%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU508^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 08:26:31 AM UTC 2026
% Result : Theorem 0.22s 0.29s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU508^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n015.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 13:50:33 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.h1c135jeMq/E---3.1_3549663.p
% 0.22/0.29 % Version: 3.5.1-ho
% 0.22/0.29 % Preprocessing class: HSMSSLSSMLLCHSA.
% 0.22/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.29 % Starting new_ho_10 with 1500s (5) cores
% 0.22/0.29 % Starting sh5l with 300s (1) cores
% 0.22/0.29 % Starting new_bool_1 with 300s (1) cores
% 0.22/0.29 % Starting new_bool_2 with 300s (1) cores
% 0.22/0.29 % new_bool_2 with pid 3549679 completed with status 0
% 0.22/0.29 % Result found by new_bool_2
% 0.22/0.29 % Preprocessing class: HSMSSLSSMLLCHSA.
% 0.22/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.29 % Starting new_ho_10 with 1500s (5) cores
% 0.22/0.29 % Starting sh5l with 300s (1) cores
% 0.22/0.29 % Starting new_bool_1 with 300s (1) cores
% 0.22/0.29 % Starting new_bool_2 with 300s (1) cores
% 0.22/0.29 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.22/0.29 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.22/0.29 % Search class: HGHSF-FFMM31-SHSSMSBN
% 0.22/0.29 % partial match(1): HGHSM-FFMM31-SHSSMSBN
% 0.22/0.29 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.29 % Starting SubtermCWHack with 31s (1) cores
% 0.22/0.29 % SubtermCWHack with pid 3549680 completed with status 0
% 0.22/0.29 % Result found by SubtermCWHack
% 0.22/0.29 % Preprocessing class: HSMSSLSSMLLCHSA.
% 0.22/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.29 % Starting new_ho_10 with 1500s (5) cores
% 0.22/0.29 % Starting sh5l with 300s (1) cores
% 0.22/0.29 % Starting new_bool_1 with 300s (1) cores
% 0.22/0.29 % Starting new_bool_2 with 300s (1) cores
% 0.22/0.29 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.22/0.29 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.22/0.29 % Search class: HGHSF-FFMM31-SHSSMSBN
% 0.22/0.29 % partial match(1): HGHSM-FFMM31-SHSSMSBN
% 0.22/0.29 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.29 % Starting SubtermCWHack with 31s (1) cores
% 0.22/0.29 % Preprocessing time : 0.002 s
% 0.22/0.29
% 0.22/0.29 % Proof found!
% 0.22/0.29 % SZS status Theorem
% 0.22/0.29 % SZS output start CNFRefutation
% 0.22/0.29 thf(decl_23, type, in: $i > $i > $o).
% 0.22/0.29 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.22/0.29 thf(decl_25, type, setextAx: $o).
% 0.22/0.29 thf(decl_26, type, emptyset: $i).
% 0.22/0.29 thf(decl_27, type, emptysetAx: $o).
% 0.22/0.29 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.22/0.29 thf(decl_29, type, setadjoinAx: $o).
% 0.22/0.29 thf(decl_30, type, powerset: $i > $i).
% 0.22/0.29 thf(decl_31, type, powersetAx: $o).
% 0.22/0.29 thf(decl_33, type, setunionAx: $o).
% 0.22/0.29 thf(decl_34, type, omega: $i).
% 0.22/0.29 thf(decl_35, type, omega0Ax: $o).
% 0.22/0.29 thf(decl_36, type, omegaSAx: $o).
% 0.22/0.29 thf(decl_37, type, omegaIndAx: $o).
% 0.22/0.29 thf(decl_38, type, replAx: $o).
% 0.22/0.29 thf(decl_39, type, foundationAx: $o).
% 0.22/0.29 thf(decl_40, type, wellorderingAx: $o).
% 0.22/0.29 thf(decl_42, type, descrp: $o).
% 0.22/0.29 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.22/0.29 thf(decl_44, type, dsetconstrI: $o).
