%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU504^1 : 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 : n010.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 08:24:17 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU504^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n010.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 13:47:18 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.25 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.VGZZexlhVo/E---3.1_2877674.p
% 0.20/0.27 % Version: 3.5.1-ho
% 0.20/0.27 % Preprocessing class: HSMSSLSSMLLCHSA.
% 0.20/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.20/0.27 % Starting sh5l with 300s (1) cores
% 0.20/0.27 % Starting new_bool_1 with 300s (1) cores
% 0.20/0.27 % Starting new_bool_2 with 300s (1) cores
% 0.20/0.27 % new_ho_10 with pid 2877687 completed with status 0
% 0.20/0.27 % Result found by new_ho_10
% 0.20/0.27 % Preprocessing class: HSMSSLSSMLLCHSA.
% 0.20/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.20/0.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.20/0.27 % No SInE strategy applied
% 0.20/0.27 % Search class: HGHSS-FFMS31-SHSSMSBN
% 0.20/0.27 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.27 % Starting SubtermCWHack with 151s (1) cores
% 0.20/0.27 % Starting new_ho_10 with 901s (1) cores
% 0.20/0.27 % Starting sh5l with 151s (1) cores
% 0.20/0.27 % Starting new_bool_1 with 151s (1) cores
% 0.20/0.27 % Starting new_bool_2 with 146s (1) cores
% 0.20/0.27 % SubtermCWHack with pid 2877691 completed with status 0
% 0.20/0.27 % Result found by SubtermCWHack
% 0.20/0.27 % Preprocessing class: HSMSSLSSMLLCHSA.
% 0.20/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.20/0.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.20/0.27 % No SInE strategy applied
% 0.20/0.27 % Search class: HGHSS-FFMS31-SHSSMSBN
% 0.20/0.27 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.27 % Starting SubtermCWHack with 151s (1) cores
% 0.20/0.27 % Preprocessing time : 0.002 s
% 0.20/0.27
% 0.20/0.27 % Proof found!
% 0.20/0.27 % SZS status Theorem
% 0.20/0.27 % SZS output start CNFRefutation
% 0.20/0.27 thf(decl_23, type, in: $i > $i > $o).
% 0.20/0.27 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.20/0.27 thf(decl_25, type, setextAx: $o).
% 0.20/0.27 thf(decl_26, type, emptyset: $i).
% 0.20/0.27 thf(decl_27, type, emptysetAx: $o).
% 0.20/0.27 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.20/0.27 thf(decl_29, type, setadjoinAx: $o).
% 0.20/0.27 thf(decl_30, type, powerset: $i > $i).
% 0.20/0.27 thf(decl_31, type, powersetAx: $o).
% 0.20/0.27 thf(decl_32, type, setunion: $i > $i).
% 0.20/0.27 thf(decl_33, type, setunionAx: $o).
% 0.20/0.27 thf(decl_34, type, omega: $i).
% 0.20/0.27 thf(decl_35, type, omega0Ax: $o).
% 0.20/0.27 thf(decl_36, type, omegaSAx: $o).
% 0.20/0.27 thf(decl_37, type, omegaIndAx: $o).
% 0.20/0.27 thf(decl_38, type, replAx: $o).
% 0.20/0.27 thf(decl_39, type, foundationAx: $o).
% 0.20/0.27 thf(decl_40, type, wellorderingAx: $o).
% 0.20/0.27 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.20/0.27 thf(decl_42, type, descrp: $o).
% 0.20/0.27 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.20/0.27 thf(decl_44, type, dsetconstrI: $o).
% 0.20/0.27 thf(decl_45, type, dsetconstrEL: $o).
% 0.20/0.27 thf(decl_46, type, dsetconstrER: $o).
% 0.20/0.27 thf(decl_47, type, exuE1: $o).
% 0.20/0.27 thf(decl_48, type, prop2set: $o > $i).
% 0.20/0.27 thf(decl_49, type, prop2setE: $o).
% 0.20/0.27 thf(decl_50, type, emptysetE: $o).
% 0.20/0.27 thf(decl_51, type, emptysetimpfalse: $o).
% 0.20/0.27 thf(decl_52, type, notinemptyset: $o).
% 0.20/0.27 thf(decl_53, type, epred1_0: $o).
% 0.20/0.27 thf(decl_54, type, esk1_2: $i > $i > $i).
% 0.20/0.27 thf(decl_55, type, esk2_2: $i > $i > $i).
% 0.20/0.27 thf(decl_56, type, esk3_2: $i > $i > $i).
