%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU565^1 : 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 : n019.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 08:24:31 AM UTC 2026
% Result : Theorem 0.21s 0.31s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU565^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n019.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:50:47 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.20 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.21/0.26 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.yEpYbuk0Mh/E---3.1_800114.p
% 0.21/0.31 % Version: 3.5.1-ho
% 0.21/0.31 % Preprocessing class: HSMSSLSSLLLCHFA.
% 0.21/0.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.31 % Starting new_ho_10 with 1500s (5) cores
% 0.21/0.31 % Starting sh5l with 300s (1) cores
% 0.21/0.31 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.31 % Starting new_bool_2 with 300s (1) cores
% 0.21/0.31 % new_bool_2 with pid 800130 completed with status 0
% 0.21/0.31 % Result found by new_bool_2
% 0.21/0.31 % Preprocessing class: HSMSSLSSLLLCHFA.
% 0.21/0.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.31 % Starting new_ho_10 with 1500s (5) cores
% 0.21/0.31 % Starting sh5l with 300s (1) cores
% 0.21/0.31 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.31 % Starting new_bool_2 with 300s (1) cores
% 0.21/0.31 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.21/0.31 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.31 % Search class: HGHSM-FSLM31-SHFMMMBN
% 0.21/0.31 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.31 % Starting SubtermCWHack with 28s (1) cores
% 0.21/0.31 % SubtermCWHack with pid 800131 completed with status 0
% 0.21/0.31 % Result found by SubtermCWHack
% 0.21/0.31 % Preprocessing class: HSMSSLSSLLLCHFA.
% 0.21/0.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.31 % Starting new_ho_10 with 1500s (5) cores
% 0.21/0.31 % Starting sh5l with 300s (1) cores
% 0.21/0.31 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.31 % Starting new_bool_2 with 300s (1) cores
% 0.21/0.31 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.21/0.31 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.31 % Search class: HGHSM-FSLM31-SHFMMMBN
% 0.21/0.31 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.31 % Starting SubtermCWHack with 28s (1) cores
% 0.21/0.31 % Preprocessing time : 0.004 s
% 0.21/0.31
% 0.21/0.31 % Proof found!
% 0.21/0.31 % SZS status Theorem
% 0.21/0.31 % SZS output start CNFRefutation
% 0.21/0.31 thf(decl_23, type, in: $i > $i > $o).
% 0.21/0.31 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.21/0.31 thf(decl_25, type, setextAx: $o).
% 0.21/0.31 thf(decl_26, type, emptyset: $i).
% 0.21/0.31 thf(decl_27, type, emptysetAx: $o).
% 0.21/0.31 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.21/0.31 thf(decl_29, type, setadjoinAx: $o).
% 0.21/0.31 thf(decl_30, type, powerset: $i > $i).
% 0.21/0.31 thf(decl_31, type, powersetAx: $o).
% 0.21/0.31 thf(decl_32, type, setunion: $i > $i).
% 0.21/0.31 thf(decl_33, type, setunionAx: $o).
% 0.21/0.31 thf(decl_34, type, omega: $i).
% 0.21/0.31 thf(decl_35, type, omega0Ax: $o).
% 0.21/0.31 thf(decl_36, type, omegaSAx: $o).
% 0.21/0.31 thf(decl_37, type, omegaIndAx: $o).
% 0.21/0.31 thf(decl_38, type, replAx: $o).
% 0.21/0.31 thf(decl_39, type, foundationAx: $o).
% 0.21/0.31 thf(decl_40, type, wellorderingAx: $o).
% 0.21/0.31 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.21/0.31 thf(decl_42, type, descrp: $o).
% 0.21/0.31 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.21/0.31 thf(decl_44, type, dsetconstrI: $o).
% 0.21/0.31 thf(decl_45, type, dsetconstrEL: $o).
% 0.21/0.31 thf(decl_46, type, dsetconstrER: $o).
% 0.21/0.31 thf(decl_47, type, exuE1: $o).
% 0.21/0.31 thf(decl_48, type, prop2set: $o > $i).
% 0.21/0.31 thf(decl_49, type, prop2setE: $o).
% 0.21/0.31 thf(decl_50, type, emptysetE: $o).
% 0.21/0.31 thf(decl_51, type, emptysetimpfalse: $o).
% 0.21/0.31 thf(decl_52, type, notinemptyset: $o).
% 0.21/0.31 thf(decl_53, type, exuE3e: $o).
% 0.21/0.31 thf(decl_54, type, setext: $o).
% 0.21/0.31 thf(decl_55, type, emptyI: $o).
% 0.21/0.31 thf(decl_56, type, noeltsimpempty: $o).
% 0.21/0.31 thf(decl_57, type, setbeta: $o).
% 0.21/0.31 thf(decl_58, type, nonempty: $i > $o).
% 0.21/0.31 thf(decl_59, type, nonemptyE1: $o).
% 0.21/0.31 thf(decl_60, type, nonemptyI: $o).
% 0.21/0.31 thf(decl_61, type, nonemptyI1: $o).
% 0.21/0.31 thf(decl_62, type, setadjoinIL: $o).
% 0.21/0.31 thf(decl_63, type, emptyinunitempty: $o).
% 0.21/0.31 thf(decl_64, type, setadjoinIR: $o).
% 0.21/0.31 thf(decl_65, type, setadjoinE: $o).
% 0.21/0.31 thf(decl_66, type, setadjoinOr: $o).
% 0.21/0.31 thf(decl_67, type, setoftrueEq: $o).
% 0.21/0.31 thf(decl_68, type, powersetI: $o).
% 0.21/0.31 thf(decl_69, type, emptyinPowerset: $o).
% 0.21/0.31 thf(decl_70, type, emptyInPowerset: $o).
% 0.21/0.31 thf(decl_71, type, powersetE: $o).
% 0.21/0.31 thf(decl_72, type, setunionI: $o).
% 0.21/0.31 thf(decl_73, type, setunionE: $o).
% 0.21/0.31 thf(decl_74, type, subPowSU: $o).
% 0.21/0.31 thf(decl_75, type, exuE2: $o).
% 0.21/0.31 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.21/0.31 thf(decl_77, type, uniqinunit: $o).
% 0.21/0.31 thf(decl_78, type, notinsingleton: $o).
% 0.21/0.31 thf(decl_79, type, eqinunit: $o).
% 0.21/0.31 thf(decl_80, type, singletonsswitch: $o).
% 0.21/0.31 thf(decl_81, type, upairsetE: $o).
% 0.21/0.31 thf(decl_82, type, upairsetIL: $o).
% 0.21/0.31 thf(decl_83, type, upairsetIR: $o).
% 0.21/0.31 thf(decl_84, type, emptyE1: $o).
% 0.21/0.31 thf(decl_85, type, vacuousDall: $o).
% 0.21/0.31 thf(decl_86, type, quantDeMorgan1: $o).
% 0.21/0.31 thf(decl_87, type, quantDeMorgan2: $o).
% 0.21/0.31 thf(decl_88, type, quantDeMorgan3: $o).
% 0.21/0.31 thf(decl_89, type, quantDeMorgan4: $o).
% 0.21/0.31 thf(decl_90, type, prop2setI: $o).
% 0.21/0.31 thf(decl_92, type, prop2set2propI: $o).
