0.11/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.13 % Command : run_portfolio.sh /export/starexec/sandbox/benchmark/theBenchmark.p /export/starexec/sandbox/tmp/tmp.txuhOxuNbu 0.13/0.35 % Computer : n024.cluster.edu 0.13/0.35 % Model : x86_64 x86_64 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.35 % Memory : 8042.1875MB 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.35 % CPULimit : 180 0.13/0.35 % DateTime : Thu Aug 29 09:12:05 EDT 2019 0.13/0.35 % CPUTime : 104.15/104.79 % Running portfolio for 180 s 104.15/104.79 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 104.15/104.79 % TempDir : /export/starexec/sandbox/tmp/tmp.txuhOxuNbu 104.15/104.79 % Recognized as monomorphic HO. 104.15/104.79 % Running /export/starexec/sandbox/solver/bin/competitive.sh for 18 104.15/104.79 % Running /export/starexec/sandbox/solver/bin/competitive.2.sh for 13 104.15/104.79 % Running /export/starexec/sandbox/solver/bin/competitive.3.sh for 3 104.15/104.79 % Running /export/starexec/sandbox/solver/bin/pragmatic.rudimentary.sh for 28 104.15/104.79 % Running /export/starexec/sandbox/solver/bin/pragmatic.rudimentary.1.sh for 12 104.15/104.79 % Running /export/starexec/sandbox/solver/bin/pragmatic.rudimentary.2.sh for 7 104.15/104.79 % Running /export/starexec/sandbox/solver/bin/pragmatic.shallow.sh for 3 104.15/104.79 % Running /export/starexec/sandbox/solver/bin/pragmatic.shallow.1.sh for 14 104.15/104.79 % Running /export/starexec/sandbox/solver/bin/pragmatic.shallow.2.sh for 12 104.15/104.79 % Running /export/starexec/sandbox/solver/bin/pragmatic.ll.e.sh for 19 104.15/104.79 % Solved by: pragmatic.ll.e.sh 104.15/104.79 % Running : timeout 16 /export/starexec/sandbox/solver/bin/eprover-ho /export/starexec/sandbox/tmp/tmp.txuhOxuNbu/e_inputd3df92 --cpu-limit=14 --auto-schedule -s -p. 104.15/104.79 % done 490 iterations in 6.080s 104.15/104.79 % hashcons stats for terms: size 4096, num 23234, sum length 37182, buckets: small 0, median 7, big 22 104.15/104.79 % proof state stats: {active 201, passive 6739, simpl 0} 104.15/104.79 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 104.15/104.79 % SZS output start Refutation 104.15/104.79 tff(secondinupair, axiom, secondinupair <=> 104.15/104.79 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 104.15/104.79 tff('0', plain, 104.15/104.79 secondinupair = (![X2,X3]: in(X3,setadjoin(X2,setadjoin(X3,emptyset)))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(symdiffIneg2, axiom, symdiffIneg2 <=> 104.15/104.79 (![A,B,Xx]: ((~in(Xx,A)) => ((~in(Xx,B)) => (~in(Xx,symdiff(A,B))))))). 104.15/104.79 tff('1', plain, 104.15/104.79 symdiffIneg2 = 104.15/104.79 (![X2,X3,X4]: 104.15/104.79 ((~in(X4,X2)) => ((~in(X4,X3)) => (~in(X4,symdiff(X2,X3)))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(symdiffIneg1, axiom, symdiffIneg1 <=> 104.15/104.79 (![A,B,Xx]: (in(Xx,A) => (in(Xx,B) => (~in(Xx,symdiff(A,B))))))). 104.15/104.79 tff('2', plain, 104.15/104.79 symdiffIneg1 = 104.15/104.79 (![X2,X3,X4]: (in(X4,X2) => (in(X4,X3) => (~in(X4,symdiff(X2,X3)))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(symdiffI2, axiom, symdiffI2 <=> 104.15/104.79 (![A,B,Xx]: ((~in(Xx,A)) => (in(Xx,B) => in(Xx,symdiff(A,B)))))). 104.15/104.79 tff('3', plain, 104.15/104.79 symdiffI2 = 104.15/104.79 (![X2,X3,X4]: ((~in(X4,X2)) => (in(X4,X3) => in(X4,symdiff(X2,X3))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(symdiffI1, axiom, symdiffI1 <=> 104.15/104.79 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => in(Xx,symdiff(A,B)))))). 104.15/104.79 tff('4', plain, 104.15/104.79 symdiffI1 = 104.15/104.79 (![X2,X3,X4]: (in(X4,X2) => ((~in(X4,X3)) => in(X4,symdiff(X2,X3))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(symdiffE, axiom, symdiffE <=> 104.15/104.79 (![A,B,Xx]: 104.15/104.79 (in(Xx,symdiff(A,B)) => 104.15/104.79 (![Xphi:$o]: 104.15/104.79 ((in(Xx,A) => ((~in(Xx,B)) => Xphi)) => 104.15/104.79 (((~in(Xx,A)) => (in(Xx,B) => Xphi)) => Xphi)))))). 104.15/104.79 tff('5', plain, 104.15/104.79 symdiffE = 104.15/104.79 (![X2,X3,X4]: 104.15/104.79 (in(X4,symdiff(X2,X3)) => 104.15/104.79 (![X5:$o]: 104.15/104.79 ((in(X4,X2) => ((~in(X4,X3)) => X5)) => 104.15/104.79 (((~in(X4,X2)) => (in(X4,X3) => X5)) => X5))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(setminusSubset1, axiom, setminusSubset1 <=> 104.15/104.79 (![A,B]: ((setminus(A,B) = emptyset) => subset(A,B)))). 104.15/104.79 tff('6', plain, 104.15/104.79 setminusSubset1 = 104.15/104.79 (![X2,X3]: ((setminus(X2,X3) = emptyset) => subset(X2,X3))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(setminusLsub, axiom, setminusLsub <=> (![A,B]: subset(setminus(A,B),A))). 104.15/104.79 tff('7', plain, setminusLsub = (![X2,X3]: subset(setminus(X2,X3),X2)), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(setminusIRneg, axiom, setminusIRneg <=> 104.15/104.79 (![A,B,Xx]: (in(Xx,B) => (~in(Xx,setminus(A,B)))))). 104.15/104.79 tff('8', plain, 104.15/104.79 setminusIRneg = (![X2,X3,X4]: (in(X4,X3) => (~in(X4,setminus(X2,X3))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(setminusILneg, axiom, setminusILneg <=> 104.15/104.79 (![A,B,Xx]: ((~in(Xx,A)) => (~in(Xx,setminus(A,B)))))). 104.15/104.79 tff('9', plain, 104.15/104.79 setminusILneg = 104.15/104.79 (![X2,X3,X4]: ((~in(X4,X2)) => (~in(X4,setminus(X2,X3))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(setminusELneg, axiom, setminusELneg <=> 104.15/104.79 (![A,B,Xx]: ((~in(Xx,setminus(A,B))) => ((~in(Xx,B)) => (~in(Xx,A)))))). 104.15/104.79 tff('10', plain, 104.15/104.79 setminusELneg = 104.15/104.79 (![X2,X3,X4]: 104.15/104.79 ((~in(X4,setminus(X2,X3))) => ((~in(X4,X3)) => (~in(X4,X2))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(setminusERneg, axiom, setminusERneg <=> 104.15/104.79 (![A,B,Xx]: ((~in(Xx,setminus(A,B))) => (in(Xx,A) => in(Xx,B))))). 104.15/104.79 tff('11', plain, 104.15/104.79 setminusERneg = 104.15/104.79 (![X2,X3,X4]: ((~in(X4,setminus(X2,X3))) => (in(X4,X2) => in(X4,X3)))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(setminusSubset2, axiom, setminusSubset2 <=> 104.15/104.79 (![A,B]: (subset(A,B) => (setminus(A,B) = emptyset)))). 104.15/104.79 tff('12', plain, 104.15/104.79 setminusSubset2 = 104.15/104.79 (![X2,X3]: (subset(X2,X3) => (setminus(X2,X3) = emptyset))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(setminusER, axiom, setminusER <=> 104.15/104.79 (![A,B,Xx]: (in(Xx,setminus(A,B)) => (~in(Xx,B))))). 104.15/104.79 tff('13', plain, 104.15/104.79 setminusER = (![X2,X3,X4]: (in(X4,setminus(X2,X3)) => (~in(X4,X3)))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(setminusEL, axiom, setminusEL <=> 104.15/104.79 (![A,B,Xx]: (in(Xx,setminus(A,B)) => in(Xx,A)))). 104.15/104.79 tff('14', plain, 104.15/104.79 setminusEL = (![X2,X3,X4]: (in(X4,setminus(X2,X3)) => in(X4,X2))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(setminusI, axiom, setminusI <=> 104.15/104.79 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => in(Xx,setminus(A,B)))))). 104.15/104.79 tff('15', plain, 104.15/104.79 setminusI = 104.15/104.79 (![X2,X3,X4]: (in(X4,X2) => ((~in(X4,X3)) => in(X4,setminus(X2,X3))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(bs114d, axiom, bs114d <=> 104.15/104.79 (![A,B,C]: 104.15/104.79 (binintersect(A,binunion(B,C)) = 104.15/104.79 binunion(binintersect(A,B),binintersect(A,C))))). 104.15/104.79 tff('16', plain, 104.15/104.79 bs114d = 104.15/104.79 (![X2,X3,X4]: 104.15/104.79 (binintersect(X2,binunion(X3,X4)) = 104.15/104.79 binunion(binintersect(X2,X3),binintersect(X2,X4)))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(binintersectSubset1, axiom, binintersectSubset1 <=> 104.15/104.79 (![A,B]: ((binintersect(A,B) = A) => subset(A,B)))). 104.15/104.79 tff('17', plain, 104.15/104.79 binintersectSubset1 = 104.15/104.79 (![X2,X3]: ((binintersect(X2,X3) = X2) => subset(X2,X3))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(binintersectSubset4, axiom, binintersectSubset4 <=> 104.15/104.79 (![A,B]: (subset(B,A) => (binintersect(A,B) = B)))). 104.15/104.79 tff('18', plain, 104.15/104.79 binintersectSubset4 = 104.15/104.79 (![X2,X3]: (subset(X3,X2) => (binintersect(X2,X3) = X3))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(binintersectRsub, axiom, binintersectRsub <=> 104.15/104.79 (![A,B]: subset(binintersect(A,B),B))). 104.15/104.79 tff('19', plain, 104.15/104.79 binintersectRsub = (![X2,X3]: subset(binintersect(X2,X3),X3)), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(disjointsetsI1, axiom, disjointsetsI1 <=> 104.15/104.79 (![A,B]: 104.15/104.79 ((~(?[Xx]: (in(Xx,B) & in(Xx,A)))) => (binintersect(A,B) = emptyset)))). 104.15/104.79 tff('20', plain, 104.15/104.79 disjointsetsI1 = 104.15/104.79 (![X2,X3]: 104.15/104.79 ((~(?[X4]: (in(X4,X3) & in(X4,X2)))) => 104.15/104.79 (binintersect(X2,X3) = emptyset))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(binintersectER, axiom, binintersectER <=> 104.15/104.79 (![A,B,Xx]: (in(Xx,binintersect(A,B)) => in(Xx,B)))). 104.15/104.79 tff('21', plain, 104.15/104.79 binintersectER = (![X2,X3,X4]: (in(X4,binintersect(X2,X3)) => in(X4,X3))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(binintersectSubset3, axiom, binintersectSubset3 <=> 104.15/104.79 (![A,B]: ((binintersect(A,B) = B) => subset(B,A)))). 104.15/104.79 tff('22', plain, 104.15/104.79 binintersectSubset3 = 104.15/104.79 (![X2,X3]: ((binintersect(X2,X3) = X3) => subset(X3,X2))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(binintersectSubset2, axiom, binintersectSubset2 <=> 104.15/104.79 (![A,B]: (subset(A,B) => (binintersect(A,B) = A)))). 104.15/104.79 tff('23', plain, 104.15/104.79 binintersectSubset2 = 104.15/104.79 (![X2,X3]: (subset(X2,X3) => (binintersect(X2,X3) = X2))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(binintersectLsub, axiom, binintersectLsub <=> 104.15/104.79 (![A,B]: subset(binintersect(A,B),A))). 104.15/104.79 tff('24', plain, 104.15/104.79 binintersectLsub = (![X2,X3]: subset(binintersect(X2,X3),X2)), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(binintersectEL, axiom, binintersectEL <=> 104.15/104.79 (![A,B,Xx]: (in(Xx,binintersect(A,B)) => in(Xx,A)))). 104.15/104.79 tff('25', plain, 104.15/104.79 binintersectEL = (![X2,X3,X4]: (in(X4,binintersect(X2,X3)) => in(X4,X2))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(binintersectSubset5, axiom, binintersectSubset5 <=> 104.15/104.79 (![A,B,C]: (subset(C,A) => (subset(C,B) => subset(C,binintersect(A,B)))))). 104.15/104.79 tff('26', plain, 104.15/104.79 binintersectSubset5 = 104.15/104.79 (![X2,X3,X4]: 104.15/104.79 (subset(X4,X2) => (subset(X4,X3) => subset(X4,binintersect(X2,X3))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(binintersectI, axiom, binintersectI <=> 104.15/104.79 (![A,B,Xx]: (in(Xx,A) => (in(Xx,B) => in(Xx,binintersect(A,B)))))). 104.15/104.79 tff('27', plain, 104.15/104.79 binintersectI = 104.15/104.79 (![X2,X3,X4]: (in(X4,X2) => (in(X4,X3) => in(X4,binintersect(X2,X3))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(binunionRsub, axiom, binunionRsub <=> (![A,B]: subset(B,binunion(A,B)))). 104.15/104.79 tff('28', plain, binunionRsub = (![X2,X3]: subset(X3,binunion(X2,X3))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(binunionLsub, axiom, binunionLsub <=> (![A,B]: subset(A,binunion(A,B)))). 104.15/104.79 tff('29', plain, binunionLsub = (![X2,X3]: subset(X2,binunion(X2,X3))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(binunionE, axiom, binunionE <=> 104.15/104.79 (![A,B,Xx]: (in(Xx,binunion(A,B)) => (in(Xx,B) | in(Xx,A))))). 104.15/104.79 tff('30', plain, 104.15/104.79 binunionE = 104.15/104.79 (![X2,X3,X4]: (in(X4,binunion(X2,X3)) => (in(X4,X3) | in(X4,X2)))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(binunionEcases, axiom, binunionEcases <=> 104.15/104.79 (![A,B,Xx,Xphi:$o]: 104.15/104.79 (in(Xx,binunion(A,B)) => 104.15/104.79 ((in(Xx,A) => Xphi) => ((in(Xx,B) => Xphi) => Xphi))))). 104.15/104.79 tff('31', plain, 104.15/104.79 binunionEcases = 104.15/104.79 (![X2,X3,X4,X5:$o]: 104.15/104.79 (in(X4,binunion(X2,X3)) => 104.15/104.79 ((in(X4,X2) => X5) => ((in(X4,X3) => X5) => X5)))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(binunionIR, axiom, binunionIR <=> 104.15/104.79 (![A,B,Xx]: (in(Xx,B) => in(Xx,binunion(A,B))))). 104.15/104.79 tff('32', plain, 104.15/104.79 binunionIR = (![X2,X3,X4]: (in(X4,X3) => in(X4,binunion(X2,X3)))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(upairset2IR, axiom, upairset2IR <=> 104.15/104.79 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 104.15/104.79 tff('33', plain, 104.15/104.79 upairset2IR = (![X2,X3]: in(X3,setadjoin(X2,setadjoin(X3,emptyset)))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(binunionIL, axiom, binunionIL <=> 104.15/104.79 (![A,B,Xx]: (in(Xx,A) => in(Xx,binunion(A,B))))). 104.15/104.79 tff('34', plain, 104.15/104.79 binunionIL = (![X2,X3,X4]: (in(X4,X2) => in(X4,binunion(X2,X3)))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(sepSubset, axiom, sepSubset <=> 104.15/104.79 (![A,Xphi:($i > $o)]: subset(dsetconstr(A,^[Xx]: Xphi(Xx)),A))). 104.15/104.79 tff('35', plain, 104.15/104.79 sepSubset = 104.15/104.79 (![X2,X3:($i > $o)]: subset(dsetconstr(X2,^[V_1]: X3(V_1)),X2)), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(sepInPowerset, axiom, sepInPowerset <=> 104.15/104.79 (![A,Xphi:($i > $o)]: in(dsetconstr(A,^[Xx]: Xphi(Xx)),powerset(A)))). 104.15/104.79 tff('36', plain, 104.15/104.79 sepInPowerset = 104.15/104.79 (![X2,X3:($i > $o)]: in(dsetconstr(X2,^[V_1]: X3(V_1)),powerset(X2))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(powersetsubset, axiom, powersetsubset <=> 104.15/104.79 (![A,B]: (subset(A,B) => subset(powerset(A),powerset(B))))). 104.15/104.79 tff('37', plain, 104.15/104.79 powersetsubset = 104.15/104.79 (![X2,X3]: (subset(X2,X3) => subset(powerset(X2),powerset(X3)))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(inPowerset, axiom, inPowerset <=> (![A]: in(A,powerset(A)))). 104.15/104.79 tff('38', plain, inPowerset = (![X2]: in(X2,powerset(X2))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(powersetE1, axiom, powersetE1 <=> 104.15/104.79 (![A,B]: (in(B,powerset(A)) => subset(B,A)))). 104.15/104.79 tff('39', plain, 104.15/104.79 powersetE1 = (![X2,X3]: (in(X3,powerset(X2)) => subset(X3,X2))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(powersetI1, axiom, powersetI1 <=> 104.15/104.79 (![A,B]: (subset(B,A) => in(B,powerset(A))))). 104.15/104.79 tff('40', plain, 104.15/104.79 powersetI1 = (![X2,X3]: (subset(X3,X2) => in(X3,powerset(X2)))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(subsetemptysetimpeq, axiom, subsetemptysetimpeq <=> 104.15/104.79 (![A]: (subset(A,emptyset) => (A = emptyset)))). 104.15/104.79 tff('41', plain, 104.15/104.79 subsetemptysetimpeq = (![X2]: (subset(X2,emptyset) => (X2 = emptyset))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(setextsub, axiom, setextsub <=> 104.15/104.79 (![A,B]: (subset(A,B) => (subset(B,A) => (A = B))))). 104.15/104.79 tff('42', plain, 104.15/104.79 setextsub = (![X2,X3]: (subset(X2,X3) => (subset(X3,X2) => (X2 = X3)))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(subset2powerset, axiom, subset2powerset <=> 104.15/104.79 (![A,B]: (subset(A,B) => in(A,powerset(B))))). 104.15/104.79 tff('43', plain, 104.15/104.79 subset2powerset = (![X2,X3]: (subset(X2,X3) => in(X2,powerset(X3)))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(setadjoinSub2, axiom, setadjoinSub2 <=> 104.15/104.79 (![A,Xx,B]: (subset(A,B) => subset(A,setadjoin(Xx,B))))). 104.15/104.79 tff('44', plain, 104.15/104.79 setadjoinSub2 = 104.15/104.79 (![X2,X3,X4]: (subset(X2,X4) => subset(X2,setadjoin(X3,X4)))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(setadjoinSub, axiom, setadjoinSub <=> 104.15/104.79 (![Xx,A]: subset(A,setadjoin(Xx,A)))). 104.15/104.79 tff('45', plain, setadjoinSub = (![X2,X3]: subset(X3,setadjoin(X2,X3))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(subsetTrans, axiom, subsetTrans <=> 104.15/104.79 (![A,B,C]: (subset(A,B) => (subset(B,C) => subset(A,C))))). 104.15/104.79 tff('46', plain, 104.15/104.79 subsetTrans = 104.15/104.79 (![X2,X3,X4]: (subset(X2,X3) => (subset(X3,X4) => subset(X2,X4)))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(subsetRefl, axiom, subsetRefl <=> (![A]: subset(A,A))). 104.15/104.79 tff('47', plain, subsetRefl = (![X2]: subset(X2,X2)), define([status(thm)])). 104.15/104.79 tff(notequalI2, axiom, notequalI2 <=> 104.15/104.79 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => (A != B))))). 104.15/104.79 tff('48', plain, 104.15/104.79 notequalI2 = (![X2,X3,X4]: (in(X4,X2) => ((~in(X4,X3)) => (X2 != X3)))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(notequalI1, axiom, notequalI1 <=> (![A,B]: ((~subset(A,B)) => (A != B)))). 104.15/104.79 tff('49', plain, notequalI1 = (![X2,X3]: ((~subset(X2,X3)) => (X2 != X3))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(notsubsetI, axiom, notsubsetI <=> 104.15/104.79 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => (~subset(A,B)))))). 104.15/104.79 tff('50', plain, 104.15/104.79 notsubsetI = 104.15/104.79 (![X2,X3,X4]: (in(X4,X2) => ((~in(X4,X3)) => (~subset(X2,X3))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(subsetE2, axiom, subsetE2 <=> 104.15/104.79 (![A,B,Xx]: (subset(A,B) => ((~in(Xx,B)) => (~in(Xx,A)))))). 104.15/104.79 tff('51', plain, 104.15/104.79 subsetE2 = 104.15/104.79 (![X2,X3,X4]: (subset(X2,X3) => ((~in(X4,X3)) => (~in(X4,X2))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(subsetE, axiom, subsetE <=> 104.15/104.79 (![A,B,Xx]: (subset(A,B) => (in(Xx,A) => in(Xx,B))))). 104.15/104.79 tff('52', plain, 104.15/104.79 subsetE = (![X2,X3,X4]: (subset(X2,X3) => (in(X4,X2) => in(X4,X3)))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(emptysetsubset, axiom, emptysetsubset <=> (![A]: subset(emptyset,A))). 104.15/104.79 tff('53', plain, emptysetsubset = (![X2]: subset(emptyset,X2)), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(subsetI2, axiom, subsetI2 <=> 104.15/104.79 (![A,B]: ((![Xx]: (in(Xx,A) => in(Xx,B))) => subset(A,B)))). 