0.04/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.04/0.13 % Command : run_portfolio.sh /export/starexec/sandbox/benchmark/theBenchmark.p /export/starexec/sandbox/tmp/tmp.Q70uateFr7 0.13/0.34 % Computer : n007.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 180 0.13/0.34 % DateTime : Thu Aug 29 14:56:51 EDT 2019 0.13/0.34 % CPUTime : 87.78/88.36 % Running portfolio for 180 s 87.78/88.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 87.78/88.36 % TempDir : /export/starexec/sandbox/tmp/tmp.Q70uateFr7 87.78/88.36 % Recognized as monomorphic HO. 87.78/88.36 % Running /export/starexec/sandbox/solver/bin/competitive.sh for 18 87.78/88.36 % Running /export/starexec/sandbox/solver/bin/competitive.2.sh for 13 87.78/88.36 % Running /export/starexec/sandbox/solver/bin/competitive.3.sh for 3 87.78/88.36 % Running /export/starexec/sandbox/solver/bin/pragmatic.rudimentary.sh for 28 87.78/88.36 % Running /export/starexec/sandbox/solver/bin/pragmatic.rudimentary.1.sh for 12 87.78/88.36 % Running /export/starexec/sandbox/solver/bin/pragmatic.rudimentary.2.sh for 7 87.78/88.36 % Running /export/starexec/sandbox/solver/bin/pragmatic.shallow.sh for 3 87.78/88.36 % Running /export/starexec/sandbox/solver/bin/pragmatic.shallow.1.sh for 14 87.78/88.36 % Solved by: pragmatic.shallow.1.sh 87.78/88.36 % done 1171 iterations in 3.961s 87.78/88.36 % hashcons stats for terms: size 4096, num 26232, sum length 38752, buckets: small 0, median 7, big 22 87.78/88.36 % proof state stats: {active 279, passive 9778, simpl 0} 87.78/88.36 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 87.78/88.36 % SZS output start Refutation 87.78/88.36 tff(symdiff, axiom, symdiff() = 87.78/88.36 ^[A,B]: dsetconstr(binunion(A,B),^[Xx]: ((~in(Xx,B)) | (~in(Xx,A))))). 87.78/88.36 tff('0', plain, 87.78/88.36 symdiff = 87.78/88.36 (^[V_1,V_2]: 87.78/88.36 dsetconstr(binunion(V_1,V_2),^[V_3]: ((~in(V_3,V_2)) | (~in(V_3,V_1))))), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(setminusSubset1, axiom, setminusSubset1 <=> 87.78/88.36 (![A,B]: ((setminus(A,B) = emptyset) => subset(A,B)))). 87.78/88.36 tff('1', plain, 87.78/88.36 setminusSubset1 = 87.78/88.36 (![X2,X3]: ((setminus(X2,X3) = emptyset) => subset(X2,X3))), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(setminusLsub, axiom, setminusLsub <=> (![A,B]: subset(setminus(A,B),A))). 87.78/88.36 tff('2', plain, setminusLsub = (![X2,X3]: subset(setminus(X2,X3),X2)), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(setminusIRneg, axiom, setminusIRneg <=> 87.78/88.36 (![A,B,Xx]: (in(Xx,B) => (~in(Xx,setminus(A,B)))))). 87.78/88.36 tff('3', plain, 87.78/88.36 setminusIRneg = (![X2,X3,X4]: (in(X4,X3) => (~in(X4,setminus(X2,X3))))), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(setminusILneg, axiom, setminusILneg <=> 87.78/88.36 (![A,B,Xx]: ((~in(Xx,A)) => (~in(Xx,setminus(A,B)))))). 87.78/88.36 tff('4', plain, 87.78/88.36 setminusILneg = 87.78/88.36 (![X2,X3,X4]: ((~in(X4,X2)) => (~in(X4,setminus(X2,X3))))), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(setminusELneg, axiom, setminusELneg <=> 87.78/88.36 (![A,B,Xx]: ((~in(Xx,setminus(A,B))) => ((~in(Xx,B)) => (~in(Xx,A)))))). 87.78/88.36 tff('5', plain, 87.78/88.36 setminusELneg = 87.78/88.36 (![X2,X3,X4]: 87.78/88.36 ((~in(X4,setminus(X2,X3))) => ((~in(X4,X3)) => (~in(X4,X2))))), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(setminusERneg, axiom, setminusERneg <=> 87.78/88.36 (![A,B,Xx]: ((~in(Xx,setminus(A,B))) => (in(Xx,A) => in(Xx,B))))). 87.78/88.36 tff('6', plain, 87.78/88.36 setminusERneg = 87.78/88.36 (![X2,X3,X4]: ((~in(X4,setminus(X2,X3))) => (in(X4,X2) => in(X4,X3)))), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(setminusSubset2, axiom, setminusSubset2 <=> 87.78/88.36 (![A,B]: (subset(A,B) => (setminus(A,B) = emptyset)))). 87.78/88.36 tff('7', plain, 87.78/88.36 setminusSubset2 = 87.78/88.36 (![X2,X3]: (subset(X2,X3) => (setminus(X2,X3) = emptyset))), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(setminusER, axiom, setminusER <=> 87.78/88.36 (![A,B,Xx]: (in(Xx,setminus(A,B)) => (~in(Xx,B))))). 87.78/88.36 tff('8', plain, 87.78/88.36 setminusER = (![X2,X3,X4]: (in(X4,setminus(X2,X3)) => (~in(X4,X3)))), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(setminusEL, axiom, setminusEL <=> 87.78/88.36 (![A,B,Xx]: (in(Xx,setminus(A,B)) => in(Xx,A)))). 87.78/88.36 tff('9', plain, 87.78/88.36 setminusEL = (![X2,X3,X4]: (in(X4,setminus(X2,X3)) => in(X4,X2))), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(setminusI, axiom, setminusI <=> 87.78/88.36 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => in(Xx,setminus(A,B)))))). 87.78/88.36 tff('10', plain, 87.78/88.36 setminusI = 87.78/88.36 (![X2,X3,X4]: (in(X4,X2) => ((~in(X4,X3)) => in(X4,setminus(X2,X3))))), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(bs114d, axiom, bs114d <=> 87.78/88.36 (![A,B,C]: 87.78/88.36 (binintersect(A,binunion(B,C)) = 87.78/88.36 binunion(binintersect(A,B),binintersect(A,C))))). 87.78/88.36 tff('11', plain, 87.78/88.36 bs114d = 87.78/88.36 (![X2,X3,X4]: 87.78/88.36 (binintersect(X2,binunion(X3,X4)) = 87.78/88.36 binunion(binintersect(X2,X3),binintersect(X2,X4)))), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(binintersectSubset1, axiom, binintersectSubset1 <=> 87.78/88.36 (![A,B]: ((binintersect(A,B) = A) => subset(A,B)))). 87.78/88.36 tff('12', plain, 87.78/88.36 binintersectSubset1 = 87.78/88.36 (![X2,X3]: ((binintersect(X2,X3) = X2) => subset(X2,X3))), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(binintersectSubset4, axiom, binintersectSubset4 <=> 87.78/88.36 (![A,B]: (subset(B,A) => (binintersect(A,B) = B)))). 87.78/88.36 tff('13', plain, 87.78/88.36 binintersectSubset4 = 87.78/88.36 (![X2,X3]: (subset(X3,X2) => (binintersect(X2,X3) = X3))), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(binintersectRsub, axiom, binintersectRsub <=> 87.78/88.36 (![A,B]: subset(binintersect(A,B),B))). 87.78/88.36 tff('14', plain, 87.78/88.36 binintersectRsub = (![X2,X3]: subset(binintersect(X2,X3),X3)), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(disjointsetsI1, axiom, disjointsetsI1 <=> 87.78/88.36 (![A,B]: 87.78/88.36 ((~(?[Xx]: (in(Xx,B) & in(Xx,A)))) => (binintersect(A,B) = emptyset)))). 87.78/88.36 tff('15', plain, 87.78/88.36 disjointsetsI1 = 87.78/88.36 (![X2,X3]: 87.78/88.36 ((~(?[X4]: (in(X4,X3) & in(X4,X2)))) => 87.78/88.36 (binintersect(X2,X3) = emptyset))), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(binintersectER, axiom, binintersectER <=> 87.78/88.36 (![A,B,Xx]: (in(Xx,binintersect(A,B)) => in(Xx,B)))). 87.78/88.36 tff('16', plain, 87.78/88.36 binintersectER = (![X2,X3,X4]: (in(X4,binintersect(X2,X3)) => in(X4,X3))), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(binintersectSubset3, axiom, binintersectSubset3 <=> 87.78/88.36 (![A,B]: ((binintersect(A,B) = B) => subset(B,A)))). 87.78/88.36 tff('17', plain, 87.78/88.36 binintersectSubset3 = 87.78/88.36 (![X2,X3]: ((binintersect(X2,X3) = X3) => subset(X3,X2))), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(binintersectSubset2, axiom, binintersectSubset2 <=> 87.78/88.36 (![A,B]: (subset(A,B) => (binintersect(A,B) = A)))). 87.78/88.36 tff('18', plain, 87.78/88.36 binintersectSubset2 = 87.78/88.36 (![X2,X3]: (subset(X2,X3) => (binintersect(X2,X3) = X2))), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(binintersectLsub, axiom, binintersectLsub <=> 87.78/88.36 (![A,B]: subset(binintersect(A,B),A))). 87.78/88.36 tff('19', plain, 87.78/88.36 binintersectLsub = (![X2,X3]: subset(binintersect(X2,X3),X2)), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(binintersectEL, axiom, binintersectEL <=> 87.78/88.36 (![A,B,Xx]: (in(Xx,binintersect(A,B)) => in(Xx,A)))). 87.78/88.36 tff('20', plain, 87.78/88.36 binintersectEL = (![X2,X3,X4]: (in(X4,binintersect(X2,X3)) => in(X4,X2))), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(binintersectSubset5, axiom, binintersectSubset5 <=> 87.78/88.36 (![A,B,C]: (subset(C,A) => (subset(C,B) => subset(C,binintersect(A,B)))))). 87.78/88.36 tff('21', plain, 87.78/88.36 binintersectSubset5 = 87.78/88.36 (![X2,X3,X4]: 87.78/88.36 (subset(X4,X2) => (subset(X4,X3) => subset(X4,binintersect(X2,X3))))), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(binintersectI, axiom, binintersectI <=> 87.78/88.36 (![A,B,Xx]: (in(Xx,A) => (in(Xx,B) => in(Xx,binintersect(A,B)))))). 87.78/88.36 tff('22', plain, 87.78/88.36 binintersectI = 87.78/88.36 (![X2,X3,X4]: (in(X4,X2) => (in(X4,X3) => in(X4,binintersect(X2,X3))))), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(binunionRsub, axiom, binunionRsub <=> (![A,B]: subset(B,binunion(A,B)))). 87.78/88.36 tff('23', plain, binunionRsub = (![X2,X3]: subset(X3,binunion(X2,X3))), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(binunionLsub, axiom, binunionLsub <=> (![A,B]: subset(A,binunion(A,B)))). 87.78/88.36 tff('24', plain, binunionLsub = (![X2,X3]: subset(X2,binunion(X2,X3))), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(binunionE, axiom, binunionE <=> 87.78/88.36 (![A,B,Xx]: (in(Xx,binunion(A,B)) => (in(Xx,B) | in(Xx,A))))). 87.78/88.36 tff('25', plain, 87.78/88.36 binunionE = 87.78/88.36 (![X2,X3,X4]: (in(X4,binunion(X2,X3)) => (in(X4,X3) | in(X4,X2)))), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(binunionEcases, axiom, binunionEcases <=> 87.78/88.36 (![A,B,Xx,Xphi:$o]: 87.78/88.36 (in(Xx,binunion(A,B)) => 87.78/88.36 ((in(Xx,A) => Xphi) => ((in(Xx,B) => Xphi) => Xphi))))). 87.78/88.36 tff('26', plain, 87.78/88.36 binunionEcases = 87.78/88.36 (![X2,X3,X4,X5:$o]: 87.78/88.36 (in(X4,binunion(X2,X3)) => 87.78/88.36 ((in(X4,X2) => X5) => ((in(X4,X3) => X5) => X5)))), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(binunionIR, axiom, binunionIR <=> 87.78/88.36 (![A,B,Xx]: (in(Xx,B) => in(Xx,binunion(A,B))))). 87.78/88.36 tff('27', plain, 87.78/88.36 binunionIR = (![X2,X3,X4]: (in(X4,X3) => in(X4,binunion(X2,X3)))), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(upairset2IR, axiom, upairset2IR <=> 87.78/88.36 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 87.78/88.36 tff('28', plain, 87.78/88.36 upairset2IR = (![X2,X3]: in(X3,setadjoin(X2,setadjoin(X3,emptyset)))), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(binunionIL, axiom, binunionIL <=> 87.78/88.36 (![A,B,Xx]: (in(Xx,A) => in(Xx,binunion(A,B))))). 87.78/88.36 tff('29', plain, 87.78/88.36 binunionIL = (![X2,X3,X4]: (in(X4,X2) => in(X4,binunion(X2,X3)))), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(sepSubset, axiom, sepSubset <=> 87.78/88.36 (![A,Xphi:($i > $o)]: subset(dsetconstr(A,^[Xx]: Xphi(Xx)),A))). 87.78/88.36 tff('30', plain, 87.78/88.36 sepSubset = 87.78/88.36 (![X2,X3:($i > $o)]: subset(dsetconstr(X2,^[V_1]: X3(V_1)),X2)), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(sepInPowerset, axiom, sepInPowerset <=> 87.78/88.36 (![A,Xphi:($i > $o)]: in(dsetconstr(A,^[Xx]: Xphi(Xx)),powerset(A)))). 87.78/88.36 tff('31', plain, 87.78/88.36 sepInPowerset = 87.78/88.36 (![X2,X3:($i > $o)]: in(dsetconstr(X2,^[V_1]: X3(V_1)),powerset(X2))), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(powersetsubset, axiom, powersetsubset <=> 87.78/88.36 (![A,B]: (subset(A,B) => subset(powerset(A),powerset(B))))). 87.78/88.36 tff('32', plain, 87.78/88.36 powersetsubset = 87.78/88.36 (![X2,X3]: (subset(X2,X3) => subset(powerset(X2),powerset(X3)))), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(inPowerset, axiom, inPowerset <=> (![A]: in(A,powerset(A)))). 87.78/88.36 tff('33', plain, inPowerset = (![X2]: in(X2,powerset(X2))), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(powersetE1, axiom, powersetE1 <=> 87.78/88.36 (![A,B]: (in(B,powerset(A)) => subset(B,A)))). 87.78/88.36 tff('34', plain, 87.78/88.36 powersetE1 = (![X2,X3]: (in(X3,powerset(X2)) => subset(X3,X2))), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(powersetI1, axiom, powersetI1 <=> 87.78/88.36 (![A,B]: (subset(B,A) => in(B,powerset(A))))). 87.78/88.36 tff('35', plain, 87.78/88.36 powersetI1 = (![X2,X3]: (subset(X3,X2) => in(X3,powerset(X2)))), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(subsetemptysetimpeq, axiom, subsetemptysetimpeq <=> 87.78/88.36 (![A]: (subset(A,emptyset) => (A = emptyset)))). 87.78/88.36 tff('36', plain, 87.78/88.36 subsetemptysetimpeq = (![X2]: (subset(X2,emptyset) => (X2 = emptyset))), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(setextsub, axiom, setextsub <=> 87.78/88.36 (![A,B]: (subset(A,B) => (subset(B,A) => (A = B))))). 87.78/88.36 tff('37', plain, 87.78/88.36 setextsub = (![X2,X3]: (subset(X2,X3) => (subset(X3,X2) => (X2 = X3)))), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(subset2powerset, axiom, subset2powerset <=> 87.78/88.36 (![A,B]: (subset(A,B) => in(A,powerset(B))))). 87.78/88.36 tff('38', plain, 87.78/88.36 subset2powerset = (![X2,X3]: (subset(X2,X3) => in(X2,powerset(X3)))), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(setadjoinSub2, axiom, setadjoinSub2 <=> 87.78/88.36 (![A,Xx,B]: (subset(A,B) => subset(A,setadjoin(Xx,B))))). 87.78/88.36 tff('39', plain, 87.78/88.36 setadjoinSub2 = 87.78/88.36 (![X2,X3,X4]: (subset(X2,X4) => subset(X2,setadjoin(X3,X4)))), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(setadjoinSub, axiom, setadjoinSub <=> 87.78/88.36 (![Xx,A]: subset(A,setadjoin(Xx,A)))). 87.78/88.36 tff('40', plain, setadjoinSub = (![X2,X3]: subset(X3,setadjoin(X2,X3))), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(subsetTrans, axiom, subsetTrans <=> 87.78/88.36 (![A,B,C]: (subset(A,B) => (subset(B,C) => subset(A,C))))). 87.78/88.36 tff('41', plain, 87.78/88.36 subsetTrans = 87.78/88.36 (![X2,X3,X4]: (subset(X2,X3) => (subset(X3,X4) => subset(X2,X4)))), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(subsetRefl, axiom, subsetRefl <=> (![A]: subset(A,A))). 87.78/88.36 tff('42', plain, subsetRefl = (![X2]: subset(X2,X2)), define([status(thm)])). 87.78/88.36 tff(notequalI2, axiom, notequalI2 <=> 87.78/88.36 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => (A != B))))). 87.78/88.36 tff('43', plain, 87.78/88.36 notequalI2 = (![X2,X3,X4]: (in(X4,X2) => ((~in(X4,X3)) => (X2 != X3)))), 87.78/88.36 define([status(thm)])). 87.78/88.36 tff(notequalI1, axiom, notequalI1 <=> (![A,B]: ((~subset(A,B)) => (A != B)))). 87.78/88.37 tff('44', plain, notequalI1 = (![X2,X3]: ((~subset(X2,X3)) => (X2 != X3))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(notsubsetI, axiom, notsubsetI <=> 87.78/88.37 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => (~subset(A,B)))))). 87.78/88.37 tff('45', plain, 87.78/88.37 notsubsetI = 87.78/88.37 (![X2,X3,X4]: (in(X4,X2) => ((~in(X4,X3)) => (~subset(X2,X3))))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(subsetE2, axiom, subsetE2 <=> 87.78/88.37 (![A,B,Xx]: (subset(A,B) => ((~in(Xx,B)) => (~in(Xx,A)))))). 87.78/88.37 tff('46', plain, 87.78/88.37 subsetE2 = 87.78/88.37 (![X2,X3,X4]: (subset(X2,X3) => ((~in(X4,X3)) => (~in(X4,X2))))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(subsetE, axiom, subsetE <=> 87.78/88.37 (![A,B,Xx]: (subset(A,B) => (in(Xx,A) => in(Xx,B))))). 87.78/88.37 tff('47', plain, 87.78/88.37 subsetE = (![X2,X3,X4]: (subset(X2,X3) => (in(X4,X2) => in(X4,X3)))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(emptysetsubset, axiom, emptysetsubset <=> (![A]: subset(emptyset,A))). 87.78/88.37 tff('48', plain, emptysetsubset = (![X2]: subset(emptyset,X2)), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(subsetI2, axiom, subsetI2 <=> 87.78/88.37 (![A,B]: ((![Xx]: (in(Xx,A) => in(Xx,B))) => subset(A,B)))). 87.78/88.37 tff('49', plain, 87.78/88.37 subsetI2 = 87.78/88.37 (![X2,X3]: ((![X4]: (in(X4,X2) => in(X4,X3))) => subset(X2,X3))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(eqimpsubset1, axiom, eqimpsubset1 <=> (![A,B]: ((A = B) => subset(A,B)))). 87.78/88.37 tff('50', plain, eqimpsubset1 = (![X2,X3]: ((X2 = X3) => subset(X2,X3))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(eqimpsubset2, axiom, eqimpsubset2 <=> (![A,B]: ((A = B) => subset(B,A)))). 87.78/88.37 tff('51', plain, eqimpsubset2 = (![X2,X3]: ((X2 = X3) => subset(X3,X2))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(subsetI1, axiom, subsetI1 <=> 87.78/88.37 (![A,B]: ((![Xx]: (in(Xx,A) => in(Xx,B))) => subset(A,B)))). 87.78/88.37 tff('52', plain, 87.78/88.37 subsetI1 = 87.78/88.37 (![X2,X3]: ((![X4]: (in(X4,X2) => in(X4,X3))) => subset(X2,X3))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(dsetconstr__Cong, axiom, dsetconstr__Cong <=> 87.78/88.37 (![A,B]: 87.78/88.37 ((A = B) => 87.78/88.37 (![Xphi:($i > $o),Xpsi:($i > $o)]: 87.78/88.37 ((![Xx]: 87.78/88.37 (in(Xx,A) => 87.78/88.37 (![Xy]: (in(Xy,B) => ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy))))))) => 87.78/88.37 (dsetconstr(A,^[Xx]: Xphi(Xx)) = dsetconstr(B,^[Xx]: Xpsi(Xx)))))))). 