0.05/0.09 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.05/0.10 % Command : run_E %s %d THM 0.08/0.29 % Computer : n006.cluster.edu 0.08/0.29 % Model : x86_64 x86_64 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.08/0.29 % Memory : 8042.1875MB 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64 0.08/0.29 % CPULimit : 960 0.08/0.29 % WCLimit : 120 0.08/0.29 % DateTime : Tue Aug 9 05:57:13 EDT 2022 0.08/0.29 % CPUTime : 0.13/0.41 Running higher-order on 8 cores theorem proving 0.13/0.41 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=120 /export/starexec/sandbox/benchmark/theBenchmark.p 0.13/0.41 # Version: 3.0pre003-ho 5.49/1.34 # Preprocessing class: HSLMSLSSLLLCHFA. 5.49/1.34 # Scheduled 8 strats onto 8 cores with 120 seconds (960 total) 5.49/1.34 # Starting ehoh_best5 with 120s (1) cores 5.49/1.34 # Starting almost_fo_3_lam with 120s (1) cores 5.49/1.34 # Starting new_bool_5 with 120s (1) cores 5.49/1.34 # Starting pre_casc_3 with 120s (1) cores 5.49/1.34 # Starting ho_unfolding_8 with 120s (1) cores 5.49/1.34 # Starting new_ho_10_cnf2 with 120s (1) cores 5.49/1.34 # Starting new_bool_3 with 120s (1) cores 5.49/1.34 # Starting new_ho_5 with 120s (1) cores 5.49/1.34 # new_ho_10_cnf2 with pid 3921 completed with status 0 5.49/1.34 # Result found by new_ho_10_cnf2 5.49/1.34 # Preprocessing class: HSLMSLSSLLLCHFA. 5.49/1.34 # Scheduled 8 strats onto 8 cores with 120 seconds (960 total) 5.49/1.34 # Starting ehoh_best5 with 120s (1) cores 5.49/1.34 # Starting almost_fo_3_lam with 120s (1) cores 5.49/1.34 # Starting new_bool_5 with 120s (1) cores 5.49/1.34 # Starting pre_casc_3 with 120s (1) cores 5.49/1.34 # Starting ho_unfolding_8 with 120s (1) cores 5.49/1.34 # Starting new_ho_10_cnf2 with 120s (1) cores 5.49/1.34 # No SInE strategy applied 5.49/1.34 # Search class: HGHSM-FSLS31-SHFMMSBN 5.49/1.34 # Scheduled 6 strats onto 1 cores with 120 seconds (120 total) 5.49/1.34 # Starting sh3 with 65s (1) cores 5.49/1.34 # sh3 with pid 3927 completed with status 0 5.49/1.34 # Result found by sh3 5.49/1.34 # Preprocessing class: HSLMSLSSLLLCHFA. 5.49/1.34 # Scheduled 8 strats onto 8 cores with 120 seconds (960 total) 5.49/1.34 # Starting ehoh_best5 with 120s (1) cores 5.49/1.34 # Starting almost_fo_3_lam with 120s (1) cores 5.49/1.34 # Starting new_bool_5 with 120s (1) cores 5.49/1.34 # Starting pre_casc_3 with 120s (1) cores 5.49/1.34 # Starting ho_unfolding_8 with 120s (1) cores 5.49/1.34 # Starting new_ho_10_cnf2 with 120s (1) cores 5.49/1.34 # No SInE strategy applied 5.49/1.34 # Search class: HGHSM-FSLS31-SHFMMSBN 5.49/1.34 # Scheduled 6 strats onto 1 cores with 120 seconds (120 total) 5.49/1.34 # Starting sh3 with 65s (1) cores 5.49/1.34 # Preprocessing time : 0.004 s 5.49/1.34 # Presaturation interreduction done 5.49/1.34 5.49/1.34 # Proof found! 5.49/1.34 # SZS status Theorem 5.49/1.34 # SZS output start CNFRefutation 5.49/1.34 thf(decl_22, type, in: $i > $i > $o). 5.49/1.34 thf(decl_23, type, exu: ($i > $o) > $o). 5.49/1.34 thf(decl_24, type, setextAx: $o). 5.49/1.34 thf(decl_25, type, emptyset: $i). 5.49/1.34 thf(decl_26, type, emptysetAx: $o). 5.49/1.34 thf(decl_27, type, setadjoin: $i > $i > $i). 5.49/1.34 thf(decl_28, type, setadjoinAx: $o). 5.49/1.34 thf(decl_29, type, powerset: $i > $i). 5.49/1.34 thf(decl_30, type, powersetAx: $o). 5.49/1.34 thf(decl_31, type, setunion: $i > $i). 5.49/1.34 thf(decl_32, type, setunionAx: $o). 5.49/1.34 thf(decl_33, type, omega: $i). 5.49/1.34 thf(decl_34, type, omega0Ax: $o). 5.49/1.34 thf(decl_35, type, omegaSAx: $o). 5.49/1.34 thf(decl_36, type, omegaIndAx: $o). 5.49/1.34 thf(decl_37, type, replAx: $o). 5.49/1.34 thf(decl_38, type, foundationAx: $o). 5.49/1.34 thf(decl_39, type, wellorderingAx: $o). 5.49/1.34 thf(decl_40, type, descr: ($i > $o) > $i). 5.49/1.34 thf(decl_41, type, descrp: $o). 5.49/1.34 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i). 5.49/1.34 thf(decl_43, type, dsetconstrI: $o). 5.49/1.34 thf(decl_44, type, dsetconstrEL: $o). 5.49/1.34 thf(decl_45, type, dsetconstrER: $o). 5.49/1.34 thf(decl_46, type, exuE1: $o). 5.49/1.34 thf(decl_47, type, prop2set: $o > $i). 5.49/1.34 thf(decl_48, type, prop2setE: $o). 5.49/1.34 thf(decl_49, type, emptysetE: $o). 5.49/1.34 thf(decl_50, type, emptysetimpfalse: $o). 5.49/1.34 thf(decl_51, type, notinemptyset: $o). 5.49/1.34 thf(decl_52, type, exuE3e: $o). 5.49/1.34 thf(decl_53, type, setext: $o). 5.49/1.34 thf(decl_54, type, emptyI: $o). 5.49/1.34 thf(decl_55, type, noeltsimpempty: $o). 5.49/1.34 thf(decl_56, type, setbeta: $o). 5.49/1.34 thf(decl_57, type, nonempty: $i > $o). 5.49/1.34 thf(decl_58, type, nonemptyE1: $o). 5.49/1.34 thf(decl_59, type, nonemptyI: $o). 5.49/1.34 thf(decl_60, type, nonemptyI1: $o). 5.49/1.34 thf(decl_61, type, setadjoinIL: $o). 5.49/1.34 thf(decl_62, type, emptyinunitempty: $o). 5.49/1.34 thf(decl_63, type, setadjoinIR: $o). 5.49/1.34 thf(decl_64, type, setadjoinE: $o). 5.49/1.34 thf(decl_65, type, setadjoinOr: $o). 5.49/1.34 thf(decl_66, type, setoftrueEq: $o). 5.49/1.34 thf(decl_67, type, powersetI: $o). 5.49/1.34 thf(decl_68, type, emptyinPowerset: $o). 5.49/1.34 thf(decl_69, type, emptyInPowerset: $o). 5.49/1.34 thf(decl_70, type, powersetE: $o). 5.49/1.34 thf(decl_71, type, setunionI: $o). 5.49/1.34 thf(decl_72, type, setunionE: $o). 5.49/1.34 thf(decl_73, type, subPowSU: $o). 5.49/1.34 thf(decl_74, type, exuE2: $o). 5.49/1.34 thf(decl_75, type, nonemptyImpWitness: $o). 5.49/1.34 thf(decl_76, type, uniqinunit: $o). 5.49/1.34 thf(decl_77, type, notinsingleton: $o). 5.49/1.34 thf(decl_78, type, eqinunit: $o). 5.49/1.34 thf(decl_79, type, singletonsswitch: $o). 5.49/1.34 thf(decl_80, type, upairsetE: $o). 5.49/1.34 thf(decl_81, type, upairsetIL: $o). 5.49/1.34 thf(decl_82, type, upairsetIR: $o). 5.49/1.34 thf(decl_83, type, emptyE1: $o). 5.49/1.34 thf(decl_84, type, vacuousDall: $o). 5.49/1.34 thf(decl_85, type, quantDeMorgan1: $o). 5.49/1.34 thf(decl_86, type, quantDeMorgan2: $o). 5.49/1.34 thf(decl_87, type, quantDeMorgan3: $o). 5.49/1.34 thf(decl_88, type, quantDeMorgan4: $o). 5.49/1.34 thf(decl_89, type, prop2setI: $o). 5.49/1.34 thf(decl_90, type, set2prop: $i > $o). 5.49/1.34 thf(decl_91, type, prop2set2propI: $o). 5.49/1.34 thf(decl_92, type, notdexE: $o). 5.49/1.34 thf(decl_93, type, notdallE: $o). 5.49/1.34 thf(decl_94, type, exuI1: $o). 5.49/1.34 thf(decl_95, type, exuI3: $o). 5.49/1.34 thf(decl_96, type, exuI2: $o). 5.49/1.34 thf(decl_97, type, inCongP: $o). 5.49/1.34 thf(decl_98, type, in__Cong: $o). 5.49/1.34 thf(decl_99, type, exuE3u: $o). 5.49/1.34 thf(decl_100, type, exu__Cong: $o). 5.49/1.34 thf(decl_101, type, emptyset__Cong: $o). 5.49/1.34 thf(decl_102, type, setadjoin__Cong: $o). 5.49/1.34 thf(decl_103, type, powerset__Cong: $o). 5.49/1.34 thf(decl_104, type, setunion__Cong: $o). 5.49/1.34 thf(decl_105, type, omega__Cong: $o). 5.49/1.34 thf(decl_106, type, exuEu: $o). 5.49/1.34 thf(decl_107, type, descr__Cong: $o). 5.49/1.34 thf(decl_108, type, dsetconstr__Cong: $o). 5.49/1.34 thf(decl_109, type, subset: $i > $i > $o). 5.49/1.34 thf(decl_110, type, disjoint: $i > $i > $o). 5.49/1.34 thf(decl_111, type, setsmeet: $i > $i > $o). 5.49/1.34 thf(decl_112, type, subsetI1: $o). 5.49/1.34 thf(decl_113, type, eqimpsubset2: $o). 5.49/1.34 thf(decl_114, type, eqimpsubset1: $o). 5.49/1.34 thf(decl_115, type, subsetI2: $o). 5.49/1.34 thf(decl_116, type, emptysetsubset: $o). 5.49/1.34 thf(decl_117, type, subsetE: $o). 5.49/1.34 thf(decl_118, type, subsetE2: $o). 5.49/1.34 thf(decl_119, type, notsubsetI: $o). 5.49/1.34 thf(decl_120, type, notequalI1: $o). 5.49/1.34 thf(decl_121, type, notequalI2: $o). 5.49/1.34 thf(decl_122, type, subsetRefl: $o). 5.49/1.34 thf(decl_123, type, subsetTrans: $o). 5.49/1.34 thf(decl_124, type, setadjoinSub: $o). 5.49/1.34 thf(decl_125, type, setadjoinSub2: $o). 