%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU545^1 : 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 : n020.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 08:26:39 AM UTC 2026
% Result : Theorem 0.21s 0.30s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU545^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n020.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 13:50:19 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.24 Running higher-order theorem proving
% 0.21/0.26 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.URlTJcQGSt/E---3.1_1083664.p
% 0.21/0.30 % Version: 3.5.1-ho
% 0.21/0.30 % Preprocessing class: HSMSSLSSMLLCHSA.
% 0.21/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.30 % Starting new_ho_10 with 1500s (5) cores
% 0.21/0.30 % Starting sh5l with 300s (1) cores
% 0.21/0.30 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.30 % Starting new_bool_2 with 300s (1) cores
% 0.21/0.30 % new_ho_10 with pid 1083677 completed with status 0
% 0.21/0.30 % Result found by new_ho_10
% 0.21/0.30 % Preprocessing class: HSMSSLSSMLLCHSA.
% 0.21/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.30 % Starting new_ho_10 with 1500s (5) cores
% 0.21/0.30 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.21/0.30 % No SInE strategy applied
% 0.21/0.30 % Search class: HGHSM-FFMM31-SHSSMSBN
% 0.21/0.30 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/0.30 % Starting SubtermCWHack with 151s (1) cores
% 0.21/0.30 % Starting new_ho_10 with 901s (1) cores
% 0.21/0.30 % Starting sh5l with 151s (1) cores
% 0.21/0.30 % Starting new_bool_1 with 151s (1) cores
% 0.21/0.30 % Starting new_bool_2 with 146s (1) cores
% 0.21/0.30 % SubtermCWHack with pid 1083681 completed with status 0
% 0.21/0.30 % Result found by SubtermCWHack
% 0.21/0.30 % Preprocessing class: HSMSSLSSMLLCHSA.
% 0.21/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.30 % Starting new_ho_10 with 1500s (5) cores
% 0.21/0.30 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.21/0.30 % No SInE strategy applied
% 0.21/0.30 % Search class: HGHSM-FFMM31-SHSSMSBN
% 0.21/0.30 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/0.30 % Starting SubtermCWHack with 151s (1) cores
% 0.21/0.30 % Preprocessing time : 0.003 s
% 0.21/0.30
% 0.21/0.30 % Proof found!
% 0.21/0.30 % SZS status Theorem
% 0.21/0.30 % SZS output start CNFRefutation
% 0.21/0.30 thf(decl_23, type, in: $i > $i > $o).
% 0.21/0.30 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.21/0.30 thf(decl_25, type, setextAx: $o).
% 0.21/0.30 thf(decl_26, type, emptyset: $i).
% 0.21/0.30 thf(decl_27, type, emptysetAx: $o).
% 0.21/0.30 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.21/0.30 thf(decl_29, type, setadjoinAx: $o).
% 0.21/0.30 thf(decl_30, type, powerset: $i > $i).
% 0.21/0.30 thf(decl_31, type, powersetAx: $o).
% 0.21/0.30 thf(decl_32, type, setunion: $i > $i).
% 0.21/0.30 thf(decl_33, type, setunionAx: $o).
% 0.21/0.30 thf(decl_34, type, omega: $i).
% 0.21/0.30 thf(decl_35, type, omega0Ax: $o).
% 0.21/0.30 thf(decl_36, type, omegaSAx: $o).
% 0.21/0.30 thf(decl_37, type, omegaIndAx: $o).
% 0.21/0.30 thf(decl_38, type, replAx: $o).
% 0.21/0.30 thf(decl_39, type, foundationAx: $o).
% 0.21/0.30 thf(decl_40, type, wellorderingAx: $o).
% 0.21/0.30 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.21/0.30 thf(decl_42, type, descrp: $o).
% 0.21/0.30 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.21/0.30 thf(decl_44, type, dsetconstrI: $o).
% 0.21/0.30 thf(decl_45, type, dsetconstrEL: $o).
% 0.21/0.30 thf(decl_46, type, dsetconstrER: $o).
% 0.21/0.30 thf(decl_47, type, exuE1: $o).
% 0.21/0.30 thf(decl_48, type, prop2set: $o > $i).
% 0.21/0.30 thf(decl_49, type, prop2setE: $o).
% 0.21/0.30 thf(decl_50, type, emptysetE: $o).
% 0.21/0.30 thf(decl_51, type, emptysetimpfalse: $o).
% 0.21/0.30 thf(decl_52, type, notinemptyset: $o).
% 0.21/0.30 thf(decl_53, type, exuE3e: $o).
% 0.21/0.30 thf(decl_54, type, setext: $o).
% 0.21/0.30 thf(decl_55, type, emptyI: $o).
% 0.21/0.30 thf(decl_56, type, noeltsimpempty: $o).
% 0.21/0.30 thf(decl_57, type, setbeta: $o).
% 0.21/0.30 thf(decl_58, type, nonempty: $i > $o).
% 0.21/0.30 thf(decl_59, type, nonemptyE1: $o).
% 0.21/0.30 thf(decl_60, type, nonemptyI: $o).
% 0.21/0.30 thf(decl_61, type, nonemptyI1: $o).
% 0.21/0.30 thf(decl_62, type, setadjoinIL: $o).
% 0.21/0.30 thf(decl_63, type, emptyinunitempty: $o).
% 0.21/0.30 thf(decl_64, type, setadjoinIR: $o).
% 0.21/0.30 thf(decl_65, type, setadjoinE: $o).
% 0.21/0.30 thf(decl_66, type, setadjoinOr: $o).
% 0.21/0.30 thf(decl_67, type, setoftrueEq: $o).
% 0.21/0.30 thf(decl_68, type, powersetI: $o).
% 0.21/0.30 thf(decl_69, type, emptyinPowerset: $o).
% 0.21/0.30 thf(decl_70, type, emptyInPowerset: $o).
% 0.21/0.30 thf(decl_71, type, powersetE: $o).
% 0.21/0.30 thf(decl_72, type, setunionI: $o).
% 0.21/0.30 thf(decl_73, type, setunionE: $o).
% 0.21/0.30 thf(decl_74, type, subPowSU: $o).
% 0.21/0.30 thf(decl_75, type, exuE2: $o).
% 0.21/0.30 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.21/0.30 thf(decl_77, type, uniqinunit: $o).
% 0.21/0.30 thf(decl_78, type, notinsingleton: $o).
% 0.21/0.30 thf(decl_79, type, eqinunit: $o).
% 0.21/0.30 thf(decl_80, type, singletonsswitch: $o).
