TSTP Solution File: SYO450^5 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO450^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n013.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 0.14s 0.40s
% Output : Refutation 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYO450^5 : TPTP v8.2.0. Released v4.0.0.
% 0.11/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon May 20 11:16:38 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a TH0_THM_EQU_NAR problem
% 0.14/0.35 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.37 % (15637)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.14/0.37 % (15636)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.37 % (15643)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.14/0.37 % (15641)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.14/0.37 % (15637)Instruction limit reached!
% 0.14/0.37 % (15637)------------------------------
% 0.14/0.37 % (15637)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (15637)Termination reason: Unknown
% 0.14/0.37 % (15637)Termination phase: shuffling
% 0.14/0.37
% 0.14/0.37 % (15637)Memory used [KB]: 1023
% 0.14/0.37 % (15637)Time elapsed: 0.004 s
% 0.14/0.37 % (15637)Instructions burned: 4 (million)
% 0.14/0.37 % (15637)------------------------------
% 0.14/0.37 % (15637)------------------------------
% 0.14/0.37 % (15643)Instruction limit reached!
% 0.14/0.37 % (15643)------------------------------
% 0.14/0.37 % (15643)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (15643)Termination reason: Unknown
% 0.14/0.37 % (15643)Termination phase: shuffling
% 0.14/0.37
% 0.14/0.37 % (15643)Memory used [KB]: 1023
% 0.14/0.37 % (15643)Time elapsed: 0.004 s
% 0.14/0.37 % (15643)Instructions burned: 4 (million)
% 0.14/0.37 % (15643)------------------------------
% 0.14/0.37 % (15643)------------------------------
% 0.14/0.38 % (15642)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.38 % (15641)Refutation not found, incomplete strategy
% 0.14/0.38 % (15641)------------------------------
% 0.14/0.38 % (15641)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (15639)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.38 % (15641)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.38
% 0.14/0.38
% 0.14/0.38 % (15641)Memory used [KB]: 5628
% 0.14/0.38 % (15641)Time elapsed: 0.010 s
% 0.14/0.38 % (15641)Instructions burned: 15 (million)
% 0.14/0.38 % (15641)------------------------------
% 0.14/0.38 % (15641)------------------------------
% 0.14/0.38 % (15638)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.14/0.38 % (15639)Instruction limit reached!
% 0.14/0.38 % (15639)------------------------------
% 0.14/0.38 % (15639)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (15639)Termination reason: Unknown
% 0.14/0.38 % (15639)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (15639)Memory used [KB]: 1023
% 0.14/0.38 % (15639)Time elapsed: 0.003 s
% 0.14/0.38 % (15639)Instructions burned: 2 (million)
% 0.14/0.38 % (15639)------------------------------
% 0.14/0.38 % (15639)------------------------------
% 0.14/0.39 % (15640)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.39 % (15642)Instruction limit reached!
% 0.14/0.39 % (15642)------------------------------
% 0.14/0.39 % (15642)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (15642)Termination reason: Unknown
% 0.14/0.39 % (15642)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (15642)Memory used [KB]: 5756
% 0.14/0.39 % (15642)Time elapsed: 0.012 s
% 0.14/0.39 % (15642)Instructions burned: 19 (million)
% 0.14/0.39 % (15642)------------------------------
% 0.14/0.39 % (15642)------------------------------
% 0.14/0.39 % (15640)Instruction limit reached!
% 0.14/0.39 % (15640)------------------------------
% 0.14/0.39 % (15640)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (15640)Termination reason: Unknown
% 0.14/0.39 % (15640)Termination phase: shuffling
% 0.14/0.39
% 0.14/0.39 % (15640)Memory used [KB]: 1023
% 0.14/0.39 % (15640)Time elapsed: 0.003 s
% 0.14/0.39 % (15640)Instructions burned: 3 (million)
% 0.14/0.39 % (15640)------------------------------
% 0.14/0.39 % (15640)------------------------------
% 0.14/0.39 % (15644)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)
% 0.14/0.39 % (15645)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)
% 0.14/0.40 % (15636)First to succeed.
% 0.14/0.40 % (15647)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)
% 0.14/0.40 % (15645)Instruction limit reached!
% 0.14/0.40 % (15645)------------------------------
% 0.14/0.40 % (15645)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (15645)Termination reason: Unknown
% 0.14/0.40 % (15645)Termination phase: Saturation
% 0.14/0.40
% 0.14/0.40 % (15645)Memory used [KB]: 5628
% 0.14/0.40 % (15645)Time elapsed: 0.010 s
% 0.14/0.40 % (15645)Instructions burned: 15 (million)
% 0.14/0.40 % (15645)------------------------------
% 0.14/0.40 % (15645)------------------------------
% 0.14/0.40 % (15646)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)
% 0.14/0.40 % (15638)Instruction limit reached!
