%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU501^1 : 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 : n011.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 08:24:16 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
% 0.00/0.02 % Problem : SEU501^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n011.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 13:46:46 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
% 0.08/0.23 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.KU9j8b2Q9B/E---3.1_118086.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 118113 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 118115 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 : 0.001 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, epred1_0: $o).
% 0.08/0.26 thf(decl_51, type, esk1_2: $i > $i > $i).
% 0.08/0.26 thf(decl_52, type, esk2_2: $i > $i > $i).
% 0.08/0.26 thf(decl_53, type, esk3_1: $i > $i).
% 0.08/0.26 thf(decl_54, type, esk4_2: ($i > $i > $o) > $i > $i).
% 0.08/0.26 thf(decl_55, type, esk5_3: ($i > $i > $o) > $i > $i > $i).
% 0.08/0.26 thf(decl_56, type, esk6_2: ($i > $i > $o) > $i > $i).
% 0.08/0.26 thf(decl_57, type, esk7_3: ($i > $i > $o) > $i > $i > $i).
% 0.08/0.26 thf(decl_58, type, esk8_1: $i > $i).
% 0.08/0.26 thf(decl_59, type, esk9_2: ($i > $o) > $i > $i).
% 0.08/0.26 thf(decl_60, type, esk10_1: ($i > $o) > $i).
% 0.08/0.26 thf(decl_61, type, esk11_0: $i).
% 0.08/0.26 thf(decl_62, type, epred2_0: $o).
% 0.08/0.26 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.KU9j8b2Q9B/E---3.1_118086.p', replAx)).
% 0.08/0.26 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.KU9j8b2Q9B/E---3.1_118086.p', exu)).
% 0.08/0.26 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.KU9j8b2Q9B/E---3.1_118086.p', exuE1)).
% 0.08/0.26 thf(prop2set, axiom, ((prop2set)=(^[X10:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[X2:$i]:((X10)))))), file('/export/starexec/sandbox/tmp/tmp.KU9j8b2Q9B/E---3.1_118086.p', prop2set)).
% 0.08/0.26 thf(emptysetE, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>![X2:$i]:(((in @ X2 @ emptyset)=>![X12:$o]:((X12))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.KU9j8b2Q9B/E---3.1_118086.p', emptysetE)).
% 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:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.KU9j8b2Q9B/E---3.1_118086.p', dsetconstrI)).
% 0.08/0.26 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.KU9j8b2Q9B/E---3.1_118086.p', dsetconstrEL)).
% 0.08/0.26 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.KU9j8b2Q9B/E---3.1_118086.p', dsetconstrER)).
% 0.08/0.26 thf(prop2setE, axiom, ((prop2setE)<=>![X11:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X11))))=>(X11)))), file('/export/starexec/sandbox/tmp/tmp.KU9j8b2Q9B/E---3.1_118086.p', prop2setE)).
% 0.08/0.26 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.KU9j8b2Q9B/E---3.1_118086.p', powersetAx)).
% 0.08/0.26 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.KU9j8b2Q9B/E---3.1_118086.p', omega0Ax)).
% 0.08/0.26 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.KU9j8b2Q9B/E---3.1_118086.p', omegaSAx)).
% 0.08/0.26 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.KU9j8b2Q9B/E---3.1_118086.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.KU9j8b2Q9B/E---3.1_118086.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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.KU9j8b2Q9B/E---3.1_118086.p', wellorderingAx)).
% 0.08/0.26 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.KU9j8b2Q9B/E---3.1_118086.p', setextAx)).
% 0.08/0.26 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.KU9j8b2Q9B/E---3.1_118086.p', emptysetAx)).
% 0.08/0.26 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.KU9j8b2Q9B/E---3.1_118086.p', setadjoinAx)).
% 0.08/0.26 thf(c_0_18, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.08/0.26 thf(c_0_19, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.08/0.26 thf(c_0_20, plain, ((exuE1)<=>![X1:$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_21, plain, ((prop2set)=(^[Z0:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[Z1:$i]:((Z0)))))), inference(fof_simplification,[status(thm)],[prop2set])).
% 0.08/0.26 thf(c_0_22, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>![X2:$i]:(((in @ X2 @ emptyset)=>![X12:$o]:((X12)))))))))))))))))))))), inference(assume_negation,[status(cth)],[emptysetE])).
% 0.08/0.26 thf(c_0_23, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X72:$i]:(((((X6 @ X2 @ X72)))&(![X73:$i]:(((((X6 @ X2 @ X73)))=>(((X72)=(X73)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_18, c_0_19])).
