%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU569^1 : 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 08:26:45 AM UTC 2026
% Result : Theorem 0.22s 0.30s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU569^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.17 % Computer : n007.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Sep 29 13:48:55 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.22 Running higher-order theorem proving
% 0.06/0.25 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.SOCSP0uuZK/E---3.1_3394720.p
% 0.22/0.30 % Version: 3.5.1-ho
% 0.22/0.30 % Preprocessing class: HSMMSLSSLLLCHFA.
% 0.22/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.30 % Starting ehoh_best3_avoidappvar with 1500s (5) cores
% 0.22/0.30 % Starting ehoh_best3_rw with 300s (1) cores
% 0.22/0.30 % Starting almost_fo_3 with 300s (1) cores
% 0.22/0.30 % Starting new_ho_13 with 300s (1) cores
% 0.22/0.30 % ehoh_best3_avoidappvar with pid 3394733 completed with status 0
% 0.22/0.30 % Result found by ehoh_best3_avoidappvar
% 0.22/0.30 % Preprocessing class: HSMMSLSSLLLCHFA.
% 0.22/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.30 % Starting ehoh_best3_avoidappvar with 1500s (5) cores
% 0.22/0.30 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.30 % No SInE strategy applied
% 0.22/0.30 % Search class: HGHSM-FSLS31-SHFMMMBN
% 0.22/0.30 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.30 % Starting SubtermCWHack with 136s (1) cores
% 0.22/0.30 % Starting ehoh_best3_avoidappvar with 151s (1) cores
% 0.22/0.30 % Starting sh5l with 136s (1) cores
% 0.22/0.30 % Starting new_bool_1 with 136s (1) cores
% 0.22/0.30 % Starting new_bool_2 with 136s (1) cores
% 0.22/0.30 % new_bool_1 with pid 3394740 completed with status 0
% 0.22/0.30 % Result found by new_bool_1
% 0.22/0.30 % Preprocessing class: HSMMSLSSLLLCHFA.
% 0.22/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.30 % Starting ehoh_best3_avoidappvar with 1500s (5) cores
% 0.22/0.30 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.30 % No SInE strategy applied
% 0.22/0.30 % Search class: HGHSM-FSLS31-SHFMMMBN
% 0.22/0.30 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.30 % Starting SubtermCWHack with 136s (1) cores
% 0.22/0.30 % Starting ehoh_best3_avoidappvar with 151s (1) cores
% 0.22/0.30 % Starting sh5l with 136s (1) cores
% 0.22/0.30 % Starting new_bool_1 with 136s (1) cores
% 0.22/0.30 % Preprocessing time : 0.003 s
% 0.22/0.30 % Presaturation interreduction done
% 0.22/0.30
% 0.22/0.30 % Proof found!
% 0.22/0.30 % SZS status Theorem
% 0.22/0.30 % SZS output start CNFRefutation
% 0.22/0.30 thf(decl_23, type, in: $i > $i > $o).
% 0.22/0.30 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.22/0.30 thf(decl_25, type, setextAx: $o).
% 0.22/0.30 thf(decl_26, type, emptyset: $i).
% 0.22/0.30 thf(decl_27, type, emptysetAx: $o).
% 0.22/0.30 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.22/0.30 thf(decl_29, type, setadjoinAx: $o).
% 0.22/0.30 thf(decl_30, type, powerset: $i > $i).
% 0.22/0.30 thf(decl_31, type, powersetAx: $o).
% 0.22/0.30 thf(decl_32, type, setunion: $i > $i).
% 0.22/0.30 thf(decl_33, type, setunionAx: $o).
% 0.22/0.30 thf(decl_34, type, omega: $i).
% 0.22/0.30 thf(decl_35, type, omega0Ax: $o).
% 0.22/0.30 thf(decl_36, type, omegaSAx: $o).
% 0.22/0.30 thf(decl_37, type, omegaIndAx: $o).
% 0.22/0.30 thf(decl_38, type, replAx: $o).
% 0.22/0.30 thf(decl_39, type, foundationAx: $o).
% 0.22/0.30 thf(decl_40, type, wellorderingAx: $o).
% 0.22/0.30 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.22/0.30 thf(decl_42, type, descrp: $o).
% 0.22/0.30 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.22/0.30 thf(decl_44, type, dsetconstrI: $o).
% 0.22/0.30 thf(decl_45, type, dsetconstrEL: $o).
% 0.22/0.30 thf(decl_46, type, dsetconstrER: $o).
% 0.22/0.30 thf(decl_47, type, exuE1: $o).
% 0.22/0.30 thf(decl_48, type, prop2set: $o > $i).
% 0.22/0.30 thf(decl_49, type, prop2setE: $o).
% 0.22/0.30 thf(decl_50, type, emptysetE: $o).
% 0.22/0.30 thf(decl_51, type, emptysetimpfalse: $o).
% 0.22/0.30 thf(decl_52, type, notinemptyset: $o).
% 0.22/0.30 thf(decl_53, type, exuE3e: $o).
% 0.22/0.30 thf(decl_54, type, setext: $o).
% 0.22/0.30 thf(decl_55, type, emptyI: $o).
% 0.22/0.30 thf(decl_56, type, noeltsimpempty: $o).
% 0.22/0.30 thf(decl_57, type, setbeta: $o).
% 0.22/0.30 thf(decl_58, type, nonempty: $i > $o).
% 0.22/0.30 thf(decl_59, type, nonemptyE1: $o).
% 0.22/0.30 thf(decl_60, type, nonemptyI: $o).
% 0.22/0.30 thf(decl_61, type, nonemptyI1: $o).
% 0.22/0.30 thf(decl_62, type, setadjoinIL: $o).
% 0.22/0.30 thf(decl_63, type, emptyinunitempty: $o).
% 0.22/0.30 thf(decl_64, type, setadjoinIR: $o).
% 0.22/0.30 thf(decl_65, type, setadjoinE: $o).
% 0.22/0.30 thf(decl_66, type, setadjoinOr: $o).
% 0.22/0.30 thf(decl_67, type, setoftrueEq: $o).
% 0.22/0.30 thf(decl_68, type, powersetI: $o).
% 0.22/0.30 thf(decl_69, type, emptyinPowerset: $o).
% 0.22/0.30 thf(decl_70, type, emptyInPowerset: $o).
% 0.22/0.30 thf(decl_71, type, powersetE: $o).
% 0.22/0.30 thf(decl_72, type, setunionI: $o).
% 0.22/0.30 thf(decl_73, type, setunionE: $o).
% 0.22/0.30 thf(decl_74, type, subPowSU: $o).
% 0.22/0.30 thf(decl_75, type, exuE2: $o).
% 0.22/0.30 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.22/0.30 thf(decl_77, type, uniqinunit: $o).
% 0.22/0.30 thf(decl_78, type, notinsingleton: $o).
% 0.22/0.30 thf(decl_79, type, eqinunit: $o).
% 0.22/0.30 thf(decl_80, type, singletonsswitch: $o).
% 0.22/0.30 thf(decl_81, type, upairsetE: $o).
% 0.22/0.30 thf(decl_82, type, upairsetIL: $o).