104.15/104.79 tff('54', plain, 104.15/104.79 subsetI2 = 104.15/104.79 (![X2,X3]: ((![X4]: (in(X4,X2) => in(X4,X3))) => subset(X2,X3))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(eqimpsubset1, axiom, eqimpsubset1 <=> (![A,B]: ((A = B) => subset(A,B)))). 104.15/104.79 tff('55', plain, eqimpsubset1 = (![X2,X3]: ((X2 = X3) => subset(X2,X3))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(eqimpsubset2, axiom, eqimpsubset2 <=> (![A,B]: ((A = B) => subset(B,A)))). 104.15/104.79 tff('56', plain, eqimpsubset2 = (![X2,X3]: ((X2 = X3) => subset(X3,X2))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(subsetI1, axiom, subsetI1 <=> 104.15/104.79 (![A,B]: ((![Xx]: (in(Xx,A) => in(Xx,B))) => subset(A,B)))). 104.15/104.79 tff('57', plain, 104.15/104.79 subsetI1 = 104.15/104.79 (![X2,X3]: ((![X4]: (in(X4,X2) => in(X4,X3))) => subset(X2,X3))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(dsetconstr__Cong, axiom, dsetconstr__Cong <=> 104.15/104.79 (![A,B]: 104.15/104.79 ((A = B) => 104.15/104.79 (![Xphi:($i > $o),Xpsi:($i > $o)]: 104.15/104.79 ((![Xx]: 104.15/104.79 (in(Xx,A) => 104.15/104.79 (![Xy]: (in(Xy,B) => ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy))))))) => 104.15/104.79 (dsetconstr(A,^[Xx]: Xphi(Xx)) = dsetconstr(B,^[Xx]: Xpsi(Xx)))))))). 104.15/104.79 tff('58', plain, 104.15/104.79 dsetconstr__Cong = 104.15/104.79 (![X2,X3]: 104.15/104.79 ((X2 = X3) => 104.15/104.79 (![X4:($i > $o),X5:($i > $o)]: 104.15/104.79 ((![X6]: 104.15/104.79 (in(X6,X2) => 104.15/104.79 (![X7]: (in(X7,X3) => ((X6 = X7) => (X4(X6) <=> X5(X7))))))) => 104.15/104.79 (dsetconstr(X2,^[V_1]: X4(V_1)) = dsetconstr(X3,^[V_2]: X5(V_2))))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(descr__Cong, axiom, descr__Cong <=> 104.15/104.79 (![Xphi:($i > $o),Xpsi:($i > $o)]: 104.15/104.79 ((![Xx,Xy]: ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy)))) => 104.15/104.79 (exu(^[Xx]: Xphi(Xx)) => 104.15/104.79 (exu(^[Xx]: Xpsi(Xx)) => 104.15/104.79 (descr(^[Xx]: Xphi(Xx)) = descr(^[Xx]: Xpsi(Xx)))))))). 104.15/104.79 tff('59', plain, 104.15/104.79 descr__Cong = 104.15/104.79 (![X2:($i > $o),X3:($i > $o)]: 104.15/104.79 ((![X4,X5]: ((X4 = X5) => (X2(X4) <=> X3(X5)))) => 104.15/104.79 (exu(^[V_1]: X2(V_1)) => 104.15/104.79 (exu(^[V_2]: X3(V_2)) => 104.15/104.79 (descr(^[V_3]: X2(V_3)) = descr(^[V_4]: X3(V_4))))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(exuEu, axiom, exuEu <=> 104.15/104.79 (![Xphi:($i > $o)]: 104.15/104.79 (exu(^[Xx]: Xphi(Xx)) => 104.15/104.79 (![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))). 104.15/104.79 tff('60', plain, 104.15/104.79 exuEu = 104.15/104.79 (![X2:($i > $o)]: 104.15/104.79 (exu(^[V_1]: X2(V_1)) => (![X3,X4]: (X2(X3) => (X2(X4) => (X3 = X4)))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(omega__Cong, axiom, omega__Cong <=> (omega = omega)). 104.15/104.79 tff('61', plain, omega__Cong = (omega = omega), define([status(thm)])). 104.15/104.79 tff(setunion__Cong, axiom, setunion__Cong <=> 104.15/104.79 (![A,B]: ((A = B) => (setunion(A) = setunion(B))))). 104.15/104.79 tff('62', plain, 104.15/104.79 setunion__Cong = (![X2,X3]: ((X2 = X3) => (setunion(X2) = setunion(X3)))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(powerset__Cong, axiom, powerset__Cong <=> 104.15/104.79 (![A,B]: ((A = B) => (powerset(A) = powerset(B))))). 104.15/104.79 tff('63', plain, 104.15/104.79 powerset__Cong = (![X2,X3]: ((X2 = X3) => (powerset(X2) = powerset(X3)))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(setadjoin__Cong, axiom, setadjoin__Cong <=> 104.15/104.79 (![Xx,Xy]: 104.15/104.79 ((Xx = Xy) => 104.15/104.79 (![Xz,Xu]: ((Xz = Xu) => (setadjoin(Xx,Xz) = setadjoin(Xy,Xu))))))). 104.15/104.79 tff('64', plain, 104.15/104.79 setadjoin__Cong = 104.15/104.79 (![X2,X3]: 104.15/104.79 ((X2 = X3) => 104.15/104.79 (![X4,X5]: ((X4 = X5) => (setadjoin(X2,X4) = setadjoin(X3,X5)))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(emptyset__Cong, axiom, emptyset__Cong <=> (emptyset = emptyset)). 104.15/104.79 tff('65', plain, emptyset__Cong = (emptyset = emptyset), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(exu__Cong, axiom, exu__Cong <=> 104.15/104.79 (![Xphi:($i > $o),Xpsi:($i > $o)]: 104.15/104.79 ((![Xx,Xy]: ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy)))) => 104.15/104.79 (exu(^[Xx]: Xphi(Xx)) <=> exu(^[Xx]: Xpsi(Xx)))))). 104.15/104.79 tff('66', plain, 104.15/104.79 exu__Cong = 104.15/104.79 (![X2:($i > $o),X3:($i > $o)]: 104.15/104.79 ((![X4,X5]: ((X4 = X5) => (X2(X4) <=> X3(X5)))) => 104.15/104.79 (exu(^[V_1]: X2(V_1)) <=> exu(^[V_2]: X3(V_2))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(exuE3u, axiom, exuE3u <=> 104.15/104.79 (![Xphi:($i > $o)]: 104.15/104.79 (exu(^[Xx]: Xphi(Xx)) => 104.15/104.79 (![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))). 104.15/104.79 tff('67', plain, 104.15/104.79 exuE3u = 104.15/104.79 (![X2:($i > $o)]: 104.15/104.79 (exu(^[V_1]: X2(V_1)) => (![X3,X4]: (X2(X3) => (X2(X4) => (X3 = X4)))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(in__Cong, axiom, in__Cong <=> 104.15/104.79 (![A,B]: ((A = B) => (![Xx,Xy]: ((Xx = Xy) => (in(Xx,A) <=> in(Xy,B))))))). 104.15/104.79 tff('68', plain, 104.15/104.79 in__Cong = 104.15/104.79 (![X2,X3]: 104.15/104.79 ((X2 = X3) => (![X4,X5]: ((X4 = X5) => (in(X4,X2) <=> in(X5,X3)))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(inCongP, axiom, inCongP <=> 104.15/104.79 (![A,B]: ((A = B) => (![Xx,Xy]: ((Xx = Xy) => (in(Xx,A) => in(Xy,B))))))). 104.15/104.79 tff('69', plain, 104.15/104.79 inCongP = 104.15/104.79 (![X2,X3]: 104.15/104.79 ((X2 = X3) => (![X4,X5]: ((X4 = X5) => (in(X4,X2) => in(X5,X3)))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(exuI2, axiom, exuI2 <=> 104.15/104.79 (![Xphi:($i > $o)]: 104.15/104.79 ((?[Xx]: (![Xy]: (Xphi(Xy) <=> (Xy = Xx)))) => exu(^[Xx]: Xphi(Xx))))). 104.15/104.79 tff('70', plain, 104.15/104.79 exuI2 = 104.15/104.79 (![X2:($i > $o)]: 104.15/104.79 ((?[X3]: (![X4]: (X2(X4) <=> (X4 = X3)))) => exu(^[V_1]: X2(V_1)))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(exuI3, axiom, exuI3 <=> 104.15/104.79 (![Xphi:($i > $o)]: 104.15/104.79 ((?[Xx]: Xphi(Xx)) => 104.15/104.79 ((![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy)))) => 104.15/104.79 exu(^[Xx]: Xphi(Xx)))))). 104.15/104.79 tff('71', plain, 104.15/104.79 exuI3 = 104.15/104.79 (![X2:($i > $o)]: 104.15/104.79 ((?[X3]: X2(X3)) => 104.15/104.79 ((![X4,X5]: (X2(X4) => (X2(X5) => (X4 = X5)))) => 104.15/104.79 exu(^[V_1]: X2(V_1))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(exuI1, axiom, exuI1 <=> 104.15/104.79 (![Xphi:($i > $o)]: 104.15/104.79 ((?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx))) => 104.15/104.79 exu(^[Xx]: Xphi(Xx))))). 104.15/104.79 tff('72', plain, 104.15/104.79 exuI1 = 104.15/104.79 (![X2:($i > $o)]: 104.15/104.79 ((?[X3]: ((![X4]: (X2(X4) => (X3 = X4))) & X2(X3))) => 104.15/104.79 exu(^[V_1]: X2(V_1)))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(notdallE, axiom, notdallE <=> 104.15/104.79 (![A,Xphi:($i > $o)]: 104.15/104.79 ((~(![Xx]: (in(Xx,A) => Xphi(Xx)))) => (?[Xx]: ((~Xphi(Xx)) & in(Xx,A)))))). 104.15/104.79 tff('73', plain, 104.15/104.79 notdallE = 104.15/104.79 (![X2,X3:($i > $o)]: 104.15/104.79 ((~(![X4]: (in(X4,X2) => X3(X4)))) => (?[X5]: ((~X3(X5)) & in(X5,X2))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(notdexE, axiom, notdexE <=> 104.15/104.79 (![A,Xphi:($i > $o)]: 104.15/104.79 ((~(?[Xx]: (Xphi(Xx) & in(Xx,A)))) => (![Xx]: (in(Xx,A) => (~Xphi(Xx))))))). 104.15/104.79 tff('74', plain, 104.15/104.79 notdexE = 104.15/104.79 (![X2,X3:($i > $o)]: 104.15/104.79 ((~(?[X4]: (X3(X4) & in(X4,X2)))) => (![X5]: (in(X5,X2) => (~X3(X5)))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(prop2set2propI, axiom, prop2set2propI <=> 104.15/104.79 (![Xphi:$o]: (Xphi => set2prop(prop2set(Xphi))))). 104.15/104.79 tff('75', plain, prop2set2propI = (![X2:$o]: (X2 => set2prop(prop2set(X2)))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(prop2setI, axiom, prop2setI <=> 104.15/104.79 (![Xphi:$o]: (Xphi => in(emptyset,prop2set(Xphi))))). 104.15/104.79 tff('76', plain, prop2setI = (![X2:$o]: (X2 => in(emptyset,prop2set(X2)))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(quantDeMorgan4, axiom, quantDeMorgan4 <=> 104.15/104.79 (![A,Xphi:($i > $o)]: 104.15/104.79 ((?[Xx]: ((~Xphi(Xx)) & in(Xx,A))) => (~(![Xx]: (in(Xx,A) => Xphi(Xx))))))). 104.15/104.79 tff('77', plain, 104.15/104.79 quantDeMorgan4 = 104.15/104.79 (![X2,X3:($i > $o)]: 104.15/104.79 ((?[X4]: ((~X3(X4)) & in(X4,X2))) => (~(![X5]: (in(X5,X2) => X3(X5)))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(quantDeMorgan3, axiom, quantDeMorgan3 <=> 104.15/104.79 (![A,Xphi:($i > $o)]: 104.15/104.79 ((~(?[Xx]: (Xphi(Xx) & in(Xx,A)))) => (![Xx]: (in(Xx,A) => (~Xphi(Xx))))))). 104.15/104.79 tff('78', plain, 104.15/104.79 quantDeMorgan3 = 104.15/104.79 (![X2,X3:($i > $o)]: 104.15/104.79 ((~(?[X4]: (X3(X4) & in(X4,X2)))) => (![X5]: (in(X5,X2) => (~X3(X5)))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(quantDeMorgan2, axiom, quantDeMorgan2 <=> 104.15/104.79 (![A,Xphi:($i > $o)]: 104.15/104.79 ((![Xx]: (in(Xx,A) => (~Xphi(Xx)))) => (~(?[Xx]: (Xphi(Xx) & in(Xx,A))))))). 104.15/104.79 tff('79', plain, 104.15/104.79 quantDeMorgan2 = 104.15/104.79 (![X2,X3:($i > $o)]: 104.15/104.79 ((![X4]: (in(X4,X2) => (~X3(X4)))) => (~(?[X5]: (X3(X5) & in(X5,X2)))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(quantDeMorgan1, axiom, quantDeMorgan1 <=> 104.15/104.79 (![A,Xphi:($i > $o)]: 104.15/104.79 ((~(![Xx]: (in(Xx,A) => Xphi(Xx)))) => (?[Xx]: ((~Xphi(Xx)) & in(Xx,A)))))). 104.15/104.79 tff('80', plain, 104.15/104.79 quantDeMorgan1 = 104.15/104.79 (![X2,X3:($i > $o)]: 104.15/104.79 ((~(![X4]: (in(X4,X2) => X3(X4)))) => (?[X5]: ((~X3(X5)) & in(X5,X2))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(vacuousDall, axiom, vacuousDall <=> 104.15/104.79 (![Xphi:($i > $o),Xx]: (in(Xx,emptyset) => Xphi(Xx)))). 104.15/104.79 tff('81', plain, 104.15/104.79 vacuousDall = (![X2:($i > $o),X3]: (in(X3,emptyset) => X2(X3))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(emptyE1, axiom, emptyE1 <=> 104.15/104.79 (![A,Xphi:($i > $o)]: 104.15/104.79 ((?[Xx]: (Xphi(Xx) & in(Xx,A))) => 104.15/104.79 ((dsetconstr(A,^[Xx]: Xphi(Xx)) = emptyset) => $false)))). 104.15/104.79 tff('82', plain, 104.15/104.79 emptyE1 = 104.15/104.79 (![X2,X3:($i > $o)]: 104.15/104.79 ((?[X4]: (X3(X4) & in(X4,X2))) => 104.15/104.79 ((dsetconstr(X2,^[V_1]: X3(V_1)) = emptyset) => $false))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(upairsetIR, axiom, upairsetIR <=> 104.15/104.79 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 104.15/104.79 tff('83', plain, 104.15/104.79 upairsetIR = (![X2,X3]: in(X3,setadjoin(X2,setadjoin(X3,emptyset)))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(upairsetIL, axiom, upairsetIL <=> 104.15/104.79 (![Xx,Xy]: in(Xx,setadjoin(Xx,setadjoin(Xy,emptyset))))). 104.15/104.79 tff('84', plain, 104.15/104.79 upairsetIL = (![X2,X3]: in(X2,setadjoin(X2,setadjoin(X3,emptyset)))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(upairsetE, axiom, upairsetE <=> 104.15/104.79 (![Xx,Xy,Xz]: 104.15/104.79 (in(Xz,setadjoin(Xx,setadjoin(Xy,emptyset))) => ((Xz = Xy) | (Xz = Xx))))). 104.15/104.79 tff('85', plain, 104.15/104.79 upairsetE = 104.15/104.79 (![X2,X3,X4]: 104.15/104.79 (in(X4,setadjoin(X2,setadjoin(X3,emptyset))) => 104.15/104.79 ((X4 = X3) | (X4 = X2)))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(singletonsswitch, axiom, singletonsswitch <=> 104.15/104.79 (![Xx,Xy]: (in(Xx,setadjoin(Xy,emptyset)) => in(Xy,setadjoin(Xx,emptyset))))). 104.15/104.79 tff('86', plain, 104.15/104.79 singletonsswitch = 104.15/104.79 (![X2,X3]: 104.15/104.79 (in(X2,setadjoin(X3,emptyset)) => in(X3,setadjoin(X2,emptyset)))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(eqinunit, axiom, eqinunit <=> 104.15/104.79 (![Xx,Xy]: ((Xx = Xy) => in(Xx,setadjoin(Xy,emptyset))))). 104.15/104.79 tff('87', plain, 104.15/104.79 eqinunit = (![X2,X3]: ((X2 = X3) => in(X2,setadjoin(X3,emptyset)))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(notinsingleton, axiom, notinsingleton <=> 104.15/104.79 (![Xx,Xy]: ((Xx != Xy) => (~in(Xy,setadjoin(Xx,emptyset)))))). 104.15/104.79 tff('88', plain, 104.15/104.79 notinsingleton = 104.15/104.79 (![X2,X3]: ((X2 != X3) => (~in(X3,setadjoin(X2,emptyset))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(uniqinunit, axiom, uniqinunit <=> 104.15/104.79 (![Xx,Xy]: (in(Xx,setadjoin(Xy,emptyset)) => (Xx = Xy)))). 104.15/104.79 tff('89', plain, 104.15/104.79 uniqinunit = (![X2,X3]: (in(X2,setadjoin(X3,emptyset)) => (X2 = X3))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(nonemptyImpWitness, axiom, nonemptyImpWitness <=> 104.15/104.79 (![A]: (nonempty(A) => (?[Xx]: (in(Xx,A)))))). 104.15/104.79 tff('90', plain, 104.15/104.79 nonemptyImpWitness = (![X2]: (nonempty(X2) => (?[X3]: (in(X3,X2))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(exuE2, axiom, exuE2 <=> 104.15/104.79 (![Xphi:($i > $o)]: 104.15/104.79 (exu(^[Xx]: Xphi(Xx)) => (?[Xx]: (![Xy]: (Xphi(Xy) <=> (Xy = Xx))))))). 104.15/104.79 tff('91', plain, 104.15/104.79 exuE2 = 104.15/104.79 (![X2:($i > $o)]: 104.15/104.79 (exu(^[V_1]: X2(V_1)) => (?[X3]: (![X4]: (X2(X4) <=> (X4 = X3)))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(subPowSU, axiom, subPowSU <=> 104.15/104.79 (![A,Xx]: (in(Xx,A) => in(Xx,powerset(setunion(A)))))). 104.15/104.79 tff('92', plain, 104.15/104.79 subPowSU = (![X2,X3]: (in(X3,X2) => in(X3,powerset(setunion(X2))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(setunionE, axiom, setunionE <=> 104.15/104.79 (![A,Xx]: 104.15/104.79 (in(Xx,setunion(A)) => 104.15/104.79 (![Xphi:$o]: ((![B]: (in(Xx,B) => (in(B,A) => Xphi))) => Xphi))))). 104.15/104.79 tff('93', plain, 104.15/104.79 setunionE = 104.15/104.79 (![X2,X3]: 104.15/104.79 (in(X3,setunion(X2)) => 104.15/104.79 (![X4:$o]: ((![X5]: (in(X3,X5) => (in(X5,X2) => X4))) => X4)))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(setunionI, axiom, setunionI <=> 104.15/104.79 (![A,Xx,B]: (in(Xx,B) => (in(B,A) => in(Xx,setunion(A)))))). 104.15/104.79 tff('94', plain, 104.15/104.79 setunionI = 104.15/104.79 (![X2,X3,X4]: (in(X3,X4) => (in(X4,X2) => in(X3,setunion(X2))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(powersetE, axiom, powersetE <=> 104.15/104.79 (![A,B,Xx]: (in(B,powerset(A)) => (in(Xx,B) => in(Xx,A))))). 104.15/104.79 tff('95', plain, 104.15/104.79 powersetE = 104.15/104.79 (![X2,X3,X4]: (in(X3,powerset(X2)) => (in(X4,X3) => in(X4,X2)))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(emptyInPowerset, axiom, emptyInPowerset <=> 104.15/104.79 (![A]: in(emptyset,powerset(A)))). 104.15/104.79 tff('96', plain, emptyInPowerset = (![X2]: in(emptyset,powerset(X2))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(emptyinPowerset, axiom, emptyinPowerset <=> 104.15/104.79 (![A]: in(emptyset,powerset(A)))). 104.15/104.79 tff('97', plain, emptyinPowerset = (![X2]: in(emptyset,powerset(X2))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(powersetI, axiom, powersetI <=> 104.15/104.79 (![A,B]: ((![Xx]: (in(Xx,B) => in(Xx,A))) => in(B,powerset(A))))). 104.15/104.79 tff('98', plain, 104.15/104.79 powersetI = 104.15/104.79 (![X2,X3]: ((![X4]: (in(X4,X3) => in(X4,X2))) => in(X3,powerset(X2)))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(setoftrueEq, axiom, setoftrueEq <=> 104.15/104.79 (![A]: (dsetconstr(A,^[Xx]: $true) = A))). 104.15/104.79 tff('99', plain, setoftrueEq = (![X2]: (dsetconstr(X2,^[V_1]: $true) = X2)), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(setadjoinOr, axiom, setadjoinOr <=> 104.15/104.79 (![Xx,A,Xy]: (in(Xy,setadjoin(Xx,A)) => (in(Xy,A) | (Xy = Xx))))). 104.15/104.79 tff('100', plain, 104.15/104.79 setadjoinOr = 104.15/104.79 (![X2,X3,X4]: (in(X4,setadjoin(X2,X3)) => (in(X4,X3) | (X4 = X2)))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(setadjoinE, axiom, setadjoinE <=> 104.15/104.79 (![Xx,A,Xy]: 104.15/104.79 (in(Xy,setadjoin(Xx,A)) => 104.15/104.79 (![Xphi:$o]: (((Xy = Xx) => Xphi) => ((in(Xy,A) => Xphi) => Xphi)))))). 104.15/104.79 tff('101', plain, 104.15/104.79 setadjoinE = 104.15/104.79 (![X2,X3,X4]: 104.15/104.79 (in(X4,setadjoin(X2,X3)) => 104.15/104.79 (![X5:$o]: (((X4 = X2) => X5) => ((in(X4,X3) => X5) => X5))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(setadjoinIR, axiom, setadjoinIR <=> 104.15/104.79 (![Xx,A,Xy]: (in(Xy,A) => in(Xy,setadjoin(Xx,A))))). 104.15/104.79 tff('102', plain, 104.15/104.79 setadjoinIR = (![X2,X3,X4]: (in(X4,X3) => in(X4,setadjoin(X2,X3)))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(emptyinunitempty, axiom, emptyinunitempty() = 104.15/104.79 in(emptyset,setadjoin(emptyset,emptyset))). 104.15/104.79 tff('103', plain, 104.15/104.79 emptyinunitempty = in(emptyset,setadjoin(emptyset,emptyset)), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(setadjoinIL, axiom, setadjoinIL <=> (![Xx,Xy]: in(Xx,setadjoin(Xx,Xy)))). 104.15/104.79 tff('104', plain, setadjoinIL = (![X2,X3]: in(X2,setadjoin(X2,X3))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(nonemptyI1, axiom, nonemptyI1 <=> 104.15/104.79 (![A]: ((?[Xx]: in(Xx,A)) => nonempty(A)))). 104.15/104.79 tff('105', plain, nonemptyI1 = (![X2]: ((?[X3]: in(X3,X2)) => nonempty(X2))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(nonemptyI, axiom, nonemptyI <=> 104.15/104.79 (![A,Xphi:($i > $o),Xx]: 104.15/104.79 (in(Xx,A) => (Xphi(Xx) => nonempty(dsetconstr(A,^[Xy]: Xphi(Xy))))))). 104.15/104.79 tff('106', plain, 104.15/104.79 nonemptyI = 104.15/104.79 (![X2,X3:($i > $o),X4]: 104.15/104.79 (in(X4,X2) => (X3(X4) => nonempty(dsetconstr(X2,^[V_1]: X3(V_1)))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(nonemptyE1, axiom, nonemptyE1 <=> 104.15/104.79 (![A]: (nonempty(A) => (?[Xx]: in(Xx,A))))). 104.15/104.79 tff('107', plain, nonemptyE1 = (![X2]: (nonempty(X2) => (?[X3]: in(X3,X2)))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(nonempty, axiom, nonempty() = ^[Xx]: (Xx != emptyset)). 104.15/104.79 tff('108', plain, nonempty = (^[V_1]: (V_1 != emptyset)), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(setbeta, axiom, setbeta <=> 104.15/104.79 (![A,Xphi:($i > $o),Xx]: 104.15/104.79 (in(Xx,A) => (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) <=> Xphi(Xx))))). 