% 0.21/0.30 thf(decl_81, type, upairsetE: $o).
% 0.21/0.30 thf(decl_82, type, upairsetIL: $o).
% 0.21/0.30 thf(decl_83, type, upairsetIR: $o).
% 0.21/0.30 thf(decl_84, type, emptyE1: $o).
% 0.21/0.30 thf(decl_85, type, vacuousDall: $o).
% 0.21/0.30 thf(decl_86, type, quantDeMorgan1: $o).
% 0.21/0.30 thf(decl_87, type, quantDeMorgan2: $o).
% 0.21/0.30 thf(decl_88, type, quantDeMorgan3: $o).
% 0.21/0.30 thf(decl_89, type, quantDeMorgan4: $o).
% 0.21/0.30 thf(decl_90, type, prop2setI: $o).
% 0.21/0.30 thf(decl_91, type, set2prop: $i > $o).
% 0.21/0.30 thf(decl_92, type, prop2set2propI: $o).
% 0.21/0.30 thf(decl_93, type, notdexE: $o).
% 0.21/0.30 thf(decl_94, type, notdallE: $o).
% 0.21/0.30 thf(decl_95, type, exuI1: $o).
% 0.21/0.30 thf(decl_96, type, epred1_0: $o).
% 0.21/0.30 thf(decl_97, type, esk1_2: $i > $i > $i).
% 0.21/0.30 thf(decl_98, type, esk2_2: $i > $i > $i).
% 0.21/0.30 thf(decl_99, type, esk3_2: $i > $i > $i).
% 0.21/0.30 thf(decl_100, type, esk4_1: $i > $i).
% 0.21/0.30 thf(decl_101, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.21/0.30 thf(decl_102, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.21/0.30 thf(decl_103, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.21/0.30 thf(decl_104, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.21/0.30 thf(decl_105, type, esk9_1: $i > $i).
% 0.21/0.30 thf(decl_106, type, esk10_2: ($i > $o) > $i > $i).
% 0.21/0.30 thf(decl_107, type, esk11_2: ($i > $o) > $i > $i).
% 0.21/0.30 thf(decl_108, type, esk12_1: ($i > $o) > $i).
% 0.21/0.30 thf(decl_109, type, esk13_2: ($i > $o) > $i > $i).
% 0.21/0.30 thf(decl_110, type, esk14_1: ($i > $o) > $i).
% 0.21/0.30 thf(decl_111, type, esk15_2: $i > $i > $i).
% 0.21/0.30 thf(decl_112, type, esk16_2: $i > $i > $i).
% 0.21/0.30 thf(decl_113, type, esk17_1: $i > $i).
% 0.21/0.30 thf(decl_114, type, esk18_1: $i > $i).
% 0.21/0.30 thf(decl_115, type, esk19_1: $i > $i).
% 0.21/0.30 thf(decl_116, type, esk20_2: $i > $i > $i).
% 0.21/0.30 thf(decl_117, type, esk21_3: $i > $i > $o > $i).
% 0.21/0.30 thf(decl_118, type, esk22_2: ($i > $o) > $i > $i).
% 0.21/0.30 thf(decl_119, type, esk23_1: ($i > $o) > $i).
% 0.21/0.30 thf(decl_120, type, esk24_1: $i > $i).
% 0.21/0.30 thf(decl_121, type, esk25_2: $i > ($i > $o) > $i).
% 0.21/0.30 thf(decl_122, type, esk26_2: $i > ($i > $o) > $i).
% 0.21/0.30 thf(decl_123, type, esk27_2: $i > ($i > $o) > $i).
% 0.21/0.30 thf(decl_124, type, esk28_2: $i > ($i > $o) > $i).
% 0.21/0.30 thf(decl_125, type, esk29_2: $i > ($i > $o) > $i).
% 0.21/0.30 thf(decl_126, type, esk30_2: $i > ($i > $o) > $i).
% 0.21/0.30 thf(decl_127, type, esk31_2: ($i > $o) > $i > $i).
% 0.21/0.30 thf(decl_128, type, esk32_1: ($i > $o) > $i).
% 0.21/0.30 thf(decl_129, type, epred2_0: $i > $o).
% 0.21/0.30 thf(decl_130, type, esk33_0: $i).
% 0.21/0.30 thf(decl_131, type, esk34_1: $i > $i).
% 0.21/0.30 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', replAx)).
% 0.21/0.30 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', exu)).
% 0.21/0.30 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', descrp)).
% 0.21/0.30 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', exuE1)).
% 0.21/0.30 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', exuE3e)).
% 0.21/0.30 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', nonempty)).
% 0.21/0.30 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', nonemptyI)).
% 0.21/0.30 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', exuE2)).
% 0.21/0.30 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', exuI1)).
% 0.21/0.30 thf(exuI3, 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)=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', exuI3)).
% 0.21/0.30 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', dsetconstrI)).
% 0.21/0.30 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', dsetconstrEL)).
% 0.21/0.30 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', dsetconstrER)).
% 0.21/0.30 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', setbeta)).
% 0.21/0.30 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', nonemptyE1)).
% 0.21/0.30 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', nonemptyI1)).
% 0.21/0.30 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', setoftrueEq)).
% 0.21/0.30 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', nonemptyImpWitness)).
% 0.21/0.30 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.URlTJcQGSt/E---3.1_1083664.p', emptyE1)).
% 0.21/0.30 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', setextAx)).
% 0.21/0.30 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', emptysetAx)).
% 0.21/0.30 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', setadjoinAx)).
% 0.21/0.30 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', powersetAx)).
% 0.21/0.30 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', setunionAx)).
% 0.21/0.30 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', omega0Ax)).
% 0.21/0.30 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', omegaSAx)).
% 0.21/0.30 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', omegaIndAx)).
% 0.21/0.30 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', foundationAx)).
% 0.21/0.30 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.URlTJcQGSt/E---3.1_1083664.p', wellorderingAx)).
% 0.21/0.30 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', prop2setE)).
% 0.21/0.30 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', emptysetE)).
% 0.21/0.30 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', emptysetimpfalse)).
% 0.21/0.30 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', notinemptyset)).
% 0.21/0.30 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', setext)).
% 0.21/0.30 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', emptyI)).
% 0.21/0.30 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', noeltsimpempty)).
% 0.21/0.30 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', setadjoinIL)).
% 0.21/0.30 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', emptyinunitempty)).
% 0.21/0.30 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', setadjoinIR)).
% 0.21/0.30 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.URlTJcQGSt/E---3.1_1083664.p', setadjoinE)).
