TSTP Solution File: SYO400^1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO400^1 : 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/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n015.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 09:04:18 EDT 2024
% Result : Theorem 0.15s 0.39s
% Output : Refutation 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO400^1 : 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/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.35 % Computer : n015.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon May 20 10:56:23 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.35 This is a TH0_THM_EQU_NAR problem
% 0.15/0.35 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/sandbox2/benchmark/theBenchmark.p
% 0.15/0.37 % (2547)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)
% 0.15/0.37 % (2545)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)
% 0.15/0.37 % (2547)Instruction limit reached!
% 0.15/0.37 % (2547)------------------------------
% 0.15/0.37 % (2547)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.37 % (2547)Termination reason: Unknown
% 0.15/0.37 % (2547)Termination phase: shuffling
% 0.15/0.37
% 0.15/0.37 % (2547)Memory used [KB]: 1023
% 0.15/0.37 % (2547)Time elapsed: 0.004 s
% 0.15/0.37 % (2547)Instructions burned: 3 (million)
% 0.15/0.37 % (2547)------------------------------
% 0.15/0.37 % (2547)------------------------------
% 0.15/0.37 % (2540)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.38 % (2545)Refutation not found, incomplete strategy
% 0.15/0.38 % (2545)------------------------------
% 0.15/0.38 % (2545)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (2545)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.38
% 0.15/0.38
% 0.15/0.38 % (2545)Memory used [KB]: 5628
% 0.15/0.38 % (2545)Time elapsed: 0.006 s
% 0.15/0.38 % (2545)Instructions burned: 9 (million)
% 0.15/0.38 % (2545)------------------------------
% 0.15/0.38 % (2545)------------------------------
% 0.15/0.38 % (2541)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)
% 0.15/0.38 % (2542)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)
% 0.15/0.38 % (2541)Instruction limit reached!
% 0.15/0.38 % (2541)------------------------------
% 0.15/0.38 % (2541)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (2541)Termination reason: Unknown
% 0.15/0.38 % (2541)Termination phase: Property scanning
% 0.15/0.38
% 0.15/0.38 % (2541)Memory used [KB]: 1023
% 0.15/0.38 % (2541)Time elapsed: 0.005 s
% 0.15/0.38 % (2541)Instructions burned: 5 (million)
% 0.15/0.38 % (2541)------------------------------
% 0.15/0.38 % (2541)------------------------------
% 0.15/0.38 % (2544)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)
% 0.15/0.38 % (2546)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.38 % (2540)First to succeed.
% 0.15/0.38 % (2543)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.38 % (2544)Instruction limit reached!
% 0.15/0.38 % (2544)------------------------------
% 0.15/0.38 % (2544)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (2544)Termination reason: Unknown
% 0.15/0.38 % (2544)Termination phase: shuffling
% 0.15/0.38 % (2543)Instruction limit reached!
% 0.15/0.38 % (2543)------------------------------
% 0.15/0.38 % (2543)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38
% 0.15/0.38 % (2543)Termination reason: Unknown
% 0.15/0.38 % (2544)Memory used [KB]: 1023
% 0.15/0.38 % (2543)Termination phase: shuffling
% 0.15/0.38
% 0.15/0.38 % (2544)Time elapsed: 0.003 s
% 0.15/0.38 % (2544)Instructions burned: 3 (million)
% 0.15/0.38 % (2543)Memory used [KB]: 1023
% 0.15/0.38 % (2544)------------------------------
% 0.15/0.38 % (2544)------------------------------
% 0.15/0.38 % (2543)Time elapsed: 0.003 s
% 0.15/0.38 % (2543)Instructions burned: 2 (million)
% 0.15/0.38 % (2543)------------------------------
% 0.15/0.38 % (2543)------------------------------
% 0.15/0.39 % (2542)Also succeeded, but the first one will report.
% 0.15/0.39 % (2540)Refutation found. Thanks to Tanya!
% 0.15/0.39 % SZS status Theorem for theBenchmark
% 0.15/0.39 % SZS output start Proof for theBenchmark
% 0.15/0.39 thf(type_def_5, type, mu: $tType).
