TSTP Solution File: SYO458^3 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO458^3 : 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/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n012.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 09:04:46 EDT 2024
% Result : Theorem 0.16s 0.34s
% Output : Refutation 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : SYO458^3 : TPTP v8.2.0. Released v4.0.0.
% 0.02/0.11 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.10/0.31 % Computer : n012.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Mon May 20 09:57:23 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.10/0.31 This is a TH0_THM_EQU_NAR problem
% 0.10/0.32 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/sandbox2/benchmark/theBenchmark.p
% 0.10/0.33 % (12151)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)
% 0.10/0.33 % (12152)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)
% 0.10/0.33 % (12153)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.10/0.33 % (12150)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.10/0.33 % (12154)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)
% 0.10/0.33 % (12155)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)
% 0.10/0.33 % (12156)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.10/0.33 % (12153)Instruction limit reached!
% 0.10/0.33 % (12153)------------------------------
% 0.10/0.33 % (12153)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.10/0.33 % (12153)Termination reason: Unknown
% 0.10/0.33 % (12153)Termination phase: shuffling
% 0.10/0.33 % (12154)Instruction limit reached!
% 0.10/0.33 % (12154)------------------------------
% 0.10/0.33 % (12154)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.10/0.33 % (12154)Termination reason: Unknown
% 0.10/0.33 % (12154)Termination phase: shuffling
% 0.10/0.33
% 0.10/0.33 % (12154)Memory used [KB]: 1023
% 0.10/0.33 % (12154)Time elapsed: 0.003 s
% 0.10/0.33 % (12154)Instructions burned: 3 (million)
% 0.10/0.33 % (12154)------------------------------
% 0.10/0.33 % (12154)------------------------------
% 0.10/0.33
% 0.10/0.33 % (12153)Memory used [KB]: 1023
% 0.10/0.33 % (12153)Time elapsed: 0.003 s
% 0.10/0.34 % (12153)Instructions burned: 3 (million)
% 0.10/0.34 % (12153)------------------------------
% 0.10/0.34 % (12153)------------------------------
% 0.10/0.34 % (12151)Instruction limit reached!
% 0.10/0.34 % (12151)------------------------------
% 0.10/0.34 % (12151)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.10/0.34 % (12151)Termination reason: Unknown
% 0.10/0.34 % (12151)Termination phase: Property scanning
% 0.10/0.34
% 0.10/0.34 % (12151)Memory used [KB]: 1023
% 0.10/0.34 % (12151)Time elapsed: 0.004 s
% 0.10/0.34 % (12151)Instructions burned: 5 (million)
% 0.10/0.34 % (12151)------------------------------
% 0.10/0.34 % (12151)------------------------------
% 0.10/0.34 % (12155)Refutation not found, incomplete strategy
% 0.10/0.34 % (12155)------------------------------
% 0.10/0.34 % (12155)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.10/0.34 % (12155)Termination reason: Refutation not found, incomplete strategy
% 0.10/0.34
% 0.10/0.34
% 0.10/0.34 % (12155)Memory used [KB]: 5628
% 0.10/0.34 % (12155)Time elapsed: 0.006 s
% 0.10/0.34 % (12155)Instructions burned: 9 (million)
% 0.10/0.34 % (12155)------------------------------
% 0.10/0.34 % (12155)------------------------------
% 0.16/0.34 % (12157)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)
% 0.16/0.34 % (12150)First to succeed.
% 0.16/0.34 % (12157)Instruction limit reached!
% 0.16/0.34 % (12157)------------------------------
% 0.16/0.34 % (12157)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.34 % (12157)Termination reason: Unknown
% 0.16/0.34 % (12157)Termination phase: shuffling
% 0.16/0.34
% 0.16/0.34 % (12157)Memory used [KB]: 1023
% 0.16/0.34 % (12157)Time elapsed: 0.003 s
% 0.16/0.34 % (12157)Instructions burned: 3 (million)
% 0.16/0.34 % (12157)------------------------------
% 0.16/0.34 % (12157)------------------------------
% 0.16/0.34 % (12152)Also succeeded, but the first one will report.
