TSTP Solution File: SEU550^2 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU550^2 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n025.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 03:49:31 EDT 2024
% Result : Theorem 0.20s 0.40s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU550^2 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.03/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.35 % Computer : n025.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun May 19 15:36:38 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a TH0_THM_EQU_NAR problem
% 0.14/0.35 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.37 % (28424)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.14/0.37 % (28427)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.14/0.37 % (28431)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (3000ds/3Mi)
% 0.14/0.37 % (28429)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 (3000ds/275Mi)
% 0.14/0.37 % (28427)Instruction limit reached!
% 0.14/0.37 % (28427)------------------------------
% 0.14/0.37 % (28427)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (28427)Termination reason: Unknown
% 0.14/0.37 % (28427)Termination phase: Property scanning
% 0.14/0.37
% 0.14/0.37 % (28427)Memory used [KB]: 895
% 0.14/0.37 % (28427)Time elapsed: 0.003 s
% 0.14/0.37 % (28427)Instructions burned: 2 (million)
% 0.14/0.37 % (28427)------------------------------
% 0.14/0.37 % (28427)------------------------------
% 0.14/0.37 % (28431)Instruction limit reached!
% 0.14/0.37 % (28431)------------------------------
% 0.14/0.37 % (28431)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (28431)Termination reason: Unknown
% 0.14/0.37 % (28431)Termination phase: Saturation
% 0.14/0.37
% 0.14/0.37 % (28431)Memory used [KB]: 5500
% 0.14/0.37 % (28431)Time elapsed: 0.004 s
% 0.14/0.37 % (28431)Instructions burned: 3 (million)
% 0.14/0.37 % (28431)------------------------------
% 0.14/0.37 % (28431)------------------------------
% 0.14/0.37 % (28429)Refutation not found, incomplete strategy
% 0.14/0.37 % (28429)------------------------------
% 0.14/0.37 % (28429)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (28429)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.37
% 0.14/0.37
% 0.14/0.37 % (28429)Memory used [KB]: 5500
% 0.14/0.37 % (28429)Time elapsed: 0.004 s
% 0.14/0.37 % (28429)Instructions burned: 2 (million)
% 0.14/0.37 % (28429)------------------------------
% 0.14/0.37 % (28429)------------------------------
% 0.20/0.37 % (28428)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 (3000ds/2Mi)
% 0.20/0.38 % (28428)Instruction limit reached!
% 0.20/0.38 % (28428)------------------------------
% 0.20/0.38 % (28428)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.38 % (28428)Termination reason: Unknown
% 0.20/0.38 % (28428)Termination phase: Saturation
% 0.20/0.38
% 0.20/0.38 % (28428)Memory used [KB]: 895
% 0.20/0.38 % (28428)Time elapsed: 0.003 s
% 0.20/0.38 % (28428)Instructions burned: 2 (million)
% 0.20/0.38 % (28428)------------------------------
% 0.20/0.38 % (28428)------------------------------
% 0.20/0.38 % (28425)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 (3000ds/4Mi)
% 0.20/0.38 % (28426)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 (3000ds/27Mi)
% 0.20/0.38 % (28430)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (3000ds/18Mi)
% 0.20/0.38 % (28425)Instruction limit reached!
% 0.20/0.38 % (28425)------------------------------
% 0.20/0.38 % (28425)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.38 % (28425)Termination reason: Unknown
% 0.20/0.38 % (28425)Termination phase: Saturation
% 0.20/0.38
% 0.20/0.38 % (28425)Memory used [KB]: 5500
% 0.20/0.38 % (28425)Time elapsed: 0.004 s
% 0.20/0.38 % (28425)Instructions burned: 4 (million)
% 0.20/0.38 % (28425)------------------------------
% 0.20/0.38 % (28425)------------------------------
% 0.20/0.38 % (28432)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)
% 0.20/0.39 % (28434)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)
% 0.20/0.39 % (28434)Instruction limit reached!
% 0.20/0.39 % (28434)------------------------------
% 0.20/0.39 % (28434)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.39 % (28434)Termination reason: Unknown
% 0.20/0.39 % (28434)Termination phase: Saturation
% 0.20/0.39
% 0.20/0.39 % (28434)Memory used [KB]: 5500
% 0.20/0.39 % (28434)Time elapsed: 0.004 s
% 0.20/0.39 % (28434)Instructions burned: 3 (million)
% 0.20/0.39 % (28434)------------------------------
% 0.20/0.39 % (28434)------------------------------
% 0.20/0.39 % (28430)Instruction limit reached!
% 0.20/0.39 % (28430)------------------------------
% 0.20/0.39 % (28430)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.39 % (28430)Termination reason: Unknown
% 0.20/0.39 % (28433)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)
% 0.20/0.39 % (28430)Termination phase: Saturation
% 0.20/0.39
% 0.20/0.39 % (28430)Memory used [KB]: 5628
% 0.20/0.39 % (28430)Time elapsed: 0.015 s
% 0.20/0.39 % (28430)Instructions burned: 19 (million)
% 0.20/0.39 % (28430)------------------------------
% 0.20/0.39 % (28430)------------------------------
% 0.20/0.39 % (28435)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)
% 0.20/0.39 % (28424)First to succeed.
% 0.20/0.39 % (28426)Instruction limit reached!
% 0.20/0.39 % (28426)------------------------------
% 0.20/0.39 % (28426)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.39 % (28426)Termination reason: Unknown
% 0.20/0.39 % (28426)Termination phase: Saturation
% 0.20/0.39
% 0.20/0.39 % (28426)Memory used [KB]: 5628
% 0.20/0.39 % (28426)Time elapsed: 0.020 s
% 0.20/0.39 % (28426)Instructions burned: 27 (million)
% 0.20/0.39 % (28426)------------------------------
% 0.20/0.39 % (28426)------------------------------
% 0.20/0.40 % (28424)Refutation found. Thanks to Tanya!
% 0.20/0.40 % SZS status Theorem for theBenchmark
% 0.20/0.40 % SZS output start Proof for theBenchmark
% 0.20/0.40 thf(func_def_0, type, exu: ($i > $o) > $o).
% 0.20/0.40 thf(func_def_13, type, sK0: $i > $o).
% 0.20/0.40 thf(func_def_14, type, sK1: $i > $o).
% 0.20/0.40 thf(func_def_16, type, sK3: $i > $i).
% 0.20/0.40 thf(func_def_17, type, sK4: $i > $i).
% 0.20/0.40 thf(func_def_18, type, sK5: $i > $i).
% 0.20/0.40 thf(f584,plain,(
% 0.20/0.40 $false),
% 0.20/0.40 inference(avatar_sat_refutation,[],[f76,f81,f86,f87,f94,f98,f105,f109,f159,f207,f293,f407,f467,f494,f502,f541,f580])).
% 0.20/0.40 thf(f580,plain,(
% 0.20/0.40 ~spl2_3 | ~spl2_11),
% 0.20/0.40 inference(avatar_contradiction_clause,[],[f579])).
% 0.20/0.40 thf(f579,plain,(
% 0.20/0.40 $false | (~spl2_3 | ~spl2_11)),
% 0.20/0.40 inference(trivial_inequality_removal,[],[f576])).
% 0.20/0.40 thf(f576,plain,(
% 0.20/0.40 ($false = $true) | (~spl2_3 | ~spl2_11)),
% 0.20/0.40 inference(superposition,[],[f80,f551])).
% 0.20/0.40 thf(f551,plain,(
% 0.20/0.40 ( ! [X0 : $i] : (((sK1 @ X0) = $false)) ) | ~spl2_11),
% 0.20/0.40 inference(trivial_inequality_removal,[],[f543])).
