%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU545^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 08:24:27 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : CNFRefutation 0.20s
% 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/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n002.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 13:52:07 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p
% 0.20/0.28 % Version: 3.5.1-ho
% 0.20/0.28 % Preprocessing class: HSMSSLSSMLLCHSA.
% 0.20/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.20/0.28 % Starting sh5l with 300s (1) cores
% 0.20/0.28 % Starting new_bool_1 with 300s (1) cores
% 0.20/0.28 % Starting new_bool_2 with 300s (1) cores
% 0.20/0.28 % new_bool_1 with pid 1317677 completed with status 0
% 0.20/0.28 % Result found by new_bool_1
% 0.20/0.28 % Preprocessing class: HSMSSLSSMLLCHSA.
% 0.20/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.20/0.28 % Starting sh5l with 300s (1) cores
% 0.20/0.28 % Starting new_bool_1 with 300s (1) cores
% 0.20/0.28 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.20/0.28 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.28 % Search class: HGHSM-FFMM31-SHSSMSBN
% 0.20/0.28 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.28 % Starting SubtermCWHack with 31s (1) cores
% 0.20/0.28 % SubtermCWHack with pid 1317681 completed with status 0
% 0.20/0.28 % Result found by SubtermCWHack
% 0.20/0.28 % Preprocessing class: HSMSSLSSMLLCHSA.
% 0.20/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.20/0.28 % Starting sh5l with 300s (1) cores
% 0.20/0.28 % Starting new_bool_1 with 300s (1) cores
% 0.20/0.28 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.20/0.28 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.28 % Search class: HGHSM-FFMM31-SHSSMSBN
% 0.20/0.28 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.28 % Starting SubtermCWHack with 31s (1) cores
% 0.20/0.28 % Preprocessing time : 0.003 s
% 0.20/0.28
% 0.20/0.28 % Proof found!
% 0.20/0.28 % SZS status Theorem
% 0.20/0.28 % SZS output start CNFRefutation
% 0.20/0.28 thf(decl_23, type, in: $i > $i > $o).
% 0.20/0.28 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.20/0.28 thf(decl_25, type, setextAx: $o).
% 0.20/0.28 thf(decl_26, type, emptyset: $i).
% 0.20/0.28 thf(decl_27, type, emptysetAx: $o).
% 0.20/0.28 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.20/0.28 thf(decl_29, type, setadjoinAx: $o).
% 0.20/0.28 thf(decl_30, type, powerset: $i > $i).
% 0.20/0.28 thf(decl_31, type, powersetAx: $o).
% 0.20/0.28 thf(decl_32, type, setunion: $i > $i).
% 0.20/0.28 thf(decl_33, type, setunionAx: $o).
% 0.20/0.28 thf(decl_34, type, omega: $i).
% 0.20/0.28 thf(decl_35, type, omega0Ax: $o).
% 0.20/0.28 thf(decl_36, type, omegaSAx: $o).
% 0.20/0.28 thf(decl_37, type, omegaIndAx: $o).
% 0.20/0.28 thf(decl_38, type, replAx: $o).
% 0.20/0.28 thf(decl_39, type, foundationAx: $o).
% 0.20/0.28 thf(decl_40, type, wellorderingAx: $o).
% 0.20/0.28 thf(decl_42, type, descrp: $o).
% 0.20/0.28 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.20/0.28 thf(decl_44, type, dsetconstrI: $o).
% 0.20/0.28 thf(decl_45, type, dsetconstrEL: $o).
% 0.20/0.28 thf(decl_46, type, dsetconstrER: $o).
% 0.20/0.28 thf(decl_47, type, exuE1: $o).
% 0.20/0.28 thf(decl_48, type, prop2set: $o > $i).
% 0.20/0.28 thf(decl_49, type, prop2setE: $o).
% 0.20/0.28 thf(decl_50, type, emptysetE: $o).
% 0.20/0.28 thf(decl_51, type, emptysetimpfalse: $o).
% 0.20/0.28 thf(decl_52, type, notinemptyset: $o).
% 0.20/0.28 thf(decl_53, type, exuE3e: $o).
% 0.20/0.28 thf(decl_54, type, setext: $o).
% 0.20/0.28 thf(decl_55, type, emptyI: $o).
% 0.20/0.28 thf(decl_56, type, noeltsimpempty: $o).
% 0.20/0.28 thf(decl_57, type, setbeta: $o).
% 0.20/0.28 thf(decl_58, type, nonempty: $i > $o).
% 0.20/0.28 thf(decl_59, type, nonemptyE1: $o).
% 0.20/0.28 thf(decl_60, type, nonemptyI: $o).
% 0.20/0.28 thf(decl_61, type, nonemptyI1: $o).
% 0.20/0.28 thf(decl_62, type, setadjoinIL: $o).
% 0.20/0.28 thf(decl_63, type, emptyinunitempty: $o).
% 0.20/0.28 thf(decl_64, type, setadjoinIR: $o).
% 0.20/0.28 thf(decl_65, type, setadjoinE: $o).
% 0.20/0.28 thf(decl_66, type, setadjoinOr: $o).
% 0.20/0.28 thf(decl_67, type, setoftrueEq: $o).
% 0.20/0.28 thf(decl_68, type, powersetI: $o).
% 0.20/0.28 thf(decl_69, type, emptyinPowerset: $o).
% 0.20/0.28 thf(decl_70, type, emptyInPowerset: $o).
% 0.20/0.28 thf(decl_71, type, powersetE: $o).
% 0.20/0.28 thf(decl_72, type, setunionI: $o).
% 0.20/0.28 thf(decl_73, type, setunionE: $o).
% 0.20/0.28 thf(decl_74, type, subPowSU: $o).
% 0.20/0.28 thf(decl_75, type, exuE2: $o).
% 0.20/0.28 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.20/0.28 thf(decl_77, type, uniqinunit: $o).
% 0.20/0.28 thf(decl_78, type, notinsingleton: $o).
% 0.20/0.28 thf(decl_79, type, eqinunit: $o).
% 0.20/0.28 thf(decl_80, type, singletonsswitch: $o).
% 0.20/0.28 thf(decl_81, type, upairsetE: $o).
% 0.20/0.28 thf(decl_82, type, upairsetIL: $o).
% 0.20/0.28 thf(decl_83, type, upairsetIR: $o).
% 0.20/0.28 thf(decl_84, type, emptyE1: $o).
