%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU502^1 : 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 : n008.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 08:26:29 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU502^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n008.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:47:24 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 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.9W1Mv4vWPJ/E---3.1_3176444.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 % new_bool_1 with pid 3176459 completed with status 0
% 0.21/0.28 % Result found by new_bool_1
% 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 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.21/0.28 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.28 % Search class: HGHSF-FFMS31-SHFSMSBN
% 0.21/0.28 % partial match(1): 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 3176461 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
% 0.21/0.28 % Starting sh5l with 300s (1) cores
% 0.21/0.28 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.28 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.21/0.28 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.28 % Search class: HGHSF-FFMS31-SHFSMSBN
% 0.21/0.28 % partial match(1): 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 % Preprocessing time : 0.002 s
% 0.21/0.28
% 0.21/0.28 % Proof found!
% 0.21/0.28 % SZS status Theorem
% 0.21/0.28 % SZS output start CNFRefutation
% 0.21/0.28 thf(decl_23, type, in: $i > $i > $o).
% 0.21/0.28 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.21/0.28 thf(decl_25, type, setextAx: $o).
% 0.21/0.28 thf(decl_26, type, emptyset: $i).
% 0.21/0.28 thf(decl_27, type, emptysetAx: $o).
% 0.21/0.28 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.21/0.28 thf(decl_29, type, setadjoinAx: $o).
% 0.21/0.28 thf(decl_30, type, powerset: $i > $i).
% 0.21/0.28 thf(decl_31, type, powersetAx: $o).
% 0.21/0.28 thf(decl_33, type, setunionAx: $o).
% 0.21/0.28 thf(decl_34, type, omega: $i).
% 0.21/0.28 thf(decl_35, type, omega0Ax: $o).
% 0.21/0.28 thf(decl_36, type, omegaSAx: $o).
% 0.21/0.28 thf(decl_37, type, omegaIndAx: $o).
% 0.21/0.28 thf(decl_38, type, replAx: $o).
% 0.21/0.28 thf(decl_39, type, foundationAx: $o).
% 0.21/0.28 thf(decl_40, type, wellorderingAx: $o).
% 0.21/0.28 thf(decl_42, type, descrp: $o).
% 0.21/0.28 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.21/0.28 thf(decl_44, type, dsetconstrI: $o).
% 0.21/0.28 thf(decl_45, type, dsetconstrEL: $o).
% 0.21/0.28 thf(decl_46, type, dsetconstrER: $o).
% 0.21/0.28 thf(decl_47, type, exuE1: $o).
% 0.21/0.28 thf(decl_48, type, prop2set: $o > $i).
% 0.21/0.28 thf(decl_49, type, prop2setE: $o).
% 0.21/0.28 thf(decl_50, type, emptysetE: $o).
% 0.21/0.28 thf(decl_51, type, epred1_0: $o).
% 0.21/0.28 thf(decl_52, type, esk1_2: $i > $i > $i).
% 0.21/0.28 thf(decl_53, type, esk2_2: $i > $i > $i).
% 0.21/0.28 thf(decl_54, type, esk3_1: $i > $i).
% 0.21/0.28 thf(decl_55, type, esk4_2: ($i > $i > $o) > $i > $i).
% 0.21/0.28 thf(decl_56, type, esk5_3: ($i > $i > $o) > $i > $i > $i).
% 0.21/0.28 thf(decl_57, type, esk6_2: ($i > $i > $o) > $i > $i).
% 0.21/0.28 thf(decl_58, type, esk7_3: ($i > $i > $o) > $i > $i > $i).
% 0.21/0.28 thf(decl_59, type, esk8_1: $i > $i).
% 0.21/0.28 thf(decl_60, type, esk9_2: ($i > $o) > $i > $i).
% 0.21/0.28 thf(decl_61, type, esk10_1: ($i > $o) > $i).
% 0.21/0.28 thf(decl_62, type, esk11_0: $i).
% 0.21/0.28 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.9W1Mv4vWPJ/E---3.1_3176444.p', replAx)).
