%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU505^1 : 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 : n004.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 08:24:17 AM UTC 2026
% Result : Theorem 0.21s 0.37s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU505^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n004.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 13:46:52 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.vEldODtZ0P/E---3.1_1308876.p
% 0.21/0.37 % Version: 3.5.1-ho
% 0.21/0.37 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.21/0.37 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.37 % Starting new_ho_10 with 1500s (5) cores
% 0.21/0.37 % Starting sh5l with 300s (1) cores
% 0.21/0.37 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.37 % Starting new_bool_2 with 300s (1) cores
% 0.21/0.37 % new_bool_2 with pid 1308892 completed with status 0
% 0.21/0.37 % Result found by new_bool_2
% 0.21/0.37 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.21/0.37 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.37 % Starting new_ho_10 with 1500s (5) cores
% 0.21/0.37 % Starting sh5l with 300s (1) cores
% 0.21/0.37 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.37 % Starting new_bool_2 with 300s (1) cores
% 0.21/0.37 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.21/0.37 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.37 % Search class: HGHSF-FFMS31-SHFSMSBN
% 0.21/0.37 % partial match(1): HGHSM-FFMS31-SHFSMSBN
% 0.21/0.37 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.37 % Starting SubtermCWHack with 31s (1) cores
% 0.21/0.37 % SubtermCWHack with pid 1308893 completed with status 0
% 0.21/0.37 % Result found by SubtermCWHack
% 0.21/0.37 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.21/0.37 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.37 % Starting new_ho_10 with 1500s (5) cores
% 0.21/0.37 % Starting sh5l with 300s (1) cores
% 0.21/0.37 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.37 % Starting new_bool_2 with 300s (1) cores
% 0.21/0.37 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.21/0.37 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.37 % Search class: HGHSF-FFMS31-SHFSMSBN
% 0.21/0.37 % partial match(1): HGHSM-FFMS31-SHFSMSBN
% 0.21/0.37 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.37 % Starting SubtermCWHack with 31s (1) cores
% 0.21/0.37 % Preprocessing time : 0.001 s
% 0.21/0.37
% 0.21/0.37 % Proof found!
% 0.21/0.37 % SZS status Theorem
% 0.21/0.37 % SZS output start CNFRefutation
% 0.21/0.37 thf(decl_23, type, in: $i > $i > $o).
% 0.21/0.37 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.21/0.37 thf(decl_25, type, setextAx: $o).
% 0.21/0.37 thf(decl_26, type, emptyset: $i).
% 0.21/0.37 thf(decl_27, type, emptysetAx: $o).
% 0.21/0.37 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.21/0.37 thf(decl_29, type, setadjoinAx: $o).
% 0.21/0.37 thf(decl_30, type, powerset: $i > $i).
% 0.21/0.37 thf(decl_31, type, powersetAx: $o).
% 0.21/0.37 thf(decl_33, type, setunionAx: $o).
% 0.21/0.37 thf(decl_34, type, omega: $i).
% 0.21/0.37 thf(decl_35, type, omega0Ax: $o).
% 0.21/0.37 thf(decl_36, type, omegaSAx: $o).
% 0.21/0.37 thf(decl_37, type, omegaIndAx: $o).
% 0.21/0.37 thf(decl_38, type, replAx: $o).
% 0.21/0.37 thf(decl_39, type, foundationAx: $o).
% 0.21/0.37 thf(decl_40, type, wellorderingAx: $o).
% 0.21/0.37 thf(decl_42, type, descrp: $o).
% 0.21/0.37 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.21/0.37 thf(decl_44, type, dsetconstrI: $o).
% 0.21/0.37 thf(decl_45, type, dsetconstrEL: $o).
% 0.21/0.37 thf(decl_46, type, dsetconstrER: $o).
% 0.21/0.37 thf(decl_47, type, exuE1: $o).
% 0.21/0.37 thf(decl_48, type, prop2set: $o > $i).
% 0.21/0.37 thf(decl_49, type, prop2setE: $o).
% 0.21/0.37 thf(decl_50, type, emptysetE: $o).
% 0.21/0.37 thf(decl_51, type, emptysetimpfalse: $o).
