TSTP Solution File: SYO049^1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO049^1 : 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 : n007.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 0.18s 0.37s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO049^1 : TPTP v8.2.0. Released v4.0.0.
% 0.11/0.13 % 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
% 0.11/0.34 % Computer : n007.cluster.edu
% 0.11/0.34 % Model : x86_64 x86_64
% 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34 % Memory : 8042.1875MB
% 0.11/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Mon May 20 08:48:08 EDT 2024
% 0.11/0.34 % CPUTime :
% 0.11/0.34 This is a TH0_THM_EQU_NAR problem
% 0.11/0.34 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
% 0.18/0.35 % (19988)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)
% 0.18/0.36 % (19984)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)
% 0.18/0.36 % (19985)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)
% 0.18/0.36 % (19987)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)
% 0.18/0.36 % (19983)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.18/0.36 % (19986)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.18/0.36 % (19987)Instruction limit reached!
% 0.18/0.36 % (19987)------------------------------
% 0.18/0.36 % (19987)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.36 % (19987)Termination reason: Unknown
% 0.18/0.36 % (19987)Termination phase: shuffling
% 0.18/0.36
% 0.18/0.36 % (19987)Memory used [KB]: 1023
% 0.18/0.36 % (19987)Time elapsed: 0.003 s
% 0.18/0.36 % (19987)Instructions burned: 2 (million)
% 0.18/0.36 % (19987)------------------------------
% 0.18/0.36 % (19987)------------------------------
% 0.18/0.36 % (19988)Refutation not found, incomplete strategy
% 0.18/0.36 % (19988)------------------------------
% 0.18/0.36 % (19988)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.36 % (19988)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.36
% 0.18/0.36 % (19984)Instruction limit reached!
% 0.18/0.36 % (19984)------------------------------
% 0.18/0.36 % (19984)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.36 % (19984)Termination reason: Unknown
% 0.18/0.36 % (19984)Termination phase: Property scanning
% 0.18/0.36
% 0.18/0.36 % (19984)Memory used [KB]: 1023
% 0.18/0.36 % (19984)Time elapsed: 0.003 s
% 0.18/0.36 % (19984)Instructions burned: 4 (million)
% 0.18/0.36 % (19984)------------------------------
% 0.18/0.36 % (19984)------------------------------
% 0.18/0.36 % (19986)Instruction limit reached!
% 0.18/0.36 % (19986)------------------------------
% 0.18/0.36 % (19986)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.36 % (19986)Termination reason: Unknown
% 0.18/0.36 % (19986)Termination phase: shuffling
% 0.18/0.36
% 0.18/0.36 % (19986)Memory used [KB]: 1023
% 0.18/0.36 % (19986)Time elapsed: 0.003 s
% 0.18/0.36 % (19986)Instructions burned: 3 (million)
% 0.18/0.36 % (19986)------------------------------
% 0.18/0.36 % (19986)------------------------------
% 0.18/0.36
% 0.18/0.36 % (19988)Memory used [KB]: 5628
% 0.18/0.36 % (19988)Time elapsed: 0.007 s
% 0.18/0.36 % (19988)Instructions burned: 7 (million)
% 0.18/0.36 % (19988)------------------------------
% 0.18/0.36 % (19988)------------------------------
% 0.18/0.36 % (19991)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)
% 0.18/0.36 % (19991)Instruction limit reached!
% 0.18/0.36 % (19991)------------------------------
% 0.18/0.36 % (19991)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.36 % (19991)Termination reason: Unknown
% 0.18/0.36 % (19991)Termination phase: Property scanning
% 0.18/0.36
% 0.18/0.36 % (19991)Memory used [KB]: 1023
% 0.18/0.36 % (19991)Time elapsed: 0.003 s
% 0.18/0.36 % (19991)Instructions burned: 5 (million)
% 0.18/0.36 % (19991)------------------------------
% 0.18/0.36 % (19991)------------------------------
% 0.18/0.37 % (19989)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.18/0.37 % (19983)First to succeed.
% 0.18/0.37 % (19985)Instruction limit reached!
% 0.18/0.37 % (19985)------------------------------
% 0.18/0.37 % (19985)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.37 % (19985)Termination reason: Unknown
% 0.18/0.37 % (19985)Termination phase: Saturation
% 0.18/0.37
% 0.18/0.37 % (19985)Memory used [KB]: 5756
% 0.18/0.37 % (19985)Time elapsed: 0.013 s
% 0.18/0.37 % (19985)Instructions burned: 27 (million)
% 0.18/0.37 % (19985)------------------------------
% 0.18/0.37 % (19985)------------------------------
% 0.18/0.37 % (19992)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)
% 0.18/0.37 % (19995)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)
% 0.18/0.37 % (19996)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)
% 0.18/0.37 % (19995)Instruction limit reached!
% 0.18/0.37 % (19995)------------------------------
% 0.18/0.37 % (19995)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.37 % (19995)Termination reason: Unknown
% 0.18/0.37 % (19995)Termination phase: shuffling
% 0.18/0.37
% 0.18/0.37 % (19995)Memory used [KB]: 1023
% 0.18/0.37 % (19995)Time elapsed: 0.003 s
% 0.18/0.37 % (19995)Instructions burned: 4 (million)
% 0.18/0.37 % (19995)------------------------------
% 0.18/0.37 % (19995)------------------------------
% 0.18/0.37 % (19983)Refutation found. Thanks to Tanya!
% 0.18/0.37 % SZS status Theorem for theBenchmark
% 0.18/0.37 % SZS output start Proof for theBenchmark
% 0.18/0.37 thf(type_def_5, type, mu: $tType).
% 0.18/0.37 thf(func_def_0, type, mu: $tType).
% 0.18/0.37 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.18/0.37 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.18/0.37 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.18/0.37 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.18/0.37 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.18/0.37 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.18/0.37 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.18/0.37 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.18/0.37 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.18/0.37 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.18/0.37 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.18/0.37 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.18/0.37 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.18/0.37 thf(func_def_15, type, mtrue: $i > $o).
% 0.18/0.37 thf(func_def_16, type, mfalse: $i > $o).
% 0.18/0.37 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.18/0.37 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.18/0.37 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.18/0.37 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.18/0.37 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.18/0.37 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.18/0.37 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.18/0.37 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.18/0.37 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.18/0.37 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.18/0.37 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.18/0.37 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.18/0.37 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.18/0.37 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.18/0.37 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.18/0.37 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.18/0.37 thf(func_def_48, type, sK0: $i > $i > $o).
% 0.18/0.37 thf(func_def_51, type, sK3: $i > $o).
% 0.18/0.37 thf(func_def_52, type, sK4: $i > $o).
% 0.18/0.37 thf(f566,plain,(
% 0.18/0.37 $false),
% 0.18/0.37 inference(avatar_sat_refutation,[],[f330,f336,f417,f422,f427,f428,f437,f442,f451,f456,f470,f477,f493,f508,f535,f550,f565])).
% 0.18/0.37 thf(f565,plain,(
% 0.18/0.37 ~spl1_1 | ~spl1_22 | ~spl1_24),
% 0.18/0.37 inference(avatar_contradiction_clause,[],[f564])).
% 0.18/0.37 thf(f564,plain,(
% 0.18/0.37 $false | (~spl1_1 | ~spl1_22 | ~spl1_24)),
% 0.18/0.37 inference(trivial_inequality_removal,[],[f561])).
% 0.18/0.37 thf(f561,plain,(
% 0.18/0.37 ($false = $true) | (~spl1_1 | ~spl1_22 | ~spl1_24)),
% 0.18/0.37 inference(superposition,[],[f441,f559])).
% 0.18/0.37 thf(f559,plain,(
% 0.18/0.37 ($false = (sK4 @ sK8)) | (~spl1_1 | ~spl1_22)),
% 0.18/0.37 inference(trivial_inequality_removal,[],[f553])).
% 0.18/0.37 thf(f553,plain,(
% 0.18/0.37 ($false = (sK4 @ sK8)) | ($false = $true) | (~spl1_1 | ~spl1_22)),
% 0.18/0.37 inference(superposition,[],[f432,f329])).
% 0.18/0.37 thf(f329,plain,(
% 0.18/0.37 ( ! [X2 : $i] : (($false = (sK0 @ sK2 @ X2)) | ($false = (sK4 @ X2))) ) | ~spl1_1),
% 0.18/0.37 inference(avatar_component_clause,[],[f328])).
% 0.18/0.37 thf(f328,plain,(
% 0.18/0.37 spl1_1 <=> ! [X2] : (($false = (sK4 @ X2)) | ($false = (sK0 @ sK2 @ X2)))),
% 0.18/0.37 introduced(avatar_definition,[new_symbols(naming,[spl1_1])])).