5.49/1.34 thf(decl_126, type, subset2powerset: $o). 5.49/1.34 thf(decl_127, type, setextsub: $o). 5.49/1.34 thf(decl_128, type, subsetemptysetimpeq: $o). 5.49/1.34 thf(decl_129, type, powersetI1: $o). 5.49/1.34 thf(decl_130, type, powersetE1: $o). 5.49/1.34 thf(decl_131, type, inPowerset: $o). 5.49/1.34 thf(decl_132, type, powersetsubset: $o). 5.49/1.34 thf(decl_133, type, sepInPowerset: $o). 5.49/1.34 thf(decl_134, type, sepSubset: $o). 5.49/1.34 thf(decl_135, type, binunion: $i > $i > $i). 5.49/1.34 thf(decl_136, type, binunionIL: $o). 5.49/1.34 thf(decl_137, type, upairset2IR: $o). 5.49/1.34 thf(decl_138, type, binunionIR: $o). 5.49/1.34 thf(decl_139, type, binunionEcases: $o). 5.49/1.34 thf(decl_140, type, binunionE: $o). 5.49/1.34 thf(decl_141, type, binunionLsub: $o). 5.49/1.34 thf(decl_142, type, binunionRsub: $o). 5.49/1.34 thf(decl_143, type, binintersect: $i > $i > $i). 5.49/1.34 thf(decl_144, type, binintersectI: $o). 5.49/1.34 thf(decl_145, type, binintersectSubset5: $o). 5.49/1.34 thf(decl_146, type, binintersectEL: $o). 5.49/1.34 thf(decl_147, type, binintersectLsub: $o). 5.49/1.34 thf(decl_148, type, binintersectSubset2: $o). 5.49/1.34 thf(decl_149, type, binintersectSubset3: $o). 5.49/1.34 thf(decl_150, type, binintersectER: $o). 5.49/1.34 thf(decl_151, type, disjointsetsI1: $o). 5.49/1.34 thf(decl_152, type, binintersectRsub: $o). 5.49/1.34 thf(decl_153, type, binintersectSubset4: $o). 5.49/1.34 thf(decl_154, type, binintersectSubset1: $o). 5.49/1.34 thf(decl_155, type, bs114d: $o). 5.49/1.34 thf(decl_156, type, regular: $i > $o). 5.49/1.34 thf(decl_157, type, setminus: $i > $i > $i). 5.49/1.34 thf(decl_158, type, setminusI: $o). 5.49/1.34 thf(decl_159, type, setminusEL: $o). 5.49/1.34 thf(decl_160, type, setminusER: $o). 5.49/1.34 thf(decl_161, type, setminusSubset2: $o). 5.49/1.34 thf(decl_162, type, setminusERneg: $o). 5.49/1.34 thf(decl_163, type, setminusELneg: $o). 5.49/1.34 thf(decl_164, type, setminusILneg: $o). 5.49/1.34 thf(decl_165, type, setminusIRneg: $o). 5.49/1.34 thf(decl_166, type, epred1_0: $o). 5.49/1.34 thf(decl_167, type, esk1_2: $i > $i > $i). 5.49/1.34 thf(decl_168, type, esk2_2: $i > $i > $i). 5.49/1.34 thf(decl_169, type, esk3_2: $i > $i > $i). 5.49/1.34 thf(decl_170, type, esk4_1: $i > $i). 5.49/1.34 thf(decl_171, type, esk5_2: ($i > $i > $o) > $i > $i). 5.49/1.34 thf(decl_172, type, esk6_3: ($i > $i > $o) > $i > $i > $i). 5.49/1.34 thf(decl_173, type, esk7_2: ($i > $i > $o) > $i > $i). 5.49/1.34 thf(decl_174, type, esk8_3: ($i > $i > $o) > $i > $i > $i). 5.49/1.34 thf(decl_175, type, esk9_1: $i > $i). 5.49/1.34 thf(decl_176, type, esk10_2: ($i > $o) > $i > $i). 5.49/1.34 thf(decl_177, type, esk11_2: ($i > $o) > $i > $i). 5.49/1.34 thf(decl_178, type, esk12_1: ($i > $o) > $i). 5.49/1.34 thf(decl_179, type, esk13_2: ($i > $o) > $i > $i). 5.49/1.34 thf(decl_180, type, esk14_1: ($i > $o) > $i). 5.49/1.34 thf(decl_181, type, esk15_2: $i > $i > $i). 5.49/1.34 thf(decl_182, type, esk16_2: $i > $i > $i). 5.49/1.34 thf(decl_183, type, esk17_1: $i > $i). 5.49/1.34 thf(decl_184, type, esk18_1: $i > $i). 5.49/1.34 thf(decl_185, type, esk19_1: $i > $i). 5.49/1.34 thf(decl_186, type, esk20_2: $i > $i > $i). 5.49/1.34 thf(decl_187, type, esk21_3: $i > $i > $o > $i). 5.49/1.34 thf(decl_188, type, esk22_2: ($i > $o) > $i > $i). 5.49/1.34 thf(decl_189, type, esk23_1: ($i > $o) > $i). 5.49/1.34 thf(decl_190, type, esk24_1: $i > $i). 5.49/1.34 thf(decl_191, type, esk25_2: $i > ($i > $o) > $i). 5.49/1.34 thf(decl_192, type, esk26_2: $i > ($i > $o) > $i). 5.49/1.34 thf(decl_193, type, esk27_2: $i > ($i > $o) > $i). 5.49/1.34 thf(decl_194, type, esk28_2: $i > ($i > $o) > $i). 5.49/1.34 thf(decl_195, type, esk29_2: $i > ($i > $o) > $i). 5.49/1.34 thf(decl_196, type, esk30_2: $i > ($i > $o) > $i). 5.49/1.34 thf(decl_197, type, esk31_2: ($i > $o) > $i > $i). 5.49/1.34 thf(decl_198, type, esk32_1: ($i > $o) > $i). 5.49/1.34 thf(decl_199, type, esk33_1: ($i > $o) > $i). 5.49/1.34 thf(decl_200, type, esk34_1: ($i > $o) > $i). 5.49/1.34 thf(decl_201, type, esk35_1: ($i > $o) > $i). 5.49/1.34 thf(decl_202, type, esk36_2: ($i > $o) > $i > $i). 5.49/1.34 thf(decl_203, type, esk37_1: ($i > $o) > $i). 5.49/1.34 thf(decl_204, type, esk38_2: ($i > $o) > $i > $i). 5.49/1.34 thf(decl_205, type, esk39_2: ($i > $o) > ($i > $o) > $i). 5.49/1.34 thf(decl_206, type, esk40_2: ($i > $o) > ($i > $o) > $i). 5.49/1.34 thf(decl_207, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i). 5.49/1.34 thf(decl_208, type, esk42_2: ($i > $o) > ($i > $o) > $i). 5.49/1.34 thf(decl_209, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i). 5.49/1.34 thf(decl_210, type, esk44_2: ($i > $o) > ($i > $o) > $i). 5.49/1.34 thf(decl_211, type, esk45_2: ($i > $o) > $i > $i). 5.49/1.34 thf(decl_212, type, esk46_2: ($i > $o) > ($i > $o) > $i). 5.49/1.34 thf(decl_213, type, esk47_2: ($i > $o) > ($i > $o) > $i). 5.49/1.34 thf(decl_214, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i). 5.49/1.34 thf(decl_215, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i). 5.49/1.34 thf(decl_216, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i). 5.49/1.34 thf(decl_217, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i). 5.49/1.34 thf(decl_218, type, esk52_2: $i > $i > $i). 5.49/1.34 thf(decl_219, type, esk53_2: $i > $i > $i). 5.49/1.34 thf(decl_220, type, esk54_2: $i > $i > $i). 5.49/1.34 thf(decl_221, type, esk55_0: $i). 5.49/1.34 thf(decl_222, type, esk56_0: $i). 5.49/1.34 thf(decl_223, type, esk57_1: $i > $i). 5.49/1.34 thf(decl_224, type, esk58_3: $i > $i > $i > $i). 5.49/1.34 thf(decl_225, type, esk59_2: $i > $i > $i). 5.49/1.34 thf(decl_226, type, esk60_2: $i > $i > $i). 5.49/1.34 thf(decl_227, type, esk61_2: $i > $i > $i). 5.49/1.34 thf(decl_228, type, epred2_0: $i > $o). 5.49/1.34 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', replAx)). 5.49/1.34 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exu)). 5.49/1.34 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', descrp)). 5.49/1.34 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuE1)). 5.49/1.34 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuE3e)). 5.49/1.34 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonempty)). 5.49/1.34 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyI)). 5.49/1.34 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuE2)). 5.49/1.34 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/benchmark/theBenchmark.p', exuI1)). 5.49/1.34 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuI3)). 5.49/1.34 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuI2)). 5.49/1.34 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/benchmark/theBenchmark.p', exuE3u)). 5.49/1.34 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exu__Cong)). 5.49/1.34 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuEu)). 5.49/1.34 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', descr__Cong)). 5.49/1.34 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstrI)). 5.49/1.34 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstrEL)). 5.49/1.34 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstrER)). 5.49/1.34 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setbeta)). 5.49/1.34 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyE1)). 5.49/1.34 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyI1)). 5.49/1.34 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setoftrueEq)). 5.49/1.34 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyImpWitness)). 5.49/1.34 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyE1)). 5.49/1.34 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstr__Cong)). 5.49/1.34 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', sepInPowerset)). 5.49/1.34 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', sepSubset)). 