TSTP Solution File: SYO460^5 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO460^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 09:04:49 EDT 2024
% Result : Theorem 0.20s 0.39s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO460^5 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon May 20 08:46:38 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a TH0_THM_EQU_NAR problem
% 0.14/0.35 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.37 % (27204)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.38 % (27198)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.20/0.38 % (27199)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.20/0.38 % (27200)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.38 % (27197)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.20/0.38 % (27204)Instruction limit reached!
% 0.20/0.38 % (27204)------------------------------
% 0.20/0.38 % (27204)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.38 % (27204)Termination reason: Unknown
% 0.20/0.38 % (27204)Termination phase: shuffling
% 0.20/0.38
% 0.20/0.38 % (27204)Memory used [KB]: 1023
% 0.20/0.38 % (27204)Time elapsed: 0.003 s
% 0.20/0.38 % (27204)Instructions burned: 3 (million)
% 0.20/0.38 % (27204)------------------------------
% 0.20/0.38 % (27204)------------------------------
% 0.20/0.38 % (27201)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.38 % (27202)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.20/0.38 % (27200)Instruction limit reached!
% 0.20/0.38 % (27200)------------------------------
% 0.20/0.38 % (27200)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.38 % (27200)Termination reason: Unknown
% 0.20/0.38 % (27200)Termination phase: shuffling
% 0.20/0.38
% 0.20/0.38 % (27201)Instruction limit reached!
% 0.20/0.38 % (27201)------------------------------
% 0.20/0.38 % (27201)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.38 % (27201)Termination reason: Unknown
% 0.20/0.38 % (27201)Termination phase: shuffling
% 0.20/0.38
% 0.20/0.38 % (27201)Memory used [KB]: 1023
% 0.20/0.38 % (27201)Time elapsed: 0.003 s
% 0.20/0.38 % (27201)Instructions burned: 2 (million)
% 0.20/0.38 % (27201)------------------------------
% 0.20/0.38 % (27201)------------------------------
% 0.20/0.38 % (27200)Memory used [KB]: 1023
% 0.20/0.38 % (27200)Time elapsed: 0.003 s
% 0.20/0.38 % (27200)Instructions burned: 2 (million)
% 0.20/0.38 % (27200)------------------------------
% 0.20/0.38 % (27200)------------------------------
% 0.20/0.38 % (27203)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.20/0.38 % (27198)Instruction limit reached!
% 0.20/0.38 % (27198)------------------------------
% 0.20/0.38 % (27198)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.38 % (27198)Termination reason: Unknown
% 0.20/0.38 % (27198)Termination phase: shuffling
% 0.20/0.38
% 0.20/0.38 % (27198)Memory used [KB]: 1023
% 0.20/0.38 % (27198)Time elapsed: 0.004 s
% 0.20/0.38 % (27198)Instructions burned: 4 (million)
% 0.20/0.38 % (27198)------------------------------
% 0.20/0.38 % (27198)------------------------------
% 0.20/0.38 % (27202)Refutation not found, incomplete strategy
% 0.20/0.38 % (27202)------------------------------
% 0.20/0.38 % (27202)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.38 % (27202)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.38
% 0.20/0.38
% 0.20/0.38 % (27202)Memory used [KB]: 5628
% 0.20/0.38 % (27202)Time elapsed: 0.007 s
% 0.20/0.38 % (27202)Instructions burned: 8 (million)
% 0.20/0.38 % (27202)------------------------------
% 0.20/0.38 % (27202)------------------------------
% 0.20/0.39 % (27197)First to succeed.
% 0.20/0.39 % (27199)Also succeeded, but the first one will report.
% 0.20/0.39 % (27205)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.20/0.39 % (27197)Refutation found. Thanks to Tanya!
% 0.20/0.39 % SZS status Theorem for theBenchmark
% 0.20/0.39 % SZS output start Proof for theBenchmark
% 0.20/0.39 thf(type_def_5, type, mu: $tType).
% 0.20/0.39 thf(func_def_0, type, mu: $tType).
% 0.20/0.39 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.20/0.39 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.39 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.20/0.39 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.39 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.39 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.39 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.39 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.39 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.39 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.20/0.39 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.20/0.39 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.20/0.39 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.20/0.39 thf(func_def_15, type, mtrue: $i > $o).
