0.04/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.16 % Command : run_portfolio.sh /export/starexec/sandbox/benchmark/theBenchmark.p /export/starexec/sandbox/tmp/tmp.njXF0ZLAA7 0.15/0.37 % Computer : n028.cluster.edu 0.15/0.37 % Model : x86_64 x86_64 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.15/0.37 % Memory : 8042.1875MB 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64 0.15/0.37 % CPULimit : 1200 0.15/0.37 % DateTime : Tue Jul 13 12:50:02 EDT 2021 0.15/0.37 % CPUTime : 0.15/0.37 % Running portfolio for 120 s 0.15/0.37 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.15/0.37 % Number of cores: 8 0.15/0.37 % Python version: Python 3.6.8 0.15/0.37 % Running in HO mode 0.59/0.68 % Estimated wc time : 1286 0.59/0.68 % Estimated cpu time (7 cpus) : 183.71428571428572 0.61/0.74 % /export/starexec/sandbox/solver/bin/lams/s6.sh running for 21s 0.62/0.77 % /export/starexec/sandbox/solver/bin/lams/new_b3.2.norw.sh running for 15s 0.62/0.78 % /export/starexec/sandbox/solver/bin/lams/b.rpo.sh running for 21s 0.62/0.79 % /export/starexec/sandbox/solver/bin/lams/s6.ds.sh running for 10s 0.62/0.79 % /export/starexec/sandbox/solver/bin/lams/c.s.2.sh running for 68s 0.62/0.80 % /export/starexec/sandbox/solver/bin/lams/c.easy.sh running for 26s 0.62/0.80 % /export/starexec/sandbox/solver/bin/lams/old_b3.avatar.sh running for 15s 70.43/10.72 % /export/starexec/sandbox/solver/bin/lams/old_sp2.sh running for 17s 105.83/15.78 % /export/starexec/sandbox/solver/bin/lams/b.sh running for 31s 105.83/15.79 % /export/starexec/sandbox/solver/bin/lams/sh1.sh running for 26s 148.57/21.88 % /export/starexec/sandbox/solver/bin/lams/b.lsimp.sh running for 17s 148.75/22.00 % /export/starexec/sandbox/solver/bin/lams/b.split.sh running for 31s 182.51/26.86 % /export/starexec/sandbox/solver/bin/lams/s4.sh running for 15s 189.03/27.82 % /export/starexec/sandbox/solver/bin/lams/b.rw.sh running for 26s 191.17/28.17 % /export/starexec/sandbox/solver/bin/lams/c_ic.sh running for 42s 265.95/38.93 % /export/starexec/sandbox/solver/bin/lams/s1.f.sh running for 15s 275.77/40.37 % Solved by lams/c_ic.sh. 275.77/40.37 % Running : timeout 32 /export/starexec/sandbox/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox/tmp/tmp.njXF0ZLAA7/e_inputb3c767 --cpu-limit=30 --auto-schedule -s -p. 275.77/40.37 % done 3844 iterations in 12.115s 275.77/40.37 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 275.77/40.37 % SZS output start Refutation 275.77/40.37 tff(contrasubsetT1, axiom, contrasubsetT1 <=> 275.77/40.37 (![A,X]: 275.77/40.37 (in(X,powerset(A)) => 275.77/40.37 (![Y]: 275.77/40.37 (in(Y,powerset(A)) => 275.77/40.37 (![Xx]: (in(Xx,A) => (subset(X,Y) => ((~in(Xx,Y)) => (~in(Xx,X))))))))))). 275.77/40.37 tff('0', plain, 275.77/40.37 contrasubsetT1 = 275.77/40.37 (![X4,X6]: 275.77/40.37 (in(X6,powerset(X4)) => 275.77/40.37 (![X8]: 275.77/40.37 (in(X8,powerset(X4)) => 275.77/40.37 (![X10]: 275.77/40.37 (in(X10,X4) => 275.77/40.37 (subset(X6,X8) => ((~in(X10,X8)) => (~in(X10,X6)))))))))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(contrasubsetT, axiom, contrasubsetT <=> 275.77/40.37 (![A,X]: 275.77/40.37 (in(X,powerset(A)) => 275.77/40.37 (![Y]: 275.77/40.37 (in(Y,powerset(A)) => 275.77/40.37 (![Xx]: 275.77/40.37 (in(Xx,A) => 275.77/40.37 (subset(X,setminus(A,Y)) => (in(Xx,Y) => (~in(Xx,X))))))))))). 275.77/40.37 tff('1', plain, 275.77/40.37 contrasubsetT = 275.77/40.37 (![X4,X6]: 275.77/40.37 (in(X6,powerset(X4)) => 275.77/40.37 (![X8]: 275.77/40.37 (in(X8,powerset(X4)) => 275.77/40.37 (![X10]: 275.77/40.37 (in(X10,X4) => 275.77/40.37 (subset(X6,setminus(X4,X8)) => (in(X10,X8) => (~in(X10,X6)))))))))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(complementTE1, axiom, complementTE1 <=> 275.77/40.37 (![A,X]: 275.77/40.37 (in(X,powerset(A)) => 275.77/40.37 (![Xx]: (in(Xx,A) => ((~in(Xx,setminus(A,X))) => in(Xx,X))))))). 275.77/40.37 tff('2', plain, 275.77/40.37 complementTE1 = 275.77/40.37 (![X4,X6]: 275.77/40.37 (in(X6,powerset(X4)) => 275.77/40.37 (![X8]: (in(X8,X4) => ((~in(X8,setminus(X4,X6))) => in(X8,X6)))))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(complementTI1, axiom, complementTI1 <=> 275.77/40.37 (![A,X]: 275.77/40.37 (in(X,powerset(A)) => 275.77/40.37 (![Xx]: (in(Xx,A) => (in(Xx,X) => (~in(Xx,setminus(A,X))))))))). 275.77/40.37 tff('3', plain, 275.77/40.37 complementTI1 = 275.77/40.37 (![X4,X6]: 275.77/40.37 (in(X6,powerset(X4)) => 275.77/40.37 (![X8]: (in(X8,X4) => (in(X8,X6) => (~in(X8,setminus(X4,X6)))))))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(powersetTE1, axiom, powersetTE1 <=> 275.77/40.37 (![A,X]: 275.77/40.37 (in(X,powerset(A)) => 275.77/40.37 (![Y]: 275.77/40.37 (in(Y,powerset(A)) => 275.77/40.37 (![Xx]: (in(Xx,A) => (in(X,powerset(Y)) => (in(Xx,X) => in(Xx,Y)))))))))). 275.77/40.37 tff('4', plain, 275.77/40.37 powersetTE1 = 275.77/40.37 (![X4,X6]: 275.77/40.37 (in(X6,powerset(X4)) => 275.77/40.37 (![X8]: 275.77/40.37 (in(X8,powerset(X4)) => 275.77/40.37 (![X10]: 275.77/40.37 (in(X10,X4) => 275.77/40.37 (in(X6,powerset(X8)) => (in(X10,X6) => in(X10,X8))))))))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(powersetTI1, axiom, powersetTI1 <=> 275.77/40.37 (![A,X]: 275.77/40.37 (in(X,powerset(A)) => 275.77/40.37 (![Y]: 275.77/40.37 (in(Y,powerset(A)) => 275.77/40.37 ((![Xx]: (in(Xx,A) => (in(Xx,X) => in(Xx,Y)))) => in(X,powerset(Y)))))))). 275.77/40.37 tff('5', plain, 275.77/40.37 powersetTI1 = 275.77/40.37 (![X4,X6]: 275.77/40.37 (in(X6,powerset(X4)) => 275.77/40.37 (![X8]: 275.77/40.37 (in(X8,powerset(X4)) => 275.77/40.37 ((![X10]: (in(X10,X4) => (in(X10,X6) => in(X10,X8)))) => 275.77/40.37 in(X6,powerset(X8))))))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(subsetTI, axiom, subsetTI <=> 275.77/40.37 (![A,X]: 275.77/40.37 (in(X,powerset(A)) => 275.77/40.37 (![Y]: 275.77/40.37 (in(Y,powerset(A)) => 275.77/40.37 ((![Xx]: (in(Xx,A) => (in(Xx,X) => in(Xx,Y)))) => subset(X,Y))))))). 275.77/40.37 tff('6', plain, 275.77/40.37 subsetTI = 275.77/40.37 (![X4,X6]: 275.77/40.37 (in(X6,powerset(X4)) => 275.77/40.37 (![X8]: 275.77/40.37 (in(X8,powerset(X4)) => 275.77/40.37 ((![X10]: (in(X10,X4) => (in(X10,X6) => in(X10,X8)))) => 275.77/40.37 subset(X6,X8)))))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(setextT, axiom, setextT <=> 275.77/40.37 (![A,X]: 275.77/40.37 (in(X,powerset(A)) => 275.77/40.37 (![Y]: 275.77/40.37 (in(Y,powerset(A)) => 275.77/40.37 ((![Xx]: (in(Xx,A) => (in(Xx,X) => in(Xx,Y)))) => 275.77/40.37 ((![Xx]: (in(Xx,A) => (in(Xx,Y) => in(Xx,X)))) => (X = Y)))))))). 275.77/40.37 tff('7', plain, 275.77/40.37 setextT = 275.77/40.37 (![X4,X6]: 275.77/40.37 (in(X6,powerset(X4)) => 275.77/40.37 (![X8]: 275.77/40.37 (in(X8,powerset(X4)) => 275.77/40.37 ((![X10]: (in(X10,X4) => (in(X10,X6) => in(X10,X8)))) => 275.77/40.37 ((![X12]: (in(X12,X4) => (in(X12,X8) => in(X12,X6)))) => 275.77/40.37 (X6 = X8))))))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(complementT_lem, axiom, complementT_lem <=> 275.77/40.37 (![A,X]: (in(X,powerset(A)) => in(setminus(A,X),powerset(A))))). 275.77/40.37 tff('8', plain, 275.77/40.37 complementT_lem = 275.77/40.37 (![X4,X6]: (in(X6,powerset(X4)) => in(setminus(X4,X6),powerset(X4)))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(setminusT_lem, axiom, setminusT_lem <=> 275.77/40.37 (![A,X]: 275.77/40.37 (in(X,powerset(A)) => 275.77/40.37 (![Y]: (in(Y,powerset(A)) => in(setminus(X,Y),powerset(A))))))). 275.77/40.37 tff('9', plain, 275.77/40.37 setminusT_lem = 275.77/40.37 (![X4,X6]: 275.77/40.37 (in(X6,powerset(X4)) => 275.77/40.37 (![X8]: (in(X8,powerset(X4)) => in(setminus(X6,X8),powerset(X4)))))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(powersetT_lem, axiom, powersetT_lem <=> 275.77/40.37 (![A,X]: (in(X,powerset(A)) => in(powerset(X),powerset(powerset(A)))))). 275.77/40.37 tff('10', plain, 275.77/40.37 powersetT_lem = 275.77/40.37 (![X4,X6]: 275.77/40.37 (in(X6,powerset(X4)) => in(powerset(X6),powerset(powerset(X4))))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(singletoninpowerset, axiom, singletoninpowerset <=> 275.77/40.37 (![A,Xx]: (in(Xx,A) => in(setadjoin(Xx,emptyset),powerset(A))))). 275.77/40.37 tff('11', plain, 275.77/40.37 singletoninpowerset = 275.77/40.37 (![X4,X6]: (in(X6,X4) => in(setadjoin(X6,emptyset),powerset(X4)))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(singletonsubset, axiom, singletonsubset <=> 275.77/40.37 (![A,Xx]: (in(Xx,A) => subset(setadjoin(Xx,emptyset),A)))). 275.77/40.37 tff('12', plain, 275.77/40.37 singletonsubset = 275.77/40.37 (![X4,X6]: (in(X6,X4) => subset(setadjoin(X6,emptyset),X4))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(setminusSubset1, axiom, setminusSubset1 <=> 275.77/40.37 (![A,B]: ((setminus(A,B) = emptyset) => subset(A,B)))). 275.77/40.37 tff('13', plain, 275.77/40.37 setminusSubset1 = 275.77/40.37 (![X4,X6]: ((setminus(X4,X6) = emptyset) => subset(X4,X6))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(setminusLsub, axiom, setminusLsub <=> (![A,B]: subset(setminus(A,B),A))). 275.77/40.37 tff('14', plain, setminusLsub = (![X4,X6]: subset(setminus(X4,X6),X4)), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(setminusIRneg, axiom, setminusIRneg <=> 275.77/40.37 (![A,B,Xx]: (in(Xx,B) => (~in(Xx,setminus(A,B)))))). 275.77/40.37 tff('15', plain, 275.77/40.37 setminusIRneg = (![X4,X6,X8]: (in(X8,X6) => (~in(X8,setminus(X4,X6))))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(setminusILneg, axiom, setminusILneg <=> 275.77/40.37 (![A,B,Xx]: ((~in(Xx,A)) => (~in(Xx,setminus(A,B)))))). 275.77/40.37 tff('16', plain, 275.77/40.37 setminusILneg = 275.77/40.37 (![X4,X6,X8]: ((~in(X8,X4)) => (~in(X8,setminus(X4,X6))))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(setminusELneg, axiom, setminusELneg <=> 275.77/40.37 (![A,B,Xx]: ((~in(Xx,setminus(A,B))) => ((~in(Xx,B)) => (~in(Xx,A)))))). 275.77/40.37 tff('17', plain, 275.77/40.37 setminusELneg = 275.77/40.37 (![X4,X6,X8]: 275.77/40.37 ((~in(X8,setminus(X4,X6))) => ((~in(X8,X6)) => (~in(X8,X4))))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(setminusERneg, axiom, setminusERneg <=> 275.77/40.37 (![A,B,Xx]: ((~in(Xx,setminus(A,B))) => (in(Xx,A) => in(Xx,B))))). 275.77/40.37 tff('18', plain, 275.77/40.37 setminusERneg = 275.77/40.37 (![X4,X6,X8]: ((~in(X8,setminus(X4,X6))) => (in(X8,X4) => in(X8,X6)))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(setminusSubset2, axiom, setminusSubset2 <=> 275.77/40.37 (![A,B]: (subset(A,B) => (setminus(A,B) = emptyset)))). 275.77/40.37 tff('19', plain, 275.77/40.37 setminusSubset2 = 275.77/40.37 (![X4,X6]: (subset(X4,X6) => (setminus(X4,X6) = emptyset))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(setminusER, axiom, setminusER <=> 275.77/40.37 (![A,B,Xx]: (in(Xx,setminus(A,B)) => (~in(Xx,B))))). 275.77/40.37 tff('20', plain, 275.77/40.37 setminusER = (![X4,X6,X8]: (in(X8,setminus(X4,X6)) => (~in(X8,X6)))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(setminusEL, axiom, setminusEL <=> 275.77/40.37 (![A,B,Xx]: (in(Xx,setminus(A,B)) => in(Xx,A)))). 275.77/40.37 tff('21', plain, 275.77/40.37 setminusEL = (![X4,X6,X8]: (in(X8,setminus(X4,X6)) => in(X8,X4))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(setminusI, axiom, setminusI <=> 275.77/40.37 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => in(Xx,setminus(A,B)))))). 