% 0.22/0.30 thf(decl_83, type, upairsetIR: $o).
% 0.22/0.30 thf(decl_84, type, emptyE1: $o).
% 0.22/0.30 thf(decl_85, type, vacuousDall: $o).
% 0.22/0.30 thf(decl_86, type, quantDeMorgan1: $o).
% 0.22/0.30 thf(decl_87, type, quantDeMorgan2: $o).
% 0.22/0.30 thf(decl_88, type, quantDeMorgan3: $o).
% 0.22/0.30 thf(decl_89, type, quantDeMorgan4: $o).
% 0.22/0.30 thf(decl_90, type, prop2setI: $o).
% 0.22/0.30 thf(decl_91, type, set2prop: $i > $o).
% 0.22/0.30 thf(decl_92, type, prop2set2propI: $o).
% 0.22/0.30 thf(decl_93, type, notdexE: $o).
% 0.22/0.30 thf(decl_94, type, notdallE: $o).
% 0.22/0.30 thf(decl_95, type, exuI1: $o).
% 0.22/0.30 thf(decl_96, type, exuI3: $o).
% 0.22/0.30 thf(decl_97, type, exuI2: $o).
% 0.22/0.30 thf(decl_98, type, inCongP: $o).
% 0.22/0.30 thf(decl_99, type, in__Cong: $o).
% 0.22/0.30 thf(decl_100, type, exuE3u: $o).
% 0.22/0.30 thf(decl_101, type, exu__Cong: $o).
% 0.22/0.30 thf(decl_102, type, emptyset__Cong: $o).
% 0.22/0.30 thf(decl_103, type, setadjoin__Cong: $o).
% 0.22/0.30 thf(decl_104, type, powerset__Cong: $o).
% 0.22/0.30 thf(decl_105, type, setunion__Cong: $o).
% 0.22/0.30 thf(decl_106, type, omega__Cong: $o).
% 0.22/0.30 thf(decl_107, type, exuEu: $o).
% 0.22/0.30 thf(decl_108, type, descr__Cong: $o).
% 0.22/0.30 thf(decl_109, type, dsetconstr__Cong: $o).
% 0.22/0.30 thf(decl_110, type, subset: $i > $i > $o).
% 0.22/0.30 thf(decl_113, type, subsetI1: $o).
% 0.22/0.30 thf(decl_114, type, eqimpsubset2: $o).
% 0.22/0.30 thf(decl_115, type, eqimpsubset1: $o).
% 0.22/0.30 thf(decl_116, type, subsetI2: $o).
% 0.22/0.30 thf(decl_117, type, emptysetsubset: $o).
% 0.22/0.30 thf(decl_118, type, subsetE: $o).
% 0.22/0.30 thf(decl_119, type, subsetE2: $o).
% 0.22/0.30 thf(decl_120, type, notsubsetI: $o).
% 0.22/0.30 thf(decl_121, type, notequalI1: $o).
% 0.22/0.30 thf(decl_122, type, notequalI2: $o).
% 0.22/0.30 thf(decl_123, type, epred1_0: $o).
% 0.22/0.30 thf(decl_124, type, esk1_2: $i > $i > $i).
% 0.22/0.30 thf(decl_125, type, esk2_2: $i > $i > $i).
% 0.22/0.30 thf(decl_126, type, esk3_2: $i > $i > $i).
% 0.22/0.30 thf(decl_127, type, esk4_1: $i > $i).
% 0.22/0.30 thf(decl_128, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.22/0.30 thf(decl_129, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.22/0.30 thf(decl_130, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.22/0.30 thf(decl_131, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.22/0.30 thf(decl_132, type, esk9_1: $i > $i).
% 0.22/0.30 thf(decl_133, type, esk10_2: ($i > $o) > $i > $i).
% 0.22/0.30 thf(decl_134, type, esk11_2: ($i > $o) > $i > $i).
% 0.22/0.30 thf(decl_135, type, esk12_1: ($i > $o) > $i).
% 0.22/0.30 thf(decl_136, type, esk13_2: ($i > $o) > $i > $i).
% 0.22/0.30 thf(decl_137, type, esk14_1: ($i > $o) > $i).
% 0.22/0.30 thf(decl_138, type, esk15_2: $i > $i > $i).
% 0.22/0.30 thf(decl_139, type, esk16_2: $i > $i > $i).
% 0.22/0.30 thf(decl_140, type, esk17_1: $i > $i).
% 0.22/0.30 thf(decl_141, type, esk18_1: $i > $i).
% 0.22/0.30 thf(decl_142, type, esk19_1: $i > $i).
% 0.22/0.30 thf(decl_143, type, esk20_2: $i > $i > $i).
% 0.22/0.30 thf(decl_144, type, esk21_3: $i > $i > $o > $i).
% 0.22/0.30 thf(decl_145, type, esk22_2: ($i > $o) > $i > $i).
% 0.22/0.30 thf(decl_146, type, esk23_1: ($i > $o) > $i).
% 0.22/0.30 thf(decl_147, type, esk24_1: $i > $i).
% 0.22/0.30 thf(decl_148, type, esk25_2: $i > ($i > $o) > $i).
% 0.22/0.30 thf(decl_149, type, esk26_2: $i > ($i > $o) > $i).
% 0.22/0.30 thf(decl_150, type, esk27_2: $i > ($i > $o) > $i).
% 0.22/0.30 thf(decl_151, type, esk28_2: $i > ($i > $o) > $i).
% 0.22/0.30 thf(decl_152, type, esk29_2: $i > ($i > $o) > $i).
% 0.22/0.30 thf(decl_153, type, esk30_2: $i > ($i > $o) > $i).
% 0.22/0.30 thf(decl_154, type, esk31_2: ($i > $o) > $i > $i).
% 0.22/0.30 thf(decl_155, type, esk32_1: ($i > $o) > $i).
% 0.22/0.30 thf(decl_156, type, esk33_1: ($i > $o) > $i).
% 0.22/0.30 thf(decl_157, type, esk34_1: ($i > $o) > $i).
% 0.22/0.30 thf(decl_158, type, esk35_1: ($i > $o) > $i).
% 0.22/0.30 thf(decl_159, type, esk36_2: ($i > $o) > $i > $i).
% 0.22/0.30 thf(decl_160, type, esk37_1: ($i > $o) > $i).
% 0.22/0.30 thf(decl_161, type, esk38_2: ($i > $o) > $i > $i).
% 0.22/0.30 thf(decl_162, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.30 thf(decl_163, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.30 thf(decl_164, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.22/0.30 thf(decl_165, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.30 thf(decl_166, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.22/0.30 thf(decl_167, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.30 thf(decl_168, type, esk45_2: ($i > $o) > $i > $i).
% 0.22/0.30 thf(decl_169, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.30 thf(decl_170, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 0.22/0.30 thf(decl_171, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.22/0.30 thf(decl_172, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.22/0.30 thf(decl_173, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.22/0.30 thf(decl_174, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.22/0.30 thf(decl_175, type, esk52_2: $i > $i > $i).
% 0.22/0.30 thf(decl_176, type, esk53_2: $i > $i > $i).
% 0.22/0.30 thf(decl_177, type, esk54_0: $i).
