%------------------------------------------------------------------------------
% File : E-SAT---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 : n019.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 0.07s 0.26s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU501^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n019.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 13:46:47 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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.jqjphAZkLJ/E---3.1_787576.p
% 0.07/0.26 % Version: 3.5.1-ho
% 0.07/0.26 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.07/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.26 % Starting sh5l with 300s (1) cores
% 0.07/0.26 % Starting new_bool_1 with 300s (1) cores
% 0.07/0.26 % Starting new_bool_2 with 300s (1) cores
% 0.07/0.26 % sh5l with pid 787590 completed with status 0
% 0.07/0.26 % Result found by sh5l
% 0.07/0.26 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.07/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.26 % Starting sh5l with 300s (1) cores
% 0.07/0.26 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.07/0.26 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.07/0.26 % Search class: HGHSF-FFMS31-SHFSMSBN
% 0.07/0.26 % partial match(1): HGHSM-FFMS31-SHFSMSBN
% 0.07/0.26 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.26 % Starting SubtermCWHack with 31s (1) cores
% 0.07/0.26 % SubtermCWHack with pid 787598 completed with status 0
% 0.07/0.26 % Result found by SubtermCWHack
% 0.07/0.26 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.07/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.26 % Starting sh5l with 300s (1) cores
% 0.07/0.26 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.07/0.26 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.07/0.26 % Search class: HGHSF-FFMS31-SHFSMSBN
% 0.07/0.26 % partial match(1): HGHSM-FFMS31-SHFSMSBN
% 0.07/0.26 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.26 % Starting SubtermCWHack with 31s (1) cores
% 0.07/0.26 % Preprocessing time : 0.002 s
% 0.07/0.26
% 0.07/0.26 % Proof found!
% 0.07/0.26 % SZS status Theorem
% 0.07/0.26 % SZS output start CNFRefutation
% 0.07/0.26 thf(decl_23, type, in: $i > $i > $o).
% 0.07/0.26 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.07/0.26 thf(decl_25, type, setextAx: $o).
% 0.07/0.26 thf(decl_26, type, emptyset: $i).
% 0.07/0.26 thf(decl_27, type, emptysetAx: $o).
% 0.07/0.26 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.07/0.26 thf(decl_29, type, setadjoinAx: $o).
% 0.07/0.26 thf(decl_30, type, powerset: $i > $i).
% 0.07/0.26 thf(decl_31, type, powersetAx: $o).
% 0.07/0.26 thf(decl_32, type, setunion: $i > $i).
% 0.07/0.26 thf(decl_33, type, setunionAx: $o).
% 0.07/0.26 thf(decl_34, type, omega: $i).
% 0.07/0.26 thf(decl_35, type, omega0Ax: $o).
% 0.07/0.26 thf(decl_36, type, omegaSAx: $o).
% 0.07/0.26 thf(decl_37, type, omegaIndAx: $o).
% 0.07/0.26 thf(decl_38, type, replAx: $o).
% 0.07/0.26 thf(decl_39, type, foundationAx: $o).
% 0.07/0.26 thf(decl_40, type, wellorderingAx: $o).
% 0.07/0.26 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.07/0.26 thf(decl_42, type, descrp: $o).
% 0.07/0.26 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.07/0.26 thf(decl_44, type, dsetconstrI: $o).
% 0.07/0.26 thf(decl_45, type, dsetconstrEL: $o).
% 0.07/0.26 thf(decl_46, type, dsetconstrER: $o).
% 0.07/0.26 thf(decl_47, type, exuE1: $o).
% 0.07/0.26 thf(decl_48, type, prop2set: $o > $i).
% 0.07/0.26 thf(decl_49, type, prop2setE: $o).
% 0.07/0.26 thf(decl_50, type, epred1_0: $o).
% 0.07/0.26 thf(decl_51, type, esk1_2: $i > $i > $i).
% 0.07/0.26 thf(decl_52, type, esk2_2: $i > $i > $i).
% 0.07/0.26 thf(decl_53, type, esk3_2: $i > $i > $i).
% 0.07/0.26 thf(decl_54, type, esk4_1: $i > $i).
% 0.07/0.26 thf(decl_55, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.07/0.26 thf(decl_56, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.07/0.26 thf(decl_57, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.07/0.26 thf(decl_58, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.07/0.26 thf(decl_59, type, esk9_1: $i > $i).