% 0.20/0.27 thf(decl_57, type, esk4_1: $i > $i).
% 0.20/0.27 thf(decl_58, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.20/0.27 thf(decl_59, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.20/0.27 thf(decl_60, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.20/0.27 thf(decl_61, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.20/0.27 thf(decl_62, type, esk9_1: $i > $i).
% 0.20/0.27 thf(decl_63, type, esk10_2: ($i > $o) > $i > $i).
% 0.20/0.27 thf(decl_64, type, esk11_2: ($i > $o) > $i > $i).
% 0.20/0.27 thf(decl_65, type, esk12_1: ($i > $o) > $i).
% 0.20/0.27 thf(decl_66, type, epred2_0: $i > $o).
% 0.20/0.27 thf(decl_67, type, esk13_0: $i).
% 0.20/0.27 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.VGZZexlhVo/E---3.1_2877674.p', replAx)).
% 0.20/0.27 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.VGZZexlhVo/E---3.1_2877674.p', exu)).
% 0.20/0.27 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.VGZZexlhVo/E---3.1_2877674.p', descrp)).
% 0.20/0.27 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.VGZZexlhVo/E---3.1_2877674.p', exuE1)).
% 0.20/0.27 thf(exuE3e, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2)))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.VGZZexlhVo/E---3.1_2877674.p', exuE3e)).
% 0.20/0.27 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.VGZZexlhVo/E---3.1_2877674.p', dsetconstrI)).
% 0.20/0.27 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.VGZZexlhVo/E---3.1_2877674.p', dsetconstrEL)).
% 0.20/0.27 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.VGZZexlhVo/E---3.1_2877674.p', dsetconstrER)).
% 0.20/0.27 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.VGZZexlhVo/E---3.1_2877674.p', setextAx)).
% 0.20/0.27 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.VGZZexlhVo/E---3.1_2877674.p', emptysetAx)).
% 0.20/0.27 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.VGZZexlhVo/E---3.1_2877674.p', setadjoinAx)).
% 0.20/0.27 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.VGZZexlhVo/E---3.1_2877674.p', powersetAx)).
% 0.20/0.27 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.VGZZexlhVo/E---3.1_2877674.p', setunionAx)).
% 0.20/0.27 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.VGZZexlhVo/E---3.1_2877674.p', omega0Ax)).
% 0.20/0.27 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.VGZZexlhVo/E---3.1_2877674.p', omegaSAx)).
% 0.20/0.27 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.VGZZexlhVo/E---3.1_2877674.p', omegaIndAx)).
% 0.20/0.27 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.VGZZexlhVo/E---3.1_2877674.p', foundationAx)).
% 0.20/0.27 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.VGZZexlhVo/E---3.1_2877674.p', wellorderingAx)).
% 0.20/0.27 thf(prop2setE, axiom, ((prop2setE)<=>![X11:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X11))))=>(X11)))), file('/export/starexec/sandbox/tmp/tmp.VGZZexlhVo/E---3.1_2877674.p', prop2setE)).
% 0.20/0.27 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X12:$o]:((X12))))), file('/export/starexec/sandbox/tmp/tmp.VGZZexlhVo/E---3.1_2877674.p', emptysetE)).
% 0.20/0.27 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.VGZZexlhVo/E---3.1_2877674.p', emptysetimpfalse)).
% 0.20/0.27 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.VGZZexlhVo/E---3.1_2877674.p', notinemptyset)).
% 0.20/0.27 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.20/0.27 thf(c_0_23, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.20/0.27 thf(c_0_24, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.20/0.27 thf(c_0_25, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.20/0.27 thf(c_0_26, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[exuE3e])).
% 0.20/0.27 thf(c_0_27, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X80:$i]:(((((X6 @ X2 @ X80)))&(![X81:$i]:(((((X6 @ X2 @ X81)))=>(((X80)=(X81)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_22, c_0_23])).
% 0.20/0.27 thf(c_0_28, plain, ((descrp)=(![X1:$i > $o]:((((?[X82:$i]:(((((X1 @ X82)))&(![X83:$i]:(((((X1 @ X83)))=>(((X82)=(X83))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_24, c_0_23])).
% 0.20/0.27 thf(c_0_29, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.20/0.27 thf(c_0_30, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.20/0.27 thf(c_0_31, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.20/0.27 thf(c_0_32, plain, ((exuE1)=(![X1:$i > $o]:((((?[X84:$i]:(((((X1 @ X84)))&(![X85:$i]:(((((X1 @ X85)))=>(((X84)=(X85))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_25, c_0_23])).
