%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU523^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:26:34 AM UTC 2026
% Result : Theorem 0.21s 0.27s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU523^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n018.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 13:50:11 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.24 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p
% 0.21/0.27 % Version: 3.5.1-ho
% 0.21/0.27 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.21/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.21/0.27 % Starting sh5l with 300s (1) cores
% 0.21/0.27 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.27 % Starting new_bool_2 with 300s (1) cores
% 0.21/0.27 % new_ho_10 with pid 96240 completed with status 0
% 0.21/0.27 % Result found by new_ho_10
% 0.21/0.27 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.21/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.21/0.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.21/0.27 % No SInE strategy applied
% 0.21/0.27 % Search class: HGHSM-FFMS31-SHFSMSBN
% 0.21/0.27 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/0.27 % Starting SubtermCWHack with 151s (1) cores
% 0.21/0.27 % Starting new_ho_10 with 901s (1) cores
% 0.21/0.27 % Starting sh5l with 151s (1) cores
% 0.21/0.27 % Starting new_bool_1 with 151s (1) cores
% 0.21/0.27 % Starting new_bool_2 with 146s (1) cores
% 0.21/0.27 % SubtermCWHack with pid 96246 completed with status 0
% 0.21/0.27 % Result found by SubtermCWHack
% 0.21/0.27 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.21/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.21/0.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.21/0.27 % No SInE strategy applied
% 0.21/0.27 % Search class: HGHSM-FFMS31-SHFSMSBN
% 0.21/0.27 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/0.27 % Starting SubtermCWHack with 151s (1) cores
% 0.21/0.27 % Preprocessing time : 0.004 s
% 0.21/0.27
% 0.21/0.27 % Proof found!
% 0.21/0.27 % SZS status Theorem
% 0.21/0.27 % SZS output start CNFRefutation
% 0.21/0.27 thf(decl_23, type, in: $i > $i > $o).
% 0.21/0.27 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.21/0.27 thf(decl_25, type, setextAx: $o).
% 0.21/0.27 thf(decl_26, type, emptyset: $i).
% 0.21/0.27 thf(decl_27, type, emptysetAx: $o).
% 0.21/0.27 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.21/0.27 thf(decl_29, type, setadjoinAx: $o).
% 0.21/0.27 thf(decl_30, type, powerset: $i > $i).
% 0.21/0.27 thf(decl_31, type, powersetAx: $o).
% 0.21/0.27 thf(decl_32, type, setunion: $i > $i).
% 0.21/0.27 thf(decl_33, type, setunionAx: $o).
% 0.21/0.27 thf(decl_34, type, omega: $i).
% 0.21/0.27 thf(decl_35, type, omega0Ax: $o).
% 0.21/0.27 thf(decl_36, type, omegaSAx: $o).
% 0.21/0.27 thf(decl_37, type, omegaIndAx: $o).
% 0.21/0.27 thf(decl_38, type, replAx: $o).
% 0.21/0.27 thf(decl_39, type, foundationAx: $o).
% 0.21/0.27 thf(decl_40, type, wellorderingAx: $o).
% 0.21/0.27 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.21/0.27 thf(decl_42, type, descrp: $o).
% 0.21/0.27 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.21/0.27 thf(decl_44, type, dsetconstrI: $o).
% 0.21/0.27 thf(decl_45, type, dsetconstrEL: $o).
% 0.21/0.27 thf(decl_46, type, dsetconstrER: $o).
% 0.21/0.27 thf(decl_47, type, exuE1: $o).
% 0.21/0.27 thf(decl_48, type, prop2set: $o > $i).
% 0.21/0.27 thf(decl_49, type, prop2setE: $o).
% 0.21/0.27 thf(decl_50, type, emptysetE: $o).
% 0.21/0.27 thf(decl_51, type, emptysetimpfalse: $o).
% 0.21/0.27 thf(decl_52, type, notinemptyset: $o).
% 0.21/0.27 thf(decl_53, type, exuE3e: $o).
% 0.21/0.27 thf(decl_54, type, setext: $o).
% 0.21/0.27 thf(decl_55, type, emptyI: $o).
% 0.21/0.27 thf(decl_56, type, noeltsimpempty: $o).
% 0.21/0.27 thf(decl_57, type, setbeta: $o).
% 0.21/0.27 thf(decl_58, type, nonempty: $i > $o).
% 0.21/0.27 thf(decl_59, type, nonemptyE1: $o).
% 0.21/0.27 thf(decl_60, type, nonemptyI: $o).
% 0.21/0.27 thf(decl_61, type, nonemptyI1: $o).
% 0.21/0.27 thf(decl_62, type, setadjoinIL: $o).
% 0.21/0.27 thf(decl_63, type, emptyinunitempty: $o).