% 0.21/0.28 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.9W1Mv4vWPJ/E---3.1_3176444.p', exu)).
% 0.21/0.28 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.9W1Mv4vWPJ/E---3.1_3176444.p', exuE1)).
% 0.21/0.28 thf(prop2set, axiom, ((prop2set)=(^[X10:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[X2:$i]:((X10)))))), file('/export/starexec/sandbox/tmp/tmp.9W1Mv4vWPJ/E---3.1_3176444.p', prop2set)).
% 0.21/0.28 thf(emptysetimpfalse, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.9W1Mv4vWPJ/E---3.1_3176444.p', emptysetimpfalse)).
% 0.21/0.28 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.9W1Mv4vWPJ/E---3.1_3176444.p', dsetconstrI)).
% 0.21/0.28 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.9W1Mv4vWPJ/E---3.1_3176444.p', dsetconstrEL)).
% 0.21/0.28 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.9W1Mv4vWPJ/E---3.1_3176444.p', dsetconstrER)).
% 0.21/0.28 thf(prop2setE, axiom, ((prop2setE)<=>![X11:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X11))))=>(X11)))), file('/export/starexec/sandbox/tmp/tmp.9W1Mv4vWPJ/E---3.1_3176444.p', prop2setE)).
% 0.21/0.28 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.9W1Mv4vWPJ/E---3.1_3176444.p', omega0Ax)).
% 0.21/0.28 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.9W1Mv4vWPJ/E---3.1_3176444.p', omegaSAx)).
% 0.21/0.28 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.9W1Mv4vWPJ/E---3.1_3176444.p', omegaIndAx)).
% 0.21/0.28 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.9W1Mv4vWPJ/E---3.1_3176444.p', foundationAx)).
% 0.21/0.28 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.9W1Mv4vWPJ/E---3.1_3176444.p', wellorderingAx)).
% 0.21/0.28 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X12:$o]:((X12))))), file('/export/starexec/sandbox/tmp/tmp.9W1Mv4vWPJ/E---3.1_3176444.p', emptysetE)).
% 0.21/0.28 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.9W1Mv4vWPJ/E---3.1_3176444.p', setextAx)).
% 0.21/0.28 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.9W1Mv4vWPJ/E---3.1_3176444.p', emptysetAx)).
% 0.21/0.28 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.9W1Mv4vWPJ/E---3.1_3176444.p', setadjoinAx)).
% 0.21/0.28 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.9W1Mv4vWPJ/E---3.1_3176444.p', powersetAx)).
% 0.21/0.28 thf(c_0_19, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.21/0.28 thf(c_0_20, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.21/0.28 thf(c_0_21, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.21/0.28 thf(c_0_22, plain, ((prop2set)=(^[Z0:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[Z1:$i]:((Z0)))))), inference(fof_simplification,[status(thm)],[prop2set])).
% 0.21/0.28 thf(c_0_23, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))))))))))))))))))))), inference(assume_negation,[status(cth)],[emptysetimpfalse])).
% 0.21/0.28 thf(c_0_24, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X73:$i]:(((((X6 @ X2 @ X73)))&(![X74:$i]:(((((X6 @ X2 @ X74)))=>(((X73)=(X74)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_19, c_0_20])).
% 0.21/0.28 thf(c_0_25, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.21/0.28 thf(c_0_26, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.21/0.28 thf(c_0_27, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.21/0.28 thf(c_0_28, plain, ((exuE1)=(![X1:$i > $o]:((((?[X75:$i]:(((((X1 @ X75)))&(![X76:$i]:(((((X1 @ X76)))=>(((X75)=(X76))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_21, c_0_20])).
% 0.21/0.28 thf(c_0_29, axiom, ((prop2setE)=(![X11:$o, X2:$i]:((((in @ X2 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:(((X11)))))))=>((X11)))))), inference(apply_def,[status(thm)],[prop2setE, c_0_22])).