% 0.18/0.37 thf(f432,plain,(
% 0.18/0.37 ($true = (sK0 @ sK2 @ sK8)) | ~spl1_22),
% 0.18/0.37 inference(avatar_component_clause,[],[f430])).
% 0.18/0.37 thf(f430,plain,(
% 0.18/0.37 spl1_22 <=> ($true = (sK0 @ sK2 @ sK8))),
% 0.18/0.37 introduced(avatar_definition,[new_symbols(naming,[spl1_22])])).
% 0.18/0.37 thf(f441,plain,(
% 0.18/0.37 ($true = (sK4 @ sK8)) | ~spl1_24),
% 0.18/0.37 inference(avatar_component_clause,[],[f439])).
% 0.18/0.37 thf(f439,plain,(
% 0.18/0.37 spl1_24 <=> ($true = (sK4 @ sK8))),
% 0.18/0.37 introduced(avatar_definition,[new_symbols(naming,[spl1_24])])).
% 0.18/0.37 thf(f550,plain,(
% 0.18/0.37 ~spl1_1 | ~spl1_26 | ~spl1_27),
% 0.18/0.37 inference(avatar_contradiction_clause,[],[f549])).
% 0.18/0.37 thf(f549,plain,(
% 0.18/0.37 $false | (~spl1_1 | ~spl1_26 | ~spl1_27)),
% 0.18/0.37 inference(trivial_inequality_removal,[],[f545])).
% 0.18/0.37 thf(f545,plain,(
% 0.18/0.37 ($false = $true) | (~spl1_1 | ~spl1_26 | ~spl1_27)),
% 0.18/0.37 inference(superposition,[],[f543,f455])).
% 0.18/0.37 thf(f455,plain,(
% 0.18/0.37 ($true = (sK4 @ sK7)) | ~spl1_27),
% 0.18/0.37 inference(avatar_component_clause,[],[f453])).
% 0.18/0.37 thf(f453,plain,(
% 0.18/0.37 spl1_27 <=> ($true = (sK4 @ sK7))),
% 0.18/0.37 introduced(avatar_definition,[new_symbols(naming,[spl1_27])])).
% 0.18/0.37 thf(f543,plain,(
% 0.18/0.37 ($false = (sK4 @ sK7)) | (~spl1_1 | ~spl1_26)),
% 0.18/0.37 inference(trivial_inequality_removal,[],[f540])).
% 0.18/0.37 thf(f540,plain,(
% 0.18/0.37 ($false = $true) | ($false = (sK4 @ sK7)) | (~spl1_1 | ~spl1_26)),
% 0.18/0.37 inference(superposition,[],[f329,f450])).
% 0.18/0.37 thf(f450,plain,(
% 0.18/0.37 ((sK0 @ sK2 @ sK7) = $true) | ~spl1_26),
% 0.18/0.37 inference(avatar_component_clause,[],[f448])).
% 0.18/0.37 thf(f448,plain,(
% 0.18/0.37 spl1_26 <=> ((sK0 @ sK2 @ sK7) = $true)),
% 0.18/0.37 introduced(avatar_definition,[new_symbols(naming,[spl1_26])])).
% 0.18/0.37 thf(f535,plain,(
% 0.18/0.37 ~spl1_2 | ~spl1_23 | ~spl1_25),
% 0.18/0.37 inference(avatar_contradiction_clause,[],[f534])).
% 0.18/0.37 thf(f534,plain,(
% 0.18/0.37 $false | (~spl1_2 | ~spl1_23 | ~spl1_25)),
% 0.18/0.37 inference(trivial_inequality_removal,[],[f530])).
% 0.18/0.37 thf(f530,plain,(
% 0.18/0.37 ($false = $true) | (~spl1_2 | ~spl1_23 | ~spl1_25)),
% 0.18/0.37 inference(superposition,[],[f528,f446])).
% 0.18/0.37 thf(f446,plain,(
% 0.18/0.37 ((sK3 @ sK6) = $true) | ~spl1_25),
% 0.18/0.37 inference(avatar_component_clause,[],[f444])).
% 0.18/0.37 thf(f444,plain,(
% 0.18/0.37 spl1_25 <=> ((sK3 @ sK6) = $true)),
% 0.18/0.37 introduced(avatar_definition,[new_symbols(naming,[spl1_25])])).
% 0.18/0.37 thf(f528,plain,(
% 0.18/0.37 ($false = (sK3 @ sK6)) | (~spl1_2 | ~spl1_23)),
% 0.18/0.37 inference(trivial_inequality_removal,[],[f524])).
% 0.18/0.37 thf(f524,plain,(
% 0.18/0.37 ($false = (sK3 @ sK6)) | ($false = $true) | (~spl1_2 | ~spl1_23)),
% 0.18/0.37 inference(superposition,[],[f333,f436])).
% 0.18/0.37 thf(f436,plain,(
% 0.18/0.37 ((sK0 @ sK2 @ sK6) = $true) | ~spl1_23),
% 0.18/0.37 inference(avatar_component_clause,[],[f434])).
% 0.18/0.37 thf(f434,plain,(
% 0.18/0.37 spl1_23 <=> ((sK0 @ sK2 @ sK6) = $true)),
% 0.18/0.37 introduced(avatar_definition,[new_symbols(naming,[spl1_23])])).
% 0.18/0.37 thf(f333,plain,(
% 0.18/0.37 ( ! [X1 : $i] : (($false = (sK0 @ sK2 @ X1)) | ($false = (sK3 @ X1))) ) | ~spl1_2),
% 0.18/0.37 inference(avatar_component_clause,[],[f332])).
% 0.18/0.37 thf(f332,plain,(
% 0.18/0.37 spl1_2 <=> ! [X1] : (($false = (sK3 @ X1)) | ($false = (sK0 @ sK2 @ X1)))),
% 0.18/0.37 introduced(avatar_definition,[new_symbols(naming,[spl1_2])])).
% 0.18/0.37 thf(f508,plain,(
% 0.18/0.37 ~spl1_2 | ~spl1_19 | ~spl1_20),
% 0.18/0.37 inference(avatar_contradiction_clause,[],[f507])).
% 0.18/0.37 thf(f507,plain,(
% 0.18/0.37 $false | (~spl1_2 | ~spl1_19 | ~spl1_20)),
% 0.18/0.37 inference(trivial_inequality_removal,[],[f503])).
% 0.18/0.37 thf(f503,plain,(
% 0.18/0.37 ($false = $true) | (~spl1_2 | ~spl1_19 | ~spl1_20)),
% 0.18/0.37 inference(superposition,[],[f502,f421])).
% 0.18/0.37 thf(f421,plain,(
% 0.18/0.37 ($true = (sK3 @ sK9)) | ~spl1_20),
% 0.18/0.37 inference(avatar_component_clause,[],[f419])).
% 0.18/0.37 thf(f419,plain,(
% 0.18/0.37 spl1_20 <=> ($true = (sK3 @ sK9))),
% 0.18/0.37 introduced(avatar_definition,[new_symbols(naming,[spl1_20])])).
% 0.18/0.37 thf(f502,plain,(
% 0.18/0.37 ($false = (sK3 @ sK9)) | (~spl1_2 | ~spl1_19)),
% 0.18/0.37 inference(trivial_inequality_removal,[],[f497])).
% 0.18/0.37 thf(f497,plain,(
% 0.18/0.37 ($false = $true) | ($false = (sK3 @ sK9)) | (~spl1_2 | ~spl1_19)),
% 0.18/0.37 inference(superposition,[],[f333,f416])).
% 0.18/0.37 thf(f416,plain,(
% 0.18/0.37 ($true = (sK0 @ sK2 @ sK9)) | ~spl1_19),
% 0.18/0.37 inference(avatar_component_clause,[],[f414])).
% 0.18/0.37 thf(f414,plain,(
% 0.18/0.37 spl1_19 <=> ($true = (sK0 @ sK2 @ sK9))),
% 0.18/0.37 introduced(avatar_definition,[new_symbols(naming,[spl1_19])])).
% 0.18/0.37 thf(f493,plain,(
% 0.18/0.37 ~spl1_1 | ~spl1_18 | ~spl1_21),
% 0.18/0.37 inference(avatar_contradiction_clause,[],[f492])).
% 0.18/0.37 thf(f492,plain,(
% 0.18/0.37 $false | (~spl1_1 | ~spl1_18 | ~spl1_21)),
% 0.18/0.37 inference(trivial_inequality_removal,[],[f488])).
% 0.18/0.37 thf(f488,plain,(
% 0.18/0.37 ($false = $true) | (~spl1_1 | ~spl1_18 | ~spl1_21)),
% 0.18/0.37 inference(superposition,[],[f485,f426])).