% 0.21/0.31 thf(decl_93, type, notdexE: $o).
% 0.21/0.31 thf(decl_94, type, notdallE: $o).
% 0.21/0.31 thf(decl_95, type, exuI1: $o).
% 0.21/0.31 thf(decl_96, type, exuI3: $o).
% 0.21/0.31 thf(decl_97, type, exuI2: $o).
% 0.21/0.31 thf(decl_98, type, inCongP: $o).
% 0.21/0.31 thf(decl_99, type, in__Cong: $o).
% 0.21/0.31 thf(decl_100, type, exuE3u: $o).
% 0.21/0.31 thf(decl_101, type, exu__Cong: $o).
% 0.21/0.31 thf(decl_102, type, emptyset__Cong: $o).
% 0.21/0.31 thf(decl_103, type, setadjoin__Cong: $o).
% 0.21/0.31 thf(decl_104, type, powerset__Cong: $o).
% 0.21/0.31 thf(decl_105, type, setunion__Cong: $o).
% 0.21/0.31 thf(decl_106, type, omega__Cong: $o).
% 0.21/0.31 thf(decl_107, type, exuEu: $o).
% 0.21/0.31 thf(decl_108, type, descr__Cong: $o).
% 0.21/0.31 thf(decl_109, type, dsetconstr__Cong: $o).
% 0.21/0.31 thf(decl_110, type, subset: $i > $i > $o).
% 0.21/0.31 thf(decl_113, type, subsetI1: $o).
% 0.21/0.31 thf(decl_114, type, eqimpsubset2: $o).
% 0.21/0.31 thf(decl_115, type, eqimpsubset1: $o).
% 0.21/0.31 thf(decl_116, type, subsetI2: $o).
% 0.21/0.31 thf(decl_117, type, emptysetsubset: $o).
% 0.21/0.31 thf(decl_118, type, subsetE: $o).
% 0.21/0.31 thf(decl_119, type, epred1_0: $o).
% 0.21/0.31 thf(decl_120, type, esk1_2: $i > $i > $i).
% 0.21/0.31 thf(decl_121, type, esk2_2: $i > $i > $i).
% 0.21/0.31 thf(decl_122, type, esk3_2: $i > $i > $i).
% 0.21/0.31 thf(decl_123, type, esk4_1: $i > $i).
% 0.21/0.31 thf(decl_124, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.21/0.31 thf(decl_125, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.21/0.31 thf(decl_126, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.21/0.31 thf(decl_127, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.21/0.31 thf(decl_128, type, esk9_1: $i > $i).
% 0.21/0.31 thf(decl_129, type, esk10_2: ($i > $o) > $i > $i).
% 0.21/0.31 thf(decl_130, type, esk11_2: ($i > $o) > $i > $i).
% 0.21/0.31 thf(decl_131, type, esk12_1: ($i > $o) > $i).
% 0.21/0.31 thf(decl_132, type, esk13_2: ($i > $o) > $i > $i).
% 0.21/0.31 thf(decl_133, type, esk14_1: ($i > $o) > $i).
% 0.21/0.31 thf(decl_134, type, esk15_2: $i > $i > $i).
% 0.21/0.31 thf(decl_135, type, esk16_2: $i > $i > $i).
% 0.21/0.31 thf(decl_136, type, esk17_1: $i > $i).
% 0.21/0.31 thf(decl_137, type, esk18_1: $i > $i).
% 0.21/0.31 thf(decl_138, type, esk19_1: $i > $i).
% 0.21/0.31 thf(decl_139, type, esk20_2: $i > $i > $i).
% 0.21/0.31 thf(decl_140, type, esk21_3: $i > $i > $o > $i).
% 0.21/0.31 thf(decl_141, type, esk22_2: ($i > $o) > $i > $i).
% 0.21/0.31 thf(decl_142, type, esk23_1: ($i > $o) > $i).
% 0.21/0.31 thf(decl_143, type, esk24_1: $i > $i).
% 0.21/0.31 thf(decl_144, type, esk25_2: $i > ($i > $o) > $i).
% 0.21/0.31 thf(decl_145, type, esk26_2: $i > ($i > $o) > $i).
% 0.21/0.31 thf(decl_146, type, esk27_2: $i > ($i > $o) > $i).
% 0.21/0.31 thf(decl_147, type, esk28_2: $i > ($i > $o) > $i).
% 0.21/0.31 thf(decl_148, type, esk29_2: $i > ($i > $o) > $i).
% 0.21/0.31 thf(decl_149, type, esk30_2: $i > ($i > $o) > $i).
% 0.21/0.31 thf(decl_150, type, esk31_2: ($i > $o) > $i > $i).
% 0.21/0.31 thf(decl_151, type, esk32_1: ($i > $o) > $i).
% 0.21/0.31 thf(decl_152, type, esk33_1: ($i > $o) > $i).
% 0.21/0.31 thf(decl_153, type, esk34_1: ($i > $o) > $i).
% 0.21/0.31 thf(decl_154, type, esk35_1: ($i > $o) > $i).
% 0.21/0.31 thf(decl_155, type, esk36_2: ($i > $o) > $i > $i).
% 0.21/0.31 thf(decl_156, type, esk37_1: ($i > $o) > $i).
% 0.21/0.31 thf(decl_157, type, esk38_2: ($i > $o) > $i > $i).
% 0.21/0.31 thf(decl_158, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 0.21/0.31 thf(decl_159, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 0.21/0.31 thf(decl_160, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.21/0.31 thf(decl_161, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 0.21/0.31 thf(decl_162, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.21/0.31 thf(decl_163, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 0.21/0.31 thf(decl_164, type, esk45_2: ($i > $o) > $i > $i).
% 0.21/0.31 thf(decl_165, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 0.21/0.31 thf(decl_166, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 0.21/0.31 thf(decl_167, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.21/0.31 thf(decl_168, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.21/0.31 thf(decl_169, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.21/0.31 thf(decl_170, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.21/0.31 thf(decl_171, type, esk52_2: $i > $i > $i).
% 0.21/0.31 thf(decl_172, type, esk53_2: $i > $i > $i).
% 0.21/0.31 thf(decl_173, type, esk54_0: $i).
% 0.21/0.31 thf(decl_174, type, esk55_0: $i).
% 0.21/0.31 thf(decl_175, type, esk56_0: $i).
% 0.21/0.31 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', exu__Cong)).
% 0.21/0.31 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', exu)).
% 0.21/0.31 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', exuE3u)).
% 0.21/0.31 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.yEpYbuk0Mh/E---3.1_800114.p', exuEu)).
% 0.21/0.31 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', descr__Cong)).
% 0.21/0.31 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', exuE1)).
% 0.21/0.31 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', descrp)).
% 0.21/0.31 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', nonemptyI)).
% 0.21/0.31 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', nonempty)).
% 0.21/0.31 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', exuE3e)).
% 0.21/0.31 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', exuE2)).
% 0.21/0.31 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', exuI3)).
% 0.21/0.31 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', exuI2)).
% 0.21/0.31 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.yEpYbuk0Mh/E---3.1_800114.p', exuI1)).
% 0.21/0.31 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', replAx)).
% 0.21/0.31 thf(subsetE2, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', subsetE2)).
% 0.21/0.31 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', dsetconstr__Cong)).