% 0.21/0.30 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', setadjoinOr)).
% 0.21/0.30 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', powersetI)).
% 0.21/0.30 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', emptyinPowerset)).
% 0.21/0.30 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', emptyInPowerset)).
% 0.21/0.30 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', powersetE)).
% 0.21/0.30 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', setunionI)).
% 0.21/0.30 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.URlTJcQGSt/E---3.1_1083664.p', setunionE)).
% 0.21/0.30 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', subPowSU)).
% 0.21/0.30 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', uniqinunit)).
% 0.21/0.30 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', notinsingleton)).
% 0.21/0.30 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', eqinunit)).
% 0.21/0.30 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', singletonsswitch)).
% 0.21/0.30 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', upairsetE)).
% 0.21/0.30 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', upairsetIL)).
% 0.21/0.30 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', upairsetIR)).
% 0.21/0.30 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', vacuousDall)).
% 0.21/0.30 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', quantDeMorgan1)).
% 0.21/0.30 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', quantDeMorgan2)).
% 0.21/0.30 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', quantDeMorgan3)).
% 0.21/0.30 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', quantDeMorgan4)).
% 0.21/0.30 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', prop2setI)).
% 0.21/0.30 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', prop2set2propI)).
% 0.21/0.30 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', notdexE)).
% 0.21/0.30 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.URlTJcQGSt/E---3.1_1083664.p', notdallE)).
% 0.21/0.30 thf(c_0_64, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.21/0.30 thf(c_0_65, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.21/0.30 thf(c_0_66, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.21/0.30 thf(c_0_67, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.21/0.30 thf(c_0_68, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.21/0.30 thf(c_0_69, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.21/0.30 thf(c_0_70, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.21/0.30 thf(c_0_71, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.21/0.30 thf(c_0_72, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 0.21/0.30 thf(c_0_73, 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)=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[exuI3])).
% 0.21/0.30 thf(c_0_74, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X190:$i]:(((((X6 @ X2 @ X190)))&(![X191:$i]:(((((X6 @ X2 @ X191)))=>(((X190)=(X191)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_64, c_0_65])).
% 0.21/0.30 thf(c_0_75, plain, ((descrp)=(![X1:$i > $o]:((((?[X192:$i]:(((((X1 @ X192)))&(![X193:$i]:(((((X1 @ X193)))=>(((X192)=(X193))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_66, c_0_65])).
% 0.21/0.30 thf(c_0_76, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.21/0.30 thf(c_0_77, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.21/0.30 thf(c_0_78, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.21/0.30 thf(c_0_79, plain, ((exuE1)=(![X1:$i > $o]:((((?[X194:$i]:(((((X1 @ X194)))&(![X195:$i]:(((((X1 @ X195)))=>(((X194)=(X195))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_67, c_0_65])).
% 0.21/0.30 thf(c_0_80, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X196:$i]:(((((X1 @ X196)))&(![X197:$i]:(((((X1 @ X197)))=>(((X196)=(X197))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_68, c_0_65])).
% 0.21/0.30 thf(c_0_81, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.21/0.30 thf(c_0_82, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_69])).
% 0.21/0.30 thf(c_0_83, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_70, c_0_69])).
% 0.21/0.30 thf(c_0_84, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_69])).
% 0.21/0.30 thf(c_0_85, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.21/0.30 thf(c_0_86, plain, ((exuE2)=(![X1:$i > $o]:((((?[X198:$i]:(((((X1 @ X198)))&(![X199:$i]:(((((X1 @ X199)))=>(((X198)=(X199))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_71, c_0_65])).
% 0.21/0.30 thf(c_0_87, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_69])).
% 0.21/0.30 thf(c_0_88, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])).
% 0.21/0.30 thf(c_0_89, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X200:$i]:(((((X1 @ X200)))&(![X201:$i]:(((((X1 @ X201)))=>(((X200)=(X201)))))))))))))), inference(apply_def,[status(thm)],[c_0_72, c_0_65])).
% 0.21/0.30 thf(c_0_90, plain, ((epred1_0)<=>![X231:$i]:(?[X232:$i]:((((![X233:$i]:(((in @ X233 @ X232)=>![X234:$i]:(((in @ X234 @ X233)=>(in @ X234 @ X231)))))&![X235:$i, X236:$i]:((((in @ X235 @ X231)&(in @ X236 @ X231))=>(![X237:$i]:(((in @ X237 @ X232)=>((in @ X235 @ X237)<=>(in @ X236 @ X237))))=>((X235)=(X236))))))&![X238:$i, X239:$i]:((((in @ X238 @ X232)&(in @ X239 @ X232))=>(![X240:$i]:(((in @ X240 @ X238)=>(in @ X240 @ X239)))|![X241:$i]:(((in @ X241 @ X239)=>(in @ X241 @ X238)))))))&![X242:$i]:(((![X243:$i]:(((in @ X243 @ X242)=>(in @ X243 @ X231)))&?[X244:$i]:((in @ X244 @ X242)))=>?[X245:$i, X246:$i]:(((((in @ X245 @ X232)&(in @ X246 @ X242))&~(?[X247:$i]:(((in @ X247 @ X245)&(in @ X247 @ X242)))))&![X248:$i]:(((in @ X248 @ X232)=>(![X249:$i]:(((in @ X249 @ X248)=>(in @ X249 @ X245)))|(in @ X246 @ X248)))))))))))), introduced(definition)).