5.49/1.34 thf(setminusLsub, conjecture, (((((powersetAx)=>((((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>(((((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>(((((noeltsimpempty)=>((((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>(((setadjoinOr)=>((((emptyinPowerset)=>(((powersetE)=>((((((nonemptyImpWitness)=>(((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((((((vacuousDall)=>(((quantDeMorgan2)=>((quantDeMorgan3)=>(((((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>(((in__Cong)=>((((emptyset__Cong)=>(((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>(((descr__Cong)=>(((subsetI1)=>((eqimpsubset2)=>(((subsetI2)=>(((((notsubsetI)=>((notequalI1)=>((notequalI2)=>(((((((setextsub)=>(((powersetI1)=>(((inPowerset)=>((((sepSubset)=>((binunionIL)=>((((binunionEcases)=>(((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>(((((((disjointsetsI1)=>(((binintersectSubset4)=>(((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((((setminusELneg)=>((![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))<=(setminusIRneg))<=(setminusILneg)))<=(setminusERneg))<=(setminusSubset2))))))<=(binintersectSubset1)))<=(binintersectRsub)))<=(binintersectER))<=(binintersectSubset3))<=(binintersectSubset2))<=(binintersectLsub))<=(binintersectEL))))))<=(binunionE)))<=(binunionIR))<=(upairset2IR))))<=(sepInPowerset))<=(powersetsubset)))<=(powersetE1)))<=(subsetemptysetimpeq)))<=(subset2powerset))<=(setadjoinSub2))<=(setadjoinSub))<=(subsetTrans))<=(subsetRefl)))))<=(subsetE2))<=(subsetE))<=(emptysetsubset)))<=(eqimpsubset1))))<=(dsetconstr__Cong)))<=(exuEu)))))<=(setadjoin__Cong)))<=(exu__Cong))<=(exuE3u)))<=(inCongP)))))))<=(prop2set2propI))<=(prop2setI))<=(quantDeMorgan4))))<=(quantDeMorgan1)))<=(emptyE1))<=(upairsetIR))<=(upairsetIL))<=(upairsetE)))))<=(uniqinunit)))<=(exuE2))<=(subPowSU))<=(setunionE))<=(setunionI)))<=(emptyInPowerset)))<=(powersetI))<=(setoftrueEq)))<=(setadjoinE)))))))<=(nonemptyE1))<=(setbeta)))<=(emptyI))<=(setext))<=(exuE3e)))))))))<=(dsetconstrI))<=(descrp))<=(wellorderingAx))))))<=(omega0Ax))<=(setunionAx)))<=(setadjoinAx))<=(emptysetAx))<=(setextAx)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusLsub)). 5.49/1.34 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setextAx)). 5.49/1.34 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetAx)). 5.49/1.34 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinAx)). 5.49/1.34 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetAx)). 5.49/1.34 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionAx)). 5.49/1.34 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', omega0Ax)). 5.49/1.34 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', omegaSAx)). 5.49/1.34 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', omegaIndAx)). 5.49/1.34 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', foundationAx)). 5.49/1.34 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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/benchmark/theBenchmark.p', wellorderingAx)). 5.49/1.34 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', prop2setE)). 5.49/1.34 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetE)). 5.49/1.34 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetimpfalse)). 5.49/1.34 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notinemptyset)). 5.49/1.34 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setext)). 5.49/1.34 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyI)). 5.49/1.34 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', noeltsimpempty)). 5.49/1.34 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinIL)). 5.49/1.34 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyinunitempty)). 5.49/1.34 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinIR)). 5.49/1.34 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/benchmark/theBenchmark.p', setadjoinE)). 5.49/1.34 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinOr)). 5.49/1.34 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetI)). 5.49/1.34 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyinPowerset)). 5.49/1.34 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyInPowerset)). 5.49/1.34 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetE)). 5.49/1.34 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionI)). 5.49/1.34 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/benchmark/theBenchmark.p', setunionE)). 5.49/1.34 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subPowSU)). 5.49/1.34 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', uniqinunit)). 5.49/1.34 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notinsingleton)). 5.49/1.34 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eqinunit)). 5.49/1.34 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletonsswitch)). 5.49/1.34 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairsetE)). 5.49/1.34 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairsetIL)). 5.49/1.34 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairsetIR)). 5.49/1.34 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', vacuousDall)). 5.49/1.34 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan1)). 5.49/1.34 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan2)). 5.49/1.34 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan3)). 5.49/1.34 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan4)). 5.49/1.34 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', prop2setI)). 5.49/1.34 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', prop2set2propI)). 5.49/1.34 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notdexE)). 5.49/1.34 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notdallE)). 5.49/1.34 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', inCongP)). 5.49/1.34 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', in__Cong)). 5.49/1.34 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyset__Cong)). 5.49/1.34 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoin__Cong)). 5.49/1.34 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powerset__Cong)). 5.49/1.34 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunion__Cong)). 5.49/1.34 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', omega__Cong)). 5.49/1.34 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetI1)). 5.49/1.34 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eqimpsubset2)). 5.49/1.34 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eqimpsubset1)). 5.49/1.34 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetI2)). 5.49/1.34 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetsubset)). 5.49/1.34 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetE)). 5.49/1.34 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetE2)). 5.49/1.34 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notsubsetI)). 5.49/1.34 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notequalI1)). 5.49/1.34 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notequalI2)). 5.49/1.34 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetRefl)). 5.49/1.34 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetTrans)). 5.49/1.34 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinSub)). 5.49/1.34 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinSub2)). 5.49/1.34 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subset2powerset)). 5.49/1.34 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setextsub)). 5.49/1.34 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetemptysetimpeq)). 5.49/1.34 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetI1)). 5.49/1.34 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetE1)). 5.49/1.34 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', inPowerset)). 