TSTP Solution File: SYO404^1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO404^1 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 09:04:18 EDT 2024
% Result : Theorem 0.13s 0.31s
% Output : Refutation 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.07 % Problem : SYO404^1 : TPTP v8.2.0. Released v4.0.0.
% 0.02/0.08 % 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
% 0.08/0.27 % Computer : n032.cluster.edu
% 0.08/0.27 % Model : x86_64 x86_64
% 0.08/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.27 % Memory : 8042.1875MB
% 0.08/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.27 % CPULimit : 300
% 0.08/0.27 % WCLimit : 300
% 0.08/0.27 % DateTime : Mon May 20 10:27:37 EDT 2024
% 0.08/0.27 % CPUTime :
% 0.08/0.27 This is a TH0_THM_EQU_NAR problem
% 0.08/0.28 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
% 0.13/0.29 % (15438)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)
% 0.13/0.29 % (15439)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)
% 0.13/0.29 % (15443)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.13/0.29 % (15438)Instruction limit reached!
% 0.13/0.29 % (15438)------------------------------
% 0.13/0.29 % (15438)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.29 % (15437)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.13/0.29 % (15440)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.13/0.29 % (15440)Instruction limit reached!
% 0.13/0.29 % (15440)------------------------------
% 0.13/0.29 % (15440)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.29 % (15440)Termination reason: Unknown
% 0.13/0.29 % (15440)Termination phase: shuffling
% 0.13/0.29
% 0.13/0.29 % (15440)Memory used [KB]: 1023
% 0.13/0.29 % (15440)Time elapsed: 0.002 s
% 0.13/0.29 % (15440)Instructions burned: 2 (million)
% 0.13/0.29 % (15440)------------------------------
% 0.13/0.29 % (15440)------------------------------
% 0.13/0.29 % (15444)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)
% 0.13/0.29 % (15441)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)
% 0.13/0.29 % (15442)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)
% 0.13/0.29 % (15441)Instruction limit reached!
% 0.13/0.29 % (15441)------------------------------
% 0.13/0.29 % (15441)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.29 % (15441)Termination reason: Unknown
% 0.13/0.29 % (15441)Termination phase: shuffling
% 0.13/0.29
% 0.13/0.29 % (15441)Memory used [KB]: 1023
% 0.13/0.29 % (15441)Time elapsed: 0.003 s
% 0.13/0.29 % (15441)Instructions burned: 3 (million)
% 0.13/0.29 % (15441)------------------------------
% 0.13/0.29 % (15441)------------------------------
% 0.13/0.29 % (15444)Instruction limit reached!
% 0.13/0.29 % (15444)------------------------------
% 0.13/0.29 % (15444)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.29 % (15444)Termination reason: Unknown
% 0.13/0.29 % (15444)Termination phase: shuffling
% 0.13/0.29
% 0.13/0.29 % (15444)Memory used [KB]: 1023
% 0.13/0.29 % (15444)Time elapsed: 0.003 s
% 0.13/0.29 % (15444)Instructions burned: 4 (million)
% 0.13/0.29 % (15444)------------------------------
% 0.13/0.29 % (15444)------------------------------
% 0.13/0.29 % (15443)Instruction limit reached!
% 0.13/0.29 % (15443)------------------------------
% 0.13/0.29 % (15443)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.29 % (15443)Termination reason: Unknown
% 0.13/0.29 % (15443)Termination phase: Saturation
% 0.13/0.29
% 0.13/0.29 % (15443)Memory used [KB]: 5628
% 0.13/0.29 % (15443)Time elapsed: 0.007 s
% 0.13/0.29 % (15443)Instructions burned: 20 (million)
% 0.13/0.29 % (15443)------------------------------
% 0.13/0.29 % (15443)------------------------------
% 0.13/0.29 % (15438)Termination reason: Unknown
% 0.13/0.29 % (15438)Termination phase: Property scanning
% 0.13/0.29
% 0.13/0.29 % (15438)Memory used [KB]: 1023
% 0.13/0.29 % (15438)Time elapsed: 0.003 s
% 0.13/0.29 % (15438)Instructions burned: 4 (million)
% 0.13/0.29 % (15438)------------------------------
% 0.13/0.29 % (15438)------------------------------
% 0.13/0.30 % (15439)Instruction limit reached!
% 0.13/0.30 % (15439)------------------------------
% 0.13/0.30 % (15439)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.30 % (15439)Termination reason: Unknown
% 0.13/0.30 % (15439)Termination phase: Saturation
% 0.13/0.30
% 0.13/0.30 % (15439)Memory used [KB]: 5756
% 0.13/0.30 % (15439)Time elapsed: 0.009 s
% 0.13/0.30 % (15439)Instructions burned: 27 (million)
% 0.13/0.30 % (15439)------------------------------
% 0.13/0.30 % (15439)------------------------------
% 0.13/0.30 % (15442)Refutation not found, incomplete strategy
% 0.13/0.30 % (15442)------------------------------
% 0.13/0.30 % (15442)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.30 % (15442)Termination reason: Refutation not found, incomplete strategy
% 0.13/0.30
% 0.13/0.30
% 0.13/0.30 % (15442)Memory used [KB]: 5628
% 0.13/0.30 % (15442)Time elapsed: 0.004 s
% 0.13/0.30 % (15442)Instructions burned: 8 (million)
% 0.13/0.30 % (15442)------------------------------
% 0.13/0.30 % (15442)------------------------------
% 0.13/0.30 % (15445)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)
% 0.13/0.30 % (15437)First to succeed.
% 0.13/0.30 % (15452)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.13/0.30 % (15448)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)
% 0.13/0.31 % (15448)Instruction limit reached!
% 0.13/0.31 % (15448)------------------------------
% 0.13/0.31 % (15448)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.31 % (15448)Termination reason: Unknown
% 0.13/0.31 % (15448)Termination phase: Clausification
% 0.13/0.31
% 0.13/0.31 % (15448)Memory used [KB]: 1023
% 0.13/0.31 % (15448)Time elapsed: 0.003 s
% 0.13/0.31 % (15448)Instructions burned: 6 (million)
% 0.13/0.31 % (15448)------------------------------
% 0.13/0.31 % (15448)------------------------------
% 0.13/0.31 % (15454)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.13/0.31 % (15437)Refutation found. Thanks to Tanya!
% 0.13/0.31 % SZS status Theorem for theBenchmark
% 0.13/0.31 % SZS output start Proof for theBenchmark
% 0.13/0.31 thf(type_def_5, type, mu: $tType).
% 0.13/0.31 thf(func_def_0, type, mu: $tType).
% 0.13/0.31 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.13/0.31 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.31 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.13/0.31 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.31 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.31 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.31 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.31 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.31 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.31 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.13/0.31 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.13/0.31 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.13/0.31 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.13/0.31 thf(func_def_15, type, mtrue: $i > $o).
% 0.13/0.31 thf(func_def_16, type, mfalse: $i > $o).
% 0.13/0.31 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.13/0.31 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.13/0.31 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.13/0.31 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.13/0.31 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.13/0.31 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.13/0.31 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.13/0.31 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.13/0.31 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.13/0.31 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.13/0.31 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.13/0.31 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.13/0.31 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.13/0.31 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.13/0.31 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.13/0.31 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.13/0.31 thf(func_def_33, type, rel_k: $i > $i > $o).
% 0.13/0.31 thf(func_def_34, type, mbox_k: ($i > $o) > $i > $o).
% 0.13/0.31 thf(func_def_35, type, mdia_k: ($i > $o) > $i > $o).
% 0.13/0.31 thf(func_def_36, type, p: $i > $o).
% 0.13/0.31 thf(func_def_37, type, q: $i > $o).
% 0.13/0.31 thf(f831,plain,(
% 0.13/0.31 $false),
% 0.13/0.31 inference(avatar_sat_refutation,[],[f364,f425,f463,f468,f477,f487,f497,f501,f510,f520,f548,f558,f572,f590,f614,f621,f647,f661,f700,f740,f801,f823,f830])).
% 0.13/0.31 thf(f830,plain,(
% 0.13/0.31 ~spl0_46 | ~spl0_54),
% 0.13/0.31 inference(avatar_contradiction_clause,[],[f829])).
% 0.13/0.31 thf(f829,plain,(
% 0.13/0.31 $false | (~spl0_46 | ~spl0_54)),
% 0.13/0.31 inference(trivial_inequality_removal,[],[f826])).
% 0.13/0.31 thf(f826,plain,(
% 0.13/0.31 ($true = $false) | (~spl0_46 | ~spl0_54)),
% 0.13/0.31 inference(superposition,[],[f713,f799])).
% 0.13/0.31 thf(f799,plain,(
% 0.13/0.31 ((q @ sK2) = $false) | ~spl0_54),
% 0.13/0.31 inference(avatar_component_clause,[],[f797])).
% 0.13/0.31 thf(f797,plain,(
% 0.13/0.31 spl0_54 <=> ((q @ sK2) = $false)),
% 0.13/0.31 introduced(avatar_definition,[new_symbols(naming,[spl0_54])])).
