TSTP Solution File: SYO048^1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO048^1 : 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 : n014.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 09:02:27 EDT 2024
% Result : Theorem 0.21s 0.40s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYO048^1 : TPTP v8.2.0. Released v4.0.0.
% 0.06/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon May 20 08:40:53 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 This is a TH0_THM_EQU_NAR problem
% 0.13/0.35 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.37 % (4692)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.13/0.37 % (4694)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)
% 0.13/0.37 % (4695)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.13/0.37 % (4693)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)
% 0.13/0.37 % (4696)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)
% 0.13/0.37 % (4698)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.13/0.37 % (4695)Instruction limit reached!
% 0.13/0.37 % (4695)------------------------------
% 0.13/0.37 % (4695)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (4696)Instruction limit reached!
% 0.13/0.37 % (4696)------------------------------
% 0.13/0.37 % (4696)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (4695)Termination reason: Unknown
% 0.13/0.37 % (4695)Termination phase: shuffling
% 0.13/0.37
% 0.13/0.37 % (4695)Memory used [KB]: 1023
% 0.13/0.37 % (4695)Time elapsed: 0.003 s
% 0.13/0.37 % (4695)Instructions burned: 2 (million)
% 0.13/0.37 % (4695)------------------------------
% 0.13/0.37 % (4695)------------------------------
% 0.13/0.37 % (4696)Termination reason: Unknown
% 0.13/0.37 % (4696)Termination phase: shuffling
% 0.13/0.37
% 0.13/0.37 % (4696)Memory used [KB]: 1023
% 0.13/0.37 % (4696)Time elapsed: 0.003 s
% 0.13/0.37 % (4696)Instructions burned: 2 (million)
% 0.13/0.37 % (4696)------------------------------
% 0.13/0.37 % (4696)------------------------------
% 0.13/0.37 % (4693)Instruction limit reached!
% 0.13/0.37 % (4693)------------------------------
% 0.13/0.37 % (4693)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (4693)Termination reason: Unknown
% 0.13/0.37 % (4693)Termination phase: shuffling
% 0.13/0.37
% 0.13/0.37 % (4693)Memory used [KB]: 1023
% 0.13/0.37 % (4693)Time elapsed: 0.004 s
% 0.13/0.37 % (4693)Instructions burned: 4 (million)
% 0.13/0.37 % (4693)------------------------------
% 0.13/0.37 % (4693)------------------------------
% 0.13/0.37 % (4697)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)
% 0.13/0.38 % (4698)Instruction limit reached!
% 0.13/0.38 % (4698)------------------------------
% 0.13/0.38 % (4698)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (4698)Termination reason: Unknown
% 0.13/0.38 % (4698)Termination phase: Saturation
% 0.13/0.38
% 0.13/0.38 % (4698)Memory used [KB]: 5628
% 0.13/0.38 % (4698)Time elapsed: 0.011 s
% 0.13/0.38 % (4698)Instructions burned: 18 (million)
% 0.13/0.38 % (4698)------------------------------
% 0.13/0.38 % (4698)------------------------------
% 0.13/0.38 % (4697)Refutation not found, incomplete strategy
% 0.13/0.38 % (4697)------------------------------
% 0.13/0.38 % (4697)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (4697)Termination reason: Refutation not found, incomplete strategy
% 0.13/0.38
% 0.13/0.38
% 0.13/0.38 % (4697)Memory used [KB]: 5628
% 0.13/0.38 % (4697)Time elapsed: 0.008 s
% 0.13/0.38 % (4697)Instructions burned: 10 (million)
% 0.13/0.38 % (4697)------------------------------
% 0.13/0.38 % (4697)------------------------------
% 0.13/0.38 % (4699)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)
% 0.21/0.38 % (4694)Instruction limit reached!
% 0.21/0.38 % (4694)------------------------------
% 0.21/0.38 % (4694)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (4699)Instruction limit reached!
% 0.21/0.38 % (4699)------------------------------
% 0.21/0.38 % (4699)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (4694)Termination reason: Unknown
% 0.21/0.38 % (4694)Termination phase: Saturation
% 0.21/0.38
% 0.21/0.38 % (4694)Memory used [KB]: 5756
% 0.21/0.38 % (4694)Time elapsed: 0.017 s
% 0.21/0.38 % (4694)Instructions burned: 28 (million)
% 0.21/0.38 % (4694)------------------------------
% 0.21/0.38 % (4694)------------------------------
% 0.21/0.38 % (4699)Termination reason: Unknown
% 0.21/0.38 % (4699)Termination phase: shuffling
% 0.21/0.38
% 0.21/0.38 % (4699)Memory used [KB]: 1023
% 0.21/0.38 % (4699)Time elapsed: 0.004 s
% 0.21/0.38 % (4699)Instructions burned: 4 (million)
% 0.21/0.38 % (4699)------------------------------
% 0.21/0.38 % (4699)------------------------------
% 0.21/0.38 % (4700)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.21/0.38 % (4701)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)
% 0.21/0.39 % (4692)First to succeed.
% 0.21/0.39 % (4702)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)
% 0.21/0.39 % (4702)Instruction limit reached!
% 0.21/0.39 % (4702)------------------------------
% 0.21/0.39 % (4702)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (4702)Termination reason: Unknown
% 0.21/0.39 % (4702)Termination phase: shuffling
% 0.21/0.39
% 0.21/0.39 % (4702)Memory used [KB]: 1023
% 0.21/0.39 % (4702)Time elapsed: 0.003 s
% 0.21/0.39 % (4702)Instructions burned: 3 (million)
% 0.21/0.39 % (4702)------------------------------
% 0.21/0.39 % (4702)------------------------------
% 0.21/0.39 % (4701)Instruction limit reached!
% 0.21/0.39 % (4701)------------------------------
% 0.21/0.39 % (4701)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (4701)Termination reason: Unknown
% 0.21/0.39 % (4701)Termination phase: Saturation
% 0.21/0.39
% 0.21/0.39 % (4701)Memory used [KB]: 5628
% 0.21/0.39 % (4701)Time elapsed: 0.009 s
% 0.21/0.39 % (4701)Instructions burned: 15 (million)
% 0.21/0.39 % (4701)------------------------------
% 0.21/0.39 % (4701)------------------------------
% 0.21/0.39 % (4703)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)
% 0.21/0.40 % (4692)Refutation found. Thanks to Tanya!
% 0.21/0.40 % SZS status Theorem for theBenchmark
% 0.21/0.40 % SZS output start Proof for theBenchmark
% 0.21/0.40 thf(type_def_5, type, mu: $tType).
% 0.21/0.40 thf(func_def_0, type, mu: $tType).
% 0.21/0.40 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.21/0.40 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_15, type, mtrue: $i > $o).
% 0.21/0.40 thf(func_def_16, type, mfalse: $i > $o).
% 0.21/0.40 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.21/0.40 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.21/0.40 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.21/0.40 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.21/0.40 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.21/0.40 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.21/0.40 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.21/0.40 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.21/0.40 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.21/0.40 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.21/0.40 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.21/0.40 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.21/0.40 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.21/0.40 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.21/0.40 thf(func_def_48, type, sK0: $i > $i > $o).
% 0.21/0.40 thf(func_def_51, type, sK3: $i > $o).
% 0.21/0.40 thf(func_def_52, type, sK4: $i > $o).
% 0.21/0.40 thf(f572,plain,(
% 0.21/0.40 $false),
% 0.21/0.40 inference(avatar_sat_refutation,[],[f316,f322,f411,f416,f425,f430,f447,f452,f457,f458,f472,f488,f502,f526,f550,f565,f571])).
% 0.21/0.40 thf(f571,plain,(
% 0.21/0.40 ~spl1_1 | ~spl1_19 | ~spl1_29),
% 0.21/0.40 inference(avatar_contradiction_clause,[],[f570])).
% 0.21/0.40 thf(f570,plain,(
% 0.21/0.40 $false | (~spl1_1 | ~spl1_19 | ~spl1_29)),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f567])).
% 0.21/0.40 thf(f567,plain,(
% 0.21/0.40 ($false = $true) | (~spl1_1 | ~spl1_19 | ~spl1_29)),
% 0.21/0.40 inference(superposition,[],[f534,f446])).
% 0.21/0.40 thf(f446,plain,(
% 0.21/0.40 ((sK3 @ sK5) = $false) | ~spl1_29),
% 0.21/0.40 inference(avatar_component_clause,[],[f444])).
