TSTP Solution File: SEV101^5 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEV101^5 : TPTP v8.1.2. 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 : n027.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 : Sun May 5 09:41:20 EDT 2024
% Result : Theorem 0.13s 0.42s
% Output : Refutation 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.14 % Problem : SEV101^5 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.15 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.13/0.36 % Computer : n027.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Fri May 3 12:31:36 EDT 2024
% 0.13/0.37 % CPUTime :
% 0.13/0.37 This is a TH0_THM_NEQ_NAR problem
% 0.13/0.37 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/tmp/tmp.pTBeMFlsT2/Vampire---4.8_14300
% 0.13/0.38 % (14412)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.13/0.38 % (14411)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.13/0.38 % (14414)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.13/0.38 % (14413)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on Vampire---4 for (2999ds/275Mi)
% 0.13/0.38 % (14415)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.13/0.39 % (14411)Instruction limit reached!
% 0.13/0.39 % (14411)------------------------------
% 0.13/0.39 % (14411)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.39 % (14411)Termination reason: Unknown
% 0.13/0.39 % (14412)Instruction limit reached!
% 0.13/0.39 % (14412)------------------------------
% 0.13/0.39 % (14412)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.39 % (14411)Termination phase: Property scanning
% 0.13/0.39
% 0.13/0.39 % (14411)Memory used [KB]: 1023
% 0.13/0.39 % (14411)Time elapsed: 0.003 s
% 0.13/0.39 % (14411)Instructions burned: 3 (million)
% 0.13/0.39 % (14411)------------------------------
% 0.13/0.39 % (14411)------------------------------
% 0.13/0.39 % (14412)Termination reason: Unknown
% 0.13/0.39 % (14412)Termination phase: Saturation
% 0.13/0.39
% 0.13/0.39 % (14412)Memory used [KB]: 895
% 0.13/0.39 % (14412)Time elapsed: 0.003 s
% 0.13/0.39 % (14412)Instructions burned: 3 (million)
% 0.13/0.39 % (14412)------------------------------
% 0.13/0.39 % (14412)------------------------------
% 0.13/0.39 % (14408)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on Vampire---4 for (2999ds/183Mi)
% 0.13/0.39 % (14415)Instruction limit reached!
% 0.13/0.39 % (14415)------------------------------
% 0.13/0.39 % (14415)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.39 % (14415)Termination reason: Unknown
% 0.13/0.39 % (14415)Termination phase: Property scanning
% 0.13/0.39
% 0.13/0.39 % (14415)Memory used [KB]: 1023
% 0.13/0.39 % (14415)Time elapsed: 0.003 s
% 0.13/0.39 % (14415)Instructions burned: 3 (million)
% 0.13/0.39 % (14415)------------------------------
% 0.13/0.39 % (14415)------------------------------
% 0.13/0.39 % (14409)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 Vampire---4 for (2999ds/4Mi)
% 0.13/0.39 % (14409)Instruction limit reached!
% 0.13/0.39 % (14409)------------------------------
% 0.13/0.39 % (14409)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.39 % (14409)Termination reason: Unknown
% 0.13/0.39 % (14409)Termination phase: Saturation
% 0.13/0.39
% 0.13/0.39 % (14409)Memory used [KB]: 5500
% 0.13/0.39 % (14409)Time elapsed: 0.004 s
% 0.13/0.39 % (14409)Instructions burned: 5 (million)
% 0.13/0.39 % (14409)------------------------------
% 0.13/0.39 % (14409)------------------------------
% 0.13/0.39 % (14414)Instruction limit reached!
% 0.13/0.39 % (14414)------------------------------
% 0.13/0.39 % (14414)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.39 % (14414)Termination reason: Unknown
% 0.13/0.39 % (14414)Termination phase: Saturation
% 0.13/0.39
% 0.13/0.39 % (14414)Memory used [KB]: 5628
% 0.13/0.39 % (14414)Time elapsed: 0.011 s
% 0.13/0.39 % (14414)Instructions burned: 20 (million)
% 0.13/0.39 % (14414)------------------------------
% 0.13/0.39 % (14414)------------------------------
% 0.13/0.40 % (14410)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 Vampire---4 for (2999ds/27Mi)
% 0.13/0.40 % (14416)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 Vampire---4 for (2999ds/37Mi)
% 0.13/0.40 % (14418)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.13/0.40 % (14418)Instruction limit reached!