% 0.20/0.40 thf(f543,plain,(
% 0.20/0.40 ( ! [X0 : $i] : (($false = $true) | ((sK1 @ X0) = $false)) ) | ~spl2_11),
% 0.20/0.40 inference(superposition,[],[f497,f69])).
% 0.20/0.40 thf(f69,plain,(
% 0.20/0.40 ( ! [X3 : $i] : (($true = (sK0 @ X3)) | ($false = (sK1 @ X3))) )),
% 0.20/0.40 inference(binary_proxy_clausification,[],[f16])).
% 0.20/0.40 thf(f16,plain,(
% 0.20/0.40 ( ! [X3 : $i] : (((sK1 @ X3) = (sK0 @ X3))) )),
% 0.20/0.40 inference(equality_resolution,[],[f13])).
% 0.20/0.40 thf(f13,plain,(
% 0.20/0.40 ( ! [X2 : $i,X3 : $i] : ((X2 != X3) | ((sK1 @ X3) = (sK0 @ X2))) )),
% 0.20/0.40 inference(cnf_transformation,[],[f11])).
% 0.20/0.40 thf(f11,plain,(
% 0.20/0.40 ((exu @ (^[Y0 : $i]: (sK0 @ Y0))) != (exu @ (^[Y0 : $i]: (sK1 @ Y0)))) & ! [X2,X3] : ((X2 != X3) | ((sK1 @ X3) = (sK0 @ X2)))),
% 0.20/0.40 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f10])).
% 0.20/0.40 thf(f10,plain,(
% 0.20/0.40 ? [X0 : $i > $o,X1 : $i > $o] : (((exu @ (^[Y0 : $i]: (X0 @ Y0))) != (exu @ (^[Y0 : $i]: (X1 @ Y0)))) & ! [X2,X3] : ((X2 != X3) | ((X0 @ X2) = (X1 @ X3)))) => (((exu @ (^[Y0 : $i]: (sK0 @ Y0))) != (exu @ (^[Y0 : $i]: (sK1 @ Y0)))) & ! [X3,X2] : ((X2 != X3) | ((sK1 @ X3) = (sK0 @ X2))))),
% 0.20/0.40 introduced(choice_axiom,[])).
% 0.20/0.40 thf(f9,plain,(
% 0.20/0.40 ? [X0 : $i > $o,X1 : $i > $o] : (((exu @ (^[Y0 : $i]: (X0 @ Y0))) != (exu @ (^[Y0 : $i]: (X1 @ Y0)))) & ! [X2,X3] : ((X2 != X3) | ((X0 @ X2) = (X1 @ X3))))),
% 0.20/0.40 inference(ennf_transformation,[],[f6])).
% 0.20/0.40 thf(f6,plain,(
% 0.20/0.40 ~! [X0 : $i > $o,X1 : $i > $o] : (! [X2,X3] : ((X2 = X3) => ((X0 @ X2) = (X1 @ X3))) => ((exu @ (^[Y0 : $i]: (X0 @ Y0))) = (exu @ (^[Y0 : $i]: (X1 @ Y0)))))),
% 0.20/0.40 inference(fool_elimination,[],[f5])).
% 0.20/0.40 thf(f5,plain,(
% 0.20/0.40 ~! [X0 : $i > $o,X1 : $i > $o] : (! [X2,X3] : ((X2 = X3) => ((X0 @ X2) <=> (X1 @ X3))) => ((exu @ (^[X4 : $i] : (X0 @ X4))) <=> (exu @ (^[X5 : $i] : (X1 @ X5)))))),
% 0.20/0.40 inference(rectify,[],[f3])).
% 0.20/0.40 thf(f3,negated_conjecture,(
% 0.20/0.40 ~! [X3 : $i > $o,X0 : $i > $o] : (! [X2,X1] : ((X1 = X2) => ((X3 @ X2) <=> (X0 @ X1))) => ((exu @ (^[X1 : $i] : (X3 @ X1))) <=> (exu @ (^[X1 : $i] : (X0 @ X1)))))),
% 0.20/0.40 inference(negated_conjecture,[],[f2])).
% 0.20/0.40 thf(f2,conjecture,(
% 0.20/0.40 ! [X3 : $i > $o,X0 : $i > $o] : (! [X2,X1] : ((X1 = X2) => ((X3 @ X2) <=> (X0 @ X1))) => ((exu @ (^[X1 : $i] : (X3 @ X1))) <=> (exu @ (^[X1 : $i] : (X0 @ X1)))))),
% 0.20/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu__Cong)).
% 0.20/0.40 thf(f497,plain,(
% 0.20/0.40 ( ! [X0 : $i] : (($false = (sK0 @ X0))) ) | ~spl2_11),
% 0.20/0.40 inference(avatar_component_clause,[],[f496])).
% 0.20/0.40 thf(f496,plain,(
% 0.20/0.40 spl2_11 <=> ! [X0] : ($false = (sK0 @ X0))),
% 0.20/0.40 introduced(avatar_definition,[new_symbols(naming,[spl2_11])])).
% 0.20/0.40 thf(f80,plain,(
% 0.20/0.40 ((sK1 @ sK6) = $true) | ~spl2_3),
% 0.20/0.40 inference(avatar_component_clause,[],[f78])).
% 0.20/0.40 thf(f78,plain,(
% 0.20/0.40 spl2_3 <=> ((sK1 @ sK6) = $true)),
% 0.20/0.40 introduced(avatar_definition,[new_symbols(naming,[spl2_3])])).
% 0.20/0.40 thf(f541,plain,(
% 0.20/0.40 ~spl2_1 | ~spl2_8 | ~spl2_10 | ~spl2_12),
% 0.20/0.40 inference(avatar_contradiction_clause,[],[f540])).
% 0.20/0.40 thf(f540,plain,(
% 0.20/0.40 $false | (~spl2_1 | ~spl2_8 | ~spl2_10 | ~spl2_12)),
% 0.20/0.40 inference(trivial_inequality_removal,[],[f533])).
% 0.20/0.40 thf(f533,plain,(
% 0.20/0.40 ($false = $true) | (~spl2_1 | ~spl2_8 | ~spl2_10 | ~spl2_12)),
% 0.20/0.40 inference(superposition,[],[f532,f501])).
% 0.20/0.40 thf(f501,plain,(
% 0.20/0.40 ($true = (sK0 @ sK6)) | ~spl2_12),
% 0.20/0.40 inference(avatar_component_clause,[],[f499])).
% 0.20/0.40 thf(f499,plain,(
% 0.20/0.40 spl2_12 <=> ($true = (sK0 @ sK6))),
% 0.20/0.40 introduced(avatar_definition,[new_symbols(naming,[spl2_12])])).
% 0.20/0.40 thf(f532,plain,(
% 0.20/0.40 ($false = (sK0 @ sK6)) | (~spl2_1 | ~spl2_8 | ~spl2_10 | ~spl2_12)),
% 0.20/0.40 inference(trivial_inequality_removal,[],[f531])).
% 0.20/0.40 thf(f531,plain,(
% 0.20/0.40 (sK6 != sK6) | ($false = (sK0 @ sK6)) | (~spl2_1 | ~spl2_8 | ~spl2_10 | ~spl2_12)),
% 0.20/0.40 inference(superposition,[],[f528,f449])).
% 0.20/0.40 thf(f449,plain,(
% 0.20/0.40 ( ! [X0 : $i] : ((sK6 = (sK4 @ X0)) | ($false = (sK0 @ X0))) ) | (~spl2_1 | ~spl2_10)),
% 0.20/0.40 inference(trivial_inequality_removal,[],[f438])).
% 0.20/0.40 thf(f438,plain,(
% 0.20/0.40 ( ! [X0 : $i] : (($false = $true) | ($false = (sK0 @ X0)) | (sK6 = (sK4 @ X0))) ) | (~spl2_1 | ~spl2_10)),
% 0.20/0.40 inference(superposition,[],[f72,f386])).