% 0.14/0.40 % (15638)------------------------------
% 0.14/0.40 % (15638)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (15638)Termination reason: Unknown
% 0.14/0.40 % (15638)Termination phase: Saturation
% 0.14/0.40
% 0.14/0.40 % (15638)Memory used [KB]: 5756
% 0.14/0.40 % (15638)Time elapsed: 0.018 s
% 0.14/0.40 % (15638)Instructions burned: 27 (million)
% 0.14/0.40 % (15638)------------------------------
% 0.14/0.40 % (15638)------------------------------
% 0.14/0.40 % (15646)Instruction limit reached!
% 0.14/0.40 % (15646)------------------------------
% 0.14/0.40 % (15646)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (15646)Termination reason: Unknown
% 0.14/0.40 % (15646)Termination phase: shuffling
% 0.14/0.40
% 0.14/0.40 % (15646)Memory used [KB]: 1023
% 0.14/0.40 % (15646)Time elapsed: 0.003 s
% 0.14/0.40 % (15646)Instructions burned: 3 (million)
% 0.14/0.40 % (15646)------------------------------
% 0.14/0.40 % (15646)------------------------------
% 0.14/0.40 % (15648)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.14/0.40 % (15636)Refutation found. Thanks to Tanya!
% 0.14/0.40 % SZS status Theorem for theBenchmark
% 0.14/0.40 % SZS output start Proof for theBenchmark
% 0.14/0.40 thf(type_def_5, type, mu: $tType).
% 0.14/0.40 thf(func_def_0, type, mu: $tType).
% 0.14/0.40 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.14/0.40 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_15, type, mtrue: $i > $o).
% 0.14/0.40 thf(func_def_16, type, mfalse: $i > $o).
% 0.14/0.40 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.14/0.40 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.14/0.40 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.14/0.40 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.14/0.40 thf(func_def_33, type, rel_s4: $i > $i > $o).
% 0.14/0.40 thf(func_def_34, type, mbox_s4: ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_35, type, mdia_s4: ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_36, type, p: $i > $o).
% 0.14/0.40 thf(func_def_37, type, q: $i > $o).
% 0.14/0.40 thf(func_def_38, type, r: $i > $o).
% 0.14/0.40 thf(func_def_56, type, sK2: $i > $i).
% 0.14/0.40 thf(f446,plain,(
% 0.14/0.40 $false),
% 0.14/0.40 inference(avatar_sat_refutation,[],[f243,f311,f328,f338,f396,f421,f438,f445])).
% 0.14/0.40 thf(f445,plain,(
% 0.14/0.40 ~spl0_6 | ~spl0_13),
% 0.14/0.40 inference(avatar_contradiction_clause,[],[f444])).
% 0.14/0.40 thf(f444,plain,(
% 0.14/0.40 $false | (~spl0_6 | ~spl0_13)),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f441])).
% 0.14/0.40 thf(f441,plain,(
% 0.14/0.40 ($false = $true) | (~spl0_6 | ~spl0_13)),
% 0.14/0.40 inference(superposition,[],[f315,f405])).
% 0.14/0.40 thf(f405,plain,(
% 0.14/0.40 ($false = (q @ (sK2 @ sK1))) | ~spl0_13),
% 0.14/0.40 inference(avatar_component_clause,[],[f403])).
% 0.14/0.40 thf(f403,plain,(
% 0.14/0.40 spl0_13 <=> ($false = (q @ (sK2 @ sK1)))),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_13])])).
% 0.14/0.40 thf(f315,plain,(
% 0.14/0.40 ((q @ (sK2 @ sK1)) = $true) | ~spl0_6),
% 0.14/0.40 inference(avatar_component_clause,[],[f313])).
% 0.14/0.40 thf(f313,plain,(
% 0.14/0.40 spl0_6 <=> ((q @ (sK2 @ sK1)) = $true)),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_6])])).
% 0.14/0.40 thf(f438,plain,(
% 0.14/0.40 ~spl0_4 | ~spl0_12),
% 0.14/0.40 inference(avatar_contradiction_clause,[],[f437])).
% 0.14/0.40 thf(f437,plain,(
% 0.14/0.40 $false | (~spl0_4 | ~spl0_12)),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f433])).
% 0.14/0.40 thf(f433,plain,(
% 0.14/0.40 ($false = $true) | (~spl0_4 | ~spl0_12)),
% 0.14/0.40 inference(superposition,[],[f401,f305])).
% 0.14/0.40 thf(f305,plain,(
% 0.14/0.40 ((r @ (sK2 @ sK1)) = $false) | ~spl0_4),
% 0.14/0.40 inference(avatar_component_clause,[],[f303])).
% 0.14/0.40 thf(f303,plain,(
% 0.14/0.40 spl0_4 <=> ((r @ (sK2 @ sK1)) = $false)),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_4])])).
% 0.14/0.40 thf(f401,plain,(
% 0.14/0.40 ((r @ (sK2 @ sK1)) = $true) | ~spl0_12),
% 0.14/0.40 inference(avatar_component_clause,[],[f399])).
