%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU499^1 : 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 : n009.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 0.09s 0.26s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU499^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n009.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 13:46:30 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.23 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.OSYiRPDhiU/E---3.1_4013534.p
% 0.09/0.26 % Version: 3.5.1-ho
% 0.09/0.26 % partial match(1): HSMSSLSSMLLCHSA
% 0.09/0.26 % Preprocessing class: HSMSSLSSMLMCHSA.
% 0.09/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.26 % Starting sh5l with 300s (1) cores
% 0.09/0.26 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.26 % Starting new_bool_2 with 300s (1) cores
% 0.09/0.26 % sh5l with pid 4013548 completed with status 0
% 0.09/0.26 % Result found by sh5l
% 0.09/0.26 % partial match(1): HSMSSLSSMLLCHSA
% 0.09/0.26 % Preprocessing class: HSMSSLSSMLMCHSA.
% 0.09/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.26 % Starting sh5l with 300s (1) cores
% 0.09/0.26 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.09/0.26 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.09/0.26 % Search class: HGHSF-FFMS31-SHSSMSBN
% 0.09/0.26 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.26 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.26 % SubtermCWHack with pid 4013553 completed with status 0
% 0.09/0.26 % Result found by SubtermCWHack
% 0.09/0.26 % partial match(1): HSMSSLSSMLLCHSA
% 0.09/0.26 % Preprocessing class: HSMSSLSSMLMCHSA.
% 0.09/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.26 % Starting sh5l with 300s (1) cores
% 0.09/0.26 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.09/0.26 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.09/0.26 % Search class: HGHSF-FFMS31-SHSSMSBN
% 0.09/0.26 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.26 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.26 % Preprocessing time : 0.001 s
% 0.09/0.26
% 0.09/0.26 % Proof found!
% 0.09/0.26 % SZS status Theorem
% 0.09/0.26 % SZS output start CNFRefutation
% 0.09/0.26 thf(decl_23, type, in: $i > $i > $o).
% 0.09/0.26 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.09/0.26 thf(decl_25, type, setextAx: $o).
% 0.09/0.26 thf(decl_26, type, emptyset: $i).
% 0.09/0.26 thf(decl_27, type, emptysetAx: $o).
% 0.09/0.26 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.09/0.26 thf(decl_29, type, setadjoinAx: $o).
% 0.09/0.26 thf(decl_30, type, powerset: $i > $i).
% 0.09/0.26 thf(decl_31, type, powersetAx: $o).
% 0.09/0.26 thf(decl_32, type, setunion: $i > $i).
% 0.09/0.26 thf(decl_33, type, setunionAx: $o).
% 0.09/0.26 thf(decl_34, type, omega: $i).
% 0.09/0.26 thf(decl_35, type, omega0Ax: $o).
% 0.09/0.26 thf(decl_36, type, omegaSAx: $o).
% 0.09/0.26 thf(decl_37, type, omegaIndAx: $o).
% 0.09/0.26 thf(decl_38, type, replAx: $o).
% 0.09/0.26 thf(decl_39, type, foundationAx: $o).
% 0.09/0.26 thf(decl_40, type, wellorderingAx: $o).
% 0.09/0.26 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.09/0.26 thf(decl_42, type, descrp: $o).
% 0.09/0.26 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.09/0.26 thf(decl_44, type, dsetconstrI: $o).
% 0.09/0.26 thf(decl_45, type, dsetconstrEL: $o).
% 0.09/0.26 thf(decl_46, type, dsetconstrER: $o).
% 0.09/0.26 thf(decl_47, type, epred1_0: $o).
% 0.09/0.26 thf(decl_48, type, esk1_2: $i > $i > $i).
% 0.09/0.26 thf(decl_49, type, esk2_2: $i > $i > $i).
% 0.09/0.26 thf(decl_50, type, esk3_2: $i > $i > $i).
% 0.09/0.26 thf(decl_51, type, esk4_1: $i > $i).
% 0.09/0.26 thf(decl_52, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.09/0.26 thf(decl_53, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.09/0.26 thf(decl_54, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.09/0.26 thf(decl_55, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.09/0.26 thf(decl_56, type, esk9_1: $i > $i).
% 0.09/0.26 thf(decl_57, type, esk10_2: ($i > $o) > $i > $i).
% 0.09/0.26 thf(decl_58, type, epred2_0: $i > $o).
