%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : PLA033^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 08:20:22 AM UTC 2026
% Result : Theorem 0.11s 0.25s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PLA033^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.16 % Computer : n008.cluster.edu
% 0.11/0.16 % Model : x86_64 x86_64
% 0.11/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.16 % Memory : 8046.5625MB
% 0.11/0.16 % OS : Linux 6.8.0-71-generic
% 0.11/0.16 % CPULimit : 300
% 0.11/0.16 % WCLimit : 300
% 0.11/0.16 % DateTime : Tue Sep 29 13:21:09 UTC 2026
% 0.11/0.16 % CPUTime :
% 0.11/0.16 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.20 Running higher-order theorem proving
% 0.11/0.22 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.k5FCpQ2n6L/E---3.1_3136056.p
% 0.11/0.25 % Version: 3.5.1-ho
% 0.11/0.25 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.11/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.25 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.11/0.25 % Starting post_as_ho3 with 300s (1) cores
% 0.11/0.25 % Starting new_ho_12 with 300s (1) cores
% 0.11/0.25 % Starting new_bool_2 with 300s (1) cores
% 0.11/0.25 % new_ho_10_cnf2 with pid 3136086 completed with status 0
% 0.11/0.25 % Result found by new_ho_10_cnf2
% 0.11/0.25 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.11/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.25 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.11/0.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.25 % No SInE strategy applied
% 0.11/0.25 % Search class: HGHNM-FFSF31-SHSSMFNN
% 0.11/0.25 % partial match(1): HGHNM-FFMF31-SHSSMFNN
% 0.11/0.25 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.25 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.25 % Starting new_ho_10_cnf2 with 151s (1) cores
% 0.11/0.25 % Starting full_lambda_10 with 136s (1) cores
% 0.11/0.25 % Starting full_lambda_9 with 136s (1) cores
% 0.11/0.25 % Starting new_ho_14 with 136s (1) cores
% 0.11/0.25 % full_lambda_9 with pid 3136095 completed with status 0
% 0.11/0.25 % Result found by full_lambda_9
% 0.11/0.25 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.11/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.25 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.11/0.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.25 % No SInE strategy applied
% 0.11/0.25 % Search class: HGHNM-FFSF31-SHSSMFNN
% 0.11/0.25 % partial match(1): HGHNM-FFMF31-SHSSMFNN
% 0.11/0.25 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.25 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.25 % Starting new_ho_10_cnf2 with 151s (1) cores
% 0.11/0.25 % Starting full_lambda_10 with 136s (1) cores
% 0.11/0.25 % Starting full_lambda_9 with 136s (1) cores
% 0.11/0.25 % Preprocessing time : 0.001 s
% 0.11/0.25 % Presaturation interreduction done
% 0.11/0.25
% 0.11/0.25 % Proof found!
% 0.11/0.25 % SZS status Theorem
% 0.11/0.25 % SZS output start CNFRefutation
% 0.11/0.25 thf(decl_sort1, type, mu: $tType).
% 0.11/0.25 thf(decl_25, type, mnot: ($i > $o) > $i > $o).
% 0.11/0.25 thf(decl_26, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.11/0.25 thf(decl_31, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.11/0.25 thf(decl_32, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.11/0.25 thf(decl_37, type, exists_in_world: mu > $i > $o).
% 0.11/0.25 thf(decl_38, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.11/0.25 thf(decl_39, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.11/0.25 thf(decl_41, type, mreflexive: ($i > $i > $o) > $o).
% 0.11/0.25 thf(decl_51, type, mvalid: ($i > $o) > $o).
% 0.11/0.25 thf(decl_55, type, rel_s4: $i > $i > $o).
% 0.11/0.25 thf(decl_56, type, mbox_s4: ($i > $o) > $i > $o).
% 0.11/0.25 thf(decl_58, type, closed: mu > $i > $o).
% 0.11/0.25 thf(decl_59, type, open: mu > $i > $o).
% 0.11/0.25 thf(decl_60, type, h: mu > $i > $o).
% 0.11/0.25 thf(decl_61, type, combo: mu > mu > $i > $o).
% 0.11/0.25 thf(decl_62, type, o: mu).
% 0.11/0.25 thf(decl_64, type, d: mu).
