%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU542^1 : 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 : n010.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 08:24:26 AM UTC 2026
% Result : Theorem 0.23s 0.30s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU542^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n010.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 13:49:33 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 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.EGc3s0JjVG/E---3.1_2885270.p
% 0.23/0.30 % Version: 3.5.1-ho
% 0.23/0.30 % Preprocessing class: HSMSSLSSMLLCHSA.
% 0.23/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.30 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.30 % Starting sh5l with 300s (1) cores
% 0.23/0.30 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.30 % Starting new_bool_2 with 300s (1) cores
% 0.23/0.30 % new_bool_2 with pid 2885286 completed with status 0
% 0.23/0.30 % Result found by new_bool_2
% 0.23/0.30 % Preprocessing class: HSMSSLSSMLLCHSA.
% 0.23/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.30 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.30 % Starting sh5l with 300s (1) cores
% 0.23/0.30 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.30 % Starting new_bool_2 with 300s (1) cores
% 0.23/0.30 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.23/0.30 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.23/0.30 % Search class: HGHSM-FFMM31-SHSSMSBN
% 0.23/0.30 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.30 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.30 % SubtermCWHack with pid 2885287 completed with status 0
% 0.23/0.30 % Result found by SubtermCWHack
% 0.23/0.30 % Preprocessing class: HSMSSLSSMLLCHSA.
% 0.23/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.30 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.30 % Starting sh5l with 300s (1) cores
% 0.23/0.30 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.30 % Starting new_bool_2 with 300s (1) cores
% 0.23/0.30 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.23/0.30 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.23/0.30 % Search class: HGHSM-FFMM31-SHSSMSBN
% 0.23/0.30 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.30 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.30 % Preprocessing time : 0.002 s
% 0.23/0.30
% 0.23/0.30 % Proof found!
% 0.23/0.30 % SZS status Theorem
% 0.23/0.30 % SZS output start CNFRefutation
% 0.23/0.30 thf(decl_23, type, in: $i > $i > $o).
% 0.23/0.30 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.23/0.30 thf(decl_25, type, setextAx: $o).
% 0.23/0.30 thf(decl_26, type, emptyset: $i).
% 0.23/0.30 thf(decl_27, type, emptysetAx: $o).
% 0.23/0.30 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.23/0.30 thf(decl_29, type, setadjoinAx: $o).
% 0.23/0.30 thf(decl_30, type, powerset: $i > $i).
% 0.23/0.30 thf(decl_31, type, powersetAx: $o).
% 0.23/0.30 thf(decl_32, type, setunion: $i > $i).
% 0.23/0.30 thf(decl_33, type, setunionAx: $o).
% 0.23/0.30 thf(decl_34, type, omega: $i).
% 0.23/0.30 thf(decl_35, type, omega0Ax: $o).
% 0.23/0.30 thf(decl_36, type, omegaSAx: $o).
% 0.23/0.30 thf(decl_37, type, omegaIndAx: $o).
% 0.23/0.30 thf(decl_38, type, replAx: $o).
% 0.23/0.30 thf(decl_39, type, foundationAx: $o).
% 0.23/0.30 thf(decl_40, type, wellorderingAx: $o).
% 0.23/0.30 thf(decl_42, type, descrp: $o).
% 0.23/0.30 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.23/0.30 thf(decl_44, type, dsetconstrI: $o).
% 0.23/0.30 thf(decl_45, type, dsetconstrEL: $o).
% 0.23/0.30 thf(decl_46, type, dsetconstrER: $o).
% 0.23/0.30 thf(decl_47, type, exuE1: $o).
% 0.23/0.30 thf(decl_48, type, prop2set: $o > $i).
% 0.23/0.30 thf(decl_49, type, prop2setE: $o).
% 0.23/0.30 thf(decl_50, type, emptysetE: $o).
% 0.23/0.30 thf(decl_51, type, emptysetimpfalse: $o).
% 0.23/0.30 thf(decl_52, type, notinemptyset: $o).
% 0.23/0.30 thf(decl_53, type, exuE3e: $o).
% 0.23/0.30 thf(decl_54, type, setext: $o).
% 0.23/0.30 thf(decl_55, type, emptyI: $o).
% 0.23/0.30 thf(decl_56, type, noeltsimpempty: $o).
% 0.23/0.30 thf(decl_57, type, setbeta: $o).
% 0.23/0.30 thf(decl_58, type, nonempty: $i > $o).
% 0.23/0.30 thf(decl_59, type, nonemptyE1: $o).
% 0.23/0.30 thf(decl_60, type, nonemptyI: $o).
% 0.23/0.30 thf(decl_61, type, nonemptyI1: $o).
% 0.23/0.30 thf(decl_62, type, setadjoinIL: $o).
% 0.23/0.30 thf(decl_63, type, emptyinunitempty: $o).
% 0.23/0.30 thf(decl_64, type, setadjoinIR: $o).
% 0.23/0.30 thf(decl_65, type, setadjoinE: $o).
% 0.23/0.30 thf(decl_66, type, setadjoinOr: $o).
% 0.23/0.30 thf(decl_67, type, setoftrueEq: $o).
% 0.23/0.30 thf(decl_68, type, powersetI: $o).
% 0.23/0.30 thf(decl_69, type, emptyinPowerset: $o).
% 0.23/0.30 thf(decl_70, type, emptyInPowerset: $o).
% 0.23/0.30 thf(decl_71, type, powersetE: $o).
% 0.23/0.30 thf(decl_72, type, setunionI: $o).
% 0.23/0.30 thf(decl_73, type, setunionE: $o).
% 0.23/0.30 thf(decl_74, type, subPowSU: $o).
% 0.23/0.30 thf(decl_75, type, exuE2: $o).
% 0.23/0.30 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.23/0.30 thf(decl_77, type, uniqinunit: $o).
% 0.23/0.30 thf(decl_78, type, notinsingleton: $o).
