0.00/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM 0.19/0.45 % Computer : n022.cluster.edu 0.19/0.45 % Model : x86_64 x86_64 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.19/0.45 % Memory : 8046.5625MB 0.19/0.45 % OS : Linux 6.8.0-71-generic 0.19/0.45 % CPULimit : 1440 0.19/0.45 % WCLimit : 180 0.19/0.45 % DateTime : Mon Jul 27 09:34:43 UTC 2026 0.19/0.46 % CPUTime : 0.19/0.46 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM 0.19/0.51 Running higher-order theorem proving 0.24/0.53 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=180 /export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p 9.14/2.16 % Version: 3.5.1-ho 9.14/2.16 % Preprocessing class: HSMMSLSSLLLCHFA. 9.14/2.16 % Scheduled 4 strats onto 8 cores with 180 seconds (1440 total) 9.14/2.16 % Starting ehoh_best3_avoidappvar with 900s (5) cores 9.14/2.16 % Starting ehoh_best3_rw with 180s (1) cores 9.14/2.16 % Starting almost_fo_3 with 180s (1) cores 9.14/2.16 % Starting new_ho_13 with 180s (1) cores 9.14/2.16 % ehoh_best3_avoidappvar with pid 710997 completed with status 0 9.14/2.16 % Result found by ehoh_best3_avoidappvar 9.14/2.16 % Preprocessing class: HSMMSLSSLLLCHFA. 9.14/2.16 % Scheduled 4 strats onto 8 cores with 180 seconds (1440 total) 9.14/2.16 % Starting ehoh_best3_avoidappvar with 900s (5) cores 9.14/2.16 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto) 9.14/2.16 % No SInE strategy applied 9.14/2.16 % Search class: HGHSM-FSLM31-SHFMMMBN 9.14/2.16 % Scheduled 7 strats onto 5 cores with 900 seconds (900 total) 9.14/2.16 % Starting SubtermCWHack with 82s (1) cores 9.14/2.16 % Starting ehoh_best3_avoidappvar with 91s (1) cores 9.14/2.16 % Starting sh5l with 82s (1) cores 9.14/2.16 % Starting lpo1_def_fix with 82s (1) cores 9.14/2.16 % Starting full_lambda_2 with 82s (1) cores 9.14/2.16 % ehoh_best3_avoidappvar with pid 711003 completed with status 0 9.14/2.16 % Result found by ehoh_best3_avoidappvar 9.14/2.16 % Preprocessing class: HSMMSLSSLLLCHFA. 9.14/2.16 % Scheduled 4 strats onto 8 cores with 180 seconds (1440 total) 9.14/2.16 % Starting ehoh_best3_avoidappvar with 900s (5) cores 9.14/2.16 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto) 9.14/2.16 % No SInE strategy applied 9.14/2.16 % Search class: HGHSM-FSLM31-SHFMMMBN 9.14/2.16 % Scheduled 7 strats onto 5 cores with 900 seconds (900 total) 9.14/2.16 % Starting SubtermCWHack with 82s (1) cores 9.14/2.16 % Starting ehoh_best3_avoidappvar with 91s (1) cores 9.14/2.16 % Preprocessing time : 0.009 s 9.14/2.16 % Presaturation interreduction done 9.14/2.16 9.14/2.16 % Proof found! 9.14/2.16 % SZS status Theorem 9.14/2.16 % SZS output start CNFRefutation 9.14/2.16 thf(decl_23, type, in: $i > $i > $o). 9.14/2.16 thf(decl_24, type, exu: ($i > $o) > $o). 9.14/2.16 thf(decl_25, type, setextAx: $o). 9.14/2.16 thf(decl_26, type, emptyset: $i). 9.14/2.16 thf(decl_27, type, emptysetAx: $o). 9.14/2.16 thf(decl_28, type, setadjoin: $i > $i > $i). 9.14/2.16 thf(decl_29, type, setadjoinAx: $o). 9.14/2.16 thf(decl_30, type, powerset: $i > $i). 9.14/2.16 thf(decl_31, type, powersetAx: $o). 9.14/2.16 thf(decl_32, type, setunion: $i > $i). 9.14/2.16 thf(decl_33, type, setunionAx: $o). 9.14/2.16 thf(decl_34, type, omega: $i). 9.14/2.16 thf(decl_35, type, omega0Ax: $o). 9.14/2.16 thf(decl_36, type, omegaSAx: $o). 9.14/2.16 thf(decl_37, type, omegaIndAx: $o). 9.14/2.16 thf(decl_38, type, replAx: $o). 9.14/2.16 thf(decl_39, type, foundationAx: $o). 9.14/2.16 thf(decl_40, type, wellorderingAx: $o). 9.14/2.16 thf(decl_41, type, descr: ($i > $o) > $i). 9.14/2.16 thf(decl_42, type, descrp: $o). 9.14/2.16 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i). 9.14/2.16 thf(decl_44, type, dsetconstrI: $o). 9.14/2.16 thf(decl_45, type, dsetconstrEL: $o). 9.14/2.16 thf(decl_46, type, dsetconstrER: $o). 9.14/2.16 thf(decl_47, type, exuE1: $o). 9.14/2.16 thf(decl_48, type, prop2set: $o > $i). 9.14/2.16 thf(decl_49, type, prop2setE: $o). 9.14/2.16 thf(decl_50, type, emptysetE: $o). 9.14/2.16 thf(decl_51, type, emptysetimpfalse: $o). 9.14/2.16 thf(decl_52, type, notinemptyset: $o). 9.14/2.16 thf(decl_53, type, exuE3e: $o). 9.14/2.16 thf(decl_54, type, setext: $o). 9.14/2.16 thf(decl_55, type, emptyI: $o). 9.14/2.16 thf(decl_56, type, noeltsimpempty: $o). 9.14/2.16 thf(decl_57, type, setbeta: $o). 9.14/2.16 thf(decl_58, type, nonempty: $i > $o). 9.14/2.16 thf(decl_59, type, nonemptyE1: $o). 9.14/2.16 thf(decl_60, type, nonemptyI: $o). 9.14/2.16 thf(decl_61, type, nonemptyI1: $o). 9.14/2.16 thf(decl_62, type, setadjoinIL: $o). 9.14/2.16 thf(decl_63, type, emptyinunitempty: $o). 9.14/2.16 thf(decl_64, type, setadjoinIR: $o). 9.14/2.16 thf(decl_65, type, setadjoinE: $o). 9.14/2.16 thf(decl_66, type, setadjoinOr: $o). 9.14/2.16 thf(decl_67, type, setoftrueEq: $o). 9.14/2.16 thf(decl_68, type, powersetI: $o). 9.14/2.16 thf(decl_69, type, emptyinPowerset: $o). 9.14/2.16 thf(decl_70, type, emptyInPowerset: $o). 9.14/2.16 thf(decl_71, type, powersetE: $o). 9.14/2.16 thf(decl_72, type, setunionI: $o). 9.14/2.16 thf(decl_73, type, setunionE: $o). 9.14/2.16 thf(decl_74, type, subPowSU: $o). 9.14/2.16 thf(decl_75, type, exuE2: $o). 9.14/2.16 thf(decl_76, type, nonemptyImpWitness: $o). 9.14/2.16 thf(decl_77, type, uniqinunit: $o). 9.14/2.16 thf(decl_78, type, notinsingleton: $o). 9.14/2.16 thf(decl_79, type, eqinunit: $o). 9.14/2.16 thf(decl_80, type, singletonsswitch: $o). 9.14/2.16 thf(decl_81, type, upairsetE: $o). 9.14/2.16 thf(decl_82, type, upairsetIL: $o). 9.14/2.16 thf(decl_83, type, upairsetIR: $o). 9.14/2.16 thf(decl_84, type, emptyE1: $o). 9.14/2.16 thf(decl_85, type, vacuousDall: $o). 9.14/2.16 thf(decl_86, type, quantDeMorgan1: $o). 9.14/2.16 thf(decl_87, type, quantDeMorgan2: $o). 9.14/2.16 thf(decl_88, type, quantDeMorgan3: $o). 9.14/2.16 thf(decl_89, type, quantDeMorgan4: $o). 9.14/2.16 thf(decl_90, type, prop2setI: $o). 9.14/2.16 thf(decl_91, type, set2prop: $i > $o). 9.14/2.16 thf(decl_92, type, prop2set2propI: $o). 9.14/2.16 thf(decl_93, type, notdexE: $o). 9.14/2.16 thf(decl_94, type, notdallE: $o). 9.14/2.16 thf(decl_95, type, exuI1: $o). 9.14/2.16 thf(decl_96, type, exuI3: $o). 9.14/2.16 thf(decl_97, type, exuI2: $o). 9.14/2.16 thf(decl_98, type, inCongP: $o). 9.14/2.16 thf(decl_99, type, in__Cong: $o). 9.14/2.16 thf(decl_100, type, exuE3u: $o). 9.14/2.16 thf(decl_101, type, exu__Cong: $o). 9.14/2.16 thf(decl_102, type, emptyset__Cong: $o). 9.14/2.16 thf(decl_103, type, setadjoin__Cong: $o). 9.14/2.16 thf(decl_104, type, powerset__Cong: $o). 9.14/2.16 thf(decl_105, type, setunion__Cong: $o). 9.14/2.16 thf(decl_106, type, omega__Cong: $o). 9.14/2.16 thf(decl_107, type, exuEu: $o). 9.14/2.16 thf(decl_108, type, descr__Cong: $o). 9.14/2.16 thf(decl_109, type, dsetconstr__Cong: $o). 9.14/2.16 thf(decl_110, type, subset: $i > $i > $o). 9.14/2.16 thf(decl_113, type, subsetI1: $o). 9.14/2.16 thf(decl_114, type, eqimpsubset2: $o). 9.14/2.16 thf(decl_115, type, eqimpsubset1: $o). 9.14/2.16 thf(decl_116, type, subsetI2: $o). 9.14/2.16 thf(decl_117, type, emptysetsubset: $o). 9.14/2.16 thf(decl_118, type, subsetE: $o). 9.14/2.16 thf(decl_119, type, subsetE2: $o). 9.14/2.16 thf(decl_120, type, notsubsetI: $o). 9.14/2.16 thf(decl_121, type, notequalI1: $o). 9.14/2.16 thf(decl_122, type, notequalI2: $o). 9.14/2.16 thf(decl_123, type, subsetRefl: $o). 9.14/2.16 thf(decl_124, type, subsetTrans: $o). 9.14/2.16 thf(decl_125, type, setadjoinSub: $o). 9.14/2.16 thf(decl_126, type, setadjoinSub2: $o). 9.14/2.16 thf(decl_127, type, subset2powerset: $o). 9.14/2.16 thf(decl_128, type, epred1_0: $o). 9.14/2.16 thf(decl_129, type, esk1_2: $i > $i > $i). 9.14/2.16 thf(decl_130, type, esk2_2: $i > $i > $i). 9.14/2.16 thf(decl_131, type, esk3_2: $i > $i > $i). 9.14/2.16 thf(decl_132, type, esk4_1: $i > $i). 9.14/2.16 thf(decl_133, type, esk5_2: ($i > $i > $o) > $i > $i). 9.14/2.16 thf(decl_134, type, esk6_3: ($i > $i > $o) > $i > $i > $i). 