% 0.21/0.27 thf(decl_64, type, setadjoinIR: $o).
% 0.21/0.27 thf(decl_65, type, setadjoinE: $o).
% 0.21/0.27 thf(decl_66, type, setadjoinOr: $o).
% 0.21/0.27 thf(decl_67, type, setoftrueEq: $o).
% 0.21/0.27 thf(decl_68, type, powersetI: $o).
% 0.21/0.27 thf(decl_69, type, emptyinPowerset: $o).
% 0.21/0.27 thf(decl_70, type, emptyInPowerset: $o).
% 0.21/0.27 thf(decl_71, type, powersetE: $o).
% 0.21/0.27 thf(decl_72, type, setunionI: $o).
% 0.21/0.27 thf(decl_73, type, epred1_0: $o).
% 0.21/0.27 thf(decl_74, type, esk1_2: $i > $i > $i).
% 0.21/0.27 thf(decl_75, type, esk2_2: $i > $i > $i).
% 0.21/0.27 thf(decl_76, type, esk3_2: $i > $i > $i).
% 0.21/0.27 thf(decl_77, type, esk4_1: $i > $i).
% 0.21/0.27 thf(decl_78, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.21/0.27 thf(decl_79, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.21/0.27 thf(decl_80, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.21/0.27 thf(decl_81, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.21/0.27 thf(decl_82, type, esk9_1: $i > $i).
% 0.21/0.27 thf(decl_83, type, esk10_2: ($i > $o) > $i > $i).
% 0.21/0.27 thf(decl_84, type, esk11_2: ($i > $o) > $i > $i).
% 0.21/0.27 thf(decl_85, type, esk12_1: ($i > $o) > $i).
% 0.21/0.27 thf(decl_86, type, esk13_2: ($i > $o) > $i > $i).
% 0.21/0.27 thf(decl_87, type, esk14_1: ($i > $o) > $i).
% 0.21/0.27 thf(decl_88, type, esk15_2: $i > $i > $i).
% 0.21/0.27 thf(decl_89, type, esk16_2: $i > $i > $i).
% 0.21/0.27 thf(decl_90, type, esk17_1: $i > $i).
% 0.21/0.27 thf(decl_91, type, esk18_1: $i > $i).
% 0.21/0.27 thf(decl_92, type, esk19_1: $i > $i).
% 0.21/0.27 thf(decl_93, type, esk20_2: $i > $i > $i).
% 0.21/0.27 thf(decl_94, type, esk21_0: $i).
% 0.21/0.27 thf(decl_95, type, esk22_0: $i).
% 0.21/0.27 thf(decl_96, type, epred2_0: $o).
% 0.21/0.27 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p', replAx)).
% 0.21/0.27 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p', exu)).
% 0.21/0.27 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p', descrp)).
% 0.21/0.27 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p', exuE1)).
% 0.21/0.27 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p', exuE3e)).
% 0.21/0.27 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p', nonempty)).
% 0.21/0.27 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p', nonemptyI)).
% 0.21/0.27 thf(setunionE, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X14:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X14))))=>(X14)))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p', setunionE)).
% 0.21/0.27 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p', dsetconstrI)).
% 0.21/0.27 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p', dsetconstrEL)).
% 0.21/0.27 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p', dsetconstrER)).
% 0.21/0.27 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p', setbeta)).
% 0.21/0.27 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p', nonemptyE1)).
% 0.21/0.27 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p', nonemptyI1)).
% 0.21/0.27 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p', setoftrueEq)).
% 0.21/0.27 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p', setextAx)).
% 0.21/0.27 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p', emptysetAx)).
% 0.21/0.27 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p', setadjoinAx)).
% 0.21/0.27 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p', powersetAx)).
% 0.21/0.27 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p', setunionAx)).
% 0.21/0.27 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p', omega0Ax)).
% 0.21/0.27 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p', omegaSAx)).
% 0.21/0.27 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p', omegaIndAx)).
% 0.21/0.27 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p', foundationAx)).
% 0.21/0.27 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p', wellorderingAx)).
% 0.21/0.27 thf(prop2setE, axiom, ((prop2setE)<=>![X11:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X11))))=>(X11)))), file('/export/starexec/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p', prop2setE)).
% 0.21/0.27 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X12:$o]:((X12))))), file('/export/starexec/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p', emptysetE)).
% 0.21/0.27 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p', emptysetimpfalse)).
% 0.21/0.27 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p', notinemptyset)).
% 0.21/0.27 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p', setext)).
% 0.21/0.27 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p', emptyI)).
% 0.21/0.27 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p', noeltsimpempty)).
% 0.21/0.27 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p', setadjoinIL)).