% 0.07/0.26 thf(decl_60, type, esk10_2: ($i > $o) > $i > $i).
% 0.27/0.26 thf(decl_61, type, esk11_2: ($i > $o) > $i > $i).
% 0.27/0.26 thf(decl_62, type, esk12_1: ($i > $o) > $i).
% 0.27/0.26 thf(decl_63, type, esk13_0: $i).
% 0.27/0.26 thf(decl_64, type, epred2_0: $o).
% 0.27/0.26 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.jqjphAZkLJ/E---3.1_787576.p', exuE1)).
% 0.27/0.26 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.jqjphAZkLJ/E---3.1_787576.p', exu)).
% 0.27/0.26 thf(prop2set, axiom, ((prop2set)=(^[X10:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[X2:$i]:((X10)))))), file('/export/starexec/sandbox/tmp/tmp.jqjphAZkLJ/E---3.1_787576.p', prop2set)).
% 0.27/0.26 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.jqjphAZkLJ/E---3.1_787576.p', descrp)).
% 0.27/0.26 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.jqjphAZkLJ/E---3.1_787576.p', replAx)).
% 0.27/0.26 thf(emptysetE, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>![X2:$i]:(((in @ X2 @ emptyset)=>![X12:$o]:((X12))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.jqjphAZkLJ/E---3.1_787576.p', emptysetE)).
% 0.27/0.26 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.jqjphAZkLJ/E---3.1_787576.p', dsetconstrEL)).
% 0.27/0.26 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.jqjphAZkLJ/E---3.1_787576.p', dsetconstrER)).
% 0.27/0.26 thf(prop2setE, axiom, ((prop2setE)<=>![X11:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X11))))=>(X11)))), file('/export/starexec/sandbox/tmp/tmp.jqjphAZkLJ/E---3.1_787576.p', prop2setE)).
% 0.27/0.26 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.jqjphAZkLJ/E---3.1_787576.p', dsetconstrI)).
% 0.27/0.26 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.jqjphAZkLJ/E---3.1_787576.p', foundationAx)).
% 0.27/0.26 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.jqjphAZkLJ/E---3.1_787576.p', wellorderingAx)).
% 0.27/0.26 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.jqjphAZkLJ/E---3.1_787576.p', omegaIndAx)).
% 0.27/0.26 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.jqjphAZkLJ/E---3.1_787576.p', omega0Ax)).
% 0.27/0.26 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.jqjphAZkLJ/E---3.1_787576.p', emptysetAx)).
% 0.27/0.26 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.jqjphAZkLJ/E---3.1_787576.p', omegaSAx)).
% 0.27/0.26 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.jqjphAZkLJ/E---3.1_787576.p', setunionAx)).
% 0.27/0.26 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.jqjphAZkLJ/E---3.1_787576.p', powersetAx)).
% 0.27/0.26 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.jqjphAZkLJ/E---3.1_787576.p', setadjoinAx)).
% 0.27/0.26 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.jqjphAZkLJ/E---3.1_787576.p', setextAx)).
% 0.27/0.26 thf(c_0_20, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.27/0.26 thf(c_0_21, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.27/0.26 thf(c_0_22, plain, ((prop2set)=(^[Z0:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[Z1:$i]:((Z0)))))), inference(fof_simplification,[status(thm)],[prop2set])).
% 0.27/0.26 thf(c_0_23, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.27/0.26 thf(c_0_24, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.27/0.26 thf(c_0_25, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>![X2:$i]:(((in @ X2 @ emptyset)=>![X12:$o]:((X12)))))))))))))))))))))), inference(assume_negation,[status(cth)],[emptysetE])).
% 0.27/0.26 thf(c_0_26, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.27/0.26 thf(c_0_27, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.27/0.26 thf(c_0_28, plain, ((exuE1)=(![X1:$i > $o]:((((?[X80:$i]:(((((X1 @ X80)))&(![X81:$i]:(((((X1 @ X81)))=>(((X80)=(X81))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_20, c_0_21])).
% 0.27/0.26 thf(c_0_29, axiom, ((prop2setE)=(![X11:$o, X2:$i]:((((in @ X2 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:(((X11)))))))=>((X11)))))), inference(apply_def,[status(thm)],[prop2setE, c_0_22])).
% 0.27/0.26 thf(c_0_30, plain, ((descrp)=(![X1:$i > $o]:((((?[X78:$i]:(((((X1 @ X78)))&(![X79:$i]:(((((X1 @ X79)))=>(((X78)=(X79))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_23, c_0_21])).
