%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU503^1 : 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 : 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 08:26:30 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU503^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n018.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 13:48:56 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.oWczu69Hy2/E---3.1_91928.p
% 0.08/0.26 % Version: 3.5.1-ho
% 0.08/0.26 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.08/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.26 % Starting sh5l with 300s (1) cores
% 0.08/0.26 % Starting new_bool_1 with 300s (1) cores
% 0.08/0.26 % Starting new_bool_2 with 300s (1) cores
% 0.08/0.26 % new_bool_2 with pid 91964 completed with status 0
% 0.08/0.26 % Result found by new_bool_2
% 0.08/0.26 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.08/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.26 % Starting sh5l with 300s (1) cores
% 0.08/0.26 % Starting new_bool_1 with 300s (1) cores
% 0.08/0.26 % Starting new_bool_2 with 300s (1) cores
% 0.08/0.26 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.08/0.26 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.08/0.26 % Search class: HGHSF-FFMS31-SHFSMSBN
% 0.08/0.26 % partial match(1): HGHSM-FFMS31-SHFSMSBN
% 0.08/0.26 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.26 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.26 % SubtermCWHack with pid 91965 completed with status 0
% 0.08/0.26 % Result found by SubtermCWHack
% 0.08/0.26 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.08/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.26 % Starting sh5l with 300s (1) cores
% 0.08/0.26 % Starting new_bool_1 with 300s (1) cores
% 0.08/0.26 % Starting new_bool_2 with 300s (1) cores
% 0.08/0.26 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.08/0.26 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.08/0.26 % Search class: HGHSF-FFMS31-SHFSMSBN
% 0.08/0.26 % partial match(1): HGHSM-FFMS31-SHFSMSBN
% 0.08/0.26 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.26 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.26 % Preprocessing time : 0.002 s
% 0.08/0.26
% 0.08/0.26 % Proof found!
% 0.08/0.26 % SZS status Theorem
% 0.08/0.26 % SZS output start CNFRefutation
% 0.08/0.26 thf(decl_23, type, in: $i > $i > $o).
% 0.08/0.26 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.08/0.26 thf(decl_25, type, setextAx: $o).
% 0.08/0.26 thf(decl_26, type, emptyset: $i).
% 0.08/0.26 thf(decl_27, type, emptysetAx: $o).
% 0.08/0.26 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.08/0.26 thf(decl_29, type, setadjoinAx: $o).
% 0.08/0.26 thf(decl_30, type, powerset: $i > $i).
% 0.08/0.26 thf(decl_31, type, powersetAx: $o).
% 0.08/0.26 thf(decl_33, type, setunionAx: $o).
% 0.08/0.26 thf(decl_34, type, omega: $i).
% 0.08/0.26 thf(decl_35, type, omega0Ax: $o).
% 0.08/0.26 thf(decl_36, type, omegaSAx: $o).
% 0.08/0.26 thf(decl_37, type, omegaIndAx: $o).
% 0.08/0.26 thf(decl_38, type, replAx: $o).
% 0.08/0.26 thf(decl_39, type, foundationAx: $o).
% 0.08/0.26 thf(decl_40, type, wellorderingAx: $o).
% 0.08/0.26 thf(decl_42, type, descrp: $o).
% 0.08/0.26 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.08/0.26 thf(decl_44, type, dsetconstrI: $o).
% 0.08/0.26 thf(decl_45, type, dsetconstrEL: $o).
% 0.08/0.26 thf(decl_46, type, dsetconstrER: $o).
% 0.08/0.26 thf(decl_47, type, exuE1: $o).
% 0.08/0.26 thf(decl_48, type, prop2set: $o > $i).
% 0.08/0.26 thf(decl_49, type, prop2setE: $o).
% 0.08/0.26 thf(decl_50, type, emptysetE: $o).
% 0.08/0.26 thf(decl_51, type, emptysetimpfalse: $o).
% 0.08/0.26 thf(decl_52, type, epred1_0: $o).
% 0.08/0.26 thf(decl_53, type, esk1_2: $i > $i > $i).
% 0.08/0.26 thf(decl_54, type, esk2_2: $i > $i > $i).
% 0.08/0.26 thf(decl_55, type, esk3_1: $i > $i).
% 0.08/0.26 thf(decl_56, type, esk4_2: ($i > $i > $o) > $i > $i).