275.77/40.37 tff('22', plain, 275.77/40.37 setminusI = 275.77/40.37 (![X4,X6,X8]: (in(X8,X4) => ((~in(X8,X6)) => in(X8,setminus(X4,X6))))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(powersetsubset, axiom, powersetsubset <=> 275.77/40.37 (![A,B]: (subset(A,B) => subset(powerset(A),powerset(B))))). 275.77/40.37 tff('23', plain, 275.77/40.37 powersetsubset = 275.77/40.37 (![X4,X6]: (subset(X4,X6) => subset(powerset(X4),powerset(X6)))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(inPowerset, axiom, inPowerset <=> (![A]: in(A,powerset(A)))). 275.77/40.37 tff('24', plain, inPowerset = (![X4]: in(X4,powerset(X4))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(powersetE1, axiom, powersetE1 <=> 275.77/40.37 (![A,B]: (in(B,powerset(A)) => subset(B,A)))). 275.77/40.37 tff('25', plain, 275.77/40.37 powersetE1 = (![X4,X6]: (in(X6,powerset(X4)) => subset(X6,X4))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(powersetI1, axiom, powersetI1 <=> 275.77/40.37 (![A,B]: (subset(B,A) => in(B,powerset(A))))). 275.77/40.37 tff('26', plain, 275.77/40.37 powersetI1 = (![X4,X6]: (subset(X6,X4) => in(X6,powerset(X4)))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(subsetemptysetimpeq, axiom, subsetemptysetimpeq <=> 275.77/40.37 (![A]: (subset(A,emptyset) => (A = emptyset)))). 275.77/40.37 tff('27', plain, 275.77/40.37 subsetemptysetimpeq = (![X4]: (subset(X4,emptyset) => (X4 = emptyset))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(setextsub, axiom, setextsub <=> 275.77/40.37 (![A,B]: (subset(A,B) => (subset(B,A) => (A = B))))). 275.77/40.37 tff('28', plain, 275.77/40.37 setextsub = (![X4,X6]: (subset(X4,X6) => (subset(X6,X4) => (X4 = X6)))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(subset2powerset, axiom, subset2powerset <=> 275.77/40.37 (![A,B]: (subset(A,B) => in(A,powerset(B))))). 275.77/40.37 tff('29', plain, 275.77/40.37 subset2powerset = (![X4,X6]: (subset(X4,X6) => in(X4,powerset(X6)))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(setadjoinSub2, axiom, setadjoinSub2 <=> 275.77/40.37 (![A,Xx,B]: (subset(A,B) => subset(A,setadjoin(Xx,B))))). 275.77/40.37 tff('30', plain, 275.77/40.37 setadjoinSub2 = 275.77/40.37 (![X4,X6,X8]: (subset(X4,X8) => subset(X4,setadjoin(X6,X8)))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(setadjoinSub, axiom, setadjoinSub <=> 275.77/40.37 (![Xx,A]: subset(A,setadjoin(Xx,A)))). 275.77/40.37 tff('31', plain, setadjoinSub = (![X4,X6]: subset(X6,setadjoin(X4,X6))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(subsetTrans, axiom, subsetTrans <=> 275.77/40.37 (![A,B,C]: (subset(A,B) => (subset(B,C) => subset(A,C))))). 275.77/40.37 tff('32', plain, 275.77/40.37 subsetTrans = 275.77/40.37 (![X4,X6,X8]: (subset(X4,X6) => (subset(X6,X8) => subset(X4,X8)))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(subsetRefl, axiom, subsetRefl <=> (![A]: subset(A,A))). 275.77/40.37 tff('33', plain, subsetRefl = (![X4]: subset(X4,X4)), define([status(thm)])). 275.77/40.37 tff(notequalI1, axiom, notequalI1 <=> (![A,B]: ((~subset(A,B)) => (A != B)))). 275.77/40.37 tff('34', plain, notequalI1 = (![X4,X6]: ((~subset(X4,X6)) => (X4 != X6))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(notsubsetI, axiom, notsubsetI <=> 275.77/40.37 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => (~subset(A,B)))))). 275.77/40.37 tff('35', plain, 275.77/40.37 notsubsetI = 275.77/40.37 (![X4,X6,X8]: (in(X8,X4) => ((~in(X8,X6)) => (~subset(X4,X6))))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(subsetE2, axiom, subsetE2 <=> 275.77/40.37 (![A,B,Xx]: (subset(A,B) => ((~in(Xx,B)) => (~in(Xx,A)))))). 275.77/40.37 tff('36', plain, 275.77/40.37 subsetE2 = 275.77/40.37 (![X4,X6,X8]: (subset(X4,X6) => ((~in(X8,X6)) => (~in(X8,X4))))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(subsetE, axiom, subsetE <=> 275.77/40.37 (![A,B,Xx]: (subset(A,B) => (in(Xx,A) => in(Xx,B))))). 275.77/40.37 tff('37', plain, 275.77/40.37 subsetE = (![X4,X6,X8]: (subset(X4,X6) => (in(X8,X4) => in(X8,X6)))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(emptysetsubset, axiom, emptysetsubset <=> (![A]: subset(emptyset,A))). 275.77/40.37 tff('38', plain, emptysetsubset = (![X4]: subset(emptyset,X4)), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(subsetI2, axiom, subsetI2 <=> 275.77/40.37 (![A,B]: ((![Xx]: (in(Xx,A) => in(Xx,B))) => subset(A,B)))). 275.77/40.37 tff('39', plain, 275.77/40.37 subsetI2 = 275.77/40.37 (![X4,X6]: ((![X8]: (in(X8,X4) => in(X8,X6))) => subset(X4,X6))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(eqimpsubset1, axiom, eqimpsubset1 <=> (![A,B]: ((A = B) => subset(A,B)))). 275.77/40.37 tff('40', plain, eqimpsubset1 = (![X4,X6]: ((X4 = X6) => subset(X4,X6))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(eqimpsubset2, axiom, eqimpsubset2 <=> (![A,B]: ((A = B) => subset(B,A)))). 275.77/40.37 tff('41', plain, eqimpsubset2 = (![X4,X6]: ((X4 = X6) => subset(X6,X4))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(subsetI1, axiom, subsetI1 <=> 275.77/40.37 (![A,B]: ((![Xx]: (in(Xx,A) => in(Xx,B))) => subset(A,B)))). 275.77/40.37 tff('42', plain, 275.77/40.37 subsetI1 = 275.77/40.37 (![X4,X6]: ((![X8]: (in(X8,X4) => in(X8,X6))) => subset(X4,X6))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(powerset__Cong, axiom, powerset__Cong <=> 275.77/40.37 (![A,B]: ((A = B) => (powerset(A) = powerset(B))))). 275.77/40.37 tff('43', plain, 275.77/40.37 powerset__Cong = (![X4,X6]: ((X4 = X6) => (powerset(X4) = powerset(X6)))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(powersetE, axiom, powersetE <=> 275.77/40.37 (![A,B,Xx]: (in(B,powerset(A)) => (in(Xx,B) => in(Xx,A))))). 275.77/40.37 tff('44', plain, 275.77/40.37 powersetE = 275.77/40.37 (![X4,X6,X8]: (in(X6,powerset(X4)) => (in(X8,X6) => in(X8,X4)))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(emptyInPowerset, axiom, emptyInPowerset <=> 275.77/40.37 (![A]: in(emptyset,powerset(A)))). 275.77/40.37 tff('45', plain, emptyInPowerset = (![X4]: in(emptyset,powerset(X4))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(emptyinPowerset, axiom, emptyinPowerset <=> 275.77/40.37 (![A]: in(emptyset,powerset(A)))). 275.77/40.37 tff('46', plain, emptyinPowerset = (![X4]: in(emptyset,powerset(X4))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(powersetI, axiom, powersetI <=> 275.77/40.37 (![A,B]: ((![Xx]: (in(Xx,B) => in(Xx,A))) => in(B,powerset(A))))). 275.77/40.37 tff('47', plain, 275.77/40.37 powersetI = 275.77/40.37 (![X4,X6]: ((![X8]: (in(X8,X6) => in(X8,X4))) => in(X6,powerset(X4)))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(powersetAx, axiom, powersetAx <=> 275.77/40.37 (![A,B]: (in(B,powerset(A)) <=> (![Xx]: (in(Xx,B) => in(Xx,A)))))). 275.77/40.37 tff('48', plain, 275.77/40.37 powersetAx = 275.77/40.37 (![X4,X6]: (in(X6,powerset(X4)) <=> (![X8]: (in(X8,X6) => in(X8,X4))))), 275.77/40.37 define([status(thm)])). 275.77/40.37 tff(contrasubsetT2, conjecture, 275.77/40.37 (setextAx => 275.77/40.37 (emptysetAx => 275.77/40.37 (setadjoinAx => 275.77/40.37 (powersetAx => 275.77/40.37 (setunionAx => 275.77/40.37 (omega0Ax => 275.77/40.37 (omegaSAx => 275.77/40.37 (omegaIndAx => 275.77/40.37 (replAx => 275.77/40.37 (foundationAx => 275.77/40.37 (wellorderingAx => 275.77/40.37 (descrp => 275.77/40.37 (dsetconstrI => 275.77/40.37 (dsetconstrEL => 275.77/40.37 (dsetconstrER => 275.77/40.37 (exuE1 => 275.77/40.37 (prop2setE => 275.77/40.37 (emptysetE => 275.77/40.37 (emptysetimpfalse => 275.77/40.37 (notinemptyset => 275.77/40.37 (exuE3e => 275.77/40.37 (setext => 275.77/40.37 (emptyI => 275.77/40.37 (noeltsimpempty => 275.77/40.37 (setbeta => 275.77/40.37 (nonemptyE1 => 275.77/40.37 (nonemptyI => 275.77/40.37 (nonemptyI1 => 275.77/40.37 (setadjoinIL => 275.77/40.37 (emptyinunitempty => 275.77/40.37 (setadjoinIR => 275.77/40.37 (setadjoinE => 275.77/40.37 (setadjoinOr => 275.77/40.37 (setoftrueEq => 275.77/40.37 (powersetI => 275.77/40.37 (emptyinPowerset => 275.77/40.37 (emptyInPowerset => 275.77/40.37 (powersetE => 275.77/40.37 (setunionI => 275.77/40.37 (setunionE => 275.77/40.37 (subPowSU => 275.77/40.37 (exuE2 => 275.77/40.37 (nonemptyImpWitness => 275.77/40.37 (uniqinunit => 275.77/40.37 (notinsingleton => 275.77/40.37 (eqinunit => 275.77/40.37 (singletonsswitch => 275.77/40.37 (upairsetE => 275.77/40.37 (upairsetIL => 275.77/40.37 (upairsetIR => 275.77/40.37 (emptyE1 => 275.77/40.37 (vacuousDall => 275.77/40.37 (quantDeMorgan1 => 275.77/40.37 (quantDeMorgan2 => 275.77/40.37 (quantDeMorgan3 => 275.77/40.37 (quantDeMorgan4 => 275.77/40.37 (prop2setI => 275.77/40.37 (prop2set2propI => 275.77/40.37 (notdexE => 275.77/40.37 (notdallE => 275.77/40.37 (exuI1 => 275.77/40.37 (exuI3 => 275.77/40.37 (exuI2 => 275.77/40.37 (inCongP => 275.77/40.37 (in__Cong => 275.77/40.37 (exuE3u => 275.77/40.37 ( 275.77/40.37 exu__Cong => 275.77/40.37 ( 275.77/40.37 emptyset__Cong => 275.77/40.37 ( 275.77/40.37 setadjoin__Cong => 275.77/40.37 ( 275.77/40.37 powerset__Cong => 275.77/40.37 ( 275.77/40.37 setunion__Cong => 275.77/40.37 ( 275.77/40.37 omega__Cong => 275.77/40.37 ( 275.77/40.37 exuEu => 275.77/40.37 ( 275.77/40.37 descr__Cong => 275.77/40.37 ( 275.77/40.37 dsetconstr__Cong => 275.77/40.37 ( 275.77/40.37 subsetI1 => 275.77/40.37 ( 275.77/40.37 eqimpsubset2 => 275.77/40.37 ( 275.77/40.37 eqimpsubset1 => 275.77/40.37 ( 275.77/40.37 subsetI2 => 275.77/40.37 ( 275.77/40.37 emptysetsubset => 275.77/40.37 ( 275.77/40.37 subsetE => 275.77/40.37 ( 275.77/40.37 subsetE2 => 275.77/40.37 ( 275.77/40.37 notsubsetI => 275.77/40.37 ( 275.77/40.37 notequalI1 => 275.77/40.37 ( 275.77/40.37 notequalI2 => 275.77/40.37 ( 275.77/40.37 subsetRefl => 275.77/40.37 ( 275.77/40.37 subsetTrans => 275.77/40.37 ( 275.77/40.37 setadjoinSub => 275.77/40.37 ( 275.77/40.37 setadjoinSub2 => 275.77/40.37 ( 275.77/40.37 subset2powerset => 275.77/40.37 ( 275.77/40.37 setextsub => 275.77/40.37 ( 275.77/40.37 subsetemptysetimpeq => 275.77/40.37 ( 275.77/40.37 powersetI1 => 275.77/40.37 ( 275.77/40.37 powersetE1 => 275.77/40.37 ( 275.77/40.37 inPowerset => 275.77/40.37 ( 275.77/40.37 powersetsubset => 275.77/40.37 ( 275.77/40.37 sepInPowerset => 275.77/40.37 ( 275.77/40.37 sepSubset => 275.77/40.37 ( 275.77/40.37 binunionIL => 275.77/40.37 ( 275.77/40.37 upairset2IR => 275.77/40.37 ( 275.77/40.37 binunionIR => 275.77/40.37 ( 275.77/40.37 binunionEcases => 275.77/40.37 ( 275.77/40.37 binunionE => 275.77/40.37 ( 275.77/40.37 binunionLsub => 275.77/40.37 ( 275.77/40.37 binunionRsub => 275.77/40.37 ( 275.77/40.37 binintersectI => 275.77/40.37 ( 275.77/40.37 binintersectSubset5 => 275.77/40.37 ( 275.77/40.37 binintersectEL => 275.77/40.37 ( 275.77/40.37 binintersectLsub => 275.77/40.37 ( 275.77/40.37 binintersectSubset2 => 275.77/40.37 ( 275.77/40.37 binintersectSubset3 => 275.77/40.37 ( 275.77/40.37 binintersectER => 275.77/40.37 ( 275.77/40.37 disjointsetsI1 => 275.77/40.37 ( 275.77/40.37 binintersectRsub => 275.77/40.37 ( 275.77/40.37 binintersectSubset4 => 275.77/40.37 ( 275.77/40.37 binintersectSubset1 => 275.77/40.37 ( 275.77/40.37 bs114d => 275.77/40.37 ( 275.77/40.37 setminusI => 275.77/40.37 ( 275.77/40.37 setminusEL => 275.77/40.37 ( 275.77/40.37 setminusER => 275.77/40.37 ( 275.77/40.37 setminusSubset2 => 275.77/40.37 ( 275.77/40.37 setminusERneg => 275.77/40.37 ( 275.77/40.37 setminusELneg => 275.77/40.37 ( 275.77/40.37 setminusILneg => 275.77/40.37 ( 275.77/40.37 setminusIRneg => 275.77/40.37 ( 275.77/40.37 setminusLsub => 275.77/40.37 ( 275.77/40.37 