% 0.18/0.37 thf(f426,plain,(
% 0.18/0.37 ($true = (sK4 @ sK10)) | ~spl1_21),
% 0.18/0.37 inference(avatar_component_clause,[],[f424])).
% 0.18/0.37 thf(f424,plain,(
% 0.18/0.37 spl1_21 <=> ($true = (sK4 @ sK10))),
% 0.18/0.37 introduced(avatar_definition,[new_symbols(naming,[spl1_21])])).
% 0.18/0.37 thf(f485,plain,(
% 0.18/0.37 ($false = (sK4 @ sK10)) | (~spl1_1 | ~spl1_18)),
% 0.18/0.37 inference(trivial_inequality_removal,[],[f483])).
% 0.18/0.37 thf(f483,plain,(
% 0.18/0.37 ($false = $true) | ($false = (sK4 @ sK10)) | (~spl1_1 | ~spl1_18)),
% 0.18/0.37 inference(superposition,[],[f329,f412])).
% 0.18/0.37 thf(f412,plain,(
% 0.18/0.37 ((sK0 @ sK2 @ sK10) = $true) | ~spl1_18),
% 0.18/0.37 inference(avatar_component_clause,[],[f410])).
% 0.18/0.37 thf(f410,plain,(
% 0.18/0.37 spl1_18 <=> ((sK0 @ sK2 @ sK10) = $true)),
% 0.18/0.37 introduced(avatar_definition,[new_symbols(naming,[spl1_18])])).
% 0.18/0.37 thf(f477,plain,(
% 0.18/0.37 ~spl1_1 | ~spl1_15 | ~spl1_17),
% 0.18/0.37 inference(avatar_contradiction_clause,[],[f476])).
% 0.18/0.37 thf(f476,plain,(
% 0.18/0.37 $false | (~spl1_1 | ~spl1_15 | ~spl1_17)),
% 0.18/0.37 inference(trivial_inequality_removal,[],[f473])).
% 0.18/0.37 thf(f473,plain,(
% 0.18/0.37 ($false = $true) | (~spl1_1 | ~spl1_15 | ~spl1_17)),
% 0.18/0.37 inference(superposition,[],[f460,f406])).
% 0.18/0.37 thf(f406,plain,(
% 0.18/0.37 ($true = (sK4 @ sK5)) | ~spl1_17),
% 0.18/0.37 inference(avatar_component_clause,[],[f404])).
% 0.18/0.37 thf(f404,plain,(
% 0.18/0.37 spl1_17 <=> ($true = (sK4 @ sK5))),
% 0.18/0.37 introduced(avatar_definition,[new_symbols(naming,[spl1_17])])).
% 0.18/0.37 thf(f460,plain,(
% 0.18/0.37 ($false = (sK4 @ sK5)) | (~spl1_1 | ~spl1_15)),
% 0.18/0.37 inference(trivial_inequality_removal,[],[f458])).
% 0.18/0.37 thf(f458,plain,(
% 0.18/0.37 ($false = $true) | ($false = (sK4 @ sK5)) | (~spl1_1 | ~spl1_15)),
% 0.18/0.37 inference(superposition,[],[f396,f329])).
% 0.18/0.37 thf(f396,plain,(
% 0.18/0.37 ($true = (sK0 @ sK2 @ sK5)) | ~spl1_15),
% 0.18/0.37 inference(avatar_component_clause,[],[f394])).
% 0.18/0.37 thf(f394,plain,(
% 0.18/0.37 spl1_15 <=> ($true = (sK0 @ sK2 @ sK5))),
% 0.18/0.37 introduced(avatar_definition,[new_symbols(naming,[spl1_15])])).
% 0.18/0.37 thf(f470,plain,(
% 0.18/0.37 ~spl1_2 | ~spl1_15 | ~spl1_16),
% 0.18/0.37 inference(avatar_contradiction_clause,[],[f469])).
% 0.18/0.37 thf(f469,plain,(
% 0.18/0.37 $false | (~spl1_2 | ~spl1_15 | ~spl1_16)),
% 0.18/0.37 inference(trivial_inequality_removal,[],[f465])).
% 0.18/0.37 thf(f465,plain,(
% 0.18/0.37 ($false = $true) | (~spl1_2 | ~spl1_15 | ~spl1_16)),
% 0.18/0.37 inference(superposition,[],[f464,f402])).
% 0.18/0.37 thf(f402,plain,(
% 0.18/0.37 ((sK3 @ sK5) = $true) | ~spl1_16),
% 0.18/0.37 inference(avatar_component_clause,[],[f400])).
% 0.18/0.37 thf(f400,plain,(
% 0.18/0.37 spl1_16 <=> ((sK3 @ sK5) = $true)),
% 0.18/0.37 introduced(avatar_definition,[new_symbols(naming,[spl1_16])])).
% 0.18/0.37 thf(f464,plain,(
% 0.18/0.37 ($false = (sK3 @ sK5)) | (~spl1_2 | ~spl1_15)),
% 0.18/0.37 inference(trivial_inequality_removal,[],[f461])).
% 0.18/0.37 thf(f461,plain,(
% 0.18/0.37 ($false = $true) | ($false = (sK3 @ sK5)) | (~spl1_2 | ~spl1_15)),
% 0.18/0.37 inference(superposition,[],[f333,f396])).
% 0.18/0.37 thf(f456,plain,(
% 0.18/0.37 spl1_25 | spl1_16 | spl1_27 | spl1_17),
% 0.18/0.37 inference(avatar_split_clause,[],[f175,f404,f453,f400,f444])).
% 0.18/0.37 thf(f175,plain,(
% 0.18/0.37 ((sK3 @ sK5) = $true) | ((sK3 @ sK6) = $true) | ($true = (sK4 @ sK7)) | ($true = (sK4 @ sK5))),
% 0.18/0.37 inference(not_proxy_clausification,[],[f174])).
% 0.18/0.37 thf(f174,plain,(
% 0.18/0.37 ((sK3 @ sK5) = $true) | ($true = (sK4 @ sK5)) | ((sK3 @ sK6) = $true) | ($false = (~ (sK4 @ sK7)))),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f172])).
% 0.18/0.37 thf(f172,plain,(
% 0.18/0.37 ($true = (sK4 @ sK5)) | ($false = ((~ (sK4 @ sK7)) | (~ (sK0 @ sK2 @ sK7)))) | ((sK3 @ sK5) = $true) | ((sK3 @ sK6) = $true)),
% 0.18/0.37 inference(beta_eta_normalization,[],[f171])).
% 0.18/0.37 thf(f171,plain,(
% 0.18/0.37 ($false = ((^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))) @ sK7)) | ((sK3 @ sK5) = $true) | ($true = (sK4 @ sK5)) | ((sK3 @ sK6) = $true)),
% 0.18/0.37 inference(sigma_clausification,[],[f170])).
% 0.18/0.37 thf(f170,plain,(
% 0.18/0.37 ((sK3 @ sK5) = $true) | ($true = (sK4 @ sK5)) | ((sK3 @ sK6) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))) = $false)),
% 0.18/0.37 inference(not_proxy_clausification,[],[f169])).
% 0.18/0.37 thf(f169,plain,(
% 0.18/0.37 ($true = (sK4 @ sK5)) | ((sK3 @ sK5) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) = $true) | ((sK3 @ sK6) = $true)),
% 0.18/0.37 inference(not_proxy_clausification,[],[f168])).
% 0.18/0.37 thf(f168,plain,(
% 0.18/0.37 ($false = (~ (sK3 @ sK6))) | ($true = (sK4 @ sK5)) | ((sK3 @ sK5) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) = $true)),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f167])).
% 0.18/0.37 thf(f167,plain,(
% 0.18/0.37 ($true = ((sK3 @ sK5) | (sK4 @ sK5))) | ($false = (~ (sK3 @ sK6))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) = $true)),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f165])).
% 0.18/0.37 thf(f165,plain,(
% 0.18/0.37 ($false = ((~ (sK3 @ sK6)) | (~ (sK0 @ sK2 @ sK6)))) | ($true = ((sK3 @ sK5) | (sK4 @ sK5))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) = $true)),
% 0.18/0.37 inference(beta_eta_normalization,[],[f164])).
% 0.18/0.37 thf(f164,plain,(
% 0.18/0.37 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) = $true) | ($false = ((^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))) @ sK6)) | ($true = ((sK3 @ sK5) | (sK4 @ sK5)))),
% 0.18/0.37 inference(sigma_clausification,[],[f163])).
% 0.18/0.37 thf(f163,plain,(
% 0.18/0.37 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) = $true) | ($true = ((sK3 @ sK5) | (sK4 @ sK5)))),
% 0.18/0.37 inference(not_proxy_clausification,[],[f162])).