% 0.20/0.40 thf(f386,plain,(
% 0.20/0.40 ( ! [X0 : $i] : (((sK1 @ (sK4 @ X0)) = $true) | ($false = (sK0 @ X0))) ) | ~spl2_10),
% 0.20/0.40 inference(trivial_inequality_removal,[],[f375])).
% 0.20/0.40 thf(f375,plain,(
% 0.20/0.40 ( ! [X0 : $i] : (((sK1 @ (sK4 @ X0)) = $true) | ($false = (sK0 @ X0)) | ($false = $true)) ) | ~spl2_10),
% 0.20/0.40 inference(superposition,[],[f108,f68])).
% 0.20/0.40 thf(f68,plain,(
% 0.20/0.40 ( ! [X3 : $i] : (($false = (sK0 @ X3)) | ((sK1 @ X3) = $true)) )),
% 0.20/0.40 inference(binary_proxy_clausification,[],[f16])).
% 0.20/0.40 thf(f108,plain,(
% 0.20/0.40 ( ! [X2 : $i] : (($true = (sK0 @ (sK4 @ X2))) | ($false = (sK0 @ X2))) ) | ~spl2_10),
% 0.20/0.40 inference(avatar_component_clause,[],[f107])).
% 0.20/0.40 thf(f107,plain,(
% 0.20/0.40 spl2_10 <=> ! [X2] : (($false = (sK0 @ X2)) | ($true = (sK0 @ (sK4 @ X2))))),
% 0.20/0.40 introduced(avatar_definition,[new_symbols(naming,[spl2_10])])).
% 0.20/0.40 thf(f72,plain,(
% 0.20/0.40 ( ! [X2 : $i] : (($false = (sK1 @ X2)) | (sK6 = X2)) ) | ~spl2_1),
% 0.20/0.40 inference(avatar_component_clause,[],[f71])).
% 0.20/0.40 thf(f71,plain,(
% 0.20/0.40 spl2_1 <=> ! [X2] : (($false = (sK1 @ X2)) | (sK6 = X2))),
% 0.20/0.40 introduced(avatar_definition,[new_symbols(naming,[spl2_1])])).
% 0.20/0.40 thf(f528,plain,(
% 0.20/0.40 (sK6 != (sK4 @ sK6)) | (~spl2_8 | ~spl2_12)),
% 0.20/0.40 inference(trivial_inequality_removal,[],[f523])).
% 0.20/0.40 thf(f523,plain,(
% 0.20/0.40 (sK6 != (sK4 @ sK6)) | ($false = $true) | (~spl2_8 | ~spl2_12)),
% 0.20/0.40 inference(superposition,[],[f501,f101])).
% 0.20/0.40 thf(f101,plain,(
% 0.20/0.40 ( ! [X2 : $i] : (($false = (sK0 @ X2)) | ((sK4 @ X2) != X2)) ) | ~spl2_8),
% 0.20/0.40 inference(avatar_component_clause,[],[f100])).
% 0.20/0.40 thf(f100,plain,(
% 0.20/0.40 spl2_8 <=> ! [X2] : (((sK4 @ X2) != X2) | ($false = (sK0 @ X2)))),
% 0.20/0.40 introduced(avatar_definition,[new_symbols(naming,[spl2_8])])).
% 0.20/0.40 thf(f502,plain,(
% 0.20/0.40 spl2_11 | spl2_12 | ~spl2_1 | ~spl2_10),
% 0.20/0.40 inference(avatar_split_clause,[],[f454,f107,f71,f499,f496])).
% 0.20/0.40 thf(f454,plain,(
% 0.20/0.40 ( ! [X0 : $i] : (($true = (sK0 @ sK6)) | ($false = (sK0 @ X0))) ) | (~spl2_1 | ~spl2_10)),
% 0.20/0.40 inference(duplicate_literal_removal,[],[f452])).
% 0.20/0.40 thf(f452,plain,(
% 0.20/0.40 ( ! [X0 : $i] : (($true = (sK0 @ sK6)) | ($false = (sK0 @ X0)) | ($false = (sK0 @ X0))) ) | (~spl2_1 | ~spl2_10)),
% 0.20/0.40 inference(superposition,[],[f108,f449])).
% 0.20/0.40 thf(f494,plain,(
% 0.20/0.40 ~spl2_1 | ~spl2_3 | ~spl2_6 | ~spl2_9),
% 0.20/0.40 inference(avatar_contradiction_clause,[],[f493])).
% 0.20/0.40 thf(f493,plain,(
% 0.20/0.40 $false | (~spl2_1 | ~spl2_3 | ~spl2_6 | ~spl2_9)),
% 0.20/0.40 inference(trivial_inequality_removal,[],[f486])).
% 0.20/0.40 thf(f486,plain,(
% 0.20/0.40 ($false = $true) | (~spl2_1 | ~spl2_3 | ~spl2_6 | ~spl2_9)),
% 0.20/0.40 inference(superposition,[],[f484,f80])).
% 0.20/0.40 thf(f484,plain,(
% 0.20/0.40 ((sK1 @ sK6) = $false) | (~spl2_1 | ~spl2_3 | ~spl2_6 | ~spl2_9)),
% 0.20/0.40 inference(trivial_inequality_removal,[],[f480])).
% 0.20/0.40 thf(f480,plain,(
% 0.20/0.40 ((sK1 @ sK6) = $false) | (sK6 != sK6) | (~spl2_1 | ~spl2_3 | ~spl2_6 | ~spl2_9)),
% 0.20/0.40 inference(superposition,[],[f334,f478])).
% 0.20/0.40 thf(f478,plain,(
% 0.20/0.40 ( ! [X0 : $i] : ((sK6 = (sK3 @ X0)) | ((sK1 @ X0) = $false)) ) | (~spl2_1 | ~spl2_9)),
% 0.20/0.40 inference(trivial_inequality_removal,[],[f471])).
% 0.20/0.40 thf(f471,plain,(
% 0.20/0.40 ( ! [X0 : $i] : (($false = $true) | (sK6 = (sK3 @ X0)) | ((sK1 @ X0) = $false)) ) | (~spl2_1 | ~spl2_9)),
% 0.20/0.40 inference(superposition,[],[f72,f104])).
% 0.20/0.40 thf(f104,plain,(
% 0.20/0.40 ( ! [X1 : $i] : (($true = (sK1 @ (sK3 @ X1))) | ($false = (sK1 @ X1))) ) | ~spl2_9),
% 0.20/0.40 inference(avatar_component_clause,[],[f103])).
% 0.20/0.40 thf(f103,plain,(
% 0.20/0.40 spl2_9 <=> ! [X1] : (($true = (sK1 @ (sK3 @ X1))) | ($false = (sK1 @ X1)))),
% 0.20/0.40 introduced(avatar_definition,[new_symbols(naming,[spl2_9])])).
% 0.20/0.40 thf(f334,plain,(
% 0.20/0.40 (sK6 != (sK3 @ sK6)) | (~spl2_3 | ~spl2_6)),
% 0.20/0.40 inference(trivial_inequality_removal,[],[f328])).
% 0.20/0.40 thf(f328,plain,(
% 0.20/0.40 ($false = $true) | (sK6 != (sK3 @ sK6)) | (~spl2_3 | ~spl2_6)),
% 0.20/0.40 inference(superposition,[],[f80,f93])).
% 0.20/0.40 thf(f93,plain,(
% 0.20/0.40 ( ! [X1 : $i] : (($false = (sK1 @ X1)) | ((sK3 @ X1) != X1)) ) | ~spl2_6),
% 0.20/0.40 inference(avatar_component_clause,[],[f92])).
