0.11/0.14 % Problem : Vampire---4.8_27962 : TPTP v0.0.0. Released v0.0.0. 0.11/0.15 % Command : run_E %s %d THM 0.15/0.35 % Computer : n028.cluster.edu 0.15/0.35 % Model : x86_64 x86_64 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.15/0.35 % Memory : 8042.1875MB 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.15/0.35 % CPULimit : 1440 0.15/0.35 % WCLimit : 180 0.15/0.35 % DateTime : Mon Jul 3 13:17:29 EDT 2023 0.15/0.35 % CPUTime : 0.20/0.50 Running higher-order theorem provingRunning: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=180 /export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962 0.20/0.51 # Version: 3.1pre001-ho 786.41/99.42 # Preprocessing class: HSLMSLSSLLLCHFA. 786.41/99.42 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 786.41/99.42 # Starting ehoh_best5 with 180s (1) cores 786.41/99.42 # Starting almost_fo_3_lam with 180s (1) cores 786.41/99.42 # Starting new_bool_5 with 180s (1) cores 786.41/99.42 # Starting pre_casc_3 with 180s (1) cores 786.41/99.42 # Starting ho_unfolding_8 with 180s (1) cores 786.41/99.42 # Starting new_ho_10_cnf2 with 180s (1) cores 786.41/99.42 # Starting new_bool_3 with 180s (1) cores 786.41/99.42 # Starting new_ho_5 with 180s (1) cores 786.41/99.42 # almost_fo_3_lam with pid 28321 completed with status 0 786.41/99.42 # Result found by almost_fo_3_lam 786.41/99.42 # Preprocessing class: HSLMSLSSLLLCHFA. 786.41/99.42 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 786.41/99.42 # Starting ehoh_best5 with 180s (1) cores 786.41/99.42 # Starting almost_fo_3_lam with 180s (1) cores 786.41/99.42 # No SInE strategy applied 786.41/99.42 # Search class: HGHSM-FSLM31-MHFMMSBN 786.41/99.42 # Scheduled 6 strats onto 1 cores with 180 seconds (180 total) 786.41/99.42 # Starting new_ho_10_cnf2 with 98s (1) cores 786.41/99.42 # new_ho_10_cnf2 with pid 28335 completed with status 7 786.41/99.42 # Starting almost_fo_3_lam with 19s (1) cores 786.41/99.42 # almost_fo_3_lam with pid 30316 completed with status 0 786.41/99.42 # Result found by almost_fo_3_lam 786.41/99.42 # Preprocessing class: HSLMSLSSLLLCHFA. 786.41/99.42 # Scheduled 8 strats onto 8 cores with 180 seconds (1440 total) 786.41/99.42 # Starting ehoh_best5 with 180s (1) cores 786.41/99.42 # Starting almost_fo_3_lam with 180s (1) cores 786.41/99.42 # No SInE strategy applied 786.41/99.42 # Search class: HGHSM-FSLM31-MHFMMSBN 786.41/99.42 # Scheduled 6 strats onto 1 cores with 180 seconds (180 total) 786.41/99.42 # Starting new_ho_10_cnf2 with 98s (1) cores 786.41/99.42 # new_ho_10_cnf2 with pid 28335 completed with status 7 786.41/99.42 # Starting almost_fo_3_lam with 19s (1) cores 786.41/99.42 # Preprocessing time : 0.005 s 786.41/99.42 # Presaturation interreduction done 786.41/99.42 786.41/99.42 # Proof found! 786.41/99.42 # SZS status Theorem 786.41/99.42 # SZS output start CNFRefutation 786.41/99.42 thf(decl_22, type, in: $i > $i > $o). 786.41/99.42 thf(decl_23, type, exu: ($i > $o) > $o). 786.41/99.42 thf(decl_24, type, setextAx: $o). 786.41/99.42 thf(decl_25, type, emptyset: $i). 786.41/99.42 thf(decl_26, type, emptysetAx: $o). 786.41/99.42 thf(decl_27, type, setadjoin: $i > $i > $i). 786.41/99.42 thf(decl_28, type, setadjoinAx: $o). 786.41/99.42 thf(decl_29, type, powerset: $i > $i). 786.41/99.42 thf(decl_30, type, powersetAx: $o). 786.41/99.42 thf(decl_31, type, setunion: $i > $i). 786.41/99.42 thf(decl_32, type, setunionAx: $o). 786.41/99.42 thf(decl_33, type, omega: $i). 786.41/99.42 thf(decl_34, type, omega0Ax: $o). 786.41/99.42 thf(decl_35, type, omegaSAx: $o). 786.41/99.42 thf(decl_36, type, omegaIndAx: $o). 786.41/99.42 thf(decl_37, type, replAx: $o). 786.41/99.42 thf(decl_38, type, foundationAx: $o). 786.41/99.42 thf(decl_39, type, wellorderingAx: $o). 786.41/99.42 thf(decl_40, type, descr: ($i > $o) > $i). 786.41/99.42 thf(decl_41, type, descrp: $o). 786.41/99.42 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i). 786.41/99.42 thf(decl_43, type, dsetconstrI: $o). 786.41/99.42 thf(decl_44, type, dsetconstrEL: $o). 786.41/99.42 thf(decl_45, type, dsetconstrER: $o). 786.41/99.42 thf(decl_46, type, exuE1: $o). 786.41/99.42 thf(decl_47, type, prop2set: $o > $i). 786.41/99.42 thf(decl_48, type, prop2setE: $o). 786.41/99.42 thf(decl_49, type, emptysetE: $o). 786.41/99.42 thf(decl_50, type, emptysetimpfalse: $o). 786.41/99.42 thf(decl_51, type, notinemptyset: $o). 786.41/99.42 thf(decl_52, type, exuE3e: $o). 786.41/99.42 thf(decl_53, type, setext: $o). 786.41/99.42 thf(decl_54, type, emptyI: $o). 786.41/99.42 thf(decl_55, type, noeltsimpempty: $o). 786.41/99.42 thf(decl_56, type, setbeta: $o). 786.41/99.42 thf(decl_57, type, nonempty: $i > $o). 786.41/99.42 thf(decl_58, type, nonemptyE1: $o). 786.41/99.42 thf(decl_59, type, nonemptyI: $o). 786.41/99.42 thf(decl_60, type, nonemptyI1: $o). 786.41/99.42 thf(decl_61, type, setadjoinIL: $o). 786.41/99.42 thf(decl_62, type, emptyinunitempty: $o). 786.41/99.42 thf(decl_63, type, setadjoinIR: $o). 786.41/99.42 thf(decl_64, type, setadjoinE: $o). 786.41/99.42 thf(decl_65, type, setadjoinOr: $o). 786.41/99.42 thf(decl_66, type, setoftrueEq: $o). 786.41/99.42 thf(decl_67, type, powersetI: $o). 786.41/99.42 thf(decl_68, type, emptyinPowerset: $o). 786.41/99.42 thf(decl_69, type, emptyInPowerset: $o). 786.41/99.42 thf(decl_70, type, powersetE: $o). 786.41/99.42 thf(decl_71, type, setunionI: $o). 786.41/99.42 thf(decl_72, type, setunionE: $o). 786.41/99.42 thf(decl_73, type, subPowSU: $o). 786.41/99.42 thf(decl_74, type, exuE2: $o). 786.41/99.42 thf(decl_75, type, nonemptyImpWitness: $o). 786.41/99.42 thf(decl_76, type, uniqinunit: $o). 786.41/99.42 thf(decl_77, type, notinsingleton: $o). 786.41/99.42 thf(decl_78, type, eqinunit: $o). 786.41/99.42 thf(decl_79, type, singletonsswitch: $o). 786.41/99.42 thf(decl_80, type, upairsetE: $o). 786.41/99.42 thf(decl_81, type, upairsetIL: $o). 786.41/99.42 thf(decl_82, type, upairsetIR: $o). 786.41/99.42 thf(decl_83, type, emptyE1: $o). 786.41/99.42 thf(decl_84, type, vacuousDall: $o). 786.41/99.42 thf(decl_85, type, quantDeMorgan1: $o). 786.41/99.42 thf(decl_86, type, quantDeMorgan2: $o). 786.41/99.42 thf(decl_87, type, quantDeMorgan3: $o). 786.41/99.42 thf(decl_88, type, quantDeMorgan4: $o). 786.41/99.42 thf(decl_89, type, prop2setI: $o). 786.41/99.42 thf(decl_90, type, set2prop: $i > $o). 786.41/99.42 thf(decl_91, type, prop2set2propI: $o). 786.41/99.42 thf(decl_92, type, notdexE: $o). 786.41/99.42 thf(decl_93, type, notdallE: $o). 786.41/99.42 thf(decl_94, type, exuI1: $o). 786.41/99.42 thf(decl_95, type, exuI3: $o). 786.41/99.42 thf(decl_96, type, exuI2: $o). 786.41/99.42 thf(decl_97, type, inCongP: $o). 786.41/99.42 thf(decl_98, type, in__Cong: $o). 786.41/99.42 thf(decl_99, type, exuE3u: $o). 786.41/99.42 thf(decl_100, type, exu__Cong: $o). 786.41/99.42 thf(decl_101, type, emptyset__Cong: $o). 786.41/99.42 thf(decl_102, type, setadjoin__Cong: $o). 786.41/99.42 thf(decl_103, type, powerset__Cong: $o). 786.41/99.42 thf(decl_104, type, setunion__Cong: $o). 786.41/99.42 thf(decl_105, type, omega__Cong: $o). 786.41/99.42 thf(decl_106, type, exuEu: $o). 786.41/99.42 thf(decl_107, type, descr__Cong: $o). 