% 0.08/0.26 thf(c_0_24, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.08/0.26 thf(c_0_25, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.08/0.26 thf(c_0_26, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.08/0.26 thf(c_0_27, plain, ((exuE1)=(![X1:$i > $o]:((((?[X74:$i]:(((((X1 @ X74)))&(![X75:$i]:(((((X1 @ X75)))=>(((X74)=(X75))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_20, c_0_19])).
% 0.08/0.26 thf(c_0_28, axiom, ((prop2setE)=(![X11:$o, X2:$i]:((((in @ X2 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:(((X11)))))))=>((X11)))))), inference(apply_def,[status(thm)],[prop2setE, c_0_21])).
% 0.08/0.26 thf(c_0_29, plain, ((epred1_0)<=>![X102:$i]:(?[X103:$i]:((((![X104:$i]:(((in @ X104 @ X103)=>![X105:$i]:(((in @ X105 @ X104)=>(in @ X105 @ X102)))))&![X106:$i, X107:$i]:((((in @ X106 @ X102)&(in @ X107 @ X102))=>(![X108:$i]:(((in @ X108 @ X103)=>((in @ X106 @ X108)<=>(in @ X107 @ X108))))=>((X106)=(X107))))))&![X109:$i, X110:$i]:((((in @ X109 @ X103)&(in @ X110 @ X103))=>(![X111:$i]:(((in @ X111 @ X109)=>(in @ X111 @ X110)))|![X112:$i]:(((in @ X112 @ X110)=>(in @ X112 @ X109)))))))&![X113:$i]:(((![X114:$i]:(((in @ X114 @ X113)=>(in @ X114 @ X102)))&?[X115:$i]:((in @ X115 @ X113)))=>?[X116:$i, X117:$i]:(((((in @ X116 @ X103)&(in @ X117 @ X113))&~(?[X118:$i]:(((in @ X118 @ X116)&(in @ X118 @ X113)))))&![X119:$i]:(((in @ X119 @ X103)=>(![X120:$i]:(((in @ X120 @ X119)=>(in @ X120 @ X116)))|(in @ X117 @ X119)))))))))))), introduced(definition)).
% 0.08/0.26 thf(c_0_30, negated_conjecture, ~((![X76:$i, X77:$i]:((![X78:$i]:(((in @ X78 @ X76)<=>(in @ X78 @ X77)))=>((X76)=(X77))))=>(![X79:$i]:(~(in @ X79 @ emptyset))=>(![X80:$i, X81:$i, X82:$i]:(((in @ X82 @ (setadjoin @ X80 @ X81))<=>(((X82)=(X80))|(in @ X82 @ X81))))=>(![X83:$i, X84:$i]:(((in @ X84 @ (powerset @ X83))<=>![X85:$i]:(((in @ X85 @ X84)=>(in @ X85 @ X83)))))=>((setunionAx)=>((in @ emptyset @ omega)=>(![X86:$i]:(((in @ X86 @ omega)=>(in @ (setadjoin @ X86 @ X86) @ omega)))=>(![X87:$i]:((((in @ emptyset @ X87)&![X88:$i]:((((in @ X88 @ omega)&(in @ X88 @ X87))=>(in @ (setadjoin @ X88 @ X88) @ X87))))=>![X89:$i]:(((in @ X89 @ omega)=>(in @ X89 @ X87)))))=>(![X90:$i > $i > $o, X91:$i]:((![X92:$i]:(((in @ X92 @ X91)=>?[X93:$i]:(((X90 @ X92 @ X93)&![X94:$i]:(((X90 @ X92 @ X94)=>((X93)=(X94))))))))=>?[X95:$i]:(![X96:$i]:(((in @ X96 @ X95)<=>?[X97:$i]:(((in @ X97 @ X91)&(X90 @ X97 @ X96))))))))=>(![X98:$i]:((?[X99:$i]:((in @ X99 @ X98))=>?[X100:$i]:(((in @ X100 @ X98)&~(?[X101:$i]:(((in @ X101 @ X100)&(in @ X101 @ X98))))))))=>((epred1_0)=>((descrp)=>(![X121:$i, X122:$i > $o, X123:$i]:(((in @ X123 @ X121)=>((X122 @ X123)=>(in @ X123 @ (dsetconstr @ X121 @ (^[Z0:$i]:((X122 @ Z0))))))))=>(![X124:$i, X125:$i > $o, X126:$i]:(((in @ X126 @ (dsetconstr @ X124 @ (^[Z0:$i]:((X125 @ Z0)))))=>(in @ X126 @ X124)))=>(![X127:$i, X128:$i > $o, X129:$i]:(((in @ X129 @ (dsetconstr @ X127 @ (^[Z0:$i]:((X128 @ Z0)))))=>(X128 @ X129)))=>(![X130:$i > $o]:((?[X131:$i]:(((X130 @ X131)&![X132:$i]:(((X130 @ X132)=>((X131)=(X132))))))=>?[X133:$i]:(((X130 @ X133)&![X134:$i]:(((X130 @ X134)=>((X133)=(X134))))))))=>(![X135:$o, X136:$i]:(((in @ X136 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X135)))))=>(X135)))=>![X2:$i]:(((in @ X2 @ emptyset)=>![X12:$o]:((X12)))))))))))))))))))))), 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)],[c_0_22, powersetAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_23]), foundationAx]), wellorderingAx]), c_0_24]), c_0_25]), c_0_26]), c_0_27]), c_0_28]), setextAx]), emptysetAx]), setadjoinAx])]), c_0_29])).