% 0.11/0.25 thf(decl_65, type, epred1_3: mu > $i > mu > $o).
% 0.11/0.25 thf(decl_67, type, esk2_1: $i > mu).
% 0.11/0.25 thf(decl_68, type, esk3_0: $i).
% 0.11/0.25 thf(decl_69, type, esk4_0: $i).
% 0.11/0.25 thf(decl_70, type, esk5_2: mu > mu > $i).
% 0.11/0.25 thf(decl_71, type, esk6_3: mu > $i > mu > mu).
% 0.11/0.25 thf(mand, axiom, ((mand)=(^[X4:$i > $o, X5:$i > $o]:(mnot @ (mor @ (mnot @ X4) @ (mnot @ X5))))), file('/export/starexec/sandbox/tmp/tmp.k5FCpQ2n6L/E---3.1_3136056.p', mand)).
% 0.11/0.25 thf(mnot, axiom, ((mnot)=(^[X4:$i > $o, X3:$i]:(~((X4 @ X3))))), file('/export/starexec/sandbox/tmp/tmp.k5FCpQ2n6L/E---3.1_3136056.p', mnot)).
% 0.11/0.25 thf(mor, axiom, ((mor)=(^[X4:$i > $o, X5:$i > $o, X3:$i]:((((X4 @ X3))|((X5 @ X3)))))), file('/export/starexec/sandbox/tmp/tmp.k5FCpQ2n6L/E---3.1_3136056.p', mor)).
% 0.11/0.25 thf(mimplies, axiom, ((mimplies)=(^[X4:$i > $o, X5:$i > $o]:(mor @ (mnot @ X4) @ X5))), file('/export/starexec/sandbox/tmp/tmp.k5FCpQ2n6L/E---3.1_3136056.p', mimplies)).
% 0.11/0.25 thf(mexists_ind, axiom, ((mexists_ind)=(^[X13:mu > $i > $o]:(mnot @ (mforall_ind @ (^[X14:mu]:(mnot @ (X13 @ X14))))))), file('/export/starexec/sandbox/tmp/tmp.k5FCpQ2n6L/E---3.1_3136056.p', mexists_ind)).
% 0.11/0.25 thf(mforall_ind, axiom, ((mforall_ind)=(^[X11:mu > $i > $o, X3:$i]:(![X12:mu]:((((exists_in_world @ X12 @ X3))=>((X11 @ X12 @ X3))))))), file('/export/starexec/sandbox/tmp/tmp.k5FCpQ2n6L/E---3.1_3136056.p', mforall_ind)).
% 0.11/0.25 thf(con, conjecture, (mvalid @ (mbox_s4 @ (mexists_ind @ (^[X25:mu]:(mexists_ind @ (^[X22:mu]:(mimplies @ (mbox_s4 @ (mand @ (combo @ d @ X25) @ (h @ X22))) @ (mbox_s4 @ (open @ d))))))))), file('/export/starexec/sandbox/tmp/tmp.k5FCpQ2n6L/E---3.1_3136056.p', con)).
% 0.11/0.25 thf(mvalid, axiom, ((mvalid)=(^[X4:$i > $o]:(![X3:$i]:((X4 @ X3))))), file('/export/starexec/sandbox/tmp/tmp.k5FCpQ2n6L/E---3.1_3136056.p', mvalid)).
% 0.11/0.25 thf(mbox_s4, axiom, ((mbox_s4)=(^[X4:$i > $o, X3:$i]:(![X7:$i]:(((~((rel_s4 @ X3 @ X7)))|((X4 @ X7))))))), file('/export/starexec/sandbox/tmp/tmp.k5FCpQ2n6L/E---3.1_3136056.p', mbox_s4)).
% 0.11/0.25 thf(ax5, axiom, (mvalid @ (mexists_ind @ (^[X24:mu]:(mbox_s4 @ (combo @ d @ X24))))), file('/export/starexec/sandbox/tmp/tmp.k5FCpQ2n6L/E---3.1_3136056.p', ax5)).
% 0.11/0.25 thf(mreflexive, axiom, ((mreflexive)=(^[X6:$i > $i > $o]:(![X16:$i]:((X6 @ X16 @ X16))))), file('/export/starexec/sandbox/tmp/tmp.k5FCpQ2n6L/E---3.1_3136056.p', mreflexive)).
