TSTP Solution File: SYO450^3 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO450^3 : 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 : n011.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 09:04:30 EDT 2024
% Result : Theorem 0.16s 0.43s
% Output : Refutation 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO450^3 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.15 % 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
% 0.16/0.39 % Computer : n011.cluster.edu
% 0.16/0.39 % Model : x86_64 x86_64
% 0.16/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.39 % Memory : 8042.1875MB
% 0.16/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.39 % CPULimit : 300
% 0.16/0.39 % WCLimit : 300
% 0.16/0.39 % DateTime : Mon May 20 10:15:23 EDT 2024
% 0.16/0.39 % CPUTime :
% 0.16/0.39 This is a TH0_THM_EQU_NAR problem
% 0.16/0.39 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
% 0.16/0.41 % (22736)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)
% 0.16/0.41 % (22735)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.16/0.41 % (22740)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)
% 0.16/0.41 % (22737)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)
% 0.16/0.41 % (22739)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)
% 0.16/0.41 % (22738)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.16/0.41 % (22741)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.16/0.41 % (22742)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)
% 0.16/0.41 % (22738)Instruction limit reached!
% 0.16/0.41 % (22738)------------------------------
% 0.16/0.41 % (22738)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.41 % (22738)Termination reason: Unknown
% 0.16/0.41 % (22738)Termination phase: shuffling
% 0.16/0.41 % (22739)Instruction limit reached!
% 0.16/0.41 % (22739)------------------------------
% 0.16/0.41 % (22739)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.41
% 0.16/0.41 % (22738)Memory used [KB]: 1023
% 0.16/0.41 % (22738)Time elapsed: 0.003 s
% 0.16/0.41 % (22738)Instructions burned: 2 (million)
% 0.16/0.41 % (22738)------------------------------
% 0.16/0.41 % (22738)------------------------------
% 0.16/0.41 % (22739)Termination reason: Unknown
% 0.16/0.41 % (22739)Termination phase: shuffling
% 0.16/0.41
% 0.16/0.41 % (22739)Memory used [KB]: 1023
% 0.16/0.41 % (22739)Time elapsed: 0.003 s
% 0.16/0.41 % (22739)Instructions burned: 2 (million)
% 0.16/0.41 % (22739)------------------------------
% 0.16/0.41 % (22739)------------------------------
% 0.16/0.42 % (22742)Instruction limit reached!
% 0.16/0.42 % (22742)------------------------------
% 0.16/0.42 % (22742)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.42 % (22742)Termination reason: Unknown
% 0.16/0.42 % (22742)Termination phase: Property scanning
% 0.16/0.42
% 0.16/0.42 % (22742)Memory used [KB]: 1023
% 0.16/0.42 % (22742)Time elapsed: 0.004 s
% 0.16/0.42 % (22736)Instruction limit reached!
% 0.16/0.42 % (22736)------------------------------
% 0.16/0.42 % (22736)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.42 % (22736)Termination reason: Unknown
% 0.16/0.42 % (22736)Termination phase: Property scanning
% 0.16/0.42
% 0.16/0.42 % (22736)Memory used [KB]: 1023
% 0.16/0.42 % (22736)Time elapsed: 0.005 s
% 0.16/0.42 % (22736)Instructions burned: 5 (million)
% 0.16/0.42 % (22736)------------------------------
% 0.16/0.42 % (22736)------------------------------
% 0.16/0.42 % (22742)Instructions burned: 4 (million)
% 0.16/0.42 % (22742)------------------------------
% 0.16/0.42 % (22742)------------------------------
% 0.16/0.42 % (22740)Refutation not found, incomplete strategy
% 0.16/0.42 % (22740)------------------------------
% 0.16/0.42 % (22740)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.42 % (22740)Termination reason: Refutation not found, incomplete strategy
% 0.16/0.42
% 0.16/0.42
% 0.16/0.42 % (22740)Memory used [KB]: 5628
% 0.16/0.42 % (22740)Time elapsed: 0.007 s
% 0.16/0.42 % (22740)Instructions burned: 8 (million)
% 0.16/0.42 % (22740)------------------------------
% 0.16/0.42 % (22740)------------------------------
% 0.16/0.42 % (22741)Instruction limit reached!
% 0.16/0.42 % (22741)------------------------------
% 0.16/0.42 % (22741)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.42 % (22741)Termination reason: Unknown
% 0.16/0.42 % (22741)Termination phase: Saturation
% 0.16/0.42
% 0.16/0.42 % (22741)Memory used [KB]: 5628
% 0.16/0.42 % (22741)Time elapsed: 0.012 s
% 0.16/0.42 % (22741)Instructions burned: 18 (million)
% 0.16/0.42 % (22741)------------------------------
% 0.16/0.42 % (22741)------------------------------
% 0.16/0.43 % (22735)First to succeed.
% 0.16/0.43 % (22737)Instruction limit reached!
% 0.16/0.43 % (22737)------------------------------
% 0.16/0.43 % (22737)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.43 % (22737)Termination reason: Unknown
% 0.16/0.43 % (22737)Termination phase: Saturation
% 0.16/0.43
% 0.16/0.43 % (22744)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.16/0.43 % (22743)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)
% 0.16/0.43 % (22737)Memory used [KB]: 5756
% 0.16/0.43 % (22737)Time elapsed: 0.018 s
% 0.16/0.43 % (22737)Instructions burned: 27 (million)
% 0.16/0.43 % (22737)------------------------------
% 0.16/0.43 % (22737)------------------------------
% 0.16/0.43 % (22745)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.16/0.43 % (22746)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.16/0.43 % (22735)Refutation found. Thanks to Tanya!
