TSTP Solution File: SYO460^1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO460^1 : 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 : n020.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 09:04:48 EDT 2024
% Result : Theorem 0.21s 0.38s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYO460^1 : TPTP v8.2.0. Released v4.0.0.
% 0.06/0.14 % 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 : n020.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 09:40:53 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 % (14263)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.37 % (14263)Instruction limit reached!
% 0.15/0.37 % (14263)------------------------------
% 0.15/0.37 % (14263)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.37 % (14263)Termination reason: Unknown
% 0.15/0.37 % (14263)Termination phase: shuffling
% 0.15/0.37
% 0.15/0.37 % (14263)Memory used [KB]: 1023
% 0.15/0.37 % (14263)Time elapsed: 0.003 s
% 0.15/0.37 % (14263)Instructions burned: 4 (million)
% 0.15/0.37 % (14263)------------------------------
% 0.15/0.37 % (14263)------------------------------
% 0.15/0.37 % (14262)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)
% 0.15/0.37 % (14260)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.37 % (14261)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)
% 0.15/0.37 % (14264)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)
% 0.15/0.37 % (14265)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 % (14266)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.37 % (14267)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 % (14264)Instruction limit reached!
% 0.15/0.37 % (14264)------------------------------
% 0.15/0.37 % (14264)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.37 % (14264)Termination reason: Unknown
% 0.15/0.37 % (14264)Termination phase: shuffling
% 0.15/0.37
% 0.15/0.37 % (14264)Memory used [KB]: 1023
% 0.15/0.37 % (14264)Time elapsed: 0.003 s
% 0.15/0.37 % (14264)Instructions burned: 2 (million)
% 0.15/0.37 % (14264)------------------------------
% 0.15/0.37 % (14264)------------------------------
% 0.15/0.37 % (14267)Instruction limit reached!
% 0.15/0.37 % (14267)------------------------------
% 0.15/0.37 % (14267)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.37 % (14267)Termination reason: Unknown
% 0.15/0.37 % (14267)Termination phase: shuffling
% 0.15/0.37
% 0.15/0.37 % (14267)Memory used [KB]: 1023
% 0.15/0.37 % (14267)Time elapsed: 0.004 s
% 0.15/0.37 % (14267)Instructions burned: 3 (million)
% 0.15/0.37 % (14267)------------------------------
% 0.15/0.37 % (14267)------------------------------
% 0.15/0.37 % (14261)Instruction limit reached!
% 0.15/0.37 % (14261)------------------------------
% 0.15/0.37 % (14261)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.37 % (14261)Termination reason: Unknown
% 0.15/0.37 % (14261)Termination phase: Property scanning
% 0.15/0.37
% 0.15/0.37 % (14261)Memory used [KB]: 1023
% 0.15/0.37 % (14261)Time elapsed: 0.005 s
% 0.15/0.37 % (14261)Instructions burned: 5 (million)
% 0.15/0.37 % (14261)------------------------------
% 0.15/0.37 % (14261)------------------------------
% 0.15/0.38 % (14265)Refutation not found, incomplete strategy
% 0.15/0.38 % (14265)------------------------------
% 0.15/0.38 % (14265)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (14265)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.38
% 0.15/0.38
% 0.15/0.38 % (14265)Memory used [KB]: 5628
% 0.15/0.38 % (14265)Time elapsed: 0.007 s
% 0.15/0.38 % (14265)Instructions burned: 7 (million)
% 0.15/0.38 % (14265)------------------------------
% 0.15/0.38 % (14265)------------------------------
% 0.15/0.38 % (14260)First to succeed.
% 0.21/0.38 % (14266)Also succeeded, but the first one will report.
% 0.21/0.38 % (14268)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)
% 0.21/0.38 % (14260)Refutation found. Thanks to Tanya!
% 0.21/0.38 % SZS status Theorem for theBenchmark
% 0.21/0.38 % SZS output start Proof for theBenchmark
% 0.21/0.38 thf(type_def_5, type, mu: $tType).
% 0.21/0.38 thf(func_def_0, type, mu: $tType).
% 0.21/0.38 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.21/0.38 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.38 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.21/0.38 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.38 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.38 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.38 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.38 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.38 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.38 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.21/0.38 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.21/0.38 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.21/0.38 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.21/0.38 thf(func_def_15, type, mtrue: $i > $o).