setminusSubset1 => 275.77/40.37 ( 275.77/40.37 symdiffE => 275.77/40.37 ( 275.77/40.37 symdiffI1 => 275.77/40.37 ( 275.77/40.37 symdiffI2 => 275.77/40.37 ( 275.77/40.37 symdiffIneg1 => 275.77/40.37 ( 275.77/40.37 symdiffIneg2 => 275.77/40.37 ( 275.77/40.37 secondinupair => 275.77/40.37 ( 275.77/40.37 setukpairIL => 275.77/40.37 ( 275.77/40.37 setukpairIR => 275.77/40.37 ( 275.77/40.37 kpairiskpair => 275.77/40.37 ( 275.77/40.37 kpairp => 275.77/40.37 ( 275.77/40.37 singletonsubset => 275.77/40.37 ( 275.77/40.37 singletoninpowerset => 275.77/40.37 ( 275.77/40.37 singletoninpowunion => 275.77/40.37 ( 275.77/40.37 upairset2E => 275.77/40.37 ( 275.77/40.37 upairsubunion => 275.77/40.37 ( 275.77/40.37 upairinpowunion => 275.77/40.37 ( 275.77/40.37 ubforcartprodlem1 => 275.77/40.37 ( 275.77/40.37 ubforcartprodlem2 => 275.77/40.37 ( 275.77/40.37 ubforcartprodlem3 => 275.77/40.37 ( 275.77/40.37 cartprodpairin => 275.77/40.37 ( 275.77/40.37 cartprodmempair1 => 275.77/40.37 ( 275.77/40.37 cartprodmempair => 275.77/40.37 ( 275.77/40.37 setunionE2 => 275.77/40.37 ( 275.77/40.37 setunionsingleton1 => 275.77/40.37 ( 275.77/40.37 setunionsingleton2 => 275.77/40.37 ( 275.77/40.37 setunionsingleton => 275.77/40.37 ( 275.77/40.37 singletonprop => 275.77/40.37 ( 275.77/40.37 ex1E1 => 275.77/40.37 ( 275.77/40.37 ex1I => 275.77/40.37 ( 275.77/40.37 ex1I2 => 275.77/40.37 ( 275.77/40.37 singletonsuniq => 275.77/40.37 ( 275.77/40.37 setukpairinjL1 => 275.77/40.37 ( 275.77/40.37 kfstsingleton => 275.77/40.37 ( 275.77/40.37 theprop => 275.77/40.37 ( 275.77/40.37 kfstpairEq => 275.77/40.37 ( 275.77/40.37 cartprodfstin => 275.77/40.37 ( 275.77/40.37 setukpairinjL2 => 275.77/40.37 ( 275.77/40.37 setukpairinjL => 275.77/40.37 ( 275.77/40.37 setukpairinjR11 => 275.77/40.37 ( 275.77/40.37 setukpairinjR12 => 275.77/40.37 ( 275.77/40.37 setukpairinjR1 => 275.77/40.37 ( 275.77/40.37 upairequniteq => 275.77/40.37 ( 275.77/40.37 setukpairinjR2 => 275.77/40.37 ( 275.77/40.37 setukpairinjR => 275.77/40.37 ( 275.77/40.37 ksndsingleton => 275.77/40.37 ( 275.77/40.37 ksndpairEq => 275.77/40.37 ( 275.77/40.37 kpairsurjEq => 275.77/40.37 ( 275.77/40.37 cartprodsndin => 275.77/40.37 ( 275.77/40.37 cartprodpairmemEL => 275.77/40.37 ( 275.77/40.37 cartprodpairmemER => 275.77/40.37 ( 275.77/40.37 cartprodmempaircEq => 275.77/40.37 ( 275.77/40.37 cartprodfstpairEq => 275.77/40.37 ( 275.77/40.37 cartprodsndpairEq => 275.77/40.37 ( 275.77/40.37 cartprodpairsurjEq => 275.77/40.37 ( 275.77/40.37 dpsetconstrI => 275.77/40.37 ( 275.77/40.37 dpsetconstrSub => 275.77/40.37 ( 275.77/40.37 setOfPairsIsBReln => 275.77/40.37 ( 275.77/40.37 dpsetconstrERa => 275.77/40.37 ( 275.77/40.37 dpsetconstrEL1 => 275.77/40.37 ( 275.77/40.37 dpsetconstrEL2 => 275.77/40.37 ( 275.77/40.37 dpsetconstrER => 275.77/40.37 ( 275.77/40.37 funcImageSingleton => 275.77/40.37 ( 275.77/40.37 apProp => 275.77/40.37 ( 275.77/40.37 app => 275.77/40.37 ( 275.77/40.37 infuncsetfunc => 275.77/40.37 ( 275.77/40.37 ap2p => 275.77/40.37 ( 275.77/40.37 funcinfuncset => 275.77/40.37 ( 275.77/40.37 lamProp => 275.77/40.37 ( 275.77/40.37 lamp => 275.77/40.37 ( 275.77/40.37 lam2p => 275.77/40.37 ( 275.77/40.37 brelnall1 => 275.77/40.37 ( 275.77/40.37 brelnall2 => 275.77/40.37 ( 275.77/40.37 ex1E2 => 275.77/40.37 ( 275.77/40.37 funcGraphProp1 => 275.77/40.37 ( 275.77/40.37 funcGraphProp3 => 275.77/40.37 ( 275.77/40.37 funcGraphProp2 => 275.77/40.37 ( 275.77/40.37 funcextLem => 275.77/40.37 ( 275.77/40.37 funcGraphProp4 => 275.77/40.37 ( 275.77/40.37 subbreln => 275.77/40.37 ( 275.77/40.37 eqbreln => 275.77/40.37 ( 275.77/40.37 funcext => 275.77/40.37 ( 275.77/40.37 funcext2 => 275.77/40.37 ( 275.77/40.37 ap2apEq1 => 275.77/40.37 ( 275.77/40.37 ap2apEq2 => 275.77/40.37 ( 275.77/40.37 beta1 => 275.77/40.37 ( 275.77/40.37 eta1 => 275.77/40.37 ( 275.77/40.37 lam2lamEq => 275.77/40.37 ( 275.77/40.37 beta2 => 275.77/40.37 ( 275.77/40.37 eta2 => 275.77/40.37 ( 275.77/40.37 iffalseProp1 => 275.77/40.37 ( 275.77/40.37 iffalseProp2 => 275.77/40.37 ( 275.77/40.37 iftrueProp1 => 275.77/40.37 ( 275.77/40.37 iftrueProp2 => 275.77/40.37 ( 275.77/40.37 ifSingleton => 275.77/40.37 ( 275.77/40.37 ifp => 275.77/40.37 ( 275.77/40.37 theeq => 275.77/40.37 ( 275.77/40.37 iftrue => 275.77/40.37 ( 275.77/40.37 iffalse => 275.77/40.37 ( 275.77/40.37 iftrueorfalse => 275.77/40.37 ( 275.77/40.37 binintersectT_lem => 275.77/40.37 ( 275.77/40.37 binunionT_lem => 275.77/40.37 ( 275.77/40.37 powersetT_lem => 275.77/40.37 ( 275.77/40.37 setminusT_lem => 275.77/40.37 ( 275.77/40.37 complementT_lem => 275.77/40.37 ( 275.77/40.37 setextT => 275.77/40.37 ( 275.77/40.37 subsetTI => 275.77/40.37 ( 275.77/40.37 powersetTI1 => 275.77/40.37 ( 275.77/40.37 powersetTE1 => 275.77/40.37 ( 275.77/40.37 complementTI1 => 275.77/40.37 ( 275.77/40.37 complementTE1 => 275.77/40.37 ( 275.77/40.37 binintersectTELcontra => 275.77/40.37 ( 275.77/40.37 binintersectTERcontra => 275.77/40.37 ( 275.77/40.37 contrasubsetT => 275.77/40.37 ( 275.77/40.37 contrasubsetT1 => 275.77/40.37 ( 275.77/40.37 ![A,X]: 275.77/40.37 (in( 275.77/40.37 X, 275.77/40.37 powerset( 275.77/40.37 A)) => 275.77/40.37 (![Y]: 275.77/40.37 (in( 275.77/40.37 Y, 275.77/40.37 powerset( 275.77/40.37 A)) => 275.77/40.37 (subset( 275.77/40.37 X,Y) => 275.77/40.37 subset( 275.77/40.37 setminus( 275.77/40.37 A,Y), 275.77/40.37 setminus( 275.77/40.37 A,X))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 275.77/40.37 tff(zf_stmt_0, conjecture, 275.77/40.37 (setextAx => 275.77/40.37 (emptysetAx => 275.77/40.37 (setadjoinAx => 275.77/40.37 ((![X4,X6]: (in(X6,powerset(X4)) <=> (![X8]: (in(X8,X6) => in(X8,X4))))) => 275.77/40.37 (setunionAx => 275.77/40.37 (omega0Ax => 275.77/40.37 (omegaSAx => 275.77/40.37 (omegaIndAx => 275.77/40.37 (replAx => 275.77/40.37 (foundationAx => 275.77/40.37 (wellorderingAx => 275.77/40.37 (descrp => 275.77/40.37 (dsetconstrI => 275.77/40.37 (dsetconstrEL => 275.77/40.37 (dsetconstrER => 275.77/40.37 (exuE1 => 275.77/40.37 (prop2setE => 275.77/40.37 (emptysetE => 275.77/40.37 (emptysetimpfalse => 275.77/40.37 (notinemptyset => 275.77/40.37 (exuE3e => 275.77/40.37 (setext => 275.77/40.37 (emptyI => 275.77/40.37 (noeltsimpempty => 275.77/40.37 (setbeta => 275.77/40.37 (nonemptyE1 => 275.77/40.37 (nonemptyI => 275.77/40.37 (nonemptyI1 => 275.77/40.37 (setadjoinIL => 275.77/40.37 (emptyinunitempty => 275.77/40.37 (setadjoinIR => 275.77/40.37 (setadjoinE => 275.77/40.37 (setadjoinOr => 275.77/40.37 (setoftrueEq => 275.77/40.37 ((![X10,X12]: 275.77/40.37 ((![X14]: 275.77/40.37 (in(X14,X12) => in(X14,X10))) => 275.77/40.37 in(X12,powerset(X10)))) => 275.77/40.37 ((![X16]: in(emptyset,powerset(X16))) => 275.77/40.37 ((![X18]: in(emptyset,powerset(X18))) => 275.77/40.37 ((![X20,X22,X24]: 275.77/40.37 (in(X22,powerset(X20)) => 275.77/40.37 (in(X24,X22) => in(X24,X20)))) => 275.77/40.37 (setunionI => 275.77/40.37 (setunionE => 275.77/40.37 (subPowSU => 275.77/40.37 (exuE2 => 275.77/40.37 (nonemptyImpWitness => 275.77/40.37 (uniqinunit => 275.77/40.37 (notinsingleton => 275.77/40.37 (eqinunit => 275.77/40.37 (singletonsswitch => 275.77/40.37 (upairsetE => 275.77/40.37 (upairsetIL => 275.77/40.37 (upairsetIR => 275.77/40.37 (emptyE1 => 275.77/40.37 (vacuousDall => 275.77/40.37 (quantDeMorgan1 => 275.77/40.37 (quantDeMorgan2 => 275.77/40.37 (quantDeMorgan3 => 275.77/40.37 (quantDeMorgan4 => 275.77/40.37 (prop2setI => 275.77/40.37 (prop2set2propI => 275.77/40.37 (notdexE => 275.77/40.37 (notdallE => 275.77/40.37 (exuI1 => 275.77/40.37 (exuI3 => 275.77/40.37 (exuI2 => 275.77/40.37 (inCongP => 275.77/40.37 (in__Cong => 275.77/40.37 (exuE3u => 275.77/40.37 ( 275.77/40.37 exu__Cong => 275.77/40.37 ( 275.77/40.37 emptyset__Cong => 275.77/40.37 ( 275.77/40.37 setadjoin__Cong => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X26,X28]: 275.77/40.37 (( 275.77/40.37 X26 = X28) => 275.77/40.37 (powerset( 275.77/40.37 X26) = 275.77/40.37 powerset( 275.77/40.37 X28)))) => 275.77/40.37 ( 275.77/40.37 setunion__Cong => 275.77/40.37 ( 275.77/40.37 omega__Cong => 275.77/40.37 ( 275.77/40.37 exuEu => 275.77/40.37 ( 275.77/40.37 descr__Cong => 275.77/40.37 ( 275.77/40.37 dsetconstr__Cong => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X30,X32]: 275.77/40.37 (( 275.77/40.37 ![X34]: 275.77/40.37 (in( 275.77/40.37 X34,X30) => 275.77/40.37 in( 275.77/40.37 X34,X32))) => 275.77/40.37 subset( 275.77/40.37 X30,X32))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X36,X38]: 275.77/40.37 (( 275.77/40.37 X36 = X38) => 275.77/40.37 subset( 275.77/40.37 X38,X36))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X40,X42]: 275.77/40.37 (( 275.77/40.37 X40 = X42) => 275.77/40.37 subset( 275.77/40.37 X40,X42))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X44,X46]: 275.77/40.37 (( 275.77/40.37 ![X48]: 275.77/40.37 (in( 275.77/40.37 X48,X44) => 275.77/40.37 in( 275.77/40.37 X48,X46))) => 275.77/40.37 subset( 275.77/40.37 X44,X46))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X50]: 275.77/40.37 subset( 275.77/40.37 emptyset, 275.77/40.37 X50)) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X52, 275.77/40.37 X54,X56]: 275.77/40.37 (subset( 275.77/40.37 X52,X54) => 275.77/40.37 (in( 275.77/40.37 X56,X52) => 275.77/40.37 in( 275.77/40.37 X56,X54)))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X58, 275.77/40.37 X60,X62]: 275.77/40.37 (subset( 275.77/40.37 X58,X60) => 275.77/40.37 (( 275.77/40.37 ~ 275.77/40.37 in( 275.77/40.37 X62,X60)) => 275.77/40.37 (~ 275.77/40.37 in( 275.77/40.37 X62,X58))))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X64, 275.77/40.37 X66,X68]: 275.77/40.37 (in( 275.77/40.37 X68,X64) => 275.77/40.37 (( 275.77/40.37 ~ 275.77/40.37 in( 275.77/40.37 X68,X66)) => 275.77/40.37 (~ 275.77/40.37 subset( 275.77/40.37 X64,X66))))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X70,X72]: 275.77/40.37 (( 275.77/40.37 ~ 275.77/40.37 subset( 275.77/40.37 X70,X72)) => 275.77/40.37 (X70 != 275.77/40.37 X72))) => 275.77/40.37 ( 275.77/40.37 notequalI2 => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X74]: 275.77/40.37 subset( 275.77/40.37 X74,X74)) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X76, 275.77/40.37 X78,X80]: 275.77/40.37 (subset( 275.77/40.37 X76,X78) => 275.77/40.37 (subset( 275.77/40.37 X78,X80) => 275.77/40.37 subset( 275.77/40.37 X76,X80)))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X82,X84]: 275.77/40.37 subset( 275.77/40.37 X84, 275.77/40.37 setadjoin( 275.77/40.37 X82,X84))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X86, 275.77/40.37 X88,X90]: 275.77/40.37 (subset( 275.77/40.37 X86,X90) => 275.77/40.37 subset( 275.77/40.37 X86, 275.77/40.37 setadjoin( 275.77/40.37 X88,X90)))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X92,X94]: 275.77/40.37 (subset( 275.77/40.37 X92,X94) => 275.77/40.37 in( 275.77/40.37 X92, 275.77/40.37 powerset( 275.77/40.37 X94)))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X96,X98]: 275.77/40.37 (subset( 275.77/40.37 X96,X98) => 275.77/40.37 (subset( 275.77/40.37 X98,X96) => 275.77/40.37 (X96 = 275.77/40.37 X98)))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X100]: 275.77/40.37 (subset( 275.77/40.37 X100, 275.77/40.37 emptyset) => 275.77/40.37 (X100 = 275.77/40.37 emptyset))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X102, 275.77/40.37 X104]: 275.77/40.37 (subset( 275.77/40.37 X104,X102) => 275.77/40.37 in( 275.77/40.37 X104, 275.77/40.37 