% 0.16/0.43 % SZS status Theorem for theBenchmark
% 0.16/0.43 % SZS output start Proof for theBenchmark
% 0.16/0.43 thf(type_def_5, type, mu: $tType).
% 0.16/0.43 thf(func_def_0, type, mu: $tType).
% 0.16/0.43 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.16/0.43 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.43 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.16/0.43 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.43 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.43 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.43 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.43 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.43 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.43 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.16/0.43 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.16/0.43 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.16/0.43 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.16/0.43 thf(func_def_15, type, mtrue: $i > $o).
% 0.16/0.43 thf(func_def_16, type, mfalse: $i > $o).
% 0.16/0.43 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.16/0.43 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.16/0.43 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.16/0.43 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.16/0.43 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.16/0.43 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.16/0.43 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.16/0.43 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.16/0.43 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.16/0.43 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.16/0.43 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.16/0.43 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.16/0.43 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.16/0.43 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.16/0.43 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.16/0.43 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.16/0.43 thf(func_def_33, type, rel_m: $i > $i > $o).
% 0.16/0.43 thf(func_def_34, type, mbox_m: ($i > $o) > $i > $o).
% 0.16/0.43 thf(func_def_35, type, mdia_m: ($i > $o) > $i > $o).
% 0.16/0.43 thf(func_def_36, type, p: $i > $o).
% 0.16/0.43 thf(func_def_37, type, q: $i > $o).
% 0.16/0.43 thf(func_def_38, type, r: $i > $o).
% 0.16/0.43 thf(func_def_56, type, sK2: $i > $i).
% 0.16/0.43 thf(f361,plain,(
% 0.16/0.43 $false),
% 0.16/0.43 inference(avatar_sat_refutation,[],[f269,f276,f283,f290,f347,f353,f360])).
% 0.16/0.43 thf(f360,plain,(
% 0.16/0.43 ~spl0_5 | ~spl0_12),
% 0.16/0.43 inference(avatar_contradiction_clause,[],[f359])).
% 0.16/0.43 thf(f359,plain,(
% 0.16/0.43 $false | (~spl0_5 | ~spl0_12)),
% 0.16/0.43 inference(trivial_inequality_removal,[],[f356])).
% 0.16/0.43 thf(f356,plain,(
% 0.16/0.43 ($true = $false) | (~spl0_5 | ~spl0_12)),
% 0.16/0.43 inference(superposition,[],[f262,f342])).
% 0.16/0.43 thf(f342,plain,(
% 0.16/0.43 ($false = (q @ (sK2 @ sK1))) | ~spl0_12),
% 0.16/0.43 inference(avatar_component_clause,[],[f340])).
% 0.16/0.43 thf(f340,plain,(
% 0.16/0.43 spl0_12 <=> ($false = (q @ (sK2 @ sK1)))),
% 0.16/0.43 introduced(avatar_definition,[new_symbols(naming,[spl0_12])])).
% 0.16/0.43 thf(f262,plain,(
% 0.16/0.43 ($true = (q @ (sK2 @ sK1))) | ~spl0_5),
% 0.16/0.43 inference(avatar_component_clause,[],[f260])).
% 0.16/0.43 thf(f260,plain,(
% 0.16/0.43 spl0_5 <=> ($true = (q @ (sK2 @ sK1)))),
% 0.16/0.43 introduced(avatar_definition,[new_symbols(naming,[spl0_5])])).
% 0.16/0.43 thf(f353,plain,(
% 0.16/0.43 ~spl0_6 | ~spl0_11),
% 0.16/0.43 inference(avatar_contradiction_clause,[],[f352])).
% 0.16/0.43 thf(f352,plain,(
% 0.16/0.43 $false | (~spl0_6 | ~spl0_11)),
% 0.16/0.43 inference(trivial_inequality_removal,[],[f349])).
% 0.16/0.43 thf(f349,plain,(
% 0.16/0.43 ($true = $false) | (~spl0_6 | ~spl0_11)),
% 0.16/0.43 inference(superposition,[],[f267,f338])).
% 0.16/0.43 thf(f338,plain,(
% 0.16/0.43 ($true = (r @ (sK2 @ sK1))) | ~spl0_11),
% 0.16/0.43 inference(avatar_component_clause,[],[f336])).
% 0.16/0.43 thf(f336,plain,(
% 0.16/0.43 spl0_11 <=> ($true = (r @ (sK2 @ sK1)))),
% 0.16/0.43 introduced(avatar_definition,[new_symbols(naming,[spl0_11])])).
% 0.16/0.43 thf(f267,plain,(
% 0.16/0.43 ((r @ (sK2 @ sK1)) = $false) | ~spl0_6),
% 0.16/0.43 inference(avatar_component_clause,[],[f265])).
% 0.16/0.43 thf(f265,plain,(
% 0.16/0.43 spl0_6 <=> ((r @ (sK2 @ sK1)) = $false)),
% 0.16/0.43 introduced(avatar_definition,[new_symbols(naming,[spl0_6])])).
% 0.16/0.43 thf(f347,plain,(
% 0.16/0.43 spl0_11 | spl0_12 | spl0_2),
% 0.16/0.43 inference(avatar_split_clause,[],[f346,f246,f340,f336])).
% 0.16/0.43 thf(f246,plain,(
% 0.16/0.43 spl0_2 <=> ($false = (p @ sK1))),
% 0.16/0.43 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.16/0.43 thf(f346,plain,(
% 0.16/0.43 ($false = (q @ (sK2 @ sK1))) | ($true = (r @ (sK2 @ sK1))) | spl0_2),
% 0.16/0.43 inference(subsumption_resolution,[],[f329,f247])).