% 0.21/0.38 thf(func_def_16, type, mfalse: $i > $o).
% 0.21/0.38 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.21/0.38 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.21/0.38 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.21/0.38 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.21/0.38 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.21/0.38 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.21/0.38 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.21/0.38 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.21/0.38 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.21/0.38 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.21/0.38 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.21/0.38 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.21/0.38 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.21/0.38 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.21/0.38 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.21/0.38 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.21/0.38 thf(func_def_33, type, rel_k: $i > $i > $o).
% 0.21/0.38 thf(func_def_34, type, mbox_k: ($i > $o) > $i > $o).
% 0.21/0.38 thf(func_def_35, type, mdia_k: ($i > $o) > $i > $o).
% 0.21/0.38 thf(func_def_36, type, p: $i > $o).
% 0.21/0.38 thf(func_def_37, type, q: $i > $o).
% 0.21/0.38 thf(func_def_38, type, r: $i > $o).
% 0.21/0.38 thf(f252,plain,(
% 0.21/0.38 $false),
% 0.21/0.38 inference(avatar_sat_refutation,[],[f207,f217,f229,f231,f241,f251])).
% 0.21/0.38 thf(f251,plain,(
% 0.21/0.38 ~spl0_1 | ~spl0_6),
% 0.21/0.38 inference(avatar_contradiction_clause,[],[f250])).
% 0.21/0.38 thf(f250,plain,(
% 0.21/0.38 $false | (~spl0_1 | ~spl0_6)),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f246])).
% 0.21/0.38 thf(f246,plain,(
% 0.21/0.38 ($false = $true) | (~spl0_1 | ~spl0_6)),
% 0.21/0.38 inference(superposition,[],[f245,f228])).
% 0.21/0.38 thf(f228,plain,(
% 0.21/0.38 ($true = (p @ sK2)) | ~spl0_6),
% 0.21/0.38 inference(avatar_component_clause,[],[f226])).
% 0.21/0.38 thf(f226,plain,(
% 0.21/0.38 spl0_6 <=> ($true = (p @ sK2))),
% 0.21/0.38 introduced(avatar_definition,[new_symbols(naming,[spl0_6])])).
% 0.21/0.38 thf(f245,plain,(
% 0.21/0.38 ($false = (p @ sK2)) | ~spl0_1),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f243])).
% 0.21/0.38 thf(f243,plain,(
% 0.21/0.38 ($false = $true) | ($false = (p @ sK2)) | ~spl0_1),
% 0.21/0.38 inference(superposition,[],[f198,f202])).
% 0.21/0.38 thf(f202,plain,(
% 0.21/0.38 ((rel_k @ sK1 @ sK2) = $true) | ~spl0_1),
% 0.21/0.38 inference(avatar_component_clause,[],[f200])).
% 0.21/0.38 thf(f200,plain,(
% 0.21/0.38 spl0_1 <=> ((rel_k @ sK1 @ sK2) = $true)),
% 0.21/0.38 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.21/0.38 thf(f198,plain,(
% 0.21/0.38 ( ! [X1 : $i] : (($false = (rel_k @ sK1 @ X1)) | ((p @ X1) = $false)) )),
% 0.21/0.38 inference(not_proxy_clausification,[],[f197])).
% 0.21/0.38 thf(f197,plain,(
% 0.21/0.38 ( ! [X1 : $i] : (((p @ X1) = $false) | ((~ (rel_k @ sK1 @ X1)) = $true)) )),
% 0.21/0.38 inference(not_proxy_clausification,[],[f196])).
% 0.21/0.38 thf(f196,plain,(
% 0.21/0.38 ( ! [X1 : $i] : (((~ (p @ X1)) = $true) | ((~ (rel_k @ sK1 @ X1)) = $true)) )),
% 0.21/0.38 inference(binary_proxy_clausification,[],[f195])).
% 0.21/0.38 thf(f195,plain,(
% 0.21/0.38 ( ! [X1 : $i] : ((((~ (p @ X1)) | (~ (rel_k @ sK1 @ X1))) = $true)) )),
% 0.21/0.38 inference(beta_eta_normalization,[],[f194])).
