%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU559^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 08:26:42 AM UTC 2026
% Result : Theorem 0.23s 0.31s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU559^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n006.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 13:49:54 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.08/0.26 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p
% 0.23/0.31 % Version: 3.5.1-ho
% 0.23/0.31 % Preprocessing class: HSMSSLSSLLLCHFA.
% 0.23/0.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.31 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.31 % Starting sh5l with 300s (1) cores
% 0.23/0.31 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.31 % Starting new_bool_2 with 300s (1) cores
% 0.23/0.31 % new_bool_2 with pid 750524 completed with status 0
% 0.23/0.31 % Result found by new_bool_2
% 0.23/0.31 % Preprocessing class: HSMSSLSSLLLCHFA.
% 0.23/0.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.31 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.31 % Starting sh5l with 300s (1) cores
% 0.23/0.31 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.31 % Starting new_bool_2 with 300s (1) cores
% 0.23/0.31 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.23/0.31 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.23/0.31 % Search class: HGHSM-FSLM31-SHFMMMBN
% 0.23/0.31 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.31 % Starting SubtermCWHack with 28s (1) cores
% 0.23/0.31 % SubtermCWHack with pid 750531 completed with status 0
% 0.23/0.31 % Result found by SubtermCWHack
% 0.23/0.31 % Preprocessing class: HSMSSLSSLLLCHFA.
% 0.23/0.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.31 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.31 % Starting sh5l with 300s (1) cores
% 0.23/0.31 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.31 % Starting new_bool_2 with 300s (1) cores
% 0.23/0.31 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.23/0.31 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.23/0.31 % Search class: HGHSM-FSLM31-SHFMMMBN
% 0.23/0.31 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.31 % Starting SubtermCWHack with 28s (1) cores
% 0.23/0.31 % Preprocessing time : 0.004 s
% 0.23/0.31
% 0.23/0.31 % Proof found!
% 0.23/0.31 % SZS status Theorem
% 0.23/0.31 % SZS output start CNFRefutation
% 0.23/0.31 thf(decl_23, type, in: $i > $i > $o).
% 0.23/0.31 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.23/0.31 thf(decl_25, type, setextAx: $o).
% 0.23/0.31 thf(decl_26, type, emptyset: $i).
% 0.23/0.31 thf(decl_27, type, emptysetAx: $o).
% 0.23/0.31 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.23/0.31 thf(decl_29, type, setadjoinAx: $o).
% 0.23/0.31 thf(decl_30, type, powerset: $i > $i).
% 0.23/0.31 thf(decl_31, type, powersetAx: $o).
% 0.23/0.31 thf(decl_32, type, setunion: $i > $i).
% 0.23/0.31 thf(decl_33, type, setunionAx: $o).
% 0.23/0.31 thf(decl_34, type, omega: $i).
% 0.23/0.31 thf(decl_35, type, omega0Ax: $o).
% 0.23/0.31 thf(decl_36, type, omegaSAx: $o).
% 0.23/0.31 thf(decl_37, type, omegaIndAx: $o).
% 0.23/0.31 thf(decl_38, type, replAx: $o).
% 0.23/0.31 thf(decl_39, type, foundationAx: $o).
% 0.23/0.31 thf(decl_40, type, wellorderingAx: $o).
% 0.23/0.31 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.23/0.31 thf(decl_42, type, descrp: $o).
% 0.23/0.31 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.23/0.31 thf(decl_44, type, dsetconstrI: $o).
% 0.23/0.31 thf(decl_45, type, dsetconstrEL: $o).
% 0.23/0.31 thf(decl_46, type, dsetconstrER: $o).
% 0.23/0.31 thf(decl_47, type, exuE1: $o).
% 0.23/0.31 thf(decl_48, type, prop2set: $o > $i).
% 0.23/0.31 thf(decl_49, type, prop2setE: $o).
% 0.23/0.31 thf(decl_50, type, emptysetE: $o).
% 0.23/0.31 thf(decl_51, type, emptysetimpfalse: $o).
% 0.23/0.31 thf(decl_52, type, notinemptyset: $o).
% 0.23/0.31 thf(decl_53, type, exuE3e: $o).
% 0.23/0.31 thf(decl_54, type, setext: $o).
% 0.23/0.31 thf(decl_55, type, emptyI: $o).
% 0.23/0.31 thf(decl_56, type, noeltsimpempty: $o).
% 0.23/0.31 thf(decl_57, type, setbeta: $o).
% 0.23/0.31 thf(decl_58, type, nonempty: $i > $o).
% 0.23/0.31 thf(decl_59, type, nonemptyE1: $o).
% 0.23/0.31 thf(decl_60, type, nonemptyI: $o).
% 0.23/0.31 thf(decl_61, type, nonemptyI1: $o).
% 0.23/0.31 thf(decl_62, type, setadjoinIL: $o).
% 0.23/0.31 thf(decl_63, type, emptyinunitempty: $o).
% 0.23/0.31 thf(decl_64, type, setadjoinIR: $o).
% 0.23/0.31 thf(decl_65, type, setadjoinE: $o).
% 0.23/0.31 thf(decl_66, type, setadjoinOr: $o).
% 0.23/0.31 thf(decl_67, type, setoftrueEq: $o).
% 0.23/0.31 thf(decl_68, type, powersetI: $o).
% 0.23/0.31 thf(decl_69, type, emptyinPowerset: $o).
% 0.23/0.31 thf(decl_70, type, emptyInPowerset: $o).
% 0.23/0.31 thf(decl_71, type, powersetE: $o).
% 0.23/0.31 thf(decl_72, type, setunionI: $o).
% 0.23/0.31 thf(decl_73, type, setunionE: $o).
% 0.23/0.31 thf(decl_74, type, subPowSU: $o).
% 0.23/0.31 thf(decl_75, type, exuE2: $o).
% 0.23/0.31 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.23/0.31 thf(decl_77, type, uniqinunit: $o).
% 0.23/0.31 thf(decl_78, type, notinsingleton: $o).
% 0.23/0.31 thf(decl_79, type, eqinunit: $o).
% 0.23/0.31 thf(decl_80, type, singletonsswitch: $o).
% 0.23/0.31 thf(decl_81, type, upairsetE: $o).
% 0.23/0.31 thf(decl_82, type, upairsetIL: $o).
% 0.23/0.31 thf(decl_83, type, upairsetIR: $o).
% 0.23/0.31 thf(decl_84, type, emptyE1: $o).
% 0.23/0.31 thf(decl_85, type, vacuousDall: $o).
% 0.23/0.31 thf(decl_86, type, quantDeMorgan1: $o).
% 0.23/0.31 thf(decl_87, type, quantDeMorgan2: $o).
% 0.23/0.31 thf(decl_88, type, quantDeMorgan3: $o).
% 0.23/0.31 thf(decl_89, type, quantDeMorgan4: $o).
% 0.23/0.31 thf(decl_90, type, prop2setI: $o).
% 0.23/0.31 thf(decl_92, type, prop2set2propI: $o).
% 0.23/0.31 thf(decl_93, type, notdexE: $o).
% 0.23/0.31 thf(decl_94, type, notdallE: $o).
% 0.23/0.31 thf(decl_95, type, exuI1: $o).