% 0.13/0.40 % (14418)------------------------------
% 0.13/0.40 % (14418)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.40 % (14418)Termination reason: Unknown
% 0.13/0.40 % (14418)Termination phase: Property scanning
% 0.13/0.40
% 0.13/0.40 % (14418)Memory used [KB]: 1023
% 0.13/0.40 % (14418)Time elapsed: 0.003 s
% 0.13/0.40 % (14418)Instructions burned: 3 (million)
% 0.13/0.40 % (14418)------------------------------
% 0.13/0.40 % (14418)------------------------------
% 0.13/0.40 % (14417)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 Vampire---4 for (2999ds/15Mi)
% 0.13/0.40 % (14410)Refutation not found, incomplete strategy
% 0.13/0.40 % (14410)------------------------------
% 0.13/0.40 % (14410)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.40 % (14410)Termination reason: Refutation not found, incomplete strategy
% 0.13/0.40
% 0.13/0.40
% 0.13/0.40 % (14410)Memory used [KB]: 5500
% 0.13/0.40 % (14410)Time elapsed: 0.010 s
% 0.13/0.40 % (14410)Instructions burned: 8 (million)
% 0.13/0.40 % (14410)------------------------------
% 0.13/0.40 % (14410)------------------------------
% 0.13/0.41 % (14420)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on Vampire---4 for (2999ds/7Mi)
% 0.13/0.41 % (14419)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 Vampire---4 for (2999ds/1041Mi)
% 0.13/0.41 % (14417)Instruction limit reached!
% 0.13/0.41 % (14417)------------------------------
% 0.13/0.41 % (14417)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.41 % (14417)Termination reason: Unknown
% 0.13/0.41 % (14417)Termination phase: Saturation
% 0.13/0.41
% 0.13/0.41 % (14417)Memory used [KB]: 5628
% 0.13/0.41 % (14417)Time elapsed: 0.009 s
% 0.13/0.41 % (14417)Instructions burned: 15 (million)
% 0.13/0.41 % (14417)------------------------------
% 0.13/0.41 % (14417)------------------------------
% 0.13/0.41 % (14420)Instruction limit reached!
% 0.13/0.41 % (14420)------------------------------
% 0.13/0.41 % (14420)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.41 % (14420)Termination reason: Unknown
% 0.13/0.41 % (14420)Termination phase: Saturation
% 0.13/0.41
% 0.13/0.41 % (14420)Memory used [KB]: 1023
% 0.13/0.41 % (14420)Time elapsed: 0.005 s
% 0.13/0.41 % (14420)Instructions burned: 7 (million)
% 0.13/0.41 % (14420)------------------------------
% 0.13/0.41 % (14420)------------------------------
% 0.13/0.41 % (14413)First to succeed.
% 0.13/0.41 % (14416)Instruction limit reached!
% 0.13/0.41 % (14416)------------------------------
% 0.13/0.41 % (14416)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.41 % (14416)Termination reason: Unknown
% 0.13/0.41 % (14416)Termination phase: Saturation
% 0.13/0.41
% 0.13/0.41 % (14416)Memory used [KB]: 5756
% 0.13/0.41 % (14416)Time elapsed: 0.018 s
% 0.13/0.41 % (14416)Instructions burned: 38 (million)
% 0.13/0.41 % (14416)------------------------------
% 0.13/0.41 % (14416)------------------------------
% 0.13/0.42 % (14421)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on Vampire---4 for (2999ds/16Mi)
% 0.13/0.42 % (14422)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.13/0.42 % (14422)Instruction limit reached!
% 0.13/0.42 % (14422)------------------------------
% 0.13/0.42 % (14422)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.42 % (14422)Termination reason: Unknown
% 0.13/0.42 % (14422)Termination phase: Twee Goal Transformation
% 0.13/0.42
% 0.13/0.42 % (14422)Memory used [KB]: 1023
% 0.13/0.42 % (14422)Time elapsed: 0.004 s
% 0.13/0.42 % (14422)Instructions burned: 4 (million)
% 0.13/0.42 % (14422)------------------------------
% 0.13/0.42 % (14422)------------------------------
% 0.13/0.42 % (14413)Refutation found. Thanks to Tanya!
% 0.13/0.42 % SZS status Theorem for Vampire---4
% 0.13/0.42 % SZS output start Proof for Vampire---4
% 0.13/0.42 thf(func_def_8, type, sK0: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i).
% 0.13/0.42 thf(func_def_9, type, sK1: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o).
% 0.13/0.42 thf(func_def_10, type, sK2: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o).
% 0.13/0.42 thf(func_def_11, type, sK3: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o).
% 0.13/0.42 thf(func_def_12, type, sK4: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o).
% 0.13/0.42 thf(func_def_13, type, sK5: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i).
% 0.13/0.42 thf(func_def_15, type, ph7: !>[X0: $tType]:(X0)).
% 0.13/0.42 thf(func_def_21, type, sK9: (($i > $o) > ($i > $o) > $i > $o) > $i).
% 0.13/0.42 thf(func_def_22, type, sK10: (($i > $o) > ($i > $o) > $i > $o) > $i).
% 0.13/0.42 thf(f383,plain,(
% 0.13/0.42 $false),
% 0.13/0.42 inference(avatar_sat_refutation,[],[f146,f150,f382])).
