => 102.30/102.93 ((![X123,X124]: 102.30/102.93 (in(X124,X123) => 102.30/102.93 in(X124, 102.30/102.93 powerset(setunion(X123))))) => 102.30/102.93 ((![X125:($i > $o)]: 102.30/102.93 ((?[X126]: 102.30/102.93 ((![X127]: 102.30/102.93 (X125(X127) => 102.30/102.93 (X126 = X127))) & 102.30/102.93 X125(X126))) => 102.30/102.93 (?[X128]: 102.30/102.93 (![X129]: 102.30/102.93 (X125(X129) <=> 102.30/102.93 (X129 = X128)))))) => 102.30/102.93 ((![X130]: 102.30/102.93 ((X130 != emptyset) => 102.30/102.93 (?[X131]: in(X131,X130)))) => 102.30/102.93 ((![X132,X133]: 102.30/102.93 (in(X132, 102.30/102.93 setadjoin(X133,emptyset)) => 102.30/102.93 (X132 = X133))) => 102.30/102.93 ((![X134,X135]: 102.30/102.93 ((X134 != X135) => 102.30/102.93 (~ 102.30/102.93 in(X135, 102.30/102.93 setadjoin(X134, 102.30/102.93 emptyset))))) => 102.30/102.93 ((![X136,X137]: 102.30/102.93 ((X136 = X137) => 102.30/102.93 in(X136, 102.30/102.93 setadjoin(X137, 102.30/102.93 emptyset)))) => 102.30/102.93 ((![X138,X139]: 102.30/102.93 (in(X138, 102.30/102.93 setadjoin(X139, 102.30/102.93 emptyset)) => 102.30/102.93 in(X139, 102.30/102.93 setadjoin(X138, 102.30/102.93 emptyset)))) => 102.30/102.93 ((![X140,X141,X142]: 102.30/102.93 (in(X142, 102.30/102.93 setadjoin(X140, 102.30/102.93 setadjoin( 102.30/102.93 X141, 102.30/102.93 emptyset))) => 102.30/102.93 ((X142 = X141) | 102.30/102.93 (X142 = X140)))) => 102.30/102.93 ((![X143,X144]: 102.30/102.93 in(X143, 102.30/102.93 setadjoin(X143, 102.30/102.93 setadjoin( 102.30/102.93 X144, 102.30/102.93 emptyset)))) => 102.30/102.93 ((![X145,X146]: 102.30/102.93 in(X146, 102.30/102.93 setadjoin(X145, 102.30/102.93 setadjoin( 102.30/102.93 X146, 102.30/102.93 emptyset)))) => 102.30/102.93 ((![X147,X148:($i > $o)]: 102.30/102.93 ((?[X149]: 102.30/102.93 (X148(X149) & 102.30/102.93 in(X149,X147))) => 102.30/102.93 ((dsetconstr( 102.30/102.93 X147,'#ll_0'(X148)) = 102.30/102.93 emptyset) => 102.30/102.93 $false))) => 102.30/102.93 ((![X150:($i > $o),X151]: 102.30/102.93 (in(X151,emptyset) => 102.30/102.93 X150(X151))) => 102.30/102.93 ((![X152,X153:($i > $o)]: 102.30/102.93 ((~ 102.30/102.93 (![X154]: 102.30/102.93 (in(X154,X152) => 102.30/102.93 X153(X154)))) => 102.30/102.93 (?[X155]: 102.30/102.93 ((~X153(X155)) & 102.30/102.93 in(X155,X152))))) => 102.30/102.93 ((![X156, 102.30/102.93 X157:($i > $o)]: 102.30/102.93 ((![X158]: 102.30/102.93 (in(X158,X156) => 102.30/102.93 (~X157(X158)))) => 102.30/102.93 (~ 102.30/102.93 (?[X159]: 102.30/102.93 (X157(X159) & 102.30/102.93 in( 102.30/102.93 X159,X156)))))) => 102.30/102.93 ((![X160, 102.30/102.93 X161:($i > $o)]: 102.30/102.93 ((~ 102.30/102.93 (?[X162]: 102.30/102.93 (X161(X162) & 102.30/102.93 in( 102.30/102.93 X162,X160)))) => 102.30/102.93 (![X163]: 102.30/102.93 (in(X163,X160) => 102.30/102.93 (~X161(X163)))))) => 102.30/102.93 ((![X164, 102.30/102.93 X165:($i > $o)]: 102.30/102.93 ((?[X166]: 102.30/102.93 ((~ 102.30/102.93 X165( 102.30/102.93 X166)) & 102.30/102.93 in( 102.30/102.93 X166,X164))) => 102.30/102.93 (~ 102.30/102.93 (![X167]: 102.30/102.93 (in( 102.30/102.93 X167,X164) => 102.30/102.93 X165( 102.30/102.93 X167)))))) => 102.30/102.93 ((![X168:$o]: 102.30/102.93 (X168 => 102.30/102.93 in(emptyset, 102.30/102.93 prop2set( 102.30/102.93 X168)))) => 102.30/102.93 ((![X169:$o]: 102.30/102.93 (X169 => 102.30/102.93 set2prop( 102.30/102.93 prop2set( 102.30/102.93 X169)))) => 102.30/102.93 ((![X170, 102.30/102.93 X171:( 102.30/102.93 $i > $o)]: 102.30/102.93 ((~ 102.30/102.93 (?[X172]: 102.30/102.93 (X171( 102.30/102.93 X172) & 102.30/102.93 in( 102.30/102.93 X172,X170)))) => 102.30/102.93 (![X173]: 102.30/102.93 ( 102.30/102.93 in( 102.30/102.93 X173,X170) => 102.30/102.93 ( 102.30/102.93 ~ 102.30/102.93 X171( 102.30/102.93 X173)))))) => 102.30/102.93 ((![X174, 102.30/102.93 X175:( 102.30/102.93 $i > $o)]: 102.30/102.93 ((~ 102.30/102.93 ( 102.30/102.93 ![X176]: 102.30/102.93 (in( 102.30/102.93 X176,X174) => 102.30/102.93 X175( 102.30/102.93 X176)))) => 102.30/102.93 (?[X177]: 102.30/102.93 (( 102.30/102.93 ~ 102.30/102.93 X175( 102.30/102.93 X177)) & 102.30/102.93 in( 102.30/102.93 X177,X174))))) => 102.30/102.93 ((![X178:( 102.30/102.93 $i > $o)]: 102.30/102.93 ((?[X179]: 102.30/102.93 (( 102.30/102.93 ![X180]: 102.30/102.93 (X178( 102.30/102.93 X180) => 102.30/102.93 (X179 = 102.30/102.93 X180))) & 102.30/102.93 X178( 102.30/102.93 X179))) => 102.30/102.93 (?[X181]: 102.30/102.93 (( 102.30/102.93 ![X182]: 102.30/102.93 (X178( 102.30/102.93 X182) => 102.30/102.93 (X181 = 102.30/102.93 X182))) & 102.30/102.93 X178( 102.30/102.93 X181))))) => 102.30/102.93 ((![X183:( 102.30/102.93 $i > $o)]: 102.30/102.93 (( 102.30/102.93 ?[X184]: 102.30/102.93 X183( 102.30/102.93 X184)) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X185, 102.30/102.93 X186]: 102.30/102.93 (X183( 102.30/102.93 X185) => 102.30/102.93 (X183( 102.30/102.93 X186) => 102.30/102.93 (X185 = 102.30/102.93 X186)))) => 102.30/102.93 ( 102.30/102.93 ?[X187]: 102.30/102.93 (( 102.30/102.93 ![X188]: 102.30/102.93 (X183( 102.30/102.93 X188) => 102.30/102.93 (X187 = 102.30/102.93 X188))) & 102.30/102.93 X183( 102.30/102.93 X187)))))) => 102.30/102.93 ((![X189:( 102.30/102.93 $i > $o)]: 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ?[X190]: 102.30/102.93 (![X191]: 102.30/102.93 (X189( 102.30/102.93 X191) <=> 102.30/102.93 (X191 = 102.30/102.93 X190)))) => 102.30/102.93 ( 102.30/102.93 ?[X192]: 102.30/102.93 (( 102.30/102.93 ![X193]: 102.30/102.93 (X189( 102.30/102.93 X193) => 102.30/102.93 (X192 = 102.30/102.93 X193))) & 102.30/102.93 X189( 102.30/102.93 X192))))) => 102.30/102.93 ((![X194, 102.30/102.93 X195]: 102.30/102.93 (( 102.30/102.93 X194 = 102.30/102.93 X195) => 102.30/102.93 (![X196, 102.30/102.93 X197]: 102.30/102.93 (( 102.30/102.93 X196 = 102.30/102.93 X197) => 102.30/102.93 (in( 102.30/102.93 X196,X194) => 102.30/102.93 in( 102.30/102.93 X197,X195)))))) => 102.30/102.93 ((![X198, 102.30/102.93 X199]: 102.30/102.93 (( 102.30/102.93 X198 = 102.30/102.93 X199) => 102.30/102.93 (![X200, 102.30/102.93 X201]: 102.30/102.93 (( 102.30/102.93 X200 = 102.30/102.93 X201) => 102.30/102.93 (in( 102.30/102.93 X200,X198) <=> 102.30/102.93 in( 102.30/102.93 X201,X199)))))) => 102.30/102.93 (( 102.30/102.93 ![X202:( 102.30/102.93 $i > $o)]: 102.30/102.93 (( 102.30/102.93 ?