0.00/0.07 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.08 % Command : run_portfolio.sh /export/starexec/sandbox/benchmark/theBenchmark.p /export/starexec/sandbox/tmp/tmp.jAi9kExPMt 0.08/0.27 % Computer : n027.cluster.edu 0.08/0.27 % Model : x86_64 x86_64 0.08/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.08/0.27 % Memory : 8042.1875MB 0.08/0.27 % OS : Linux 3.10.0-693.el7.x86_64 0.08/0.27 % CPULimit : 1200 0.08/0.27 % DateTime : Tue Jul 13 15:35:55 EDT 2021 0.08/0.27 % CPUTime : 0.08/0.27 % Running portfolio for 120 s 0.08/0.27 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.08/0.27 % Number of cores: 8 0.08/0.27 % Python version: Python 3.6.8 0.08/0.27 % Running in HO mode 0.12/0.54 % Estimated wc time : 1286 0.12/0.54 % Estimated cpu time (7 cpus) : 183.71428571428572 0.53/0.60 % /export/starexec/sandbox/solver/bin/lams/s6.sh running for 21s 0.81/0.63 % /export/starexec/sandbox/solver/bin/lams/new_b3.2.norw.sh running for 15s 0.81/0.65 % /export/starexec/sandbox/solver/bin/lams/s6.ds.sh running for 10s 0.81/0.65 % /export/starexec/sandbox/solver/bin/lams/b.rpo.sh running for 21s 0.81/0.65 % /export/starexec/sandbox/solver/bin/lams/c.s.2.sh running for 68s 0.81/0.65 % /export/starexec/sandbox/solver/bin/lams/c.easy.sh running for 26s 0.81/0.65 % /export/starexec/sandbox/solver/bin/lams/old_b3.avatar.sh running for 15s 70.32/10.62 % /export/starexec/sandbox/solver/bin/lams/old_sp2.sh running for 17s 105.89/15.66 % /export/starexec/sandbox/solver/bin/lams/b.sh running for 31s 105.89/15.67 % /export/starexec/sandbox/solver/bin/lams/sh1.sh running for 26s 147.08/21.58 % /export/starexec/sandbox/solver/bin/lams/b.lsimp.sh running for 17s 147.62/21.68 % /export/starexec/sandbox/solver/bin/lams/b.split.sh running for 31s 183.50/26.89 % /export/starexec/sandbox/solver/bin/lams/s4.sh running for 15s 188.91/27.64 % /export/starexec/sandbox/solver/bin/lams/b.rw.sh running for 26s 191.09/27.96 % /export/starexec/sandbox/solver/bin/lams/c_ic.sh running for 42s 191.81/28.10 % Solved by lams/c_ic.sh. 191.81/28.10 % done 216 iterations in 0.104s 191.81/28.10 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 191.81/28.10 % SZS output start Refutation 191.81/28.10 tff(funcextLem, axiom, funcextLem <=> 191.81/28.10 (![A,B,Xf]: 191.81/28.10 (func(A,B,Xf) => 191.81/28.10 (![Xg]: 191.81/28.10 (func(A,B,Xg) => 191.81/28.10 ((![Xx]: (in(Xx,A) => (ap(A,B,Xf,Xx) = ap(A,B,Xg,Xx)))) => 191.81/28.10 (![Xx]: 191.81/28.10 (in(Xx,A) => 191.81/28.10 (![Xy]: 191.81/28.10 (in(Xy,B) => (in(kpair(Xx,Xy),Xg) => in(kpair(Xx,Xy),Xf)))))))))))). 191.81/28.10 tff('0', plain, 191.81/28.10 funcextLem = 191.81/28.10 (![X4,X6,X8]: 191.81/28.10 (func(X4,X6,X8) => 191.81/28.10 (![X10]: 191.81/28.10 (func(X4,X6,X10) => 191.81/28.10 ((![X12]: (in(X12,X4) => (ap(X4,X6,X8,X12) = ap(X4,X6,X10,X12)))) => 191.81/28.10 (![X14]: 191.81/28.10 (in(X14,X4) => 191.81/28.10 (![X16]: 191.81/28.10 (in(X16,X6) => 191.81/28.10 (in(kpair(X14,X16),X10) => in(kpair(X14,X16),X8))))))))))), 191.81/28.10 define([status(thm)])). 191.81/28.10 tff(funcGraphProp2, axiom, funcGraphProp2 <=> 191.81/28.10 (![A,B,Xf]: 191.81/28.10 (func(A,B,Xf) => 191.81/28.10 (![Xx]: 191.81/28.10 (in(Xx,A) => 191.81/28.10 (![Xy]: (in(Xy,B) => (in(kpair(Xx,Xy),Xf) => (ap(A,B,Xf,Xx) = Xy))))))))). 191.81/28.10 tff('1', plain, 191.81/28.10 funcGraphProp2 = 191.81/28.10 (![X4,X6,X8]: 191.81/28.10 (func(X4,X6,X8) => 191.81/28.10 (![X10]: 191.81/28.10 (in(X10,X4) => 191.81/28.10 (![X12]: 191.81/28.10 (in(X12,X6) => 191.81/28.10 (in(kpair(X10,X12),X8) => (ap(X4,X6,X8,X10) = X12)))))))), 191.81/28.10 define([status(thm)])). 191.81/28.10 tff(funcGraphProp3, axiom, funcGraphProp3 <=> 191.81/28.10 (![A,B,Xf]: 191.81/28.10 (in(Xf,funcSet(A,B)) => 191.81/28.10 (![Xx]: (in(Xx,A) => in(kpair(Xx,ap(A,B,Xf,Xx)),Xf)))))). 191.81/28.10 tff('2', plain, 191.81/28.10 funcGraphProp3 = 191.81/28.10 (![X4,X6,X8]: 191.81/28.10 (in(X8,funcSet(X4,X6)) => 191.81/28.10 (![X10]: (in(X10,X4) => in(kpair(X10,ap(X4,X6,X8,X10)),X8))))), 191.81/28.10 define([status(thm)])). 191.81/28.10 tff(funcGraphProp1, axiom, funcGraphProp1 <=> 191.81/28.10 (![A,B,Xf]: 191.81/28.10 (func(A,B,Xf) => (![Xx]: (in(Xx,A) => in(kpair(Xx,ap(A,B,Xf,Xx)),Xf)))))). 191.81/28.10 tff('3', plain, 191.81/28.10 funcGraphProp1 = 191.81/28.10 (![X4,X6,X8]: 191.81/28.10 (func(X4,X6,X8) => 191.81/28.10 (![X10]: (in(X10,X4) => in(kpair(X10,ap(X4,X6,X8,X10)),X8))))), 191.81/28.10 define([status(thm)])). 191.81/28.10 tff(funcinfuncset, axiom, funcinfuncset <=> 191.81/28.10 (![A,B,Xf]: (func(A,B,Xf) => in(Xf,funcSet(A,B))))). 191.81/28.10 tff('4', plain, 191.81/28.10 funcinfuncset = (![X4,X6,X8]: (func(X4,X6,X8) => in(X8,funcSet(X4,X6)))), 191.81/28.10 define([status(thm)])). 191.81/28.10 tff(ap2p, axiom, ap2p <=> 191.81/28.10 (![A,B,Xf]: 191.81/28.10 (in(Xf,funcSet(A,B)) => (![Xx]: (in(Xx,A) => in(ap(A,B,Xf,Xx),B)))))). 191.81/28.10 tff('5', plain, 191.81/28.10 ap2p = 191.81/28.10 (![X4,X6,X8]: 191.81/28.10 (in(X8,funcSet(X4,X6)) => 191.81/28.10 (![X10]: (in(X10,X4) => in(ap(X4,X6,X8,X10),X6))))), 191.81/28.10 define([status(thm)])). 