% 0.16/0.43 thf(f247,plain,(
% 0.16/0.43 ($false != (p @ sK1)) | spl0_2),
% 0.16/0.43 inference(avatar_component_clause,[],[f246])).
% 0.16/0.43 thf(f329,plain,(
% 0.16/0.43 ($false = (p @ sK1)) | ($true = (r @ (sK2 @ sK1))) | ($false = (q @ (sK2 @ sK1)))),
% 0.16/0.43 inference(trivial_inequality_removal,[],[f326])).
% 0.16/0.43 thf(f326,plain,(
% 0.16/0.43 ($false = (q @ (sK2 @ sK1))) | ($true = (r @ (sK2 @ sK1))) | ($true = $false) | ($false = (p @ sK1))),
% 0.16/0.43 inference(superposition,[],[f197,f171])).
% 0.16/0.43 thf(f171,plain,(
% 0.16/0.43 ( ! [X1 : $i] : (((rel_m @ sK1 @ X1) = $false) | ($false = (p @ X1)) | ($true = (r @ (sK2 @ X1))) | ((q @ (sK2 @ X1)) = $false)) )),
% 0.16/0.43 inference(not_proxy_clausification,[],[f170])).
% 0.16/0.43 thf(f170,plain,(
% 0.16/0.43 ( ! [X1 : $i] : (($false = (p @ X1)) | ($true = (~ (q @ (sK2 @ X1)))) | ((rel_m @ sK1 @ X1) = $false) | ($true = (r @ (sK2 @ X1)))) )),
% 0.16/0.43 inference(binary_proxy_clausification,[],[f169])).
% 0.16/0.43 thf(f169,plain,(
% 0.16/0.43 ( ! [X1 : $i] : (($false = (p @ X1)) | ((rel_m @ sK1 @ X1) = $false) | ($true = ((~ (q @ (sK2 @ X1))) | (r @ (sK2 @ X1))))) )),
% 0.16/0.43 inference(not_proxy_clausification,[],[f168])).
% 0.16/0.43 thf(f168,plain,(
% 0.16/0.43 ( ! [X1 : $i] : (((rel_m @ sK1 @ X1) = $false) | ($false = (p @ X1)) | ($false = (~ ((~ (q @ (sK2 @ X1))) | (r @ (sK2 @ X1)))))) )),
% 0.16/0.43 inference(binary_proxy_clausification,[],[f166])).
% 0.16/0.43 thf(f166,plain,(
% 0.16/0.43 ( ! [X1 : $i] : (($false = ((~ ((~ (q @ (sK2 @ X1))) | (r @ (sK2 @ X1)))) | (~ (rel_m @ X1 @ (sK2 @ X1))))) | ($false = (p @ X1)) | ((rel_m @ sK1 @ X1) = $false)) )),
% 0.16/0.43 inference(beta_eta_normalization,[],[f165])).
% 0.16/0.43 thf(f165,plain,(
% 0.16/0.43 ( ! [X1 : $i] : (($false = (p @ X1)) | ((rel_m @ sK1 @ X1) = $false) | ($false = ((^[Y0 : $i]: ((~ ((~ (q @ Y0)) | (r @ Y0))) | (~ (rel_m @ X1 @ Y0)))) @ (sK2 @ X1)))) )),
% 0.16/0.43 inference(sigma_clausification,[],[f164])).
% 0.16/0.43 thf(f164,plain,(
% 0.16/0.43 ( ! [X1 : $i] : (((rel_m @ sK1 @ X1) = $false) | ($false = (p @ X1)) | ($false = (!! @ $i @ (^[Y0 : $i]: ((~ ((~ (q @ Y0)) | (r @ Y0))) | (~ (rel_m @ X1 @ Y0))))))) )),
% 0.16/0.43 inference(not_proxy_clausification,[],[f163])).
% 0.16/0.43 thf(f163,plain,(
% 0.16/0.43 ( ! [X1 : $i] : (((rel_m @ sK1 @ X1) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ ((~ (q @ Y0)) | (r @ Y0))) | (~ (rel_m @ X1 @ Y0))))))) | ($false = (p @ X1))) )),
% 0.16/0.43 inference(not_proxy_clausification,[],[f162])).
% 0.16/0.43 thf(f162,plain,(
% 0.16/0.43 ( ! [X1 : $i] : (((~ (p @ X1)) = $true) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ ((~ (q @ Y0)) | (r @ Y0))) | (~ (rel_m @ X1 @ Y0))))))) | ((rel_m @ sK1 @ X1) = $false)) )),
% 0.16/0.43 inference(not_proxy_clausification,[],[f161])).
% 0.16/0.43 thf(f161,plain,(
% 0.16/0.43 ( ! [X1 : $i] : (($true = (~ (rel_m @ sK1 @ X1))) | ((~ (p @ X1)) = $true) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ ((~ (q @ Y0)) | (r @ Y0))) | (~ (rel_m @ X1 @ Y0)))))))) )),
% 0.16/0.43 inference(binary_proxy_clausification,[],[f160])).
% 0.16/0.43 thf(f160,plain,(
% 0.16/0.43 ( ! [X1 : $i] : ((((~ (p @ X1)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ ((~ (q @ Y0)) | (r @ Y0))) | (~ (rel_m @ X1 @ Y0))))))) = $true) | ($true = (~ (rel_m @ sK1 @ X1)))) )),
% 0.16/0.43 inference(binary_proxy_clausification,[],[f159])).