% 0.08/0.26 thf(c_0_31, negated_conjecture, ![X137:$i, X138:$i, X140:$i, X141:$i, X142:$i, X143:$i, X144:$i, X145:$i, X146:$i, X147:$i, X148:$i, X150:$i, X151:$i, X153:$i, X154:$i > $i > $o, X155:$i, X157:$i, X160:$i, X162:$i, X163:$i, X164:$i, X165:$i, X167:$i, X168:$i, X169:$i > $o, X170:$i, X171:$i, X172:$i > $o, X173:$i, X174:$i, X175:$i > $o, X176:$i, X177:$i > $o, X178:$i, X181:$i, X182:$o, X183:$i]:((((~(in @ (esk1_2 @ X137 @ X138) @ X137)|~(in @ (esk1_2 @ X137 @ X138) @ X138)|((X137)=(X138)))&((in @ (esk1_2 @ X137 @ X138) @ X137)|(in @ (esk1_2 @ X137 @ X138) @ X138)|((X137)=(X138))))&(~(in @ X140 @ emptyset)&(((~(in @ X143 @ (setadjoin @ X141 @ X142))|(((X143)=(X141))|(in @ X143 @ X142)))&((((X143)!=(X141))|(in @ X143 @ (setadjoin @ X141 @ X142)))&(~(in @ X143 @ X142)|(in @ X143 @ (setadjoin @ X141 @ X142)))))&(((~(in @ X145 @ (powerset @ X144))|(~(in @ X146 @ X145)|(in @ X146 @ X144)))&(((in @ (esk2_2 @ X147 @ X148) @ X148)|(in @ X148 @ (powerset @ X147)))&(~(in @ (esk2_2 @ X147 @ X148) @ X147)|(in @ X148 @ (powerset @ X147)))))&((setunionAx)&((in @ emptyset @ omega)&((~(in @ X150 @ omega)|(in @ (setadjoin @ X150 @ X150) @ omega))&(((((in @ (esk3_1 @ X151) @ omega)|~(in @ emptyset @ X151)|(~(in @ X153 @ omega)|(in @ X153 @ X151)))&((in @ (esk3_1 @ X151) @ X151)|~(in @ emptyset @ X151)|(~(in @ X153 @ omega)|(in @ X153 @ X151))))&(~(in @ (setadjoin @ (esk3_1 @ X151) @ (esk3_1 @ X151)) @ X151)|~(in @ emptyset @ X151)|(~(in @ X153 @ omega)|(in @ X153 @ X151))))&((((((in @ (esk7_3 @ X154 @ X155 @ X160) @ X155)|~(in @ X160 @ (esk6_2 @ X154 @ X155))|(in @ (esk4_2 @ X154 @ X155) @ X155))&((X154 @ (esk7_3 @ X154 @ X155 @ X160) @ X160)|~(in @ X160 @ (esk6_2 @ X154 @ X155))|(in @ (esk4_2 @ X154 @ X155) @ X155)))&(~(in @ X163 @ X155)|~(X154 @ X163 @ X162)|(in @ X162 @ (esk6_2 @ X154 @ X155))|(in @ (esk4_2 @ X154 @ X155) @ X155)))&(((((in @ (esk7_3 @ X154 @ X155 @ X160) @ X155)|~(in @ X160 @ (esk6_2 @ X154 @ X155))|((X154 @ (esk4_2 @ X154 @ X155) @ (esk5_3 @ X154 @ X155 @ X157))|~(X154 @ (esk4_2 @ X154 @ X155) @ X157)))&((X154 @ (esk7_3 @ X154 @ X155 @ X160) @ X160)|~(in @ X160 @ (esk6_2 @ X154 @ X155))|((X154 @ (esk4_2 @ X154 @ X155) @ (esk5_3 @ X154 @ X155 @ X157))|~(X154 @ (esk4_2 @ X154 @ X155) @ X157))))&(~(in @ X163 @ X155)|~(X154 @ X163 @ X162)|(in @ X162 @ (esk6_2 @ X154 @ X155))|((X154 @ (esk4_2 @ X154 @ X155) @ (esk5_3 @ X154 @ X155 @ X157))|~(X154 @ (esk4_2 @ X154 @ X155) @ X157))))&((((in @ (esk7_3 @ X154 @ X155 @ X160) @ X155)|~(in @ X160 @ (esk6_2 @ X154 @ X155))|(((X157)!=(esk5_3 @ X154 @ X155 @ X157))|~(X154 @ (esk4_2 @ X154 @ X155) @ X157)))&((X154 @ (esk7_3 @ X154 @ X155 @ X160) @ X160)|~(in @ X160 @ (esk6_2 @ X154 @ X155))|(((X157)!=(esk5_3 @ X154 @ X155 @ X157))|~(X154 @ (esk4_2 @ X154 @ X155) @ X157))))&(~(in @ X163 @ X155)|~(X154 @ X163 @ X162)|(in @ X162 @ (esk6_2 @ X154 @ X155))|(((X157)!