%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU526^1 : 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 : n011.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 08:24:22 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU526^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n011.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:48:16 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.25 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.E0UF7sI0qN/E---3.1_123094.p
% 0.21/0.28 % Version: 3.5.1-ho
% 0.21/0.28 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.21/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.21/0.28 % Starting sh5l with 300s (1) cores
% 0.21/0.28 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.28 % Starting new_bool_2 with 300s (1) cores
% 0.21/0.28 % sh5l with pid 123129 completed with status 0
% 0.21/0.28 % Result found by sh5l
% 0.21/0.28 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.21/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.21/0.28 % Starting sh5l with 300s (1) cores
% 0.21/0.28 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.21/0.28 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.21/0.28 % Search class: HGHSM-FFMS31-SHFSMSBN
% 0.21/0.28 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.28 % Starting SubtermCWHack with 31s (1) cores
% 0.21/0.28 % SubtermCWHack with pid 123139 completed with status 0
% 0.21/0.28 % Result found by SubtermCWHack
% 0.21/0.28 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.21/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.21/0.29 % Starting sh5l with 300s (1) cores
% 0.21/0.29 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.21/0.29 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.21/0.29 % Search class: HGHSM-FFMS31-SHFSMSBN
% 0.21/0.29 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.29 % Starting SubtermCWHack with 31s (1) cores
% 0.21/0.29 % Preprocessing time : 0.002 s
% 0.21/0.29
% 0.21/0.29 % Proof found!
% 0.21/0.29 % SZS status Theorem
% 0.21/0.29 % SZS output start CNFRefutation
% 0.21/0.29 thf(decl_23, type, in: $i > $i > $o).
% 0.21/0.29 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.21/0.29 thf(decl_25, type, setextAx: $o).
% 0.21/0.29 thf(decl_26, type, emptyset: $i).
% 0.21/0.29 thf(decl_27, type, emptysetAx: $o).
% 0.21/0.29 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.21/0.29 thf(decl_29, type, setadjoinAx: $o).
% 0.21/0.29 thf(decl_30, type, powerset: $i > $i).
% 0.21/0.29 thf(decl_31, type, powersetAx: $o).
% 0.21/0.29 thf(decl_32, type, setunion: $i > $i).
% 0.21/0.29 thf(decl_33, type, setunionAx: $o).
% 0.21/0.29 thf(decl_34, type, omega: $i).
% 0.21/0.29 thf(decl_35, type, omega0Ax: $o).
% 0.21/0.29 thf(decl_36, type, omegaSAx: $o).
% 0.21/0.29 thf(decl_37, type, omegaIndAx: $o).
% 0.21/0.29 thf(decl_38, type, replAx: $o).
% 0.21/0.29 thf(decl_39, type, foundationAx: $o).
% 0.21/0.29 thf(decl_40, type, wellorderingAx: $o).
% 0.21/0.29 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.21/0.29 thf(decl_42, type, descrp: $o).
% 0.21/0.29 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.21/0.29 thf(decl_44, type, dsetconstrI: $o).
% 0.21/0.29 thf(decl_45, type, dsetconstrEL: $o).
% 0.21/0.29 thf(decl_46, type, dsetconstrER: $o).
% 0.21/0.29 thf(decl_47, type, exuE1: $o).
% 0.21/0.29 thf(decl_48, type, prop2set: $o > $i).
% 0.21/0.29 thf(decl_49, type, prop2setE: $o).
% 0.21/0.29 thf(decl_50, type, emptysetE: $o).
% 0.21/0.29 thf(decl_51, type, emptysetimpfalse: $o).
% 0.21/0.29 thf(decl_52, type, notinemptyset: $o).
% 0.21/0.29 thf(decl_53, type, exuE3e: $o).
% 0.21/0.29 thf(decl_54, type, setext: $o).
% 0.21/0.29 thf(decl_55, type, emptyI: $o).
% 0.21/0.29 thf(decl_56, type, noeltsimpempty: $o).
% 0.21/0.29 thf(decl_57, type, setbeta: $o).
% 0.21/0.29 thf(decl_58, type, nonempty: $i > $o).
% 0.21/0.29 thf(decl_59, type, nonemptyE1: $o).
% 0.21/0.29 thf(decl_60, type, nonemptyI: $o).
% 0.21/0.29 thf(decl_61, type, nonemptyI1: $o).
% 0.21/0.29 thf(decl_62, type, setadjoinIL: $o).
% 0.21/0.29 thf(decl_63, type, emptyinunitempty: $o).
% 0.21/0.29 thf(decl_64, type, setadjoinIR: $o).
% 0.21/0.29 thf(decl_65, type, setadjoinE: $o).
% 0.21/0.29 thf(decl_66, type, setadjoinOr: $o).
% 0.21/0.29 thf(decl_67, type, setoftrueEq: $o).
% 0.21/0.29 thf(decl_68, type, powersetI: $o).
% 0.21/0.29 thf(decl_69, type, emptyinPowerset: $o).
% 0.21/0.29 thf(decl_70, type, emptyInPowerset: $o).