% 0.16/0.43 thf(f159,plain,(
% 0.16/0.43 ( ! [X1 : $i] : (($true = (((~ (p @ X1)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ ((~ (q @ Y0)) | (r @ Y0))) | (~ (rel_m @ X1 @ Y0))))))) | (~ (rel_m @ sK1 @ X1))))) )),
% 0.16/0.43 inference(beta_eta_normalization,[],[f158])).
% 0.16/0.43 thf(f158,plain,(
% 0.16/0.43 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (((~ (p @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ ((~ (q @ Y1)) | (r @ Y1))) | (~ (rel_m @ Y0 @ Y1))))))) | (~ (rel_m @ sK1 @ Y0)))) @ X1))) )),
% 0.16/0.43 inference(pi_clausification,[],[f157])).
% 0.16/0.43 thf(f157,plain,(
% 0.16/0.43 ($true = (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ ((~ (q @ Y1)) | (r @ Y1))) | (~ (rel_m @ Y0 @ Y1))))))) | (~ (rel_m @ sK1 @ Y0))))))),
% 0.16/0.43 inference(not_proxy_clausification,[],[f156])).
% 0.16/0.43 thf(f156,plain,(
% 0.16/0.43 ($false = (~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ ((~ (q @ Y1)) | (r @ Y1))) | (~ (rel_m @ Y0 @ Y1))))))) | (~ (rel_m @ sK1 @ Y0)))))))),
% 0.16/0.43 inference(binary_proxy_clausification,[],[f154])).
% 0.16/0.43 thf(f154,plain,(
% 0.16/0.43 (((~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ ((~ (q @ Y1)) | (r @ Y1))) | (~ (rel_m @ Y0 @ Y1))))))) | (~ (rel_m @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ ((~ (q @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_m @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (r @ Y1)) | (~ (rel_m @ Y0 @ Y1))))))))) | (~ (rel_m @ sK1 @ Y0))))))) = $false)),
% 0.16/0.43 inference(beta_eta_normalization,[],[f153])).
% 0.16/0.43 thf(f153,plain,(
% 0.16/0.43 (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ ((~ (q @ Y2)) | (r @ Y2))) | (~ (rel_m @ Y1 @ Y2))))))) | (~ (rel_m @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ ((~ (q @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((p @ Y2) | (~ (rel_m @ Y1 @ Y2)))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (r @ Y2)) | (~ (rel_m @ Y1 @ Y2))))))))) | (~ (rel_m @ Y0 @ Y1)))))))) @ sK1) = $false)),
% 0.16/0.43 inference(sigma_clausification,[],[f152])).
% 0.16/0.43 thf(f152,plain,(
% 0.16/0.43 ($true != (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ ((~ (q @ Y2)) | (r @ Y2))) | (~ (rel_m @ Y1 @ Y2))))))) | (~ (rel_m @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ ((~ (q @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((p @ Y2) | (~ (rel_m @ Y1 @ Y2)))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (r @ Y2)) | (~ (rel_m @ Y1 @ Y2))))))))) | (~ (rel_m @ Y0 @ Y1))))))))))),
% 0.16/0.43 inference(beta_eta_normalization,[],[f150])).
% 0.16/0.43 thf(f150,plain,(
% 0.16/0.43 (((^[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]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_m @ Y1 @ Y2)))))))) @ ((^[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)))) @ p @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_m @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[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)))) @ q @ r)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_m @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[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)))) @ q @ ((^[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]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_m @ Y1 @ Y2)))))))) @ p) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_m @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ r)))))) != $true)),
% 0.16/0.43 inference(definition_unfolding,[],[f109,f111,f141,f139,f141,f149,f141,f149,f141,f141,f139,f149])).
% 0.16/0.43 thf(f149,plain,(
% 0.16/0.43 (mdia_m = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_m @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))))),
% 0.16/0.43 inference(definition_unfolding,[],[f137,f106,f139,f106])).
% 0.16/0.43 thf(f106,plain,(
% 0.16/0.43 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.16/0.43 inference(cnf_transformation,[],[f47])).
% 0.16/0.43 thf(f47,plain,(
% 0.16/0.43 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.16/0.43 inference(fool_elimination,[],[f46])).
% 0.16/0.43 thf(f46,plain,(
% 0.16/0.43 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.16/0.43 inference(rectify,[],[f3])).
% 0.16/0.43 thf(f3,axiom,(
% 0.16/0.43 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.16/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.16/0.43 thf(f137,plain,(
% 0.16/0.43 (mdia_m = (^[Y0 : $i > $o]: (mnot @ (mbox_m @ (mnot @ Y0)))))),
% 0.16/0.43 inference(cnf_transformation,[],[f39])).
% 0.16/0.43 thf(f39,plain,(
% 0.16/0.43 (mdia_m = (^[Y0 : $i > $o]: (mnot @ (mbox_m @ (mnot @ Y0)))))),
% 0.16/0.43 inference(fool_elimination,[],[f38])).
% 0.16/0.43 thf(f38,plain,(
% 0.16/0.43 ((^[X0 : $i > $o] : (mnot @ (mbox_m @ (mnot @ X0)))) = mdia_m)),
% 0.16/0.43 inference(rectify,[],[f33])).
% 0.16/0.43 thf(f33,axiom,(
% 0.16/0.43 ((^[X3 : $i > $o] : (mnot @ (mbox_m @ (mnot @ X3)))) = mdia_m)),
% 0.16/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_m)).