% 0.22/0.30 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', replAx)).
% 0.22/0.30 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', exu)).
% 0.22/0.30 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', descrp)).
% 0.22/0.30 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', exuE1)).
% 0.22/0.30 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', exuE3e)).
% 0.22/0.30 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', nonempty)).
% 0.22/0.30 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', nonemptyI)).
% 0.22/0.30 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', exuE2)).
% 0.22/0.30 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.SOCSP0uuZK/E---3.1_3394720.p', exuI1)).
% 0.22/0.30 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', exuI3)).
% 0.22/0.30 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', exuI2)).
% 0.22/0.30 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.SOCSP0uuZK/E---3.1_3394720.p', exuE3u)).
% 0.22/0.30 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', exu__Cong)).
% 0.22/0.30 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', exuEu)).
% 0.22/0.30 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', descr__Cong)).
% 0.22/0.30 thf(subsetRefl, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>![X4:$i]:((subset @ X4 @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', subsetRefl)).
% 0.22/0.30 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', dsetconstrI)).
% 0.22/0.30 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', dsetconstrEL)).
% 0.22/0.30 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', dsetconstrER)).
% 0.22/0.30 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', setbeta)).
% 0.22/0.30 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', nonemptyE1)).
% 0.22/0.30 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', nonemptyI1)).
% 0.22/0.30 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', setoftrueEq)).
% 0.22/0.30 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', nonemptyImpWitness)).
% 0.22/0.30 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.SOCSP0uuZK/E---3.1_3394720.p', emptyE1)).
% 0.22/0.30 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', dsetconstr__Cong)).
% 0.22/0.30 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', setextAx)).
% 0.22/0.30 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', emptysetAx)).
% 0.22/0.30 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', setadjoinAx)).
% 0.22/0.30 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', powersetAx)).
% 0.22/0.30 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', setunionAx)).
% 0.22/0.30 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', omega0Ax)).
% 0.22/0.30 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', omegaSAx)).
% 0.22/0.30 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.SOCSP0uuZK/E---3.1_3394720.p', omegaIndAx)).
% 0.22/0.30 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.SOCSP0uuZK/E---3.1_3394720.p', foundationAx)).
% 0.22/0.30 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', wellorderingAx)).
% 0.22/0.30 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', prop2setE)).
% 0.22/0.30 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', emptysetE)).
% 0.22/0.30 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', emptysetimpfalse)).
% 0.22/0.30 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', notinemptyset)).
% 0.22/0.30 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.SOCSP0uuZK/E---3.1_3394720.p', setext)).
% 0.22/0.30 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', emptyI)).
% 0.22/0.30 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', noeltsimpempty)).
% 0.22/0.30 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', setadjoinIL)).
% 0.22/0.30 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', emptyinunitempty)).
% 0.22/0.30 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', setadjoinIR)).
% 0.22/0.30 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', setadjoinE)).
% 0.22/0.30 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', setadjoinOr)).
% 0.22/0.30 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', powersetI)).
% 0.22/0.30 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', emptyinPowerset)).
% 0.22/0.30 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', emptyInPowerset)).
% 0.22/0.30 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', powersetE)).
% 0.22/0.30 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', setunionI)).
% 0.22/0.30 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', setunionE)).
% 0.22/0.30 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', subPowSU)).
% 0.22/0.30 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', uniqinunit)).
% 0.22/0.30 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', notinsingleton)).
% 0.22/0.30 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', eqinunit)).
% 0.22/0.30 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', singletonsswitch)).
% 0.22/0.30 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', upairsetE)).
% 0.22/0.30 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', upairsetIL)).
% 0.22/0.30 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', upairsetIR)).
% 0.22/0.30 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', vacuousDall)).
% 0.22/0.30 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', quantDeMorgan1)).
% 0.22/0.30 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', quantDeMorgan2)).
% 0.22/0.30 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', quantDeMorgan3)).
% 0.22/0.30 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', quantDeMorgan4)).
% 0.22/0.30 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', prop2setI)).
% 0.22/0.30 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', prop2set2propI)).
% 0.22/0.30 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', notdexE)).
% 0.22/0.30 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', notdallE)).
% 0.22/0.30 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', inCongP)).
% 0.22/0.30 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', in__Cong)).
% 0.22/0.30 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', emptyset__Cong)).
% 0.22/0.30 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', setadjoin__Cong)).
% 0.22/0.30 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', powerset__Cong)).
% 0.22/0.30 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', setunion__Cong)).
% 0.22/0.30 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', omega__Cong)).
% 0.22/0.30 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', subsetI1)).
% 0.22/0.30 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', eqimpsubset2)).
% 0.22/0.30 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', eqimpsubset1)).
% 0.22/0.30 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', subsetI2)).
% 0.22/0.30 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', emptysetsubset)).
% 0.22/0.30 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', subsetE)).
% 0.22/0.30 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', subsetE2)).
% 0.22/0.30 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', notsubsetI)).
% 0.22/0.30 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', notequalI1)).
% 0.22/0.30 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.SOCSP0uuZK/E---3.1_3394720.p', notequalI2)).
% 0.22/0.30 thf(c_0_88, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.22/0.30 thf(c_0_89, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.22/0.30 thf(c_0_90, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.22/0.30 thf(c_0_91, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.22/0.30 thf(c_0_92, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.22/0.30 thf(c_0_93, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.22/0.30 thf(c_0_94, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.22/0.30 thf(c_0_95, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.22/0.30 thf(c_0_96, 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])).
% 0.22/0.30 thf(c_0_97, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.22/0.30 thf(c_0_98, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.22/0.30 thf(c_0_99, 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])).
% 0.22/0.30 thf(c_0_100, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 0.22/0.30 thf(c_0_101, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 0.22/0.30 thf(c_0_102, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 0.22/0.30 thf(c_0_103, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>![X4:$i]:((subset @ X4 @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[subsetRefl])).
% 0.22/0.30 thf(c_0_104, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X257:$i]:(((((X6 @ X2 @ X257)))&(![X258:$i]:(((((X6 @ X2 @ X258)))=>(((X257)=(X258)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_88, c_0_89])).
% 0.22/0.30 thf(c_0_105, plain, ((descrp)=(![X1:$i > $o]:((((?[X259:$i]:(((((X1 @ X259)))&(![X260:$i]:(((((X1 @ X260)))=>(((X259)=(X260))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_90, c_0_89])).
% 0.22/0.30 thf(c_0_106, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.22/0.30 thf(c_0_107, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.22/0.30 thf(c_0_108, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.22/0.30 thf(c_0_109, plain, ((exuE1)=(![X1:$i > $o]:((((?[X261:$i]:(((((X1 @ X261)))&(![X262:$i]:(((((X1 @ X262)))=>(((X261)=(X262))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_91, c_0_89])).
% 0.22/0.30 thf(c_0_110, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X263:$i]:(((((X1 @ X263)))&(![X264:$i]:(((((X1 @ X264)))=>(((X263)=(X264))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_92, c_0_89])).
% 0.22/0.30 thf(c_0_111, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.22/0.30 thf(c_0_112, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_93])).
% 0.22/0.30 thf(c_0_113, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_94, c_0_93])).