% 0.16/0.34 % (12156)Also succeeded, but the first one will report.
% 0.16/0.34 % (12150)Refutation found. Thanks to Tanya!
% 0.16/0.34 % SZS status Theorem for theBenchmark
% 0.16/0.34 % SZS output start Proof for theBenchmark
% 0.16/0.34 thf(type_def_5, type, mu: $tType).
% 0.16/0.34 thf(func_def_0, type, mu: $tType).
% 0.16/0.34 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.16/0.34 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.34 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.16/0.34 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.34 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.34 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.34 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.34 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.34 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.34 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.16/0.34 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.16/0.34 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.16/0.34 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.16/0.34 thf(func_def_15, type, mtrue: $i > $o).
% 0.16/0.34 thf(func_def_16, type, mfalse: $i > $o).
% 0.16/0.34 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.16/0.34 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.16/0.34 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.16/0.34 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.16/0.34 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.16/0.34 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.16/0.34 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.16/0.34 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.16/0.34 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.16/0.34 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.16/0.34 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.16/0.34 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.16/0.34 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.16/0.34 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.16/0.34 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.16/0.34 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.16/0.34 thf(func_def_33, type, rel_m: $i > $i > $o).
% 0.16/0.34 thf(func_def_34, type, mbox_m: ($i > $o) > $i > $o).
% 0.16/0.34 thf(func_def_35, type, mdia_m: ($i > $o) > $i > $o).
% 0.16/0.34 thf(func_def_36, type, p: $i > $o).
% 0.16/0.34 thf(func_def_37, type, q: $i > $o).
% 0.16/0.34 thf(f247,plain,(
% 0.16/0.34 $false),
% 0.16/0.34 inference(avatar_sat_refutation,[],[f200,f221,f227,f233,f246])).
% 0.16/0.34 thf(f246,plain,(
% 0.16/0.34 spl0_4),
% 0.16/0.34 inference(avatar_contradiction_clause,[],[f245])).
% 0.16/0.34 thf(f245,plain,(
% 0.16/0.34 $false | spl0_4),
% 0.16/0.34 inference(subsumption_resolution,[],[f239,f208])).
% 0.16/0.34 thf(f208,plain,(
% 0.16/0.34 ($true != (q @ sK2)) | spl0_4),
% 0.16/0.34 inference(avatar_component_clause,[],[f207])).
% 0.16/0.34 thf(f207,plain,(
% 0.16/0.34 spl0_4 <=> ($true = (q @ sK2))),
% 0.16/0.34 introduced(avatar_definition,[new_symbols(naming,[spl0_4])])).
% 0.16/0.34 thf(f239,plain,(
% 0.16/0.34 ($true = (q @ sK2))),
% 0.16/0.34 inference(trivial_inequality_removal,[],[f236])).
% 0.16/0.34 thf(f236,plain,(
% 0.16/0.34 ($false = $true) | ($true = (q @ sK2))),
% 0.16/0.34 inference(superposition,[],[f172,f177])).
% 0.16/0.34 thf(f177,plain,(
% 0.16/0.34 ((rel_m @ sK1 @ sK2) = $true)),
% 0.16/0.34 inference(not_proxy_clausification,[],[f176])).
% 0.16/0.34 thf(f176,plain,(
% 0.16/0.34 ($false = (~ (rel_m @ sK1 @ sK2)))),
% 0.16/0.34 inference(binary_proxy_clausification,[],[f174])).
% 0.16/0.34 thf(f174,plain,(
% 0.16/0.34 (((~ (rel_m @ sK1 @ sK2)) | (~ ((~ ((~ (p @ sK2)) | (q @ sK2))) | (~ ((~ (q @ sK2)) | (p @ sK2)))))) = $false)),
% 0.16/0.34 inference(beta_eta_normalization,[],[f173])).