% 0.21/0.30 thf(c_0_91, negated_conjecture, ~((![X202:$i, X203:$i]:((![X204:$i]:(((in @ X204 @ X202)<=>(in @ X204 @ X203)))=>((X202)=(X203))))=>(![X205:$i]:(~(in @ X205 @ emptyset))=>(![X206:$i, X207:$i, X208:$i]:(((in @ X208 @ (setadjoin @ X206 @ X207))<=>(((X208)=(X206))|(in @ X208 @ X207))))=>(![X209:$i, X210:$i]:(((in @ X210 @ (powerset @ X209))<=>![X211:$i]:(((in @ X211 @ X210)=>(in @ X211 @ X209)))))=>(![X212:$i, X213:$i]:(((in @ X213 @ (setunion @ X212))<=>?[X214:$i]:(((in @ X213 @ X214)&(in @ X214 @ X212)))))=>((in @ emptyset @ omega)=>(![X215:$i]:(((in @ X215 @ omega)=>(in @ (setadjoin @ X215 @ X215) @ omega)))=>(![X216:$i]:((((in @ emptyset @ X216)&![X217:$i]:((((in @ X217 @ omega)&(in @ X217 @ X216))=>(in @ (setadjoin @ X217 @ X217) @ X216))))=>![X218:$i]:(((in @ X218 @ omega)=>(in @ X218 @ X216)))))=>(![X219:$i > $i > $o, X220:$i]:((![X221:$i]:(((in @ X221 @ X220)=>?[X222:$i]:(((X219 @ X221 @ X222)&![X223:$i]:(((X219 @ X221 @ X223)=>((X222)=(X223))))))))=>?[X224:$i]:(![X225:$i]:(((in @ X225 @ X224)<=>?[X226:$i]:(((in @ X226 @ X220)&(X219 @ X226 @ X225))))))))=>(![X227:$i]:((?[X228:$i]:((in @ X228 @ X227))=>?[X229:$i]:(((in @ X229 @ X227)&~(?[X230:$i]:(((in @ X230 @ X229)&(in @ X230 @ X227))))))))=>((epred1_0)=>(![X250:$i > $o]:((?[X251:$i]:(((X250 @ X251)&![X252:$i]:(((X250 @ X252)=>((X251)=(X252))))))=>(X250 @ (descr @ (^[Z0:$i]:(X250 @ Z0))))))=>(![X253:$i, X254:$i > $o, X255:$i]:(((in @ X255 @ X253)=>((X254 @ X255)=>(in @ X255 @ (dsetconstr @ X253 @ X254)))))=>(![X256:$i, X257:$i > $o, X258:$i]:(((in @ X258 @ (dsetconstr @ X256 @ X257))=>(in @ X258 @ X256)))=>(![X259:$i, X260:$i > $o, X261:$i]:(((in @ X261 @ (dsetconstr @ X259 @ X260))=>(X260 @ X261)))=>(![X262:$i > $o]:((?[X263:$i]:(((X262 @ X263)&![X264:$i]:(((X262 @ X264)=>((X263)=(X264))))))=>?[X265:$i]:(((X262 @ X265)&![X266:$i]:(((X262 @ X266)=>((X265)=(X266))))))))=>(![X267:$o, X268:$i]:(((in @ X268 @ (prop2set @ ((X267))))=>(X267)))=>(![X269:$i]:(((in @ X269 @ emptyset)=>![X270:$o]:((X270))))=>(![X271:$i]:(((in @ X271 @ emptyset)=>~($true)))=>(![X272:$i]:(~(in @ X272 @ emptyset))=>(![X273:$i > $o]:((?[X274:$i]:(((X273 @ X274)&![X275:$i]:(((X273 @ X275)=>((X274)=(X275))))))=>?[X276:$i]:((X273 @ X276))))=>(![X277:$i, X278:$i]:((![X279:$i]:(((in @ X279 @ X277)=>(in @ X279 @ X278)))=>(![X280:$i]:(((in @ X280 @ X278)=>(in @ X280 @ X277)))=>((X277)=(X278)))))=>(![X281:$i]:((![X282:$i]:(~(in @ X282 @ X281))=>((X281)=(emptyset))))=>(![X283:$i]:((![X284:$i]:(~(in @ X284 @ X283))=>((X283)=(emptyset))))=>(![X285:$i, X286:$i > $o, X287:$i]:(((in @ X287 @ X285)=>((in @ X287 @ (dsetconstr @ X285 @ X286))<=>(X286 @ X287))))=>(![X288:$i]:((((X288)!=(emptyset))=>?[X289:$i]:((in @ X289 @ X288))))=>(![X290:$i, X291:$i > $o, X292:$i]:(((in @ X292 @ X290)=>((X291 @ X292)=>((dsetconstr @ X290 @ X291)!=(emptyset)))))=>(![X293:$i]:((?[X294:$i]:((in @ X294 @ X293))=>((X293)!=(emptyset))))=>(![X295:$i, X296:$i]:((in @ X295 @ (setadjoin @ X295 @ X296)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X297:$i, X298:$i, X299:$i]:(((in @ X299 @ X298)=>(in @ X299 @ (setadjoin @ X297 @ X298))))=>(![X300:$i, X301:$i, X302:$i]:(((in @ X302 @ (setadjoin @ X300 @ X301))=>![X303:$o]:(((((X302)=(X300))=>(X303))=>(((in @ X302 @ X301)=>(X303))=>(X303))))))=>(![X304:$i, X305:$i, X306:$i]:(((in @ X306 @ (setadjoin @ X304 @ X305))=>(((X306)=(X304))|(in @ X306 @ X305))))=>(![X307:$i]:(((dsetconstr @ X307 @ (^[Z0:$i]:($true)))=(X307)))=>(![X308:$i, X309:$i]:((![X310:$i]:(((in @ X310 @ X309)=>(in @ X310 @ X308)))=>(in @ X309 @ (powerset @ X308))))=>(![X311:$i]:((in @ emptyset @ (powerset @ X311)))=>(![X312:$i]:((in @ emptyset @ (powerset @ X312)))=>(![X313:$i, X314:$i, X315:$i]:(((in @ X314 @ (powerset @ X313))=>((in @ X315 @ X314)=>(in @ X315 @ X313))))=>(![X316:$i, X317:$i, X318:$i]:(((in @ X317 @ X318)=>((in @ X318 @ X316)=>(in @ X317 @ (setunion @ X316)))))=>(![X319:$i, X320:$i]:(((in @ X320 @ (setunion @ X319))=>![X321:$o]:((![X322:$i]:(((in @ X320 @ X322)=>((in @ X322 @ X319)=>(X321))))=>(X321)))))=>(![X323:$i, X324:$i]:(((in @ X324 @ X323)=>(in @ X324 @ (powerset @ (setunion @ X323)))))=>(![X325:$i > $o]:((?[X326:$i]:(((X325 @ X326)&![X327:$i]:(((X325 @ X327)=>((X326)=(X327))))))=>?[X328:$i]:(![X329:$i]:(((X325 @ X329)<=>((X329)=(X328)))))))=>(![X330:$i]:((((X330)!=(emptyset))=>?