%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU505^1 : 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 : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:26:30 AM UTC 2026
% Result : Theorem 0.21s 0.34s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU505^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n003.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:48:43 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 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.8tEP1LpT1L/E---3.1_2523989.p
% 0.21/0.34 % Version: 3.5.1-ho
% 0.21/0.34 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.21/0.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.34 % Starting new_ho_10 with 1500s (5) cores
% 0.21/0.34 % Starting sh5l with 300s (1) cores
% 0.21/0.34 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.34 % Starting new_bool_2 with 300s (1) cores
% 0.21/0.34 % new_ho_10 with pid 2524002 completed with status 0
% 0.21/0.34 % Result found by new_ho_10
% 0.21/0.34 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.21/0.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.34 % Starting new_ho_10 with 1500s (5) cores
% 0.21/0.34 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.21/0.34 % No SInE strategy applied
% 0.21/0.34 % Search class: HGHSS-FFMF31-SHFSMSBN
% 0.21/0.34 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/0.34 % Starting SubtermCWHack with 151s (1) cores
% 0.21/0.34 % Starting new_ho_10 with 901s (1) cores
% 0.21/0.34 % Starting sh5l with 151s (1) cores
% 0.21/0.34 % Starting new_bool_1 with 151s (1) cores
% 0.21/0.34 % Starting new_bool_2 with 146s (1) cores
% 0.21/0.34 % new_ho_10 with pid 2524010 completed with status 0
% 0.21/0.34 % Result found by new_ho_10
% 0.21/0.34 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.21/0.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.34 % Starting new_ho_10 with 1500s (5) cores
% 0.21/0.34 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.21/0.34 % No SInE strategy applied
% 0.21/0.34 % Search class: HGHSS-FFMF31-SHFSMSBN
% 0.21/0.34 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/0.34 % Starting SubtermCWHack with 151s (1) cores
% 0.21/0.34 % Starting new_ho_10 with 901s (1) cores
% 0.21/0.34 % Preprocessing time : 0.003 s
% 0.21/0.34 % Presaturation interreduction done
% 0.21/0.34
% 0.21/0.34 % Proof found!
% 0.21/0.34 % SZS status Theorem
% 0.21/0.34 % SZS output start CNFRefutation
% 0.21/0.34 thf(decl_23, type, in: $i > $i > $o).
% 0.21/0.34 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.21/0.34 thf(decl_25, type, setextAx: $o).
% 0.21/0.34 thf(decl_26, type, emptyset: $i).
% 0.21/0.34 thf(decl_27, type, emptysetAx: $o).
% 0.21/0.34 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.21/0.34 thf(decl_29, type, setadjoinAx: $o).
% 0.21/0.34 thf(decl_30, type, powerset: $i > $i).
% 0.21/0.34 thf(decl_31, type, powersetAx: $o).
% 0.21/0.34 thf(decl_32, type, setunion: $i > $i).
% 0.21/0.34 thf(decl_33, type, setunionAx: $o).
% 0.21/0.34 thf(decl_34, type, omega: $i).
% 0.21/0.34 thf(decl_35, type, omega0Ax: $o).
% 0.21/0.34 thf(decl_36, type, omegaSAx: $o).
% 0.21/0.34 thf(decl_37, type, omegaIndAx: $o).
% 0.21/0.34 thf(decl_38, type, replAx: $o).
% 0.21/0.34 thf(decl_39, type, foundationAx: $o).
% 0.21/0.34 thf(decl_40, type, wellorderingAx: $o).
% 0.21/0.34 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.21/0.34 thf(decl_42, type, descrp: $o).
% 0.21/0.34 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.21/0.34 thf(decl_44, type, dsetconstrI: $o).
% 0.21/0.34 thf(decl_45, type, dsetconstrEL: $o).
% 0.21/0.34 thf(decl_46, type, dsetconstrER: $o).
% 0.21/0.34 thf(decl_47, type, exuE1: $o).
% 0.21/0.34 thf(decl_48, type, prop2set: $o > $i).
% 0.21/0.34 thf(decl_49, type, prop2setE: $o).
% 0.21/0.34 thf(decl_50, type, emptysetE: $o).
% 0.21/0.34 thf(decl_51, type, emptysetimpfalse: $o).