% 0.22/0.30 thf(c_0_114, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_93])).
% 0.22/0.30 thf(c_0_115, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.22/0.30 thf(c_0_116, plain, ((exuE2)=(![X1:$i > $o]:((((?[X265:$i]:(((((X1 @ X265)))&(![X266:$i]:(((((X1 @ X266)))=>(((X265)=(X266))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_95, c_0_89])).
% 0.22/0.30 thf(c_0_117, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_93])).
% 0.22/0.30 thf(c_0_118, 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])).
% 0.22/0.30 thf(c_0_119, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X267:$i]:(((((X1 @ X267)))&(![X268:$i]:(((((X1 @ X268)))=>(((X267)=(X268)))))))))))))), inference(apply_def,[status(thm)],[c_0_96, c_0_89])).
% 0.22/0.30 thf(c_0_120, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X269:$i]:(((((X1 @ X269)))&(![X270:$i]:(((((X1 @ X270)))=>(((X269)=(X270)))))))))))))))), inference(apply_def,[status(thm)],[c_0_97, c_0_89])).
% 0.22/0.30 thf(c_0_121, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X271:$i]:(((((X1 @ X271)))&(![X272:$i]:(((((X1 @ X272)))=>(((X271)=(X272)))))))))))))), inference(apply_def,[status(thm)],[c_0_98, c_0_89])).
% 0.22/0.30 thf(c_0_122, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X273:$i]:(((((X1 @ X273)))&(![X274:$i]:(((((X1 @ X274)))=>(((X273)=(X274))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_99, c_0_89])).
% 0.22/0.30 thf(c_0_123, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X275:$i]:(((((X1 @ X275)))&(![X276:$i]:(((((X1 @ X276)))=>(((X275)=(X276))))))))))<=>((?[X277:$i]:(((((X17 @ X277)))&(![X278:$i]:(((((X17 @ X278)))=>(((X277)=(X278)))))))))))))))), inference(apply_def,[status(thm)],[c_0_100, c_0_89])).
% 0.22/0.30 thf(c_0_124, plain, ((exuEu)=(![X1:$i > $o]:((((?[X279:$i]:(((((X1 @ X279)))&(![X280:$i]:(((((X1 @ X280)))=>(((X279)=(X280))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_101, c_0_89])).
% 0.22/0.30 thf(c_0_125, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X281:$i]:(((((X1 @ X281)))&(![X282:$i]:(((((X1 @ X282)))=>(((X281)=(X282))))))))))=>((((?[X283:$i]:(((((X17 @ X283)))&(![X284:$i]:(((((X17 @ X284)))=>(((X283)=(X284))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_102, c_0_89])).
% 0.22/0.30 thf(c_0_126, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 0.22/0.30 thf(c_0_127, plain, ((epred1_0)<=>![X314:$i]:(?[X315:$i]:((((![X316:$i]:(((in @ X316 @ X315)=>![X317:$i]:(((in @ X317 @ X316)=>(in @ X317 @ X314)))))&![X318:$i, X319:$i]:((((in @ X318 @ X314)&(in @ X319 @ X314))=>(![X320:$i]:(((in @ X320 @ X315)=>((in @ X318 @ X320)<=>(in @ X319 @ X320))))=>((X318)=(X319))))))&![X321:$i, X322:$i]:((((in @ X321 @ X315)&(in @ X322 @ X315))=>(![X323:$i]:(((in @ X323 @ X321)=>(in @ X323 @ X322)))|![X324:$i]:(((in @ X324 @ X322)=>(in @ X324 @ X321)))))))&![X325:$i]:(((![X326:$i]:(((in @ X326 @ X325)=>(in @ X326 @ X314)))&?[X327:$i]:((in @ X327 @ X325)))=>?[X328:$i, X329:$i]:(((((in @ X328 @ X315)&(in @ X329 @ X325))&~(?[X330:$i]:(((in @ X330 @ X328)&(in @ X330 @ X325)))))&![X331:$i]:(((in @ X331 @ X315)=>(![X332:$i]:(((in @ X332 @ X331)=>(in @ X332 @ X328)))|(in @ X329 @ X331)))))))))))), introduced(definition)).
% 0.22/0.30 thf(c_0_128, negated_conjecture, ~((![X285:$i, X286:$i]:((![X287:$i]:(((in @ X287 @ X285)<=>(in @ X287 @ X286)))=>((X285)=(X286))))=>(![X288:$i]:(~(in @ X288 @ emptyset))=>(![X289:$i, X290:$i, X291:$i]:(((in @ X291 @ (setadjoin @ X289 @ X290))<=>(((X291)=(X289))|(in @ X291 @ X290))))=>(![X292:$i, X293:$i]:(((in @ X293 @ (powerset @ X292))<=>![X294:$i]:(((in @ X294 @ X293)=>(in @ X294 @ X292)))))=>(![X295:$i, X296:$i]:(((in @ X296 @ (setunion @ X295))<=>?[X297:$i]:(((in @ X296 @ X297)&(in @ X297 @ X295)))))=>((in @ emptyset @ omega)=>(![X298:$i]:(((in @ X298 @ omega)=>(in @ (setadjoin @ X298 @ X298) @ omega)))=>(![X299:$i]:((((in @ emptyset @ X299)&![X300:$i]:((((in @ X300 @ omega)&(in @ X300 @ X299))=>(in @ (setadjoin @ X300 @ X300) @ X299))))=>![X301:$i]:(((in @ X301 @ omega)=>(in @ X301 @ X299)))))=>(![X302:$i > $i > $o, X303:$i]:((![X304:$i]:(((in @ X304 @ X303)=>?[X305:$i]:(((X302 @ X304 @ X305)&![X306:$i]:(((X302 @ X304 @ X306)=>((X305)=(X306))))))))=>?[X307:$i]:(![X308:$i]:(((in @ X308 @ X307)<=>?[X309:$i]:(((in @ X309 @ X303)&(X302 @ X309 @ X308))))))))=>(![X310:$i]:((?[X311:$i]:((in @ X311 @ X310))=>?[X312:$i]:(((in @ X312 @ X310)&~(?[X313:$i]:(((in @ X313 @ X312)&(in @ X313 @ X310))))))))=>((epred1_0)=>(![X333:$i > $o]:((?