%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU514^1 : 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 : n014.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 08:24:19 AM UTC 2026
% Result : Theorem 0.08s 0.27s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU514^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n014.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 13:47:15 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 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.VEGEQz3UX7/E---3.1_2684968.p
% 0.08/0.27 % Version: 3.5.1-ho
% 0.08/0.27 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.08/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.27 % Starting sh5l with 300s (1) cores
% 0.08/0.27 % Starting new_bool_1 with 300s (1) cores
% 0.08/0.27 % Starting new_bool_2 with 300s (1) cores
% 0.08/0.27 % new_bool_2 with pid 2684984 completed with status 0
% 0.08/0.27 % Result found by new_bool_2
% 0.08/0.27 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.08/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.27 % Starting sh5l with 300s (1) cores
% 0.08/0.27 % Starting new_bool_1 with 300s (1) cores
% 0.08/0.27 % Starting new_bool_2 with 300s (1) cores
% 0.08/0.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.08/0.27 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.08/0.27 % Search class: HGHSF-FFMM31-SHFSMSBN
% 0.08/0.27 % partial match(2): HGHSM-FFMS31-SHFSMSBN
% 0.08/0.27 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.27 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.27 % SubtermCWHack with pid 2684985 completed with status 0
% 0.08/0.27 % Result found by SubtermCWHack
% 0.08/0.27 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.08/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.27 % Starting sh5l with 300s (1) cores
% 0.08/0.27 % Starting new_bool_1 with 300s (1) cores
% 0.08/0.27 % Starting new_bool_2 with 300s (1) cores
% 0.08/0.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.08/0.27 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.08/0.27 % Search class: HGHSF-FFMM31-SHFSMSBN
% 0.08/0.27 % partial match(2): HGHSM-FFMS31-SHFSMSBN
% 0.08/0.27 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.27 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.27 % Preprocessing time : 0.002 s
% 0.08/0.27
% 0.08/0.27 % Proof found!
% 0.08/0.27 % SZS status Theorem
% 0.08/0.27 % SZS output start CNFRefutation
% 0.08/0.27 thf(decl_23, type, in: $i > $i > $o).
% 0.08/0.27 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.08/0.27 thf(decl_25, type, setextAx: $o).
% 0.08/0.27 thf(decl_26, type, emptyset: $i).
% 0.08/0.27 thf(decl_27, type, emptysetAx: $o).
% 0.08/0.27 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.08/0.27 thf(decl_29, type, setadjoinAx: $o).
% 0.08/0.27 thf(decl_30, type, powerset: $i > $i).
% 0.08/0.27 thf(decl_31, type, powersetAx: $o).
% 0.08/0.27 thf(decl_33, type, setunionAx: $o).
% 0.08/0.27 thf(decl_34, type, omega: $i).
% 0.08/0.27 thf(decl_35, type, omega0Ax: $o).
% 0.08/0.27 thf(decl_36, type, omegaSAx: $o).
% 0.08/0.27 thf(decl_37, type, omegaIndAx: $o).
% 0.08/0.27 thf(decl_38, type, replAx: $o).
% 0.08/0.27 thf(decl_39, type, foundationAx: $o).
% 0.08/0.27 thf(decl_40, type, wellorderingAx: $o).
% 0.08/0.27 thf(decl_42, type, descrp: $o).
% 0.08/0.27 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.08/0.27 thf(decl_44, type, dsetconstrI: $o).
% 0.08/0.27 thf(decl_45, type, dsetconstrEL: $o).
% 0.08/0.27 thf(decl_46, type, dsetconstrER: $o).
% 0.08/0.27 thf(decl_47, type, exuE1: $o).
% 0.08/0.27 thf(decl_48, type, prop2set: $o > $i).
% 0.08/0.27 thf(decl_49, type, prop2setE: $o).
% 0.08/0.27 thf(decl_50, type, emptysetE: $o).
% 0.08/0.27 thf(decl_51, type, emptysetimpfalse: $o).
% 0.08/0.27 thf(decl_52, type, notinemptyset: $o).
% 0.08/0.27 thf(decl_53, type, exuE3e: $o).
% 0.08/0.27 thf(decl_54, type, setext: $o).