% 0.21/0.40 thf(f444,plain,(
% 0.21/0.40 spl1_29 <=> ((sK3 @ sK5) = $false)),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl1_29])])).
% 0.21/0.40 thf(f534,plain,(
% 0.21/0.40 ((sK3 @ sK5) = $true) | (~spl1_1 | ~spl1_19)),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f531])).
% 0.21/0.40 thf(f531,plain,(
% 0.21/0.40 ($false = $true) | ((sK3 @ sK5) = $true) | (~spl1_1 | ~spl1_19)),
% 0.21/0.40 inference(superposition,[],[f315,f402])).
% 0.21/0.40 thf(f402,plain,(
% 0.21/0.40 ((sK0 @ sK2 @ sK5) = $true) | ~spl1_19),
% 0.21/0.40 inference(avatar_component_clause,[],[f400])).
% 0.21/0.40 thf(f400,plain,(
% 0.21/0.40 spl1_19 <=> ((sK0 @ sK2 @ sK5) = $true)),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl1_19])])).
% 0.21/0.40 thf(f315,plain,(
% 0.21/0.40 ( ! [X2 : $i] : (((sK0 @ sK2 @ X2) = $false) | ((sK3 @ X2) = $true)) ) | ~spl1_1),
% 0.21/0.40 inference(avatar_component_clause,[],[f314])).
% 0.21/0.40 thf(f314,plain,(
% 0.21/0.40 spl1_1 <=> ! [X2] : (((sK3 @ X2) = $true) | ((sK0 @ sK2 @ X2) = $false))),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl1_1])])).
% 0.21/0.40 thf(f565,plain,(
% 0.21/0.40 ~spl1_2 | ~spl1_28 | ~spl1_30),
% 0.21/0.40 inference(avatar_contradiction_clause,[],[f564])).
% 0.21/0.40 thf(f564,plain,(
% 0.21/0.40 $false | (~spl1_2 | ~spl1_28 | ~spl1_30)),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f561])).
% 0.21/0.40 thf(f561,plain,(
% 0.21/0.40 ($false = $true) | (~spl1_2 | ~spl1_28 | ~spl1_30)),
% 0.21/0.40 inference(superposition,[],[f451,f557])).
% 0.21/0.40 thf(f557,plain,(
% 0.21/0.40 ((sK4 @ sK6) = $true) | (~spl1_2 | ~spl1_28)),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f552])).
% 0.21/0.40 thf(f552,plain,(
% 0.21/0.40 ((sK4 @ sK6) = $true) | ($false = $true) | (~spl1_2 | ~spl1_28)),
% 0.21/0.40 inference(superposition,[],[f442,f319])).
% 0.21/0.40 thf(f319,plain,(
% 0.21/0.40 ( ! [X1 : $i] : (((sK0 @ sK2 @ X1) = $false) | ((sK4 @ X1) = $true)) ) | ~spl1_2),
% 0.21/0.40 inference(avatar_component_clause,[],[f318])).
% 0.21/0.40 thf(f318,plain,(
% 0.21/0.40 spl1_2 <=> ! [X1] : (((sK0 @ sK2 @ X1) = $false) | ((sK4 @ X1) = $true))),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl1_2])])).
% 0.21/0.40 thf(f442,plain,(
% 0.21/0.40 ((sK0 @ sK2 @ sK6) = $true) | ~spl1_28),
% 0.21/0.40 inference(avatar_component_clause,[],[f440])).
% 0.21/0.40 thf(f440,plain,(
% 0.21/0.40 spl1_28 <=> ((sK0 @ sK2 @ sK6) = $true)),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl1_28])])).
% 0.21/0.40 thf(f451,plain,(
% 0.21/0.40 ((sK4 @ sK6) = $false) | ~spl1_30),
% 0.21/0.40 inference(avatar_component_clause,[],[f449])).
% 0.21/0.40 thf(f449,plain,(
% 0.21/0.40 spl1_30 <=> ((sK4 @ sK6) = $false)),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl1_30])])).
% 0.21/0.40 thf(f550,plain,(
% 0.21/0.40 ~spl1_1 | ~spl1_27 | ~spl1_31),
% 0.21/0.40 inference(avatar_contradiction_clause,[],[f549])).
% 0.21/0.40 thf(f549,plain,(
% 0.21/0.40 $false | (~spl1_1 | ~spl1_27 | ~spl1_31)),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f546])).
% 0.21/0.40 thf(f546,plain,(
% 0.21/0.40 ($false = $true) | (~spl1_1 | ~spl1_27 | ~spl1_31)),
% 0.21/0.40 inference(superposition,[],[f456,f543])).
% 0.21/0.40 thf(f543,plain,(
% 0.21/0.40 ((sK3 @ sK7) = $true) | (~spl1_1 | ~spl1_27)),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f539])).
% 0.21/0.40 thf(f539,plain,(
% 0.21/0.40 ((sK3 @ sK7) = $true) | ($false = $true) | (~spl1_1 | ~spl1_27)),
% 0.21/0.40 inference(superposition,[],[f315,f438])).
% 0.21/0.40 thf(f438,plain,(
% 0.21/0.40 ((sK0 @ sK2 @ sK7) = $true) | ~spl1_27),
% 0.21/0.40 inference(avatar_component_clause,[],[f436])).
% 0.21/0.40 thf(f436,plain,(
% 0.21/0.40 spl1_27 <=> ((sK0 @ sK2 @ sK7) = $true)),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl1_27])])).
% 0.21/0.40 thf(f456,plain,(
% 0.21/0.40 ((sK3 @ sK7) = $false) | ~spl1_31),
% 0.21/0.40 inference(avatar_component_clause,[],[f454])).
% 0.21/0.40 thf(f454,plain,(
% 0.21/0.40 spl1_31 <=> ((sK3 @ sK7) = $false)),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl1_31])])).
% 0.21/0.40 thf(f526,plain,(
% 0.21/0.40 ~spl1_2 | ~spl1_24 | ~spl1_25),
% 0.21/0.40 inference(avatar_contradiction_clause,[],[f525])).
% 0.21/0.40 thf(f525,plain,(
% 0.21/0.40 $false | (~spl1_2 | ~spl1_24 | ~spl1_25)),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f521])).
% 0.21/0.40 thf(f521,plain,(
% 0.21/0.40 ($false = $true) | (~spl1_2 | ~spl1_24 | ~spl1_25)),
% 0.21/0.40 inference(superposition,[],[f517,f429])).
% 0.21/0.40 thf(f429,plain,(
% 0.21/0.40 ((sK4 @ sK9) = $false) | ~spl1_25),
% 0.21/0.40 inference(avatar_component_clause,[],[f427])).
% 0.21/0.40 thf(f427,plain,(
% 0.21/0.40 spl1_25 <=> ((sK4 @ sK9) = $false)),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl1_25])])).
% 0.21/0.40 thf(f517,plain,(
% 0.21/0.40 ((sK4 @ sK9) = $true) | (~spl1_2 | ~spl1_24)),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f512])).
% 0.21/0.40 thf(f512,plain,(
% 0.21/0.40 ($false = $true) | ((sK4 @ sK9) = $true) | (~spl1_2 | ~spl1_24)),
% 0.21/0.40 inference(superposition,[],[f424,f319])).
% 0.21/0.40 thf(f424,plain,(
% 0.21/0.40 ((sK0 @ sK2 @ sK9) = $true) | ~spl1_24),
% 0.21/0.40 inference(avatar_component_clause,[],[f422])).
% 0.21/0.40 thf(f422,plain,(
% 0.21/0.40 spl1_24 <=> ((sK0 @ sK2 @ sK9) = $true)),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl1_24])])).
% 0.21/0.40 thf(f502,plain,(
% 0.21/0.40 ~spl1_2 | ~spl1_20 | ~spl1_22),
% 0.21/0.40 inference(avatar_contradiction_clause,[],[f501])).
% 0.21/0.40 thf(f501,plain,(
% 0.21/0.40 $false | (~spl1_2 | ~spl1_20 | ~spl1_22)),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f498])).
% 0.21/0.40 thf(f498,plain,(
% 0.21/0.40 ($false = $true) | (~spl1_2 | ~spl1_20 | ~spl1_22)),
% 0.21/0.40 inference(superposition,[],[f415,f495])).