9.14/2.16 thf(decl_135, type, esk7_2: ($i > $i > $o) > $i > $i). 9.14/2.16 thf(decl_136, type, esk8_3: ($i > $i > $o) > $i > $i > $i). 9.14/2.16 thf(decl_137, type, esk9_1: $i > $i). 9.14/2.16 thf(decl_138, type, esk10_2: ($i > $o) > $i > $i). 9.14/2.16 thf(decl_139, type, esk11_2: ($i > $o) > $i > $i). 9.14/2.16 thf(decl_140, type, esk12_1: ($i > $o) > $i). 9.14/2.16 thf(decl_141, type, esk13_2: ($i > $o) > $i > $i). 9.14/2.16 thf(decl_142, type, esk14_1: ($i > $o) > $i). 9.14/2.16 thf(decl_143, type, esk15_2: $i > $i > $i). 9.14/2.16 thf(decl_144, type, esk16_2: $i > $i > $i). 9.14/2.16 thf(decl_145, type, esk17_1: $i > $i). 9.14/2.16 thf(decl_146, type, esk18_1: $i > $i). 9.14/2.16 thf(decl_147, type, esk19_1: $i > $i). 9.14/2.16 thf(decl_148, type, esk20_2: $i > $i > $i). 9.14/2.16 thf(decl_149, type, esk21_3: $i > $i > $o > $i). 9.14/2.16 thf(decl_150, type, esk22_2: ($i > $o) > $i > $i). 9.14/2.16 thf(decl_151, type, esk23_1: ($i > $o) > $i). 9.14/2.16 thf(decl_152, type, esk24_1: $i > $i). 9.14/2.16 thf(decl_153, type, esk25_2: $i > ($i > $o) > $i). 9.14/2.16 thf(decl_154, type, esk26_2: $i > ($i > $o) > $i). 9.14/2.16 thf(decl_155, type, esk27_2: $i > ($i > $o) > $i). 9.14/2.16 thf(decl_156, type, esk28_2: $i > ($i > $o) > $i). 9.14/2.16 thf(decl_157, type, esk29_2: $i > ($i > $o) > $i). 9.14/2.16 thf(decl_158, type, esk30_2: $i > ($i > $o) > $i). 9.14/2.16 thf(decl_159, type, esk31_2: ($i > $o) > $i > $i). 9.14/2.16 thf(decl_160, type, esk32_1: ($i > $o) > $i). 9.14/2.16 thf(decl_161, type, esk33_1: ($i > $o) > $i). 9.14/2.16 thf(decl_162, type, esk34_1: ($i > $o) > $i). 9.14/2.16 thf(decl_163, type, esk35_1: ($i > $o) > $i). 9.14/2.16 thf(decl_164, type, esk36_2: ($i > $o) > $i > $i). 9.14/2.16 thf(decl_165, type, esk37_1: ($i > $o) > $i). 9.14/2.16 thf(decl_166, type, esk38_2: ($i > $o) > $i > $i). 9.14/2.16 thf(decl_167, type, esk39_2: ($i > $o) > ($i > $o) > $i). 9.14/2.16 thf(decl_168, type, esk40_2: ($i > $o) > ($i > $o) > $i). 9.14/2.16 thf(decl_169, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i). 9.14/2.16 thf(decl_170, type, esk42_2: ($i > $o) > ($i > $o) > $i). 9.14/2.16 thf(decl_171, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i). 9.14/2.16 thf(decl_172, type, esk44_2: ($i > $o) > ($i > $o) > $i). 9.14/2.16 thf(decl_173, type, esk45_2: ($i > $o) > $i > $i). 9.14/2.16 thf(decl_174, type, esk46_2: ($i > $o) > ($i > $o) > $i). 9.14/2.16 thf(decl_175, type, esk47_2: ($i > $o) > ($i > $o) > $i). 9.14/2.16 thf(decl_176, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i). 9.14/2.16 thf(decl_177, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i). 9.14/2.16 thf(decl_178, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i). 9.14/2.16 thf(decl_179, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i). 9.14/2.16 thf(decl_180, type, esk52_2: $i > $i > $i). 9.14/2.16 thf(decl_181, type, esk53_2: $i > $i > $i). 9.14/2.16 thf(decl_182, type, esk54_0: $i). 9.14/2.16 thf(decl_183, type, esk55_0: $i). 9.14/2.16 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', replAx)). 9.14/2.16 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', exu)). 9.14/2.16 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', descrp)). 9.14/2.16 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', exuE1)). 9.14/2.16 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', exuE3e)). 9.14/2.16 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', nonempty)). 9.14/2.16 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', nonemptyI)). 9.14/2.16 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', exuE2)). 9.14/2.16 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', exuI1)). 9.14/2.16 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', exuI3)). 9.14/2.16 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', exuI2)). 9.14/2.16 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', exuE3u)). 9.14/2.16 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', exu__Cong)). 9.14/2.16 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', exuEu)). 9.14/2.16 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', descr__Cong)). 9.14/2.16 thf(setextsub, conjecture, (((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>(((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((((emptyI)=>((noeltsimpempty)=>(((nonemptyE1)=>((((((setadjoinIR)=>((setadjoinE)=>((((powersetI)=>(((emptyInPowerset)=>((powersetE)=>((((subPowSU)=>(((((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>(((((emptyE1)=>(((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>(((prop2set2propI)=>(((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>(((exuE3u)=>((((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>(((((subsetI1)=>(((((emptysetsubset)=>(((subsetE2)=>((notsubsetI)=>((notequalI1)=>(((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))<=(subset2powerset))<=(setadjoinSub2)))))<=(notequalI2)))))<=(subsetE)))<=(subsetI2))<=(eqimpsubset1))<=(eqimpsubset2)))<=(dsetconstr__Cong))<=(descr__Cong))<=(exuEu))))))<=(emptyset__Cong))<=(exu__Cong)))<=(in__Cong)))))))<=(notdexE)))<=(prop2setI))))))<=(vacuousDall)))<=(upairsetIR))<=(upairsetIL))<=(upairsetE)))))<=(uniqinunit))<=(nonemptyImpWitness))<=(exuE2)))<=(setunionE))<=(setunionI))))<=(emptyinPowerset)))<=(setoftrueEq))<=(setadjoinOr))))<=(emptyinunitempty))<=(setadjoinIL))<=(nonemptyI1))<=(nonemptyI)))<=(setbeta))))<=(setext))<=(exuE3e))))))<=(exuE1)))))<=(descrp))<=(wellorderingAx))))))<=(omega0Ax))<=(setunionAx)))))<=(setextAx)), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', setextsub)). 9.14/2.16 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', dsetconstrI)). 9.14/2.16 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', dsetconstrEL)). 9.14/2.16 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', dsetconstrER)). 9.14/2.16 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', setbeta)). 9.14/2.16 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', nonemptyE1)). 9.14/2.16 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', nonemptyI1)). 9.14/2.16 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', setoftrueEq)). 9.14/2.16 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', nonemptyImpWitness)). 9.14/2.16 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', emptyE1)). 9.14/2.16 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', dsetconstr__Cong)). 9.14/2.16 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', setextAx)). 9.14/2.16 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', emptysetAx)). 9.14/2.16 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', setadjoinAx)). 9.14/2.16 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', powersetAx)). 9.14/2.16 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', setunionAx)). 9.14/2.16 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', omega0Ax)). 9.14/2.16 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', omegaSAx)). 9.14/2.16 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', omegaIndAx)). 9.14/2.16 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', foundationAx)). 9.14/2.16 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', wellorderingAx)). 9.14/2.16 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', prop2setE)). 9.14/2.16 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', emptysetE)). 9.14/2.16 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', emptysetimpfalse)). 9.14/2.16 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', notinemptyset)). 9.14/2.16 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', setext)). 9.14/2.16 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', emptyI)). 9.14/2.16 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', noeltsimpempty)). 9.14/2.16 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', setadjoinIL)). 9.14/2.16 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', emptyinunitempty)). 