% 0.09/0.26 thf(decl_59, type, esk11_0: $i).
% 0.09/0.26 thf(decl_60, type, esk12_1: $i > $i).
% 0.09/0.26 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.OSYiRPDhiU/E---3.1_4013534.p', descrp)).
% 0.09/0.26 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.OSYiRPDhiU/E---3.1_4013534.p', exu)).
% 0.09/0.26 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.OSYiRPDhiU/E---3.1_4013534.p', replAx)).
% 0.09/0.26 thf(exuE1, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.OSYiRPDhiU/E---3.1_4013534.p', exuE1)).
% 0.09/0.26 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.OSYiRPDhiU/E---3.1_4013534.p', dsetconstrI)).
% 0.09/0.26 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.OSYiRPDhiU/E---3.1_4013534.p', dsetconstrEL)).
% 0.09/0.26 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.OSYiRPDhiU/E---3.1_4013534.p', dsetconstrER)).
% 0.09/0.26 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.OSYiRPDhiU/E---3.1_4013534.p', setextAx)).
% 0.09/0.26 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/sandbox2/tmp/tmp.OSYiRPDhiU/E---3.1_4013534.p', foundationAx)).
% 0.09/0.26 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.OSYiRPDhiU/E---3.1_4013534.p', setadjoinAx)).
% 0.09/0.26 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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/sandbox2/tmp/tmp.OSYiRPDhiU/E---3.1_4013534.p', omegaIndAx)).
% 0.09/0.26 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.OSYiRPDhiU/E---3.1_4013534.p', powersetAx)).
% 0.09/0.26 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.OSYiRPDhiU/E---3.1_4013534.p', setunionAx)).
% 0.09/0.26 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.OSYiRPDhiU/E---3.1_4013534.p', wellorderingAx)).
% 0.09/0.26 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.OSYiRPDhiU/E---3.1_4013534.p', emptysetAx)).
% 0.09/0.26 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.OSYiRPDhiU/E---3.1_4013534.p', omega0Ax)).
% 0.09/0.26 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.OSYiRPDhiU/E---3.1_4013534.p', omegaSAx)).
% 0.09/0.26 thf(c_0_17, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.09/0.26 thf(c_0_18, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.09/0.26 thf(c_0_19, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.09/0.26 thf(c_0_20, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))))))))))))))))), inference(assume_negation,[status(cth)],[exuE1])).
% 0.09/0.26 thf(c_0_21, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.09/0.26 thf(c_0_22, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.09/0.26 thf(c_0_23, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.09/0.26 thf(c_0_24, plain, ((descrp)=(![X1:$i > $o]:((((?[X71:$i]:(((((X1 @ X71)))&(![X72:$i]:(((((X1 @ X72)))=>(((X71)=(X72))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_17, c_0_18])).
% 0.09/0.26 thf(c_0_25, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X69:$i]:(((((X6 @ X2 @ X69)))&(![X70:$i]:(((((X6 @ X2 @ X70)))=>(((X69)=(X70)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_19, c_0_18])).
% 0.09/0.26 thf(c_0_26, 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:$i]:(((in @ X120 @ X119)=>(in @ X120 @ X116)))|(in @ X117 @ X119)))))))))))), introduced(definition)).
% 0.09/0.26 thf(c_0_27, negated_conjecture, ~((![X73:$i, X74:$i]:((![X75:$i]:(((in @ X75 @ X73)<=>(in @ X75 @ X74)))=>((X73)=(X74))))=>(![X76:$i]:(~(in @ X76 @ emptyset))=>(![X77:$i, X78:$i, X79:$i]:(((in @ X79 @ (setadjoin @ X77 @ X78))<=>(((X79)=(X77))|(in @ X79 @ X78))))=>(![X80:$i, X81:$i]:(((in @ X81 @ (powerset @ X80))<=>![X82:$i]:(((in @ X82 @ X81)=>(in @ X82 @ X80)))))=>(![X83:$i, X84:$i]:(((in @ X84 @ (setunion @ X83))<=>?[X85:$i]:(((in @ X84 @ X85)&(in @ X85 @ X83)))))=>((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)=>(![X121:$i > $o]:((?[X122:$i]:(((X121 @ X122)&![X123:$i]:(((X121 @ X123)=>((X122)=(X123))))))=>(X121 @ (descr @ (^[Z0:$i]:(X121 @ Z0))))))=>(![X124:$i, X125:$i > $o, X126:$i]:(((in @ X126 @ X124)=>((X125 @ X126)=>(in @ X126 @ (dsetconstr @ X124 @ X125)))))=>(![X127:$i, X128:$i > $o, X129:$i]:(((in @ X129 @ (dsetconstr @ X127 @ X128))=>(in @ X129 @ X127)))=>(![X130:$i, X131:$i > $o, X132:$i]:(((in @ X132 @ (dsetconstr @ X130 @ X131))=>(X131 @ X132)))=>![X1:$i > $o]:((?[X133:$i]:(((X1 @ X133)&![X134:$i]:(((X1 @ X134)=>((X133)=(X134))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_20]), setextAx]), foundationAx]), setadjoinAx]), omegaIndAx]), powersetAx]), setunionAx]), wellorderingAx]), c_0_21]), c_0_22]), c_0_23]), c_0_24]), c_0_25]), c_0_18]), emptysetAx]), omega0Ax]), omegaSAx])])]), c_0_26])).