% 0.21/0.29 thf(decl_71, type, powersetE: $o).
% 0.21/0.29 thf(decl_72, type, setunionI: $o).
% 0.21/0.29 thf(decl_73, type, setunionE: $o).
% 0.21/0.29 thf(decl_74, type, subPowSU: $o).
% 0.21/0.29 thf(decl_75, type, exuE2: $o).
% 0.21/0.29 thf(decl_76, type, epred1_0: $o).
% 0.21/0.29 thf(decl_77, type, esk1_2: $i > $i > $i).
% 0.21/0.29 thf(decl_78, type, esk2_2: $i > $i > $i).
% 0.21/0.29 thf(decl_79, type, esk3_2: $i > $i > $i).
% 0.21/0.29 thf(decl_80, type, esk4_1: $i > $i).
% 0.21/0.29 thf(decl_81, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.21/0.29 thf(decl_82, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.21/0.29 thf(decl_83, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.21/0.29 thf(decl_84, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.21/0.29 thf(decl_85, type, esk9_1: $i > $i).
% 0.21/0.29 thf(decl_86, type, esk10_2: ($i > $o) > $i > $i).
% 0.21/0.29 thf(decl_87, type, esk11_2: ($i > $o) > $i > $i).
% 0.21/0.29 thf(decl_88, type, esk12_1: ($i > $o) > $i).
% 0.21/0.29 thf(decl_89, type, esk13_2: ($i > $o) > $i > $i).
% 0.21/0.29 thf(decl_90, type, esk14_1: ($i > $o) > $i).
% 0.21/0.29 thf(decl_91, type, esk15_2: $i > $i > $i).
% 0.21/0.29 thf(decl_92, type, esk16_2: $i > $i > $i).
% 0.21/0.29 thf(decl_93, type, esk17_1: $i > $i).
% 0.21/0.29 thf(decl_94, type, esk18_1: $i > $i).
% 0.21/0.29 thf(decl_95, type, esk19_1: $i > $i).
% 0.21/0.29 thf(decl_96, type, esk20_2: $i > $i > $i).
% 0.21/0.29 thf(decl_97, type, esk21_3: $i > $i > $o > $i).
% 0.21/0.29 thf(decl_98, type, esk22_2: ($i > $o) > $i > $i).
% 0.21/0.29 thf(decl_99, type, esk23_1: ($i > $o) > $i).
% 0.21/0.29 thf(decl_100, type, esk24_0: $i).
% 0.21/0.29 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', exuE2)).
% 0.21/0.29 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', exu)).
% 0.21/0.29 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', nonempty)).
% 0.21/0.29 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', nonemptyI)).
% 0.21/0.29 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', descrp)).
% 0.21/0.29 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', replAx)).
% 0.21/0.29 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', exuE3e)).
% 0.21/0.29 thf(prop2set, axiom, ((prop2set)=(^[X10:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[X2:$i]:((X10)))))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', prop2set)).
% 0.21/0.29 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', exuE1)).
% 0.21/0.29 thf(nonemptyImpWitness, 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)=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', nonemptyImpWitness)).
% 0.21/0.29 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', nonemptyI1)).
% 0.21/0.29 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', nonemptyE1)).
% 0.21/0.29 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', dsetconstrEL)).
% 0.21/0.29 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', dsetconstrI)).
% 0.21/0.29 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', dsetconstrER)).
% 0.21/0.29 thf(prop2setE, axiom, ((prop2setE)<=>![X11:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X11))))=>(X11)))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', prop2setE)).
% 0.21/0.29 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', setbeta)).
% 0.21/0.29 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', setoftrueEq)).
% 0.21/0.29 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', setunionI)).
% 0.21/0.29 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', powersetI)).
% 0.21/0.29 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', emptyinPowerset)).
% 0.21/0.29 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', emptyInPowerset)).
% 0.21/0.29 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X14:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X14))))=>(X14)))))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', setunionE)).
% 0.21/0.29 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', subPowSU)).
% 0.21/0.29 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', omega0Ax)).
% 0.21/0.29 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', setunionAx)).
% 0.21/0.29 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', powersetAx)).
% 0.21/0.29 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', setadjoinAx)).
% 0.21/0.29 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', emptysetAx)).
% 0.21/0.29 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', setextAx)).
% 0.21/0.29 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', omegaSAx)).
% 0.21/0.29 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', wellorderingAx)).
% 0.21/0.29 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', foundationAx)).
% 0.21/0.29 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.E0UF7sI0qN/E---3.1_123094.p', omegaIndAx)).
% 0.21/0.29 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.E0UF7sI0qN/E---3.1_123094.p', setext)).
% 0.21/0.29 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', notinemptyset)).
% 0.21/0.29 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', emptysetimpfalse)).
% 0.21/0.29 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X12:$o]:((X12))))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', emptysetE)).
% 0.21/0.29 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', emptyI)).
% 0.21/0.29 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', setadjoinOr)).
% 0.21/0.29 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X13:$o]:(((((X3)=(X2))=>(X13))=>(((in @ X3 @ X4)=>(X13))=>(X13))))))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', setadjoinE)).