% 0.08/0.26 thf(decl_57, type, esk5_3: ($i > $i > $o) > $i > $i > $i).
% 0.08/0.26 thf(decl_58, type, esk6_2: ($i > $i > $o) > $i > $i).
% 0.08/0.26 thf(decl_59, type, esk7_3: ($i > $i > $o) > $i > $i > $i).
% 0.08/0.26 thf(decl_60, type, esk8_1: $i > $i).
% 0.08/0.26 thf(decl_61, type, esk9_2: ($i > $o) > $i > $i).
% 0.08/0.26 thf(decl_62, type, esk10_1: ($i > $o) > $i).
% 0.08/0.26 thf(decl_63, type, esk11_0: $i).
% 0.08/0.26 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.oWczu69Hy2/E---3.1_91928.p', replAx)).
% 0.08/0.26 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.oWczu69Hy2/E---3.1_91928.p', exu)).
% 0.08/0.26 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.oWczu69Hy2/E---3.1_91928.p', exuE1)).
% 0.08/0.26 thf(prop2set, axiom, ((prop2set)=(^[X10:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[X2:$i]:((X10)))))), file('/export/starexec/sandbox/tmp/tmp.oWczu69Hy2/E---3.1_91928.p', prop2set)).
% 0.08/0.26 thf(notinemptyset, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>![X2:$i]:(~((in @ X2 @ emptyset)))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.oWczu69Hy2/E---3.1_91928.p', notinemptyset)).
% 0.08/0.26 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.oWczu69Hy2/E---3.1_91928.p', dsetconstrI)).
% 0.08/0.26 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.oWczu69Hy2/E---3.1_91928.p', dsetconstrEL)).
% 0.08/0.26 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.oWczu69Hy2/E---3.1_91928.p', dsetconstrER)).
% 0.08/0.26 thf(prop2setE, axiom, ((prop2setE)<=>![X11:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X11))))=>(X11)))), file('/export/starexec/sandbox/tmp/tmp.oWczu69Hy2/E---3.1_91928.p', prop2setE)).
% 0.08/0.26 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.oWczu69Hy2/E---3.1_91928.p', omegaSAx)).
% 0.08/0.26 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.oWczu69Hy2/E---3.1_91928.p', omegaIndAx)).
% 0.08/0.26 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.oWczu69Hy2/E---3.1_91928.p', foundationAx)).
% 0.08/0.26 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.oWczu69Hy2/E---3.1_91928.p', wellorderingAx)).
% 0.08/0.26 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X12:$o]:((X12))))), file('/export/starexec/sandbox/tmp/tmp.oWczu69Hy2/E---3.1_91928.p', emptysetE)).
% 0.08/0.26 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.oWczu69Hy2/E---3.1_91928.p', emptysetimpfalse)).
% 0.08/0.26 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.oWczu69Hy2/E---3.1_91928.p', emptysetAx)).
% 0.08/0.26 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.oWczu69Hy2/E---3.1_91928.p', setadjoinAx)).
% 0.08/0.26 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.oWczu69Hy2/E---3.1_91928.p', powersetAx)).
% 0.08/0.26 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.oWczu69Hy2/E---3.1_91928.p', omega0Ax)).
% 0.08/0.26 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.oWczu69Hy2/E---3.1_91928.p', setextAx)).
% 0.08/0.26 thf(c_0_20, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.08/0.26 thf(c_0_21, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.08/0.26 thf(c_0_22, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.08/0.26 thf(c_0_23, plain, ((prop2set)=(^[Z0:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[Z1:$i]:((Z0)))))), inference(fof_simplification,[status(thm)],[prop2set])).
% 0.08/0.26 thf(c_0_24, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>![X2:$i]:(~((in @ X2 @ emptyset))))))))))))))))))))))), inference(assume_negation,[status(cth)],[notinemptyset])).
% 0.08/0.26 thf(c_0_25, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X74:$i]:(((((X6 @ X2 @ X74)))&(![X75:$i]:(((((X6 @ X2 @ X75)))=>(((X74)=(X75)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_20, c_0_21])).