% 0.14/0.40 thf(f399,plain,(
% 0.14/0.40 spl0_12 <=> ((r @ (sK2 @ sK1)) = $true)),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_12])])).
% 0.14/0.40 thf(f421,plain,(
% 0.14/0.40 spl0_12 | spl0_13 | spl0_3),
% 0.14/0.40 inference(avatar_split_clause,[],[f420,f299,f403,f399])).
% 0.14/0.40 thf(f299,plain,(
% 0.14/0.40 spl0_3 <=> ((p @ sK1) = $false)),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_3])])).
% 0.14/0.40 thf(f420,plain,(
% 0.14/0.40 ($false = (q @ (sK2 @ sK1))) | ((r @ (sK2 @ sK1)) = $true) | spl0_3),
% 0.14/0.40 inference(subsumption_resolution,[],[f389,f300])).
% 0.14/0.40 thf(f300,plain,(
% 0.14/0.40 ((p @ sK1) != $false) | spl0_3),
% 0.14/0.40 inference(avatar_component_clause,[],[f299])).
% 0.14/0.40 thf(f389,plain,(
% 0.14/0.40 ($false = (q @ (sK2 @ sK1))) | ((r @ (sK2 @ sK1)) = $true) | ((p @ sK1) = $false)),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f381])).
% 0.14/0.40 thf(f381,plain,(
% 0.14/0.40 ((p @ sK1) = $false) | ($false = $true) | ($false = (q @ (sK2 @ sK1))) | ((r @ (sK2 @ sK1)) = $true)),
% 0.14/0.40 inference(superposition,[],[f205,f200])).
% 0.14/0.40 thf(f200,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($false = (rel_s4 @ sK1 @ X1)) | ((p @ X1) = $false) | ((r @ (sK2 @ X1)) = $true) | ($false = (q @ (sK2 @ X1)))) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f199])).
% 0.14/0.40 thf(f199,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((r @ (sK2 @ X1)) = $true) | ((~ (q @ (sK2 @ X1))) = $true) | ((p @ X1) = $false) | ($false = (rel_s4 @ sK1 @ X1))) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f198])).
% 0.14/0.40 thf(f198,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((p @ X1) = $false) | ((~ (rel_s4 @ sK1 @ X1)) = $true) | ((r @ (sK2 @ X1)) = $true) | ((~ (q @ (sK2 @ X1))) = $true)) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f197])).
% 0.14/0.40 thf(f197,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($true = ((r @ (sK2 @ X1)) | (~ (q @ (sK2 @ X1))))) | ((p @ X1) = $false) | ((~ (rel_s4 @ sK1 @ X1)) = $true)) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f196])).
% 0.14/0.40 thf(f196,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((p @ X1) = $false) | ($false = (~ ((r @ (sK2 @ X1)) | (~ (q @ (sK2 @ X1)))))) | ((~ (rel_s4 @ sK1 @ X1)) = $true)) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f194])).
% 0.14/0.40 thf(f194,plain,(
% 0.14/0.40 ( ! [X1 : $i] : ((((~ ((r @ (sK2 @ X1)) | (~ (q @ (sK2 @ X1))))) | (~ (rel_s4 @ X1 @ (sK2 @ X1)))) = $false) | ((~ (rel_s4 @ sK1 @ X1)) = $true) | ((p @ X1) = $false)) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f193])).
% 0.14/0.40 thf(f193,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((p @ X1) = $false) | ((~ (rel_s4 @ sK1 @ X1)) = $true) | (((^[Y0 : $i]: ((~ ((r @ Y0) | (~ (q @ Y0)))) | (~ (rel_s4 @ X1 @ Y0)))) @ (sK2 @ X1)) = $false)) )),
% 0.14/0.40 inference(sigma_clausification,[],[f192])).
% 0.14/0.40 thf(f192,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((~ ((r @ Y0) | (~ (q @ Y0)))) | (~ (rel_s4 @ X1 @ Y0))))) = $false) | ((p @ X1) = $false) | ((~ (rel_s4 @ sK1 @ X1)) = $true)) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f191])).
% 0.14/0.40 thf(f191,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((p @ X1) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ ((r @ Y0) | (~ (q @ Y0)))) | (~ (rel_s4 @ X1 @ Y0)))))) = $true) | ((~ (rel_s4 @ sK1 @ X1)) = $true)) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f190])).
% 0.14/0.40 thf(f190,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((~ (p @ X1)) = $true) | ((~ (rel_s4 @ sK1 @ X1)) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ ((r @ Y0) | (~ (q @ Y0)))) | (~ (rel_s4 @ X1 @ Y0)))))) = $true)) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f189])).
% 0.14/0.40 thf(f189,plain,(
% 0.14/0.40 ( ! [X1 : $i] : ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ ((r @ Y0) | (~ (q @ Y0)))) | (~ (rel_s4 @ X1 @ Y0)))))) | (~ (p @ X1))) = $true) | ((~ (rel_s4 @ sK1 @ X1)) = $true)) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f188])).