191.81/28.10 tff(infuncsetfunc, axiom, infuncsetfunc <=> 191.81/28.10 (![A,B,Xf]: (in(Xf,funcSet(A,B)) => func(A,B,Xf)))). 191.81/28.10 tff('6', plain, 191.81/28.10 infuncsetfunc = (![X4,X6,X8]: (in(X8,funcSet(X4,X6)) => func(X4,X6,X8))), 191.81/28.10 define([status(thm)])). 191.81/28.10 tff(app, axiom, app <=> 191.81/28.10 (![A,B,Xf]: (func(A,B,Xf) => (![Xx]: (in(Xx,A) => in(ap(A,B,Xf,Xx),B)))))). 191.81/28.10 tff('7', plain, 191.81/28.10 app = 191.81/28.10 (![X4,X6,X8]: 191.81/28.10 (func(X4,X6,X8) => (![X10]: (in(X10,X4) => in(ap(X4,X6,X8,X10),X6))))), 191.81/28.10 define([status(thm)])). 191.81/28.10 tff(cartprodmempaircEq, axiom, cartprodmempaircEq <=> 191.81/28.10 (![A,B,Xx]: 191.81/28.10 (in(Xx,A) => (![Xy]: (in(Xy,B) => (kpair(Xx,Xy) = kpair(Xx,Xy))))))). 191.81/28.10 tff('8', plain, 191.81/28.10 cartprodmempaircEq = 191.81/28.10 (![X4,X6,X8]: 191.81/28.10 (in(X8,X4) => 191.81/28.10 (![X10]: (in(X10,X6) => (kpair(X8,X10) = kpair(X8,X10)))))), 191.81/28.10 define([status(thm)])). 191.81/28.10 tff(setukpairinjR, axiom, setukpairinjR <=> 191.81/28.10 (![Xx,Xy,Xz,Xu]: ((kpair(Xx,Xy) = kpair(Xz,Xu)) => (Xy = Xu)))). 191.81/28.10 tff('9', plain, 191.81/28.10 setukpairinjR = 191.81/28.10 (![X4,X6,X8,X10]: ((kpair(X4,X6) = kpair(X8,X10)) => (X6 = X10))), 191.81/28.10 define([status(thm)])). 191.81/28.10 tff(setukpairinjL, axiom, setukpairinjL <=> 191.81/28.10 (![Xx,Xy,Xz,Xu]: ((kpair(Xx,Xy) = kpair(Xz,Xu)) => (Xx = Xz)))). 191.81/28.10 tff('10', plain, 191.81/28.10 setukpairinjL = 191.81/28.10 (![X4,X6,X8,X10]: ((kpair(X4,X6) = kpair(X8,X10)) => (X4 = X8))), 191.81/28.10 define([status(thm)])). 191.81/28.10 tff(funcGraphProp4, conjecture, 191.81/28.10 (setextAx => 191.81/28.10 (emptysetAx => 191.81/28.10 (setadjoinAx => 191.81/28.10 (powersetAx => 191.81/28.10 (setunionAx => 191.81/28.10 (omega0Ax => 191.81/28.10 (omegaSAx => 191.81/28.10 (omegaIndAx => 191.81/28.10 (replAx => 191.81/28.10 (foundationAx => 191.81/28.10 (wellorderingAx => 191.81/28.10 (descrp => 191.81/28.10 (dsetconstrI => 191.81/28.10 (dsetconstrEL => 191.81/28.10 (dsetconstrER => 191.81/28.10 (exuE1 => 191.81/28.10 (prop2setE => 191.81/28.10 (emptysetE => 191.81/28.10 (emptysetimpfalse => 191.81/28.10 (notinemptyset => 191.81/28.10 (exuE3e => 191.81/28.10 (setext => 191.81/28.10 (emptyI => 191.81/28.10 (noeltsimpempty => 191.81/28.10 (setbeta => 191.81/28.10 (nonemptyE1 => 191.81/28.10 (nonemptyI => 191.81/28.10 (nonemptyI1 => 191.81/28.10 (setadjoinIL => 191.81/28.10 (emptyinunitempty => 191.81/28.10 (setadjoinIR => 191.81/28.10 (setadjoinE => 191.81/28.10 (setadjoinOr => 191.81/28.10 (setoftrueEq => 191.81/28.10 (powersetI => 191.81/28.10 (emptyinPowerset => 191.81/28.10 (emptyInPowerset => 191.81/28.10 (powersetE => 191.81/28.10 (setunionI => 191.81/28.10 (setunionE => 191.81/28.10 (subPowSU => 191.81/28.10 (exuE2 => 191.81/28.10 (nonemptyImpWitness => 191.81/28.10 (uniqinunit => 191.81/28.10 (notinsingleton => 191.81/28.10 (eqinunit => 191.81/28.10 (singletonsswitch => 191.81/28.10 (upairsetE => 191.81/28.10 (upairsetIL => 191.81/28.10 (upairsetIR => 191.81/28.10 (emptyE1 => 191.81/28.10 (vacuousDall => 191.81/28.10 (quantDeMorgan1 => 191.81/28.10 (quantDeMorgan2 => 191.81/28.10 (quantDeMorgan3 => 191.81/28.10 (quantDeMorgan4 => 191.81/28.10 (prop2setI => 191.81/28.10 (prop2set2propI => 191.81/28.10 (notdexE => 191.81/28.10 (notdallE => 191.81/28.10 (exuI1 => 191.81/28.10 (exuI3 => 191.81/28.10 (exuI2 => 191.81/28.10 (inCongP => 191.81/28.10 (in__Cong => 191.81/28.10 (exuE3u => 191.81/28.10 ( 191.81/28.10 exu__Cong => 191.81/28.10 ( 191.81/28.10 emptyset__Cong => 191.81/28.10 ( 191.81/28.10 setadjoin__Cong => 191.81/28.10 ( 191.81/28.10 powerset__Cong => 191.81/28.10 ( 191.81/28.10 setunion__Cong => 191.81/28.10 ( 191.81/28.10 omega__Cong => 191.81/28.10 ( 191.81/28.10 exuEu => 191.81/28.10 ( 191.81/28.10 descr__Cong => 191.81/28.10 ( 191.81/28.10 dsetconstr__Cong => 191.81/28.10 ( 191.81/28.10 subsetI1 => 191.81/28.10 ( 191.81/28.10 eqimpsubset2 => 191.81/28.10 ( 191.81/28.10 eqimpsubset1 => 191.81/28.10 ( 191.81/28.10 subsetI2 => 191.81/28.10 ( 191.81/28.10 emptysetsubset => 191.81/28.10 ( 191.81/28.10 subsetE => 191.81/28.10 ( 191.81/28.10 subsetE2 => 191.81/28.10 ( 191.81/28.10 notsubsetI => 191.81/28.10 ( 191.81/28.10 notequalI1 => 191.81/28.10 ( 191.81/28.10 notequalI2 => 191.81/28.10 ( 191.81/28.10 subsetRefl => 191.81/28.10 ( 191.81/28.10 subsetTrans => 191.81/28.10 ( 191.81/28.10 setadjoinSub => 191.81/28.10 ( 191.81/28.10 setadjoinSub2 => 191.81/28.10 ( 191.81/28.10 subset2powerset => 191.81/28.10 ( 191.81/28.10 setextsub => 191.81/28.10 ( 191.81/28.10 subsetemptysetimpeq => 191.81/28.10 ( 191.81/28.10 powersetI1 => 191.81/28.10 ( 191.81/28.10 powersetE1 => 191.81/28.10 ( 191.81/28.10 inPowerset => 191.81/28.10 ( 191.81/28.10 powersetsubset => 191.81/28.10 ( 191.81/28.10 sepInPowerset => 191.81/28.10 ( 191.81/28.10 sepSubset => 191.81/28.10 ( 191.81/28.10 binunionIL => 191.81/28.10 ( 191.81/28.10 upairset2IR => 191.81/28.10 ( 191.81/28.10 binunionIR => 191.81/28.10 ( 191.81/28.10 binunionEcases => 191.81/28.10 ( 191.81/28.10 