% 0.08/0.26 thf(c_0_26, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.08/0.26 thf(c_0_27, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.08/0.26 thf(c_0_28, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.08/0.26 thf(c_0_29, plain, ((exuE1)=(![X1:$i > $o]:((((?[X76:$i]:(((((X1 @ X76)))&(![X77:$i]:(((((X1 @ X77)))=>(((X76)=(X77))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_22, c_0_21])).
% 0.08/0.26 thf(c_0_30, axiom, ((prop2setE)=(![X11:$o, X2:$i]:((((in @ X2 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:(((X11)))))))=>((X11)))))), inference(apply_def,[status(thm)],[prop2setE, c_0_23])).
% 0.08/0.26 thf(c_0_31, plain, ((epred1_0)<=>![X104:$i]:(?[X105:$i]:((((![X106:$i]:(((in @ X106 @ X105)=>![X107:$i]:(((in @ X107 @ X106)=>(in @ X107 @ X104)))))&![X108:$i, X109:$i]:((((in @ X108 @ X104)&(in @ X109 @ X104))=>(![X110:$i]:(((in @ X110 @ X105)=>((in @ X108 @ X110)<=>(in @ X109 @ X110))))=>((X108)=(X109))))))&![X111:$i, X112:$i]:((((in @ X111 @ X105)&(in @ X112 @ X105))=>(![X113:$i]:(((in @ X113 @ X111)=>(in @ X113 @ X112)))|![X114:$i]:(((in @ X114 @ X112)=>(in @ X114 @ X111)))))))&![X115:$i]:(((![X116:$i]:(((in @ X116 @ X115)=>(in @ X116 @ X104)))&?[X117:$i]:((in @ X117 @ X115)))=>?[X118:$i, X119:$i]:(((((in @ X118 @ X105)&(in @ X119 @ X115))&~(?[X120:$i]:(((in @ X120 @ X118)&(in @ X120 @ X115)))))&![X121:$i]:(((in @ X121 @ X105)=>(![X122:$i]:(((in @ X122 @ X121)=>(in @ X122 @ X118)))|(in @ X119 @ X121)))))))))))), introduced(definition)).
% 0.08/0.26 thf(c_0_32, negated_conjecture, ~((![X78:$i, X79:$i]:((![X80:$i]:(((in @ X80 @ X78)<=>(in @ X80 @ X79)))=>((X78)=(X79))))=>(![X81:$i]:(~(in @ X81 @ emptyset))=>(![X82:$i, X83:$i, X84:$i]:(((in @ X84 @ (setadjoin @ X82 @ X83))<=>(((X84)=(X82))|(in @ X84 @ X83))))=>(![X85:$i, X86:$i]:(((in @ X86 @ (powerset @ X85))<=>![X87:$i]:(((in @ X87 @ X86)=>(in @ X87 @ X85)))))=>((setunionAx)=>((in @ emptyset @ omega)=>(![X88:$i]:(((in @ X88 @ omega)=>(in @ (setadjoin @ X88 @ X88) @ omega)))=>(![X89:$i]:((((in @ emptyset @ X89)&![X90:$i]:((((in @ X90 @ omega)&(in @ X90 @ X89))=>(in @ (setadjoin @ X90 @ X90) @ X89))))=>![X91:$i]:(((in @ X91 @ omega)=>(in @ X91 @ X89)))))=>(![X92:$i > $i > $o, X93:$i]:((![X94:$i]:(((in @ X94 @ X93)=>?[X95:$i]:(((X92 @ X94 @ X95)&![X96:$i]:(((X92 @ X94 @ X96)=>((X95)=(X96))))))))=>?[X97:$i]:(![X98:$i]:(((in @ X98 @ X97)<=>?[X99:$i]:(((in @ X99 @ X93)&(X92 @ X99 @ X98))))))))=>(![X100:$i]:((?[X101:$i]:((in @ X101 @ X100))=>?[X102:$i]:(((in @ X102 @ X100)&~(?