% 0.21/0.34 thf(decl_52, type, notinemptyset: $o).
% 0.21/0.34 thf(decl_53, type, exuE3e: $o).
% 0.21/0.34 thf(decl_54, type, epred1_0: $o).
% 0.21/0.34 thf(decl_55, type, esk1_2: $i > $i > $i).
% 0.21/0.34 thf(decl_56, type, esk2_2: $i > $i > $i).
% 0.21/0.34 thf(decl_57, type, esk3_2: $i > $i > $i).
% 0.21/0.34 thf(decl_58, type, esk4_1: $i > $i).
% 0.21/0.34 thf(decl_59, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.21/0.34 thf(decl_60, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.21/0.34 thf(decl_61, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.21/0.34 thf(decl_62, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.21/0.34 thf(decl_63, type, esk9_1: $i > $i).
% 0.21/0.34 thf(decl_64, type, esk10_2: ($i > $o) > $i > $i).
% 0.21/0.34 thf(decl_65, type, esk11_2: ($i > $o) > $i > $i).
% 0.21/0.34 thf(decl_66, type, esk12_1: ($i > $o) > $i).
% 0.21/0.34 thf(decl_67, type, esk13_2: ($i > $o) > $i > $i).
% 0.21/0.34 thf(decl_68, type, esk14_1: ($i > $o) > $i).
% 0.21/0.34 thf(decl_69, type, esk15_0: $i).
% 0.21/0.34 thf(decl_70, type, esk16_0: $i).
% 0.21/0.34 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.8tEP1LpT1L/E---3.1_2523989.p', replAx)).
% 0.21/0.34 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.8tEP1LpT1L/E---3.1_2523989.p', exu)).
% 0.21/0.34 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.8tEP1LpT1L/E---3.1_2523989.p', descrp)).
% 0.21/0.34 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.8tEP1LpT1L/E---3.1_2523989.p', exuE1)).
% 0.21/0.34 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.8tEP1LpT1L/E---3.1_2523989.p', exuE3e)).
% 0.21/0.34 thf(setext, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.8tEP1LpT1L/E---3.1_2523989.p', setext)).
% 0.21/0.34 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.8tEP1LpT1L/E---3.1_2523989.p', dsetconstrI)).
% 0.21/0.34 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.8tEP1LpT1L/E---3.1_2523989.p', dsetconstrEL)).
% 0.21/0.34 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.8tEP1LpT1L/E---3.1_2523989.p', dsetconstrER)).
% 0.21/0.34 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.8tEP1LpT1L/E---3.1_2523989.p', setextAx)).
% 0.21/0.34 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.8tEP1LpT1L/E---3.1_2523989.p', emptysetAx)).
% 0.21/0.34 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.8tEP1LpT1L/E---3.1_2523989.p', setadjoinAx)).
% 0.21/0.34 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.8tEP1LpT1L/E---3.1_2523989.p', powersetAx)).
% 0.21/0.34 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.8tEP1LpT1L/E---3.1_2523989.p', setunionAx)).
% 0.21/0.34 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.8tEP1LpT1L/E---3.1_2523989.p', omega0Ax)).
% 0.21/0.34 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.8tEP1LpT1L/E---3.1_2523989.p', omegaSAx)).
% 0.21/0.34 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.8tEP1LpT1L/E---3.1_2523989.p', omegaIndAx)).
% 0.21/0.34 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.8tEP1LpT1L/E---3.1_2523989.p', foundationAx)).
% 0.21/0.34 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.8tEP1LpT1L/E---3.1_2523989.p', wellorderingAx)).
% 0.21/0.34 thf(prop2setE, axiom, ((prop2setE)<=>![X11:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X11))))=>(X11)))), file('/export/starexec/sandbox/tmp/tmp.8tEP1LpT1L/E---3.1_2523989.p', prop2setE)).
% 0.21/0.34 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X12:$o]:((X12))))), file('/export/starexec/sandbox/tmp/tmp.8tEP1LpT1L/E---3.1_2523989.p', emptysetE)).
% 0.21/0.34 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.8tEP1LpT1L/E---3.1_2523989.p', emptysetimpfalse)).
% 0.21/0.34 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.8tEP1LpT1L/E---3.1_2523989.p', notinemptyset)).