% 0.22/0.29 thf(decl_45, type, dsetconstrEL: $o).
% 0.22/0.29 thf(decl_46, type, dsetconstrER: $o).
% 0.22/0.29 thf(decl_47, type, exuE1: $o).
% 0.22/0.29 thf(decl_48, type, prop2set: $o > $i).
% 0.22/0.29 thf(decl_49, type, prop2setE: $o).
% 0.22/0.29 thf(decl_50, type, emptysetE: $o).
% 0.22/0.29 thf(decl_51, type, emptysetimpfalse: $o).
% 0.22/0.29 thf(decl_52, type, notinemptyset: $o).
% 0.22/0.29 thf(decl_53, type, exuE3e: $o).
% 0.22/0.29 thf(decl_54, type, setext: $o).
% 0.22/0.29 thf(decl_55, type, emptyI: $o).
% 0.22/0.29 thf(decl_56, type, noeltsimpempty: $o).
% 0.22/0.29 thf(decl_57, type, epred1_0: $o).
% 0.22/0.29 thf(decl_58, type, esk1_2: $i > $i > $i).
% 0.22/0.29 thf(decl_59, type, esk2_2: $i > $i > $i).
% 0.22/0.29 thf(decl_60, type, esk3_1: $i > $i).
% 0.22/0.29 thf(decl_61, type, esk4_2: ($i > $i > $o) > $i > $i).
% 0.22/0.29 thf(decl_62, type, esk5_3: ($i > $i > $o) > $i > $i > $i).
% 0.22/0.29 thf(decl_63, type, esk6_2: ($i > $i > $o) > $i > $i).
% 0.22/0.29 thf(decl_64, type, esk7_3: ($i > $i > $o) > $i > $i > $i).
% 0.22/0.29 thf(decl_65, type, esk8_1: $i > $i).
% 0.22/0.29 thf(decl_66, type, esk9_2: ($i > $o) > $i > $i).
% 0.22/0.29 thf(decl_67, type, esk10_1: ($i > $o) > $i).
% 0.22/0.29 thf(decl_68, type, esk11_2: ($i > $o) > $i > $i).
% 0.22/0.29 thf(decl_69, type, esk12_1: ($i > $o) > $i).
% 0.22/0.29 thf(decl_70, type, esk13_2: $i > $i > $i).
% 0.22/0.29 thf(decl_71, type, esk14_2: $i > $i > $i).
% 0.22/0.29 thf(decl_72, type, esk15_1: $i > $i).
% 0.22/0.29 thf(decl_73, type, esk16_1: $i > $i).
% 0.22/0.29 thf(decl_74, type, esk17_0: $i).
% 0.22/0.29 thf(decl_75, type, epred2_0: $i > $o).
% 0.22/0.29 thf(decl_76, type, esk18_0: $i).
% 0.22/0.29 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.h1c135jeMq/E---3.1_3549663.p', exuE1)).
% 0.22/0.29 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.h1c135jeMq/E---3.1_3549663.p', exu)).
% 0.22/0.29 thf(prop2set, axiom, ((prop2set)=(^[X10:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[X2:$i]:((X10)))))), file('/export/starexec/sandbox2/tmp/tmp.h1c135jeMq/E---3.1_3549663.p', prop2set)).
% 0.22/0.29 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.h1c135jeMq/E---3.1_3549663.p', exuE3e)).
% 0.22/0.29 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.h1c135jeMq/E---3.1_3549663.p', replAx)).
% 0.22/0.29 thf(setbeta, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2)))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.h1c135jeMq/E---3.1_3549663.p', setbeta)).
% 0.22/0.29 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.h1c135jeMq/E---3.1_3549663.p', dsetconstrI)).
% 0.22/0.29 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.h1c135jeMq/E---3.1_3549663.p', dsetconstrEL)).
% 0.22/0.29 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.h1c135jeMq/E---3.1_3549663.p', dsetconstrER)).