% 0.27/0.26 thf(c_0_31, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.27/0.26 thf(c_0_32, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X76:$i]:(((((X6 @ X2 @ X76)))&(![X77:$i]:(((((X6 @ X2 @ X77)))=>(((X76)=(X77)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_24, c_0_21])).
% 0.27/0.26 thf(c_0_33, plain, ((epred1_0)<=>![X111:$i]:(?[X112:$i]:((((![X113:$i]:(((in @ X113 @ X112)=>![X114:$i]:(((in @ X114 @ X113)=>(in @ X114 @ X111)))))&![X115:$i, X116:$i]:((((in @ X115 @ X111)&(in @ X116 @ X111))=>(![X117:$i]:(((in @ X117 @ X112)=>((in @ X115 @ X117)<=>(in @ X116 @ X117))))=>((X115)=(X116))))))&![X118:$i, X119:$i]:((((in @ X118 @ X112)&(in @ X119 @ X112))=>(![X120:$i]:(((in @ X120 @ X118)=>(in @ X120 @ X119)))|![X121:$i]:(((in @ X121 @ X119)=>(in @ X121 @ X118)))))))&![X122:$i]:(((![X123:$i]:(((in @ X123 @ X122)=>(in @ X123 @ X111)))&?[X124:$i]:((in @ X124 @ X122)))=>?[X125:$i, X126:$i]:(((((in @ X125 @ X112)&(in @ X126 @ X122))&~(?[X127:$i]:(((in @ X127 @ X125)&(in @ X127 @ X122)))))&![X128:$i]:(((in @ X128 @ X112)=>(![X129:$i]:(((in @ X129 @ X128)=>(in @ X129 @ X125)))|(in @ X126 @ X128)))))))))))), introduced(definition)).
% 0.27/0.26 thf(c_0_34, negated_conjecture, ~((![X82:$i, X83:$i]:((![X84:$i]:(((in @ X84 @ X82)<=>(in @ X84 @ X83)))=>((X82)=(X83))))=>(![X85:$i]:(~(in @ X85 @ emptyset))=>(![X86:$i, X87:$i, X88:$i]:(((in @ X88 @ (setadjoin @ X86 @ X87))<=>(((X88)=(X86))|(in @ X88 @ X87))))=>(![X89:$i, X90:$i]:(((in @ X90 @ (powerset @ X89))<=>![X91:$i]:(((in @ X91 @ X90)=>(in @ X91 @ X89)))))=>(![X92:$i, X93:$i]:(((in @ X93 @ (setunion @ X92))<=>?[X94:$i]:(((in @ X93 @ X94)&(in @ X94 @ X92)))))=>((in @ emptyset @ omega)=>(![X95:$i]:(((in @ X95 @ omega)=>(in @ (setadjoin @ X95 @ X95) @ omega)))=>(![X96:$i]:((((in @ emptyset @ X96)&![X97:$i]:((((in @ X97 @ omega)&(in @ X97 @ X96))=>(in @ (setadjoin @ X97 @ X97) @ X96))))=>![X98:$i]:(((in @ X98 @ omega)=>(in @ X98 @ X96)))))=>(![X99:$i > $i > $o, X100:$i]:((![X101:$i]:(((in @ X101 @ X100)=>?[X102:$i]:(((X99 @ X101 @ X102)&![X103:$i]:(((X99 @ X101 @ X103)=>((X102)=(X103))))))))=>?[X104:$i]:(![X105:$i]:(((in @ X105 @ X104)<=>?[X106:$i]:(((in @ X106 @ X100)&(X99 @ X106 @ X105))))))))=>(![X107:$i]:((?[X108:$i]:((in @ X108 @ X107))=>?[X109:$i]:(((in @ X109 @ X107)&~(?[X110:$i]:(((in @ X110 @ X109)&(in @ X110 @ X107))))))))=>((epred1_0)=>(![X130:$i > $o]:((?[X131:$i]:(((X130 @ X131)&![X132:$i]:(((X130 @ X132)=>((X131)=(X132))))))=>(X130 @ (descr @ (^[Z0:$i]:(X130 @ Z0))))))=>(![X133:$i, X134:$i > $o, X135:$i]:(((in @ X135 @ X133)=>((X134 @ X135)=>(in @ X135 @ (dsetconstr @ X133 @ X134)))))=>(![X136:$i, X137:$i > $o, X138:$i]:(((in @ X138 @ (dsetconstr @ X136 @ X137))=>(in @ X138 @ X136)))=>(![X139:$i, X140:$i > $o, X141:$i]:(((in @ X141 @ (dsetconstr @ X139 @ X140))=>(X140 @ X141)))=>(![X142:$i > $o]:((?[X143:$i]:(((X142 @ X143)&![X144:$i]:(((X142 @ X144)=>((X143)=(X144))))))=>?[X145:$i]:(((X142 @ X145)&![X146:$i]:(((X142 @ X146)=>((X145)=(X146))))))))=>(![X147:$o, X148:$i]:(((in @ X148 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X147)))))=>(X147)))=>![X2:$i]:(((in @ X2 @ emptyset)=>![X12:$o]:((X12)))))))))))))))))))))), 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_25, c_0_26]), foundationAx]), wellorderingAx]), c_0_27]), c_0_28]), c_0_29]), omegaIndAx]), omega0Ax]), emptysetAx]), omegaSAx]), setunionAx]), powersetAx]), setadjoinAx]), setextAx]), c_0_30]), c_0_31]), c_0_32])])]), c_0_33])).
