TSTP Solution File: SYO462^4 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO462^4 : 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 : n017.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 09:04:53 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
% 0.07/0.12 % Problem : SYO462^4 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.35 % Computer : n017.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 09:05:53 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/sandbox2/benchmark/theBenchmark.p
% 0.14/0.37 % (20408)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.37 % (20405)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.37 % (20407)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 % (20404)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.14/0.37 % (20406)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.37 % (20402)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 % (20403)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 % (20405)Instruction limit reached!
% 0.14/0.37 % (20405)------------------------------
% 0.14/0.37 % (20405)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (20405)Termination reason: Unknown
% 0.14/0.37 % (20405)Termination phase: shuffling
% 0.14/0.37 % (20406)Instruction limit reached!
% 0.14/0.37 % (20406)------------------------------
% 0.14/0.37 % (20406)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (20406)Termination reason: Unknown
% 0.14/0.37 % (20406)Termination phase: shuffling
% 0.14/0.37
% 0.14/0.37 % (20406)Memory used [KB]: 1023
% 0.14/0.37 % (20406)Time elapsed: 0.002 s
% 0.14/0.37 % (20406)Instructions burned: 2 (million)
% 0.14/0.37 % (20406)------------------------------
% 0.14/0.37 % (20406)------------------------------
% 0.14/0.37
% 0.14/0.37 % (20405)Memory used [KB]: 1023
% 0.14/0.37 % (20405)Time elapsed: 0.002 s
% 0.14/0.37 % (20405)Instructions burned: 2 (million)
% 0.14/0.37 % (20405)------------------------------
% 0.14/0.37 % (20405)------------------------------
% 0.14/0.38 % (20409)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)
% 0.14/0.38 % (20403)Instruction limit reached!
% 0.14/0.38 % (20403)------------------------------
% 0.14/0.38 % (20403)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (20403)Termination reason: Unknown
% 0.14/0.38 % (20403)Termination phase: Property scanning
% 0.14/0.38
% 0.14/0.38 % (20403)Memory used [KB]: 1023
% 0.14/0.38 % (20403)Time elapsed: 0.004 s
% 0.14/0.38 % (20403)Instructions burned: 5 (million)
% 0.14/0.38 % (20403)------------------------------
% 0.14/0.38 % (20403)------------------------------
% 0.14/0.38 % (20409)Instruction limit reached!
% 0.14/0.38 % (20409)------------------------------
% 0.14/0.38 % (20409)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (20409)Termination reason: Unknown
% 0.14/0.38 % (20409)Termination phase: Property scanning
% 0.14/0.38
% 0.14/0.38 % (20409)Memory used [KB]: 1023
% 0.14/0.38 % (20409)Time elapsed: 0.004 s
% 0.14/0.38 % (20409)Instructions burned: 4 (million)
% 0.14/0.38 % (20409)------------------------------
% 0.14/0.38 % (20409)------------------------------
% 0.14/0.38 % (20407)Refutation not found, incomplete strategy
% 0.14/0.38 % (20407)------------------------------
% 0.14/0.38 % (20407)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (20407)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.38
% 0.14/0.38
% 0.14/0.38 % (20407)Memory used [KB]: 5628
% 0.14/0.38 % (20407)Time elapsed: 0.007 s
% 0.14/0.38 % (20407)Instructions burned: 8 (million)
% 0.14/0.38 % (20407)------------------------------
% 0.14/0.38 % (20407)------------------------------
% 0.14/0.38 % (20408)Instruction limit reached!
% 0.14/0.38 % (20408)------------------------------
% 0.14/0.38 % (20408)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (20408)Termination reason: Unknown
% 0.14/0.38 % (20408)Termination phase: Saturation
% 0.14/0.38
% 0.14/0.38 % (20408)Memory used [KB]: 5756
% 0.14/0.38 % (20408)Time elapsed: 0.012 s
% 0.14/0.38 % (20408)Instructions burned: 18 (million)
% 0.14/0.38 % (20408)------------------------------
% 0.14/0.38 % (20408)------------------------------
% 0.14/0.39 % (20411)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)
% 0.14/0.39 % (20410)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 % (20404)Instruction limit reached!
% 0.14/0.39 % (20404)------------------------------
% 0.14/0.39 % (20404)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (20404)Termination reason: Unknown
% 0.14/0.39 % (20404)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (20404)Memory used [KB]: 5756
% 0.14/0.39 % (20404)Time elapsed: 0.018 s
% 0.14/0.39 % (20404)Instructions burned: 27 (million)
% 0.14/0.39 % (20404)------------------------------
% 0.14/0.39 % (20404)------------------------------
% 0.14/0.39 % (20412)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)
% 0.14/0.39 % (20413)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)
% 0.14/0.39 % (20412)Instruction limit reached!
% 0.14/0.39 % (20412)------------------------------
% 0.14/0.39 % (20412)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (20412)Termination reason: Unknown
% 0.14/0.39 % (20412)Termination phase: shuffling
% 0.14/0.39
% 0.14/0.39 % (20412)Memory used [KB]: 1023
% 0.14/0.39 % (20412)Time elapsed: 0.004 s
% 0.14/0.39 % (20412)Instructions burned: 4 (million)
% 0.14/0.39 % (20412)------------------------------
% 0.14/0.39 % (20412)------------------------------
% 0.14/0.39 % (20414)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.14/0.39 % (20402)First to succeed.
% 0.14/0.40 % (20411)Instruction limit reached!