% 0.20/0.28 thf(decl_85, type, vacuousDall: $o).
% 0.20/0.28 thf(decl_86, type, quantDeMorgan1: $o).
% 0.20/0.28 thf(decl_87, type, quantDeMorgan2: $o).
% 0.20/0.28 thf(decl_88, type, quantDeMorgan3: $o).
% 0.20/0.28 thf(decl_89, type, quantDeMorgan4: $o).
% 0.20/0.28 thf(decl_90, type, prop2setI: $o).
% 0.20/0.28 thf(decl_92, type, prop2set2propI: $o).
% 0.20/0.28 thf(decl_93, type, notdexE: $o).
% 0.20/0.28 thf(decl_94, type, notdallE: $o).
% 0.20/0.28 thf(decl_95, type, exuI1: $o).
% 0.20/0.28 thf(decl_96, type, epred1_0: $o).
% 0.20/0.28 thf(decl_97, type, esk1_2: $i > $i > $i).
% 0.20/0.28 thf(decl_98, type, esk2_2: $i > $i > $i).
% 0.20/0.28 thf(decl_99, type, esk3_2: $i > $i > $i).
% 0.20/0.28 thf(decl_100, type, esk4_1: $i > $i).
% 0.20/0.28 thf(decl_101, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.20/0.28 thf(decl_102, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.20/0.28 thf(decl_103, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.20/0.28 thf(decl_104, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.20/0.28 thf(decl_105, type, esk9_1: $i > $i).
% 0.20/0.28 thf(decl_106, type, esk10_2: ($i > $o) > $i > $i).
% 0.20/0.28 thf(decl_107, type, esk11_1: ($i > $o) > $i).
% 0.20/0.28 thf(decl_108, type, esk12_2: ($i > $o) > $i > $i).
% 0.20/0.28 thf(decl_109, type, esk13_1: ($i > $o) > $i).
% 0.20/0.28 thf(decl_110, type, esk14_2: $i > $i > $i).
% 0.20/0.28 thf(decl_111, type, esk15_2: $i > $i > $i).
% 0.20/0.28 thf(decl_112, type, esk16_1: $i > $i).
% 0.20/0.28 thf(decl_113, type, esk17_1: $i > $i).
% 0.20/0.28 thf(decl_114, type, esk18_1: $i > $i).
% 0.20/0.28 thf(decl_115, type, esk19_2: $i > $i > $i).
% 0.20/0.28 thf(decl_116, type, esk20_3: $i > $i > $o > $i).
% 0.20/0.28 thf(decl_117, type, esk21_2: ($i > $o) > $i > $i).
% 0.20/0.28 thf(decl_118, type, esk22_1: ($i > $o) > $i).
% 0.20/0.28 thf(decl_119, type, esk23_1: $i > $i).
% 0.20/0.28 thf(decl_120, type, esk24_2: $i > ($i > $o) > $i).
% 0.20/0.28 thf(decl_121, type, esk25_2: $i > ($i > $o) > $i).
% 0.20/0.28 thf(decl_122, type, esk26_2: $i > ($i > $o) > $i).
% 0.20/0.28 thf(decl_123, type, esk27_2: $i > ($i > $o) > $i).
% 0.20/0.28 thf(decl_124, type, esk28_2: $i > ($i > $o) > $i).
% 0.20/0.28 thf(decl_125, type, esk29_2: $i > ($i > $o) > $i).
% 0.20/0.28 thf(decl_126, type, esk30_2: ($i > $o) > $i > $i).
% 0.20/0.28 thf(decl_127, type, esk31_1: ($i > $o) > $i).
% 0.20/0.28 thf(decl_128, type, epred2_0: $i > $o).
% 0.20/0.28 thf(decl_129, type, esk32_0: $i).
% 0.20/0.28 thf(decl_130, type, esk33_1: $i > $i).
% 0.20/0.28 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', replAx)).
% 0.20/0.28 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', exu)).
% 0.20/0.28 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', exuI1)).
% 0.20/0.28 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', exuE1)).
% 0.20/0.28 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', exuE3e)).
% 0.20/0.28 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', nonempty)).
% 0.20/0.28 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', nonemptyI)).
% 0.20/0.28 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', exuE2)).
% 0.20/0.28 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:$i]:((X1 @ X2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', exuI3)).
% 0.20/0.28 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', emptyE1)).
% 0.20/0.28 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', dsetconstrER)).
% 0.20/0.28 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', dsetconstrEL)).
% 0.20/0.28 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', dsetconstrI)).
% 0.20/0.28 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', setbeta)).
% 0.20/0.28 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', nonemptyE1)).
% 0.20/0.28 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', nonemptyI1)).
% 0.20/0.28 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', setoftrueEq)).
% 0.20/0.28 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', nonemptyImpWitness)).
% 0.20/0.28 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', upairsetE)).
% 0.20/0.28 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', singletonsswitch)).
% 0.20/0.28 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', upairsetIL)).
% 0.20/0.28 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', upairsetIR)).
% 0.20/0.28 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', omegaIndAx)).
% 0.20/0.28 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', omegaSAx)).
% 0.20/0.28 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', vacuousDall)).
% 0.20/0.28 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', omega0Ax)).
% 0.20/0.28 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', quantDeMorgan1)).
% 0.20/0.28 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', setunionAx)).
% 0.20/0.28 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', quantDeMorgan2)).
% 0.20/0.28 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', powersetAx)).
% 0.20/0.28 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', quantDeMorgan3)).
% 0.20/0.28 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', setadjoinAx)).
% 0.20/0.28 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', quantDeMorgan4)).
% 0.20/0.28 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', emptysetAx)).
% 0.20/0.28 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', prop2setI)).
% 0.20/0.28 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', notdexE)).
% 0.20/0.28 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', notdallE)).
% 0.20/0.28 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', setadjoinOr)).
% 0.20/0.28 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', prop2setE)).
% 0.20/0.28 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', wellorderingAx)).
% 0.20/0.28 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', foundationAx)).
% 0.20/0.28 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', emptysetE)).
% 0.20/0.28 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', noeltsimpempty)).
% 0.20/0.28 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', emptyI)).
% 0.20/0.28 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', setext)).
% 0.20/0.28 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', notinemptyset)).
% 0.20/0.28 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', emptysetimpfalse)).
% 0.20/0.28 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', setadjoinE)).
% 0.20/0.28 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', setadjoinIR)).