% 0.21/0.38 thf(f194,plain,(
% 0.21/0.38 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0)))) @ X1) = $true)) )),
% 0.21/0.38 inference(pi_clausification,[],[f193])).
% 0.21/0.38 thf(f193,plain,(
% 0.21/0.38 ((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0))))) = $true)),
% 0.21/0.38 inference(not_proxy_clausification,[],[f152])).
% 0.21/0.38 thf(f152,plain,(
% 0.21/0.38 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))))),
% 0.21/0.38 inference(binary_proxy_clausification,[],[f151])).
% 0.21/0.38 thf(f151,plain,(
% 0.21/0.38 ($false = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (~ (r @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0))))))))),
% 0.21/0.38 inference(beta_eta_normalization,[],[f150])).
% 0.21/0.38 thf(f150,plain,(
% 0.21/0.38 (((^[Y0 : $i]: ((~ ((~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (~ (q @ Y1))) | (~ (rel_k @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (~ (r @ Y1))) | (~ (rel_k @ Y0 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_k @ Y0 @ Y1)))))))) @ sK1) = $false)),
% 0.21/0.38 inference(sigma_clausification,[],[f149])).
% 0.21/0.38 thf(f149,plain,(
% 0.21/0.38 ((!! @ $i @ (^[Y0 : $i]: ((~ ((~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (~ (q @ Y1))) | (~ (rel_k @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (~ (r @ Y1))) | (~ (rel_k @ Y0 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_k @ Y0 @ Y1))))))))) != $true)),
% 0.21/0.38 inference(boolean_simplification,[],[f148])).
% 0.21/0.38 thf(f148,plain,(
% 0.21/0.38 ((!! @ $i @ (^[Y0 : $i]: ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (~ ((~ (p @ Y1)) | (~ (q @ Y1))))) | (~ (rel_k @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (~ (r @ Y1))) | (~ (rel_k @ Y0 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_k @ Y0 @ Y1))))))))) != $true)),
% 0.21/0.38 inference(boolean_simplification,[],[f147])).
% 0.21/0.38 thf(f147,plain,(
% 0.21/0.38 ($true != (!! @ $i @ (^[Y0 : $i]: ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (~ ((~ (p @ Y1)) | (~ (q @ Y1))))) | (~ (rel_k @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (~ ((~ (p @ Y1)) | (~ (r @ Y1))))) | (~ (rel_k @ Y0 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_k @ Y0 @ Y1))))))))))),
% 0.21/0.38 inference(beta_eta_normalization,[],[f146])).
% 0.21/0.38 thf(f146,plain,(
% 0.21/0.38 (((^[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]: ((Y1 @ Y3) | (~ (rel_k @ Y2 @ 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]: ((Y1 @ Y3) | (~ (rel_k @ Y2 @ 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]: ((Y1 @ Y3) | (~ (rel_k @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ p))) != $true)),
% 0.21/0.38 inference(definition_unfolding,[],[f121,f115,f137,f127,f145,f136,f145,f136,f145])).
% 0.21/0.38 thf(f136,plain,(
% 0.21/0.38 (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)))))))),
% 0.21/0.38 inference(definition_unfolding,[],[f105,f102,f127,f102,f102])).
% 0.21/0.38 thf(f102,plain,(
% 0.21/0.38 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.21/0.38 inference(cnf_transformation,[],[f94])).
% 0.21/0.38 thf(f94,plain,(
% 0.21/0.38 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.21/0.38 inference(fool_elimination,[],[f93])).
% 0.21/0.38 thf(f93,plain,(
% 0.21/0.38 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.21/0.38 inference(rectify,[],[f3])).
% 0.21/0.38 thf(f3,axiom,(
% 0.21/0.38 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)),
% 0.21/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.21/0.38 thf(f105,plain,(
% 0.21/0.38 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.21/0.38 inference(cnf_transformation,[],[f77])).
% 0.21/0.38 thf(f77,plain,(
% 0.21/0.38 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.21/0.38 inference(fool_elimination,[],[f76])).
% 0.21/0.38 thf(f76,plain,(
% 0.21/0.38 (mand = (^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))))),
% 0.21/0.38 inference(rectify,[],[f5])).