% 0.14/0.40 % (20411)------------------------------
% 0.14/0.40 % (20411)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (20411)Termination reason: Unknown
% 0.14/0.40 % (20411)Termination phase: Saturation
% 0.14/0.40
% 0.14/0.40 % (20411)Memory used [KB]: 5628
% 0.14/0.40 % (20411)Time elapsed: 0.010 s
% 0.14/0.40 % (20411)Instructions burned: 15 (million)
% 0.14/0.40 % (20411)------------------------------
% 0.14/0.40 % (20411)------------------------------
% 0.14/0.40 % (20414)Instruction limit reached!
% 0.14/0.40 % (20414)------------------------------
% 0.14/0.40 % (20414)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (20414)Termination reason: Unknown
% 0.14/0.40 % (20414)Termination phase: Property scanning
% 0.14/0.40
% 0.14/0.40 % (20414)Memory used [KB]: 1023
% 0.14/0.40 % (20414)Time elapsed: 0.006 s
% 0.14/0.40 % (20414)Instructions burned: 7 (million)
% 0.14/0.40 % (20414)------------------------------
% 0.14/0.40 % (20414)------------------------------
% 0.14/0.40 % (20415)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.14/0.40 % (20402)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_b: $i > $i > $o).
% 0.14/0.40 thf(func_def_34, type, mbox_b: ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_35, type, mdia_b: ($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(f570,plain,(
% 0.14/0.40 $false),
% 0.14/0.40 inference(avatar_sat_refutation,[],[f255,f260,f273,f278,f287,f292,f293,f357,f371,f378,f404,f450,f494,f501,f569])).
% 0.14/0.40 thf(f569,plain,(
% 0.14/0.40 ~spl0_5 | ~spl0_7 | ~spl0_8),
% 0.14/0.40 inference(avatar_contradiction_clause,[],[f568])).
% 0.14/0.40 thf(f568,plain,(
% 0.14/0.40 $false | (~spl0_5 | ~spl0_7 | ~spl0_8)),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f565])).
% 0.14/0.40 thf(f565,plain,(
% 0.14/0.40 ($false = $true) | (~spl0_5 | ~spl0_7 | ~spl0_8)),
% 0.14/0.40 inference(superposition,[],[f277,f554])).
% 0.14/0.40 thf(f554,plain,(
% 0.14/0.40 ((q @ sK4) = $true) | (~spl0_5 | ~spl0_8)),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f544])).
% 0.14/0.40 thf(f544,plain,(
% 0.14/0.40 ($false = $true) | ((q @ sK4) = $true) | (~spl0_5 | ~spl0_8)),
% 0.14/0.40 inference(superposition,[],[f282,f268])).
% 0.14/0.40 thf(f268,plain,(
% 0.14/0.40 ((rel_b @ sK1 @ sK4) = $true) | ~spl0_5),
% 0.14/0.40 inference(avatar_component_clause,[],[f266])).
% 0.14/0.40 thf(f266,plain,(
% 0.14/0.40 spl0_5 <=> ((rel_b @ sK1 @ sK4) = $true)),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_5])])).
% 0.14/0.40 thf(f282,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((rel_b @ sK1 @ X1) = $false) | ($true = (q @ X1))) ) | ~spl0_8),
% 0.14/0.40 inference(avatar_component_clause,[],[f281])).
% 0.14/0.40 thf(f281,plain,(
% 0.14/0.40 spl0_8 <=> ! [X1] : (($true = (q @ X1)) | ((rel_b @ sK1 @ X1) = $false))),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_8])])).
% 0.14/0.40 thf(f277,plain,(
% 0.14/0.40 ((q @ sK4) = $false) | ~spl0_7),
% 0.14/0.40 inference(avatar_component_clause,[],[f275])).
% 0.14/0.40 thf(f275,plain,(
% 0.14/0.40 spl0_7 <=> ((q @ sK4) = $false)),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_7])])).
% 0.14/0.40 thf(f501,plain,(
% 0.14/0.40 ~spl0_10 | ~spl0_20),
% 0.14/0.40 inference(avatar_contradiction_clause,[],[f500])).
% 0.14/0.40 thf(f500,plain,(
% 0.14/0.40 $false | (~spl0_10 | ~spl0_20)),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f497])).
% 0.14/0.40 thf(f497,plain,(
% 0.14/0.40 ($false = $true) | (~spl0_10 | ~spl0_20)),
% 0.14/0.40 inference(superposition,[],[f291,f448])).
% 0.14/0.40 thf(f448,plain,(
% 0.14/0.40 ($true = (q @ sK2)) | ~spl0_20),
% 0.14/0.40 inference(avatar_component_clause,[],[f446])).
% 0.14/0.40 thf(f446,plain,(
% 0.14/0.40 spl0_20 <=> ($true = (q @ sK2))),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_20])])).
% 0.14/0.40 thf(f291,plain,(
% 0.14/0.40 ($false = (q @ sK2)) | ~spl0_10),
% 0.14/0.40 inference(avatar_component_clause,[],[f289])).
% 0.14/0.40 thf(f289,plain,(
% 0.14/0.40 spl0_10 <=> ($false = (q @ sK2))),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_10])])).
% 0.14/0.40 thf(f494,plain,(
% 0.14/0.40 ~spl0_4 | ~spl0_9 | ~spl0_19),
% 0.14/0.40 inference(avatar_contradiction_clause,[],[f493])).