[X334:$i]:(((X333 @ X334)&![X335:$i]:(((X333 @ X335)=>((X334)=(X335))))))=>(X333 @ (descr @ (^[Z0:$i]:(X333 @ Z0))))))=>(![X336:$i, X337:$i > $o, X338:$i]:(((in @ X338 @ X336)=>((X337 @ X338)=>(in @ X338 @ (dsetconstr @ X336 @ X337)))))=>(![X339:$i, X340:$i > $o, X341:$i]:(((in @ X341 @ (dsetconstr @ X339 @ X340))=>(in @ X341 @ X339)))=>(![X342:$i, X343:$i > $o, X344:$i]:(((in @ X344 @ (dsetconstr @ X342 @ X343))=>(X343 @ X344)))=>(![X345:$i > $o]:((?[X346:$i]:(((X345 @ X346)&![X347:$i]:(((X345 @ X347)=>((X346)=(X347))))))=>?[X348:$i]:(((X345 @ X348)&![X349:$i]:(((X345 @ X349)=>((X348)=(X349))))))))=>(![X350:$o, X351:$i]:(((in @ X351 @ (prop2set @ ((X350))))=>(X350)))=>(![X352:$i]:(((in @ X352 @ emptyset)=>![X353:$o]:((X353))))=>(![X354:$i]:(((in @ X354 @ emptyset)=>~($true)))=>(![X355:$i]:(~(in @ X355 @ emptyset))=>(![X356:$i > $o]:((?[X357:$i]:(((X356 @ X357)&![X358:$i]:(((X356 @ X358)=>((X357)=(X358))))))=>?[X359:$i]:((X356 @ X359))))=>(![X360:$i, X361:$i]:((![X362:$i]:(((in @ X362 @ X360)=>(in @ X362 @ X361)))=>(![X363:$i]:(((in @ X363 @ X361)=>(in @ X363 @ X360)))=>((X360)=(X361)))))=>(![X364:$i]:((![X365:$i]:(~(in @ X365 @ X364))=>((X364)=(emptyset))))=>(![X366:$i]:((![X367:$i]:(~(in @ X367 @ X366))=>((X366)=(emptyset))))=>(![X368:$i, X369:$i > $o, X370:$i]:(((in @ X370 @ X368)=>((in @ X370 @ (dsetconstr @ X368 @ X369))<=>(X369 @ X370))))=>(![X371:$i]:((((X371)!=(emptyset))=>?[X372:$i]:((in @ X372 @ X371))))=>(![X373:$i, X374:$i > $o, X375:$i]:(((in @ X375 @ X373)=>((X374 @ X375)=>((dsetconstr @ X373 @ X374)!=(emptyset)))))=>(![X376:$i]:((?[X377:$i]:((in @ X377 @ X376))=>((X376)!=(emptyset))))=>(![X378:$i, X379:$i]:((in @ X378 @ (setadjoin @ X378 @ X379)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X380:$i, X381:$i, X382:$i]:(((in @ X382 @ X381)=>(in @ X382 @ (setadjoin @ X380 @ X381))))=>(![X383:$i, X384:$i, X385:$i]:(((in @ X385 @ (setadjoin @ X383 @ X384))=>![X386:$o]:(((((X385)=(X383))=>(X386))=>(((in @ X385 @ X384)=>(X386))=>(X386))))))=>(![X387:$i, X388:$i, X389:$i]:(((in @ X389 @ (setadjoin @ X387 @ X388))=>(((X389)=(X387))|(in @ X389 @ X388))))=>(![X390:$i]:(((dsetconstr @ X390 @ (^[Z0:$i]:($true)))=(X390)))=>(![X391:$i, X392:$i]:((![X393:$i]:(((in @ X393 @ X392)=>(in @ X393 @ X391)))=>(in @ X392 @ (powerset @ X391))))=>(![X394:$i]:((in @ emptyset @ (powerset @ X394)))=>(![X395:$i]:((in @ emptyset @ (powerset @ X395)))=>(![X396:$i, X397:$i, X398:$i]:(((in @ X397 @ (powerset @ X396))=>((in @ X398 @ X397)=>(in @ X398 @ X396))))=>(![X399:$i, X400:$i, X401:$i]:(((in @ X400 @ X401)=>((in @ X401 @ X399)=>(in @ X400 @ (setunion @ X399)))))=>(![X402:$i, X403:$i]:(((in @ X403 @ (setunion @ X402))=>![X404:$o]:((![X405:$i]:(((in @ X403 @ X405)=>((in @ X405 @ X402)=>(X404))))=>(X404)))))=>(![X406:$i, X407:$i]:(((in @ X407 @ X406)=>(in @ X407 @ (powerset @ (setunion @ X406)))))=>(![X408:$i > $o]:((?[X409:$i]:(((X408 @ X409)&![X410:$i]:(((X408 @ X410)=>((X409)=(X410))))))=>?[X411:$i]:(![X412:$i]:(((X408 @ X412)<=>((X412)=(X411)))))))=>(![X413:$i]:((((X413)!=(emptyset))=>?[X414:$i]:(((in @ X414 @ X413)&$true))))=>(![X415:$i, X416:$i]:(((in @ X415 @ (setadjoin @ X416 @ emptyset))=>((X415)=(X416))))=>(![X417:$i, X418:$i]:((((X417)!=(X418))=>~(in @ X418 @ (setadjoin @ X417 @ emptyset))))=>(![X419:$i, X420:$i]:((((X419)=(X420))=>(in @ X419 @ (setadjoin @ X420 @ emptyset))))=>(![X421:$i, X422:$i]:(((in @ X421 @ (setadjoin @ X422 @ emptyset))=>(in @ X422 @ (setadjoin @ X421 @ emptyset))))=>(![X423:$i, X424:$i, X425:$i]:(((in @ X425 @ (setadjoin @ X423 @ (setadjoin @ X424 @ emptyset)))=>(((X425)=(X423))|((X425)=(X424)))))=>(![X426:$i, X427:$i]:((in @ X426 @ (setadjoin @ X426 @ (setadjoin @ X427 @ emptyset))))=>(![X428:$i, X429:$i]:((in @ X429 @ (setadjoin @ X428 @ (setadjoin @ X429 @ emptyset))))=>(![X430:$i, X431:$i > $o]:((?[X432:$i]:(((in @ X432 @ X430)&(X431 @ X432)))=>(((dsetconstr @ X430 @ X431)=(emptyset))=>~($true))))=>(![X433:$i > $o, X434:$i]:(((in @ X434 @ emptyset)=>(X433 @ X434)))=>(![X435:$i, X436:$i > $o]:((~(![X437:$i]:(((in @ X437 @ X435)=>(X436 @ X437))))=>?[X438:$i]:(((in @ X438 @ X435)&~((X436 @ X438))))))=>(![X439:$i, X440:$i > $o]:((![X441:$i]:(((in @ X441 @ X439)=>~((X440 @ X441))))=>~(?[X442:$i]:(((in @ X442 @ X439)&(X440 @ X442))))))=>(![X443:$i, X444:$i > $o]:((~(?[X445:$i]:(((in @ X445 @ X443)&(X444 @ X445))))=>![X446:$i]:(((in @ X446 @ X443)=>~((X444 @ X446))))))=>(![X447:$i, X448:$i > $o]:((?