9.14/2.16 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', setadjoinIR)). 9.14/2.16 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', setadjoinE)). 9.14/2.16 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', setadjoinOr)). 9.14/2.16 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', powersetI)). 9.14/2.16 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', emptyinPowerset)). 9.14/2.16 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', emptyInPowerset)). 9.14/2.16 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', powersetE)). 9.14/2.16 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', setunionI)). 9.14/2.16 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', setunionE)). 9.14/2.16 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', subPowSU)). 9.14/2.16 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', uniqinunit)). 9.14/2.16 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', notinsingleton)). 9.14/2.16 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', eqinunit)). 9.14/2.16 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', singletonsswitch)). 9.14/2.16 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', upairsetE)). 9.14/2.16 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', upairsetIL)). 9.14/2.16 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', upairsetIR)). 9.14/2.16 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', vacuousDall)). 9.14/2.16 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', quantDeMorgan1)). 9.14/2.16 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', quantDeMorgan2)). 9.14/2.16 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', quantDeMorgan3)). 9.14/2.16 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', quantDeMorgan4)). 9.14/2.16 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', prop2setI)). 9.14/2.16 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', prop2set2propI)). 9.14/2.16 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', notdexE)). 9.14/2.16 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', notdallE)). 9.14/2.16 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', inCongP)). 9.14/2.16 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', in__Cong)). 9.14/2.16 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', emptyset__Cong)). 9.14/2.16 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', setadjoin__Cong)). 9.14/2.16 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', powerset__Cong)). 9.14/2.16 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', setunion__Cong)). 9.14/2.16 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', omega__Cong)). 9.14/2.16 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', subsetI1)). 9.14/2.16 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', eqimpsubset2)). 9.14/2.16 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', eqimpsubset1)). 9.14/2.16 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', subsetI2)). 9.14/2.16 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', emptysetsubset)). 9.14/2.16 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', subsetE)). 9.14/2.16 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', subsetE2)). 9.14/2.16 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', notsubsetI)). 9.14/2.16 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', notequalI1)). 9.14/2.16 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', notequalI2)). 9.14/2.16 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', subsetRefl)). 9.14/2.16 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', subsetTrans)). 9.14/2.16 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', setadjoinSub)). 9.14/2.16 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', setadjoinSub2)). 9.14/2.16 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.4MKMsy6vPZ/E---3.1_710984.p', subset2powerset)). 9.14/2.16 thf(c_0_93, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 9.14/2.16 thf(c_0_94, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])). 9.14/2.16 thf(c_0_95, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 9.14/2.16 thf(c_0_96, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 9.14/2.16 thf(c_0_97, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 9.14/2.16 thf(c_0_98, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])). 9.14/2.16 thf(c_0_99, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 9.14/2.16 thf(c_0_100, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])). 9.14/2.16 thf(c_0_101, 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])). 9.14/2.16 thf(c_0_102, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 9.14/2.16 thf(c_0_103, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 9.14/2.16 thf(c_0_104, 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])). 9.14/2.16 thf(c_0_105, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 9.14/2.16 thf(c_0_106, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 9.14/2.16 thf(c_0_107, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 9.14/2.16 thf(c_0_108, negated_conjecture, ~((((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>(((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((((emptyI)=>((noeltsimpempty)=>(((nonemptyE1)=>((((((setadjoinIR)=>((setadjoinE)=>((((powersetI)=>(((emptyInPowerset)=>((powersetE)=>((((subPowSU)=>(((((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>(((((emptyE1)=>(((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>(((prop2set2propI)=>(((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>(((exuE3u)=>((((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>(((((subsetI1)=>(((((emptysetsubset)=>(((subsetE2)=>((notsubsetI)=>((notequalI1)=>(((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))<=(subset2powerset))<=(setadjoinSub2)))))<=(notequalI2)))))<=(subsetE)))<=(subsetI2))<=(eqimpsubset1))<=(eqimpsubset2)))<=(dsetconstr__Cong))<=(descr__Cong))<=(exuEu))))))<=(emptyset__Cong))<=(exu__Cong)))<=(in__Cong)))))))<=(notdexE)))<=(prop2setI))))))<=(vacuousDall)))<=(upairsetIR))<=(upairsetIL))<=(upairsetE)))))<=(uniqinunit))<=(nonemptyImpWitness))<=(exuE2)))<=(setunionE))<=(setunionI))))<=(emptyinPowerset)))<=(setoftrueEq))<=(setadjoinOr))))<=(emptyinunitempty))<=(setadjoinIL))<=(nonemptyI1))<=(nonemptyI)))<=(setbeta))))<=(setext))<=(exuE3e))))))<=(exuE1)))))<=(descrp))<=(wellorderingAx))))))<=(omega0Ax))<=(setunionAx)))))<=(setextAx))), inference(assume_negation,[status(cth)],[setextsub])). 9.14/2.16 thf(c_0_109, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X269:$i]:(((((X6 @ X2 @ X269)))&(![X270:$i]:(((((X6 @ X2 @ X270)))=>(((X269)=(X270)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_93, c_0_94])). 9.14/2.16 thf(c_0_110, plain, ((descrp)=(![X1:$i > $o]:((((?[X271:$i]:(((((X1 @ X271)))&(![X272:$i]:(((((X1 @ X272)))=>(((X271)=(X272))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_95, c_0_94])). 9.14/2.16 thf(c_0_111, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 9.14/2.16 thf(c_0_112, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 9.14/2.16 thf(c_0_113, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 9.14/2.16 thf(c_0_114, plain, ((exuE1)=(![X1:$i > $o]:((((?[X273:$i]:(((((X1 @ X273)))&(![X274:$i]:(((((X1 @ X274)))=>(((X273)=(X274))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_96, c_0_94])). 9.14/2.16 thf(c_0_115, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X275:$i]:(((((X1 @ X275)))&(![X276:$i]:(((((X1 @ X276)))=>(((X275)=(X276))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_97, c_0_94])). 9.14/2.16 thf(c_0_116, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 9.14/2.16 thf(c_0_117, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_98])). 9.14/2.16 thf(c_0_118, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_99, c_0_98])). 