% 0.20/0.40 thf(f92,plain,(
% 0.20/0.40 spl2_6 <=> ! [X1] : (($false = (sK1 @ X1)) | ((sK3 @ X1) != X1))),
% 0.20/0.40 introduced(avatar_definition,[new_symbols(naming,[spl2_6])])).
% 0.20/0.40 thf(f467,plain,(
% 0.20/0.40 ~spl2_1 | ~spl2_3 | ~spl2_4 | ~spl2_8 | ~spl2_10),
% 0.20/0.40 inference(avatar_contradiction_clause,[],[f466])).
% 0.20/0.40 thf(f466,plain,(
% 0.20/0.40 $false | (~spl2_1 | ~spl2_3 | ~spl2_4 | ~spl2_8 | ~spl2_10)),
% 0.20/0.40 inference(trivial_inequality_removal,[],[f460])).
% 0.20/0.40 thf(f460,plain,(
% 0.20/0.40 ($false = $true) | (~spl2_1 | ~spl2_3 | ~spl2_4 | ~spl2_8 | ~spl2_10)),
% 0.20/0.40 inference(superposition,[],[f421,f456])).
% 0.20/0.40 thf(f456,plain,(
% 0.20/0.40 ($false = (sK0 @ sK6)) | (~spl2_1 | ~spl2_3 | ~spl2_8 | ~spl2_10)),
% 0.20/0.40 inference(trivial_inequality_removal,[],[f453])).
% 0.20/0.40 thf(f453,plain,(
% 0.20/0.40 ($false = (sK0 @ sK6)) | (sK6 != sK6) | (~spl2_1 | ~spl2_3 | ~spl2_8 | ~spl2_10)),
% 0.20/0.40 inference(superposition,[],[f371,f449])).
% 0.20/0.40 thf(f371,plain,(
% 0.20/0.40 (sK6 != (sK4 @ sK6)) | (~spl2_3 | ~spl2_8)),
% 0.20/0.40 inference(trivial_inequality_removal,[],[f365])).
% 0.20/0.40 thf(f365,plain,(
% 0.20/0.40 ($false = $true) | (sK6 != (sK4 @ sK6)) | (~spl2_3 | ~spl2_8)),
% 0.20/0.40 inference(superposition,[],[f80,f358])).
% 0.20/0.40 thf(f358,plain,(
% 0.20/0.40 ( ! [X0 : $i] : (((sK1 @ X0) = $false) | ((sK4 @ X0) != X0)) ) | ~spl2_8),
% 0.20/0.40 inference(trivial_inequality_removal,[],[f348])).
% 0.20/0.40 thf(f348,plain,(
% 0.20/0.40 ( ! [X0 : $i] : (((sK1 @ X0) = $false) | ((sK4 @ X0) != X0) | ($false = $true)) ) | ~spl2_8),
% 0.20/0.40 inference(superposition,[],[f101,f69])).
% 0.20/0.40 thf(f421,plain,(
% 0.20/0.40 ($true = (sK0 @ sK6)) | (~spl2_1 | ~spl2_4)),
% 0.20/0.40 inference(superposition,[],[f85,f415])).
% 0.20/0.40 thf(f415,plain,(
% 0.20/0.40 (sK6 = sK7) | (~spl2_1 | ~spl2_4)),
% 0.20/0.40 inference(trivial_inequality_removal,[],[f413])).
% 0.20/0.40 thf(f413,plain,(
% 0.20/0.40 ($false = $true) | (sK6 = sK7) | (~spl2_1 | ~spl2_4)),
% 0.20/0.40 inference(superposition,[],[f301,f72])).
% 0.20/0.40 thf(f301,plain,(
% 0.20/0.40 ((sK1 @ sK7) = $true) | ~spl2_4),
% 0.20/0.40 inference(trivial_inequality_removal,[],[f297])).
% 0.20/0.40 thf(f297,plain,(
% 0.20/0.40 ((sK1 @ sK7) = $true) | ($false = $true) | ~spl2_4),
% 0.20/0.40 inference(superposition,[],[f68,f85])).
% 0.20/0.40 thf(f85,plain,(
% 0.20/0.40 ((sK0 @ sK7) = $true) | ~spl2_4),
% 0.20/0.40 inference(avatar_component_clause,[],[f83])).
% 0.20/0.40 thf(f83,plain,(
% 0.20/0.40 spl2_4 <=> ((sK0 @ sK7) = $true)),
% 0.20/0.40 introduced(avatar_definition,[new_symbols(naming,[spl2_4])])).
% 0.20/0.40 thf(f407,plain,(
% 0.20/0.40 ~spl2_2 | ~spl2_4 | ~spl2_8 | ~spl2_10),
% 0.20/0.40 inference(avatar_contradiction_clause,[],[f406])).
% 0.20/0.40 thf(f406,plain,(
% 0.20/0.40 $false | (~spl2_2 | ~spl2_4 | ~spl2_8 | ~spl2_10)),
% 0.20/0.40 inference(subsumption_resolution,[],[f399,f357])).
% 0.20/0.40 thf(f357,plain,(
% 0.20/0.40 ((sK4 @ sK7) != sK7) | (~spl2_4 | ~spl2_8)),
% 0.20/0.40 inference(trivial_inequality_removal,[],[f349])).
% 0.20/0.40 thf(f349,plain,(
% 0.20/0.40 ($false = $true) | ((sK4 @ sK7) != sK7) | (~spl2_4 | ~spl2_8)),
% 0.20/0.40 inference(superposition,[],[f101,f85])).
% 0.20/0.40 thf(f399,plain,(
% 0.20/0.40 ((sK4 @ sK7) = sK7) | (~spl2_2 | ~spl2_4 | ~spl2_10)),
% 0.20/0.40 inference(trivial_inequality_removal,[],[f391])).
% 0.20/0.40 thf(f391,plain,(
% 0.20/0.40 ((sK4 @ sK7) = sK7) | ($false = $true) | (~spl2_2 | ~spl2_4 | ~spl2_10)),
% 0.20/0.40 inference(superposition,[],[f387,f85])).
% 0.20/0.40 thf(f387,plain,(
% 0.20/0.40 ( ! [X0 : $i] : (($false = (sK0 @ X0)) | ((sK4 @ X0) = sK7)) ) | (~spl2_2 | ~spl2_10)),
% 0.20/0.40 inference(trivial_inequality_removal,[],[f373])).
% 0.20/0.40 thf(f373,plain,(
% 0.20/0.40 ( ! [X0 : $i] : (((sK4 @ X0) = sK7) | ($false = (sK0 @ X0)) | ($false = $true)) ) | (~spl2_2 | ~spl2_10)),
% 0.20/0.40 inference(superposition,[],[f108,f75])).
% 0.20/0.40 thf(f75,plain,(
% 0.20/0.40 ( ! [X1 : $i] : (($false = (sK0 @ X1)) | (sK7 = X1)) ) | ~spl2_2),
% 0.20/0.40 inference(avatar_component_clause,[],[f74])).
% 0.20/0.40 thf(f74,plain,(
% 0.20/0.40 spl2_2 <=> ! [X1] : (($false = (sK0 @ X1)) | (sK7 = X1))),
% 0.20/0.40 introduced(avatar_definition,[new_symbols(naming,[spl2_2])])).
% 0.20/0.40 thf(f293,plain,(
% 0.20/0.40 ~spl2_1 | ~spl2_3 | ~spl2_5 | ~spl2_7),
% 0.20/0.40 inference(avatar_contradiction_clause,[],[f292])).
% 0.20/0.40 thf(f292,plain,(
% 0.20/0.40 $false | (~spl2_1 | ~spl2_3 | ~spl2_5 | ~spl2_7)),
% 0.20/0.40 inference(subsumption_resolution,[],[f287,f219])).
% 0.20/0.40 thf(f219,plain,(
% 0.20/0.40 ((sK5 @ sK6) != sK6) | (~spl2_3 | ~spl2_5)),
% 0.20/0.40 inference(trivial_inequality_removal,[],[f211])).