87.78/88.37 tff('53', plain, 87.78/88.37 dsetconstr__Cong = 87.78/88.37 (![X2,X3]: 87.78/88.37 ((X2 = X3) => 87.78/88.37 (![X4:($i > $o),X5:($i > $o)]: 87.78/88.37 ((![X6]: 87.78/88.37 (in(X6,X2) => 87.78/88.37 (![X7]: (in(X7,X3) => ((X6 = X7) => (X4(X6) <=> X5(X7))))))) => 87.78/88.37 (dsetconstr(X2,^[V_1]: X4(V_1)) = dsetconstr(X3,^[V_2]: X5(V_2))))))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(descr__Cong, axiom, descr__Cong <=> 87.78/88.37 (![Xphi:($i > $o),Xpsi:($i > $o)]: 87.78/88.37 ((![Xx,Xy]: ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy)))) => 87.78/88.37 (exu(^[Xx]: Xphi(Xx)) => 87.78/88.37 (exu(^[Xx]: Xpsi(Xx)) => 87.78/88.37 (descr(^[Xx]: Xphi(Xx)) = descr(^[Xx]: Xpsi(Xx)))))))). 87.78/88.37 tff('54', plain, 87.78/88.37 descr__Cong = 87.78/88.37 (![X2:($i > $o),X3:($i > $o)]: 87.78/88.37 ((![X4,X5]: ((X4 = X5) => (X2(X4) <=> X3(X5)))) => 87.78/88.37 (exu(^[V_1]: X2(V_1)) => 87.78/88.37 (exu(^[V_2]: X3(V_2)) => 87.78/88.37 (descr(^[V_3]: X2(V_3)) = descr(^[V_4]: X3(V_4))))))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(exuEu, axiom, exuEu <=> 87.78/88.37 (![Xphi:($i > $o)]: 87.78/88.37 (exu(^[Xx]: Xphi(Xx)) => 87.78/88.37 (![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))). 87.78/88.37 tff('55', plain, 87.78/88.37 exuEu = 87.78/88.37 (![X2:($i > $o)]: 87.78/88.37 (exu(^[V_1]: X2(V_1)) => (![X3,X4]: (X2(X3) => (X2(X4) => (X3 = X4)))))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(omega__Cong, axiom, omega__Cong <=> (omega = omega)). 87.78/88.37 tff('56', plain, omega__Cong = (omega = omega), define([status(thm)])). 87.78/88.37 tff(setunion__Cong, axiom, setunion__Cong <=> 87.78/88.37 (![A,B]: ((A = B) => (setunion(A) = setunion(B))))). 87.78/88.37 tff('57', plain, 87.78/88.37 setunion__Cong = (![X2,X3]: ((X2 = X3) => (setunion(X2) = setunion(X3)))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(powerset__Cong, axiom, powerset__Cong <=> 87.78/88.37 (![A,B]: ((A = B) => (powerset(A) = powerset(B))))). 87.78/88.37 tff('58', plain, 87.78/88.37 powerset__Cong = (![X2,X3]: ((X2 = X3) => (powerset(X2) = powerset(X3)))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(setadjoin__Cong, axiom, setadjoin__Cong <=> 87.78/88.37 (![Xx,Xy]: 87.78/88.37 ((Xx = Xy) => 87.78/88.37 (![Xz,Xu]: ((Xz = Xu) => (setadjoin(Xx,Xz) = setadjoin(Xy,Xu))))))). 87.78/88.37 tff('59', plain, 87.78/88.37 setadjoin__Cong = 87.78/88.37 (![X2,X3]: 87.78/88.37 ((X2 = X3) => 87.78/88.37 (![X4,X5]: ((X4 = X5) => (setadjoin(X2,X4) = setadjoin(X3,X5)))))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(emptyset__Cong, axiom, emptyset__Cong <=> (emptyset = emptyset)). 87.78/88.37 tff('60', plain, emptyset__Cong = (emptyset = emptyset), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(exu__Cong, axiom, exu__Cong <=> 87.78/88.37 (![Xphi:($i > $o),Xpsi:($i > $o)]: 87.78/88.37 ((![Xx,Xy]: ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy)))) => 87.78/88.37 (exu(^[Xx]: Xphi(Xx)) <=> exu(^[Xx]: Xpsi(Xx)))))). 87.78/88.37 tff('61', plain, 87.78/88.37 exu__Cong = 87.78/88.37 (![X2:($i > $o),X3:($i > $o)]: 87.78/88.37 ((![X4,X5]: ((X4 = X5) => (X2(X4) <=> X3(X5)))) => 87.78/88.37 (exu(^[V_1]: X2(V_1)) <=> exu(^[V_2]: X3(V_2))))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(exuE3u, axiom, exuE3u <=> 87.78/88.37 (![Xphi:($i > $o)]: 87.78/88.37 (exu(^[Xx]: Xphi(Xx)) => 87.78/88.37 (![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))). 87.78/88.37 tff('62', plain, 87.78/88.37 exuE3u = 87.78/88.37 (![X2:($i > $o)]: 87.78/88.37 (exu(^[V_1]: X2(V_1)) => (![X3,X4]: (X2(X3) => (X2(X4) => (X3 = X4)))))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(in__Cong, axiom, in__Cong <=> 87.78/88.37 (![A,B]: ((A = B) => (![Xx,Xy]: ((Xx = Xy) => (in(Xx,A) <=> in(Xy,B))))))). 87.78/88.37 tff('63', plain, 87.78/88.37 in__Cong = 87.78/88.37 (![X2,X3]: 87.78/88.37 ((X2 = X3) => (![X4,X5]: ((X4 = X5) => (in(X4,X2) <=> in(X5,X3)))))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(inCongP, axiom, inCongP <=> 87.78/88.37 (![A,B]: ((A = B) => (![Xx,Xy]: ((Xx = Xy) => (in(Xx,A) => in(Xy,B))))))). 87.78/88.37 tff('64', plain, 87.78/88.37 inCongP = 87.78/88.37 (![X2,X3]: 87.78/88.37 ((X2 = X3) => (![X4,X5]: ((X4 = X5) => (in(X4,X2) => in(X5,X3)))))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(exuI2, axiom, exuI2 <=> 87.78/88.37 (![Xphi:($i > $o)]: 87.78/88.37 ((?[Xx]: (![Xy]: (Xphi(Xy) <=> (Xy = Xx)))) => exu(^[Xx]: Xphi(Xx))))). 87.78/88.37 tff('65', plain, 87.78/88.37 exuI2 = 87.78/88.37 (![X2:($i > $o)]: 87.78/88.37 ((?[X3]: (![X4]: (X2(X4) <=> (X4 = X3)))) => exu(^[V_1]: X2(V_1)))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(exuI3, axiom, exuI3 <=> 87.78/88.37 (![Xphi:($i > $o)]: 87.78/88.37 ((?[Xx]: Xphi(Xx)) => 87.78/88.37 ((![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy)))) => 87.78/88.37 exu(^[Xx]: Xphi(Xx)))))). 87.78/88.37 tff('66', plain, 87.78/88.37 exuI3 = 87.78/88.37 (![X2:($i > $o)]: 87.78/88.37 ((?[X3]: X2(X3)) => 87.78/88.37 ((![X4,X5]: (X2(X4) => (X2(X5) => (X4 = X5)))) => 87.78/88.37 exu(^[V_1]: X2(V_1))))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(exuI1, axiom, exuI1 <=> 87.78/88.37 (![Xphi:($i > $o)]: 87.78/88.37 ((?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx))) => 87.78/88.37 exu(^[Xx]: Xphi(Xx))))). 87.78/88.37 tff('67', plain, 87.78/88.37 exuI1 = 87.78/88.37 (![X2:($i > $o)]: 87.78/88.37 ((?[X3]: ((![X4]: (X2(X4) => (X3 = X4))) & X2(X3))) => 87.78/88.37 exu(^[V_1]: X2(V_1)))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(notdallE, axiom, notdallE <=> 87.78/88.37 (![A,Xphi:($i > $o)]: 87.78/88.37 ((~(![Xx]: (in(Xx,A) => Xphi(Xx)))) => (?[Xx]: ((~Xphi(Xx)) & in(Xx,A)))))). 87.78/88.37 tff('68', plain, 87.78/88.37 notdallE = 87.78/88.37 (![X2,X3:($i > $o)]: 87.78/88.37 ((~(![X4]: (in(X4,X2) => X3(X4)))) => (?[X5]: ((~X3(X5)) & in(X5,X2))))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(notdexE, axiom, notdexE <=> 87.78/88.37 (![A,Xphi:($i > $o)]: 87.78/88.37 ((~(?[Xx]: (Xphi(Xx) & in(Xx,A)))) => (![Xx]: (in(Xx,A) => (~Xphi(Xx))))))). 87.78/88.37 tff('69', plain, 87.78/88.37 notdexE = 87.78/88.37 (![X2,X3:($i > $o)]: 87.78/88.37 ((~(?[X4]: (X3(X4) & in(X4,X2)))) => (![X5]: (in(X5,X2) => (~X3(X5)))))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(prop2set2propI, axiom, prop2set2propI <=> 87.78/88.37 (![Xphi:$o]: (Xphi => set2prop(prop2set(Xphi))))). 87.78/88.37 tff('70', plain, prop2set2propI = (![X2:$o]: (X2 => set2prop(prop2set(X2)))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(prop2setI, axiom, prop2setI <=> 87.78/88.37 (![Xphi:$o]: (Xphi => in(emptyset,prop2set(Xphi))))). 87.78/88.37 tff('71', plain, prop2setI = (![X2:$o]: (X2 => in(emptyset,prop2set(X2)))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(quantDeMorgan4, axiom, quantDeMorgan4 <=> 87.78/88.37 (![A,Xphi:($i > $o)]: 87.78/88.37 ((?[Xx]: ((~Xphi(Xx)) & in(Xx,A))) => (~(![Xx]: (in(Xx,A) => Xphi(Xx))))))). 87.78/88.37 tff('72', plain, 87.78/88.37 quantDeMorgan4 = 87.78/88.37 (![X2,X3:($i > $o)]: 87.78/88.37 ((?[X4]: ((~X3(X4)) & in(X4,X2))) => (~(![X5]: (in(X5,X2) => X3(X5)))))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(quantDeMorgan3, axiom, quantDeMorgan3 <=> 87.78/88.37 (![A,Xphi:($i > $o)]: 87.78/88.37 ((~(?[Xx]: (Xphi(Xx) & in(Xx,A)))) => (![Xx]: (in(Xx,A) => (~Xphi(Xx))))))). 87.78/88.37 tff('73', plain, 87.78/88.37 quantDeMorgan3 = 87.78/88.37 (![X2,X3:($i > $o)]: 87.78/88.37 ((~(?[X4]: (X3(X4) & in(X4,X2)))) => (![X5]: (in(X5,X2) => (~X3(X5)))))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(quantDeMorgan2, axiom, quantDeMorgan2 <=> 87.78/88.37 (![A,Xphi:($i > $o)]: 87.78/88.37 ((![Xx]: (in(Xx,A) => (~Xphi(Xx)))) => (~(?[Xx]: (Xphi(Xx) & in(Xx,A))))))). 87.78/88.37 tff('74', plain, 87.78/88.37 quantDeMorgan2 = 87.78/88.37 (![X2,X3:($i > $o)]: 87.78/88.37 ((![X4]: (in(X4,X2) => (~X3(X4)))) => (~(?[X5]: (X3(X5) & in(X5,X2)))))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(quantDeMorgan1, axiom, quantDeMorgan1 <=> 87.78/88.37 (![A,Xphi:($i > $o)]: 87.78/88.37 ((~(![Xx]: (in(Xx,A) => Xphi(Xx)))) => (?[Xx]: ((~Xphi(Xx)) & in(Xx,A)))))). 87.78/88.37 tff('75', plain, 87.78/88.37 quantDeMorgan1 = 87.78/88.37 (![X2,X3:($i > $o)]: 87.78/88.37 ((~(![X4]: (in(X4,X2) => X3(X4)))) => (?[X5]: ((~X3(X5)) & in(X5,X2))))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(vacuousDall, axiom, vacuousDall <=> 87.78/88.37 (![Xphi:($i > $o),Xx]: (in(Xx,emptyset) => Xphi(Xx)))). 87.78/88.37 tff('76', plain, 87.78/88.37 vacuousDall = (![X2:($i > $o),X3]: (in(X3,emptyset) => X2(X3))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(emptyE1, axiom, emptyE1 <=> 87.78/88.37 (![A,Xphi:($i > $o)]: 87.78/88.37 ((?[Xx]: (Xphi(Xx) & in(Xx,A))) => 87.78/88.37 ((dsetconstr(A,^[Xx]: Xphi(Xx)) = emptyset) => $false)))). 87.78/88.37 tff('77', plain, 87.78/88.37 emptyE1 = 87.78/88.37 (![X2,X3:($i > $o)]: 87.78/88.37 ((?[X4]: (X3(X4) & in(X4,X2))) => 87.78/88.37 ((dsetconstr(X2,^[V_1]: X3(V_1)) = emptyset) => $false))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(upairsetIR, axiom, upairsetIR <=> 87.78/88.37 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 87.78/88.37 tff('78', plain, 87.78/88.37 upairsetIR = (![X2,X3]: in(X3,setadjoin(X2,setadjoin(X3,emptyset)))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(upairsetIL, axiom, upairsetIL <=> 87.78/88.37 (![Xx,Xy]: in(Xx,setadjoin(Xx,setadjoin(Xy,emptyset))))). 87.78/88.37 tff('79', plain, 87.78/88.37 upairsetIL = (![X2,X3]: in(X2,setadjoin(X2,setadjoin(X3,emptyset)))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(upairsetE, axiom, upairsetE <=> 87.78/88.37 (![Xx,Xy,Xz]: 87.78/88.37 (in(Xz,setadjoin(Xx,setadjoin(Xy,emptyset))) => ((Xz = Xy) | (Xz = Xx))))). 87.78/88.37 tff('80', plain, 87.78/88.37 upairsetE = 87.78/88.37 (![X2,X3,X4]: 87.78/88.37 (in(X4,setadjoin(X2,setadjoin(X3,emptyset))) => 87.78/88.37 ((X4 = X3) | (X4 = X2)))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(singletonsswitch, axiom, singletonsswitch <=> 87.78/88.37 (![Xx,Xy]: (in(Xx,setadjoin(Xy,emptyset)) => in(Xy,setadjoin(Xx,emptyset))))). 87.78/88.37 tff('81', plain, 87.78/88.37 singletonsswitch = 87.78/88.37 (![X2,X3]: 87.78/88.37 (in(X2,setadjoin(X3,emptyset)) => in(X3,setadjoin(X2,emptyset)))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(eqinunit, axiom, eqinunit <=> 87.78/88.37 (![Xx,Xy]: ((Xx = Xy) => in(Xx,setadjoin(Xy,emptyset))))). 87.78/88.37 tff('82', plain, 87.78/88.37 eqinunit = (![X2,X3]: ((X2 = X3) => in(X2,setadjoin(X3,emptyset)))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(notinsingleton, axiom, notinsingleton <=> 87.78/88.37 (![Xx,Xy]: ((Xx != Xy) => (~in(Xy,setadjoin(Xx,emptyset)))))). 87.78/88.37 tff('83', plain, 87.78/88.37 notinsingleton = 87.78/88.37 (![X2,X3]: ((X2 != X3) => (~in(X3,setadjoin(X2,emptyset))))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(uniqinunit, axiom, uniqinunit <=> 87.78/88.37 (![Xx,Xy]: (in(Xx,setadjoin(Xy,emptyset)) => (Xx = Xy)))). 87.78/88.37 tff('84', plain, 87.78/88.37 uniqinunit = (![X2,X3]: (in(X2,setadjoin(X3,emptyset)) => (X2 = X3))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(nonemptyImpWitness, axiom, nonemptyImpWitness <=> 87.78/88.37 (![A]: (nonempty(A) => (?[Xx]: (in(Xx,A)))))). 87.78/88.37 tff('85', plain, 87.78/88.37 nonemptyImpWitness = (![X2]: (nonempty(X2) => (?[X3]: (in(X3,X2))))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(exuE2, axiom, exuE2 <=> 87.78/88.37 (![Xphi:($i > $o)]: 87.78/88.37 (exu(^[Xx]: Xphi(Xx)) => (?[Xx]: (![Xy]: (Xphi(Xy) <=> (Xy = Xx))))))). 87.78/88.37 tff('86', plain, 87.78/88.37 exuE2 = 87.78/88.37 (![X2:($i > $o)]: 87.78/88.37 (exu(^[V_1]: X2(V_1)) => (?[X3]: (![X4]: (X2(X4) <=> (X4 = X3)))))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(subPowSU, axiom, subPowSU <=> 87.78/88.37 (![A,Xx]: (in(Xx,A) => in(Xx,powerset(setunion(A)))))). 87.78/88.37 tff('87', plain, 87.78/88.37 subPowSU = (![X2,X3]: (in(X3,X2) => in(X3,powerset(setunion(X2))))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(setunionE, axiom, setunionE <=> 87.78/88.37 (![A,Xx]: 87.78/88.37 (in(Xx,setunion(A)) => 87.78/88.37 (![Xphi:$o]: ((![B]: (in(Xx,B) => (in(B,A) => Xphi))) => Xphi))))). 87.78/88.37 tff('88', plain, 87.78/88.37 setunionE = 87.78/88.37 (![X2,X3]: 87.78/88.37 (in(X3,setunion(X2)) => 87.78/88.37 (![X4:$o]: ((![X5]: (in(X3,X5) => (in(X5,X2) => X4))) => X4)))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(setunionI, axiom, setunionI <=> 87.78/88.37 (![A,Xx,B]: (in(Xx,B) => (in(B,A) => in(Xx,setunion(A)))))). 87.78/88.37 tff('89', plain, 87.78/88.37 setunionI = 87.78/88.37 (![X2,X3,X4]: (in(X3,X4) => (in(X4,X2) => in(X3,setunion(X2))))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(powersetE, axiom, powersetE <=> 87.78/88.37 (![A,B,Xx]: (in(B,powerset(A)) => (in(Xx,B) => in(Xx,A))))). 87.78/88.37 tff('90', plain, 87.78/88.37 powersetE = 87.78/88.37 (![X2,X3,X4]: (in(X3,powerset(X2)) => (in(X4,X3) => in(X4,X2)))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(emptyInPowerset, axiom, emptyInPowerset <=> 87.78/88.37 (![A]: in(emptyset,powerset(A)))). 87.78/88.37 tff('91', plain, emptyInPowerset = (![X2]: in(emptyset,powerset(X2))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(emptyinPowerset, axiom, emptyinPowerset <=> 87.78/88.37 (![A]: in(emptyset,powerset(A)))). 87.78/88.37 tff('92', plain, emptyinPowerset = (![X2]: in(emptyset,powerset(X2))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(powersetI, axiom, powersetI <=> 87.78/88.37 (![A,B]: ((![Xx]: (in(Xx,B) => in(Xx,A))) => in(B,powerset(A))))). 87.78/88.37 tff('93', plain, 87.78/88.37 powersetI = 87.78/88.37 (![X2,X3]: ((![X4]: (in(X4,X3) => in(X4,X2))) => in(X3,powerset(X2)))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(setoftrueEq, axiom, setoftrueEq <=> 87.78/88.37 (![A]: (dsetconstr(A,^[Xx]: $true) = A))). 87.78/88.37 tff('94', plain, setoftrueEq = (![X2]: (dsetconstr(X2,^[V_1]: $true) = X2)), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(setadjoinOr, axiom, setadjoinOr <=> 87.78/88.37 (![Xx,A,Xy]: (in(Xy,setadjoin(Xx,A)) => (in(Xy,A) | (Xy = Xx))))). 87.78/88.37 tff('95', plain, 87.78/88.37 setadjoinOr = 87.78/88.37 (![X2,X3,X4]: (in(X4,setadjoin(X2,X3)) => (in(X4,X3) | (X4 = X2)))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(setadjoinE, axiom, setadjoinE <=> 87.78/88.37 (![Xx,A,Xy]: 87.78/88.37 (in(Xy,setadjoin(Xx,A)) => 87.78/88.37 (![Xphi:$o]: (((Xy = Xx) => Xphi) => ((in(Xy,A) => Xphi) => Xphi)))))). 87.78/88.37 tff('96', plain, 87.78/88.37 setadjoinE = 87.78/88.37 (![X2,X3,X4]: 87.78/88.37 (in(X4,setadjoin(X2,X3)) => 87.78/88.37 (![X5:$o]: (((X4 = X2) => X5) => ((in(X4,X3) => X5) => X5))))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(setadjoinIR, axiom, setadjoinIR <=> 87.78/88.37 (![Xx,A,Xy]: (in(Xy,A) => in(Xy,setadjoin(Xx,A))))). 87.78/88.37 tff('97', plain, 87.78/88.37 setadjoinIR = (![X2,X3,X4]: (in(X4,X3) => in(X4,setadjoin(X2,X3)))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(emptyinunitempty, axiom, emptyinunitempty() = 87.78/88.37 in(emptyset,setadjoin(emptyset,emptyset))). 87.78/88.37 tff('98', plain, 87.78/88.37 emptyinunitempty = in(emptyset,setadjoin(emptyset,emptyset)), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(setadjoinIL, axiom, setadjoinIL <=> (![Xx,Xy]: in(Xx,setadjoin(Xx,Xy)))). 87.78/88.37 tff('99', plain, setadjoinIL = (![X2,X3]: in(X2,setadjoin(X2,X3))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(nonemptyI1, axiom, nonemptyI1 <=> 87.78/88.37 (![A]: ((?[Xx]: in(Xx,A)) => nonempty(A)))). 87.78/88.37 tff('100', plain, nonemptyI1 = (![X2]: ((?[X3]: in(X3,X2)) => nonempty(X2))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(nonemptyI, axiom, nonemptyI <=> 87.78/88.37 (![A,Xphi:($i > $o),Xx]: 87.78/88.37 (in(Xx,A) => (Xphi(Xx) => nonempty(dsetconstr(A,^[Xy]: Xphi(Xy))))))). 87.78/88.37 tff('101', plain, 87.78/88.37 nonemptyI = 87.78/88.37 (![X2,X3:($i > $o),X4]: 87.78/88.37 (in(X4,X2) => (X3(X4) => nonempty(dsetconstr(X2,^[V_1]: X3(V_1)))))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(nonemptyE1, axiom, nonemptyE1 <=> 87.78/88.37 (![A]: (nonempty(A) => (?[Xx]: in(Xx,A))))). 87.78/88.37 tff('102', plain, nonemptyE1 = (![X2]: (nonempty(X2) => (?[X3]: in(X3,X2)))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(nonempty, axiom, nonempty() = ^[Xx]: (Xx != emptyset)). 87.78/88.37 tff('103', plain, nonempty = (^[V_1]: (V_1 != emptyset)), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(setbeta, axiom, setbeta <=> 87.78/88.37 (![A,Xphi:($i > $o),Xx]: 87.78/88.37 (in(Xx,A) => (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) <=> Xphi(Xx))))). 87.78/88.37 tff('104', plain, 87.78/88.37 setbeta = 87.78/88.37 (![X2,X3:($i > $o),X4]: 87.78/88.37 (in(X4,X2) => (in(X4,dsetconstr(X2,^[V_1]: X3(V_1))) <=> X3(X4)))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(noeltsimpempty, axiom, noeltsimpempty <=> 87.78/88.37 (![A]: ((![Xx]: (~in(Xx,A))) => (A = emptyset)))). 