% 0.21/0.31 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', dsetconstrER)).
% 0.21/0.31 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', dsetconstrEL)).
% 0.21/0.31 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', dsetconstrI)).
% 0.21/0.31 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', nonemptyE1)).
% 0.21/0.31 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', setbeta)).
% 0.21/0.31 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', nonemptyI1)).
% 0.21/0.31 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', setoftrueEq)).
% 0.21/0.31 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', nonemptyImpWitness)).
% 0.21/0.31 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.yEpYbuk0Mh/E---3.1_800114.p', emptyE1)).
% 0.21/0.31 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', emptyset__Cong)).
% 0.21/0.31 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.yEpYbuk0Mh/E---3.1_800114.p', setadjoin__Cong)).
% 0.21/0.31 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', powerset__Cong)).
% 0.21/0.31 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', setunion__Cong)).
% 0.21/0.31 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', omega__Cong)).
% 0.21/0.31 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', subsetI1)).
% 0.21/0.31 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', emptysetimpfalse)).
% 0.21/0.31 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', eqimpsubset2)).
% 0.21/0.31 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', emptysetE)).
% 0.21/0.31 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', eqimpsubset1)).
% 0.21/0.31 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', prop2setE)).
% 0.21/0.31 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', subsetI2)).
% 0.21/0.31 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', emptysetsubset)).
% 0.21/0.31 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', subsetE)).
% 0.21/0.31 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', notinemptyset)).
% 0.21/0.31 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', emptyinPowerset)).
% 0.21/0.31 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', noeltsimpempty)).
% 0.21/0.31 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', emptyI)).
% 0.21/0.31 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.yEpYbuk0Mh/E---3.1_800114.p', setext)).
% 0.21/0.31 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', powersetI)).
% 0.21/0.31 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', setadjoinOr)).
% 0.21/0.31 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.yEpYbuk0Mh/E---3.1_800114.p', setadjoinE)).
% 0.21/0.31 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', setadjoinIR)).
% 0.21/0.31 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', emptyinunitempty)).
% 0.21/0.31 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', setadjoinIL)).
% 0.21/0.31 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', subPowSU)).
% 0.21/0.31 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', setunionE)).
% 0.21/0.31 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', setunionI)).
% 0.21/0.31 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', powersetE)).
% 0.21/0.31 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', emptyInPowerset)).
% 0.21/0.31 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', uniqinunit)).
% 0.21/0.31 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', upairsetIR)).
% 0.21/0.31 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', upairsetIL)).
% 0.21/0.31 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', upairsetE)).
% 0.21/0.31 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', singletonsswitch)).
% 0.21/0.31 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', eqinunit)).
% 0.21/0.31 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', notinsingleton)).
% 0.21/0.31 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', vacuousDall)).
% 0.21/0.31 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', notdallE)).
% 0.21/0.31 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', notdexE)).
% 0.21/0.31 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', prop2setI)).
% 0.21/0.31 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', quantDeMorgan4)).
% 0.21/0.31 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', quantDeMorgan3)).
% 0.21/0.31 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', quantDeMorgan2)).
% 0.21/0.31 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', quantDeMorgan1)).
% 0.21/0.31 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', inCongP)).
% 0.21/0.31 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', in__Cong)).
% 0.21/0.31 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.yEpYbuk0Mh/E---3.1_800114.p', wellorderingAx)).
% 0.21/0.31 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.yEpYbuk0Mh/E---3.1_800114.p', foundationAx)).
% 0.21/0.31 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', omegaIndAx)).
% 0.21/0.31 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', omegaSAx)).
% 0.21/0.31 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', omega0Ax)).
% 0.21/0.31 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', setunionAx)).
% 0.21/0.31 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', powersetAx)).
% 0.21/0.31 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', setadjoinAx)).
% 0.21/0.31 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', emptysetAx)).
% 0.21/0.31 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.yEpYbuk0Mh/E---3.1_800114.p', setextAx)).
% 0.21/0.31 thf(c_0_83, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 0.21/0.31 thf(c_0_84, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.21/0.31 thf(c_0_85, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 0.21/0.31 thf(c_0_86, 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])).
% 0.21/0.31 thf(c_0_87, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 0.21/0.31 thf(c_0_88, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.21/0.31 thf(c_0_89, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.21/0.31 thf(c_0_90, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.21/0.31 thf(c_0_91, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.21/0.31 thf(c_0_92, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.21/0.31 thf(c_0_93, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.21/0.31 thf(c_0_94, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.21/0.31 thf(c_0_95, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.21/0.31 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])).
% 0.21/0.31 thf(c_0_97, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.21/0.31 thf(c_0_98, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[subsetE2])).
% 0.21/0.31 thf(c_0_99, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X265:$i]:(((((X1 @ X265)))&(![X266:$i]:(((((X1 @ X266)))=>(((X265)=(X266))))))))))<=>((?[X267:$i]:(((((X17 @ X267)))&(![X268:$i]:(((((X17 @ X268)))=>(((X267)=(X268)))))))))))))))), inference(apply_def,[status(thm)],[c_0_83, c_0_84])).
% 0.21/0.31 thf(c_0_100, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X263:$i]:(((((X1 @ X263)))&(![X264:$i]:(((((X1 @ X264)))=>(((X263)=(X264))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_85, c_0_84])).
% 0.21/0.31 thf(c_0_101, plain, ((exuEu)=(![X1:$i > $o]:((((?[X269:$i]:(((((X1 @ X269)))&(![X270:$i]:(((((X1 @ X270)))=>(((X269)=(X270))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_86, c_0_84])).
% 0.21/0.31 thf(c_0_102, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X271:$i]:(((((X1 @ X271)))&(![X272:$i]:(((((X1 @ X272)))=>(((X271)=(X272))))))))))=>((((?[X273:$i]:(((((X17 @ X273)))&(![X274:$i]:(((((X17 @ X274)))=>(((X273)=(X274))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_87, c_0_84])).
% 0.21/0.31 thf(c_0_103, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 0.21/0.31 thf(c_0_104, plain, ((exuE1)=(![X1:$i > $o]:((((?[X251:$i]:(((((X1 @ X251)))&(![X252:$i]:(((((X1 @ X252)))=>(((X251)=(X252))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_88, c_0_84])).
% 0.21/0.31 thf(c_0_105, plain, ((descrp)=(![X1:$i > $o]:((((?[X249:$i]:(((((X1 @ X249)))&(![X250:$i]:(((((X1 @ X250)))=>(((X249)=(X250))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_89, c_0_84])).
% 0.21/0.31 thf(c_0_106, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.21/0.31 thf(c_0_107, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.21/0.31 thf(c_0_108, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.21/0.31 thf(c_0_109, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_90, c_0_91])).
% 0.21/0.31 thf(c_0_110, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_91])).
% 0.21/0.31 thf(c_0_111, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.21/0.31 thf(c_0_112, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X253:$i]:(((((X1 @ X253)))&(![X254:$i]:(((((X1 @ X254)))=>(((X253)=(X254))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_92, c_0_84])).
% 0.21/0.31 thf(c_0_113, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_91])).
% 0.21/0.31 thf(c_0_114, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.21/0.31 thf(c_0_115, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_91])).