% 0.21/0.29 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', setadjoinIR)).
% 0.21/0.29 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', emptyinunitempty)).
% 0.21/0.29 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', setadjoinIL)).
% 0.21/0.29 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', noeltsimpempty)).
% 0.21/0.29 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.E0UF7sI0qN/E---3.1_123094.p', powersetE)).
% 0.21/0.29 thf(c_0_46, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.21/0.29 thf(c_0_47, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.21/0.29 thf(c_0_48, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.21/0.29 thf(c_0_49, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.21/0.29 thf(c_0_50, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.21/0.29 thf(c_0_51, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.21/0.29 thf(c_0_52, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.21/0.29 thf(c_0_53, plain, ((prop2set)=(^[Z0:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[Z1:$i]:((Z0)))))), inference(fof_simplification,[status(thm)],[prop2set])).
% 0.21/0.29 thf(c_0_54, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.21/0.29 thf(c_0_55, 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)=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[nonemptyImpWitness])).
% 0.21/0.29 thf(c_0_56, plain, ((exuE2)=(![X1:$i > $o]:((((?[X143:$i]:(((((X1 @ X143)))&(![X144:$i]:(((((X1 @ X144)))=>(((X143)=(X144))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_46, c_0_47])).
% 0.21/0.29 thf(c_0_57, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_48])).
% 0.21/0.29 thf(c_0_58, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_49, c_0_48])).
% 0.21/0.29 thf(c_0_59, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_48])).
% 0.21/0.29 thf(c_0_60, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.21/0.29 thf(c_0_61, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.21/0.29 thf(c_0_62, plain, ((descrp)=(![X1:$i > $o]:((((?[X137:$i]:(((((X1 @ X137)))&(![X138:$i]:(((((X1 @ X138)))=>(((X137)=(X138))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_50, c_0_47])).
% 0.21/0.29 thf(c_0_63, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X135:$i]:(((((X6 @ X2 @ X135)))&(![X136:$i]:(((((X6 @ X2 @ X136)))=>(((X135)=(X136)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_51, c_0_47])).
% 0.21/0.29 thf(c_0_64, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.21/0.29 thf(c_0_65, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X141:$i]:(((((X1 @ X141)))&(![X142:$i]:(((((X1 @ X142)))=>(((X141)=(X142))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_52, c_0_47])).
% 0.21/0.29 thf(c_0_66, axiom, ((prop2setE)=(![X11:$o, X2:$i]:((((in @ X2 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:(((X11)))))))=>((X11)))))), inference(apply_def,[status(thm)],[prop2setE, c_0_53])).
% 0.21/0.29 thf(c_0_67, plain, ((exuE1)=(![X1:$i > $o]:((((?[X139:$i]:(((((X1 @ X139)))&(![X140:$i]:(((((X1 @ X140)))=>(((X139)=(X140))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_54, c_0_47])).
% 0.21/0.29 thf(c_0_68, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.21/0.29 thf(c_0_69, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.21/0.29 thf(c_0_70, plain, ((epred1_0)<=>![X174:$i]:(?[X175:$i]:((((![X176:$i]:(((in @ X176 @ X175)=>![X177:$i]:(((in @ X177 @ X176)=>(in @ X177 @ X174)))))&![X178:$i, X179:$i]:((((in @ X178 @ X174)&(in @ X179 @ X174))=>(![X180:$i]:(((in @ X180 @ X175)=>((in @ X178 @ X180)<=>(in @ X179 @ X180))))=>((X178)=(X179))))))&![X181:$i, X182:$i]:((((in @ X181 @ X175)&(in @ X182 @ X175))=>(![X183:$i]:(((in @ X183 @ X181)=>(in @ X183 @ X182)))|![X184:$i]:(((in @ X184 @ X182)=>(in @ X184 @ X181)))))))&![X185:$i]:(((![X186:$i]:(((in @ X186 @ X185)=>(in @ X186 @ X174)))&?[X187:$i]:((in @ X187 @ X185)))=>?[X188:$i, X189:$i]:(((((in @ X188 @ X175)&(in @ X189 @ X185))&~(?[X190:$i]:(((in @ X190 @ X188)&(in @ X190 @ X185)))))&![X191:$i]:(((in @ X191 @ X175)=>(![X192:$i]:(((in @ X192 @ X191)=>(in @ X192 @ X188)))|(in @ X189 @ X191)))))))))))), introduced(definition)).