% 0.13/0.42 thf(f382,plain,(
% 0.13/0.42 spl6_2 | ~spl6_5),
% 0.13/0.42 inference(avatar_contradiction_clause,[],[f381])).
% 0.13/0.42 thf(f381,plain,(
% 0.13/0.42 $false | (spl6_2 | ~spl6_5)),
% 0.13/0.42 inference(subsumption_resolution,[],[f380,f300])).
% 0.13/0.42 thf(f300,plain,(
% 0.13/0.42 ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) != (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | (spl6_2 | ~spl6_5)),
% 0.13/0.42 inference(subsumption_resolution,[],[f298,f86])).
% 0.13/0.42 thf(f86,plain,(
% 0.13/0.42 ((^[Y0 : $i]: ($false)) != (^[Y0 : $i]: ($true))) | spl6_2),
% 0.13/0.42 inference(avatar_component_clause,[],[f84])).
% 0.13/0.42 thf(f84,plain,(
% 0.13/0.42 spl6_2 <=> ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))),
% 0.13/0.42 introduced(avatar_definition,[new_symbols(naming,[spl6_2])])).
% 0.13/0.42 thf(f298,plain,(
% 0.13/0.42 ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) != (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ~spl6_5),
% 0.13/0.42 inference(equality_proxy_clausification,[],[f297])).
% 0.13/0.42 thf(f297,plain,(
% 0.13/0.42 ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) != (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ~spl6_5),
% 0.13/0.42 inference(equality_proxy_clausification,[],[f296])).
% 0.13/0.42 thf(f296,plain,(
% 0.13/0.42 (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) != $true) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ~spl6_5),
% 0.13/0.42 inference(beta_eta_normalization,[],[f282])).
% 0.13/0.42 thf(f282,plain,(
% 0.13/0.42 ( ! [X4 : $i] : (($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4) = $true)) ) | ~spl6_5),
% 0.13/0.42 inference(primitive_instantiation,[],[f149])).
% 0.13/0.42 thf(f149,plain,(
% 0.13/0.42 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X4 : $i] : (((X0 @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) != $true) | ($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4))) ) | ~spl6_5),
% 0.13/0.42 inference(avatar_component_clause,[],[f148])).
% 0.13/0.42 thf(f148,plain,(
% 0.13/0.42 spl6_5 <=> ! [X4,X0 : ($i > $o) > ($i > $o) > $i > $o] : (($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4)) | ((X0 @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) != $true))),
% 0.13/0.42 introduced(avatar_definition,[new_symbols(naming,[spl6_5])])).
% 0.13/0.42 thf(f380,plain,(
% 0.13/0.42 ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | spl6_2),
% 0.13/0.42 inference(forward_demodulation,[],[f379,f323])).
% 0.13/0.42 thf(f323,plain,(
% 0.13/0.42 ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | spl6_2),
% 0.13/0.42 inference(subsumption_resolution,[],[f317,f86])).
% 0.13/0.42 thf(f317,plain,(
% 0.13/0.42 ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | spl6_2),
% 0.13/0.42 inference(duplicate_literal_removal,[],[f316])).
% 0.13/0.42 thf(f316,plain,(
% 0.13/0.42 ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | spl6_2),
% 0.13/0.42 inference(equality_proxy_clausification,[],[f315])).
% 0.13/0.42 thf(f315,plain,(
% 0.13/0.42 ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) = $true) | ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | spl6_2),
% 0.13/0.42 inference(equality_proxy_clausification,[],[f314])).
% 0.13/0.42 thf(f314,plain,(
% 0.13/0.42 (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) = $true) | ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | spl6_2),
% 0.13/0.42 inference(beta_eta_normalization,[],[f301])).
% 0.13/0.42 thf(f301,plain,(
% 0.13/0.42 ( ! [X8 : $i,X4 : $i] : ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X8) = $true) | ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4) = $true)) ) | spl6_2),
% 0.13/0.42 inference(primitive_instantiation,[],[f197])).
% 0.13/0.42 thf(f197,plain,(
% 0.13/0.42 ( ! [X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X4 : $i] : (((X1 @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X8) = $true) | ((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4) = $true)) ) | spl6_2),
% 0.13/0.42 inference(subsumption_resolution,[],[f196,f86])).
% 0.13/0.42 thf(f196,plain,(
% 0.13/0.42 ( ! [X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X4 : $i] : (((X1 @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X8) = $true) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4) = $true) | ((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) )),
% 0.13/0.42 inference(equality_proxy_clausification,[],[f195])).
% 0.13/0.42 thf(f195,plain,(
% 0.13/0.42 ( ! [X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X4 : $i] : (((X1 @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X8) = $true) | ((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4) = $true)) )),
% 0.13/0.42 inference(equality_proxy_clausification,[],[f194])).
% 0.13/0.42 thf(f194,plain,(
% 0.13/0.42 ( ! [X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X4 : $i] : (((X1 @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X8) = $true) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4) = $true) | (((sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) = $true) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true)) )),
% 0.13/0.42 inference(trivial_inequality_removal,[],[f193])).