[X449:$i]:(((in @ X449 @ X447)&~((X448 @ X449))))=>~(![X450:$i]:(((in @ X450 @ X447)=>(X448 @ X450))))))=>(![X451:$o]:(((X451)=>(in @ emptyset @ (prop2set @ ((X451))))))=>(![X452:$o]:(((X452)=>(set2prop @ (prop2set @ ((X452))))))=>(![X453:$i, X454:$i > $o]:((~(?[X455:$i]:(((in @ X455 @ X453)&(X454 @ X455))))=>![X456:$i]:(((in @ X456 @ X453)=>~((X454 @ X456))))))=>(![X457:$i, X458:$i > $o]:((~(![X459:$i]:(((in @ X459 @ X457)=>(X458 @ X459))))=>?[X460:$i]:(((in @ X460 @ X457)&~((X458 @ X460))))))=>(![X461:$i > $o]:((?[X462:$i]:(((X461 @ X462)&![X463:$i]:(((X461 @ X463)=>((X462)=(X463))))))=>?[X464:$i]:(((X461 @ X464)&![X465:$i]:(((X461 @ X465)=>((X464)=(X465))))))))=>(![X466:$i > $o]:((?[X467:$i]:((X466 @ X467))=>(![X468:$i, X469:$i]:(((X466 @ X468)=>((X466 @ X469)=>((X468)=(X469)))))=>?[X470:$i]:(((X466 @ X470)&![X471:$i]:(((X466 @ X471)=>((X470)=(X471)))))))))=>(![X472:$i > $o]:((?[X473:$i]:(![X474:$i]:(((X472 @ X474)<=>((X474)=(X473)))))=>?[X475:$i]:(((X472 @ X475)&![X476:$i]:(((X472 @ X476)=>((X475)=(X476))))))))=>(![X477:$i, X478:$i]:((((X477)=(X478))=>![X479:$i, X480:$i]:((((X479)=(X480))=>((in @ X479 @ X477)=>(in @ X480 @ X478))))))=>(![X481:$i, X482:$i]:((((X481)=(X482))=>![X483:$i, X484:$i]:((((X483)=(X484))=>((in @ X483 @ X481)<=>(in @ X484 @ X482))))))=>(![X485:$i > $o]:((?[X486:$i]:(((X485 @ X486)&![X487:$i]:(((X485 @ X487)=>((X486)=(X487))))))=>![X488:$i, X489:$i]:(((X485 @ X488)=>((X485 @ X489)=>((X488)=(X489)))))))=>(![X490:$i > $o, X491:$i > $o]:((![X492:$i, X493:$i]:((((X492)=(X493))=>((X490 @ X492)<=>(X491 @ X493))))=>(?[X494:$i]:(((X490 @ X494)&![X495:$i]:(((X490 @ X495)=>((X494)=(X495))))))<=>?[X496:$i]:(((X491 @ X496)&![X497:$i]:(((X491 @ X497)=>((X496)=(X497)))))))))=>(((emptyset)=(emptyset))=>(![X498:$i, X499:$i]:((((X498)=(X499))=>![X500:$i, X501:$i]:((((X500)=(X501))=>((setadjoin @ X498 @ X500)=(setadjoin @ X499 @ X501))))))=>(![X502:$i, X503:$i]:((((X502)=(X503))=>((powerset @ X502)=(powerset @ X503))))=>(![X504:$i, X505:$i]:((((X504)=(X505))=>((setunion @ X504)=(setunion @ X505))))=>(((omega)=(omega))=>(![X506:$i > $o]:((?[X507:$i]:(((X506 @ X507)&![X508:$i]:(((X506 @ X508)=>((X507)=(X508))))))=>![X509:$i, X510:$i]:(((X506 @ X509)=>((X506 @ X510)=>((X509)=(X510)))))))=>(![X511:$i > $o, X512:$i > $o]:((![X513:$i, X514:$i]:((((X513)=(X514))=>((X511 @ X513)<=>(X512 @ X514))))=>(?[X515:$i]:(((X511 @ X515)&![X516:$i]:(((X511 @ X516)=>((X515)=(X516))))))=>(?[X517:$i]:(((X512 @ X517)&![X518:$i]:(((X512 @ X518)=>((X517)=(X518))))))=>((descr @ X511)=(descr @ X512))))))=>(![X519:$i, X520:$i]:((((X519)=(X520))=>![X521:$i > $o, X522:$i > $o]:((![X523:$i]:(((in @ X523 @ X519)=>![X524:$i]:(((in @ X524 @ X520)=>(((X523)=(X524))=>((X521 @ X523)<=>(X522 @ X524)))))))=>((dsetconstr @ X519 @ X521)=(dsetconstr @ X520 @ X522))))))=>(![X525:$i, X526:$i]:((![X527:$i]:(((in @ X527 @ X525)=>(in @ X527 @ X526)))=>(subset @ X525 @ X526)))=>(![X528:$i, X529:$i]:((((X528)=(X529))=>(subset @ X529 @ X528)))=>(![X530:$i, X531:$i]:((((X530)=(X531))=>(subset @ X530 @ X531)))=>(![X532:$i, X533:$i]:((![X534:$i]:(((in @ X534 @ X532)=>(in @ X534 @ X533)))=>(subset @ X532 @ X533)))=>(![X535:$i]:((subset @ emptyset @ X535))=>(![X536:$i, X537:$i, X538:$i]:(((subset @ X536 @ X537)=>((in @ X538 @ X536)=>(in @ X538 @ X537))))=>(![X539:$i, X540:$i, X541:$i]:(((subset @ X539 @ X540)=>(~(in @ X541 @ X540)=>~(in @ X541 @ X539))))=>(![X542:$i, X543:$i, X544:$i]:(((in @ X544 @ X542)=>(~(in @ X544 @ X543)=>~(subset @ X542 @ X543))))=>(![X545:$i, X546:$i]:((~(subset @ X545 @ X546)=>((X545)!=(X546))))=>(![X547:$i, X548:$i, X549:$i]:(((in @ X549 @ X547)=>(~(in @ X549 @ X548)=>((X547)!=(X548)))))=>![X4:$i]:((subset @ X4 @ 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)],[c_0_103, setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_104]), foundationAx]), wellorderingAx]), c_0_105]), c_0_106]), c_0_107]), c_0_108]), c_0_109]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_110]), setext]), emptyI]), noeltsimpempty]), c_0_111]), c_0_112]), c_0_113]), c_0_114]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_115]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_116]), c_0_117]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_118]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_119]), c_0_120]), c_0_121]), inCongP]), in__Cong]), c_0_122]), c_0_123]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_124]), c_0_125]), c_0_126]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2])])]), c_0_127])).