% 0.11/0.25 thf(ax1, axiom, (mvalid @ (mbox_s4 @ (mforall_ind @ (^[X20:mu]:(mforall_ind @ (^[X21:mu]:(mexists_ind @ (^[X22:mu]:(mand @ (mbox_s4 @ (mimplies @ (mand @ (closed @ X20) @ (mand @ (combo @ X20 @ X21) @ (h @ X22))) @ (mbox_s4 @ (open @ X20)))) @ (mbox_s4 @ (mimplies @ (mand @ (closed @ X20) @ (mand @ (mnot @ (combo @ X20 @ X21)) @ (h @ o))) @ (mbox_s4 @ (closed @ X20))))))))))))), file('/export/starexec/sandbox/tmp/tmp.k5FCpQ2n6L/E---3.1_3136056.p', ax1)).
% 0.11/0.25 thf(a1, axiom, (mreflexive @ rel_s4), file('/export/starexec/sandbox/tmp/tmp.k5FCpQ2n6L/E---3.1_3136056.p', a1)).
% 0.11/0.25 thf(ax2, axiom, (mvalid @ (mbox_s4 @ (closed @ d))), file('/export/starexec/sandbox/tmp/tmp.k5FCpQ2n6L/E---3.1_3136056.p', ax2)).
% 0.11/0.25 thf(existence_of_d_ax, axiom, ![X7:$i]:((exists_in_world @ d @ X7)), file('/export/starexec/sandbox/tmp/tmp.k5FCpQ2n6L/E---3.1_3136056.p', existence_of_d_ax)).
% 0.11/0.25 thf(ax4, axiom, (mvalid @ (mbox_s4 @ (mforall_ind @ (^[X23:mu]:(mnot @ (mand @ (open @ X23) @ (closed @ X23))))))), file('/export/starexec/sandbox/tmp/tmp.k5FCpQ2n6L/E---3.1_3136056.p', ax4)).
% 0.11/0.25 thf(c_0_16, plain, ((mand)=(^[Z0:$i > $o, Z1:$i > $o, Z2:$i]:(~(((((~((Z0 @ Z2))))|((~((Z1 @ Z2)))))))))), inference(fof_simplification,[status(thm)],[mand])).
% 0.11/0.25 thf(c_0_17, plain, ((mnot)=(^[Z0:$i > $o, Z1:$i]:(~((Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[mnot])).
% 0.11/0.25 thf(c_0_18, plain, ((mor)=(^[Z0:$i > $o, Z1:$i > $o, Z2:$i]:((((Z0 @ Z2))|((Z1 @ Z2)))))), inference(fof_simplification,[status(thm)],[mor])).
% 0.11/0.25 thf(c_0_19, plain, ((mimplies)=(^[Z0:$i > $o, Z1:$i > $o, Z2:$i]:((((~((Z0 @ Z2))))|((Z1 @ Z2)))))), inference(fof_simplification,[status(thm)],[mimplies])).
% 0.11/0.25 thf(c_0_20, plain, ((mexists_ind)=(^[Z0:mu > $i > $o, Z1:$i]:(~((![X35:mu]:((((exists_in_world @ X35 @ Z1))=>((~((Z0 @ X35 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[mexists_ind])).
% 0.11/0.25 thf(c_0_21, plain, ((mforall_ind)=(^[Z0:mu > $i > $o, Z1:$i]:(![X12:mu]:((((exists_in_world @ X12 @ Z1))=>((Z0 @ X12 @ Z1))))))), inference(fof_simplification,[status(thm)],[mforall_ind])).
% 0.11/0.25 thf(c_0_22, negated_conjecture, ~((mvalid @ (mbox_s4 @ (mexists_ind @ (^[X25:mu]:(mexists_ind @ (^[X22:mu]:(mimplies @ (mbox_s4 @ (mand @ (combo @ d @ X25) @ (h @ X22))) @ (mbox_s4 @ (open @ d)))))))))), inference(assume_negation,[status(cth)],[con])).
% 0.11/0.25 thf(c_0_23, plain, ((mand)=(^[Z0:$i > $o, Z1:$i > $o, Z2:$i]:(~(((((~((Z0 @ Z2))))|((~((Z1 @ Z2)))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_16, c_0_17]), c_0_18])).