786.41/99.42 thf(decl_108, type, dsetconstr__Cong: $o). 786.41/99.42 thf(decl_109, type, subset: $i > $i > $o). 786.41/99.42 thf(decl_112, type, subsetI1: $o). 786.41/99.42 thf(decl_113, type, eqimpsubset2: $o). 786.41/99.42 thf(decl_114, type, eqimpsubset1: $o). 786.41/99.42 thf(decl_115, type, subsetI2: $o). 786.41/99.42 thf(decl_116, type, emptysetsubset: $o). 786.41/99.42 thf(decl_117, type, subsetE: $o). 786.41/99.42 thf(decl_118, type, subsetE2: $o). 786.41/99.42 thf(decl_119, type, notsubsetI: $o). 786.41/99.42 thf(decl_120, type, notequalI1: $o). 786.41/99.42 thf(decl_121, type, notequalI2: $o). 786.41/99.42 thf(decl_122, type, subsetRefl: $o). 786.41/99.42 thf(decl_123, type, subsetTrans: $o). 786.41/99.42 thf(decl_124, type, setadjoinSub: $o). 786.41/99.42 thf(decl_125, type, setadjoinSub2: $o). 786.41/99.42 thf(decl_126, type, subset2powerset: $o). 786.41/99.42 thf(decl_127, type, setextsub: $o). 786.41/99.42 thf(decl_128, type, subsetemptysetimpeq: $o). 786.41/99.42 thf(decl_129, type, powersetI1: $o). 786.41/99.42 thf(decl_130, type, powersetE1: $o). 786.41/99.42 thf(decl_131, type, inPowerset: $o). 786.41/99.42 thf(decl_132, type, powersetsubset: $o). 786.41/99.42 thf(decl_133, type, sepInPowerset: $o). 786.41/99.42 thf(decl_134, type, sepSubset: $o). 786.41/99.42 thf(decl_135, type, binunion: $i > $i > $i). 786.41/99.42 thf(decl_136, type, binunionIL: $o). 786.41/99.42 thf(decl_137, type, upairset2IR: $o). 786.41/99.42 thf(decl_138, type, binunionIR: $o). 786.41/99.42 thf(decl_139, type, binunionEcases: $o). 786.41/99.42 thf(decl_140, type, binunionE: $o). 786.41/99.42 thf(decl_141, type, binunionLsub: $o). 786.41/99.42 thf(decl_142, type, binunionRsub: $o). 786.41/99.42 thf(decl_143, type, binintersect: $i > $i > $i). 786.41/99.42 thf(decl_144, type, binintersectI: $o). 786.41/99.42 thf(decl_145, type, epred1_0: $o). 786.41/99.42 thf(decl_146, type, esk1_2: $i > $i > $i). 786.41/99.42 thf(decl_147, type, esk2_2: $i > $i > $i). 786.41/99.42 thf(decl_148, type, esk3_2: $i > $i > $i). 786.41/99.42 thf(decl_149, type, esk4_1: $i > $i). 786.41/99.42 thf(decl_150, type, esk5_2: ($i > $i > $o) > $i > $i). 786.41/99.42 thf(decl_151, type, esk6_3: ($i > $i > $o) > $i > $i > $i). 786.41/99.42 thf(decl_152, type, esk7_2: ($i > $i > $o) > $i > $i). 786.41/99.42 thf(decl_153, type, esk8_3: ($i > $i > $o) > $i > $i > $i). 786.41/99.42 thf(decl_154, type, esk9_1: $i > $i). 786.41/99.42 thf(decl_155, type, esk10_2: ($i > $o) > $i > $i). 786.41/99.42 thf(decl_156, type, esk11_2: ($i > $o) > $i > $i). 786.41/99.42 thf(decl_157, type, esk12_1: ($i > $o) > $i). 786.41/99.42 thf(decl_158, type, esk13_2: ($i > $o) > $i > $i). 786.41/99.42 thf(decl_159, type, esk14_1: ($i > $o) > $i). 786.41/99.42 thf(decl_160, type, esk15_2: $i > $i > $i). 786.41/99.42 thf(decl_161, type, esk16_2: $i > $i > $i). 786.41/99.42 thf(decl_162, type, esk17_1: $i > $i). 786.41/99.42 thf(decl_163, type, esk18_1: $i > $i). 786.41/99.42 thf(decl_164, type, esk19_1: $i > $i). 786.41/99.42 thf(decl_165, type, esk20_2: $i > $i > $i). 786.41/99.42 thf(decl_166, type, esk21_3: $i > $i > $o > $i). 786.41/99.42 thf(decl_167, type, esk22_2: ($i > $o) > $i > $i). 786.41/99.42 thf(decl_168, type, esk23_1: ($i > $o) > $i). 786.41/99.42 thf(decl_169, type, esk24_1: $i > $i). 786.41/99.42 thf(decl_170, type, esk25_2: $i > ($i > $o) > $i). 786.41/99.42 thf(decl_171, type, esk26_2: $i > ($i > $o) > $i). 786.41/99.42 thf(decl_172, type, esk27_2: $i > ($i > $o) > $i). 786.41/99.42 thf(decl_173, type, esk28_2: $i > ($i > $o) > $i). 786.41/99.42 thf(decl_174, type, esk29_2: $i > ($i > $o) > $i). 786.41/99.42 thf(decl_175, type, esk30_2: $i > ($i > $o) > $i). 786.41/99.42 thf(decl_176, type, esk31_2: ($i > $o) > $i > $i). 786.41/99.42 thf(decl_177, type, esk32_1: ($i > $o) > $i). 786.41/99.42 thf(decl_178, type, esk33_1: ($i > $o) > $i). 786.41/99.42 thf(decl_179, type, esk34_1: ($i > $o) > $i). 786.41/99.42 thf(decl_180, type, esk35_1: ($i > $o) > $i). 786.41/99.42 thf(decl_181, type, esk36_2: ($i > $o) > $i > $i). 786.41/99.42 thf(decl_182, type, esk37_1: ($i > $o) > $i). 786.41/99.42 thf(decl_183, type, esk38_2: ($i > $o) > $i > $i). 786.41/99.42 thf(decl_184, type, esk39_2: ($i > $o) > ($i > $o) > $i). 786.41/99.42 thf(decl_185, type, esk40_2: ($i > $o) > ($i > $o) > $i). 786.41/99.42 thf(decl_186, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i). 786.41/99.42 thf(decl_187, type, esk42_2: ($i > $o) > ($i > $o) > $i). 786.41/99.42 thf(decl_188, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i). 786.41/99.42 thf(decl_189, type, esk44_2: ($i > $o) > ($i > $o) > $i). 786.41/99.42 thf(decl_190, type, esk45_2: ($i > $o) > $i > $i). 786.41/99.42 thf(decl_191, type, esk46_2: ($i > $o) > ($i > $o) > $i). 786.41/99.42 thf(decl_192, type, esk47_2: ($i > $o) > ($i > $o) > $i). 786.41/99.42 thf(decl_193, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i). 786.41/99.42 thf(decl_194, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i). 786.41/99.42 thf(decl_195, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i). 786.41/99.42 thf(decl_196, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i). 786.41/99.42 thf(decl_197, type, esk52_2: $i > $i > $i). 786.41/99.42 thf(decl_198, type, esk53_2: $i > $i > $i). 786.41/99.42 thf(decl_199, type, esk54_0: $i). 786.41/99.42 thf(decl_200, type, esk55_0: $i). 786.41/99.42 thf(decl_201, type, esk56_0: $i). 786.41/99.42 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', replAx)). 786.41/99.42 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', exu)). 786.41/99.42 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', descrp)). 786.41/99.42 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', exuE1)). 786.41/99.42 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', exuE3e)). 786.41/99.42 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', nonempty)). 786.41/99.42 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', nonemptyI)). 786.41/99.42 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', exuE2)). 786.41/99.42 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', exuI1)). 786.41/99.42 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', exuI3)). 786.41/99.42 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', exuI2)). 786.41/99.42 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', exuE3u)). 786.41/99.42 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', exu__Cong)). 786.41/99.42 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', exuEu)). 786.41/99.42 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', descr__Cong)). 786.41/99.42 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', dsetconstrI)). 786.41/99.42 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', dsetconstrEL)). 786.41/99.42 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', dsetconstrER)). 786.41/99.42 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', setbeta)). 786.41/99.42 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', nonemptyE1)). 786.41/99.42 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', nonemptyI1)). 