%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU571^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:24:33 AM UTC 2026
% Result : Theorem 4.69s 1.02s
% Output : CNFRefutation 4.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU571^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n007.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:49:11 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.27 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=300 /export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p
% 4.69/1.02 % Version: 3.5.1-ho
% 4.69/1.02 % Preprocessing class: HSMMSLSSLLLCHFA.
% 4.69/1.02 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.69/1.02 % Starting ehoh_best3_avoidappvar with 1500s (5) cores
% 4.69/1.02 % Starting ehoh_best3_rw with 300s (1) cores
% 4.69/1.02 % Starting almost_fo_3 with 300s (1) cores
% 4.69/1.02 % Starting new_ho_13 with 300s (1) cores
% 4.69/1.02 % ehoh_best3_avoidappvar with pid 3395679 completed with status 0
% 4.69/1.02 % Result found by ehoh_best3_avoidappvar
% 4.69/1.02 % Preprocessing class: HSMMSLSSLLLCHFA.
% 4.69/1.02 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.69/1.02 % Starting ehoh_best3_avoidappvar with 1500s (5) cores
% 4.69/1.02 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 4.69/1.02 % No SInE strategy applied
% 4.69/1.02 % Search class: HGHSM-FSLS31-SHFMMMBN
% 4.69/1.02 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 4.69/1.02 % Starting SubtermCWHack with 136s (1) cores
% 4.69/1.02 % Starting ehoh_best3_avoidappvar with 151s (1) cores
% 4.69/1.02 % Starting sh5l with 136s (1) cores
% 4.69/1.02 % Starting new_bool_1 with 136s (1) cores
% 4.69/1.02 % Starting new_bool_2 with 136s (1) cores
% 4.69/1.02 % ehoh_best3_avoidappvar with pid 3395691 completed with status 0
% 4.69/1.02 % Result found by ehoh_best3_avoidappvar
% 4.69/1.02 % Preprocessing class: HSMMSLSSLLLCHFA.
% 4.69/1.02 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.69/1.02 % Starting ehoh_best3_avoidappvar with 1500s (5) cores
% 4.69/1.02 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 4.69/1.02 % No SInE strategy applied
% 4.69/1.02 % Search class: HGHSM-FSLS31-SHFMMMBN
% 4.69/1.02 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 4.69/1.02 % Starting SubtermCWHack with 136s (1) cores
% 4.69/1.02 % Starting ehoh_best3_avoidappvar with 151s (1) cores
% 4.69/1.02 % Preprocessing time : 0.004 s
% 4.69/1.02 % Presaturation interreduction done
% 4.69/1.02
% 4.69/1.02 % Proof found!
% 4.69/1.02 % SZS status Theorem
% 4.69/1.02 % SZS output start CNFRefutation
% 4.69/1.02 thf(decl_23, type, in: $i > $i > $o).
% 4.69/1.02 thf(decl_24, type, exu: ($i > $o) > $o).
% 4.69/1.02 thf(decl_25, type, setextAx: $o).
% 4.69/1.02 thf(decl_26, type, emptyset: $i).
% 4.69/1.02 thf(decl_27, type, emptysetAx: $o).
% 4.69/1.02 thf(decl_28, type, setadjoin: $i > $i > $i).
% 4.69/1.02 thf(decl_29, type, setadjoinAx: $o).
% 4.69/1.02 thf(decl_30, type, powerset: $i > $i).
% 4.69/1.02 thf(decl_31, type, powersetAx: $o).
% 4.69/1.02 thf(decl_32, type, setunion: $i > $i).
% 4.69/1.02 thf(decl_33, type, setunionAx: $o).
% 4.69/1.02 thf(decl_34, type, omega: $i).
% 4.69/1.02 thf(decl_35, type, omega0Ax: $o).
% 4.69/1.02 thf(decl_36, type, omegaSAx: $o).
% 4.69/1.02 thf(decl_37, type, omegaIndAx: $o).
% 4.69/1.02 thf(decl_38, type, replAx: $o).
% 4.69/1.02 thf(decl_39, type, foundationAx: $o).
% 4.69/1.02 thf(decl_40, type, wellorderingAx: $o).
% 4.69/1.02 thf(decl_41, type, descr: ($i > $o) > $i).
% 4.69/1.02 thf(decl_42, type, descrp: $o).
% 4.69/1.02 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 4.69/1.02 thf(decl_44, type, dsetconstrI: $o).
% 4.69/1.02 thf(decl_45, type, dsetconstrEL: $o).
% 4.69/1.02 thf(decl_46, type, dsetconstrER: $o).
% 4.69/1.02 thf(decl_47, type, exuE1: $o).
% 4.69/1.02 thf(decl_48, type, prop2set: $o > $i).
% 4.69/1.02 thf(decl_49, type, prop2setE: $o).
% 4.69/1.02 thf(decl_50, type, emptysetE: $o).
% 4.69/1.02 thf(decl_51, type, emptysetimpfalse: $o).
% 4.69/1.02 thf(decl_52, type, notinemptyset: $o).
% 4.69/1.02 thf(decl_53, type, exuE3e: $o).
% 4.69/1.02 thf(decl_54, type, setext: $o).
% 4.69/1.02 thf(decl_55, type, emptyI: $o).
% 4.69/1.02 thf(decl_56, type, noeltsimpempty: $o).
% 4.69/1.02 thf(decl_57, type, setbeta: $o).
% 4.69/1.02 thf(decl_58, type, nonempty: $i > $o).
% 4.69/1.02 thf(decl_59, type, nonemptyE1: $o).
% 4.69/1.02 thf(decl_60, type, nonemptyI: $o).
% 4.69/1.02 thf(decl_61, type, nonemptyI1: $o).
% 4.69/1.02 thf(decl_62, type, setadjoinIL: $o).
% 4.69/1.02 thf(decl_63, type, emptyinunitempty: $o).
% 4.69/1.02 thf(decl_64, type, setadjoinIR: $o).
% 4.69/1.02 thf(decl_65, type, setadjoinE: $o).
% 4.69/1.02 thf(decl_66, type, setadjoinOr: $o).
% 4.69/1.02 thf(decl_67, type, setoftrueEq: $o).
% 4.69/1.02 thf(decl_68, type, powersetI: $o).
% 4.69/1.02 thf(decl_69, type, emptyinPowerset: $o).
% 4.69/1.02 thf(decl_70, type, emptyInPowerset: $o).
% 4.69/1.02 thf(decl_71, type, powersetE: $o).
% 4.69/1.02 thf(decl_72, type, setunionI: $o).
% 4.69/1.02 thf(decl_73, type, setunionE: $o).
% 4.69/1.02 thf(decl_74, type, subPowSU: $o).
% 4.69/1.02 thf(decl_75, type, exuE2: $o).
% 4.69/1.02 thf(decl_76, type, nonemptyImpWitness: $o).
% 4.69/1.02 thf(decl_77, type, uniqinunit: $o).
% 4.69/1.02 thf(decl_78, type, notinsingleton: $o).
% 4.69/1.02 thf(decl_79, type, eqinunit: $o).
% 4.69/1.02 thf(decl_80, type, singletonsswitch: $o).
% 4.69/1.02 thf(decl_81, type, upairsetE: $o).
% 4.69/1.02 thf(decl_82, type, upairsetIL: $o).
% 4.69/1.02 thf(decl_83, type, upairsetIR: $o).
% 4.69/1.02 thf(decl_84, type, emptyE1: $o).
% 4.69/1.02 thf(decl_85, type, vacuousDall: $o).
% 4.69/1.02 thf(decl_86, type, quantDeMorgan1: $o).
% 4.69/1.02 thf(decl_87, type, quantDeMorgan2: $o).
% 4.69/1.02 thf(decl_88, type, quantDeMorgan3: $o).
% 4.69/1.02 thf(decl_89, type, quantDeMorgan4: $o).
% 4.69/1.02 thf(decl_90, type, prop2setI: $o).
% 4.69/1.02 thf(decl_91, type, set2prop: $i > $o).
% 4.69/1.02 thf(decl_92, type, prop2set2propI: $o).
% 4.69/1.02 thf(decl_93, type, notdexE: $o).
% 4.69/1.02 thf(decl_94, type, notdallE: $o).
% 4.69/1.02 thf(decl_95, type, exuI1: $o).
% 4.69/1.02 thf(decl_96, type, exuI3: $o).
% 4.69/1.02 thf(decl_97, type, exuI2: $o).
% 4.69/1.02 thf(decl_98, type, inCongP: $o).
% 4.69/1.02 thf(decl_99, type, in__Cong: $o).
% 4.69/1.02 thf(decl_100, type, exuE3u: $o).
% 4.69/1.02 thf(decl_101, type, exu__Cong: $o).
% 4.69/1.02 thf(decl_102, type, emptyset__Cong: $o).
% 4.69/1.02 thf(decl_103, type, setadjoin__Cong: $o).
% 4.69/1.02 thf(decl_104, type, powerset__Cong: $o).
% 4.69/1.02 thf(decl_105, type, setunion__Cong: $o).
% 4.69/1.02 thf(decl_106, type, omega__Cong: $o).
% 4.69/1.02 thf(decl_107, type, exuEu: $o).
% 4.69/1.02 thf(decl_108, type, descr__Cong: $o).
% 4.69/1.02 thf(decl_109, type, dsetconstr__Cong: $o).
% 4.69/1.02 thf(decl_110, type, subset: $i > $i > $o).
% 4.69/1.02 thf(decl_113, type, subsetI1: $o).
% 4.69/1.02 thf(decl_114, type, eqimpsubset2: $o).
% 4.69/1.02 thf(decl_115, type, eqimpsubset1: $o).
% 4.69/1.02 thf(decl_116, type, subsetI2: $o).
% 4.69/1.02 thf(decl_117, type, emptysetsubset: $o).
% 4.69/1.02 thf(decl_118, type, subsetE: $o).
% 4.69/1.02 thf(decl_119, type, subsetE2: $o).
% 4.69/1.02 thf(decl_120, type, notsubsetI: $o).
% 4.69/1.02 thf(decl_121, type, notequalI1: $o).
% 4.69/1.02 thf(decl_122, type, notequalI2: $o).
% 4.69/1.02 thf(decl_123, type, subsetRefl: $o).