powerset( 275.77/40.37 X102)))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X106, 275.77/40.37 X108]: 275.77/40.37 (in( 275.77/40.37 X108, 275.77/40.37 powerset( 275.77/40.37 X106)) => 275.77/40.37 subset( 275.77/40.37 X108,X106))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X110]: 275.77/40.37 in( 275.77/40.37 X110, 275.77/40.37 powerset( 275.77/40.37 X110))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X112, 275.77/40.37 X114]: 275.77/40.37 (subset( 275.77/40.37 X112,X114) => 275.77/40.37 subset( 275.77/40.37 powerset( 275.77/40.37 X112), 275.77/40.37 powerset( 275.77/40.37 X114)))) => 275.77/40.37 ( 275.77/40.37 sepInPowerset => 275.77/40.37 ( 275.77/40.37 sepSubset => 275.77/40.37 ( 275.77/40.37 binunionIL => 275.77/40.37 ( 275.77/40.37 upairset2IR => 275.77/40.37 ( 275.77/40.37 binunionIR => 275.77/40.37 ( 275.77/40.37 binunionEcases => 275.77/40.37 ( 275.77/40.37 binunionE => 275.77/40.37 ( 275.77/40.37 binunionLsub => 275.77/40.37 ( 275.77/40.37 binunionRsub => 275.77/40.37 ( 275.77/40.37 binintersectI => 275.77/40.37 ( 275.77/40.37 binintersectSubset5 => 275.77/40.37 ( 275.77/40.37 binintersectEL => 275.77/40.37 ( 275.77/40.37 binintersectLsub => 275.77/40.37 ( 275.77/40.37 binintersectSubset2 => 275.77/40.37 ( 275.77/40.37 binintersectSubset3 => 275.77/40.37 ( 275.77/40.37 binintersectER => 275.77/40.37 ( 275.77/40.37 disjointsetsI1 => 275.77/40.37 ( 275.77/40.37 binintersectRsub => 275.77/40.37 ( 275.77/40.37 binintersectSubset4 => 275.77/40.37 ( 275.77/40.37 binintersectSubset1 => 275.77/40.37 ( 275.77/40.37 bs114d => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X116, 275.77/40.37 X118,X120]: 275.77/40.37 (in( 275.77/40.37 X120,X116) => 275.77/40.37 (( 275.77/40.37 ~ 275.77/40.37 in( 275.77/40.37 X120,X118)) => 275.77/40.37 in( 275.77/40.37 X120, 275.77/40.37 setminus( 275.77/40.37 X116,X118))))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X122, 275.77/40.37 X124,X126]: 275.77/40.37 (in( 275.77/40.37 X126, 275.77/40.37 setminus( 275.77/40.37 X122,X124)) => 275.77/40.37 in( 275.77/40.37 X126,X122))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X128, 275.77/40.37 X130,X132]: 275.77/40.37 (in( 275.77/40.37 X132, 275.77/40.37 setminus( 275.77/40.37 X128,X130)) => 275.77/40.37 (~ 275.77/40.37 in( 275.77/40.37 X132,X130)))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X134, 275.77/40.37 X136]: 275.77/40.37 (subset( 275.77/40.37 X134,X136) => 275.77/40.37 (setminus( 275.77/40.37 X134,X136) = 275.77/40.37 emptyset))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X138, 275.77/40.37 X140,X142]: 275.77/40.37 (( 275.77/40.37 ~ 275.77/40.37 in( 275.77/40.37 X142, 275.77/40.37 setminus( 275.77/40.37 X138,X140))) => 275.77/40.37 (in( 275.77/40.37 X142,X138) => 275.77/40.37 in( 275.77/40.37 X142,X140)))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X144, 275.77/40.37 X146,X148]: 275.77/40.37 (( 275.77/40.37 ~ 275.77/40.37 in( 275.77/40.37 X148, 275.77/40.37 setminus( 275.77/40.37 X144,X146))) => 275.77/40.37 (( 275.77/40.37 ~ 275.77/40.37 in( 275.77/40.37 X148,X146)) => 275.77/40.37 (~ 275.77/40.37 in( 275.77/40.37 X148,X144))))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X150, 275.77/40.37 X152,X154]: 275.77/40.37 (( 275.77/40.37 ~ 275.77/40.37 in( 275.77/40.37 X154,X150)) => 275.77/40.37 (~ 275.77/40.37 in( 275.77/40.37 X154, 275.77/40.37 setminus( 275.77/40.37 X150,X152))))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X156, 275.77/40.37 X158,X160]: 275.77/40.37 (in( 275.77/40.37 X160,X158) => 275.77/40.37 (~ 275.77/40.37 in( 275.77/40.37 X160, 275.77/40.37 setminus( 275.77/40.37 X156,X158))))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X162, 275.77/40.37 X164]: 275.77/40.37 subset( 275.77/40.37 setminus( 275.77/40.37 X162,X164), 275.77/40.37 X162)) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X166, 275.77/40.37 X168]: 275.77/40.37 (( 275.77/40.37 setminus( 275.77/40.37 X166,X168) = 275.77/40.37 emptyset) => 275.77/40.37 subset( 275.77/40.37 X166,X168))) => 275.77/40.37 ( 275.77/40.37 symdiffE => 275.77/40.37 ( 275.77/40.37 symdiffI1 => 275.77/40.37 ( 275.77/40.37 symdiffI2 => 275.77/40.37 ( 275.77/40.37 symdiffIneg1 => 275.77/40.37 ( 275.77/40.37 symdiffIneg2 => 275.77/40.37 ( 275.77/40.37 secondinupair => 275.77/40.37 ( 275.77/40.37 setukpairIL => 275.77/40.37 ( 275.77/40.37 setukpairIR => 275.77/40.37 ( 275.77/40.37 kpairiskpair => 275.77/40.37 ( 275.77/40.37 kpairp => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X170, 275.77/40.37 X172]: 275.77/40.37 (in( 275.77/40.37 X172,X170) => 275.77/40.37 subset( 275.77/40.37 setadjoin( 275.77/40.37 X172, 275.77/40.37 emptyset), 275.77/40.37 X170))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X174, 275.77/40.37 X176]: 275.77/40.37 (in( 275.77/40.37 X176,X174) => 275.77/40.37 in( 275.77/40.37 setadjoin( 275.77/40.37 X176, 275.77/40.37 emptyset), 275.77/40.37 powerset( 275.77/40.37 X174)))) => 275.77/40.37 ( 275.77/40.37 singletoninpowunion => 275.77/40.37 ( 275.77/40.37 upairset2E => 275.77/40.37 ( 275.77/40.37 upairsubunion => 275.77/40.37 ( 275.77/40.37 upairinpowunion => 275.77/40.37 ( 275.77/40.37 ubforcartprodlem1 => 275.77/40.37 ( 275.77/40.37 ubforcartprodlem2 => 275.77/40.37 ( 275.77/40.37 ubforcartprodlem3 => 275.77/40.37 ( 275.77/40.37 cartprodpairin => 275.77/40.37 ( 275.77/40.37 cartprodmempair1 => 275.77/40.37 ( 275.77/40.37 cartprodmempair => 275.77/40.37 ( 275.77/40.37 setunionE2 => 275.77/40.37 ( 275.77/40.37 setunionsingleton1 => 275.77/40.37 ( 275.77/40.37 setunionsingleton2 => 275.77/40.37 ( 275.77/40.37 setunionsingleton => 275.77/40.37 ( 275.77/40.37 singletonprop => 275.77/40.37 ( 275.77/40.37 ex1E1 => 275.77/40.37 ( 275.77/40.37 ex1I => 275.77/40.37 ( 275.77/40.37 ex1I2 => 275.77/40.37 ( 275.77/40.37 singletonsuniq => 275.77/40.37 ( 275.77/40.37 setukpairinjL1 => 275.77/40.37 ( 275.77/40.37 kfstsingleton => 275.77/40.37 ( 275.77/40.37 theprop => 275.77/40.37 ( 275.77/40.37 kfstpairEq => 275.77/40.37 ( 275.77/40.37 cartprodfstin => 275.77/40.37 ( 275.77/40.37 setukpairinjL2 => 275.77/40.37 ( 275.77/40.37 setukpairinjL => 275.77/40.37 ( 275.77/40.37 setukpairinjR11 => 275.77/40.37 ( 275.77/40.37 setukpairinjR12 => 275.77/40.37 ( 275.77/40.37 setukpairinjR1 => 275.77/40.37 ( 275.77/40.37 upairequniteq => 275.77/40.37 ( 275.77/40.37 setukpairinjR2 => 275.77/40.37 ( 275.77/40.37 setukpairinjR => 275.77/40.37 ( 275.77/40.37 ksndsingleton => 275.77/40.37 ( 275.77/40.37 ksndpairEq => 275.77/40.37 ( 275.77/40.37 kpairsurjEq => 275.77/40.37 ( 275.77/40.37 cartprodsndin => 275.77/40.37 ( 275.77/40.37 cartprodpairmemEL => 275.77/40.37 ( 275.77/40.37 cartprodpairmemER => 275.77/40.37 ( 275.77/40.37 cartprodmempaircEq => 275.77/40.37 ( 275.77/40.37 cartprodfstpairEq => 275.77/40.37 ( 275.77/40.37 cartprodsndpairEq => 275.77/40.37 ( 275.77/40.37 cartprodpairsurjEq => 275.77/40.37 ( 275.77/40.37 dpsetconstrI => 275.77/40.37 ( 275.77/40.37 dpsetconstrSub => 275.77/40.37 ( 275.77/40.37 setOfPairsIsBReln => 275.77/40.37 ( 275.77/40.37 dpsetconstrERa => 275.77/40.37 ( 275.77/40.37 dpsetconstrEL1 => 275.77/40.37 ( 275.77/40.37 dpsetconstrEL2 => 275.77/40.37 ( 275.77/40.37 dpsetconstrER => 275.77/40.37 ( 275.77/40.37 funcImageSingleton => 275.77/40.37 ( 275.77/40.37 apProp => 275.77/40.37 ( 275.77/40.37 app => 275.77/40.37 ( 275.77/40.37 infuncsetfunc => 275.77/40.37 ( 275.77/40.37 ap2p => 275.77/40.37 ( 275.77/40.37 funcinfuncset => 275.77/40.37 ( 275.77/40.37 lamProp => 275.77/40.37 ( 275.77/40.37 lamp => 275.77/40.37 ( 275.77/40.37 lam2p => 275.77/40.37 ( 275.77/40.37 brelnall1 => 275.77/40.37 ( 275.77/40.37 brelnall2 => 275.77/40.37 ( 275.77/40.37 ex1E2 => 275.77/40.37 ( 275.77/40.37 funcGraphProp1 => 275.77/40.37 ( 275.77/40.37 funcGraphProp3 => 275.77/40.37 ( 275.77/40.37 funcGraphProp2 => 275.77/40.37 ( 275.77/40.37 funcextLem => 275.77/40.37 ( 275.77/40.37 funcGraphProp4 => 275.77/40.37 ( 275.77/40.37 subbreln => 275.77/40.37 ( 275.77/40.37 eqbreln => 275.77/40.37 ( 275.77/40.37 funcext => 275.77/40.37 ( 275.77/40.37 funcext2 => 275.77/40.37 ( 275.77/40.37 ap2apEq1 => 275.77/40.37 ( 275.77/40.37 ap2apEq2 => 275.77/40.37 ( 275.77/40.37 beta1 => 275.77/40.37 ( 275.77/40.37 eta1 => 275.77/40.37 ( 275.77/40.37 lam2lamEq => 275.77/40.37 ( 275.77/40.37 beta2 => 275.77/40.37 ( 275.77/40.37 eta2 => 275.77/40.37 ( 275.77/40.37 iffalseProp1 => 275.77/40.37 ( 275.77/40.37 iffalseProp2 => 275.77/40.37 ( 275.77/40.37 iftrueProp1 => 275.77/40.37 ( 275.77/40.37 iftrueProp2 => 275.77/40.37 ( 275.77/40.37 ifSingleton => 275.77/40.37 ( 275.77/40.37 ifp => 275.77/40.37 ( 275.77/40.37 theeq => 275.77/40.37 ( 275.77/40.37 iftrue => 275.77/40.37 ( 275.77/40.37 iffalse => 275.77/40.37 ( 275.77/40.37 iftrueorfalse => 275.77/40.37 ( 275.77/40.37 binintersectT_lem => 275.77/40.37 ( 275.77/40.37 binunionT_lem => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X178, 275.77/40.37 X180]: 275.77/40.37 (in( 275.77/40.37 X180, 275.77/40.37 powerset( 275.77/40.37 X178)) => 275.77/40.37 in( 275.77/40.37 powerset( 275.77/40.37 X180), 275.77/40.37 powerset( 275.77/40.37 powerset( 275.77/40.37 X178))))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X182, 275.77/40.37 X184]: 275.77/40.37 (in( 275.77/40.37 X184, 275.77/40.37 powerset( 275.77/40.37 X182)) => 275.77/40.37 (![X186]: 275.77/40.37 (in( 275.77/40.37 X186, 275.77/40.37 powerset( 275.77/40.37 X182)) => 275.77/40.37 in( 275.77/40.37 setminus( 275.77/40.37 X184,X186), 275.77/40.37 powerset( 275.77/40.37 X182)))))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X188, 275.77/40.37 X190]: 275.77/40.37 (in( 275.77/40.37 X190, 275.77/40.37 powerset( 275.77/40.37 X188)) => 275.77/40.37 in( 275.77/40.37 setminus( 275.77/40.37 X188,X190), 275.77/40.37 powerset( 275.77/40.37 X188)))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X192, 275.77/40.37 X194]: 275.77/40.37 (in( 275.77/40.37 X194, 275.77/40.37 powerset( 275.77/40.37 X192)) => 275.77/40.37 (![X196]: 275.77/40.37 (in( 275.77/40.37 X196, 275.77/40.37 powerset( 275.77/40.37 X192)) => 275.77/40.37 (( 275.77/40.37 ![X198]: 275.77/40.37 (in( 275.77/40.37 X198,X192) => 275.77/40.37 (in( 275.77/40.37 X198,X194) => 275.77/40.37 in( 275.77/40.37 X198,X196)))) => 275.77/40.37 (( 275.77/40.37 ![X200]: 275.77/40.37 (in( 275.77/40.37 X200,X192) => 275.77/40.37 (in( 275.77/40.37 X200,X196) => 275.77/40.37 in( 275.77/40.37 X200,X194)))) => 275.77/40.37 (X194 = 275.77/40.37 X196))))))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X202, 275.77/40.37 X204]: 275.77/40.37 (in( 275.77/40.37 X204, 275.77/40.37 powerset( 275.77/40.37 X202)) => 275.77/40.37 (![X206]: 275.77/40.37 (in( 275.77/40.37 X206, 275.77/40.37 powerset( 275.77/40.37 X202)) => 275.77/40.37 (( 275.77/40.37 ![X208]: 275.77/40.37 (in( 275.77/40.37 X208,X202) => 275.77/40.37 (in( 275.77/40.37 X208,X204) => 275.77/40.37 in( 275.77/40.37 X208,X206)))) => 275.77/40.37 subset( 275.77/40.37 X204,X206)))))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X210, 275.77/40.37 X212]: 275.77/40.37 (in( 275.77/40.37 X212, 275.77/40.37 powerset( 275.77/40.37 X210)) => 275.77/40.37 (![X214]: 275.77/40.37 (in( 275.77/40.37 X214, 275.77/40.37 powerset( 275.77/40.37 X210)) => 275.77/40.37 (( 275.77/40.37 ![X216]: 275.77/40.37 (in( 275.77/40.37 X216,X210) => 275.77/40.37 (in( 275.77/40.37 X216,X212) => 275.77/40.37 in( 275.77/40.37 X216,X214)))) => 275.77/40.37 in( 275.77/40.37 X212, 275.77/40.37 powerset( 275.77/40.37 