9.14/2.16 thf(c_0_119, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_98])). 9.14/2.16 thf(c_0_120, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 9.14/2.16 thf(c_0_121, plain, ((exuE2)=(![X1:$i > $o]:((((?[X277:$i]:(((((X1 @ X277)))&(![X278:$i]:(((((X1 @ X278)))=>(((X277)=(X278))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_100, c_0_94])). 9.14/2.16 thf(c_0_122, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_98])). 9.14/2.16 thf(c_0_123, 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])). 9.14/2.16 thf(c_0_124, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X279:$i]:(((((X1 @ X279)))&(![X280:$i]:(((((X1 @ X280)))=>(((X279)=(X280)))))))))))))), inference(apply_def,[status(thm)],[c_0_101, c_0_94])). 9.14/2.16 thf(c_0_125, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X281:$i]:(((((X1 @ X281)))&(![X282:$i]:(((((X1 @ X282)))=>(((X281)=(X282)))))))))))))))), inference(apply_def,[status(thm)],[c_0_102, c_0_94])). 9.14/2.16 thf(c_0_126, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X283:$i]:(((((X1 @ X283)))&(![X284:$i]:(((((X1 @ X284)))=>(((X283)=(X284)))))))))))))), inference(apply_def,[status(thm)],[c_0_103, c_0_94])). 9.14/2.16 thf(c_0_127, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X285:$i]:(((((X1 @ X285)))&(![X286:$i]:(((((X1 @ X286)))=>(((X285)=(X286))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_104, c_0_94])). 9.14/2.16 thf(c_0_128, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X287:$i]:(((((X1 @ X287)))&(![X288:$i]:(((((X1 @ X288)))=>(((X287)=(X288))))))))))<=>((?[X289:$i]:(((((X17 @ X289)))&(![X290:$i]:(((((X17 @ X290)))=>(((X289)=(X290)))))))))))))))), inference(apply_def,[status(thm)],[c_0_105, c_0_94])). 9.14/2.16 thf(c_0_129, plain, ((exuEu)=(![X1:$i > $o]:((((?[X291:$i]:(((((X1 @ X291)))&(![X292:$i]:(((((X1 @ X292)))=>(((X291)=(X292))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_106, c_0_94])). 9.14/2.16 thf(c_0_130, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X293:$i]:(((((X1 @ X293)))&(![X294:$i]:(((((X1 @ X294)))=>(((X293)=(X294))))))))))=>((((?[X295:$i]:(((((X17 @ X295)))&(![X296:$i]:(((((X17 @ X296)))=>(((X295)=(X296))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_107, c_0_94])). 9.14/2.16 thf(c_0_131, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 9.14/2.16 thf(c_0_132, plain, ((epred1_0)<=>![X548:$i]:(?[X549:$i]:((((![X550:$i]:(((in @ X550 @ X549)=>![X551:$i]:(((in @ X551 @ X550)=>(in @ X551 @ X548)))))&![X552:$i, X553:$i]:((((in @ X552 @ X548)&(in @ X553 @ X548))=>(![X554:$i]:(((in @ X554 @ X549)=>((in @ X552 @ X554)<=>(in @ X553 @ X554))))=>((X552)=(X553))))))&![X555:$i, X556:$i]:((((in @ X555 @ X549)&(in @ X556 @ X549))=>(![X557:$i]:(((in @ X557 @ X555)=>(in @ X557 @ X556)))|![X558:$i]:(((in @ X558 @ X556)=>(in @ X558 @ X555)))))))&![X559:$i]:(((![X560:$i]:(((in @ X560 @ X559)=>(in @ X560 @ X548)))&?[X561:$i]:((in @ X561 @ X559)))=>?[X562:$i, X563:$i]:(((((in @ X562 @ X549)&(in @ X563 @ X559))&~(?[X564:$i]:(((in @ X564 @ X562)&(in @ X564 @ X559)))))&![X565:$i]:(((in @ X565 @ X549)=>(![X566:$i]:(((in @ X566 @ X565)=>(in @ X566 @ X562)))|(in @ X563 @ X565)))))))))))), introduced(definition)). 9.14/2.16 thf(c_0_133, negated_conjecture, ~((![X570:$i, X571:$i]:((![X572:$i]:(((in @ X572 @ X570)<=>(in @ X572 @ X571)))=>((X570)=(X571))))=>(![X297:$i]:(~(in @ X297 @ emptyset))=>(![X298:$i, X299:$i, X300:$i]:(((in @ X300 @ (setadjoin @ X298 @ X299))<=>(((X300)=(X298))|(in @ X300 @ X299))))=>(![X301:$i, X302:$i]:(((in @ X302 @ (powerset @ X301))<=>![X303:$i]:(((in @ X303 @ X302)=>(in @ X303 @ X301)))))=>(![X567:$i, X568:$i]:(((in @ X568 @ (setunion @ X567))<=>?[X569:$i]:(((in @ X568 @ X569)&(in @ X569 @ X567)))))=>((in @ emptyset @ omega)=>(![X304:$i]:(((in @ X304 @ omega)=>(in @ (setadjoin @ X304 @ X304) @ omega)))=>(![X305:$i]:((((in @ emptyset @ X305)&![X306:$i]:((((in @ X306 @ omega)&(in @ X306 @ X305))=>(in @ (setadjoin @ X306 @ X306) @ X305))))=>![X307:$i]:(((in @ X307 @ omega)=>(in @ X307 @ X305)))))=>(![X308:$i > $i > $o, X309:$i]:((![X310:$i]:(((in @ X310 @ X309)=>?[X311:$i]:(((X308 @ X310 @ X311)&![X312:$i]:(((X308 @ X310 @ X312)=>((X311)=(X312))))))))=>?[X313:$i]:(![X314:$i]:(((in @ X314 @ X313)<=>?[X315:$i]:(((in @ X315 @ X309)&(X308 @ X315 @ X314))))))))=>(![X316:$i]:((?[X317:$i]:((in @ X317 @ X316))=>?[X318:$i]:(((in @ X318 @ X316)&~(?[X319:$i]:(((in @ X319 @ X318)&(in @ X319 @ X316))))))))=>((epred1_0)=>(![X545:$i > $o]:((?[X546:$i]:(((X545 @ X546)&![X547:$i]:(((X545 @ X547)=>((X546)=(X547))))))=>(X545 @ (descr @ (^[Z0:$i]:(X545 @ Z0))))))=>(![X320:$i, X321:$i > $o, X322:$i]:(((in @ X322 @ X320)=>((X321 @ X322)=>(in @ X322 @ (dsetconstr @ X320 @ X321)))))=>(![X323:$i, X324:$i > $o, X325:$i]:(((in @ X325 @ (dsetconstr @ X323 @ X324))=>(in @ X325 @ X323)))=>(![X326:$i, X327:$i > $o, X328:$i]:(((in @ X328 @ (dsetconstr @ X326 @ X327))=>(X327 @ X328)))=>(![X540:$i > $o]:((?[X541:$i]:(((X540 @ X541)&![X542:$i]:(((X540 @ X542)=>((X541)=(X542))))))=>?[X543:$i]:(((X540 @ X543)&![X544:$i]:(((X540 @ X544)=>((X543)=(X544))))))))=>(![X329:$o, X330:$i]:(((in @ X330 @ (prop2set @ ((X329))))=>(X329)))=>(![X331:$i]:(((in @ X331 @ emptyset)=>![X332:$o]:((X332))))=>(![X333:$i]:(((in @ X333 @ emptyset)=>~($true)))=>(![X334:$i]:(~(in @ X334 @ emptyset))=>(![X536:$i > $o]:((?[X537:$i]:(((X536 @ X537)&![X538:$i]:(((X536 @ X538)=>((X537)=(X538))))))=>?[X539:$i]:((X536 @ X539))))=>(![X532:$i, X533:$i]:((![X534:$i]:(((in @ X534 @ X532)=>(in @ X534 @ X533)))=>(![X535:$i]:(((in @ X535 @ X533)=>(in @ X535 @ X532)))=>((X532)=(X533)))))=>(![X335:$i]:((![X336:$i]:(~(in @ X336 @ X335))=>((X335)=(emptyset))))=>(![X337:$i]:((![X338:$i]:(~(in @ X338 @ X337))=>((X337)=(emptyset))))=>(![X529:$i, X530:$i > $o, X531:$i]:(((in @ X531 @ X529)=>((in @ X531 @ (dsetconstr @ X529 @ X530))<=>(X530 @ X531))))=>(![X339:$i]:((((X339)!=(emptyset))=>?[X340:$i]:((in @ X340 @ X339))))=>(![X526:$i, X527:$i > $o, X528:$i]:(((in @ X528 @ X526)=>((X527 @ X528)=>((dsetconstr @ X526 @ X527)!=(emptyset)))))=>(![X524:$i]:((?[X525:$i]:((in @ X525 @ X524))=>((X524)!=(emptyset))))=>(![X522:$i, X523:$i]:((in @ X522 @ (setadjoin @ X522 @ X523)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X341:$i, X342:$i, X343:$i]:(((in @ X343 @ X342)=>(in @ X343 @ (setadjoin @ X341 @ X342))))=>(![X344:$i, X345:$i, X346:$i]:(((in @ X346 @ (setadjoin @ X344 @ X345))=>![X347:$o]:(((((X346)=(X344))=>(X347))=>(((in @ X346 @ X345)=>(X347))=>(X347))))))=>(![X519:$i, X520:$i, X521:$i]:(((in @ X521 @ (setadjoin @ X519 @ X520))=>(((X521)=(X519))|(in @ X521 @ X520))))=>(![X518:$i]:(((dsetconstr @ X518 @ (^[Z0:$i]:($true)))=(X518)))=>(![X348:$i, X349:$i]:((![X350:$i]:(((in @ X350 @ X349)=>(in @ X350 @ X348)))=>(in @ X349 @ (powerset @ X348))))=>(![X517:$i]:((in @ emptyset @ (powerset @ X517)))=>(![X351:$i]:((in @ emptyset @ (powerset @ X351)))=>(![X352:$i, X353:$i, X354:$i]:(((in @ X353 @ (powerset @ X352))=>((in @ X354 @ X353)=>(in @ X354 @ X352))))=>(![X514:$i, X515:$i, X516:$i]:(((in @ X515 @ X516)=>((in @ X516 @ X514)=>(in @ X515 @ (setunion @ X514)))))=>(![X510:$i, X511:$i]:(((in @ X511 @ (setunion @ X510))=>![X512:$o]:((![X513:$i]:(((in @ X511 @ X513)=>((in @ X513 @ X510)=>(X512))))=>(X512)))))=>(![X355:$i, X356:$i]:(((in @ X356 @ X355)=>(in @ X356 @ (powerset @ (setunion @ X355)))))=>(![X505:$i > $o]:((?[X506:$i]:(((X505 @ X506)&![X507:$i]:(((X505 @ X507)=>((X506)=(X507))))))=>?[X508:$i]:(![X509:$i]:(((X505 @ X509)<=>((X509)=(X508)))))))=>(![X503:$i]:((((X503)!=(emptyset))=>?[X504:$i]:(((in @ X504 @ X503)&$true))))=>(![X501:$i, X502:$i]:(((in @ X501 @ (setadjoin @ X502 @ emptyset))=>((X501)=(X502))))=>(![X357:$i, X358:$i]:((((X357)!