786.41/99.42 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', setoftrueEq)). 786.41/99.42 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', nonemptyImpWitness)). 786.41/99.42 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', emptyE1)). 786.41/99.42 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', dsetconstr__Cong)). 786.41/99.42 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', sepInPowerset)). 786.41/99.42 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', sepSubset)). 786.41/99.42 thf(binintersectSubset5, conjecture, ((((((((((replAx)=>(((wellorderingAx)=>(((dsetconstrI)=>(((((((((exuE3e)=>((setext)=>(((noeltsimpempty)=>((setbeta)=>(((nonemptyI)=>((nonemptyI1)=>(((emptyinunitempty)=>((setadjoinIR)=>(((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((((powersetE)=>(((((((((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>(((((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((((inCongP)=>((((exu__Cong)=>((emptyset__Cong)=>(((powerset__Cong)=>(((omega__Cong)=>((((((eqimpsubset2)=>(((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>(((((((setadjoinSub)=>((((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>(((sepInPowerset)=>(((binunionIL)=>((((binunionEcases)=>(((binunionLsub)=>((![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))<=(binintersectI))<=(binunionRsub)))<=(binunionE)))<=(binunionIR))<=(upairset2IR)))<=(sepSubset)))<=(powersetsubset)))))))<=(subset2powerset))<=(setadjoinSub2)))<=(subsetTrans))<=(subsetRefl))<=(notequalI2))<=(notequalI1))<=(notsubsetI))))))<=(eqimpsubset1)))<=(subsetI1))<=(dsetconstr__Cong))<=(descr__Cong))<=(exuEu)))<=(setunion__Cong)))<=(setadjoin__Cong))))<=(exuE3u))<=(in__Cong)))<=(exuI2))<=(exuI3)))))))<=(quantDeMorgan4))<=(quantDeMorgan3))<=(quantDeMorgan2))))))))))<=(notinsingleton))<=(uniqinunit))<=(nonemptyImpWitness))<=(exuE2))<=(subPowSU))<=(setunionE))<=(setunionI)))<=(emptyInPowerset))<=(emptyinPowerset)))))<=(setadjoinE))))<=(setadjoinIL))))<=(nonemptyE1))))<=(emptyI))))<=(notinemptyset))<=(emptysetimpfalse))<=(emptysetE))<=(prop2setE))<=(exuE1))<=(dsetconstrER))<=(dsetconstrEL)))<=(descrp)))<=(foundationAx)))<=(omegaIndAx))<=(omegaSAx))<=(omega0Ax))<=(setunionAx))<=(powersetAx))<=(setadjoinAx))<=(emptysetAx))<=(setextAx)), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', binintersectSubset5)). 786.41/99.42 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', setextAx)). 786.41/99.42 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', emptysetAx)). 786.41/99.42 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', setadjoinAx)). 786.41/99.42 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', powersetAx)). 786.41/99.42 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', setunionAx)). 786.41/99.42 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', omega0Ax)). 786.41/99.42 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', omegaSAx)). 786.41/99.42 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', omegaIndAx)). 786.41/99.42 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', foundationAx)). 786.41/99.42 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', wellorderingAx)). 786.41/99.42 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', prop2setE)). 786.41/99.42 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', emptysetE)). 786.41/99.42 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', emptysetimpfalse)). 786.41/99.42 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', notinemptyset)). 786.41/99.42 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', setext)). 786.41/99.42 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', emptyI)). 786.41/99.42 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', noeltsimpempty)). 786.41/99.42 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', setadjoinIL)). 786.41/99.42 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', emptyinunitempty)). 786.41/99.42 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', setadjoinIR)). 786.41/99.42 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', setadjoinE)). 786.41/99.42 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', setadjoinOr)). 786.41/99.42 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', powersetI)). 786.41/99.42 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', emptyinPowerset)). 786.41/99.42 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', emptyInPowerset)). 786.41/99.42 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', powersetE)). 786.41/99.42 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', setunionI)). 786.41/99.42 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', setunionE)). 786.41/99.42 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', subPowSU)). 786.41/99.42 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', uniqinunit)). 786.41/99.42 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', notinsingleton)). 786.41/99.42 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', eqinunit)). 786.41/99.42 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', singletonsswitch)). 786.41/99.42 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', upairsetE)). 786.41/99.42 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', upairsetIL)). 786.41/99.42 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', upairsetIR)). 786.41/99.42 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', vacuousDall)). 786.41/99.42 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', quantDeMorgan1)). 786.41/99.42 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', quantDeMorgan2)). 786.41/99.42 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', quantDeMorgan3)). 786.41/99.42 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', quantDeMorgan4)). 786.41/99.42 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', prop2setI)). 786.41/99.42 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', prop2set2propI)). 786.41/99.42 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', notdexE)). 786.41/99.42 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', notdallE)). 786.41/99.42 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', inCongP)). 786.41/99.42 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', in__Cong)). 786.41/99.42 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', emptyset__Cong)). 786.41/99.42 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', setadjoin__Cong)). 786.41/99.42 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', powerset__Cong)). 786.41/99.42 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', setunion__Cong)). 786.41/99.42 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', omega__Cong)). 786.41/99.42 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', subsetI1)). 786.41/99.42 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', eqimpsubset2)). 786.41/99.42 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', eqimpsubset1)). 786.41/99.42 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', subsetI2)). 786.41/99.42 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', emptysetsubset)). 