% 0.21/0.38 thf(f5,axiom,(
% 0.21/0.38 (mand = (^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))))),
% 0.21/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand)).
% 0.21/0.38 thf(f145,plain,(
% 0.21/0.38 (mdia_k = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_k @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))))),
% 0.21/0.38 inference(definition_unfolding,[],[f126,f102,f117,f102])).
% 0.21/0.38 thf(f117,plain,(
% 0.21/0.38 (mbox_k = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_k @ Y1 @ Y2)))))))))),
% 0.21/0.38 inference(cnf_transformation,[],[f46])).
% 0.21/0.38 thf(f46,plain,(
% 0.21/0.38 (mbox_k = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_k @ Y1 @ Y2)))))))))),
% 0.21/0.38 inference(fool_elimination,[],[f45])).
% 0.21/0.38 thf(f45,plain,(
% 0.21/0.38 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : (~(rel_k @ X1 @ X2) | (X0 @ X2)))) = mbox_k)),
% 0.21/0.38 inference(rectify,[],[f32])).
% 0.21/0.38 thf(f32,axiom,(
% 0.21/0.38 ((^[X3 : $i > $o, X2 : $i] : (! [X7] : (~(rel_k @ X2 @ X7) | (X3 @ X7)))) = mbox_k)),
% 0.21/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_k)).
% 0.21/0.38 thf(f126,plain,(
% 0.21/0.38 (mdia_k = (^[Y0 : $i > $o]: (mnot @ (mbox_k @ (mnot @ Y0)))))),
% 0.21/0.38 inference(cnf_transformation,[],[f75])).
% 0.21/0.38 thf(f75,plain,(
% 0.21/0.38 (mdia_k = (^[Y0 : $i > $o]: (mnot @ (mbox_k @ (mnot @ Y0)))))),
% 0.21/0.38 inference(fool_elimination,[],[f74])).
% 0.21/0.38 thf(f74,plain,(
% 0.21/0.38 (mdia_k = (^[X0 : $i > $o] : (mnot @ (mbox_k @ (mnot @ X0)))))),
% 0.21/0.38 inference(rectify,[],[f33])).
% 0.21/0.38 thf(f33,axiom,(
% 0.21/0.38 (mdia_k = (^[X3 : $i > $o] : (mnot @ (mbox_k @ (mnot @ X3)))))),
% 0.21/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_k)).
% 0.21/0.38 thf(f127,plain,(
% 0.21/0.38 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.21/0.38 inference(cnf_transformation,[],[f96])).
% 0.21/0.38 thf(f96,plain,(
% 0.21/0.38 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.21/0.38 inference(fool_elimination,[],[f95])).
% 0.21/0.38 thf(f95,plain,(
% 0.21/0.38 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))) = mor)),
% 0.21/0.38 inference(rectify,[],[f4])).
% 0.21/0.38 thf(f4,axiom,(
% 0.21/0.38 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))) = mor)),
% 0.21/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.21/0.38 thf(f137,plain,(
% 0.21/0.38 (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)))))),
% 0.21/0.38 inference(definition_unfolding,[],[f108,f127,f102])).
% 0.21/0.38 thf(f108,plain,(
% 0.21/0.38 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.21/0.38 inference(cnf_transformation,[],[f42])).
% 0.21/0.38 thf(f42,plain,(
% 0.21/0.38 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.21/0.38 inference(fool_elimination,[],[f41])).
% 0.21/0.38 thf(f41,plain,(
% 0.21/0.38 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.21/0.38 inference(rectify,[],[f6])).
% 0.21/0.38 thf(f6,axiom,(
% 0.21/0.38 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.21/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.21/0.38 thf(f115,plain,(
% 0.21/0.38 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.21/0.38 inference(cnf_transformation,[],[f100])).
% 0.21/0.38 thf(f100,plain,(
% 0.21/0.38 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.21/0.38 inference(fool_elimination,[],[f99])).
% 0.21/0.38 thf(f99,plain,(
% 0.21/0.38 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.21/0.38 inference(rectify,[],[f28])).