% 0.20/0.40 thf(f211,plain,(
% 0.20/0.40 ((sK5 @ sK6) != sK6) | ($false = $true) | (~spl2_3 | ~spl2_5)),
% 0.20/0.40 inference(superposition,[],[f168,f80])).
% 0.20/0.40 thf(f168,plain,(
% 0.20/0.40 ( ! [X0 : $i] : (((sK1 @ X0) = $false) | ((sK5 @ X0) != X0)) ) | ~spl2_5),
% 0.20/0.40 inference(trivial_inequality_removal,[],[f161])).
% 0.20/0.40 thf(f161,plain,(
% 0.20/0.40 ( ! [X0 : $i] : (((sK1 @ X0) = $false) | ($false = $true) | ((sK5 @ X0) != X0)) ) | ~spl2_5),
% 0.20/0.40 inference(superposition,[],[f90,f69])).
% 0.20/0.40 thf(f90,plain,(
% 0.20/0.40 ( ! [X2 : $i] : (($false = (sK0 @ X2)) | ((sK5 @ X2) != X2)) ) | ~spl2_5),
% 0.20/0.40 inference(avatar_component_clause,[],[f89])).
% 0.20/0.40 thf(f89,plain,(
% 0.20/0.40 spl2_5 <=> ! [X2] : (($false = (sK0 @ X2)) | ((sK5 @ X2) != X2))),
% 0.20/0.40 introduced(avatar_definition,[new_symbols(naming,[spl2_5])])).
% 0.20/0.40 thf(f287,plain,(
% 0.20/0.40 ((sK5 @ sK6) = sK6) | (~spl2_1 | ~spl2_3 | ~spl2_7)),
% 0.20/0.40 inference(trivial_inequality_removal,[],[f278])).
% 0.20/0.40 thf(f278,plain,(
% 0.20/0.40 ($false = $true) | ((sK5 @ sK6) = sK6) | (~spl2_1 | ~spl2_3 | ~spl2_7)),
% 0.20/0.40 inference(superposition,[],[f272,f80])).
% 0.20/0.40 thf(f272,plain,(
% 0.20/0.40 ( ! [X0 : $i] : (((sK1 @ X0) = $false) | ((sK5 @ X0) = sK6)) ) | (~spl2_1 | ~spl2_7)),
% 0.20/0.40 inference(trivial_inequality_removal,[],[f266])).
% 0.20/0.40 thf(f266,plain,(
% 0.20/0.40 ( ! [X0 : $i] : (($false = $true) | ((sK1 @ X0) = $false) | ((sK5 @ X0) = sK6)) ) | (~spl2_1 | ~spl2_7)),
% 0.20/0.40 inference(superposition,[],[f264,f69])).
% 0.20/0.40 thf(f264,plain,(
% 0.20/0.40 ( ! [X0 : $i] : (($false = (sK0 @ X0)) | ((sK5 @ X0) = sK6)) ) | (~spl2_1 | ~spl2_7)),
% 0.20/0.40 inference(trivial_inequality_removal,[],[f258])).
% 0.20/0.40 thf(f258,plain,(
% 0.20/0.40 ( ! [X0 : $i] : (($false = $true) | ((sK5 @ X0) = sK6) | ($false = (sK0 @ X0))) ) | (~spl2_1 | ~spl2_7)),
% 0.20/0.40 inference(superposition,[],[f191,f72])).
% 0.20/0.40 thf(f191,plain,(
% 0.20/0.40 ( ! [X0 : $i] : (($true = (sK1 @ (sK5 @ X0))) | ($false = (sK0 @ X0))) ) | ~spl2_7),
% 0.20/0.40 inference(trivial_inequality_removal,[],[f185])).
% 0.20/0.40 thf(f185,plain,(
% 0.20/0.40 ( ! [X0 : $i] : (($true = (sK1 @ (sK5 @ X0))) | ($false = (sK0 @ X0)) | ($false = $true)) ) | ~spl2_7),
% 0.20/0.40 inference(superposition,[],[f68,f97])).
% 0.20/0.40 thf(f97,plain,(
% 0.20/0.40 ( ! [X2 : $i] : (((sK0 @ (sK5 @ X2)) = $true) | ($false = (sK0 @ X2))) ) | ~spl2_7),
% 0.20/0.40 inference(avatar_component_clause,[],[f96])).
% 0.20/0.40 thf(f96,plain,(
% 0.20/0.40 spl2_7 <=> ! [X2] : (($false = (sK0 @ X2)) | ((sK0 @ (sK5 @ X2)) = $true))),
% 0.20/0.40 introduced(avatar_definition,[new_symbols(naming,[spl2_7])])).
% 0.20/0.40 thf(f207,plain,(
% 0.20/0.40 ~spl2_2 | ~spl2_4 | ~spl2_5 | ~spl2_7),
% 0.20/0.40 inference(avatar_contradiction_clause,[],[f206])).
% 0.20/0.40 thf(f206,plain,(
% 0.20/0.40 $false | (~spl2_2 | ~spl2_4 | ~spl2_5 | ~spl2_7)),
% 0.20/0.40 inference(subsumption_resolution,[],[f202,f167])).
% 0.20/0.40 thf(f167,plain,(
% 0.20/0.40 ((sK5 @ sK7) != sK7) | (~spl2_4 | ~spl2_5)),
% 0.20/0.40 inference(trivial_inequality_removal,[],[f164])).
% 0.20/0.40 thf(f164,plain,(
% 0.20/0.40 ((sK5 @ sK7) != sK7) | ($false = $true) | (~spl2_4 | ~spl2_5)),
% 0.20/0.40 inference(superposition,[],[f85,f90])).
% 0.20/0.40 thf(f202,plain,(
% 0.20/0.40 ((sK5 @ sK7) = sK7) | (~spl2_2 | ~spl2_4 | ~spl2_7)),
% 0.20/0.40 inference(trivial_inequality_removal,[],[f196])).
% 0.20/0.40 thf(f196,plain,(
% 0.20/0.40 ($false = $true) | ((sK5 @ sK7) = sK7) | (~spl2_2 | ~spl2_4 | ~spl2_7)),
% 0.20/0.40 inference(superposition,[],[f85,f189])).
% 0.20/0.40 thf(f189,plain,(
% 0.20/0.40 ( ! [X0 : $i] : (($false = (sK0 @ X0)) | ((sK5 @ X0) = sK7)) ) | (~spl2_2 | ~spl2_7)),
% 0.20/0.40 inference(trivial_inequality_removal,[],[f184])).
% 0.20/0.40 thf(f184,plain,(
% 0.20/0.40 ( ! [X0 : $i] : (((sK5 @ X0) = sK7) | ($false = (sK0 @ X0)) | ($false = $true)) ) | (~spl2_2 | ~spl2_7)),
% 0.20/0.40 inference(superposition,[],[f75,f97])).
% 0.20/0.40 thf(f159,plain,(
% 0.20/0.40 ~spl2_2 | ~spl2_4 | ~spl2_6 | ~spl2_9),
% 0.20/0.40 inference(avatar_contradiction_clause,[],[f158])).
% 0.20/0.40 thf(f158,plain,(
% 0.20/0.40 $false | (~spl2_2 | ~spl2_4 | ~spl2_6 | ~spl2_9)),
% 0.20/0.40 inference(subsumption_resolution,[],[f154,f136])).
% 0.20/0.40 thf(f136,plain,(
% 0.20/0.40 ((sK3 @ sK7) != sK7) | (~spl2_4 | ~spl2_6)),
% 0.20/0.40 inference(trivial_inequality_removal,[],[f130])).