% 4.69/1.02 thf(decl_124, type, subsetTrans: $o).
% 4.69/1.02 thf(decl_125, type, epred1_0: $o).
% 4.69/1.02 thf(decl_126, type, esk1_2: $i > $i > $i).
% 4.69/1.02 thf(decl_127, type, esk2_2: $i > $i > $i).
% 4.69/1.02 thf(decl_128, type, esk3_2: $i > $i > $i).
% 4.69/1.02 thf(decl_129, type, esk4_1: $i > $i).
% 4.69/1.02 thf(decl_130, type, esk5_2: ($i > $i > $o) > $i > $i).
% 4.69/1.02 thf(decl_131, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 4.69/1.02 thf(decl_132, type, esk7_2: ($i > $i > $o) > $i > $i).
% 4.69/1.02 thf(decl_133, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 4.69/1.02 thf(decl_134, type, esk9_1: $i > $i).
% 4.69/1.02 thf(decl_135, type, esk10_2: ($i > $o) > $i > $i).
% 4.69/1.02 thf(decl_136, type, esk11_2: ($i > $o) > $i > $i).
% 4.69/1.02 thf(decl_137, type, esk12_1: ($i > $o) > $i).
% 4.69/1.02 thf(decl_138, type, esk13_2: ($i > $o) > $i > $i).
% 4.69/1.02 thf(decl_139, type, esk14_1: ($i > $o) > $i).
% 4.69/1.02 thf(decl_140, type, esk15_2: $i > $i > $i).
% 4.69/1.02 thf(decl_141, type, esk16_2: $i > $i > $i).
% 4.69/1.02 thf(decl_142, type, esk17_1: $i > $i).
% 4.69/1.02 thf(decl_143, type, esk18_1: $i > $i).
% 4.69/1.02 thf(decl_144, type, esk19_1: $i > $i).
% 4.69/1.02 thf(decl_145, type, esk20_2: $i > $i > $i).
% 4.69/1.02 thf(decl_146, type, esk21_3: $i > $i > $o > $i).
% 4.69/1.02 thf(decl_147, type, esk22_2: ($i > $o) > $i > $i).
% 4.69/1.02 thf(decl_148, type, esk23_1: ($i > $o) > $i).
% 4.69/1.02 thf(decl_149, type, esk24_1: $i > $i).
% 4.69/1.02 thf(decl_150, type, esk25_2: $i > ($i > $o) > $i).
% 4.69/1.02 thf(decl_151, type, esk26_2: $i > ($i > $o) > $i).
% 4.69/1.02 thf(decl_152, type, esk27_2: $i > ($i > $o) > $i).
% 4.69/1.02 thf(decl_153, type, esk28_2: $i > ($i > $o) > $i).
% 4.69/1.02 thf(decl_154, type, esk29_2: $i > ($i > $o) > $i).
% 4.69/1.02 thf(decl_155, type, esk30_2: $i > ($i > $o) > $i).
% 4.69/1.02 thf(decl_156, type, esk31_2: ($i > $o) > $i > $i).
% 4.69/1.02 thf(decl_157, type, esk32_1: ($i > $o) > $i).
% 4.69/1.02 thf(decl_158, type, esk33_1: ($i > $o) > $i).
% 4.69/1.02 thf(decl_159, type, esk34_1: ($i > $o) > $i).
% 4.69/1.02 thf(decl_160, type, esk35_1: ($i > $o) > $i).
% 4.69/1.02 thf(decl_161, type, esk36_2: ($i > $o) > $i > $i).
% 4.69/1.02 thf(decl_162, type, esk37_1: ($i > $o) > $i).
% 4.69/1.02 thf(decl_163, type, esk38_2: ($i > $o) > $i > $i).
% 4.69/1.02 thf(decl_164, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 4.69/1.02 thf(decl_165, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 4.69/1.02 thf(decl_166, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 4.69/1.02 thf(decl_167, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 4.69/1.02 thf(decl_168, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 4.69/1.02 thf(decl_169, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 4.69/1.02 thf(decl_170, type, esk45_2: ($i > $o) > $i > $i).
% 4.69/1.02 thf(decl_171, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 4.69/1.02 thf(decl_172, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 4.69/1.02 thf(decl_173, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 4.69/1.02 thf(decl_174, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 4.69/1.02 thf(decl_175, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 4.69/1.02 thf(decl_176, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 4.69/1.02 thf(decl_177, type, esk52_2: $i > $i > $i).
% 4.69/1.02 thf(decl_178, type, esk53_2: $i > $i > $i).
% 4.69/1.02 thf(decl_179, type, esk54_0: $i).
% 4.69/1.02 thf(decl_180, type, esk55_0: $i).
% 4.69/1.02 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', replAx)).
% 4.69/1.02 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', exu)).
% 4.69/1.02 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', descrp)).
% 4.69/1.02 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', exuE1)).
% 4.69/1.02 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', exuE3e)).
% 4.69/1.02 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', nonempty)).
% 4.69/1.02 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', nonemptyI)).
% 4.69/1.02 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', exuE2)).
% 4.69/1.02 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', exuI1)).
% 4.69/1.02 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', exuI3)).
% 4.69/1.02 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', exuI2)).
% 4.69/1.02 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', exuE3u)).
% 4.69/1.02 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', exu__Cong)).
% 4.69/1.02 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', exuEu)).
% 4.69/1.02 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', descr__Cong)).
% 4.69/1.02 thf(setadjoinSub, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', setadjoinSub)).
% 4.69/1.02 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', dsetconstrI)).
% 4.69/1.02 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', dsetconstrEL)).
% 4.69/1.02 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', dsetconstrER)).
% 4.69/1.02 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', setbeta)).
% 4.69/1.02 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', nonemptyE1)).
% 4.69/1.02 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', nonemptyI1)).
% 4.69/1.02 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', setoftrueEq)).
% 4.69/1.02 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', nonemptyImpWitness)).
% 4.69/1.02 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', emptyE1)).
% 4.69/1.02 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', dsetconstr__Cong)).
% 4.69/1.02 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', setextAx)).
% 4.69/1.02 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', emptysetAx)).
% 4.69/1.02 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', setadjoinAx)).
% 4.69/1.02 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', powersetAx)).
% 4.69/1.02 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', setunionAx)).
% 4.69/1.02 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', omega0Ax)).
% 4.69/1.02 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', omegaSAx)).
% 4.69/1.02 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', omegaIndAx)).
% 4.69/1.02 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', foundationAx)).
% 4.69/1.02 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', wellorderingAx)).
% 4.69/1.02 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', prop2setE)).
% 4.69/1.02 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', emptysetE)).
% 4.69/1.02 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', emptysetimpfalse)).
% 4.69/1.02 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', notinemptyset)).
% 4.69/1.02 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', setext)).
% 4.69/1.02 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', emptyI)).
% 4.69/1.02 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', noeltsimpempty)).
% 4.69/1.02 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', setadjoinIL)).
% 4.69/1.02 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', emptyinunitempty)).
% 4.69/1.02 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', setadjoinIR)).
% 4.69/1.02 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', setadjoinE)).
% 4.69/1.02 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', setadjoinOr)).
% 4.69/1.02 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', powersetI)).
% 4.69/1.02 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', emptyinPowerset)).
% 4.69/1.02 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', emptyInPowerset)).
% 4.69/1.02 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', powersetE)).
% 4.69/1.02 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', setunionI)).
% 4.69/1.02 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', setunionE)).
% 4.69/1.02 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', subPowSU)).
% 4.69/1.02 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', uniqinunit)).
% 4.69/1.02 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', notinsingleton)).
% 4.69/1.02 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', eqinunit)).
% 4.69/1.02 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', singletonsswitch)).
% 4.69/1.02 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', upairsetE)).
% 4.69/1.02 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', upairsetIL)).
% 4.69/1.02 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', upairsetIR)).
% 4.69/1.02 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', vacuousDall)).
% 4.69/1.02 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', quantDeMorgan1)).
% 4.69/1.02 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', quantDeMorgan2)).
% 4.69/1.02 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', quantDeMorgan3)).
% 4.69/1.02 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', quantDeMorgan4)).
% 4.69/1.02 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', prop2setI)).
% 4.69/1.02 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', prop2set2propI)).
% 4.69/1.02 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', notdexE)).
% 4.69/1.02 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', notdallE)).
% 4.69/1.02 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', inCongP)).
% 4.69/1.02 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', in__Cong)).
% 4.69/1.02 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', emptyset__Cong)).
% 4.69/1.02 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', setadjoin__Cong)).
% 4.69/1.02 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', powerset__Cong)).
% 4.69/1.02 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', setunion__Cong)).
% 4.69/1.02 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', omega__Cong)).
% 4.69/1.02 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', subsetI1)).
% 4.69/1.02 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', eqimpsubset2)).
% 4.69/1.02 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', eqimpsubset1)).
% 4.69/1.02 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', subsetI2)).
% 4.69/1.02 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', emptysetsubset)).
% 4.69/1.02 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', subsetE)).
% 4.69/1.02 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', subsetE2)).
% 4.69/1.02 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', notsubsetI)).
% 4.69/1.02 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', notequalI1)).
% 4.69/1.02 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', notequalI2)).
% 4.69/1.02 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', subsetRefl)).
% 4.69/1.02 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/tmp/tmp.s21nsgANhV/E---3.1_3395646.p', subsetTrans)).
% 4.69/1.02 thf(c_0_90, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 4.69/1.02 thf(c_0_91, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 4.69/1.02 thf(c_0_92, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 4.69/1.02 thf(c_0_93, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 4.69/1.02 thf(c_0_94, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 4.69/1.02 thf(c_0_95, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 4.69/1.02 thf(c_0_96, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 4.69/1.02 thf(c_0_97, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 4.69/1.02 thf(c_0_98, 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])).
% 4.69/1.02 thf(c_0_99, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 4.69/1.02 thf(c_0_100, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 4.69/1.02 thf(c_0_101, 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])).
% 4.69/1.02 thf(c_0_102, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 4.69/1.02 thf(c_0_103, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 4.69/1.02 thf(c_0_104, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 4.69/1.02 thf(c_0_105, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[setadjoinSub])).