% 0.23/0.30 thf(decl_79, type, eqinunit: $o).
% 0.23/0.30 thf(decl_80, type, singletonsswitch: $o).
% 0.23/0.30 thf(decl_81, type, upairsetE: $o).
% 0.23/0.30 thf(decl_82, type, upairsetIL: $o).
% 0.23/0.30 thf(decl_83, type, upairsetIR: $o).
% 0.23/0.30 thf(decl_84, type, emptyE1: $o).
% 0.23/0.30 thf(decl_85, type, vacuousDall: $o).
% 0.23/0.30 thf(decl_86, type, quantDeMorgan1: $o).
% 0.23/0.30 thf(decl_87, type, quantDeMorgan2: $o).
% 0.23/0.30 thf(decl_88, type, quantDeMorgan3: $o).
% 0.23/0.30 thf(decl_89, type, quantDeMorgan4: $o).
% 0.23/0.30 thf(decl_90, type, prop2setI: $o).
% 0.23/0.30 thf(decl_92, type, prop2set2propI: $o).
% 0.23/0.30 thf(decl_93, type, epred1_0: $o).
% 0.23/0.30 thf(decl_94, type, esk1_2: $i > $i > $i).
% 0.23/0.30 thf(decl_95, type, esk2_2: $i > $i > $i).
% 0.23/0.30 thf(decl_96, type, esk3_2: $i > $i > $i).
% 0.23/0.30 thf(decl_97, type, esk4_1: $i > $i).
% 0.23/0.30 thf(decl_98, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.23/0.30 thf(decl_99, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.23/0.30 thf(decl_100, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.23/0.30 thf(decl_101, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.23/0.30 thf(decl_102, type, esk9_1: $i > $i).
% 0.23/0.30 thf(decl_103, type, esk10_2: ($i > $o) > $i > $i).
% 0.23/0.30 thf(decl_104, type, esk11_1: ($i > $o) > $i).
% 0.23/0.30 thf(decl_105, type, esk12_2: ($i > $o) > $i > $i).
% 0.23/0.30 thf(decl_106, type, esk13_1: ($i > $o) > $i).
% 0.23/0.30 thf(decl_107, type, esk14_2: $i > $i > $i).
% 0.23/0.30 thf(decl_108, type, esk15_2: $i > $i > $i).
% 0.23/0.30 thf(decl_109, type, esk16_1: $i > $i).
% 0.23/0.30 thf(decl_110, type, esk17_1: $i > $i).
% 0.23/0.30 thf(decl_111, type, esk18_1: $i > $i).
% 0.23/0.30 thf(decl_112, type, esk19_2: $i > $i > $i).
% 0.23/0.30 thf(decl_113, type, esk20_3: $i > $i > $o > $i).
% 0.23/0.30 thf(decl_114, type, esk21_2: ($i > $o) > $i > $i).
% 0.23/0.30 thf(decl_115, type, esk22_1: ($i > $o) > $i).
% 0.23/0.30 thf(decl_116, type, esk23_1: $i > $i).
% 0.23/0.30 thf(decl_117, type, esk24_2: $i > ($i > $o) > $i).
% 0.23/0.30 thf(decl_118, type, esk25_2: $i > ($i > $o) > $i).
% 0.23/0.30 thf(decl_119, type, esk26_2: $i > ($i > $o) > $i).
% 0.23/0.30 thf(decl_120, type, esk27_2: $i > ($i > $o) > $i).
% 0.23/0.30 thf(decl_121, type, esk28_0: $i).
% 0.23/0.30 thf(decl_122, type, epred2_0: $i > $o).
% 0.23/0.30 thf(decl_123, type, esk29_0: $i).
% 0.23/0.30 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', nonempty)).
% 0.23/0.30 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', nonemptyI)).
% 0.23/0.30 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', replAx)).
% 0.23/0.30 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', exu)).
% 0.23/0.30 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', exuE3e)).
% 0.23/0.30 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', exuE1)).
% 0.23/0.30 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', exuE2)).
% 0.23/0.30 thf(notdexE, 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)=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', notdexE)).
% 0.23/0.30 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', nonemptyImpWitness)).
% 0.23/0.30 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', emptyE1)).
% 0.23/0.30 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', nonemptyE1)).
% 0.23/0.30 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', dsetconstrI)).
% 0.23/0.30 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', dsetconstrEL)).
% 0.23/0.30 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', dsetconstrER)).
% 0.23/0.30 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', nonemptyI1)).
% 0.23/0.30 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', setbeta)).
% 0.23/0.30 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', setoftrueEq)).
% 0.23/0.30 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', uniqinunit)).
% 0.23/0.30 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', notinsingleton)).
% 0.23/0.30 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', eqinunit)).
% 0.23/0.30 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', powersetAx)).
% 0.23/0.30 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', singletonsswitch)).
% 0.23/0.30 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', setadjoinAx)).
% 0.23/0.30 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', upairsetE)).
% 0.23/0.30 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', emptysetAx)).
% 0.23/0.30 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', upairsetIL)).
% 0.23/0.30 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', setunionAx)).
% 0.23/0.30 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', upairsetIR)).
% 0.23/0.30 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', vacuousDall)).
% 0.23/0.30 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', quantDeMorgan1)).
% 0.23/0.30 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', quantDeMorgan2)).
% 0.23/0.30 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', quantDeMorgan3)).
% 0.23/0.30 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', quantDeMorgan4)).
% 0.23/0.30 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', prop2setI)).
% 0.23/0.30 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', wellorderingAx)).
% 0.23/0.30 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', foundationAx)).
% 0.23/0.30 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', omegaIndAx)).
% 0.23/0.30 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', omegaSAx)).
% 0.23/0.30 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', omega0Ax)).
% 0.23/0.30 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', notinemptyset)).
% 0.23/0.30 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', emptysetimpfalse)).
% 0.23/0.30 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', emptysetE)).
% 0.23/0.30 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', prop2setE)).