% 0.20/0.40 thf(f130,plain,(
% 0.20/0.40 ((sK3 @ sK7) != sK7) | ($false = $true) | (~spl2_4 | ~spl2_6)),
% 0.20/0.40 inference(superposition,[],[f93,f113])).
% 0.20/0.40 thf(f113,plain,(
% 0.20/0.40 ((sK1 @ sK7) = $true) | ~spl2_4),
% 0.20/0.40 inference(trivial_inequality_removal,[],[f111])).
% 0.20/0.40 thf(f111,plain,(
% 0.20/0.40 ($false = $true) | ((sK1 @ sK7) = $true) | ~spl2_4),
% 0.20/0.40 inference(superposition,[],[f68,f85])).
% 0.20/0.40 thf(f154,plain,(
% 0.20/0.40 ((sK3 @ sK7) = sK7) | (~spl2_2 | ~spl2_4 | ~spl2_9)),
% 0.20/0.40 inference(trivial_inequality_removal,[],[f145])).
% 0.20/0.40 thf(f145,plain,(
% 0.20/0.40 ($false = $true) | ((sK3 @ sK7) = sK7) | (~spl2_2 | ~spl2_4 | ~spl2_9)),
% 0.20/0.40 inference(superposition,[],[f144,f113])).
% 0.20/0.40 thf(f144,plain,(
% 0.20/0.40 ( ! [X0 : $i] : (((sK1 @ X0) = $false) | ((sK3 @ X0) = sK7)) ) | (~spl2_2 | ~spl2_9)),
% 0.20/0.40 inference(trivial_inequality_removal,[],[f138])).
% 0.20/0.40 thf(f138,plain,(
% 0.20/0.40 ( ! [X0 : $i] : (($false = $true) | ((sK1 @ X0) = $false) | ((sK3 @ X0) = sK7)) ) | (~spl2_2 | ~spl2_9)),
% 0.20/0.40 inference(superposition,[],[f104,f122])).
% 0.20/0.40 thf(f122,plain,(
% 0.20/0.40 ( ! [X0 : $i] : (((sK1 @ X0) = $false) | (sK7 = X0)) ) | ~spl2_2),
% 0.20/0.40 inference(trivial_inequality_removal,[],[f118])).
% 0.20/0.40 thf(f118,plain,(
% 0.20/0.40 ( ! [X0 : $i] : ((sK7 = X0) | ((sK1 @ X0) = $false) | ($false = $true)) ) | ~spl2_2),
% 0.20/0.40 inference(superposition,[],[f75,f69])).
% 0.20/0.40 thf(f109,plain,(
% 0.20/0.40 spl2_10 | spl2_9),
% 0.20/0.40 inference(avatar_split_clause,[],[f33,f103,f107])).
% 0.20/0.40 thf(f33,plain,(
% 0.20/0.40 ( ! [X2 : $i,X1 : $i] : (($false = (sK0 @ X2)) | ($true = (sK1 @ (sK3 @ X1))) | ($false = (sK1 @ X1)) | ($true = (sK0 @ (sK4 @ X2)))) )),
% 0.20/0.40 inference(binary_proxy_clausification,[],[f31])).
% 0.20/0.40 thf(f31,plain,(
% 0.20/0.40 ( ! [X2 : $i,X1 : $i] : (($false = (sK0 @ X2)) | ($false = ((sK0 @ (sK4 @ X2)) => (X2 = (sK4 @ X2)))) | ($true = (sK1 @ (sK3 @ X1))) | ($false = (sK1 @ X1))) )),
% 0.20/0.40 inference(beta_eta_normalization,[],[f30])).
% 0.20/0.40 thf(f30,plain,(
% 0.20/0.40 ( ! [X2 : $i,X1 : $i] : (($true = (sK1 @ (sK3 @ X1))) | (((^[Y0 : $i]: ((sK0 @ Y0) => (X2 = Y0))) @ (sK4 @ X2)) = $false) | ($false = (sK1 @ X1)) | ($false = (sK0 @ X2))) )),
% 0.20/0.40 inference(sigma_clausification,[],[f29])).
% 0.20/0.40 thf(f29,plain,(
% 0.20/0.40 ( ! [X2 : $i,X1 : $i] : (($true = (sK1 @ (sK3 @ X1))) | ($false = (sK0 @ X2)) | ($false = (!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (X2 = Y0))))) | ($false = (sK1 @ X1))) )),
% 0.20/0.40 inference(binary_proxy_clausification,[],[f28])).
% 0.20/0.40 thf(f28,plain,(
% 0.20/0.40 ( ! [X2 : $i,X1 : $i] : (($false = (sK1 @ X1)) | ($true = (sK1 @ (sK3 @ X1))) | ($false = ((sK0 @ X2) & (!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (X2 = Y0))))))) )),
% 0.20/0.40 inference(binary_proxy_clausification,[],[f26])).
% 0.20/0.40 thf(f26,plain,(
% 0.20/0.40 ( ! [X2 : $i,X1 : $i] : (($false = ((sK1 @ (sK3 @ X1)) => (X1 = (sK3 @ X1)))) | ($false = (sK1 @ X1)) | ($false = ((sK0 @ X2) & (!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (X2 = Y0))))))) )),
% 0.20/0.40 inference(beta_eta_normalization,[],[f25])).
% 0.20/0.40 thf(f25,plain,(
% 0.20/0.40 ( ! [X2 : $i,X1 : $i] : (($false = ((^[Y0 : $i]: ((sK1 @ Y0) => (X1 = Y0))) @ (sK3 @ X1))) | ($false = (sK1 @ X1)) | ($false = ((sK0 @ X2) & (!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (X2 = Y0))))))) )),
% 0.20/0.40 inference(sigma_clausification,[],[f24])).
% 0.20/0.40 thf(f24,plain,(
% 0.20/0.40 ( ! [X2 : $i,X1 : $i] : (($false = (sK1 @ X1)) | ($false = (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) => (X1 = Y0))))) | ($false = ((sK0 @ X2) & (!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (X2 = Y0))))))) )),
% 0.20/0.40 inference(beta_eta_normalization,[],[f23])).
% 0.20/0.40 thf(f23,plain,(
% 0.20/0.40 ( ! [X2 : $i,X1 : $i] : (($false = ((^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))))) @ X2)) | ($false = (sK1 @ X1)) | ($false = (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) => (X1 = Y0)))))) )),
% 0.20/0.40 inference(pi_clausification,[],[f22])).
% 0.20/0.40 thf(f22,plain,(
% 0.20/0.40 ( ! [X1 : $i] : (($false = (?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))))))) | ($false = (sK1 @ X1)) | ($false = (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) => (X1 = Y0)))))) )),
% 0.20/0.40 inference(binary_proxy_clausification,[],[f21])).
% 0.20/0.40 thf(f21,plain,(
% 0.20/0.40 ( ! [X1 : $i] : (($false = ((sK1 @ X1) & (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) => (X1 = Y0)))))) | ($false = (?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1))))))))) )),
% 0.20/0.40 inference(beta_eta_normalization,[],[f20])).
% 0.20/0.40 thf(f20,plain,(
% 0.20/0.40 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: ((sK1 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) => (Y0 = Y1)))))) @ X1)) | ($false = (?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1))))))))) )),
% 0.20/0.40 inference(pi_clausification,[],[f19])).
% 0.20/0.40 thf(f19,plain,(
% 0.20/0.40 ($false = (?? @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) => (Y0 = Y1)))))))) | ($false = (?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1))))))))),
% 0.20/0.40 inference(binary_proxy_clausification,[],[f17])).
% 0.20/0.40 thf(f17,plain,(
% 0.20/0.40 ((?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1))))))) != (?? @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) => (Y0 = Y1))))))))),
% 0.20/0.40 inference(beta_eta_normalization,[],[f15])).