% 4.69/1.02 thf(c_0_106, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X262:$i]:(((((X6 @ X2 @ X262)))&(![X263:$i]:(((((X6 @ X2 @ X263)))=>(((X262)=(X263)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_90, c_0_91])).
% 4.69/1.02 thf(c_0_107, plain, ((descrp)=(![X1:$i > $o]:((((?[X264:$i]:(((((X1 @ X264)))&(![X265:$i]:(((((X1 @ X265)))=>(((X264)=(X265))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_92, c_0_91])).
% 4.69/1.02 thf(c_0_108, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 4.69/1.02 thf(c_0_109, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 4.69/1.02 thf(c_0_110, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 4.69/1.02 thf(c_0_111, plain, ((exuE1)=(![X1:$i > $o]:((((?[X266:$i]:(((((X1 @ X266)))&(![X267:$i]:(((((X1 @ X267)))=>(((X266)=(X267))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_93, c_0_91])).
% 4.69/1.02 thf(c_0_112, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X268:$i]:(((((X1 @ X268)))&(![X269:$i]:(((((X1 @ X269)))=>(((X268)=(X269))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_94, c_0_91])).
% 4.69/1.02 thf(c_0_113, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 4.69/1.02 thf(c_0_114, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_95])).
% 4.69/1.02 thf(c_0_115, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_96, c_0_95])).
% 4.69/1.02 thf(c_0_116, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_95])).
% 4.69/1.02 thf(c_0_117, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 4.69/1.02 thf(c_0_118, plain, ((exuE2)=(![X1:$i > $o]:((((?[X270:$i]:(((((X1 @ X270)))&(![X271:$i]:(((((X1 @ X271)))=>(((X270)=(X271))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_97, c_0_91])).
% 4.69/1.02 thf(c_0_119, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_95])).
% 4.69/1.02 thf(c_0_120, 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])).
% 4.69/1.02 thf(c_0_121, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X272:$i]:(((((X1 @ X272)))&(![X273:$i]:(((((X1 @ X273)))=>(((X272)=(X273)))))))))))))), inference(apply_def,[status(thm)],[c_0_98, c_0_91])).
% 4.69/1.02 thf(c_0_122, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X274:$i]:(((((X1 @ X274)))&(![X275:$i]:(((((X1 @ X275)))=>(((X274)=(X275)))))))))))))))), inference(apply_def,[status(thm)],[c_0_99, c_0_91])).
% 4.69/1.02 thf(c_0_123, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X276:$i]:(((((X1 @ X276)))&(![X277:$i]:(((((X1 @ X277)))=>(((X276)=(X277)))))))))))))), inference(apply_def,[status(thm)],[c_0_100, c_0_91])).
% 4.69/1.02 thf(c_0_124, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X278:$i]:(((((X1 @ X278)))&(![X279:$i]:(((((X1 @ X279)))=>(((X278)=(X279))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_101, c_0_91])).
% 4.69/1.02 thf(c_0_125, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X280:$i]:(((((X1 @ X280)))&(![X281:$i]:(((((X1 @ X281)))=>(((X280)=(X281))))))))))<=>((?[X282:$i]:(((((X17 @ X282)))&(![X283:$i]:(((((X17 @ X283)))=>(((X282)=(X283)))))))))))))))), inference(apply_def,[status(thm)],[c_0_102, c_0_91])).
% 4.69/1.02 thf(c_0_126, plain, ((exuEu)=(![X1:$i > $o]:((((?[X284:$i]:(((((X1 @ X284)))&(![X285:$i]:(((((X1 @ X285)))=>(((X284)=(X285))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_103, c_0_91])).
% 4.69/1.02 thf(c_0_127, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X286:$i]:(((((X1 @ X286)))&(![X287:$i]:(((((X1 @ X287)))=>(((X286)=(X287))))))))))=>((((?[X288:$i]:(((((X17 @ X288)))&(![X289:$i]:(((((X17 @ X289)))=>(((X288)=(X289))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_104, c_0_91])).
% 4.69/1.02 thf(c_0_128, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 4.69/1.02 thf(c_0_129, plain, ((epred1_0)<=>![X319:$i]:(?[X320:$i]:((((![X321:$i]:(((in @ X321 @ X320)=>![X322:$i]:(((in @ X322 @ X321)=>(in @ X322 @ X319)))))&![X323:$i, X324:$i]:((((in @ X323 @ X319)&(in @ X324 @ X319))=>(![X325:$i]:(((in @ X325 @ X320)=>((in @ X323 @ X325)<=>(in @ X324 @ X325))))=>((X323)=(X324))))))&![X326:$i, X327:$i]:((((in @ X326 @ X320)&(in @ X327 @ X320))=>(![X328:$i]:(((in @ X328 @ X326)=>(in @ X328 @ X327)))|![X329:$i]:(((in @ X329 @ X327)=>(in @ X329 @ X326)))))))&![X330:$i]:(((![X331:$i]:(((in @ X331 @ X330)=>(in @ X331 @ X319)))&?[X332:$i]:((in @ X332 @ X330)))=>?[X333:$i, X334:$i]:(((((in @ X333 @ X320)&(in @ X334 @ X330))&~(?[X335:$i]:(((in @ X335 @ X333)&(in @ X335 @ X330)))))&![X336:$i]:(((in @ X336 @ X320)=>(![X337:$i]:(((in @ X337 @ X336)=>(in @ X337 @ X333)))|(in @ X334 @ X336)))))))))))), introduced(definition)).
% 4.69/1.02 thf(c_0_130, negated_conjecture, ~((![X290:$i, X291:$i]:((![X292:$i]:(((in @ X292 @ X290)<=>(in @ X292 @ X291)))=>((X290)=(X291))))=>(![X293:$i]:(~(in @ X293 @ emptyset))=>(![X294:$i, X295:$i, X296:$i]:(((in @ X296 @ (setadjoin @ X294 @ X295))<=>(((X296)=(X294))|(in @ X296 @ X295))))=>(![X297:$i, X298:$i]:(((in @ X298 @ (powerset @ X297))<=>![X299:$i]:(((in @ X299 @ X298)=>(in @ X299 @ X297)))))=>(![X300:$i, X301:$i]:(((in @ X301 @ (setunion @ X300))<=>?[X302:$i]:(((in @ X301 @ X302)&(in @ X302 @ X300)))))=>((in @ emptyset @ omega)=>(![X303:$i]:(((in @ X303 @ omega)=>(in @ (setadjoin @ X303 @ X303) @ omega)))=>(![X304:$i]:((((in @ emptyset @ X304)&![X305:$i]:((((in @ X305 @ omega)&(in @ X305 @ X304))=>(in @ (setadjoin @ X305 @ X305) @ X304))))=>![X306:$i]:(((in @ X306 @ omega)=>(in @ X306 @ X304)))))=>(![X307:$i > $i > $o, X308:$i]:((![X309:$i]:(((in @ X309 @ X308)=>?[X310:$i]:(((X307 @ X309 @ X310)&![X311:$i]:(((X307 @ X309 @ X311)=>((X310)=(X311))))))))=>?[X312:$i]:(![X313:$i]:(((in @ X313 @ X312)<=>?[X314:$i]:(((in @ X314 @ X308)&(X307 @ X314 @ X313))))))))=>(![X315:$i]:((?[X316:$i]:((in @ X316 @ X315))=>?[X317:$i]:(((in @ X317 @ X315)&~(?[X318:$i]:(((in @ X318 @ X317)&(in @ X318 @ X315))))))))=>((epred1_0)=>(![X338:$i > $o]:((?[X339:$i]:(((X338 @ X339)&![X340:$i]:(((X338 @ X340)=>((X339)=(X340))))))=>(X338 @ (descr @ (^[Z0:$i]:(X338 @ Z0))))))=>(![X341:$i, X342:$i > $o, X343:$i]:(((in @ X343 @ X341)=>((X342 @ X343)=>(in @ X343 @ (dsetconstr @ X341 @ X342)))))=>(![X344:$i, X345:$i > $o, X346:$i]:(((in @ X346 @ (dsetconstr @ X344 @ X345))=>(in @ X346 @ X344)))=>(![X347:$i, X348:$i > $o, X349:$i]:(((in @ X349 @ (dsetconstr @ X347 @ X348))=>(X348 @ X349)))=>(![X350:$i > $o]:((?[X351:$i]:(((X350 @ X351)&![X352:$i]:(((X350 @ X352)=>((X351)=(X352))))))=>?[X353:$i]:(((X350 @ X353)&![X354:$i]:(((X350 @ X354)=>((X353)=(X354))))))))=>(![X355:$o, X356:$i]:(((in @ X356 @ (prop2set @ ((X355))))=>(X355)))=>(![X357:$i]:(((in @ X357 @ emptyset)=>![X358:$o]:((X358))))=>(![X359:$i]:(((in @ X359 @ emptyset)=>~($true)))=>(![X360:$i]:(~(in @ X360 @ emptyset))=>(![X361:$i > $o]:((?[X362:$i]:(((X361 @ X362)&![X363:$i]:(((X361 @ X363)=>((X362)=(X363))))))=>?[X364:$i]:((X361 @ X364))))=>(![X365:$i, X366:$i]:((![X367:$i]:(((in @ X367 @ X365)=>(in @ X367 @ X366)))=>(![X368:$i]:(((in @ X368 @ X366)=>(in @ X368 @ X365)))=>((X365)=(X366)))))=>(![X369:$i]:((![X370:$i]:(~(in @ X370 @ X369))=>((X369)=(emptyset))))=>(![X371:$i]:((![X372:$i]:(~(in @ X372 @ X371))=>((X371)=(emptyset))))=>(![X373:$i, X374:$i > $o, X375:$i]:(((in @ X375 @ X373)=>((in @ X375 @ (dsetconstr @ X373 @ X374))<=>(X374 @ X375))))=>(![X376:$i]:((((X376)!=(emptyset))=>?[X377:$i]:((in @ X377 @ X376))))=>(![X378:$i, X379:$i > $o, X380:$i]:(((in @ X380 @ X378)=>((X379 @ X380)=>((dsetconstr @ X378 @ X379)!=(emptyset)))))=>(![X381:$i]:((?[X382:$i]:((in @ X382 @ X381))=>((X381)!