[X103:$i]:(((in @ X103 @ X102)&(in @ X103 @ X100))))))))=>((epred1_0)=>((descrp)=>(![X123:$i, X124:$i > $o, X125:$i]:(((in @ X125 @ X123)=>((X124 @ X125)=>(in @ X125 @ (dsetconstr @ X123 @ (^[Z0:$i]:((X124 @ Z0))))))))=>(![X126:$i, X127:$i > $o, X128:$i]:(((in @ X128 @ (dsetconstr @ X126 @ (^[Z0:$i]:((X127 @ Z0)))))=>(in @ X128 @ X126)))=>(![X129:$i, X130:$i > $o, X131:$i]:(((in @ X131 @ (dsetconstr @ X129 @ (^[Z0:$i]:((X130 @ Z0)))))=>(X130 @ X131)))=>(![X132:$i > $o]:((?[X133:$i]:(((X132 @ X133)&![X134:$i]:(((X132 @ X134)=>((X133)=(X134))))))=>?[X135:$i]:(((X132 @ X135)&![X136:$i]:(((X132 @ X136)=>((X135)=(X136))))))))=>(![X137:$o, X138:$i]:(((in @ X138 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X137)))))=>(X137)))=>(![X139:$i]:(((in @ X139 @ emptyset)=>![X140:$o]:((X140))))=>(![X141:$i]:(~(in @ X141 @ emptyset))=>![X2:$i]:(~(in @ X2 @ emptyset)))))))))))))))))))))), 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)],[c_0_24, omegaSAx]), omegaIndAx]), c_0_25]), foundationAx]), wellorderingAx]), c_0_26]), c_0_27]), c_0_28]), c_0_29]), c_0_30]), emptysetE]), emptysetimpfalse]), emptysetAx]), setadjoinAx]), powersetAx]), omega0Ax]), setextAx])]), c_0_31])).
% 0.08/0.26 thf(c_0_33, negated_conjecture, ![X142:$i, X143:$i, X145:$i, X146:$i, X147:$i, X148:$i, X149:$i, X150:$i, X151:$i, X152:$i, X153:$i, X155:$i, X156:$i, X158:$i, X159:$i > $i > $o, X160:$i, X162:$i, X165:$i, X167:$i, X168:$i, X169:$i, X170:$i, X172:$i, X173:$i, X174:$i > $o, X175:$i, X176:$i, X177:$i > $o, X178:$i, X179:$i, X180:$i > $o, X181:$i, X182:$i > $o, X183:$i, X186:$i, X187:$o, X188:$i, X189:$i, X190:$o, X191:$i]:((((~(in @ (esk1_2 @ X142 @ X143) @ X142)|~(in @ (esk1_2 @ X142 @ X143) @ X143)|((X142)=(X143)))&((in @ (esk1_2 @ X142 @ X143) @ X142)|(in @ (esk1_2 @ X142 @ X143) @ X143)|((X142)=(X143))))&(~(in @ X145 @ emptyset)&(((~(in @ X148 @ (setadjoin @ X146 @ X147))|(((X148)=(X146))|(in @ X148 @ X147)))&((((X148)!=(X146))|(in @ X148 @ (setadjoin @ X146 @ X147)))&(~(in @ X148 @ X147)|(in @ X148 @ (setadjoin @ X146 @ X147)))))&(((~(in @ X150 @ (powerset @ X149))|(~(in @ X151 @ X150)|(in @ X151 @ X149)))&(((in @ (esk2_2 @ X152 @ X153) @ X153)|(in @ X153 @ (powerset @ X152)))&(~(in @ (esk2_2 @ X152 @ X153) @ X152)|(in @ X153 @ (powerset @ X152)))))&((setunionAx)&((in @ emptyset @ omega)&((~(in @ X155 @ omega)|(in @ (setadjoin @ X155 @ X155) @ omega))&(((((in @ (esk3_1 @ X156) @ omega)|~(in @ emptyset @ X156)|(~(in @ X158 @ omega)|(in @ X158 @ X156)))&((in @ (esk3_1 @ X156) @ X156)|~(in @ emptyset @ X156)|(~(in @ X158 @ omega)|(in @ X158 @ X156))))&(~(in @ (setadjoin @ (esk3_1 @ X156) @ (esk3_1 @ X156)) @ X156)|~(in @ emptyset @ X156)|(~(in @ X158 @ omega)|(in @ X158 @ X156))))&((((((in @ (esk7_3 @ X159 @ X160 @ X165) @ X160)|~(in @ X165 @ (esk6_2 @ X159 @ X160))|(in @ (esk4_2 @ X159 @ X160) @ X160))&((X159 @ (esk7_3 @ X159 @ X160 @ X165) @ X165)|~(in @ X165 @ (esk6_2 @ X159 @ X160))|(in @ (esk4_2 @ X159 @ X160) @ X160)))&(~(in @ X168 @ X160)|~(X159 @ X168 @ X167)|(in @ X167 @ (esk6_2 @ X159 @ X160))|(in @ (esk4_2 @ X159 @ X160) @ X160)))&(((((in @ (esk7_3 @ X159 @ X160 @ X165) @ X160)|~(in @ X165 @ (esk6_2 @ X159 @ X160))|((X159 @ (esk4_2 @ X159 @ X160) @ (esk5_3 @ X159 @ X160 @ X162))|~(X159 @ (esk4_2 @ X159 @ X160) @ X162)))&((X159 @ (esk7_3 @ X159 @ X160 @ X165) @ X165)|~(in @ X165 @ (esk6_2 @ X159 @ X160))|((X159 @ (esk4_2 @ X159 @ X160) @ (esk5_3 @ X159 @ X160 @ X162))|~(X159 @ (esk4_2 @ X159 @ X160) @ X162))))&(~(in @ X168 @ X160)|~(X159 @ X168 @ X167)|(in @ X167 @ (esk6_2 @ X159 @ X160))|((X159 @ (esk4_2 @ X159 @ X160) @ (esk5_3 @ X159 @ X160 @ X162))|~(X159 @ (esk4_2 @ X159 @ X160) @ X162))))&((((in @ (esk7_3 @ X159 @ X160 @ X165) @ X160)|~(in @ X165 @ (esk6_2 @ X159 @ X160))|(((X162)!=(esk5_3 @ X159 @ X160 @ X162))|~(X159 @ (esk4_2 @ X159 @ X160) @ X162)))&((X159 @ (esk7_3 @ X159 @ X160 @ X165) @ X165)|~(in @ X165 @ (esk6_2 @ X159 @ X160))|(((X162)!=(esk5_3 @ X159 @ X160 @ X162))|~(X159 @ (esk4_2 @ X159 @ X160) @ X162))))&(~(in @ X168 @ X160)|~(X159 @ X168 @ X167)|(in @ X167 @ (esk6_2 @ X159 @ X160))|(((X162)!=(esk5_3 @ X159 @ X160 @ X162))|~(X159 @ (esk4_2 @ X159 @ X160) @ X162))))))&((((in @ (esk8_1 @ X169) @ X169)|~(in @ X170 @ X169))&(~(in @ X172 @ (esk8_1 @ X169))|~(in @ X172 @ X169)|~(in @ X170 @ X169)))&((epred1_0)&((descrp)&((~(in @ X175 @ X173)|(~(X174 @ X175)|(in @ X175 @ (dsetconstr @ X173 @ (^[Z0:$i]:((X174 @ Z0)))))))&((~(in @ X178 @ (dsetconstr @ X176 @ (^[Z0:$i]:((X177 @ Z0)))))|(in @ X178 @ X176))&((~(in @ X181 @ (dsetconstr @ X179 @ (^[Z0:$i]:((X180 @ Z0)))))|(X180 @ X181))&(((((X182 @ (esk10_1 @ X182))|((X182 @ (esk9_2 @ X182 @ X183))|~(X182 @ X183)))&(~(X182 @ X186)|((esk10_1 @ X182)=(X186))|((X182 @ (esk9_2 @ X182 @ X183))|~(X182 @ X183))))&(((X182 @ (esk10_1 @ X182))|(((X183)!=(esk9_2 @ X182 @ X183))|~(X182 @ X183)))&(~(X182 @ X186)|((esk10_1 @ X182)=(X186))|(((X183)!=(esk9_2 @ X182 @ X183))|~(X182 @ X183)))))&((~(in @ X188 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X187)))))|(X187))&((~(in @ X189 @ emptyset)|(X190))&(~(in @ X191 @ emptyset)&(in @ esk11_0 @ emptyset))))))))))))))))))))), 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_32])])])])])])).
% 0.08/0.26 thf(c_0_34, negated_conjecture, (in @ esk11_0 @ emptyset), inference(split_conjunct,[status(thm)],[c_0_33])).
% 0.08/0.26 thf(c_0_35, negated_conjecture, ![X2:$i]:(~((in @ X2 @ emptyset))), inference(split_conjunct,[status(thm)],[c_0_33])).