% 0.21/0.38 thf(f28,axiom,(
% 0.21/0.38 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.21/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.21/0.38 thf(f121,plain,(
% 0.21/0.38 ((mvalid @ (mimplies @ (mor @ (mdia_k @ (mand @ p @ q)) @ (mdia_k @ (mand @ p @ r))) @ (mdia_k @ p))) != $true)),
% 0.21/0.38 inference(cnf_transformation,[],[f101])).
% 0.21/0.38 thf(f101,plain,(
% 0.21/0.38 ((mvalid @ (mimplies @ (mor @ (mdia_k @ (mand @ p @ q)) @ (mdia_k @ (mand @ p @ r))) @ (mdia_k @ p))) != $true)),
% 0.21/0.38 inference(flattening,[],[f63])).
% 0.21/0.38 thf(f63,plain,(
% 0.21/0.38 ~((mvalid @ (mimplies @ (mor @ (mdia_k @ (mand @ p @ q)) @ (mdia_k @ (mand @ p @ r))) @ (mdia_k @ p))) = $true)),
% 0.21/0.38 inference(fool_elimination,[],[f62])).
% 0.21/0.38 thf(f62,plain,(
% 0.21/0.38 ~(mvalid @ (mimplies @ (mor @ (mdia_k @ (mand @ p @ q)) @ (mdia_k @ (mand @ p @ r))) @ (mdia_k @ p)))),
% 0.21/0.38 inference(rectify,[],[f35])).
% 0.21/0.38 thf(f35,negated_conjecture,(
% 0.21/0.38 ~(mvalid @ (mimplies @ (mor @ (mdia_k @ (mand @ p @ q)) @ (mdia_k @ (mand @ p @ r))) @ (mdia_k @ p)))),
% 0.21/0.38 inference(negated_conjecture,[],[f34])).
% 0.21/0.38 thf(f34,conjecture,(
% 0.21/0.38 (mvalid @ (mimplies @ (mor @ (mdia_k @ (mand @ p @ q)) @ (mdia_k @ (mand @ p @ r))) @ (mdia_k @ p)))),
% 0.21/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove)).
% 0.21/0.38 thf(f241,plain,(
% 0.21/0.38 ~spl0_2 | ~spl0_4),
% 0.21/0.38 inference(avatar_contradiction_clause,[],[f240])).
% 0.21/0.38 thf(f240,plain,(
% 0.21/0.38 $false | (~spl0_2 | ~spl0_4)),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f237])).
% 0.21/0.38 thf(f237,plain,(
% 0.21/0.38 ($false = $true) | (~spl0_2 | ~spl0_4)),
% 0.21/0.38 inference(superposition,[],[f216,f235])).
% 0.21/0.38 thf(f235,plain,(
% 0.21/0.38 ($false = (p @ sK3)) | ~spl0_2),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f233])).
% 0.21/0.38 thf(f233,plain,(
% 0.21/0.38 ($false = $true) | ($false = (p @ sK3)) | ~spl0_2),
% 0.21/0.38 inference(superposition,[],[f198,f206])).
% 0.21/0.38 thf(f206,plain,(
% 0.21/0.38 ((rel_k @ sK1 @ sK3) = $true) | ~spl0_2),
% 0.21/0.38 inference(avatar_component_clause,[],[f204])).
% 0.21/0.38 thf(f204,plain,(
% 0.21/0.38 spl0_2 <=> ((rel_k @ sK1 @ sK3) = $true)),
% 0.21/0.38 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.21/0.38 thf(f216,plain,(
% 0.21/0.38 ($true = (p @ sK3)) | ~spl0_4),
% 0.21/0.38 inference(avatar_component_clause,[],[f214])).
% 0.21/0.38 thf(f214,plain,(
% 0.21/0.38 spl0_4 <=> ($true = (p @ sK3))),
% 0.21/0.38 introduced(avatar_definition,[new_symbols(naming,[spl0_4])])).
% 0.21/0.38 thf(f231,plain,(
% 0.21/0.38 spl0_4 | spl0_6),
% 0.21/0.38 inference(avatar_split_clause,[],[f171,f226,f214])).
% 0.21/0.38 thf(f171,plain,(
% 0.21/0.38 ($true = (p @ sK3)) | ($true = (p @ sK2))),
% 0.21/0.38 inference(not_proxy_clausification,[],[f170])).