% 0.23/0.30 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', setext)).
% 0.23/0.30 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', setadjoinIL)).
% 0.23/0.30 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', noeltsimpempty)).
% 0.23/0.30 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', emptyI)).
% 0.23/0.30 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', emptyinunitempty)).
% 0.23/0.30 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', emptyInPowerset)).
% 0.23/0.30 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', emptyinPowerset)).
% 0.23/0.30 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', powersetI)).
% 0.23/0.30 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', setadjoinOr)).
% 0.23/0.30 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', setadjoinE)).
% 0.23/0.30 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', setadjoinIR)).
% 0.23/0.30 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', setunionI)).
% 0.23/0.30 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', setunionE)).
% 0.23/0.30 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', subPowSU)).
% 0.23/0.30 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', powersetE)).
% 0.23/0.30 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.EGc3s0JjVG/E---3.1_2885270.p', setextAx)).
% 0.23/0.30 thf(c_0_59, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.23/0.30 thf(c_0_60, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.23/0.30 thf(c_0_61, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.23/0.30 thf(c_0_62, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.23/0.30 thf(c_0_63, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.23/0.30 thf(c_0_64, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.23/0.30 thf(c_0_65, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.23/0.30 thf(c_0_66, 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)=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[notdexE])).
% 0.23/0.30 thf(c_0_67, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_59])).
% 0.23/0.30 thf(c_0_68, 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])).
% 0.23/0.30 thf(c_0_69, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_60, c_0_59])).
% 0.23/0.30 thf(c_0_70, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_59])).
% 0.23/0.30 thf(c_0_71, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.23/0.30 thf(c_0_72, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X177:$i]:(((((X6 @ X2 @ X177)))&(![X178:$i]:(((((X6 @ X2 @ X178)))=>(((X177)=(X178)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_61, c_0_62])).
% 0.23/0.30 thf(c_0_73, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.23/0.30 thf(c_0_74, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X181:$i]:(((((X1 @ X181)))&(![X182:$i]:(((((X1 @ X182)))=>(((X181)=(X182))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_63, c_0_62])).
% 0.23/0.30 thf(c_0_75, plain, ((exuE1)=(![X1:$i > $o]:((((?[X179:$i]:(((((X1 @ X179)))&(![X180:$i]:(((((X1 @ X180)))=>(((X179)=(X180))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_64, c_0_62])).
% 0.23/0.30 thf(c_0_76, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.23/0.30 thf(c_0_77, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_59])).
% 0.23/0.30 thf(c_0_78, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.23/0.30 thf(c_0_79, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.23/0.30 thf(c_0_80, plain, ((exuE2)=(![X1:$i > $o]:((((?[X183:$i]:(((((X1 @ X183)))&(![X184:$i]:(((((X1 @ X184)))=>(((X183)=(X184))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_65, c_0_62])).
% 0.23/0.30 thf(c_0_81, plain, ((epred1_0)<=>![X214:$i]:(?[X215:$i]:((((![X216:$i]:(((in @ X216 @ X215)=>![X217:$i]:(((in @ X217 @ X216)=>(in @ X217 @ X214)))))&![X218:$i, X219:$i]:((((in @ X218 @ X214)&(in @ X219 @ X214))=>(![X220:$i]:(((in @ X220 @ X215)=>((in @ X218 @ X220)<=>(in @ X219 @ X220))))=>((X218)=(X219))))))&![X221:$i, X222:$i]:((((in @ X221 @ X215)&(in @ X222 @ X215))=>(![X223:$i]:(((in @ X223 @ X221)=>(in @ X223 @ X222)))|![X224:$i]:(((in @ X224 @ X222)=>(in @ X224 @ X221)))))))&![X225:$i]:(((![X226:$i]:(((in @ X226 @ X225)=>(in @ X226 @ X214)))&?[X227:$i]:((in @ X227 @ X225)))=>?[X228:$i, X229:$i]:(((((in @ X228 @ X215)&(in @ X229 @ X225))&~(?[X230:$i]:(((in @ X230 @ X228)&(in @ X230 @ X225)))))&![X231:$i]:(((in @ X231 @ X215)=>(![X232:$i]:(((in @ X232 @ X231)=>(in @ X232 @ X228)))|(in @ X229 @ X231)))))))))))), introduced(definition)).