% 0.21/0.37 thf(decl_52, type, notinemptyset: $o).
% 0.21/0.37 thf(decl_53, type, exuE3e: $o).
% 0.21/0.37 thf(decl_54, type, epred1_0: $o).
% 0.21/0.37 thf(decl_55, type, esk1_2: $i > $i > $i).
% 0.21/0.37 thf(decl_56, type, esk2_2: $i > $i > $i).
% 0.21/0.37 thf(decl_57, type, esk3_1: $i > $i).
% 0.21/0.37 thf(decl_58, type, esk4_2: ($i > $i > $o) > $i > $i).
% 0.21/0.37 thf(decl_59, type, esk5_3: ($i > $i > $o) > $i > $i > $i).
% 0.21/0.37 thf(decl_60, type, esk6_2: ($i > $i > $o) > $i > $i).
% 0.21/0.37 thf(decl_61, type, esk7_3: ($i > $i > $o) > $i > $i > $i).
% 0.21/0.37 thf(decl_62, type, esk8_1: $i > $i).
% 0.21/0.37 thf(decl_63, type, esk9_2: ($i > $o) > $i > $i).
% 0.21/0.37 thf(decl_64, type, esk10_1: ($i > $o) > $i).
% 0.21/0.37 thf(decl_65, type, esk11_2: ($i > $o) > $i > $i).
% 0.21/0.37 thf(decl_66, type, esk12_1: ($i > $o) > $i).
% 0.21/0.37 thf(decl_67, type, esk13_0: $i).
% 0.21/0.37 thf(decl_68, type, esk14_0: $i).
% 0.21/0.37 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.vEldODtZ0P/E---3.1_1308876.p', replAx)).
% 0.21/0.37 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.vEldODtZ0P/E---3.1_1308876.p', exu)).
% 0.21/0.37 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.vEldODtZ0P/E---3.1_1308876.p', exuE1)).
% 0.21/0.37 thf(prop2set, axiom, ((prop2set)=(^[X10:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[X2:$i]:((X10)))))), file('/export/starexec/sandbox2/tmp/tmp.vEldODtZ0P/E---3.1_1308876.p', prop2set)).
% 0.21/0.37 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.vEldODtZ0P/E---3.1_1308876.p', exuE3e)).
% 0.21/0.37 thf(setext, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.vEldODtZ0P/E---3.1_1308876.p', setext)).
% 0.21/0.37 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.vEldODtZ0P/E---3.1_1308876.p', dsetconstrI)).
% 0.21/0.37 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.vEldODtZ0P/E---3.1_1308876.p', dsetconstrEL)).
% 0.21/0.37 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.vEldODtZ0P/E---3.1_1308876.p', dsetconstrER)).
% 0.21/0.37 thf(prop2setE, axiom, ((prop2setE)<=>![X11:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X11))))=>(X11)))), file('/export/starexec/sandbox2/tmp/tmp.vEldODtZ0P/E---3.1_1308876.p', prop2setE)).
% 0.21/0.37 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.vEldODtZ0P/E---3.1_1308876.p', foundationAx)).
% 0.21/0.37 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.vEldODtZ0P/E---3.1_1308876.p', wellorderingAx)).
% 0.21/0.37 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X12:$o]:((X12))))), file('/export/starexec/sandbox2/tmp/tmp.vEldODtZ0P/E---3.1_1308876.p', emptysetE)).
% 0.21/0.37 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.vEldODtZ0P/E---3.1_1308876.p', emptysetimpfalse)).
% 0.21/0.37 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.vEldODtZ0P/E---3.1_1308876.p', notinemptyset)).
% 0.21/0.37 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.vEldODtZ0P/E---3.1_1308876.p', emptysetAx)).
% 0.21/0.37 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.vEldODtZ0P/E---3.1_1308876.p', setextAx)).
% 0.21/0.37 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.vEldODtZ0P/E---3.1_1308876.p', powersetAx)).
% 0.21/0.37 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.vEldODtZ0P/E---3.1_1308876.p', omega0Ax)).
% 0.21/0.37 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.vEldODtZ0P/E---3.1_1308876.p', omegaSAx)).
% 0.21/0.37 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.vEldODtZ0P/E---3.1_1308876.p', omegaIndAx)).