% 0.23/0.31 thf(decl_96, type, exuI3: $o).
% 0.23/0.31 thf(decl_97, type, exuI2: $o).
% 0.23/0.31 thf(decl_98, type, inCongP: $o).
% 0.23/0.31 thf(decl_99, type, in__Cong: $o).
% 0.23/0.31 thf(decl_100, type, exuE3u: $o).
% 0.23/0.31 thf(decl_101, type, exu__Cong: $o).
% 0.23/0.31 thf(decl_102, type, emptyset__Cong: $o).
% 0.23/0.31 thf(decl_103, type, setadjoin__Cong: $o).
% 0.23/0.31 thf(decl_104, type, powerset__Cong: $o).
% 0.23/0.31 thf(decl_105, type, setunion__Cong: $o).
% 0.23/0.31 thf(decl_106, type, omega__Cong: $o).
% 0.23/0.31 thf(decl_107, type, exuEu: $o).
% 0.23/0.31 thf(decl_108, type, descr__Cong: $o).
% 0.23/0.31 thf(decl_109, type, dsetconstr__Cong: $o).
% 0.23/0.31 thf(decl_110, type, subset: $i > $i > $o).
% 0.23/0.31 thf(decl_113, type, epred1_0: $o).
% 0.23/0.31 thf(decl_114, type, esk1_2: $i > $i > $i).
% 0.23/0.31 thf(decl_115, type, esk2_2: $i > $i > $i).
% 0.23/0.31 thf(decl_116, type, esk3_2: $i > $i > $i).
% 0.23/0.31 thf(decl_117, type, esk4_1: $i > $i).
% 0.23/0.31 thf(decl_118, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.23/0.31 thf(decl_119, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.23/0.31 thf(decl_120, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.23/0.31 thf(decl_121, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.23/0.31 thf(decl_122, type, esk9_1: $i > $i).
% 0.23/0.31 thf(decl_123, type, esk10_2: ($i > $o) > $i > $i).
% 0.23/0.31 thf(decl_124, type, esk11_2: ($i > $o) > $i > $i).
% 0.23/0.31 thf(decl_125, type, esk12_1: ($i > $o) > $i).
% 0.23/0.31 thf(decl_126, type, esk13_2: ($i > $o) > $i > $i).
% 0.23/0.31 thf(decl_127, type, esk14_1: ($i > $o) > $i).
% 0.23/0.31 thf(decl_128, type, esk15_2: $i > $i > $i).
% 0.23/0.31 thf(decl_129, type, esk16_2: $i > $i > $i).
% 0.23/0.31 thf(decl_130, type, esk17_1: $i > $i).
% 0.23/0.31 thf(decl_131, type, esk18_1: $i > $i).
% 0.23/0.31 thf(decl_132, type, esk19_1: $i > $i).
% 0.23/0.31 thf(decl_133, type, esk20_2: $i > $i > $i).
% 0.23/0.31 thf(decl_134, type, esk21_3: $i > $i > $o > $i).
% 0.23/0.31 thf(decl_135, type, esk22_2: ($i > $o) > $i > $i).
% 0.23/0.31 thf(decl_136, type, esk23_1: ($i > $o) > $i).
% 0.23/0.31 thf(decl_137, type, esk24_1: $i > $i).
% 0.23/0.31 thf(decl_138, type, esk25_2: $i > ($i > $o) > $i).
% 0.23/0.31 thf(decl_139, type, esk26_2: $i > ($i > $o) > $i).
% 0.23/0.31 thf(decl_140, type, esk27_2: $i > ($i > $o) > $i).
% 0.23/0.31 thf(decl_141, type, esk28_2: $i > ($i > $o) > $i).
% 0.23/0.31 thf(decl_142, type, esk29_2: $i > ($i > $o) > $i).
% 0.23/0.31 thf(decl_143, type, esk30_2: $i > ($i > $o) > $i).
% 0.23/0.31 thf(decl_144, type, esk31_2: ($i > $o) > $i > $i).
% 0.23/0.31 thf(decl_145, type, esk32_1: ($i > $o) > $i).
% 0.23/0.31 thf(decl_146, type, esk33_1: ($i > $o) > $i).
% 0.23/0.31 thf(decl_147, type, esk34_1: ($i > $o) > $i).
% 0.23/0.31 thf(decl_148, type, esk35_1: ($i > $o) > $i).
% 0.23/0.31 thf(decl_149, type, esk36_2: ($i > $o) > $i > $i).
% 0.23/0.31 thf(decl_150, type, esk37_1: ($i > $o) > $i).
% 0.23/0.31 thf(decl_151, type, esk38_2: ($i > $o) > $i > $i).
% 0.23/0.31 thf(decl_152, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 0.23/0.31 thf(decl_153, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 0.23/0.31 thf(decl_154, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.23/0.31 thf(decl_155, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 0.23/0.31 thf(decl_156, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.23/0.31 thf(decl_157, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 0.23/0.31 thf(decl_158, type, esk45_2: ($i > $o) > $i > $i).
% 0.23/0.31 thf(decl_159, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 0.23/0.31 thf(decl_160, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 0.23/0.31 thf(decl_161, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.23/0.31 thf(decl_162, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.23/0.31 thf(decl_163, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.23/0.31 thf(decl_164, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.23/0.31 thf(decl_165, type, esk52_0: $i).
% 0.23/0.31 thf(decl_166, type, esk53_0: $i).
% 0.23/0.31 thf(decl_167, type, esk54_0: $i).
% 0.23/0.31 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', exuI2)).
% 0.23/0.31 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', exu)).
% 0.23/0.31 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', exuE3u)).
% 0.23/0.31 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/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', exuE1)).
% 0.23/0.31 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', exu__Cong)).
% 0.23/0.31 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', descrp)).
% 0.23/0.31 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', exuEu)).
% 0.23/0.31 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', descr__Cong)).
% 0.23/0.31 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', exuE3e)).
% 0.23/0.31 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', nonempty)).
% 0.23/0.31 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', nonemptyI)).
% 0.23/0.31 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', exuE2)).
% 0.23/0.31 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/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', exuI1)).
% 0.23/0.31 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', exuI3)).
% 0.23/0.31 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', replAx)).
% 0.23/0.31 thf(subsetI1, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', subsetI1)).
% 0.23/0.31 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', dsetconstrER)).
% 0.23/0.31 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', dsetconstrEL)).
% 0.23/0.31 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', dsetconstrI)).
% 0.23/0.31 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', dsetconstr__Cong)).
% 0.23/0.31 thf(subset, axiom, ((subset)=(^[X4:$i, X5:$i]:(![X2:$i]:((((in @ X2 @ X4))=>((in @ X2 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', subset)).
% 0.23/0.31 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', setbeta)).
% 0.23/0.31 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', nonemptyI1)).
% 0.23/0.31 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', nonemptyE1)).
% 0.23/0.31 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', setoftrueEq)).
% 0.23/0.31 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', nonemptyImpWitness)).
% 0.23/0.31 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', emptyE1)).
% 0.23/0.31 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/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', inCongP)).
% 0.23/0.31 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/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', in__Cong)).
% 0.23/0.31 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', emptyset__Cong)).
% 0.23/0.31 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/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', setadjoin__Cong)).
% 0.23/0.31 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', powerset__Cong)).