% 0.23/0.30 thf(c_0_82, negated_conjecture, ~((![X185:$i, X186:$i]:((![X187:$i]:(((in @ X187 @ X185)<=>(in @ X187 @ X186)))=>((X185)=(X186))))=>(![X188:$i]:(~(in @ X188 @ emptyset))=>(![X189:$i, X190:$i, X191:$i]:(((in @ X191 @ (setadjoin @ X189 @ X190))<=>(((X191)=(X189))|(in @ X191 @ X190))))=>(![X192:$i, X193:$i]:(((in @ X193 @ (powerset @ X192))<=>![X194:$i]:(((in @ X194 @ X193)=>(in @ X194 @ X192)))))=>(![X195:$i, X196:$i]:(((in @ X196 @ (setunion @ X195))<=>?[X197:$i]:(((in @ X196 @ X197)&(in @ X197 @ X195)))))=>((in @ emptyset @ omega)=>(![X198:$i]:(((in @ X198 @ omega)=>(in @ (setadjoin @ X198 @ X198) @ omega)))=>(![X199:$i]:((((in @ emptyset @ X199)&![X200:$i]:((((in @ X200 @ omega)&(in @ X200 @ X199))=>(in @ (setadjoin @ X200 @ X200) @ X199))))=>![X201:$i]:(((in @ X201 @ omega)=>(in @ X201 @ X199)))))=>(![X202:$i > $i > $o, X203:$i]:((![X204:$i]:(((in @ X204 @ X203)=>?[X205:$i]:(((X202 @ X204 @ X205)&![X206:$i]:(((X202 @ X204 @ X206)=>((X205)=(X206))))))))=>?[X207:$i]:(![X208:$i]:(((in @ X208 @ X207)<=>?[X209:$i]:(((in @ X209 @ X203)&(X202 @ X209 @ X208))))))))=>(![X210:$i]:((?[X211:$i]:((in @ X211 @ X210))=>?[X212:$i]:(((in @ X212 @ X210)&~(?[X213:$i]:(((in @ X213 @ X212)&(in @ X213 @ X210))))))))=>((epred1_0)=>((descrp)=>(![X233:$i, X234:$i > $o, X235:$i]:(((in @ X235 @ X233)=>((X234 @ X235)=>(in @ X235 @ (dsetconstr @ X233 @ (^[Z0:$i]:((X234 @ Z0))))))))=>(![X236:$i, X237:$i > $o, X238:$i]:(((in @ X238 @ (dsetconstr @ X236 @ (^[Z0:$i]:((X237 @ Z0)))))=>(in @ X238 @ X236)))=>(![X239:$i, X240:$i > $o, X241:$i]:(((in @ X241 @ (dsetconstr @ X239 @ (^[Z0:$i]:((X240 @ Z0)))))=>(X240 @ X241)))=>(![X242:$i > $o]:((?[X243:$i]:(((X242 @ X243)&![X244:$i]:(((X242 @ X244)=>((X243)=(X244))))))=>?[X245:$i]:(((X242 @ X245)&![X246:$i]:(((X242 @ X246)=>((X245)=(X246))))))))=>(![X247:$o, X248:$i]:(((in @ X248 @ (prop2set @ ((X247))))=>(X247)))=>(![X249:$i]:(((in @ X249 @ emptyset)=>![X250:$o]:((X250))))=>(![X251:$i]:(~(in @ X251 @ emptyset))=>(![X252:$i]:(~(in @ X252 @ emptyset))=>(![X253:$i > $o]:((?[X254:$i]:(((X253 @ X254)&![X255:$i]:(((X253 @ X255)=>((X254)=(X255))))))=>?[X256:$i]:((X253 @ X256))))=>(![X257:$i, X258:$i]:((![X259:$i]:(((in @ X259 @ X257)=>(in @ X259 @ X258)))=>(![X260:$i]:(((in @ X260 @ X258)=>(in @ X260 @ X257)))=>((X257)=(X258)))))=>(![X261:$i]:((![X262:$i]:(~(in @ X262 @ X261))=>((X261)=(emptyset))))=>(![X263:$i]:((![X264:$i]:(~(in @ X264 @ X263))=>((X263)=(emptyset))))=>(![X265:$i, X266:$i > $o, X267:$i]:(((in @ X267 @ X265)=>((in @ X267 @ (dsetconstr @ X265 @ (^[Z0:$i]:((X266 @ Z0)))))<=>(X266 @ X267))))=>(![X268:$i]:((((X268)!=(emptyset))=>?[X269:$i]:((in @ X269 @ X268))))=>(![X270:$i, X271:$i > $o, X272:$i]:(((in @ X272 @ X270)=>((X271 @ X272)=>((dsetconstr @ X270 @ (^[Z0:$i]:((X271 @ Z0))))!=(emptyset)))))=>(![X273:$i]:((?[X274:$i]:((in @ X274 @ X273))=>((X273)!=(emptyset))))=>(![X275:$i, X276:$i]:((in @ X275 @ (setadjoin @ X275 @ X276)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X277:$i, X278:$i, X279:$i]:(((in @ X279 @ X278)=>(in @ X279 @ (setadjoin @ X277 @ X278))))=>(![X280:$i, X281:$i, X282:$i]:(((in @ X282 @ (setadjoin @ X280 @ X281))=>![X283:$o]:(((((X282)=(X280))=>(X283))=>(((in @ X282 @ X281)=>(X283))=>(X283))))))=>(![X284:$i, X285:$i, X286:$i]:(((in @ X286 @ (setadjoin @ X284 @ X285))=>(((X286)=(X284))|(in @ X286 @ X285))))=>(![X287:$i]:(((dsetconstr @ X287 @ (^[Z0:$i]:(($true))))=(X287)))=>(![X288:$i, X289:$i]:((![X290:$i]:(((in @ X290 @ X289)=>(in @ X290 @ X288)))=>(in @ X289 @ (powerset @ X288))))=>(![X291:$i]:((in @ emptyset @ (powerset @ X291)))=>(![X292:$i]:((in @ emptyset @ (powerset @ X292)))=>(![X293:$i, X294:$i, X295:$i]:(((in @ X294 @ (powerset @ X293))=>((in @ X295 @ X294)=>(in @ X295 @ X293))))=>(![X296:$i, X297:$i, X298:$i]:(((in @ X297 @ X298)=>((in @ X298 @ X296)=>(in @ X297 @ (setunion @ X296)))))=>(![X299:$i, X300:$i]:(((in @ X300 @ (setunion @ X299))=>![X301:$o]:((![X302:$i]:(((in @ X300 @ X302)=>((in @ X302 @ X299)=>(X301))))=>(X301)))))=>(![X303:$i, X304:$i]:(((in @ X304 @ X303)=>(in @ X304 @ (powerset @ (setunion @ X303)))))=>(![X305:$i > $o]:((?