% 0.16/0.34 thf(f173,plain,(
% 0.16/0.34 ($false = ((^[Y0 : $i]: ((~ (rel_m @ sK1 @ Y0)) | (~ ((~ ((~ (p @ Y0)) | (q @ Y0))) | (~ ((~ (q @ Y0)) | (p @ Y0))))))) @ sK2))),
% 0.16/0.34 inference(sigma_clausification,[],[f159])).
% 0.16/0.34 thf(f159,plain,(
% 0.16/0.34 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_m @ sK1 @ Y0)) | (~ ((~ ((~ (p @ Y0)) | (q @ Y0))) | (~ ((~ (q @ Y0)) | (p @ Y0)))))))))),
% 0.16/0.34 inference(binary_proxy_clausification,[],[f158])).
% 0.16/0.34 thf(f158,plain,(
% 0.16/0.34 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_m @ sK1 @ Y0)) | (p @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_m @ sK1 @ Y0)) | (q @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_m @ sK1 @ Y0)) | (~ ((~ ((~ (p @ Y0)) | (q @ Y0))) | (~ ((~ (q @ Y0)) | (p @ Y0))))))))))),
% 0.16/0.34 inference(beta_eta_normalization,[],[f157])).
% 0.16/0.34 thf(f157,plain,(
% 0.16/0.34 (((^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_m @ Y0 @ Y1)) | (p @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_m @ Y0 @ Y1)) | (q @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_m @ Y0 @ Y1)) | (~ ((~ ((~ (p @ Y1)) | (q @ Y1))) | (~ ((~ (q @ Y1)) | (p @ Y1)))))))))) @ sK1) = $false)),
% 0.16/0.34 inference(sigma_clausification,[],[f156])).
% 0.16/0.34 thf(f156,plain,(
% 0.16/0.34 ((!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_m @ Y0 @ Y1)) | (p @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_m @ Y0 @ Y1)) | (q @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_m @ Y0 @ Y1)) | (~ ((~ ((~ (p @ Y1)) | (q @ Y1))) | (~ ((~ (q @ Y1)) | (p @ Y1))))))))))) != $true)),
% 0.16/0.34 inference(boolean_simplification,[],[f155])).
% 0.16/0.34 thf(f155,plain,(
% 0.16/0.34 ((!! @ $i @ (^[Y0 : $i]: ((~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_m @ Y0 @ Y1)) | (p @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_m @ Y0 @ Y1)) | (q @ Y1)))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_m @ Y0 @ Y1)) | (~ ((~ ((~ (p @ Y1)) | (q @ Y1))) | (~ ((~ (q @ Y1)) | (p @ Y1))))))))))) != $true)),
% 0.16/0.34 inference(beta_eta_normalization,[],[f150])).
% 0.16/0.34 thf(f150,plain,(
% 0.16/0.34 ($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 > $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)))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_m @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ p) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_m @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ q)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_m @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y1 @ Y0))))) @ p @ q)))))),
% 0.16/0.34 inference(definition_unfolding,[],[f116,f106,f141,f140,f139,f139,f139,f143])).
% 0.16/0.34 thf(f143,plain,(
% 0.16/0.34 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y1 @ Y0))))))),
% 0.16/0.35 inference(definition_unfolding,[],[f123,f140,f141,f141])).
% 0.16/0.35 thf(f123,plain,(
% 0.16/0.35 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.16/0.35 inference(cnf_transformation,[],[f89])).
% 0.16/0.35 thf(f89,plain,(
% 0.16/0.35 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.16/0.35 inference(fool_elimination,[],[f88])).
% 0.16/0.35 thf(f88,plain,(
% 0.16/0.35 ((^[X0 : $i > $o, X1 : $i > $o] : (mand @ (mimplies @ X0 @ X1) @ (mimplies @ X1 @ X0))) = mequiv)),
% 0.16/0.35 inference(rectify,[],[f8])).