% 0.18/0.37 thf(f162,plain,(
% 0.18/0.37 ($false = (~ ((sK3 @ sK5) | (sK4 @ sK5)))) | ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) = $true)),
% 0.18/0.37 inference(not_proxy_clausification,[],[f161])).
% 0.18/0.37 thf(f161,plain,(
% 0.18/0.37 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) = $true) | ($false = (~ ((sK3 @ sK5) | (sK4 @ sK5))))),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f160])).
% 0.18/0.37 thf(f160,plain,(
% 0.18/0.37 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))))) = $true) | ($false = (~ ((sK3 @ sK5) | (sK4 @ sK5))))),
% 0.18/0.37 inference(not_proxy_clausification,[],[f159])).
% 0.18/0.37 thf(f159,plain,(
% 0.18/0.37 ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))))) = $false) | ($false = (~ ((sK3 @ sK5) | (sK4 @ sK5))))),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f157])).
% 0.18/0.37 thf(f157,plain,(
% 0.18/0.37 ($false = ((~ ((sK3 @ sK5) | (sK4 @ sK5))) | (~ (sK0 @ sK2 @ sK5)))) | ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))))) = $false)),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f155])).
% 0.18/0.37 thf(f155,plain,(
% 0.18/0.37 ($false = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ ((sK3 @ Y0) | (sK4 @ Y0))) | (~ (sK0 @ sK2 @ Y0)))))))) | ($false = ((~ ((sK3 @ sK5) | (sK4 @ sK5))) | (~ (sK0 @ sK2 @ sK5))))),
% 0.18/0.37 inference(beta_eta_normalization,[],[f154])).
% 0.18/0.37 thf(f154,plain,(
% 0.18/0.37 ($false = ((^[Y0 : $i]: ((~ ((sK3 @ Y0) | (sK4 @ Y0))) | (~ (sK0 @ sK2 @ Y0)))) @ sK5)) | ($false = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ ((sK3 @ Y0) | (sK4 @ Y0))) | (~ (sK0 @ sK2 @ Y0))))))))),
% 0.18/0.37 inference(sigma_clausification,[],[f153])).
% 0.18/0.37 thf(f153,plain,(
% 0.18/0.37 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ ((sK3 @ Y0) | (sK4 @ Y0))) | (~ (sK0 @ sK2 @ Y0)))))) | ($false = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ ((sK3 @ Y0) | (sK4 @ Y0))) | (~ (sK0 @ sK2 @ Y0))))))))),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f151])).
% 0.18/0.37 thf(f151,plain,(
% 0.18/0.37 (((!! @ $i @ (^[Y0 : $i]: ((~ ((sK3 @ Y0) | (sK4 @ Y0))) | (~ (sK0 @ sK2 @ Y0))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))))) = $false) | ($false = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ ((sK3 @ Y0) | (sK4 @ Y0))) | (~ (sK0 @ sK2 @ Y0))))))))),
% 0.18/0.37 inference(not_proxy_clausification,[],[f150])).
% 0.18/0.37 thf(f150,plain,(
% 0.18/0.37 ($true = (~ ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ ((sK3 @ Y0) | (sK4 @ Y0))) | (~ (sK0 @ sK2 @ Y0))))))))) | (((!! @ $i @ (^[Y0 : $i]: ((~ ((sK3 @ Y0) | (sK4 @ Y0))) | (~ (sK0 @ sK2 @ Y0))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))))) = $false)),
% 0.18/0.37 inference(not_proxy_clausification,[],[f149])).
% 0.18/0.37 thf(f149,plain,(
% 0.18/0.37 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: ((~ ((sK3 @ Y0) | (sK4 @ Y0))) | (~ (sK0 @ sK2 @ Y0))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))))))) | ($true = (~ ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ ((sK3 @ Y0) | (sK4 @ Y0))) | (~ (sK0 @ sK2 @ Y0)))))))))),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f148])).
% 0.18/0.37 thf(f148,plain,(
% 0.18/0.37 ($true = ((~ ((!! @ $i @ (^[Y0 : $i]: ((~ ((sK3 @ Y0) | (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)) | (~ (sK0 @ sK2 @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ ((sK3 @ Y0) | (sK4 @ Y0))) | (~ (sK0 @ sK2 @ Y0))))))))))),
% 0.18/0.37 inference(not_proxy_clausification,[],[f147])).
% 0.18/0.37 thf(f147,plain,(
% 0.18/0.37 ($false = (~ ((~ ((!! @ $i @ (^[Y0 : $i]: ((~ ((sK3 @ Y0) | (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)) | (~ (sK0 @ sK2 @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ ((sK3 @ Y0) | (sK4 @ Y0))) | (~ (sK0 @ sK2 @ Y0)))))))))))),
% 0.18/0.37 inference(beta_eta_normalization,[],[f146])).
% 0.18/0.37 thf(f146,plain,(
% 0.18/0.37 ($false = ((^[Y0 : $i > $o]: (~ ((~ ((!! @ $i @ (^[Y1 : $i]: ((~ ((sK3 @ Y1) | (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)) | (~ (sK0 @ sK2 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ ((sK3 @ Y1) | (Y0 @ Y1))) | (~ (sK0 @ sK2 @ Y1))))))))))) @ sK4))),
% 0.18/0.37 inference(sigma_clausification,[],[f145])).
% 0.18/0.37 thf(f145,plain,(
% 0.18/0.37 ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (~ ((~ ((!! @ $i @ (^[Y1 : $i]: ((~ ((sK3 @ Y1) | (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)) | (~ (sK0 @ sK2 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ ((sK3 @ Y1) | (Y0 @ Y1))) | (~ (sK0 @ sK2 @ Y1)))))))))))))),
% 0.18/0.37 inference(beta_eta_normalization,[],[f144])).
% 0.18/0.37 thf(f144,plain,(
% 0.18/0.37 ($false = ((^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (~ ((~ ((!! @ $i @ (^[Y2 : $i]: ((~ ((Y0 @ Y2) | (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)) | (~ (sK0 @ sK2 @ Y2)))))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ ((Y0 @ Y2) | (Y1 @ Y2))) | (~ (sK0 @ sK2 @ Y2))))))))))))) @ sK3))),
% 0.18/0.37 inference(sigma_clausification,[],[f143])).
% 0.18/0.37 thf(f143,plain,(
% 0.18/0.37 ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (~ ((~ ((!! @ $i @ (^[Y2 : $i]: ((~ ((Y0 @ Y2) | (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)) | (~ (sK0 @ sK2 @ Y2)))))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ ((Y0 @ Y2) | (Y1 @ Y2))) | (~ (sK0 @ sK2 @ Y2)))))))))))))))),
% 0.18/0.37 inference(beta_eta_normalization,[],[f142])).
% 0.18/0.37 thf(f142,plain,(
% 0.18/0.37 ($false = ((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (~ ((~ ((!! @ $i @ (^[Y3 : $i]: ((~ ((Y1 @ Y3) | (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)) | (~ (sK0 @ Y0 @ Y3)))))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ ((Y1 @ Y3) | (Y2 @ Y3))) | (~ (sK0 @ Y0 @ Y3))))))))))))))) @ sK2))),
% 0.18/0.37 inference(sigma_clausification,[],[f141])).
% 0.18/0.37 thf(f141,plain,(
% 0.18/0.37 ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (~ ((~ ((!! @ $i @ (^[Y3 : $i]: ((~ ((Y1 @ Y3) | (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)) | (~ (sK0 @ Y0 @ Y3)))))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ ((Y1 @ Y3) | (Y2 @ Y3))) | (~ (sK0 @ Y0 @ Y3)))))))))))))))))),
% 0.18/0.37 inference(boolean_simplification,[],[f140])).
% 0.18/0.37 thf(f140,plain,(
% 0.18/0.37 ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (~ ((~ ((~ (~ (!! @ $i @ (^[Y3 : $i]: ((~ ((Y1 @ Y3) | (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)) | (~ (sK0 @ Y0 @ Y3)))))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ ((Y1 @ Y3) | (Y2 @ Y3))) | (~ (sK0 @ Y0 @ Y3)))))))))))))))))),
% 0.18/0.37 inference(beta_eta_normalization,[],[f139])).
% 0.18/0.37 thf(f139,plain,(
% 0.18/0.37 ($true != ((^[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]: ((Y6 @ Y8) | (Y7 @ 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]: ((Y6 @ Y8) | (Y7 @ 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]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ Y3 @ Y2))))) @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7) | (~ (Y4 @ Y6 @ Y7)))))))))) @ Y2 @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ sK0 @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ Y0 @ Y1)) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7) | (~ (Y4 @ Y6 @ Y7)))))))))) @ Y2 @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ sK0 @ Y0) @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7) | (~ (Y4 @ Y6 @ Y7)))))))))) @ Y2 @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ sK0 @ Y1)))))))))),
% 0.18/0.37 inference(definition_unfolding,[],[f109,f104,f115,f115,f133,f138,f125,f125,f138,f138])).