[X331:$i]:(((in @ X331 @ X330)&$true))))=>(![X332:$i, X333:$i]:(((in @ X332 @ (setadjoin @ X333 @ emptyset))=>((X332)=(X333))))=>(![X334:$i, X335:$i]:((((X334)!=(X335))=>~(in @ X335 @ (setadjoin @ X334 @ emptyset))))=>(![X336:$i, X337:$i]:((((X336)=(X337))=>(in @ X336 @ (setadjoin @ X337 @ emptyset))))=>(![X338:$i, X339:$i]:(((in @ X338 @ (setadjoin @ X339 @ emptyset))=>(in @ X339 @ (setadjoin @ X338 @ emptyset))))=>(![X340:$i, X341:$i, X342:$i]:(((in @ X342 @ (setadjoin @ X340 @ (setadjoin @ X341 @ emptyset)))=>(((X342)=(X340))|((X342)=(X341)))))=>(![X343:$i, X344:$i]:((in @ X343 @ (setadjoin @ X343 @ (setadjoin @ X344 @ emptyset))))=>(![X345:$i, X346:$i]:((in @ X346 @ (setadjoin @ X345 @ (setadjoin @ X346 @ emptyset))))=>(![X347:$i, X348:$i > $o]:((?[X349:$i]:(((in @ X349 @ X347)&(X348 @ X349)))=>(((dsetconstr @ X347 @ X348)=(emptyset))=>~($true))))=>(![X350:$i > $o, X351:$i]:(((in @ X351 @ emptyset)=>(X350 @ X351)))=>(![X352:$i, X353:$i > $o]:((~(![X354:$i]:(((in @ X354 @ X352)=>(X353 @ X354))))=>?[X355:$i]:(((in @ X355 @ X352)&~((X353 @ X355))))))=>(![X356:$i, X357:$i > $o]:((![X358:$i]:(((in @ X358 @ X356)=>~((X357 @ X358))))=>~(?[X359:$i]:(((in @ X359 @ X356)&(X357 @ X359))))))=>(![X360:$i, X361:$i > $o]:((~(?[X362:$i]:(((in @ X362 @ X360)&(X361 @ X362))))=>![X363:$i]:(((in @ X363 @ X360)=>~((X361 @ X363))))))=>(![X364:$i, X365:$i > $o]:((?[X366:$i]:(((in @ X366 @ X364)&~((X365 @ X366))))=>~(![X367:$i]:(((in @ X367 @ X364)=>(X365 @ X367))))))=>(![X368:$o]:(((X368)=>(in @ emptyset @ (prop2set @ ((X368))))))=>(![X369:$o]:(((X369)=>(set2prop @ (prop2set @ ((X369))))))=>(![X370:$i, X371:$i > $o]:((~(?[X372:$i]:(((in @ X372 @ X370)&(X371 @ X372))))=>![X373:$i]:(((in @ X373 @ X370)=>~((X371 @ X373))))))=>(![X374:$i, X375:$i > $o]:((~(![X376:$i]:(((in @ X376 @ X374)=>(X375 @ X376))))=>?[X377:$i]:(((in @ X377 @ X374)&~((X375 @ X377))))))=>(![X378:$i > $o]:((?[X379:$i]:(((X378 @ X379)&![X380:$i]:(((X378 @ X380)=>((X379)=(X380))))))=>?[X381:$i]:(((X378 @ X381)&![X382:$i]:(((X378 @ X382)=>((X381)=(X382))))))))=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>?[X383:$i]:(((X1 @ X383)&![X384:$i]:(((X1 @ X384)=>((X383)=(X384))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_73]), c_0_65]), setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_74]), foundationAx]), wellorderingAx]), c_0_75]), c_0_76]), c_0_77]), c_0_78]), c_0_79]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_80]), setext]), emptyI]), noeltsimpempty]), c_0_81]), c_0_82]), c_0_83]), c_0_84]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_85]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_86]), c_0_87]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_88]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_89])])]), c_0_90])).
% 0.21/0.30 thf(c_0_92, negated_conjecture, ![X385:$i, X386:$i, X388:$i, X389:$i, X390:$i, X391:$i, X392:$i, X393:$i, X394:$i, X395:$i, X396:$i, X398:$i, X399:$i, X401:$i, X402:$i, X403:$i, X404:$i, X405:$i, X407:$i, X408:$i > $i > $o, X409:$i, X411:$i, X414:$i, X416:$i, X417:$i, X418:$i, X419:$i, X421:$i, X422:$i > $o, X423:$i, X425:$i, X426:$i > $o, X427:$i, X428:$i, X429:$i > $o, X430:$i, X431:$i, X432:$i > $o, X433:$i, X434:$i > $o, X435:$i, X438:$i, X439:$o, X440:$i, X441:$i, X442:$o, X443:$i, X444:$i, X445:$i > $o, X446:$i, X449:$i, X450:$i, X453:$i, X455:$i, X457:$i, X458:$i > $o, X459:$i, X460:$i, X462:$i, X463:$i > $o, X464:$i, X465:$i, X466:$i, X467:$i, X468:$i, X469:$i, X470:$i, X471:$i, X472:$i, X473:$i, X474:$i, X475:$o, X476:$i, X477:$i, X478:$i, X479:$i, X480:$i, X481:$i, X483:$i, X484:$i, X485:$i, X486:$i, X487:$i, X488:$i, X489:$i, X490:$i, X491:$i, X492:$i, X493:$o, X495:$i, X496:$i, X497:$i > $o, X498:$i, X501:$i, X502:$i, X503:$i, X505:$i, X506:$i, X507:$i, X508:$i, X509:$i, X510:$i, X511:$i, X512:$i, X513:$i, X514:$i, X515:$i, X516:$i, X517:$i, X518:$i, X519:$i, X520:$i, X521:$i > $o, X522:$i, X523:$i > $o, X524:$i, X525:$i, X526:$i > $o, X527:$i, X529:$i, X530:$i > $o, X532:$i, X533:$i, X534:$i > $o, X536:$i, X537:$i, X538:$i > $o, X539:$i, X541:$o, X542:$o, X543:$i, X544:$i > $o, X546:$i, X547:$i, X548:$i > $o, X549:$i, X551:$i > $o, X552:$i, X555:$i, X558:$i, X559:$i, X560:$i]:((((~(in @ (esk1_2 @ X385 @ X386) @ X385)|~(in @ (esk1_2 @ X385 @ X386) @ X386)|((X385)=(X386)))&((in @ (esk1_2 @ X385 @ X386) @ X385)|(in @ (esk1_2 @ X385 @ X386) @ X386)|((X385)=(X386))))&(~(in @ X388 @ emptyset)&(((~(in @ X391 @ (setadjoin @ X389 @ X390))|(((X391)=(X389))|(in @ X391 @ X390)))&((((X391)!