104.15/104.79 tff('109', plain, 104.15/104.79 setbeta = 104.15/104.79 (![X2,X3:($i > $o),X4]: 104.15/104.79 (in(X4,X2) => (in(X4,dsetconstr(X2,^[V_1]: X3(V_1))) <=> X3(X4)))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(noeltsimpempty, axiom, noeltsimpempty <=> 104.15/104.79 (![A]: ((![Xx]: (~in(Xx,A))) => (A = emptyset)))). 104.15/104.79 tff('110', plain, 104.15/104.79 noeltsimpempty = (![X2]: ((![X3]: (~in(X3,X2))) => (X2 = emptyset))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(emptyI, axiom, emptyI <=> 104.15/104.79 (![A]: ((![Xx]: (~in(Xx,A))) => (A = emptyset)))). 104.15/104.79 tff('111', plain, 104.15/104.79 emptyI = (![X2]: ((![X3]: (~in(X3,X2))) => (X2 = emptyset))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(setext, axiom, setext <=> 104.15/104.79 (![A,B]: 104.15/104.79 ((![Xx]: (in(Xx,A) => in(Xx,B))) => 104.15/104.79 ((![Xx]: (in(Xx,B) => in(Xx,A))) => (A = B))))). 104.15/104.79 tff('112', plain, 104.15/104.79 setext = 104.15/104.79 (![X2,X3]: 104.15/104.79 ((![X4]: (in(X4,X2) => in(X4,X3))) => 104.15/104.79 ((![X5]: (in(X5,X3) => in(X5,X2))) => (X2 = X3)))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(exuE3e, axiom, exuE3e <=> 104.15/104.79 (![Xphi:($i > $o)]: (exu(^[Xx]: Xphi(Xx)) => (?[Xx]: Xphi(Xx))))). 104.15/104.79 tff('113', plain, 104.15/104.79 exuE3e = (![X2:($i > $o)]: (exu(^[V_1]: X2(V_1)) => (?[X3]: X2(X3)))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(notinemptyset, axiom, notinemptyset <=> (![Xx]: (~in(Xx,emptyset)))). 104.15/104.79 tff('114', plain, notinemptyset = (![X2]: (~in(X2,emptyset))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(emptysetimpfalse, axiom, emptysetimpfalse <=> 104.15/104.79 (![Xx]: (in(Xx,emptyset) => $false))). 104.15/104.79 tff('115', plain, emptysetimpfalse = (![X2]: (in(X2,emptyset) => $false)), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(emptysetE, axiom, emptysetE <=> 104.15/104.79 (![Xx]: (in(Xx,emptyset) => (![Xphi:$o]: Xphi)))). 104.15/104.79 tff('116', plain, emptysetE = (![X2]: (in(X2,emptyset) => (![X3:$o]: X3))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(prop2setE, axiom, prop2setE <=> 104.15/104.79 (![Xphi:$o,Xx]: (in(Xx,prop2set(Xphi)) => Xphi))). 104.15/104.79 tff('117', plain, prop2setE = (![X2:$o,X3]: (in(X3,prop2set(X2)) => X2)), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(exuE1, axiom, exuE1 <=> 104.15/104.79 (![Xphi:($i > $o)]: 104.15/104.79 (exu(^[Xx]: Xphi(Xx)) => 104.15/104.79 (?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx)))))). 104.15/104.79 tff('118', plain, 104.15/104.79 exuE1 = 104.15/104.79 (![X2:($i > $o)]: 104.15/104.79 (exu(^[V_1]: X2(V_1)) => 104.15/104.79 (?[X3]: ((![X4]: (X2(X4) => (X3 = X4))) & X2(X3))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(dsetconstrER, axiom, dsetconstrER <=> 104.15/104.79 (![A,Xphi:($i > $o),Xx]: (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) => Xphi(Xx)))). 104.15/104.79 tff('119', plain, 104.15/104.79 dsetconstrER = 104.15/104.79 (![X2,X3:($i > $o),X4]: (in(X4,dsetconstr(X2,^[V_1]: X3(V_1))) => X3(X4))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(dsetconstrEL, axiom, dsetconstrEL <=> 104.15/104.79 (![A,Xphi:($i > $o),Xx]: (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) => in(Xx,A)))). 104.15/104.79 tff('120', plain, 104.15/104.79 dsetconstrEL = 104.15/104.79 (![X2,X3:($i > $o),X4]: 104.15/104.79 (in(X4,dsetconstr(X2,^[V_1]: X3(V_1))) => in(X4,X2))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(dsetconstrI, axiom, dsetconstrI <=> 104.15/104.79 (![A,Xphi:($i > $o),Xx]: 104.15/104.79 (in(Xx,A) => (Xphi(Xx) => in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))))))). 104.15/104.79 tff('121', plain, 104.15/104.79 dsetconstrI = 104.15/104.79 (![X2,X3:($i > $o),X4]: 104.15/104.79 (in(X4,X2) => (X3(X4) => in(X4,dsetconstr(X2,^[V_1]: X3(V_1)))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(descrp, axiom, descrp <=> 104.15/104.79 (![Xphi:($i > $o)]: (exu(^[Xx]: Xphi(Xx)) => Xphi(descr(^[Xx]: Xphi(Xx)))))). 104.15/104.79 tff('122', plain, 104.15/104.79 descrp = 104.15/104.79 (![X2:($i > $o)]: (exu(^[V_1]: X2(V_1)) => X2(descr(^[V_2]: X2(V_2))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(wellorderingAx, axiom, wellorderingAx <=> 104.15/104.79 (![A]: 104.15/104.79 (?[B]: 104.15/104.79 ((![C]: 104.15/104.79 (((?[Xx]: in(Xx,C)) & (![Xx]: (in(Xx,C) => in(Xx,A)))) => 104.15/104.79 (?[D,Xx]: 104.15/104.79 ((![E]: 104.15/104.79 (in(E,B) => (in(Xx,E) | (![Xy]: (in(Xy,E) => in(Xy,D)))))) & 104.15/104.79 (~(?[Xy]: (in(Xy,C) & in(Xy,D)))) & in(Xx,C) & in(D,B))))) & 104.15/104.79 (![C,D]: 104.15/104.79 ((in(D,B) & in(C,B)) => 104.15/104.79 ((![Xx]: (in(Xx,D) => in(Xx,C))) | 104.15/104.79 (![Xx]: (in(Xx,C) => in(Xx,D)))))) & 104.15/104.79 (![Xx,Xy]: 104.15/104.79 ((in(Xy,A) & in(Xx,A)) => 104.15/104.79 ((![C]: (in(C,B) => (in(Xx,C) <=> in(Xy,C)))) => (Xx = Xy)))) & 104.15/104.79 (![C]: (in(C,B) => (![Xx]: (in(Xx,C) => in(Xx,A))))))))). 104.15/104.79 tff('123', plain, 104.15/104.79 wellorderingAx = 104.15/104.79 (![X2]: 104.15/104.79 (?[X3]: 104.15/104.79 ((![X4]: 104.15/104.79 (((?[X5]: in(X5,X4)) & (![X6]: (in(X6,X4) => in(X6,X2)))) => 104.15/104.79 (?[X7,X8]: 104.15/104.79 ((![X9]: 104.15/104.79 (in(X9,X3) => 104.15/104.79 (in(X8,X9) | (![X10]: (in(X10,X9) => in(X10,X7)))))) & 104.15/104.79 (~(?[X11]: (in(X11,X4) & in(X11,X7)))) & in(X8,X4) & 104.15/104.79 in(X7,X3))))) & 104.15/104.79 (![X12,X13]: 104.15/104.79 ((in(X13,X3) & in(X12,X3)) => 104.15/104.79 ((![X14]: (in(X14,X13) => in(X14,X12))) | 104.15/104.79 (![X15]: (in(X15,X12) => in(X15,X13)))))) & 104.15/104.79 (![X16,X17]: 104.15/104.79 ((in(X17,X2) & in(X16,X2)) => 104.15/104.79 ((![X18]: (in(X18,X3) => (in(X16,X18) <=> in(X17,X18)))) => 104.15/104.79 (X16 = X17)))) & 104.15/104.79 (![X19]: (in(X19,X3) => (![X20]: (in(X20,X19) => in(X20,X2)))))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(foundationAx, axiom, foundationAx <=> 104.15/104.79 (![A]: 104.15/104.79 ((?[Xx]: in(Xx,A)) => 104.15/104.79 (?[B]: ((~(?[Xx]: (in(Xx,A) & in(Xx,B)))) & in(B,A)))))). 104.15/104.79 tff('124', plain, 104.15/104.79 foundationAx = 104.15/104.79 (![X2]: 104.15/104.79 ((?[X3]: in(X3,X2)) => 104.15/104.79 (?[X4]: ((~(?[X5]: (in(X5,X2) & in(X5,X4)))) & in(X4,X2))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(replAx, axiom, replAx <=> 104.15/104.79 (![Xphi:(($i * $i) > $o),A]: 104.15/104.79 ((![Xx]: (in(Xx,A) => exu(^[Xy]: Xphi(Xx,Xy)))) => 104.15/104.79 (?[B]: (![Xx]: (in(Xx,B) <=> (?[Xy]: (Xphi(Xy,Xx) & in(Xy,A))))))))). 104.15/104.79 tff('125', plain, 104.15/104.79 replAx = 104.15/104.79 (![X2:(($i * $i) > $o),X3]: 104.15/104.79 ((![X4]: (in(X4,X3) => exu(^[V_1]: X2(X4,V_1)))) => 104.15/104.79 (?[X5]: (![X6]: (in(X6,X5) <=> (?[X7]: (X2(X7,X6) & in(X7,X3)))))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(omegaIndAx, axiom, omegaIndAx <=> 104.15/104.79 (![A]: 104.15/104.79 (((![Xx]: ((in(Xx,A) & in(Xx,omega)) => in(setadjoin(Xx,Xx),A))) & 104.15/104.79 in(emptyset,A)) => 104.15/104.79 (![Xx]: (in(Xx,omega) => in(Xx,A)))))). 104.15/104.79 tff('126', plain, 104.15/104.79 omegaIndAx = 104.15/104.79 (![X2]: 104.15/104.79 (((![X3]: ((in(X3,X2) & in(X3,omega)) => in(setadjoin(X3,X3),X2))) & 104.15/104.79 in(emptyset,X2)) => 104.15/104.79 (![X4]: (in(X4,omega) => in(X4,X2))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(omegaSAx, axiom, omegaSAx <=> 104.15/104.79 (![Xx]: (in(Xx,omega) => in(setadjoin(Xx,Xx),omega)))). 104.15/104.79 tff('127', plain, 104.15/104.79 omegaSAx = (![X2]: (in(X2,omega) => in(setadjoin(X2,X2),omega))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(omega0Ax, axiom, omega0Ax() = in(emptyset,omega)). 104.15/104.79 tff('128', plain, omega0Ax = in(emptyset,omega), define([status(thm)])). 104.15/104.79 tff(setunionAx, axiom, setunionAx <=> 104.15/104.79 (![A,Xx]: (in(Xx,setunion(A)) <=> (?[B]: (in(B,A) & in(Xx,B)))))). 104.15/104.79 tff('129', plain, 104.15/104.79 setunionAx = 104.15/104.79 (![X2,X3]: (in(X3,setunion(X2)) <=> (?[X4]: (in(X4,X2) & in(X3,X4))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(powersetAx, axiom, powersetAx <=> 104.15/104.79 (![A,B]: (in(B,powerset(A)) <=> (![Xx]: (in(Xx,B) => in(Xx,A)))))). 104.15/104.79 tff('130', plain, 104.15/104.79 powersetAx = 104.15/104.79 (![X2,X3]: (in(X3,powerset(X2)) <=> (![X4]: (in(X4,X3) => in(X4,X2))))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(setadjoinAx, axiom, setadjoinAx <=> 104.15/104.79 (![Xx,A,Xy]: (in(Xy,setadjoin(Xx,A)) <=> (in(Xy,A) | (Xy = Xx))))). 104.15/104.79 tff('131', plain, 104.15/104.79 setadjoinAx = 104.15/104.79 (![X2,X3,X4]: (in(X4,setadjoin(X2,X3)) <=> (in(X4,X3) | (X4 = X2)))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(emptysetAx, axiom, emptysetAx <=> (![Xx]: (~in(Xx,emptyset)))). 104.15/104.79 tff('132', plain, emptysetAx = (![X2]: (~in(X2,emptyset))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(setextAx, axiom, setextAx <=> 104.15/104.79 (![A,B]: ((![Xx]: (in(Xx,A) <=> in(Xx,B))) => (A = B)))). 104.15/104.79 tff('133', plain, 104.15/104.79 setextAx = (![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(exu, axiom, exu() = 104.15/104.79 ^[Xphi:($i > $o)]: (?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx)))). 104.15/104.79 tff('134', plain, 104.15/104.79 exu = 104.15/104.79 (^[V_1:($i > $o)]: (?[X2]: ((![X3]: (V_1(X3) => (X2 = X3))) & V_1(X2)))), 104.15/104.79 define([status(thm)])). 104.15/104.79 tff(setukpairIL, conjecture, 104.15/104.79 (setextAx => 104.15/104.79 (emptysetAx => 104.15/104.79 (setadjoinAx => 104.15/104.79 (powersetAx => 104.15/104.79 (setunionAx => 104.15/104.79 (omega0Ax => 104.15/104.79 (omegaSAx => 104.15/104.79 (omegaIndAx => 104.15/104.79 (replAx => 104.15/104.79 (foundationAx => 104.15/104.79 (wellorderingAx => 104.15/104.79 (descrp => 104.15/104.79 (dsetconstrI => 104.15/104.79 (dsetconstrEL => 104.15/104.79 (dsetconstrER => 104.15/104.79 (exuE1 => 104.15/104.79 (prop2setE => 104.15/104.79 (emptysetE => 104.15/104.79 (emptysetimpfalse => 104.15/104.79 (notinemptyset => 104.15/104.79 (exuE3e => 104.15/104.79 (setext => 104.15/104.79 (emptyI => 104.15/104.79 (noeltsimpempty => 104.15/104.79 (setbeta => 104.15/104.79 (nonemptyE1 => 104.15/104.79 (nonemptyI => 104.15/104.79 (nonemptyI1 => 104.15/104.79 (setadjoinIL => 104.15/104.79 (emptyinunitempty => 104.15/104.79 (setadjoinIR => 104.15/104.79 (setadjoinE => 104.15/104.79 (setadjoinOr => 104.15/104.79 (setoftrueEq => 104.15/104.79 (powersetI => 104.15/104.79 (emptyinPowerset => 104.15/104.79 (emptyInPowerset => 104.15/104.79 (powersetE => 104.15/104.79 (setunionI => 104.15/104.79 (setunionE => 104.15/104.79 (subPowSU => 104.15/104.79 (exuE2 => 104.15/104.79 (nonemptyImpWitness => 104.15/104.79 (uniqinunit => 104.15/104.79 (notinsingleton => 104.15/104.79 (eqinunit => 104.15/104.79 (singletonsswitch => 104.15/104.79 (upairsetE => 104.15/104.79 (upairsetIL => 104.15/104.79 (upairsetIR => 104.15/104.79 (emptyE1 => 104.15/104.79 (vacuousDall => 104.15/104.79 (quantDeMorgan1 => 104.15/104.79 (quantDeMorgan2 => 104.15/104.79 (quantDeMorgan3 => 104.15/104.79 (quantDeMorgan4 => 104.15/104.79 (prop2setI => 104.15/104.79 (prop2set2propI => 104.15/104.79 (notdexE => 104.15/104.79 (notdallE => 104.15/104.79 (exuI1 => 104.15/104.79 (exuI3 => 104.15/104.79 (exuI2 => 104.15/104.79 (inCongP => 104.15/104.79 (in__Cong => 104.15/104.79 (exuE3u => 104.15/104.79 ( 104.15/104.79 exu__Cong => 104.15/104.79 ( 104.15/104.79 emptyset__Cong => 104.15/104.79 ( 104.15/104.79 setadjoin__Cong => 104.15/104.79 ( 104.15/104.79 powerset__Cong => 104.15/104.79 ( 104.15/104.79 setunion__Cong => 104.15/104.79 ( 104.15/104.79 omega__Cong => 104.15/104.79 ( 104.15/104.79 exuEu => 104.15/104.79 ( 104.15/104.79 descr__Cong => 104.15/104.79 ( 104.15/104.79 dsetconstr__Cong => 104.15/104.79 ( 104.15/104.79 subsetI1 => 104.15/104.79 ( 104.15/104.79 eqimpsubset2 => 104.15/104.79 ( 104.15/104.79 eqimpsubset1 => 104.15/104.79 ( 104.15/104.79 subsetI2 => 104.15/104.79 ( 104.15/104.79 emptysetsubset => 104.15/104.79 ( 104.15/104.79 subsetE => 104.15/104.79 ( 104.15/104.79 subsetE2 => 104.15/104.79 ( 104.15/104.79 notsubsetI => 104.15/104.79 ( 104.15/104.79 notequalI1 => 104.15/104.79 ( 104.15/104.79 notequalI2 => 104.15/104.79 ( 104.15/104.79 subsetRefl => 104.15/104.79 ( 104.15/104.79 subsetTrans => 104.15/104.79 ( 104.15/104.79 setadjoinSub => 104.15/104.79 ( 104.15/104.79 setadjoinSub2 => 104.15/104.79 ( 104.15/104.79 subset2powerset => 104.15/104.79 ( 104.15/104.79 setextsub => 104.15/104.79 ( 104.15/104.79 subsetemptysetimpeq => 104.15/104.79 ( 104.15/104.79 powersetI1 => 104.15/104.79 ( 104.15/104.79 powersetE1 => 104.15/104.79 ( 104.15/104.79 inPowerset => 104.15/104.79 ( 104.15/104.79 powersetsubset => 104.15/104.79 ( 104.15/104.79 sepInPowerset => 104.15/104.79 ( 104.15/104.79 sepSubset => 104.15/104.79 ( 104.15/104.79 binunionIL => 104.15/104.79 ( 104.15/104.79 upairset2IR => 104.15/104.79 ( 104.15/104.79 binunionIR => 104.15/104.79 ( 104.15/104.79 binunionEcases => 104.15/104.79 ( 104.15/104.79 binunionE => 104.15/104.79 ( 104.15/104.79 binunionLsub => 104.15/104.79 ( 104.15/104.79 binunionRsub => 104.15/104.79 ( 104.15/104.79 binintersectI => 104.15/104.79 ( 104.15/104.79 binintersectSubset5 => 104.15/104.79 ( 104.15/104.79 binintersectEL => 104.15/104.79 ( 104.15/104.79 binintersectLsub => 104.15/104.79 ( 104.15/104.79 binintersectSubset2 => 104.15/104.79 ( 104.15/104.79 binintersectSubset3 => 104.15/104.79 ( 104.15/104.79 binintersectER => 104.15/104.79 ( 104.15/104.79 disjointsetsI1 => 104.15/104.79 ( 104.15/104.79 binintersectRsub => 104.15/104.79 ( 104.15/104.79 binintersectSubset4 => 104.15/104.79 ( 104.15/104.79 binintersectSubset1 => 104.15/104.79 ( 104.15/104.79 bs114d => 104.15/104.79 ( 104.15/104.79 setminusI => 104.15/104.79 ( 104.15/104.79 setminusEL => 104.15/104.79 ( 104.15/104.79 setminusER => 104.15/104.79 ( 104.15/104.79 setminusSubset2 => 104.15/104.79 ( 104.15/104.79 setminusERneg => 104.15/104.79 ( 104.15/104.79 setminusELneg => 104.15/104.79 ( 104.15/104.79 setminusILneg => 104.15/104.79 ( 104.15/104.79 setminusIRneg => 104.15/104.79 ( 104.15/104.79 setminusLsub => 104.15/104.79 ( 104.15/104.79 setminusSubset1 => 104.15/104.79 ( 104.15/104.79 symdiffE => 104.15/104.79 ( 104.15/104.79 symdiffI1 => 104.15/104.79 ( 104.15/104.79 symdiffI2 => 104.15/104.79 ( 104.15/104.79 symdiffIneg1 => 104.15/104.79 ( 104.15/104.79 symdiffIneg2 => 104.15/104.79 ( 104.15/104.79 secondinupair => 104.15/104.79 ( 104.15/104.79 ![Xx,Xy]: 104.15/104.79 in( 104.15/104.79 Xx, 104.15/104.79 setunion( 104.15/104.79 setadjoin( 104.15/104.79 setadjoin( 104.15/104.79 Xx, 104.15/104.79 emptyset), 104.15/104.79 setadjoin( 104.15/104.79 setadjoin( 104.15/104.79 Xx, 104.15/104.79 setadjoin( 104.15/104.79 Xy, 104.15/104.79 emptyset)), 104.15/104.79 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 104.15/104.79 tff(zf_stmt_0, conjecture, 104.15/104.79 ((![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))) => 104.15/104.79 ((![X5]: (~in(X5,emptyset))) => 104.15/104.79 ((![X6,X7,X8]: (in(X8,setadjoin(X6,X7)) <=> ((X8 = X6) | in(X8,X7)))) => 104.15/104.79 ((![X9,X10]: 104.15/104.79 (in(X10,powerset(X9)) <=> (![X11]: (in(X11,X10) => in(X11,X9))))) => 104.15/104.79 ((![X12,X13]: 104.15/104.79 (in(X13,setunion(X12)) <=> (?[X14]: (in(X13,X14) & in(X14,X12))))) => 104.15/104.79 (in(emptyset,omega) => 104.15/104.79 ((![X15]: (in(X15,omega) => in(setadjoin(X15,X15),omega))) => 104.15/104.79 ((![X16]: 104.15/104.79 ((in(emptyset,X16) & 104.15/104.79 (![X17]: 104.15/104.79 ((in(X17,omega) & in(X17,X16)) => 104.15/104.79 in(setadjoin(X17,X17),X16)))) => 104.15/104.79 (![X18]: (in(X18,omega) => in(X18,X16))))) => 104.15/104.79 ((![X19:(($i * $i) > $o),X20]: 104.15/104.79 ((![X21]: 104.15/104.79 (in(X21,X20) => 104.15/104.79 (?[X22]: 104.15/104.79 (X19(X21,X22) & (![X23]: (X19(X21,X23) => (X22 = X23))))))) => 104.15/104.79 (?[X24]: 104.15/104.79 (![X25]: 104.15/104.79 (in(X25,X24) <=> (?[X26]: (in(X26,X20) & X19(X26,X25)))))))) => 104.15/104.79 ((![X27]: 104.15/104.79 ((?[X28]: in(X28,X27)) => 104.15/104.79 (?[X29]: 104.15/104.79 (in(X29,X27) & (~(?[X30]: (in(X30,X29) & in(X30,X27)))))))) => 104.15/104.79 ((![X31]: 104.15/104.79 (?[X32]: 104.15/104.79 ((![X48]: 104.15/104.79 (in(X48,X32) => (![X49]: (in(X49,X48) => in(X49,X31))))) & 104.15/104.79 (![X45,X46]: 104.15/104.79 ((in(X45,X31) & in(X46,X31)) => 104.15/104.79 ((![X47]: 104.15/104.79 (in(X47,X32) => (in(X45,X47) <=> in(X46,X47)))) => 104.15/104.79 (X45 = X46)))) & 104.15/104.79 (![X41,X42]: 104.15/104.79 ((in(X41,X32) & in(X42,X32)) => 104.15/104.79 ((![X44]: (in(X44,X41) => in(X44,X42))) | 104.15/104.79 (![X43]: (in(X43,X42) => in(X43,X41)))))) & 104.15/104.79 (![X33]: 104.15/104.79 (((![X35]: (in(X35,X33) => in(X35,X31))) & 104.15/104.79 (?[X34]: in(X34,X33))) => 104.15/104.79 (?[X36,X37]: 104.15/104.79 (in(X36,X32) & in(X37,X33) & 104.15/104.79 (~(?[X40]: (in(X40,X36) & in(X40,X33)))) & 104.15/104.79 (![X38]: 104.15/104.79 (in(X38,X32) => 104.15/104.79 ((![X39]: (in(X39,X38) => in(X39,X36))) | 104.15/104.79 in(X37,X38))))))))))) => 104.15/104.79 ((![X50:($i > $o)]: 104.15/104.79 ((?[X51]: (X50(X51) & (![X52]: (X50(X52) => (X51 = X52))))) => 104.15/104.79 X50(descr('#ll_0'(X50))))) => 104.15/104.79 ((![X53,X54:($i > $o),X55]: 104.15/104.79 (in(X55,X53) => 104.15/104.79 (X54(X55) => in(X55,dsetconstr(X53,'#ll_0'(X54)))))) => 104.15/104.79 ((![X56,X57:($i > $o),X58]: 104.15/104.79 (in(X58,dsetconstr(X56,'#ll_0'(X57))) => in(X58,X56))) => 104.15/104.79 ((![X59,X60:($i > $o),X61]: 104.15/104.79 (in(X61,dsetconstr(X59,'#ll_0'(X60))) => X60(X61))) => 104.15/104.79 ((![X62:($i > $o)]: 104.15/104.79 ((?[X63]: 104.15/104.79 (X62(X63) & (![X64]: (X62(X64) => (X63 = X64))))) => 104.15/104.79 (?[X65]: 104.15/104.79 (X62(X65) & (![X66]: (X62(X66) => (X65 = X66))))))) => 104.15/104.79 ((![X67:$o,X68]: (in(X68,prop2set(X67)) => X67)) => 104.15/104.79 ((![X69]: (in(X69,emptyset) => (![X70:$o]: X70))) => 104.15/104.79 ((![X71]: (in(X71,emptyset) => $false)) => 104.15/104.79 ((![X72]: (~in(X72,emptyset))) => 104.15/104.79 ((![X73:($i > $o)]: 104.15/104.79 ((?