%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU500^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:26:29 AM UTC 2026
% Result : Theorem 0.23s 0.27s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU500^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.18 % Computer : n018.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Tue Sep 29 13:48:41 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.23 Running higher-order theorem proving
% 0.06/0.24 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.5hMBbazZV6/E---3.1_91069.p
% 0.23/0.27 % Version: 3.5.1-ho
% 0.23/0.27 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.23/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.27 % Starting sh5l with 300s (1) cores
% 0.23/0.27 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.27 % Starting new_bool_2 with 300s (1) cores
% 0.23/0.27 % sh5l with pid 91101 completed with status 0
% 0.23/0.27 % Result found by sh5l
% 0.23/0.27 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.23/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.27 % Starting sh5l with 300s (1) cores
% 0.23/0.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.23/0.27 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.23/0.27 % Search class: HGHSF-FFMS31-SHFSMSBN
% 0.23/0.27 % partial match(1): HGHSM-FFMS31-SHFSMSBN
% 0.23/0.27 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.27 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.27 % SubtermCWHack with pid 91105 completed with status 0
% 0.23/0.27 % Result found by SubtermCWHack
% 0.23/0.27 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.23/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.27 % Starting sh5l with 300s (1) cores
% 0.23/0.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.23/0.27 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.23/0.27 % Search class: HGHSF-FFMS31-SHFSMSBN
% 0.23/0.27 % partial match(1): HGHSM-FFMS31-SHFSMSBN
% 0.23/0.27 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.27 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.27 % Preprocessing time : 0.001 s
% 0.23/0.27
% 0.23/0.27 % Proof found!
% 0.23/0.27 % SZS status Theorem
% 0.23/0.27 % SZS output start CNFRefutation
% 0.23/0.27 thf(decl_23, type, in: $i > $i > $o).
% 0.23/0.27 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.23/0.27 thf(decl_25, type, setextAx: $o).
% 0.23/0.27 thf(decl_26, type, emptyset: $i).
% 0.23/0.27 thf(decl_27, type, emptysetAx: $o).
% 0.23/0.27 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.23/0.27 thf(decl_29, type, setadjoinAx: $o).
% 0.23/0.27 thf(decl_30, type, powerset: $i > $i).
% 0.23/0.27 thf(decl_31, type, powersetAx: $o).
% 0.23/0.27 thf(decl_32, type, setunion: $i > $i).
% 0.23/0.27 thf(decl_33, type, setunionAx: $o).
% 0.23/0.27 thf(decl_34, type, omega: $i).
% 0.23/0.27 thf(decl_35, type, omega0Ax: $o).
% 0.23/0.27 thf(decl_36, type, omegaSAx: $o).
% 0.23/0.27 thf(decl_37, type, omegaIndAx: $o).
% 0.23/0.27 thf(decl_38, type, replAx: $o).
% 0.23/0.27 thf(decl_39, type, foundationAx: $o).
% 0.23/0.27 thf(decl_40, type, wellorderingAx: $o).
% 0.23/0.27 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.23/0.27 thf(decl_42, type, descrp: $o).
% 0.23/0.27 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.23/0.27 thf(decl_44, type, dsetconstrI: $o).
% 0.23/0.27 thf(decl_45, type, dsetconstrEL: $o).
% 0.23/0.27 thf(decl_46, type, dsetconstrER: $o).
% 0.23/0.27 thf(decl_47, type, exuE1: $o).
% 0.23/0.27 thf(decl_48, type, prop2set: $o > $i).
% 0.23/0.27 thf(decl_49, type, epred1_0: $o).
% 0.23/0.27 thf(decl_50, type, esk1_2: $i > $i > $i).
% 0.23/0.27 thf(decl_51, type, esk2_2: $i > $i > $i).
% 0.23/0.27 thf(decl_52, type, esk3_2: $i > $i > $i).
% 0.23/0.27 thf(decl_53, type, esk4_1: $i > $i).
% 0.23/0.27 thf(decl_54, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.23/0.27 thf(decl_55, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.23/0.27 thf(decl_56, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.23/0.27 thf(decl_57, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.23/0.27 thf(decl_58, type, esk9_1: $i > $i).
% 0.23/0.27 thf(decl_59, type, esk10_2: ($i > $o) > $i > $i).