% 0.21/0.37 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.vEldODtZ0P/E---3.1_1308876.p', setadjoinAx)).
% 0.21/0.37 thf(c_0_22, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.21/0.37 thf(c_0_23, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.21/0.37 thf(c_0_24, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.21/0.37 thf(c_0_25, plain, ((prop2set)=(^[Z0:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[Z1:$i]:((Z0)))))), inference(fof_simplification,[status(thm)],[prop2set])).
% 0.21/0.37 thf(c_0_26, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.21/0.37 thf(c_0_27, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[setext])).
% 0.21/0.37 thf(c_0_28, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X80:$i]:(((((X6 @ X2 @ X80)))&(![X81:$i]:(((((X6 @ X2 @ X81)))=>(((X80)=(X81)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_22, c_0_23])).
% 0.21/0.37 thf(c_0_29, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.21/0.37 thf(c_0_30, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.21/0.37 thf(c_0_31, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.21/0.37 thf(c_0_32, plain, ((exuE1)=(![X1:$i > $o]:((((?[X82:$i]:(((((X1 @ X82)))&(![X83:$i]:(((((X1 @ X83)))=>(((X82)=(X83))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_24, c_0_23])).
% 0.21/0.37 thf(c_0_33, axiom, ((prop2setE)=(![X11:$o, X2:$i]:((((in @ X2 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:(((X11)))))))=>((X11)))))), inference(apply_def,[status(thm)],[prop2setE, c_0_25])).
% 0.21/0.37 thf(c_0_34, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X84:$i]:(((((X1 @ X84)))&(![X85:$i]:(((((X1 @ X85)))=>(((X84)=(X85))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_26, c_0_23])).
% 0.21/0.37 thf(c_0_35, plain, ((epred1_0)<=>![X112:$i]:(?[X113:$i]:((((![X114:$i]:(((in @ X114 @ X113)=>![X115:$i]:(((in @ X115 @ X114)=>(in @ X115 @ X112)))))&![X116:$i, X117:$i]:((((in @ X116 @ X112)&(in @ X117 @ X112))=>(![X118:$i]:(((in @ X118 @ X113)=>((in @ X116 @ X118)<=>(in @ X117 @ X118))))=>((X116)=(X117))))))&![X119:$i, X120:$i]:((((in @ X119 @ X113)&(in @ X120 @ X113))=>(![X121:$i]:(((in @ X121 @ X119)=>(in @ X121 @ X120)))|![X122:$i]:(((in @ X122 @ X120)=>(in @ X122 @ X119)))))))&![X123:$i]:(((![X124:$i]:(((in @ X124 @ X123)=>(in @ X124 @ X112)))&?[X125:$i]:((in @ X125 @ X123)))=>?[X126:$i, X127:$i]:(((((in @ X126 @ X113)&(in @ X127 @ X123))&~(?[X128:$i]:(((in @ X128 @ X126)&(in @ X128 @ X123)))))&![X129:$i]:(((in @ X129 @ X113)=>(![X130:$i]:(((in @ X130 @ X129)=>(in @ X130 @ X126)))|(in @ X127 @ X129)))))))))))), introduced(definition)).