[X74]: 104.15/104.79 (X73(X74) & (![X75]: (X73(X75) => (X74 = X75))))) => 104.15/104.79 (?[X76]: X73(X76)))) => 104.15/104.79 ((![X77,X78]: 104.15/104.79 ((![X79]: (in(X79,X77) => in(X79,X78))) => 104.15/104.79 ((![X80]: (in(X80,X78) => in(X80,X77))) => 104.15/104.79 (X77 = X78)))) => 104.15/104.79 ((![X81]: 104.15/104.79 ((![X82]: (~in(X82,X81))) => (X81 = emptyset))) => 104.15/104.79 ((![X83]: 104.15/104.79 ((![X84]: (~in(X84,X83))) => (X83 = emptyset))) => 104.15/104.79 ((![X85,X86:($i > $o),X87]: 104.15/104.79 (in(X87,X85) => 104.15/104.79 (in(X87,dsetconstr(X85,'#ll_0'(X86))) <=> 104.15/104.79 X86(X87)))) => 104.15/104.79 ((![X88]: 104.15/104.79 ((X88 != emptyset) => (?[X89]: in(X89,X88)))) => 104.15/104.79 ((![X90,X91:($i > $o),X92]: 104.15/104.79 (in(X92,X90) => 104.15/104.79 (X91(X92) => 104.15/104.79 (dsetconstr(X90,'#ll_0'(X91)) != emptyset)))) => 104.15/104.79 ((![X93]: 104.15/104.79 ((?[X94]: in(X94,X93)) => (X93 != emptyset))) => 104.15/104.79 ((![X95,X96]: in(X95,setadjoin(X95,X96))) => 104.15/104.79 (in(emptyset,setadjoin(emptyset,emptyset)) => 104.15/104.79 ((![X97,X98,X99]: 104.15/104.79 (in(X99,X98) => 104.15/104.79 in(X99,setadjoin(X97,X98)))) => 104.15/104.79 ((![X100,X101,X102]: 104.15/104.79 (in(X102,setadjoin(X100,X101)) => 104.15/104.79 (![X103:$o]: 104.15/104.79 (((X102 = X100) => X103) => 104.15/104.79 ((in(X102,X101) => X103) => X103))))) => 104.15/104.79 ((![X104,X105,X106]: 104.15/104.79 (in(X106,setadjoin(X104,X105)) => 104.15/104.79 ((X106 = X104) | in(X106,X105)))) => 104.15/104.79 ((![X107]: 104.15/104.79 (dsetconstr(X107,'#ll_1') = X107)) => 104.15/104.79 ((![X108,X109]: 104.15/104.79 ((![X110]: 104.15/104.79 (in(X110,X109) => in(X110,X108))) => 104.15/104.79 in(X109,powerset(X108)))) => 104.15/104.79 ((![X111]: in(emptyset,powerset(X111))) => 104.15/104.79 ((![X112]: in(emptyset,powerset(X112))) => 104.15/104.79 ((![X113,X114,X115]: 104.15/104.79 (in(X114,powerset(X113)) => 104.15/104.79 (in(X115,X114) => in(X115,X113)))) => 104.15/104.79 ((![X116,X117,X118]: 104.15/104.79 (in(X117,X118) => 104.15/104.79 (in(X118,X116) => 104.15/104.79 in(X117,setunion(X116))))) => 104.15/104.79 ((![X119,X120]: 104.15/104.79 (in(X120,setunion(X119)) => 104.15/104.79 (![X121:$o]: 104.15/104.79 ((![X122]: 104.15/104.79 (in(X120,X122) => 104.15/104.79 (in(X122,X119) => X121))) => 104.15/104.79 X121)))) => 104.15/104.79 ((![X123,X124]: 104.15/104.79 (in(X124,X123) => 104.15/104.79 in(X124, 104.15/104.79 powerset(setunion(X123))))) => 104.15/104.79 ((![X125:($i > $o)]: 104.15/104.79 ((?[X126]: 104.15/104.79 (X125(X126) & 104.15/104.79 (![X127]: 104.15/104.79 (X125(X127) => 104.15/104.79 (X126 = X127))))) => 104.15/104.79 (?[X128]: 104.15/104.79 (![X129]: 104.15/104.79 (X125(X129) <=> 104.15/104.79 (X129 = X128)))))) => 104.15/104.79 ((![X130]: 104.15/104.79 ((X130 != emptyset) => 104.15/104.79 (?[X131]: in(X131,X130)))) => 104.15/104.79 ((![X132,X133]: 104.15/104.79 (in(X132, 104.15/104.79 setadjoin(X133,emptyset)) => 104.15/104.79 (X132 = X133))) => 104.15/104.79 ((![X134,X135]: 104.15/104.79 ((X134 != X135) => 104.15/104.79 (~ 104.15/104.79 in(X135, 104.15/104.79 setadjoin(X134, 104.15/104.79 emptyset))))) => 104.15/104.79 ((![X136,X137]: 104.15/104.79 ((X136 = X137) => 104.15/104.79 in(X136, 104.15/104.79 setadjoin(X137, 104.15/104.79 emptyset)))) => 104.15/104.79 ((![X138,X139]: 104.15/104.79 (in(X138, 104.15/104.79 setadjoin(X139, 104.15/104.79 emptyset)) => 104.15/104.79 in(X139, 104.15/104.79 setadjoin(X138, 104.15/104.79 emptyset)))) => 104.15/104.79 ((![X140,X141,X142]: 104.15/104.79 (in(X142, 104.15/104.79 setadjoin(X140, 104.15/104.79 setadjoin( 104.15/104.79 X141, 104.15/104.79 emptyset))) => 104.15/104.79 ((X142 = X140) | 104.15/104.79 (X142 = X141)))) => 104.15/104.79 ((![X143,X144]: 104.15/104.79 in(X143, 104.15/104.79 setadjoin(X143, 104.15/104.79 setadjoin( 104.15/104.79 X144, 104.15/104.79 emptyset)))) => 104.15/104.79 ((![X145,X146]: 104.15/104.79 in(X146, 104.15/104.79 setadjoin(X145, 104.15/104.79 setadjoin( 104.15/104.79 X146, 104.15/104.79 emptyset)))) => 104.15/104.79 ((![X147,X148:($i > $o)]: 104.15/104.79 ((?[X149]: 104.15/104.79 (in(X149,X147) & 104.15/104.79 X148(X149))) => 104.15/104.79 ((dsetconstr( 104.15/104.79 X147,'#ll_0'(X148)) = 104.15/104.79 emptyset) => 104.15/104.79 $false))) => 104.15/104.79 ((![X150:($i > $o),X151]: 104.15/104.79 (in(X151,emptyset) => 104.15/104.79 X150(X151))) => 104.15/104.79 ((![X152,X153:($i > $o)]: 104.15/104.79 ((~ 104.15/104.79 (![X154]: 104.15/104.79 (in(X154,X152) => 104.15/104.79 X153(X154)))) => 104.15/104.79 (?[X155]: 104.15/104.79 (in(X155,X152) & 104.15/104.79 (~X153(X155)))))) => 104.15/104.79 ((![X156, 104.15/104.79 X157:($i > $o)]: 104.15/104.79 ((![X158]: 104.15/104.79 (in(X158,X156) => 104.15/104.79 (~X157(X158)))) => 104.15/104.79 (~ 104.15/104.79 (?[X159]: 104.15/104.79 (in( 104.15/104.79 X159,X156) & 104.15/104.79 X157(X159)))))) => 104.15/104.79 ((![X160, 104.15/104.79 X161:($i > $o)]: 104.15/104.79 ((~ 104.15/104.79 (?[X162]: 104.15/104.79 (in( 104.15/104.79 X162,X160) & 104.15/104.79 X161(X162)))) => 104.15/104.79 (![X163]: 104.15/104.79 (in(X163,X160) => 104.15/104.79 (~X161(X163)))))) => 104.15/104.79 ((![X164, 104.15/104.79 X165:($i > $o)]: 104.15/104.79 ((?[X166]: 104.15/104.79 (in( 104.15/104.79 X166,X164) & 104.15/104.79 (~ 104.15/104.79 X165( 104.15/104.79 X166)))) => 104.15/104.79 (~ 104.15/104.79 (![X167]: 104.15/104.79 (in( 104.15/104.79 X167,X164) => 104.15/104.79 X165( 104.15/104.79 X167)))))) => 104.15/104.79 ((![X168:$o]: 104.15/104.79 (X168 => 104.15/104.79 in(emptyset, 104.15/104.79 prop2set( 104.15/104.79 X168)))) => 104.15/104.79 ((![X169:$o]: 104.15/104.79 (X169 => 104.15/104.79 set2prop( 104.15/104.79 prop2set( 104.15/104.79 X169)))) => 104.15/104.79 ((![X170, 104.15/104.79 X171:( 104.15/104.79 $i > $o)]: 104.15/104.79 ((~ 104.15/104.79 (?[X172]: 104.15/104.79 (in( 104.15/104.79 X172,X170) & 104.15/104.79 X171( 104.15/104.79 X172)))) => 104.15/104.79 (![X173]: 104.15/104.79 ( 104.15/104.79 in( 104.15/104.79 X173,X170) => 104.15/104.79 ( 104.15/104.79 ~ 104.15/104.79 X171( 104.15/104.79 X173)))))) => 104.15/104.79 ((![X174, 104.15/104.79 X175:( 104.15/104.79 $i > $o)]: 104.15/104.79 ((~ 104.15/104.79 ( 104.15/104.79 ![X176]: 104.15/104.79 (in( 104.15/104.79 X176,X174) => 104.15/104.79 X175( 104.15/104.79 X176)))) => 104.15/104.79 (?[X177]: 104.15/104.79 (in( 104.15/104.79 X177,X174) & 104.15/104.79 (~ 104.15/104.79 X175( 104.15/104.79 X177)))))) => 104.15/104.79 ((![X178:( 104.15/104.79 $i > $o)]: 104.15/104.79 ((?[X179]: 104.15/104.79 (X178( 104.15/104.79 X179) & 104.15/104.79 (![X180]: 104.15/104.79 (X178( 104.15/104.79 X180) => 104.15/104.79 (X179 = 104.15/104.79 X180))))) => 104.15/104.79 (?[X181]: 104.15/104.79 (X178( 104.15/104.79 X181) & 104.15/104.79 (![X182]: 104.15/104.79 (X178( 104.15/104.79 X182) => 104.15/104.79 (X181 = 104.15/104.79 X182))))))) => 104.15/104.79 ((![X183:( 104.15/104.79 $i > $o)]: 104.15/104.79 (( 104.15/104.79 ?[X184]: 104.15/104.79 X183( 104.15/104.79 X184)) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X185, 104.15/104.79 X186]: 104.15/104.79 (X183( 104.15/104.79 X185) => 104.15/104.79 (X183( 104.15/104.79 X186) => 104.15/104.79 (X185 = 104.15/104.79 X186)))) => 104.15/104.79 ( 104.15/104.79 ?[X187]: 104.15/104.79 (X183( 104.15/104.79 X187) & 104.15/104.79 (![X188]: 104.15/104.79 (X183( 104.15/104.79 X188) => 104.15/104.79 (X187 = 104.15/104.79 X188)))))))) => 104.15/104.79 ((![X189:( 104.15/104.79 $i > $o)]: 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ?[X190]: 104.15/104.79 (![X191]: 104.15/104.79 (X189( 104.15/104.79 X191) <=> 104.15/104.79 (X191 = 104.15/104.79 X190)))) => 104.15/104.79 ( 104.15/104.79 ?[X192]: 104.15/104.79 (X189( 104.15/104.79 X192) & 104.15/104.79 (![X193]: 104.15/104.79 (X189( 104.15/104.79 X193) => 104.15/104.79 (X192 = 104.15/104.79 X193))))))) => 104.15/104.79 ((![X194, 104.15/104.79 X195]: 104.15/104.79 (( 104.15/104.79 X194 = 104.15/104.79 X195) => 104.15/104.79 (![X196, 104.15/104.79 X197]: 104.15/104.79 (( 104.15/104.79 X196 = 104.15/104.79 X197) => 104.15/104.79 (in( 104.15/104.79 X196,X194) => 104.15/104.79 in( 104.15/104.79 X197,X195)))))) => 104.15/104.79 ((![X198, 104.15/104.79 X199]: 104.15/104.79 (( 104.15/104.79 X198 = 104.15/104.79 X199) => 104.15/104.79 (![X200, 104.15/104.79 X201]: 104.15/104.79 (( 104.15/104.79 X200 = 104.15/104.79 X201) => 104.15/104.79 (in( 104.15/104.79 X200,X198) <=> 104.15/104.79 in( 104.15/104.79 X201,X199)))))) => 104.15/104.79 (( 104.15/104.79 ![X202:( 104.15/104.79 $i > $o)]: 104.15/104.79 (( 104.15/104.79 ?[X203]: 104.15/104.79 (X202( 104.15/104.79 X203) & 104.15/104.79 (![X204]: 104.15/104.79 (X202( 104.15/104.79 X204) => 104.15/104.79 (X203 = 104.15/104.79 X204))))) => 104.15/104.79 (![X205, 104.15/104.79 X206]: 104.15/104.79 (X202( 104.15/104.79 X205) => 104.15/104.79 (X202( 104.15/104.79 X206) => 104.15/104.79 (X205 = 104.15/104.79 X206)))))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X207:( 104.15/104.79 $i > $o), 104.15/104.79 X208:( 104.15/104.79 $i > $o)]: 104.15/104.79 (( 104.15/104.79 ![X209, 104.15/104.79 X210]: 104.15/104.79 (( 104.15/104.79 X209 = 104.15/104.79 X210) => 104.15/104.79 (X207( 104.15/104.79 X209) <=> 104.15/104.79 X208( 104.15/104.79 X210)))) => 104.15/104.79 (( 104.15/104.79 ?[X211]: 104.15/104.79 (X207( 104.15/104.79 X211) & 104.15/104.79 (![X212]: 104.15/104.79 (X207( 104.15/104.79 X212) => 104.15/104.79 (X211 = 104.15/104.79 X212))))) <=> 104.15/104.79 (?[X213]: 104.15/104.79 (X208( 104.15/104.79 X213) & 104.15/104.79 (![X214]: 104.15/104.79 (X208( 104.15/104.79 X214) => 104.15/104.79 (X213 = 104.15/104.79 X214)))))))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 emptyset = 104.15/104.79 emptyset) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X215, 104.15/104.79 X216]: 104.15/104.79 (( 104.15/104.79 X215 = 104.15/104.79 X216) => 104.15/104.79 (![X217, 104.15/104.79 X218]: 104.15/104.79 (( 104.15/104.79 X217 = 104.15/104.79 X218) => 104.15/104.79 (setadjoin( 104.15/104.79 X215,X217) = 104.15/104.79 setadjoin( 104.15/104.79 X216,X218)))))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X219, 104.15/104.79 X220]: 104.15/104.79 (( 104.15/104.79 X219 = 104.15/104.79 X220) => 104.15/104.79 (powerset( 104.15/104.79 X219) = 104.15/104.79 powerset( 104.15/104.79 X220)))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X221, 104.15/104.79 X222]: 104.15/104.79 (( 104.15/104.79 X221 = 104.15/104.79 X222) => 104.15/104.79 (setunion( 104.15/104.79 X221) = 104.15/104.79 setunion( 104.15/104.79 X222)))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 omega = 104.15/104.79 omega) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X223:( 104.15/104.79 $i > $o)]: 104.15/104.79 (( 104.15/104.79 ?[X224]: 104.15/104.79 (X223( 104.15/104.79 X224) & 104.15/104.79 (![X225]: 104.15/104.79 (X223( 104.15/104.79 X225) => 104.15/104.79 (X224 = 104.15/104.79 X225))))) => 104.15/104.79 (![X226, 104.15/104.79 X227]: 104.15/104.79 (X223( 104.15/104.79 X226) => 104.15/104.79 (X223( 104.15/104.79 X227) => 104.15/104.79 (X226 = 104.15/104.79 X227)))))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X228:( 104.15/104.79 $i > $o), 104.15/104.79 X229:( 104.15/104.79 $i > $o)]: 104.15/104.79 (( 104.15/104.79 ![X230, 104.15/104.79 X231]: 104.15/104.79 (( 104.15/104.79 X230 = 104.15/104.79 X231) => 104.15/104.79 (X228( 104.15/104.79 X230) <=> 104.15/104.79 X229( 104.15/104.79 X231)))) => 104.15/104.79 (( 104.15/104.79 ?[X232]: 104.15/104.79 (X228( 104.15/104.79 X232) & 104.15/104.79 (![X233]: 104.15/104.79 (X228( 104.15/104.79 X233) => 104.15/104.79 (X232 = 104.15/104.79 X233))))) => 104.15/104.79 (( 104.15/104.79 ?[X234]: 104.15/104.79 (X229( 104.15/104.79 X234) & 104.15/104.79 (![X235]: 104.15/104.79 (X229( 104.15/104.79 X235) => 104.15/104.79 (X234 = 104.15/104.79 X235))))) => 104.15/104.79 (descr( 104.15/104.79 '#ll_0'( 104.15/104.79 X228)) = 104.15/104.79 descr( 104.15/104.79 '#ll_0'( 104.15/104.79 X229))))))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X236, 104.15/104.79 X237]: 104.15/104.79 (( 104.15/104.79 X236 = 104.15/104.79 X237) => 104.15/104.79 (![X238:( 104.15/104.79 $i > $o), 104.15/104.79 X239:( 104.15/104.79 $i > $o)]: 104.15/104.79 (( 104.15/104.79 ![X240]: 104.15/104.79 (in( 104.15/104.79 X240,X236) => 104.15/104.79 (![X241]: 104.15/104.79 (in( 104.15/104.79 X241,X237) => 104.15/104.79 (( 104.15/104.79 X240 = 104.15/104.79 X241) => 104.15/104.79 (X238( 104.15/104.79 X240) <=> 104.15/104.79 X239( 104.15/104.79 X241))))))) => 104.15/104.79 (dsetconstr( 104.15/104.79 X236, 104.15/104.79 '#ll_0'( 104.15/104.79 X238)) = 104.15/104.79 dsetconstr( 104.15/104.79 X237, 104.15/104.79 '#ll_0'( 104.15/104.79 X239))))))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X242, 104.15/104.79 X243]: 104.15/104.79 (( 104.15/104.79 ![X244]: 104.15/104.79 (in( 104.15/104.79 X244,X242) => 104.15/104.79 in( 104.15/104.79 X244,X243))) => 104.15/104.79 subset( 104.15/104.79 X242,X243))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X245, 104.15/104.79 X246]: 104.15/104.79 (( 104.15/104.79 X245 = 104.15/104.79 X246) => 104.15/104.79 subset( 104.15/104.79 X246,X245))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X247, 104.15/104.79 X248]: 104.15/104.79 (( 104.15/104.79 X247 = 104.15/104.79 X248) => 104.15/104.79 subset( 104.15/104.79 X247,X248))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X249, 104.15/104.79 X250]: 104.15/104.79 (( 104.15/104.79 ![X251]: 104.15/104.79 (in( 104.15/104.79 X251,X249) => 104.15/104.79 in( 104.15/104.79 X251,X250))) => 104.15/104.79 subset( 104.15/104.79 X249,X250))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X252]: 104.15/104.79 subset( 104.15/104.79 emptyset, 104.15/104.79 X252)) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X253, 104.15/104.79 X254,X255]: 104.15/104.79 (subset( 104.15/104.79 X253,X254) => 104.15/104.79 (in( 104.15/104.79 X255,X253) => 104.15/104.79 in( 104.15/104.79 X255,X254)))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X256, 104.15/104.79 X257,X258]: 104.15/104.79 (subset( 104.15/104.79 X256,X257) => 104.15/104.79 (( 104.15/104.79 ~ 104.15/104.79 in( 104.15/104.79 X258,X257)) => 104.15/104.79 (~ 104.15/104.79 in( 104.15/104.79 X258,X256))))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X259, 104.15/104.79 X260,X261]: 104.15/104.79 (in( 104.15/104.79 X261,X259) => 104.15/104.79 (( 104.15/104.79 ~ 104.15/104.79 in( 104.15/104.79 X261,X260)) => 104.15/104.79 (~ 104.15/104.79 subset( 104.15/104.79 X259,X260))))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X262, 104.15/104.79 X263]: 104.15/104.79 (( 104.15/104.79 ~ 104.15/104.79 subset( 104.15/104.79 X262,X263)) => 104.15/104.79 (X262 != 104.15/104.79 X263))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X264, 104.15/104.79 X265,X266]: 104.15/104.79 (in( 104.15/104.79 X266,X264) => 104.15/104.79 (( 104.15/104.79 ~ 104.15/104.79 in( 104.15/104.79 X266,X265)) => 104.15/104.79 (X264 != 104.15/104.79 X265)))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X267]: 104.15/104.79 subset( 104.15/104.79 X267,X267)) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X268, 104.15/104.79 X269,X270]: 104.15/104.79 (subset( 104.15/104.79 X268,X269) => 104.15/104.79 (subset( 104.15/104.79 X269,X270) => 104.15/104.79 subset( 104.15/104.79 X268,X270)))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X271, 104.15/104.79 X272]: 104.15/104.79 subset( 104.15/104.79 X272, 104.15/104.79 setadjoin( 104.15/104.79 X271,X272))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X273, 104.15/104.79 X274,X275]: 104.15/104.79 (subset( 104.15/104.79 X273,X275) => 104.15/104.79 subset( 104.15/104.79 X273, 104.15/104.79 setadjoin( 104.15/104.79 X274,X275)))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X276, 104.15/104.79 X277]: 104.15/104.79 (subset( 104.15/104.79 X276,X277) => 104.15/104.79 in( 104.15/104.79 X276, 104.15/104.79 powerset( 104.15/104.79 X277)))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X278, 104.15/104.79 X279]: 104.15/104.79 (subset( 104.15/104.79 X278,X279) => 104.15/104.79 (subset( 104.15/104.79 X279,X278) => 104.15/104.79 (X278 = 104.15/104.79 X279)))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X280]: 104.15/104.79 (subset( 104.15/104.79 X280, 104.15/104.79 emptyset) => 104.15/104.79 (X280 = 104.15/104.79 emptyset))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X281, 104.15/104.79 X282]: 104.15/104.79 (subset( 104.15/104.79 X282,X281) => 104.15/104.79 in( 104.15/104.79 X282, 104.15/104.79 powerset( 104.15/104.79 X281)))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X283, 104.15/104.79 X284]: 104.15/104.79 (in( 104.15/104.79 X284, 104.15/104.79 powerset( 104.15/104.79 X283)) => 104.15/104.79 subset( 104.15/104.79 X284,X283))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X285]: 104.15/104.79 in( 104.15/104.79 X285, 104.15/104.79 powerset( 104.15/104.79 X285))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X286, 104.15/104.79 X287]: 104.15/104.79 (subset( 104.15/104.79 X286,X287) => 104.15/104.79 subset( 104.15/104.79 powerset( 104.15/104.79 X286), 104.15/104.79 powerset( 104.15/104.79 X287)))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X288, 104.15/104.79 X289:( 104.15/104.79 $i > $o)]: 104.15/104.79 in( 104.15/104.79 dsetconstr( 104.15/104.79 X288, 104.15/104.79 '#ll_0'( 104.15/104.79 X289)), 104.15/104.79 powerset( 104.15/104.79 X288))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X290, 104.15/104.79 X291:( 104.15/104.79 $i > $o)]: 104.15/104.79 subset( 104.15/104.79 dsetconstr( 104.15/104.79 X290, 104.15/104.79 '#ll_0'( 104.15/104.79 X291)), 104.15/104.79 X290)) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X292, 104.15/104.79 X293,X294]: 104.15/104.79 (in( 104.15/104.79 X294,X292) => 104.15/104.79 in( 104.15/104.79 X294, 104.15/104.79 binunion( 104.15/104.79 X292,X293)))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X295, 104.15/104.79 X296]: 104.15/104.79 in( 104.15/104.79 X296, 104.15/104.79 setadjoin( 104.15/104.79 X295, 104.15/104.79 setadjoin( 104.15/104.79 X296, 104.15/104.79 