% 0.23/0.27 thf(decl_60, type, esk11_2: ($i > $o) > $i > $i).
% 0.23/0.27 thf(decl_61, type, esk12_1: ($i > $o) > $i).
% 0.23/0.27 thf(decl_62, type, epred2_0: $o).
% 0.23/0.27 thf(decl_63, type, esk13_0: $i).
% 0.23/0.27 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.5hMBbazZV6/E---3.1_91069.p', descrp)).
% 0.23/0.27 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.5hMBbazZV6/E---3.1_91069.p', exu)).
% 0.23/0.27 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.5hMBbazZV6/E---3.1_91069.p', exuE1)).
% 0.23/0.27 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.5hMBbazZV6/E---3.1_91069.p', replAx)).
% 0.23/0.27 thf(prop2setE, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>![X11:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X11))))=>(X11))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.5hMBbazZV6/E---3.1_91069.p', prop2setE)).
% 0.23/0.27 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.5hMBbazZV6/E---3.1_91069.p', dsetconstrI)).
% 0.23/0.27 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.5hMBbazZV6/E---3.1_91069.p', dsetconstrEL)).
% 0.23/0.27 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.5hMBbazZV6/E---3.1_91069.p', dsetconstrER)).
% 0.23/0.27 thf(prop2set, axiom, ((prop2set)=(^[X10:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[X2:$i]:((X10)))))), file('/export/starexec/sandbox/tmp/tmp.5hMBbazZV6/E---3.1_91069.p', prop2set)).
% 0.23/0.27 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.5hMBbazZV6/E---3.1_91069.p', foundationAx)).
% 0.23/0.27 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.5hMBbazZV6/E---3.1_91069.p', omega0Ax)).
% 0.23/0.27 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.5hMBbazZV6/E---3.1_91069.p', omegaSAx)).
% 0.23/0.27 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.5hMBbazZV6/E---3.1_91069.p', wellorderingAx)).
% 0.23/0.27 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.5hMBbazZV6/E---3.1_91069.p', powersetAx)).
% 0.23/0.27 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.5hMBbazZV6/E---3.1_91069.p', setadjoinAx)).
% 0.23/0.27 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.5hMBbazZV6/E---3.1_91069.p', emptysetAx)).
% 0.23/0.27 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.5hMBbazZV6/E---3.1_91069.p', setextAx)).
% 0.23/0.27 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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/sandbox/tmp/tmp.5hMBbazZV6/E---3.1_91069.p', omegaIndAx)).
% 0.23/0.27 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.5hMBbazZV6/E---3.1_91069.p', setunionAx)).
% 0.23/0.27 thf(c_0_19, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.23/0.27 thf(c_0_20, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.23/0.27 thf(c_0_21, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.23/0.27 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.23/0.27 thf(c_0_23, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>![X11:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X11))))=>(X11)))))))))))))))))))), inference(assume_negation,[status(cth)],[prop2setE])).
% 0.23/0.27 thf(c_0_24, plain, ((descrp)=(![X1:$i > $o]:((((?[X75:$i]:(((((X1 @ X75)))&(![X76:$i]:(((((X1 @ X76)))=>(((X75)=(X76))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_19, c_0_20])).
% 0.23/0.27 thf(c_0_25, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.23/0.27 thf(c_0_26, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.23/0.27 thf(c_0_27, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.23/0.27 thf(c_0_28, plain, ((exuE1)=(![X1:$i > $o]:((((?[X77:$i]:(((((X1 @ X77)))&(![X78:$i]:(((((X1 @ X78)))=>(((X77)=(X78))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_21, c_0_20])).
% 0.23/0.27 thf(c_0_29, plain, ((prop2set)=(^[Z0:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[Z1:$i]:((Z0)))))), inference(fof_simplification,[status(thm)],[prop2set])).
% 0.23/0.27 thf(c_0_30, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X73:$i]:(((((X6 @ X2 @ X73)))&(![X74:$i]:(((((X6 @ X2 @ X74)))=>(((X73)=(X74)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_22, c_0_20])).