% 0.20/0.28 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', emptyinunitempty)).
% 0.20/0.28 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', setadjoinIL)).
% 0.20/0.28 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', subPowSU)).
% 0.20/0.28 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', setunionE)).
% 0.20/0.28 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', setunionI)).
% 0.20/0.28 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', powersetE)).
% 0.20/0.28 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', emptyInPowerset)).
% 0.20/0.28 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', emptyinPowerset)).
% 0.20/0.28 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', powersetI)).
% 0.20/0.28 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', uniqinunit)).
% 0.20/0.28 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', notinsingleton)).
% 0.20/0.28 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', eqinunit)).
% 0.20/0.28 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.2oBm3XkwAC/E---3.1_1317643.p', setextAx)).
% 0.20/0.28 thf(c_0_62, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.20/0.28 thf(c_0_63, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.20/0.28 thf(c_0_64, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 0.20/0.28 thf(c_0_65, 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])).
% 0.20/0.28 thf(c_0_66, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.20/0.28 thf(c_0_67, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.20/0.28 thf(c_0_68, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.20/0.28 thf(c_0_69, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.20/0.28 thf(c_0_70, 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:$i]:((X1 @ X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[exuI3])).
% 0.20/0.28 thf(c_0_71, plain, ((emptyE1)<=>![X4:$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])).
% 0.20/0.28 thf(c_0_72, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X188:$i]:(((((X6 @ X2 @ X188)))&(![X189:$i]:(((((X6 @ X2 @ X189)))=>(((X188)=(X189)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_62, c_0_63])).
% 0.20/0.28 thf(c_0_73, plain, ((exuI1)=(![X1:$i > $o]:(((?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3)))))))))=>((?[X196:$i]:(((((X1 @ X196)))&(![X197:$i]:(((((X1 @ X197)))=>(((X196)=(X197)))))))))))))), inference(apply_def,[status(thm)],[c_0_64, c_0_63])).
% 0.20/0.28 thf(c_0_74, plain, ((exuE1)=(![X1:$i > $o]:((((?[X190:$i]:(((((X1 @ X190)))&(![X191:$i]:(((((X1 @ X191)))=>(((X190)=(X191))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_65, c_0_63])).
% 0.20/0.28 thf(c_0_75, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.20/0.28 thf(c_0_76, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.20/0.28 thf(c_0_77, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.20/0.28 thf(c_0_78, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.20/0.28 thf(c_0_79, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X192:$i]:(((((X1 @ X192)))&(![X193:$i]:(((((X1 @ X193)))=>(((X192)=(X193))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_66, c_0_63])).
% 0.20/0.28 thf(c_0_80, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_67])).
% 0.20/0.28 thf(c_0_81, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_67])).
% 0.20/0.28 thf(c_0_82, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_68, c_0_67])).
% 0.20/0.28 thf(c_0_83, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.20/0.28 thf(c_0_84, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_67])).
% 0.20/0.28 thf(c_0_85, plain, ((exuE2)=(![X1:$i > $o]:((((?[X194:$i]:(((((X1 @ X194)))&(![X195:$i]:(((((X1 @ X195)))=>(((X194)=(X195))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_69, c_0_63])).
% 0.20/0.28 thf(c_0_86, plain, ((epred1_0)<=>![X227:$i]:(?[X228:$i]:((((![X229:$i]:(((in @ X229 @ X228)=>![X230:$i]:(((in @ X230 @ X229)=>(in @ X230 @ X227)))))&![X231:$i, X232:$i]:((((in @ X231 @ X227)&(in @ X232 @ X227))=>(![X233:$i]:(((in @ X233 @ X228)=>((in @ X231 @ X233)<=>(in @ X232 @ X233))))=>((X231)=(X232))))))&![X234:$i, X235:$i]:((((in @ X234 @ X228)&(in @ X235 @ X228))=>(![X236:$i]:(((in @ X236 @ X234)=>(in @ X236 @ X235)))|![X237:$i]:(((in @ X237 @ X235)=>(in @ X237 @ X234)))))))&![X238:$i]:(((![X239:$i]:(((in @ X239 @ X238)=>(in @ X239 @ X227)))&?[X240:$i]:((in @ X240 @ X238)))=>?[X241:$i, X242:$i]:(((((in @ X241 @ X228)&(in @ X242 @ X238))&~(?[X243:$i]:(((in @ X243 @ X241)&(in @ X243 @ X238)))))&![X244:$i]:(((in @ X244 @ X228)=>(![X245:$i]:(((in @ X245 @ X244)=>(in @ X245 @ X241)))|(in @ X242 @ X244)))))))))))), introduced(definition)).
