%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU509^1 : 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 : n003.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 08:26:31 AM UTC 2026
% Result : Theorem 0.22s 0.27s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU509^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n003.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 13:48:59 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.24 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.ZZfI315NuB/E---3.1_2524933.p
% 0.22/0.27 % Version: 3.5.1-ho
% 0.22/0.27 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.22/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.22/0.27 % Starting sh5l with 300s (1) cores
% 0.22/0.27 % Starting new_bool_1 with 300s (1) cores
% 0.22/0.27 % Starting new_bool_2 with 300s (1) cores
% 0.22/0.27 % new_bool_1 with pid 2524962 completed with status 0
% 0.22/0.27 % Result found by new_bool_1
% 0.22/0.27 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.22/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.22/0.27 % Starting sh5l with 300s (1) cores
% 0.22/0.27 % Starting new_bool_1 with 300s (1) cores
% 0.22/0.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.22/0.27 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.22/0.27 % Search class: HGHSF-FFMS31-SHFSMSBN
% 0.22/0.27 % partial match(1): HGHSM-FFMS31-SHFSMSBN
% 0.22/0.27 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.27 % Starting SubtermCWHack with 31s (1) cores
% 0.22/0.27 % SubtermCWHack with pid 2524968 completed with status 0
% 0.22/0.27 % Result found by SubtermCWHack
% 0.22/0.27 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.22/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.22/0.27 % Starting sh5l with 300s (1) cores
% 0.22/0.27 % Starting new_bool_1 with 300s (1) cores
% 0.22/0.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.22/0.27 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.22/0.27 % Search class: HGHSF-FFMS31-SHFSMSBN
% 0.22/0.27 % partial match(1): HGHSM-FFMS31-SHFSMSBN
% 0.22/0.27 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.27 % Starting SubtermCWHack with 31s (1) cores
% 0.22/0.27 % Preprocessing time : 0.002 s
% 0.22/0.27
% 0.22/0.27 % Proof found!
% 0.22/0.27 % SZS status Theorem
% 0.22/0.27 % SZS output start CNFRefutation
% 0.22/0.27 thf(decl_23, type, in: $i > $i > $o).
% 0.22/0.27 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.22/0.27 thf(decl_25, type, setextAx: $o).
% 0.22/0.27 thf(decl_26, type, emptyset: $i).
% 0.22/0.27 thf(decl_27, type, emptysetAx: $o).
% 0.22/0.27 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.22/0.27 thf(decl_29, type, setadjoinAx: $o).
% 0.22/0.27 thf(decl_30, type, powerset: $i > $i).
% 0.22/0.27 thf(decl_31, type, powersetAx: $o).
% 0.22/0.27 thf(decl_33, type, setunionAx: $o).
% 0.22/0.27 thf(decl_34, type, omega: $i).
% 0.22/0.27 thf(decl_35, type, omega0Ax: $o).
% 0.22/0.27 thf(decl_36, type, omegaSAx: $o).
% 0.22/0.27 thf(decl_37, type, omegaIndAx: $o).
% 0.22/0.27 thf(decl_38, type, replAx: $o).
% 0.22/0.27 thf(decl_39, type, foundationAx: $o).
% 0.22/0.27 thf(decl_40, type, wellorderingAx: $o).
% 0.22/0.27 thf(decl_42, type, descrp: $o).
% 0.22/0.27 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.22/0.27 thf(decl_44, type, dsetconstrI: $o).
% 0.22/0.27 thf(decl_45, type, dsetconstrEL: $o).
% 0.22/0.27 thf(decl_46, type, dsetconstrER: $o).
% 0.22/0.27 thf(decl_47, type, exuE1: $o).
% 0.22/0.27 thf(decl_48, type, prop2set: $o > $i).
% 0.22/0.27 thf(decl_49, type, prop2setE: $o).
% 0.22/0.27 thf(decl_50, type, emptysetE: $o).
% 0.22/0.27 thf(decl_51, type, emptysetimpfalse: $o).
% 0.22/0.27 thf(decl_52, type, notinemptyset: $o).
% 0.22/0.27 thf(decl_53, type, exuE3e: $o).
% 0.22/0.27 thf(decl_54, type, setext: $o).
% 0.22/0.27 thf(decl_55, type, emptyI: $o).
% 0.22/0.27 thf(decl_56, type, noeltsimpempty: $o).