% 0.21/0.40 thf(f495,plain,(
% 0.21/0.40 ((sK4 @ sK10) = $true) | (~spl1_2 | ~spl1_20)),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f489])).
% 0.21/0.40 thf(f489,plain,(
% 0.21/0.40 ($false = $true) | ((sK4 @ sK10) = $true) | (~spl1_2 | ~spl1_20)),
% 0.21/0.40 inference(superposition,[],[f406,f319])).
% 0.21/0.40 thf(f406,plain,(
% 0.21/0.40 ((sK0 @ sK2 @ sK10) = $true) | ~spl1_20),
% 0.21/0.40 inference(avatar_component_clause,[],[f404])).
% 0.21/0.40 thf(f404,plain,(
% 0.21/0.40 spl1_20 <=> ((sK0 @ sK2 @ sK10) = $true)),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl1_20])])).
% 0.21/0.40 thf(f415,plain,(
% 0.21/0.40 ((sK4 @ sK10) = $false) | ~spl1_22),
% 0.21/0.40 inference(avatar_component_clause,[],[f413])).
% 0.21/0.40 thf(f413,plain,(
% 0.21/0.40 spl1_22 <=> ((sK4 @ sK10) = $false)),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl1_22])])).
% 0.21/0.40 thf(f488,plain,(
% 0.21/0.40 ~spl1_1 | ~spl1_21 | ~spl1_23),
% 0.21/0.40 inference(avatar_contradiction_clause,[],[f487])).
% 0.21/0.40 thf(f487,plain,(
% 0.21/0.40 $false | (~spl1_1 | ~spl1_21 | ~spl1_23)),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f483])).
% 0.21/0.40 thf(f483,plain,(
% 0.21/0.40 ($false = $true) | (~spl1_1 | ~spl1_21 | ~spl1_23)),
% 0.21/0.40 inference(superposition,[],[f481,f420])).
% 0.21/0.40 thf(f420,plain,(
% 0.21/0.40 ((sK3 @ sK8) = $false) | ~spl1_23),
% 0.21/0.40 inference(avatar_component_clause,[],[f418])).
% 0.21/0.40 thf(f418,plain,(
% 0.21/0.40 spl1_23 <=> ((sK3 @ sK8) = $false)),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl1_23])])).
% 0.21/0.40 thf(f481,plain,(
% 0.21/0.40 ((sK3 @ sK8) = $true) | (~spl1_1 | ~spl1_21)),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f478])).
% 0.21/0.40 thf(f478,plain,(
% 0.21/0.40 ($false = $true) | ((sK3 @ sK8) = $true) | (~spl1_1 | ~spl1_21)),
% 0.21/0.40 inference(superposition,[],[f315,f410])).
% 0.21/0.40 thf(f410,plain,(
% 0.21/0.40 ((sK0 @ sK2 @ sK8) = $true) | ~spl1_21),
% 0.21/0.40 inference(avatar_component_clause,[],[f408])).
% 0.21/0.40 thf(f408,plain,(
% 0.21/0.40 spl1_21 <=> ((sK0 @ sK2 @ sK8) = $true)),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl1_21])])).
% 0.21/0.40 thf(f472,plain,(
% 0.21/0.40 ~spl1_2 | ~spl1_19 | ~spl1_26),
% 0.21/0.40 inference(avatar_contradiction_clause,[],[f471])).
% 0.21/0.40 thf(f471,plain,(
% 0.21/0.40 $false | (~spl1_2 | ~spl1_19 | ~spl1_26)),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f468])).
% 0.21/0.40 thf(f468,plain,(
% 0.21/0.40 ($false = $true) | (~spl1_2 | ~spl1_19 | ~spl1_26)),
% 0.21/0.40 inference(superposition,[],[f434,f466])).
% 0.21/0.40 thf(f466,plain,(
% 0.21/0.40 ((sK4 @ sK5) = $true) | (~spl1_2 | ~spl1_19)),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f464])).
% 0.21/0.40 thf(f464,plain,(
% 0.21/0.40 ($false = $true) | ((sK4 @ sK5) = $true) | (~spl1_2 | ~spl1_19)),
% 0.21/0.40 inference(superposition,[],[f402,f319])).
% 0.21/0.40 thf(f434,plain,(
% 0.21/0.40 ((sK4 @ sK5) = $false) | ~spl1_26),
% 0.21/0.40 inference(avatar_component_clause,[],[f432])).
% 0.21/0.40 thf(f432,plain,(
% 0.21/0.40 spl1_26 <=> ((sK4 @ sK5) = $false)),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl1_26])])).
% 0.21/0.40 thf(f458,plain,(
% 0.21/0.40 spl1_29 | spl1_30 | spl1_31 | spl1_26),
% 0.21/0.40 inference(avatar_split_clause,[],[f175,f432,f454,f449,f444])).
% 0.21/0.40 thf(f175,plain,(
% 0.21/0.40 ((sK4 @ sK6) = $false) | ((sK3 @ sK5) = $false) | ((sK3 @ sK7) = $false) | ((sK4 @ sK5) = $false)),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f173])).
% 0.21/0.40 thf(f173,plain,(
% 0.21/0.40 ((sK4 @ sK5) = $false) | ((sK3 @ sK5) = $false) | (((sK4 @ sK6) | (~ (sK0 @ sK2 @ sK6))) = $false) | ((sK3 @ sK7) = $false)),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f171])).
% 0.21/0.40 thf(f171,plain,(
% 0.21/0.40 ($false = ((sK3 @ sK7) | (~ (sK0 @ sK2 @ sK7)))) | (((sK4 @ sK6) | (~ (sK0 @ sK2 @ sK6))) = $false) | ((sK4 @ sK5) = $false) | ((sK3 @ sK5) = $false)),
% 0.21/0.40 inference(beta_eta_normalization,[],[f170])).
% 0.21/0.40 thf(f170,plain,(
% 0.21/0.40 ((sK4 @ sK5) = $false) | (((sK4 @ sK6) | (~ (sK0 @ sK2 @ sK6))) = $false) | ($false = ((^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0)))) @ sK7)) | ((sK3 @ sK5) = $false)),
% 0.21/0.40 inference(sigma_clausification,[],[f169])).
% 0.21/0.40 thf(f169,plain,(
% 0.21/0.40 ((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0))))) = $false) | ((sK4 @ sK5) = $false) | (((sK4 @ sK6) | (~ (sK0 @ sK2 @ sK6))) = $false) | ((sK3 @ sK5) = $false)),
% 0.21/0.40 inference(beta_eta_normalization,[],[f168])).
% 0.21/0.40 thf(f168,plain,(
% 0.21/0.40 ((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0))))) = $false) | (((^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0)))) @ sK6) = $false) | ((sK3 @ sK5) = $false) | ((sK4 @ sK5) = $false)),
% 0.21/0.40 inference(sigma_clausification,[],[f167])).
% 0.21/0.40 thf(f167,plain,(
% 0.21/0.40 ((sK4 @ sK5) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0))))) = $false) | ((sK3 @ sK5) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0))))) = $false)),
% 0.21/0.40 inference(not_proxy_clausification,[],[f166])).
% 0.21/0.40 thf(f166,plain,(
% 0.21/0.40 ((~ (sK4 @ sK5)) = $true) | ((sK3 @ sK5) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0))))) = $false)),
% 0.21/0.40 inference(not_proxy_clausification,[],[f165])).
% 0.21/0.40 thf(f165,plain,(
% 0.21/0.40 ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))) = $true) | ((~ (sK4 @ sK5)) = $true) | ((sK3 @ sK5) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0))))) = $false)),
% 0.21/0.40 inference(not_proxy_clausification,[],[f164])).
% 0.21/0.40 thf(f164,plain,(
% 0.21/0.40 ((~ (sK3 @ sK5)) = $true) | ((~ (sK4 @ sK5)) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0))))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))) = $true)),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f163])).
% 0.21/0.40 thf(f163,plain,(
% 0.21/0.40 (((~ (sK4 @ sK5)) | (~ (sK3 @ sK5))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0))))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))) = $true)),
% 0.21/0.40 inference(not_proxy_clausification,[],[f162])).
% 0.21/0.40 thf(f162,plain,(
% 0.21/0.40 ((~ ((~ (sK4 @ sK5)) | (~ (sK3 @ sK5)))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0))))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))) = $true)),
% 0.21/0.40 inference(not_proxy_clausification,[],[f161])).