% 0.21/0.34 thf(c_0_23, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.21/0.34 thf(c_0_24, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.21/0.34 thf(c_0_25, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.21/0.34 thf(c_0_26, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.21/0.34 thf(c_0_27, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.21/0.34 thf(c_0_28, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[setext])).
% 0.21/0.34 thf(c_0_29, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X84:$i]:(((((X6 @ X2 @ X84)))&(![X85:$i]:(((((X6 @ X2 @ X85)))=>(((X84)=(X85)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_23, c_0_24])).
% 0.21/0.34 thf(c_0_30, plain, ((descrp)=(![X1:$i > $o]:((((?[X86:$i]:(((((X1 @ X86)))&(![X87:$i]:(((((X1 @ X87)))=>(((X86)=(X87))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_25, c_0_24])).
% 0.21/0.34 thf(c_0_31, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.21/0.34 thf(c_0_32, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.21/0.34 thf(c_0_33, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.21/0.34 thf(c_0_34, plain, ((exuE1)=(![X1:$i > $o]:((((?[X88:$i]:(((((X1 @ X88)))&(![X89:$i]:(((((X1 @ X89)))=>(((X88)=(X89))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_26, c_0_24])).
% 0.21/0.34 thf(c_0_35, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X90:$i]:(((((X1 @ X90)))&(![X91:$i]:(((((X1 @ X91)))=>(((X90)=(X91))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_27, c_0_24])).
% 0.21/0.34 thf(c_0_36, plain, ((epred1_0)<=>![X121:$i]:(?[X122:$i]:((((![X123:$i]:(((in @ X123 @ X122)=>![X124:$i]:(((in @ X124 @ X123)=>(in @ X124 @ X121)))))&![X125:$i, X126:$i]:((((in @ X125 @ X121)&(in @ X126 @ X121))=>(![X127:$i]:(((in @ X127 @ X122)=>((in @ X125 @ X127)<=>(in @ X126 @ X127))))=>((X125)=(X126))))))&![X128:$i, X129:$i]:((((in @ X128 @ X122)&(in @ X129 @ X122))=>(![X130:$i]:(((in @ X130 @ X128)=>(in @ X130 @ X129)))|![X131:$i]:(((in @ X131 @ X129)=>(in @ X131 @ X128)))))))&![X132:$i]:(((![X133:$i]:(((in @ X133 @ X132)=>(in @ X133 @ X121)))&?[X134:$i]:((in @ X134 @ X132)))=>?[X135:$i, X136:$i]:(((((in @ X135 @ X122)&(in @ X136 @ X132))&~(?[X137:$i]:(((in @ X137 @ X135)&(in @ X137 @ X132)))))&![X138:$i]:(((in @ X138 @ X122)=>(![X139:$i]:(((in @ X139 @ X138)=>(in @ X139 @ X135)))|(in @ X136 @ X138)))))))))))), introduced(definition)).