% 0.21/0.31 thf(c_0_116, plain, ((exuE2)=(![X1:$i > $o]:((((?[X255:$i]:(((((X1 @ X255)))&(![X256:$i]:(((((X1 @ X256)))=>(((X255)=(X256))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_93, c_0_84])).
% 0.21/0.31 thf(c_0_117, plain, ((emptyE1)<=>![X4:$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])).
% 0.21/0.31 thf(c_0_118, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X259:$i]:(((((X1 @ X259)))&(![X260:$i]:(((((X1 @ X260)))=>(((X259)=(X260)))))))))))))))), inference(apply_def,[status(thm)],[c_0_94, c_0_84])).
% 0.21/0.31 thf(c_0_119, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X261:$i]:(((((X1 @ X261)))&(![X262:$i]:(((((X1 @ X262)))=>(((X261)=(X262)))))))))))))), inference(apply_def,[status(thm)],[c_0_95, c_0_84])).
% 0.21/0.31 thf(c_0_120, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X257:$i]:(((((X1 @ X257)))&(![X258:$i]:(((((X1 @ X258)))=>(((X257)=(X258)))))))))))))), inference(apply_def,[status(thm)],[c_0_96, c_0_84])).
% 0.21/0.31 thf(c_0_121, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X247:$i]:(((((X6 @ X2 @ X247)))&(![X248:$i]:(((((X6 @ X2 @ X248)))=>(((X247)=(X248)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_97, c_0_84])).
% 0.21/0.31 thf(c_0_122, plain, ((epred1_0)<=>![X304:$i]:(?[X305:$i]:((((![X306:$i]:(((in @ X306 @ X305)=>![X307:$i]:(((in @ X307 @ X306)=>(in @ X307 @ X304)))))&![X308:$i, X309:$i]:((((in @ X308 @ X304)&(in @ X309 @ X304))=>(![X310:$i]:(((in @ X310 @ X305)=>((in @ X308 @ X310)<=>(in @ X309 @ X310))))=>((X308)=(X309))))))&![X311:$i, X312:$i]:((((in @ X311 @ X305)&(in @ X312 @ X305))=>(![X313:$i]:(((in @ X313 @ X311)=>(in @ X313 @ X312)))|![X314:$i]:(((in @ X314 @ X312)=>(in @ X314 @ X311)))))))&![X315:$i]:(((![X316:$i]:(((in @ X316 @ X315)=>(in @ X316 @ X304)))&?[X317:$i]:((in @ X317 @ X315)))=>?[X318:$i, X319:$i]:(((((in @ X318 @ X305)&(in @ X319 @ X315))&~(?[X320:$i]:(((in @ X320 @ X318)&(in @ X320 @ X315)))))&![X321:$i]:(((in @ X321 @ X305)=>(![X322:$i]:(((in @ X322 @ X321)=>(in @ X322 @ X318)))|(in @ X319 @ X321)))))))))))), introduced(definition)).
% 0.21/0.31 thf(c_0_123, negated_conjecture, ~((![X275:$i, X276:$i]:((![X277:$i]:(((in @ X277 @ X275)<=>(in @ X277 @ X276)))=>((X275)=(X276))))=>(![X278:$i]:(~(in @ X278 @ emptyset))=>(![X279:$i, X280:$i, X281:$i]:(((in @ X281 @ (setadjoin @ X279 @ X280))<=>(((X281)=(X279))|(in @ X281 @ X280))))=>(![X282:$i, X283:$i]:(((in @ X283 @ (powerset @ X282))<=>![X284:$i]:(((in @ X284 @ X283)=>(in @ X284 @ X282)))))=>(![X285:$i, X286:$i]:(((in @ X286 @ (setunion @ X285))<=>?[X287:$i]:(((in @ X286 @ X287)&(in @ X287 @ X285)))))=>((in @ emptyset @ omega)=>(![X288:$i]:(((in @ X288 @ omega)=>(in @ (setadjoin @ X288 @ X288) @ omega)))=>(![X289:$i]:((((in @ emptyset @ X289)&![X290:$i]:((((in @ X290 @ omega)&(in @ X290 @ X289))=>(in @ (setadjoin @ X290 @ X290) @ X289))))=>![X291:$i]:(((in @ X291 @ omega)=>(in @ X291 @ X289)))))=>(![X292:$i > $i > $o, X293:$i]:((![X294:$i]:(((in @ X294 @ X293)=>?[X295:$i]:(((X292 @ X294 @ X295)&![X296:$i]:(((X292 @ X294 @ X296)=>((X295)=(X296))))))))=>?[X297:$i]:(![X298:$i]:(((in @ X298 @ X297)<=>?[X299:$i]:(((in @ X299 @ X293)&(X292 @ X299 @ X298))))))))=>(![X300:$i]:((?[X301:$i]:((in @ X301 @ X300))=>?[X302:$i]:(((in @ X302 @ X300)&~(?[X303:$i]:(((in @ X303 @ X302)&(in @ X303 @ X300))))))))=>((epred1_0)=>(![X323:$i > $o]:((?[X324:$i]:(((X323 @ X324)&![X325:$i]:(((X323 @ X325)=>((X324)=(X325))))))=>(X323 @ (descr @ (^[Z0:$i]:((X323 @ Z0)))))))=>(![X326:$i, X327:$i > $o, X328:$i]:(((in @ X328 @ X326)=>((X327 @ X328)=>(in @ X328 @ (dsetconstr @ X326 @ (^[Z0:$i]:((X327 @ Z0))))))))=>(![X329:$i, X330:$i > $o, X331:$i]:(((in @ X331 @ (dsetconstr @ X329 @ (^[Z0:$i]:((X330 @ Z0)))))=>(in @ X331 @ X329)))=>(![X332:$i, X333:$i > $o, X334:$i]:(((in @ X334 @ (dsetconstr @ X332 @ (^[Z0:$i]:((X333 @ Z0)))))=>(X333 @ X334)))=>(![X335:$i > $o]:((?[X336:$i]:(((X335 @ X336)&![X337:$i]:(((X335 @ X337)=>((X336)=(X337))))))=>?[X338:$i]:(((X335 @ X338)&![X339:$i]:(((X335 @ X339)=>((X338)=(X339))))))))=>(![X340:$o, X341:$i]:(((in @ X341 @ (prop2set @ ((X340))))=>(X340)))=>(![X342:$i]:(((in @ X342 @ emptyset)=>![X343:$o]:((X343))))=>(![X344:$i]:(~(in @ X344 @ emptyset))=>(![X345:$i]:(~(in @ X345 @ emptyset))=>(![X346:$i > $o]:((?[X347:$i]:(((X346 @ X347)&![X348:$i]:(((X346 @ X348)=>((X347)=(X348))))))=>?[X349:$i]:((X346 @ X349))))=>(![X350:$i, X351:$i]:((![X352:$i]:(((in @ X352 @ X350)=>(in @ X352 @ X351)))=>(![X353:$i]:(((in @ X353 @ X351)=>(in @ X353 @ X350)))=>((X350)=(X351)))))=>(![X354:$i]:((![X355:$i]:(~(in @ X355 @ X354))=>((X354)=(emptyset))))=>(![X356:$i]:((![X357:$i]:(~(in @ X357 @ X356))=>((X356)=(emptyset))))=>(![X358:$i, X359:$i > $o, X360:$i]:(((in @ X360 @ X358)=>((in @ X360 @ (dsetconstr @ X358 @ (^[Z0:$i]:((X359 @ Z0)))))<=>(X359 @ X360))))=>(![X361:$i]:((((X361)!