% 0.23/0.31 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', setunion__Cong)).
% 0.23/0.31 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', wellorderingAx)).
% 0.23/0.31 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', omega__Cong)).
% 0.23/0.31 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', foundationAx)).
% 0.23/0.31 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', prop2setE)).
% 0.23/0.31 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', noeltsimpempty)).
% 0.23/0.31 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', emptyI)).
% 0.23/0.31 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', setext)).
% 0.23/0.31 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', notinemptyset)).
% 0.23/0.31 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', emptysetimpfalse)).
% 0.23/0.31 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', emptysetE)).
% 0.23/0.31 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/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', setadjoinE)).
% 0.23/0.31 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', setadjoinIR)).
% 0.23/0.31 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', emptyinunitempty)).
% 0.23/0.31 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', setadjoinIL)).
% 0.23/0.31 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', setadjoinOr)).
% 0.23/0.31 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/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', setunionE)).
% 0.23/0.31 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', setunionI)).
% 0.23/0.31 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', powersetE)).
% 0.23/0.31 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', emptyInPowerset)).
% 0.23/0.31 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', emptyinPowerset)).
% 0.23/0.31 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', powersetI)).
% 0.23/0.31 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', subPowSU)).
% 0.23/0.31 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', upairsetE)).
% 0.23/0.31 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', singletonsswitch)).
% 0.23/0.31 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', eqinunit)).
% 0.23/0.31 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', notinsingleton)).
% 0.23/0.31 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', uniqinunit)).
% 0.23/0.31 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', upairsetIL)).
% 0.23/0.31 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', quantDeMorgan4)).
% 0.23/0.31 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', quantDeMorgan3)).
% 0.23/0.31 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', quantDeMorgan2)).
% 0.23/0.31 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', quantDeMorgan1)).
% 0.23/0.31 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', vacuousDall)).
% 0.23/0.31 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', upairsetIR)).
% 0.23/0.31 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', notdexE)).
% 0.23/0.31 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', notdallE)).
% 0.23/0.31 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', prop2setI)).
% 0.23/0.31 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', omegaIndAx)).
% 0.23/0.31 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', omegaSAx)).
% 0.23/0.31 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', omega0Ax)).
% 0.23/0.31 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', setunionAx)).
% 0.23/0.31 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', powersetAx)).
% 0.23/0.31 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', setadjoinAx)).
% 0.23/0.31 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', emptysetAx)).
% 0.23/0.31 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.7p0XOfJVHV/E---3.1_750491.p', setextAx)).
% 0.23/0.31 thf(c_0_78, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.23/0.31 thf(c_0_79, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.23/0.31 thf(c_0_80, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 0.23/0.31 thf(c_0_81, 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])).
% 0.23/0.31 thf(c_0_82, 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:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 0.23/0.31 thf(c_0_83, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.23/0.31 thf(c_0_84, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 0.23/0.31 thf(c_0_85, 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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 0.23/0.31 thf(c_0_86, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.23/0.31 thf(c_0_87, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.23/0.31 thf(c_0_88, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.23/0.31 thf(c_0_89, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.23/0.31 thf(c_0_90, 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])).
% 0.23/0.31 thf(c_0_91, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.23/0.31 thf(c_0_92, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.23/0.31 thf(c_0_93, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[subsetI1])).
% 0.23/0.31 thf(c_0_94, plain, ((exuI2)=(![X1:$i > $o]:(((?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2)))))))=>((?[X247:$i]:(((((X1 @ X247)))&(![X248:$i]:(((((X1 @ X248)))=>(((X247)=(X248)))))))))))))), inference(apply_def,[status(thm)],[c_0_78, c_0_79])).
% 0.23/0.31 thf(c_0_95, plain, ((exuE3u)=(![X1:$i > $o]:((((?[X249:$i]:(((((X1 @ X249)))&(![X250:$i]:(((((X1 @ X250)))=>(((X249)=(X250))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_80, c_0_79])).
% 0.23/0.31 thf(c_0_96, plain, ((exuE1)=(![X1:$i > $o]:((((?[X237:$i]:(((((X1 @ X237)))&(![X238:$i]:(((((X1 @ X238)))=>(((X237)=(X238))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_81, c_0_79])).
% 0.23/0.31 thf(c_0_97, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X251:$i]:(((((X1 @ X251)))&(![X252:$i]:(((((X1 @ X252)))=>(((X251)=(X252))))))))))<=>((?[X253:$i]:(((((X17 @ X253)))&(![X254:$i]:(((((X17 @ X254)))=>(((X253)=(X254)))))))))))))))), inference(apply_def,[status(thm)],[c_0_82, c_0_79])).
% 0.23/0.31 thf(c_0_98, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.23/0.31 thf(c_0_99, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.23/0.31 thf(c_0_100, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.23/0.31 thf(c_0_101, plain, ((descrp)=(![X1:$i > $o]:((((?[X235:$i]:(((((X1 @ X235)))&(![X236:$i]:(((((X1 @ X236)))=>(((X235)=(X236))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_83, c_0_79])).
% 0.23/0.31 thf(c_0_102, plain, ((exuEu)=(![X1:$i > $o]:((((?[X255:$i]:(((((X1 @ X255)))&(![X256:$i]:(((((X1 @ X256)))=>(((X255)=(X256))))))))))=>(![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3)))))))))))), inference(apply_def,[status(thm)],[c_0_84, c_0_79])).
% 0.23/0.31 thf(c_0_103, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:(((![X2:$i, X3:$i]:(((((X2)=(X3)))=>((((X1 @ X2))<=>((X17 @ X3)))))))=>((((?[X257:$i]:(((((X1 @ X257)))&(![X258:$i]:(((((X1 @ X258)))=>(((X257)=(X258))))))))))=>((((?[X259:$i]:(((((X17 @ X259)))&(![X260:$i]:(((((X17 @ X260)))=>(((X259)=(X260))))))))))=>(((descr @ (^[Z0:$i]:((X1 @ Z0))))=(descr @ (^[Z0:$i]:((X17 @ Z0)))))))))))))), inference(apply_def,[status(thm)],[c_0_85, c_0_79])).
% 0.23/0.31 thf(c_0_104, plain, ((dsetconstr__Cong)<=>![X4:$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:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 0.23/0.31 thf(c_0_105, plain, ((subset)=(^[Z0:$i, Z1:$i]:(![X2:$i]:((((in @ X2 @ Z0))=>((in @ X2 @ Z1))))))), inference(fof_simplification,[status(thm)],[subset])).
% 0.23/0.31 thf(c_0_106, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X239:$i]:(((((X1 @ X239)))&(![X240:$i]:(((((X1 @ X240)))=>(((X239)=(X240))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_86, c_0_79])).
% 0.23/0.31 thf(c_0_107, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.23/0.31 thf(c_0_108, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_87])).
% 0.23/0.31 thf(c_0_109, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_88, c_0_87])).
% 0.23/0.31 thf(c_0_110, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_87])).
% 0.23/0.31 thf(c_0_111, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.23/0.31 thf(c_0_112, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_87])).
% 0.23/0.31 thf(c_0_113, plain, ((exuE2)=(![X1:$i > $o]:((((?[X241:$i]:(((((X1 @ X241)))&(![X242:$i]:(((((X1 @ X242)))=>(((X241)=(X242))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_89, c_0_79])).
