TSTP Solution File: SEV066^5 by Vampire---4.9
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEV066^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n026.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 : Mon Jun 24 16:01:41 EDT 2024
% Result : Theorem 0.15s 0.39s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11 % Problem : SEV066^5 : TPTP v8.2.0. Released v4.0.0.
% 0.05/0.11 % Command : run_vampire %s %d THM
% 0.10/0.31 % Computer : n026.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Fri Jun 21 19:03:09 EDT 2024
% 0.15/0.31 % CPUTime :
% 0.15/0.33 This is a TH0_THM_NEQ_NAR problem
% 0.15/0.33 Running higher-order theorem proving
% 0.15/0.33 Running /export/starexec/sandbox2/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/benchmark/theBenchmark.p -m 16384 -t 300
% 0.15/0.35 % (19949)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.35 % (19952)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.35 % (19953)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.35 % (19954)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.15/0.35 % (19951)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.15/0.35 % (19950)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.15/0.35 % (19955)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.35 % (19952)Instruction limit reached!
% 0.15/0.35 % (19952)------------------------------
% 0.15/0.35 % (19952)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.15/0.35 % (19952)Termination reason: Unknown
% 0.15/0.35 % (19952)Termination phase: Preprocessing 3
% 0.15/0.35
% 0.15/0.35 % (19952)Memory used [KB]: 1023
% 0.15/0.35 % (19952)Time elapsed: 0.003 s
% 0.15/0.35 % (19952)Instructions burned: 2 (million)
% 0.15/0.35 % (19952)------------------------------
% 0.15/0.35 % (19952)------------------------------
% 0.15/0.35 % (19953)Instruction limit reached!
% 0.15/0.35 % (19953)------------------------------
% 0.15/0.35 % (19953)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.15/0.35 % (19953)Termination reason: Unknown
% 0.15/0.35 % (19953)Termination phase: Saturation
% 0.15/0.35
% 0.15/0.35 % (19953)Memory used [KB]: 1023
% 0.15/0.35 % (19953)Time elapsed: 0.003 s
% 0.15/0.35 % (19953)Instructions burned: 2 (million)
% 0.15/0.35 % (19953)------------------------------
% 0.15/0.35 % (19953)------------------------------
% 0.15/0.35 % (19950)Instruction limit reached!
% 0.15/0.35 % (19950)------------------------------
% 0.15/0.35 % (19950)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.15/0.35 % (19950)Termination reason: Unknown
% 0.15/0.35 % (19950)Termination phase: Saturation
% 0.15/0.35
% 0.15/0.35 % (19950)Memory used [KB]: 5500
% 0.15/0.35 % (19950)Time elapsed: 0.004 s
% 0.15/0.35 % (19950)Instructions burned: 4 (million)
% 0.15/0.35 % (19950)------------------------------
% 0.15/0.35 % (19950)------------------------------
% 0.15/0.35 % (19951)Refutation not found, incomplete strategy
% 0.15/0.35 % (19951)------------------------------
% 0.15/0.35 % (19951)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.15/0.35 % (19951)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.35
% 0.15/0.35
% 0.15/0.35 % (19951)Memory used [KB]: 5500
% 0.15/0.35 % (19951)Time elapsed: 0.005 s
% 0.15/0.35 % (19951)Instructions burned: 5 (million)
% 0.15/0.35 % (19951)------------------------------
% 0.15/0.35 % (19951)------------------------------
% 0.15/0.36 % (19955)Instruction limit reached!
% 0.15/0.36 % (19955)------------------------------
% 0.15/0.36 % (19955)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.15/0.36 % (19955)Termination reason: Unknown
% 0.15/0.36 % (19955)Termination phase: Saturation
% 0.15/0.36
% 0.15/0.36 % (19955)Memory used [KB]: 5628
% 0.15/0.36 % (19955)Time elapsed: 0.011 s
% 0.15/0.36 % (19955)Instructions burned: 18 (million)
% 0.15/0.36 % (19955)------------------------------
% 0.15/0.36 % (19955)------------------------------
% 0.15/0.36 % (19958)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)
% 0.15/0.36 % (19957)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)
% 0.15/0.36 % (19956)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.15/0.36 % (19956)Instruction limit reached!