emptyset)))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X297, 104.15/104.79 X298,X299]: 104.15/104.79 (in( 104.15/104.79 X299,X298) => 104.15/104.79 in( 104.15/104.79 X299, 104.15/104.79 binunion( 104.15/104.79 X297,X298)))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X300, 104.15/104.79 X301, 104.15/104.79 X302, 104.15/104.79 X303:$o]: 104.15/104.79 (in( 104.15/104.79 X302, 104.15/104.79 binunion( 104.15/104.79 X300,X301)) => 104.15/104.79 (( 104.15/104.79 in( 104.15/104.79 X302,X300) => 104.15/104.79 X303) => 104.15/104.79 (( 104.15/104.79 in( 104.15/104.79 X302,X301) => 104.15/104.79 X303) => 104.15/104.79 X303)))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X304, 104.15/104.79 X305,X306]: 104.15/104.79 (in( 104.15/104.79 X306, 104.15/104.79 binunion( 104.15/104.79 X304,X305)) => 104.15/104.79 (in( 104.15/104.79 X306,X304) | 104.15/104.79 in( 104.15/104.79 X306,X305)))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X307, 104.15/104.79 X308]: 104.15/104.79 subset( 104.15/104.79 X307, 104.15/104.79 binunion( 104.15/104.79 X307,X308))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X309, 104.15/104.79 X310]: 104.15/104.79 subset( 104.15/104.79 X310, 104.15/104.79 binunion( 104.15/104.79 X309,X310))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X311, 104.15/104.79 X312,X313]: 104.15/104.79 (in( 104.15/104.79 X313,X311) => 104.15/104.79 (in( 104.15/104.79 X313,X312) => 104.15/104.79 in( 104.15/104.79 X313, 104.15/104.79 binintersect( 104.15/104.79 X311,X312))))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X314, 104.15/104.79 X315,X316]: 104.15/104.79 (subset( 104.15/104.79 X316,X314) => 104.15/104.79 (subset( 104.15/104.79 X316,X315) => 104.15/104.79 subset( 104.15/104.79 X316, 104.15/104.79 binintersect( 104.15/104.79 X314,X315))))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X317, 104.15/104.79 X318,X319]: 104.15/104.79 (in( 104.15/104.79 X319, 104.15/104.79 binintersect( 104.15/104.79 X317,X318)) => 104.15/104.79 in( 104.15/104.79 X319,X317))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X320, 104.15/104.79 X321]: 104.15/104.79 subset( 104.15/104.79 binintersect( 104.15/104.79 X320,X321), 104.15/104.79 X320)) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X322, 104.15/104.79 X323]: 104.15/104.79 (subset( 104.15/104.79 X322,X323) => 104.15/104.79 (binintersect( 104.15/104.79 X322,X323) = 104.15/104.79 X322))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X324, 104.15/104.79 X325]: 104.15/104.79 (( 104.15/104.79 binintersect( 104.15/104.79 X324,X325) = 104.15/104.79 X325) => 104.15/104.79 subset( 104.15/104.79 X325,X324))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X326, 104.15/104.79 X327,X328]: 104.15/104.79 (in( 104.15/104.79 X328, 104.15/104.79 binintersect( 104.15/104.79 X326,X327)) => 104.15/104.79 in( 104.15/104.79 X328,X327))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X329, 104.15/104.79 X330]: 104.15/104.79 (( 104.15/104.79 ~ 104.15/104.79 ( 104.15/104.79 ?[X331]: 104.15/104.79 (in( 104.15/104.79 X331,X329) & 104.15/104.79 in( 104.15/104.79 X331,X330)))) => 104.15/104.79 (binintersect( 104.15/104.79 X329,X330) = 104.15/104.79 emptyset))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X332, 104.15/104.79 X333]: 104.15/104.79 subset( 104.15/104.79 binintersect( 104.15/104.79 X332,X333), 104.15/104.79 X333)) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X334, 104.15/104.79 X335]: 104.15/104.79 (subset( 104.15/104.79 X335,X334) => 104.15/104.79 (binintersect( 104.15/104.79 X334,X335) = 104.15/104.79 X335))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X336, 104.15/104.79 X337]: 104.15/104.79 (( 104.15/104.79 binintersect( 104.15/104.79 X336,X337) = 104.15/104.79 X336) => 104.15/104.79 subset( 104.15/104.79 X336,X337))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X338, 104.15/104.79 X339,X340]: 104.15/104.79 (binintersect( 104.15/104.79 X338, 104.15/104.79 binunion( 104.15/104.79 X339,X340)) = 104.15/104.79 binunion( 104.15/104.79 binintersect( 104.15/104.79 X338,X339), 104.15/104.79 binintersect( 104.15/104.79 X338,X340)))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X341, 104.15/104.79 X342,X343]: 104.15/104.79 (in( 104.15/104.79 X343,X341) => 104.15/104.79 (( 104.15/104.79 ~ 104.15/104.79 in( 104.15/104.79 X343,X342)) => 104.15/104.79 in( 104.15/104.79 X343, 104.15/104.79 setminus( 104.15/104.79 X341,X342))))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X344, 104.15/104.79 X345,X346]: 104.15/104.79 (in( 104.15/104.79 X346, 104.15/104.79 setminus( 104.15/104.79 X344,X345)) => 104.15/104.79 in( 104.15/104.79 X346,X344))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X347, 104.15/104.79 X348,X349]: 104.15/104.79 (in( 104.15/104.79 X349, 104.15/104.79 setminus( 104.15/104.79 X347,X348)) => 104.15/104.79 (~ 104.15/104.79 in( 104.15/104.79 X349,X348)))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X350, 104.15/104.79 X351]: 104.15/104.79 (subset( 104.15/104.79 X350,X351) => 104.15/104.79 (setminus( 104.15/104.79 X350,X351) = 104.15/104.79 emptyset))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X352, 104.15/104.79 X353,X354]: 104.15/104.79 (( 104.15/104.79 ~ 104.15/104.79 in( 104.15/104.79 X354, 104.15/104.79 setminus( 104.15/104.79 X352,X353))) => 104.15/104.79 (in( 104.15/104.79 X354,X352) => 104.15/104.79 in( 104.15/104.79 X354,X353)))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X355, 104.15/104.79 X356,X357]: 104.15/104.79 (( 104.15/104.79 ~ 104.15/104.79 in( 104.15/104.79 X357, 104.15/104.79 setminus( 104.15/104.79 X355,X356))) => 104.15/104.79 (( 104.15/104.79 ~ 104.15/104.79 in( 104.15/104.79 X357,X356)) => 104.15/104.79 (~ 104.15/104.79 in( 104.15/104.79 X357,X355))))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X358, 104.15/104.79 X359,X360]: 104.15/104.79 (( 104.15/104.79 ~ 104.15/104.79 in( 104.15/104.79 X360,X358)) => 104.15/104.79 (~ 104.15/104.79 in( 104.15/104.79 X360, 104.15/104.79 setminus( 104.15/104.79 X358,X359))))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X361, 104.15/104.79 X362,X363]: 104.15/104.79 (in( 104.15/104.79 X363,X362) => 104.15/104.79 (~ 104.15/104.79 in( 104.15/104.79 X363, 104.15/104.79 setminus( 104.15/104.79 X361,X362))))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X364, 104.15/104.79 X365]: 104.15/104.79 subset( 104.15/104.79 setminus( 104.15/104.79 X364,X365), 104.15/104.79 X364)) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X366, 104.15/104.79 X367]: 104.15/104.79 (( 104.15/104.79 setminus( 104.15/104.79 X366,X367) = 104.15/104.79 emptyset) => 104.15/104.79 subset( 104.15/104.79 X366,X367))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X368, 104.15/104.79 X369,X370]: 104.15/104.79 (in( 104.15/104.79 X370, 104.15/104.79 symdiff( 104.15/104.79 X368,X369)) => 104.15/104.79 (![X371:$o]: 104.15/104.79 (( 104.15/104.79 in( 104.15/104.79 X370,X368) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ~ 104.15/104.79 in( 104.15/104.79 X370,X369)) => 104.15/104.79 X371)) => 104.15/104.79 (( 104.15/104.79 ( 104.15/104.79 ~ 104.15/104.79 in( 104.15/104.79 X370,X368)) => 104.15/104.79 ( 104.15/104.79 in( 104.15/104.79 X370,X369) => 104.15/104.79 X371)) => 104.15/104.79 X371))))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X372, 104.15/104.79 X373,X374]: 104.15/104.79 (in( 104.15/104.79 X374,X372) => 104.15/104.79 (( 104.15/104.79 ~ 104.15/104.79 in( 104.15/104.79 X374,X373)) => 104.15/104.79 in( 104.15/104.79 X374, 104.15/104.79 symdiff( 104.15/104.79 X372,X373))))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X375, 104.15/104.79 X376,X377]: 104.15/104.79 (( 104.15/104.79 ~ 104.15/104.79 in( 104.15/104.79 X377,X375)) => 104.15/104.79 (in( 104.15/104.79 X377,X376) => 104.15/104.79 in( 104.15/104.79 X377, 104.15/104.79 symdiff( 104.15/104.79 X375,X376))))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X378, 104.15/104.79 X379,X380]: 104.15/104.79 (in( 104.15/104.79 X380,X378) => 104.15/104.79 (in( 104.15/104.79 X380,X379) => 104.15/104.79 (~ 104.15/104.79 in( 104.15/104.79 X380, 104.15/104.79 symdiff( 104.15/104.79 X378,X379)))))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X381, 104.15/104.79 X382,X383]: 104.15/104.79 (( 104.15/104.79 ~ 104.15/104.79 in( 104.15/104.79 X383,X381)) => 104.15/104.79 (( 104.15/104.79 ~ 104.15/104.79 in( 104.15/104.79 X383,X382)) => 104.15/104.79 (~ 104.15/104.79 in( 104.15/104.79 X383, 104.15/104.79 symdiff( 104.15/104.79 X381,X382)))))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X384, 104.15/104.79 X385]: 104.15/104.79 in( 104.15/104.79 X385, 104.15/104.79 setadjoin( 104.15/104.79 X384, 104.15/104.79 setadjoin( 104.15/104.79 X385, 104.15/104.79 emptyset)))) => 104.15/104.79 ( 104.15/104.79 ![X386, 104.15/104.79 X387]: 104.15/104.79 in( 104.15/104.79 X386, 104.15/104.79 setunion( 104.15/104.79 setadjoin( 104.15/104.79 setadjoin( 104.15/104.79 X386, 104.15/104.79 emptyset), 104.15/104.79 setadjoin( 104.15/104.79 setadjoin( 104.15/104.79 X386, 104.15/104.79 setadjoin( 104.15/104.79 X387, 104.15/104.79 emptyset)), 104.15/104.79 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 104.15/104.79 tff(zf_stmt_1, type, zip_tseitin5 : ($i * $i > $o) > $o). 104.15/104.79 tff(zf_stmt_2, axiom, 104.15/104.79 (zip_tseitin5(X211,X207) <=> 104.15/104.79 ((![X212]: zip_tseitin4(X212,X211,X207)) & X207(X211)))). 104.15/104.79 tff(zf_stmt_3, type, zip_tseitin4 : ($i * $i * $i > $o) > $o). 104.15/104.79 tff(zf_stmt_4, axiom, 104.15/104.79 (zip_tseitin4(X212,X211,X207) <=> (X207(X212) => (X211 = X212)))). 104.15/104.79 tff(zf_stmt_5, type, zip_tseitin3 : ($i * $i * $i * ($i * $i) > $o) > $o). 104.15/104.79 tff(zf_stmt_6, axiom, 104.15/104.79 (zip_tseitin3(X26,X25,X20,X19) <=> (X19(X26,X25) & in(X26,X20)))). 104.15/104.79 tff(zf_stmt_7, type, zip_tseitin2 : ($i * $i * $i) > $o). 104.15/104.79 tff(zf_stmt_8, axiom, 104.15/104.79 (zip_tseitin2(X14,X13,X12) <=> (in(X14,X12) & in(X13,X14)))). 104.15/104.79 tff(zf_stmt_9, type, zip_tseitin1 : ($i * $i * $i) > $o). 104.15/104.79 tff(zf_stmt_10, axiom, 104.15/104.79 (zip_tseitin1(X11,X10,X9) <=> (in(X11,X10) => in(X11,X9)))). 104.15/104.79 tff(zf_stmt_11, type, zip_tseitin0 : ($i * $i * $i) > $o). 104.15/104.79 tff(zf_stmt_12, axiom, (zip_tseitin0(X8,X7,X6) <=> (in(X8,X7) | (X8 = X6)))). 104.15/104.79 tff(zf_stmt_13, conjecture, 104.15/104.79 ((![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))) => 104.15/104.79 ((![X5]: (~in(X5,emptyset))) => 104.15/104.79 ((![X6,X7,X8]: (in(X8,setadjoin(X6,X7)) <=> zip_tseitin0(X8,X7,X6))) => 104.15/104.79 ((![X9,X10]: 104.15/104.79 (in(X10,powerset(X9)) <=> (![X11]: zip_tseitin1(X11,X10,X9)))) => 104.15/104.79 ((![X12,X13]: 104.15/104.79 (in(X13,setunion(X12)) <=> (?[X14]: zip_tseitin2(X14,X13,X12)))) => 104.15/104.79 (in(emptyset,omega) => 104.15/104.79 ((![X15]: (in(X15,omega) => in(setadjoin(X15,X15),omega))) => 104.15/104.79 ((![X16]: 104.15/104.79 (((![X17]: 104.15/104.79 ((in(X17,X16) & in(X17,omega)) => 104.15/104.79 in(setadjoin(X17,X17),X16))) & 104.15/104.79 in(emptyset,X16)) => 104.15/104.79 (![X18]: (in(X18,omega) => in(X18,X16))))) => 104.15/104.79 ((![X19:(($i * $i) > $o),X20]: 104.15/104.79 ((![X21]: 104.15/104.79 (in(X21,X20) => 104.15/104.79 (?[X22]: 104.15/104.79 ((![X23]: (X19(X21,X23) => (X22 = X23))) & X19(X21,X22))))) => 104.15/104.79 (?[X24]: 104.15/104.79 (![X25]: 104.15/104.79 (in(X25,X24) <=> (?[X26]: zip_tseitin3(X26,X25,X20,X19))))))) => 104.15/104.79 ((![X27]: 104.15/104.79 ((?[X28]: in(X28,X27)) => 104.15/104.79 (?[X29]: 104.15/104.79 ((~(?[X30]: (in(X30,X27) & in(X30,X29)))) & in(X29,X27))))) => 104.15/104.79 ((![X31]: 104.15/104.79 (?[X32]: 104.15/104.79 ((![X33]: 104.15/104.79 (((?[X34]: in(X34,X33)) & 104.15/104.79 (![X35]: (in(X35,X33) => in(X35,X31)))) => 104.15/104.79 (?[X36,X37]: 104.15/104.79 ((![X38]: 104.15/104.79 (in(X38,X32) => 104.15/104.79 (in(X37,X38) | 104.15/104.79 (![X39]: (in(X39,X38) => in(X39,X36)))))) & 104.15/104.79 (~(?[X40]: (in(X40,X33) & in(X40,X36)))) & 104.15/104.79 in(X37,X33) & in(X36,X32))))) & 104.15/104.79 (![X41,X42]: 104.15/104.79 ((in(X42,X32) & in(X41,X32)) => 104.15/104.79 ((![X43]: (in(X43,X42) => in(X43,X41))) | 104.15/104.79 (![X44]: (in(X44,X41) => in(X44,X42)))))) & 104.15/104.79 (![X45,X46]: 104.15/104.79 ((in(X46,X31) & in(X45,X31)) => 104.15/104.79 ((![X47]: 104.15/104.79 (in(X47,X32) => (in(X45,X47) <=> in(X46,X47)))) => 104.15/104.79 (X45 = X46)))) & 104.15/104.79 (![X48]: 104.15/104.79 (in(X48,X32) => (![X49]: (in(X49,X48) => in(X49,X31)))))))) => 104.15/104.79 ((![X50:($i > $o)]: 104.15/104.79 ((?[X51]: ((![X52]: (X50(X52) => (X51 = X52))) & X50(X51))) => 104.15/104.79 X50(descr('#ll_0'(X50))))) => 104.15/104.79 ((![X53,X54:($i > $o),X55]: 104.15/104.79 (in(X55,X53) => 104.15/104.79 (X54(X55) => in(X55,dsetconstr(X53,'#ll_0'(X54)))))) => 104.15/104.79 ((![X56,X57:($i > $o),X58]: 104.15/104.79 (in(X58,dsetconstr(X56,'#ll_0'(X57))) => in(X58,X56))) => 104.15/104.79 ((![X59,X60:($i > $o),X61]: 104.15/104.79 (in(X61,dsetconstr(X59,'#ll_0'(X60))) => X60(X61))) => 104.15/104.79 ((![X62:($i > $o)]: 104.15/104.79 ((?[X63]: 104.15/104.79 ((![X64]: (X62(X64) => (X63 = X64))) & X62(X63))) => 104.15/104.79 (?[X65]: 104.15/104.79 ((![X66]: (X62(X66) => (X65 = X66))) & X62(X65))))) => 104.15/104.79 ((![X67:$o,X68]: (in(X68,prop2set(X67)) => X67)) => 104.15/104.79 ((![X69]: (in(X69,emptyset) => (![X70:$o]: X70))) => 104.15/104.79 ((![X71]: (in(X71,emptyset) => $false)) => 104.15/104.79 ((![X72]: (~in(X72,emptyset))) => 104.15/104.79 ((![X73:($i > $o)]: 104.15/104.79 ((?[X74]: 104.15/104.79 ((![X75]: (X73(X75) => (X74 = X75))) & X73(X74))) => 104.15/104.79 (?[X76]: X73(X76)))) => 104.15/104.79 ((![X77,X78]: 104.15/104.79 ((![X79]: (in(X79,X77) => in(X79,X78))) => 104.15/104.79 ((![X80]: (in(X80,X78) => in(X80,X77))) => 104.15/104.79 (X77 = X78)))) => 104.15/104.79 ((![X81]: 104.15/104.79 ((![X82]: (~in(X82,X81))) => (X81 = emptyset))) => 104.15/104.79 ((![X83]: 104.15/104.79 ((![X84]: (~in(X84,X83))) => (X83 = emptyset))) => 104.15/104.79 ((![X85,X86:($i > $o),X87]: 104.15/104.79 (in(X87,X85) => 104.15/104.79 (in(X87,dsetconstr(X85,'#ll_0'(X86))) <=> 104.15/104.79 X86(X87)))) => 104.15/104.79 ((![X88]: 104.15/104.79 ((X88 != emptyset) => (?[X89]: in(X89,X88)))) => 104.15/104.79 ((![X90,X91:($i > $o),X92]: 104.15/104.79 (in(X92,X90) => 104.15/104.79 (X91(X92) => 104.15/104.79 (dsetconstr(X90,'#ll_0'(X91)) != emptyset)))) => 104.15/104.79 ((![X93]: 104.15/104.79 ((?[X94]: in(X94,X93)) => (X93 != emptyset))) => 104.15/104.79 ((![X95,X96]: in(X95,setadjoin(X95,X96))) => 104.15/104.79 (in(emptyset,setadjoin(emptyset,emptyset)) => 104.15/104.79 ((![X97,X98,X99]: 104.15/104.79 (in(X99,X98) => 104.15/104.79 in(X99,setadjoin(X97,X98)))) => 104.15/104.79 ((![X100,X101,X102]: 104.15/104.79 (in(X102,setadjoin(X100,X101)) => 104.15/104.79 (![X103:$o]: 104.15/104.79 (((X102 = X100) => X103) => 104.15/104.79 ((in(X102,X101) => X103) => X103))))) => 104.15/104.79 ((![X104,X105,X106]: 104.15/104.79 (in(X106,setadjoin(X104,X105)) => 104.15/104.79 (in(X106,X105) | (X106 = X104)))) => 104.15/104.79 ((![X107]: 104.15/104.79 (dsetconstr(X107,'#ll_1') = X107)) => 104.15/104.79 ((![X108,X109]: 104.15/104.79 ((![X110]: 104.15/104.79 (in(X110,X109) => in(X110,X108))) => 104.15/104.79 in(X109,powerset(X108)))) => 104.15/104.79 ((![X111]: in(emptyset,powerset(X111))) => 104.15/104.79 ((![X112]: in(emptyset,powerset(X112))) => 104.15/104.79 ((![X113,X114,X115]: 104.15/104.79 (in(X114,powerset(X113)) => 104.15/104.79 (in(X115,X114) => in(X115,X113)))) => 104.15/104.79 ((![X116,X117,X118]: 104.15/104.79 (in(X117,X118) => 104.15/104.79 (in(X118,X116) => 104.15/104.79 in(X117,setunion(X116))))) => 104.15/104.79 ((![X119,X120]: 104.15/104.79 (in(X120,setunion(X119)) => 104.15/104.79 (![X121:$o]: 104.15/104.79 ((![X122]: 104.15/104.79 (in(X120,X122) => 104.15/104.79 (in(X122,X119) => X121))) => 104.15/104.79 X121)))) => 104.15/104.79 ((![X123,X124]: 104.15/104.79 (in(X124,X123) => 104.15/104.79 in(X124, 104.15/104.79 powerset(setunion(X123))))) => 104.15/104.79 ((![X125:($i > $o)]: 104.15/104.79 ((?[X126]: 104.15/104.79 ((![X127]: 104.15/104.79 (X125(X127) => 104.15/104.79 (X126 = X127))) & 104.15/104.79 X125(X126))) => 104.15/104.79 (?[X128]: 104.15/104.79 (![X129]: 104.15/104.79 (X125(X129) <=> 104.15/104.79 (X129 = X128)))))) => 104.15/104.79 ((![X130]: 104.15/104.79 ((X130 != emptyset) => 104.15/104.79 (?[X131]: in(X131,X130)))) => 104.15/104.79 ((![X132,X133]: 104.15/104.79 (in(X132, 104.15/104.79 setadjoin(X133,emptyset)) => 104.15/104.79 (X132 = X133))) => 104.15/104.79 ((![X134,X135]: 104.15/104.79 ((X134 != X135) => 104.15/104.79 (~ 104.15/104.79 in(X135, 104.15/104.79 setadjoin(X134, 104.15/104.79 emptyset))))) => 104.15/104.79 ((![X136,X137]: 104.15/104.79 ((X136 = X137) => 104.15/104.79 in(X136, 104.15/104.79 setadjoin(X137, 104.15/104.79 emptyset)))) => 104.15/104.79 ((![X138,X139]: 104.15/104.79 (in(X138, 104.15/104.79 setadjoin(X139, 104.15/104.79 emptyset)) => 104.15/104.79 in(X139, 104.15/104.79 setadjoin(X138, 104.15/104.79 emptyset)))) => 104.15/104.79 ((![X140,X141,X142]: 104.15/104.79 (in(X142, 104.15/104.79 setadjoin(X140, 104.15/104.79 setadjoin( 104.15/104.79 X141, 104.15/104.79 emptyset))) => 104.15/104.79 ((X142 = X141) | 104.15/104.79 (X142 = X140)))) => 104.15/104.79 ((![X143,X144]: 104.15/104.79 in(X143, 104.15/104.79 setadjoin(X143, 104.15/104.79 setadjoin( 104.15/104.79 X144, 104.15/104.79 emptyset)))) => 104.15/104.79 ((![X145,X146]: 104.15/104.79 in(X146, 104.15/104.79 setadjoin(X145, 104.15/104.79 setadjoin( 104.15/104.79 X146, 104.15/104.79 emptyset)))) => 104.15/104.79 ((![X147,X148:($i > $o)]: 104.15/104.79 ((?[X149]: 104.15/104.79 (X148(X149) & 104.15/104.79 in(X149,X147))) => 104.15/104.79 ((dsetconstr( 104.15/104.79 X147,'#ll_0'(X148)) = 104.15/104.79 emptyset) => 104.15/104.79 $false))) => 104.15/104.79 ((![X150:($i > $o),X151]: 104.15/104.79 (in(X151,emptyset) => 104.15/104.79 X150(X151))) => 104.15/104.79 ((![X152,X153:($i > $o)]: 104.15/104.79 ((~ 104.15/104.79 (![X154]: 104.15/104.79 (in(X154,X152) => 104.15/104.79 X153(X154)))) => 104.15/104.79 (?