0.02/0.09 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.02/0.12 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.1ZaiBOux6G true 0.11/0.32 % Computer : n005.cluster.edu 0.11/0.32 % Model : x86_64 x86_64 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.32 % Memory : 8042.1875MB 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.32 % CPULimit : 1200 0.11/0.32 % WCLimit : 120 0.11/0.32 % DateTime : Tue Jul 13 14:00:03 EDT 2021 0.11/0.32 % CPUTime : 0.11/0.32 % Running portfolio for 120 s 0.11/0.32 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.11/0.32 % Number of cores: 8 0.11/0.32 % Python version: Python 3.6.8 0.11/0.32 % Running in HO mode 0.17/0.58 % Total configuration time : 828 0.17/0.58 % Estimated wc time : 983 0.17/0.58 % Estimated cpu time (8 cpus) : 122.875 0.83/0.65 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 47s 0.83/0.65 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 47s 0.83/0.65 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 18s 0.83/0.65 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 53s 0.83/0.66 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 47s 0.83/0.66 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 24s 0.83/0.66 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 41s 1.24/0.70 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 35s 1.25/0.79 % Solved by lams/40_c_ic.sh. 1.25/0.79 % done 143 iterations in 0.083s 1.25/0.79 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 1.25/0.79 % SZS output start Refutation 1.25/0.79 thf(binintersectER_type, type, binintersectER: $o). 1.25/0.79 thf(setadjoinSub_type, type, setadjoinSub: $o). 1.25/0.79 thf(ex1_type, type, ex1: $i > ($i > $o) > $o). 1.25/0.79 thf(setukpairinjR2_type, type, setukpairinjR2: $o). 1.25/0.79 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o). 1.25/0.79 thf(setunion_type, type, setunion: $i > $i). 1.25/0.79 thf(vacuousDall_type, type, vacuousDall: $o). 1.25/0.79 thf(setadjoinIR_type, type, setadjoinIR: $o). 1.25/0.79 thf(omega0Ax_type, type, omega0Ax: $o). 1.25/0.79 thf(subsetE_type, type, subsetE: $o). 1.25/0.79 thf(binintersectSubset3_type, type, binintersectSubset3: $o). 1.25/0.79 thf(setminusER_type, type, setminusER: $o). 1.25/0.79 thf(binunionE_type, type, binunionE: $o). 1.25/0.79 thf(setadjoinSub2_type, type, setadjoinSub2: $o). 1.25/0.79 thf(powersetE_type, type, powersetE: $o). 1.25/0.79 thf(binunionRsub_type, type, binunionRsub: $o). 1.25/0.79 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o). 1.25/0.79 thf(powerset__Cong_type, type, powerset__Cong: $o). 1.25/0.79 thf(ksndsingleton_type, type, ksndsingleton: $o). 1.25/0.79 thf(omegaIndAx_type, type, omegaIndAx: $o). 1.25/0.79 thf(uniqinunit_type, type, uniqinunit: $o). 1.25/0.79 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o). 1.25/0.79 thf(exu__Cong_type, type, exu__Cong: $o). 1.25/0.79 thf(subset2powerset_type, type, subset2powerset: $o). 1.25/0.79 thf(setoftrueEq_type, type, setoftrueEq: $o). 1.25/0.79 thf(setukpairinjR12_type, type, setukpairinjR12: $o). 1.25/0.79 thf(upairsetIL_type, type, upairsetIL: $o). 1.25/0.79 thf(disjointsetsI1_type, type, disjointsetsI1: $o). 1.25/0.79 thf(emptyI_type, type, emptyI: $o). 1.25/0.79 thf(setukpairIL_type, type, setukpairIL: $o). 1.25/0.79 thf(setukpairinjL1_type, type, setukpairinjL1: $o). 1.25/0.79 thf(func_type, type, func: $i > $i > $i > $o). 1.25/0.79 thf(exuI3_type, type, exuI3: $o). 1.25/0.79 thf(emptysetAx_type, type, emptysetAx: $o). 1.25/0.79 thf(setukpairIR_type, type, setukpairIR: $o). 1.25/0.79 thf(emptyInPowerset_type, type, emptyInPowerset: $o). 1.25/0.79 thf(setadjoinIL_type, type, setadjoinIL: $o). 1.25/0.79 thf(upairsubunion_type, type, upairsubunion: $o). 1.25/0.79 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o). 1.25/0.79 thf(ksndpairEq_type, type, ksndpairEq: $o). 1.25/0.79 thf(emptyinunitempty_type, type, emptyinunitempty: $o). 1.25/0.79 thf(upairsetIR_type, type, upairsetIR: $o). 1.25/0.79 thf(ex1I2_type, type, ex1I2: $o). 1.25/0.79 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o). 1.25/0.79 thf(emptyset__Cong_type, type, emptyset__Cong: $o). 1.25/0.79 thf(sk__9_type, type, sk__9: $i > $i > $i > $i). 1.25/0.79 thf(ex1I_type, type, ex1I: $o). 1.25/0.79 thf(cartprodsndin_type, type, cartprodsndin: $o). 1.25/0.79 thf(setminusI_type, type, setminusI: $o). 1.25/0.79 thf(ap_type, type, ap: $i > $i > $i > $i > $i). 1.25/0.79 thf(descrp_type, type, descrp: $o). 1.25/0.79 thf(binintersectI_type, type, binintersectI: $o). 1.25/0.79 thf(nonemptyI1_type, type, nonemptyI1: $o). 1.25/0.79 thf(emptysetsubset_type, type, emptysetsubset: $o). 1.25/0.79 thf(setunionAx_type, type, setunionAx: $o). 1.25/0.79 thf(notsubsetI_type, type, notsubsetI: $o). 1.25/0.79 thf(theprop_type, type, theprop: $o). 1.25/0.79 thf(binintersectSubset5_type, type, binintersectSubset5: $o). 1.25/0.79 thf(upairset2IR_type, type, upairset2IR: $o). 1.25/0.79 thf(binunionLsub_type, type, binunionLsub: $o). 1.25/0.79 thf(subsetRefl_type, type, subsetRefl: $o). 1.25/0.79 thf(nonemptyI_type, type, nonemptyI: $o). 1.25/0.79 thf(emptysetE_type, type, emptysetE: $o). 1.25/0.79 thf(sepInPowerset_type, type, sepInPowerset: $o). 1.25/0.79 thf(upairequniteq_type, type, upairequniteq: $o). 1.25/0.79 thf(kpairsurjEq_type, type, kpairsurjEq: $o). 1.25/0.79 thf(cartprodmempair1_type, type, cartprodmempair1: $o). 1.25/0.79 thf(singletonprop_type, type, singletonprop: $o). 1.25/0.79 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o). 1.25/0.79 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o). 1.25/0.79 thf(powersetI_type, type, powersetI: $o). 1.25/0.79 thf(exuE2_type, type, exuE2: $o). 1.25/0.79 thf(setukpairinjL_type, type, setukpairinjL: $o). 1.25/0.79 thf(exuE3e_type, type, exuE3e: $o). 1.25/0.79 thf(setminusSubset1_type, type, setminusSubset1: $o). 1.25/0.79 thf(notequalI2_type, type, notequalI2: $o). 1.25/0.79 thf(descr__Cong_type, type, descr__Cong: $o). 1.25/0.79 thf(setextAx_type, type, setextAx: $o). 1.25/0.79 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o). 1.25/0.79 thf(eqinunit_type, type, eqinunit: $o). 1.25/0.79 thf(symdiffE_type, type, symdiffE: $o). 1.25/0.79 thf(upairinpowunion_type, type, upairinpowunion: $o). 1.25/0.79 thf(binintersectSubset1_type, type, binintersectSubset1: $o). 1.25/0.79 thf(powersetAx_type, type, powersetAx: $o). 1.25/0.79 thf(upairset2E_type, type, upairset2E: $o). 1.25/0.79 thf(sk__13_type, type, sk__13: $i). 1.25/0.79 thf(subsetI2_type, type, subsetI2: $o). 1.25/0.79 thf(symdiffI1_type, type, symdiffI1: $o). 1.25/0.79 thf(kpair_type, type, kpair: $i > $i > $i). 1.25/0.79 thf(setukpairinjR11_type, type, setukpairinjR11: $o). 1.25/0.79 thf(subsetI1_type, type, subsetI1: $o). 1.25/0.79 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o). 1.25/0.79 thf(breln_type, type, breln: $i > $i > $i > $o). 1.25/0.79 thf(replAx_type, type, replAx: $o). 1.25/0.79 thf(subPowSU_type, type, subPowSU: $o). 1.25/0.79 thf(funcImageSingleton_type, type, funcImageSingleton: $o). 1.25/0.79 thf(setunionE_type, type, setunionE: $o). 1.25/0.79 thf(setunionsingleton_type, type, setunionsingleton: $o). 1.25/0.79 thf(setunion__Cong_type, type, setunion__Cong: $o). 1.25/0.79 thf(bs114d_type, type, bs114d: $o). 1.25/0.79 thf(setminusSubset2_type, type, setminusSubset2: $o). 1.25/0.79 thf(powersetE1_type, type, powersetE1: $o). 1.25/0.79 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o). 1.25/0.79 thf(dpsetconstrI_type, type, dpsetconstrI: $o). 1.25/0.79 thf(omegaSAx_type, type, omegaSAx: $o). 1.25/0.79 thf(sk__10_type, type, sk__10: $i). 1.25/0.79 thf(setext_type, type, setext: $o). 1.25/0.79 thf(cartprodfstin_type, type, cartprodfstin: $o). 