% 0.22/0.29 thf(prop2setE, axiom, ((prop2setE)<=>![X11:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X11))))=>(X11)))), file('/export/starexec/sandbox2/tmp/tmp.h1c135jeMq/E---3.1_3549663.p', prop2setE)).
% 0.22/0.29 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X12:$o]:((X12))))), file('/export/starexec/sandbox2/tmp/tmp.h1c135jeMq/E---3.1_3549663.p', emptysetE)).
% 0.22/0.29 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.h1c135jeMq/E---3.1_3549663.p', emptysetimpfalse)).
% 0.22/0.29 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.h1c135jeMq/E---3.1_3549663.p', notinemptyset)).
% 0.22/0.29 thf(setext, axiom, ((setext)<=>![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/sandbox2/tmp/tmp.h1c135jeMq/E---3.1_3549663.p', setext)).
% 0.22/0.29 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.h1c135jeMq/E---3.1_3549663.p', emptyI)).
% 0.22/0.29 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.h1c135jeMq/E---3.1_3549663.p', noeltsimpempty)).
% 0.22/0.29 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.h1c135jeMq/E---3.1_3549663.p', omega0Ax)).
% 0.22/0.29 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.h1c135jeMq/E---3.1_3549663.p', powersetAx)).
% 0.22/0.29 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.h1c135jeMq/E---3.1_3549663.p', setadjoinAx)).
% 0.22/0.29 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.h1c135jeMq/E---3.1_3549663.p', emptysetAx)).
% 0.22/0.29 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.h1c135jeMq/E---3.1_3549663.p', setextAx)).
% 0.22/0.29 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.h1c135jeMq/E---3.1_3549663.p', omegaIndAx)).
% 0.22/0.29 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.h1c135jeMq/E---3.1_3549663.p', foundationAx)).
% 0.22/0.29 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.h1c135jeMq/E---3.1_3549663.p', wellorderingAx)).
% 0.22/0.29 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.h1c135jeMq/E---3.1_3549663.p', omegaSAx)).
% 0.22/0.29 thf(c_0_25, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.22/0.29 thf(c_0_26, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.22/0.29 thf(c_0_27, plain, ((prop2set)=(^[Z0:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[Z1:$i]:((Z0)))))), inference(fof_simplification,[status(thm)],[prop2set])).
% 0.22/0.29 thf(c_0_28, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.22/0.29 thf(c_0_29, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.22/0.29 thf(c_0_30, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[setbeta])).
% 0.22/0.29 thf(c_0_31, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.22/0.29 thf(c_0_32, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.22/0.29 thf(c_0_33, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.22/0.29 thf(c_0_34, plain, ((exuE1)=(![X1:$i > $o]:((((?[X89:$i]:(((((X1 @ X89)))&(![X90:$i]:(((((X1 @ X90)))=>(((X89)=(X90))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_25, c_0_26])).
% 0.22/0.29 thf(c_0_35, axiom, ((prop2setE)=(![X11:$o, X2:$i]:((((in @ X2 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:(((X11)))))))=>((X11)))))), inference(apply_def,[status(thm)],[prop2setE, c_0_27])).
% 0.22/0.29 thf(c_0_36, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X91:$i]:(((((X1 @ X91)))&(![X92:$i]:(((((X1 @ X92)))=>(((X91)=(X92))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_28, c_0_26])).
% 0.22/0.29 thf(c_0_37, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X87:$i]:(((((X6 @ X2 @ X87)))&(![X88:$i]:(((((X6 @ X2 @ X88)))=>(((X87)=(X88)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_29, c_0_26])).