% 0.08/0.27 thf(decl_55, type, emptyI: $o).
% 0.08/0.27 thf(decl_56, type, noeltsimpempty: $o).
% 0.08/0.27 thf(decl_57, type, setbeta: $o).
% 0.08/0.27 thf(decl_58, type, nonempty: $i > $o).
% 0.08/0.27 thf(decl_59, type, nonemptyE1: $o).
% 0.08/0.27 thf(decl_60, type, nonemptyI: $o).
% 0.08/0.27 thf(decl_61, type, nonemptyI1: $o).
% 0.08/0.27 thf(decl_62, type, setadjoinIL: $o).
% 0.08/0.27 thf(decl_63, type, emptyinunitempty: $o).
% 0.08/0.27 thf(decl_64, type, epred1_0: $o).
% 0.08/0.27 thf(decl_65, type, esk1_2: $i > $i > $i).
% 0.08/0.27 thf(decl_66, type, esk2_2: $i > $i > $i).
% 0.08/0.27 thf(decl_67, type, esk3_1: $i > $i).
% 0.08/0.27 thf(decl_68, type, esk4_2: ($i > $i > $o) > $i > $i).
% 0.08/0.27 thf(decl_69, type, esk5_3: ($i > $i > $o) > $i > $i > $i).
% 0.08/0.27 thf(decl_70, type, esk6_2: ($i > $i > $o) > $i > $i).
% 0.08/0.27 thf(decl_71, type, esk7_3: ($i > $i > $o) > $i > $i > $i).
% 0.08/0.27 thf(decl_72, type, esk8_1: $i > $i).
% 0.08/0.27 thf(decl_73, type, esk9_2: ($i > $o) > $i > $i).
% 0.08/0.27 thf(decl_74, type, esk10_1: ($i > $o) > $i).
% 0.08/0.27 thf(decl_75, type, esk11_2: ($i > $o) > $i > $i).
% 0.08/0.27 thf(decl_76, type, esk12_1: ($i > $o) > $i).
% 0.08/0.27 thf(decl_77, type, esk13_2: $i > $i > $i).
% 0.08/0.27 thf(decl_78, type, esk14_2: $i > $i > $i).
% 0.08/0.27 thf(decl_79, type, esk15_1: $i > $i).
% 0.08/0.27 thf(decl_80, type, esk16_1: $i > $i).
% 0.08/0.27 thf(decl_81, type, esk17_1: $i > $i).
% 0.08/0.27 thf(decl_82, type, esk18_0: $i).
% 0.08/0.27 thf(decl_83, type, esk19_0: $i).
% 0.08/0.27 thf(decl_84, type, esk20_0: $i).
% 0.08/0.27 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.VEGEQz3UX7/E---3.1_2684968.p', exuE3e)).
% 0.08/0.27 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.VEGEQz3UX7/E---3.1_2684968.p', exu)).
% 0.08/0.27 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.VEGEQz3UX7/E---3.1_2684968.p', nonempty)).
% 0.08/0.27 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.VEGEQz3UX7/E---3.1_2684968.p', nonemptyI)).
% 0.08/0.27 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.VEGEQz3UX7/E---3.1_2684968.p', replAx)).
% 0.08/0.27 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.VEGEQz3UX7/E---3.1_2684968.p', exuE1)).
% 0.08/0.27 thf(prop2set, axiom, ((prop2set)=(^[X10:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[X2:$i]:((X10)))))), file('/export/starexec/sandbox2/tmp/tmp.VEGEQz3UX7/E---3.1_2684968.p', prop2set)).
% 0.08/0.27 thf(setadjoinIR, 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)=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4)))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.VEGEQz3UX7/E---3.1_2684968.p', setadjoinIR)).
% 0.08/0.27 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.VEGEQz3UX7/E---3.1_2684968.p', setbeta)).
% 0.08/0.27 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.VEGEQz3UX7/E---3.1_2684968.p', nonemptyE1)).
% 0.08/0.27 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.VEGEQz3UX7/E---3.1_2684968.p', nonemptyI1)).
% 0.08/0.27 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.VEGEQz3UX7/E---3.1_2684968.p', dsetconstrI)).