% 0.20/0.28 thf(c_0_87, negated_conjecture, ~((![X198:$i, X199:$i]:((![X200:$i]:(((in @ X200 @ X198)<=>(in @ X200 @ X199)))=>((X198)=(X199))))=>(![X201:$i]:(~(in @ X201 @ emptyset))=>(![X202:$i, X203:$i, X204:$i]:(((in @ X204 @ (setadjoin @ X202 @ X203))<=>(((X204)=(X202))|(in @ X204 @ X203))))=>(![X205:$i, X206:$i]:(((in @ X206 @ (powerset @ X205))<=>![X207:$i]:(((in @ X207 @ X206)=>(in @ X207 @ X205)))))=>(![X208:$i, X209:$i]:(((in @ X209 @ (setunion @ X208))<=>?[X210:$i]:(((in @ X209 @ X210)&(in @ X210 @ X208)))))=>((in @ emptyset @ omega)=>(![X211:$i]:(((in @ X211 @ omega)=>(in @ (setadjoin @ X211 @ X211) @ omega)))=>(![X212:$i]:((((in @ emptyset @ X212)&![X213:$i]:((((in @ X213 @ omega)&(in @ X213 @ X212))=>(in @ (setadjoin @ X213 @ X213) @ X212))))=>![X214:$i]:(((in @ X214 @ omega)=>(in @ X214 @ X212)))))=>(![X215:$i > $i > $o, X216:$i]:((![X217:$i]:(((in @ X217 @ X216)=>?[X218:$i]:(((X215 @ X217 @ X218)&![X219:$i]:(((X215 @ X217 @ X219)=>((X218)=(X219))))))))=>?[X220:$i]:(![X221:$i]:(((in @ X221 @ X220)<=>?[X222:$i]:(((in @ X222 @ X216)&(X215 @ X222 @ X221))))))))=>(![X223:$i]:((?[X224:$i]:((in @ X224 @ X223))=>?[X225:$i]:(((in @ X225 @ X223)&~(?[X226:$i]:(((in @ X226 @ X225)&(in @ X226 @ X223))))))))=>((epred1_0)=>((descrp)=>(![X246:$i, X247:$i > $o, X248:$i]:(((in @ X248 @ X246)=>((X247 @ X248)=>(in @ X248 @ (dsetconstr @ X246 @ X247)))))=>(![X249:$i, X250:$i > $o, X251:$i]:(((in @ X251 @ (dsetconstr @ X249 @ X250))=>(in @ X251 @ X249)))=>(![X252:$i, X253:$i > $o, X254:$i]:(((in @ X254 @ (dsetconstr @ X252 @ X253))=>(X253 @ X254)))=>(![X255:$i > $o]:((?[X256:$i]:(((X255 @ X256)&![X257:$i]:(((X255 @ X257)=>((X256)=(X257))))))=>?[X258:$i]:(((X255 @ X258)&![X259:$i]:(((X255 @ X259)=>((X258)=(X259))))))))=>(![X260:$o, X261:$i]:(((in @ X261 @ (prop2set @ ((X260))))=>(X260)))=>(![X262:$i]:(((in @ X262 @ emptyset)=>![X263:$o]:((X263))))=>(![X264:$i]:(((in @ X264 @ emptyset)=>~($true)))=>(![X265:$i]:(~(in @ X265 @ emptyset))=>(![X266:$i > $o]:((?[X267:$i]:(((X266 @ X267)&![X268:$i]:(((X266 @ X268)=>((X267)=(X268))))))=>?[X269:$i]:((X266 @ X269))))=>(![X270:$i, X271:$i]:((![X272:$i]:(((in @ X272 @ X270)=>(in @ X272 @ X271)))=>(![X273:$i]:(((in @ X273 @ X271)=>(in @ X273 @ X270)))=>((X270)=(X271)))))=>(![X274:$i]:((![X275:$i]:(~(in @ X275 @ X274))=>((X274)=(emptyset))))=>(![X276:$i]:((![X277:$i]:(~(in @ X277 @ X276))=>((X276)=(emptyset))))=>(![X278:$i, X279:$i > $o, X280:$i]:(((in @ X280 @ X278)=>((in @ X280 @ (dsetconstr @ X278 @ X279))<=>(X279 @ X280))))=>(![X281:$i]:((((X281)!=(emptyset))=>?[X282:$i]:((in @ X282 @ X281))))=>(![X283:$i, X284:$i > $o, X285:$i]:(((in @ X285 @ X283)=>((X284 @ X285)=>((dsetconstr @ X283 @ X284)!=(emptyset)))))=>(![X286:$i]:((?[X287:$i]:((in @ X287 @ X286))=>((X286)!=(emptyset))))=>(![X288:$i, X289:$i]:((in @ X288 @ (setadjoin @ X288 @ X289)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X290:$i, X291:$i, X292:$i]:(((in @ X292 @ X291)=>(in @ X292 @ (setadjoin @ X290 @ X291))))=>(![X293:$i, X294:$i, X295:$i]:(((in @ X295 @ (setadjoin @ X293 @ X294))=>![X296:$o]:(((((X295)=(X293))=>(X296))=>(((in @ X295 @ X294)=>(X296))=>(X296))))))=>(![X297:$i, X298:$i, X299:$i]:(((in @ X299 @ (setadjoin @ X297 @ X298))=>(((X299)=(X297))|(in @ X299 @ X298))))=>(![X300:$i]:(((dsetconstr @ X300 @ (^[Z0:$i]:($true)))=(X300)))=>(![X301:$i, X302:$i]:((![X303:$i]:(((in @ X303 @ X302)=>(in @ X303 @ X301)))=>(in @ X302 @ (powerset @ X301))))=>(![X304:$i]:((in @ emptyset @ (powerset @ X304)))=>(![X305:$i]:((in @ emptyset @ (powerset @ X305)))=>(![X306:$i, X307:$i, X308:$i]:(((in @ X307 @ (powerset @ X306))=>((in @ X308 @ X307)=>(in @ X308 @ X306))))=>(![X309:$i, X310:$i, X311:$i]:(((in @ X310 @ X311)=>((in @ X311 @ X309)=>(in @ X310 @ (setunion @ X309)))))=>(![X312:$i, X313:$i]:(((in @ X313 @ (setunion @ X312))=>![X314:$o]:((![X315:$i]:(((in @ X313 @ X315)=>((in @ X315 @ X312)=>(X314))))=>(X314)))))=>(![X316:$i, X317:$i]:(((in @ X317 @ X316)=>(in @ X317 @ (powerset @ (setunion @ X316)))))=>(![X318:$i > $o]:((?[X319:$i]:(((X318 @ X319)&![X320:$i]:(((X318 @ X320)=>((X319)=(X320))))))=>?[X321:$i]:(![X322:$i]:(((X318 @ X322)<=>((X322)=(X321)))))))=>(![X323:$i]:((((X323)!=(emptyset))=>?[X324:$i]:(((in @ X324 @ X323)&$true))))=>(![X325:$i, X326:$i]:(((in @ X325 @ (setadjoin @ X326 @ emptyset))=>((X325)=(X326))))=>(![X327:$i, X328:$i]:((((X327)!