% 0.21/0.27 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p', emptyinunitempty)).
% 0.21/0.27 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p', setadjoinIR)).
% 0.21/0.27 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/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p', setadjoinE)).
% 0.21/0.27 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p', setadjoinOr)).
% 0.21/0.27 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p', powersetI)).
% 0.21/0.27 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p', emptyinPowerset)).
% 0.21/0.27 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p', emptyInPowerset)).
% 0.21/0.27 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p', powersetE)).
% 0.21/0.27 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.gy1mavG0wC/E---3.1_96209.p', setunionI)).
% 0.21/0.27 thf(c_0_42, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.21/0.27 thf(c_0_43, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.21/0.27 thf(c_0_44, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.21/0.27 thf(c_0_45, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.21/0.27 thf(c_0_46, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.21/0.27 thf(c_0_47, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.21/0.27 thf(c_0_48, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.21/0.27 thf(c_0_49, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X14:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X14))))=>(X14))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[setunionE])).
% 0.21/0.27 thf(c_0_50, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X128:$i]:(((((X6 @ X2 @ X128)))&(![X129:$i]:(((((X6 @ X2 @ X129)))=>(((X128)=(X129)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_42, c_0_43])).
% 0.21/0.27 thf(c_0_51, plain, ((descrp)=(![X1:$i > $o]:((((?[X130:$i]:(((((X1 @ X130)))&(![X131:$i]:(((((X1 @ X131)))=>(((X130)=(X131))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_44, c_0_43])).
% 0.21/0.27 thf(c_0_52, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.21/0.27 thf(c_0_53, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.21/0.27 thf(c_0_54, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.21/0.27 thf(c_0_55, plain, ((exuE1)=(![X1:$i > $o]:((((?[X132:$i]:(((((X1 @ X132)))&(![X133:$i]:(((((X1 @ X133)))=>(((X132)=(X133))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_45, c_0_43])).
% 0.21/0.27 thf(c_0_56, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X134:$i]:(((((X1 @ X134)))&(![X135:$i]:(((((X1 @ X135)))=>(((X134)=(X135))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_46, c_0_43])).
% 0.21/0.27 thf(c_0_57, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.21/0.27 thf(c_0_58, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_47])).
% 0.21/0.27 thf(c_0_59, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_48, c_0_47])).
% 0.21/0.27 thf(c_0_60, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_47])).
% 0.21/0.27 thf(c_0_61, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.21/0.27 thf(c_0_62, plain, ((epred1_0)<=>![X165:$i]:(?[X166:$i]:((((![X167:$i]:(((in @ X167 @ X166)=>![X168:$i]:(((in @ X168 @ X167)=>(in @ X168 @ X165)))))&![X169:$i, X170:$i]:((((in @ X169 @ X165)&(in @ X170 @ X165))=>(![X171:$i]:(((in @ X171 @ X166)=>((in @ X169 @ X171)<=>(in @ X170 @ X171))))=>((X169)=(X170))))))&![X172:$i, X173:$i]:((((in @ X172 @ X166)&(in @ X173 @ X166))=>(![X174:$i]:(((in @ X174 @ X172)=>(in @ X174 @ X173)))|![X175:$i]:(((in @ X175 @ X173)=>(in @ X175 @ X172)))))))&![X176:$i]:(((![X177:$i]:(((in @ X177 @ X176)=>(in @ X177 @ X165)))&?[X178:$i]:((in @ X178 @ X176)))=>?[X179:$i, X180:$i]:(((((in @ X179 @ X166)&(in @ X180 @ X176))&~(?[X181:$i]:(((in @ X181 @ X179)&(in @ X181 @ X176)))))&![X182:$i]:(((in @ X182 @ X166)=>(![X183:$i]:(((in @ X183 @ X182)=>(in @ X183 @ X179)))|(in @ X180 @ X182)))))))))))), introduced(definition)).