% 0.22/0.29 thf(c_0_38, plain, ((epred1_0)<=>![X119:$i]:(?[X120:$i]:((((![X121:$i]:(((in @ X121 @ X120)=>![X122:$i]:(((in @ X122 @ X121)=>(in @ X122 @ X119)))))&![X123:$i, X124:$i]:((((in @ X123 @ X119)&(in @ X124 @ X119))=>(![X125:$i]:(((in @ X125 @ X120)=>((in @ X123 @ X125)<=>(in @ X124 @ X125))))=>((X123)=(X124))))))&![X126:$i, X127:$i]:((((in @ X126 @ X120)&(in @ X127 @ X120))=>(![X128:$i]:(((in @ X128 @ X126)=>(in @ X128 @ X127)))|![X129:$i]:(((in @ X129 @ X127)=>(in @ X129 @ X126)))))))&![X130:$i]:(((![X131:$i]:(((in @ X131 @ X130)=>(in @ X131 @ X119)))&?[X132:$i]:((in @ X132 @ X130)))=>?[X133:$i, X134:$i]:(((((in @ X133 @ X120)&(in @ X134 @ X130))&~(?[X135:$i]:(((in @ X135 @ X133)&(in @ X135 @ X130)))))&![X136:$i]:(((in @ X136 @ X120)=>(![X137:$i]:(((in @ X137 @ X136)=>(in @ X137 @ X133)))|(in @ X134 @ X136)))))))))))), introduced(definition)).
% 0.22/0.29 thf(c_0_39, negated_conjecture, ~((![X93:$i, X94:$i]:((![X95:$i]:(((in @ X95 @ X93)<=>(in @ X95 @ X94)))=>((X93)=(X94))))=>(![X96:$i]:(~(in @ X96 @ emptyset))=>(![X97:$i, X98:$i, X99:$i]:(((in @ X99 @ (setadjoin @ X97 @ X98))<=>(((X99)=(X97))|(in @ X99 @ X98))))=>(![X100:$i, X101:$i]:(((in @ X101 @ (powerset @ X100))<=>![X102:$i]:(((in @ X102 @ X101)=>(in @ X102 @ X100)))))=>((setunionAx)=>((in @ emptyset @ omega)=>(![X103:$i]:(((in @ X103 @ omega)=>(in @ (setadjoin @ X103 @ X103) @ omega)))=>(![X104:$i]:((((in @ emptyset @ X104)&![X105:$i]:((((in @ X105 @ omega)&(in @ X105 @ X104))=>(in @ (setadjoin @ X105 @ X105) @ X104))))=>![X106:$i]:(((in @ X106 @ omega)=>(in @ X106 @ X104)))))=>(![X107:$i > $i > $o, X108:$i]:((![X109:$i]:(((in @ X109 @ X108)=>?[X110:$i]:(((X107 @ X109 @ X110)&![X111:$i]:(((X107 @ X109 @ X111)=>((X110)=(X111))))))))=>?[X112:$i]:(![X113:$i]:(((in @ X113 @ X112)<=>?[X114:$i]:(((in @ X114 @ X108)&(X107 @ X114 @ X113))))))))=>(![X115:$i]:((?[X116:$i]:((in @ X116 @ X115))=>?[X117:$i]:(((in @ X117 @ X115)&~(?[X118:$i]:(((in @ X118 @ X117)&(in @ X118 @ X115))))))))=>((epred1_0)=>((descrp)=>(![X138:$i, X139:$i > $o, X140:$i]:(((in @ X140 @ X138)=>((X139 @ X140)=>(in @ X140 @ (dsetconstr @ X138 @ (^[Z0:$i]:((X139 @ Z0))))))))=>(![X141:$i, X142:$i > $o, X143:$i]:(((in @ X143 @ (dsetconstr @ X141 @ (^[Z0:$i]:((X142 @ Z0)))))=>(in @ X143 @ X141)))=>(![X144:$i, X145:$i > $o, X146:$i]:(((in @ X146 @ (dsetconstr @ X144 @ (^[Z0:$i]:((X145 @ Z0)))))=>(X145 @ X146)))=>(![X147:$i > $o]:((?