% 0.13/0.31 thf(f713,plain,(
% 0.13/0.31 ($true = (q @ sK2)) | ~spl0_46),
% 0.13/0.31 inference(avatar_component_clause,[],[f711])).
% 0.13/0.31 thf(f711,plain,(
% 0.13/0.31 spl0_46 <=> ($true = (q @ sK2))),
% 0.13/0.31 introduced(avatar_definition,[new_symbols(naming,[spl0_46])])).
% 0.13/0.31 thf(f823,plain,(
% 0.13/0.31 ~spl0_23 | ~spl0_47),
% 0.13/0.31 inference(avatar_contradiction_clause,[],[f822])).
% 0.13/0.31 thf(f822,plain,(
% 0.13/0.31 $false | (~spl0_23 | ~spl0_47)),
% 0.13/0.31 inference(trivial_inequality_removal,[],[f819])).
% 0.13/0.31 thf(f819,plain,(
% 0.13/0.31 ($true = $false) | (~spl0_23 | ~spl0_47)),
% 0.13/0.31 inference(superposition,[],[f467,f717])).
% 0.13/0.31 thf(f717,plain,(
% 0.13/0.31 ($true = (p @ sK2)) | ~spl0_47),
% 0.13/0.31 inference(avatar_component_clause,[],[f715])).
% 0.13/0.31 thf(f715,plain,(
% 0.13/0.31 spl0_47 <=> ($true = (p @ sK2))),
% 0.13/0.31 introduced(avatar_definition,[new_symbols(naming,[spl0_47])])).
% 0.13/0.31 thf(f467,plain,(
% 0.13/0.31 ((p @ sK2) = $false) | ~spl0_23),
% 0.13/0.31 inference(avatar_component_clause,[],[f465])).
% 0.13/0.31 thf(f465,plain,(
% 0.13/0.31 spl0_23 <=> ((p @ sK2) = $false)),
% 0.13/0.31 introduced(avatar_definition,[new_symbols(naming,[spl0_23])])).
% 0.13/0.31 thf(f801,plain,(
% 0.13/0.31 spl0_54 | spl0_47 | ~spl0_1 | ~spl0_22),
% 0.13/0.31 inference(avatar_split_clause,[],[f784,f460,f359,f715,f797])).
% 0.13/0.31 thf(f359,plain,(
% 0.13/0.31 spl0_1 <=> ! [X1] : (($false = (q @ X1)) | ($true = (p @ X1)) | ($false = (rel_k @ sK1 @ X1)))),
% 0.13/0.31 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.13/0.31 thf(f460,plain,(
% 0.13/0.31 spl0_22 <=> ($true = (rel_k @ sK1 @ sK2))),
% 0.13/0.31 introduced(avatar_definition,[new_symbols(naming,[spl0_22])])).
% 0.13/0.31 thf(f784,plain,(
% 0.13/0.31 ((q @ sK2) = $false) | ($true = (p @ sK2)) | (~spl0_1 | ~spl0_22)),
% 0.13/0.31 inference(trivial_inequality_removal,[],[f768])).
% 0.13/0.31 thf(f768,plain,(
% 0.13/0.31 ((q @ sK2) = $false) | ($true = (p @ sK2)) | ($true = $false) | (~spl0_1 | ~spl0_22)),
% 0.13/0.31 inference(superposition,[],[f462,f360])).
% 0.13/0.31 thf(f360,plain,(
% 0.13/0.31 ( ! [X1 : $i] : (($false = (rel_k @ sK1 @ X1)) | ($true = (p @ X1)) | ($false = (q @ X1))) ) | ~spl0_1),
% 0.13/0.31 inference(avatar_component_clause,[],[f359])).
% 0.13/0.31 thf(f462,plain,(
% 0.13/0.31 ($true = (rel_k @ sK1 @ sK2)) | ~spl0_22),
% 0.13/0.31 inference(avatar_component_clause,[],[f460])).
% 0.13/0.31 thf(f740,plain,(
% 0.13/0.31 spl0_46 | spl0_47 | ~spl0_15 | ~spl0_22),
% 0.13/0.31 inference(avatar_split_clause,[],[f628,f460,f423,f715,f711])).
% 0.13/0.31 thf(f423,plain,(
% 0.13/0.31 spl0_15 <=> ! [X1] : (($false = (rel_k @ sK1 @ X1)) | ($true = (q @ X1)) | ($true = (p @ X1)))),
% 0.13/0.31 introduced(avatar_definition,[new_symbols(naming,[spl0_15])])).
% 0.13/0.31 thf(f628,plain,(
% 0.13/0.31 ($true = (q @ sK2)) | ($true = (p @ sK2)) | (~spl0_15 | ~spl0_22)),
% 0.13/0.31 inference(trivial_inequality_removal,[],[f625])).
% 0.13/0.31 thf(f625,plain,(
% 0.13/0.31 ($true = (q @ sK2)) | ($true = (p @ sK2)) | ($true = $false) | (~spl0_15 | ~spl0_22)),
% 0.13/0.31 inference(superposition,[],[f424,f462])).
% 0.13/0.31 thf(f424,plain,(
% 0.13/0.31 ( ! [X1 : $i] : (($false = (rel_k @ sK1 @ X1)) | ($true = (p @ X1)) | ($true = (q @ X1))) ) | ~spl0_15),
% 0.13/0.31 inference(avatar_component_clause,[],[f423])).
% 0.13/0.31 thf(f700,plain,(
% 0.13/0.31 ~spl0_2 | ~spl0_38 | ~spl0_41),
% 0.13/0.31 inference(avatar_contradiction_clause,[],[f699])).
% 0.13/0.31 thf(f699,plain,(
% 0.13/0.31 $false | (~spl0_2 | ~spl0_38 | ~spl0_41)),
% 0.13/0.31 inference(trivial_inequality_removal,[],[f695])).
% 0.13/0.31 thf(f695,plain,(
% 0.13/0.31 ($true = $false) | (~spl0_2 | ~spl0_38 | ~spl0_41)),
% 0.13/0.31 inference(superposition,[],[f694,f557])).
% 0.13/0.31 thf(f557,plain,(
% 0.13/0.31 ((p @ sK4) = $false) | ~spl0_41),
% 0.13/0.31 inference(avatar_component_clause,[],[f555])).
% 0.13/0.31 thf(f555,plain,(
% 0.13/0.31 spl0_41 <=> ((p @ sK4) = $false)),
% 0.13/0.31 introduced(avatar_definition,[new_symbols(naming,[spl0_41])])).
% 0.13/0.31 thf(f694,plain,(
% 0.13/0.31 ($true = (p @ sK4)) | (~spl0_2 | ~spl0_38)),
% 0.13/0.31 inference(trivial_inequality_removal,[],[f688])).
% 0.13/0.31 thf(f688,plain,(
% 0.13/0.31 ($true = (p @ sK4)) | ($true = $false) | (~spl0_2 | ~spl0_38)),
% 0.13/0.31 inference(superposition,[],[f543,f363])).
% 0.13/0.31 thf(f363,plain,(
% 0.13/0.31 ( ! [X2 : $i] : (((rel_k @ sK1 @ X2) = $false) | ($true = (p @ X2))) ) | ~spl0_2),
% 0.13/0.31 inference(avatar_component_clause,[],[f362])).
% 0.13/0.31 thf(f362,plain,(
% 0.13/0.31 spl0_2 <=> ! [X2] : (((rel_k @ sK1 @ X2) = $false) | ($true = (p @ X2)))),
% 0.13/0.31 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.13/0.31 thf(f543,plain,(
% 0.13/0.31 ($true = (rel_k @ sK1 @ sK4)) | ~spl0_38),
% 0.13/0.31 inference(avatar_component_clause,[],[f541])).
% 0.13/0.31 thf(f541,plain,(
% 0.13/0.31 spl0_38 <=> ($true = (rel_k @ sK1 @ sK4))),
% 0.13/0.31 introduced(avatar_definition,[new_symbols(naming,[spl0_38])])).
% 0.13/0.31 thf(f661,plain,(
% 0.13/0.31 ~spl0_2 | ~spl0_30 | ~spl0_33),
% 0.13/0.31 inference(avatar_contradiction_clause,[],[f660])).
% 0.13/0.31 thf(f660,plain,(
% 0.13/0.31 $false | (~spl0_2 | ~spl0_30 | ~spl0_33)),
% 0.13/0.31 inference(trivial_inequality_removal,[],[f656])).
% 0.13/0.31 thf(f656,plain,(
% 0.13/0.31 ($true = $false) | (~spl0_2 | ~spl0_30 | ~spl0_33)),
% 0.13/0.31 inference(superposition,[],[f655,f519])).
% 0.13/0.31 thf(f519,plain,(
% 0.13/0.31 ((p @ sK6) = $false) | ~spl0_33),
% 0.13/0.31 inference(avatar_component_clause,[],[f517])).