% 0.22/0.27 thf(decl_57, type, setbeta: $o).
% 0.22/0.27 thf(decl_58, type, nonempty: $i > $o).
% 0.22/0.27 thf(decl_59, type, epred1_0: $o).
% 0.22/0.27 thf(decl_60, type, esk1_2: $i > $i > $i).
% 0.22/0.27 thf(decl_61, type, esk2_2: $i > $i > $i).
% 0.22/0.27 thf(decl_62, type, esk3_1: $i > $i).
% 0.22/0.27 thf(decl_63, type, esk4_2: ($i > $i > $o) > $i > $i).
% 0.22/0.27 thf(decl_64, type, esk5_3: ($i > $i > $o) > $i > $i > $i).
% 0.22/0.27 thf(decl_65, type, esk6_2: ($i > $i > $o) > $i > $i).
% 0.22/0.27 thf(decl_66, type, esk7_3: ($i > $i > $o) > $i > $i > $i).
% 0.22/0.27 thf(decl_67, type, esk8_1: $i > $i).
% 0.22/0.27 thf(decl_68, type, esk9_2: ($i > $o) > $i > $i).
% 0.22/0.27 thf(decl_69, type, esk10_1: ($i > $o) > $i).
% 0.22/0.27 thf(decl_70, type, esk11_2: ($i > $o) > $i > $i).
% 0.22/0.27 thf(decl_71, type, esk12_1: ($i > $o) > $i).
% 0.22/0.27 thf(decl_72, type, esk13_2: $i > $i > $i).
% 0.22/0.27 thf(decl_73, type, esk14_2: $i > $i > $i).
% 0.22/0.27 thf(decl_74, type, esk15_1: $i > $i).
% 0.22/0.27 thf(decl_75, type, esk16_1: $i > $i).
% 0.22/0.27 thf(decl_76, type, esk17_0: $i).
% 0.22/0.27 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.ZZfI315NuB/E---3.1_2524933.p', exuE1)).
% 0.22/0.27 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ZZfI315NuB/E---3.1_2524933.p', exu)).
% 0.22/0.27 thf(prop2set, axiom, ((prop2set)=(^[X10:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[X2:$i]:((X10)))))), file('/export/starexec/sandbox2/tmp/tmp.ZZfI315NuB/E---3.1_2524933.p', prop2set)).
% 0.22/0.27 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.ZZfI315NuB/E---3.1_2524933.p', exuE3e)).
% 0.22/0.27 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.ZZfI315NuB/E---3.1_2524933.p', replAx)).
% 0.22/0.27 thf(nonemptyE1, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ZZfI315NuB/E---3.1_2524933.p', nonemptyE1)).
% 0.22/0.27 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.ZZfI315NuB/E---3.1_2524933.p', dsetconstrER)).
% 0.22/0.27 thf(prop2setE, axiom, ((prop2setE)<=>![X11:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X11))))=>(X11)))), file('/export/starexec/sandbox2/tmp/tmp.ZZfI315NuB/E---3.1_2524933.p', prop2setE)).
% 0.22/0.27 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.ZZfI315NuB/E---3.1_2524933.p', setbeta)).
% 0.22/0.27 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ZZfI315NuB/E---3.1_2524933.p', nonempty)).
% 0.22/0.27 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.ZZfI315NuB/E---3.1_2524933.p', dsetconstrI)).
% 0.22/0.27 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.ZZfI315NuB/E---3.1_2524933.p', dsetconstrEL)).
% 0.22/0.27 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X12:$o]:((X12))))), file('/export/starexec/sandbox2/tmp/tmp.ZZfI315NuB/E---3.1_2524933.p', emptysetE)).
% 0.22/0.27 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.ZZfI315NuB/E---3.1_2524933.p', emptysetimpfalse)).
% 0.22/0.27 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.ZZfI315NuB/E---3.1_2524933.p', notinemptyset)).
% 0.22/0.27 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.ZZfI315NuB/E---3.1_2524933.p', setext)).
% 0.22/0.27 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ZZfI315NuB/E---3.1_2524933.p', emptyI)).
% 0.22/0.27 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.ZZfI315NuB/E---3.1_2524933.p', noeltsimpempty)).
% 0.22/0.27 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ZZfI315NuB/E---3.1_2524933.p', omegaIndAx)).