=(emptyset))))=>(![X383:$i, X384:$i]:((in @ X383 @ (setadjoin @ X383 @ X384)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X385:$i, X386:$i, X387:$i]:(((in @ X387 @ X386)=>(in @ X387 @ (setadjoin @ X385 @ X386))))=>(![X388:$i, X389:$i, X390:$i]:(((in @ X390 @ (setadjoin @ X388 @ X389))=>![X391:$o]:(((((X390)=(X388))=>(X391))=>(((in @ X390 @ X389)=>(X391))=>(X391))))))=>(![X392:$i, X393:$i, X394:$i]:(((in @ X394 @ (setadjoin @ X392 @ X393))=>(((X394)=(X392))|(in @ X394 @ X393))))=>(![X395:$i]:(((dsetconstr @ X395 @ (^[Z0:$i]:($true)))=(X395)))=>(![X396:$i, X397:$i]:((![X398:$i]:(((in @ X398 @ X397)=>(in @ X398 @ X396)))=>(in @ X397 @ (powerset @ X396))))=>(![X399:$i]:((in @ emptyset @ (powerset @ X399)))=>(![X400:$i]:((in @ emptyset @ (powerset @ X400)))=>(![X401:$i, X402:$i, X403:$i]:(((in @ X402 @ (powerset @ X401))=>((in @ X403 @ X402)=>(in @ X403 @ X401))))=>(![X404:$i, X405:$i, X406:$i]:(((in @ X405 @ X406)=>((in @ X406 @ X404)=>(in @ X405 @ (setunion @ X404)))))=>(![X407:$i, X408:$i]:(((in @ X408 @ (setunion @ X407))=>![X409:$o]:((![X410:$i]:(((in @ X408 @ X410)=>((in @ X410 @ X407)=>(X409))))=>(X409)))))=>(![X411:$i, X412:$i]:(((in @ X412 @ X411)=>(in @ X412 @ (powerset @ (setunion @ X411)))))=>(![X413:$i > $o]:((?[X414:$i]:(((X413 @ X414)&![X415:$i]:(((X413 @ X415)=>((X414)=(X415))))))=>?[X416:$i]:(![X417:$i]:(((X413 @ X417)<=>((X417)=(X416)))))))=>(![X418:$i]:((((X418)!=(emptyset))=>?[X419:$i]:(((in @ X419 @ X418)&$true))))=>(![X420:$i, X421:$i]:(((in @ X420 @ (setadjoin @ X421 @ emptyset))=>((X420)=(X421))))=>(![X422:$i, X423:$i]:((((X422)!=(X423))=>~(in @ X423 @ (setadjoin @ X422 @ emptyset))))=>(![X424:$i, X425:$i]:((((X424)=(X425))=>(in @ X424 @ (setadjoin @ X425 @ emptyset))))=>(![X426:$i, X427:$i]:(((in @ X426 @ (setadjoin @ X427 @ emptyset))=>(in @ X427 @ (setadjoin @ X426 @ emptyset))))=>(![X428:$i, X429:$i, X430:$i]:(((in @ X430 @ (setadjoin @ X428 @ (setadjoin @ X429 @ emptyset)))=>(((X430)=(X428))|((X430)=(X429)))))=>(![X431:$i, X432:$i]:((in @ X431 @ (setadjoin @ X431 @ (setadjoin @ X432 @ emptyset))))=>(![X433:$i, X434:$i]:((in @ X434 @ (setadjoin @ X433 @ (setadjoin @ X434 @ emptyset))))=>(![X435:$i, X436:$i > $o]:((?[X437:$i]:(((in @ X437 @ X435)&(X436 @ X437)))=>(((dsetconstr @ X435 @ X436)=(emptyset))=>~($true))))=>(![X438:$i > $o, X439:$i]:(((in @ X439 @ emptyset)=>(X438 @ X439)))=>(![X440:$i, X441:$i > $o]:((~(![X442:$i]:(((in @ X442 @ X440)=>(X441 @ X442))))=>?[X443:$i]:(((in @ X443 @ X440)&~((X441 @ X443))))))=>(![X444:$i, X445:$i > $o]:((![X446:$i]:(((in @ X446 @ X444)=>~((X445 @ X446))))=>~(?[X447:$i]:(((in @ X447 @ X444)&(X445 @ X447))))))=>(![X448:$i, X449:$i > $o]:((~(?[X450:$i]:(((in @ X450 @ X448)&(X449 @ X450))))=>![X451:$i]:(((in @ X451 @ X448)=>~((X449 @ X451))))))=>(![X452:$i, X453:$i > $o]:((?[X454:$i]:(((in @ X454 @ X452)&~((X453 @ X454))))=>~(![X455:$i]:(((in @ X455 @ X452)=>(X453 @ X455))))))=>(![X456:$o]:(((X456)=>(in @ emptyset @ (prop2set @ ((X456))))))=>(![X457:$o]:(((X457)=>(set2prop @ (prop2set @ ((X457))))))=>(![X458:$i, X459:$i > $o]:((~(?[X460:$i]:(((in @ X460 @ X458)&(X459 @ X460))))=>![X461:$i]:(((in @ X461 @ X458)=>~((X459 @ X461))))))=>(![X462:$i, X463:$i > $o]:((~(![X464:$i]:(((in @ X464 @ X462)=>(X463 @ X464))))=>?[X465:$i]:(((in @ X465 @ X462)&~((X463 @ X465))))))=>(![X466:$i > $o]:((?[X467:$i]:(((X466 @ X467)&![X468:$i]:(((X466 @ X468)=>((X467)=(X468))))))=>?[X469:$i]:(((X466 @ X469)&![X470:$i]:(((X466 @ X470)=>((X469)=(X470))))))))=>(![X471:$i > $o]:((?[X472:$i]:((X471 @ X472))=>(![X473:$i, X474:$i]:(((X471 @ X473)=>((X471 @ X474)=>((X473)=(X474)))))=>?[X475:$i]:(((X471 @ X475)&![X476:$i]:(((X471 @ X476)=>((X475)=(X476)))))))))=>(![X477:$i > $o]:((?[X478:$i]:(![X479:$i]:(((X477 @ X479)<=>((X479)=(X478)))))=>?[X480:$i]:(((X477 @ X480)&![X481:$i]:(((X477 @ X481)=>((X480)=(X481))))))))=>(![X482:$i, X483:$i]:((((X482)=(X483))=>![X484:$i, X485:$i]:((((X484)=(X485))=>((in @ X484 @ X482)=>(in @ X485 @ X483))))))=>(![X486:$i, X487:$i]:((((X486)=(X487))=>![X488:$i, X489:$i]:((((X488)=(X489))=>((in @ X488 @ X486)<=>(in @ X489 @ X487))))))=>(![X490:$i > $o]:((?[X491:$i]:(((X490 @ X491)&![X492:$i]:(((X490 @ X492)=>((X491)=(X492))))))=>![X493:$i, X494:$i]:(((X490 @ X493)=>((X490 @ X494)=>((X493)=(X494)))))))=>(![X495:$i > $o, X496:$i > $o]:((![X497:$i, X498:$i]:((((X497)=(X498))=>((X495 @ X497)<=>(X496 @ X498))))=>(?[X499:$i]:(((X495 @ X499)&![X500:$i]:(((X495 @ X500)=>((X499)=(X500))))))<=>?[X501:$i]:(((X496 @ X501)&![X502:$i]:(((X496 @ X502)=>((X501)=(X502)))))))))=>(((emptyset)=(emptyset))=>(![X503:$i, X504:$i]:((((X503)=(X504))=>![X505:$i, X506:$i]:((((X505)=(X506))=>((setadjoin @ X503 @ X505)=(setadjoin @ X504 @ X506))))))=>(![X507:$i, X508:$i]:((((X507)=(X508))=>((powerset @ X507)=(powerset @ X508))))=>(![X509:$i, X510:$i]:((((X509)=(X510))=>((setunion @ X509)=(setunion @ X510))))=>(((omega)=(omega))=>(![X511:$i > $o]:((?[X512:$i]:(((X511 @ X512)&![X513:$i]:(((X511 @ X513)=>((X512)=(X513))))))=>![X514:$i, X515:$i]:(((X511 @ X514)=>((X511 @ X515)=>((X514)=(X515)))))))=>(![X516:$i > $o, X517:$i > $o]:((![X518:$i, X519:$i]:((((X518)=(X519))=>((X516 @ X518)<=>(X517 @ X519))))=>(?[X520:$i]:(((X516 @ X520)&![X521:$i]:(((X516 @ X521)=>((X520)=(X521))))))=>(?[X522:$i]:(((X517 @ X522)&![X523:$i]:(((X517 @ X523)=>((X522)=(X523))))))=>((descr @ X516)=(descr @ X517))))))=>(![X524:$i, X525:$i]:((((X524)=(X525))=>![X526:$i > $o, X527:$i > $o]:((![X528:$i]:(((in @ X528 @ X524)=>![X529:$i]:(((in @ X529 @ X525)=>(((X528)=(X529))=>((X526 @ X528)<=>(X527 @ X529)))))))=>((dsetconstr @ X524 @ X526)=(dsetconstr @ X525 @ X527))))))=>(![X530:$i, X531:$i]:((![X532:$i]:(((in @ X532 @ X530)=>(in @ X532 @ X531)))=>(subset @ X530 @ X531)))=>(![X533:$i, X534:$i]:((((X533)=(X534))=>(subset @ X534 @ X533)))=>(![X535:$i, X536:$i]:((((X535)=(X536))=>(subset @ X535 @ X536)))=>(![X537:$i, X538:$i]:((![X539:$i]:(((in @ X539 @ X537)=>(in @ X539 @ X538)))=>(subset @ X537 @ X538)))=>(![X540:$i]:((subset @ emptyset @ X540))=>(![X541:$i, X542:$i, X543:$i]:(((subset @ X541 @ X542)=>((in @ X543 @ X541)=>(in @ X543 @ X542))))=>(![X544:$i, X545:$i, X546:$i]:(((subset @ X544 @ X545)=>(~(in @ X546 @ X545)=>~(in @ X546 @ X544))))=>(![X547:$i, X548:$i, X549:$i]:(((in @ X549 @ X547)=>(~(in @ X549 @ X548)=>~(subset @ X547 @ X548))))=>(![X550:$i, X551:$i]:((~(subset @ X550 @ X551)=>((X550)!=(X551))))=>(![X552:$i, X553:$i, X554:$i]:(((in @ X554 @ X552)=>(~(in @ X554 @ X553)=>((X552)!=(X553)))))=>(![X555:$i]:((subset @ X555 @ X555))=>(![X556:$i, X557:$i, X558:$i]:(((subset @ X556 @ X557)=>((subset @ X557 @ X558)=>(subset @ X556 @ X558))))=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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)],[c_0_105, setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_106]), foundationAx]), wellorderingAx]), c_0_107]), c_0_108]), c_0_109]), c_0_110]), c_0_111]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_112]), setext]), emptyI]), noeltsimpempty]), c_0_113]), c_0_114]), c_0_115]), c_0_116]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_117]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_118]), c_0_119]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_120]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_121]), c_0_122]), c_0_123]), inCongP]), in__Cong]), c_0_124]), c_0_125]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_126]), c_0_127]), c_0_128]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans])])]), c_0_129])).