% 0.13/0.31 thf(f517,plain,(
% 0.13/0.31 spl0_33 <=> ((p @ sK6) = $false)),
% 0.13/0.31 introduced(avatar_definition,[new_symbols(naming,[spl0_33])])).
% 0.13/0.31 thf(f655,plain,(
% 0.13/0.31 ($true = (p @ sK6)) | (~spl0_2 | ~spl0_30)),
% 0.13/0.31 inference(trivial_inequality_removal,[],[f649])).
% 0.13/0.31 thf(f649,plain,(
% 0.13/0.31 ($true = (p @ sK6)) | ($true = $false) | (~spl0_2 | ~spl0_30)),
% 0.13/0.31 inference(superposition,[],[f505,f363])).
% 0.13/0.31 thf(f505,plain,(
% 0.13/0.31 ($true = (rel_k @ sK1 @ sK6)) | ~spl0_30),
% 0.13/0.31 inference(avatar_component_clause,[],[f503])).
% 0.13/0.31 thf(f503,plain,(
% 0.13/0.31 spl0_30 <=> ($true = (rel_k @ sK1 @ sK6))),
% 0.13/0.31 introduced(avatar_definition,[new_symbols(naming,[spl0_30])])).
% 0.13/0.31 thf(f647,plain,(
% 0.13/0.31 ~spl0_2 | ~spl0_31 | ~spl0_39),
% 0.13/0.31 inference(avatar_contradiction_clause,[],[f646])).
% 0.13/0.31 thf(f646,plain,(
% 0.13/0.31 $false | (~spl0_2 | ~spl0_31 | ~spl0_39)),
% 0.13/0.31 inference(trivial_inequality_removal,[],[f642])).
% 0.13/0.31 thf(f642,plain,(
% 0.13/0.31 ($true = $false) | (~spl0_2 | ~spl0_31 | ~spl0_39)),
% 0.13/0.31 inference(superposition,[],[f641,f547])).
% 0.13/0.31 thf(f547,plain,(
% 0.13/0.31 ((p @ sK3) = $false) | ~spl0_39),
% 0.13/0.31 inference(avatar_component_clause,[],[f545])).
% 0.13/0.31 thf(f545,plain,(
% 0.13/0.31 spl0_39 <=> ((p @ sK3) = $false)),
% 0.13/0.31 introduced(avatar_definition,[new_symbols(naming,[spl0_39])])).
% 0.13/0.31 thf(f641,plain,(
% 0.13/0.31 ($true = (p @ sK3)) | (~spl0_2 | ~spl0_31)),
% 0.13/0.31 inference(trivial_inequality_removal,[],[f637])).
% 0.13/0.31 thf(f637,plain,(
% 0.13/0.31 ($true = $false) | ($true = (p @ sK3)) | (~spl0_2 | ~spl0_31)),
% 0.13/0.31 inference(superposition,[],[f363,f509])).
% 0.13/0.31 thf(f509,plain,(
% 0.13/0.31 ($true = (rel_k @ sK1 @ sK3)) | ~spl0_31),
% 0.13/0.31 inference(avatar_component_clause,[],[f507])).
% 0.13/0.31 thf(f507,plain,(
% 0.13/0.31 spl0_31 <=> ($true = (rel_k @ sK1 @ sK3))),
% 0.13/0.31 introduced(avatar_definition,[new_symbols(naming,[spl0_31])])).
% 0.13/0.31 thf(f621,plain,(
% 0.13/0.31 ~spl0_29 | ~spl0_43),
% 0.13/0.31 inference(avatar_contradiction_clause,[],[f620])).
% 0.13/0.31 thf(f620,plain,(
% 0.13/0.31 $false | (~spl0_29 | ~spl0_43)),
% 0.13/0.31 inference(trivial_inequality_removal,[],[f617])).
% 0.13/0.31 thf(f617,plain,(
% 0.13/0.31 ($true = $false) | (~spl0_29 | ~spl0_43)),
% 0.13/0.31 inference(superposition,[],[f496,f611])).
% 0.13/0.31 thf(f611,plain,(
% 0.13/0.31 ($true = (p @ sK8)) | ~spl0_43),
% 0.13/0.31 inference(avatar_component_clause,[],[f609])).
% 0.13/0.31 thf(f609,plain,(
% 0.13/0.31 spl0_43 <=> ($true = (p @ sK8))),
% 0.13/0.31 introduced(avatar_definition,[new_symbols(naming,[spl0_43])])).
% 0.13/0.31 thf(f496,plain,(
% 0.13/0.31 ((p @ sK8) = $false) | ~spl0_29),
% 0.13/0.31 inference(avatar_component_clause,[],[f494])).
% 0.13/0.31 thf(f494,plain,(
% 0.13/0.31 spl0_29 <=> ((p @ sK8) = $false)),
% 0.13/0.31 introduced(avatar_definition,[new_symbols(naming,[spl0_29])])).
% 0.13/0.31 thf(f614,plain,(
% 0.13/0.31 spl0_43 | ~spl0_2 | ~spl0_24),
% 0.13/0.31 inference(avatar_split_clause,[],[f601,f470,f362,f609])).
% 0.13/0.31 thf(f470,plain,(
% 0.13/0.31 spl0_24 <=> ($true = (rel_k @ sK1 @ sK8))),
% 0.13/0.31 introduced(avatar_definition,[new_symbols(naming,[spl0_24])])).
% 0.13/0.31 thf(f601,plain,(
% 0.13/0.31 ($true = (p @ sK8)) | (~spl0_2 | ~spl0_24)),
% 0.13/0.31 inference(trivial_inequality_removal,[],[f597])).
% 0.13/0.31 thf(f597,plain,(
% 0.13/0.31 ($true = $false) | ($true = (p @ sK8)) | (~spl0_2 | ~spl0_24)),
% 0.13/0.31 inference(superposition,[],[f472,f363])).
% 0.13/0.31 thf(f472,plain,(
% 0.13/0.31 ($true = (rel_k @ sK1 @ sK8)) | ~spl0_24),
% 0.13/0.31 inference(avatar_component_clause,[],[f470])).
% 0.13/0.31 thf(f590,plain,(
% 0.13/0.31 ~spl0_2 | ~spl0_25 | ~spl0_27),
% 0.13/0.31 inference(avatar_contradiction_clause,[],[f589])).
% 0.13/0.31 thf(f589,plain,(
% 0.13/0.31 $false | (~spl0_2 | ~spl0_25 | ~spl0_27)),
% 0.13/0.31 inference(trivial_inequality_removal,[],[f586])).
% 0.13/0.31 thf(f586,plain,(
% 0.13/0.31 ($true = $false) | (~spl0_2 | ~spl0_25 | ~spl0_27)),
% 0.13/0.31 inference(superposition,[],[f486,f584])).
% 0.13/0.31 thf(f584,plain,(
% 0.13/0.31 ((p @ sK7) = $true) | (~spl0_2 | ~spl0_25)),
% 0.13/0.31 inference(trivial_inequality_removal,[],[f582])).
% 0.13/0.31 thf(f582,plain,(
% 0.13/0.31 ((p @ sK7) = $true) | ($true = $false) | (~spl0_2 | ~spl0_25)),
% 0.13/0.31 inference(superposition,[],[f363,f476])).
% 0.13/0.31 thf(f476,plain,(
% 0.13/0.31 ($true = (rel_k @ sK1 @ sK7)) | ~spl0_25),
% 0.13/0.31 inference(avatar_component_clause,[],[f474])).
% 0.13/0.31 thf(f474,plain,(
% 0.13/0.31 spl0_25 <=> ($true = (rel_k @ sK1 @ sK7))),
% 0.13/0.31 introduced(avatar_definition,[new_symbols(naming,[spl0_25])])).
% 0.13/0.31 thf(f486,plain,(
% 0.13/0.31 ((p @ sK7) = $false) | ~spl0_27),
% 0.13/0.31 inference(avatar_component_clause,[],[f484])).
% 0.13/0.31 thf(f484,plain,(
% 0.13/0.31 spl0_27 <=> ((p @ sK7) = $false)),
% 0.13/0.31 introduced(avatar_definition,[new_symbols(naming,[spl0_27])])).
% 0.13/0.31 thf(f572,plain,(
% 0.13/0.31 ~spl0_2 | ~spl0_22 | ~spl0_23),
% 0.13/0.31 inference(avatar_contradiction_clause,[],[f571])).
% 0.13/0.31 thf(f571,plain,(
% 0.13/0.31 $false | (~spl0_2 | ~spl0_22 | ~spl0_23)),
% 0.13/0.31 inference(trivial_inequality_removal,[],[f568])).
% 0.13/0.31 thf(f568,plain,(
% 0.13/0.31 ($true = $false) | (~spl0_2 | ~spl0_22 | ~spl0_23)),
% 0.13/0.31 inference(superposition,[],[f467,f566])).
% 0.13/0.31 thf(f566,plain,(
% 0.13/0.31 ($true = (p @ sK2)) | (~spl0_2 | ~spl0_22)),
% 0.13/0.31 inference(trivial_inequality_removal,[],[f561])).