% 0.18/0.37 thf(f125,plain,(
% 0.18/0.37 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.18/0.37 inference(cnf_transformation,[],[f38])).
% 0.18/0.37 thf(f38,plain,(
% 0.18/0.37 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.18/0.37 inference(fool_elimination,[],[f37])).
% 0.18/0.37 thf(f37,plain,(
% 0.18/0.37 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 0.18/0.37 inference(rectify,[],[f4])).
% 0.18/0.37 thf(f4,axiom,(
% 0.18/0.37 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))))),
% 0.18/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.18/0.37 thf(f138,plain,(
% 0.18/0.37 (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5) | (~ (Y2 @ Y4 @ Y5)))))))))) @ Y0 @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 0.18/0.37 inference(definition_unfolding,[],[f111,f101,f102,f101])).
% 0.18/0.37 thf(f102,plain,(
% 0.18/0.37 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (Y0 @ Y2 @ Y3)))))))))))),
% 0.18/0.37 inference(cnf_transformation,[],[f53])).
% 0.18/0.37 thf(f53,plain,(
% 0.18/0.37 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (Y0 @ Y2 @ Y3)))))))))))),
% 0.18/0.37 inference(fool_elimination,[],[f52])).
% 0.18/0.37 thf(f52,plain,(
% 0.18/0.37 ((^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i] : (! [X3] : (~(X0 @ X2 @ X3) | (X1 @ X3)))) = mbox)),
% 0.18/0.37 inference(rectify,[],[f16])).
% 0.18/0.37 thf(f16,axiom,(
% 0.18/0.37 ((^[X6 : $i > $i > $o, X3 : $i > $o, X2 : $i] : (! [X7] : (~(X6 @ X2 @ X7) | (X3 @ X7)))) = mbox)),
% 0.18/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox)).
% 0.18/0.37 thf(f101,plain,(
% 0.18/0.37 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.18/0.37 inference(cnf_transformation,[],[f67])).
% 0.18/0.37 thf(f67,plain,(
% 0.18/0.37 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.18/0.37 inference(fool_elimination,[],[f66])).
% 0.18/0.37 thf(f66,plain,(
% 0.18/0.37 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.18/0.37 inference(rectify,[],[f3])).
% 0.18/0.37 thf(f3,axiom,(
% 0.18/0.37 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.18/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.18/0.37 thf(f111,plain,(
% 0.18/0.37 (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mbox @ Y0 @ (mnot @ Y1)))))))),
% 0.18/0.37 inference(cnf_transformation,[],[f55])).
% 0.18/0.37 thf(f55,plain,(
% 0.18/0.37 (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mbox @ Y0 @ (mnot @ Y1)))))))),
% 0.18/0.37 inference(fool_elimination,[],[f54])).
% 0.18/0.37 thf(f54,plain,(
% 0.18/0.37 (mdia = (^[X0 : $i > $i > $o, X1 : $i > $o] : (mnot @ (mbox @ X0 @ (mnot @ X1)))))),
% 0.18/0.37 inference(rectify,[],[f17])).
% 0.18/0.37 thf(f17,axiom,(
% 0.18/0.37 (mdia = (^[X6 : $i > $i > $o, X3 : $i > $o] : (mnot @ (mbox @ X6 @ (mnot @ X3)))))),
% 0.18/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia)).
% 0.18/0.37 thf(f133,plain,(
% 0.18/0.37 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y1 @ Y0))))))),
% 0.18/0.37 inference(definition_unfolding,[],[f103,f130,f131,f131])).
% 0.18/0.37 thf(f131,plain,(
% 0.18/0.37 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.18/0.37 inference(definition_unfolding,[],[f126,f125,f101])).
% 0.18/0.37 thf(f126,plain,(
% 0.18/0.37 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.18/0.37 inference(cnf_transformation,[],[f94])).
% 0.18/0.37 thf(f94,plain,(
% 0.18/0.37 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.18/0.37 inference(fool_elimination,[],[f93])).
% 0.18/0.37 thf(f93,plain,(
% 0.18/0.37 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.18/0.37 inference(rectify,[],[f6])).
% 0.18/0.37 thf(f6,axiom,(
% 0.18/0.37 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.18/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.18/0.37 thf(f130,plain,(
% 0.18/0.37 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 0.18/0.37 inference(definition_unfolding,[],[f121,f101,f125,f101,f101])).
% 0.18/0.37 thf(f121,plain,(
% 0.18/0.37 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.18/0.37 inference(cnf_transformation,[],[f63])).
% 0.18/0.37 thf(f63,plain,(
% 0.18/0.37 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.18/0.37 inference(fool_elimination,[],[f62])).
% 0.18/0.37 thf(f62,plain,(
% 0.18/0.37 (mand = (^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))))),
% 0.18/0.37 inference(rectify,[],[f5])).
% 0.18/0.37 thf(f5,axiom,(
% 0.18/0.37 (mand = (^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))))),
% 0.18/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand)).
% 0.18/0.37 thf(f103,plain,(
% 0.18/0.37 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.18/0.37 inference(cnf_transformation,[],[f77])).
% 0.18/0.37 thf(f77,plain,(
% 0.18/0.37 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.18/0.37 inference(fool_elimination,[],[f76])).
% 0.18/0.37 thf(f76,plain,(
% 0.18/0.37 (mequiv = (^[X0 : $i > $o, X1 : $i > $o] : (mand @ (mimplies @ X0 @ X1) @ (mimplies @ X1 @ X0))))),
% 0.18/0.37 inference(rectify,[],[f8])).
% 0.18/0.37 thf(f8,axiom,(
% 0.18/0.37 (mequiv = (^[X3 : $i > $o, X4 : $i > $o] : (mand @ (mimplies @ X3 @ X4) @ (mimplies @ X4 @ X3))))),
% 0.18/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mequiv)).
% 0.18/0.37 thf(f115,plain,(
% 0.18/0.37 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.18/0.37 inference(cnf_transformation,[],[f59])).
% 0.18/0.37 thf(f59,plain,(
% 0.18/0.37 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.18/0.37 inference(fool_elimination,[],[f58])).
% 0.18/0.37 thf(f58,plain,(
% 0.18/0.37 (mforall_prop = (^[X0 : ($i > $o) > $i > $o, X1 : $i] : (! [X2 : $i > $o] : (X0 @ X2 @ X1))))),
% 0.18/0.37 inference(rectify,[],[f11])).
% 0.18/0.37 thf(f11,axiom,(
% 0.18/0.37 (mforall_prop = (^[X3 : ($i > $o) > $i > $o, X2 : $i] : (! [X5 : $i > $o] : (X3 @ X5 @ X2))))),
% 0.18/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_prop)).
% 0.18/0.37 thf(f104,plain,(
% 0.18/0.37 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.18/0.37 inference(cnf_transformation,[],[f83])).
% 0.18/0.37 thf(f83,plain,(
% 0.18/0.37 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.18/0.37 inference(fool_elimination,[],[f82])).
% 0.18/0.37 thf(f82,plain,(
% 0.18/0.37 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.18/0.37 inference(rectify,[],[f28])).
% 0.18/0.37 thf(f28,axiom,(
% 0.18/0.37 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.18/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.18/0.37 thf(f109,plain,(
% 0.18/0.37 ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mforall_prop @ (^[Y1 : $i > $o]: (mequiv @ (mdia @ sK0 @ (mor @ Y0 @ Y1)) @ (mor @ (mdia @ sK0 @ Y0) @ (mdia @ sK0 @ Y1)))))))) != $true)),
% 0.18/0.37 inference(cnf_transformation,[],[f97])).
% 0.18/0.37 thf(f97,plain,(
% 0.18/0.37 ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mforall_prop @ (^[Y1 : $i > $o]: (mequiv @ (mdia @ sK0 @ (mor @ Y0 @ Y1)) @ (mor @ (mdia @ sK0 @ Y0) @ (mdia @ sK0 @ Y1)))))))) != $true)),
% 0.18/0.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f95,f96])).
% 0.18/0.37 thf(f96,plain,(
% 0.18/0.37 ? [X0 : $i > $i > $o] : ($true != (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mforall_prop @ (^[Y1 : $i > $o]: (mequiv @ (mdia @ X0 @ (mor @ Y0 @ Y1)) @ (mor @ (mdia @ X0 @ Y0) @ (mdia @ X0 @ Y1))))))))) => ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mforall_prop @ (^[Y1 : $i > $o]: (mequiv @ (mdia @ sK0 @ (mor @ Y0 @ Y1)) @ (mor @ (mdia @ sK0 @ Y0) @ (mdia @ sK0 @ Y1)))))))) != $true)),
% 0.18/0.37 introduced(choice_axiom,[])).