=(X358))=>~(in @ X358 @ (setadjoin @ X357 @ emptyset))))=>(![X359:$i, X360:$i]:((((X359)=(X360))=>(in @ X359 @ (setadjoin @ X360 @ emptyset))))=>(![X361:$i, X362:$i]:(((in @ X361 @ (setadjoin @ X362 @ emptyset))=>(in @ X362 @ (setadjoin @ X361 @ emptyset))))=>(![X498:$i, X499:$i, X500:$i]:(((in @ X500 @ (setadjoin @ X498 @ (setadjoin @ X499 @ emptyset)))=>(((X500)=(X498))|((X500)=(X499)))))=>(![X496:$i, X497:$i]:((in @ X496 @ (setadjoin @ X496 @ (setadjoin @ X497 @ emptyset))))=>(![X494:$i, X495:$i]:((in @ X495 @ (setadjoin @ X494 @ (setadjoin @ X495 @ emptyset))))=>(![X363:$i, X364:$i > $o]:((?[X365:$i]:(((in @ X365 @ X363)&(X364 @ X365)))=>(((dsetconstr @ X363 @ X364)=(emptyset))=>~($true))))=>(![X492:$i > $o, X493:$i]:(((in @ X493 @ emptyset)=>(X492 @ X493)))=>(![X366:$i, X367:$i > $o]:((~(![X368:$i]:(((in @ X368 @ X366)=>(X367 @ X368))))=>?[X369:$i]:(((in @ X369 @ X366)&~((X367 @ X369))))))=>(![X370:$i, X371:$i > $o]:((![X372:$i]:(((in @ X372 @ X370)=>~((X371 @ X372))))=>~(?[X373:$i]:(((in @ X373 @ X370)&(X371 @ X373))))))=>(![X374:$i, X375:$i > $o]:((~(?[X376:$i]:(((in @ X376 @ X374)&(X375 @ X376))))=>![X377:$i]:(((in @ X377 @ X374)=>~((X375 @ X377))))))=>(![X378:$i, X379:$i > $o]:((?[X380:$i]:(((in @ X380 @ X378)&~((X379 @ X380))))=>~(![X381:$i]:(((in @ X381 @ X378)=>(X379 @ X381))))))=>(![X491:$o]:(((X491)=>(in @ emptyset @ (prop2set @ ((X491))))))=>(![X382:$o]:(((X382)=>(set2prop @ (prop2set @ ((X382))))))=>(![X487:$i, X488:$i > $o]:((~(?[X489:$i]:(((in @ X489 @ X487)&(X488 @ X489))))=>![X490:$i]:(((in @ X490 @ X487)=>~((X488 @ X490))))))=>(![X383:$i, X384:$i > $o]:((~(![X385:$i]:(((in @ X385 @ X383)=>(X384 @ X385))))=>?[X386:$i]:(((in @ X386 @ X383)&~((X384 @ X386))))))=>(![X387:$i > $o]:((?[X388:$i]:(((X387 @ X388)&![X389:$i]:(((X387 @ X389)=>((X388)=(X389))))))=>?[X390:$i]:(((X387 @ X390)&![X391:$i]:(((X387 @ X391)=>((X390)=(X391))))))))=>(![X392:$i > $o]:((?[X393:$i]:((X392 @ X393))=>(![X394:$i, X395:$i]:(((X392 @ X394)=>((X392 @ X395)=>((X394)=(X395)))))=>?[X396:$i]:(((X392 @ X396)&![X397:$i]:(((X392 @ X397)=>((X396)=(X397)))))))))=>(![X398:$i > $o]:((?[X399:$i]:(![X400:$i]:(((X398 @ X400)<=>((X400)=(X399)))))=>?[X401:$i]:(((X398 @ X401)&![X402:$i]:(((X398 @ X402)=>((X401)=(X402))))))))=>(![X403:$i, X404:$i]:((((X403)=(X404))=>![X405:$i, X406:$i]:((((X405)=(X406))=>((in @ X405 @ X403)=>(in @ X406 @ X404))))))=>(![X483:$i, X484:$i]:((((X483)=(X484))=>![X485:$i, X486:$i]:((((X485)=(X486))=>((in @ X485 @ X483)<=>(in @ X486 @ X484))))))=>(![X407:$i > $o]:((?[X408:$i]:(((X407 @ X408)&![X409:$i]:(((X407 @ X409)=>((X408)=(X409))))))=>![X410:$i, X411:$i]:(((X407 @ X410)=>((X407 @ X411)=>((X410)=(X411)))))))=>(![X475:$i > $o, X476:$i > $o]:((![X477:$i, X478:$i]:((((X477)=(X478))=>((X475 @ X477)<=>(X476 @ X478))))=>(?[X479:$i]:(((X475 @ X479)&![X480:$i]:(((X475 @ X480)=>((X479)=(X480))))))<=>?[X481:$i]:(((X476 @ X481)&![X482:$i]:(((X476 @ X482)=>((X481)=(X482)))))))))=>(((emptyset)=(emptyset))=>(![X412:$i, X413:$i]:((((X412)=(X413))=>![X414:$i, X415:$i]:((((X414)=(X415))=>((setadjoin @ X412 @ X414)=(setadjoin @ X413 @ X415))))))=>(![X416:$i, X417:$i]:((((X416)=(X417))=>((powerset @ X416)=(powerset @ X417))))=>(![X418:$i, X419:$i]:((((X418)=(X419))=>((setunion @ X418)=(setunion @ X419))))=>(((omega)=(omega))=>(![X470:$i > $o]:((?[X471:$i]:(((X470 @ X471)&![X472:$i]:(((X470 @ X472)=>((X471)=(X472))))))=>![X473:$i, X474:$i]:(((X470 @ X473)=>((X470 @ X474)=>((X473)=(X474)))))))=>(![X462:$i > $o, X463:$i > $o]:((![X464:$i, X465:$i]:((((X464)=(X465))=>((X462 @ X464)<=>(X463 @ X465))))=>(?[X466:$i]:(((X462 @ X466)&![X467:$i]:(((X462 @ X467)=>((X466)=(X467))))))=>(?[X468:$i]:(((X463 @ X468)&![X469:$i]:(((X463 @ X469)=>((X468)=(X469))))))=>((descr @ X462)=(descr @ X463))))))=>(![X456:$i, X457:$i]:((((X456)=(X457))=>![X458:$i > $o, X459:$i > $o]:((![X460:$i]:(((in @ X460 @ X456)=>![X461:$i]:(((in @ X461 @ X457)=>(((X460)=(X461))=>((X458 @ X460)<=>(X459 @ X461)))))))=>((dsetconstr @ X456 @ X458)=(dsetconstr @ X457 @ X459))))))=>(![X420:$i, X421:$i]:((![X422:$i]:(((in @ X422 @ X420)=>(in @ X422 @ X421)))=>(subset @ X420 @ X421)))=>(![X454:$i, X455:$i]:((((X454)=(X455))=>(subset @ X455 @ X454)))=>(![X452:$i, X453:$i]:((((X452)=(X453))=>(subset @ X452 @ X453)))=>(![X449:$i, X450:$i]:((![X451:$i]:(((in @ X451 @ X449)=>(in @ X451 @ X450)))=>(subset @ X449 @ X450)))=>(![X423:$i]:((subset @ emptyset @ X423))=>(![X446:$i, X447:$i, X448:$i]:(((subset @ X446 @ X447)=>((in @ X448 @ X446)=>(in @ X448 @ X447))))=>(![X424:$i, X425:$i, X426:$i]:(((subset @ X424 @ X425)=>(~(in @ X426 @ X425)=>~(in @ X426 @ X424))))=>(![X427:$i, X428:$i, X429:$i]:(((in @ X429 @ X427)=>(~(in @ X429 @ X428)=>~(subset @ X427 @ X428))))=>(![X430:$i, X431:$i]:((~(subset @ X430 @ X431)=>((X430)!=(X431))))=>(![X443:$i, X444:$i, X445:$i]:(((in @ X445 @ X443)=>(~(in @ X445 @ X444)=>((X443)!=(X444)))))=>(![X432:$i]:((subset @ X432 @ X432))=>(![X433:$i, X434:$i, X435:$i]:(((subset @ X433 @ X434)=>((subset @ X434 @ X435)=>(subset @ X433 @ X435))))=>(![X436:$i, X437:$i]:((subset @ X437 @ (setadjoin @ X436 @ X437)))=>(![X440:$i, X441:$i, X442:$i]:(((subset @ X440 @ X442)=>(subset @ X440 @ (setadjoin @ X441 @ X442))))=>(![X438:$i, X439:$i]:(((subset @ X438 @ X439)=>(in @ X438 @ (powerset @ X439))))=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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)],[c_0_108, setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_109]), foundationAx]), wellorderingAx]), c_0_110]), c_0_111]), c_0_112]), c_0_113]), c_0_114]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_115]), setext]), emptyI]), noeltsimpempty]), c_0_116]), c_0_117]), c_0_118]), c_0_119]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_120]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_121]), c_0_122]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_123]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_124]), c_0_125]), c_0_126]), inCongP]), in__Cong]), c_0_127]), c_0_128]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_129]), c_0_130]), c_0_131]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset])])]), c_0_132])). 9.14/2.16 thf(c_0_134, negated_conjecture, ![X573:$i, X574:$i, X576:$i, X577:$i, X578:$i, X579:$i, X580:$i, X581:$i, X582:$i, X583:$i, X584:$i, X586:$i, X587:$i, X589:$i, X590:$i, X591:$i, X592:$i, X593:$i, X595:$i, X596:$i > $i > $o, X597:$i, X599:$i, X602:$i, X604:$i, X605:$i, X606:$i, X607:$i, X609:$i, X610:$i > $o, X611:$i, X613:$i, X614:$i > $o, X615:$i, X616:$i, X617:$i > $o, X618:$i, X619:$i, X620:$i > $o, X621:$i, X622:$i > $o, X623:$i, X626:$i, X627:$o, X628:$i, X629:$i, X630:$o, X631:$i, X632:$i, X633:$i > $o, X634:$i, X637:$i, X638:$i, X641:$i, X643:$i, X645:$i, X646:$i > $o, X647:$i, X648:$i, X650:$i, X651:$i > $o, X652:$i, X653:$i, X654:$i, X655:$i, X656:$i, X657:$i, X658:$i, X659:$i, X660:$i, X661:$i, X662:$i, X663:$o, X664:$i, X665:$i, X666:$i, X667:$i, X668:$i, X669:$i, X671:$i, X672:$i, X673:$i, X674:$i, X675:$i, X676:$i, X677:$i, X678:$i, X679:$i, X680:$i, X681:$o, X683:$i, X684:$i, X685:$i > $o, X686:$i, X689:$i, X690:$i, X691:$i, X693:$i, X694:$i, X695:$i, X696:$i, X697:$i, X698:$i, X699:$i, X700:$i, X701:$i, X702:$i, X703:$i, X704:$i, X705:$i, X706:$i, X707:$i, X708:$i, X709:$i > $o, X710:$i, X711:$i > $o, X712:$i, X713:$i, X714:$i > $o, X715:$i, X717:$i, X718:$i > $o, X720:$i, X721:$i, X722:$i > $o, X724:$i, X725:$i, X726:$i > $o, X727:$i, X729:$o, X730:$o, X731:$i, X732:$i > $o, X734:$i, X735:$i, X736:$i > $o, X737:$i, X739:$i > $o, X740:$i, X743:$i, X744:$i > $o, X745:$i, X749:$i, X750:$i > $o, X751:$i, X754:$i, X755:$i, X756:$i, X757:$i, X758:$i, X759:$i, X760:$i, X761:$i, X762:$i, X763:$i > $o, X764:$i, X766:$i, X767:$i, X768:$i > $o, X769:$i > $o, X772:$i, X775:$i, X776:$i, X779:$i, X780:$i, X781:$i, X782:$i, X783:$i, X784:$i, X785:$i, X786:$i, X787:$i, X788:$i > $o, X789:$i, X791:$i, X792:$i, X793:$i > $o, X794:$i > $o, X797:$i, X799:$i, X801:$i, X802:$i, X803:$i > $o, X804:$i > $o, X807:$i, X808:$i, X810:$i, X811:$i, X812:$i, X813:$i, X814:$i, X815:$i, X817:$i, X818:$i, X819:$i, X820:$i, X821:$i, X822:$i, X823:$i, X824:$i, X825:$i, X826:$i, X827:$i, X828:$i, X829:$i, X830:$i, X831:$i, X832:$i, X833:$i, X834:$i, X835:$i, X836:$i, X837:$i, X838:$i, X839:$i, X840:$i, X841:$i, X842:$i]:((((~(in @ (esk1_2 @ X573 @ X574) @ X573)|~(in @ (esk1_2 @ X573 @ X574) @ X574)|((X573)=(X574)))&((in @ (esk1_2 @ X573 @ X574) @ X573)|(in @ (esk1_2 @ X573 @ X574) @ X574)|((X573)=(X574))))&(~(in @ X576 @ emptyset)&(((~(in @ X579 @ (setadjoin @ X577 @ X578))|(((X579)=(X577))|(in @ X579 @ X578)))&((((X579)!