% 0.15/0.39 thf(func_def_0, type, mu: $tType).
% 0.15/0.39 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.15/0.39 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_15, type, mtrue: $i > $o).
% 0.15/0.39 thf(func_def_16, type, mfalse: $i > $o).
% 0.15/0.39 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.15/0.39 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.15/0.39 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.15/0.39 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.15/0.39 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.15/0.39 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.15/0.39 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.15/0.39 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.15/0.39 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.15/0.39 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.15/0.39 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.15/0.39 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.15/0.39 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.15/0.39 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.15/0.39 thf(func_def_33, type, rel_k: $i > $i > $o).
% 0.15/0.39 thf(func_def_34, type, mbox_k: ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_35, type, mdia_k: ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_36, type, p: $i > $o).
% 0.15/0.39 thf(func_def_37, type, q: $i > $o).
% 0.15/0.39 thf(f214,plain,(
% 0.15/0.39 $false),
% 0.15/0.39 inference(avatar_sat_refutation,[],[f190,f200,f206,f213])).
% 0.15/0.39 thf(f213,plain,(
% 0.15/0.39 ~spl0_2 | ~spl0_3),
% 0.15/0.39 inference(avatar_contradiction_clause,[],[f212])).
% 0.15/0.39 thf(f212,plain,(
% 0.15/0.39 $false | (~spl0_2 | ~spl0_3)),
% 0.15/0.39 inference(trivial_inequality_removal,[],[f208])).
% 0.15/0.39 thf(f208,plain,(
% 0.15/0.39 ($false = $true) | (~spl0_2 | ~spl0_3)),
% 0.15/0.39 inference(superposition,[],[f198,f188])).
% 0.15/0.39 thf(f188,plain,(
% 0.15/0.39 ($false = (q @ sK2)) | ~spl0_2),
% 0.15/0.39 inference(avatar_component_clause,[],[f186])).
% 0.15/0.39 thf(f186,plain,(
% 0.15/0.39 spl0_2 <=> ($false = (q @ sK2))),
% 0.15/0.39 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.15/0.39 thf(f198,plain,(
% 0.15/0.39 ($true = (q @ sK2)) | ~spl0_3),
% 0.15/0.39 inference(avatar_component_clause,[],[f196])).
% 0.15/0.39 thf(f196,plain,(
% 0.15/0.39 spl0_3 <=> ($true = (q @ sK2))),
% 0.15/0.39 introduced(avatar_definition,[new_symbols(naming,[spl0_3])])).
% 0.15/0.39 thf(f206,plain,(
% 0.15/0.39 ~spl0_1),
% 0.15/0.39 inference(avatar_contradiction_clause,[],[f205])).
% 0.15/0.39 thf(f205,plain,(
% 0.15/0.39 $false | ~spl0_1),
% 0.15/0.39 inference(trivial_inequality_removal,[],[f201])).
% 0.15/0.39 thf(f201,plain,(
% 0.15/0.39 ($false = $true) | ~spl0_1),
% 0.15/0.39 inference(superposition,[],[f184,f159])).
% 0.15/0.39 thf(f159,plain,(
% 0.15/0.39 ((p @ sK2) = $true)),
% 0.15/0.39 inference(not_proxy_clausification,[],[f156])).
% 0.15/0.39 thf(f156,plain,(
% 0.15/0.39 ($false = (~ (p @ sK2)))),
% 0.15/0.39 inference(binary_proxy_clausification,[],[f155])).
% 0.15/0.39 thf(f155,plain,(
% 0.15/0.39 ($false = ((~ (rel_k @ sK1 @ sK2)) | (~ (p @ sK2))))),
% 0.15/0.39 inference(beta_eta_normalization,[],[f154])).
% 0.15/0.39 thf(f154,plain,(
% 0.15/0.39 ($false = ((^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (p @ Y0)))) @ sK2))),
% 0.15/0.39 inference(sigma_clausification,[],[f153])).
% 0.15/0.39 thf(f153,plain,(
% 0.15/0.39 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (p @ Y0))))))),
% 0.15/0.39 inference(binary_proxy_clausification,[],[f151])).