% 0.21/0.40 thf(f161,plain,(
% 0.21/0.40 ((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))) = $true) | ((~ ((~ (sK4 @ sK5)) | (~ (sK3 @ sK5)))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))) = $true)),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f160])).
% 0.21/0.40 thf(f160,plain,(
% 0.21/0.40 (((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0))))))) = $true) | ((~ ((~ (sK4 @ sK5)) | (~ (sK3 @ sK5)))) = $false)),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f158])).
% 0.21/0.40 thf(f158,plain,(
% 0.21/0.40 (((~ ((~ (sK4 @ sK5)) | (~ (sK3 @ sK5)))) | (~ (sK0 @ sK2 @ sK5))) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0))))))) = $true)),
% 0.21/0.40 inference(not_proxy_clausification,[],[f157])).
% 0.21/0.40 thf(f157,plain,(
% 0.21/0.40 ($false = (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0))))))))) | (((~ ((~ (sK4 @ sK5)) | (~ (sK3 @ sK5)))) | (~ (sK0 @ sK2 @ sK5))) = $false)),
% 0.21/0.40 inference(beta_eta_normalization,[],[f156])).
% 0.21/0.40 thf(f156,plain,(
% 0.21/0.40 ($false = (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0))))))))) | ($false = ((^[Y0 : $i]: ((~ ((~ (sK4 @ Y0)) | (~ (sK3 @ Y0)))) | (~ (sK0 @ sK2 @ Y0)))) @ sK5))),
% 0.21/0.40 inference(sigma_clausification,[],[f155])).
% 0.21/0.40 thf(f155,plain,(
% 0.21/0.40 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ ((~ (sK4 @ Y0)) | (~ (sK3 @ Y0)))) | (~ (sK0 @ sK2 @ Y0)))))) | ($false = (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))))))),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f153])).
% 0.21/0.40 thf(f153,plain,(
% 0.21/0.40 (((!! @ $i @ (^[Y0 : $i]: ((~ ((~ (sK4 @ Y0)) | (~ (sK3 @ Y0)))) | (~ (sK0 @ sK2 @ Y0))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))))) = $false) | ($false = (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))))))),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f151])).
% 0.21/0.40 thf(f151,plain,(
% 0.21/0.40 (((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ ((~ (sK4 @ Y0)) | (~ (sK3 @ Y0)))) | (~ (sK0 @ sK2 @ Y0))))))) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((~ ((~ (sK4 @ Y0)) | (~ (sK3 @ Y0)))) | (~ (sK0 @ sK2 @ Y0))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))))) = $false)),
% 0.21/0.40 inference(not_proxy_clausification,[],[f150])).
% 0.21/0.40 thf(f150,plain,(
% 0.21/0.40 ((~ ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ ((~ (sK4 @ Y0)) | (~ (sK3 @ Y0)))) | (~ (sK0 @ sK2 @ Y0)))))))) = $true) | (((!! @ $i @ (^[Y0 : $i]: ((~ ((~ (sK4 @ Y0)) | (~ (sK3 @ Y0)))) | (~ (sK0 @ sK2 @ Y0))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))))) = $false)),
% 0.21/0.40 inference(not_proxy_clausification,[],[f149])).
% 0.21/0.40 thf(f149,plain,(
% 0.21/0.40 ((~ ((!! @ $i @ (^[Y0 : $i]: ((~ ((~ (sK4 @ Y0)) | (~ (sK3 @ Y0)))) | (~ (sK0 @ sK2 @ Y0))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0))))))))) = $true) | ((~ ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ ((~ (sK4 @ Y0)) | (~ (sK3 @ Y0)))) | (~ (sK0 @ sK2 @ Y0)))))))) = $true)),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f148])).
% 0.21/0.40 thf(f148,plain,(
% 0.21/0.40 (((~ ((!! @ $i @ (^[Y0 : $i]: ((~ ((~ (sK4 @ Y0)) | (~ (sK3 @ Y0)))) | (~ (sK0 @ sK2 @ Y0))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0))))))))) | (~ ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ ((~ (sK4 @ Y0)) | (~ (sK3 @ Y0)))) | (~ (sK0 @ sK2 @ Y0))))))))) = $true)),
% 0.21/0.40 inference(not_proxy_clausification,[],[f147])).
% 0.21/0.40 thf(f147,plain,(
% 0.21/0.40 ($false = (~ ((~ ((!! @ $i @ (^[Y0 : $i]: ((~ ((~ (sK4 @ Y0)) | (~ (sK3 @ Y0)))) | (~ (sK0 @ sK2 @ Y0))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0))))))))) | (~ ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ ((~ (sK4 @ Y0)) | (~ (sK3 @ Y0)))) | (~ (sK0 @ sK2 @ Y0)))))))))))),
% 0.21/0.40 inference(beta_eta_normalization,[],[f146])).
% 0.21/0.40 thf(f146,plain,(
% 0.21/0.40 (((^[Y0 : $i > $o]: (~ ((~ ((!! @ $i @ (^[Y1 : $i]: ((~ ((~ (Y0 @ Y1)) | (~ (sK3 @ Y1)))) | (~ (sK0 @ sK2 @ Y1))))) | ((~ (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) | (~ (sK0 @ sK2 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (sK0 @ sK2 @ Y1))))))))) | (~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) | (~ (sK0 @ sK2 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (sK0 @ sK2 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ ((~ (Y0 @ Y1)) | (~ (sK3 @ Y1)))) | (~ (sK0 @ sK2 @ Y1))))))))))) @ sK4) = $false)),
% 0.21/0.40 inference(sigma_clausification,[],[f145])).
% 0.21/0.40 thf(f145,plain,(
% 0.21/0.40 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (~ ((~ ((!! @ $i @ (^[Y1 : $i]: ((~ ((~ (Y0 @ Y1)) | (~ (sK3 @ Y1)))) | (~ (sK0 @ sK2 @ Y1))))) | ((~ (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) | (~ (sK0 @ sK2 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (sK0 @ sK2 @ Y1))))))))) | (~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) | (~ (sK0 @ sK2 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (sK0 @ sK2 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ ((~ (Y0 @ Y1)) | (~ (sK3 @ Y1)))) | (~ (sK0 @ sK2 @ Y1)))))))))))) = $false)),
% 0.21/0.40 inference(beta_eta_normalization,[],[f144])).
% 0.21/0.40 thf(f144,plain,(
% 0.21/0.40 (((^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (~ ((~ ((!! @ $i @ (^[Y2 : $i]: ((~ ((~ (Y1 @ Y2)) | (~ (Y0 @ Y2)))) | (~ (sK0 @ sK2 @ Y2))))) | ((~ (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) | (~ (sK0 @ sK2 @ Y2)))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (sK0 @ sK2 @ Y2))))))))) | (~ ((~ ((~ (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) | (~ (sK0 @ sK2 @ Y2)))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (sK0 @ sK2 @ Y2)))))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ ((~ (Y1 @ Y2)) | (~ (Y0 @ Y2)))) | (~ (sK0 @ sK2 @ Y2))))))))))))) @ sK3) = $false)),
% 0.21/0.40 inference(sigma_clausification,[],[f143])).
% 0.21/0.40 thf(f143,plain,(
% 0.21/0.40 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (~ ((~ ((!! @ $i @ (^[Y2 : $i]: ((~ ((~ (Y1 @ Y2)) | (~ (Y0 @ Y2)))) | (~ (sK0 @ sK2 @ Y2))))) | ((~ (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) | (~ (sK0 @ sK2 @ Y2)))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (sK0 @ sK2 @ Y2))))))))) | (~ ((~ ((~ (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) | (~ (sK0 @ sK2 @ Y2)))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (sK0 @ sK2 @ Y2)))))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ ((~ (Y1 @ Y2)) | (~ (Y0 @ Y2)))) | (~ (sK0 @ sK2 @ Y2)))))))))))))) = $false)),
% 0.21/0.40 inference(beta_eta_normalization,[],[f142])).