X214))))))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X218, 275.77/40.37 X220]: 275.77/40.37 (in( 275.77/40.37 X220, 275.77/40.37 powerset( 275.77/40.37 X218)) => 275.77/40.37 (![X222]: 275.77/40.37 (in( 275.77/40.37 X222, 275.77/40.37 powerset( 275.77/40.37 X218)) => 275.77/40.37 (![X224]: 275.77/40.37 (in( 275.77/40.37 X224,X218) => 275.77/40.37 (in( 275.77/40.37 X220, 275.77/40.37 powerset( 275.77/40.37 X222)) => 275.77/40.37 (in( 275.77/40.37 X224,X220) => 275.77/40.37 in( 275.77/40.37 X224,X222))))))))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X226, 275.77/40.37 X228]: 275.77/40.37 (in( 275.77/40.37 X228, 275.77/40.37 powerset( 275.77/40.37 X226)) => 275.77/40.37 (![X230]: 275.77/40.37 (in( 275.77/40.37 X230,X226) => 275.77/40.37 (in( 275.77/40.37 X230,X228) => 275.77/40.37 (~ 275.77/40.37 in( 275.77/40.37 X230, 275.77/40.37 setminus( 275.77/40.37 X226,X228)))))))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X232, 275.77/40.37 X234]: 275.77/40.37 (in( 275.77/40.37 X234, 275.77/40.37 powerset( 275.77/40.37 X232)) => 275.77/40.37 (![X236]: 275.77/40.37 (in( 275.77/40.37 X236,X232) => 275.77/40.37 (( 275.77/40.37 ~ 275.77/40.37 in( 275.77/40.37 X236, 275.77/40.37 setminus( 275.77/40.37 X232,X234))) => 275.77/40.37 in( 275.77/40.37 X236,X234)))))) => 275.77/40.37 ( 275.77/40.37 binintersectTELcontra => 275.77/40.37 ( 275.77/40.37 binintersectTERcontra => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X238, 275.77/40.37 X240]: 275.77/40.37 (in( 275.77/40.37 X240, 275.77/40.37 powerset( 275.77/40.37 X238)) => 275.77/40.37 (![X242]: 275.77/40.37 (in( 275.77/40.37 X242, 275.77/40.37 powerset( 275.77/40.37 X238)) => 275.77/40.37 (![X244]: 275.77/40.37 (in( 275.77/40.37 X244,X238) => 275.77/40.37 (subset( 275.77/40.37 X240, 275.77/40.37 setminus( 275.77/40.37 X238,X242)) => 275.77/40.37 (in( 275.77/40.37 X244,X242) => 275.77/40.37 (~ 275.77/40.37 in( 275.77/40.37 X244,X240)))))))))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X246, 275.77/40.37 X248]: 275.77/40.37 (in( 275.77/40.37 X248, 275.77/40.37 powerset( 275.77/40.37 X246)) => 275.77/40.37 (![X250]: 275.77/40.37 (in( 275.77/40.37 X250, 275.77/40.37 powerset( 275.77/40.37 X246)) => 275.77/40.37 (![X252]: 275.77/40.37 (in( 275.77/40.37 X252,X246) => 275.77/40.37 (subset( 275.77/40.37 X248,X250) => 275.77/40.37 (( 275.77/40.37 ~ 275.77/40.37 in( 275.77/40.37 X252,X250)) => 275.77/40.37 (~ 275.77/40.37 in( 275.77/40.37 X252,X248)))))))))) => 275.77/40.37 ( 275.77/40.37 ![X254, 275.77/40.37 X256]: 275.77/40.37 (in( 275.77/40.37 X256, 275.77/40.37 powerset( 275.77/40.37 X254)) => 275.77/40.37 (![X258]: 275.77/40.37 (in( 275.77/40.37 X258, 275.77/40.37 powerset( 275.77/40.37 X254)) => 275.77/40.37 (subset( 275.77/40.37 X256,X258) => 275.77/40.37 subset( 275.77/40.37 setminus( 275.77/40.37 X254,X258), 275.77/40.37 setminus( 275.77/40.37 X254,X256))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 275.77/40.37 tff(zf_stmt_1, type, zip_tseitin_0 : ($i * $i * $i) > $o). 275.77/40.37 tff(zf_stmt_2, axiom, (zip_tseitin_0(X8,X6,X4) <=> (in(X8,X6) => in(X8,X4)))). 275.77/40.37 tff(zf_stmt_3, conjecture, 275.77/40.37 (setextAx => 275.77/40.37 (emptysetAx => 275.77/40.37 (setadjoinAx => 275.77/40.37 ((![X4,X6]: (in(X6,powerset(X4)) <=> (![X8]: zip_tseitin_0(X8,X6,X4)))) => 275.77/40.37 (setunionAx => 275.77/40.37 (omega0Ax => 275.77/40.37 (omegaSAx => 275.77/40.37 (omegaIndAx => 275.77/40.37 (replAx => 275.77/40.37 (foundationAx => 275.77/40.37 (wellorderingAx => 275.77/40.37 (descrp => 275.77/40.37 (dsetconstrI => 275.77/40.37 (dsetconstrEL => 275.77/40.37 (dsetconstrER => 275.77/40.37 (exuE1 => 275.77/40.37 (prop2setE => 275.77/40.37 (emptysetE => 275.77/40.37 (emptysetimpfalse => 275.77/40.37 (notinemptyset => 275.77/40.37 (exuE3e => 275.77/40.37 (setext => 275.77/40.37 (emptyI => 275.77/40.37 (noeltsimpempty => 275.77/40.37 (setbeta => 275.77/40.37 (nonemptyE1 => 275.77/40.37 (nonemptyI => 275.77/40.37 (nonemptyI1 => 275.77/40.37 (setadjoinIL => 275.77/40.37 (emptyinunitempty => 275.77/40.37 (setadjoinIR => 275.77/40.37 (setadjoinE => 275.77/40.37 (setadjoinOr => 275.77/40.37 (setoftrueEq => 275.77/40.37 ((![X10,X12]: 275.77/40.37 ((![X14]: 275.77/40.37 (in(X14,X12) => in(X14,X10))) => 275.77/40.37 in(X12,powerset(X10)))) => 275.77/40.37 ((![X16]: in(emptyset,powerset(X16))) => 275.77/40.37 ((![X18]: in(emptyset,powerset(X18))) => 275.77/40.37 ((![X20,X22,X24]: 275.77/40.37 (in(X22,powerset(X20)) => 275.77/40.37 (in(X24,X22) => in(X24,X20)))) => 275.77/40.37 (setunionI => 275.77/40.37 (setunionE => 275.77/40.37 (subPowSU => 275.77/40.37 (exuE2 => 275.77/40.37 (nonemptyImpWitness => 275.77/40.37 (uniqinunit => 275.77/40.37 (notinsingleton => 275.77/40.37 (eqinunit => 275.77/40.37 (singletonsswitch => 275.77/40.37 (upairsetE => 275.77/40.37 (upairsetIL => 275.77/40.37 (upairsetIR => 275.77/40.37 (emptyE1 => 275.77/40.37 (vacuousDall => 275.77/40.37 (quantDeMorgan1 => 275.77/40.37 (quantDeMorgan2 => 275.77/40.37 (quantDeMorgan3 => 275.77/40.37 (quantDeMorgan4 => 275.77/40.37 (prop2setI => 275.77/40.37 (prop2set2propI => 275.77/40.37 (notdexE => 275.77/40.37 (notdallE => 275.77/40.37 (exuI1 => 275.77/40.37 (exuI3 => 275.77/40.37 (exuI2 => 275.77/40.37 (inCongP => 275.77/40.37 (in__Cong => 275.77/40.37 (exuE3u => 275.77/40.37 ( 275.77/40.37 exu__Cong => 275.77/40.37 ( 275.77/40.37 emptyset__Cong => 275.77/40.37 ( 275.77/40.37 setadjoin__Cong => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X26,X28]: 275.77/40.37 (( 275.77/40.37 X26 = X28) => 275.77/40.37 (powerset( 275.77/40.37 X26) = 275.77/40.37 powerset( 275.77/40.37 X28)))) => 275.77/40.37 ( 275.77/40.37 setunion__Cong => 275.77/40.37 ( 275.77/40.37 omega__Cong => 275.77/40.37 ( 275.77/40.37 exuEu => 275.77/40.37 ( 275.77/40.37 descr__Cong => 275.77/40.37 ( 275.77/40.37 dsetconstr__Cong => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X30,X32]: 275.77/40.37 (( 275.77/40.37 ![X34]: 275.77/40.37 (in( 275.77/40.37 X34,X30) => 275.77/40.37 in( 275.77/40.37 X34,X32))) => 275.77/40.37 subset( 275.77/40.37 X30,X32))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X36,X38]: 275.77/40.37 (( 275.77/40.37 X36 = X38) => 275.77/40.37 subset( 275.77/40.37 X38,X36))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X40,X42]: 275.77/40.37 (( 275.77/40.37 X40 = X42) => 275.77/40.37 subset( 275.77/40.37 X40,X42))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X44,X46]: 275.77/40.37 (( 275.77/40.37 ![X48]: 275.77/40.37 (in( 275.77/40.37 X48,X44) => 275.77/40.37 in( 275.77/40.37 X48,X46))) => 275.77/40.37 subset( 275.77/40.37 X44,X46))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X50]: 275.77/40.37 subset( 275.77/40.37 emptyset, 275.77/40.37 X50)) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X52, 275.77/40.37 X54,X56]: 275.77/40.37 (subset( 275.77/40.37 X52,X54) => 275.77/40.37 (in( 275.77/40.37 X56,X52) => 275.77/40.37 in( 275.77/40.37 X56,X54)))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X58, 275.77/40.37 X60,X62]: 275.77/40.37 (subset( 275.77/40.37 X58,X60) => 275.77/40.37 (( 275.77/40.37 ~ 275.77/40.37 in( 275.77/40.37 X62,X60)) => 275.77/40.37 (~ 275.77/40.37 in( 275.77/40.37 X62,X58))))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X64, 275.77/40.37 X66,X68]: 275.77/40.37 (in( 275.77/40.37 X68,X64) => 275.77/40.37 (( 275.77/40.37 ~ 275.77/40.37 in( 275.77/40.37 X68,X66)) => 275.77/40.37 (~ 275.77/40.37 subset( 275.77/40.37 X64,X66))))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X70,X72]: 275.77/40.37 (( 275.77/40.37 ~ 275.77/40.37 subset( 275.77/40.37 X70,X72)) => 275.77/40.37 (X70 != 275.77/40.37 X72))) => 275.77/40.37 ( 275.77/40.37 notequalI2 => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X74]: 275.77/40.37 subset( 275.77/40.37 X74,X74)) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X76, 275.77/40.37 X78,X80]: 275.77/40.37 (subset( 275.77/40.37 X76,X78) => 275.77/40.37 (subset( 275.77/40.37 X78,X80) => 275.77/40.37 subset( 275.77/40.37 X76,X80)))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X82,X84]: 275.77/40.37 subset( 275.77/40.37 X84, 275.77/40.37 setadjoin( 275.77/40.37 X82,X84))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X86, 275.77/40.37 X88,X90]: 275.77/40.37 (subset( 275.77/40.37 X86,X90) => 275.77/40.37 subset( 275.77/40.37 X86, 275.77/40.37 setadjoin( 275.77/40.37 X88,X90)))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X92,X94]: 275.77/40.37 (subset( 275.77/40.37 X92,X94) => 275.77/40.37 in( 275.77/40.37 X92, 275.77/40.37 powerset( 275.77/40.37 X94)))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X96,X98]: 275.77/40.37 (subset( 275.77/40.37 X96,X98) => 275.77/40.37 (subset( 275.77/40.37 X98,X96) => 275.77/40.37 (X96 = 275.77/40.37 X98)))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X100]: 275.77/40.37 (subset( 275.77/40.37 X100, 275.77/40.37 emptyset) => 275.77/40.37 (X100 = 275.77/40.37 emptyset))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X102, 275.77/40.37 X104]: 275.77/40.37 (subset( 275.77/40.37 X104,X102) => 275.77/40.37 in( 275.77/40.37 X104, 275.77/40.37 powerset( 275.77/40.37 X102)))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X106, 275.77/40.37 X108]: 275.77/40.37 (in( 275.77/40.37 X108, 275.77/40.37 powerset( 275.77/40.37 X106)) => 275.77/40.37 subset( 275.77/40.37 X108,X106))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X110]: 275.77/40.37 in( 275.77/40.37 X110, 275.77/40.37 powerset( 275.77/40.37 X110))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X112, 275.77/40.37 X114]: 275.77/40.37 (subset( 275.77/40.37 X112,X114) => 275.77/40.37 subset( 275.77/40.37 powerset( 275.77/40.37 X112), 275.77/40.37 powerset( 275.77/40.37 X114)))) => 275.77/40.37 ( 275.77/40.37 sepInPowerset => 275.77/40.37 ( 275.77/40.37 sepSubset => 275.77/40.37 ( 275.77/40.37 binunionIL => 275.77/40.37 ( 275.77/40.37 upairset2IR => 275.77/40.37 ( 275.77/40.37 binunionIR => 275.77/40.37 ( 275.77/40.37 binunionEcases => 275.77/40.37 ( 275.77/40.37 binunionE => 275.77/40.37 ( 275.77/40.37 binunionLsub => 275.77/40.37 ( 275.77/40.37 binunionRsub => 275.77/40.37 ( 275.77/40.37 binintersectI => 275.77/40.37 ( 275.77/40.37 binintersectSubset5 => 275.77/40.37 ( 275.77/40.37 binintersectEL => 275.77/40.37 ( 275.77/40.37 binintersectLsub => 275.77/40.37 ( 275.77/40.37 binintersectSubset2 => 275.77/40.37 ( 275.77/40.37 binintersectSubset3 => 275.77/40.37 ( 275.77/40.37 binintersectER => 275.77/40.37 ( 275.77/40.37 disjointsetsI1 => 275.77/40.37 ( 275.77/40.37 binintersectRsub => 275.77/40.37 ( 275.77/40.37 binintersectSubset4 => 275.77/40.37 ( 275.77/40.37 binintersectSubset1 => 275.77/40.37 ( 275.77/40.37 bs114d => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X116, 275.77/40.37 X118,X120]: 275.77/40.37 (in( 275.77/40.37 X120,X116) => 275.77/40.37 (( 275.77/40.37 ~ 275.77/40.37 in( 275.77/40.37 X120,X118)) => 275.77/40.37 in( 275.77/40.37 X120, 275.77/40.37 setminus( 275.77/40.37 X116,X118))))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X122, 275.77/40.37 X124,X126]: 275.77/40.37 (in( 275.77/40.37 X126, 275.77/40.37 setminus( 275.77/40.37 X122,X124)) => 275.77/40.37 in( 275.77/40.37 X126,X122))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X128, 275.77/40.37 X130,X132]: 275.77/40.37 (in( 275.77/40.37 X132, 275.77/40.37 setminus( 275.77/40.37 X128,X130)) => 275.77/40.37 (~ 275.77/40.37 in( 275.77/40.37 