% 0.21/0.38 thf(f170,plain,(
% 0.21/0.38 ((~ (p @ sK3)) = $false) | ($true = (p @ sK2))),
% 0.21/0.38 inference(binary_proxy_clausification,[],[f168])).
% 0.21/0.38 thf(f168,plain,(
% 0.21/0.38 ($true = (p @ sK2)) | ($false = ((~ (p @ sK3)) | (~ (q @ sK3))))),
% 0.21/0.38 inference(binary_proxy_clausification,[],[f166])).
% 0.21/0.38 thf(f166,plain,(
% 0.21/0.38 ($false = (((~ (p @ sK3)) | (~ (q @ sK3))) | (~ (rel_k @ sK1 @ sK3)))) | ($true = (p @ sK2))),
% 0.21/0.38 inference(not_proxy_clausification,[],[f165])).
% 0.21/0.38 thf(f165,plain,(
% 0.21/0.38 ($false = (~ (p @ sK2))) | ($false = (((~ (p @ sK3)) | (~ (q @ sK3))) | (~ (rel_k @ sK1 @ sK3))))),
% 0.21/0.38 inference(binary_proxy_clausification,[],[f163])).
% 0.21/0.38 thf(f163,plain,(
% 0.21/0.38 ($false = ((~ (p @ sK2)) | (~ (r @ sK2)))) | ($false = (((~ (p @ sK3)) | (~ (q @ sK3))) | (~ (rel_k @ sK1 @ sK3))))),
% 0.21/0.38 inference(binary_proxy_clausification,[],[f161])).
% 0.21/0.38 thf(f161,plain,(
% 0.21/0.38 ($false = (((~ (p @ sK2)) | (~ (r @ sK2))) | (~ (rel_k @ sK1 @ sK2)))) | ($false = (((~ (p @ sK3)) | (~ (q @ sK3))) | (~ (rel_k @ sK1 @ sK3))))),
% 0.21/0.38 inference(beta_eta_normalization,[],[f160])).
% 0.21/0.38 thf(f160,plain,(
% 0.21/0.38 (((^[Y0 : $i]: (((~ (p @ Y0)) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0)))) @ sK3) = $false) | ($false = (((~ (p @ sK2)) | (~ (r @ sK2))) | (~ (rel_k @ sK1 @ sK2))))),
% 0.21/0.38 inference(sigma_clausification,[],[f159])).
% 0.21/0.38 thf(f159,plain,(
% 0.21/0.38 ($false = (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))) | ($false = (((~ (p @ sK2)) | (~ (r @ sK2))) | (~ (rel_k @ sK1 @ sK2))))),
% 0.21/0.38 inference(beta_eta_normalization,[],[f158])).
% 0.21/0.38 thf(f158,plain,(
% 0.21/0.38 (((^[Y0 : $i]: (((~ (p @ Y0)) | (~ (r @ Y0))) | (~ (rel_k @ sK1 @ Y0)))) @ sK2) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0))))))),
% 0.21/0.38 inference(sigma_clausification,[],[f157])).
% 0.21/0.38 thf(f157,plain,(
% 0.21/0.38 ((!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (~ (r @ Y0))) | (~ (rel_k @ sK1 @ Y0))))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0))))))),
% 0.21/0.38 inference(not_proxy_clausification,[],[f156])).
% 0.21/0.38 thf(f156,plain,(
% 0.21/0.38 ((~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (~ (r @ Y0))) | (~ (rel_k @ sK1 @ Y0))))) = $false)),
% 0.21/0.38 inference(not_proxy_clausification,[],[f155])).
% 0.21/0.38 thf(f155,plain,(
% 0.21/0.38 ((~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (~ (r @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))) = $true)),
% 0.21/0.38 inference(binary_proxy_clausification,[],[f154])).
% 0.21/0.38 thf(f154,plain,(
% 0.21/0.38 (((~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (~ (r @ Y0))) | (~ (rel_k @ sK1 @ Y0))))))) = $true)),
% 0.21/0.38 inference(not_proxy_clausification,[],[f153])).
% 0.21/0.38 thf(f153,plain,(
% 0.21/0.38 ((~ ((~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (~ (r @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))))) = $false)),
% 0.21/0.38 inference(binary_proxy_clausification,[],[f151])).