% 0.23/0.31 thf(c_0_114, plain, ((emptyE1)<=>![X4:$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])).
% 0.23/0.31 thf(c_0_115, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X243:$i]:(((((X1 @ X243)))&(![X244:$i]:(((((X1 @ X244)))=>(((X243)=(X244)))))))))))))), inference(apply_def,[status(thm)],[c_0_90, c_0_79])).
% 0.23/0.31 thf(c_0_116, plain, ((exuI3)=(![X1:$i > $o]:(((?[X2:$i]:((X1 @ X2)))=>(((![X2:$i, X3:$i]:((((X1 @ X2))=>((((X1 @ X3))=>(((X2)=(X3))))))))=>((?[X245:$i]:(((((X1 @ X245)))&(![X246:$i]:(((((X1 @ X246)))=>(((X245)=(X246)))))))))))))))), inference(apply_def,[status(thm)],[c_0_91, c_0_79])).
% 0.23/0.31 thf(c_0_117, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X233:$i]:(((((X6 @ X2 @ X233)))&(![X234:$i]:(((((X6 @ X2 @ X234)))=>(((X233)=(X234)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_92, c_0_79])).
% 0.23/0.31 thf(c_0_118, plain, ((epred1_0)<=>![X290:$i]:(?[X291:$i]:((((![X292:$i]:(((in @ X292 @ X291)=>![X293:$i]:(((in @ X293 @ X292)=>(in @ X293 @ X290)))))&![X294:$i, X295:$i]:((((in @ X294 @ X290)&(in @ X295 @ X290))=>(![X296:$i]:(((in @ X296 @ X291)=>((in @ X294 @ X296)<=>(in @ X295 @ X296))))=>((X294)=(X295))))))&![X297:$i, X298:$i]:((((in @ X297 @ X291)&(in @ X298 @ X291))=>(![X299:$i]:(((in @ X299 @ X297)=>(in @ X299 @ X298)))|![X300:$i]:(((in @ X300 @ X298)=>(in @ X300 @ X297)))))))&![X301:$i]:(((![X302:$i]:(((in @ X302 @ X301)=>(in @ X302 @ X290)))&?[X303:$i]:((in @ X303 @ X301)))=>?[X304:$i, X305:$i]:(((((in @ X304 @ X291)&(in @ X305 @ X301))&~(?[X306:$i]:(((in @ X306 @ X304)&(in @ X306 @ X301)))))&![X307:$i]:(((in @ X307 @ X291)=>(![X308:$i]:(((in @ X308 @ X307)=>(in @ X308 @ X304)))|(in @ X305 @ X307)))))))))))), introduced(definition)).
% 0.23/0.31 thf(c_0_119, negated_conjecture, ~((![X261:$i, X262:$i]:((![X263:$i]:(((in @ X263 @ X261)<=>(in @ X263 @ X262)))=>((X261)=(X262))))=>(![X264:$i]:(~(in @ X264 @ emptyset))=>(![X265:$i, X266:$i, X267:$i]:(((in @ X267 @ (setadjoin @ X265 @ X266))<=>(((X267)=(X265))|(in @ X267 @ X266))))=>(![X268:$i, X269:$i]:(((in @ X269 @ (powerset @ X268))<=>![X270:$i]:(((in @ X270 @ X269)=>(in @ X270 @ X268)))))=>(![X271:$i, X272:$i]:(((in @ X272 @ (setunion @ X271))<=>?[X273:$i]:(((in @ X272 @ X273)&(in @ X273 @ X271)))))=>((in @ emptyset @ omega)=>(![X274:$i]:(((in @ X274 @ omega)=>(in @ (setadjoin @ X274 @ X274) @ omega)))=>(![X275:$i]:((((in @ emptyset @ X275)&![X276:$i]:((((in @ X276 @ omega)&(in @ X276 @ X275))=>(in @ (setadjoin @ X276 @ X276) @ X275))))=>![X277:$i]:(((in @ X277 @ omega)=>(in @ X277 @ X275)))))=>(![X278:$i > $i > $o, X279:$i]:((![X280:$i]:(((in @ X280 @ X279)=>?[X281:$i]:(((X278 @ X280 @ X281)&![X282:$i]:(((X278 @ X280 @ X282)=>((X281)=(X282))))))))=>?[X283:$i]:(![X284:$i]:(((in @ X284 @ X283)<=>?[X285:$i]:(((in @ X285 @ X279)&(X278 @ X285 @ X284))))))))=>(![X286:$i]:((?[X287:$i]:((in @ X287 @ X286))=>?[X288:$i]:(((in @ X288 @ X286)&~(?[X289:$i]:(((in @ X289 @ X288)&(in @ X289 @ X286))))))))=>((epred1_0)=>(![X309:$i > $o]:((?[X310:$i]:(((X309 @ X310)&![X311:$i]:(((X309 @ X311)=>((X310)=(X311))))))=>(X309 @ (descr @ (^[Z0:$i]:((X309 @ Z0)))))))=>(![X312:$i, X313:$i > $o, X314:$i]:(((in @ X314 @ X312)=>((X313 @ X314)=>(in @ X314 @ (dsetconstr @ X312 @ (^[Z0:$i]:((X313 @ Z0))))))))=>(![X315:$i, X316:$i > $o, X317:$i]:(((in @ X317 @ (dsetconstr @ X315 @ (^[Z0:$i]:((X316 @ Z0)))))=>(in @ X317 @ X315)))=>(![X318:$i, X319:$i > $o, X320:$i]:(((in @ X320 @ (dsetconstr @ X318 @ (^[Z0:$i]:((X319 @ Z0)))))=>(X319 @ X320)))=>(![X321:$i > $o]:((?[X322:$i]:(((X321 @ X322)&![X323:$i]:(((X321 @ X323)=>((X322)=(X323))))))=>?[X324:$i]:(((X321 @ X324)&![X325:$i]:(((X321 @ X325)=>((X324)=(X325))))))))=>(![X326:$o, X327:$i]:(((in @ X327 @ (prop2set @ ((X326))))=>(X326)))=>(![X328:$i]:(((in @ X328 @ emptyset)=>![X329:$o]:((X329))))=>(![X330:$i]:(~(in @ X330 @ emptyset))=>(![X331:$i]:(~(in @ X331 @ emptyset))=>(![X332:$i > $o]:((?[X333:$i]:(((X332 @ X333)&![X334:$i]:(((X332 @ X334)=>((X333)=(X334))))))=>?[X335:$i]:((X332 @ X335))))=>(![X336:$i, X337:$i]:((![X338:$i]:(((in @ X338 @ X336)=>(in @ X338 @ X337)))=>(![X339:$i]:(((in @ X339 @ X337)=>(in @ X339 @ X336)))=>((X336)=(X337)))))=>(![X340:$i]:((![X341:$i]:(~(in @ X341 @ X340))=>((X340)=(emptyset))))=>(![X342:$i]:((![X343:$i]:(~(in @ X343 @ X342))=>((X342)=(emptyset))))=>(![X344:$i, X345:$i > $o, X346:$i]:(((in @ X346 @ X344)=>((in @ X346 @ (dsetconstr @ X344 @ (^[Z0:$i]:((X345 @ Z0)))))<=>(X345 @ X346))))=>(![X347:$i]:((((X347)!=(emptyset))=>?