% 4.69/1.02 thf(c_0_131, negated_conjecture, ![X559:$i, X560:$i, X562:$i, X563:$i, X564:$i, X565:$i, X566:$i, X567:$i, X568:$i, X569:$i, X570:$i, X572:$i, X573:$i, X575:$i, X576:$i, X577:$i, X578:$i, X579:$i, X581:$i, X582:$i > $i > $o, X583:$i, X585:$i, X588:$i, X590:$i, X591:$i, X592:$i, X593:$i, X595:$i, X596:$i > $o, X597:$i, X599:$i, X600:$i > $o, X601:$i, X602:$i, X603:$i > $o, X604:$i, X605:$i, X606:$i > $o, X607:$i, X608:$i > $o, X609:$i, X612:$i, X613:$o, X614:$i, X615:$i, X616:$o, X617:$i, X618:$i, X619:$i > $o, X620:$i, X623:$i, X624:$i, X627:$i, X629:$i, X631:$i, X632:$i > $o, X633:$i, X634:$i, X636:$i, X637:$i > $o, X638:$i, X639:$i, X640:$i, X641:$i, X642:$i, X643:$i, X644:$i, X645:$i, X646:$i, X647:$i, X648:$i, X649:$o, X650:$i, X651:$i, X652:$i, X653:$i, X654:$i, X655:$i, X657:$i, X658:$i, X659:$i, X660:$i, X661:$i, X662:$i, X663:$i, X664:$i, X665:$i, X666:$i, X667:$o, X669:$i, X670:$i, X671:$i > $o, X672:$i, X675:$i, X676:$i, X677:$i, X679:$i, X680:$i, X681:$i, X682:$i, X683:$i, X684:$i, X685:$i, X686:$i, X687:$i, X688:$i, X689:$i, X690:$i, X691:$i, X692:$i, X693:$i, X694:$i, X695:$i > $o, X696:$i, X697:$i > $o, X698:$i, X699:$i, X700:$i > $o, X701:$i, X703:$i, X704:$i > $o, X706:$i, X707:$i, X708:$i > $o, X710:$i, X711:$i, X712:$i > $o, X713:$i, X715:$o, X716:$o, X717:$i, X718:$i > $o, X720:$i, X721:$i, X722:$i > $o, X723:$i, X725:$i > $o, X726:$i, X729:$i, X730:$i > $o, X731:$i, X735:$i, X736:$i > $o, X737:$i, X740:$i, X741:$i, X742:$i, X743:$i, X744:$i, X745:$i, X746:$i, X747:$i, X748:$i, X749:$i > $o, X750:$i, X752:$i, X753:$i, X754:$i > $o, X755:$i > $o, X758:$i, X761:$i, X762:$i, X765:$i, X766:$i, X767:$i, X768:$i, X769:$i, X770:$i, X771:$i, X772:$i, X773:$i, X774:$i > $o, X775:$i, X777:$i, X778:$i, X779:$i > $o, X780:$i > $o, X783:$i, X785:$i, X787:$i, X788:$i, X789:$i > $o, X790:$i > $o, X793:$i, X794:$i, X796:$i, X797:$i, X798:$i, X799:$i, X800:$i, X801:$i, X803:$i, X804:$i, X805:$i, X806:$i, X807:$i, X808:$i, X809:$i, X810:$i, X811:$i, X812:$i, X813:$i, X814:$i, X815:$i, X816:$i, X817:$i, X818:$i, X819:$i, X820:$i, X821:$i]:((((~(in @ (esk1_2 @ X559 @ X560) @ X559)|~(in @ (esk1_2 @ X559 @ X560) @ X560)|((X559)=(X560)))&((in @ (esk1_2 @ X559 @ X560) @ X559)|(in @ (esk1_2 @ X559 @ X560) @ X560)|((X559)=(X560))))&(~(in @ X562 @ emptyset)&(((~(in @ X565 @ (setadjoin @ X563 @ X564))|(((X565)=(X563))|(in @ X565 @ X564)))&((((X565)!=(X563))|(in @ X565 @ (setadjoin @ X563 @ X564)))&(~(in @ X565 @ X564)|(in @ X565 @ (setadjoin @ X563 @ X564)))))&(((~(in @ X567 @ (powerset @ X566))|(~(in @ X568 @ X567)|(in @ X568 @ X566)))&(((in @ (esk2_2 @ X569 @ X570) @ X570)|(in @ X570 @ (powerset @ X569)))&(~(in @ (esk2_2 @ X569 @ X570) @ X569)|(in @ X570 @ (powerset @ X569)))))&(((((in @ X573 @ (esk3_2 @ X572 @ X573))|~(in @ X573 @ (setunion @ X572)))&((in @ (esk3_2 @ X572 @ X573) @ X572)|~(in @ X573 @ (setunion @ X572))))&(~(in @ X576 @ X577)|~(in @ X577 @ X575)|(in @ X576 @ (setunion @ X575))))&((in @ emptyset @ omega)&((~(in @ X578 @ omega)|(in @ (setadjoin @ X578 @ X578) @ omega))&(((((in @ (esk4_1 @ X579) @ omega)|~(in @ emptyset @ X579)|(~(in @ X581 @ omega)|(in @ X581 @ X579)))&((in @ (esk4_1 @ X579) @ X579)|~(in @ emptyset @ X579)|(~(in @ X581 @ omega)|(in @ X581 @ X579))))&(~(in @ (setadjoin @ (esk4_1 @ X579) @ (esk4_1 @ X579)) @ X579)|~(in @ emptyset @ X579)|(~(in @ X581 @ omega)|(in @ X581 @ X579))))&((((((in @ (esk8_3 @ X582 @ X583 @ X588) @ X583)|~(in @ X588 @ (esk7_2 @ X582 @ X583))|(in @ (esk5_2 @ X582 @ X583) @ X583))&((X582 @ (esk8_3 @ X582 @ X583 @ X588) @ X588)|~(in @ X588 @ (esk7_2 @ X582 @ X583))|(in @ (esk5_2 @ X582 @ X583) @ X583)))&(~(in @ X591 @ X583)|~(X582 @ X591 @ X590)|(in @ X590 @ (esk7_2 @ X582 @ X583))|(in @ (esk5_2 @ X582 @ X583) @ X583)))&(((((in @ (esk8_3 @ X582 @ X583 @ X588) @ X583)|~(in @ X588 @ (esk7_2 @ X582 @ X583))|((X582 @ (esk5_2 @ X582 @ X583) @ (esk6_3 @ X582 @ X583 @ X585))|~(X582 @ (esk5_2 @ X582 @ X583) @ X585)))&((X582 @ (esk8_3 @ X582 @ X583 @ X588) @ X588)|~(in @ X588 @ (esk7_2 @ X582 @ X583))|((X582 @ (esk5_2 @ X582 @ X583) @ (esk6_3 @ X582 @ X583 @ X585))|~(X582 @ (esk5_2 @ X582 @ X583) @ X585))))&(~(in @ X591 @ X583)|~(X582 @ X591 @ X590)|(in @ X590 @ (esk7_2 @ X582 @ X583))|((X582 @ (esk5_2 @ X582 @ X583) @ (esk6_3 @ X582 @ X583 @ X585))|~(X582 @ (esk5_2 @ X582 @ X583) @ X585))))&((((in @ (esk8_3 @ X582 @ X583 @ X588) @ X583)|~(in @ X588 @ (esk7_2 @ X582 @ X583))|(((X585)!=(esk6_3 @ X582 @ X583 @ X585))|~(X582 @ (esk5_2 @ X582 @ X583) @ X585)))&((X582 @ (esk8_3 @ X582 @ X583 @ X588) @ X588)|~(in @ X588 @ (esk7_2 @ X582 @ X583))|(((X585)!=(esk6_3 @ X582 @ X583 @ X585))|~(X582 @ (esk5_2 @ X582 @ X583) @ X585))))&(~(in @ X591 @ X583)|~(X582 @ X591 @ X590)|(in @ X590 @ (esk7_2 @ X582 @ X583))|(((X585)!=(esk6_3 @ X582 @ X583 @ X585))|~(X582 @ (esk5_2 @ X582 @ X583) @ X585))))))&((((in @ (esk9_1 @ X592) @ X592)|~(in @ X593 @ X592))&(~(in @ X595 @ (esk9_1 @ X592))|~(in @ X595 @ X592)|~(in @ X593 @ X592)))&((epred1_0)&((((X596 @ (esk10_2 @ X596 @ X597))|~(X596 @ X597)|(X596 @ (descr @ X596)))&(((X597)!=(esk10_2 @ X596 @ X597))|~(X596 @ X597)|(X596 @ (descr @ X596))))&((~(in @ X601 @ X599)|(~(X600 @ X601)|(in @ X601 @ (dsetconstr @ X599 @ X600))))&((~(in @ X604 @ (dsetconstr @ X602 @ X603))|(in @ X604 @ X602))&((~(in @ X607 @ (dsetconstr @ X605 @ X606))|(X606 @ X607))&(((((X608 @ (esk12_1 @ X608))|((X608 @ (esk11_2 @ X608 @ X609))|~(X608 @ X609)))&(~(X608 @ X612)|((esk12_1 @ X608)=(X612))|((X608 @ (esk11_2 @ X608 @ X609))|~(X608 @ X609))))&(((X608 @ (esk12_1 @ X608))|(((X609)!=(esk11_2 @ X608 @ X609))|~(X608 @ X609)))&(~(X608 @ X612)|((esk12_1 @ X608)=(X612))|(((X609)!=(esk11_2 @ X608 @ X609))|~(X608 @ X609)))))&((~(in @ X614 @ (prop2set @ ((X613))))|(X613))&((~(in @ X615 @ emptyset)|(X616))&((~(in @ X617 @ emptyset)|~($true))&(~(in @ X618 @ emptyset)&((((X619 @ (esk13_2 @ X619 @ X620))|~(X619 @ X620)|(X619 @ (esk14_1 @ X619)))&(((X620)!