% 0.13/0.42 thf(f193,plain,(
% 0.13/0.42 ( ! [X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X4 : $i] : ((((sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) = $true) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ((X1 @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X8) = $true) | ($true != $true) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4) = $true)) )),
% 0.13/0.42 inference(boolean_simplification,[],[f192])).
% 0.13/0.42 thf(f192,plain,(
% 0.13/0.42 ( ! [X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X4 : $i] : ((((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ((X1 @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X8) = $true) | (((sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) = $true) | (((sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) != $true) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4) = $true)) )),
% 0.13/0.42 inference(beta_eta_normalization,[],[f172])).
% 0.13/0.42 thf(f172,plain,(
% 0.13/0.42 ( ! [X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X4 : $i] : (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4) = $true) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) != $true) | ((X1 @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X8) = $true) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4) = $true) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK2 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X8) = $true)) )),
% 0.13/0.42 inference(primitive_instantiation,[],[f25])).
% 0.13/0.42 thf(f25,plain,(
% 0.13/0.42 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X4 : $i] : (((X0 @ (sK1 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0)) != $true) | ($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4)) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4) = $true) | ((X1 @ (sK4 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X8) = $true) | ($true = (X0 @ (sK4 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X8))) )),
% 0.13/0.42 inference(boolean_simplification,[],[f24])).
% 0.13/0.42 thf(f24,plain,(
% 0.13/0.42 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X4 : $i] : (((X1 @ (sK4 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X8) = $true) | ((X0 @ (sK1 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0)) != $true) | ($true = (X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X4)) | ($true = (X0 @ (sK4 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X8)) | ($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4))) )),
% 0.13/0.42 inference(boolean_simplification,[],[f23])).
% 0.13/0.42 thf(f23,plain,(
% 0.13/0.42 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X4 : $i] : (((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X4) = $true) | ($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4)) | ($true = (X0 @ (sK4 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X8)) | ((X0 @ (sK1 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0)) != $true) | ((X1 @ (sK4 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X8) = $true)) )),
% 0.13/0.42 inference(boolean_simplification,[],[f22])).
% 0.13/0.42 thf(f22,plain,(
% 0.13/0.42 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X4 : $i] : (($true = (X0 @ (sK4 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X8)) | ((X1 @ (sK4 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X8) = $true) | ($true = (X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ($false)) @ X4)) | ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X4) = $true) | ((X0 @ (sK1 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0)) != $true)) )),
% 0.13/0.42 inference(boolean_simplification,[],[f17])).
% 0.13/0.42 thf(f17,plain,(
% 0.13/0.42 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i,X4 : $i] : (((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X4) = $true) | ((X1 @ (sK4 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X8) = $true) | ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X4) = $true) | ((X0 @ (sK1 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0)) != $true) | ($true = (X0 @ (sK4 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X8))) )),
% 0.13/0.42 inference(cnf_transformation,[],[f13])).
% 0.13/0.42 thf(f13,plain,(
% 0.13/0.42 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : ((((X1 @ (sK1 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0)) != $true) & ((X0 @ (sK1 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0)) != $true)) | ! [X4] : (((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X4) = $true) | ((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X4) = $true)) | (! [X8] : (((X1 @ (sK4 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X8) = $true) | ($true = (X0 @ (sK4 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X8))) & (((X0 @ (sK3 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK5 @ X1 @ X0)) != $true) & ((X1 @ (sK3 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK5 @ X1 @ X0)) != $true)) & ! [X10] : (((X1 @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X10) = $true) | ($true = (X0 @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X10)))))),
% 0.13/0.42 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f9,f12,f11,f10])).
% 0.13/0.42 thf(f10,plain,(
% 0.13/0.42 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X2,X3 : $i > $o] : (((X1 @ X3 @ X3 @ X2) != $true) & ((X0 @ X3 @ X3 @ X2) != $true)) => (((X1 @ (sK1 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0)) != $true) & ((X0 @ (sK1 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0)) != $true)))),
% 0.13/0.42 introduced(choice_axiom,[])).
% 0.13/0.42 thf(f11,plain,(
% 0.13/0.42 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X5 : $i > $o,X6 : $i > $o,X7 : $i > $o] : (! [X8] : (((X1 @ X7 @ X5 @ X8) = $true) | ($true = (X0 @ X7 @ X5 @ X8))) & ? [X9] : (((X0 @ X6 @ X5 @ X9) != $true) & ((X1 @ X6 @ X5 @ X9) != $true)) & ! [X10] : (((X1 @ X6 @ X7 @ X10) = $true) | ((X0 @ X6 @ X7 @ X10) = $true))) => (! [X8] : (((X1 @ (sK4 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X8) = $true) | ($true = (X0 @ (sK4 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X8))) & ? [X9] : (($true != (X0 @ (sK3 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X9)) & ((X1 @ (sK3 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X9) != $true)) & ! [X10] : (((X1 @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X10) = $true) | ($true = (X0 @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X10)))))),
% 0.13/0.42 introduced(choice_axiom,[])).
