0.00/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.11 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 240 THM 0.11/0.32 % Computer : n027.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 : 1920 0.11/0.32 % WCLimit : 240 0.11/0.32 % DateTime : Wed Jul 30 07:24:34 EDT 2025 0.11/0.32 % CPUTime : 0.19/0.45 Running higher-order theorem proving 0.19/0.48 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=240 /export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p 0.92/0.59 # Version: 3.0.0-ho 0.92/0.59 # Preprocessing class: HSLMSLSSLLLCHFA. 0.92/0.59 # Scheduled 8 strats onto 8 cores with 240 seconds (1920 total) 0.92/0.59 # Starting ehoh_best5 with 240s (1) cores 0.92/0.59 # Starting almost_fo_3_lam with 240s (1) cores 0.92/0.59 # Starting new_bool_5 with 240s (1) cores 0.92/0.59 # Starting pre_casc_3 with 240s (1) cores 0.92/0.59 # Starting ho_unfolding_8 with 240s (1) cores 0.92/0.59 # Starting new_ho_10_cnf2 with 240s (1) cores 0.92/0.59 # Starting new_bool_3 with 240s (1) cores 0.92/0.59 # Starting new_ho_5 with 240s (1) cores 0.92/0.59 # new_bool_3 with pid 3338 completed with status 0 0.92/0.59 # Result found by new_bool_3 0.92/0.59 # Preprocessing class: HSLMSLSSLLLCHFA. 0.92/0.59 # Scheduled 8 strats onto 8 cores with 240 seconds (1920 total) 0.92/0.59 # Starting ehoh_best5 with 240s (1) cores 0.92/0.59 # Starting almost_fo_3_lam with 240s (1) cores 0.92/0.59 # Starting new_bool_5 with 240s (1) cores 0.92/0.59 # Starting pre_casc_3 with 240s (1) cores 0.92/0.59 # Starting ho_unfolding_8 with 240s (1) cores 0.92/0.59 # Starting new_ho_10_cnf2 with 240s (1) cores 0.92/0.59 # Starting new_bool_3 with 240s (1) cores 0.92/0.59 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0) 0.92/0.59 # Search class: HGHSM-FSLM31-MHFMMSBN 0.92/0.59 # Scheduled 6 strats onto 1 cores with 240 seconds (240 total) 0.92/0.59 # Starting new_ho_10_cnf2 with 130s (1) cores 0.92/0.59 # new_ho_10_cnf2 with pid 3340 completed with status 0 0.92/0.59 # Result found by new_ho_10_cnf2 0.92/0.59 # Preprocessing class: HSLMSLSSLLLCHFA. 0.92/0.59 # Scheduled 8 strats onto 8 cores with 240 seconds (1920 total) 0.92/0.59 # Starting ehoh_best5 with 240s (1) cores 0.92/0.59 # Starting almost_fo_3_lam with 240s (1) cores 0.92/0.59 # Starting new_bool_5 with 240s (1) cores 0.92/0.59 # Starting pre_casc_3 with 240s (1) cores 0.92/0.59 # Starting ho_unfolding_8 with 240s (1) cores 0.92/0.59 # Starting new_ho_10_cnf2 with 240s (1) cores 0.92/0.59 # Starting new_bool_3 with 240s (1) cores 0.92/0.59 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0) 0.92/0.59 # Search class: HGHSM-FSLM31-MHFMMSBN 0.92/0.59 # Scheduled 6 strats onto 1 cores with 240 seconds (240 total) 0.92/0.59 # Starting new_ho_10_cnf2 with 130s (1) cores 0.92/0.59 # Preprocessing time : 0.004 s 0.92/0.59 # Presaturation interreduction done 0.92/0.59 0.92/0.59 # Proof found! 0.92/0.59 # SZS status Theorem 0.92/0.59 # SZS output start CNFRefutation 0.92/0.59 thf(decl_23, type, in: $i > $i > $o). 0.92/0.59 thf(decl_24, type, exu: ($i > $o) > $o). 0.92/0.59 thf(decl_25, type, setextAx: $o). 0.92/0.59 thf(decl_26, type, emptyset: $i). 0.92/0.59 thf(decl_27, type, emptysetAx: $o). 0.92/0.59 thf(decl_28, type, setadjoin: $i > $i > $i). 0.92/0.59 thf(decl_29, type, setadjoinAx: $o). 0.92/0.59 thf(decl_30, type, powerset: $i > $i). 0.92/0.59 thf(decl_31, type, powersetAx: $o). 0.92/0.59 thf(decl_32, type, setunion: $i > $i). 0.92/0.59 thf(decl_33, type, setunionAx: $o). 0.92/0.59 thf(decl_34, type, omega: $i). 0.92/0.59 thf(decl_35, type, omega0Ax: $o). 0.92/0.59 thf(decl_36, type, omegaSAx: $o). 0.92/0.59 thf(decl_37, type, omegaIndAx: $o). 0.92/0.59 thf(decl_38, type, replAx: $o). 0.92/0.59 thf(decl_39, type, foundationAx: $o). 0.92/0.59 thf(decl_40, type, wellorderingAx: $o). 0.92/0.59 thf(decl_41, type, descr: ($i > $o) > $i). 0.92/0.59 thf(decl_42, type, descrp: $o). 0.92/0.59 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i). 0.92/0.59 thf(decl_44, type, dsetconstrI: $o). 0.92/0.59 thf(decl_45, type, dsetconstrEL: $o). 0.92/0.59 thf(decl_46, type, dsetconstrER: $o). 0.92/0.59 thf(decl_47, type, exuE1: $o). 0.92/0.59 thf(decl_48, type, prop2set: $o > $i). 0.92/0.59 thf(decl_49, type, prop2setE: $o). 0.92/0.59 thf(decl_50, type, emptysetE: $o). 0.92/0.59 thf(decl_51, type, emptysetimpfalse: $o). 0.92/0.59 thf(decl_52, type, notinemptyset: $o). 0.92/0.59 thf(decl_53, type, exuE3e: $o). 0.92/0.59 thf(decl_54, type, setext: $o). 0.92/0.59 thf(decl_55, type, emptyI: $o). 0.92/0.59 thf(decl_56, type, noeltsimpempty: $o). 0.92/0.59 thf(decl_57, type, setbeta: $o). 0.92/0.59 thf(decl_58, type, nonempty: $i > $o). 0.92/0.59 thf(decl_59, type, nonemptyE1: $o). 0.92/0.59 thf(decl_60, type, nonemptyI: $o). 0.92/0.59 thf(decl_61, type, nonemptyI1: $o). 0.92/0.59 thf(decl_62, type, setadjoinIL: $o). 0.92/0.59 thf(decl_63, type, emptyinunitempty: $o). 0.92/0.59 thf(decl_64, type, setadjoinIR: $o). 0.92/0.59 thf(decl_65, type, setadjoinE: $o). 0.92/0.59 thf(decl_66, type, setadjoinOr: $o). 0.92/0.59 thf(decl_67, type, setoftrueEq: $o). 0.92/0.59 thf(decl_68, type, powersetI: $o). 0.92/0.59 thf(decl_69, type, emptyinPowerset: $o). 0.92/0.59 thf(decl_70, type, emptyInPowerset: $o). 0.92/0.59 thf(decl_71, type, powersetE: $o). 0.92/0.59 thf(decl_72, type, setunionI: $o). 0.92/0.59 thf(decl_73, type, setunionE: $o). 0.92/0.59 thf(decl_74, type, subPowSU: $o). 0.92/0.59 thf(decl_75, type, exuE2: $o). 0.92/0.59 thf(decl_76, type, nonemptyImpWitness: $o). 0.92/0.59 thf(decl_77, type, uniqinunit: $o). 0.92/0.59 thf(decl_78, type, notinsingleton: $o). 0.92/0.59 thf(decl_79, type, eqinunit: $o). 0.92/0.59 thf(decl_80, type, singletonsswitch: $o). 0.92/0.59 thf(decl_81, type, upairsetE: $o). 0.92/0.59 thf(decl_82, type, upairsetIL: $o). 0.92/0.59 thf(decl_83, type, upairsetIR: $o). 0.92/0.59 thf(decl_84, type, emptyE1: $o). 0.92/0.59 thf(decl_85, type, vacuousDall: $o). 0.92/0.59 thf(decl_86, type, quantDeMorgan1: $o). 0.92/0.59 thf(decl_87, type, quantDeMorgan2: $o). 0.92/0.59 thf(decl_88, type, quantDeMorgan3: $o). 0.92/0.59 thf(decl_89, type, quantDeMorgan4: $o). 0.92/0.59 thf(decl_90, type, prop2setI: $o). 0.92/0.59 thf(decl_92, type, prop2set2propI: $o). 0.92/0.59 thf(decl_93, type, notdexE: $o). 0.92/0.59 thf(decl_94, type, notdallE: $o). 0.92/0.59 thf(decl_95, type, exuI1: $o). 0.92/0.59 thf(decl_96, type, exuI3: $o). 0.92/0.59 thf(decl_97, type, exuI2: $o). 0.92/0.59 thf(decl_98, type, inCongP: $o). 0.92/0.59 thf(decl_99, type, in__Cong: $o). 0.92/0.59 thf(decl_100, type, exuE3u: $o). 0.92/0.59 thf(decl_101, type, exu__Cong: $o). 0.92/0.59 thf(decl_102, type, emptyset__Cong: $o). 0.92/0.59 thf(decl_103, type, setadjoin__Cong: $o). 0.92/0.59 thf(decl_104, type, powerset__Cong: $o). 0.92/0.59 thf(decl_105, type, setunion__Cong: $o). 0.92/0.59 thf(decl_106, type, omega__Cong: $o). 0.92/0.59 thf(decl_107, type, exuEu: $o). 0.92/0.59 thf(decl_108, type, descr__Cong: $o). 0.92/0.59 thf(decl_109, type, dsetconstr__Cong: $o). 0.92/0.59 thf(decl_110, type, subset: $i > $i > $o). 0.92/0.59 thf(decl_113, type, subsetI1: $o). 0.92/0.59 thf(decl_114, type, eqimpsubset2: $o). 0.92/0.59 thf(decl_115, type, eqimpsubset1: $o). 0.92/0.59 thf(decl_116, type, subsetI2: $o). 0.92/0.59 thf(decl_117, type, emptysetsubset: $o). 