87.78/88.37 tff('105', plain, 87.78/88.37 noeltsimpempty = (![X2]: ((![X3]: (~in(X3,X2))) => (X2 = emptyset))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(emptyI, axiom, emptyI <=> 87.78/88.37 (![A]: ((![Xx]: (~in(Xx,A))) => (A = emptyset)))). 87.78/88.37 tff('106', plain, 87.78/88.37 emptyI = (![X2]: ((![X3]: (~in(X3,X2))) => (X2 = emptyset))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(setext, axiom, setext <=> 87.78/88.37 (![A,B]: 87.78/88.37 ((![Xx]: (in(Xx,A) => in(Xx,B))) => 87.78/88.37 ((![Xx]: (in(Xx,B) => in(Xx,A))) => (A = B))))). 87.78/88.37 tff('107', plain, 87.78/88.37 setext = 87.78/88.37 (![X2,X3]: 87.78/88.37 ((![X4]: (in(X4,X2) => in(X4,X3))) => 87.78/88.37 ((![X5]: (in(X5,X3) => in(X5,X2))) => (X2 = X3)))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(exuE3e, axiom, exuE3e <=> 87.78/88.37 (![Xphi:($i > $o)]: (exu(^[Xx]: Xphi(Xx)) => (?[Xx]: Xphi(Xx))))). 87.78/88.37 tff('108', plain, 87.78/88.37 exuE3e = (![X2:($i > $o)]: (exu(^[V_1]: X2(V_1)) => (?[X3]: X2(X3)))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(notinemptyset, axiom, notinemptyset <=> (![Xx]: (~in(Xx,emptyset)))). 87.78/88.37 tff('109', plain, notinemptyset = (![X2]: (~in(X2,emptyset))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(emptysetimpfalse, axiom, emptysetimpfalse <=> 87.78/88.37 (![Xx]: (in(Xx,emptyset) => $false))). 87.78/88.37 tff('110', plain, emptysetimpfalse = (![X2]: (in(X2,emptyset) => $false)), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(emptysetE, axiom, emptysetE <=> 87.78/88.37 (![Xx]: (in(Xx,emptyset) => (![Xphi:$o]: Xphi)))). 87.78/88.37 tff('111', plain, emptysetE = (![X2]: (in(X2,emptyset) => (![X3:$o]: X3))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(prop2setE, axiom, prop2setE <=> 87.78/88.37 (![Xphi:$o,Xx]: (in(Xx,prop2set(Xphi)) => Xphi))). 87.78/88.37 tff('112', plain, prop2setE = (![X2:$o,X3]: (in(X3,prop2set(X2)) => X2)), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(exuE1, axiom, exuE1 <=> 87.78/88.37 (![Xphi:($i > $o)]: 87.78/88.37 (exu(^[Xx]: Xphi(Xx)) => 87.78/88.37 (?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx)))))). 87.78/88.37 tff('113', plain, 87.78/88.37 exuE1 = 87.78/88.37 (![X2:($i > $o)]: 87.78/88.37 (exu(^[V_1]: X2(V_1)) => 87.78/88.37 (?[X3]: ((![X4]: (X2(X4) => (X3 = X4))) & X2(X3))))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(dsetconstrER, axiom, dsetconstrER <=> 87.78/88.37 (![A,Xphi:($i > $o),Xx]: (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) => Xphi(Xx)))). 87.78/88.37 tff('114', plain, 87.78/88.37 dsetconstrER = 87.78/88.37 (![X2,X3:($i > $o),X4]: (in(X4,dsetconstr(X2,^[V_1]: X3(V_1))) => X3(X4))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(dsetconstrEL, axiom, dsetconstrEL <=> 87.78/88.37 (![A,Xphi:($i > $o),Xx]: (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) => in(Xx,A)))). 87.78/88.37 tff('115', plain, 87.78/88.37 dsetconstrEL = 87.78/88.37 (![X2,X3:($i > $o),X4]: 87.78/88.37 (in(X4,dsetconstr(X2,^[V_1]: X3(V_1))) => in(X4,X2))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(dsetconstrI, axiom, dsetconstrI <=> 87.78/88.37 (![A,Xphi:($i > $o),Xx]: 87.78/88.37 (in(Xx,A) => (Xphi(Xx) => in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))))))). 87.78/88.37 tff('116', plain, 87.78/88.37 dsetconstrI = 87.78/88.37 (![X2,X3:($i > $o),X4]: 87.78/88.37 (in(X4,X2) => (X3(X4) => in(X4,dsetconstr(X2,^[V_1]: X3(V_1)))))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(descrp, axiom, descrp <=> 87.78/88.37 (![Xphi:($i > $o)]: (exu(^[Xx]: Xphi(Xx)) => Xphi(descr(^[Xx]: Xphi(Xx)))))). 87.78/88.37 tff('117', plain, 87.78/88.37 descrp = 87.78/88.37 (![X2:($i > $o)]: (exu(^[V_1]: X2(V_1)) => X2(descr(^[V_2]: X2(V_2))))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(wellorderingAx, axiom, wellorderingAx <=> 87.78/88.37 (![A]: 87.78/88.37 (?[B]: 87.78/88.37 ((![C]: 87.78/88.37 (((?[Xx]: in(Xx,C)) & (![Xx]: (in(Xx,C) => in(Xx,A)))) => 87.78/88.37 (?[D,Xx]: 87.78/88.37 ((![E]: 87.78/88.37 (in(E,B) => (in(Xx,E) | (![Xy]: (in(Xy,E) => in(Xy,D)))))) & 87.78/88.37 (~(?[Xy]: (in(Xy,C) & in(Xy,D)))) & in(Xx,C) & in(D,B))))) & 87.78/88.37 (![C,D]: 87.78/88.37 ((in(D,B) & in(C,B)) => 87.78/88.37 ((![Xx]: (in(Xx,D) => in(Xx,C))) | 87.78/88.37 (![Xx]: (in(Xx,C) => in(Xx,D)))))) & 87.78/88.37 (![Xx,Xy]: 87.78/88.37 ((in(Xy,A) & in(Xx,A)) => 87.78/88.37 ((![C]: (in(C,B) => (in(Xx,C) <=> in(Xy,C)))) => (Xx = Xy)))) & 87.78/88.37 (![C]: (in(C,B) => (![Xx]: (in(Xx,C) => in(Xx,A))))))))). 87.78/88.37 tff('118', plain, 87.78/88.37 wellorderingAx = 87.78/88.37 (![X2]: 87.78/88.37 (?[X3]: 87.78/88.37 ((![X4]: 87.78/88.37 (((?[X5]: in(X5,X4)) & (![X6]: (in(X6,X4) => in(X6,X2)))) => 87.78/88.37 (?[X7,X8]: 87.78/88.37 ((![X9]: 87.78/88.37 (in(X9,X3) => 87.78/88.37 (in(X8,X9) | (![X10]: (in(X10,X9) => in(X10,X7)))))) & 87.78/88.37 (~(?[X11]: (in(X11,X4) & in(X11,X7)))) & in(X8,X4) & 87.78/88.37 in(X7,X3))))) & 87.78/88.37 (![X12,X13]: 87.78/88.37 ((in(X13,X3) & in(X12,X3)) => 87.78/88.37 ((![X14]: (in(X14,X13) => in(X14,X12))) | 87.78/88.37 (![X15]: (in(X15,X12) => in(X15,X13)))))) & 87.78/88.37 (![X16,X17]: 87.78/88.37 ((in(X17,X2) & in(X16,X2)) => 87.78/88.37 ((![X18]: (in(X18,X3) => (in(X16,X18) <=> in(X17,X18)))) => 87.78/88.37 (X16 = X17)))) & 87.78/88.37 (![X19]: (in(X19,X3) => (![X20]: (in(X20,X19) => in(X20,X2)))))))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(foundationAx, axiom, foundationAx <=> 87.78/88.37 (![A]: 87.78/88.37 ((?[Xx]: in(Xx,A)) => 87.78/88.37 (?[B]: ((~(?[Xx]: (in(Xx,A) & in(Xx,B)))) & in(B,A)))))). 87.78/88.37 tff('119', plain, 87.78/88.37 foundationAx = 87.78/88.37 (![X2]: 87.78/88.37 ((?[X3]: in(X3,X2)) => 87.78/88.37 (?[X4]: ((~(?[X5]: (in(X5,X2) & in(X5,X4)))) & in(X4,X2))))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(replAx, axiom, replAx <=> 87.78/88.37 (![Xphi:(($i * $i) > $o),A]: 87.78/88.37 ((![Xx]: (in(Xx,A) => exu(^[Xy]: Xphi(Xx,Xy)))) => 87.78/88.37 (?[B]: (![Xx]: (in(Xx,B) <=> (?[Xy]: (Xphi(Xy,Xx) & in(Xy,A))))))))). 87.78/88.37 tff('120', plain, 87.78/88.37 replAx = 87.78/88.37 (![X2:(($i * $i) > $o),X3]: 87.78/88.37 ((![X4]: (in(X4,X3) => exu(^[V_1]: X2(X4,V_1)))) => 87.78/88.37 (?[X5]: (![X6]: (in(X6,X5) <=> (?[X7]: (X2(X7,X6) & in(X7,X3)))))))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(omegaIndAx, axiom, omegaIndAx <=> 87.78/88.37 (![A]: 87.78/88.37 (((![Xx]: ((in(Xx,A) & in(Xx,omega)) => in(setadjoin(Xx,Xx),A))) & 87.78/88.37 in(emptyset,A)) => 87.78/88.37 (![Xx]: (in(Xx,omega) => in(Xx,A)))))). 87.78/88.37 tff('121', plain, 87.78/88.37 omegaIndAx = 87.78/88.37 (![X2]: 87.78/88.37 (((![X3]: ((in(X3,X2) & in(X3,omega)) => in(setadjoin(X3,X3),X2))) & 87.78/88.37 in(emptyset,X2)) => 87.78/88.37 (![X4]: (in(X4,omega) => in(X4,X2))))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(omegaSAx, axiom, omegaSAx <=> 87.78/88.37 (![Xx]: (in(Xx,omega) => in(setadjoin(Xx,Xx),omega)))). 87.78/88.37 tff('122', plain, 87.78/88.37 omegaSAx = (![X2]: (in(X2,omega) => in(setadjoin(X2,X2),omega))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(omega0Ax, axiom, omega0Ax() = in(emptyset,omega)). 87.78/88.37 tff('123', plain, omega0Ax = in(emptyset,omega), define([status(thm)])). 87.78/88.37 tff(setunionAx, axiom, setunionAx <=> 87.78/88.37 (![A,Xx]: (in(Xx,setunion(A)) <=> (?[B]: (in(B,A) & in(Xx,B)))))). 87.78/88.37 tff('124', plain, 87.78/88.37 setunionAx = 87.78/88.37 (![X2,X3]: (in(X3,setunion(X2)) <=> (?[X4]: (in(X4,X2) & in(X3,X4))))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(powersetAx, axiom, powersetAx <=> 87.78/88.37 (![A,B]: (in(B,powerset(A)) <=> (![Xx]: (in(Xx,B) => in(Xx,A)))))). 87.78/88.37 tff('125', plain, 87.78/88.37 powersetAx = 87.78/88.37 (![X2,X3]: (in(X3,powerset(X2)) <=> (![X4]: (in(X4,X3) => in(X4,X2))))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(setadjoinAx, axiom, setadjoinAx <=> 87.78/88.37 (![Xx,A,Xy]: (in(Xy,setadjoin(Xx,A)) <=> (in(Xy,A) | (Xy = Xx))))). 87.78/88.37 tff('126', plain, 87.78/88.37 setadjoinAx = 87.78/88.37 (![X2,X3,X4]: (in(X4,setadjoin(X2,X3)) <=> (in(X4,X3) | (X4 = X2)))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(emptysetAx, axiom, emptysetAx <=> (![Xx]: (~in(Xx,emptyset)))). 87.78/88.37 tff('127', plain, emptysetAx = (![X2]: (~in(X2,emptyset))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(setextAx, axiom, setextAx <=> 87.78/88.37 (![A,B]: ((![Xx]: (in(Xx,A) <=> in(Xx,B))) => (A = B)))). 87.78/88.37 tff('128', plain, 87.78/88.37 setextAx = (![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(exu, axiom, exu() = 87.78/88.37 ^[Xphi:($i > $o)]: (?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx)))). 87.78/88.37 tff('129', plain, 87.78/88.37 exu = 87.78/88.37 (^[V_1:($i > $o)]: (?[X2]: ((![X3]: (V_1(X3) => (X2 = X3))) & V_1(X2)))), 87.78/88.37 define([status(thm)])). 87.78/88.37 tff(symdiffE, conjecture, 87.78/88.37 (setextAx => 87.78/88.37 (emptysetAx => 87.78/88.37 (setadjoinAx => 87.78/88.37 (powersetAx => 87.78/88.37 (setunionAx => 87.78/88.37 (omega0Ax => 87.78/88.37 (omegaSAx => 87.78/88.37 (omegaIndAx => 87.78/88.37 (replAx => 87.78/88.37 (foundationAx => 87.78/88.37 (wellorderingAx => 87.78/88.37 (descrp => 87.78/88.37 (dsetconstrI => 87.78/88.37 (dsetconstrEL => 87.78/88.37 (dsetconstrER => 87.78/88.37 (exuE1 => 87.78/88.37 (prop2setE => 87.78/88.37 (emptysetE => 87.78/88.37 (emptysetimpfalse => 87.78/88.37 (notinemptyset => 87.78/88.37 (exuE3e => 87.78/88.37 (setext => 87.78/88.37 (emptyI => 87.78/88.37 (noeltsimpempty => 87.78/88.37 (setbeta => 87.78/88.37 (nonemptyE1 => 87.78/88.37 (nonemptyI => 87.78/88.37 (nonemptyI1 => 87.78/88.37 (setadjoinIL => 87.78/88.37 (emptyinunitempty => 87.78/88.37 (setadjoinIR => 87.78/88.37 (setadjoinE => 87.78/88.37 (setadjoinOr => 87.78/88.37 (setoftrueEq => 87.78/88.37 (powersetI => 87.78/88.37 (emptyinPowerset => 87.78/88.37 (emptyInPowerset => 87.78/88.37 (powersetE => 87.78/88.37 (setunionI => 87.78/88.37 (setunionE => 87.78/88.37 (subPowSU => 87.78/88.37 (exuE2 => 87.78/88.37 (nonemptyImpWitness => 87.78/88.37 (uniqinunit => 87.78/88.37 (notinsingleton => 87.78/88.37 (eqinunit => 87.78/88.37 (singletonsswitch => 87.78/88.37 (upairsetE => 87.78/88.37 (upairsetIL => 87.78/88.37 (upairsetIR => 87.78/88.37 (emptyE1 => 87.78/88.37 (vacuousDall => 87.78/88.37 (quantDeMorgan1 => 87.78/88.37 (quantDeMorgan2 => 87.78/88.37 (quantDeMorgan3 => 87.78/88.37 (quantDeMorgan4 => 87.78/88.37 (prop2setI => 87.78/88.37 (prop2set2propI => 87.78/88.37 (notdexE => 87.78/88.37 (notdallE => 87.78/88.37 (exuI1 => 87.78/88.37 (exuI3 => 87.78/88.37 (exuI2 => 87.78/88.37 (inCongP => 87.78/88.37 (in__Cong => 87.78/88.37 (exuE3u => 87.78/88.37 ( 87.78/88.37 exu__Cong => 87.78/88.37 ( 87.78/88.37 emptyset__Cong => 87.78/88.37 ( 87.78/88.37 setadjoin__Cong => 87.78/88.37 ( 87.78/88.37 powerset__Cong => 87.78/88.37 ( 87.78/88.37 setunion__Cong => 87.78/88.37 ( 87.78/88.37 omega__Cong => 87.78/88.37 ( 87.78/88.37 exuEu => 87.78/88.37 ( 87.78/88.37 descr__Cong => 87.78/88.37 ( 87.78/88.37 dsetconstr__Cong => 87.78/88.37 ( 87.78/88.37 subsetI1 => 87.78/88.37 ( 87.78/88.37 eqimpsubset2 => 87.78/88.37 ( 87.78/88.37 eqimpsubset1 => 87.78/88.37 ( 87.78/88.37 subsetI2 => 87.78/88.37 ( 87.78/88.37 emptysetsubset => 87.78/88.37 ( 87.78/88.37 subsetE => 87.78/88.37 ( 87.78/88.37 subsetE2 => 87.78/88.37 ( 87.78/88.37 notsubsetI => 87.78/88.37 ( 87.78/88.37 notequalI1 => 87.78/88.37 ( 87.78/88.37 notequalI2 => 87.78/88.37 ( 87.78/88.37 subsetRefl => 87.78/88.37 ( 87.78/88.37 subsetTrans => 87.78/88.37 ( 87.78/88.37 setadjoinSub => 87.78/88.37 ( 87.78/88.37 setadjoinSub2 => 87.78/88.37 ( 87.78/88.37 subset2powerset => 87.78/88.37 ( 87.78/88.37 setextsub => 87.78/88.37 ( 87.78/88.37 subsetemptysetimpeq => 87.78/88.37 ( 87.78/88.37 powersetI1 => 87.78/88.37 ( 87.78/88.37 powersetE1 => 87.78/88.37 ( 87.78/88.37 inPowerset => 87.78/88.37 ( 87.78/88.37 powersetsubset => 87.78/88.37 ( 87.78/88.37 sepInPowerset => 87.78/88.37 ( 87.78/88.37 sepSubset => 87.78/88.37 ( 87.78/88.37 binunionIL => 87.78/88.37 ( 87.78/88.37 upairset2IR => 87.78/88.37 ( 87.78/88.37 binunionIR => 87.78/88.37 ( 87.78/88.37 binunionEcases => 87.78/88.37 ( 87.78/88.37 binunionE => 87.78/88.37 ( 87.78/88.37 binunionLsub => 87.78/88.37 ( 87.78/88.37 binunionRsub => 87.78/88.37 ( 87.78/88.37 binintersectI => 87.78/88.37 ( 87.78/88.37 binintersectSubset5 => 87.78/88.37 ( 87.78/88.37 binintersectEL => 87.78/88.37 ( 87.78/88.37 binintersectLsub => 87.78/88.37 ( 87.78/88.37 binintersectSubset2 => 87.78/88.37 ( 87.78/88.37 binintersectSubset3 => 87.78/88.37 ( 87.78/88.37 binintersectER => 87.78/88.37 ( 87.78/88.37 disjointsetsI1 => 87.78/88.37 ( 87.78/88.37 binintersectRsub => 87.78/88.37 ( 87.78/88.37 binintersectSubset4 => 87.78/88.37 ( 87.78/88.37 binintersectSubset1 => 87.78/88.37 ( 87.78/88.37 bs114d => 87.78/88.37 ( 87.78/88.37 setminusI => 87.78/88.37 ( 87.78/88.37 setminusEL => 87.78/88.37 ( 87.78/88.37 setminusER => 87.78/88.37 ( 87.78/88.37 setminusSubset2 => 87.78/88.37 ( 87.78/88.37 setminusERneg => 87.78/88.37 ( 87.78/88.37 setminusELneg => 87.78/88.37 ( 87.78/88.37 setminusILneg => 87.78/88.37 ( 87.78/88.37 setminusIRneg => 87.78/88.37 ( 87.78/88.37 setminusLsub => 87.78/88.37 ( 87.78/88.37 setminusSubset1 => 87.78/88.37 ( 87.78/88.37 ![A,B,Xx]: 87.78/88.37 (in( 87.78/88.37 Xx, 87.78/88.37 symdiff( 87.78/88.37 A,B)) => 87.78/88.37 (![Xphi:$o]: 87.78/88.37 (( 87.78/88.37 in(Xx,A) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ~in(Xx,B)) => 87.78/88.37 Xphi)) => 87.78/88.37 (( 87.78/88.37 ( 87.78/88.37 ~in(Xx,A)) => 87.78/88.37 ( 87.78/88.37 in(Xx,B) => 87.78/88.37 Xphi)) => 87.78/88.37 Xphi))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 87.78/88.37 tff(zf_stmt_0, conjecture, 87.78/88.37 ((![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))) => 87.78/88.37 ((![X5]: (~in(X5,emptyset))) => 87.78/88.37 ((![X6,X7,X8]: (in(X8,setadjoin(X6,X7)) <=> ((X8 = X6) | in(X8,X7)))) => 87.78/88.37 ((![X9,X10]: 87.78/88.37 (in(X10,powerset(X9)) <=> (![X11]: (in(X11,X10) => in(X11,X9))))) => 87.78/88.37 ((![X12,X13]: 87.78/88.37 (in(X13,setunion(X12)) <=> (?[X14]: (in(X13,X14) & in(X14,X12))))) => 87.78/88.37 (in(emptyset,omega) => 87.78/88.37 ((![X15]: (in(X15,omega) => in(setadjoin(X15,X15),omega))) => 87.78/88.37 ((![X16]: 87.78/88.37 ((in(emptyset,X16) & 87.78/88.37 (![X17]: 87.78/88.37 ((in(X17,omega) & in(X17,X16)) => 87.78/88.37 in(setadjoin(X17,X17),X16)))) => 87.78/88.37 (![X18]: (in(X18,omega) => in(X18,X16))))) => 87.78/88.37 ((![X19:(($i * $i) > $o),X20]: 87.78/88.37 ((![X21]: 87.78/88.37 (in(X21,X20) => 87.78/88.37 (?[X22]: 87.78/88.37 (X19(X21,X22) & (![X23]: (X19(X21,X23) => (X22 = X23))))))) => 87.78/88.37 (?[X24]: 87.78/88.37 (![X25]: 87.78/88.37 (in(X25,X24) <=> (?[X26]: (in(X26,X20) & X19(X26,X25)))))))) => 87.78/88.37 ((![X27]: 87.78/88.37 ((?[X28]: in(X28,X27)) => 87.78/88.37 (?[X29]: 87.78/88.37 (in(X29,X27) & (~(?[X30]: (in(X30,X29) & in(X30,X27)))))))) => 87.78/88.37 ((![X31]: 87.78/88.37 (?[X32]: 87.78/88.37 ((![X48]: 87.78/88.37 (in(X48,X32) => (![X49]: (in(X49,X48) => in(X49,X31))))) & 87.78/88.37 (![X45,X46]: 87.78/88.37 ((in(X45,X31) & in(X46,X31)) => 87.78/88.37 ((![X47]: 87.78/88.37 (in(X47,X32) => (in(X45,X47) <=> in(X46,X47)))) => 87.78/88.37 (X45 = X46)))) & 87.78/88.37 (![X41,X42]: 87.78/88.37 ((in(X41,X32) & in(X42,X32)) => 87.78/88.37 ((![X44]: (in(X44,X41) => in(X44,X42))) | 87.78/88.37 (![X43]: (in(X43,X42) => in(X43,X41)))))) & 87.78/88.37 (![X33]: 87.78/88.37 (((![X35]: (in(X35,X33) => in(X35,X31))) & 87.78/88.37 (?[X34]: in(X34,X33))) => 87.78/88.37 (?[X36,X37]: 87.78/88.37 (in(X36,X32) & in(X37,X33) & 87.78/88.37 (~(?[X40]: (in(X40,X36) & in(X40,X33)))) & 87.78/88.37 (![X38]: 87.78/88.37 (in(X38,X32) => 87.78/88.37 ((![X39]: (in(X39,X38) => in(X39,X36))) | 87.78/88.37 in(X37,X38))))))))))) => 87.78/88.37 ((![X50:($i > $o)]: 87.78/88.37 ((?[X51]: (X50(X51) & (![X52]: (X50(X52) => (X51 = X52))))) => 87.78/88.37 X50(descr(^[V_1]: X50(V_1))))) => 87.78/88.37 ((![X53,X54:($i > $o),X55]: 87.78/88.37 (in(X55,X53) => 87.78/88.37 (X54(X55) => in(X55,dsetconstr(X53,^[V_2]: X54(V_2)))))) => 87.78/88.37 ((![X56,X57:($i > $o),X58]: 87.78/88.37 (in(X58,dsetconstr(X56,^[V_3]: X57(V_3))) => in(X58,X56))) => 87.78/88.37 ((![X59,X60:($i > $o),X61]: 87.78/88.37 (in(X61,dsetconstr(X59,^[V_4]: X60(V_4))) => X60(X61))) => 87.78/88.37 ((![X62:($i > $o)]: 87.78/88.37 ((?[X63]: 87.78/88.37 (X62(X63) & (![X64]: (X62(X64) => (X63 = X64))))) => 87.78/88.37 (?[X65]: 87.78/88.37 (X62(X65) & (![X66]: (X62(X66) => (X65 = X66))))))) => 87.78/88.37 ((![X67:$o,X68]: (in(X68,prop2set(X67)) => X67)) => 87.78/88.37 ((![X69]: (in(X69,emptyset) => (![X70:$o]: X70))) => 87.78/88.37 ((![X71]: (in(X71,emptyset) => $false)) => 87.78/88.37 ((![X72]: (~in(X72,emptyset))) => 87.78/88.37 ((![X73:($i > $o)]: 87.78/88.37 ((?