% 0.11/0.25 thf(c_0_24, plain, ((mimplies)=(^[Z0:$i > $o, Z1:$i > $o, Z2:$i]:((((~((Z0 @ Z2))))|((Z1 @ Z2)))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_19, c_0_17]), c_0_18])).
% 0.11/0.25 thf(c_0_25, plain, ((mexists_ind)=(^[Z0:mu > $i > $o, Z1:$i]:(~((![X35:mu]:((((exists_in_world @ X35 @ Z1))=>((~((Z0 @ X35 @ Z1))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_20, c_0_17]), c_0_21])).
% 0.11/0.25 thf(c_0_26, plain, ((mvalid)=(^[Z0:$i > $o]:(![X3:$i]:((Z0 @ X3))))), inference(fof_simplification,[status(thm)],[mvalid])).
% 0.11/0.25 thf(c_0_27, plain, ((mbox_s4)=(^[Z0:$i > $o, Z1:$i]:(![X7:$i]:(((~((rel_s4 @ Z1 @ X7)))|((Z0 @ X7))))))), inference(fof_simplification,[status(thm)],[mbox_s4])).
% 0.11/0.25 thf(c_0_28, plain, ![X47:mu, X49:$i, X48:mu]:(((epred1_3 @ X48 @ X49 @ X47)<=>~(![X46:mu]:(((exists_in_world @ X46 @ X49)=>~(~((~(![X43:$i]:((~(rel_s4 @ X49 @ X43)|(~(~((~(closed @ X48 @ X43)|~(~((~(combo @ X48 @ X47 @ X43)|~(h @ X46 @ X43)))))))|![X42:$i]:((~(rel_s4 @ X43 @ X42)|(open @ X48 @ X42)))))))|~(![X45:$i]:((~(rel_s4 @ X49 @ X45)|(~(~((~(closed @ X48 @ X45)|~(~(((combo @ X48 @ X47 @ X45)|~(h @ o @ X45)))))))|![X44:$i]:((~(rel_s4 @ X45 @ X44)|(closed @ X48 @ X44))))))))))))))), introduced(definition)).
% 0.11/0.25 thf(c_0_29, negated_conjecture, ~(![X66:$i, X65:$i]:((~(rel_s4 @ X66 @ X65)|~(![X64:mu]:(((exists_in_world @ X64 @ X65)=>~(~(![X63:mu]:(((exists_in_world @ X63 @ X65)=>~((~(![X61:$i]:((~(rel_s4 @ X65 @ X61)|~((~(combo @ d @ X64 @ X61)|~(h @ X63 @ X61))))))|![X62:$i]:((~(rel_s4 @ X65 @ X62)|(open @ d @ X62))))))))))))))), 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(fof_simplification,[status(thm)],[c_0_22]), c_0_23]), c_0_24]), c_0_25]), c_0_26]), c_0_27])])).
% 0.11/0.25 thf(c_0_30, plain, ![X60:$i]:(~(![X59:mu]:(((exists_in_world @ X59 @ X60)=>~(![X58:$i]:((~(rel_s4 @ X60 @ X58)|(combo @ d @ X59 @ X58)))))))), inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[ax5]), c_0_25]), c_0_26]), c_0_27])])).
% 0.11/0.25 thf(c_0_31, plain, ![X47:mu, X49:$i, X48:mu]:(((epred1_3 @ X48 @ X49 @ X47)=>~(![X46:mu]:(((exists_in_world @ X46 @ X49)=>~(~((~(![X43:$i]:((~(rel_s4 @ X49 @ X43)|(~(~((~(closed @ X48 @ X43)|~(~((~(combo @ X48 @ X47 @ X43)|~(h @ X46 @ X43)))))))|![X42:$i]:((~(rel_s4 @ X43 @ X42)|(open @ X48 @ X42)))))))|~(![X45:$i]:((~(rel_s4 @ X49 @ X45)|(~(~((~(closed @ X48 @ X45)|~(~(((combo @ X48 @ X47 @ X45)|~(h @ o @ X45)))))))|![X44:$i]:((~(rel_s4 @ X45 @ X44)|(closed @ X48 @ X44))))))))))))))), inference(split_equiv,[status(thm)],[c_0_28])).