% 0.08/0.27 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.VEGEQz3UX7/E---3.1_2684968.p', dsetconstrER)).
% 0.08/0.27 thf(prop2setE, axiom, ((prop2setE)<=>![X11:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X11))))=>(X11)))), file('/export/starexec/sandbox2/tmp/tmp.VEGEQz3UX7/E---3.1_2684968.p', prop2setE)).
% 0.08/0.27 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.VEGEQz3UX7/E---3.1_2684968.p', dsetconstrEL)).
% 0.08/0.27 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.VEGEQz3UX7/E---3.1_2684968.p', emptysetimpfalse)).
% 0.08/0.27 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.VEGEQz3UX7/E---3.1_2684968.p', notinemptyset)).
% 0.08/0.27 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.VEGEQz3UX7/E---3.1_2684968.p', setext)).
% 0.08/0.27 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.VEGEQz3UX7/E---3.1_2684968.p', emptyI)).
% 0.08/0.27 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.VEGEQz3UX7/E---3.1_2684968.p', noeltsimpempty)).
% 0.08/0.27 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.VEGEQz3UX7/E---3.1_2684968.p', setadjoinIL)).
% 0.08/0.27 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.VEGEQz3UX7/E---3.1_2684968.p', emptyinunitempty)).
% 0.08/0.27 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.VEGEQz3UX7/E---3.1_2684968.p', setadjoinAx)).
% 0.08/0.27 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.VEGEQz3UX7/E---3.1_2684968.p', emptysetAx)).
% 0.08/0.27 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.VEGEQz3UX7/E---3.1_2684968.p', setextAx)).
% 0.08/0.27 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.VEGEQz3UX7/E---3.1_2684968.p', powersetAx)).
% 0.08/0.27 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.VEGEQz3UX7/E---3.1_2684968.p', wellorderingAx)).
% 0.08/0.27 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.VEGEQz3UX7/E---3.1_2684968.p', foundationAx)).
% 0.08/0.27 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.VEGEQz3UX7/E---3.1_2684968.p', omegaIndAx)).
% 0.08/0.27 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.VEGEQz3UX7/E---3.1_2684968.p', omegaSAx)).
% 0.08/0.27 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.VEGEQz3UX7/E---3.1_2684968.p', omega0Ax)).
% 0.08/0.27 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X12:$o]:((X12))))), file('/export/starexec/sandbox2/tmp/tmp.VEGEQz3UX7/E---3.1_2684968.p', emptysetE)).
% 0.08/0.27 thf(c_0_32, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.08/0.27 thf(c_0_33, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.08/0.27 thf(c_0_34, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.08/0.27 thf(c_0_35, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.08/0.27 thf(c_0_36, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.08/0.27 thf(c_0_37, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.08/0.27 thf(c_0_38, plain, ((prop2set)=(^[Z0:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[Z1:$i]:((Z0)))))), inference(fof_simplification,[status(thm)],[prop2set])).
% 0.08/0.27 thf(c_0_39, 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)=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[setadjoinIR])).
% 0.08/0.27 thf(c_0_40, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X103:$i]:(((((X1 @ X103)))&(![X104:$i]:(((((X1 @ X104)))=>(((X103)=(X104))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_32, c_0_33])).
% 0.08/0.27 thf(c_0_41, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.08/0.27 thf(c_0_42, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_34])).
% 0.08/0.27 thf(c_0_43, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_35, c_0_34])).
% 0.08/0.27 thf(c_0_44, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_34])).
% 0.08/0.27 thf(c_0_45, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.08/0.27 thf(c_0_46, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X99:$i]:(((((X6 @ X2 @ X99)))&(![X100:$i]:(((((X6 @ X2 @ X100)))=>(((X99)=(X100)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_36, c_0_33])).
% 0.08/0.27 thf(c_0_47, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.08/0.27 thf(c_0_48, plain, ((exuE1)=(![X1:$i > $o]:((((?[X101:$i]:(((((X1 @ X101)))&(![X102:$i]:(((((X1 @ X102)))=>(((X101)=(X102))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_37, c_0_33])).
% 0.08/0.27 thf(c_0_49, axiom, ((prop2setE)=(![X11:$o, X2:$i]:((((in @ X2 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:(((X11)))))))=>((X11)))))), inference(apply_def,[status(thm)],[prop2setE, c_0_38])).