% 0.15/0.36 % (19956)------------------------------
% 0.15/0.36 % (19956)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.15/0.36 % (19956)Termination reason: Unknown
% 0.15/0.36 % (19956)Termination phase: Saturation
% 0.15/0.36
% 0.15/0.36 % (19956)Memory used [KB]: 5500
% 0.15/0.36 % (19956)Time elapsed: 0.004 s
% 0.15/0.36 % (19956)Instructions burned: 4 (million)
% 0.15/0.36 % (19956)------------------------------
% 0.15/0.36 % (19956)------------------------------
% 0.15/0.36 % (19959)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)
% 0.15/0.37 % (19959)Instruction limit reached!
% 0.15/0.37 % (19959)------------------------------
% 0.15/0.37 % (19959)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.15/0.37 % (19959)Termination reason: Unknown
% 0.15/0.37 % (19959)Termination phase: Saturation
% 0.15/0.37
% 0.15/0.37 % (19959)Memory used [KB]: 1023
% 0.15/0.37 % (19959)Time elapsed: 0.003 s
% 0.15/0.37 % (19959)Instructions burned: 3 (million)
% 0.15/0.37 % (19959)------------------------------
% 0.15/0.37 % (19959)------------------------------
% 0.15/0.37 % (19958)Instruction limit reached!
% 0.15/0.37 % (19958)------------------------------
% 0.15/0.37 % (19958)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.15/0.37 % (19958)Termination reason: Unknown
% 0.15/0.37 % (19958)Termination phase: Saturation
% 0.15/0.37
% 0.15/0.37 % (19958)Memory used [KB]: 5628
% 0.15/0.37 % (19958)Time elapsed: 0.007 s
% 0.15/0.37 % (19958)Instructions burned: 15 (million)
% 0.15/0.37 % (19958)------------------------------
% 0.15/0.37 % (19958)------------------------------
% 0.15/0.37 % (19960)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)
% 0.15/0.38 % (19961)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.15/0.38 % (19957)Instruction limit reached!
% 0.15/0.38 % (19957)------------------------------
% 0.15/0.38 % (19957)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.15/0.38 % (19957)Termination reason: Unknown
% 0.15/0.38 % (19957)Termination phase: Saturation
% 0.15/0.38 % (19962)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.15/0.38
% 0.15/0.38 % (19957)Memory used [KB]: 5884
% 0.15/0.38 % (19957)Time elapsed: 0.019 s
% 0.15/0.38 % (19957)Instructions burned: 37 (million)
% 0.15/0.38 % (19957)------------------------------
% 0.15/0.38 % (19957)------------------------------
% 0.15/0.38 % (19961)Instruction limit reached!
% 0.15/0.38 % (19961)------------------------------
% 0.15/0.38 % (19961)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.15/0.38 % (19961)Termination reason: Unknown
% 0.15/0.38 % (19961)Termination phase: Saturation
% 0.15/0.38
% 0.15/0.38 % (19961)Memory used [KB]: 1023
% 0.15/0.38 % (19961)Time elapsed: 0.006 s
% 0.15/0.38 % (19961)Instructions burned: 7 (million)
% 0.15/0.38 % (19961)------------------------------
% 0.15/0.38 % (19961)------------------------------
% 0.15/0.39 % (19962)Instruction limit reached!
% 0.15/0.39 % (19962)------------------------------
% 0.15/0.39 % (19962)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.15/0.39 % (19962)Termination reason: Unknown
% 0.15/0.39 % (19962)Termination phase: Saturation
% 0.15/0.39
% 0.15/0.39 % (19962)Memory used [KB]: 5628
% 0.15/0.39 % (19962)Time elapsed: 0.010 s
% 0.15/0.39 % (19962)Instructions burned: 16 (million)
% 0.15/0.39 % (19962)------------------------------
% 0.15/0.39 % (19962)------------------------------
% 0.15/0.39 % (19963)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.15/0.39 % (19954)First to succeed.
% 0.15/0.39 % (19963)Instruction limit reached!
% 0.15/0.39 % (19963)------------------------------
% 0.15/0.39 % (19963)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.15/0.39 % (19963)Termination reason: Unknown
% 0.15/0.39 % (19963)Termination phase: Twee Goal Transformation
% 0.15/0.39
% 0.15/0.39 % (19963)Memory used [KB]: 1023
% 0.15/0.39 % (19963)Time elapsed: 0.004 s
% 0.15/0.39 % (19963)Instructions burned: 4 (million)
% 0.15/0.39 % (19963)------------------------------
% 0.15/0.39 % (19963)------------------------------
% 0.15/0.39 % (19954)Refutation found. Thanks to Tanya!