=(X328))=>~(in @ X328 @ (setadjoin @ X327 @ emptyset))))=>(![X329:$i, X330:$i]:((((X329)=(X330))=>(in @ X329 @ (setadjoin @ X330 @ emptyset))))=>(![X331:$i, X332:$i]:(((in @ X331 @ (setadjoin @ X332 @ emptyset))=>(in @ X332 @ (setadjoin @ X331 @ emptyset))))=>(![X333:$i, X334:$i, X335:$i]:(((in @ X335 @ (setadjoin @ X333 @ (setadjoin @ X334 @ emptyset)))=>(((X335)=(X333))|((X335)=(X334)))))=>(![X336:$i, X337:$i]:((in @ X336 @ (setadjoin @ X336 @ (setadjoin @ X337 @ emptyset))))=>(![X338:$i, X339:$i]:((in @ X339 @ (setadjoin @ X338 @ (setadjoin @ X339 @ emptyset))))=>(![X340:$i, X341:$i > $o]:((?[X342:$i]:(((in @ X342 @ X340)&(X341 @ X342)))=>(((dsetconstr @ X340 @ X341)=(emptyset))=>~($true))))=>(![X343:$i > $o, X344:$i]:(((in @ X344 @ emptyset)=>(X343 @ X344)))=>(![X345:$i, X346:$i > $o]:((~(![X347:$i]:(((in @ X347 @ X345)=>(X346 @ X347))))=>?[X348:$i]:(((in @ X348 @ X345)&~((X346 @ X348))))))=>(![X349:$i, X350:$i > $o]:((![X351:$i]:(((in @ X351 @ X349)=>~((X350 @ X351))))=>~(?[X352:$i]:(((in @ X352 @ X349)&(X350 @ X352))))))=>(![X353:$i, X354:$i > $o]:((~(?[X355:$i]:(((in @ X355 @ X353)&(X354 @ X355))))=>![X356:$i]:(((in @ X356 @ X353)=>~((X354 @ X356))))))=>(![X357:$i, X358:$i > $o]:((?[X359:$i]:(((in @ X359 @ X357)&~((X358 @ X359))))=>~(![X360:$i]:(((in @ X360 @ X357)=>(X358 @ X360))))))=>(![X361:$o]:(((X361)=>(in @ emptyset @ (prop2set @ ((X361))))))=>((prop2set2propI)=>(![X362:$i, X363:$i > $o]:((~(?[X364:$i]:(((in @ X364 @ X362)&(X363 @ X364))))=>![X365:$i]:(((in @ X365 @ X362)=>~((X363 @ X365))))))=>(![X366:$i, X367:$i > $o]:((~(![X368:$i]:(((in @ X368 @ X366)=>(X367 @ X368))))=>?[X369:$i]:(((in @ X369 @ X366)&~((X367 @ X369))))))=>(![X370:$i > $o]:((?[X371:$i]:(((X370 @ X371)&![X372:$i]:(((X370 @ X372)=>((X371)=(X372))))))=>?[X373:$i]:(((X370 @ X373)&![X374:$i]:(((X370 @ X374)=>((X373)=(X374))))))))=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>?[X375:$i]:(((X1 @ X375)&![X376:$i]:(((X1 @ X376)=>((X375)=(X376))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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(fof_simplification,[status(thm)],[c_0_70]), upairsetE]), singletonsswitch]), upairsetIL]), upairsetIR]), omegaIndAx]), c_0_71]), omegaSAx]), vacuousDall]), omega0Ax]), quantDeMorgan1]), setunionAx]), quantDeMorgan2]), powersetAx]), quantDeMorgan3]), setadjoinAx]), quantDeMorgan4]), emptysetAx]), prop2setI]), c_0_72]), notdexE]), notdallE]), c_0_73]), c_0_63]), setadjoinOr]), prop2setE]), c_0_74]), c_0_75]), c_0_76]), c_0_77]), wellorderingAx]), foundationAx]), emptysetE]), c_0_78]), noeltsimpempty]), emptyI]), setext]), c_0_79]), notinemptyset]), emptysetimpfalse]), c_0_80]), setadjoinE]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), c_0_81]), c_0_82]), c_0_83]), subPowSU]), setunionE]), setunionI]), powersetE]), emptyInPowerset]), emptyinPowerset]), powersetI]), c_0_84]), uniqinunit]), notinsingleton]), eqinunit]), c_0_85]), setextAx])])]), c_0_86])).
% 0.20/0.28 thf(c_0_88, negated_conjecture, ![X377:$i, X378:$i, X380:$i, X381:$i, X382:$i, X383:$i, X384:$i, X385:$i, X386:$i, X387:$i, X388:$i, X390:$i, X391:$i, X393:$i, X394:$i, X395:$i, X396:$i, X397:$i, X399:$i, X400:$i > $i > $o, X401:$i, X403:$i, X406:$i, X408:$i, X409:$i, X410:$i, X411:$i, X413:$i, X414:$i, X415:$i > $o, X416:$i, X417:$i, X418:$i > $o, X419:$i, X420:$i, X421:$i > $o, X422:$i, X423:$i > $o, X424:$i, X427:$i, X428:$o, X429:$i, X430:$i, X431:$o, X432:$i, X433:$i, X434:$i > $o, X435:$i, X438:$i, X439:$i, X442:$i, X444:$i, X446:$i, X447:$i > $o, X448:$i, X449:$i, X451:$i, X452:$i > $o, X453:$i, X454:$i, X455:$i, X456:$i, X457:$i, X458:$i, X459:$i, X460:$i, X461:$i, X462:$i, X463:$i, X464:$o, X465:$i, X466:$i, X467:$i, X468:$i, X469:$i, X470:$i, X472:$i, X473:$i, X474:$i, X475:$i, X476:$i, X477:$i, X478:$i, X479:$i, X480:$i, X481:$i, X482:$o, X484:$i, X485:$i, X486:$i > $o, X487:$i, X490:$i, X491:$i, X492:$i, X494:$i, X495:$i, X496:$i, X497:$i, X498:$i, X499:$i, X500:$i, X501:$i, X502:$i, X503:$i, X504:$i, X505:$i, X506:$i, X507:$i, X508:$i, X509:$i, X510:$i > $o, X511:$i, X512:$i > $o, X513:$i, X514:$i, X515:$i > $o, X516:$i, X518:$i, X519:$i > $o, X521:$i, X522:$i, X523:$i > $o, X525:$i, X526:$i, X527:$i > $o, X528:$i, X530:$o, X531:$i, X532:$i > $o, X534:$i, X535:$i, X536:$i > $o, X537:$i, X539:$i > $o, X540:$i, X543:$i, X546:$i, X547:$i, X548:$i]:((((~(in @ (esk1_2 @ X377 @ X378) @ X377)|~(in @ (esk1_2 @ X377 @ X378) @ X378)|((X377)=(X378)))&((in @ (esk1_2 @ X377 @ X378) @ X377)|(in @ (esk1_2 @ X377 @ X378) @ X378)|((X377)=(X378))))&(~(in @ X380 @ emptyset)&(((~(in @ X383 @ (setadjoin @ X381 @ X382))|(((X383)=(X381))|(in @ X383 @ X382)))&((((X383)!