% 0.21/0.37 thf(c_0_36, negated_conjecture, ~((![X86:$i, X87:$i]:((![X88:$i]:(((in @ X88 @ X86)<=>(in @ X88 @ X87)))=>((X86)=(X87))))=>(![X89:$i]:(~(in @ X89 @ emptyset))=>(![X90:$i, X91:$i, X92:$i]:(((in @ X92 @ (setadjoin @ X90 @ X91))<=>(((X92)=(X90))|(in @ X92 @ X91))))=>(![X93:$i, X94:$i]:(((in @ X94 @ (powerset @ X93))<=>![X95:$i]:(((in @ X95 @ X94)=>(in @ X95 @ X93)))))=>((setunionAx)=>((in @ emptyset @ omega)=>(![X96:$i]:(((in @ X96 @ omega)=>(in @ (setadjoin @ X96 @ X96) @ omega)))=>(![X97:$i]:((((in @ emptyset @ X97)&![X98:$i]:((((in @ X98 @ omega)&(in @ X98 @ X97))=>(in @ (setadjoin @ X98 @ X98) @ X97))))=>![X99:$i]:(((in @ X99 @ omega)=>(in @ X99 @ X97)))))=>(![X100:$i > $i > $o, X101:$i]:((![X102:$i]:(((in @ X102 @ X101)=>?[X103:$i]:(((X100 @ X102 @ X103)&![X104:$i]:(((X100 @ X102 @ X104)=>((X103)=(X104))))))))=>?[X105:$i]:(![X106:$i]:(((in @ X106 @ X105)<=>?[X107:$i]:(((in @ X107 @ X101)&(X100 @ X107 @ X106))))))))=>(![X108:$i]:((?[X109:$i]:((in @ X109 @ X108))=>?[X110:$i]:(((in @ X110 @ X108)&~(?[X111:$i]:(((in @ X111 @ X110)&(in @ X111 @ X108))))))))=>((epred1_0)=>((descrp)=>(![X131:$i, X132:$i > $o, X133:$i]:(((in @ X133 @ X131)=>((X132 @ X133)=>(in @ X133 @ (dsetconstr @ X131 @ (^[Z0:$i]:((X132 @ Z0))))))))=>(![X134:$i, X135:$i > $o, X136:$i]:(((in @ X136 @ (dsetconstr @ X134 @ (^[Z0:$i]:((X135 @ Z0)))))=>(in @ X136 @ X134)))=>(![X137:$i, X138:$i > $o, X139:$i]:(((in @ X139 @ (dsetconstr @ X137 @ (^[Z0:$i]:((X138 @ Z0)))))=>(X138 @ X139)))=>(![X140:$i > $o]:((?[X141:$i]:(((X140 @ X141)&![X142:$i]:(((X140 @ X142)=>((X141)=(X142))))))=>?[X143:$i]:(((X140 @ X143)&![X144:$i]:(((X140 @ X144)=>((X143)=(X144))))))))=>(![X145:$o, X146:$i]:(((in @ X146 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X145)))))=>(X145)))=>(![X147:$i]:(((in @ X147 @ emptyset)=>![X148:$o]:((X148))))=>(![X149:$i]:(~(in @ X149 @ emptyset))=>(![X150:$i]:(~(in @ X150 @ emptyset))=>(![X151:$i > $o]:((?[X152:$i]:(((X151 @ X152)&![X153:$i]:(((X151 @ X153)=>((X152)=(X153))))))=>?[X154:$i]:((X151 @ X154))))=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5))))))))))))))))))))))))))), 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)],[c_0_27, c_0_28]), foundationAx]), wellorderingAx]), c_0_29]), c_0_30]), c_0_31]), c_0_32]), c_0_33]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_34]), emptysetAx]), setextAx]), powersetAx]), omega0Ax]), omegaSAx]), omegaIndAx]), setadjoinAx])]), c_0_35])).