[X148:$i]:(((X147 @ X148)&![X149:$i]:(((X147 @ X149)=>((X148)=(X149))))))=>?[X150:$i]:(((X147 @ X150)&![X151:$i]:(((X147 @ X151)=>((X150)=(X151))))))))=>(![X152:$o, X153:$i]:(((in @ X153 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X152)))))=>(X152)))=>(![X154:$i]:(((in @ X154 @ emptyset)=>![X155:$o]:((X155))))=>(![X156:$i]:(~(in @ X156 @ emptyset))=>(![X157:$i]:(~(in @ X157 @ emptyset))=>(![X158:$i > $o]:((?[X159:$i]:(((X158 @ X159)&![X160:$i]:(((X158 @ X160)=>((X159)=(X160))))))=>?[X161:$i]:((X158 @ X161))))=>(![X162:$i, X163:$i]:((![X164:$i]:(((in @ X164 @ X162)=>(in @ X164 @ X163)))=>(![X165:$i]:(((in @ X165 @ X163)=>(in @ X165 @ X162)))=>((X162)=(X163)))))=>(![X166:$i]:((![X167:$i]:(~(in @ X167 @ X166))=>((X166)=(emptyset))))=>(![X168:$i]:((![X169:$i]:(~(in @ X169 @ X168))=>((X168)=(emptyset))))=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_30]), c_0_31]), c_0_32]), c_0_33]), c_0_34]), c_0_35]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_36]), setext]), emptyI]), noeltsimpempty]), omega0Ax]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx]), omegaIndAx]), c_0_37]), foundationAx]), wellorderingAx]), omegaSAx])]), c_0_38])).
% 0.22/0.29 thf(c_0_40, negated_conjecture, ![X170:$i, X171:$i, X173:$i, X174:$i, X175:$i, X176:$i, X177:$i, X178:$i, X179:$i, X180:$i, X181:$i, X183:$i, X184:$i, X186:$i, X187:$i > $i > $o, X188:$i, X190:$i, X193:$i, X195:$i, X196:$i, X197:$i, X198:$i, X200:$i, X201:$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:$i, X221:$i > $o, X222:$i, X225:$i, X226:$i, X229:$i, X231:$i]:((((~(in @ (esk1_2 @ X170 @ X171) @ X170)|~(in @ (esk1_2 @ X170 @ X171) @ X171)|((X170)=(X171)))&((in @ (esk1_2 @ X170 @ X171) @ X170)|(in @ (esk1_2 @ X170 @ X171) @ X171)|((X170)=(X171))))&(~(in @ X173 @ emptyset)&(((~(in @ X176 @ (setadjoin @ X174 @ X175))|(((X176)=(X174))|(in @ X176 @ X175)))&((((X176)!=(X174))|(in @ X176 @ (setadjoin @ X174 @ X175)))&(~(in @ X176 @ X175)|(in @ X176 @ (setadjoin @ X174 @ X175)))))&(((~(in @ X178 @ (powerset @ X177))|(~(in @ X179 @ X178)|(in @ X179 @ X177)))&(((in @ (esk2_2 @ X180 @ X181) @ X181)|(in @ X181 @ (powerset @ X180)))&(~(in @ (esk2_2 @ X180 @ X181) @ X180)|(in @ X181 @ (powerset @ X180)))))&((setunionAx)&((in @ emptyset @ omega)&((~(in @ X183 @ omega)|(in @ (setadjoin @ X183 @ X183) @ omega))&(((((in @ (esk3_1 @ X184) @ omega)|~(in @ emptyset @ X184)|(~(in @ X186 @ omega)|(in @ X186 @ X184)))&((in @ (esk3_1 @ X184) @ X184)|~(in @ emptyset @ X184)|(~(in @ X186 @ omega)|(in @ X186 @ X184))))&(~(in @ (setadjoin @ (esk3_1 @ X184) @ (esk3_1 @ X184)) @ X184)|~(in @ emptyset @ X184)|(~(in @ X186 @ omega)|(in @ X186 @ X184))))&((((((in @ (esk7_3 @ X187 @ X188 @ X193) @ X188)|~(in @ X193 @ (esk6_2 @ X187 @ X188))|(in @ (esk4_2 @ X187 @ X188) @ X188))&((X187 @ (esk7_3 @ X187 @ X188 @ X193) @ X193)|~(in @ X193 @ (esk6_2 @ X187 @ X188))|(in @ (esk4_2 @ X187 @ X188) @ X188)))&(~(in @ X196 @ X188)|~(X187 @ X196 @ X195)|(in @ X195 @ (esk6_2 @ X187 @ X188))|(in @ (esk4_2 @ X187 @ X188) @ X188)))&(((((in @ (esk7_3 @ X187 @ X188 @ X193) @ X188)|~(in @ X193 @ (esk6_2 @ X187 @ X188))|((X187 @ (esk4_2 @ X187 @ X188) @ (esk5_3 @ X187 @ X188 @ X190))|~(X187 @ (esk4_2 @ X187 @ X188) @ X190)))&((X187 @ (esk7_3 @ X187 @ X188 @ X193) @ X193)|~(in @ X193 @ (esk6_2 @ X187 @ X188))|((X187 @ (esk4_2 @ X187 @ X188) @ (esk5_3 @ X187 @ X188 @ X190))|~(X187 @ (esk4_2 @ X187 @ X188) @ X190))))&(~(in @ X196 @ X188)|~(X187 @ X196 @ X195)|(in @ X195 @ (esk6_2 @ X187 @ X188))|((X187 @ (esk4_2 @ X187 @ X188) @ (esk5_3 @ X187 @ X188 @ X190))|~(X187 @ (esk4_2 @ X187 @ X188) @ X190))))&((((in @ (esk7_3 @ X187 @ X188 @ X193) @ X188)|~(in @ X193 @ (esk6_2 @ X187 @ X188))|(((X190)!=(esk5_3 @ X187 @ X188 @ X190))|~(X187 @ (esk4_2 @ X187 @ X188) @ X190)))&((X187 @ (esk7_3 @ X187 @ X188 @ X193) @ X193)|~(in @ X193 @ (esk6_2 @ X187 @ X188))|(((X190)!=(esk5_3 @ X187 @ X188 @ X190))|~(X187 @ (esk4_2 @ X187 @ X188) @ X190))))&(~(in @ X196 @ X188)|~(X187 @ X196 @ X195)|(in @ X195 @ (esk6_2 @ X187 @ X188))|(((X190)!=(esk5_3 @ X187 @ X188 @ X190))|~(X187 @ (esk4_2 @ X187 @ X188) @ X190))))))&((((in @ (esk8_1 @ X197) @ X197)|~(in @ X198 @ X197))&(~(in @ X200 @ (esk8_1 @ X197))|~(in @ X200 @ X197)|~(in @ X198 @ X197)))&((epred1_0)&((descrp)&((~(in @ X203 @ X201)|(~(X202 @ X203)|(in @ X203 @ (dsetconstr @ X201 @ (^[Z0:$i]:((X202 @ Z0)))))))&((~(in @ X206 @ (dsetconstr @ X204 @ (^[Z0:$i]:((X205 @ Z0)))))|(in @ X206 @ X204))&((~(in @ X209 @ (dsetconstr @ X207 @ (^[Z0:$i]:((X208 @ Z0)))))|(X208 @ X209))&(((((X210 @ (esk10_1 @ X210))|((X210 @ (esk9_2 @ X210 @ X211))|~(X210 @ X211)))&(~(X210 @ X214)|((esk10_1 @ X210)=(X214))|((X210 @ (esk9_2 @ X210 @ X211))|~(X210 @ X211))))&(((X210 @ (esk10_1 @ X210))|(((X211)!=(esk9_2 @ X210 @ X211))|~(X210 @ X211)))&(~(X210 @ X214)|((esk10_1 @ X210)=(X214))|(((X211)!