TSTP Solution File: SYO408^1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO408^1 : 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 : n004.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 09:04:19 EDT 2024
% Result : Theorem 0.14s 0.38s
% Output : Refutation 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO408^1 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.14 % 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 : n004.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 08:33:38 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
% 0.14/0.37 % (7411)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)
% 0.14/0.37 % (7410)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.37 % (7412)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)
% 0.14/0.37 % (7414)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)
% 0.14/0.37 % (7413)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.37 % (7416)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.37 % (7415)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)
% 0.14/0.37 % (7417)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)
% 0.14/0.37 % (7414)Instruction limit reached!
% 0.14/0.37 % (7414)------------------------------
% 0.14/0.37 % (7414)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (7414)Termination reason: Unknown
% 0.14/0.37 % (7414)Termination phase: shuffling
% 0.14/0.37
% 0.14/0.37 % (7414)Memory used [KB]: 1023
% 0.14/0.37 % (7414)Time elapsed: 0.003 s
% 0.14/0.37 % (7414)Instructions burned: 2 (million)
% 0.14/0.37 % (7414)------------------------------
% 0.14/0.37 % (7414)------------------------------
% 0.14/0.37 % (7413)Instruction limit reached!
% 0.14/0.37 % (7413)------------------------------
% 0.14/0.37 % (7413)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (7413)Termination reason: Unknown
% 0.14/0.37 % (7413)Termination phase: shuffling
% 0.14/0.37
% 0.14/0.37 % (7413)Memory used [KB]: 1023
% 0.14/0.37 % (7413)Time elapsed: 0.004 s
% 0.14/0.37 % (7413)Instructions burned: 3 (million)
% 0.14/0.37 % (7413)------------------------------
% 0.14/0.37 % (7413)------------------------------
% 0.14/0.37 % (7417)Instruction limit reached!
% 0.14/0.37 % (7417)------------------------------
% 0.14/0.37 % (7417)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (7417)Termination reason: Unknown
% 0.14/0.37 % (7417)Termination phase: shuffling
% 0.14/0.37
% 0.14/0.37 % (7417)Memory used [KB]: 1023
% 0.14/0.37 % (7417)Time elapsed: 0.004 s
% 0.14/0.37 % (7417)Instructions burned: 3 (million)
% 0.14/0.37 % (7417)------------------------------
% 0.14/0.37 % (7417)------------------------------
% 0.14/0.37 % (7411)Instruction limit reached!
% 0.14/0.37 % (7411)------------------------------
% 0.14/0.37 % (7411)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (7411)Termination reason: Unknown
% 0.14/0.37 % (7411)Termination phase: Property scanning
% 0.14/0.37
% 0.14/0.37 % (7411)Memory used [KB]: 1023
% 0.14/0.37 % (7411)Time elapsed: 0.005 s
% 0.14/0.37 % (7411)Instructions burned: 5 (million)
% 0.14/0.37 % (7411)------------------------------
% 0.14/0.37 % (7411)------------------------------
% 0.14/0.38 % (7415)Refutation not found, incomplete strategy
% 0.14/0.38 % (7415)------------------------------
% 0.14/0.38 % (7415)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (7415)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.38
% 0.14/0.38
% 0.14/0.38 % (7415)Memory used [KB]: 5628
% 0.14/0.38 % (7415)Time elapsed: 0.007 s
% 0.14/0.38 % (7415)Instructions burned: 8 (million)
% 0.14/0.38 % (7415)------------------------------
% 0.14/0.38 % (7415)------------------------------
% 0.14/0.38 % (7410)First to succeed.
% 0.14/0.38 % (7412)Also succeeded, but the first one will report.
% 0.14/0.38 % (7410)Refutation found. Thanks to Tanya!
% 0.14/0.38 % SZS status Theorem for theBenchmark
% 0.14/0.38 % SZS output start Proof for theBenchmark
% 0.14/0.38 thf(type_def_5, type, mu: $tType).
% 0.14/0.38 thf(func_def_0, type, mu: $tType).