% 0.13/0.31 thf(f561,plain,(
% 0.13/0.31 ($true = $false) | ($true = (p @ sK2)) | (~spl0_2 | ~spl0_22)),
% 0.13/0.31 inference(superposition,[],[f462,f363])).
% 0.13/0.31 thf(f558,plain,(
% 0.13/0.31 spl0_41 | spl0_39 | spl0_23),
% 0.13/0.31 inference(avatar_split_clause,[],[f179,f465,f545,f555])).
% 0.13/0.31 thf(f179,plain,(
% 0.13/0.31 ((p @ sK4) = $false) | ((p @ sK3) = $false) | ((p @ sK2) = $false)),
% 0.13/0.31 inference(binary_proxy_clausification,[],[f177])).
% 0.13/0.31 thf(f177,plain,(
% 0.13/0.31 ((p @ sK3) = $false) | ((p @ sK2) = $false) | (((p @ sK4) | (q @ sK4)) = $false)),
% 0.13/0.31 inference(binary_proxy_clausification,[],[f175])).
% 0.13/0.31 thf(f175,plain,(
% 0.13/0.31 ((p @ sK2) = $false) | ((((p @ sK4) | (q @ sK4)) | (~ (rel_k @ sK1 @ sK4))) = $false) | ((p @ sK3) = $false)),
% 0.13/0.31 inference(beta_eta_normalization,[],[f174])).
% 0.13/0.31 thf(f174,plain,(
% 0.13/0.31 ((p @ sK2) = $false) | ((p @ sK3) = $false) | (((^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))) @ sK4) = $false)),
% 0.13/0.31 inference(sigma_clausification,[],[f173])).
% 0.13/0.31 thf(f173,plain,(
% 0.13/0.31 ((p @ sK3) = $false) | ((!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0))))) = $false) | ((p @ sK2) = $false)),
% 0.13/0.31 inference(not_proxy_clausification,[],[f172])).
% 0.13/0.31 thf(f172,plain,(
% 0.13/0.31 ((p @ sK3) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0))))))) | ((p @ sK2) = $false)),
% 0.13/0.31 inference(binary_proxy_clausification,[],[f170])).
% 0.13/0.31 thf(f170,plain,(
% 0.13/0.31 ((p @ sK2) = $false) | (((p @ sK3) | (~ (q @ sK3))) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))))),
% 0.13/0.31 inference(binary_proxy_clausification,[],[f168])).
% 0.13/0.31 thf(f168,plain,(
% 0.13/0.31 ((p @ sK2) = $false) | ((((p @ sK3) | (~ (q @ sK3))) | (~ (rel_k @ sK1 @ sK3))) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))))),
% 0.13/0.31 inference(beta_eta_normalization,[],[f167])).
% 0.13/0.31 thf(f167,plain,(
% 0.13/0.31 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0))))))) | ((p @ sK2) = $false) | ($false = ((^[Y0 : $i]: (((p @ Y0) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0)))) @ sK3))),
% 0.13/0.31 inference(sigma_clausification,[],[f166])).
% 0.13/0.31 thf(f166,plain,(
% 0.13/0.31 ((p @ sK2) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))))),
% 0.13/0.31 inference(binary_proxy_clausification,[],[f164])).
% 0.13/0.31 thf(f164,plain,(
% 0.13/0.31 (((p @ sK2) | (~ (rel_k @ sK1 @ sK2))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))))),
% 0.13/0.31 inference(not_proxy_clausification,[],[f163])).
% 0.13/0.31 thf(f163,plain,(
% 0.13/0.31 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0))))))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0))))))) | (((p @ sK2) | (~ (rel_k @ sK1 @ sK2))) = $false)),
% 0.13/0.31 inference(binary_proxy_clausification,[],[f162])).
% 0.13/0.31 thf(f162,plain,(
% 0.13/0.31 ($true = ((~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))))) | (((p @ sK2) | (~ (rel_k @ sK1 @ sK2))) = $false)),
% 0.13/0.31 inference(not_proxy_clausification,[],[f161])).
% 0.13/0.31 thf(f161,plain,(
% 0.13/0.31 ($false = (~ ((~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0))))))))) | (((p @ sK2) | (~ (rel_k @ sK1 @ sK2))) = $false)),
% 0.13/0.31 inference(binary_proxy_clausification,[],[f159])).
% 0.13/0.31 thf(f159,plain,(
% 0.13/0.31 (((~ ((~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0))))))) = $false) | (((p @ sK2) | (~ (rel_k @ sK1 @ sK2))) = $false)),
% 0.13/0.31 inference(beta_eta_normalization,[],[f158])).
% 0.13/0.31 thf(f158,plain,(
% 0.13/0.31 (((~ ((~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0))))))) = $false) | ($false = ((^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0)))) @ sK2))),
% 0.13/0.31 inference(sigma_clausification,[],[f157])).
% 0.13/0.31 thf(f157,plain,(
% 0.13/0.31 ((!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0))))) = $false) | (((~ ((~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0))))))) = $false)),
% 0.13/0.31 inference(not_proxy_clausification,[],[f156])).
% 0.13/0.31 thf(f156,plain,(
% 0.13/0.31 ($true = (~ ((~ ((~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0))))))))) | ((!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0))))) = $false)),
% 0.13/0.31 inference(binary_proxy_clausification,[],[f154])).
% 0.13/0.31 thf(f154,plain,(
% 0.13/0.31 (((!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0))))) | ((~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))))) = $false) | ($true = (~ ((~ ((~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0)))))))))),
% 0.13/0.31 inference(not_proxy_clausification,[],[f153])).
% 0.13/0.31 thf(f153,plain,(
% 0.13/0.31 ((~ ((!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0))))) | ((~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0))))))))) = $true) | ($true = (~ ((~ ((~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0)))))))))),
% 0.13/0.31 inference(binary_proxy_clausification,[],[f152])).
% 0.13/0.31 thf(f152,plain,(
% 0.13/0.31 ($true = ((~ ((~ ((~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0)))))))) | (~ ((!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0))))) | ((~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))))))))),
% 0.13/0.31 inference(not_proxy_clausification,[],[f151])).
% 0.13/0.31 thf(f151,plain,(
% 0.13/0.31 ($false = (~ ((~ ((~ ((~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0)))))))) | (~ ((!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0))))) | ((~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0))))))))))))),
% 0.13/0.31 inference(beta_eta_normalization,[],[f150])).
% 0.13/0.31 thf(f150,plain,(
% 0.13/0.31 (((^[Y0 : $i]: (~ ((~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: (((p @ Y1) | (q @ Y1)) | (~ (rel_k @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((p @ Y1) | (~ (q @ Y1))) | (~ (rel_k @ Y0 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_k @ Y0 @ Y1)))))))) | (~ ((!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_k @ Y0 @ Y1))))) | ((~ (!! @ $i @ (^[Y1 : $i]: (((p @ Y1) | (q @ Y1)) | (~ (rel_k @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((p @ Y1) | (~ (q @ Y1))) | (~ (rel_k @ Y0 @ Y1)))))))))))) @ sK1) = $false)),
% 0.13/0.31 inference(sigma_clausification,[],[f149])).
% 0.13/0.31 thf(f149,plain,(
% 0.13/0.31 ($true != (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: (((p @ Y1) | (q @ Y1)) | (~ (rel_k @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((p @ Y1) | (~ (q @ Y1))) | (~ (rel_k @ Y0 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_k @ Y0 @ Y1)))))))) | (~ ((!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_k @ Y0 @ Y1))))) | ((~ (!! @ $i @ (^[Y1 : $i]: (((p @ Y1) | (q @ Y1)) | (~ (rel_k @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((p @ Y1) | (~ (q @ Y1))) | (~ (rel_k @ Y0 @ Y1))))))))))))))),
% 0.13/0.31 inference(boolean_simplification,[],[f148])).
% 0.13/0.31 thf(f148,plain,(
% 0.13/0.31 ($true != (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: (((p @ Y1) | (~ (~ (q @ Y1)))) | (~ (rel_k @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((p @ Y1) | (~ (q @ Y1))) | (~ (rel_k @ Y0 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_k @ Y0 @ Y1)))))))) | (~ ((!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_k @ Y0 @ Y1))))) | ((~ (!! @ $i @ (^[Y1 : $i]: (((p @ Y1) | (~ (~ (q @ Y1)))) | (~ (rel_k @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((p @ Y1) | (~ (q @ Y1))) | (~ (rel_k @ Y0 @ Y1))))))))))))))),
% 0.13/0.31 inference(boolean_simplification,[],[f147])).
% 0.13/0.31 thf(f147,plain,(
% 0.13/0.31 ($true != (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: (((p @ Y1) | (~ (~ (q @ Y1)))) | (~ (rel_k @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((p @ Y1) | (~ (q @ Y1))) | (~ (rel_k @ Y0 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_k @ Y0 @ Y1)))))))) | (~ ((!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_k @ Y0 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: (((p @ Y1) | (~ (~ (q @ Y1)))) | (~ (rel_k @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((p @ Y1) | (~ (q @ Y1))) | (~ (rel_k @ Y0 @ Y1))))))))))))))))),
% 0.13/0.31 inference(beta_eta_normalization,[],[f146])).