% 0.16/0.43 thf(f139,plain,(
% 0.16/0.43 (mbox_m = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_m @ Y1 @ Y2)))))))))),
% 0.16/0.43 inference(cnf_transformation,[],[f58])).
% 0.16/0.43 thf(f58,plain,(
% 0.16/0.43 (mbox_m = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_m @ Y1 @ Y2)))))))))),
% 0.16/0.43 inference(fool_elimination,[],[f57])).
% 0.16/0.43 thf(f57,plain,(
% 0.16/0.43 (mbox_m = (^[X0 : $i > $o, X1 : $i] : (! [X2] : (~(rel_m @ X1 @ X2) | (X0 @ X2)))))),
% 0.16/0.43 inference(rectify,[],[f32])).
% 0.16/0.43 thf(f32,axiom,(
% 0.16/0.43 (mbox_m = (^[X3 : $i > $o, X2 : $i] : (! [X7] : (~(rel_m @ X2 @ X7) | (X3 @ X7)))))),
% 0.16/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_m)).
% 0.16/0.43 thf(f141,plain,(
% 0.16/0.43 (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)))))),
% 0.16/0.43 inference(definition_unfolding,[],[f134,f107,f106])).
% 0.16/0.43 thf(f107,plain,(
% 0.16/0.43 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.16/0.43 inference(cnf_transformation,[],[f101])).
% 0.16/0.43 thf(f101,plain,(
% 0.16/0.43 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.16/0.43 inference(fool_elimination,[],[f100])).
% 0.16/0.43 thf(f100,plain,(
% 0.16/0.43 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 0.16/0.43 inference(rectify,[],[f4])).
% 0.16/0.43 thf(f4,axiom,(
% 0.16/0.43 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))))),
% 0.16/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.16/0.43 thf(f134,plain,(
% 0.16/0.43 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.16/0.43 inference(cnf_transformation,[],[f91])).
% 0.16/0.43 thf(f91,plain,(
% 0.16/0.43 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.16/0.43 inference(fool_elimination,[],[f90])).
% 0.16/0.43 thf(f90,plain,(
% 0.16/0.43 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.16/0.43 inference(rectify,[],[f6])).
% 0.16/0.43 thf(f6,axiom,(
% 0.16/0.43 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.16/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.16/0.43 thf(f111,plain,(
% 0.16/0.43 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.16/0.43 inference(cnf_transformation,[],[f43])).
% 0.16/0.43 thf(f43,plain,(
% 0.16/0.43 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.16/0.43 inference(fool_elimination,[],[f42])).
% 0.16/0.43 thf(f42,plain,(
% 0.16/0.43 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.16/0.43 inference(rectify,[],[f28])).
% 0.16/0.43 thf(f28,axiom,(
% 0.16/0.43 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.16/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.16/0.43 thf(f109,plain,(
% 0.16/0.43 ((mvalid @ (mimplies @ (mbox_m @ (mimplies @ p @ (mdia_m @ (mimplies @ q @ r)))) @ (mdia_m @ (mimplies @ q @ (mimplies @ (mbox_m @ p) @ (mdia_m @ r)))))) != $true)),
% 0.16/0.43 inference(cnf_transformation,[],[f104])).
% 0.16/0.43 thf(f104,plain,(
% 0.16/0.43 ((mvalid @ (mimplies @ (mbox_m @ (mimplies @ p @ (mdia_m @ (mimplies @ q @ r)))) @ (mdia_m @ (mimplies @ q @ (mimplies @ (mbox_m @ p) @ (mdia_m @ r)))))) != $true)),
% 0.16/0.43 inference(flattening,[],[f49])).
% 0.16/0.43 thf(f49,plain,(
% 0.16/0.43 ~((mvalid @ (mimplies @ (mbox_m @ (mimplies @ p @ (mdia_m @ (mimplies @ q @ r)))) @ (mdia_m @ (mimplies @ q @ (mimplies @ (mbox_m @ p) @ (mdia_m @ r)))))) = $true)),
% 0.16/0.43 inference(fool_elimination,[],[f48])).
% 0.16/0.43 thf(f48,plain,(
% 0.16/0.43 ~(mvalid @ (mimplies @ (mbox_m @ (mimplies @ p @ (mdia_m @ (mimplies @ q @ r)))) @ (mdia_m @ (mimplies @ q @ (mimplies @ (mbox_m @ p) @ (mdia_m @ r))))))),
% 0.16/0.43 inference(rectify,[],[f36])).
% 0.16/0.43 thf(f36,negated_conjecture,(
% 0.16/0.43 ~(mvalid @ (mimplies @ (mbox_m @ (mimplies @ p @ (mdia_m @ (mimplies @ q @ r)))) @ (mdia_m @ (mimplies @ q @ (mimplies @ (mbox_m @ p) @ (mdia_m @ r))))))),
% 0.16/0.43 inference(negated_conjecture,[],[f35])).
% 0.16/0.43 thf(f35,conjecture,(
% 0.16/0.43 (mvalid @ (mimplies @ (mbox_m @ (mimplies @ p @ (mdia_m @ (mimplies @ q @ r)))) @ (mdia_m @ (mimplies @ q @ (mimplies @ (mbox_m @ p) @ (mdia_m @ r))))))),
% 0.16/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove)).
% 0.16/0.43 thf(f197,plain,(
% 0.16/0.43 ( ! [X1 : $i] : (((rel_m @ X1 @ X1) = $true)) )),
% 0.16/0.43 inference(beta_eta_normalization,[],[f196])).