5.49/1.34 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetsubset)). 5.49/1.34 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionIL)). 5.49/1.34 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairset2IR)). 5.49/1.34 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionIR)). 5.49/1.34 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionEcases)). 5.49/1.34 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionE)). 5.49/1.34 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionLsub)). 5.49/1.34 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionRsub)). 5.49/1.34 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectI)). 5.49/1.34 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset5)). 5.49/1.34 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectEL)). 5.49/1.34 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectLsub)). 5.49/1.34 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset2)). 5.49/1.34 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset3)). 5.49/1.34 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectER)). 5.49/1.34 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', disjointsetsI1)). 5.49/1.34 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectRsub)). 5.49/1.34 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset4)). 5.49/1.34 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset1)). 5.49/1.34 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', bs114d)). 5.49/1.34 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusI)). 5.49/1.34 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusEL)). 5.49/1.34 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusER)). 5.49/1.34 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusSubset2)). 5.49/1.34 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusERneg)). 5.49/1.34 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusELneg)). 5.49/1.34 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusILneg)). 5.49/1.34 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusIRneg)). 5.49/1.34 thf(c_0_128, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 5.49/1.34 thf(c_0_129, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])). 5.49/1.34 thf(c_0_130, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 5.49/1.34 thf(c_0_131, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 5.49/1.34 thf(c_0_132, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 5.49/1.34 thf(c_0_133, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])). 5.49/1.34 thf(c_0_134, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 5.49/1.34 thf(c_0_135, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])). 5.49/1.34 thf(c_0_136, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])). 5.49/1.34 thf(c_0_137, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 5.49/1.34 thf(c_0_138, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 5.49/1.34 thf(c_0_139, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])). 5.49/1.34 thf(c_0_140, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 5.49/1.34 thf(c_0_141, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 5.49/1.34 thf(c_0_142, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))=>((exu @ (^[Z0:$i]:((X17 @ Z0))))=>((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 5.49/1.34 thf(c_0_143, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X356:$i]:((((X6 @ X2 @ X356))&![X357:$i]:((((X6 @ X2 @ X357))=>((X356)=(X357)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_128, c_0_129])). 5.49/1.34 thf(c_0_144, plain, ((descrp)=(![X1:$i > $o]:(((?[X358:$i]:((((X1 @ X358))&![X359:$i]:((((X1 @ X359))=>((X358)=(X359)))))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_130, c_0_129])). 5.49/1.34 thf(c_0_145, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 5.49/1.34 thf(c_0_146, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 5.49/1.34 thf(c_0_147, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 5.49/1.34 thf(c_0_148, plain, ((exuE1)=(![X1:$i > $o]:(((?[X360:$i]:((((X1 @ X360))&![X361:$i]:((((X1 @ X361))=>((X360)=(X361)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_131, c_0_129])). 5.49/1.34 thf(c_0_149, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X362:$i]:((((X1 @ X362))&![X363:$i]:((((X1 @ X363))=>((X362)=(X363)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_132, c_0_129])). 5.49/1.34 thf(c_0_150, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 5.49/1.34 thf(c_0_151, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_133])). 5.49/1.34 thf(c_0_152, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_134, c_0_133])). 5.49/1.34 thf(c_0_153, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_133])). 5.49/1.34 thf(c_0_154, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 5.49/1.34 thf(c_0_155, plain, ((exuE2)=(![X1:$i > $o]:(((?[X364:$i]:((((X1 @ X364))&![X365:$i]:((((X1 @ X365))=>((X364)=(X365)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_135, c_0_129])). 5.49/1.34 thf(c_0_156, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_133])). 5.49/1.34 thf(c_0_157, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])). 5.49/1.34 thf(c_0_158, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X366:$i]:((((X1 @ X366))&![X367:$i]:((((X1 @ X367))=>((X366)=(X367))))))))))), inference(apply_def,[status(thm)],[c_0_136, c_0_129])). 5.49/1.34 thf(c_0_159, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X368:$i]:((((X1 @ X368))&![X369:$i]:((((X1 @ X369))=>((X368)=(X369)))))))))))), inference(apply_def,[status(thm)],[c_0_137, c_0_129])). 5.49/1.34 thf(c_0_160, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X370:$i]:((((X1 @ X370))&![X371:$i]:((((X1 @ X371))=>((X370)=(X371))))))))))), inference(apply_def,[status(thm)],[c_0_138, c_0_129])). 5.49/1.34 thf(c_0_161, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X372:$i]:((((X1 @ X372))&![X373:$i]:((((X1 @ X373))=>((X372)=(X373)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_139, c_0_129])). 5.49/1.34 thf(c_0_162, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X374:$i]:((((X1 @ X374))&![X375:$i]:((((X1 @ X375))=>((X374)=(X375)))))))<=>(?[X376:$i]:((((X17 @ X376))&![X377:$i]:((((X17 @ X377))=>((X376)=(X377)))))))))))), inference(apply_def,[status(thm)],[c_0_140, c_0_129])). 5.49/1.34 thf(c_0_163, plain, ((exuEu)=(![X1:$i > $o]:(((?[X378:$i]:((((X1 @ X378))&![X379:$i]:((((X1 @ X379))=>((X378)=(X379)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_141, c_0_129])). 5.49/1.34 thf(c_0_164, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X380:$i]:((((X1 @ X380))&![X381:$i]:((((X1 @ X381))=>((X380)=(X381)))))))=>((?[X382:$i]:((((X17 @ X382))&![X383:$i]:((((X17 @ X383))=>((X382)=(X383)))))))=>((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_142, c_0_129])). 5.49/1.34 thf(c_0_165, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 5.49/1.34 thf(c_0_166, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])). 5.49/1.34 thf(c_0_167, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])). 5.49/1.34 thf(c_0_168, plain, ((epred1_0)<=>![X717:$i]:(?[X718:$i]:((((![X719:$i]:(((in @ X719 @ X718)=>![X720:$i]:(((in @ X720 @ X719)=>(in @ X720 @ X717)))))&![X721:$i, X722:$i]:((((in @ X721 @ X717)&(in @ X722 @ X717))=>(![X723:$i]:(((in @ X723 @ X718)=>((in @ X721 @ X723)<=>(in @ X722 @ X723))))=>((X721)=(X722))))))&![X724:$i, X725:$i]:((((in @ X724 @ X718)&(in @ X725 @ X718))=>(![X726:$i]:(((in @ X726 @ X724)=>(in @ X726 @ X725)))|![X727:$i]:(((in @ X727 @ X725)=>(in @ X727 @ X724)))))))&![X728:$i]:(((![X729:$i]:(((in @ X729 @ X728)=>(in @ X729 @ X717)))&?[X730:$i]:((in @ X730 @ X728)))=>?[X731:$i, X732:$i]:(((((in @ X731 @ X718)&(in @ X732 @ X728))&~(?[X733:$i]:(((in @ X733 @ X731)&(in @ X733 @ X728)))))&![X734:$i]:(((in @ X734 @ X718)=>(![X735:$i]:(((in @ X735 @ X734)=>(in @ X735 @ X731)))|(in @ X732 @ X734)))))))))))), introduced(definition)). 