% 0.08/0.27 thf(c_0_50, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.08/0.27 thf(c_0_51, plain, ((epred1_0)<=>![X131:$i]:(?[X132:$i]:((((![X133:$i]:(((in @ X133 @ X132)=>![X134:$i]:(((in @ X134 @ X133)=>(in @ X134 @ X131)))))&![X135:$i, X136:$i]:((((in @ X135 @ X131)&(in @ X136 @ X131))=>(![X137:$i]:(((in @ X137 @ X132)=>((in @ X135 @ X137)<=>(in @ X136 @ X137))))=>((X135)=(X136))))))&![X138:$i, X139:$i]:((((in @ X138 @ X132)&(in @ X139 @ X132))=>(![X140:$i]:(((in @ X140 @ X138)=>(in @ X140 @ X139)))|![X141:$i]:(((in @ X141 @ X139)=>(in @ X141 @ X138)))))))&![X142:$i]:(((![X143:$i]:(((in @ X143 @ X142)=>(in @ X143 @ X131)))&?[X144:$i]:((in @ X144 @ X142)))=>?[X145:$i, X146:$i]:(((((in @ X145 @ X132)&(in @ X146 @ X142))&~(?[X147:$i]:(((in @ X147 @ X145)&(in @ X147 @ X142)))))&![X148:$i]:(((in @ X148 @ X132)=>(![X149:$i]:(((in @ X149 @ X148)=>(in @ X149 @ X145)))|(in @ X146 @ X148)))))))))))), introduced(definition)).
% 0.08/0.27 thf(c_0_52, negated_conjecture, ~((![X105:$i, X106:$i]:((![X107:$i]:(((in @ X107 @ X105)<=>(in @ X107 @ X106)))=>((X105)=(X106))))=>(![X108:$i]:(~(in @ X108 @ emptyset))=>(![X109:$i, X110:$i, X111:$i]:(((in @ X111 @ (setadjoin @ X109 @ X110))<=>(((X111)=(X109))|(in @ X111 @ X110))))=>(![X112:$i, X113:$i]:(((in @ X113 @ (powerset @ X112))<=>![X114:$i]:(((in @ X114 @ X113)=>(in @ X114 @ X112)))))=>((setunionAx)=>((in @ emptyset @ omega)=>(![X115:$i]:(((in @ X115 @ omega)=>(in @ (setadjoin @ X115 @ X115) @ omega)))=>(![X116:$i]:((((in @ emptyset @ X116)&![X117:$i]:((((in @ X117 @ omega)&(in @ X117 @ X116))=>(in @ (setadjoin @ X117 @ X117) @ X116))))=>![X118:$i]:(((in @ X118 @ omega)=>(in @ X118 @ X116)))))=>(![X119:$i > $i > $o, X120:$i]:((![X121:$i]:(((in @ X121 @ X120)=>?[X122:$i]:(((X119 @ X121 @ X122)&![X123:$i]:(((X119 @ X121 @ X123)=>((X122)=(X123))))))))=>?[X124:$i]:(![X125:$i]:(((in @ X125 @ X124)<=>?[X126:$i]:(((in @ X126 @ X120)&(X119 @ X126 @ X125))))))))=>(![X127:$i]:((?[X128:$i]:((in @ X128 @ X127))=>?[X129:$i]:(((in @ X129 @ X127)&~(?[X130:$i]:(((in @ X130 @ X129)&(in @ X130 @ X127))))))))=>((epred1_0)=>((descrp)=>(![X150:$i, X151:$i > $o, X152:$i]:(((in @ X152 @ X150)=>((X151 @ X152)=>(in @ X152 @ (dsetconstr @ X150 @ (^[Z0:$i]:((X151 @ Z0))))))))=>(![X153:$i, X154:$i > $o, X155:$i]:(((in @ X155 @ (dsetconstr @ X153 @ (^[Z0:$i]:((X154 @ Z0)))))=>(in @ X155 @ X153)))=>(![X156:$i, X157:$i > $o, X158:$i]:(((in @ X158 @ (dsetconstr @ X156 @ (^[Z0:$i]:((X157 @ Z0)))))=>(X157 @ X158)))=>(![X159:$i > $o]:((?[X160:$i]:(((X159 @ X160)&![X161:$i]:(((X159 @ X161)=>((X160)=(X161))))))=>?