% 0.21/0.34 thf(c_0_37, negated_conjecture, ~((![X92:$i, X93:$i]:((![X94:$i]:(((in @ X94 @ X92)<=>(in @ X94 @ X93)))=>((X92)=(X93))))=>(![X95:$i]:(~(in @ X95 @ emptyset))=>(![X96:$i, X97:$i, X98:$i]:(((in @ X98 @ (setadjoin @ X96 @ X97))<=>(((X98)=(X96))|(in @ X98 @ X97))))=>(![X99:$i, X100:$i]:(((in @ X100 @ (powerset @ X99))<=>![X101:$i]:(((in @ X101 @ X100)=>(in @ X101 @ X99)))))=>(![X102:$i, X103:$i]:(((in @ X103 @ (setunion @ X102))<=>?[X104:$i]:(((in @ X103 @ X104)&(in @ X104 @ X102)))))=>((in @ emptyset @ omega)=>(![X105:$i]:(((in @ X105 @ omega)=>(in @ (setadjoin @ X105 @ X105) @ omega)))=>(![X106:$i]:((((in @ emptyset @ X106)&![X107:$i]:((((in @ X107 @ omega)&(in @ X107 @ X106))=>(in @ (setadjoin @ X107 @ X107) @ X106))))=>![X108:$i]:(((in @ X108 @ omega)=>(in @ X108 @ X106)))))=>(![X109:$i > $i > $o, X110:$i]:((![X111:$i]:(((in @ X111 @ X110)=>?[X112:$i]:(((X109 @ X111 @ X112)&![X113:$i]:(((X109 @ X111 @ X113)=>((X112)=(X113))))))))=>?[X114:$i]:(![X115:$i]:(((in @ X115 @ X114)<=>?[X116:$i]:(((in @ X116 @ X110)&(X109 @ X116 @ X115))))))))=>(![X117:$i]:((?[X118:$i]:((in @ X118 @ X117))=>?[X119:$i]:(((in @ X119 @ X117)&~(?[X120:$i]:(((in @ X120 @ X119)&(in @ X120 @ X117))))))))=>((epred1_0)=>(![X140:$i > $o]:((?[X141:$i]:(((X140 @ X141)&![X142:$i]:(((X140 @ X142)=>((X141)=(X142))))))=>(X140 @ (descr @ (^[Z0:$i]:(X140 @ Z0))))))=>(![X143:$i, X144:$i > $o, X145:$i]:(((in @ X145 @ X143)=>((X144 @ X145)=>(in @ X145 @ (dsetconstr @ X143 @ X144)))))=>(![X146:$i, X147:$i > $o, X148:$i]:(((in @ X148 @ (dsetconstr @ X146 @ X147))=>(in @ X148 @ X146)))=>(![X149:$i, X150:$i > $o, X151:$i]:(((in @ X151 @ (dsetconstr @ X149 @ X150))=>(X150 @ X151)))=>(![X152:$i > $o]:((?[X153:$i]:(((X152 @ X153)&![X154:$i]:(((X152 @ X154)=>((X153)=(X154))))))=>?[X155:$i]:(((X152 @ X155)&![X156:$i]:(((X152 @ X156)=>((X155)=(X156))))))))=>(![X157:$o, X158:$i]:(((in @ X158 @ (prop2set @ ((X157))))=>(X157)))=>(![X159:$i]:(((in @ X159 @ emptyset)=>![X160:$o]:((X160))))=>(![X161:$i]:(((in @ X161 @ emptyset)=>~($true)))=>(![X162:$i]:(~(in @ X162 @ emptyset))=>(![X163:$i > $o]:((?[X164:$i]:(((X163 @ X164)&![X165:$i]:(((X163 @ X165)=>((X164)=(X165))))))=>?[X166:$i]:((X163 @ X166))))=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_28, setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_29]), foundationAx]), wellorderingAx]), c_0_30]), c_0_31]), c_0_32]), c_0_33]), c_0_34]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_35])])]), c_0_36])).
% 0.21/0.34 thf(c_0_38, negated_conjecture, ![X169:$i, X170:$i, X172:$i, X173:$i, X174:$i, X175:$i, X176:$i, X177:$i, X178:$i, X179:$i, X180:$i, X182:$i, X183:$i, X185:$i, X186:$i, X187:$i, X188:$i, X189:$i, X191:$i, X192:$i > $i > $o, X193:$i, X195:$i, X198:$i, X200:$i, X201:$i, X202:$i, X203:$i, X205:$i, X206:$i > $o, X207:$i, X209:$i, X210:$i > $o, X211:$i, X212:$i, X213:$i > $o, X214:$i, X215:$i, X216:$i > $o, X217:$i, X218:$i > $o, X219:$i, X222:$i, X223:$o, X224:$i, X225:$i, X226:$o, X227:$i, X228:$i, X229:$i > $o, X230:$i, X235:$i, X236:$i]:((((~(in @ (esk1_2 @ X169 @ X170) @ X169)|~(in @ (esk1_2 @ X169 @ X170) @ X170)|((X169)=(X170)))&((in @ (esk1_2 @ X169 @ X170) @ X169)|(in @ (esk1_2 @ X169 @ X170) @ X170)|((X169)=(X170))))&(~(in @ X172 @ emptyset)&(((~(in @ X175 @ (setadjoin @ X173 @ X174))|(((X175)=(X173))|(in @ X175 @ X174)))&((((X175)!