5.49/1.34 thf(c_0_169, negated_conjecture, ~((![X743:$i, X744:$i]:((![X745:$i]:(((in @ X745 @ X743)<=>(in @ X745 @ X744)))=>((X743)=(X744))))=>(![X742:$i]:(~(in @ X742 @ emptyset))=>(![X739:$i, X740:$i, X741:$i]:(((in @ X741 @ (setadjoin @ X739 @ X740))<=>(((X741)=(X739))|(in @ X741 @ X740))))=>(![X384:$i, X385:$i]:(((in @ X385 @ (powerset @ X384))<=>![X386:$i]:(((in @ X386 @ X385)=>(in @ X386 @ X384)))))=>(![X736:$i, X737:$i]:(((in @ X737 @ (setunion @ X736))<=>?[X738:$i]:(((in @ X737 @ X738)&(in @ X738 @ X736)))))=>((in @ emptyset @ omega)=>(![X387:$i]:(((in @ X387 @ omega)=>(in @ (setadjoin @ X387 @ X387) @ omega)))=>(![X388:$i]:((((in @ emptyset @ X388)&![X389:$i]:((((in @ X389 @ omega)&(in @ X389 @ X388))=>(in @ (setadjoin @ X389 @ X389) @ X388))))=>![X390:$i]:(((in @ X390 @ omega)=>(in @ X390 @ X388)))))=>(![X391:$i > $i > $o, X392:$i]:((![X393:$i]:(((in @ X393 @ X392)=>?[X394:$i]:(((X391 @ X393 @ X394)&![X395:$i]:(((X391 @ X393 @ X395)=>((X394)=(X395))))))))=>?[X396:$i]:(![X397:$i]:(((in @ X397 @ X396)<=>?[X398:$i]:(((in @ X398 @ X392)&(X391 @ X398 @ X397))))))))=>(![X399:$i]:((?[X400:$i]:((in @ X400 @ X399))=>?[X401:$i]:(((in @ X401 @ X399)&~(?[X402:$i]:(((in @ X402 @ X401)&(in @ X402 @ X399))))))))=>((epred1_0)=>(![X714:$i > $o]:((?[X715:$i]:(((X714 @ X715)&![X716:$i]:(((X714 @ X716)=>((X715)=(X716))))))=>(X714 @ (descr @ (^[Z0:$i]:((X714 @ Z0)))))))=>(![X711:$i, X712:$i > $o, X713:$i]:(((in @ X713 @ X711)=>((X712 @ X713)=>(in @ X713 @ (dsetconstr @ X711 @ (^[Z0:$i]:((X712 @ Z0))))))))=>(![X403:$i, X404:$i > $o, X405:$i]:(((in @ X405 @ (dsetconstr @ X403 @ (^[Z0:$i]:((X404 @ Z0)))))=>(in @ X405 @ X403)))=>(![X406:$i, X407:$i > $o, X408:$i]:(((in @ X408 @ (dsetconstr @ X406 @ (^[Z0:$i]:((X407 @ Z0)))))=>(X407 @ X408)))=>(![X409:$i > $o]:((?[X410:$i]:(((X409 @ X410)&![X411:$i]:(((X409 @ X411)=>((X410)=(X411))))))=>?[X412:$i]:(((X409 @ X412)&![X413:$i]:(((X409 @ X413)=>((X412)=(X413))))))))=>(![X414:$o, X415:$i]:(((in @ X415 @ (prop2set @ ((X414))))=>(X414)))=>(![X416:$i]:(((in @ X416 @ emptyset)=>![X417:$o]:((X417))))=>(![X418:$i]:(~(in @ X418 @ emptyset))=>(![X419:$i]:(~(in @ X419 @ emptyset))=>(![X707:$i > $o]:((?[X708:$i]:(((X707 @ X708)&![X709:$i]:(((X707 @ X709)=>((X708)=(X709))))))=>?[X710:$i]:((X707 @ X710))))=>(![X703:$i, X704:$i]:((![X705:$i]:(((in @ X705 @ X703)=>(in @ X705 @ X704)))=>(![X706:$i]:(((in @ X706 @ X704)=>(in @ X706 @ X703)))=>((X703)=(X704)))))=>(![X701:$i]:((![X702:$i]:(~(in @ X702 @ X701))=>((X701)=(emptyset))))=>(![X420:$i]:((![X421:$i]:(~(in @ X421 @ X420))=>((X420)=(emptyset))))=>(![X698:$i, X699:$i > $o, X700:$i]:(((in @ X700 @ X698)=>((in @ X700 @ (dsetconstr @ X698 @ (^[Z0:$i]:((X699 @ Z0)))))<=>(X699 @ X700))))=>(![X696:$i]:((((X696)!=(emptyset))=>?[X697:$i]:((in @ X697 @ X696))))=>(![X422:$i, X423:$i > $o, X424:$i]:(((in @ X424 @ X422)=>((X423 @ X424)=>((dsetconstr @ X422 @ (^[Z0:$i]:((X423 @ Z0))))!=(emptyset)))))=>(![X425:$i]:((?[X426:$i]:((in @ X426 @ X425))=>((X425)!=(emptyset))))=>(![X427:$i, X428:$i]:((in @ X427 @ (setadjoin @ X427 @ X428)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X429:$i, X430:$i, X431:$i]:(((in @ X431 @ X430)=>(in @ X431 @ (setadjoin @ X429 @ X430))))=>(![X692:$i, X693:$i, X694:$i]:(((in @ X694 @ (setadjoin @ X692 @ X693))=>![X695:$o]:(((((X694)=(X692))=>(X695))=>(((in @ X694 @ X693)=>(X695))=>(X695))))))=>(![X432:$i, X433:$i, X434:$i]:(((in @ X434 @ (setadjoin @ X432 @ X433))=>(((X434)=(X432))|(in @ X434 @ X433))))=>(![X691:$i]:(((dsetconstr @ X691 @ (^[Z0:$i]:(($true))))=(X691)))=>(![X688:$i, X689:$i]:((![X690:$i]:(((in @ X690 @ X689)=>(in @ X690 @ X688)))=>(in @ X689 @ (powerset @ X688))))=>(![X435:$i]:((in @ emptyset @ (powerset @ X435)))=>(![X687:$i]:((in @ emptyset @ (powerset @ X687)))=>(![X436:$i, X437:$i, X438:$i]:(((in @ X437 @ (powerset @ X436))=>((in @ X438 @ X437)=>(in @ X438 @ X436))))=>(![X684:$i, X685:$i, X686:$i]:(((in @ X685 @ X686)=>((in @ X686 @ X684)=>(in @ X685 @ (setunion @ X684)))))=>(![X680:$i, X681:$i]:(((in @ X681 @ (setunion @ X680))=>![X682:$o]:((![X683:$i]:(((in @ X681 @ X683)=>((in @ X683 @ X680)=>(X682))))=>(X682)))))=>(![X678:$i, X679:$i]:(((in @ X679 @ X678)=>(in @ X679 @ (powerset @ (setunion @ X678)))))=>(![X673:$i > $o]:((?[X674:$i]:(((X673 @ X674)&![X675:$i]:(((X673 @ X675)=>((X674)=(X675))))))=>?[X676:$i]:(![X677:$i]:(((X673 @ X677)<=>((X677)=(X676)))))))=>(![X439:$i]:((((X439)!=(emptyset))=>?[X440:$i]:((in @ X440 @ X439))))=>(![X671:$i, X672:$i]:(((in @ X671 @ (setadjoin @ X672 @ emptyset))=>((X671)=(X672))))=>(![X441:$i, X442:$i]:((((X441)!=(X442))=>~(in @ X442 @ (setadjoin @ X441 @ emptyset))))=>(![X443:$i, X444:$i]:((((X443)=(X444))=>(in @ X443 @ (setadjoin @ X444 @ emptyset))))=>(![X445:$i, X446:$i]:(((in @ X445 @ (setadjoin @ X446 @ emptyset))=>(in @ X446 @ (setadjoin @ X445 @ emptyset))))=>(![X668:$i, X669:$i, X670:$i]:(((in @ X670 @ (setadjoin @ X668 @ (setadjoin @ X669 @ emptyset)))=>(((X670)=(X668))|((X670)=(X669)))))=>(![X666:$i, X667:$i]:((in @ X666 @ (setadjoin @ X666 @ (setadjoin @ X667 @ emptyset))))=>(![X664:$i, X665:$i]:((in @ X665 @ (setadjoin @ X664 @ (setadjoin @ X665 @ emptyset))))=>(![X661:$i, X662:$i > $o]:((?[X663:$i]:(((in @ X663 @ X661)&(X662 @ X663)))=>((dsetconstr @ X661 @ (^[Z0:$i]:((X662 @ Z0))))!=(emptyset))))=>(![X447:$i > $o, X448:$i]:(((in @ X448 @ emptyset)=>(X447 @ X448)))=>(![X657:$i, X658:$i > $o]:((~(![X659:$i]:(((in @ X659 @ X657)=>(X658 @ X659))))=>?[X660:$i]:(((in @ X660 @ X657)&~(X658 @ X660)))))=>(![X449:$i, X450:$i > $o]:((![X451:$i]:(((in @ X451 @ X449)=>~(X450 @ X451)))=>~(?[X452:$i]:(((in @ X452 @ X449)&(X450 @ X452))))))=>(![X453:$i, X454:$i > $o]:((~(?[X455:$i]:(((in @ X455 @ X453)&(X454 @ X455))))=>![X456:$i]:(((in @ X456 @ X453)=>~(X454 @ X456)))))=>(![X653:$i, X654:$i > $o]:((?[X655:$i]:(((in @ X655 @ X653)&~(X654 @ X655)))=>~(![X656:$i]:(((in @ X656 @ X653)=>(X654 @ X656))))))=>(![X652:$o]:(((X652)=>(in @ emptyset @ (prop2set @ ((X652))))))=>(![X651:$o]:(((X651)=>(set2prop @ (prop2set @ ((X651))))))=>(![X457:$i, X458:$i > $o]:((~(?[X459:$i]:(((in @ X459 @ X457)&(X458 @ X459))))=>![X460:$i]:(((in @ X460 @ X457)=>~(X458 @ X460)))))=>(![X461:$i, X462:$i > $o]:((~(![X463:$i]:(((in @ X463 @ X461)=>(X462 @ X463))))=>?[X464:$i]:(((in @ X464 @ X461)&~(X462 @ X464)))))=>(![X465:$i > $o]:((?[X466:$i]:(((X465 @ X466)&![X467:$i]:(((X465 @ X467)=>((X466)=(X467))))))=>?[X468:$i]:(((X465 @ X468)&![X469:$i]:(((X465 @ X469)=>((X468)=(X469))))))))=>(![X470:$i > $o]:((?[X471:$i]:((X470 @ X471))=>(![X472:$i, X473:$i]:(((X470 @ X472)=>((X470 @ X473)=>((X472)=(X473)))))=>?[X474:$i]:(((X470 @ X474)&![X475:$i]:(((X470 @ X475)=>((X474)=(X475)))))))))=>(![X476:$i > $o]:((?[X477:$i]:(![X478:$i]:(((X476 @ X478)<=>((X478)=(X477)))))=>?[X479:$i]:(((X476 @ X479)&![X480:$i]:(((X476 @ X480)=>((X479)=(X480))))))))=>(![X647:$i, X648:$i]:((((X647)=(X648))=>![X649:$i, X650:$i]:((((X649)=(X650))=>((in @ X649 @ X647)=>(in @ X650 @ X648))))))=>(![X481:$i, X482:$i]:((((X481)=(X482))=>![X483:$i, X484:$i]:((((X483)=(X484))=>((in @ X483 @ X481)<=>(in @ X484 @ X482))))))=>(![X642:$i > $o]:((?[X643:$i]:(((X642 @ X643)&![X644:$i]:(((X642 @ X644)=>((X643)=(X644))))))=>![X645:$i, X646:$i]:(((X642 @ X645)=>((X642 @ X646)=>((X645)=(X646)))))))=>(![X634:$i > $o, X635:$i > $o]:((![X636:$i, X637:$i]:((((X636)=(X637))=>((X634 @ X636)<=>(X635 @ X637))))=>(?[X638:$i]:(((X634 @ X638)&![X639:$i]:(((X634 @ X639)=>((X638)=(X639))))))<=>?[X640:$i]:(((X635 @ X640)&![X641:$i]:(((X635 @ X641)=>((X640)=(X641)))))))))=>(((emptyset)=(emptyset))=>(![X630:$i, X631:$i]:((((X630)=(X631))=>![X632:$i, X633:$i]:((((X632)=(X633))=>((setadjoin @ X630 @ X632)=(setadjoin @ X631 @ X633))))))=>(![X485:$i, X486:$i]:((((X485)=(X486))=>((powerset @ X485)=(powerset @ X486))))=>(![X487:$i, X488:$i]:((((X487)=(X488))=>((setunion @ X487)=(setunion @ X488))))=>(((omega)=(omega))=>(![X625:$i > $o]:((?