% 0.14/0.40 thf(f493,plain,(
% 0.14/0.40 $false | (~spl0_4 | ~spl0_9 | ~spl0_19)),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f489])).
% 0.14/0.40 thf(f489,plain,(
% 0.14/0.40 ($false = $true) | (~spl0_4 | ~spl0_9 | ~spl0_19)),
% 0.14/0.40 inference(superposition,[],[f486,f444])).
% 0.14/0.40 thf(f444,plain,(
% 0.14/0.40 ($false = (p @ sK2)) | ~spl0_19),
% 0.14/0.40 inference(avatar_component_clause,[],[f442])).
% 0.14/0.40 thf(f442,plain,(
% 0.14/0.40 spl0_19 <=> ($false = (p @ sK2))),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_19])])).
% 0.14/0.40 thf(f486,plain,(
% 0.14/0.40 ($true = (p @ sK2)) | (~spl0_4 | ~spl0_9)),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f474])).
% 0.14/0.40 thf(f474,plain,(
% 0.14/0.40 ($false = $true) | ($true = (p @ sK2)) | (~spl0_4 | ~spl0_9)),
% 0.14/0.40 inference(superposition,[],[f263,f286])).
% 0.14/0.40 thf(f286,plain,(
% 0.14/0.40 ((rel_b @ sK1 @ sK2) = $true) | ~spl0_9),
% 0.14/0.40 inference(avatar_component_clause,[],[f284])).
% 0.14/0.40 thf(f284,plain,(
% 0.14/0.40 spl0_9 <=> ((rel_b @ sK1 @ sK2) = $true)),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_9])])).
% 0.14/0.40 thf(f263,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((rel_b @ sK1 @ X1) = $false) | ((p @ X1) = $true)) ) | ~spl0_4),
% 0.14/0.40 inference(avatar_component_clause,[],[f262])).
% 0.14/0.40 thf(f262,plain,(
% 0.14/0.40 spl0_4 <=> ! [X1] : (((p @ X1) = $true) | ((rel_b @ sK1 @ X1) = $false))),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_4])])).
% 0.14/0.40 thf(f450,plain,(
% 0.14/0.40 spl0_20 | spl0_19 | ~spl0_9),
% 0.14/0.40 inference(avatar_split_clause,[],[f437,f284,f442,f446])).
% 0.14/0.40 thf(f437,plain,(
% 0.14/0.40 ($false = (p @ sK2)) | ($true = (q @ sK2)) | ~spl0_9),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f434])).
% 0.14/0.40 thf(f434,plain,(
% 0.14/0.40 ($true = (q @ sK2)) | ($false = $true) | ($false = (p @ sK2)) | ~spl0_9),
% 0.14/0.40 inference(superposition,[],[f286,f172])).
% 0.14/0.40 thf(f172,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((rel_b @ sK1 @ X1) = $false) | ($true = (q @ X1)) | ((p @ X1) = $false)) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f171])).
% 0.14/0.40 thf(f171,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($true = (q @ X1)) | ((~ (p @ X1)) = $true) | ((rel_b @ sK1 @ X1) = $false)) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f170])).
% 0.14/0.40 thf(f170,plain,(
% 0.14/0.40 ( ! [X1 : $i] : ((((~ (p @ X1)) | (q @ X1)) = $true) | ((rel_b @ sK1 @ X1) = $false)) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f169])).
% 0.14/0.40 thf(f169,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($false = (~ ((~ (p @ X1)) | (q @ X1)))) | ((rel_b @ sK1 @ X1) = $false)) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f167])).
% 0.14/0.40 thf(f167,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($false = ((~ ((~ (p @ X1)) | (q @ X1))) | (~ ((~ (q @ X1)) | (p @ X1))))) | ((rel_b @ sK1 @ X1) = $false)) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f166])).
% 0.14/0.40 thf(f166,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($true = (~ (rel_b @ sK1 @ X1))) | ($false = ((~ ((~ (p @ X1)) | (q @ X1))) | (~ ((~ (q @ X1)) | (p @ X1)))))) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f165])).
% 0.14/0.40 thf(f165,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((~ ((~ ((~ (p @ X1)) | (q @ X1))) | (~ ((~ (q @ X1)) | (p @ X1))))) = $true) | ($true = (~ (rel_b @ sK1 @ X1)))) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f164])).
% 0.14/0.40 thf(f164,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($true = ((~ ((~ ((~ (p @ X1)) | (q @ X1))) | (~ ((~ (q @ X1)) | (p @ X1))))) | (~ (rel_b @ sK1 @ X1))))) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f163])).
% 0.14/0.40 thf(f163,plain,(
% 0.14/0.40 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ ((~ ((~ (p @ Y0)) | (q @ Y0))) | (~ ((~ (q @ Y0)) | (p @ Y0))))) | (~ (rel_b @ sK1 @ Y0)))) @ X1) = $true)) )),
% 0.14/0.40 inference(pi_clausification,[],[f162])).
% 0.14/0.40 thf(f162,plain,(
% 0.14/0.40 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ ((~ ((~ (p @ Y0)) | (q @ Y0))) | (~ ((~ (q @ Y0)) | (p @ Y0))))) | (~ (rel_b @ sK1 @ Y0))))))),
% 0.14/0.40 inference(not_proxy_clausification,[],[f161])).