% 0.14/0.38 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.14/0.38 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.38 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.14/0.38 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.38 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.38 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.38 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.38 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.38 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.38 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.14/0.38 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.14/0.38 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.14/0.38 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.14/0.38 thf(func_def_15, type, mtrue: $i > $o).
% 0.14/0.38 thf(func_def_16, type, mfalse: $i > $o).
% 0.14/0.38 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.14/0.38 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.14/0.38 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.14/0.38 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.14/0.38 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.14/0.38 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.14/0.38 thf(func_def_33, type, rel_k: $i > $i > $o).
% 0.14/0.38 thf(func_def_34, type, mbox_k: ($i > $o) > $i > $o).
% 0.14/0.38 thf(func_def_35, type, mdia_k: ($i > $o) > $i > $o).
% 0.14/0.38 thf(func_def_36, type, p: $i > $o).
% 0.14/0.38 thf(func_def_37, type, q: $i > $o).
% 0.14/0.38 thf(f232,plain,(
% 0.14/0.38 $false),
% 0.14/0.38 inference(avatar_sat_refutation,[],[f192,f209,f215,f221,f231])).
% 0.14/0.38 thf(f231,plain,(
% 0.14/0.38 spl0_4),
% 0.14/0.38 inference(avatar_contradiction_clause,[],[f230])).
% 0.14/0.38 thf(f230,plain,(
% 0.14/0.38 $false | spl0_4),
% 0.14/0.38 inference(subsumption_resolution,[],[f226,f200])).
% 0.14/0.38 thf(f200,plain,(
% 0.14/0.38 ((q @ sK2) != $true) | spl0_4),
% 0.14/0.38 inference(avatar_component_clause,[],[f199])).
% 0.14/0.38 thf(f199,plain,(
% 0.14/0.38 spl0_4 <=> ((q @ sK2) = $true)),
% 0.14/0.38 introduced(avatar_definition,[new_symbols(naming,[spl0_4])])).
% 0.14/0.38 thf(f226,plain,(
% 0.14/0.38 ((q @ sK2) = $true)),
% 0.14/0.38 inference(trivial_inequality_removal,[],[f225])).
% 0.14/0.38 thf(f225,plain,(
% 0.14/0.38 ($true = $false) | ((q @ sK2) = $true)),
% 0.14/0.38 inference(superposition,[],[f169,f164])).
% 0.14/0.38 thf(f164,plain,(
% 0.14/0.38 ( ! [X1 : $i] : (((rel_k @ sK1 @ X1) = $false) | ((q @ X1) = $true)) )),
% 0.14/0.38 inference(not_proxy_clausification,[],[f163])).
% 0.14/0.38 thf(f163,plain,(
% 0.14/0.38 ( ! [X1 : $i] : (($true = (~ (rel_k @ sK1 @ X1))) | ((q @ X1) = $true)) )),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f162])).
% 0.14/0.38 thf(f162,plain,(
% 0.14/0.38 ( ! [X1 : $i] : ((((~ (rel_k @ sK1 @ X1)) | (q @ X1)) = $true)) )),
% 0.14/0.38 inference(beta_eta_normalization,[],[f161])).
% 0.14/0.38 thf(f161,plain,(
% 0.14/0.38 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (q @ Y0))) @ X1) = $true)) )),
% 0.14/0.38 inference(pi_clausification,[],[f160])).
% 0.14/0.38 thf(f160,plain,(
% 0.14/0.38 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (q @ Y0)))) = $true)),
% 0.14/0.38 inference(not_proxy_clausification,[],[f153])).
% 0.14/0.38 thf(f153,plain,(
% 0.14/0.38 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (q @ Y0))))))),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f152])).
% 0.14/0.38 thf(f152,plain,(
% 0.14/0.38 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (p @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (q @ Y0)))))))),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f150])).
% 0.14/0.38 thf(f150,plain,(
% 0.14/0.38 ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (p @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (q @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ ((~ ((~ (p @ Y0)) | (q @ Y0))) | (~ ((~ (q @ Y0)) | (p @ Y0))))))))) = $false)),
% 0.14/0.38 inference(beta_eta_normalization,[],[f149])).