% 0.22/0.27 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.ZZfI315NuB/E---3.1_2524933.p', omegaSAx)).
% 0.22/0.27 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.ZZfI315NuB/E---3.1_2524933.p', omega0Ax)).
% 0.22/0.27 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.ZZfI315NuB/E---3.1_2524933.p', powersetAx)).
% 0.22/0.27 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.ZZfI315NuB/E---3.1_2524933.p', setadjoinAx)).
% 0.22/0.27 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.ZZfI315NuB/E---3.1_2524933.p', emptysetAx)).
% 0.22/0.27 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.ZZfI315NuB/E---3.1_2524933.p', setextAx)).
% 0.22/0.27 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.ZZfI315NuB/E---3.1_2524933.p', foundationAx)).
% 0.22/0.27 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.ZZfI315NuB/E---3.1_2524933.p', wellorderingAx)).
% 0.22/0.27 thf(c_0_27, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.22/0.27 thf(c_0_28, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.22/0.27 thf(c_0_29, plain, ((prop2set)=(^[Z0:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[Z1:$i]:((Z0)))))), inference(fof_simplification,[status(thm)],[prop2set])).
% 0.22/0.27 thf(c_0_30, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.22/0.27 thf(c_0_31, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.22/0.27 thf(c_0_32, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4)))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[nonemptyE1])).
% 0.22/0.27 thf(c_0_33, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.22/0.27 thf(c_0_34, plain, ((exuE1)=(![X1:$i > $o]:((((?[X91:$i]:(((((X1 @ X91)))&(![X92:$i]:(((((X1 @ X92)))=>(((X91)=(X92))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_27, c_0_28])).
% 0.22/0.27 thf(c_0_35, axiom, ((prop2setE)=(![X11:$o, X2:$i]:((((in @ X2 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:(((X11)))))))=>((X11)))))), inference(apply_def,[status(thm)],[prop2setE, c_0_29])).
% 0.22/0.27 thf(c_0_36, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X93:$i]:(((((X1 @ X93)))&(![X94:$i]:(((((X1 @ X94)))=>(((X93)=(X94))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_30, c_0_28])).
% 0.22/0.27 thf(c_0_37, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.22/0.27 thf(c_0_38, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.22/0.27 thf(c_0_39, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.22/0.27 thf(c_0_40, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.22/0.27 thf(c_0_41, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X89:$i]:(((((X6 @ X2 @ X89)))&(![X90:$i]:(((((X6 @ X2 @ X90)))=>(((X89)=(X90)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_31, c_0_28])).
% 0.22/0.27 thf(c_0_42, plain, ((epred1_0)<=>![X121:$i]:(?[X122:$i]:((((![X123:$i]:(((in @ X123 @ X122)=>![X124:$i]:(((in @ X124 @ X123)=>(in @ X124 @ X121)))))&![X125:$i, X126:$i]:((((in @ X125 @ X121)&(in @ X126 @ X121))=>(![X127:$i]:(((in @ X127 @ X122)=>((in @ X125 @ X127)<=>(in @ X126 @ X127))))=>((X125)=(X126))))))&![X128:$i, X129:$i]:((((in @ X128 @ X122)&(in @ X129 @ X122))=>(![X130:$i]:(((in @ X130 @ X128)=>(in @ X130 @ X129)))|![X131:$i]:(((in @ X131 @ X129)=>(in @ X131 @ X128)))))))&![X132:$i]:(((![X133:$i]:(((in @ X133 @ X132)=>(in @ X133 @ X121)))&?[X134:$i]:((in @ X134 @ X132)))=>?[X135:$i, X136:$i]:(((((in @ X135 @ X122)&(in @ X136 @ X132))&~(?[X137:$i]:(((in @ X137 @ X135)&(in @ X137 @ X132)))))&![X138:$i]:(((in @ X138 @ X122)=>(![X139:$i]:(((in @ X139 @ X138)=>(in @ X139 @ X135)))|(in @ X136 @ X138)))))))))))), introduced(definition)).