% 0.14/0.40 thf(f161,plain,(
% 0.14/0.40 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ ((~ ((~ (p @ Y0)) | (q @ Y0))) | (~ ((~ (q @ Y0)) | (p @ Y0))))) | (~ (rel_b @ 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]: ((~ ((~ ((~ (p @ Y0)) | (q @ Y0))) | (~ ((~ (q @ Y0)) | (p @ Y0))))) | (~ (rel_b @ sK1 @ Y0)))))) | (~ ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ sK1 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0))))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ 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]: ((~ ((~ ((~ (p @ Y1)) | (q @ Y1))) | (~ ((~ (q @ Y1)) | (p @ Y1))))) | (~ (rel_b @ Y0 @ Y1)))))) | (~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_b @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_b @ Y0 @ Y1))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_b @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_b @ Y0 @ Y1))))))))))) @ sK1) = $false)),
% 0.14/0.40 inference(sigma_clausification,[],[f157])).
% 0.14/0.40 thf(f157,plain,(
% 0.14/0.40 ($true != (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ ((~ ((~ (p @ Y1)) | (q @ Y1))) | (~ ((~ (q @ Y1)) | (p @ Y1))))) | (~ (rel_b @ Y0 @ Y1)))))) | (~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_b @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_b @ Y0 @ Y1))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_b @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_b @ Y0 @ Y1)))))))))))))),
% 0.14/0.40 inference(beta_eta_normalization,[],[f156])).
% 0.14/0.40 thf(f156,plain,(
% 0.14/0.40 ($true != ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_b @ Y1 @ Y2)))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y1 @ Y0))))) @ p @ q)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y1 @ Y0))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_b @ Y1 @ Y2)))))))) @ p) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_b @ Y1 @ Y2)))))))) @ q)))))),
% 0.14/0.40 inference(definition_unfolding,[],[f129,f125,f145,f133,f147,f147,f133,f133])).
% 0.14/0.40 thf(f147,plain,(
% 0.14/0.40 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y1 @ Y0))))))),
% 0.14/0.40 inference(definition_unfolding,[],[f119,f144,f145,f145])).
% 0.14/0.40 thf(f144,plain,(
% 0.14/0.40 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 0.14/0.40 inference(definition_unfolding,[],[f121,f126,f109,f126,f126])).
% 0.14/0.40 thf(f109,plain,(
% 0.14/0.40 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f70])).
% 0.14/0.40 thf(f70,plain,(
% 0.14/0.40 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.14/0.40 inference(fool_elimination,[],[f69])).
% 0.14/0.40 thf(f69,plain,(
% 0.14/0.40 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ 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] : ((X4 @ X2) | (X3 @ X2))))),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.14/0.40 thf(f126,plain,(
% 0.14/0.40 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f58])).
% 0.14/0.40 thf(f58,plain,(
% 0.14/0.40 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.14/0.40 inference(fool_elimination,[],[f57])).
% 0.14/0.40 thf(f57,plain,(
% 0.14/0.40 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.14/0.40 inference(rectify,[],[f3])).
% 0.14/0.40 thf(f3,axiom,(
% 0.14/0.40 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.14/0.40 thf(f121,plain,(
% 0.14/0.40 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f86])).
% 0.14/0.40 thf(f86,plain,(
% 0.14/0.40 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.14/0.40 inference(fool_elimination,[],[f85])).
% 0.14/0.40 thf(f85,plain,(
% 0.14/0.40 (mand = (^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))))),
% 0.14/0.40 inference(rectify,[],[f5])).
% 0.14/0.40 thf(f5,axiom,(
% 0.14/0.40 (mand = (^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))))),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand)).
% 0.14/0.40 thf(f119,plain,(
% 0.14/0.40 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f96])).
% 0.14/0.40 thf(f96,plain,(
% 0.14/0.40 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.14/0.40 inference(fool_elimination,[],[f95])).
% 0.14/0.40 thf(f95,plain,(
% 0.14/0.40 (mequiv = (^[X0 : $i > $o, X1 : $i > $o] : (mand @ (mimplies @ X0 @ X1) @ (mimplies @ X1 @ X0))))),
% 0.14/0.40 inference(rectify,[],[f8])).
% 0.14/0.40 thf(f8,axiom,(
% 0.14/0.40 (mequiv = (^[X3 : $i > $o, X4 : $i > $o] : (mand @ (mimplies @ X3 @ X4) @ (mimplies @ X4 @ X3))))),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv)).
% 0.14/0.40 thf(f133,plain,(
% 0.14/0.40 (mbox_b = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_b @ Y1 @ Y2)))))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f102])).
% 0.14/0.40 thf(f102,plain,(
% 0.14/0.40 (mbox_b = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_b @ Y1 @ Y2)))))))))),
% 0.14/0.40 inference(fool_elimination,[],[f101])).
% 0.14/0.40 thf(f101,plain,(
% 0.14/0.40 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : (~(rel_b @ X1 @ X2) | (X0 @ X2)))) = mbox_b)),
% 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_b @ X2 @ X7) | (X3 @ X7)))) = mbox_b)),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_b)).
% 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]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.14/0.40 inference(definition_unfolding,[],[f110,f109,f126])).
% 0.14/0.40 thf(f110,plain,(
% 0.14/0.40 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.14/0.40 inference(cnf_transformation,[],[f100])).
% 0.14/0.40 thf(f100,plain,(
% 0.14/0.40 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.14/0.40 inference(fool_elimination,[],[f99])).
% 0.14/0.40 thf(f99,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/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.14/0.40 thf(f125,plain,(
% 0.14/0.40 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.14/0.40 inference(cnf_transformation,[],[f93])).