% 0.16/0.35 thf(f8,axiom,(
% 0.16/0.35 ((^[X3 : $i > $o, X4 : $i > $o] : (mand @ (mimplies @ X3 @ X4) @ (mimplies @ X4 @ X3))) = mequiv)),
% 0.16/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv)).
% 0.16/0.35 thf(f139,plain,(
% 0.16/0.35 (mbox_m = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_m @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.16/0.35 inference(cnf_transformation,[],[f43])).
% 0.16/0.35 thf(f43,plain,(
% 0.16/0.35 (mbox_m = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_m @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.16/0.35 inference(fool_elimination,[],[f42])).
% 0.16/0.35 thf(f42,plain,(
% 0.16/0.35 (mbox_m = (^[X0 : $i > $o, X1 : $i] : (! [X2] : ((X0 @ X2) | ~(rel_m @ X1 @ X2)))))),
% 0.16/0.35 inference(rectify,[],[f32])).
% 0.16/0.35 thf(f32,axiom,(
% 0.16/0.35 (mbox_m = (^[X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(rel_m @ X2 @ X7)))))),
% 0.16/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_m)).
% 0.16/0.35 thf(f140,plain,(
% 0.16/0.35 (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)))))))),
% 0.16/0.35 inference(definition_unfolding,[],[f124,f136,f107,f136,f136])).
% 0.16/0.35 thf(f107,plain,(
% 0.16/0.35 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.16/0.35 inference(cnf_transformation,[],[f91])).
% 0.16/0.35 thf(f91,plain,(
% 0.16/0.35 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.16/0.35 inference(fool_elimination,[],[f90])).
% 0.16/0.35 thf(f90,plain,(
% 0.16/0.35 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 0.16/0.35 inference(rectify,[],[f4])).
% 0.16/0.35 thf(f4,axiom,(
% 0.16/0.35 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))))),
% 0.16/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.16/0.35 thf(f136,plain,(
% 0.16/0.35 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.16/0.35 inference(cnf_transformation,[],[f95])).
% 0.16/0.35 thf(f95,plain,(
% 0.16/0.35 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.16/0.35 inference(fool_elimination,[],[f94])).
% 0.16/0.35 thf(f94,plain,(
% 0.16/0.35 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.16/0.35 inference(rectify,[],[f3])).
% 0.16/0.35 thf(f3,axiom,(
% 0.16/0.35 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)),
% 0.16/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.16/0.35 thf(f124,plain,(
% 0.16/0.35 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.16/0.35 inference(cnf_transformation,[],[f99])).
% 0.16/0.35 thf(f99,plain,(
% 0.16/0.35 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.16/0.35 inference(fool_elimination,[],[f98])).
% 0.16/0.35 thf(f98,plain,(
% 0.16/0.35 (mand = (^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))))),
% 0.16/0.35 inference(rectify,[],[f5])).
% 0.16/0.35 thf(f5,axiom,(
% 0.16/0.35 (mand = (^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))))),
% 0.16/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand)).
% 0.16/0.35 thf(f141,plain,(
% 0.16/0.35 (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)))))),
% 0.16/0.35 inference(definition_unfolding,[],[f118,f107,f136])).
% 0.16/0.35 thf(f118,plain,(
% 0.16/0.35 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.16/0.35 inference(cnf_transformation,[],[f76])).
% 0.16/0.35 thf(f76,plain,(
% 0.16/0.35 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.16/0.35 inference(fool_elimination,[],[f75])).
% 0.16/0.35 thf(f75,plain,(
% 0.16/0.35 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.16/0.35 inference(rectify,[],[f6])).
% 0.16/0.35 thf(f6,axiom,(
% 0.16/0.35 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.16/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.16/0.35 thf(f106,plain,(
% 0.16/0.35 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.16/0.35 inference(cnf_transformation,[],[f51])).
% 0.16/0.35 thf(f51,plain,(
% 0.16/0.35 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.16/0.35 inference(fool_elimination,[],[f50])).