X132,X130)))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X134, 275.77/40.37 X136]: 275.77/40.37 (subset( 275.77/40.37 X134,X136) => 275.77/40.37 (setminus( 275.77/40.37 X134,X136) = 275.77/40.37 emptyset))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X138, 275.77/40.37 X140,X142]: 275.77/40.37 (( 275.77/40.37 ~ 275.77/40.37 in( 275.77/40.37 X142, 275.77/40.37 setminus( 275.77/40.37 X138,X140))) => 275.77/40.37 (in( 275.77/40.37 X142,X138) => 275.77/40.37 in( 275.77/40.37 X142,X140)))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X144, 275.77/40.37 X146,X148]: 275.77/40.37 (( 275.77/40.37 ~ 275.77/40.37 in( 275.77/40.37 X148, 275.77/40.37 setminus( 275.77/40.37 X144,X146))) => 275.77/40.37 (( 275.77/40.37 ~ 275.77/40.37 in( 275.77/40.37 X148,X146)) => 275.77/40.37 (~ 275.77/40.37 in( 275.77/40.37 X148,X144))))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X150, 275.77/40.37 X152,X154]: 275.77/40.37 (( 275.77/40.37 ~ 275.77/40.37 in( 275.77/40.37 X154,X150)) => 275.77/40.37 (~ 275.77/40.37 in( 275.77/40.37 X154, 275.77/40.37 setminus( 275.77/40.37 X150,X152))))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X156, 275.77/40.37 X158,X160]: 275.77/40.37 (in( 275.77/40.37 X160,X158) => 275.77/40.37 (~ 275.77/40.37 in( 275.77/40.37 X160, 275.77/40.37 setminus( 275.77/40.37 X156,X158))))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X162, 275.77/40.37 X164]: 275.77/40.37 subset( 275.77/40.37 setminus( 275.77/40.37 X162,X164), 275.77/40.37 X162)) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X166, 275.77/40.37 X168]: 275.77/40.37 (( 275.77/40.37 setminus( 275.77/40.37 X166,X168) = 275.77/40.37 emptyset) => 275.77/40.37 subset( 275.77/40.37 X166,X168))) => 275.77/40.37 ( 275.77/40.37 symdiffE => 275.77/40.37 ( 275.77/40.37 symdiffI1 => 275.77/40.37 ( 275.77/40.37 symdiffI2 => 275.77/40.37 ( 275.77/40.37 symdiffIneg1 => 275.77/40.37 ( 275.77/40.37 symdiffIneg2 => 275.77/40.37 ( 275.77/40.37 secondinupair => 275.77/40.37 ( 275.77/40.37 setukpairIL => 275.77/40.37 ( 275.77/40.37 setukpairIR => 275.77/40.37 ( 275.77/40.37 kpairiskpair => 275.77/40.37 ( 275.77/40.37 kpairp => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X170, 275.77/40.37 X172]: 275.77/40.37 (in( 275.77/40.37 X172,X170) => 275.77/40.37 subset( 275.77/40.37 setadjoin( 275.77/40.37 X172, 275.77/40.37 emptyset), 275.77/40.37 X170))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X174, 275.77/40.37 X176]: 275.77/40.37 (in( 275.77/40.37 X176,X174) => 275.77/40.37 in( 275.77/40.37 setadjoin( 275.77/40.37 X176, 275.77/40.37 emptyset), 275.77/40.37 powerset( 275.77/40.37 X174)))) => 275.77/40.37 ( 275.77/40.37 singletoninpowunion => 275.77/40.37 ( 275.77/40.37 upairset2E => 275.77/40.37 ( 275.77/40.37 upairsubunion => 275.77/40.37 ( 275.77/40.37 upairinpowunion => 275.77/40.37 ( 275.77/40.37 ubforcartprodlem1 => 275.77/40.37 ( 275.77/40.37 ubforcartprodlem2 => 275.77/40.37 ( 275.77/40.37 ubforcartprodlem3 => 275.77/40.37 ( 275.77/40.37 cartprodpairin => 275.77/40.37 ( 275.77/40.37 cartprodmempair1 => 275.77/40.37 ( 275.77/40.37 cartprodmempair => 275.77/40.37 ( 275.77/40.37 setunionE2 => 275.77/40.37 ( 275.77/40.37 setunionsingleton1 => 275.77/40.37 ( 275.77/40.37 setunionsingleton2 => 275.77/40.37 ( 275.77/40.37 setunionsingleton => 275.77/40.37 ( 275.77/40.37 singletonprop => 275.77/40.37 ( 275.77/40.37 ex1E1 => 275.77/40.37 ( 275.77/40.37 ex1I => 275.77/40.37 ( 275.77/40.37 ex1I2 => 275.77/40.37 ( 275.77/40.37 singletonsuniq => 275.77/40.37 ( 275.77/40.37 setukpairinjL1 => 275.77/40.37 ( 275.77/40.37 kfstsingleton => 275.77/40.37 ( 275.77/40.37 theprop => 275.77/40.37 ( 275.77/40.37 kfstpairEq => 275.77/40.37 ( 275.77/40.37 cartprodfstin => 275.77/40.37 ( 275.77/40.37 setukpairinjL2 => 275.77/40.37 ( 275.77/40.37 setukpairinjL => 275.77/40.37 ( 275.77/40.37 setukpairinjR11 => 275.77/40.37 ( 275.77/40.37 setukpairinjR12 => 275.77/40.37 ( 275.77/40.37 setukpairinjR1 => 275.77/40.37 ( 275.77/40.37 upairequniteq => 275.77/40.37 ( 275.77/40.37 setukpairinjR2 => 275.77/40.37 ( 275.77/40.37 setukpairinjR => 275.77/40.37 ( 275.77/40.37 ksndsingleton => 275.77/40.37 ( 275.77/40.37 ksndpairEq => 275.77/40.37 ( 275.77/40.37 kpairsurjEq => 275.77/40.37 ( 275.77/40.37 cartprodsndin => 275.77/40.37 ( 275.77/40.37 cartprodpairmemEL => 275.77/40.37 ( 275.77/40.37 cartprodpairmemER => 275.77/40.37 ( 275.77/40.37 cartprodmempaircEq => 275.77/40.37 ( 275.77/40.37 cartprodfstpairEq => 275.77/40.37 ( 275.77/40.37 cartprodsndpairEq => 275.77/40.37 ( 275.77/40.37 cartprodpairsurjEq => 275.77/40.37 ( 275.77/40.37 dpsetconstrI => 275.77/40.37 ( 275.77/40.37 dpsetconstrSub => 275.77/40.37 ( 275.77/40.37 setOfPairsIsBReln => 275.77/40.37 ( 275.77/40.37 dpsetconstrERa => 275.77/40.37 ( 275.77/40.37 dpsetconstrEL1 => 275.77/40.37 ( 275.77/40.37 dpsetconstrEL2 => 275.77/40.37 ( 275.77/40.37 dpsetconstrER => 275.77/40.37 ( 275.77/40.37 funcImageSingleton => 275.77/40.37 ( 275.77/40.37 apProp => 275.77/40.37 ( 275.77/40.37 app => 275.77/40.37 ( 275.77/40.37 infuncsetfunc => 275.77/40.37 ( 275.77/40.37 ap2p => 275.77/40.37 ( 275.77/40.37 funcinfuncset => 275.77/40.37 ( 275.77/40.37 lamProp => 275.77/40.37 ( 275.77/40.37 lamp => 275.77/40.37 ( 275.77/40.37 lam2p => 275.77/40.37 ( 275.77/40.37 brelnall1 => 275.77/40.37 ( 275.77/40.37 brelnall2 => 275.77/40.37 ( 275.77/40.37 ex1E2 => 275.77/40.37 ( 275.77/40.37 funcGraphProp1 => 275.77/40.37 ( 275.77/40.37 funcGraphProp3 => 275.77/40.37 ( 275.77/40.37 funcGraphProp2 => 275.77/40.37 ( 275.77/40.37 funcextLem => 275.77/40.37 ( 275.77/40.37 funcGraphProp4 => 275.77/40.37 ( 275.77/40.37 subbreln => 275.77/40.37 ( 275.77/40.37 eqbreln => 275.77/40.37 ( 275.77/40.37 funcext => 275.77/40.37 ( 275.77/40.37 funcext2 => 275.77/40.37 ( 275.77/40.37 ap2apEq1 => 275.77/40.37 ( 275.77/40.37 ap2apEq2 => 275.77/40.37 ( 275.77/40.37 beta1 => 275.77/40.37 ( 275.77/40.37 eta1 => 275.77/40.37 ( 275.77/40.37 lam2lamEq => 275.77/40.37 ( 275.77/40.37 beta2 => 275.77/40.37 ( 275.77/40.37 eta2 => 275.77/40.37 ( 275.77/40.37 iffalseProp1 => 275.77/40.37 ( 275.77/40.37 iffalseProp2 => 275.77/40.37 ( 275.77/40.37 iftrueProp1 => 275.77/40.37 ( 275.77/40.37 iftrueProp2 => 275.77/40.37 ( 275.77/40.37 ifSingleton => 275.77/40.37 ( 275.77/40.37 ifp => 275.77/40.37 ( 275.77/40.37 theeq => 275.77/40.37 ( 275.77/40.37 iftrue => 275.77/40.37 ( 275.77/40.37 iffalse => 275.77/40.37 ( 275.77/40.37 iftrueorfalse => 275.77/40.37 ( 275.77/40.37 binintersectT_lem => 275.77/40.37 ( 275.77/40.37 binunionT_lem => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X178, 275.77/40.37 X180]: 275.77/40.37 (in( 275.77/40.37 X180, 275.77/40.37 powerset( 275.77/40.37 X178)) => 275.77/40.37 in( 275.77/40.37 powerset( 275.77/40.37 X180), 275.77/40.37 powerset( 275.77/40.37 powerset( 275.77/40.37 X178))))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X182, 275.77/40.37 X184]: 275.77/40.37 (in( 275.77/40.37 X184, 275.77/40.37 powerset( 275.77/40.37 X182)) => 275.77/40.37 (![X186]: 275.77/40.37 (in( 275.77/40.37 X186, 275.77/40.37 powerset( 275.77/40.37 X182)) => 275.77/40.37 in( 275.77/40.37 setminus( 275.77/40.37 X184,X186), 275.77/40.37 powerset( 275.77/40.37 X182)))))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X188, 275.77/40.37 X190]: 275.77/40.37 (in( 275.77/40.37 X190, 275.77/40.37 powerset( 275.77/40.37 X188)) => 275.77/40.37 in( 275.77/40.37 setminus( 275.77/40.37 X188,X190), 275.77/40.37 powerset( 275.77/40.37 X188)))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X192, 275.77/40.37 X194]: 275.77/40.37 (in( 275.77/40.37 X194, 275.77/40.37 powerset( 275.77/40.37 X192)) => 275.77/40.37 (![X196]: 275.77/40.37 (in( 275.77/40.37 X196, 275.77/40.37 powerset( 275.77/40.37 X192)) => 275.77/40.37 (( 275.77/40.37 ![X198]: 275.77/40.37 (in( 275.77/40.37 X198,X192) => 275.77/40.37 (in( 275.77/40.37 X198,X194) => 275.77/40.37 in( 275.77/40.37 X198,X196)))) => 275.77/40.37 (( 275.77/40.37 ![X200]: 275.77/40.37 (in( 275.77/40.37 X200,X192) => 275.77/40.37 (in( 275.77/40.37 X200,X196) => 275.77/40.37 in( 275.77/40.37 X200,X194)))) => 275.77/40.37 (X194 = 275.77/40.37 X196))))))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X202, 275.77/40.37 X204]: 275.77/40.37 (in( 275.77/40.37 X204, 275.77/40.37 powerset( 275.77/40.37 X202)) => 275.77/40.37 (![X206]: 275.77/40.37 (in( 275.77/40.37 X206, 275.77/40.37 powerset( 275.77/40.37 X202)) => 275.77/40.37 (( 275.77/40.37 ![X208]: 275.77/40.37 (in( 275.77/40.37 X208,X202) => 275.77/40.37 (in( 275.77/40.37 X208,X204) => 275.77/40.37 in( 275.77/40.37 X208,X206)))) => 275.77/40.37 subset( 275.77/40.37 X204,X206)))))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X210, 275.77/40.37 X212]: 275.77/40.37 (in( 275.77/40.37 X212, 275.77/40.37 powerset( 275.77/40.37 X210)) => 275.77/40.37 (![X214]: 275.77/40.37 (in( 275.77/40.37 X214, 275.77/40.37 powerset( 275.77/40.37 X210)) => 275.77/40.37 (( 275.77/40.37 ![X216]: 275.77/40.37 (in( 275.77/40.37 X216,X210) => 275.77/40.37 (in( 275.77/40.37 X216,X212) => 275.77/40.37 in( 275.77/40.37 X216,X214)))) => 275.77/40.37 in( 275.77/40.37 X212, 275.77/40.37 powerset( 275.77/40.37 X214))))))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X218, 275.77/40.37 X220]: 275.77/40.37 (in( 275.77/40.37 X220, 275.77/40.37 powerset( 275.77/40.37 X218)) => 275.77/40.37 (![X222]: 275.77/40.37 (in( 275.77/40.37 X222, 275.77/40.37 powerset( 275.77/40.37 X218)) => 275.77/40.37 (![X224]: 275.77/40.37 (in( 275.77/40.37 X224,X218) => 275.77/40.37 (in( 275.77/40.37 X220, 275.77/40.37 powerset( 275.77/40.37 X222)) => 275.77/40.37 (in( 275.77/40.37 X224,X220) => 275.77/40.37 in( 275.77/40.37 X224,X222))))))))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X226, 275.77/40.37 X228]: 275.77/40.37 (in( 275.77/40.37 X228, 275.77/40.37 powerset( 275.77/40.37 X226)) => 275.77/40.37 (![X230]: 275.77/40.37 (in( 275.77/40.37 X230,X226) => 275.77/40.37 (in( 275.77/40.37 X230,X228) => 275.77/40.37 (~ 275.77/40.37 in( 275.77/40.37 X230, 275.77/40.37 setminus( 275.77/40.37 X226,X228)))))))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X232, 275.77/40.37 X234]: 275.77/40.37 (in( 275.77/40.37 X234, 275.77/40.37 powerset( 275.77/40.37 X232)) => 275.77/40.37 (![X236]: 275.77/40.37 (in( 275.77/40.37 X236,X232) => 275.77/40.37 (( 275.77/40.37 ~ 275.77/40.37 in( 275.77/40.37 X236, 275.77/40.37 setminus( 275.77/40.37 X232,X234))) => 275.77/40.37 in( 275.77/40.37 X236,X234)))))) => 275.77/40.37 ( 275.77/40.37 binintersectTELcontra => 275.77/40.37 ( 275.77/40.37 binintersectTERcontra => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X238, 275.77/40.37 X240]: 275.77/40.37 (in( 275.77/40.37 X240, 275.77/40.37 powerset( 275.77/40.37 X238)) => 275.77/40.37 (![X242]: 275.77/40.37 (in( 275.77/40.37 X242, 275.77/40.37 powerset( 275.77/40.37 X238)) => 275.77/40.37 (![X244]: 275.77/40.37 (in( 275.77/40.37 X244,X238) => 275.77/40.37 (subset( 275.77/40.37 X240, 275.77/40.37 setminus( 275.77/40.37 X238,X242)) => 275.77/40.37 (in( 275.77/40.37 X244,X242) => 275.77/40.37 (~ 275.77/40.37 in( 275.77/40.37 X244,X240)))))))))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X246, 275.77/40.37 X248]: 275.77/40.37 (in( 275.77/40.37 X248, 275.77/40.37 powerset( 275.77/40.37 X246)) => 275.77/40.37 (![X250]: 275.77/40.37 (in( 275.77/40.37 X250, 275.77/40.37 powerset( 275.77/40.37 X246)) => 275.77/40.37 (![X252]: 275.77/40.37 (in( 275.77/40.37 X252,X246) => 275.77/40.37 (subset( 275.77/40.37 X248,X250) => 