% 0.14/0.40 thf(f93,plain,(
% 0.14/0.40 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.14/0.40 inference(fool_elimination,[],[f92])).
% 0.14/0.40 thf(f92,plain,(
% 0.14/0.40 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.14/0.40 inference(rectify,[],[f28])).
% 0.14/0.40 thf(f28,axiom,(
% 0.14/0.40 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.14/0.40 thf(f129,plain,(
% 0.14/0.40 ((mvalid @ (mimplies @ (mbox_b @ (mequiv @ p @ q)) @ (mequiv @ (mbox_b @ p) @ (mbox_b @ q)))) != $true)),
% 0.14/0.40 inference(cnf_transformation,[],[f107])).
% 0.14/0.40 thf(f107,plain,(
% 0.14/0.40 ((mvalid @ (mimplies @ (mbox_b @ (mequiv @ p @ q)) @ (mequiv @ (mbox_b @ p) @ (mbox_b @ q)))) != $true)),
% 0.14/0.40 inference(flattening,[],[f50])).
% 0.14/0.40 thf(f50,plain,(
% 0.14/0.40 ~((mvalid @ (mimplies @ (mbox_b @ (mequiv @ p @ q)) @ (mequiv @ (mbox_b @ p) @ (mbox_b @ q)))) = $true)),
% 0.14/0.40 inference(fool_elimination,[],[f49])).
% 0.14/0.40 thf(f49,plain,(
% 0.14/0.40 ~(mvalid @ (mimplies @ (mbox_b @ (mequiv @ p @ q)) @ (mequiv @ (mbox_b @ p) @ (mbox_b @ q))))),
% 0.14/0.40 inference(rectify,[],[f37])).
% 0.14/0.40 thf(f37,negated_conjecture,(
% 0.14/0.40 ~(mvalid @ (mimplies @ (mbox_b @ (mequiv @ p @ q)) @ (mequiv @ (mbox_b @ p) @ (mbox_b @ q))))),
% 0.14/0.40 inference(negated_conjecture,[],[f36])).
% 0.14/0.40 thf(f36,conjecture,(
% 0.14/0.40 (mvalid @ (mimplies @ (mbox_b @ (mequiv @ p @ q)) @ (mequiv @ (mbox_b @ p) @ (mbox_b @ q))))),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove)).
% 0.14/0.40 thf(f404,plain,(
% 0.14/0.40 ~spl0_1 | ~spl0_3 | ~spl0_8),
% 0.14/0.40 inference(avatar_contradiction_clause,[],[f403])).
% 0.14/0.40 thf(f403,plain,(
% 0.14/0.40 $false | (~spl0_1 | ~spl0_3 | ~spl0_8)),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f399])).
% 0.14/0.40 thf(f399,plain,(
% 0.14/0.40 ($false = $true) | (~spl0_1 | ~spl0_3 | ~spl0_8)),
% 0.14/0.40 inference(superposition,[],[f390,f259])).
% 0.14/0.40 thf(f259,plain,(
% 0.14/0.40 ($false = (q @ sK5)) | ~spl0_3),
% 0.14/0.40 inference(avatar_component_clause,[],[f257])).
% 0.14/0.40 thf(f257,plain,(
% 0.14/0.40 spl0_3 <=> ($false = (q @ sK5))),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_3])])).
% 0.14/0.40 thf(f390,plain,(
% 0.14/0.40 ($true = (q @ sK5)) | (~spl0_1 | ~spl0_8)),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f384])).
% 0.14/0.40 thf(f384,plain,(
% 0.14/0.40 ($false = $true) | ($true = (q @ sK5)) | (~spl0_1 | ~spl0_8)),
% 0.14/0.40 inference(superposition,[],[f282,f250])).
% 0.14/0.40 thf(f250,plain,(
% 0.14/0.40 ((rel_b @ sK1 @ sK5) = $true) | ~spl0_1),
% 0.14/0.40 inference(avatar_component_clause,[],[f248])).
% 0.14/0.40 thf(f248,plain,(
% 0.14/0.40 spl0_1 <=> ((rel_b @ sK1 @ sK5) = $true)),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.14/0.40 thf(f378,plain,(
% 0.14/0.40 ~spl0_2 | ~spl0_8 | ~spl0_12),
% 0.14/0.40 inference(avatar_contradiction_clause,[],[f377])).
% 0.14/0.40 thf(f377,plain,(
% 0.14/0.40 $false | (~spl0_2 | ~spl0_8 | ~spl0_12)),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f374])).
% 0.14/0.40 thf(f374,plain,(
% 0.14/0.40 ($false = $true) | (~spl0_2 | ~spl0_8 | ~spl0_12)),
% 0.14/0.40 inference(superposition,[],[f301,f346])).
% 0.14/0.40 thf(f346,plain,(
% 0.14/0.40 ($false = (q @ sK3)) | ~spl0_12),
% 0.14/0.40 inference(avatar_component_clause,[],[f344])).
% 0.14/0.40 thf(f344,plain,(
% 0.14/0.40 spl0_12 <=> ($false = (q @ sK3))),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_12])])).
% 0.14/0.40 thf(f301,plain,(
% 0.14/0.40 ((q @ sK3) = $true) | (~spl0_2 | ~spl0_8)),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f297])).