% 0.13/0.42 thf(f12,plain,(
% 0.13/0.42 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X9] : (($true != (X0 @ (sK3 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X9)) & ((X1 @ (sK3 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X9) != $true)) => (((X0 @ (sK3 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK5 @ X1 @ X0)) != $true) & ((X1 @ (sK3 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK5 @ X1 @ X0)) != $true)))),
% 0.13/0.42 introduced(choice_axiom,[])).
% 0.13/0.42 thf(f9,plain,(
% 0.13/0.42 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X2,X3 : $i > $o] : (((X1 @ X3 @ X3 @ X2) != $true) & ((X0 @ X3 @ X3 @ X2) != $true)) | ! [X4] : (((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X4) = $true) | ((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X4) = $true)) | ? [X5 : $i > $o,X6 : $i > $o,X7 : $i > $o] : (! [X8] : (((X1 @ X7 @ X5 @ X8) = $true) | ($true = (X0 @ X7 @ X5 @ X8))) & ? [X9] : (((X0 @ X6 @ X5 @ X9) != $true) & ((X1 @ X6 @ X5 @ X9) != $true)) & ! [X10] : (((X1 @ X6 @ X7 @ X10) = $true) | ((X0 @ X6 @ X7 @ X10) = $true))))),
% 0.13/0.42 inference(rectify,[],[f8])).
% 0.13/0.42 thf(f8,plain,(
% 0.13/0.42 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X9,X10 : $i > $o] : (((X1 @ X10 @ X10 @ X9) != $true) & ((X0 @ X10 @ X10 @ X9) != $true)) | ! [X2] : (((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2) = $true) | ($true = (X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) | ? [X5 : $i > $o,X4 : $i > $o,X3 : $i > $o] : (! [X7] : (((X1 @ X3 @ X5 @ X7) = $true) | ($true = (X0 @ X3 @ X5 @ X7))) & ? [X8] : (((X0 @ X4 @ X5 @ X8) != $true) & ($true != (X1 @ X4 @ X5 @ X8))) & ! [X6] : (((X1 @ X4 @ X3 @ X6) = $true) | ($true = (X0 @ X4 @ X3 @ X6)))))),
% 0.13/0.42 inference(flattening,[],[f7])).
% 0.13/0.42 thf(f7,plain,(
% 0.13/0.42 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (! [X2] : (((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2) = $true) | ($true = (X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) | ? [X9,X10 : $i > $o] : (((X1 @ X10 @ X10 @ X9) != $true) & ((X0 @ X10 @ X10 @ X9) != $true)) | ? [X5 : $i > $o,X4 : $i > $o,X3 : $i > $o] : (? [X8] : (((X0 @ X4 @ X5 @ X8) != $true) & ($true != (X1 @ X4 @ X5 @ X8))) & (! [X6] : (((X1 @ X4 @ X3 @ X6) = $true) | ($true = (X0 @ X4 @ X3 @ X6))) & ! [X7] : (((X1 @ X3 @ X5 @ X7) = $true) | ($true = (X0 @ X3 @ X5 @ X7))))))),
% 0.13/0.42 inference(ennf_transformation,[],[f6])).
% 0.13/0.42 thf(f6,plain,(
% 0.13/0.42 ~? [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (~! [X2] : (((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2) = $true) | ($true = (X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) & ! [X9,X10 : $i > $o] : (((X0 @ X10 @ X10 @ X9) = $true) | ((X1 @ X10 @ X10 @ X9) = $true)) & ! [X5 : $i > $o,X4 : $i > $o,X3 : $i > $o] : ((! [X6] : (((X1 @ X4 @ X3 @ X6) = $true) | ($true = (X0 @ X4 @ X3 @ X6))) & ! [X7] : (((X1 @ X3 @ X5 @ X7) = $true) | ($true = (X0 @ X3 @ X5 @ X7)))) => ! [X8] : (((X0 @ X4 @ X5 @ X8) = $true) | ($true = (X1 @ X4 @ X5 @ X8)))))),
% 0.13/0.42 inference(rectify,[],[f5])).
% 0.13/0.42 thf(f5,plain,(
% 0.13/0.42 ~? [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (~! [X2] : (((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X2) = $true) | ($true = (X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X2))) & ! [X7 : $i > $o,X8 : $i > $o,X9 : $i > $o] : ((! [X10] : (($true = (X1 @ X8 @ X7 @ X10)) | ($true = (X0 @ X8 @ X7 @ X10))) & ! [X11] : (($true = (X0 @ X7 @ X9 @ X11)) | ($true = (X1 @ X7 @ X9 @ X11)))) => ! [X12] : (($true = (X0 @ X8 @ X9 @ X12)) | ($true = (X1 @ X8 @ X9 @ X12)))) & ! [X13,X14 : $i > $o] : (((X1 @ X14 @ X14 @ X13) = $true) | ($true = (X0 @ X14 @ X14 @ X13))))),
% 0.13/0.42 inference(fool_elimination,[],[f4])).