% 0.16/0.43 thf(f196,plain,(
% 0.16/0.43 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (rel_m @ Y0 @ Y0)) @ X1))) )),
% 0.16/0.43 inference(pi_clausification,[],[f195])).
% 0.16/0.43 thf(f195,plain,(
% 0.16/0.43 ($true = (!! @ $i @ (^[Y0 : $i]: (rel_m @ Y0 @ Y0))))),
% 0.16/0.43 inference(beta_eta_normalization,[],[f151])).
% 0.16/0.43 thf(f151,plain,(
% 0.16/0.43 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) @ rel_m))),
% 0.16/0.43 inference(definition_unfolding,[],[f138,f132])).
% 0.16/0.43 thf(f132,plain,(
% 0.16/0.43 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.16/0.43 inference(cnf_transformation,[],[f77])).
% 0.16/0.43 thf(f77,plain,(
% 0.16/0.43 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.16/0.43 inference(fool_elimination,[],[f76])).
% 0.16/0.43 thf(f76,plain,(
% 0.16/0.43 ((^[X0 : $i > $i > $o] : (! [X1] : (X0 @ X1 @ X1))) = mreflexive)),
% 0.16/0.43 inference(rectify,[],[f18])).
% 0.16/0.43 thf(f18,axiom,(
% 0.16/0.43 ((^[X6 : $i > $i > $o] : (! [X8] : (X6 @ X8 @ X8))) = mreflexive)),
% 0.16/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mreflexive)).
% 0.16/0.43 thf(f138,plain,(
% 0.16/0.43 ((mreflexive @ rel_m) = $true)),
% 0.16/0.43 inference(cnf_transformation,[],[f51])).
% 0.16/0.43 thf(f51,plain,(
% 0.16/0.43 ((mreflexive @ rel_m) = $true)),
% 0.16/0.43 inference(fool_elimination,[],[f50])).
% 0.16/0.43 thf(f50,plain,(
% 0.16/0.43 (mreflexive @ rel_m)),
% 0.16/0.43 inference(rectify,[],[f34])).
% 0.16/0.43 thf(f34,axiom,(
% 0.16/0.43 (mreflexive @ rel_m)),
% 0.16/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1)).
% 0.16/0.43 thf(f290,plain,(
% 0.16/0.43 ~spl0_3),
% 0.16/0.43 inference(avatar_contradiction_clause,[],[f289])).
% 0.16/0.43 thf(f289,plain,(
% 0.16/0.43 $false | ~spl0_3),
% 0.16/0.43 inference(trivial_inequality_removal,[],[f285])).
% 0.16/0.43 thf(f285,plain,(
% 0.16/0.43 ($true = $false) | ~spl0_3),
% 0.16/0.43 inference(superposition,[],[f252,f197])).
% 0.16/0.43 thf(f252,plain,(
% 0.16/0.43 ((rel_m @ sK1 @ sK1) = $false) | ~spl0_3),
% 0.16/0.43 inference(avatar_component_clause,[],[f250])).
% 0.16/0.43 thf(f250,plain,(
% 0.16/0.43 spl0_3 <=> ((rel_m @ sK1 @ sK1) = $false)),
% 0.16/0.43 introduced(avatar_definition,[new_symbols(naming,[spl0_3])])).
% 0.16/0.43 thf(f283,plain,(
% 0.16/0.43 ~spl0_2),
% 0.16/0.43 inference(avatar_contradiction_clause,[],[f282])).
% 0.16/0.43 thf(f282,plain,(
% 0.16/0.43 $false | ~spl0_2),
% 0.16/0.43 inference(trivial_inequality_removal,[],[f278])).
% 0.16/0.43 thf(f278,plain,(
% 0.16/0.43 ($true = $false) | ~spl0_2),
% 0.16/0.43 inference(superposition,[],[f248,f211])).
% 0.16/0.43 thf(f211,plain,(
% 0.16/0.43 ($true = (p @ sK1))),
% 0.16/0.43 inference(trivial_inequality_removal,[],[f209])).
% 0.16/0.43 thf(f209,plain,(
% 0.16/0.43 ($true = $false) | ($true = (p @ sK1))),
% 0.16/0.43 inference(superposition,[],[f197,f207])).
% 0.16/0.43 thf(f207,plain,(
% 0.16/0.43 ( ! [X0 : $i] : (($false = (rel_m @ sK1 @ X0)) | ((p @ X0) = $true)) )),
% 0.16/0.43 inference(trivial_inequality_removal,[],[f202])).
% 0.16/0.43 thf(f202,plain,(
% 0.16/0.43 ( ! [X0 : $i] : (($true = $false) | ($false = (rel_m @ sK1 @ X0)) | ((p @ X0) = $true)) )),
% 0.16/0.43 inference(superposition,[],[f188,f197])).
% 0.16/0.43 thf(f188,plain,(
% 0.16/0.43 ( ! [X2 : $i,X1 : $i] : (((rel_m @ sK1 @ X1) = $false) | ($true = (p @ X2)) | ((rel_m @ X1 @ X2) = $false)) )),
% 0.16/0.43 inference(not_proxy_clausification,[],[f187])).
% 0.16/0.43 thf(f187,plain,(
% 0.16/0.43 ( ! [X2 : $i,X1 : $i] : (((rel_m @ sK1 @ X1) = $false) | ($true = (p @ X2)) | ($true = (~ (rel_m @ X1 @ X2)))) )),
% 0.16/0.43 inference(binary_proxy_clausification,[],[f186])).