% 0.11/0.25 thf(c_0_32, negated_conjecture, ![X95:mu, X96:mu, X97:$i]:(((rel_s4 @ esk3_0 @ esk4_0)&((((combo @ d @ X95 @ X97)|~(rel_s4 @ esk4_0 @ X97)|~(exists_in_world @ X96 @ esk4_0)|~(exists_in_world @ X95 @ esk4_0))&((h @ X96 @ X97)|~(rel_s4 @ esk4_0 @ X97)|~(exists_in_world @ X96 @ esk4_0)|~(exists_in_world @ X95 @ esk4_0)))&(((rel_s4 @ esk4_0 @ (esk5_2 @ X95 @ X96))|~(exists_in_world @ X96 @ esk4_0)|~(exists_in_world @ X95 @ esk4_0))&(~(open @ d @ (esk5_2 @ X95 @ X96))|~(exists_in_world @ X96 @ esk4_0)|~(exists_in_world @ X95 @ esk4_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(fof_nnf,[status(thm)],[c_0_29])])])])])])).
% 0.11/0.25 thf(c_0_33, plain, ![X90:$i, X92:$i]:(((exists_in_world @ (esk2_1 @ X90) @ X90)&(~(rel_s4 @ X90 @ X92)|(combo @ d @ (esk2_1 @ X90) @ X92)))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])])])])).
% 0.11/0.25 thf(c_0_34, plain, ((mreflexive)=(^[Z0:$i > $i > $o]:(![X16:$i]:((Z0 @ X16 @ X16))))), inference(fof_simplification,[status(thm)],[mreflexive])).
% 0.11/0.25 thf(c_0_35, plain, ![X99:mu, X100:$i, X101:mu, X103:$i, X104:$i, X105:$i, X106:$i]:((((exists_in_world @ (esk6_3 @ X99 @ X100 @ X101) @ X100)|~(epred1_3 @ X101 @ X100 @ X99))&((~(rel_s4 @ X100 @ X103)|(~(closed @ X101 @ X103)|(~(combo @ X101 @ X99 @ X103)|~(h @ (esk6_3 @ X99 @ X100 @ X101) @ X103))|(~(rel_s4 @ X103 @ X104)|(open @ X101 @ X104)))|~(epred1_3 @ X101 @ X100 @ X99))&(~(rel_s4 @ X100 @ X105)|(~(closed @ X101 @ X105)|((combo @ X101 @ X99 @ X105)|~(h @ o @ X105))|(~(rel_s4 @ X105 @ X106)|(closed @ X101 @ X106)))|~(epred1_3 @ X101 @ X100 @ X99))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])])])])])).
% 0.11/0.25 thf(c_0_36, negated_conjecture, ![X3:$i, X10:mu, X12:mu]:(((h @ X10 @ X3)|~((rel_s4 @ esk4_0 @ X3))|~((exists_in_world @ X10 @ esk4_0))|~((exists_in_world @ X12 @ esk4_0)))), inference(split_conjunct,[status(thm)],[c_0_32])).
% 0.11/0.25 thf(c_0_37, plain, ![X3:$i]:((exists_in_world @ (esk2_1 @ X3) @ X3)), inference(split_conjunct,[status(thm)],[c_0_33])).
% 0.11/0.25 thf(c_0_38, plain, ![X50:$i, X49:$i]:((~(rel_s4 @ X50 @ X49)|![X48:mu]:(((exists_in_world @ X48 @ X49)=>![X47:mu]:(((exists_in_world @ X47 @ X49)=>(epred1_3 @ X48 @ X49 @ X47))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[ax1]), c_0_17]), c_0_23]), c_0_24]), c_0_21]), c_0_25]), c_0_26]), c_0_27])]), c_0_28])).
% 0.11/0.25 thf(c_0_39, plain, ![X38:$i]:((rel_s4 @ X38 @ X38)), inference(apply_def,[status(thm)],[a1, c_0_34])).
% 0.11/0.25 thf(c_0_40, plain, ![X3:$i, X10:mu, X7:$i, X16:$i, X12:mu]:(((open @ X10 @ X16)|~((rel_s4 @ X3 @ X7))|~((closed @ X10 @ X7))|~((combo @ X10 @ X12 @ X7))|~((h @ (esk6_3 @ X12 @ X3 @ X10) @ X7))|~((rel_s4 @ X7 @ X16))|~((epred1_3 @ X10 @ X3 @ X12)))), inference(split_conjunct,[status(thm)],[c_0_35])).