[X626:$i]:(((X625 @ X626)&![X627:$i]:(((X625 @ X627)=>((X626)=(X627))))))=>![X628:$i, X629:$i]:(((X625 @ X628)=>((X625 @ X629)=>((X628)=(X629)))))))=>(![X489:$i > $o, X490:$i > $o]:((![X491:$i, X492:$i]:((((X491)=(X492))=>((X489 @ X491)<=>(X490 @ X492))))=>(?[X493:$i]:(((X489 @ X493)&![X494:$i]:(((X489 @ X494)=>((X493)=(X494))))))=>(?[X495:$i]:(((X490 @ X495)&![X496:$i]:(((X490 @ X496)=>((X495)=(X496))))))=>((descr @ (^[Z0:$i]:((X489 @ Z0))))=(descr @ (^[Z0:$i]:((X490 @ Z0)))))))))=>(![X619:$i, X620:$i]:((((X619)=(X620))=>![X621:$i > $o, X622:$i > $o]:((![X623:$i]:(((in @ X623 @ X619)=>![X624:$i]:(((in @ X624 @ X620)=>(((X623)=(X624))=>((X621 @ X623)<=>(X622 @ X624)))))))=>((dsetconstr @ X619 @ (^[Z0:$i]:((X621 @ Z0))))=(dsetconstr @ X620 @ (^[Z0:$i]:((X622 @ Z0)))))))))=>(![X497:$i, X498:$i]:((![X499:$i]:(((in @ X499 @ X497)=>(in @ X499 @ X498)))=>(subset @ X497 @ X498)))=>(![X500:$i, X501:$i]:((((X500)=(X501))=>(subset @ X501 @ X500)))=>(![X617:$i, X618:$i]:((((X617)=(X618))=>(subset @ X617 @ X618)))=>(![X502:$i, X503:$i]:((![X504:$i]:(((in @ X504 @ X502)=>(in @ X504 @ X503)))=>(subset @ X502 @ X503)))=>(![X616:$i]:((subset @ emptyset @ X616))=>(![X613:$i, X614:$i, X615:$i]:(((subset @ X613 @ X614)=>((in @ X615 @ X613)=>(in @ X615 @ X614))))=>(![X610:$i, X611:$i, X612:$i]:(((subset @ X610 @ X611)=>(~(in @ X612 @ X611)=>~(in @ X612 @ X610))))=>(![X505:$i, X506:$i, X507:$i]:(((in @ X507 @ X505)=>(~(in @ X507 @ X506)=>~(subset @ X505 @ X506))))=>(![X508:$i, X509:$i]:((~(subset @ X508 @ X509)=>((X508)!=(X509))))=>(![X510:$i, X511:$i, X512:$i]:(((in @ X512 @ X510)=>(~(in @ X512 @ X511)=>((X510)!=(X511)))))=>(![X609:$i]:((subset @ X609 @ X609))=>(![X606:$i, X607:$i, X608:$i]:(((subset @ X606 @ X607)=>((subset @ X607 @ X608)=>(subset @ X606 @ X608))))=>(![X604:$i, X605:$i]:((subset @ X605 @ (setadjoin @ X604 @ X605)))=>(![X601:$i, X602:$i, X603:$i]:(((subset @ X601 @ X603)=>(subset @ X601 @ (setadjoin @ X602 @ X603))))=>(![X599:$i, X600:$i]:(((subset @ X599 @ X600)=>(in @ X599 @ (powerset @ X600))))=>(![X513:$i, X514:$i]:(((subset @ X513 @ X514)=>((subset @ X514 @ X513)=>((X513)=(X514)))))=>(![X598:$i]:(((subset @ X598 @ emptyset)=>((X598)=(emptyset))))=>(![X515:$i, X516:$i]:(((subset @ X516 @ X515)=>(in @ X516 @ (powerset @ X515))))=>(![X596:$i, X597:$i]:(((in @ X597 @ (powerset @ X596))=>(subset @ X597 @ X596)))=>(![X517:$i]:((in @ X517 @ (powerset @ X517)))=>(![X594:$i, X595:$i]:(((subset @ X594 @ X595)=>(subset @ (powerset @ X594) @ (powerset @ X595))))=>(![X592:$i, X593:$i > $o]:((in @ (dsetconstr @ X592 @ (^[Z0:$i]:((X593 @ Z0)))) @ (powerset @ X592)))=>(![X518:$i, X519:$i > $o]:((subset @ (dsetconstr @ X518 @ (^[Z0:$i]:((X519 @ Z0)))) @ X518))=>(![X520:$i, X521:$i, X522:$i]:(((in @ X522 @ X520)=>(in @ X522 @ (binunion @ X520 @ X521))))=>(![X590:$i, X591:$i]:((in @ X591 @ (setadjoin @ X590 @ (setadjoin @ X591 @ emptyset))))=>(![X587:$i, X588:$i, X589:$i]:(((in @ X589 @ X588)=>(in @ X589 @ (binunion @ X587 @ X588))))=>(![X523:$i, X524:$i, X525:$i, X526:$o]:(((in @ X525 @ (binunion @ X523 @ X524))=>(((in @ X525 @ X523)=>(X526))=>(((in @ X525 @ X524)=>(X526))=>(X526)))))=>(![X584:$i, X585:$i, X586:$i]:(((in @ X586 @ (binunion @ X584 @ X585))=>((in @ X586 @ X584)|(in @ X586 @ X585))))=>(![X527:$i, X528:$i]:((subset @ X527 @ (binunion @ X527 @ X528)))=>(![X529:$i, X530:$i]:((subset @ X530 @ (binunion @ X529 @ X530)))=>(![X531:$i, X532:$i, X533:$i]:(((in @ X533 @ X531)=>((in @ X533 @ X532)=>(in @ X533 @ (binintersect @ X531 @ X532)))))=>(![X534:$i, X535:$i, X536:$i]:(((subset @ X536 @ X534)=>((subset @ X536 @ X535)=>(subset @ X536 @ (binintersect @ X534 @ X535)))))=>(![X581:$i, X582:$i, X583:$i]:(((in @ X583 @ (binintersect @ X581 @ X582))=>(in @ X583 @ X581)))=>(![X579:$i, X580:$i]:((subset @ (binintersect @ X579 @ X580) @ X579))=>(![X577:$i, X578:$i]:(((subset @ X577 @ X578)=>((binintersect @ X577 @ X578)=(X577))))=>(![X575:$i, X576:$i]:((((binintersect @ X575 @ X576)=(X576))=>(subset @ X576 @ X575)))=>(![X572:$i, X573:$i, X574:$i]:(((in @ X574 @ (binintersect @ X572 @ X573))=>(in @ X574 @ X573)))=>(![X537:$i, X538:$i]:((~(?[X539:$i]:(((in @ X539 @ X537)&(in @ X539 @ X538))))=>((binintersect @ X537 @ X538)=(emptyset))))=>(![X570:$i, X571:$i]:((subset @ (binintersect @ X570 @ X571) @ X571))=>(![X540:$i, X541:$i]:(((subset @ X541 @ X540)=>((binintersect @ X540 @ X541)=(X541))))=>(![X568:$i, X569:$i]:((((binintersect @ X568 @ X569)=(X568))=>(subset @ X568 @ X569)))=>(![X542:$i, X543:$i, X544:$i]:(((binintersect @ X542 @ (binunion @ X543 @ X544))=(binunion @ (binintersect @ X542 @ X543) @ (binintersect @ X542 @ X544))))=>(![X545:$i, X546:$i, X547:$i]:(((in @ X547 @ X545)=>(~(in @ X547 @ X546)=>(in @ X547 @ (setminus @ X545 @ X546)))))=>(![X548:$i, X549:$i, X550:$i]:(((in @ X550 @ (setminus @ X548 @ X549))=>(in @ X550 @ X548)))=>(![X551:$i, X552:$i, X553:$i]:(((in @ X553 @ (setminus @ X551 @ X552))=>~(in @ X553 @ X552)))=>(![X566:$i, X567:$i]:(((subset @ X566 @ X567)=>((setminus @ X566 @ X567)=(emptyset))))=>(![X563:$i, X564:$i, X565:$i]:((~(in @ X565 @ (setminus @ X563 @ X564))=>((in @ X565 @ X563)=>(in @ X565 @ X564))))=>(![X554:$i, X555:$i, X556:$i]:((~(in @ X556 @ (setminus @ X554 @ X555))=>(~(in @ X556 @ X555)=>~(in @ X556 @ X554))))=>(![X560:$i, X561:$i, X562:$i]:((~(in @ X562 @ X560)=>~(in @ X562 @ (setminus @ X560 @ X561))))=>(![X557:$i, X558:$i, X559:$i]:(((in @ X559 @ X558)=>~(in @ X559 @ (setminus @ X557 @ X558))))=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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(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)],[setminusLsub]), setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_143]), foundationAx]), wellorderingAx]), c_0_144]), c_0_145]), c_0_146]), c_0_147]), c_0_148]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_149]), setext]), emptyI]), noeltsimpempty]), c_0_150]), c_0_151]), c_0_152]), c_0_153]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_154]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_155]), c_0_156]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_157]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_158]), c_0_159]), c_0_160]), inCongP]), in__Cong]), c_0_161]), c_0_162]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_163]), c_0_164]), c_0_165]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_166]), c_0_167]), binunionIL]), upairset2IR]), binunionIR]), binunionEcases]), binunionE]), binunionLsub]), binunionRsub]), binintersectI]), binintersectSubset5]), binintersectEL]), binintersectLsub]), binintersectSubset2]), binintersectSubset3]), binintersectER]), disjointsetsI1]), binintersectRsub]), binintersectSubset4]), binintersectSubset1]), bs114d]), setminusI]), setminusEL]), setminusER]), setminusSubset2]), setminusERneg]), setminusELneg]), setminusILneg]), setminusIRneg])]), c_0_168])). 