% 0.21/0.40 thf(f142,plain,(
% 0.21/0.40 ($false = ((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (~ ((~ ((!! @ $i @ (^[Y3 : $i]: ((~ ((~ (Y2 @ Y3)) | (~ (Y1 @ Y3)))) | (~ (sK0 @ Y0 @ Y3))))) | ((~ (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) | (~ (sK0 @ Y0 @ Y3)))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (sK0 @ Y0 @ Y3))))))))) | (~ ((~ ((~ (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) | (~ (sK0 @ Y0 @ Y3)))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (sK0 @ Y0 @ Y3)))))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ ((~ (Y2 @ Y3)) | (~ (Y1 @ Y3)))) | (~ (sK0 @ Y0 @ Y3))))))))))))))) @ sK2))),
% 0.21/0.40 inference(sigma_clausification,[],[f141])).
% 0.21/0.40 thf(f141,plain,(
% 0.21/0.40 ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (~ ((~ ((!! @ $i @ (^[Y3 : $i]: ((~ ((~ (Y2 @ Y3)) | (~ (Y1 @ Y3)))) | (~ (sK0 @ Y0 @ Y3))))) | ((~ (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) | (~ (sK0 @ Y0 @ Y3)))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (sK0 @ Y0 @ Y3))))))))) | (~ ((~ ((~ (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) | (~ (sK0 @ Y0 @ Y3)))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (sK0 @ Y0 @ Y3)))))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ ((~ (Y2 @ Y3)) | (~ (Y1 @ Y3)))) | (~ (sK0 @ Y0 @ Y3)))))))))))))))) != $true)),
% 0.21/0.40 inference(boolean_simplification,[],[f140])).
% 0.21/0.40 thf(f140,plain,(
% 0.21/0.40 ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (~ ((~ ((!! @ $i @ (^[Y3 : $i]: ((~ ((~ (Y2 @ Y3)) | (~ (Y1 @ Y3)))) | (~ (sK0 @ Y0 @ Y3))))) | (~ (~ ((~ (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) | (~ (sK0 @ Y0 @ Y3)))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (sK0 @ Y0 @ Y3))))))))))) | (~ ((~ ((~ (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) | (~ (sK0 @ Y0 @ Y3)))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (sK0 @ Y0 @ Y3)))))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ ((~ (Y2 @ Y3)) | (~ (Y1 @ Y3)))) | (~ (sK0 @ Y0 @ Y3)))))))))))))))))),
% 0.21/0.40 inference(beta_eta_normalization,[],[f139])).
% 0.21/0.40 thf(f139,plain,(
% 0.21/0.40 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : ($i > $o) > $i > $o]: ((^[Y2 : $i]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y7 @ Y8) | (Y6 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y5)))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y7 @ Y8) | (Y6 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ Y2 @ Y3) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y7 @ Y8) | (Y6 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ Y3 @ Y2))))) @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5) | (~ (Y2 @ Y4 @ Y5)))))))))) @ sK0 @ ((^[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)))))) @ Y0 @ Y1)) @ ((^[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 > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5) | (~ (Y2 @ Y4 @ Y5)))))))))) @ sK0 @ Y0) @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5) | (~ (Y2 @ Y4 @ Y5)))))))))) @ sK0 @ Y1)))))))) != $true)),
% 0.21/0.40 inference(definition_unfolding,[],[f128,f113,f127,f127,f133,f105,f130,f130,f105,f105])).
% 0.21/0.40 thf(f130,plain,(
% 0.21/0.40 (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)))))))),
% 0.21/0.40 inference(definition_unfolding,[],[f114,f124,f120,f124,f124])).
% 0.21/0.40 thf(f120,plain,(
% 0.21/0.40 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.21/0.40 inference(cnf_transformation,[],[f48])).
% 0.21/0.40 thf(f48,plain,(
% 0.21/0.40 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.21/0.40 inference(fool_elimination,[],[f47])).
% 0.21/0.40 thf(f47,plain,(
% 0.21/0.40 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))))),
% 0.21/0.40 inference(rectify,[],[f4])).
% 0.21/0.40 thf(f4,axiom,(
% 0.21/0.40 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))))),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.21/0.40 thf(f124,plain,(
% 0.21/0.40 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.21/0.40 inference(cnf_transformation,[],[f44])).
% 0.21/0.40 thf(f44,plain,(
% 0.21/0.40 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.21/0.40 inference(fool_elimination,[],[f43])).
% 0.21/0.40 thf(f43,plain,(
% 0.21/0.40 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.21/0.40 inference(rectify,[],[f3])).
% 0.21/0.40 thf(f3,axiom,(
% 0.21/0.40 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.21/0.40 thf(f114,plain,(
% 0.21/0.40 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.21/0.40 inference(cnf_transformation,[],[f70])).
% 0.21/0.40 thf(f70,plain,(
% 0.21/0.40 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.21/0.40 inference(fool_elimination,[],[f69])).
% 0.21/0.40 thf(f69,plain,(
% 0.21/0.40 ((^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))) = mand)),
% 0.21/0.40 inference(rectify,[],[f5])).
% 0.21/0.40 thf(f5,axiom,(
% 0.21/0.40 ((^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))) = mand)),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand)).
% 0.21/0.40 thf(f105,plain,(
% 0.21/0.40 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (Y0 @ Y2 @ Y3)))))))))))),
% 0.21/0.40 inference(cnf_transformation,[],[f60])).
% 0.21/0.40 thf(f60,plain,(
% 0.21/0.40 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (Y0 @ Y2 @ Y3)))))))))))),
% 0.21/0.40 inference(fool_elimination,[],[f59])).
% 0.21/0.40 thf(f59,plain,(
% 0.21/0.40 (mbox = (^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i] : (! [X3] : (~(X0 @ X2 @ X3) | (X1 @ X3)))))),
% 0.21/0.40 inference(rectify,[],[f16])).
% 0.21/0.40 thf(f16,axiom,(
% 0.21/0.40 (mbox = (^[X6 : $i > $i > $o, X3 : $i > $o, X2 : $i] : (! [X7] : (~(X6 @ X2 @ X7) | (X3 @ X7)))))),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox)).
% 0.21/0.40 thf(f133,plain,(
% 0.21/0.40 (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]: ((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))))))),
% 0.21/0.40 inference(definition_unfolding,[],[f110,f130,f131,f131])).
% 0.21/0.40 thf(f131,plain,(
% 0.21/0.40 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.21/0.40 inference(definition_unfolding,[],[f121,f120,f124])).
% 0.21/0.40 thf(f121,plain,(
% 0.21/0.40 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.21/0.40 inference(cnf_transformation,[],[f42])).
% 0.21/0.40 thf(f42,plain,(
% 0.21/0.40 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.21/0.40 inference(fool_elimination,[],[f41])).
% 0.21/0.40 thf(f41,plain,(
% 0.21/0.40 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.21/0.40 inference(rectify,[],[f6])).
% 0.21/0.40 thf(f6,axiom,(
% 0.21/0.40 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.21/0.40 thf(f110,plain,(
% 0.21/0.40 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.21/0.40 inference(cnf_transformation,[],[f89])).
% 0.21/0.40 thf(f89,plain,(
% 0.21/0.40 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.21/0.40 inference(fool_elimination,[],[f88])).
% 0.21/0.40 thf(f88,plain,(
% 0.21/0.40 (mequiv = (^[X0 : $i > $o, X1 : $i > $o] : (mand @ (mimplies @ X0 @ X1) @ (mimplies @ X1 @ X0))))),
% 0.21/0.40 inference(rectify,[],[f8])).
% 0.21/0.40 thf(f8,axiom,(
% 0.21/0.40 (mequiv = (^[X3 : $i > $o, X4 : $i > $o] : (mand @ (mimplies @ X3 @ X4) @ (mimplies @ X4 @ X3))))),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mequiv)).
% 0.21/0.40 thf(f127,plain,(
% 0.21/0.40 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.21/0.40 inference(cnf_transformation,[],[f66])).
% 0.21/0.40 thf(f66,plain,(
% 0.21/0.40 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.21/0.40 inference(fool_elimination,[],[f65])).
% 0.21/0.40 thf(f65,plain,(
% 0.21/0.40 ((^[X0 : ($i > $o) > $i > $o, X1 : $i] : (! [X2 : $i > $o] : (X0 @ X2 @ X1))) = mforall_prop)),
% 0.21/0.40 inference(rectify,[],[f11])).
% 0.21/0.40 thf(f11,axiom,(
% 0.21/0.40 ((^[X3 : ($i > $o) > $i > $o, X2 : $i] : (! [X5 : $i > $o] : (X3 @ X5 @ X2))) = mforall_prop)),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_prop)).