% 0.22/0.27 thf(c_0_43, negated_conjecture, ~((![X95:$i, X96:$i]:((![X97:$i]:(((in @ X97 @ X95)<=>(in @ X97 @ X96)))=>((X95)=(X96))))=>(![X98:$i]:(~(in @ X98 @ emptyset))=>(![X99:$i, X100:$i, X101:$i]:(((in @ X101 @ (setadjoin @ X99 @ X100))<=>(((X101)=(X99))|(in @ X101 @ X100))))=>(![X102:$i, X103:$i]:(((in @ X103 @ (powerset @ X102))<=>![X104:$i]:(((in @ X104 @ X103)=>(in @ X104 @ X102)))))=>((setunionAx)=>((in @ emptyset @ omega)=>(![X105:$i]:(((in @ X105 @ omega)=>(in @ (setadjoin @ X105 @ X105) @ omega)))=>(![X106:$i]:((((in @ emptyset @ X106)&![X107:$i]:((((in @ X107 @ omega)&(in @ X107 @ X106))=>(in @ (setadjoin @ X107 @ X107) @ X106))))=>![X108:$i]:(((in @ X108 @ omega)=>(in @ X108 @ X106)))))=>(![X109:$i > $i > $o, X110:$i]:((![X111:$i]:(((in @ X111 @ X110)=>?[X112:$i]:(((X109 @ X111 @ X112)&![X113:$i]:(((X109 @ X111 @ X113)=>((X112)=(X113))))))))=>?[X114:$i]:(![X115:$i]:(((in @ X115 @ X114)<=>?[X116:$i]:(((in @ X116 @ X110)&(X109 @ X116 @ X115))))))))=>(![X117:$i]:((?[X118:$i]:((in @ X118 @ X117))=>?[X119:$i]:(((in @ X119 @ X117)&~(?[X120:$i]:(((in @ X120 @ X119)&(in @ X120 @ X117))))))))=>((epred1_0)=>((descrp)=>(![X140:$i, X141:$i > $o, X142:$i]:(((in @ X142 @ X140)=>((X141 @ X142)=>(in @ X142 @ (dsetconstr @ X140 @ X141)))))=>(![X143:$i, X144:$i > $o, X145:$i]:(((in @ X145 @ (dsetconstr @ X143 @ X144))=>(in @ X145 @ X143)))=>(![X146:$i, X147:$i > $o, X148:$i]:(((in @ X148 @ (dsetconstr @ X146 @ X147))=>(X147 @ X148)))=>(![X149:$i > $o]:((?[X150:$i]:(((X149 @ X150)&![X151:$i]:(((X149 @ X151)=>((X150)=(X151))))))=>?[X152:$i]:(((X149 @ X152)&![X153:$i]:(((X149 @ X153)=>((X152)=(X153))))))))=>(![X154:$o, X155:$i]:(((in @ X155 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X154)))))=>(X154)))=>(![X156:$i]:(((in @ X156 @ emptyset)=>![X157:$o]:((X157))))=>(![X158:$i]:(((in @ X158 @ emptyset)=>~($true)))=>(![X159:$i]:(~(in @ X159 @ emptyset))=>(![X160:$i > $o]:((?[X161:$i]:(((X160 @ X161)&![X162:$i]:(((X160 @ X162)=>((X161)=(X162))))))=>?[X163:$i]:((X160 @ X163))))=>(![X164:$i, X165:$i]:((![X166:$i]:(((in @ X166 @ X164)=>(in @ X166 @ X165)))=>(![X167:$i]:(((in @ X167 @ X165)=>(in @ X167 @ X164)))=>((X164)=(X165)))))=>(![X168:$i]:((![X169:$i]:(~(in @ X169 @ X168))=>((X168)=(emptyset))))=>(![X170:$i]:((![X171:$i]:(~(in @ X171 @ X170))=>((X170)=(emptyset))))=>(![X172:$i, X173:$i > $o, X174:$i]:(((in @ X174 @ X172)=>((in @ X174 @ (dsetconstr @ X172 @ X173))<=>(X173 @ X174))))=>![X4:$i]:((((X4)!=(emptyset))=>?[X2:$i]:((in @ X2 @ X4)))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_32, c_0_33]), c_0_34]), c_0_35]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_36]), setext]), emptyI]), noeltsimpempty]), c_0_37]), c_0_38]), omegaIndAx]), omegaSAx]), omega0Ax]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx]), foundationAx]), wellorderingAx]), c_0_39]), c_0_40]), c_0_41])])]), c_0_42])).