% 0.21/0.29 thf(c_0_71, negated_conjecture, ~((![X145:$i, X146:$i]:((![X147:$i]:(((in @ X147 @ X145)<=>(in @ X147 @ X146)))=>((X145)=(X146))))=>(![X148:$i]:(~(in @ X148 @ emptyset))=>(![X149:$i, X150:$i, X151:$i]:(((in @ X151 @ (setadjoin @ X149 @ X150))<=>(((X151)=(X149))|(in @ X151 @ X150))))=>(![X152:$i, X153:$i]:(((in @ X153 @ (powerset @ X152))<=>![X154:$i]:(((in @ X154 @ X153)=>(in @ X154 @ X152)))))=>(![X155:$i, X156:$i]:(((in @ X156 @ (setunion @ X155))<=>?[X157:$i]:(((in @ X156 @ X157)&(in @ X157 @ X155)))))=>((in @ emptyset @ omega)=>(![X158:$i]:(((in @ X158 @ omega)=>(in @ (setadjoin @ X158 @ X158) @ omega)))=>(![X159:$i]:((((in @ emptyset @ X159)&![X160:$i]:((((in @ X160 @ omega)&(in @ X160 @ X159))=>(in @ (setadjoin @ X160 @ X160) @ X159))))=>![X161:$i]:(((in @ X161 @ omega)=>(in @ X161 @ X159)))))=>(![X162:$i > $i > $o, X163:$i]:((![X164:$i]:(((in @ X164 @ X163)=>?[X165:$i]:(((X162 @ X164 @ X165)&![X166:$i]:(((X162 @ X164 @ X166)=>((X165)=(X166))))))))=>?[X167:$i]:(![X168:$i]:(((in @ X168 @ X167)<=>?[X169:$i]:(((in @ X169 @ X163)&(X162 @ X169 @ X168))))))))=>(![X170:$i]:((?[X171:$i]:((in @ X171 @ X170))=>?[X172:$i]:(((in @ X172 @ X170)&~(?[X173:$i]:(((in @ X173 @ X172)&(in @ X173 @ X170))))))))=>((epred1_0)=>(![X193:$i > $o]:((?[X194:$i]:(((X193 @ X194)&![X195:$i]:(((X193 @ X195)=>((X194)=(X195))))))=>(X193 @ (descr @ (^[Z0:$i]:(X193 @ Z0))))))=>(![X196:$i, X197:$i > $o, X198:$i]:(((in @ X198 @ X196)=>((X197 @ X198)=>(in @ X198 @ (dsetconstr @ X196 @ X197)))))=>(![X199:$i, X200:$i > $o, X201:$i]:(((in @ X201 @ (dsetconstr @ X199 @ X200))=>(in @ X201 @ X199)))=>(![X202:$i, X203:$i > $o, X204:$i]:(((in @ X204 @ (dsetconstr @ X202 @ X203))=>(X203 @ X204)))=>(![X205:$i > $o]:((?[X206:$i]:(((X205 @ X206)&![X207:$i]:(((X205 @ X207)=>((X206)=(X207))))))=>?[X208:$i]:(((X205 @ X208)&![X209:$i]:(((X205 @ X209)=>((X208)=(X209))))))))=>(![X210:$o, X211:$i]:(((in @ X211 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X210)))))=>(X210)))=>(![X212:$i]:(((in @ X212 @ emptyset)=>![X213:$o]:((X213))))=>(![X214:$i]:(((in @ X214 @ emptyset)=>~($true)))=>(![X215:$i]:(~(in @ X215 @ emptyset))=>(![X216:$i > $o]:((?[X217:$i]:(((X216 @ X217)&![X218:$i]:(((X216 @ X218)=>((X217)=(X218))))))=>?[X219:$i]:((X216 @ X219))))=>(![X220:$i, X221:$i]:((![X222:$i]:(((in @ X222 @ X220)=>(in @ X222 @ X221)))=>(![X223:$i]:(((in @ X223 @ X221)=>(in @ X223 @ X220)))=>((X220)=(X221)))))=>(![X224:$i]:((![X225:$i]:(~(in @ X225 @ X224))=>((X224)=(emptyset))))=>(![X226:$i]:((![X227:$i]:(~(in @ X227 @ X226))=>((X226)=(emptyset))))=>(![X228:$i, X229:$i > $o, X230:$i]:(((in @ X230 @ X228)=>((in @ X230 @ (dsetconstr @ X228 @ X229))<=>(X229 @ X230))))=>(![X231:$i]:((((X231)!=(emptyset))=>?[X232:$i]:((in @ X232 @ X231))))=>(![X233:$i, X234:$i > $o, X235:$i]:(((in @ X235 @ X233)=>((X234 @ X235)=>((dsetconstr @ X233 @ X234)!=(emptyset)))))=>(![X236:$i]:((?[X237:$i]:((in @ X237 @ X236))=>((X236)!