=(X577))|(in @ X579 @ (setadjoin @ X577 @ X578)))&(~(in @ X579 @ X578)|(in @ X579 @ (setadjoin @ X577 @ X578)))))&(((~(in @ X581 @ (powerset @ X580))|(~(in @ X582 @ X581)|(in @ X582 @ X580)))&(((in @ (esk2_2 @ X583 @ X584) @ X584)|(in @ X584 @ (powerset @ X583)))&(~(in @ (esk2_2 @ X583 @ X584) @ X583)|(in @ X584 @ (powerset @ X583)))))&(((((in @ X587 @ (esk3_2 @ X586 @ X587))|~(in @ X587 @ (setunion @ X586)))&((in @ (esk3_2 @ X586 @ X587) @ X586)|~(in @ X587 @ (setunion @ X586))))&(~(in @ X590 @ X591)|~(in @ X591 @ X589)|(in @ X590 @ (setunion @ X589))))&((in @ emptyset @ omega)&((~(in @ X592 @ omega)|(in @ (setadjoin @ X592 @ X592) @ omega))&(((((in @ (esk4_1 @ X593) @ omega)|~(in @ emptyset @ X593)|(~(in @ X595 @ omega)|(in @ X595 @ X593)))&((in @ (esk4_1 @ X593) @ X593)|~(in @ emptyset @ X593)|(~(in @ X595 @ omega)|(in @ X595 @ X593))))&(~(in @ (setadjoin @ (esk4_1 @ X593) @ (esk4_1 @ X593)) @ X593)|~(in @ emptyset @ X593)|(~(in @ X595 @ omega)|(in @ X595 @ X593))))&((((((in @ (esk8_3 @ X596 @ X597 @ X602) @ X597)|~(in @ X602 @ (esk7_2 @ X596 @ X597))|(in @ (esk5_2 @ X596 @ X597) @ X597))&((X596 @ (esk8_3 @ X596 @ X597 @ X602) @ X602)|~(in @ X602 @ (esk7_2 @ X596 @ X597))|(in @ (esk5_2 @ X596 @ X597) @ X597)))&(~(in @ X605 @ X597)|~(X596 @ X605 @ X604)|(in @ X604 @ (esk7_2 @ X596 @ X597))|(in @ (esk5_2 @ X596 @ X597) @ X597)))&(((((in @ (esk8_3 @ X596 @ X597 @ X602) @ X597)|~(in @ X602 @ (esk7_2 @ X596 @ X597))|((X596 @ (esk5_2 @ X596 @ X597) @ (esk6_3 @ X596 @ X597 @ X599))|~(X596 @ (esk5_2 @ X596 @ X597) @ X599)))&((X596 @ (esk8_3 @ X596 @ X597 @ X602) @ X602)|~(in @ X602 @ (esk7_2 @ X596 @ X597))|((X596 @ (esk5_2 @ X596 @ X597) @ (esk6_3 @ X596 @ X597 @ X599))|~(X596 @ (esk5_2 @ X596 @ X597) @ X599))))&(~(in @ X605 @ X597)|~(X596 @ X605 @ X604)|(in @ X604 @ (esk7_2 @ X596 @ X597))|((X596 @ (esk5_2 @ X596 @ X597) @ (esk6_3 @ X596 @ X597 @ X599))|~(X596 @ (esk5_2 @ X596 @ X597) @ X599))))&((((in @ (esk8_3 @ X596 @ X597 @ X602) @ X597)|~(in @ X602 @ (esk7_2 @ X596 @ X597))|(((X599)!=(esk6_3 @ X596 @ X597 @ X599))|~(X596 @ (esk5_2 @ X596 @ X597) @ X599)))&((X596 @ (esk8_3 @ X596 @ X597 @ X602) @ X602)|~(in @ X602 @ (esk7_2 @ X596 @ X597))|(((X599)!=(esk6_3 @ X596 @ X597 @ X599))|~(X596 @ (esk5_2 @ X596 @ X597) @ X599))))&(~(in @ X605 @ X597)|~(X596 @ X605 @ X604)|(in @ X604 @ (esk7_2 @ X596 @ X597))|(((X599)!=(esk6_3 @ X596 @ X597 @ X599))|~(X596 @ (esk5_2 @ X596 @ X597) @ X599))))))&((((in @ (esk9_1 @ X606) @ X606)|~(in @ X607 @ X606))&(~(in @ X609 @ (esk9_1 @ X606))|~(in @ X609 @ X606)|~(in @ X607 @ X606)))&((epred1_0)&((((X610 @ (esk10_2 @ X610 @ X611))|~(X610 @ X611)|(X610 @ (descr @ X610)))&(((X611)!=(esk10_2 @ X610 @ X611))|~(X610 @ X611)|(X610 @ (descr @ X610))))&((~(in @ X615 @ X613)|(~(X614 @ X615)|(in @ X615 @ (dsetconstr @ X613 @ X614))))&((~(in @ X618 @ (dsetconstr @ X616 @ X617))|(in @ X618 @ X616))&((~(in @ X621 @ (dsetconstr @ X619 @ X620))|(X620 @ X621))&(((((X622 @ (esk12_1 @ X622))|((X622 @ (esk11_2 @ X622 @ X623))|~(X622 @ X623)))&(~(X622 @ X626)|((esk12_1 @ X622)=(X626))|((X622 @ (esk11_2 @ X622 @ X623))|~(X622 @ X623))))&(((X622 @ (esk12_1 @ X622))|(((X623)!=(esk11_2 @ X622 @ X623))|~(X622 @ X623)))&(~(X622 @ X626)|((esk12_1 @ X622)=(X626))|(((X623)!=(esk11_2 @ X622 @ X623))|~(X622 @ X623)))))&((~(in @ X628 @ (prop2set @ ((X627))))|(X627))&((~(in @ X629 @ emptyset)|(X630))&((~(in @ X631 @ emptyset)|~($true))&(~(in @ X632 @ emptyset)&((((X633 @ (esk13_2 @ X633 @ X634))|~(X633 @ X634)|(X633 @ (esk14_1 @ X633)))&(((X634)!=(esk13_2 @ X633 @ X634))|~(X633 @ X634)|(X633 @ (esk14_1 @ X633))))&(((((in @ (esk16_2 @ X637 @ X638) @ X638)|((X637)=(X638))|(in @ (esk15_2 @ X637 @ X638) @ X637))&(~(in @ (esk16_2 @ X637 @ X638) @ X637)|((X637)=(X638))|(in @ (esk15_2 @ X637 @ X638) @ X637)))&(((in @ (esk16_2 @ X637 @ X638) @ X638)|((X637)=(X638))|~(in @ (esk15_2 @ X637 @ X638) @ X638))&(~(in @ (esk16_2 @ X637 @ X638) @ X637)|((X637)=(X638))|~(in @ (esk15_2 @ X637 @ X638) @ X638))))&(((in @ (esk17_1 @ X641) @ X641)|((X641)=(emptyset)))&(((in @ (esk18_1 @ X643) @ X643)|((X643)=(emptyset)))&(((~(in @ X647 @ (dsetconstr @ X645 @ X646))|(X646 @ X647)|~(in @ X647 @ X645))&(~(X646 @ X647)|(in @ X647 @ (dsetconstr @ X645 @ X646))|~(in @ X647 @ X645)))&((((X648)=(emptyset))|(in @ (esk19_1 @ X648) @ X648))&((~(in @ X652 @ X650)|(~(X651 @ X652)|((dsetconstr @ X650 @ X651)!=(emptyset))))&((~(in @ X654 @ X653)|((X653)!=(emptyset)))&((in @ X655 @ (setadjoin @ X655 @ X656))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X659 @ X658)|(in @ X659 @ (setadjoin @ X657 @ X658)))&(((((in @ X662 @ X661)|(X663)|((X662)=(X660))|~(in @ X662 @ (setadjoin @ X660 @ X661)))&(~(X663)|(X663)|((X662)=(X660))|~(in @ X662 @ (setadjoin @ X660 @ X661))))&(((in @ X662 @ X661)|(X663)|~(X663)|~(in @ X662 @ (setadjoin @ X660 @ X661)))&(~(X663)|(X663)|~(X663)|~(in @ X662 @ (setadjoin @ X660 @ X661)))))&((~(in @ X666 @ (setadjoin @ X664 @ X665))|(((X666)=(X664))|(in @ X666 @ X665)))&(((dsetconstr @ X667 @ (^[Z0:$i]:($true)))=(X667))&((((in @ (esk20_2 @ X668 @ X669) @ X669)|(in @ X669 @ (powerset @ X668)))&(~(in @ (esk20_2 @ X668 @ X669) @ X668)|(in @ X669 @ (powerset @ X668))))&((in @ emptyset @ (powerset @ X671))&((in @ emptyset @ (powerset @ X672))&((~(in @ X674 @ (powerset @ X673))|(~(in @ X675 @ X674)|(in @ X675 @ X673)))&((~(in @ X677 @ X678)|(~(in @ X678 @ X676)|(in @ X677 @ (setunion @ X676))))&((((in @ X680 @ (esk21_3 @ X679 @ X680 @ X681))|(X681)|~(in @ X680 @ (setunion @ X679)))&(((in @ (esk21_3 @ X679 @ X680 @ X681) @ X679)|(X681)|~(in @ X680 @ (setunion @ X679)))&(~(X681)|(X681)|~(in @ X680 @ (setunion @ X679)))))&((~(in @ X684 @ X683)|(in @ X684 @ (powerset @ (setunion @ X683))))&((((~(X685 @ X689)|((X689)=(esk23_1 @ X685))|((X685 @ (esk22_2 @ X685 @ X686))|~(X685 @ X686)))&(((X690)!=(esk23_1 @ X685))|(X685 @ X690)|((X685 @ (esk22_2 @ X685 @ X686))|~(X685 @ X686))))&((~(X685 @ X689)|((X689)=(esk23_1 @ X685))|(((X686)!=(esk22_2 @ X685 @ X686))|~(X685 @ X686)))&(((X690)!=(esk23_1 @ X685))|(X685 @ X690)|(((X686)!=(esk22_2 @ X685 @ X686))|~(X685 @ X686)))))&((((in @ (esk24_1 @ X691) @ X691)|((X691)=(emptyset)))&(($true)|((X691)=(emptyset))))&((~(in @ X693 @ (setadjoin @ X694 @ emptyset))|((X693)=(X694)))&((((X695)=(X696))|~(in @ X696 @ (setadjoin @ X695 @ emptyset)))&((((X697)!=(X698))|(in @ X697 @ (setadjoin @ X698 @ emptyset)))&((~(in @ X699 @ (setadjoin @ X700 @ emptyset))|(in @ X700 @ (setadjoin @ X699 @ emptyset)))&((~(in @ X703 @ (setadjoin @ X701 @ (setadjoin @ X702 @ emptyset)))|(((X703)=(X701))|((X703)=(X702))))&((in @ X704 @ (setadjoin @ X704 @ (setadjoin @ X705 @ emptyset)))&((in @ X707 @ (setadjoin @ X706 @ (setadjoin @ X707 @ emptyset)))&((~(in @ X710 @ X708)|~(X709 @ X710)|(((dsetconstr @ X708 @ X709)!=(emptyset))|~($true)))&((~(in @ X712 @ emptyset)|(X711 @ X712))&((((in @ (esk25_2 @ X713 @ X714) @ X713)|(~(in @ X715 @ X713)|(X714 @ X715)))&(~(X714 @ (esk25_2 @ X713 @ X714))|(~(in @ X715 @ X713)|(X714 @ X715))))&((((in @ (esk26_2 @ X717 @ X718) @ X717)|(~(in @ X720 @ X717)|~(X718 @ X720)))&((X718 @ (esk26_2 @ X717 @ X718))|(~(in @ X720 @ X717)|~(X718 @ X720))))&((((in @ (esk27_2 @ X721 @ X722) @ X721)|(~(in @ X724 @ X721)|~(X722 @ X724)))&((X722 @ (esk27_2 @ X721 @ X722))|(~(in @ X724 @ X721)|~(X722 @ X724))))&((((in @ (esk28_2 @ X725 @ X726) @ X725)|(~(in @ X727 @ X725)|(X726 @ X727)))&(~(X726 @ (esk28_2 @ X725 @ X726))|(~(in @ X727 @ X725)|(X726 @ X727))))&((~(X729)|(in @ emptyset @ (prop2set @ ((X729)))))&((~(X730)|(set2prop @ (prop2set @ ((X730)))))&((((in @ (esk29_2 @ X731 @ X732) @ X731)|(~(in @ X734 @ X731)|~(X732 @ X734)))&((X732 @ (esk29_2 @ X731 @ X732))|(~(in @ X734 @ X731)|~(X732 @ X734))))&((((in @ (esk30_2 @ X735 @ X736) @ X735)|(~(in @ X737 @ X735)|(X736 @ X737)))&(~(X736 @ (esk30_2 @ X735 @ X736))|(~(in @ X737 @ X735)|(X736 @ X737))))&(((((X739 @ (esk32_1 @ X739))|((X739 @ (esk31_2 @ X739 @ X740))|~(X739 @ X740)))&(~(X739 @ X743)|((esk32_1 @ X739)=(X743))|((X739 @ (esk31_2 @ X739 @ X740))|~(X739 @ X740))))&(((X739 @ (esk32_1 @ X739))|(((X740)!