% 0.09/0.26 thf(c_0_28, negated_conjecture, ![X135:$i, X136:$i, X138:$i, X139:$i, X140:$i, X141:$i, X142:$i, X143:$i, X144:$i, X145:$i, X146:$i, X148:$i, X149:$i, X151:$i, X152:$i, X153:$i, X154:$i, X155:$i, X157:$i, X158:$i > $i > $o, X159:$i, X161:$i, X164:$i, X166:$i, X167:$i, X168:$i, X169:$i, X171:$i, X172:$i > $o, X173:$i, X175:$i, X176:$i > $o, X177:$i, X178:$i, X179:$i > $o, X180:$i, X181:$i, X182:$i > $o, X183:$i, X186:$i, X187:$i]:((((~(in @ (esk1_2 @ X135 @ X136) @ X135)|~(in @ (esk1_2 @ X135 @ X136) @ X136)|((X135)=(X136)))&((in @ (esk1_2 @ X135 @ X136) @ X135)|(in @ (esk1_2 @ X135 @ X136) @ X136)|((X135)=(X136))))&(~(in @ X138 @ emptyset)&(((~(in @ X141 @ (setadjoin @ X139 @ X140))|(((X141)=(X139))|(in @ X141 @ X140)))&((((X141)!=(X139))|(in @ X141 @ (setadjoin @ X139 @ X140)))&(~(in @ X141 @ X140)|(in @ X141 @ (setadjoin @ X139 @ X140)))))&(((~(in @ X143 @ (powerset @ X142))|(~(in @ X144 @ X143)|(in @ X144 @ X142)))&(((in @ (esk2_2 @ X145 @ X146) @ X146)|(in @ X146 @ (powerset @ X145)))&(~(in @ (esk2_2 @ X145 @ X146) @ X145)|(in @ X146 @ (powerset @ X145)))))&(((((in @ X149 @ (esk3_2 @ X148 @ X149))|~(in @ X149 @ (setunion @ X148)))&((in @ (esk3_2 @ X148 @ X149) @ X148)|~(in @ X149 @ (setunion @ X148))))&(~(in @ X152 @ X153)|~(in @ X153 @ X151)|(in @ X152 @ (setunion @ X151))))&((in @ emptyset @ omega)&((~(in @ X154 @ omega)|(in @ (setadjoin @ X154 @ X154) @ omega))&(((((in @ (esk4_1 @ X155) @ omega)|~(in @ emptyset @ X155)|(~(in @ X157 @ omega)|(in @ X157 @ X155)))&((in @ (esk4_1 @ X155) @ X155)|~(in @ emptyset @ X155)|(~(in @ X157 @ omega)|(in @ X157 @ X155))))&(~(in @ (setadjoin @ (esk4_1 @ X155) @ (esk4_1 @ X155)) @ X155)|~(in @ emptyset @ X155)|(~(in @ X157 @ omega)|(in @ X157 @ X155))))&((((((in @ (esk8_3 @ X158 @ X159 @ X164) @ X159)|~(in @ X164 @ (esk7_2 @ X158 @ X159))|(in @ (esk5_2 @ X158 @ X159) @ X159))&((X158 @ (esk8_3 @ X158 @ X159 @ X164) @ X164)|~(in @ X164 @ (esk7_2 @ X158 @ X159))|(in @ (esk5_2 @ X158 @ X159) @ X159)))&(~(in @ X167 @ X159)|~(X158 @ X167 @ X166)|(in @ X166 @ (esk7_2 @ X158 @ X159))|(in @ (esk5_2 @ X158 @ X159) @ X159)))&(((((in @ (esk8_3 @ X158 @ X159 @ X164) @ X159)|~(in @ X164 @ (esk7_2 @ X158 @ X159))|((X158 @ (esk5_2 @ X158 @ X159) @ (esk6_3 @ X158 @ X159 @ X161))|~(X158 @ (esk5_2 @ X158 @ X159) @ X161)))&((X158 @ (esk8_3 @ X158 @ X159 @ X164) @ X164)|~(in @ X164 @ (esk7_2 @ X158 @ X159))|((X158 @ (esk5_2 @ X158 @ X159) @ (esk6_3 @ X158 @ X159 @ X161))|~(X158 @ (esk5_2 @ X158 @ X159) @ X161))))&(~(in @ X167 @ X159)|~(X158 @ X167 @ X166)|(in @ X166 @ (esk7_2 @ X158 @ X159))|((X158 @ (esk5_2 @ X158 @ X159) @ (esk6_3 @ X158 @ X159 @ X161))|~(X158 @ (esk5_2 @ X158 @ X159) @ X161))))&((((in @ (esk8_3 @ X158 @ X159 @ X164) @ X159)|~(in @ X164 @ (esk7_2 @ X158 @ X159))|(((X161)!=(esk6_3 @ X158 @ X159 @ X161))|~(X158 @ (esk5_2 @ X158 @ X159) @ X161)))&((X158 @ (esk8_3 @ X158 @ X159 @ X164) @ X164)|~(in @ X164 @ (esk7_2 @ X158 @ X159))|(((X161)!=(esk6_3 @ X158 @ X159 @ X161))|~(X158 @ (esk5_2 @ X158 @ X159) @ X161))))&(~(in @ X167 @ X159)|~(X158 @ X167 @ X166)|(in @ X166 @ (esk7_2 @ X158 @ X159))|(((X161)!=(esk6_3 @ X158 @ X159 @ X161))|~(X158 @ (esk5_2 @ X158 @ X159) @ X161))))))&((((in @ (esk9_1 @ X168) @ X168)|~(in @ X169 @ X168))&(~(in @ X171 @ (esk9_1 @ X168))|~(in @ X171 @ X168)|~(in @ X169 @ X168)))&((epred1_0)&((((X172 @ (esk10_2 @ X172 @ X173))|~(X172 @ X173)|(X172 @ (descr @ X172)))&(((X173)!=(esk10_2 @ X172 @ X173))|~(X172 @ X173)|(X172 @ (descr @ X172))))&((~(in @ X177 @ X175)|(~(X176 @ X177)|(in @ X177 @ (dsetconstr @ X175 @ X176))))&((~(in @ X180 @ (dsetconstr @ X178 @ X179))|(in @ X180 @ X178))&((~(in @ X183 @ (dsetconstr @ X181 @ X182))|(X182 @ X183))&(((epred2_0 @ esk11_0)&(~(epred2_0 @ X186)|((esk11_0)=(X186))))&(((epred2_0 @ (esk12_1 @ X187))|~(epred2_0 @ X187))&(((X187)!=(esk12_1 @ X187))|~(epred2_0 @ X187)))))))))))))))))))), 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_27])])])])])])])).
% 0.09/0.26 thf(c_0_29, negated_conjecture, ![X2:$i]:((((esk11_0)=(X2))|~((epred2_0 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_28])).
% 0.09/0.26 thf(c_0_30, negated_conjecture, ![X2:$i]:(((epred2_0 @ (esk12_1 @ X2))|~((epred2_0 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_28])).
% 0.09/0.26 thf(c_0_31, negated_conjecture, ![X2:$i]:((((X2)!=(esk12_1 @ X2))|~((epred2_0 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_28])).
% 0.09/0.26 thf(c_0_32, negated_conjecture, ![X2:$i]:((((esk12_1 @ X2)=(esk11_0))|~((epred2_0 @ X2)))), inference(spm,[status(thm)],[c_0_29, c_0_30])).
% 0.09/0.26 thf(c_0_33, negated_conjecture, (epred2_0 @ esk11_0), inference(split_conjunct,[status(thm)],[c_0_28])).