% 0.21/0.40 thf(f113,plain,(
% 0.21/0.40 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.21/0.40 inference(cnf_transformation,[],[f50])).
% 0.21/0.40 thf(f50,plain,(
% 0.21/0.40 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.21/0.40 inference(fool_elimination,[],[f49])).
% 0.21/0.40 thf(f49,plain,(
% 0.21/0.40 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.21/0.40 inference(rectify,[],[f28])).
% 0.21/0.40 thf(f28,axiom,(
% 0.21/0.40 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.21/0.40 thf(f128,plain,(
% 0.21/0.40 ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mforall_prop @ (^[Y1 : $i > $o]: (mequiv @ (mbox @ sK0 @ (mand @ Y0 @ Y1)) @ (mand @ (mbox @ sK0 @ Y0) @ (mbox @ sK0 @ Y1)))))))) != $true)),
% 0.21/0.40 inference(cnf_transformation,[],[f97])).
% 0.21/0.40 thf(f97,plain,(
% 0.21/0.40 ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mforall_prop @ (^[Y1 : $i > $o]: (mequiv @ (mbox @ sK0 @ (mand @ Y0 @ Y1)) @ (mand @ (mbox @ sK0 @ Y0) @ (mbox @ sK0 @ Y1)))))))) != $true)),
% 0.21/0.40 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f95,f96])).
% 0.21/0.40 thf(f96,plain,(
% 0.21/0.40 ? [X0 : $i > $i > $o] : ($true != (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mforall_prop @ (^[Y1 : $i > $o]: (mequiv @ (mbox @ X0 @ (mand @ Y0 @ Y1)) @ (mand @ (mbox @ X0 @ Y0) @ (mbox @ X0 @ Y1))))))))) => ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mforall_prop @ (^[Y1 : $i > $o]: (mequiv @ (mbox @ sK0 @ (mand @ Y0 @ Y1)) @ (mand @ (mbox @ sK0 @ Y0) @ (mbox @ sK0 @ Y1)))))))) != $true)),
% 0.21/0.40 introduced(choice_axiom,[])).
% 0.21/0.40 thf(f95,plain,(
% 0.21/0.40 ? [X0 : $i > $i > $o] : ($true != (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mforall_prop @ (^[Y1 : $i > $o]: (mequiv @ (mbox @ X0 @ (mand @ Y0 @ Y1)) @ (mand @ (mbox @ X0 @ Y0) @ (mbox @ X0 @ Y1)))))))))),
% 0.21/0.40 inference(ennf_transformation,[],[f74])).
% 0.21/0.40 thf(f74,plain,(
% 0.21/0.40 ~! [X0 : $i > $i > $o] : ($true = (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mforall_prop @ (^[Y1 : $i > $o]: (mequiv @ (mbox @ X0 @ (mand @ Y0 @ Y1)) @ (mand @ (mbox @ X0 @ Y0) @ (mbox @ X0 @ Y1)))))))))),
% 0.21/0.40 inference(fool_elimination,[],[f73])).
% 0.21/0.40 thf(f73,plain,(
% 0.21/0.40 ~! [X0 : $i > $i > $o] : (mvalid @ (mforall_prop @ (^[X1 : $i > $o] : (mforall_prop @ (^[X2 : $i > $o] : (mequiv @ (mbox @ X0 @ (mand @ X1 @ X2)) @ (mand @ (mbox @ X0 @ X1) @ (mbox @ X0 @ X2))))))))),
% 0.21/0.40 inference(rectify,[],[f33])).
% 0.21/0.40 thf(f33,negated_conjecture,(
% 0.21/0.40 ~! [X6 : $i > $i > $o] : (mvalid @ (mforall_prop @ (^[X11 : $i > $o] : (mforall_prop @ (^[X12 : $i > $o] : (mequiv @ (mbox @ X6 @ (mand @ X11 @ X12)) @ (mand @ (mbox @ X6 @ X11) @ (mbox @ X6 @ X12))))))))),
% 0.21/0.40 inference(negated_conjecture,[],[f32])).
% 0.21/0.40 thf(f32,conjecture,(
% 0.21/0.40 ! [X6 : $i > $i > $o] : (mvalid @ (mforall_prop @ (^[X11 : $i > $o] : (mforall_prop @ (^[X12 : $i > $o] : (mequiv @ (mbox @ X6 @ (mand @ X11 @ X12)) @ (mand @ (mbox @ X6 @ X11) @ (mbox @ X6 @ X12))))))))),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj)).
% 0.21/0.40 thf(f457,plain,(
% 0.21/0.40 spl1_29 | spl1_26 | spl1_28 | spl1_31),
% 0.21/0.40 inference(avatar_split_clause,[],[f176,f454,f440,f432,f444])).
% 0.21/0.40 thf(f176,plain,(
% 0.21/0.40 ((sK4 @ sK5) = $false) | ((sK0 @ sK2 @ sK6) = $true) | ((sK3 @ sK5) = $false) | ((sK3 @ sK7) = $false)),
% 0.21/0.40 inference(not_proxy_clausification,[],[f174])).
% 0.21/0.40 thf(f174,plain,(
% 0.21/0.40 ((sK4 @ sK5) = $false) | ((sK3 @ sK7) = $false) | ((~ (sK0 @ sK2 @ sK6)) = $false) | ((sK3 @ sK5) = $false)),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f173])).
% 0.21/0.40 thf(f452,plain,(
% 0.21/0.40 spl1_30 | spl1_26 | spl1_27 | spl1_29),
% 0.21/0.40 inference(avatar_split_clause,[],[f179,f444,f436,f432,f449])).
% 0.21/0.40 thf(f179,plain,(
% 0.21/0.40 ((sK0 @ sK2 @ sK7) = $true) | ((sK3 @ sK5) = $false) | ((sK4 @ sK5) = $false) | ((sK4 @ sK6) = $false)),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f177])).
% 0.21/0.40 thf(f177,plain,(
% 0.21/0.40 ((sK0 @ sK2 @ sK7) = $true) | ((sK3 @ sK5) = $false) | ((sK4 @ sK5) = $false) | (((sK4 @ sK6) | (~ (sK0 @ sK2 @ sK6))) = $false)),
% 0.21/0.40 inference(not_proxy_clausification,[],[f172])).
% 0.21/0.40 thf(f172,plain,(
% 0.21/0.40 ((sK4 @ sK5) = $false) | ((~ (sK0 @ sK2 @ sK7)) = $false) | ((sK3 @ sK5) = $false) | (((sK4 @ sK6) | (~ (sK0 @ sK2 @ sK6))) = $false)),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f171])).
% 0.21/0.40 thf(f447,plain,(
% 0.21/0.40 spl1_26 | spl1_27 | spl1_28 | spl1_29),
% 0.21/0.40 inference(avatar_split_clause,[],[f180,f444,f440,f436,f432])).
% 0.21/0.40 thf(f180,plain,(
% 0.21/0.40 ((sK3 @ sK5) = $false) | ((sK0 @ sK2 @ sK7) = $true) | ((sK0 @ sK2 @ sK6) = $true) | ((sK4 @ sK5) = $false)),
% 0.21/0.40 inference(not_proxy_clausification,[],[f178])).
% 0.21/0.40 thf(f178,plain,(
% 0.21/0.40 ((sK4 @ sK5) = $false) | ((sK0 @ sK2 @ sK7) = $true) | ((~ (sK0 @ sK2 @ sK6)) = $false) | ((sK3 @ sK5) = $false)),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f177])).
% 0.21/0.40 thf(f430,plain,(
% 0.21/0.40 spl1_25 | spl1_19 | spl1_23),
% 0.21/0.40 inference(avatar_split_clause,[],[f192,f418,f400,f427])).
% 0.21/0.40 thf(f192,plain,(
% 0.21/0.40 ((sK4 @ sK9) = $false) | ((sK3 @ sK8) = $false) | ((sK0 @ sK2 @ sK5) = $true)),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f190])).
% 0.21/0.40 thf(f190,plain,(
% 0.21/0.40 ((sK0 @ sK2 @ sK5) = $true) | (((sK4 @ sK9) | (~ (sK0 @ sK2 @ sK9))) = $false) | ((sK3 @ sK8) = $false)),
% 0.21/0.40 inference(beta_eta_normalization,[],[f189])).