% 0.21/0.37 thf(c_0_37, negated_conjecture, ![X155:$i, X156:$i, X158:$i, X159:$i, X160:$i, X161:$i, X162:$i, X163:$i, X164:$i, X165:$i, X166:$i, X168:$i, X169:$i, X171:$i, X172:$i > $i > $o, X173:$i, X175:$i, X178:$i, X180:$i, X181:$i, X182:$i, X183:$i, X185:$i, X186:$i, X187:$i > $o, X188:$i, X189:$i, X190:$i > $o, X191:$i, X192:$i, X193:$i > $o, X194:$i, X195:$i > $o, X196:$i, X199:$i, X200:$o, X201:$i, X202:$i, X203:$o, X204:$i, X205:$i, X206:$i > $o, X207:$i, X212:$i, X213:$i]:((((~(in @ (esk1_2 @ X155 @ X156) @ X155)|~(in @ (esk1_2 @ X155 @ X156) @ X156)|((X155)=(X156)))&((in @ (esk1_2 @ X155 @ X156) @ X155)|(in @ (esk1_2 @ X155 @ X156) @ X156)|((X155)=(X156))))&(~(in @ X158 @ emptyset)&(((~(in @ X161 @ (setadjoin @ X159 @ X160))|(((X161)=(X159))|(in @ X161 @ X160)))&((((X161)!=(X159))|(in @ X161 @ (setadjoin @ X159 @ X160)))&(~(in @ X161 @ X160)|(in @ X161 @ (setadjoin @ X159 @ X160)))))&(((~(in @ X163 @ (powerset @ X162))|(~(in @ X164 @ X163)|(in @ X164 @ X162)))&(((in @ (esk2_2 @ X165 @ X166) @ X166)|(in @ X166 @ (powerset @ X165)))&(~(in @ (esk2_2 @ X165 @ X166) @ X165)|(in @ X166 @ (powerset @ X165)))))&((setunionAx)&((in @ emptyset @ omega)&((~(in @ X168 @ omega)|(in @ (setadjoin @ X168 @ X168) @ omega))&(((((in @ (esk3_1 @ X169) @ omega)|~(in @ emptyset @ X169)|(~(in @ X171 @ omega)|(in @ X171 @ X169)))&((in @ (esk3_1 @ X169) @ X169)|~(in @ emptyset @ X169)|(~(in @ X171 @ omega)|(in @ X171 @ X169))))&(~(in @ (setadjoin @ (esk3_1 @ X169) @ (esk3_1 @ X169)) @ X169)|~(in @ emptyset @ X169)|(~(in @ X171 @ omega)|(in @ X171 @ X169))))&((((((in @ (esk7_3 @ X172 @ X173 @ X178) @ X173)|~(in @ X178 @ (esk6_2 @ X172 @ X173))|(in @ (esk4_2 @ X172 @ X173) @ X173))&((X172 @ (esk7_3 @ X172 @ X173 @ X178) @ X178)|~(in @ X178 @ (esk6_2 @ X172 @ X173))|(in @ (esk4_2 @ X172 @ X173) @ X173)))&(~(in @ X181 @ X173)|~(X172 @ X181 @ X180)|(in @ X180 @ (esk6_2 @ X172 @ X173))|(in @ (esk4_2 @ X172 @ X173) @ X173)))&(((((in @ (esk7_3 @ X172 @ X173 @ X178) @ X173)|~(in @ X178 @ (esk6_2 @ X172 @ X173))|((X172 @ (esk4_2 @ X172 @ X173) @ (esk5_3 @ X172 @ X173 @ X175))|~(X172 @ (esk4_2 @ X172 @ X173) @ X175)))&((X172 @ (esk7_3 @ X172 @ X173 @ X178) @ X178)|~(in @ X178 @ (esk6_2 @ X172 @ X173))|((X172 @ (esk4_2 @ X172 @ X173) @ (esk5_3 @ X172 @ X173 @ X175))|~(X172 @ (esk4_2 @ X172 @ X173) @ X175))))&(~(in @ X181 @ X173)|~(X172 @ X181 @ X180)|(in @ X180 @ (esk6_2 @ X172 @ X173))|((X172 @ (esk4_2 @ X172 @ X173) @ (esk5_3 @ X172 @ X173 @ X175))|~(X172 @ (esk4_2 @ X172 @ X173) @ X175))))&((((in @ (esk7_3 @ X172 @ X173 @ X178) @ X173)|~(in @ X178 @ (esk6_2 @ X172 @ X173))|(((X175)!=(esk5_3 @ X172 @ X173 @ X175))|~(X172 @ (esk4_2 @ X172 @ X173) @ X175)))&((X172 @ (esk7_3 @ X172 @ X173 @ X178) @ X178)|~(in @ X178 @ (esk6_2 @ X172 @ X173))|(((X175)!=(esk5_3 @ X172 @ X173 @ X175))|~(X172 @ (esk4_2 @ X172 @ X173) @ X175))))&(~(in @ X181 @ X173)|~(X172 @ X181 @ X180)|(in @ X180 @ (esk6_2 @ X172 @ X173))|(((X175)!