% 0.21/0.28 thf(c_0_30, plain, ((epred1_0)<=>![X103:$i]:(?[X104:$i]:((((![X105:$i]:(((in @ X105 @ X104)=>![X106:$i]:(((in @ X106 @ X105)=>(in @ X106 @ X103)))))&![X107:$i, X108:$i]:((((in @ X107 @ X103)&(in @ X108 @ X103))=>(![X109:$i]:(((in @ X109 @ X104)=>((in @ X107 @ X109)<=>(in @ X108 @ X109))))=>((X107)=(X108))))))&![X110:$i, X111:$i]:((((in @ X110 @ X104)&(in @ X111 @ X104))=>(![X112:$i]:(((in @ X112 @ X110)=>(in @ X112 @ X111)))|![X113:$i]:(((in @ X113 @ X111)=>(in @ X113 @ X110)))))))&![X114:$i]:(((![X115:$i]:(((in @ X115 @ X114)=>(in @ X115 @ X103)))&?[X116:$i]:((in @ X116 @ X114)))=>?[X117:$i, X118:$i]:(((((in @ X117 @ X104)&(in @ X118 @ X114))&~(?[X119:$i]:(((in @ X119 @ X117)&(in @ X119 @ X114)))))&![X120:$i]:(((in @ X120 @ X104)=>(![X121:$i]:(((in @ X121 @ X120)=>(in @ X121 @ X117)))|(in @ X118 @ X120)))))))))))), introduced(definition)).
% 0.21/0.28 thf(c_0_31, negated_conjecture, ~((![X77:$i, X78:$i]:((![X79:$i]:(((in @ X79 @ X77)<=>(in @ X79 @ X78)))=>((X77)=(X78))))=>(![X80:$i]:(~(in @ X80 @ emptyset))=>(![X81:$i, X82:$i, X83:$i]:(((in @ X83 @ (setadjoin @ X81 @ X82))<=>(((X83)=(X81))|(in @ X83 @ X82))))=>(![X84:$i, X85:$i]:(((in @ X85 @ (powerset @ X84))<=>![X86:$i]:(((in @ X86 @ X85)=>(in @ X86 @ X84)))))=>((setunionAx)=>((in @ emptyset @ omega)=>(![X87:$i]:(((in @ X87 @ omega)=>(in @ (setadjoin @ X87 @ X87) @ omega)))=>(![X88:$i]:((((in @ emptyset @ X88)&![X89:$i]:((((in @ X89 @ omega)&(in @ X89 @ X88))=>(in @ (setadjoin @ X89 @ X89) @ X88))))=>![X90:$i]:(((in @ X90 @ omega)=>(in @ X90 @ X88)))))=>(![X91:$i > $i > $o, X92:$i]:((![X93:$i]:(((in @ X93 @ X92)=>?[X94:$i]:(((X91 @ X93 @ X94)&![X95:$i]:(((X91 @ X93 @ X95)=>((X94)=(X95))))))))=>?[X96:$i]:(![X97:$i]:(((in @ X97 @ X96)<=>?[X98:$i]:(((in @ X98 @ X92)&(X91 @ X98 @ X97))))))))=>(![X99:$i]:((?[X100:$i]:((in @ X100 @ X99))=>?[X101:$i]:(((in @ X101 @ X99)&~(?[X102:$i]:(((in @ X102 @ X101)&(in @ X102 @ X99))))))))=>((epred1_0)=>((descrp)=>(![X122:$i, X123:$i > $o, X124:$i]:(((in @ X124 @ X122)=>((X123 @ X124)=>(in @ X124 @ (dsetconstr @ X122 @ X123)))))=>(![X125:$i, X126:$i > $o, X127:$i]:(((in @ X127 @ (dsetconstr @ X125 @ X126))=>(in @ X127 @ X125)))=>(![X128:$i, X129:$i > $o, X130:$i]:(((in @ X130 @ (dsetconstr @ X128 @ X129))=>(X129 @ X130)))=>(![X131:$i > $o]:((?[X132:$i]:(((X131 @ X132)&![X133:$i]:(((X131 @ X133)=>((X132)=(X133))))))=>?[X134:$i]:(((X131 @ X134)&![X135:$i]:(((X131 @ X135)=>((X134)=(X135))))))))=>(![X136:$o, X137:$i]:(((in @ X137 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X136)))))=>(X136)))=>(![X138:$i]:(((in @ X138 @ emptyset)=>![X139:$o]:((X139))))=>![X2:$i]:(((in @ X2 @ emptyset)=>~($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)],[c_0_23, omega0Ax]), omegaSAx]), omegaIndAx]), c_0_24]), foundationAx]), wellorderingAx]), c_0_25]), c_0_26]), c_0_27]), c_0_28]), c_0_29]), emptysetE]), setextAx]), emptysetAx]), setadjoinAx]), powersetAx])])]), c_0_30])).