% 0.21/0.38 thf(f229,plain,(
% 0.21/0.38 spl0_6 | spl0_2),
% 0.21/0.38 inference(avatar_split_clause,[],[f173,f204,f226])).
% 0.21/0.38 thf(f173,plain,(
% 0.21/0.38 ($true = (p @ sK2)) | ((rel_k @ sK1 @ sK3) = $true)),
% 0.21/0.38 inference(not_proxy_clausification,[],[f167])).
% 0.21/0.38 thf(f167,plain,(
% 0.21/0.38 ((~ (rel_k @ sK1 @ sK3)) = $false) | ($true = (p @ sK2))),
% 0.21/0.38 inference(binary_proxy_clausification,[],[f166])).
% 0.21/0.38 thf(f217,plain,(
% 0.21/0.38 spl0_1 | spl0_4),
% 0.21/0.38 inference(avatar_split_clause,[],[f188,f214,f200])).
% 0.21/0.38 thf(f188,plain,(
% 0.21/0.38 ($true = (p @ sK3)) | ((rel_k @ sK1 @ sK2) = $true)),
% 0.21/0.38 inference(not_proxy_clausification,[],[f187])).
% 0.21/0.38 thf(f187,plain,(
% 0.21/0.38 ((rel_k @ sK1 @ sK2) = $true) | ((~ (p @ sK3)) = $false)),
% 0.21/0.38 inference(not_proxy_clausification,[],[f186])).
% 0.21/0.38 thf(f186,plain,(
% 0.21/0.38 ((~ (rel_k @ sK1 @ sK2)) = $false) | ((~ (p @ sK3)) = $false)),
% 0.21/0.38 inference(binary_proxy_clausification,[],[f184])).
% 0.21/0.38 thf(f184,plain,(
% 0.21/0.38 ($false = ((~ (p @ sK3)) | (~ (q @ sK3)))) | ((~ (rel_k @ sK1 @ sK2)) = $false)),
% 0.21/0.38 inference(binary_proxy_clausification,[],[f162])).
% 0.21/0.38 thf(f162,plain,(
% 0.21/0.38 ($false = (((~ (p @ sK3)) | (~ (q @ sK3))) | (~ (rel_k @ sK1 @ sK3)))) | ((~ (rel_k @ sK1 @ sK2)) = $false)),
% 0.21/0.38 inference(binary_proxy_clausification,[],[f161])).
% 0.21/0.38 thf(f207,plain,(
% 0.21/0.38 spl0_1 | spl0_2),
% 0.21/0.38 inference(avatar_split_clause,[],[f192,f204,f200])).
% 0.21/0.38 thf(f192,plain,(
% 0.21/0.38 ((rel_k @ sK1 @ sK2) = $true) | ((rel_k @ sK1 @ sK3) = $true)),
% 0.21/0.38 inference(not_proxy_clausification,[],[f191])).
% 0.21/0.38 thf(f191,plain,(
% 0.21/0.38 ((~ (rel_k @ sK1 @ sK3)) = $false) | ((rel_k @ sK1 @ sK2) = $true)),
% 0.21/0.38 inference(not_proxy_clausification,[],[f183])).
% 0.21/0.38 thf(f183,plain,(
% 0.21/0.38 ((~ (rel_k @ sK1 @ sK2)) = $false) | ((~ (rel_k @ sK1 @ sK3)) = $false)),
% 0.21/0.38 inference(binary_proxy_clausification,[],[f162])).
% 0.21/0.38 % SZS output end Proof for theBenchmark
% 0.21/0.38 % (14260)------------------------------
% 0.21/0.38 % (14260)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (14260)Termination reason: Refutation
% 0.21/0.38
% 0.21/0.38 % (14260)Memory used [KB]: 5756
% 0.21/0.38 % (14260)Time elapsed: 0.014 s
% 0.21/0.38 % (14260)Instructions burned: 14 (million)
% 0.21/0.38 % (14260)------------------------------
% 0.21/0.38 % (14260)------------------------------
% 0.21/0.38 % (14259)Success in time 0.014 s
% 0.21/0.38 % Vampire---4.8 exiting
%------------------------------------------------------------------------------