275.77/40.37 (( 275.77/40.37 ~ 275.77/40.37 in( 275.77/40.37 X252,X250)) => 275.77/40.37 (~ 275.77/40.37 in( 275.77/40.37 X252,X248)))))))))) => 275.77/40.37 ( 275.77/40.37 ![X254, 275.77/40.37 X256]: 275.77/40.37 (in( 275.77/40.37 X256, 275.77/40.37 powerset( 275.77/40.37 X254)) => 275.77/40.37 (![X258]: 275.77/40.37 (in( 275.77/40.37 X258, 275.77/40.37 powerset( 275.77/40.37 X254)) => 275.77/40.37 (subset( 275.77/40.37 X256,X258) => 275.77/40.37 subset( 275.77/40.37 setminus( 275.77/40.37 X254,X258), 275.77/40.37 setminus( 275.77/40.37 X254,X256))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 275.77/40.37 tff(zf_stmt_4, negated_conjecture, 275.77/40.37 (~ 275.77/40.37 (setextAx => 275.77/40.37 (emptysetAx => 275.77/40.37 (setadjoinAx => 275.77/40.37 ((![X4,X6]: (in(X6,powerset(X4)) <=> (![X8]: zip_tseitin_0(X8,X6,X4)))) => 275.77/40.37 (setunionAx => 275.77/40.37 (omega0Ax => 275.77/40.37 (omegaSAx => 275.77/40.37 (omegaIndAx => 275.77/40.37 (replAx => 275.77/40.37 (foundationAx => 275.77/40.37 (wellorderingAx => 275.77/40.37 (descrp => 275.77/40.37 (dsetconstrI => 275.77/40.37 (dsetconstrEL => 275.77/40.37 (dsetconstrER => 275.77/40.37 (exuE1 => 275.77/40.37 (prop2setE => 275.77/40.37 (emptysetE => 275.77/40.37 (emptysetimpfalse => 275.77/40.37 (notinemptyset => 275.77/40.37 (exuE3e => 275.77/40.37 (setext => 275.77/40.37 (emptyI => 275.77/40.37 (noeltsimpempty => 275.77/40.37 (setbeta => 275.77/40.37 (nonemptyE1 => 275.77/40.37 (nonemptyI => 275.77/40.37 (nonemptyI1 => 275.77/40.37 (setadjoinIL => 275.77/40.37 (emptyinunitempty => 275.77/40.37 (setadjoinIR => 275.77/40.37 (setadjoinE => 275.77/40.37 (setadjoinOr => 275.77/40.37 (setoftrueEq => 275.77/40.37 ((![X10,X12]: 275.77/40.37 ((![X14]: 275.77/40.37 (in(X14,X12) => in(X14,X10))) => 275.77/40.37 in(X12,powerset(X10)))) => 275.77/40.37 ((![X16]: in(emptyset,powerset(X16))) => 275.77/40.37 ((![X18]: in(emptyset,powerset(X18))) => 275.77/40.37 ((![X20,X22,X24]: 275.77/40.37 (in(X22,powerset(X20)) => 275.77/40.37 (in(X24,X22) => in(X24,X20)))) => 275.77/40.37 (setunionI => 275.77/40.37 (setunionE => 275.77/40.37 (subPowSU => 275.77/40.37 (exuE2 => 275.77/40.37 (nonemptyImpWitness => 275.77/40.37 (uniqinunit => 275.77/40.37 (notinsingleton => 275.77/40.37 (eqinunit => 275.77/40.37 (singletonsswitch => 275.77/40.37 (upairsetE => 275.77/40.37 (upairsetIL => 275.77/40.37 (upairsetIR => 275.77/40.37 (emptyE1 => 275.77/40.37 (vacuousDall => 275.77/40.37 (quantDeMorgan1 => 275.77/40.37 (quantDeMorgan2 => 275.77/40.37 (quantDeMorgan3 => 275.77/40.37 (quantDeMorgan4 => 275.77/40.37 (prop2setI => 275.77/40.37 (prop2set2propI => 275.77/40.37 (notdexE => 275.77/40.37 (notdallE => 275.77/40.37 (exuI1 => 275.77/40.37 (exuI3 => 275.77/40.37 (exuI2 => 275.77/40.37 (inCongP => 275.77/40.37 ( 275.77/40.37 in__Cong => 275.77/40.37 ( 275.77/40.37 exuE3u => 275.77/40.37 ( 275.77/40.37 exu__Cong => 275.77/40.37 ( 275.77/40.37 emptyset__Cong => 275.77/40.37 ( 275.77/40.37 setadjoin__Cong => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X26,X28]: 275.77/40.37 (( 275.77/40.37 X26 = X28) => 275.77/40.37 (powerset( 275.77/40.37 X26) = 275.77/40.37 powerset( 275.77/40.37 X28)))) => 275.77/40.37 ( 275.77/40.37 setunion__Cong => 275.77/40.37 ( 275.77/40.37 omega__Cong => 275.77/40.37 ( 275.77/40.37 exuEu => 275.77/40.37 ( 275.77/40.37 descr__Cong => 275.77/40.37 ( 275.77/40.37 dsetconstr__Cong => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X30,X32]: 275.77/40.37 (( 275.77/40.37 ![X34]: 275.77/40.37 (in( 275.77/40.37 X34,X30) => 275.77/40.37 in( 275.77/40.37 X34,X32))) => 275.77/40.37 subset( 275.77/40.37 X30,X32))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X36,X38]: 275.77/40.37 (( 275.77/40.37 X36 = X38) => 275.77/40.37 subset( 275.77/40.37 X38,X36))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X40,X42]: 275.77/40.37 (( 275.77/40.37 X40 = X42) => 275.77/40.37 subset( 275.77/40.37 X40,X42))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X44,X46]: 275.77/40.37 (( 275.77/40.37 ![X48]: 275.77/40.37 (in( 275.77/40.37 X48,X44) => 275.77/40.37 in( 275.77/40.37 X48,X46))) => 275.77/40.37 subset( 275.77/40.37 X44,X46))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X50]: 275.77/40.37 subset( 275.77/40.37 emptyset, 275.77/40.37 X50)) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X52, 275.77/40.37 X54,X56]: 275.77/40.37 (subset( 275.77/40.37 X52,X54) => 275.77/40.37 (in( 275.77/40.37 X56,X52) => 275.77/40.37 in( 275.77/40.37 X56,X54)))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X58, 275.77/40.37 X60,X62]: 275.77/40.37 (subset( 275.77/40.37 X58,X60) => 275.77/40.37 (( 275.77/40.37 ~ 275.77/40.37 in( 275.77/40.37 X62,X60)) => 275.77/40.37 (~ 275.77/40.37 in( 275.77/40.37 X62,X58))))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X64, 275.77/40.37 X66,X68]: 275.77/40.37 (in( 275.77/40.37 X68,X64) => 275.77/40.37 (( 275.77/40.37 ~ 275.77/40.37 in( 275.77/40.37 X68,X66)) => 275.77/40.37 (~ 275.77/40.37 subset( 275.77/40.37 X64,X66))))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X70,X72]: 275.77/40.37 (( 275.77/40.37 ~ 275.77/40.37 subset( 275.77/40.37 X70,X72)) => 275.77/40.37 (X70 != 275.77/40.37 X72))) => 275.77/40.37 ( 275.77/40.37 notequalI2 => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X74]: 275.77/40.37 subset( 275.77/40.37 X74,X74)) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X76, 275.77/40.37 X78,X80]: 275.77/40.37 (subset( 275.77/40.37 X76,X78) => 275.77/40.37 (subset( 275.77/40.37 X78,X80) => 275.77/40.37 subset( 275.77/40.37 X76,X80)))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X82,X84]: 275.77/40.37 subset( 275.77/40.37 X84, 275.77/40.37 setadjoin( 275.77/40.37 X82,X84))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X86, 275.77/40.37 X88,X90]: 275.77/40.37 (subset( 275.77/40.37 X86,X90) => 275.77/40.37 subset( 275.77/40.37 X86, 275.77/40.37 setadjoin( 275.77/40.37 X88,X90)))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X92,X94]: 275.77/40.37 (subset( 275.77/40.37 X92,X94) => 275.77/40.37 in( 275.77/40.37 X92, 275.77/40.37 powerset( 275.77/40.37 X94)))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X96,X98]: 275.77/40.37 (subset( 275.77/40.37 X96,X98) => 275.77/40.37 (subset( 275.77/40.37 X98,X96) => 275.77/40.37 (X96 = 275.77/40.37 X98)))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X100]: 275.77/40.37 (subset( 275.77/40.37 X100, 275.77/40.37 emptyset) => 275.77/40.37 (X100 = 275.77/40.37 emptyset))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X102, 275.77/40.37 X104]: 275.77/40.37 (subset( 275.77/40.37 X104,X102) => 275.77/40.37 in( 275.77/40.37 X104, 275.77/40.37 powerset( 275.77/40.37 X102)))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X106, 275.77/40.37 X108]: 275.77/40.37 (in( 275.77/40.37 X108, 275.77/40.37 powerset( 275.77/40.37 X106)) => 275.77/40.37 subset( 275.77/40.37 X108,X106))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X110]: 275.77/40.37 in( 275.77/40.37 X110, 275.77/40.37 powerset( 275.77/40.37 X110))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X112, 275.77/40.37 X114]: 275.77/40.37 (subset( 275.77/40.37 X112,X114) => 275.77/40.37 subset( 275.77/40.37 powerset( 275.77/40.37 X112), 275.77/40.37 powerset( 275.77/40.37 X114)))) => 275.77/40.37 ( 275.77/40.37 sepInPowerset => 275.77/40.37 ( 275.77/40.37 sepSubset => 275.77/40.37 ( 275.77/40.37 binunionIL => 275.77/40.37 ( 275.77/40.37 upairset2IR => 275.77/40.37 ( 275.77/40.37 binunionIR => 275.77/40.37 ( 275.77/40.37 binunionEcases => 275.77/40.37 ( 275.77/40.37 binunionE => 275.77/40.37 ( 275.77/40.37 binunionLsub => 275.77/40.37 ( 275.77/40.37 binunionRsub => 275.77/40.37 ( 275.77/40.37 binintersectI => 275.77/40.37 ( 275.77/40.37 binintersectSubset5 => 275.77/40.37 ( 275.77/40.37 binintersectEL => 275.77/40.37 ( 275.77/40.37 binintersectLsub => 275.77/40.37 ( 275.77/40.37 binintersectSubset2 => 275.77/40.37 ( 275.77/40.37 binintersectSubset3 => 275.77/40.37 ( 275.77/40.37 binintersectER => 275.77/40.37 ( 275.77/40.37 disjointsetsI1 => 275.77/40.37 ( 275.77/40.37 binintersectRsub => 275.77/40.37 ( 275.77/40.37 binintersectSubset4 => 275.77/40.37 ( 275.77/40.37 binintersectSubset1 => 275.77/40.37 ( 275.77/40.37 bs114d => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X116, 275.77/40.37 X118,X120]: 275.77/40.37 (in( 275.77/40.37 X120,X116) => 275.77/40.37 (( 275.77/40.37 ~ 275.77/40.37 in( 275.77/40.37 X120,X118)) => 275.77/40.37 in( 275.77/40.37 X120, 275.77/40.37 setminus( 275.77/40.37 X116,X118))))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X122, 275.77/40.37 X124,X126]: 275.77/40.37 (in( 275.77/40.37 X126, 275.77/40.37 setminus( 275.77/40.37 X122,X124)) => 275.77/40.37 in( 275.77/40.37 X126,X122))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X128, 275.77/40.37 X130,X132]: 275.77/40.37 (in( 275.77/40.37 X132, 275.77/40.37 setminus( 275.77/40.37 X128,X130)) => 275.77/40.37 (~ 275.77/40.37 in( 275.77/40.37 X132,X130)))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X134, 275.77/40.37 X136]: 275.77/40.37 (subset( 275.77/40.37 X134,X136) => 275.77/40.37 (setminus( 275.77/40.37 X134,X136) = 275.77/40.37 emptyset))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X138, 275.77/40.37 X140,X142]: 275.77/40.37 (( 275.77/40.37 ~ 275.77/40.37 in( 275.77/40.37 X142, 275.77/40.37 setminus( 275.77/40.37 X138,X140))) => 275.77/40.37 (in( 275.77/40.37 X142,X138) => 275.77/40.37 in( 275.77/40.37 X142,X140)))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X144, 275.77/40.37 X146,X148]: 275.77/40.37 (( 275.77/40.37 ~ 275.77/40.37 in( 275.77/40.37 X148, 275.77/40.37 setminus( 275.77/40.37 X144,X146))) => 275.77/40.37 (( 275.77/40.37 ~ 275.77/40.37 in( 275.77/40.37 X148,X146)) => 275.77/40.37 (~ 275.77/40.37 in( 275.77/40.37 X148,X144))))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X150, 275.77/40.37 X152,X154]: 275.77/40.37 (( 275.77/40.37 ~ 275.77/40.37 in( 275.77/40.37 X154,X150)) => 275.77/40.37 (~ 275.77/40.37 in( 275.77/40.37 X154, 275.77/40.37 setminus( 275.77/40.37 X150,X152))))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X156, 275.77/40.37 X158,X160]: 275.77/40.37 (in( 275.77/40.37 X160,X158) => 275.77/40.37 (~ 275.77/40.37 in( 275.77/40.37 X160, 275.77/40.37 setminus( 275.77/40.37 X156,X158))))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X162, 275.77/40.37 X164]: 275.77/40.37 subset( 275.77/40.37 setminus( 275.77/40.37 X162,X164), 275.77/40.37 X162)) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X166, 275.77/40.37 X168]: 275.77/40.37 (( 275.77/40.37 setminus( 275.77/40.37 X166,X168) = 275.77/40.37 emptyset) => 275.77/40.37 subset( 275.77/40.37 X166,X168))) => 275.77/40.37 ( 275.77/40.37 symdiffE => 275.77/40.37 ( 275.77/40.37 symdiffI1 => 275.77/40.37 ( 275.77/40.37 symdiffI2 => 275.77/40.37 ( 275.77/40.37 symdiffIneg1 => 275.77/40.37 ( 275.77/40.37 symdiffIneg2 => 275.77/40.37 ( 275.77/40.37 secondinupair => 275.77/40.37 ( 275.77/40.37 setukpairIL => 275.77/40.37 ( 275.77/40.37 setukpairIR => 275.77/40.37 ( 275.77/40.37 kpairiskpair => 275.77/40.37 ( 275.77/40.37 kpairp => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X170, 275.77/40.37 X172]: 275.77/40.37 (in( 275.77/40.37 X172,X170) => 275.77/40.37 subset( 275.77/40.37 setadjoin( 275.77/40.37 X172, 275.77/40.37 emptyset), 275.77/40.37 X170))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X174, 275.77/40.37 X176]: 275.77/40.37 (in( 275.77/40.37 X176,X174) => 275.77/40.37 in( 275.77/40.37 setadjoin( 275.77/40.37 X176, 275.77/40.37 emptyset), 275.77/40.37 powerset( 275.77/40.37 X174)))) => 275.77/40.37 ( 275.77/40.37 singletoninpowunion => 275.77/40.37 ( 275.77/40.37 upairset2E => 275.77/40.37 ( 275.77/40.37 upairsubunion => 275.77/40.37 ( 275.77/40.37 upairinpowunion => 275.77/40.37 ( 275.77/40.37 ubforcartprodlem1 => 275.77/40.37 ( 275.77/40.37 ubforcartprodlem2 => 275.77/40.37 ( 275.77/40.37 ubforcartprodlem3 => 275.77/40.37 ( 275.77/40.37 cartprodpairin => 275.77/40.37 ( 275.77/40.37 cartprodmempair1 => 275.77/40.37 ( 275.77/40.37 cartprodmempair => 275.77/40.37 ( 275.77/40.37 setunionE2 => 275.77/40.37 ( 275.77/40.37 setunionsingleton1 => 275.77/40.37 ( 275.77/40.37 setunionsingleton2 => 275.77/40.37 ( 275.77/40.37 setunionsingleton => 275.77/40.37 ( 275.77/40.37 singletonprop => 275.77/40.37 ( 275.77/40.37 ex1E1 => 275.77/40.37 ( 275.77/40.37 ex1I => 275.77/40.37 ( 275.77/40.37 ex1I2 => 275.77/40.37 ( 275.77/40.37 singletonsuniq => 275.77/40.37 ( 275.77/40.37 setukpairinjL1 => 275.77/40.37 ( 275.77/40.37 kfstsingleton => 275.77/40.37 ( 275.77/40.37 theprop => 275.77/40.37 ( 275.77/40.37 kfstpairEq => 275.77/40.37 ( 275.77/40.37 cartprodfstin => 275.77/40.37 ( 275.77/40.37 setukpairinjL2 => 275.77/40.37 ( 275.77/40.37 setukpairinjL => 275.77/40.37 ( 275.77/40.37 setukpairinjR11 => 275.77/40.37 ( 275.77/40.37 setukpairinjR12 => 275.77/40.37 ( 275.77/40.37 setukpairinjR1 => 275.77/40.37 ( 275.77/40.37 upairequniteq => 275.77/40.37 ( 275.77/40.37 setukpairinjR2 => 275.77/40.37 ( 275.77/40.37 setukpairinjR => 275.77/40.37 ( 275.77/40.37 ksndsingleton => 275.77/40.37 ( 275.77/40.37 ksndpairEq => 275.77/40.37 ( 275.77/40.37 kpairsurjEq => 275.77/40.37 ( 275.77/40.37 cartprodsndin => 275.77/40.37 ( 275.77/40.37 cartprodpairmemEL => 275.77/40.37 ( 275.77/40.37 cartprodpairmemER => 275.77/40.37 ( 275.77/40.37 cartprodmempaircEq => 275.77/40.37 ( 275.77/40.37 cartprodfstpairEq => 275.77/40.37 ( 275.77/40.37 cartprodsndpairEq => 275.77/40.37 ( 275.77/40.37 cartprodpairsurjEq => 275.77/40.37 ( 275.77/40.37 dpsetconstrI => 275.77/40.37 ( 275.77/40.37 dpsetconstrSub => 275.77/40.37 ( 275.77/40.37 setOfPairsIsBReln => 275.77/40.37 ( 275.77/40.37 dpsetconstrERa => 275.77/40.37 ( 275.77/40.37 dpsetconstrEL1 => 275.77/40.37 ( 275.77/40.37 dpsetconstrEL2 => 275.77/40.37 ( 275.77/40.37 dpsetconstrER => 275.77/40.37 ( 275.77/40.37 funcImageSingleton => 275.77/40.37 ( 275.77/40.37 apProp => 275.77/40.37 ( 275.77/40.37 app => 275.77/40.37 ( 275.77/40.37 infuncsetfunc => 275.77/40.37 ( 275.77/40.37 ap2p => 275.77/40.37 ( 275.77/40.37 funcinfuncset => 275.77/40.37 ( 275.77/40.37 lamProp => 275.77/40.37 ( 275.77/40.37 lamp => 275.77/40.37 ( 275.77/40.37 lam2p => 275.77/40.37 ( 275.77/40.37 brelnall1 => 275.77/40.37 ( 275.77/40.37 brelnall2 => 275.77/40.37 ( 275.77/40.37 ex1E2 => 275.77/40.37 ( 275.77/40.37 funcGraphProp1 => 275.77/40.37 ( 275.77/40.37 funcGraphProp3 => 275.77/40.37 ( 275.77/40.37 funcGraphProp2 => 275.77/40.37 ( 275.77/40.37 funcextLem => 275.77/40.37 ( 275.77/40.37 funcGraphProp4 => 275.77/40.37 ( 275.77/40.37 subbreln => 275.77/40.37 ( 275.77/40.37 eqbreln => 275.77/40.37 ( 275.77/40.37 funcext => 275.77/40.37 ( 275.77/40.37 funcext2 => 275.77/40.37 ( 275.77/40.37 ap2apEq1 => 275.77/40.37 ( 275.77/40.37 ap2apEq2 => 275.77/40.37 ( 275.77/40.37 beta1 => 275.77/40.37 ( 275.77/40.37 eta1 => 275.77/40.37 ( 275.77/40.37 lam2lamEq => 275.77/40.37 ( 275.77/40.37 beta2 => 275.77/40.37 ( 275.77/40.37 eta2 => 275.77/40.37 ( 275.77/40.37 iffalseProp1 => 275.77/40.37 ( 275.77/40.37 iffalseProp2 => 275.77/40.37 ( 275.77/40.37 iftrueProp1 => 275.77/40.37 ( 275.77/40.37 iftrueProp2 => 275.77/40.37 ( 275.77/40.37 ifSingleton => 275.77/40.37 ( 275.77/40.37 ifp => 275.77/40.37 ( 275.77/40.37 theeq => 275.77/40.37 ( 275.77/40.37 iftrue => 275.77/40.37 ( 275.77/40.37 iffalse => 275.77/40.37 ( 275.77/40.37 iftrueorfalse => 275.77/40.37 ( 275.77/40.37 binintersectT_lem => 275.77/40.37 ( 275.77/40.37 binunionT_lem => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X178, 275.77/40.37 X180]: 275.77/40.37 (in( 275.77/40.37 X180, 275.77/40.37 powerset( 275.77/40.37 X178)) => 275.77/40.37 in( 275.77/40.37 powerset( 275.77/40.37 X180), 275.77/40.37 powerset( 275.77/40.37 powerset( 275.77/40.37 X178))))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X182, 275.77/40.37 X184]: 275.77/40.37 (in( 275.77/40.37 X184, 275.77/40.37 powerset( 275.77/40.37 X182)) => 275.77/40.37 (![X186]: 275.77/40.37 (in( 275.77/40.37 X186, 275.77/40.37 powerset( 275.77/40.37 X182)) => 275.77/40.37 in( 275.77/40.37 setminus( 275.77/40.37 X184,X186), 275.77/40.37 powerset( 275.77/40.37 X182)))))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X188, 275.77/40.37 X190]: 275.77/40.37 (in( 275.77/40.37 X190, 275.77/40.37 powerset( 275.77/40.37 X188)) => 275.77/40.37 in( 275.77/40.37 setminus( 275.77/40.37 X188,X190), 275.77/40.37 powerset( 275.77/40.37 X188)))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X192, 275.77/40.37 X194]: 275.77/40.37 (in( 275.77/40.37 X194, 275.77/40.37 powerset( 275.77/40.37 X192)) => 275.77/40.37 (![X196]: 275.77/40.37 (in( 275.77/40.37 X196, 275.77/40.37 powerset( 275.77/40.37 X192)) => 275.77/40.37 (( 275.77/40.37 ![X198]: 275.77/40.37 (in( 275.77/40.37 X198,X192) => 275.77/40.37 (in( 275.77/40.37 X198,X194) => 275.77/40.37 in( 275.77/40.37 X198,X196)))) => 275.77/40.37 (( 275.77/40.37 ![X200]: 275.77/40.37 (in( 275.77/40.37 X200,X192) => 275.77/40.37 (in( 275.77/40.37 X200,X196) => 275.77/40.37 in( 275.77/40.37 X200,X194)))) => 275.77/40.37 (X194 = 275.77/40.37 X196))))))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X202, 275.77/40.37 X204]: 275.77/40.37 (in( 275.77/40.37 X204, 275.77/40.37 powerset( 275.77/40.37 X202)) => 275.77/40.37 (![X206]: 275.77/40.37 (in( 275.77/40.37 X206, 275.77/40.37 powerset( 275.77/40.37 X202)) => 275.77/40.37 (( 275.77/40.37 ![X208]: 275.77/40.37 (in( 275.77/40.37 X208,X202) => 275.77/40.37 (in( 275.77/40.37 X208,X204) => 275.77/40.37 in( 275.77/40.37 X208,X206)))) => 275.77/40.37 subset( 275.77/40.37 X204,X206)))))) => 275.77/40.37 ( 275.77/40.37 ( 275.77/40.37 ![X210, 275.77/40.37 X212]: 275.77/40.37 (in( 275.77/40.37 X212, 275.77/40.37 powerset( 275.77/40.37 X210)) => 275.77/40.37 (![X214]: 275.77/40.37 (in( 275.77/40.37 X214, 275.77/40.37 powerset( 275.77/40.37 X210)) => 275.77/40.37 (( 275.77/40.37 ![X216]: 275.77/40.37 (in( 275.77/40.37 X216,X210) => 275.77/40.37 (in( 275.77/40.37 X216,X212) => 275.77/40.37 in( 275.77/40.37 X216,X214)))) => 275.77/40.37 in( 275.77/40.37 X212, 275.77/40.37 powerset( 275.77/40.37 X214))))))) => 275.77/40.37 ( 275.77/40.38 ( 275.77/40.38 ![X218, 275.77/40.38 X220]: 275.77/40.38 (in( 275.77/40.38 X220, 275.77/40.38 powerset( 275.77/40.38 X218)) => 275.77/40.38 (![X222]: 275.77/40.38 (in( 275.77/40.38 X222, 275.77/40.38 powerset( 275.77/40.38 X218)) => 275.77/40.38 (![X224]: 275.77/40.38 (in( 275.77/40.38 X224,X218) => 275.77/40.38 (in( 275.77/40.38 X220, 275.77/40.38 powerset( 275.77/40.38 X222)) => 275.77/40.38 (in( 275.77/40.38 X224,X220) => 275.77/40.38 in( 275.77/40.38 X224,X222))))))))) => 275.77/40.38 ( 275.77/40.38 ( 275.77/40.38 ![X226, 275.77/40.38 X228]: 275.77/40.38 (in( 275.77/40.38 X228, 275.77/40.38 powerset( 275.77/40.38 X226)) => 275.77/40.38 (![X230]: 275.77/40.38 (in( 275.77/40.38 X230,X226) => 275.77/40.38 (in( 275.77/40.38 X230,X228) => 275.77/40.38 (~ 275.77/40.38 in( 275.77/40.38 X230, 275.77/40.38 setminus( 275.77/40.38 X226,X228)))))))) => 275.77/40.38 ( 275.77/40.38 ( 275.77/40.38 ![X232, 275.77/40.38 X234]: 275.77/40.38 (in( 275.77/40.38 X234, 275.77/40.38 powerset( 275.77/40.38 X232)) => 275.77/40.38 (![X236]: 275.77/40.38 (in( 275.77/40.38 X236,X232) => 275.77/40.38 (( 275.77/40.38 ~ 275.77/40.38 in( 275.77/40.38 X236, 275.77/40.38 setminus( 275.77/40.38 X232,X234))) => 275.77/40.38 in( 275.77/40.38 X236,X234)))))) => 275.77/40.38 ( 275.77/40.38 binintersectTELcontra => 275.77/40.38 ( 275.77/40.38 binintersectTERcontra => 275.77/40.38 ( 275.77/40.38 ( 275.77/40.38 ![X238, 275.77/40.38 X240]: 275.77/40.38 (in( 275.77/40.38 X240, 275.77/40.38 powerset( 275.77/40.38 X238)) => 275.77/40.38 (![X242]: 275.77/40.38 (in( 275.77/40.38 X242, 275.77/40.38 powerset( 275.77/40.38 X238)) => 275.77/40.38 (![X244]: 275.77/40.38 (in( 275.77/40.38 X244,X238) => 275.77/40.38 (subset( 275.77/40.38 X240, 275.77/40.38 setminus( 275.77/40.38 X238,X242)) => 275.77/40.38 (in( 275.77/40.38 X244,X242) => 275.77/40.38 (~ 275.77/40.38 in( 275.77/40.38 X244,X240)))))))))) => 275.77/40.38 ( 275.77/40.38 ( 275.77/40.38 ![X246, 275.77/40.38 X248]: 275.77/40.38 (in( 275.77/40.38 X248, 275.77/40.38 powerset( 275.77/40.38 X246)) => 275.77/40.38 (![X250]: 275.77/40.38 (in( 275.77/40.38 X250, 275.77/40.38 powerset( 275.77/40.38 X246)) => 275.77/40.38 (![X252]: 275.77/40.38 (in( 275.77/40.38 X252,X246) => 275.77/40.38 (subset( 275.77/40.38 X248,X250) => 275.77/40.38 (( 275.77/40.38 ~ 275.77/40.38 in( 275.77/40.38 X252,X250)) => 275.77/40.38 (~ 275.77/40.38 in( 275.77/40.38 X252,X248)))))))))) => 275.77/40.38 ( 275.77/40.38 ![X254, 275.77/40.38 X256]: 275.77/40.38 (in( 275.77/40.38 X256, 275.77/40.38 powerset( 275.77/40.38 X254)) => 275.77/40.38 (![X258]: 275.77/40.38 (in( 275.77/40.38 X258, 275.77/40.38 powerset( 275.77/40.38 X254)) => 275.77/40.38 (subset( 275.77/40.38 X256,X258) => 275.77/40.38 subset( 275.77/40.38 setminus( 275.77/40.38 X254,X258), 275.77/40.38 setminus( 275.77/40.38 X254,X256)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 275.77/40.38 tff('49', plain, 275.77/40.38 ~ subset(setminus(sk_X254, sk_X258), setminus(sk_X254, sk_X256)), 275.77/40.38 inference('cnf', [status(esa)], [zf_stmt_4])). 275.77/40.38 tff('50', plain, subset(sk_X256, sk_X258), 275.77/40.38 inference('cnf', [status(esa)], [zf_stmt_4])). 275.77/40.38 tff('51', plain, 275.77/40.38 ![X154, X155, X156]: ( in(X154, X155) | ~ in(X154, setminus(X155, X156))), 275.77/40.38 inference('cnf', [status(esa)], [zf_stmt_4])). 275.77/40.38 tff('52', plain, 275.77/40.38 ![X210, X211, X212]: 275.77/40.38 (~ in(X210, X211) | in(X210, X212) | in(X210, setminus(X211, X212))), 275.77/40.38 inference('cnf', [status(esa)], [zf_stmt_4])). 275.77/40.38 tff('53', plain, 275.77/40.38 ![X135, X136]: ( subset(X135, X136) | ~ in(sk_X48(X136, X135), X136)), 275.77/40.38 inference('cnf', [status(esa)], [zf_stmt_4])). 275.77/40.38 tff('54', plain, 275.77/40.38 ![X137, X138, X139]: 275.77/40.38 (~ subset(X137, X138) | in(X139, X138) | ~ in(X139, X137)), 275.77/40.38 inference('cnf', [status(esa)], [zf_stmt_4])). 275.77/40.38 tff('55', plain, 275.77/40.38 ![X135, X136]: ( subset(X135, X136) | in(sk_X48(X136, X135), X135)), 275.77/40.38 inference('cnf', [status(esa)], [zf_stmt_4])). 275.77/40.38 tff('56', plain, 275.77/40.38 ![X162, X163, X164]: 275.77/40.38 (~ in(X162, setminus(X163, X164)) | ~ in(X162, X164)), 275.77/40.38 inference('cnf', [status(esa)], [zf_stmt_4])). 275.77/40.38 tff('57', plain, $false, 275.77/40.38 inference('eprover', [status(thm)], 275.77/40.38 ['49', '50', '51', '52', '53', '54', '55', '56'])). 275.77/40.38 275.77/40.38 % SZS output end Refutation 275.77/40.38 275.77/40.38 275.77/40.38 % Terminating... 275.77/40.38 % /export/starexec/sandbox/solver/bin/lams/c.preprocess2.sh running for 21s 276.45/40.49 % Runner terminated. 276.45/40.50 % Zipperpin 1.5 exiting 276.45/40.50 EOF