=(emptyset))=>?[X362:$i]:((in @ X362 @ X361))))=>(![X363:$i, X364:$i > $o, X365:$i]:(((in @ X365 @ X363)=>((X364 @ X365)=>((dsetconstr @ X363 @ (^[Z0:$i]:((X364 @ Z0))))!=(emptyset)))))=>(![X366:$i]:((?[X367:$i]:((in @ X367 @ X366))=>((X366)!=(emptyset))))=>(![X368:$i, X369:$i]:((in @ X368 @ (setadjoin @ X368 @ X369)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X370:$i, X371:$i, X372:$i]:(((in @ X372 @ X371)=>(in @ X372 @ (setadjoin @ X370 @ X371))))=>(![X373:$i, X374:$i, X375:$i]:(((in @ X375 @ (setadjoin @ X373 @ X374))=>![X376:$o]:(((((X375)=(X373))=>(X376))=>(((in @ X375 @ X374)=>(X376))=>(X376))))))=>(![X377:$i, X378:$i, X379:$i]:(((in @ X379 @ (setadjoin @ X377 @ X378))=>(((X379)=(X377))|(in @ X379 @ X378))))=>(![X380:$i]:(((dsetconstr @ X380 @ (^[Z0:$i]:(($true))))=(X380)))=>(![X381:$i, X382:$i]:((![X383:$i]:(((in @ X383 @ X382)=>(in @ X383 @ X381)))=>(in @ X382 @ (powerset @ X381))))=>(![X384:$i]:((in @ emptyset @ (powerset @ X384)))=>(![X385:$i]:((in @ emptyset @ (powerset @ X385)))=>(![X386:$i, X387:$i, X388:$i]:(((in @ X387 @ (powerset @ X386))=>((in @ X388 @ X387)=>(in @ X388 @ X386))))=>(![X389:$i, X390:$i, X391:$i]:(((in @ X390 @ X391)=>((in @ X391 @ X389)=>(in @ X390 @ (setunion @ X389)))))=>(![X392:$i, X393:$i]:(((in @ X393 @ (setunion @ X392))=>![X394:$o]:((![X395:$i]:(((in @ X393 @ X395)=>((in @ X395 @ X392)=>(X394))))=>(X394)))))=>(![X396:$i, X397:$i]:(((in @ X397 @ X396)=>(in @ X397 @ (powerset @ (setunion @ X396)))))=>(![X398:$i > $o]:((?[X399:$i]:(((X398 @ X399)&![X400:$i]:(((X398 @ X400)=>((X399)=(X400))))))=>?[X401:$i]:(![X402:$i]:(((X398 @ X402)<=>((X402)=(X401)))))))=>(![X403:$i]:((((X403)!=(emptyset))=>?[X404:$i]:((in @ X404 @ X403))))=>(![X405:$i, X406:$i]:(((in @ X405 @ (setadjoin @ X406 @ emptyset))=>((X405)=(X406))))=>(![X407:$i, X408:$i]:((((X407)!=(X408))=>~(in @ X408 @ (setadjoin @ X407 @ emptyset))))=>(![X409:$i, X410:$i]:((((X409)=(X410))=>(in @ X409 @ (setadjoin @ X410 @ emptyset))))=>(![X411:$i, X412:$i]:(((in @ X411 @ (setadjoin @ X412 @ emptyset))=>(in @ X412 @ (setadjoin @ X411 @ emptyset))))=>(![X413:$i, X414:$i, X415:$i]:(((in @ X415 @ (setadjoin @ X413 @ (setadjoin @ X414 @ emptyset)))=>(((X415)=(X413))|((X415)=(X414)))))=>(![X416:$i, X417:$i]:((in @ X416 @ (setadjoin @ X416 @ (setadjoin @ X417 @ emptyset))))=>(![X418:$i, X419:$i]:((in @ X419 @ (setadjoin @ X418 @ (setadjoin @ X419 @ emptyset))))=>(![X420:$i, X421:$i > $o]:((?[X422:$i]:(((in @ X422 @ X420)&(X421 @ X422)))=>((dsetconstr @ X420 @ (^[Z0:$i]:((X421 @ Z0))))!=(emptyset))))=>(![X423:$i > $o, X424:$i]:(((in @ X424 @ emptyset)=>(X423 @ X424)))=>(![X425:$i, X426:$i > $o]:((~(![X427:$i]:(((in @ X427 @ X425)=>(X426 @ X427))))=>?[X428:$i]:(((in @ X428 @ X425)&~(X426 @ X428)))))=>(![X429:$i, X430:$i > $o]:((![X431:$i]:(((in @ X431 @ X429)=>~(X430 @ X431)))=>~(?[X432:$i]:(((in @ X432 @ X429)&(X430 @ X432))))))=>(![X433:$i, X434:$i > $o]:((~(?[X435:$i]:(((in @ X435 @ X433)&(X434 @ X435))))=>![X436:$i]:(((in @ X436 @ X433)=>~(X434 @ X436)))))=>(![X437:$i, X438:$i > $o]:((?[X439:$i]:(((in @ X439 @ X437)&~(X438 @ X439)))=>~(![X440:$i]:(((in @ X440 @ X437)=>(X438 @ X440))))))=>(![X441:$o]:(((X441)=>(in @ emptyset @ (prop2set @ ((X441))))))=>((prop2set2propI)=>(![X442:$i, X443:$i > $o]:((~(?[X444:$i]:(((in @ X444 @ X442)&(X443 @ X444))))=>![X445:$i]:(((in @ X445 @ X442)=>~(X443 @ X445)))))=>(![X446:$i, X447:$i > $o]:((~(![X448:$i]:(((in @ X448 @ X446)=>(X447 @ X448))))=>?[X449:$i]:(((in @ X449 @ X446)&~(X447 @ X449)))))=>(![X450:$i > $o]:((?[X451:$i]:(((X450 @ X451)&![X452:$i]:(((X450 @ X452)=>((X451)=(X452))))))=>?[X453:$i]:(((X450 @ X453)&![X454:$i]:(((X450 @ X454)=>((X453)=(X454))))))))=>(![X455:$i > $o]:((?[X456:$i]:((X455 @ X456))=>(![X457:$i, X458:$i]:(((X455 @ X457)=>((X455 @ X458)=>((X457)=(X458)))))=>?[X459:$i]:(((X455 @ X459)&![X460:$i]:(((X455 @ X460)=>((X459)=(X460)))))))))=>(![X461:$i > $o]:((?[X462:$i]:(![X463:$i]:(((X461 @ X463)<=>((X463)=(X462)))))=>?[X464:$i]:(((X461 @ X464)&![X465:$i]:(((X461 @ X465)=>((X464)=(X465))))))))=>(![X466:$i, X467:$i]:((((X466)=(X467))=>![X468:$i, X469:$i]:((((X468)=(X469))=>((in @ X468 @ X466)=>(in @ X469 @ X467))))))=>(![X470:$i, X471:$i]:((((X470)=(X471))=>![X472:$i, X473:$i]:((((X472)=(X473))=>((in @ X472 @ X470)<=>(in @ X473 @ X471))))))=>(![X474:$i > $o]:((?[X475:$i]:(((X474 @ X475)&![X476:$i]:(((X474 @ X476)=>((X475)=(X476))))))=>![X477:$i, X478:$i]:(((X474 @ X477)=>((X474 @ X478)=>((X477)=(X478)))))))=>(![X479:$i > $o, X480:$i > $o]:((![X481:$i, X482:$i]:((((X481)=(X482))=>((X479 @ X481)<=>(X480 @ X482))))=>(?[X483:$i]:(((X479 @ X483)&![X484:$i]:(((X479 @ X484)=>((X483)=(X484))))))<=>?