% 0.20/0.40 thf(f15,plain,(
% 0.20/0.40 (((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))) @ (^[Y0 : $i]: (sK1 @ Y0))) != ((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))) @ (^[Y0 : $i]: (sK0 @ Y0))))),
% 0.20/0.40 inference(definition_unfolding,[],[f14,f12,f12])).
% 0.20/0.40 thf(f12,plain,(
% 0.20/0.40 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))),
% 0.20/0.40 inference(cnf_transformation,[],[f8])).
% 0.20/0.40 thf(f8,plain,(
% 0.20/0.40 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))),
% 0.20/0.40 inference(fool_elimination,[],[f7])).
% 0.20/0.40 thf(f7,plain,(
% 0.20/0.40 (exu = (^[X0 : $i > $o] : (? [X1] : (! [X2] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))))),
% 0.20/0.40 inference(rectify,[],[f1])).
% 0.20/0.40 thf(f1,axiom,(
% 0.20/0.40 (exu = (^[X0 : $i > $o] : (? [X1] : (! [X2] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))))),
% 0.20/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu_def)).
% 0.20/0.40 thf(f14,plain,(
% 0.20/0.40 ((exu @ (^[Y0 : $i]: (sK0 @ Y0))) != (exu @ (^[Y0 : $i]: (sK1 @ Y0))))),
% 0.20/0.40 inference(cnf_transformation,[],[f11])).
% 0.20/0.40 thf(f105,plain,(
% 0.20/0.40 spl2_8 | spl2_9),
% 0.20/0.40 inference(avatar_split_clause,[],[f34,f103,f100])).
% 0.20/0.40 thf(f34,plain,(
% 0.20/0.40 ( ! [X2 : $i,X1 : $i] : (((sK4 @ X2) != X2) | ($true = (sK1 @ (sK3 @ X1))) | ($false = (sK1 @ X1)) | ($false = (sK0 @ X2))) )),
% 0.20/0.40 inference(equality_proxy_clausification,[],[f32])).
% 0.20/0.40 thf(f32,plain,(
% 0.20/0.40 ( ! [X2 : $i,X1 : $i] : (($false = (X2 = (sK4 @ X2))) | ($false = (sK0 @ X2)) | ($true = (sK1 @ (sK3 @ X1))) | ($false = (sK1 @ X1))) )),
% 0.20/0.40 inference(binary_proxy_clausification,[],[f31])).
% 0.20/0.40 thf(f98,plain,(
% 0.20/0.40 spl2_7 | spl2_6),
% 0.20/0.40 inference(avatar_split_clause,[],[f40,f92,f96])).
% 0.20/0.40 thf(f40,plain,(
% 0.20/0.40 ( ! [X2 : $i,X1 : $i] : (($false = (sK0 @ X2)) | ($false = (sK1 @ X1)) | ((sK3 @ X1) != X1) | ((sK0 @ (sK5 @ X2)) = $true)) )),
% 0.20/0.40 inference(binary_proxy_clausification,[],[f38])).
% 0.20/0.40 thf(f38,plain,(
% 0.20/0.40 ( ! [X2 : $i,X1 : $i] : (($false = (sK1 @ X1)) | ($false = ((sK0 @ (sK5 @ X2)) => (X2 = (sK5 @ X2)))) | ((sK3 @ X1) != X1) | ($false = (sK0 @ X2))) )),
% 0.20/0.40 inference(beta_eta_normalization,[],[f37])).
% 0.20/0.40 thf(f37,plain,(
% 0.20/0.40 ( ! [X2 : $i,X1 : $i] : (((sK3 @ X1) != X1) | ($false = (sK1 @ X1)) | ($false = ((^[Y0 : $i]: ((sK0 @ Y0) => (X2 = Y0))) @ (sK5 @ X2))) | ($false = (sK0 @ X2))) )),
% 0.20/0.40 inference(sigma_clausification,[],[f36])).
% 0.20/0.40 thf(f36,plain,(
% 0.20/0.40 ( ! [X2 : $i,X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (X2 = Y0))))) | ((sK3 @ X1) != X1) | ($false = (sK0 @ X2)) | ($false = (sK1 @ X1))) )),
% 0.20/0.40 inference(equality_proxy_clausification,[],[f35])).
% 0.20/0.40 thf(f35,plain,(
% 0.20/0.40 ( ! [X2 : $i,X1 : $i] : (($false = (sK0 @ X2)) | ($false = (X1 = (sK3 @ X1))) | ($false = (sK1 @ X1)) | ($false = (!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (X2 = Y0)))))) )),
% 0.20/0.40 inference(binary_proxy_clausification,[],[f27])).
% 0.20/0.40 thf(f27,plain,(
% 0.20/0.40 ( ! [X2 : $i,X1 : $i] : (($false = ((sK0 @ X2) & (!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (X2 = Y0)))))) | ($false = (X1 = (sK3 @ X1))) | ($false = (sK1 @ X1))) )),
% 0.20/0.40 inference(binary_proxy_clausification,[],[f26])).
% 0.20/0.40 thf(f94,plain,(
% 0.20/0.40 spl2_5 | spl2_6),
% 0.20/0.40 inference(avatar_split_clause,[],[f41,f92,f89])).
% 0.20/0.40 thf(f41,plain,(
% 0.20/0.40 ( ! [X2 : $i,X1 : $i] : (($false = (sK1 @ X1)) | ($false = (sK0 @ X2)) | ((sK5 @ X2) != X2) | ((sK3 @ X1) != X1)) )),
% 0.20/0.40 inference(equality_proxy_clausification,[],[f39])).
% 0.20/0.40 thf(f39,plain,(
% 0.20/0.40 ( ! [X2 : $i,X1 : $i] : (($false = (X2 = (sK5 @ X2))) | ((sK3 @ X1) != X1) | ($false = (sK1 @ X1)) | ($false = (sK0 @ X2))) )),
% 0.20/0.40 inference(binary_proxy_clausification,[],[f38])).
% 0.20/0.40 thf(f87,plain,(
% 0.20/0.40 spl2_4 | spl2_3),
% 0.20/0.40 inference(avatar_split_clause,[],[f49,f78,f83])).
% 0.20/0.40 thf(f49,plain,(
% 0.20/0.40 ((sK1 @ sK6) = $true) | ((sK0 @ sK7) = $true)),
% 0.20/0.40 inference(binary_proxy_clausification,[],[f47])).
% 0.20/0.40 thf(f47,plain,(
% 0.20/0.40 ((sK0 @ sK7) = $true) | ($true = ((sK1 @ sK6) & (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) => (sK6 = Y0))))))),
% 0.20/0.40 inference(binary_proxy_clausification,[],[f45])).
% 0.20/0.40 thf(f45,plain,(
% 0.20/0.40 (((sK0 @ sK7) & (!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (sK7 = Y0))))) = $true) | ($true = ((sK1 @ sK6) & (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) => (sK6 = Y0))))))),
% 0.20/0.40 inference(beta_eta_normalization,[],[f44])).
% 0.20/0.40 thf(f44,plain,(
% 0.20/0.40 ($true = ((^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))))) @ sK7)) | ($true = ((sK1 @ sK6) & (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) => (sK6 = Y0))))))),
% 0.20/0.40 inference(sigma_clausification,[],[f43])).
% 0.20/0.40 thf(f43,plain,(
% 0.20/0.40 ($true = (?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))))))) | ($true = ((sK1 @ sK6) & (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) => (sK6 = Y0))))))),
% 0.20/0.40 inference(beta_eta_normalization,[],[f42])).
% 0.20/0.40 thf(f42,plain,(
% 0.20/0.40 ($true = (?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))))))) | ($true = ((^[Y0 : $i]: ((sK1 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) => (Y0 = Y1)))))) @ sK6))),
% 0.20/0.40 inference(sigma_clausification,[],[f18])).