% 0.20/0.39 thf(func_def_16, type, mfalse: $i > $o).
% 0.20/0.39 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.20/0.39 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.20/0.39 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.20/0.39 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.20/0.39 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.20/0.39 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.20/0.39 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.20/0.39 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.20/0.39 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.20/0.39 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.20/0.39 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.20/0.39 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.20/0.39 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.20/0.39 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.20/0.39 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.20/0.39 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.20/0.39 thf(func_def_33, type, rel_s4: $i > $i > $o).
% 0.20/0.39 thf(func_def_34, type, mbox_s4: ($i > $o) > $i > $o).
% 0.20/0.39 thf(func_def_35, type, mdia_s4: ($i > $o) > $i > $o).
% 0.20/0.39 thf(func_def_36, type, p: $i > $o).
% 0.20/0.39 thf(func_def_37, type, q: $i > $o).
% 0.20/0.39 thf(func_def_38, type, r: $i > $o).
% 0.20/0.39 thf(f286,plain,(
% 0.20/0.39 $false),
% 0.20/0.39 inference(avatar_sat_refutation,[],[f241,f247,f253,f254,f268,f285])).
% 0.20/0.39 thf(f285,plain,(
% 0.20/0.39 ~spl0_3 | ~spl0_5),
% 0.20/0.39 inference(avatar_contradiction_clause,[],[f284])).
% 0.20/0.39 thf(f284,plain,(
% 0.20/0.39 $false | (~spl0_3 | ~spl0_5)),
% 0.20/0.39 inference(trivial_inequality_removal,[],[f281])).
% 0.20/0.39 thf(f281,plain,(
% 0.20/0.39 ($true = $false) | (~spl0_3 | ~spl0_5)),
% 0.20/0.39 inference(superposition,[],[f234,f279])).
% 0.20/0.39 thf(f279,plain,(
% 0.20/0.39 ($false = (p @ sK2)) | ~spl0_5),
% 0.20/0.39 inference(trivial_inequality_removal,[],[f276])).
% 0.20/0.39 thf(f276,plain,(
% 0.20/0.39 ($true = $false) | ($false = (p @ sK2)) | ~spl0_5),
% 0.20/0.39 inference(superposition,[],[f245,f212])).
% 0.20/0.39 thf(f212,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (($false = (rel_s4 @ sK1 @ X1)) | ($false = (p @ X1))) )),
% 0.20/0.39 inference(not_proxy_clausification,[],[f211])).
% 0.20/0.39 thf(f211,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (($true = (~ (p @ X1))) | ($false = (rel_s4 @ sK1 @ X1))) )),
% 0.20/0.39 inference(not_proxy_clausification,[],[f210])).
% 0.20/0.39 thf(f210,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (($true = (~ (rel_s4 @ sK1 @ X1))) | ($true = (~ (p @ X1)))) )),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f209])).
% 0.20/0.39 thf(f209,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (($true = ((~ (rel_s4 @ sK1 @ X1)) | (~ (p @ X1))))) )),
% 0.20/0.39 inference(beta_eta_normalization,[],[f208])).
% 0.20/0.39 thf(f208,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_s4 @ sK1 @ Y0)) | (~ (p @ Y0)))) @ X1))) )),
% 0.20/0.39 inference(pi_clausification,[],[f207])).
% 0.20/0.39 thf(f207,plain,(
% 0.20/0.39 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK1 @ Y0)) | (~ (p @ Y0))))))),
% 0.20/0.39 inference(not_proxy_clausification,[],[f165])).
% 0.20/0.39 thf(f165,plain,(
% 0.20/0.39 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK1 @ Y0)) | (~ (p @ Y0)))))))),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f164])).
% 0.20/0.39 thf(f164,plain,(
% 0.20/0.39 ($false = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK1 @ Y0)) | ((~ (p @ Y0)) | (~ (q @ Y0))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK1 @ Y0)) | ((~ (p @ Y0)) | (~ (r @ Y0))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK1 @ Y0)) | (~ (p @ Y0))))))))),
% 0.20/0.39 inference(beta_eta_normalization,[],[f163])).