% 0.21/0.27 thf(c_0_63, negated_conjecture, ~((![X136:$i, X137:$i]:((![X138:$i]:(((in @ X138 @ X136)<=>(in @ X138 @ X137)))=>((X136)=(X137))))=>(![X139:$i]:(~(in @ X139 @ emptyset))=>(![X140:$i, X141:$i, X142:$i]:(((in @ X142 @ (setadjoin @ X140 @ X141))<=>(((X142)=(X140))|(in @ X142 @ X141))))=>(![X143:$i, X144:$i]:(((in @ X144 @ (powerset @ X143))<=>![X145:$i]:(((in @ X145 @ X144)=>(in @ X145 @ X143)))))=>(![X146:$i, X147:$i]:(((in @ X147 @ (setunion @ X146))<=>?[X148:$i]:(((in @ X147 @ X148)&(in @ X148 @ X146)))))=>((in @ emptyset @ omega)=>(![X149:$i]:(((in @ X149 @ omega)=>(in @ (setadjoin @ X149 @ X149) @ omega)))=>(![X150:$i]:((((in @ emptyset @ X150)&![X151:$i]:((((in @ X151 @ omega)&(in @ X151 @ X150))=>(in @ (setadjoin @ X151 @ X151) @ X150))))=>![X152:$i]:(((in @ X152 @ omega)=>(in @ X152 @ X150)))))=>(![X153:$i > $i > $o, X154:$i]:((![X155:$i]:(((in @ X155 @ X154)=>?[X156:$i]:(((X153 @ X155 @ X156)&![X157:$i]:(((X153 @ X155 @ X157)=>((X156)=(X157))))))))=>?[X158:$i]:(![X159:$i]:(((in @ X159 @ X158)<=>?[X160:$i]:(((in @ X160 @ X154)&(X153 @ X160 @ X159))))))))=>(![X161:$i]:((?[X162:$i]:((in @ X162 @ X161))=>?[X163:$i]:(((in @ X163 @ X161)&~(?[X164:$i]:(((in @ X164 @ X163)&(in @ X164 @ X161))))))))=>((epred1_0)=>(![X184:$i > $o]:((?[X185:$i]:(((X184 @ X185)&![X186:$i]:(((X184 @ X186)=>((X185)=(X186))))))=>(X184 @ (descr @ (^[Z0:$i]:(X184 @ Z0))))))=>(![X187:$i, X188:$i > $o, X189:$i]:(((in @ X189 @ X187)=>((X188 @ X189)=>(in @ X189 @ (dsetconstr @ X187 @ X188)))))=>(![X190:$i, X191:$i > $o, X192:$i]:(((in @ X192 @ (dsetconstr @ X190 @ X191))=>(in @ X192 @ X190)))=>(![X193:$i, X194:$i > $o, X195:$i]:(((in @ X195 @ (dsetconstr @ X193 @ X194))=>(X194 @ X195)))=>(![X196:$i > $o]:((?[X197:$i]:(((X196 @ X197)&![X198:$i]:(((X196 @ X198)=>((X197)=(X198))))))=>?[X199:$i]:(((X196 @ X199)&![X200:$i]:(((X196 @ X200)=>((X199)=(X200))))))))=>(![X201:$o, X202:$i]:(((in @ X202 @ (prop2set @ ((X201))))=>(X201)))=>(![X203:$i]:(((in @ X203 @ emptyset)=>![X204:$o]:((X204))))=>(![X205:$i]:(((in @ X205 @ emptyset)=>~($true)))=>(![X206:$i]:(~(in @ X206 @ emptyset))=>(![X207:$i > $o]:((?[X208:$i]:(((X207 @ X208)&![X209:$i]:(((X207 @ X209)=>((X208)=(X209))))))=>?[X210:$i]:((X207 @ X210))))=>(![X211:$i, X212:$i]:((![X213:$i]:(((in @ X213 @ X211)=>(in @ X213 @ X212)))=>(![X214:$i]:(((in @ X214 @ X212)=>(in @ X214 @ X211)))=>((X211)=(X212)))))=>(![X215:$i]:((![X216:$i]:(~(in @ X216 @ X215))=>((X215)=(emptyset))))=>(![X217:$i]:((![X218:$i]:(~(in @ X218 @ X217))=>((X217)=(emptyset))))=>(![X219:$i, X220:$i > $o, X221:$i]:(((in @ X221 @ X219)=>((in @ X221 @ (dsetconstr @ X219 @ X220))<=>(X220 @ X221))))=>(![X222:$i]:((((X222)!=(emptyset))=>?[X223:$i]:((in @ X223 @ X222))))=>(![X224:$i, X225:$i > $o, X226:$i]:(((in @ X226 @ X224)=>((X225 @ X226)=>((dsetconstr @ X224 @ X225)!=(emptyset)))))=>(![X227:$i]:((?[X228:$i]:((in @ X228 @ X227))=>((X227)!=(emptyset))))=>(![X229:$i, X230:$i]:((in @ X229 @ (setadjoin @ X229 @ X230)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X231:$i, X232:$i, X233:$i]:(((in @ X233 @ X232)=>(in @ X233 @ (setadjoin @ X231 @ X232))))=>(![X234:$i, X235:$i, X236:$i]:(((in @ X236 @ (setadjoin @ X234 @ X235))=>![X237:$o]:(((((X236)=(X234))=>(X237))=>(((in @ X236 @ X235)=>(X237))=>(X237))))))=>(![X238:$i, X239:$i, X240:$i]:(((in @ X240 @ (setadjoin @ X238 @ X239))=>(((X240)=(X238))|(in @ X240 @ X239))))=>(![X241:$i]:(((dsetconstr @ X241 @ (^[Z0:$i]:($true)))=(X241)))=>(![X242:$i, X243:$i]:((![X244:$i]:(((in @ X244 @ X243)=>(in @ X244 @ X242)))=>(in @ X243 @ (powerset @ X242))))=>(![X245:$i]:((in @ emptyset @ (powerset @ X245)))=>(![X246:$i]:((in @ emptyset @ (powerset @ X246)))=>(![X247:$i, X248:$i, X249:$i]:(((in @ X248 @ (powerset @ X247))=>((in @ X249 @ X248)=>(in @ X249 @ X247))))=>(![X250:$i, X251:$i, X252:$i]:(((in @ X251 @ X252)=>((in @ X252 @ X250)=>(in @ X251 @ (setunion @ X250)))))=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X14:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X14))))=>(X14))))))))))))))))))))))))))))))))))))))))))))), 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)],[c_0_49, setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_50]), foundationAx]), wellorderingAx]), c_0_51]), c_0_52]), c_0_53]), c_0_54]), c_0_55]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_56]), setext]), emptyI]), noeltsimpempty]), c_0_57]), c_0_58]), c_0_59]), c_0_60]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_61]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI])])]), c_0_62])).