=(X389))|(in @ X391 @ (setadjoin @ X389 @ X390)))&(~(in @ X391 @ X390)|(in @ X391 @ (setadjoin @ X389 @ X390)))))&(((~(in @ X393 @ (powerset @ X392))|(~(in @ X394 @ X393)|(in @ X394 @ X392)))&(((in @ (esk2_2 @ X395 @ X396) @ X396)|(in @ X396 @ (powerset @ X395)))&(~(in @ (esk2_2 @ X395 @ X396) @ X395)|(in @ X396 @ (powerset @ X395)))))&(((((in @ X399 @ (esk3_2 @ X398 @ X399))|~(in @ X399 @ (setunion @ X398)))&((in @ (esk3_2 @ X398 @ X399) @ X398)|~(in @ X399 @ (setunion @ X398))))&(~(in @ X402 @ X403)|~(in @ X403 @ X401)|(in @ X402 @ (setunion @ X401))))&((in @ emptyset @ omega)&((~(in @ X404 @ omega)|(in @ (setadjoin @ X404 @ X404) @ omega))&(((((in @ (esk4_1 @ X405) @ omega)|~(in @ emptyset @ X405)|(~(in @ X407 @ omega)|(in @ X407 @ X405)))&((in @ (esk4_1 @ X405) @ X405)|~(in @ emptyset @ X405)|(~(in @ X407 @ omega)|(in @ X407 @ X405))))&(~(in @ (setadjoin @ (esk4_1 @ X405) @ (esk4_1 @ X405)) @ X405)|~(in @ emptyset @ X405)|(~(in @ X407 @ omega)|(in @ X407 @ X405))))&((((((in @ (esk8_3 @ X408 @ X409 @ X414) @ X409)|~(in @ X414 @ (esk7_2 @ X408 @ X409))|(in @ (esk5_2 @ X408 @ X409) @ X409))&((X408 @ (esk8_3 @ X408 @ X409 @ X414) @ X414)|~(in @ X414 @ (esk7_2 @ X408 @ X409))|(in @ (esk5_2 @ X408 @ X409) @ X409)))&(~(in @ X417 @ X409)|~(X408 @ X417 @ X416)|(in @ X416 @ (esk7_2 @ X408 @ X409))|(in @ (esk5_2 @ X408 @ X409) @ X409)))&(((((in @ (esk8_3 @ X408 @ X409 @ X414) @ X409)|~(in @ X414 @ (esk7_2 @ X408 @ X409))|((X408 @ (esk5_2 @ X408 @ X409) @ (esk6_3 @ X408 @ X409 @ X411))|~(X408 @ (esk5_2 @ X408 @ X409) @ X411)))&((X408 @ (esk8_3 @ X408 @ X409 @ X414) @ X414)|~(in @ X414 @ (esk7_2 @ X408 @ X409))|((X408 @ (esk5_2 @ X408 @ X409) @ (esk6_3 @ X408 @ X409 @ X411))|~(X408 @ (esk5_2 @ X408 @ X409) @ X411))))&(~(in @ X417 @ X409)|~(X408 @ X417 @ X416)|(in @ X416 @ (esk7_2 @ X408 @ X409))|((X408 @ (esk5_2 @ X408 @ X409) @ (esk6_3 @ X408 @ X409 @ X411))|~(X408 @ (esk5_2 @ X408 @ X409) @ X411))))&((((in @ (esk8_3 @ X408 @ X409 @ X414) @ X409)|~(in @ X414 @ (esk7_2 @ X408 @ X409))|(((X411)!=(esk6_3 @ X408 @ X409 @ X411))|~(X408 @ (esk5_2 @ X408 @ X409) @ X411)))&((X408 @ (esk8_3 @ X408 @ X409 @ X414) @ X414)|~(in @ X414 @ (esk7_2 @ X408 @ X409))|(((X411)!=(esk6_3 @ X408 @ X409 @ X411))|~(X408 @ (esk5_2 @ X408 @ X409) @ X411))))&(~(in @ X417 @ X409)|~(X408 @ X417 @ X416)|(in @ X416 @ (esk7_2 @ X408 @ X409))|(((X411)!=(esk6_3 @ X408 @ X409 @ X411))|~(X408 @ (esk5_2 @ X408 @ X409) @ X411))))))&((((in @ (esk9_1 @ X418) @ X418)|~(in @ X419 @ X418))&(~(in @ X421 @ (esk9_1 @ X418))|~(in @ X421 @ X418)|~(in @ X419 @ X418)))&((epred1_0)&((((X422 @ (esk10_2 @ X422 @ X423))|~(X422 @ X423)|(X422 @ (descr @ X422)))&(((X423)!=(esk10_2 @ X422 @ X423))|~(X422 @ X423)|(X422 @ (descr @ X422))))&((~(in @ X427 @ X425)|(~(X426 @ X427)|(in @ X427 @ (dsetconstr @ X425 @ X426))))&((~(in @ X430 @ (dsetconstr @ X428 @ X429))|(in @ X430 @ X428))&((~(in @ X433 @ (dsetconstr @ X431 @ X432))|(X432 @ X433))&(((((X434 @ (esk12_1 @ X434))|((X434 @ (esk11_2 @ X434 @ X435))|~(X434 @ X435)))&(~(X434 @ X438)|((esk12_1 @ X434)=(X438))|((X434 @ (esk11_2 @ X434 @ X435))|~(X434 @ X435))))&(((X434 @ (esk12_1 @ X434))|(((X435)!=(esk11_2 @ X434 @ X435))|~(X434 @ X435)))&(~(X434 @ X438)|((esk12_1 @ X434)=(X438))|(((X435)!=(esk11_2 @ X434 @ X435))|~(X434 @ X435)))))&((~(in @ X440 @ (prop2set @ ((X439))))|(X439))&((~(in @ X441 @ emptyset)|(X442))&((~(in @ X443 @ emptyset)|~($true))&(~(in @ X444 @ emptyset)&((((X445 @ (esk13_2 @ X445 @ X446))|~(X445 @ X446)|(X445 @ (esk14_1 @ X445)))&(((X446)!=(esk13_2 @ X445 @ X446))|~(X445 @ X446)|(X445 @ (esk14_1 @ X445))))&(((((in @ (esk16_2 @ X449 @ X450) @ X450)|((X449)=(X450))|(in @ (esk15_2 @ X449 @ X450) @ X449))&(~(in @ (esk16_2 @ X449 @ X450) @ X449)|((X449)=(X450))|(in @ (esk15_2 @ X449 @ X450) @ X449)))&(((in @ (esk16_2 @ X449 @ X450) @ X450)|((X449)=(X450))|~(in @ (esk15_2 @ X449 @ X450) @ X450))&(~(in @ (esk16_2 @ X449 @ X450) @ X449)|((X449)=(X450))|~(in @ (esk15_2 @ X449 @ X450) @ X450))))&(((in @ (esk17_1 @ X453) @ X453)|((X453)=(emptyset)))&(((in @ (esk18_1 @ X455) @ X455)|((X455)=(emptyset)))&(((~(in @ X459 @ (dsetconstr @ X457 @ X458))|(X458 @ X459)|~(in @ X459 @ X457))&(~(X458 @ X459)|(in @ X459 @ (dsetconstr @ X457 @ X458))|~(in @ X459 @ X457)))&((((X460)=(emptyset))|(in @ (esk19_1 @ X460) @ X460))&((~(in @ X464 @ X462)|(~(X463 @ X464)|((dsetconstr @ X462 @ X463)!