% 0.20/0.39 thf(f163,plain,(
% 0.20/0.39 (((^[Y0 : $i]: ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | ((~ (p @ Y1)) | (~ (q @ Y1))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | ((~ (p @ Y1)) | (~ (r @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (p @ Y1)))))))) @ sK1) = $false)),
% 0.20/0.39 inference(sigma_clausification,[],[f162])).
% 0.20/0.39 thf(f162,plain,(
% 0.20/0.39 ($true != (!! @ $i @ (^[Y0 : $i]: ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | ((~ (p @ Y1)) | (~ (q @ Y1))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | ((~ (p @ Y1)) | (~ (r @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (p @ Y1))))))))))),
% 0.20/0.39 inference(boolean_simplification,[],[f161])).
% 0.20/0.39 thf(f161,plain,(
% 0.20/0.39 ($true != (!! @ $i @ (^[Y0 : $i]: ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (~ ((~ (p @ Y1)) | (~ (q @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | ((~ (p @ Y1)) | (~ (r @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (p @ Y1))))))))))),
% 0.20/0.39 inference(boolean_simplification,[],[f160])).
% 0.20/0.39 thf(f160,plain,(
% 0.20/0.39 ($true != (!! @ $i @ (^[Y0 : $i]: ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (~ ((~ (p @ Y1)) | (~ (q @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (~ ((~ (p @ Y1)) | (~ (r @ Y1))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (p @ Y1))))))))))),
% 0.20/0.39 inference(beta_eta_normalization,[],[f155])).
% 0.20/0.39 thf(f155,plain,(
% 0.20/0.39 ($true != ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))) @ p @ q)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))) @ p @ r))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ p))))),
% 0.20/0.39 inference(definition_unfolding,[],[f137,f135,f145,f121,f153,f144,f153,f144,f153])).
% 0.20/0.39 thf(f144,plain,(
% 0.20/0.39 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 0.20/0.39 inference(definition_unfolding,[],[f129,f133,f121,f133,f133])).
% 0.20/0.39 thf(f133,plain,(
% 0.20/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.20/0.39 inference(cnf_transformation,[],[f55])).
% 0.20/0.39 thf(f55,plain,(
% 0.20/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.20/0.39 inference(fool_elimination,[],[f54])).
% 0.20/0.39 thf(f54,plain,(
% 0.20/0.39 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.20/0.39 inference(rectify,[],[f3])).
% 0.20/0.39 thf(f3,axiom,(
% 0.20/0.39 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)),
% 0.20/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.20/0.39 thf(f129,plain,(
% 0.20/0.39 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.20/0.39 inference(cnf_transformation,[],[f94])).
% 0.20/0.39 thf(f94,plain,(
% 0.20/0.39 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.20/0.39 inference(fool_elimination,[],[f93])).
% 0.20/0.39 thf(f93,plain,(
% 0.20/0.39 (mand = (^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))))),
% 0.20/0.39 inference(rectify,[],[f5])).
% 0.20/0.39 thf(f5,axiom,(
% 0.20/0.39 (mand = (^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))))),
% 0.20/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand)).
% 0.20/0.39 thf(f153,plain,(
% 0.20/0.39 (mdia_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))))),
% 0.20/0.39 inference(definition_unfolding,[],[f122,f133,f132,f133])).
% 0.20/0.39 thf(f132,plain,(
% 0.20/0.39 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.20/0.39 inference(cnf_transformation,[],[f63])).
% 0.20/0.39 thf(f63,plain,(
% 0.20/0.39 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.20/0.39 inference(fool_elimination,[],[f62])).
% 0.20/0.39 thf(f62,plain,(
% 0.20/0.39 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : ((X0 @ X2) | ~(rel_s4 @ X1 @ X2)))) = mbox_s4)),
% 0.20/0.39 inference(rectify,[],[f32])).
% 0.20/0.39 thf(f32,axiom,(
% 0.20/0.39 ((^[X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(rel_s4 @ X2 @ X7)))) = mbox_s4)),
% 0.20/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_s4)).
% 0.20/0.39 thf(f122,plain,(
% 0.20/0.39 (mdia_s4 = (^[Y0 : $i > $o]: (mnot @ (mbox_s4 @ (mnot @ Y0)))))),
% 0.20/0.39 inference(cnf_transformation,[],[f100])).