% 0.11/0.25 thf(c_0_41, negated_conjecture, ![X10:mu, X3:$i]:(((h @ X10 @ X3)|~((exists_in_world @ X10 @ esk4_0))|~((rel_s4 @ esk4_0 @ X3)))), inference(spm,[status(thm)],[c_0_36, c_0_37])).
% 0.11/0.25 thf(c_0_42, plain, ![X79:$i, X80:$i, X81:mu, X82:mu]:((~(rel_s4 @ X79 @ X80)|(~(exists_in_world @ X81 @ X80)|(~(exists_in_world @ X82 @ X80)|(epred1_3 @ X81 @ X80 @ X82))))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])])])])).
% 0.11/0.25 thf(c_0_43, plain, ![X69:$i]:((rel_s4 @ X69 @ X69)), inference(variable_rename,[status(thm)],[c_0_39])).
% 0.11/0.25 thf(c_0_44, plain, ![X52:$i, X51:$i]:((~(rel_s4 @ X52 @ X51)|(closed @ d @ X51))), inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[ax2, c_0_26]), c_0_27])])).
% 0.11/0.25 thf(c_0_45, plain, ![X3:$i, X7:$i, X10:mu, X12:mu, X16:$i]:(((open @ X10 @ X3)|~((exists_in_world @ (esk6_3 @ X12 @ X7 @ X10) @ esk4_0))|~((epred1_3 @ X10 @ X7 @ X12))|~((combo @ X10 @ X12 @ X16))|~((rel_s4 @ esk4_0 @ X16))|~((rel_s4 @ X16 @ X3))|~((rel_s4 @ X7 @ X16))|~((closed @ X10 @ X16)))), inference(spm,[status(thm)],[c_0_40, c_0_41])).
% 0.11/0.25 thf(c_0_46, plain, ![X3:$i, X12:mu, X10:mu]:(((exists_in_world @ (esk6_3 @ X10 @ X3 @ X12) @ X3)|~((epred1_3 @ X12 @ X3 @ X10)))), inference(split_conjunct,[status(thm)],[c_0_35])).
% 0.11/0.25 thf(c_0_47, plain, ![X3:$i, X12:mu, X10:mu, X7:$i]:(((epred1_3 @ X10 @ X7 @ X12)|~((rel_s4 @ X3 @ X7))|~((exists_in_world @ X10 @ X7))|~((exists_in_world @ X12 @ X7)))), inference(split_conjunct,[status(thm)],[c_0_42])).
% 0.11/0.25 thf(c_0_48, plain, ![X3:$i]:((rel_s4 @ X3 @ X3)), inference(split_conjunct,[status(thm)],[c_0_43])).
% 0.11/0.25 thf(c_0_49, plain, ![X83:$i, X84:$i]:((~(rel_s4 @ X83 @ X84)|(closed @ d @ X84))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_44])])).
% 0.11/0.25 thf(c_0_50, plain, ![X3:$i, X12:mu, X10:mu, X7:$i]:(((open @ X10 @ X3)|~((epred1_3 @ X10 @ esk4_0 @ X12))|~((combo @ X10 @ X12 @ X7))|~((rel_s4 @ esk4_0 @ X7))|~((rel_s4 @ X7 @ X3))|~((closed @ X10 @ X7)))), inference(spm,[status(thm)],[c_0_45, c_0_46])).
% 0.11/0.25 thf(c_0_51, plain, ![X12:mu, X10:mu, X3:$i]:(((epred1_3 @ X10 @ X3 @ X12)|~((exists_in_world @ X12 @ X3))|~((exists_in_world @ X10 @ X3)))), inference(spm,[status(thm)],[c_0_47, c_0_48])).
% 0.11/0.25 thf(c_0_52, negated_conjecture, ![X3:$i, X12:mu, X10:mu]:(((combo @ d @ X10 @ X3)|~((rel_s4 @ esk4_0 @ X3))|~((exists_in_world @ X12 @ esk4_0))|~((exists_in_world @ X10 @ esk4_0)))), inference(split_conjunct,[status(thm)],[c_0_32])).