% 0.13/0.42 thf(f4,plain,(
% 0.13/0.42 ~? [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (~! [X2] : ((X1 @ (^[X3 : $i] : (~p | p)) @ (^[X4 : $i] : (~p & p)) @ X2) | (X0 @ (^[X5 : $i] : (p | ~p)) @ (^[X6 : $i] : (~p & p)) @ X2)) & ! [X7 : $i > $o,X8 : $i > $o,X9 : $i > $o] : ((! [X10] : ((X1 @ X8 @ X7 @ X10) | (X0 @ X8 @ X7 @ X10)) & ! [X11] : ((X0 @ X7 @ X9 @ X11) | (X1 @ X7 @ X9 @ X11))) => ! [X12] : ((X0 @ X8 @ X9 @ X12) | (X1 @ X8 @ X9 @ X12))) & ! [X13,X14 : $i > $o] : ((X1 @ X14 @ X14 @ X13) | (X0 @ X14 @ X14 @ X13)))),
% 0.13/0.42 inference(rectify,[],[f2])).
% 0.13/0.42 thf(f2,negated_conjecture,(
% 0.13/0.42 ~? [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (~! [X3] : ((X1 @ (^[X2 : $i] : (~p | p)) @ (^[X2 : $i] : (~p & p)) @ X3) | (X0 @ (^[X2 : $i] : (p | ~p)) @ (^[X2 : $i] : (~p & p)) @ X3)) & ! [X4 : $i > $o,X2 : $i > $o,X5 : $i > $o] : ((! [X3] : ((X1 @ X2 @ X4 @ X3) | (X0 @ X2 @ X4 @ X3)) & ! [X3] : ((X0 @ X4 @ X5 @ X3) | (X1 @ X4 @ X5 @ X3))) => ! [X3] : ((X0 @ X2 @ X5 @ X3) | (X1 @ X2 @ X5 @ X3))) & ! [X3,X2 : $i > $o] : ((X1 @ X2 @ X2 @ X3) | (X0 @ X2 @ X2 @ X3)))),
% 0.13/0.42 inference(negated_conjecture,[],[f1])).
% 0.13/0.42 thf(f1,conjecture,(
% 0.13/0.42 ? [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (~! [X3] : ((X1 @ (^[X2 : $i] : (~p | p)) @ (^[X2 : $i] : (~p & p)) @ X3) | (X0 @ (^[X2 : $i] : (p | ~p)) @ (^[X2 : $i] : (~p & p)) @ X3)) & ! [X4 : $i > $o,X2 : $i > $o,X5 : $i > $o] : ((! [X3] : ((X1 @ X2 @ X4 @ X3) | (X0 @ X2 @ X4 @ X3)) & ! [X3] : ((X0 @ X4 @ X5 @ X3) | (X1 @ X4 @ X5 @ X3))) => ! [X3] : ((X0 @ X2 @ X5 @ X3) | (X1 @ X2 @ X5 @ X3))) & ! [X3,X2 : $i > $o] : ((X1 @ X2 @ X2 @ X3) | (X0 @ X2 @ X2 @ X3)))),
% 0.13/0.42 file('/export/starexec/sandbox/tmp/tmp.pTBeMFlsT2/Vampire---4.8_14300',cTHM120E_pme)).
% 0.13/0.42 thf(f379,plain,(
% 0.13/0.42 ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | spl6_2),
% 0.13/0.42 inference(subsumption_resolution,[],[f366,f86])).
% 0.13/0.42 thf(f366,plain,(
% 0.13/0.42 ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | spl6_2),
% 0.13/0.42 inference(equality_proxy_clausification,[],[f365])).
% 0.13/0.42 thf(f365,plain,(
% 0.13/0.42 (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | spl6_2),
% 0.13/0.42 inference(duplicate_literal_removal,[],[f364])).
% 0.13/0.42 thf(f364,plain,(
% 0.13/0.42 ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | spl6_2),
% 0.13/0.42 inference(equality_proxy_clausification,[],[f363])).
% 0.13/0.42 thf(f363,plain,(
% 0.13/0.42 ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | (((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) = $true) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | spl6_2),
% 0.13/0.42 inference(beta_eta_normalization,[],[f354])).
% 0.13/0.42 thf(f354,plain,(
% 0.13/0.42 ( ! [X10 : $i,X4 : $i] : (($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X10)) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4) = $true) | ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) ) | spl6_2),
% 0.13/0.42 inference(primitive_instantiation,[],[f255])).