=(esk5_3 @ X154 @ X155 @ X157))|~(X154 @ (esk4_2 @ X154 @ X155) @ X157))))))&((((in @ (esk8_1 @ X164) @ X164)|~(in @ X165 @ X164))&(~(in @ X167 @ (esk8_1 @ X164))|~(in @ X167 @ X164)|~(in @ X165 @ X164)))&((epred1_0)&((descrp)&((~(in @ X170 @ X168)|(~(X169 @ X170)|(in @ X170 @ (dsetconstr @ X168 @ (^[Z0:$i]:((X169 @ Z0)))))))&((~(in @ X173 @ (dsetconstr @ X171 @ (^[Z0:$i]:((X172 @ Z0)))))|(in @ X173 @ X171))&((~(in @ X176 @ (dsetconstr @ X174 @ (^[Z0:$i]:((X175 @ Z0)))))|(X175 @ X176))&(((((X177 @ (esk10_1 @ X177))|((X177 @ (esk9_2 @ X177 @ X178))|~(X177 @ X178)))&(~(X177 @ X181)|((esk10_1 @ X177)=(X181))|((X177 @ (esk9_2 @ X177 @ X178))|~(X177 @ X178))))&(((X177 @ (esk10_1 @ X177))|(((X178)!=(esk9_2 @ X177 @ X178))|~(X177 @ X178)))&(~(X177 @ X181)|((esk10_1 @ X177)=(X181))|(((X178)!=(esk9_2 @ X177 @ X178))|~(X177 @ X178)))))&((~(in @ X183 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X182)))))|(X182))&((in @ esk11_0 @ emptyset)&~(epred2_0)))))))))))))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])])])])])).
% 0.08/0.26 thf(c_0_32, negated_conjecture, (in @ esk11_0 @ emptyset), inference(split_conjunct,[status(thm)],[c_0_31])).
% 0.08/0.26 thf(c_0_33, negated_conjecture, ![X2:$i]:(~((in @ X2 @ emptyset))), inference(split_conjunct,[status(thm)],[c_0_31])).
% 0.08/0.26 thf(c_0_34, negated_conjecture, ($false), inference(sr,[status(thm)],[c_0_32, c_0_33]), ['proof']).
% 0.08/0.26 % SZS output end CNFRefutation
% 0.08/0.26 % Parsed axioms : 47
% 0.08/0.26 % Removed by relevancy pruning/SinE : 29
% 0.08/0.26 % Initial clauses : 51
% 0.08/0.26 % Removed in clause preprocessing : 0
% 0.08/0.26 % Initial clauses in saturation : 51
% 0.08/0.26 % Processed clauses : 7
% 0.08/0.26 % ...of these trivial : 0
% 0.08/0.26 % ...subsumed : 0
% 0.08/0.26 % ...remaining for further processing : 7
% 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 : 6
% 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 : 2
% 0.08/0.26 % Non-unit-clauses : 0
% 0.08/0.26 % Current number of unprocessed clauses: 44
% 0.08/0.26 % ...number of literals in the above : 165
% 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 : 5172
% 0.08/0.26 % Search garbage collected termcells : 1863
% 0.08/0.26
% 0.08/0.26 % -------------------------------------------------
% 0.08/0.26 % User time : 0.007 s
% 0.08/0.26 % System time : 0.002 s
% 0.08/0.26 % Total time : 0.010 s
% 0.08/0.26 % Maximum resident set size: 3944 pages
% 0.08/0.26
% 0.08/0.26 % -------------------------------------------------
% 0.08/0.26 % User time : 0.009 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: 4864 pages
% 0.08/0.26 % E exiting
%------------------------------------------------------------------------------