=(esk9_2 @ X210 @ X211))|~(X210 @ X211)))))&((~(in @ X216 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X215)))))|(X215))&((~(in @ X217 @ emptyset)|(X218))&(~(in @ X219 @ emptyset)&(~(in @ X220 @ emptyset)&((((X221 @ (esk11_2 @ X221 @ X222))|~(X221 @ X222)|(X221 @ (esk12_1 @ X221)))&(((X222)!=(esk11_2 @ X221 @ X222))|~(X221 @ X222)|(X221 @ (esk12_1 @ X221))))&(((((in @ (esk14_2 @ X225 @ X226) @ X226)|((X225)=(X226))|(in @ (esk13_2 @ X225 @ X226) @ X225))&(~(in @ (esk14_2 @ X225 @ X226) @ X225)|((X225)=(X226))|(in @ (esk13_2 @ X225 @ X226) @ X225)))&(((in @ (esk14_2 @ X225 @ X226) @ X226)|((X225)=(X226))|~(in @ (esk13_2 @ X225 @ X226) @ X226))&(~(in @ (esk14_2 @ X225 @ X226) @ X225)|((X225)=(X226))|~(in @ (esk13_2 @ X225 @ X226) @ X226))))&(((in @ (esk15_1 @ X229) @ X229)|((X229)=(emptyset)))&(((in @ (esk16_1 @ X231) @ X231)|((X231)=(emptyset)))&((in @ esk18_0 @ esk17_0)&((~(in @ esk18_0 @ (dsetconstr @ esk17_0 @ (^[Z0:$i]:((epred2_0 @ Z0)))))|~(epred2_0 @ esk18_0))&((in @ esk18_0 @ (dsetconstr @ esk17_0 @ (^[Z0:$i]:((epred2_0 @ Z0)))))|(epred2_0 @ esk18_0))))))))))))))))))))))))))))), inference(distribute,[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_39])])])])])])).
% 0.22/0.29 thf(c_0_41, negated_conjecture, ![X3:$i, X2:$i, X1:$i > $o]:(((X1 @ X2)|~((in @ X2 @ (dsetconstr @ X3 @ X1))))), inference(split_conjunct,[status(thm)],[c_0_40])).
% 0.22/0.29 thf(c_0_42, negated_conjecture, ((in @ esk18_0 @ (dsetconstr @ esk17_0 @ epred2_0))|(epred2_0 @ esk18_0)), inference(split_conjunct,[status(thm)],[c_0_40])).
% 0.22/0.29 thf(c_0_43, negated_conjecture, (~((in @ esk18_0 @ (dsetconstr @ esk17_0 @ epred2_0)))|~((epred2_0 @ esk18_0))), inference(split_conjunct,[status(thm)],[c_0_40])).
% 0.22/0.29 thf(c_0_44, negated_conjecture, (epred2_0 @ esk18_0), inference(spm,[status(thm)],[c_0_41, c_0_42])).
% 0.22/0.29 thf(c_0_45, negated_conjecture, ~((in @ esk18_0 @ (dsetconstr @ esk17_0 @ epred2_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43, c_0_44])])).
% 0.22/0.29 thf(c_0_46, negated_conjecture, ![X1:$i > $o, X3:$i, X2:$i]:(((in @ X2 @ (dsetconstr @ X3 @ X1))|~((in @ X2 @ X3))|~((X1 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_40])).
% 0.22/0.29 thf(c_0_47, negated_conjecture, (in @ esk18_0 @ esk17_0), inference(split_conjunct,[status(thm)],[c_0_40])).
% 0.22/0.29 thf(c_0_48, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45, c_0_46]), c_0_47]), c_0_44])]), ['proof']).