% 0.21/0.40 thf(f189,plain,(
% 0.21/0.40 ((sK0 @ sK2 @ sK5) = $true) | (((^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0)))) @ sK9) = $false) | ((sK3 @ sK8) = $false)),
% 0.21/0.40 inference(sigma_clausification,[],[f188])).
% 0.21/0.40 thf(f188,plain,(
% 0.21/0.40 ((!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0))))) = $false) | ((sK3 @ sK8) = $false) | ((sK0 @ sK2 @ sK5) = $true)),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f186])).
% 0.21/0.40 thf(f186,plain,(
% 0.21/0.40 ((sK0 @ sK2 @ sK5) = $true) | ($false = ((sK3 @ sK8) | (~ (sK0 @ sK2 @ sK8)))) | ((!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0))))) = $false)),
% 0.21/0.40 inference(not_proxy_clausification,[],[f185])).
% 0.21/0.40 thf(f185,plain,(
% 0.21/0.40 ((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))) = $true) | ($false = ((sK3 @ sK8) | (~ (sK0 @ sK2 @ sK8)))) | ((sK0 @ sK2 @ sK5) = $true)),
% 0.21/0.40 inference(not_proxy_clausification,[],[f184])).
% 0.21/0.40 thf(f184,plain,(
% 0.21/0.40 ((~ (sK0 @ sK2 @ sK5)) = $false) | ($false = ((sK3 @ sK8) | (~ (sK0 @ sK2 @ sK8)))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))) = $true)),
% 0.21/0.40 inference(beta_eta_normalization,[],[f183])).
% 0.21/0.40 thf(f183,plain,(
% 0.21/0.40 ((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))) = $true) | ((~ (sK0 @ sK2 @ sK5)) = $false) | (((^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0)))) @ sK8) = $false)),
% 0.21/0.40 inference(sigma_clausification,[],[f182])).
% 0.21/0.40 thf(f182,plain,(
% 0.21/0.40 ((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0))))) = $false) | ((~ (sK0 @ sK2 @ sK5)) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))) = $true)),
% 0.21/0.40 inference(not_proxy_clausification,[],[f181])).
% 0.21/0.40 thf(f181,plain,(
% 0.21/0.40 ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))) = $true) | ((~ (sK0 @ sK2 @ sK5)) = $false)),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f159])).
% 0.21/0.40 thf(f159,plain,(
% 0.21/0.40 (((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0))))))) = $true) | ((~ (sK0 @ sK2 @ sK5)) = $false)),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f158])).
% 0.21/0.40 thf(f425,plain,(
% 0.21/0.40 spl1_23 | spl1_24 | spl1_19),
% 0.21/0.40 inference(avatar_split_clause,[],[f193,f400,f422,f418])).
% 0.21/0.40 thf(f193,plain,(
% 0.21/0.40 ((sK0 @ sK2 @ sK5) = $true) | ((sK0 @ sK2 @ sK9) = $true) | ((sK3 @ sK8) = $false)),
% 0.21/0.40 inference(not_proxy_clausification,[],[f191])).
% 0.21/0.40 thf(f191,plain,(
% 0.21/0.40 ((sK0 @ sK2 @ sK5) = $true) | ((~ (sK0 @ sK2 @ sK9)) = $false) | ((sK3 @ sK8) = $false)),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f190])).
% 0.21/0.40 thf(f416,plain,(
% 0.21/0.40 spl1_19 | spl1_22 | spl1_21),
% 0.21/0.40 inference(avatar_split_clause,[],[f198,f408,f413,f400])).
% 0.21/0.40 thf(f198,plain,(
% 0.21/0.40 ((sK0 @ sK2 @ sK5) = $true) | ((sK0 @ sK2 @ sK8) = $true) | ((sK4 @ sK10) = $false)),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f196])).
% 0.21/0.40 thf(f196,plain,(
% 0.21/0.40 ((sK0 @ sK2 @ sK5) = $true) | (((sK4 @ sK10) | (~ (sK0 @ sK2 @ sK10))) = $false) | ((sK0 @ sK2 @ sK8) = $true)),
% 0.21/0.40 inference(beta_eta_normalization,[],[f195])).
% 0.21/0.40 thf(f195,plain,(
% 0.21/0.40 ((sK0 @ sK2 @ sK5) = $true) | ((sK0 @ sK2 @ sK8) = $true) | (((^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0)))) @ sK10) = $false)),
% 0.21/0.40 inference(sigma_clausification,[],[f194])).
% 0.21/0.40 thf(f194,plain,(
% 0.21/0.40 ((sK0 @ sK2 @ sK5) = $true) | ((sK0 @ sK2 @ sK8) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0))))) = $false)),
% 0.21/0.40 inference(not_proxy_clausification,[],[f187])).
% 0.21/0.40 thf(f187,plain,(
% 0.21/0.40 ((~ (sK0 @ sK2 @ sK8)) = $false) | ((sK0 @ sK2 @ sK5) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0))))) = $false)),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f186])).
% 0.21/0.40 thf(f411,plain,(
% 0.21/0.40 spl1_19 | spl1_20 | spl1_21),
% 0.21/0.40 inference(avatar_split_clause,[],[f199,f408,f404,f400])).
% 0.21/0.40 thf(f199,plain,(
% 0.21/0.40 ((sK0 @ sK2 @ sK10) = $true) | ((sK0 @ sK2 @ sK8) = $true) | ((sK0 @ sK2 @ sK5) = $true)),
% 0.21/0.40 inference(not_proxy_clausification,[],[f197])).
% 0.21/0.40 thf(f197,plain,(
% 0.21/0.40 ((sK0 @ sK2 @ sK5) = $true) | ((sK0 @ sK2 @ sK8) = $true) | ((~ (sK0 @ sK2 @ sK10)) = $false)),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f196])).
% 0.21/0.40 thf(f322,plain,(
% 0.21/0.40 spl1_2 | spl1_2),
% 0.21/0.40 inference(avatar_split_clause,[],[f295,f318,f318])).
% 0.21/0.40 thf(f295,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i] : (((sK0 @ sK2 @ X2) = $false) | ((sK4 @ X1) = $true) | ((sK0 @ sK2 @ X1) = $false) | ((sK4 @ X2) = $true)) )),
% 0.21/0.40 inference(not_proxy_clausification,[],[f294])).
% 0.21/0.40 thf(f294,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i] : (((sK4 @ X1) = $true) | ((sK0 @ sK2 @ X2) = $false) | ((~ (sK0 @ sK2 @ X1)) = $true) | ((sK4 @ X2) = $true)) )),
% 0.21/0.40 inference(not_proxy_clausification,[],[f293])).
% 0.21/0.40 thf(f293,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i] : (((sK0 @ sK2 @ X2) = $false) | ((sK4 @ X2) = $true) | ((~ (sK4 @ X1)) = $false) | ((~ (sK0 @ sK2 @ X1)) = $true)) )),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f291])).
% 0.21/0.40 thf(f291,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i] : ((((~ (sK4 @ X1)) | (~ (sK3 @ X1))) = $false) | ((~ (sK0 @ sK2 @ X1)) = $true) | ((sK0 @ sK2 @ X2) = $false) | ((sK4 @ X2) = $true)) )),
% 0.21/0.40 inference(not_proxy_clausification,[],[f290])).
% 0.21/0.40 thf(f290,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i] : (((~ ((~ (sK4 @ X1)) | (~ (sK3 @ X1)))) = $true) | ((sK0 @ sK2 @ X2) = $false) | ((sK4 @ X2) = $true) | ((~ (sK0 @ sK2 @ X1)) = $true)) )),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f289])).
% 0.21/0.40 thf(f289,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i] : (((sK4 @ X2) = $true) | ((sK0 @ sK2 @ X2) = $false) | (((~ ((~ (sK4 @ X1)) | (~ (sK3 @ X1)))) | (~ (sK0 @ sK2 @ X1))) = $true)) )),
% 0.21/0.40 inference(not_proxy_clausification,[],[f288])).
% 0.21/0.40 thf(f288,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i] : (((sK4 @ X2) = $true) | ((~ (sK0 @ sK2 @ X2)) = $true) | (((~ ((~ (sK4 @ X1)) | (~ (sK3 @ X1)))) | (~ (sK0 @ sK2 @ X1))) = $true)) )),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f287])).