% 0.23/0.27 thf(c_0_31, plain, ((epred1_0)<=>![X108:$i]:(?[X109:$i]:((((![X110:$i]:(((in @ X110 @ X109)=>![X111:$i]:(((in @ X111 @ X110)=>(in @ X111 @ X108)))))&![X112:$i, X113:$i]:((((in @ X112 @ X108)&(in @ X113 @ X108))=>(![X114:$i]:(((in @ X114 @ X109)=>((in @ X112 @ X114)<=>(in @ X113 @ X114))))=>((X112)=(X113))))))&![X115:$i, X116:$i]:((((in @ X115 @ X109)&(in @ X116 @ X109))=>(![X117:$i]:(((in @ X117 @ X115)=>(in @ X117 @ X116)))|![X118:$i]:(((in @ X118 @ X116)=>(in @ X118 @ X115)))))))&![X119:$i]:(((![X120:$i]:(((in @ X120 @ X119)=>(in @ X120 @ X108)))&?[X121:$i]:((in @ X121 @ X119)))=>?[X122:$i, X123:$i]:(((((in @ X122 @ X109)&(in @ X123 @ X119))&~(?[X124:$i]:(((in @ X124 @ X122)&(in @ X124 @ X119)))))&![X125:$i]:(((in @ X125 @ X109)=>(![X126:$i]:(((in @ X126 @ X125)=>(in @ X126 @ X122)))|(in @ X123 @ X125)))))))))))), introduced(definition)).
% 0.23/0.27 thf(c_0_32, negated_conjecture, ~((![X79:$i, X80:$i]:((![X81:$i]:(((in @ X81 @ X79)<=>(in @ X81 @ X80)))=>((X79)=(X80))))=>(![X82:$i]:(~(in @ X82 @ emptyset))=>(![X83:$i, X84:$i, X85:$i]:(((in @ X85 @ (setadjoin @ X83 @ X84))<=>(((X85)=(X83))|(in @ X85 @ X84))))=>(![X86:$i, X87:$i]:(((in @ X87 @ (powerset @ X86))<=>![X88:$i]:(((in @ X88 @ X87)=>(in @ X88 @ X86)))))=>(![X89:$i, X90:$i]:(((in @ X90 @ (setunion @ X89))<=>?[X91:$i]:(((in @ X90 @ X91)&(in @ X91 @ X89)))))=>((in @ emptyset @ omega)=>(![X92:$i]:(((in @ X92 @ omega)=>(in @ (setadjoin @ X92 @ X92) @ omega)))=>(![X93:$i]:((((in @ emptyset @ X93)&![X94:$i]:((((in @ X94 @ omega)&(in @ X94 @ X93))=>(in @ (setadjoin @ X94 @ X94) @ X93))))=>![X95:$i]:(((in @ X95 @ omega)=>(in @ X95 @ X93)))))=>(![X96:$i > $i > $o, X97:$i]:((![X98:$i]:(((in @ X98 @ X97)=>?[X99:$i]:(((X96 @ X98 @ X99)&![X100:$i]:(((X96 @ X98 @ X100)=>((X99)=(X100))))))))=>?[X101:$i]:(![X102:$i]:(((in @ X102 @ X101)<=>?[X103:$i]:(((in @ X103 @ X97)&(X96 @ X103 @ X102))))))))=>(![X104:$i]:((?[X105:$i]:((in @ X105 @ X104))=>?[X106:$i]:(((in @ X106 @ X104)&~(?[X107:$i]:(((in @ X107 @ X106)&(in @ X107 @ X104))))))))=>((epred1_0)=>(![X127:$i > $o]:((?[X128:$i]:(((X127 @ X128)&![X129:$i]:(((X127 @ X129)=>((X128)=(X129))))))=>(X127 @ (descr @ (^[Z0:$i]:(X127 @ Z0))))))=>(![X130:$i, X131:$i > $o, X132:$i]:(((in @ X132 @ X130)=>((X131 @ X132)=>(in @ X132 @ (dsetconstr @ X130 @ X131)))))=>(![X133:$i, X134:$i > $o, X135:$i]:(((in @ X135 @ (dsetconstr @ X133 @ X134))=>(in @ X135 @ X133)))=>(![X136:$i, X137:$i > $o, X138:$i]:(((in @ X138 @ (dsetconstr @ X136 @ X137))=>(X137 @ X138)))=>(![X139:$i > $o]:((?[X140:$i]:(((X139 @ X140)&![X141:$i]:(((X139 @ X141)=>((X140)=(X141))))))=>?[X142:$i]:(((X139 @ X142)&![X143:$i]:(((X139 @ X143)=>((X142)=(X143))))))))=>![X11:$o, X2:$i]:(((in @ X2 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X11)))))=>(X11)))))))))))))))))))), 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)],[c_0_23, foundationAx]), omega0Ax]), omegaSAx]), wellorderingAx]), c_0_24]), c_0_25]), c_0_26]), c_0_27]), c_0_28]), c_0_29]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx]), omegaIndAx]), c_0_30]), setunionAx])])]), c_0_31])).