binunionE => 191.81/28.10 ( 191.81/28.10 binunionLsub => 191.81/28.10 ( 191.81/28.10 binunionRsub => 191.81/28.10 ( 191.81/28.10 binintersectI => 191.81/28.10 ( 191.81/28.10 binintersectSubset5 => 191.81/28.10 ( 191.81/28.10 binintersectEL => 191.81/28.10 ( 191.81/28.10 binintersectLsub => 191.81/28.10 ( 191.81/28.10 binintersectSubset2 => 191.81/28.10 ( 191.81/28.10 binintersectSubset3 => 191.81/28.10 ( 191.81/28.10 binintersectER => 191.81/28.10 ( 191.81/28.10 disjointsetsI1 => 191.81/28.10 ( 191.81/28.10 binintersectRsub => 191.81/28.10 ( 191.81/28.10 binintersectSubset4 => 191.81/28.10 ( 191.81/28.10 binintersectSubset1 => 191.81/28.10 ( 191.81/28.10 bs114d => 191.81/28.10 ( 191.81/28.10 setminusI => 191.81/28.10 ( 191.81/28.10 setminusEL => 191.81/28.10 ( 191.81/28.10 setminusER => 191.81/28.10 ( 191.81/28.10 setminusSubset2 => 191.81/28.10 ( 191.81/28.10 setminusERneg => 191.81/28.10 ( 191.81/28.10 setminusELneg => 191.81/28.10 ( 191.81/28.10 setminusILneg => 191.81/28.10 ( 191.81/28.10 setminusIRneg => 191.81/28.10 ( 191.81/28.10 setminusLsub => 191.81/28.10 ( 191.81/28.10 setminusSubset1 => 191.81/28.10 ( 191.81/28.10 symdiffE => 191.81/28.10 ( 191.81/28.10 symdiffI1 => 191.81/28.10 ( 191.81/28.10 symdiffI2 => 191.81/28.10 ( 191.81/28.10 symdiffIneg1 => 191.81/28.10 ( 191.81/28.10 symdiffIneg2 => 191.81/28.10 ( 191.81/28.10 secondinupair => 191.81/28.10 ( 191.81/28.10 setukpairIL => 191.81/28.10 ( 191.81/28.10 setukpairIR => 191.81/28.10 ( 191.81/28.10 kpairiskpair => 191.81/28.10 ( 191.81/28.10 kpairp => 191.81/28.10 ( 191.81/28.10 singletonsubset => 191.81/28.10 ( 191.81/28.10 singletoninpowerset => 191.81/28.10 ( 191.81/28.10 singletoninpowunion => 191.81/28.10 ( 191.81/28.10 upairset2E => 191.81/28.10 ( 191.81/28.10 upairsubunion => 191.81/28.10 ( 191.81/28.10 upairinpowunion => 191.81/28.10 ( 191.81/28.10 ubforcartprodlem1 => 191.81/28.10 ( 191.81/28.10 ubforcartprodlem2 => 191.81/28.10 ( 191.81/28.10 ubforcartprodlem3 => 191.81/28.10 ( 191.81/28.10 cartprodpairin => 191.81/28.10 ( 191.81/28.10 cartprodmempair1 => 191.81/28.10 ( 191.81/28.10 cartprodmempair => 191.81/28.10 ( 191.81/28.10 setunionE2 => 191.81/28.10 ( 191.81/28.10 setunionsingleton1 => 191.81/28.10 ( 191.81/28.10 setunionsingleton2 => 191.81/28.10 ( 191.81/28.10 setunionsingleton => 191.81/28.10 ( 191.81/28.10 singletonprop => 191.81/28.10 ( 191.81/28.10 ex1E1 => 191.81/28.10 ( 191.81/28.10 ex1I => 191.81/28.10 ( 191.81/28.10 ex1I2 => 191.81/28.10 ( 191.81/28.10 singletonsuniq => 191.81/28.10 ( 191.81/28.10 setukpairinjL1 => 191.81/28.10 ( 191.81/28.10 kfstsingleton => 191.81/28.10 ( 191.81/28.10 theprop => 191.81/28.10 ( 191.81/28.10 kfstpairEq => 191.81/28.10 ( 191.81/28.10 cartprodfstin => 191.81/28.10 ( 191.81/28.10 setukpairinjL2 => 191.81/28.10 ( 191.81/28.10 setukpairinjL => 191.81/28.10 ( 191.81/28.10 setukpairinjR11 => 191.81/28.10 ( 191.81/28.10 setukpairinjR12 => 191.81/28.10 ( 191.81/28.10 setukpairinjR1 => 191.81/28.10 ( 191.81/28.10 upairequniteq => 191.81/28.10 ( 191.81/28.10 setukpairinjR2 => 191.81/28.10 ( 191.81/28.10 setukpairinjR => 191.81/28.10 ( 191.81/28.10 ksndsingleton => 191.81/28.10 ( 191.81/28.10 ksndpairEq => 191.81/28.10 ( 191.81/28.10 kpairsurjEq => 191.81/28.10 ( 191.81/28.10 cartprodsndin => 191.81/28.10 ( 191.81/28.10 cartprodpairmemEL => 191.81/28.10 ( 191.81/28.10 cartprodpairmemER => 191.81/28.10 ( 191.81/28.10 cartprodmempaircEq => 191.81/28.10 ( 191.81/28.10 cartprodfstpairEq => 191.81/28.10 ( 191.81/28.10 cartprodsndpairEq => 191.81/28.10 ( 191.81/28.10 cartprodpairsurjEq => 191.81/28.10 ( 191.81/28.10 dpsetconstrI => 191.81/28.10 ( 191.81/28.10 dpsetconstrSub => 191.81/28.10 ( 191.81/28.10 setOfPairsIsBReln => 191.81/28.10 ( 191.81/28.10 dpsetconstrERa => 191.81/28.10 ( 191.81/28.10 dpsetconstrEL1 => 191.81/28.10 ( 191.81/28.10 dpsetconstrEL2 => 191.81/28.10 ( 191.81/28.10 dpsetconstrER => 191.81/28.10 ( 191.81/28.10 funcImageSingleton => 191.81/28.10 ( 191.81/28.10 apProp => 191.81/28.10 ( 191.81/28.10 app => 191.81/28.10 ( 191.81/28.10 infuncsetfunc => 191.81/28.10 ( 191.81/28.10 ap2p => 191.81/28.10 ( 191.81/28.10 funcinfuncset => 191.81/28.10 ( 191.81/28.10 lamProp => 191.81/28.10 ( 191.81/28.10 lamp => 191.81/28.10 ( 191.81/28.10 lam2p => 191.81/28.10 ( 191.81/28.10 brelnall1 => 191.81/28.10 ( 191.81/28.10 brelnall2 => 191.81/28.10 ( 191.81/28.10 ex1E2 => 191.81/28.10 ( 191.81/28.10 funcGraphProp1 => 191.81/28.10 ( 191.81/28.10 funcGraphProp3 => 191.81/28.10 ( 191.81/28.10 funcGraphProp2 => 191.81/28.10 ( 191.81/28.10 funcextLem => 191.81/28.10 ( 191.81/28.10 ![A,B,Xf]: 191.81/28.10 (in( 191.81/28.10 Xf, 191.81/28.10 funcSet( 191.81/28.10 A,B)) => 191.81/28.10 (![Xx]: 191.81/28.10 (in(Xx,A) => 191.81/28.10 (![Xy]: 191.81/28.10 (in(Xy,B) => 191.81/28.10 (in( 191.81/28.10 kpair( 191.81/28.10 Xx,Xy),Xf) => 191.81/28.10 (ap( 191.81/28.10 A,B,Xf,Xx) = 191.81/28.10 Xy))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 191.81/28.10 tff(zf_stmt_0, conjecture, 191.81/28.10 (setextAx => 191.81/28.10 (emptysetAx => 191.81/28.10 (setadjoinAx => 191.81/28.10 (powersetAx => 191.81/28.10 (setunionAx => 191.81/28.10 (omega0Ax => 191.81/28.10 (omegaSAx => 191.81/28.10 (omegaIndAx => 191.81/28.10 (replAx => 191.81/28.10 (foundationAx => 191.81/28.10 (wellorderingAx => 191.81/28.10 (descrp => 191.81/28.10 (dsetconstrI => 191.81/28.10 (dsetconstrEL => 191.81/28.10 (dsetconstrER => 191.81/28.10 (exuE1 => 191.81/28.10 (prop2setE => 191.81/28.10 (emptysetE => 191.81/28.10 (emptysetimpfalse => 191.81/28.10 (notinemptyset => 191.81/28.10 (exuE3e => 191.81/28.10 (setext => 191.81/28.10 (emptyI => 191.81/28.10 (noeltsimpempty => 191.81/28.10 (setbeta => 191.81/28.10 (nonemptyE1 => 191.81/28.10 (nonemptyI => 191.81/28.10 (nonemptyI1 => 191.81/28.10 (setadjoinIL => 191.81/28.10 (emptyinunitempty => 191.81/28.10 (setadjoinIR => 191.81/28.10 (setadjoinE => 191.81/28.10 (setadjoinOr => 191.81/28.10 (setoftrueEq => 191.81/28.10 (powersetI => 191.81/28.10 (emptyinPowerset => 191.81/28.10 (emptyInPowerset => 191.81/28.10 (powersetE => 191.81/28.10 (setunionI => 191.81/28.10 (setunionE => 191.81/28.10 (subPowSU => 191.81/28.10 (exuE2 => 191.81/28.10 (nonemptyImpWitness => 191.81/28.10 (uniqinunit => 191.81/28.10 (notinsingleton => 191.81/28.10 (eqinunit => 191.81/28.10 (singletonsswitch => 191.81/28.10 (upairsetE => 191.81/28.10 (upairsetIL => 191.81/28.10 (upairsetIR => 191.81/28.10 (emptyE1 => 191.81/28.10 (vacuousDall => 191.81/28.10 (quantDeMorgan1 => 191.81/28.10 (quantDeMorgan2 => 191.81/28.10 (quantDeMorgan3 => 191.81/28.10 (quantDeMorgan4 => 191.81/28.10 (prop2setI => 191.81/28.10 (prop2set2propI => 191.81/28.10 (notdexE => 191.81/28.10 (notdallE => 191.81/28.10 (exuI1 => 191.81/28.10 (exuI3 => 191.81/28.10 (exuI2 => 191.81/28.10 (inCongP => 191.81/28.10 (in__Cong => 191.81/28.10 (exuE3u => 191.81/28.10 ( 191.81/28.10 exu__Cong => 191.81/28.10 ( 191.81/28.10 emptyset__Cong => 191.81/28.10 ( 191.81/28.10 setadjoin__Cong => 191.81/28.10 ( 191.81/28.10 powerset__Cong => 191.81/28.10 ( 191.81/28.10 setunion__Cong => 191.81/28.10 ( 191.81/28.10 omega__Cong => 191.81/28.10 ( 191.81/28.10 exuEu => 191.81/28.10 ( 191.81/28.10 descr__Cong => 191.81/28.10 ( 191.81/28.10 dsetconstr__Cong => 191.81/28.10 ( 191.81/28.10 subsetI1 => 191.81/28.10 ( 191.81/28.10 eqimpsubset2 => 191.81/28.10 ( 191.81/28.10 eqimpsubset1 => 191.81/28.10 ( 191.81/28.10 subsetI2 => 191.81/28.10 ( 191.81/28.10 emptysetsubset => 191.81/28.10 ( 191.81/28.10 subsetE => 191.81/28.10 ( 191.81/28.10 subsetE2 => 191.81/28.10 ( 191.81/28.10 notsubsetI => 191.81/28.10 ( 191.81/28.10 notequalI1 => 191.81/28.10 ( 191.81/28.10 notequalI2 => 191.81/28.10 ( 191.81/28.10 subsetRefl => 191.81/28.10 ( 191.81/28.10 subsetTrans => 191.81/28.10 ( 191.81/28.10 setadjoinSub => 191.81/28.10 ( 191.81/28.10 setadjoinSub2 => 191.81/28.10 ( 191.81/28.10 subset2powerset => 191.81/28.10 ( 191.81/28.10 setextsub => 191.81/28.10 ( 191.81/28.10 subsetemptysetimpeq => 191.81/28.10 ( 191.81/28.10 powersetI1 => 191.81/28.10 ( 191.81/28.10 powersetE1 => 191.81/28.10 ( 191.81/28.10 inPowerset => 191.81/28.10 ( 191.81/28.10 powersetsubset => 191.81/28.10 ( 191.81/28.10 sepInPowerset => 191.81/28.10 ( 191.81/28.10 sepSubset => 191.81/28.10 ( 191.81/28.10 binunionIL => 191.81/28.10 ( 191.81/28.10 upairset2IR => 191.81/28.10 ( 191.81/28.10 binunionIR => 191.81/28.10 ( 191.81/28.10 binunionEcases => 191.81/28.10 ( 191.81/28.10 binunionE => 191.81/28.10 ( 191.81/28.10 binunionLsub => 191.81/28.10 ( 191.81/28.10 binunionRsub => 191.81/28.10 ( 191.81/28.10 binintersectI => 191.81/28.10 ( 191.81/28.10 binintersectSubset5 => 191.81/28.10 ( 191.81/28.10 binintersectEL => 191.81/28.10 ( 191.81/28.10 binintersectLsub => 191.81/28.10 ( 191.81/28.10 binintersectSubset2 => 191.81/28.10 ( 191.81/28.10 binintersectSubset3 => 191.81/28.10 ( 191.81/28.10 binintersectER => 191.81/28.10 ( 191.81/28.10 disjointsetsI1 => 191.81/28.10 ( 191.81/28.10 binintersectRsub => 191.81/28.10 ( 191.81/28.10 binintersectSubset4 => 191.81/28.10 ( 191.81/28.10 binintersectSubset1 => 191.81/28.10 ( 191.81/28.10 bs114d => 191.81/28.10 ( 191.81/28.10 setminusI => 191.81/28.10 ( 191.81/28.10 setminusEL => 191.81/28.10 ( 191.81/28.10 setminusER => 191.81/28.10 ( 191.81/28.10 setminusSubset2 => 191.81/28.10 ( 191.81/28.10 setminusERneg => 191.81/28.10 ( 191.81/28.10 setminusELneg => 191.81/28.10 ( 191.81/28.10 setminusILneg => 191.81/28.10 ( 191.81/28.10 setminusIRneg => 191.81/28.10 ( 191.81/28.10 setminusLsub => 191.81/28.10 ( 191.81/28.10 setminusSubset1 => 191.81/28.10 ( 191.81/28.10 symdiffE => 191.81/28.10 ( 191.81/28.10 symdiffI1 => 191.81/28.10 ( 191.81/28.10 symdiffI2 => 191.81/28.10 ( 191.81/28.10 symdiffIneg1 => 191.81/28.10 ( 191.81/28.10 symdiffIneg2 => 191.81/28.10 ( 191.81/28.10 secondinupair => 191.81/28.10 ( 191.81/28.10 setukpairIL => 191.81/28.10 ( 191.81/28.10 setukpairIR => 191.81/28.10 ( 191.81/28.10 kpairiskpair => 191.81/28.10 ( 191.81/28.10 kpairp => 191.81/28.10 ( 191.81/28.10 singletonsubset => 191.81/28.10 ( 191.81/28.10 singletoninpowerset => 191.81/28.10 ( 191.81/28.10 singletoninpowunion => 191.81/28.10 ( 191.81/28.10 upairset2E => 191.81/28.10 ( 191.81/28.10 upairsubunion => 191.81/28.10 ( 