=(esk5_3 @ X172 @ X173 @ X175))|~(X172 @ (esk4_2 @ X172 @ X173) @ X175))))))&((((in @ (esk8_1 @ X182) @ X182)|~(in @ X183 @ X182))&(~(in @ X185 @ (esk8_1 @ X182))|~(in @ X185 @ X182)|~(in @ X183 @ X182)))&((epred1_0)&((descrp)&((~(in @ X188 @ X186)|(~(X187 @ X188)|(in @ X188 @ (dsetconstr @ X186 @ (^[Z0:$i]:((X187 @ Z0)))))))&((~(in @ X191 @ (dsetconstr @ X189 @ (^[Z0:$i]:((X190 @ Z0)))))|(in @ X191 @ X189))&((~(in @ X194 @ (dsetconstr @ X192 @ (^[Z0:$i]:((X193 @ Z0)))))|(X193 @ X194))&(((((X195 @ (esk10_1 @ X195))|((X195 @ (esk9_2 @ X195 @ X196))|~(X195 @ X196)))&(~(X195 @ X199)|((esk10_1 @ X195)=(X199))|((X195 @ (esk9_2 @ X195 @ X196))|~(X195 @ X196))))&(((X195 @ (esk10_1 @ X195))|(((X196)!=(esk9_2 @ X195 @ X196))|~(X195 @ X196)))&(~(X195 @ X199)|((esk10_1 @ X195)=(X199))|(((X196)!=(esk9_2 @ X195 @ X196))|~(X195 @ X196)))))&((~(in @ X201 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X200)))))|(X200))&((~(in @ X202 @ emptyset)|(X203))&(~(in @ X204 @ emptyset)&(~(in @ X205 @ emptyset)&((((X206 @ (esk11_2 @ X206 @ X207))|~(X206 @ X207)|(X206 @ (esk12_1 @ X206)))&(((X207)!=(esk11_2 @ X206 @ X207))|~(X206 @ X207)|(X206 @ (esk12_1 @ X206))))&((~(in @ X212 @ esk13_0)|(in @ X212 @ esk14_0))&((~(in @ X213 @ esk14_0)|(in @ X213 @ esk13_0))&((esk13_0)!=(esk14_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_36])])])])])])).
% 0.21/0.37 thf(c_0_38, negated_conjecture, ![X2:$i]:(((in @ X2 @ esk13_0)|~((in @ X2 @ esk14_0)))), inference(split_conjunct,[status(thm)],[c_0_37])).
% 0.21/0.37 thf(c_0_39, negated_conjecture, ![X2:$i, X3:$i]:(((in @ (esk1_2 @ X2 @ X3) @ X2)|(in @ (esk1_2 @ X2 @ X3) @ X3)|((X2)=(X3)))), inference(split_conjunct,[status(thm)],[c_0_37])).
% 0.21/0.37 thf(c_0_40, negated_conjecture, ![X2:$i]:((((esk14_0)=(X2))|(in @ (esk1_2 @ esk14_0 @ X2) @ esk13_0)|(in @ (esk1_2 @ esk14_0 @ X2) @ X2))), inference(spm,[status(thm)],[c_0_38, c_0_39])).
% 0.21/0.37 thf(c_0_41, negated_conjecture, ((esk13_0)!=(esk14_0)), inference(split_conjunct,[status(thm)],[c_0_37])).
% 0.21/0.37 thf(c_0_42, negated_conjecture, ![X2:$i, X3:$i]:((((X2)=(X3))|~((in @ (esk1_2 @ X2 @ X3) @ X2))|~((in @ (esk1_2 @ X2 @ X3) @ X3)))), inference(split_conjunct,[status(thm)],[c_0_37])).
% 0.21/0.37 thf(c_0_43, negated_conjecture, (in @ (esk1_2 @ esk14_0 @ esk13_0) @ esk13_0), inference(sr,[status(thm)],[inference(ef,[status(thm)],[c_0_40]), c_0_41])).
% 0.21/0.37 thf(c_0_44, negated_conjecture, ~((in @ (esk1_2 @ esk14_0 @ esk13_0) @ esk14_0)), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42, c_0_43]), c_0_41])).
% 0.21/0.37 thf(c_0_45, negated_conjecture, ![X2:$i]:(((in @ X2 @ esk14_0)|~((in @ X2 @ esk13_0)))), inference(split_conjunct,[status(thm)],[c_0_37])).
% 0.21/0.37 thf(c_0_46, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44, c_0_45]), c_0_43])]), ['proof']).