1.25/0.79 thf(notequalI1_type, type, notequalI1: $o). 1.25/0.79 thf(setextsub_type, type, setextsub: $o). 1.25/0.79 thf(kpairp_type, type, kpairp: $o). 1.25/0.79 thf(omega__Cong_type, type, omega__Cong: $o). 1.25/0.79 thf(symdiffI2_type, type, symdiffI2: $o). 1.25/0.79 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o). 1.25/0.79 thf(setbeta_type, type, setbeta: $o). 1.25/0.79 thf(dsetconstrER_type, type, dsetconstrER: $o). 1.25/0.79 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o). 1.25/0.79 thf(nonemptyE1_type, type, nonemptyE1: $o). 1.25/0.79 thf(binunionIL_type, type, binunionIL: $o). 1.25/0.79 thf(prop2setE_type, type, prop2setE: $o). 1.25/0.79 thf(prop2set2propI_type, type, prop2set2propI: $o). 1.25/0.79 thf(notdallE_type, type, notdallE: $o). 1.25/0.79 thf(eqimpsubset1_type, type, eqimpsubset1: $o). 1.25/0.79 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o). 1.25/0.79 thf(exuEu_type, type, exuEu: $o). 1.25/0.79 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o). 1.25/0.79 thf(singletoninpowerset_type, type, singletoninpowerset: $o). 1.25/0.79 thf(notinsingleton_type, type, notinsingleton: $o). 1.25/0.79 thf(upairsetE_type, type, upairsetE: $o). 1.25/0.79 thf(emptyE1_type, type, emptyE1: $o). 1.25/0.79 thf(emptyinPowerset_type, type, emptyinPowerset: $o). 1.25/0.79 thf(cartprodmempair_type, type, cartprodmempair: $o). 1.25/0.79 thf(binunionEcases_type, type, binunionEcases: $o). 1.25/0.79 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o). 1.25/0.79 thf(symdiffIneg1_type, type, symdiffIneg1: $o). 1.25/0.79 thf(binintersectSubset4_type, type, binintersectSubset4: $o). 1.25/0.79 thf(wellorderingAx_type, type, wellorderingAx: $o). 1.25/0.79 thf(singletoninpowunion_type, type, singletoninpowunion: $o). 1.25/0.79 thf(binintersectLsub_type, type, binintersectLsub: $o). 1.25/0.79 thf(binintersectRsub_type, type, binintersectRsub: $o). 1.25/0.79 thf(powersetsubset_type, type, powersetsubset: $o). 1.25/0.79 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o). 1.25/0.79 thf(noeltsimpempty_type, type, noeltsimpempty: $o). 1.25/0.79 thf(exuE1_type, type, exuE1: $o). 1.25/0.79 thf(inPowerset_type, type, inPowerset: $o). 1.25/0.79 thf(dpsetconstrER_type, type, dpsetconstrER: $o). 1.25/0.79 thf(in_type, type, in: $i > $i > $o). 1.25/0.79 thf(cartprodpairin_type, type, cartprodpairin: $o). 1.25/0.79 thf(setunionI_type, type, setunionI: $o). 1.25/0.79 thf(in__Cong_type, type, in__Cong: $o). 1.25/0.79 thf(setadjoinE_type, type, setadjoinE: $o). 1.25/0.79 thf(subsetTrans_type, type, subsetTrans: $o). 1.25/0.79 thf(dsetconstrEL_type, type, dsetconstrEL: $o). 1.25/0.79 thf(sk__11_type, type, sk__11: $i). 1.25/0.79 thf(symdiffIneg2_type, type, symdiffIneg2: $o). 1.25/0.79 thf(setminusIRneg_type, type, setminusIRneg: $o). 1.25/0.79 thf(setminusELneg_type, type, setminusELneg: $o). 1.25/0.79 thf(foundationAx_type, type, foundationAx: $o). 1.25/0.79 thf(sepSubset_type, type, sepSubset: $o). 1.25/0.79 thf(exuE3u_type, type, exuE3u: $o). 1.25/0.79 thf(kpairiskpair_type, type, kpairiskpair: $o). 1.25/0.79 thf(setadjoinOr_type, type, setadjoinOr: $o). 1.25/0.79 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o). 1.25/0.79 thf(apProp_type, type, apProp: $o). 1.25/0.79 thf(exuI1_type, type, exuI1: $o). 1.25/0.79 thf(kfstsingleton_type, type, kfstsingleton: $o). 1.25/0.79 thf(setukpairinjL2_type, type, setukpairinjL2: $o). 1.25/0.79 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o). 1.25/0.79 thf(binunionIR_type, type, binunionIR: $o). 1.25/0.79 thf(inCongP_type, type, inCongP: $o). 1.25/0.79 thf(setminusLsub_type, type, setminusLsub: $o). 1.25/0.79 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o). 1.25/0.79 thf(binintersectSubset2_type, type, binintersectSubset2: $o). 1.25/0.79 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o). 1.25/0.79 thf(eqimpsubset2_type, type, eqimpsubset2: $o). 1.25/0.79 thf(setukpairinjR1_type, type, setukpairinjR1: $o). 1.25/0.79 thf(setminusERneg_type, type, setminusERneg: $o). 1.25/0.79 thf(exuI2_type, type, exuI2: $o). 1.25/0.79 thf(powersetI1_type, type, powersetI1: $o). 1.25/0.79 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o). 1.25/0.79 thf(kfstpairEq_type, type, kfstpairEq: $o). 1.25/0.79 thf(setunionsingleton1_type, type, setunionsingleton1: $o). 1.25/0.79 thf(setminusILneg_type, type, setminusILneg: $o). 1.25/0.79 thf(dsetconstrI_type, type, dsetconstrI: $o). 1.25/0.79 thf(setminusEL_type, type, setminusEL: $o). 1.25/0.79 thf(singletonsubset_type, type, singletonsubset: $o). 1.25/0.79 thf(setukpairinjR_type, type, setukpairinjR: $o). 1.25/0.79 thf(secondinupair_type, type, secondinupair: $o). 1.25/0.79 thf(ex1E1_type, type, ex1E1: $o). 1.25/0.79 thf(singletonsuniq_type, type, singletonsuniq: $o). 1.25/0.79 thf(dsetconstr_type, type, dsetconstr: $i > ($i > $o) > $i). 1.25/0.79 thf(sk__12_type, type, sk__12: $i). 1.25/0.79 thf(subsetE2_type, type, subsetE2: $o). 1.25/0.79 thf(singletonsswitch_type, type, singletonsswitch: $o). 1.25/0.79 thf(singleton_type, type, singleton: $i > $o). 1.25/0.79 thf(binintersectEL_type, type, binintersectEL: $o). 1.25/0.79 thf(setadjoinAx_type, type, setadjoinAx: $o). 1.25/0.79 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o). 1.25/0.79 thf(notinemptyset_type, type, notinemptyset: $o). 1.25/0.79 thf(prop2setI_type, type, prop2setI: $o). 1.25/0.79 thf(setunionsingleton2_type, type, setunionsingleton2: $o). 1.25/0.79 thf(setunionE2_type, type, setunionE2: $o). 1.25/0.79 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o). 1.25/0.79 thf(notdexE_type, type, notdexE: $o). 1.25/0.79 thf(ap, axiom,(( ap ) = 1.25/0.79 (^[A:$i,B:$i,Xf:$i,Xx:$i]: 1.25/0.79 ( setunion @ 1.25/0.79 ( dsetconstr @ B @ ( ^[Xy:$i]: ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) )))). 1.25/0.79 thf('0', plain, 1.25/0.79 (( ap ) = 1.25/0.79 ( ^[A:$i,B:$i,Xf:$i,Xx:$i]: 1.25/0.79 ( setunion @ 1.25/0.79 ( dsetconstr @ B @ ( ^[Xy:$i]: ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) )), 1.25/0.79 inference('simplify_rw_rule', [status(thm)], [ap])). 1.25/0.79 thf('1', plain, 1.25/0.79 (( ap ) = 1.25/0.79 ( ^[V_1:$i,V_2:$i,V_3:$i,V_4:$i]: 1.25/0.79 ( setunion @ 1.25/0.79 ( dsetconstr @ 1.25/0.79 V_2 @ ( ^[V_5:$i]: ( in @ ( kpair @ V_4 @ V_5 ) @ V_3 ) ) ) ) )), 1.25/0.79 define([status(thm)])). 1.25/0.79 thf(apProp, axiom, apProp = 1.25/0.79 (![A:$i,B:$i,Xf:$i]: 1.25/0.79 ( ( func @ A @ B @ Xf ) => 1.25/0.79 ( ![Xx:$i]: 1.25/0.79 ( ( in @ Xx @ A ) => 1.25/0.79 ( in @ 1.25/0.79 ( setunion @ 1.25/0.79 ( dsetconstr @ 1.25/0.79 B @ ( ^[Xy:$i]: ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) @ 1.25/0.79 B ) ) ) ))). 1.25/0.79 thf('2', plain, 1.25/0.79 (( apProp ) = 1.25/0.79 ( ![X4:$i,X6:$i,X8:$i]: 1.25/0.79 ( ( func @ X4 @ X6 @ X8 ) => 1.25/0.79 ( ![X10:$i]: 1.25/0.79 ( ( in @ X10 @ X4 ) => 1.25/0.79 ( in @ 1.25/0.79 ( setunion @ 1.25/0.79 ( dsetconstr @ 1.25/0.79 X6 @ ( ^[V_1:$i]: ( in @ ( kpair @ X10 @ V_1 ) @ X8 ) ) ) ) @ 1.25/0.79 X6 ) ) ) ) )), 1.25/0.79 define([status(thm)])). 1.25/0.79 thf(funcImageSingleton, axiom, funcImageSingleton = 1.25/0.79 (![A:$i,B:$i,Xf:$i]: 1.25/0.79 ( ( func @ A @ B @ Xf ) => 1.25/0.79 ( ![Xx:$i]: 1.25/0.79 ( ( in @ Xx @ A ) => 1.25/0.79 ( singleton @ 1.25/0.79 ( dsetconstr @ B @ ( ^[Xy:$i]: ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ))). 1.25/0.79 thf('3', plain, 1.25/0.79 (( funcImageSingleton ) = 1.25/0.79 ( ![X4:$i,X6:$i,X8:$i]: 1.25/0.79 ( ( func @ X4 @ X6 @ X8 ) => 1.25/0.79 ( ![X10:$i]: 1.25/0.79 ( ( in @ X10 @ X4 ) => 1.25/0.79 ( singleton @ 1.25/0.79 ( dsetconstr @ 1.25/0.79 X6 @ ( ^[V_1:$i]: ( in @ ( kpair @ X10 @ V_1 ) @ X8 ) ) ) ) ) ) ) )), 1.25/0.79 define([status(thm)])). 