% 0.18/0.37 thf(f95,plain,(
% 0.18/0.37 ? [X0 : $i > $i > $o] : ($true != (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mforall_prop @ (^[Y1 : $i > $o]: (mequiv @ (mdia @ X0 @ (mor @ Y0 @ Y1)) @ (mor @ (mdia @ X0 @ Y0) @ (mdia @ X0 @ Y1)))))))))),
% 0.18/0.37 inference(ennf_transformation,[],[f40])).
% 0.18/0.37 thf(f40,plain,(
% 0.18/0.37 ~! [X0 : $i > $i > $o] : ($true = (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mforall_prop @ (^[Y1 : $i > $o]: (mequiv @ (mdia @ X0 @ (mor @ Y0 @ Y1)) @ (mor @ (mdia @ X0 @ Y0) @ (mdia @ X0 @ Y1)))))))))),
% 0.18/0.37 inference(fool_elimination,[],[f39])).
% 0.18/0.37 thf(f39,plain,(
% 0.18/0.37 ~! [X0 : $i > $i > $o] : (mvalid @ (mforall_prop @ (^[X1 : $i > $o] : (mforall_prop @ (^[X2 : $i > $o] : (mequiv @ (mdia @ X0 @ (mor @ X1 @ X2)) @ (mor @ (mdia @ X0 @ X1) @ (mdia @ X0 @ X2))))))))),
% 0.18/0.37 inference(rectify,[],[f33])).
% 0.18/0.37 thf(f33,negated_conjecture,(
% 0.18/0.37 ~! [X6 : $i > $i > $o] : (mvalid @ (mforall_prop @ (^[X11 : $i > $o] : (mforall_prop @ (^[X12 : $i > $o] : (mequiv @ (mdia @ X6 @ (mor @ X11 @ X12)) @ (mor @ (mdia @ X6 @ X11) @ (mdia @ X6 @ X12))))))))),
% 0.18/0.37 inference(negated_conjecture,[],[f32])).
% 0.18/0.37 thf(f32,conjecture,(
% 0.18/0.37 ! [X6 : $i > $i > $o] : (mvalid @ (mforall_prop @ (^[X11 : $i > $o] : (mforall_prop @ (^[X12 : $i > $o] : (mequiv @ (mdia @ X6 @ (mor @ X11 @ X12)) @ (mor @ (mdia @ X6 @ X11) @ (mdia @ X6 @ X12))))))))),
% 0.18/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj)).
% 0.18/0.37 thf(f451,plain,(
% 0.18/0.37 spl1_16 | spl1_17 | spl1_25 | spl1_26),
% 0.18/0.37 inference(avatar_split_clause,[],[f176,f448,f444,f404,f400])).
% 0.18/0.37 thf(f176,plain,(
% 0.18/0.37 ((sK0 @ sK2 @ sK7) = $true) | ((sK3 @ sK5) = $true) | ($true = (sK4 @ sK5)) | ((sK3 @ sK6) = $true)),
% 0.18/0.37 inference(not_proxy_clausification,[],[f173])).
% 0.18/0.37 thf(f173,plain,(
% 0.18/0.37 ($true = (sK4 @ sK5)) | ((sK3 @ sK5) = $true) | ($false = (~ (sK0 @ sK2 @ sK7))) | ((sK3 @ sK6) = $true)),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f172])).
% 0.18/0.37 thf(f442,plain,(
% 0.18/0.37 spl1_24 | spl1_16 | spl1_23 | spl1_17),
% 0.18/0.37 inference(avatar_split_clause,[],[f184,f404,f434,f400,f439])).
% 0.18/0.37 thf(f184,plain,(
% 0.18/0.37 ($true = (sK4 @ sK8)) | ((sK3 @ sK5) = $true) | ($true = (sK4 @ sK5)) | ((sK0 @ sK2 @ sK6) = $true)),
% 0.18/0.37 inference(not_proxy_clausification,[],[f183])).
% 0.18/0.37 thf(f183,plain,(
% 0.18/0.37 ($false = (~ (sK4 @ sK8))) | ($true = (sK4 @ sK5)) | ((sK0 @ sK2 @ sK6) = $true) | ((sK3 @ sK5) = $true)),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f181])).
% 0.18/0.37 thf(f181,plain,(
% 0.18/0.37 ($true = (sK4 @ sK5)) | ($false = ((~ (sK4 @ sK8)) | (~ (sK0 @ sK2 @ sK8)))) | ((sK3 @ sK5) = $true) | ((sK0 @ sK2 @ sK6) = $true)),
% 0.18/0.37 inference(not_proxy_clausification,[],[f180])).
% 0.18/0.37 thf(f180,plain,(
% 0.18/0.37 ($true = (sK4 @ sK5)) | ($false = (~ (sK0 @ sK2 @ sK6))) | ((sK3 @ sK5) = $true) | ($false = ((~ (sK4 @ sK8)) | (~ (sK0 @ sK2 @ sK8))))),
% 0.18/0.37 inference(beta_eta_normalization,[],[f179])).
% 0.18/0.37 thf(f179,plain,(
% 0.18/0.37 ($false = (~ (sK0 @ sK2 @ sK6))) | ($true = (sK4 @ sK5)) | ($false = ((^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))) @ sK8)) | ((sK3 @ sK5) = $true)),
% 0.18/0.37 inference(sigma_clausification,[],[f178])).
% 0.18/0.37 thf(f178,plain,(
% 0.18/0.37 ((!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))) = $false) | ($true = (sK4 @ sK5)) | ((sK3 @ sK5) = $true) | ($false = (~ (sK0 @ sK2 @ sK6)))),
% 0.18/0.37 inference(not_proxy_clausification,[],[f177])).
% 0.18/0.37 thf(f177,plain,(
% 0.18/0.37 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) = $true) | ($true = (sK4 @ sK5)) | ($false = (~ (sK0 @ sK2 @ sK6))) | ((sK3 @ sK5) = $true)),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f166])).
% 0.18/0.37 thf(f166,plain,(
% 0.18/0.37 ($true = ((sK3 @ sK5) | (sK4 @ sK5))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) = $true) | ($false = (~ (sK0 @ sK2 @ sK6)))),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f165])).
% 0.18/0.37 thf(f437,plain,(
% 0.18/0.37 spl1_17 | spl1_22 | spl1_23 | spl1_16),
% 0.18/0.37 inference(avatar_split_clause,[],[f185,f400,f434,f430,f404])).
% 0.18/0.37 thf(f185,plain,(
% 0.18/0.37 ($true = (sK4 @ sK5)) | ($true = (sK0 @ sK2 @ sK8)) | ((sK3 @ sK5) = $true) | ((sK0 @ sK2 @ sK6) = $true)),
% 0.18/0.37 inference(not_proxy_clausification,[],[f182])).
% 0.18/0.37 thf(f182,plain,(
% 0.18/0.37 ((sK0 @ sK2 @ sK6) = $true) | ((sK3 @ sK5) = $true) | ($true = (sK4 @ sK5)) | ($false = (~ (sK0 @ sK2 @ sK8)))),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f181])).
% 0.18/0.37 thf(f428,plain,(
% 0.18/0.37 spl1_20 | spl1_21 | spl1_15),
% 0.18/0.37 inference(avatar_split_clause,[],[f200,f394,f424,f419])).
% 0.18/0.37 thf(f200,plain,(
% 0.18/0.37 ($true = (sK0 @ sK2 @ sK5)) | ($true = (sK4 @ sK10)) | ($true = (sK3 @ sK9))),
% 0.18/0.37 inference(not_proxy_clausification,[],[f199])).
% 0.18/0.37 thf(f199,plain,(
% 0.18/0.37 ($true = (sK0 @ sK2 @ sK5)) | ($true = (sK4 @ sK10)) | ($false = (~ (sK3 @ sK9)))),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f197])).
% 0.18/0.37 thf(f197,plain,(
% 0.18/0.37 (((~ (sK3 @ sK9)) | (~ (sK0 @ sK2 @ sK9))) = $false) | ($true = (sK4 @ sK10)) | ($true = (sK0 @ sK2 @ sK5))),
% 0.18/0.37 inference(not_proxy_clausification,[],[f196])).
% 0.18/0.37 thf(f196,plain,(
% 0.18/0.37 ($false = (~ (sK4 @ sK10))) | ($true = (sK0 @ sK2 @ sK5)) | (((~ (sK3 @ sK9)) | (~ (sK0 @ sK2 @ sK9))) = $false)),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f194])).