% 0.08/0.26 thf(c_0_36, negated_conjecture, ($false), inference(sr,[status(thm)],[c_0_34, c_0_35]), ['proof']).
% 0.08/0.26 % SZS output end CNFRefutation
% 0.08/0.26 % Parsed axioms : 51
% 0.08/0.26 % Removed by relevancy pruning/SinE : 31
% 0.08/0.26 % Initial clauses : 52
% 0.08/0.26 % Removed in clause preprocessing : 0
% 0.08/0.26 % Initial clauses in saturation : 52
% 0.08/0.26 % Processed clauses : 6
% 0.08/0.26 % ...of these trivial : 0
% 0.08/0.26 % ...subsumed : 0
% 0.08/0.26 % ...remaining for further processing : 6
% 0.08/0.26 % Other redundant clauses eliminated : 0
% 0.08/0.26 % Clauses deleted for lack of memory : 0
% 0.08/0.26 % Backward-subsumed : 0
% 0.08/0.26 % Backward-rewritten : 0
% 0.08/0.26 % Generated clauses : 1
% 0.08/0.26 % ...of the previous two non-redundant : 0
% 0.08/0.26 % ...aggressively subsumed : 0
% 0.08/0.26 % Contextual simplify-reflections : 0
% 0.08/0.26 % Paramodulations : 0
% 0.08/0.26 % Factorizations : 0
% 0.08/0.26 % NegExts : 0
% 0.08/0.26 % Equation resolutions : 0
% 0.08/0.26 % Disequality decompositions : 0
% 0.08/0.26 % Total rewrite steps : 0
% 0.08/0.26 % ...of those cached : 0
% 0.08/0.26 % Propositional unsat checks : 0
% 0.08/0.26 % Propositional check models : 0
% 0.08/0.26 % Propositional check unsatisfiable : 0
% 0.08/0.26 % Propositional clauses : 0
% 0.08/0.26 % Propositional clauses after purity: 0
% 0.08/0.26 % Propositional unsat core size : 0
% 0.08/0.26 % Propositional preprocessing time : 0.000
% 0.08/0.26 % Propositional encoding time : 0.000
% 0.08/0.26 % Propositional solver time : 0.000
% 0.08/0.26 % Success case prop preproc time : 0.000
% 0.08/0.26 % Success case prop encoding time : 0.000
% 0.08/0.26 % Success case prop solver time : 0.000
% 0.08/0.26 % Current number of processed clauses : 5
% 0.08/0.26 % Positive orientable unit clauses : 4
% 0.08/0.26 % Positive unorientable unit clauses: 0
% 0.08/0.26 % Negative unit clauses : 1
% 0.08/0.26 % Non-unit-clauses : 0
% 0.08/0.26 % Current number of unprocessed clauses: 46
% 0.08/0.26 % ...number of literals in the above : 167
% 0.08/0.26 % Current number of archived formulas : 0
% 0.08/0.26 % Current number of archived clauses : 1
% 0.08/0.26 % Clause-clause subsumption calls (NU) : 0
% 0.08/0.26 % Rec. Clause-clause subsumption calls : 0
% 0.08/0.26 % Non-unit clause-clause subsumptions : 0
% 0.08/0.26 % Unit Clause-clause subsumption calls : 0
% 0.08/0.26 % Rewrite failures with RHS unbound : 0
% 0.08/0.26 % BW rewrite match attempts : 0
% 0.08/0.26 % BW rewrite match successes : 0
% 0.08/0.26 % Condensation attempts : 0
% 0.08/0.26 % Condensation successes : 0
% 0.08/0.26 % Termbank termtop insertions : 5356
% 0.08/0.26 % Search garbage collected termcells : 1939
% 0.08/0.26
% 0.08/0.26 % -------------------------------------------------
% 0.08/0.26 % User time : 0.006 s
% 0.08/0.26 % System time : 0.002 s
% 0.08/0.26 % Total time : 0.008 s
% 0.08/0.26 % Maximum resident set size: 4460 pages
% 0.08/0.26
% 0.08/0.26 % -------------------------------------------------
% 0.08/0.26 % User time : 0.008 s
% 0.08/0.26 % System time : 0.007 s
% 0.08/0.26 % Total time : 0.016 s
% 0.08/0.26 % Maximum resident set size: 4608 pages
% 0.08/0.26 % E exiting
%------------------------------------------------------------------------------