% 0.13/0.42 thf(f255,plain,(
% 0.13/0.42 ( ! [X10 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X4 : $i] : (((X1 @ (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X10) = $true) | ((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4) = $true)) ) | spl6_2),
% 0.13/0.42 inference(subsumption_resolution,[],[f254,f86])).
% 0.13/0.42 thf(f254,plain,(
% 0.13/0.42 ( ! [X10 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X4 : $i] : (((X1 @ (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X10) = $true) | ((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4) = $true) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) )),
% 0.13/0.42 inference(equality_proxy_clausification,[],[f253])).
% 0.13/0.42 thf(f253,plain,(
% 0.13/0.42 ( ! [X10 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X4 : $i] : (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4) = $true) | ((X1 @ (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X10) = $true) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))))) )),
% 0.13/0.42 inference(equality_proxy_clausification,[],[f252])).
% 0.13/0.42 thf(f252,plain,(
% 0.13/0.42 ( ! [X10 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X4 : $i] : ((((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) = $true) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ((X1 @ (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X10) = $true) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4) = $true)) )),
% 0.13/0.42 inference(trivial_inequality_removal,[],[f251])).
% 0.13/0.42 thf(f251,plain,(
% 0.13/0.42 ( ! [X10 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X4 : $i] : (((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4) = $true) | (((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) = $true) | ($true != $true) | ((X1 @ (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X10) = $true) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true)) )),
% 0.13/0.42 inference(boolean_simplification,[],[f250])).
% 0.13/0.42 thf(f250,plain,(
% 0.13/0.42 ( ! [X10 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X4 : $i] : (((X1 @ (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X10) = $true) | (((sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) != $true) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4) = $true) | (((sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) = (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) = $true)) )),
% 0.13/0.42 inference(beta_eta_normalization,[],[f230])).
% 0.13/0.42 thf(f230,plain,(
% 0.13/0.42 ( ! [X10 : $i,X1 : ($i > $o) > ($i > $o) > $i > $o,X4 : $i] : (((X1 @ (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X10) = $true) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK1 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK0 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))))) != $true) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4) = $true) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4) = $true) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK3 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ (sK4 @ X1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0))))))) @ X10) = $true)) )),
% 0.13/0.42 inference(primitive_instantiation,[],[f49])).
% 0.13/0.42 thf(f49,plain,(
% 0.13/0.42 ( ! [X10 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X4 : $i] : (((X0 @ (sK1 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0)) != $true) | ($true = (X0 @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X10)) | ($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4)) | ((X1 @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X10) = $true) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4) = $true)) )),
% 0.13/0.42 inference(boolean_simplification,[],[f48])).
% 0.13/0.42 thf(f48,plain,(
% 0.13/0.42 ( ! [X10 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X4 : $i] : (((X0 @ (sK1 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0)) != $true) | ($true = (X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ($false)) @ X4)) | ($true = (X0 @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X10)) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4) = $true) | ((X1 @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X10) = $true)) )),
% 0.13/0.42 inference(boolean_simplification,[],[f47])).
% 0.13/0.42 thf(f47,plain,(
% 0.13/0.42 ( ! [X10 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X4 : $i] : (($true = (X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X4)) | ($true = (X0 @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X10)) | ($true = (X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ($false)) @ X4)) | ((X1 @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X10) = $true) | ((X0 @ (sK1 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0)) != $true)) )),
% 0.13/0.42 inference(boolean_simplification,[],[f46])).
% 0.13/0.42 thf(f46,plain,(
% 0.13/0.42 ( ! [X10 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X4 : $i] : (((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X4) = $true) | ($true = (X0 @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X10)) | ($true = (X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X4)) | ((X1 @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X10) = $true) | ((X0 @ (sK1 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0)) != $true)) )),
% 0.13/0.42 inference(boolean_simplification,[],[f14])).
% 0.13/0.42 thf(f14,plain,(
% 0.13/0.42 ( ! [X10 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X4 : $i] : (((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X4) = $true) | ((X1 @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X10) = $true) | ((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X4) = $true) | ((X0 @ (sK1 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0)) != $true) | ($true = (X0 @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X10))) )),
% 0.13/0.42 inference(cnf_transformation,[],[f13])).
% 0.13/0.42 thf(f150,plain,(
% 0.13/0.42 spl6_2 | spl6_5),
% 0.13/0.42 inference(avatar_split_clause,[],[f113,f148,f84])).
% 0.13/0.42 thf(f113,plain,(
% 0.13/0.42 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X4 : $i] : (($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4)) | ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ((X0 @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) != $true)) )),
% 0.13/0.42 inference(equality_proxy_clausification,[],[f112])).
% 0.13/0.42 thf(f112,plain,(
% 0.13/0.42 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X4 : $i] : (($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4)) | ((X0 @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) != $true) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true)) )),
% 0.13/0.42 inference(trivial_inequality_removal,[],[f111])).