=(X381))|(in @ X383 @ (setadjoin @ X381 @ X382)))&(~(in @ X383 @ X382)|(in @ X383 @ (setadjoin @ X381 @ X382)))))&(((~(in @ X385 @ (powerset @ X384))|(~(in @ X386 @ X385)|(in @ X386 @ X384)))&(((in @ (esk2_2 @ X387 @ X388) @ X388)|(in @ X388 @ (powerset @ X387)))&(~(in @ (esk2_2 @ X387 @ X388) @ X387)|(in @ X388 @ (powerset @ X387)))))&(((((in @ X391 @ (esk3_2 @ X390 @ X391))|~(in @ X391 @ (setunion @ X390)))&((in @ (esk3_2 @ X390 @ X391) @ X390)|~(in @ X391 @ (setunion @ X390))))&(~(in @ X394 @ X395)|~(in @ X395 @ X393)|(in @ X394 @ (setunion @ X393))))&((in @ emptyset @ omega)&((~(in @ X396 @ omega)|(in @ (setadjoin @ X396 @ X396) @ omega))&(((((in @ (esk4_1 @ X397) @ omega)|~(in @ emptyset @ X397)|(~(in @ X399 @ omega)|(in @ X399 @ X397)))&((in @ (esk4_1 @ X397) @ X397)|~(in @ emptyset @ X397)|(~(in @ X399 @ omega)|(in @ X399 @ X397))))&(~(in @ (setadjoin @ (esk4_1 @ X397) @ (esk4_1 @ X397)) @ X397)|~(in @ emptyset @ X397)|(~(in @ X399 @ omega)|(in @ X399 @ X397))))&((((((in @ (esk8_3 @ X400 @ X401 @ X406) @ X401)|~(in @ X406 @ (esk7_2 @ X400 @ X401))|(in @ (esk5_2 @ X400 @ X401) @ X401))&((X400 @ (esk8_3 @ X400 @ X401 @ X406) @ X406)|~(in @ X406 @ (esk7_2 @ X400 @ X401))|(in @ (esk5_2 @ X400 @ X401) @ X401)))&(~(in @ X409 @ X401)|~(X400 @ X409 @ X408)|(in @ X408 @ (esk7_2 @ X400 @ X401))|(in @ (esk5_2 @ X400 @ X401) @ X401)))&(((((in @ (esk8_3 @ X400 @ X401 @ X406) @ X401)|~(in @ X406 @ (esk7_2 @ X400 @ X401))|((X400 @ (esk5_2 @ X400 @ X401) @ (esk6_3 @ X400 @ X401 @ X403))|~(X400 @ (esk5_2 @ X400 @ X401) @ X403)))&((X400 @ (esk8_3 @ X400 @ X401 @ X406) @ X406)|~(in @ X406 @ (esk7_2 @ X400 @ X401))|((X400 @ (esk5_2 @ X400 @ X401) @ (esk6_3 @ X400 @ X401 @ X403))|~(X400 @ (esk5_2 @ X400 @ X401) @ X403))))&(~(in @ X409 @ X401)|~(X400 @ X409 @ X408)|(in @ X408 @ (esk7_2 @ X400 @ X401))|((X400 @ (esk5_2 @ X400 @ X401) @ (esk6_3 @ X400 @ X401 @ X403))|~(X400 @ (esk5_2 @ X400 @ X401) @ X403))))&((((in @ (esk8_3 @ X400 @ X401 @ X406) @ X401)|~(in @ X406 @ (esk7_2 @ X400 @ X401))|(((X403)!=(esk6_3 @ X400 @ X401 @ X403))|~(X400 @ (esk5_2 @ X400 @ X401) @ X403)))&((X400 @ (esk8_3 @ X400 @ X401 @ X406) @ X406)|~(in @ X406 @ (esk7_2 @ X400 @ X401))|(((X403)!=(esk6_3 @ X400 @ X401 @ X403))|~(X400 @ (esk5_2 @ X400 @ X401) @ X403))))&(~(in @ X409 @ X401)|~(X400 @ X409 @ X408)|(in @ X408 @ (esk7_2 @ X400 @ X401))|(((X403)!=(esk6_3 @ X400 @ X401 @ X403))|~(X400 @ (esk5_2 @ X400 @ X401) @ X403))))))&((((in @ (esk9_1 @ X410) @ X410)|~(in @ X411 @ X410))&(~(in @ X413 @ (esk9_1 @ X410))|~(in @ X413 @ X410)|~(in @ X411 @ X410)))&((epred1_0)&((descrp)&((~(in @ X416 @ X414)|(~(X415 @ X416)|(in @ X416 @ (dsetconstr @ X414 @ X415))))&((~(in @ X419 @ (dsetconstr @ X417 @ X418))|(in @ X419 @ X417))&((~(in @ X422 @ (dsetconstr @ X420 @ X421))|(X421 @ X422))&(((((X423 @ (esk11_1 @ X423))|((X423 @ (esk10_2 @ X423 @ X424))|~(X423 @ X424)))&(~(X423 @ X427)|((esk11_1 @ X423)=(X427))|((X423 @ (esk10_2 @ X423 @ X424))|~(X423 @ X424))))&(((X423 @ (esk11_1 @ X423))|(((X424)!=(esk10_2 @ X423 @ X424))|~(X423 @ X424)))&(~(X423 @ X427)|((esk11_1 @ X423)=(X427))|(((X424)!=(esk10_2 @ X423 @ X424))|~(X423 @ X424)))))&((~(in @ X429 @ (prop2set @ ((X428))))|(X428))&((~(in @ X430 @ emptyset)|(X431))&((~(in @ X432 @ emptyset)|~($true))&(~(in @ X433 @ emptyset)&((((X434 @ (esk12_2 @ X434 @ X435))|~(X434 @ X435)|(X434 @ (esk13_1 @ X434)))&(((X435)!=(esk12_2 @ X434 @ X435))|~(X434 @ X435)|(X434 @ (esk13_1 @ X434))))&(((((in @ (esk15_2 @ X438 @ X439) @ X439)|((X438)=(X439))|(in @ (esk14_2 @ X438 @ X439) @ X438))&(~(in @ (esk15_2 @ X438 @ X439) @ X438)|((X438)=(X439))|(in @ (esk14_2 @ X438 @ X439) @ X438)))&(((in @ (esk15_2 @ X438 @ X439) @ X439)|((X438)=(X439))|~(in @ (esk14_2 @ X438 @ X439) @ X439))&(~(in @ (esk15_2 @ X438 @ X439) @ X438)|((X438)=(X439))|~(in @ (esk14_2 @ X438 @ X439) @ X439))))&(((in @ (esk16_1 @ X442) @ X442)|((X442)=(emptyset)))&(((in @ (esk17_1 @ X444) @ X444)|((X444)=(emptyset)))&(((~(in @ X448 @ (dsetconstr @ X446 @ X447))|(X447 @ X448)|~(in @ X448 @ X446))&(~(X447 @ X448)|(in @ X448 @ (dsetconstr @ X446 @ X447))|~(in @ X448 @ X446)))&((((X449)=(emptyset))|(in @ (esk18_1 @ X449) @ X449))&((~(in @ X453 @ X451)|(~(X452 @ X453)|((dsetconstr @ X451 @ X452)!