% 0.15/0.39 % SZS status Theorem for theBenchmark
% 0.15/0.39 % SZS output start Proof for theBenchmark
% 0.15/0.39 thf(func_def_4, type, sK0: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_5, type, sK1: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i).
% 0.15/0.39 thf(func_def_6, type, sK2: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_7, type, sK3: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_8, type, sK4: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_9, type, sK5: (($i > $o) > ($i > $o) > $i > $o) > (($i > $o) > ($i > $o) > $i > $o) > $i).
% 0.15/0.39 thf(func_def_11, type, ph7: !>[X0: $tType]:(X0)).
% 0.15/0.39 thf(func_def_18, type, sK9: (($i > $o) > ($i > $o) > $i > $o) > $i).
% 0.15/0.39 thf(func_def_19, type, sK10: (($i > $o) > ($i > $o) > $i > $o) > $i).
% 0.15/0.39 thf(f449,plain,(
% 0.15/0.39 $false),
% 0.15/0.39 inference(avatar_sat_refutation,[],[f78,f448])).
% 0.15/0.39 thf(f448,plain,(
% 0.15/0.39 spl6_2),
% 0.15/0.39 inference(avatar_contradiction_clause,[],[f447])).
% 0.15/0.39 thf(f447,plain,(
% 0.15/0.39 $false | spl6_2),
% 0.15/0.39 inference(subsumption_resolution,[],[f446,f45])).
% 0.15/0.39 thf(f45,plain,(
% 0.15/0.39 ((^[Y0 : $i]: ($true)) != (^[Y0 : $i]: ($false))) | spl6_2),
% 0.15/0.39 inference(avatar_component_clause,[],[f44])).
% 0.15/0.39 thf(f44,plain,(
% 0.15/0.39 spl6_2 <=> ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))),
% 0.15/0.39 introduced(avatar_definition,[new_symbols(naming,[spl6_2])])).
% 0.15/0.39 thf(f446,plain,(
% 0.15/0.39 ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | spl6_2),
% 0.15/0.39 inference(equality_proxy_clausification,[],[f445])).
% 0.15/0.39 thf(f445,plain,(
% 0.15/0.39 ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | spl6_2),
% 0.15/0.39 inference(trivial_inequality_removal,[],[f444])).
% 0.15/0.39 thf(f444,plain,(
% 0.15/0.39 ($true != $true) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | spl6_2),
% 0.15/0.39 inference(boolean_simplification,[],[f443])).
% 0.15/0.39 thf(f443,plain,(
% 0.15/0.39 ($true != ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | spl6_2),
% 0.15/0.39 inference(trivial_inequality_removal,[],[f442])).
% 0.15/0.39 thf(f442,plain,(
% 0.15/0.39 ($true != $true) | ($true = ((^[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 : $i]: ($false))))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | spl6_2),
% 0.15/0.39 inference(boolean_simplification,[],[f441])).
% 0.15/0.39 thf(f441,plain,(
% 0.15/0.39 ($true != ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | ($true = ((^[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 : $i]: ($false))))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | spl6_2),
% 0.15/0.39 inference(trivial_inequality_removal,[],[f440])).
% 0.15/0.39 thf(f440,plain,(
% 0.15/0.39 ($true = $false) | ($true = ((^[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 : $i]: ($false))))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | ($true != ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | spl6_2),
% 0.15/0.39 inference(beta_eta_normalization,[],[f424])).
% 0.15/0.39 thf(f424,plain,(
% 0.15/0.39 ( ! [X0 : $i] : (($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X0)) | ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X0)) | ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) | ($true != ((^[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 : $i]: ($false))))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))))) ) | spl6_2),
% 0.15/0.39 inference(superposition,[],[f15,f297])).
% 0.15/0.39 thf(f297,plain,(
% 0.15/0.39 ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | spl6_2),
% 0.15/0.39 inference(trivial_inequality_removal,[],[f296])).
% 0.15/0.39 thf(f296,plain,(
% 0.15/0.39 ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | ($true = $false) | spl6_2),
% 0.15/0.39 inference(duplicate_literal_removal,[],[f295])).
% 0.15/0.39 thf(f295,plain,(
% 0.15/0.39 ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | ($true = $false) | ($true = $false) | spl6_2),
% 0.15/0.39 inference(beta_eta_normalization,[],[f294])).