% 0.16/0.35 thf(f50,plain,(
% 0.16/0.35 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.16/0.35 inference(rectify,[],[f28])).
% 0.16/0.35 thf(f28,axiom,(
% 0.16/0.35 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.16/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.16/0.35 thf(f116,plain,(
% 0.16/0.35 ((mvalid @ (mimplies @ (mand @ (mbox_m @ p) @ (mbox_m @ q)) @ (mbox_m @ (mequiv @ p @ q)))) != $true)),
% 0.16/0.35 inference(cnf_transformation,[],[f104])).
% 0.16/0.35 thf(f104,plain,(
% 0.16/0.35 ((mvalid @ (mimplies @ (mand @ (mbox_m @ p) @ (mbox_m @ q)) @ (mbox_m @ (mequiv @ p @ q)))) != $true)),
% 0.16/0.35 inference(flattening,[],[f101])).
% 0.16/0.35 thf(f101,plain,(
% 0.16/0.35 ~((mvalid @ (mimplies @ (mand @ (mbox_m @ p) @ (mbox_m @ q)) @ (mbox_m @ (mequiv @ p @ q)))) = $true)),
% 0.16/0.35 inference(fool_elimination,[],[f100])).
% 0.16/0.35 thf(f100,plain,(
% 0.16/0.35 ~(mvalid @ (mimplies @ (mand @ (mbox_m @ p) @ (mbox_m @ q)) @ (mbox_m @ (mequiv @ p @ q))))),
% 0.16/0.35 inference(rectify,[],[f36])).
% 0.16/0.35 thf(f36,negated_conjecture,(
% 0.16/0.35 ~(mvalid @ (mimplies @ (mand @ (mbox_m @ p) @ (mbox_m @ q)) @ (mbox_m @ (mequiv @ p @ q))))),
% 0.16/0.35 inference(negated_conjecture,[],[f35])).
% 0.16/0.35 thf(f35,conjecture,(
% 0.16/0.35 (mvalid @ (mimplies @ (mand @ (mbox_m @ p) @ (mbox_m @ q)) @ (mbox_m @ (mequiv @ p @ q))))),
% 0.16/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove)).
% 0.16/0.35 thf(f172,plain,(
% 0.16/0.35 ( ! [X1 : $i] : (($false = (rel_m @ sK1 @ X1)) | ($true = (q @ X1))) )),
% 0.16/0.35 inference(not_proxy_clausification,[],[f171])).
% 0.16/0.35 thf(f171,plain,(
% 0.16/0.35 ( ! [X1 : $i] : (($true = (q @ X1)) | ($true = (~ (rel_m @ sK1 @ X1)))) )),
% 0.16/0.35 inference(binary_proxy_clausification,[],[f170])).
% 0.16/0.35 thf(f170,plain,(
% 0.16/0.35 ( ! [X1 : $i] : ((((~ (rel_m @ sK1 @ X1)) | (q @ X1)) = $true)) )),
% 0.16/0.35 inference(beta_eta_normalization,[],[f169])).
% 0.16/0.35 thf(f169,plain,(
% 0.16/0.35 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_m @ sK1 @ Y0)) | (q @ Y0))) @ X1))) )),
% 0.16/0.35 inference(pi_clausification,[],[f168])).
% 0.16/0.35 thf(f168,plain,(
% 0.16/0.35 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_m @ sK1 @ Y0)) | (q @ Y0)))) = $true)),
% 0.16/0.35 inference(not_proxy_clausification,[],[f161])).
% 0.16/0.35 thf(f161,plain,(
% 0.16/0.35 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_m @ sK1 @ Y0)) | (q @ Y0))))))),
% 0.16/0.35 inference(binary_proxy_clausification,[],[f160])).
% 0.16/0.35 thf(f160,plain,(
% 0.16/0.35 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_m @ sK1 @ Y0)) | (p @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_m @ sK1 @ Y0)) | (q @ Y0)))))))),
% 0.16/0.35 inference(binary_proxy_clausification,[],[f158])).