[X203]: 102.30/102.93 (( 102.30/102.93 ![X204]: 102.30/102.93 (X202( 102.30/102.93 X204) => 102.30/102.93 (X203 = 102.30/102.93 X204))) & 102.30/102.93 X202( 102.30/102.93 X203))) => 102.30/102.93 (![X205, 102.30/102.93 X206]: 102.30/102.93 (X202( 102.30/102.93 X205) => 102.30/102.93 (X202( 102.30/102.93 X206) => 102.30/102.93 (X205 = 102.30/102.93 X206)))))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X207:( 102.30/102.93 $i > $o), 102.30/102.93 X208:( 102.30/102.93 $i > $o)]: 102.30/102.93 (( 102.30/102.93 ![X209, 102.30/102.93 X210]: 102.30/102.93 (( 102.30/102.93 X209 = 102.30/102.93 X210) => 102.30/102.93 (X207( 102.30/102.93 X209) <=> 102.30/102.93 X208( 102.30/102.93 X210)))) => 102.30/102.93 (( 102.30/102.93 ?[X211]: 102.30/102.93 zip_tseitin5( 102.30/102.93 X211,X207)) <=> 102.30/102.93 (?[X213]: 102.30/102.93 zip_tseitin5( 102.30/102.93 X213,X208))))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 emptyset = 102.30/102.93 emptyset) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X215, 102.30/102.93 X216]: 102.30/102.93 (( 102.30/102.93 X215 = 102.30/102.93 X216) => 102.30/102.93 (![X217, 102.30/102.93 X218]: 102.30/102.93 (( 102.30/102.93 X217 = 102.30/102.93 X218) => 102.30/102.93 (setadjoin( 102.30/102.93 X215,X217) = 102.30/102.93 setadjoin( 102.30/102.93 X216,X218)))))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X219, 102.30/102.93 X220]: 102.30/102.93 (( 102.30/102.93 X219 = 102.30/102.93 X220) => 102.30/102.93 (powerset( 102.30/102.93 X219) = 102.30/102.93 powerset( 102.30/102.93 X220)))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X221, 102.30/102.93 X222]: 102.30/102.93 (( 102.30/102.93 X221 = 102.30/102.93 X222) => 102.30/102.93 (setunion( 102.30/102.93 X221) = 102.30/102.93 setunion( 102.30/102.93 X222)))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 omega = 102.30/102.93 omega) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X223:( 102.30/102.93 $i > $o)]: 102.30/102.93 (( 102.30/102.93 ?[X224]: 102.30/102.93 (( 102.30/102.93 ![X225]: 102.30/102.93 (X223( 102.30/102.93 X225) => 102.30/102.93 (X224 = 102.30/102.93 X225))) & 102.30/102.93 X223( 102.30/102.93 X224))) => 102.30/102.93 (![X226, 102.30/102.93 X227]: 102.30/102.93 (X223( 102.30/102.93 X226) => 102.30/102.93 (X223( 102.30/102.93 X227) => 102.30/102.93 (X226 = 102.30/102.93 X227)))))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X228:( 102.30/102.93 $i > $o), 102.30/102.93 X229:( 102.30/102.93 $i > $o)]: 102.30/102.93 (( 102.30/102.93 ![X230, 102.30/102.93 X231]: 102.30/102.93 (( 102.30/102.93 X230 = 102.30/102.93 X231) => 102.30/102.93 (X228( 102.30/102.93 X230) <=> 102.30/102.93 X229( 102.30/102.93 X231)))) => 102.30/102.93 (( 102.30/102.93 ?[X232]: 102.30/102.93 (( 102.30/102.93 ![X233]: 102.30/102.93 (X228( 102.30/102.93 X233) => 102.30/102.93 (X232 = 102.30/102.93 X233))) & 102.30/102.93 X228( 102.30/102.93 X232))) => 102.30/102.93 (( 102.30/102.93 ?[X234]: 102.30/102.93 (( 102.30/102.93 ![X235]: 102.30/102.93 (X229( 102.30/102.93 X235) => 102.30/102.93 (X234 = 102.30/102.93 X235))) & 102.30/102.93 X229( 102.30/102.93 X234))) => 102.30/102.93 (descr( 102.30/102.93 '#ll_0'( 102.30/102.93 X228)) = 102.30/102.93 descr( 102.30/102.93 '#ll_0'( 102.30/102.93 X229))))))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X236, 102.30/102.93 X237]: 102.30/102.93 (( 102.30/102.93 X236 = 102.30/102.93 X237) => 102.30/102.93 (![X238:( 102.30/102.93 $i > $o), 102.30/102.93 X239:( 102.30/102.93 $i > $o)]: 102.30/102.93 (( 102.30/102.93 ![X240]: 102.30/102.93 (in( 102.30/102.93 X240,X236) => 102.30/102.93 (![X241]: 102.30/102.93 (in( 102.30/102.93 X241,X237) => 102.30/102.93 (( 102.30/102.93 X240 = 102.30/102.93 X241) => 102.30/102.93 (X238( 102.30/102.93 X240) <=> 102.30/102.93 X239( 102.30/102.93 X241))))))) => 102.30/102.93 (dsetconstr( 102.30/102.93 X236, 102.30/102.93 '#ll_0'( 102.30/102.93 X238)) = 102.30/102.93 dsetconstr( 102.30/102.93 X237, 102.30/102.93 '#ll_0'( 102.30/102.93 X239))))))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X242, 102.30/102.93 X243]: 102.30/102.93 (( 102.30/102.93 ![X244]: 102.30/102.93 (in( 102.30/102.93 X244,X242) => 102.30/102.93 in( 102.30/102.93 X244,X243))) => 102.30/102.93 subset( 102.30/102.93 X242,X243))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X245, 102.30/102.93 X246]: 102.30/102.93 (( 102.30/102.93 X245 = 102.30/102.93 X246) => 102.30/102.93 subset( 102.30/102.93 X246,X245))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X247, 102.30/102.93 X248]: 102.30/102.93 (( 102.30/102.93 X247 = 102.30/102.93 X248) => 102.30/102.93 subset( 102.30/102.93 X247,X248))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X249, 102.30/102.93 X250]: 102.30/102.93 (( 102.30/102.93 ![X251]: 102.30/102.93 (in( 102.30/102.93 X251,X249) => 102.30/102.93 in( 102.30/102.93 X251,X250))) => 102.30/102.93 subset( 102.30/102.93 X249,X250))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X252]: 102.30/102.93 subset( 102.30/102.93 emptyset, 102.30/102.93 X252)) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X253, 102.30/102.93 X254,X255]: 102.30/102.93 (subset( 102.30/102.93 X253,X254) => 102.30/102.93 (in( 102.30/102.93 X255,X253) => 102.30/102.93 in( 102.30/102.93 X255,X254)))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X256, 102.30/102.93 X257,X258]: 102.30/102.93 (subset( 102.30/102.93 X256,X257) => 102.30/102.93 (( 102.30/102.93 ~ 102.30/102.93 in( 102.30/102.93 X258,X257)) => 102.30/102.93 (~ 102.30/102.93 in( 102.30/102.93 X258,X256))))) => 102.30/102.93 ( 102.30/102.93 ( 102.30/102.93 ![X259, 102.30/102.93 X260,X261]: 102.30/102.93 (in( 102.38/102.93 X261,X259) => 102.38/102.93 (( 102.38/102.93 ~ 102.38/102.93 in( 102.38/102.93 X261,X260)) => 102.38/102.93 (~ 102.38/102.93 subset( 102.38/102.93 X259,X260))))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X262, 102.38/102.93 X263]: 102.38/102.93 (( 102.38/102.93 ~ 102.38/102.93 subset( 102.38/102.93 