% 0.15/0.39 thf(f294,plain,(
% 0.15/0.39 ( ! [X0 : $i,X1 : $i] : (($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ X0)) | ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X1))) ) | spl6_2),
% 0.15/0.39 inference(superposition,[],[f186,f280])).
% 0.15/0.39 thf(f280,plain,(
% 0.15/0.39 ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | spl6_2),
% 0.15/0.39 inference(trivial_inequality_removal,[],[f279])).
% 0.15/0.39 thf(f279,plain,(
% 0.15/0.39 ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | ($true = $false) | spl6_2),
% 0.15/0.39 inference(duplicate_literal_removal,[],[f278])).
% 0.15/0.39 thf(f278,plain,(
% 0.15/0.39 ($true = $false) | ($true = $false) | ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))))) | spl6_2),
% 0.15/0.39 inference(beta_eta_normalization,[],[f265])).
% 0.15/0.39 thf(f265,plain,(
% 0.15/0.39 ( ! [X2 : $i,X10 : $i] : (($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) @ X10)) | ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) | ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ($false))))))))) ) | spl6_2),
% 0.15/0.39 inference(primitive_instantiation,[],[f157])).
% 0.15/0.39 thf(f157,plain,(
% 0.15/0.39 ( ! [X2 : $i,X10 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o] : (($true = (X0 @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X10)) | ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) | ($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) ) | spl6_2),
% 0.15/0.39 inference(subsumption_resolution,[],[f141,f45])).
% 0.15/0.39 thf(f141,plain,(
% 0.15/0.39 ( ! [X2 : $i,X10 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o] : (($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) | ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) | ($true = (X0 @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X10)) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false)))) )),
% 0.15/0.39 inference(equality_proxy_clausification,[],[f140])).
% 0.15/0.39 thf(f140,plain,(
% 0.15/0.39 ( ! [X2 : $i,X10 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o] : (($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) | ($true = (X0 @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X10)) | ((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))))) )),
% 0.15/0.39 inference(equality_proxy_clausification,[],[f139])).
% 0.15/0.39 thf(f139,plain,(
% 0.15/0.39 ( ! [X2 : $i,X10 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o] : (($true = ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0))) | ($true = (X0 @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X10)) | ($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))))) )),
% 0.15/0.39 inference(trivial_inequality_removal,[],[f138])).
% 0.15/0.39 thf(f138,plain,(
% 0.15/0.39 ( ! [X2 : $i,X10 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o] : (($true != $true) | ($true = (X0 @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X10)) | ($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) | ($true = ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0))) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))))) )),
% 0.15/0.39 inference(boolean_simplification,[],[f137])).
% 0.15/0.39 thf(f137,plain,(
% 0.15/0.39 ( ! [X2 : $i,X10 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o] : (($true != ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0))) | ($true = ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0))) | ($true = (X0 @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X10)) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | ($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) )),
% 0.15/0.39 inference(beta_eta_normalization,[],[f132])).
% 0.15/0.39 thf(f132,plain,(
% 0.15/0.39 ( ! [X2 : $i,X10 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o] : (($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) | ($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) | ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK0 @ (^[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 > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X10)) | ($true = (X0 @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X10))) )),
% 0.15/0.39 inference(primitive_instantiation,[],[f13])).
% 0.15/0.39 thf(f13,plain,(
% 0.15/0.39 ( ! [X2 : $i,X10 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (($true != (X1 @ (sK0 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0))) | ((X1 @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X10) = $true) | ($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) | ($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) | ($true = (X0 @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X10))) )),
% 0.15/0.39 inference(cnf_transformation,[],[f12])).
% 0.15/0.39 thf(f12,plain,(
% 0.15/0.39 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (! [X2] : (($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) | ($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | (($true != (X0 @ (sK0 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0))) & ($true != (X1 @ (sK0 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0)))) | (! [X8] : (($true = (X1 @ (sK4 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X8)) | ($true = (X0 @ (sK4 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X8))) & (($true != (X1 @ (sK3 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK5 @ X1 @ X0))) & ((X0 @ (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)))))),
% 0.15/0.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f8,f11,f10,f9])).
% 0.15/0.39 thf(f9,plain,(
% 0.15/0.39 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X3 : $i > $o,X4] : (($true != (X0 @ X3 @ X3 @ X4)) & ($true != (X1 @ X3 @ X3 @ X4))) => (($true != (X0 @ (sK0 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0))) & ($true != (X1 @ (sK0 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0)))))),
% 0.15/0.39 introduced(choice_axiom,[])).