% 0.20/0.39 thf(f100,plain,(
% 0.20/0.39 (mdia_s4 = (^[Y0 : $i > $o]: (mnot @ (mbox_s4 @ (mnot @ Y0)))))),
% 0.20/0.39 inference(fool_elimination,[],[f99])).
% 0.20/0.39 thf(f99,plain,(
% 0.20/0.39 ((^[X0 : $i > $o] : (mnot @ (mbox_s4 @ (mnot @ X0)))) = mdia_s4)),
% 0.20/0.39 inference(rectify,[],[f33])).
% 0.20/0.39 thf(f33,axiom,(
% 0.20/0.39 ((^[X3 : $i > $o] : (mnot @ (mbox_s4 @ (mnot @ X3)))) = mdia_s4)),
% 0.20/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_s4)).
% 0.20/0.39 thf(f121,plain,(
% 0.20/0.39 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.20/0.39 inference(cnf_transformation,[],[f78])).
% 0.20/0.39 thf(f78,plain,(
% 0.20/0.39 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.20/0.39 inference(fool_elimination,[],[f77])).
% 0.20/0.39 thf(f77,plain,(
% 0.20/0.39 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 0.20/0.39 inference(rectify,[],[f4])).
% 0.20/0.39 thf(f4,axiom,(
% 0.20/0.39 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))))),
% 0.20/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.20/0.39 thf(f145,plain,(
% 0.20/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.20/0.39 inference(definition_unfolding,[],[f140,f121,f133])).
% 0.20/0.39 thf(f140,plain,(
% 0.20/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.20/0.39 inference(cnf_transformation,[],[f67])).
% 0.20/0.39 thf(f67,plain,(
% 0.20/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.20/0.39 inference(fool_elimination,[],[f66])).
% 0.20/0.39 thf(f66,plain,(
% 0.20/0.39 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.20/0.39 inference(rectify,[],[f6])).
% 0.20/0.39 thf(f6,axiom,(
% 0.20/0.39 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.20/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.20/0.39 thf(f135,plain,(
% 0.20/0.39 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.20/0.39 inference(cnf_transformation,[],[f106])).
% 0.20/0.39 thf(f106,plain,(
% 0.20/0.39 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.20/0.39 inference(fool_elimination,[],[f105])).
% 0.20/0.39 thf(f105,plain,(
% 0.20/0.39 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.20/0.39 inference(rectify,[],[f28])).
% 0.20/0.39 thf(f28,axiom,(
% 0.20/0.39 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.20/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.20/0.39 thf(f137,plain,(
% 0.20/0.39 ((mvalid @ (mimplies @ (mor @ (mdia_s4 @ (mand @ p @ q)) @ (mdia_s4 @ (mand @ p @ r))) @ (mdia_s4 @ p))) != $true)),
% 0.20/0.39 inference(cnf_transformation,[],[f107])).
% 0.20/0.39 thf(f107,plain,(
% 0.20/0.39 ((mvalid @ (mimplies @ (mor @ (mdia_s4 @ (mand @ p @ q)) @ (mdia_s4 @ (mand @ p @ r))) @ (mdia_s4 @ p))) != $true)),
% 0.20/0.39 inference(flattening,[],[f61])).
% 0.20/0.39 thf(f61,plain,(
% 0.20/0.39 ~((mvalid @ (mimplies @ (mor @ (mdia_s4 @ (mand @ p @ q)) @ (mdia_s4 @ (mand @ p @ r))) @ (mdia_s4 @ p))) = $true)),
% 0.20/0.39 inference(fool_elimination,[],[f60])).
% 0.20/0.39 thf(f60,plain,(
% 0.20/0.39 ~(mvalid @ (mimplies @ (mor @ (mdia_s4 @ (mand @ p @ q)) @ (mdia_s4 @ (mand @ p @ r))) @ (mdia_s4 @ p)))),
% 0.20/0.39 inference(rectify,[],[f37])).
% 0.20/0.39 thf(f37,negated_conjecture,(
% 0.20/0.39 ~(mvalid @ (mimplies @ (mor @ (mdia_s4 @ (mand @ p @ q)) @ (mdia_s4 @ (mand @ p @ r))) @ (mdia_s4 @ p)))),
% 0.20/0.39 inference(negated_conjecture,[],[f36])).