786.41/99.42 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', subsetE)). 786.41/99.42 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', subsetE2)). 786.41/99.42 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', notsubsetI)). 786.41/99.42 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', notequalI1)). 786.41/99.42 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', notequalI2)). 786.41/99.42 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', subsetRefl)). 786.41/99.42 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', subsetTrans)). 786.41/99.42 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', setadjoinSub)). 786.41/99.42 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', setadjoinSub2)). 786.41/99.42 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', subset2powerset)). 786.41/99.42 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', setextsub)). 786.41/99.42 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', subsetemptysetimpeq)). 786.41/99.42 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', powersetI1)). 786.41/99.42 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', powersetE1)). 786.41/99.42 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', inPowerset)). 786.41/99.42 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', powersetsubset)). 786.41/99.42 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', binunionIL)). 786.41/99.42 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', upairset2IR)). 786.41/99.42 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', binunionIR)). 786.41/99.42 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', binunionEcases)). 786.41/99.42 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', binunionE)). 786.41/99.42 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', binunionLsub)). 786.41/99.42 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', binunionRsub)). 786.41/99.42 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.mw7bZXKnZp/Vampire---4.8_27962', binintersectI)). 786.41/99.42 thf(c_0_109, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0/* 3 */:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 786.41/99.42 thf(c_0_110, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])). 786.41/99.42 thf(c_0_111, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 786.41/99.42 thf(c_0_112, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 786.41/99.42 thf(c_0_113, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 786.41/99.42 thf(c_0_114, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])). 786.41/99.42 thf(c_0_115, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 786.41/99.42 thf(c_0_116, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])). 786.41/99.42 thf(c_0_117, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])). 786.41/99.42 thf(c_0_118, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 786.41/99.42 thf(c_0_119, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 786.41/99.42 thf(c_0_120, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])). 786.41/99.42 thf(c_0_121, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 786.41/99.42 thf(c_0_122, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 786.41/99.42 thf(c_0_123, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>((exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 786.41/99.42 thf(c_0_124, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X307:$i]:((((X6 @ X2 @ X307))&![X308:$i]:((((X6 @ X2 @ X308))=>((X307)=(X308)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_109, c_0_110])). 786.41/99.42 thf(c_0_125, plain, ((descrp)=(![X1:$i > $o]:(((?[X309:$i]:((((X1 @ X309))&![X310:$i]:((((X1 @ X310))=>((X309)=(X310)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_111, c_0_110])). 786.41/99.42 thf(c_0_126, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 786.41/99.42 thf(c_0_127, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 786.41/99.42 thf(c_0_128, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 786.41/99.42 thf(c_0_129, plain, ((exuE1)=(![X1:$i > $o]:(((?[X311:$i]:((((X1 @ X311))&![X312:$i]:((((X1 @ X312))=>((X311)=(X312)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_112, c_0_110])). 786.41/99.42 thf(c_0_130, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X313:$i]:((((X1 @ X313))&![X314:$i]:((((X1 @ X314))=>((X313)=(X314)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_113, c_0_110])). 786.41/99.42 thf(c_0_131, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 786.41/99.42 thf(c_0_132, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_114])). 786.41/99.42 thf(c_0_133, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_115, c_0_114])). 786.41/99.42 thf(c_0_134, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_114])). 786.41/99.42 thf(c_0_135, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 786.41/99.42 thf(c_0_136, plain, ((exuE2)=(![X1:$i > $o]:(((?[X315:$i]:((((X1 @ X315))&![X316:$i]:((((X1 @ X316))=>((X315)=(X316)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_116, c_0_110])). 786.41/99.42 thf(c_0_137, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_114])). 786.41/99.42 thf(c_0_138, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])). 786.41/99.42 thf(c_0_139, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X317:$i]:((((X1 @ X317))&![X318:$i]:((((X1 @ X318))=>((X317)=(X318))))))))))), inference(apply_def,[status(thm)],[c_0_117, c_0_110])). 786.41/99.42 thf(c_0_140, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X319:$i]:((((X1 @ X319))&![X320:$i]:((((X1 @ X320))=>((X319)=(X320)))))))))))), inference(apply_def,[status(thm)],[c_0_118, c_0_110])). 786.41/99.42 thf(c_0_141, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X321:$i]:((((X1 @ X321))&![X322:$i]:((((X1 @ X322))=>((X321)=(X322))))))))))), inference(apply_def,[status(thm)],[c_0_119, c_0_110])). 786.41/99.42 thf(c_0_142, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X323:$i]:((((X1 @ X323))&![X324:$i]:((((X1 @ X324))=>((X323)=(X324)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_120, c_0_110])). 786.41/99.42 thf(c_0_143, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X325:$i]:((((X1 @ X325))&![X326:$i]:((((X1 @ X326))=>((X325)=(X326)))))))<=>(?[X327:$i]:((((X17 @ X327))&![X328:$i]:((((X17 @ X328))=>((X327)=(X328)))))))))))), inference(apply_def,[status(thm)],[c_0_121, c_0_110])). 786.41/99.42 thf(c_0_144, plain, ((exuEu)=(![X1:$i > $o]:(((?[X329:$i]:((((X1 @ X329))&![X330:$i]:((((X1 @ X330))=>((X329)=(X330)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_122, c_0_110])). 786.41/99.42 thf(c_0_145, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X331:$i]:((((X1 @ X331))&![X332:$i]:((((X1 @ X332))=>((X331)=(X332)))))))=>((?[X333:$i]:((((X17 @ X333))&![X334:$i]:((((X17 @ X334))=>((X333)=(X334)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_123, c_0_110])). 786.41/99.42 thf(c_0_146, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 786.41/99.42 thf(c_0_147, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 786.41/99.42 thf(c_0_148, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 786.41/99.42 thf(c_0_149, plain, ((epred1_0)<=>![X343:$i]:(?