% 0.21/0.27 thf(c_0_64, negated_conjecture, ![X255:$i, X256:$i, X258:$i, X259:$i, X260:$i, X261:$i, X262:$i, X263:$i, X264:$i, X265:$i, X266:$i, X268:$i, X269:$i, X271:$i, X272:$i, X273:$i, X274:$i, X275:$i, X277:$i, X278:$i > $i > $o, X279:$i, X281:$i, X284:$i, X286:$i, X287:$i, X288:$i, X289:$i, X291:$i, X292:$i > $o, X293:$i, X295:$i, X296:$i > $o, X297:$i, X298:$i, X299:$i > $o, X300:$i, X301:$i, X302:$i > $o, X303:$i, X304:$i > $o, X305:$i, X308:$i, X309:$o, X310:$i, X311:$i, X312:$o, X313:$i, X314:$i, X315:$i > $o, X316:$i, X319:$i, X320:$i, X323:$i, X325:$i, X327:$i, X328:$i > $o, X329:$i, X330:$i, X332:$i, X333:$i > $o, X334:$i, X335:$i, X336:$i, X337:$i, X338:$i, X339:$i, X340:$i, X341:$i, X342:$i, X343:$i, X344:$i, X345:$o, X346:$i, X347:$i, X348:$i, X349:$i, X350:$i, X351:$i, X353:$i, X354:$i, X355:$i, X356:$i, X357:$i, X358:$i, X359:$i, X360:$i, X364:$i]:((((~(in @ (esk1_2 @ X255 @ X256) @ X255)|~(in @ (esk1_2 @ X255 @ X256) @ X256)|((X255)=(X256)))&((in @ (esk1_2 @ X255 @ X256) @ X255)|(in @ (esk1_2 @ X255 @ X256) @ X256)|((X255)=(X256))))&(~(in @ X258 @ emptyset)&(((~(in @ X261 @ (setadjoin @ X259 @ X260))|(((X261)=(X259))|(in @ X261 @ X260)))&((((X261)!=(X259))|(in @ X261 @ (setadjoin @ X259 @ X260)))&(~(in @ X261 @ X260)|(in @ X261 @ (setadjoin @ X259 @ X260)))))&(((~(in @ X263 @ (powerset @ X262))|(~(in @ X264 @ X263)|(in @ X264 @ X262)))&(((in @ (esk2_2 @ X265 @ X266) @ X266)|(in @ X266 @ (powerset @ X265)))&(~(in @ (esk2_2 @ X265 @ X266) @ X265)|(in @ X266 @ (powerset @ X265)))))&(((((in @ X269 @ (esk3_2 @ X268 @ X269))|~(in @ X269 @ (setunion @ X268)))&((in @ (esk3_2 @ X268 @ X269) @ X268)|~(in @ X269 @ (setunion @ X268))))&(~(in @ X272 @ X273)|~(in @ X273 @ X271)|(in @ X272 @ (setunion @ X271))))&((in @ emptyset @ omega)&((~(in @ X274 @ omega)|(in @ (setadjoin @ X274 @ X274) @ omega))&(((((in @ (esk4_1 @ X275) @ omega)|~(in @ emptyset @ X275)|(~(in @ X277 @ omega)|(in @ X277 @ X275)))&((in @ (esk4_1 @ X275) @ X275)|~(in @ emptyset @ X275)|(~(in @ X277 @ omega)|(in @ X277 @ X275))))&(~(in @ (setadjoin @ (esk4_1 @ X275) @ (esk4_1 @ X275)) @ X275)|~(in @ emptyset @ X275)|(~(in @ X277 @ omega)|(in @ X277 @ X275))))&((((((in @ (esk8_3 @ X278 @ X279 @ X284) @ X279)|~(in @ X284 @ (esk7_2 @ X278 @ X279))|(in @ (esk5_2 @ X278 @ X279) @ X279))&((X278 @ (esk8_3 @ X278 @ X279 @ X284) @ X284)|~(in @ X284 @ (esk7_2 @ X278 @ X279))|(in @ (esk5_2 @ X278 @ X279) @ X279)))&(~(in @ X287 @ X279)|~(X278 @ X287 @ X286)|(in @ X286 @ (esk7_2 @ X278 @ X279))|(in @ (esk5_2 @ X278 @ X279) @ X279)))&(((((in @ (esk8_3 @ X278 @ X279 @ X284) @ X279)|~(in @ X284 @ (esk7_2 @ X278 @ X279))|((X278 @ (esk5_2 @ X278 @ X279) @ (esk6_3 @ X278 @ X279 @ X281))|~(X278 @ (esk5_2 @ X278 @ X279) @ X281)))&((X278 @ (esk8_3 @ X278 @ X279 @ X284) @ X284)|~(in @ X284 @ (esk7_2 @ X278 @ X279))|((X278 @ (esk5_2 @ X278 @ X279) @ (esk6_3 @ X278 @ X279 @ X281))|~(X278 @ (esk5_2 @ X278 @ X279) @ X281))))&(~(in @ X287 @ X279)|~(X278 @ X287 @ X286)|(in @ X286 @ (esk7_2 @ X278 @ X279))|((X278 @ (esk5_2 @ X278 @ X279) @ (esk6_3 @ X278 @ X279 @ X281))|~(X278 @ (esk5_2 @ X278 @ X279) @ X281))))&((((in @ (esk8_3 @ X278 @ X279 @ X284) @ X279)|~(in @ X284 @ (esk7_2 @ X278 @ X279))|(((X281)!=(esk6_3 @ X278 @ X279 @ X281))|~(X278 @ (esk5_2 @ X278 @ X279) @ X281)))&((X278 @ (esk8_3 @ X278 @ X279 @ X284) @ X284)|~(in @ X284 @ (esk7_2 @ X278 @ X279))|(((X281)!=(esk6_3 @ X278 @ X279 @ X281))|~(X278 @ (esk5_2 @ X278 @ X279) @ X281))))&(~(in @ X287 @ X279)|~(X278 @ X287 @ X286)|(in @ X286 @ (esk7_2 @ X278 @ X279))|(((X281)!=(esk6_3 @ X278 @ X279 @ X281))|~(X278 @ (esk5_2 @ X278 @ X279) @ X281))))))&((((in @ (esk9_1 @ X288) @ X288)|~(in @ X289 @ X288))&(~(in @ X291 @ (esk9_1 @ X288))|~(in @ X291 @ X288)|~(in @ X289 @ X288)))&((epred1_0)&((((X292 @ (esk10_2 @ X292 @ X293))|~(X292 @ X293)|(X292 @ (descr @ X292)))&(((X293)!=(esk10_2 @ X292 @ X293))|~(X292 @ X293)|(X292 @ (descr @ X292))))&((~(in @ X297 @ X295)|(~(X296 @ X297)|(in @ X297 @ (dsetconstr @ X295 @ X296))))&((~(in @ X300 @ (dsetconstr @ X298 @ X299))|(in @ X300 @ X298))&((~(in @ X303 @ (dsetconstr @ X301 @ X302))|(X302 @ X303))&(((((X304 @ (esk12_1 @ X304))|((X304 @ (esk11_2 @ X304 @ X305))|~(X304 @ X305)))&(~(X304 @ X308)|((esk12_1 @ X304)=(X308))|((X304 @ (esk11_2 @ X304 @ X305))|~(X304 @ X305))))&(((X304 @ (esk12_1 @ X304))|(((X305)!=(esk11_2 @ X304 @ X305))|~(X304 @ X305)))&(~(X304 @ X308)|((esk12_1 @ X304)=(X308))|(((X305)!=(esk11_2 @ X304 @ X305))|~(X304 @ X305)))))&((~(in @ X310 @ (prop2set @ ((X309))))|(X309))&((~(in @ X311 @ emptyset)|(X312))&((~(in @ X313 @ emptyset)|~($true))&(~(in @ X314 @ emptyset)&((((X315 @ (esk13_2 @ X315 @ X316))|~(X315 @ X316)|(X315 @ (esk14_1 @ X315)))&(((X316)!