=(emptyset))))=>(![X238:$i, X239:$i]:((in @ X238 @ (setadjoin @ X238 @ X239)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X240:$i, X241:$i, X242:$i]:(((in @ X242 @ X241)=>(in @ X242 @ (setadjoin @ X240 @ X241))))=>(![X243:$i, X244:$i, X245:$i]:(((in @ X245 @ (setadjoin @ X243 @ X244))=>![X246:$o]:(((((X245)=(X243))=>(X246))=>(((in @ X245 @ X244)=>(X246))=>(X246))))))=>(![X247:$i, X248:$i, X249:$i]:(((in @ X249 @ (setadjoin @ X247 @ X248))=>(((X249)=(X247))|(in @ X249 @ X248))))=>(![X250:$i]:(((dsetconstr @ X250 @ (^[Z0:$i]:($true)))=(X250)))=>(![X251:$i, X252:$i]:((![X253:$i]:(((in @ X253 @ X252)=>(in @ X253 @ X251)))=>(in @ X252 @ (powerset @ X251))))=>(![X254:$i]:((in @ emptyset @ (powerset @ X254)))=>(![X255:$i]:((in @ emptyset @ (powerset @ X255)))=>(![X256:$i, X257:$i, X258:$i]:(((in @ X257 @ (powerset @ X256))=>((in @ X258 @ X257)=>(in @ X258 @ X256))))=>(![X259:$i, X260:$i, X261:$i]:(((in @ X260 @ X261)=>((in @ X261 @ X259)=>(in @ X260 @ (setunion @ X259)))))=>(![X262:$i, X263:$i]:(((in @ X263 @ (setunion @ X262))=>![X264:$o]:((![X265:$i]:(((in @ X263 @ X265)=>((in @ X265 @ X262)=>(X264))))=>(X264)))))=>(![X266:$i, X267:$i]:(((in @ X267 @ X266)=>(in @ X267 @ (powerset @ (setunion @ X266)))))=>(![X268:$i > $o]:((?[X269:$i]:(((X268 @ X269)&![X270:$i]:(((X268 @ X270)=>((X269)=(X270))))))=>?[X271:$i]:(![X272:$i]:(((X268 @ X272)<=>((X272)=(X271)))))))=>![X4:$i]:((((X4)!=(emptyset))=>?[X2:$i]:(((in @ X2 @ X4)&$true))))))))))))))))))))))))))))))))))))))))))))))), 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)],[c_0_55, setunionI]), powersetI]), emptyinPowerset]), emptyInPowerset]), setunionE]), subPowSU]), omega0Ax]), c_0_56]), setunionAx]), c_0_57]), powersetAx]), c_0_58]), setadjoinAx]), c_0_59]), emptysetAx]), c_0_48]), setextAx]), omegaSAx]), c_0_60]), c_0_61]), c_0_62]), wellorderingAx]), foundationAx]), c_0_63]), omegaIndAx]), c_0_64]), setext]), c_0_65]), notinemptyset]), emptysetimpfalse]), emptysetE]), c_0_66]), c_0_67]), emptyI]), setadjoinOr]), setadjoinE]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), c_0_68]), noeltsimpempty]), powersetE]), c_0_69])])]), c_0_70])).
% 0.21/0.29 thf(c_0_72, negated_conjecture, ![X273:$i, X274:$i, X276:$i, X277:$i, X278:$i, X279:$i, X280:$i, X281:$i, X282:$i, X283:$i, X284:$i, X286:$i, X287:$i, X289:$i, X290:$i, X291:$i, X292:$i, X293:$i, X295:$i, X296:$i > $i > $o, X297:$i, X299:$i, X302:$i, X304:$i, X305:$i, X306:$i, X307:$i, X309:$i, X310:$i > $o, X311:$i, X313:$i, X314:$i > $o, X315:$i, X316:$i, X317:$i > $o, X318:$i, X319:$i, X320:$i > $o, X321:$i, X322:$i > $o, X323:$i, X326:$i, X327:$o, X328:$i, X329:$i, X330:$o, X331:$i, X332:$i, X333:$i > $o, X334:$i, X337:$i, X338:$i, X341:$i, X343:$i, X345:$i, X346:$i > $o, X347:$i, X348:$i, X350:$i, X351:$i > $o, X352:$i, X353:$i, X354:$i, X355:$i, X356:$i, X357:$i, X358:$i, X359:$i, X360:$i, X361:$i, X362:$i, X363:$o, X364:$i, X365:$i, X366:$i, X367:$i, X368:$i, X369:$i, X371:$i, X372:$i, X373:$i, X374:$i, X375:$i, X376:$i, X377:$i, X378:$i, X379:$i, X380:$i, X381:$o, X383:$i, X384:$i, X385:$i > $o, X386:$i, X389:$i, X390:$i, X392:$i]:((((~(in @ (esk1_2 @ X273 @ X274) @ X273)|~(in @ (esk1_2 @ X273 @ X274) @ X274)|((X273)=(X274)))&((in @ (esk1_2 @ X273 @ X274) @ X273)|(in @ (esk1_2 @ X273 @ X274) @ X274)|((X273)=(X274))))&(~(in @ X276 @ emptyset)&(((~(in @ X279 @ (setadjoin @ X277 @ X278))|(((X279)=(X277))|(in @ X279 @ X278)))&((((X279)!