=(esk13_2 @ X619 @ X620))|~(X619 @ X620)|(X619 @ (esk14_1 @ X619))))&(((((in @ (esk16_2 @ X623 @ X624) @ X624)|((X623)=(X624))|(in @ (esk15_2 @ X623 @ X624) @ X623))&(~(in @ (esk16_2 @ X623 @ X624) @ X623)|((X623)=(X624))|(in @ (esk15_2 @ X623 @ X624) @ X623)))&(((in @ (esk16_2 @ X623 @ X624) @ X624)|((X623)=(X624))|~(in @ (esk15_2 @ X623 @ X624) @ X624))&(~(in @ (esk16_2 @ X623 @ X624) @ X623)|((X623)=(X624))|~(in @ (esk15_2 @ X623 @ X624) @ X624))))&(((in @ (esk17_1 @ X627) @ X627)|((X627)=(emptyset)))&(((in @ (esk18_1 @ X629) @ X629)|((X629)=(emptyset)))&(((~(in @ X633 @ (dsetconstr @ X631 @ X632))|(X632 @ X633)|~(in @ X633 @ X631))&(~(X632 @ X633)|(in @ X633 @ (dsetconstr @ X631 @ X632))|~(in @ X633 @ X631)))&((((X634)=(emptyset))|(in @ (esk19_1 @ X634) @ X634))&((~(in @ X638 @ X636)|(~(X637 @ X638)|((dsetconstr @ X636 @ X637)!=(emptyset))))&((~(in @ X640 @ X639)|((X639)!=(emptyset)))&((in @ X641 @ (setadjoin @ X641 @ X642))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X645 @ X644)|(in @ X645 @ (setadjoin @ X643 @ X644)))&(((((in @ X648 @ X647)|(X649)|((X648)=(X646))|~(in @ X648 @ (setadjoin @ X646 @ X647)))&(~(X649)|(X649)|((X648)=(X646))|~(in @ X648 @ (setadjoin @ X646 @ X647))))&(((in @ X648 @ X647)|(X649)|~(X649)|~(in @ X648 @ (setadjoin @ X646 @ X647)))&(~(X649)|(X649)|~(X649)|~(in @ X648 @ (setadjoin @ X646 @ X647)))))&((~(in @ X652 @ (setadjoin @ X650 @ X651))|(((X652)=(X650))|(in @ X652 @ X651)))&(((dsetconstr @ X653 @ (^[Z0:$i]:($true)))=(X653))&((((in @ (esk20_2 @ X654 @ X655) @ X655)|(in @ X655 @ (powerset @ X654)))&(~(in @ (esk20_2 @ X654 @ X655) @ X654)|(in @ X655 @ (powerset @ X654))))&((in @ emptyset @ (powerset @ X657))&((in @ emptyset @ (powerset @ X658))&((~(in @ X660 @ (powerset @ X659))|(~(in @ X661 @ X660)|(in @ X661 @ X659)))&((~(in @ X663 @ X664)|(~(in @ X664 @ X662)|(in @ X663 @ (setunion @ X662))))&((((in @ X666 @ (esk21_3 @ X665 @ X666 @ X667))|(X667)|~(in @ X666 @ (setunion @ X665)))&(((in @ (esk21_3 @ X665 @ X666 @ X667) @ X665)|(X667)|~(in @ X666 @ (setunion @ X665)))&(~(X667)|(X667)|~(in @ X666 @ (setunion @ X665)))))&((~(in @ X670 @ X669)|(in @ X670 @ (powerset @ (setunion @ X669))))&((((~(X671 @ X675)|((X675)=(esk23_1 @ X671))|((X671 @ (esk22_2 @ X671 @ X672))|~(X671 @ X672)))&(((X676)!=(esk23_1 @ X671))|(X671 @ X676)|((X671 @ (esk22_2 @ X671 @ X672))|~(X671 @ X672))))&((~(X671 @ X675)|((X675)=(esk23_1 @ X671))|(((X672)!=(esk22_2 @ X671 @ X672))|~(X671 @ X672)))&(((X676)!=(esk23_1 @ X671))|(X671 @ X676)|(((X672)!=(esk22_2 @ X671 @ X672))|~(X671 @ X672)))))&((((in @ (esk24_1 @ X677) @ X677)|((X677)=(emptyset)))&(($true)|((X677)=(emptyset))))&((~(in @ X679 @ (setadjoin @ X680 @ emptyset))|((X679)=(X680)))&((((X681)=(X682))|~(in @ X682 @ (setadjoin @ X681 @ emptyset)))&((((X683)!=(X684))|(in @ X683 @ (setadjoin @ X684 @ emptyset)))&((~(in @ X685 @ (setadjoin @ X686 @ emptyset))|(in @ X686 @ (setadjoin @ X685 @ emptyset)))&((~(in @ X689 @ (setadjoin @ X687 @ (setadjoin @ X688 @ emptyset)))|(((X689)=(X687))|((X689)=(X688))))&((in @ X690 @ (setadjoin @ X690 @ (setadjoin @ X691 @ emptyset)))&((in @ X693 @ (setadjoin @ X692 @ (setadjoin @ X693 @ emptyset)))&((~(in @ X696 @ X694)|~(X695 @ X696)|(((dsetconstr @ X694 @ X695)!=(emptyset))|~($true)))&((~(in @ X698 @ emptyset)|(X697 @ X698))&((((in @ (esk25_2 @ X699 @ X700) @ X699)|(~(in @ X701 @ X699)|(X700 @ X701)))&(~(X700 @ (esk25_2 @ X699 @ X700))|(~(in @ X701 @ X699)|(X700 @ X701))))&((((in @ (esk26_2 @ X703 @ X704) @ X703)|(~(in @ X706 @ X703)|~(X704 @ X706)))&((X704 @ (esk26_2 @ X703 @ X704))|(~(in @ X706 @ X703)|~(X704 @ X706))))&((((in @ (esk27_2 @ X707 @ X708) @ X707)|(~(in @ X710 @ X707)|~(X708 @ X710)))&((X708 @ (esk27_2 @ X707 @ X708))|(~(in @ X710 @ X707)|~(X708 @ X710))))&((((in @ (esk28_2 @ X711 @ X712) @ X711)|(~(in @ X713 @ X711)|(X712 @ X713)))&(~(X712 @ (esk28_2 @ X711 @ X712))|(~(in @ X713 @ X711)|(X712 @ X713))))&((~(X715)|(in @ emptyset @ (prop2set @ ((X715)))))&((~(X716)|(set2prop @ (prop2set @ ((X716)))))&((((in @ (esk29_2 @ X717 @ X718) @ X717)|(~(in @ X720 @ X717)|~(X718 @ X720)))&((X718 @ (esk29_2 @ X717 @ X718))|(~(in @ X720 @ X717)|~(X718 @ X720))))&((((in @ (esk30_2 @ X721 @ X722) @ X721)|(~(in @ X723 @ X721)|(X722 @ X723)))&(~(X722 @ (esk30_2 @ X721 @ X722))|(~(in @ X723 @ X721)|(X722 @ X723))))&(((((X725 @ (esk32_1 @ X725))|((X725 @ (esk31_2 @ X725 @ X726))|~(X725 @ X726)))&(~(X725 @ X729)|((esk32_1 @ X725)=(X729))|((X725 @ (esk31_2 @ X725 @ X726))|~(X725 @ X726))))&(((X725 @ (esk32_1 @ X725))|(((X726)!=(esk31_2 @ X725 @ X726))|~(X725 @ X726)))&(~(X725 @ X729)|((esk32_1 @ X725)=(X729))|(((X726)!=(esk31_2 @ X725 @ X726))|~(X725 @ X726)))))&(((((X730 @ (esk35_1 @ X730))|(X730 @ (esk33_1 @ X730))|~(X730 @ X731))&(~(X730 @ X735)|((esk35_1 @ X730)=(X735))|(X730 @ (esk33_1 @ X730))|~(X730 @ X731)))&((((X730 @ (esk35_1 @ X730))|(X730 @ (esk34_1 @ X730))|~(X730 @ X731))&(~(X730 @ X735)|((esk35_1 @ X730)=(X735))|(X730 @ (esk34_1 @ X730))|~(X730 @ X731)))&(((X730 @ (esk35_1 @ X730))|((esk33_1 @ X730)!=(esk34_1 @ X730))|~(X730 @ X731))&(~(X730 @ X735)|((esk35_1 @ X730)=(X735))|((esk33_1 @ X730)!=(esk34_1 @ X730))|~(X730 @ X731)))))&(((((X736 @ (esk37_1 @ X736))|(~(X736 @ (esk36_2 @ X736 @ X737))|((esk36_2 @ X736 @ X737)!=(X737))))&(~(X736 @ X740)|((esk37_1 @ X736)=(X740))|(~(X736 @ (esk36_2 @ X736 @ X737))|((esk36_2 @ X736 @ X737)!=(X737)))))&(((X736 @ (esk37_1 @ X736))|((X736 @ (esk36_2 @ X736 @ X737))|((esk36_2 @ X736 @ X737)=(X737))))&(~(X736 @ X740)|((esk37_1 @ X736)=(X740))|((X736 @ (esk36_2 @ X736 @ X737))|((esk36_2 @ X736 @ X737)=(X737))))))&((((X741)!=(X742))|(((X743)!=(X744))|(~(in @ X743 @ X741)|(in @ X744 @ X742))))&(((~(in @ X747 @ X745)|(in @ X748 @ X746)|((X747)!=(X748))|((X745)!=(X746)))&(~(in @ X748 @ X746)|(in @ X747 @ X745)|((X747)!=(X748))|((X745)!=(X746))))&((((X749 @ (esk38_2 @ X749 @ X750))|~(X749 @ X750)|(~(X749 @ X752)|(~(X749 @ X753)|((X752)=(X753)))))&(((X750)!=(esk38_2 @ X749 @ X750))|~(X749 @ X750)|(~(X749 @ X752)|(~(X749 @ X753)|((X752)=(X753))))))&(((((((X755 @ (esk42_2 @ X754 @ X755))|((X754 @ (esk41_3 @ X754 @ X755 @ X758))|~(X754 @ X758))|((esk39_2 @ X754 @ X755)=(esk40_2 @ X754 @ X755)))&(~(X755 @ X761)|((esk42_2 @ X754 @ X755)=(X761))|((X754 @ (esk41_3 @ X754 @ X755 @ X758))|~(X754 @ X758))|((esk39_2 @ X754 @ X755)=(esk40_2 @ X754 @ X755))))&(((X755 @ (esk42_2 @ X754 @ X755))|(((X758)!=(esk41_3 @ X754 @ X755 @ X758))|~(X754 @ X758))|((esk39_2 @ X754 @ X755)=(esk40_2 @ X754 @ X755)))&(~(X755 @ X761)|((esk42_2 @ X754 @ X755)=(X761))|(((X758)!