=(emptyset))))&((~(in @ X466 @ X465)|((X465)!=(emptyset)))&((in @ X467 @ (setadjoin @ X467 @ X468))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X471 @ X470)|(in @ X471 @ (setadjoin @ X469 @ X470)))&(((((in @ X474 @ X473)|(X475)|((X474)=(X472))|~(in @ X474 @ (setadjoin @ X472 @ X473)))&(~(X475)|(X475)|((X474)=(X472))|~(in @ X474 @ (setadjoin @ X472 @ X473))))&(((in @ X474 @ X473)|(X475)|~(X475)|~(in @ X474 @ (setadjoin @ X472 @ X473)))&(~(X475)|(X475)|~(X475)|~(in @ X474 @ (setadjoin @ X472 @ X473)))))&((~(in @ X478 @ (setadjoin @ X476 @ X477))|(((X478)=(X476))|(in @ X478 @ X477)))&(((dsetconstr @ X479 @ (^[Z0:$i]:($true)))=(X479))&((((in @ (esk20_2 @ X480 @ X481) @ X481)|(in @ X481 @ (powerset @ X480)))&(~(in @ (esk20_2 @ X480 @ X481) @ X480)|(in @ X481 @ (powerset @ X480))))&((in @ emptyset @ (powerset @ X483))&((in @ emptyset @ (powerset @ X484))&((~(in @ X486 @ (powerset @ X485))|(~(in @ X487 @ X486)|(in @ X487 @ X485)))&((~(in @ X489 @ X490)|(~(in @ X490 @ X488)|(in @ X489 @ (setunion @ X488))))&((((in @ X492 @ (esk21_3 @ X491 @ X492 @ X493))|(X493)|~(in @ X492 @ (setunion @ X491)))&(((in @ (esk21_3 @ X491 @ X492 @ X493) @ X491)|(X493)|~(in @ X492 @ (setunion @ X491)))&(~(X493)|(X493)|~(in @ X492 @ (setunion @ X491)))))&((~(in @ X496 @ X495)|(in @ X496 @ (powerset @ (setunion @ X495))))&((((~(X497 @ X501)|((X501)=(esk23_1 @ X497))|((X497 @ (esk22_2 @ X497 @ X498))|~(X497 @ X498)))&(((X502)!=(esk23_1 @ X497))|(X497 @ X502)|((X497 @ (esk22_2 @ X497 @ X498))|~(X497 @ X498))))&((~(X497 @ X501)|((X501)=(esk23_1 @ X497))|(((X498)!=(esk22_2 @ X497 @ X498))|~(X497 @ X498)))&(((X502)!=(esk23_1 @ X497))|(X497 @ X502)|(((X498)!=(esk22_2 @ X497 @ X498))|~(X497 @ X498)))))&((((in @ (esk24_1 @ X503) @ X503)|((X503)=(emptyset)))&(($true)|((X503)=(emptyset))))&((~(in @ X505 @ (setadjoin @ X506 @ emptyset))|((X505)=(X506)))&((((X507)=(X508))|~(in @ X508 @ (setadjoin @ X507 @ emptyset)))&((((X509)!=(X510))|(in @ X509 @ (setadjoin @ X510 @ emptyset)))&((~(in @ X511 @ (setadjoin @ X512 @ emptyset))|(in @ X512 @ (setadjoin @ X511 @ emptyset)))&((~(in @ X515 @ (setadjoin @ X513 @ (setadjoin @ X514 @ emptyset)))|(((X515)=(X513))|((X515)=(X514))))&((in @ X516 @ (setadjoin @ X516 @ (setadjoin @ X517 @ emptyset)))&((in @ X519 @ (setadjoin @ X518 @ (setadjoin @ X519 @ emptyset)))&((~(in @ X522 @ X520)|~(X521 @ X522)|(((dsetconstr @ X520 @ X521)!=(emptyset))|~($true)))&((~(in @ X524 @ emptyset)|(X523 @ X524))&((((in @ (esk25_2 @ X525 @ X526) @ X525)|(~(in @ X527 @ X525)|(X526 @ X527)))&(~(X526 @ (esk25_2 @ X525 @ X526))|(~(in @ X527 @ X525)|(X526 @ X527))))&((((in @ (esk26_2 @ X529 @ X530) @ X529)|(~(in @ X532 @ X529)|~(X530 @ X532)))&((X530 @ (esk26_2 @ X529 @ X530))|(~(in @ X532 @ X529)|~(X530 @ X532))))&((((in @ (esk27_2 @ X533 @ X534) @ X533)|(~(in @ X536 @ X533)|~(X534 @ X536)))&((X534 @ (esk27_2 @ X533 @ X534))|(~(in @ X536 @ X533)|~(X534 @ X536))))&((((in @ (esk28_2 @ X537 @ X538) @ X537)|(~(in @ X539 @ X537)|(X538 @ X539)))&(~(X538 @ (esk28_2 @ X537 @ X538))|(~(in @ X539 @ X537)|(X538 @ X539))))&((~(X541)|(in @ emptyset @ (prop2set @ ((X541)))))&((~(X542)|(set2prop @ (prop2set @ ((X542)))))&((((in @ (esk29_2 @ X543 @ X544) @ X543)|(~(in @ X546 @ X543)|~(X544 @ X546)))&((X544 @ (esk29_2 @ X543 @ X544))|(~(in @ X546 @ X543)|~(X544 @ X546))))&((((in @ (esk30_2 @ X547 @ X548) @ X547)|(~(in @ X549 @ X547)|(X548 @ X549)))&(~(X548 @ (esk30_2 @ X547 @ X548))|(~(in @ X549 @ X547)|(X548 @ X549))))&(((((X551 @ (esk32_1 @ X551))|((X551 @ (esk31_2 @ X551 @ X552))|~(X551 @ X552)))&(~(X551 @ X555)|((esk32_1 @ X551)=(X555))|((X551 @ (esk31_2 @ X551 @ X552))|~(X551 @ X552))))&(((X551 @ (esk32_1 @ X551))|(((X552)!=(esk31_2 @ X551 @ X552))|~(X551 @ X552)))&(~(X551 @ X555)|((esk32_1 @ X551)=(X555))|(((X552)!=(esk31_2 @ X551 @ X552))|~(X551 @ X552)))))&((epred2_0 @ esk33_0)&((~(epred2_0 @ X558)|(~(epred2_0 @ X559)|((X558)=(X559))))&(((epred2_0 @ (esk34_1 @ X560))|~(epred2_0 @ X560))&(((X560)!=(esk34_1 @ X560))|~(epred2_0 @ X560))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_91])])])])])])])).