[X348:$i]:((in @ X348 @ X347))))=>(![X349:$i, X350:$i > $o, X351:$i]:(((in @ X351 @ X349)=>((X350 @ X351)=>((dsetconstr @ X349 @ (^[Z0:$i]:((X350 @ Z0))))!=(emptyset)))))=>(![X352:$i]:((?[X353:$i]:((in @ X353 @ X352))=>((X352)!=(emptyset))))=>(![X354:$i, X355:$i]:((in @ X354 @ (setadjoin @ X354 @ X355)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X356:$i, X357:$i, X358:$i]:(((in @ X358 @ X357)=>(in @ X358 @ (setadjoin @ X356 @ X357))))=>(![X359:$i, X360:$i, X361:$i]:(((in @ X361 @ (setadjoin @ X359 @ X360))=>![X362:$o]:(((((X361)=(X359))=>(X362))=>(((in @ X361 @ X360)=>(X362))=>(X362))))))=>(![X363:$i, X364:$i, X365:$i]:(((in @ X365 @ (setadjoin @ X363 @ X364))=>(((X365)=(X363))|(in @ X365 @ X364))))=>(![X366:$i]:(((dsetconstr @ X366 @ (^[Z0:$i]:(($true))))=(X366)))=>(![X367:$i, X368:$i]:((![X369:$i]:(((in @ X369 @ X368)=>(in @ X369 @ X367)))=>(in @ X368 @ (powerset @ X367))))=>(![X370:$i]:((in @ emptyset @ (powerset @ X370)))=>(![X371:$i]:((in @ emptyset @ (powerset @ X371)))=>(![X372:$i, X373:$i, X374:$i]:(((in @ X373 @ (powerset @ X372))=>((in @ X374 @ X373)=>(in @ X374 @ X372))))=>(![X375:$i, X376:$i, X377:$i]:(((in @ X376 @ X377)=>((in @ X377 @ X375)=>(in @ X376 @ (setunion @ X375)))))=>(![X378:$i, X379:$i]:(((in @ X379 @ (setunion @ X378))=>![X380:$o]:((![X381:$i]:(((in @ X379 @ X381)=>((in @ X381 @ X378)=>(X380))))=>(X380)))))=>(![X382:$i, X383:$i]:(((in @ X383 @ X382)=>(in @ X383 @ (powerset @ (setunion @ X382)))))=>(![X384:$i > $o]:((?[X385:$i]:(((X384 @ X385)&![X386:$i]:(((X384 @ X386)=>((X385)=(X386))))))=>?[X387:$i]:(![X388:$i]:(((X384 @ X388)<=>((X388)=(X387)))))))=>(![X389:$i]:((((X389)!=(emptyset))=>?[X390:$i]:((in @ X390 @ X389))))=>(![X391:$i, X392:$i]:(((in @ X391 @ (setadjoin @ X392 @ emptyset))=>((X391)=(X392))))=>(![X393:$i, X394:$i]:((((X393)!=(X394))=>~(in @ X394 @ (setadjoin @ X393 @ emptyset))))=>(![X395:$i, X396:$i]:((((X395)=(X396))=>(in @ X395 @ (setadjoin @ X396 @ emptyset))))=>(![X397:$i, X398:$i]:(((in @ X397 @ (setadjoin @ X398 @ emptyset))=>(in @ X398 @ (setadjoin @ X397 @ emptyset))))=>(![X399:$i, X400:$i, X401:$i]:(((in @ X401 @ (setadjoin @ X399 @ (setadjoin @ X400 @ emptyset)))=>(((X401)=(X399))|((X401)=(X400)))))=>(![X402:$i, X403:$i]:((in @ X402 @ (setadjoin @ X402 @ (setadjoin @ X403 @ emptyset))))=>(![X404:$i, X405:$i]:((in @ X405 @ (setadjoin @ X404 @ (setadjoin @ X405 @ emptyset))))=>(![X406:$i, X407:$i > $o]:((?[X408:$i]:(((in @ X408 @ X406)&(X407 @ X408)))=>((dsetconstr @ X406 @ (^[Z0:$i]:((X407 @ Z0))))!=(emptyset))))=>(![X409:$i > $o, X410:$i]:(((in @ X410 @ emptyset)=>(X409 @ X410)))=>(![X411:$i, X412:$i > $o]:((~(![X413:$i]:(((in @ X413 @ X411)=>(X412 @ X413))))=>?[X414:$i]:(((in @ X414 @ X411)&~(X412 @ X414)))))=>(![X415:$i, X416:$i > $o]:((![X417:$i]:(((in @ X417 @ X415)=>~(X416 @ X417)))=>~(?[X418:$i]:(((in @ X418 @ X415)&(X416 @ X418))))))=>(![X419:$i, X420:$i > $o]:((~(?[X421:$i]:(((in @ X421 @ X419)&(X420 @ X421))))=>![X422:$i]:(((in @ X422 @ X419)=>~(X420 @ X422)))))=>(![X423:$i, X424:$i > $o]:((?[X425:$i]:(((in @ X425 @ X423)&~(X424 @ X425)))=>~(![X426:$i]:(((in @ X426 @ X423)=>(X424 @ X426))))))=>(![X427:$o]:(((X427)=>(in @ emptyset @ (prop2set @ ((X427))))))=>((prop2set2propI)=>(![X428:$i, X429:$i > $o]:((~(?[X430:$i]:(((in @ X430 @ X428)&(X429 @ X430))))=>![X431:$i]:(((in @ X431 @ X428)=>~(X429 @ X431)))))=>(![X432:$i, X433:$i > $o]:((~(![X434:$i]:(((in @ X434 @ X432)=>(X433 @ X434))))=>?[X435:$i]:(((in @ X435 @ X432)&~(X433 @ X435)))))=>(![X436:$i > $o]:((?[X437:$i]:(((X436 @ X437)&![X438:$i]:(((X436 @ X438)=>((X437)=(X438))))))=>?[X439:$i]:(((X436 @ X439)&![X440:$i]:(((X436 @ X440)=>((X439)=(X440))))))))=>(![X441:$i > $o]:((?[X442:$i]:((X441 @ X442))=>(![X443:$i, X444:$i]:(((X441 @ X443)=>((X441 @ X444)=>((X443)=(X444)))))=>?[X445:$i]:(((X441 @ X445)&![X446:$i]:(((X441 @ X446)=>((X445)=(X446)))))))))=>(![X447:$i > $o]:((?[X448:$i]:(![X449:$i]:(((X447 @ X449)<=>((X449)=(X448)))))=>?[X450:$i]:(((X447 @ X450)&![X451:$i]:(((X447 @ X451)=>((X450)=(X451))))))))=>(![X452:$i, X453:$i]:((((X452)=(X453))=>![X454:$i, X455:$i]:((((X454)=(X455))=>((in @ X454 @ X452)=>(in @ X455 @ X453))))))=>(![X456:$i, X457:$i]:((((X456)=(X457))=>![X458:$i, X459:$i]:((((X458)=(X459))=>((in @ X458 @ X456)<=>(in @ X459 @ X457))))))=>(![X460:$i > $o]:((?[X461:$i]:(((X460 @ X461)&![X462:$i]:(((X460 @ X462)=>((X461)=(X462))))))=>![X463:$i, X464:$i]:(((X460 @ X463)=>((X460 @ X464)=>((X463)=(X464)))))))=>(![X465:$i > $o, X466:$i > $o]:((![X467:$i, X468:$i]:((((X467)=(X468))=>((X465 @ X467)<=>(X466 @ X468))))=>(?[X469:$i]:(((X465 @ X469)&![X470:$i]:(((X465 @ X470)=>((X469)=(X470))))))<=>?