[X485:$i]:(((X480 @ X485)&![X486:$i]:(((X480 @ X486)=>((X485)=(X486)))))))))=>(((emptyset)=(emptyset))=>(![X487:$i, X488:$i]:((((X487)=(X488))=>![X489:$i, X490:$i]:((((X489)=(X490))=>((setadjoin @ X487 @ X489)=(setadjoin @ X488 @ X490))))))=>(![X491:$i, X492:$i]:((((X491)=(X492))=>((powerset @ X491)=(powerset @ X492))))=>(![X493:$i, X494:$i]:((((X493)=(X494))=>((setunion @ X493)=(setunion @ X494))))=>(((omega)=(omega))=>(![X495:$i > $o]:((?[X496:$i]:(((X495 @ X496)&![X497:$i]:(((X495 @ X497)=>((X496)=(X497))))))=>![X498:$i, X499:$i]:(((X495 @ X498)=>((X495 @ X499)=>((X498)=(X499)))))))=>(![X500:$i > $o, X501:$i > $o]:((![X502:$i, X503:$i]:((((X502)=(X503))=>((X500 @ X502)<=>(X501 @ X503))))=>(?[X504:$i]:(((X500 @ X504)&![X505:$i]:(((X500 @ X505)=>((X504)=(X505))))))=>(?[X506:$i]:(((X501 @ X506)&![X507:$i]:(((X501 @ X507)=>((X506)=(X507))))))=>((descr @ (^[Z0:$i]:((X500 @ Z0))))=(descr @ (^[Z0:$i]:((X501 @ Z0)))))))))=>(![X508:$i, X509:$i]:((((X508)=(X509))=>![X510:$i > $o, X511:$i > $o]:((![X512:$i]:(((in @ X512 @ X508)=>![X513:$i]:(((in @ X513 @ X509)=>(((X512)=(X513))=>((X510 @ X512)<=>(X511 @ X513)))))))=>((dsetconstr @ X508 @ (^[Z0:$i]:((X510 @ Z0))))=(dsetconstr @ X509 @ (^[Z0:$i]:((X511 @ Z0)))))))))=>(![X514:$i, X515:$i]:((![X516:$i]:(((in @ X516 @ X514)=>(in @ X516 @ X515)))=>(subset @ X514 @ X515)))=>(![X517:$i, X518:$i]:((((X517)=(X518))=>(subset @ X518 @ X517)))=>(![X519:$i, X520:$i]:((((X519)=(X520))=>(subset @ X519 @ X520)))=>(![X521:$i, X522:$i]:((![X523:$i]:(((in @ X523 @ X521)=>(in @ X523 @ X522)))=>(subset @ X521 @ X522)))=>(![X524:$i]:((subset @ emptyset @ X524))=>(![X525:$i, X526:$i, X527:$i]:(((subset @ X525 @ X526)=>((in @ X527 @ X525)=>(in @ X527 @ X526))))=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~(in @ X2 @ X5)=>~(in @ X2 @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_98, c_0_99]), c_0_100]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_101]), c_0_102]), c_0_103]), subsetI1]), emptysetimpfalse]), eqimpsubset2]), emptysetE]), eqimpsubset1]), prop2setE]), subsetI2]), c_0_104]), emptysetsubset]), c_0_105]), subsetE]), c_0_106]), c_0_107]), c_0_108]), notinemptyset]), emptyinPowerset]), c_0_109]), c_0_110]), c_0_111]), noeltsimpempty]), emptyI]), setext]), c_0_112]), c_0_113]), powersetI]), c_0_114]), setadjoinOr]), setadjoinE]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), c_0_115]), c_0_116]), subPowSU]), setunionE]), setunionI]), powersetE]), emptyInPowerset]), uniqinunit]), c_0_117]), upairsetIR]), upairsetIL]), upairsetE]), singletonsswitch]), eqinunit]), notinsingleton]), vacuousDall]), notdallE]), notdexE]), prop2setI]), quantDeMorgan4]), quantDeMorgan3]), quantDeMorgan2]), quantDeMorgan1]), c_0_118]), c_0_119]), inCongP]), in__Cong]), c_0_120]), wellorderingAx]), foundationAx]), c_0_121]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])]), c_0_122])).
% 0.21/0.31 thf(c_0_124, negated_conjecture, ![X528:$i, X529:$i, X531:$i, X532:$i, X533:$i, X534:$i, X535:$i, X536:$i, X537:$i, X538:$i, X539:$i, X541:$i, X542:$i, X544:$i, X545:$i, X546:$i, X547:$i, X548:$i, X550:$i, X551:$i > $i > $o, X552:$i, X554:$i, X557:$i, X559:$i, X560:$i, X561:$i, X562:$i, X564:$i, X565:$i > $o, X566:$i, X568:$i, X569:$i > $o, X570:$i, X571:$i, X572:$i > $o, X573:$i, X574:$i, X575:$i > $o, X576:$i, X577:$i > $o, X578:$i, X581:$i, X582:$o, X583:$i, X584:$i, X585:$o, X586:$i, X587:$i, X588:$i > $o, X589:$i, X592:$i, X593:$i, X596:$i, X598:$i, X600:$i, X601:$i > $o, X602:$i, X603:$i, X605:$i, X606:$i > $o, X607:$i, X608:$i, X609:$i, X610:$i, X611:$i, X612:$i, X613:$i, X614:$i, X615:$i, X616:$i, X617:$i, X618:$o, X619:$i, X620:$i, X621:$i, X622:$i, X623:$i, X624:$i, X626:$i, X627:$i, X628:$i, X629:$i, X630:$i, X631:$i, X632:$i, X633:$i, X634:$i, X635:$i, X636:$o, X638:$i, X639:$i, X640:$i > $o, X641:$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:$i, X658:$i, X659:$i, X660:$i, X661:$i, X662:$i, X663:$i, X664:$i > $o, X665:$i, X666:$i > $o, X667:$i, X668:$i, X669:$i > $o, X670:$i, X672:$i, X673:$i > $o, X675:$i, X676:$i, X677:$i > $o, X679:$i, X680:$i, X681:$i > $o, X682:$i, X684:$o, X685:$i, X686:$i > $o, X688:$i, X689:$i, X690:$i > $o, X691:$i, X693:$i > $o, X694:$i, X697:$i, X698:$i > $o, X699:$i, X703:$i, X704:$i > $o, X705:$i, X708:$i, X709:$i, X710:$i, X711:$i, X712:$i, X713:$i, X714:$i, X715:$i, X716:$i, X717:$i > $o, X718:$i, X720:$i, X721:$i, X722:$i > $o, X723:$i > $o, X726:$i, X729:$i, X730:$i, X733:$i, X734:$i, X735:$i, X736:$i, X737:$i, X738:$i, X739:$i, X740:$i, X741:$i, X742:$i > $o, X743:$i, X745:$i, X746:$i, X747:$i > $o, X748:$i > $o, X751:$i, X753:$i, X755:$i, X756:$i, X757:$i > $o, X758:$i > $o, X761:$i, X762:$i, X764:$i, X765:$i, X766:$i, X767:$i, X768:$i, X769:$i, X771:$i, X772:$i, X773:$i, X774:$i]:((((~(in @ (esk1_2 @ X528 @ X529) @ X528)|~(in @ (esk1_2 @ X528 @ X529) @ X529)|((X528)=(X529)))&((in @ (esk1_2 @ X528 @ X529) @ X528)|(in @ (esk1_2 @ X528 @ X529) @ X529)|((X528)=(X529))))&(~(in @ X531 @ emptyset)&(((~(in @ X534 @ (setadjoin @ X532 @ X533))|(((X534)=(X532))|(in @ X534 @ X533)))&((((X534)!