X262,X263)) => 102.38/102.93 (X262 != 102.38/102.93 X263))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X264, 102.38/102.93 X265,X266]: 102.38/102.93 (in( 102.38/102.93 X266,X264) => 102.38/102.93 (( 102.38/102.93 ~ 102.38/102.93 in( 102.38/102.93 X266,X265)) => 102.38/102.93 (X264 != 102.38/102.93 X265)))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X267]: 102.38/102.93 subset( 102.38/102.93 X267,X267)) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X268, 102.38/102.93 X269,X270]: 102.38/102.93 (subset( 102.38/102.93 X268,X269) => 102.38/102.93 (subset( 102.38/102.93 X269,X270) => 102.38/102.93 subset( 102.38/102.93 X268,X270)))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X271, 102.38/102.93 X272]: 102.38/102.93 subset( 102.38/102.93 X272, 102.38/102.93 setadjoin( 102.38/102.93 X271,X272))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X273, 102.38/102.93 X274,X275]: 102.38/102.93 (subset( 102.38/102.93 X273,X275) => 102.38/102.93 subset( 102.38/102.93 X273, 102.38/102.93 setadjoin( 102.38/102.93 X274,X275)))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X276, 102.38/102.93 X277]: 102.38/102.93 (subset( 102.38/102.93 X276,X277) => 102.38/102.93 in( 102.38/102.93 X276, 102.38/102.93 powerset( 102.38/102.93 X277)))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X278, 102.38/102.93 X279]: 102.38/102.93 (subset( 102.38/102.93 X278,X279) => 102.38/102.93 (subset( 102.38/102.93 X279,X278) => 102.38/102.93 (X278 = 102.38/102.93 X279)))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X280]: 102.38/102.93 (subset( 102.38/102.93 X280, 102.38/102.93 emptyset) => 102.38/102.93 (X280 = 102.38/102.93 emptyset))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X281, 102.38/102.93 X282]: 102.38/102.93 (subset( 102.38/102.93 X282,X281) => 102.38/102.93 in( 102.38/102.93 X282, 102.38/102.93 powerset( 102.38/102.93 X281)))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X283, 102.38/102.93 X284]: 102.38/102.93 (in( 102.38/102.93 X284, 102.38/102.93 powerset( 102.38/102.93 X283)) => 102.38/102.93 subset( 102.38/102.93 X284,X283))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X285]: 102.38/102.93 in( 102.38/102.93 X285, 102.38/102.93 powerset( 102.38/102.93 X285))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X286, 102.38/102.93 X287]: 102.38/102.93 (subset( 102.38/102.93 X286,X287) => 102.38/102.93 subset( 102.38/102.93 powerset( 102.38/102.93 X286), 102.38/102.93 powerset( 102.38/102.93 X287)))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X288, 102.38/102.93 X289:( 102.38/102.93 $i > $o)]: 102.38/102.93 in( 102.38/102.93 dsetconstr( 102.38/102.93 X288, 102.38/102.93 '#ll_0'( 102.38/102.93 X289)), 102.38/102.93 powerset( 102.38/102.93 X288))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X290, 102.38/102.93 X291:( 102.38/102.93 $i > $o)]: 102.38/102.93 subset( 102.38/102.93 dsetconstr( 102.38/102.93 X290, 102.38/102.93 '#ll_0'( 102.38/102.93 X291)), 102.38/102.93 X290)) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X292, 102.38/102.93 X293,X294]: 102.38/102.93 (in( 102.38/102.93 X294,X292) => 102.38/102.93 in( 102.38/102.93 X294, 102.38/102.93 binunion( 102.38/102.93 X292,X293)))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X295, 102.38/102.93 X296]: 102.38/102.93 in( 102.38/102.93 X296, 102.38/102.93 setadjoin( 102.38/102.93 X295, 102.38/102.93 setadjoin( 102.38/102.93 X296, 102.38/102.93 emptyset)))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X297, 102.38/102.93 X298,X299]: 102.38/102.93 (in( 102.38/102.93 X299,X298) => 102.38/102.93 in( 102.38/102.93 X299, 102.38/102.93 binunion( 102.38/102.93 X297,X298)))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X300, 102.38/102.93 X301, 102.38/102.93 X302, 102.38/102.93 X303:$o]: 102.38/102.93 (in( 102.38/102.93 X302, 102.38/102.93 binunion( 102.38/102.93 X300,X301)) => 102.38/102.93 (( 102.38/102.93 in( 102.38/102.93 X302,X300) => 102.38/102.93 X303) => 102.38/102.93 (( 102.38/102.93 in( 102.38/102.93 X302,X301) => 102.38/102.93 X303) => 102.38/102.93 X303)))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X304, 102.38/102.93 X305,X306]: 102.38/102.93 (in( 102.38/102.93 X306, 102.38/102.93 binunion( 102.38/102.93 X304,X305)) => 102.38/102.93 (in( 102.38/102.93 X306,X305) | 102.38/102.93 in( 102.38/102.93 X306,X304)))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X307, 102.38/102.93 X308]: 102.38/102.93 subset( 102.38/102.93 X307, 102.38/102.93 binunion( 102.38/102.93 X307,X308))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X309, 102.38/102.93 X310]: 102.38/102.93 subset( 102.38/102.93 X310, 102.38/102.93 binunion( 102.38/102.93 X309,X310))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X311, 102.38/102.93 X312,X313]: 102.38/102.93 (in( 102.38/102.93 X313,X311) => 102.38/102.93 (in( 102.38/102.93 X313,X312) => 102.38/102.93 in( 102.38/102.93 X313, 102.38/102.93 binintersect( 102.38/102.93 X311,X312))))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X314, 102.38/102.93 X315,X316]: 102.38/102.93 (subset( 102.38/102.93 X316,X314) => 102.38/102.93 (subset( 102.38/102.93 X316,X315) => 102.38/102.93 subset( 102.38/102.93 X316, 102.38/102.93 binintersect( 102.38/102.93 X314,X315))))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X317, 102.38/102.93 X318,X319]: 102.38/102.93 (in( 102.38/102.93 X319, 102.38/102.93 binintersect( 102.38/102.93 X317,X318)) => 102.38/102.93 in( 102.38/102.93 X319,X317))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X320, 102.38/102.93 X321]: 102.38/102.93 subset( 102.38/102.93 binintersect( 102.38/102.93 X320,X321), 102.38/102.93 X320)) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X322, 102.38/102.93 X323]: 102.38/102.93 (subset( 102.38/102.93 X322,X323) => 102.38/102.93 (binintersect( 102.38/102.93 X322,X323) = 102.38/102.93 X322))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X324, 102.38/102.93 X325]: 102.38/102.93 (( 102.38/102.93 binintersect( 102.38/102.93 X324,X325) = 102.38/102.93 X325) => 102.38/102.93 subset( 102.38/102.93 X325,X324))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X326, 102.38/102.93 X327,X328]: 102.38/102.93 (in( 102.38/102.93 X328, 102.38/102.93 binintersect( 102.38/102.93 X326,X327)) => 102.38/102.93 in( 102.38/102.93 X328,X327))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X329, 102.38/102.93 X330]: 102.38/102.93 (( 102.38/102.93 ~ 102.38/102.93 ( 102.38/102.93 ?