% 0.21/0.28 thf(c_0_32, negated_conjecture, ![X140:$i, X141:$i, X143:$i, X144:$i, X145:$i, X146:$i, X147:$i, X148:$i, X149:$i, X150:$i, X151:$i, X153:$i, X154:$i, X156:$i, X157:$i > $i > $o, X158:$i, X160:$i, X163:$i, X165:$i, X166:$i, X167:$i, X168:$i, X170:$i, X171:$i, X172:$i > $o, X173:$i, X174:$i, X175:$i > $o, X176:$i, X177:$i, X178:$i > $o, X179:$i, X180:$i > $o, X181:$i, X184:$i, X185:$o, X186:$i, X187:$i, X188:$o]:((((~(in @ (esk1_2 @ X140 @ X141) @ X140)|~(in @ (esk1_2 @ X140 @ X141) @ X141)|((X140)=(X141)))&((in @ (esk1_2 @ X140 @ X141) @ X140)|(in @ (esk1_2 @ X140 @ X141) @ X141)|((X140)=(X141))))&(~(in @ X143 @ emptyset)&(((~(in @ X146 @ (setadjoin @ X144 @ X145))|(((X146)=(X144))|(in @ X146 @ X145)))&((((X146)!=(X144))|(in @ X146 @ (setadjoin @ X144 @ X145)))&(~(in @ X146 @ X145)|(in @ X146 @ (setadjoin @ X144 @ X145)))))&(((~(in @ X148 @ (powerset @ X147))|(~(in @ X149 @ X148)|(in @ X149 @ X147)))&(((in @ (esk2_2 @ X150 @ X151) @ X151)|(in @ X151 @ (powerset @ X150)))&(~(in @ (esk2_2 @ X150 @ X151) @ X150)|(in @ X151 @ (powerset @ X150)))))&((setunionAx)&((in @ emptyset @ omega)&((~(in @ X153 @ omega)|(in @ (setadjoin @ X153 @ X153) @ omega))&(((((in @ (esk3_1 @ X154) @ omega)|~(in @ emptyset @ X154)|(~(in @ X156 @ omega)|(in @ X156 @ X154)))&((in @ (esk3_1 @ X154) @ X154)|~(in @ emptyset @ X154)|(~(in @ X156 @ omega)|(in @ X156 @ X154))))&(~(in @ (setadjoin @ (esk3_1 @ X154) @ (esk3_1 @ X154)) @ X154)|~(in @ emptyset @ X154)|(~(in @ X156 @ omega)|(in @ X156 @ X154))))&((((((in @ (esk7_3 @ X157 @ X158 @ X163) @ X158)|~(in @ X163 @ (esk6_2 @ X157 @ X158))|(in @ (esk4_2 @ X157 @ X158) @ X158))&((X157 @ (esk7_3 @ X157 @ X158 @ X163) @ X163)|~(in @ X163 @ (esk6_2 @ X157 @ X158))|(in @ (esk4_2 @ X157 @ X158) @ X158)))&(~(in @ X166 @ X158)|~(X157 @ X166 @ X165)|(in @ X165 @ (esk6_2 @ X157 @ X158))|(in @ (esk4_2 @ X157 @ X158) @ X158)))&(((((in @ (esk7_3 @ X157 @ X158 @ X163) @ X158)|~(in @ X163 @ (esk6_2 @ X157 @ X158))|((X157 @ (esk4_2 @ X157 @ X158) @ (esk5_3 @ X157 @ X158 @ X160))|~(X157 @ (esk4_2 @ X157 @ X158) @ X160)))&((X157 @ (esk7_3 @ X157 @ X158 @ X163) @ X163)|~(in @ X163 @ (esk6_2 @ X157 @ X158))|((X157 @ (esk4_2 @ X157 @ X158) @ (esk5_3 @ X157 @ X158 @ X160))|~(X157 @ (esk4_2 @ X157 @ X158) @ X160))))&(~(in @ X166 @ X158)|~(X157 @ X166 @ X165)|(in @ X165 @ (esk6_2 @ X157 @ X158))|((X157 @ (esk4_2 @ X157 @ X158) @ (esk5_3 @ X157 @ X158 @ X160))|~(X157 @ (esk4_2 @ X157 @ X158) @ X160))))&((((in @ (esk7_3 @ X157 @ X158 @ X163) @ X158)|~(in @ X163 @ (esk6_2 @ X157 @ X158))|(((X160)!=(esk5_3 @ X157 @ X158 @ X160))|~(X157 @ (esk4_2 @ X157 @ X158) @ X160)))&((X157 @ (esk7_3 @ X157 @ X158 @ X163) @ X163)|~(in @ X163 @ (esk6_2 @ X157 @ X158))|(((X160)!=(esk5_3 @ X157 @ X158 @ X160))|~(X157 @ (esk4_2 @ X157 @ X158) @ X160))))&(~(in @ X166 @ X158)|~(X157 @ X166 @ X165)|(in @ X165 @ (esk6_2 @ X157 @ X158))|(((X160)!=(esk5_3 @ X157 @ X158 @ X160))|~(X157 @ (esk4_2 @ X157 @ X158) @ X160))))))&((((in @ (esk8_1 @ X167) @ X167)|~(in @ X168 @ X167))&(~(in @ X170 @ (esk8_1 @ X167))|~(in @ X170 @ X167)|~(in @ X168 @ X167)))&((epred1_0)&((descrp)&((~(in @ X173 @ X171)|(~(X172 @ X173)|(in @ X173 @ (dsetconstr @ X171 @ X172))))&((~(in @ X176 @ (dsetconstr @ X174 @ X175))|(in @ X176 @ X174))&((~(in @ X179 @ (dsetconstr @ X177 @ X178))|(X178 @ X179))&(((((X180 @ (esk10_1 @ X180))|((X180 @ (esk9_2 @ X180 @ X181))|~(X180 @ X181)))&(~(X180 @ X184)|((esk10_1 @ X180)=(X184))|((X180 @ (esk9_2 @ X180 @ X181))|~(X180 @ X181))))&(((X180 @ (esk10_1 @ X180))|(((X181)!=(esk9_2 @ X180 @ X181))|~(X180 @ X181)))&(~(X180 @ X184)|((esk10_1 @ X180)=(X184))|(((X181)!=(esk9_2 @ X180 @ X181))|~(X180 @ X181)))))&((~(in @ X186 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X185)))))|(X185))&((~(in @ X187 @ emptyset)|(X188))&((in @ esk11_0 @ emptyset)&($true))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])])])])])])).
% 0.21/0.28 thf(c_0_33, negated_conjecture, (in @ esk11_0 @ emptyset), inference(split_conjunct,[status(thm)],[c_0_32])).
% 0.21/0.28 thf(c_0_34, negated_conjecture, ![X2:$i]:(~((in @ X2 @ emptyset))), inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_32])])])).
% 0.21/0.28 thf(c_0_35, negated_conjecture, ($false), inference(sr,[status(thm)],[c_0_33, c_0_34]), ['proof']).