=(X532))|(in @ X534 @ (setadjoin @ X532 @ X533)))&(~(in @ X534 @ X533)|(in @ X534 @ (setadjoin @ X532 @ X533)))))&(((~(in @ X536 @ (powerset @ X535))|(~(in @ X537 @ X536)|(in @ X537 @ X535)))&(((in @ (esk2_2 @ X538 @ X539) @ X539)|(in @ X539 @ (powerset @ X538)))&(~(in @ (esk2_2 @ X538 @ X539) @ X538)|(in @ X539 @ (powerset @ X538)))))&(((((in @ X542 @ (esk3_2 @ X541 @ X542))|~(in @ X542 @ (setunion @ X541)))&((in @ (esk3_2 @ X541 @ X542) @ X541)|~(in @ X542 @ (setunion @ X541))))&(~(in @ X545 @ X546)|~(in @ X546 @ X544)|(in @ X545 @ (setunion @ X544))))&((in @ emptyset @ omega)&((~(in @ X547 @ omega)|(in @ (setadjoin @ X547 @ X547) @ omega))&(((((in @ (esk4_1 @ X548) @ omega)|~(in @ emptyset @ X548)|(~(in @ X550 @ omega)|(in @ X550 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X751))|~(X747 @ X751))|((esk46_2 @ X747 @ X748)=(esk47_2 @ X747 @ X748)))&(((X753)!=(esk49_3 @ X747 @ X748 @ X753))|~(X748 @ X753)|((descr @ (^[Z0:$i]:((X747 @ Z0))))=(descr @ (^[Z0:$i]:((X748 @ Z0)))))|(((X751)!=(esk48_3 @ X747 @ X748 @ X751))|~(X747 @ X751))|((esk46_2 @ X747 @ X748)=(esk47_2 @ X747 @ X748)))))&(((((X748 @ (esk49_3 @ X747 @ X748 @ X753))|~(X748 @ X753)|((descr @ (^[Z0:$i]:((X747 @ Z0))))=(descr @ (^[Z0:$i]:((X748 @ Z0)))))|((X747 @ (esk48_3 @ X747 @ X748 @ X751))|~(X747 @ X751))|(~(X747 @ (esk46_2 @ X747 @ X748))|~(X748 @ (esk47_2 @ X747 @ X748))))&(((X753)!=(esk49_3 @ X747 @ X748 @ X753))|~(X748 @ X753)|((descr @ (^[Z0:$i]:((X747 @ Z0))))=(descr @ (^[Z0:$i]:((X748 @ Z0)))))|((X747 @ (esk48_3 @ X747 @ X748 @ X751))|~(X747 @ X751))|(~(X747 @ (esk46_2 @ X747 @ X748))|~(X748 @ (esk47_2 @ X747 @ X748)))))&(((X748 @ (esk49_3 @ X747 @ X748 @ X753))|~(X748 @ X753)|((descr @ (^[Z0:$i]:((X747 @ Z0))))=(descr @ (^[Z0:$i]:((X748 @ Z0)))))|(((X751)!=(esk48_3 @ X747 @ X748 @ X751))|~(X747 @ X751))|(~(X747 @ (esk46_2 @ X747 @ X748))|~(X748 @ (esk47_2 @ X747 @ X748))))&(((X753)!=(esk49_3 @ X747 @ X748 @ X753))|~(X748 @ X753)|((descr @ (^[Z0:$i]:((X747 @ Z0))))=(descr @ (^[Z0:$i]:((X748 @ Z0)))))|(((X751)!=(esk48_3 @ X747 @ X748 @ X751))|~(X747 @ X751))|(~(X747 @ (esk46_2 @ X747 @ X748))|~(X748 @ (esk47_2 @ X747 @ X748))))))&((((X748 @ (esk49_3 @ X747 @ X748 @ X753))|~(X748 @ X753)|((descr @ (^[Z0:$i]:((X747 @ Z0))))=(descr @ (^[Z0:$i]:((X748 @ Z0)))))|((X747 @ (esk48_3 @ X747 @ X748 @ X751))|~(X747 @ X751))|((X747 @ (esk46_2 @ X747 @ X748))|(X748 @ (esk47_2 @ X747 @ X748))))&(((X753)!=(esk49_3 @ X747 @ X748 @ X753))|~(X748 @ X753)|((descr @ (^[Z0:$i]:((X747 @ Z0))))=(descr @ (^[Z0:$i]:((X748 @ Z0)))))|((X747 @ (esk48_3 @ X747 @ X748 @ X751))|~(X747 @ X751))|((X747 @ (esk46_2 @ X747 @ X748))|(X748 @ (esk47_2 @ X747 @ X748)))))&(((X748 @ (esk49_3 @ X747 @ X748 @ X753))|~(X748 @ X753)|((descr @ (^[Z0:$i]:((X747 @ Z0))))=(descr @ (^[Z0:$i]:((X748 @ Z0)))))|(((X751)!=(esk48_3 @ X747 @ X748 @ X751))|~(X747 @ X751))|((X747 @ (esk46_2 @ X747 @ X748))|(X748 @ (esk47_2 @ X747 @ X748))))&(((X753)!=(esk49_3 @ X747 @ X748 @ X753))|~(X748 @ X753)|((descr @ (^[Z0:$i]:((X747 @ Z0))))=(descr @ (^[Z0:$i]:((X748 @ Z0)))))|(((X751)!=(esk48_3 @ X747 @ X748 @ X751))|~(X747 @ X751))|((X747 @ (esk46_2 @ X747 @ X748))|(X748 @ (esk47_2 @ X747 @ X748))))))))&((((in @ (esk50_4 @ X755 @ X756 @ X757 @ X758) @ X755)|((dsetconstr @ X755 @ (^[Z0:$i]:((X757 @ Z0))))=(dsetconstr @ X756 @ (^[Z0:$i]:((X758 @ Z0)))))|((X755)!=(X756)))&(((in @ (esk51_4 @ X755 @ X756 @ X757 @ X758) @ X756)|((dsetconstr @ X755 @ (^[Z0:$i]:((X757 @ Z0))))=(dsetconstr @ X756 @ (^[Z0:$i]:((X758 @ Z0)))))|((X755)!=(X756)))&((((esk50_4 @ X755 @ X756 @ X757 @ X758)=(esk51_4 @ X755 @ X756 @ X757 @ X758))|((dsetconstr @ X755 @ (^[Z0:$i]:((X757 @ Z0))))=(dsetconstr @ X756 @ (^[Z0:$i]:((X758 @ Z0)))))|((X755)!=(X756)))&((~(X757 @ (esk50_4 @ X755 @ X756 @ X757 @ X758))|~(X758 @ (esk51_4 @ X755 @ X756 @ X757 @ X758))|((dsetconstr @ X755 @ (^[Z0:$i]:((X757 @ Z0))))=(dsetconstr @ X756 @ (^[Z0:$i]:((X758 @ Z0)))))|((X755)!=(X756)))&((X757 @ (esk50_4 @ X755 @ X756 @ X757 @ X758))|(X758 @ (esk51_4 @ X755 @ X756 @ X757 @ X758))|((dsetconstr @ X755 @ (^[Z0:$i]:((X757 @ Z0))))=(dsetconstr @ X756 @ (^[Z0:$i]:((X758 @ Z0)))))|((X755)!=(X756)))))))&((((in @ (esk52_2 @ X761 @ X762) @ X761)|(subset @ X761 @ X762))&(~(in @ (esk52_2 @ X761 @ X762) @ X762)|(subset @ X761 @ X762)))&((((X764)!=(X765))|(subset @ X765 @ X764))&((((X766)!=(X767))|(subset @ X766 @ X767))&((((in @ (esk53_2 @ X768 @ X769) @ X768)|(subset @ X768 @ X769))&(~(in @ (esk53_2 @ X768 @ X769) @ X769)|(subset @ X768 @ X769)))&((subset @ emptyset @ X771)&((~(subset @ X772 @ X773)|(~(in @ X774 @ X772)|(in @ X774 @ X773)))&((subset @ esk54_0 @ esk55_0)&(~(in @ esk56_0 @ esk55_0)&(in @ esk56_0 @ esk54_0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_123])])])])])])).