0.92/0.59 thf(decl_118, type, subsetE: $o). 0.92/0.59 thf(decl_119, type, subsetE2: $o). 0.92/0.59 thf(decl_120, type, notsubsetI: $o). 0.92/0.59 thf(decl_121, type, notequalI1: $o). 0.92/0.59 thf(decl_122, type, notequalI2: $o). 0.92/0.59 thf(decl_123, type, subsetRefl: $o). 0.92/0.59 thf(decl_124, type, subsetTrans: $o). 0.92/0.59 thf(decl_125, type, setadjoinSub: $o). 0.92/0.59 thf(decl_126, type, setadjoinSub2: $o). 0.92/0.59 thf(decl_127, type, subset2powerset: $o). 0.92/0.59 thf(decl_128, type, setextsub: $o). 0.92/0.59 thf(decl_129, type, subsetemptysetimpeq: $o). 0.92/0.59 thf(decl_130, type, powersetI1: $o). 0.92/0.59 thf(decl_131, type, powersetE1: $o). 0.92/0.59 thf(decl_132, type, inPowerset: $o). 0.92/0.59 thf(decl_133, type, powersetsubset: $o). 0.92/0.59 thf(decl_134, type, sepInPowerset: $o). 0.92/0.59 thf(decl_135, type, sepSubset: $o). 0.92/0.59 thf(decl_136, type, binunion: $i > $i > $i). 0.92/0.59 thf(decl_137, type, binunionIL: $o). 0.92/0.59 thf(decl_138, type, upairset2IR: $o). 0.92/0.59 thf(decl_139, type, binunionIR: $o). 0.92/0.59 thf(decl_140, type, binunionEcases: $o). 0.92/0.59 thf(decl_141, type, binunionE: $o). 0.92/0.59 thf(decl_142, type, binunionLsub: $o). 0.92/0.59 thf(decl_143, type, binunionRsub: $o). 0.92/0.59 thf(decl_144, type, binintersect: $i > $i > $i). 0.92/0.59 thf(decl_145, type, binintersectI: $o). 0.92/0.59 thf(decl_146, type, binintersectSubset5: $o). 0.92/0.59 thf(decl_147, type, binintersectEL: $o). 0.92/0.59 thf(decl_148, type, binintersectLsub: $o). 0.92/0.59 thf(decl_149, type, binintersectSubset2: $o). 0.92/0.59 thf(decl_150, type, binintersectSubset3: $o). 0.92/0.59 thf(decl_151, type, binintersectER: $o). 0.92/0.59 thf(decl_152, type, disjointsetsI1: $o). 0.92/0.59 thf(decl_153, type, binintersectRsub: $o). 0.92/0.59 thf(decl_154, type, binintersectSubset4: $o). 0.92/0.59 thf(decl_155, type, binintersectSubset1: $o). 0.92/0.59 thf(decl_156, type, bs114d: $o). 0.92/0.59 thf(decl_158, type, setminus: $i > $i > $i). 0.92/0.59 thf(decl_159, type, setminusI: $o). 0.92/0.59 thf(decl_160, type, setminusEL: $o). 0.92/0.59 thf(decl_161, type, setminusER: $o). 0.92/0.59 thf(decl_162, type, setminusSubset2: $o). 0.92/0.59 thf(decl_163, type, setminusERneg: $o). 0.92/0.59 thf(decl_164, type, setminusELneg: $o). 0.92/0.59 thf(decl_165, type, setminusILneg: $o). 0.92/0.59 thf(decl_166, type, setminusIRneg: $o). 0.92/0.59 thf(decl_167, type, setminusLsub: $o). 0.92/0.59 thf(decl_168, type, setminusSubset1: $o). 0.92/0.59 thf(decl_169, type, symdiff: $i > $i > $i). 0.92/0.59 thf(decl_170, type, symdiffE: $o). 0.92/0.59 thf(decl_171, type, epred1_0: $o). 0.92/0.59 thf(decl_172, type, esk1_2: $i > $i > $i). 0.92/0.59 thf(decl_173, type, esk2_2: $i > $i > $i). 0.92/0.59 thf(decl_174, type, esk3_2: $i > $i > $i). 0.92/0.59 thf(decl_175, type, esk4_1: $i > $i). 0.92/0.59 thf(decl_176, type, esk5_2: ($i > $i > $o) > $i > $i). 0.92/0.59 thf(decl_177, type, esk6_3: ($i > $i > $o) > $i > $i > $i). 0.92/0.59 thf(decl_178, type, esk7_2: ($i > $i > $o) > $i > $i). 0.92/0.59 thf(decl_179, type, esk8_3: ($i > $i > $o) > $i > $i > $i). 0.92/0.59 thf(decl_180, type, esk9_1: $i > $i). 0.92/0.59 thf(decl_181, type, esk10_2: ($i > $o) > $i > $i). 0.92/0.59 thf(decl_182, type, esk11_2: ($i > $o) > $i > $i). 0.92/0.59 thf(decl_183, type, esk12_1: ($i > $o) > $i). 0.92/0.59 thf(decl_184, type, esk13_2: ($i > $o) > $i > $i). 0.92/0.59 thf(decl_185, type, esk14_1: ($i > $o) > $i). 0.92/0.59 thf(decl_186, type, esk15_2: $i > $i > $i). 0.92/0.59 thf(decl_187, type, esk16_2: $i > $i > $i). 0.92/0.59 thf(decl_188, type, esk17_1: $i > $i). 0.92/0.59 thf(decl_189, type, esk18_1: $i > $i). 0.92/0.59 thf(decl_190, type, esk19_1: $i > $i). 0.92/0.59 thf(decl_191, type, esk20_2: $i > $i > $i). 0.92/0.59 thf(decl_192, type, esk21_3: $i > $i > $o > $i). 0.92/0.59 thf(decl_193, type, esk22_2: ($i > $o) > $i > $i). 0.92/0.59 thf(decl_194, type, esk23_1: ($i > $o) > $i). 0.92/0.59 thf(decl_195, type, esk24_1: $i > $i). 0.92/0.59 thf(decl_196, type, esk25_2: $i > ($i > $o) > $i). 0.92/0.59 thf(decl_197, type, esk26_2: $i > ($i > $o) > $i). 0.92/0.59 thf(decl_198, type, esk27_2: $i > ($i > $o) > $i). 0.92/0.59 thf(decl_199, type, esk28_2: $i > ($i > $o) > $i). 0.92/0.59 thf(decl_200, type, esk29_2: $i > ($i > $o) > $i). 0.92/0.59 thf(decl_201, type, esk30_2: $i > ($i > $o) > $i). 0.92/0.59 thf(decl_202, type, esk31_2: ($i > $o) > $i > $i). 0.92/0.59 thf(decl_203, type, esk32_1: ($i > $o) > $i). 0.92/0.59 thf(decl_204, type, esk33_1: ($i > $o) > $i). 0.92/0.59 thf(decl_205, type, esk34_1: ($i > $o) > $i). 0.92/0.59 thf(decl_206, type, esk35_1: ($i > $o) > $i). 0.92/0.59 thf(decl_207, type, esk36_2: ($i > $o) > $i > $i). 0.92/0.59 thf(decl_208, type, esk37_1: ($i > $o) > $i). 0.92/0.59 thf(decl_209, type, esk38_2: ($i > $o) > $i > $i). 0.92/0.59 thf(decl_210, type, esk39_2: ($i > $o) > ($i > $o) > $i). 0.92/0.59 thf(decl_211, type, esk40_2: ($i > $o) > ($i > $o) > $i). 0.92/0.59 thf(decl_212, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i). 0.92/0.59 thf(decl_213, type, esk42_2: ($i > $o) > ($i > $o) > $i). 0.92/0.59 thf(decl_214, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i). 0.92/0.59 thf(decl_215, type, esk44_2: ($i > $o) > ($i > $o) > $i). 0.92/0.59 thf(decl_216, type, esk45_2: ($i > $o) > $i > $i). 0.92/0.59 thf(decl_217, type, esk46_2: ($i > $o) > ($i > $o) > $i). 0.92/0.59 thf(decl_218, type, esk47_2: ($i > $o) > ($i > $o) > $i). 0.92/0.59 thf(decl_219, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i). 0.92/0.59 thf(decl_220, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i). 0.92/0.59 thf(decl_221, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i). 0.92/0.59 thf(decl_222, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i). 0.92/0.59 thf(decl_223, type, esk52_2: $i > $i > $i). 0.92/0.59 thf(decl_224, type, esk53_2: $i > $i > $i). 0.92/0.59 thf(decl_225, type, esk54_2: $i > $i > $i). 0.92/0.59 thf(decl_226, type, esk55_0: $i). 0.92/0.59 thf(decl_227, type, esk56_0: $i). 0.92/0.59 thf(decl_228, type, esk57_0: $i). 0.92/0.59 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', nonemptyI)). 0.92/0.59 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', nonempty)). 0.92/0.59 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/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', exuEu)). 0.92/0.59 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', exu)). 0.92/0.59 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', exuE1)). 0.92/0.59 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', descrp)). 0.92/0.59 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', descr__Cong)). 0.92/0.59 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', replAx)). 0.92/0.59 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', exuE3u)). 0.92/0.59 thf(symdiff, axiom, ((symdiff)=(^[X4:$i, X5:$i]:(dsetconstr @ (binunion @ X4 @ X5) @ (^[X2:$i]:((~((in @ X2 @ X4))|~((in @ X2 @ X5)))))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', symdiff)). 0.92/0.59 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', exu__Cong)). 0.92/0.59 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', exuI3)). 0.92/0.59 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', exuI2)). 