[X344:$i]:((((![X345:$i]:(((in @ X345 @ X344)=>![X346:$i]:(((in @ X346 @ X345)=>(in @ X346 @ X343)))))&![X347:$i, X348:$i]:((((in @ X347 @ X343)&(in @ X348 @ X343))=>(![X349:$i]:(((in @ X349 @ X344)=>((in @ X347 @ X349)<=>(in @ X348 @ X349))))=>((X347)=(X348))))))&![X350:$i, X351:$i]:((((in @ X350 @ X344)&(in @ X351 @ X344))=>(![X352:$i]:(((in @ X352 @ X350)=>(in @ X352 @ X351)))|![X353:$i]:(((in @ X353 @ X351)=>(in @ X353 @ X350)))))))&![X354:$i]:(((![X355:$i]:(((in @ X355 @ X354)=>(in @ X355 @ X343)))&?[X356:$i]:((in @ X356 @ X354)))=>?[X357:$i, X358:$i]:(((((in @ X357 @ X344)&(in @ X358 @ X354))&~(?[X359:$i]:(((in @ X359 @ X357)&(in @ X359 @ X354)))))&![X360:$i]:(((in @ X360 @ X344)=>(![X361:$i]:(((in @ X361 @ X360)=>(in @ X361 @ X357)))|(in @ X358 @ X360)))))))))))), introduced(definition)). 786.41/99.42 thf(c_0_150, negated_conjecture, ~((![X644:$i, X645:$i]:((![X646:$i]:(((in @ X646 @ X644)<=>(in @ X646 @ X645)))=>((X644)=(X645))))=>(![X643:$i]:(~(in @ X643 @ emptyset))=>(![X640:$i, X641:$i, X642:$i]:(((in @ X642 @ (setadjoin @ X640 @ X641))<=>(((X642)=(X640))|(in @ X642 @ X641))))=>(![X637:$i, X638:$i]:(((in @ X638 @ (powerset @ X637))<=>![X639:$i]:(((in @ X639 @ X638)=>(in @ X639 @ X637)))))=>(![X634:$i, X635:$i]:(((in @ X635 @ (setunion @ X634))<=>?[X636:$i]:(((in @ X635 @ X636)&(in @ X636 @ X634)))))=>((in @ emptyset @ omega)=>(![X633:$i]:(((in @ X633 @ omega)=>(in @ (setadjoin @ X633 @ X633) @ omega)))=>(![X630:$i]:((((in @ emptyset @ X630)&![X631:$i]:((((in @ X631 @ omega)&(in @ X631 @ X630))=>(in @ (setadjoin @ X631 @ X631) @ X630))))=>![X632:$i]:(((in @ X632 @ omega)=>(in @ X632 @ X630)))))=>(![X335:$i > $i > $o, X336:$i]:((![X337:$i]:(((in @ X337 @ X336)=>?[X338:$i]:(((X335 @ X337 @ X338)&![X339:$i]:(((X335 @ X337 @ X339)=>((X338)=(X339))))))))=>?[X340:$i]:(![X341:$i]:(((in @ X341 @ X340)<=>?[X342:$i]:(((in @ X342 @ X336)&(X335 @ X342 @ X341))))))))=>(![X626:$i]:((?[X627:$i]:((in @ X627 @ X626))=>?[X628:$i]:(((in @ X628 @ X626)&~(?[X629:$i]:(((in @ X629 @ X628)&(in @ X629 @ X626))))))))=>((epred1_0)=>(![X623:$i > $o]:((?[X624:$i]:(((X623 @ X624)&![X625:$i]:(((X623 @ X625)=>((X624)=(X625))))))=>(X623 @ (descr @ (^[Z0/* 3 */:$i]:((X623 @ Z0)))))))=>(![X362:$i, X363:$i > $o, X364:$i]:(((in @ X364 @ X362)=>((X363 @ X364)=>(in @ X364 @ (dsetconstr @ X362 @ (^[Z0/* 3 */:$i]:((X363 @ Z0))))))))=>(![X620:$i, X621:$i > $o, X622:$i]:(((in @ X622 @ (dsetconstr @ X620 @ (^[Z0/* 3 */:$i]:((X621 @ Z0)))))=>(in @ X622 @ X620)))=>(![X617:$i, X618:$i > $o, X619:$i]:(((in @ X619 @ (dsetconstr @ X617 @ (^[Z0/* 3 */:$i]:((X618 @ Z0)))))=>(X618 @ X619)))=>(![X612:$i > $o]:((?[X613:$i]:(((X612 @ X613)&![X614:$i]:(((X612 @ X614)=>((X613)=(X614))))))=>?[X615:$i]:(((X612 @ X615)&![X616:$i]:(((X612 @ X616)=>((X615)=(X616))))))))=>(![X610:$o, X611:$i]:(((in @ X611 @ (prop2set @ ((X610))))=>(X610)))=>(![X608:$i]:(((in @ X608 @ emptyset)=>![X609:$o]:((X609))))=>(![X607:$i]:(~(in @ X607 @ emptyset))=>(![X606:$i]:(~(in @ X606 @ emptyset))=>(![X365:$i > $o]:((?[X366:$i]:(((X365 @ X366)&![X367:$i]:(((X365 @ X367)=>((X366)=(X367))))))=>?[X368:$i]:((X365 @ X368))))=>(![X369:$i, X370:$i]:((![X371:$i]:(((in @ X371 @ X369)=>(in @ X371 @ X370)))=>(![X372:$i]:(((in @ X372 @ X370)=>(in @ X372 @ X369)))=>((X369)=(X370)))))=>(![X604:$i]:((![X605:$i]:(~(in @ X605 @ X604))=>((X604)=(emptyset))))=>(![X373:$i]:((![X374:$i]:(~(in @ X374 @ X373))=>((X373)=(emptyset))))=>(![X375:$i, X376:$i > $o, X377:$i]:(((in @ X377 @ X375)=>((in @ X377 @ (dsetconstr @ X375 @ (^[Z0/* 3 */:$i]:((X376 @ Z0)))))<=>(X376 @ X377))))=>(![X602:$i]:((((X602)!=(emptyset))=>?[X603:$i]:((in @ X603 @ X602))))=>(![X378:$i, X379:$i > $o, X380:$i]:(((in @ X380 @ X378)=>((X379 @ X380)=>((dsetconstr @ X378 @ (^[Z0/* 3 */:$i]:((X379 @ Z0))))!=(emptyset)))))=>(![X381:$i]:((?[X382:$i]:((in @ X382 @ X381))=>((X381)!=(emptyset))))=>(![X600:$i, X601:$i]:((in @ X600 @ (setadjoin @ X600 @ X601)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X383:$i, X384:$i, X385:$i]:(((in @ X385 @ X384)=>(in @ X385 @ (setadjoin @ X383 @ X384))))=>(![X596:$i, X597:$i, X598:$i]:(((in @ X598 @ (setadjoin @ X596 @ X597))=>![X599:$o]:(((((X598)=(X596))=>(X599))=>(((in @ X598 @ X597)=>(X599))=>(X599))))))=>(![X386:$i, X387:$i, X388:$i]:(((in @ X388 @ (setadjoin @ X386 @ X387))=>(((X388)=(X386))|(in @ X388 @ X387))))=>(![X389:$i]:(((dsetconstr @ X389 @ (^[Z0/* 3 */:$i]:(($true))))=(X389)))=>(![X390:$i, X391:$i]:((![X392:$i]:(((in @ X392 @ X391)=>(in @ X392 @ X390)))=>(in @ X391 @ (powerset @ X390))))=>(![X595:$i]:((in @ emptyset @ (powerset @ X595)))=>(![X594:$i]:((in @ emptyset @ (powerset @ X594)))=>(![X393:$i, X394:$i, X395:$i]:(((in @ X394 @ (powerset @ X393))=>((in @ X395 @ X394)=>(in @ X395 @ X393))))=>(![X591:$i, X592:$i, X593:$i]:(((in @ X592 @ X593)=>((in @ X593 @ X591)=>(in @ X592 @ (setunion @ X591)))))=>(![X587:$i, X588:$i]:(((in @ X588 @ (setunion @ X587))=>![X589:$o]:((![X590:$i]:(((in @ X588 @ X590)=>((in @ X590 @ X587)=>(X589))))=>(X589)))))=>(![X585:$i, X586:$i]:(((in @ X586 @ X585)=>(in @ X586 @ (powerset @ (setunion @ X585)))))=>(![X580:$i > $o]:((?[X581:$i]:(((X580 @ X581)&![X582:$i]:(((X580 @ X582)=>((X581)=(X582))))))=>?[X583:$i]:(![X584:$i]:(((X580 @ X584)<=>((X584)=(X583)))))))=>(![X578:$i]:((((X578)!=(emptyset))=>?[X579:$i]:((in @ X579 @ X578))))=>(![X576:$i, X577:$i]:(((in @ X576 @ (setadjoin @ X577 @ emptyset))=>((X576)=(X577))))=>(![X574:$i, X575:$i]:((((X574)!=(X575))=>~(in @ X575 @ (setadjoin @ X574 @ emptyset))))=>(![X396:$i, X397:$i]:((((X396)=(X397))=>(in @ X396 @ (setadjoin @ X397 @ emptyset))))=>(![X398:$i, X399:$i]:(((in @ X398 @ (setadjoin @ X399 @ emptyset))=>(in @ X399 @ (setadjoin @ X398 @ emptyset))))=>(![X400:$i, X401:$i, X402:$i]:(((in @ X402 @ (setadjoin @ X400 @ (setadjoin @ X401 @ emptyset)))=>(((X402)=(X400))|((X402)=(X401)))))=>(![X403:$i, X404:$i]:((in @ X403 @ (setadjoin @ X403 @ (setadjoin @ X404 @ emptyset))))=>(![X405:$i, X406:$i]:((in @ X406 @ (setadjoin @ X405 @ (setadjoin @ X406 @ emptyset))))=>(![X407:$i, X408:$i > $o]:((?[X409:$i]:(((in @ X409 @ X407)&(X408 @ X409)))=>((dsetconstr @ X407 @ (^[Z0/* 3 */:$i]:((X408 @ Z0))))!=(emptyset))))=>(![X410:$i > $o, X411:$i]:(((in @ X411 @ emptyset)=>(X410 @ X411)))=>(![X412:$i, X413:$i > $o]:((~(![X414:$i]:(((in @ X414 @ X412)=>(X413 @ X414))))=>?[X415:$i]:(((in @ X415 @ X412)&~(X413 @ X415)))))=>(![X570:$i, X571:$i > $o]:((![X572:$i]:(((in @ X572 @ X570)=>~(X571 @ X572)))=>~(?[X573:$i]:(((in @ X573 @ X570)&(X571 @ X573))))))=>(![X566:$i, X567:$i > $o]:((~(?[X568:$i]:(((in @ X568 @ X566)&(X567 @ X568))))=>![X569:$i]:(((in @ X569 @ X566)=>~(X567 @ X569)))))=>(![X562:$i, X563:$i > $o]:((?[X564:$i]:(((in @ X564 @ X562)&~(X563 @ X564)))=>~(![X565:$i]:(((in @ X565 @ X562)=>(X563 @ X565))))))=>(![X416:$o]:(((X416)=>(in @ emptyset @ (prop2set @ ((X416))))))=>(![X417:$o]:(((X417)=>(set2prop @ (prop2set @ ((X417))))))=>(![X418:$i, X419:$i > $o]:((~(?[X420:$i]:(((in @ X420 @ X418)&(X419 @ X420))))=>![X421:$i]:(((in @ X421 @ X418)=>~(X419 @ X421)))))=>(![X422:$i, X423:$i > $o]:((~(![X424:$i]:(((in @ X424 @ X422)=>(X423 @ X424))))=>?[X425:$i]:(((in @ X425 @ X422)&~(X423 @ X425)))))=>(![X426:$i > $o]:((?