% 0.20/0.39 thf(f36,conjecture,(
% 0.20/0.39 (mvalid @ (mimplies @ (mor @ (mdia_s4 @ (mand @ p @ q)) @ (mdia_s4 @ (mand @ p @ r))) @ (mdia_s4 @ p)))),
% 0.20/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove)).
% 0.20/0.39 thf(f245,plain,(
% 0.20/0.39 ($true = (rel_s4 @ sK1 @ sK2)) | ~spl0_5),
% 0.20/0.39 inference(avatar_component_clause,[],[f243])).
% 0.20/0.39 thf(f243,plain,(
% 0.20/0.39 spl0_5 <=> ($true = (rel_s4 @ sK1 @ sK2))),
% 0.20/0.39 introduced(avatar_definition,[new_symbols(naming,[spl0_5])])).
% 0.20/0.39 thf(f234,plain,(
% 0.20/0.39 ($true = (p @ sK2)) | ~spl0_3),
% 0.20/0.39 inference(avatar_component_clause,[],[f232])).
% 0.20/0.39 thf(f232,plain,(
% 0.20/0.39 spl0_3 <=> ($true = (p @ sK2))),
% 0.20/0.39 introduced(avatar_definition,[new_symbols(naming,[spl0_3])])).
% 0.20/0.39 thf(f268,plain,(
% 0.20/0.39 ~spl0_4 | ~spl0_6),
% 0.20/0.39 inference(avatar_contradiction_clause,[],[f267])).
% 0.20/0.39 thf(f267,plain,(
% 0.20/0.39 $false | (~spl0_4 | ~spl0_6)),
% 0.20/0.39 inference(trivial_inequality_removal,[],[f263])).
% 0.20/0.39 thf(f263,plain,(
% 0.20/0.39 ($true = $false) | (~spl0_4 | ~spl0_6)),
% 0.20/0.39 inference(superposition,[],[f261,f239])).
% 0.20/0.39 thf(f239,plain,(
% 0.20/0.39 ($true = (p @ sK3)) | ~spl0_4),
% 0.20/0.39 inference(avatar_component_clause,[],[f237])).
% 0.20/0.39 thf(f237,plain,(
% 0.20/0.39 spl0_4 <=> ($true = (p @ sK3))),
% 0.20/0.39 introduced(avatar_definition,[new_symbols(naming,[spl0_4])])).
% 0.20/0.39 thf(f261,plain,(
% 0.20/0.39 ($false = (p @ sK3)) | ~spl0_6),
% 0.20/0.39 inference(trivial_inequality_removal,[],[f258])).
% 0.20/0.39 thf(f258,plain,(
% 0.20/0.39 ($true = $false) | ($false = (p @ sK3)) | ~spl0_6),
% 0.20/0.39 inference(superposition,[],[f251,f212])).
% 0.20/0.39 thf(f251,plain,(
% 0.20/0.39 ($true = (rel_s4 @ sK1 @ sK3)) | ~spl0_6),
% 0.20/0.39 inference(avatar_component_clause,[],[f249])).
% 0.20/0.39 thf(f249,plain,(
% 0.20/0.39 spl0_6 <=> ($true = (rel_s4 @ sK1 @ sK3))),
% 0.20/0.39 introduced(avatar_definition,[new_symbols(naming,[spl0_6])])).
% 0.20/0.39 thf(f254,plain,(
% 0.20/0.39 spl0_6 | spl0_5),
% 0.20/0.39 inference(avatar_split_clause,[],[f180,f243,f249])).
% 0.20/0.39 thf(f180,plain,(
% 0.20/0.39 ($true = (rel_s4 @ sK1 @ sK3)) | ($true = (rel_s4 @ sK1 @ sK2))),
% 0.20/0.39 inference(not_proxy_clausification,[],[f179])).
% 0.20/0.39 thf(f179,plain,(
% 0.20/0.39 ($true = (rel_s4 @ sK1 @ sK3)) | ($false = (~ (rel_s4 @ sK1 @ sK2)))),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f177])).