0.92/0.59 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/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', exuI1)). 0.92/0.59 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', exuE2)). 0.92/0.59 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', exuE3e)). 0.92/0.59 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', nonemptyE1)). 0.92/0.59 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', setbeta)). 0.92/0.59 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', dsetconstrI)). 0.92/0.59 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', sepInPowerset)). 0.92/0.59 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', sepSubset)). 0.92/0.59 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', nonemptyImpWitness)). 0.92/0.59 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', symdiffE)). 0.92/0.59 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', dsetconstr__Cong)). 0.92/0.59 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', emptyE1)). 0.92/0.59 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', setoftrueEq)). 0.92/0.59 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', nonemptyI1)). 0.92/0.59 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', dsetconstrER)). 0.92/0.59 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', dsetconstrEL)). 0.92/0.59 thf(symdiffI1, conjecture, (((emptysetAx)=>((((((((((wellorderingAx)=>((((dsetconstrEL)=>((dsetconstrER)=>(((prop2setE)=>((emptysetE)=>(((notinemptyset)=>((exuE3e)=>((setext)=>(((noeltsimpempty)=>(((((nonemptyI1)=>((((setadjoinIR)=>((setadjoinE)=>(((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((((subPowSU)=>((exuE2)=>((((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((((emptyE1)=>((vacuousDall)=>(((quantDeMorgan2)=>((((prop2setI)=>(((notdexE)=>((notdallE)=>((exuI1)=>(((exuI2)=>(((in__Cong)=>((exuE3u)=>(((emptyset__Cong)=>((setadjoin__Cong)=>(((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>(((subsetI1)=>(((((((subsetE2)=>((notsubsetI)=>((notequalI1)=>(((subsetRefl)=>(((setadjoinSub)=>(((subset2powerset)=>((setextsub)=>((((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((((binunionEcases)=>(((binunionLsub)=>(((binintersectI)=>((binintersectSubset5)=>((((((((binintersectRsub)=>(((((setminusI)=>((setminusEL)=>(((((((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>![X4:$i, X5:$i, X2:$i]:(((~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))<=(in @ X2 @ X4)))))))<=(setminusILneg))<=(setminusELneg))<=(setminusERneg))<=(setminusSubset2))<=(setminusER))))<=(bs114d))<=(binintersectSubset1))<=(binintersectSubset4)))<=(disjointsetsI1))<=(binintersectER))<=(binintersectSubset3))<=(binintersectSubset2))<=(binintersectLsub))<=(binintersectEL))))<=(binunionRsub)))<=(binunionE)))<=(binunionIR))<=(upairset2IR))))))))<=(powersetI1))<=(subsetemptysetimpeq))))<=(setadjoinSub2)))<=(subsetTrans)))<=(notequalI2)))))<=(subsetE))<=(emptysetsubset))<=(subsetI2))<=(eqimpsubset1))<=(eqimpsubset2)))<=(dsetconstr__Cong))))))<=(powerset__Cong))))<=(exu__Cong))))<=(inCongP)))<=(exuI3)))))<=(prop2set2propI)))<=(quantDeMorgan4))<=(quantDeMorgan3)))<=(quantDeMorgan1))))<=(upairsetIR))<=(upairsetIL))))))<=(uniqinunit))<=(nonemptyImpWitness))))<=(setunionE))<=(setunionI)))))))<=(setadjoinOr))))<=(emptyinunitempty))<=(setadjoinIL)))<=(nonemptyI))<=(nonemptyE1))<=(setbeta)))<=(emptyI)))))<=(emptysetimpfalse))))<=(exuE1))))<=(dsetconstrI))<=(descrp)))<=(foundationAx))<=(replAx))<=(omegaIndAx))<=(omegaSAx))<=(omega0Ax))<=(setunionAx))<=(powersetAx))<=(setadjoinAx)))<=(setextAx)), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', symdiffI1)). 0.92/0.59 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', notsubsetI)). 0.92/0.59 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', setextAx)). 0.92/0.59 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', setadjoinOr)). 0.92/0.59 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', emptyinunitempty)). 0.92/0.59 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', setadjoinIL)). 0.92/0.59 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', setunion__Cong)). 0.92/0.59 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', omega__Cong)). 0.92/0.59 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', emptyI)). 0.92/0.59 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', emptysetimpfalse)). 0.92/0.59 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', foundationAx)). 0.92/0.59 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', subsetI1)). 0.92/0.59 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', omegaIndAx)). 0.92/0.59 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', in__Cong)). 0.92/0.59 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', omegaSAx)). 0.92/0.59 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', omega0Ax)). 0.92/0.59 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', setunionAx)). 0.92/0.59 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', subsetE2)). 0.92/0.59 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', powersetAx)). 0.92/0.59 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', setadjoinAx)). 0.92/0.59 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', binintersectSubset5)). 0.92/0.59 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', notequalI1)). 0.92/0.59 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', subsetRefl)). 0.92/0.59 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', setadjoinSub)). 0.92/0.59 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', subset2powerset)). 0.92/0.59 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', setextsub)). 0.92/0.59 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', powersetE1)). 0.92/0.59 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', inPowerset)). 0.92/0.59 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', powersetsubset)). 0.92/0.59 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', emptyset__Cong)). 0.92/0.59 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', binunionIL)). 0.92/0.59 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/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', binunionEcases)). 0.92/0.59 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', binunionLsub)). 0.92/0.59 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', binintersectI)). 0.92/0.59 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', quantDeMorgan1)). 0.92/0.59 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', upairsetIR)). 0.92/0.59 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', upairsetIL)). 0.92/0.59 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', uniqinunit)). 0.92/0.59 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', setunionE)). 0.92/0.59 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', binintersectRsub)). 0.92/0.59 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', setminusI)). 0.92/0.59 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', setminusEL)). 0.92/0.59 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', setminusIRneg)). 0.92/0.59 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', setminusLsub)). 0.92/0.59 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', setminusSubset1)). 