% 0.11/0.25 thf(c_0_53, plain, ![X78:$i]:((exists_in_world @ d @ X78)), inference(variable_rename,[status(thm)],[existence_of_d_ax])).
% 0.11/0.25 thf(c_0_54, plain, ![X3:$i, X7:$i]:(((closed @ d @ X7)|~((rel_s4 @ X3 @ X7)))), inference(split_conjunct,[status(thm)],[c_0_49])).
% 0.11/0.25 thf(c_0_55, plain, ![X57:$i, X56:$i]:((~(rel_s4 @ X57 @ X56)|![X55:mu]:(((exists_in_world @ X55 @ X56)=>~(~((~(open @ X55 @ X56)|~(closed @ X55 @ X56)))))))), inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[ax4]), c_0_17]), c_0_23]), c_0_21]), c_0_26]), c_0_27])])).
% 0.11/0.25 thf(c_0_56, plain, ![X3:$i, X12:mu, X10:mu, X7:$i]:(((open @ X10 @ X3)|~((combo @ X10 @ X12 @ X7))|~((rel_s4 @ esk4_0 @ X7))|~((exists_in_world @ X12 @ esk4_0))|~((exists_in_world @ X10 @ esk4_0))|~((rel_s4 @ X7 @ X3))|~((closed @ X10 @ X7)))), inference(spm,[status(thm)],[c_0_50, c_0_51])).
% 0.11/0.25 thf(c_0_57, negated_conjecture, ![X10:mu, X3:$i]:(((combo @ d @ X10 @ X3)|~((exists_in_world @ X10 @ esk4_0))|~((rel_s4 @ esk4_0 @ X3)))), inference(spm,[status(thm)],[c_0_52, c_0_37])).
% 0.11/0.25 thf(c_0_58, plain, ![X3:$i]:((exists_in_world @ d @ X3)), inference(split_conjunct,[status(thm)],[c_0_53])).
% 0.11/0.25 thf(c_0_59, plain, ![X3:$i]:((closed @ d @ X3)), inference(spm,[status(thm)],[c_0_54, c_0_48])).
% 0.11/0.25 thf(c_0_60, plain, ![X87:$i, X88:$i, X89:mu]:((~(rel_s4 @ X87 @ X88)|(~(exists_in_world @ X89 @ X88)|(~(open @ X89 @ X88)|~(closed @ X89 @ X88))))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_55])])])])).
% 0.11/0.25 thf(c_0_61, negated_conjecture, ![X10:mu, X7:$i, X3:$i]:(((open @ d @ X3)|~((rel_s4 @ esk4_0 @ X7))|~((exists_in_world @ X10 @ esk4_0))|~((rel_s4 @ X7 @ X3)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56, c_0_57]), c_0_58]), c_0_59])])).
% 0.11/0.25 thf(c_0_62, plain, ![X3:$i, X10:mu, X7:$i]:((~((rel_s4 @ X3 @ X7))|~((exists_in_world @ X10 @ X7))|~((open @ X10 @ X7))|~((closed @ X10 @ X7)))), inference(split_conjunct,[status(thm)],[c_0_60])).
% 0.11/0.25 thf(c_0_63, negated_conjecture, ![X10:mu, X3:$i]:(((open @ d @ X3)|~((exists_in_world @ X10 @ esk4_0))|~((rel_s4 @ esk4_0 @ X3)))), inference(spm,[status(thm)],[c_0_61, c_0_48])).
% 0.11/0.25 thf(c_0_64, plain, ![X10:mu, X3:$i]:((~((exists_in_world @ X10 @ X3))|~((closed @ X10 @ X3))|~((open @ X10 @ X3)))), inference(spm,[status(thm)],[c_0_62, c_0_48])).
% 0.11/0.25 thf(c_0_65, negated_conjecture, ![X3:$i]:(((open @ d @ X3)|~((rel_s4 @ esk4_0 @ X3)))), inference(spm,[status(thm)],[c_0_63, c_0_37])).
% 0.11/0.25 thf(c_0_66, negated_conjecture, ![X3:$i]:(~((rel_s4 @ esk4_0 @ X3))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64, c_0_65]), c_0_58]), c_0_59])])).
% 0.11/0.25 thf(c_0_67, negated_conjecture, ($false), inference(spm,[status(thm)],[c_0_66, c_0_48]), ['proof']).