% 0.14/0.40 thf(f188,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ ((r @ Y0) | (~ (q @ Y0)))) | (~ (rel_s4 @ X1 @ Y0)))))) | (~ (p @ X1))) | (~ (rel_s4 @ sK1 @ X1))) = $true)) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f187])).
% 0.14/0.40 thf(f187,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((~ ((r @ Y1) | (~ (q @ Y1)))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (p @ Y0))) | (~ (rel_s4 @ sK1 @ Y0)))) @ X1))) )),
% 0.14/0.40 inference(pi_clausification,[],[f186])).
% 0.14/0.40 thf(f186,plain,(
% 0.14/0.40 ((!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((~ ((r @ Y1) | (~ (q @ Y1)))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (p @ Y0))) | (~ (rel_s4 @ sK1 @ Y0))))) = $true)),
% 0.14/0.40 inference(not_proxy_clausification,[],[f160])).
% 0.14/0.40 thf(f160,plain,(
% 0.14/0.40 ((~ (!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((~ ((r @ Y1) | (~ (q @ Y1)))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (p @ Y0))) | (~ (rel_s4 @ sK1 @ Y0)))))) = $false)),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f159])).
% 0.14/0.40 thf(f159,plain,(
% 0.14/0.40 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (((~ (!! @ $i @ (^[Y1 : $i]: ((~ (r @ Y1)) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_s4 @ Y0 @ Y1))))))) | (~ (q @ Y0)))) | (~ (rel_s4 @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((~ ((r @ Y1) | (~ (q @ Y1)))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (p @ Y0))) | (~ (rel_s4 @ sK1 @ Y0))))))) = $false)),
% 0.14/0.40 inference(beta_eta_normalization,[],[f158])).
% 0.14/0.40 thf(f158,plain,(
% 0.14/0.40 (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (((~ (!! @ $i @ (^[Y2 : $i]: ((~ (r @ Y2)) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((p @ Y2) | (~ (rel_s4 @ Y1 @ Y2))))))) | (~ (q @ Y1)))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (!! @ $i @ (^[Y2 : $i]: ((~ ((r @ Y2) | (~ (q @ Y2)))) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (p @ Y1))) | (~ (rel_s4 @ Y0 @ Y1)))))))) @ sK1) = $false)),
% 0.14/0.40 inference(sigma_clausification,[],[f157])).
% 0.14/0.40 thf(f157,plain,(
% 0.14/0.40 ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (((~ (!! @ $i @ (^[Y2 : $i]: ((~ (r @ Y2)) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((p @ Y2) | (~ (rel_s4 @ Y1 @ Y2))))))) | (~ (q @ Y1)))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (!! @ $i @ (^[Y2 : $i]: ((~ ((r @ Y2) | (~ (q @ Y2)))) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (p @ Y1))) | (~ (rel_s4 @ Y0 @ Y1))))))))) != $true)),
% 0.14/0.40 inference(beta_eta_normalization,[],[f154])).
% 0.14/0.40 thf(f154,plain,(
% 0.14/0.40 (((^[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]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ 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 > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[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)))) @ q @ r)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[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)))) @ q @ ((^[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]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))) @ p) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ r)))))) != $true)),
% 0.14/0.40 inference(definition_unfolding,[],[f133,f128,f145,f124,f145,f153,f145,f153,f145,f145,f124,f153])).
% 0.14/0.40 thf(f153,plain,(
% 0.14/0.40 (mdia_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))))),
% 0.14/0.40 inference(definition_unfolding,[],[f121,f135,f124,f135])).
% 0.14/0.40 thf(f135,plain,(
% 0.14/0.40 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f48])).
% 0.14/0.40 thf(f48,plain,(
% 0.14/0.40 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.14/0.40 inference(fool_elimination,[],[f47])).
% 0.14/0.40 thf(f47,plain,(
% 0.14/0.40 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.14/0.40 inference(rectify,[],[f3])).
% 0.14/0.40 thf(f3,axiom,(
% 0.14/0.40 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.14/0.40 thf(f121,plain,(
% 0.14/0.40 (mdia_s4 = (^[Y0 : $i > $o]: (mnot @ (mbox_s4 @ (mnot @ Y0)))))),
% 0.14/0.40 inference(cnf_transformation,[],[f62])).
% 0.14/0.40 thf(f62,plain,(
% 0.14/0.40 (mdia_s4 = (^[Y0 : $i > $o]: (mnot @ (mbox_s4 @ (mnot @ Y0)))))),
% 0.14/0.40 inference(fool_elimination,[],[f61])).
% 0.14/0.40 thf(f61,plain,(
% 0.14/0.40 (mdia_s4 = (^[X0 : $i > $o] : (mnot @ (mbox_s4 @ (mnot @ X0)))))),
% 0.14/0.40 inference(rectify,[],[f33])).
% 0.14/0.40 thf(f33,axiom,(
% 0.14/0.40 (mdia_s4 = (^[X3 : $i > $o] : (mnot @ (mbox_s4 @ (mnot @ X3)))))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_s4)).