1.25/0.79 thf(func, axiom,(( func ) = 1.25/0.79 (^[A:$i,B:$i,R:$i]: 1.25/0.79 ( ( breln @ A @ B @ R ) & 1.25/0.79 ( ![Xx:$i]: 1.25/0.79 ( ( in @ Xx @ A ) => 1.25/0.79 ( ex1 @ B @ ( ^[Xy:$i]: ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) )))). 1.25/0.79 thf('4', plain, 1.25/0.79 (( func ) = 1.25/0.79 ( ^[A:$i,B:$i,R:$i]: 1.25/0.79 ( ( breln @ A @ B @ R ) & 1.25/0.79 ( ![Xx:$i]: 1.25/0.79 ( ( in @ Xx @ A ) => 1.25/0.79 ( ex1 @ B @ ( ^[Xy:$i]: ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) )), 1.25/0.79 inference('simplify_rw_rule', [status(thm)], [func])). 1.25/0.79 thf('5', plain, 1.25/0.79 (( func ) = 1.25/0.79 ( ^[V_1:$i,V_2:$i,V_3:$i]: 1.25/0.79 ( ( breln @ V_1 @ V_2 @ V_3 ) & 1.25/0.79 ( ![X4:$i]: 1.25/0.79 ( ( in @ X4 @ V_1 ) => 1.25/0.79 ( ex1 @ V_2 @ ( ^[V_4:$i]: ( in @ ( kpair @ X4 @ V_4 ) @ V_3 ) ) ) ) ) ) )), 1.25/0.79 define([status(thm)])). 1.25/0.79 thf(app, conjecture, 1.25/0.79 (( setextAx ) => 1.25/0.79 ( ( emptysetAx ) => 1.25/0.79 ( ( setadjoinAx ) => 1.25/0.79 ( ( powersetAx ) => 1.25/0.79 ( ( setunionAx ) => 1.25/0.79 ( ( omega0Ax ) => 1.25/0.79 ( ( omegaSAx ) => 1.25/0.79 ( ( omegaIndAx ) => 1.25/0.79 ( ( replAx ) => 1.25/0.79 ( ( foundationAx ) => 1.25/0.79 ( ( wellorderingAx ) => 1.25/0.79 ( ( descrp ) => 1.25/0.79 ( ( dsetconstrI ) => 1.25/0.79 ( ( dsetconstrEL ) => 1.25/0.79 ( ( dsetconstrER ) => 1.25/0.79 ( ( exuE1 ) => 1.25/0.79 ( ( prop2setE ) => 1.25/0.79 ( ( emptysetE ) => 1.25/0.79 ( ( emptysetimpfalse ) => 1.25/0.79 ( ( notinemptyset ) => 1.25/0.79 ( ( exuE3e ) => 1.25/0.79 ( ( setext ) => 1.25/0.79 ( ( emptyI ) => 1.25/0.79 ( ( noeltsimpempty ) => 1.25/0.79 ( ( setbeta ) => 1.25/0.79 ( ( nonemptyE1 ) => 1.25/0.79 ( ( nonemptyI ) => 1.25/0.79 ( ( nonemptyI1 ) => 1.25/0.79 ( ( setadjoinIL ) => 1.25/0.79 ( ( emptyinunitempty ) => 1.25/0.79 ( ( setadjoinIR ) => 1.25/0.79 ( ( setadjoinE ) => 1.25/0.79 ( ( 1.25/0.79 setadjoinOr ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setoftrueEq ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 powersetI ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 emptyinPowerset ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 emptyInPowerset ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 powersetE ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setunionI ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setunionE ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 subPowSU ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 exuE2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 nonemptyImpWitness ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 uniqinunit ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 notinsingleton ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 eqinunit ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 singletonsswitch ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 upairsetE ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 upairsetIL ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 upairsetIR ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 emptyE1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 vacuousDall ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 quantDeMorgan1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 quantDeMorgan2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 quantDeMorgan3 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 quantDeMorgan4 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 prop2setI ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 prop2set2propI ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 notdexE ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 notdallE ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 exuI1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 exuI3 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 exuI2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 inCongP ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 in__Cong ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 exuE3u ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 exu__Cong ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 emptyset__Cong ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setadjoin__Cong ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 powerset__Cong ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setunion__Cong ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 omega__Cong ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 exuEu ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 descr__Cong ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 dsetconstr__Cong ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 subsetI1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 eqimpsubset2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 eqimpsubset1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 subsetI2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 emptysetsubset ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 subsetE ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 subsetE2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 notsubsetI ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 notequalI1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 notequalI2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 subsetRefl ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 subsetTrans ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setadjoinSub ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setadjoinSub2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 subset2powerset ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setextsub ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 subsetemptysetimpeq ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 powersetI1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 powersetE1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 inPowerset ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 powersetsubset ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 sepInPowerset ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 sepSubset ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 binunionIL ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 upairset2IR ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 binunionIR ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 binunionEcases ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 binunionE ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 binunionLsub ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 binunionRsub ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 binintersectI ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 binintersectSubset5 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 binintersectEL ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 binintersectLsub ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 binintersectSubset2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 binintersectSubset3 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 binintersectER ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 disjointsetsI1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 binintersectRsub ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 binintersectSubset4 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 binintersectSubset1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 bs114d ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setminusI ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setminusEL ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setminusER ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setminusSubset2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setminusERneg ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setminusELneg ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setminusILneg ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setminusIRneg ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setminusLsub ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setminusSubset1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 symdiffE ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 symdiffI1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 symdiffI2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 symdiffIneg1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 symdiffIneg2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 secondinupair ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setukpairIL ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setukpairIR ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 kpairiskpair ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 kpairp ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 singletonsubset ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 singletoninpowerset ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 singletoninpowunion ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 upairset2E ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 upairsubunion ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 upairinpowunion ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 ubforcartprodlem1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 ubforcartprodlem2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 ubforcartprodlem3 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 cartprodpairin ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 cartprodmempair1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 cartprodmempair ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setunionE2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setunionsingleton1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setunionsingleton2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setunionsingleton ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 singletonprop ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 ex1E1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 ex1I ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 ex1I2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 singletonsuniq ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setukpairinjL1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 kfstsingleton ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 theprop ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 kfstpairEq ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 cartprodfstin ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setukpairinjL2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setukpairinjL ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setukpairinjR11 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setukpairinjR12 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setukpairinjR1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 upairequniteq ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setukpairinjR2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setukpairinjR ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 ksndsingleton ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 ksndpairEq ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 kpairsurjEq ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 cartprodsndin ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 cartprodpairmemEL ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 cartprodpairmemER ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 cartprodmempaircEq ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 cartprodfstpairEq ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 cartprodsndpairEq ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 cartprodpairsurjEq ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 dpsetconstrI ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 dpsetconstrSub ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setOfPairsIsBReln ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 dpsetconstrERa ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 dpsetconstrEL1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 dpsetconstrEL2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 dpsetconstrER ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 funcImageSingleton ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 apProp ) => 1.25/0.79 ( 1.25/0.79 ![ 1.25/0.79 A:$i,B:$i, 1.25/0.79 Xf:$i]: 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 func @ 1.25/0.79 A @ B @ Xf ) => 1.25/0.79 ( 1.25/0.79 ![ 1.25/0.79 Xx:$i]: 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 in @ 1.25/0.79 Xx @ A ) => 1.25/0.79 ( 1.25/0.79 in @ 1.25/0.79 ( 1.25/0.79 ap @ 1.25/0.79 A @ B @ 1.25/0.79 Xf @ Xx ) @ 1.25/0.79 B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 1.25/0.79 thf(zf_stmt_0, conjecture, 1.25/0.79 (( setextAx ) => 1.25/0.79 ( ( emptysetAx ) => 1.25/0.79 ( ( setadjoinAx ) => 1.25/0.79 ( ( powersetAx ) => 1.25/0.79 ( ( setunionAx ) => 1.25/0.79 ( ( omega0Ax ) => 1.25/0.79 ( ( omegaSAx ) => 1.25/0.79 ( ( omegaIndAx ) => 1.25/0.79 ( ( replAx ) => 1.25/0.79 ( ( foundationAx ) => 1.25/0.79 ( ( wellorderingAx ) => 1.25/0.79 ( ( descrp ) => 1.25/0.79 ( ( dsetconstrI ) => 1.25/0.79 ( ( dsetconstrEL ) => 1.25/0.79 ( ( dsetconstrER ) => 1.25/0.79 ( ( exuE1 ) => 1.25/0.79 ( ( prop2setE ) => 1.25/0.79 ( ( emptysetE ) => 1.25/0.79 ( ( emptysetimpfalse ) => 1.25/0.79 ( ( notinemptyset ) => 1.25/0.79 ( ( exuE3e ) => 1.25/0.79 ( ( setext ) => 1.25/0.79 ( ( emptyI ) => 1.25/0.79 ( ( noeltsimpempty ) => 1.25/0.79 ( ( setbeta ) => 1.25/0.79 ( ( nonemptyE1 ) => 1.25/0.79 ( ( nonemptyI ) => 1.25/0.79 ( ( nonemptyI1 ) => 1.25/0.79 ( ( setadjoinIL ) => 1.25/0.79 ( ( emptyinunitempty ) => 1.25/0.79 ( ( setadjoinIR ) => 1.25/0.79 ( ( setadjoinE ) => 1.25/0.79 ( ( 1.25/0.79 setadjoinOr ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setoftrueEq ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 powersetI ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 emptyinPowerset ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 emptyInPowerset ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 powersetE ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setunionI ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setunionE ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 subPowSU ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 exuE2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 nonemptyImpWitness ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 uniqinunit ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 notinsingleton ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 eqinunit ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 singletonsswitch ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 upairsetE ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 upairsetIL ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 upairsetIR ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 emptyE1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 vacuousDall ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 quantDeMorgan1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 quantDeMorgan2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 quantDeMorgan3 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 quantDeMorgan4 