% 0.14/0.38 thf(f149,plain,(
% 0.14/0.38 ($false = ((^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (p @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (q @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ ((~ ((~ (p @ Y1)) | (q @ Y1))) | (~ ((~ (q @ Y1)) | (p @ Y1)))))))))) @ sK1))),
% 0.14/0.38 inference(sigma_clausification,[],[f148])).
% 0.14/0.38 thf(f148,plain,(
% 0.14/0.38 ((!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (p @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (q @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ ((~ ((~ (p @ Y1)) | (q @ Y1))) | (~ ((~ (q @ Y1)) | (p @ Y1))))))))))) != $true)),
% 0.14/0.38 inference(boolean_simplification,[],[f147])).
% 0.14/0.38 thf(f147,plain,(
% 0.14/0.38 ($true != (!! @ $i @ (^[Y0 : $i]: ((~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (p @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (q @ Y1)))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ ((~ ((~ (p @ Y1)) | (q @ Y1))) | (~ ((~ (q @ Y1)) | (p @ Y1))))))))))))),
% 0.14/0.38 inference(beta_eta_normalization,[],[f146])).
% 0.14/0.38 thf(f146,plain,(
% 0.14/0.38 ($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_k @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ p) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_k @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ q)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_k @ 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)))))),
% 0.14/0.38 inference(definition_unfolding,[],[f116,f122,f137,f136,f114,f114,f114,f139])).
% 0.14/0.38 thf(f139,plain,(
% 0.14/0.38 (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))))))),
% 0.14/0.38 inference(definition_unfolding,[],[f127,f136,f137,f137])).
% 0.14/0.38 thf(f127,plain,(
% 0.14/0.38 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.14/0.38 inference(cnf_transformation,[],[f77])).
% 0.14/0.38 thf(f77,plain,(
% 0.14/0.38 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.14/0.38 inference(fool_elimination,[],[f76])).
% 0.14/0.38 thf(f76,plain,(
% 0.14/0.38 (mequiv = (^[X0 : $i > $o, X1 : $i > $o] : (mand @ (mimplies @ X0 @ X1) @ (mimplies @ X1 @ X0))))),
% 0.14/0.38 inference(rectify,[],[f8])).
% 0.14/0.38 thf(f8,axiom,(
% 0.14/0.38 (mequiv = (^[X3 : $i > $o, X4 : $i > $o] : (mand @ (mimplies @ X3 @ X4) @ (mimplies @ X4 @ X3))))),
% 0.14/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mequiv)).
% 0.14/0.38 thf(f114,plain,(
% 0.14/0.38 (mbox_k = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_k @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.14/0.38 inference(cnf_transformation,[],[f63])).
% 0.14/0.38 thf(f63,plain,(
% 0.14/0.38 (mbox_k = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_k @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.14/0.38 inference(fool_elimination,[],[f62])).
% 0.14/0.38 thf(f62,plain,(
% 0.14/0.38 (mbox_k = (^[X0 : $i > $o, X1 : $i] : (! [X2] : ((X0 @ X2) | ~(rel_k @ X1 @ X2)))))),
% 0.14/0.38 inference(rectify,[],[f32])).
% 0.14/0.38 thf(f32,axiom,(
% 0.14/0.38 (mbox_k = (^[X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(rel_k @ X2 @ X7)))))),
% 0.14/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_k)).
% 0.14/0.38 thf(f136,plain,(
% 0.14/0.38 (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)))))))),
% 0.14/0.38 inference(definition_unfolding,[],[f107,f124,f125,f124,f124])).
% 0.14/0.38 thf(f125,plain,(
% 0.14/0.38 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.14/0.38 inference(cnf_transformation,[],[f67])).
% 0.14/0.38 thf(f67,plain,(
% 0.14/0.38 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.14/0.38 inference(fool_elimination,[],[f66])).
% 0.14/0.38 thf(f66,plain,(
% 0.14/0.38 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))) = mor)),
% 0.14/0.38 inference(rectify,[],[f4])).
% 0.14/0.38 thf(f4,axiom,(
% 0.14/0.38 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))) = mor)),
% 0.14/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.14/0.39 thf(f124,plain,(
% 0.14/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.14/0.39 inference(cnf_transformation,[],[f51])).