% 0.15/0.39 thf(f151,plain,(
% 0.15/0.39 ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (p @ Y0))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | ((~ (q @ Y0)) | (~ (p @ Y0))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | ((q @ Y0) | (~ (p @ Y0))))))))))),
% 0.15/0.39 inference(beta_eta_normalization,[],[f150])).
% 0.15/0.39 thf(f150,plain,(
% 0.15/0.39 ($false = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ (p @ Y1))))) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | ((~ (q @ Y1)) | (~ (p @ Y1))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | ((q @ Y1) | (~ (p @ Y1)))))))))) @ sK1))),
% 0.15/0.39 inference(sigma_clausification,[],[f149])).
% 0.15/0.39 thf(f149,plain,(
% 0.15/0.39 ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ (p @ Y1))))) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | ((~ (q @ Y1)) | (~ (p @ Y1))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | ((q @ Y1) | (~ (p @ Y1))))))))))) != $true)),
% 0.15/0.39 inference(boolean_simplification,[],[f148])).
% 0.15/0.39 thf(f148,plain,(
% 0.15/0.39 ($true != (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | ((~ (p @ Y1)) | (~ (p @ Y1)))))) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | ((~ (q @ Y1)) | (~ (p @ Y1))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | ((q @ Y1) | (~ (p @ Y1))))))))))))),
% 0.15/0.39 inference(boolean_simplification,[],[f147])).
% 0.15/0.39 thf(f147,plain,(
% 0.15/0.39 ($true != (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | ((~ (p @ Y1)) | (~ (p @ Y1)))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | ((~ (q @ Y1)) | (~ (p @ Y1))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | ((q @ Y1) | (~ (p @ Y1))))))))))))))),
% 0.15/0.39 inference(beta_eta_normalization,[],[f146])).
% 0.15/0.39 thf(f146,plain,(
% 0.15/0.39 ($true != ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ 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]: ((Y3 @ Y4) | (Y2 @ 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))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))) @ p @ 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]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))) @ p @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))) @ 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]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))) @ p @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))) @ p))))))),
% 0.15/0.39 inference(definition_unfolding,[],[f130,f111,f137,f136,f131,f137,f131,f137,f126,f131,f137,f126])).
% 0.15/0.39 thf(f126,plain,(
% 0.15/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.15/0.39 inference(cnf_transformation,[],[f58])).
% 0.15/0.39 thf(f58,plain,(
% 0.15/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.15/0.39 inference(fool_elimination,[],[f57])).
% 0.15/0.39 thf(f57,plain,(
% 0.15/0.39 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.15/0.39 inference(rectify,[],[f3])).
% 0.15/0.39 thf(f3,axiom,(
% 0.15/0.39 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)),
% 0.15/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.15/0.39 thf(f131,plain,(
% 0.15/0.39 (mbox_k = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_k @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.15/0.39 inference(cnf_transformation,[],[f100])).
% 0.15/0.39 thf(f100,plain,(
% 0.15/0.39 (mbox_k = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_k @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.15/0.39 inference(fool_elimination,[],[f99])).
% 0.15/0.39 thf(f99,plain,(
% 0.15/0.39 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : ((X0 @ X2) | ~(rel_k @ X1 @ X2)))) = mbox_k)),
% 0.15/0.39 inference(rectify,[],[f32])).
% 0.15/0.39 thf(f32,axiom,(
% 0.15/0.39 ((^[X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(rel_k @ X2 @ X7)))) = mbox_k)),
% 0.15/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_k)).
% 0.15/0.39 thf(f136,plain,(
% 0.15/0.39 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 0.15/0.39 inference(definition_unfolding,[],[f117,f126,f116,f126,f126])).
% 0.15/0.39 thf(f116,plain,(
% 0.15/0.39 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.15/0.39 inference(cnf_transformation,[],[f94])).
% 0.15/0.39 thf(f94,plain,(
% 0.15/0.39 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.15/0.39 inference(fool_elimination,[],[f93])).
% 0.15/0.39 thf(f93,plain,(
% 0.15/0.39 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))))),
% 0.15/0.39 inference(rectify,[],[f4])).