% 0.14/0.40 thf(f124,plain,(
% 0.14/0.40 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f67])).
% 0.14/0.40 thf(f67,plain,(
% 0.14/0.40 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))))),
% 0.14/0.40 inference(fool_elimination,[],[f66])).
% 0.14/0.40 thf(f66,plain,(
% 0.14/0.40 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : (~(rel_s4 @ X1 @ X2) | (X0 @ X2)))) = mbox_s4)),
% 0.14/0.40 inference(rectify,[],[f32])).
% 0.14/0.40 thf(f32,axiom,(
% 0.14/0.40 ((^[X3 : $i > $o, X2 : $i] : (! [X7] : (~(rel_s4 @ X2 @ X7) | (X3 @ X7)))) = mbox_s4)),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_s4)).
% 0.14/0.40 thf(f145,plain,(
% 0.14/0.40 (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)))))),
% 0.14/0.40 inference(definition_unfolding,[],[f139,f130,f135])).
% 0.14/0.40 thf(f130,plain,(
% 0.14/0.40 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f40])).
% 0.14/0.40 thf(f40,plain,(
% 0.14/0.40 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.14/0.40 inference(fool_elimination,[],[f39])).
% 0.14/0.40 thf(f39,plain,(
% 0.14/0.40 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))))),
% 0.14/0.40 inference(rectify,[],[f4])).
% 0.14/0.40 thf(f4,axiom,(
% 0.14/0.40 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.14/0.40 thf(f139,plain,(
% 0.14/0.40 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.14/0.40 inference(cnf_transformation,[],[f84])).
% 0.14/0.40 thf(f84,plain,(
% 0.14/0.40 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.14/0.40 inference(fool_elimination,[],[f83])).
% 0.14/0.40 thf(f83,plain,(
% 0.14/0.40 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.14/0.40 inference(rectify,[],[f6])).
% 0.14/0.40 thf(f6,axiom,(
% 0.14/0.40 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.14/0.40 thf(f128,plain,(
% 0.14/0.40 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.14/0.40 inference(cnf_transformation,[],[f94])).
% 0.14/0.40 thf(f94,plain,(
% 0.14/0.40 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.14/0.40 inference(fool_elimination,[],[f93])).
% 0.14/0.40 thf(f93,plain,(
% 0.14/0.40 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.14/0.40 inference(rectify,[],[f28])).
% 0.14/0.40 thf(f28,axiom,(
% 0.14/0.40 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.14/0.40 thf(f133,plain,(
% 0.14/0.40 ((mvalid @ (mimplies @ (mbox_s4 @ (mimplies @ p @ (mdia_s4 @ (mimplies @ q @ r)))) @ (mdia_s4 @ (mimplies @ q @ (mimplies @ (mbox_s4 @ p) @ (mdia_s4 @ r)))))) != $true)),
% 0.14/0.40 inference(cnf_transformation,[],[f107])).
% 0.14/0.40 thf(f107,plain,(
% 0.14/0.40 ((mvalid @ (mimplies @ (mbox_s4 @ (mimplies @ p @ (mdia_s4 @ (mimplies @ q @ r)))) @ (mdia_s4 @ (mimplies @ q @ (mimplies @ (mbox_s4 @ p) @ (mdia_s4 @ r)))))) != $true)),
% 0.14/0.40 inference(flattening,[],[f71])).
% 0.14/0.40 thf(f71,plain,(
% 0.14/0.40 ~((mvalid @ (mimplies @ (mbox_s4 @ (mimplies @ p @ (mdia_s4 @ (mimplies @ q @ r)))) @ (mdia_s4 @ (mimplies @ q @ (mimplies @ (mbox_s4 @ p) @ (mdia_s4 @ r)))))) = $true)),
% 0.14/0.40 inference(fool_elimination,[],[f70])).
% 0.14/0.40 thf(f70,plain,(
% 0.14/0.40 ~(mvalid @ (mimplies @ (mbox_s4 @ (mimplies @ p @ (mdia_s4 @ (mimplies @ q @ r)))) @ (mdia_s4 @ (mimplies @ q @ (mimplies @ (mbox_s4 @ p) @ (mdia_s4 @ r))))))),
% 0.14/0.40 inference(rectify,[],[f37])).
% 0.14/0.40 thf(f37,negated_conjecture,(
% 0.14/0.40 ~(mvalid @ (mimplies @ (mbox_s4 @ (mimplies @ p @ (mdia_s4 @ (mimplies @ q @ r)))) @ (mdia_s4 @ (mimplies @ q @ (mimplies @ (mbox_s4 @ p) @ (mdia_s4 @ r))))))),
% 0.14/0.40 inference(negated_conjecture,[],[f36])).
% 0.14/0.40 thf(f36,conjecture,(
% 0.14/0.40 (mvalid @ (mimplies @ (mbox_s4 @ (mimplies @ p @ (mdia_s4 @ (mimplies @ q @ r)))) @ (mdia_s4 @ (mimplies @ q @ (mimplies @ (mbox_s4 @ p) @ (mdia_s4 @ r))))))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove)).