[X74]: 87.78/88.37 (X73(X74) & (![X75]: (X73(X75) => (X74 = X75))))) => 87.78/88.37 (?[X76]: X73(X76)))) => 87.78/88.37 ((![X77,X78]: 87.78/88.37 ((![X79]: (in(X79,X77) => in(X79,X78))) => 87.78/88.37 ((![X80]: (in(X80,X78) => in(X80,X77))) => 87.78/88.37 (X77 = X78)))) => 87.78/88.37 ((![X81]: 87.78/88.37 ((![X82]: (~in(X82,X81))) => (X81 = emptyset))) => 87.78/88.37 ((![X83]: 87.78/88.37 ((![X84]: (~in(X84,X83))) => (X83 = emptyset))) => 87.78/88.37 ((![X85,X86:($i > $o),X87]: 87.78/88.37 (in(X87,X85) => 87.78/88.37 (in(X87,dsetconstr(X85,^[V_5]: X86(V_5))) <=> 87.78/88.37 X86(X87)))) => 87.78/88.37 ((![X88]: 87.78/88.37 ((X88 != emptyset) => (?[X89]: in(X89,X88)))) => 87.78/88.37 ((![X90,X91:($i > $o),X92]: 87.78/88.37 (in(X92,X90) => 87.78/88.37 (X91(X92) => 87.78/88.37 (dsetconstr(X90,^[V_6]: X91(V_6)) != 87.78/88.37 emptyset)))) => 87.78/88.37 ((![X93]: 87.78/88.37 ((?[X94]: in(X94,X93)) => (X93 != emptyset))) => 87.78/88.37 ((![X95,X96]: in(X95,setadjoin(X95,X96))) => 87.78/88.37 (in(emptyset,setadjoin(emptyset,emptyset)) => 87.78/88.37 ((![X97,X98,X99]: 87.78/88.37 (in(X99,X98) => 87.78/88.37 in(X99,setadjoin(X97,X98)))) => 87.78/88.37 ((![X100,X101,X102]: 87.78/88.37 (in(X102,setadjoin(X100,X101)) => 87.78/88.37 (![X103:$o]: 87.78/88.37 (((X102 = X100) => X103) => 87.78/88.37 ((in(X102,X101) => X103) => X103))))) => 87.78/88.37 ((![X104,X105,X106]: 87.78/88.37 (in(X106,setadjoin(X104,X105)) => 87.78/88.37 ((X106 = X104) | in(X106,X105)))) => 87.78/88.37 ((![X107]: 87.78/88.37 (dsetconstr(X107,^[V_7]: $true) = X107)) => 87.78/88.37 ((![X108,X109]: 87.78/88.37 ((![X110]: 87.78/88.37 (in(X110,X109) => in(X110,X108))) => 87.78/88.37 in(X109,powerset(X108)))) => 87.78/88.37 ((![X111]: in(emptyset,powerset(X111))) => 87.78/88.37 ((![X112]: in(emptyset,powerset(X112))) => 87.78/88.37 ((![X113,X114,X115]: 87.78/88.37 (in(X114,powerset(X113)) => 87.78/88.37 (in(X115,X114) => in(X115,X113)))) => 87.78/88.37 ((![X116,X117,X118]: 87.78/88.37 (in(X117,X118) => 87.78/88.37 (in(X118,X116) => 87.78/88.37 in(X117,setunion(X116))))) => 87.78/88.37 ((![X119,X120]: 87.78/88.37 (in(X120,setunion(X119)) => 87.78/88.37 (![X121:$o]: 87.78/88.37 ((![X122]: 87.78/88.37 (in(X120,X122) => 87.78/88.37 (in(X122,X119) => X121))) => 87.78/88.37 X121)))) => 87.78/88.37 ((![X123,X124]: 87.78/88.37 (in(X124,X123) => 87.78/88.37 in(X124, 87.78/88.37 powerset(setunion(X123))))) => 87.78/88.37 ((![X125:($i > $o)]: 87.78/88.37 ((?[X126]: 87.78/88.37 (X125(X126) & 87.78/88.37 (![X127]: 87.78/88.37 (X125(X127) => 87.78/88.37 (X126 = X127))))) => 87.78/88.37 (?[X128]: 87.78/88.37 (![X129]: 87.78/88.37 (X125(X129) <=> 87.78/88.37 (X129 = X128)))))) => 87.78/88.37 ((![X130]: 87.78/88.37 ((X130 != emptyset) => 87.78/88.37 (?[X131]: in(X131,X130)))) => 87.78/88.37 ((![X132,X133]: 87.78/88.37 (in(X132, 87.78/88.37 setadjoin(X133,emptyset)) => 87.78/88.37 (X132 = X133))) => 87.78/88.37 ((![X134,X135]: 87.78/88.37 ((X134 != X135) => 87.78/88.37 (~ 87.78/88.37 in(X135, 87.78/88.37 setadjoin(X134, 87.78/88.37 emptyset))))) => 87.78/88.37 ((![X136,X137]: 87.78/88.37 ((X136 = X137) => 87.78/88.37 in(X136, 87.78/88.37 setadjoin(X137, 87.78/88.37 emptyset)))) => 87.78/88.37 ((![X138,X139]: 87.78/88.37 (in(X138, 87.78/88.37 setadjoin(X139, 87.78/88.37 emptyset)) => 87.78/88.37 in(X139, 87.78/88.37 setadjoin(X138, 87.78/88.37 emptyset)))) => 87.78/88.37 ((![X140,X141,X142]: 87.78/88.37 (in(X142, 87.78/88.37 setadjoin(X140, 87.78/88.37 setadjoin( 87.78/88.37 X141, 87.78/88.37 emptyset))) => 87.78/88.37 ((X142 = X140) | 87.78/88.37 (X142 = X141)))) => 87.78/88.37 ((![X143,X144]: 87.78/88.37 in(X143, 87.78/88.37 setadjoin(X143, 87.78/88.37 setadjoin( 87.78/88.37 X144, 87.78/88.37 emptyset)))) => 87.78/88.37 ((![X145,X146]: 87.78/88.37 in(X146, 87.78/88.37 setadjoin(X145, 87.78/88.37 setadjoin( 87.78/88.37 X146, 87.78/88.37 emptyset)))) => 87.78/88.37 ((![X147,X148:($i > $o)]: 87.78/88.37 ((?[X149]: 87.78/88.37 (in(X149,X147) & 87.78/88.37 X148(X149))) => 87.78/88.37 ((dsetconstr( 87.78/88.37 X147, 87.78/88.37 ^[V_8]: X148(V_8)) = 87.78/88.37 emptyset) => 87.78/88.37 $false))) => 87.78/88.37 ((![X150:($i > $o),X151]: 87.78/88.37 (in(X151,emptyset) => 87.78/88.37 X150(X151))) => 87.78/88.37 ((![X152,X153:($i > $o)]: 87.78/88.37 ((~ 87.78/88.37 (![X154]: 87.78/88.37 (in(X154,X152) => 87.78/88.37 X153(X154)))) => 87.78/88.37 (?[X155]: 87.78/88.37 (in(X155,X152) & 87.78/88.37 (~X153(X155)))))) => 87.78/88.37 ((![X156, 87.78/88.37 X157:($i > $o)]: 87.78/88.37 ((![X158]: 87.78/88.37 (in(X158,X156) => 87.78/88.37 (~X157(X158)))) => 87.78/88.37 (~ 87.78/88.37 (?[X159]: 87.78/88.37 (in( 87.78/88.37 X159,X156) & 87.78/88.37 X157(X159)))))) => 87.78/88.37 ((![X160, 87.78/88.37 X161:($i > $o)]: 87.78/88.37 ((~ 87.78/88.37 (?[X162]: 87.78/88.37 (in( 87.78/88.37 X162,X160) & 87.78/88.37 X161(X162)))) => 87.78/88.37 (![X163]: 87.78/88.37 (in(X163,X160) => 87.78/88.37 (~X161(X163)))))) => 87.78/88.37 ((![X164, 87.78/88.37 X165:($i > $o)]: 87.78/88.37 ((?[X166]: 87.78/88.37 (in( 87.78/88.37 X166,X164) & 87.78/88.37 (~ 87.78/88.37 X165( 87.78/88.37 X166)))) => 87.78/88.37 (~ 87.78/88.37 (![X167]: 87.78/88.37 (in( 87.78/88.37 X167,X164) => 87.78/88.37 X165( 87.78/88.37 X167)))))) => 87.78/88.37 ((![X168:$o]: 87.78/88.37 (X168 => 87.78/88.37 in(emptyset, 87.78/88.37 prop2set( 87.78/88.37 X168)))) => 87.78/88.37 ((![X169:$o]: 87.78/88.37 (X169 => 87.78/88.37 set2prop( 87.78/88.37 prop2set( 87.78/88.37 X169)))) => 87.78/88.37 ((![X170, 87.78/88.37 X171:( 87.78/88.37 $i > $o)]: 87.78/88.37 ((~ 87.78/88.37 (?[X172]: 87.78/88.37 (in( 87.78/88.37 X172,X170) & 87.78/88.37 X171( 87.78/88.37 X172)))) => 87.78/88.37 (![X173]: 87.78/88.37 ( 87.78/88.37 in( 87.78/88.37 X173,X170) => 87.78/88.37 ( 87.78/88.37 ~ 87.78/88.37 X171( 87.78/88.37 X173)))))) => 87.78/88.37 ((![X174, 87.78/88.37 X175:( 87.78/88.37 $i > $o)]: 87.78/88.37 ((~ 87.78/88.37 ( 87.78/88.37 ![X176]: 87.78/88.37 (in( 87.78/88.37 X176,X174) => 87.78/88.37 X175( 87.78/88.37 X176)))) => 87.78/88.37 (?[X177]: 87.78/88.37 (in( 87.78/88.37 X177,X174) & 87.78/88.37 (~ 87.78/88.37 X175( 87.78/88.37 X177)))))) => 87.78/88.37 ((![X178:( 87.78/88.37 $i > $o)]: 87.78/88.37 ((?[X179]: 87.78/88.37 (X178( 87.78/88.37 X179) & 87.78/88.37 (![X180]: 87.78/88.37 (X178( 87.78/88.37 X180) => 87.78/88.37 (X179 = 87.78/88.37 X180))))) => 87.78/88.37 (?[X181]: 87.78/88.37 (X178( 87.78/88.37 X181) & 87.78/88.37 (![X182]: 87.78/88.37 (X178( 87.78/88.37 X182) => 87.78/88.37 (X181 = 87.78/88.37 X182))))))) => 87.78/88.37 ((![X183:( 87.78/88.37 $i > $o)]: 87.78/88.37 (( 87.78/88.37 ?[X184]: 87.78/88.37 X183( 87.78/88.37 X184)) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X185, 87.78/88.37 X186]: 87.78/88.37 (X183( 87.78/88.37 X185) => 87.78/88.37 (X183( 87.78/88.37 X186) => 87.78/88.37 (X185 = 87.78/88.37 X186)))) => 87.78/88.37 ( 87.78/88.37 ?[X187]: 87.78/88.37 (X183( 87.78/88.37 X187) & 87.78/88.37 (![X188]: 87.78/88.37 (X183( 87.78/88.37 X188) => 87.78/88.37 (X187 = 87.78/88.37 X188)))))))) => 87.78/88.37 ((![X189:( 87.78/88.37 $i > $o)]: 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ?[X190]: 87.78/88.37 (![X191]: 87.78/88.37 (X189( 87.78/88.37 X191) <=> 87.78/88.37 (X191 = 87.78/88.37 X190)))) => 87.78/88.37 ( 87.78/88.37 ?[X192]: 87.78/88.37 (X189( 87.78/88.37 X192) & 87.78/88.37 (![X193]: 87.78/88.37 (X189( 87.78/88.37 X193) => 87.78/88.37 (X192 = 87.78/88.37 X193))))))) => 87.78/88.37 ((![X194, 87.78/88.37 X195]: 87.78/88.37 (( 87.78/88.37 X194 = 87.78/88.37 X195) => 87.78/88.37 (![X196, 87.78/88.37 X197]: 87.78/88.37 (( 87.78/88.37 X196 = 87.78/88.37 X197) => 87.78/88.37 (in( 87.78/88.37 X196,X194) => 87.78/88.37 in( 87.78/88.37 X197,X195)))))) => 87.78/88.37 ((![X198, 87.78/88.37 X199]: 87.78/88.37 (( 87.78/88.37 X198 = 87.78/88.37 X199) => 87.78/88.37 (![X200, 87.78/88.37 X201]: 87.78/88.37 (( 87.78/88.37 X200 = 87.78/88.37 X201) => 87.78/88.37 (in( 87.78/88.37 X200,X198) <=> 87.78/88.37 in( 87.78/88.37 X201,X199)))))) => 87.78/88.37 (( 87.78/88.37 ![X202:( 87.78/88.37 $i > $o)]: 87.78/88.37 (( 87.78/88.37 ?[X203]: 87.78/88.37 (X202( 87.78/88.37 X203) & 87.78/88.37 (![X204]: 87.78/88.37 (X202( 87.78/88.37 X204) => 87.78/88.37 (X203 = 87.78/88.37 X204))))) => 87.78/88.37 (![X205, 87.78/88.37 X206]: 87.78/88.37 (X202( 87.78/88.37 X205) => 87.78/88.37 (X202( 87.78/88.37 X206) => 87.78/88.37 (X205 = 87.78/88.37 X206)))))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X207:( 87.78/88.37 $i > $o), 87.78/88.37 X208:( 87.78/88.37 $i > $o)]: 87.78/88.37 (( 87.78/88.37 ![X209, 87.78/88.37 X210]: 87.78/88.37 (( 87.78/88.37 X209 = 87.78/88.37 X210) => 87.78/88.37 (X207( 87.78/88.37 X209) <=> 87.78/88.37 X208( 87.78/88.37 X210)))) => 87.78/88.37 (( 87.78/88.37 ?[X211]: 87.78/88.37 (X207( 87.78/88.37 X211) & 87.78/88.37 (![X212]: 87.78/88.37 (X207( 87.78/88.37 X212) => 87.78/88.37 (X211 = 87.78/88.37 X212))))) <=> 87.78/88.37 (?[X213]: 87.78/88.37 (X208( 87.78/88.37 X213) & 87.78/88.37 (![X214]: 87.78/88.37 (X208( 87.78/88.37 X214) => 87.78/88.37 (X213 = 87.78/88.37 X214)))))))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 emptyset = 87.78/88.37 emptyset) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X215, 87.78/88.37 X216]: 87.78/88.37 (( 87.78/88.37 X215 = 87.78/88.37 X216) => 87.78/88.37 (![X217, 87.78/88.37 X218]: 87.78/88.37 (( 87.78/88.37 X217 = 87.78/88.37 X218) => 87.78/88.37 (setadjoin( 87.78/88.37 X215,X217) = 87.78/88.37 setadjoin( 87.78/88.37 X216,X218)))))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X219, 87.78/88.37 X220]: 87.78/88.37 (( 87.78/88.37 X219 = 87.78/88.37 X220) => 87.78/88.37 (powerset( 87.78/88.37 X219) = 87.78/88.37 powerset( 87.78/88.37 X220)))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X221, 87.78/88.37 X222]: 87.78/88.37 (( 87.78/88.37 X221 = 87.78/88.37 X222) => 87.78/88.37 (setunion( 87.78/88.37 X221) = 87.78/88.37 setunion( 87.78/88.37 X222)))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 omega = 87.78/88.37 omega) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X223:( 87.78/88.37 $i > $o)]: 87.78/88.37 (( 87.78/88.37 ?[X224]: 87.78/88.37 (X223( 87.78/88.37 X224) & 87.78/88.37 (![X225]: 87.78/88.37 (X223( 87.78/88.37 X225) => 87.78/88.37 (X224 = 87.78/88.37 X225))))) => 87.78/88.37 (![X226, 87.78/88.37 X227]: 87.78/88.37 (X223( 87.78/88.37 X226) => 87.78/88.37 (X223( 87.78/88.37 X227) => 87.78/88.37 (X226 = 87.78/88.37 X227)))))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X228:( 87.78/88.37 $i > $o), 87.78/88.37 X229:( 87.78/88.37 $i > $o)]: 87.78/88.37 (( 87.78/88.37 ![X230, 87.78/88.37 X231]: 87.78/88.37 (( 87.78/88.37 X230 = 87.78/88.37 X231) => 87.78/88.37 (X228( 87.78/88.37 X230) <=> 87.78/88.37 X229( 87.78/88.37 X231)))) => 87.78/88.37 (( 87.78/88.37 ?[X232]: 87.78/88.37 (X228( 87.78/88.37 X232) & 87.78/88.37 (![X233]: 87.78/88.37 (X228( 87.78/88.37 X233) => 87.78/88.37 (X232 = 87.78/88.37 X233))))) => 87.78/88.37 (( 87.78/88.37 ?[X234]: 87.78/88.37 (X229( 87.78/88.37 X234) & 87.78/88.37 (![X235]: 87.78/88.37 (X229( 87.78/88.37 X235) => 87.78/88.37 (X234 = 87.78/88.37 X235))))) => 87.78/88.37 (descr( 87.78/88.37 ^[V_9]: 87.78/88.37 X228(V_9)) = 87.78/88.37 descr( 87.78/88.37 ^[V_10]: 87.78/88.37 X229( 87.78/88.37 V_10))))))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X236, 87.78/88.37 X237]: 87.78/88.37 (( 87.78/88.37 X236 = 87.78/88.37 X237) => 87.78/88.37 (![X238:( 87.78/88.37 $i > $o), 87.78/88.37 X239:( 87.78/88.37 $i > $o)]: 87.78/88.37 (( 87.78/88.37 ![X240]: 87.78/88.37 (in( 87.78/88.37 X240,X236) => 87.78/88.37 (![X241]: 87.78/88.37 (in( 87.78/88.37 X241,X237) => 87.78/88.37 (( 87.78/88.37 X240 = 87.78/88.37 X241) => 87.78/88.37 (X238( 87.78/88.37 X240) <=> 87.78/88.37 X239( 87.78/88.37 X241))))))) => 87.78/88.37 (dsetconstr( 87.78/88.37 X236, 87.78/88.37 ^[V_11]: 87.78/88.37 X238( 87.78/88.37 V_11)) = 87.78/88.37 dsetconstr( 87.78/88.37 X237, 87.78/88.37 ^[V_12]: 87.78/88.37 X239( 87.78/88.37 V_12))))))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X242, 87.78/88.37 X243]: 87.78/88.37 (( 87.78/88.37 ![X244]: 87.78/88.37 (in( 87.78/88.37 X244,X242) => 87.78/88.37 in( 87.78/88.37 X244,X243))) => 87.78/88.37 subset( 87.78/88.37 X242,X243))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X245, 87.78/88.37 X246]: 87.78/88.37 (( 87.78/88.37 X245 = 87.78/88.37 X246) => 87.78/88.37 subset( 87.78/88.37 X246,X245))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X247, 87.78/88.37 X248]: 87.78/88.37 (( 87.78/88.37 X247 = 87.78/88.37 X248) => 87.78/88.37 subset( 87.78/88.37 X247,X248))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X249, 87.78/88.37 X250]: 87.78/88.37 (( 87.78/88.37 ![X251]: 87.78/88.37 (in( 87.78/88.37 X251,X249) => 87.78/88.37 in( 87.78/88.37 X251,X250))) => 87.78/88.37 subset( 87.78/88.37 X249,X250))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X252]: 87.78/88.37 subset( 87.78/88.37 emptyset, 87.78/88.37 X252)) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X253, 87.78/88.37 X254,X255]: 87.78/88.37 (subset( 87.78/88.37 X253,X254) => 87.78/88.37 (in( 87.78/88.37 X255,X253) => 87.78/88.37 in( 87.78/88.37 X255,X254)))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X256, 87.78/88.37 X257,X258]: 87.78/88.37 (subset( 87.78/88.37 X256,X257) => 87.78/88.37 (( 87.78/88.37 ~ 87.78/88.37 in( 87.78/88.37 X258,X257)) => 87.78/88.37 (~ 87.78/88.37 in( 87.78/88.37 X258,X256))))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X259, 87.78/88.37 X260,X261]: 87.78/88.37 (in( 87.78/88.37 X261,X259) => 87.78/88.37 (( 87.78/88.37 ~ 87.78/88.37 in( 87.78/88.37 X261,X260)) => 87.78/88.37 (~ 87.78/88.37 subset( 87.78/88.37 X259,X260))))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X262, 87.78/88.37 X263]: 87.78/88.37 (( 87.78/88.37 ~ 87.78/88.37 subset( 87.78/88.37 X262,X263)) => 87.78/88.37 (X262 != 87.78/88.37 X263))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X264, 87.78/88.37 X265,X266]: 87.78/88.37 (in( 87.78/88.37 X266,X264) => 87.78/88.37 (( 87.78/88.37 ~ 87.78/88.37 in( 87.78/88.37 X266,X265)) => 87.78/88.37 (X264 != 87.78/88.37 X265)))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X267]: 87.78/88.37 subset( 87.78/88.37 X267,X267)) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X268, 87.78/88.37 X269,X270]: 87.78/88.37 (subset( 87.78/88.37 X268,X269) => 87.78/88.37 (subset( 87.78/88.37 X269,X270) => 87.78/88.37 subset( 87.78/88.37 X268,X270)))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X271, 87.78/88.37 X272]: 87.78/88.37 subset( 87.78/88.37 X272, 87.78/88.37 setadjoin( 87.78/88.37 X271,X272))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X273, 87.78/88.37 X274,X275]: 87.78/88.37 (subset( 87.78/88.37 X273,X275) => 87.78/88.37 subset( 87.78/88.37 X273, 87.78/88.37 setadjoin( 87.78/88.37 X274,X275)))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X276, 87.78/88.37 X277]: 87.78/88.37 (subset( 87.78/88.37 X276,X277) => 87.78/88.37 in( 87.78/88.37 X276, 87.78/88.37 powerset( 87.78/88.37 X277)))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X278, 87.78/88.37 X279]: 87.78/88.37 (subset( 87.78/88.37 X278,X279) => 87.78/88.37 (subset( 87.78/88.37 X279,X278) => 87.78/88.37 (X278 = 87.78/88.37 X279)))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X280]: 87.78/88.37 (subset( 87.78/88.37 X280, 87.78/88.37 emptyset) => 87.78/88.37 (X280 = 87.78/88.37 emptyset))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X281, 87.78/88.37 X282]: 87.78/88.37 (subset( 87.78/88.37 X282,X281) => 87.78/88.37 in( 87.78/88.37 X282, 87.78/88.37 powerset( 87.78/88.37 X281)))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X283, 87.78/88.37 X284]: 87.78/88.37 (in( 87.78/88.37 X284, 87.78/88.37 powerset( 87.78/88.37 X283)) => 87.78/88.37 subset( 87.78/88.37 X284,X283))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X285]: 87.78/88.37 in( 87.78/88.37 X285, 87.78/88.37 powerset( 87.78/88.37 X285))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X286, 87.78/88.37 X287]: 87.78/88.37 (subset( 87.78/88.37 X286,X287) => 87.78/88.37 subset( 87.78/88.37 powerset( 87.78/88.37 X286), 87.78/88.37 powerset( 87.78/88.37 X287)))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X288, 87.78/88.37 X289:( 87.78/88.37 $i > $o)]: 87.78/88.37 in( 87.78/88.37 dsetconstr( 87.78/88.37 X288, 87.78/88.37 ^[V_13]: 87.78/88.37 X289( 87.78/88.37 V_13)), 87.78/88.37 powerset( 87.78/88.37 X288))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X290, 87.78/88.37 X291:( 87.78/88.37 $i > $o)]: 87.78/88.37 subset( 87.78/88.37 dsetconstr( 87.78/88.37 X290, 87.78/88.37 ^[V_14]: 87.78/88.37 X291( 87.78/88.37 V_14)), 87.78/88.37 X290)) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X292, 