=(emptyset))))&((~(in @ X455 @ X454)|((X454)!=(emptyset)))&((in @ X456 @ (setadjoin @ X456 @ X457))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X460 @ X459)|(in @ X460 @ (setadjoin @ X458 @ X459)))&(((((in @ X463 @ X462)|(X464)|((X463)=(X461))|~(in @ X463 @ (setadjoin @ X461 @ X462)))&(~(X464)|(X464)|((X463)=(X461))|~(in @ X463 @ (setadjoin @ X461 @ X462))))&(((in @ X463 @ X462)|(X464)|~(X464)|~(in @ X463 @ (setadjoin @ X461 @ X462)))&(~(X464)|(X464)|~(X464)|~(in @ X463 @ (setadjoin @ X461 @ X462)))))&((~(in @ X467 @ (setadjoin @ X465 @ X466))|(((X467)=(X465))|(in @ X467 @ X466)))&(((dsetconstr @ X468 @ (^[Z0:$i]:($true)))=(X468))&((((in @ (esk19_2 @ X469 @ X470) @ X470)|(in @ X470 @ (powerset @ X469)))&(~(in @ (esk19_2 @ X469 @ X470) @ X469)|(in @ X470 @ (powerset @ X469))))&((in @ emptyset @ (powerset @ X472))&((in @ emptyset @ (powerset @ X473))&((~(in @ X475 @ (powerset @ X474))|(~(in @ X476 @ X475)|(in @ X476 @ X474)))&((~(in @ X478 @ X479)|(~(in @ X479 @ X477)|(in @ X478 @ (setunion @ X477))))&((((in @ X481 @ (esk20_3 @ X480 @ X481 @ X482))|(X482)|~(in @ X481 @ (setunion @ X480)))&(((in @ (esk20_3 @ X480 @ X481 @ X482) @ X480)|(X482)|~(in @ X481 @ (setunion @ X480)))&(~(X482)|(X482)|~(in @ X481 @ (setunion @ X480)))))&((~(in @ X485 @ X484)|(in @ X485 @ (powerset @ (setunion @ X484))))&((((~(X486 @ X490)|((X490)=(esk22_1 @ X486))|((X486 @ (esk21_2 @ X486 @ X487))|~(X486 @ X487)))&(((X491)!=(esk22_1 @ X486))|(X486 @ X491)|((X486 @ (esk21_2 @ X486 @ X487))|~(X486 @ X487))))&((~(X486 @ X490)|((X490)=(esk22_1 @ X486))|(((X487)!=(esk21_2 @ X486 @ X487))|~(X486 @ X487)))&(((X491)!=(esk22_1 @ X486))|(X486 @ X491)|(((X487)!=(esk21_2 @ X486 @ X487))|~(X486 @ X487)))))&((((in @ (esk23_1 @ X492) @ X492)|((X492)=(emptyset)))&(($true)|((X492)=(emptyset))))&((~(in @ X494 @ (setadjoin @ X495 @ emptyset))|((X494)=(X495)))&((((X496)=(X497))|~(in @ X497 @ (setadjoin @ X496 @ emptyset)))&((((X498)!=(X499))|(in @ X498 @ (setadjoin @ X499 @ emptyset)))&((~(in @ X500 @ (setadjoin @ X501 @ emptyset))|(in @ X501 @ (setadjoin @ X500 @ emptyset)))&((~(in @ X504 @ (setadjoin @ X502 @ (setadjoin @ X503 @ emptyset)))|(((X504)=(X502))|((X504)=(X503))))&((in @ X505 @ (setadjoin @ X505 @ (setadjoin @ X506 @ emptyset)))&((in @ X508 @ (setadjoin @ X507 @ (setadjoin @ X508 @ emptyset)))&((~(in @ X511 @ X509)|~(X510 @ X511)|(((dsetconstr @ X509 @ X510)!=(emptyset))|~($true)))&((~(in @ X513 @ emptyset)|(X512 @ X513))&((((in @ (esk24_2 @ X514 @ X515) @ X514)|(~(in @ X516 @ X514)|(X515 @ X516)))&(~(X515 @ (esk24_2 @ X514 @ X515))|(~(in @ X516 @ X514)|(X515 @ X516))))&((((in @ (esk25_2 @ X518 @ X519) @ X518)|(~(in @ X521 @ X518)|~(X519 @ X521)))&((X519 @ (esk25_2 @ X518 @ X519))|(~(in @ X521 @ X518)|~(X519 @ X521))))&((((in @ (esk26_2 @ X522 @ X523) @ X522)|(~(in @ X525 @ X522)|~(X523 @ X525)))&((X523 @ (esk26_2 @ X522 @ X523))|(~(in @ X525 @ X522)|~(X523 @ X525))))&((((in @ (esk27_2 @ X526 @ X527) @ X526)|(~(in @ X528 @ X526)|(X527 @ X528)))&(~(X527 @ (esk27_2 @ X526 @ X527))|(~(in @ X528 @ X526)|(X527 @ X528))))&((~(X530)|(in @ emptyset @ (prop2set @ ((X530)))))&((prop2set2propI)&((((in @ (esk28_2 @ X531 @ X532) @ X531)|(~(in @ X534 @ X531)|~(X532 @ X534)))&((X532 @ (esk28_2 @ X531 @ X532))|(~(in @ X534 @ X531)|~(X532 @ X534))))&((((in @ (esk29_2 @ X535 @ X536) @ X535)|(~(in @ X537 @ X535)|(X536 @ X537)))&(~(X536 @ (esk29_2 @ X535 @ X536))|(~(in @ X537 @ X535)|(X536 @ X537))))&(((((X539 @ (esk31_1 @ X539))|((X539 @ (esk30_2 @ X539 @ X540))|~(X539 @ X540)))&(~(X539 @ X543)|((esk31_1 @ X539)=(X543))|((X539 @ (esk30_2 @ X539 @ X540))|~(X539 @ X540))))&(((X539 @ (esk31_1 @ X539))|(((X540)!=(esk30_2 @ X539 @ X540))|~(X539 @ X540)))&(~(X539 @ X543)|((esk31_1 @ X539)=(X543))|(((X540)!=(esk30_2 @ X539 @ X540))|~(X539 @ X540)))))&((epred2_0 @ esk32_0)&((~(epred2_0 @ X546)|(~(epred2_0 @ X547)|((X546)=(X547))))&(((epred2_0 @ (esk33_1 @ X548))|~(epred2_0 @ X548))&(((X548)!=(esk33_1 @ X548))|~(epred2_0 @ X548))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_87])])])])])])])).