% 0.16/0.43 thf(f186,plain,(
% 0.16/0.43 ( ! [X2 : $i,X1 : $i] : (((rel_m @ sK1 @ X1) = $false) | (((p @ X2) | (~ (rel_m @ X1 @ X2))) = $true)) )),
% 0.16/0.43 inference(beta_eta_normalization,[],[f185])).
% 0.16/0.43 thf(f185,plain,(
% 0.16/0.43 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((p @ Y0) | (~ (rel_m @ X1 @ Y0)))) @ X2)) | ((rel_m @ sK1 @ X1) = $false)) )),
% 0.16/0.43 inference(pi_clausification,[],[f184])).
% 0.16/0.43 thf(f184,plain,(
% 0.16/0.43 ( ! [X1 : $i] : (((rel_m @ sK1 @ X1) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_m @ X1 @ Y0))))))) )),
% 0.16/0.43 inference(not_proxy_clausification,[],[f183])).
% 0.16/0.43 thf(f183,plain,(
% 0.16/0.43 ( ! [X1 : $i] : (((rel_m @ sK1 @ X1) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_m @ X1 @ Y0)))))) = $false)) )),
% 0.16/0.43 inference(binary_proxy_clausification,[],[f179])).
% 0.16/0.43 thf(f179,plain,(
% 0.16/0.43 ( ! [X1 : $i] : (($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_m @ X1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (r @ Y0)) | (~ (rel_m @ X1 @ Y0)))))))) | ((rel_m @ sK1 @ X1) = $false)) )),
% 0.16/0.43 inference(binary_proxy_clausification,[],[f178])).
% 0.16/0.43 thf(f178,plain,(
% 0.16/0.43 ( ! [X1 : $i] : (($false = ((~ (q @ X1)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_m @ X1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (r @ Y0)) | (~ (rel_m @ X1 @ Y0))))))))) | ((rel_m @ sK1 @ X1) = $false)) )),
% 0.16/0.43 inference(not_proxy_clausification,[],[f177])).
% 0.16/0.43 thf(f177,plain,(
% 0.16/0.43 ( ! [X1 : $i] : (((rel_m @ sK1 @ X1) = $false) | ($true = (~ ((~ (q @ X1)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_m @ X1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (r @ Y0)) | (~ (rel_m @ X1 @ Y0))))))))))) )),
% 0.16/0.43 inference(not_proxy_clausification,[],[f176])).
% 0.16/0.43 thf(f176,plain,(
% 0.16/0.43 ( ! [X1 : $i] : (($true = (~ (rel_m @ sK1 @ X1))) | ($true = (~ ((~ (q @ X1)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_m @ X1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (r @ Y0)) | (~ (rel_m @ X1 @ Y0))))))))))) )),
% 0.16/0.43 inference(binary_proxy_clausification,[],[f175])).
% 0.16/0.43 thf(f175,plain,(
% 0.16/0.43 ( ! [X1 : $i] : (($true = ((~ ((~ (q @ X1)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_m @ X1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (r @ Y0)) | (~ (rel_m @ X1 @ Y0))))))))) | (~ (rel_m @ sK1 @ X1))))) )),
% 0.16/0.43 inference(beta_eta_normalization,[],[f174])).
% 0.16/0.43 thf(f174,plain,(
% 0.16/0.43 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ ((~ (q @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_m @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (r @ Y1)) | (~ (rel_m @ Y0 @ Y1))))))))) | (~ (rel_m @ sK1 @ Y0)))) @ X1))) )),
% 0.16/0.43 inference(pi_clausification,[],[f173])).
% 0.16/0.43 thf(f173,plain,(
% 0.16/0.43 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ ((~ (q @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_m @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (r @ Y1)) | (~ (rel_m @ Y0 @ Y1))))))))) | (~ (rel_m @ sK1 @ Y0))))))),
% 0.16/0.43 inference(not_proxy_clausification,[],[f155])).
% 0.16/0.43 thf(f155,plain,(
% 0.16/0.43 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ ((~ (q @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_m @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (r @ Y1)) | (~ (rel_m @ Y0 @ Y1))))))))) | (~ (rel_m @ sK1 @ Y0)))))) = $false)),
% 0.16/0.43 inference(binary_proxy_clausification,[],[f154])).
% 0.16/0.43 thf(f248,plain,(
% 0.16/0.43 ($false = (p @ sK1)) | ~spl0_2),
% 0.16/0.43 inference(avatar_component_clause,[],[f246])).
% 0.16/0.43 thf(f276,plain,(
% 0.16/0.43 spl0_3 | spl0_2 | spl0_6),
% 0.16/0.43 inference(avatar_split_clause,[],[f233,f265,f246,f250])).
% 0.16/0.43 thf(f233,plain,(
% 0.16/0.43 ($false = (p @ sK1)) | ((r @ (sK2 @ sK1)) = $false) | ((rel_m @ sK1 @ sK1) = $false)),
% 0.16/0.43 inference(trivial_inequality_removal,[],[f227])).
% 0.16/0.43 thf(f227,plain,(
% 0.16/0.43 ((r @ (sK2 @ sK1)) = $false) | ($true = $false) | ((rel_m @ sK1 @ sK1) = $false) | ($false = (p @ sK1))),
% 0.16/0.43 inference(superposition,[],[f217,f172])).
% 0.16/0.43 thf(f172,plain,(
% 0.16/0.43 ( ! [X1 : $i] : (($true = (rel_m @ X1 @ (sK2 @ X1))) | ($false = (p @ X1)) | ((rel_m @ sK1 @ X1) = $false)) )),
% 0.16/0.43 inference(not_proxy_clausification,[],[f167])).