[X471:$i]:(((X466 @ X471)&![X472:$i]:(((X466 @ X472)=>((X471)=(X472)))))))))=>(((emptyset)=(emptyset))=>(![X473:$i, X474:$i]:((((X473)=(X474))=>![X475:$i, X476:$i]:((((X475)=(X476))=>((setadjoin @ X473 @ X475)=(setadjoin @ X474 @ X476))))))=>(![X477:$i, X478:$i]:((((X477)=(X478))=>((powerset @ X477)=(powerset @ X478))))=>(![X479:$i, X480:$i]:((((X479)=(X480))=>((setunion @ X479)=(setunion @ X480))))=>(((omega)=(omega))=>(![X481:$i > $o]:((?[X482:$i]:(((X481 @ X482)&![X483:$i]:(((X481 @ X483)=>((X482)=(X483))))))=>![X484:$i, X485:$i]:(((X481 @ X484)=>((X481 @ X485)=>((X484)=(X485)))))))=>(![X486:$i > $o, X487:$i > $o]:((![X488:$i, X489:$i]:((((X488)=(X489))=>((X486 @ X488)<=>(X487 @ X489))))=>(?[X490:$i]:(((X486 @ X490)&![X491:$i]:(((X486 @ X491)=>((X490)=(X491))))))=>(?[X492:$i]:(((X487 @ X492)&![X493:$i]:(((X487 @ X493)=>((X492)=(X493))))))=>((descr @ (^[Z0:$i]:((X486 @ Z0))))=(descr @ (^[Z0:$i]:((X487 @ Z0)))))))))=>(![X494:$i, X495:$i]:((((X494)=(X495))=>![X496:$i > $o, X497:$i > $o]:((![X498:$i]:(((in @ X498 @ X494)=>![X499:$i]:(((in @ X499 @ X495)=>(((X498)=(X499))=>((X496 @ X498)<=>(X497 @ X499)))))))=>((dsetconstr @ X494 @ (^[Z0:$i]:((X496 @ Z0))))=(dsetconstr @ X495 @ (^[Z0:$i]:((X497 @ Z0)))))))))=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>![X500:$i]:(((in @ X500 @ X4)=>(in @ X500 @ X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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)],[c_0_93, c_0_94]), inCongP]), in__Cong]), c_0_95]), c_0_96]), c_0_97]), c_0_98]), emptyset__Cong]), c_0_99]), setadjoin__Cong]), c_0_100]), powerset__Cong]), c_0_101]), setunion__Cong]), wellorderingAx]), omega__Cong]), foundationAx]), c_0_102]), prop2setE]), c_0_103]), c_0_104]), c_0_105]), noeltsimpempty]), emptyI]), setext]), c_0_106]), notinemptyset]), emptysetimpfalse]), emptysetE]), c_0_107]), setadjoinE]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), c_0_108]), c_0_109]), c_0_110]), setadjoinOr]), setunionE]), setunionI]), powersetE]), emptyInPowerset]), emptyinPowerset]), powersetI]), c_0_111]), subPowSU]), upairsetE]), singletonsswitch]), eqinunit]), notinsingleton]), uniqinunit]), c_0_112]), c_0_113]), upairsetIL]), quantDeMorgan4]), quantDeMorgan3]), quantDeMorgan2]), quantDeMorgan1]), vacuousDall]), c_0_114]), upairsetIR]), notdexE]), notdallE]), c_0_115]), c_0_116]), prop2setI]), c_0_117]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])]), c_0_118])).
% 0.23/0.31 thf(c_0_120, negated_conjecture, ![X501:$i, X502:$i, X504:$i, X505:$i, X506:$i, X507:$i, X508:$i, X509:$i, X510:$i, X511:$i, X512:$i, X514:$i, X515:$i, X517:$i, X518:$i, X519:$i, X520:$i, X521:$i, X523:$i, X524:$i > $i > $o, X525:$i, X527:$i, X530:$i, X532:$i, X533:$i, X534:$i, X535:$i, X537:$i, X538:$i > $o, X539:$i, X541:$i, X542:$i > $o, X543:$i, X544:$i, X545:$i > $o, X546:$i, X547:$i, X548:$i > $o, X549:$i, X550:$i > $o, X551:$i, X554:$i, X555:$o, X556:$i, X557:$i, X558:$o, X559:$i, X560:$i, X561:$i > $o, X562:$i, X565:$i, X566:$i, X569:$i, X571:$i, X573:$i, X574:$i > $o, X575:$i, X576:$i, X578:$i, X579:$i > $o, X580:$i, X581:$i, X582:$i, X583:$i, X584:$i, X585:$i, X586:$i, X587:$i, X588:$i, X589:$i, X590:$i, X591:$o, X592:$i, X593:$i, X594:$i, X595:$i, X596:$i, X597:$i, X599:$i, X600:$i, X601:$i, X602:$i, X603:$i, X604:$i, X605:$i, X606:$i, X607:$i, X608:$i, X609:$o, X611:$i, X612:$i, X613:$i > $o, X614:$i, X617:$i, X618:$i, X619:$i, X621:$i, X622:$i, X623:$i, X624:$i, X625:$i, X626:$i, X627:$i, X628:$i, X629:$i, X630:$i, X631:$i, X632:$i, X633:$i, X634:$i, X635:$i, X636:$i, X637:$i > $o, X638:$i, X639:$i > $o, X640:$i, X641:$i, X642:$i > $o, X643:$i, X645:$i, X646:$i > $o, X648:$i, X649:$i, X650:$i > $o, X652:$i, X653:$i, X654:$i > $o, X655:$i, X657:$o, X658:$i, X659:$i > $o, X661:$i, X662:$i, X663:$i > $o, X664:$i, X666:$i > $o, X667:$i, X670:$i, X671:$i > $o, X672:$i, X676:$i, X677:$i > $o, X678:$i, X681:$i, X682:$i, X683:$i, X684:$i, X685:$i, X686:$i, X687:$i, X688:$i, X689:$i, X690:$i > $o, X691:$i, X693:$i, X694:$i, X695:$i > $o, X696:$i > $o, X699:$i, X702:$i, X703:$i, X706:$i, X707:$i, X708:$i, X709:$i, X710:$i, X711:$i, X712:$i, X713:$i, X714:$i, X715:$i > $o, X716:$i, X718:$i, X719:$i, X720:$i > $o, X721:$i > $o, X724:$i, X726:$i, X728:$i, X729:$i, X730:$i > $o, X731:$i > $o, X736:$i]:((((~(in @ (esk1_2 @ X501 @ X502) @ X501)|~(in @ (esk1_2 @ X501 @ X502) @ X502)|((X501)=(X502)))&((in @ (esk1_2 @ X501 @ X502) @ X501)|(in @ (esk1_2 @ X501 @ X502) @ X502)|((X501)=(X502))))&(~(in @ X504 @ emptyset)&(((~(in @ X507 @ (setadjoin @ X505 @ X506))|(((X507)=(X505))|(in @ X507 @ X506)))&((((X507)!