% 0.27/0.26 thf(c_0_35, negated_conjecture, ![X149:$i, X150:$i, X152:$i, X153:$i, X154:$i, X155:$i, X156:$i, X157:$i, X158:$i, X159:$i, X160:$i, X162:$i, X163:$i, X165:$i, X166:$i, X167:$i, X168:$i, X169:$i, X171:$i, X172:$i > $i > $o, X173:$i, X175:$i, X178:$i, X180:$i, X181:$i, X182:$i, X183:$i, X185:$i, X186:$i > $o, X187:$i, X189:$i, X190:$i > $o, X191:$i, X192:$i, X193:$i > $o, X194:$i, X195:$i, X196:$i > $o, X197:$i, X198:$i > $o, X199:$i, X202:$i, X203:$o, X204:$i]:((((~(in @ (esk1_2 @ X149 @ X150) @ X149)|~(in @ (esk1_2 @ X149 @ X150) @ X150)|((X149)=(X150)))&((in @ (esk1_2 @ X149 @ X150) @ X149)|(in @ (esk1_2 @ X149 @ X150) @ X150)|((X149)=(X150))))&(~(in @ X152 @ emptyset)&(((~(in @ X155 @ (setadjoin @ X153 @ X154))|(((X155)=(X153))|(in @ X155 @ X154)))&((((X155)!=(X153))|(in @ X155 @ (setadjoin @ X153 @ X154)))&(~(in @ X155 @ X154)|(in @ X155 @ (setadjoin @ X153 @ X154)))))&(((~(in @ X157 @ (powerset @ X156))|(~(in @ X158 @ X157)|(in @ X158 @ X156)))&(((in @ (esk2_2 @ X159 @ X160) @ X160)|(in @ X160 @ (powerset @ X159)))&(~(in @ (esk2_2 @ X159 @ X160) @ X159)|(in @ X160 @ (powerset @ X159)))))&(((((in @ X163 @ (esk3_2 @ X162 @ X163))|~(in @ X163 @ (setunion @ X162)))&((in @ (esk3_2 @ X162 @ X163) @ X162)|~(in @ X163 @ (setunion @ X162))))&(~(in @ X166 @ X167)|~(in @ X167 @ X165)|(in @ X166 @ (setunion @ X165))))&((in @ emptyset @ omega)&((~(in @ X168 @ omega)|(in @ (setadjoin @ X168 @ X168) @ omega))&(((((in @ (esk4_1 @ X169) @ omega)|~(in @ emptyset @ X169)|(~(in @ X171 @ omega)|(in @ X171 @ X169)))&((in @ (esk4_1 @ X169) @ X169)|~(in @ emptyset @ X169)|(~(in @ X171 @ omega)|(in @ X171 @ X169))))&(~(in @ (setadjoin @ (esk4_1 @ X169) @ (esk4_1 @ X169)) @ X169)|~(in @ emptyset @ X169)|(~(in @ X171 @ omega)|(in @ X171 @ X169))))&((((((in @ (esk8_3 @ X172 @ X173 @ X178) @ X173)|~(in @ X178 @ (esk7_2 @ X172 @ X173))|(in @ (esk5_2 @ X172 @ X173) @ X173))&((X172 @ (esk8_3 @ X172 @ X173 @ X178) @ X178)|~(in @ X178 @ (esk7_2 @ X172 @ X173))|(in @ (esk5_2 @ X172 @ X173) @ X173)))&(~(in @ X181 @ X173)|~(X172 @ X181 @ X180)|(in @ X180 @ (esk7_2 @ X172 @ X173))|(in @ (esk5_2 @ X172 @ X173) @ X173)))&(((((in @ (esk8_3 @ X172 @ X173 @ X178) @ X173)|~(in @ X178 @ (esk7_2 @ X172 @ X173))|((X172 @ (esk5_2 @ X172 @ X173) @ (esk6_3 @ X172 @ X173 @ X175))|~(X172 @ (esk5_2 @ X172 @ X173) @ X175)))&((X172 @ (esk8_3 @ X172 @ X173 @ X178) @ X178)|~(in @ X178 @ (esk7_2 @ X172 @ X173))|((X172 @ (esk5_2 @ X172 @ X173) @ (esk6_3 @ X172 @ X173 @ X175))|~(X172 @ (esk5_2 @ X172 @ X173) @ X175))))&(~(in @ X181 @ X173)|~(X172 @ X181 @ X180)|(in @ X180 @ (esk7_2 @ X172 @ X173))|((X172 @ (esk5_2 @ X172 @ X173) @ (esk6_3 @ X172 @ X173 @ X175))|~(X172 @ (esk5_2 @ X172 @ X173) @ X175))))&((((in @ (esk8_3 @ X172 @ X173 @ X178) @ X173)|~(in @ X178 @ (esk7_2 @ X172 @ X173))|(((X175)!=(esk6_3 @ X172 @ X173 @ X175))|~(X172 @ (esk5_2 @ X172 @ X173) @ X175)))&((X172 @ (esk8_3 @ X172 @ X173 @ X178) @ X178)|~(in @ X178 @ (esk7_2 @ X172 @ X173))|(((X175)!=(esk6_3 @ X172 @ X173 @ X175))|~(X172 @ (esk5_2 @ X172 @ X173) @ X175))))&(~(in @ X181 @ X173)|~(X172 @ X181 @ X180)|(in @ X180 @ (esk7_2 @ X172 @ X173))|(((X175)!=(esk6_3 @ X172 @ X173 @ X175))|~(X172 @ (esk5_2 @ X172 @ X173) @ X175))))))&((((in @ (esk9_1 @ X182) @ X182)|~(in @ X183 @ X182))&(~(in @ X185 @ (esk9_1 @ X182))|~(in @ X185 @ X182)|~(in @ X183 @ X182)))&((epred1_0)&((((X186 @ (esk10_2 @ X186 @ X187))|~(X186 @ X187)|(X186 @ (descr @ X186)))&(((X187)!=(esk10_2 @ X186 @ X187))|~(X186 @ X187)|(X186 @ (descr @ X186))))&((~(in @ X191 @ X189)|(~(X190 @ X191)|(in @ X191 @ (dsetconstr @ X189 @ X190))))&((~(in @ X194 @ (dsetconstr @ X192 @ X193))|(in @ X194 @ X192))&((~(in @ X197 @ (dsetconstr @ X195 @ X196))|(X196 @ X197))&(((((X198 @ (esk12_1 @ X198))|((X198 @ (esk11_2 @ X198 @ X199))|~(X198 @ X199)))&(~(X198 @ X202)|((esk12_1 @ X198)=(X202))|((X198 @ (esk11_2 @ X198 @ X199))|~(X198 @ X199))))&(((X198 @ (esk12_1 @ X198))|(((X199)!=(esk11_2 @ X198 @ X199))|~(X198 @ X199)))&(~(X198 @ X202)|((esk12_1 @ X198)=(X202))|(((X199)!=(esk11_2 @ X198 @ X199))|~(X198 @ X199)))))&((~(in @ X204 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X203)))))|(X203))&((in @ esk13_0 @ emptyset)&~(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_34])])])])])])])).
% 0.27/0.26 thf(c_0_36, negated_conjecture, (in @ esk13_0 @ emptyset), inference(split_conjunct,[status(thm)],[c_0_35])).
% 0.27/0.26 thf(c_0_37, negated_conjecture, ![X2:$i]:(~((in @ X2 @ emptyset))), inference(split_conjunct,[status(thm)],[c_0_35])).