% 0.22/0.29 % SZS output end CNFRefutation
% 0.22/0.29 % Parsed axioms : 61
% 0.22/0.29 % Removed by relevancy pruning/SinE : 36
% 0.22/0.29 % Initial clauses : 63
% 0.22/0.29 % Removed in clause preprocessing : 0
% 0.22/0.29 % Initial clauses in saturation : 63
% 0.22/0.29 % Processed clauses : 49
% 0.22/0.29 % ...of these trivial : 0
% 0.22/0.29 % ...subsumed : 10
% 0.22/0.29 % ...remaining for further processing : 39
% 0.22/0.29 % Other redundant clauses eliminated : 1
% 0.22/0.29 % Clauses deleted for lack of memory : 0
% 0.22/0.29 % Backward-subsumed : 0
% 0.22/0.29 % Backward-rewritten : 3
% 0.22/0.29 % Generated clauses : 64
% 0.22/0.29 % ...of the previous two non-redundant : 51
% 0.22/0.29 % ...aggressively subsumed : 0
% 0.22/0.29 % Contextual simplify-reflections : 0
% 0.22/0.29 % Paramodulations : 63
% 0.22/0.29 % Factorizations : 0
% 0.22/0.29 % NegExts : 0
% 0.22/0.29 % Equation resolutions : 1
% 0.22/0.29 % Disequality decompositions : 0
% 0.22/0.29 % Total rewrite steps : 13
% 0.22/0.29 % ...of those cached : 5
% 0.22/0.29 % Propositional unsat checks : 0
% 0.22/0.29 % Propositional check models : 0
% 0.22/0.29 % Propositional check unsatisfiable : 0
% 0.22/0.29 % Propositional clauses : 0
% 0.22/0.29 % Propositional clauses after purity: 0
% 0.22/0.29 % Propositional unsat core size : 0
% 0.22/0.29 % Propositional preprocessing time : 0.000
% 0.22/0.29 % Propositional encoding time : 0.000
% 0.22/0.29 % Propositional solver time : 0.000
% 0.22/0.29 % Success case prop preproc time : 0.000
% 0.22/0.29 % Success case prop encoding time : 0.000
% 0.22/0.29 % Success case prop solver time : 0.000
% 0.22/0.29 % Current number of processed clauses : 35
% 0.22/0.29 % Positive orientable unit clauses : 14
% 0.22/0.29 % Positive unorientable unit clauses: 0
% 0.22/0.29 % Negative unit clauses : 2
% 0.22/0.29 % Non-unit-clauses : 19
% 0.22/0.29 % Current number of unprocessed clauses: 65
% 0.22/0.29 % ...number of literals in the above : 220
% 0.22/0.29 % Current number of archived formulas : 0
% 0.22/0.29 % Current number of archived clauses : 3
% 0.22/0.29 % Clause-clause subsumption calls (NU) : 73
% 0.22/0.29 % Rec. Clause-clause subsumption calls : 68
% 0.22/0.29 % Non-unit clause-clause subsumptions : 3
% 0.22/0.29 % Unit Clause-clause subsumption calls : 7
% 0.22/0.29 % Rewrite failures with RHS unbound : 0
% 0.22/0.29 % BW rewrite match attempts : 6
% 0.22/0.29 % BW rewrite match successes : 2
% 0.22/0.29 % Condensation attempts : 0
% 0.22/0.29 % Condensation successes : 0
% 0.22/0.29 % Termbank termtop insertions : 7325
% 0.22/0.29 % Search garbage collected termcells : 2446
% 0.22/0.29
% 0.22/0.29 % -------------------------------------------------
% 0.22/0.29 % User time : 0.010 s
% 0.22/0.29 % System time : 0.003 s
% 0.22/0.29 % Total time : 0.013 s
% 0.22/0.29 % Maximum resident set size: 4416 pages
% 0.22/0.29
% 0.22/0.29 % -------------------------------------------------
% 0.22/0.29 % User time : 0.015 s
% 0.22/0.29 % System time : 0.007 s
% 0.22/0.29 % Total time : 0.021 s
% 0.22/0.29 % Maximum resident set size: 4864 pages
% 0.22/0.29 % E exiting
%------------------------------------------------------------------------------