87.78/88.37 X293,X294]: 87.78/88.37 (in( 87.78/88.37 X294,X292) => 87.78/88.37 in( 87.78/88.37 X294, 87.78/88.37 binunion( 87.78/88.37 X292,X293)))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X295, 87.78/88.37 X296]: 87.78/88.37 in( 87.78/88.37 X296, 87.78/88.37 setadjoin( 87.78/88.37 X295, 87.78/88.37 setadjoin( 87.78/88.37 X296, 87.78/88.37 emptyset)))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X297, 87.78/88.37 X298,X299]: 87.78/88.37 (in( 87.78/88.37 X299,X298) => 87.78/88.37 in( 87.78/88.37 X299, 87.78/88.37 binunion( 87.78/88.37 X297,X298)))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X300, 87.78/88.37 X301, 87.78/88.37 X302, 87.78/88.37 X303:$o]: 87.78/88.37 (in( 87.78/88.37 X302, 87.78/88.37 binunion( 87.78/88.37 X300,X301)) => 87.78/88.37 (( 87.78/88.37 in( 87.78/88.37 X302,X300) => 87.78/88.37 X303) => 87.78/88.37 (( 87.78/88.37 in( 87.78/88.37 X302,X301) => 87.78/88.37 X303) => 87.78/88.37 X303)))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X304, 87.78/88.37 X305,X306]: 87.78/88.37 (in( 87.78/88.37 X306, 87.78/88.37 binunion( 87.78/88.37 X304,X305)) => 87.78/88.37 (in( 87.78/88.37 X306,X304) | 87.78/88.37 in( 87.78/88.37 X306,X305)))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X307, 87.78/88.37 X308]: 87.78/88.37 subset( 87.78/88.37 X307, 87.78/88.37 binunion( 87.78/88.37 X307,X308))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X309, 87.78/88.37 X310]: 87.78/88.37 subset( 87.78/88.37 X310, 87.78/88.37 binunion( 87.78/88.37 X309,X310))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X311, 87.78/88.37 X312,X313]: 87.78/88.37 (in( 87.78/88.37 X313,X311) => 87.78/88.37 (in( 87.78/88.37 X313,X312) => 87.78/88.37 in( 87.78/88.37 X313, 87.78/88.37 binintersect( 87.78/88.37 X311,X312))))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X314, 87.78/88.37 X315,X316]: 87.78/88.37 (subset( 87.78/88.37 X316,X314) => 87.78/88.37 (subset( 87.78/88.37 X316,X315) => 87.78/88.37 subset( 87.78/88.37 X316, 87.78/88.37 binintersect( 87.78/88.37 X314,X315))))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X317, 87.78/88.37 X318,X319]: 87.78/88.37 (in( 87.78/88.37 X319, 87.78/88.37 binintersect( 87.78/88.37 X317,X318)) => 87.78/88.37 in( 87.78/88.37 X319,X317))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X320, 87.78/88.37 X321]: 87.78/88.37 subset( 87.78/88.37 binintersect( 87.78/88.37 X320,X321), 87.78/88.37 X320)) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X322, 87.78/88.37 X323]: 87.78/88.37 (subset( 87.78/88.37 X322,X323) => 87.78/88.37 (binintersect( 87.78/88.37 X322,X323) = 87.78/88.37 X322))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X324, 87.78/88.37 X325]: 87.78/88.37 (( 87.78/88.37 binintersect( 87.78/88.37 X324,X325) = 87.78/88.37 X325) => 87.78/88.37 subset( 87.78/88.37 X325,X324))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X326, 87.78/88.37 X327,X328]: 87.78/88.37 (in( 87.78/88.37 X328, 87.78/88.37 binintersect( 87.78/88.37 X326,X327)) => 87.78/88.37 in( 87.78/88.37 X328,X327))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X329, 87.78/88.37 X330]: 87.78/88.37 (( 87.78/88.37 ~ 87.78/88.37 ( 87.78/88.37 ?[X331]: 87.78/88.37 (in( 87.78/88.37 X331,X329) & 87.78/88.37 in( 87.78/88.37 X331,X330)))) => 87.78/88.37 (binintersect( 87.78/88.37 X329,X330) = 87.78/88.37 emptyset))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X332, 87.78/88.37 X333]: 87.78/88.37 subset( 87.78/88.37 binintersect( 87.78/88.37 X332,X333), 87.78/88.37 X333)) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X334, 87.78/88.37 X335]: 87.78/88.37 (subset( 87.78/88.37 X335,X334) => 87.78/88.37 (binintersect( 87.78/88.37 X334,X335) = 87.78/88.37 X335))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X336, 87.78/88.37 X337]: 87.78/88.37 (( 87.78/88.37 binintersect( 87.78/88.37 X336,X337) = 87.78/88.37 X336) => 87.78/88.37 subset( 87.78/88.37 X336,X337))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X338, 87.78/88.37 X339,X340]: 87.78/88.37 (binintersect( 87.78/88.37 X338, 87.78/88.37 binunion( 87.78/88.37 X339,X340)) = 87.78/88.37 binunion( 87.78/88.37 binintersect( 87.78/88.37 X338,X339), 87.78/88.37 binintersect( 87.78/88.37 X338,X340)))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X341, 87.78/88.37 X342,X343]: 87.78/88.37 (in( 87.78/88.37 X343,X341) => 87.78/88.37 (( 87.78/88.37 ~ 87.78/88.37 in( 87.78/88.37 X343,X342)) => 87.78/88.37 in( 87.78/88.37 X343, 87.78/88.37 setminus( 87.78/88.37 X341,X342))))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X344, 87.78/88.37 X345,X346]: 87.78/88.37 (in( 87.78/88.37 X346, 87.78/88.37 setminus( 87.78/88.37 X344,X345)) => 87.78/88.37 in( 87.78/88.37 X346,X344))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X347, 87.78/88.37 X348,X349]: 87.78/88.37 (in( 87.78/88.37 X349, 87.78/88.37 setminus( 87.78/88.37 X347,X348)) => 87.78/88.37 (~ 87.78/88.37 in( 87.78/88.37 X349,X348)))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X350, 87.78/88.37 X351]: 87.78/88.37 (subset( 87.78/88.37 X350,X351) => 87.78/88.37 (setminus( 87.78/88.37 X350,X351) = 87.78/88.37 emptyset))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X352, 87.78/88.37 X353,X354]: 87.78/88.37 (( 87.78/88.37 ~ 87.78/88.37 in( 87.78/88.37 X354, 87.78/88.37 setminus( 87.78/88.37 X352,X353))) => 87.78/88.37 (in( 87.78/88.37 X354,X352) => 87.78/88.37 in( 87.78/88.37 X354,X353)))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X355, 87.78/88.37 X356,X357]: 87.78/88.37 (( 87.78/88.37 ~ 87.78/88.37 in( 87.78/88.37 X357, 87.78/88.37 setminus( 87.78/88.37 X355,X356))) => 87.78/88.37 (( 87.78/88.37 ~ 87.78/88.37 in( 87.78/88.37 X357,X356)) => 87.78/88.37 (~ 87.78/88.37 in( 87.78/88.37 X357,X355))))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X358, 87.78/88.37 X359,X360]: 87.78/88.37 (( 87.78/88.37 ~ 87.78/88.37 in( 87.78/88.37 X360,X358)) => 87.78/88.37 (~ 87.78/88.37 in( 87.78/88.37 X360, 87.78/88.37 setminus( 87.78/88.37 X358,X359))))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X361, 87.78/88.37 X362,X363]: 87.78/88.37 (in( 87.78/88.37 X363,X362) => 87.78/88.37 (~ 87.78/88.37 in( 87.78/88.37 X363, 87.78/88.37 setminus( 87.78/88.37 X361,X362))))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X364, 87.78/88.37 X365]: 87.78/88.37 subset( 87.78/88.37 setminus( 87.78/88.37 X364,X365), 87.78/88.37 X364)) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X366, 87.78/88.37 X367]: 87.78/88.37 (( 87.78/88.37 setminus( 87.78/88.37 X366,X367) = 87.78/88.37 emptyset) => 87.78/88.37 subset( 87.78/88.37 X366,X367))) => 87.78/88.37 ( 87.78/88.37 ![X368, 87.78/88.37 X369,X370]: 87.78/88.37 (in( 87.78/88.37 X370, 87.78/88.37 dsetconstr( 87.78/88.37 binunion( 87.78/88.37 X368,X369), 87.78/88.37 ^[V_15]: 87.78/88.37 (( 87.78/88.37 ~ 87.78/88.37 in( 87.78/88.37 V_15,X368)) | 87.78/88.37 (~ 87.78/88.37 in( 87.78/88.37 V_15,X369))))) => 87.78/88.37 (![X371:$o]: 87.78/88.37 (( 87.78/88.37 in( 87.78/88.37 X370,X368) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ~ 87.78/88.37 in( 87.78/88.37 X370,X369)) => 87.78/88.37 X371)) => 87.78/88.37 (( 87.78/88.37 ( 87.78/88.37 ~ 87.78/88.37 in( 87.78/88.37 X370,X368)) => 87.78/88.37 ( 87.78/88.37 in( 87.78/88.37 X370,X369) => 87.78/88.37 X371)) => 87.78/88.37 X371))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 87.78/88.37 tff(zf_stmt_1, type, zip_tseitin5 : ($i * $i > $o) > $o). 87.78/88.37 tff(zf_stmt_2, axiom, 87.78/88.37 (zip_tseitin5(X211,X207) <=> 87.78/88.37 ((![X212]: zip_tseitin4(X212,X211,X207)) & X207(X211)))). 87.78/88.37 tff(zf_stmt_3, type, zip_tseitin4 : ($i * $i * $i > $o) > $o). 87.78/88.37 tff(zf_stmt_4, axiom, 87.78/88.37 (zip_tseitin4(X212,X211,X207) <=> (X207(X212) => (X211 = X212)))). 87.78/88.37 tff(zf_stmt_5, type, zip_tseitin3 : ($i * $i * $i * ($i * $i) > $o) > $o). 87.78/88.37 tff(zf_stmt_6, axiom, 87.78/88.37 (zip_tseitin3(X26,X25,X20,X19) <=> (X19(X26,X25) & in(X26,X20)))). 87.78/88.37 tff(zf_stmt_7, type, zip_tseitin2 : ($i * $i * $i) > $o). 87.78/88.37 tff(zf_stmt_8, axiom, 87.78/88.37 (zip_tseitin2(X14,X13,X12) <=> (in(X14,X12) & in(X13,X14)))). 87.78/88.37 tff(zf_stmt_9, type, zip_tseitin1 : ($i * $i * $i) > $o). 87.78/88.37 tff(zf_stmt_10, axiom, 87.78/88.37 (zip_tseitin1(X11,X10,X9) <=> (in(X11,X10) => in(X11,X9)))). 87.78/88.37 tff(zf_stmt_11, type, zip_tseitin0 : ($i * $i * $i) > $o). 87.78/88.37 tff(zf_stmt_12, axiom, (zip_tseitin0(X8,X7,X6) <=> (in(X8,X7) | (X8 = X6)))). 87.78/88.37 tff(zf_stmt_13, conjecture, 87.78/88.37 ((![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))) => 87.78/88.37 ((![X5]: (~in(X5,emptyset))) => 87.78/88.37 ((![X6,X7,X8]: (in(X8,setadjoin(X6,X7)) <=> zip_tseitin0(X8,X7,X6))) => 87.78/88.37 ((![X9,X10]: 87.78/88.37 (in(X10,powerset(X9)) <=> (![X11]: zip_tseitin1(X11,X10,X9)))) => 87.78/88.37 ((![X12,X13]: 87.78/88.37 (in(X13,setunion(X12)) <=> (?[X14]: zip_tseitin2(X14,X13,X12)))) => 87.78/88.37 (in(emptyset,omega) => 87.78/88.37 ((![X15]: (in(X15,omega) => in(setadjoin(X15,X15),omega))) => 87.78/88.37 ((![X16]: 87.78/88.37 (((![X17]: 87.78/88.37 ((in(X17,X16) & in(X17,omega)) => 87.78/88.37 in(setadjoin(X17,X17),X16))) & 87.78/88.37 in(emptyset,X16)) => 87.78/88.37 (![X18]: (in(X18,omega) => in(X18,X16))))) => 87.78/88.37 ((![X19:(($i * $i) > $o),X20]: 87.78/88.37 ((![X21]: 87.78/88.37 (in(X21,X20) => 87.78/88.37 (?[X22]: 87.78/88.37 ((![X23]: (X19(X21,X23) => (X22 = X23))) & X19(X21,X22))))) => 87.78/88.37 (?[X24]: 87.78/88.37 (![X25]: 87.78/88.37 (in(X25,X24) <=> (?[X26]: zip_tseitin3(X26,X25,X20,X19))))))) => 87.78/88.37 ((![X27]: 87.78/88.37 ((?[X28]: in(X28,X27)) => 87.78/88.37 (?[X29]: 87.78/88.37 ((~(?[X30]: (in(X30,X27) & in(X30,X29)))) & in(X29,X27))))) => 87.78/88.37 ((![X31]: 87.78/88.37 (?[X32]: 87.78/88.37 ((![X33]: 87.78/88.37 (((?[X34]: in(X34,X33)) & 87.78/88.37 (![X35]: (in(X35,X33) => in(X35,X31)))) => 87.78/88.37 (?[X36,X37]: 87.78/88.37 ((![X38]: 87.78/88.37 (in(X38,X32) => 87.78/88.37 (in(X37,X38) | 87.78/88.37 (![X39]: (in(X39,X38) => in(X39,X36)))))) & 87.78/88.37 (~(?[X40]: (in(X40,X33) & in(X40,X36)))) & 87.78/88.37 in(X37,X33) & in(X36,X32))))) & 87.78/88.37 (![X41,X42]: 87.78/88.37 ((in(X42,X32) & in(X41,X32)) => 87.78/88.37 ((![X43]: (in(X43,X42) => in(X43,X41))) | 87.78/88.37 (![X44]: (in(X44,X41) => in(X44,X42)))))) & 87.78/88.37 (![X45,X46]: 87.78/88.37 ((in(X46,X31) & in(X45,X31)) => 87.78/88.37 ((![X47]: 87.78/88.37 (in(X47,X32) => (in(X45,X47) <=> in(X46,X47)))) => 87.78/88.37 (X45 = X46)))) & 87.78/88.37 (![X48]: 87.78/88.37 (in(X48,X32) => (![X49]: (in(X49,X48) => in(X49,X31)))))))) => 87.78/88.37 ((![X50:($i > $o)]: 87.78/88.37 ((?[X51]: ((![X52]: (X50(X52) => (X51 = X52))) & X50(X51))) => 87.78/88.37 X50(descr(^[V_1]: X50(V_1))))) => 87.78/88.37 ((![X53,X54:($i > $o),X55]: 87.78/88.37 (in(X55,X53) => 87.78/88.37 (X54(X55) => in(X55,dsetconstr(X53,^[V_2]: X54(V_2)))))) => 87.78/88.37 ((![X56,X57:($i > $o),X58]: 87.78/88.37 (in(X58,dsetconstr(X56,^[V_3]: X57(V_3))) => in(X58,X56))) => 87.78/88.37 ((![X59,X60:($i > $o),X61]: 87.78/88.37 (in(X61,dsetconstr(X59,^[V_4]: X60(V_4))) => X60(X61))) => 87.78/88.37 ((![X62:($i > $o)]: 87.78/88.37 ((?[X63]: 87.78/88.37 ((![X64]: (X62(X64) => (X63 = X64))) & X62(X63))) => 87.78/88.37 (?[X65]: 87.78/88.37 ((![X66]: (X62(X66) => (X65 = X66))) & X62(X65))))) => 87.78/88.37 ((![X67:$o,X68]: (in(X68,prop2set(X67)) => X67)) => 87.78/88.37 ((![X69]: (in(X69,emptyset) => (![X70:$o]: X70))) => 87.78/88.37 ((![X71]: (in(X71,emptyset) => $false)) => 87.78/88.37 ((![X72]: (~in(X72,emptyset))) => 87.78/88.37 ((![X73:($i > $o)]: 87.78/88.37 ((?[X74]: 87.78/88.37 ((![X75]: (X73(X75) => (X74 = X75))) & X73(X74))) => 87.78/88.37 (?[X76]: X73(X76)))) => 87.78/88.37 ((![X77,X78]: 87.78/88.37 ((![X79]: (in(X79,X77) => in(X79,X78))) => 87.78/88.37 ((![X80]: (in(X80,X78) => in(X80,X77))) => 87.78/88.37 (X77 = X78)))) => 87.78/88.37 ((![X81]: 87.78/88.37 ((![X82]: (~in(X82,X81))) => (X81 = emptyset))) => 87.78/88.37 ((![X83]: 87.78/88.37 ((![X84]: (~in(X84,X83))) => (X83 = emptyset))) => 87.78/88.37 ((![X85,X86:($i > $o),X87]: 87.78/88.37 (in(X87,X85) => 87.78/88.37 (in(X87,dsetconstr(X85,^[V_5]: X86(V_5))) <=> 87.78/88.37 X86(X87)))) => 87.78/88.37 ((![X88]: 87.78/88.37 ((X88 != emptyset) => (?[X89]: in(X89,X88)))) => 87.78/88.37 ((![X90,X91:($i > $o),X92]: 87.78/88.37 (in(X92,X90) => 87.78/88.37 (X91(X92) => 87.78/88.37 (dsetconstr(X90,^[V_6]: X91(V_6)) != 87.78/88.37 emptyset)))) => 87.78/88.37 ((![X93]: 87.78/88.37 ((?[X94]: in(X94,X93)) => (X93 != emptyset))) => 87.78/88.37 ((![X95,X96]: in(X95,setadjoin(X95,X96))) => 87.78/88.37 (in(emptyset,setadjoin(emptyset,emptyset)) => 87.78/88.37 ((![X97,X98,X99]: 87.78/88.37 (in(X99,X98) => 87.78/88.37 in(X99,setadjoin(X97,X98)))) => 87.78/88.37 ((![X100,X101,X102]: 87.78/88.37 (in(X102,setadjoin(X100,X101)) => 87.78/88.37 (![X103:$o]: 87.78/88.37 (((X102 = X100) => X103) => 87.78/88.37 ((in(X102,X101) => X103) => X103))))) => 87.78/88.37 ((![X104,X105,X106]: 87.78/88.37 (in(X106,setadjoin(X104,X105)) => 87.78/88.37 (in(X106,X105) | (X106 = X104)))) => 87.78/88.37 ((![X107]: 87.78/88.37 (dsetconstr(X107,^[V_7]: $true) = X107)) => 87.78/88.37 ((![X108,X109]: 87.78/88.37 ((![X110]: 87.78/88.37 (in(X110,X109) => in(X110,X108))) => 87.78/88.37 in(X109,powerset(X108)))) => 87.78/88.37 ((![X111]: in(emptyset,powerset(X111))) => 87.78/88.37 ((![X112]: in(emptyset,powerset(X112))) => 87.78/88.37 ((![X113,X114,X115]: 87.78/88.37 (in(X114,powerset(X113)) => 87.78/88.37 (in(X115,X114) => in(X115,X113)))) => 87.78/88.37 ((![X116,X117,X118]: 87.78/88.37 (in(X117,X118) => 87.78/88.37 (in(X118,X116) => 87.78/88.37 in(X117,setunion(X116))))) => 87.78/88.37 ((![X119,X120]: 87.78/88.37 (in(X120,setunion(X119)) => 87.78/88.37 (![X121:$o]: 87.78/88.37 ((![X122]: 87.78/88.37 (in(X120,X122) => 87.78/88.37 (in(X122,X119) => X121))) => 87.78/88.37 X121)))) => 87.78/88.37 ((![X123,X124]: 87.78/88.37 (in(X124,X123) => 87.78/88.37 in(X124, 87.78/88.37 powerset(setunion(X123))))) => 87.78/88.37 ((![X125:($i > $o)]: 87.78/88.37 ((?[X126]: 87.78/88.37 ((![X127]: 87.78/88.37 (X125(X127) => 87.78/88.37 (X126 = X127))) & 87.78/88.37 X125(X126))) => 87.78/88.37 (?[X128]: 87.78/88.37 (![X129]: 87.78/88.37 (X125(X129) <=> 87.78/88.37 (X129 = X128)))))) => 87.78/88.37 ((![X130]: 87.78/88.37 ((X130 != emptyset) => 87.78/88.37 (?[X131]: in(X131,X130)))) => 87.78/88.37 ((![X132,X133]: 87.78/88.37 (in(X132, 87.78/88.37 setadjoin(X133,emptyset)) => 87.78/88.37 (X132 = X133))) => 87.78/88.37 ((![X134,X135]: 87.78/88.37 ((X134 != X135) => 87.78/88.37 (~ 87.78/88.37 in(X135, 87.78/88.37 setadjoin(X134, 87.78/88.37 emptyset))))) => 87.78/88.37 ((![X136,X137]: 87.78/88.37 ((X136 = X137) => 87.78/88.37 in(X136, 87.78/88.37 setadjoin(X137, 87.78/88.37 emptyset)))) => 87.78/88.37 ((![X138,X139]: 87.78/88.37 (in(X138, 87.78/88.37 setadjoin(X139, 87.78/88.37 emptyset)) => 87.78/88.37 in(X139, 87.78/88.37 setadjoin(X138, 87.78/88.37 emptyset)))) => 87.78/88.37 ((![X140,X141,X142]: 87.78/88.37 (in(X142, 87.78/88.37 setadjoin(X140, 87.78/88.37 setadjoin( 87.78/88.37 X141, 87.78/88.37 emptyset))) => 87.78/88.37 ((X142 = X141) | 87.78/88.37 (X142 = X140)))) => 87.78/88.37 ((![X143,X144]: 87.78/88.37 in(X143, 87.78/88.37 setadjoin(X143, 87.78/88.37 setadjoin( 87.78/88.37 X144, 87.78/88.37 emptyset)))) => 87.78/88.37 ((![X145,X146]: 87.78/88.37 in(X146, 87.78/88.37 setadjoin(X145, 87.78/88.37 setadjoin( 87.78/88.37 X146, 87.78/88.37 emptyset)))) => 87.78/88.37 ((![X147,X148:($i > $o)]: 87.78/88.37 ((?[X149]: 87.78/88.37 (X148(X149) & 87.78/88.37 in(X149,X147))) => 87.78/88.37 ((dsetconstr( 87.78/88.37 X147, 87.78/88.37 ^[V_8]: X148(V_8)) = 87.78/88.37 emptyset) => 87.78/88.37 $false))) => 87.78/88.37 ((![X150:($i > $o),X151]: 87.78/88.37 (in(X151,emptyset) => 87.78/88.37 X150(X151))) => 87.78/88.37 ((![X152,X153:($i > $o)]: 87.78/88.37 ((~ 87.78/88.37 (![X154]: 87.78/88.37 (in(X154,X152) => 87.78/88.37 X153(X154)))) => 87.78/88.37 (?[X155]: 87.78/88.37 ((~X153(X155)) & 87.78/88.37 in(X155,X152))))) => 87.78/88.37 ((![X156, 87.78/88.37 X157:($i > $o)]: 87.78/88.37 ((![X158]: 87.78/88.37 (in(X158,X156) => 87.78/88.37 (~X157(X158)))) => 87.78/88.37 (~ 87.78/88.37 (?[X159]: 87.78/88.37 (X157(X159) & 87.78/88.37 in( 87.78/88.37 X159,X156)))))) => 87.78/88.37 ((![X160, 87.78/88.37 X161:($i > $o)]: 87.78/88.37 ((~ 87.78/88.37 (?[X162]: 87.78/88.37 (X161(X162) & 87.78/88.37 in( 87.78/88.37 X162,X160)))) => 87.78/88.37 (![X163]: 87.78/88.37 (in(X163,X160) => 87.78/88.37 (~X161(X163)))))) => 87.78/88.37 ((![X164, 87.78/88.37 X165:($i > $o)]: 87.78/88.37 ((?