% 0.14/0.40 thf(f297,plain,(
% 0.14/0.40 ($false = $true) | ((q @ sK3) = $true) | (~spl0_2 | ~spl0_8)),
% 0.14/0.40 inference(superposition,[],[f254,f282])).
% 0.14/0.40 thf(f254,plain,(
% 0.14/0.40 ($true = (rel_b @ sK1 @ sK3)) | ~spl0_2),
% 0.14/0.40 inference(avatar_component_clause,[],[f252])).
% 0.14/0.40 thf(f252,plain,(
% 0.14/0.40 spl0_2 <=> ($true = (rel_b @ sK1 @ sK3))),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.14/0.40 thf(f371,plain,(
% 0.14/0.40 ~spl0_6 | ~spl0_11),
% 0.14/0.40 inference(avatar_contradiction_clause,[],[f370])).
% 0.14/0.40 thf(f370,plain,(
% 0.14/0.40 $false | (~spl0_6 | ~spl0_11)),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f366])).
% 0.14/0.40 thf(f366,plain,(
% 0.14/0.40 ($false = $true) | (~spl0_6 | ~spl0_11)),
% 0.14/0.40 inference(superposition,[],[f342,f272])).
% 0.14/0.40 thf(f272,plain,(
% 0.14/0.40 ($false = (p @ sK3)) | ~spl0_6),
% 0.14/0.40 inference(avatar_component_clause,[],[f270])).
% 0.14/0.40 thf(f270,plain,(
% 0.14/0.40 spl0_6 <=> ($false = (p @ sK3))),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_6])])).
% 0.14/0.40 thf(f342,plain,(
% 0.14/0.40 ($true = (p @ sK3)) | ~spl0_11),
% 0.14/0.40 inference(avatar_component_clause,[],[f340])).
% 0.14/0.40 thf(f340,plain,(
% 0.14/0.40 spl0_11 <=> ($true = (p @ sK3))),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_11])])).
% 0.14/0.40 thf(f357,plain,(
% 0.14/0.40 spl0_11 | spl0_12 | ~spl0_2),
% 0.14/0.40 inference(avatar_split_clause,[],[f335,f252,f344,f340])).
% 0.14/0.40 thf(f335,plain,(
% 0.14/0.40 ($false = (q @ sK3)) | ($true = (p @ sK3)) | ~spl0_2),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f329])).
% 0.14/0.40 thf(f329,plain,(
% 0.14/0.40 ($false = (q @ sK3)) | ($false = $true) | ($true = (p @ sK3)) | ~spl0_2),
% 0.14/0.40 inference(superposition,[],[f175,f254])).
% 0.14/0.40 thf(f175,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((rel_b @ sK1 @ X1) = $false) | ($false = (q @ X1)) | ((p @ X1) = $true)) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f174])).
% 0.14/0.40 thf(f174,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((p @ X1) = $true) | ($true = (~ (q @ X1))) | ((rel_b @ sK1 @ X1) = $false)) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f173])).
% 0.14/0.40 thf(f173,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((rel_b @ sK1 @ X1) = $false) | (((~ (q @ X1)) | (p @ X1)) = $true)) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f168])).
% 0.14/0.40 thf(f168,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((rel_b @ sK1 @ X1) = $false) | ($false = (~ ((~ (q @ X1)) | (p @ X1))))) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f167])).
% 0.14/0.40 thf(f293,plain,(
% 0.14/0.40 spl0_8 | spl0_4),
% 0.14/0.40 inference(avatar_split_clause,[],[f193,f262,f281])).
% 0.14/0.40 thf(f193,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : (($false = (rel_b @ sK1 @ X2)) | ($true = (q @ X1)) | ((rel_b @ sK1 @ X1) = $false) | ($true = (p @ X2))) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f192])).
% 0.14/0.40 thf(f192,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : (($true = (p @ X2)) | ((rel_b @ sK1 @ X1) = $false) | ($true = (q @ X1)) | ((~ (rel_b @ sK1 @ X2)) = $true)) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f191])).
% 0.14/0.40 thf(f191,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : (((rel_b @ sK1 @ X1) = $false) | ($true = (q @ X1)) | ($true = ((p @ X2) | (~ (rel_b @ sK1 @ X2))))) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f190])).
% 0.14/0.40 thf(f190,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : (($true = (q @ X1)) | ($true = (~ (rel_b @ sK1 @ X1))) | ($true = ((p @ X2) | (~ (rel_b @ sK1 @ X2))))) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f189])).
% 0.14/0.40 thf(f189,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : (($true = (~ (rel_b @ sK1 @ X1))) | (((^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ sK1 @ Y0)))) @ X2) = $true) | ($true = (q @ X1))) )),
% 0.14/0.40 inference(pi_clausification,[],[f188])).
% 0.14/0.40 thf(f188,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ sK1 @ Y0))))) = $true) | ($true = (q @ X1)) | ($true = (~ (rel_b @ sK1 @ X1)))) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f187])).
% 0.14/0.40 thf(f187,plain,(
% 0.14/0.40 ( ! [X1 : $i] : ((((q @ X1) | (~ (rel_b @ sK1 @ X1))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ sK1 @ Y0))))) = $true)) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f186])).
% 0.14/0.40 thf(f186,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ sK1 @ Y0))))) = $true) | ($true = ((^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0)))) @ X1))) )),
% 0.14/0.40 inference(pi_clausification,[],[f185])).
% 0.14/0.40 thf(f185,plain,(
% 0.14/0.40 ($true = (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0)))))) | ((!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ sK1 @ Y0))))) = $true)),
% 0.14/0.40 inference(not_proxy_clausification,[],[f184])).