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 prop2setI ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 prop2set2propI ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 notdexE ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 notdallE ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 exuI1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 exuI3 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 exuI2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 inCongP ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 in__Cong ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 exuE3u ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 exu__Cong ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 emptyset__Cong ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setadjoin__Cong ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 powerset__Cong ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setunion__Cong ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 omega__Cong ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 exuEu ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 descr__Cong ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 dsetconstr__Cong ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 subsetI1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 eqimpsubset2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 eqimpsubset1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 subsetI2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 emptysetsubset ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 subsetE ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 subsetE2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 notsubsetI ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 notequalI1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 notequalI2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 subsetRefl ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 subsetTrans ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setadjoinSub ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setadjoinSub2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 subset2powerset ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setextsub ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 subsetemptysetimpeq ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 powersetI1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 powersetE1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 inPowerset ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 powersetsubset ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 sepInPowerset ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 sepSubset ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 binunionIL ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 upairset2IR ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 binunionIR ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 binunionEcases ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 binunionE ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 binunionLsub ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 binunionRsub ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 binintersectI ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 binintersectSubset5 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 binintersectEL ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 binintersectLsub ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 binintersectSubset2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 binintersectSubset3 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 binintersectER ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 disjointsetsI1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 binintersectRsub ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 binintersectSubset4 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 binintersectSubset1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 bs114d ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setminusI ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setminusEL ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setminusER ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setminusSubset2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setminusERneg ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setminusELneg ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setminusILneg ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setminusIRneg ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setminusLsub ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setminusSubset1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 symdiffE ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 symdiffI1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 symdiffI2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 symdiffIneg1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 symdiffIneg2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 secondinupair ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setukpairIL ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setukpairIR ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 kpairiskpair ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 kpairp ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 singletonsubset ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 singletoninpowerset ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 singletoninpowunion ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 upairset2E ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 upairsubunion ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 upairinpowunion ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 ubforcartprodlem1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 ubforcartprodlem2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 ubforcartprodlem3 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 cartprodpairin ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 cartprodmempair1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 cartprodmempair ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setunionE2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setunionsingleton1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setunionsingleton2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setunionsingleton ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 singletonprop ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 ex1E1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 ex1I ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 ex1I2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 singletonsuniq ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setukpairinjL1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 kfstsingleton ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 theprop ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 kfstpairEq ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 cartprodfstin ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setukpairinjL2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setukpairinjL ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setukpairinjR11 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setukpairinjR12 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setukpairinjR1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 upairequniteq ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setukpairinjR2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setukpairinjR ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 