% 0.15/0.39 thf(f4,axiom,(
% 0.15/0.39 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))))),
% 0.15/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.15/0.39 thf(f117,plain,(
% 0.15/0.39 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.15/0.39 inference(cnf_transformation,[],[f68])).
% 0.15/0.39 thf(f68,plain,(
% 0.15/0.39 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.15/0.39 inference(fool_elimination,[],[f67])).
% 0.15/0.39 thf(f67,plain,(
% 0.15/0.39 (mand = (^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))))),
% 0.15/0.39 inference(rectify,[],[f5])).
% 0.15/0.39 thf(f5,axiom,(
% 0.15/0.39 (mand = (^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))))),
% 0.15/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand)).
% 0.15/0.39 thf(f137,plain,(
% 0.15/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.15/0.39 inference(definition_unfolding,[],[f113,f116,f126])).
% 0.15/0.39 thf(f113,plain,(
% 0.15/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.15/0.39 inference(cnf_transformation,[],[f79])).
% 0.15/0.39 thf(f79,plain,(
% 0.15/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.15/0.39 inference(fool_elimination,[],[f78])).
% 0.15/0.39 thf(f78,plain,(
% 0.15/0.39 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.15/0.39 inference(rectify,[],[f6])).
% 0.15/0.39 thf(f6,axiom,(
% 0.15/0.39 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.15/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.15/0.39 thf(f111,plain,(
% 0.15/0.39 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.15/0.39 inference(cnf_transformation,[],[f40])).
% 0.15/0.39 thf(f40,plain,(
% 0.15/0.39 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.15/0.39 inference(fool_elimination,[],[f39])).
% 0.15/0.39 thf(f39,plain,(
% 0.15/0.39 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.15/0.39 inference(rectify,[],[f28])).
% 0.15/0.39 thf(f28,axiom,(
% 0.15/0.39 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.15/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.15/0.39 thf(f130,plain,(
% 0.15/0.39 ((mvalid @ (mimplies @ (mand @ (mbox_k @ (mimplies @ p @ q)) @ (mbox_k @ (mimplies @ p @ (mnot @ q)))) @ (mbox_k @ (mimplies @ p @ (mnot @ p))))) != $true)),
% 0.15/0.39 inference(cnf_transformation,[],[f101])).
% 0.15/0.39 thf(f101,plain,(
% 0.15/0.39 ((mvalid @ (mimplies @ (mand @ (mbox_k @ (mimplies @ p @ q)) @ (mbox_k @ (mimplies @ p @ (mnot @ q)))) @ (mbox_k @ (mimplies @ p @ (mnot @ p))))) != $true)),
% 0.15/0.39 inference(flattening,[],[f84])).
% 0.15/0.39 thf(f84,plain,(
% 0.15/0.39 ~((mvalid @ (mimplies @ (mand @ (mbox_k @ (mimplies @ p @ q)) @ (mbox_k @ (mimplies @ p @ (mnot @ q)))) @ (mbox_k @ (mimplies @ p @ (mnot @ p))))) = $true)),
% 0.15/0.39 inference(fool_elimination,[],[f83])).
% 0.15/0.39 thf(f83,plain,(
% 0.15/0.39 ~(mvalid @ (mimplies @ (mand @ (mbox_k @ (mimplies @ p @ q)) @ (mbox_k @ (mimplies @ p @ (mnot @ q)))) @ (mbox_k @ (mimplies @ p @ (mnot @ p)))))),
% 0.15/0.39 inference(rectify,[],[f35])).
% 0.15/0.39 thf(f35,negated_conjecture,(
% 0.15/0.39 ~(mvalid @ (mimplies @ (mand @ (mbox_k @ (mimplies @ p @ q)) @ (mbox_k @ (mimplies @ p @ (mnot @ q)))) @ (mbox_k @ (mimplies @ p @ (mnot @ p)))))),
% 0.15/0.39 inference(negated_conjecture,[],[f34])).
% 0.15/0.39 thf(f34,conjecture,(
% 0.15/0.39 (mvalid @ (mimplies @ (mand @ (mbox_k @ (mimplies @ p @ q)) @ (mbox_k @ (mimplies @ p @ (mnot @ q)))) @ (mbox_k @ (mimplies @ p @ (mnot @ p)))))),
% 0.15/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove)).