[X155]: 104.15/104.79 ((~X153(X155)) & 104.15/104.79 in(X155,X152))))) => 104.15/104.79 ((![X156, 104.15/104.79 X157:($i > $o)]: 104.15/104.79 ((![X158]: 104.15/104.79 (in(X158,X156) => 104.15/104.79 (~X157(X158)))) => 104.15/104.79 (~ 104.15/104.79 (?[X159]: 104.15/104.79 (X157(X159) & 104.15/104.79 in( 104.15/104.79 X159,X156)))))) => 104.15/104.79 ((![X160, 104.15/104.79 X161:($i > $o)]: 104.15/104.79 ((~ 104.15/104.79 (?[X162]: 104.15/104.79 (X161(X162) & 104.15/104.79 in( 104.15/104.79 X162,X160)))) => 104.15/104.79 (![X163]: 104.15/104.79 (in(X163,X160) => 104.15/104.79 (~X161(X163)))))) => 104.15/104.79 ((![X164, 104.15/104.79 X165:($i > $o)]: 104.15/104.79 ((?[X166]: 104.15/104.79 ((~ 104.15/104.79 X165( 104.15/104.79 X166)) & 104.15/104.79 in( 104.15/104.79 X166,X164))) => 104.15/104.79 (~ 104.15/104.79 (![X167]: 104.15/104.79 (in( 104.15/104.79 X167,X164) => 104.15/104.79 X165( 104.15/104.79 X167)))))) => 104.15/104.79 ((![X168:$o]: 104.15/104.79 (X168 => 104.15/104.79 in(emptyset, 104.15/104.79 prop2set( 104.15/104.79 X168)))) => 104.15/104.79 ((![X169:$o]: 104.15/104.79 (X169 => 104.15/104.79 set2prop( 104.15/104.79 prop2set( 104.15/104.79 X169)))) => 104.15/104.79 ((![X170, 104.15/104.79 X171:( 104.15/104.79 $i > $o)]: 104.15/104.79 ((~ 104.15/104.79 (?[X172]: 104.15/104.79 (X171( 104.15/104.79 X172) & 104.15/104.79 in( 104.15/104.79 X172,X170)))) => 104.15/104.79 (![X173]: 104.15/104.79 ( 104.15/104.79 in( 104.15/104.79 X173,X170) => 104.15/104.79 ( 104.15/104.79 ~ 104.15/104.79 X171( 104.15/104.79 X173)))))) => 104.15/104.79 ((![X174, 104.15/104.79 X175:( 104.15/104.79 $i > $o)]: 104.15/104.79 ((~ 104.15/104.79 ( 104.15/104.79 ![X176]: 104.15/104.79 (in( 104.15/104.79 X176,X174) => 104.15/104.79 X175( 104.15/104.79 X176)))) => 104.15/104.79 (?[X177]: 104.15/104.79 (( 104.15/104.79 ~ 104.15/104.79 X175( 104.15/104.79 X177)) & 104.15/104.79 in( 104.15/104.79 X177,X174))))) => 104.15/104.79 ((![X178:( 104.15/104.79 $i > $o)]: 104.15/104.79 ((?[X179]: 104.15/104.79 (( 104.15/104.79 ![X180]: 104.15/104.79 (X178( 104.15/104.79 X180) => 104.15/104.79 (X179 = 104.15/104.79 X180))) & 104.15/104.79 X178( 104.15/104.79 X179))) => 104.15/104.79 (?[X181]: 104.15/104.79 (( 104.15/104.79 ![X182]: 104.15/104.79 (X178( 104.15/104.79 X182) => 104.15/104.79 (X181 = 104.15/104.79 X182))) & 104.15/104.79 X178( 104.15/104.79 X181))))) => 104.15/104.79 ((![X183:( 104.15/104.79 $i > $o)]: 104.15/104.79 (( 104.15/104.79 ?[X184]: 104.15/104.79 X183( 104.15/104.79 X184)) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X185, 104.15/104.79 X186]: 104.15/104.79 (X183( 104.15/104.79 X185) => 104.15/104.79 (X183( 104.15/104.79 X186) => 104.15/104.79 (X185 = 104.15/104.79 X186)))) => 104.15/104.79 ( 104.15/104.79 ?[X187]: 104.15/104.79 (( 104.15/104.79 ![X188]: 104.15/104.79 (X183( 104.15/104.79 X188) => 104.15/104.79 (X187 = 104.15/104.79 X188))) & 104.15/104.79 X183( 104.15/104.79 X187)))))) => 104.15/104.79 ((![X189:( 104.15/104.79 $i > $o)]: 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ?[X190]: 104.15/104.79 (![X191]: 104.15/104.79 (X189( 104.15/104.79 X191) <=> 104.15/104.79 (X191 = 104.15/104.79 X190)))) => 104.15/104.79 ( 104.15/104.79 ?[X192]: 104.15/104.79 (( 104.15/104.79 ![X193]: 104.15/104.79 (X189( 104.15/104.79 X193) => 104.15/104.79 (X192 = 104.15/104.79 X193))) & 104.15/104.79 X189( 104.15/104.79 X192))))) => 104.15/104.79 ((![X194, 104.15/104.79 X195]: 104.15/104.79 (( 104.15/104.79 X194 = 104.15/104.79 X195) => 104.15/104.79 (![X196, 104.15/104.79 X197]: 104.15/104.79 (( 104.15/104.79 X196 = 104.15/104.79 X197) => 104.15/104.79 (in( 104.15/104.79 X196,X194) => 104.15/104.79 in( 104.15/104.79 X197,X195)))))) => 104.15/104.79 ((![X198, 104.15/104.79 X199]: 104.15/104.79 (( 104.15/104.79 X198 = 104.15/104.79 X199) => 104.15/104.79 (![X200, 104.15/104.79 X201]: 104.15/104.79 (( 104.15/104.79 X200 = 104.15/104.79 X201) => 104.15/104.79 (in( 104.15/104.79 X200,X198) <=> 104.15/104.79 in( 104.15/104.79 X201,X199)))))) => 104.15/104.79 (( 104.15/104.79 ![X202:( 104.15/104.79 $i > $o)]: 104.15/104.79 (( 104.15/104.79 ?[X203]: 104.15/104.79 (( 104.15/104.79 ![X204]: 104.15/104.79 (X202( 104.15/104.79 X204) => 104.15/104.79 (X203 = 104.15/104.79 X204))) & 104.15/104.79 X202( 104.15/104.79 X203))) => 104.15/104.79 (![X205, 104.15/104.79 X206]: 104.15/104.79 (X202( 104.15/104.79 X205) => 104.15/104.79 (X202( 104.15/104.79 X206) => 104.15/104.79 (X205 = 104.15/104.79 X206)))))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X207:( 104.15/104.79 $i > $o), 104.15/104.79 X208:( 104.15/104.79 $i > $o)]: 104.15/104.79 (( 104.15/104.79 ![X209, 104.15/104.79 X210]: 104.15/104.79 (( 104.15/104.79 X209 = 104.15/104.79 X210) => 104.15/104.79 (X207( 104.15/104.79 X209) <=> 104.15/104.79 X208( 104.15/104.79 X210)))) => 104.15/104.79 (( 104.15/104.79 ?[X211]: 104.15/104.79 zip_tseitin5( 104.15/104.79 X211,X207)) <=> 104.15/104.79 (?[X213]: 104.15/104.79 zip_tseitin5( 104.15/104.79 X213,X208))))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 emptyset = 104.15/104.79 emptyset) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X215, 104.15/104.79 X216]: 104.15/104.79 (( 104.15/104.79 X215 = 104.15/104.79 X216) => 104.15/104.79 (![X217, 104.15/104.79 X218]: 104.15/104.79 (( 104.15/104.79 X217 = 104.15/104.79 X218) => 104.15/104.79 (setadjoin( 104.15/104.79 X215,X217) = 104.15/104.79 setadjoin( 104.15/104.79 X216,X218)))))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X219, 104.15/104.79 X220]: 104.15/104.79 (( 104.15/104.79 X219 = 104.15/104.79 X220) => 104.15/104.79 (powerset( 104.15/104.79 X219) = 104.15/104.79 powerset( 104.15/104.79 X220)))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X221, 104.15/104.79 X222]: 104.15/104.79 (( 104.15/104.79 X221 = 104.15/104.79 X222) => 104.15/104.79 (setunion( 104.15/104.79 X221) = 104.15/104.79 setunion( 104.15/104.79 X222)))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 omega = 104.15/104.79 omega) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X223:( 104.15/104.79 $i > $o)]: 104.15/104.79 (( 104.15/104.79 ?[X224]: 104.15/104.79 (( 104.15/104.79 ![X225]: 104.15/104.79 (X223( 104.15/104.79 X225) => 104.15/104.79 (X224 = 104.15/104.79 X225))) & 104.15/104.79 X223( 104.15/104.79 X224))) => 104.15/104.79 (![X226, 104.15/104.79 X227]: 104.15/104.79 (X223( 104.15/104.79 X226) => 104.15/104.79 (X223( 104.15/104.79 X227) => 104.15/104.79 (X226 = 104.15/104.79 X227)))))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X228:( 104.15/104.79 $i > $o), 104.15/104.79 X229:( 104.15/104.79 $i > $o)]: 104.15/104.79 (( 104.15/104.79 ![X230, 104.15/104.79 X231]: 104.15/104.79 (( 104.15/104.79 X230 = 104.15/104.79 X231) => 104.15/104.79 (X228( 104.15/104.79 X230) <=> 104.15/104.79 X229( 104.15/104.79 X231)))) => 104.15/104.79 (( 104.15/104.79 ?[X232]: 104.15/104.79 (( 104.15/104.79 ![X233]: 104.15/104.79 (X228( 104.15/104.79 X233) => 104.15/104.79 (X232 = 104.15/104.79 X233))) & 104.15/104.79 X228( 104.15/104.79 X232))) => 104.15/104.79 (( 104.15/104.79 ?[X234]: 104.15/104.79 (( 104.15/104.79 ![X235]: 104.15/104.79 (X229( 104.15/104.79 X235) => 104.15/104.79 (X234 = 104.15/104.79 X235))) & 104.15/104.79 X229( 104.15/104.79 X234))) => 104.15/104.79 (descr( 104.15/104.79 '#ll_0'( 104.15/104.79 X228)) = 104.15/104.79 descr( 104.15/104.79 '#ll_0'( 104.15/104.79 X229))))))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X236, 104.15/104.79 X237]: 104.15/104.79 (( 104.15/104.79 X236 = 104.15/104.79 X237) => 104.15/104.79 (![X238:( 104.15/104.79 $i > $o), 104.15/104.79 X239:( 104.15/104.79 $i > $o)]: 104.15/104.79 (( 104.15/104.79 ![X240]: 104.15/104.79 (in( 104.15/104.79 X240,X236) => 104.15/104.79 (![X241]: 104.15/104.79 (in( 104.15/104.79 X241,X237) => 104.15/104.79 (( 104.15/104.79 X240 = 104.15/104.79 X241) => 104.15/104.79 (X238( 104.15/104.79 X240) <=> 104.15/104.79 X239( 104.15/104.79 X241))))))) => 104.15/104.79 (dsetconstr( 104.15/104.79 X236, 104.15/104.79 '#ll_0'( 104.15/104.79 X238)) = 104.15/104.79 dsetconstr( 104.15/104.79 X237, 104.15/104.79 '#ll_0'( 104.15/104.79 X239))))))) => 104.15/104.79 ( 104.15/104.79 ( 104.15/104.79 ![X242, 104.15/104.79 X243]: 104.15/104.79 (( 104.15/104.79 ![X244]: 104.15/104.79 (in( 104.15/104.79 X244,X242) => 104.15/104.79 in( 104.15/104.79 X244,X243))) => 104.15/104.79 subset( 104.15/104.79 X242,X243))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X245, 104.15/104.80 X246]: 104.15/104.80 (( 104.15/104.80 X245 = 104.15/104.80 X246) => 104.15/104.80 subset( 104.15/104.80 X246,X245))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X247, 104.15/104.80 X248]: 104.15/104.80 (( 104.15/104.80 X247 = 104.15/104.80 X248) => 104.15/104.80 subset( 104.15/104.80 X247,X248))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X249, 104.15/104.80 X250]: 104.15/104.80 (( 104.15/104.80 ![X251]: 104.15/104.80 (in( 104.15/104.80 X251,X249) => 104.15/104.80 in( 104.15/104.80 X251,X250))) => 104.15/104.80 subset( 104.15/104.80 X249,X250))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X252]: 104.15/104.80 subset( 104.15/104.80 emptyset, 104.15/104.80 X252)) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X253, 104.15/104.80 X254,X255]: 104.15/104.80 (subset( 104.15/104.80 X253,X254) => 104.15/104.80 (in( 104.15/104.80 X255,X253) => 104.15/104.80 in( 104.15/104.80 X255,X254)))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X256, 104.15/104.80 X257,X258]: 104.15/104.80 (subset( 104.15/104.80 X256,X257) => 104.15/104.80 (( 104.15/104.80 ~ 104.15/104.80 in( 104.15/104.80 X258,X257)) => 104.15/104.80 (~ 104.15/104.80 in( 104.15/104.80 X258,X256))))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X259, 104.15/104.80 X260,X261]: 104.15/104.80 (in( 104.15/104.80 X261,X259) => 104.15/104.80 (( 104.15/104.80 ~ 104.15/104.80 in( 104.15/104.80 X261,X260)) => 104.15/104.80 (~ 104.15/104.80 subset( 104.15/104.80 X259,X260))))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X262, 104.15/104.80 X263]: 104.15/104.80 (( 104.15/104.80 ~ 104.15/104.80 subset( 104.15/104.80 X262,X263)) => 104.15/104.80 (X262 != 104.15/104.80 X263))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X264, 104.15/104.80 X265,X266]: 104.15/104.80 (in( 104.15/104.80 X266,X264) => 104.15/104.80 (( 104.15/104.80 ~ 104.15/104.80 in( 104.15/104.80 X266,X265)) => 104.15/104.80 (X264 != 104.15/104.80 X265)))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X267]: 104.15/104.80 subset( 104.15/104.80 X267,X267)) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X268, 104.15/104.80 X269,X270]: 104.15/104.80 (subset( 104.15/104.80 X268,X269) => 104.15/104.80 (subset( 104.15/104.80 X269,X270) => 104.15/104.80 subset( 104.15/104.80 X268,X270)))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X271, 104.15/104.80 X272]: 104.15/104.80 subset( 104.15/104.80 X272, 104.15/104.80 setadjoin( 104.15/104.80 X271,X272))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X273, 104.15/104.80 X274,X275]: 104.15/104.80 (subset( 104.15/104.80 X273,X275) => 104.15/104.80 subset( 104.15/104.80 X273, 104.15/104.80 setadjoin( 104.15/104.80 X274,X275)))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X276, 104.15/104.80 X277]: 104.15/104.80 (subset( 104.15/104.80 X276,X277) => 104.15/104.80 in( 104.15/104.80 X276, 104.15/104.80 powerset( 104.15/104.80 X277)))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X278, 104.15/104.80 X279]: 104.15/104.80 (subset( 104.15/104.80 X278,X279) => 104.15/104.80 (subset( 104.15/104.80 X279,X278) => 104.15/104.80 (X278 = 104.15/104.80 X279)))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X280]: 104.15/104.80 (subset( 104.15/104.80 X280, 104.15/104.80 emptyset) => 104.15/104.80 (X280 = 104.15/104.80 emptyset))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X281, 104.15/104.80 X282]: 104.15/104.80 (subset( 104.15/104.80 X282,X281) => 104.15/104.80 in( 104.15/104.80 X282, 104.15/104.80 powerset( 104.15/104.80 X281)))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X283, 104.15/104.80 X284]: 104.15/104.80 (in( 104.15/104.80 X284, 104.15/104.80 powerset( 104.15/104.80 X283)) => 104.15/104.80 subset( 104.15/104.80 X284,X283))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X285]: 104.15/104.80 in( 104.15/104.80 X285, 104.15/104.80 powerset( 104.15/104.80 X285))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X286, 104.15/104.80 X287]: 104.15/104.80 (subset( 104.15/104.80 X286,X287) => 104.15/104.80 subset( 104.15/104.80 powerset( 104.15/104.80 X286), 104.15/104.80 powerset( 104.15/104.80 X287)))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X288, 104.15/104.80 X289:( 104.15/104.80 $i > $o)]: 104.15/104.80 in( 104.15/104.80 dsetconstr( 104.15/104.80 X288, 104.15/104.80 '#ll_0'( 104.15/104.80 X289)), 104.15/104.80 powerset( 104.15/104.80 X288))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X290, 104.15/104.80 X291:( 104.15/104.80 $i > $o)]: 104.15/104.80 subset( 104.15/104.80 dsetconstr( 104.15/104.80 X290, 104.15/104.80 '#ll_0'( 104.15/104.80 X291)), 104.15/104.80 X290)) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X292, 104.15/104.80 X293,X294]: 104.15/104.80 (in( 104.15/104.80 X294,X292) => 104.15/104.80 in( 104.15/104.80 X294, 104.15/104.80 binunion( 104.15/104.80 X292,X293)))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X295, 104.15/104.80 X296]: 104.15/104.80 in( 104.15/104.80 X296, 104.15/104.80 setadjoin( 104.15/104.80 X295, 104.15/104.80 setadjoin( 104.15/104.80 X296, 104.15/104.80 emptyset)))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X297, 104.15/104.80 X298,X299]: 104.15/104.80 (in( 104.15/104.80 X299,X298) => 104.15/104.80 in( 104.15/104.80 X299, 104.15/104.80 binunion( 104.15/104.80 X297,X298)))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X300, 104.15/104.80 X301, 104.15/104.80 X302, 104.15/104.80 X303:$o]: 104.15/104.80 (in( 104.15/104.80 X302, 104.15/104.80 binunion( 104.15/104.80 X300,X301)) => 104.15/104.80 (( 104.15/104.80 in( 104.15/104.80 X302,X300) => 104.15/104.80 X303) => 104.15/104.80 (( 104.15/104.80 in( 104.15/104.80 X302,X301) => 104.15/104.80 X303) => 104.15/104.80 X303)))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X304, 104.15/104.80 X305,X306]: 104.15/104.80 (in( 104.15/104.80 X306, 104.15/104.80 binunion( 104.15/104.80 X304,X305)) => 104.15/104.80 (in( 104.15/104.80 X306,X305) | 104.15/104.80 in( 104.15/104.80 X306,X304)))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X307, 104.15/104.80 X308]: 104.15/104.80 subset( 104.15/104.80 X307, 104.15/104.80 binunion( 104.15/104.80 X307,X308))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X309, 104.15/104.80 X310]: 104.15/104.80 subset( 104.15/104.80 X310, 104.15/104.80 binunion( 104.15/104.80 X309,X310))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X311, 104.15/104.80 X312,X313]: 104.15/104.80 (in( 104.15/104.80 X313,X311) => 104.15/104.80 (in( 104.15/104.80 X313,X312) => 104.15/104.80 in( 104.15/104.80 X313, 104.15/104.80 binintersect( 104.15/104.80 X311,X312))))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X314, 104.15/104.80 X315,X316]: 104.15/104.80 (subset( 104.15/104.80 X316,X314) => 104.15/104.80 (subset( 104.15/104.80 X316,X315) => 104.15/104.80 subset( 104.15/104.80 X316, 104.15/104.80 binintersect( 104.15/104.80 X314,X315))))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X317, 104.15/104.80 X318,X319]: 104.15/104.80 (in( 104.15/104.80 X319, 104.15/104.80 binintersect( 104.15/104.80 X317,X318)) => 104.15/104.80 in( 104.15/104.80 X319,X317))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X320, 104.15/104.80 X321]: 104.15/104.80 subset( 104.15/104.80 binintersect( 104.15/104.80 X320,X321), 104.15/104.80 X320)) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X322, 104.15/104.80 X323]: 104.15/104.80 (subset( 104.15/104.80 X322,X323) => 104.15/104.80 (binintersect( 104.15/104.80 X322,X323) = 104.15/104.80 X322))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X324, 104.15/104.80 X325]: 104.15/104.80 (( 104.15/104.80 binintersect( 104.15/104.80 X324,X325) = 104.15/104.80 X325) => 104.15/104.80 subset( 104.15/104.80 X325,X324))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X326, 104.15/104.80 X327,X328]: 104.15/104.80 (in( 104.15/104.80 X328, 104.15/104.80 binintersect( 104.15/104.80 X326,X327)) => 104.15/104.80 in( 104.15/104.80 X328,X327))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X329, 104.15/104.80 X330]: 104.15/104.80 (( 104.15/104.80 ~ 104.15/104.80 ( 104.15/104.80 ?