% 0.21/0.31 thf(c_0_125, negated_conjecture, ![X4:$i, X3:$i, X2:$i]:(((in @ X4 @ X3)|~((subset @ X2 @ X3))|~((in @ X4 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_124])).
% 0.21/0.31 thf(c_0_126, negated_conjecture, (subset @ esk54_0 @ esk55_0), inference(split_conjunct,[status(thm)],[c_0_124])).
% 0.21/0.31 thf(c_0_127, negated_conjecture, ~((in @ esk56_0 @ esk55_0)), inference(split_conjunct,[status(thm)],[c_0_124])).
% 0.21/0.31 thf(c_0_128, negated_conjecture, ![X2:$i]:(((in @ X2 @ esk55_0)|~((in @ X2 @ esk54_0)))), inference(spm,[status(thm)],[c_0_125, c_0_126])).
% 0.21/0.31 thf(c_0_129, negated_conjecture, (in @ esk56_0 @ esk54_0), inference(split_conjunct,[status(thm)],[c_0_124])).
% 0.21/0.31 thf(c_0_130, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127, c_0_128]), c_0_129])]), ['proof']).
% 0.21/0.31 % SZS output end CNFRefutation
% 0.21/0.31 % Parsed axioms : 180
% 0.21/0.31 % Removed by relevancy pruning/SinE : 97
% 0.21/0.31 % Initial clauses : 193
% 0.21/0.31 % Removed in clause preprocessing : 12
% 0.21/0.31 % Initial clauses in saturation : 181
% 0.21/0.31 % Processed clauses : 67
% 0.21/0.31 % ...of these trivial : 2
% 0.21/0.31 % ...subsumed : 15
% 0.21/0.31 % ...remaining for further processing : 50
% 0.21/0.31 % Other redundant clauses eliminated : 5
% 0.21/0.31 % Clauses deleted for lack of memory : 0
% 0.21/0.31 % Backward-subsumed : 0
% 0.21/0.31 % Backward-rewritten : 2
% 0.21/0.31 % Generated clauses : 129
% 0.21/0.31 % ...of the previous two non-redundant : 104
% 0.21/0.31 % ...aggressively subsumed : 0
% 0.21/0.31 % Contextual simplify-reflections : 0
% 0.21/0.31 % Paramodulations : 124
% 0.21/0.31 % Factorizations : 0
% 0.21/0.31 % NegExts : 0
% 0.21/0.31 % Equation resolutions : 5
% 0.21/0.31 % Disequality decompositions : 0
% 0.21/0.32 % Total rewrite steps : 27
% 0.21/0.32 % ...of those cached : 9
% 0.21/0.32 % Propositional unsat checks : 0
% 0.21/0.32 % Propositional check models : 0
% 0.21/0.32 % Propositional check unsatisfiable : 0
% 0.21/0.32 % Propositional clauses : 0
% 0.21/0.32 % Propositional clauses after purity: 0
% 0.21/0.32 % Propositional unsat core size : 0
% 0.21/0.32 % Propositional preprocessing time : 0.000
% 0.21/0.32 % Propositional encoding time : 0.000
% 0.21/0.32 % Propositional solver time : 0.000
% 0.21/0.32 % Success case prop preproc time : 0.000
% 0.21/0.32 % Success case prop encoding time : 0.000
% 0.21/0.32 % Success case prop solver time : 0.000
% 0.21/0.32 % Current number of processed clauses : 43
% 0.21/0.32 % Positive orientable unit clauses : 19
% 0.21/0.32 % Positive unorientable unit clauses: 0
% 0.21/0.32 % Negative unit clauses : 2
% 0.21/0.32 % Non-unit-clauses : 22
% 0.21/0.32 % Current number of unprocessed clauses: 216
% 0.21/0.32 % ...number of literals in the above : 741
% 0.21/0.32 % Current number of archived formulas : 0
% 0.21/0.32 % Current number of archived clauses : 2
% 0.21/0.32 % Clause-clause subsumption calls (NU) : 54
% 0.21/0.32 % Rec. Clause-clause subsumption calls : 48
% 0.21/0.32 % Non-unit clause-clause subsumptions : 8
% 0.21/0.32 % Unit Clause-clause subsumption calls : 15
% 0.21/0.32 % Rewrite failures with RHS unbound : 0
% 0.21/0.32 % BW rewrite match attempts : 4
% 0.21/0.32 % BW rewrite match successes : 2
% 0.21/0.32 % Condensation attempts : 0
% 0.21/0.32 % Condensation successes : 0
% 0.21/0.32 % Termbank termtop insertions : 22216
% 0.21/0.32 % Search garbage collected termcells : 7896
% 0.21/0.32
% 0.21/0.32 % -------------------------------------------------
% 0.21/0.32 % User time : 0.017 s
% 0.21/0.32 % System time : 0.008 s
% 0.21/0.32 % Total time : 0.026 s
% 0.21/0.32 % Maximum resident set size: 6116 pages
% 0.21/0.32
% 0.21/0.32 % -------------------------------------------------
% 0.21/0.32 % User time : 0.022 s
% 0.21/0.32 % System time : 0.013 s
% 0.21/0.32 % Total time : 0.036 s
% 0.21/0.32 % Maximum resident set size: 5120 pages
% 0.21/0.32 % E exiting
%------------------------------------------------------------------------------