191.81/28.10 upairinpowunion => 191.81/28.10 ( 191.81/28.10 ubforcartprodlem1 => 191.81/28.10 ( 191.81/28.10 ubforcartprodlem2 => 191.81/28.10 ( 191.81/28.10 ubforcartprodlem3 => 191.81/28.10 ( 191.81/28.10 cartprodpairin => 191.81/28.10 ( 191.81/28.10 cartprodmempair1 => 191.81/28.10 ( 191.81/28.10 cartprodmempair => 191.81/28.10 ( 191.81/28.10 setunionE2 => 191.81/28.10 ( 191.81/28.10 setunionsingleton1 => 191.81/28.10 ( 191.81/28.10 setunionsingleton2 => 191.81/28.10 ( 191.81/28.10 setunionsingleton => 191.81/28.10 ( 191.81/28.10 singletonprop => 191.81/28.10 ( 191.81/28.10 ex1E1 => 191.81/28.10 ( 191.81/28.10 ex1I => 191.81/28.10 ( 191.81/28.10 ex1I2 => 191.81/28.10 ( 191.81/28.10 singletonsuniq => 191.81/28.10 ( 191.81/28.10 setukpairinjL1 => 191.81/28.10 ( 191.81/28.10 kfstsingleton => 191.81/28.10 ( 191.81/28.10 theprop => 191.81/28.10 ( 191.81/28.10 kfstpairEq => 191.81/28.10 ( 191.81/28.10 cartprodfstin => 191.81/28.10 ( 191.81/28.10 setukpairinjL2 => 191.81/28.10 ( 191.81/28.10 ( 191.81/28.10 ![X4,X6, 191.81/28.10 X8,X10]: 191.81/28.10 (( 191.81/28.10 kpair( 191.81/28.10 X4,X6) = 191.81/28.10 kpair( 191.81/28.10 X8,X10)) => 191.81/28.10 (X4 = X8))) => 191.81/28.10 ( 191.81/28.10 setukpairinjR11 => 191.81/28.10 ( 191.81/28.10 setukpairinjR12 => 191.81/28.10 ( 191.81/28.10 setukpairinjR1 => 191.81/28.10 ( 191.81/28.10 upairequniteq => 191.81/28.10 ( 191.81/28.10 setukpairinjR2 => 191.81/28.10 ( 191.81/28.10 ( 191.81/28.10 ![X12, 191.81/28.10 X14,X16, 191.81/28.10 X18]: 191.81/28.10 (( 191.81/28.10 kpair( 191.81/28.10 X12,X14) = 191.81/28.10 kpair( 191.81/28.10 X16,X18)) => 191.81/28.10 (X14 = 191.81/28.10 X18))) => 191.81/28.10 ( 191.81/28.10 ksndsingleton => 191.81/28.10 ( 191.81/28.10 ksndpairEq => 191.81/28.10 ( 191.81/28.10 kpairsurjEq => 191.81/28.10 ( 191.81/28.10 cartprodsndin => 191.81/28.10 ( 191.81/28.10 cartprodpairmemEL => 191.81/28.10 ( 191.81/28.10 cartprodpairmemER => 191.81/28.10 ( 191.81/28.10 ( 191.81/28.10 ![X20, 191.81/28.10 X22,X24]: 191.81/28.10 (in( 191.81/28.10 X24,X20) => 191.81/28.10 (![X26]: 191.81/28.10 (in( 191.81/28.10 X26,X22) => 191.81/28.10 (kpair( 191.81/28.10 X24,X26) = 191.81/28.10 kpair( 191.81/28.10 X24,X26)))))) => 191.81/28.10 ( 191.81/28.10 cartprodfstpairEq => 191.81/28.10 ( 191.81/28.10 cartprodsndpairEq => 191.81/28.10 ( 191.81/28.10 cartprodpairsurjEq => 191.81/28.10 ( 191.81/28.10 dpsetconstrI => 191.81/28.10 ( 191.81/28.10 dpsetconstrSub => 191.81/28.10 ( 191.81/28.10 setOfPairsIsBReln => 191.81/28.10 ( 191.81/28.10 dpsetconstrERa => 191.81/28.10 ( 191.81/28.10 dpsetconstrEL1 => 191.81/28.10 ( 191.81/28.10 dpsetconstrEL2 => 191.81/28.10 ( 191.81/28.10 dpsetconstrER => 191.81/28.10 ( 191.81/28.10 funcImageSingleton => 191.81/28.10 ( 191.81/28.10 apProp => 191.81/28.10 ( 191.81/28.10 ( 191.81/28.10 ![X28, 191.81/28.10 X30,X32]: 191.81/28.10 (func( 191.81/28.10 X28,X30, 191.81/28.10 X32) => 191.81/28.10 (![X34]: 191.81/28.10 (in( 191.81/28.10 X34,X28) => 191.81/28.10 in( 191.81/28.10 ap( 191.81/28.10 X28,X30, 191.81/28.10 X32,X34), 191.81/28.10 X30))))) => 191.81/28.10 ( 191.81/28.10 ( 191.81/28.10 ![X36, 191.81/28.10 X38,X40]: 191.81/28.10 (in( 191.81/28.10 X40, 191.81/28.10 funcSet( 191.81/28.10 X36,X38)) => 191.81/28.10 func( 191.81/28.10 X36,X38, 191.81/28.10 X40))) => 191.81/28.10 ( 191.81/28.10 ( 191.81/28.10 ![X42, 191.81/28.10 X44,X46]: 191.81/28.10 (in( 191.81/28.10 X46, 191.81/28.10 funcSet( 191.81/28.10 X42,X44)) => 191.81/28.10 (![X48]: 191.81/28.10 (in( 191.81/28.10 X48,X42) => 191.81/28.10 in( 191.81/28.10 ap( 191.81/28.10 X42,X44, 191.81/28.10 X46,X48), 191.81/28.10 X44))))) => 191.81/28.10 ( 191.81/28.10 ( 191.81/28.10 ![X50, 191.81/28.10 X52,X54]: 191.81/28.10 (func( 191.81/28.10 X50,X52, 191.81/28.10 X54) => 191.81/28.10 in( 191.81/28.10 X54, 191.81/28.10 funcSet( 191.81/28.10 X50,X52)))) => 191.81/28.10 ( 191.81/28.10 lamProp => 191.81/28.10 ( 191.81/28.10 lamp => 191.81/28.10 ( 191.81/28.10 lam2p => 191.81/28.10 ( 191.81/28.10 brelnall1 => 191.81/28.10 ( 191.81/28.10 brelnall2 => 191.81/28.10 ( 191.81/28.10 ex1E2 => 191.81/28.10 ( 191.81/28.10 ( 191.81/28.10 ![X56, 191.81/28.10 X58,X60]: 191.81/28.10 (func( 191.81/28.10 X56,X58, 191.81/28.10 X60) => 191.81/28.10 (![X62]: 191.81/28.10 (in( 191.81/28.10 X62,X56) => 191.81/28.10 in( 191.81/28.10 kpair( 191.81/28.10 X62, 191.81/28.10 ap( 191.81/28.10 X56,X58, 191.81/28.10 X60,X62)), 191.81/28.10 X60))))) => 191.81/28.10 ( 191.81/28.10 ( 191.81/28.10 ![X64, 191.81/28.10 X66,X68]: 191.81/28.10 (in( 191.81/28.10 X68, 191.81/28.10 funcSet( 191.81/28.10 X64,X66)) => 191.81/28.10 (![X70]: 191.81/28.10 (in( 191.81/28.10 X70,X64) => 191.81/28.10 in( 191.81/28.10 kpair( 191.81/28.10 X70, 191.81/28.10 ap( 191.81/28.10 X64,X66, 191.81/28.10 X68,X70)), 191.81/28.10 X68))))) => 191.81/28.10 ( 191.81/28.10 ( 191.81/28.10 ![X72, 191.81/28.10 X74,X76]: 191.81/28.10 (func( 191.81/28.10 X72,X74, 191.81/28.10 X76) => 191.81/28.10 (![X78]: 191.81/28.10 (in( 191.81/28.10 X78,X72) => 191.81/28.10 (![X80]: 191.81/28.10 (in( 191.81/28.10 X80,X74) => 191.81/28.10 (in( 191.81/28.10 kpair( 191.81/28.10 X78,X80), 191.81/28.10 