[X162:$i]:(((X159 @ X162)&![X163:$i]:(((X159 @ X163)=>((X162)=(X163))))))))=>(![X164:$o, X165:$i]:(((in @ X165 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X164)))))=>(X164)))=>(![X166:$i]:(((in @ X166 @ emptyset)=>![X167:$o]:((X167))))=>(![X168:$i]:(~(in @ X168 @ emptyset))=>(![X169:$i]:(~(in @ X169 @ emptyset))=>(![X170:$i > $o]:((?[X171:$i]:(((X170 @ X171)&![X172:$i]:(((X170 @ X172)=>((X171)=(X172))))))=>?[X173:$i]:((X170 @ X173))))=>(![X174:$i, X175:$i]:((![X176:$i]:(((in @ X176 @ X174)=>(in @ X176 @ X175)))=>(![X177:$i]:(((in @ X177 @ X175)=>(in @ X177 @ X174)))=>((X174)=(X175)))))=>(![X178:$i]:((![X179:$i]:(~(in @ X179 @ X178))=>((X178)=(emptyset))))=>(![X180:$i]:((![X181:$i]:(~(in @ X181 @ X180))=>((X180)=(emptyset))))=>(![X182:$i, X183:$i > $o, X184:$i]:(((in @ X184 @ X182)=>((in @ X184 @ (dsetconstr @ X182 @ (^[Z0:$i]:((X183 @ Z0)))))<=>(X183 @ X184))))=>(![X185:$i]:((((X185)!=(emptyset))=>?[X186:$i]:((in @ X186 @ X185))))=>(![X187:$i, X188:$i > $o, X189:$i]:(((in @ X189 @ X187)=>((X188 @ X189)=>((dsetconstr @ X187 @ (^[Z0:$i]:((X188 @ Z0))))!=(emptyset)))))=>(![X190:$i]:((?[X191:$i]:((in @ X191 @ X190))=>((X190)!=(emptyset))))=>(![X192:$i, X193:$i]:((in @ X192 @ (setadjoin @ X192 @ X193)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_39, emptysetimpfalse]), notinemptyset]), c_0_40]), setext]), emptyI]), noeltsimpempty]), c_0_41]), c_0_42]), c_0_43]), c_0_44]), setadjoinIL]), emptyinunitempty]), setadjoinAx]), emptysetAx]), setextAx]), powersetAx]), c_0_45]), wellorderingAx]), foundationAx]), c_0_46]), omegaIndAx]), omegaSAx]), omega0Ax]), c_0_47]), c_0_48]), c_0_49]), emptysetE]), c_0_50])]), c_0_51])).
% 0.08/0.27 thf(c_0_53, negated_conjecture, ![X194:$i, X195:$i, X197:$i, X198:$i, X199:$i, X200:$i, X201:$i, X202:$i, X203:$i, X204:$i, X205:$i, X207:$i, X208:$i, X210:$i, X211:$i > $i > $o, X212:$i, X214:$i, X217:$i, X219:$i, X220:$i, X221:$i, X222:$i, X224:$i, X225:$i, X226:$i > $o, X227:$i, X228:$i, X229:$i > $o, X230:$i, X231:$i, X232:$i > $o, X233:$i, X234:$i > $o, X235:$i, X238:$i, X239:$o, X240:$i, X241:$i, X242:$o, X243:$i, X244:$i, X245:$i > $o, X246:$i, X249:$i, X250:$i, X253:$i, X255:$i, X257:$i, X258:$i > $o, X259:$i, X260:$i, X262:$i, X263:$i > $o, X264:$i, X265:$i, X266:$i, X267:$i, X268:$i]:((((~(in @ (esk1_2 @ X194 @ X195) @ X194)|~(in @ (esk1_2 @ X194 @ X195) @ X195)|((X194)=(X195)))&((in @ (esk1_2 @ X194 @ X195) @ X194)|(in @ (esk1_2 @ X194 @ X195) @ X195)|((X194)=(X195))))&(~(in @ X197 @ emptyset)&(((~(in @ X200 @ (setadjoin @ X198 @ X199))|(((X200)=(X198))|(in @ X200 @ X199)))&((((X200)!