% 0.22/0.30 thf(c_0_129, negated_conjecture, ![X550:$i, X551:$i, X553:$i, X554:$i, X555:$i, X556:$i, X557:$i, X558:$i, X559:$i, X560:$i, X561:$i, X563:$i, X564:$i, X566:$i, X567:$i, X568:$i, X569:$i, X570:$i, X572:$i, X573:$i > $i > $o, X574:$i, X576:$i, X579:$i, X581:$i, X582:$i, X583:$i, X584:$i, X586:$i, X587:$i > $o, X588:$i, X590:$i, X591:$i > $o, X592:$i, X593:$i, X594:$i > $o, X595:$i, X596:$i, X597:$i > $o, X598:$i, X599:$i > $o, X600:$i, X603:$i, X604:$o, X605:$i, X606:$i, X607:$o, X608:$i, X609:$i, X610:$i > $o, X611:$i, X614:$i, X615:$i, X618:$i, X620:$i, X622:$i, X623:$i > $o, X624:$i, X625:$i, X627:$i, X628:$i > $o, X629:$i, X630:$i, X631:$i, X632:$i, X633:$i, X634:$i, X635:$i, X636:$i, X637:$i, X638:$i, X639:$i, X640:$o, X641:$i, X642:$i, X643:$i, X644:$i, X645:$i, X646:$i, X648:$i, X649:$i, X650:$i, X651:$i, X652:$i, X653:$i, X654:$i, X655:$i, X656:$i, X657:$i, X658:$o, X660:$i, X661:$i, X662:$i > $o, X663:$i, X666:$i, X667:$i, X668:$i, X670:$i, X671:$i, X672:$i, X673:$i, X674:$i, X675:$i, X676:$i, X677:$i, X678:$i, X679:$i, X680:$i, X681:$i, X682:$i, X683:$i, X684:$i, X685:$i, X686:$i > $o, X687:$i, X688:$i > $o, X689:$i, X690:$i, X691:$i > $o, X692:$i, X694:$i, X695:$i > $o, X697:$i, X698:$i, X699:$i > $o, X701:$i, X702:$i, X703:$i > $o, X704:$i, X706:$o, X707:$o, X708:$i, X709:$i > $o, X711:$i, X712:$i, X713:$i > $o, X714:$i, X716:$i > $o, X717:$i, X720:$i, X721:$i > $o, X722:$i, X726:$i, X727:$i > $o, X728:$i, X731:$i, X732:$i, X733:$i, X734:$i, X735:$i, X736:$i, X737:$i, X738:$i, X739:$i, X740:$i > $o, X741:$i, X743:$i, X744:$i, X745:$i > $o, X746:$i > $o, X749:$i, X752:$i, X753:$i, X756:$i, X757:$i, X758:$i, X759:$i, X760:$i, X761:$i, X762:$i, X763:$i, X764:$i, X765:$i > $o, X766:$i, X768:$i, X769:$i, X770:$i > $o, X771:$i > $o, X774:$i, X776:$i, X778:$i, X779:$i, X780:$i > $o, X781:$i > $o, X784:$i, X785:$i, X787:$i, X788:$i, X789:$i, X790:$i, X791:$i, X792:$i, X794:$i, X795:$i, X796:$i, X797:$i, X798:$i, X799:$i, X800:$i, X801:$i, X802:$i, X803:$i, X804:$i, X805:$i, X806:$i, X807:$i, X808:$i]:((((~(in @ (esk1_2 @ X550 @ X551) @ X550)|~(in @ (esk1_2 @ X550 @ X551) @ X551)|((X550)=(X551)))&((in @ (esk1_2 @ X550 @ X551) @ X550)|(in @ (esk1_2 @ X550 @ X551) @ X551)|((X550)=(X551))))&(~(in @ X553 @ emptyset)&(((~(in @ X556 @ (setadjoin @ X554 @ X555))|(((X556)=(X554))|(in @ X556 @ X555)))&((((X556)!=(X554))|(in @ X556 @ (setadjoin @ X554 @ X555)))&(~(in @ X556 @ X555)|(in @ X556 @ (setadjoin @ X554 @ X555)))))&(((~(in @ X558 @ (powerset @ X557))|(~(in @ X559 @ X558)|(in @ X559 @ X557)))&(((in @ (esk2_2 @ X560 @ X561) @ X561)|(in @ X561 @ (powerset @ X560)))&(~(in @ (esk2_2 @ X560 @ X561) @ X560)|(in @ X561 @ (powerset @ X560)))))&(((((in @ X564 @ (esk3_2 @ X563 @ X564))|~(in @ X564 @ (setunion @ X563)))&((in @ (esk3_2 @ X563 @ X564) @ X563)|~(in @ X564 @ (setunion @ X563))))&(~(in @ X567 @ X568)|~(in @ X568 @ X566)|(in @ X567 @ (setunion @ X566))))&((in @ emptyset @ omega)&((~(in @ X569 @ omega)|(in @ (setadjoin @ 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X771 @ X776))|~(X771 @ X776)|((descr @ X770)=(descr @ X771))|(((X774)!=(esk48_3 @ X770 @ X771 @ X774))|~(X770 @ X774))|((esk46_2 @ X770 @ X771)=(esk47_2 @ X770 @ X771)))))&(((((X771 @ (esk49_3 @ X770 @ X771 @ X776))|~(X771 @ X776)|((descr @ X770)=(descr @ X771))|((X770 @ (esk48_3 @ X770 @ X771 @ X774))|~(X770 @ X774))|(~(X770 @ (esk46_2 @ X770 @ X771))|~(X771 @ (esk47_2 @ X770 @ X771))))&(((X776)!=(esk49_3 @ X770 @ X771 @ X776))|~(X771 @ X776)|((descr @ X770)=(descr @ X771))|((X770 @ (esk48_3 @ X770 @ X771 @ X774))|~(X770 @ X774))|(~(X770 @ (esk46_2 @ X770 @ X771))|~(X771 @ (esk47_2 @ X770 @ X771)))))&(((X771 @ (esk49_3 @ X770 @ X771 @ X776))|~(X771 @ X776)|((descr @ X770)=(descr @ X771))|(((X774)!=(esk48_3 @ X770 @ X771 @ X774))|~(X770 @ X774))|(~(X770 @ (esk46_2 @ X770 @ X771))|~(X771 @ (esk47_2 @ X770 @ X771))))&(((X776)!=(esk49_3 @ X770 @ X771 @ X776))|~(X771 @ X776)|((descr @ X770)=(descr @ X771))|(((X774)!=(esk48_3 @ X770 @ X771 @ X774))|~(X770 @ X774))|(~(X770 @ (esk46_2 @ X770 @ X771))|~(X771 @ (esk47_2 @ X770 @ X771))))))&((((X771 @ (esk49_3 @ X770 @ X771 @ X776))|~(X771 @ X776)|((descr @ X770)=(descr @ X771))|((X770 @ (esk48_3 @ X770 @ X771 @ X774))|~(X770 @ X774))|((X770 @ (esk46_2 @ X770 @ X771))|(X771 @ (esk47_2 @ X770 @ X771))))&(((X776)!=(esk49_3 @ X770 @ X771 @ X776))|~(X771 @ X776)|((descr @ X770)=(descr @ X771))|((X770 @ (esk48_3 @ X770 @ X771 @ X774))|~(X770 @ X774))|((X770 @ (esk46_2 @ X770 @ X771))|(X771 @ (esk47_2 @ X770 @ X771)))))&(((X771 @ (esk49_3 @ X770 @ X771 @ X776))|~(X771 @ X776)|((descr @ X770)=(descr @ X771))|(((X774)!=(esk48_3 @ X770 @ X771 @ X774))|~(X770 @ X774))|((X770 @ (esk46_2 @ X770 @ X771))|(X771 @ (esk47_2 @ X770 @ X771))))&(((X776)!=(esk49_3 @ X770 @ X771 @ X776))|~(X771 @ X776)|((descr @ X770)=(descr @ X771))|(((X774)!=(esk48_3 @ X770 @ X771 @ X774))|~(X770 @ X774))|((X770 @ (esk46_2 @ X770 @ X771))|(X771 @ (esk47_2 @ X770 @ X771))))))))&((((in @ (esk50_4 @ X778 @ X779 @ X780 @ X781) @ X778)|((dsetconstr @ X778 @ X780)=(dsetconstr @ X779 @ X781))|((X778)!