% 0.16/0.35 thf(f233,plain,(
% 0.16/0.35 ~spl0_1 | ~spl0_4),
% 0.16/0.35 inference(avatar_contradiction_clause,[],[f232])).
% 0.16/0.35 thf(f232,plain,(
% 0.16/0.35 $false | (~spl0_1 | ~spl0_4)),
% 0.16/0.35 inference(trivial_inequality_removal,[],[f228])).
% 0.16/0.35 thf(f228,plain,(
% 0.16/0.35 ($false = $true) | (~spl0_1 | ~spl0_4)),
% 0.16/0.35 inference(superposition,[],[f195,f209])).
% 0.16/0.35 thf(f209,plain,(
% 0.16/0.35 ($true = (q @ sK2)) | ~spl0_4),
% 0.16/0.35 inference(avatar_component_clause,[],[f207])).
% 0.16/0.35 thf(f195,plain,(
% 0.16/0.35 ($false = (q @ sK2)) | ~spl0_1),
% 0.16/0.35 inference(avatar_component_clause,[],[f193])).
% 0.16/0.35 thf(f193,plain,(
% 0.16/0.35 spl0_1 <=> ($false = (q @ sK2))),
% 0.16/0.35 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.16/0.35 thf(f227,plain,(
% 0.16/0.35 ~spl0_2 | ~spl0_3),
% 0.16/0.35 inference(avatar_contradiction_clause,[],[f226])).
% 0.16/0.35 thf(f226,plain,(
% 0.16/0.35 $false | (~spl0_2 | ~spl0_3)),
% 0.16/0.35 inference(trivial_inequality_removal,[],[f223])).
% 0.16/0.35 thf(f223,plain,(
% 0.16/0.35 ($false = $true) | (~spl0_2 | ~spl0_3)),
% 0.16/0.35 inference(superposition,[],[f199,f204])).
% 0.16/0.35 thf(f204,plain,(
% 0.16/0.35 ($true = (p @ sK2)) | ~spl0_3),
% 0.16/0.35 inference(avatar_component_clause,[],[f202])).
% 0.16/0.35 thf(f202,plain,(
% 0.16/0.35 spl0_3 <=> ($true = (p @ sK2))),
% 0.16/0.35 introduced(avatar_definition,[new_symbols(naming,[spl0_3])])).
% 0.16/0.35 thf(f199,plain,(
% 0.16/0.35 ($false = (p @ sK2)) | ~spl0_2),
% 0.16/0.35 inference(avatar_component_clause,[],[f197])).
% 0.16/0.35 thf(f197,plain,(
% 0.16/0.35 spl0_2 <=> ($false = (p @ sK2))),
% 0.16/0.35 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.16/0.35 thf(f221,plain,(
% 0.16/0.35 spl0_3),
% 0.16/0.35 inference(avatar_split_clause,[],[f216,f202])).
% 0.16/0.35 thf(f216,plain,(
% 0.16/0.35 ($true = (p @ sK2))),
% 0.16/0.35 inference(trivial_inequality_removal,[],[f213])).
% 0.16/0.35 thf(f213,plain,(
% 0.16/0.35 ($true = (p @ sK2)) | ($false = $true)),
% 0.16/0.35 inference(superposition,[],[f167,f177])).
% 0.16/0.35 thf(f167,plain,(
% 0.16/0.35 ( ! [X1 : $i] : (($false = (rel_m @ sK1 @ X1)) | ((p @ X1) = $true)) )),
% 0.16/0.35 inference(not_proxy_clausification,[],[f166])).
% 0.16/0.35 thf(f166,plain,(
% 0.16/0.35 ( ! [X1 : $i] : (((p @ X1) = $true) | ($true = (~ (rel_m @ sK1 @ X1)))) )),
% 0.16/0.35 inference(binary_proxy_clausification,[],[f165])).