0.92/0.59 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', setminusILneg)). 0.92/0.59 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', setadjoin__Cong)). 0.92/0.59 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', setminusELneg)). 0.92/0.59 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', setminusERneg)). 0.92/0.59 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', setminusSubset2)). 0.92/0.59 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', setminusER)). 0.92/0.59 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', bs114d)). 0.92/0.59 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', binintersectSubset1)). 0.92/0.59 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', binintersectSubset4)). 0.92/0.59 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', disjointsetsI1)). 0.92/0.59 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', binintersectER)). 0.92/0.59 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', binintersectSubset3)). 0.92/0.59 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', binintersectSubset2)). 0.92/0.59 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', binintersectLsub)). 0.92/0.59 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', binintersectEL)). 0.92/0.59 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', binunionRsub)). 0.92/0.59 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', binunionE)). 0.92/0.59 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', binunionIR)). 0.92/0.59 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', upairset2IR)). 0.92/0.59 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', powersetI1)). 0.92/0.59 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', subsetemptysetimpeq)). 0.92/0.59 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', setadjoinSub2)). 0.92/0.59 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', subsetTrans)). 0.92/0.59 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', notequalI2)). 0.92/0.59 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', subsetE)). 0.92/0.59 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', emptysetsubset)). 0.92/0.59 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', subsetI2)). 0.92/0.59 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', eqimpsubset1)). 0.92/0.59 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', eqimpsubset2)). 0.92/0.59 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', powerset__Cong)). 0.92/0.59 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', inCongP)). 0.92/0.59 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', quantDeMorgan4)). 0.92/0.59 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', quantDeMorgan3)). 0.92/0.59 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', setunionI)). 0.92/0.59 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', notdallE)). 0.92/0.59 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', notdexE)). 0.92/0.59 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', prop2setI)). 0.92/0.59 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', quantDeMorgan2)). 0.92/0.59 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', vacuousDall)). 0.92/0.59 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', upairsetE)). 0.92/0.59 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', singletonsswitch)). 0.92/0.59 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', eqinunit)). 0.92/0.59 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', notinsingleton)). 0.92/0.59 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', subPowSU)). 0.92/0.59 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', powersetE)). 0.92/0.59 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', emptyInPowerset)). 0.92/0.59 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', emptyinPowerset)). 0.92/0.59 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', powersetI)). 0.92/0.59 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', setadjoinE)). 0.92/0.59 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', setadjoinIR)). 0.92/0.59 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', noeltsimpempty)). 0.92/0.59 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/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', setext)). 0.92/0.59 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', notinemptyset)). 0.92/0.59 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', emptysetE)). 0.92/0.59 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', prop2setE)). 0.92/0.59 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', wellorderingAx)). 0.92/0.59 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.4S6zL42VeA/E---3.1_3253.p', emptysetAx)). 0.92/0.59 thf(c_0_131, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 0.92/0.59 thf(c_0_132, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])). 0.92/0.59 thf(c_0_133, 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])). 0.92/0.59 thf(c_0_134, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])). 0.92/0.59 thf(c_0_135, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 0.92/0.59 thf(c_0_136, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 0.92/0.59 thf(c_0_137, plain, ((descr__Cong)<=>![X1:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 0.92/0.59 thf(c_0_138, plain, ((replAx)<=>![X6:$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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 0.92/0.59 thf(c_0_139, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])). 0.92/0.59 thf(c_0_140, plain, ((symdiff)=(^[Z0/* 19 */:$i, Z1:$i]:(dsetconstr @ (binunion @ Z0 @ Z1) @ (^[Z2/* 9 */:$i]:((~((in @ Z2 @ Z0))|~((in @ Z2 @ Z1)))))))), inference(fof_simplification,[status(thm)],[symdiff])). 0.92/0.59 thf(c_0_141, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 0.92/0.59 thf(c_0_142, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 0.92/0.59 thf(c_0_143, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 0.92/0.59 thf(c_0_144, 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])). 0.92/0.59 thf(c_0_145, 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])). 0.92/0.59 thf(c_0_146, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 0.92/0.59 thf(c_0_147, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_131, c_0_132])). 0.92/0.59 thf(c_0_148, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_132])). 0.92/0.59 thf(c_0_149, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 0.92/0.59 thf(c_0_150, plain, ((exuEu)=(![X1:$i > $o]:(((?[X387:$i]:((((X1 @ X387))&![X388:$i]:((((X1 @ X388))=>((X387)=(X388)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_133, c_0_134])). 0.92/0.59 thf(c_0_151, plain, ((exuE1)=(![X1:$i > $o]:(((?[X369:$i]:((((X1 @ X369))&![X370:$i]:((((X1 @ X370))=>((X369)=(X370)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_135, c_0_134])). 0.92/0.59 thf(c_0_152, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 0.92/0.59 thf(c_0_153, plain, ((descrp)=(![X1:$i > $o]:(((?[X367:$i]:((((X1 @ X367))&![X368:$i]:((((X1 @ X368))=>((X367)=(X368)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_136, c_0_134])). 0.92/0.59 thf(c_0_154, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X389:$i]:((((X1 @ X389))&![X390:$i]:((((X1 @ X390))=>((X389)=(X390)))))))=>((?