% 0.14/0.39 thf(f51,plain,(
% 0.14/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.14/0.39 inference(fool_elimination,[],[f50])).
% 0.14/0.39 thf(f50,plain,(
% 0.14/0.39 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.14/0.39 inference(rectify,[],[f3])).
% 0.14/0.39 thf(f3,axiom,(
% 0.14/0.39 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.14/0.39 thf(f107,plain,(
% 0.14/0.39 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.14/0.39 inference(cnf_transformation,[],[f47])).
% 0.14/0.39 thf(f47,plain,(
% 0.14/0.39 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.14/0.39 inference(fool_elimination,[],[f46])).
% 0.14/0.39 thf(f46,plain,(
% 0.14/0.39 ((^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))) = mand)),
% 0.14/0.39 inference(rectify,[],[f5])).
% 0.14/0.39 thf(f5,axiom,(
% 0.14/0.39 ((^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))) = mand)),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand)).
% 0.14/0.39 thf(f137,plain,(
% 0.14/0.39 (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)))))),
% 0.14/0.39 inference(definition_unfolding,[],[f129,f125,f124])).
% 0.14/0.39 thf(f129,plain,(
% 0.14/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.14/0.39 inference(cnf_transformation,[],[f41])).
% 0.14/0.39 thf(f41,plain,(
% 0.14/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.14/0.39 inference(fool_elimination,[],[f40])).
% 0.14/0.39 thf(f40,plain,(
% 0.14/0.39 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.14/0.39 inference(rectify,[],[f6])).
% 0.14/0.39 thf(f6,axiom,(
% 0.14/0.39 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.14/0.39 thf(f122,plain,(
% 0.14/0.39 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.14/0.39 inference(cnf_transformation,[],[f71])).
% 0.14/0.39 thf(f71,plain,(
% 0.14/0.39 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.14/0.39 inference(fool_elimination,[],[f70])).
% 0.14/0.39 thf(f70,plain,(
% 0.14/0.39 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.14/0.39 inference(rectify,[],[f28])).
% 0.14/0.39 thf(f28,axiom,(
% 0.14/0.39 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.14/0.39 thf(f116,plain,(
% 0.14/0.39 ((mvalid @ (mimplies @ (mand @ (mbox_k @ p) @ (mbox_k @ q)) @ (mbox_k @ (mequiv @ p @ q)))) != $true)),
% 0.14/0.39 inference(cnf_transformation,[],[f101])).
% 0.14/0.39 thf(f101,plain,(
% 0.14/0.39 ((mvalid @ (mimplies @ (mand @ (mbox_k @ p) @ (mbox_k @ q)) @ (mbox_k @ (mequiv @ p @ q)))) != $true)),
% 0.14/0.39 inference(flattening,[],[f100])).
% 0.14/0.39 thf(f100,plain,(
% 0.14/0.39 ~((mvalid @ (mimplies @ (mand @ (mbox_k @ p) @ (mbox_k @ q)) @ (mbox_k @ (mequiv @ p @ q)))) = $true)),
% 0.14/0.39 inference(fool_elimination,[],[f99])).
% 0.14/0.39 thf(f99,plain,(
% 0.14/0.39 ~(mvalid @ (mimplies @ (mand @ (mbox_k @ p) @ (mbox_k @ q)) @ (mbox_k @ (mequiv @ p @ q))))),
% 0.14/0.39 inference(rectify,[],[f35])).
% 0.14/0.39 thf(f35,negated_conjecture,(
% 0.14/0.39 ~(mvalid @ (mimplies @ (mand @ (mbox_k @ p) @ (mbox_k @ q)) @ (mbox_k @ (mequiv @ p @ q))))),
% 0.14/0.39 inference(negated_conjecture,[],[f34])).
% 0.14/0.39 thf(f34,conjecture,(
% 0.14/0.39 (mvalid @ (mimplies @ (mand @ (mbox_k @ p) @ (mbox_k @ q)) @ (mbox_k @ (mequiv @ p @ q))))),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove)).
% 0.14/0.39 thf(f169,plain,(
% 0.14/0.39 ((rel_k @ sK1 @ sK2) = $true)),
% 0.14/0.39 inference(not_proxy_clausification,[],[f168])).