[X331]: 102.38/102.93 (in( 102.38/102.93 X331,X330) & 102.38/102.93 in( 102.38/102.93 X331,X329)))) => 102.38/102.93 (binintersect( 102.38/102.93 X329,X330) = 102.38/102.93 emptyset))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X332, 102.38/102.93 X333]: 102.38/102.93 subset( 102.38/102.93 binintersect( 102.38/102.93 X332,X333), 102.38/102.93 X333)) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X334, 102.38/102.93 X335]: 102.38/102.93 (subset( 102.38/102.93 X335,X334) => 102.38/102.93 (binintersect( 102.38/102.93 X334,X335) = 102.38/102.93 X335))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X336, 102.38/102.93 X337]: 102.38/102.93 (( 102.38/102.93 binintersect( 102.38/102.93 X336,X337) = 102.38/102.93 X336) => 102.38/102.93 subset( 102.38/102.93 X336,X337))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X338, 102.38/102.93 X339,X340]: 102.38/102.93 (binintersect( 102.38/102.93 X338, 102.38/102.93 binunion( 102.38/102.93 X339,X340)) = 102.38/102.93 binunion( 102.38/102.93 binintersect( 102.38/102.93 X338,X339), 102.38/102.93 binintersect( 102.38/102.93 X338,X340)))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X341, 102.38/102.93 X342,X343]: 102.38/102.93 (in( 102.38/102.93 X343,X341) => 102.38/102.93 (( 102.38/102.93 ~ 102.38/102.93 in( 102.38/102.93 X343,X342)) => 102.38/102.93 in( 102.38/102.93 X343, 102.38/102.93 setminus( 102.38/102.93 X341,X342))))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X344, 102.38/102.93 X345,X346]: 102.38/102.93 (in( 102.38/102.93 X346, 102.38/102.93 setminus( 102.38/102.93 X344,X345)) => 102.38/102.93 in( 102.38/102.93 X346,X344))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X347, 102.38/102.93 X348,X349]: 102.38/102.93 (in( 102.38/102.93 X349, 102.38/102.93 setminus( 102.38/102.93 X347,X348)) => 102.38/102.93 (~ 102.38/102.93 in( 102.38/102.93 X349,X348)))) => 102.38/102.93 ( 102.38/102.93 ![X350, 102.38/102.93 X351]: 102.38/102.93 (subset( 102.38/102.93 X350,X351) => 102.38/102.93 (setminus( 102.38/102.93 X350,X351) = 102.38/102.93 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 102.38/102.93 tff(zf_stmt_14, negated_conjecture, 102.38/102.93 (~ 102.38/102.93 ((![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))) => 102.38/102.93 ((![X5]: (~in(X5,emptyset))) => 102.38/102.93 ((![X6,X7,X8]: (in(X8,setadjoin(X6,X7)) <=> zip_tseitin0(X8,X7,X6))) => 102.38/102.93 ((![X9,X10]: 102.38/102.93 (in(X10,powerset(X9)) <=> (![X11]: zip_tseitin1(X11,X10,X9)))) => 102.38/102.93 ((![X12,X13]: 102.38/102.93 (in(X13,setunion(X12)) <=> (?[X14]: zip_tseitin2(X14,X13,X12)))) => 102.38/102.93 (in(emptyset,omega) => 102.38/102.93 ((![X15]: (in(X15,omega) => in(setadjoin(X15,X15),omega))) => 102.38/102.93 ((![X16]: 102.38/102.93 (((![X17]: 102.38/102.93 ((in(X17,X16) & in(X17,omega)) => 102.38/102.93 in(setadjoin(X17,X17),X16))) & 102.38/102.93 in(emptyset,X16)) => 102.38/102.93 (![X18]: (in(X18,omega) => in(X18,X16))))) => 102.38/102.93 ((![X19:(($i * $i) > $o),X20]: 102.38/102.93 ((![X21]: 102.38/102.93 (in(X21,X20) => 102.38/102.93 (?[X22]: 102.38/102.93 ((![X23]: (X19(X21,X23) => (X22 = X23))) & 102.38/102.93 X19(X21,X22))))) => 102.38/102.93 (?[X24]: 102.38/102.93 (![X25]: 102.38/102.93 (in(X25,X24) <=> 102.38/102.93 (?[X26]: zip_tseitin3(X26,X25,X20,X19))))))) => 102.38/102.93 ((![X27]: 102.38/102.93 ((?[X28]: in(X28,X27)) => 102.38/102.93 (?[X29]: 102.38/102.93 ((~(?[X30]: (in(X30,X27) & in(X30,X29)))) & in(X29,X27))))) => 102.38/102.93 ((![X31]: 102.38/102.93 (?[X32]: 102.38/102.93 ((![X33]: 102.38/102.93 (((?[X34]: in(X34,X33)) & 102.38/102.93 (![X35]: (in(X35,X33) => in(X35,X31)))) => 102.38/102.93 (?[X36,X37]: 102.38/102.93 ((![X38]: 102.38/102.93 (in(X38,X32) => 102.38/102.93 (in(X37,X38) | 102.38/102.93 (![X39]: (in(X39,X38) => in(X39,X36)))))) & 102.38/102.93 (~(?[X40]: (in(X40,X33) & in(X40,X36)))) & 102.38/102.93 in(X37,X33) & in(X36,X32))))) & 102.38/102.93 (![X41,X42]: 102.38/102.93 ((in(X42,X32) & in(X41,X32)) => 102.38/102.93 ((![X43]: (in(X43,X42) => in(X43,X41))) | 102.38/102.93 (![X44]: (in(X44,X41) => in(X44,X42)))))) & 102.38/102.93 (![X45,X46]: 102.38/102.93 ((in(X46,X31) & in(X45,X31)) => 102.38/102.93 ((![X47]: 102.38/102.93 (in(X47,X32) => (in(X45,X47) <=> in(X46,X47)))) => 102.38/102.93 (X45 = X46)))) & 102.38/102.93 (![X48]: 102.38/102.93 (in(X48,X32) => 102.38/102.93 (![X49]: (in(X49,X48) => in(X49,X31)))))))) => 102.38/102.93 ((![X50:($i > $o)]: 102.38/102.93 ((?[X51]: ((![X52]: (X50(X52) => (X51 = X52))) & X50(X51))) => 102.38/102.93 X50(descr('#ll_0'(X50))))) => 102.38/102.93 ((![X53,X54:($i > $o),X55]: 102.38/102.93 (in(X55,X53) => 102.38/102.93 (X54(X55) => in(X55,dsetconstr(X53,'#ll_0'(X54)))))) => 102.38/102.93 ((![X56,X57:($i > $o),X58]: 102.38/102.93 (in(X58,dsetconstr(X56,'#ll_0'(X57))) => in(X58,X56))) => 102.38/102.93 ((![X59,X60:($i > $o),X61]: 102.38/102.93 (in(X61,dsetconstr(X59,'#ll_0'(X60))) => X60(X61))) => 102.38/102.93 ((![X62:($i > $o)]: 102.38/102.93 ((?[X63]: 102.38/102.93 ((![X64]: (X62(X64) => (X63 = X64))) & X62(X63))) => 102.38/102.93 (?[X65]: 102.38/102.93 ((![X66]: (X62(X66) => (X65 = X66))) & X62(X65))))) => 102.38/102.93 ((![X67:$o,X68]: (in(X68,prop2set(X67)) => X67)) => 102.38/102.93 ((![X69]: (in(X69,emptyset) => (![X70:$o]: X70))) => 102.38/102.93 ((![X71]: (in(X71,emptyset) => $false)) => 102.38/102.93 ((![X72]: (~in(X72,emptyset))) => 102.38/102.93 ((![X73:($i > $o)]: 102.38/102.93 ((?[X74]: 102.38/102.93 ((![X75]: (X73(X75) => (X74 = X75))) & 102.38/102.93 X73(X74))) => 102.38/102.93 (?[X76]: X73(X76)))) => 102.38/102.93 ((![X77,X78]: 102.38/102.93 ((![X79]: (in(X79,X77) => in(X79,X78))) => 102.38/102.93 ((![X80]: (in(X80,X78) => in(X80,X77))) => 102.38/102.93 (X77 = X78)))) => 102.38/102.93 ((![X81]: 102.38/102.93 ((![X82]: (~in(X82,X81))) => (X81 = emptyset))) => 102.38/102.93 ((![X83]: 102.38/102.93 ((![X84]: (~in(X84,X83))) => (X83 = emptyset))) => 102.38/102.93 ((![X85,X86:($i > $o),X87]: 102.38/102.93 (in(X87,X85) => 102.38/102.93 (in(X87,dsetconstr(X85,'#ll_0'(X86))) <=> 102.38/102.93 X86(X87)))) => 102.38/102.93 ((![X88]: 102.38/102.93 ((X88 != emptyset) => (?