=(X173))|(in @ X175 @ (setadjoin @ X173 @ X174)))&(~(in @ X175 @ X174)|(in @ X175 @ (setadjoin @ X173 @ X174)))))&(((~(in @ X177 @ (powerset @ X176))|(~(in @ X178 @ X177)|(in @ X178 @ X176)))&(((in @ (esk2_2 @ X179 @ X180) @ X180)|(in @ X180 @ (powerset @ X179)))&(~(in @ (esk2_2 @ X179 @ X180) @ X179)|(in @ X180 @ (powerset @ X179)))))&(((((in @ X183 @ (esk3_2 @ X182 @ X183))|~(in @ X183 @ (setunion @ X182)))&((in @ (esk3_2 @ X182 @ X183) @ X182)|~(in @ X183 @ (setunion @ X182))))&(~(in @ X186 @ X187)|~(in @ X187 @ X185)|(in @ X186 @ (setunion @ X185))))&((in @ emptyset @ omega)&((~(in @ X188 @ omega)|(in @ (setadjoin @ X188 @ X188) @ omega))&(((((in @ (esk4_1 @ X189) @ omega)|~(in @ emptyset @ X189)|(~(in @ X191 @ omega)|(in @ X191 @ X189)))&((in @ (esk4_1 @ X189) @ X189)|~(in @ emptyset @ X189)|(~(in @ X191 @ omega)|(in @ X191 @ X189))))&(~(in @ (setadjoin @ (esk4_1 @ X189) @ (esk4_1 @ X189)) @ X189)|~(in @ emptyset @ X189)|(~(in @ X191 @ omega)|(in @ X191 @ X189))))&((((((in @ (esk8_3 @ X192 @ X193 @ X198) @ X193)|~(in @ X198 @ (esk7_2 @ X192 @ X193))|(in @ (esk5_2 @ X192 @ X193) @ X193))&((X192 @ (esk8_3 @ X192 @ X193 @ X198) @ X198)|~(in @ X198 @ (esk7_2 @ X192 @ X193))|(in @ (esk5_2 @ X192 @ X193) @ X193)))&(~(in @ X201 @ X193)|~(X192 @ X201 @ X200)|(in @ X200 @ (esk7_2 @ X192 @ X193))|(in @ (esk5_2 @ X192 @ X193) @ X193)))&(((((in @ (esk8_3 @ X192 @ X193 @ X198) @ X193)|~(in @ X198 @ (esk7_2 @ X192 @ X193))|((X192 @ (esk5_2 @ X192 @ X193) @ (esk6_3 @ X192 @ X193 @ X195))|~(X192 @ (esk5_2 @ X192 @ X193) @ X195)))&((X192 @ (esk8_3 @ X192 @ X193 @ X198) @ X198)|~(in @ X198 @ (esk7_2 @ X192 @ X193))|((X192 @ (esk5_2 @ X192 @ X193) @ (esk6_3 @ X192 @ X193 @ X195))|~(X192 @ (esk5_2 @ X192 @ X193) @ X195))))&(~(in @ X201 @ X193)|~(X192 @ X201 @ X200)|(in @ X200 @ (esk7_2 @ X192 @ X193))|((X192 @ (esk5_2 @ X192 @ X193) @ (esk6_3 @ X192 @ X193 @ X195))|~(X192 @ (esk5_2 @ X192 @ X193) @ X195))))&((((in @ (esk8_3 @ X192 @ X193 @ X198) @ X193)|~(in @ X198 @ (esk7_2 @ X192 @ X193))|(((X195)!=(esk6_3 @ X192 @ X193 @ X195))|~(X192 @ (esk5_2 @ X192 @ X193) @ X195)))&((X192 @ (esk8_3 @ X192 @ X193 @ X198) @ X198)|~(in @ X198 @ (esk7_2 @ X192 @ X193))|(((X195)!=(esk6_3 @ X192 @ X193 @ X195))|~(X192 @ (esk5_2 @ X192 @ X193) @ X195))))&(~(in @ X201 @ X193)|~(X192 @ X201 @ X200)|(in @ X200 @ (esk7_2 @ X192 @ X193))|(((X195)!