% 0.20/0.39 thf(f177,plain,(
% 0.20/0.39 ($false = ((~ (rel_s4 @ sK1 @ sK2)) | ((~ (p @ sK2)) | (~ (q @ sK2))))) | ($true = (rel_s4 @ sK1 @ sK3))),
% 0.20/0.39 inference(not_proxy_clausification,[],[f176])).
% 0.20/0.39 thf(f176,plain,(
% 0.20/0.39 ($false = (~ (rel_s4 @ sK1 @ sK3))) | ($false = ((~ (rel_s4 @ sK1 @ sK2)) | ((~ (p @ sK2)) | (~ (q @ sK2)))))),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f174])).
% 0.20/0.39 thf(f174,plain,(
% 0.20/0.39 ($false = ((~ (rel_s4 @ sK1 @ sK3)) | ((~ (p @ sK3)) | (~ (r @ sK3))))) | ($false = ((~ (rel_s4 @ sK1 @ sK2)) | ((~ (p @ sK2)) | (~ (q @ sK2)))))),
% 0.20/0.39 inference(beta_eta_normalization,[],[f173])).
% 0.20/0.39 thf(f173,plain,(
% 0.20/0.39 (((^[Y0 : $i]: ((~ (rel_s4 @ sK1 @ Y0)) | ((~ (p @ Y0)) | (~ (r @ Y0))))) @ sK3) = $false) | ($false = ((~ (rel_s4 @ sK1 @ sK2)) | ((~ (p @ sK2)) | (~ (q @ sK2)))))),
% 0.20/0.39 inference(sigma_clausification,[],[f172])).
% 0.20/0.39 thf(f172,plain,(
% 0.20/0.39 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK1 @ Y0)) | ((~ (p @ Y0)) | (~ (r @ Y0))))))) | ($false = ((~ (rel_s4 @ sK1 @ sK2)) | ((~ (p @ sK2)) | (~ (q @ sK2)))))),
% 0.20/0.39 inference(not_proxy_clausification,[],[f171])).
% 0.20/0.39 thf(f171,plain,(
% 0.20/0.39 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK1 @ Y0)) | ((~ (p @ Y0)) | (~ (r @ Y0)))))))) | ($false = ((~ (rel_s4 @ sK1 @ sK2)) | ((~ (p @ sK2)) | (~ (q @ sK2)))))),
% 0.20/0.39 inference(beta_eta_normalization,[],[f170])).
% 0.20/0.39 thf(f170,plain,(
% 0.20/0.39 (((^[Y0 : $i]: ((~ (rel_s4 @ sK1 @ Y0)) | ((~ (p @ Y0)) | (~ (q @ Y0))))) @ sK2) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK1 @ Y0)) | ((~ (p @ Y0)) | (~ (r @ Y0))))))))),
% 0.20/0.39 inference(sigma_clausification,[],[f169])).
% 0.20/0.39 thf(f169,plain,(
% 0.20/0.39 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK1 @ Y0)) | ((~ (p @ Y0)) | (~ (q @ Y0)))))) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK1 @ Y0)) | ((~ (p @ Y0)) | (~ (r @ Y0))))))))),
% 0.20/0.39 inference(not_proxy_clausification,[],[f168])).
% 0.20/0.39 thf(f168,plain,(
% 0.20/0.39 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK1 @ Y0)) | ((~ (p @ Y0)) | (~ (q @ Y0)))))))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK1 @ Y0)) | ((~ (p @ Y0)) | (~ (r @ Y0))))))))),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f167])).
% 0.20/0.39 thf(f167,plain,(
% 0.20/0.39 ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK1 @ Y0)) | ((~ (p @ Y0)) | (~ (q @ Y0))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK1 @ Y0)) | ((~ (p @ Y0)) | (~ (r @ Y0)))))))))),
% 0.20/0.39 inference(not_proxy_clausification,[],[f166])).
% 0.20/0.39 thf(f166,plain,(
% 0.20/0.39 ($false = (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK1 @ Y0)) | ((~ (p @ Y0)) | (~ (q @ Y0))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK1 @ Y0)) | ((~ (p @ Y0)) | (~ (r @ Y0))))))))))),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f164])).
% 0.20/0.39 thf(f253,plain,(
% 0.20/0.39 spl0_3 | spl0_6),
% 0.20/0.39 inference(avatar_split_clause,[],[f183,f249,f232])).