% 0.13/0.31 thf(f146,plain,(
% 0.13/0.31 ($true != ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[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]: ((Y5 @ Y6) | (Y4 @ 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]: ((Y5 @ Y6) | (Y4 @ 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]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y1 @ Y0))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_k @ 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)))) @ q @ p)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_k @ 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)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))) @ q) @ p))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_k @ Y1 @ Y2)))))))) @ p))))),
% 0.13/0.31 inference(definition_unfolding,[],[f117,f115,f139,f136,f124,f137,f124,f137,f110,f124])).
% 0.13/0.31 thf(f110,plain,(
% 0.13/0.31 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.13/0.31 inference(cnf_transformation,[],[f38])).
% 0.13/0.31 thf(f38,plain,(
% 0.13/0.31 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.13/0.31 inference(fool_elimination,[],[f37])).
% 0.13/0.31 thf(f37,plain,(
% 0.13/0.31 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.13/0.31 inference(rectify,[],[f3])).
% 0.13/0.31 thf(f3,axiom,(
% 0.13/0.31 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)),
% 0.13/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.13/0.31 thf(f137,plain,(
% 0.13/0.31 (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)))))),
% 0.13/0.31 inference(definition_unfolding,[],[f132,f102,f110])).
% 0.13/0.31 thf(f102,plain,(
% 0.13/0.31 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.13/0.31 inference(cnf_transformation,[],[f94])).
% 0.13/0.31 thf(f94,plain,(
% 0.13/0.31 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.13/0.31 inference(fool_elimination,[],[f93])).
% 0.13/0.31 thf(f93,plain,(
% 0.13/0.31 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))) = mor)),
% 0.13/0.31 inference(rectify,[],[f4])).
% 0.13/0.31 thf(f4,axiom,(
% 0.13/0.31 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))) = mor)),
% 0.13/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.13/0.31 thf(f132,plain,(
% 0.13/0.31 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.13/0.31 inference(cnf_transformation,[],[f40])).
% 0.13/0.31 thf(f40,plain,(
% 0.13/0.31 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.13/0.31 inference(fool_elimination,[],[f39])).
% 0.13/0.31 thf(f39,plain,(
% 0.13/0.31 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.13/0.31 inference(rectify,[],[f6])).
% 0.13/0.31 thf(f6,axiom,(
% 0.13/0.31 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.13/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.13/0.31 thf(f124,plain,(
% 0.13/0.31 (mbox_k = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_k @ Y1 @ Y2)))))))))),
% 0.13/0.31 inference(cnf_transformation,[],[f42])).
% 0.13/0.31 thf(f42,plain,(
% 0.13/0.31 (mbox_k = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_k @ Y1 @ Y2)))))))))),
% 0.13/0.31 inference(fool_elimination,[],[f41])).
% 0.13/0.31 thf(f41,plain,(
% 0.13/0.31 (mbox_k = (^[X0 : $i > $o, X1 : $i] : (! [X2] : (~(rel_k @ X1 @ X2) | (X0 @ X2)))))),
% 0.13/0.31 inference(rectify,[],[f32])).
% 0.13/0.31 thf(f32,axiom,(
% 0.13/0.31 (mbox_k = (^[X3 : $i > $o, X2 : $i] : (! [X7] : (~(rel_k @ X2 @ X7) | (X3 @ X7)))))),
% 0.13/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_k)).
% 0.13/0.31 thf(f136,plain,(
% 0.13/0.31 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 0.13/0.31 inference(definition_unfolding,[],[f130,f110,f102,f110,f110])).
% 0.13/0.31 thf(f130,plain,(
% 0.13/0.31 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.13/0.31 inference(cnf_transformation,[],[f69])).
% 0.13/0.31 thf(f69,plain,(
% 0.13/0.31 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.13/0.31 inference(fool_elimination,[],[f68])).
% 0.13/0.31 thf(f68,plain,(
% 0.13/0.31 (mand = (^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))))),
% 0.13/0.31 inference(rectify,[],[f5])).
% 0.13/0.31 thf(f5,axiom,(
% 0.13/0.31 (mand = (^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))))),
% 0.13/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand)).
% 0.13/0.31 thf(f139,plain,(
% 0.13/0.31 (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]: ((Y5 @ Y6) | (Y4 @ 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]: ((Y5 @ Y6) | (Y4 @ 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]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y1 @ Y0))))))),
% 0.13/0.31 inference(definition_unfolding,[],[f133,f136,f137,f137])).
% 0.13/0.31 thf(f133,plain,(
% 0.13/0.31 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.13/0.31 inference(cnf_transformation,[],[f98])).
% 0.13/0.31 thf(f98,plain,(
% 0.13/0.31 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.13/0.31 inference(fool_elimination,[],[f97])).
% 0.13/0.31 thf(f97,plain,(
% 0.13/0.31 ((^[X0 : $i > $o, X1 : $i > $o] : (mand @ (mimplies @ X0 @ X1) @ (mimplies @ X1 @ X0))) = mequiv)),
% 0.13/0.31 inference(rectify,[],[f8])).
% 0.13/0.31 thf(f8,axiom,(
% 0.13/0.31 ((^[X3 : $i > $o, X4 : $i > $o] : (mand @ (mimplies @ X3 @ X4) @ (mimplies @ X4 @ X3))) = mequiv)),
% 0.13/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mequiv)).
% 0.13/0.31 thf(f115,plain,(
% 0.13/0.31 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.13/0.31 inference(cnf_transformation,[],[f83])).
% 0.13/0.31 thf(f83,plain,(
% 0.13/0.31 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.13/0.31 inference(fool_elimination,[],[f82])).
% 0.13/0.31 thf(f82,plain,(
% 0.13/0.31 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.13/0.31 inference(rectify,[],[f28])).
% 0.13/0.31 thf(f28,axiom,(
% 0.13/0.31 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.13/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.13/0.31 thf(f117,plain,(
% 0.13/0.31 ((mvalid @ (mequiv @ (mand @ (mbox_k @ (mimplies @ q @ p)) @ (mbox_k @ (mimplies @ (mnot @ q) @ p))) @ (mbox_k @ p))) != $true)),
% 0.13/0.31 inference(cnf_transformation,[],[f101])).
% 0.13/0.31 thf(f101,plain,(
% 0.13/0.31 ((mvalid @ (mequiv @ (mand @ (mbox_k @ (mimplies @ q @ p)) @ (mbox_k @ (mimplies @ (mnot @ q) @ p))) @ (mbox_k @ p))) != $true)),
% 0.13/0.31 inference(flattening,[],[f87])).
% 0.13/0.31 thf(f87,plain,(
% 0.13/0.31 ~((mvalid @ (mequiv @ (mand @ (mbox_k @ (mimplies @ q @ p)) @ (mbox_k @ (mimplies @ (mnot @ q) @ p))) @ (mbox_k @ p))) = $true)),
% 0.13/0.31 inference(fool_elimination,[],[f86])).
% 0.13/0.31 thf(f86,plain,(
% 0.13/0.31 ~(mvalid @ (mequiv @ (mand @ (mbox_k @ (mimplies @ q @ p)) @ (mbox_k @ (mimplies @ (mnot @ q) @ p))) @ (mbox_k @ p)))),
% 0.13/0.31 inference(rectify,[],[f35])).
% 0.13/0.31 thf(f35,negated_conjecture,(
% 0.13/0.31 ~(mvalid @ (mequiv @ (mand @ (mbox_k @ (mimplies @ q @ p)) @ (mbox_k @ (mimplies @ (mnot @ q) @ p))) @ (mbox_k @ p)))),
% 0.13/0.31 inference(negated_conjecture,[],[f34])).
% 0.13/0.31 thf(f34,conjecture,(
% 0.13/0.31 (mvalid @ (mequiv @ (mand @ (mbox_k @ (mimplies @ q @ p)) @ (mbox_k @ (mimplies @ (mnot @ q) @ p))) @ (mbox_k @ p)))),
% 0.13/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove)).
% 0.13/0.31 thf(f548,plain,(
% 0.13/0.31 spl0_38 | spl0_39 | spl0_23),
% 0.13/0.31 inference(avatar_split_clause,[],[f180,f465,f545,f541])).
% 0.13/0.31 thf(f180,plain,(
% 0.13/0.31 ((p @ sK3) = $false) | ((p @ sK2) = $false) | ($true = (rel_k @ sK1 @ sK4))),
% 0.13/0.31 inference(not_proxy_clausification,[],[f176])).
% 0.13/0.31 thf(f176,plain,(
% 0.13/0.31 ((p @ sK3) = $false) | ((~ (rel_k @ sK1 @ sK4)) = $false) | ((p @ sK2) = $false)),
% 0.13/0.31 inference(binary_proxy_clausification,[],[f175])).