[X89]: in(X89,X88)))) => 102.38/102.93 ((![X90,X91:($i > $o),X92]: 102.38/102.93 (in(X92,X90) => 102.38/102.93 (X91(X92) => 102.38/102.93 (dsetconstr(X90,'#ll_0'(X91)) != emptyset)))) => 102.38/102.93 ((![X93]: 102.38/102.93 ((?[X94]: in(X94,X93)) => 102.38/102.93 (X93 != emptyset))) => 102.38/102.93 ((![X95,X96]: in(X95,setadjoin(X95,X96))) => 102.38/102.93 (in(emptyset,setadjoin(emptyset,emptyset)) => 102.38/102.93 ((![X97,X98,X99]: 102.38/102.93 (in(X99,X98) => 102.38/102.93 in(X99,setadjoin(X97,X98)))) => 102.38/102.93 ((![X100,X101,X102]: 102.38/102.93 (in(X102,setadjoin(X100,X101)) => 102.38/102.93 (![X103:$o]: 102.38/102.93 (((X102 = X100) => X103) => 102.38/102.93 ((in(X102,X101) => X103) => X103))))) => 102.38/102.93 ((![X104,X105,X106]: 102.38/102.93 (in(X106,setadjoin(X104,X105)) => 102.38/102.93 (in(X106,X105) | (X106 = X104)))) => 102.38/102.93 ((![X107]: 102.38/102.93 (dsetconstr(X107,'#ll_1') = X107)) => 102.38/102.93 ((![X108,X109]: 102.38/102.93 ((![X110]: 102.38/102.93 (in(X110,X109) => in(X110,X108))) => 102.38/102.93 in(X109,powerset(X108)))) => 102.38/102.93 ((![X111]: in(emptyset,powerset(X111))) => 102.38/102.93 ((![X112]: 102.38/102.93 in(emptyset,powerset(X112))) => 102.38/102.93 ((![X113,X114,X115]: 102.38/102.93 (in(X114,powerset(X113)) => 102.38/102.93 (in(X115,X114) => in(X115,X113)))) => 102.38/102.93 ((![X116,X117,X118]: 102.38/102.93 (in(X117,X118) => 102.38/102.93 (in(X118,X116) => 102.38/102.93 in(X117,setunion(X116))))) => 102.38/102.93 ((![X119,X120]: 102.38/102.93 (in(X120,setunion(X119)) => 102.38/102.93 (![X121:$o]: 102.38/102.93 ((![X122]: 102.38/102.93 (in(X120,X122) => 102.38/102.93 (in(X122,X119) => 102.38/102.93 X121))) => 102.38/102.93 X121)))) => 102.38/102.93 ((![X123,X124]: 102.38/102.93 (in(X124,X123) => 102.38/102.93 in(X124, 102.38/102.93 powerset(setunion(X123))))) => 102.38/102.93 ((![X125:($i > $o)]: 102.38/102.93 ((?[X126]: 102.38/102.93 ((![X127]: 102.38/102.93 (X125(X127) => 102.38/102.93 (X126 = X127))) & 102.38/102.93 X125(X126))) => 102.38/102.93 (?[X128]: 102.38/102.93 (![X129]: 102.38/102.93 (X125(X129) <=> 102.38/102.93 (X129 = X128)))))) => 102.38/102.93 ((![X130]: 102.38/102.93 ((X130 != emptyset) => 102.38/102.93 (?[X131]: in(X131,X130)))) => 102.38/102.93 ((![X132,X133]: 102.38/102.93 (in(X132, 102.38/102.93 setadjoin(X133, 102.38/102.93 emptyset)) => 102.38/102.93 (X132 = X133))) => 102.38/102.93 ((![X134,X135]: 102.38/102.93 ((X134 != X135) => 102.38/102.93 (~ 102.38/102.93 in(X135, 102.38/102.93 setadjoin(X134, 102.38/102.93 emptyset))))) => 102.38/102.93 ((![X136,X137]: 102.38/102.93 ((X136 = X137) => 102.38/102.93 in(X136, 102.38/102.93 setadjoin(X137, 102.38/102.93 emptyset)))) => 102.38/102.93 ((![X138,X139]: 102.38/102.93 (in(X138, 102.38/102.93 setadjoin(X139, 102.38/102.93 emptyset)) => 102.38/102.93 in(X139, 102.38/102.93 setadjoin(X138, 102.38/102.93 emptyset)))) => 102.38/102.93 ((![X140,X141,X142]: 102.38/102.93 (in(X142, 102.38/102.93 setadjoin( 102.38/102.93 X140, 102.38/102.93 setadjoin( 102.38/102.93 X141,emptyset))) => 102.38/102.93 ((X142 = X141) | 102.38/102.93 (X142 = X140)))) => 102.38/102.93 ((![X143,X144]: 102.38/102.93 in(X143, 102.38/102.93 setadjoin( 102.38/102.93 X143, 102.38/102.93 setadjoin( 102.38/102.93 X144,emptyset)))) => 102.38/102.93 ((![X145,X146]: 102.38/102.93 in(X146, 102.38/102.93 setadjoin( 102.38/102.93 X145, 102.38/102.93 setadjoin( 102.38/102.93 X146,emptyset)))) => 102.38/102.93 ((![X147,X148:($i > $o)]: 102.38/102.93 ((?[X149]: 102.38/102.93 (X148(X149) & 102.38/102.93 in(X149,X147))) => 102.38/102.93 ((dsetconstr( 102.38/102.93 X147, 102.38/102.93 '#ll_0'(X148)) = 102.38/102.93 emptyset) => 102.38/102.93 $false))) => 102.38/102.93 ((![X150:($i > $o), 102.38/102.93 X151]: 102.38/102.93 (in(X151,emptyset) => 102.38/102.93 X150(X151))) => 102.38/102.93 ((![X152, 102.38/102.93 X153:($i > $o)]: 102.38/102.93 ((~ 102.38/102.93 (![X154]: 102.38/102.93 (in( 102.38/102.93 X154,X152) => 102.38/102.93 X153(X154)))) => 102.38/102.93 (?[X155]: 102.38/102.93 ((~X153(X155)) & 102.38/102.93 in(X155,X152))))) => 102.38/102.93 ((![X156, 102.38/102.93 X157:($i > $o)]: 102.38/102.93 ((![X158]: 102.38/102.93 (in( 102.38/102.93 X158,X156) => 102.38/102.93 (~ 102.38/102.93 X157( 102.38/102.93 X158)))) => 102.38/102.93 (~ 102.38/102.93 (?[X159]: 102.38/102.93 (X157( 102.38/102.93 X159) & 102.38/102.93 in( 102.38/102.93 X159,X156)))))) => 102.38/102.93 ((![X160, 102.38/102.93 X161:($i > $o)]: 102.38/102.93 ((~ 102.38/102.93 (?[X162]: 102.38/102.93 ( 102.38/102.93 X161( 102.38/102.93 X162) & 102.38/102.93 in( 102.38/102.93 X162,X160)))) => 102.38/102.93 (![X163]: 102.38/102.93 (in( 102.38/102.93 X163,X160) => 102.38/102.93 (~ 102.38/102.93 X161( 102.38/102.93 X163)))))) => 102.38/102.93 ((![X164, 102.38/102.93 X165:( 102.38/102.93 $i > $o)]: 102.38/102.93 ((?[X166]: 102.38/102.93 (( 102.38/102.93 ~ 102.38/102.93 X165( 102.38/102.93 X166)) & 102.38/102.93 in( 102.38/102.93 X166,X164))) => 102.38/102.93 (~ 102.38/102.93 (![X167]: 102.38/102.93 (in( 102.38/102.93 X167,X164) => 102.38/102.93 X165( 102.38/102.93 X167)))))) => 102.38/102.93 ((![X168:$o]: 102.38/102.93 (X168 => 102.38/102.93 in(emptyset, 102.38/102.93 prop2set( 102.38/102.93 X168)))) => 102.38/102.93 ((![X169:$o]: 102.38/102.93 (X169 => 102.38/102.93 set2prop( 102.38/102.93 prop2set( 102.38/102.93 X169)))) => 102.38/102.93 ((![X170, 102.38/102.93 X171:( 102.38/102.93 $i > $o)]: 102.38/102.93 ((~ 102.38/102.93 ( 102.38/102.93 ?[X172]: 102.38/102.93 (X171( 102.38/102.93 X172) & 102.38/102.93 in( 102.38/102.93 X172,X170)))) => 102.38/102.93 (![X173]: 102.38/102.93 (in( 102.38/102.93 X173,X170) => 102.38/102.93 (~ 102.38/102.93 X171( 102.38/102.93 X173)))))) => 102.38/102.93 ((![X174, 102.38/102.93 X175:( 102.38/102.93 $i > $o)]: 102.38/102.93 (( 102.38/102.93 ~ 102.38/102.93 ( 102.38/102.93 ![X176]: 102.38/102.93 (in( 102.38/102.93 X176,X174) => 102.38/102.93 X175( 102.38/102.93 X176)))) => 102.38/102.93 ( 102.38/102.93 ?