% 0.22/0.27 thf(c_0_44, negated_conjecture, ![X175:$i, X176:$i, X178:$i, X179:$i, X180:$i, X181:$i, X182:$i, X183:$i, X184:$i, X185:$i, X186:$i, X188:$i, X189:$i, X191:$i, X192:$i > $i > $o, X193:$i, X195:$i, X198:$i, X200:$i, X201:$i, X202:$i, X203:$i, X205:$i, X206:$i, X207:$i > $o, X208:$i, X209:$i, X210:$i > $o, X211:$i, X212:$i, X213:$i > $o, X214:$i, X215:$i > $o, X216:$i, X219:$i, X220:$o, X221:$i, X222:$i, X223:$o, X224:$i, X225:$i, X226:$i > $o, X227:$i, X230:$i, X231:$i, X234:$i, X236:$i, X238:$i, X239:$i > $o, X240:$i, X242:$i]:((((~(in @ (esk1_2 @ X175 @ X176) @ X175)|~(in @ (esk1_2 @ X175 @ X176) @ X176)|((X175)=(X176)))&((in @ (esk1_2 @ X175 @ X176) @ X175)|(in @ (esk1_2 @ X175 @ X176) @ X176)|((X175)=(X176))))&(~(in @ X178 @ emptyset)&(((~(in @ X181 @ (setadjoin @ X179 @ X180))|(((X181)=(X179))|(in @ X181 @ X180)))&((((X181)!=(X179))|(in @ X181 @ (setadjoin @ X179 @ X180)))&(~(in @ X181 @ X180)|(in @ X181 @ (setadjoin @ X179 @ X180)))))&(((~(in @ X183 @ (powerset @ X182))|(~(in @ X184 @ X183)|(in @ X184 @ X182)))&(((in @ (esk2_2 @ X185 @ X186) @ X186)|(in @ X186 @ (powerset @ X185)))&(~(in @ (esk2_2 @ X185 @ X186) @ X185)|(in @ X186 @ (powerset @ X185)))))&((setunionAx)&((in @ emptyset @ omega)&((~(in @ X188 @ omega)|(in @ (setadjoin @ X188 @ X188) @ omega))&(((((in @ (esk3_1 @ X189) @ omega)|~(in @ emptyset @ X189)|(~(in @ X191 @ omega)|(in @ X191 @ X189)))&((in @ (esk3_1 @ X189) @ X189)|~(in @ emptyset @ X189)|(~(in @ X191 @ omega)|(in @ X191 @ X189))))&(~(in @ (setadjoin @ (esk3_1 @ X189) @ (esk3_1 @ X189)) @ X189)|~(in @ emptyset @ X189)|(~(in @ X191 @ omega)|(in @ X191 @ X189))))&((((((in @ (esk7_3 @ X192 @ X193 @ X198) @ X193)|~(in @ X198 @ (esk6_2 @ X192 @ X193))|(in @ (esk4_2 @ X192 @ X193) @ X193))&((X192 @ (esk7_3 @ X192 @ X193 @ X198) @ X198)|~(in @ X198 @ (esk6_2 @ X192 @ X193))|(in @ (esk4_2 @ X192 @ X193) @ X193)))&(~(in @ X201 @ X193)|~(X192 @ X201 @ X200)|(in @ X200 @ (esk6_2 @ X192 @ X193))|(in @ (esk4_2 @ X192 @ X193) @ X193)))&(((((in @ (esk7_3 @ X192 @ X193 @ X198) @ X193)|~(in @ X198 @ (esk6_2 @ X192 @ X193))|((X192 @ (esk4_2 @ X192 @ X193) @ (esk5_3 @ X192 @ X193 @ X195))|~(X192 @ (esk4_2 @ X192 @ X193) @ X195)))&((X192 @ (esk7_3 @ X192 @ X193 @ X198) @ X198)|~(in @ X198 @ (esk6_2 @ X192 @ X193))|((X192 @ (esk4_2 @ X192 @ X193) @ (esk5_3 @ X192 @ X193 @ X195))|~(X192 @ (esk4_2 @ X192 @ X193) @ X195))))&(~(in @ X201 @ X193)|~(X192 @ X201 @ X200)|(in @ X200 @ (esk6_2 @ X192 @ X193))|((X192 @ (esk4_2 @ X192 @ X193) @ (esk5_3 @ X192 @ X193 @ X195))|~(X192 @ (esk4_2 @ X192 @ X193) @ X195))))&((((in @ (esk7_3 @ X192 @ X193 @ X198) @ X193)|~(in @ X198 @ (esk6_2 @ X192 @ X193))|(((X195)!