% 0.20/0.28 thf(c_0_89, negated_conjecture, ![X2:$i, X3:$i]:((((X2)=(X3))|~((epred2_0 @ X2))|~((epred2_0 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_88])).
% 0.20/0.28 thf(c_0_90, negated_conjecture, (epred2_0 @ esk32_0), inference(split_conjunct,[status(thm)],[c_0_88])).
% 0.20/0.28 thf(c_0_91, negated_conjecture, ![X2:$i]:((((X2)=(esk32_0))|~((epred2_0 @ X2)))), inference(spm,[status(thm)],[c_0_89, c_0_90])).
% 0.20/0.28 thf(c_0_92, negated_conjecture, ![X2:$i]:(((epred2_0 @ (esk33_1 @ X2))|~((epred2_0 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_88])).
% 0.20/0.28 thf(c_0_93, negated_conjecture, ![X2:$i]:((((X2)!=(esk33_1 @ X2))|~((epred2_0 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_88])).
% 0.20/0.28 thf(c_0_94, negated_conjecture, ![X2:$i]:((((esk33_1 @ X2)=(esk32_0))|~((epred2_0 @ X2)))), inference(spm,[status(thm)],[c_0_91, c_0_92])).
% 0.20/0.28 thf(c_0_95, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_93, c_0_94])]), c_0_90])]), ['proof']).
% 0.20/0.28 % SZS output end CNFRefutation
% 0.20/0.28 % Parsed axioms : 137
% 0.20/0.28 % Removed by relevancy pruning/SinE : 75
% 0.20/0.28 % Initial clauses : 123
% 0.20/0.28 % Removed in clause preprocessing : 5
% 0.20/0.28 % Initial clauses in saturation : 118
% 0.20/0.28 % Processed clauses : 24
% 0.20/0.28 % ...of these trivial : 1
% 0.20/0.28 % ...subsumed : 5
% 0.20/0.28 % ...remaining for further processing : 18
% 0.20/0.28 % Other redundant clauses eliminated : 2
% 0.20/0.28 % Clauses deleted for lack of memory : 0
% 0.20/0.28 % Backward-subsumed : 0
% 0.20/0.28 % Backward-rewritten : 1
% 0.20/0.28 % Generated clauses : 7
% 0.20/0.28 % ...of the previous two non-redundant : 4
% 0.20/0.28 % ...aggressively subsumed : 0
% 0.20/0.28 % Contextual simplify-reflections : 0
% 0.20/0.28 % Paramodulations : 5
% 0.20/0.28 % Factorizations : 0
% 0.20/0.28 % NegExts : 0
% 0.20/0.28 % Equation resolutions : 2
% 0.20/0.28 % Disequality decompositions : 0
% 0.20/0.28 % Total rewrite steps : 4
% 0.20/0.28 % ...of those cached : 1
% 0.20/0.28 % Propositional unsat checks : 0
% 0.20/0.28 % Propositional check models : 0
% 0.20/0.28 % Propositional check unsatisfiable : 0
% 0.20/0.28 % Propositional clauses : 0
% 0.20/0.28 % Propositional clauses after purity: 0
% 0.20/0.28 % Propositional unsat core size : 0
% 0.20/0.28 % Propositional preprocessing time : 0.000
% 0.20/0.28 % Propositional encoding time : 0.000
% 0.20/0.28 % Propositional solver time : 0.000
% 0.20/0.28 % Success case prop preproc time : 0.000
% 0.20/0.28 % Success case prop encoding time : 0.000
% 0.20/0.28 % Success case prop solver time : 0.000
% 0.20/0.28 % Current number of processed clauses : 16
% 0.20/0.28 % Positive orientable unit clauses : 9
% 0.20/0.28 % Positive unorientable unit clauses: 0
% 0.20/0.28 % Negative unit clauses : 2
% 0.20/0.28 % Non-unit-clauses : 5
% 0.20/0.28 % Current number of unprocessed clauses: 98
% 0.20/0.28 % ...number of literals in the above : 315
% 0.20/0.28 % Current number of archived formulas : 0
% 0.20/0.28 % Current number of archived clauses : 1
% 0.20/0.28 % Clause-clause subsumption calls (NU) : 6
% 0.20/0.28 % Rec. Clause-clause subsumption calls : 6
% 0.20/0.28 % Non-unit clause-clause subsumptions : 0
% 0.20/0.28 % Unit Clause-clause subsumption calls : 1
% 0.20/0.28 % Rewrite failures with RHS unbound : 0
% 0.20/0.28 % BW rewrite match attempts : 1
% 0.20/0.28 % BW rewrite match successes : 1
% 0.20/0.28 % Condensation attempts : 0
% 0.20/0.28 % Condensation successes : 0
% 0.20/0.28 % Termbank termtop insertions : 15836
% 0.20/0.28 % Search garbage collected termcells : 6479
% 0.20/0.28
% 0.20/0.28 % -------------------------------------------------
% 0.20/0.28 % User time : 0.014 s
% 0.20/0.28 % System time : 0.003 s
% 0.20/0.28 % Total time : 0.017 s
% 0.20/0.28 % Maximum resident set size: 5564 pages
% 0.20/0.28
% 0.20/0.28 % -------------------------------------------------
% 0.20/0.28 % User time : 0.018 s
% 0.20/0.28 % System time : 0.007 s
% 0.20/0.28 % Total time : 0.026 s
% 0.20/0.28 % Maximum resident set size: 5120 pages
% 0.20/0.28 % E exiting
%------------------------------------------------------------------------------