X76) => 191.81/28.10 (ap( 191.81/28.10 X72,X74, 191.81/28.10 X76,X78) = 191.81/28.10 X80)))))))) => 191.81/28.10 ( 191.81/28.10 ( 191.81/28.10 ![X82, 191.81/28.10 X84,X86]: 191.81/28.10 (func( 191.81/28.10 X82,X84, 191.81/28.10 X86) => 191.81/28.10 (![X88]: 191.81/28.10 (func( 191.81/28.10 X82,X84, 191.81/28.10 X88) => 191.81/28.10 (( 191.81/28.10 ![X90]: 191.81/28.10 (in( 191.81/28.10 X90,X82) => 191.81/28.10 (ap( 191.81/28.10 X82,X84, 191.81/28.10 X86,X90) = 191.81/28.10 ap( 191.81/28.10 X82,X84, 191.81/28.10 X88,X90)))) => 191.81/28.10 (![X92]: 191.81/28.10 (in( 191.81/28.10 X92,X82) => 191.81/28.10 (![X94]: 191.81/28.10 (in( 191.81/28.10 X94,X84) => 191.81/28.10 (in( 191.81/28.10 kpair( 191.81/28.10 X92,X94), 191.81/28.10 X88) => 191.81/28.10 in( 191.81/28.10 kpair( 191.81/28.10 X92,X94), 191.81/28.10 X86))))))))))) => 191.81/28.10 ( 191.81/28.10 ![X96, 191.81/28.10 X98,X100]: 191.81/28.10 (in( 191.81/28.10 X100, 191.81/28.10 funcSet( 191.81/28.10 X96,X98)) => 191.81/28.10 (![X102]: 191.81/28.10 (in( 191.81/28.10 X102,X96) => 191.81/28.10 (![X104]: 191.81/28.10 (in( 191.81/28.10 X104,X98) => 191.81/28.10 (in( 191.81/28.10 kpair( 191.81/28.10 X102,X104), 191.81/28.10 X100) => 191.81/28.10 (ap( 191.81/28.10 X96,X98, 191.81/28.10 X100,X102) = 191.81/28.10 X104))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 191.81/28.10 tff(zf_stmt_1, negated_conjecture, 191.81/28.10 (~ 191.81/28.10 (setextAx => 191.81/28.10 (emptysetAx => 191.81/28.10 (setadjoinAx => 191.81/28.10 (powersetAx => 191.81/28.10 (setunionAx => 191.81/28.10 (omega0Ax => 191.81/28.10 (omegaSAx => 191.81/28.10 (omegaIndAx => 191.81/28.10 (replAx => 191.81/28.10 (foundationAx => 191.81/28.10 (wellorderingAx => 191.81/28.10 (descrp => 191.81/28.10 (dsetconstrI => 191.81/28.10 (dsetconstrEL => 191.81/28.10 (dsetconstrER => 191.81/28.10 (exuE1 => 191.81/28.10 (prop2setE => 191.81/28.10 (emptysetE => 191.81/28.10 (emptysetimpfalse => 191.81/28.10 (notinemptyset => 191.81/28.10 (exuE3e => 191.81/28.10 (setext => 191.81/28.10 (emptyI => 191.81/28.10 (noeltsimpempty => 191.81/28.10 (setbeta => 191.81/28.10 (nonemptyE1 => 191.81/28.10 (nonemptyI => 191.81/28.10 (nonemptyI1 => 191.81/28.10 (setadjoinIL => 191.81/28.10 (emptyinunitempty => 191.81/28.10 (setadjoinIR => 191.81/28.10 (setadjoinE => 191.81/28.10 (setadjoinOr => 191.81/28.10 (setoftrueEq => 191.81/28.10 (powersetI => 191.81/28.10 (emptyinPowerset => 191.81/28.10 (emptyInPowerset => 191.81/28.10 (powersetE => 191.81/28.10 (setunionI => 191.81/28.10 (setunionE => 191.81/28.10 (subPowSU => 191.81/28.10 (exuE2 => 191.81/28.10 (nonemptyImpWitness => 191.81/28.10 (uniqinunit => 191.81/28.10 (notinsingleton => 191.81/28.10 (eqinunit => 191.81/28.10 (singletonsswitch => 191.81/28.10 (upairsetE => 191.81/28.10 (upairsetIL => 191.81/28.10 (upairsetIR => 191.81/28.10 (emptyE1 => 191.81/28.10 (vacuousDall => 191.81/28.10 (quantDeMorgan1 => 191.81/28.10 (quantDeMorgan2 => 191.81/28.10 (quantDeMorgan3 => 191.81/28.10 (quantDeMorgan4 => 191.81/28.10 (prop2setI => 191.81/28.10 (prop2set2propI => 191.81/28.10 (notdexE => 191.81/28.10 (notdallE => 191.81/28.10 (exuI1 => 191.81/28.10 (exuI3 => 191.81/28.10 (exuI2 => 191.81/28.10 (inCongP => 191.81/28.10 ( 191.81/28.10 in__Cong => 191.81/28.10 ( 191.81/28.10 exuE3u => 191.81/28.10 ( 191.81/28.10 exu__Cong => 191.81/28.10 ( 191.81/28.10 emptyset__Cong => 191.81/28.10 ( 191.81/28.10 setadjoin__Cong => 191.81/28.10 ( 191.81/28.10 powerset__Cong => 191.81/28.10 ( 191.81/28.10 setunion__Cong => 191.81/28.10 ( 191.81/28.10 omega__Cong => 191.81/28.10 ( 191.81/28.10 exuEu => 191.81/28.10 ( 191.81/28.10 descr__Cong => 191.81/28.10 ( 191.81/28.10 dsetconstr__Cong => 191.81/28.10 ( 191.81/28.10 subsetI1 => 191.81/28.10 ( 191.81/28.10 eqimpsubset2 => 191.81/28.10 ( 191.81/28.10 eqimpsubset1 => 191.81/28.10 ( 191.81/28.10 subsetI2 => 191.81/28.10 ( 191.81/28.10 emptysetsubset => 191.81/28.10 ( 191.81/28.10 subsetE => 191.81/28.10 ( 191.81/28.10 subsetE2 => 191.81/28.10 ( 191.81/28.10 notsubsetI => 191.81/28.10 ( 191.81/28.10 notequalI1 => 191.81/28.10 ( 191.81/28.10 notequalI2 => 191.81/28.10 ( 191.81/28.10 subsetRefl => 191.81/28.10 ( 191.81/28.10 subsetTrans => 191.81/28.10 ( 191.81/28.10 setadjoinSub => 191.81/28.10 ( 191.81/28.10 setadjoinSub2 => 191.81/28.10 ( 191.81/28.10 subset2powerset => 191.81/28.10 ( 191.81/28.10 setextsub => 191.81/28.10 ( 191.81/28.10 subsetemptysetimpeq => 191.81/28.10 ( 191.81/28.10 powersetI1 => 191.81/28.10 ( 191.81/28.10 powersetE1 => 191.81/28.10 ( 191.81/28.10 inPowerset => 191.81/28.10 ( 191.81/28.10 powersetsubset => 191.81/28.10 ( 191.81/28.10 sepInPowerset => 191.81/28.10 ( 191.81/28.10 sepSubset => 191.81/28.10 ( 191.81/28.10 binunionIL => 191.81/28.10 ( 191.81/28.10 upairset2IR => 191.81/28.10 ( 191.81/28.10 binunionIR => 191.81/28.10 ( 191.81/28.10 binunionEcases => 191.81/28.10 ( 191.81/28.10 binunionE => 191.81/28.10 ( 191.81/28.10 binunionLsub => 191.81/28.10 ( 191.81/28.10 binunionRsub => 191.81/28.10 ( 191.81/28.10 binintersectI => 191.81/28.10 ( 191.81/28.10 binintersectSubset5 => 191.81/28.10 ( 191.81/28.10 