=(esk6_3 @ X192 @ X193 @ X195))|~(X192 @ (esk5_2 @ X192 @ X193) @ X195))))))&((((in @ (esk9_1 @ X202) @ X202)|~(in @ X203 @ X202))&(~(in @ X205 @ (esk9_1 @ X202))|~(in @ X205 @ X202)|~(in @ X203 @ X202)))&((epred1_0)&((((X206 @ (esk10_2 @ X206 @ X207))|~(X206 @ X207)|(X206 @ (descr @ X206)))&(((X207)!=(esk10_2 @ X206 @ X207))|~(X206 @ X207)|(X206 @ (descr @ X206))))&((~(in @ X211 @ X209)|(~(X210 @ X211)|(in @ X211 @ (dsetconstr @ X209 @ X210))))&((~(in @ X214 @ (dsetconstr @ X212 @ X213))|(in @ X214 @ X212))&((~(in @ X217 @ (dsetconstr @ X215 @ X216))|(X216 @ X217))&(((((X218 @ (esk12_1 @ X218))|((X218 @ (esk11_2 @ X218 @ X219))|~(X218 @ X219)))&(~(X218 @ X222)|((esk12_1 @ X218)=(X222))|((X218 @ (esk11_2 @ X218 @ X219))|~(X218 @ X219))))&(((X218 @ (esk12_1 @ X218))|(((X219)!=(esk11_2 @ X218 @ X219))|~(X218 @ X219)))&(~(X218 @ X222)|((esk12_1 @ X218)=(X222))|(((X219)!=(esk11_2 @ X218 @ X219))|~(X218 @ X219)))))&((~(in @ X224 @ (prop2set @ ((X223))))|(X223))&((~(in @ X225 @ emptyset)|(X226))&((~(in @ X227 @ emptyset)|~($true))&(~(in @ X228 @ emptyset)&((((X229 @ (esk13_2 @ X229 @ X230))|~(X229 @ X230)|(X229 @ (esk14_1 @ X229)))&(((X230)!=(esk13_2 @ X229 @ X230))|~(X229 @ X230)|(X229 @ (esk14_1 @ X229))))&((~(in @ X235 @ esk15_0)|(in @ X235 @ esk16_0))&((~(in @ X236 @ esk16_0)|(in @ X236 @ esk15_0))&((esk15_0)!=(esk16_0)))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])])])])])])).
% 0.21/0.34 thf(c_0_39, negated_conjecture, ![X2:$i]:(((in @ X2 @ esk15_0)|~((in @ X2 @ esk16_0)))), inference(split_conjunct,[status(thm)],[c_0_38])).
% 0.21/0.34 thf(c_0_40, negated_conjecture, ![X2:$i, X3:$i]:(((in @ (esk1_2 @ X2 @ X3) @ X2)|(in @ (esk1_2 @ X2 @ X3) @ X3)|((X2)=(X3)))), inference(split_conjunct,[status(thm)],[c_0_38])).
% 0.21/0.34 thf(c_0_41, negated_conjecture, ![X2:$i]:((((esk16_0)=(X2))|(in @ (esk1_2 @ esk16_0 @ X2) @ esk15_0)|(in @ (esk1_2 @ esk16_0 @ X2) @ X2))), inference(spm,[status(thm)],[c_0_39, c_0_40])).
% 0.21/0.34 thf(c_0_42, negated_conjecture, ((esk15_0)!=(esk16_0)), inference(split_conjunct,[status(thm)],[c_0_38])).
% 0.21/0.34 thf(c_0_43, negated_conjecture, ![X2:$i, X3:$i]:((((X2)=(X3))|~((in @ (esk1_2 @ X2 @ X3) @ X2))|~((in @ (esk1_2 @ X2 @ X3) @ X3)))), inference(split_conjunct,[status(thm)],[c_0_38])).
% 0.21/0.34 thf(c_0_44, negated_conjecture, (in @ (esk1_2 @ esk16_0 @ esk15_0) @ esk15_0), inference(sr,[status(thm)],[inference(ef,[status(thm)],[c_0_41]), c_0_42])).
% 0.21/0.34 thf(c_0_45, negated_conjecture, ~((in @ (esk1_2 @ esk16_0 @ esk15_0) @ esk16_0)), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43, c_0_44]), c_0_42])).
% 0.21/0.34 thf(c_0_46, negated_conjecture, ![X2:$i]:(((in @ X2 @ esk16_0)|~((in @ X2 @ esk15_0)))), inference(split_conjunct,[status(thm)],[c_0_38])).
% 0.21/0.34 thf(c_0_47, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45, c_0_46]), c_0_44])]), ['proof']).