[X166]: 87.78/88.37 ((~ 87.78/88.37 X165( 87.78/88.37 X166)) & 87.78/88.37 in( 87.78/88.37 X166,X164))) => 87.78/88.37 (~ 87.78/88.37 (![X167]: 87.78/88.37 (in( 87.78/88.37 X167,X164) => 87.78/88.37 X165( 87.78/88.37 X167)))))) => 87.78/88.37 ((![X168:$o]: 87.78/88.37 (X168 => 87.78/88.37 in(emptyset, 87.78/88.37 prop2set( 87.78/88.37 X168)))) => 87.78/88.37 ((![X169:$o]: 87.78/88.37 (X169 => 87.78/88.37 set2prop( 87.78/88.37 prop2set( 87.78/88.37 X169)))) => 87.78/88.37 ((![X170, 87.78/88.37 X171:( 87.78/88.37 $i > $o)]: 87.78/88.37 ((~ 87.78/88.37 (?[X172]: 87.78/88.37 (X171( 87.78/88.37 X172) & 87.78/88.37 in( 87.78/88.37 X172,X170)))) => 87.78/88.37 (![X173]: 87.78/88.37 ( 87.78/88.37 in( 87.78/88.37 X173,X170) => 87.78/88.37 ( 87.78/88.37 ~ 87.78/88.37 X171( 87.78/88.37 X173)))))) => 87.78/88.37 ((![X174, 87.78/88.37 X175:( 87.78/88.37 $i > $o)]: 87.78/88.37 ((~ 87.78/88.37 ( 87.78/88.37 ![X176]: 87.78/88.37 (in( 87.78/88.37 X176,X174) => 87.78/88.37 X175( 87.78/88.37 X176)))) => 87.78/88.37 (?[X177]: 87.78/88.37 (( 87.78/88.37 ~ 87.78/88.37 X175( 87.78/88.37 X177)) & 87.78/88.37 in( 87.78/88.37 X177,X174))))) => 87.78/88.37 ((![X178:( 87.78/88.37 $i > $o)]: 87.78/88.37 ((?[X179]: 87.78/88.37 (( 87.78/88.37 ![X180]: 87.78/88.37 (X178( 87.78/88.37 X180) => 87.78/88.37 (X179 = 87.78/88.37 X180))) & 87.78/88.37 X178( 87.78/88.37 X179))) => 87.78/88.37 (?[X181]: 87.78/88.37 (( 87.78/88.37 ![X182]: 87.78/88.37 (X178( 87.78/88.37 X182) => 87.78/88.37 (X181 = 87.78/88.37 X182))) & 87.78/88.37 X178( 87.78/88.37 X181))))) => 87.78/88.37 ((![X183:( 87.78/88.37 $i > $o)]: 87.78/88.37 (( 87.78/88.37 ?[X184]: 87.78/88.37 X183( 87.78/88.37 X184)) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X185, 87.78/88.37 X186]: 87.78/88.37 (X183( 87.78/88.37 X185) => 87.78/88.37 (X183( 87.78/88.37 X186) => 87.78/88.37 (X185 = 87.78/88.37 X186)))) => 87.78/88.37 ( 87.78/88.37 ?[X187]: 87.78/88.37 (( 87.78/88.37 ![X188]: 87.78/88.37 (X183( 87.78/88.37 X188) => 87.78/88.37 (X187 = 87.78/88.37 X188))) & 87.78/88.37 X183( 87.78/88.37 X187)))))) => 87.78/88.37 ((![X189:( 87.78/88.37 $i > $o)]: 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ?[X190]: 87.78/88.37 (![X191]: 87.78/88.37 (X189( 87.78/88.37 X191) <=> 87.78/88.37 (X191 = 87.78/88.37 X190)))) => 87.78/88.37 ( 87.78/88.37 ?[X192]: 87.78/88.37 (( 87.78/88.37 ![X193]: 87.78/88.37 (X189( 87.78/88.37 X193) => 87.78/88.37 (X192 = 87.78/88.37 X193))) & 87.78/88.37 X189( 87.78/88.37 X192))))) => 87.78/88.37 ((![X194, 87.78/88.37 X195]: 87.78/88.37 (( 87.78/88.37 X194 = 87.78/88.37 X195) => 87.78/88.37 (![X196, 87.78/88.37 X197]: 87.78/88.37 (( 87.78/88.37 X196 = 87.78/88.37 X197) => 87.78/88.37 (in( 87.78/88.37 X196,X194) => 87.78/88.37 in( 87.78/88.37 X197,X195)))))) => 87.78/88.37 ((![X198, 87.78/88.37 X199]: 87.78/88.37 (( 87.78/88.37 X198 = 87.78/88.37 X199) => 87.78/88.37 (![X200, 87.78/88.37 X201]: 87.78/88.37 (( 87.78/88.37 X200 = 87.78/88.37 X201) => 87.78/88.37 (in( 87.78/88.37 X200,X198) <=> 87.78/88.37 in( 87.78/88.37 X201,X199)))))) => 87.78/88.37 (( 87.78/88.37 ![X202:( 87.78/88.37 $i > $o)]: 87.78/88.37 (( 87.78/88.37 ?[X203]: 87.78/88.37 (( 87.78/88.37 ![X204]: 87.78/88.37 (X202( 87.78/88.37 X204) => 87.78/88.37 (X203 = 87.78/88.37 X204))) & 87.78/88.37 X202( 87.78/88.37 X203))) => 87.78/88.37 (![X205, 87.78/88.37 X206]: 87.78/88.37 (X202( 87.78/88.37 X205) => 87.78/88.37 (X202( 87.78/88.37 X206) => 87.78/88.37 (X205 = 87.78/88.37 X206)))))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X207:( 87.78/88.37 $i > $o), 87.78/88.37 X208:( 87.78/88.37 $i > $o)]: 87.78/88.37 (( 87.78/88.37 ![X209, 87.78/88.37 X210]: 87.78/88.37 (( 87.78/88.37 X209 = 87.78/88.37 X210) => 87.78/88.37 (X207( 87.78/88.37 X209) <=> 87.78/88.37 X208( 87.78/88.37 X210)))) => 87.78/88.37 (( 87.78/88.37 ?[X211]: 87.78/88.37 zip_tseitin5( 87.78/88.37 X211,X207)) <=> 87.78/88.37 (?[X213]: 87.78/88.37 zip_tseitin5( 87.78/88.37 X213,X208))))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 emptyset = 87.78/88.37 emptyset) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X215, 87.78/88.37 X216]: 87.78/88.37 (( 87.78/88.37 X215 = 87.78/88.37 X216) => 87.78/88.37 (![X217, 87.78/88.37 X218]: 87.78/88.37 (( 87.78/88.37 X217 = 87.78/88.37 X218) => 87.78/88.37 (setadjoin( 87.78/88.37 X215,X217) = 87.78/88.37 setadjoin( 87.78/88.37 X216,X218)))))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X219, 87.78/88.37 X220]: 87.78/88.37 (( 87.78/88.37 X219 = 87.78/88.37 X220) => 87.78/88.37 (powerset( 87.78/88.37 X219) = 87.78/88.37 powerset( 87.78/88.37 X220)))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X221, 87.78/88.37 X222]: 87.78/88.37 (( 87.78/88.37 X221 = 87.78/88.37 X222) => 87.78/88.37 (setunion( 87.78/88.37 X221) = 87.78/88.37 setunion( 87.78/88.37 X222)))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 omega = 87.78/88.37 omega) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X223:( 87.78/88.37 $i > $o)]: 87.78/88.37 (( 87.78/88.37 ?[X224]: 87.78/88.37 (( 87.78/88.37 ![X225]: 87.78/88.37 (X223( 87.78/88.37 X225) => 87.78/88.37 (X224 = 87.78/88.37 X225))) & 87.78/88.37 X223( 87.78/88.37 X224))) => 87.78/88.37 (![X226, 87.78/88.37 X227]: 87.78/88.37 (X223( 87.78/88.37 X226) => 87.78/88.37 (X223( 87.78/88.37 X227) => 87.78/88.37 (X226 = 87.78/88.37 X227)))))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X228:( 87.78/88.37 $i > $o), 87.78/88.37 X229:( 87.78/88.37 $i > $o)]: 87.78/88.37 (( 87.78/88.37 ![X230, 87.78/88.37 X231]: 87.78/88.37 (( 87.78/88.37 X230 = 87.78/88.37 X231) => 87.78/88.37 (X228( 87.78/88.37 X230) <=> 87.78/88.37 X229( 87.78/88.37 X231)))) => 87.78/88.37 (( 87.78/88.37 ?[X232]: 87.78/88.37 (( 87.78/88.37 ![X233]: 87.78/88.37 (X228( 87.78/88.37 X233) => 87.78/88.37 (X232 = 87.78/88.37 X233))) & 87.78/88.37 X228( 87.78/88.37 X232))) => 87.78/88.37 (( 87.78/88.37 ?[X234]: 87.78/88.37 (( 87.78/88.37 ![X235]: 87.78/88.37 (X229( 87.78/88.37 X235) => 87.78/88.37 (X234 = 87.78/88.37 X235))) & 87.78/88.37 X229( 87.78/88.37 X234))) => 87.78/88.37 (descr( 87.78/88.37 ^[V_9]: 87.78/88.37 X228(V_9)) = 87.78/88.37 descr( 87.78/88.37 ^[V_10]: 87.78/88.37 X229( 87.78/88.37 V_10))))))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X236, 87.78/88.37 X237]: 87.78/88.37 (( 87.78/88.37 X236 = 87.78/88.37 X237) => 87.78/88.37 (![X238:( 87.78/88.37 $i > $o), 87.78/88.37 X239:( 87.78/88.37 $i > $o)]: 87.78/88.37 (( 87.78/88.37 ![X240]: 87.78/88.37 (in( 87.78/88.37 X240,X236) => 87.78/88.37 (![X241]: 87.78/88.37 (in( 87.78/88.37 X241,X237) => 87.78/88.37 (( 87.78/88.37 X240 = 87.78/88.37 X241) => 87.78/88.37 (X238( 87.78/88.37 X240) <=> 87.78/88.37 X239( 87.78/88.37 X241))))))) => 87.78/88.37 (dsetconstr( 87.78/88.37 X236, 87.78/88.37 ^[V_11]: 87.78/88.37 X238( 87.78/88.37 V_11)) = 87.78/88.37 dsetconstr( 87.78/88.37 X237, 87.78/88.37 ^[V_12]: 87.78/88.37 X239( 87.78/88.37 V_12))))))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X242, 87.78/88.37 X243]: 87.78/88.37 (( 87.78/88.37 ![X244]: 87.78/88.37 (in( 87.78/88.37 X244,X242) => 87.78/88.37 in( 87.78/88.37 X244,X243))) => 87.78/88.37 subset( 87.78/88.37 X242,X243))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X245, 87.78/88.37 X246]: 87.78/88.37 (( 87.78/88.37 X245 = 87.78/88.37 X246) => 87.78/88.37 subset( 87.78/88.37 X246,X245))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X247, 87.78/88.37 X248]: 87.78/88.37 (( 87.78/88.37 X247 = 87.78/88.37 X248) => 87.78/88.37 subset( 87.78/88.37 X247,X248))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X249, 87.78/88.37 X250]: 87.78/88.37 (( 87.78/88.37 ![X251]: 87.78/88.37 (in( 87.78/88.37 X251,X249) => 87.78/88.37 in( 87.78/88.37 X251,X250))) => 87.78/88.37 subset( 87.78/88.37 X249,X250))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X252]: 87.78/88.37 subset( 87.78/88.37 emptyset, 87.78/88.37 X252)) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X253, 87.78/88.37 X254,X255]: 87.78/88.37 (subset( 87.78/88.37 X253,X254) => 87.78/88.37 (in( 87.78/88.37 X255,X253) => 87.78/88.37 in( 87.78/88.37 X255,X254)))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X256, 87.78/88.37 X257,X258]: 87.78/88.37 (subset( 87.78/88.37 X256,X257) => 87.78/88.37 (( 87.78/88.37 ~ 87.78/88.37 in( 87.78/88.37 X258,X257)) => 87.78/88.37 (~ 87.78/88.37 in( 87.78/88.37 X258,X256))))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X259, 87.78/88.37 X260,X261]: 87.78/88.37 (in( 87.78/88.37 X261,X259) => 87.78/88.37 (( 87.78/88.37 ~ 87.78/88.37 in( 87.78/88.37 X261,X260)) => 87.78/88.37 (~ 87.78/88.37 subset( 87.78/88.37 X259,X260))))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X262, 87.78/88.37 X263]: 87.78/88.37 (( 87.78/88.37 ~ 87.78/88.37 subset( 87.78/88.37 X262,X263)) => 87.78/88.37 (X262 != 87.78/88.37 X263))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X264, 87.78/88.37 X265,X266]: 87.78/88.37 (in( 87.78/88.37 X266,X264) => 87.78/88.37 (( 87.78/88.37 ~ 87.78/88.37 in( 87.78/88.37 X266,X265)) => 87.78/88.37 (X264 != 87.78/88.37 X265)))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X267]: 87.78/88.37 subset( 87.78/88.37 X267,X267)) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X268, 87.78/88.37 X269,X270]: 87.78/88.37 (subset( 87.78/88.37 X268,X269) => 87.78/88.37 (subset( 87.78/88.37 X269,X270) => 87.78/88.37 subset( 87.78/88.37 X268,X270)))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X271, 87.78/88.37 X272]: 87.78/88.37 subset( 87.78/88.37 X272, 87.78/88.37 setadjoin( 87.78/88.37 X271,X272))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X273, 87.78/88.37 X274,X275]: 87.78/88.37 (subset( 87.78/88.37 X273,X275) => 87.78/88.37 subset( 87.78/88.37 X273, 87.78/88.37 setadjoin( 87.78/88.37 X274,X275)))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X276, 87.78/88.37 X277]: 87.78/88.37 (subset( 87.78/88.37 X276,X277) => 87.78/88.37 in( 87.78/88.37 X276, 87.78/88.37 powerset( 87.78/88.37 X277)))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X278, 87.78/88.37 X279]: 87.78/88.37 (subset( 87.78/88.37 X278,X279) => 87.78/88.37 (subset( 87.78/88.37 X279,X278) => 87.78/88.37 (X278 = 87.78/88.37 X279)))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X280]: 87.78/88.37 (subset( 87.78/88.37 X280, 87.78/88.37 emptyset) => 87.78/88.37 (X280 = 87.78/88.37 emptyset))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X281, 87.78/88.37 X282]: 87.78/88.37 (subset( 87.78/88.37 X282,X281) => 87.78/88.37 in( 87.78/88.37 X282, 87.78/88.37 powerset( 87.78/88.37 X281)))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X283, 87.78/88.37 X284]: 87.78/88.37 (in( 87.78/88.37 X284, 87.78/88.37 powerset( 87.78/88.37 X283)) => 87.78/88.37 subset( 87.78/88.37 X284,X283))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X285]: 87.78/88.37 in( 87.78/88.37 X285, 87.78/88.37 powerset( 87.78/88.37 X285))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X286, 87.78/88.37 X287]: 87.78/88.37 (subset( 87.78/88.37 X286,X287) => 87.78/88.37 subset( 87.78/88.37 powerset( 87.78/88.37 X286), 87.78/88.37 powerset( 87.78/88.37 X287)))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X288, 87.78/88.37 X289:( 87.78/88.37 $i > $o)]: 87.78/88.37 in( 87.78/88.37 dsetconstr( 87.78/88.37 X288, 87.78/88.37 ^[V_13]: 87.78/88.37 X289( 87.78/88.37 V_13)), 87.78/88.37 powerset( 87.78/88.37 X288))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X290, 87.78/88.37 X291:( 87.78/88.37 $i > $o)]: 87.78/88.37 subset( 87.78/88.37 dsetconstr( 87.78/88.37 X290, 87.78/88.37 ^[V_14]: 87.78/88.37 X291( 87.78/88.37 V_14)), 87.78/88.37 X290)) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X292, 87.78/88.37 X293,X294]: 87.78/88.37 (in( 87.78/88.37 X294,X292) => 87.78/88.37 in( 87.78/88.37 X294, 87.78/88.37 binunion( 87.78/88.37 X292,X293)))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X295, 87.78/88.37 X296]: 87.78/88.37 in( 87.78/88.37 X296, 87.78/88.37 setadjoin( 87.78/88.37 X295, 87.78/88.37 setadjoin( 87.78/88.37 X296, 87.78/88.37 emptyset)))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X297, 87.78/88.37 X298,X299]: 87.78/88.37 (in( 87.78/88.37 X299,X298) => 87.78/88.37 in( 87.78/88.37 X299, 87.78/88.37 binunion( 87.78/88.37 X297,X298)))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X300, 87.78/88.37 X301, 87.78/88.37 X302, 87.78/88.37 X303:$o]: 87.78/88.37 (in( 87.78/88.37 X302, 87.78/88.37 binunion( 87.78/88.37 X300,X301)) => 87.78/88.37 (( 87.78/88.37 in( 87.78/88.37 X302,X300) => 87.78/88.37 X303) => 87.78/88.37 (( 87.78/88.37 in( 87.78/88.37 X302,X301) => 87.78/88.37 X303) => 87.78/88.37 X303)))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X304, 87.78/88.37 X305,X306]: 87.78/88.37 (in( 87.78/88.37 X306, 87.78/88.37 binunion( 87.78/88.37 X304,X305)) => 87.78/88.37 (in( 87.78/88.37 X306,X305) | 87.78/88.37 in( 87.78/88.37 X306,X304)))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X307, 87.78/88.37 X308]: 87.78/88.37 subset( 87.78/88.37 X307, 87.78/88.37 binunion( 87.78/88.37 X307,X308))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X309, 87.78/88.37 X310]: 87.78/88.37 subset( 87.78/88.37 X310, 87.78/88.37 binunion( 87.78/88.37 X309,X310))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X311, 87.78/88.37 X312,X313]: 87.78/88.37 (in( 87.78/88.37 X313,X311) => 87.78/88.37 (in( 87.78/88.37 X313,X312) => 87.78/88.37 in( 87.78/88.37 X313, 87.78/88.37 binintersect( 87.78/88.37 X311,X312))))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X314, 87.78/88.37 X315,X316]: 87.78/88.37 (subset( 87.78/88.37 X316,X314) => 87.78/88.37 (subset( 87.78/88.37 X316,X315) => 87.78/88.37 subset( 87.78/88.37 X316, 87.78/88.37 binintersect( 87.78/88.37 X314,X315))))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X317, 87.78/88.37 X318,X319]: 87.78/88.37 (in( 87.78/88.37 X319, 87.78/88.37 binintersect( 87.78/88.37 X317,X318)) => 87.78/88.37 in( 87.78/88.37 X319,X317))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X320, 87.78/88.37 X321]: 87.78/88.37 subset( 87.78/88.37 binintersect( 87.78/88.37 X320,X321), 87.78/88.37 X320)) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X322, 87.78/88.37 X323]: 87.78/88.37 (subset( 87.78/88.37 X322,X323) => 87.78/88.37 (binintersect( 87.78/88.37 X322,X323) = 87.78/88.37 X322))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X324, 87.78/88.37 X325]: 87.78/88.37 (( 87.78/88.37 binintersect( 87.78/88.37 X324,X325) = 87.78/88.37 X325) => 87.78/88.37 subset( 87.78/88.37 X325,X324))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X326, 87.78/88.37 X327,X328]: 87.78/88.37 (in( 87.78/88.37 X328, 87.78/88.37 binintersect( 87.78/88.37 X326,X327)) => 87.78/88.37 in( 87.78/88.37 X328,X327))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X329, 87.78/88.37 X330]: 87.78/88.37 (( 87.78/88.37 ~ 87.78/88.37 ( 87.78/88.37 ?