% 0.14/0.40 thf(f205,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((rel_s4 @ X1 @ X1) = $true)) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f204])).
% 0.14/0.40 thf(f204,plain,(
% 0.14/0.40 ( ! [X1 : $i] : ((((^[Y0 : $i]: (rel_s4 @ Y0 @ Y0)) @ X1) = $true)) )),
% 0.14/0.40 inference(pi_clausification,[],[f203])).
% 0.14/0.40 thf(f203,plain,(
% 0.14/0.40 ((!! @ $i @ (^[Y0 : $i]: (rel_s4 @ Y0 @ Y0))) = $true)),
% 0.14/0.40 inference(beta_eta_normalization,[],[f155])).
% 0.14/0.40 thf(f155,plain,(
% 0.14/0.40 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) @ rel_s4) = $true)),
% 0.14/0.40 inference(definition_unfolding,[],[f140,f125])).
% 0.14/0.40 thf(f125,plain,(
% 0.14/0.40 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.14/0.40 inference(cnf_transformation,[],[f106])).
% 0.14/0.40 thf(f106,plain,(
% 0.14/0.40 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.14/0.40 inference(fool_elimination,[],[f105])).
% 0.14/0.40 thf(f105,plain,(
% 0.14/0.40 ((^[X0 : $i > $i > $o] : (! [X1] : (X0 @ X1 @ X1))) = mreflexive)),
% 0.14/0.40 inference(rectify,[],[f18])).
% 0.14/0.40 thf(f18,axiom,(
% 0.14/0.40 ((^[X6 : $i > $i > $o] : (! [X8] : (X6 @ X8 @ X8))) = mreflexive)),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mreflexive)).
% 0.14/0.40 thf(f140,plain,(
% 0.14/0.40 ((mreflexive @ rel_s4) = $true)),
% 0.14/0.40 inference(cnf_transformation,[],[f73])).
% 0.14/0.40 thf(f73,plain,(
% 0.14/0.40 ((mreflexive @ rel_s4) = $true)),
% 0.14/0.40 inference(fool_elimination,[],[f72])).
% 0.14/0.40 thf(f72,plain,(
% 0.14/0.40 (mreflexive @ rel_s4)),
% 0.14/0.40 inference(rectify,[],[f34])).
% 0.14/0.40 thf(f34,axiom,(
% 0.14/0.40 (mreflexive @ rel_s4)),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1)).
% 0.14/0.40 thf(f396,plain,(
% 0.14/0.40 ~spl0_2 | ~spl0_3),
% 0.14/0.40 inference(avatar_contradiction_clause,[],[f395])).
% 0.14/0.40 thf(f395,plain,(
% 0.14/0.40 $false | (~spl0_2 | ~spl0_3)),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f392])).
% 0.14/0.40 thf(f392,plain,(
% 0.14/0.40 ($false = $true) | (~spl0_2 | ~spl0_3)),
% 0.14/0.40 inference(superposition,[],[f242,f301])).
% 0.14/0.40 thf(f301,plain,(
% 0.14/0.40 ((p @ sK1) = $false) | ~spl0_3),
% 0.14/0.40 inference(avatar_component_clause,[],[f299])).
% 0.14/0.40 thf(f242,plain,(
% 0.14/0.40 ((p @ sK1) = $true) | ~spl0_2),
% 0.14/0.40 inference(avatar_component_clause,[],[f240])).
% 0.14/0.40 thf(f240,plain,(
% 0.14/0.40 spl0_2 <=> ((p @ sK1) = $true)),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.14/0.40 thf(f338,plain,(
% 0.14/0.40 ~spl0_1),
% 0.14/0.40 inference(avatar_contradiction_clause,[],[f337])).
% 0.14/0.40 thf(f337,plain,(
% 0.14/0.40 $false | ~spl0_1),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f330])).
% 0.14/0.40 thf(f330,plain,(
% 0.14/0.40 ($false = $true) | ~spl0_1),
% 0.14/0.40 inference(superposition,[],[f238,f205])).
% 0.14/0.40 thf(f238,plain,(
% 0.14/0.40 ((rel_s4 @ sK1 @ sK1) = $false) | ~spl0_1),
% 0.14/0.40 inference(avatar_component_clause,[],[f236])).
% 0.14/0.40 thf(f236,plain,(
% 0.14/0.40 spl0_1 <=> ((rel_s4 @ sK1 @ sK1) = $false)),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.14/0.40 thf(f328,plain,(
% 0.14/0.40 spl0_3 | spl0_1 | spl0_6),
% 0.14/0.40 inference(avatar_split_clause,[],[f288,f313,f236,f299])).
% 0.14/0.40 thf(f288,plain,(
% 0.14/0.40 ((rel_s4 @ sK1 @ sK1) = $false) | ((q @ (sK2 @ sK1)) = $true) | ((p @ sK1) = $false)),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f278])).