% 0.21/0.34 % SZS output end CNFRefutation
% 0.21/0.34 % Parsed axioms : 55
% 0.21/0.34 % Removed by relevancy pruning/SinE : 0
% 0.21/0.34 % Initial clauses : 94
% 0.21/0.34 % Removed in clause preprocessing : 31
% 0.21/0.34 % Initial clauses in saturation : 63
% 0.21/0.34 % Processed clauses : 264
% 0.21/0.34 % ...of these trivial : 21
% 0.21/0.34 % ...subsumed : 30
% 0.21/0.34 % ...remaining for further processing : 213
% 0.21/0.34 % Other redundant clauses eliminated : 1
% 0.21/0.34 % Clauses deleted for lack of memory : 0
% 0.21/0.34 % Backward-subsumed : 0
% 0.21/0.34 % Backward-rewritten : 8
% 0.21/0.34 % Generated clauses : 1719
% 0.21/0.34 % ...of the previous two non-redundant : 1674
% 0.21/0.34 % ...aggressively subsumed : 0
% 0.21/0.34 % Contextual simplify-reflections : 0
% 0.21/0.34 % Paramodulations : 1712
% 0.21/0.34 % Factorizations : 6
% 0.21/0.34 % NegExts : 0
% 0.21/0.34 % Equation resolutions : 1
% 0.21/0.34 % Disequality decompositions : 0
% 0.21/0.34 % Total rewrite steps : 498
% 0.21/0.34 % ...of those cached : 476
% 0.21/0.34 % Propositional unsat checks : 0
% 0.21/0.34 % Propositional check models : 0
% 0.21/0.34 % Propositional check unsatisfiable : 0
% 0.21/0.34 % Propositional clauses : 0
% 0.21/0.34 % Propositional clauses after purity: 0
% 0.21/0.34 % Propositional unsat core size : 0
% 0.21/0.34 % Propositional preprocessing time : 0.000
% 0.21/0.34 % Propositional encoding time : 0.000
% 0.21/0.34 % Propositional solver time : 0.000
% 0.21/0.34 % Success case prop preproc time : 0.000
% 0.21/0.34 % Success case prop encoding time : 0.000
% 0.21/0.34 % Success case prop solver time : 0.000
% 0.21/0.34 % Current number of processed clauses : 144
% 0.21/0.34 % Positive orientable unit clauses : 23
% 0.21/0.34 % Positive unorientable unit clauses: 0
% 0.21/0.34 % Negative unit clauses : 17
% 0.21/0.34 % Non-unit-clauses : 104
% 0.21/0.34 % Current number of unprocessed clauses: 1522
% 0.21/0.34 % ...number of literals in the above : 5422
% 0.21/0.34 % Current number of archived formulas : 0
% 0.21/0.34 % Current number of archived clauses : 68
% 0.21/0.34 % Clause-clause subsumption calls (NU) : 6135
% 0.21/0.34 % Rec. Clause-clause subsumption calls : 3000
% 0.21/0.34 % Non-unit clause-clause subsumptions : 8
% 0.21/0.34 % Unit Clause-clause subsumption calls : 446
% 0.21/0.34 % Rewrite failures with RHS unbound : 0
% 0.21/0.34 % BW rewrite match attempts : 11
% 0.21/0.34 % BW rewrite match successes : 4
% 0.21/0.34 % Condensation attempts : 264
% 0.21/0.34 % Condensation successes : 3
% 0.21/0.34 % Termbank termtop insertions : 38183
% 0.21/0.34 % Search garbage collected termcells : 2906
% 0.21/0.34
% 0.21/0.34 % -------------------------------------------------
% 0.21/0.34 % User time : 0.067 s
% 0.21/0.34 % System time : 0.008 s
% 0.21/0.34 % Total time : 0.075 s
% 0.21/0.34 % Maximum resident set size: 4208 pages
% 0.21/0.34
% 0.21/0.34 % -------------------------------------------------
% 0.21/0.34 % User time : 0.313 s
% 0.21/0.34 % System time : 0.036 s
% 0.21/0.34 % Total time : 0.348 s
% 0.21/0.34 % Maximum resident set size: 4864 pages
% 0.21/0.34 % E exiting
%------------------------------------------------------------------------------