=(X277))|(in @ X279 @ (setadjoin @ X277 @ X278)))&(~(in @ X279 @ X278)|(in @ X279 @ (setadjoin @ X277 @ X278)))))&(((~(in @ X281 @ (powerset @ X280))|(~(in @ X282 @ X281)|(in @ X282 @ X280)))&(((in @ (esk2_2 @ X283 @ X284) @ X284)|(in @ X284 @ (powerset @ X283)))&(~(in @ (esk2_2 @ X283 @ X284) @ X283)|(in @ X284 @ (powerset @ X283)))))&(((((in @ X287 @ (esk3_2 @ X286 @ X287))|~(in @ X287 @ (setunion @ X286)))&((in @ (esk3_2 @ X286 @ X287) @ X286)|~(in @ X287 @ (setunion @ X286))))&(~(in @ X290 @ X291)|~(in @ X291 @ X289)|(in @ X290 @ (setunion @ X289))))&((in @ emptyset @ omega)&((~(in @ X292 @ omega)|(in @ (setadjoin @ X292 @ X292) @ omega))&(((((in @ (esk4_1 @ X293) @ omega)|~(in @ emptyset @ X293)|(~(in @ X295 @ omega)|(in @ X295 @ X293)))&((in @ (esk4_1 @ X293) @ X293)|~(in @ emptyset @ X293)|(~(in @ X295 @ omega)|(in @ X295 @ X293))))&(~(in @ (setadjoin @ (esk4_1 @ X293) @ (esk4_1 @ X293)) @ X293)|~(in @ emptyset @ X293)|(~(in @ X295 @ omega)|(in @ X295 @ X293))))&((((((in @ (esk8_3 @ X296 @ X297 @ X302) @ X297)|~(in @ X302 @ (esk7_2 @ X296 @ X297))|(in @ (esk5_2 @ X296 @ X297) @ X297))&((X296 @ (esk8_3 @ X296 @ X297 @ X302) @ X302)|~(in @ X302 @ (esk7_2 @ X296 @ X297))|(in @ (esk5_2 @ X296 @ X297) @ X297)))&(~(in @ X305 @ X297)|~(X296 @ X305 @ X304)|(in @ X304 @ (esk7_2 @ X296 @ X297))|(in @ (esk5_2 @ X296 @ X297) @ X297)))&(((((in @ (esk8_3 @ X296 @ X297 @ X302) @ X297)|~(in @ X302 @ (esk7_2 @ X296 @ X297))|((X296 @ (esk5_2 @ X296 @ X297) @ (esk6_3 @ X296 @ X297 @ X299))|~(X296 @ (esk5_2 @ X296 @ X297) @ X299)))&((X296 @ (esk8_3 @ X296 @ X297 @ X302) @ X302)|~(in @ X302 @ (esk7_2 @ X296 @ X297))|((X296 @ (esk5_2 @ X296 @ X297) @ (esk6_3 @ X296 @ X297 @ X299))|~(X296 @ (esk5_2 @ X296 @ X297) @ X299))))&(~(in @ X305 @ X297)|~(X296 @ X305 @ X304)|(in @ X304 @ (esk7_2 @ X296 @ X297))|((X296 @ (esk5_2 @ X296 @ X297) @ (esk6_3 @ X296 @ X297 @ X299))|~(X296 @ (esk5_2 @ X296 @ X297) @ X299))))&((((in @ (esk8_3 @ X296 @ X297 @ X302) @ X297)|~(in @ X302 @ (esk7_2 @ X296 @ X297))|(((X299)!=(esk6_3 @ X296 @ X297 @ X299))|~(X296 @ (esk5_2 @ X296 @ X297) @ X299)))&((X296 @ (esk8_3 @ X296 @ X297 @ X302) @ X302)|~(in @ X302 @ (esk7_2 @ X296 @ X297))|(((X299)!=(esk6_3 @ X296 @ X297 @ X299))|~(X296 @ (esk5_2 @ X296 @ X297) @ X299))))&(~(in @ X305 @ X297)|~(X296 @ X305 @ X304)|(in @ X304 @ (esk7_2 @ X296 @ X297))|(((X299)!=(esk6_3 @ X296 @ X297 @ X299))|~(X296 @ (esk5_2 @ X296 @ X297) @ X299))))))&((((in @ (esk9_1 @ X306) @ X306)|~(in @ X307 @ X306))&(~(in @ X309 @ (esk9_1 @ X306))|~(in @ X309 @ X306)|~(in @ X307 @ X306)))&((epred1_0)&((((X310 @ (esk10_2 @ X310 @ X311))|~(X310 @ X311)|(X310 @ (descr @ X310)))&(((X311)!=(esk10_2 @ X310 @ X311))|~(X310 @ X311)|(X310 @ (descr @ X310))))&((~(in @ X315 @ X313)|(~(X314 @ X315)|(in @ X315 @ (dsetconstr @ X313 @ X314))))&((~(in @ X318 @ (dsetconstr @ X316 @ X317))|(in @ X318 @ X316))&((~(in @ X321 @ (dsetconstr @ X319 @ X320))|(X320 @ X321))&(((((X322 @ (esk12_1 @ X322))|((X322 @ (esk11_2 @ X322 @ X323))|~(X322 @ X323)))&(~(X322 @ X326)|((esk12_1 @ X322)=(X326))|((X322 @ (esk11_2 @ X322 @ X323))|~(X322 @ X323))))&(((X322 @ (esk12_1 @ X322))|(((X323)!