% 0.14/0.40 thf(f184,plain,(
% 0.14/0.40 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ sK1 @ Y0))))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0))))))),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f182])).
% 0.14/0.40 thf(f182,plain,(
% 0.14/0.40 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ sK1 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0))))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0))))))),
% 0.14/0.40 inference(not_proxy_clausification,[],[f181])).
% 0.14/0.40 thf(f181,plain,(
% 0.14/0.40 ($true = (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ sK1 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0)))))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0))))))),
% 0.14/0.40 inference(not_proxy_clausification,[],[f180])).
% 0.14/0.40 thf(f180,plain,(
% 0.14/0.40 ((~ (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0)))))) = $false) | ($true = (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ sK1 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0))))))))),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f178])).
% 0.14/0.40 thf(f178,plain,(
% 0.14/0.40 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ sK1 @ Y0))))))) | ($true = (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ sK1 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0))))))))),
% 0.14/0.40 inference(not_proxy_clausification,[],[f177])).
% 0.14/0.40 thf(f177,plain,(
% 0.14/0.40 ($true = (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ sK1 @ Y0)))))))) | ($true = (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ sK1 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0))))))))),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f176])).
% 0.14/0.40 thf(f176,plain,(
% 0.14/0.40 (((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ sK1 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0))))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ sK1 @ Y0)))))))) = $true)),
% 0.14/0.40 inference(not_proxy_clausification,[],[f160])).
% 0.14/0.40 thf(f160,plain,(
% 0.14/0.40 ($false = (~ ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ sK1 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0))))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ sK1 @ Y0))))))))))),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f159])).
% 0.14/0.40 thf(f292,plain,(
% 0.14/0.40 spl0_8 | spl0_10),
% 0.14/0.40 inference(avatar_split_clause,[],[f201,f289,f281])).
% 0.14/0.40 thf(f201,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($false = (q @ sK2)) | ((rel_b @ sK1 @ X1) = $false) | ($true = (q @ X1))) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f200])).
% 0.14/0.40 thf(f200,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($false = (q @ sK2)) | ($true = (~ (rel_b @ sK1 @ X1))) | ($true = (q @ X1))) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f199])).
% 0.14/0.40 thf(f199,plain,(
% 0.14/0.40 ( ! [X1 : $i] : ((((q @ X1) | (~ (rel_b @ sK1 @ X1))) = $true) | ($false = (q @ sK2))) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f198])).
% 0.14/0.40 thf(f198,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0)))) @ X1)) | ($false = (q @ sK2))) )),
% 0.14/0.40 inference(pi_clausification,[],[f197])).
% 0.14/0.40 thf(f197,plain,(
% 0.14/0.40 ($false = (q @ sK2)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0))))))),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f195])).
% 0.14/0.40 thf(f195,plain,(
% 0.14/0.40 (((q @ sK2) | (~ (rel_b @ sK1 @ sK2))) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0))))))),
% 0.14/0.40 inference(beta_eta_normalization,[],[f194])).
% 0.14/0.40 thf(f194,plain,(
% 0.14/0.40 ($true = (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0)))))) | ($false = ((^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0)))) @ sK2))),
% 0.14/0.40 inference(sigma_clausification,[],[f183])).
% 0.14/0.40 thf(f183,plain,(
% 0.14/0.40 ($false = (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0)))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0))))))),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f182])).
% 0.14/0.40 thf(f287,plain,(
% 0.14/0.40 spl0_8 | spl0_9),
% 0.14/0.40 inference(avatar_split_clause,[],[f206,f284,f281])).
% 0.14/0.40 thf(f206,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($true = (q @ X1)) | ((rel_b @ sK1 @ sK2) = $true) | ((rel_b @ sK1 @ X1) = $false)) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f205])).
% 0.14/0.40 thf(f205,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($true = (~ (rel_b @ sK1 @ X1))) | ($true = (q @ X1)) | ((rel_b @ sK1 @ sK2) = $true)) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f204])).
% 0.14/0.40 thf(f204,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((rel_b @ sK1 @ sK2) = $true) | (((q @ X1) | (~ (rel_b @ sK1 @ X1))) = $true)) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f203])).
% 0.14/0.40 thf(f203,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0)))) @ X1)) | ((rel_b @ sK1 @ sK2) = $true)) )),
% 0.14/0.40 inference(pi_clausification,[],[f202])).
% 0.14/0.40 thf(f202,plain,(
% 0.14/0.40 ((rel_b @ sK1 @ sK2) = $true) | ($true = (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0))))))),
% 0.14/0.40 inference(not_proxy_clausification,[],[f196])).
% 0.14/0.40 thf(f196,plain,(
% 0.14/0.40 ((~ (rel_b @ sK1 @ sK2)) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0))))))),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f195])).
% 0.14/0.40 thf(f278,plain,(
% 0.14/0.40 spl0_7 | spl0_6),
% 0.14/0.40 inference(avatar_split_clause,[],[f222,f270,f275])).
% 0.14/0.40 thf(f222,plain,(
% 0.14/0.40 ($false = (p @ sK3)) | ((q @ sK4) = $false)),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f220])).
% 0.14/0.40 thf(f220,plain,(
% 0.14/0.40 (((q @ sK4) | (~ (rel_b @ sK1 @ sK4))) = $false) | ($false = (p @ sK3))),
% 0.14/0.40 inference(beta_eta_normalization,[],[f219])).