=(X505))|(in @ X507 @ (setadjoin @ X505 @ X506)))&(~(in @ X507 @ X506)|(in @ X507 @ (setadjoin @ X505 @ X506)))))&(((~(in @ X509 @ (powerset @ X508))|(~(in @ X510 @ X509)|(in @ X510 @ X508)))&(((in @ (esk2_2 @ X511 @ X512) @ X512)|(in @ X512 @ (powerset @ X511)))&(~(in @ (esk2_2 @ X511 @ X512) @ X511)|(in @ X512 @ (powerset @ X511)))))&(((((in @ X515 @ (esk3_2 @ X514 @ X515))|~(in @ X515 @ (setunion @ X514)))&((in @ (esk3_2 @ X514 @ X515) @ X514)|~(in @ X515 @ (setunion @ X514))))&(~(in @ X518 @ X519)|~(in @ X519 @ X517)|(in @ X518 @ (setunion @ X517))))&((in @ emptyset @ omega)&((~(in @ X520 @ omega)|(in @ (setadjoin @ X520 @ X520) @ omega))&(((((in @ (esk4_1 @ X521) @ omega)|~(in @ emptyset @ X521)|(~(in @ X523 @ omega)|(in @ X523 @ X521)))&((in @ (esk4_1 @ X521) @ X521)|~(in @ emptyset @ X521)|(~(in @ X523 @ omega)|(in @ X523 @ X521))))&(~(in @ (setadjoin @ (esk4_1 @ X521) @ (esk4_1 @ X521)) @ X521)|~(in @ emptyset @ X521)|(~(in @ X523 @ omega)|(in @ X523 @ X521))))&((((((in @ (esk8_3 @ X524 @ X525 @ X530) @ X525)|~(in @ X530 @ (esk7_2 @ X524 @ X525))|(in @ (esk5_2 @ X524 @ X525) @ X525))&((X524 @ (esk8_3 @ X524 @ X525 @ X530) @ X530)|~(in @ X530 @ (esk7_2 @ X524 @ X525))|(in @ (esk5_2 @ X524 @ X525) @ X525)))&(~(in @ X533 @ X525)|~(X524 @ X533 @ X532)|(in @ X532 @ (esk7_2 @ X524 @ X525))|(in @ (esk5_2 @ X524 @ X525) @ X525)))&(((((in @ (esk8_3 @ X524 @ X525 @ X530) @ X525)|~(in @ X530 @ (esk7_2 @ X524 @ X525))|((X524 @ (esk5_2 @ X524 @ X525) @ (esk6_3 @ X524 @ X525 @ X527))|~(X524 @ (esk5_2 @ X524 @ X525) @ X527)))&((X524 @ (esk8_3 @ X524 @ X525 @ X530) @ X530)|~(in @ X530 @ (esk7_2 @ X524 @ X525))|((X524 @ (esk5_2 @ X524 @ X525) @ (esk6_3 @ X524 @ X525 @ X527))|~(X524 @ (esk5_2 @ X524 @ X525) @ X527))))&(~(in @ X533 @ X525)|~(X524 @ X533 @ X532)|(in @ X532 @ (esk7_2 @ X524 @ X525))|((X524 @ (esk5_2 @ X524 @ X525) @ (esk6_3 @ X524 @ X525 @ X527))|~(X524 @ (esk5_2 @ X524 @ X525) @ X527))))&((((in @ (esk8_3 @ X524 @ X525 @ X530) @ X525)|~(in @ X530 @ (esk7_2 @ X524 @ X525))|(((X527)!=(esk6_3 @ X524 @ X525 @ X527))|~(X524 @ (esk5_2 @ X524 @ X525) @ X527)))&((X524 @ (esk8_3 @ X524 @ X525 @ X530) @ X530)|~(in @ X530 @ (esk7_2 @ X524 @ X525))|(((X527)!=(esk6_3 @ X524 @ X525 @ X527))|~(X524 @ (esk5_2 @ X524 @ X525) @ X527))))&(~(in @ X533 @ X525)|~(X524 @ X533 @ X532)|(in @ X532 @ (esk7_2 @ X524 @ X525))|(((X527)!=(esk6_3 @ X524 @ X525 @ X527))|~(X524 @ (esk5_2 @ X524 @ X525) @ X527))))))&((((in @ (esk9_1 @ X534) @ X534)|~(in @ X535 @ X534))&(~(in @ X537 @ (esk9_1 @ X534))|~(in @ X537 @ X534)|~(in @ X535 @ X534)))&((epred1_0)&((((X538 @ (esk10_2 @ X538 @ X539))|~(X538 @ X539)|(X538 @ (descr @ (^[Z0:$i]:((X538 @ Z0))))))&(((X539)!=(esk10_2 @ X538 @ X539))|~(X538 @ X539)|(X538 @ (descr @ (^[Z0:$i]:((X538 @ Z0)))))))&((~(in @ X543 @ X541)|(~(X542 @ X543)|(in @ X543 @ (dsetconstr @ X541 @ (^[Z0:$i]:((X542 @ Z0)))))))&((~(in @ X546 @ (dsetconstr @ X544 @ (^[Z0:$i]:((X545 @ Z0)))))|(in @ X546 @ X544))&((~(in @ X549 @ (dsetconstr @ X547 @ (^[Z0:$i]:((X548 @ Z0)))))|(X548 @ X549))&(((((X550 @ (esk12_1 @ X550))|((X550 @ (esk11_2 @ X550 @ X551))|~(X550 @ X551)))&(~(X550 @ X554)|((esk12_1 @ X550)=(X554))|((X550 @ (esk11_2 @ X550 @ X551))|~(X550 @ X551))))&(((X550 @ (esk12_1 @ X550))|(((X551)!=(esk11_2 @ X550 @ X551))|~(X550 @ X551)))&(~(X550 @ X554)|((esk12_1 @ X550)=(X554))|(((X551)!=(esk11_2 @ X550 @ X551))|~(X550 @ X551)))))&((~(in @ X556 @ (prop2set @ ((X555))))|(X555))&((~(in @ X557 @ emptyset)|(X558))&(~(in @ X559 @ emptyset)&(~(in @ X560 @ emptyset)&((((X561 @ (esk13_2 @ X561 @ X562))|~(X561 @ X562)|(X561 @ (esk14_1 @ X561)))&(((X562)!=(esk13_2 @ X561 @ X562))|~(X561 @ X562)|(X561 @ (esk14_1 @ X561))))&(((((in @ (esk16_2 @ X565 @ X566) @ X566)|((X565)=(X566))|(in @ (esk15_2 @ X565 @ X566) @ X565))&(~(in @ (esk16_2 @ X565 @ X566) @ X565)|((X565)=(X566))|(in @ (esk15_2 @ 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X721))))&(((X726)!=(esk49_3 @ X720 @ X721 @ X726))|~(X721 @ X726)|((descr @ (^[Z0:$i]:((X720 @ Z0))))=(descr @ (^[Z0:$i]:((X721 @ Z0)))))|(((X724)!=(esk48_3 @ X720 @ X721 @ X724))|~(X720 @ X724))|((X720 @ (esk46_2 @ X720 @ X721))|(X721 @ (esk47_2 @ X720 @ X721))))))))&((((in @ (esk50_4 @ X728 @ X729 @ X730 @ X731) @ X728)|((dsetconstr @ X728 @ (^[Z0:$i]:((X730 @ Z0))))=(dsetconstr @ X729 @ (^[Z0:$i]:((X731 @ Z0)))))|((X728)!=(X729)))&(((in @ (esk51_4 @ X728 @ X729 @ X730 @ X731) @ X729)|((dsetconstr @ X728 @ (^[Z0:$i]:((X730 @ Z0))))=(dsetconstr @ X729 @ (^[Z0:$i]:((X731 @ Z0)))))|((X728)!