[X331]: 104.15/104.80 (in( 104.15/104.80 X331,X330) & 104.15/104.80 in( 104.15/104.80 X331,X329)))) => 104.15/104.80 (binintersect( 104.15/104.80 X329,X330) = 104.15/104.80 emptyset))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X332, 104.15/104.80 X333]: 104.15/104.80 subset( 104.15/104.80 binintersect( 104.15/104.80 X332,X333), 104.15/104.80 X333)) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X334, 104.15/104.80 X335]: 104.15/104.80 (subset( 104.15/104.80 X335,X334) => 104.15/104.80 (binintersect( 104.15/104.80 X334,X335) = 104.15/104.80 X335))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X336, 104.15/104.80 X337]: 104.15/104.80 (( 104.15/104.80 binintersect( 104.15/104.80 X336,X337) = 104.15/104.80 X336) => 104.15/104.80 subset( 104.15/104.80 X336,X337))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X338, 104.15/104.80 X339,X340]: 104.15/104.80 (binintersect( 104.15/104.80 X338, 104.15/104.80 binunion( 104.15/104.80 X339,X340)) = 104.15/104.80 binunion( 104.15/104.80 binintersect( 104.15/104.80 X338,X339), 104.15/104.80 binintersect( 104.15/104.80 X338,X340)))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X341, 104.15/104.80 X342,X343]: 104.15/104.80 (in( 104.15/104.80 X343,X341) => 104.15/104.80 (( 104.15/104.80 ~ 104.15/104.80 in( 104.15/104.80 X343,X342)) => 104.15/104.80 in( 104.15/104.80 X343, 104.15/104.80 setminus( 104.15/104.80 X341,X342))))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X344, 104.15/104.80 X345,X346]: 104.15/104.80 (in( 104.15/104.80 X346, 104.15/104.80 setminus( 104.15/104.80 X344,X345)) => 104.15/104.80 in( 104.15/104.80 X346,X344))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X347, 104.15/104.80 X348,X349]: 104.15/104.80 (in( 104.15/104.80 X349, 104.15/104.80 setminus( 104.15/104.80 X347,X348)) => 104.15/104.80 (~ 104.15/104.80 in( 104.15/104.80 X349,X348)))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X350, 104.15/104.80 X351]: 104.15/104.80 (subset( 104.15/104.80 X350,X351) => 104.15/104.80 (setminus( 104.15/104.80 X350,X351) = 104.15/104.80 emptyset))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X352, 104.15/104.80 X353,X354]: 104.15/104.80 (( 104.15/104.80 ~ 104.15/104.80 in( 104.15/104.80 X354, 104.15/104.80 setminus( 104.15/104.80 X352,X353))) => 104.15/104.80 (in( 104.15/104.80 X354,X352) => 104.15/104.80 in( 104.15/104.80 X354,X353)))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X355, 104.15/104.80 X356,X357]: 104.15/104.80 (( 104.15/104.80 ~ 104.15/104.80 in( 104.15/104.80 X357, 104.15/104.80 setminus( 104.15/104.80 X355,X356))) => 104.15/104.80 (( 104.15/104.80 ~ 104.15/104.80 in( 104.15/104.80 X357,X356)) => 104.15/104.80 (~ 104.15/104.80 in( 104.15/104.80 X357,X355))))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X358, 104.15/104.80 X359,X360]: 104.15/104.80 (( 104.15/104.80 ~ 104.15/104.80 in( 104.15/104.80 X360,X358)) => 104.15/104.80 (~ 104.15/104.80 in( 104.15/104.80 X360, 104.15/104.80 setminus( 104.15/104.80 X358,X359))))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X361, 104.15/104.80 X362,X363]: 104.15/104.80 (in( 104.15/104.80 X363,X362) => 104.15/104.80 (~ 104.15/104.80 in( 104.15/104.80 X363, 104.15/104.80 setminus( 104.15/104.80 X361,X362))))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X364, 104.15/104.80 X365]: 104.15/104.80 subset( 104.15/104.80 setminus( 104.15/104.80 X364,X365), 104.15/104.80 X364)) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X366, 104.15/104.80 X367]: 104.15/104.80 (( 104.15/104.80 setminus( 104.15/104.80 X366,X367) = 104.15/104.80 emptyset) => 104.15/104.80 subset( 104.15/104.80 X366,X367))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X368, 104.15/104.80 X369,X370]: 104.15/104.80 (in( 104.15/104.80 X370, 104.15/104.80 symdiff( 104.15/104.80 X368,X369)) => 104.15/104.80 (![X371:$o]: 104.15/104.80 (( 104.15/104.80 in( 104.15/104.80 X370,X368) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ~ 104.15/104.80 in( 104.15/104.80 X370,X369)) => 104.15/104.80 X371)) => 104.15/104.80 (( 104.15/104.80 ( 104.15/104.80 ~ 104.15/104.80 in( 104.15/104.80 X370,X368)) => 104.15/104.80 ( 104.15/104.80 in( 104.15/104.80 X370,X369) => 104.15/104.80 X371)) => 104.15/104.80 X371))))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X372, 104.15/104.80 X373,X374]: 104.15/104.80 (in( 104.15/104.80 X374,X372) => 104.15/104.80 (( 104.15/104.80 ~ 104.15/104.80 in( 104.15/104.80 X374,X373)) => 104.15/104.80 in( 104.15/104.80 X374, 104.15/104.80 symdiff( 104.15/104.80 X372,X373))))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X375, 104.15/104.80 X376,X377]: 104.15/104.80 (( 104.15/104.80 ~ 104.15/104.80 in( 104.15/104.80 X377,X375)) => 104.15/104.80 (in( 104.15/104.80 X377,X376) => 104.15/104.80 in( 104.15/104.80 X377, 104.15/104.80 symdiff( 104.15/104.80 X375,X376))))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X378, 104.15/104.80 X379,X380]: 104.15/104.80 (in( 104.15/104.80 X380,X378) => 104.15/104.80 (in( 104.15/104.80 X380,X379) => 104.15/104.80 (~ 104.15/104.80 in( 104.15/104.80 X380, 104.15/104.80 symdiff( 104.15/104.80 X378,X379)))))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X381, 104.15/104.80 X382,X383]: 104.15/104.80 (( 104.15/104.80 ~ 104.15/104.80 in( 104.15/104.80 X383,X381)) => 104.15/104.80 (( 104.15/104.80 ~ 104.15/104.80 in( 104.15/104.80 X383,X382)) => 104.15/104.80 (~ 104.15/104.80 in( 104.15/104.80 X383, 104.15/104.80 symdiff( 104.15/104.80 X381,X382)))))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X384, 104.15/104.80 X385]: 104.15/104.80 in( 104.15/104.80 X385, 104.15/104.80 setadjoin( 104.15/104.80 X384, 104.15/104.80 setadjoin( 104.15/104.80 X385, 104.15/104.80 emptyset)))) => 104.15/104.80 ( 104.15/104.80 ![X386, 104.15/104.80 X387]: 104.15/104.80 in( 104.15/104.80 X386, 104.15/104.80 setunion( 104.15/104.80 setadjoin( 104.15/104.80 setadjoin( 104.15/104.80 X386, 104.15/104.80 emptyset), 104.15/104.80 setadjoin( 104.15/104.80 setadjoin( 104.15/104.80 X386, 104.15/104.80 setadjoin( 104.15/104.80 X387, 104.15/104.80 emptyset)), 104.15/104.80 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 104.15/104.80 tff(zf_stmt_14, negated_conjecture, 104.15/104.80 (~ 104.15/104.80 ((![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))) => 104.15/104.80 ((![X5]: (~in(X5,emptyset))) => 104.15/104.80 ((![X6,X7,X8]: (in(X8,setadjoin(X6,X7)) <=> zip_tseitin0(X8,X7,X6))) => 104.15/104.80 ((![X9,X10]: 104.15/104.80 (in(X10,powerset(X9)) <=> (![X11]: zip_tseitin1(X11,X10,X9)))) => 104.15/104.80 ((![X12,X13]: 104.15/104.80 (in(X13,setunion(X12)) <=> (?[X14]: zip_tseitin2(X14,X13,X12)))) => 104.15/104.80 (in(emptyset,omega) => 104.15/104.80 ((![X15]: (in(X15,omega) => in(setadjoin(X15,X15),omega))) => 104.15/104.80 ((![X16]: 104.15/104.80 (((![X17]: 104.15/104.80 ((in(X17,X16) & in(X17,omega)) => 104.15/104.80 in(setadjoin(X17,X17),X16))) & 104.15/104.80 in(emptyset,X16)) => 104.15/104.80 (![X18]: (in(X18,omega) => in(X18,X16))))) => 104.15/104.80 ((![X19:(($i * $i) > $o),X20]: 104.15/104.80 ((![X21]: 104.15/104.80 (in(X21,X20) => 104.15/104.80 (?[X22]: 104.15/104.80 ((![X23]: (X19(X21,X23) => (X22 = X23))) & 104.15/104.80 X19(X21,X22))))) => 104.15/104.80 (?[X24]: 104.15/104.80 (![X25]: 104.15/104.80 (in(X25,X24) <=> 104.15/104.80 (?[X26]: zip_tseitin3(X26,X25,X20,X19))))))) => 104.15/104.80 ((![X27]: 104.15/104.80 ((?[X28]: in(X28,X27)) => 104.15/104.80 (?[X29]: 104.15/104.80 ((~(?[X30]: (in(X30,X27) & in(X30,X29)))) & in(X29,X27))))) => 104.15/104.80 ((![X31]: 104.15/104.80 (?[X32]: 104.15/104.80 ((![X33]: 104.15/104.80 (((?[X34]: in(X34,X33)) & 104.15/104.80 (![X35]: (in(X35,X33) => in(X35,X31)))) => 104.15/104.80 (?[X36,X37]: 104.15/104.80 ((![X38]: 104.15/104.80 (in(X38,X32) => 104.15/104.80 (in(X37,X38) | 104.15/104.80 (![X39]: (in(X39,X38) => in(X39,X36)))))) & 104.15/104.80 (~(?[X40]: (in(X40,X33) & in(X40,X36)))) & 104.15/104.80 in(X37,X33) & in(X36,X32))))) & 104.15/104.80 (![X41,X42]: 104.15/104.80 ((in(X42,X32) & in(X41,X32)) => 104.15/104.80 ((![X43]: (in(X43,X42) => in(X43,X41))) | 104.15/104.80 (![X44]: (in(X44,X41) => in(X44,X42)))))) & 104.15/104.80 (![X45,X46]: 104.15/104.80 ((in(X46,X31) & in(X45,X31)) => 104.15/104.80 ((![X47]: 104.15/104.80 (in(X47,X32) => (in(X45,X47) <=> in(X46,X47)))) => 104.15/104.80 (X45 = X46)))) & 104.15/104.80 (![X48]: 104.15/104.80 (in(X48,X32) => 104.15/104.80 (![X49]: (in(X49,X48) => in(X49,X31)))))))) => 104.15/104.80 ((![X50:($i > $o)]: 104.15/104.80 ((?[X51]: ((![X52]: (X50(X52) => (X51 = X52))) & X50(X51))) => 104.15/104.80 X50(descr('#ll_0'(X50))))) => 104.15/104.80 ((![X53,X54:($i > $o),X55]: 104.15/104.80 (in(X55,X53) => 104.15/104.80 (X54(X55) => in(X55,dsetconstr(X53,'#ll_0'(X54)))))) => 104.15/104.80 ((![X56,X57:($i > $o),X58]: 104.15/104.80 (in(X58,dsetconstr(X56,'#ll_0'(X57))) => in(X58,X56))) => 104.15/104.80 ((![X59,X60:($i > $o),X61]: 104.15/104.80 (in(X61,dsetconstr(X59,'#ll_0'(X60))) => X60(X61))) => 104.15/104.80 ((![X62:($i > $o)]: 104.15/104.80 ((?[X63]: 104.15/104.80 ((![X64]: (X62(X64) => (X63 = X64))) & X62(X63))) => 104.15/104.80 (?[X65]: 104.15/104.80 ((![X66]: (X62(X66) => (X65 = X66))) & X62(X65))))) => 104.15/104.80 ((![X67:$o,X68]: (in(X68,prop2set(X67)) => X67)) => 104.15/104.80 ((![X69]: (in(X69,emptyset) => (![X70:$o]: X70))) => 104.15/104.80 ((![X71]: (in(X71,emptyset) => $false)) => 104.15/104.80 ((![X72]: (~in(X72,emptyset))) => 104.15/104.80 ((![X73:($i > $o)]: 104.15/104.80 ((?[X74]: 104.15/104.80 ((![X75]: (X73(X75) => (X74 = X75))) & 104.15/104.80 X73(X74))) => 104.15/104.80 (?[X76]: X73(X76)))) => 104.15/104.80 ((![X77,X78]: 104.15/104.80 ((![X79]: (in(X79,X77) => in(X79,X78))) => 104.15/104.80 ((![X80]: (in(X80,X78) => in(X80,X77))) => 104.15/104.80 (X77 = X78)))) => 104.15/104.80 ((![X81]: 104.15/104.80 ((![X82]: (~in(X82,X81))) => (X81 = emptyset))) => 104.15/104.80 ((![X83]: 104.15/104.80 ((![X84]: (~in(X84,X83))) => (X83 = emptyset))) => 104.15/104.80 ((![X85,X86:($i > $o),X87]: 104.15/104.80 (in(X87,X85) => 104.15/104.80 (in(X87,dsetconstr(X85,'#ll_0'(X86))) <=> 104.15/104.80 X86(X87)))) => 104.15/104.80 ((![X88]: 104.15/104.80 ((X88 != emptyset) => (?[X89]: in(X89,X88)))) => 104.15/104.80 ((![X90,X91:($i > $o),X92]: 104.15/104.80 (in(X92,X90) => 104.15/104.80 (X91(X92) => 104.15/104.80 (dsetconstr(X90,'#ll_0'(X91)) != emptyset)))) => 104.15/104.80 ((![X93]: 104.15/104.80 ((?[X94]: in(X94,X93)) => 104.15/104.80 (X93 != emptyset))) => 104.15/104.80 ((![X95,X96]: in(X95,setadjoin(X95,X96))) => 104.15/104.80 (in(emptyset,setadjoin(emptyset,emptyset)) => 104.15/104.80 ((![X97,X98,X99]: 104.15/104.80 (in(X99,X98) => 104.15/104.80 in(X99,setadjoin(X97,X98)))) => 104.15/104.80 ((![X100,X101,X102]: 104.15/104.80 (in(X102,setadjoin(X100,X101)) => 104.15/104.80 (![X103:$o]: 104.15/104.80 (((X102 = X100) => X103) => 104.15/104.80 ((in(X102,X101) => X103) => X103))))) => 104.15/104.80 ((![X104,X105,X106]: 104.15/104.80 (in(X106,setadjoin(X104,X105)) => 104.15/104.80 (in(X106,X105) | (X106 = X104)))) => 104.15/104.80 ((![X107]: 104.15/104.80 (dsetconstr(X107,'#ll_1') = X107)) => 104.15/104.80 ((![X108,X109]: 104.15/104.80 ((![X110]: 104.15/104.80 (in(X110,X109) => in(X110,X108))) => 104.15/104.80 in(X109,powerset(X108)))) => 104.15/104.80 ((![X111]: in(emptyset,powerset(X111))) => 104.15/104.80 ((![X112]: 104.15/104.80 in(emptyset,powerset(X112))) => 104.15/104.80 ((![X113,X114,X115]: 104.15/104.80 (in(X114,powerset(X113)) => 104.15/104.80 (in(X115,X114) => in(X115,X113)))) => 104.15/104.80 ((![X116,X117,X118]: 104.15/104.80 (in(X117,X118) => 104.15/104.80 (in(X118,X116) => 104.15/104.80 in(X117,setunion(X116))))) => 104.15/104.80 ((![X119,X120]: 104.15/104.80 (in(X120,setunion(X119)) => 104.15/104.80 (![X121:$o]: 104.15/104.80 ((![X122]: 104.15/104.80 (in(X120,X122) => 104.15/104.80 (in(X122,X119) => 104.15/104.80 X121))) => 104.15/104.80 X121)))) => 104.15/104.80 ((![X123,X124]: 104.15/104.80 (in(X124,X123) => 104.15/104.80 in(X124, 104.15/104.80 powerset(setunion(X123))))) => 104.15/104.80 ((![X125:($i > $o)]: 104.15/104.80 ((?[X126]: 104.15/104.80 ((![X127]: 104.15/104.80 (X125(X127) => 104.15/104.80 (X126 = X127))) & 104.15/104.80 X125(X126))) => 104.15/104.80 (?[X128]: 104.15/104.80 (![X129]: 104.15/104.80 (X125(X129) <=> 104.15/104.80 (X129 = X128)))))) => 104.15/104.80 ((![X130]: 104.15/104.80 ((X130 != emptyset) => 104.15/104.80 (?[X131]: in(X131,X130)))) => 104.15/104.80 ((![X132,X133]: 104.15/104.80 (in(X132, 104.15/104.80 setadjoin(X133, 104.15/104.80 emptyset)) => 104.15/104.80 (X132 = X133))) => 104.15/104.80 ((![X134,X135]: 104.15/104.80 ((X134 != X135) => 104.15/104.80 (~ 104.15/104.80 in(X135, 104.15/104.80 setadjoin(X134, 104.15/104.80 emptyset))))) => 104.15/104.80 ((![X136,X137]: 104.15/104.80 ((X136 = X137) => 104.15/104.80 in(X136, 104.15/104.80 setadjoin(X137, 104.15/104.80 emptyset)))) => 104.15/104.80 ((![X138,X139]: 104.15/104.80 (in(X138, 104.15/104.80 setadjoin(X139, 104.15/104.80 emptyset)) => 104.15/104.80 in(X139, 104.15/104.80 setadjoin(X138, 104.15/104.80 emptyset)))) => 104.15/104.80 ((![X140,X141,X142]: 104.15/104.80 (in(X142, 104.15/104.80 setadjoin( 104.15/104.80 X140, 104.15/104.80 setadjoin( 104.15/104.80 X141,emptyset))) => 104.15/104.80 ((X142 = X141) | 104.15/104.80 (X142 = X140)))) => 104.15/104.80 ((![X143,X144]: 104.15/104.80 in(X143, 104.15/104.80 setadjoin( 104.15/104.80 X143, 104.15/104.80 setadjoin( 104.15/104.80 X144,emptyset)))) => 104.15/104.80 ((![X145,X146]: 104.15/104.80 in(X146, 104.15/104.80 setadjoin( 104.15/104.80 X145, 104.15/104.80 setadjoin( 104.15/104.80 X146,emptyset)))) => 104.15/104.80 ((![X147,X148:($i > $o)]: 104.15/104.80 ((?[X149]: 104.15/104.80 (X148(X149) & 104.15/104.80 in(X149,X147))) => 104.15/104.80 ((dsetconstr( 104.15/104.80 X147, 104.15/104.80 '#ll_0'(X148)) = 104.15/104.80 emptyset) => 104.15/104.80 $false))) => 104.15/104.80 ((![X150:($i > $o), 104.15/104.80 X151]: 104.15/104.80 (in(X151,emptyset) => 104.15/104.80 X150(X151))) => 104.15/104.80 ((![X152, 104.15/104.80 X153:($i > $o)]: 104.15/104.80 ((~ 104.15/104.80 (![X154]: 104.15/104.80 (in( 104.15/104.80 X154,X152) => 104.15/104.80 X153(X154)))) => 104.15/104.80 (?[X155]: 104.15/104.80 ((~X153(X155)) & 104.15/104.80 in(X155,X152))))) => 104.15/104.80 ((![X156, 104.15/104.80 X157:($i > $o)]: 104.15/104.80 ((![X158]: 104.15/104.80 (in( 104.15/104.80 X158,X156) => 104.15/104.80 (~ 104.15/104.80 X157( 104.15/104.80 X158)))) => 104.15/104.80 (~ 104.15/104.80 (?[X159]: 104.15/104.80 (X157( 104.15/104.80 X159) & 104.15/104.80 in( 104.15/104.80 X159,X156)))))) => 104.15/104.80 ((![X160, 104.15/104.80 X161:($i > $o)]: 104.15/104.80 ((~ 104.15/104.80 (?[X162]: 104.15/104.80 ( 104.15/104.80 X161( 104.15/104.80 X162) & 104.15/104.80 in( 104.15/104.80 X162,X160)))) => 104.15/104.80 (![X163]: 104.15/104.80 (in( 104.15/104.80 X163,X160) => 104.15/104.80 (~ 104.15/104.80 X161( 104.15/104.80 X163)))))) => 104.15/104.80 ((![X164, 104.15/104.80 X165:( 104.15/104.80 $i > $o)]: 104.15/104.80 ((?[X166]: 104.15/104.80 (( 104.15/104.80 ~ 104.15/104.80 X165( 104.15/104.80 X166)) & 104.15/104.80 in( 104.15/104.80 X166,X164))) => 104.15/104.80 (~ 104.15/104.80 (![X167]: 104.15/104.80 (in( 104.15/104.80 X167,X164) => 104.15/104.80 X165( 104.15/104.80 X167)))))) => 104.15/104.80 ((![X168:$o]: 104.15/104.80 (X168 => 104.15/104.80 in(emptyset, 104.15/104.80 prop2set( 104.15/104.80 X168)))) => 104.15/104.80 ((![X169:$o]: 104.15/104.80 (X169 => 104.15/104.80 set2prop( 104.15/104.80 prop2set( 104.15/104.80 X169)))) => 104.15/104.80 ((![X170, 104.15/104.80 X171:( 104.15/104.80 $i > $o)]: 104.15/104.80 ((~ 104.15/104.80 ( 104.15/104.80 ?[X172]: 104.15/104.80 (X171( 104.15/104.80 X172) & 104.15/104.80 in( 104.15/104.80 X172,X170)))) => 104.15/104.80 (![X173]: 104.15/104.80 (in( 104.15/104.80 X173,X170) => 104.15/104.80 (~ 104.15/104.80 X171( 104.15/104.80 X173)))))) => 104.15/104.80 ((![X174, 104.15/104.80 X175:( 104.15/104.80 $i > $o)]: 104.15/104.80 (( 104.15/104.80 ~ 104.15/104.80 ( 104.15/104.80 ![X176]: 104.15/104.80 (in( 104.15/104.80 X176,X174) => 104.15/104.80 X175( 104.15/104.80 X176)))) => 104.15/104.80 ( 104.15/104.80 ?[X177]: 104.15/104.80 (( 104.15/104.80 ~ 104.15/104.80 X175( 104.15/104.80 X177)) & 104.15/104.80 in( 104.15/104.80 X177,X174))))) => 104.15/104.80 ((![X178:( 104.15/104.80 $i > $o)]: 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ?[X179]: 104.15/104.80 (( 104.15/104.80 ![X180]: 104.15/104.80 (X178( 104.15/104.80 X180) => 104.15/104.80 (X179 = 104.15/104.80 X180))) & 104.15/104.80 X178( 104.15/104.80 X179))) => 104.15/104.80 ( 104.15/104.80 ?[X181]: 104.15/104.80 (( 104.15/104.80 ![X182]: 104.15/104.80 (X178( 104.15/104.80 X182) => 104.15/104.80 (X181 = 104.15/104.80 X182))) & 104.15/104.80 X178( 104.15/104.80 X181))))) => 104.15/104.80 ((![X183:( 104.15/104.80 $i > $o)]: 104.15/104.80 (( 104.15/104.80 ?[X184]: 104.15/104.80 X183( 104.15/104.80 X184)) => 104.15/104.80 (( 104.15/104.80 ![X185, 104.15/104.80 X186]: 104.15/104.80 (X183( 104.15/104.80 X185) => 104.15/104.80 (X183( 104.15/104.80 X186) => 104.15/104.80 (X185 = 104.15/104.80 X186)))) => 104.15/104.80 (?[X187]: 104.15/104.80 (( 104.15/104.80 ![X188]: 104.15/104.80 (X183( 104.15/104.80 X188) => 104.15/104.80 (X187 = 104.15/104.80 X188))) & 104.15/104.80 X183( 104.15/104.80 X187)))))) => 104.15/104.80 ((![X189:( 104.15/104.80 $i > $o)]: 104.15/104.80 (( 104.15/104.80 ?[X190]: 104.15/104.80 (![X191]: 104.15/104.80 (X189( 104.15/104.80 X191) <=> 104.15/104.80 (X191 = 104.15/104.80 X190)))) => 104.15/104.80 (?[X192]: 104.15/104.80 (( 104.15/104.80 ![X193]: 104.15/104.80 (X189( 104.15/104.80 X193) => 104.15/104.80 (X192 = 104.15/104.80 X193))) & 104.15/104.80 X189( 104.15/104.80 X192))))) => 104.15/104.80 (( 104.15/104.80 ![X194, 104.15/104.80 X195]: 104.15/104.80 (( 104.15/104.80 X194 = 104.15/104.80 X195) => 104.15/104.80 (![X196, 104.15/104.80 X197]: 104.15/104.80 (( 104.15/104.80 X196 = 104.15/104.80 X197) => 104.15/104.80 (in( 104.15/104.80 X196,X194) => 104.15/104.80 in( 104.15/104.80 X197,X195)))))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X198, 104.15/104.80 X199]: 104.15/104.80 (( 104.15/104.80 X198 = 104.15/104.80 X199) => 104.15/104.80 (![X200, 104.15/104.80 X201]: 104.15/104.80 (( 104.15/104.80 X200 = 104.15/104.80 X201) => 104.15/104.80 (in( 104.15/104.80 X200,X198) <=> 104.15/104.80 in( 104.15/104.80 X201,X199)))))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X202:( 104.15/104.80 $i > $o)]: 104.15/104.80 (( 104.15/104.80 ?[X203]: 104.15/104.80 (( 104.15/104.80 ![X204]: 104.15/104.80 (X202( 104.15/104.80 X204) => 104.15/104.80 (X203 = 104.15/104.80 X204))) & 104.15/104.80 X202( 104.15/104.80 X203))) => 104.15/104.80 (![X205, 104.15/104.80 X206]: 104.15/104.80 (X202( 104.15/104.80 X205) => 104.15/104.80 (X202( 104.15/104.80 X206) => 104.15/104.80 (X205 = 104.15/104.80 X206)))))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X207:( 104.15/104.80 $i > $o), 104.15/104.80 X208:( 104.15/104.80 $i > $o)]: 104.15/104.80 (( 104.15/104.80 ![X209, 104.15/104.80 X210]: 104.15/104.80 (( 104.15/104.80 X209 = 104.15/104.80 X210) => 104.15/104.80 (X207( 104.15/104.80 X209) <=> 104.15/104.80 X208( 104.15/104.80 X210)))) => 104.15/104.80 (( 104.15/104.80 ?[X211]: 104.15/104.80 zip_tseitin5( 104.15/104.80 X211,X207)) <=> 104.15/104.80 (?[X213]: 104.15/104.80 zip_tseitin5( 104.15/104.80 X213,X208))))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 emptyset = 104.15/104.80 emptyset) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X215, 104.15/104.80 X216]: 104.15/104.80 (( 104.15/104.80 X215 = 104.15/104.80 X216) => 104.15/104.80 (![X217, 104.15/104.80 X218]: 104.15/104.80 (( 104.15/104.80 X217 = 104.15/104.80 X218) => 104.15/104.80 (setadjoin( 104.15/104.80 X215,X217) = 104.15/104.80 setadjoin( 104.15/104.80 X216,X218)))))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X219, 104.15/104.80 X220]: 104.15/104.80 (( 104.15/104.80 X219 = 104.15/104.80 X220) => 104.15/104.80 (powerset( 104.15/104.80 X219) = 104.15/104.80 powerset( 104.15/104.80 X220)))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X221, 104.15/104.80 X222]: 104.15/104.80 (( 104.15/104.80 X221 = 104.15/104.80 X222) => 104.15/104.80 (setunion( 104.15/104.80 X221) = 104.15/104.80 setunion( 104.15/104.80 X222)))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 omega = 104.15/104.80 omega) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X223:( 104.15/104.80 $i > $o)]: 104.15/104.80 (( 104.15/104.80 ?