[X427:$i]:(((X426 @ X427)&![X428:$i]:(((X426 @ X428)=>((X427)=(X428))))))=>?[X429:$i]:(((X426 @ X429)&![X430:$i]:(((X426 @ X430)=>((X429)=(X430))))))))=>(![X556:$i > $o]:((?[X557:$i]:((X556 @ X557))=>(![X558:$i, X559:$i]:(((X556 @ X558)=>((X556 @ X559)=>((X558)=(X559)))))=>?[X560:$i]:(((X556 @ X560)&![X561:$i]:(((X556 @ X561)=>((X560)=(X561)))))))))=>(![X551:$i > $o]:((?[X552:$i]:(![X553:$i]:(((X551 @ X553)<=>((X553)=(X552)))))=>?[X554:$i]:(((X551 @ X554)&![X555:$i]:(((X551 @ X555)=>((X554)=(X555))))))))=>(![X431:$i, X432:$i]:((((X431)=(X432))=>![X433:$i, X434:$i]:((((X433)=(X434))=>((in @ X433 @ X431)=>(in @ X434 @ X432))))))=>(![X547:$i, X548:$i]:((((X547)=(X548))=>![X549:$i, X550:$i]:((((X549)=(X550))=>((in @ X549 @ X547)<=>(in @ X550 @ X548))))))=>(![X542:$i > $o]:((?[X543:$i]:(((X542 @ X543)&![X544:$i]:(((X542 @ X544)=>((X543)=(X544))))))=>![X545:$i, X546:$i]:(((X542 @ X545)=>((X542 @ X546)=>((X545)=(X546)))))))=>(![X435:$i > $o, X436:$i > $o]:((![X437:$i, X438:$i]:((((X437)=(X438))=>((X435 @ X437)<=>(X436 @ X438))))=>(?[X439:$i]:(((X435 @ X439)&![X440:$i]:(((X435 @ X440)=>((X439)=(X440))))))<=>?[X441:$i]:(((X436 @ X441)&![X442:$i]:(((X436 @ X442)=>((X441)=(X442)))))))))=>(((emptyset)=(emptyset))=>(![X538:$i, X539:$i]:((((X538)=(X539))=>![X540:$i, X541:$i]:((((X540)=(X541))=>((setadjoin @ X538 @ X540)=(setadjoin @ X539 @ X541))))))=>(![X443:$i, X444:$i]:((((X443)=(X444))=>((powerset @ X443)=(powerset @ X444))))=>(![X536:$i, X537:$i]:((((X536)=(X537))=>((setunion @ X536)=(setunion @ X537))))=>(((omega)=(omega))=>(![X531:$i > $o]:((?[X532:$i]:(((X531 @ X532)&![X533:$i]:(((X531 @ X533)=>((X532)=(X533))))))=>![X534:$i, X535:$i]:(((X531 @ X534)=>((X531 @ X535)=>((X534)=(X535)))))))=>(![X523:$i > $o, X524:$i > $o]:((![X525:$i, X526:$i]:((((X525)=(X526))=>((X523 @ X525)<=>(X524 @ X526))))=>(?[X527:$i]:(((X523 @ X527)&![X528:$i]:(((X523 @ X528)=>((X527)=(X528))))))=>(?[X529:$i]:(((X524 @ X529)&![X530:$i]:(((X524 @ X530)=>((X529)=(X530))))))=>((descr @ (^[Z0/* 3 */:$i]:((X523 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X524 @ Z0)))))))))=>(![X517:$i, X518:$i]:((((X517)=(X518))=>![X519:$i > $o, X520:$i > $o]:((![X521:$i]:(((in @ X521 @ X517)=>![X522:$i]:(((in @ X522 @ X518)=>(((X521)=(X522))=>((X519 @ X521)<=>(X520 @ X522)))))))=>((dsetconstr @ X517 @ (^[Z0/* 3 */:$i]:((X519 @ Z0))))=(dsetconstr @ X518 @ (^[Z0/* 3 */:$i]:((X520 @ Z0)))))))))=>(![X514:$i, X515:$i]:((![X516:$i]:(((in @ X516 @ X514)=>(in @ X516 @ X515)))=>(subset @ X514 @ X515)))=>(![X445:$i, X446:$i]:((((X445)=(X446))=>(subset @ X446 @ X445)))=>(![X512:$i, X513:$i]:((((X512)=(X513))=>(subset @ X512 @ X513)))=>(![X447:$i, X448:$i]:((![X449:$i]:(((in @ X449 @ X447)=>(in @ X449 @ X448)))=>(subset @ X447 @ X448)))=>(![X450:$i]:((subset @ emptyset @ X450))=>(![X451:$i, X452:$i, X453:$i]:(((subset @ X451 @ X452)=>((in @ X453 @ X451)=>(in @ X453 @ X452))))=>(![X454:$i, X455:$i, X456:$i]:(((subset @ X454 @ X455)=>(~(in @ X456 @ X455)=>~(in @ X456 @ X454))))=>(![X509:$i, X510:$i, X511:$i]:(((in @ X511 @ X509)=>(~(in @ X511 @ X510)=>~(subset @ X509 @ X510))))=>(![X507:$i, X508:$i]:((~(subset @ X507 @ X508)=>((X507)!=(X508))))=>(![X504:$i, X505:$i, X506:$i]:(((in @ X506 @ X504)=>(~(in @ X506 @ X505)=>((X504)!=(X505)))))=>(![X503:$i]:((subset @ X503 @ X503))=>(![X500:$i, X501:$i, X502:$i]:(((subset @ X500 @ X501)=>((subset @ X501 @ X502)=>(subset @ X500 @ X502))))=>(![X457:$i, X458:$i]:((subset @ X458 @ (setadjoin @ X457 @ X458)))=>(![X497:$i, X498:$i, X499:$i]:(((subset @ X497 @ X499)=>(subset @ X497 @ (setadjoin @ X498 @ X499))))=>(![X495:$i, X496:$i]:(((subset @ X495 @ X496)=>(in @ X495 @ (powerset @ X496))))=>(![X459:$i, X460:$i]:(((subset @ X459 @ X460)=>((subset @ X460 @ X459)=>((X459)=(X460)))))=>(![X461:$i]:(((subset @ X461 @ emptyset)=>((X461)=(emptyset))))=>(![X462:$i, X463:$i]:(((subset @ X463 @ X462)=>(in @ X463 @ (powerset @ X462))))=>(![X464:$i, X465:$i]:(((in @ X465 @ (powerset @ X464))=>(subset @ X465 @ X464)))=>(![X466:$i]:((in @ X466 @ (powerset @ X466)))=>(![X493:$i, X494:$i]:(((subset @ X493 @ X494)=>(subset @ (powerset @ X493) @ (powerset @ X494))))=>(![X467:$i, X468:$i > $o]:((in @ (dsetconstr @ X467 @ (^[Z0/* 3 */:$i]:((X468 @ Z0)))) @ (powerset @ X467)))=>(![X491:$i, X492:$i > $o]:((subset @ (dsetconstr @ X491 @ (^[Z0/* 3 */:$i]:((X492 @ Z0)))) @ X491))=>(![X469:$i, X470:$i, X471:$i]:(((in @ X471 @ X469)=>(in @ X471 @ (binunion @ X469 @ X470))))=>(![X489:$i, X490:$i]:((in @ X490 @ (setadjoin @ X489 @ (setadjoin @ X490 @ emptyset))))=>(![X486:$i, X487:$i, X488:$i]:(((in @ X488 @ X487)=>(in @ X488 @ (binunion @ X486 @ X487))))=>(![X472:$i, X473:$i, X474:$i, X475:$o]:(((in @ X474 @ (binunion @ X472 @ X473))=>(((in @ X474 @ X472)=>(X475))=>(((in @ X474 @ X473)=>(X475))=>(X475)))))=>(![X483:$i, X484:$i, X485:$i]:(((in @ X485 @ (binunion @ X483 @ X484))=>((in @ X485 @ X483)|(in @ X485 @ X484))))=>(![X476:$i, X477:$i]:((subset @ X476 @ (binunion @ X476 @ X477)))=>(![X481:$i, X482:$i]:((subset @ X482 @ (binunion @ X481 @ X482)))=>(![X478:$i, X479:$i, X480:$i]:(((in @ X480 @ X478)=>((in @ X480 @ X479)=>(in @ X480 @ (binintersect @ X478 @ X479)))))=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[binintersectSubset5]), setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_124]), foundationAx]), wellorderingAx]), c_0_125]), c_0_126]), c_0_127]), c_0_128]), c_0_129]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_130]), setext]), emptyI]), noeltsimpempty]), c_0_131]), c_0_132]), c_0_133]), c_0_134]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_135]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_136]), c_0_137]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_138]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_139]), c_0_140]), c_0_141]), inCongP]), in__Cong]), c_0_142]), c_0_143]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_144]), c_0_145]), c_0_146]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_147]), c_0_148]), binunionIL]), upairset2IR]), binunionIR]), binunionEcases]), binunionE]), binunionLsub]), binunionRsub]), binintersectI])]), c_0_149])). 