[X391:$i]:((((X17 @ X391))&![X392:$i]:((((X17 @ X392))=>((X391)=(X392)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_137, c_0_134])). 0.92/0.59 thf(c_0_155, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X365:$i]:((((X6 @ X2 @ X365))&![X366:$i]:((((X6 @ X2 @ X366))=>((X365)=(X366)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_138, c_0_134])). 0.92/0.59 thf(c_0_156, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X381:$i]:((((X1 @ X381))&![X382:$i]:((((X1 @ X382))=>((X381)=(X382)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_139, c_0_134])). 0.92/0.59 thf(c_0_157, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 0.92/0.59 thf(c_0_158, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 0.92/0.59 thf(c_0_159, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_132])). 0.92/0.59 thf(c_0_160, axiom, ((symdiffE)=(![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (dsetconstr @ (binunion @ X4 @ X5) @ (^[Z0/* 9 */:$i]:((~((in @ Z0 @ X4))|~((in @ Z0 @ X5)))))))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20)))))))), inference(apply_def,[status(thm)],[symdiffE, c_0_140])). 0.92/0.59 thf(c_0_161, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 0.92/0.59 thf(c_0_162, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X383:$i]:((((X1 @ X383))&![X384:$i]:((((X1 @ X384))=>((X383)=(X384)))))))<=>(?[X385:$i]:((((X17 @ X385))&![X386:$i]:((((X17 @ X386))=>((X385)=(X386)))))))))))), inference(apply_def,[status(thm)],[c_0_141, c_0_134])). 0.92/0.59 thf(c_0_163, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X377:$i]:((((X1 @ X377))&![X378:$i]:((((X1 @ X378))=>((X377)=(X378)))))))))))), inference(apply_def,[status(thm)],[c_0_142, c_0_134])). 0.92/0.59 thf(c_0_164, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X379:$i]:((((X1 @ X379))&![X380:$i]:((((X1 @ X380))=>((X379)=(X380))))))))))), inference(apply_def,[status(thm)],[c_0_143, c_0_134])). 0.92/0.59 thf(c_0_165, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X375:$i]:((((X1 @ X375))&![X376:$i]:((((X1 @ X376))=>((X375)=(X376))))))))))), inference(apply_def,[status(thm)],[c_0_144, c_0_134])). 0.92/0.59 thf(c_0_166, plain, ((emptyE1)<=>![X4:$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])). 0.92/0.59 thf(c_0_167, plain, ((exuE2)=(![X1:$i > $o]:(((?[X373:$i]:((((X1 @ X373))&![X374:$i]:((((X1 @ X374))=>((X373)=(X374)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_145, c_0_134])). 0.92/0.59 thf(c_0_168, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 0.92/0.59 thf(c_0_169, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_132])). 0.92/0.59 thf(c_0_170, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X371:$i]:((((X1 @ X371))&![X372:$i]:((((X1 @ X372))=>((X371)=(X372)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_146, c_0_134])). 0.92/0.59 thf(c_0_171, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 0.92/0.59 thf(c_0_172, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 0.92/0.59 thf(c_0_173, plain, ((epred1_0)<=>![X394:$i]:(?[X395:$i]:((((![X396:$i]:(((in @ X396 @ X395)=>![X397:$i]:(((in @ X397 @ X396)=>(in @ X397 @ X394)))))&![X398:$i, X399:$i]:((((in @ X398 @ X394)&(in @ X399 @ X394))=>(![X400:$i]:(((in @ X400 @ X395)=>((in @ X398 @ X400)<=>(in @ X399 @ X400))))=>((X398)=(X399))))))&![X401:$i, X402:$i]:((((in @ X401 @ X395)&(in @ X402 @ X395))=>(![X403:$i]:(((in @ X403 @ X401)=>(in @ X403 @ X402)))|![X404:$i]:(((in @ X404 @ X402)=>(in @ X404 @ X401)))))))&![X405:$i]:(((![X406:$i]:(((in @ X406 @ X405)=>(in @ X406 @ X394)))&?[X407:$i]:((in @ X407 @ X405)))=>?[X408:$i, X409:$i]:(((((in @ X408 @ X395)&(in @ X409 @ X405))&~(?[X410:$i]:(((in @ X410 @ X408)&(in @ X410 @ X405)))))&![X411:$i]:(((in @ X411 @ X395)=>(![X412:$i]:(((in @ X412 @ X411)=>(in @ X412 @ X408)))|(in @ X409 @ X411)))))))))))), introduced(definition)). 0.92/0.59 thf(c_0_174, negated_conjecture, ~((![X759:$i, X760:$i]:((![X761:$i]:(((in @ X761 @ X759)<=>(in @ X761 @ X760)))=>((X759)=(X760))))=>(![X393:$i]:(~(in @ X393 @ emptyset))=>(![X756:$i, X757:$i, X758:$i]:(((in @ X758 @ (setadjoin @ X756 @ X757))<=>(((X758)=(X756))|(in @ X758 @ X757))))=>(![X753:$i, X754:$i]:(((in @ X754 @ (powerset @ X753))<=>![X755:$i]:(((in @ X755 @ X754)=>(in @ X755 @ X753)))))=>(![X750:$i, X751:$i]:(((in @ X751 @ (setunion @ X750))<=>?[X752:$i]:(((in @ X751 @ X752)&(in @ X752 @ X750)))))=>((in @ emptyset @ omega)=>(![X749:$i]:(((in @ X749 @ omega)=>(in @ (setadjoin @ X749 @ X749) @ omega)))=>(![X746:$i]:((((in @ emptyset @ X746)&![X747:$i]:((((in @ X747 @ omega)&(in @ X747 @ X746))=>(in @ (setadjoin @ X747 @ X747) @ X746))))=>![X748:$i]:(((in @ X748 @ omega)=>(in @ X748 @ X746)))))=>(![X738:$i > $i > $o, X739:$i]:((![X740:$i]:(((in @ X740 @ X739)=>?[X741:$i]:(((X738 @ X740 @ X741)&![X742:$i]:(((X738 @ X740 @ X742)=>((X741)=(X742))))))))=>?[X743:$i]:(![X744:$i]:(((in @ X744 @ X743)<=>?[X745:$i]:(((in @ X745 @ X739)&(X738 @ X745 @ X744))))))))=>(![X734:$i]:((?[X735:$i]:((in @ X735 @ X734))=>?[X736:$i]:(((in @ X736 @ X734)&~(?[X737:$i]:(((in @ X737 @ X736)&(in @ X737 @ X734))))))))=>((epred1_0)=>(![X731:$i > $o]:((?[X732:$i]:(((X731 @ X732)&![X733:$i]:(((X731 @ X733)=>((X732)=(X733))))))=>(X731 @ (descr @ (^[Z0/* 17 */:$i]:(X731 @ Z0))))))=>(![X728:$i, X729:$i > $o, X730:$i]:(((in @ X730 @ X728)=>((X729 @ X730)=>(in @ X730 @ (dsetconstr @ X728 @ X729)))))=>(![X413:$i, X414:$i > $o, X415:$i]:(((in @ X415 @ (dsetconstr @ X413 @ X414))=>(in @ X415 @ X413)))=>(![X416:$i, X417:$i > $o, X418:$i]:(((in @ X418 @ (dsetconstr @ X416 @ X417))=>(X417 @ X418)))=>(![X723:$i > $o]:((?[X724:$i]:(((X723 @ X724)&![X725:$i]:(((X723 @ X725)=>((X724)=(X725))))))=>?[X726:$i]:(((X723 @ X726)&![X727:$i]:(((X723 @ X727)=>((X726)=(X727))))))))=>(![X419:$o, X420:$i]:(((in @ X420 @ (prop2set @ ((X419))))=>(X419)))=>(![X421:$i]:(((in @ X421 @ emptyset)=>![X422:$o]:((X422))))=>(![X722:$i]:(((in @ X722 @ emptyset)=>~($true)))=>(![X423:$i]:(~(in @ X423 @ emptyset))=>(![X424:$i > $o]:((?[X425:$i]:(((X424 @ X425)&![X426:$i]:(((X424 @ X426)=>((X425)=(X426))))))=>?[X427:$i]:((X424 @ X427))))=>(![X428:$i, X429:$i]:((![X430:$i]:(((in @ X430 @ X428)=>(in @ X430 @ X429)))=>(![X431:$i]:(((in @ X431 @ X429)=>(in @ X431 @ X428)))=>((X428)=(X429)))))=>(![X720:$i]:((![X721:$i]:(~(in @ X721 @ X720))=>((X720)=(emptyset))))=>(![X432:$i]:((![X433:$i]:(~(in @ X433 @ X432))=>((X432)=(emptyset))))=>(![X717:$i, X718:$i > $o, X719:$i]:(((in @ X719 @ X717)=>((in @ X719 @ (dsetconstr @ X717 @ X718))<=>(X718 @ X719))))=>(![X715:$i]:((((X715)!=(emptyset))=>?[X716:$i]:((in @ X716 @ X715))))=>(![X712:$i, X713:$i > $o, X714:$i]:(((in @ X714 @ X712)=>((X713 @ X714)=>((dsetconstr @ X712 @ X713)!=(emptyset)))))=>(![X434:$i]:((?[X435:$i]:((in @ X435 @ X434))=>((X434)!