% 0.14/0.39 thf(f168,plain,(
% 0.14/0.39 ($false = (~ (rel_k @ sK1 @ sK2)))),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f166])).
% 0.14/0.39 thf(f166,plain,(
% 0.14/0.39 (((~ (rel_k @ sK1 @ sK2)) | (~ ((~ ((~ (p @ sK2)) | (q @ sK2))) | (~ ((~ (q @ sK2)) | (p @ sK2)))))) = $false)),
% 0.14/0.39 inference(beta_eta_normalization,[],[f165])).
% 0.14/0.39 thf(f165,plain,(
% 0.14/0.39 (((^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ ((~ ((~ (p @ Y0)) | (q @ Y0))) | (~ ((~ (q @ Y0)) | (p @ Y0))))))) @ sK2) = $false)),
% 0.14/0.39 inference(sigma_clausification,[],[f151])).
% 0.14/0.39 thf(f151,plain,(
% 0.14/0.39 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ ((~ ((~ (p @ Y0)) | (q @ Y0))) | (~ ((~ (q @ Y0)) | (p @ Y0)))))))) = $false)),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f150])).
% 0.14/0.39 thf(f221,plain,(
% 0.14/0.39 ~spl0_1 | ~spl0_4),
% 0.14/0.39 inference(avatar_contradiction_clause,[],[f220])).
% 0.14/0.39 thf(f220,plain,(
% 0.14/0.39 $false | (~spl0_1 | ~spl0_4)),
% 0.14/0.39 inference(trivial_inequality_removal,[],[f216])).
% 0.14/0.39 thf(f216,plain,(
% 0.14/0.39 ($true = $false) | (~spl0_1 | ~spl0_4)),
% 0.14/0.39 inference(superposition,[],[f187,f201])).
% 0.14/0.39 thf(f201,plain,(
% 0.14/0.39 ((q @ sK2) = $true) | ~spl0_4),
% 0.14/0.39 inference(avatar_component_clause,[],[f199])).
% 0.14/0.39 thf(f187,plain,(
% 0.14/0.39 ((q @ sK2) = $false) | ~spl0_1),
% 0.14/0.39 inference(avatar_component_clause,[],[f185])).
% 0.14/0.39 thf(f185,plain,(
% 0.14/0.39 spl0_1 <=> ((q @ sK2) = $false)),
% 0.14/0.39 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.14/0.39 thf(f215,plain,(
% 0.14/0.39 ~spl0_2 | ~spl0_3),
% 0.14/0.39 inference(avatar_contradiction_clause,[],[f214])).
% 0.14/0.39 thf(f214,plain,(
% 0.14/0.39 $false | (~spl0_2 | ~spl0_3)),
% 0.14/0.39 inference(trivial_inequality_removal,[],[f211])).
% 0.14/0.39 thf(f211,plain,(
% 0.14/0.39 ($true = $false) | (~spl0_2 | ~spl0_3)),
% 0.14/0.39 inference(superposition,[],[f191,f196])).
% 0.14/0.39 thf(f196,plain,(
% 0.14/0.39 ((p @ sK2) = $true) | ~spl0_3),
% 0.14/0.39 inference(avatar_component_clause,[],[f194])).
% 0.14/0.39 thf(f194,plain,(
% 0.14/0.39 spl0_3 <=> ((p @ sK2) = $true)),
% 0.14/0.39 introduced(avatar_definition,[new_symbols(naming,[spl0_3])])).
% 0.14/0.39 thf(f191,plain,(
% 0.14/0.39 ((p @ sK2) = $false) | ~spl0_2),
% 0.14/0.39 inference(avatar_component_clause,[],[f189])).
% 0.14/0.39 thf(f189,plain,(
% 0.14/0.39 spl0_2 <=> ((p @ sK2) = $false)),
% 0.14/0.39 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.14/0.39 thf(f209,plain,(
% 0.14/0.39 spl0_3),
% 0.14/0.39 inference(avatar_split_clause,[],[f206,f194])).