% 0.13/0.31 thf(f520,plain,(
% 0.13/0.31 spl0_31 | spl0_33 | spl0_23),
% 0.13/0.31 inference(avatar_split_clause,[],[f197,f465,f517,f507])).
% 0.13/0.31 thf(f197,plain,(
% 0.13/0.31 ((p @ sK6) = $false) | ($true = (rel_k @ sK1 @ sK3)) | ((p @ sK2) = $false)),
% 0.13/0.31 inference(binary_proxy_clausification,[],[f195])).
% 0.13/0.31 thf(f195,plain,(
% 0.13/0.31 ($false = ((p @ sK6) | (q @ sK6))) | ($true = (rel_k @ sK1 @ sK3)) | ((p @ sK2) = $false)),
% 0.13/0.31 inference(binary_proxy_clausification,[],[f193])).
% 0.13/0.31 thf(f193,plain,(
% 0.13/0.31 ($true = (rel_k @ sK1 @ sK3)) | ((p @ sK2) = $false) | ((((p @ sK6) | (q @ sK6)) | (~ (rel_k @ sK1 @ sK6))) = $false)),
% 0.13/0.31 inference(beta_eta_normalization,[],[f192])).
% 0.13/0.31 thf(f192,plain,(
% 0.13/0.31 ($true = (rel_k @ sK1 @ sK3)) | ((p @ sK2) = $false) | (((^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))) @ sK6) = $false)),
% 0.13/0.31 inference(sigma_clausification,[],[f191])).
% 0.13/0.31 thf(f191,plain,(
% 0.13/0.31 ((p @ sK2) = $false) | ((!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0))))) = $false) | ($true = (rel_k @ sK1 @ sK3))),
% 0.13/0.31 inference(not_proxy_clausification,[],[f190])).
% 0.13/0.31 thf(f190,plain,(
% 0.13/0.31 ((p @ sK2) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0))))))) | ($true = (rel_k @ sK1 @ sK3))),
% 0.13/0.31 inference(not_proxy_clausification,[],[f169])).
% 0.13/0.31 thf(f169,plain,(
% 0.13/0.31 ((~ (rel_k @ sK1 @ sK3)) = $false) | ((p @ sK2) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))))),
% 0.13/0.31 inference(binary_proxy_clausification,[],[f168])).
% 0.13/0.31 thf(f510,plain,(
% 0.13/0.31 spl0_23 | spl0_30 | spl0_31),
% 0.13/0.31 inference(avatar_split_clause,[],[f198,f507,f503,f465])).
% 0.13/0.31 thf(f198,plain,(
% 0.13/0.31 ((p @ sK2) = $false) | ($true = (rel_k @ sK1 @ sK6)) | ($true = (rel_k @ sK1 @ sK3))),
% 0.13/0.31 inference(not_proxy_clausification,[],[f194])).
% 0.13/0.31 thf(f194,plain,(
% 0.13/0.31 ((p @ sK2) = $false) | ((~ (rel_k @ sK1 @ sK6)) = $false) | ($true = (rel_k @ sK1 @ sK3))),
% 0.13/0.31 inference(binary_proxy_clausification,[],[f193])).
% 0.13/0.31 thf(f501,plain,(
% 0.13/0.31 spl0_29 | spl0_22 | spl0_27),
% 0.13/0.31 inference(avatar_split_clause,[],[f212,f484,f460,f494])).
% 0.13/0.31 thf(f212,plain,(
% 0.13/0.31 ((p @ sK7) = $false) | ((p @ sK8) = $false) | ($true = (rel_k @ sK1 @ sK2))),
% 0.13/0.31 inference(binary_proxy_clausification,[],[f210])).
% 0.13/0.31 thf(f210,plain,(
% 0.13/0.31 ($false = ((p @ sK8) | (q @ sK8))) | ($true = (rel_k @ sK1 @ sK2)) | ((p @ sK7) = $false)),
% 0.13/0.31 inference(not_proxy_clausification,[],[f209])).
% 0.13/0.31 thf(f209,plain,(
% 0.13/0.31 ((~ (rel_k @ sK1 @ sK2)) = $false) | ((p @ sK7) = $false) | ($false = ((p @ sK8) | (q @ sK8)))),
% 0.13/0.31 inference(binary_proxy_clausification,[],[f207])).
% 0.13/0.31 thf(f207,plain,(
% 0.13/0.31 (((p @ sK7) | (~ (q @ sK7))) = $false) | ((~ (rel_k @ sK1 @ sK2)) = $false) | ($false = ((p @ sK8) | (q @ sK8)))),
% 0.13/0.31 inference(binary_proxy_clausification,[],[f205])).
% 0.13/0.31 thf(f205,plain,(
% 0.13/0.31 ((((p @ sK7) | (~ (q @ sK7))) | (~ (rel_k @ sK1 @ sK7))) = $false) | ($false = ((p @ sK8) | (q @ sK8))) | ((~ (rel_k @ sK1 @ sK2)) = $false)),
% 0.13/0.31 inference(binary_proxy_clausification,[],[f203])).
% 0.13/0.31 thf(f203,plain,(
% 0.13/0.31 ((((p @ sK8) | (q @ sK8)) | (~ (rel_k @ sK1 @ sK8))) = $false) | ((~ (rel_k @ sK1 @ sK2)) = $false) | ((((p @ sK7) | (~ (q @ sK7))) | (~ (rel_k @ sK1 @ sK7))) = $false)),
% 0.13/0.31 inference(beta_eta_normalization,[],[f202])).
% 0.13/0.31 thf(f202,plain,(
% 0.13/0.31 ((~ (rel_k @ sK1 @ sK2)) = $false) | ((((p @ sK7) | (~ (q @ sK7))) | (~ (rel_k @ sK1 @ sK7))) = $false) | (((^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))) @ sK8) = $false)),
% 0.13/0.31 inference(sigma_clausification,[],[f201])).
% 0.13/0.31 thf(f201,plain,(
% 0.13/0.31 ((!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0))))) = $false) | ((~ (rel_k @ sK1 @ sK2)) = $false) | ((((p @ sK7) | (~ (q @ sK7))) | (~ (rel_k @ sK1 @ sK7))) = $false)),
% 0.13/0.31 inference(not_proxy_clausification,[],[f200])).
% 0.13/0.31 thf(f200,plain,(
% 0.13/0.31 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0))))))) | ((((p @ sK7) | (~ (q @ sK7))) | (~ (rel_k @ sK1 @ sK7))) = $false) | ((~ (rel_k @ sK1 @ sK2)) = $false)),
% 0.13/0.31 inference(beta_eta_normalization,[],[f199])).
% 0.13/0.31 thf(f199,plain,(
% 0.13/0.31 (((^[Y0 : $i]: (((p @ Y0) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0)))) @ sK7) = $false) | ((~ (rel_k @ sK1 @ sK2)) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))))),
% 0.13/0.31 inference(sigma_clausification,[],[f165])).
% 0.13/0.31 thf(f165,plain,(
% 0.13/0.31 ($false = (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0))))))) | ((~ (rel_k @ sK1 @ sK2)) = $false)),
% 0.13/0.31 inference(binary_proxy_clausification,[],[f164])).
% 0.13/0.31 thf(f497,plain,(
% 0.13/0.31 spl0_29 | spl0_25 | spl0_22),
% 0.13/0.31 inference(avatar_split_clause,[],[f221,f460,f474,f494])).
% 0.13/0.31 thf(f221,plain,(
% 0.13/0.31 ($true = (rel_k @ sK1 @ sK7)) | ((p @ sK8) = $false) | ($true = (rel_k @ sK1 @ sK2))),
% 0.13/0.31 inference(not_proxy_clausification,[],[f220])).
% 0.13/0.31 thf(f220,plain,(
% 0.13/0.31 ((~ (rel_k @ sK1 @ sK2)) = $false) | ($true = (rel_k @ sK1 @ sK7)) | ((p @ sK8) = $false)),
% 0.13/0.31 inference(not_proxy_clausification,[],[f219])).
% 0.13/0.31 thf(f219,plain,(
% 0.13/0.31 ((~ (rel_k @ sK1 @ sK7)) = $false) | ((p @ sK8) = $false) | ((~ (rel_k @ sK1 @ sK2)) = $false)),
% 0.13/0.31 inference(binary_proxy_clausification,[],[f206])).
% 0.13/0.31 thf(f206,plain,(
% 0.13/0.31 ($false = ((p @ sK8) | (q @ sK8))) | ((~ (rel_k @ sK1 @ sK7)) = $false) | ((~ (rel_k @ sK1 @ sK2)) = $false)),
% 0.13/0.31 inference(binary_proxy_clausification,[],[f205])).
% 0.13/0.31 thf(f487,plain,(
% 0.13/0.31 spl0_27 | spl0_22 | spl0_24),
% 0.13/0.31 inference(avatar_split_clause,[],[f229,f470,f460,f484])).