[X177]: 102.38/102.93 (( 102.38/102.93 ~ 102.38/102.93 X175( 102.38/102.93 X177)) & 102.38/102.93 in( 102.38/102.93 X177,X174))))) => 102.38/102.93 ((![X178:( 102.38/102.93 $i > $o)]: 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ?[X179]: 102.38/102.93 (( 102.38/102.93 ![X180]: 102.38/102.93 (X178( 102.38/102.93 X180) => 102.38/102.93 (X179 = 102.38/102.93 X180))) & 102.38/102.93 X178( 102.38/102.93 X179))) => 102.38/102.93 ( 102.38/102.93 ?[X181]: 102.38/102.93 (( 102.38/102.93 ![X182]: 102.38/102.93 (X178( 102.38/102.93 X182) => 102.38/102.93 (X181 = 102.38/102.93 X182))) & 102.38/102.93 X178( 102.38/102.93 X181))))) => 102.38/102.93 ((![X183:( 102.38/102.93 $i > $o)]: 102.38/102.93 (( 102.38/102.93 ?[X184]: 102.38/102.93 X183( 102.38/102.93 X184)) => 102.38/102.93 (( 102.38/102.93 ![X185, 102.38/102.93 X186]: 102.38/102.93 (X183( 102.38/102.93 X185) => 102.38/102.93 (X183( 102.38/102.93 X186) => 102.38/102.93 (X185 = 102.38/102.93 X186)))) => 102.38/102.93 (?[X187]: 102.38/102.93 (( 102.38/102.93 ![X188]: 102.38/102.93 (X183( 102.38/102.93 X188) => 102.38/102.93 (X187 = 102.38/102.93 X188))) & 102.38/102.93 X183( 102.38/102.93 X187)))))) => 102.38/102.93 ((![X189:( 102.38/102.93 $i > $o)]: 102.38/102.93 (( 102.38/102.93 ?[X190]: 102.38/102.93 (![X191]: 102.38/102.93 (X189( 102.38/102.93 X191) <=> 102.38/102.93 (X191 = 102.38/102.93 X190)))) => 102.38/102.93 (?[X192]: 102.38/102.93 (( 102.38/102.93 ![X193]: 102.38/102.93 (X189( 102.38/102.93 X193) => 102.38/102.93 (X192 = 102.38/102.93 X193))) & 102.38/102.93 X189( 102.38/102.93 X192))))) => 102.38/102.93 (( 102.38/102.93 ![X194, 102.38/102.93 X195]: 102.38/102.93 (( 102.38/102.93 X194 = 102.38/102.93 X195) => 102.38/102.93 (![X196, 102.38/102.93 X197]: 102.38/102.93 (( 102.38/102.93 X196 = 102.38/102.93 X197) => 102.38/102.93 (in( 102.38/102.93 X196,X194) => 102.38/102.93 in( 102.38/102.93 X197,X195)))))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X198, 102.38/102.93 X199]: 102.38/102.93 (( 102.38/102.93 X198 = 102.38/102.93 X199) => 102.38/102.93 (![X200, 102.38/102.93 X201]: 102.38/102.93 (( 102.38/102.93 X200 = 102.38/102.93 X201) => 102.38/102.93 (in( 102.38/102.93 X200,X198) <=> 102.38/102.93 in( 102.38/102.93 X201,X199)))))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X202:( 102.38/102.93 $i > $o)]: 102.38/102.93 (( 102.38/102.93 ?[X203]: 102.38/102.93 (( 102.38/102.93 ![X204]: 102.38/102.93 (X202( 102.38/102.93 X204) => 102.38/102.93 (X203 = 102.38/102.93 X204))) & 102.38/102.93 X202( 102.38/102.93 X203))) => 102.38/102.93 (![X205, 102.38/102.93 X206]: 102.38/102.93 (X202( 102.38/102.93 X205) => 102.38/102.93 (X202( 102.38/102.93 X206) => 102.38/102.93 (X205 = 102.38/102.93 X206)))))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X207:( 102.38/102.93 $i > $o), 102.38/102.93 X208:( 102.38/102.93 $i > $o)]: 102.38/102.93 (( 102.38/102.93 ![X209, 102.38/102.93 X210]: 102.38/102.93 (( 102.38/102.93 X209 = 102.38/102.93 X210) => 102.38/102.93 (X207( 102.38/102.93 X209) <=> 102.38/102.93 X208( 102.38/102.93 X210)))) => 102.38/102.93 (( 102.38/102.93 ?[X211]: 102.38/102.93 zip_tseitin5( 102.38/102.93 X211,X207)) <=> 102.38/102.93 (?[X213]: 102.38/102.93 zip_tseitin5( 102.38/102.93 X213,X208))))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 emptyset = 102.38/102.93 emptyset) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X215, 102.38/102.93 X216]: 102.38/102.93 (( 102.38/102.93 X215 = 102.38/102.93 X216) => 102.38/102.93 (![X217, 102.38/102.93 X218]: 102.38/102.93 (( 102.38/102.93 X217 = 102.38/102.93 X218) => 102.38/102.93 (setadjoin( 102.38/102.93 X215,X217) = 102.38/102.93 setadjoin( 102.38/102.93 X216,X218)))))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X219, 102.38/102.93 X220]: 102.38/102.93 (( 102.38/102.93 X219 = 102.38/102.93 X220) => 102.38/102.93 (powerset( 102.38/102.93 X219) = 102.38/102.93 powerset( 102.38/102.93 X220)))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X221, 102.38/102.93 X222]: 102.38/102.93 (( 102.38/102.93 X221 = 102.38/102.93 X222) => 102.38/102.93 (setunion( 102.38/102.93 X221) = 102.38/102.93 setunion( 102.38/102.93 X222)))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 omega = 102.38/102.93 omega) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X223:( 102.38/102.93 $i > $o)]: 102.38/102.93 (( 102.38/102.93 ?[X224]: 102.38/102.93 (( 102.38/102.93 ![X225]: 102.38/102.93 (X223( 102.38/102.93 X225) => 102.38/102.93 (X224 = 102.38/102.93 X225))) & 102.38/102.93 X223( 102.38/102.93 X224))) => 102.38/102.93 (![X226, 102.38/102.93 X227]: 102.38/102.93 (X223( 102.38/102.93 X226) => 102.38/102.93 (X223( 102.38/102.93 X227) => 102.38/102.93 (X226 = 102.38/102.93 X227)))))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X228:( 102.38/102.93 $i > $o), 102.38/102.93 X229:( 102.38/102.93 $i > $o)]: 102.38/102.93 (( 102.38/102.93 ![X230, 102.38/102.93 X231]: 102.38/102.93 (( 102.38/102.93 X230 = 102.38/102.93 X231) => 102.38/102.93 (X228( 102.38/102.93 X230) <=> 102.38/102.93 X229( 102.38/102.93 X231)))) => 102.38/102.93 (( 102.38/102.93 ?[X232]: 102.38/102.93 (( 102.38/102.93 ![X233]: 102.38/102.93 (X228( 102.38/102.93 X233) => 102.38/102.93 (X232 = 102.38/102.93 X233))) & 102.38/102.93 X228( 102.38/102.93 X232))) => 102.38/102.93 (( 102.38/102.93 ?