% 0.20/0.27 thf(c_0_33, plain, ((epred1_0)<=>![X115:$i]:(?[X116:$i]:((((![X117:$i]:(((in @ X117 @ X116)=>![X118:$i]:(((in @ X118 @ X117)=>(in @ X118 @ X115)))))&![X119:$i, X120:$i]:((((in @ X119 @ X115)&(in @ X120 @ X115))=>(![X121:$i]:(((in @ X121 @ X116)=>((in @ X119 @ X121)<=>(in @ X120 @ X121))))=>((X119)=(X120))))))&![X122:$i, X123:$i]:((((in @ X122 @ X116)&(in @ X123 @ X116))=>(![X124:$i]:(((in @ X124 @ X122)=>(in @ X124 @ X123)))|![X125:$i]:(((in @ X125 @ X123)=>(in @ X125 @ X122)))))))&![X126:$i]:(((![X127:$i]:(((in @ X127 @ X126)=>(in @ X127 @ X115)))&?[X128:$i]:((in @ X128 @ X126)))=>?[X129:$i, X130:$i]:(((((in @ X129 @ X116)&(in @ X130 @ X126))&~(?[X131:$i]:(((in @ X131 @ X129)&(in @ X131 @ X126)))))&![X132:$i]:(((in @ X132 @ X116)=>(![X133:$i]:(((in @ X133 @ X132)=>(in @ X133 @ X129)))|(in @ X130 @ X132)))))))))))), introduced(definition)).
% 0.20/0.27 thf(c_0_34, negated_conjecture, ~((![X86:$i, X87:$i]:((![X88:$i]:(((in @ X88 @ X86)<=>(in @ X88 @ X87)))=>((X86)=(X87))))=>(![X89:$i]:(~(in @ X89 @ emptyset))=>(![X90:$i, X91:$i, X92:$i]:(((in @ X92 @ (setadjoin @ X90 @ X91))<=>(((X92)=(X90))|(in @ X92 @ X91))))=>(![X93:$i, X94:$i]:(((in @ X94 @ (powerset @ X93))<=>![X95:$i]:(((in @ X95 @ X94)=>(in @ X95 @ X93)))))=>(![X96:$i, X97:$i]:(((in @ X97 @ (setunion @ X96))<=>?[X98:$i]:(((in @ X97 @ X98)&(in @ X98 @ X96)))))=>((in @ emptyset @ omega)=>(![X99:$i]:(((in @ X99 @ omega)=>(in @ (setadjoin @ X99 @ X99) @ omega)))=>(![X100:$i]:((((in @ emptyset @ X100)&![X101:$i]:((((in @ X101 @ omega)&(in @ X101 @ X100))=>(in @ (setadjoin @ X101 @ X101) @ X100))))=>![X102:$i]:(((in @ X102 @ omega)=>(in @ X102 @ X100)))))=>(![X103:$i > $i > $o, X104:$i]:((![X105:$i]:(((in @ X105 @ X104)=>?[X106:$i]:(((X103 @ X105 @ X106)&![X107:$i]:(((X103 @ X105 @ X107)=>((X106)=(X107))))))))=>?[X108:$i]:(![X109:$i]:(((in @ X109 @ X108)<=>?[X110:$i]:(((in @ X110 @ X104)&(X103 @ X110 @ X109))))))))=>(![X111:$i]:((?[X112:$i]:((in @ X112 @ X111))=>?[X113:$i]:(((in @ X113 @ X111)&~(?[X114:$i]:(((in @ X114 @ X113)&(in @ X114 @ X111))))))))=>((epred1_0)=>(![X134:$i > $o]:((?[X135:$i]:(((X134 @ X135)&![X136:$i]:(((X134 @ X136)=>((X135)=(X136))))))=>(X134 @ (descr @ (^[Z0:$i]:(X134 @ Z0))))))=>(![X137:$i, X138:$i > $o, X139:$i]:(((in @ X139 @ X137)=>((X138 @ X139)=>(in @ X139 @ (dsetconstr @ X137 @ X138)))))=>(![X140:$i, X141:$i > $o, X142:$i]:(((in @ X142 @ (dsetconstr @ X140 @ X141))=>(in @ X142 @ X140)))=>(![X143:$i, X144:$i > $o, X145:$i]:(((in @ X145 @ (dsetconstr @ X143 @ X144))=>(X144 @ X145)))=>(![X146:$i > $o]:((?[X147:$i]:(((X146 @ X147)&![X148:$i]:(((X146 @ X148)=>((X147)=(X148))))))=>?[X149:$i]:(((X146 @ X149)&![X150:$i]:(((X146 @ X150)=>((X149)=(X150))))))))=>(![X151:$o, X152:$i]:(((in @ X152 @ (prop2set @ ((X151))))=>(X151)))=>(![X153:$i]:(((in @ X153 @ emptyset)=>![X154:$o]:((X154))))=>(![X155:$i]:(((in @ X155 @ emptyset)=>~($true)))=>(![X156:$i]:(~(in @ X156 @ emptyset))=>![X1:$i > $o]:((?[X157:$i]:(((X1 @ X157)&![X158:$i]:(((X1 @ X158)=>((X157)=(X158))))))=>?[X2:$i]:((X1 @ X2))))))))))))))))))))))))), 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)],[inference(fof_simplification,[status(thm)],[c_0_26]), c_0_23]), setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_27]), foundationAx]), wellorderingAx]), c_0_28]), c_0_29]), c_0_30]), c_0_31]), c_0_32]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset])])]), c_0_33])).