786.41/99.42 thf(c_0_151, negated_conjecture, ![X651:$i, X652:$i, X654:$i, X655:$i, X656:$i, X657:$i, X658:$i, X659:$i, X660:$i, X661:$i, X662:$i, X664:$i, X665:$i, X667:$i, X668:$i, X669:$i, X670:$i, X671:$i, X673:$i, X674:$i > $i > $o, X675:$i, X677:$i, X680:$i, X682:$i, X683:$i, X684:$i, X685:$i, X687:$i, X688:$i > $o, X689:$i, X691:$i, X692:$i > $o, X693:$i, X694:$i, X695:$i > $o, X696:$i, X697:$i, X698:$i > $o, X699:$i, X700:$i > $o, X701:$i, X704:$i, X705:$o, X706:$i, X707:$i, X708:$o, X709:$i, X710:$i, X711:$i > $o, X712:$i, X715:$i, X716:$i, X719:$i, X721:$i, X723:$i, X724:$i > $o, X725:$i, X726:$i, X728:$i, X729:$i > $o, X730:$i, X731:$i, X732:$i, X733:$i, X734:$i, X735:$i, X736:$i, X737:$i, X738:$i, X739:$i, X740:$i, X741:$o, X742:$i, X743:$i, X744:$i, X745:$i, X746:$i, X747:$i, X749:$i, X750:$i, X751:$i, X752:$i, X753:$i, X754:$i, X755:$i, X756:$i, X757:$i, X758:$i, X759:$o, X761:$i, X762:$i, X763:$i > $o, X764:$i, X767:$i, X768:$i, X769:$i, X771:$i, X772:$i, X773:$i, X774:$i, X775:$i, X776:$i, X777:$i, X778:$i, X779:$i, X780:$i, X781:$i, X782:$i, X783:$i, X784:$i, X785:$i, X786:$i, X787:$i > $o, X788:$i, X789:$i > $o, X790:$i, X791:$i, X792:$i > $o, X793:$i, X795:$i, X796:$i > $o, X798:$i, X799:$i, X800:$i > $o, X802:$i, X803:$i, X804:$i > $o, X805:$i, X807:$o, X808:$o, X809:$i, X810:$i > $o, X812:$i, X813:$i, X814:$i > $o, X815:$i, X817:$i > $o, X818:$i, X821:$i, X822:$i > $o, X823:$i, X827:$i, X828:$i > $o, X829:$i, X832:$i, X833:$i, X834:$i, X835:$i, X836:$i, X837:$i, X838:$i, X839:$i, X840:$i, X841:$i > $o, X842:$i, X844:$i, X845:$i, X846:$i > $o, X847:$i > $o, X850:$i, X853:$i, X854:$i, X857:$i, X858:$i, X859:$i, X860:$i, X861:$i, X862:$i, X863:$i, X864:$i, X865:$i, X866:$i > $o, X867:$i, X869:$i, X870:$i, X871:$i > $o, X872:$i > $o, X875:$i, X877:$i, X879:$i, X880:$i, X881:$i > $o, X882:$i > $o, X885:$i, X886:$i, X888:$i, X889:$i, X890:$i, X891:$i, X892:$i, X893:$i, X895:$i, X896:$i, X897:$i, X898:$i, X899:$i, X900:$i, X901:$i, X902:$i, X903:$i, X904:$i, X905:$i, X906:$i, X907:$i, X908:$i, X909:$i, X910:$i, X911:$i, X912:$i, X913:$i, X914:$i, X915:$i, X916:$i, X917:$i, X918:$i, X919:$i, X920:$i, X921:$i, X922:$i, X923:$i, X924:$i, X925:$i, X926:$i, X927:$i, X928:$i, X929:$i, X930:$i, X931:$i, X932:$i > $o, X933:$i, X934:$i > $o, X935:$i, X936:$i, X937:$i, X938:$i, X939:$i, X940:$i, X941:$i, X942:$i, X943:$i, X944:$i, X945:$i, X946:$o, X947:$i, X948:$i, X949:$i, X950:$i, X951:$i, X952:$i, X953:$i, X954:$i, X955:$i, X956:$i]:((((~(in @ (esk1_2 @ X651 @ X652) @ X651)|~(in @ (esk1_2 @ X651 @ X652) @ X652)|((X651)=(X652)))&((in @ (esk1_2 @ X651 @ X652) @ X651)|(in @ (esk1_2 @ X651 @ X652) @ X652)|((X651)=(X652))))&(~(in @ X654 @ emptyset)&(((~(in @ X657 @ (setadjoin @ X655 @ X656))|(((X657)=(X655))|(in @ X657 @ X656)))&((((X657)!=(X655))|(in @ X657 @ (setadjoin @ X655 @ X656)))&(~(in @ X657 @ X656)|(in @ X657 @ (setadjoin @ X655 @ X656)))))&(((~(in @ X659 @ (powerset @ X658))|(~(in @ X660 @ X659)|(in @ X660 @ X658)))&(((in @ (esk2_2 @ X661 @ X662) @ X662)|(in @ X662 @ (powerset @ X661)))&(~(in @ (esk2_2 @ X661 @ X662) @ X661)|(in @ X662 @ (powerset @ X661)))))&(((((in @ X665 @ (esk3_2 @ X664 @ X665))|~(in @ X665 @ (setunion @ X664)))&((in @ (esk3_2 @ X664 @ X665) @ X664)|~(in @ X665 @ (setunion @ X664))))&(~(in @ X668 @ X669)|~(in @ X669 @ X667)|(in @ X668 @ (setunion @ X667))))&((in @ emptyset @ omega)&((~(in @ X670 @ omega)|(in @ (setadjoin @ X670 @ X670) @ omega))&(((((in @ (esk4_1 @ X671) @ 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X872))))&(((X872 @ (esk49_3 @ X871 @ X872 @ X877))|~(X872 @ X877)|((descr @ (^[Z0/* 3 */:$i]:((X871 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X872 @ Z0)))))|(((X875)!=(esk48_3 @ X871 @ X872 @ X875))|~(X871 @ X875))|((esk46_2 @ X871 @ X872)=(esk47_2 @ X871 @ X872)))&(((X877)!=(esk49_3 @ X871 @ X872 @ X877))|~(X872 @ X877)|((descr @ (^[Z0/* 3 */:$i]:((X871 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X872 @ Z0)))))|(((X875)!=(esk48_3 @ X871 @ X872 @ X875))|~(X871 @ X875))|((esk46_2 @ X871 @ X872)=(esk47_2 @ X871 @ X872)))))&(((((X872 @ (esk49_3 @ X871 @ X872 @ X877))|~(X872 @ X877)|((descr @ (^[Z0/* 3 */:$i]:((X871 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X872 @ Z0)))))|((X871 @ (esk48_3 @ X871 @ X872 @ X875))|~(X871 @ X875))|(~(X871 @ (esk46_2 @ X871 @ X872))|~(X872 @ (esk47_2 @ X871 @ X872))))&(((X877)!=(esk49_3 @ X871 @ X872 @ X877))|~(X872 @ X877)|((descr @ (^[Z0/* 3 */:$i]:((X871 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X872 @ Z0)))))|((X871 @ (esk48_3 @ X871 @ X872 @ X875))|~(X871 @ X875))|(~(X871 @ (esk46_2 @ X871 @ X872))|~(X872 @ (esk47_2 @ X871 @ X872)))))&(((X872 @ (esk49_3 @ X871 @ X872 @ X877))|~(X872 @ X877)|((descr @ (^[Z0/* 3 */:$i]:((X871 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X872 @ Z0)))))|(((X875)!=(esk48_3 @ X871 @ X872 @ X875))|~(X871 @ X875))|(~(X871 @ (esk46_2 @ X871 @ X872))|~(X872 @ (esk47_2 @ X871 @ X872))))&(((X877)!=(esk49_3 @ X871 @ X872 @ X877))|~(X872 @ X877)|((descr @ (^[Z0/* 3 */:$i]:((X871 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X872 @ Z0)))))|(((X875)!=(esk48_3 @ X871 @ X872 @ X875))|~(X871 @ X875))|(~(X871 @ (esk46_2 @ X871 @ X872))|~(X872 @ (esk47_2 @ X871 @ X872))))))&((((X872 @ (esk49_3 @ X871 @ X872 @ X877))|~(X872 @ X877)|((descr @ (^[Z0/* 3 */:$i]:((X871 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X872 @ Z0)))))|((X871 @ (esk48_3 @ X871 @ X872 @ X875))|~(X871 @ X875))|((X871 @ (esk46_2 @ X871 @ X872))|(X872 @ (esk47_2 @ X871 @ X872))))&(((X877)!=(esk49_3 @ X871 @ X872 @ X877))|~(X872 @ X877)|((descr @ (^[Z0/* 3 */:$i]:((X871 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X872 @ Z0)))))|((X871 @ (esk48_3 @ X871 @ X872 @ X875))|~(X871 @ X875))|((X871 @ (esk46_2 @ X871 @ X872))|(X872 @ (esk47_2 @ X871 @ X872)))))&(((X872 @ (esk49_3 @ X871 @ X872 @ X877))|~(X872 @ X877)|((descr @ (^[Z0/* 3 */:$i]:((X871 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X872 @ Z0)))))|(((X875)!=(esk48_3 @ X871 @ X872 @ X875))|~(X871 @ X875))|((X871 @ (esk46_2 @ X871 @ X872))|(X872 @ (esk47_2 @ X871 @ X872))))&(((X877)!=(esk49_3 @ X871 @ X872 @ X877))|~(X872 @ X877)|((descr @ (^[Z0/* 3 */:$i]:((X871 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X872 @ Z0)))))|(((X875)!=(esk48_3 @ X871 @ X872 @ X875))|~(X871 @ X875))|((X871 @ (esk46_2 @ X871 @ X872))|(X872 @ (esk47_2 @ X871 @ X872))))))))&((((in @ (esk50_4 @ X879 @ X880 @ X881 @ X882) @ X879)|((dsetconstr @ X879 @ (^[Z0/* 3 */:$i]:((X881 @ Z0))))=(dsetconstr @ X880 @ (^[Z0/* 3 */:$i]:((X882 @ Z0)))))|((X879)!=(X880)))&(((in @ (esk51_4 @ X879 @ X880 @ X881 @ X882) @ X880)|((dsetconstr @ X879 @ (^[Z0/* 3 */:$i]:((X881 @ Z0))))=(dsetconstr @ X880 @ (^[Z0/* 3 */:$i]:((X882 @ Z0)))))|((X879)!=(X880)))&((((esk50_4 @ X879 @ X880 @ X881 @ X882)=(esk51_4 @ X879 @ X880 @ X881 @ X882))|((dsetconstr @ X879 @ (^[Z0/* 3 */:$i]:((X881 @ Z0))))=(dsetconstr @ X880 @ (^[Z0/* 3 */:$i]:((X882 @ Z0)))))|((X879)!=(X880)))&((~(X881 @ (esk50_4 @ X879 @ X880 @ X881 @ X882))|~(X882 @ (esk51_4 @ X879 @ X880 @ X881 @ X882))|((dsetconstr @ X879 @ (^[Z0/* 3 */:$i]:((X881 @ Z0))))=(dsetconstr @ X880 @ (^[Z0/* 3 */:$i]:((X882 @ Z0)))))|((X879)!=(X880)))&((X881 @ (esk50_4 @ X879 @ X880 @ X881 @ X882))|(X882 @ (esk51_4 @ X879 @ X880 @ X881 @ X882))|((dsetconstr @ X879 @ (^[Z0/* 3 */:$i]:((X881 @ Z0))))=(dsetconstr @ X880 @ (^[Z0/* 3 */:$i]:((X882 @ Z0)))))|((X879)!=(X880)))))))&((((in @ (esk52_2 @ X885 @ X886) @ X885)|(subset @ X885 @ X886))&(~(in @ (esk52_2 @ X885 @ X886) @ X886)|(subset @ X885 @ X886)))&((((X888)!=(X889))|(subset @ X889 @ X888))&((((X890)!=(X891))|(subset @ X890 @ X891))&((((in @ (esk53_2 @ X892 @ X893) @ X892)|(subset @ X892 @ X893))&(~(in @ (esk53_2 @ X892 @ X893) @ X893)|(subset @ X892 @ X893)))&((subset @ emptyset @ X895)&((~(subset @ X896 @ X897)|(~(in @ X898 @ X896)|(in @ X898 @ X897)))&((~(subset @ X899 @ X900)|((in @ X901 @ X900)|~(in @ X901 @ X899)))&((~(in @ X904 @ X902)|((in @ X904 @ X903)|~(subset @ X902 @ X903)))&(((subset @ X905 @ X906)|((X905)!=(X906)))&((~(in @ X909 @ X907)|((in @ X909 @ X908)|((X907)!