% 0.20/0.40 thf(f18,plain,(
% 0.20/0.40 ($true = (?? @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) => (Y0 = Y1)))))))) | ($true = (?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1))))))))),
% 0.20/0.40 inference(binary_proxy_clausification,[],[f17])).
% 0.20/0.40 thf(f86,plain,(
% 0.20/0.40 spl2_1 | spl2_4),
% 0.20/0.40 inference(avatar_split_clause,[],[f53,f83,f71])).
% 0.20/0.40 thf(f53,plain,(
% 0.20/0.40 ( ! [X1 : $i] : (($false = (sK1 @ X1)) | (sK6 = X1) | ((sK0 @ sK7) = $true)) )),
% 0.20/0.40 inference(equality_proxy_clausification,[],[f52])).
% 0.20/0.40 thf(f52,plain,(
% 0.20/0.40 ( ! [X1 : $i] : (($false = (sK1 @ X1)) | ((sK0 @ sK7) = $true) | ($true = (sK6 = X1))) )),
% 0.20/0.40 inference(binary_proxy_clausification,[],[f51])).
% 0.20/0.40 thf(f51,plain,(
% 0.20/0.40 ( ! [X1 : $i] : (((sK0 @ sK7) = $true) | ($true = ((sK1 @ X1) => (sK6 = X1)))) )),
% 0.20/0.40 inference(beta_eta_normalization,[],[f50])).
% 0.20/0.40 thf(f50,plain,(
% 0.20/0.40 ( ! [X1 : $i] : (((sK0 @ sK7) = $true) | (((^[Y0 : $i]: ((sK1 @ Y0) => (sK6 = Y0))) @ X1) = $true)) )),
% 0.20/0.40 inference(pi_clausification,[],[f48])).
% 0.20/0.40 thf(f48,plain,(
% 0.20/0.40 ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) => (sK6 = Y0)))) = $true) | ((sK0 @ sK7) = $true)),
% 0.20/0.40 inference(binary_proxy_clausification,[],[f47])).
% 0.20/0.40 thf(f81,plain,(
% 0.20/0.40 spl2_2 | spl2_3),
% 0.20/0.40 inference(avatar_split_clause,[],[f59,f78,f74])).
% 0.20/0.40 thf(f59,plain,(
% 0.20/0.40 ( ! [X1 : $i] : (($false = (sK0 @ X1)) | ((sK1 @ sK6) = $true) | (sK7 = X1)) )),
% 0.20/0.40 inference(equality_proxy_clausification,[],[f58])).
% 0.20/0.40 thf(f58,plain,(
% 0.20/0.40 ( ! [X1 : $i] : (($false = (sK0 @ X1)) | ((sK1 @ sK6) = $true) | ($true = (sK7 = X1))) )),
% 0.20/0.40 inference(binary_proxy_clausification,[],[f57])).
% 0.20/0.40 thf(f57,plain,(
% 0.20/0.40 ( ! [X1 : $i] : (((sK1 @ sK6) = $true) | (((sK0 @ X1) => (sK7 = X1)) = $true)) )),
% 0.20/0.40 inference(beta_eta_normalization,[],[f56])).
% 0.20/0.40 thf(f56,plain,(
% 0.20/0.40 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((sK0 @ Y0) => (sK7 = Y0))) @ X1)) | ((sK1 @ sK6) = $true)) )),
% 0.20/0.40 inference(pi_clausification,[],[f55])).
% 0.20/0.40 thf(f55,plain,(
% 0.20/0.40 ((sK1 @ sK6) = $true) | ($true = (!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (sK7 = Y0)))))),
% 0.20/0.40 inference(binary_proxy_clausification,[],[f46])).
% 0.20/0.40 thf(f46,plain,(
% 0.20/0.40 ($true = ((sK1 @ sK6) & (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) => (sK6 = Y0)))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (sK7 = Y0)))))),
% 0.20/0.40 inference(binary_proxy_clausification,[],[f45])).
% 0.20/0.40 thf(f76,plain,(
% 0.20/0.40 spl2_1 | spl2_2),
% 0.20/0.40 inference(avatar_split_clause,[],[f67,f74,f71])).
% 0.20/0.40 thf(f67,plain,(
% 0.20/0.40 ( ! [X2 : $i,X1 : $i] : (($false = (sK1 @ X2)) | ($false = (sK0 @ X1)) | (sK7 = X1) | (sK6 = X2)) )),
% 0.20/0.40 inference(equality_proxy_clausification,[],[f66])).
% 0.20/0.40 thf(f66,plain,(
% 0.20/0.40 ( ! [X2 : $i,X1 : $i] : (($false = (sK1 @ X2)) | ($true = (sK6 = X2)) | ($false = (sK0 @ X1)) | (sK7 = X1)) )),
% 0.20/0.40 inference(binary_proxy_clausification,[],[f65])).
% 0.20/0.40 thf(f65,plain,(
% 0.20/0.40 ( ! [X2 : $i,X1 : $i] : ((sK7 = X1) | ($false = (sK0 @ X1)) | ($true = ((sK1 @ X2) => (sK6 = X2)))) )),
% 0.20/0.40 inference(equality_proxy_clausification,[],[f64])).
% 0.20/0.40 thf(f64,plain,(
% 0.20/0.40 ( ! [X2 : $i,X1 : $i] : (($true = (sK7 = X1)) | ($true = ((sK1 @ X2) => (sK6 = X2))) | ($false = (sK0 @ X1))) )),
% 0.20/0.40 inference(beta_eta_normalization,[],[f63])).
% 0.20/0.40 thf(f63,plain,(
% 0.20/0.40 ( ! [X2 : $i,X1 : $i] : (($false = (sK0 @ X1)) | ($true = (sK7 = X1)) | ($true = ((^[Y0 : $i]: ((sK1 @ Y0) => (sK6 = Y0))) @ X2))) )),
% 0.20/0.40 inference(pi_clausification,[],[f62])).
% 0.20/0.40 thf(f62,plain,(
% 0.20/0.40 ( ! [X1 : $i] : (($false = (sK0 @ X1)) | ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) => (sK6 = Y0)))) = $true) | ($true = (sK7 = X1))) )),
% 0.20/0.40 inference(binary_proxy_clausification,[],[f61])).
% 0.20/0.40 thf(f61,plain,(
% 0.20/0.40 ( ! [X1 : $i] : ((((sK0 @ X1) => (sK7 = X1)) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) => (sK6 = Y0)))) = $true)) )),
% 0.20/0.40 inference(beta_eta_normalization,[],[f60])).
% 0.20/0.40 thf(f60,plain,(
% 0.20/0.40 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) => (sK6 = Y0)))) = $true) | ($true = ((^[Y0 : $i]: ((sK0 @ Y0) => (sK7 = Y0))) @ X1))) )),
% 0.20/0.40 inference(pi_clausification,[],[f54])).
% 0.20/0.40 thf(f54,plain,(
% 0.20/0.40 ($true = (!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (sK7 = Y0))))) | ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) => (sK6 = Y0)))) = $true)),
% 0.20/0.40 inference(binary_proxy_clausification,[],[f46])).
% 0.20/0.40 % SZS output end Proof for theBenchmark
% 0.20/0.40 % (28424)------------------------------
% 0.20/0.40 % (28424)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.40 % (28424)Termination reason: Refutation
% 0.20/0.40
% 0.20/0.40 % (28424)Memory used [KB]: 5756
% 0.20/0.40 % (28424)Time elapsed: 0.030 s
% 0.20/0.40 % (28424)Instructions burned: 34 (million)
% 0.20/0.40 % (28424)------------------------------
% 0.20/0.40 % (28424)------------------------------
% 0.20/0.40 % (28423)Success in time 0.03 s
% 0.20/0.40 % Vampire---4.8 exiting
%------------------------------------------------------------------------------