% 0.14/0.40 thf(f219,plain,(
% 0.14/0.40 (((^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0)))) @ sK4) = $false) | ($false = (p @ sK3))),
% 0.14/0.40 inference(sigma_clausification,[],[f212])).
% 0.14/0.40 thf(f212,plain,(
% 0.14/0.40 ($false = (p @ sK3)) | ($false = (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0))))))),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f211])).
% 0.14/0.40 thf(f211,plain,(
% 0.14/0.40 ($false = (p @ sK3)) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ sK1 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0)))))))),
% 0.14/0.40 inference(not_proxy_clausification,[],[f210])).
% 0.14/0.40 thf(f210,plain,(
% 0.14/0.40 ($true = (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ sK1 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0)))))))) | ($false = (p @ sK3))),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f208])).
% 0.14/0.40 thf(f208,plain,(
% 0.14/0.40 (((p @ sK3) | (~ (rel_b @ sK1 @ sK3))) = $false) | ($true = (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ sK1 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0))))))))),
% 0.14/0.40 inference(beta_eta_normalization,[],[f207])).
% 0.14/0.40 thf(f207,plain,(
% 0.14/0.40 ($true = (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ sK1 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0)))))))) | ($false = ((^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ sK1 @ Y0)))) @ sK3))),
% 0.14/0.40 inference(sigma_clausification,[],[f179])).
% 0.14/0.40 thf(f179,plain,(
% 0.14/0.40 ($false = (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ sK1 @ Y0)))))) | ($true = (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ sK1 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0))))))))),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f178])).
% 0.14/0.40 thf(f273,plain,(
% 0.14/0.40 spl0_5 | spl0_6),
% 0.14/0.40 inference(avatar_split_clause,[],[f223,f270,f266])).
% 0.14/0.40 thf(f223,plain,(
% 0.14/0.40 ($false = (p @ sK3)) | ((rel_b @ sK1 @ sK4) = $true)),
% 0.14/0.40 inference(not_proxy_clausification,[],[f221])).
% 0.14/0.40 thf(f221,plain,(
% 0.14/0.40 ($false = (p @ sK3)) | ($false = (~ (rel_b @ sK1 @ sK4)))),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f220])).
% 0.14/0.40 thf(f260,plain,(
% 0.14/0.40 spl0_2 | spl0_3),
% 0.14/0.40 inference(avatar_split_clause,[],[f236,f257,f252])).
% 0.14/0.40 thf(f236,plain,(
% 0.14/0.40 ($true = (rel_b @ sK1 @ sK3)) | ($false = (q @ sK5))),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f234])).
% 0.14/0.40 thf(f234,plain,(
% 0.14/0.40 ($true = (rel_b @ sK1 @ sK3)) | ($false = ((q @ sK5) | (~ (rel_b @ sK1 @ sK5))))),
% 0.14/0.40 inference(beta_eta_normalization,[],[f233])).
% 0.14/0.40 thf(f233,plain,(
% 0.14/0.40 ($true = (rel_b @ sK1 @ sK3)) | (((^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0)))) @ sK5) = $false)),
% 0.14/0.40 inference(sigma_clausification,[],[f226])).
% 0.14/0.40 thf(f226,plain,(
% 0.14/0.40 ($false = (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0)))))) | ($true = (rel_b @ sK1 @ sK3))),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f225])).
% 0.14/0.40 thf(f225,plain,(
% 0.14/0.40 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ sK1 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0))))))) | ($true = (rel_b @ sK1 @ sK3))),
% 0.14/0.40 inference(not_proxy_clausification,[],[f224])).
% 0.14/0.40 thf(f224,plain,(
% 0.14/0.40 ($false = (~ (rel_b @ sK1 @ sK3))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ sK1 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0)))))))),
% 0.14/0.40 inference(not_proxy_clausification,[],[f209])).
% 0.14/0.40 thf(f209,plain,(
% 0.14/0.40 ($true = (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ sK1 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0)))))))) | ($false = (~ (rel_b @ sK1 @ sK3)))),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f208])).
% 0.14/0.40 thf(f255,plain,(
% 0.14/0.40 spl0_1 | spl0_2),
% 0.14/0.40 inference(avatar_split_clause,[],[f237,f252,f248])).
% 0.14/0.40 thf(f237,plain,(
% 0.14/0.40 ((rel_b @ sK1 @ sK5) = $true) | ($true = (rel_b @ sK1 @ sK3))),
% 0.14/0.40 inference(not_proxy_clausification,[],[f235])).
% 0.14/0.40 thf(f235,plain,(
% 0.14/0.40 ($false = (~ (rel_b @ sK1 @ sK5))) | ($true = (rel_b @ sK1 @ sK3))),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f234])).
% 0.14/0.40 % SZS output end Proof for theBenchmark
% 0.14/0.40 % (20402)------------------------------
% 0.14/0.40 % (20402)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (20402)Termination reason: Refutation
% 0.14/0.40
% 0.14/0.40 % (20402)Memory used [KB]: 5884
% 0.14/0.40 % (20402)Time elapsed: 0.028 s
% 0.14/0.40 % (20402)Instructions burned: 33 (million)
% 0.14/0.40 % (20402)------------------------------
% 0.14/0.40 % (20402)------------------------------
% 0.14/0.40 % (20401)Success in time 0.029 s
% 0.14/0.40 % Vampire---4.8 exiting
%------------------------------------------------------------------------------