% 0.14/0.39 thf(f206,plain,(
% 0.14/0.39 ((p @ sK2) = $true)),
% 0.14/0.39 inference(trivial_inequality_removal,[],[f205])).
% 0.14/0.39 thf(f205,plain,(
% 0.14/0.39 ((p @ sK2) = $true) | ($true = $false)),
% 0.14/0.39 inference(superposition,[],[f169,f159])).
% 0.14/0.39 thf(f159,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (((rel_k @ sK1 @ X1) = $false) | ((p @ X1) = $true)) )),
% 0.14/0.39 inference(not_proxy_clausification,[],[f158])).
% 0.14/0.39 thf(f158,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (($true = (~ (rel_k @ sK1 @ X1))) | ((p @ X1) = $true)) )),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f157])).
% 0.14/0.39 thf(f157,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (($true = ((~ (rel_k @ sK1 @ X1)) | (p @ X1)))) )),
% 0.14/0.39 inference(beta_eta_normalization,[],[f156])).
% 0.14/0.39 thf(f156,plain,(
% 0.14/0.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (p @ Y0))) @ X1) = $true)) )),
% 0.14/0.39 inference(pi_clausification,[],[f155])).
% 0.14/0.39 thf(f155,plain,(
% 0.14/0.39 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (p @ Y0)))))),
% 0.14/0.39 inference(not_proxy_clausification,[],[f154])).
% 0.14/0.39 thf(f154,plain,(
% 0.14/0.39 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (p @ Y0))))))),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f152])).
% 0.14/0.39 thf(f192,plain,(
% 0.14/0.39 spl0_1 | spl0_2),
% 0.14/0.39 inference(avatar_split_clause,[],[f181,f189,f185])).
% 0.14/0.39 thf(f181,plain,(
% 0.14/0.39 ((p @ sK2) = $false) | ((q @ sK2) = $false)),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f180])).
% 0.14/0.39 thf(f180,plain,(
% 0.14/0.39 ($false = ((~ (p @ sK2)) | (q @ sK2))) | ((p @ sK2) = $false)),
% 0.14/0.39 inference(not_proxy_clausification,[],[f173])).
% 0.14/0.39 thf(f173,plain,(
% 0.14/0.39 ($true = (~ ((~ (p @ sK2)) | (q @ sK2)))) | ((p @ sK2) = $false)),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f172])).
% 0.14/0.39 thf(f172,plain,(
% 0.14/0.39 ($false = ((~ (q @ sK2)) | (p @ sK2))) | ($true = (~ ((~ (p @ sK2)) | (q @ sK2))))),
% 0.14/0.39 inference(not_proxy_clausification,[],[f171])).
% 0.14/0.39 thf(f171,plain,(
% 0.14/0.39 ($true = (~ ((~ (q @ sK2)) | (p @ sK2)))) | ($true = (~ ((~ (p @ sK2)) | (q @ sK2))))),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f170])).
% 0.14/0.39 thf(f170,plain,(
% 0.14/0.39 (((~ ((~ (p @ sK2)) | (q @ sK2))) | (~ ((~ (q @ sK2)) | (p @ sK2)))) = $true)),
% 0.14/0.39 inference(not_proxy_clausification,[],[f167])).
% 0.14/0.39 thf(f167,plain,(
% 0.14/0.39 ($false = (~ ((~ ((~ (p @ sK2)) | (q @ sK2))) | (~ ((~ (q @ sK2)) | (p @ sK2))))))),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f166])).
% 0.14/0.39 % SZS output end Proof for theBenchmark
% 0.14/0.39 % (7410)------------------------------
% 0.14/0.39 % (7410)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (7410)Termination reason: Refutation
% 0.14/0.39
% 0.14/0.39 % (7410)Memory used [KB]: 5756
% 0.14/0.39 % (7410)Time elapsed: 0.012 s
% 0.14/0.39 % (7410)Instructions burned: 13 (million)
% 0.14/0.39 % (7410)------------------------------
% 0.14/0.39 % (7410)------------------------------
% 0.14/0.39 % (7409)Success in time 0.012 s
% 0.14/0.39 % Vampire---4.8 exiting
%------------------------------------------------------------------------------