=(X908))))&((subset @ X910 @ X910)&((~(subset @ X911 @ X912)|(~(subset @ X912 @ X913)|(subset @ X911 @ X913)))&((subset @ X915 @ (setadjoin @ X914 @ X915))&((~(subset @ X916 @ X918)|(subset @ X916 @ (setadjoin @ X917 @ X918)))&((~(subset @ X919 @ X920)|(in @ X919 @ (powerset @ X920)))&((~(subset @ X921 @ X922)|(~(subset @ X922 @ X921)|((X921)=(X922))))&((~(subset @ X923 @ emptyset)|((X923)=(emptyset)))&((~(subset @ X925 @ X924)|(in @ X925 @ (powerset @ X924)))&((~(in @ X927 @ (powerset @ X926))|(subset @ X927 @ X926))&((in @ X928 @ (powerset @ X928))&((~(subset @ X929 @ X930)|(subset @ (powerset @ X929) @ (powerset @ X930)))&((in @ (dsetconstr @ X931 @ (^[Z0/* 3 */:$i]:((X932 @ Z0)))) @ (powerset @ X931))&((subset @ (dsetconstr @ X933 @ (^[Z0/* 3 */:$i]:((X934 @ Z0)))) @ X933)&((~(in @ X937 @ X935)|(in @ X937 @ (binunion @ X935 @ X936)))&((in @ X939 @ (setadjoin @ X938 @ (setadjoin @ X939 @ emptyset)))&((~(in @ X942 @ X941)|(in @ X942 @ (binunion @ X940 @ X941)))&(((((in @ X945 @ X944)|(X946)|(in @ X945 @ X943)|~(in @ X945 @ (binunion @ X943 @ X944)))&(~(X946)|(X946)|(in @ X945 @ X943)|~(in @ X945 @ (binunion @ X943 @ X944))))&(((in @ X945 @ X944)|(X946)|~(X946)|~(in @ X945 @ (binunion @ X943 @ X944)))&(~(X946)|(X946)|~(X946)|~(in @ X945 @ (binunion @ X943 @ X944)))))&((~(in @ X949 @ (binunion @ X947 @ X948))|((in @ X949 @ X947)|(in @ X949 @ X948)))&((subset @ X950 @ (binunion @ X950 @ X951))&((subset @ X953 @ (binunion @ X952 @ X953))&((~(in @ X956 @ X954)|(~(in @ X956 @ X955)|(in @ X956 @ (binintersect @ X954 @ X955))))&((subset @ esk56_0 @ esk54_0)&((subset @ esk56_0 @ esk55_0)&~(subset @ esk56_0 @ (binintersect @ esk54_0 @ esk55_0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_150])])])])])])). 786.41/99.42 thf(c_0_152, negated_conjecture, ~((subset @ esk56_0 @ (binintersect @ esk54_0 @ esk55_0))), inference(split_conjunct,[status(thm)],[c_0_151])). 786.41/99.42 thf(c_0_153, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X2 @ X3)|~((in @ (esk53_2 @ X2 @ X3) @ X3)))), inference(split_conjunct,[status(thm)],[c_0_151])). 786.41/99.42 thf(c_0_154, negated_conjecture, ~((in @ (esk53_2 @ esk56_0 @ (binintersect @ esk54_0 @ esk55_0)) @ (binintersect @ esk54_0 @ esk55_0))), inference(spm,[status(thm)],[c_0_152, c_0_153])). 786.41/99.42 thf(c_0_155, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ X2 @ (binintersect @ X3 @ X4))|~((in @ X2 @ X3))|~((in @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_151])). 786.41/99.42 thf(c_0_156, negated_conjecture, ![X4:$i, X3:$i, X2:$i]:(((in @ X4 @ X3)|~((subset @ X2 @ X3))|~((in @ X4 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_151])). 786.41/99.42 thf(c_0_157, negated_conjecture, (subset @ esk56_0 @ esk55_0), inference(split_conjunct,[status(thm)],[c_0_151])). 786.41/99.42 thf(c_0_158, negated_conjecture, ![X2:$i, X3:$i]:(((in @ (esk53_2 @ X2 @ X3) @ X2)|(subset @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_151])). 786.41/99.42 thf(c_0_159, negated_conjecture, (~((in @ (esk53_2 @ esk56_0 @ (binintersect @ esk54_0 @ esk55_0)) @ esk55_0))|~((in @ (esk53_2 @ esk56_0 @ (binintersect @ esk54_0 @ esk55_0)) @ esk54_0))), inference(spm,[status(thm)],[c_0_154, c_0_155])). 786.41/99.42 thf(c_0_160, negated_conjecture, ![X2:$i]:(((in @ X2 @ esk55_0)|~((in @ X2 @ esk56_0)))), inference(spm,[status(thm)],[c_0_156, c_0_157])). 786.41/99.42 thf(c_0_161, negated_conjecture, (in @ (esk53_2 @ esk56_0 @ (binintersect @ esk54_0 @ esk55_0)) @ esk56_0), inference(spm,[status(thm)],[c_0_152, c_0_158])). 786.41/99.42 thf(c_0_162, negated_conjecture, (subset @ esk56_0 @ esk54_0), inference(split_conjunct,[status(thm)],[c_0_151])). 786.41/99.42 thf(c_0_163, negated_conjecture, ~((in @ (esk53_2 @ esk56_0 @ (binintersect @ esk54_0 @ esk55_0)) @ esk54_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159, c_0_160]), c_0_161])])). 786.41/99.42 thf(c_0_164, negated_conjecture, ![X2:$i]:(((in @ X2 @ esk54_0)|~((in @ X2 @ esk56_0)))), inference(spm,[status(thm)],[c_0_156, c_0_162])). 786.41/99.42 thf(c_0_165, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163, c_0_164]), c_0_161])]), ['proof']). 786.41/99.42 # SZS output end CNFRefutation 786.41/99.42 # Parsed axioms : 233 786.41/99.42 # Removed by relevancy pruning/SinE : 0 786.41/99.42 # Initial clauses : 345 786.41/99.42 # Removed in clause preprocessing : 139 786.41/99.42 # Initial clauses in saturation : 206 786.41/99.42 # Processed clauses : 478 786.41/99.42 # ...of these trivial : 12 786.41/99.42 # ...subsumed : 47 786.41/99.42 # ...remaining for further processing : 419 786.41/99.42 # Other redundant clauses eliminated : 16 786.41/99.42 # Clauses deleted for lack of memory : 0 786.41/99.42 # Backward-subsumed : 3 786.41/99.42 # Backward-rewritten : 5 786.41/99.42 # Generated clauses : 1330 786.41/99.42 # ...of the previous two non-redundant : 1241 786.41/99.42 # ...aggressively subsumed : 0 786.41/99.42 # Contextual simplify-reflections : 0 786.41/99.42 # Paramodulations : 1311 786.41/99.42 # Factorizations : 0 786.41/99.42 # NegExts : 0 786.41/99.42 # Equation resolutions : 16 786.41/99.42 # Total rewrite steps : 152 786.41/99.42 # Propositional unsat checks : 0 786.41/99.42 # Propositional check models : 0 786.41/99.42 # Propositional check unsatisfiable : 0 786.41/99.42 # Propositional clauses : 0 786.41/99.42 # Propositional clauses after purity: 0 786.41/99.42 # Propositional unsat core size : 0 786.41/99.42 # Propositional preprocessing time : 0.000 786.41/99.42 # Propositional encoding time : 0.000 786.41/99.42 # Propositional solver time : 0.000 786.41/99.42 # Success case prop preproc time : 0.000 786.41/99.42 # Success case prop encoding time : 0.000 786.41/99.42 # Success case prop solver time : 0.000 786.41/99.42 # Current number of processed clauses : 219 786.41/99.42 # Positive orientable unit clauses : 54 786.41/99.42 # Positive unorientable unit clauses: 1 786.41/99.42 # Negative unit clauses : 8 786.41/99.42 # Non-unit-clauses : 156 786.41/99.42 # Current number of unprocessed clauses: 1133 786.41/99.42 # ...number of literals in the above : 2908 786.41/99.42 # Current number of archived formulas : 0 786.41/99.42 # Current number of archived clauses : 187 786.41/99.42 # Clause-clause subsumption calls (NU) : 9235 786.41/99.42 # Rec. Clause-clause subsumption calls : 3866 786.41/99.42 # Non-unit clause-clause subsumptions : 24 786.41/99.42 # Unit Clause-clause subsumption calls : 108 786.41/99.42 # Rewrite failures with RHS unbound : 0 786.41/99.42 # BW rewrite match attempts : 16 786.41/99.42 # BW rewrite match successes : 7 786.41/99.42 # Condensation attempts : 0 786.41/99.42 # Condensation successes : 0 786.41/99.42 # Termbank termtop insertions : 62470 786.41/99.42 786.41/99.42 # ------------------------------------------------- 786.41/99.42 # User time : 96.776 s 786.41/99.42 # System time : 1.499 s 786.41/99.42 # Total time : 98.275 s 786.41/99.42 # Maximum resident set size: 4468 pages 788.82/99.76 788.82/99.76 # ------------------------------------------------- 788.82/99.76 # User time : 96.784 s 788.82/99.76 # System time : 1.503 s 788.82/99.76 # Total time : 98.287 s 788.82/99.76 # Maximum resident set size: 2060 pages 788.82/99.76 % E---3.1 exiting 788.82/99.76 EOF