[X306:$i]:(((X305 @ X306)&![X307:$i]:(((X305 @ X307)=>((X306)=(X307))))))=>?[X308:$i]:(![X309:$i]:(((X305 @ X309)<=>((X309)=(X308)))))))=>(![X310:$i]:((((X310)!=(emptyset))=>?[X311:$i]:((in @ X311 @ X310))))=>(![X312:$i, X313:$i]:(((in @ X312 @ (setadjoin @ X313 @ emptyset))=>((X312)=(X313))))=>(![X314:$i, X315:$i]:((((X314)!=(X315))=>~(in @ X315 @ (setadjoin @ X314 @ emptyset))))=>(![X316:$i, X317:$i]:((((X316)=(X317))=>(in @ X316 @ (setadjoin @ X317 @ emptyset))))=>(![X318:$i, X319:$i]:(((in @ X318 @ (setadjoin @ X319 @ emptyset))=>(in @ X319 @ (setadjoin @ X318 @ emptyset))))=>(![X320:$i, X321:$i, X322:$i]:(((in @ X322 @ (setadjoin @ X320 @ (setadjoin @ X321 @ emptyset)))=>(((X322)=(X320))|((X322)=(X321)))))=>(![X323:$i, X324:$i]:((in @ X323 @ (setadjoin @ X323 @ (setadjoin @ X324 @ emptyset))))=>(![X325:$i, X326:$i]:((in @ X326 @ (setadjoin @ X325 @ (setadjoin @ X326 @ emptyset))))=>(![X327:$i, X328:$i > $o]:((?[X329:$i]:(((in @ X329 @ X327)&(X328 @ X329)))=>((dsetconstr @ X327 @ (^[Z0:$i]:((X328 @ Z0))))!=(emptyset))))=>(![X330:$i > $o, X331:$i]:(((in @ X331 @ emptyset)=>(X330 @ X331)))=>(![X332:$i, X333:$i > $o]:((~(![X334:$i]:(((in @ X334 @ X332)=>(X333 @ X334))))=>?[X335:$i]:(((in @ X335 @ X332)&~(X333 @ X335)))))=>(![X336:$i, X337:$i > $o]:((![X338:$i]:(((in @ X338 @ X336)=>~(X337 @ X338)))=>~(?[X339:$i]:(((in @ X339 @ X336)&(X337 @ X339))))))=>(![X340:$i, X341:$i > $o]:((~(?[X342:$i]:(((in @ X342 @ X340)&(X341 @ X342))))=>![X343:$i]:(((in @ X343 @ X340)=>~(X341 @ X343)))))=>(![X344:$i, X345:$i > $o]:((?[X346:$i]:(((in @ X346 @ X344)&~(X345 @ X346)))=>~(![X347:$i]:(((in @ X347 @ X344)=>(X345 @ X347))))))=>(![X348:$o]:(((X348)=>(in @ emptyset @ (prop2set @ ((X348))))))=>((prop2set2propI)=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~(X1 @ X2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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)],[c_0_66, uniqinunit]), c_0_67]), notinsingleton]), eqinunit]), powersetAx]), singletonsswitch]), setadjoinAx]), upairsetE]), emptysetAx]), upairsetIL]), setunionAx]), upairsetIR]), c_0_68]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), c_0_69]), c_0_70]), c_0_71]), wellorderingAx]), foundationAx]), c_0_72]), omegaIndAx]), omegaSAx]), omega0Ax]), c_0_73]), c_0_74]), notinemptyset]), emptysetimpfalse]), emptysetE]), prop2setE]), c_0_75]), c_0_76]), setext]), setadjoinIL]), c_0_77]), c_0_78]), noeltsimpempty]), emptyI]), emptyinunitempty]), emptyInPowerset]), emptyinPowerset]), powersetI]), c_0_79]), setadjoinOr]), setadjoinE]), setadjoinIR]), setunionI]), setunionE]), subPowSU]), c_0_80]), powersetE]), setextAx])]), c_0_81])).
% 0.23/0.30 thf(c_0_83, negated_conjecture, ![X349:$i, X350:$i, X352:$i, X353:$i, X354:$i, X355:$i, X356:$i, X357:$i, X358:$i, X359:$i, X360:$i, X362:$i, X363:$i, X365:$i, X366:$i, X367:$i, X368:$i, X369:$i, X371:$i, X372:$i > $i > $o, X373:$i, X375:$i, X378:$i, X380:$i, X381:$i, X382:$i, X383:$i, X385:$i, X386:$i, X387:$i > $o, X388:$i, X389:$i, X390:$i > $o, X391:$i, X392:$i, X393:$i > $o, X394:$i, X395:$i > $o, X396:$i, X399:$i, X400:$o, X401:$i, X402:$i, X403:$o, X404:$i, X405:$i, X406:$i > $o, X407:$i, X410:$i, X411:$i, X414:$i, X416:$i, X418:$i, X419:$i > $o, X420:$i, X421:$i, X423:$i, X424:$i > $o, X425:$i, X426:$i, X427:$i, X428:$i, X429:$i, X430:$i, X431:$i, X432:$i, X433:$i, X434:$i, X435:$i, X436:$o, X437:$i, X438:$i, X439:$i, X440:$i, X441:$i, X442:$i, X444:$i, X445:$i, X446:$i, X447:$i, X448:$i, X449:$i, X450:$i, X451:$i, X452:$i, X453:$i, X454:$o, X456:$i, X457:$i, X458:$i > $o, X459:$i, X462:$i, X463:$i, X464:$i, X466:$i, X467:$i, X468:$i, X469:$i, X470:$i, X471:$i, X472:$i, X473:$i, X474:$i, X475:$i, X476:$i, X477:$i, X478:$i, X479:$i, X480:$i, X481:$i, X482:$i > $o, X483:$i, X484:$i > $o, X485:$i, X486:$i, X487:$i > $o, X488:$i, X490:$i, X491:$i > $o, X493:$i, X494:$i, X495:$i > $o, X497:$i, X498:$i, X499:$i > $o, X500:$i, X502:$o, X505:$i]:((((~(in @ (esk1_2 @ X349 @ X350) @ X349)|~(in @ (esk1_2 @ X349 @ X350) @ X350)|((X349)=(X350)))&((in @ (esk1_2 @ X349 @ X350) @ X349)|(in @ (esk1_2 @ X349 @ X350) @ X350)|((X349)=(X350))))&(~(in @ X352 @ emptyset)&(((~(in @ X355 @ (setadjoin @ X353 @ X354))|(((X355)=(X353))|(in @ X355 @ X354)))&((((X355)!