% 0.16/0.43 thf(f167,plain,(
% 0.16/0.43 ( ! [X1 : $i] : (((~ (rel_m @ X1 @ (sK2 @ X1))) = $false) | ((rel_m @ sK1 @ X1) = $false) | ($false = (p @ X1))) )),
% 0.16/0.43 inference(binary_proxy_clausification,[],[f166])).
% 0.16/0.43 thf(f217,plain,(
% 0.16/0.43 ( ! [X0 : $i] : (($false = (rel_m @ sK1 @ X0)) | ($false = (r @ X0))) )),
% 0.16/0.43 inference(trivial_inequality_removal,[],[f212])).
% 0.16/0.43 thf(f212,plain,(
% 0.16/0.43 ( ! [X0 : $i] : (($false = (r @ X0)) | ($true = $false) | ($false = (rel_m @ sK1 @ X0))) )),
% 0.16/0.43 inference(superposition,[],[f194,f197])).
% 0.16/0.43 thf(f194,plain,(
% 0.16/0.43 ( ! [X2 : $i,X1 : $i] : (((rel_m @ sK1 @ X1) = $false) | ((r @ X2) = $false) | ((rel_m @ X1 @ X2) = $false)) )),
% 0.16/0.43 inference(not_proxy_clausification,[],[f193])).
% 0.16/0.43 thf(f193,plain,(
% 0.16/0.43 ( ! [X2 : $i,X1 : $i] : (((r @ X2) = $false) | ($true = (~ (rel_m @ X1 @ X2))) | ((rel_m @ sK1 @ X1) = $false)) )),
% 0.16/0.43 inference(not_proxy_clausification,[],[f192])).
% 0.16/0.43 thf(f192,plain,(
% 0.16/0.43 ( ! [X2 : $i,X1 : $i] : (($true = (~ (r @ X2))) | ((rel_m @ sK1 @ X1) = $false) | ($true = (~ (rel_m @ X1 @ X2)))) )),
% 0.16/0.43 inference(binary_proxy_clausification,[],[f191])).
% 0.16/0.43 thf(f191,plain,(
% 0.16/0.43 ( ! [X2 : $i,X1 : $i] : ((((~ (r @ X2)) | (~ (rel_m @ X1 @ X2))) = $true) | ((rel_m @ sK1 @ X1) = $false)) )),
% 0.16/0.43 inference(beta_eta_normalization,[],[f190])).
% 0.16/0.43 thf(f190,plain,(
% 0.16/0.43 ( ! [X2 : $i,X1 : $i] : (((rel_m @ sK1 @ X1) = $false) | ($true = ((^[Y0 : $i]: ((~ (r @ Y0)) | (~ (rel_m @ X1 @ Y0)))) @ X2))) )),
% 0.16/0.43 inference(pi_clausification,[],[f189])).
% 0.16/0.43 thf(f189,plain,(
% 0.16/0.43 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (r @ Y0)) | (~ (rel_m @ X1 @ Y0)))))) | ((rel_m @ sK1 @ X1) = $false)) )),
% 0.16/0.43 inference(not_proxy_clausification,[],[f182])).
% 0.16/0.43 thf(f182,plain,(
% 0.16/0.43 ( ! [X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (r @ Y0)) | (~ (rel_m @ X1 @ Y0)))))) = $false) | ((rel_m @ sK1 @ X1) = $false)) )),
% 0.16/0.43 inference(binary_proxy_clausification,[],[f179])).
% 0.16/0.43 thf(f269,plain,(
% 0.16/0.43 spl0_2 | spl0_3 | spl0_5),
% 0.16/0.43 inference(avatar_split_clause,[],[f237,f260,f250,f246])).
% 0.16/0.43 thf(f237,plain,(
% 0.16/0.43 ((rel_m @ sK1 @ sK1) = $false) | ($false = (p @ sK1)) | ($true = (q @ (sK2 @ sK1)))),
% 0.16/0.43 inference(trivial_inequality_removal,[],[f231])).
% 0.16/0.43 thf(f231,plain,(
% 0.16/0.43 ($false = (p @ sK1)) | ($true = $false) | ((rel_m @ sK1 @ sK1) = $false) | ($true = (q @ (sK2 @ sK1)))),
% 0.16/0.43 inference(superposition,[],[f181,f172])).
% 0.16/0.43 thf(f181,plain,(
% 0.16/0.43 ( ! [X1 : $i] : (((rel_m @ sK1 @ X1) = $false) | ($true = (q @ X1))) )),
% 0.16/0.43 inference(not_proxy_clausification,[],[f180])).
% 0.16/0.43 thf(f180,plain,(
% 0.16/0.43 ( ! [X1 : $i] : (((rel_m @ sK1 @ X1) = $false) | ($false = (~ (q @ X1)))) )),
% 0.16/0.43 inference(binary_proxy_clausification,[],[f178])).
% 0.16/0.43 % SZS output end Proof for theBenchmark
% 0.16/0.43 % (22735)------------------------------
% 0.16/0.43 % (22735)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.43 % (22735)Termination reason: Refutation
% 0.16/0.43
% 0.16/0.43 % (22735)Memory used [KB]: 5884
% 0.16/0.43 % (22735)Time elapsed: 0.019 s
% 0.16/0.43 % (22735)Instructions burned: 23 (million)
% 0.16/0.43 % (22735)------------------------------
% 0.16/0.43 % (22735)------------------------------
% 0.16/0.43 % (22734)Success in time 0.041 s
% 0.16/0.43 % Vampire---4.8 exiting
%------------------------------------------------------------------------------