% 0.21/0.28 % SZS output end CNFRefutation
% 0.21/0.28 % Parsed axioms : 49
% 0.21/0.28 % Removed by relevancy pruning/SinE : 30
% 0.21/0.28 % Initial clauses : 52
% 0.21/0.28 % Removed in clause preprocessing : 1
% 0.21/0.28 % Initial clauses in saturation : 51
% 0.21/0.28 % Processed clauses : 6
% 0.21/0.28 % ...of these trivial : 0
% 0.21/0.28 % ...subsumed : 0
% 0.21/0.28 % ...remaining for further processing : 6
% 0.21/0.28 % Other redundant clauses eliminated : 0
% 0.21/0.28 % Clauses deleted for lack of memory : 0
% 0.21/0.28 % Backward-subsumed : 0
% 0.21/0.28 % Backward-rewritten : 0
% 0.21/0.28 % Generated clauses : 1
% 0.21/0.28 % ...of the previous two non-redundant : 0
% 0.21/0.28 % ...aggressively subsumed : 0
% 0.21/0.28 % Contextual simplify-reflections : 0
% 0.21/0.28 % Paramodulations : 0
% 0.21/0.28 % Factorizations : 0
% 0.21/0.28 % NegExts : 0
% 0.21/0.28 % Equation resolutions : 0
% 0.21/0.28 % Disequality decompositions : 0
% 0.21/0.28 % Total rewrite steps : 0
% 0.21/0.28 % ...of those cached : 0
% 0.21/0.28 % Propositional unsat checks : 0
% 0.21/0.28 % Propositional check models : 0
% 0.21/0.28 % Propositional check unsatisfiable : 0
% 0.21/0.28 % Propositional clauses : 0
% 0.21/0.28 % Propositional clauses after purity: 0
% 0.21/0.28 % Propositional unsat core size : 0
% 0.21/0.28 % Propositional preprocessing time : 0.000
% 0.21/0.28 % Propositional encoding time : 0.000
% 0.21/0.28 % Propositional solver time : 0.000
% 0.21/0.28 % Success case prop preproc time : 0.000
% 0.21/0.28 % Success case prop encoding time : 0.000
% 0.21/0.28 % Success case prop solver time : 0.000
% 0.21/0.28 % Current number of processed clauses : 5
% 0.21/0.28 % Positive orientable unit clauses : 4
% 0.21/0.28 % Positive unorientable unit clauses: 0
% 0.21/0.28 % Negative unit clauses : 1
% 0.21/0.28 % Non-unit-clauses : 0
% 0.21/0.28 % Current number of unprocessed clauses: 45
% 0.21/0.28 % ...number of literals in the above : 166
% 0.21/0.28 % Current number of archived formulas : 0
% 0.21/0.28 % Current number of archived clauses : 1
% 0.21/0.28 % Clause-clause subsumption calls (NU) : 0
% 0.21/0.28 % Rec. Clause-clause subsumption calls : 0
% 0.21/0.28 % Non-unit clause-clause subsumptions : 0
% 0.21/0.28 % Unit Clause-clause subsumption calls : 0
% 0.21/0.28 % Rewrite failures with RHS unbound : 0
% 0.21/0.28 % BW rewrite match attempts : 0
% 0.21/0.28 % BW rewrite match successes : 0
% 0.21/0.28 % Condensation attempts : 0
% 0.21/0.28 % Condensation successes : 0
% 0.21/0.28 % Termbank termtop insertions : 6027
% 0.21/0.28 % Search garbage collected termcells : 2271
% 0.21/0.28
% 0.21/0.28 % -------------------------------------------------
% 0.21/0.28 % User time : 0.006 s
% 0.21/0.28 % System time : 0.003 s
% 0.21/0.28 % Total time : 0.009 s
% 0.21/0.28 % Maximum resident set size: 4204 pages
% 0.21/0.28
% 0.21/0.28 % -------------------------------------------------
% 0.21/0.28 % User time : 0.009 s
% 0.21/0.28 % System time : 0.008 s
% 0.21/0.28 % Total time : 0.017 s
% 0.21/0.28 % Maximum resident set size: 4864 pages
% 0.21/0.28 % E exiting
%------------------------------------------------------------------------------