% 0.16/0.35 thf(f165,plain,(
% 0.16/0.35 ( ! [X1 : $i] : ((((~ (rel_m @ sK1 @ X1)) | (p @ X1)) = $true)) )),
% 0.16/0.35 inference(beta_eta_normalization,[],[f164])).
% 0.16/0.35 thf(f164,plain,(
% 0.16/0.35 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_m @ sK1 @ Y0)) | (p @ Y0))) @ X1))) )),
% 0.16/0.35 inference(pi_clausification,[],[f163])).
% 0.16/0.35 thf(f163,plain,(
% 0.16/0.35 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_m @ sK1 @ Y0)) | (p @ Y0)))) = $true)),
% 0.16/0.35 inference(not_proxy_clausification,[],[f162])).
% 0.16/0.35 thf(f162,plain,(
% 0.16/0.35 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_m @ sK1 @ Y0)) | (p @ Y0))))))),
% 0.16/0.35 inference(binary_proxy_clausification,[],[f160])).
% 0.16/0.35 thf(f200,plain,(
% 0.16/0.35 spl0_1 | spl0_2),
% 0.16/0.35 inference(avatar_split_clause,[],[f189,f197,f193])).
% 0.16/0.35 thf(f189,plain,(
% 0.16/0.35 ($false = (p @ sK2)) | ($false = (q @ sK2))),
% 0.16/0.35 inference(binary_proxy_clausification,[],[f188])).
% 0.16/0.35 thf(f188,plain,(
% 0.16/0.35 ($false = (p @ sK2)) | ($false = ((~ (p @ sK2)) | (q @ sK2)))),
% 0.16/0.35 inference(not_proxy_clausification,[],[f181])).
% 0.16/0.35 thf(f181,plain,(
% 0.16/0.35 ($true = (~ ((~ (p @ sK2)) | (q @ sK2)))) | ($false = (p @ sK2))),
% 0.16/0.35 inference(binary_proxy_clausification,[],[f180])).
% 0.16/0.35 thf(f180,plain,(
% 0.16/0.35 ($false = ((~ (q @ sK2)) | (p @ sK2))) | ($true = (~ ((~ (p @ sK2)) | (q @ sK2))))),
% 0.16/0.35 inference(not_proxy_clausification,[],[f179])).
% 0.16/0.35 thf(f179,plain,(
% 0.16/0.35 ((~ ((~ (q @ sK2)) | (p @ sK2))) = $true) | ($true = (~ ((~ (p @ sK2)) | (q @ sK2))))),
% 0.16/0.35 inference(binary_proxy_clausification,[],[f178])).
% 0.16/0.35 thf(f178,plain,(
% 0.16/0.35 (((~ ((~ (p @ sK2)) | (q @ sK2))) | (~ ((~ (q @ sK2)) | (p @ sK2)))) = $true)),
% 0.16/0.35 inference(not_proxy_clausification,[],[f175])).
% 0.16/0.35 thf(f175,plain,(
% 0.16/0.35 ($false = (~ ((~ ((~ (p @ sK2)) | (q @ sK2))) | (~ ((~ (q @ sK2)) | (p @ sK2))))))),
% 0.16/0.35 inference(binary_proxy_clausification,[],[f174])).
% 0.16/0.35 % SZS output end Proof for theBenchmark
% 0.16/0.35 % (12150)------------------------------
% 0.16/0.35 % (12150)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.35 % (12150)Termination reason: Refutation
% 0.16/0.35
% 0.16/0.35 % (12150)Memory used [KB]: 5756
% 0.16/0.35 % (12150)Time elapsed: 0.011 s
% 0.16/0.35 % (12150)Instructions burned: 13 (million)
% 0.16/0.35 % (12150)------------------------------
% 0.16/0.35 % (12150)------------------------------
% 0.16/0.35 % (12149)Success in time 0.022 s
% 0.16/0.35 % Vampire---4.8 exiting
%------------------------------------------------------------------------------