% 0.13/0.42 thf(f111,plain,(
% 0.13/0.42 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X4 : $i] : ((((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4)) | ($true != $true) | ((X0 @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) != $true)) )),
% 0.13/0.42 inference(boolean_simplification,[],[f110])).
% 0.13/0.42 thf(f110,plain,(
% 0.13/0.42 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X4 : $i] : (($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4)) | (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) != $true) | (((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) = $true) | ((X0 @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) != $true)) )),
% 0.13/0.42 inference(beta_eta_normalization,[],[f95])).
% 0.13/0.42 thf(f95,plain,(
% 0.13/0.42 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X4 : $i] : ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4) = $true) | ((X0 @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) != $true) | ($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4)) | ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)))) )),
% 0.13/0.42 inference(primitive_instantiation,[],[f37])).
% 0.13/0.42 thf(f37,plain,(
% 0.13/0.42 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X4 : $i] : (((X1 @ (sK1 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0)) != $true) | ((X0 @ (sK3 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK5 @ X1 @ X0)) != $true) | ($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4)) | ((X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4) = $true)) )),
% 0.13/0.42 inference(boolean_simplification,[],[f36])).
% 0.13/0.42 thf(f36,plain,(
% 0.13/0.42 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X4 : $i] : (($true = (X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X4)) | ((X0 @ (sK3 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK5 @ X1 @ X0)) != $true) | ($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X4)) | ((X1 @ (sK1 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0)) != $true)) )),
% 0.13/0.42 inference(boolean_simplification,[],[f35])).
% 0.13/0.42 thf(f35,plain,(
% 0.13/0.42 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X4 : $i] : (((X0 @ (sK3 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK5 @ X1 @ X0)) != $true) | ((X1 @ (sK1 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0)) != $true) | ($true = (X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: ($false)) @ X4)) | ($true = (X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X4))) )),
% 0.13/0.42 inference(boolean_simplification,[],[f34])).
% 0.13/0.42 thf(f34,plain,(
% 0.13/0.42 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X4 : $i] : (((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X4) = $true) | ((X0 @ (sK3 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK5 @ X1 @ X0)) != $true) | ((X1 @ (sK1 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0)) != $true) | ($true = (X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: ($false)) @ X4))) )),
% 0.13/0.42 inference(boolean_simplification,[],[f20])).
% 0.13/0.42 thf(f20,plain,(
% 0.13/0.42 ( ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X4 : $i] : (((X1 @ (sK1 @ X1 @ X0) @ (sK1 @ X1 @ X0) @ (sK0 @ X1 @ X0)) != $true) | ((X0 @ (sK3 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK5 @ X1 @ X0)) != $true) | ((X1 @ (^[Y0 : $i]: (p | (~ p))) @ (^[Y0 : $i]: (p & (~ p))) @ X4) = $true) | ((X0 @ (^[Y0 : $i]: ((~ p) | p)) @ (^[Y0 : $i]: (p & (~ p))) @ X4) = $true)) )),
% 0.13/0.42 inference(cnf_transformation,[],[f13])).
% 0.13/0.42 thf(f146,plain,(
% 0.13/0.42 ~spl6_2),
% 0.13/0.42 inference(avatar_contradiction_clause,[],[f145])).
% 0.13/0.42 thf(f145,plain,(
% 0.13/0.42 $false | ~spl6_2),
% 0.13/0.42 inference(trivial_inequality_removal,[],[f144])).
% 0.13/0.42 thf(f144,plain,(
% 0.13/0.42 ($false = $true) | ~spl6_2),
% 0.13/0.42 inference(beta_eta_normalization,[],[f143])).
% 0.13/0.42 thf(f143,plain,(
% 0.13/0.42 ( ! [X1 : $i] : ((((^[Y0 : $i]: ($false)) @ X1) = ((^[Y0 : $i]: ($true)) @ X1))) ) | ~spl6_2),
% 0.13/0.42 inference(argument_congruence,[],[f85])).
% 0.13/0.42 thf(f85,plain,(
% 0.13/0.42 ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))) | ~spl6_2),
% 0.13/0.42 inference(avatar_component_clause,[],[f84])).
% 0.13/0.42 % SZS output end Proof for Vampire---4
% 0.13/0.42 % (14413)------------------------------
% 0.13/0.42 % (14413)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.42 % (14413)Termination reason: Refutation
% 0.13/0.42
% 0.13/0.42 % (14413)Memory used [KB]: 6012
% 0.13/0.42 % (14413)Time elapsed: 0.038 s
% 0.13/0.42 % (14413)Instructions burned: 63 (million)
% 0.13/0.42 % (14413)------------------------------
% 0.13/0.42 % (14413)------------------------------
% 0.13/0.42 % (14407)Success in time 0.046 s
% 0.13/0.42 % Vampire---4.8 exiting
%------------------------------------------------------------------------------