% 0.13/0.31 thf(f229,plain,(
% 0.13/0.31 ((p @ sK7) = $false) | ($true = (rel_k @ sK1 @ sK2)) | ($true = (rel_k @ sK1 @ sK8))),
% 0.13/0.31 inference(binary_proxy_clausification,[],[f227])).
% 0.13/0.31 thf(f227,plain,(
% 0.13/0.31 ($true = (rel_k @ sK1 @ sK2)) | ($true = (rel_k @ sK1 @ sK8)) | (((p @ sK7) | (~ (q @ sK7))) = $false)),
% 0.13/0.31 inference(binary_proxy_clausification,[],[f225])).
% 0.13/0.31 thf(f225,plain,(
% 0.13/0.31 ((((p @ sK7) | (~ (q @ sK7))) | (~ (rel_k @ sK1 @ sK7))) = $false) | ($true = (rel_k @ sK1 @ sK2)) | ($true = (rel_k @ sK1 @ sK8))),
% 0.13/0.31 inference(not_proxy_clausification,[],[f224])).
% 0.13/0.31 thf(f224,plain,(
% 0.13/0.31 ((~ (rel_k @ sK1 @ sK2)) = $false) | ($true = (rel_k @ sK1 @ sK8)) | ((((p @ sK7) | (~ (q @ sK7))) | (~ (rel_k @ sK1 @ sK7))) = $false)),
% 0.13/0.31 inference(not_proxy_clausification,[],[f204])).
% 0.13/0.31 thf(f204,plain,(
% 0.13/0.31 ((~ (rel_k @ sK1 @ sK8)) = $false) | ((~ (rel_k @ sK1 @ sK2)) = $false) | ((((p @ sK7) | (~ (q @ sK7))) | (~ (rel_k @ sK1 @ sK7))) = $false)),
% 0.13/0.31 inference(binary_proxy_clausification,[],[f203])).
% 0.13/0.31 thf(f477,plain,(
% 0.13/0.31 spl0_24 | spl0_22 | spl0_25),
% 0.13/0.31 inference(avatar_split_clause,[],[f231,f474,f460,f470])).
% 0.13/0.31 thf(f231,plain,(
% 0.13/0.31 ($true = (rel_k @ sK1 @ sK7)) | ($true = (rel_k @ sK1 @ sK8)) | ($true = (rel_k @ sK1 @ sK2))),
% 0.13/0.31 inference(not_proxy_clausification,[],[f226])).
% 0.13/0.31 thf(f226,plain,(
% 0.13/0.31 ((~ (rel_k @ sK1 @ sK7)) = $false) | ($true = (rel_k @ sK1 @ sK8)) | ($true = (rel_k @ sK1 @ sK2))),
% 0.13/0.31 inference(binary_proxy_clausification,[],[f225])).
% 0.13/0.31 thf(f468,plain,(
% 0.13/0.31 spl0_2 | spl0_23),
% 0.13/0.31 inference(avatar_split_clause,[],[f238,f465,f362])).
% 0.13/0.31 thf(f238,plain,(
% 0.13/0.31 ( ! [X1 : $i] : (($true = (p @ X1)) | ($false = (rel_k @ sK1 @ X1)) | ((p @ sK2) = $false)) )),
% 0.13/0.31 inference(not_proxy_clausification,[],[f237])).
% 0.13/0.31 thf(f237,plain,(
% 0.13/0.31 ( ! [X1 : $i] : (((p @ sK2) = $false) | ($true = (~ (rel_k @ sK1 @ X1))) | ($true = (p @ X1))) )),
% 0.13/0.31 inference(binary_proxy_clausification,[],[f236])).
% 0.13/0.31 thf(f236,plain,(
% 0.13/0.31 ( ! [X1 : $i] : (((p @ sK2) = $false) | ($true = ((p @ X1) | (~ (rel_k @ sK1 @ X1))))) )),
% 0.13/0.31 inference(beta_eta_normalization,[],[f235])).
% 0.13/0.31 thf(f235,plain,(
% 0.13/0.31 ( ! [X1 : $i] : (((p @ sK2) = $false) | ($true = ((^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0)))) @ X1))) )),
% 0.13/0.31 inference(pi_clausification,[],[f234])).
% 0.13/0.31 thf(f234,plain,(
% 0.13/0.31 ((p @ sK2) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0))))))),
% 0.13/0.31 inference(not_proxy_clausification,[],[f233])).
% 0.13/0.31 thf(f233,plain,(
% 0.13/0.31 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0))))))) | ((p @ sK2) = $false)),
% 0.13/0.31 inference(binary_proxy_clausification,[],[f160])).
% 0.13/0.31 thf(f160,plain,(
% 0.13/0.31 (((p @ sK2) | (~ (rel_k @ sK1 @ sK2))) = $false) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0)))))))),
% 0.13/0.31 inference(binary_proxy_clausification,[],[f159])).
% 0.13/0.31 thf(f463,plain,(
% 0.13/0.31 spl0_22 | spl0_2),
% 0.13/0.31 inference(avatar_split_clause,[],[f244,f362,f460])).
% 0.13/0.31 thf(f244,plain,(
% 0.13/0.31 ( ! [X1 : $i] : (($false = (rel_k @ sK1 @ X1)) | ($true = (rel_k @ sK1 @ sK2)) | ($true = (p @ X1))) )),
% 0.13/0.31 inference(not_proxy_clausification,[],[f243])).
% 0.13/0.31 thf(f243,plain,(
% 0.13/0.31 ( ! [X1 : $i] : (($true = (p @ X1)) | ($true = (~ (rel_k @ sK1 @ X1))) | ($true = (rel_k @ sK1 @ sK2))) )),
% 0.13/0.31 inference(binary_proxy_clausification,[],[f242])).
% 0.13/0.31 thf(f242,plain,(
% 0.13/0.31 ( ! [X1 : $i] : (($true = (rel_k @ sK1 @ sK2)) | ($true = ((p @ X1) | (~ (rel_k @ sK1 @ X1))))) )),
% 0.13/0.31 inference(beta_eta_normalization,[],[f241])).
% 0.13/0.31 thf(f241,plain,(
% 0.13/0.31 ( ! [X1 : $i] : (($true = (rel_k @ sK1 @ sK2)) | ($true = ((^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0)))) @ X1))) )),
% 0.13/0.31 inference(pi_clausification,[],[f240])).
% 0.13/0.31 thf(f240,plain,(
% 0.13/0.31 ($true = (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0)))))) | ($true = (rel_k @ sK1 @ sK2))),
% 0.13/0.31 inference(not_proxy_clausification,[],[f239])).
% 0.13/0.31 thf(f239,plain,(
% 0.13/0.31 ((~ (rel_k @ sK1 @ sK2)) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0))))))),
% 0.13/0.31 inference(not_proxy_clausification,[],[f232])).
% 0.13/0.31 thf(f232,plain,(
% 0.13/0.31 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0))))))) | ((~ (rel_k @ sK1 @ sK2)) = $false)),
% 0.13/0.31 inference(binary_proxy_clausification,[],[f160])).
% 0.13/0.31 thf(f425,plain,(
% 0.13/0.31 spl0_15 | spl0_2),
% 0.13/0.31 inference(avatar_split_clause,[],[f298,f362,f423])).
% 0.13/0.31 thf(f298,plain,(
% 0.13/0.31 ( ! [X2 : $i,X1 : $i] : (($true = (p @ X2)) | ((rel_k @ sK1 @ X2) = $false) | ($false = (rel_k @ sK1 @ X1)) | ($true = (p @ X1)) | ($true = (q @ X1))) )),
% 0.13/0.31 inference(not_proxy_clausification,[],[f297])).
% 0.13/0.31 thf(f297,plain,(
% 0.13/0.31 ( ! [X2 : $i,X1 : $i] : (($false = (rel_k @ sK1 @ X1)) | ($true = (q @ X1)) | ($true = (~ (rel_k @ sK1 @ X2))) | ($true = (p @ X1)) | ($true = (p @ X2))) )),
% 0.13/0.31 inference(binary_proxy_clausification,[],[f296])).
% 0.13/0.31 thf(f296,plain,(
% 0.13/0.31 ( ! [X2 : $i,X1 : $i] : (($true = (q @ X1)) | (((p @ X2) | (~ (rel_k @ sK1 @ X2))) = $true) | ($false = (rel_k @ sK1 @ X1)) | ($true = (p @ X1))) )),
% 0.13/0.31 inference(beta_eta_normalization,[],[f295])).
% 0.13/0.31 thf(f295,plain,(
% 0.13/0.31 ( ! [X2 : $i,X1 : $i] : (($true = (q @ X1)) | ($true = (p @ X1)) | ($true = ((^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0)))) @ X2)) | ($false = (rel_k @ sK1 @ X1))) )),
% 0.13/0.31 inference(pi_clausification,[],[f294])).
% 0.13/0.31 thf(f294,plain,(
% 0.13/0.31 ( ! [X1 : $i] : (($true = (q @ X1)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0)))))) | ($false = (rel_k @ sK1 @ X1)) | ($true = (p @ X1))) )),
% 0.13/0.31 inference(binary_proxy_clausification,[],[f293])).