5.49/1.34 thf(c_0_170, negated_conjecture, ![X746:$i, X747:$i, X749:$i, X750:$i, X751:$i, X752:$i, X753:$i, X754:$i, X755:$i, X756:$i, X757:$i, X759:$i, X760:$i, X762:$i, X763:$i, X764:$i, X765:$i, X766:$i, X768:$i, X769:$i > $i > $o, X770:$i, X772:$i, X775:$i, X777:$i, X778:$i, X779:$i, X780:$i, X782:$i, X783:$i > $o, X784:$i, X786:$i, X787:$i > $o, X788:$i, X789:$i, X790:$i > $o, X791:$i, X792:$i, X793:$i > $o, X794:$i, X795:$i > $o, X796:$i, X799:$i, X800:$o, X801:$i, X802:$i, X803:$o, X804:$i, X805:$i, X806:$i > $o, X807:$i, X810:$i, X811:$i, X814:$i, X816:$i, X818:$i, X819:$i > $o, X820:$i, X821:$i, X823:$i, X824:$i > $o, X825:$i, X826:$i, X827:$i, X828:$i, X829:$i, X830:$i, X831:$i, X832:$i, X833:$i, X834:$i, X835:$i, X836:$o, X837:$i, X838:$i, X839:$i, X840:$i, X841:$i, X842:$i, X844:$i, X845:$i, X846:$i, X847:$i, X848:$i, X849:$i, X850:$i, X851:$i, X852:$i, X853:$i, X854:$o, X856:$i, X857:$i, X858:$i > $o, X859:$i, X862:$i, X863:$i, X864:$i, X866:$i, X867:$i, X868:$i, X869:$i, X870:$i, X871:$i, X872:$i, X873:$i, X874:$i, X875:$i, X876:$i, X877:$i, X878:$i, X879:$i, X880:$i, X881:$i, X882:$i > $o, X883:$i, X884:$i > $o, X885:$i, X886:$i, X887:$i > $o, X888:$i, X890:$i, X891:$i > $o, X893:$i, X894:$i, X895:$i > $o, X897:$i, X898:$i, X899:$i > $o, X900:$i, X902:$o, X903:$o, X904:$i, X905:$i > $o, X907:$i, X908:$i, X909:$i > $o, X910:$i, X912:$i > $o, X913:$i, X916:$i, X917:$i > $o, X918:$i, X922:$i, X923:$i > $o, X924:$i, X927:$i, X928:$i, X929:$i, X930:$i, X931:$i, X932:$i, X933:$i, X934:$i, X935:$i, X936:$i > $o, X937:$i, X939:$i, X940:$i, X941:$i > $o, X942:$i > $o, X945:$i, X948:$i, X949:$i, X952:$i, X953:$i, X954:$i, X955:$i, X956:$i, X957:$i, X958:$i, X959:$i, X960:$i, X961:$i > $o, X962:$i, X964:$i, X965:$i, X966:$i > $o, X967:$i > $o, X970:$i, X972:$i, X974:$i, X975:$i, X976:$i > $o, X977:$i > $o, X980:$i, X981:$i, X983:$i, X984:$i, X985:$i, X986:$i, X987:$i, X988:$i, X990:$i, X991:$i, X992:$i, X993:$i, X994:$i, X995:$i, X996:$i, X997:$i, X998:$i, X999:$i, X1000:$i, X1001:$i, X1002:$i, X1003:$i, X1004:$i, X1005:$i, X1006:$i, X1007:$i, X1008:$i, X1009:$i, X1010:$i, X1011:$i, X1012:$i, X1013:$i, 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X941 @ X942 @ X949))|~(X942 @ X949))|(~(X941 @ (esk39_2 @ X941 @ X942))|~(X942 @ (esk40_2 @ X941 @ X942)))))&(((X941 @ (esk44_2 @ X941 @ X942))|(((X949)!=(esk43_3 @ X941 @ X942 @ X949))|~(X942 @ X949))|(~(X941 @ (esk39_2 @ X941 @ X942))|~(X942 @ (esk40_2 @ X941 @ X942))))&(~(X941 @ X952)|((esk44_2 @ X941 @ X942)=(X952))|(((X949)!=(esk43_3 @ X941 @ X942 @ X949))|~(X942 @ X949))|(~(X941 @ (esk39_2 @ X941 @ X942))|~(X942 @ (esk40_2 @ X941 @ X942)))))))&(((((X942 @ (esk42_2 @ X941 @ X942))|((X941 @ (esk41_3 @ X941 @ X942 @ X945))|~(X941 @ X945))|((X941 @ (esk39_2 @ X941 @ X942))|(X942 @ (esk40_2 @ X941 @ X942))))&(~(X942 @ X948)|((esk42_2 @ X941 @ X942)=(X948))|((X941 @ (esk41_3 @ X941 @ X942 @ X945))|~(X941 @ X945))|((X941 @ (esk39_2 @ X941 @ X942))|(X942 @ (esk40_2 @ X941 @ X942)))))&(((X942 @ (esk42_2 @ X941 @ X942))|(((X945)!=(esk41_3 @ X941 @ X942 @ X945))|~(X941 @ X945))|((X941 @ (esk39_2 @ X941 @ X942))|(X942 @ (esk40_2 @ X941 @ X942))))&(~(X942 @ X948)|((esk42_2 @ X941 @ X942)=(X948))|(((X945)!=(esk41_3 @ X941 @ X942 @ X945))|~(X941 @ X945))|((X941 @ (esk39_2 @ X941 @ X942))|(X942 @ (esk40_2 @ X941 @ X942))))))&((((X941 @ (esk44_2 @ X941 @ X942))|((X942 @ (esk43_3 @ X941 @ X942 @ X949))|~(X942 @ X949))|((X941 @ (esk39_2 @ X941 @ X942))|(X942 @ (esk40_2 @ X941 @ X942))))&(~(X941 @ X952)|((esk44_2 @ X941 @ X942)=(X952))|((X942 @ (esk43_3 @ X941 @ X942 @ X949))|~(X942 @ X949))|((X941 @ (esk39_2 @ X941 @ X942))|(X942 @ (esk40_2 @ X941 @ X942)))))&(((X941 @ (esk44_2 @ X941 @ X942))|(((X949)!=(esk43_3 @ X941 @ X942 @ X949))|~(X942 @ X949))|((X941 @ (esk39_2 @ X941 @ X942))|(X942 @ (esk40_2 @ X941 @ X942))))&(~(X941 @ X952)|((esk44_2 @ X941 @ X942)=(X952))|(((X949)!=(esk43_3 @ X941 @ X942 @ X949))|~(X942 @ X949))|((X941 @ (esk39_2 @ X941 @ X942))|(X942 @ (esk40_2 @ X941 @ X942)))))))))&(((emptyset)=(emptyset))&((((X953)!=(X954))|(((X955)!=(X956))|((setadjoin @ X953 @ X955)=(setadjoin @ X954 @ X956))))&((((X957)!=(X958))|((powerset @ X957)=(powerset @ X958)))&((((X959)!=(X960))|((setunion @ X959)=(setunion @ X960)))&(((omega)=(omega))&((((X961 @ (esk45_2 @ X961 @ X962))|~(X961 @ X962)|(~(X961 @ X964)|(~(X961 @ X965)|((X964)=(X965)))))&(((X962)!=(esk45_2 @ X961 @ X962))|~(X961 @ X962)|(~(X961 @ X964)|(~(X961 @ X965)|((X964)=(X965))))))&((((((X967 @ (esk49_3 @ X966 @ X967 @ X972))|~(X967 @ X972)|((descr @ (^[Z0:$i]:((X966 @ Z0))))=(descr @ (^[Z0:$i]:((X967 @ Z0)))))|((X966 @ (esk48_3 @ X966 @ X967 @ X970))|~(X966 @ X970))|((esk46_2 @ X966 @ X967)=(esk47_2 @ X966 @ X967)))&(((X972)!=(esk49_3 @ X966 @ X967 @ X972))|~(X967 @ X972)|((descr @ (^[Z0:$i]:((X966 @ Z0))))=(descr @ (^[Z0:$i]:((X967 @ Z0)))))|((X966 @ (esk48_3 @ X966 @ X967 @ X970))|~(X966 @ X970))|((esk46_2 @ X966 @ X967)=(esk47_2 @ X966 @ X967))))&(((X967 @ (esk49_3 @ X966 @ X967 @ X972))|~(X967 @ X972)|((descr @ (^[Z0:$i]:((X966 @ Z0))))=(descr @ (^[Z0:$i]:((X967 @ Z0)))))|(((X970)!=(esk48_3 @ X966 @ X967 @ X970))|~(X966 @ X970))|((esk46_2 @ X966 @ X967)=(esk47_2 @ X966 @ X967)))&(((X972)!=(esk49_3 @ X966 @ X967 @ X972))|~(X967 @ X972)|((descr @ (^[Z0:$i]:((X966 @ Z0))))=(descr @ (^[Z0:$i]:((X967 @ Z0)))))|(((X970)!=(esk48_3 @ X966 @ X967 @ X970))|~(X966 @ X970))|((esk46_2 @ X966 @ X967)=(esk47_2 @ X966 @ X967)))))&(((((X967 @ (esk49_3 @ X966 @ X967 @ X972))|~(X967 @ X972)|((descr @ (^[Z0:$i]:((X966 @ Z0))))=(descr @ (^[Z0:$i]:((X967 @ Z0)))))|((X966 @ (esk48_3 @ X966 @ X967 @ X970))|~(X966 @ X970))|(~(X966 @ (esk46_2 @ X966 @ X967))|~(X967 @ (esk47_2 @ X966 @ X967))))&(((X972)!=(esk49_3 @ X966 @ X967 @ X972))|~(X967 @ X972)|((descr @ (^[Z0:$i]:((X966 @ Z0))))=(descr @ (^[Z0:$i]:((X967 @ Z0)))))|((X966 @ (esk48_3 @ X966 @ X967 @ X970))|~(X966 @ X970))|(~(X966 @ (esk46_2 @ X966 @ X967))|~(X967 @ (esk47_2 @ X966 @ X967)))))&(((X967 @ (esk49_3 @ X966 @ X967 @ X972))|~(X967 @ X972)|((descr @ (^[Z0:$i]:((X966 @ Z0))))=(descr @ (^[Z0:$i]:((X967 @ Z0)))))|(((X970)!=(esk48_3 @ X966 @ X967 @ X970))|~(X966 @ X970))|(~(X966 @ (esk46_2 @ X966 @ X967))|~(X967 @ (esk47_2 @ X966 @ X967))))&(((X972)!=(esk49_3 @ X966 @ X967 @ X972))|~(X967 @ X972)|((descr @ (^[Z0:$i]:((X966 @ Z0))))=(descr @ (^[Z0:$i]:((X967 @ Z0)))))|(((X970)!=(esk48_3 @ X966 @ X967 @ X970))|~(X966 @ X970))|(~(X966 @ (esk46_2 @ X966 @ X967))|~(X967 @ (esk47_2 @ X966 @ X967))))))&((((X967 @ (esk49_3 @ X966 @ X967 @ X972))|~(X967 @ X972)|((descr @ (^[Z0:$i]:((X966 @ Z0))))=(descr @ (^[Z0:$i]:((X967 @ Z0)))))|((X966 @ (esk48_3 @ X966 @ X967 @ X970))|~(X966 @ X970))|((X966 @ (esk46_2 @ X966 @ X967))|(X967 @ (esk47_2 @ X966 @ X967))))&(((X972)!=(esk49_3 @ X966 @ X967 @ X972))|~(X967 @ X972)|((descr @ (^[Z0:$i]:((X966 @ Z0))))=(descr @ (^[Z0:$i]:((X967 @ Z0)))))|((X966 @ (esk48_3 @ X966 @ X967 @ X970))|~(X966 @ X970))|((X966 @ (esk46_2 @ X966 @ X967))|(X967 @ (esk47_2 @ X966 @ X967)))))&(((X967 @ (esk49_3 @ X966 @ X967 @ X972))|~(X967 @ X972)|((descr @ (^[Z0:$i]:((X966 @ Z0))))=(descr @ (^[Z0:$i]:((X967 @ Z0)))))|(((X970)!=(esk48_3 @ X966 @ X967 @ X970))|~(X966 @ X970))|((X966 @ (esk46_2 @ X966 @ X967))|(X967 @ (esk47_2 @ X966 @ X967))))&(((X972)!=(esk49_3 @ X966 @ X967 @ X972))|~(X967 @ X972)|((descr @ (^[Z0:$i]:((X966 @ Z0))))=(descr @ (^[Z0:$i]:((X967 @ Z0)))))|(((X970)!=(esk48_3 @ X966 @ X967 @ X970))|~(X966 @ X970))|((X966 @ (esk46_2 @ X966 @ X967))|(X967 @ (esk47_2 @ X966 @ X967))))))))&((((in @ (esk50_4 @ X974 @ X975 @ X976 @ X977) @ X974)|((dsetconstr @ X974 @ (^[Z0:$i]:((X976 @ Z0))))=(dsetconstr @ X975 @ (^[Z0:$i]:((X977 @ Z0)))))|((X974)!=(X975)))&(((in @ (esk51_4 @ X974 @ X975 @ X976 @ X977) @ X975)|((dsetconstr @ X974 @ (^[Z0:$i]:((X976 @ Z0))))=(dsetconstr @ X975 @ (^[Z0:$i]:((X977 @ Z0)))))|((X974)!=(X975)))&((((esk50_4 @ X974 @ X975 @ X976 @ X977)=(esk51_4 @ X974 @ X975 @ X976 @ X977))|((dsetconstr @ X974 @ (^[Z0:$i]:((X976 @ Z0))))=(dsetconstr @ X975 @ (^[Z0:$i]:((X977 @ Z0)))))|((X974)!=(X975)))&((~(X976 @ (esk50_4 @ X974 @ X975 @ X976 @ X977))|~(X977 @ (esk51_4 @ X974 @ X975 @ X976 @ X977))|((dsetconstr @ X974 @ (^[Z0:$i]:((X976 @ Z0))))=(dsetconstr @ X975 @ (^[Z0:$i]:((X977 @ Z0)))))|((X974)!=(X975)))&((X976 @ (esk50_4 @ X974 @ X975 @ X976 @ X977))|(X977 @ (esk51_4 @ X974 @ X975 @ X976 @ X977))|((dsetconstr @ X974 @ (^[Z0:$i]:((X976 @ Z0))))=(dsetconstr @ X975 @ (^[Z0:$i]:((X977 @ Z0)))))|((X974)!=(X975)))))))&((((in @ (esk52_2 @ X980 @ X981) @ X980)|(subset @ X980 @ X981))&(~(in @ (esk52_2 @ X980 @ X981) @ X981)|(subset @ X980 @ X981)))&((((X983)!=(X984))|(subset @ X984 @ X983))&((((X985)!