% 0.15/0.39 thf(f184,plain,(
% 0.15/0.39 ($false = (p @ sK2)) | ~spl0_1),
% 0.15/0.39 inference(avatar_component_clause,[],[f182])).
% 0.15/0.39 thf(f182,plain,(
% 0.15/0.39 spl0_1 <=> ($false = (p @ sK2))),
% 0.15/0.39 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.15/0.39 thf(f200,plain,(
% 0.15/0.39 spl0_1 | spl0_3),
% 0.15/0.39 inference(avatar_split_clause,[],[f193,f196,f182])).
% 0.15/0.39 thf(f193,plain,(
% 0.15/0.39 ($false = (p @ sK2)) | ($true = (q @ sK2))),
% 0.15/0.39 inference(trivial_inequality_removal,[],[f191])).
% 0.15/0.39 thf(f191,plain,(
% 0.15/0.39 ($false = (p @ sK2)) | ($true = (q @ sK2)) | ($false = $true)),
% 0.15/0.39 inference(superposition,[],[f176,f158])).
% 0.15/0.39 thf(f158,plain,(
% 0.15/0.39 ((rel_k @ sK1 @ sK2) = $true)),
% 0.15/0.39 inference(not_proxy_clausification,[],[f157])).
% 0.15/0.39 thf(f157,plain,(
% 0.15/0.39 ($false = (~ (rel_k @ sK1 @ sK2)))),
% 0.15/0.39 inference(binary_proxy_clausification,[],[f155])).
% 0.15/0.39 thf(f176,plain,(
% 0.15/0.39 ( ! [X1 : $i] : (($false = (rel_k @ sK1 @ X1)) | ($true = (q @ X1)) | ($false = (p @ X1))) )),
% 0.15/0.39 inference(not_proxy_clausification,[],[f175])).
% 0.15/0.39 thf(f175,plain,(
% 0.15/0.39 ( ! [X1 : $i] : (((~ (p @ X1)) = $true) | ($true = (q @ X1)) | ($false = (rel_k @ sK1 @ X1))) )),
% 0.15/0.39 inference(binary_proxy_clausification,[],[f174])).
% 0.15/0.39 thf(f174,plain,(
% 0.15/0.39 ( ! [X1 : $i] : ((((q @ X1) | (~ (p @ X1))) = $true) | ($false = (rel_k @ sK1 @ X1))) )),
% 0.15/0.39 inference(not_proxy_clausification,[],[f173])).
% 0.15/0.39 thf(f173,plain,(
% 0.15/0.39 ( ! [X1 : $i] : (((~ (rel_k @ sK1 @ X1)) = $true) | (((q @ X1) | (~ (p @ X1))) = $true)) )),
% 0.15/0.39 inference(binary_proxy_clausification,[],[f172])).
% 0.15/0.39 thf(f172,plain,(
% 0.15/0.39 ( ! [X1 : $i] : (($true = ((~ (rel_k @ sK1 @ X1)) | ((q @ X1) | (~ (p @ X1)))))) )),
% 0.15/0.39 inference(beta_eta_normalization,[],[f171])).
% 0.15/0.39 thf(f171,plain,(
% 0.15/0.39 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | ((q @ Y0) | (~ (p @ Y0))))) @ X1))) )),
% 0.15/0.39 inference(pi_clausification,[],[f170])).
% 0.15/0.39 thf(f170,plain,(
% 0.15/0.39 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | ((q @ Y0) | (~ (p @ Y0)))))) = $true)),
% 0.15/0.39 inference(not_proxy_clausification,[],[f160])).
% 0.15/0.39 thf(f160,plain,(
% 0.15/0.39 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | ((q @ Y0) | (~ (p @ Y0))))))))),
% 0.15/0.39 inference(binary_proxy_clausification,[],[f152])).
% 0.15/0.39 thf(f152,plain,(
% 0.15/0.39 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | ((~ (q @ Y0)) | (~ (p @ Y0))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | ((q @ Y0) | (~ (p @ Y0)))))))))),
% 0.15/0.39 inference(binary_proxy_clausification,[],[f151])).