=(esk5_3 @ X192 @ X193 @ X195))|~(X192 @ (esk4_2 @ X192 @ X193) @ X195)))&((X192 @ (esk7_3 @ X192 @ X193 @ X198) @ X198)|~(in @ X198 @ (esk6_2 @ X192 @ X193))|(((X195)!=(esk5_3 @ X192 @ X193 @ X195))|~(X192 @ (esk4_2 @ X192 @ X193) @ X195))))&(~(in @ X201 @ X193)|~(X192 @ X201 @ X200)|(in @ X200 @ (esk6_2 @ X192 @ X193))|(((X195)!=(esk5_3 @ X192 @ X193 @ X195))|~(X192 @ (esk4_2 @ X192 @ X193) @ X195))))))&((((in @ (esk8_1 @ X202) @ X202)|~(in @ X203 @ X202))&(~(in @ X205 @ (esk8_1 @ X202))|~(in @ X205 @ X202)|~(in @ X203 @ X202)))&((epred1_0)&((descrp)&((~(in @ X208 @ X206)|(~(X207 @ X208)|(in @ X208 @ (dsetconstr @ X206 @ X207))))&((~(in @ X211 @ (dsetconstr @ X209 @ X210))|(in @ X211 @ X209))&((~(in @ X214 @ (dsetconstr @ X212 @ X213))|(X213 @ X214))&(((((X215 @ (esk10_1 @ X215))|((X215 @ (esk9_2 @ X215 @ X216))|~(X215 @ X216)))&(~(X215 @ X219)|((esk10_1 @ X215)=(X219))|((X215 @ (esk9_2 @ X215 @ X216))|~(X215 @ X216))))&(((X215 @ (esk10_1 @ X215))|(((X216)!=(esk9_2 @ X215 @ X216))|~(X215 @ X216)))&(~(X215 @ X219)|((esk10_1 @ X215)=(X219))|(((X216)!=(esk9_2 @ X215 @ X216))|~(X215 @ X216)))))&((~(in @ X221 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X220)))))|(X220))&((~(in @ X222 @ emptyset)|(X223))&((~(in @ X224 @ emptyset)|~($true))&(~(in @ X225 @ emptyset)&((((X226 @ (esk11_2 @ X226 @ X227))|~(X226 @ X227)|(X226 @ (esk12_1 @ X226)))&(((X227)!=(esk11_2 @ X226 @ X227))|~(X226 @ X227)|(X226 @ (esk12_1 @ X226))))&(((((in @ (esk14_2 @ X230 @ X231) @ X231)|((X230)=(X231))|(in @ (esk13_2 @ X230 @ X231) @ X230))&(~(in @ (esk14_2 @ X230 @ X231) @ X230)|((X230)=(X231))|(in @ (esk13_2 @ X230 @ X231) @ X230)))&(((in @ (esk14_2 @ X230 @ X231) @ X231)|((X230)=(X231))|~(in @ (esk13_2 @ X230 @ X231) @ X231))&(~(in @ (esk14_2 @ X230 @ X231) @ X230)|((X230)=(X231))|~(in @ (esk13_2 @ X230 @ X231) @ X231))))&(((in @ (esk15_1 @ X234) @ X234)|((X234)=(emptyset)))&(((in @ (esk16_1 @ X236) @ X236)|((X236)=(emptyset)))&(((~(in @ X240 @ (dsetconstr @ X238 @ X239))|(X239 @ X240)|~(in @ X240 @ X238))&(~(X239 @ X240)|(in @ X240 @ (dsetconstr @ X238 @ X239))|~(in @ X240 @ X238)))&(((esk17_0)!=(emptyset))&~(in @ X242 @ esk17_0)))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])])])])])])])).
% 0.22/0.27 thf(c_0_45, negated_conjecture, ![X2:$i]:(~((in @ X2 @ esk17_0))), inference(split_conjunct,[status(thm)],[c_0_44])).
% 0.22/0.27 thf(c_0_46, negated_conjecture, ![X2:$i]:(((in @ (esk15_1 @ X2) @ X2)|((X2)=(emptyset)))), inference(split_conjunct,[status(thm)],[c_0_44])).
% 0.22/0.27 thf(c_0_47, negated_conjecture, ((esk17_0)!=(emptyset)), inference(split_conjunct,[status(thm)],[c_0_44])).