[X331]: 87.78/88.37 (in( 87.78/88.37 X331,X330) & 87.78/88.37 in( 87.78/88.37 X331,X329)))) => 87.78/88.37 (binintersect( 87.78/88.37 X329,X330) = 87.78/88.37 emptyset))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X332, 87.78/88.37 X333]: 87.78/88.37 subset( 87.78/88.37 binintersect( 87.78/88.37 X332,X333), 87.78/88.37 X333)) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X334, 87.78/88.37 X335]: 87.78/88.37 (subset( 87.78/88.37 X335,X334) => 87.78/88.37 (binintersect( 87.78/88.37 X334,X335) = 87.78/88.37 X335))) => 87.78/88.37 ( 87.78/88.37 ( 87.78/88.37 ![X336, 87.78/88.37 X337]: 87.78/88.37 (( 87.78/88.37 binintersect( 87.78/88.37 X336,X337) = 87.78/88.37 X336) => 87.78/88.37 subset( 87.78/88.38 X336,X337))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X338, 87.78/88.38 X339,X340]: 87.78/88.38 (binintersect( 87.78/88.38 X338, 87.78/88.38 binunion( 87.78/88.38 X339,X340)) = 87.78/88.38 binunion( 87.78/88.38 binintersect( 87.78/88.38 X338,X339), 87.78/88.38 binintersect( 87.78/88.38 X338,X340)))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X341, 87.78/88.38 X342,X343]: 87.78/88.38 (in( 87.78/88.38 X343,X341) => 87.78/88.38 (( 87.78/88.38 ~ 87.78/88.38 in( 87.78/88.38 X343,X342)) => 87.78/88.38 in( 87.78/88.38 X343, 87.78/88.38 setminus( 87.78/88.38 X341,X342))))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X344, 87.78/88.38 X345,X346]: 87.78/88.38 (in( 87.78/88.38 X346, 87.78/88.38 setminus( 87.78/88.38 X344,X345)) => 87.78/88.38 in( 87.78/88.38 X346,X344))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X347, 87.78/88.38 X348,X349]: 87.78/88.38 (in( 87.78/88.38 X349, 87.78/88.38 setminus( 87.78/88.38 X347,X348)) => 87.78/88.38 (~ 87.78/88.38 in( 87.78/88.38 X349,X348)))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X350, 87.78/88.38 X351]: 87.78/88.38 (subset( 87.78/88.38 X350,X351) => 87.78/88.38 (setminus( 87.78/88.38 X350,X351) = 87.78/88.38 emptyset))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X352, 87.78/88.38 X353,X354]: 87.78/88.38 (( 87.78/88.38 ~ 87.78/88.38 in( 87.78/88.38 X354, 87.78/88.38 setminus( 87.78/88.38 X352,X353))) => 87.78/88.38 (in( 87.78/88.38 X354,X352) => 87.78/88.38 in( 87.78/88.38 X354,X353)))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X355, 87.78/88.38 X356,X357]: 87.78/88.38 (( 87.78/88.38 ~ 87.78/88.38 in( 87.78/88.38 X357, 87.78/88.38 setminus( 87.78/88.38 X355,X356))) => 87.78/88.38 (( 87.78/88.38 ~ 87.78/88.38 in( 87.78/88.38 X357,X356)) => 87.78/88.38 (~ 87.78/88.38 in( 87.78/88.38 X357,X355))))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X358, 87.78/88.38 X359,X360]: 87.78/88.38 (( 87.78/88.38 ~ 87.78/88.38 in( 87.78/88.38 X360,X358)) => 87.78/88.38 (~ 87.78/88.38 in( 87.78/88.38 X360, 87.78/88.38 setminus( 87.78/88.38 X358,X359))))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X361, 87.78/88.38 X362,X363]: 87.78/88.38 (in( 87.78/88.38 X363,X362) => 87.78/88.38 (~ 87.78/88.38 in( 87.78/88.38 X363, 87.78/88.38 setminus( 87.78/88.38 X361,X362))))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X364, 87.78/88.38 X365]: 87.78/88.38 subset( 87.78/88.38 setminus( 87.78/88.38 X364,X365), 87.78/88.38 X364)) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X366, 87.78/88.38 X367]: 87.78/88.38 (( 87.78/88.38 setminus( 87.78/88.38 X366,X367) = 87.78/88.38 emptyset) => 87.78/88.38 subset( 87.78/88.38 X366,X367))) => 87.78/88.38 ( 87.78/88.38 ![X368, 87.78/88.38 X369,X370]: 87.78/88.38 (in( 87.78/88.38 X370, 87.78/88.38 dsetconstr( 87.78/88.38 binunion( 87.78/88.38 X368,X369), 87.78/88.38 ^[V_15]: 87.78/88.38 (( 87.78/88.38 ~ 87.78/88.38 in( 87.78/88.38 V_15,X368)) | 87.78/88.38 (~ 87.78/88.38 in( 87.78/88.38 V_15,X369))))) => 87.78/88.38 (![X371:$o]: 87.78/88.38 (( 87.78/88.38 in( 87.78/88.38 X370,X368) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ~ 87.78/88.38 in( 87.78/88.38 X370,X369)) => 87.78/88.38 X371)) => 87.78/88.38 (( 87.78/88.38 ( 87.78/88.38 ~ 87.78/88.38 in( 87.78/88.38 X370,X368)) => 87.78/88.38 ( 87.78/88.38 in( 87.78/88.38 X370,X369) => 87.78/88.38 X371)) => 87.78/88.38 X371))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 87.78/88.38 tff(zf_stmt_14, negated_conjecture, 87.78/88.38 (~ 87.78/88.38 ((![X2,X3]: ((![X4]: (in(X4,X2) <=> in(X4,X3))) => (X2 = X3))) => 87.78/88.38 ((![X5]: (~in(X5,emptyset))) => 87.78/88.38 ((![X6,X7,X8]: (in(X8,setadjoin(X6,X7)) <=> zip_tseitin0(X8,X7,X6))) => 87.78/88.38 ((![X9,X10]: 87.78/88.38 (in(X10,powerset(X9)) <=> (![X11]: zip_tseitin1(X11,X10,X9)))) => 87.78/88.38 ((![X12,X13]: 87.78/88.38 (in(X13,setunion(X12)) <=> (?[X14]: zip_tseitin2(X14,X13,X12)))) => 87.78/88.38 (in(emptyset,omega) => 87.78/88.38 ((![X15]: (in(X15,omega) => in(setadjoin(X15,X15),omega))) => 87.78/88.38 ((![X16]: 87.78/88.38 (((![X17]: 87.78/88.38 ((in(X17,X16) & in(X17,omega)) => 87.78/88.38 in(setadjoin(X17,X17),X16))) & 87.78/88.38 in(emptyset,X16)) => 87.78/88.38 (![X18]: (in(X18,omega) => in(X18,X16))))) => 87.78/88.38 ((![X19:(($i * $i) > $o),X20]: 87.78/88.38 ((![X21]: 87.78/88.38 (in(X21,X20) => 87.78/88.38 (?[X22]: 87.78/88.38 ((![X23]: (X19(X21,X23) => (X22 = X23))) & 87.78/88.38 X19(X21,X22))))) => 87.78/88.38 (?[X24]: 87.78/88.38 (![X25]: 87.78/88.38 (in(X25,X24) <=> 87.78/88.38 (?[X26]: zip_tseitin3(X26,X25,X20,X19))))))) => 87.78/88.38 ((![X27]: 87.78/88.38 ((?[X28]: in(X28,X27)) => 87.78/88.38 (?[X29]: 87.78/88.38 ((~(?[X30]: (in(X30,X27) & in(X30,X29)))) & in(X29,X27))))) => 87.78/88.38 ((![X31]: 87.78/88.38 (?[X32]: 87.78/88.38 ((![X33]: 87.78/88.38 (((?[X34]: in(X34,X33)) & 87.78/88.38 (![X35]: (in(X35,X33) => in(X35,X31)))) => 87.78/88.38 (?[X36,X37]: 87.78/88.38 ((![X38]: 87.78/88.38 (in(X38,X32) => 87.78/88.38 (in(X37,X38) | 87.78/88.38 (![X39]: (in(X39,X38) => in(X39,X36)))))) & 87.78/88.38 (~(?[X40]: (in(X40,X33) & in(X40,X36)))) & 87.78/88.38 in(X37,X33) & in(X36,X32))))) & 87.78/88.38 (![X41,X42]: 87.78/88.38 ((in(X42,X32) & in(X41,X32)) => 87.78/88.38 ((![X43]: (in(X43,X42) => in(X43,X41))) | 87.78/88.38 (![X44]: (in(X44,X41) => in(X44,X42)))))) & 87.78/88.38 (![X45,X46]: 87.78/88.38 ((in(X46,X31) & in(X45,X31)) => 87.78/88.38 ((![X47]: 87.78/88.38 (in(X47,X32) => (in(X45,X47) <=> in(X46,X47)))) => 87.78/88.38 (X45 = X46)))) & 87.78/88.38 (![X48]: 87.78/88.38 (in(X48,X32) => 87.78/88.38 (![X49]: (in(X49,X48) => in(X49,X31)))))))) => 87.78/88.38 ((![X50:($i > $o)]: 87.78/88.38 ((?[X51]: ((![X52]: (X50(X52) => (X51 = X52))) & X50(X51))) => 87.78/88.38 X50(descr(^[V_1]: X50(V_1))))) => 87.78/88.38 ((![X53,X54:($i > $o),X55]: 87.78/88.38 (in(X55,X53) => 87.78/88.38 (X54(X55) => in(X55,dsetconstr(X53,^[V_2]: X54(V_2)))))) => 87.78/88.38 ((![X56,X57:($i > $o),X58]: 87.78/88.38 (in(X58,dsetconstr(X56,^[V_3]: X57(V_3))) => in(X58,X56))) => 87.78/88.38 ((![X59,X60:($i > $o),X61]: 87.78/88.38 (in(X61,dsetconstr(X59,^[V_4]: X60(V_4))) => X60(X61))) => 87.78/88.38 ((![X62:($i > $o)]: 87.78/88.38 ((?[X63]: 87.78/88.38 ((![X64]: (X62(X64) => (X63 = X64))) & X62(X63))) => 87.78/88.38 (?[X65]: 87.78/88.38 ((![X66]: (X62(X66) => (X65 = X66))) & X62(X65))))) => 87.78/88.38 ((![X67:$o,X68]: (in(X68,prop2set(X67)) => X67)) => 87.78/88.38 ((![X69]: (in(X69,emptyset) => (![X70:$o]: X70))) => 87.78/88.38 ((![X71]: (in(X71,emptyset) => $false)) => 87.78/88.38 ((![X72]: (~in(X72,emptyset))) => 87.78/88.38 ((![X73:($i > $o)]: 87.78/88.38 ((?[X74]: 87.78/88.38 ((![X75]: (X73(X75) => (X74 = X75))) & 87.78/88.38 X73(X74))) => 87.78/88.38 (?[X76]: X73(X76)))) => 87.78/88.38 ((![X77,X78]: 87.78/88.38 ((![X79]: (in(X79,X77) => in(X79,X78))) => 87.78/88.38 ((![X80]: (in(X80,X78) => in(X80,X77))) => 87.78/88.38 (X77 = X78)))) => 87.78/88.38 ((![X81]: 87.78/88.38 ((![X82]: (~in(X82,X81))) => (X81 = emptyset))) => 87.78/88.38 ((![X83]: 87.78/88.38 ((![X84]: (~in(X84,X83))) => (X83 = emptyset))) => 87.78/88.38 ((![X85,X86:($i > $o),X87]: 87.78/88.38 (in(X87,X85) => 87.78/88.38 (in(X87,dsetconstr(X85,^[V_5]: X86(V_5))) <=> 87.78/88.38 X86(X87)))) => 87.78/88.38 ((![X88]: 87.78/88.38 ((X88 != emptyset) => (?[X89]: in(X89,X88)))) => 87.78/88.38 ((![X90,X91:($i > $o),X92]: 87.78/88.38 (in(X92,X90) => 87.78/88.38 (X91(X92) => 87.78/88.38 (dsetconstr(X90,^[V_6]: X91(V_6)) != 87.78/88.38 emptyset)))) => 87.78/88.38 ((![X93]: 87.78/88.38 ((?[X94]: in(X94,X93)) => 87.78/88.38 (X93 != emptyset))) => 87.78/88.38 ((![X95,X96]: in(X95,setadjoin(X95,X96))) => 87.78/88.38 (in(emptyset,setadjoin(emptyset,emptyset)) => 87.78/88.38 ((![X97,X98,X99]: 87.78/88.38 (in(X99,X98) => 87.78/88.38 in(X99,setadjoin(X97,X98)))) => 87.78/88.38 ((![X100,X101,X102]: 87.78/88.38 (in(X102,setadjoin(X100,X101)) => 87.78/88.38 (![X103:$o]: 87.78/88.38 (((X102 = X100) => X103) => 87.78/88.38 ((in(X102,X101) => X103) => X103))))) => 87.78/88.38 ((![X104,X105,X106]: 87.78/88.38 (in(X106,setadjoin(X104,X105)) => 87.78/88.38 (in(X106,X105) | (X106 = X104)))) => 87.78/88.38 ((![X107]: 87.78/88.38 (dsetconstr(X107,^[V_7]: $true) = 87.78/88.38 X107)) => 87.78/88.38 ((![X108,X109]: 87.78/88.38 ((![X110]: 87.78/88.38 (in(X110,X109) => in(X110,X108))) => 87.78/88.38 in(X109,powerset(X108)))) => 87.78/88.38 ((![X111]: in(emptyset,powerset(X111))) => 87.78/88.38 ((![X112]: 87.78/88.38 in(emptyset,powerset(X112))) => 87.78/88.38 ((![X113,X114,X115]: 87.78/88.38 (in(X114,powerset(X113)) => 87.78/88.38 (in(X115,X114) => in(X115,X113)))) => 87.78/88.38 ((![X116,X117,X118]: 87.78/88.38 (in(X117,X118) => 87.78/88.38 (in(X118,X116) => 87.78/88.38 in(X117,setunion(X116))))) => 87.78/88.38 ((![X119,X120]: 87.78/88.38 (in(X120,setunion(X119)) => 87.78/88.38 (![X121:$o]: 87.78/88.38 ((![X122]: 87.78/88.38 (in(X120,X122) => 87.78/88.38 (in(X122,X119) => 87.78/88.38 X121))) => 87.78/88.38 X121)))) => 87.78/88.38 ((![X123,X124]: 87.78/88.38 (in(X124,X123) => 87.78/88.38 in(X124, 87.78/88.38 powerset(setunion(X123))))) => 87.78/88.38 ((![X125:($i > $o)]: 87.78/88.38 ((?[X126]: 87.78/88.38 ((![X127]: 87.78/88.38 (X125(X127) => 87.78/88.38 (X126 = X127))) & 87.78/88.38 X125(X126))) => 87.78/88.38 (?[X128]: 87.78/88.38 (![X129]: 87.78/88.38 (X125(X129) <=> 87.78/88.38 (X129 = X128)))))) => 87.78/88.38 ((![X130]: 87.78/88.38 ((X130 != emptyset) => 87.78/88.38 (?[X131]: in(X131,X130)))) => 87.78/88.38 ((![X132,X133]: 87.78/88.38 (in(X132, 87.78/88.38 setadjoin(X133, 87.78/88.38 emptyset)) => 87.78/88.38 (X132 = X133))) => 87.78/88.38 ((![X134,X135]: 87.78/88.38 ((X134 != X135) => 87.78/88.38 (~ 87.78/88.38 in(X135, 87.78/88.38 setadjoin(X134, 87.78/88.38 emptyset))))) => 87.78/88.38 ((![X136,X137]: 87.78/88.38 ((X136 = X137) => 87.78/88.38 in(X136, 87.78/88.38 setadjoin(X137, 87.78/88.38 emptyset)))) => 87.78/88.38 ((![X138,X139]: 87.78/88.38 (in(X138, 87.78/88.38 setadjoin(X139, 87.78/88.38 emptyset)) => 87.78/88.38 in(X139, 87.78/88.38 setadjoin(X138, 87.78/88.38 emptyset)))) => 87.78/88.38 ((![X140,X141,X142]: 87.78/88.38 (in(X142, 87.78/88.38 setadjoin( 87.78/88.38 X140, 87.78/88.38 setadjoin( 87.78/88.38 X141,emptyset))) => 87.78/88.38 ((X142 = X141) | 87.78/88.38 (X142 = X140)))) => 87.78/88.38 ((![X143,X144]: 87.78/88.38 in(X143, 87.78/88.38 setadjoin( 87.78/88.38 X143, 87.78/88.38 setadjoin( 87.78/88.38 X144,emptyset)))) => 87.78/88.38 ((![X145,X146]: 87.78/88.38 in(X146, 87.78/88.38 setadjoin( 87.78/88.38 X145, 87.78/88.38 setadjoin( 87.78/88.38 X146,emptyset)))) => 87.78/88.38 ((![X147,X148:($i > $o)]: 87.78/88.38 ((?[X149]: 87.78/88.38 (X148(X149) & 87.78/88.38 in(X149,X147))) => 87.78/88.38 ((dsetconstr( 87.78/88.38 X147, 87.78/88.38 ^[V_8]: 87.78/88.38 X148(V_8)) = 87.78/88.38 emptyset) => 87.78/88.38 $false))) => 87.78/88.38 ((![X150:($i > $o), 87.78/88.38 X151]: 87.78/88.38 (in(X151,emptyset) => 87.78/88.38 X150(X151))) => 87.78/88.38 ((![X152, 87.78/88.38 X153:($i > $o)]: 87.78/88.38 ((~ 87.78/88.38 (![X154]: 87.78/88.38 (in( 87.78/88.38 X154,X152) => 87.78/88.38 X153(X154)))) => 87.78/88.38 (?[X155]: 87.78/88.38 ((~X153(X155)) & 87.78/88.38 in(X155,X152))))) => 87.78/88.38 ((![X156, 87.78/88.38 X157:($i > $o)]: 87.78/88.38 ((![X158]: 87.78/88.38 (in( 87.78/88.38 X158,X156) => 87.78/88.38 (~ 87.78/88.38 X157( 87.78/88.38 X158)))) => 87.78/88.38 (~ 87.78/88.38 (?[X159]: 87.78/88.38 (X157( 87.78/88.38 X159) & 87.78/88.38 in( 87.78/88.38 X159,X156)))))) => 87.78/88.38 ((![X160, 87.78/88.38 X161:($i > $o)]: 87.78/88.38 ((~ 87.78/88.38 (?[X162]: 87.78/88.38 ( 87.78/88.38 X161( 87.78/88.38 X162) & 87.78/88.38 in( 87.78/88.38 X162,X160)))) => 87.78/88.38 (![X163]: 87.78/88.38 (in( 87.78/88.38 X163,X160) => 87.78/88.38 (~ 87.78/88.38 X161( 87.78/88.38 X163)))))) => 87.78/88.38 ((![X164, 87.78/88.38 X165:( 87.78/88.38 $i > $o)]: 87.78/88.38 ((?[X166]: 87.78/88.38 (( 87.78/88.38 ~ 87.78/88.38 X165( 87.78/88.38 X166)) & 87.78/88.38 in( 87.78/88.38 X166,X164))) => 87.78/88.38 (~ 87.78/88.38 (![X167]: 87.78/88.38 (in( 87.78/88.38 X167,X164) => 87.78/88.38 X165( 87.78/88.38 X167)))))) => 87.78/88.38 ((![X168:$o]: 87.78/88.38 (X168 => 87.78/88.38 in(emptyset, 87.78/88.38 prop2set( 87.78/88.38 X168)))) => 87.78/88.38 ((![X169:$o]: 87.78/88.38 (X169 => 87.78/88.38 set2prop( 87.78/88.38 prop2set( 87.78/88.38 X169)))) => 87.78/88.38 ((![X170, 87.78/88.38 X171:( 87.78/88.38 $i > $o)]: 87.78/88.38 ((~ 87.78/88.38 ( 87.78/88.38 ?[X172]: 87.78/88.38 (X171( 87.78/88.38 X172) & 87.78/88.38 in( 87.78/88.38 X172,X170)))) => 87.78/88.38 (![X173]: 87.78/88.38 (in( 87.78/88.38 X173,X170) => 87.78/88.38 (~ 87.78/88.38 X171( 87.78/88.38 X173)))))) => 87.78/88.38 ((![X174, 87.78/88.38 X175:( 87.78/88.38 $i > $o)]: 87.78/88.38 (( 87.78/88.38 ~ 87.78/88.38 ( 87.78/88.38 ![X176]: 87.78/88.38 (in( 87.78/88.38 X176,X174) => 87.78/88.38 X175( 87.78/88.38 X176)))) => 87.78/88.38 ( 87.78/88.38 ?[X177]: 87.78/88.38 (( 87.78/88.38 ~ 87.78/88.38 X175( 87.78/88.38 X177)) & 87.78/88.38 in( 87.78/88.38 X177,X174))))) => 87.78/88.38 ((![X178:( 87.78/88.38 $i > $o)]: 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ?[X179]: 87.78/88.38 (( 87.78/88.38 ![X180]: 87.78/88.38 (X178( 87.78/88.38 X180) => 87.78/88.38 (X179 = 87.78/88.38 X180))) & 87.78/88.38 X178( 87.78/88.38 X179))) => 87.78/88.38 ( 87.78/88.38 ?[X181]: 87.78/88.38 (( 87.78/88.38 ![X182]: 87.78/88.38 (X178( 87.78/88.38 X182) => 87.78/88.38 (X181 = 87.78/88.38 X182))) & 87.78/88.38 X178( 87.78/88.38 X181))))) => 87.78/88.38 ((![X183:( 87.78/88.38 $i > $o)]: 87.78/88.38 (( 87.78/88.38 ?[X184]: 87.78/88.38 X183( 87.78/88.38 X184)) => 87.78/88.38 (( 87.78/88.38 ![X185, 87.78/88.38 X186]: 87.78/88.38 (X183( 87.78/88.38 X185) => 87.78/88.38 (X183( 87.78/88.38 X186) => 87.78/88.38 (X185 = 87.78/88.38 X186)))) => 87.78/88.38 (?[X187]: 87.78/88.38 (( 87.78/88.38 ![X188]: 87.78/88.38 (X183( 87.78/88.38 X188) => 87.78/88.38 (X187 = 87.78/88.38 X188))) & 87.78/88.38 X183( 87.78/88.38 X187)))))) => 87.78/88.38 ((![X189:( 87.78/88.38 $i > $o)]: 87.78/88.38 (( 87.78/88.38 ?[X190]: 87.78/88.38 (![X191]: 87.78/88.38 (X189( 87.78/88.38 X191) <=> 87.78/88.38 (X191 = 87.78/88.38 X190)))) => 87.78/88.38 (?[X192]: 87.78/88.38 (( 87.78/88.38 ![X193]: 87.78/88.38 (X189( 87.78/88.38 X193) => 87.78/88.38 (X192 = 87.78/88.38 X193))) & 87.78/88.38 X189( 87.78/88.38 X192))))) => 87.78/88.38 (( 87.78/88.38 ![X194, 87.78/88.38 X195]: 87.78/88.38 (( 87.78/88.38 X194 = 87.78/88.38 X195) => 87.78/88.38 (![X196, 87.78/88.38 X197]: 87.78/88.38 (( 87.78/88.38 X196 = 87.78/88.38 X197) => 87.78/88.38 (in( 87.78/88.38 X196,X194) => 87.78/88.38 in( 87.78/88.38 X197,X195)))))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X198, 87.78/88.38 X199]: 87.78/88.38 (( 87.78/88.38 X198 = 87.78/88.38 X199) => 87.78/88.38 (![X200, 87.78/88.38 X201]: 87.78/88.38 (( 87.78/88.38 X200 = 87.78/88.38 X201) => 87.78/88.38 (in( 87.78/88.38 X200,X198) <=> 87.78/88.38 in( 87.78/88.38 X201,X199)))))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X202:( 87.78/88.38 $i > $o)]: 87.78/88.38 (( 87.78/88.38 ?[X203]: 87.78/88.38 (( 87.78/88.38 ![X204]: 87.78/88.38 (X202( 87.78/88.38 X204) => 87.78/88.38 (X203 = 87.78/88.38 X204))) & 87.78/88.38 X202( 87.78/88.38 X203))) => 87.78/88.38 (![X205, 87.78/88.38 X206]: 87.78/88.38 (X202( 87.78/88.38 X205) => 87.78/88.38 (X202( 87.78/88.38 X206) => 87.78/88.38 (X205 = 87.78/88.38 X206)))))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X207:( 87.78/88.38 $i > $o), 87.78/88.38 X208:( 87.78/88.38 $i > $o)]: 87.78/88.38 (( 87.78/88.38 ![X209, 87.78/88.38 X210]: 87.78/88.38 (( 87.78/88.38 X209 = 87.78/88.38 X210) => 87.78/88.38 (X207( 87.78/88.38 X209) <=> 87.78/88.38 X208( 87.78/88.38 X210)))) => 87.78/88.38 (( 87.78/88.38 ?[X211]: 87.78/88.38 zip_tseitin5( 87.78/88.38 X211,X207)) <=> 87.78/88.38 (?[X213]: 87.78/88.38 zip_tseitin5( 87.78/88.38 X213,X208))))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 emptyset = 87.78/88.38 emptyset) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X215, 87.78/88.38 X216]: 87.78/88.38 (( 87.78/88.38 X215 = 87.78/88.38 X216) => 87.78/88.38 (![X217, 87.78/88.38 X218]: 87.78/88.38 (( 87.78/88.38 X217 = 87.78/88.38 X218) => 87.78/88.38 (setadjoin( 87.78/88.38 X215,X217) = 87.78/88.38 setadjoin( 87.78/88.38 X216,X218)))))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X219, 87.78/88.38 X220]: 87.78/88.38 (( 87.78/88.38 X219 = 87.78/88.38 X220) => 87.78/88.38 (powerset( 87.78/88.38 X219) = 87.78/88.38 powerset( 87.78/88.38 X220)))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X221, 87.78/88.38 X222]: 87.78/88.38 (( 87.78/88.38 X221 = 87.78/88.38 X222) => 87.78/88.38 (setunion( 87.78/88.38 X221) = 87.78/88.38 setunion( 87.78/88.38 X222)))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 omega = 87.78/88.38 omega) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X223:( 87.78/88.38 $i > $o)]: 87.78/88.38 (( 87.78/88.38 ?[X224]: 87.78/88.38 (( 87.78/88.38 ![X225]: 87.78/88.38 (X223( 87.78/88.38 X225) => 87.78/88.38 (X224 = 87.78/88.38 X225))) & 87.78/88.38 X223( 87.78/88.38 X224))) => 87.78/88.38 (![X226, 87.78/88.38 X227]: 87.78/88.38 (X223( 87.78/88.38 X226) => 87.78/88.38 (X223( 87.78/88.38 X227) => 87.78/88.38 (X226 = 87.78/88.38 X227)))))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X228:( 87.78/88.38 $i > $o), 87.78/88.38 X229:( 87.78/88.38 $i > $o)]: 87.78/88.38 (( 87.78/88.38 ![X230, 87.78/88.38 X231]: 87.78/88.38 (( 87.78/88.38 X230 = 87.78/88.38 X231) => 87.78/88.38 (X228( 87.78/88.38 X230) <=> 87.78/88.38 X229( 87.78/88.38 X231)))) => 87.78/88.38 (( 87.78/88.38 ?[X232]: 87.78/88.38 (( 87.78/88.38 ![X233]: 87.78/88.38 (X228( 87.78/88.38 X233) => 87.78/88.38 (X232 = 87.78/88.38 X233))) & 87.78/88.38 X228( 87.78/88.38 X232))) => 87.78/88.38 (( 87.78/88.38 ?