=(esk31_2 @ X739 @ X740))|~(X739 @ X740)))&(~(X739 @ X743)|((esk32_1 @ X739)=(X743))|(((X740)!=(esk31_2 @ X739 @ X740))|~(X739 @ X740)))))&(((((X744 @ (esk35_1 @ X744))|(X744 @ (esk33_1 @ X744))|~(X744 @ X745))&(~(X744 @ X749)|((esk35_1 @ X744)=(X749))|(X744 @ (esk33_1 @ X744))|~(X744 @ X745)))&((((X744 @ (esk35_1 @ X744))|(X744 @ (esk34_1 @ X744))|~(X744 @ X745))&(~(X744 @ X749)|((esk35_1 @ X744)=(X749))|(X744 @ (esk34_1 @ X744))|~(X744 @ X745)))&(((X744 @ (esk35_1 @ X744))|((esk33_1 @ X744)!=(esk34_1 @ X744))|~(X744 @ X745))&(~(X744 @ X749)|((esk35_1 @ X744)=(X749))|((esk33_1 @ X744)!=(esk34_1 @ X744))|~(X744 @ X745)))))&(((((X750 @ (esk37_1 @ X750))|(~(X750 @ (esk36_2 @ X750 @ X751))|((esk36_2 @ X750 @ X751)!=(X751))))&(~(X750 @ X754)|((esk37_1 @ X750)=(X754))|(~(X750 @ (esk36_2 @ X750 @ X751))|((esk36_2 @ X750 @ X751)!=(X751)))))&(((X750 @ (esk37_1 @ X750))|((X750 @ (esk36_2 @ X750 @ X751))|((esk36_2 @ X750 @ X751)=(X751))))&(~(X750 @ X754)|((esk37_1 @ X750)=(X754))|((X750 @ (esk36_2 @ X750 @ X751))|((esk36_2 @ X750 @ X751)=(X751))))))&((((X755)!=(X756))|(((X757)!=(X758))|(~(in @ X757 @ X755)|(in @ X758 @ X756))))&(((~(in @ X761 @ X759)|(in @ X762 @ X760)|((X761)!=(X762))|((X759)!=(X760)))&(~(in @ X762 @ X760)|(in @ X761 @ X759)|((X761)!=(X762))|((X759)!=(X760))))&((((X763 @ (esk38_2 @ X763 @ X764))|~(X763 @ X764)|(~(X763 @ X766)|(~(X763 @ X767)|((X766)=(X767)))))&(((X764)!=(esk38_2 @ X763 @ X764))|~(X763 @ X764)|(~(X763 @ X766)|(~(X763 @ X767)|((X766)=(X767))))))&(((((((X769 @ (esk42_2 @ X768 @ X769))|((X768 @ (esk41_3 @ X768 @ X769 @ X772))|~(X768 @ X772))|((esk39_2 @ X768 @ X769)=(esk40_2 @ X768 @ X769)))&(~(X769 @ X775)|((esk42_2 @ X768 @ X769)=(X775))|((X768 @ (esk41_3 @ X768 @ X769 @ X772))|~(X768 @ X772))|((esk39_2 @ X768 @ X769)=(esk40_2 @ X768 @ X769))))&(((X769 @ (esk42_2 @ X768 @ X769))|(((X772)!=(esk41_3 @ X768 @ X769 @ X772))|~(X768 @ X772))|((esk39_2 @ X768 @ X769)=(esk40_2 @ X768 @ X769)))&(~(X769 @ X775)|((esk42_2 @ X768 @ X769)=(X775))|(((X772)!=(esk41_3 @ X768 @ X769 @ X772))|~(X768 @ X772))|((esk39_2 @ X768 @ X769)=(esk40_2 @ X768 @ X769)))))&((((X768 @ (esk44_2 @ X768 @ X769))|((X769 @ (esk43_3 @ X768 @ X769 @ X776))|~(X769 @ X776))|((esk39_2 @ X768 @ X769)=(esk40_2 @ X768 @ X769)))&(~(X768 @ X779)|((esk44_2 @ X768 @ X769)=(X779))|((X769 @ (esk43_3 @ X768 @ X769 @ X776))|~(X769 @ X776))|((esk39_2 @ X768 @ X769)=(esk40_2 @ X768 @ X769))))&(((X768 @ (esk44_2 @ X768 @ X769))|(((X776)!=(esk43_3 @ X768 @ X769 @ X776))|~(X769 @ X776))|((esk39_2 @ X768 @ X769)=(esk40_2 @ X768 @ X769)))&(~(X768 @ X779)|((esk44_2 @ X768 @ X769)=(X779))|(((X776)!=(esk43_3 @ X768 @ X769 @ X776))|~(X769 @ X776))|((esk39_2 @ X768 @ X769)=(esk40_2 @ X768 @ X769))))))&((((((X769 @ (esk42_2 @ X768 @ X769))|((X768 @ (esk41_3 @ X768 @ X769 @ X772))|~(X768 @ X772))|(~(X768 @ (esk39_2 @ X768 @ X769))|~(X769 @ (esk40_2 @ X768 @ X769))))&(~(X769 @ X775)|((esk42_2 @ X768 @ X769)=(X775))|((X768 @ (esk41_3 @ X768 @ X769 @ X772))|~(X768 @ X772))|(~(X768 @ (esk39_2 @ X768 @ X769))|~(X769 @ (esk40_2 @ X768 @ X769)))))&(((X769 @ (esk42_2 @ X768 @ X769))|(((X772)!=(esk41_3 @ X768 @ X769 @ X772))|~(X768 @ X772))|(~(X768 @ (esk39_2 @ X768 @ X769))|~(X769 @ (esk40_2 @ X768 @ X769))))&(~(X769 @ X775)|((esk42_2 @ X768 @ X769)=(X775))|(((X772)!=(esk41_3 @ X768 @ X769 @ X772))|~(X768 @ X772))|(~(X768 @ (esk39_2 @ X768 @ X769))|~(X769 @ (esk40_2 @ X768 @ X769))))))&((((X768 @ (esk44_2 @ X768 @ X769))|((X769 @ (esk43_3 @ X768 @ X769 @ X776))|~(X769 @ X776))|(~(X768 @ (esk39_2 @ X768 @ X769))|~(X769 @ (esk40_2 @ X768 @ X769))))&(~(X768 @ X779)|((esk44_2 @ X768 @ X769)=(X779))|((X769 @ (esk43_3 @ X768 @ X769 @ X776))|~(X769 @ X776))|(~(X768 @ (esk39_2 @ X768 @ X769))|~(X769 @ (esk40_2 @ X768 @ X769)))))&(((X768 @ (esk44_2 @ X768 @ X769))|(((X776)!=(esk43_3 @ X768 @ X769 @ X776))|~(X769 @ X776))|(~(X768 @ (esk39_2 @ X768 @ X769))|~(X769 @ (esk40_2 @ X768 @ X769))))&(~(X768 @ X779)|((esk44_2 @ X768 @ X769)=(X779))|(((X776)!=(esk43_3 @ X768 @ X769 @ X776))|~(X769 @ X776))|(~(X768 @ (esk39_2 @ X768 @ X769))|~(X769 @ (esk40_2 @ X768 @ X769)))))))&(((((X769 @ (esk42_2 @ X768 @ X769))|((X768 @ (esk41_3 @ X768 @ X769 @ X772))|~(X768 @ X772))|((X768 @ (esk39_2 @ X768 @ X769))|(X769 @ (esk40_2 @ X768 @ X769))))&(~(X769 @ X775)|((esk42_2 @ X768 @ X769)=(X775))|((X768 @ (esk41_3 @ X768 @ X769 @ X772))|~(X768 @ X772))|((X768 @ (esk39_2 @ X768 @ X769))|(X769 @ (esk40_2 @ X768 @ X769)))))&(((X769 @ (esk42_2 @ X768 @ X769))|(((X772)!=(esk41_3 @ X768 @ X769 @ X772))|~(X768 @ X772))|((X768 @ (esk39_2 @ X768 @ X769))|(X769 @ (esk40_2 @ X768 @ X769))))&(~(X769 @ X775)|((esk42_2 @ X768 @ X769)=(X775))|(((X772)!=(esk41_3 @ X768 @ X769 @ X772))|~(X768 @ X772))|((X768 @ (esk39_2 @ X768 @ X769))|(X769 @ (esk40_2 @ X768 @ X769))))))&((((X768 @ (esk44_2 @ X768 @ X769))|((X769 @ (esk43_3 @ X768 @ X769 @ X776))|~(X769 @ X776))|((X768 @ (esk39_2 @ X768 @ X769))|(X769 @ (esk40_2 @ X768 @ X769))))&(~(X768 @ X779)|((esk44_2 @ X768 @ X769)=(X779))|((X769 @ (esk43_3 @ X768 @ X769 @ X776))|~(X769 @ X776))|((X768 @ (esk39_2 @ X768 @ X769))|(X769 @ (esk40_2 @ X768 @ X769)))))&(((X768 @ (esk44_2 @ X768 @ X769))|(((X776)!=(esk43_3 @ X768 @ X769 @ X776))|~(X769 @ X776))|((X768 @ (esk39_2 @ X768 @ X769))|(X769 @ (esk40_2 @ X768 @ X769))))&(~(X768 @ X779)|((esk44_2 @ X768 @ X769)=(X779))|(((X776)!=(esk43_3 @ X768 @ X769 @ X776))|~(X769 @ X776))|((X768 @ (esk39_2 @ X768 @ X769))|(X769 @ (esk40_2 @ X768 @ X769)))))))))&(((emptyset)=(emptyset))&((((X780)!=(X781))|(((X782)!=(X783))|((setadjoin @ X780 @ X782)=(setadjoin @ X781 @ X783))))&((((X784)!=(X785))|((powerset @ X784)=(powerset @ X785)))&((((X786)!=(X787))|((setunion @ X786)=(setunion @ X787)))&(((omega)=(omega))&((((X788 @ (esk45_2 @ X788 @ X789))|~(X788 @ X789)|(~(X788 @ X791)|(~(X788 @ X792)|((X791)=(X792)))))&(((X789)!=(esk45_2 @ X788 @ X789))|~(X788 @ X789)|(~(X788 @ X791)|(~(X788 @ X792)|((X791)=(X792))))))&((((((X794 @ (esk49_3 @ X793 @ X794 @ X799))|~(X794 @ X799)|((descr @ X793)=(descr @ X794))|((X793 @ (esk48_3 @ X793 @ X794 @ X797))|~(X793 @ X797))|((esk46_2 @ X793 @ X794)=(esk47_2 @ X793 @ X794)))&(((X799)!=(esk49_3 @ X793 @ X794 @ X799))|~(X794 @ X799)|((descr @ X793)=(descr @ X794))|((X793 @ (esk48_3 @ X793 @ X794 @ X797))|~(X793 @ X797))|((esk46_2 @ X793 @ X794)=(esk47_2 @ X793 @ X794))))&(((X794 @ (esk49_3 @ X793 @ X794 @ X799))|~(X794 @ X799)|((descr @ X793)=(descr @ X794))|(((X797)!=(esk48_3 @ X793 @ X794 @ X797))|~(X793 @ X797))|((esk46_2 @ X793 @ X794)=(esk47_2 @ X793 @ X794)))&(((X799)!=(esk49_3 @ X793 @ X794 @ X799))|~(X794 @ X799)|((descr @ X793)=(descr @ X794))|(((X797)!=(esk48_3 @ X793 @ X794 @ X797))|~(X793 @ X797))|((esk46_2 @ X793 @ X794)=(esk47_2 @ X793 @ X794)))))&(((((X794 @ (esk49_3 @ X793 @ X794 @ X799))|~(X794 @ X799)|((descr @ X793)=(descr @ X794))|((X793 @ (esk48_3 @ X793 @ X794 @ X797))|~(X793 @ X797))|(~(X793 @ (esk46_2 @ X793 @ X794))|~(X794 @ (esk47_2 @ X793 @ X794))))&(((X799)!=(esk49_3 @ X793 @ X794 @ X799))|~(X794 @ X799)|((descr @ X793)=(descr @ X794))|((X793 @ (esk48_3 @ X793 @ X794 @ X797))|~(X793 @ X797))|(~(X793 @ (esk46_2 @ X793 @ X794))|~(X794 @ (esk47_2 @ X793 @ X794)))))&(((X794 @ (esk49_3 @ X793 @ X794 @ X799))|~(X794 @ X799)|((descr @ X793)=(descr @ X794))|(((X797)!=(esk48_3 @ X793 @ X794 @ X797))|~(X793 @ X797))|(~(X793 @ (esk46_2 @ X793 @ X794))|~(X794 @ (esk47_2 @ X793 @ X794))))&(((X799)!