ksndsingleton ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 ksndpairEq ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 kpairsurjEq ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 cartprodsndin ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 cartprodpairmemEL ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 cartprodpairmemER ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 cartprodmempaircEq ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 cartprodfstpairEq ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 cartprodsndpairEq ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 cartprodpairsurjEq ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 dpsetconstrI ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 dpsetconstrSub ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setOfPairsIsBReln ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 dpsetconstrERa ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 dpsetconstrEL1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 dpsetconstrEL2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 dpsetconstrER ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 ![ 1.25/0.79 X4:$i, 1.25/0.79 X6:$i, 1.25/0.79 X8:$i]: 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 breln @ 1.25/0.79 X4 @ X6 @ 1.25/0.79 X8 ) & 1.25/0.79 ( 1.25/0.79 ![ 1.25/0.79 X10:$i]: 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 in @ 1.25/0.79 X10 @ X4 ) => 1.25/0.79 ( 1.25/0.79 ex1 @ 1.25/0.79 X6 @ 1.25/0.79 ( 1.25/0.79 ^[ 1.25/0.79 V_1:$i]: 1.25/0.79 ( 1.25/0.79 in @ 1.25/0.79 ( 1.25/0.79 kpair @ 1.25/0.79 X10 @ V_1 ) @ 1.25/0.79 X8 ) ) ) ) ) ) => 1.25/0.79 ( 1.25/0.79 ![ 1.25/0.79 X12:$i]: 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 in @ 1.25/0.79 X12 @ X4 ) => 1.25/0.79 ( 1.25/0.79 singleton 1.25/0.79 @ 1.25/0.79 ( 1.25/0.79 dsetconstr 1.25/0.79 @ 1.25/0.79 X6 @ 1.25/0.79 ( 1.25/0.79 ^[ 1.25/0.79 V_2:$i]: 1.25/0.79 ( 1.25/0.79 in @ 1.25/0.79 ( 1.25/0.79 kpair @ 1.25/0.79 X12 @ V_2 ) @ 1.25/0.79 X8 ) ) ) ) ) ) ) ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 ![ 1.25/0.79 X14:$i, 1.25/0.79 X16:$i, 1.25/0.79 X18:$i]: 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 breln @ 1.25/0.79 X14 @ 1.25/0.79 X16 @ X18 ) & 1.25/0.79 ( 1.25/0.79 ![ 1.25/0.79 X20:$i]: 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 in @ 1.25/0.79 X20 @ X14 ) => 1.25/0.79 ( 1.25/0.79 ex1 @ 1.25/0.79 X16 @ 1.25/0.79 ( 1.25/0.79 ^[ 1.25/0.79 V_3:$i]: 1.25/0.79 ( 1.25/0.79 in @ 1.25/0.79 ( 1.25/0.79 kpair @ 1.25/0.79 X20 @ V_3 ) @ 1.25/0.79 X18 ) ) ) ) ) ) => 1.25/0.79 ( 1.25/0.79 ![ 1.25/0.79 X22:$i]: 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 in @ 1.25/0.79 X22 @ X14 ) => 1.25/0.79 ( 1.25/0.79 in @ 1.25/0.79 ( 1.25/0.79 setunion @ 1.25/0.79 ( 1.25/0.79 dsetconstr 1.25/0.79 @ 1.25/0.79 X16 @ 1.25/0.79 ( 1.25/0.79 ^[ 1.25/0.79 V_4:$i]: 1.25/0.79 ( 1.25/0.79 in @ 1.25/0.79 ( 1.25/0.79 kpair @ 1.25/0.79 X22 @ V_4 ) @ 1.25/0.79 X18 ) ) ) ) @ 1.25/0.79 X16 ) ) ) ) ) => 1.25/0.79 ( 1.25/0.79 ![ 1.25/0.79 X24:$i, 1.25/0.79 X26:$i, 1.25/0.79 X28:$i]: 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 breln @ 1.25/0.79 X24 @ 1.25/0.79 X26 @ X28 ) & 1.25/0.79 ( 1.25/0.79 ![ 1.25/0.79 X30:$i]: 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 in @ 1.25/0.79 X30 @ X24 ) => 1.25/0.79 ( 1.25/0.79 ex1 @ 1.25/0.79 X26 @ 1.25/0.79 ( 1.25/0.79 ^[ 1.25/0.79 V_5:$i]: 1.25/0.79 ( 1.25/0.79 in @ 1.25/0.79 ( 1.25/0.79 kpair @ 1.25/0.79 X30 @ V_5 ) @ 1.25/0.79 X28 ) ) ) ) ) ) => 1.25/0.79 ( 1.25/0.79 ![ 1.25/0.79 X32:$i]: 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 in @ 1.25/0.79 X32 @ X24 ) => 1.25/0.79 ( 1.25/0.79 in @ 1.25/0.79 ( 1.25/0.79 setunion @ 1.25/0.79 ( 1.25/0.79 dsetconstr 1.25/0.79 @ 1.25/0.79 X26 @ 1.25/0.79 ( 1.25/0.79 ^[ 1.25/0.79 V_6:$i]: 1.25/0.79 ( 1.25/0.79 in @ 1.25/0.79 ( 1.25/0.79 kpair @ 1.25/0.79 X32 @ V_6 ) @ 1.25/0.79 X28 ) ) ) ) @ 1.25/0.79 X26 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 1.25/0.79 thf(zf_stmt_1, negated_conjecture, 1.25/0.79 (~( ( setextAx ) => 1.25/0.79 ( ( emptysetAx ) => 1.25/0.79 ( ( setadjoinAx ) => 1.25/0.79 ( ( powersetAx ) => 1.25/0.79 ( ( setunionAx ) => 1.25/0.79 ( ( omega0Ax ) => 1.25/0.79 ( ( omegaSAx ) => 1.25/0.79 ( ( omegaIndAx ) => 1.25/0.79 ( ( replAx ) => 1.25/0.79 ( ( foundationAx ) => 1.25/0.79 ( ( wellorderingAx ) => 1.25/0.79 ( ( descrp ) => 1.25/0.79 ( ( dsetconstrI ) => 1.25/0.79 ( ( dsetconstrEL ) => 1.25/0.79 ( ( dsetconstrER ) => 1.25/0.79 ( ( exuE1 ) => 1.25/0.79 ( ( prop2setE ) => 1.25/0.79 ( ( emptysetE ) => 1.25/0.79 ( ( emptysetimpfalse ) => 1.25/0.79 ( ( notinemptyset ) => 1.25/0.79 ( ( exuE3e ) => 1.25/0.79 ( ( setext ) => 1.25/0.79 ( ( emptyI ) => 1.25/0.79 ( ( noeltsimpempty ) => 1.25/0.79 ( ( setbeta ) => 1.25/0.79 ( ( nonemptyE1 ) => 1.25/0.79 ( ( nonemptyI ) => 1.25/0.79 ( ( nonemptyI1 ) => 1.25/0.79 ( ( setadjoinIL ) => 1.25/0.79 ( ( emptyinunitempty ) => 1.25/0.79 ( ( setadjoinIR ) => 1.25/0.79 ( ( 1.25/0.79 setadjoinE ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setadjoinOr ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setoftrueEq ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 powersetI ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 emptyinPowerset ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 emptyInPowerset ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 powersetE ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setunionI ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setunionE ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 subPowSU ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 exuE2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 nonemptyImpWitness ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 uniqinunit ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 notinsingleton ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 eqinunit ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 singletonsswitch ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 upairsetE ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 upairsetIL ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 upairsetIR ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 emptyE1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 vacuousDall ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 quantDeMorgan1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 quantDeMorgan2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 quantDeMorgan3 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 quantDeMorgan4 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 prop2setI ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 prop2set2propI ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 notdexE ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 notdallE ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 exuI1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 exuI3 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 exuI2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 inCongP ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 in__Cong ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 exuE3u ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 exu__Cong ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 emptyset__Cong ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setadjoin__Cong ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 powerset__Cong ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 setunion__Cong ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 omega__Cong ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 exuEu ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 descr__Cong ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 dsetconstr__Cong ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 subsetI1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 eqimpsubset2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 eqimpsubset1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 subsetI2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 emptysetsubset ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 subsetE ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 subsetE2 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 notsubsetI ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.79 notequalI1 ) => 1.25/0.79 ( 1.25/0.79 ( 1.25/0.80 notequalI2 ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 subsetRefl ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 subsetTrans ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 setadjoinSub ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 setadjoinSub2 ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 subset2powerset ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 setextsub ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 subsetemptysetimpeq ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 powersetI1 ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 powersetE1 ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 inPowerset ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 powersetsubset ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 sepInPowerset ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 sepSubset ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 binunionIL ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 upairset2IR ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 binunionIR ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 binunionEcases ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 binunionE ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 binunionLsub ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 binunionRsub ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 binintersectI ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 binintersectSubset5 ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 binintersectEL ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 binintersectLsub ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 binintersectSubset2 ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 binintersectSubset3 ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 binintersectER ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 disjointsetsI1 ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 binintersectRsub ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 binintersectSubset4 ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 binintersectSubset1 ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 bs114d ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 setminusI ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 setminusEL ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 setminusER ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 setminusSubset2 ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 setminusERneg ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 setminusELneg ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 setminusILneg ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 setminusIRneg ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 setminusLsub ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 setminusSubset1 ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 symdiffE ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 symdiffI1 ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 symdiffI2 ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 symdiffIneg1 ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 symdiffIneg2 ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 secondinupair ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 setukpairIL ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 setukpairIR ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 kpairiskpair ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 kpairp ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 singletonsubset ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 singletoninpowerset ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 singletoninpowunion ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 upairset2E ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 upairsubunion ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 upairinpowunion ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 ubforcartprodlem1 ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 ubforcartprodlem2 ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 ubforcartprodlem3 ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 cartprodpairin ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 cartprodmempair1 ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 cartprodmempair ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 setunionE2 ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 setunionsingleton1 ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 setunionsingleton2 ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 setunionsingleton ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 singletonprop ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 ex1E1 ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 ex1I ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 ex1I2 ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 singletonsuniq ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 setukpairinjL1 ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 kfstsingleton ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 theprop ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 kfstpairEq ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 cartprodfstin ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 setukpairinjL2 ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 setukpairinjL ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 setukpairinjR11 ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 setukpairinjR12 ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 setukpairinjR1 ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 upairequniteq ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 setukpairinjR2 ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 setukpairinjR ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 ksndsingleton ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 ksndpairEq ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 kpairsurjEq ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 cartprodsndin ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 cartprodpairmemEL ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 cartprodpairmemER ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 cartprodmempaircEq ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 cartprodfstpairEq ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 cartprodsndpairEq ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 cartprodpairsurjEq ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 dpsetconstrI ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 dpsetconstrSub ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 setOfPairsIsBReln ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 dpsetconstrERa ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 dpsetconstrEL1 ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 