=(emptyset))))=>(![X710:$i, X711:$i]:((in @ X710 @ (setadjoin @ X710 @ X711)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X436:$i, X437:$i, X438:$i]:(((in @ X438 @ X437)=>(in @ X438 @ (setadjoin @ X436 @ X437))))=>(![X439:$i, X440:$i, X441:$i]:(((in @ X441 @ (setadjoin @ X439 @ X440))=>![X442:$o]:(((((X441)=(X439))=>(X442))=>(((in @ X441 @ X440)=>(X442))=>(X442))))))=>(![X707:$i, X708:$i, X709:$i]:(((in @ X709 @ (setadjoin @ X707 @ X708))=>(((X709)=(X707))|(in @ X709 @ X708))))=>(![X443:$i]:(((dsetconstr @ X443 @ (^[Z0/* 1 */:$i]:($true)))=(X443)))=>(![X444:$i, X445:$i]:((![X446:$i]:(((in @ X446 @ X445)=>(in @ X446 @ X444)))=>(in @ X445 @ (powerset @ X444))))=>(![X447:$i]:((in @ emptyset @ (powerset @ X447)))=>(![X448:$i]:((in @ emptyset @ (powerset @ X448)))=>(![X449:$i, X450:$i, X451:$i]:(((in @ X450 @ (powerset @ X449))=>((in @ X451 @ X450)=>(in @ X451 @ X449))))=>(![X704:$i, X705:$i, X706:$i]:(((in @ X705 @ X706)=>((in @ X706 @ X704)=>(in @ X705 @ (setunion @ X704)))))=>(![X700:$i, X701:$i]:(((in @ X701 @ (setunion @ X700))=>![X702:$o]:((![X703:$i]:(((in @ X701 @ X703)=>((in @ X703 @ X700)=>(X702))))=>(X702)))))=>(![X452:$i, X453:$i]:(((in @ X453 @ X452)=>(in @ X453 @ (powerset @ (setunion @ X452)))))=>(![X454:$i > $o]:((?[X455:$i]:(((X454 @ X455)&![X456:$i]:(((X454 @ X456)=>((X455)=(X456))))))=>?[X457:$i]:(![X458:$i]:(((X454 @ X458)<=>((X458)=(X457)))))))=>(![X698:$i]:((((X698)!=(emptyset))=>?[X699:$i]:(((in @ X699 @ X698)&$true))))=>(![X696:$i, X697:$i]:(((in @ X696 @ (setadjoin @ X697 @ emptyset))=>((X696)=(X697))))=>(![X459:$i, X460:$i]:((((X459)!=(X460))=>~(in @ X460 @ (setadjoin @ X459 @ emptyset))))=>(![X461:$i, X462:$i]:((((X461)=(X462))=>(in @ X461 @ (setadjoin @ X462 @ emptyset))))=>(![X463:$i, X464:$i]:(((in @ X463 @ (setadjoin @ X464 @ emptyset))=>(in @ X464 @ (setadjoin @ X463 @ emptyset))))=>(![X465:$i, X466:$i, X467:$i]:(((in @ X467 @ (setadjoin @ X465 @ (setadjoin @ X466 @ emptyset)))=>(((X467)=(X465))|((X467)=(X466)))))=>(![X694:$i, X695:$i]:((in @ X694 @ (setadjoin @ X694 @ (setadjoin @ X695 @ emptyset))))=>(![X692:$i, X693:$i]:((in @ X693 @ (setadjoin @ X692 @ (setadjoin @ X693 @ emptyset))))=>(![X468:$i, X469:$i > $o]:((?[X470:$i]:(((in @ X470 @ X468)&(X469 @ X470)))=>(((dsetconstr @ X468 @ X469)=(emptyset))=>~($true))))=>(![X471:$i > $o, X472:$i]:(((in @ X472 @ emptyset)=>(X471 @ X472)))=>(![X688:$i, X689:$i > $o]:((~(![X690:$i]:(((in @ X690 @ X688)=>(X689 @ X690))))=>?[X691:$i]:(((in @ X691 @ X688)&~((X689 @ X691))))))=>(![X473:$i, X474:$i > $o]:((![X475:$i]:(((in @ X475 @ X473)=>~((X474 @ X475))))=>~(?[X476:$i]:(((in @ X476 @ X473)&(X474 @ X476))))))=>(![X684:$i, X685:$i > $o]:((~(?[X686:$i]:(((in @ X686 @ X684)&(X685 @ X686))))=>![X687:$i]:(((in @ X687 @ X684)=>~((X685 @ X687))))))=>(![X680:$i, X681:$i > $o]:((?[X682:$i]:(((in @ X682 @ X680)&~((X681 @ X682))))=>~(![X683:$i]:(((in @ X683 @ X680)=>(X681 @ X683))))))=>(![X477:$o]:(((X477)=>(in @ emptyset @ (prop2set @ ((X477))))))=>((prop2set2propI)=>(![X478:$i, X479:$i > $o]:((~(?[X480:$i]:(((in @ X480 @ X478)&(X479 @ X480))))=>![X481:$i]:(((in @ X481 @ X478)=>~((X479 @ X481))))))=>(![X482:$i, X483:$i > $o]:((~(![X484:$i]:(((in @ X484 @ X482)=>(X483 @ X484))))=>?[X485:$i]:(((in @ X485 @ X482)&~((X483 @ X485))))))=>(![X486:$i > $o]:((?[X487:$i]:(((X486 @ X487)&![X488:$i]:(((X486 @ X488)=>((X487)=(X488))))))=>?[X489:$i]:(((X486 @ X489)&![X490:$i]:(((X486 @ X490)=>((X489)=(X490))))))))=>(![X674:$i > $o]:((?[X675:$i]:((X674 @ X675))=>(![X676:$i, X677:$i]:(((X674 @ X676)=>((X674 @ X677)=>((X676)=(X677)))))=>?[X678:$i]:(((X674 @ X678)&![X679:$i]:(((X674 @ X679)=>((X678)=(X679)))))))))=>(![X491:$i > $o]:((?[X492:$i]:(![X493:$i]:(((X491 @ X493)<=>((X493)=(X492)))))=>?[X494:$i]:(((X491 @ X494)&![X495:$i]:(((X491 @ X495)=>((X494)=(X495))))))))=>(![X670:$i, X671:$i]:((((X670)=(X671))=>![X672:$i, X673:$i]:((((X672)=(X673))=>((in @ X672 @ X670)=>(in @ X673 @ X671))))))=>(![X496:$i, X497:$i]:((((X496)=(X497))=>![X498:$i, X499:$i]:((((X498)=(X499))=>((in @ X498 @ X496)<=>(in @ X499 @ X497))))))=>(![X500:$i > $o]:((?[X501:$i]:(((X500 @ X501)&![X502:$i]:(((X500 @ X502)=>((X501)=(X502))))))=>![X503:$i, X504:$i]:(((X500 @ X503)=>((X500 @ X504)=>((X503)=(X504)))))))=>(![X662:$i > $o, X663:$i > 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inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[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(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)],[symdiffI1]), notsubsetI]), setextAx]), setadjoinOr]), emptyinunitempty]), setadjoinIL]), setunion__Cong]), c_0_147]), c_0_148]), c_0_149]), omega__Cong]), emptyI]), emptysetimpfalse]), c_0_150]), c_0_151]), c_0_152]), c_0_153]), c_0_154]), foundationAx]), c_0_155]), subsetI1]), omegaIndAx]), in__Cong]), omegaSAx]), omega0Ax]), setunionAx]), subsetE2]), powersetAx]), setadjoinAx]), binintersectSubset5]), notequalI1]), c_0_156]), subsetRefl]), setadjoinSub]), subset2powerset]), setextsub]), powersetE1]), inPowerset]), powersetsubset]), emptyset__Cong]), c_0_157]), c_0_158]), binunionIL]), binunionEcases]), binunionLsub]), binintersectI]), quantDeMorgan1]), upairsetIR]), upairsetIL]), uniqinunit]), c_0_159]), setunionE]), binintersectRsub]), setminusI]), setminusEL]), setminusIRneg]), setminusLsub]), setminusSubset1]), c_0_160]), c_0_140]), setminusILneg]), setadjoin__Cong]), setminusELneg]), setminusERneg]), setminusSubset2]), setminusER]), bs114d]), binintersectSubset1]), binintersectSubset4]), disjointsetsI1]), binintersectER]), binintersectSubset3]), binintersectSubset2]), binintersectLsub]), binintersectEL]), binunionRsub]), binunionE]), binunionIR]), upairset2IR]), powersetI1]), subsetemptysetimpeq]), setadjoinSub2]), subsetTrans]), notequalI2]), subsetE]), emptysetsubset]), subsetI2]), eqimpsubset1]), eqimpsubset2]), c_0_161]), powerset__Cong]), c_0_162]), inCongP]), c_0_163]), quantDeMorgan4]), quantDeMorgan3]), setunionI]), c_0_164]), c_0_165]), notdallE]), notdexE]), prop2setI]), quantDeMorgan2]), vacuousDall]), c_0_166]), upairsetE]), singletonsswitch]), eqinunit]), notinsingleton]), c_0_167]), subPowSU]), powersetE]), emptyInPowerset]), emptyinPowerset]), powersetI]), c_0_168]), setadjoinE]), setadjoinIR]), c_0_169]), noeltsimpempty]), setext]), c_0_170]), notinemptyset]), emptysetE]), prop2setE]), c_0_171]), c_0_172]), wellorderingAx]), emptysetAx])])]), c_0_173])). 0.92/0.59 thf(c_0_175, negated_conjecture, ![X762:$i, X763:$i, X765:$i, X766:$i, X767:$i, X768:$i, X769:$i, X770:$i, X771:$i, X772:$i, X773:$i, X775:$i, X776:$i, X778:$i, X779:$i, X780:$i, X781:$i, X782:$i, X784:$i, X785:$i > $i > $o, X786:$i, X788:$i, X791:$i, X793:$i, X794:$i, X795:$i, X796:$i, X798:$i, X799:$i > $o, X800:$i, X802:$i, X803:$i > $o, X804:$i, X805:$i, X806:$i > $o, X807:$i, X808:$i, X809:$i > $o, X810:$i, X811:$i > $o, X812:$i, X815:$i, X816:$o, X817:$i, X818:$i, X819:$o, X820:$i, X821:$i, X822:$i > $o, X823:$i, X826:$i, X827:$i, X830:$i, X832:$i, X834:$i, X835:$i > $o, X836:$i, X837:$i, X839:$i, X840:$i > $o, X841:$i, X842:$i, X843:$i, X844:$i, X845:$i, X846:$i, X847:$i, X848:$i, X849:$i, X850:$i, X851:$i, X852:$o, X853:$i, X854:$i, X855:$i, X856:$i, X857:$i, X858:$i, X860:$i, X861:$i, X862:$i, X863:$i, X864:$i, X865:$i, X866:$i, X867:$i, X868:$i, X869:$i, X870:$o, X872:$i, X873:$i, X874:$i > $o, X875:$i, X878:$i, X879:$i, X880:$i, X882:$i, X883:$i, X884:$i, X885:$i, X886:$i, X887:$i, X888:$i, X889:$i, X890:$i, X891:$i, X892:$i, X893:$i, X894:$i, X895:$i, X896:$i, X897:$i, X898:$i > $o, X899:$i, X900:$i > $o, X901:$i, X902:$i, X903:$i > $o, X904:$i, X906:$i, X907:$i > $o, X909:$i, X910:$i, X911:$i > $o, X913:$i, X914:$i, X915:$i > $o, X916:$i, X918:$o, X919:$i, X920:$i > $o, X922:$i, X923:$i, X924:$i > $o, X925:$i, X927:$i > $o, X928:$i, X931:$i, X932:$i > $o, X933:$i, X937:$i, X938:$i > $o, X939:$i, X942:$i, X943:$i, X944:$i, X945:$i, X946:$i, X947:$i, X948:$i, X949:$i, X950:$i, X951:$i > $o, X952:$i, X954:$i, X955:$i, X956:$i > $o, X957:$i > $o, X960:$i, X963:$i, X964:$i, X967:$i, X968:$i, X969:$i, X970:$i, X971:$i, X972:$i, X973:$i, X974:$i, X975:$i, X976:$i > $o, X977:$i, X979:$i, X980:$i, X981:$i > $o, X982:$i > $o, X985:$i, X987:$i, X989:$i, X990:$i, X991:$i > $o, X992:$i > $o, X995:$i, X996:$i, X998:$i, X999:$i, X1000:$i, X1001:$i, X1002:$i, X1003:$i, X1005:$i, X1006:$i, X1007:$i, X1008:$i, X1009:$i, X1010:$i, X1011:$i, X1012:$i, X1013:$i, X1014:$i, X1015:$i, X1016:$i, X1017:$i, X1018:$i, X1019:$i, X1020:$i, X1021:$i, X1022:$i, X1023:$i, X1024:$i, X1025:$i, X1026:$i, X1027:$i, X1028:$i, X1029:$i, X1030:$i, X1031:$i, X1032:$i, X1033:$i, X1034:$i, X1035:$i, X1036:$i, X1037:$i, X1038:$i, X1039:$i, X1040:$i, X1041:$i, X1042:$i > $o, X1043:$i, X1044:$i > $o, X1045:$i, X1046:$i, X1047:$i, X1048:$i, X1049:$i, X1050:$i, X1051:$i, X1052:$i, X1053:$i, X1054:$i, X1055:$i, X1056:$o, X1057:$i, X1058:$i, X1059:$i, X1060:$i, X1061:$i, X1062:$i, X1063:$i, X1064:$i, X1065:$i, X1066:$i, X1067:$i, X1068:$i, X1069:$i, X1070:$i, X1071:$i, X1072:$i, X1073:$i, X1074:$i, X1075:$i, X1076:$i, X1077:$i, X1078:$i, X1079:$i, X1080:$i, X1081:$i, X1082:$i, X1083:$i, X1085:$i, X1086:$i, X1087:$i, X1088:$i, X1089:$i, X1090:$i, X1091:$i, X1092:$i, X1093:$i, X1094:$i, X1095:$i, X1096:$i, X1097:$i, X1098:$i, X1099:$i, X1100:$i, X1101:$i, X1102:$i, X1103:$i, X1104:$i, X1105:$i, X1106:$i, X1107:$i, X1108:$i, X1109:$i, X1110:$i, X1111:$i, X1112:$i, X1113:$i, X1114:$i, X1115:$i, X1116:$i, X1117:$i, X1118:$i, X1119:$i, X1120:$i, X1121:$i, X1122:$i, X1123:$i, X1124:$o]:((((~(in @ (esk1_2 @ X762 @ X763) @ X762)|~(in @ (esk1_2 @ X762 @ X763) @ X763)|((X762)=(X763)))&((in @ (esk1_2 @ X762 @ X763) @ X762)|(in @ (esk1_2 @ X762 @ X763) @ X763)|((X762)=(X763))))&(~(in @ X765 @ emptyset)&(((~(in @ X768 @ (setadjoin @ X766 @ X767))|(((X768)=(X766))|(in @ X768 @ X767)))&((((X768)!=(X766))|(in @ X768 @ (setadjoin @ X766 @ X767)))&(~(in @ X768 @ X767)|(in @ X768 @ (setadjoin @ X766 @ X767)))))&(((~(in @ X770 @ (powerset @ X769))|(~(in @ X771 @ X770)|(in @ X771 @ X769)))&(((in @ (esk2_2 @ X772 @ X773) @ X773)|(in @ X773 @ (powerset @ X772)))&(~(in @ (esk2_2 @ X772 @ X773) @ X772)|(in @ X773 @ (powerset @ X772)))))&(((((in @ X776 @ (esk3_2 @ X775 @ X776))|~(in @ X776 @ (setunion @ X775)))&((in @ (esk3_2 @ X775 @ X776) @ X775)|~(in @ X776 @ (setunion @ X775))))&(~(in @ X779 @ X780)|~(in @ X780 @ X778)|(in @ X779 @ (setunion @ X778))))&((in @ emptyset @ omega)&((~(in @ X781 @ omega)|(in @ (setadjoin @ X781 @ X781) @ omega))&(((((in @ (esk4_1 @ X782) @ omega)|~(in @ emptyset @ X782)|(~(in @ X784 @ omega)|(in @ X784 @ X782)))&((in @ (esk4_1 @ X782) @ X782)|~(in @ emptyset @ X782)|(~(in @ X784 @ omega)|(in @ X784 @ X782))))&(~(in @ (setadjoin @ (esk4_1 @ X782) @ (esk4_1 @ X782)) @ X782)|~(in @ emptyset @ X782)|(~(in @ X784 @ omega)|(in @ X784 @ X782))))&((((((in @ (esk8_3 @ X785 @ X786 @ X791) @ X786)|~(in @ X791 @ (esk7_2 @ X785 @ X786))|(in @ (esk5_2 @ X785 @ X786) @ X786))&((X785 @ (esk8_3 @ X785 @ X786 @ X791) @ X791)|~(in @ X791 @ (esk7_2 @ X785 @ X786))|(in @ (esk5_2 @ X785 @ X786) @ X786)))&(~(in @ X794 @ X786)|~(X785 @ X794 @ X793)|(in @ X793 @ (esk7_2 @ X785 @ X786))|(in @ (esk5_2 @ X785 @ X786) @ X786)))&(((((in @ (esk8_3 @ X785 @ X786 @ X791) @ X786)|~(in @ X791 @ (esk7_2 @ X785 @ X786))|((X785 @ (esk5_2 @ X785 @ X786) @ (esk6_3 @ X785 @ X786 @ X788))|~(X785 @ (esk5_2 @ X785 @ X786) @ X788)))&((X785 @ (esk8_3 @ X785 @ X786 @ X791) @ X791)|~(in @ X791 @ (esk7_2 @ X785 @ X786))|((X785 @ (esk5_2 @ X785 @ X786) @ (esk6_3 @ X785 @ X786 @ X788))|~(X785 @ (esk5_2 @ X785 @ X786) @ X788))))&(~(in @ X794 @ X786)|~(X785 @ X794 @ X793)|(in @ X793 @ (esk7_2 @ X785 @ X786))|((X785 @ (esk5_2 @ X785 @ X786) @ (esk6_3 @ X785 @ X786 @ X788))|~(X785 @ (esk5_2 @ X785 @ X786) @ X788))))&((((in @ (esk8_3 @ X785 @ X786 @ X791) @ X786)|~(in @ X791 @ (esk7_2 @ X785 @ X786))|(((X788)!=(esk6_3 @ X785 @ X786 @ X788))|~(X785 @ (esk5_2 @ X785 @ X786) @ X788)))&((X785 @ (esk8_3 @ X785 @ X786 @ X791) @ X791)|~(in @ X791 @ (esk7_2 @ X785 @ X786))|(((X788)!=(esk6_3 @ X785 @ X786 @ X788))|~(X785 @ (esk5_2 @ X785 @ X786) @ X788))))&(~(in @ X794 @ X786)|~(X785 @ X794 @ X793)|(in @ X793 @ (esk7_2 @ X785 @ X786))|(((X788)!=(esk6_3 @ X785 @ X786 @ X788))|~(X785 @ (esk5_2 @ X785 @ X786) @ X788))))))&((((in @ (esk9_1 @ X795) @ X795)|~(in @ X796 @ X795))&(~(in @ X798 @ (esk9_1 @ X795))|~(in @ X798 @ X795)|~(in @ X796 @ X795)))&((epred1_0)&((((X799 @ (esk10_2 @ X799 @ X800))|~(X799 @ X800)|(X799 @ (descr @ X799)))&(((X800)!=(esk10_2 @ X799 @ X800))|~(X799 @ X800)|(X799 @ (descr @ X799))))&((~(in @ X804 @ X802)|(~(X803 @ X804)|(in @ X804 @ (dsetconstr @ X802 @ X803))))&((~(in @ X807 @ (dsetconstr @ X805 @ X806))|(in @ X807 @ X805))&((~(in @ X810 @ (dsetconstr @ X808 @ X809))|(X809 @ X810))&(((((X811 @ (esk12_1 @ X811))|((X811 @ (esk11_2 @ X811 @ X812))|~(X811 @ X812)))&(~(X811 @ X815)|((esk12_1 @ X811)=(X815))|((X811 @ (esk11_2 @ X811 @ X812))|~(X811 @ X812))))&(((X811 @ (esk12_1 @ X811))|(((X812)!=(esk11_2 @ X811 @ X812))|~(X811 @ X812)))&(~(X811 @ X815)|((esk12_1 @ X811)=(X815))|(((X812)!=(esk11_2 @ X811 @ X812))|~(X811 @ X812)))))&((~(in @ X817 @ (prop2set @ ((X816))))|(X816))&((~(in @ X818 @ emptyset)|(X819))&((~(in @ X820 @ emptyset)|~($true))&(~(in @ X821 @ emptyset)&((((X822 @ (esk13_2 @ X822 @ X823))|~(X822 @ X823)|(X822 @ (esk14_1 @ X822)))&(((X823)!=(esk13_2 @ X822 @ X823))|~(X822 @ X823)|(X822 @ (esk14_1 @ X822))))&(((((in @ (esk16_2 @ X826 @ X827) @ X827)|((X826)=(X827))|(in @ (esk15_2 @ X826 @ X827) @ 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X1007)|(~(in @ X1008 @ X1006)|(in @ X1008 @ X1007)))&((~(subset @ X1009 @ X1010)|((in @ X1011 @ X1010)|~(in @ X1011 @ X1009)))&((~(in @ X1014 @ X1012)|((in @ X1014 @ X1013)|~(subset @ X1012 @ X1013)))&(((subset @ X1015 @ X1016)|((X1015)!=(X1016)))&((~(in @ X1019 @ X1017)|((in @ X1019 @ X1018)|((X1017)!=(X1018))))&((subset @ X1020 @ X1020)&((~(subset @ X1021 @ X1022)|(~(subset @ X1022 @ X1023)|(subset @ X1021 @ X1023)))&((subset @ X1025 @ (setadjoin @ X1024 @ X1025))&((~(subset @ X1026 @ X1028)|(subset @ X1026 @ (setadjoin @ X1027 @ X1028)))&((~(subset @ X1029 @ X1030)|(in @ X1029 @ (powerset @ X1030)))&((~(subset @ X1031 @ X1032)|(~(subset @ X1032 @ X1031)|((X1031)=(X1032))))&((~(subset @ X1033 @ emptyset)|((X1033)=(emptyset)))&((~(subset @ X1035 @ X1034)|(in @ X1035 @ (powerset @ X1034)))&((~(in @ X1037 @ (powerset @ X1036))|(subset @ X1037 @ X1036))&((in @ X1038 @ (powerset @ X1038))&((~(subset @ X1039 @ X1040)|(subset @ (powerset @ X1039) @ (powerset @ X1040)))&((in @ (dsetconstr @ 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X1067 @ X1068))))&((~(in @ X1072 @ (binintersect @ X1070 @ X1071))|(in @ X1072 @ X1070))&((subset @ (binintersect @ X1073 @ X1074) @ X1073)&((~(subset @ X1075 @ X1076)|((binintersect @ X1075 @ X1076)=(X1075)))&((((binintersect @ X1077 @ X1078)!=(X1078))|(subset @ X1078 @ X1077))&((~(in @ X1081 @ (binintersect @ X1079 @ X1080))|(in @ X1081 @ X1080))&((((in @ (esk54_2 @ X1082 @ X1083) @ X1082)|((binintersect @ X1082 @ X1083)=(emptyset)))&((in @ (esk54_2 @ X1082 @ X1083) @ X1083)|((binintersect @ X1082 @ X1083)=(emptyset))))&((subset @ (binintersect @ X1085 @ X1086) @ X1086)&((~(subset @ X1088 @ X1087)|((binintersect @ X1087 @ X1088)=(X1088)))&((((binintersect @ X1089 @ X1090)!