% 0.13/0.31 thf(f293,plain,(
% 0.13/0.31 ( ! [X1 : $i] : ((((p @ X1) | (q @ X1)) = $true) | ($true = (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0)))))) | ($false = (rel_k @ sK1 @ X1))) )),
% 0.13/0.31 inference(not_proxy_clausification,[],[f292])).
% 0.13/0.31 thf(f292,plain,(
% 0.13/0.31 ( ! [X1 : $i] : (($false = (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0))))))) | ($false = (rel_k @ sK1 @ X1)) | (((p @ X1) | (q @ X1)) = $true)) )),
% 0.13/0.31 inference(not_proxy_clausification,[],[f291])).
% 0.13/0.31 thf(f291,plain,(
% 0.13/0.31 ( ! [X1 : $i] : (($true = (~ (rel_k @ sK1 @ X1))) | (((p @ X1) | (q @ X1)) = $true) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0)))))))) )),
% 0.13/0.31 inference(binary_proxy_clausification,[],[f290])).
% 0.13/0.31 thf(f290,plain,(
% 0.13/0.31 ( ! [X1 : $i] : (((((p @ X1) | (q @ X1)) | (~ (rel_k @ sK1 @ X1))) = $true) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0)))))))) )),
% 0.13/0.31 inference(beta_eta_normalization,[],[f289])).
% 0.13/0.31 thf(f289,plain,(
% 0.13/0.31 ( ! [X1 : $i] : (($false = (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0))))))) | ($true = ((^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))) @ X1))) )),
% 0.13/0.31 inference(pi_clausification,[],[f249])).
% 0.13/0.31 thf(f249,plain,(
% 0.13/0.31 ($true = (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0)))))))),
% 0.13/0.31 inference(binary_proxy_clausification,[],[f248])).
% 0.13/0.31 thf(f248,plain,(
% 0.13/0.31 (((~ ((~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0))))))) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0))))))),
% 0.13/0.31 inference(not_proxy_clausification,[],[f247])).
% 0.13/0.31 thf(f247,plain,(
% 0.13/0.31 ($false = (~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0))))))) | (((~ ((~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0))))))) = $false)),
% 0.13/0.31 inference(not_proxy_clausification,[],[f246])).
% 0.13/0.31 thf(f246,plain,(
% 0.13/0.31 ($true = (~ ((~ ((~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0))))))))) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))))),
% 0.13/0.31 inference(binary_proxy_clausification,[],[f155])).
% 0.13/0.31 thf(f155,plain,(
% 0.13/0.31 (((~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0))))))) = $false) | ($true = (~ ((~ ((~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0)))))))))),
% 0.13/0.31 inference(binary_proxy_clausification,[],[f154])).
% 0.13/0.31 thf(f364,plain,(
% 0.13/0.31 spl0_1 | spl0_2),
% 0.13/0.31 inference(avatar_split_clause,[],[f357,f362,f359])).
% 0.13/0.31 thf(f357,plain,(
% 0.13/0.31 ( ! [X2 : $i,X1 : $i] : (($false = (q @ X1)) | ((rel_k @ sK1 @ X2) = $false) | ($true = (p @ X2)) | ($false = (rel_k @ sK1 @ X1)) | ($true = (p @ X1))) )),
% 0.13/0.31 inference(not_proxy_clausification,[],[f356])).
% 0.13/0.31 thf(f356,plain,(
% 0.13/0.31 ( ! [X2 : $i,X1 : $i] : (((rel_k @ sK1 @ X2) = $false) | ($true = (p @ X1)) | ((~ (q @ X1)) = $true) | ($false = (rel_k @ sK1 @ X1)) | ($true = (p @ X2))) )),
% 0.13/0.31 inference(binary_proxy_clausification,[],[f355])).
% 0.13/0.31 thf(f355,plain,(
% 0.13/0.31 ( ! [X2 : $i,X1 : $i] : (($true = (p @ X2)) | ($true = ((p @ X1) | (~ (q @ X1)))) | ($false = (rel_k @ sK1 @ X1)) | ((rel_k @ sK1 @ X2) = $false)) )),
% 0.13/0.31 inference(not_proxy_clausification,[],[f354])).
% 0.13/0.31 thf(f354,plain,(
% 0.13/0.31 ( ! [X2 : $i,X1 : $i] : (($false = (rel_k @ sK1 @ X1)) | ($true = (p @ X2)) | ($true = (~ (rel_k @ sK1 @ X2))) | ($true = ((p @ X1) | (~ (q @ X1))))) )),
% 0.13/0.31 inference(not_proxy_clausification,[],[f353])).
% 0.13/0.31 thf(f353,plain,(
% 0.13/0.31 ( ! [X2 : $i,X1 : $i] : (($true = (~ (rel_k @ sK1 @ X1))) | ($true = ((p @ X1) | (~ (q @ X1)))) | ($true = (p @ X2)) | ($true = (~ (rel_k @ sK1 @ X2)))) )),
% 0.13/0.31 inference(binary_proxy_clausification,[],[f352])).
% 0.13/0.31 thf(f352,plain,(
% 0.13/0.31 ( ! [X2 : $i,X1 : $i] : ((((p @ X2) | (~ (rel_k @ sK1 @ X2))) = $true) | ($true = (~ (rel_k @ sK1 @ X1))) | ($true = ((p @ X1) | (~ (q @ X1))))) )),
% 0.13/0.31 inference(beta_eta_normalization,[],[f351])).
% 0.13/0.31 thf(f351,plain,(
% 0.13/0.31 ( ! [X2 : $i,X1 : $i] : (($true = ((p @ X1) | (~ (q @ X1)))) | ($true = (~ (rel_k @ sK1 @ X1))) | ($true = ((^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0)))) @ X2))) )),
% 0.13/0.31 inference(pi_clausification,[],[f350])).
% 0.13/0.31 thf(f350,plain,(
% 0.13/0.31 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0)))))) | ($true = (~ (rel_k @ sK1 @ X1))) | ($true = ((p @ X1) | (~ (q @ X1))))) )),
% 0.13/0.31 inference(binary_proxy_clausification,[],[f349])).
% 0.13/0.31 thf(f349,plain,(
% 0.13/0.31 ( ! [X1 : $i] : (($true = (((p @ X1) | (~ (q @ X1))) | (~ (rel_k @ sK1 @ X1)))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0))))))) )),
% 0.13/0.31 inference(not_proxy_clausification,[],[f303])).
% 0.13/0.31 thf(f303,plain,(
% 0.13/0.31 ( ! [X1 : $i] : (($false = (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0))))))) | ($true = (((p @ X1) | (~ (q @ X1))) | (~ (rel_k @ sK1 @ X1))))) )),
% 0.13/0.31 inference(binary_proxy_clausification,[],[f302])).
% 0.13/0.31 thf(f302,plain,(
% 0.13/0.31 ( ! [X1 : $i] : ((((~ ((~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0))))))) = $false) | ($true = (((p @ X1) | (~ (q @ X1))) | (~ (rel_k @ sK1 @ X1))))) )),
% 0.13/0.31 inference(beta_eta_normalization,[],[f301])).
% 0.13/0.31 thf(f301,plain,(
% 0.13/0.31 ( ! [X1 : $i] : ((((~ ((~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0))))))) = $false) | ($true = ((^[Y0 : $i]: (((p @ Y0) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0)))) @ X1))) )),
% 0.13/0.31 inference(pi_clausification,[],[f300])).
% 0.13/0.31 thf(f300,plain,(
% 0.13/0.31 ($true = (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))) | (((~ ((~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0))))))) = $false)),
% 0.13/0.31 inference(not_proxy_clausification,[],[f299])).
% 0.13/0.31 thf(f299,plain,(
% 0.13/0.31 ($true = (~ ((~ ((~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0))))))))) | ($true = (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0))))))),
% 0.13/0.31 inference(not_proxy_clausification,[],[f245])).
% 0.13/0.31 thf(f245,plain,(
% 0.13/0.31 ((~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))) = $false) | ($true = (~ ((~ ((~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((p @ Y0) | (~ (q @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_k @ sK1 @ Y0)))))))))),
% 0.13/0.31 inference(binary_proxy_clausification,[],[f155])).
% 0.13/0.31 % SZS output end Proof for theBenchmark
% 0.13/0.31 % (15437)------------------------------
% 0.13/0.31 % (15437)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.31 % (15437)Termination reason: Refutation
% 0.13/0.31
% 0.13/0.31 % (15437)Memory used [KB]: 6012
% 0.13/0.31 % (15437)Time elapsed: 0.018 s
% 0.13/0.31 % (15437)Instructions burned: 38 (million)
% 0.13/0.31 % (15437)------------------------------
% 0.13/0.31 % (15437)------------------------------
% 0.13/0.31 % (15436)Success in time 0.024 s
% 0.13/0.31 % Vampire---4.8 exiting
%------------------------------------------------------------------------------