% 0.23/0.27 thf(c_0_33, negated_conjecture, ![X144:$i, X145:$i, X147:$i, X148:$i, X149:$i, X150:$i, X151:$i, X152:$i, X153:$i, X154:$i, X155:$i, X157:$i, X158:$i, X160:$i, X161:$i, X162:$i, X163:$i, X164:$i, X166:$i, X167:$i > $i > $o, X168:$i, X170:$i, X173:$i, X175:$i, X176:$i, X177:$i, X178:$i, X180:$i, X181:$i > $o, X182:$i, X184:$i, X185:$i > $o, X186:$i, X187:$i, X188:$i > $o, X189:$i, X190:$i, X191:$i > $o, X192:$i, X193:$i > $o, X194:$i, X197:$i]:((((~(in @ (esk1_2 @ X144 @ X145) @ X144)|~(in @ (esk1_2 @ X144 @ X145) @ X145)|((X144)=(X145)))&((in @ (esk1_2 @ X144 @ X145) @ X144)|(in @ (esk1_2 @ X144 @ X145) @ X145)|((X144)=(X145))))&(~(in @ X147 @ emptyset)&(((~(in @ X150 @ (setadjoin @ X148 @ X149))|(((X150)=(X148))|(in @ X150 @ X149)))&((((X150)!=(X148))|(in @ X150 @ (setadjoin @ X148 @ X149)))&(~(in @ X150 @ X149)|(in @ X150 @ (setadjoin @ X148 @ X149)))))&(((~(in @ X152 @ (powerset @ X151))|(~(in @ X153 @ X152)|(in @ X153 @ X151)))&(((in @ (esk2_2 @ X154 @ X155) @ X155)|(in @ X155 @ (powerset @ X154)))&(~(in @ (esk2_2 @ X154 @ X155) @ X154)|(in @ X155 @ (powerset @ X154)))))&(((((in @ X158 @ (esk3_2 @ X157 @ X158))|~(in @ X158 @ (setunion @ X157)))&((in @ (esk3_2 @ X157 @ X158) @ X157)|~(in @ X158 @ (setunion @ X157))))&(~(in @ X161 @ X162)|~(in @ X162 @ X160)|(in @ X161 @ (setunion @ X160))))&((in @ emptyset @ omega)&((~(in @ X163 @ omega)|(in @ (setadjoin @ X163 @ X163) @ omega))&(((((in @ (esk4_1 @ X164) @ omega)|~(in @ emptyset @ X164)|(~(in @ X166 @ omega)|(in @ X166 @ X164)))&((in @ (esk4_1 @ X164) @ X164)|~(in @ emptyset @ X164)|(~(in @ X166 @ omega)|(in @ X166 @ X164))))&(~(in @ (setadjoin @ (esk4_1 @ X164) @ (esk4_1 @ X164)) @ X164)|~(in @ emptyset @ X164)|(~(in @ X166 @ omega)|(in @ X166 @ X164))))&((((((in @ (esk8_3 @ X167 @ X168 @ X173) @ X168)|~(in @ X173 @ (esk7_2 @ X167 @ X168))|(in @ (esk5_2 @ X167 @ X168) @ X168))&((X167 @ (esk8_3 @ X167 @ X168 @ X173) @ X173)|~(in @ X173 @ (esk7_2 @ X167 @ X168))|(in @ (esk5_2 @ X167 @ X168) @ X168)))&(~(in @ X176 @ X168)|~(X167 @ X176 @ X175)|(in @ X175 @ (esk7_2 @ X167 @ X168))|(in @ (esk5_2 @ X167 @ X168) @ X168)))&(((((in @ (esk8_3 @ X167 @ X168 @ X173) @ X168)|~(in @ X173 @ (esk7_2 @ X167 @ X168))|((X167 @ (esk5_2 @ X167 @ X168) @ (esk6_3 @ X167 @ X168 @ X170))|~(X167 @ (esk5_2 @ X167 @ X168) @ X170)))&((X167 @ (esk8_3 @ X167 @ X168 @ X173) @ X173)|~(in @ X173 @ (esk7_2 @ X167 @ X168))|((X167 @ (esk5_2 @ X167 @ X168) @ (esk6_3 @ X167 @ X168 @ X170))|~(X167 @ (esk5_2 @ X167 @ X168) @ X170))))&(~(in @ X176 @ X168)|~(X167 @ X176 @ X175)|(in @ X175 @ (esk7_2 @ X167 @ X168))|((X167 @ (esk5_2 @ X167 @ X168) @ (esk6_3 @ X167 @ X168 @ X170))|~(X167 @ (esk5_2 @ X167 @ X168) @ X170))))&((((in @ (esk8_3 @ X167 @ X168 @ X173) @ X168)|~(in @ X173 @ (esk7_2 @ X167 @ X168))|(((X170)!=(esk6_3 @ X167 @ X168 @ X170))|~(X167 @ (esk5_2 @ X167 @ X168) @ X170)))&((X167 @ (esk8_3 @ X167 @ X168 @ X173) @ X173)|~(in @ X173 @ (esk7_2 @ X167 @ X168))|(((X170)!=(esk6_3 @ X167 @ X168 @ X170))|~(X167 @ (esk5_2 @ X167 @ X168) @ X170))))&(~(in @ X176 @ X168)|~(X167 @ X176 @ X175)|(in @ X175 @ (esk7_2 @ X167 @ X168))|(((X170)!=(esk6_3 @ X167 @ X168 @ X170))|~(X167 @ (esk5_2 @ X167 @ X168) @ X170))))))&((((in @ (esk9_1 @ X177) @ X177)|~(in @ X178 @ X177))&(~(in @ X180 @ (esk9_1 @ X177))|~(in @ X180 @ X177)|~(in @ X178 @ X177)))&((epred1_0)&((((X181 @ (esk10_2 @ X181 @ X182))|~(X181 @ X182)|(X181 @ (descr @ X181)))&(((X182)!=(esk10_2 @ X181 @ X182))|~(X181 @ X182)|(X181 @ (descr @ X181))))&((~(in @ X186 @ X184)|(~(X185 @ X186)|(in @ X186 @ (dsetconstr @ X184 @ X185))))&((~(in @ X189 @ (dsetconstr @ X187 @ X188))|(in @ X189 @ X187))&((~(in @ X192 @ (dsetconstr @ X190 @ X191))|(X191 @ X192))&(((((X193 @ (esk12_1 @ X193))|((X193 @ (esk11_2 @ X193 @ X194))|~(X193 @ X194)))&(~(X193 @ X197)|((esk12_1 @ X193)=(X197))|((X193 @ (esk11_2 @ X193 @ X194))|~(X193 @ X194))))&(((X193 @ (esk12_1 @ X193))|(((X194)!=(esk11_2 @ X193 @ X194))|~(X193 @ X194)))&(~(X193 @ X197)|((esk12_1 @ X193)=(X197))|(((X194)!=(esk11_2 @ X193 @ X194))|~(X193 @ X194)))))&((in @ esk13_0 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((epred2_0)))))&~(epred2_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_32])])])])])])])).
% 0.23/0.27 thf(c_0_34, negated_conjecture, ![X3:$i, X2:$i, X1:$i > $o]:(((X1 @ X2)|~((in @ X2 @ (dsetconstr @ X3 @ X1))))), inference(split_conjunct,[status(thm)],[c_0_33])).
% 0.23/0.27 thf(c_0_35, negated_conjecture, (in @ esk13_0 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((epred2_0))))), inference(split_conjunct,[status(thm)],[c_0_33])).
% 0.23/0.27 thf(c_0_36, negated_conjecture, ~((epred2_0)), inference(split_conjunct,[status(thm)],[c_0_33])).
% 0.23/0.27 thf(c_0_37, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34, c_0_35]), c_0_36]), ['proof']).