=(esk41_3 @ X754 @ X755 @ X758))|~(X754 @ X758))|((esk39_2 @ X754 @ X755)=(esk40_2 @ X754 @ X755)))))&((((X754 @ (esk44_2 @ X754 @ X755))|((X755 @ (esk43_3 @ X754 @ X755 @ X762))|~(X755 @ X762))|((esk39_2 @ X754 @ X755)=(esk40_2 @ X754 @ X755)))&(~(X754 @ X765)|((esk44_2 @ X754 @ X755)=(X765))|((X755 @ (esk43_3 @ X754 @ X755 @ X762))|~(X755 @ X762))|((esk39_2 @ X754 @ X755)=(esk40_2 @ X754 @ X755))))&(((X754 @ (esk44_2 @ X754 @ X755))|(((X762)!=(esk43_3 @ X754 @ X755 @ X762))|~(X755 @ X762))|((esk39_2 @ X754 @ X755)=(esk40_2 @ X754 @ X755)))&(~(X754 @ X765)|((esk44_2 @ X754 @ X755)=(X765))|(((X762)!=(esk43_3 @ X754 @ X755 @ X762))|~(X755 @ X762))|((esk39_2 @ X754 @ X755)=(esk40_2 @ X754 @ X755))))))&((((((X755 @ (esk42_2 @ X754 @ X755))|((X754 @ (esk41_3 @ X754 @ X755 @ X758))|~(X754 @ X758))|(~(X754 @ (esk39_2 @ X754 @ X755))|~(X755 @ (esk40_2 @ X754 @ X755))))&(~(X755 @ X761)|((esk42_2 @ X754 @ X755)=(X761))|((X754 @ (esk41_3 @ X754 @ X755 @ X758))|~(X754 @ X758))|(~(X754 @ (esk39_2 @ X754 @ X755))|~(X755 @ (esk40_2 @ X754 @ X755)))))&(((X755 @ (esk42_2 @ X754 @ X755))|(((X758)!=(esk41_3 @ X754 @ X755 @ X758))|~(X754 @ X758))|(~(X754 @ (esk39_2 @ X754 @ X755))|~(X755 @ (esk40_2 @ X754 @ X755))))&(~(X755 @ X761)|((esk42_2 @ X754 @ X755)=(X761))|(((X758)!=(esk41_3 @ X754 @ X755 @ X758))|~(X754 @ X758))|(~(X754 @ (esk39_2 @ X754 @ X755))|~(X755 @ (esk40_2 @ X754 @ X755))))))&((((X754 @ (esk44_2 @ X754 @ X755))|((X755 @ (esk43_3 @ X754 @ X755 @ X762))|~(X755 @ X762))|(~(X754 @ (esk39_2 @ X754 @ X755))|~(X755 @ (esk40_2 @ X754 @ X755))))&(~(X754 @ X765)|((esk44_2 @ X754 @ X755)=(X765))|((X755 @ (esk43_3 @ X754 @ X755 @ X762))|~(X755 @ X762))|(~(X754 @ (esk39_2 @ X754 @ X755))|~(X755 @ (esk40_2 @ X754 @ X755)))))&(((X754 @ (esk44_2 @ X754 @ X755))|(((X762)!=(esk43_3 @ X754 @ X755 @ X762))|~(X755 @ X762))|(~(X754 @ (esk39_2 @ X754 @ X755))|~(X755 @ (esk40_2 @ X754 @ X755))))&(~(X754 @ X765)|((esk44_2 @ X754 @ X755)=(X765))|(((X762)!=(esk43_3 @ X754 @ X755 @ X762))|~(X755 @ X762))|(~(X754 @ (esk39_2 @ X754 @ X755))|~(X755 @ (esk40_2 @ X754 @ X755)))))))&(((((X755 @ (esk42_2 @ X754 @ X755))|((X754 @ (esk41_3 @ X754 @ X755 @ X758))|~(X754 @ X758))|((X754 @ (esk39_2 @ X754 @ X755))|(X755 @ (esk40_2 @ X754 @ X755))))&(~(X755 @ X761)|((esk42_2 @ X754 @ X755)=(X761))|((X754 @ (esk41_3 @ X754 @ X755 @ X758))|~(X754 @ X758))|((X754 @ (esk39_2 @ X754 @ X755))|(X755 @ (esk40_2 @ X754 @ X755)))))&(((X755 @ (esk42_2 @ X754 @ X755))|(((X758)!=(esk41_3 @ X754 @ X755 @ X758))|~(X754 @ X758))|((X754 @ (esk39_2 @ X754 @ X755))|(X755 @ (esk40_2 @ X754 @ X755))))&(~(X755 @ X761)|((esk42_2 @ X754 @ X755)=(X761))|(((X758)!=(esk41_3 @ X754 @ X755 @ X758))|~(X754 @ X758))|((X754 @ (esk39_2 @ X754 @ X755))|(X755 @ (esk40_2 @ X754 @ X755))))))&((((X754 @ (esk44_2 @ X754 @ X755))|((X755 @ (esk43_3 @ X754 @ X755 @ X762))|~(X755 @ X762))|((X754 @ (esk39_2 @ X754 @ X755))|(X755 @ (esk40_2 @ X754 @ X755))))&(~(X754 @ X765)|((esk44_2 @ X754 @ X755)=(X765))|((X755 @ (esk43_3 @ X754 @ X755 @ X762))|~(X755 @ X762))|((X754 @ (esk39_2 @ X754 @ X755))|(X755 @ (esk40_2 @ X754 @ X755)))))&(((X754 @ (esk44_2 @ X754 @ X755))|(((X762)!=(esk43_3 @ X754 @ X755 @ X762))|~(X755 @ X762))|((X754 @ (esk39_2 @ X754 @ X755))|(X755 @ (esk40_2 @ X754 @ X755))))&(~(X754 @ X765)|((esk44_2 @ X754 @ X755)=(X765))|(((X762)!=(esk43_3 @ X754 @ X755 @ X762))|~(X755 @ X762))|((X754 @ (esk39_2 @ X754 @ X755))|(X755 @ (esk40_2 @ X754 @ X755)))))))))&(((emptyset)=(emptyset))&((((X766)!=(X767))|(((X768)!=(X769))|((setadjoin @ X766 @ X768)=(setadjoin @ X767 @ X769))))&((((X770)!=(X771))|((powerset @ X770)=(powerset @ X771)))&((((X772)!=(X773))|((setunion @ X772)=(setunion @ X773)))&(((omega)=(omega))&((((X774 @ (esk45_2 @ X774 @ X775))|~(X774 @ X775)|(~(X774 @ X777)|(~(X774 @ X778)|((X777)=(X778)))))&(((X775)!=(esk45_2 @ X774 @ X775))|~(X774 @ X775)|(~(X774 @ X777)|(~(X774 @ X778)|((X777)=(X778))))))&((((((X780 @ (esk49_3 @ X779 @ X780 @ X785))|~(X780 @ X785)|((descr @ X779)=(descr @ X780))|((X779 @ (esk48_3 @ X779 @ X780 @ X783))|~(X779 @ X783))|((esk46_2 @ X779 @ X780)=(esk47_2 @ X779 @ X780)))&(((X785)!=(esk49_3 @ X779 @ X780 @ X785))|~(X780 @ X785)|((descr @ X779)=(descr @ X780))|((X779 @ (esk48_3 @ X779 @ X780 @ X783))|~(X779 @ X783))|((esk46_2 @ X779 @ X780)=(esk47_2 @ X779 @ X780))))&(((X780 @ (esk49_3 @ X779 @ X780 @ X785))|~(X780 @ X785)|((descr @ X779)=(descr @ X780))|(((X783)!=(esk48_3 @ X779 @ X780 @ X783))|~(X779 @ X783))|((esk46_2 @ X779 @ X780)=(esk47_2 @ X779 @ X780)))&(((X785)!=(esk49_3 @ X779 @ X780 @ X785))|~(X780 @ X785)|((descr @ X779)=(descr @ X780))|(((X783)!=(esk48_3 @ X779 @ X780 @ X783))|~(X779 @ X783))|((esk46_2 @ X779 @ X780)=(esk47_2 @ X779 @ X780)))))&(((((X780 @ (esk49_3 @ X779 @ X780 @ X785))|~(X780 @ X785)|((descr @ X779)=(descr @ X780))|((X779 @ (esk48_3 @ X779 @ X780 @ X783))|~(X779 @ X783))|(~(X779 @ (esk46_2 @ X779 @ X780))|~(X780 @ (esk47_2 @ X779 @ X780))))&(((X785)!=(esk49_3 @ X779 @ X780 @ X785))|~(X780 @ X785)|((descr @ X779)=(descr @ X780))|((X779 @ (esk48_3 @ X779 @ X780 @ X783))|~(X779 @ X783))|(~(X779 @ (esk46_2 @ X779 @ X780))|~(X780 @ (esk47_2 @ X779 @ X780)))))&(((X780 @ (esk49_3 @ X779 @ X780 @ X785))|~(X780 @ X785)|((descr @ X779)=(descr @ X780))|(((X783)!=(esk48_3 @ X779 @ X780 @ X783))|~(X779 @ X783))|(~(X779 @ (esk46_2 @ X779 @ X780))|~(X780 @ (esk47_2 @ X779 @ X780))))&(((X785)!=(esk49_3 @ X779 @ X780 @ X785))|~(X780 @ X785)|((descr @ X779)=(descr @ X780))|(((X783)!=(esk48_3 @ X779 @ X780 @ X783))|~(X779 @ X783))|(~(X779 @ (esk46_2 @ X779 @ X780))|~(X780 @ (esk47_2 @ X779 @ X780))))))&((((X780 @ (esk49_3 @ X779 @ X780 @ X785))|~(X780 @ X785)|((descr @ X779)=(descr @ X780))|((X779 @ (esk48_3 @ X779 @ X780 @ X783))|~(X779 @ X783))|((X779 @ (esk46_2 @ X779 @ X780))|(X780 @ (esk47_2 @ X779 @ X780))))&(((X785)!=(esk49_3 @ X779 @ X780 @ X785))|~(X780 @ X785)|((descr @ X779)=(descr @ X780))|((X779 @ (esk48_3 @ X779 @ X780 @ X783))|~(X779 @ X783))|((X779 @ (esk46_2 @ X779 @ X780))|(X780 @ (esk47_2 @ X779 @ X780)))))&(((X780 @ (esk49_3 @ X779 @ X780 @ X785))|~(X780 @ X785)|((descr @ X779)=(descr @ X780))|(((X783)!=(esk48_3 @ X779 @ X780 @ X783))|~(X779 @ X783))|((X779 @ (esk46_2 @ X779 @ X780))|(X780 @ (esk47_2 @ X779 @ X780))))&(((X785)!