% 0.21/0.30 thf(c_0_93, negated_conjecture, ![X2:$i, X3:$i]:((((X2)=(X3))|~((epred2_0 @ X2))|~((epred2_0 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_92])).
% 0.21/0.30 thf(c_0_94, negated_conjecture, (epred2_0 @ esk33_0), inference(split_conjunct,[status(thm)],[c_0_92])).
% 0.21/0.30 thf(c_0_95, negated_conjecture, ![X2:$i]:((((X2)=(esk33_0))|~((epred2_0 @ X2)))), inference(spm,[status(thm)],[c_0_93, c_0_94])).
% 0.21/0.30 thf(c_0_96, negated_conjecture, ![X2:$i]:(((epred2_0 @ (esk34_1 @ X2))|~((epred2_0 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_92])).
% 0.21/0.30 thf(c_0_97, negated_conjecture, ![X2:$i]:((((X2)!=(esk34_1 @ X2))|~((epred2_0 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_92])).
% 0.21/0.30 thf(c_0_98, negated_conjecture, ![X2:$i]:((((esk34_1 @ X2)=(esk33_0))|~((epred2_0 @ X2)))), inference(spm,[status(thm)],[c_0_95, c_0_96])).
% 0.21/0.30 thf(c_0_99, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_97, c_0_98])]), c_0_94])]), ['proof']).
% 0.21/0.30 % SZS output end CNFRefutation
% 0.21/0.30 % Parsed axioms : 137
% 0.21/0.30 % Removed by relevancy pruning/SinE : 0
% 0.21/0.30 % Initial clauses : 199
% 0.21/0.30 % Removed in clause preprocessing : 79
% 0.21/0.30 % Initial clauses in saturation : 120
% 0.21/0.30 % Processed clauses : 24
% 0.21/0.30 % ...of these trivial : 1
% 0.21/0.30 % ...subsumed : 5
% 0.21/0.30 % ...remaining for further processing : 18
% 0.21/0.30 % Other redundant clauses eliminated : 2
% 0.21/0.30 % Clauses deleted for lack of memory : 0
% 0.21/0.30 % Backward-subsumed : 0
% 0.21/0.30 % Backward-rewritten : 1
% 0.21/0.30 % Generated clauses : 7
% 0.21/0.30 % ...of the previous two non-redundant : 4
% 0.21/0.30 % ...aggressively subsumed : 0
% 0.21/0.30 % Contextual simplify-reflections : 0
% 0.21/0.30 % Paramodulations : 5
% 0.21/0.30 % Factorizations : 0
% 0.21/0.30 % NegExts : 0
% 0.21/0.30 % Equation resolutions : 2
% 0.21/0.30 % Disequality decompositions : 0
% 0.21/0.30 % Total rewrite steps : 4
% 0.21/0.30 % ...of those cached : 1
% 0.21/0.30 % Propositional unsat checks : 0
% 0.21/0.30 % Propositional check models : 0
% 0.21/0.30 % Propositional check unsatisfiable : 0
% 0.21/0.30 % Propositional clauses : 0
% 0.21/0.30 % Propositional clauses after purity: 0
% 0.21/0.30 % Propositional unsat core size : 0
% 0.21/0.30 % Propositional preprocessing time : 0.000
% 0.21/0.30 % Propositional encoding time : 0.000
% 0.21/0.30 % Propositional solver time : 0.000
% 0.21/0.30 % Success case prop preproc time : 0.000
% 0.21/0.30 % Success case prop encoding time : 0.000
% 0.21/0.30 % Success case prop solver time : 0.000
% 0.21/0.30 % Current number of processed clauses : 16
% 0.21/0.30 % Positive orientable unit clauses : 9
% 0.21/0.30 % Positive unorientable unit clauses: 0
% 0.21/0.30 % Negative unit clauses : 2
% 0.21/0.30 % Non-unit-clauses : 5
% 0.21/0.30 % Current number of unprocessed clauses: 100
% 0.21/0.30 % ...number of literals in the above : 321
% 0.21/0.30 % Current number of archived formulas : 0
% 0.21/0.30 % Current number of archived clauses : 1
% 0.21/0.30 % Clause-clause subsumption calls (NU) : 5
% 0.21/0.30 % Rec. Clause-clause subsumption calls : 3
% 0.21/0.30 % Non-unit clause-clause subsumptions : 0
% 0.21/0.30 % Unit Clause-clause subsumption calls : 0
% 0.21/0.30 % Rewrite failures with RHS unbound : 0
% 0.21/0.30 % BW rewrite match attempts : 1
% 0.21/0.30 % BW rewrite match successes : 1
% 0.21/0.30 % Condensation attempts : 0
% 0.21/0.30 % Condensation successes : 0
% 0.21/0.30 % Termbank termtop insertions : 17127
% 0.21/0.30 % Search garbage collected termcells : 6682
% 0.21/0.30
% 0.21/0.30 % -------------------------------------------------
% 0.21/0.30 % User time : 0.014 s
% 0.21/0.30 % System time : 0.006 s
% 0.21/0.30 % Total time : 0.020 s
% 0.21/0.30 % Maximum resident set size: 5308 pages
% 0.21/0.30
% 0.21/0.30 % -------------------------------------------------
% 0.21/0.30 % User time : 0.038 s
% 0.21/0.30 % System time : 0.024 s
% 0.21/0.30 % Total time : 0.062 s
% 0.21/0.30 % Maximum resident set size: 4864 pages
% 0.21/0.30 % E exiting
%------------------------------------------------------------------------------