% 0.20/0.27 thf(c_0_35, negated_conjecture, ![X161:$i, X162:$i, X164:$i, X165:$i, X166:$i, X167:$i, X168:$i, X169:$i, X170:$i, X171:$i, X172:$i, X174:$i, X175:$i, X177:$i, X178:$i, X179:$i, X180:$i, X181:$i, X183:$i, X184:$i > $i > $o, X185:$i, X187:$i, X190:$i, X192:$i, X193:$i, X194:$i, X195:$i, X197:$i, X198:$i > $o, X199:$i, X201:$i, X202:$i > $o, X203:$i, X204:$i, X205:$i > $o, X206:$i, X207:$i, X208:$i > $o, X209:$i, X210:$i > $o, X211:$i, X214:$i, X215:$o, X216:$i, X217:$i, X218:$o, X219:$i, X220:$i, X223:$i, X224:$i]:((((~(in @ (esk1_2 @ X161 @ X162) @ X161)|~(in @ (esk1_2 @ X161 @ X162) @ X162)|((X161)=(X162)))&((in @ (esk1_2 @ X161 @ X162) @ X161)|(in @ (esk1_2 @ X161 @ X162) @ X162)|((X161)=(X162))))&(~(in @ X164 @ emptyset)&(((~(in @ X167 @ (setadjoin @ X165 @ X166))|(((X167)=(X165))|(in @ X167 @ X166)))&((((X167)!=(X165))|(in @ X167 @ (setadjoin @ X165 @ X166)))&(~(in @ X167 @ X166)|(in @ X167 @ (setadjoin @ X165 @ X166)))))&(((~(in @ X169 @ (powerset @ X168))|(~(in @ X170 @ X169)|(in @ X170 @ X168)))&(((in @ (esk2_2 @ X171 @ X172) @ X172)|(in @ X172 @ (powerset @ X171)))&(~(in @ (esk2_2 @ X171 @ X172) @ X171)|(in @ X172 @ (powerset @ X171)))))&(((((in @ X175 @ (esk3_2 @ X174 @ X175))|~(in @ X175 @ (setunion @ X174)))&((in @ (esk3_2 @ X174 @ X175) @ X174)|~(in @ X175 @ (setunion @ X174))))&(~(in @ X178 @ X179)|~(in @ X179 @ X177)|(in @ X178 @ (setunion @ X177))))&((in @ emptyset @ omega)&((~(in @ X180 @ omega)|(in @ (setadjoin @ X180 @ X180) @ omega))&(((((in @ (esk4_1 @ X181) @ omega)|~(in @ emptyset @ X181)|(~(in @ X183 @ omega)|(in @ X183 @ X181)))&((in @ (esk4_1 @ X181) @ X181)|~(in @ emptyset @ X181)|(~(in @ X183 @ omega)|(in @ X183 @ X181))))&(~(in @ (setadjoin @ (esk4_1 @ X181) @ (esk4_1 @ X181)) @ X181)|~(in @ emptyset @ X181)|(~(in @ X183 @ omega)|(in @ X183 @ X181))))&((((((in @ (esk8_3 @ X184 @ X185 @ X190) @ X185)|~(in @ X190 @ (esk7_2 @ X184 @ X185))|(in @ (esk5_2 @ X184 @ X185) @ X185))&((X184 @ (esk8_3 @ X184 @ X185 @ X190) @ X190)|~(in @ X190 @ (esk7_2 @ X184 @ X185))|(in @ (esk5_2 @ X184 @ X185) @ X185)))&(~(in @ X193 @ X185)|~(X184 @ X193 @ X192)|(in @ X192 @ (esk7_2 @ X184 @ X185))|(in @ (esk5_2 @ X184 @ X185) @ X185)))&(((((in @ (esk8_3 @ X184 @ X185 @ X190) @ X185)|~(in @ X190 @ (esk7_2 @ X184 @ X185))|((X184 @ (esk5_2 @ X184 @ X185) @ (esk6_3 @ X184 @ X185 @ X187))|~(X184 @ (esk5_2 @ X184 @ X185) @ X187)))&((X184 @ (esk8_3 @ X184 @ X185 @ X190) @ X190)|~(in @ X190 @ (esk7_2 @ X184 @ X185))|((X184 @ (esk5_2 @ X184 @ X185) @ (esk6_3 @ X184 @ X185 @ X187))|~(X184 @ (esk5_2 @ X184 @ X185) @ X187))))&(~(in @ X193 @ X185)|~(X184 @ X193 @ X192)|(in @ X192 @ (esk7_2 @ X184 @ X185))|((X184 @ (esk5_2 @ X184 @ X185) @ (esk6_3 @ X184 @ X185 @ X187))|~(X184 @ (esk5_2 @ X184 @ X185) @ X187))))&((((in @ (esk8_3 @ X184 @ X185 @ X190) @ X185)|~(in @ X190 @ (esk7_2 @ X184 @ X185))|(((X187)!=(esk6_3 @ X184 @ X185 @ X187))|~(X184 @ (esk5_2 @ X184 @ X185) @ X187)))&((X184 @ (esk8_3 @ X184 @ X185 @ X190) @ X190)|~(in @ X190 @ (esk7_2 @ X184 @ X185))|(((X187)!=(esk6_3 @ X184 @ X185 @ X187))|~(X184 @ (esk5_2 @ X184 @ X185) @ X187))))&(~(in @ X193 @ X185)|~(X184 @ X193 @ X192)|(in @ X192 @ (esk7_2 @ X184 @ X185))|(((X187)!=(esk6_3 @ X184 @ X185 @ X187))|~(X184 @ (esk5_2 @ X184 @ X185) @ X187))))))&((((in @ (esk9_1 @ X194) @ X194)|~(in @ X195 @ X194))&(~(in @ X197 @ (esk9_1 @ X194))|~(in @ X197 @ X194)|~(in @ X195 @ X194)))&((epred1_0)&((((X198 @ (esk10_2 @ X198 @ X199))|~(X198 @ X199)|(X198 @ (descr @ X198)))&(((X199)!=(esk10_2 @ X198 @ X199))|~(X198 @ X199)|(X198 @ (descr @ X198))))&((~(in @ X203 @ X201)|(~(X202 @ X203)|(in @ X203 @ (dsetconstr @ X201 @ X202))))&((~(in @ X206 @ (dsetconstr @ X204 @ X205))|(in @ X206 @ X204))&((~(in @ X209 @ (dsetconstr @ X207 @ X208))|(X208 @ X209))&(((((X210 @ (esk12_1 @ X210))|((X210 @ (esk11_2 @ X210 @ X211))|~(X210 @ X211)))&(~(X210 @ X214)|((esk12_1 @ X210)=(X214))|((X210 @ (esk11_2 @ X210 @ X211))|~(X210 @ X211))))&(((X210 @ (esk12_1 @ X210))|(((X211)!=(esk11_2 @ X210 @ X211))|~(X210 @ X211)))&(~(X210 @ X214)|((esk12_1 @ X210)=(X214))|(((X211)!=(esk11_2 @ X210 @ X211))|~(X210 @ X211)))))&((~(in @ X216 @ (prop2set @ ((X215))))|(X215))&((~(in @ X217 @ emptyset)|(X218))&((~(in @ X219 @ emptyset)|~($true))&(~(in @ X220 @ emptyset)&(((epred2_0 @ esk13_0)&(~(epred2_0 @ X223)|((esk13_0)=(X223))))&~(epred2_0 @ X224))))))))))))))))))))))), 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])])])])])])])).
% 0.20/0.27 thf(c_0_36, negated_conjecture, (epred2_0 @ esk13_0), inference(split_conjunct,[status(thm)],[c_0_35])).