% 0.23/0.27 % SZS output end CNFRefutation
% 0.23/0.27 % Parsed axioms : 45
% 0.23/0.27 % Removed by relevancy pruning/SinE : 26
% 0.23/0.27 % Initial clauses : 53
% 0.23/0.27 % Removed in clause preprocessing : 0
% 0.23/0.27 % Initial clauses in saturation : 53
% 0.23/0.27 % Processed clauses : 8
% 0.23/0.27 % ...of these trivial : 0
% 0.23/0.27 % ...subsumed : 0
% 0.23/0.27 % ...remaining for further processing : 8
% 0.23/0.27 % Other redundant clauses eliminated : 0
% 0.23/0.27 % Clauses deleted for lack of memory : 0
% 0.23/0.27 % Backward-subsumed : 0
% 0.23/0.27 % Backward-rewritten : 0
% 0.23/0.27 % Generated clauses : 4
% 0.23/0.27 % ...of the previous two non-redundant : 2
% 0.23/0.27 % ...aggressively subsumed : 0
% 0.23/0.27 % Contextual simplify-reflections : 0
% 0.23/0.27 % Paramodulations : 4
% 0.23/0.27 % Factorizations : 0
% 0.23/0.27 % NegExts : 0
% 0.23/0.27 % Equation resolutions : 0
% 0.23/0.27 % Disequality decompositions : 0
% 0.23/0.27 % Total rewrite steps : 1
% 0.23/0.27 % ...of those cached : 0
% 0.23/0.27 % Propositional unsat checks : 0
% 0.23/0.27 % Propositional check models : 0
% 0.23/0.27 % Propositional check unsatisfiable : 0
% 0.23/0.27 % Propositional clauses : 0
% 0.23/0.27 % Propositional clauses after purity: 0
% 0.23/0.27 % Propositional unsat core size : 0
% 0.23/0.27 % Propositional preprocessing time : 0.000
% 0.23/0.27 % Propositional encoding time : 0.000
% 0.23/0.27 % Propositional solver time : 0.000
% 0.23/0.27 % Success case prop preproc time : 0.000
% 0.23/0.27 % Success case prop encoding time : 0.000
% 0.23/0.27 % Success case prop solver time : 0.000
% 0.23/0.27 % Current number of processed clauses : 8
% 0.23/0.27 % Positive orientable unit clauses : 4
% 0.23/0.27 % Positive unorientable unit clauses: 0
% 0.23/0.27 % Negative unit clauses : 2
% 0.23/0.27 % Non-unit-clauses : 2
% 0.23/0.27 % Current number of unprocessed clauses: 47
% 0.23/0.27 % ...number of literals in the above : 174
% 0.23/0.27 % Current number of archived formulas : 0
% 0.23/0.27 % Current number of archived clauses : 0
% 0.23/0.27 % Clause-clause subsumption calls (NU) : 0
% 0.23/0.27 % Rec. Clause-clause subsumption calls : 0
% 0.23/0.27 % Non-unit clause-clause subsumptions : 0
% 0.23/0.27 % Unit Clause-clause subsumption calls : 0
% 0.23/0.27 % Rewrite failures with RHS unbound : 0
% 0.23/0.27 % BW rewrite match attempts : 0
% 0.23/0.27 % BW rewrite match successes : 0
% 0.23/0.27 % Condensation attempts : 0
% 0.23/0.27 % Condensation successes : 0
% 0.23/0.27 % Termbank termtop insertions : 6428
% 0.23/0.27 % Search garbage collected termcells : 2429
% 0.23/0.27
% 0.23/0.27 % -------------------------------------------------
% 0.23/0.27 % User time : 0.003 s
% 0.23/0.27 % System time : 0.004 s
% 0.23/0.27 % Total time : 0.008 s
% 0.23/0.27 % Maximum resident set size: 4200 pages
% 0.23/0.27
% 0.23/0.27 % -------------------------------------------------
% 0.23/0.27 % User time : 0.006 s
% 0.23/0.27 % System time : 0.010 s
% 0.23/0.27 % Total time : 0.016 s
% 0.23/0.27 % Maximum resident set size: 4864 pages
% 0.23/0.27 % E exiting
%------------------------------------------------------------------------------