% 0.14/0.40 thf(f278,plain,(
% 0.14/0.40 ((q @ (sK2 @ sK1)) = $true) | ((rel_s4 @ sK1 @ sK1) = $false) | ((p @ sK1) = $false) | ($false = $true)),
% 0.14/0.40 inference(superposition,[],[f202,f185])).
% 0.14/0.40 thf(f185,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($false = (rel_s4 @ sK1 @ X1)) | ((q @ X1) = $true)) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f184])).
% 0.14/0.40 thf(f184,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($false = (~ (q @ X1))) | ($false = (rel_s4 @ sK1 @ X1))) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f167])).
% 0.14/0.40 thf(f167,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((~ (rel_s4 @ sK1 @ X1)) = $true) | ($false = (~ (q @ X1)))) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f166])).
% 0.14/0.40 thf(f166,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (r @ Y0)) | (~ (rel_s4 @ X1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s4 @ X1 @ Y0))))))) | (~ (q @ X1))) = $false) | ((~ (rel_s4 @ sK1 @ X1)) = $true)) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f165])).
% 0.14/0.40 thf(f165,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($true = (~ (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (r @ Y0)) | (~ (rel_s4 @ X1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s4 @ X1 @ Y0))))))) | (~ (q @ X1))))) | ((~ (rel_s4 @ sK1 @ X1)) = $true)) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f164])).
% 0.14/0.40 thf(f164,plain,(
% 0.14/0.40 ( ! [X1 : $i] : ((((~ (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (r @ Y0)) | (~ (rel_s4 @ X1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s4 @ X1 @ Y0))))))) | (~ (q @ X1)))) | (~ (rel_s4 @ sK1 @ X1))) = $true)) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f163])).
% 0.14/0.40 thf(f163,plain,(
% 0.14/0.40 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (((~ (!! @ $i @ (^[Y1 : $i]: ((~ (r @ Y1)) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_s4 @ Y0 @ Y1))))))) | (~ (q @ Y0)))) | (~ (rel_s4 @ sK1 @ Y0)))) @ X1) = $true)) )),
% 0.14/0.40 inference(pi_clausification,[],[f162])).
% 0.14/0.40 thf(f162,plain,(
% 0.14/0.40 ((!! @ $i @ (^[Y0 : $i]: ((~ (((~ (!! @ $i @ (^[Y1 : $i]: ((~ (r @ Y1)) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_s4 @ Y0 @ Y1))))))) | (~ (q @ Y0)))) | (~ (rel_s4 @ sK1 @ Y0))))) = $true)),
% 0.14/0.40 inference(not_proxy_clausification,[],[f161])).
% 0.14/0.40 thf(f161,plain,(
% 0.14/0.40 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (((~ (!! @ $i @ (^[Y1 : $i]: ((~ (r @ Y1)) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_s4 @ Y0 @ Y1))))))) | (~ (q @ Y0)))) | (~ (rel_s4 @ sK1 @ Y0)))))) = $false)),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f159])).
% 0.14/0.40 thf(f202,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((rel_s4 @ X1 @ (sK2 @ X1)) = $true) | ((p @ X1) = $false) | ($false = (rel_s4 @ sK1 @ X1))) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f201])).
% 0.14/0.40 thf(f201,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((p @ X1) = $false) | ($false = (rel_s4 @ sK1 @ X1)) | ((~ (rel_s4 @ X1 @ (sK2 @ X1))) = $false)) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f195])).
% 0.14/0.40 thf(f195,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((p @ X1) = $false) | ((~ (rel_s4 @ sK1 @ X1)) = $true) | ((~ (rel_s4 @ X1 @ (sK2 @ X1))) = $false)) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f194])).
% 0.14/0.40 thf(f311,plain,(
% 0.14/0.40 spl0_3 | spl0_4 | spl0_1),
% 0.14/0.40 inference(avatar_split_clause,[],[f295,f236,f303,f299])).
% 0.14/0.40 thf(f295,plain,(
% 0.14/0.40 ((r @ (sK2 @ sK1)) = $false) | ((p @ sK1) = $false) | ((rel_s4 @ sK1 @ sK1) = $false)),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f282])).
% 0.14/0.40 thf(f282,plain,(
% 0.14/0.40 ($false = $true) | ((p @ sK1) = $false) | ((r @ (sK2 @ sK1)) = $false) | ((rel_s4 @ sK1 @ sK1) = $false)),
% 0.14/0.40 inference(superposition,[],[f224,f202])).
% 0.14/0.40 thf(f224,plain,(
% 0.14/0.40 ( ! [X0 : $i] : (((rel_s4 @ sK1 @ X0) = $false) | ($false = (r @ X0))) )),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f220])).
% 0.14/0.40 thf(f220,plain,(
% 0.14/0.40 ( ! [X0 : $i] : (((rel_s4 @ sK1 @ X0) = $false) | ($false = $true) | ($false = (r @ X0))) )),
% 0.14/0.40 inference(superposition,[],[f205,f177])).