=(esk11_2 @ X322 @ X323))|~(X322 @ X323)))&(~(X322 @ X326)|((esk12_1 @ X322)=(X326))|(((X323)!=(esk11_2 @ X322 @ X323))|~(X322 @ X323)))))&((~(in @ X328 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X327)))))|(X327))&((~(in @ X329 @ emptyset)|(X330))&((~(in @ X331 @ emptyset)|~($true))&(~(in @ X332 @ emptyset)&((((X333 @ (esk13_2 @ X333 @ X334))|~(X333 @ X334)|(X333 @ (esk14_1 @ X333)))&(((X334)!=(esk13_2 @ X333 @ X334))|~(X333 @ X334)|(X333 @ (esk14_1 @ X333))))&(((((in @ (esk16_2 @ X337 @ X338) @ X338)|((X337)=(X338))|(in @ (esk15_2 @ X337 @ X338) @ X337))&(~(in @ (esk16_2 @ X337 @ X338) @ X337)|((X337)=(X338))|(in @ (esk15_2 @ X337 @ X338) @ X337)))&(((in @ (esk16_2 @ X337 @ X338) @ X338)|((X337)=(X338))|~(in @ (esk15_2 @ X337 @ X338) @ X338))&(~(in @ (esk16_2 @ X337 @ X338) @ X337)|((X337)=(X338))|~(in @ (esk15_2 @ X337 @ X338) @ X338))))&(((in @ (esk17_1 @ X341) @ X341)|((X341)=(emptyset)))&(((in @ (esk18_1 @ X343) @ X343)|((X343)=(emptyset)))&(((~(in @ X347 @ (dsetconstr @ X345 @ X346))|(X346 @ X347)|~(in @ X347 @ X345))&(~(X346 @ X347)|(in @ X347 @ (dsetconstr @ X345 @ X346))|~(in @ X347 @ X345)))&((((X348)=(emptyset))|(in @ (esk19_1 @ X348) @ X348))&((~(in @ X352 @ X350)|(~(X351 @ X352)|((dsetconstr @ X350 @ X351)!=(emptyset))))&((~(in @ X354 @ X353)|((X353)!=(emptyset)))&((in @ X355 @ (setadjoin @ X355 @ X356))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X359 @ X358)|(in @ X359 @ (setadjoin @ X357 @ X358)))&(((((in @ X362 @ X361)|(X363)|((X362)=(X360))|~(in @ X362 @ (setadjoin @ X360 @ X361)))&(~(X363)|(X363)|((X362)=(X360))|~(in @ X362 @ (setadjoin @ X360 @ X361))))&(((in @ X362 @ X361)|(X363)|~(X363)|~(in @ X362 @ (setadjoin @ X360 @ X361)))&(~(X363)|(X363)|~(X363)|~(in @ X362 @ (setadjoin @ X360 @ X361)))))&((~(in @ X366 @ (setadjoin @ X364 @ X365))|(((X366)=(X364))|(in @ X366 @ X365)))&(((dsetconstr @ X367 @ (^[Z0:$i]:($true)))=(X367))&((((in @ (esk20_2 @ X368 @ X369) @ X369)|(in @ X369 @ (powerset @ X368)))&(~(in @ (esk20_2 @ X368 @ X369) @ X368)|(in @ X369 @ (powerset @ X368))))&((in @ emptyset @ (powerset @ X371))&((in @ emptyset @ (powerset @ X372))&((~(in @ X374 @ (powerset @ X373))|(~(in @ X375 @ X374)|(in @ X375 @ X373)))&((~(in @ X377 @ X378)|(~(in @ X378 @ X376)|(in @ X377 @ (setunion @ X376))))&((((in @ X380 @ (esk21_3 @ X379 @ X380 @ X381))|(X381)|~(in @ X380 @ (setunion @ X379)))&(((in @ (esk21_3 @ X379 @ X380 @ X381) @ X379)|(X381)|~(in @ X380 @ (setunion @ X379)))&(~(X381)|(X381)|~(in @ X380 @ (setunion @ X379)))))&((~(in @ X384 @ X383)|(in @ X384 @ (powerset @ (setunion @ X383))))&((((~(X385 @ X389)|((X389)=(esk23_1 @ X385))|((X385 @ (esk22_2 @ X385 @ X386))|~(X385 @ X386)))&(((X390)!=(esk23_1 @ X385))|(X385 @ X390)|((X385 @ (esk22_2 @ X385 @ X386))|~(X385 @ X386))))&((~(X385 @ X389)|((X389)=(esk23_1 @ X385))|(((X386)!=(esk22_2 @ X385 @ X386))|~(X385 @ X386)))&(((X390)!=(esk23_1 @ X385))|(X385 @ X390)|(((X386)!=(esk22_2 @ X385 @ X386))|~(X385 @ X386)))))&(((esk24_0)!=(emptyset))&(~(in @ X392 @ esk24_0)|~($true)))))))))))))))))))))))))))))))))))))))))))))), 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_71])])])])])])])).