% 0.18/0.37 thf(f194,plain,(
% 0.18/0.37 (((~ (sK4 @ sK10)) | (~ (sK0 @ sK2 @ sK10))) = $false) | (((~ (sK3 @ sK9)) | (~ (sK0 @ sK2 @ sK9))) = $false) | ($true = (sK0 @ sK2 @ sK5))),
% 0.18/0.37 inference(beta_eta_normalization,[],[f193])).
% 0.18/0.37 thf(f193,plain,(
% 0.18/0.37 (((^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))) @ sK10) = $false) | (((~ (sK3 @ sK9)) | (~ (sK0 @ sK2 @ sK9))) = $false) | ($true = (sK0 @ sK2 @ sK5))),
% 0.18/0.37 inference(sigma_clausification,[],[f192])).
% 0.18/0.37 thf(f192,plain,(
% 0.18/0.37 ($true = (sK0 @ sK2 @ sK5)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))) = $false) | (((~ (sK3 @ sK9)) | (~ (sK0 @ sK2 @ sK9))) = $false)),
% 0.18/0.37 inference(not_proxy_clausification,[],[f191])).
% 0.18/0.37 thf(f191,plain,(
% 0.18/0.37 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) = $true) | (((~ (sK3 @ sK9)) | (~ (sK0 @ sK2 @ sK9))) = $false) | ($true = (sK0 @ sK2 @ sK5))),
% 0.18/0.37 inference(beta_eta_normalization,[],[f190])).
% 0.18/0.37 thf(f190,plain,(
% 0.18/0.37 ($false = ((^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))) @ sK9)) | ($true = (sK0 @ sK2 @ sK5)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) = $true)),
% 0.18/0.37 inference(sigma_clausification,[],[f189])).
% 0.18/0.37 thf(f189,plain,(
% 0.18/0.37 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | ($true = (sK0 @ sK2 @ sK5)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) = $true)),
% 0.18/0.37 inference(not_proxy_clausification,[],[f188])).
% 0.18/0.37 thf(f188,plain,(
% 0.18/0.37 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))))) | ($true = (sK0 @ sK2 @ sK5)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) = $true)),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f187])).
% 0.18/0.37 thf(f187,plain,(
% 0.18/0.37 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))))) = $true) | ($true = (sK0 @ sK2 @ sK5))),
% 0.18/0.37 inference(not_proxy_clausification,[],[f186])).
% 0.18/0.37 thf(f186,plain,(
% 0.18/0.37 ($true = (sK0 @ sK2 @ sK5)) | ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))))) = $false)),
% 0.18/0.37 inference(not_proxy_clausification,[],[f158])).
% 0.18/0.37 thf(f158,plain,(
% 0.18/0.37 ($false = (~ (sK0 @ sK2 @ sK5))) | ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))))) = $false)),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f157])).
% 0.18/0.37 thf(f427,plain,(
% 0.18/0.37 spl1_15 | spl1_21 | spl1_19),
% 0.18/0.37 inference(avatar_split_clause,[],[f201,f414,f424,f394])).
% 0.18/0.37 thf(f201,plain,(
% 0.18/0.37 ($true = (sK0 @ sK2 @ sK5)) | ($true = (sK4 @ sK10)) | ($true = (sK0 @ sK2 @ sK9))),
% 0.18/0.37 inference(not_proxy_clausification,[],[f198])).
% 0.18/0.37 thf(f198,plain,(
% 0.18/0.37 ($false = (~ (sK0 @ sK2 @ sK9))) | ($true = (sK4 @ sK10)) | ($true = (sK0 @ sK2 @ sK5))),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f197])).
% 0.18/0.37 thf(f422,plain,(
% 0.18/0.37 spl1_20 | spl1_15 | spl1_18),
% 0.18/0.37 inference(avatar_split_clause,[],[f205,f410,f394,f419])).
% 0.18/0.37 thf(f205,plain,(
% 0.18/0.37 ($true = (sK3 @ sK9)) | ((sK0 @ sK2 @ sK10) = $true) | ($true = (sK0 @ sK2 @ sK5))),
% 0.18/0.37 inference(not_proxy_clausification,[],[f204])).
% 0.18/0.37 thf(f204,plain,(
% 0.18/0.37 ($false = (~ (sK0 @ sK2 @ sK10))) | ($true = (sK3 @ sK9)) | ($true = (sK0 @ sK2 @ sK5))),
% 0.18/0.37 inference(not_proxy_clausification,[],[f203])).
% 0.18/0.37 thf(f203,plain,(
% 0.18/0.37 ($true = (sK0 @ sK2 @ sK5)) | ($false = (~ (sK3 @ sK9))) | ($false = (~ (sK0 @ sK2 @ sK10)))),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f195])).
% 0.18/0.37 thf(f195,plain,(
% 0.18/0.37 ($true = (sK0 @ sK2 @ sK5)) | (((~ (sK3 @ sK9)) | (~ (sK0 @ sK2 @ sK9))) = $false) | ($false = (~ (sK0 @ sK2 @ sK10)))),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f194])).
% 0.18/0.37 thf(f417,plain,(
% 0.18/0.37 spl1_18 | spl1_19 | spl1_15),
% 0.18/0.37 inference(avatar_split_clause,[],[f207,f394,f414,f410])).
% 0.18/0.37 thf(f207,plain,(
% 0.18/0.37 ($true = (sK0 @ sK2 @ sK9)) | ((sK0 @ sK2 @ sK10) = $true) | ($true = (sK0 @ sK2 @ sK5))),
% 0.18/0.37 inference(not_proxy_clausification,[],[f206])).
% 0.18/0.37 thf(f206,plain,(
% 0.18/0.37 ($false = (~ (sK0 @ sK2 @ sK10))) | ($true = (sK0 @ sK2 @ sK5)) | ($true = (sK0 @ sK2 @ sK9))),
% 0.18/0.37 inference(not_proxy_clausification,[],[f202])).
% 0.18/0.37 thf(f202,plain,(
% 0.18/0.37 ($false = (~ (sK0 @ sK2 @ sK9))) | ($false = (~ (sK0 @ sK2 @ sK10))) | ($true = (sK0 @ sK2 @ sK5))),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f195])).
% 0.18/0.37 thf(f336,plain,(
% 0.18/0.37 spl1_2 | spl1_2),
% 0.18/0.37 inference(avatar_split_clause,[],[f308,f332,f332])).
% 0.18/0.37 thf(f308,plain,(
% 0.18/0.37 ( ! [X2 : $i,X1 : $i] : (($false = (sK3 @ X2)) | ($false = (sK0 @ sK2 @ X1)) | ($false = (sK0 @ sK2 @ X2)) | ($false = (sK3 @ X1))) )),
% 0.18/0.37 inference(not_proxy_clausification,[],[f307])).
% 0.18/0.37 thf(f307,plain,(
% 0.18/0.37 ( ! [X2 : $i,X1 : $i] : (($true = (~ (sK3 @ X1))) | ($false = (sK3 @ X2)) | ($false = (sK0 @ sK2 @ X2)) | ($false = (sK0 @ sK2 @ X1))) )),
% 0.18/0.37 inference(not_proxy_clausification,[],[f306])).
% 0.18/0.37 thf(f306,plain,(
% 0.18/0.37 ( ! [X2 : $i,X1 : $i] : (($true = (~ (sK0 @ sK2 @ X1))) | ($false = (sK0 @ sK2 @ X2)) | ($false = (sK3 @ X2)) | ($true = (~ (sK3 @ X1)))) )),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f304])).
% 0.18/0.37 thf(f304,plain,(
% 0.18/0.37 ( ! [X2 : $i,X1 : $i] : (($false = (sK0 @ sK2 @ X2)) | ($false = ((sK3 @ X2) | (sK4 @ X2))) | ($true = (~ (sK3 @ X1))) | ($true = (~ (sK0 @ sK2 @ X1)))) )),
% 0.18/0.37 inference(not_proxy_clausification,[],[f303])).
% 0.18/0.37 thf(f303,plain,(
% 0.18/0.37 ( ! [X2 : $i,X1 : $i] : (($true = (~ ((sK3 @ X2) | (sK4 @ X2)))) | ($true = (~ (sK3 @ X1))) | ($false = (sK0 @ sK2 @ X2)) | ($true = (~ (sK0 @ sK2 @ X1)))) )),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f302])).
% 0.18/0.37 thf(f302,plain,(
% 0.18/0.37 ( ! [X2 : $i,X1 : $i] : (($false = (sK0 @ sK2 @ X2)) | ($true = ((~ (sK3 @ X1)) | (~ (sK0 @ sK2 @ X1)))) | ($true = (~ ((sK3 @ X2) | (sK4 @ X2))))) )),
% 0.18/0.37 inference(not_proxy_clausification,[],[f301])).