=(esk49_3 @ X779 @ X780 @ X785))|~(X780 @ X785)|((descr @ X779)=(descr @ X780))|(((X783)!=(esk48_3 @ X779 @ X780 @ X783))|~(X779 @ X783))|((X779 @ (esk46_2 @ X779 @ X780))|(X780 @ (esk47_2 @ X779 @ X780))))))))&((((in @ (esk50_4 @ X787 @ X788 @ X789 @ X790) @ X787)|((dsetconstr @ X787 @ X789)=(dsetconstr @ X788 @ X790))|((X787)!=(X788)))&(((in @ (esk51_4 @ X787 @ X788 @ X789 @ X790) @ X788)|((dsetconstr @ X787 @ X789)=(dsetconstr @ X788 @ X790))|((X787)!=(X788)))&((((esk50_4 @ X787 @ X788 @ X789 @ X790)=(esk51_4 @ X787 @ X788 @ X789 @ X790))|((dsetconstr @ X787 @ X789)=(dsetconstr @ X788 @ X790))|((X787)!=(X788)))&((~(X789 @ (esk50_4 @ X787 @ X788 @ X789 @ X790))|~(X790 @ (esk51_4 @ X787 @ X788 @ X789 @ X790))|((dsetconstr @ X787 @ X789)=(dsetconstr @ X788 @ X790))|((X787)!=(X788)))&((X789 @ (esk50_4 @ X787 @ X788 @ X789 @ X790))|(X790 @ (esk51_4 @ X787 @ X788 @ X789 @ X790))|((dsetconstr @ X787 @ X789)=(dsetconstr @ X788 @ X790))|((X787)!=(X788)))))))&((((in @ (esk52_2 @ X793 @ X794) @ X793)|(subset @ X793 @ X794))&(~(in @ (esk52_2 @ X793 @ X794) @ X794)|(subset @ X793 @ X794)))&((((X796)!=(X797))|(subset @ X797 @ X796))&((((X798)!=(X799))|(subset @ X798 @ X799))&((((in @ (esk53_2 @ X800 @ X801) @ X800)|(subset @ X800 @ X801))&(~(in @ (esk53_2 @ X800 @ X801) @ X801)|(subset @ X800 @ X801)))&((subset @ emptyset @ X803)&((~(subset @ X804 @ X805)|(~(in @ X806 @ X804)|(in @ X806 @ X805)))&((~(subset @ X807 @ X808)|((in @ X809 @ X808)|~(in @ X809 @ X807)))&((~(in @ X812 @ X810)|((in @ X812 @ X811)|~(subset @ X810 @ X811)))&(((subset @ X813 @ X814)|((X813)!=(X814)))&((~(in @ X817 @ X815)|((in @ X817 @ X816)|((X815)!=(X816))))&((subset @ X818 @ X818)&((~(subset @ X819 @ X820)|(~(subset @ X820 @ X821)|(subset @ X819 @ X821)))&~(subset @ esk55_0 @ (setadjoin @ 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_130])])])])])])])).
% 4.69/1.02 thf(c_0_132, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X2 @ X3)|~((in @ (esk52_2 @ X2 @ X3) @ X3)))), inference(split_conjunct,[status(thm)],[c_0_131])).
% 4.69/1.02 thf(c_0_133, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X4 @ X3))|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_131])).
% 4.69/1.02 thf(c_0_134, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((subset @ X2 @ (setadjoin @ X3 @ X4))|~((in @ (esk52_2 @ X2 @ (setadjoin @ X3 @ X4)) @ X4)))), inference(spm,[status(thm)],[c_0_132, c_0_133])).
% 4.69/1.02 thf(c_0_135, negated_conjecture, ![X2:$i, X3:$i]:(((in @ (esk52_2 @ X2 @ X3) @ X2)|(subset @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_131])).
% 4.69/1.02 thf(c_0_136, negated_conjecture, ~((subset @ esk55_0 @ (setadjoin @ esk54_0 @ esk55_0))), inference(split_conjunct,[status(thm)],[c_0_131])).
% 4.69/1.02 thf(c_0_137, negated_conjecture, ![X3:$i, X2:$i]:((subset @ X2 @ (setadjoin @ X3 @ X2))), inference(spm,[status(thm)],[c_0_134, c_0_135])).
% 4.69/1.02 thf(c_0_138, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_136, c_0_137])]), ['proof']).
% 4.69/1.02 % SZS output end CNFRefutation
% 4.69/1.02 % Parsed axioms : 192
% 4.69/1.02 % Removed by relevancy pruning/SinE : 0
% 4.69/1.02 % Initial clauses : 300
% 4.69/1.02 % Removed in clause preprocessing : 116
% 4.69/1.02 % Initial clauses in saturation : 184
% 4.69/1.02 % Processed clauses : 1177
% 4.69/1.02 % ...of these trivial : 45
% 4.69/1.02 % ...subsumed : 383
% 4.69/1.02 % ...remaining for further processing : 749
% 4.69/1.02 % Other redundant clauses eliminated : 49
% 4.69/1.02 % Clauses deleted for lack of memory : 0
% 4.69/1.02 % Backward-subsumed : 0
% 4.69/1.02 % Backward-rewritten : 10
% 4.69/1.02 % Generated clauses : 22922
% 4.69/1.02 % ...of the previous two non-redundant : 21166
% 4.69/1.02 % ...aggressively subsumed : 0
% 4.69/1.02 % Contextual simplify-reflections : 0
% 4.69/1.02 % Paramodulations : 22414
% 4.69/1.02 % Factorizations : 2
% 4.69/1.02 % NegExts : 0
% 4.69/1.02 % Equation resolutions : 49
% 4.69/1.02 % Disequality decompositions : 0
% 4.69/1.02 % Total rewrite steps : 2359
% 4.69/1.02 % ...of those cached : 2183
% 4.69/1.02 % Propositional unsat checks : 0
% 4.69/1.02 % Propositional check models : 0
% 4.69/1.02 % Propositional check unsatisfiable : 0
% 4.69/1.02 % Propositional clauses : 0
% 4.69/1.02 % Propositional clauses after purity: 0
% 4.69/1.02 % Propositional unsat core size : 0
% 4.69/1.02 % Propositional preprocessing time : 0.000
% 4.69/1.02 % Propositional encoding time : 0.000
% 4.69/1.02 % Propositional solver time : 0.000
% 4.69/1.02 % Success case prop preproc time : 0.000
% 4.69/1.02 % Success case prop encoding time : 0.000
% 4.69/1.02 % Success case prop solver time : 0.000
% 4.69/1.02 % Current number of processed clauses : 566
% 4.69/1.02 % Positive orientable unit clauses : 173
% 4.69/1.02 % Positive unorientable unit clauses: 0
% 4.69/1.02 % Negative unit clauses : 1
% 4.69/1.02 % Non-unit-clauses : 392
% 4.69/1.02 % Current number of unprocessed clauses: 20267
% 4.69/1.02 % ...number of literals in the above : 60207
% 4.69/1.02 % Current number of archived formulas : 0
% 4.69/1.02 % Current number of archived clauses : 170
% 4.69/1.02 % Clause-clause subsumption calls (NU) : 35205
% 4.69/1.02 % Rec. Clause-clause subsumption calls : 16976
% 4.69/1.02 % Non-unit clause-clause subsumptions : 347
% 4.69/1.02 % Unit Clause-clause subsumption calls : 2828
% 4.69/1.02 % Rewrite failures with RHS unbound : 0
% 4.69/1.02 % BW rewrite match attempts : 170
% 4.69/1.02 % BW rewrite match successes : 10
% 4.69/1.02 % Condensation attempts : 0
% 4.69/1.02 % Condensation successes : 0
% 4.69/1.02 % Termbank termtop insertions : 1299463
% 4.69/1.02 % Search garbage collected termcells : 9948
% 4.69/1.02
% 4.69/1.02 % -------------------------------------------------
% 4.69/1.02 % User time : 0.603 s
% 4.69/1.02 % System time : 0.035 s
% 4.69/1.02 % Total time : 0.637 s
% 4.69/1.02 % Maximum resident set size: 6076 pages
% 4.69/1.02
% 4.69/1.02 % -------------------------------------------------
% 4.69/1.02 % User time : 2.998 s
% 4.69/1.02 % System time : 0.142 s
% 4.69/1.02 % Total time : 3.139 s
% 4.69/1.02 % Maximum resident set size: 4864 pages
% 4.69/1.02 % E exiting
%------------------------------------------------------------------------------