=(X986))|(subset @ X985 @ X986))&((((in @ (esk53_2 @ X987 @ X988) @ X987)|(subset @ X987 @ X988))&(~(in @ (esk53_2 @ X987 @ X988) @ X988)|(subset @ X987 @ X988)))&((subset @ emptyset @ X990)&((~(subset @ X991 @ X992)|(~(in @ X993 @ X991)|(in @ X993 @ X992)))&((~(subset @ X994 @ X995)|((in @ X996 @ X995)|~(in @ X996 @ X994)))&((~(in @ X999 @ X997)|((in @ X999 @ X998)|~(subset @ X997 @ X998)))&(((subset @ X1000 @ X1001)|((X1000)!=(X1001)))&((~(in @ X1004 @ X1002)|((in @ X1004 @ X1003)|((X1002)!=(X1003))))&((subset @ X1005 @ X1005)&((~(subset @ X1006 @ X1007)|(~(subset @ X1007 @ X1008)|(subset @ X1006 @ X1008)))&((subset @ X1010 @ (setadjoin @ X1009 @ X1010))&((~(subset @ X1011 @ X1013)|(subset @ X1011 @ (setadjoin @ X1012 @ X1013)))&((~(subset @ X1014 @ X1015)|(in @ X1014 @ (powerset @ X1015)))&((~(subset @ X1016 @ X1017)|(~(subset @ X1017 @ X1016)|((X1016)=(X1017))))&((~(subset @ X1018 @ emptyset)|((X1018)=(emptyset)))&((~(subset @ X1020 @ X1019)|(in @ X1020 @ (powerset @ X1019)))&((~(in @ X1022 @ (powerset @ X1021))|(subset @ X1022 @ X1021))&((in @ X1023 @ (powerset @ X1023))&((~(subset @ X1024 @ X1025)|(subset @ (powerset @ X1024) @ (powerset @ X1025)))&((in @ (dsetconstr @ X1026 @ (^[Z0:$i]:((X1027 @ Z0)))) @ (powerset @ X1026))&((subset @ (dsetconstr @ X1028 @ (^[Z0:$i]:((X1029 @ Z0)))) @ X1028)&((~(in @ X1032 @ X1030)|(in @ X1032 @ (binunion @ X1030 @ X1031)))&((in @ X1034 @ (setadjoin @ X1033 @ (setadjoin @ X1034 @ emptyset)))&((~(in @ X1037 @ X1036)|(in @ X1037 @ (binunion @ X1035 @ X1036)))&(((((in @ X1040 @ X1039)|(X1041)|(in @ X1040 @ X1038)|~(in @ X1040 @ (binunion @ X1038 @ X1039)))&(~(X1041)|(X1041)|(in @ X1040 @ X1038)|~(in @ X1040 @ (binunion @ X1038 @ X1039))))&(((in @ X1040 @ X1039)|(X1041)|~(X1041)|~(in @ X1040 @ (binunion @ X1038 @ X1039)))&(~(X1041)|(X1041)|~(X1041)|~(in @ X1040 @ (binunion @ X1038 @ X1039)))))&((~(in @ X1044 @ (binunion @ X1042 @ X1043))|((in @ X1044 @ X1042)|(in @ X1044 @ X1043)))&((subset @ X1045 @ (binunion @ X1045 @ X1046))&((subset @ X1048 @ (binunion @ X1047 @ X1048))&((~(in @ X1051 @ X1049)|(~(in @ X1051 @ X1050)|(in @ X1051 @ (binintersect @ X1049 @ X1050))))&((~(subset @ X1054 @ X1052)|(~(subset @ X1054 @ X1053)|(subset @ X1054 @ (binintersect @ X1052 @ X1053))))&((~(in @ X1057 @ (binintersect @ X1055 @ X1056))|(in @ X1057 @ X1055))&((subset @ (binintersect @ X1058 @ X1059) @ X1058)&((~(subset @ X1060 @ X1061)|((binintersect @ X1060 @ X1061)=(X1060)))&((((binintersect @ X1062 @ X1063)!=(X1063))|(subset @ X1063 @ X1062))&((~(in @ X1066 @ (binintersect @ X1064 @ X1065))|(in @ X1066 @ X1065))&((((in @ (esk54_2 @ X1067 @ X1068) @ X1067)|((binintersect @ X1067 @ X1068)=(emptyset)))&((in @ (esk54_2 @ X1067 @ X1068) @ X1068)|((binintersect @ X1067 @ X1068)=(emptyset))))&((subset @ (binintersect @ X1070 @ X1071) @ X1071)&((~(subset @ X1073 @ X1072)|((binintersect @ X1072 @ X1073)=(X1073)))&((((binintersect @ X1074 @ X1075)!=(X1074))|(subset @ X1074 @ X1075))&(((binintersect @ X1076 @ (binunion @ X1077 @ X1078))=(binunion @ (binintersect @ X1076 @ X1077) @ (binintersect @ X1076 @ X1078)))&((~(in @ X1081 @ X1079)|((in @ X1081 @ X1080)|(in @ X1081 @ (setminus @ X1079 @ X1080))))&((~(in @ X1084 @ (setminus @ X1082 @ X1083))|(in @ X1084 @ X1082))&((~(in @ X1087 @ (setminus @ X1085 @ X1086))|~(in @ X1087 @ X1086))&((~(subset @ X1088 @ X1089)|((setminus @ X1088 @ X1089)=(emptyset)))&(((in @ X1092 @ (setminus @ X1090 @ X1091))|(~(in @ X1092 @ X1090)|(in @ X1092 @ X1091)))&(((in @ X1095 @ (setminus @ X1093 @ X1094))|((in @ X1095 @ X1094)|~(in @ X1095 @ X1093)))&(((in @ X1098 @ X1096)|~(in @ X1098 @ (setminus @ X1096 @ X1097)))&((~(in @ X1101 @ X1100)|~(in @ X1101 @ (setminus @ X1099 @ X1100)))&~(subset @ (setminus @ esk55_0 @ esk56_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_169])])])])])])). 5.49/1.34 thf(c_0_171, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ X2 @ X3)|~((in @ X2 @ (setminus @ X3 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_170])). 5.49/1.34 thf(c_0_172, negated_conjecture, ![X2:$i, X3:$i]:(((in @ (esk52_2 @ X2 @ X3) @ X2)|(subset @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_170])). 5.49/1.34 thf(c_0_173, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X2 @ X3)|~((in @ (esk52_2 @ X2 @ X3) @ X3)))), inference(split_conjunct,[status(thm)],[c_0_170])). 5.49/1.34 thf(c_0_174, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ (esk52_2 @ (setminus @ X2 @ X3) @ X4) @ X2)|(subset @ (setminus @ X2 @ X3) @ X4))), inference(spm,[status(thm)],[c_0_171, c_0_172])). 5.49/1.34 thf(c_0_175, negated_conjecture, ~((subset @ (setminus @ esk55_0 @ esk56_0) @ esk55_0)), inference(split_conjunct,[status(thm)],[c_0_170])). 5.49/1.34 thf(c_0_176, negated_conjecture, ![X3:$i, X2:$i]:((subset @ (setminus @ X2 @ X3) @ X2)), inference(spm,[status(thm)],[c_0_173, c_0_174])). 5.49/1.34 thf(c_0_177, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_175, c_0_176])]), ['proof']). 5.49/1.34 # SZS output end CNFRefutation 5.49/1.34 # Parsed axioms : 272 5.49/1.34 # Removed by relevancy pruning/SinE : 0 5.49/1.34 # Initial clauses : 384 5.49/1.34 # Removed in clause preprocessing : 160 5.49/1.34 # Initial clauses in saturation : 224 5.49/1.34 # Processed clauses : 3571 5.49/1.34 # ...of these trivial : 29 5.49/1.34 # ...subsumed : 2094 5.49/1.34 # ...remaining for further processing : 1448 5.49/1.34 # Other redundant clauses eliminated : 35 5.49/1.34 # Clauses deleted for lack of memory : 0 5.49/1.34 # Backward-subsumed : 100 5.49/1.34 # Backward-rewritten : 8 5.49/1.34 # Generated clauses : 42829 5.49/1.34 # ...of the previous two non-redundant : 40803 5.49/1.34 # ...aggressively subsumed : 0 5.49/1.34 # Contextual simplify-reflections : 4 5.49/1.34 # Paramodulations : 42791 5.49/1.34 # Factorizations : 2 5.49/1.34 # NegExts : 0 5.49/1.34 # Equation resolutions : 35 5.49/1.34 # Propositional unsat checks : 0 5.49/1.34 # Propositional check models : 0 5.49/1.34 # Propositional check unsatisfiable : 0 5.49/1.34 # Propositional clauses : 0 5.49/1.34 # Propositional clauses after purity: 0 5.49/1.34 # Propositional unsat core size : 0 5.49/1.34 # Propositional preprocessing time : 0.000 5.49/1.34 # Propositional encoding time : 0.000 5.49/1.34 # Propositional solver time : 0.000 5.49/1.34 # Success case prop preproc time : 0.000 5.49/1.34 # Success case prop encoding time : 0.000 5.49/1.34 # Success case prop solver time : 0.000 5.49/1.34 # Current number of processed clauses : 1134 5.49/1.34 # Positive orientable unit clauses : 72 5.49/1.34 # Positive unorientable unit clauses: 0 5.49/1.34 # Negative unit clauses : 155 5.49/1.34 # Non-unit-clauses : 907 5.49/1.34 # Current number of unprocessed clauses: 37501 5.49/1.34 # ...number of literals in the above : 123284 5.49/1.34 # Current number of archived formulas : 0 5.49/1.34 # Current number of archived clauses : 301 5.49/1.34 # Clause-clause subsumption calls (NU) : 88774 5.49/1.34 # Rec. Clause-clause subsumption calls : 67962 5.49/1.34 # Non-unit clause-clause subsumptions : 1349 5.49/1.34 # Unit Clause-clause subsumption calls : 18305 5.49/1.34 # Rewrite failures with RHS unbound : 0 5.49/1.34 # BW rewrite match attempts : 34 5.49/1.34 # BW rewrite match successes : 8 5.49/1.34 # Condensation attempts : 0 5.49/1.34 # Condensation successes : 0 5.49/1.34 # Termbank termtop insertions : 734671 5.49/1.34 5.49/1.34 # ------------------------------------------------- 5.49/1.34 # User time : 0.898 s 5.49/1.34 # System time : 0.024 s 5.49/1.34 # Total time : 0.923 s 5.49/1.34 # Maximum resident set size: 4704 pages 5.49/1.34 5.49/1.34 # ------------------------------------------------- 5.49/1.34 # User time : 0.902 s 5.49/1.34 # System time : 0.029 s 5.49/1.34 # Total time : 0.931 s 5.49/1.34 # Maximum resident set size: 2068 pages 5.49/1.35 EOF