=(esk49_3 @ X793 @ X794 @ X799))|~(X794 @ X799)|((descr @ X793)=(descr @ X794))|(((X797)!=(esk48_3 @ X793 @ X794 @ X797))|~(X793 @ X797))|(~(X793 @ (esk46_2 @ X793 @ X794))|~(X794 @ (esk47_2 @ X793 @ X794))))))&((((X794 @ (esk49_3 @ X793 @ X794 @ X799))|~(X794 @ X799)|((descr @ X793)=(descr @ X794))|((X793 @ (esk48_3 @ X793 @ X794 @ X797))|~(X793 @ X797))|((X793 @ (esk46_2 @ X793 @ X794))|(X794 @ (esk47_2 @ X793 @ X794))))&(((X799)!=(esk49_3 @ X793 @ X794 @ X799))|~(X794 @ X799)|((descr @ X793)=(descr @ X794))|((X793 @ (esk48_3 @ X793 @ X794 @ X797))|~(X793 @ X797))|((X793 @ (esk46_2 @ X793 @ X794))|(X794 @ (esk47_2 @ X793 @ X794)))))&(((X794 @ (esk49_3 @ X793 @ X794 @ X799))|~(X794 @ X799)|((descr @ X793)=(descr @ X794))|(((X797)!=(esk48_3 @ X793 @ X794 @ X797))|~(X793 @ X797))|((X793 @ (esk46_2 @ X793 @ X794))|(X794 @ (esk47_2 @ X793 @ X794))))&(((X799)!=(esk49_3 @ X793 @ X794 @ X799))|~(X794 @ X799)|((descr @ X793)=(descr @ X794))|(((X797)!=(esk48_3 @ X793 @ X794 @ X797))|~(X793 @ X797))|((X793 @ (esk46_2 @ X793 @ X794))|(X794 @ (esk47_2 @ X793 @ X794))))))))&((((in @ (esk50_4 @ X801 @ X802 @ X803 @ X804) @ X801)|((dsetconstr @ X801 @ X803)=(dsetconstr @ X802 @ X804))|((X801)!=(X802)))&(((in @ (esk51_4 @ X801 @ X802 @ X803 @ X804) @ X802)|((dsetconstr @ X801 @ X803)=(dsetconstr @ X802 @ X804))|((X801)!=(X802)))&((((esk50_4 @ X801 @ X802 @ X803 @ X804)=(esk51_4 @ X801 @ X802 @ X803 @ X804))|((dsetconstr @ X801 @ X803)=(dsetconstr @ X802 @ X804))|((X801)!=(X802)))&((~(X803 @ (esk50_4 @ X801 @ X802 @ X803 @ X804))|~(X804 @ (esk51_4 @ X801 @ X802 @ X803 @ X804))|((dsetconstr @ X801 @ X803)=(dsetconstr @ X802 @ X804))|((X801)!=(X802)))&((X803 @ (esk50_4 @ X801 @ X802 @ X803 @ X804))|(X804 @ (esk51_4 @ X801 @ X802 @ X803 @ X804))|((dsetconstr @ X801 @ X803)=(dsetconstr @ X802 @ X804))|((X801)!=(X802)))))))&((((in @ (esk52_2 @ X807 @ X808) @ X807)|(subset @ X807 @ X808))&(~(in @ (esk52_2 @ X807 @ X808) @ X808)|(subset @ X807 @ X808)))&((((X810)!=(X811))|(subset @ X811 @ X810))&((((X812)!=(X813))|(subset @ X812 @ X813))&((((in @ (esk53_2 @ X814 @ X815) @ X814)|(subset @ X814 @ X815))&(~(in @ (esk53_2 @ X814 @ X815) @ X815)|(subset @ X814 @ X815)))&((subset @ emptyset @ X817)&((~(subset @ X818 @ X819)|(~(in @ X820 @ X818)|(in @ X820 @ X819)))&((~(subset @ X821 @ X822)|((in @ X823 @ X822)|~(in @ X823 @ X821)))&((~(in @ X826 @ X824)|((in @ X826 @ X825)|~(subset @ X824 @ X825)))&(((subset @ X827 @ X828)|((X827)!=(X828)))&((~(in @ X831 @ X829)|((in @ X831 @ X830)|((X829)!=(X830))))&((subset @ X832 @ X832)&((~(subset @ X833 @ X834)|(~(subset @ X834 @ X835)|(subset @ X833 @ X835)))&((subset @ X837 @ (setadjoin @ X836 @ X837))&((~(subset @ X838 @ X840)|(subset @ X838 @ (setadjoin @ X839 @ X840)))&((~(subset @ X841 @ X842)|(in @ X841 @ (powerset @ X842)))&((subset @ esk54_0 @ esk55_0)&((subset @ esk55_0 @ esk54_0)&((esk54_0)!=(esk55_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_133])])])])])])])). 9.14/2.16 thf(c_0_135, negated_conjecture, ![X4:$i, X3:$i, X2:$i]:(((in @ X4 @ X3)|~((subset @ X2 @ X3))|~((in @ X4 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_134])). 9.14/2.16 thf(c_0_136, negated_conjecture, (subset @ esk55_0 @ esk54_0), inference(split_conjunct,[status(thm)],[c_0_134])). 9.14/2.16 thf(c_0_137, negated_conjecture, ![X2:$i]:(((in @ X2 @ esk54_0)|~((in @ X2 @ esk55_0)))), inference(spm,[status(thm)],[c_0_135, c_0_136])). 9.14/2.16 thf(c_0_138, negated_conjecture, ![X2:$i, X3:$i]:(((in @ (esk1_2 @ X2 @ X3) @ X2)|(in @ (esk1_2 @ X2 @ X3) @ X3)|((X2)=(X3)))), inference(split_conjunct,[status(thm)],[c_0_134])). 9.14/2.16 thf(c_0_139, negated_conjecture, ![X2:$i]:((((esk55_0)=(X2))|(in @ (esk1_2 @ esk55_0 @ X2) @ esk54_0)|(in @ (esk1_2 @ esk55_0 @ X2) @ X2))), inference(spm,[status(thm)],[c_0_137, c_0_138])). 9.14/2.16 thf(c_0_140, negated_conjecture, ((esk54_0)!=(esk55_0)), inference(split_conjunct,[status(thm)],[c_0_134])). 9.14/2.16 thf(c_0_141, negated_conjecture, ![X2:$i, X3:$i]:((((X2)=(X3))|~((in @ (esk1_2 @ X2 @ X3) @ X2))|~((in @ (esk1_2 @ X2 @ X3) @ X3)))), inference(split_conjunct,[status(thm)],[c_0_134])). 9.14/2.16 thf(c_0_142, negated_conjecture, (in @ (esk1_2 @ esk55_0 @ esk54_0) @ esk54_0), inference(sr,[status(thm)],[inference(ef,[status(thm)],[c_0_139]), c_0_140])). 9.14/2.16 thf(c_0_143, negated_conjecture, (subset @ esk54_0 @ esk55_0), inference(split_conjunct,[status(thm)],[c_0_134])). 9.14/2.16 thf(c_0_144, negated_conjecture, ~((in @ (esk1_2 @ esk55_0 @ esk54_0) @ esk55_0)), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_141, c_0_142]), c_0_140])). 9.14/2.16 thf(c_0_145, negated_conjecture, ![X2:$i]:(((in @ X2 @ esk55_0)|~((in @ X2 @ esk54_0)))), inference(spm,[status(thm)],[c_0_135, c_0_143])). 9.14/2.16 thf(c_0_146, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144, c_0_145]), c_0_142])]), ['proof']). 9.14/2.16 % SZS output end CNFRefutation 9.14/2.16 % Parsed axioms : 198 9.14/2.16 % Removed by relevancy pruning/SinE : 0 9.14/2.16 % Initial clauses : 308 9.14/2.16 % Removed in clause preprocessing : 119 9.14/2.16 % Initial clauses in saturation : 189 9.14/2.16 % Processed clauses : 1335 9.14/2.16 % ...of these trivial : 75 9.14/2.16 % ...subsumed : 429 9.14/2.16 % ...remaining for further processing : 831 9.14/2.16 % Other redundant clauses eliminated : 49 9.14/2.16 % Clauses deleted for lack of memory : 0 9.14/2.16 % Backward-subsumed : 20 9.14/2.16 % Backward-rewritten : 25 9.14/2.16 % Generated clauses : 25764 9.14/2.16 % ...of the previous two non-redundant : 24385 9.14/2.16 % ...aggressively subsumed : 0 9.14/2.16 % Contextual simplify-reflections : 0 9.14/2.16 % Paramodulations : 25296 9.14/2.16 % Factorizations : 4 9.14/2.16 % NegExts : 0 9.14/2.16 % Equation resolutions : 49 9.14/2.16 % Disequality decompositions : 0 9.14/2.16 % Total rewrite steps : 1701 9.14/2.16 % ...of those cached : 1458 9.14/2.16 % Propositional unsat checks : 0 9.14/2.16 % Propositional check models : 0 9.14/2.16 % Propositional check unsatisfiable : 0 9.14/2.16 % Propositional clauses : 0 9.14/2.16 % Propositional clauses after purity: 0 9.14/2.16 % Propositional unsat core size : 0 9.14/2.16 % Propositional preprocessing time : 0.000 9.14/2.16 % Propositional encoding time : 0.000 9.14/2.16 % Propositional solver time : 0.000 9.14/2.16 % Success case prop preproc time : 0.000 9.14/2.16 % Success case prop encoding time : 0.000 9.14/2.16 % Success case prop solver time : 0.000 9.14/2.16 % Current number of processed clauses : 608 9.14/2.16 % Positive orientable unit clauses : 150 9.14/2.16 % Positive unorientable unit clauses: 0 9.14/2.16 % Negative unit clauses : 3 9.14/2.16 % Non-unit-clauses : 455 9.14/2.16 % Current number of unprocessed clauses: 23353 9.14/2.16 % ...number of literals in the above : 76774 9.14/2.16 % Current number of archived formulas : 0 9.14/2.16 % Current number of archived clauses : 210 9.14/2.16 % Clause-clause subsumption calls (NU) : 28952 9.14/2.16 % Rec. Clause-clause subsumption calls : 15603 9.14/2.16 % Non-unit clause-clause subsumptions : 392 9.14/2.16 % Unit Clause-clause subsumption calls : 9655 9.14/2.16 % Rewrite failures with RHS unbound : 0 9.14/2.16 % BW rewrite match attempts : 111 9.14/2.16 % BW rewrite match successes : 17 9.14/2.16 % Condensation attempts : 0 9.14/2.16 % Condensation successes : 0 9.14/2.16 % Termbank termtop insertions : 1323737 9.14/2.16 % Search garbage collected termcells : 10174 9.14/2.16 9.14/2.16 % ------------------------------------------------- 9.14/2.16 % User time : 1.356 s 9.14/2.16 % System time : 0.045 s 9.14/2.16 % Total time : 1.401 s 9.14/2.16 % Maximum resident set size: 5876 pages 9.14/2.16 9.14/2.16 % ------------------------------------------------- 9.14/2.16 % User time : 6.245 s 9.14/2.16 % System time : 0.245 s 9.14/2.16 % Total time : 6.490 s 9.14/2.16 % Maximum resident set size: 5120 pages 9.14/2.16 % E exiting 9.14/2.17 EOF