% 0.21/0.37 % SZS output end CNFRefutation
% 0.21/0.37 % Parsed axioms : 55
% 0.21/0.37 % Removed by relevancy pruning/SinE : 33
% 0.21/0.37 % Initial clauses : 57
% 0.21/0.37 % Removed in clause preprocessing : 0
% 0.21/0.37 % Initial clauses in saturation : 57
% 0.21/0.37 % Processed clauses : 714
% 0.21/0.37 % ...of these trivial : 5
% 0.21/0.37 % ...subsumed : 367
% 0.21/0.37 % ...remaining for further processing : 342
% 0.21/0.37 % Other redundant clauses eliminated : 7
% 0.21/0.37 % Clauses deleted for lack of memory : 0
% 0.21/0.37 % Backward-subsumed : 40
% 0.21/0.37 % Backward-rewritten : 20
% 0.21/0.37 % Generated clauses : 7941
% 0.21/0.37 % ...of the previous two non-redundant : 7057
% 0.21/0.37 % ...aggressively subsumed : 0
% 0.21/0.37 % Contextual simplify-reflections : 0
% 0.21/0.37 % Paramodulations : 7924
% 0.21/0.37 % Factorizations : 10
% 0.21/0.37 % NegExts : 0
% 0.21/0.37 % Equation resolutions : 7
% 0.21/0.37 % Disequality decompositions : 0
% 0.21/0.37 % Total rewrite steps : 1200
% 0.21/0.37 % ...of those cached : 1110
% 0.21/0.37 % Propositional unsat checks : 0
% 0.21/0.37 % Propositional check models : 0
% 0.21/0.37 % Propositional check unsatisfiable : 0
% 0.21/0.37 % Propositional clauses : 0
% 0.21/0.37 % Propositional clauses after purity: 0
% 0.21/0.37 % Propositional unsat core size : 0
% 0.21/0.37 % Propositional preprocessing time : 0.000
% 0.21/0.37 % Propositional encoding time : 0.000
% 0.21/0.37 % Propositional solver time : 0.000
% 0.21/0.37 % Success case prop preproc time : 0.000
% 0.21/0.37 % Success case prop encoding time : 0.000
% 0.21/0.37 % Success case prop solver time : 0.000
% 0.21/0.37 % Current number of processed clauses : 281
% 0.21/0.37 % Positive orientable unit clauses : 31
% 0.21/0.37 % Positive unorientable unit clauses: 0
% 0.21/0.37 % Negative unit clauses : 3
% 0.21/0.37 % Non-unit-clauses : 247
% 0.21/0.37 % Current number of unprocessed clauses: 6287
% 0.21/0.37 % ...number of literals in the above : 23974
% 0.21/0.37 % Current number of archived formulas : 0
% 0.21/0.37 % Current number of archived clauses : 60
% 0.21/0.37 % Clause-clause subsumption calls (NU) : 19996
% 0.21/0.37 % Rec. Clause-clause subsumption calls : 14282
% 0.21/0.37 % Non-unit clause-clause subsumptions : 319
% 0.21/0.37 % Unit Clause-clause subsumption calls : 894
% 0.21/0.37 % Rewrite failures with RHS unbound : 0
% 0.21/0.37 % BW rewrite match attempts : 20
% 0.21/0.37 % BW rewrite match successes : 6
% 0.21/0.37 % Condensation attempts : 0
% 0.21/0.37 % Condensation successes : 0
% 0.21/0.37 % Termbank termtop insertions : 144904
% 0.21/0.37 % Search garbage collected termcells : 2190
% 0.21/0.37
% 0.21/0.37 % -------------------------------------------------
% 0.21/0.37 % User time : 0.102 s
% 0.21/0.37 % System time : 0.007 s
% 0.21/0.37 % Total time : 0.109 s
% 0.21/0.37 % Maximum resident set size: 4208 pages
% 0.21/0.37
% 0.21/0.37 % -------------------------------------------------
% 0.21/0.37 % User time : 0.104 s
% 0.21/0.37 % System time : 0.009 s
% 0.21/0.37 % Total time : 0.114 s
% 0.21/0.37 % Maximum resident set size: 4864 pages
% 0.21/0.37 % E exiting
%------------------------------------------------------------------------------