% 0.15/0.39 thf(f10,plain,(
% 0.15/0.39 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X5 : $i > $o,X6 : $i > $o,X7 : $i > $o] : (! [X8] : (($true = (X1 @ X7 @ X5 @ X8)) | ((X0 @ X7 @ X5 @ X8) = $true)) & ? [X9] : (($true != (X1 @ X6 @ X5 @ X9)) & ($true != (X0 @ X6 @ X5 @ X9))) & ! [X10] : (($true = (X1 @ X6 @ X7 @ X10)) | ($true = (X0 @ X6 @ X7 @ X10)))) => (! [X8] : (($true = (X1 @ (sK4 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X8)) | ($true = (X0 @ (sK4 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X8))) & ? [X9] : (($true != (X1 @ (sK3 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X9)) & ($true != (X0 @ (sK3 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X9))) & ! [X10] : (((X1 @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X10) = $true) | ($true = (X0 @ (sK3 @ X1 @ X0) @ (sK4 @ X1 @ X0) @ X10)))))),
% 0.15/0.39 introduced(choice_axiom,[])).
% 0.15/0.39 thf(f11,plain,(
% 0.15/0.39 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (? [X9] : (($true != (X1 @ (sK3 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X9)) & ($true != (X0 @ (sK3 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X9))) => (($true != (X1 @ (sK3 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK5 @ X1 @ X0))) & ((X0 @ (sK3 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK5 @ X1 @ X0)) != $true)))),
% 0.15/0.39 introduced(choice_axiom,[])).
% 0.15/0.39 thf(f8,plain,(
% 0.15/0.39 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (! [X2] : (($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) | ($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) | ? [X3 : $i > $o,X4] : (($true != (X0 @ X3 @ X3 @ X4)) & ($true != (X1 @ X3 @ X3 @ X4))) | ? [X5 : $i > $o,X6 : $i > $o,X7 : $i > $o] : (! [X8] : (($true = (X1 @ X7 @ X5 @ X8)) | ((X0 @ X7 @ X5 @ X8) = $true)) & ? [X9] : (($true != (X1 @ X6 @ X5 @ X9)) & ($true != (X0 @ X6 @ X5 @ X9))) & ! [X10] : (($true = (X1 @ X6 @ X7 @ X10)) | ($true = (X0 @ X6 @ X7 @ X10)))))),
% 0.15/0.39 inference(rectify,[],[f7])).
% 0.15/0.39 thf(f7,plain,(
% 0.15/0.39 ! [X1 : ($i > $o) > ($i > $o) > $i > $o,X0 : ($i > $o) > ($i > $o) > $i > $o] : (! [X10] : (($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) | ($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) | ? [X3 : $i > $o,X2] : (($true != (X1 @ X3 @ X3 @ X2)) & ($true != (X0 @ X3 @ X3 @ X2))) | ? [X4 : $i > $o,X5 : $i > $o,X6 : $i > $o] : (! [X8] : (($true = (X0 @ X6 @ X4 @ X8)) | ($true = (X1 @ X6 @ X4 @ X8))) & ? [X9] : (($true != (X0 @ X5 @ X4 @ X9)) & ($true != (X1 @ X5 @ X4 @ X9))) & ! [X7] : (($true = (X0 @ X5 @ X6 @ X7)) | ((X1 @ X5 @ X6 @ X7) = $true))))),
% 0.15/0.39 inference(flattening,[],[f6])).
% 0.15/0.39 thf(f6,plain,(
% 0.15/0.39 ! [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (! [X10] : (($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) | ($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) | ? [X3 : $i > $o,X2] : (($true != (X1 @ X3 @ X3 @ X2)) & ($true != (X0 @ X3 @ X3 @ X2))) | ? [X4 : $i > $o,X6 : $i > $o,X5 : $i > $o] : (? [X9] : (($true != (X0 @ X5 @ X4 @ X9)) & ($true != (X1 @ X5 @ X4 @ X9))) & (! [X8] : (($true = (X0 @ X6 @ X4 @ X8)) | ($true = (X1 @ X6 @ X4 @ X8))) & ! [X7] : (($true = (X0 @ X5 @ X6 @ X7)) | ((X1 @ X5 @ X6 @ X7) = $true)))))),
% 0.15/0.39 inference(ennf_transformation,[],[f5])).