[X234]: 102.38/102.93 (( 102.38/102.93 ![X235]: 102.38/102.93 (X229( 102.38/102.93 X235) => 102.38/102.93 (X234 = 102.38/102.93 X235))) & 102.38/102.93 X229( 102.38/102.93 X234))) => 102.38/102.93 (descr( 102.38/102.93 '#ll_0'( 102.38/102.93 X228)) = 102.38/102.93 descr( 102.38/102.93 '#ll_0'( 102.38/102.93 X229))))))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X236, 102.38/102.93 X237]: 102.38/102.93 (( 102.38/102.93 X236 = 102.38/102.93 X237) => 102.38/102.93 (![X238:( 102.38/102.93 $i > $o), 102.38/102.93 X239:( 102.38/102.93 $i > $o)]: 102.38/102.93 (( 102.38/102.93 ![X240]: 102.38/102.93 (in( 102.38/102.93 X240,X236) => 102.38/102.93 (![X241]: 102.38/102.93 (in( 102.38/102.93 X241,X237) => 102.38/102.93 (( 102.38/102.93 X240 = 102.38/102.93 X241) => 102.38/102.93 (X238( 102.38/102.93 X240) <=> 102.38/102.93 X239( 102.38/102.93 X241))))))) => 102.38/102.93 (dsetconstr( 102.38/102.93 X236, 102.38/102.93 '#ll_0'( 102.38/102.93 X238)) = 102.38/102.93 dsetconstr( 102.38/102.93 X237, 102.38/102.93 '#ll_0'( 102.38/102.93 X239))))))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X242, 102.38/102.93 X243]: 102.38/102.93 (( 102.38/102.93 ![X244]: 102.38/102.93 (in( 102.38/102.93 X244,X242) => 102.38/102.93 in( 102.38/102.93 X244,X243))) => 102.38/102.93 subset( 102.38/102.93 X242,X243))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X245, 102.38/102.93 X246]: 102.38/102.93 (( 102.38/102.93 X245 = 102.38/102.93 X246) => 102.38/102.93 subset( 102.38/102.93 X246,X245))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X247, 102.38/102.93 X248]: 102.38/102.93 (( 102.38/102.93 X247 = 102.38/102.93 X248) => 102.38/102.93 subset( 102.38/102.93 X247,X248))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X249, 102.38/102.93 X250]: 102.38/102.93 (( 102.38/102.93 ![X251]: 102.38/102.93 (in( 102.38/102.93 X251,X249) => 102.38/102.93 in( 102.38/102.93 X251,X250))) => 102.38/102.93 subset( 102.38/102.93 X249,X250))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X252]: 102.38/102.93 subset( 102.38/102.93 emptyset, 102.38/102.93 X252)) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X253, 102.38/102.93 X254,X255]: 102.38/102.93 (subset( 102.38/102.93 X253,X254) => 102.38/102.93 (in( 102.38/102.93 X255,X253) => 102.38/102.93 in( 102.38/102.93 X255,X254)))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X256, 102.38/102.93 X257,X258]: 102.38/102.93 (subset( 102.38/102.93 X256,X257) => 102.38/102.93 (( 102.38/102.93 ~ 102.38/102.93 in( 102.38/102.93 X258,X257)) => 102.38/102.93 (~ 102.38/102.93 in( 102.38/102.93 X258,X256))))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X259, 102.38/102.93 X260,X261]: 102.38/102.93 (in( 102.38/102.93 X261,X259) => 102.38/102.93 (( 102.38/102.93 ~ 102.38/102.93 in( 102.38/102.93 X261,X260)) => 102.38/102.93 (~ 102.38/102.93 subset( 102.38/102.93 X259,X260))))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X262, 102.38/102.93 X263]: 102.38/102.93 (( 102.38/102.93 ~ 102.38/102.93 subset( 102.38/102.93 X262,X263)) => 102.38/102.93 (X262 != 102.38/102.93 X263))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X264, 102.38/102.93 X265,X266]: 102.38/102.93 (in( 102.38/102.93 X266,X264) => 102.38/102.93 (( 102.38/102.93 ~ 102.38/102.93 in( 102.38/102.93 X266,X265)) => 102.38/102.93 (X264 != 102.38/102.93 X265)))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X267]: 102.38/102.93 subset( 102.38/102.93 X267,X267)) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X268, 102.38/102.93 X269,X270]: 102.38/102.93 (subset( 102.38/102.93 X268,X269) => 102.38/102.93 (subset( 102.38/102.93 X269,X270) => 102.38/102.93 subset( 102.38/102.93 X268,X270)))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X271, 102.38/102.93 X272]: 102.38/102.93 subset( 102.38/102.93 X272, 102.38/102.93 setadjoin( 102.38/102.93 X271,X272))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X273, 102.38/102.93 X274,X275]: 102.38/102.93 (subset( 102.38/102.93 X273,X275) => 102.38/102.93 subset( 102.38/102.93 X273, 102.38/102.93 setadjoin( 102.38/102.93 X274,X275)))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X276, 102.38/102.93 X277]: 102.38/102.93 (subset( 102.38/102.93 X276,X277) => 102.38/102.93 in( 102.38/102.93 X276, 102.38/102.93 powerset( 102.38/102.93 X277)))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X278, 102.38/102.93 X279]: 102.38/102.93 (subset( 102.38/102.93 X278,X279) => 102.38/102.93 (subset( 102.38/102.93 X279,X278) => 102.38/102.93 (X278 = 102.38/102.93 X279)))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X280]: 102.38/102.93 (subset( 102.38/102.93 X280, 102.38/102.93 emptyset) => 102.38/102.93 (X280 = 102.38/102.93 emptyset))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X281, 102.38/102.93 X282]: 102.38/102.93 (subset( 102.38/102.93 X282,X281) => 102.38/102.93 in( 102.38/102.93 X282, 102.38/102.93 powerset( 102.38/102.93 X281)))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X283, 102.38/102.93 X284]: 102.38/102.93 (in( 102.38/102.93 X284, 102.38/102.93 powerset( 102.38/102.93 X283)) => 102.38/102.93 subset( 102.38/102.93 X284,X283))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X285]: 102.38/102.93 in( 102.38/102.93 X285, 102.38/102.93 powerset( 102.38/102.93 X285))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X286, 102.38/102.93 X287]: 102.38/102.93 (subset( 102.38/102.93 X286,X287) => 102.38/102.93 subset( 102.38/102.93 powerset( 102.38/102.93 X286), 102.38/102.93 powerset( 102.38/102.93 X287)))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X288, 102.38/102.93 X289:( 102.38/102.93 $i > $o)]: 102.38/102.93 in( 102.38/102.93 dsetconstr( 102.38/102.93 X288, 102.38/102.93 '#ll_0'( 102.38/102.93 X289)), 102.38/102.93 powerset( 102.38/102.93 X288))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X290, 102.38/102.93 X291:( 102.38/102.93 $i > $o)]: 102.38/102.93 subset( 102.38/102.93 dsetconstr( 102.38/102.93 X290, 102.38/102.93 '#ll_0'( 102.38/102.93 X291)), 102.38/102.93 X290)) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X292, 102.38/102.93 X293,X294]: 102.38/102.93 (in( 102.38/102.93 X294,X292) => 102.38/102.93 in( 102.38/102.93 X294, 102.38/102.93 binunion( 102.38/102.93 X292,X293)))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X295, 102.38/102.93 X296]: 102.38/102.93 in( 102.38/102.93 X296, 102.38/102.93 setadjoin( 102.38/102.93 X295, 102.38/102.93 setadjoin( 102.38/102.93 X296, 102.38/102.93 emptyset)))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X297, 102.38/102.93 X298,X299]: 102.38/102.93 (in( 102.38/102.93 X299,X298) => 102.38/102.93 in( 102.38/102.93 X299, 102.38/102.93 binunion( 102.38/102.93 X297,X298)))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X300, 102.38/102.93 X301, 102.38/102.93 X302, 102.38/102.93 X303:$o]: 102.38/102.93 (in( 102.38/102.93 X302, 102.38/102.93 