% 0.09/0.26 thf(c_0_34, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_31, c_0_32])]), c_0_33])]), ['proof']).
% 0.09/0.26 % SZS output end CNFRefutation
% 0.09/0.26 % Parsed axioms : 41
% 0.09/0.26 % Removed by relevancy pruning/SinE : 24
% 0.09/0.26 % Initial clauses : 51
% 0.09/0.26 % Removed in clause preprocessing : 0
% 0.09/0.26 % Initial clauses in saturation : 51
% 0.09/0.26 % Processed clauses : 8
% 0.09/0.26 % ...of these trivial : 0
% 0.09/0.26 % ...subsumed : 0
% 0.09/0.26 % ...remaining for further processing : 8
% 0.09/0.26 % Other redundant clauses eliminated : 1
% 0.09/0.26 % Clauses deleted for lack of memory : 0
% 0.09/0.26 % Backward-subsumed : 0
% 0.09/0.26 % Backward-rewritten : 0
% 0.09/0.26 % Generated clauses : 4
% 0.09/0.26 % ...of the previous two non-redundant : 1
% 0.09/0.26 % ...aggressively subsumed : 0
% 0.09/0.26 % Contextual simplify-reflections : 0
% 0.09/0.26 % Paramodulations : 3
% 0.09/0.26 % Factorizations : 0
% 0.09/0.26 % NegExts : 0
% 0.09/0.26 % Equation resolutions : 1
% 0.09/0.26 % Disequality decompositions : 0
% 0.09/0.26 % Total rewrite steps : 2
% 0.09/0.26 % ...of those cached : 1
% 0.09/0.26 % Propositional unsat checks : 0
% 0.09/0.26 % Propositional check models : 0
% 0.09/0.26 % Propositional check unsatisfiable : 0
% 0.09/0.26 % Propositional clauses : 0
% 0.09/0.26 % Propositional clauses after purity: 0
% 0.09/0.26 % Propositional unsat core size : 0
% 0.09/0.26 % Propositional preprocessing time : 0.000
% 0.09/0.26 % Propositional encoding time : 0.000
% 0.09/0.26 % Propositional solver time : 0.000
% 0.09/0.26 % Success case prop preproc time : 0.000
% 0.09/0.26 % Success case prop encoding time : 0.000
% 0.09/0.26 % Success case prop solver time : 0.000
% 0.09/0.26 % Current number of processed clauses : 8
% 0.09/0.26 % Positive orientable unit clauses : 3
% 0.09/0.26 % Positive unorientable unit clauses: 0
% 0.09/0.26 % Negative unit clauses : 1
% 0.09/0.26 % Non-unit-clauses : 4
% 0.09/0.26 % Current number of unprocessed clauses: 44
% 0.09/0.26 % ...number of literals in the above : 163
% 0.09/0.26 % Current number of archived formulas : 0
% 0.09/0.26 % Current number of archived clauses : 0
% 0.09/0.26 % Clause-clause subsumption calls (NU) : 6
% 0.09/0.26 % Rec. Clause-clause subsumption calls : 5
% 0.09/0.26 % Non-unit clause-clause subsumptions : 0
% 0.09/0.26 % Unit Clause-clause subsumption calls : 0
% 0.09/0.26 % Rewrite failures with RHS unbound : 0
% 0.09/0.26 % BW rewrite match attempts : 0
% 0.09/0.26 % BW rewrite match successes : 0
% 0.09/0.26 % Condensation attempts : 0
% 0.09/0.26 % Condensation successes : 0
% 0.09/0.26 % Termbank termtop insertions : 6141
% 0.09/0.26 % Search garbage collected termcells : 2357
% 0.09/0.26
% 0.09/0.26 % -------------------------------------------------
% 0.09/0.26 % User time : 0.006 s
% 0.09/0.26 % System time : 0.004 s
% 0.09/0.26 % Total time : 0.010 s
% 0.09/0.26 % Maximum resident set size: 4140 pages
% 0.09/0.26
% 0.09/0.26 % -------------------------------------------------
% 0.09/0.26 % User time : 0.009 s
% 0.09/0.26 % System time : 0.008 s
% 0.09/0.26 % Total time : 0.017 s
% 0.09/0.26 % Maximum resident set size: 4864 pages
% 0.09/0.26 % E exiting
%------------------------------------------------------------------------------