=(X1089))|(subset @ X1089 @ X1090))&(((binintersect @ X1091 @ (binunion @ X1092 @ X1093))=(binunion @ (binintersect @ X1091 @ X1092) @ (binintersect @ X1091 @ X1093)))&((~(in @ X1096 @ X1094)|((in @ X1096 @ X1095)|(in @ X1096 @ (setminus @ X1094 @ X1095))))&((~(in @ X1099 @ (setminus @ X1097 @ X1098))|(in @ X1099 @ X1097))&((~(in @ X1102 @ (setminus @ X1100 @ X1101))|~(in @ X1102 @ X1101))&((~(subset @ X1103 @ X1104)|((setminus @ X1103 @ X1104)=(emptyset)))&(((in @ X1107 @ (setminus @ X1105 @ X1106))|(~(in @ X1107 @ X1105)|(in @ X1107 @ X1106)))&(((in @ X1110 @ (setminus @ X1108 @ X1109))|((in @ X1110 @ X1109)|~(in @ X1110 @ X1108)))&(((in @ X1113 @ X1111)|~(in @ X1113 @ (setminus @ X1111 @ X1112)))&((~(in @ X1116 @ X1115)|~(in @ X1116 @ (setminus @ X1114 @ X1115)))&((subset @ (setminus @ X1117 @ X1118) @ X1117)&((((setminus @ X1119 @ X1120)!=(emptyset))|(subset @ X1119 @ X1120))&((((~(in @ X1123 @ X1121)|(X1124)|(in @ X1123 @ X1121)|~(in @ X1123 @ (dsetconstr @ (binunion @ X1121 @ X1122) @ (^[Z0/* 9 */:$i]:((~((in @ Z0 @ X1121))|~((in @ Z0 @ X1122))))))))&(((in @ X1123 @ X1122)|(X1124)|(in @ X1123 @ X1121)|~(in @ X1123 @ (dsetconstr @ (binunion @ X1121 @ X1122) @ (^[Z0/* 9 */:$i]:((~((in @ Z0 @ X1121))|~((in @ Z0 @ X1122))))))))&(~(X1124)|(X1124)|(in @ X1123 @ X1121)|~(in @ X1123 @ (dsetconstr @ (binunion @ X1121 @ X1122) @ (^[Z0/* 9 */:$i]:((~((in @ Z0 @ X1121))|~((in @ Z0 @ X1122))))))))))&(((~(in @ X1123 @ X1121)|(X1124)|~(in @ X1123 @ X1122)|~(in @ X1123 @ (dsetconstr @ (binunion @ X1121 @ X1122) @ (^[Z0/* 9 */:$i]:((~((in @ Z0 @ X1121))|~((in @ Z0 @ X1122))))))))&(((in @ X1123 @ X1122)|(X1124)|~(in @ X1123 @ X1122)|~(in @ X1123 @ (dsetconstr @ (binunion @ X1121 @ X1122) @ (^[Z0/* 9 */:$i]:((~((in @ Z0 @ X1121))|~((in @ Z0 @ X1122))))))))&(~(X1124)|(X1124)|~(in @ X1123 @ X1122)|~(in @ X1123 @ (dsetconstr @ (binunion @ X1121 @ X1122) @ (^[Z0/* 9 */:$i]:((~((in @ Z0 @ X1121))|~((in @ Z0 @ X1122))))))))))&((~(in @ X1123 @ X1121)|(X1124)|~(X1124)|~(in @ X1123 @ (dsetconstr @ (binunion @ X1121 @ X1122) @ (^[Z0/* 9 */:$i]:((~((in @ Z0 @ X1121))|~((in @ Z0 @ X1122))))))))&(((in @ X1123 @ X1122)|(X1124)|~(X1124)|~(in @ X1123 @ (dsetconstr @ (binunion @ X1121 @ X1122) @ (^[Z0/* 9 */:$i]:((~((in @ Z0 @ X1121))|~((in @ Z0 @ X1122))))))))&(~(X1124)|(X1124)|~(X1124)|~(in @ X1123 @ (dsetconstr @ (binunion @ X1121 @ X1122) @ (^[Z0/* 9 */:$i]:((~((in @ Z0 @ X1121))|~((in @ Z0 @ X1122))))))))))))&((in @ esk57_0 @ esk55_0)&(~(in @ esk57_0 @ esk56_0)&~(in @ esk57_0 @ (dsetconstr @ (binunion @ esk55_0 @ esk56_0) @ (^[Z0/* 9 */:$i]:((~((in @ Z0 @ esk55_0))|~((in @ Z0 @ esk56_0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_174])])])])])])])). 0.92/0.59 thf(c_0_176, negated_conjecture, ~((in @ esk57_0 @ (dsetconstr @ (binunion @ esk55_0 @ esk56_0) @ (^[Z0/* 9 */:$i]:((~((in @ Z0 @ esk55_0))|~((in @ Z0 @ esk56_0)))))))), inference(split_conjunct,[status(thm)],[c_0_175])). 0.92/0.59 thf(c_0_177, negated_conjecture, ![X1:$i > $o, X2:$i, X3:$i]:(((in @ X2 @ (dsetconstr @ X3 @ X1))|~((X1 @ X2))|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_175])). 0.92/0.59 thf(c_0_178, negated_conjecture, (in @ esk57_0 @ esk55_0), inference(split_conjunct,[status(thm)],[c_0_175])). 0.92/0.59 thf(c_0_179, negated_conjecture, (~((in @ esk57_0 @ (binunion @ esk55_0 @ esk56_0)))|~(~((in @ esk57_0 @ esk56_0)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176, c_0_177]), c_0_178])])). 0.92/0.59 thf(c_0_180, negated_conjecture, ~((in @ esk57_0 @ esk56_0)), inference(split_conjunct,[status(thm)],[c_0_175])). 0.92/0.59 thf(c_0_181, negated_conjecture, ~((in @ esk57_0 @ (binunion @ esk55_0 @ esk56_0))), inference(sr,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_179]), c_0_180])). 0.92/0.59 thf(c_0_182, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (binunion @ X3 @ X4))|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_175])). 0.92/0.59 thf(c_0_183, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181, c_0_182]), c_0_178])]), ['proof']). 0.92/0.59 # SZS output end CNFRefutation 0.92/0.59 # Parsed axioms : 280 0.92/0.59 # Removed by relevancy pruning/SinE : 149 0.92/0.59 # Initial clauses : 253 0.92/0.59 # Removed in clause preprocessing : 24 0.92/0.59 # Initial clauses in saturation : 229 0.92/0.59 # Processed clauses : 408 0.92/0.59 # ...of these trivial : 6 0.92/0.59 # ...subsumed : 52 0.92/0.59 # ...remaining for further processing : 350 0.92/0.59 # Other redundant clauses eliminated : 18 0.92/0.59 # Clauses deleted for lack of memory : 0 0.92/0.59 # Backward-subsumed : 0 0.92/0.59 # Backward-rewritten : 3 0.92/0.59 # Generated clauses : 1119 0.92/0.59 # ...of the previous two non-redundant : 1018 0.92/0.59 # ...aggressively subsumed : 0 0.92/0.59 # Contextual simplify-reflections : 0 0.92/0.59 # Paramodulations : 1100 0.92/0.59 # Factorizations : 0 0.92/0.59 # NegExts : 0 0.92/0.59 # Equation resolutions : 18 0.92/0.59 # Disequality decompositions : 0 0.92/0.59 # Total rewrite steps : 103 0.92/0.59 # ...of those cached : 65 0.92/0.59 # Propositional unsat checks : 0 0.92/0.59 # Propositional check models : 0 0.92/0.59 # Propositional check unsatisfiable : 0 0.92/0.59 # Propositional clauses : 0 0.92/0.59 # Propositional clauses after purity: 0 0.92/0.59 # Propositional unsat core size : 0 0.92/0.59 # Propositional preprocessing time : 0.000 0.92/0.59 # Propositional encoding time : 0.000 0.92/0.59 # Propositional solver time : 0.000 0.92/0.59 # Success case prop preproc time : 0.000 0.92/0.59 # Success case prop encoding time : 0.000 0.92/0.59 # Success case prop solver time : 0.000 0.92/0.59 # Current number of processed clauses : 135 0.92/0.59 # Positive orientable unit clauses : 31 0.92/0.59 # Positive unorientable unit clauses: 0 0.92/0.59 # Negative unit clauses : 4 0.92/0.59 # Non-unit-clauses : 100 0.92/0.59 # Current number of unprocessed clauses: 1029 0.92/0.59 # ...number of literals in the above : 3046 0.92/0.59 # Current number of archived formulas : 0 0.92/0.59 # Current number of archived clauses : 202 0.92/0.59 # Clause-clause subsumption calls (NU) : 8268 0.92/0.59 # Rec. Clause-clause subsumption calls : 3000 0.92/0.59 # Non-unit clause-clause subsumptions : 30 0.92/0.59 # Unit Clause-clause subsumption calls : 47 0.92/0.59 # Rewrite failures with RHS unbound : 0 0.92/0.59 # BW rewrite match attempts : 13 0.92/0.59 # BW rewrite match successes : 3 0.92/0.59 # Condensation attempts : 408 0.92/0.59 # Condensation successes : 4 0.92/0.59 # Termbank termtop insertions : 52086 0.92/0.59 # Search garbage collected termcells : 12811 0.92/0.59 0.92/0.59 # ------------------------------------------------- 0.92/0.59 # User time : 0.071 s 0.92/0.59 # System time : 0.006 s 0.92/0.59 # Total time : 0.077 s 0.92/0.59 # Maximum resident set size: 5120 pages 0.92/0.59 0.92/0.59 # ------------------------------------------------- 0.92/0.59 # User time : 0.078 s 0.92/0.59 # System time : 0.009 s 0.92/0.59 # Total time : 0.087 s 0.92/0.59 # Maximum resident set size: 2060 pages 0.92/0.59 % E exiting 0.92/0.59 % E exiting 0.92/0.59 EOF