binintersectEL => 191.81/28.10 ( 191.81/28.10 binintersectLsub => 191.81/28.10 ( 191.81/28.10 binintersectSubset2 => 191.81/28.10 ( 191.81/28.10 binintersectSubset3 => 191.81/28.10 ( 191.81/28.10 binintersectER => 191.81/28.10 ( 191.81/28.10 disjointsetsI1 => 191.81/28.10 ( 191.81/28.10 binintersectRsub => 191.81/28.10 ( 191.81/28.10 binintersectSubset4 => 191.81/28.10 ( 191.81/28.10 binintersectSubset1 => 191.81/28.10 ( 191.81/28.10 bs114d => 191.81/28.10 ( 191.81/28.10 setminusI => 191.81/28.10 ( 191.81/28.10 setminusEL => 191.81/28.10 ( 191.81/28.10 setminusER => 191.81/28.10 ( 191.81/28.10 setminusSubset2 => 191.81/28.10 ( 191.81/28.10 setminusERneg => 191.81/28.10 ( 191.81/28.10 setminusELneg => 191.81/28.10 ( 191.81/28.10 setminusILneg => 191.81/28.10 ( 191.81/28.10 setminusIRneg => 191.81/28.10 ( 191.81/28.10 setminusLsub => 191.81/28.10 ( 191.81/28.10 setminusSubset1 => 191.81/28.10 ( 191.81/28.10 symdiffE => 191.81/28.10 ( 191.81/28.10 symdiffI1 => 191.81/28.10 ( 191.81/28.10 symdiffI2 => 191.81/28.10 ( 191.81/28.10 symdiffIneg1 => 191.81/28.10 ( 191.81/28.10 symdiffIneg2 => 191.81/28.10 ( 191.81/28.10 secondinupair => 191.81/28.10 ( 191.81/28.10 setukpairIL => 191.81/28.10 ( 191.81/28.10 setukpairIR => 191.81/28.10 ( 191.81/28.10 kpairiskpair => 191.81/28.10 ( 191.81/28.10 kpairp => 191.81/28.10 ( 191.81/28.10 singletonsubset => 191.81/28.10 ( 191.81/28.10 singletoninpowerset => 191.81/28.10 ( 191.81/28.10 singletoninpowunion => 191.81/28.10 ( 191.81/28.10 upairset2E => 191.81/28.10 ( 191.81/28.10 upairsubunion => 191.81/28.10 ( 191.81/28.10 upairinpowunion => 191.81/28.10 ( 191.81/28.10 ubforcartprodlem1 => 191.81/28.10 ( 191.81/28.10 ubforcartprodlem2 => 191.81/28.10 ( 191.81/28.10 ubforcartprodlem3 => 191.81/28.10 ( 191.81/28.10 cartprodpairin => 191.81/28.10 ( 191.81/28.10 cartprodmempair1 => 191.81/28.10 ( 191.81/28.10 cartprodmempair => 191.81/28.10 ( 191.81/28.10 setunionE2 => 191.81/28.10 ( 191.81/28.10 setunionsingleton1 => 191.81/28.10 ( 191.81/28.10 setunionsingleton2 => 191.81/28.10 ( 191.81/28.10 setunionsingleton => 191.81/28.10 ( 191.81/28.10 singletonprop => 191.81/28.10 ( 191.81/28.10 ex1E1 => 191.81/28.10 ( 191.81/28.10 ex1I => 191.81/28.10 ( 191.81/28.10 ex1I2 => 191.81/28.10 ( 191.81/28.10 singletonsuniq => 191.81/28.10 ( 191.81/28.10 setukpairinjL1 => 191.81/28.10 ( 191.81/28.10 kfstsingleton => 191.81/28.10 ( 191.81/28.10 theprop => 191.81/28.10 ( 191.81/28.10 kfstpairEq => 191.81/28.10 ( 191.81/28.10 cartprodfstin => 191.81/28.10 ( 191.81/28.10 setukpairinjL2 => 191.81/28.10 ( 191.81/28.10 ( 191.81/28.10 ![X4,X6, 191.81/28.10 X8,X10]: 191.81/28.10 (( 191.81/28.10 kpair( 191.81/28.10 X4,X6) = 191.81/28.10 kpair( 191.81/28.10 X8,X10)) => 191.81/28.10 (X4 = X8))) => 191.81/28.10 ( 191.81/28.10 setukpairinjR11 => 191.81/28.10 ( 191.81/28.10 setukpairinjR12 => 191.81/28.10 ( 191.81/28.10 setukpairinjR1 => 191.81/28.10 ( 191.81/28.10 upairequniteq => 191.81/28.10 ( 191.81/28.10 setukpairinjR2 => 191.81/28.10 ( 191.81/28.10 ( 191.81/28.10 ![X12, 191.81/28.10 X14,X16, 191.81/28.10 X18]: 191.81/28.10 (( 191.81/28.10 kpair( 191.81/28.10 X12,X14) = 191.81/28.10 kpair( 191.81/28.10 X16,X18)) => 191.81/28.10 (X14 = 191.81/28.10 X18))) => 191.81/28.10 ( 191.81/28.10 ksndsingleton => 191.81/28.10 ( 191.81/28.10 ksndpairEq => 191.81/28.10 ( 191.81/28.10 kpairsurjEq => 191.81/28.10 ( 191.81/28.10 cartprodsndin => 191.81/28.10 ( 191.81/28.10 cartprodpairmemEL => 191.81/28.10 ( 191.81/28.10 cartprodpairmemER => 191.81/28.10 ( 191.81/28.10 ( 191.81/28.10 ![X20, 191.81/28.10 X22,X24]: 191.81/28.10 (in( 191.81/28.10 X24,X20) => 191.81/28.10 (![X26]: 191.81/28.10 (in( 191.81/28.10 X26,X22) => 191.81/28.10 (kpair( 191.81/28.10 X24,X26) = 191.81/28.10 kpair( 191.81/28.10 X24,X26)))))) => 191.81/28.10 ( 191.81/28.10 cartprodfstpairEq => 191.81/28.10 ( 191.81/28.10 cartprodsndpairEq => 191.81/28.10 ( 191.81/28.10 cartprodpairsurjEq => 191.81/28.10 ( 191.81/28.10 dpsetconstrI => 191.81/28.10 ( 191.81/28.10 dpsetconstrSub => 191.81/28.10 ( 191.81/28.10 setOfPairsIsBReln => 191.81/28.10 ( 191.81/28.10 dpsetconstrERa => 191.81/28.10 ( 191.81/28.10 dpsetconstrEL1 => 191.81/28.10 ( 191.81/28.10 dpsetconstrEL2 => 191.81/28.10 ( 191.81/28.10 dpsetconstrER => 191.81/28.10 ( 191.81/28.10 funcImageSingleton => 191.81/28.10 ( 191.81/28.10 apProp => 191.81/28.10 ( 191.81/28.10 ( 191.81/28.10 ![X28, 191.81/28.10 X30,X32]: 191.81/28.10 (func( 191.81/28.10 X28,X30, 191.81/28.10 X32) => 191.81/28.10 (![X34]: 191.81/28.10 (in( 191.81/28.10 X34,X28) => 191.81/28.10 in( 191.81/28.10 ap( 191.81/28.10 X28,X30, 191.81/28.10 X32,X34), 191.81/28.10 X30))))) => 191.81/28.10 ( 191.81/28.10 ( 191.81/28.10 ![X36, 191.81/28.10 X38,X40]: 191.81/28.10 (in( 191.81/28.10 X40, 191.81/28.10 funcSet( 191.81/28.10 X36,X38)) => 191.81/28.10 func( 191.81/28.10 X36,X38, 191.81/28.10 X40))) => 191.81/28.10 ( 191.81/28.10 ( 191.81/28.10 ![X42, 191.81/28.10 X44,X46]: 191.81/28.10 (in( 191.81/28.10 X46, 191.81/28.10 funcSet( 191.81/28.10 X42,X44)) => 191.81/28.10 (![X48]: 191.81/28.10 (in( 191.81/28.10 X48,X42) => 191.81/28.10 in( 191.81/28.10 ap( 