=(X198))|(in @ X200 @ (setadjoin @ X198 @ X199)))&(~(in @ X200 @ X199)|(in @ X200 @ (setadjoin @ X198 @ X199)))))&(((~(in @ X202 @ (powerset @ X201))|(~(in @ X203 @ X202)|(in @ X203 @ X201)))&(((in @ (esk2_2 @ X204 @ X205) @ X205)|(in @ X205 @ (powerset @ X204)))&(~(in @ (esk2_2 @ X204 @ X205) @ X204)|(in @ X205 @ (powerset @ X204)))))&((setunionAx)&((in @ emptyset @ omega)&((~(in @ X207 @ omega)|(in @ (setadjoin @ X207 @ X207) @ omega))&(((((in @ (esk3_1 @ X208) @ omega)|~(in @ emptyset @ X208)|(~(in @ X210 @ omega)|(in @ X210 @ X208)))&((in @ (esk3_1 @ X208) @ X208)|~(in @ emptyset @ X208)|(~(in @ X210 @ omega)|(in @ X210 @ X208))))&(~(in @ (setadjoin @ (esk3_1 @ X208) @ (esk3_1 @ X208)) @ X208)|~(in @ emptyset @ X208)|(~(in @ X210 @ omega)|(in @ X210 @ X208))))&((((((in @ (esk7_3 @ X211 @ X212 @ X217) @ X212)|~(in @ X217 @ (esk6_2 @ X211 @ X212))|(in @ (esk4_2 @ X211 @ X212) @ X212))&((X211 @ (esk7_3 @ X211 @ X212 @ X217) @ X217)|~(in @ X217 @ (esk6_2 @ X211 @ X212))|(in @ (esk4_2 @ X211 @ X212) @ X212)))&(~(in @ X220 @ X212)|~(X211 @ X220 @ X219)|(in @ X219 @ (esk6_2 @ X211 @ X212))|(in @ (esk4_2 @ X211 @ X212) @ X212)))&(((((in @ (esk7_3 @ X211 @ X212 @ X217) @ X212)|~(in @ X217 @ (esk6_2 @ X211 @ X212))|((X211 @ (esk4_2 @ X211 @ X212) @ (esk5_3 @ X211 @ X212 @ X214))|~(X211 @ (esk4_2 @ X211 @ X212) @ X214)))&((X211 @ (esk7_3 @ X211 @ X212 @ X217) @ X217)|~(in @ X217 @ (esk6_2 @ X211 @ X212))|((X211 @ (esk4_2 @ X211 @ X212) @ (esk5_3 @ X211 @ X212 @ X214))|~(X211 @ (esk4_2 @ X211 @ X212) @ X214))))&(~(in @ X220 @ X212)|~(X211 @ X220 @ X219)|(in @ X219 @ (esk6_2 @ X211 @ X212))|((X211 @ (esk4_2 @ X211 @ X212) @ (esk5_3 @ X211 @ X212 @ X214))|~(X211 @ (esk4_2 @ X211 @ X212) @ X214))))&((((in @ (esk7_3 @ X211 @ X212 @ X217) @ X212)|~(in @ X217 @ (esk6_2 @ X211 @ X212))|(((X214)!=(esk5_3 @ X211 @ X212 @ X214))|~(X211 @ (esk4_2 @ X211 @ X212) @ X214)))&((X211 @ (esk7_3 @ X211 @ X212 @ X217) @ X217)|~(in @ X217 @ (esk6_2 @ X211 @ X212))|(((X214)!=(esk5_3 @ X211 @ X212 @ X214))|~(X211 @ (esk4_2 @ X211 @ X212) @ X214))))&(~(in @ X220 @ X212)|~(X211 @ X220 @ X219)|(in @ X219 @ (esk6_2 @ X211 @ X212))|(((X214)!