=(X353))|(in @ X355 @ (setadjoin @ X353 @ X354)))&(~(in @ X355 @ X354)|(in @ X355 @ (setadjoin @ X353 @ X354)))))&(((~(in @ X357 @ (powerset @ X356))|(~(in @ X358 @ X357)|(in @ X358 @ X356)))&(((in @ (esk2_2 @ X359 @ X360) @ X360)|(in @ X360 @ (powerset @ X359)))&(~(in @ (esk2_2 @ X359 @ X360) @ X359)|(in @ X360 @ (powerset @ X359)))))&(((((in @ X363 @ (esk3_2 @ X362 @ X363))|~(in @ X363 @ (setunion @ X362)))&((in @ (esk3_2 @ X362 @ X363) @ X362)|~(in @ X363 @ (setunion @ X362))))&(~(in @ X366 @ X367)|~(in @ X367 @ X365)|(in @ X366 @ (setunion @ X365))))&((in @ emptyset @ omega)&((~(in @ X368 @ omega)|(in @ (setadjoin @ X368 @ X368) @ omega))&(((((in @ (esk4_1 @ X369) @ omega)|~(in @ emptyset @ X369)|(~(in @ X371 @ omega)|(in @ X371 @ X369)))&((in @ (esk4_1 @ X369) @ X369)|~(in @ emptyset @ X369)|(~(in @ X371 @ omega)|(in @ X371 @ X369))))&(~(in @ (setadjoin @ (esk4_1 @ X369) @ (esk4_1 @ X369)) @ X369)|~(in @ emptyset @ X369)|(~(in @ X371 @ omega)|(in @ X371 @ X369))))&((((((in @ (esk8_3 @ X372 @ X373 @ X378) @ X373)|~(in @ X378 @ (esk7_2 @ X372 @ X373))|(in @ (esk5_2 @ X372 @ X373) @ X373))&((X372 @ (esk8_3 @ X372 @ X373 @ X378) @ X378)|~(in @ X378 @ (esk7_2 @ X372 @ X373))|(in @ (esk5_2 @ X372 @ X373) @ X373)))&(~(in @ X381 @ X373)|~(X372 @ X381 @ X380)|(in @ X380 @ (esk7_2 @ X372 @ X373))|(in @ (esk5_2 @ X372 @ X373) @ X373)))&(((((in @ (esk8_3 @ X372 @ X373 @ X378) @ X373)|~(in @ X378 @ (esk7_2 @ X372 @ X373))|((X372 @ (esk5_2 @ X372 @ X373) @ (esk6_3 @ X372 @ X373 @ X375))|~(X372 @ (esk5_2 @ X372 @ X373) @ X375)))&((X372 @ (esk8_3 @ X372 @ X373 @ X378) @ X378)|~(in @ X378 @ (esk7_2 @ X372 @ X373))|((X372 @ (esk5_2 @ X372 @ X373) @ (esk6_3 @ X372 @ X373 @ X375))|~(X372 @ (esk5_2 @ X372 @ X373) @ X375))))&(~(in @ X381 @ X373)|~(X372 @ X381 @ X380)|(in @ X380 @ (esk7_2 @ X372 @ X373))|((X372 @ (esk5_2 @ X372 @ X373) @ (esk6_3 @ X372 @ X373 @ X375))|~(X372 @ (esk5_2 @ X372 @ X373) @ X375))))&((((in @ (esk8_3 @ X372 @ X373 @ X378) @ X373)|~(in @ X378 @ (esk7_2 @ X372 @ X373))|(((X375)!=(esk6_3 @ X372 @ X373 @ X375))|~(X372 @ (esk5_2 @ X372 @ X373) @ X375)))&((X372 @ (esk8_3 @ X372 @ X373 @ X378) @ X378)|~(in @ X378 @ (esk7_2 @ X372 @ X373))|(((X375)!=(esk6_3 @ X372 @ X373 @ X375))|~(X372 @ (esk5_2 @ X372 @ X373) @ X375))))&(~(in @ X381 @ X373)|~(X372 @ X381 @ X380)|(in @ X380 @ (esk7_2 @ X372 @ X373))|(((X375)!=(esk6_3 @ X372 @ X373 @ X375))|~(X372 @ (esk5_2 @ X372 @ X373) @ X375))))))&((((in @ (esk9_1 @ X382) @ X382)|~(in @ X383 @ X382))&(~(in @ X385 @ (esk9_1 @ X382))|~(in @ X385 @ X382)|~(in @ X383 @ X382)))&((epred1_0)&((descrp)&((~(in @ X388 @ X386)|(~(X387 @ X388)|(in @ X388 @ (dsetconstr @ X386 @ (^[Z0:$i]:((X387 @ Z0)))))))&((~(in @ X391 @ (dsetconstr @ X389 @ (^[Z0:$i]:((X390 @ Z0)))))|(in @ X391 @ X389))&((~(in @ X394 @ (dsetconstr @ X392 @ (^[Z0:$i]:((X393 @ Z0)))))|(X393 @ X394))&(((((X395 @ (esk11_1 @ X395))|((X395 @ (esk10_2 @ X395 @ X396))|~(X395 @ X396)))&(~(X395 @ X399)|((esk11_1 @ X395)=(X399))|((X395 @ (esk10_2 @ X395 @ X396))|~(X395 @ X396))))&(((X395 @ (esk11_1 @ X395))|(((X396)!=(esk10_2 @ X395 @ X396))|~(X395 @ X396)))&(~(X395 @ X399)|((esk11_1 @ X395)=(X399))|(((X396)!=(esk10_2 @ X395 @ X396))|~(X395 @ X396)))))&((~(in @ X401 @ (prop2set @ ((X400))))|(X400))&((~(in @ X402 @ emptyset)|(X403))&(~(in @ X404 @ emptyset)&(~(in @ X405 @ emptyset)&((((X406 @ (esk12_2 @ X406 @ X407))|~(X406 @ X407)|(X406 @ (esk13_1 @ X406)))&(((X407)!