=(X729)))&((((esk50_4 @ X728 @ X729 @ X730 @ X731)=(esk51_4 @ X728 @ X729 @ X730 @ X731))|((dsetconstr @ X728 @ (^[Z0:$i]:((X730 @ Z0))))=(dsetconstr @ X729 @ (^[Z0:$i]:((X731 @ Z0)))))|((X728)!=(X729)))&((~(X730 @ (esk50_4 @ X728 @ X729 @ X730 @ X731))|~(X731 @ (esk51_4 @ X728 @ X729 @ X730 @ X731))|((dsetconstr @ X728 @ (^[Z0:$i]:((X730 @ Z0))))=(dsetconstr @ X729 @ (^[Z0:$i]:((X731 @ Z0)))))|((X728)!=(X729)))&((X730 @ (esk50_4 @ X728 @ X729 @ X730 @ X731))|(X731 @ (esk51_4 @ X728 @ X729 @ X730 @ X731))|((dsetconstr @ X728 @ (^[Z0:$i]:((X730 @ Z0))))=(dsetconstr @ X729 @ (^[Z0:$i]:((X731 @ Z0)))))|((X728)!=(X729)))))))&((~(in @ X736 @ esk52_0)|(in @ X736 @ esk53_0))&((in @ esk54_0 @ esk52_0)&~(in @ esk54_0 @ esk53_0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_119])])])])])])).
% 0.23/0.31 thf(c_0_121, negated_conjecture, ~((in @ esk54_0 @ esk53_0)), inference(split_conjunct,[status(thm)],[c_0_120])).
% 0.23/0.31 thf(c_0_122, negated_conjecture, ![X2:$i]:(((in @ X2 @ esk53_0)|~((in @ X2 @ esk52_0)))), inference(split_conjunct,[status(thm)],[c_0_120])).
% 0.23/0.31 thf(c_0_123, negated_conjecture, (in @ esk54_0 @ esk52_0), inference(split_conjunct,[status(thm)],[c_0_120])).
% 0.23/0.31 thf(c_0_124, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121, c_0_122]), c_0_123])]), ['proof']).
% 0.23/0.31 % SZS output end CNFRefutation
% 0.23/0.31 % Parsed axioms : 169
% 0.23/0.31 % Removed by relevancy pruning/SinE : 91
% 0.23/0.31 % Initial clauses : 185
% 0.23/0.31 % Removed in clause preprocessing : 12
% 0.23/0.31 % Initial clauses in saturation : 173
% 0.23/0.31 % Processed clauses : 20
% 0.23/0.31 % ...of these trivial : 1
% 0.23/0.31 % ...subsumed : 5
% 0.23/0.31 % ...remaining for further processing : 14
% 0.23/0.31 % Other redundant clauses eliminated : 1
% 0.23/0.31 % Clauses deleted for lack of memory : 0
% 0.23/0.31 % Backward-subsumed : 0
% 0.23/0.31 % Backward-rewritten : 1
% 0.23/0.31 % Generated clauses : 2
% 0.23/0.31 % ...of the previous two non-redundant : 1
% 0.23/0.31 % ...aggressively subsumed : 0
% 0.23/0.31 % Contextual simplify-reflections : 0
% 0.23/0.31 % Paramodulations : 1
% 0.23/0.31 % Factorizations : 0
% 0.23/0.31 % NegExts : 0
% 0.23/0.31 % Equation resolutions : 1
% 0.23/0.31 % Disequality decompositions : 0
% 0.23/0.31 % Total rewrite steps : 3
% 0.23/0.31 % ...of those cached : 0
% 0.23/0.31 % Propositional unsat checks : 0
% 0.23/0.31 % Propositional check models : 0
% 0.23/0.31 % Propositional check unsatisfiable : 0
% 0.23/0.31 % Propositional clauses : 0
% 0.23/0.31 % Propositional clauses after purity: 0
% 0.23/0.31 % Propositional unsat core size : 0
% 0.23/0.31 % Propositional preprocessing time : 0.000
% 0.23/0.31 % Propositional encoding time : 0.000
% 0.23/0.31 % Propositional solver time : 0.000
% 0.23/0.31 % Success case prop preproc time : 0.000
% 0.23/0.31 % Success case prop encoding time : 0.000
% 0.23/0.31 % Success case prop solver time : 0.000
% 0.23/0.31 % Current number of processed clauses : 12
% 0.23/0.31 % Positive orientable unit clauses : 8
% 0.23/0.31 % Positive unorientable unit clauses: 0
% 0.23/0.31 % Negative unit clauses : 3
% 0.23/0.31 % Non-unit-clauses : 1
% 0.23/0.31 % Current number of unprocessed clauses: 154
% 0.23/0.31 % ...number of literals in the above : 594
% 0.23/0.31 % Current number of archived formulas : 0
% 0.23/0.31 % Current number of archived clauses : 1
% 0.23/0.31 % Clause-clause subsumption calls (NU) : 0
% 0.23/0.31 % Rec. Clause-clause subsumption calls : 0
% 0.23/0.31 % Non-unit clause-clause subsumptions : 0
% 0.23/0.31 % Unit Clause-clause subsumption calls : 2
% 0.23/0.31 % Rewrite failures with RHS unbound : 0
% 0.23/0.31 % BW rewrite match attempts : 1
% 0.23/0.31 % BW rewrite match successes : 1
% 0.23/0.31 % Condensation attempts : 0
% 0.23/0.31 % Condensation successes : 0
% 0.23/0.31 % Termbank termtop insertions : 19794
% 0.23/0.31 % Search garbage collected termcells : 7555
% 0.23/0.31
% 0.23/0.31 % -------------------------------------------------
% 0.23/0.31 % User time : 0.021 s
% 0.23/0.31 % System time : 0.009 s
% 0.23/0.31 % Total time : 0.030 s
% 0.23/0.31 % Maximum resident set size: 5852 pages
% 0.23/0.31
% 0.23/0.31 % -------------------------------------------------
% 0.23/0.31 % User time : 0.021 s
% 0.23/0.31 % System time : 0.016 s
% 0.23/0.31 % Total time : 0.037 s
% 0.23/0.31 % Maximum resident set size: 5120 pages
% 0.23/0.31 % E exiting
%------------------------------------------------------------------------------