191.81/28.10 X42,X44, 191.81/28.10 X46,X48), 191.81/28.10 X44))))) => 191.81/28.10 ( 191.81/28.10 ( 191.81/28.10 ![X50, 191.81/28.10 X52,X54]: 191.81/28.10 (func( 191.81/28.10 X50,X52, 191.81/28.10 X54) => 191.81/28.10 in( 191.81/28.10 X54, 191.81/28.10 funcSet( 191.81/28.10 X50,X52)))) => 191.81/28.10 ( 191.81/28.10 lamProp => 191.81/28.10 ( 191.81/28.10 lamp => 191.81/28.10 ( 191.81/28.10 lam2p => 191.81/28.10 ( 191.81/28.10 brelnall1 => 191.81/28.10 ( 191.81/28.10 brelnall2 => 191.81/28.10 ( 191.81/28.10 ex1E2 => 191.81/28.10 ( 191.81/28.10 ( 191.81/28.10 ![X56, 191.81/28.10 X58,X60]: 191.81/28.10 (func( 191.81/28.10 X56,X58, 191.81/28.10 X60) => 191.81/28.10 (![X62]: 191.81/28.10 (in( 191.81/28.10 X62,X56) => 191.81/28.10 in( 191.81/28.10 kpair( 191.81/28.10 X62, 191.81/28.10 ap( 191.81/28.10 X56,X58, 191.81/28.10 X60,X62)), 191.81/28.10 X60))))) => 191.81/28.10 ( 191.81/28.10 ( 191.81/28.10 ![X64, 191.81/28.10 X66,X68]: 191.81/28.10 (in( 191.81/28.10 X68, 191.81/28.10 funcSet( 191.81/28.10 X64,X66)) => 191.81/28.10 (![X70]: 191.81/28.10 (in( 191.81/28.10 X70,X64) => 191.81/28.10 in( 191.81/28.10 kpair( 191.81/28.10 X70, 191.81/28.10 ap( 191.81/28.10 X64,X66, 191.81/28.10 X68,X70)), 191.81/28.10 X68))))) => 191.81/28.10 ( 191.81/28.10 ( 191.81/28.10 ![X72, 191.81/28.10 X74,X76]: 191.81/28.10 (func( 191.81/28.10 X72,X74, 191.81/28.10 X76) => 191.81/28.10 (![X78]: 191.81/28.10 (in( 191.81/28.10 X78,X72) => 191.81/28.10 (![X80]: 191.81/28.10 (in( 191.81/28.10 X80,X74) => 191.81/28.10 (in( 191.81/28.10 kpair( 191.81/28.10 X78,X80), 191.81/28.10 X76) => 191.81/28.10 (ap( 191.81/28.10 X72,X74, 191.81/28.10 X76,X78) = 191.81/28.10 X80)))))))) => 191.81/28.10 ( 191.81/28.10 ( 191.81/28.10 ![X82, 191.81/28.10 X84,X86]: 191.81/28.10 (func( 191.81/28.10 X82,X84, 191.81/28.10 X86) => 191.81/28.10 (![X88]: 191.81/28.10 (func( 191.81/28.10 X82,X84, 191.81/28.10 X88) => 191.81/28.10 (( 191.81/28.10 ![X90]: 191.81/28.10 (in( 191.81/28.10 X90,X82) => 191.81/28.10 (ap( 191.81/28.10 X82,X84, 191.81/28.10 X86,X90) = 191.81/28.10 ap( 191.81/28.10 X82,X84, 191.81/28.10 X88,X90)))) => 191.81/28.10 (![X92]: 191.81/28.10 (in( 191.81/28.10 X92,X82) => 191.81/28.10 (![X94]: 191.81/28.10 (in( 191.81/28.10 X94,X84) => 191.81/28.10 (in( 191.81/28.10 kpair( 191.81/28.10 X92,X94), 191.81/28.10 X88) => 191.81/28.10 in( 191.81/28.10 kpair( 191.81/28.10 X92,X94), 191.81/28.10 X86))))))))))) => 191.81/28.10 ( 191.81/28.10 ![X96, 191.81/28.10 X98,X100]: 191.81/28.10 (in( 191.81/28.10 X100, 191.81/28.10 funcSet( 191.81/28.10 X96,X98)) => 191.81/28.10 (![X102]: 191.81/28.10 (in( 191.81/28.10 X102,X96) => 191.81/28.10 (![X104]: 191.81/28.10 (in( 191.81/28.10 X104,X98) => 191.81/28.10 (in( 191.81/28.10 kpair( 191.81/28.10 X102,X104), 191.81/28.10 X100) => 191.81/28.10 (ap( 191.81/28.10 X96,X98, 191.81/28.10 X100,X102) = 191.81/28.10 X104)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 191.81/28.10 tff('11', plain, in(sk_X100, funcSet(sk_X96, sk_X98)), 191.81/28.10 inference('cnf', [status(esa)], [zf_stmt_1])). 191.81/28.10 tff('12', plain, 191.81/28.10 ![X84, X85, X86]: ( func(X84, X85, X86) | ~ in(X86, funcSet(X84, X85))), 191.81/28.10 inference('cnf', [status(esa)], [zf_stmt_1])). 191.81/28.10 tff('13', plain, func(sk_X96, sk_X98, sk_X100), 191.81/28.10 inference('sup-', [status(thm)], ['11', '12'])). 191.81/28.10 tff('14', plain, in(kpair(sk_X102, sk_X104), sk_X100), 191.81/28.10 inference('cnf', [status(esa)], [zf_stmt_1])). 191.81/28.10 tff('15', plain, 191.81/28.10 ![X66, X67, X68, X69, X70]: 191.81/28.10 (~ in(X66, X67) 191.81/28.10 | ~ in(kpair(X66, X68), X69) 191.81/28.10 | ap(X67, X70, X69, X66) = X68 191.81/28.10 | ~ in(X68, X70) 191.81/28.10 | ~ func(X67, X70, X69)), 191.81/28.10 inference('cnf', [status(esa)], [zf_stmt_1])). 191.81/28.10 tff('16', plain, 191.81/28.10 ![X0, X1]: 191.81/28.10 (~ func(X1, X0, sk_X100) 191.81/28.10 | ~ in(sk_X104, X0) 191.81/28.10 | ap(X1, X0, sk_X100, sk_X102) = sk_X104 191.81/28.10 | ~ in(sk_X102, X1)), 191.81/28.10 inference('sup-', [status(thm)], ['14', '15'])). 191.81/28.10 tff('17', plain, 191.81/28.10 (~ in(sk_X102, sk_X96) 191.81/28.10 | ap(sk_X96, sk_X98, sk_X100, sk_X102) = sk_X104 191.81/28.10 | ~ in(sk_X104, sk_X98)), 191.81/28.10 inference('sup-', [status(thm)], ['13', '16'])). 191.81/28.10 tff('18', plain, in(sk_X102, sk_X96), 191.81/28.10 inference('cnf', [status(esa)], [zf_stmt_1])). 191.81/28.10 tff('19', plain, in(sk_X104, sk_X98), 191.81/28.10 inference('cnf', [status(esa)], [zf_stmt_1])). 191.81/28.10 tff('20', plain, ap(sk_X96, sk_X98, sk_X100, sk_X102) = sk_X104, 191.81/28.10 inference('demod', [status(thm)], ['17', '18', '19'])). 191.81/28.10 tff('21', plain, ap(sk_X96, sk_X98, sk_X100, sk_X102) != sk_X104, 191.81/28.10 inference('cnf', [status(esa)], [zf_stmt_1])). 191.81/28.10 tff('22', plain, $false, 191.81/28.10 inference('simplify_reflect-', [status(thm)], ['20', '21'])). 191.81/28.10 191.81/28.10 % SZS output end Refutation 191.81/28.10 191.81/28.10 191.81/28.10 % Terminating... 192.57/28.21 % Runner terminated. 192.57/28.22 % Zipperpin 1.5 exiting 192.57/28.22 EOF