% 0.18/0.37 thf(f301,plain,(
% 0.18/0.37 ( ! [X2 : $i,X1 : $i] : (($true = (~ (sK0 @ sK2 @ X2))) | ($true = (~ ((sK3 @ X2) | (sK4 @ X2)))) | ($true = ((~ (sK3 @ X1)) | (~ (sK0 @ sK2 @ X1))))) )),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f300])).
% 0.18/0.37 thf(f300,plain,(
% 0.18/0.37 ( ! [X2 : $i,X1 : $i] : ((((~ ((sK3 @ X2) | (sK4 @ X2))) | (~ (sK0 @ sK2 @ X2))) = $true) | ($true = ((~ (sK3 @ X1)) | (~ (sK0 @ sK2 @ X1))))) )),
% 0.18/0.37 inference(beta_eta_normalization,[],[f299])).
% 0.18/0.37 thf(f299,plain,(
% 0.18/0.37 ( ! [X2 : $i,X1 : $i] : (($true = ((~ (sK3 @ X1)) | (~ (sK0 @ sK2 @ X1)))) | ($true = ((^[Y0 : $i]: ((~ ((sK3 @ Y0) | (sK4 @ Y0))) | (~ (sK0 @ sK2 @ Y0)))) @ X2))) )),
% 0.18/0.37 inference(pi_clausification,[],[f298])).
% 0.18/0.37 thf(f298,plain,(
% 0.18/0.37 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ ((sK3 @ Y0) | (sK4 @ Y0))) | (~ (sK0 @ sK2 @ Y0)))))) | ($true = ((~ (sK3 @ X1)) | (~ (sK0 @ sK2 @ X1))))) )),
% 0.18/0.37 inference(beta_eta_normalization,[],[f297])).
% 0.18/0.37 thf(f297,plain,(
% 0.18/0.37 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ ((sK3 @ Y0) | (sK4 @ Y0))) | (~ (sK0 @ sK2 @ Y0)))))) | (((^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))) @ X1) = $true)) )),
% 0.18/0.37 inference(pi_clausification,[],[f296])).
% 0.18/0.37 thf(f296,plain,(
% 0.18/0.37 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ ((sK3 @ Y0) | (sK4 @ Y0))) | (~ (sK0 @ sK2 @ Y0))))))),
% 0.18/0.37 inference(not_proxy_clausification,[],[f295])).
% 0.18/0.37 thf(f295,plain,(
% 0.18/0.37 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ ((sK3 @ Y0) | (sK4 @ Y0))) | (~ (sK0 @ sK2 @ Y0))))))),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f293])).
% 0.18/0.37 thf(f293,plain,(
% 0.18/0.37 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ ((sK3 @ Y0) | (sK4 @ Y0))) | (~ (sK0 @ sK2 @ Y0))))))),
% 0.18/0.37 inference(not_proxy_clausification,[],[f228])).
% 0.18/0.37 thf(f228,plain,(
% 0.18/0.37 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ ((sK3 @ Y0) | (sK4 @ Y0))) | (~ (sK0 @ sK2 @ Y0))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))))))),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f152])).
% 0.18/0.37 thf(f152,plain,(
% 0.18/0.37 ($false = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ ((sK3 @ Y0) | (sK4 @ Y0))) | (~ (sK0 @ sK2 @ Y0)))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))))))),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f151])).
% 0.18/0.37 thf(f330,plain,(
% 0.18/0.37 spl1_1 | spl1_1),
% 0.18/0.37 inference(avatar_split_clause,[],[f326,f328,f328])).
% 0.18/0.37 thf(f326,plain,(
% 0.18/0.37 ( ! [X2 : $i,X1 : $i] : (($false = (sK4 @ X2)) | ($false = (sK0 @ sK2 @ X1)) | ((sK4 @ X1) = $false) | ($false = (sK0 @ sK2 @ X2))) )),
% 0.18/0.37 inference(not_proxy_clausification,[],[f325])).
% 0.18/0.37 thf(f325,plain,(
% 0.18/0.37 ( ! [X2 : $i,X1 : $i] : (($false = (sK0 @ sK2 @ X1)) | ($false = (sK4 @ X2)) | ((sK4 @ X1) = $false) | ($true = (~ (sK0 @ sK2 @ X2)))) )),
% 0.18/0.37 inference(not_proxy_clausification,[],[f324])).
% 0.18/0.37 thf(f324,plain,(
% 0.18/0.37 ( ! [X2 : $i,X1 : $i] : (((sK4 @ X1) = $false) | ($false = (sK0 @ sK2 @ X1)) | ((~ (sK4 @ X2)) = $true) | ($true = (~ (sK0 @ sK2 @ X2)))) )),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f319])).
% 0.18/0.37 thf(f319,plain,(
% 0.18/0.37 ( ! [X2 : $i,X1 : $i] : (($false = (sK0 @ sK2 @ X1)) | ((sK4 @ X1) = $false) | ($true = ((~ (sK4 @ X2)) | (~ (sK0 @ sK2 @ X2))))) )),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f318])).
% 0.18/0.37 thf(f318,plain,(
% 0.18/0.37 ( ! [X2 : $i,X1 : $i] : (($false = (sK0 @ sK2 @ X1)) | ($false = ((sK3 @ X1) | (sK4 @ X1))) | ($true = ((~ (sK4 @ X2)) | (~ (sK0 @ sK2 @ X2))))) )),
% 0.18/0.37 inference(not_proxy_clausification,[],[f317])).
% 0.18/0.37 thf(f317,plain,(
% 0.18/0.37 ( ! [X2 : $i,X1 : $i] : (($true = (~ (sK0 @ sK2 @ X1))) | ($true = ((~ (sK4 @ X2)) | (~ (sK0 @ sK2 @ X2)))) | ($false = ((sK3 @ X1) | (sK4 @ X1)))) )),
% 0.18/0.37 inference(beta_eta_normalization,[],[f316])).
% 0.18/0.37 thf(f316,plain,(
% 0.18/0.37 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))) @ X2)) | ($false = ((sK3 @ X1) | (sK4 @ X1))) | ($true = (~ (sK0 @ sK2 @ X1)))) )),
% 0.18/0.37 inference(pi_clausification,[],[f315])).
% 0.18/0.37 thf(f315,plain,(
% 0.18/0.37 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))) = $true) | ($true = (~ (sK0 @ sK2 @ X1))) | ($false = ((sK3 @ X1) | (sK4 @ X1)))) )),
% 0.18/0.37 inference(not_proxy_clausification,[],[f314])).
% 0.18/0.37 thf(f314,plain,(
% 0.18/0.37 ( ! [X1 : $i] : (($true = (~ ((sK3 @ X1) | (sK4 @ X1)))) | ((!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))) = $true) | ($true = (~ (sK0 @ sK2 @ X1)))) )),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f313])).
% 0.18/0.37 thf(f313,plain,(
% 0.18/0.37 ( ! [X1 : $i] : (($true = ((~ ((sK3 @ X1) | (sK4 @ X1))) | (~ (sK0 @ sK2 @ X1)))) | ((!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))) = $true)) )),
% 0.18/0.37 inference(not_proxy_clausification,[],[f312])).
% 0.18/0.37 thf(f312,plain,(
% 0.18/0.37 ( ! [X1 : $i] : (($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))))) | ($true = ((~ ((sK3 @ X1) | (sK4 @ X1))) | (~ (sK0 @ sK2 @ X1))))) )),
% 0.18/0.37 inference(beta_eta_normalization,[],[f311])).
% 0.18/0.37 thf(f311,plain,(
% 0.18/0.37 ( ! [X1 : $i] : (($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))))) | ($true = ((^[Y0 : $i]: ((~ ((sK3 @ Y0) | (sK4 @ Y0))) | (~ (sK0 @ sK2 @ Y0)))) @ X1))) )),
% 0.18/0.37 inference(pi_clausification,[],[f294])).
% 0.18/0.37 thf(f294,plain,(
% 0.18/0.37 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ ((sK3 @ Y0) | (sK4 @ Y0))) | (~ (sK0 @ sK2 @ Y0)))))) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))))),
% 0.18/0.37 inference(binary_proxy_clausification,[],[f293])).
% 0.18/0.37 % SZS output end Proof for theBenchmark
% 0.18/0.37 % (19983)------------------------------
% 0.18/0.37 % (19983)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.37 % (19983)Termination reason: Refutation
% 0.18/0.37
% 0.18/0.37 % (19983)Memory used [KB]: 6012
% 0.18/0.37 % (19983)Time elapsed: 0.017 s
% 0.18/0.37 % (19983)Instructions burned: 31 (million)
% 0.18/0.37 % (19983)------------------------------
% 0.18/0.37 % (19983)------------------------------
% 0.18/0.37 % (19982)Success in time 0.026 s
% 0.18/0.37 % Vampire---4.8 exiting
%------------------------------------------------------------------------------