=(X779)))&(((in @ (esk51_4 @ X778 @ X779 @ X780 @ X781) @ X779)|((dsetconstr @ X778 @ X780)=(dsetconstr @ X779 @ X781))|((X778)!=(X779)))&((((esk50_4 @ X778 @ X779 @ X780 @ X781)=(esk51_4 @ X778 @ X779 @ X780 @ X781))|((dsetconstr @ X778 @ X780)=(dsetconstr @ X779 @ X781))|((X778)!=(X779)))&((~(X780 @ (esk50_4 @ X778 @ X779 @ X780 @ X781))|~(X781 @ (esk51_4 @ X778 @ X779 @ X780 @ X781))|((dsetconstr @ X778 @ X780)=(dsetconstr @ X779 @ X781))|((X778)!=(X779)))&((X780 @ (esk50_4 @ X778 @ X779 @ X780 @ X781))|(X781 @ (esk51_4 @ X778 @ X779 @ X780 @ X781))|((dsetconstr @ X778 @ X780)=(dsetconstr @ X779 @ X781))|((X778)!=(X779)))))))&((((in @ (esk52_2 @ X784 @ X785) @ X784)|(subset @ X784 @ X785))&(~(in @ (esk52_2 @ X784 @ X785) @ X785)|(subset @ X784 @ X785)))&((((X787)!=(X788))|(subset @ X788 @ X787))&((((X789)!=(X790))|(subset @ X789 @ X790))&((((in @ (esk53_2 @ X791 @ X792) @ X791)|(subset @ X791 @ X792))&(~(in @ (esk53_2 @ X791 @ X792) @ X792)|(subset @ X791 @ X792)))&((subset @ emptyset @ X794)&((~(subset @ X795 @ X796)|(~(in @ X797 @ X795)|(in @ X797 @ X796)))&((~(subset @ X798 @ X799)|((in @ X800 @ X799)|~(in @ X800 @ X798)))&((~(in @ X803 @ X801)|((in @ X803 @ X802)|~(subset @ X801 @ X802)))&(((subset @ X804 @ X805)|((X804)!=(X805)))&((~(in @ X808 @ X806)|((in @ X808 @ X807)|((X806)!=(X807))))&~(subset @ esk54_0 @ esk54_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_128])])])])])])])).
% 0.22/0.30 thf(c_0_130, negated_conjecture, ![X2:$i, X3:$i]:(((subset @ X3 @ X2)|((X2)!=(X3)))), inference(split_conjunct,[status(thm)],[c_0_129])).
% 0.22/0.30 thf(c_0_131, negated_conjecture, ~((subset @ esk54_0 @ esk54_0)), inference(split_conjunct,[status(thm)],[c_0_129])).
% 0.22/0.30 thf(c_0_132, negated_conjecture, ![X2:$i]:((subset @ X2 @ X2)), inference(er,[status(thm)],[c_0_130])).
% 0.22/0.30 thf(c_0_133, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_131, c_0_132])]), ['proof']).
% 0.22/0.30 % SZS output end CNFRefutation
% 0.22/0.30 % Parsed axioms : 188
% 0.22/0.30 % Removed by relevancy pruning/SinE : 0
% 0.22/0.30 % Initial clauses : 296
% 0.22/0.30 % Removed in clause preprocessing : 114
% 0.22/0.30 % Initial clauses in saturation : 182
% 0.22/0.30 % Processed clauses : 18
% 0.22/0.30 % ...of these trivial : 1
% 0.22/0.30 % ...subsumed : 4
% 0.22/0.30 % ...remaining for further processing : 13
% 0.22/0.30 % Other redundant clauses eliminated : 2
% 0.22/0.30 % Clauses deleted for lack of memory : 0
% 0.22/0.30 % Backward-subsumed : 0
% 0.22/0.30 % Backward-rewritten : 1
% 0.22/0.30 % Generated clauses : 2
% 0.22/0.30 % ...of the previous two non-redundant : 2
% 0.22/0.30 % ...aggressively subsumed : 0
% 0.22/0.30 % Contextual simplify-reflections : 0
% 0.22/0.30 % Paramodulations : 0
% 0.22/0.30 % Factorizations : 0
% 0.22/0.30 % NegExts : 0
% 0.22/0.30 % Equation resolutions : 2
% 0.22/0.30 % Disequality decompositions : 0
% 0.22/0.30 % Total rewrite steps : 2
% 0.22/0.30 % ...of those cached : 0
% 0.22/0.30 % Propositional unsat checks : 0
% 0.22/0.30 % Propositional check models : 0
% 0.22/0.30 % Propositional check unsatisfiable : 0
% 0.22/0.30 % Propositional clauses : 0
% 0.22/0.30 % Propositional clauses after purity: 0
% 0.22/0.30 % Propositional unsat core size : 0
% 0.22/0.30 % Propositional preprocessing time : 0.000
% 0.22/0.30 % Propositional encoding time : 0.000
% 0.22/0.30 % Propositional solver time : 0.000
% 0.22/0.30 % Success case prop preproc time : 0.000
% 0.22/0.30 % Success case prop encoding time : 0.000
% 0.22/0.30 % Success case prop solver time : 0.000
% 0.22/0.30 % Current number of processed clauses : 10
% 0.22/0.30 % Positive orientable unit clauses : 8
% 0.22/0.30 % Positive unorientable unit clauses: 0
% 0.22/0.30 % Negative unit clauses : 2
% 0.22/0.30 % Non-unit-clauses : 0
% 0.22/0.30 % Current number of unprocessed clauses: 166
% 0.22/0.30 % ...number of literals in the above : 619
% 0.22/0.30 % Current number of archived formulas : 0
% 0.22/0.30 % Current number of archived clauses : 1
% 0.22/0.30 % Clause-clause subsumption calls (NU) : 0
% 0.22/0.30 % Rec. Clause-clause subsumption calls : 0
% 0.22/0.30 % Non-unit clause-clause subsumptions : 0
% 0.22/0.30 % Unit Clause-clause subsumption calls : 1
% 0.22/0.30 % Rewrite failures with RHS unbound : 0
% 0.22/0.30 % BW rewrite match attempts : 2
% 0.22/0.30 % BW rewrite match successes : 1
% 0.22/0.30 % Condensation attempts : 0
% 0.22/0.30 % Condensation successes : 0
% 0.22/0.30 % Termbank termtop insertions : 29985
% 0.22/0.30 % Search garbage collected termcells : 9835
% 0.22/0.30
% 0.22/0.30 % -------------------------------------------------
% 0.22/0.30 % User time : 0.018 s
% 0.22/0.30 % System time : 0.007 s
% 0.22/0.30 % Total time : 0.025 s
% 0.22/0.30 % Maximum resident set size: 6124 pages
% 0.22/0.30
% 0.22/0.30 % -------------------------------------------------
% 0.22/0.30 % User time : 0.055 s
% 0.22/0.30 % System time : 0.022 s
% 0.22/0.30 % Total time : 0.078 s
% 0.22/0.30 % Maximum resident set size: 5120 pages
% 0.22/0.30 % E exiting
%------------------------------------------------------------------------------