=(esk13_2 @ X315 @ X316))|~(X315 @ X316)|(X315 @ (esk14_1 @ X315))))&(((((in @ (esk16_2 @ X319 @ X320) @ X320)|((X319)=(X320))|(in @ (esk15_2 @ X319 @ X320) @ X319))&(~(in @ (esk16_2 @ X319 @ X320) @ X319)|((X319)=(X320))|(in @ (esk15_2 @ X319 @ X320) @ X319)))&(((in @ (esk16_2 @ X319 @ X320) @ X320)|((X319)=(X320))|~(in @ (esk15_2 @ X319 @ X320) @ X320))&(~(in @ (esk16_2 @ X319 @ X320) @ X319)|((X319)=(X320))|~(in @ (esk15_2 @ X319 @ X320) @ X320))))&(((in @ (esk17_1 @ X323) @ X323)|((X323)=(emptyset)))&(((in @ (esk18_1 @ X325) @ X325)|((X325)=(emptyset)))&(((~(in @ X329 @ (dsetconstr @ X327 @ X328))|(X328 @ X329)|~(in @ X329 @ X327))&(~(X328 @ X329)|(in @ X329 @ (dsetconstr @ X327 @ X328))|~(in @ X329 @ X327)))&((((X330)=(emptyset))|(in @ (esk19_1 @ X330) @ X330))&((~(in @ X334 @ X332)|(~(X333 @ X334)|((dsetconstr @ X332 @ X333)!=(emptyset))))&((~(in @ X336 @ X335)|((X335)!=(emptyset)))&((in @ X337 @ (setadjoin @ X337 @ X338))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X341 @ X340)|(in @ X341 @ (setadjoin @ X339 @ X340)))&(((((in @ X344 @ X343)|(X345)|((X344)=(X342))|~(in @ X344 @ (setadjoin @ X342 @ X343)))&(~(X345)|(X345)|((X344)=(X342))|~(in @ X344 @ (setadjoin @ X342 @ X343))))&(((in @ X344 @ X343)|(X345)|~(X345)|~(in @ X344 @ (setadjoin @ X342 @ X343)))&(~(X345)|(X345)|~(X345)|~(in @ X344 @ (setadjoin @ X342 @ X343)))))&((~(in @ X348 @ (setadjoin @ X346 @ X347))|(((X348)=(X346))|(in @ X348 @ X347)))&(((dsetconstr @ X349 @ (^[Z0:$i]:($true)))=(X349))&((((in @ (esk20_2 @ X350 @ X351) @ X351)|(in @ X351 @ (powerset @ X350)))&(~(in @ (esk20_2 @ X350 @ X351) @ X350)|(in @ X351 @ (powerset @ X350))))&((in @ emptyset @ (powerset @ X353))&((in @ emptyset @ (powerset @ X354))&((~(in @ X356 @ (powerset @ X355))|(~(in @ X357 @ X356)|(in @ X357 @ X355)))&((~(in @ X359 @ X360)|(~(in @ X360 @ X358)|(in @ X359 @ (setunion @ X358))))&((in @ esk22_0 @ (setunion @ esk21_0))&((~(in @ esk22_0 @ X364)|(~(in @ X364 @ esk21_0)|(epred2_0)))&~(epred2_0))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_63])])])])])])])).
% 0.21/0.27 thf(c_0_65, negated_conjecture, ![X2:$i]:(((epred2_0)|~((in @ esk22_0 @ X2))|~((in @ X2 @ esk21_0)))), inference(split_conjunct,[status(thm)],[c_0_64])).
% 0.21/0.27 thf(c_0_66, negated_conjecture, ~((epred2_0)), inference(split_conjunct,[status(thm)],[c_0_64])).
% 0.21/0.27 thf(c_0_67, negated_conjecture, ![X2:$i]:((~((in @ X2 @ esk21_0))|~((in @ esk22_0 @ X2)))), inference(sr,[status(thm)],[c_0_65, c_0_66])).
% 0.21/0.27 thf(c_0_68, negated_conjecture, ![X3:$i, X2:$i]:(((in @ (esk3_2 @ X2 @ X3) @ X2)|~((in @ X3 @ (setunion @ X2))))), inference(split_conjunct,[status(thm)],[c_0_64])).
% 0.21/0.27 thf(c_0_69, negated_conjecture, ![X2:$i]:((~((in @ esk22_0 @ (esk3_2 @ esk21_0 @ X2)))|~((in @ X2 @ (setunion @ esk21_0))))), inference(spm,[status(thm)],[c_0_67, c_0_68])).