=(esk12_2 @ X406 @ X407))|~(X406 @ X407)|(X406 @ (esk13_1 @ X406))))&(((((in @ (esk15_2 @ X410 @ X411) @ X411)|((X410)=(X411))|(in @ (esk14_2 @ X410 @ X411) @ X410))&(~(in @ (esk15_2 @ X410 @ X411) @ X410)|((X410)=(X411))|(in @ (esk14_2 @ X410 @ X411) @ X410)))&(((in @ (esk15_2 @ X410 @ X411) @ X411)|((X410)=(X411))|~(in @ (esk14_2 @ X410 @ X411) @ X411))&(~(in @ (esk15_2 @ X410 @ X411) @ X410)|((X410)=(X411))|~(in @ (esk14_2 @ X410 @ X411) @ X411))))&(((in @ (esk16_1 @ X414) @ X414)|((X414)=(emptyset)))&(((in @ (esk17_1 @ X416) @ X416)|((X416)=(emptyset)))&(((~(in @ X420 @ (dsetconstr @ X418 @ (^[Z0:$i]:((X419 @ Z0)))))|(X419 @ X420)|~(in @ X420 @ X418))&(~(X419 @ X420)|(in @ X420 @ (dsetconstr @ X418 @ (^[Z0:$i]:((X419 @ Z0)))))|~(in @ X420 @ X418)))&((((X421)=(emptyset))|(in @ (esk18_1 @ X421) @ X421))&((~(in @ X425 @ X423)|(~(X424 @ X425)|((dsetconstr @ X423 @ (^[Z0:$i]:((X424 @ Z0))))!=(emptyset))))&((~(in @ X427 @ X426)|((X426)!=(emptyset)))&((in @ X428 @ (setadjoin @ X428 @ X429))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X432 @ X431)|(in @ X432 @ (setadjoin @ X430 @ X431)))&(((((in @ X435 @ X434)|(X436)|((X435)=(X433))|~(in @ X435 @ (setadjoin @ X433 @ X434)))&(~(X436)|(X436)|((X435)=(X433))|~(in @ X435 @ (setadjoin @ X433 @ X434))))&(((in @ X435 @ X434)|(X436)|~(X436)|~(in @ X435 @ (setadjoin @ X433 @ X434)))&(~(X436)|(X436)|~(X436)|~(in @ X435 @ (setadjoin @ X433 @ X434)))))&((~(in @ X439 @ (setadjoin @ X437 @ X438))|(((X439)=(X437))|(in @ X439 @ X438)))&(((dsetconstr @ X440 @ (^[Z0:$i]:(($true))))=(X440))&((((in @ (esk19_2 @ X441 @ X442) @ X442)|(in @ X442 @ (powerset @ X441)))&(~(in @ (esk19_2 @ X441 @ X442) @ X441)|(in @ X442 @ (powerset @ X441))))&((in @ emptyset @ (powerset @ X444))&((in @ emptyset @ (powerset @ X445))&((~(in @ X447 @ (powerset @ X446))|(~(in @ X448 @ X447)|(in @ X448 @ X446)))&((~(in @ X450 @ X451)|(~(in @ X451 @ X449)|(in @ X450 @ (setunion @ X449))))&((((in @ X453 @ (esk20_3 @ X452 @ X453 @ X454))|(X454)|~(in @ X453 @ (setunion @ X452)))&(((in @ (esk20_3 @ X452 @ X453 @ X454) @ X452)|(X454)|~(in @ X453 @ (setunion @ X452)))&(~(X454)|(X454)|~(in @ X453 @ (setunion @ X452)))))&((~(in @ X457 @ X456)|(in @ X457 @ (powerset @ (setunion @ X456))))&((((~(X458 @ X462)|((X462)=(esk22_1 @ X458))|((X458 @ (esk21_2 @ X458 @ X459))|~(X458 @ X459)))&(((X463)!=(esk22_1 @ X458))|(X458 @ X463)|((X458 @ (esk21_2 @ X458 @ X459))|~(X458 @ X459))))&((~(X458 @ X462)|((X462)=(esk22_1 @ X458))|(((X459)!=(esk21_2 @ X458 @ X459))|~(X458 @ X459)))&(((X463)!=(esk22_1 @ X458))|(X458 @ X463)|(((X459)!=(esk21_2 @ X458 @ X459))|~(X458 @ X459)))))&((((X464)=(emptyset))|(in @ (esk23_1 @ X464) @ X464))&((~(in @ X466 @ (setadjoin @ X467 @ emptyset))|((X466)=(X467)))&((((X468)=(X469))|~(in @ X469 @ (setadjoin @ X468 @ emptyset)))&((((X470)!=(X471))|(in @ X470 @ (setadjoin @ X471 @ emptyset)))&((~(in @ X472 @ (setadjoin @ X473 @ emptyset))|(in @ X473 @ (setadjoin @ X472 @ emptyset)))&((~(in @ X476 @ (setadjoin @ X474 @ (setadjoin @ X475 @ emptyset)))|(((X476)=(X474))|((X476)=(X475))))&((in @ X477 @ (setadjoin @ X477 @ (setadjoin @ X478 @ emptyset)))&((in @ X480 @ (setadjoin @ X479 @ (setadjoin @ X480 @ emptyset)))&((~(in @ X483 @ X481)|~(X482 @ X483)|((dsetconstr @ X481 @ (^[Z0:$i]:((X482 @ Z0))))!=(emptyset)))&((~(in @ X485 @ emptyset)|(X484 @ X485))&((((in @ (esk24_2 @ X486 @ X487) @ X486)|(~(in @ X488 @ X486)|(X487 @ X488)))&(~(X487 @ (esk24_2 @ X486 @ X487))|(~(in @ X488 @ X486)|(X487 @ X488))))&((((in @ (esk25_2 @ X490 @ X491) @ X490)|(~(in @ X493 @ X490)|~(X491 @ X493)))&((X491 @ (esk25_2 @ X490 @ X491))|(~(in @ X493 @ X490)|~(X491 @ X493))))&((((in @ (esk26_2 @ X494 @ X495) @ X494)|(~(in @ X497 @ X494)|~(X495 @ X497)))&((X495 @ (esk26_2 @ X494 @ X495))|(~(in @ X497 @ X494)|~(X495 @ X497))))&((((in @ (esk27_2 @ X498 @ X499) @ X498)|(~(in @ X500 @ X498)|(X499 @ X500)))&(~(X499 @ (esk27_2 @ X498 @ X499))|(~(in @ X500 @ X498)|(X499 @ X500))))&((~(X502)|(in @ emptyset @ (prop2set @ ((X502)))))&((prop2set2propI)&((~(in @ X505 @ esk28_0)|~(epred2_0 @ X505))&((in @ esk29_0 @ esk28_0)&(epred2_0 @ esk29_0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_82])])])])])])).