% 0.20/0.39 thf(f183,plain,(
% 0.20/0.39 ($true = (p @ sK2)) | ($true = (rel_s4 @ sK1 @ sK3))),
% 0.20/0.39 inference(not_proxy_clausification,[],[f182])).
% 0.20/0.39 thf(f182,plain,(
% 0.20/0.39 ((~ (p @ sK2)) = $false) | ($true = (rel_s4 @ sK1 @ sK3))),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f178])).
% 0.20/0.39 thf(f178,plain,(
% 0.20/0.39 (((~ (p @ sK2)) | (~ (q @ sK2))) = $false) | ($true = (rel_s4 @ sK1 @ sK3))),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f177])).
% 0.20/0.39 thf(f247,plain,(
% 0.20/0.39 spl0_5 | spl0_4),
% 0.20/0.39 inference(avatar_split_clause,[],[f190,f237,f243])).
% 0.20/0.39 thf(f190,plain,(
% 0.20/0.39 ($true = (rel_s4 @ sK1 @ sK2)) | ($true = (p @ sK3))),
% 0.20/0.39 inference(not_proxy_clausification,[],[f189])).
% 0.20/0.39 thf(f189,plain,(
% 0.20/0.39 ((~ (p @ sK3)) = $false) | ($true = (rel_s4 @ sK1 @ sK2))),
% 0.20/0.39 inference(not_proxy_clausification,[],[f188])).
% 0.20/0.39 thf(f188,plain,(
% 0.20/0.39 ($false = (~ (rel_s4 @ sK1 @ sK2))) | ((~ (p @ sK3)) = $false)),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f186])).
% 0.20/0.39 thf(f186,plain,(
% 0.20/0.39 ($false = ((~ (p @ sK3)) | (~ (r @ sK3)))) | ($false = (~ (rel_s4 @ sK1 @ sK2)))),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f175])).
% 0.20/0.39 thf(f175,plain,(
% 0.20/0.39 ($false = ((~ (rel_s4 @ sK1 @ sK2)) | ((~ (p @ sK2)) | (~ (q @ sK2))))) | ($false = ((~ (p @ sK3)) | (~ (r @ sK3))))),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f174])).
% 0.20/0.39 thf(f241,plain,(
% 0.20/0.39 spl0_3 | spl0_4),
% 0.20/0.39 inference(avatar_split_clause,[],[f198,f237,f232])).
% 0.20/0.39 thf(f198,plain,(
% 0.20/0.39 ($true = (p @ sK3)) | ($true = (p @ sK2))),
% 0.20/0.39 inference(not_proxy_clausification,[],[f197])).
% 0.20/0.39 thf(f197,plain,(
% 0.20/0.39 ((~ (p @ sK2)) = $false) | ($true = (p @ sK3))),
% 0.20/0.39 inference(not_proxy_clausification,[],[f196])).
% 0.20/0.39 thf(f196,plain,(
% 0.20/0.39 ((~ (p @ sK3)) = $false) | ((~ (p @ sK2)) = $false)),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f194])).
% 0.20/0.39 thf(f194,plain,(
% 0.20/0.39 (((~ (p @ sK2)) | (~ (q @ sK2))) = $false) | ((~ (p @ sK3)) = $false)),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f185])).
% 0.20/0.39 thf(f185,plain,(
% 0.20/0.39 ($false = ((~ (p @ sK3)) | (~ (r @ sK3)))) | (((~ (p @ sK2)) | (~ (q @ sK2))) = $false)),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f175])).
% 0.20/0.39 % SZS output end Proof for theBenchmark
% 0.20/0.39 % (27197)------------------------------
% 0.20/0.39 % (27197)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.39 % (27197)Termination reason: Refutation
% 0.20/0.39
% 0.20/0.39 % (27197)Memory used [KB]: 5756
% 0.20/0.39 % (27197)Time elapsed: 0.014 s
% 0.20/0.39 % (27197)Instructions burned: 17 (million)
% 0.20/0.39 % (27197)------------------------------
% 0.20/0.39 % (27197)------------------------------
% 0.20/0.39 % (27196)Success in time 0.016 s
% 0.20/0.39 % Vampire---4.8 exiting
%------------------------------------------------------------------------------