binunion( 102.38/102.93 X300,X301)) => 102.38/102.93 (( 102.38/102.93 in( 102.38/102.93 X302,X300) => 102.38/102.93 X303) => 102.38/102.93 (( 102.38/102.93 in( 102.38/102.93 X302,X301) => 102.38/102.93 X303) => 102.38/102.93 X303)))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X304, 102.38/102.93 X305,X306]: 102.38/102.93 (in( 102.38/102.93 X306, 102.38/102.93 binunion( 102.38/102.93 X304,X305)) => 102.38/102.93 (in( 102.38/102.93 X306,X305) | 102.38/102.93 in( 102.38/102.93 X306,X304)))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X307, 102.38/102.93 X308]: 102.38/102.93 subset( 102.38/102.93 X307, 102.38/102.93 binunion( 102.38/102.93 X307,X308))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X309, 102.38/102.93 X310]: 102.38/102.93 subset( 102.38/102.93 X310, 102.38/102.93 binunion( 102.38/102.93 X309,X310))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X311, 102.38/102.93 X312,X313]: 102.38/102.93 (in( 102.38/102.93 X313,X311) => 102.38/102.93 (in( 102.38/102.93 X313,X312) => 102.38/102.93 in( 102.38/102.93 X313, 102.38/102.93 binintersect( 102.38/102.93 X311,X312))))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X314, 102.38/102.93 X315,X316]: 102.38/102.93 (subset( 102.38/102.93 X316,X314) => 102.38/102.93 (subset( 102.38/102.93 X316,X315) => 102.38/102.93 subset( 102.38/102.93 X316, 102.38/102.93 binintersect( 102.38/102.93 X314,X315))))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X317, 102.38/102.93 X318,X319]: 102.38/102.93 (in( 102.38/102.93 X319, 102.38/102.93 binintersect( 102.38/102.93 X317,X318)) => 102.38/102.93 in( 102.38/102.93 X319,X317))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X320, 102.38/102.93 X321]: 102.38/102.93 subset( 102.38/102.93 binintersect( 102.38/102.93 X320,X321), 102.38/102.93 X320)) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X322, 102.38/102.93 X323]: 102.38/102.93 (subset( 102.38/102.93 X322,X323) => 102.38/102.93 (binintersect( 102.38/102.93 X322,X323) = 102.38/102.93 X322))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X324, 102.38/102.93 X325]: 102.38/102.93 (( 102.38/102.93 binintersect( 102.38/102.93 X324,X325) = 102.38/102.93 X325) => 102.38/102.93 subset( 102.38/102.93 X325,X324))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X326, 102.38/102.93 X327,X328]: 102.38/102.93 (in( 102.38/102.93 X328, 102.38/102.93 binintersect( 102.38/102.93 X326,X327)) => 102.38/102.93 in( 102.38/102.93 X328,X327))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X329, 102.38/102.93 X330]: 102.38/102.93 (( 102.38/102.93 ~ 102.38/102.93 ( 102.38/102.93 ?[X331]: 102.38/102.93 (in( 102.38/102.93 X331,X330) & 102.38/102.93 in( 102.38/102.93 X331,X329)))) => 102.38/102.93 (binintersect( 102.38/102.93 X329,X330) = 102.38/102.93 emptyset))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X332, 102.38/102.93 X333]: 102.38/102.93 subset( 102.38/102.93 binintersect( 102.38/102.93 X332,X333), 102.38/102.93 X333)) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X334, 102.38/102.93 X335]: 102.38/102.93 (subset( 102.38/102.93 X335,X334) => 102.38/102.93 (binintersect( 102.38/102.93 X334,X335) = 102.38/102.93 X335))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X336, 102.38/102.93 X337]: 102.38/102.93 (( 102.38/102.93 binintersect( 102.38/102.93 X336,X337) = 102.38/102.93 X336) => 102.38/102.93 subset( 102.38/102.93 X336,X337))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X338, 102.38/102.93 X339,X340]: 102.38/102.93 (binintersect( 102.38/102.93 X338, 102.38/102.93 binunion( 102.38/102.93 X339,X340)) = 102.38/102.93 binunion( 102.38/102.93 binintersect( 102.38/102.93 X338,X339), 102.38/102.93 binintersect( 102.38/102.93 X338,X340)))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X341, 102.38/102.93 X342,X343]: 102.38/102.93 (in( 102.38/102.93 X343,X341) => 102.38/102.93 (( 102.38/102.93 ~ 102.38/102.93 in( 102.38/102.93 X343,X342)) => 102.38/102.93 in( 102.38/102.93 X343, 102.38/102.93 setminus( 102.38/102.93 X341,X342))))) => 102.38/102.93 ( 102.38/102.93 ( 102.38/102.93 ![X344, 102.38/102.93 X345,X346]: 102.38/102.94 (in( 102.38/102.94 X346, 102.38/102.94 setminus( 102.38/102.94 X344,X345)) => 102.38/102.94 in( 102.38/102.94 X346,X344))) => 102.38/102.94 ( 102.38/102.94 ( 102.38/102.94 ![X347, 102.38/102.94 X348,X349]: 102.38/102.94 (in( 102.38/102.94 X349, 102.38/102.94 setminus( 102.38/102.94 X347,X348)) => 102.38/102.94 (~ 102.38/102.94 in( 102.38/102.94 X349,X348)))) => 102.38/102.94 ( 102.38/102.94 ![X350, 102.38/102.94 X351]: 102.38/102.94 (subset( 102.38/102.94 X350,X351) => 102.38/102.94 (setminus( 102.38/102.94 X350,X351) = 102.38/102.94 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 102.38/102.94 tff('122', plain, setminus(sk_X350_, sk_X351_) != emptyset, 102.38/102.94 inference('cnf', [status(esa)], [zf_stmt_14])). 102.38/102.94 tff('123', plain, 102.38/102.94 ![X515, X516, X517]: (in(X515, X516) | ~ in(X515, setminus(X516, X517))), 102.38/102.94 inference('cnf', [status(esa)], [zf_stmt_14])). 102.38/102.94 tff('124', plain, subset(sk_X350_, sk_X351_), 102.38/102.94 inference('cnf', [status(esa)], [zf_stmt_14])). 102.38/102.94 tff('125', plain, ![X393]: (X393 = emptyset | in(sk_X82_(X393), X393)), 102.38/102.94 inference('cnf', [status(esa)], [zf_stmt_14])). 102.38/102.94 tff('126', plain, 102.38/102.94 ![X518, X519, X520]: 102.38/102.94 (~ in(X518, X519) | ~ in(X518, setminus(X520, X519))), 102.38/102.94 inference('cnf', [status(esa)], [zf_stmt_14])). 102.38/102.94 tff('127', plain, 102.38/102.94 ![X531, X532]: (binintersect(X531, X532) = X531 | ~ subset(X531, X532)), 102.38/102.94 inference('cnf', [status(esa)], [zf_stmt_14])). 102.38/102.94 tff('128', plain, 102.38/102.94 ![X528, X529, X530]: 102.38/102.94 (in(X528, X529) | ~ in(X528, binintersect(X530, X529))), 102.38/102.94 inference('cnf', [status(esa)], [zf_stmt_14])). 102.38/102.94 tff('129', plain, $false, 102.38/102.94 inference('eprover', [status(thm)], 102.38/102.94 ['122', '123', '124', '125', '126', '127', '128'])). 102.38/102.94 102.38/102.94 % SZS output end Refutation 102.38/102.94 % Zipperpin 1.5 exiting 102.38/102.94 EOF