% 0.23/0.30 thf(c_0_84, negated_conjecture, ![X2:$i]:((~((in @ X2 @ esk28_0))|~((epred2_0 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_83])).
% 0.23/0.30 thf(c_0_85, negated_conjecture, (in @ esk29_0 @ esk28_0), inference(split_conjunct,[status(thm)],[c_0_83])).
% 0.23/0.30 thf(c_0_86, negated_conjecture, (epred2_0 @ esk29_0), inference(split_conjunct,[status(thm)],[c_0_83])).
% 0.23/0.30 thf(c_0_87, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84, c_0_85]), c_0_86])]), ['proof']).
% 0.23/0.30 % SZS output end CNFRefutation
% 0.23/0.30 % Parsed axioms : 131
% 0.23/0.30 % Removed by relevancy pruning/SinE : 72
% 0.23/0.30 % Initial clauses : 113
% 0.23/0.30 % Removed in clause preprocessing : 4
% 0.23/0.30 % Initial clauses in saturation : 109
% 0.23/0.30 % Processed clauses : 15
% 0.23/0.30 % ...of these trivial : 1
% 0.23/0.30 % ...subsumed : 3
% 0.23/0.30 % ...remaining for further processing : 11
% 0.23/0.30 % Other redundant clauses eliminated : 0
% 0.23/0.30 % Clauses deleted for lack of memory : 0
% 0.23/0.30 % Backward-subsumed : 0
% 0.23/0.30 % Backward-rewritten : 0
% 0.23/0.30 % Generated clauses : 1
% 0.23/0.30 % ...of the previous two non-redundant : 0
% 0.23/0.30 % ...aggressively subsumed : 0
% 0.23/0.30 % Contextual simplify-reflections : 0
% 0.23/0.30 % Paramodulations : 1
% 0.23/0.30 % Factorizations : 0
% 0.23/0.30 % NegExts : 0
% 0.23/0.30 % Equation resolutions : 0
% 0.23/0.30 % Disequality decompositions : 0
% 0.23/0.30 % Total rewrite steps : 2
% 0.23/0.30 % ...of those cached : 0
% 0.23/0.30 % Propositional unsat checks : 0
% 0.23/0.30 % Propositional check models : 0
% 0.23/0.30 % Propositional check unsatisfiable : 0
% 0.23/0.30 % Propositional clauses : 0
% 0.23/0.30 % Propositional clauses after purity: 0
% 0.23/0.30 % Propositional unsat core size : 0
% 0.23/0.30 % Propositional preprocessing time : 0.000
% 0.23/0.30 % Propositional encoding time : 0.000
% 0.23/0.30 % Propositional solver time : 0.000
% 0.23/0.30 % Success case prop preproc time : 0.000
% 0.23/0.30 % Success case prop encoding time : 0.000
% 0.23/0.30 % Success case prop solver time : 0.000
% 0.23/0.30 % Current number of processed clauses : 11
% 0.23/0.30 % Positive orientable unit clauses : 8
% 0.23/0.30 % Positive unorientable unit clauses: 0
% 0.23/0.30 % Negative unit clauses : 2
% 0.23/0.30 % Non-unit-clauses : 1
% 0.23/0.30 % Current number of unprocessed clauses: 94
% 0.23/0.30 % ...number of literals in the above : 293
% 0.23/0.30 % Current number of archived formulas : 0
% 0.23/0.30 % Current number of archived clauses : 0
% 0.23/0.30 % Clause-clause subsumption calls (NU) : 0
% 0.23/0.30 % Rec. Clause-clause subsumption calls : 0
% 0.23/0.30 % Non-unit clause-clause subsumptions : 0
% 0.23/0.30 % Unit Clause-clause subsumption calls : 1
% 0.23/0.30 % Rewrite failures with RHS unbound : 0
% 0.23/0.30 % BW rewrite match attempts : 0
% 0.23/0.30 % BW rewrite match successes : 0
% 0.23/0.30 % Condensation attempts : 0
% 0.23/0.30 % Condensation successes : 0
% 0.23/0.30 % Termbank termtop insertions : 12501
% 0.23/0.30 % Search garbage collected termcells : 4856
% 0.23/0.30
% 0.23/0.30 % -------------------------------------------------
% 0.23/0.30 % User time : 0.011 s
% 0.23/0.30 % System time : 0.007 s
% 0.23/0.30 % Total time : 0.018 s
% 0.23/0.30 % Maximum resident set size: 5048 pages
% 0.23/0.30
% 0.23/0.30 % -------------------------------------------------
% 0.23/0.30 % User time : 0.014 s
% 0.23/0.30 % System time : 0.013 s
% 0.23/0.30 % Total time : 0.027 s
% 0.23/0.30 % Maximum resident set size: 4864 pages
% 0.23/0.30 % E exiting
%------------------------------------------------------------------------------