% 0.14/0.40 thf(f177,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : (($false = (rel_s4 @ sK1 @ X1)) | ((rel_s4 @ X1 @ X2) = $false) | ((r @ X2) = $false)) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f176])).
% 0.14/0.40 thf(f176,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : (($false = (rel_s4 @ sK1 @ X1)) | ((~ (rel_s4 @ X1 @ X2)) = $true) | ((r @ X2) = $false)) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f175])).
% 0.14/0.40 thf(f175,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : (((~ (r @ X2)) = $true) | ((~ (rel_s4 @ X1 @ X2)) = $true) | ($false = (rel_s4 @ sK1 @ X1))) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f174])).
% 0.14/0.40 thf(f174,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : ((((~ (r @ X2)) | (~ (rel_s4 @ X1 @ X2))) = $true) | ($false = (rel_s4 @ sK1 @ X1))) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f173])).
% 0.14/0.40 thf(f173,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : (((~ (rel_s4 @ sK1 @ X1)) = $true) | (((~ (r @ X2)) | (~ (rel_s4 @ X1 @ X2))) = $true)) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f172])).
% 0.14/0.40 thf(f172,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((~ (r @ Y0)) | (~ (rel_s4 @ X1 @ Y0)))) @ X2) = $true) | ((~ (rel_s4 @ sK1 @ X1)) = $true)) )),
% 0.14/0.40 inference(pi_clausification,[],[f171])).
% 0.14/0.40 thf(f171,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((~ (r @ Y0)) | (~ (rel_s4 @ X1 @ Y0))))) = $true) | ((~ (rel_s4 @ sK1 @ X1)) = $true)) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f170])).
% 0.14/0.40 thf(f170,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (r @ Y0)) | (~ (rel_s4 @ X1 @ Y0)))))) = $false) | ((~ (rel_s4 @ sK1 @ X1)) = $true)) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f168])).
% 0.14/0.40 thf(f168,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (r @ Y0)) | (~ (rel_s4 @ X1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s4 @ X1 @ Y0)))))))) | ((~ (rel_s4 @ sK1 @ X1)) = $true)) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f166])).
% 0.14/0.40 thf(f243,plain,(
% 0.14/0.40 spl0_1 | spl0_2),
% 0.14/0.40 inference(avatar_split_clause,[],[f234,f240,f236])).
% 0.14/0.40 thf(f234,plain,(
% 0.14/0.40 ((p @ sK1) = $true) | ((rel_s4 @ sK1 @ sK1) = $false)),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f231])).
% 0.14/0.40 thf(f231,plain,(
% 0.14/0.40 ($false != $false) | ((p @ sK1) = $true) | ((rel_s4 @ sK1 @ sK1) = $false)),
% 0.14/0.40 inference(equality_factoring,[],[f183])).
% 0.14/0.40 thf(f183,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : (($false = (rel_s4 @ sK1 @ X1)) | ((p @ X2) = $true) | ((rel_s4 @ X1 @ X2) = $false)) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f182])).
% 0.14/0.40 thf(f182,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : (((~ (rel_s4 @ X1 @ X2)) = $true) | ($false = (rel_s4 @ sK1 @ X1)) | ((p @ X2) = $true)) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f181])).
% 0.14/0.40 thf(f181,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : ((((p @ X2) | (~ (rel_s4 @ X1 @ X2))) = $true) | ($false = (rel_s4 @ sK1 @ X1))) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f180])).
% 0.14/0.40 thf(f180,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : (($false = (rel_s4 @ sK1 @ X1)) | (((^[Y0 : $i]: ((p @ Y0) | (~ (rel_s4 @ X1 @ Y0)))) @ X2) = $true)) )),
% 0.14/0.40 inference(pi_clausification,[],[f179])).
% 0.14/0.40 thf(f179,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s4 @ X1 @ Y0))))) = $true) | ($false = (rel_s4 @ sK1 @ X1))) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f178])).
% 0.14/0.40 thf(f178,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($false = (rel_s4 @ sK1 @ X1)) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s4 @ X1 @ Y0)))))))) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f169])).
% 0.14/0.40 thf(f169,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((~ (rel_s4 @ sK1 @ X1)) = $true) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s4 @ X1 @ Y0)))))))) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f168])).
% 0.14/0.40 % SZS output end Proof for theBenchmark
% 0.14/0.40 % (15636)------------------------------
% 0.14/0.40 % (15636)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (15636)Termination reason: Refutation
% 0.14/0.40
% 0.14/0.40 % (15636)Memory used [KB]: 5884
% 0.14/0.40 % (15636)Time elapsed: 0.026 s
% 0.14/0.40 % (15636)Instructions burned: 31 (million)
% 0.14/0.40 % (15636)------------------------------
% 0.14/0.40 % (15636)------------------------------
% 0.14/0.40 % (15635)Success in time 0.05 s
% 0.14/0.40 % Vampire---4.8 exiting
%------------------------------------------------------------------------------