[X224]: 104.15/104.80 (( 104.15/104.80 ![X225]: 104.15/104.80 (X223( 104.15/104.80 X225) => 104.15/104.80 (X224 = 104.15/104.80 X225))) & 104.15/104.80 X223( 104.15/104.80 X224))) => 104.15/104.80 (![X226, 104.15/104.80 X227]: 104.15/104.80 (X223( 104.15/104.80 X226) => 104.15/104.80 (X223( 104.15/104.80 X227) => 104.15/104.80 (X226 = 104.15/104.80 X227)))))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X228:( 104.15/104.80 $i > $o), 104.15/104.80 X229:( 104.15/104.80 $i > $o)]: 104.15/104.80 (( 104.15/104.80 ![X230, 104.15/104.80 X231]: 104.15/104.80 (( 104.15/104.80 X230 = 104.15/104.80 X231) => 104.15/104.80 (X228( 104.15/104.80 X230) <=> 104.15/104.80 X229( 104.15/104.80 X231)))) => 104.15/104.80 (( 104.15/104.80 ?[X232]: 104.15/104.80 (( 104.15/104.80 ![X233]: 104.15/104.80 (X228( 104.15/104.80 X233) => 104.15/104.80 (X232 = 104.15/104.80 X233))) & 104.15/104.80 X228( 104.15/104.80 X232))) => 104.15/104.80 (( 104.15/104.80 ?[X234]: 104.15/104.80 (( 104.15/104.80 ![X235]: 104.15/104.80 (X229( 104.15/104.80 X235) => 104.15/104.80 (X234 = 104.15/104.80 X235))) & 104.15/104.80 X229( 104.15/104.80 X234))) => 104.15/104.80 (descr( 104.15/104.80 '#ll_0'( 104.15/104.80 X228)) = 104.15/104.80 descr( 104.15/104.80 '#ll_0'( 104.15/104.80 X229))))))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X236, 104.15/104.80 X237]: 104.15/104.80 (( 104.15/104.80 X236 = 104.15/104.80 X237) => 104.15/104.80 (![X238:( 104.15/104.80 $i > $o), 104.15/104.80 X239:( 104.15/104.80 $i > $o)]: 104.15/104.80 (( 104.15/104.80 ![X240]: 104.15/104.80 (in( 104.15/104.80 X240,X236) => 104.15/104.80 (![X241]: 104.15/104.80 (in( 104.15/104.80 X241,X237) => 104.15/104.80 (( 104.15/104.80 X240 = 104.15/104.80 X241) => 104.15/104.80 (X238( 104.15/104.80 X240) <=> 104.15/104.80 X239( 104.15/104.80 X241))))))) => 104.15/104.80 (dsetconstr( 104.15/104.80 X236, 104.15/104.80 '#ll_0'( 104.15/104.80 X238)) = 104.15/104.80 dsetconstr( 104.15/104.80 X237, 104.15/104.80 '#ll_0'( 104.15/104.80 X239))))))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X242, 104.15/104.80 X243]: 104.15/104.80 (( 104.15/104.80 ![X244]: 104.15/104.80 (in( 104.15/104.80 X244,X242) => 104.15/104.80 in( 104.15/104.80 X244,X243))) => 104.15/104.80 subset( 104.15/104.80 X242,X243))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X245, 104.15/104.80 X246]: 104.15/104.80 (( 104.15/104.80 X245 = 104.15/104.80 X246) => 104.15/104.80 subset( 104.15/104.80 X246,X245))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X247, 104.15/104.80 X248]: 104.15/104.80 (( 104.15/104.80 X247 = 104.15/104.80 X248) => 104.15/104.80 subset( 104.15/104.80 X247,X248))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X249, 104.15/104.80 X250]: 104.15/104.80 (( 104.15/104.80 ![X251]: 104.15/104.80 (in( 104.15/104.80 X251,X249) => 104.15/104.80 in( 104.15/104.80 X251,X250))) => 104.15/104.80 subset( 104.15/104.80 X249,X250))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X252]: 104.15/104.80 subset( 104.15/104.80 emptyset, 104.15/104.80 X252)) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X253, 104.15/104.80 X254,X255]: 104.15/104.80 (subset( 104.15/104.80 X253,X254) => 104.15/104.80 (in( 104.15/104.80 X255,X253) => 104.15/104.80 in( 104.15/104.80 X255,X254)))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X256, 104.15/104.80 X257,X258]: 104.15/104.80 (subset( 104.15/104.80 X256,X257) => 104.15/104.80 (( 104.15/104.80 ~ 104.15/104.80 in( 104.15/104.80 X258,X257)) => 104.15/104.80 (~ 104.15/104.80 in( 104.15/104.80 X258,X256))))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X259, 104.15/104.80 X260,X261]: 104.15/104.80 (in( 104.15/104.80 X261,X259) => 104.15/104.80 (( 104.15/104.80 ~ 104.15/104.80 in( 104.15/104.80 X261,X260)) => 104.15/104.80 (~ 104.15/104.80 subset( 104.15/104.80 X259,X260))))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X262, 104.15/104.80 X263]: 104.15/104.80 (( 104.15/104.80 ~ 104.15/104.80 subset( 104.15/104.80 X262,X263)) => 104.15/104.80 (X262 != 104.15/104.80 X263))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X264, 104.15/104.80 X265,X266]: 104.15/104.80 (in( 104.15/104.80 X266,X264) => 104.15/104.80 (( 104.15/104.80 ~ 104.15/104.80 in( 104.15/104.80 X266,X265)) => 104.15/104.80 (X264 != 104.15/104.80 X265)))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X267]: 104.15/104.80 subset( 104.15/104.80 X267,X267)) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X268, 104.15/104.80 X269,X270]: 104.15/104.80 (subset( 104.15/104.80 X268,X269) => 104.15/104.80 (subset( 104.15/104.80 X269,X270) => 104.15/104.80 subset( 104.15/104.80 X268,X270)))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X271, 104.15/104.80 X272]: 104.15/104.80 subset( 104.15/104.80 X272, 104.15/104.80 setadjoin( 104.15/104.80 X271,X272))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X273, 104.15/104.80 X274,X275]: 104.15/104.80 (subset( 104.15/104.80 X273,X275) => 104.15/104.80 subset( 104.15/104.80 X273, 104.15/104.80 setadjoin( 104.15/104.80 X274,X275)))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X276, 104.15/104.80 X277]: 104.15/104.80 (subset( 104.15/104.80 X276,X277) => 104.15/104.80 in( 104.15/104.80 X276, 104.15/104.80 powerset( 104.15/104.80 X277)))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X278, 104.15/104.80 X279]: 104.15/104.80 (subset( 104.15/104.80 X278,X279) => 104.15/104.80 (subset( 104.15/104.80 X279,X278) => 104.15/104.80 (X278 = 104.15/104.80 X279)))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X280]: 104.15/104.80 (subset( 104.15/104.80 X280, 104.15/104.80 emptyset) => 104.15/104.80 (X280 = 104.15/104.80 emptyset))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X281, 104.15/104.80 X282]: 104.15/104.80 (subset( 104.15/104.80 X282,X281) => 104.15/104.80 in( 104.15/104.80 X282, 104.15/104.80 powerset( 104.15/104.80 X281)))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X283, 104.15/104.80 X284]: 104.15/104.80 (in( 104.15/104.80 X284, 104.15/104.80 powerset( 104.15/104.80 X283)) => 104.15/104.80 subset( 104.15/104.80 X284,X283))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X285]: 104.15/104.80 in( 104.15/104.80 X285, 104.15/104.80 powerset( 104.15/104.80 X285))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X286, 104.15/104.80 X287]: 104.15/104.80 (subset( 104.15/104.80 X286,X287) => 104.15/104.80 subset( 104.15/104.80 powerset( 104.15/104.80 X286), 104.15/104.80 powerset( 104.15/104.80 X287)))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X288, 104.15/104.80 X289:( 104.15/104.80 $i > $o)]: 104.15/104.80 in( 104.15/104.80 dsetconstr( 104.15/104.80 X288, 104.15/104.80 '#ll_0'( 104.15/104.80 X289)), 104.15/104.80 powerset( 104.15/104.80 X288))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X290, 104.15/104.80 X291:( 104.15/104.80 $i > $o)]: 104.15/104.80 subset( 104.15/104.80 dsetconstr( 104.15/104.80 X290, 104.15/104.80 '#ll_0'( 104.15/104.80 X291)), 104.15/104.80 X290)) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X292, 104.15/104.80 X293,X294]: 104.15/104.80 (in( 104.15/104.80 X294,X292) => 104.15/104.80 in( 104.15/104.80 X294, 104.15/104.80 binunion( 104.15/104.80 X292,X293)))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X295, 104.15/104.80 X296]: 104.15/104.80 in( 104.15/104.80 X296, 104.15/104.80 setadjoin( 104.15/104.80 X295, 104.15/104.80 setadjoin( 104.15/104.80 X296, 104.15/104.80 emptyset)))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X297, 104.15/104.80 X298,X299]: 104.15/104.80 (in( 104.15/104.80 X299,X298) => 104.15/104.80 in( 104.15/104.80 X299, 104.15/104.80 binunion( 104.15/104.80 X297,X298)))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X300, 104.15/104.80 X301, 104.15/104.80 X302, 104.15/104.80 X303:$o]: 104.15/104.80 (in( 104.15/104.80 X302, 104.15/104.80 binunion( 104.15/104.80 X300,X301)) => 104.15/104.80 (( 104.15/104.80 in( 104.15/104.80 X302,X300) => 104.15/104.80 X303) => 104.15/104.80 (( 104.15/104.80 in( 104.15/104.80 X302,X301) => 104.15/104.80 X303) => 104.15/104.80 X303)))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X304, 104.15/104.80 X305,X306]: 104.15/104.80 (in( 104.15/104.80 X306, 104.15/104.80 binunion( 104.15/104.80 X304,X305)) => 104.15/104.80 (in( 104.15/104.80 X306,X305) | 104.15/104.80 in( 104.15/104.80 X306,X304)))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X307, 104.15/104.80 X308]: 104.15/104.80 subset( 104.15/104.80 X307, 104.15/104.80 binunion( 104.15/104.80 X307,X308))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X309, 104.15/104.80 X310]: 104.15/104.80 subset( 104.15/104.80 X310, 104.15/104.80 binunion( 104.15/104.80 X309,X310))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X311, 104.15/104.80 X312,X313]: 104.15/104.80 (in( 104.15/104.80 X313,X311) => 104.15/104.80 (in( 104.15/104.80 X313,X312) => 104.15/104.80 in( 104.15/104.80 X313, 104.15/104.80 binintersect( 104.15/104.80 X311,X312))))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X314, 104.15/104.80 X315,X316]: 104.15/104.80 (subset( 104.15/104.80 X316,X314) => 104.15/104.80 (subset( 104.15/104.80 X316,X315) => 104.15/104.80 subset( 104.15/104.80 X316, 104.15/104.80 binintersect( 104.15/104.80 X314,X315))))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X317, 104.15/104.80 X318,X319]: 104.15/104.80 (in( 104.15/104.80 X319, 104.15/104.80 binintersect( 104.15/104.80 X317,X318)) => 104.15/104.80 in( 104.15/104.80 X319,X317))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X320, 104.15/104.80 X321]: 104.15/104.80 subset( 104.15/104.80 binintersect( 104.15/104.80 X320,X321), 104.15/104.80 X320)) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X322, 104.15/104.80 X323]: 104.15/104.80 (subset( 104.15/104.80 X322,X323) => 104.15/104.80 (binintersect( 104.15/104.80 X322,X323) = 104.15/104.80 X322))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X324, 104.15/104.80 X325]: 104.15/104.80 (( 104.15/104.80 binintersect( 104.15/104.80 X324,X325) = 104.15/104.80 X325) => 104.15/104.80 subset( 104.15/104.80 X325,X324))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X326, 104.15/104.80 X327,X328]: 104.15/104.80 (in( 104.15/104.80 X328, 104.15/104.80 binintersect( 104.15/104.80 X326,X327)) => 104.15/104.80 in( 104.15/104.80 X328,X327))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X329, 104.15/104.80 X330]: 104.15/104.80 (( 104.15/104.80 ~ 104.15/104.80 ( 104.15/104.80 ?[X331]: 104.15/104.80 (in( 104.15/104.80 X331,X330) & 104.15/104.80 in( 104.15/104.80 X331,X329)))) => 104.15/104.80 (binintersect( 104.15/104.80 X329,X330) = 104.15/104.80 emptyset))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X332, 104.15/104.80 X333]: 104.15/104.80 subset( 104.15/104.80 binintersect( 104.15/104.80 X332,X333), 104.15/104.80 X333)) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X334, 104.15/104.80 X335]: 104.15/104.80 (subset( 104.15/104.80 X335,X334) => 104.15/104.80 (binintersect( 104.15/104.80 X334,X335) = 104.15/104.80 X335))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X336, 104.15/104.80 X337]: 104.15/104.80 (( 104.15/104.80 binintersect( 104.15/104.80 X336,X337) = 104.15/104.80 X336) => 104.15/104.80 subset( 104.15/104.80 X336,X337))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X338, 104.15/104.80 X339,X340]: 104.15/104.80 (binintersect( 104.15/104.80 X338, 104.15/104.80 binunion( 104.15/104.80 X339,X340)) = 104.15/104.80 binunion( 104.15/104.80 binintersect( 104.15/104.80 X338,X339), 104.15/104.80 binintersect( 104.15/104.80 X338,X340)))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X341, 104.15/104.80 X342,X343]: 104.15/104.80 (in( 104.15/104.80 X343,X341) => 104.15/104.80 (( 104.15/104.80 ~ 104.15/104.80 in( 104.15/104.80 X343,X342)) => 104.15/104.80 in( 104.15/104.80 X343, 104.15/104.80 setminus( 104.15/104.80 X341,X342))))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X344, 104.15/104.80 X345,X346]: 104.15/104.80 (in( 104.15/104.80 X346, 104.15/104.80 setminus( 104.15/104.80 X344,X345)) => 104.15/104.80 in( 104.15/104.80 X346,X344))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X347, 104.15/104.80 X348,X349]: 104.15/104.80 (in( 104.15/104.80 X349, 104.15/104.80 setminus( 104.15/104.80 X347,X348)) => 104.15/104.80 (~ 104.15/104.80 in( 104.15/104.80 X349,X348)))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X350, 104.15/104.80 X351]: 104.15/104.80 (subset( 104.15/104.80 X350,X351) => 104.15/104.80 (setminus( 104.15/104.80 X350,X351) = 104.15/104.80 emptyset))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X352, 104.15/104.80 X353,X354]: 104.15/104.80 (( 104.15/104.80 ~ 104.15/104.80 in( 104.15/104.80 X354, 104.15/104.80 setminus( 104.15/104.80 X352,X353))) => 104.15/104.80 (in( 104.15/104.80 X354,X352) => 104.15/104.80 in( 104.15/104.80 X354,X353)))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X355, 104.15/104.80 X356,X357]: 104.15/104.80 (( 104.15/104.80 ~ 104.15/104.80 in( 104.15/104.80 X357, 104.15/104.80 setminus( 104.15/104.80 X355,X356))) => 104.15/104.80 (( 104.15/104.80 ~ 104.15/104.80 in( 104.15/104.80 X357,X356)) => 104.15/104.80 (~ 104.15/104.80 in( 104.15/104.80 X357,X355))))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X358, 104.15/104.80 X359,X360]: 104.15/104.80 (( 104.15/104.80 ~ 104.15/104.80 in( 104.15/104.80 X360,X358)) => 104.15/104.80 (~ 104.15/104.80 in( 104.15/104.80 X360, 104.15/104.80 setminus( 104.15/104.80 X358,X359))))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X361, 104.15/104.80 X362,X363]: 104.15/104.80 (in( 104.15/104.80 X363,X362) => 104.15/104.80 (~ 104.15/104.80 in( 104.15/104.80 X363, 104.15/104.80 setminus( 104.15/104.80 X361,X362))))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X364, 104.15/104.80 X365]: 104.15/104.80 subset( 104.15/104.80 setminus( 104.15/104.80 X364,X365), 104.15/104.80 X364)) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X366, 104.15/104.80 X367]: 104.15/104.80 (( 104.15/104.80 setminus( 104.15/104.80 X366,X367) = 104.15/104.80 emptyset) => 104.15/104.80 subset( 104.15/104.80 X366,X367))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X368, 104.15/104.80 X369,X370]: 104.15/104.80 (in( 104.15/104.80 X370, 104.15/104.80 symdiff( 104.15/104.80 X368,X369)) => 104.15/104.80 (![X371:$o]: 104.15/104.80 (( 104.15/104.80 in( 104.15/104.80 X370,X368) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ~ 104.15/104.80 in( 104.15/104.80 X370,X369)) => 104.15/104.80 X371)) => 104.15/104.80 (( 104.15/104.80 ( 104.15/104.80 ~ 104.15/104.80 in( 104.15/104.80 X370,X368)) => 104.15/104.80 ( 104.15/104.80 in( 104.15/104.80 X370,X369) => 104.15/104.80 X371)) => 104.15/104.80 X371))))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X372, 104.15/104.80 X373,X374]: 104.15/104.80 (in( 104.15/104.80 X374,X372) => 104.15/104.80 (( 104.15/104.80 ~ 104.15/104.80 in( 104.15/104.80 X374,X373)) => 104.15/104.80 in( 104.15/104.80 X374, 104.15/104.80 symdiff( 104.15/104.80 X372,X373))))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X375, 104.15/104.80 X376,X377]: 104.15/104.80 (( 104.15/104.80 ~ 104.15/104.80 in( 104.15/104.80 X377,X375)) => 104.15/104.80 (in( 104.15/104.80 X377,X376) => 104.15/104.80 in( 104.15/104.80 X377, 104.15/104.80 symdiff( 104.15/104.80 X375,X376))))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X378, 104.15/104.80 X379,X380]: 104.15/104.80 (in( 104.15/104.80 X380,X378) => 104.15/104.80 (in( 104.15/104.80 X380,X379) => 104.15/104.80 (~ 104.15/104.80 in( 104.15/104.80 X380, 104.15/104.80 symdiff( 104.15/104.80 X378,X379)))))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X381, 104.15/104.80 X382,X383]: 104.15/104.80 (( 104.15/104.80 ~ 104.15/104.80 in( 104.15/104.80 X383,X381)) => 104.15/104.80 (( 104.15/104.80 ~ 104.15/104.80 in( 104.15/104.80 X383,X382)) => 104.15/104.80 (~ 104.15/104.80 in( 104.15/104.80 X383, 104.15/104.80 symdiff( 104.15/104.80 X381,X382)))))) => 104.15/104.80 ( 104.15/104.80 ( 104.15/104.80 ![X384, 104.15/104.80 X385]: 104.15/104.80 in( 104.15/104.80 X385, 104.15/104.80 setadjoin( 104.15/104.80 X384, 104.15/104.80 setadjoin( 104.15/104.80 X385, 104.15/104.80 emptyset)))) => 104.15/104.80 ( 104.15/104.80 ![X386, 104.15/104.80 X387]: 104.15/104.80 in( 104.15/104.80 X386, 104.15/104.80 setunion( 104.15/104.80 setadjoin( 104.15/104.80 setadjoin( 104.15/104.80 X386, 104.15/104.80 emptyset), 104.15/104.80 setadjoin( 104.15/104.80 setadjoin( 104.15/104.80 X386, 104.15/104.80 setadjoin( 104.15/104.80 X387, 104.15/104.80 emptyset)), 104.15/104.80 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 104.15/104.80 tff('135', plain, ![X439, X440]: in(X439, setadjoin(X439, X440)), 104.15/104.80 inference('cnf', [status(esa)], [zf_stmt_14])). 104.15/104.80 tff('136', plain, 104.15/104.80 ~ in(sk_X386_, 104.15/104.80 setunion( 104.15/104.80 setadjoin(setadjoin(sk_X386_, emptyset), 104.15/104.80 setadjoin(setadjoin(sk_X386_, setadjoin(sk_X387_, emptyset)), 104.15/104.80 emptyset)))), 104.15/104.80 inference('cnf', [status(esa)], [zf_stmt_14])). 104.15/104.80 tff('137', plain, 104.15/104.80 ![X573, X574]: in(X573, setadjoin(X574, setadjoin(X573, emptyset))), 104.15/104.80 inference('cnf', [status(esa)], [zf_stmt_14])). 104.15/104.80 tff('138', plain, 104.15/104.80 ![X450, X451, X452]: 104.15/104.80 (in(X450, setunion(X451)) | ~ in(X450, X452) | ~ in(X452, X451)), 104.15/104.80 inference('cnf', [status(esa)], [zf_stmt_14])). 104.15/104.80 tff('139', plain, $false, 104.15/104.80 inference('eprover', [status(thm)], ['135', '136', '137', '138'])). 104.15/104.80 104.15/104.80 % SZS output end Refutation 104.15/104.80 % Zipperpin 1.5 exiting 104.15/104.81 EOF