[X234]: 87.78/88.38 (( 87.78/88.38 ![X235]: 87.78/88.38 (X229( 87.78/88.38 X235) => 87.78/88.38 (X234 = 87.78/88.38 X235))) & 87.78/88.38 X229( 87.78/88.38 X234))) => 87.78/88.38 (descr( 87.78/88.38 ^[V_9]: 87.78/88.38 X228(V_9)) = 87.78/88.38 descr( 87.78/88.38 ^[V_10]: 87.78/88.38 X229( 87.78/88.38 V_10))))))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X236, 87.78/88.38 X237]: 87.78/88.38 (( 87.78/88.38 X236 = 87.78/88.38 X237) => 87.78/88.38 (![X238:( 87.78/88.38 $i > $o), 87.78/88.38 X239:( 87.78/88.38 $i > $o)]: 87.78/88.38 (( 87.78/88.38 ![X240]: 87.78/88.38 (in( 87.78/88.38 X240,X236) => 87.78/88.38 (![X241]: 87.78/88.38 (in( 87.78/88.38 X241,X237) => 87.78/88.38 (( 87.78/88.38 X240 = 87.78/88.38 X241) => 87.78/88.38 (X238( 87.78/88.38 X240) <=> 87.78/88.38 X239( 87.78/88.38 X241))))))) => 87.78/88.38 (dsetconstr( 87.78/88.38 X236, 87.78/88.38 ^[V_11]: 87.78/88.38 X238( 87.78/88.38 V_11)) = 87.78/88.38 dsetconstr( 87.78/88.38 X237, 87.78/88.38 ^[V_12]: 87.78/88.38 X239( 87.78/88.38 V_12))))))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X242, 87.78/88.38 X243]: 87.78/88.38 (( 87.78/88.38 ![X244]: 87.78/88.38 (in( 87.78/88.38 X244,X242) => 87.78/88.38 in( 87.78/88.38 X244,X243))) => 87.78/88.38 subset( 87.78/88.38 X242,X243))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X245, 87.78/88.38 X246]: 87.78/88.38 (( 87.78/88.38 X245 = 87.78/88.38 X246) => 87.78/88.38 subset( 87.78/88.38 X246,X245))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X247, 87.78/88.38 X248]: 87.78/88.38 (( 87.78/88.38 X247 = 87.78/88.38 X248) => 87.78/88.38 subset( 87.78/88.38 X247,X248))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X249, 87.78/88.38 X250]: 87.78/88.38 (( 87.78/88.38 ![X251]: 87.78/88.38 (in( 87.78/88.38 X251,X249) => 87.78/88.38 in( 87.78/88.38 X251,X250))) => 87.78/88.38 subset( 87.78/88.38 X249,X250))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X252]: 87.78/88.38 subset( 87.78/88.38 emptyset, 87.78/88.38 X252)) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X253, 87.78/88.38 X254,X255]: 87.78/88.38 (subset( 87.78/88.38 X253,X254) => 87.78/88.38 (in( 87.78/88.38 X255,X253) => 87.78/88.38 in( 87.78/88.38 X255,X254)))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X256, 87.78/88.38 X257,X258]: 87.78/88.38 (subset( 87.78/88.38 X256,X257) => 87.78/88.38 (( 87.78/88.38 ~ 87.78/88.38 in( 87.78/88.38 X258,X257)) => 87.78/88.38 (~ 87.78/88.38 in( 87.78/88.38 X258,X256))))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X259, 87.78/88.38 X260,X261]: 87.78/88.38 (in( 87.78/88.38 X261,X259) => 87.78/88.38 (( 87.78/88.38 ~ 87.78/88.38 in( 87.78/88.38 X261,X260)) => 87.78/88.38 (~ 87.78/88.38 subset( 87.78/88.38 X259,X260))))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X262, 87.78/88.38 X263]: 87.78/88.38 (( 87.78/88.38 ~ 87.78/88.38 subset( 87.78/88.38 X262,X263)) => 87.78/88.38 (X262 != 87.78/88.38 X263))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X264, 87.78/88.38 X265,X266]: 87.78/88.38 (in( 87.78/88.38 X266,X264) => 87.78/88.38 (( 87.78/88.38 ~ 87.78/88.38 in( 87.78/88.38 X266,X265)) => 87.78/88.38 (X264 != 87.78/88.38 X265)))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X267]: 87.78/88.38 subset( 87.78/88.38 X267,X267)) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X268, 87.78/88.38 X269,X270]: 87.78/88.38 (subset( 87.78/88.38 X268,X269) => 87.78/88.38 (subset( 87.78/88.38 X269,X270) => 87.78/88.38 subset( 87.78/88.38 X268,X270)))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X271, 87.78/88.38 X272]: 87.78/88.38 subset( 87.78/88.38 X272, 87.78/88.38 setadjoin( 87.78/88.38 X271,X272))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X273, 87.78/88.38 X274,X275]: 87.78/88.38 (subset( 87.78/88.38 X273,X275) => 87.78/88.38 subset( 87.78/88.38 X273, 87.78/88.38 setadjoin( 87.78/88.38 X274,X275)))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X276, 87.78/88.38 X277]: 87.78/88.38 (subset( 87.78/88.38 X276,X277) => 87.78/88.38 in( 87.78/88.38 X276, 87.78/88.38 powerset( 87.78/88.38 X277)))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X278, 87.78/88.38 X279]: 87.78/88.38 (subset( 87.78/88.38 X278,X279) => 87.78/88.38 (subset( 87.78/88.38 X279,X278) => 87.78/88.38 (X278 = 87.78/88.38 X279)))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X280]: 87.78/88.38 (subset( 87.78/88.38 X280, 87.78/88.38 emptyset) => 87.78/88.38 (X280 = 87.78/88.38 emptyset))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X281, 87.78/88.38 X282]: 87.78/88.38 (subset( 87.78/88.38 X282,X281) => 87.78/88.38 in( 87.78/88.38 X282, 87.78/88.38 powerset( 87.78/88.38 X281)))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X283, 87.78/88.38 X284]: 87.78/88.38 (in( 87.78/88.38 X284, 87.78/88.38 powerset( 87.78/88.38 X283)) => 87.78/88.38 subset( 87.78/88.38 X284,X283))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X285]: 87.78/88.38 in( 87.78/88.38 X285, 87.78/88.38 powerset( 87.78/88.38 X285))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X286, 87.78/88.38 X287]: 87.78/88.38 (subset( 87.78/88.38 X286,X287) => 87.78/88.38 subset( 87.78/88.38 powerset( 87.78/88.38 X286), 87.78/88.38 powerset( 87.78/88.38 X287)))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X288, 87.78/88.38 X289:( 87.78/88.38 $i > $o)]: 87.78/88.38 in( 87.78/88.38 dsetconstr( 87.78/88.38 X288, 87.78/88.38 ^[V_13]: 87.78/88.38 X289( 87.78/88.38 V_13)), 87.78/88.38 powerset( 87.78/88.38 X288))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X290, 87.78/88.38 X291:( 87.78/88.38 $i > $o)]: 87.78/88.38 subset( 87.78/88.38 dsetconstr( 87.78/88.38 X290, 87.78/88.38 ^[V_14]: 87.78/88.38 X291( 87.78/88.38 V_14)), 87.78/88.38 X290)) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X292, 87.78/88.38 X293,X294]: 87.78/88.38 (in( 87.78/88.38 X294,X292) => 87.78/88.38 in( 87.78/88.38 X294, 87.78/88.38 binunion( 87.78/88.38 X292,X293)))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X295, 87.78/88.38 X296]: 87.78/88.38 in( 87.78/88.38 X296, 87.78/88.38 setadjoin( 87.78/88.38 X295, 87.78/88.38 setadjoin( 87.78/88.38 X296, 87.78/88.38 emptyset)))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X297, 87.78/88.38 X298,X299]: 87.78/88.38 (in( 87.78/88.38 X299,X298) => 87.78/88.38 in( 87.78/88.38 X299, 87.78/88.38 binunion( 87.78/88.38 X297,X298)))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X300, 87.78/88.38 X301, 87.78/88.38 X302, 87.78/88.38 X303:$o]: 87.78/88.38 (in( 87.78/88.38 X302, 87.78/88.38 binunion( 87.78/88.38 X300,X301)) => 87.78/88.38 (( 87.78/88.38 in( 87.78/88.38 X302,X300) => 87.78/88.38 X303) => 87.78/88.38 (( 87.78/88.38 in( 87.78/88.38 X302,X301) => 87.78/88.38 X303) => 87.78/88.38 X303)))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X304, 87.78/88.38 X305,X306]: 87.78/88.38 (in( 87.78/88.38 X306, 87.78/88.38 binunion( 87.78/88.38 X304,X305)) => 87.78/88.38 (in( 87.78/88.38 X306,X305) | 87.78/88.38 in( 87.78/88.38 X306,X304)))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X307, 87.78/88.38 X308]: 87.78/88.38 subset( 87.78/88.38 X307, 87.78/88.38 binunion( 87.78/88.38 X307,X308))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X309, 87.78/88.38 X310]: 87.78/88.38 subset( 87.78/88.38 X310, 87.78/88.38 binunion( 87.78/88.38 X309,X310))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X311, 87.78/88.38 X312,X313]: 87.78/88.38 (in( 87.78/88.38 X313,X311) => 87.78/88.38 (in( 87.78/88.38 X313,X312) => 87.78/88.38 in( 87.78/88.38 X313, 87.78/88.38 binintersect( 87.78/88.38 X311,X312))))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X314, 87.78/88.38 X315,X316]: 87.78/88.38 (subset( 87.78/88.38 X316,X314) => 87.78/88.38 (subset( 87.78/88.38 X316,X315) => 87.78/88.38 subset( 87.78/88.38 X316, 87.78/88.38 binintersect( 87.78/88.38 X314,X315))))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X317, 87.78/88.38 X318,X319]: 87.78/88.38 (in( 87.78/88.38 X319, 87.78/88.38 binintersect( 87.78/88.38 X317,X318)) => 87.78/88.38 in( 87.78/88.38 X319,X317))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X320, 87.78/88.38 X321]: 87.78/88.38 subset( 87.78/88.38 binintersect( 87.78/88.38 X320,X321), 87.78/88.38 X320)) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X322, 87.78/88.38 X323]: 87.78/88.38 (subset( 87.78/88.38 X322,X323) => 87.78/88.38 (binintersect( 87.78/88.38 X322,X323) = 87.78/88.38 X322))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X324, 87.78/88.38 X325]: 87.78/88.38 (( 87.78/88.38 binintersect( 87.78/88.38 X324,X325) = 87.78/88.38 X325) => 87.78/88.38 subset( 87.78/88.38 X325,X324))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X326, 87.78/88.38 X327,X328]: 87.78/88.38 (in( 87.78/88.38 X328, 87.78/88.38 binintersect( 87.78/88.38 X326,X327)) => 87.78/88.38 in( 87.78/88.38 X328,X327))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X329, 87.78/88.38 X330]: 87.78/88.38 (( 87.78/88.38 ~ 87.78/88.38 ( 87.78/88.38 ?[X331]: 87.78/88.38 (in( 87.78/88.38 X331,X330) & 87.78/88.38 in( 87.78/88.38 X331,X329)))) => 87.78/88.38 (binintersect( 87.78/88.38 X329,X330) = 87.78/88.38 emptyset))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X332, 87.78/88.38 X333]: 87.78/88.38 subset( 87.78/88.38 binintersect( 87.78/88.38 X332,X333), 87.78/88.38 X333)) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X334, 87.78/88.38 X335]: 87.78/88.38 (subset( 87.78/88.38 X335,X334) => 87.78/88.38 (binintersect( 87.78/88.38 X334,X335) = 87.78/88.38 X335))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X336, 87.78/88.38 X337]: 87.78/88.38 (( 87.78/88.38 binintersect( 87.78/88.38 X336,X337) = 87.78/88.38 X336) => 87.78/88.38 subset( 87.78/88.38 X336,X337))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X338, 87.78/88.38 X339,X340]: 87.78/88.38 (binintersect( 87.78/88.38 X338, 87.78/88.38 binunion( 87.78/88.38 X339,X340)) = 87.78/88.38 binunion( 87.78/88.38 binintersect( 87.78/88.38 X338,X339), 87.78/88.38 binintersect( 87.78/88.38 X338,X340)))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X341, 87.78/88.38 X342,X343]: 87.78/88.38 (in( 87.78/88.38 X343,X341) => 87.78/88.38 (( 87.78/88.38 ~ 87.78/88.38 in( 87.78/88.38 X343,X342)) => 87.78/88.38 in( 87.78/88.38 X343, 87.78/88.38 setminus( 87.78/88.38 X341,X342))))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X344, 87.78/88.38 X345,X346]: 87.78/88.38 (in( 87.78/88.38 X346, 87.78/88.38 setminus( 87.78/88.38 X344,X345)) => 87.78/88.38 in( 87.78/88.38 X346,X344))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X347, 87.78/88.38 X348,X349]: 87.78/88.38 (in( 87.78/88.38 X349, 87.78/88.38 setminus( 87.78/88.38 X347,X348)) => 87.78/88.38 (~ 87.78/88.38 in( 87.78/88.38 X349,X348)))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X350, 87.78/88.38 X351]: 87.78/88.38 (subset( 87.78/88.38 X350,X351) => 87.78/88.38 (setminus( 87.78/88.38 X350,X351) = 87.78/88.38 emptyset))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X352, 87.78/88.38 X353,X354]: 87.78/88.38 (( 87.78/88.38 ~ 87.78/88.38 in( 87.78/88.38 X354, 87.78/88.38 setminus( 87.78/88.38 X352,X353))) => 87.78/88.38 (in( 87.78/88.38 X354,X352) => 87.78/88.38 in( 87.78/88.38 X354,X353)))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X355, 87.78/88.38 X356,X357]: 87.78/88.38 (( 87.78/88.38 ~ 87.78/88.38 in( 87.78/88.38 X357, 87.78/88.38 setminus( 87.78/88.38 X355,X356))) => 87.78/88.38 (( 87.78/88.38 ~ 87.78/88.38 in( 87.78/88.38 X357,X356)) => 87.78/88.38 (~ 87.78/88.38 in( 87.78/88.38 X357,X355))))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X358, 87.78/88.38 X359,X360]: 87.78/88.38 (( 87.78/88.38 ~ 87.78/88.38 in( 87.78/88.38 X360,X358)) => 87.78/88.38 (~ 87.78/88.38 in( 87.78/88.38 X360, 87.78/88.38 setminus( 87.78/88.38 X358,X359))))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X361, 87.78/88.38 X362,X363]: 87.78/88.38 (in( 87.78/88.38 X363,X362) => 87.78/88.38 (~ 87.78/88.38 in( 87.78/88.38 X363, 87.78/88.38 setminus( 87.78/88.38 X361,X362))))) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X364, 87.78/88.38 X365]: 87.78/88.38 subset( 87.78/88.38 setminus( 87.78/88.38 X364,X365), 87.78/88.38 X364)) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ![X366, 87.78/88.38 X367]: 87.78/88.38 (( 87.78/88.38 setminus( 87.78/88.38 X366,X367) = 87.78/88.38 emptyset) => 87.78/88.38 subset( 87.78/88.38 X366,X367))) => 87.78/88.38 ( 87.78/88.38 ![X368, 87.78/88.38 X369,X370]: 87.78/88.38 (in( 87.78/88.38 X370, 87.78/88.38 dsetconstr( 87.78/88.38 binunion( 87.78/88.38 X368,X369), 87.78/88.38 ^[V_15]: 87.78/88.38 (( 87.78/88.38 ~ 87.78/88.38 in( 87.78/88.38 V_15,X368)) | 87.78/88.38 (~ 87.78/88.38 in( 87.78/88.38 V_15,X369))))) => 87.78/88.38 (![X371:$o]: 87.78/88.38 (( 87.78/88.38 in( 87.78/88.38 X370,X368) => 87.78/88.38 ( 87.78/88.38 ( 87.78/88.38 ~ 87.78/88.38 in( 87.78/88.38 X370,X369)) => 87.78/88.38 X371)) => 87.78/88.38 (( 87.78/88.38 ( 87.78/88.38 ~ 87.78/88.38 in( 87.78/88.38 X370,X368)) => 87.78/88.38 ( 87.78/88.38 in( 87.78/88.38 X370,X369) => 87.78/88.38 X371)) => 87.78/88.38 X371)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 87.78/88.38 tff('130', plain, 87.78/88.38 in(sk_X370_, 87.78/88.38 dsetconstr(binunion(sk_X368_, sk_X369_), 87.78/88.38 (^[Y0 : $i]: ((~ in(Y0, sk_X368_)) | (~ in(Y0, sk_X369_)))))), 87.78/88.38 inference('cnf', [status(esa)], [zf_stmt_14])). 87.78/88.38 tff('131', plain, 87.78/88.38 ![X673, X674, X675 : $i > $o]: 87.78/88.38 (in(X673, X674) | ~ in(X673, dsetconstr(X674, (^[Y0 : $i]: X675(Y0))))), 87.78/88.38 inference('cnf', [status(esa)], [zf_stmt_14])). 87.78/88.38 tff('132', plain, 87.78/88.38 ![X673, X674, X675 : $i > $o]: 87.78/88.38 (in(X673, X674) | ~ in(X673, dsetconstr(X674, X675))), 87.78/88.38 inference('lambda-normalize', [status(thm)], ['131'])). 87.78/88.38 tff('133', plain, in(sk_X370_, binunion(sk_X368_, sk_X369_)), 87.78/88.38 inference('sup-', [status(thm)], ['130', '132'])). 87.78/88.38 tff('134', plain, 87.78/88.38 ![X516, X517, X518]: 87.78/88.38 (in(X516, X517) | in(X516, X518) | ~ in(X516, binunion(X517, X518))), 87.78/88.38 inference('cnf', [status(esa)], [zf_stmt_14])). 87.78/88.38 tff('135', plain, (in(sk_X370_, sk_X369_) | in(sk_X370_, sk_X368_)), 87.78/88.38 inference('sup-', [status(thm)], ['133', '134'])). 87.78/88.38 tff('136', plain, 87.78/88.38 (~ in(sk_X370_, sk_X369_) | sk_X371_ | in(sk_X370_, sk_X368_)), 87.78/88.38 inference('cnf', [status(esa)], [zf_stmt_14])). 87.78/88.38 tff('137', plain, ~ sk_X371_, inference('cnf', [status(esa)], [zf_stmt_14])). 87.78/88.38 tff('138', plain, (~ in(sk_X370_, sk_X369_) | in(sk_X370_, sk_X368_)), 87.78/88.38 inference('demod', [status(thm)], ['136', '137'])). 87.78/88.38 tff('139', plain, (~ in(sk_X370_, sk_X369_)) <= (~ (in(sk_X370_, sk_X369_))), 87.78/88.38 inference('split', [status(esa)], ['138'])). 87.78/88.38 tff('140', plain, ~ (in(sk_X370_, sk_X369_)) | (in(sk_X370_, sk_X368_)), 87.78/88.38 inference('split', [status(esa)], ['138'])). 87.78/88.38 tff('141', plain, 87.78/88.38 ![X405 : $i > $o, X406, X407]: 87.78/88.38 (X405(X406) | ~ in(X406, dsetconstr(X407, (^[Y0 : $i]: X405(Y0))))), 87.78/88.38 inference('cnf', [status(esa)], [zf_stmt_14])). 87.78/88.38 tff('142', plain, 87.78/88.38 ![X405 : $i > $o, X406, X407]: 87.78/88.38 (X405(X406) | ~ in(X406, dsetconstr(X407, X405))), 87.78/88.38 inference('lambda-normalize', [status(thm)], ['141'])). 87.78/88.38 tff('143', plain, 87.78/88.38 (^[Y0 : $i]: ((~ in(Y0, sk_X368_)) | (~ in(Y0, sk_X369_))))(sk_X370_), 87.78/88.38 inference('sup-', [status(thm)], ['130', '142'])). 87.78/88.38 tff('144', plain, ((~ in(sk_X370_, sk_X368_)) | (~ in(sk_X370_, sk_X369_))), 87.78/88.38 inference('lambda-normalize', [status(thm)], ['143'])). 87.78/88.38 tff('145', plain, (~ in(sk_X370_, sk_X369_) | ~ in(sk_X370_, sk_X368_)), 87.78/88.38 inference('cnf_otf', [status(thm)], ['144'])). 87.78/88.38 tff('146', plain, ~ (in(sk_X370_, sk_X369_)) | ~ (in(sk_X370_, sk_X368_)), 87.78/88.38 inference('split', [status(esa)], ['145'])). 87.78/88.38 tff('147', plain, 87.78/88.38 (in(sk_X370_, sk_X369_) | sk_X371_ | ~ in(sk_X370_, sk_X368_)), 87.78/88.38 inference('cnf', [status(esa)], [zf_stmt_14])). 87.78/88.38 tff('148', plain, (in(sk_X370_, sk_X369_) | ~ in(sk_X370_, sk_X368_)), 87.78/88.38 inference('demod', [status(thm)], ['147', '137'])). 87.78/88.38 tff('149', plain, ~ (in(sk_X370_, sk_X368_)) | (in(sk_X370_, sk_X369_)), 87.78/88.38 inference('split', [status(esa)], ['148'])). 87.78/88.38 tff('150', plain, ~ (in(sk_X370_, sk_X368_)), 87.78/88.38 inference('sat_resolution', [status(thm)], ['146', '149'])). 87.78/88.38 tff('151', plain, ~ (in(sk_X370_, sk_X369_)), 87.78/88.38 inference('sat_resolution', [status(thm)], ['140', '150'])). 87.78/88.38 tff('152', plain, ~ in(sk_X370_, sk_X369_), 87.78/88.38 inference('simpl_trail', [status(thm)], ['139', '151'])). 87.78/88.38 tff('153', plain, in(sk_X370_, sk_X368_), 87.78/88.38 inference('clc', [status(thm)], ['135', '152'])). 87.78/88.38 tff('154', plain, (~ in(sk_X370_, sk_X368_)) <= (~ (in(sk_X370_, sk_X368_))), 87.78/88.38 inference('split', [status(esa)], ['148'])). 87.78/88.38 tff('155', plain, ~ in(sk_X370_, sk_X368_), 87.78/88.38 inference('simpl_trail', [status(thm)], ['154', '150'])). 87.78/88.38 tff('156', plain, $false, inference('sup-', [status(thm)], ['153', '155'])). 87.78/88.38 87.78/88.38 % SZS output end Refutation 87.78/88.38 % Zipperpin 1.5 exiting 87.78/88.38 EOF