% 0.21/0.29 thf(c_0_73, negated_conjecture, ![X2:$i]:((~((in @ X2 @ esk24_0))|~(($true)))), inference(split_conjunct,[status(thm)],[c_0_72])).
% 0.21/0.29 thf(c_0_74, negated_conjecture, ![X2:$i]:(~((in @ X2 @ esk24_0))), inference(cn,[status(thm)],[c_0_73])).
% 0.21/0.29 thf(c_0_75, negated_conjecture, ![X2:$i]:(((in @ (esk17_1 @ X2) @ X2)|((X2)=(emptyset)))), inference(split_conjunct,[status(thm)],[c_0_72])).
% 0.21/0.29 thf(c_0_76, negated_conjecture, ((esk24_0)!=(emptyset)), inference(split_conjunct,[status(thm)],[c_0_72])).
% 0.21/0.29 thf(c_0_77, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_74, c_0_75]), c_0_76]), ['proof']).
% 0.21/0.29 % SZS output end CNFRefutation
% 0.21/0.29 % Parsed axioms : 99
% 0.21/0.29 % Removed by relevancy pruning/SinE : 53
% 0.21/0.29 % Initial clauses : 93
% 0.21/0.29 % Removed in clause preprocessing : 4
% 0.21/0.29 % Initial clauses in saturation : 89
% 0.21/0.29 % Processed clauses : 11
% 0.21/0.29 % ...of these trivial : 1
% 0.21/0.29 % ...subsumed : 3
% 0.21/0.29 % ...remaining for further processing : 7
% 0.21/0.29 % Other redundant clauses eliminated : 0
% 0.21/0.29 % Clauses deleted for lack of memory : 0
% 0.21/0.29 % Backward-subsumed : 0
% 0.21/0.29 % Backward-rewritten : 0
% 0.21/0.29 % Generated clauses : 1
% 0.21/0.29 % ...of the previous two non-redundant : 0
% 0.21/0.29 % ...aggressively subsumed : 0
% 0.21/0.29 % Contextual simplify-reflections : 0
% 0.21/0.29 % Paramodulations : 1
% 0.21/0.29 % Factorizations : 0
% 0.21/0.29 % NegExts : 0
% 0.21/0.29 % Equation resolutions : 0
% 0.21/0.29 % Disequality decompositions : 0
% 0.21/0.29 % Total rewrite steps : 1
% 0.21/0.29 % ...of those cached : 0
% 0.21/0.29 % Propositional unsat checks : 0
% 0.21/0.29 % Propositional check models : 0
% 0.21/0.29 % Propositional check unsatisfiable : 0
% 0.21/0.29 % Propositional clauses : 0
% 0.21/0.29 % Propositional clauses after purity: 0
% 0.21/0.29 % Propositional unsat core size : 0
% 0.21/0.29 % Propositional preprocessing time : 0.000
% 0.21/0.29 % Propositional encoding time : 0.000
% 0.21/0.29 % Propositional solver time : 0.000
% 0.21/0.29 % Success case prop preproc time : 0.000
% 0.21/0.29 % Success case prop encoding time : 0.000
% 0.21/0.29 % Success case prop solver time : 0.000
% 0.21/0.29 % Current number of processed clauses : 7
% 0.21/0.29 % Positive orientable unit clauses : 3
% 0.21/0.29 % Positive unorientable unit clauses: 0
% 0.21/0.29 % Negative unit clauses : 3
% 0.21/0.29 % Non-unit-clauses : 1
% 0.21/0.29 % Current number of unprocessed clauses: 78
% 0.21/0.29 % ...number of literals in the above : 254
% 0.21/0.29 % Current number of archived formulas : 0
% 0.21/0.29 % Current number of archived clauses : 0
% 0.21/0.29 % Clause-clause subsumption calls (NU) : 0
% 0.21/0.29 % Rec. Clause-clause subsumption calls : 0
% 0.21/0.29 % Non-unit clause-clause subsumptions : 0
% 0.21/0.29 % Unit Clause-clause subsumption calls : 0
% 0.21/0.29 % Rewrite failures with RHS unbound : 0
% 0.21/0.29 % BW rewrite match attempts : 0
% 0.21/0.29 % BW rewrite match successes : 0
% 0.21/0.29 % Condensation attempts : 0
% 0.21/0.29 % Condensation successes : 0
% 0.21/0.29 % Termbank termtop insertions : 11672
% 0.21/0.29 % Search garbage collected termcells : 4654
% 0.21/0.29
% 0.21/0.29 % -------------------------------------------------
% 0.21/0.29 % User time : 0.011 s
% 0.21/0.29 % System time : 0.004 s
% 0.21/0.29 % Total time : 0.016 s
% 0.21/0.29 % Maximum resident set size: 5012 pages
% 0.21/0.29
% 0.21/0.29 % -------------------------------------------------
% 0.21/0.29 % User time : 0.015 s
% 0.21/0.29 % System time : 0.007 s
% 0.21/0.29 % Total time : 0.023 s
% 0.21/0.29 % Maximum resident set size: 4864 pages
% 0.21/0.29 % E exiting
%------------------------------------------------------------------------------