% 0.15/0.39 thf(f5,plain,(
% 0.15/0.39 ~? [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (~! [X10] : (($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10)) | ($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X10))) & ! [X2,X3 : $i > $o] : (($true = (X1 @ X3 @ X3 @ X2)) | ($true = (X0 @ X3 @ X3 @ X2))) & ! [X4 : $i > $o,X6 : $i > $o,X5 : $i > $o] : ((! [X8] : (($true = (X0 @ X6 @ X4 @ X8)) | ($true = (X1 @ X6 @ X4 @ X8))) & ! [X7] : (($true = (X0 @ X5 @ X6 @ X7)) | ((X1 @ X5 @ X6 @ X7) = $true))) => ! [X9] : (($true = (X1 @ X5 @ X4 @ X9)) | ($true = (X0 @ X5 @ X4 @ X9)))))),
% 0.15/0.39 inference(fool_elimination,[],[f4])).
% 0.15/0.39 thf(f4,plain,(
% 0.15/0.39 ~? [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (! [X2,X3 : $i > $o] : ((X0 @ X3 @ X3 @ X2) | (X1 @ X3 @ X3 @ X2)) & ! [X4 : $i > $o,X5 : $i > $o,X6 : $i > $o] : ((! [X7] : ((X0 @ X5 @ X6 @ X7) | (X1 @ X5 @ X6 @ X7)) & ! [X8] : ((X0 @ X6 @ X4 @ X8) | (X1 @ X6 @ X4 @ X8))) => ! [X9] : ((X0 @ X5 @ X4 @ X9) | (X1 @ X5 @ X4 @ X9))) & ~! [X10] : ((X1 @ (^[X11 : $i] : ($true)) @ (^[X12 : $i] : ($false)) @ X10) | (X0 @ (^[X13 : $i] : ($true)) @ (^[X14 : $i] : ($false)) @ X10)))),
% 0.15/0.39 inference(rectify,[],[f2])).
% 0.15/0.39 thf(f2,negated_conjecture,(
% 0.15/0.39 ~? [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (! [X3,X2 : $i > $o] : ((X0 @ X2 @ X2 @ X3) | (X1 @ X2 @ X2 @ X3)) & ! [X5 : $i > $o,X2 : $i > $o,X4 : $i > $o] : ((! [X3] : ((X0 @ X2 @ X4 @ X3) | (X1 @ X2 @ X4 @ X3)) & ! [X3] : ((X0 @ X4 @ X5 @ X3) | (X1 @ X4 @ X5 @ X3))) => ! [X3] : ((X0 @ X2 @ X5 @ X3) | (X1 @ X2 @ X5 @ X3))) & ~! [X3] : ((X1 @ (^[X2 : $i] : ($true)) @ (^[X2 : $i] : ($false)) @ X3) | (X0 @ (^[X2 : $i] : ($true)) @ (^[X2 : $i] : ($false)) @ X3)))),
% 0.15/0.39 inference(negated_conjecture,[],[f1])).
% 0.15/0.39 thf(f1,conjecture,(
% 0.15/0.39 ? [X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (! [X3,X2 : $i > $o] : ((X0 @ X2 @ X2 @ X3) | (X1 @ X2 @ X2 @ X3)) & ! [X5 : $i > $o,X2 : $i > $o,X4 : $i > $o] : ((! [X3] : ((X0 @ X2 @ X4 @ X3) | (X1 @ X2 @ X4 @ X3)) & ! [X3] : ((X0 @ X4 @ X5 @ X3) | (X1 @ X4 @ X5 @ X3))) => ! [X3] : ((X0 @ X2 @ X5 @ X3) | (X1 @ X2 @ X5 @ X3))) & ~! [X3] : ((X1 @ (^[X2 : $i] : ($true)) @ (^[X2 : $i] : ($false)) @ X3) | (X0 @ (^[X2 : $i] : ($true)) @ (^[X2 : $i] : ($false)) @ X3)))),
% 0.15/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM120D_pme)).
% 0.15/0.39 thf(f186,plain,(
% 0.15/0.39 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (((X0 @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X8) = $true) | ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) | ($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) ) | spl6_2),
% 0.15/0.39 inference(subsumption_resolution,[],[f170,f45])).
% 0.15/0.39 thf(f170,plain,(
% 0.15/0.39 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) | ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ((X0 @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X8) = $true) | ($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) )),
% 0.15/0.39 inference(equality_proxy_clausification,[],[f169])).