% 0.15/0.39 thf(f190,plain,(
% 0.15/0.39 spl0_2 | spl0_1),
% 0.15/0.39 inference(avatar_split_clause,[],[f179,f182,f186])).
% 0.15/0.39 thf(f179,plain,(
% 0.15/0.39 ($false = (q @ sK2)) | ($false = (p @ sK2))),
% 0.15/0.39 inference(trivial_inequality_removal,[],[f178])).
% 0.15/0.39 thf(f178,plain,(
% 0.15/0.39 ($false = (p @ sK2)) | ($false = (q @ sK2)) | ($false = $true)),
% 0.15/0.39 inference(superposition,[],[f158,f169])).
% 0.15/0.39 thf(f169,plain,(
% 0.15/0.39 ( ! [X1 : $i] : (($false = (rel_k @ sK1 @ X1)) | ($false = (p @ X1)) | ($false = (q @ X1))) )),
% 0.15/0.39 inference(not_proxy_clausification,[],[f168])).
% 0.15/0.39 thf(f168,plain,(
% 0.15/0.39 ( ! [X1 : $i] : (((~ (q @ X1)) = $true) | ($false = (rel_k @ sK1 @ X1)) | ($false = (p @ X1))) )),
% 0.15/0.39 inference(not_proxy_clausification,[],[f167])).
% 0.15/0.39 thf(f167,plain,(
% 0.15/0.39 ( ! [X1 : $i] : (((~ (rel_k @ sK1 @ X1)) = $true) | ($false = (p @ X1)) | ((~ (q @ X1)) = $true)) )),
% 0.15/0.39 inference(not_proxy_clausification,[],[f166])).
% 0.15/0.39 thf(f166,plain,(
% 0.15/0.39 ( ! [X1 : $i] : (((~ (p @ X1)) = $true) | ((~ (rel_k @ sK1 @ X1)) = $true) | ((~ (q @ X1)) = $true)) )),
% 0.15/0.39 inference(binary_proxy_clausification,[],[f165])).
% 0.15/0.39 thf(f165,plain,(
% 0.15/0.39 ( ! [X1 : $i] : (($true = ((~ (q @ X1)) | (~ (p @ X1)))) | ((~ (rel_k @ sK1 @ X1)) = $true)) )),
% 0.15/0.39 inference(binary_proxy_clausification,[],[f164])).
% 0.15/0.39 thf(f164,plain,(
% 0.15/0.39 ( ! [X1 : $i] : (($true = ((~ (rel_k @ sK1 @ X1)) | ((~ (q @ X1)) | (~ (p @ X1)))))) )),
% 0.15/0.39 inference(beta_eta_normalization,[],[f163])).
% 0.15/0.39 thf(f163,plain,(
% 0.15/0.39 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | ((~ (q @ Y0)) | (~ (p @ Y0))))) @ X1))) )),
% 0.15/0.39 inference(pi_clausification,[],[f162])).
% 0.15/0.39 thf(f162,plain,(
% 0.15/0.39 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | ((~ (q @ Y0)) | (~ (p @ Y0)))))) = $true)),
% 0.15/0.39 inference(not_proxy_clausification,[],[f161])).
% 0.15/0.39 thf(f161,plain,(
% 0.15/0.39 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | ((~ (q @ Y0)) | (~ (p @ Y0))))))))),
% 0.15/0.39 inference(binary_proxy_clausification,[],[f152])).
% 0.15/0.39 % SZS output end Proof for theBenchmark
% 0.15/0.39 % (2540)------------------------------
% 0.15/0.39 % (2540)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (2540)Termination reason: Refutation
% 0.15/0.39
% 0.15/0.39 % (2540)Memory used [KB]: 5628
% 0.15/0.39 % (2540)Time elapsed: 0.013 s
% 0.15/0.39 % (2540)Instructions burned: 12 (million)
% 0.15/0.39 % (2540)------------------------------
% 0.15/0.39 % (2540)------------------------------
% 0.15/0.39 % (2539)Success in time 0.029 s
% 0.15/0.39 % Vampire---4.8 exiting
%------------------------------------------------------------------------------