% 0.27/0.26 thf(c_0_38, negated_conjecture, ($false), inference(sr,[status(thm)],[c_0_36, c_0_37]), ['proof']).
% 0.27/0.26 % SZS output end CNFRefutation
% 0.27/0.26 % Parsed axioms : 47
% 0.27/0.26 % Removed by relevancy pruning/SinE : 27
% 0.27/0.26 % Initial clauses : 54
% 0.27/0.26 % Removed in clause preprocessing : 0
% 0.27/0.26 % Initial clauses in saturation : 54
% 0.27/0.26 % Processed clauses : 5
% 0.27/0.26 % ...of these trivial : 0
% 0.27/0.26 % ...subsumed : 0
% 0.27/0.26 % ...remaining for further processing : 5
% 0.27/0.26 % Other redundant clauses eliminated : 0
% 0.27/0.26 % Clauses deleted for lack of memory : 0
% 0.27/0.26 % Backward-subsumed : 0
% 0.27/0.26 % Backward-rewritten : 0
% 0.27/0.26 % Generated clauses : 1
% 0.27/0.26 % ...of the previous two non-redundant : 0
% 0.27/0.26 % ...aggressively subsumed : 0
% 0.27/0.26 % Contextual simplify-reflections : 0
% 0.27/0.26 % Paramodulations : 0
% 0.27/0.26 % Factorizations : 0
% 0.27/0.26 % NegExts : 0
% 0.27/0.26 % Equation resolutions : 0
% 0.27/0.26 % Disequality decompositions : 0
% 0.27/0.26 % Total rewrite steps : 0
% 0.27/0.26 % ...of those cached : 0
% 0.27/0.26 % Propositional unsat checks : 0
% 0.27/0.26 % Propositional check models : 0
% 0.27/0.26 % Propositional check unsatisfiable : 0
% 0.27/0.26 % Propositional clauses : 0
% 0.27/0.26 % Propositional clauses after purity: 0
% 0.27/0.26 % Propositional unsat core size : 0
% 0.27/0.26 % Propositional preprocessing time : 0.000
% 0.27/0.26 % Propositional encoding time : 0.000
% 0.27/0.26 % Propositional solver time : 0.000
% 0.27/0.26 % Success case prop preproc time : 0.000
% 0.27/0.26 % Success case prop encoding time : 0.000
% 0.27/0.26 % Success case prop solver time : 0.000
% 0.27/0.26 % Current number of processed clauses : 4
% 0.27/0.26 % Positive orientable unit clauses : 2
% 0.27/0.26 % Positive unorientable unit clauses: 0
% 0.27/0.26 % Negative unit clauses : 2
% 0.27/0.26 % Non-unit-clauses : 0
% 0.27/0.26 % Current number of unprocessed clauses: 49
% 0.27/0.26 % ...number of literals in the above : 178
% 0.27/0.26 % Current number of archived formulas : 0
% 0.27/0.26 % Current number of archived clauses : 1
% 0.27/0.26 % Clause-clause subsumption calls (NU) : 0
% 0.27/0.26 % Rec. Clause-clause subsumption calls : 0
% 0.27/0.26 % Non-unit clause-clause subsumptions : 0
% 0.27/0.26 % Unit Clause-clause subsumption calls : 0
% 0.27/0.26 % Rewrite failures with RHS unbound : 0
% 0.27/0.26 % BW rewrite match attempts : 0
% 0.27/0.26 % BW rewrite match successes : 0
% 0.27/0.26 % Condensation attempts : 0
% 0.27/0.26 % Condensation successes : 0
% 0.27/0.26 % Termbank termtop insertions : 6503
% 0.27/0.26 % Search garbage collected termcells : 2485
% 0.27/0.26
% 0.27/0.26 % -------------------------------------------------
% 0.27/0.26 % User time : 0.011 s
% 0.27/0.26 % System time : 0.001 s
% 0.27/0.26 % Total time : 0.012 s
% 0.27/0.26 % Maximum resident set size: 4456 pages
% 0.27/0.26
% 0.27/0.26 % -------------------------------------------------
% 0.27/0.26 % User time : 0.013 s
% 0.27/0.26 % System time : 0.006 s
% 0.27/0.26 % Total time : 0.020 s
% 0.27/0.26 % Maximum resident set size: 4864 pages
% 0.27/0.26 % E exiting
%------------------------------------------------------------------------------