% 0.15/0.39 thf(f169,plain,(
% 0.15/0.39 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) | ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0)) | ((X0 @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X8) = $true) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))))) )),
% 0.15/0.39 inference(equality_proxy_clausification,[],[f168])).
% 0.15/0.39 thf(f168,plain,(
% 0.15/0.39 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) | ((X0 @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X8) = $true) | ($true = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0))) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true))))) )),
% 0.15/0.39 inference(trivial_inequality_removal,[],[f167])).
% 0.15/0.39 thf(f167,plain,(
% 0.15/0.39 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (($true = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0))) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | ($true != $true) | ($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) | ((X0 @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X8) = $true)) )),
% 0.15/0.39 inference(boolean_simplification,[],[f166])).
% 0.15/0.39 thf(f166,plain,(
% 0.15/0.39 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (((X0 @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X8) = $true) | ($true = ((^[Y0 : $i]: ($false)) = (^[Y0 : $i]: ($true)))) | ($true != ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0))) | ($true = ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0))) | ($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2))) )),
% 0.15/0.39 inference(beta_eta_normalization,[],[f161])).
% 0.15/0.39 thf(f161,plain,(
% 0.15/0.39 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (((X0 @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X8) = $true) | ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK0 @ (^[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 > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) | ($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 = Y0)))))) @ X0) @ X8) = $true)) )),
% 0.15/0.39 inference(primitive_instantiation,[],[f16])).
% 0.15/0.39 thf(f16,plain,(
% 0.15/0.39 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o,X8 : $i] : (($true != (X1 @ (sK0 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0))) | ($true = (X1 @ (sK4 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X8)) | ($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) | ($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) | ($true = (X0 @ (sK4 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ X8))) )),
% 0.15/0.39 inference(cnf_transformation,[],[f12])).
% 0.15/0.39 thf(f15,plain,(
% 0.15/0.39 ( ! [X2 : $i,X0 : ($i > $o) > ($i > $o) > $i > $o,X1 : ($i > $o) > ($i > $o) > $i > $o] : (($true != (X1 @ (sK3 @ X1 @ X0) @ (sK2 @ X1 @ X0) @ (sK5 @ X1 @ X0))) | ($true = (X1 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) | ($true = (X0 @ (^[Y0 : $i]: ($true)) @ (^[Y0 : $i]: ($false)) @ X2)) | ($true != (X1 @ (sK0 @ X1 @ X0) @ (sK0 @ X1 @ X0) @ (sK1 @ X1 @ X0)))) )),
% 0.18/0.39 inference(cnf_transformation,[],[f12])).
% 0.18/0.39 thf(f78,plain,(
% 0.18/0.39 ~spl6_2),
% 0.18/0.39 inference(avatar_contradiction_clause,[],[f77])).
% 0.18/0.39 thf(f77,plain,(
% 0.18/0.39 $false | ~spl6_2),
% 0.18/0.39 inference(trivial_inequality_removal,[],[f76])).
% 0.18/0.39 thf(f76,plain,(
% 0.18/0.39 ($true = $false) | ~spl6_2),
% 0.18/0.39 inference(beta_eta_normalization,[],[f75])).
% 0.18/0.39 thf(f75,plain,(
% 0.18/0.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: ($true)) @ X1) = ((^[Y0 : $i]: ($false)) @ X1))) ) | ~spl6_2),
% 0.18/0.39 inference(argument_congruence,[],[f46])).
% 0.18/0.39 thf(f46,plain,(
% 0.18/0.39 ((^[Y0 : $i]: ($true)) = (^[Y0 : $i]: ($false))) | ~spl6_2),
% 0.18/0.39 inference(avatar_component_clause,[],[f44])).
% 0.18/0.39 % SZS output end Proof for theBenchmark
% 0.18/0.39 % (19954)------------------------------
% 0.18/0.39 % (19954)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.18/0.39 % (19954)Termination reason: Refutation
% 0.18/0.39
% 0.18/0.39 % (19954)Memory used [KB]: 6012
% 0.18/0.39 % (19954)Time elapsed: 0.046 s
% 0.18/0.39 % (19954)Instructions burned: 81 (million)
% 0.18/0.39 % (19954)------------------------------
% 0.18/0.39 % (19954)------------------------------
% 0.18/0.39 % (19948)Success in time 0.054 s
%------------------------------------------------------------------------------