% 0.11/0.25 % SZS output end CNFRefutation
% 0.11/0.25 % Parsed axioms : 88
% 0.11/0.25 % Removed by relevancy pruning/SinE : 0
% 0.11/0.25 % Initial clauses : 64
% 0.11/0.25 % Removed in clause preprocessing : 44
% 0.11/0.25 % Initial clauses in saturation : 20
% 0.11/0.25 % Processed clauses : 67
% 0.11/0.25 % ...of these trivial : 0
% 0.11/0.25 % ...subsumed : 1
% 0.11/0.25 % ...remaining for further processing : 66
% 0.11/0.25 % Other redundant clauses eliminated : 0
% 0.11/0.25 % Clauses deleted for lack of memory : 0
% 0.11/0.25 % Backward-subsumed : 15
% 0.11/0.25 % Backward-rewritten : 2
% 0.11/0.25 % Generated clauses : 66
% 0.11/0.25 % ...of the previous two non-redundant : 58
% 0.11/0.25 % ...aggressively subsumed : 0
% 0.11/0.25 % Contextual simplify-reflections : 0
% 0.11/0.25 % Paramodulations : 66
% 0.11/0.25 % Factorizations : 0
% 0.11/0.25 % NegExts : 0
% 0.11/0.25 % Equation resolutions : 0
% 0.11/0.25 % Disequality decompositions : 0
% 0.11/0.25 % Total rewrite steps : 15
% 0.11/0.25 % ...of those cached : 5
% 0.11/0.25 % Propositional unsat checks : 0
% 0.11/0.25 % Propositional check models : 0
% 0.11/0.25 % Propositional check unsatisfiable : 0
% 0.11/0.25 % Propositional clauses : 0
% 0.11/0.25 % Propositional clauses after purity: 0
% 0.11/0.25 % Propositional unsat core size : 0
% 0.11/0.25 % Propositional preprocessing time : 0.000
% 0.11/0.25 % Propositional encoding time : 0.000
% 0.11/0.25 % Propositional solver time : 0.000
% 0.11/0.25 % Success case prop preproc time : 0.000
% 0.11/0.25 % Success case prop encoding time : 0.000
% 0.11/0.25 % Success case prop solver time : 0.000
% 0.11/0.25 % Current number of processed clauses : 29
% 0.11/0.25 % Positive orientable unit clauses : 10
% 0.11/0.25 % Positive unorientable unit clauses: 0
% 0.11/0.25 % Negative unit clauses : 1
% 0.11/0.25 % Non-unit-clauses : 18
% 0.11/0.25 % Current number of unprocessed clauses: 17
% 0.11/0.25 % ...number of literals in the above : 64
% 0.11/0.25 % Current number of archived formulas : 0
% 0.11/0.25 % Current number of archived clauses : 37
% 0.11/0.25 % Clause-clause subsumption calls (NU) : 185
% 0.11/0.25 % Rec. Clause-clause subsumption calls : 81
% 0.11/0.25 % Non-unit clause-clause subsumptions : 8
% 0.11/0.25 % Unit Clause-clause subsumption calls : 15
% 0.11/0.25 % Rewrite failures with RHS unbound : 0
% 0.11/0.25 % BW rewrite match attempts : 4
% 0.11/0.25 % BW rewrite match successes : 2
% 0.11/0.25 % Condensation attempts : 0
% 0.11/0.25 % Condensation successes : 0
% 0.11/0.25 % Termbank termtop insertions : 7497
% 0.11/0.25 % Search garbage collected termcells : 2283
% 0.11/0.25
% 0.11/0.25 % -------------------------------------------------
% 0.11/0.25 % User time : 0.008 s
% 0.11/0.25 % System time : 0.003 s
% 0.11/0.25 % Total time : 0.011 s
% 0.11/0.25 % Maximum resident set size: 3972 pages
% 0.11/0.25
% 0.11/0.25 % -------------------------------------------------
% 0.11/0.25 % User time : 0.036 s
% 0.11/0.25 % System time : 0.020 s
% 0.11/0.25 % Total time : 0.056 s
% 0.11/0.25 % Maximum resident set size: 4864 pages
% 0.11/0.25 % E exiting
%------------------------------------------------------------------------------