=(esk5_3 @ X211 @ X212 @ X214))|~(X211 @ (esk4_2 @ X211 @ X212) @ X214))))))&((((in @ (esk8_1 @ X221) @ X221)|~(in @ X222 @ X221))&(~(in @ X224 @ (esk8_1 @ X221))|~(in @ X224 @ X221)|~(in @ X222 @ X221)))&((epred1_0)&((descrp)&((~(in @ X227 @ X225)|(~(X226 @ X227)|(in @ X227 @ (dsetconstr @ X225 @ (^[Z0:$i]:((X226 @ Z0)))))))&((~(in @ X230 @ (dsetconstr @ X228 @ (^[Z0:$i]:((X229 @ Z0)))))|(in @ X230 @ X228))&((~(in @ X233 @ (dsetconstr @ X231 @ (^[Z0:$i]:((X232 @ Z0)))))|(X232 @ X233))&(((((X234 @ (esk10_1 @ X234))|((X234 @ (esk9_2 @ X234 @ X235))|~(X234 @ X235)))&(~(X234 @ X238)|((esk10_1 @ X234)=(X238))|((X234 @ (esk9_2 @ X234 @ X235))|~(X234 @ X235))))&(((X234 @ (esk10_1 @ X234))|(((X235)!=(esk9_2 @ X234 @ X235))|~(X234 @ X235)))&(~(X234 @ X238)|((esk10_1 @ X234)=(X238))|(((X235)!=(esk9_2 @ X234 @ X235))|~(X234 @ X235)))))&((~(in @ X240 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X239)))))|(X239))&((~(in @ X241 @ emptyset)|(X242))&(~(in @ X243 @ emptyset)&(~(in @ X244 @ emptyset)&((((X245 @ (esk11_2 @ X245 @ X246))|~(X245 @ X246)|(X245 @ (esk12_1 @ X245)))&(((X246)!=(esk11_2 @ X245 @ X246))|~(X245 @ X246)|(X245 @ (esk12_1 @ X245))))&(((((in @ (esk14_2 @ X249 @ X250) @ X250)|((X249)=(X250))|(in @ (esk13_2 @ X249 @ X250) @ X249))&(~(in @ (esk14_2 @ X249 @ X250) @ X249)|((X249)=(X250))|(in @ (esk13_2 @ X249 @ X250) @ X249)))&(((in @ (esk14_2 @ X249 @ X250) @ X250)|((X249)=(X250))|~(in @ (esk13_2 @ X249 @ X250) @ X250))&(~(in @ (esk14_2 @ X249 @ X250) @ X249)|((X249)=(X250))|~(in @ (esk13_2 @ X249 @ X250) @ X250))))&(((in @ (esk15_1 @ X253) @ X253)|((X253)=(emptyset)))&(((in @ (esk16_1 @ X255) @ X255)|((X255)=(emptyset)))&(((~(in @ X259 @ (dsetconstr @ X257 @ (^[Z0:$i]:((X258 @ Z0)))))|(X258 @ X259)|~(in @ X259 @ X257))&(~(X258 @ X259)|(in @ X259 @ (dsetconstr @ X257 @ (^[Z0:$i]:((X258 @ Z0)))))|~(in @ X259 @ X257)))&((((X260)=(emptyset))|(in @ (esk17_1 @ X260) @ X260))&((~(in @ X264 @ X262)|(~(X263 @ X264)|((dsetconstr @ X262 @ (^[Z0:$i]:((X263 @ Z0))))!=(emptyset))))&((~(in @ X266 @ X265)|((X265)!=(emptyset)))&((in @ X267 @ (setadjoin @ X267 @ X268))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((in @ esk20_0 @ esk19_0)&~(in @ esk20_0 @ (setadjoin @ esk18_0 @ esk19_0)))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])])])])])])).
% 0.08/0.27 thf(c_0_54, negated_conjecture, ~((in @ esk20_0 @ (setadjoin @ esk18_0 @ esk19_0))), inference(split_conjunct,[status(thm)],[c_0_53])).
% 0.08/0.27 thf(c_0_55, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X4 @ X3))|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_53])).
% 0.08/0.27 thf(c_0_56, negated_conjecture, (in @ esk20_0 @ esk19_0), inference(split_conjunct,[status(thm)],[c_0_53])).
% 0.08/0.27 thf(c_0_57, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54, c_0_55]), c_0_56])]), ['proof']).