% 0.21/0.40 thf(f287,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i] : ((((sK4 @ X2) | (~ (sK0 @ sK2 @ X2))) = $true) | (((~ ((~ (sK4 @ X1)) | (~ (sK3 @ X1)))) | (~ (sK0 @ sK2 @ X1))) = $true)) )),
% 0.21/0.40 inference(beta_eta_normalization,[],[f286])).
% 0.21/0.40 thf(f286,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0)))) @ X2)) | (((~ ((~ (sK4 @ X1)) | (~ (sK3 @ X1)))) | (~ (sK0 @ sK2 @ X1))) = $true)) )),
% 0.21/0.40 inference(pi_clausification,[],[f285])).
% 0.21/0.40 thf(f285,plain,(
% 0.21/0.40 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0))))) = $true) | (((~ ((~ (sK4 @ X1)) | (~ (sK3 @ X1)))) | (~ (sK0 @ sK2 @ X1))) = $true)) )),
% 0.21/0.40 inference(beta_eta_normalization,[],[f284])).
% 0.21/0.40 thf(f284,plain,(
% 0.21/0.40 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ ((~ (sK4 @ Y0)) | (~ (sK3 @ Y0)))) | (~ (sK0 @ sK2 @ Y0)))) @ X1) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0))))) = $true)) )),
% 0.21/0.40 inference(pi_clausification,[],[f283])).
% 0.21/0.40 thf(f283,plain,(
% 0.21/0.40 ((!! @ $i @ (^[Y0 : $i]: ((~ ((~ (sK4 @ Y0)) | (~ (sK3 @ Y0)))) | (~ (sK0 @ sK2 @ Y0))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0))))) = $true)),
% 0.21/0.40 inference(not_proxy_clausification,[],[f282])).
% 0.21/0.40 thf(f282,plain,(
% 0.21/0.40 ((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ ((~ (sK4 @ Y0)) | (~ (sK3 @ Y0)))) | (~ (sK0 @ sK2 @ Y0))))) = $true)),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f251])).
% 0.21/0.40 thf(f251,plain,(
% 0.21/0.40 (((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0))))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ ((~ (sK4 @ Y0)) | (~ (sK3 @ Y0)))) | (~ (sK0 @ sK2 @ Y0))))) = $true)),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f250])).
% 0.21/0.40 thf(f250,plain,(
% 0.21/0.40 (((!! @ $i @ (^[Y0 : $i]: ((~ ((~ (sK4 @ Y0)) | (~ (sK3 @ Y0)))) | (~ (sK0 @ sK2 @ Y0))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ ((~ (sK4 @ Y0)) | (~ (sK3 @ Y0)))) | (~ (sK0 @ sK2 @ Y0))))) = $true)),
% 0.21/0.40 inference(not_proxy_clausification,[],[f152])).
% 0.21/0.40 thf(f152,plain,(
% 0.21/0.40 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ ((~ (sK4 @ Y0)) | (~ (sK3 @ Y0)))) | (~ (sK0 @ sK2 @ Y0)))))) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((~ ((~ (sK4 @ Y0)) | (~ (sK3 @ Y0)))) | (~ (sK0 @ sK2 @ Y0))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))))) = $false)),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f151])).
% 0.21/0.40 thf(f316,plain,(
% 0.21/0.40 spl1_1 | spl1_1),
% 0.21/0.40 inference(avatar_split_clause,[],[f312,f314,f314])).
% 0.21/0.40 thf(f312,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i] : (((sK3 @ X2) = $true) | ((sK0 @ sK2 @ X2) = $false) | ($true = (sK3 @ X1)) | ((sK0 @ sK2 @ X1) = $false)) )),
% 0.21/0.40 inference(not_proxy_clausification,[],[f311])).
% 0.21/0.40 thf(f311,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i] : (((sK3 @ X2) = $true) | ((sK0 @ sK2 @ X2) = $false) | ((sK0 @ sK2 @ X1) = $false) | ((~ (sK3 @ X1)) = $false)) )),
% 0.21/0.40 inference(not_proxy_clausification,[],[f307])).
% 0.21/0.40 thf(f307,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i] : (((sK0 @ sK2 @ X1) = $false) | ((sK3 @ X2) = $true) | ((~ (sK0 @ sK2 @ X2)) = $true) | ((~ (sK3 @ X1)) = $false)) )),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f306])).
% 0.21/0.40 thf(f306,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i] : ((((~ (sK4 @ X1)) | (~ (sK3 @ X1))) = $false) | ((sK0 @ sK2 @ X1) = $false) | ((~ (sK0 @ sK2 @ X2)) = $true) | ((sK3 @ X2) = $true)) )),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f305])).
% 0.21/0.40 thf(f305,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i] : ((((sK3 @ X2) | (~ (sK0 @ sK2 @ X2))) = $true) | ((sK0 @ sK2 @ X1) = $false) | (((~ (sK4 @ X1)) | (~ (sK3 @ X1))) = $false)) )),
% 0.21/0.40 inference(beta_eta_normalization,[],[f304])).
% 0.21/0.40 thf(f304,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i] : (((sK0 @ sK2 @ X1) = $false) | (((^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0)))) @ X2) = $true) | (((~ (sK4 @ X1)) | (~ (sK3 @ X1))) = $false)) )),
% 0.21/0.40 inference(pi_clausification,[],[f303])).
% 0.21/0.40 thf(f303,plain,(
% 0.21/0.40 ( ! [X1 : $i] : (((sK0 @ sK2 @ X1) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0))))) = $true) | (((~ (sK4 @ X1)) | (~ (sK3 @ X1))) = $false)) )),
% 0.21/0.40 inference(not_proxy_clausification,[],[f302])).
% 0.21/0.40 thf(f302,plain,(
% 0.21/0.40 ( ! [X1 : $i] : (((~ ((~ (sK4 @ X1)) | (~ (sK3 @ X1)))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0))))) = $true) | ((sK0 @ sK2 @ X1) = $false)) )),
% 0.21/0.40 inference(not_proxy_clausification,[],[f301])).
% 0.21/0.40 thf(f301,plain,(
% 0.21/0.40 ( ! [X1 : $i] : (((~ (sK0 @ sK2 @ X1)) = $true) | ((~ ((~ (sK4 @ X1)) | (~ (sK3 @ X1)))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0))))) = $true)) )),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f300])).
% 0.21/0.40 thf(f300,plain,(
% 0.21/0.40 ( ! [X1 : $i] : ((((~ ((~ (sK4 @ X1)) | (~ (sK3 @ X1)))) | (~ (sK0 @ sK2 @ X1))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0))))) = $true)) )),
% 0.21/0.40 inference(beta_eta_normalization,[],[f299])).
% 0.21/0.40 thf(f299,plain,(
% 0.21/0.40 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ ((~ (sK4 @ Y0)) | (~ (sK3 @ Y0)))) | (~ (sK0 @ sK2 @ Y0)))) @ X1) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0))))) = $true)) )),
% 0.21/0.40 inference(pi_clausification,[],[f298])).
% 0.21/0.40 thf(f298,plain,(
% 0.21/0.40 ((!! @ $i @ (^[Y0 : $i]: ((~ ((~ (sK4 @ Y0)) | (~ (sK3 @ Y0)))) | (~ (sK0 @ sK2 @ Y0))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0))))) = $true)),
% 0.21/0.40 inference(not_proxy_clausification,[],[f281])).
% 0.21/0.40 thf(f281,plain,(
% 0.21/0.40 ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK2 @ Y0)))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ ((~ (sK4 @ Y0)) | (~ (sK3 @ Y0)))) | (~ (sK0 @ sK2 @ Y0))))) = $true)),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f251])).
% 0.21/0.40 % SZS output end Proof for theBenchmark
% 0.21/0.40 % (4692)------------------------------
% 0.21/0.40 % (4692)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (4692)Termination reason: Refutation
% 0.21/0.40
% 0.21/0.40 % (4692)Memory used [KB]: 6012
% 0.21/0.40 % (4692)Time elapsed: 0.029 s
% 0.21/0.40 % (4692)Instructions burned: 31 (million)
% 0.21/0.40 % (4692)------------------------------
% 0.21/0.40 % (4692)------------------------------
% 0.21/0.40 % (4691)Success in time 0.028 s
% 0.21/0.40 % Vampire---4.8 exiting
%------------------------------------------------------------------------------