% 0.22/0.27 thf(c_0_48, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45, c_0_46]), c_0_47]), ['proof']).
% 0.22/0.27 % SZS output end CNFRefutation
% 0.22/0.27 % Parsed axioms : 65
% 0.22/0.27 % Removed by relevancy pruning/SinE : 38
% 0.22/0.27 % Initial clauses : 64
% 0.22/0.27 % Removed in clause preprocessing : 0
% 0.22/0.27 % Initial clauses in saturation : 64
% 0.22/0.27 % Processed clauses : 11
% 0.22/0.27 % ...of these trivial : 0
% 0.22/0.27 % ...subsumed : 3
% 0.22/0.27 % ...remaining for further processing : 8
% 0.22/0.27 % Other redundant clauses eliminated : 0
% 0.22/0.27 % Clauses deleted for lack of memory : 0
% 0.22/0.27 % Backward-subsumed : 0
% 0.22/0.27 % Backward-rewritten : 0
% 0.22/0.27 % Generated clauses : 1
% 0.22/0.27 % ...of the previous two non-redundant : 0
% 0.22/0.27 % ...aggressively subsumed : 0
% 0.22/0.27 % Contextual simplify-reflections : 0
% 0.22/0.27 % Paramodulations : 1
% 0.22/0.27 % Factorizations : 0
% 0.22/0.27 % NegExts : 0
% 0.22/0.27 % Equation resolutions : 0
% 0.22/0.27 % Disequality decompositions : 0
% 0.22/0.27 % Total rewrite steps : 0
% 0.22/0.27 % ...of those cached : 0
% 0.22/0.27 % Propositional unsat checks : 0
% 0.22/0.27 % Propositional check models : 0
% 0.22/0.27 % Propositional check unsatisfiable : 0
% 0.22/0.27 % Propositional clauses : 0
% 0.22/0.27 % Propositional clauses after purity: 0
% 0.22/0.27 % Propositional unsat core size : 0
% 0.22/0.27 % Propositional preprocessing time : 0.000
% 0.22/0.27 % Propositional encoding time : 0.000
% 0.22/0.27 % Propositional solver time : 0.000
% 0.22/0.27 % Success case prop preproc time : 0.000
% 0.22/0.27 % Success case prop encoding time : 0.000
% 0.22/0.27 % Success case prop solver time : 0.000
% 0.22/0.27 % Current number of processed clauses : 8
% 0.22/0.27 % Positive orientable unit clauses : 4
% 0.22/0.27 % Positive unorientable unit clauses: 0
% 0.22/0.27 % Negative unit clauses : 3
% 0.22/0.27 % Non-unit-clauses : 1
% 0.22/0.27 % Current number of unprocessed clauses: 53
% 0.22/0.27 % ...number of literals in the above : 191
% 0.22/0.27 % Current number of archived formulas : 0
% 0.22/0.27 % Current number of archived clauses : 0
% 0.22/0.27 % Clause-clause subsumption calls (NU) : 0
% 0.22/0.27 % Rec. Clause-clause subsumption calls : 0
% 0.22/0.27 % Non-unit clause-clause subsumptions : 0
% 0.22/0.27 % Unit Clause-clause subsumption calls : 0
% 0.22/0.27 % Rewrite failures with RHS unbound : 0
% 0.22/0.27 % BW rewrite match attempts : 0
% 0.22/0.27 % BW rewrite match successes : 0
% 0.22/0.27 % Condensation attempts : 0
% 0.22/0.27 % Condensation successes : 0
% 0.22/0.27 % Termbank termtop insertions : 7623
% 0.22/0.27 % Search garbage collected termcells : 2964
% 0.22/0.27
% 0.22/0.27 % -------------------------------------------------
% 0.22/0.27 % User time : 0.010 s
% 0.22/0.27 % System time : 0.003 s
% 0.22/0.27 % Total time : 0.013 s
% 0.22/0.27 % Maximum resident set size: 4216 pages
% 0.22/0.27
% 0.22/0.27 % -------------------------------------------------
% 0.22/0.27 % User time : 0.013 s
% 0.22/0.27 % System time : 0.006 s
% 0.22/0.27 % Total time : 0.019 s
% 0.22/0.27 % Maximum resident set size: 4864 pages
% 0.22/0.27 % E exiting
%------------------------------------------------------------------------------