% 0.08/0.27 % SZS output end CNFRefutation
% 0.08/0.27 % Parsed axioms : 75
% 0.08/0.27 % Removed by relevancy pruning/SinE : 43
% 0.08/0.27 % Initial clauses : 69
% 0.08/0.27 % Removed in clause preprocessing : 0
% 0.08/0.27 % Initial clauses in saturation : 69
% 0.08/0.27 % Processed clauses : 32
% 0.08/0.27 % ...of these trivial : 0
% 0.08/0.27 % ...subsumed : 9
% 0.08/0.27 % ...remaining for further processing : 23
% 0.08/0.27 % Other redundant clauses eliminated : 2
% 0.08/0.27 % Clauses deleted for lack of memory : 0
% 0.08/0.27 % Backward-subsumed : 0
% 0.08/0.27 % Backward-rewritten : 2
% 0.08/0.27 % Generated clauses : 20
% 0.08/0.27 % ...of the previous two non-redundant : 15
% 0.08/0.27 % ...aggressively subsumed : 0
% 0.08/0.27 % Contextual simplify-reflections : 0
% 0.08/0.27 % Paramodulations : 18
% 0.08/0.27 % Factorizations : 0
% 0.08/0.27 % NegExts : 0
% 0.08/0.27 % Equation resolutions : 2
% 0.08/0.27 % Disequality decompositions : 0
% 0.08/0.27 % Total rewrite steps : 7
% 0.08/0.27 % ...of those cached : 1
% 0.08/0.27 % Propositional unsat checks : 0
% 0.08/0.27 % Propositional check models : 0
% 0.08/0.27 % Propositional check unsatisfiable : 0
% 0.08/0.27 % Propositional clauses : 0
% 0.08/0.27 % Propositional clauses after purity: 0
% 0.08/0.27 % Propositional unsat core size : 0
% 0.08/0.27 % Propositional preprocessing time : 0.000
% 0.08/0.27 % Propositional encoding time : 0.000
% 0.08/0.27 % Propositional solver time : 0.000
% 0.08/0.27 % Success case prop preproc time : 0.000
% 0.08/0.27 % Success case prop encoding time : 0.000
% 0.08/0.27 % Success case prop solver time : 0.000
% 0.08/0.27 % Current number of processed clauses : 19
% 0.08/0.27 % Positive orientable unit clauses : 9
% 0.08/0.27 % Positive unorientable unit clauses: 0
% 0.08/0.27 % Negative unit clauses : 2
% 0.08/0.27 % Non-unit-clauses : 8
% 0.08/0.27 % Current number of unprocessed clauses: 52
% 0.08/0.27 % ...number of literals in the above : 190
% 0.08/0.27 % Current number of archived formulas : 0
% 0.08/0.27 % Current number of archived clauses : 2
% 0.08/0.27 % Clause-clause subsumption calls (NU) : 22
% 0.08/0.27 % Rec. Clause-clause subsumption calls : 21
% 0.08/0.27 % Non-unit clause-clause subsumptions : 3
% 0.08/0.27 % Unit Clause-clause subsumption calls : 5
% 0.08/0.27 % Rewrite failures with RHS unbound : 0
% 0.08/0.27 % BW rewrite match attempts : 2
% 0.08/0.27 % BW rewrite match successes : 2
% 0.08/0.27 % Condensation attempts : 0
% 0.08/0.27 % Condensation successes : 0
% 0.08/0.27 % Termbank termtop insertions : 7493
% 0.08/0.27 % Search garbage collected termcells : 2710
% 0.08/0.27
% 0.08/0.27 % -------------------------------------------------
% 0.08/0.27 % User time : 0.010 s
% 0.08/0.27 % System time : 0.003 s
% 0.08/0.27 % Total time : 0.013 s
% 0.08/0.27 % Maximum resident set size: 4480 pages
% 0.08/0.27
% 0.08/0.27 % -------------------------------------------------
% 0.08/0.27 % User time : 0.012 s
% 0.08/0.27 % System time : 0.006 s
% 0.08/0.27 % Total time : 0.018 s
% 0.08/0.27 % Maximum resident set size: 4864 pages
% 0.08/0.27 % E exiting
%------------------------------------------------------------------------------