% 0.20/0.27 thf(c_0_37, negated_conjecture, ![X2:$i]:(~((epred2_0 @ X2))), inference(split_conjunct,[status(thm)],[c_0_35])).
% 0.20/0.27 thf(c_0_38, negated_conjecture, ($false), inference(sr,[status(thm)],[c_0_36, c_0_37]), ['proof']).
% 0.20/0.27 % SZS output end CNFRefutation
% 0.20/0.27 % Parsed axioms : 53
% 0.20/0.27 % Removed by relevancy pruning/SinE : 0
% 0.20/0.27 % Initial clauses : 91
% 0.20/0.27 % Removed in clause preprocessing : 30
% 0.20/0.27 % Initial clauses in saturation : 61
% 0.20/0.27 % Processed clauses : 3
% 0.20/0.27 % ...of these trivial : 0
% 0.20/0.27 % ...subsumed : 0
% 0.20/0.27 % ...remaining for further processing : 3
% 0.20/0.27 % Other redundant clauses eliminated : 0
% 0.20/0.27 % Clauses deleted for lack of memory : 0
% 0.20/0.27 % Backward-subsumed : 0
% 0.20/0.27 % Backward-rewritten : 0
% 0.20/0.27 % Generated clauses : 1
% 0.20/0.27 % ...of the previous two non-redundant : 0
% 0.20/0.27 % ...aggressively subsumed : 0
% 0.20/0.27 % Contextual simplify-reflections : 0
% 0.20/0.27 % Paramodulations : 0
% 0.20/0.27 % Factorizations : 0
% 0.20/0.27 % NegExts : 0
% 0.20/0.27 % Equation resolutions : 0
% 0.20/0.27 % Disequality decompositions : 0
% 0.20/0.27 % Total rewrite steps : 0
% 0.20/0.27 % ...of those cached : 0
% 0.20/0.27 % Propositional unsat checks : 0
% 0.20/0.27 % Propositional check models : 0
% 0.20/0.27 % Propositional check unsatisfiable : 0
% 0.20/0.27 % Propositional clauses : 0
% 0.20/0.27 % Propositional clauses after purity: 0
% 0.20/0.27 % Propositional unsat core size : 0
% 0.20/0.27 % Propositional preprocessing time : 0.000
% 0.20/0.27 % Propositional encoding time : 0.000
% 0.20/0.27 % Propositional solver time : 0.000
% 0.20/0.27 % Success case prop preproc time : 0.000
% 0.20/0.27 % Success case prop encoding time : 0.000
% 0.20/0.27 % Success case prop solver time : 0.000
% 0.20/0.27 % Current number of processed clauses : 2
% 0.20/0.27 % Positive orientable unit clauses : 1
% 0.20/0.27 % Positive unorientable unit clauses: 0
% 0.20/0.27 % Negative unit clauses : 1
% 0.20/0.27 % Non-unit-clauses : 0
% 0.20/0.27 % Current number of unprocessed clauses: 58
% 0.20/0.27 % ...number of literals in the above : 188
% 0.20/0.27 % Current number of archived formulas : 0
% 0.20/0.27 % Current number of archived clauses : 1
% 0.20/0.27 % Clause-clause subsumption calls (NU) : 0
% 0.20/0.27 % Rec. Clause-clause subsumption calls : 0
% 0.20/0.27 % Non-unit clause-clause subsumptions : 0
% 0.20/0.27 % Unit Clause-clause subsumption calls : 0
% 0.20/0.27 % Rewrite failures with RHS unbound : 0
% 0.20/0.27 % BW rewrite match attempts : 0
% 0.20/0.27 % BW rewrite match successes : 0
% 0.20/0.27 % Condensation attempts : 0
% 0.20/0.27 % Condensation successes : 0
% 0.20/0.27 % Termbank termtop insertions : 7489
% 0.20/0.27 % Search garbage collected termcells : 2787
% 0.20/0.27
% 0.20/0.27 % -------------------------------------------------
% 0.20/0.27 % User time : 0.007 s
% 0.20/0.27 % System time : 0.004 s
% 0.20/0.27 % Total time : 0.011 s
% 0.20/0.27 % Maximum resident set size: 4204 pages
% 0.20/0.27
% 0.20/0.27 % -------------------------------------------------
% 0.20/0.27 % User time : 0.019 s
% 0.20/0.27 % System time : 0.014 s
% 0.20/0.27 % Total time : 0.033 s
% 0.20/0.27 % Maximum resident set size: 4864 pages
% 0.20/0.27 % E exiting
%------------------------------------------------------------------------------