% 0.21/0.27 thf(c_0_70, negated_conjecture, ![X2:$i, X3:$i]:(((in @ X2 @ (esk3_2 @ X3 @ X2))|~((in @ X2 @ (setunion @ X3))))), inference(split_conjunct,[status(thm)],[c_0_64])).
% 0.21/0.27 thf(c_0_71, negated_conjecture, (in @ esk22_0 @ (setunion @ esk21_0)), inference(split_conjunct,[status(thm)],[c_0_64])).
% 0.21/0.27 thf(c_0_72, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69, c_0_70]), c_0_71])]), ['proof']).
% 0.21/0.27 % SZS output end CNFRefutation
% 0.21/0.27 % Parsed axioms : 93
% 0.21/0.27 % Removed by relevancy pruning/SinE : 0
% 0.21/0.27 % Initial clauses : 139
% 0.21/0.27 % Removed in clause preprocessing : 53
% 0.21/0.27 % Initial clauses in saturation : 86
% 0.21/0.27 % Processed clauses : 98
% 0.21/0.27 % ...of these trivial : 2
% 0.21/0.27 % ...subsumed : 26
% 0.21/0.27 % ...remaining for further processing : 70
% 0.21/0.27 % Other redundant clauses eliminated : 2
% 0.21/0.27 % Clauses deleted for lack of memory : 0
% 0.21/0.27 % Backward-subsumed : 2
% 0.21/0.27 % Backward-rewritten : 3
% 0.21/0.27 % Generated clauses : 184
% 0.21/0.27 % ...of the previous two non-redundant : 156
% 0.21/0.27 % ...aggressively subsumed : 0
% 0.21/0.27 % Contextual simplify-reflections : 0
% 0.21/0.27 % Paramodulations : 182
% 0.21/0.27 % Factorizations : 0
% 0.21/0.27 % NegExts : 0
% 0.21/0.27 % Equation resolutions : 2
% 0.21/0.27 % Disequality decompositions : 0
% 0.21/0.27 % Total rewrite steps : 33
% 0.21/0.27 % ...of those cached : 16
% 0.21/0.27 % Propositional unsat checks : 0
% 0.21/0.27 % Propositional check models : 0
% 0.21/0.27 % Propositional check unsatisfiable : 0
% 0.21/0.27 % Propositional clauses : 0
% 0.21/0.27 % Propositional clauses after purity: 0
% 0.21/0.27 % Propositional unsat core size : 0
% 0.21/0.27 % Propositional preprocessing time : 0.000
% 0.21/0.27 % Propositional encoding time : 0.000
% 0.21/0.27 % Propositional solver time : 0.000
% 0.21/0.27 % Success case prop preproc time : 0.000
% 0.21/0.27 % Success case prop encoding time : 0.000
% 0.21/0.27 % Success case prop solver time : 0.000
% 0.21/0.27 % Current number of processed clauses : 63
% 0.21/0.27 % Positive orientable unit clauses : 17
% 0.21/0.27 % Positive unorientable unit clauses: 0
% 0.21/0.27 % Negative unit clauses : 4
% 0.21/0.27 % Non-unit-clauses : 42
% 0.21/0.27 % Current number of unprocessed clauses: 137
% 0.21/0.27 % ...number of literals in the above : 386
% 0.21/0.27 % Current number of archived formulas : 0
% 0.21/0.27 % Current number of archived clauses : 5
% 0.21/0.27 % Clause-clause subsumption calls (NU) : 262
% 0.21/0.27 % Rec. Clause-clause subsumption calls : 241
% 0.21/0.27 % Non-unit clause-clause subsumptions : 11
% 0.21/0.27 % Unit Clause-clause subsumption calls : 27
% 0.21/0.27 % Rewrite failures with RHS unbound : 0
% 0.21/0.27 % BW rewrite match attempts : 8
% 0.21/0.27 % BW rewrite match successes : 3
% 0.21/0.27 % Condensation attempts : 0
% 0.21/0.27 % Condensation successes : 0
% 0.21/0.27 % Termbank termtop insertions : 13459
% 0.21/0.27 % Search garbage collected termcells : 4250
% 0.21/0.27
% 0.21/0.27 % -------------------------------------------------
% 0.21/0.27 % User time : 0.013 s
% 0.21/0.27 % System time : 0.008 s
% 0.21/0.27 % Total time : 0.021 s
% 0.21/0.27 % Maximum resident set size: 4496 pages
% 0.21/0.27
% 0.21/0.27 % -------------------------------------------------
% 0.21/0.27 % User time : 0.053 s
% 0.21/0.27 % System time : 0.020 s
% 0.21/0.28 % Total time : 0.072 s
% 0.21/0.28 % Maximum resident set size: 4864 pages
% 0.21/0.28 % E exiting
%------------------------------------------------------------------------------