dpsetconstrEL2 ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 dpsetconstrER ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 ![ 1.25/0.80 X4:$i, 1.25/0.80 X6:$i, 1.25/0.80 X8:$i]: 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 breln @ 1.25/0.80 X4 @ 1.25/0.80 X6 @ X8 ) & 1.25/0.80 ( 1.25/0.80 ![ 1.25/0.80 X10:$i]: 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 in @ 1.25/0.80 X10 @ X4 ) => 1.25/0.80 ( 1.25/0.80 ex1 @ 1.25/0.80 X6 @ 1.25/0.80 ( 1.25/0.80 ^[ 1.25/0.80 V_1:$i]: 1.25/0.80 ( 1.25/0.80 in @ 1.25/0.80 ( 1.25/0.80 kpair @ 1.25/0.80 X10 @ V_1 ) @ 1.25/0.80 X8 ) ) ) ) ) ) => 1.25/0.80 ( 1.25/0.80 ![ 1.25/0.80 X12:$i]: 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 in @ 1.25/0.80 X12 @ X4 ) => 1.25/0.80 ( 1.25/0.80 singleton 1.25/0.80 @ 1.25/0.80 ( 1.25/0.80 dsetconstr 1.25/0.80 @ 1.25/0.80 X6 @ 1.25/0.80 ( 1.25/0.80 ^[ 1.25/0.80 V_2:$i]: 1.25/0.80 ( 1.25/0.80 in @ 1.25/0.80 ( 1.25/0.80 kpair @ 1.25/0.80 X12 @ V_2 ) @ 1.25/0.80 X8 ) ) ) ) ) ) ) ) => 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 ![ 1.25/0.80 X14:$i, 1.25/0.80 X16:$i, 1.25/0.80 X18:$i]: 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 breln @ 1.25/0.80 X14 @ 1.25/0.80 X16 @ X18 ) & 1.25/0.80 ( 1.25/0.80 ![ 1.25/0.80 X20:$i]: 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 in @ 1.25/0.80 X20 @ X14 ) => 1.25/0.80 ( 1.25/0.80 ex1 @ 1.25/0.80 X16 @ 1.25/0.80 ( 1.25/0.80 ^[ 1.25/0.80 V_3:$i]: 1.25/0.80 ( 1.25/0.80 in @ 1.25/0.80 ( 1.25/0.80 kpair @ 1.25/0.80 X20 @ V_3 ) @ 1.25/0.80 X18 ) ) ) ) ) ) => 1.25/0.80 ( 1.25/0.80 ![ 1.25/0.80 X22:$i]: 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 in @ 1.25/0.80 X22 @ X14 ) => 1.25/0.80 ( 1.25/0.80 in @ 1.25/0.80 ( 1.25/0.80 setunion 1.25/0.80 @ 1.25/0.80 ( 1.25/0.80 dsetconstr 1.25/0.80 @ 1.25/0.80 X16 @ 1.25/0.80 ( 1.25/0.80 ^[ 1.25/0.80 V_4:$i]: 1.25/0.80 ( 1.25/0.80 in @ 1.25/0.80 ( 1.25/0.80 kpair @ 1.25/0.80 X22 @ V_4 ) @ 1.25/0.80 X18 ) ) ) ) @ 1.25/0.80 X16 ) ) ) ) ) => 1.25/0.80 ( 1.25/0.80 ![ 1.25/0.80 X24:$i, 1.25/0.80 X26:$i, 1.25/0.80 X28:$i]: 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 breln @ 1.25/0.80 X24 @ 1.25/0.80 X26 @ X28 ) & 1.25/0.80 ( 1.25/0.80 ![ 1.25/0.80 X30:$i]: 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 in @ 1.25/0.80 X30 @ X24 ) => 1.25/0.80 ( 1.25/0.80 ex1 @ 1.25/0.80 X26 @ 1.25/0.80 ( 1.25/0.80 ^[ 1.25/0.80 V_5:$i]: 1.25/0.80 ( 1.25/0.80 in @ 1.25/0.80 ( 1.25/0.80 kpair @ 1.25/0.80 X30 @ V_5 ) @ 1.25/0.80 X28 ) ) ) ) ) ) => 1.25/0.80 ( 1.25/0.80 ![ 1.25/0.80 X32:$i]: 1.25/0.80 ( 1.25/0.80 ( 1.25/0.80 in @ 1.25/0.80 X32 @ X24 ) => 1.25/0.80 ( 1.25/0.80 in @ 1.25/0.80 ( 1.25/0.80 setunion 1.25/0.80 @ 1.25/0.80 ( 1.25/0.80 dsetconstr 1.25/0.80 @ 1.25/0.80 X26 @ 1.25/0.80 ( 1.25/0.80 ^[ 1.25/0.80 V_6:$i]: 1.25/0.80 ( 1.25/0.80 in @ 1.25/0.80 ( 1.25/0.80 kpair @ 1.25/0.80 X32 @ V_6 ) @ 1.25/0.80 X28 ) ) ) ) @ 1.25/0.80 X26 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )), 1.25/0.80 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 1.25/0.80 thf(zip_derived_cl96, plain, ( (in @ sk__13 @ sk__10)), 1.25/0.80 inference('cnf', [status(esa)], [zf_stmt_1])). 1.25/0.80 thf(zip_derived_cl99, plain, ( (breln @ sk__10 @ sk__11 @ sk__12)), 1.25/0.80 inference('cnf', [status(esa)], [zf_stmt_1])). 1.25/0.80 thf(zip_derived_cl101, plain, 1.25/0.80 (![X5 : $i, X6 : $i, X7 : $i, X8 : $i]: 1.25/0.80 (~ (in @ X5 @ X6) 1.25/0.80 | (in @ 1.25/0.80 (setunion @ 1.25/0.80 (dsetconstr @ X7 @ (^[Y0 : $i]: (in @ (kpair @ X5 @ Y0) @ X8)))) @ 1.25/0.80 X7) 1.25/0.80 | (in @ (sk__9 @ X8 @ X7 @ X6) @ X6) 1.25/0.80 | ~ (breln @ X6 @ X7 @ X8))), 1.25/0.80 inference('cnf', [status(esa)], [zf_stmt_1])). 1.25/0.80 thf(zip_derived_cl198, plain, 1.25/0.80 (![X0 : $i]: 1.25/0.80 ( (in @ (sk__9 @ sk__12 @ sk__11 @ sk__10) @ sk__10) 1.25/0.80 | (in @ 1.25/0.80 (setunion @ 1.25/0.80 (dsetconstr @ sk__11 @ 1.25/0.80 (^[Y0 : $i]: (in @ (kpair @ X0 @ Y0) @ sk__12)))) @ 1.25/0.80 sk__11) 1.25/0.80 | ~ (in @ X0 @ sk__10))), 1.25/0.80 inference('sup-', [status(thm)], [zip_derived_cl99, zip_derived_cl101])). 1.25/0.80 thf(zip_derived_cl204, plain, 1.25/0.80 (( (in @ 1.25/0.80 (setunion @ 1.25/0.80 (dsetconstr @ sk__11 @ 1.25/0.80 (^[Y0 : $i]: (in @ (kpair @ sk__13 @ Y0) @ sk__12)))) @ 1.25/0.80 sk__11) 1.25/0.80 | (in @ (sk__9 @ sk__12 @ sk__11 @ sk__10) @ sk__10))), 1.25/0.80 inference('sup-', [status(thm)], [zip_derived_cl96, zip_derived_cl198])). 1.25/0.80 thf(zip_derived_cl97, plain, 1.25/0.80 (~ (in @ 1.25/0.80 (setunion @ 1.25/0.80 (dsetconstr @ sk__11 @ 1.25/0.80 (^[Y0 : $i]: (in @ (kpair @ sk__13 @ Y0) @ sk__12)))) @ 1.25/0.80 sk__11)), 1.25/0.80 inference('cnf', [status(esa)], [zf_stmt_1])). 1.25/0.80 thf(zip_derived_cl206, plain, 1.25/0.80 ( (in @ (sk__9 @ sk__12 @ sk__11 @ sk__10) @ sk__10)), 1.25/0.80 inference('clc', [status(thm)], [zip_derived_cl204, zip_derived_cl97])). 1.25/0.80 thf(zip_derived_cl98, plain, 1.25/0.80 (![X4 : $i]: 1.25/0.80 ( (ex1 @ sk__11 @ (^[Y0 : $i]: (in @ (kpair @ X4 @ Y0) @ sk__12))) 1.25/0.80 | ~ (in @ X4 @ sk__10))), 1.25/0.80 inference('cnf', [status(esa)], [zf_stmt_1])). 1.25/0.80 thf(zip_derived_cl100, plain, 1.25/0.80 (![X5 : $i, X6 : $i, X7 : $i, X8 : $i]: 1.25/0.80 (~ (in @ X5 @ X6) 1.25/0.80 | (in @ 1.25/0.80 (setunion @ 1.25/0.80 (dsetconstr @ X7 @ (^[Y0 : $i]: (in @ (kpair @ X5 @ Y0) @ X8)))) @ 1.25/0.80 X7) 1.25/0.80 | ~ (ex1 @ X7 @ 1.25/0.80 (^[Y0 : $i]: (in @ (kpair @ (sk__9 @ X8 @ X7 @ X6) @ Y0) @ X8))) 1.25/0.80 | ~ (breln @ X6 @ X7 @ X8))), 1.25/0.80 inference('cnf', [status(esa)], [zf_stmt_1])). 1.25/0.80 thf(zip_derived_cl197, plain, 1.25/0.80 (![X0 : $i, X1 : $i]: 1.25/0.80 (~ (in @ (sk__9 @ sk__12 @ sk__11 @ X0) @ sk__10) 1.25/0.80 | ~ (breln @ X0 @ sk__11 @ sk__12) 1.25/0.80 | (in @ 1.25/0.80 (setunion @ 1.25/0.80 (dsetconstr @ sk__11 @ 1.25/0.80 (^[Y0 : $i]: (in @ (kpair @ X1 @ Y0) @ sk__12)))) @ 1.25/0.80 sk__11) 1.25/0.80 | ~ (in @ X1 @ X0))), 1.25/0.80 inference('sup-', [status(thm)], [zip_derived_cl98, zip_derived_cl100])). 1.25/0.80 thf(zip_derived_cl207, plain, 1.25/0.80 (![X0 : $i]: 1.25/0.80 (~ (in @ X0 @ sk__10) 1.25/0.80 | (in @ 1.25/0.80 (setunion @ 1.25/0.80 (dsetconstr @ sk__11 @ 1.25/0.80 (^[Y0 : $i]: (in @ (kpair @ X0 @ Y0) @ sk__12)))) @ 1.25/0.80 sk__11) 1.25/0.80 | ~ (breln @ sk__10 @ sk__11 @ sk__12))), 1.25/0.80 inference('sup-', [status(thm)], [zip_derived_cl206, zip_derived_cl197])). 1.25/0.80 thf(zip_derived_cl99, plain, ( (breln @ sk__10 @ sk__11 @ sk__12)), 1.25/0.80 inference('cnf', [status(esa)], [zf_stmt_1])). 1.25/0.80 thf(zip_derived_cl211, plain, 1.25/0.80 (![X0 : $i]: 1.25/0.80 (~ (in @ X0 @ sk__10) 1.25/0.80 | (in @ 1.25/0.80 (setunion @ 1.25/0.80 (dsetconstr @ sk__11 @ 1.25/0.80 (^[Y0 : $i]: (in @ (kpair @ X0 @ Y0) @ sk__12)))) @ 1.25/0.80 sk__11))), 1.25/0.80 inference('demod', [status(thm)], [zip_derived_cl207, zip_derived_cl99])). 1.25/0.80 thf(zip_derived_cl97, plain, 1.25/0.80 (~ (in @ 1.25/0.80 (setunion @ 1.25/0.80 (dsetconstr @ sk__11 @ 1.25/0.80 (^[Y0 : $i]: (in @ (kpair @ sk__13 @ Y0) @ sk__12)))) @ 1.25/0.80 sk__11)), 1.25/0.80 inference('cnf', [status(esa)], [zf_stmt_1])). 1.25/0.80 thf(zip_derived_cl213, plain, (~ (in @ sk__13 @ sk__10)), 1.25/0.80 inference('sup-', [status(thm)], [zip_derived_cl211, zip_derived_cl97])). 1.25/0.80 thf(zip_derived_cl96, plain, ( (in @ sk__13 @ sk__10)), 1.25/0.80 inference('cnf', [status(esa)], [zf_stmt_1])). 1.25/0.80 thf(zip_derived_cl214, plain, ($false), 1.25/0.80 inference('demod', [status(thm)], [zip_derived_cl213, zip_derived_cl96])). 1.25/0.80 1.25/0.80 % SZS output end Refutation 1.25/0.80 1.25/0.80 1.25/0.80 % Terminating... 1.57/0.89 % Runner terminated. 1.57/0.91 % Zipperpin 1.5 exiting 1.57/0.91 EOF